LMFDB - Embedded newform 8023.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.554958 q^{2} +2.69202 q^{3} -1.69202 q^{4} -0.109916 q^{5} +1.49396 q^{6} -2.24698 q^{7} -2.04892 q^{8} +4.24698 q^{9} +O(q^{10})$	\(q+0.554958 q^{2} +2.69202 q^{3} -1.69202 q^{4} -0.109916 q^{5} +1.49396 q^{6} -2.24698 q^{7} -2.04892 q^{8} +4.24698 q^{9} -0.0609989 q^{10} -1.19806 q^{11} -4.55496 q^{12} -1.69202 q^{13} -1.24698 q^{14} -0.295897 q^{15} +2.24698 q^{16} +4.46681 q^{17} +2.35690 q^{18} +5.85086 q^{19} +0.185981 q^{20} -6.04892 q^{21} -0.664874 q^{22} -1.66487 q^{23} -5.51573 q^{24} -4.98792 q^{25} -0.939001 q^{26} +3.35690 q^{27} +3.80194 q^{28} +0.692021 q^{29} -0.164210 q^{30} -8.23490 q^{31} +5.34481 q^{32} -3.22521 q^{33} +2.47889 q^{34} +0.246980 q^{35} -7.18598 q^{36} +0.951083 q^{37} +3.24698 q^{38} -4.55496 q^{39} +0.225209 q^{40} -8.54288 q^{41} -3.35690 q^{42} +10.6528 q^{43} +2.02715 q^{44} -0.466812 q^{45} -0.923936 q^{46} +1.97823 q^{47} +6.04892 q^{48} -1.95108 q^{49} -2.76809 q^{50} +12.0248 q^{51} +2.86294 q^{52} +9.15883 q^{53} +1.86294 q^{54} +0.131687 q^{55} +4.60388 q^{56} +15.7506 q^{57} +0.384043 q^{58} -3.95108 q^{59} +0.500664 q^{60} -3.97823 q^{61} -4.57002 q^{62} -9.54288 q^{63} -1.52781 q^{64} +0.185981 q^{65} -1.78986 q^{66} -9.03684 q^{67} -7.55794 q^{68} -4.48188 q^{69} +0.137063 q^{70} -1.00000 q^{71} -8.70171 q^{72} -11.5646 q^{73} +0.527811 q^{74} -13.4276 q^{75} -9.89977 q^{76} +2.69202 q^{77} -2.52781 q^{78} -3.56465 q^{79} -0.246980 q^{80} -3.70410 q^{81} -4.74094 q^{82} -9.04892 q^{83} +10.2349 q^{84} -0.490975 q^{85} +5.91185 q^{86} +1.86294 q^{87} +2.45473 q^{88} -14.0804 q^{89} -0.259061 q^{90} +3.80194 q^{91} +2.81700 q^{92} -22.1685 q^{93} +1.09783 q^{94} -0.643104 q^{95} +14.3884 q^{96} -1.25906 q^{97} -1.08277 q^{98} -5.08815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} - q^{5} - 5 q^{6} - 2 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 - q^5 - 5 * q^6 - 2 * q^7 + 3 * q^8 + 8 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} - q^{5} - 5 q^{6} - 2 q^{7} + 3 q^{8} + 8 q^{9} - 10 q^{10} - 8 q^{11} - 14 q^{12} + q^{14} + 13 q^{15} + 2 q^{16} + 10 q^{17} + 3 q^{18} + 4 q^{19} - 14 q^{20} - 9 q^{21} - 3 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} + 7 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} + 11 q^{30} - q^{31} - 7 q^{32} - 8 q^{33} + 23 q^{34} - 4 q^{35} - 7 q^{36} + 12 q^{37} + 5 q^{38} - 14 q^{39} - q^{40} - 7 q^{41} - 6 q^{42} + 14 q^{43} + 2 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} - 15 q^{49} + 12 q^{50} - 11 q^{51} + 14 q^{52} + 19 q^{53} + 11 q^{54} - 2 q^{55} + 5 q^{56} + 11 q^{57} - 9 q^{58} - 21 q^{59} + 14 q^{60} - 15 q^{61} + 11 q^{62} - 10 q^{63} - 11 q^{64} - 14 q^{65} + 18 q^{66} + q^{67} + 21 q^{68} + 15 q^{69} - 5 q^{70} - 3 q^{71} + q^{72} - 13 q^{73} + 8 q^{74} - 24 q^{75} - 7 q^{76} + 3 q^{77} - 14 q^{78} + 11 q^{79} + 4 q^{80} - 25 q^{81} - 18 q^{83} + 7 q^{84} - 36 q^{85} + 14 q^{86} + 11 q^{87} - 15 q^{88} - 8 q^{89} - 15 q^{90} + 7 q^{91} - 21 q^{92} - 36 q^{93} - 15 q^{94} - 6 q^{95} + 14 q^{96} - 18 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 - q^5 - 5 * q^6 - 2 * q^7 + 3 * q^8 + 8 * q^9 - 10 * q^10 - 8 * q^11 - 14 * q^12 + q^14 + 13 * q^15 + 2 * q^16 + 10 * q^17 + 3 * q^18 + 4 * q^19 - 14 * q^20 - 9 * q^21 - 3 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 + 7 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 + 11 * q^30 - q^31 - 7 * q^32 - 8 * q^33 + 23 * q^34 - 4 * q^35 - 7 * q^36 + 12 * q^37 + 5 * q^38 - 14 * q^39 - q^40 - 7 * q^41 - 6 * q^42 + 14 * q^43 + 2 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 - 15 * q^49 + 12 * q^50 - 11 * q^51 + 14 * q^52 + 19 * q^53 + 11 * q^54 - 2 * q^55 + 5 * q^56 + 11 * q^57 - 9 * q^58 - 21 * q^59 + 14 * q^60 - 15 * q^61 + 11 * q^62 - 10 * q^63 - 11 * q^64 - 14 * q^65 + 18 * q^66 + q^67 + 21 * q^68 + 15 * q^69 - 5 * q^70 - 3 * q^71 + q^72 - 13 * q^73 + 8 * q^74 - 24 * q^75 - 7 * q^76 + 3 * q^77 - 14 * q^78 + 11 * q^79 + 4 * q^80 - 25 * q^81 - 18 * q^83 + 7 * q^84 - 36 * q^85 + 14 * q^86 + 11 * q^87 - 15 * q^88 - 8 * q^89 - 15 * q^90 + 7 * q^91 - 21 * q^92 - 36 * q^93 - 15 * q^94 - 6 * q^95 + 14 * q^96 - 18 * q^97 - 10 * q^98 - 19 * 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 $

$2$	0.554958	0.392415	0.196207	−	0.980562i	$-0.437137\pi$
$2$	0.554958	0.392415	0.196207	+	0.980562i	$0.437137\pi$
$3$	2.69202	1.55424	0.777120	−	0.629353i	$-0.216680\pi$
$3$	2.69202	1.55424	0.777120	+	0.629353i	$0.216680\pi$
$4$	−1.69202	−0.846011
$5$	−0.109916	−0.0491560	−0.0245780	−	0.999698i	$-0.507824\pi$
$5$	−0.109916	−0.0491560	−0.0245780	+	0.999698i	$0.507824\pi$
$6$	1.49396	0.609906
$7$	−2.24698	−0.849278	−0.424639	−	0.905363i	$-0.639599\pi$
$7$	−2.24698	−0.849278	−0.424639	+	0.905363i	$0.639599\pi$
$8$	−2.04892	−0.724402
$9$	4.24698	1.41566
$10$	−0.0609989	−0.0192896
$11$	−1.19806	−0.361229	−0.180615	−	0.983554i	$-0.557809\pi$
$11$	−1.19806	−0.361229	−0.180615	+	0.983554i	$0.557809\pi$
$12$	−4.55496	−1.31490
$13$	−1.69202	−0.469282	−0.234641	−	0.972082i	$-0.575392\pi$
$13$	−1.69202	−0.469282	−0.234641	+	0.972082i	$0.575392\pi$
$14$	−1.24698	−0.333269
$15$	−0.295897	−0.0764003
$16$	2.24698	0.561745
$17$	4.46681	1.08336	0.541681	−	0.840584i	$-0.317788\pi$
$17$	4.46681	1.08336	0.541681	+	0.840584i	$0.317788\pi$
$18$	2.35690	0.555526
$19$	5.85086	1.34228	0.671139	−	0.741331i	$-0.265805\pi$
$19$	5.85086	1.34228	0.671139	+	0.741331i	$0.265805\pi$
$20$	0.185981	0.0415865
$21$	−6.04892	−1.31998
$22$	−0.664874	−0.141752
$23$	−1.66487	−0.347150	−0.173575	−	0.984821i	$-0.555532\pi$
$23$	−1.66487	−0.347150	−0.173575	+	0.984821i	$0.555532\pi$
$24$	−5.51573	−1.12589
$25$	−4.98792	−0.997584
$26$	−0.939001	−0.184153
$27$	3.35690	0.646035
$28$	3.80194	0.718499
$29$	0.692021	0.128505	0.0642526	−	0.997934i	$-0.479534\pi$
$29$	0.692021	0.128505	0.0642526	+	0.997934i	$0.479534\pi$
$30$	−0.164210	−0.0299806
$31$	−8.23490	−1.47903	−0.739516	−	0.673139i	$-0.764945\pi$
$31$	−8.23490	−1.47903	−0.739516	+	0.673139i	$0.764945\pi$
$32$	5.34481	0.944839
$33$	−3.22521	−0.561437
$34$	2.47889	0.425127
$35$	0.246980	0.0417472
$36$	−7.18598	−1.19766
$37$	0.951083	0.156357	0.0781785	−	0.996939i	$-0.475090\pi$
$37$	0.951083	0.156357	0.0781785	+	0.996939i	$0.475090\pi$
$38$	3.24698	0.526730
$39$	−4.55496	−0.729377
$40$	0.225209	0.0356087
$41$	−8.54288	−1.33417	−0.667087	−	0.744980i	$-0.732459\pi$
$41$	−8.54288	−1.33417	−0.667087	+	0.744980i	$0.732459\pi$
$42$	−3.35690	−0.517980
$43$	10.6528	1.62454	0.812268	−	0.583285i	$-0.198233\pi$
$43$	10.6528	1.62454	0.812268	+	0.583285i	$0.198233\pi$
$44$	2.02715	0.305604
$45$	−0.466812	−0.0695882
$46$	−0.923936	−0.136227
$47$	1.97823	0.288554	0.144277	−	0.989537i	$-0.453914\pi$
$47$	1.97823	0.288554	0.144277	+	0.989537i	$0.453914\pi$
$48$	6.04892	0.873086
$49$	−1.95108	−0.278726
$50$	−2.76809	−0.391466
$51$	12.0248	1.68380
$52$	2.86294	0.397018
$53$	9.15883	1.25806	0.629031	−	0.777380i	$-0.283452\pi$
$53$	9.15883	1.25806	0.629031	+	0.777380i	$0.283452\pi$
$54$	1.86294	0.253514
$55$	0.131687	0.0177566
$56$	4.60388	0.615219
$57$	15.7506	2.08622
$58$	0.384043	0.0504273
$59$	−3.95108	−0.514387	−0.257194	−	0.966360i	$-0.582798\pi$
$59$	−3.95108	−0.514387	−0.257194	+	0.966360i	$0.582798\pi$
$60$	0.500664	0.0646354
$61$	−3.97823	−0.509360	−0.254680	−	0.967025i	$-0.581970\pi$
$61$	−3.97823	−0.509360	−0.254680	+	0.967025i	$0.581970\pi$
$62$	−4.57002	−0.580394
$63$	−9.54288	−1.20229
$64$	−1.52781	−0.190976
$65$	0.185981	0.0230681
$66$	−1.78986	−0.220316
$67$	−9.03684	−1.10403	−0.552013	−	0.833836i	$-0.686140\pi$
$67$	−9.03684	−1.10403	−0.552013	+	0.833836i	$0.686140\pi$
$68$	−7.55794	−0.916535
$69$	−4.48188	−0.539555
$70$	0.137063	0.0163822
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−8.70171	−1.02551
$73$	−11.5646	−1.35354	−0.676770	−	0.736195i	$-0.736621\pi$
$73$	−11.5646	−1.35354	−0.676770	+	0.736195i	$0.736621\pi$
$74$	0.527811	0.0613568
$75$	−13.4276	−1.55048
$76$	−9.89977	−1.13558
$77$	2.69202	0.306784
$78$	−2.52781	−0.286218
$79$	−3.56465	−0.401054	−0.200527	−	0.979688i	$-0.564265\pi$
$79$	−3.56465	−0.401054	−0.200527	+	0.979688i	$0.564265\pi$
$80$	−0.246980	−0.0276132
$81$	−3.70410	−0.411567
$82$	−4.74094	−0.523549
$83$	−9.04892	−0.993248	−0.496624	−	0.867966i	$-0.665427\pi$
$83$	−9.04892	−0.993248	−0.496624	+	0.867966i	$0.665427\pi$
$84$	10.2349	1.11672
$85$	−0.490975	−0.0532537
$86$	5.91185	0.637492
$87$	1.86294	0.199728
$88$	2.45473	0.261675
$89$	−14.0804	−1.49252	−0.746258	−	0.665656i	$-0.768152\pi$
$89$	−14.0804	−1.49252	−0.746258	+	0.665656i	$0.768152\pi$
$90$	−0.259061	−0.0273074
$91$	3.80194	0.398551
$92$	2.81700	0.293693
$93$	−22.1685	−2.29877
$94$	1.09783	0.113233
$95$	−0.643104	−0.0659811
$96$	14.3884	1.46851
$97$	−1.25906	−0.127838	−0.0639191	−	0.997955i	$-0.520360\pi$
$97$	−1.25906	−0.127838	−0.0639191	+	0.997955i	$0.520360\pi$
$98$	−1.08277	−0.109376
$99$	−5.08815	−0.511378
$100$	8.43967	0.843967
$101$	1.81163	0.180264	0.0901318	−	0.995930i	$-0.471271\pi$
$101$	1.81163	0.180264	0.0901318	+	0.995930i	$0.471271\pi$
$102$	6.67324	0.660749
$103$	10.3056	1.01544	0.507720	−	0.861522i	$-0.330489\pi$
$103$	10.3056	1.01544	0.507720	+	0.861522i	$0.330489\pi$
$104$	3.46681	0.339949
$105$	0.664874	0.0648851
$106$	5.08277	0.493682
$107$	−10.4993	−1.01501	−0.507505	−	0.861649i	$-0.669432\pi$
$107$	−10.4993	−1.01501	−0.507505	+	0.861649i	$0.669432\pi$
$108$	−5.67994	−0.546552
$109$	−3.39612	−0.325290	−0.162645	−	0.986685i	$-0.552002\pi$
$109$	−3.39612	−0.325290	−0.162645	+	0.986685i	$0.552002\pi$
$110$	0.0730805	0.00696795
$111$	2.56033	0.243016
$112$	−5.04892	−0.477078
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	8.74094	0.818664
$115$	0.182997	0.0170645
$116$	−1.17092	−0.108717
$117$	−7.18598	−0.664344
$118$	−2.19269	−0.201853
$119$	−10.0368	−0.920075
$120$	0.606268	0.0553445
$121$	−9.56465	−0.869513
$122$	−2.20775	−0.199880
$123$	−22.9976	−2.07362
$124$	13.9336	1.25128
$125$	1.09783	0.0981933
$126$	−5.29590	−0.471796
$127$	3.36658	0.298736	0.149368	−	0.988782i	$-0.452276\pi$
$127$	3.36658	0.298736	0.149368	+	0.988782i	$0.452276\pi$
$128$	−11.5375	−1.01978
$129$	28.6775	2.52492
$130$	0.103211	0.00905225
$131$	−11.4330	−0.998902	−0.499451	−	0.866342i	$-0.666465\pi$
$131$	−11.4330	−0.998902	−0.499451	+	0.866342i	$0.666465\pi$
$132$	5.45712	0.474982
$133$	−13.1468	−1.13997
$134$	−5.01507	−0.433236
$135$	−0.368977	−0.0317565
$136$	−9.15213	−0.784789
$137$	−7.15883	−0.611620	−0.305810	−	0.952092i	$-0.598927\pi$
$137$	−7.15883	−0.611620	−0.305810	+	0.952092i	$0.598927\pi$
$138$	−2.48725	−0.211729
$139$	2.02715	0.171940	0.0859702	−	0.996298i	$-0.472601\pi$
$139$	2.02715	0.171940	0.0859702	+	0.996298i	$0.472601\pi$
$140$	−0.417895	−0.0353186
$141$	5.32544	0.448483
$142$	−0.554958	−0.0465711
$143$	2.02715	0.169519
$144$	9.54288	0.795240
$145$	−0.0760644	−0.00631681
$146$	−6.41789	−0.531149
$147$	−5.25236	−0.433207
$148$	−1.60925	−0.132280
$149$	19.1347	1.56757	0.783787	−	0.621030i	$-0.213286\pi$
$149$	19.1347	1.56757	0.783787	+	0.621030i	$0.213286\pi$
$150$	−7.45175	−0.608433
$151$	−22.4426	−1.82636	−0.913178	−	0.407560i	$-0.866380\pi$
$151$	−22.4426	−1.82636	−0.913178	+	0.407560i	$0.866380\pi$
$152$	−11.9879	−0.972349
$153$	18.9705	1.53367
$154$	1.49396	0.120387
$155$	0.905149	0.0727033
$156$	7.70709	0.617061
$157$	7.36227	0.587573	0.293787	−	0.955871i	$-0.405084\pi$
$157$	7.36227	0.587573	0.293787	+	0.955871i	$0.405084\pi$
$158$	−1.97823	−0.157380
$159$	24.6558	1.95533
$160$	−0.587482	−0.0464445
$161$	3.74094	0.294827
$162$	−2.05562	−0.161505
$163$	4.16123	0.325932	0.162966	−	0.986632i	$-0.447894\pi$
$163$	4.16123	0.325932	0.162966	+	0.986632i	$0.447894\pi$
$164$	14.4547	1.12872
$165$	0.354503	0.0275980
$166$	−5.02177	−0.389765
$167$	1.76271	0.136403	0.0682013	−	0.997672i	$-0.478274\pi$
$167$	1.76271	0.136403	0.0682013	+	0.997672i	$0.478274\pi$
$168$	12.3937	0.956197
$169$	−10.1371	−0.779774
$170$	−0.272471	−0.0208976
$171$	24.8485	1.90021
$172$	−18.0248	−1.37437
$173$	12.9215	0.982407	0.491203	−	0.871045i	$-0.336557\pi$
$173$	12.9215	0.982407	0.491203	+	0.871045i	$0.336557\pi$
$174$	1.03385	0.0783761
$175$	11.2078	0.847226
$176$	−2.69202	−0.202919
$177$	−10.6364	−0.799481
$178$	−7.81402	−0.585686
$179$	13.0954	0.978799	0.489400	−	0.872060i	$-0.337216\pi$
$179$	13.0954	0.978799	0.489400	+	0.872060i	$0.337216\pi$
$180$	0.789856	0.0588724
$181$	−15.5942	−1.15911	−0.579553	−	0.814934i	$-0.696773\pi$
$181$	−15.5942	−1.15911	−0.579553	+	0.814934i	$0.696773\pi$
$182$	2.10992	0.156397
$183$	−10.7095	−0.791668
$184$	3.41119	0.251476
$185$	−0.104539	−0.00768589
$186$	−12.3026	−0.902071
$187$	−5.35152	−0.391342
$188$	−3.34721	−0.244120
$189$	−7.54288	−0.548664
$190$	−0.356896	−0.0258919
$191$	2.05861	0.148956	0.0744778	−	0.997223i	$-0.476271\pi$
$191$	2.05861	0.148956	0.0744778	+	0.997223i	$0.476271\pi$
$192$	−4.11290	−0.296823
$193$	26.8267	1.93103	0.965514	−	0.260352i	$-0.0838386\pi$
$193$	26.8267	1.93103	0.965514	+	0.260352i	$0.0838386\pi$
$194$	−0.698726	−0.0501656
$195$	0.500664	0.0358533
$196$	3.30127	0.235805
$197$	21.2935	1.51710	0.758550	−	0.651615i	$-0.225908\pi$
$197$	21.2935	1.51710	0.758550	+	0.651615i	$0.225908\pi$
$198$	−2.82371	−0.200672
$199$	−16.3937	−1.16212	−0.581060	−	0.813860i	$-0.697362\pi$
$199$	−16.3937	−1.16212	−0.581060	+	0.813860i	$0.697362\pi$
$200$	10.2198	0.722651
$201$	−24.3274	−1.71592
$202$	1.00538	0.0707381
$203$	−1.55496	−0.109137
$204$	−20.3461	−1.42451
$205$	0.939001	0.0655827
$206$	5.71917	0.398473
$207$	−7.07069	−0.491447
$208$	−3.80194	−0.263617
$209$	−7.00969	−0.484870
$210$	0.368977	0.0254619
$211$	3.40044	0.234096	0.117048	−	0.993126i	$-0.462657\pi$
$211$	3.40044	0.234096	0.117048	+	0.993126i	$0.462657\pi$
$212$	−15.4969	−1.06433
$213$	−2.69202	−0.184454
$214$	−5.82669	−0.398304
$215$	−1.17092	−0.0798558
$216$	−6.87800	−0.467989
$217$	18.5036	1.25611
$218$	−1.88471	−0.127648
$219$	−31.1323	−2.10372
$220$	−0.222816	−0.0150223
$221$	−7.55794	−0.508402
$222$	1.42088	0.0953631
$223$	−14.9976	−1.00431	−0.502157	−	0.864776i	$-0.667460\pi$
$223$	−14.9976	−1.00431	−0.502157	+	0.864776i	$0.667460\pi$
$224$	−12.0097	−0.802431
$225$	−21.1836	−1.41224
$226$	−0.554958	−0.0369153
$227$	−17.5690	−1.16609	−0.583046	−	0.812439i	$-0.698139\pi$
$227$	−17.5690	−1.16609	−0.583046	+	0.812439i	$0.698139\pi$
$228$	−26.6504	−1.76497
$229$	−26.0586	−1.72200	−0.861001	−	0.508604i	$-0.830162\pi$
$229$	−26.0586	−1.72200	−0.861001	+	0.508604i	$0.830162\pi$
$230$	0.101556	0.00669637
$231$	7.24698	0.476816
$232$	−1.41789	−0.0930894
$233$	1.33513	0.0874670	0.0437335	−	0.999043i	$-0.486075\pi$
$233$	1.33513	0.0874670	0.0437335	+	0.999043i	$0.486075\pi$
$234$	−3.98792	−0.260698
$235$	−0.217440	−0.0141842
$236$	6.68532	0.435177
$237$	−9.59611	−0.623334
$238$	−5.57002	−0.361051
$239$	−19.9782	−1.29228	−0.646142	−	0.763217i	$-0.723619\pi$
$239$	−19.9782	−1.29228	−0.646142	+	0.763217i	$0.723619\pi$
$240$	−0.664874	−0.0429175
$241$	−22.7681	−1.46662	−0.733311	−	0.679894i	$-0.762026\pi$
$241$	−22.7681	−1.46662	−0.733311	+	0.679894i	$0.762026\pi$
$242$	−5.30798	−0.341210
$243$	−20.0422	−1.28571
$244$	6.73125	0.430924
$245$	0.214456	0.0137011
$246$	−12.7627	−0.813721
$247$	−9.89977	−0.629907
$248$	16.8726	1.07141
$249$	−24.3599	−1.54374
$250$	0.609252	0.0385325
$251$	−24.2107	−1.52817	−0.764084	−	0.645117i	$-0.776809\pi$
$251$	−24.2107	−1.52817	−0.764084	+	0.645117i	$0.776809\pi$
$252$	16.1468	1.01715
$253$	1.99462	0.125401
$254$	1.86831	0.117228
$255$	−1.32172	−0.0827691
$256$	−3.34721	−0.209200
$257$	2.86831	0.178920	0.0894602	−	0.995990i	$-0.471486\pi$
$257$	2.86831	0.178920	0.0894602	+	0.995990i	$0.471486\pi$
$258$	15.9148	0.990815
$259$	−2.13706	−0.132791
$260$	−0.314683	−0.0195158
$261$	2.93900	0.181920
$262$	−6.34481	−0.391984
$263$	27.4892	1.69506	0.847528	−	0.530751i	$-0.178090\pi$
$263$	27.4892	1.69506	0.847528	+	0.530751i	$0.178090\pi$
$264$	6.60819	0.406706
$265$	−1.00670	−0.0618414
$266$	−7.29590	−0.447340
$267$	−37.9047	−2.31973
$268$	15.2905	0.934017
$269$	−17.4426	−1.06350	−0.531749	−	0.846902i	$-0.678465\pi$
$269$	−17.4426	−1.06350	−0.531749	+	0.846902i	$0.678465\pi$
$270$	−0.204767	−0.0124617
$271$	15.7627	0.957516	0.478758	−	0.877947i	$-0.341087\pi$
$271$	15.7627	0.957516	0.478758	+	0.877947i	$0.341087\pi$
$272$	10.0368	0.608573
$273$	10.2349	0.619444
$274$	−3.97285	−0.240009
$275$	5.97584	0.360357
$276$	7.58343	0.456469
$277$	29.2121	1.75518	0.877591	−	0.479409i	$-0.159149\pi$
$277$	29.2121	1.75518	0.877591	+	0.479409i	$0.159149\pi$
$278$	1.12498	0.0674719
$279$	−34.9734	−2.09381
$280$	−0.506041	−0.0302417
$281$	−24.8377	−1.48169	−0.740847	−	0.671674i	$-0.765576\pi$
$281$	−24.8377	−1.48169	−0.740847	+	0.671674i	$0.765576\pi$
$282$	2.95539	0.175991
$283$	−1.30559	−0.0776090	−0.0388045	−	0.999247i	$-0.512355\pi$
$283$	−1.30559	−0.0776090	−0.0388045	+	0.999247i	$0.512355\pi$
$284$	1.69202	0.100403
$285$	−1.73125	−0.102550
$286$	1.12498	0.0665216
$287$	19.1957	1.13308
$288$	22.6993	1.33757
$289$	2.95241	0.173671
$290$	−0.0422126	−0.00247881
$291$	−3.38942	−0.198691
$292$	19.5676	1.14511
$293$	−19.6082	−1.14552	−0.572761	−	0.819722i	$-0.694128\pi$
$293$	−19.6082	−1.14552	−0.572761	+	0.819722i	$0.694128\pi$
$294$	−2.91484	−0.169997
$295$	0.434288	0.0252852
$296$	−1.94869	−0.113265
$297$	−4.02177	−0.233367
$298$	10.6189	0.615139
$299$	2.81700	0.162912
$300$	22.7198	1.31173
$301$	−23.9366	−1.37968
$302$	−12.4547	−0.716689
$303$	4.87694	0.280173
$304$	13.1468	0.754018
$305$	0.437272	0.0250381
$306$	10.5278	0.601835
$307$	−22.0344	−1.25757	−0.628786	−	0.777578i	$-0.716448\pi$
$307$	−22.0344	−1.25757	−0.628786	+	0.777578i	$0.716448\pi$
$308$	−4.55496	−0.259543
$309$	27.7429	1.57824
$310$	0.502320	0.0285299
$311$	−20.9312	−1.18690	−0.593451	−	0.804870i	$-0.702235\pi$
$311$	−20.9312	−1.18690	−0.593451	+	0.804870i	$0.702235\pi$
$312$	9.33273	0.528362
$313$	−9.72587	−0.549739	−0.274869	−	0.961482i	$-0.588635\pi$
$313$	−9.72587	−0.549739	−0.274869	+	0.961482i	$0.588635\pi$
$314$	4.08575	0.230572
$315$	1.04892	0.0590998
$316$	6.03146	0.339296
$317$	2.45712	0.138006	0.0690029	−	0.997616i	$-0.478018\pi$
$317$	2.45712	0.138006	0.0690029	+	0.997616i	$0.478018\pi$
$318$	13.6829	0.767300
$319$	−0.829085	−0.0464198
$320$	0.167931	0.00938764
$321$	−28.2644	−1.57757
$322$	2.07606	0.115695
$323$	26.1347	1.45417
$324$	6.26742	0.348190
$325$	8.43967	0.468148
$326$	2.30931	0.127901
$327$	−9.14244	−0.505578
$328$	17.5036	0.966477
$329$	−4.44504	−0.245063
$330$	0.196734	0.0108299
$331$	20.5090	1.12728	0.563639	−	0.826021i	$-0.309401\pi$
$331$	20.5090	1.12728	0.563639	+	0.826021i	$0.309401\pi$
$332$	15.3110	0.840298
$333$	4.03923	0.221348
$334$	0.978230	0.0535263
$335$	0.993295	0.0542695
$336$	−13.5918	−0.741493
$337$	23.9855	1.30657	0.653287	−	0.757110i	$-0.273389\pi$
$337$	23.9855	1.30657	0.653287	+	0.757110i	$0.273389\pi$
$338$	−5.62565	−0.305995
$339$	−2.69202	−0.146211
$340$	0.830741	0.0450532
$341$	9.86592	0.534270
$342$	13.7899	0.745670
$343$	20.1129	1.08599
$344$	−21.8267	−1.17682
$345$	0.492631	0.0265224
$346$	7.17092	0.385511
$347$	24.4450	1.31228	0.656139	−	0.754640i	$-0.272188\pi$
$347$	24.4450	1.31228	0.656139	+	0.754640i	$0.272188\pi$
$348$	−3.15213	−0.168972
$349$	8.83207	0.472770	0.236385	−	0.971659i	$-0.424037\pi$
$349$	8.83207	0.472770	0.236385	+	0.971659i	$0.424037\pi$
$350$	6.21983	0.332464
$351$	−5.67994	−0.303173
$352$	−6.40342	−0.341303
$353$	17.0030	0.904978	0.452489	−	0.891770i	$-0.350536\pi$
$353$	17.0030	0.904978	0.452489	+	0.891770i	$0.350536\pi$
$354$	−5.90276	−0.313728
$355$	0.109916	0.00583375
$356$	23.8243	1.26269
$357$	−27.0194	−1.43002
$358$	7.26742	0.384095
$359$	−0.857560	−0.0452603	−0.0226301	−	0.999744i	$-0.507204\pi$
$359$	−0.857560	−0.0452603	−0.0226301	+	0.999744i	$0.507204\pi$
$360$	0.956459	0.0504098
$361$	15.2325	0.801711
$362$	−8.65412	−0.454850
$363$	−25.7482	−1.35143
$364$	−6.43296	−0.337179
$365$	1.27114	0.0665347
$366$	−5.94331	−0.310662
$367$	34.3196	1.79147	0.895734	−	0.444591i	$-0.146651\pi$
$367$	34.3196	1.79147	0.895734	+	0.444591i	$0.146651\pi$
$368$	−3.74094	−0.195010
$369$	−36.2814	−1.88874
$370$	−0.0580150	−0.00301606
$371$	−20.5797	−1.06845
$372$	37.5096	1.94478
$373$	−14.5942	−0.755658	−0.377829	−	0.925875i	$-0.623329\pi$
$373$	−14.5942	−0.755658	−0.377829	+	0.925875i	$0.623329\pi$
$374$	−2.96987	−0.153568
$375$	2.95539	0.152616
$376$	−4.05323	−0.209029
$377$	−1.17092	−0.0603052
$378$	−4.18598	−0.215304
$379$	−15.0218	−0.771617	−0.385808	−	0.922579i	$-0.626077\pi$
$379$	−15.0218	−0.771617	−0.385808	+	0.922579i	$0.626077\pi$
$380$	1.08815	0.0558207
$381$	9.06292	0.464307
$382$	1.14244	0.0584523
$383$	29.7899	1.52219	0.761095	−	0.648640i	$-0.224662\pi$
$383$	29.7899	1.52219	0.761095	+	0.648640i	$0.224662\pi$
$384$	−31.0592	−1.58498
$385$	−0.295897	−0.0150803
$386$	14.8877	0.757764
$387$	45.2422	2.29979
$388$	2.13036	0.108153
$389$	5.95348	0.301853	0.150927	−	0.988545i	$-0.451774\pi$
$389$	5.95348	0.301853	0.150927	+	0.988545i	$0.451774\pi$
$390$	0.277848	0.0140694
$391$	−7.43668	−0.376089
$392$	3.99761	0.201910
$393$	−30.7778	−1.55253
$394$	11.8170	0.595332
$395$	0.391813	0.0197142
$396$	8.60925	0.432631
$397$	−5.12737	−0.257336	−0.128668	−	0.991688i	$-0.541070\pi$
$397$	−5.12737	−0.257336	−0.128668	+	0.991688i	$0.541070\pi$
$398$	−9.09783	−0.456033
$399$	−35.3913	−1.77178
$400$	−11.2078	−0.560388
$401$	14.4437	0.721285	0.360642	−	0.932704i	$-0.382558\pi$
$401$	14.4437	0.721285	0.360642	+	0.932704i	$0.382558\pi$
$402$	−13.5007	−0.673352
$403$	13.9336	0.694083
$404$	−3.06531	−0.152505
$405$	0.407141	0.0202310
$406$	−0.862937	−0.0428268
$407$	−1.13946	−0.0564807
$408$	−24.6377	−1.21975
$409$	−31.6668	−1.56582	−0.782911	−	0.622134i	$-0.786266\pi$
$409$	−31.6668	−1.56582	−0.782911	+	0.622134i	$0.786266\pi$
$410$	0.521106	0.0257356
$411$	−19.2717	−0.950605
$412$	−17.4373	−0.859073
$413$	8.87800	0.436858
$414$	−3.92394	−0.192851
$415$	0.994623	0.0488241
$416$	−9.04354	−0.443396
$417$	5.45712	0.267236
$418$	−3.89008	−0.190270
$419$	−35.4698	−1.73281	−0.866406	−	0.499339i	$-0.833576\pi$
$419$	−35.4698	−1.73281	−0.866406	+	0.499339i	$0.833576\pi$
$420$	−1.12498	−0.0548935
$421$	28.6775	1.39766	0.698829	−	0.715289i	$-0.253705\pi$
$421$	28.6775	1.39766	0.698829	+	0.715289i	$0.253705\pi$
$422$	1.88710	0.0918626
$423$	8.40150	0.408495
$424$	−18.7657	−0.911343
$425$	−22.2801	−1.08074
$426$	−1.49396	−0.0723826
$427$	8.93900	0.432589
$428$	17.7651	0.858709
$429$	5.45712	0.263472
$430$	−0.649809	−0.0313366
$431$	−11.7125	−0.564170	−0.282085	−	0.959389i	$-0.591026\pi$
$431$	−11.7125	−0.564170	−0.282085	+	0.959389i	$0.591026\pi$
$432$	7.54288	0.362907
$433$	6.38644	0.306913	0.153456	−	0.988155i	$-0.450960\pi$
$433$	6.38644	0.306913	0.153456	+	0.988155i	$0.450960\pi$
$434$	10.2687	0.492916
$435$	−0.204767	−0.00981783
$436$	5.74632	0.275199
$437$	−9.74094	−0.465972
$438$	−17.2771	−0.825532
$439$	30.7802	1.46906	0.734529	−	0.678578i	$-0.237403\pi$
$439$	30.7802	1.46906	0.734529	+	0.678578i	$0.237403\pi$
$440$	−0.269815	−0.0128629
$441$	−8.28621	−0.394581
$442$	−4.19434	−0.199504
$443$	−17.8950	−0.850216	−0.425108	−	0.905143i	$-0.639764\pi$
$443$	−17.8950	−0.850216	−0.425108	+	0.905143i	$0.639764\pi$
$444$	−4.33214	−0.205594
$445$	1.54766	0.0733662
$446$	−8.32304	−0.394108
$447$	51.5109	2.43638
$448$	3.43296	0.162192
$449$	9.95646	0.469874	0.234937	−	0.972011i	$-0.424512\pi$
$449$	9.95646	0.469874	0.234937	+	0.972011i	$0.424512\pi$
$450$	−11.7560	−0.554183
$451$	10.2349	0.481943
$452$	1.69202	0.0795860
$453$	−60.4161	−2.83860
$454$	−9.75004	−0.457592
$455$	−0.417895	−0.0195912
$456$	−32.2717	−1.51126
$457$	19.3099	0.903279	0.451639	−	0.892201i	$-0.350839\pi$
$457$	19.3099	0.903279	0.451639	+	0.892201i	$0.350839\pi$
$458$	−14.4614	−0.675738
$459$	14.9946	0.699889
$460$	−0.309634	−0.0144368
$461$	0.191357	0.00891241	0.00445620	−	0.999990i	$-0.498582\pi$
$461$	0.191357	0.00891241	0.00445620	+	0.999990i	$0.498582\pi$
$462$	4.02177	0.187110
$463$	−6.73556	−0.313028	−0.156514	−	0.987676i	$-0.550026\pi$
$463$	−6.73556	−0.313028	−0.156514	+	0.987676i	$0.550026\pi$
$464$	1.55496	0.0721871
$465$	2.43668	0.112998
$466$	0.740939	0.0343233
$467$	11.9729	0.554038	0.277019	−	0.960865i	$-0.410654\pi$
$467$	11.9729	0.554038	0.277019	+	0.960865i	$0.410654\pi$
$468$	12.1588	0.562042
$469$	20.3056	0.937625
$470$	−0.120670	−0.00556609
$471$	19.8194	0.913230
$472$	8.09544	0.372623
$473$	−12.7627	−0.586830
$474$	−5.32544	−0.244605
$475$	−29.1836	−1.33903
$476$	16.9825	0.778394
$477$	38.8974	1.78099
$478$	−11.0871	−0.507111
$479$	5.37734	0.245697	0.122848	−	0.992425i	$-0.460797\pi$
$479$	5.37734	0.245697	0.122848	+	0.992425i	$0.460797\pi$
$480$	−1.58151	−0.0721859
$481$	−1.60925	−0.0733756
$482$	−12.6353	−0.575524
$483$	10.0707	0.458232
$484$	16.1836	0.735618
$485$	0.138391	0.00628403
$486$	−11.1226	−0.504531
$487$	−4.08144	−0.184948	−0.0924739	−	0.995715i	$-0.529477\pi$
$487$	−4.08144	−0.184948	−0.0924739	+	0.995715i	$0.529477\pi$
$488$	8.15106	0.368981
$489$	11.2021	0.506577
$490$	0.119014	0.00537650
$491$	17.1444	0.773714	0.386857	−	0.922140i	$-0.373561\pi$
$491$	17.1444	0.773714	0.386857	+	0.922140i	$0.373561\pi$
$492$	38.9124	1.75431
$493$	3.09113	0.139217
$494$	−5.49396	−0.247185
$495$	0.559270	0.0251373
$496$	−18.5036	−0.830838
$497$	2.24698	0.100791
$498$	−13.5187	−0.605788
$499$	−9.22388	−0.412918	−0.206459	−	0.978455i	$-0.566194\pi$
$499$	−9.22388	−0.412918	−0.206459	+	0.978455i	$0.566194\pi$
$500$	−1.85756	−0.0830726
$501$	4.74525	0.212002
$502$	−13.4359	−0.599676
$503$	−5.89248	−0.262733	−0.131366	−	0.991334i	$-0.541936\pi$
$503$	−5.89248	−0.262733	−0.131366	+	0.991334i	$0.541936\pi$
$504$	19.5526	0.870940
$505$	−0.199127	−0.00886104
$506$	1.10693	0.0492091
$507$	−27.2892	−1.21196
$508$	−5.69633	−0.252734
$509$	−0.309043	−0.0136981	−0.00684906	−	0.999977i	$-0.502180\pi$
$509$	−0.309043	−0.0136981	−0.00684906	+	0.999977i	$0.502180\pi$
$510$	−0.733497	−0.0324798
$511$	25.9855	1.14953
$512$	21.2174	0.937687
$513$	19.6407	0.867159
$514$	1.59179	0.0702110
$515$	−1.13275	−0.0499150
$516$	−48.5230	−2.13611
$517$	−2.37004	−0.104234
$518$	−1.18598	−0.0521090
$519$	34.7851	1.52690
$520$	−0.381059	−0.0167105
$521$	−9.91425	−0.434351	−0.217176	−	0.976133i	$-0.569684\pi$
$521$	−9.91425	−0.434351	−0.217176	+	0.976133i	$0.569684\pi$
$522$	1.63102	0.0713879
$523$	−45.0887	−1.97159	−0.985796	−	0.167945i	$-0.946287\pi$
$523$	−45.0887	−1.97159	−0.985796	+	0.167945i	$0.946287\pi$
$524$	19.3448	0.845082
$525$	30.1715	1.31679
$526$	15.2553	0.665164
$527$	−36.7837	−1.60232
$528$	−7.24698	−0.315384
$529$	−20.2282	−0.879487
$530$	−0.558679	−0.0242675
$531$	−16.7802	−0.728197
$532$	22.2446	0.964425
$533$	14.4547	0.626104
$534$	−21.0355	−0.910295
$535$	1.15405	0.0498938
$536$	18.5157	0.799758
$537$	35.2532	1.52129
$538$	−9.67994	−0.417332
$539$	2.33752	0.100684
$540$	0.624318	0.0268664
$541$	0.166603	0.00716284	0.00358142	−	0.999994i	$-0.498860\pi$
$541$	0.166603	0.00716284	0.00358142	+	0.999994i	$0.498860\pi$
$542$	8.74764	0.375743
$543$	−41.9799	−1.80153
$544$	23.8743	1.02360
$545$	0.373289	0.0159900
$546$	5.67994	0.243079
$547$	8.78687	0.375700	0.187850	−	0.982198i	$-0.439848\pi$
$547$	8.78687	0.375700	0.187850	+	0.982198i	$0.439848\pi$
$548$	12.1129	0.517437
$549$	−16.8955	−0.721081
$550$	3.31634	0.141409
$551$	4.04892	0.172490
$552$	9.18300	0.390854
$553$	8.00969	0.340607
$554$	16.2115	0.688759
$555$	−0.281422	−0.0119457
$556$	−3.42998	−0.145463
$557$	30.4179	1.28885	0.644424	−	0.764669i	$-0.277097\pi$
$557$	30.4179	1.28885	0.644424	+	0.764669i	$0.277097\pi$
$558$	−19.4088	−0.821640
$559$	−18.0248	−0.762366
$560$	0.554958	0.0234513
$561$	−14.4064	−0.608239
$562$	−13.7839	−0.581438
$563$	−34.2911	−1.44520	−0.722599	−	0.691267i	$-0.757053\pi$
$563$	−34.2911	−1.44520	−0.722599	+	0.691267i	$0.757053\pi$
$564$	−9.01075	−0.379421
$565$	0.109916	0.00462421
$566$	−0.724545	−0.0304549
$567$	8.32304	0.349535
$568$	2.04892	0.0859707
$569$	33.6625	1.41120	0.705602	−	0.708608i	$-0.250677\pi$
$569$	33.6625	1.41120	0.705602	+	0.708608i	$0.250677\pi$
$570$	−0.960771	−0.0402423
$571$	−23.7181	−0.992572	−0.496286	−	0.868159i	$-0.665303\pi$
$571$	−23.7181	−0.992572	−0.496286	+	0.868159i	$0.665303\pi$
$572$	−3.42998	−0.143415
$573$	5.54181	0.231513
$574$	10.6528	0.444639
$575$	8.30426	0.346311
$576$	−6.48858	−0.270358
$577$	−8.22713	−0.342500	−0.171250	−	0.985228i	$-0.554781\pi$
$577$	−8.22713	−0.342500	−0.171250	+	0.985228i	$0.554781\pi$
$578$	1.63846	0.0681511
$579$	72.2180	3.00128
$580$	0.128703	0.00534409
$581$	20.3327	0.843544
$582$	−1.88099	−0.0779694
$583$	−10.9729	−0.454449
$584$	23.6950	0.980506
$585$	0.789856	0.0326565
$586$	−10.8817	−0.449520
$587$	9.09113	0.375231	0.187616	−	0.982243i	$-0.439924\pi$
$587$	9.09113	0.375231	0.187616	+	0.982243i	$0.439924\pi$
$588$	8.88710	0.366498
$589$	−48.1812	−1.98527
$590$	0.241012	0.00992230
$591$	57.3226	2.35794
$592$	2.13706	0.0878328
$593$	30.2398	1.24180	0.620900	−	0.783890i	$-0.286767\pi$
$593$	30.2398	1.24180	0.620900	+	0.783890i	$0.286767\pi$
$594$	−2.23191	−0.0915765
$595$	1.10321	0.0452273
$596$	−32.3763	−1.32618
$597$	−44.1323	−1.80621
$598$	1.56332	0.0639289
$599$	27.6002	1.12771	0.563856	−	0.825873i	$-0.309317\pi$
$599$	27.6002	1.12771	0.563856	+	0.825873i	$0.309317\pi$
$600$	27.5120	1.12317
$601$	−25.7778	−1.05150	−0.525749	−	0.850640i	$-0.676215\pi$
$601$	−25.7778	−1.05150	−0.525749	+	0.850640i	$0.676215\pi$
$602$	−13.2838	−0.541408
$603$	−38.3793	−1.56292
$604$	37.9734	1.54512
$605$	1.05131	0.0427418
$606$	2.70650	0.109944
$607$	26.2543	1.06563	0.532814	−	0.846232i	$-0.321135\pi$
$607$	26.2543	1.06563	0.532814	+	0.846232i	$0.321135\pi$
$608$	31.2717	1.26824
$609$	−4.18598	−0.169624
$610$	0.242668	0.00982533
$611$	−3.34721	−0.135414
$612$	−32.0984	−1.29750
$613$	7.10454	0.286950	0.143475	−	0.989654i	$-0.454172\pi$
$613$	7.10454	0.286950	0.143475	+	0.989654i	$0.454172\pi$
$614$	−12.2282	−0.493490
$615$	2.52781	0.101931
$616$	−5.51573	−0.222235
$617$	31.8998	1.28424	0.642118	−	0.766606i	$-0.278056\pi$
$617$	31.8998	1.28424	0.642118	+	0.766606i	$0.278056\pi$
$618$	15.3961	0.619323
$619$	25.8767	1.04007	0.520036	−	0.854145i	$-0.325919\pi$
$619$	25.8767	1.04007	0.520036	+	0.854145i	$0.325919\pi$
$620$	−1.53153	−0.0615078
$621$	−5.58881	−0.224271
$622$	−11.6160	−0.465757
$623$	31.6383	1.26756
$624$	−10.2349	−0.409724
$625$	24.8189	0.992757
$626$	−5.39745	−0.215726
$627$	−18.8702	−0.753604
$628$	−12.4571	−0.497093
$629$	4.24831	0.169391
$630$	0.582105	0.0231916
$631$	28.1608	1.12106	0.560531	−	0.828133i	$-0.310597\pi$
$631$	28.1608	1.12106	0.560531	+	0.828133i	$0.310597\pi$
$632$	7.30367	0.290524
$633$	9.15405	0.363841
$634$	1.36360	0.0541555
$635$	−0.370042	−0.0146847
$636$	−41.7181	−1.65423
$637$	3.30127	0.130801
$638$	−0.460107	−0.0182158
$639$	−4.24698	−0.168008
$640$	1.26816	0.0501284
$641$	5.08516	0.200852	0.100426	−	0.994945i	$-0.467979\pi$
$641$	5.08516	0.200852	0.100426	+	0.994945i	$0.467979\pi$
$642$	−15.6856	−0.619060
$643$	−49.6631	−1.95852	−0.979260	−	0.202607i	$-0.935059\pi$
$643$	−49.6631	−1.95852	−0.979260	+	0.202607i	$0.935059\pi$
$644$	−6.32975	−0.249427
$645$	−3.15213	−0.124115
$646$	14.5036	0.570638
$647$	−14.0508	−0.552395	−0.276198	−	0.961101i	$-0.589074\pi$
$647$	−14.0508	−0.552395	−0.276198	+	0.961101i	$0.589074\pi$
$648$	7.58940	0.298140
$649$	4.73364	0.185812
$650$	4.68366	0.183708
$651$	49.8122	1.95229
$652$	−7.04088	−0.275742
$653$	31.7894	1.24401	0.622007	−	0.783011i	$-0.286317\pi$
$653$	31.7894	1.24401	0.622007	+	0.783011i	$0.286317\pi$
$654$	−5.07367	−0.198396
$655$	1.25667	0.0491021
$656$	−19.1957	−0.749465
$657$	−49.1148	−1.91615
$658$	−2.46681	−0.0961663
$659$	4.16613	0.162289	0.0811447	−	0.996702i	$-0.474142\pi$
$659$	4.16613	0.162289	0.0811447	+	0.996702i	$0.474142\pi$
$660$	−0.599827	−0.0233482
$661$	−47.4107	−1.84406	−0.922032	−	0.387115i	$-0.873472\pi$
$661$	−47.4107	−1.84406	−0.922032	+	0.387115i	$0.873472\pi$
$662$	11.3817	0.442360
$663$	−20.3461	−0.790179
$664$	18.5405	0.719510
$665$	1.44504	0.0560363
$666$	2.24160	0.0868603
$667$	−1.15213	−0.0446106
$668$	−2.98254	−0.115398
$669$	−40.3739	−1.56094
$670$	0.551237	0.0212962
$671$	4.76617	0.183996
$672$	−32.3303	−1.24717
$673$	23.6420	0.911334	0.455667	−	0.890150i	$-0.349401\pi$
$673$	23.6420	0.911334	0.455667	+	0.890150i	$0.349401\pi$
$674$	13.3110	0.512719
$675$	−16.7439	−0.644474
$676$	17.1521	0.659697
$677$	5.28860	0.203257	0.101629	−	0.994822i	$-0.467595\pi$
$677$	5.28860	0.203257	0.101629	+	0.994822i	$0.467595\pi$
$678$	−1.49396	−0.0573752
$679$	2.82908	0.108570
$680$	1.00597	0.0385771
$681$	−47.2960	−1.81239
$682$	5.47517	0.209655
$683$	12.0847	0.462408	0.231204	−	0.972905i	$-0.425734\pi$
$683$	12.0847	0.462408	0.231204	+	0.972905i	$0.425734\pi$
$684$	−42.0441	−1.60760
$685$	0.786872	0.0300648
$686$	11.1618	0.426160
$687$	−70.1503	−2.67640
$688$	23.9366	0.912575
$689$	−15.4969	−0.590387
$690$	0.273390	0.0104078
$691$	21.2674	0.809051	0.404525	−	0.914527i	$-0.367437\pi$
$691$	21.2674	0.809051	0.404525	+	0.914527i	$0.367437\pi$
$692$	−21.8635	−0.831127
$693$	11.4330	0.434302
$694$	13.5660	0.514957
$695$	−0.222816	−0.00845191
$696$	−3.81700	−0.144683
$697$	−38.1594	−1.44539
$698$	4.90143	0.185522
$699$	3.59419	0.135945
$700$	−18.9638	−0.716763
$701$	28.1661	1.06382	0.531910	−	0.846801i	$-0.321474\pi$
$701$	28.1661	1.06382	0.531910	+	0.846801i	$0.321474\pi$
$702$	−3.15213	−0.118969
$703$	5.56465	0.209875
$704$	1.83041	0.0689863
$705$	−0.585352	−0.0220456
$706$	9.43594	0.355126
$707$	−4.07069	−0.153094
$708$	17.9970	0.676369
$709$	−1.58151	−0.0593950	−0.0296975	−	0.999559i	$-0.509454\pi$
$709$	−1.58151	−0.0593950	−0.0296975	+	0.999559i	$0.509454\pi$
$710$	0.0609989	0.00228925
$711$	−15.1390	−0.567756
$712$	28.8495	1.08118
$713$	13.7101	0.513446
$714$	−14.9946	−0.561160
$715$	−0.222816	−0.00833286
$716$	−22.1578	−0.828075
$717$	−53.7818	−2.00852
$718$	−0.475910	−0.0177608
$719$	−6.54958	−0.244258	−0.122129	−	0.992514i	$-0.538972\pi$
$719$	−6.54958	−0.244258	−0.122129	+	0.992514i	$0.538972\pi$
$720$	−1.04892	−0.0390908
$721$	−23.1564	−0.862391
$722$	8.45340	0.314603
$723$	−61.2922	−2.27948
$724$	26.3857	0.980617
$725$	−3.45175	−0.128195
$726$	−14.2892	−0.530322
$727$	42.4330	1.57375	0.786876	−	0.617112i	$-0.211697\pi$
$727$	42.4330	1.57375	0.786876	+	0.617112i	$0.211697\pi$
$728$	−7.78986	−0.288711
$729$	−42.8418	−1.58673
$730$	0.705431	0.0261092
$731$	47.5840	1.75996
$732$	18.1207	0.669759
$733$	−36.2892	−1.34037	−0.670186	−	0.742193i	$-0.733786\pi$
$733$	−36.2892	−1.34037	−0.670186	+	0.742193i	$0.733786\pi$
$734$	19.0459	0.702998
$735$	0.577319	0.0212947
$736$	−8.89844	−0.328001
$737$	10.8267	0.398806
$738$	−20.1347	−0.741167
$739$	42.8896	1.57772	0.788860	−	0.614573i	$-0.210672\pi$
$739$	42.8896	1.57772	0.788860	+	0.614573i	$0.210672\pi$
$740$	0.176883	0.00650235
$741$	−26.6504	−0.979027
$742$	−11.4209	−0.419274
$743$	14.5512	0.533833	0.266917	−	0.963720i	$-0.413995\pi$
$743$	14.5512	0.533833	0.266917	+	0.963720i	$0.413995\pi$
$744$	45.4215	1.66523
$745$	−2.10321	−0.0770557
$746$	−8.09916	−0.296531
$747$	−38.4306	−1.40610
$748$	9.05489	0.331079
$749$	23.5918	0.862025
$750$	1.64012	0.0598887
$751$	12.8364	0.468406	0.234203	−	0.972188i	$-0.424752\pi$
$751$	12.8364	0.468406	0.234203	+	0.972188i	$0.424752\pi$
$752$	4.44504	0.162094
$753$	−65.1758	−2.37514
$754$	−0.649809	−0.0236646
$755$	2.46681	0.0897765
$756$	12.7627	0.464175
$757$	−10.7248	−0.389800	−0.194900	−	0.980823i	$-0.562438\pi$
$757$	−10.7248	−0.389800	−0.194900	+	0.980823i	$0.562438\pi$
$758$	−8.33645	−0.302794
$759$	5.36957	0.194903
$760$	1.31767	0.0477968
$761$	22.9608	0.832327	0.416164	−	0.909290i	$-0.363374\pi$
$761$	22.9608	0.832327	0.416164	+	0.909290i	$0.363374\pi$
$762$	5.02954	0.182201
$763$	7.63102	0.276262
$764$	−3.48321	−0.126018
$765$	−2.08516	−0.0753892
$766$	16.5321	0.597330
$767$	6.68532	0.241393
$768$	−9.01075	−0.325148
$769$	18.2577	0.658391	0.329195	−	0.944262i	$-0.393223\pi$
$769$	18.2577	0.658391	0.329195	+	0.944262i	$0.393223\pi$
$770$	−0.164210	−0.00591773
$771$	7.72156	0.278085
$772$	−45.3913	−1.63367
$773$	−48.1309	−1.73115	−0.865575	−	0.500779i	$-0.833047\pi$
$773$	−48.1309	−1.73115	−0.865575	+	0.500779i	$0.833047\pi$
$774$	25.1075	0.902471
$775$	41.0750	1.47546
$776$	2.57971	0.0926063
$777$	−5.75302	−0.206388
$778$	3.30393	0.118452
$779$	−49.9831	−1.79083
$780$	−0.847134	−0.0303323
$781$	1.19806	0.0428700
$782$	−4.12705	−0.147583
$783$	2.32304	0.0830188
$784$	−4.38404	−0.156573
$785$	−0.809234	−0.0288828
$786$	−17.0804	−0.609237
$787$	15.6679	0.558499	0.279249	−	0.960219i	$-0.409914\pi$
$787$	15.6679	0.558499	0.279249	+	0.960219i	$0.409914\pi$
$788$	−36.0291	−1.28348
$789$	74.0014	2.63452
$790$	0.217440	0.00773615
$791$	2.24698	0.0798934
$792$	10.4252	0.370443
$793$	6.73125	0.239034
$794$	−2.84548	−0.100982
$795$	−2.71007	−0.0961163
$796$	27.7385	0.983167
$797$	−23.5719	−0.834961	−0.417481	−	0.908686i	$-0.637087\pi$
$797$	−23.5719	−0.834961	−0.417481	+	0.908686i	$0.637087\pi$
$798$	−19.6407	−0.695274
$799$	8.83638	0.312609
$800$	−26.6595	−0.942556
$801$	−59.7991	−2.11290
$802$	8.01566	0.283043
$803$	13.8552	0.488938
$804$	41.1624	1.45169
$805$	−0.411190	−0.0144925
$806$	7.73258	0.272368
$807$	−46.9560	−1.65293
$808$	−3.71187	−0.130583
$809$	−4.77048	−0.167721	−0.0838606	−	0.996477i	$-0.526725\pi$
$809$	−4.77048	−0.167721	−0.0838606	+	0.996477i	$0.526725\pi$
$810$	0.225946	0.00793894
$811$	−25.0605	−0.879994	−0.439997	−	0.897999i	$-0.645021\pi$
$811$	−25.0605	−0.879994	−0.439997	+	0.897999i	$0.645021\pi$
$812$	2.63102	0.0923308
$813$	42.4336	1.48821
$814$	−0.632351	−0.0221639
$815$	−0.457386	−0.0160215
$816$	27.0194	0.945867
$817$	62.3279	2.18058
$818$	−17.5737	−0.614452
$819$	16.1468	0.564213
$820$	−1.58881	−0.0554837
$821$	31.3599	1.09447	0.547234	−	0.836980i	$-0.315681\pi$
$821$	31.3599	1.09447	0.547234	+	0.836980i	$0.315681\pi$
$822$	−10.6950	−0.373031
$823$	12.4316	0.433339	0.216670	−	0.976245i	$-0.430481\pi$
$823$	12.4316	0.433339	0.216670	+	0.976245i	$0.430481\pi$
$824$	−21.1153	−0.735586
$825$	16.0871	0.560080
$826$	4.92692	0.171429
$827$	−34.5907	−1.20284	−0.601419	−	0.798934i	$-0.705398\pi$
$827$	−34.5907	−1.20284	−0.601419	+	0.798934i	$0.705398\pi$
$828$	11.9638	0.415769
$829$	9.06638	0.314888	0.157444	−	0.987528i	$-0.449675\pi$
$829$	9.06638	0.314888	0.157444	+	0.987528i	$0.449675\pi$
$830$	0.551974	0.0191593
$831$	78.6395	2.72797
$832$	2.58509	0.0896218
$833$	−8.71512	−0.301961
$834$	3.02848	0.104868
$835$	−0.193750	−0.00670501
$836$	11.8605	0.410205
$837$	−27.6437	−0.955506
$838$	−19.6843	−0.679981
$839$	0.823708	0.0284376	0.0142188	−	0.999899i	$-0.495474\pi$
$839$	0.823708	0.0284376	0.0142188	+	0.999899i	$0.495474\pi$
$840$	−1.36227	−0.0470029
$841$	−28.5211	−0.983486
$842$	15.9148	0.548462
$843$	−66.8636	−2.30291
$844$	−5.75361	−0.198047
$845$	1.11423	0.0383306
$846$	4.66248	0.160299
$847$	21.4916	0.738459
$848$	20.5797	0.706710
$849$	−3.51466	−0.120623
$850$	−12.3645	−0.424100
$851$	−1.58343	−0.0542794
$852$	4.55496	0.156050
$853$	−5.33704	−0.182737	−0.0913685	−	0.995817i	$-0.529124\pi$
$853$	−5.33704	−0.182737	−0.0913685	+	0.995817i	$0.529124\pi$
$854$	4.96077	0.169754
$855$	−2.73125	−0.0934068
$856$	21.5123	0.735274
$857$	25.9162	0.885279	0.442640	−	0.896700i	$-0.354042\pi$
$857$	25.9162	0.885279	0.442640	+	0.896700i	$0.354042\pi$
$858$	3.02848	0.103390
$859$	−43.9318	−1.49893	−0.749467	−	0.662041i	$-0.769690\pi$
$859$	−43.9318	−1.49893	−0.749467	+	0.662041i	$0.769690\pi$
$860$	1.98121	0.0675588
$861$	51.6752	1.76108
$862$	−6.49993	−0.221388
$863$	−22.6450	−0.770846	−0.385423	−	0.922740i	$-0.625944\pi$
$863$	−22.6450	−0.770846	−0.385423	+	0.922740i	$0.625944\pi$
$864$	17.9420	0.610399
$865$	−1.42029	−0.0482912
$866$	3.54420	0.120437
$867$	7.94795	0.269927
$868$	−31.3086	−1.06268
$869$	4.27067	0.144873
$870$	−0.113637	−0.00385266
$871$	15.2905	0.518100
$872$	6.95838	0.235640
$873$	−5.34721	−0.180976
$874$	−5.40581	−0.182854
$875$	−2.46681	−0.0833935
$876$	52.6765	1.77977
$877$	−18.5405	−0.626068	−0.313034	−	0.949742i	$-0.601345\pi$
$877$	−18.5405	−0.626068	−0.313034	+	0.949742i	$0.601345\pi$
$878$	17.0817	0.576480
$879$	−52.7857	−1.78042
$880$	0.295897	0.00997468
$881$	−0.0416216	−0.00140227	−0.000701133	−	1.00000i	$-0.500223\pi$
$881$	−0.0416216	−0.00140227	−0.000701133		1.00000i	$0.500223\pi$
$882$	−4.59850	−0.154840
$883$	8.53425	0.287200	0.143600	−	0.989636i	$-0.454132\pi$
$883$	8.53425	0.287200	0.143600	+	0.989636i	$0.454132\pi$
$884$	12.7882	0.430114
$885$	1.16911	0.0392993
$886$	−9.93097	−0.333637
$887$	44.1420	1.48214	0.741071	−	0.671427i	$-0.234318\pi$
$887$	44.1420	1.48214	0.741071	+	0.671427i	$0.234318\pi$
$888$	−5.24591	−0.176041
$889$	−7.56465	−0.253710
$890$	0.858888	0.0287900
$891$	4.43775	0.148670
$892$	25.3763	0.849660
$893$	11.5743	0.387320
$894$	28.5864	0.956073
$895$	−1.43940	−0.0481139
$896$	25.9245	0.866078
$897$	7.58343	0.253203
$898$	5.52542	0.184386
$899$	−5.69873	−0.190063
$900$	35.8431	1.19477
$901$	40.9108	1.36294
$902$	5.67994	0.189121
$903$	−64.4379	−2.14436
$904$	2.04892	0.0681460
$905$	1.71405	0.0569771
$906$	−33.5284	−1.11391
$907$	50.6031	1.68025	0.840125	−	0.542393i	$-0.182482\pi$
$907$	50.6031	1.68025	0.840125	+	0.542393i	$0.182482\pi$
$908$	29.7271	0.986527
$909$	7.69394	0.255192
$910$	−0.231914	−0.00768788
$911$	−4.50663	−0.149311	−0.0746557	−	0.997209i	$-0.523786\pi$
$911$	−4.50663	−0.149311	−0.0746557	+	0.997209i	$0.523786\pi$
$912$	35.3913	1.17192
$913$	10.8412	0.358790
$914$	10.7162	0.354460
$915$	1.17715	0.0389152
$916$	44.0917	1.45683
$917$	25.6896	0.848346
$918$	8.32139	0.274647
$919$	43.2556	1.42687	0.713435	−	0.700721i	$-0.247138\pi$
$919$	43.2556	1.42687	0.713435	+	0.700721i	$0.247138\pi$
$920$	−0.374945	−0.0123616
$921$	−59.3172	−1.95457
$922$	0.106195	0.00349736
$923$	1.69202	0.0556936
$924$	−12.2620	−0.403392
$925$	−4.74392	−0.155979
$926$	−3.73795	−0.122837
$927$	43.7676	1.43752
$928$	3.69873	0.121417
$929$	−4.79358	−0.157272	−0.0786361	−	0.996903i	$-0.525057\pi$
$929$	−4.79358	−0.157272	−0.0786361	+	0.996903i	$0.525057\pi$
$930$	1.35226	0.0443422
$931$	−11.4155	−0.374128
$932$	−2.25906	−0.0739980
$933$	−56.3473	−1.84473
$934$	6.64443	0.217412
$935$	0.588219	0.0192368
$936$	14.7235	0.481252
$937$	−31.2470	−1.02079	−0.510397	−	0.859939i	$-0.670502\pi$
$937$	−31.2470	−1.02079	−0.510397	+	0.859939i	$0.670502\pi$
$938$	11.2687	0.367938
$939$	−26.1823	−0.854426
$940$	0.367913	0.0120000
$941$	−35.1530	−1.14595	−0.572977	−	0.819571i	$-0.694212\pi$
$941$	−35.1530	−1.14595	−0.572977	+	0.819571i	$0.694212\pi$
$942$	10.9989	0.358365
$943$	14.2228	0.463159
$944$	−8.87800	−0.288954
$945$	0.829085	0.0269701
$946$	−7.08277	−0.230281
$947$	−46.5846	−1.51380	−0.756898	−	0.653533i	$-0.773286\pi$
$947$	−46.5846	−1.51380	−0.756898	+	0.653533i	$0.773286\pi$
$948$	16.2368	0.527347
$949$	19.5676	0.635192
$950$	−16.1957	−0.525457
$951$	6.61463	0.214494
$952$	20.5646	0.666504
$953$	56.8437	1.84135	0.920674	−	0.390333i	$-0.127640\pi$
$953$	56.8437	1.84135	0.920674	+	0.390333i	$0.127640\pi$
$954$	21.5864	0.698886
$955$	−0.226274	−0.00732206
$956$	33.8036	1.09329
$957$	−2.23191	−0.0721475
$958$	2.98420	0.0964150
$959$	16.0858	0.519436
$960$	0.452075	0.0145906
$961$	36.8135	1.18753
$962$	−0.893068	−0.0287937
$963$	−44.5905	−1.43691
$964$	38.5241	1.24078
$965$	−2.94869	−0.0949217
$966$	5.58881	0.179817
$967$	34.1511	1.09822	0.549112	−	0.835749i	$-0.314966\pi$
$967$	34.1511	1.09822	0.549112	+	0.835749i	$0.314966\pi$
$968$	19.5972	0.629877
$969$	70.3551	2.26013
$970$	0.0768014	0.00246594
$971$	11.0707	0.355275	0.177638	−	0.984096i	$-0.443155\pi$
$971$	11.0707	0.355275	0.177638	+	0.984096i	$0.443155\pi$
$972$	33.9119	1.08772
$973$	−4.55496	−0.146025
$974$	−2.26503	−0.0725762
$975$	22.7198	0.727615
$976$	−8.93900	−0.286130
$977$	−36.4239	−1.16530	−0.582651	−	0.812722i	$-0.697985\pi$
$977$	−36.4239	−1.16530	−0.582651	+	0.812722i	$0.697985\pi$
$978$	6.21670	0.198788
$979$	16.8692	0.539141
$980$	−0.362864	−0.0115913
$981$	−14.4233	−0.460500
$982$	9.51440	0.303617
$983$	20.3056	0.647648	0.323824	−	0.946117i	$-0.395031\pi$
$983$	20.3056	0.647648	0.323824	+	0.946117i	$0.395031\pi$
$984$	47.1202	1.50214
$985$	−2.34050	−0.0745746
$986$	1.71545	0.0546310
$987$	−11.9661	−0.380887
$988$	16.7506	0.532908
$989$	−17.7356	−0.563958
$990$	0.310371	0.00986425
$991$	−6.69096	−0.212545	−0.106273	−	0.994337i	$-0.533892\pi$
$991$	−6.69096	−0.212545	−0.106273	+	0.994337i	$0.533892\pi$
$992$	−44.0140	−1.39745
$993$	55.2107	1.75206
$994$	1.24698	0.0395518
$995$	1.80194	0.0571253
$996$	41.2174	1.30602
$997$	−8.30021	−0.262870	−0.131435	−	0.991325i	$-0.541959\pi$
$997$	−8.30021	−0.262870	−0.131435	+	0.991325i	$0.541959\pi$
$998$	−5.11887	−0.162035
$999$	3.19269	0.101012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.a.1.2	✓	3	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q+0.554958 q^{2} +2.69202 q^{3} -1.69202 q^{4} -0.109916 q^{5} +1.49396 q^{6} -2.24698 q^{7} -2.04892 q^{8} +4.24698 q^{9} +O(q^{10})\)	\(q+0.554958 q^{2} +2.69202 q^{3} -1.69202 q^{4} -0.109916 q^{5} +1.49396 q^{6} -2.24698 q^{7} -2.04892 q^{8} +4.24698 q^{9} -0.0609989 q^{10} -1.19806 q^{11} -4.55496 q^{12} -1.69202 q^{13} -1.24698 q^{14} -0.295897 q^{15} +2.24698 q^{16} +4.46681 q^{17} +2.35690 q^{18} +5.85086 q^{19} +0.185981 q^{20} -6.04892 q^{21} -0.664874 q^{22} -1.66487 q^{23} -5.51573 q^{24} -4.98792 q^{25} -0.939001 q^{26} +3.35690 q^{27} +3.80194 q^{28} +0.692021 q^{29} -0.164210 q^{30} -8.23490 q^{31} +5.34481 q^{32} -3.22521 q^{33} +2.47889 q^{34} +0.246980 q^{35} -7.18598 q^{36} +0.951083 q^{37} +3.24698 q^{38} -4.55496 q^{39} +0.225209 q^{40} -8.54288 q^{41} -3.35690 q^{42} +10.6528 q^{43} +2.02715 q^{44} -0.466812 q^{45} -0.923936 q^{46} +1.97823 q^{47} +6.04892 q^{48} -1.95108 q^{49} -2.76809 q^{50} +12.0248 q^{51} +2.86294 q^{52} +9.15883 q^{53} +1.86294 q^{54} +0.131687 q^{55} +4.60388 q^{56} +15.7506 q^{57} +0.384043 q^{58} -3.95108 q^{59} +0.500664 q^{60} -3.97823 q^{61} -4.57002 q^{62} -9.54288 q^{63} -1.52781 q^{64} +0.185981 q^{65} -1.78986 q^{66} -9.03684 q^{67} -7.55794 q^{68} -4.48188 q^{69} +0.137063 q^{70} -1.00000 q^{71} -8.70171 q^{72} -11.5646 q^{73} +0.527811 q^{74} -13.4276 q^{75} -9.89977 q^{76} +2.69202 q^{77} -2.52781 q^{78} -3.56465 q^{79} -0.246980 q^{80} -3.70410 q^{81} -4.74094 q^{82} -9.04892 q^{83} +10.2349 q^{84} -0.490975 q^{85} +5.91185 q^{86} +1.86294 q^{87} +2.45473 q^{88} -14.0804 q^{89} -0.259061 q^{90} +3.80194 q^{91} +2.81700 q^{92} -22.1685 q^{93} +1.09783 q^{94} -0.643104 q^{95} +14.3884 q^{96} -1.25906 q^{97} -1.08277 q^{98} -5.08815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} - q^{5} - 5 q^{6} - 2 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 - q^5 - 5 * q^6 - 2 * q^7 + 3 * q^8 + 8 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} - q^{5} - 5 q^{6} - 2 q^{7} + 3 q^{8} + 8 q^{9} - 10 q^{10} - 8 q^{11} - 14 q^{12} + q^{14} + 13 q^{15} + 2 q^{16} + 10 q^{17} + 3 q^{18} + 4 q^{19} - 14 q^{20} - 9 q^{21} - 3 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} + 7 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} + 11 q^{30} - q^{31} - 7 q^{32} - 8 q^{33} + 23 q^{34} - 4 q^{35} - 7 q^{36} + 12 q^{37} + 5 q^{38} - 14 q^{39} - q^{40} - 7 q^{41} - 6 q^{42} + 14 q^{43} + 2 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} - 15 q^{49} + 12 q^{50} - 11 q^{51} + 14 q^{52} + 19 q^{53} + 11 q^{54} - 2 q^{55} + 5 q^{56} + 11 q^{57} - 9 q^{58} - 21 q^{59} + 14 q^{60} - 15 q^{61} + 11 q^{62} - 10 q^{63} - 11 q^{64} - 14 q^{65} + 18 q^{66} + q^{67} + 21 q^{68} + 15 q^{69} - 5 q^{70} - 3 q^{71} + q^{72} - 13 q^{73} + 8 q^{74} - 24 q^{75} - 7 q^{76} + 3 q^{77} - 14 q^{78} + 11 q^{79} + 4 q^{80} - 25 q^{81} - 18 q^{83} + 7 q^{84} - 36 q^{85} + 14 q^{86} + 11 q^{87} - 15 q^{88} - 8 q^{89} - 15 q^{90} + 7 q^{91} - 21 q^{92} - 36 q^{93} - 15 q^{94} - 6 q^{95} + 14 q^{96} - 18 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 - q^5 - 5 * q^6 - 2 * q^7 + 3 * q^8 + 8 * q^9 - 10 * q^10 - 8 * q^11 - 14 * q^12 + q^14 + 13 * q^15 + 2 * q^16 + 10 * q^17 + 3 * q^18 + 4 * q^19 - 14 * q^20 - 9 * q^21 - 3 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 + 7 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 + 11 * q^30 - q^31 - 7 * q^32 - 8 * q^33 + 23 * q^34 - 4 * q^35 - 7 * q^36 + 12 * q^37 + 5 * q^38 - 14 * q^39 - q^40 - 7 * q^41 - 6 * q^42 + 14 * q^43 + 2 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 - 15 * q^49 + 12 * q^50 - 11 * q^51 + 14 * q^52 + 19 * q^53 + 11 * q^54 - 2 * q^55 + 5 * q^56 + 11 * q^57 - 9 * q^58 - 21 * q^59 + 14 * q^60 - 15 * q^61 + 11 * q^62 - 10 * q^63 - 11 * q^64 - 14 * q^65 + 18 * q^66 + q^67 + 21 * q^68 + 15 * q^69 - 5 * q^70 - 3 * q^71 + q^72 - 13 * q^73 + 8 * q^74 - 24 * q^75 - 7 * q^76 + 3 * q^77 - 14 * q^78 + 11 * q^79 + 4 * q^80 - 25 * q^81 - 18 * q^83 + 7 * q^84 - 36 * q^85 + 14 * q^86 + 11 * q^87 - 15 * q^88 - 8 * q^89 - 15 * q^90 + 7 * q^91 - 21 * q^92 - 36 * q^93 - 15 * q^94 - 6 * q^95 + 14 * q^96 - 18 * q^97 - 10 * q^98 - 19 * q^99

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