LMFDB - Embedded newform 6026.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.69112 q^{3} +1.00000 q^{4} -3.34531 q^{5} -1.69112 q^{6} +0.398747 q^{7} +1.00000 q^{8} -0.140113 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.69112 q^{3} +1.00000 q^{4} -3.34531 q^{5} -1.69112 q^{6} +0.398747 q^{7} +1.00000 q^{8} -0.140113 q^{9} -3.34531 q^{10} +2.98081 q^{11} -1.69112 q^{12} +4.90018 q^{13} +0.398747 q^{14} +5.65732 q^{15} +1.00000 q^{16} -7.88643 q^{17} -0.140113 q^{18} +7.38263 q^{19} -3.34531 q^{20} -0.674329 q^{21} +2.98081 q^{22} -1.00000 q^{23} -1.69112 q^{24} +6.19110 q^{25} +4.90018 q^{26} +5.31031 q^{27} +0.398747 q^{28} +1.12944 q^{29} +5.65732 q^{30} -10.3238 q^{31} +1.00000 q^{32} -5.04091 q^{33} -7.88643 q^{34} -1.33393 q^{35} -0.140113 q^{36} -8.61735 q^{37} +7.38263 q^{38} -8.28680 q^{39} -3.34531 q^{40} -6.81371 q^{41} -0.674329 q^{42} +10.1069 q^{43} +2.98081 q^{44} +0.468720 q^{45} -1.00000 q^{46} -2.44759 q^{47} -1.69112 q^{48} -6.84100 q^{49} +6.19110 q^{50} +13.3369 q^{51} +4.90018 q^{52} +9.95047 q^{53} +5.31031 q^{54} -9.97175 q^{55} +0.398747 q^{56} -12.4849 q^{57} +1.12944 q^{58} -2.60393 q^{59} +5.65732 q^{60} -1.65551 q^{61} -10.3238 q^{62} -0.0558695 q^{63} +1.00000 q^{64} -16.3926 q^{65} -5.04091 q^{66} -9.23411 q^{67} -7.88643 q^{68} +1.69112 q^{69} -1.33393 q^{70} +8.52385 q^{71} -0.140113 q^{72} +2.01849 q^{73} -8.61735 q^{74} -10.4699 q^{75} +7.38263 q^{76} +1.18859 q^{77} -8.28680 q^{78} +6.10594 q^{79} -3.34531 q^{80} -8.56003 q^{81} -6.81371 q^{82} +16.5674 q^{83} -0.674329 q^{84} +26.3825 q^{85} +10.1069 q^{86} -1.91002 q^{87} +2.98081 q^{88} -11.6112 q^{89} +0.468720 q^{90} +1.95393 q^{91} -1.00000 q^{92} +17.4588 q^{93} -2.44759 q^{94} -24.6972 q^{95} -1.69112 q^{96} -2.06658 q^{97} -6.84100 q^{98} -0.417650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−1.69112	−0.976369	−0.488184	−	0.872741i	$-0.662341\pi$
$3$	−1.69112	−0.976369	−0.488184	+	0.872741i	$0.662341\pi$
$4$	1.00000	0.500000
$5$	−3.34531	−1.49607	−0.748034	−	0.663660i	$-0.769002\pi$
$5$	−3.34531	−1.49607	−0.748034	+	0.663660i	$0.769002\pi$
$6$	−1.69112	−0.690397
$7$	0.398747	0.150712	0.0753561	−	0.997157i	$-0.475991\pi$
$7$	0.398747	0.150712	0.0753561	+	0.997157i	$0.475991\pi$
$8$	1.00000	0.353553
$9$	−0.140113	−0.0467042
$10$	−3.34531	−1.05788
$11$	2.98081	0.898749	0.449375	−	0.893343i	$-0.351647\pi$
$11$	2.98081	0.898749	0.449375	+	0.893343i	$0.351647\pi$
$12$	−1.69112	−0.488184
$13$	4.90018	1.35907	0.679533	−	0.733645i	$-0.262182\pi$
$13$	4.90018	1.35907	0.679533	+	0.733645i	$0.262182\pi$
$14$	0.398747	0.106570
$15$	5.65732	1.46071
$16$	1.00000	0.250000
$17$	−7.88643	−1.91274	−0.956370	−	0.292159i	$-0.905626\pi$
$17$	−7.88643	−1.91274	−0.956370	+	0.292159i	$0.905626\pi$
$18$	−0.140113	−0.0330249
$19$	7.38263	1.69369	0.846846	−	0.531838i	$-0.178499\pi$
$19$	7.38263	1.69369	0.846846	+	0.531838i	$0.178499\pi$
$20$	−3.34531	−0.748034
$21$	−0.674329	−0.147151
$22$	2.98081	0.635512
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.69112	−0.345198
$25$	6.19110	1.23822
$26$	4.90018	0.961005
$27$	5.31031	1.02197
$28$	0.398747	0.0753561
$29$	1.12944	0.209732	0.104866	−	0.994486i	$-0.466559\pi$
$29$	1.12944	0.209732	0.104866	+	0.994486i	$0.466559\pi$
$30$	5.65732	1.03288
$31$	−10.3238	−1.85421	−0.927104	−	0.374804i	$-0.877710\pi$
$31$	−10.3238	−1.85421	−0.927104	+	0.374804i	$0.877710\pi$
$32$	1.00000	0.176777
$33$	−5.04091	−0.877510
$34$	−7.88643	−1.35251
$35$	−1.33393	−0.225476
$36$	−0.140113	−0.0233521
$37$	−8.61735	−1.41668	−0.708342	−	0.705870i	$-0.750556\pi$
$37$	−8.61735	−1.41668	−0.708342	+	0.705870i	$0.750556\pi$
$38$	7.38263	1.19762
$39$	−8.28680	−1.32695
$40$	−3.34531	−0.528940
$41$	−6.81371	−1.06412	−0.532061	−	0.846706i	$-0.678582\pi$
$41$	−6.81371	−1.06412	−0.532061	+	0.846706i	$0.678582\pi$
$42$	−0.674329	−0.104051
$43$	10.1069	1.54129	0.770643	−	0.637267i	$-0.219935\pi$
$43$	10.1069	1.54129	0.770643	+	0.637267i	$0.219935\pi$
$44$	2.98081	0.449375
$45$	0.468720	0.0698727
$46$	−1.00000	−0.147442
$47$	−2.44759	−0.357018	−0.178509	−	0.983938i	$-0.557127\pi$
$47$	−2.44759	−0.357018	−0.178509	+	0.983938i	$0.557127\pi$
$48$	−1.69112	−0.244092
$49$	−6.84100	−0.977286
$50$	6.19110	0.875554
$51$	13.3369	1.86754
$52$	4.90018	0.679533
$53$	9.95047	1.36680	0.683401	−	0.730043i	$-0.260500\pi$
$53$	9.95047	1.36680	0.683401	+	0.730043i	$0.260500\pi$
$54$	5.31031	0.722641
$55$	−9.97175	−1.34459
$56$	0.398747	0.0532848
$57$	−12.4849	−1.65367
$58$	1.12944	0.148303
$59$	−2.60393	−0.339003	−0.169501	−	0.985530i	$-0.554216\pi$
$59$	−2.60393	−0.339003	−0.169501	+	0.985530i	$0.554216\pi$
$60$	5.65732	0.730357
$61$	−1.65551	−0.211966	−0.105983	−	0.994368i	$-0.533799\pi$
$61$	−1.65551	−0.211966	−0.105983	+	0.994368i	$0.533799\pi$
$62$	−10.3238	−1.31112
$63$	−0.0558695	−0.00703890
$64$	1.00000	0.125000
$65$	−16.3926	−2.03326
$66$	−5.04091	−0.620494
$67$	−9.23411	−1.12813	−0.564063	−	0.825732i	$-0.690762\pi$
$67$	−9.23411	−1.12813	−0.564063	+	0.825732i	$0.690762\pi$
$68$	−7.88643	−0.956370
$69$	1.69112	0.203587
$70$	−1.33393	−0.159435
$71$	8.52385	1.01159	0.505797	−	0.862652i	$-0.331198\pi$
$71$	8.52385	1.01159	0.505797	+	0.862652i	$0.331198\pi$
$72$	−0.140113	−0.0165124
$73$	2.01849	0.236246	0.118123	−	0.992999i	$-0.462312\pi$
$73$	2.01849	0.236246	0.118123	+	0.992999i	$0.462312\pi$
$74$	−8.61735	−1.00175
$75$	−10.4699	−1.20896
$76$	7.38263	0.846846
$77$	1.18859	0.135452
$78$	−8.28680	−0.938295
$79$	6.10594	0.686972	0.343486	−	0.939158i	$-0.388392\pi$
$79$	6.10594	0.686972	0.343486	+	0.939158i	$0.388392\pi$
$80$	−3.34531	−0.374017
$81$	−8.56003	−0.951115
$82$	−6.81371	−0.752449
$83$	16.5674	1.81851	0.909253	−	0.416245i	$-0.136654\pi$
$83$	16.5674	1.81851	0.909253	+	0.416245i	$0.136654\pi$
$84$	−0.674329	−0.0735754
$85$	26.3825	2.86159
$86$	10.1069	1.08985
$87$	−1.91002	−0.204776
$88$	2.98081	0.317756
$89$	−11.6112	−1.23078	−0.615390	−	0.788223i	$-0.711001\pi$
$89$	−11.6112	−1.23078	−0.615390	+	0.788223i	$0.711001\pi$
$90$	0.468720	0.0494074
$91$	1.95393	0.204828
$92$	−1.00000	−0.104257
$93$	17.4588	1.81039
$94$	−2.44759	−0.252450
$95$	−24.6972	−2.53388
$96$	−1.69112	−0.172599
$97$	−2.06658	−0.209829	−0.104914	−	0.994481i	$-0.533457\pi$
$97$	−2.06658	−0.209829	−0.104914	+	0.994481i	$0.533457\pi$
$98$	−6.84100	−0.691045
$99$	−0.417650	−0.0419754
$100$	6.19110	0.619110
$101$	7.77656	0.773797	0.386899	−	0.922122i	$-0.373546\pi$
$101$	7.77656	0.773797	0.386899	+	0.922122i	$0.373546\pi$
$102$	13.3369	1.32055
$103$	7.06993	0.696621	0.348310	−	0.937379i	$-0.386755\pi$
$103$	7.06993	0.696621	0.348310	+	0.937379i	$0.386755\pi$
$104$	4.90018	0.480502
$105$	2.25584	0.220148
$106$	9.95047	0.966475
$107$	0.729573	0.0705305	0.0352652	−	0.999378i	$-0.488772\pi$
$107$	0.729573	0.0705305	0.0352652	+	0.999378i	$0.488772\pi$
$108$	5.31031	0.510985
$109$	−17.2040	−1.64785	−0.823924	−	0.566701i	$-0.808220\pi$
$109$	−17.2040	−1.64785	−0.823924	+	0.566701i	$0.808220\pi$
$110$	−9.97175	−0.950769
$111$	14.5730	1.38321
$112$	0.398747	0.0376781
$113$	10.6507	1.00193	0.500966	−	0.865467i	$-0.332978\pi$
$113$	10.6507	1.00193	0.500966	+	0.865467i	$0.332978\pi$
$114$	−12.4849	−1.16932
$115$	3.34531	0.311952
$116$	1.12944	0.104866
$117$	−0.686577	−0.0634741
$118$	−2.60393	−0.239711
$119$	−3.14469	−0.288273
$120$	5.65732	0.516440
$121$	−2.11475	−0.192250
$122$	−1.65551	−0.149882
$123$	11.5228	1.03898
$124$	−10.3238	−0.927104
$125$	−3.98460	−0.356394
$126$	−0.0558695	−0.00497725
$127$	14.7506	1.30890	0.654452	−	0.756103i	$-0.272899\pi$
$127$	14.7506	1.30890	0.654452	+	0.756103i	$0.272899\pi$
$128$	1.00000	0.0883883
$129$	−17.0920	−1.50486
$130$	−16.3926	−1.43773
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−5.04091	−0.438755
$133$	2.94380	0.255260
$134$	−9.23411	−0.797705
$135$	−17.7646	−1.52894
$136$	−7.88643	−0.676255
$137$	−9.49328	−0.811066	−0.405533	−	0.914081i	$-0.632914\pi$
$137$	−9.49328	−0.811066	−0.405533	+	0.914081i	$0.632914\pi$
$138$	1.69112	0.143958
$139$	20.5900	1.74642	0.873211	−	0.487342i	$-0.162034\pi$
$139$	20.5900	1.74642	0.873211	+	0.487342i	$0.162034\pi$
$140$	−1.33393	−0.112738
$141$	4.13918	0.348581
$142$	8.52385	0.715305
$143$	14.6065	1.22146
$144$	−0.140113	−0.0116761
$145$	−3.77833	−0.313773
$146$	2.01849	0.167051
$147$	11.5690	0.954191
$148$	−8.61735	−0.708342
$149$	16.7943	1.37584	0.687921	−	0.725786i	$-0.258524\pi$
$149$	16.7943	1.37584	0.687921	+	0.725786i	$0.258524\pi$
$150$	−10.4699	−0.854863
$151$	16.6685	1.35647	0.678233	−	0.734847i	$-0.262746\pi$
$151$	16.6685	1.35647	0.678233	+	0.734847i	$0.262746\pi$
$152$	7.38263	0.598810
$153$	1.10499	0.0893330
$154$	1.18859	0.0957794
$155$	34.5363	2.77402
$156$	−8.28680	−0.663475
$157$	0.394782	0.0315071	0.0157535	−	0.999876i	$-0.494985\pi$
$157$	0.394782	0.0315071	0.0157535	+	0.999876i	$0.494985\pi$
$158$	6.10594	0.485763
$159$	−16.8274	−1.33450
$160$	−3.34531	−0.264470
$161$	−0.398747	−0.0314257
$162$	−8.56003	−0.672540
$163$	17.0469	1.33521	0.667607	−	0.744514i	$-0.267319\pi$
$163$	17.0469	1.33521	0.667607	+	0.744514i	$0.267319\pi$
$164$	−6.81371	−0.532061
$165$	16.8634	1.31282
$166$	16.5674	1.28588
$167$	−11.0024	−0.851393	−0.425696	−	0.904866i	$-0.639971\pi$
$167$	−11.0024	−0.851393	−0.425696	+	0.904866i	$0.639971\pi$
$168$	−0.674329	−0.0520256
$169$	11.0118	0.847061
$170$	26.3825	2.02345
$171$	−1.03440	−0.0791025
$172$	10.1069	0.770643
$173$	14.2018	1.07974	0.539870	−	0.841748i	$-0.318473\pi$
$173$	14.2018	1.07974	0.539870	+	0.841748i	$0.318473\pi$
$174$	−1.91002	−0.144798
$175$	2.46868	0.186615
$176$	2.98081	0.224687
$177$	4.40356	0.330992
$178$	−11.6112	−0.870293
$179$	13.4742	1.00711	0.503554	−	0.863964i	$-0.332025\pi$
$179$	13.4742	1.00711	0.503554	+	0.863964i	$0.332025\pi$
$180$	0.468720	0.0349363
$181$	−6.06855	−0.451071	−0.225536	−	0.974235i	$-0.572413\pi$
$181$	−6.06855	−0.451071	−0.225536	+	0.974235i	$0.572413\pi$
$182$	1.95393	0.144835
$183$	2.79966	0.206957
$184$	−1.00000	−0.0737210
$185$	28.8277	2.11945
$186$	17.4588	1.28014
$187$	−23.5080	−1.71907
$188$	−2.44759	−0.178509
$189$	2.11747	0.154023
$190$	−24.6972	−1.79172
$191$	−14.2715	−1.03265	−0.516325	−	0.856393i	$-0.672700\pi$
$191$	−14.2715	−1.03265	−0.516325	+	0.856393i	$0.672700\pi$
$192$	−1.69112	−0.122046
$193$	17.6604	1.27122	0.635611	−	0.772010i	$-0.280748\pi$
$193$	17.6604	1.27122	0.635611	+	0.772010i	$0.280748\pi$
$194$	−2.06658	−0.148371
$195$	27.7219	1.98521
$196$	−6.84100	−0.488643
$197$	−17.1607	−1.22265	−0.611324	−	0.791381i	$-0.709363\pi$
$197$	−17.1607	−1.22265	−0.611324	+	0.791381i	$0.709363\pi$
$198$	−0.417650	−0.0296811
$199$	17.8353	1.26431	0.632156	−	0.774841i	$-0.282170\pi$
$199$	17.8353	1.26431	0.632156	+	0.774841i	$0.282170\pi$
$200$	6.19110	0.437777
$201$	15.6160	1.10147
$202$	7.77656	0.547157
$203$	0.450361	0.0316092
$204$	13.3369	0.933769
$205$	22.7940	1.59200
$206$	7.06993	0.492585
$207$	0.140113	0.00973850
$208$	4.90018	0.339767
$209$	22.0062	1.52220
$210$	2.25584	0.155668
$211$	23.4130	1.61182	0.805909	−	0.592040i	$-0.201677\pi$
$211$	23.4130	1.61182	0.805909	+	0.592040i	$0.201677\pi$
$212$	9.95047	0.683401
$213$	−14.4149	−0.987689
$214$	0.729573	0.0498726
$215$	−33.8107	−2.30587
$216$	5.31031	0.361321
$217$	−4.11658	−0.279452
$218$	−17.2040	−1.16520
$219$	−3.41350	−0.230663
$220$	−9.97175	−0.672295
$221$	−38.6449	−2.59954
$222$	14.5730	0.978074
$223$	4.93290	0.330332	0.165166	−	0.986266i	$-0.447184\pi$
$223$	4.93290	0.330332	0.165166	+	0.986266i	$0.447184\pi$
$224$	0.398747	0.0266424
$225$	−0.867451	−0.0578301
$226$	10.6507	0.708473
$227$	10.5215	0.698334	0.349167	−	0.937061i	$-0.386465\pi$
$227$	10.5215	0.698334	0.349167	+	0.937061i	$0.386465\pi$
$228$	−12.4849	−0.826834
$229$	17.1728	1.13481	0.567405	−	0.823439i	$-0.307947\pi$
$229$	17.1728	1.13481	0.567405	+	0.823439i	$0.307947\pi$
$230$	3.34531	0.220583
$231$	−2.01005	−0.132252
$232$	1.12944	0.0741514
$233$	−20.8477	−1.36578	−0.682888	−	0.730523i	$-0.739276\pi$
$233$	−20.8477	−1.36578	−0.682888	+	0.730523i	$0.739276\pi$
$234$	−0.686577	−0.0448830
$235$	8.18796	0.534124
$236$	−2.60393	−0.169501
$237$	−10.3259	−0.670738
$238$	−3.14469	−0.203840
$239$	4.42195	0.286032	0.143016	−	0.989720i	$-0.454320\pi$
$239$	4.42195	0.286032	0.143016	+	0.989720i	$0.454320\pi$
$240$	5.65732	0.365179
$241$	−3.25503	−0.209675	−0.104838	−	0.994489i	$-0.533432\pi$
$241$	−3.25503	−0.209675	−0.104838	+	0.994489i	$0.533432\pi$
$242$	−2.11475	−0.135941
$243$	−1.45488	−0.0933308
$244$	−1.65551	−0.105983
$245$	22.8853	1.46209
$246$	11.5228	0.734667
$247$	36.1762	2.30184
$248$	−10.3238	−0.655562
$249$	−28.0174	−1.77553
$250$	−3.98460	−0.252008
$251$	−27.6635	−1.74610	−0.873052	−	0.487627i	$-0.837863\pi$
$251$	−27.6635	−1.74610	−0.873052	+	0.487627i	$0.837863\pi$
$252$	−0.0558695	−0.00351945
$253$	−2.98081	−0.187402
$254$	14.7506	0.925536
$255$	−44.6160	−2.79397
$256$	1.00000	0.0625000
$257$	−12.3217	−0.768607	−0.384303	−	0.923207i	$-0.625558\pi$
$257$	−12.3217	−0.768607	−0.384303	+	0.923207i	$0.625558\pi$
$258$	−17.0920	−1.06410
$259$	−3.43614	−0.213512
$260$	−16.3926	−1.01663
$261$	−0.158249	−0.00979536
$262$	−1.00000	−0.0617802
$263$	−12.0683	−0.744165	−0.372083	−	0.928200i	$-0.621356\pi$
$263$	−12.0683	−0.744165	−0.372083	+	0.928200i	$0.621356\pi$
$264$	−5.04091	−0.310247
$265$	−33.2874	−2.04483
$266$	2.94380	0.180496
$267$	19.6359	1.20169
$268$	−9.23411	−0.564063
$269$	−13.4417	−0.819556	−0.409778	−	0.912185i	$-0.634394\pi$
$269$	−13.4417	−0.819556	−0.409778	+	0.912185i	$0.634394\pi$
$270$	−17.7646	−1.08112
$271$	20.0729	1.21934	0.609671	−	0.792655i	$-0.291302\pi$
$271$	20.0729	1.21934	0.609671	+	0.792655i	$0.291302\pi$
$272$	−7.88643	−0.478185
$273$	−3.30434	−0.199988
$274$	−9.49328	−0.573510
$275$	18.4545	1.11285
$276$	1.69112	0.101793
$277$	14.5074	0.871665	0.435833	−	0.900028i	$-0.356454\pi$
$277$	14.5074	0.871665	0.435833	+	0.900028i	$0.356454\pi$
$278$	20.5900	1.23491
$279$	1.44649	0.0865993
$280$	−1.33393	−0.0797177
$281$	30.0849	1.79472	0.897358	−	0.441304i	$-0.145484\pi$
$281$	30.0849	1.79472	0.897358	+	0.441304i	$0.145484\pi$
$282$	4.13918	0.246484
$283$	9.46204	0.562460	0.281230	−	0.959640i	$-0.409258\pi$
$283$	9.46204	0.562460	0.281230	+	0.959640i	$0.409258\pi$
$284$	8.52385	0.505797
$285$	41.7659	2.47400
$286$	14.6065	0.863702
$287$	−2.71695	−0.160376
$288$	−0.140113	−0.00825621
$289$	45.1957	2.65857
$290$	−3.77833	−0.221871
$291$	3.49483	0.204870
$292$	2.01849	0.118123
$293$	−1.13587	−0.0663583	−0.0331792	−	0.999449i	$-0.510563\pi$
$293$	−1.13587	−0.0663583	−0.0331792	+	0.999449i	$0.510563\pi$
$294$	11.5690	0.674715
$295$	8.71096	0.507172
$296$	−8.61735	−0.500873
$297$	15.8290	0.918494
$298$	16.7943	0.972867
$299$	−4.90018	−0.283385
$300$	−10.4699	−0.604480
$301$	4.03009	0.232291
$302$	16.6685	0.959166
$303$	−13.1511	−0.755511
$304$	7.38263	0.423423
$305$	5.53818	0.317115
$306$	1.10499	0.0631679
$307$	−6.32668	−0.361083	−0.180541	−	0.983567i	$-0.557785\pi$
$307$	−6.32668	−0.361083	−0.180541	+	0.983567i	$0.557785\pi$
$308$	1.18859	0.0677262
$309$	−11.9561	−0.680159
$310$	34.5363	1.96153
$311$	−24.8883	−1.41129	−0.705644	−	0.708567i	$-0.749342\pi$
$311$	−24.8883	−1.41129	−0.705644	+	0.708567i	$0.749342\pi$
$312$	−8.28680	−0.469148
$313$	−11.3813	−0.643308	−0.321654	−	0.946857i	$-0.604239\pi$
$313$	−11.3813	−0.643308	−0.321654	+	0.946857i	$0.604239\pi$
$314$	0.394782	0.0222789
$315$	0.186901	0.0105307
$316$	6.10594	0.343486
$317$	−29.5327	−1.65872	−0.829362	−	0.558712i	$-0.811296\pi$
$317$	−29.5327	−1.65872	−0.829362	+	0.558712i	$0.811296\pi$
$318$	−16.8274	−0.943636
$319$	3.36665	0.188496
$320$	−3.34531	−0.187009
$321$	−1.23380	−0.0688637
$322$	−0.398747	−0.0222213
$323$	−58.2226	−3.23959
$324$	−8.56003	−0.475557
$325$	30.3375	1.68282
$326$	17.0469	0.944139
$327$	29.0941	1.60891
$328$	−6.81371	−0.376224
$329$	−0.975971	−0.0538070
$330$	16.8634	0.928301
$331$	−1.27736	−0.0702102	−0.0351051	−	0.999384i	$-0.511177\pi$
$331$	−1.27736	−0.0702102	−0.0351051	+	0.999384i	$0.511177\pi$
$332$	16.5674	0.909253
$333$	1.20740	0.0661651
$334$	−11.0024	−0.602026
$335$	30.8910	1.68775
$336$	−0.674329	−0.0367877
$337$	11.4394	0.623145	0.311572	−	0.950222i	$-0.399144\pi$
$337$	11.4394	0.623145	0.311572	+	0.950222i	$0.399144\pi$
$338$	11.0118	0.598963
$339$	−18.0116	−0.978256
$340$	26.3825	1.43079
$341$	−30.7733	−1.66647
$342$	−1.03440	−0.0559339
$343$	−5.51906	−0.298001
$344$	10.1069	0.544927
$345$	−5.65732	−0.304580
$346$	14.2018	0.763492
$347$	0.861282	0.0462360	0.0231180	−	0.999733i	$-0.492641\pi$
$347$	0.861282	0.0462360	0.0231180	+	0.999733i	$0.492641\pi$
$348$	−1.91002	−0.102388
$349$	28.3641	1.51829	0.759147	−	0.650919i	$-0.225616\pi$
$349$	28.3641	1.51829	0.759147	+	0.650919i	$0.225616\pi$
$350$	2.46868	0.131957
$351$	26.0215	1.38892
$352$	2.98081	0.158878
$353$	6.93270	0.368990	0.184495	−	0.982833i	$-0.440935\pi$
$353$	6.93270	0.368990	0.184495	+	0.982833i	$0.440935\pi$
$354$	4.40356	0.234047
$355$	−28.5149	−1.51341
$356$	−11.6112	−0.615390
$357$	5.31805	0.281461
$358$	13.4742	0.712133
$359$	26.6306	1.40551	0.702756	−	0.711431i	$-0.251953\pi$
$359$	26.6306	1.40551	0.702756	+	0.711431i	$0.251953\pi$
$360$	0.468720	0.0247037
$361$	35.5032	1.86859
$362$	−6.06855	−0.318956
$363$	3.57630	0.187707
$364$	1.95393	0.102414
$365$	−6.75246	−0.353440
$366$	2.79966	0.146341
$367$	15.4687	0.807460	0.403730	−	0.914878i	$-0.367714\pi$
$367$	15.4687	0.807460	0.403730	+	0.914878i	$0.367714\pi$
$368$	−1.00000	−0.0521286
$369$	0.954687	0.0496990
$370$	28.8277	1.49868
$371$	3.96772	0.205994
$372$	17.4588	0.905196
$373$	−8.47870	−0.439010	−0.219505	−	0.975611i	$-0.570444\pi$
$373$	−8.47870	−0.439010	−0.219505	+	0.975611i	$0.570444\pi$
$374$	−23.5080	−1.21557
$375$	6.73844	0.347972
$376$	−2.44759	−0.126225
$377$	5.53447	0.285040
$378$	2.11747	0.108911
$379$	18.9708	0.974462	0.487231	−	0.873273i	$-0.338007\pi$
$379$	18.9708	0.974462	0.487231	+	0.873273i	$0.338007\pi$
$380$	−24.6972	−1.26694
$381$	−24.9451	−1.27797
$382$	−14.2715	−0.730194
$383$	22.6777	1.15878	0.579389	−	0.815051i	$-0.303291\pi$
$383$	22.6777	1.15878	0.579389	+	0.815051i	$0.303291\pi$
$384$	−1.69112	−0.0862996
$385$	−3.97620	−0.202646
$386$	17.6604	0.898889
$387$	−1.41610	−0.0719846
$388$	−2.06658	−0.104914
$389$	35.5592	1.80292	0.901461	−	0.432860i	$-0.142495\pi$
$389$	35.5592	1.80292	0.901461	+	0.432860i	$0.142495\pi$
$390$	27.7219	1.40375
$391$	7.88643	0.398834
$392$	−6.84100	−0.345523
$393$	1.69112	0.0853057
$394$	−17.1607	−0.864542
$395$	−20.4263	−1.02776
$396$	−0.417650	−0.0209877
$397$	23.0310	1.15589	0.577947	−	0.816074i	$-0.303854\pi$
$397$	23.0310	1.15589	0.577947	+	0.816074i	$0.303854\pi$
$398$	17.8353	0.894004
$399$	−4.97832	−0.249228
$400$	6.19110	0.309555
$401$	10.3837	0.518538	0.259269	−	0.965805i	$-0.416518\pi$
$401$	10.3837	0.518538	0.259269	+	0.965805i	$0.416518\pi$
$402$	15.6160	0.778854
$403$	−50.5885	−2.51999
$404$	7.77656	0.386899
$405$	28.6360	1.42293
$406$	0.450361	0.0223511
$407$	−25.6867	−1.27324
$408$	13.3369	0.660275
$409$	−21.1070	−1.04368	−0.521838	−	0.853045i	$-0.674753\pi$
$409$	−21.1070	−1.04368	−0.521838	+	0.853045i	$0.674753\pi$
$410$	22.7940	1.12571
$411$	16.0543	0.791899
$412$	7.06993	0.348310
$413$	−1.03831	−0.0510919
$414$	0.140113	0.00688616
$415$	−55.4230	−2.72061
$416$	4.90018	0.240251
$417$	−34.8202	−1.70515
$418$	22.0062	1.07636
$419$	29.0263	1.41803	0.709013	−	0.705195i	$-0.249141\pi$
$419$	29.0263	1.41803	0.709013	+	0.705195i	$0.249141\pi$
$420$	2.25584	0.110074
$421$	17.7367	0.864436	0.432218	−	0.901769i	$-0.357731\pi$
$421$	17.7367	0.864436	0.432218	+	0.901769i	$0.357731\pi$
$422$	23.4130	1.13973
$423$	0.342939	0.0166743
$424$	9.95047	0.483238
$425$	−48.8257	−2.36839
$426$	−14.4149	−0.698402
$427$	−0.660128	−0.0319458
$428$	0.729573	0.0352652
$429$	−24.7014	−1.19259
$430$	−33.8107	−1.63050
$431$	−1.32217	−0.0636865	−0.0318433	−	0.999493i	$-0.510138\pi$
$431$	−1.32217	−0.0636865	−0.0318433	+	0.999493i	$0.510138\pi$
$432$	5.31031	0.255492
$433$	−23.7185	−1.13984	−0.569920	−	0.821700i	$-0.693026\pi$
$433$	−23.7185	−1.13984	−0.569920	+	0.821700i	$0.693026\pi$
$434$	−4.11658	−0.197602
$435$	6.38961	0.306358
$436$	−17.2040	−0.823924
$437$	−7.38263	−0.353159
$438$	−3.41350	−0.163103
$439$	−9.55440	−0.456007	−0.228003	−	0.973660i	$-0.573220\pi$
$439$	−9.55440	−0.456007	−0.228003	+	0.973660i	$0.573220\pi$
$440$	−9.97175	−0.475384
$441$	0.958510	0.0456434
$442$	−38.6449	−1.83815
$443$	−37.7969	−1.79579	−0.897893	−	0.440214i	$-0.854902\pi$
$443$	−37.7969	−1.79579	−0.897893	+	0.440214i	$0.854902\pi$
$444$	14.5730	0.691603
$445$	38.8429	1.84133
$446$	4.93290	0.233580
$447$	−28.4011	−1.34333
$448$	0.398747	0.0188390
$449$	−18.8766	−0.890841	−0.445420	−	0.895322i	$-0.646946\pi$
$449$	−18.8766	−0.890841	−0.445420	+	0.895322i	$0.646946\pi$
$450$	−0.867451	−0.0408920
$451$	−20.3104	−0.956380
$452$	10.6507	0.500966
$453$	−28.1885	−1.32441
$454$	10.5215	0.493797
$455$	−6.53651	−0.306437
$456$	−12.4849	−0.584660
$457$	1.67639	0.0784182	0.0392091	−	0.999231i	$-0.487516\pi$
$457$	1.67639	0.0784182	0.0392091	+	0.999231i	$0.487516\pi$
$458$	17.1728	0.802432
$459$	−41.8794	−1.95476
$460$	3.34531	0.155976
$461$	20.9332	0.974958	0.487479	−	0.873135i	$-0.337917\pi$
$461$	20.9332	0.974958	0.487479	+	0.873135i	$0.337917\pi$
$462$	−2.01005	−0.0935160
$463$	17.8898	0.831411	0.415705	−	0.909499i	$-0.363535\pi$
$463$	17.8898	0.831411	0.415705	+	0.909499i	$0.363535\pi$
$464$	1.12944	0.0524330
$465$	−58.4050	−2.70847
$466$	−20.8477	−0.965749
$467$	−3.59838	−0.166513	−0.0832565	−	0.996528i	$-0.526532\pi$
$467$	−3.59838	−0.166513	−0.0832565	+	0.996528i	$0.526532\pi$
$468$	−0.686577	−0.0317371
$469$	−3.68207	−0.170022
$470$	8.18796	0.377683
$471$	−0.667624	−0.0307625
$472$	−2.60393	−0.119856
$473$	30.1268	1.38523
$474$	−10.3259	−0.474283
$475$	45.7066	2.09716
$476$	−3.14469	−0.144137
$477$	−1.39419	−0.0638354
$478$	4.42195	0.202255
$479$	−4.43104	−0.202460	−0.101230	−	0.994863i	$-0.532278\pi$
$479$	−4.43104	−0.202460	−0.101230	+	0.994863i	$0.532278\pi$
$480$	5.65732	0.258220
$481$	−42.2266	−1.92537
$482$	−3.25503	−0.148263
$483$	0.674329	0.0306830
$484$	−2.11475	−0.0961251
$485$	6.91333	0.313918
$486$	−1.45488	−0.0659948
$487$	4.11562	0.186497	0.0932483	−	0.995643i	$-0.470275\pi$
$487$	4.11562	0.186497	0.0932483	+	0.995643i	$0.470275\pi$
$488$	−1.65551	−0.0749412
$489$	−28.8283	−1.30366
$490$	22.8853	1.03385
$491$	−37.1681	−1.67737	−0.838687	−	0.544614i	$-0.816676\pi$
$491$	−37.1681	−1.67737	−0.838687	+	0.544614i	$0.816676\pi$
$492$	11.5228	0.519488
$493$	−8.90725	−0.401163
$494$	36.1762	1.62765
$495$	1.39717	0.0627980
$496$	−10.3238	−0.463552
$497$	3.39886	0.152460
$498$	−28.0174	−1.25549
$499$	−2.03818	−0.0912414	−0.0456207	−	0.998959i	$-0.514527\pi$
$499$	−2.03818	−0.0912414	−0.0456207	+	0.998959i	$0.514527\pi$
$500$	−3.98460	−0.178197
$501$	18.6064	0.831273
$502$	−27.6635	−1.23468
$503$	−18.6971	−0.833660	−0.416830	−	0.908984i	$-0.636859\pi$
$503$	−18.6971	−0.833660	−0.416830	+	0.908984i	$0.636859\pi$
$504$	−0.0558695	−0.00248863
$505$	−26.0150	−1.15765
$506$	−2.98081	−0.132513
$507$	−18.6223	−0.827044
$508$	14.7506	0.654452
$509$	−28.4027	−1.25893	−0.629464	−	0.777029i	$-0.716726\pi$
$509$	−28.4027	−1.25893	−0.629464	+	0.777029i	$0.716726\pi$
$510$	−44.6160	−1.97563
$511$	0.804865	0.0356051
$512$	1.00000	0.0441942
$513$	39.2040	1.73090
$514$	−12.3217	−0.543487
$515$	−23.6511	−1.04219
$516$	−17.0920	−0.752432
$517$	−7.29582	−0.320870
$518$	−3.43614	−0.150975
$519$	−24.0169	−1.05423
$520$	−16.3926	−0.718864
$521$	14.8649	0.651245	0.325622	−	0.945500i	$-0.394426\pi$
$521$	14.8649	0.651245	0.325622	+	0.945500i	$0.394426\pi$
$522$	−0.158249	−0.00692637
$523$	6.36608	0.278369	0.139185	−	0.990266i	$-0.455552\pi$
$523$	6.36608	0.278369	0.139185	+	0.990266i	$0.455552\pi$
$524$	−1.00000	−0.0436852
$525$	−4.17484	−0.182205
$526$	−12.0683	−0.526204
$527$	81.4179	3.54662
$528$	−5.04091	−0.219378
$529$	1.00000	0.0434783
$530$	−33.2874	−1.44591
$531$	0.364844	0.0158329
$532$	2.94380	0.127630
$533$	−33.3884	−1.44621
$534$	19.6359	0.849727
$535$	−2.44065	−0.105518
$536$	−9.23411	−0.398853
$537$	−22.7865	−0.983309
$538$	−13.4417	−0.579514
$539$	−20.3917	−0.878335
$540$	−17.7646	−0.764468
$541$	−3.96084	−0.170290	−0.0851449	−	0.996369i	$-0.527135\pi$
$541$	−3.96084	−0.170290	−0.0851449	+	0.996369i	$0.527135\pi$
$542$	20.0729	0.862204
$543$	10.2626	0.440412
$544$	−7.88643	−0.338128
$545$	57.5528	2.46529
$546$	−3.30434	−0.141413
$547$	32.9566	1.40912	0.704562	−	0.709643i	$-0.251144\pi$
$547$	32.9566	1.40912	0.704562	+	0.709643i	$0.251144\pi$
$548$	−9.49328	−0.405533
$549$	0.231957	0.00989969
$550$	18.4545	0.786903
$551$	8.33825	0.355221
$552$	1.69112	0.0719789
$553$	2.43473	0.103535
$554$	14.5074	0.616360
$555$	−48.7511	−2.06937
$556$	20.5900	0.873211
$557$	43.2090	1.83083	0.915413	−	0.402517i	$-0.131865\pi$
$557$	43.2090	1.83083	0.915413	+	0.402517i	$0.131865\pi$
$558$	1.44649	0.0612350
$559$	49.5256	2.09471
$560$	−1.33393	−0.0563689
$561$	39.7548	1.67845
$562$	30.0849	1.26906
$563$	−4.40745	−0.185752	−0.0928759	−	0.995678i	$-0.529606\pi$
$563$	−4.40745	−0.185752	−0.0928759	+	0.995678i	$0.529606\pi$
$564$	4.13918	0.174291
$565$	−35.6299	−1.49896
$566$	9.46204	0.397719
$567$	−3.41329	−0.143345
$568$	8.52385	0.357653
$569$	11.5451	0.483995	0.241997	−	0.970277i	$-0.422197\pi$
$569$	11.5451	0.483995	0.241997	+	0.970277i	$0.422197\pi$
$570$	41.7659	1.74938
$571$	31.0080	1.29764	0.648821	−	0.760941i	$-0.275262\pi$
$571$	31.0080	1.29764	0.648821	+	0.760941i	$0.275262\pi$
$572$	14.6065	0.610730
$573$	24.1348	1.00825
$574$	−2.71695	−0.113403
$575$	−6.19110	−0.258187
$576$	−0.140113	−0.00583803
$577$	−29.8033	−1.24073	−0.620363	−	0.784315i	$-0.713015\pi$
$577$	−29.8033	−1.24073	−0.620363	+	0.784315i	$0.713015\pi$
$578$	45.1957	1.87989
$579$	−29.8658	−1.24118
$580$	−3.77833	−0.156887
$581$	6.60619	0.274071
$582$	3.49483	0.144865
$583$	29.6605	1.22841
$584$	2.01849	0.0835255
$585$	2.29681	0.0949616
$586$	−1.13587	−0.0469224
$587$	5.38240	0.222155	0.111078	−	0.993812i	$-0.464570\pi$
$587$	5.38240	0.222155	0.111078	+	0.993812i	$0.464570\pi$
$588$	11.5690	0.477096
$589$	−76.2168	−3.14046
$590$	8.71096	0.358624
$591$	29.0208	1.19375
$592$	−8.61735	−0.354171
$593$	−13.0421	−0.535573	−0.267787	−	0.963478i	$-0.586292\pi$
$593$	−13.0421	−0.535573	−0.267787	+	0.963478i	$0.586292\pi$
$594$	15.8290	0.649473
$595$	10.5200	0.431276
$596$	16.7943	0.687921
$597$	−30.1617	−1.23444
$598$	−4.90018	−0.200383
$599$	8.65606	0.353677	0.176838	−	0.984240i	$-0.443413\pi$
$599$	8.65606	0.353677	0.176838	+	0.984240i	$0.443413\pi$
$600$	−10.4699	−0.427432
$601$	−44.7785	−1.82655	−0.913277	−	0.407338i	$-0.866457\pi$
$601$	−44.7785	−1.82655	−0.913277	+	0.407338i	$0.866457\pi$
$602$	4.03009	0.164254
$603$	1.29381	0.0526882
$604$	16.6685	0.678233
$605$	7.07450	0.287619
$606$	−13.1511	−0.534227
$607$	−39.1954	−1.59089	−0.795445	−	0.606025i	$-0.792763\pi$
$607$	−39.1954	−1.59089	−0.795445	+	0.606025i	$0.792763\pi$
$608$	7.38263	0.299405
$609$	−0.761615	−0.0308622
$610$	5.53818	0.224234
$611$	−11.9937	−0.485212
$612$	1.10499	0.0446665
$613$	25.1519	1.01588	0.507938	−	0.861394i	$-0.330408\pi$
$613$	25.1519	1.01588	0.507938	+	0.861394i	$0.330408\pi$
$614$	−6.32668	−0.255324
$615$	−38.5474	−1.55438
$616$	1.18859	0.0478897
$617$	−10.2581	−0.412976	−0.206488	−	0.978449i	$-0.566204\pi$
$617$	−10.2581	−0.412976	−0.206488	+	0.978449i	$0.566204\pi$
$618$	−11.9561	−0.480945
$619$	5.20382	0.209159	0.104579	−	0.994517i	$-0.466650\pi$
$619$	5.20382	0.209159	0.104579	+	0.994517i	$0.466650\pi$
$620$	34.5363	1.38701
$621$	−5.31031	−0.213095
$622$	−24.8883	−0.997931
$623$	−4.62991	−0.185494
$624$	−8.28680	−0.331737
$625$	−17.6258	−0.705031
$626$	−11.3813	−0.454888
$627$	−37.2152	−1.48623
$628$	0.394782	0.0157535
$629$	67.9601	2.70975
$630$	0.186901	0.00744631
$631$	27.7446	1.10449	0.552247	−	0.833680i	$-0.313771\pi$
$631$	27.7446	1.10449	0.552247	+	0.833680i	$0.313771\pi$
$632$	6.10594	0.242881
$633$	−39.5942	−1.57373
$634$	−29.5327	−1.17289
$635$	−49.3454	−1.95821
$636$	−16.8274	−0.667252
$637$	−33.5222	−1.32820
$638$	3.36665	0.133287
$639$	−1.19430	−0.0472457
$640$	−3.34531	−0.132235
$641$	44.7103	1.76595	0.882976	−	0.469419i	$-0.155537\pi$
$641$	44.7103	1.76595	0.882976	+	0.469419i	$0.155537\pi$
$642$	−1.23380	−0.0486940
$643$	6.49673	0.256206	0.128103	−	0.991761i	$-0.459111\pi$
$643$	6.49673	0.256206	0.128103	+	0.991761i	$0.459111\pi$
$644$	−0.398747	−0.0157128
$645$	57.1779	2.25138
$646$	−58.2226	−2.29074
$647$	11.2046	0.440497	0.220248	−	0.975444i	$-0.429313\pi$
$647$	11.2046	0.440497	0.220248	+	0.975444i	$0.429313\pi$
$648$	−8.56003	−0.336270
$649$	−7.76183	−0.304679
$650$	30.3375	1.18994
$651$	6.96164	0.272848
$652$	17.0469	0.667607
$653$	−39.9768	−1.56441	−0.782206	−	0.623020i	$-0.785906\pi$
$653$	−39.9768	−1.56441	−0.782206	+	0.623020i	$0.785906\pi$
$654$	29.0941	1.13767
$655$	3.34531	0.130712
$656$	−6.81371	−0.266031
$657$	−0.282815	−0.0110337
$658$	−0.975971	−0.0380473
$659$	5.61124	0.218583	0.109291	−	0.994010i	$-0.465142\pi$
$659$	5.61124	0.218583	0.109291	+	0.994010i	$0.465142\pi$
$660$	16.8634	0.656408
$661$	2.13770	0.0831469	0.0415734	−	0.999135i	$-0.486763\pi$
$661$	2.13770	0.0831469	0.0415734	+	0.999135i	$0.486763\pi$
$662$	−1.27736	−0.0496461
$663$	65.3532	2.53811
$664$	16.5674	0.642939
$665$	−9.84793	−0.381887
$666$	1.20740	0.0467858
$667$	−1.12944	−0.0437321
$668$	−11.0024	−0.425696
$669$	−8.34213	−0.322525
$670$	30.8910	1.19342
$671$	−4.93475	−0.190504
$672$	−0.674329	−0.0260128
$673$	−5.79650	−0.223439	−0.111719	−	0.993740i	$-0.535636\pi$
$673$	−5.79650	−0.223439	−0.111719	+	0.993740i	$0.535636\pi$
$674$	11.4394	0.440630
$675$	32.8767	1.26542
$676$	11.0118	0.423531
$677$	4.18229	0.160739	0.0803693	−	0.996765i	$-0.474390\pi$
$677$	4.18229	0.160739	0.0803693	+	0.996765i	$0.474390\pi$
$678$	−18.0116	−0.691731
$679$	−0.824041	−0.0316238
$680$	26.3825	1.01172
$681$	−17.7931	−0.681831
$682$	−30.7733	−1.17837
$683$	−43.6102	−1.66870	−0.834350	−	0.551236i	$-0.814157\pi$
$683$	−43.6102	−1.66870	−0.834350	+	0.551236i	$0.814157\pi$
$684$	−1.03440	−0.0395513
$685$	31.7580	1.21341
$686$	−5.51906	−0.210719
$687$	−29.0412	−1.10799
$688$	10.1069	0.385322
$689$	48.7591	1.85758
$690$	−5.65732	−0.215371
$691$	13.7094	0.521530	0.260765	−	0.965402i	$-0.416025\pi$
$691$	13.7094	0.521530	0.260765	+	0.965402i	$0.416025\pi$
$692$	14.2018	0.539870
$693$	−0.166537	−0.00632620
$694$	0.861282	0.0326938
$695$	−68.8800	−2.61277
$696$	−1.91002	−0.0723991
$697$	53.7358	2.03539
$698$	28.3641	1.07360
$699$	35.2559	1.33350
$700$	2.46868	0.0933075
$701$	30.4949	1.15178	0.575888	−	0.817529i	$-0.304657\pi$
$701$	30.4949	1.15178	0.575888	+	0.817529i	$0.304657\pi$
$702$	26.0215	0.982117
$703$	−63.6187	−2.39942
$704$	2.98081	0.112344
$705$	−13.8468	−0.521502
$706$	6.93270	0.260916
$707$	3.10088	0.116621
$708$	4.40356	0.165496
$709$	−9.70873	−0.364619	−0.182310	−	0.983241i	$-0.558357\pi$
$709$	−9.70873	−0.364619	−0.182310	+	0.983241i	$0.558357\pi$
$710$	−28.5149	−1.07015
$711$	−0.855519	−0.0320845
$712$	−11.6112	−0.435146
$713$	10.3238	0.386629
$714$	5.31805	0.199023
$715$	−48.8634	−1.82739
$716$	13.4742	0.503554
$717$	−7.47804	−0.279273
$718$	26.6306	0.993847
$719$	−39.2505	−1.46380	−0.731898	−	0.681414i	$-0.761365\pi$
$719$	−39.2505	−1.46380	−0.731898	+	0.681414i	$0.761365\pi$
$720$	0.468720	0.0174682
$721$	2.81911	0.104989
$722$	35.5032	1.32129
$723$	5.50465	0.204720
$724$	−6.06855	−0.225536
$725$	6.99248	0.259694
$726$	3.57630	0.132729
$727$	−34.1185	−1.26538	−0.632692	−	0.774403i	$-0.718050\pi$
$727$	−34.1185	−1.26538	−0.632692	+	0.774403i	$0.718050\pi$
$728$	1.95393	0.0724176
$729$	28.1405	1.04224
$730$	−6.75246	−0.249920
$731$	−79.7073	−2.94808
$732$	2.79966	0.103478
$733$	42.3763	1.56521	0.782603	−	0.622521i	$-0.213892\pi$
$733$	42.3763	1.56521	0.782603	+	0.622521i	$0.213892\pi$
$734$	15.4687	0.570960
$735$	−38.7017	−1.42754
$736$	−1.00000	−0.0368605
$737$	−27.5251	−1.01390
$738$	0.954687	0.0351425
$739$	22.3727	0.822992	0.411496	−	0.911412i	$-0.365006\pi$
$739$	22.3727	0.822992	0.411496	+	0.911412i	$0.365006\pi$
$740$	28.8277	1.05973
$741$	−61.1784	−2.24744
$742$	3.96772	0.145660
$743$	20.4205	0.749157	0.374578	−	0.927195i	$-0.377787\pi$
$743$	20.4205	0.749157	0.374578	+	0.927195i	$0.377787\pi$
$744$	17.4588	0.640070
$745$	−56.1821	−2.05835
$746$	−8.47870	−0.310427
$747$	−2.32130	−0.0849318
$748$	−23.5080	−0.859536
$749$	0.290915	0.0106298
$750$	6.73844	0.246053
$751$	−3.33252	−0.121605	−0.0608027	−	0.998150i	$-0.519366\pi$
$751$	−3.33252	−0.121605	−0.0608027	+	0.998150i	$0.519366\pi$
$752$	−2.44759	−0.0892546
$753$	46.7823	1.70484
$754$	5.53447	0.201553
$755$	−55.7614	−2.02937
$756$	2.11747	0.0770116
$757$	0.920065	0.0334403	0.0167202	−	0.999860i	$-0.494678\pi$
$757$	0.920065	0.0334403	0.0167202	+	0.999860i	$0.494678\pi$
$758$	18.9708	0.689049
$759$	5.04091	0.182974
$760$	−24.6972	−0.895861
$761$	25.0130	0.906721	0.453360	−	0.891327i	$-0.350225\pi$
$761$	25.0130	0.906721	0.453360	+	0.891327i	$0.350225\pi$
$762$	−24.9451	−0.903664
$763$	−6.86006	−0.248351
$764$	−14.2715	−0.516325
$765$	−3.69653	−0.133648
$766$	22.6777	0.819380
$767$	−12.7597	−0.460727
$768$	−1.69112	−0.0610230
$769$	18.5150	0.667668	0.333834	−	0.942632i	$-0.391658\pi$
$769$	18.5150	0.667668	0.333834	+	0.942632i	$0.391658\pi$
$770$	−3.97620	−0.143292
$771$	20.8375	0.750444
$772$	17.6604	0.635611
$773$	−25.6398	−0.922201	−0.461100	−	0.887348i	$-0.652545\pi$
$773$	−25.6398	−0.922201	−0.461100	+	0.887348i	$0.652545\pi$
$774$	−1.41610	−0.0509008
$775$	−63.9157	−2.29592
$776$	−2.06658	−0.0741857
$777$	5.81093	0.208466
$778$	35.5592	1.27486
$779$	−50.3031	−1.80230
$780$	27.7219	0.992604
$781$	25.4080	0.909170
$782$	7.88643	0.282018
$783$	5.99768	0.214340
$784$	−6.84100	−0.244321
$785$	−1.32067	−0.0471367
$786$	1.69112	0.0603203
$787$	−27.7398	−0.988816	−0.494408	−	0.869230i	$-0.664615\pi$
$787$	−27.7398	−0.988816	−0.494408	+	0.869230i	$0.664615\pi$
$788$	−17.1607	−0.611324
$789$	20.4090	0.726580
$790$	−20.4263	−0.726734
$791$	4.24693	0.151004
$792$	−0.417650	−0.0148405
$793$	−8.11228	−0.288076
$794$	23.0310	0.817340
$795$	56.2930	1.99651
$796$	17.8353	0.632156
$797$	11.3733	0.402864	0.201432	−	0.979502i	$-0.435440\pi$
$797$	11.3733	0.402864	0.201432	+	0.979502i	$0.435440\pi$
$798$	−4.97832	−0.176231
$799$	19.3028	0.682883
$800$	6.19110	0.218888
$801$	1.62687	0.0574826
$802$	10.3837	0.366662
$803$	6.01673	0.212326
$804$	15.6160	0.550733
$805$	1.33393	0.0470150
$806$	−50.5885	−1.78190
$807$	22.7316	0.800189
$808$	7.77656	0.273579
$809$	47.0000	1.65243	0.826216	−	0.563353i	$-0.190489\pi$
$809$	47.0000	1.65243	0.826216	+	0.563353i	$0.190489\pi$
$810$	28.6360	1.00617
$811$	−53.4041	−1.87527	−0.937637	−	0.347617i	$-0.886991\pi$
$811$	−53.4041	−1.87527	−0.937637	+	0.347617i	$0.886991\pi$
$812$	0.450361	0.0158046
$813$	−33.9457	−1.19053
$814$	−25.6867	−0.900319
$815$	−57.0271	−1.99757
$816$	13.3369	0.466885
$817$	74.6155	2.61046
$818$	−21.1070	−0.737990
$819$	−0.273771	−0.00956632
$820$	22.7940	0.796000
$821$	19.0881	0.666179	0.333089	−	0.942895i	$-0.391909\pi$
$821$	19.0881	0.666179	0.333089	+	0.942895i	$0.391909\pi$
$822$	16.0543	0.559957
$823$	15.8257	0.551649	0.275825	−	0.961208i	$-0.411049\pi$
$823$	15.8257	0.551649	0.275825	+	0.961208i	$0.411049\pi$
$824$	7.06993	0.246293
$825$	−31.2088	−1.08655
$826$	−1.03831	−0.0361274
$827$	−26.6832	−0.927867	−0.463934	−	0.885870i	$-0.653562\pi$
$827$	−26.6832	−0.927867	−0.463934	+	0.885870i	$0.653562\pi$
$828$	0.140113	0.00486925
$829$	−11.3382	−0.393791	−0.196896	−	0.980424i	$-0.563086\pi$
$829$	−11.3382	−0.393791	−0.196896	+	0.980424i	$0.563086\pi$
$830$	−55.4230	−1.92376
$831$	−24.5338	−0.851067
$832$	4.90018	0.169883
$833$	53.9510	1.86929
$834$	−34.8202	−1.20572
$835$	36.8065	1.27374
$836$	22.0062	0.761102
$837$	−54.8225	−1.89494
$838$	29.0263	1.00270
$839$	−14.9570	−0.516374	−0.258187	−	0.966095i	$-0.583125\pi$
$839$	−14.9570	−0.516374	−0.258187	+	0.966095i	$0.583125\pi$
$840$	2.25584	0.0778339
$841$	−27.7244	−0.956013
$842$	17.7367	0.611248
$843$	−50.8772	−1.75230
$844$	23.4130	0.805909
$845$	−36.8379	−1.26726
$846$	0.342939	0.0117905
$847$	−0.843251	−0.0289745
$848$	9.95047	0.341701
$849$	−16.0015	−0.549168
$850$	−48.8257	−1.67471
$851$	8.61735	0.295399
$852$	−14.4149	−0.493845
$853$	38.1773	1.30717	0.653583	−	0.756855i	$-0.273265\pi$
$853$	38.1773	1.30717	0.653583	+	0.756855i	$0.273265\pi$
$854$	−0.660128	−0.0225891
$855$	3.46039	0.118343
$856$	0.729573	0.0249363
$857$	5.48304	0.187297	0.0936486	−	0.995605i	$-0.470147\pi$
$857$	5.48304	0.187297	0.0936486	+	0.995605i	$0.470147\pi$
$858$	−24.7014	−0.843292
$859$	44.2340	1.50924	0.754622	−	0.656160i	$-0.227820\pi$
$859$	44.2340	1.50924	0.754622	+	0.656160i	$0.227820\pi$
$860$	−33.8107	−1.15293
$861$	4.59469	0.156586
$862$	−1.32217	−0.0450332
$863$	−15.6041	−0.531169	−0.265585	−	0.964088i	$-0.585565\pi$
$863$	−15.6041	−0.531169	−0.265585	+	0.964088i	$0.585565\pi$
$864$	5.31031	0.180660
$865$	−47.5093	−1.61537
$866$	−23.7185	−0.805989
$867$	−76.4314	−2.59575
$868$	−4.11658	−0.139726
$869$	18.2007	0.617415
$870$	6.38961	0.216628
$871$	−45.2488	−1.53320
$872$	−17.2040	−0.582602
$873$	0.289553	0.00979989
$874$	−7.38263	−0.249721
$875$	−1.58885	−0.0537129
$876$	−3.41350	−0.115332
$877$	30.3279	1.02410	0.512050	−	0.858956i	$-0.328886\pi$
$877$	30.3279	1.02410	0.512050	+	0.858956i	$0.328886\pi$
$878$	−9.55440	−0.322445
$879$	1.92090	0.0647902
$880$	−9.97175	−0.336147
$881$	45.0759	1.51865	0.759323	−	0.650714i	$-0.225530\pi$
$881$	45.0759	1.51865	0.759323	+	0.650714i	$0.225530\pi$
$882$	0.958510	0.0322747
$883$	−49.5202	−1.66649	−0.833244	−	0.552905i	$-0.813519\pi$
$883$	−49.5202	−1.66649	−0.833244	+	0.552905i	$0.813519\pi$
$884$	−38.6449	−1.29977
$885$	−14.7313	−0.495186
$886$	−37.7969	−1.26981
$887$	42.8414	1.43847	0.719237	−	0.694765i	$-0.244492\pi$
$887$	42.8414	1.43847	0.719237	+	0.694765i	$0.244492\pi$
$888$	14.5730	0.489037
$889$	5.88176	0.197268
$890$	38.8429	1.30202
$891$	−25.5159	−0.854813
$892$	4.93290	0.165166
$893$	−18.0697	−0.604679
$894$	−28.4011	−0.949876
$895$	−45.0753	−1.50670
$896$	0.398747	0.0133212
$897$	8.28680	0.276688
$898$	−18.8766	−0.629920
$899$	−11.6601	−0.388887
$900$	−0.867451	−0.0289150
$901$	−78.4737	−2.61434
$902$	−20.3104	−0.676262
$903$	−6.81537	−0.226801
$904$	10.6507	0.354237
$905$	20.3012	0.674834
$906$	−28.1885	−0.936500
$907$	−8.47602	−0.281442	−0.140721	−	0.990049i	$-0.544942\pi$
$907$	−8.47602	−0.281442	−0.140721	+	0.990049i	$0.544942\pi$
$908$	10.5215	0.349167
$909$	−1.08959	−0.0361396
$910$	−6.53651	−0.216683
$911$	20.5111	0.679562	0.339781	−	0.940505i	$-0.389647\pi$
$911$	20.5111	0.679562	0.339781	+	0.940505i	$0.389647\pi$
$912$	−12.4849	−0.413417
$913$	49.3842	1.63438
$914$	1.67639	0.0554500
$915$	−9.36573	−0.309621
$916$	17.1728	0.567405
$917$	−0.398747	−0.0131678
$918$	−41.8794	−1.38222
$919$	−22.8009	−0.752133	−0.376067	−	0.926593i	$-0.622724\pi$
$919$	−22.8009	−0.752133	−0.376067	+	0.926593i	$0.622724\pi$
$920$	3.34531	0.110292
$921$	10.6992	0.352550
$922$	20.9332	0.689399
$923$	41.7684	1.37482
$924$	−2.01005	−0.0661258
$925$	−53.3509	−1.75417
$926$	17.8898	0.587896
$927$	−0.990586	−0.0325351
$928$	1.12944	0.0370757
$929$	39.6390	1.30051	0.650256	−	0.759715i	$-0.274662\pi$
$929$	39.6390	1.30051	0.650256	+	0.759715i	$0.274662\pi$
$930$	−58.4050	−1.91518
$931$	−50.5046	−1.65522
$932$	−20.8477	−0.682888
$933$	42.0892	1.37794
$934$	−3.59838	−0.117743
$935$	78.6414	2.57185
$936$	−0.686577	−0.0224415
$937$	−22.2069	−0.725469	−0.362734	−	0.931893i	$-0.618157\pi$
$937$	−22.2069	−0.725469	−0.362734	+	0.931893i	$0.618157\pi$
$938$	−3.68207	−0.120224
$939$	19.2471	0.628106
$940$	8.18796	0.267062
$941$	−0.872461	−0.0284414	−0.0142207	−	0.999899i	$-0.504527\pi$
$941$	−0.872461	−0.0284414	−0.0142207	+	0.999899i	$0.504527\pi$
$942$	−0.667624	−0.0217524
$943$	6.81371	0.221885
$944$	−2.60393	−0.0847507
$945$	−7.08359	−0.230429
$946$	30.1268	0.979505
$947$	12.1635	0.395260	0.197630	−	0.980277i	$-0.436676\pi$
$947$	12.1635	0.395260	0.197630	+	0.980277i	$0.436676\pi$
$948$	−10.3259	−0.335369
$949$	9.89095	0.321074
$950$	45.7066	1.48292
$951$	49.9434	1.61953
$952$	−3.14469	−0.101920
$953$	−55.3131	−1.79177	−0.895883	−	0.444290i	$-0.853456\pi$
$953$	−55.3131	−1.79177	−0.895883	+	0.444290i	$0.853456\pi$
$954$	−1.39419	−0.0451385
$955$	47.7426	1.54492
$956$	4.42195	0.143016
$957$	−5.69342	−0.184042
$958$	−4.43104	−0.143161
$959$	−3.78542	−0.122238
$960$	5.65732	0.182589
$961$	75.5808	2.43809
$962$	−42.2266	−1.36144
$963$	−0.102222	−0.00329407
$964$	−3.25503	−0.104838
$965$	−59.0794	−1.90183
$966$	0.674329	0.0216962
$967$	29.2712	0.941297	0.470648	−	0.882321i	$-0.344020\pi$
$967$	29.2712	0.941297	0.470648	+	0.882321i	$0.344020\pi$
$968$	−2.11475	−0.0679707
$969$	98.4614	3.16304
$970$	6.91333	0.221974
$971$	45.8636	1.47183	0.735916	−	0.677073i	$-0.236752\pi$
$971$	45.8636	1.47183	0.735916	+	0.677073i	$0.236752\pi$
$972$	−1.45488	−0.0466654
$973$	8.21021	0.263207
$974$	4.11562	0.131873
$975$	−51.3044	−1.64306
$976$	−1.65551	−0.0529914
$977$	−16.2676	−0.520447	−0.260224	−	0.965548i	$-0.583796\pi$
$977$	−16.2676	−0.520447	−0.260224	+	0.965548i	$0.583796\pi$
$978$	−28.8283	−0.921828
$979$	−34.6107	−1.10616
$980$	22.8853	0.731043
$981$	2.41050	0.0769614
$982$	−37.1681	−1.18608
$983$	−30.9398	−0.986827	−0.493414	−	0.869795i	$-0.664251\pi$
$983$	−30.9398	−0.986827	−0.493414	+	0.869795i	$0.664251\pi$
$984$	11.5228	0.367334
$985$	57.4078	1.82916
$986$	−8.90725	−0.283665
$987$	1.65048	0.0525355
$988$	36.1762	1.15092
$989$	−10.1069	−0.321380
$990$	1.39717	0.0444049
$991$	27.6883	0.879549	0.439775	−	0.898108i	$-0.355058\pi$
$991$	27.6883	0.879549	0.439775	+	0.898108i	$0.355058\pi$
$992$	−10.3238	−0.327781
$993$	2.16017	0.0685511
$994$	3.39886	0.107805
$995$	−59.6647	−1.89150
$996$	−28.0174	−0.887766
$997$	31.1672	0.987076	0.493538	−	0.869724i	$-0.335703\pi$
$997$	31.1672	0.987076	0.493538	+	0.869724i	$0.335703\pi$
$998$	−2.03818	−0.0645174
$999$	−45.7608	−1.44781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.11	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.11	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.69112 q^{3} +1.00000 q^{4} -3.34531 q^{5} -1.69112 q^{6} +0.398747 q^{7} +1.00000 q^{8} -0.140113 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.69112 q^{3} +1.00000 q^{4} -3.34531 q^{5} -1.69112 q^{6} +0.398747 q^{7} +1.00000 q^{8} -0.140113 q^{9} -3.34531 q^{10} +2.98081 q^{11} -1.69112 q^{12} +4.90018 q^{13} +0.398747 q^{14} +5.65732 q^{15} +1.00000 q^{16} -7.88643 q^{17} -0.140113 q^{18} +7.38263 q^{19} -3.34531 q^{20} -0.674329 q^{21} +2.98081 q^{22} -1.00000 q^{23} -1.69112 q^{24} +6.19110 q^{25} +4.90018 q^{26} +5.31031 q^{27} +0.398747 q^{28} +1.12944 q^{29} +5.65732 q^{30} -10.3238 q^{31} +1.00000 q^{32} -5.04091 q^{33} -7.88643 q^{34} -1.33393 q^{35} -0.140113 q^{36} -8.61735 q^{37} +7.38263 q^{38} -8.28680 q^{39} -3.34531 q^{40} -6.81371 q^{41} -0.674329 q^{42} +10.1069 q^{43} +2.98081 q^{44} +0.468720 q^{45} -1.00000 q^{46} -2.44759 q^{47} -1.69112 q^{48} -6.84100 q^{49} +6.19110 q^{50} +13.3369 q^{51} +4.90018 q^{52} +9.95047 q^{53} +5.31031 q^{54} -9.97175 q^{55} +0.398747 q^{56} -12.4849 q^{57} +1.12944 q^{58} -2.60393 q^{59} +5.65732 q^{60} -1.65551 q^{61} -10.3238 q^{62} -0.0558695 q^{63} +1.00000 q^{64} -16.3926 q^{65} -5.04091 q^{66} -9.23411 q^{67} -7.88643 q^{68} +1.69112 q^{69} -1.33393 q^{70} +8.52385 q^{71} -0.140113 q^{72} +2.01849 q^{73} -8.61735 q^{74} -10.4699 q^{75} +7.38263 q^{76} +1.18859 q^{77} -8.28680 q^{78} +6.10594 q^{79} -3.34531 q^{80} -8.56003 q^{81} -6.81371 q^{82} +16.5674 q^{83} -0.674329 q^{84} +26.3825 q^{85} +10.1069 q^{86} -1.91002 q^{87} +2.98081 q^{88} -11.6112 q^{89} +0.468720 q^{90} +1.95393 q^{91} -1.00000 q^{92} +17.4588 q^{93} -2.44759 q^{94} -24.6972 q^{95} -1.69112 q^{96} -2.06658 q^{97} -6.84100 q^{98} -0.417650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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