LMFDB - Embedded newform 6033.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38207 q^{2} +1.00000 q^{3} +3.67426 q^{4} -3.40207 q^{5} -2.38207 q^{6} +2.20870 q^{7} -3.98822 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38207 q^{2} +1.00000 q^{3} +3.67426 q^{4} -3.40207 q^{5} -2.38207 q^{6} +2.20870 q^{7} -3.98822 q^{8} +1.00000 q^{9} +8.10396 q^{10} +2.73993 q^{11} +3.67426 q^{12} -3.19286 q^{13} -5.26129 q^{14} -3.40207 q^{15} +2.15169 q^{16} -6.10538 q^{17} -2.38207 q^{18} +6.99358 q^{19} -12.5001 q^{20} +2.20870 q^{21} -6.52670 q^{22} +6.57298 q^{23} -3.98822 q^{24} +6.57405 q^{25} +7.60562 q^{26} +1.00000 q^{27} +8.11536 q^{28} +4.52261 q^{29} +8.10396 q^{30} +3.70127 q^{31} +2.85096 q^{32} +2.73993 q^{33} +14.5435 q^{34} -7.51415 q^{35} +3.67426 q^{36} +8.18575 q^{37} -16.6592 q^{38} -3.19286 q^{39} +13.5682 q^{40} -8.18505 q^{41} -5.26129 q^{42} +0.739971 q^{43} +10.0672 q^{44} -3.40207 q^{45} -15.6573 q^{46} -9.91389 q^{47} +2.15169 q^{48} -2.12163 q^{49} -15.6599 q^{50} -6.10538 q^{51} -11.7314 q^{52} -2.29526 q^{53} -2.38207 q^{54} -9.32141 q^{55} -8.80878 q^{56} +6.99358 q^{57} -10.7732 q^{58} -1.00891 q^{59} -12.5001 q^{60} -4.03018 q^{61} -8.81668 q^{62} +2.20870 q^{63} -11.0946 q^{64} +10.8623 q^{65} -6.52670 q^{66} +10.7693 q^{67} -22.4328 q^{68} +6.57298 q^{69} +17.8992 q^{70} +8.17783 q^{71} -3.98822 q^{72} -4.72401 q^{73} -19.4990 q^{74} +6.57405 q^{75} +25.6963 q^{76} +6.05169 q^{77} +7.60562 q^{78} +3.28856 q^{79} -7.32018 q^{80} +1.00000 q^{81} +19.4974 q^{82} +11.3211 q^{83} +8.11536 q^{84} +20.7709 q^{85} -1.76266 q^{86} +4.52261 q^{87} -10.9274 q^{88} -11.8352 q^{89} +8.10396 q^{90} -7.05207 q^{91} +24.1509 q^{92} +3.70127 q^{93} +23.6156 q^{94} -23.7926 q^{95} +2.85096 q^{96} +0.303612 q^{97} +5.05388 q^{98} +2.73993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.38207	−1.68438	−0.842189	−	0.539182i	$-0.818734\pi$
$2$	−2.38207	−1.68438	−0.842189	+	0.539182i	$0.818734\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.67426	1.83713
$5$	−3.40207	−1.52145	−0.760725	−	0.649074i	$-0.775156\pi$
$5$	−3.40207	−1.52145	−0.760725	+	0.649074i	$0.775156\pi$
$6$	−2.38207	−0.972477
$7$	2.20870	0.834811	0.417406	−	0.908720i	$-0.362939\pi$
$7$	2.20870	0.834811	0.417406	+	0.908720i	$0.362939\pi$
$8$	−3.98822	−1.41005
$9$	1.00000	0.333333
$10$	8.10396	2.56270
$11$	2.73993	0.826119	0.413060	−	0.910704i	$-0.364460\pi$
$11$	2.73993	0.826119	0.413060	+	0.910704i	$0.364460\pi$
$12$	3.67426	1.06067
$13$	−3.19286	−0.885539	−0.442770	−	0.896635i	$-0.646004\pi$
$13$	−3.19286	−0.885539	−0.442770	+	0.896635i	$0.646004\pi$
$14$	−5.26129	−1.40614
$15$	−3.40207	−0.878410
$16$	2.15169	0.537922
$17$	−6.10538	−1.48077	−0.740386	−	0.672182i	$-0.765357\pi$
$17$	−6.10538	−1.48077	−0.740386	+	0.672182i	$0.765357\pi$
$18$	−2.38207	−0.561460
$19$	6.99358	1.60444	0.802219	−	0.597030i	$-0.203653\pi$
$19$	6.99358	1.60444	0.802219	+	0.597030i	$0.203653\pi$
$20$	−12.5001	−2.79510
$21$	2.20870	0.481978
$22$	−6.52670	−1.39150
$23$	6.57298	1.37056	0.685281	−	0.728279i	$-0.259679\pi$
$23$	6.57298	1.37056	0.685281	+	0.728279i	$0.259679\pi$
$24$	−3.98822	−0.814091
$25$	6.57405	1.31481
$26$	7.60562	1.49158
$27$	1.00000	0.192450
$28$	8.11536	1.53366
$29$	4.52261	0.839828	0.419914	−	0.907564i	$-0.362060\pi$
$29$	4.52261	0.839828	0.419914	+	0.907564i	$0.362060\pi$
$30$	8.10396	1.47957
$31$	3.70127	0.664767	0.332384	−	0.943144i	$-0.392147\pi$
$31$	3.70127	0.664767	0.332384	+	0.943144i	$0.392147\pi$
$32$	2.85096	0.503983
$33$	2.73993	0.476960
$34$	14.5435	2.49418
$35$	−7.51415	−1.27012
$36$	3.67426	0.612377
$37$	8.18575	1.34573	0.672865	−	0.739766i	$-0.265064\pi$
$37$	8.18575	1.34573	0.672865	+	0.739766i	$0.265064\pi$
$38$	−16.6592	−2.70248
$39$	−3.19286	−0.511266
$40$	13.5682	2.14532
$41$	−8.18505	−1.27829	−0.639145	−	0.769086i	$-0.720712\pi$
$41$	−8.18505	−1.27829	−0.639145	+	0.769086i	$0.720712\pi$
$42$	−5.26129	−0.811834
$43$	0.739971	0.112844	0.0564222	−	0.998407i	$-0.482031\pi$
$43$	0.739971	0.112844	0.0564222	+	0.998407i	$0.482031\pi$
$44$	10.0672	1.51769
$45$	−3.40207	−0.507150
$46$	−15.6573	−2.30855
$47$	−9.91389	−1.44609	−0.723044	−	0.690801i	$-0.757258\pi$
$47$	−9.91389	−1.44609	−0.723044	+	0.690801i	$0.757258\pi$
$48$	2.15169	0.310569
$49$	−2.12163	−0.303090
$50$	−15.6599	−2.21464
$51$	−6.10538	−0.854924
$52$	−11.7314	−1.62685
$53$	−2.29526	−0.315278	−0.157639	−	0.987497i	$-0.550388\pi$
$53$	−2.29526	−0.315278	−0.157639	+	0.987497i	$0.550388\pi$
$54$	−2.38207	−0.324159
$55$	−9.32141	−1.25690
$56$	−8.80878	−1.17712
$57$	6.99358	0.926322
$58$	−10.7732	−1.41459
$59$	−1.00891	−0.131349	−0.0656747	−	0.997841i	$-0.520920\pi$
$59$	−1.00891	−0.131349	−0.0656747	+	0.997841i	$0.520920\pi$
$60$	−12.5001	−1.61375
$61$	−4.03018	−0.516012	−0.258006	−	0.966143i	$-0.583065\pi$
$61$	−4.03018	−0.516012	−0.258006	+	0.966143i	$0.583065\pi$
$62$	−8.81668	−1.11972
$63$	2.20870	0.278270
$64$	−11.0946	−1.38682
$65$	10.8623	1.34730
$66$	−6.52670	−0.803382
$67$	10.7693	1.31568	0.657842	−	0.753156i	$-0.271469\pi$
$67$	10.7693	1.31568	0.657842	+	0.753156i	$0.271469\pi$
$68$	−22.4328	−2.72037
$69$	6.57298	0.791294
$70$	17.8992	2.13937
$71$	8.17783	0.970530	0.485265	−	0.874367i	$-0.338723\pi$
$71$	8.17783	0.970530	0.485265	+	0.874367i	$0.338723\pi$
$72$	−3.98822	−0.470016
$73$	−4.72401	−0.552904	−0.276452	−	0.961028i	$-0.589159\pi$
$73$	−4.72401	−0.552904	−0.276452	+	0.961028i	$0.589159\pi$
$74$	−19.4990	−2.26672
$75$	6.57405	0.759106
$76$	25.6963	2.94756
$77$	6.05169	0.689654
$78$	7.60562	0.861166
$79$	3.28856	0.369992	0.184996	−	0.982739i	$-0.440773\pi$
$79$	3.28856	0.369992	0.184996	+	0.982739i	$0.440773\pi$
$80$	−7.32018	−0.818421
$81$	1.00000	0.111111
$82$	19.4974	2.15313
$83$	11.3211	1.24265	0.621325	−	0.783553i	$-0.286594\pi$
$83$	11.3211	1.24265	0.621325	+	0.783553i	$0.286594\pi$
$84$	8.11536	0.885458
$85$	20.7709	2.25292
$86$	−1.76266	−0.190073
$87$	4.52261	0.484875
$88$	−10.9274	−1.16487
$89$	−11.8352	−1.25453	−0.627266	−	0.778805i	$-0.715826\pi$
$89$	−11.8352	−1.25453	−0.627266	+	0.778805i	$0.715826\pi$
$90$	8.10396	0.854233
$91$	−7.05207	−0.739258
$92$	24.1509	2.51790
$93$	3.70127	0.383804
$94$	23.6156	2.43576
$95$	−23.7926	−2.44107
$96$	2.85096	0.290975
$97$	0.303612	0.0308272	0.0154136	−	0.999881i	$-0.495094\pi$
$97$	0.303612	0.0308272	0.0154136	+	0.999881i	$0.495094\pi$
$98$	5.05388	0.510519
$99$	2.73993	0.275373
$100$	24.1548	2.41548
$101$	−3.12654	−0.311102	−0.155551	−	0.987828i	$-0.549715\pi$
$101$	−3.12654	−0.311102	−0.155551	+	0.987828i	$0.549715\pi$
$102$	14.5435	1.44002
$103$	−4.59439	−0.452699	−0.226349	−	0.974046i	$-0.572679\pi$
$103$	−4.59439	−0.452699	−0.226349	+	0.974046i	$0.572679\pi$
$104$	12.7338	1.24865
$105$	−7.51415	−0.733306
$106$	5.46747	0.531048
$107$	9.92362	0.959353	0.479676	−	0.877445i	$-0.340754\pi$
$107$	9.92362	0.959353	0.479676	+	0.877445i	$0.340754\pi$
$108$	3.67426	0.353556
$109$	−13.1655	−1.26103	−0.630513	−	0.776179i	$-0.717155\pi$
$109$	−13.1655	−1.26103	−0.630513	+	0.776179i	$0.717155\pi$
$110$	22.2043	2.11709
$111$	8.18575	0.776957
$112$	4.75244	0.449063
$113$	9.52435	0.895975	0.447988	−	0.894040i	$-0.352141\pi$
$113$	9.52435	0.895975	0.447988	+	0.894040i	$0.352141\pi$
$114$	−16.6592	−1.56028
$115$	−22.3617	−2.08524
$116$	16.6173	1.54288
$117$	−3.19286	−0.295180
$118$	2.40331	0.221242
$119$	−13.4850	−1.23617
$120$	13.5682	1.23860
$121$	−3.49279	−0.317527
$122$	9.60017	0.869159
$123$	−8.18505	−0.738022
$124$	13.5994	1.22127
$125$	−5.35502	−0.478968
$126$	−5.26129	−0.468713
$127$	16.4966	1.46384	0.731920	−	0.681390i	$-0.238624\pi$
$127$	16.4966	1.46384	0.731920	+	0.681390i	$0.238624\pi$
$128$	20.7261	1.83195
$129$	0.739971	0.0651508
$130$	−25.8748	−2.26937
$131$	−10.8120	−0.944646	−0.472323	−	0.881425i	$-0.656584\pi$
$131$	−10.8120	−0.944646	−0.472323	+	0.881425i	$0.656584\pi$
$132$	10.0672	0.876239
$133$	15.4467	1.33940
$134$	−25.6533	−2.21611
$135$	−3.40207	−0.292803
$136$	24.3496	2.08796
$137$	−0.753253	−0.0643548	−0.0321774	−	0.999482i	$-0.510244\pi$
$137$	−0.753253	−0.0643548	−0.0321774	+	0.999482i	$0.510244\pi$
$138$	−15.6573	−1.33284
$139$	11.9964	1.01752	0.508759	−	0.860909i	$-0.330104\pi$
$139$	11.9964	1.01752	0.508759	+	0.860909i	$0.330104\pi$
$140$	−27.6090	−2.33338
$141$	−9.91389	−0.834900
$142$	−19.4802	−1.63474
$143$	−8.74820	−0.731561
$144$	2.15169	0.179307
$145$	−15.3862	−1.27776
$146$	11.2529	0.931299
$147$	−2.12163	−0.174989
$148$	30.0766	2.47228
$149$	−18.0637	−1.47984	−0.739919	−	0.672696i	$-0.765136\pi$
$149$	−18.0637	−1.47984	−0.739919	+	0.672696i	$0.765136\pi$
$150$	−15.6599	−1.27862
$151$	17.6993	1.44035	0.720175	−	0.693793i	$-0.244062\pi$
$151$	17.6993	1.44035	0.720175	+	0.693793i	$0.244062\pi$
$152$	−27.8919	−2.26233
$153$	−6.10538	−0.493591
$154$	−14.4155	−1.16164
$155$	−12.5920	−1.01141
$156$	−11.7314	−0.939264
$157$	11.5436	0.921277	0.460638	−	0.887588i	$-0.347620\pi$
$157$	11.5436	0.921277	0.460638	+	0.887588i	$0.347620\pi$
$158$	−7.83359	−0.623207
$159$	−2.29526	−0.182026
$160$	−9.69915	−0.766785
$161$	14.5178	1.14416
$162$	−2.38207	−0.187153
$163$	3.40393	0.266616	0.133308	−	0.991075i	$-0.457440\pi$
$163$	3.40393	0.266616	0.133308	+	0.991075i	$0.457440\pi$
$164$	−30.0741	−2.34839
$165$	−9.32141	−0.725671
$166$	−26.9676	−2.09309
$167$	18.2451	1.41185	0.705924	−	0.708288i	$-0.250532\pi$
$167$	18.2451	1.41185	0.705924	+	0.708288i	$0.250532\pi$
$168$	−8.80878	−0.679612
$169$	−2.80566	−0.215820
$170$	−49.4778	−3.79477
$171$	6.99358	0.534813
$172$	2.71885	0.207310
$173$	14.7282	1.11977	0.559883	−	0.828571i	$-0.310846\pi$
$173$	14.7282	1.11977	0.559883	+	0.828571i	$0.310846\pi$
$174$	−10.7732	−0.816713
$175$	14.5201	1.09762
$176$	5.89547	0.444388
$177$	−1.00891	−0.0758347
$178$	28.1924	2.11311
$179$	−4.40330	−0.329118	−0.164559	−	0.986367i	$-0.552620\pi$
$179$	−4.40330	−0.329118	−0.164559	+	0.986367i	$0.552620\pi$
$180$	−12.5001	−0.931701
$181$	−14.4972	−1.07757	−0.538785	−	0.842443i	$-0.681117\pi$
$181$	−14.4972	−1.07757	−0.538785	+	0.842443i	$0.681117\pi$
$182$	16.7985	1.24519
$183$	−4.03018	−0.297919
$184$	−26.2145	−1.93256
$185$	−27.8485	−2.04746
$186$	−8.81668	−0.646471
$187$	−16.7283	−1.22329
$188$	−36.4262	−2.65666
$189$	2.20870	0.160659
$190$	56.6757	4.11169
$191$	−12.6675	−0.916588	−0.458294	−	0.888801i	$-0.651539\pi$
$191$	−12.6675	−0.916588	−0.458294	+	0.888801i	$0.651539\pi$
$192$	−11.0946	−0.800681
$193$	1.58860	0.114350	0.0571750	−	0.998364i	$-0.481791\pi$
$193$	1.58860	0.114350	0.0571750	+	0.998364i	$0.481791\pi$
$194$	−0.723226	−0.0519246
$195$	10.8623	0.777866
$196$	−7.79544	−0.556817
$197$	−10.0763	−0.717905	−0.358953	−	0.933356i	$-0.616866\pi$
$197$	−10.0763	−0.717905	−0.358953	+	0.933356i	$0.616866\pi$
$198$	−6.52670	−0.463833
$199$	−7.68834	−0.545012	−0.272506	−	0.962154i	$-0.587852\pi$
$199$	−7.68834	−0.545012	−0.272506	+	0.962154i	$0.587852\pi$
$200$	−26.2187	−1.85394
$201$	10.7693	0.759610
$202$	7.44763	0.524014
$203$	9.98911	0.701098
$204$	−22.4328	−1.57061
$205$	27.8461	1.94486
$206$	10.9442	0.762516
$207$	6.57298	0.456854
$208$	−6.87003	−0.476351
$209$	19.1619	1.32546
$210$	17.8992	1.23517
$211$	−12.5153	−0.861590	−0.430795	−	0.902450i	$-0.641767\pi$
$211$	−12.5153	−0.861590	−0.430795	+	0.902450i	$0.641767\pi$
$212$	−8.43339	−0.579207
$213$	8.17783	0.560336
$214$	−23.6388	−1.61591
$215$	−2.51743	−0.171687
$216$	−3.98822	−0.271364
$217$	8.17500	0.554955
$218$	31.3612	2.12405
$219$	−4.72401	−0.319219
$220$	−34.2493	−2.30909
$221$	19.4936	1.31128
$222$	−19.4990	−1.30869
$223$	−1.94232	−0.130068	−0.0650338	−	0.997883i	$-0.520716\pi$
$223$	−1.94232	−0.130068	−0.0650338	+	0.997883i	$0.520716\pi$
$224$	6.29692	0.420731
$225$	6.57405	0.438270
$226$	−22.6877	−1.50916
$227$	9.54709	0.633663	0.316831	−	0.948482i	$-0.397381\pi$
$227$	9.54709	0.633663	0.316831	+	0.948482i	$0.397381\pi$
$228$	25.6963	1.70178
$229$	−6.70824	−0.443293	−0.221646	−	0.975127i	$-0.571143\pi$
$229$	−6.70824	−0.443293	−0.221646	+	0.975127i	$0.571143\pi$
$230$	53.2672	3.51234
$231$	6.05169	0.398172
$232$	−18.0372	−1.18420
$233$	−15.8281	−1.03693	−0.518467	−	0.855098i	$-0.673497\pi$
$233$	−15.8281	−1.03693	−0.518467	+	0.855098i	$0.673497\pi$
$234$	7.60562	0.497195
$235$	33.7277	2.20015
$236$	−3.70702	−0.241306
$237$	3.28856	0.213615
$238$	32.1222	2.08217
$239$	13.9717	0.903755	0.451878	−	0.892080i	$-0.350754\pi$
$239$	13.9717	0.903755	0.451878	+	0.892080i	$0.350754\pi$
$240$	−7.32018	−0.472516
$241$	24.1219	1.55383	0.776914	−	0.629607i	$-0.216784\pi$
$241$	24.1219	1.55383	0.776914	+	0.629607i	$0.216784\pi$
$242$	8.32009	0.534835
$243$	1.00000	0.0641500
$244$	−14.8079	−0.947981
$245$	7.21794	0.461137
$246$	19.4974	1.24311
$247$	−22.3295	−1.42079
$248$	−14.7615	−0.937353
$249$	11.3211	0.717445
$250$	12.7560	0.806763
$251$	−18.7613	−1.18421	−0.592103	−	0.805863i	$-0.701702\pi$
$251$	−18.7613	−1.18421	−0.592103	+	0.805863i	$0.701702\pi$
$252$	8.11536	0.511219
$253$	18.0095	1.13225
$254$	−39.2962	−2.46566
$255$	20.7709	1.30072
$256$	−27.1820	−1.69887
$257$	26.7593	1.66920	0.834600	−	0.550857i	$-0.185699\pi$
$257$	26.7593	1.66920	0.834600	+	0.550857i	$0.185699\pi$
$258$	−1.76266	−0.109739
$259$	18.0799	1.12343
$260$	39.9110	2.47518
$261$	4.52261	0.279943
$262$	25.7549	1.59114
$263$	−3.10313	−0.191347	−0.0956737	−	0.995413i	$-0.530501\pi$
$263$	−3.10313	−0.191347	−0.0956737	+	0.995413i	$0.530501\pi$
$264$	−10.9274	−0.672536
$265$	7.80862	0.479680
$266$	−36.7952	−2.25606
$267$	−11.8352	−0.724304
$268$	39.5694	2.41708
$269$	19.8618	1.21100	0.605499	−	0.795846i	$-0.292974\pi$
$269$	19.8618	1.21100	0.605499	+	0.795846i	$0.292974\pi$
$270$	8.10396	0.493191
$271$	−30.9211	−1.87832	−0.939160	−	0.343480i	$-0.888394\pi$
$271$	−30.9211	−1.87832	−0.939160	+	0.343480i	$0.888394\pi$
$272$	−13.1369	−0.796540
$273$	−7.05207	−0.426811
$274$	1.79430	0.108398
$275$	18.0124	1.08619
$276$	24.1509	1.45371
$277$	−10.8137	−0.649733	−0.324867	−	0.945760i	$-0.605319\pi$
$277$	−10.8137	−0.649733	−0.324867	+	0.945760i	$0.605319\pi$
$278$	−28.5762	−1.71389
$279$	3.70127	0.221589
$280$	29.9681	1.79093
$281$	8.09905	0.483149	0.241574	−	0.970382i	$-0.422336\pi$
$281$	8.09905	0.483149	0.241574	+	0.970382i	$0.422336\pi$
$282$	23.6156	1.40629
$283$	6.87657	0.408770	0.204385	−	0.978891i	$-0.434481\pi$
$283$	6.87657	0.408770	0.204385	+	0.978891i	$0.434481\pi$
$284$	30.0475	1.78299
$285$	−23.7926	−1.40935
$286$	20.8388	1.23223
$287$	−18.0784	−1.06713
$288$	2.85096	0.167994
$289$	20.2757	1.19269
$290$	36.6511	2.15223
$291$	0.303612	0.0177981
$292$	−17.3573	−1.01576
$293$	8.29429	0.484557	0.242279	−	0.970207i	$-0.422105\pi$
$293$	8.29429	0.484557	0.242279	+	0.970207i	$0.422105\pi$
$294$	5.05388	0.294748
$295$	3.43239	0.199842
$296$	−32.6465	−1.89754
$297$	2.73993	0.158987
$298$	43.0291	2.49261
$299$	−20.9866	−1.21369
$300$	24.1548	1.39458
$301$	1.63438	0.0942038
$302$	−42.1610	−2.42609
$303$	−3.12654	−0.179615
$304$	15.0480	0.863062
$305$	13.7109	0.785086
$306$	14.5435	0.831394
$307$	−14.3917	−0.821380	−0.410690	−	0.911775i	$-0.634712\pi$
$307$	−14.3917	−0.821380	−0.410690	+	0.911775i	$0.634712\pi$
$308$	22.2355	1.26698
$309$	−4.59439	−0.261366
$310$	29.9949	1.70360
$311$	−25.1416	−1.42565	−0.712823	−	0.701343i	$-0.752584\pi$
$311$	−25.1416	−1.42565	−0.712823	+	0.701343i	$0.752584\pi$
$312$	12.7338	0.720910
$313$	21.0681	1.19084	0.595418	−	0.803416i	$-0.296986\pi$
$313$	21.0681	1.19084	0.595418	+	0.803416i	$0.296986\pi$
$314$	−27.4976	−1.55178
$315$	−7.51415	−0.423374
$316$	12.0831	0.679725
$317$	−28.7332	−1.61382	−0.806908	−	0.590677i	$-0.798861\pi$
$317$	−28.7332	−1.61382	−0.806908	+	0.590677i	$0.798861\pi$
$318$	5.46747	0.306600
$319$	12.3916	0.693798
$320$	37.7444	2.10998
$321$	9.92362	0.553883
$322$	−34.5824	−1.92720
$323$	−42.6985	−2.37581
$324$	3.67426	0.204126
$325$	−20.9900	−1.16432
$326$	−8.10841	−0.449083
$327$	−13.1655	−0.728054
$328$	32.6438	1.80245
$329$	−21.8968	−1.20721
$330$	22.2043	1.22231
$331$	18.1533	0.997794	0.498897	−	0.866661i	$-0.333739\pi$
$331$	18.1533	0.997794	0.498897	+	0.866661i	$0.333739\pi$
$332$	41.5967	2.28291
$333$	8.18575	0.448576
$334$	−43.4611	−2.37809
$335$	−36.6380	−2.00175
$336$	4.75244	0.259267
$337$	20.5662	1.12031	0.560156	−	0.828387i	$-0.310741\pi$
$337$	20.5662	1.12031	0.560156	+	0.828387i	$0.310741\pi$
$338$	6.68328	0.363522
$339$	9.52435	0.517291
$340$	76.3178	4.13891
$341$	10.1412	0.549177
$342$	−16.6592	−0.900827
$343$	−20.1470	−1.08783
$344$	−2.95116	−0.159116
$345$	−22.3617	−1.20391
$346$	−35.0837	−1.88611
$347$	17.6923	0.949773	0.474887	−	0.880047i	$-0.342489\pi$
$347$	17.6923	0.949773	0.474887	+	0.880047i	$0.342489\pi$
$348$	16.6173	0.890779
$349$	23.0338	1.23297	0.616485	−	0.787367i	$-0.288556\pi$
$349$	23.0338	1.23297	0.616485	+	0.787367i	$0.288556\pi$
$350$	−34.5880	−1.84880
$351$	−3.19286	−0.170422
$352$	7.81143	0.416350
$353$	20.7462	1.10421	0.552105	−	0.833775i	$-0.313825\pi$
$353$	20.7462	1.10421	0.552105	+	0.833775i	$0.313825\pi$
$354$	2.40331	0.127734
$355$	−27.8215	−1.47661
$356$	−43.4858	−2.30474
$357$	−13.4850	−0.713700
$358$	10.4890	0.554359
$359$	13.6899	0.722525	0.361263	−	0.932464i	$-0.382346\pi$
$359$	13.6899	0.722525	0.361263	+	0.932464i	$0.382346\pi$
$360$	13.5682	0.715105
$361$	29.9102	1.57422
$362$	34.5334	1.81504
$363$	−3.49279	−0.183324
$364$	−25.9112	−1.35811
$365$	16.0714	0.841215
$366$	9.60017	0.501809
$367$	−17.6928	−0.923556	−0.461778	−	0.886996i	$-0.652788\pi$
$367$	−17.6928	−0.923556	−0.461778	+	0.886996i	$0.652788\pi$
$368$	14.1430	0.737255
$369$	−8.18505	−0.426097
$370$	66.3370	3.44870
$371$	−5.06954	−0.263198
$372$	13.5994	0.705098
$373$	−3.14795	−0.162995	−0.0814975	−	0.996674i	$-0.525970\pi$
$373$	−3.14795	−0.162995	−0.0814975	+	0.996674i	$0.525970\pi$
$374$	39.8480	2.06049
$375$	−5.35502	−0.276532
$376$	39.5387	2.03905
$377$	−14.4401	−0.743701
$378$	−5.26129	−0.270611
$379$	−30.2466	−1.55366	−0.776831	−	0.629710i	$-0.783174\pi$
$379$	−30.2466	−1.55366	−0.776831	+	0.629710i	$0.783174\pi$
$380$	−87.4204	−4.48457
$381$	16.4966	0.845149
$382$	30.1749	1.54388
$383$	33.9271	1.73359	0.866796	−	0.498662i	$-0.166175\pi$
$383$	33.9271	1.73359	0.866796	+	0.498662i	$0.166175\pi$
$384$	20.7261	1.05768
$385$	−20.5882	−1.04927
$386$	−3.78416	−0.192609
$387$	0.739971	0.0376148
$388$	1.11555	0.0566336
$389$	−0.0988699	−0.00501290	−0.00250645	−	0.999997i	$-0.500798\pi$
$389$	−0.0988699	−0.00501290	−0.00250645	+	0.999997i	$0.500798\pi$
$390$	−25.8748	−1.31022
$391$	−40.1306	−2.02949
$392$	8.46153	0.427372
$393$	−10.8120	−0.545392
$394$	24.0024	1.20922
$395$	−11.1879	−0.562925
$396$	10.0672	0.505897
$397$	22.7529	1.14193	0.570967	−	0.820973i	$-0.306568\pi$
$397$	22.7529	1.14193	0.570967	+	0.820973i	$0.306568\pi$
$398$	18.3142	0.918007
$399$	15.4467	0.773304
$400$	14.1453	0.707265
$401$	−14.6641	−0.732291	−0.366146	−	0.930558i	$-0.619323\pi$
$401$	−14.6641	−0.732291	−0.366146	+	0.930558i	$0.619323\pi$
$402$	−25.6533	−1.27947
$403$	−11.8176	−0.588678
$404$	−11.4877	−0.571535
$405$	−3.40207	−0.169050
$406$	−23.7948	−1.18091
$407$	22.4284	1.11173
$408$	24.3496	1.20548
$409$	−39.2586	−1.94121	−0.970607	−	0.240672i	$-0.922632\pi$
$409$	−39.2586	−1.94121	−0.970607	+	0.240672i	$0.922632\pi$
$410$	−66.3314	−3.27587
$411$	−0.753253	−0.0371553
$412$	−16.8810	−0.831668
$413$	−2.22839	−0.109652
$414$	−15.6573	−0.769515
$415$	−38.5151	−1.89063
$416$	−9.10271	−0.446297
$417$	11.9964	0.587464
$418$	−45.6450	−2.23257
$419$	17.8937	0.874166	0.437083	−	0.899421i	$-0.356012\pi$
$419$	17.8937	0.874166	0.437083	+	0.899421i	$0.356012\pi$
$420$	−27.6090	−1.34718
$421$	31.7185	1.54587	0.772933	−	0.634488i	$-0.218789\pi$
$421$	31.7185	1.54587	0.772933	+	0.634488i	$0.218789\pi$
$422$	29.8124	1.45124
$423$	−9.91389	−0.482030
$424$	9.15399	0.444557
$425$	−40.1371	−1.94693
$426$	−19.4802	−0.943818
$427$	−8.90147	−0.430772
$428$	36.4620	1.76246
$429$	−8.74820	−0.422367
$430$	5.99670	0.289186
$431$	38.8190	1.86985	0.934923	−	0.354851i	$-0.115468\pi$
$431$	38.8190	1.86985	0.934923	+	0.354851i	$0.115468\pi$
$432$	2.15169	0.103523
$433$	10.6070	0.509742	0.254871	−	0.966975i	$-0.417967\pi$
$433$	10.6070	0.509742	0.254871	+	0.966975i	$0.417967\pi$
$434$	−19.4734	−0.934755
$435$	−15.3862	−0.737713
$436$	−48.3735	−2.31667
$437$	45.9687	2.19898
$438$	11.2529	0.537686
$439$	31.9011	1.52256	0.761278	−	0.648425i	$-0.224572\pi$
$439$	31.9011	1.52256	0.761278	+	0.648425i	$0.224572\pi$
$440$	37.1758	1.77229
$441$	−2.12163	−0.101030
$442$	−46.4352	−2.20870
$443$	6.94349	0.329895	0.164948	−	0.986302i	$-0.447254\pi$
$443$	6.94349	0.329895	0.164948	+	0.986302i	$0.447254\pi$
$444$	30.0766	1.42737
$445$	40.2642	1.90871
$446$	4.62675	0.219083
$447$	−18.0637	−0.854385
$448$	−24.5046	−1.15773
$449$	−17.1990	−0.811670	−0.405835	−	0.913946i	$-0.633019\pi$
$449$	−17.1990	−0.811670	−0.405835	+	0.913946i	$0.633019\pi$
$450$	−15.6599	−0.738213
$451$	−22.4265	−1.05602
$452$	34.9950	1.64602
$453$	17.6993	0.831586
$454$	−22.7418	−1.06733
$455$	23.9916	1.12474
$456$	−27.8919	−1.30616
$457$	−0.668271	−0.0312604	−0.0156302	−	0.999878i	$-0.504975\pi$
$457$	−0.668271	−0.0312604	−0.0156302	+	0.999878i	$0.504975\pi$
$458$	15.9795	0.746673
$459$	−6.10538	−0.284975
$460$	−82.1629	−3.83086
$461$	28.9117	1.34655	0.673277	−	0.739390i	$-0.264886\pi$
$461$	28.9117	1.34655	0.673277	+	0.739390i	$0.264886\pi$
$462$	−14.4155	−0.670672
$463$	−21.6332	−1.00538	−0.502689	−	0.864467i	$-0.667656\pi$
$463$	−21.6332	−1.00538	−0.502689	+	0.864467i	$0.667656\pi$
$464$	9.73125	0.451762
$465$	−12.5920	−0.583938
$466$	37.7037	1.74659
$467$	36.6681	1.69680	0.848398	−	0.529359i	$-0.177567\pi$
$467$	36.6681	1.69680	0.848398	+	0.529359i	$0.177567\pi$
$468$	−11.7314	−0.542284
$469$	23.7863	1.09835
$470$	−80.3418	−3.70589
$471$	11.5436	0.531900
$472$	4.02377	0.185209
$473$	2.02747	0.0932230
$474$	−7.83359	−0.359809
$475$	45.9762	2.10953
$476$	−49.5473	−2.27100
$477$	−2.29526	−0.105093
$478$	−33.2816	−1.52227
$479$	−6.90176	−0.315349	−0.157675	−	0.987491i	$-0.550400\pi$
$479$	−6.90176	−0.315349	−0.157675	+	0.987491i	$0.550400\pi$
$480$	−9.69915	−0.442704
$481$	−26.1359	−1.19170
$482$	−57.4601	−2.61723
$483$	14.5178	0.660581
$484$	−12.8334	−0.583339
$485$	−1.03291	−0.0469020
$486$	−2.38207	−0.108053
$487$	−9.06955	−0.410980	−0.205490	−	0.978659i	$-0.565879\pi$
$487$	−9.06955	−0.410980	−0.205490	+	0.978659i	$0.565879\pi$
$488$	16.0732	0.727601
$489$	3.40393	0.153931
$490$	−17.1936	−0.776729
$491$	20.4240	0.921722	0.460861	−	0.887472i	$-0.347541\pi$
$491$	20.4240	0.921722	0.460861	+	0.887472i	$0.347541\pi$
$492$	−30.0741	−1.35584
$493$	−27.6123	−1.24359
$494$	53.1905	2.39315
$495$	−9.32141	−0.418966
$496$	7.96397	0.357593
$497$	18.0624	0.810209
$498$	−26.9676	−1.20845
$499$	30.4105	1.36136	0.680681	−	0.732580i	$-0.261684\pi$
$499$	30.4105	1.36136	0.680681	+	0.732580i	$0.261684\pi$
$500$	−19.6758	−0.879927
$501$	18.2451	0.815130
$502$	44.6909	1.99465
$503$	−17.3619	−0.774127	−0.387064	−	0.922053i	$-0.626511\pi$
$503$	−17.3619	−0.774127	−0.387064	+	0.922053i	$0.626511\pi$
$504$	−8.80878	−0.392374
$505$	10.6367	0.473326
$506$	−42.8999	−1.90713
$507$	−2.80566	−0.124604
$508$	60.6130	2.68927
$509$	16.9904	0.753088	0.376544	−	0.926399i	$-0.377112\pi$
$509$	16.9904	0.753088	0.376544	+	0.926399i	$0.377112\pi$
$510$	−49.4778	−2.19091
$511$	−10.4339	−0.461570
$512$	23.2972	1.02960
$513$	6.99358	0.308774
$514$	−63.7426	−2.81156
$515$	15.6304	0.688759
$516$	2.71885	0.119691
$517$	−27.1633	−1.19464
$518$	−43.0676	−1.89228
$519$	14.7282	0.646498
$520$	−43.3212	−1.89976
$521$	11.2151	0.491343	0.245671	−	0.969353i	$-0.420992\pi$
$521$	11.2151	0.491343	0.245671	+	0.969353i	$0.420992\pi$
$522$	−10.7732	−0.471530
$523$	23.1347	1.01161	0.505804	−	0.862648i	$-0.331196\pi$
$523$	23.1347	1.01161	0.505804	+	0.862648i	$0.331196\pi$
$524$	−39.7260	−1.73544
$525$	14.5201	0.633710
$526$	7.39189	0.322302
$527$	−22.5976	−0.984369
$528$	5.89547	0.256567
$529$	20.2041	0.878440
$530$	−18.6007	−0.807962
$531$	−1.00891	−0.0437832
$532$	56.7554	2.46066
$533$	26.1337	1.13198
$534$	28.1924	1.22000
$535$	−33.7608	−1.45961
$536$	−42.9504	−1.85518
$537$	−4.40330	−0.190016
$538$	−47.3123	−2.03978
$539$	−5.81312	−0.250389
$540$	−12.5001	−0.537918
$541$	1.81751	0.0781408	0.0390704	−	0.999236i	$-0.487560\pi$
$541$	1.81751	0.0781408	0.0390704	+	0.999236i	$0.487560\pi$
$542$	73.6561	3.16380
$543$	−14.4972	−0.622136
$544$	−17.4062	−0.746285
$545$	44.7899	1.91859
$546$	16.7985	0.718911
$547$	11.1524	0.476841	0.238421	−	0.971162i	$-0.423370\pi$
$547$	11.1524	0.476841	0.238421	+	0.971162i	$0.423370\pi$
$548$	−2.76765	−0.118228
$549$	−4.03018	−0.172004
$550$	−42.9069	−1.82956
$551$	31.6293	1.34745
$552$	−26.2145	−1.11576
$553$	7.26346	0.308874
$554$	25.7590	1.09440
$555$	−27.8485	−1.18210
$556$	44.0778	1.86931
$557$	37.5541	1.59122	0.795608	−	0.605811i	$-0.207151\pi$
$557$	37.5541	1.59122	0.795608	+	0.605811i	$0.207151\pi$
$558$	−8.81668	−0.373240
$559$	−2.36262	−0.0999282
$560$	−16.1681	−0.683227
$561$	−16.7283	−0.706270
$562$	−19.2925	−0.813805
$563$	21.6637	0.913018	0.456509	−	0.889719i	$-0.349100\pi$
$563$	21.6637	0.913018	0.456509	+	0.889719i	$0.349100\pi$
$564$	−36.4262	−1.53382
$565$	−32.4025	−1.36318
$566$	−16.3805	−0.688523
$567$	2.20870	0.0927568
$568$	−32.6150	−1.36849
$569$	36.8819	1.54617	0.773084	−	0.634304i	$-0.218713\pi$
$569$	36.8819	1.54617	0.773084	+	0.634304i	$0.218713\pi$
$570$	56.6757	2.37388
$571$	3.17674	0.132942	0.0664711	−	0.997788i	$-0.478826\pi$
$571$	3.17674	0.132942	0.0664711	+	0.997788i	$0.478826\pi$
$572$	−32.1432	−1.34397
$573$	−12.6675	−0.529193
$574$	43.0639	1.79745
$575$	43.2111	1.80203
$576$	−11.0946	−0.462273
$577$	−3.27870	−0.136494	−0.0682470	−	0.997668i	$-0.521741\pi$
$577$	−3.27870	−0.136494	−0.0682470	+	0.997668i	$0.521741\pi$
$578$	−48.2981	−2.00894
$579$	1.58860	0.0660200
$580$	−56.5331	−2.34741
$581$	25.0049	1.03738
$582$	−0.723226	−0.0299787
$583$	−6.28884	−0.260457
$584$	18.8404	0.779620
$585$	10.8623	0.449101
$586$	−19.7576	−0.816178
$587$	−25.0780	−1.03508	−0.517539	−	0.855660i	$-0.673152\pi$
$587$	−25.0780	−1.03508	−0.517539	+	0.855660i	$0.673152\pi$
$588$	−7.79544	−0.321479
$589$	25.8851	1.06658
$590$	−8.17621	−0.336609
$591$	−10.0763	−0.414483
$592$	17.6132	0.723897
$593$	−29.5494	−1.21345	−0.606724	−	0.794913i	$-0.707517\pi$
$593$	−29.5494	−1.21345	−0.606724	+	0.794913i	$0.707517\pi$
$594$	−6.52670	−0.267794
$595$	45.8767	1.88076
$596$	−66.3709	−2.71866
$597$	−7.68834	−0.314663
$598$	49.9916	2.04431
$599$	20.8958	0.853781	0.426891	−	0.904303i	$-0.359609\pi$
$599$	20.8958	0.853781	0.426891	+	0.904303i	$0.359609\pi$
$600$	−26.2187	−1.07038
$601$	22.5263	0.918868	0.459434	−	0.888212i	$-0.348052\pi$
$601$	22.5263	0.918868	0.459434	+	0.888212i	$0.348052\pi$
$602$	−3.89320	−0.158675
$603$	10.7693	0.438561
$604$	65.0320	2.64611
$605$	11.8827	0.483101
$606$	7.44763	0.302539
$607$	−16.7496	−0.679844	−0.339922	−	0.940454i	$-0.610401\pi$
$607$	−16.7496	−0.679844	−0.339922	+	0.940454i	$0.610401\pi$
$608$	19.9384	0.808610
$609$	9.98911	0.404779
$610$	−32.6604	−1.32238
$611$	31.6536	1.28057
$612$	−22.4328	−0.906791
$613$	38.4986	1.55494	0.777472	−	0.628917i	$-0.216501\pi$
$613$	38.4986	1.55494	0.777472	+	0.628917i	$0.216501\pi$
$614$	34.2822	1.38352
$615$	27.8461	1.12286
$616$	−24.1354	−0.972444
$617$	38.1978	1.53779	0.768894	−	0.639377i	$-0.220808\pi$
$617$	38.1978	1.53779	0.768894	+	0.639377i	$0.220808\pi$
$618$	10.9442	0.440239
$619$	1.50146	0.0603489	0.0301745	−	0.999545i	$-0.490394\pi$
$619$	1.50146	0.0603489	0.0301745	+	0.999545i	$0.490394\pi$
$620$	−46.2662	−1.85809
$621$	6.57298	0.263765
$622$	59.8890	2.40133
$623$	−26.1405	−1.04730
$624$	−6.87003	−0.275021
$625$	−14.6521	−0.586085
$626$	−50.1856	−2.00582
$627$	19.1619	0.765253
$628$	42.4141	1.69251
$629$	−49.9771	−1.99272
$630$	17.8992	0.713123
$631$	−10.4412	−0.415657	−0.207828	−	0.978165i	$-0.566640\pi$
$631$	−10.4412	−0.415657	−0.207828	+	0.978165i	$0.566640\pi$
$632$	−13.1155	−0.521707
$633$	−12.5153	−0.497439
$634$	68.4445	2.71828
$635$	−56.1227	−2.22716
$636$	−8.43339	−0.334405
$637$	6.77407	0.268399
$638$	−29.5178	−1.16862
$639$	8.17783	0.323510
$640$	−70.5116	−2.78722
$641$	10.9767	0.433555	0.216778	−	0.976221i	$-0.430445\pi$
$641$	10.9767	0.433555	0.216778	+	0.976221i	$0.430445\pi$
$642$	−23.6388	−0.932948
$643$	−49.4497	−1.95010	−0.975052	−	0.221976i	$-0.928749\pi$
$643$	−49.4497	−1.95010	−0.975052	+	0.221976i	$0.928749\pi$
$644$	53.3421	2.10197
$645$	−2.51743	−0.0991237
$646$	101.711	4.00176
$647$	34.1749	1.34355	0.671776	−	0.740754i	$-0.265532\pi$
$647$	34.1749	1.34355	0.671776	+	0.740754i	$0.265532\pi$
$648$	−3.98822	−0.156672
$649$	−2.76435	−0.108510
$650$	49.9997	1.96115
$651$	8.17500	0.320403
$652$	12.5069	0.489810
$653$	10.9381	0.428041	0.214021	−	0.976829i	$-0.431344\pi$
$653$	10.9381	0.428041	0.214021	+	0.976829i	$0.431344\pi$
$654$	31.3612	1.22632
$655$	36.7830	1.43723
$656$	−17.6117	−0.687620
$657$	−4.72401	−0.184301
$658$	52.1598	2.03340
$659$	−44.5710	−1.73624	−0.868120	−	0.496354i	$-0.834672\pi$
$659$	−44.5710	−1.73624	−0.868120	+	0.496354i	$0.834672\pi$
$660$	−34.2493	−1.33315
$661$	27.6698	1.07623	0.538115	−	0.842872i	$-0.319137\pi$
$661$	27.6698	1.07623	0.538115	+	0.842872i	$0.319137\pi$
$662$	−43.2424	−1.68066
$663$	19.4936	0.757069
$664$	−45.1509	−1.75220
$665$	−52.5508	−2.03783
$666$	−19.4990	−0.755573
$667$	29.7271	1.15104
$668$	67.0373	2.59375
$669$	−1.94232	−0.0750945
$670$	87.2743	3.37170
$671$	−11.0424	−0.426287
$672$	6.29692	0.242909
$673$	−12.3776	−0.477121	−0.238561	−	0.971128i	$-0.576676\pi$
$673$	−12.3776	−0.477121	−0.238561	+	0.971128i	$0.576676\pi$
$674$	−48.9902	−1.88703
$675$	6.57405	0.253035
$676$	−10.3087	−0.396490
$677$	−38.1339	−1.46560	−0.732802	−	0.680442i	$-0.761788\pi$
$677$	−38.1339	−1.46560	−0.732802	+	0.680442i	$0.761788\pi$
$678$	−22.6877	−0.871315
$679$	0.670589	0.0257349
$680$	−82.8389	−3.17672
$681$	9.54709	0.365845
$682$	−24.1571	−0.925022
$683$	−3.85474	−0.147497	−0.0737487	−	0.997277i	$-0.523496\pi$
$683$	−3.85474	−0.147497	−0.0737487	+	0.997277i	$0.523496\pi$
$684$	25.6963	0.982521
$685$	2.56262	0.0979126
$686$	47.9915	1.83233
$687$	−6.70824	−0.255935
$688$	1.59219	0.0607015
$689$	7.32843	0.279191
$690$	53.2672	2.02785
$691$	−29.3201	−1.11539	−0.557695	−	0.830046i	$-0.688314\pi$
$691$	−29.3201	−1.11539	−0.557695	+	0.830046i	$0.688314\pi$
$692$	54.1154	2.05716
$693$	6.05169	0.229885
$694$	−42.1444	−1.59978
$695$	−40.8124	−1.54810
$696$	−18.0372	−0.683697
$697$	49.9729	1.89286
$698$	−54.8681	−2.07679
$699$	−15.8281	−0.598674
$700$	53.3508	2.01647
$701$	25.0390	0.945710	0.472855	−	0.881140i	$-0.343224\pi$
$701$	25.0390	0.945710	0.472855	+	0.881140i	$0.343224\pi$
$702$	7.60562	0.287055
$703$	57.2477	2.15914
$704$	−30.3983	−1.14568
$705$	33.7277	1.27026
$706$	−49.4190	−1.85991
$707$	−6.90559	−0.259711
$708$	−3.70702	−0.139318
$709$	16.7394	0.628660	0.314330	−	0.949314i	$-0.398220\pi$
$709$	16.7394	0.628660	0.314330	+	0.949314i	$0.398220\pi$
$710$	66.2728	2.48718
$711$	3.28856	0.123331
$712$	47.2015	1.76895
$713$	24.3284	0.911105
$714$	32.1222	1.20214
$715$	29.7620	1.11303
$716$	−16.1789	−0.604633
$717$	13.9717	0.521783
$718$	−32.6103	−1.21701
$719$	26.4563	0.986652	0.493326	−	0.869844i	$-0.335781\pi$
$719$	26.4563	0.986652	0.493326	+	0.869844i	$0.335781\pi$
$720$	−7.32018	−0.272807
$721$	−10.1476	−0.377918
$722$	−71.2482	−2.65158
$723$	24.1219	0.897103
$724$	−53.2667	−1.97964
$725$	29.7319	1.10421
$726$	8.32009	0.308787
$727$	21.4459	0.795384	0.397692	−	0.917519i	$-0.369811\pi$
$727$	21.4459	0.795384	0.397692	+	0.917519i	$0.369811\pi$
$728$	28.1252	1.04239
$729$	1.00000	0.0370370
$730$	−38.2832	−1.41693
$731$	−4.51780	−0.167097
$732$	−14.8079	−0.547317
$733$	−26.0700	−0.962919	−0.481459	−	0.876468i	$-0.659893\pi$
$733$	−26.0700	−0.962919	−0.481459	+	0.876468i	$0.659893\pi$
$734$	42.1455	1.55562
$735$	7.21794	0.266238
$736$	18.7393	0.690740
$737$	29.5072	1.08691
$738$	19.4974	0.717709
$739$	−39.4195	−1.45007	−0.725035	−	0.688712i	$-0.758176\pi$
$739$	−39.4195	−1.45007	−0.725035	+	0.688712i	$0.758176\pi$
$740$	−102.323	−3.76145
$741$	−22.3295	−0.820295
$742$	12.0760	0.443324
$743$	17.8168	0.653636	0.326818	−	0.945087i	$-0.394024\pi$
$743$	17.8168	0.653636	0.326818	+	0.945087i	$0.394024\pi$
$744$	−14.7615	−0.541181
$745$	61.4540	2.25150
$746$	7.49865	0.274545
$747$	11.3211	0.414217
$748$	−61.4642	−2.24735
$749$	21.9183	0.800878
$750$	12.7560	0.465785
$751$	25.6545	0.936145	0.468073	−	0.883690i	$-0.344949\pi$
$751$	25.6545	0.936145	0.468073	+	0.883690i	$0.344949\pi$
$752$	−21.3316	−0.777883
$753$	−18.7613	−0.683701
$754$	34.3973	1.25267
$755$	−60.2142	−2.19142
$756$	8.11536	0.295153
$757$	−28.5675	−1.03830	−0.519151	−	0.854683i	$-0.673752\pi$
$757$	−28.5675	−1.03830	−0.519151	+	0.854683i	$0.673752\pi$
$758$	72.0495	2.61695
$759$	18.0095	0.653704
$760$	94.8901	3.44203
$761$	34.0077	1.23278	0.616388	−	0.787442i	$-0.288595\pi$
$761$	34.0077	1.23278	0.616388	+	0.787442i	$0.288595\pi$
$762$	−39.2962	−1.42355
$763$	−29.0787	−1.05272
$764$	−46.5438	−1.68389
$765$	20.7709	0.750974
$766$	−80.8167	−2.92003
$767$	3.22132	0.116315
$768$	−27.1820	−0.980845
$769$	19.6015	0.706848	0.353424	−	0.935463i	$-0.385017\pi$
$769$	19.6015	0.706848	0.353424	+	0.935463i	$0.385017\pi$
$770$	49.0426	1.76737
$771$	26.7593	0.963713
$772$	5.83693	0.210076
$773$	6.92429	0.249049	0.124525	−	0.992217i	$-0.460259\pi$
$773$	6.92429	0.249049	0.124525	+	0.992217i	$0.460259\pi$
$774$	−1.76266	−0.0633576
$775$	24.3323	0.874043
$776$	−1.21087	−0.0434678
$777$	18.0799	0.648612
$778$	0.235515	0.00844363
$779$	−57.2428	−2.05094
$780$	39.9110	1.42904
$781$	22.4067	0.801774
$782$	95.5939	3.41843
$783$	4.52261	0.161625
$784$	−4.56509	−0.163039
$785$	−39.2720	−1.40168
$786$	25.7549	0.918646
$787$	−30.5589	−1.08931	−0.544654	−	0.838661i	$-0.683339\pi$
$787$	−30.5589	−1.08931	−0.544654	+	0.838661i	$0.683339\pi$
$788$	−37.0229	−1.31889
$789$	−3.10313	−0.110475
$790$	26.6504	0.948179
$791$	21.0364	0.747970
$792$	−10.9274	−0.388289
$793$	12.8678	0.456949
$794$	−54.1990	−1.92345
$795$	7.80862	0.276943
$796$	−28.2490	−1.00126
$797$	−20.8230	−0.737587	−0.368794	−	0.929511i	$-0.620229\pi$
$797$	−20.8230	−0.737587	−0.368794	+	0.929511i	$0.620229\pi$
$798$	−36.7952	−1.30254
$799$	60.5281	2.14133
$800$	18.7424	0.662642
$801$	−11.8352	−0.418177
$802$	34.9310	1.23346
$803$	−12.9435	−0.456765
$804$	39.5694	1.39550
$805$	−49.3904	−1.74078
$806$	28.1504	0.991556
$807$	19.8618	0.699170
$808$	12.4693	0.438668
$809$	−37.3689	−1.31382	−0.656909	−	0.753969i	$-0.728137\pi$
$809$	−37.3689	−1.31382	−0.656909	+	0.753969i	$0.728137\pi$
$810$	8.10396	0.284744
$811$	−18.5133	−0.650090	−0.325045	−	0.945699i	$-0.605379\pi$
$811$	−18.5133	−0.650090	−0.325045	+	0.945699i	$0.605379\pi$
$812$	36.7026	1.28801
$813$	−30.9211	−1.08445
$814$	−53.4260	−1.87258
$815$	−11.5804	−0.405644
$816$	−13.1369	−0.459882
$817$	5.17505	0.181052
$818$	93.5168	3.26974
$819$	−7.05207	−0.246419
$820$	102.314	3.57296
$821$	32.3663	1.12959	0.564795	−	0.825231i	$-0.308955\pi$
$821$	32.3663	1.12959	0.564795	+	0.825231i	$0.308955\pi$
$822$	1.79430	0.0625835
$823$	40.1278	1.39877	0.699384	−	0.714746i	$-0.253458\pi$
$823$	40.1278	1.39877	0.699384	+	0.714746i	$0.253458\pi$
$824$	18.3234	0.638327
$825$	18.0124	0.627112
$826$	5.30819	0.184695
$827$	10.0112	0.348124	0.174062	−	0.984735i	$-0.444311\pi$
$827$	10.0112	0.348124	0.174062	+	0.984735i	$0.444311\pi$
$828$	24.1509	0.839301
$829$	−13.3876	−0.464972	−0.232486	−	0.972600i	$-0.574686\pi$
$829$	−13.3876	−0.464972	−0.232486	+	0.972600i	$0.574686\pi$
$830$	91.7457	3.18454
$831$	−10.8137	−0.375124
$832$	35.4234	1.22808
$833$	12.9534	0.448808
$834$	−28.5762	−0.989512
$835$	−62.0710	−2.14805
$836$	70.4059	2.43504
$837$	3.70127	0.127935
$838$	−42.6242	−1.47243
$839$	−6.60903	−0.228169	−0.114084	−	0.993471i	$-0.536393\pi$
$839$	−6.60903	−0.228169	−0.114084	+	0.993471i	$0.536393\pi$
$840$	29.9681	1.03400
$841$	−8.54597	−0.294689
$842$	−75.5557	−2.60382
$843$	8.09905	0.278946
$844$	−45.9846	−1.58285
$845$	9.54504	0.328359
$846$	23.6156	0.811921
$847$	−7.71454	−0.265075
$848$	−4.93868	−0.169595
$849$	6.87657	0.236003
$850$	95.6094	3.27937
$851$	53.8048	1.84441
$852$	30.0475	1.02941
$853$	51.0390	1.74754	0.873770	−	0.486339i	$-0.161668\pi$
$853$	51.0390	1.74754	0.873770	+	0.486339i	$0.161668\pi$
$854$	21.2039	0.725583
$855$	−23.7926	−0.813691
$856$	−39.5775	−1.35273
$857$	−4.27606	−0.146068	−0.0730338	−	0.997329i	$-0.523268\pi$
$857$	−4.27606	−0.146068	−0.0730338	+	0.997329i	$0.523268\pi$
$858$	20.8388	0.711426
$859$	−23.7792	−0.811337	−0.405668	−	0.914020i	$-0.632961\pi$
$859$	−23.7792	−0.811337	−0.405668	+	0.914020i	$0.632961\pi$
$860$	−9.24970	−0.315412
$861$	−18.0784	−0.616109
$862$	−92.4697	−3.14953
$863$	−17.2436	−0.586979	−0.293490	−	0.955962i	$-0.594817\pi$
$863$	−17.2436	−0.586979	−0.293490	+	0.955962i	$0.594817\pi$
$864$	2.85096	0.0969916
$865$	−50.1064	−1.70367
$866$	−25.2667	−0.858598
$867$	20.2757	0.688598
$868$	30.0371	1.01953
$869$	9.01043	0.305658
$870$	36.6511	1.24259
$871$	−34.3850	−1.16509
$872$	52.5068	1.77811
$873$	0.303612	0.0102757
$874$	−109.501	−3.70392
$875$	−11.8277	−0.399848
$876$	−17.3573	−0.586448
$877$	23.5680	0.795834	0.397917	−	0.917422i	$-0.369733\pi$
$877$	23.5680	0.795834	0.397917	+	0.917422i	$0.369733\pi$
$878$	−75.9907	−2.56456
$879$	8.29429	0.279759
$880$	−20.0568	−0.676113
$881$	−20.0113	−0.674198	−0.337099	−	0.941469i	$-0.609446\pi$
$881$	−20.0113	−0.674198	−0.337099	+	0.941469i	$0.609446\pi$
$882$	5.05388	0.170173
$883$	−11.3690	−0.382598	−0.191299	−	0.981532i	$-0.561270\pi$
$883$	−11.3690	−0.382598	−0.191299	+	0.981532i	$0.561270\pi$
$884$	71.6247	2.40900
$885$	3.43239	0.115379
$886$	−16.5399	−0.555669
$887$	19.2489	0.646316	0.323158	−	0.946345i	$-0.395255\pi$
$887$	19.2489	0.646316	0.323158	+	0.946345i	$0.395255\pi$
$888$	−32.6465	−1.09555
$889$	36.4362	1.22203
$890$	−95.9123	−3.21499
$891$	2.73993	0.0917910
$892$	−7.13660	−0.238951
$893$	−69.3336	−2.32016
$894$	43.0291	1.43911
$895$	14.9803	0.500736
$896$	45.7778	1.52933
$897$	−20.9866	−0.700722
$898$	40.9692	1.36716
$899$	16.7394	0.558290
$900$	24.1548	0.805160
$901$	14.0134	0.466855
$902$	53.4214	1.77874
$903$	1.63438	0.0543886
$904$	−37.9851	−1.26337
$905$	49.3205	1.63947
$906$	−42.1610	−1.40071
$907$	36.5174	1.21254	0.606270	−	0.795259i	$-0.292665\pi$
$907$	36.5174	1.21254	0.606270	+	0.795259i	$0.292665\pi$
$908$	35.0785	1.16412
$909$	−3.12654	−0.103701
$910$	−57.1497	−1.89450
$911$	45.7614	1.51614	0.758071	−	0.652172i	$-0.226142\pi$
$911$	45.7614	1.51614	0.758071	+	0.652172i	$0.226142\pi$
$912$	15.0480	0.498289
$913$	31.0190	1.02658
$914$	1.59187	0.0526544
$915$	13.7109	0.453269
$916$	−24.6478	−0.814387
$917$	−23.8804	−0.788601
$918$	14.5435	0.480005
$919$	−14.4144	−0.475488	−0.237744	−	0.971328i	$-0.576408\pi$
$919$	−14.4144	−0.475488	−0.237744	+	0.971328i	$0.576408\pi$
$920$	89.1834	2.94029
$921$	−14.3917	−0.474224
$922$	−68.8698	−2.26811
$923$	−26.1107	−0.859443
$924$	22.2355	0.731494
$925$	53.8135	1.76938
$926$	51.5317	1.69344
$927$	−4.59439	−0.150900
$928$	12.8938	0.423259
$929$	−2.93931	−0.0964355	−0.0482178	−	0.998837i	$-0.515354\pi$
$929$	−2.93931	−0.0964355	−0.0482178	+	0.998837i	$0.515354\pi$
$930$	29.9949	0.983573
$931$	−14.8378	−0.486290
$932$	−58.1566	−1.90498
$933$	−25.1416	−0.823098
$934$	−87.3460	−2.85805
$935$	56.9108	1.86118
$936$	12.7338	0.416217
$937$	−16.0993	−0.525940	−0.262970	−	0.964804i	$-0.584702\pi$
$937$	−16.0993	−0.525940	−0.262970	+	0.964804i	$0.584702\pi$
$938$	−56.6606	−1.85003
$939$	21.0681	0.687530
$940$	123.924	4.04197
$941$	7.16287	0.233503	0.116752	−	0.993161i	$-0.462752\pi$
$941$	7.16287	0.233503	0.116752	+	0.993161i	$0.462752\pi$
$942$	−27.4976	−0.895920
$943$	−53.8002	−1.75198
$944$	−2.17087	−0.0706557
$945$	−7.51415	−0.244435
$946$	−4.82957	−0.157023
$947$	12.4876	0.405793	0.202897	−	0.979200i	$-0.434964\pi$
$947$	12.4876	0.405793	0.202897	+	0.979200i	$0.434964\pi$
$948$	12.0831	0.392439
$949$	15.0831	0.489618
$950$	−109.518	−3.55325
$951$	−28.7332	−0.931737
$952$	53.7810	1.74305
$953$	−34.7365	−1.12523	−0.562613	−	0.826720i	$-0.690204\pi$
$953$	−34.7365	−1.12523	−0.562613	+	0.826720i	$0.690204\pi$
$954$	5.46747	0.177016
$955$	43.0957	1.39454
$956$	51.3358	1.66032
$957$	12.3916	0.400565
$958$	16.4405	0.531168
$959$	−1.66371	−0.0537241
$960$	37.7444	1.21820
$961$	−17.3006	−0.558084
$962$	62.2577	2.00727
$963$	9.92362	0.319784
$964$	88.6302	2.85459
$965$	−5.40452	−0.173978
$966$	−34.5824	−1.11267
$967$	17.4745	0.561941	0.280971	−	0.959716i	$-0.409344\pi$
$967$	17.4745	0.561941	0.280971	+	0.959716i	$0.409344\pi$
$968$	13.9300	0.447728
$969$	−42.6985	−1.37167
$970$	2.46046	0.0790007
$971$	−16.2293	−0.520824	−0.260412	−	0.965498i	$-0.583858\pi$
$971$	−16.2293	−0.520824	−0.260412	+	0.965498i	$0.583858\pi$
$972$	3.67426	0.117852
$973$	26.4964	0.849435
$974$	21.6043	0.692247
$975$	−20.9900	−0.672218
$976$	−8.67168	−0.277574
$977$	45.9531	1.47017	0.735086	−	0.677974i	$-0.237142\pi$
$977$	45.9531	1.47017	0.735086	+	0.677974i	$0.237142\pi$
$978$	−8.10841	−0.259278
$979$	−32.4277	−1.03639
$980$	26.5206	0.847169
$981$	−13.1655	−0.420342
$982$	−48.6514	−1.55253
$983$	−41.2333	−1.31514	−0.657568	−	0.753395i	$-0.728415\pi$
$983$	−41.2333	−1.31514	−0.657568	+	0.753395i	$0.728415\pi$
$984$	32.6438	1.04065
$985$	34.2802	1.09226
$986$	65.7744	2.09468
$987$	−21.8968	−0.696984
$988$	−82.0445	−2.61018
$989$	4.86382	0.154660
$990$	22.2043	0.705698
$991$	14.4894	0.460272	0.230136	−	0.973159i	$-0.426083\pi$
$991$	14.4894	0.460272	0.230136	+	0.973159i	$0.426083\pi$
$992$	10.5522	0.335032
$993$	18.1533	0.576077
$994$	−43.0259	−1.36470
$995$	26.1562	0.829209
$996$	41.5967	1.31804
$997$	26.7960	0.848637	0.424319	−	0.905513i	$-0.360514\pi$
$997$	26.7960	0.848637	0.424319	+	0.905513i	$0.360514\pi$
$998$	−72.4400	−2.29305
$999$	8.18575	0.258986

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.10	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.10	✓	97	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38207 q^{2} +1.00000 q^{3} +3.67426 q^{4} -3.40207 q^{5} -2.38207 q^{6} +2.20870 q^{7} -3.98822 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38207 q^{2} +1.00000 q^{3} +3.67426 q^{4} -3.40207 q^{5} -2.38207 q^{6} +2.20870 q^{7} -3.98822 q^{8} +1.00000 q^{9} +8.10396 q^{10} +2.73993 q^{11} +3.67426 q^{12} -3.19286 q^{13} -5.26129 q^{14} -3.40207 q^{15} +2.15169 q^{16} -6.10538 q^{17} -2.38207 q^{18} +6.99358 q^{19} -12.5001 q^{20} +2.20870 q^{21} -6.52670 q^{22} +6.57298 q^{23} -3.98822 q^{24} +6.57405 q^{25} +7.60562 q^{26} +1.00000 q^{27} +8.11536 q^{28} +4.52261 q^{29} +8.10396 q^{30} +3.70127 q^{31} +2.85096 q^{32} +2.73993 q^{33} +14.5435 q^{34} -7.51415 q^{35} +3.67426 q^{36} +8.18575 q^{37} -16.6592 q^{38} -3.19286 q^{39} +13.5682 q^{40} -8.18505 q^{41} -5.26129 q^{42} +0.739971 q^{43} +10.0672 q^{44} -3.40207 q^{45} -15.6573 q^{46} -9.91389 q^{47} +2.15169 q^{48} -2.12163 q^{49} -15.6599 q^{50} -6.10538 q^{51} -11.7314 q^{52} -2.29526 q^{53} -2.38207 q^{54} -9.32141 q^{55} -8.80878 q^{56} +6.99358 q^{57} -10.7732 q^{58} -1.00891 q^{59} -12.5001 q^{60} -4.03018 q^{61} -8.81668 q^{62} +2.20870 q^{63} -11.0946 q^{64} +10.8623 q^{65} -6.52670 q^{66} +10.7693 q^{67} -22.4328 q^{68} +6.57298 q^{69} +17.8992 q^{70} +8.17783 q^{71} -3.98822 q^{72} -4.72401 q^{73} -19.4990 q^{74} +6.57405 q^{75} +25.6963 q^{76} +6.05169 q^{77} +7.60562 q^{78} +3.28856 q^{79} -7.32018 q^{80} +1.00000 q^{81} +19.4974 q^{82} +11.3211 q^{83} +8.11536 q^{84} +20.7709 q^{85} -1.76266 q^{86} +4.52261 q^{87} -10.9274 q^{88} -11.8352 q^{89} +8.10396 q^{90} -7.05207 q^{91} +24.1509 q^{92} +3.70127 q^{93} +23.6156 q^{94} -23.7926 q^{95} +2.85096 q^{96} +0.303612 q^{97} +5.05388 q^{98} +2.73993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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