LMFDB - Embedded newform 4334.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.614404 q^{3} +1.00000 q^{4} +2.62767 q^{5} -0.614404 q^{6} -2.77855 q^{7} +1.00000 q^{8} -2.62251 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.614404 q^{3} +1.00000 q^{4} +2.62767 q^{5} -0.614404 q^{6} -2.77855 q^{7} +1.00000 q^{8} -2.62251 q^{9} +2.62767 q^{10} +1.00000 q^{11} -0.614404 q^{12} -0.846497 q^{13} -2.77855 q^{14} -1.61445 q^{15} +1.00000 q^{16} +1.92541 q^{17} -2.62251 q^{18} -2.31790 q^{19} +2.62767 q^{20} +1.70715 q^{21} +1.00000 q^{22} +8.38848 q^{23} -0.614404 q^{24} +1.90465 q^{25} -0.846497 q^{26} +3.45449 q^{27} -2.77855 q^{28} -4.26515 q^{29} -1.61445 q^{30} +5.79622 q^{31} +1.00000 q^{32} -0.614404 q^{33} +1.92541 q^{34} -7.30111 q^{35} -2.62251 q^{36} +6.76334 q^{37} -2.31790 q^{38} +0.520091 q^{39} +2.62767 q^{40} -1.47998 q^{41} +1.70715 q^{42} -0.213650 q^{43} +1.00000 q^{44} -6.89108 q^{45} +8.38848 q^{46} +3.39698 q^{47} -0.614404 q^{48} +0.720332 q^{49} +1.90465 q^{50} -1.18298 q^{51} -0.846497 q^{52} +5.38730 q^{53} +3.45449 q^{54} +2.62767 q^{55} -2.77855 q^{56} +1.42413 q^{57} -4.26515 q^{58} -0.740266 q^{59} -1.61445 q^{60} +10.2166 q^{61} +5.79622 q^{62} +7.28676 q^{63} +1.00000 q^{64} -2.22431 q^{65} -0.614404 q^{66} +2.32060 q^{67} +1.92541 q^{68} -5.15392 q^{69} -7.30111 q^{70} +10.5738 q^{71} -2.62251 q^{72} -3.71486 q^{73} +6.76334 q^{74} -1.17023 q^{75} -2.31790 q^{76} -2.77855 q^{77} +0.520091 q^{78} -2.62028 q^{79} +2.62767 q^{80} +5.74507 q^{81} -1.47998 q^{82} +9.53327 q^{83} +1.70715 q^{84} +5.05933 q^{85} -0.213650 q^{86} +2.62053 q^{87} +1.00000 q^{88} +10.3091 q^{89} -6.89108 q^{90} +2.35203 q^{91} +8.38848 q^{92} -3.56122 q^{93} +3.39698 q^{94} -6.09068 q^{95} -0.614404 q^{96} +5.94742 q^{97} +0.720332 q^{98} -2.62251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	−0.614404	−0.354727	−0.177363	−	0.984145i	$-0.556757\pi$
$3$	−0.614404	−0.354727	−0.177363	+	0.984145i	$0.556757\pi$
$4$	1.00000	0.500000
$5$	2.62767	1.17513	0.587565	−	0.809177i	$-0.300087\pi$
$5$	2.62767	1.17513	0.587565	+	0.809177i	$0.300087\pi$
$6$	−0.614404	−0.250830
$7$	−2.77855	−1.05019	−0.525096	−	0.851043i	$-0.675971\pi$
$7$	−2.77855	−1.05019	−0.525096	+	0.851043i	$0.675971\pi$
$8$	1.00000	0.353553
$9$	−2.62251	−0.874169
$10$	2.62767	0.830942
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.614404	−0.177363
$13$	−0.846497	−0.234776	−0.117388	−	0.993086i	$-0.537452\pi$
$13$	−0.846497	−0.234776	−0.117388	+	0.993086i	$0.537452\pi$
$14$	−2.77855	−0.742598
$15$	−1.61445	−0.416850
$16$	1.00000	0.250000
$17$	1.92541	0.466980	0.233490	−	0.972359i	$-0.424985\pi$
$17$	1.92541	0.466980	0.233490	+	0.972359i	$0.424985\pi$
$18$	−2.62251	−0.618131
$19$	−2.31790	−0.531763	−0.265882	−	0.964006i	$-0.585663\pi$
$19$	−2.31790	−0.531763	−0.265882	+	0.964006i	$0.585663\pi$
$20$	2.62767	0.587565
$21$	1.70715	0.372531
$22$	1.00000	0.213201
$23$	8.38848	1.74912	0.874559	−	0.484919i	$-0.161151\pi$
$23$	8.38848	1.74912	0.874559	+	0.484919i	$0.161151\pi$
$24$	−0.614404	−0.125415
$25$	1.90465	0.380930
$26$	−0.846497	−0.166012
$27$	3.45449	0.664818
$28$	−2.77855	−0.525096
$29$	−4.26515	−0.792018	−0.396009	−	0.918247i	$-0.629605\pi$
$29$	−4.26515	−0.792018	−0.396009	+	0.918247i	$0.629605\pi$
$30$	−1.61445	−0.294757
$31$	5.79622	1.04103	0.520516	−	0.853852i	$-0.325740\pi$
$31$	5.79622	1.04103	0.520516	+	0.853852i	$0.325740\pi$
$32$	1.00000	0.176777
$33$	−0.614404	−0.106954
$34$	1.92541	0.330204
$35$	−7.30111	−1.23411
$36$	−2.62251	−0.437085
$37$	6.76334	1.11189	0.555944	−	0.831220i	$-0.312357\pi$
$37$	6.76334	1.11189	0.555944	+	0.831220i	$0.312357\pi$
$38$	−2.31790	−0.376013
$39$	0.520091	0.0832813
$40$	2.62767	0.415471
$41$	−1.47998	−0.231134	−0.115567	−	0.993300i	$-0.536869\pi$
$41$	−1.47998	−0.231134	−0.115567	+	0.993300i	$0.536869\pi$
$42$	1.70715	0.263419
$43$	−0.213650	−0.0325813	−0.0162906	−	0.999867i	$-0.505186\pi$
$43$	−0.213650	−0.0325813	−0.0162906	+	0.999867i	$0.505186\pi$
$44$	1.00000	0.150756
$45$	−6.89108	−1.02726
$46$	8.38848	1.23681
$47$	3.39698	0.495501	0.247750	−	0.968824i	$-0.420309\pi$
$47$	3.39698	0.495501	0.247750	+	0.968824i	$0.420309\pi$
$48$	−0.614404	−0.0886816
$49$	0.720332	0.102905
$50$	1.90465	0.269358
$51$	−1.18298	−0.165650
$52$	−0.846497	−0.117388
$53$	5.38730	0.740003	0.370002	−	0.929031i	$-0.379357\pi$
$53$	5.38730	0.740003	0.370002	+	0.929031i	$0.379357\pi$
$54$	3.45449	0.470097
$55$	2.62767	0.354315
$56$	−2.77855	−0.371299
$57$	1.42413	0.188631
$58$	−4.26515	−0.560041
$59$	−0.740266	−0.0963744	−0.0481872	−	0.998838i	$-0.515344\pi$
$59$	−0.740266	−0.0963744	−0.0481872	+	0.998838i	$0.515344\pi$
$60$	−1.61445	−0.208425
$61$	10.2166	1.30810	0.654051	−	0.756450i	$-0.273068\pi$
$61$	10.2166	1.30810	0.654051	+	0.756450i	$0.273068\pi$
$62$	5.79622	0.736120
$63$	7.28676	0.918046
$64$	1.00000	0.125000
$65$	−2.22431	−0.275892
$66$	−0.614404	−0.0756280
$67$	2.32060	0.283506	0.141753	−	0.989902i	$-0.454726\pi$
$67$	2.32060	0.283506	0.141753	+	0.989902i	$0.454726\pi$
$68$	1.92541	0.233490
$69$	−5.15392	−0.620459
$70$	−7.30111	−0.872650
$71$	10.5738	1.25488	0.627442	−	0.778664i	$-0.284102\pi$
$71$	10.5738	1.25488	0.627442	+	0.778664i	$0.284102\pi$
$72$	−2.62251	−0.309065
$73$	−3.71486	−0.434791	−0.217396	−	0.976084i	$-0.569756\pi$
$73$	−3.71486	−0.434791	−0.217396	+	0.976084i	$0.569756\pi$
$74$	6.76334	0.786223
$75$	−1.17023	−0.135126
$76$	−2.31790	−0.265882
$77$	−2.77855	−0.316645
$78$	0.520091	0.0588887
$79$	−2.62028	−0.294805	−0.147402	−	0.989077i	$-0.547091\pi$
$79$	−2.62028	−0.294805	−0.147402	+	0.989077i	$0.547091\pi$
$80$	2.62767	0.293782
$81$	5.74507	0.638341
$82$	−1.47998	−0.163437
$83$	9.53327	1.04641	0.523206	−	0.852206i	$-0.324736\pi$
$83$	9.53327	1.04641	0.523206	+	0.852206i	$0.324736\pi$
$84$	1.70715	0.186266
$85$	5.05933	0.548762
$86$	−0.213650	−0.0230385
$87$	2.62053	0.280950
$88$	1.00000	0.106600
$89$	10.3091	1.09276	0.546382	−	0.837536i	$-0.316005\pi$
$89$	10.3091	1.09276	0.546382	+	0.837536i	$0.316005\pi$
$90$	−6.89108	−0.726384
$91$	2.35203	0.246560
$92$	8.38848	0.874559
$93$	−3.56122	−0.369281
$94$	3.39698	0.350372
$95$	−6.09068	−0.624891
$96$	−0.614404	−0.0627074
$97$	5.94742	0.603869	0.301934	−	0.953329i	$-0.402368\pi$
$97$	5.94742	0.603869	0.301934	+	0.953329i	$0.402368\pi$
$98$	0.720332	0.0727646
$99$	−2.62251	−0.263572
$100$	1.90465	0.190465
$101$	1.05910	0.105385	0.0526924	−	0.998611i	$-0.483220\pi$
$101$	1.05910	0.105385	0.0526924	+	0.998611i	$0.483220\pi$
$102$	−1.18298	−0.117132
$103$	−5.38912	−0.531006	−0.265503	−	0.964110i	$-0.585538\pi$
$103$	−5.38912	−0.531006	−0.265503	+	0.964110i	$0.585538\pi$
$104$	−0.846497	−0.0830058
$105$	4.48583	0.437773
$106$	5.38730	0.523261
$107$	4.04065	0.390625	0.195312	−	0.980741i	$-0.437428\pi$
$107$	4.04065	0.390625	0.195312	+	0.980741i	$0.437428\pi$
$108$	3.45449	0.332409
$109$	9.26109	0.887051	0.443526	−	0.896262i	$-0.353728\pi$
$109$	9.26109	0.887051	0.443526	+	0.896262i	$0.353728\pi$
$110$	2.62767	0.250539
$111$	−4.15543	−0.394416
$112$	−2.77855	−0.262548
$113$	−2.02007	−0.190032	−0.0950160	−	0.995476i	$-0.530290\pi$
$113$	−2.02007	−0.190032	−0.0950160	+	0.995476i	$0.530290\pi$
$114$	1.42413	0.133382
$115$	22.0421	2.05544
$116$	−4.26515	−0.396009
$117$	2.21994	0.205234
$118$	−0.740266	−0.0681470
$119$	−5.34983	−0.490418
$120$	−1.61445	−0.147379
$121$	1.00000	0.0909091
$122$	10.2166	0.924968
$123$	0.909307	0.0819894
$124$	5.79622	0.520516
$125$	−8.13355	−0.727487
$126$	7.28676	0.649157
$127$	−17.6186	−1.56340	−0.781698	−	0.623657i	$-0.785646\pi$
$127$	−17.6186	−1.56340	−0.781698	+	0.623657i	$0.785646\pi$
$128$	1.00000	0.0883883
$129$	0.131267	0.0115575
$130$	−2.22431	−0.195085
$131$	21.3290	1.86353	0.931763	−	0.363068i	$-0.118271\pi$
$131$	21.3290	1.86353	0.931763	+	0.363068i	$0.118271\pi$
$132$	−0.614404	−0.0534770
$133$	6.44040	0.558454
$134$	2.32060	0.200469
$135$	9.07727	0.781247
$136$	1.92541	0.165102
$137$	16.0262	1.36921	0.684606	−	0.728914i	$-0.259974\pi$
$137$	16.0262	1.36921	0.684606	+	0.728914i	$0.259974\pi$
$138$	−5.15392	−0.438731
$139$	−14.6432	−1.24202	−0.621008	−	0.783804i	$-0.713277\pi$
$139$	−14.6432	−1.24202	−0.621008	+	0.783804i	$0.713277\pi$
$140$	−7.30111	−0.617056
$141$	−2.08712	−0.175767
$142$	10.5738	0.887337
$143$	−0.846497	−0.0707876
$144$	−2.62251	−0.218542
$145$	−11.2074	−0.930724
$146$	−3.71486	−0.307444
$147$	−0.442575	−0.0365030
$148$	6.76334	0.555944
$149$	−16.2370	−1.33019	−0.665094	−	0.746760i	$-0.731608\pi$
$149$	−16.2370	−1.33019	−0.665094	+	0.746760i	$0.731608\pi$
$150$	−1.17023	−0.0955486
$151$	−13.1879	−1.07321	−0.536607	−	0.843832i	$-0.680294\pi$
$151$	−13.1879	−1.07321	−0.536607	+	0.843832i	$0.680294\pi$
$152$	−2.31790	−0.188007
$153$	−5.04939	−0.408219
$154$	−2.77855	−0.223902
$155$	15.2305	1.22335
$156$	0.520091	0.0416406
$157$	−5.52568	−0.440997	−0.220499	−	0.975387i	$-0.570768\pi$
$157$	−5.52568	−0.440997	−0.220499	+	0.975387i	$0.570768\pi$
$158$	−2.62028	−0.208458
$159$	−3.30998	−0.262499
$160$	2.62767	0.207736
$161$	−23.3078	−1.83691
$162$	5.74507	0.451375
$163$	13.9287	1.09098	0.545490	−	0.838117i	$-0.316343\pi$
$163$	13.9287	1.09098	0.545490	+	0.838117i	$0.316343\pi$
$164$	−1.47998	−0.115567
$165$	−1.61445	−0.125685
$166$	9.53327	0.739925
$167$	13.7010	1.06022	0.530108	−	0.847930i	$-0.322151\pi$
$167$	13.7010	1.06022	0.530108	+	0.847930i	$0.322151\pi$
$168$	1.70715	0.131710
$169$	−12.2834	−0.944880
$170$	5.05933	0.388033
$171$	6.07871	0.464851
$172$	−0.213650	−0.0162906
$173$	−20.7113	−1.57465	−0.787324	−	0.616539i	$-0.788534\pi$
$173$	−20.7113	−1.57465	−0.787324	+	0.616539i	$0.788534\pi$
$174$	2.62053	0.198662
$175$	−5.29217	−0.400050
$176$	1.00000	0.0753778
$177$	0.454823	0.0341866
$178$	10.3091	0.772701
$179$	10.5316	0.787170	0.393585	−	0.919288i	$-0.371235\pi$
$179$	10.5316	0.787170	0.393585	+	0.919288i	$0.371235\pi$
$180$	−6.89108	−0.513631
$181$	3.53657	0.262871	0.131436	−	0.991325i	$-0.458041\pi$
$181$	3.53657	0.262871	0.131436	+	0.991325i	$0.458041\pi$
$182$	2.35203	0.174344
$183$	−6.27713	−0.464019
$184$	8.38848	0.618407
$185$	17.7718	1.30661
$186$	−3.56122	−0.261121
$187$	1.92541	0.140800
$188$	3.39698	0.247750
$189$	−9.59848	−0.698187
$190$	−6.09068	−0.441865
$191$	−5.17249	−0.374269	−0.187134	−	0.982334i	$-0.559920\pi$
$191$	−5.17249	−0.374269	−0.187134	+	0.982334i	$0.559920\pi$
$192$	−0.614404	−0.0443408
$193$	−23.3212	−1.67870	−0.839349	−	0.543593i	$-0.817064\pi$
$193$	−23.3212	−1.67870	−0.839349	+	0.543593i	$0.817064\pi$
$194$	5.94742	0.427000
$195$	1.36663	0.0978663
$196$	0.720332	0.0514523
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−2.62251	−0.186373
$199$	−6.94661	−0.492432	−0.246216	−	0.969215i	$-0.579187\pi$
$199$	−6.94661	−0.492432	−0.246216	+	0.969215i	$0.579187\pi$
$200$	1.90465	0.134679
$201$	−1.42579	−0.100567
$202$	1.05910	0.0745183
$203$	11.8509	0.831772
$204$	−1.18298	−0.0828250
$205$	−3.88890	−0.271613
$206$	−5.38912	−0.375478
$207$	−21.9988	−1.52902
$208$	−0.846497	−0.0586940
$209$	−2.31790	−0.160333
$210$	4.48583	0.309552
$211$	8.19484	0.564156	0.282078	−	0.959391i	$-0.408976\pi$
$211$	8.19484	0.564156	0.282078	+	0.959391i	$0.408976\pi$
$212$	5.38730	0.370002
$213$	−6.49661	−0.445140
$214$	4.04065	0.276213
$215$	−0.561401	−0.0382873
$216$	3.45449	0.235048
$217$	−16.1051	−1.09328
$218$	9.26109	0.627240
$219$	2.28242	0.154232
$220$	2.62767	0.177158
$221$	−1.62985	−0.109636
$222$	−4.15543	−0.278894
$223$	−12.5617	−0.841195	−0.420598	−	0.907247i	$-0.638180\pi$
$223$	−12.5617	−0.841195	−0.420598	+	0.907247i	$0.638180\pi$
$224$	−2.77855	−0.185650
$225$	−4.99496	−0.332998
$226$	−2.02007	−0.134373
$227$	15.2928	1.01502	0.507511	−	0.861646i	$-0.330566\pi$
$227$	15.2928	1.01502	0.507511	+	0.861646i	$0.330566\pi$
$228$	1.42413	0.0943153
$229$	−11.7631	−0.777325	−0.388662	−	0.921380i	$-0.627063\pi$
$229$	−11.7631	−0.777325	−0.388662	+	0.921380i	$0.627063\pi$
$230$	22.0421	1.45342
$231$	1.70715	0.112322
$232$	−4.26515	−0.280021
$233$	2.46526	0.161504	0.0807522	−	0.996734i	$-0.474268\pi$
$233$	2.46526	0.161504	0.0807522	+	0.996734i	$0.474268\pi$
$234$	2.21994	0.145122
$235$	8.92615	0.582278
$236$	−0.740266	−0.0481872
$237$	1.60991	0.104575
$238$	−5.34983	−0.346778
$239$	26.2625	1.69878	0.849389	−	0.527768i	$-0.176971\pi$
$239$	26.2625	1.69878	0.849389	+	0.527768i	$0.176971\pi$
$240$	−1.61445	−0.104212
$241$	8.37771	0.539656	0.269828	−	0.962909i	$-0.413033\pi$
$241$	8.37771	0.539656	0.269828	+	0.962909i	$0.413033\pi$
$242$	1.00000	0.0642824
$243$	−13.8933	−0.891254
$244$	10.2166	0.654051
$245$	1.89280	0.120926
$246$	0.909307	0.0579753
$247$	1.96210	0.124845
$248$	5.79622	0.368060
$249$	−5.85728	−0.371190
$250$	−8.13355	−0.514411
$251$	10.3519	0.653407	0.326703	−	0.945127i	$-0.394062\pi$
$251$	10.3519	0.653407	0.326703	+	0.945127i	$0.394062\pi$
$252$	7.28676	0.459023
$253$	8.38848	0.527379
$254$	−17.6186	−1.10549
$255$	−3.10848	−0.194660
$256$	1.00000	0.0625000
$257$	12.4238	0.774972	0.387486	−	0.921875i	$-0.373343\pi$
$257$	12.4238	0.774972	0.387486	+	0.921875i	$0.373343\pi$
$258$	0.131267	0.00817235
$259$	−18.7923	−1.16770
$260$	−2.22431	−0.137946
$261$	11.1854	0.692358
$262$	21.3290	1.31771
$263$	20.0342	1.23536	0.617682	−	0.786428i	$-0.288072\pi$
$263$	20.0342	1.23536	0.617682	+	0.786428i	$0.288072\pi$
$264$	−0.614404	−0.0378140
$265$	14.1561	0.869600
$266$	6.44040	0.394886
$267$	−6.33397	−0.387632
$268$	2.32060	0.141753
$269$	2.29186	0.139737	0.0698687	−	0.997556i	$-0.477742\pi$
$269$	2.29186	0.139737	0.0698687	+	0.997556i	$0.477742\pi$
$270$	9.07727	0.552425
$271$	−11.6859	−0.709865	−0.354933	−	0.934892i	$-0.615496\pi$
$271$	−11.6859	−0.709865	−0.354933	+	0.934892i	$0.615496\pi$
$272$	1.92541	0.116745
$273$	−1.44510	−0.0874614
$274$	16.0262	0.968179
$275$	1.90465	0.114855
$276$	−5.15392	−0.310229
$277$	−10.0225	−0.602193	−0.301096	−	0.953594i	$-0.597353\pi$
$277$	−10.0225	−0.602193	−0.301096	+	0.953594i	$0.597353\pi$
$278$	−14.6432	−0.878238
$279$	−15.2006	−0.910037
$280$	−7.30111	−0.436325
$281$	−3.88966	−0.232038	−0.116019	−	0.993247i	$-0.537013\pi$
$281$	−3.88966	−0.232038	−0.116019	+	0.993247i	$0.537013\pi$
$282$	−2.08712	−0.124286
$283$	22.8380	1.35758	0.678790	−	0.734332i	$-0.262505\pi$
$283$	22.8380	1.35758	0.678790	+	0.734332i	$0.262505\pi$
$284$	10.5738	0.627442
$285$	3.74214	0.221665
$286$	−0.846497	−0.0500544
$287$	4.11220	0.242735
$288$	−2.62251	−0.154533
$289$	−13.2928	−0.781930
$290$	−11.2074	−0.658121
$291$	−3.65412	−0.214208
$292$	−3.71486	−0.217396
$293$	−11.5401	−0.674180	−0.337090	−	0.941472i	$-0.609443\pi$
$293$	−11.5401	−0.674180	−0.337090	+	0.941472i	$0.609443\pi$
$294$	−0.442575	−0.0258115
$295$	−1.94517	−0.113252
$296$	6.76334	0.393111
$297$	3.45449	0.200450
$298$	−16.2370	−0.940585
$299$	−7.10082	−0.410651
$300$	−1.17023	−0.0675631
$301$	0.593636	0.0342166
$302$	−13.1879	−0.758877
$303$	−0.650718	−0.0373828
$304$	−2.31790	−0.132941
$305$	26.8459	1.53719
$306$	−5.04939	−0.288654
$307$	0.802154	0.0457813	0.0228907	−	0.999738i	$-0.492713\pi$
$307$	0.802154	0.0457813	0.0228907	+	0.999738i	$0.492713\pi$
$308$	−2.77855	−0.158323
$309$	3.31110	0.188362
$310$	15.2305	0.865037
$311$	0.295618	0.0167630	0.00838149	−	0.999965i	$-0.497332\pi$
$311$	0.295618	0.0167630	0.00838149	+	0.999965i	$0.497332\pi$
$312$	0.520091	0.0294444
$313$	6.32460	0.357488	0.178744	−	0.983896i	$-0.442797\pi$
$313$	6.32460	0.357488	0.178744	+	0.983896i	$0.442797\pi$
$314$	−5.52568	−0.311832
$315$	19.1472	1.07882
$316$	−2.62028	−0.147402
$317$	26.7362	1.50166	0.750828	−	0.660498i	$-0.229655\pi$
$317$	26.7362	1.50166	0.750828	+	0.660498i	$0.229655\pi$
$318$	−3.30998	−0.185615
$319$	−4.26515	−0.238802
$320$	2.62767	0.146891
$321$	−2.48259	−0.138565
$322$	−23.3078	−1.29889
$323$	−4.46290	−0.248323
$324$	5.74507	0.319170
$325$	−1.61228	−0.0894333
$326$	13.9287	0.771440
$327$	−5.69005	−0.314661
$328$	−1.47998	−0.0817183
$329$	−9.43868	−0.520371
$330$	−1.61445	−0.0888727
$331$	−26.1507	−1.43737	−0.718687	−	0.695333i	$-0.755257\pi$
$331$	−26.1507	−1.43737	−0.718687	+	0.695333i	$0.755257\pi$
$332$	9.53327	0.523206
$333$	−17.7369	−0.971977
$334$	13.7010	0.749686
$335$	6.09777	0.333157
$336$	1.70715	0.0931328
$337$	19.3600	1.05461	0.527303	−	0.849678i	$-0.323203\pi$
$337$	19.3600	1.05461	0.527303	+	0.849678i	$0.323203\pi$
$338$	−12.2834	−0.668131
$339$	1.24114	0.0674094
$340$	5.05933	0.274381
$341$	5.79622	0.313883
$342$	6.07871	0.328699
$343$	17.4484	0.942123
$344$	−0.213650	−0.0115192
$345$	−13.5428	−0.729120
$346$	−20.7113	−1.11344
$347$	−2.10163	−0.112821	−0.0564107	−	0.998408i	$-0.517966\pi$
$347$	−2.10163	−0.112821	−0.0564107	+	0.998408i	$0.517966\pi$
$348$	2.62053	0.140475
$349$	−34.2049	−1.83095	−0.915474	−	0.402377i	$-0.868184\pi$
$349$	−34.2049	−1.83095	−0.915474	+	0.402377i	$0.868184\pi$
$350$	−5.29217	−0.282878
$351$	−2.92422	−0.156083
$352$	1.00000	0.0533002
$353$	−0.224933	−0.0119720	−0.00598598	−	0.999982i	$-0.501905\pi$
$353$	−0.224933	−0.0119720	−0.00598598	+	0.999982i	$0.501905\pi$
$354$	0.454823	0.0241735
$355$	27.7846	1.47465
$356$	10.3091	0.546382
$357$	3.28696	0.173964
$358$	10.5316	0.556613
$359$	28.2205	1.48942	0.744710	−	0.667388i	$-0.232588\pi$
$359$	28.2205	1.48942	0.744710	+	0.667388i	$0.232588\pi$
$360$	−6.89108	−0.363192
$361$	−13.6273	−0.717228
$362$	3.53657	0.185878
$363$	−0.614404	−0.0322479
$364$	2.35203	0.123280
$365$	−9.76142	−0.510936
$366$	−6.27713	−0.328111
$367$	15.0074	0.783382	0.391691	−	0.920097i	$-0.371890\pi$
$367$	15.0074	0.783382	0.391691	+	0.920097i	$0.371890\pi$
$368$	8.38848	0.437280
$369$	3.88126	0.202050
$370$	17.7718	0.923914
$371$	−14.9689	−0.777146
$372$	−3.56122	−0.184641
$373$	−25.2478	−1.30728	−0.653641	−	0.756805i	$-0.726759\pi$
$373$	−25.2478	−1.30728	−0.653641	+	0.756805i	$0.726759\pi$
$374$	1.92541	0.0995604
$375$	4.99729	0.258059
$376$	3.39698	0.175186
$377$	3.61043	0.185947
$378$	−9.59848	−0.493692
$379$	16.3972	0.842269	0.421134	−	0.906998i	$-0.361632\pi$
$379$	16.3972	0.842269	0.421134	+	0.906998i	$0.361632\pi$
$380$	−6.09068	−0.312445
$381$	10.8249	0.554578
$382$	−5.17249	−0.264648
$383$	−6.55363	−0.334875	−0.167438	−	0.985883i	$-0.553549\pi$
$383$	−6.55363	−0.334875	−0.167438	+	0.985883i	$0.553549\pi$
$384$	−0.614404	−0.0313537
$385$	−7.30111	−0.372099
$386$	−23.3212	−1.18702
$387$	0.560298	0.0284816
$388$	5.94742	0.301934
$389$	−28.3182	−1.43579	−0.717895	−	0.696151i	$-0.754894\pi$
$389$	−28.3182	−1.43579	−0.717895	+	0.696151i	$0.754894\pi$
$390$	1.36663	0.0692019
$391$	16.1512	0.816802
$392$	0.720332	0.0363823
$393$	−13.1046	−0.661042
$394$	1.00000	0.0503793
$395$	−6.88524	−0.346434
$396$	−2.62251	−0.131786
$397$	−27.0154	−1.35586	−0.677932	−	0.735125i	$-0.737124\pi$
$397$	−27.0154	−1.35586	−0.677932	+	0.735125i	$0.737124\pi$
$398$	−6.94661	−0.348202
$399$	−3.95701	−0.198098
$400$	1.90465	0.0952326
$401$	11.3669	0.567637	0.283818	−	0.958878i	$-0.408399\pi$
$401$	11.3669	0.567637	0.283818	+	0.958878i	$0.408399\pi$
$402$	−1.42579	−0.0711118
$403$	−4.90648	−0.244409
$404$	1.05910	0.0526924
$405$	15.0961	0.750133
$406$	11.8509	0.588151
$407$	6.76334	0.335247
$408$	−1.18298	−0.0585661
$409$	−15.5266	−0.767741	−0.383870	−	0.923387i	$-0.625409\pi$
$409$	−15.5266	−0.767741	−0.383870	+	0.923387i	$0.625409\pi$
$410$	−3.88890	−0.192059
$411$	−9.84657	−0.485696
$412$	−5.38912	−0.265503
$413$	2.05686	0.101212
$414$	−21.9988	−1.08118
$415$	25.0503	1.22967
$416$	−0.846497	−0.0415029
$417$	8.99682	0.440576
$418$	−2.31790	−0.113372
$419$	−27.2928	−1.33334	−0.666670	−	0.745353i	$-0.732281\pi$
$419$	−27.2928	−1.33334	−0.666670	+	0.745353i	$0.732281\pi$
$420$	4.48583	0.218886
$421$	9.66471	0.471029	0.235515	−	0.971871i	$-0.424322\pi$
$421$	9.66471	0.471029	0.235515	+	0.971871i	$0.424322\pi$
$422$	8.19484	0.398919
$423$	−8.90861	−0.433151
$424$	5.38730	0.261631
$425$	3.66723	0.177887
$426$	−6.49661	−0.314762
$427$	−28.3873	−1.37376
$428$	4.04065	0.195312
$429$	0.520091	0.0251102
$430$	−0.561401	−0.0270732
$431$	−9.66390	−0.465494	−0.232747	−	0.972537i	$-0.574771\pi$
$431$	−9.66390	−0.465494	−0.232747	+	0.972537i	$0.574771\pi$
$432$	3.45449	0.166204
$433$	4.60349	0.221229	0.110615	−	0.993863i	$-0.464718\pi$
$433$	4.60349	0.221229	0.110615	+	0.993863i	$0.464718\pi$
$434$	−16.1051	−0.773068
$435$	6.88588	0.330153
$436$	9.26109	0.443526
$437$	−19.4437	−0.930117
$438$	2.28242	0.109058
$439$	24.0485	1.14777	0.573887	−	0.818934i	$-0.305435\pi$
$439$	24.0485	1.14777	0.573887	+	0.818934i	$0.305435\pi$
$440$	2.62767	0.125269
$441$	−1.88908	−0.0899560
$442$	−1.62985	−0.0775240
$443$	1.57221	0.0746981	0.0373490	−	0.999302i	$-0.488109\pi$
$443$	1.57221	0.0746981	0.0373490	+	0.999302i	$0.488109\pi$
$444$	−4.15543	−0.197208
$445$	27.0890	1.28414
$446$	−12.5617	−0.594815
$447$	9.97609	0.471853
$448$	−2.77855	−0.131274
$449$	−39.3486	−1.85698	−0.928488	−	0.371364i	$-0.878890\pi$
$449$	−39.3486	−1.85698	−0.928488	+	0.371364i	$0.878890\pi$
$450$	−4.99496	−0.235465
$451$	−1.47998	−0.0696896
$452$	−2.02007	−0.0950160
$453$	8.10269	0.380697
$454$	15.2928	0.717728
$455$	6.18037	0.289740
$456$	1.42413	0.0666910
$457$	−17.0307	−0.796662	−0.398331	−	0.917242i	$-0.630410\pi$
$457$	−17.0307	−0.796662	−0.398331	+	0.917242i	$0.630410\pi$
$458$	−11.7631	−0.549652
$459$	6.65130	0.310456
$460$	22.0421	1.02772
$461$	0.779505	0.0363052	0.0181526	−	0.999835i	$-0.494222\pi$
$461$	0.779505	0.0363052	0.0181526	+	0.999835i	$0.494222\pi$
$462$	1.70715	0.0794239
$463$	−15.8188	−0.735163	−0.367582	−	0.929991i	$-0.619814\pi$
$463$	−15.8188	−0.735163	−0.367582	+	0.929991i	$0.619814\pi$
$464$	−4.26515	−0.198005
$465$	−9.35771	−0.433954
$466$	2.46526	0.114201
$467$	34.7698	1.60895	0.804477	−	0.593984i	$-0.202446\pi$
$467$	34.7698	1.60895	0.804477	+	0.593984i	$0.202446\pi$
$468$	2.21994	0.102617
$469$	−6.44790	−0.297736
$470$	8.92615	0.411733
$471$	3.39500	0.156433
$472$	−0.740266	−0.0340735
$473$	−0.213650	−0.00982363
$474$	1.60991	0.0739457
$475$	−4.41480	−0.202565
$476$	−5.34983	−0.245209
$477$	−14.1282	−0.646888
$478$	26.2625	1.20122
$479$	7.30783	0.333903	0.166952	−	0.985965i	$-0.446608\pi$
$479$	7.30783	0.333903	0.166952	+	0.985965i	$0.446608\pi$
$480$	−1.61445	−0.0736893
$481$	−5.72515	−0.261044
$482$	8.37771	0.381594
$483$	14.3204	0.651601
$484$	1.00000	0.0454545
$485$	15.6279	0.709624
$486$	−13.8933	−0.630212
$487$	−5.84907	−0.265047	−0.132523	−	0.991180i	$-0.542308\pi$
$487$	−5.84907	−0.265047	−0.132523	+	0.991180i	$0.542308\pi$
$488$	10.2166	0.462484
$489$	−8.55786	−0.387000
$490$	1.89280	0.0855078
$491$	−37.0872	−1.67372	−0.836860	−	0.547417i	$-0.815611\pi$
$491$	−37.0872	−1.67372	−0.836860	+	0.547417i	$0.815611\pi$
$492$	0.909307	0.0409947
$493$	−8.21214	−0.369856
$494$	1.96210	0.0882789
$495$	−6.89108	−0.309731
$496$	5.79622	0.260258
$497$	−29.3799	−1.31787
$498$	−5.85728	−0.262471
$499$	15.6262	0.699524	0.349762	−	0.936839i	$-0.386262\pi$
$499$	15.6262	0.699524	0.349762	+	0.936839i	$0.386262\pi$
$500$	−8.13355	−0.363744
$501$	−8.41796	−0.376087
$502$	10.3519	0.462028
$503$	27.8551	1.24200	0.620998	−	0.783812i	$-0.286728\pi$
$503$	27.8551	1.24200	0.620998	+	0.783812i	$0.286728\pi$
$504$	7.28676	0.324578
$505$	2.78297	0.123841
$506$	8.38848	0.372913
$507$	7.54700	0.335174
$508$	−17.6186	−0.781698
$509$	−28.2673	−1.25293	−0.626463	−	0.779452i	$-0.715498\pi$
$509$	−28.2673	−1.25293	−0.626463	+	0.779452i	$0.715498\pi$
$510$	−3.10848	−0.137646
$511$	10.3219	0.456614
$512$	1.00000	0.0441942
$513$	−8.00718	−0.353525
$514$	12.4238	0.547988
$515$	−14.1608	−0.624001
$516$	0.131267	0.00577873
$517$	3.39698	0.149399
$518$	−18.7923	−0.825685
$519$	12.7251	0.558570
$520$	−2.22431	−0.0975426
$521$	13.6897	0.599759	0.299879	−	0.953977i	$-0.403054\pi$
$521$	13.6897	0.599759	0.299879	+	0.953977i	$0.403054\pi$
$522$	11.1854	0.489571
$523$	−37.2911	−1.63063	−0.815313	−	0.579021i	$-0.803435\pi$
$523$	−37.2911	−1.63063	−0.815313	+	0.579021i	$0.803435\pi$
$524$	21.3290	0.931763
$525$	3.25153	0.141908
$526$	20.0342	0.873534
$527$	11.1601	0.486140
$528$	−0.614404	−0.0267385
$529$	47.3665	2.05941
$530$	14.1561	0.614900
$531$	1.94135	0.0842475
$532$	6.44040	0.279227
$533$	1.25280	0.0542647
$534$	−6.33397	−0.274098
$535$	10.6175	0.459035
$536$	2.32060	0.100235
$537$	−6.47067	−0.279230
$538$	2.29186	0.0988092
$539$	0.720332	0.0310269
$540$	9.07727	0.390624
$541$	23.6855	1.01832	0.509159	−	0.860672i	$-0.329956\pi$
$541$	23.6855	1.01832	0.509159	+	0.860672i	$0.329956\pi$
$542$	−11.6859	−0.501950
$543$	−2.17289	−0.0932474
$544$	1.92541	0.0825511
$545$	24.3351	1.04240
$546$	−1.44510	−0.0618445
$547$	24.3801	1.04242	0.521208	−	0.853430i	$-0.325482\pi$
$547$	24.3801	1.04242	0.521208	+	0.853430i	$0.325482\pi$
$548$	16.0262	0.684606
$549$	−26.7931	−1.14350
$550$	1.90465	0.0812146
$551$	9.88619	0.421166
$552$	−5.15392	−0.219365
$553$	7.28058	0.309602
$554$	−10.0225	−0.425815
$555$	−10.9191	−0.463490
$556$	−14.6432	−0.621008
$557$	8.61492	0.365026	0.182513	−	0.983203i	$-0.441577\pi$
$557$	8.61492	0.365026	0.182513	+	0.983203i	$0.441577\pi$
$558$	−15.2006	−0.643493
$559$	0.180854	0.00764930
$560$	−7.30111	−0.308528
$561$	−1.18298	−0.0499454
$562$	−3.88966	−0.164075
$563$	24.2193	1.02072	0.510362	−	0.859960i	$-0.329511\pi$
$563$	24.2193	1.02072	0.510362	+	0.859960i	$0.329511\pi$
$564$	−2.08712	−0.0878836
$565$	−5.30808	−0.223312
$566$	22.8380	0.959954
$567$	−15.9629	−0.670381
$568$	10.5738	0.443668
$569$	38.1418	1.59899	0.799494	−	0.600675i	$-0.205101\pi$
$569$	38.1418	1.59899	0.799494	+	0.600675i	$0.205101\pi$
$570$	3.74214	0.156741
$571$	4.90752	0.205373	0.102687	−	0.994714i	$-0.467256\pi$
$571$	4.90752	0.205373	0.102687	+	0.994714i	$0.467256\pi$
$572$	−0.846497	−0.0353938
$573$	3.17800	0.132763
$574$	4.11220	0.171640
$575$	15.9771	0.666292
$576$	−2.62251	−0.109271
$577$	−14.7101	−0.612390	−0.306195	−	0.951969i	$-0.599056\pi$
$577$	−14.7101	−0.612390	−0.306195	+	0.951969i	$0.599056\pi$
$578$	−13.2928	−0.552908
$579$	14.3287	0.595479
$580$	−11.2074	−0.465362
$581$	−26.4887	−1.09893
$582$	−3.65412	−0.151468
$583$	5.38730	0.223119
$584$	−3.71486	−0.153722
$585$	5.83328	0.241176
$586$	−11.5401	−0.476718
$587$	−18.8132	−0.776504	−0.388252	−	0.921553i	$-0.626921\pi$
$587$	−18.8132	−0.776504	−0.388252	+	0.921553i	$0.626921\pi$
$588$	−0.442575	−0.0182515
$589$	−13.4351	−0.553582
$590$	−1.94517	−0.0800816
$591$	−0.614404	−0.0252732
$592$	6.76334	0.277972
$593$	−21.0053	−0.862584	−0.431292	−	0.902212i	$-0.641942\pi$
$593$	−21.0053	−0.862584	−0.431292	+	0.902212i	$0.641942\pi$
$594$	3.45449	0.141740
$595$	−14.0576	−0.576305
$596$	−16.2370	−0.665094
$597$	4.26803	0.174679
$598$	−7.10082	−0.290374
$599$	16.3414	0.667693	0.333846	−	0.942628i	$-0.391653\pi$
$599$	16.3414	0.667693	0.333846	+	0.942628i	$0.391653\pi$
$600$	−1.17023	−0.0477743
$601$	7.13350	0.290982	0.145491	−	0.989360i	$-0.453524\pi$
$601$	7.13350	0.290982	0.145491	+	0.989360i	$0.453524\pi$
$602$	0.593636	0.0241948
$603$	−6.08579	−0.247833
$604$	−13.1879	−0.536607
$605$	2.62767	0.106830
$606$	−0.650718	−0.0264336
$607$	31.8436	1.29249	0.646247	−	0.763128i	$-0.276338\pi$
$607$	31.8436	1.29249	0.646247	+	0.763128i	$0.276338\pi$
$608$	−2.31790	−0.0940033
$609$	−7.28126	−0.295051
$610$	26.8459	1.08696
$611$	−2.87553	−0.116332
$612$	−5.04939	−0.204110
$613$	12.5251	0.505886	0.252943	−	0.967481i	$-0.418602\pi$
$613$	12.5251	0.505886	0.252943	+	0.967481i	$0.418602\pi$
$614$	0.802154	0.0323723
$615$	2.38936	0.0963482
$616$	−2.77855	−0.111951
$617$	−15.6495	−0.630026	−0.315013	−	0.949087i	$-0.602009\pi$
$617$	−15.6495	−0.630026	−0.315013	+	0.949087i	$0.602009\pi$
$618$	3.31110	0.133192
$619$	28.2106	1.13388	0.566940	−	0.823759i	$-0.308127\pi$
$619$	28.2106	1.13388	0.566940	+	0.823759i	$0.308127\pi$
$620$	15.2305	0.611673
$621$	28.9779	1.16284
$622$	0.295618	0.0118532
$623$	−28.6444	−1.14761
$624$	0.520091	0.0208203
$625$	−30.8956	−1.23582
$626$	6.32460	0.252782
$627$	1.42413	0.0568742
$628$	−5.52568	−0.220499
$629$	13.0222	0.519228
$630$	19.1472	0.762843
$631$	−9.28648	−0.369689	−0.184845	−	0.982768i	$-0.559178\pi$
$631$	−9.28648	−0.369689	−0.184845	+	0.982768i	$0.559178\pi$
$632$	−2.62028	−0.104229
$633$	−5.03495	−0.200121
$634$	26.7362	1.06183
$635$	−46.2958	−1.83719
$636$	−3.30998	−0.131249
$637$	−0.609759	−0.0241595
$638$	−4.26515	−0.168859
$639$	−27.7300	−1.09698
$640$	2.62767	0.103868
$641$	−1.61921	−0.0639548	−0.0319774	−	0.999489i	$-0.510180\pi$
$641$	−1.61921	−0.0639548	−0.0319774	+	0.999489i	$0.510180\pi$
$642$	−2.48259	−0.0979802
$643$	−21.7783	−0.858851	−0.429426	−	0.903102i	$-0.641284\pi$
$643$	−21.7783	−0.858851	−0.429426	+	0.903102i	$0.641284\pi$
$644$	−23.3078	−0.918455
$645$	0.344927	0.0135815
$646$	−4.46290	−0.175591
$647$	12.6554	0.497535	0.248768	−	0.968563i	$-0.419974\pi$
$647$	12.6554	0.497535	0.248768	+	0.968563i	$0.419974\pi$
$648$	5.74507	0.225687
$649$	−0.740266	−0.0290580
$650$	−1.61228	−0.0632389
$651$	9.89502	0.387817
$652$	13.9287	0.545490
$653$	−27.4302	−1.07343	−0.536713	−	0.843765i	$-0.680334\pi$
$653$	−27.4302	−1.07343	−0.536713	+	0.843765i	$0.680334\pi$
$654$	−5.69005	−0.222499
$655$	56.0456	2.18988
$656$	−1.47998	−0.0577835
$657$	9.74224	0.380081
$658$	−9.43868	−0.367958
$659$	−31.5994	−1.23094	−0.615469	−	0.788161i	$-0.711033\pi$
$659$	−31.5994	−1.23094	−0.615469	+	0.788161i	$0.711033\pi$
$660$	−1.61445	−0.0628425
$661$	−26.0912	−1.01483	−0.507416	−	0.861701i	$-0.669399\pi$
$661$	−26.0912	−1.01483	−0.507416	+	0.861701i	$0.669399\pi$
$662$	−26.1507	−1.01638
$663$	1.00139	0.0388906
$664$	9.53327	0.369963
$665$	16.9233	0.656256
$666$	−17.7369	−0.687292
$667$	−35.7781	−1.38533
$668$	13.7010	0.530108
$669$	7.71798	0.298394
$670$	6.09777	0.235577
$671$	10.2166	0.394408
$672$	1.70715	0.0658548
$673$	−36.2597	−1.39771	−0.698855	−	0.715263i	$-0.746307\pi$
$673$	−36.2597	−1.39771	−0.698855	+	0.715263i	$0.746307\pi$
$674$	19.3600	0.745718
$675$	6.57961	0.253249
$676$	−12.2834	−0.472440
$677$	−3.81839	−0.146753	−0.0733763	−	0.997304i	$-0.523377\pi$
$677$	−3.81839	−0.146753	−0.0733763	+	0.997304i	$0.523377\pi$
$678$	1.24114	0.0476657
$679$	−16.5252	−0.634178
$680$	5.05933	0.194017
$681$	−9.39599	−0.360055
$682$	5.79622	0.221949
$683$	14.5522	0.556825	0.278413	−	0.960462i	$-0.410192\pi$
$683$	14.5522	0.556825	0.278413	+	0.960462i	$0.410192\pi$
$684$	6.07871	0.232425
$685$	42.1116	1.60900
$686$	17.4484	0.666182
$687$	7.22728	0.275738
$688$	−0.213650	−0.00814532
$689$	−4.56034	−0.173735
$690$	−13.5428	−0.515565
$691$	4.04686	0.153950	0.0769749	−	0.997033i	$-0.475474\pi$
$691$	4.04686	0.153950	0.0769749	+	0.997033i	$0.475474\pi$
$692$	−20.7113	−0.787324
$693$	7.28676	0.276801
$694$	−2.10163	−0.0797768
$695$	−38.4774	−1.45953
$696$	2.62053	0.0993308
$697$	−2.84956	−0.107935
$698$	−34.2049	−1.29468
$699$	−1.51467	−0.0572899
$700$	−5.29217	−0.200025
$701$	9.12342	0.344587	0.172293	−	0.985046i	$-0.444882\pi$
$701$	9.12342	0.344587	0.172293	+	0.985046i	$0.444882\pi$
$702$	−2.92422	−0.110367
$703$	−15.6768	−0.591261
$704$	1.00000	0.0376889
$705$	−5.48427	−0.206549
$706$	−0.224933	−0.00846546
$707$	−2.94277	−0.110674
$708$	0.454823	0.0170933
$709$	29.4303	1.10528	0.552639	−	0.833421i	$-0.313621\pi$
$709$	29.4303	1.10528	0.552639	+	0.833421i	$0.313621\pi$
$710$	27.7846	1.04274
$711$	6.87171	0.257709
$712$	10.3091	0.386350
$713$	48.6214	1.82089
$714$	3.28696	0.123011
$715$	−2.22431	−0.0831846
$716$	10.5316	0.393585
$717$	−16.1358	−0.602601
$718$	28.2205	1.05318
$719$	31.7601	1.18445	0.592226	−	0.805772i	$-0.298249\pi$
$719$	31.7601	1.18445	0.592226	+	0.805772i	$0.298249\pi$
$720$	−6.89108	−0.256816
$721$	14.9739	0.557658
$722$	−13.6273	−0.507157
$723$	−5.14730	−0.191430
$724$	3.53657	0.131436
$725$	−8.12362	−0.301704
$726$	−0.614404	−0.0228027
$727$	−33.5503	−1.24431	−0.622157	−	0.782893i	$-0.713743\pi$
$727$	−33.5503	−1.24431	−0.622157	+	0.782893i	$0.713743\pi$
$728$	2.35203	0.0871721
$729$	−8.69911	−0.322189
$730$	−9.76142	−0.361286
$731$	−0.411363	−0.0152148
$732$	−6.27713	−0.232009
$733$	−11.2722	−0.416347	−0.208174	−	0.978092i	$-0.566752\pi$
$733$	−11.2722	−0.416347	−0.208174	+	0.978092i	$0.566752\pi$
$734$	15.0074	0.553935
$735$	−1.16294	−0.0428958
$736$	8.38848	0.309203
$737$	2.32060	0.0854804
$738$	3.88126	0.142871
$739$	12.8960	0.474387	0.237194	−	0.971462i	$-0.423772\pi$
$739$	12.8960	0.474387	0.237194	+	0.971462i	$0.423772\pi$
$740$	17.7718	0.653306
$741$	−1.20552	−0.0442859
$742$	−14.9689	−0.549525
$743$	−16.2490	−0.596118	−0.298059	−	0.954547i	$-0.596339\pi$
$743$	−16.2490	−0.596118	−0.298059	+	0.954547i	$0.596339\pi$
$744$	−3.56122	−0.130561
$745$	−42.6655	−1.56314
$746$	−25.2478	−0.924387
$747$	−25.0011	−0.914741
$748$	1.92541	0.0703998
$749$	−11.2271	−0.410231
$750$	4.99729	0.182475
$751$	−17.7206	−0.646634	−0.323317	−	0.946291i	$-0.604798\pi$
$751$	−17.7206	−0.646634	−0.323317	+	0.946291i	$0.604798\pi$
$752$	3.39698	0.123875
$753$	−6.36026	−0.231781
$754$	3.61043	0.131484
$755$	−34.6534	−1.26117
$756$	−9.59848	−0.349093
$757$	40.8409	1.48439	0.742194	−	0.670186i	$-0.233786\pi$
$757$	40.8409	1.48439	0.742194	+	0.670186i	$0.233786\pi$
$758$	16.3972	0.595574
$759$	−5.15392	−0.187075
$760$	−6.09068	−0.220932
$761$	−17.1521	−0.621764	−0.310882	−	0.950448i	$-0.600624\pi$
$761$	−17.1521	−0.621764	−0.310882	+	0.950448i	$0.600624\pi$
$762$	10.8249	0.392146
$763$	−25.7324	−0.931575
$764$	−5.17249	−0.187134
$765$	−13.2681	−0.479710
$766$	−6.55363	−0.236792
$767$	0.626632	0.0226264
$768$	−0.614404	−0.0221704
$769$	1.54456	0.0556981	0.0278491	−	0.999612i	$-0.491134\pi$
$769$	1.54456	0.0556981	0.0278491	+	0.999612i	$0.491134\pi$
$770$	−7.30111	−0.263114
$771$	−7.63321	−0.274903
$772$	−23.3212	−0.839349
$773$	−22.7474	−0.818166	−0.409083	−	0.912497i	$-0.634151\pi$
$773$	−22.7474	−0.818166	−0.409083	+	0.912497i	$0.634151\pi$
$774$	0.560298	0.0201395
$775$	11.0398	0.396560
$776$	5.94742	0.213500
$777$	11.5461	0.414213
$778$	−28.3182	−1.01526
$779$	3.43045	0.122909
$780$	1.36663	0.0489331
$781$	10.5738	0.378362
$782$	16.1512	0.577566
$783$	−14.7339	−0.526548
$784$	0.720332	0.0257262
$785$	−14.5197	−0.518229
$786$	−13.1046	−0.467427
$787$	−39.3876	−1.40402	−0.702008	−	0.712169i	$-0.747713\pi$
$787$	−39.3876	−1.40402	−0.702008	+	0.712169i	$0.747713\pi$
$788$	1.00000	0.0356235
$789$	−12.3091	−0.438216
$790$	−6.88524	−0.244966
$791$	5.61286	0.199570
$792$	−2.62251	−0.0931867
$793$	−8.64832	−0.307111
$794$	−27.0154	−0.958740
$795$	−8.69755	−0.308470
$796$	−6.94661	−0.246216
$797$	−13.6221	−0.482520	−0.241260	−	0.970461i	$-0.577561\pi$
$797$	−13.6221	−0.482520	−0.241260	+	0.970461i	$0.577561\pi$
$798$	−3.95701	−0.140077
$799$	6.54057	0.231389
$800$	1.90465	0.0673396
$801$	−27.0357	−0.955261
$802$	11.3669	0.401380
$803$	−3.71486	−0.131094
$804$	−1.42579	−0.0502836
$805$	−61.2452	−2.15861
$806$	−4.90648	−0.172823
$807$	−1.40813	−0.0495685
$808$	1.05910	0.0372591
$809$	16.2245	0.570422	0.285211	−	0.958465i	$-0.407936\pi$
$809$	16.2245	0.570422	0.285211	+	0.958465i	$0.407936\pi$
$810$	15.0961	0.530424
$811$	−32.9102	−1.15563	−0.577817	−	0.816166i	$-0.696095\pi$
$811$	−32.9102	−1.15563	−0.577817	+	0.816166i	$0.696095\pi$
$812$	11.8509	0.415886
$813$	7.17984	0.251808
$814$	6.76334	0.237055
$815$	36.6001	1.28204
$816$	−1.18298	−0.0414125
$817$	0.495219	0.0173255
$818$	−15.5266	−0.542875
$819$	−6.16822	−0.215535
$820$	−3.88890	−0.135806
$821$	−32.5207	−1.13498	−0.567490	−	0.823380i	$-0.692085\pi$
$821$	−32.5207	−1.13498	−0.567490	+	0.823380i	$0.692085\pi$
$822$	−9.84657	−0.343439
$823$	−23.2294	−0.809727	−0.404864	−	0.914377i	$-0.632681\pi$
$823$	−23.2294	−0.809727	−0.404864	+	0.914377i	$0.632681\pi$
$824$	−5.38912	−0.187739
$825$	−1.17023	−0.0407421
$826$	2.05686	0.0715675
$827$	−17.5918	−0.611728	−0.305864	−	0.952075i	$-0.598945\pi$
$827$	−17.5918	−0.611728	−0.305864	+	0.952075i	$0.598945\pi$
$828$	−21.9988	−0.764512
$829$	7.75690	0.269408	0.134704	−	0.990886i	$-0.456992\pi$
$829$	7.75690	0.269408	0.134704	+	0.990886i	$0.456992\pi$
$830$	25.0503	0.869508
$831$	6.15786	0.213614
$832$	−0.846497	−0.0293470
$833$	1.38693	0.0480544
$834$	8.99682	0.311534
$835$	36.0017	1.24589
$836$	−2.31790	−0.0801663
$837$	20.0230	0.692096
$838$	−27.2928	−0.942813
$839$	7.98056	0.275520	0.137760	−	0.990466i	$-0.456010\pi$
$839$	7.98056	0.275520	0.137760	+	0.990466i	$0.456010\pi$
$840$	4.48583	0.154776
$841$	−10.8085	−0.372707
$842$	9.66471	0.333068
$843$	2.38983	0.0823100
$844$	8.19484	0.282078
$845$	−32.2768	−1.11036
$846$	−8.90861	−0.306284
$847$	−2.77855	−0.0954721
$848$	5.38730	0.185001
$849$	−14.0318	−0.481570
$850$	3.66723	0.125785
$851$	56.7342	1.94482
$852$	−6.49661	−0.222570
$853$	−32.2063	−1.10272	−0.551361	−	0.834267i	$-0.685891\pi$
$853$	−32.2063	−1.10272	−0.551361	+	0.834267i	$0.685891\pi$
$854$	−28.3873	−0.971395
$855$	15.9729	0.546260
$856$	4.04065	0.138107
$857$	−0.945691	−0.0323042	−0.0161521	−	0.999870i	$-0.505142\pi$
$857$	−0.945691	−0.0323042	−0.0161521	+	0.999870i	$0.505142\pi$
$858$	0.520091	0.0177556
$859$	−44.4969	−1.51822	−0.759108	−	0.650965i	$-0.774365\pi$
$859$	−44.4969	−1.51822	−0.759108	+	0.650965i	$0.774365\pi$
$860$	−0.561401	−0.0191436
$861$	−2.52655	−0.0861047
$862$	−9.66390	−0.329154
$863$	5.96998	0.203220	0.101610	−	0.994824i	$-0.467601\pi$
$863$	5.96998	0.203220	0.101610	+	0.994824i	$0.467601\pi$
$864$	3.45449	0.117524
$865$	−54.4224	−1.85042
$866$	4.60349	0.156433
$867$	8.16716	0.277371
$868$	−16.1051	−0.546642
$869$	−2.62028	−0.0888870
$870$	6.88588	0.233453
$871$	−1.96438	−0.0665605
$872$	9.26109	0.313620
$873$	−15.5971	−0.527883
$874$	−19.4437	−0.657692
$875$	22.5995	0.764002
$876$	2.28242	0.0771160
$877$	−30.2306	−1.02082	−0.510408	−	0.859933i	$-0.670505\pi$
$877$	−30.2306	−1.02082	−0.510408	+	0.859933i	$0.670505\pi$
$878$	24.0485	0.811599
$879$	7.09029	0.239150
$880$	2.62767	0.0885788
$881$	−0.713098	−0.0240249	−0.0120124	−	0.999928i	$-0.503824\pi$
$881$	−0.713098	−0.0240249	−0.0120124	+	0.999928i	$0.503824\pi$
$882$	−1.88908	−0.0636085
$883$	53.1129	1.78739	0.893696	−	0.448672i	$-0.148103\pi$
$883$	53.1129	1.78739	0.893696	+	0.448672i	$0.148103\pi$
$884$	−1.62985	−0.0548178
$885$	1.19512	0.0401736
$886$	1.57221	0.0528195
$887$	−3.85753	−0.129523	−0.0647616	−	0.997901i	$-0.520629\pi$
$887$	−3.85753	−0.129523	−0.0647616	+	0.997901i	$0.520629\pi$
$888$	−4.15543	−0.139447
$889$	48.9541	1.64187
$890$	27.0890	0.908024
$891$	5.74507	0.192467
$892$	−12.5617	−0.420598
$893$	−7.87387	−0.263489
$894$	9.97609	0.333650
$895$	27.6736	0.925026
$896$	−2.77855	−0.0928248
$897$	4.36277	0.145669
$898$	−39.3486	−1.31308
$899$	−24.7217	−0.824515
$900$	−4.99496	−0.166499
$901$	10.3727	0.345566
$902$	−1.47998	−0.0492780
$903$	−0.364733	−0.0121375
$904$	−2.02007	−0.0671865
$905$	9.29294	0.308908
$906$	8.10269	0.269194
$907$	−46.2568	−1.53593	−0.767967	−	0.640490i	$-0.778731\pi$
$907$	−46.2568	−1.53593	−0.767967	+	0.640490i	$0.778731\pi$
$908$	15.2928	0.507511
$909$	−2.77751	−0.0921241
$910$	6.18037	0.204877
$911$	−7.12414	−0.236033	−0.118017	−	0.993012i	$-0.537654\pi$
$911$	−7.12414	−0.236033	−0.118017	+	0.993012i	$0.537654\pi$
$912$	1.42413	0.0471576
$913$	9.53327	0.315505
$914$	−17.0307	−0.563325
$915$	−16.4942	−0.545282
$916$	−11.7631	−0.388662
$917$	−59.2637	−1.95706
$918$	6.65130	0.219526
$919$	−17.7620	−0.585915	−0.292957	−	0.956126i	$-0.594639\pi$
$919$	−17.7620	−0.585915	−0.292957	+	0.956126i	$0.594639\pi$
$920$	22.0421	0.726708
$921$	−0.492847	−0.0162399
$922$	0.779505	0.0256716
$923$	−8.95072	−0.294616
$924$	1.70715	0.0561612
$925$	12.8818	0.423552
$926$	−15.8188	−0.519839
$927$	14.1330	0.464189
$928$	−4.26515	−0.140010
$929$	29.1518	0.956438	0.478219	−	0.878241i	$-0.341282\pi$
$929$	29.1518	0.956438	0.478219	+	0.878241i	$0.341282\pi$
$930$	−9.35771	−0.306852
$931$	−1.66966	−0.0547209
$932$	2.46526	0.0807522
$933$	−0.181629	−0.00594627
$934$	34.7698	1.13770
$935$	5.05933	0.165458
$936$	2.21994	0.0725611
$937$	−3.78352	−0.123602	−0.0618011	−	0.998088i	$-0.519684\pi$
$937$	−3.78352	−0.123602	−0.0618011	+	0.998088i	$0.519684\pi$
$938$	−6.44790	−0.210531
$939$	−3.88586	−0.126810
$940$	8.92615	0.291139
$941$	38.5139	1.25552	0.627759	−	0.778408i	$-0.283973\pi$
$941$	38.5139	1.25552	0.627759	+	0.778408i	$0.283973\pi$
$942$	3.39500	0.110615
$943$	−12.4148	−0.404281
$944$	−0.740266	−0.0240936
$945$	−25.2216	−0.820460
$946$	−0.213650	−0.00694636
$947$	43.1434	1.40197	0.700986	−	0.713175i	$-0.252743\pi$
$947$	43.1434	1.40197	0.700986	+	0.713175i	$0.252743\pi$
$948$	1.60991	0.0522875
$949$	3.14461	0.102078
$950$	−4.41480	−0.143235
$951$	−16.4269	−0.532677
$952$	−5.34983	−0.173389
$953$	−0.253226	−0.00820281	−0.00410140	−	0.999992i	$-0.501306\pi$
$953$	−0.253226	−0.00820281	−0.00410140	+	0.999992i	$0.501306\pi$
$954$	−14.1282	−0.457419
$955$	−13.5916	−0.439814
$956$	26.2625	0.849389
$957$	2.62053	0.0847096
$958$	7.30783	0.236105
$959$	−44.5296	−1.43794
$960$	−1.61445	−0.0521062
$961$	2.59612	0.0837458
$962$	−5.72515	−0.184586
$963$	−10.5966	−0.341472
$964$	8.37771	0.269828
$965$	−61.2805	−1.97269
$966$	14.3204	0.460752
$967$	−33.7788	−1.08625	−0.543127	−	0.839650i	$-0.682760\pi$
$967$	−33.7788	−1.08625	−0.543127	+	0.839650i	$0.682760\pi$
$968$	1.00000	0.0321412
$969$	2.74203	0.0880866
$970$	15.6279	0.501780
$971$	23.7129	0.760983	0.380491	−	0.924784i	$-0.375755\pi$
$971$	23.7129	0.760983	0.380491	+	0.924784i	$0.375755\pi$
$972$	−13.8933	−0.445627
$973$	40.6867	1.30436
$974$	−5.84907	−0.187416
$975$	0.990593	0.0317244
$976$	10.2166	0.327026
$977$	−11.2114	−0.358684	−0.179342	−	0.983787i	$-0.557397\pi$
$977$	−11.2114	−0.358684	−0.179342	+	0.983787i	$0.557397\pi$
$978$	−8.55786	−0.273650
$979$	10.3091	0.329481
$980$	1.89280	0.0604632
$981$	−24.2873	−0.775433
$982$	−37.0872	−1.18350
$983$	17.5793	0.560693	0.280346	−	0.959899i	$-0.409551\pi$
$983$	17.5793	0.560693	0.280346	+	0.959899i	$0.409551\pi$
$984$	0.909307	0.0289876
$985$	2.62767	0.0837245
$986$	−8.21214	−0.261528
$987$	5.79917	0.184589
$988$	1.96210	0.0624226
$989$	−1.79220	−0.0569885
$990$	−6.89108	−0.219013
$991$	9.61960	0.305577	0.152788	−	0.988259i	$-0.451175\pi$
$991$	9.61960	0.305577	0.152788	+	0.988259i	$0.451175\pi$
$992$	5.79622	0.184030
$993$	16.0671	0.509875
$994$	−29.3799	−0.931874
$995$	−18.2534	−0.578672
$996$	−5.85728	−0.185595
$997$	−31.9615	−1.01223	−0.506115	−	0.862466i	$-0.668919\pi$
$997$	−31.9615	−1.01223	−0.506115	+	0.862466i	$0.668919\pi$
$998$	15.6262	0.494638
$999$	23.3639	0.739202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.10	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.10	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.614404 q^{3} +1.00000 q^{4} +2.62767 q^{5} -0.614404 q^{6} -2.77855 q^{7} +1.00000 q^{8} -2.62251 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.614404 q^{3} +1.00000 q^{4} +2.62767 q^{5} -0.614404 q^{6} -2.77855 q^{7} +1.00000 q^{8} -2.62251 q^{9} +2.62767 q^{10} +1.00000 q^{11} -0.614404 q^{12} -0.846497 q^{13} -2.77855 q^{14} -1.61445 q^{15} +1.00000 q^{16} +1.92541 q^{17} -2.62251 q^{18} -2.31790 q^{19} +2.62767 q^{20} +1.70715 q^{21} +1.00000 q^{22} +8.38848 q^{23} -0.614404 q^{24} +1.90465 q^{25} -0.846497 q^{26} +3.45449 q^{27} -2.77855 q^{28} -4.26515 q^{29} -1.61445 q^{30} +5.79622 q^{31} +1.00000 q^{32} -0.614404 q^{33} +1.92541 q^{34} -7.30111 q^{35} -2.62251 q^{36} +6.76334 q^{37} -2.31790 q^{38} +0.520091 q^{39} +2.62767 q^{40} -1.47998 q^{41} +1.70715 q^{42} -0.213650 q^{43} +1.00000 q^{44} -6.89108 q^{45} +8.38848 q^{46} +3.39698 q^{47} -0.614404 q^{48} +0.720332 q^{49} +1.90465 q^{50} -1.18298 q^{51} -0.846497 q^{52} +5.38730 q^{53} +3.45449 q^{54} +2.62767 q^{55} -2.77855 q^{56} +1.42413 q^{57} -4.26515 q^{58} -0.740266 q^{59} -1.61445 q^{60} +10.2166 q^{61} +5.79622 q^{62} +7.28676 q^{63} +1.00000 q^{64} -2.22431 q^{65} -0.614404 q^{66} +2.32060 q^{67} +1.92541 q^{68} -5.15392 q^{69} -7.30111 q^{70} +10.5738 q^{71} -2.62251 q^{72} -3.71486 q^{73} +6.76334 q^{74} -1.17023 q^{75} -2.31790 q^{76} -2.77855 q^{77} +0.520091 q^{78} -2.62028 q^{79} +2.62767 q^{80} +5.74507 q^{81} -1.47998 q^{82} +9.53327 q^{83} +1.70715 q^{84} +5.05933 q^{85} -0.213650 q^{86} +2.62053 q^{87} +1.00000 q^{88} +10.3091 q^{89} -6.89108 q^{90} +2.35203 q^{91} +8.38848 q^{92} -3.56122 q^{93} +3.39698 q^{94} -6.09068 q^{95} -0.614404 q^{96} +5.94742 q^{97} +0.720332 q^{98} -2.62251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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