LMFDB - Embedded newform 8033.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65443 q^{2} -2.20662 q^{3} +5.04598 q^{4} +0.185737 q^{5} +5.85731 q^{6} -3.52416 q^{7} -8.08534 q^{8} +1.86917 q^{9} +O(q^{10})$	\(q-2.65443 q^{2} -2.20662 q^{3} +5.04598 q^{4} +0.185737 q^{5} +5.85731 q^{6} -3.52416 q^{7} -8.08534 q^{8} +1.86917 q^{9} -0.493026 q^{10} +3.86758 q^{11} -11.1346 q^{12} +0.687005 q^{13} +9.35462 q^{14} -0.409851 q^{15} +11.3700 q^{16} -5.48861 q^{17} -4.96158 q^{18} +2.98606 q^{19} +0.937226 q^{20} +7.77648 q^{21} -10.2662 q^{22} +6.01762 q^{23} +17.8413 q^{24} -4.96550 q^{25} -1.82361 q^{26} +2.49531 q^{27} -17.7828 q^{28} -1.00000 q^{29} +1.08792 q^{30} -1.76949 q^{31} -14.0101 q^{32} -8.53427 q^{33} +14.5691 q^{34} -0.654567 q^{35} +9.43181 q^{36} +8.63655 q^{37} -7.92627 q^{38} -1.51596 q^{39} -1.50175 q^{40} -7.26301 q^{41} -20.6421 q^{42} -6.66460 q^{43} +19.5157 q^{44} +0.347175 q^{45} -15.9733 q^{46} -0.513091 q^{47} -25.0892 q^{48} +5.41969 q^{49} +13.1806 q^{50} +12.1113 q^{51} +3.46662 q^{52} -6.01532 q^{53} -6.62361 q^{54} +0.718353 q^{55} +28.4940 q^{56} -6.58910 q^{57} +2.65443 q^{58} -1.51392 q^{59} -2.06810 q^{60} +9.52113 q^{61} +4.69698 q^{62} -6.58726 q^{63} +14.4488 q^{64} +0.127602 q^{65} +22.6536 q^{66} -10.1845 q^{67} -27.6954 q^{68} -13.2786 q^{69} +1.73750 q^{70} +14.0760 q^{71} -15.1129 q^{72} -8.21024 q^{73} -22.9251 q^{74} +10.9570 q^{75} +15.0676 q^{76} -13.6300 q^{77} +4.02400 q^{78} +1.31338 q^{79} +2.11183 q^{80} -11.1137 q^{81} +19.2791 q^{82} +1.58517 q^{83} +39.2400 q^{84} -1.01944 q^{85} +17.6907 q^{86} +2.20662 q^{87} -31.2707 q^{88} -0.478790 q^{89} -0.921550 q^{90} -2.42111 q^{91} +30.3648 q^{92} +3.90459 q^{93} +1.36196 q^{94} +0.554622 q^{95} +30.9150 q^{96} -1.09910 q^{97} -14.3862 q^{98} +7.22917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.65443	−1.87696	−0.938482	−	0.345329i	$-0.887767\pi$
$2$	−2.65443	−1.87696	−0.938482	+	0.345329i	$0.887767\pi$
$3$	−2.20662	−1.27399	−0.636996	−	0.770867i	$-0.719823\pi$
$3$	−2.20662	−1.27399	−0.636996	+	0.770867i	$0.719823\pi$
$4$	5.04598	2.52299
$5$	0.185737	0.0830642	0.0415321	−	0.999137i	$-0.486776\pi$
$5$	0.185737	0.0830642	0.0415321	+	0.999137i	$0.486776\pi$
$6$	5.85731	2.39124
$7$	−3.52416	−1.33201	−0.666003	−	0.745949i	$-0.731996\pi$
$7$	−3.52416	−1.33201	−0.666003	+	0.745949i	$0.731996\pi$
$8$	−8.08534	−2.85860
$9$	1.86917	0.623057
$10$	−0.493026	−0.155908
$11$	3.86758	1.16612	0.583059	−	0.812430i	$-0.301856\pi$
$11$	3.86758	1.16612	0.583059	+	0.812430i	$0.301856\pi$
$12$	−11.1346	−3.21427
$13$	0.687005	0.190541	0.0952705	−	0.995451i	$-0.469628\pi$
$13$	0.687005	0.190541	0.0952705	+	0.995451i	$0.469628\pi$
$14$	9.35462	2.50013
$15$	−0.409851	−0.105823
$16$	11.3700	2.84250
$17$	−5.48861	−1.33118	−0.665591	−	0.746316i	$-0.731821\pi$
$17$	−5.48861	−1.33118	−0.665591	+	0.746316i	$0.731821\pi$
$18$	−4.96158	−1.16946
$19$	2.98606	0.685049	0.342524	−	0.939509i	$-0.388718\pi$
$19$	2.98606	0.685049	0.342524	+	0.939509i	$0.388718\pi$
$20$	0.937226	0.209570
$21$	7.77648	1.69697
$22$	−10.2662	−2.18876
$23$	6.01762	1.25476	0.627380	−	0.778713i	$-0.284127\pi$
$23$	6.01762	1.25476	0.627380	+	0.778713i	$0.284127\pi$
$24$	17.8413	3.64184
$25$	−4.96550	−0.993100
$26$	−1.82361	−0.357638
$27$	2.49531	0.480222
$28$	−17.7828	−3.36064
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.08792	0.198626
$31$	−1.76949	−0.317810	−0.158905	−	0.987294i	$-0.550796\pi$
$31$	−1.76949	−0.317810	−0.158905	+	0.987294i	$0.550796\pi$
$32$	−14.0101	−2.47666
$33$	−8.53427	−1.48563
$34$	14.5691	2.49858
$35$	−0.654567	−0.110642
$36$	9.43181	1.57197
$37$	8.63655	1.41984	0.709920	−	0.704282i	$-0.248731\pi$
$37$	8.63655	1.41984	0.709920	+	0.704282i	$0.248731\pi$
$38$	−7.92627	−1.28581
$39$	−1.51596	−0.242748
$40$	−1.50175	−0.237447
$41$	−7.26301	−1.13429	−0.567146	−	0.823617i	$-0.691952\pi$
$41$	−7.26301	−1.13429	−0.567146	+	0.823617i	$0.691952\pi$
$42$	−20.6421	−3.18514
$43$	−6.66460	−1.01634	−0.508171	−	0.861256i	$-0.669678\pi$
$43$	−6.66460	−1.01634	−0.508171	+	0.861256i	$0.669678\pi$
$44$	19.5157	2.94211
$45$	0.347175	0.0517537
$46$	−15.9733	−2.35514
$47$	−0.513091	−0.0748420	−0.0374210	−	0.999300i	$-0.511914\pi$
$47$	−0.513091	−0.0748420	−0.0374210	+	0.999300i	$0.511914\pi$
$48$	−25.0892	−3.62132
$49$	5.41969	0.774242
$50$	13.1806	1.86401
$51$	12.1113	1.69592
$52$	3.46662	0.480733
$53$	−6.01532	−0.826267	−0.413134	−	0.910670i	$-0.635566\pi$
$53$	−6.01532	−0.826267	−0.413134	+	0.910670i	$0.635566\pi$
$54$	−6.62361	−0.901360
$55$	0.718353	0.0968627
$56$	28.4940	3.80767
$57$	−6.58910	−0.872747
$58$	2.65443	0.348543
$59$	−1.51392	−0.197096	−0.0985479	−	0.995132i	$-0.531420\pi$
$59$	−1.51392	−0.197096	−0.0985479	+	0.995132i	$0.531420\pi$
$60$	−2.06810	−0.266991
$61$	9.52113	1.21906	0.609528	−	0.792765i	$-0.291359\pi$
$61$	9.52113	1.21906	0.609528	+	0.792765i	$0.291359\pi$
$62$	4.69698	0.596518
$63$	−6.58726	−0.829916
$64$	14.4488	1.80611
$65$	0.127602	0.0158271
$66$	22.6536	2.78847
$67$	−10.1845	−1.24423	−0.622114	−	0.782926i	$-0.713726\pi$
$67$	−10.1845	−1.24423	−0.622114	+	0.782926i	$0.713726\pi$
$68$	−27.6954	−3.35856
$69$	−13.2786	−1.59855
$70$	1.73750	0.207671
$71$	14.0760	1.67051	0.835255	−	0.549864i	$-0.185320\pi$
$71$	14.0760	1.67051	0.835255	+	0.549864i	$0.185320\pi$
$72$	−15.1129	−1.78107
$73$	−8.21024	−0.960936	−0.480468	−	0.877012i	$-0.659533\pi$
$73$	−8.21024	−0.960936	−0.480468	+	0.877012i	$0.659533\pi$
$74$	−22.9251	−2.66499
$75$	10.9570	1.26520
$76$	15.0676	1.72837
$77$	−13.6300	−1.55328
$78$	4.02400	0.455629
$79$	1.31338	0.147766	0.0738831	−	0.997267i	$-0.476461\pi$
$79$	1.31338	0.147766	0.0738831	+	0.997267i	$0.476461\pi$
$80$	2.11183	0.236110
$81$	−11.1137	−1.23486
$82$	19.2791	2.12902
$83$	1.58517	0.173995	0.0869976	−	0.996209i	$-0.472273\pi$
$83$	1.58517	0.173995	0.0869976	+	0.996209i	$0.472273\pi$
$84$	39.2400	4.28143
$85$	−1.01944	−0.110574
$86$	17.6907	1.90764
$87$	2.20662	0.236574
$88$	−31.2707	−3.33347
$89$	−0.478790	−0.0507516	−0.0253758	−	0.999678i	$-0.508078\pi$
$89$	−0.478790	−0.0507516	−0.0253758	+	0.999678i	$0.508078\pi$
$90$	−0.921550	−0.0971399
$91$	−2.42111	−0.253802
$92$	30.3648	3.16575
$93$	3.90459	0.404887
$94$	1.36196	0.140476
$95$	0.554622	0.0569030
$96$	30.9150	3.15525
$97$	−1.09910	−0.111597	−0.0557983	−	0.998442i	$-0.517770\pi$
$97$	−1.09910	−0.111597	−0.0557983	+	0.998442i	$0.517770\pi$
$98$	−14.3862	−1.45322
$99$	7.22917	0.726559
$100$	−25.0558	−2.50558
$101$	8.15136	0.811090	0.405545	−	0.914075i	$-0.367082\pi$
$101$	8.15136	0.811090	0.405545	+	0.914075i	$0.367082\pi$
$102$	−32.1485	−3.18317
$103$	3.37773	0.332817	0.166409	−	0.986057i	$-0.446783\pi$
$103$	3.37773	0.332817	0.166409	+	0.986057i	$0.446783\pi$
$104$	−5.55467	−0.544680
$105$	1.44438	0.140957
$106$	15.9672	1.55087
$107$	−2.58409	−0.249814	−0.124907	−	0.992168i	$-0.539863\pi$
$107$	−2.58409	−0.249814	−0.124907	+	0.992168i	$0.539863\pi$
$108$	12.5913	1.21160
$109$	11.5090	1.10236	0.551179	−	0.834387i	$-0.314178\pi$
$109$	11.5090	1.10236	0.551179	+	0.834387i	$0.314178\pi$
$110$	−1.90682	−0.181808
$111$	−19.0576	−1.80887
$112$	−40.0696	−3.78622
$113$	−8.15598	−0.767250	−0.383625	−	0.923489i	$-0.625324\pi$
$113$	−8.15598	−0.767250	−0.383625	+	0.923489i	$0.625324\pi$
$114$	17.4903	1.63811
$115$	1.11769	0.104226
$116$	−5.04598	−0.468508
$117$	1.28413	0.118718
$118$	4.01859	0.369941
$119$	19.3427	1.77314
$120$	3.31379	0.302506
$121$	3.95816	0.359833
$122$	−25.2731	−2.28812
$123$	16.0267	1.44508
$124$	−8.92882	−0.801832
$125$	−1.85096	−0.165555
$126$	17.4854	1.55772
$127$	8.40824	0.746111	0.373055	−	0.927809i	$-0.378310\pi$
$127$	8.40824	0.746111	0.373055	+	0.927809i	$0.378310\pi$
$128$	−10.3332	−0.913334
$129$	14.7062	1.29481
$130$	−0.338711	−0.0297069
$131$	13.5777	1.18629	0.593144	−	0.805096i	$-0.297886\pi$
$131$	13.5777	1.18629	0.593144	+	0.805096i	$0.297886\pi$
$132$	−43.0638	−3.74822
$133$	−10.5233	−0.912489
$134$	27.0339	2.33537
$135$	0.463471	0.0398893
$136$	44.3773	3.80532
$137$	20.4287	1.74534	0.872669	−	0.488312i	$-0.162387\pi$
$137$	20.4287	1.74534	0.872669	+	0.488312i	$0.162387\pi$
$138$	35.2471	3.00043
$139$	0.258099	0.0218917	0.0109459	−	0.999940i	$-0.496516\pi$
$139$	0.258099	0.0218917	0.0109459	+	0.999940i	$0.496516\pi$
$140$	−3.30293	−0.279149
$141$	1.13220	0.0953482
$142$	−37.3636	−3.13548
$143$	2.65705	0.222193
$144$	21.2524	1.77104
$145$	−0.185737	−0.0154246
$146$	21.7935	1.80364
$147$	−11.9592	−0.986378
$148$	43.5799	3.58224
$149$	−14.1675	−1.16065	−0.580323	−	0.814386i	$-0.697074\pi$
$149$	−14.1675	−1.16065	−0.580323	+	0.814386i	$0.697074\pi$
$150$	−29.0845	−2.37474
$151$	−8.81353	−0.717235	−0.358617	−	0.933485i	$-0.616752\pi$
$151$	−8.81353	−0.717235	−0.358617	+	0.933485i	$0.616752\pi$
$152$	−24.1433	−1.95828
$153$	−10.2591	−0.829403
$154$	36.1797	2.91545
$155$	−0.328660	−0.0263986
$156$	−7.64951	−0.612451
$157$	5.09224	0.406405	0.203202	−	0.979137i	$-0.434865\pi$
$157$	5.09224	0.406405	0.203202	+	0.979137i	$0.434865\pi$
$158$	−3.48626	−0.277352
$159$	13.2735	1.05266
$160$	−2.60220	−0.205722
$161$	−21.2070	−1.67135
$162$	29.5005	2.31778
$163$	−21.7277	−1.70184	−0.850922	−	0.525292i	$-0.823956\pi$
$163$	−21.7277	−1.70184	−0.850922	+	0.525292i	$0.823956\pi$
$164$	−36.6490	−2.86181
$165$	−1.58513	−0.123402
$166$	−4.20772	−0.326583
$167$	−13.1965	−1.02118	−0.510590	−	0.859824i	$-0.670573\pi$
$167$	−13.1965	−1.02118	−0.510590	+	0.859824i	$0.670573\pi$
$168$	−62.8755	−4.85095
$169$	−12.5280	−0.963694
$170$	2.70602	0.207543
$171$	5.58146	0.426825
$172$	−33.6295	−2.56422
$173$	21.2080	1.61241	0.806206	−	0.591635i	$-0.201517\pi$
$173$	21.2080	1.61241	0.806206	+	0.591635i	$0.201517\pi$
$174$	−5.85731	−0.444042
$175$	17.4992	1.32282
$176$	43.9743	3.31469
$177$	3.34065	0.251099
$178$	1.27091	0.0952589
$179$	−3.38974	−0.253361	−0.126680	−	0.991944i	$-0.540432\pi$
$179$	−3.38974	−0.253361	−0.126680	+	0.991944i	$0.540432\pi$
$180$	1.75184	0.130574
$181$	−13.1861	−0.980115	−0.490058	−	0.871690i	$-0.663024\pi$
$181$	−13.1861	−0.980115	−0.490058	+	0.871690i	$0.663024\pi$
$182$	6.42667	0.476377
$183$	−21.0095	−1.55307
$184$	−48.6545	−3.58686
$185$	1.60413	0.117938
$186$	−10.3645	−0.759959
$187$	−21.2276	−1.55232
$188$	−2.58905	−0.188826
$189$	−8.79386	−0.639659
$190$	−1.47220	−0.106805
$191$	3.41301	0.246957	0.123479	−	0.992347i	$-0.460595\pi$
$191$	3.41301	0.246957	0.123479	+	0.992347i	$0.460595\pi$
$192$	−31.8831	−2.30097
$193$	−3.25634	−0.234396	−0.117198	−	0.993109i	$-0.537391\pi$
$193$	−3.25634	−0.234396	−0.117198	+	0.993109i	$0.537391\pi$
$194$	2.91748	0.209463
$195$	−0.281570	−0.0201636
$196$	27.3477	1.95340
$197$	−1.36227	−0.0970580	−0.0485290	−	0.998822i	$-0.515453\pi$
$197$	−1.36227	−0.0970580	−0.0485290	+	0.998822i	$0.515453\pi$
$198$	−19.1893	−1.36372
$199$	−19.5953	−1.38908	−0.694539	−	0.719455i	$-0.744392\pi$
$199$	−19.5953	−1.38908	−0.694539	+	0.719455i	$0.744392\pi$
$200$	40.1478	2.83888
$201$	22.4732	1.58514
$202$	−21.6372	−1.52239
$203$	3.52416	0.247347
$204$	61.1133	4.27878
$205$	−1.34901	−0.0942190
$206$	−8.96593	−0.624686
$207$	11.2480	0.781787
$208$	7.81124	0.541612
$209$	11.5488	0.798848
$210$	−3.83400	−0.264571
$211$	−10.1801	−0.700829	−0.350415	−	0.936595i	$-0.613959\pi$
$211$	−10.1801	−0.700829	−0.350415	+	0.936595i	$0.613959\pi$
$212$	−30.3532	−2.08467
$213$	−31.0603	−2.12822
$214$	6.85928	0.468891
$215$	−1.23786	−0.0844216
$216$	−20.1754	−1.37276
$217$	6.23596	0.423325
$218$	−30.5497	−2.06909
$219$	18.1169	1.22423
$220$	3.62480	0.244384
$221$	−3.77070	−0.253645
$222$	50.5870	3.39517
$223$	23.2535	1.55717	0.778584	−	0.627540i	$-0.215938\pi$
$223$	23.2535	1.55717	0.778584	+	0.627540i	$0.215938\pi$
$224$	49.3738	3.29893
$225$	−9.28138	−0.618758
$226$	21.6494	1.44010
$227$	−27.5776	−1.83039	−0.915196	−	0.403008i	$-0.867965\pi$
$227$	−27.5776	−1.83039	−0.915196	+	0.403008i	$0.867965\pi$
$228$	−33.2485	−2.20193
$229$	28.2876	1.86930	0.934649	−	0.355571i	$-0.115714\pi$
$229$	28.2876	1.86930	0.934649	+	0.355571i	$0.115714\pi$
$230$	−2.96684	−0.195628
$231$	30.0761	1.97886
$232$	8.08534	0.530829
$233$	13.5063	0.884830	0.442415	−	0.896810i	$-0.354122\pi$
$233$	13.5063	0.884830	0.442415	+	0.896810i	$0.354122\pi$
$234$	−3.40863	−0.222829
$235$	−0.0953001	−0.00621669
$236$	−7.63922	−0.497271
$237$	−2.89812	−0.188253
$238$	−51.3438	−3.32813
$239$	1.67778	0.108526	0.0542632	−	0.998527i	$-0.482719\pi$
$239$	1.67778	0.108526	0.0542632	+	0.998527i	$0.482719\pi$
$240$	−4.66000	−0.300802
$241$	1.73455	0.111732	0.0558661	−	0.998438i	$-0.482208\pi$
$241$	1.73455	0.111732	0.0558661	+	0.998438i	$0.482208\pi$
$242$	−10.5066	−0.675393
$243$	17.0378	1.09298
$244$	48.0435	3.07567
$245$	1.00664	0.0643117
$246$	−42.5417	−2.71236
$247$	2.05144	0.130530
$248$	14.3069	0.908491
$249$	−3.49787	−0.221669
$250$	4.91325	0.310741
$251$	0.148060	0.00934544	0.00467272	−	0.999989i	$-0.498513\pi$
$251$	0.148060	0.00934544	0.00467272	+	0.999989i	$0.498513\pi$
$252$	−33.2392	−2.09387
$253$	23.2736	1.46320
$254$	−22.3191	−1.40042
$255$	2.24951	0.140870
$256$	−1.46899	−0.0918117
$257$	26.8894	1.67732	0.838658	−	0.544658i	$-0.183340\pi$
$257$	26.8894	1.67732	0.838658	+	0.544658i	$0.183340\pi$
$258$	−39.0366	−2.43032
$259$	−30.4366	−1.89124
$260$	0.643879	0.0399317
$261$	−1.86917	−0.115699
$262$	−36.0410	−2.22662
$263$	15.5145	0.956666	0.478333	−	0.878179i	$-0.341241\pi$
$263$	15.5145	0.956666	0.478333	+	0.878179i	$0.341241\pi$
$264$	69.0025	4.24681
$265$	−1.11727	−0.0686332
$266$	27.9334	1.71271
$267$	1.05651	0.0646572
$268$	−51.3906	−3.13918
$269$	−14.7293	−0.898060	−0.449030	−	0.893517i	$-0.648230\pi$
$269$	−14.7293	−0.898060	−0.449030	+	0.893517i	$0.648230\pi$
$270$	−1.23025	−0.0748707
$271$	9.26580	0.562857	0.281429	−	0.959582i	$-0.409192\pi$
$271$	9.26580	0.562857	0.281429	+	0.959582i	$0.409192\pi$
$272$	−62.4054	−3.78388
$273$	5.34248	0.323342
$274$	−54.2264	−3.27594
$275$	−19.2045	−1.15807
$276$	−67.0036	−4.03314
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−0.685106	−0.0410899
$279$	−3.30748	−0.198014
$280$	5.29240	0.316281
$281$	27.1958	1.62237	0.811183	−	0.584792i	$-0.198824\pi$
$281$	27.1958	1.62237	0.811183	+	0.584792i	$0.198824\pi$
$282$	−3.00534	−0.178965
$283$	12.2090	0.725749	0.362874	−	0.931838i	$-0.381795\pi$
$283$	12.2090	0.725749	0.362874	+	0.931838i	$0.381795\pi$
$284$	71.0271	4.21468
$285$	−1.22384	−0.0724940
$286$	−7.05293	−0.417049
$287$	25.5960	1.51088
$288$	−26.1873	−1.54310
$289$	13.1248	0.772047
$290$	0.493026	0.0289515
$291$	2.42529	0.142173
$292$	−41.4288	−2.42443
$293$	8.51975	0.497729	0.248864	−	0.968538i	$-0.419943\pi$
$293$	8.51975	0.497729	0.248864	+	0.968538i	$0.419943\pi$
$294$	31.7448	1.85140
$295$	−0.281191	−0.0163716
$296$	−69.8294	−4.05875
$297$	9.65080	0.559996
$298$	37.6066	2.17849
$299$	4.13413	0.239083
$300$	55.2887	3.19210
$301$	23.4871	1.35377
$302$	23.3949	1.34622
$303$	−17.9869	−1.03332
$304$	33.9514	1.94725
$305$	1.76843	0.101260
$306$	27.2322	1.55676
$307$	−25.0774	−1.43125	−0.715623	−	0.698487i	$-0.753857\pi$
$307$	−25.0774	−1.43125	−0.715623	+	0.698487i	$0.753857\pi$
$308$	−68.7765	−3.91891
$309$	−7.45336	−0.424007
$310$	0.872404	0.0495492
$311$	11.7774	0.667835	0.333917	−	0.942602i	$-0.391629\pi$
$311$	11.7774	0.667835	0.333917	+	0.942602i	$0.391629\pi$
$312$	12.2570	0.693919
$313$	17.1139	0.967336	0.483668	−	0.875252i	$-0.339304\pi$
$313$	17.1139	0.967336	0.483668	+	0.875252i	$0.339304\pi$
$314$	−13.5170	−0.762807
$315$	−1.22350	−0.0689363
$316$	6.62727	0.372813
$317$	21.0637	1.18306	0.591528	−	0.806285i	$-0.298525\pi$
$317$	21.0637	1.18306	0.591528	+	0.806285i	$0.298525\pi$
$318$	−35.2336	−1.97580
$319$	−3.86758	−0.216543
$320$	2.68369	0.150023
$321$	5.70211	0.318261
$322$	56.2925	3.13706
$323$	−16.3893	−0.911925
$324$	−56.0796	−3.11553
$325$	−3.41133	−0.189226
$326$	57.6746	3.19430
$327$	−25.3959	−1.40440
$328$	58.7239	3.24249
$329$	1.80821	0.0996901
$330$	4.20762	0.231622
$331$	−2.60399	−0.143128	−0.0715641	−	0.997436i	$-0.522799\pi$
$331$	−2.60399	−0.143128	−0.0715641	+	0.997436i	$0.522799\pi$
$332$	7.99875	0.438989
$333$	16.1432	0.884642
$334$	35.0293	1.91672
$335$	−1.89163	−0.103351
$336$	88.4184	4.82362
$337$	27.9194	1.52087	0.760434	−	0.649415i	$-0.224986\pi$
$337$	27.9194	1.52087	0.760434	+	0.649415i	$0.224986\pi$
$338$	33.2547	1.80882
$339$	17.9971	0.977471
$340$	−5.14407	−0.278976
$341$	−6.84364	−0.370604
$342$	−14.8156	−0.801134
$343$	5.56926	0.300712
$344$	53.8856	2.90532
$345$	−2.46633	−0.132783
$346$	−56.2950	−3.02644
$347$	3.76005	0.201850	0.100925	−	0.994894i	$-0.467820\pi$
$347$	3.76005	0.201850	0.100925	+	0.994894i	$0.467820\pi$
$348$	11.1346	0.596875
$349$	24.9909	1.33773	0.668867	−	0.743382i	$-0.266779\pi$
$349$	24.9909	1.33773	0.668867	+	0.743382i	$0.266779\pi$
$350$	−46.4504	−2.48288
$351$	1.71429	0.0915020
$352$	−54.1852	−2.88808
$353$	−11.3515	−0.604182	−0.302091	−	0.953279i	$-0.597685\pi$
$353$	−11.3515	−0.604182	−0.302091	+	0.953279i	$0.597685\pi$
$354$	−8.86751	−0.471303
$355$	2.61443	0.138759
$356$	−2.41597	−0.128046
$357$	−42.6820	−2.25897
$358$	8.99781	0.475549
$359$	19.8585	1.04809	0.524046	−	0.851690i	$-0.324422\pi$
$359$	19.8585	1.04809	0.524046	+	0.851690i	$0.324422\pi$
$360$	−2.80702	−0.147943
$361$	−10.0835	−0.530708
$362$	35.0016	1.83964
$363$	−8.73415	−0.458424
$364$	−12.2169	−0.640340
$365$	−1.52495	−0.0798194
$366$	55.7682	2.91505
$367$	−5.20601	−0.271751	−0.135876	−	0.990726i	$-0.543385\pi$
$367$	−5.20601	−0.271751	−0.135876	+	0.990726i	$0.543385\pi$
$368$	68.4202	3.56665
$369$	−13.5758	−0.706729
$370$	−4.25804	−0.221365
$371$	21.1989	1.10059
$372$	19.7025	1.02153
$373$	−30.9825	−1.60421	−0.802105	−	0.597183i	$-0.796287\pi$
$373$	−30.9825	−1.60421	−0.802105	+	0.597183i	$0.796287\pi$
$374$	56.3471	2.91364
$375$	4.08437	0.210916
$376$	4.14852	0.213943
$377$	−0.687005	−0.0353826
$378$	23.3427	1.20062
$379$	22.6544	1.16368	0.581840	−	0.813304i	$-0.302333\pi$
$379$	22.6544	1.16368	0.581840	+	0.813304i	$0.302333\pi$
$380$	2.79861	0.143566
$381$	−18.5538	−0.950540
$382$	−9.05960	−0.463529
$383$	−10.8509	−0.554456	−0.277228	−	0.960804i	$-0.589416\pi$
$383$	−10.8509	−0.554456	−0.277228	+	0.960804i	$0.589416\pi$
$384$	22.8014	1.16358
$385$	−2.53159	−0.129022
$386$	8.64370	0.439953
$387$	−12.4573	−0.633239
$388$	−5.54603	−0.281557
$389$	29.9971	1.52091	0.760457	−	0.649388i	$-0.224975\pi$
$389$	29.9971	1.52091	0.760457	+	0.649388i	$0.224975\pi$
$390$	0.747407	0.0378464
$391$	−33.0283	−1.67031
$392$	−43.8200	−2.21325
$393$	−29.9608	−1.51132
$394$	3.61606	0.182174
$395$	0.243943	0.0122741
$396$	36.4783	1.83310
$397$	8.80216	0.441768	0.220884	−	0.975300i	$-0.429106\pi$
$397$	8.80216	0.441768	0.220884	+	0.975300i	$0.429106\pi$
$398$	52.0144	2.60725
$399$	23.2210	1.16250
$400$	−56.4577	−2.82288
$401$	7.91199	0.395106	0.197553	−	0.980292i	$-0.436701\pi$
$401$	7.91199	0.395106	0.197553	+	0.980292i	$0.436701\pi$
$402$	−59.6535	−2.97525
$403$	−1.21565	−0.0605558
$404$	41.1316	2.04637
$405$	−2.06423	−0.102572
$406$	−9.35462	−0.464262
$407$	33.4025	1.65570
$408$	−97.9237	−4.84795
$409$	−23.0601	−1.14025	−0.570125	−	0.821558i	$-0.693105\pi$
$409$	−23.0601	−1.14025	−0.570125	+	0.821558i	$0.693105\pi$
$410$	3.58085	0.176846
$411$	−45.0783	−2.22355
$412$	17.0440	0.839696
$413$	5.33530	0.262533
$414$	−29.8569	−1.46739
$415$	0.294425	0.0144528
$416$	−9.62502	−0.471905
$417$	−0.569527	−0.0278899
$418$	−30.6555	−1.49941
$419$	−5.90615	−0.288534	−0.144267	−	0.989539i	$-0.546082\pi$
$419$	−5.90615	−0.288534	−0.144267	+	0.989539i	$0.546082\pi$
$420$	7.28832	0.355634
$421$	−12.2024	−0.594711	−0.297355	−	0.954767i	$-0.596105\pi$
$421$	−12.2024	−0.594711	−0.297355	+	0.954767i	$0.596105\pi$
$422$	27.0224	1.31543
$423$	−0.959056	−0.0466309
$424$	48.6359	2.36197
$425$	27.2537	1.32200
$426$	82.4473	3.99458
$427$	−33.5540	−1.62379
$428$	−13.0393	−0.630278
$429$	−5.86309	−0.283073
$430$	3.28582	0.158456
$431$	−26.3884	−1.27108	−0.635542	−	0.772066i	$-0.719223\pi$
$431$	−26.3884	−1.27108	−0.635542	+	0.772066i	$0.719223\pi$
$432$	28.3716	1.36503
$433$	9.52155	0.457576	0.228788	−	0.973476i	$-0.426524\pi$
$433$	9.52155	0.457576	0.228788	+	0.973476i	$0.426524\pi$
$434$	−16.5529	−0.794565
$435$	0.409851	0.0196509
$436$	58.0740	2.78124
$437$	17.9690	0.859572
$438$	−48.0900	−2.29783
$439$	16.6026	0.792401	0.396200	−	0.918164i	$-0.370329\pi$
$439$	16.6026	0.792401	0.396200	+	0.918164i	$0.370329\pi$
$440$	−5.80813	−0.276892
$441$	10.1303	0.482397
$442$	10.0091	0.476082
$443$	−10.6449	−0.505754	−0.252877	−	0.967498i	$-0.581377\pi$
$443$	−10.6449	−0.505754	−0.252877	+	0.967498i	$0.581377\pi$
$444$	−96.1642	−4.56375
$445$	−0.0889291	−0.00421564
$446$	−61.7247	−2.92275
$447$	31.2623	1.47865
$448$	−50.9200	−2.40574
$449$	31.1159	1.46845	0.734225	−	0.678906i	$-0.237546\pi$
$449$	31.1159	1.46845	0.734225	+	0.678906i	$0.237546\pi$
$450$	24.6367	1.16139
$451$	−28.0903	−1.32272
$452$	−41.1549	−1.93577
$453$	19.4481	0.913752
$454$	73.2029	3.43558
$455$	−0.449691	−0.0210818
$456$	53.2751	2.49483
$457$	−23.2314	−1.08672	−0.543360	−	0.839500i	$-0.682848\pi$
$457$	−23.2314	−1.08672	−0.543360	+	0.839500i	$0.682848\pi$
$458$	−75.0874	−3.50860
$459$	−13.6958	−0.639264
$460$	5.63987	0.262960
$461$	−12.4512	−0.579908	−0.289954	−	0.957041i	$-0.593640\pi$
$461$	−12.4512	−0.579908	−0.289954	+	0.957041i	$0.593640\pi$
$462$	−79.8349	−3.71426
$463$	−4.60142	−0.213846	−0.106923	−	0.994267i	$-0.534100\pi$
$463$	−4.60142	−0.213846	−0.106923	+	0.994267i	$0.534100\pi$
$464$	−11.3700	−0.527838
$465$	0.725228	0.0336316
$466$	−35.8516	−1.66079
$467$	35.2881	1.63294	0.816469	−	0.577389i	$-0.195928\pi$
$467$	35.2881	1.63294	0.816469	+	0.577389i	$0.195928\pi$
$468$	6.47970	0.299524
$469$	35.8916	1.65732
$470$	0.252967	0.0116685
$471$	−11.2366	−0.517757
$472$	12.2406	0.563418
$473$	−25.7759	−1.18518
$474$	7.69285	0.353344
$475$	−14.8273	−0.680322
$476$	97.6030	4.47363
$477$	−11.2437	−0.514812
$478$	−4.45354	−0.203700
$479$	−3.15184	−0.144011	−0.0720056	−	0.997404i	$-0.522940\pi$
$479$	−3.15184	−0.144011	−0.0720056	+	0.997404i	$0.522940\pi$
$480$	5.74206	0.262088
$481$	5.93335	0.270538
$482$	−4.60424	−0.209717
$483$	46.7959	2.12929
$484$	19.9728	0.907855
$485$	−0.204143	−0.00926968
$486$	−45.2256	−2.05148
$487$	28.9530	1.31198	0.655992	−	0.754768i	$-0.272250\pi$
$487$	28.9530	1.31198	0.655992	+	0.754768i	$0.272250\pi$
$488$	−76.9816	−3.48479
$489$	47.9447	2.16814
$490$	−2.67205	−0.120711
$491$	23.2371	1.04867	0.524337	−	0.851511i	$-0.324313\pi$
$491$	23.2371	1.04867	0.524337	+	0.851511i	$0.324313\pi$
$492$	80.8705	3.64592
$493$	5.48861	0.247194
$494$	−5.44539	−0.245000
$495$	1.34272	0.0603510
$496$	−20.1191	−0.903373
$497$	−49.6059	−2.22513
$498$	9.28485	0.416064
$499$	−35.1151	−1.57197	−0.785984	−	0.618247i	$-0.787843\pi$
$499$	−35.1151	−1.57197	−0.785984	+	0.618247i	$0.787843\pi$
$500$	−9.33993	−0.417694
$501$	29.1198	1.30098
$502$	−0.393014	−0.0175411
$503$	−7.44433	−0.331926	−0.165963	−	0.986132i	$-0.553073\pi$
$503$	−7.44433	−0.331926	−0.165963	+	0.986132i	$0.553073\pi$
$504$	53.2602	2.37240
$505$	1.51401	0.0673726
$506$	−61.7781	−2.74637
$507$	27.6446	1.22774
$508$	42.4278	1.88243
$509$	−14.0540	−0.622934	−0.311467	−	0.950257i	$-0.600820\pi$
$509$	−14.0540	−0.622934	−0.311467	+	0.950257i	$0.600820\pi$
$510$	−5.97117	−0.264408
$511$	28.9342	1.27997
$512$	24.5657	1.08566
$513$	7.45114	0.328976
$514$	−71.3760	−3.14826
$515$	0.627370	0.0276452
$516$	74.2075	3.26680
$517$	−1.98442	−0.0872747
$518$	80.7916	3.54978
$519$	−46.7979	−2.05420
$520$	−1.03171	−0.0452434
$521$	11.5423	0.505676	0.252838	−	0.967509i	$-0.418636\pi$
$521$	11.5423	0.505676	0.252838	+	0.967509i	$0.418636\pi$
$522$	4.96158	0.217162
$523$	−30.5076	−1.33400	−0.667002	−	0.745056i	$-0.732423\pi$
$523$	−30.5076	−1.33400	−0.667002	+	0.745056i	$0.732423\pi$
$524$	68.5128	2.99300
$525$	−38.6141	−1.68526
$526$	−41.1822	−1.79563
$527$	9.71204	0.423063
$528$	−97.0346	−4.22289
$529$	13.2117	0.574422
$530$	2.96571	0.128822
$531$	−2.82978	−0.122802
$532$	−53.1006	−2.30220
$533$	−4.98973	−0.216129
$534$	−2.80442	−0.121359
$535$	−0.479962	−0.0207506
$536$	82.3448	3.55675
$537$	7.47986	0.322780
$538$	39.0978	1.68563
$539$	20.9611	0.902857
$540$	2.33867	0.100640
$541$	−13.1536	−0.565516	−0.282758	−	0.959191i	$-0.591249\pi$
$541$	−13.1536	−0.565516	−0.282758	+	0.959191i	$0.591249\pi$
$542$	−24.5954	−1.05646
$543$	29.0967	1.24866
$544$	76.8960	3.29689
$545$	2.13764	0.0915664
$546$	−14.1812	−0.606900
$547$	−20.1421	−0.861213	−0.430606	−	0.902540i	$-0.641700\pi$
$547$	−20.1421	−0.861213	−0.430606	+	0.902540i	$0.641700\pi$
$548$	103.083	4.40347
$549$	17.7966	0.759541
$550$	50.9769	2.17366
$551$	−2.98606	−0.127210
$552$	107.362	4.56963
$553$	−4.62854	−0.196826
$554$	2.65443	0.112776
$555$	−3.53970	−0.150252
$556$	1.30237	0.0552326
$557$	26.8864	1.13921	0.569607	−	0.821917i	$-0.307095\pi$
$557$	26.8864	1.13921	0.569607	+	0.821917i	$0.307095\pi$
$558$	8.77947	0.371665
$559$	−4.57862	−0.193655
$560$	−7.44242	−0.314499
$561$	46.8413	1.97764
$562$	−72.1893	−3.04512
$563$	−14.4221	−0.607820	−0.303910	−	0.952701i	$-0.598292\pi$
$563$	−14.4221	−0.607820	−0.303910	+	0.952701i	$0.598292\pi$
$564$	5.71305	0.240563
$565$	−1.51487	−0.0637310
$566$	−32.4079	−1.36220
$567$	39.1665	1.64484
$568$	−113.809	−4.77532
$569$	23.8407	0.999454	0.499727	−	0.866183i	$-0.333434\pi$
$569$	23.8407	0.999454	0.499727	+	0.866183i	$0.333434\pi$
$570$	3.24859	0.136069
$571$	−39.3078	−1.64498	−0.822489	−	0.568781i	$-0.807415\pi$
$571$	−39.3078	−1.64498	−0.822489	+	0.568781i	$0.807415\pi$
$572$	13.4074	0.560592
$573$	−7.53123	−0.314621
$574$	−67.9427	−2.83587
$575$	−29.8805	−1.24610
$576$	27.0074	1.12531
$577$	6.06488	0.252484	0.126242	−	0.991999i	$-0.459708\pi$
$577$	6.06488	0.252484	0.126242	+	0.991999i	$0.459708\pi$
$578$	−34.8388	−1.44910
$579$	7.18549	0.298619
$580$	−0.937226	−0.0389162
$581$	−5.58640	−0.231763
$582$	−6.43776	−0.266854
$583$	−23.2647	−0.963526
$584$	66.3826	2.74693
$585$	0.238511	0.00986121
$586$	−22.6150	−0.934219
$587$	−6.66495	−0.275092	−0.137546	−	0.990495i	$-0.543922\pi$
$587$	−6.66495	−0.275092	−0.137546	+	0.990495i	$0.543922\pi$
$588$	−60.3459	−2.48862
$589$	−5.28380	−0.217715
$590$	0.746402	0.0307289
$591$	3.00602	0.123651
$592$	98.1974	4.03589
$593$	−21.6373	−0.888539	−0.444269	−	0.895893i	$-0.646537\pi$
$593$	−21.6373	−0.888539	−0.444269	+	0.895893i	$0.646537\pi$
$594$	−25.6173	−1.05109
$595$	3.59266	0.147285
$596$	−71.4889	−2.92830
$597$	43.2395	1.76967
$598$	−10.9738	−0.448750
$599$	19.7994	0.808981	0.404490	−	0.914542i	$-0.367449\pi$
$599$	19.7994	0.808981	0.404490	+	0.914542i	$0.367449\pi$
$600$	−88.5909	−3.61671
$601$	−35.7827	−1.45961	−0.729804	−	0.683657i	$-0.760389\pi$
$601$	−35.7827	−1.45961	−0.729804	+	0.683657i	$0.760389\pi$
$602$	−62.3448	−2.54099
$603$	−19.0365	−0.775226
$604$	−44.4729	−1.80958
$605$	0.735177	0.0298892
$606$	47.7450	1.93951
$607$	0.0826529	0.00335478	0.00167739	−	0.999999i	$-0.499466\pi$
$607$	0.0826529	0.00335478	0.00167739	+	0.999999i	$0.499466\pi$
$608$	−41.8350	−1.69663
$609$	−7.77648	−0.315119
$610$	−4.69416	−0.190061
$611$	−0.352496	−0.0142605
$612$	−51.7675	−2.09258
$613$	−34.4076	−1.38971	−0.694854	−	0.719151i	$-0.744531\pi$
$613$	−34.4076	−1.38971	−0.694854	+	0.719151i	$0.744531\pi$
$614$	66.5663	2.68640
$615$	2.97675	0.120034
$616$	110.203	4.44020
$617$	36.3587	1.46375	0.731873	−	0.681442i	$-0.238647\pi$
$617$	36.3587	1.46375	0.731873	+	0.681442i	$0.238647\pi$
$618$	19.7844	0.795846
$619$	−0.116831	−0.00469582	−0.00234791	−	0.999997i	$-0.500747\pi$
$619$	−0.116831	−0.00469582	−0.00234791	+	0.999997i	$0.500747\pi$
$620$	−1.65841	−0.0666035
$621$	15.0158	0.602564
$622$	−31.2622	−1.25350
$623$	1.68733	0.0676015
$624$	−17.2364	−0.690009
$625$	24.4837	0.979349
$626$	−45.4277	−1.81565
$627$	−25.4838	−1.01773
$628$	25.6954	1.02536
$629$	−47.4026	−1.89007
$630$	3.24769	0.129391
$631$	12.3999	0.493633	0.246817	−	0.969062i	$-0.420615\pi$
$631$	12.3999	0.493633	0.246817	+	0.969062i	$0.420615\pi$
$632$	−10.6191	−0.422405
$633$	22.4637	0.892851
$634$	−55.9121	−2.22055
$635$	1.56172	0.0619751
$636$	66.9780	2.65585
$637$	3.72336	0.147525
$638$	10.2662	0.406443
$639$	26.3104	1.04082
$640$	−1.91926	−0.0758653
$641$	−9.58420	−0.378553	−0.189277	−	0.981924i	$-0.560614\pi$
$641$	−9.58420	−0.378553	−0.189277	+	0.981924i	$0.560614\pi$
$642$	−15.1358	−0.597364
$643$	−33.5027	−1.32122	−0.660609	−	0.750730i	$-0.729702\pi$
$643$	−33.5027	−1.32122	−0.660609	+	0.750730i	$0.729702\pi$
$644$	−107.010	−4.21680
$645$	2.73150	0.107553
$646$	43.5042	1.71165
$647$	−12.6467	−0.497195	−0.248597	−	0.968607i	$-0.579970\pi$
$647$	−12.6467	−0.497195	−0.248597	+	0.968607i	$0.579970\pi$
$648$	89.8582	3.52996
$649$	−5.85521	−0.229837
$650$	9.05511	0.355171
$651$	−13.7604	−0.539313
$652$	−109.638	−4.29374
$653$	−31.1725	−1.21987	−0.609937	−	0.792450i	$-0.708805\pi$
$653$	−31.1725	−1.21987	−0.609937	+	0.792450i	$0.708805\pi$
$654$	67.4115	2.63600
$655$	2.52188	0.0985381
$656$	−82.5803	−3.22422
$657$	−15.3464	−0.598718
$658$	−4.79977	−0.187115
$659$	−9.43742	−0.367630	−0.183815	−	0.982961i	$-0.558845\pi$
$659$	−9.43742	−0.367630	−0.183815	+	0.982961i	$0.558845\pi$
$660$	−7.99855	−0.311343
$661$	20.5862	0.800712	0.400356	−	0.916360i	$-0.368887\pi$
$661$	20.5862	0.800712	0.400356	+	0.916360i	$0.368887\pi$
$662$	6.91210	0.268647
$663$	8.32050	0.323142
$664$	−12.8167	−0.497383
$665$	−1.95458	−0.0757952
$666$	−42.8509	−1.66044
$667$	−6.01762	−0.233003
$668$	−66.5896	−2.57643
$669$	−51.3116	−1.98382
$670$	5.02120	0.193986
$671$	36.8237	1.42156
$672$	−108.949	−4.20281
$673$	−41.2312	−1.58934	−0.794672	−	0.607039i	$-0.792357\pi$
$673$	−41.2312	−1.58934	−0.794672	+	0.607039i	$0.792357\pi$
$674$	−74.1101	−2.85461
$675$	−12.3905	−0.476909
$676$	−63.2162	−2.43139
$677$	−26.9460	−1.03562	−0.517809	−	0.855496i	$-0.673252\pi$
$677$	−26.9460	−1.03562	−0.517809	+	0.855496i	$0.673252\pi$
$678$	−47.7721	−1.83468
$679$	3.87340	0.148647
$680$	8.24250	0.316086
$681$	60.8534	2.33191
$682$	18.1659	0.695610
$683$	21.4648	0.821328	0.410664	−	0.911787i	$-0.365297\pi$
$683$	21.4648	0.821328	0.410664	+	0.911787i	$0.365297\pi$
$684$	28.1639	1.07687
$685$	3.79436	0.144975
$686$	−14.7832	−0.564425
$687$	−62.4200	−2.38147
$688$	−75.7764	−2.88895
$689$	−4.13255	−0.157438
$690$	6.54669	0.249228
$691$	−35.5309	−1.35166	−0.675829	−	0.737059i	$-0.736214\pi$
$691$	−35.5309	−1.35166	−0.675829	+	0.737059i	$0.736214\pi$
$692$	107.015	4.06810
$693$	−25.4767	−0.967781
$694$	−9.98078	−0.378865
$695$	0.0479386	0.00181842
$696$	−17.8413	−0.676272
$697$	39.8638	1.50995
$698$	−66.3366	−2.51088
$699$	−29.8034	−1.12727
$700$	88.3007	3.33745
$701$	22.3776	0.845190	0.422595	−	0.906319i	$-0.361119\pi$
$701$	22.3776	0.845190	0.422595	+	0.906319i	$0.361119\pi$
$702$	−4.55046	−0.171746
$703$	25.7892	0.972660
$704$	55.8820	2.10613
$705$	0.210291	0.00792002
$706$	30.1319	1.13403
$707$	−28.7267	−1.08038
$708$	16.8569	0.633520
$709$	−14.9769	−0.562469	−0.281235	−	0.959639i	$-0.590744\pi$
$709$	−14.9769	−0.562469	−0.281235	+	0.959639i	$0.590744\pi$
$710$	−6.93981	−0.260446
$711$	2.45492	0.0920669
$712$	3.87118	0.145079
$713$	−10.6481	−0.398775
$714$	113.296	4.24001
$715$	0.493512	0.0184563
$716$	−17.1045	−0.639227
$717$	−3.70222	−0.138262
$718$	−52.7130	−1.96723
$719$	22.3739	0.834406	0.417203	−	0.908813i	$-0.363010\pi$
$719$	22.3739	0.834406	0.417203	+	0.908813i	$0.363010\pi$
$720$	3.94737	0.147110
$721$	−11.9036	−0.443315
$722$	26.7658	0.996120
$723$	−3.82750	−0.142346
$724$	−66.5369	−2.47282
$725$	4.96550	0.184414
$726$	23.1842	0.860445
$727$	−34.5377	−1.28093	−0.640467	−	0.767986i	$-0.721259\pi$
$727$	−34.5377	−1.28093	−0.640467	+	0.767986i	$0.721259\pi$
$728$	19.5755	0.725518
$729$	−4.25485	−0.157587
$730$	4.04786	0.149818
$731$	36.5794	1.35294
$732$	−106.014	−3.91838
$733$	7.23037	0.267060	0.133530	−	0.991045i	$-0.457369\pi$
$733$	7.23037	0.267060	0.133530	+	0.991045i	$0.457369\pi$
$734$	13.8190	0.510067
$735$	−2.22127	−0.0819327
$736$	−84.3075	−3.10761
$737$	−39.3892	−1.45092
$738$	36.0360	1.32650
$739$	−18.3469	−0.674900	−0.337450	−	0.941343i	$-0.609564\pi$
$739$	−18.3469	−0.674900	−0.337450	+	0.941343i	$0.609564\pi$
$740$	8.09440	0.297556
$741$	−4.52674	−0.166294
$742$	−56.2710	−2.06577
$743$	−24.8296	−0.910911	−0.455455	−	0.890259i	$-0.650524\pi$
$743$	−24.8296	−0.910911	−0.455455	+	0.890259i	$0.650524\pi$
$744$	−31.5700	−1.15741
$745$	−2.63143	−0.0964081
$746$	82.2407	3.01104
$747$	2.96296	0.108409
$748$	−107.114	−3.91648
$749$	9.10675	0.332753
$750$	−10.8417	−0.395882
$751$	−5.71904	−0.208691	−0.104345	−	0.994541i	$-0.533275\pi$
$751$	−5.71904	−0.208691	−0.104345	+	0.994541i	$0.533275\pi$
$752$	−5.83384	−0.212738
$753$	−0.326711	−0.0119060
$754$	1.82361	0.0664118
$755$	−1.63700	−0.0595765
$756$	−44.3737	−1.61386
$757$	11.8000	0.428878	0.214439	−	0.976737i	$-0.431208\pi$
$757$	11.8000	0.428878	0.214439	+	0.976737i	$0.431208\pi$
$758$	−60.1345	−2.18418
$759$	−51.3560	−1.86410
$760$	−4.48431	−0.162663
$761$	−29.4437	−1.06733	−0.533667	−	0.845695i	$-0.679186\pi$
$761$	−29.4437	−1.06733	−0.533667	+	0.845695i	$0.679186\pi$
$762$	49.2497	1.78413
$763$	−40.5594	−1.46835
$764$	17.2220	0.623071
$765$	−1.90550	−0.0688937
$766$	28.8030	1.04069
$767$	−1.04007	−0.0375548
$768$	3.24150	0.116967
$769$	−20.0466	−0.722899	−0.361450	−	0.932392i	$-0.617718\pi$
$769$	−20.0466	−0.722899	−0.361450	+	0.932392i	$0.617718\pi$
$770$	6.71992	0.242169
$771$	−59.3348	−2.13689
$772$	−16.4314	−0.591379
$773$	12.1668	0.437608	0.218804	−	0.975769i	$-0.429784\pi$
$773$	12.1668	0.437608	0.218804	+	0.975769i	$0.429784\pi$
$774$	33.0670	1.18857
$775$	8.78641	0.315617
$776$	8.88659	0.319010
$777$	67.1619	2.40942
$778$	−79.6252	−2.85470
$779$	−21.6878	−0.777045
$780$	−1.42080	−0.0508727
$781$	54.4399	1.94801
$782$	87.6713	3.13512
$783$	−2.49531	−0.0891750
$784$	61.6218	2.20078
$785$	0.945818	0.0337577
$786$	79.5288	2.83670
$787$	−0.950017	−0.0338644	−0.0169322	−	0.999857i	$-0.505390\pi$
$787$	−0.950017	−0.0338644	−0.0169322	+	0.999857i	$0.505390\pi$
$788$	−6.87401	−0.244877
$789$	−34.2346	−1.21879
$790$	−0.647528	−0.0230380
$791$	28.7430	1.02198
$792$	−58.4503	−2.07694
$793$	6.54106	0.232280
$794$	−23.3647	−0.829182
$795$	2.46539	0.0874382
$796$	−98.8778	−3.50463
$797$	9.83505	0.348375	0.174188	−	0.984712i	$-0.444270\pi$
$797$	9.83505	0.348375	0.174188	+	0.984712i	$0.444270\pi$
$798$	−61.6385	−2.18198
$799$	2.81616	0.0996284
$800$	69.5672	2.45957
$801$	−0.894940	−0.0316212
$802$	−21.0018	−0.741599
$803$	−31.7538	−1.12057
$804$	113.399	3.99929
$805$	−3.93893	−0.138829
$806$	3.22685	0.113661
$807$	32.5019	1.14412
$808$	−65.9065	−2.31858
$809$	−9.38230	−0.329864	−0.164932	−	0.986305i	$-0.552740\pi$
$809$	−9.38230	−0.329864	−0.164932	+	0.986305i	$0.552740\pi$
$810$	5.47935	0.192525
$811$	−31.9872	−1.12322	−0.561611	−	0.827401i	$-0.689818\pi$
$811$	−31.9872	−1.12322	−0.561611	+	0.827401i	$0.689818\pi$
$812$	17.7828	0.624055
$813$	−20.4461	−0.717076
$814$	−88.6646	−3.10769
$815$	−4.03564	−0.141362
$816$	137.705	4.82064
$817$	−19.9009	−0.696244
$818$	61.2115	2.14021
$819$	−4.52548	−0.158133
$820$	−6.80709	−0.237714
$821$	−4.79581	−0.167375	−0.0836875	−	0.996492i	$-0.526670\pi$
$821$	−4.79581	−0.167375	−0.0836875	+	0.996492i	$0.526670\pi$
$822$	119.657	4.17352
$823$	−7.28190	−0.253831	−0.126916	−	0.991914i	$-0.540508\pi$
$823$	−7.28190	−0.253831	−0.126916	+	0.991914i	$0.540508\pi$
$824$	−27.3101	−0.951392
$825$	42.3770	1.47538
$826$	−14.1622	−0.492765
$827$	44.9772	1.56401	0.782005	−	0.623272i	$-0.214197\pi$
$827$	44.9772	1.56401	0.782005	+	0.623272i	$0.214197\pi$
$828$	56.7570	1.97244
$829$	30.6167	1.06336	0.531681	−	0.846945i	$-0.321560\pi$
$829$	30.6167	1.06336	0.531681	+	0.846945i	$0.321560\pi$
$830$	−0.781531	−0.0271273
$831$	2.20662	0.0765468
$832$	9.92643	0.344137
$833$	−29.7465	−1.03066
$834$	1.51177	0.0523483
$835$	−2.45109	−0.0848234
$836$	58.2751	2.01549
$837$	−4.41542	−0.152619
$838$	15.6774	0.541568
$839$	−16.1153	−0.556363	−0.278182	−	0.960529i	$-0.589732\pi$
$839$	−16.1153	−0.556363	−0.278182	+	0.960529i	$0.589732\pi$
$840$	−11.6783	−0.402940
$841$	1.00000	0.0344828
$842$	32.3905	1.11625
$843$	−60.0108	−2.06688
$844$	−51.3688	−1.76819
$845$	−2.32692	−0.0800485
$846$	2.54574	0.0875245
$847$	−13.9492	−0.479299
$848$	−68.3941	−2.34866
$849$	−26.9406	−0.924599
$850$	−72.3429	−2.48134
$851$	51.9714	1.78156
$852$	−156.730	−5.36947
$853$	−52.1418	−1.78530	−0.892650	−	0.450750i	$-0.851157\pi$
$853$	−52.1418	−1.78530	−0.892650	+	0.450750i	$0.851157\pi$
$854$	89.0665	3.04779
$855$	1.03668	0.0354538
$856$	20.8933	0.714117
$857$	7.23788	0.247241	0.123621	−	0.992330i	$-0.460549\pi$
$857$	7.23788	0.247241	0.123621	+	0.992330i	$0.460549\pi$
$858$	15.5631	0.531317
$859$	−8.15290	−0.278173	−0.139087	−	0.990280i	$-0.544417\pi$
$859$	−8.15290	−0.278173	−0.139087	+	0.990280i	$0.544417\pi$
$860$	−6.24624	−0.212995
$861$	−56.4806	−1.92485
$862$	70.0460	2.38578
$863$	27.6982	0.942857	0.471428	−	0.881904i	$-0.343739\pi$
$863$	27.6982	0.942857	0.471428	+	0.881904i	$0.343739\pi$
$864$	−34.9595	−1.18935
$865$	3.93911	0.133934
$866$	−25.2743	−0.858854
$867$	−28.9614	−0.983582
$868$	31.4666	1.06805
$869$	5.07958	0.172313
$870$	−1.08792	−0.0368840
$871$	−6.99677	−0.237077
$872$	−93.0538	−3.15120
$873$	−2.05440	−0.0695310
$874$	−47.6973	−1.61338
$875$	6.52309	0.220521
$876$	91.4175	3.08871
$877$	15.8773	0.536138	0.268069	−	0.963400i	$-0.413614\pi$
$877$	15.8773	0.536138	0.268069	+	0.963400i	$0.413614\pi$
$878$	−44.0705	−1.48731
$879$	−18.7998	−0.634103
$880$	8.16766	0.275332
$881$	−54.4352	−1.83397	−0.916984	−	0.398924i	$-0.869384\pi$
$881$	−54.4352	−1.83397	−0.916984	+	0.398924i	$0.869384\pi$
$882$	−26.8902	−0.905441
$883$	43.9074	1.47760	0.738802	−	0.673923i	$-0.235392\pi$
$883$	43.9074	1.47760	0.738802	+	0.673923i	$0.235392\pi$
$884$	−19.0269	−0.639944
$885$	0.620482	0.0208573
$886$	28.2561	0.949282
$887$	36.9712	1.24137	0.620686	−	0.784059i	$-0.286854\pi$
$887$	36.9712	1.24137	0.620686	+	0.784059i	$0.286854\pi$
$888$	154.087	5.17082
$889$	−29.6320	−0.993824
$890$	0.236056	0.00791260
$891$	−42.9831	−1.43999
$892$	117.337	3.92872
$893$	−1.53212	−0.0512705
$894$	−82.9834	−2.77538
$895$	−0.629600	−0.0210452
$896$	36.4158	1.21657
$897$	−9.12246	−0.304590
$898$	−82.5949	−2.75623
$899$	1.76949	0.0590158
$900$	−46.8337	−1.56112
$901$	33.0157	1.09991
$902$	74.5635	2.48269
$903$	−51.8271	−1.72470
$904$	65.9439	2.19326
$905$	−2.44915	−0.0814125
$906$	−51.6236	−1.71508
$907$	21.2040	0.704066	0.352033	−	0.935988i	$-0.385490\pi$
$907$	21.2040	0.704066	0.352033	+	0.935988i	$0.385490\pi$
$908$	−139.156	−4.61807
$909$	15.2363	0.505356
$910$	1.19367	0.0395698
$911$	22.2794	0.738151	0.369076	−	0.929399i	$-0.379674\pi$
$911$	22.2794	0.738151	0.369076	+	0.929399i	$0.379674\pi$
$912$	−74.9179	−2.48078
$913$	6.13078	0.202899
$914$	61.6661	2.03973
$915$	−3.90225	−0.129004
$916$	142.739	4.71622
$917$	−47.8499	−1.58014
$918$	36.3544	1.19987
$919$	−0.0527560	−0.00174026	−0.000870130	−	1.00000i	$-0.500277\pi$
$919$	−0.0527560	−0.00174026	−0.000870130		1.00000i	$0.500277\pi$
$920$	−9.03694	−0.297939
$921$	55.3364	1.82340
$922$	33.0507	1.08847
$923$	9.67026	0.318300
$924$	151.764	4.99266
$925$	−42.8848	−1.41004
$926$	12.2141	0.401381
$927$	6.31355	0.207364
$928$	14.0101	0.459904
$929$	−54.3135	−1.78197	−0.890984	−	0.454035i	$-0.849984\pi$
$929$	−54.3135	−1.78197	−0.890984	+	0.454035i	$0.849984\pi$
$930$	−1.92506	−0.0631254
$931$	16.1835	0.530393
$932$	68.1528	2.23242
$933$	−25.9882	−0.850817
$934$	−93.6697	−3.06497
$935$	−3.94276	−0.128942
$936$	−10.3826	−0.339367
$937$	−12.6846	−0.414387	−0.207193	−	0.978300i	$-0.566433\pi$
$937$	−12.6846	−0.414387	−0.207193	+	0.978300i	$0.566433\pi$
$938$	−95.2717	−3.11073
$939$	−37.7639	−1.23238
$940$	−0.480883	−0.0156847
$941$	−23.8743	−0.778281	−0.389140	−	0.921178i	$-0.627228\pi$
$941$	−23.8743	−0.778281	−0.389140	+	0.921178i	$0.627228\pi$
$942$	29.8268	0.971811
$943$	−43.7060	−1.42326
$944$	−17.2133	−0.560244
$945$	−1.63335	−0.0531328
$946$	68.4202	2.22453
$947$	−5.74415	−0.186660	−0.0933300	−	0.995635i	$-0.529751\pi$
$947$	−5.74415	−0.186660	−0.0933300	+	0.995635i	$0.529751\pi$
$948$	−14.6239	−0.474961
$949$	−5.64048	−0.183098
$950$	39.3579	1.27694
$951$	−46.4796	−1.50720
$952$	−156.392	−5.06871
$953$	−58.8431	−1.90612	−0.953058	−	0.302789i	$-0.902082\pi$
$953$	−58.8431	−1.90612	−0.953058	+	0.302789i	$0.902082\pi$
$954$	29.8455	0.966283
$955$	0.633924	0.0205133
$956$	8.46603	0.273811
$957$	8.53427	0.275874
$958$	8.36633	0.270304
$959$	−71.9938	−2.32480
$960$	−5.92188	−0.191128
$961$	−27.8689	−0.898997
$962$	−15.7497	−0.507789
$963$	−4.83011	−0.155648
$964$	8.75252	0.281900
$965$	−0.604822	−0.0194699
$966$	−124.216	−3.99659
$967$	−35.3489	−1.13674	−0.568372	−	0.822772i	$-0.692426\pi$
$967$	−35.3489	−1.13674	−0.568372	+	0.822772i	$0.692426\pi$
$968$	−32.0031	−1.02862
$969$	36.1650	1.16179
$970$	0.541884	0.0173988
$971$	−32.2350	−1.03447	−0.517236	−	0.855843i	$-0.673039\pi$
$971$	−32.2350	−1.03447	−0.517236	+	0.855843i	$0.673039\pi$
$972$	85.9725	2.75757
$973$	−0.909583	−0.0291599
$974$	−76.8536	−2.46255
$975$	7.52750	0.241073
$976$	108.255	3.46516
$977$	15.8248	0.506279	0.253139	−	0.967430i	$-0.418537\pi$
$977$	15.8248	0.506279	0.253139	+	0.967430i	$0.418537\pi$
$978$	−127.266	−4.06951
$979$	−1.85176	−0.0591824
$980$	5.07948	0.162258
$981$	21.5122	0.686832
$982$	−61.6811	−1.96832
$983$	−45.5678	−1.45339	−0.726694	−	0.686961i	$-0.758944\pi$
$983$	−45.5678	−1.45339	−0.726694	+	0.686961i	$0.758944\pi$
$984$	−129.581	−4.13090
$985$	−0.253025	−0.00806204
$986$	−14.5691	−0.463975
$987$	−3.99004	−0.127004
$988$	10.3515	0.329326
$989$	−40.1050	−1.27527
$990$	−3.56416	−0.113277
$991$	−41.1709	−1.30784	−0.653918	−	0.756565i	$-0.726876\pi$
$991$	−41.1709	−1.30784	−0.653918	+	0.756565i	$0.726876\pi$
$992$	24.7908	0.787107
$993$	5.74602	0.182344
$994$	131.675	4.17649
$995$	−3.63958	−0.115383
$996$	−17.6502	−0.559268
$997$	28.3540	0.897981	0.448990	−	0.893537i	$-0.351784\pi$
$997$	28.3540	0.897981	0.448990	+	0.893537i	$0.351784\pi$
$998$	93.2105	2.95053
$999$	21.5509	0.681839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.3	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.3	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65443 q^{2} -2.20662 q^{3} +5.04598 q^{4} +0.185737 q^{5} +5.85731 q^{6} -3.52416 q^{7} -8.08534 q^{8} +1.86917 q^{9} +O(q^{10})\)	\(q-2.65443 q^{2} -2.20662 q^{3} +5.04598 q^{4} +0.185737 q^{5} +5.85731 q^{6} -3.52416 q^{7} -8.08534 q^{8} +1.86917 q^{9} -0.493026 q^{10} +3.86758 q^{11} -11.1346 q^{12} +0.687005 q^{13} +9.35462 q^{14} -0.409851 q^{15} +11.3700 q^{16} -5.48861 q^{17} -4.96158 q^{18} +2.98606 q^{19} +0.937226 q^{20} +7.77648 q^{21} -10.2662 q^{22} +6.01762 q^{23} +17.8413 q^{24} -4.96550 q^{25} -1.82361 q^{26} +2.49531 q^{27} -17.7828 q^{28} -1.00000 q^{29} +1.08792 q^{30} -1.76949 q^{31} -14.0101 q^{32} -8.53427 q^{33} +14.5691 q^{34} -0.654567 q^{35} +9.43181 q^{36} +8.63655 q^{37} -7.92627 q^{38} -1.51596 q^{39} -1.50175 q^{40} -7.26301 q^{41} -20.6421 q^{42} -6.66460 q^{43} +19.5157 q^{44} +0.347175 q^{45} -15.9733 q^{46} -0.513091 q^{47} -25.0892 q^{48} +5.41969 q^{49} +13.1806 q^{50} +12.1113 q^{51} +3.46662 q^{52} -6.01532 q^{53} -6.62361 q^{54} +0.718353 q^{55} +28.4940 q^{56} -6.58910 q^{57} +2.65443 q^{58} -1.51392 q^{59} -2.06810 q^{60} +9.52113 q^{61} +4.69698 q^{62} -6.58726 q^{63} +14.4488 q^{64} +0.127602 q^{65} +22.6536 q^{66} -10.1845 q^{67} -27.6954 q^{68} -13.2786 q^{69} +1.73750 q^{70} +14.0760 q^{71} -15.1129 q^{72} -8.21024 q^{73} -22.9251 q^{74} +10.9570 q^{75} +15.0676 q^{76} -13.6300 q^{77} +4.02400 q^{78} +1.31338 q^{79} +2.11183 q^{80} -11.1137 q^{81} +19.2791 q^{82} +1.58517 q^{83} +39.2400 q^{84} -1.01944 q^{85} +17.6907 q^{86} +2.20662 q^{87} -31.2707 q^{88} -0.478790 q^{89} -0.921550 q^{90} -2.42111 q^{91} +30.3648 q^{92} +3.90459 q^{93} +1.36196 q^{94} +0.554622 q^{95} +30.9150 q^{96} -1.09910 q^{97} -14.3862 q^{98} +7.22917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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