LMFDB - Embedded newform 1014.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.04892 q^{5} +1.00000 q^{6} -0.692021 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.04892 q^{5} +1.00000 q^{6} -0.692021 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.04892 q^{10} +4.85086 q^{11} +1.00000 q^{12} -0.692021 q^{14} -4.04892 q^{15} +1.00000 q^{16} +7.38404 q^{17} +1.00000 q^{18} +1.78017 q^{19} -4.04892 q^{20} -0.692021 q^{21} +4.85086 q^{22} +5.10992 q^{23} +1.00000 q^{24} +11.3937 q^{25} +1.00000 q^{27} -0.692021 q^{28} -3.34481 q^{29} -4.04892 q^{30} -0.972853 q^{31} +1.00000 q^{32} +4.85086 q^{33} +7.38404 q^{34} +2.80194 q^{35} +1.00000 q^{36} -1.28621 q^{37} +1.78017 q^{38} -4.04892 q^{40} -1.50604 q^{41} -0.692021 q^{42} -8.31767 q^{43} +4.85086 q^{44} -4.04892 q^{45} +5.10992 q^{46} +7.20775 q^{47} +1.00000 q^{48} -6.52111 q^{49} +11.3937 q^{50} +7.38404 q^{51} +13.4765 q^{53} +1.00000 q^{54} -19.6407 q^{55} -0.692021 q^{56} +1.78017 q^{57} -3.34481 q^{58} -1.30798 q^{59} -4.04892 q^{60} -0.396125 q^{61} -0.972853 q^{62} -0.692021 q^{63} +1.00000 q^{64} +4.85086 q^{66} -6.05429 q^{67} +7.38404 q^{68} +5.10992 q^{69} +2.80194 q^{70} +1.32975 q^{71} +1.00000 q^{72} +7.65279 q^{73} -1.28621 q^{74} +11.3937 q^{75} +1.78017 q^{76} -3.35690 q^{77} -8.33944 q^{79} -4.04892 q^{80} +1.00000 q^{81} -1.50604 q^{82} -15.3274 q^{83} -0.692021 q^{84} -29.8974 q^{85} -8.31767 q^{86} -3.34481 q^{87} +4.85086 q^{88} -3.10992 q^{89} -4.04892 q^{90} +5.10992 q^{92} -0.972853 q^{93} +7.20775 q^{94} -7.20775 q^{95} +1.00000 q^{96} +8.54288 q^{97} -6.52111 q^{98} +4.85086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + q^{11} + 3 q^{12} + 3 q^{14} - 3 q^{15} + 3 q^{16} + 12 q^{17} + 3 q^{18} + 4 q^{19} - 3 q^{20} + 3 q^{21} + q^{22} + 16 q^{23} + 3 q^{24} + 2 q^{25} + 3 q^{27} + 3 q^{28} + 13 q^{29} - 3 q^{30} - 9 q^{31} + 3 q^{32} + q^{33} + 12 q^{34} + 4 q^{35} + 3 q^{36} - 12 q^{37} + 4 q^{38} - 3 q^{40} - 14 q^{41} + 3 q^{42} - 8 q^{43} + q^{44} - 3 q^{45} + 16 q^{46} + 4 q^{47} + 3 q^{48} - 4 q^{49} + 2 q^{50} + 12 q^{51} + 15 q^{53} + 3 q^{54} - 22 q^{55} + 3 q^{56} + 4 q^{57} + 13 q^{58} - 9 q^{59} - 3 q^{60} - 10 q^{61} - 9 q^{62} + 3 q^{63} + 3 q^{64} + q^{66} - 6 q^{67} + 12 q^{68} + 16 q^{69} + 4 q^{70} + 6 q^{71} + 3 q^{72} + 5 q^{73} - 12 q^{74} + 2 q^{75} + 4 q^{76} - 6 q^{77} - 5 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} - 7 q^{83} + 3 q^{84} - 26 q^{85} - 8 q^{86} + 13 q^{87} + q^{88} - 10 q^{89} - 3 q^{90} + 16 q^{92} - 9 q^{93} + 4 q^{94} - 4 q^{95} + 3 q^{96} + 7 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + q^11 + 3 * q^12 + 3 * q^14 - 3 * q^15 + 3 * q^16 + 12 * q^17 + 3 * q^18 + 4 * q^19 - 3 * q^20 + 3 * q^21 + q^22 + 16 * q^23 + 3 * q^24 + 2 * q^25 + 3 * q^27 + 3 * q^28 + 13 * q^29 - 3 * q^30 - 9 * q^31 + 3 * q^32 + q^33 + 12 * q^34 + 4 * q^35 + 3 * q^36 - 12 * q^37 + 4 * q^38 - 3 * q^40 - 14 * q^41 + 3 * q^42 - 8 * q^43 + q^44 - 3 * q^45 + 16 * q^46 + 4 * q^47 + 3 * q^48 - 4 * q^49 + 2 * q^50 + 12 * q^51 + 15 * q^53 + 3 * q^54 - 22 * q^55 + 3 * q^56 + 4 * q^57 + 13 * q^58 - 9 * q^59 - 3 * q^60 - 10 * q^61 - 9 * q^62 + 3 * q^63 + 3 * q^64 + q^66 - 6 * q^67 + 12 * q^68 + 16 * q^69 + 4 * q^70 + 6 * q^71 + 3 * q^72 + 5 * q^73 - 12 * q^74 + 2 * q^75 + 4 * q^76 - 6 * q^77 - 5 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 - 7 * q^83 + 3 * q^84 - 26 * q^85 - 8 * q^86 + 13 * q^87 + q^88 - 10 * q^89 - 3 * q^90 + 16 * q^92 - 9 * q^93 + 4 * q^94 - 4 * q^95 + 3 * q^96 + 7 * q^97 - 4 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−4.04892	−1.81073	−0.905365	−	0.424633i	$-0.860403\pi$
$5$	−4.04892	−1.81073	−0.905365	+	0.424633i	$0.860403\pi$
$6$	1.00000	0.408248
$7$	−0.692021	−0.261560	−0.130780	−	0.991411i	$-0.541748\pi$
$7$	−0.692021	−0.261560	−0.130780	+	0.991411i	$0.541748\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−4.04892	−1.28038
$11$	4.85086	1.46259	0.731294	−	0.682062i	$-0.238917\pi$
$11$	4.85086	1.46259	0.731294	+	0.682062i	$0.238917\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−0.692021	−0.184951
$15$	−4.04892	−1.04543
$16$	1.00000	0.250000
$17$	7.38404	1.79089	0.895447	−	0.445169i	$-0.146856\pi$
$17$	7.38404	1.79089	0.895447	+	0.445169i	$0.146856\pi$
$18$	1.00000	0.235702
$19$	1.78017	0.408398	0.204199	−	0.978929i	$-0.434541\pi$
$19$	1.78017	0.408398	0.204199	+	0.978929i	$0.434541\pi$
$20$	−4.04892	−0.905365
$21$	−0.692021	−0.151011
$22$	4.85086	1.03421
$23$	5.10992	1.06549	0.532746	−	0.846275i	$-0.321160\pi$
$23$	5.10992	1.06549	0.532746	+	0.846275i	$0.321160\pi$
$24$	1.00000	0.204124
$25$	11.3937	2.27875
$26$	0	0
$27$	1.00000	0.192450
$28$	−0.692021	−0.130780
$29$	−3.34481	−0.621116	−0.310558	−	0.950554i	$-0.600516\pi$
$29$	−3.34481	−0.621116	−0.310558	+	0.950554i	$0.600516\pi$
$30$	−4.04892	−0.739228
$31$	−0.972853	−0.174730	−0.0873648	−	0.996176i	$-0.527845\pi$
$31$	−0.972853	−0.174730	−0.0873648	+	0.996176i	$0.527845\pi$
$32$	1.00000	0.176777
$33$	4.85086	0.844425
$34$	7.38404	1.26635
$35$	2.80194	0.473614
$36$	1.00000	0.166667
$37$	−1.28621	−0.211451	−0.105726	−	0.994395i	$-0.533717\pi$
$37$	−1.28621	−0.211451	−0.105726	+	0.994395i	$0.533717\pi$
$38$	1.78017	0.288781
$39$	0	0
$40$	−4.04892	−0.640190
$41$	−1.50604	−0.235204	−0.117602	−	0.993061i	$-0.537521\pi$
$41$	−1.50604	−0.235204	−0.117602	+	0.993061i	$0.537521\pi$
$42$	−0.692021	−0.106781
$43$	−8.31767	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$43$	−8.31767	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$44$	4.85086	0.731294
$45$	−4.04892	−0.603577
$46$	5.10992	0.753416
$47$	7.20775	1.05136	0.525679	−	0.850683i	$-0.323811\pi$
$47$	7.20775	1.05136	0.525679	+	0.850683i	$0.323811\pi$
$48$	1.00000	0.144338
$49$	−6.52111	−0.931587
$50$	11.3937	1.61132
$51$	7.38404	1.03397
$52$	0	0
$53$	13.4765	1.85114	0.925570	−	0.378577i	$-0.123586\pi$
$53$	13.4765	1.85114	0.925570	+	0.378577i	$0.123586\pi$
$54$	1.00000	0.136083
$55$	−19.6407	−2.64835
$56$	−0.692021	−0.0924753
$57$	1.78017	0.235789
$58$	−3.34481	−0.439196
$59$	−1.30798	−0.170284	−0.0851422	−	0.996369i	$-0.527134\pi$
$59$	−1.30798	−0.170284	−0.0851422	+	0.996369i	$0.527134\pi$
$60$	−4.04892	−0.522713
$61$	−0.396125	−0.0507185	−0.0253593	−	0.999678i	$-0.508073\pi$
$61$	−0.396125	−0.0507185	−0.0253593	+	0.999678i	$0.508073\pi$
$62$	−0.972853	−0.123552
$63$	−0.692021	−0.0871865
$64$	1.00000	0.125000
$65$	0	0
$66$	4.85086	0.597099
$67$	−6.05429	−0.739650	−0.369825	−	0.929101i	$-0.620582\pi$
$67$	−6.05429	−0.739650	−0.369825	+	0.929101i	$0.620582\pi$
$68$	7.38404	0.895447
$69$	5.10992	0.615162
$70$	2.80194	0.334896
$71$	1.32975	0.157812	0.0789061	−	0.996882i	$-0.474857\pi$
$71$	1.32975	0.157812	0.0789061	+	0.996882i	$0.474857\pi$
$72$	1.00000	0.117851
$73$	7.65279	0.895692	0.447846	−	0.894111i	$-0.352191\pi$
$73$	7.65279	0.895692	0.447846	+	0.894111i	$0.352191\pi$
$74$	−1.28621	−0.149519
$75$	11.3937	1.31563
$76$	1.78017	0.204199
$77$	−3.35690	−0.382554
$78$	0	0
$79$	−8.33944	−0.938260	−0.469130	−	0.883129i	$-0.655432\pi$
$79$	−8.33944	−0.938260	−0.469130	+	0.883129i	$0.655432\pi$
$80$	−4.04892	−0.452683
$81$	1.00000	0.111111
$82$	−1.50604	−0.166314
$83$	−15.3274	−1.68240	−0.841198	−	0.540727i	$-0.818149\pi$
$83$	−15.3274	−1.68240	−0.841198	+	0.540727i	$0.818149\pi$
$84$	−0.692021	−0.0755057
$85$	−29.8974	−3.24283
$86$	−8.31767	−0.896917
$87$	−3.34481	−0.358602
$88$	4.85086	0.517103
$89$	−3.10992	−0.329650	−0.164825	−	0.986323i	$-0.552706\pi$
$89$	−3.10992	−0.329650	−0.164825	+	0.986323i	$0.552706\pi$
$90$	−4.04892	−0.426793
$91$	0	0
$92$	5.10992	0.532746
$93$	−0.972853	−0.100880
$94$	7.20775	0.743423
$95$	−7.20775	−0.739500
$96$	1.00000	0.102062
$97$	8.54288	0.867398	0.433699	−	0.901058i	$-0.357208\pi$
$97$	8.54288	0.867398	0.433699	+	0.901058i	$0.357208\pi$
$98$	−6.52111	−0.658731
$99$	4.85086	0.487529
$100$	11.3937	1.13937
$101$	−11.9976	−1.19381	−0.596903	−	0.802313i	$-0.703602\pi$
$101$	−11.9976	−1.19381	−0.596903	+	0.802313i	$0.703602\pi$
$102$	7.38404	0.731129
$103$	−12.3230	−1.21423	−0.607113	−	0.794616i	$-0.707672\pi$
$103$	−12.3230	−1.21423	−0.607113	+	0.794616i	$0.707672\pi$
$104$	0	0
$105$	2.80194	0.273441
$106$	13.4765	1.30895
$107$	5.89977	0.570353	0.285176	−	0.958475i	$-0.407948\pi$
$107$	5.89977	0.570353	0.285176	+	0.958475i	$0.407948\pi$
$108$	1.00000	0.0962250
$109$	−0.792249	−0.0758837	−0.0379418	−	0.999280i	$-0.512080\pi$
$109$	−0.792249	−0.0758837	−0.0379418	+	0.999280i	$0.512080\pi$
$110$	−19.6407	−1.87267
$111$	−1.28621	−0.122081
$112$	−0.692021	−0.0653899
$113$	6.21983	0.585113	0.292556	−	0.956248i	$-0.405494\pi$
$113$	6.21983	0.585113	0.292556	+	0.956248i	$0.405494\pi$
$114$	1.78017	0.166728
$115$	−20.6896	−1.92932
$116$	−3.34481	−0.310558
$117$	0	0
$118$	−1.30798	−0.120409
$119$	−5.10992	−0.468425
$120$	−4.04892	−0.369614
$121$	12.5308	1.13916
$122$	−0.396125	−0.0358634
$123$	−1.50604	−0.135795
$124$	−0.972853	−0.0873648
$125$	−25.8877	−2.31547
$126$	−0.692021	−0.0616502
$127$	−6.00538	−0.532891	−0.266446	−	0.963850i	$-0.585849\pi$
$127$	−6.00538	−0.532891	−0.266446	+	0.963850i	$0.585849\pi$
$128$	1.00000	0.0883883
$129$	−8.31767	−0.732330
$130$	0	0
$131$	8.81700	0.770345	0.385173	−	0.922845i	$-0.374142\pi$
$131$	8.81700	0.770345	0.385173	+	0.922845i	$0.374142\pi$
$132$	4.85086	0.422213
$133$	−1.23191	−0.106821
$134$	−6.05429	−0.523011
$135$	−4.04892	−0.348475
$136$	7.38404	0.633176
$137$	15.7560	1.34613	0.673063	−	0.739585i	$-0.264978\pi$
$137$	15.7560	1.34613	0.673063	+	0.739585i	$0.264978\pi$
$138$	5.10992	0.434985
$139$	−6.09783	−0.517212	−0.258606	−	0.965983i	$-0.583263\pi$
$139$	−6.09783	−0.517212	−0.258606	+	0.965983i	$0.583263\pi$
$140$	2.80194	0.236807
$141$	7.20775	0.607002
$142$	1.32975	0.111590
$143$	0	0
$144$	1.00000	0.0833333
$145$	13.5429	1.12467
$146$	7.65279	0.633350
$147$	−6.52111	−0.537852
$148$	−1.28621	−0.105726
$149$	2.55257	0.209114	0.104557	−	0.994519i	$-0.466657\pi$
$149$	2.55257	0.209114	0.104557	+	0.994519i	$0.466657\pi$
$150$	11.3937	0.930294
$151$	17.7168	1.44177	0.720885	−	0.693054i	$-0.243735\pi$
$151$	17.7168	1.44177	0.720885	+	0.693054i	$0.243735\pi$
$152$	1.78017	0.144391
$153$	7.38404	0.596964
$154$	−3.35690	−0.270506
$155$	3.93900	0.316388
$156$	0	0
$157$	−6.31767	−0.504205	−0.252102	−	0.967701i	$-0.581122\pi$
$157$	−6.31767	−0.504205	−0.252102	+	0.967701i	$0.581122\pi$
$158$	−8.33944	−0.663450
$159$	13.4765	1.06876
$160$	−4.04892	−0.320095
$161$	−3.53617	−0.278689
$162$	1.00000	0.0785674
$163$	14.5918	1.14292	0.571459	−	0.820631i	$-0.306378\pi$
$163$	14.5918	1.14292	0.571459	+	0.820631i	$0.306378\pi$
$164$	−1.50604	−0.117602
$165$	−19.6407	−1.52903
$166$	−15.3274	−1.18963
$167$	−19.5013	−1.50905	−0.754526	−	0.656270i	$-0.772133\pi$
$167$	−19.5013	−1.50905	−0.754526	+	0.656270i	$0.772133\pi$
$168$	−0.692021	−0.0533906
$169$	0	0
$170$	−29.8974	−2.29302
$171$	1.78017	0.136133
$172$	−8.31767	−0.634216
$173$	−9.29052	−0.706345	−0.353173	−	0.935558i	$-0.614897\pi$
$173$	−9.29052	−0.706345	−0.353173	+	0.935558i	$0.614897\pi$
$174$	−3.34481	−0.253570
$175$	−7.88471	−0.596028
$176$	4.85086	0.365647
$177$	−1.30798	−0.0983137
$178$	−3.10992	−0.233098
$179$	22.7928	1.70362	0.851808	−	0.523853i	$-0.175506\pi$
$179$	22.7928	1.70362	0.851808	+	0.523853i	$0.175506\pi$
$180$	−4.04892	−0.301788
$181$	0.537500	0.0399520	0.0199760	−	0.999800i	$-0.493641\pi$
$181$	0.537500	0.0399520	0.0199760	+	0.999800i	$0.493641\pi$
$182$	0	0
$183$	−0.396125	−0.0292824
$184$	5.10992	0.376708
$185$	5.20775	0.382881
$186$	−0.972853	−0.0713330
$187$	35.8189	2.61934
$188$	7.20775	0.525679
$189$	−0.692021	−0.0503372
$190$	−7.20775	−0.522905
$191$	−9.79954	−0.709070	−0.354535	−	0.935043i	$-0.615361\pi$
$191$	−9.79954	−0.709070	−0.354535	+	0.935043i	$0.615361\pi$
$192$	1.00000	0.0721688
$193$	−14.1957	−1.02183	−0.510913	−	0.859632i	$-0.670693\pi$
$193$	−14.1957	−1.02183	−0.510913	+	0.859632i	$0.670693\pi$
$194$	8.54288	0.613343
$195$	0	0
$196$	−6.52111	−0.465793
$197$	−3.00969	−0.214431	−0.107216	−	0.994236i	$-0.534194\pi$
$197$	−3.00969	−0.214431	−0.107216	+	0.994236i	$0.534194\pi$
$198$	4.85086	0.344735
$199$	12.8944	0.914059	0.457030	−	0.889451i	$-0.348913\pi$
$199$	12.8944	0.914059	0.457030	+	0.889451i	$0.348913\pi$
$200$	11.3937	0.805658
$201$	−6.05429	−0.427037
$202$	−11.9976	−0.844149
$203$	2.31468	0.162459
$204$	7.38404	0.516986
$205$	6.09783	0.425891
$206$	−12.3230	−0.858587
$207$	5.10992	0.355164
$208$	0	0
$209$	8.63533	0.597319
$210$	2.80194	0.193352
$211$	7.79954	0.536943	0.268471	−	0.963288i	$-0.413482\pi$
$211$	7.79954	0.536943	0.268471	+	0.963288i	$0.413482\pi$
$212$	13.4765	0.925570
$213$	1.32975	0.0911129
$214$	5.89977	0.403300
$215$	33.6775	2.29679
$216$	1.00000	0.0680414
$217$	0.673235	0.0457022
$218$	−0.792249	−0.0536579
$219$	7.65279	0.517128
$220$	−19.6407	−1.32418
$221$	0	0
$222$	−1.28621	−0.0863246
$223$	−12.1957	−0.816682	−0.408341	−	0.912829i	$-0.633893\pi$
$223$	−12.1957	−0.816682	−0.408341	+	0.912829i	$0.633893\pi$
$224$	−0.692021	−0.0462376
$225$	11.3937	0.759582
$226$	6.21983	0.413737
$227$	6.74333	0.447571	0.223785	−	0.974638i	$-0.428159\pi$
$227$	6.74333	0.447571	0.223785	+	0.974638i	$0.428159\pi$
$228$	1.78017	0.117894
$229$	−19.8237	−1.30999	−0.654994	−	0.755634i	$-0.727329\pi$
$229$	−19.8237	−1.30999	−0.654994	+	0.755634i	$0.727329\pi$
$230$	−20.6896	−1.36423
$231$	−3.35690	−0.220868
$232$	−3.34481	−0.219598
$233$	−30.0301	−1.96734	−0.983670	−	0.179983i	$-0.942396\pi$
$233$	−30.0301	−1.96734	−0.983670	+	0.179983i	$0.942396\pi$
$234$	0	0
$235$	−29.1836	−1.90373
$236$	−1.30798	−0.0851422
$237$	−8.33944	−0.541705
$238$	−5.10992	−0.331227
$239$	22.0978	1.42939	0.714695	−	0.699436i	$-0.246565\pi$
$239$	22.0978	1.42939	0.714695	+	0.699436i	$0.246565\pi$
$240$	−4.04892	−0.261356
$241$	10.1274	0.652362	0.326181	−	0.945307i	$-0.394238\pi$
$241$	10.1274	0.652362	0.326181	+	0.945307i	$0.394238\pi$
$242$	12.5308	0.805510
$243$	1.00000	0.0641500
$244$	−0.396125	−0.0253593
$245$	26.4034	1.68685
$246$	−1.50604	−0.0960217
$247$	0	0
$248$	−0.972853	−0.0617762
$249$	−15.3274	−0.971332
$250$	−25.8877	−1.63728
$251$	5.54719	0.350135	0.175068	−	0.984556i	$-0.443986\pi$
$251$	5.54719	0.350135	0.175068	+	0.984556i	$0.443986\pi$
$252$	−0.692021	−0.0435933
$253$	24.7875	1.55837
$254$	−6.00538	−0.376811
$255$	−29.8974	−1.87225
$256$	1.00000	0.0625000
$257$	−13.7995	−0.860792	−0.430396	−	0.902640i	$-0.641626\pi$
$257$	−13.7995	−0.860792	−0.430396	+	0.902640i	$0.641626\pi$
$258$	−8.31767	−0.517835
$259$	0.890084	0.0553071
$260$	0	0
$261$	−3.34481	−0.207039
$262$	8.81700	0.544716
$263$	−22.4698	−1.38555	−0.692773	−	0.721155i	$-0.743611\pi$
$263$	−22.4698	−1.38555	−0.692773	+	0.721155i	$0.743611\pi$
$264$	4.85086	0.298549
$265$	−54.5652	−3.35192
$266$	−1.23191	−0.0755335
$267$	−3.10992	−0.190324
$268$	−6.05429	−0.369825
$269$	−26.0140	−1.58610	−0.793051	−	0.609156i	$-0.791509\pi$
$269$	−26.0140	−1.58610	−0.793051	+	0.609156i	$0.791509\pi$
$270$	−4.04892	−0.246409
$271$	2.88471	0.175233	0.0876167	−	0.996154i	$-0.472075\pi$
$271$	2.88471	0.175233	0.0876167	+	0.996154i	$0.472075\pi$
$272$	7.38404	0.447723
$273$	0	0
$274$	15.7560	0.951855
$275$	55.2693	3.33287
$276$	5.10992	0.307581
$277$	−1.46250	−0.0878731	−0.0439366	−	0.999034i	$-0.513990\pi$
$277$	−1.46250	−0.0878731	−0.0439366	+	0.999034i	$0.513990\pi$
$278$	−6.09783	−0.365724
$279$	−0.972853	−0.0582432
$280$	2.80194	0.167448
$281$	5.68233	0.338980	0.169490	−	0.985532i	$-0.445788\pi$
$281$	5.68233	0.338980	0.169490	+	0.985532i	$0.445788\pi$
$282$	7.20775	0.429215
$283$	−25.2078	−1.49845	−0.749223	−	0.662318i	$-0.769573\pi$
$283$	−25.2078	−1.49845	−0.749223	+	0.662318i	$0.769573\pi$
$284$	1.32975	0.0789061
$285$	−7.20775	−0.426950
$286$	0	0
$287$	1.04221	0.0615199
$288$	1.00000	0.0589256
$289$	37.5241	2.20730
$290$	13.5429	0.795265
$291$	8.54288	0.500792
$292$	7.65279	0.447846
$293$	−7.14914	−0.417658	−0.208829	−	0.977952i	$-0.566965\pi$
$293$	−7.14914	−0.417658	−0.208829	+	0.977952i	$0.566965\pi$
$294$	−6.52111	−0.380319
$295$	5.29590	0.308339
$296$	−1.28621	−0.0747593
$297$	4.85086	0.281475
$298$	2.55257	0.147866
$299$	0	0
$300$	11.3937	0.657817
$301$	5.75600	0.331771
$302$	17.7168	1.01949
$303$	−11.9976	−0.689245
$304$	1.78017	0.102100
$305$	1.60388	0.0918376
$306$	7.38404	0.422118
$307$	−17.9952	−1.02704	−0.513521	−	0.858077i	$-0.671659\pi$
$307$	−17.9952	−1.02704	−0.513521	+	0.858077i	$0.671659\pi$
$308$	−3.35690	−0.191277
$309$	−12.3230	−0.701033
$310$	3.93900	0.223720
$311$	3.32975	0.188813	0.0944064	−	0.995534i	$-0.469905\pi$
$311$	3.32975	0.188813	0.0944064	+	0.995534i	$0.469905\pi$
$312$	0	0
$313$	−17.8834	−1.01083	−0.505414	−	0.862877i	$-0.668660\pi$
$313$	−17.8834	−1.01083	−0.505414	+	0.862877i	$0.668660\pi$
$314$	−6.31767	−0.356527
$315$	2.80194	0.157871
$316$	−8.33944	−0.469130
$317$	4.39373	0.246777	0.123388	−	0.992358i	$-0.460624\pi$
$317$	4.39373	0.246777	0.123388	+	0.992358i	$0.460624\pi$
$318$	13.4765	0.755725
$319$	−16.2252	−0.908437
$320$	−4.04892	−0.226341
$321$	5.89977	0.329293
$322$	−3.53617	−0.197063
$323$	13.1448	0.731398
$324$	1.00000	0.0555556
$325$	0	0
$326$	14.5918	0.808165
$327$	−0.792249	−0.0438115
$328$	−1.50604	−0.0831572
$329$	−4.98792	−0.274993
$330$	−19.6407	−1.08119
$331$	−25.6775	−1.41137	−0.705683	−	0.708528i	$-0.749360\pi$
$331$	−25.6775	−1.41137	−0.705683	+	0.708528i	$0.749360\pi$
$332$	−15.3274	−0.841198
$333$	−1.28621	−0.0704838
$334$	−19.5013	−1.06706
$335$	24.5133	1.33931
$336$	−0.692021	−0.0377529
$337$	−24.6504	−1.34279	−0.671396	−	0.741098i	$-0.734305\pi$
$337$	−24.6504	−1.34279	−0.671396	+	0.741098i	$0.734305\pi$
$338$	0	0
$339$	6.21983	0.337815
$340$	−29.8974	−1.62141
$341$	−4.71917	−0.255557
$342$	1.78017	0.0962604
$343$	9.35690	0.505225
$344$	−8.31767	−0.448459
$345$	−20.6896	−1.11389
$346$	−9.29052	−0.499461
$347$	14.2959	0.767444	0.383722	−	0.923449i	$-0.374642\pi$
$347$	14.2959	0.767444	0.383722	+	0.923449i	$0.374642\pi$
$348$	−3.34481	−0.179301
$349$	11.0616	0.592113	0.296057	−	0.955170i	$-0.404328\pi$
$349$	11.0616	0.592113	0.296057	+	0.955170i	$0.404328\pi$
$350$	−7.88471	−0.421455
$351$	0	0
$352$	4.85086	0.258551
$353$	−10.5047	−0.559109	−0.279555	−	0.960130i	$-0.590187\pi$
$353$	−10.5047	−0.559109	−0.279555	+	0.960130i	$0.590187\pi$
$354$	−1.30798	−0.0695183
$355$	−5.38404	−0.285755
$356$	−3.10992	−0.164825
$357$	−5.10992	−0.270445
$358$	22.7928	1.20464
$359$	5.10992	0.269691	0.134846	−	0.990867i	$-0.456946\pi$
$359$	5.10992	0.269691	0.134846	+	0.990867i	$0.456946\pi$
$360$	−4.04892	−0.213397
$361$	−15.8310	−0.833211
$362$	0.537500	0.0282504
$363$	12.5308	0.657696
$364$	0	0
$365$	−30.9855	−1.62186
$366$	−0.396125	−0.0207058
$367$	−8.44803	−0.440983	−0.220492	−	0.975389i	$-0.570766\pi$
$367$	−8.44803	−0.440983	−0.220492	+	0.975389i	$0.570766\pi$
$368$	5.10992	0.266373
$369$	−1.50604	−0.0784014
$370$	5.20775	0.270738
$371$	−9.32603	−0.484183
$372$	−0.972853	−0.0504401
$373$	7.69096	0.398223	0.199111	−	0.979977i	$-0.436194\pi$
$373$	7.69096	0.398223	0.199111	+	0.979977i	$0.436194\pi$
$374$	35.8189	1.85215
$375$	−25.8877	−1.33683
$376$	7.20775	0.371711
$377$	0	0
$378$	−0.692021	−0.0355937
$379$	−11.4034	−0.585754	−0.292877	−	0.956150i	$-0.594613\pi$
$379$	−11.4034	−0.585754	−0.292877	+	0.956150i	$0.594613\pi$
$380$	−7.20775	−0.369750
$381$	−6.00538	−0.307665
$382$	−9.79954	−0.501388
$383$	20.6703	1.05620	0.528100	−	0.849182i	$-0.322905\pi$
$383$	20.6703	1.05620	0.528100	+	0.849182i	$0.322905\pi$
$384$	1.00000	0.0510310
$385$	13.5918	0.692702
$386$	−14.1957	−0.722541
$387$	−8.31767	−0.422811
$388$	8.54288	0.433699
$389$	17.4776	0.886148	0.443074	−	0.896485i	$-0.353888\pi$
$389$	17.4776	0.886148	0.443074	+	0.896485i	$0.353888\pi$
$390$	0	0
$391$	37.7318	1.90818
$392$	−6.52111	−0.329366
$393$	8.81700	0.444759
$394$	−3.00969	−0.151626
$395$	33.7657	1.69894
$396$	4.85086	0.243765
$397$	−19.3599	−0.971645	−0.485822	−	0.874058i	$-0.661480\pi$
$397$	−19.3599	−0.971645	−0.485822	+	0.874058i	$0.661480\pi$
$398$	12.8944	0.646338
$399$	−1.23191	−0.0616728
$400$	11.3937	0.569687
$401$	−14.4832	−0.723257	−0.361628	−	0.932322i	$-0.617779\pi$
$401$	−14.4832	−0.723257	−0.361628	+	0.932322i	$0.617779\pi$
$402$	−6.05429	−0.301961
$403$	0	0
$404$	−11.9976	−0.596903
$405$	−4.04892	−0.201192
$406$	2.31468	0.114876
$407$	−6.23921	−0.309266
$408$	7.38404	0.365565
$409$	−18.8984	−0.934468	−0.467234	−	0.884134i	$-0.654749\pi$
$409$	−18.8984	−0.934468	−0.467234	+	0.884134i	$0.654749\pi$
$410$	6.09783	0.301151
$411$	15.7560	0.777186
$412$	−12.3230	−0.607113
$413$	0.905149	0.0445395
$414$	5.10992	0.251139
$415$	62.0592	3.04637
$416$	0	0
$417$	−6.09783	−0.298612
$418$	8.63533	0.422368
$419$	−21.7603	−1.06306	−0.531531	−	0.847039i	$-0.678383\pi$
$419$	−21.7603	−1.06306	−0.531531	+	0.847039i	$0.678383\pi$
$420$	2.80194	0.136721
$421$	20.5918	1.00358	0.501791	−	0.864989i	$-0.332675\pi$
$421$	20.5918	1.00358	0.501791	+	0.864989i	$0.332675\pi$
$422$	7.79954	0.379676
$423$	7.20775	0.350453
$424$	13.4765	0.654477
$425$	84.1318	4.08099
$426$	1.32975	0.0644265
$427$	0.274127	0.0132659
$428$	5.89977	0.285176
$429$	0	0
$430$	33.6775	1.62408
$431$	34.5133	1.66245	0.831224	−	0.555937i	$-0.187640\pi$
$431$	34.5133	1.66245	0.831224	+	0.555937i	$0.187640\pi$
$432$	1.00000	0.0481125
$433$	−2.12631	−0.102184	−0.0510920	−	0.998694i	$-0.516270\pi$
$433$	−2.12631	−0.102184	−0.0510920	+	0.998694i	$0.516270\pi$
$434$	0.673235	0.0323163
$435$	13.5429	0.649331
$436$	−0.792249	−0.0379418
$437$	9.09651	0.435145
$438$	7.65279	0.365665
$439$	21.8321	1.04199	0.520994	−	0.853560i	$-0.325561\pi$
$439$	21.8321	1.04199	0.520994	+	0.853560i	$0.325561\pi$
$440$	−19.6407	−0.936334
$441$	−6.52111	−0.310529
$442$	0	0
$443$	−7.54048	−0.358259	−0.179130	−	0.983825i	$-0.557328\pi$
$443$	−7.54048	−0.358259	−0.179130	+	0.983825i	$0.557328\pi$
$444$	−1.28621	−0.0610407
$445$	12.5918	0.596908
$446$	−12.1957	−0.577482
$447$	2.55257	0.120732
$448$	−0.692021	−0.0326949
$449$	19.7560	0.932343	0.466172	−	0.884694i	$-0.345633\pi$
$449$	19.7560	0.932343	0.466172	+	0.884694i	$0.345633\pi$
$450$	11.3937	0.537106
$451$	−7.30559	−0.344007
$452$	6.21983	0.292556
$453$	17.7168	0.832407
$454$	6.74333	0.316480
$455$	0	0
$456$	1.78017	0.0833640
$457$	23.8582	1.11604	0.558019	−	0.829828i	$-0.311562\pi$
$457$	23.8582	1.11604	0.558019	+	0.829828i	$0.311562\pi$
$458$	−19.8237	−0.926301
$459$	7.38404	0.344658
$460$	−20.6896	−0.964659
$461$	−17.5773	−0.818657	−0.409329	−	0.912387i	$-0.634237\pi$
$461$	−17.5773	−0.818657	−0.409329	+	0.912387i	$0.634237\pi$
$462$	−3.35690	−0.156177
$463$	23.8431	1.10808	0.554041	−	0.832489i	$-0.313085\pi$
$463$	23.8431	1.10808	0.554041	+	0.832489i	$0.313085\pi$
$464$	−3.34481	−0.155279
$465$	3.93900	0.182667
$466$	−30.0301	−1.39112
$467$	8.61058	0.398450	0.199225	−	0.979954i	$-0.436158\pi$
$467$	8.61058	0.398450	0.199225	+	0.979954i	$0.436158\pi$
$468$	0	0
$469$	4.18970	0.193462
$470$	−29.1836	−1.34614
$471$	−6.31767	−0.291103
$472$	−1.30798	−0.0602046
$473$	−40.3478	−1.85519
$474$	−8.33944	−0.383043
$475$	20.2828	0.930636
$476$	−5.10992	−0.234213
$477$	13.4765	0.617047
$478$	22.0978	1.01073
$479$	6.58104	0.300695	0.150348	−	0.988633i	$-0.451961\pi$
$479$	6.58104	0.300695	0.150348	+	0.988633i	$0.451961\pi$
$480$	−4.04892	−0.184807
$481$	0	0
$482$	10.1274	0.461289
$483$	−3.53617	−0.160901
$484$	12.5308	0.569582
$485$	−34.5894	−1.57062
$486$	1.00000	0.0453609
$487$	−23.2760	−1.05474	−0.527369	−	0.849636i	$-0.676822\pi$
$487$	−23.2760	−1.05474	−0.527369	+	0.849636i	$0.676822\pi$
$488$	−0.396125	−0.0179317
$489$	14.5918	0.659864
$490$	26.4034	1.19278
$491$	−15.5405	−0.701332	−0.350666	−	0.936501i	$-0.614045\pi$
$491$	−15.5405	−0.701332	−0.350666	+	0.936501i	$0.614045\pi$
$492$	−1.50604	−0.0678976
$493$	−24.6983	−1.11235
$494$	0	0
$495$	−19.6407	−0.882784
$496$	−0.972853	−0.0436824
$497$	−0.920215	−0.0412773
$498$	−15.3274	−0.686835
$499$	9.53617	0.426898	0.213449	−	0.976954i	$-0.431530\pi$
$499$	9.53617	0.426898	0.213449	+	0.976954i	$0.431530\pi$
$500$	−25.8877	−1.15773
$501$	−19.5013	−0.871252
$502$	5.54719	0.247583
$503$	−13.8345	−0.616848	−0.308424	−	0.951249i	$-0.599802\pi$
$503$	−13.8345	−0.616848	−0.308424	+	0.951249i	$0.599802\pi$
$504$	−0.692021	−0.0308251
$505$	48.5773	2.16166
$506$	24.7875	1.10194
$507$	0	0
$508$	−6.00538	−0.266446
$509$	−40.9638	−1.81569	−0.907843	−	0.419310i	$-0.862272\pi$
$509$	−40.9638	−1.81569	−0.907843	+	0.419310i	$0.862272\pi$
$510$	−29.8974	−1.32388
$511$	−5.29590	−0.234277
$512$	1.00000	0.0441942
$513$	1.78017	0.0785963
$514$	−13.7995	−0.608672
$515$	49.8950	2.19864
$516$	−8.31767	−0.366165
$517$	34.9638	1.53770
$518$	0.890084	0.0391080
$519$	−9.29052	−0.407809
$520$	0	0
$521$	36.3672	1.59327	0.796637	−	0.604457i	$-0.206610\pi$
$521$	36.3672	1.59327	0.796637	+	0.604457i	$0.206610\pi$
$522$	−3.34481	−0.146399
$523$	−6.03013	−0.263679	−0.131840	−	0.991271i	$-0.542088\pi$
$523$	−6.03013	−0.263679	−0.131840	+	0.991271i	$0.542088\pi$
$524$	8.81700	0.385173
$525$	−7.88471	−0.344117
$526$	−22.4698	−0.979730
$527$	−7.18359	−0.312922
$528$	4.85086	0.211106
$529$	3.11124	0.135271
$530$	−54.5652	−2.37016
$531$	−1.30798	−0.0567614
$532$	−1.23191	−0.0534103
$533$	0	0
$534$	−3.10992	−0.134579
$535$	−23.8877	−1.03275
$536$	−6.05429	−0.261506
$537$	22.7928	0.983584
$538$	−26.0140	−1.12154
$539$	−31.6329	−1.36253
$540$	−4.04892	−0.174238
$541$	−7.92154	−0.340574	−0.170287	−	0.985395i	$-0.554469\pi$
$541$	−7.92154	−0.340574	−0.170287	+	0.985395i	$0.554469\pi$
$542$	2.88471	0.123909
$543$	0.537500	0.0230663
$544$	7.38404	0.316588
$545$	3.20775	0.137405
$546$	0	0
$547$	18.4155	0.787390	0.393695	−	0.919241i	$-0.371197\pi$
$547$	18.4155	0.787390	0.393695	+	0.919241i	$0.371197\pi$
$548$	15.7560	0.673063
$549$	−0.396125	−0.0169062
$550$	55.2693	2.35669
$551$	−5.95433	−0.253663
$552$	5.10992	0.217492
$553$	5.77107	0.245411
$554$	−1.46250	−0.0621357
$555$	5.20775	0.221057
$556$	−6.09783	−0.258606
$557$	−23.9758	−1.01589	−0.507944	−	0.861390i	$-0.669594\pi$
$557$	−23.9758	−1.01589	−0.507944	+	0.861390i	$0.669594\pi$
$558$	−0.972853	−0.0411841
$559$	0	0
$560$	2.80194	0.118403
$561$	35.8189	1.51228
$562$	5.68233	0.239695
$563$	−2.29291	−0.0966348	−0.0483174	−	0.998832i	$-0.515386\pi$
$563$	−2.29291	−0.0966348	−0.0483174	+	0.998832i	$0.515386\pi$
$564$	7.20775	0.303501
$565$	−25.1836	−1.05948
$566$	−25.2078	−1.05956
$567$	−0.692021	−0.0290622
$568$	1.32975	0.0557950
$569$	−44.3430	−1.85896	−0.929478	−	0.368878i	$-0.879742\pi$
$569$	−44.3430	−1.85896	−0.929478	+	0.368878i	$0.879742\pi$
$570$	−7.20775	−0.301899
$571$	−15.2707	−0.639058	−0.319529	−	0.947577i	$-0.603525\pi$
$571$	−15.2707	−0.639058	−0.319529	+	0.947577i	$0.603525\pi$
$572$	0	0
$573$	−9.79954	−0.409382
$574$	1.04221	0.0435011
$575$	58.2210	2.42798
$576$	1.00000	0.0416667
$577$	8.77048	0.365120	0.182560	−	0.983195i	$-0.441562\pi$
$577$	8.77048	0.365120	0.182560	+	0.983195i	$0.441562\pi$
$578$	37.5241	1.56080
$579$	−14.1957	−0.589952
$580$	13.5429	0.562337
$581$	10.6069	0.440047
$582$	8.54288	0.354114
$583$	65.3726	2.70745
$584$	7.65279	0.316675
$585$	0	0
$586$	−7.14914	−0.295328
$587$	−38.1430	−1.57433	−0.787166	−	0.616742i	$-0.788452\pi$
$587$	−38.1430	−1.57433	−0.787166	+	0.616742i	$0.788452\pi$
$588$	−6.52111	−0.268926
$589$	−1.73184	−0.0713593
$590$	5.29590	0.218029
$591$	−3.00969	−0.123802
$592$	−1.28621	−0.0528628
$593$	−37.9517	−1.55849	−0.779244	−	0.626720i	$-0.784397\pi$
$593$	−37.9517	−1.55849	−0.779244	+	0.626720i	$0.784397\pi$
$594$	4.85086	0.199033
$595$	20.6896	0.848192
$596$	2.55257	0.104557
$597$	12.8944	0.527732
$598$	0	0
$599$	−3.57971	−0.146263	−0.0731315	−	0.997322i	$-0.523299\pi$
$599$	−3.57971	−0.146263	−0.0731315	+	0.997322i	$0.523299\pi$
$600$	11.3937	0.465147
$601$	−5.71678	−0.233192	−0.116596	−	0.993179i	$-0.537198\pi$
$601$	−5.71678	−0.233192	−0.116596	+	0.993179i	$0.537198\pi$
$602$	5.75600	0.234597
$603$	−6.05429	−0.246550
$604$	17.7168	0.720885
$605$	−50.7362	−2.06272
$606$	−11.9976	−0.487369
$607$	22.4286	0.910351	0.455175	−	0.890402i	$-0.349577\pi$
$607$	22.4286	0.910351	0.455175	+	0.890402i	$0.349577\pi$
$608$	1.78017	0.0721953
$609$	2.31468	0.0937957
$610$	1.60388	0.0649390
$611$	0	0
$612$	7.38404	0.298482
$613$	−39.9603	−1.61398	−0.806991	−	0.590564i	$-0.798905\pi$
$613$	−39.9603	−1.61398	−0.806991	+	0.590564i	$0.798905\pi$
$614$	−17.9952	−0.726228
$615$	6.09783	0.245888
$616$	−3.35690	−0.135253
$617$	31.4470	1.26601	0.633003	−	0.774149i	$-0.281822\pi$
$617$	31.4470	1.26601	0.633003	+	0.774149i	$0.281822\pi$
$618$	−12.3230	−0.495706
$619$	−29.3685	−1.18042	−0.590210	−	0.807250i	$-0.700955\pi$
$619$	−29.3685	−1.18042	−0.590210	+	0.807250i	$0.700955\pi$
$620$	3.93900	0.158194
$621$	5.10992	0.205054
$622$	3.32975	0.133511
$623$	2.15213	0.0862232
$624$	0	0
$625$	47.8485	1.91394
$626$	−17.8834	−0.714764
$627$	8.63533	0.344862
$628$	−6.31767	−0.252102
$629$	−9.49742	−0.378687
$630$	2.80194	0.111632
$631$	21.6799	0.863065	0.431532	−	0.902097i	$-0.357973\pi$
$631$	21.6799	0.863065	0.431532	+	0.902097i	$0.357973\pi$
$632$	−8.33944	−0.331725
$633$	7.79954	0.310004
$634$	4.39373	0.174497
$635$	24.3153	0.964922
$636$	13.4765	0.534378
$637$	0	0
$638$	−16.2252	−0.642362
$639$	1.32975	0.0526040
$640$	−4.04892	−0.160048
$641$	14.0108	0.553391	0.276696	−	0.960958i	$-0.410761\pi$
$641$	14.0108	0.553391	0.276696	+	0.960958i	$0.410761\pi$
$642$	5.89977	0.232845
$643$	30.7875	1.21414	0.607070	−	0.794649i	$-0.292345\pi$
$643$	30.7875	1.21414	0.607070	+	0.794649i	$0.292345\pi$
$644$	−3.53617	−0.139345
$645$	33.6775	1.32605
$646$	13.1448	0.517177
$647$	−16.6025	−0.652713	−0.326357	−	0.945247i	$-0.605821\pi$
$647$	−16.6025	−0.652713	−0.326357	+	0.945247i	$0.605821\pi$
$648$	1.00000	0.0392837
$649$	−6.34481	−0.249056
$650$	0	0
$651$	0.673235	0.0263862
$652$	14.5918	0.571459
$653$	28.5459	1.11709	0.558543	−	0.829476i	$-0.311361\pi$
$653$	28.5459	1.11709	0.558543	+	0.829476i	$0.311361\pi$
$654$	−0.792249	−0.0309794
$655$	−35.6993	−1.39489
$656$	−1.50604	−0.0588010
$657$	7.65279	0.298564
$658$	−4.98792	−0.194449
$659$	27.7187	1.07977	0.539884	−	0.841740i	$-0.318468\pi$
$659$	27.7187	1.07977	0.539884	+	0.841740i	$0.318468\pi$
$660$	−19.6407	−0.764514
$661$	10.8009	0.420105	0.210053	−	0.977690i	$-0.432636\pi$
$661$	10.8009	0.420105	0.210053	+	0.977690i	$0.432636\pi$
$662$	−25.6775	−0.997986
$663$	0	0
$664$	−15.3274	−0.594817
$665$	4.98792	0.193423
$666$	−1.28621	−0.0498396
$667$	−17.0917	−0.661794
$668$	−19.5013	−0.754526
$669$	−12.1957	−0.471512
$670$	24.5133	0.947033
$671$	−1.92154	−0.0741803
$672$	−0.692021	−0.0266953
$673$	16.3260	0.629322	0.314661	−	0.949204i	$-0.398109\pi$
$673$	16.3260	0.629322	0.314661	+	0.949204i	$0.398109\pi$
$674$	−24.6504	−0.949498
$675$	11.3937	0.438545
$676$	0	0
$677$	41.4252	1.59210	0.796050	−	0.605231i	$-0.206919\pi$
$677$	41.4252	1.59210	0.796050	+	0.605231i	$0.206919\pi$
$678$	6.21983	0.238871
$679$	−5.91185	−0.226876
$680$	−29.8974	−1.14651
$681$	6.74333	0.258405
$682$	−4.71917	−0.180706
$683$	31.2325	1.19508	0.597539	−	0.801840i	$-0.296145\pi$
$683$	31.2325	1.19508	0.597539	+	0.801840i	$0.296145\pi$
$684$	1.78017	0.0680664
$685$	−63.7948	−2.43747
$686$	9.35690	0.357248
$687$	−19.8237	−0.756322
$688$	−8.31767	−0.317108
$689$	0	0
$690$	−20.6896	−0.787641
$691$	24.9638	0.949666	0.474833	−	0.880076i	$-0.342508\pi$
$691$	24.9638	0.949666	0.474833	+	0.880076i	$0.342508\pi$
$692$	−9.29052	−0.353173
$693$	−3.35690	−0.127518
$694$	14.2959	0.542665
$695$	24.6896	0.936531
$696$	−3.34481	−0.126785
$697$	−11.1207	−0.421225
$698$	11.0616	0.418687
$699$	−30.0301	−1.13584
$700$	−7.88471	−0.298014
$701$	8.17151	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$701$	8.17151	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$702$	0	0
$703$	−2.28967	−0.0863564
$704$	4.85086	0.182823
$705$	−29.1836	−1.09912
$706$	−10.5047	−0.395350
$707$	8.30260	0.312251
$708$	−1.30798	−0.0491568
$709$	−36.7982	−1.38199	−0.690993	−	0.722861i	$-0.742826\pi$
$709$	−36.7982	−1.38199	−0.690993	+	0.722861i	$0.742826\pi$
$710$	−5.38404	−0.202060
$711$	−8.33944	−0.312753
$712$	−3.10992	−0.116549
$713$	−4.97120	−0.186173
$714$	−5.10992	−0.191234
$715$	0	0
$716$	22.7928	0.851808
$717$	22.0978	0.825259
$718$	5.10992	0.190700
$719$	35.2223	1.31357	0.656786	−	0.754077i	$-0.271916\pi$
$719$	35.2223	1.31357	0.656786	+	0.754077i	$0.271916\pi$
$720$	−4.04892	−0.150894
$721$	8.52781	0.317592
$722$	−15.8310	−0.589169
$723$	10.1274	0.376641
$724$	0.537500	0.0199760
$725$	−38.1099	−1.41537
$726$	12.5308	0.465061
$727$	40.6872	1.50901	0.754503	−	0.656297i	$-0.227878\pi$
$727$	40.6872	1.50901	0.754503	+	0.656297i	$0.227878\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−30.9855	−1.14683
$731$	−61.4180	−2.27163
$732$	−0.396125	−0.0146412
$733$	27.1400	1.00244	0.501220	−	0.865320i	$-0.332885\pi$
$733$	27.1400	1.00244	0.501220	+	0.865320i	$0.332885\pi$
$734$	−8.44803	−0.311822
$735$	26.4034	0.973905
$736$	5.10992	0.188354
$737$	−29.3685	−1.08180
$738$	−1.50604	−0.0554381
$739$	3.72587	0.137058	0.0685292	−	0.997649i	$-0.478169\pi$
$739$	3.72587	0.137058	0.0685292	+	0.997649i	$0.478169\pi$
$740$	5.20775	0.191441
$741$	0	0
$742$	−9.32603	−0.342369
$743$	21.8586	0.801915	0.400958	−	0.916097i	$-0.368677\pi$
$743$	21.8586	0.801915	0.400958	+	0.916097i	$0.368677\pi$
$744$	−0.972853	−0.0356665
$745$	−10.3351	−0.378650
$746$	7.69096	0.281586
$747$	−15.3274	−0.560799
$748$	35.8189	1.30967
$749$	−4.08277	−0.149181
$750$	−25.8877	−0.945285
$751$	53.3642	1.94729	0.973644	−	0.228075i	$-0.0732432\pi$
$751$	53.3642	1.94729	0.973644	+	0.228075i	$0.0732432\pi$
$752$	7.20775	0.262840
$753$	5.54719	0.202151
$754$	0	0
$755$	−71.7338	−2.61066
$756$	−0.692021	−0.0251686
$757$	−4.63533	−0.168474	−0.0842370	−	0.996446i	$-0.526845\pi$
$757$	−4.63533	−0.168474	−0.0842370	+	0.996446i	$0.526845\pi$
$758$	−11.4034	−0.414191
$759$	24.7875	0.899728
$760$	−7.20775	−0.261453
$761$	11.5603	0.419062	0.209531	−	0.977802i	$-0.432806\pi$
$761$	11.5603	0.419062	0.209531	+	0.977802i	$0.432806\pi$
$762$	−6.00538	−0.217552
$763$	0.548253	0.0198481
$764$	−9.79954	−0.354535
$765$	−29.8974	−1.08094
$766$	20.6703	0.746847
$767$	0	0
$768$	1.00000	0.0360844
$769$	14.7439	0.531679	0.265840	−	0.964017i	$-0.414351\pi$
$769$	14.7439	0.531679	0.265840	+	0.964017i	$0.414351\pi$
$770$	13.5918	0.489814
$771$	−13.7995	−0.496978
$772$	−14.1957	−0.510913
$773$	−6.42268	−0.231008	−0.115504	−	0.993307i	$-0.536848\pi$
$773$	−6.42268	−0.231008	−0.115504	+	0.993307i	$0.536848\pi$
$774$	−8.31767	−0.298972
$775$	−11.0844	−0.398164
$776$	8.54288	0.306671
$777$	0.890084	0.0319316
$778$	17.4776	0.626601
$779$	−2.68100	−0.0960570
$780$	0	0
$781$	6.45042	0.230814
$782$	37.7318	1.34929
$783$	−3.34481	−0.119534
$784$	−6.52111	−0.232897
$785$	25.5797	0.912979
$786$	8.81700	0.314492
$787$	43.4336	1.54824	0.774119	−	0.633040i	$-0.218193\pi$
$787$	43.4336	1.54824	0.774119	+	0.633040i	$0.218193\pi$
$788$	−3.00969	−0.107216
$789$	−22.4698	−0.799946
$790$	33.7657	1.20133
$791$	−4.30426	−0.153042
$792$	4.85086	0.172368
$793$	0	0
$794$	−19.3599	−0.687056
$795$	−54.5652	−1.93523
$796$	12.8944	0.457030
$797$	21.0164	0.744439	0.372219	−	0.928145i	$-0.378597\pi$
$797$	21.0164	0.744439	0.372219	+	0.928145i	$0.378597\pi$
$798$	−1.23191	−0.0436093
$799$	53.2223	1.88287
$800$	11.3937	0.402829
$801$	−3.10992	−0.109883
$802$	−14.4832	−0.511420
$803$	37.1226	1.31003
$804$	−6.05429	−0.213518
$805$	14.3177	0.504631
$806$	0	0
$807$	−26.0140	−0.915736
$808$	−11.9976	−0.422074
$809$	−8.32245	−0.292602	−0.146301	−	0.989240i	$-0.546737\pi$
$809$	−8.32245	−0.292602	−0.146301	+	0.989240i	$0.546737\pi$
$810$	−4.04892	−0.142264
$811$	14.4638	0.507894	0.253947	−	0.967218i	$-0.418271\pi$
$811$	14.4638	0.507894	0.253947	+	0.967218i	$0.418271\pi$
$812$	2.31468	0.0812295
$813$	2.88471	0.101171
$814$	−6.23921	−0.218684
$815$	−59.0810	−2.06952
$816$	7.38404	0.258493
$817$	−14.8068	−0.518026
$818$	−18.8984	−0.660769
$819$	0	0
$820$	6.09783	0.212946
$821$	38.4161	1.34073	0.670365	−	0.742031i	$-0.266137\pi$
$821$	38.4161	1.34073	0.670365	+	0.742031i	$0.266137\pi$
$822$	15.7560	0.549554
$823$	−40.9748	−1.42829	−0.714145	−	0.699997i	$-0.753184\pi$
$823$	−40.9748	−1.42829	−0.714145	+	0.699997i	$0.753184\pi$
$824$	−12.3230	−0.429294
$825$	55.2693	1.92423
$826$	0.905149	0.0314942
$827$	−3.51035	−0.122067	−0.0610335	−	0.998136i	$-0.519440\pi$
$827$	−3.51035	−0.122067	−0.0610335	+	0.998136i	$0.519440\pi$
$828$	5.10992	0.177582
$829$	−13.2185	−0.459098	−0.229549	−	0.973297i	$-0.573725\pi$
$829$	−13.2185	−0.459098	−0.229549	+	0.973297i	$0.573725\pi$
$830$	62.0592	2.15411
$831$	−1.46250	−0.0507336
$832$	0	0
$833$	−48.1521	−1.66837
$834$	−6.09783	−0.211151
$835$	78.9590	2.73249
$836$	8.63533	0.298659
$837$	−0.972853	−0.0336267
$838$	−21.7603	−0.751698
$839$	−55.8491	−1.92812	−0.964062	−	0.265678i	$-0.914404\pi$
$839$	−55.8491	−1.92812	−0.964062	+	0.265678i	$0.914404\pi$
$840$	2.80194	0.0966760
$841$	−17.8122	−0.614214
$842$	20.5918	0.709640
$843$	5.68233	0.195710
$844$	7.79954	0.268471
$845$	0	0
$846$	7.20775	0.247808
$847$	−8.67158	−0.297959
$848$	13.4765	0.462785
$849$	−25.2078	−0.865128
$850$	84.1318	2.88570
$851$	−6.57242	−0.225300
$852$	1.32975	0.0455564
$853$	−21.8103	−0.746770	−0.373385	−	0.927676i	$-0.621803\pi$
$853$	−21.8103	−0.746770	−0.373385	+	0.927676i	$0.621803\pi$
$854$	0.274127	0.00938042
$855$	−7.20775	−0.246500
$856$	5.89977	0.201650
$857$	28.8961	0.987070	0.493535	−	0.869726i	$-0.335704\pi$
$857$	28.8961	0.987070	0.493535	+	0.869726i	$0.335704\pi$
$858$	0	0
$859$	−17.2755	−0.589431	−0.294715	−	0.955585i	$-0.595225\pi$
$859$	−17.2755	−0.589431	−0.294715	+	0.955585i	$0.595225\pi$
$860$	33.6775	1.14839
$861$	1.04221	0.0355185
$862$	34.5133	1.17553
$863$	−44.7741	−1.52413	−0.762063	−	0.647503i	$-0.775813\pi$
$863$	−44.7741	−1.52413	−0.762063	+	0.647503i	$0.775813\pi$
$864$	1.00000	0.0340207
$865$	37.6165	1.27900
$866$	−2.12631	−0.0722549
$867$	37.5241	1.27438
$868$	0.673235	0.0228511
$869$	−40.4534	−1.37229
$870$	13.5429	0.459147
$871$	0	0
$872$	−0.792249	−0.0268289
$873$	8.54288	0.289133
$874$	9.09651	0.307694
$875$	17.9148	0.605632
$876$	7.65279	0.258564
$877$	−40.2741	−1.35996	−0.679980	−	0.733230i	$-0.738012\pi$
$877$	−40.2741	−1.35996	−0.679980	+	0.733230i	$0.738012\pi$
$878$	21.8321	0.736797
$879$	−7.14914	−0.241135
$880$	−19.6407	−0.662088
$881$	9.40821	0.316971	0.158485	−	0.987361i	$-0.449339\pi$
$881$	9.40821	0.316971	0.158485	+	0.987361i	$0.449339\pi$
$882$	−6.52111	−0.219577
$883$	−51.2271	−1.72393	−0.861965	−	0.506968i	$-0.830766\pi$
$883$	−51.2271	−1.72393	−0.861965	+	0.506968i	$0.830766\pi$
$884$	0	0
$885$	5.29590	0.178020
$886$	−7.54048	−0.253328
$887$	−39.9215	−1.34043	−0.670217	−	0.742165i	$-0.733799\pi$
$887$	−39.9215	−1.34043	−0.670217	+	0.742165i	$0.733799\pi$
$888$	−1.28621	−0.0431623
$889$	4.15585	0.139383
$890$	12.5918	0.422078
$891$	4.85086	0.162510
$892$	−12.1957	−0.408341
$893$	12.8310	0.429373
$894$	2.55257	0.0853706
$895$	−92.2863	−3.08479
$896$	−0.692021	−0.0231188
$897$	0	0
$898$	19.7560	0.659266
$899$	3.25401	0.108527
$900$	11.3937	0.379791
$901$	99.5111	3.31519
$902$	−7.30559	−0.243249
$903$	5.75600	0.191548
$904$	6.21983	0.206869
$905$	−2.17629	−0.0723424
$906$	17.7168	0.588600
$907$	−34.8310	−1.15654	−0.578272	−	0.815844i	$-0.696273\pi$
$907$	−34.8310	−1.15654	−0.578272	+	0.815844i	$0.696273\pi$
$908$	6.74333	0.223785
$909$	−11.9976	−0.397936
$910$	0	0
$911$	13.2125	0.437751	0.218875	−	0.975753i	$-0.429761\pi$
$911$	13.2125	0.437751	0.218875	+	0.975753i	$0.429761\pi$
$912$	1.78017	0.0589472
$913$	−74.3508	−2.46065
$914$	23.8582	0.789157
$915$	1.60388	0.0530225
$916$	−19.8237	−0.654994
$917$	−6.10156	−0.201491
$918$	7.38404	0.243710
$919$	21.0175	0.693302	0.346651	−	0.937994i	$-0.387319\pi$
$919$	21.0175	0.693302	0.346651	+	0.937994i	$0.387319\pi$
$920$	−20.6896	−0.682117
$921$	−17.9952	−0.592962
$922$	−17.5773	−0.578878
$923$	0	0
$924$	−3.35690	−0.110434
$925$	−14.6547	−0.481844
$926$	23.8431	0.783532
$927$	−12.3230	−0.404742
$928$	−3.34481	−0.109799
$929$	−26.9965	−0.885728	−0.442864	−	0.896589i	$-0.646038\pi$
$929$	−26.9965	−0.885728	−0.442864	+	0.896589i	$0.646038\pi$
$930$	3.93900	0.129165
$931$	−11.6087	−0.380459
$932$	−30.0301	−0.983670
$933$	3.32975	0.109011
$934$	8.61058	0.281747
$935$	−145.028	−4.74292
$936$	0	0
$937$	23.1745	0.757078	0.378539	−	0.925585i	$-0.376427\pi$
$937$	23.1745	0.757078	0.378539	+	0.925585i	$0.376427\pi$
$938$	4.18970	0.136799
$939$	−17.8834	−0.583602
$940$	−29.1836	−0.951864
$941$	7.54048	0.245813	0.122906	−	0.992418i	$-0.460779\pi$
$941$	7.54048	0.245813	0.122906	+	0.992418i	$0.460779\pi$
$942$	−6.31767	−0.205841
$943$	−7.69574	−0.250608
$944$	−1.30798	−0.0425711
$945$	2.80194	0.0911470
$946$	−40.3478	−1.31182
$947$	20.6601	0.671363	0.335681	−	0.941976i	$-0.391033\pi$
$947$	20.6601	0.671363	0.335681	+	0.941976i	$0.391033\pi$
$948$	−8.33944	−0.270852
$949$	0	0
$950$	20.2828	0.658059
$951$	4.39373	0.142477
$952$	−5.10992	−0.165613
$953$	−30.2935	−0.981303	−0.490651	−	0.871356i	$-0.663241\pi$
$953$	−30.2935	−0.981303	−0.490651	+	0.871356i	$0.663241\pi$
$954$	13.4765	0.436318
$955$	39.6775	1.28394
$956$	22.0978	0.714695
$957$	−16.2252	−0.524487
$958$	6.58104	0.212624
$959$	−10.9035	−0.352092
$960$	−4.04892	−0.130678
$961$	−30.0536	−0.969470
$962$	0	0
$963$	5.89977	0.190118
$964$	10.1274	0.326181
$965$	57.4771	1.85025
$966$	−3.53617	−0.113774
$967$	−20.7289	−0.666595	−0.333298	−	0.942822i	$-0.608161\pi$
$967$	−20.7289	−0.666595	−0.333298	+	0.942822i	$0.608161\pi$
$968$	12.5308	0.402755
$969$	13.1448	0.422273
$970$	−34.5894	−1.11060
$971$	−39.1094	−1.25508	−0.627541	−	0.778584i	$-0.715938\pi$
$971$	−39.1094	−1.25508	−0.627541	+	0.778584i	$0.715938\pi$
$972$	1.00000	0.0320750
$973$	4.21983	0.135282
$974$	−23.2760	−0.745813
$975$	0	0
$976$	−0.396125	−0.0126796
$977$	7.27545	0.232762	0.116381	−	0.993205i	$-0.462871\pi$
$977$	7.27545	0.232762	0.116381	+	0.993205i	$0.462871\pi$
$978$	14.5918	0.466594
$979$	−15.0858	−0.482143
$980$	26.4034	0.843426
$981$	−0.792249	−0.0252946
$982$	−15.5405	−0.495917
$983$	53.4857	1.70593	0.852965	−	0.521969i	$-0.174802\pi$
$983$	53.4857	1.70593	0.852965	+	0.521969i	$0.174802\pi$
$984$	−1.50604	−0.0480108
$985$	12.1860	0.388278
$986$	−24.6983	−0.786553
$987$	−4.98792	−0.158767
$988$	0	0
$989$	−42.5026	−1.35150
$990$	−19.6407	−0.624223
$991$	16.0575	0.510085	0.255042	−	0.966930i	$-0.417911\pi$
$991$	16.0575	0.510085	0.255042	+	0.966930i	$0.417911\pi$
$992$	−0.972853	−0.0308881
$993$	−25.6775	−0.814852
$994$	−0.920215	−0.0291874
$995$	−52.2083	−1.65512
$996$	−15.3274	−0.485666
$997$	22.4263	0.710247	0.355123	−	0.934819i	$-0.384439\pi$
$997$	22.4263	0.710247	0.355123	+	0.934819i	$0.384439\pi$
$998$	9.53617	0.301862
$999$	−1.28621	−0.0406938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.o.1.1	yes	3
3.2	odd	2		3042.2.a.bd.1.3		3
4.3	odd	2		8112.2.a.bz.1.1		3
13.2	odd	12		1014.2.i.g.823.6		12
13.3	even	3		1014.2.e.k.529.1		6
13.4	even	6		1014.2.e.m.991.3		6
13.5	odd	4		1014.2.b.g.337.3		6
13.6	odd	12		1014.2.i.g.361.3		12
13.7	odd	12		1014.2.i.g.361.4		12
13.8	odd	4		1014.2.b.g.337.4		6
13.9	even	3		1014.2.e.k.991.1		6
13.10	even	6		1014.2.e.m.529.3		6
13.11	odd	12		1014.2.i.g.823.1		12
13.12	even	2		1014.2.a.m.1.3	✓	3
39.5	even	4		3042.2.b.r.1351.4		6
39.8	even	4		3042.2.b.r.1351.3		6
39.38	odd	2		3042.2.a.be.1.1		3
52.51	odd	2		8112.2.a.ce.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.3	✓	3	13.12	even	2
1014.2.a.o.1.1	yes	3	1.1	even	1	trivial
1014.2.b.g.337.3		6	13.5	odd	4
1014.2.b.g.337.4		6	13.8	odd	4
1014.2.e.k.529.1		6	13.3	even	3
1014.2.e.k.991.1		6	13.9	even	3
1014.2.e.m.529.3		6	13.10	even	6
1014.2.e.m.991.3		6	13.4	even	6
1014.2.i.g.361.3		12	13.6	odd	12
1014.2.i.g.361.4		12	13.7	odd	12
1014.2.i.g.823.1		12	13.11	odd	12
1014.2.i.g.823.6		12	13.2	odd	12
3042.2.a.bd.1.3		3	3.2	odd	2
3042.2.a.be.1.1		3	39.38	odd	2
3042.2.b.r.1351.3		6	39.8	even	4
3042.2.b.r.1351.4		6	39.5	even	4
8112.2.a.bz.1.1		3	4.3	odd	2
8112.2.a.ce.1.3		3	52.51	odd	2

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.04892 q^{5} +1.00000 q^{6} -0.692021 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.04892 q^{5} +1.00000 q^{6} -0.692021 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.04892 q^{10} +4.85086 q^{11} +1.00000 q^{12} -0.692021 q^{14} -4.04892 q^{15} +1.00000 q^{16} +7.38404 q^{17} +1.00000 q^{18} +1.78017 q^{19} -4.04892 q^{20} -0.692021 q^{21} +4.85086 q^{22} +5.10992 q^{23} +1.00000 q^{24} +11.3937 q^{25} +1.00000 q^{27} -0.692021 q^{28} -3.34481 q^{29} -4.04892 q^{30} -0.972853 q^{31} +1.00000 q^{32} +4.85086 q^{33} +7.38404 q^{34} +2.80194 q^{35} +1.00000 q^{36} -1.28621 q^{37} +1.78017 q^{38} -4.04892 q^{40} -1.50604 q^{41} -0.692021 q^{42} -8.31767 q^{43} +4.85086 q^{44} -4.04892 q^{45} +5.10992 q^{46} +7.20775 q^{47} +1.00000 q^{48} -6.52111 q^{49} +11.3937 q^{50} +7.38404 q^{51} +13.4765 q^{53} +1.00000 q^{54} -19.6407 q^{55} -0.692021 q^{56} +1.78017 q^{57} -3.34481 q^{58} -1.30798 q^{59} -4.04892 q^{60} -0.396125 q^{61} -0.972853 q^{62} -0.692021 q^{63} +1.00000 q^{64} +4.85086 q^{66} -6.05429 q^{67} +7.38404 q^{68} +5.10992 q^{69} +2.80194 q^{70} +1.32975 q^{71} +1.00000 q^{72} +7.65279 q^{73} -1.28621 q^{74} +11.3937 q^{75} +1.78017 q^{76} -3.35690 q^{77} -8.33944 q^{79} -4.04892 q^{80} +1.00000 q^{81} -1.50604 q^{82} -15.3274 q^{83} -0.692021 q^{84} -29.8974 q^{85} -8.31767 q^{86} -3.34481 q^{87} +4.85086 q^{88} -3.10992 q^{89} -4.04892 q^{90} +5.10992 q^{92} -0.972853 q^{93} +7.20775 q^{94} -7.20775 q^{95} +1.00000 q^{96} +8.54288 q^{97} -6.52111 q^{98} +4.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + q^{11} + 3 q^{12} + 3 q^{14} - 3 q^{15} + 3 q^{16} + 12 q^{17} + 3 q^{18} + 4 q^{19} - 3 q^{20} + 3 q^{21} + q^{22} + 16 q^{23} + 3 q^{24} + 2 q^{25} + 3 q^{27} + 3 q^{28} + 13 q^{29} - 3 q^{30} - 9 q^{31} + 3 q^{32} + q^{33} + 12 q^{34} + 4 q^{35} + 3 q^{36} - 12 q^{37} + 4 q^{38} - 3 q^{40} - 14 q^{41} + 3 q^{42} - 8 q^{43} + q^{44} - 3 q^{45} + 16 q^{46} + 4 q^{47} + 3 q^{48} - 4 q^{49} + 2 q^{50} + 12 q^{51} + 15 q^{53} + 3 q^{54} - 22 q^{55} + 3 q^{56} + 4 q^{57} + 13 q^{58} - 9 q^{59} - 3 q^{60} - 10 q^{61} - 9 q^{62} + 3 q^{63} + 3 q^{64} + q^{66} - 6 q^{67} + 12 q^{68} + 16 q^{69} + 4 q^{70} + 6 q^{71} + 3 q^{72} + 5 q^{73} - 12 q^{74} + 2 q^{75} + 4 q^{76} - 6 q^{77} - 5 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} - 7 q^{83} + 3 q^{84} - 26 q^{85} - 8 q^{86} + 13 q^{87} + q^{88} - 10 q^{89} - 3 q^{90} + 16 q^{92} - 9 q^{93} + 4 q^{94} - 4 q^{95} + 3 q^{96} + 7 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + q^11 + 3 * q^12 + 3 * q^14 - 3 * q^15 + 3 * q^16 + 12 * q^17 + 3 * q^18 + 4 * q^19 - 3 * q^20 + 3 * q^21 + q^22 + 16 * q^23 + 3 * q^24 + 2 * q^25 + 3 * q^27 + 3 * q^28 + 13 * q^29 - 3 * q^30 - 9 * q^31 + 3 * q^32 + q^33 + 12 * q^34 + 4 * q^35 + 3 * q^36 - 12 * q^37 + 4 * q^38 - 3 * q^40 - 14 * q^41 + 3 * q^42 - 8 * q^43 + q^44 - 3 * q^45 + 16 * q^46 + 4 * q^47 + 3 * q^48 - 4 * q^49 + 2 * q^50 + 12 * q^51 + 15 * q^53 + 3 * q^54 - 22 * q^55 + 3 * q^56 + 4 * q^57 + 13 * q^58 - 9 * q^59 - 3 * q^60 - 10 * q^61 - 9 * q^62 + 3 * q^63 + 3 * q^64 + q^66 - 6 * q^67 + 12 * q^68 + 16 * q^69 + 4 * q^70 + 6 * q^71 + 3 * q^72 + 5 * q^73 - 12 * q^74 + 2 * q^75 + 4 * q^76 - 6 * q^77 - 5 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 - 7 * q^83 + 3 * q^84 - 26 * q^85 - 8 * q^86 + 13 * q^87 + q^88 - 10 * q^89 - 3 * q^90 + 16 * q^92 - 9 * q^93 + 4 * q^94 - 4 * q^95 + 3 * q^96 + 7 * q^97 - 4 * q^98 + q^99

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