LMFDB - Embedded newform 8026.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.57686 q^{3} +1.00000 q^{4} -0.429942 q^{5} -2.57686 q^{6} +3.15501 q^{7} +1.00000 q^{8} +3.64023 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.57686 q^{3} +1.00000 q^{4} -0.429942 q^{5} -2.57686 q^{6} +3.15501 q^{7} +1.00000 q^{8} +3.64023 q^{9} -0.429942 q^{10} -0.939170 q^{11} -2.57686 q^{12} -0.174791 q^{13} +3.15501 q^{14} +1.10790 q^{15} +1.00000 q^{16} +6.62770 q^{17} +3.64023 q^{18} +0.936792 q^{19} -0.429942 q^{20} -8.13004 q^{21} -0.939170 q^{22} -3.00807 q^{23} -2.57686 q^{24} -4.81515 q^{25} -0.174791 q^{26} -1.64979 q^{27} +3.15501 q^{28} -2.77938 q^{29} +1.10790 q^{30} -9.38904 q^{31} +1.00000 q^{32} +2.42011 q^{33} +6.62770 q^{34} -1.35647 q^{35} +3.64023 q^{36} -8.71854 q^{37} +0.936792 q^{38} +0.450413 q^{39} -0.429942 q^{40} -7.10711 q^{41} -8.13004 q^{42} -9.56175 q^{43} -0.939170 q^{44} -1.56509 q^{45} -3.00807 q^{46} +1.70301 q^{47} -2.57686 q^{48} +2.95410 q^{49} -4.81515 q^{50} -17.0787 q^{51} -0.174791 q^{52} +3.59248 q^{53} -1.64979 q^{54} +0.403789 q^{55} +3.15501 q^{56} -2.41399 q^{57} -2.77938 q^{58} +10.9021 q^{59} +1.10790 q^{60} +5.86500 q^{61} -9.38904 q^{62} +11.4850 q^{63} +1.00000 q^{64} +0.0751500 q^{65} +2.42011 q^{66} +14.5707 q^{67} +6.62770 q^{68} +7.75138 q^{69} -1.35647 q^{70} +1.79758 q^{71} +3.64023 q^{72} -5.60047 q^{73} -8.71854 q^{74} +12.4080 q^{75} +0.936792 q^{76} -2.96309 q^{77} +0.450413 q^{78} -7.13386 q^{79} -0.429942 q^{80} -6.66941 q^{81} -7.10711 q^{82} -15.7861 q^{83} -8.13004 q^{84} -2.84953 q^{85} -9.56175 q^{86} +7.16208 q^{87} -0.939170 q^{88} +2.62998 q^{89} -1.56509 q^{90} -0.551468 q^{91} -3.00807 q^{92} +24.1943 q^{93} +1.70301 q^{94} -0.402767 q^{95} -2.57686 q^{96} -3.24787 q^{97} +2.95410 q^{98} -3.41879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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
$3$	−2.57686	−1.48775	−0.743877	−	0.668317i	$-0.767015\pi$
$3$	−2.57686	−1.48775	−0.743877	+	0.668317i	$0.767015\pi$
$4$	1.00000	0.500000
$5$	−0.429942	−0.192276	−0.0961380	−	0.995368i	$-0.530649\pi$
$5$	−0.429942	−0.192276	−0.0961380	+	0.995368i	$0.530649\pi$
$6$	−2.57686	−1.05200
$7$	3.15501	1.19248	0.596241	−	0.802805i	$-0.296660\pi$
$7$	3.15501	1.19248	0.596241	+	0.802805i	$0.296660\pi$
$8$	1.00000	0.353553
$9$	3.64023	1.21341
$10$	−0.429942	−0.135960
$11$	−0.939170	−0.283170	−0.141585	−	0.989926i	$-0.545220\pi$
$11$	−0.939170	−0.283170	−0.141585	+	0.989926i	$0.545220\pi$
$12$	−2.57686	−0.743877
$13$	−0.174791	−0.0484783	−0.0242391	−	0.999706i	$-0.507716\pi$
$13$	−0.174791	−0.0484783	−0.0242391	+	0.999706i	$0.507716\pi$
$14$	3.15501	0.843212
$15$	1.10790	0.286059
$16$	1.00000	0.250000
$17$	6.62770	1.60745	0.803726	−	0.594999i	$-0.202848\pi$
$17$	6.62770	1.60745	0.803726	+	0.594999i	$0.202848\pi$
$18$	3.64023	0.858011
$19$	0.936792	0.214915	0.107457	−	0.994210i	$-0.465729\pi$
$19$	0.936792	0.214915	0.107457	+	0.994210i	$0.465729\pi$
$20$	−0.429942	−0.0961380
$21$	−8.13004	−1.77412
$22$	−0.939170	−0.200232
$23$	−3.00807	−0.627225	−0.313612	−	0.949551i	$-0.601539\pi$
$23$	−3.00807	−0.627225	−0.313612	+	0.949551i	$0.601539\pi$
$24$	−2.57686	−0.526000
$25$	−4.81515	−0.963030
$26$	−0.174791	−0.0342793
$27$	−1.64979	−0.317502
$28$	3.15501	0.596241
$29$	−2.77938	−0.516118	−0.258059	−	0.966129i	$-0.583083\pi$
$29$	−2.77938	−0.516118	−0.258059	+	0.966129i	$0.583083\pi$
$30$	1.10790	0.202275
$31$	−9.38904	−1.68632	−0.843161	−	0.537661i	$-0.819308\pi$
$31$	−9.38904	−1.68632	−0.843161	+	0.537661i	$0.819308\pi$
$32$	1.00000	0.176777
$33$	2.42011	0.421288
$34$	6.62770	1.13664
$35$	−1.35647	−0.229286
$36$	3.64023	0.606705
$37$	−8.71854	−1.43332	−0.716659	−	0.697423i	$-0.754330\pi$
$37$	−8.71854	−1.43332	−0.716659	+	0.697423i	$0.754330\pi$
$38$	0.936792	0.151968
$39$	0.450413	0.0721237
$40$	−0.429942	−0.0679799
$41$	−7.10711	−1.10994	−0.554972	−	0.831869i	$-0.687271\pi$
$41$	−7.10711	−1.10994	−0.554972	+	0.831869i	$0.687271\pi$
$42$	−8.13004	−1.25449
$43$	−9.56175	−1.45815	−0.729077	−	0.684432i	$-0.760050\pi$
$43$	−9.56175	−1.45815	−0.729077	+	0.684432i	$0.760050\pi$
$44$	−0.939170	−0.141585
$45$	−1.56509	−0.233310
$46$	−3.00807	−0.443515
$47$	1.70301	0.248410	0.124205	−	0.992257i	$-0.460362\pi$
$47$	1.70301	0.248410	0.124205	+	0.992257i	$0.460362\pi$
$48$	−2.57686	−0.371938
$49$	2.95410	0.422015
$50$	−4.81515	−0.680965
$51$	−17.0787	−2.39149
$52$	−0.174791	−0.0242391
$53$	3.59248	0.493465	0.246732	−	0.969084i	$-0.420643\pi$
$53$	3.59248	0.493465	0.246732	+	0.969084i	$0.420643\pi$
$54$	−1.64979	−0.224508
$55$	0.403789	0.0544469
$56$	3.15501	0.421606
$57$	−2.41399	−0.319740
$58$	−2.77938	−0.364950
$59$	10.9021	1.41934	0.709668	−	0.704537i	$-0.248845\pi$
$59$	10.9021	1.41934	0.709668	+	0.704537i	$0.248845\pi$
$60$	1.10790	0.143030
$61$	5.86500	0.750937	0.375468	−	0.926835i	$-0.377482\pi$
$61$	5.86500	0.750937	0.375468	+	0.926835i	$0.377482\pi$
$62$	−9.38904	−1.19241
$63$	11.4850	1.44697
$64$	1.00000	0.125000
$65$	0.0751500	0.00932121
$66$	2.42011	0.297895
$67$	14.5707	1.78009	0.890047	−	0.455868i	$-0.150671\pi$
$67$	14.5707	1.78009	0.890047	+	0.455868i	$0.150671\pi$
$68$	6.62770	0.803726
$69$	7.75138	0.933156
$70$	−1.35647	−0.162130
$71$	1.79758	0.213334	0.106667	−	0.994295i	$-0.465982\pi$
$71$	1.79758	0.213334	0.106667	+	0.994295i	$0.465982\pi$
$72$	3.64023	0.429005
$73$	−5.60047	−0.655486	−0.327743	−	0.944767i	$-0.606288\pi$
$73$	−5.60047	−0.655486	−0.327743	+	0.944767i	$0.606288\pi$
$74$	−8.71854	−1.01351
$75$	12.4080	1.43275
$76$	0.936792	0.107457
$77$	−2.96309	−0.337676
$78$	0.450413	0.0509992
$79$	−7.13386	−0.802622	−0.401311	−	0.915942i	$-0.631445\pi$
$79$	−7.13386	−0.802622	−0.401311	+	0.915942i	$0.631445\pi$
$80$	−0.429942	−0.0480690
$81$	−6.66941	−0.741046
$82$	−7.10711	−0.784849
$83$	−15.7861	−1.73275	−0.866377	−	0.499390i	$-0.833558\pi$
$83$	−15.7861	−1.73275	−0.866377	+	0.499390i	$0.833558\pi$
$84$	−8.13004	−0.887060
$85$	−2.84953	−0.309075
$86$	−9.56175	−1.03107
$87$	7.16208	0.767856
$88$	−0.939170	−0.100116
$89$	2.62998	0.278777	0.139389	−	0.990238i	$-0.455486\pi$
$89$	2.62998	0.278777	0.139389	+	0.990238i	$0.455486\pi$
$90$	−1.56509	−0.164975
$91$	−0.551468	−0.0578095
$92$	−3.00807	−0.313612
$93$	24.1943	2.50883
$94$	1.70301	0.175652
$95$	−0.402767	−0.0413230
$96$	−2.57686	−0.263000
$97$	−3.24787	−0.329771	−0.164886	−	0.986313i	$-0.552726\pi$
$97$	−3.24787	−0.329771	−0.164886	+	0.986313i	$0.552726\pi$
$98$	2.95410	0.298409
$99$	−3.41879	−0.343602
$100$	−4.81515	−0.481515
$101$	−5.78679	−0.575807	−0.287903	−	0.957659i	$-0.592958\pi$
$101$	−5.78679	−0.575807	−0.287903	+	0.957659i	$0.592958\pi$
$102$	−17.0787	−1.69104
$103$	−1.13543	−0.111877	−0.0559386	−	0.998434i	$-0.517815\pi$
$103$	−1.13543	−0.111877	−0.0559386	+	0.998434i	$0.517815\pi$
$104$	−0.174791	−0.0171397
$105$	3.49545	0.341121
$106$	3.59248	0.348932
$107$	8.97683	0.867823	0.433912	−	0.900955i	$-0.357133\pi$
$107$	8.97683	0.867823	0.433912	+	0.900955i	$0.357133\pi$
$108$	−1.64979	−0.158751
$109$	10.0067	0.958464	0.479232	−	0.877688i	$-0.340915\pi$
$109$	10.0067	0.958464	0.479232	+	0.877688i	$0.340915\pi$
$110$	0.403789	0.0384997
$111$	22.4665	2.13242
$112$	3.15501	0.298121
$113$	−16.9937	−1.59864	−0.799318	−	0.600908i	$-0.794806\pi$
$113$	−16.9937	−1.59864	−0.799318	+	0.600908i	$0.794806\pi$
$114$	−2.41399	−0.226091
$115$	1.29329	0.120600
$116$	−2.77938	−0.258059
$117$	−0.636279	−0.0588240
$118$	10.9021	1.00362
$119$	20.9105	1.91686
$120$	1.10790	0.101137
$121$	−10.1180	−0.919815
$122$	5.86500	0.530992
$123$	18.3141	1.65132
$124$	−9.38904	−0.843161
$125$	4.21995	0.377444
$126$	11.4850	1.02316
$127$	−3.93384	−0.349072	−0.174536	−	0.984651i	$-0.555843\pi$
$127$	−3.93384	−0.349072	−0.174536	+	0.984651i	$0.555843\pi$
$128$	1.00000	0.0883883
$129$	24.6393	2.16937
$130$	0.0751500	0.00659109
$131$	1.35166	0.118095	0.0590477	−	0.998255i	$-0.481194\pi$
$131$	1.35166	0.118095	0.0590477	+	0.998255i	$0.481194\pi$
$132$	2.42011	0.210644
$133$	2.95559	0.256282
$134$	14.5707	1.25872
$135$	0.709313	0.0610480
$136$	6.62770	0.568320
$137$	4.65644	0.397826	0.198913	−	0.980017i	$-0.436259\pi$
$137$	4.65644	0.397826	0.198913	+	0.980017i	$0.436259\pi$
$138$	7.75138	0.659841
$139$	−0.187908	−0.0159382	−0.00796909	−	0.999968i	$-0.502537\pi$
$139$	−0.187908	−0.0159382	−0.00796909	+	0.999968i	$0.502537\pi$
$140$	−1.35647	−0.114643
$141$	−4.38843	−0.369573
$142$	1.79758	0.150850
$143$	0.164158	0.0137276
$144$	3.64023	0.303353
$145$	1.19497	0.0992371
$146$	−5.60047	−0.463498
$147$	−7.61232	−0.627854
$148$	−8.71854	−0.716659
$149$	5.00328	0.409885	0.204942	−	0.978774i	$-0.434299\pi$
$149$	5.00328	0.409885	0.204942	+	0.978774i	$0.434299\pi$
$150$	12.4080	1.01311
$151$	5.02039	0.408553	0.204277	−	0.978913i	$-0.434516\pi$
$151$	5.02039	0.408553	0.204277	+	0.978913i	$0.434516\pi$
$152$	0.936792	0.0759839
$153$	24.1263	1.95050
$154$	−2.96309	−0.238773
$155$	4.03675	0.324239
$156$	0.450413	0.0360619
$157$	−15.2459	−1.21675	−0.608376	−	0.793649i	$-0.708179\pi$
$157$	−15.2459	−1.21675	−0.608376	+	0.793649i	$0.708179\pi$
$158$	−7.13386	−0.567540
$159$	−9.25733	−0.734154
$160$	−0.429942	−0.0339899
$161$	−9.49048	−0.747955
$162$	−6.66941	−0.523999
$163$	11.5888	0.907708	0.453854	−	0.891076i	$-0.350049\pi$
$163$	11.5888	0.907708	0.453854	+	0.891076i	$0.350049\pi$
$164$	−7.10711	−0.554972
$165$	−1.04051	−0.0810035
$166$	−15.7861	−1.22524
$167$	−14.4829	−1.12072	−0.560359	−	0.828250i	$-0.689337\pi$
$167$	−14.4829	−1.12072	−0.560359	+	0.828250i	$0.689337\pi$
$168$	−8.13004	−0.627246
$169$	−12.9694	−0.997650
$170$	−2.84953	−0.218549
$171$	3.41014	0.260780
$172$	−9.56175	−0.729077
$173$	−2.25487	−0.171434	−0.0857172	−	0.996320i	$-0.527318\pi$
$173$	−2.25487	−0.171434	−0.0857172	+	0.996320i	$0.527318\pi$
$174$	7.16208	0.542956
$175$	−15.1919	−1.14840
$176$	−0.939170	−0.0707926
$177$	−28.0933	−2.11162
$178$	2.62998	0.197125
$179$	−15.7254	−1.17537	−0.587684	−	0.809091i	$-0.699960\pi$
$179$	−15.7254	−1.17537	−0.587684	+	0.809091i	$0.699960\pi$
$180$	−1.56509	−0.116655
$181$	0.565643	0.0420439	0.0210220	−	0.999779i	$-0.493308\pi$
$181$	0.565643	0.0420439	0.0210220	+	0.999779i	$0.493308\pi$
$182$	−0.551468	−0.0408775
$183$	−15.1133	−1.11721
$184$	−3.00807	−0.221758
$185$	3.74847	0.275593
$186$	24.1943	1.77401
$187$	−6.22453	−0.455183
$188$	1.70301	0.124205
$189$	−5.20510	−0.378615
$190$	−0.402767	−0.0292198
$191$	12.1006	0.875571	0.437786	−	0.899079i	$-0.355763\pi$
$191$	12.1006	0.875571	0.437786	+	0.899079i	$0.355763\pi$
$192$	−2.57686	−0.185969
$193$	1.09328	0.0786960	0.0393480	−	0.999226i	$-0.487472\pi$
$193$	1.09328	0.0786960	0.0393480	+	0.999226i	$0.487472\pi$
$194$	−3.24787	−0.233184
$195$	−0.193651	−0.0138677
$196$	2.95410	0.211007
$197$	19.9795	1.42348	0.711741	−	0.702442i	$-0.247907\pi$
$197$	19.9795	1.42348	0.711741	+	0.702442i	$0.247907\pi$
$198$	−3.41879	−0.242963
$199$	12.1436	0.860839	0.430420	−	0.902629i	$-0.358366\pi$
$199$	12.1436	0.860839	0.430420	+	0.902629i	$0.358366\pi$
$200$	−4.81515	−0.340482
$201$	−37.5467	−2.64834
$202$	−5.78679	−0.407157
$203$	−8.76898	−0.615461
$204$	−17.0787	−1.19575
$205$	3.05565	0.213416
$206$	−1.13543	−0.0791091
$207$	−10.9501	−0.761081
$208$	−0.174791	−0.0121196
$209$	−0.879807	−0.0608575
$210$	3.49545	0.241209
$211$	20.4723	1.40937	0.704686	−	0.709520i	$-0.251088\pi$
$211$	20.4723	1.40937	0.704686	+	0.709520i	$0.251088\pi$
$212$	3.59248	0.246732
$213$	−4.63213	−0.317388
$214$	8.97683	0.613644
$215$	4.11100	0.280368
$216$	−1.64979	−0.112254
$217$	−29.6225	−2.01091
$218$	10.0067	0.677737
$219$	14.4317	0.975201
$220$	0.403789	0.0272234
$221$	−1.15846	−0.0779265
$222$	22.4665	1.50785
$223$	−5.09721	−0.341335	−0.170667	−	0.985329i	$-0.554592\pi$
$223$	−5.09721	−0.341335	−0.170667	+	0.985329i	$0.554592\pi$
$224$	3.15501	0.210803
$225$	−17.5283	−1.16855
$226$	−16.9937	−1.13041
$227$	−22.8126	−1.51413	−0.757063	−	0.653342i	$-0.773366\pi$
$227$	−22.8126	−1.51413	−0.757063	+	0.653342i	$0.773366\pi$
$228$	−2.41399	−0.159870
$229$	−9.74494	−0.643964	−0.321982	−	0.946746i	$-0.604349\pi$
$229$	−9.74494	−0.643964	−0.321982	+	0.946746i	$0.604349\pi$
$230$	1.29329	0.0852773
$231$	7.63549	0.502378
$232$	−2.77938	−0.182475
$233$	−12.1643	−0.796908	−0.398454	−	0.917188i	$-0.630453\pi$
$233$	−12.1643	−0.796908	−0.398454	+	0.917188i	$0.630453\pi$
$234$	−0.636279	−0.0415949
$235$	−0.732197	−0.0477633
$236$	10.9021	0.709668
$237$	18.3830	1.19410
$238$	20.9105	1.35542
$239$	−12.4483	−0.805214	−0.402607	−	0.915373i	$-0.631896\pi$
$239$	−12.4483	−0.805214	−0.402607	+	0.915373i	$0.631896\pi$
$240$	1.10790	0.0715148
$241$	11.2765	0.726382	0.363191	−	0.931715i	$-0.381687\pi$
$241$	11.2765	0.726382	0.363191	+	0.931715i	$0.381687\pi$
$242$	−10.1180	−0.650407
$243$	22.1355	1.42000
$244$	5.86500	0.375468
$245$	−1.27009	−0.0811433
$246$	18.3141	1.16766
$247$	−0.163743	−0.0104187
$248$	−9.38904	−0.596205
$249$	40.6788	2.57791
$250$	4.21995	0.266893
$251$	17.3614	1.09584	0.547919	−	0.836531i	$-0.315420\pi$
$251$	17.3614	1.09584	0.547919	+	0.836531i	$0.315420\pi$
$252$	11.4850	0.723485
$253$	2.82508	0.177611
$254$	−3.93384	−0.246831
$255$	7.34285	0.459827
$256$	1.00000	0.0625000
$257$	−9.25982	−0.577612	−0.288806	−	0.957388i	$-0.593258\pi$
$257$	−9.25982	−0.577612	−0.288806	+	0.957388i	$0.593258\pi$
$258$	24.6393	1.53398
$259$	−27.5071	−1.70921
$260$	0.0751500	0.00466061
$261$	−10.1176	−0.626263
$262$	1.35166	0.0835061
$263$	−9.43288	−0.581656	−0.290828	−	0.956775i	$-0.593931\pi$
$263$	−9.43288	−0.581656	−0.290828	+	0.956775i	$0.593931\pi$
$264$	2.42011	0.148948
$265$	−1.54456	−0.0948814
$266$	2.95559	0.181219
$267$	−6.77710	−0.414752
$268$	14.5707	0.890047
$269$	7.27251	0.443413	0.221706	−	0.975113i	$-0.428837\pi$
$269$	7.27251	0.443413	0.221706	+	0.975113i	$0.428837\pi$
$270$	0.709313	0.0431674
$271$	−28.1830	−1.71200	−0.855999	−	0.516978i	$-0.827057\pi$
$271$	−28.1830	−1.71200	−0.855999	+	0.516978i	$0.827057\pi$
$272$	6.62770	0.401863
$273$	1.42106	0.0860063
$274$	4.65644	0.281306
$275$	4.52224	0.272701
$276$	7.75138	0.466578
$277$	−23.1323	−1.38989	−0.694943	−	0.719065i	$-0.744570\pi$
$277$	−23.1323	−1.38989	−0.694943	+	0.719065i	$0.744570\pi$
$278$	−0.187908	−0.0112700
$279$	−34.1783	−2.04620
$280$	−1.35647	−0.0810648
$281$	−29.7464	−1.77452	−0.887260	−	0.461270i	$-0.847394\pi$
$281$	−29.7464	−1.77452	−0.887260	+	0.461270i	$0.847394\pi$
$282$	−4.38843	−0.261327
$283$	12.9932	0.772365	0.386183	−	0.922422i	$-0.373793\pi$
$283$	12.9932	0.772365	0.386183	+	0.922422i	$0.373793\pi$
$284$	1.79758	0.106667
$285$	1.03787	0.0614784
$286$	0.164158	0.00970689
$287$	−22.4230	−1.32359
$288$	3.64023	0.214503
$289$	26.9264	1.58390
$290$	1.19497	0.0701712
$291$	8.36933	0.490619
$292$	−5.60047	−0.327743
$293$	−3.46729	−0.202561	−0.101281	−	0.994858i	$-0.532294\pi$
$293$	−3.46729	−0.202561	−0.101281	+	0.994858i	$0.532294\pi$
$294$	−7.61232	−0.443959
$295$	−4.68728	−0.272904
$296$	−8.71854	−0.506755
$297$	1.54943	0.0899070
$298$	5.00328	0.289832
$299$	0.525783	0.0304068
$300$	12.4080	0.716376
$301$	−30.1674	−1.73882
$302$	5.02039	0.288891
$303$	14.9118	0.856659
$304$	0.936792	0.0537287
$305$	−2.52161	−0.144387
$306$	24.1263	1.37921
$307$	−30.7807	−1.75675	−0.878373	−	0.477976i	$-0.841371\pi$
$307$	−30.7807	−1.75675	−0.878373	+	0.477976i	$0.841371\pi$
$308$	−2.96309	−0.168838
$309$	2.92585	0.166446
$310$	4.03675	0.229272
$311$	14.9106	0.845503	0.422752	−	0.906246i	$-0.361064\pi$
$311$	14.9106	0.845503	0.422752	+	0.906246i	$0.361064\pi$
$312$	0.450413	0.0254996
$313$	−4.21595	−0.238299	−0.119150	−	0.992876i	$-0.538017\pi$
$313$	−4.21595	−0.238299	−0.119150	+	0.992876i	$0.538017\pi$
$314$	−15.2459	−0.860373
$315$	−4.93788	−0.278218
$316$	−7.13386	−0.401311
$317$	1.42586	0.0800843	0.0400422	−	0.999198i	$-0.487251\pi$
$317$	1.42586	0.0800843	0.0400422	+	0.999198i	$0.487251\pi$
$318$	−9.25733	−0.519125
$319$	2.61031	0.146149
$320$	−0.429942	−0.0240345
$321$	−23.1321	−1.29111
$322$	−9.49048	−0.528884
$323$	6.20877	0.345465
$324$	−6.66941	−0.370523
$325$	0.841645	0.0466860
$326$	11.5888	0.641846
$327$	−25.7858	−1.42596
$328$	−7.10711	−0.392424
$329$	5.37303	0.296225
$330$	−1.04051	−0.0572781
$331$	−15.9295	−0.875566	−0.437783	−	0.899081i	$-0.644236\pi$
$331$	−15.9295	−0.875566	−0.437783	+	0.899081i	$0.644236\pi$
$332$	−15.7861	−0.866377
$333$	−31.7375	−1.73920
$334$	−14.4829	−0.792467
$335$	−6.26456	−0.342270
$336$	−8.13004	−0.443530
$337$	27.1463	1.47875	0.739377	−	0.673292i	$-0.235120\pi$
$337$	27.1463	1.47875	0.739377	+	0.673292i	$0.235120\pi$
$338$	−12.9694	−0.705445
$339$	43.7906	2.37838
$340$	−2.84953	−0.154537
$341$	8.81790	0.477516
$342$	3.41014	0.184399
$343$	−12.7649	−0.689238
$344$	−9.56175	−0.515535
$345$	−3.33264	−0.179424
$346$	−2.25487	−0.121222
$347$	−13.6423	−0.732358	−0.366179	−	0.930544i	$-0.619334\pi$
$347$	−13.6423	−0.732358	−0.366179	+	0.930544i	$0.619334\pi$
$348$	7.16208	0.383928
$349$	5.37710	0.287830	0.143915	−	0.989590i	$-0.454031\pi$
$349$	5.37710	0.287830	0.143915	+	0.989590i	$0.454031\pi$
$350$	−15.1919	−0.812039
$351$	0.288368	0.0153919
$352$	−0.939170	−0.0500579
$353$	−25.6936	−1.36753	−0.683766	−	0.729701i	$-0.739659\pi$
$353$	−25.6936	−1.36753	−0.683766	+	0.729701i	$0.739659\pi$
$354$	−28.0933	−1.49314
$355$	−0.772858	−0.0410190
$356$	2.62998	0.139389
$357$	−53.8834	−2.85181
$358$	−15.7254	−0.831111
$359$	9.76663	0.515463	0.257731	−	0.966217i	$-0.417025\pi$
$359$	9.76663	0.515463	0.257731	+	0.966217i	$0.417025\pi$
$360$	−1.56509	−0.0824874
$361$	−18.1224	−0.953812
$362$	0.565643	0.0297296
$363$	26.0726	1.36846
$364$	−0.551468	−0.0289048
$365$	2.40788	0.126034
$366$	−15.1133	−0.789986
$367$	−6.84402	−0.357255	−0.178627	−	0.983917i	$-0.557166\pi$
$367$	−6.84402	−0.357255	−0.178627	+	0.983917i	$0.557166\pi$
$368$	−3.00807	−0.156806
$369$	−25.8715	−1.34682
$370$	3.74847	0.194874
$371$	11.3343	0.588448
$372$	24.1943	1.25442
$373$	18.5281	0.959350	0.479675	−	0.877446i	$-0.340755\pi$
$373$	18.5281	0.959350	0.479675	+	0.877446i	$0.340755\pi$
$374$	−6.22453	−0.321863
$375$	−10.8742	−0.561543
$376$	1.70301	0.0878262
$377$	0.485810	0.0250205
$378$	−5.20510	−0.267721
$379$	33.0383	1.69706	0.848532	−	0.529145i	$-0.177487\pi$
$379$	33.0383	1.69706	0.848532	+	0.529145i	$0.177487\pi$
$380$	−0.402767	−0.0206615
$381$	10.1370	0.519333
$382$	12.1006	0.619122
$383$	−8.82681	−0.451029	−0.225515	−	0.974240i	$-0.572406\pi$
$383$	−8.82681	−0.451029	−0.225515	+	0.974240i	$0.572406\pi$
$384$	−2.57686	−0.131500
$385$	1.27396	0.0649269
$386$	1.09328	0.0556465
$387$	−34.8070	−1.76934
$388$	−3.24787	−0.164886
$389$	−17.6604	−0.895419	−0.447710	−	0.894179i	$-0.647760\pi$
$389$	−17.6604	−0.895419	−0.447710	+	0.894179i	$0.647760\pi$
$390$	−0.193651	−0.00980592
$391$	−19.9365	−1.00823
$392$	2.95410	0.149205
$393$	−3.48306	−0.175697
$394$	19.9795	1.00655
$395$	3.06715	0.154325
$396$	−3.41879	−0.171801
$397$	16.7091	0.838607	0.419304	−	0.907846i	$-0.362274\pi$
$397$	16.7091	0.838607	0.419304	+	0.907846i	$0.362274\pi$
$398$	12.1436	0.608705
$399$	−7.61616	−0.381285
$400$	−4.81515	−0.240757
$401$	−21.3786	−1.06760	−0.533798	−	0.845612i	$-0.679236\pi$
$401$	−21.3786	−1.06760	−0.533798	+	0.845612i	$0.679236\pi$
$402$	−37.5467	−1.87266
$403$	1.64112	0.0817500
$404$	−5.78679	−0.287903
$405$	2.86746	0.142485
$406$	−8.76898	−0.435197
$407$	8.18819	0.405873
$408$	−17.0787	−0.845520
$409$	25.2976	1.25089	0.625443	−	0.780270i	$-0.284918\pi$
$409$	25.2976	1.25089	0.625443	+	0.780270i	$0.284918\pi$
$410$	3.05565	0.150908
$411$	−11.9990	−0.591867
$412$	−1.13543	−0.0559386
$413$	34.3963	1.69253
$414$	−10.9501	−0.538166
$415$	6.78713	0.333167
$416$	−0.174791	−0.00856983
$417$	0.484215	0.0237121
$418$	−0.879807	−0.0430328
$419$	−9.90459	−0.483871	−0.241935	−	0.970292i	$-0.577782\pi$
$419$	−9.90459	−0.483871	−0.241935	+	0.970292i	$0.577782\pi$
$420$	3.49545	0.170560
$421$	−18.0686	−0.880609	−0.440304	−	0.897849i	$-0.645129\pi$
$421$	−18.0686	−0.880609	−0.440304	+	0.897849i	$0.645129\pi$
$422$	20.4723	0.996576
$423$	6.19936	0.301423
$424$	3.59248	0.174466
$425$	−31.9134	−1.54802
$426$	−4.63213	−0.224428
$427$	18.5042	0.895479
$428$	8.97683	0.433912
$429$	−0.423014	−0.0204233
$430$	4.11100	0.198250
$431$	−12.4829	−0.601281	−0.300641	−	0.953738i	$-0.597200\pi$
$431$	−12.4829	−0.601281	−0.300641	+	0.953738i	$0.597200\pi$
$432$	−1.64979	−0.0793754
$433$	−0.937072	−0.0450328	−0.0225164	−	0.999746i	$-0.507168\pi$
$433$	−0.937072	−0.0450328	−0.0225164	+	0.999746i	$0.507168\pi$
$434$	−29.6225	−1.42193
$435$	−3.07928	−0.147640
$436$	10.0067	0.479232
$437$	−2.81793	−0.134800
$438$	14.4317	0.689571
$439$	3.32439	0.158664	0.0793322	−	0.996848i	$-0.474721\pi$
$439$	3.32439	0.158664	0.0793322	+	0.996848i	$0.474721\pi$
$440$	0.403789	0.0192499
$441$	10.7536	0.512077
$442$	−1.15846	−0.0551024
$443$	4.73887	0.225151	0.112575	−	0.993643i	$-0.464090\pi$
$443$	4.73887	0.225151	0.112575	+	0.993643i	$0.464090\pi$
$444$	22.4665	1.06621
$445$	−1.13074	−0.0536022
$446$	−5.09721	−0.241360
$447$	−12.8928	−0.609807
$448$	3.15501	0.149060
$449$	−8.76916	−0.413842	−0.206921	−	0.978358i	$-0.566344\pi$
$449$	−8.76916	−0.413842	−0.206921	+	0.978358i	$0.566344\pi$
$450$	−17.5283	−0.826290
$451$	6.67478	0.314303
$452$	−16.9937	−0.799318
$453$	−12.9369	−0.607827
$454$	−22.8126	−1.07065
$455$	0.237099	0.0111154
$456$	−2.41399	−0.113045
$457$	19.5897	0.916366	0.458183	−	0.888858i	$-0.348500\pi$
$457$	19.5897	0.916366	0.458183	+	0.888858i	$0.348500\pi$
$458$	−9.74494	−0.455351
$459$	−10.9343	−0.510369
$460$	1.29329	0.0603002
$461$	−0.988261	−0.0460279	−0.0230139	−	0.999735i	$-0.507326\pi$
$461$	−0.988261	−0.0460279	−0.0230139	+	0.999735i	$0.507326\pi$
$462$	7.63549	0.355235
$463$	9.08129	0.422044	0.211022	−	0.977481i	$-0.432321\pi$
$463$	9.08129	0.422044	0.211022	+	0.977481i	$0.432321\pi$
$464$	−2.77938	−0.129029
$465$	−10.4022	−0.482388
$466$	−12.1643	−0.563499
$467$	−33.4831	−1.54941	−0.774706	−	0.632322i	$-0.782102\pi$
$467$	−33.4831	−1.54941	−0.774706	+	0.632322i	$0.782102\pi$
$468$	−0.636279	−0.0294120
$469$	45.9707	2.12273
$470$	−0.732197	−0.0337737
$471$	39.2865	1.81023
$472$	10.9021	0.501811
$473$	8.98011	0.412906
$474$	18.3830	0.844359
$475$	−4.51079	−0.206969
$476$	20.9105	0.958430
$477$	13.0774	0.598775
$478$	−12.4483	−0.569372
$479$	9.03571	0.412852	0.206426	−	0.978462i	$-0.433817\pi$
$479$	9.03571	0.412852	0.206426	+	0.978462i	$0.433817\pi$
$480$	1.10790	0.0505686
$481$	1.52392	0.0694848
$482$	11.2765	0.513630
$483$	24.4557	1.11277
$484$	−10.1180	−0.459907
$485$	1.39640	0.0634072
$486$	22.1355	1.00409
$487$	0.0148551	0.000673149 0	0.000336575	−	1.00000i	$-0.499893\pi$
$487$	0.0148551	0.000673149 0	0.000336575		1.00000i	$0.499893\pi$
$488$	5.86500	0.265496
$489$	−29.8629	−1.35044
$490$	−1.27009	−0.0573770
$491$	1.56381	0.0705739	0.0352869	−	0.999377i	$-0.488765\pi$
$491$	1.56381	0.0705739	0.0352869	+	0.999377i	$0.488765\pi$
$492$	18.3141	0.825662
$493$	−18.4209	−0.829635
$494$	−0.163743	−0.00736714
$495$	1.46988	0.0660664
$496$	−9.38904	−0.421580
$497$	5.67140	0.254397
$498$	40.6788	1.82286
$499$	27.4848	1.23039	0.615195	−	0.788375i	$-0.289077\pi$
$499$	27.4848	1.23039	0.615195	+	0.788375i	$0.289077\pi$
$500$	4.21995	0.188722
$501$	37.3204	1.66735
$502$	17.3614	0.774875
$503$	−4.00403	−0.178531	−0.0892655	−	0.996008i	$-0.528452\pi$
$503$	−4.00403	−0.178531	−0.0892655	+	0.996008i	$0.528452\pi$
$504$	11.4850	0.511581
$505$	2.48798	0.110714
$506$	2.82508	0.125590
$507$	33.4205	1.48426
$508$	−3.93384	−0.174536
$509$	−5.11126	−0.226553	−0.113276	−	0.993564i	$-0.536135\pi$
$509$	−5.11126	−0.226553	−0.113276	+	0.993564i	$0.536135\pi$
$510$	7.34285	0.325147
$511$	−17.6696	−0.781655
$512$	1.00000	0.0441942
$513$	−1.54551	−0.0682358
$514$	−9.25982	−0.408433
$515$	0.488169	0.0215113
$516$	24.6393	1.08469
$517$	−1.59942	−0.0703423
$518$	−27.5071	−1.20859
$519$	5.81049	0.255052
$520$	0.0751500	0.00329555
$521$	0.770484	0.0337555	0.0168778	−	0.999858i	$-0.494627\pi$
$521$	0.770484	0.0337555	0.0168778	+	0.999858i	$0.494627\pi$
$522$	−10.1176	−0.442834
$523$	35.5960	1.55650	0.778251	−	0.627953i	$-0.216107\pi$
$523$	35.5960	1.55650	0.778251	+	0.627953i	$0.216107\pi$
$524$	1.35166	0.0590477
$525$	39.1474	1.70853
$526$	−9.43288	−0.411293
$527$	−62.2277	−2.71068
$528$	2.42011	0.105322
$529$	−13.9515	−0.606589
$530$	−1.54456	−0.0670913
$531$	39.6862	1.72224
$532$	2.95559	0.128141
$533$	1.24226	0.0538082
$534$	−6.77710	−0.293274
$535$	−3.85952	−0.166862
$536$	14.5707	0.629359
$537$	40.5221	1.74866
$538$	7.27251	0.313540
$539$	−2.77440	−0.119502
$540$	0.709313	0.0305240
$541$	−31.0727	−1.33592	−0.667961	−	0.744197i	$-0.732833\pi$
$541$	−31.0727	−1.33592	−0.667961	+	0.744197i	$0.732833\pi$
$542$	−28.1830	−1.21057
$543$	−1.45759	−0.0625510
$544$	6.62770	0.284160
$545$	−4.30229	−0.184290
$546$	1.42106	0.0608156
$547$	24.0392	1.02784	0.513921	−	0.857837i	$-0.328192\pi$
$547$	24.0392	1.02784	0.513921	+	0.857837i	$0.328192\pi$
$548$	4.65644	0.198913
$549$	21.3500	0.911194
$550$	4.52224	0.192829
$551$	−2.60370	−0.110921
$552$	7.75138	0.329921
$553$	−22.5074	−0.957113
$554$	−23.1323	−0.982797
$555$	−9.65929	−0.410014
$556$	−0.187908	−0.00796909
$557$	−18.6460	−0.790057	−0.395029	−	0.918669i	$-0.629265\pi$
$557$	−18.6460	−0.790057	−0.395029	+	0.918669i	$0.629265\pi$
$558$	−34.1783	−1.44688
$559$	1.67131	0.0706888
$560$	−1.35647	−0.0573215
$561$	16.0398	0.677200
$562$	−29.7464	−1.25477
$563$	4.58219	0.193116	0.0965582	−	0.995327i	$-0.469217\pi$
$563$	4.58219	0.193116	0.0965582	+	0.995327i	$0.469217\pi$
$564$	−4.38843	−0.184786
$565$	7.30633	0.307380
$566$	12.9932	0.546145
$567$	−21.0421	−0.883684
$568$	1.79758	0.0754250
$569$	−16.1142	−0.675544	−0.337772	−	0.941228i	$-0.609673\pi$
$569$	−16.1142	−0.675544	−0.337772	+	0.941228i	$0.609673\pi$
$570$	1.03787	0.0434718
$571$	−22.1512	−0.927000	−0.463500	−	0.886097i	$-0.653407\pi$
$571$	−22.1512	−0.927000	−0.463500	+	0.886097i	$0.653407\pi$
$572$	0.164158	0.00686381
$573$	−31.1817	−1.30263
$574$	−22.4230	−0.935919
$575$	14.4843	0.604036
$576$	3.64023	0.151676
$577$	13.0436	0.543013	0.271506	−	0.962437i	$-0.412478\pi$
$577$	13.0436	0.543013	0.271506	+	0.962437i	$0.412478\pi$
$578$	26.9264	1.11999
$579$	−2.81723	−0.117080
$580$	1.19497	0.0496185
$581$	−49.8055	−2.06628
$582$	8.36933	0.346920
$583$	−3.37395	−0.139735
$584$	−5.60047	−0.231749
$585$	0.273563	0.0113105
$586$	−3.46729	−0.143232
$587$	−18.8598	−0.778428	−0.389214	−	0.921147i	$-0.627253\pi$
$587$	−18.8598	−0.778428	−0.389214	+	0.921147i	$0.627253\pi$
$588$	−7.61232	−0.313927
$589$	−8.79558	−0.362416
$590$	−4.68728	−0.192972
$591$	−51.4845	−2.11779
$592$	−8.71854	−0.358330
$593$	−27.5971	−1.13328	−0.566638	−	0.823967i	$-0.691756\pi$
$593$	−27.5971	−1.13328	−0.566638	+	0.823967i	$0.691756\pi$
$594$	1.54943	0.0635739
$595$	−8.99029	−0.368566
$596$	5.00328	0.204942
$597$	−31.2925	−1.28072
$598$	0.525783	0.0215008
$599$	−31.8690	−1.30213	−0.651066	−	0.759021i	$-0.725678\pi$
$599$	−31.8690	−1.30213	−0.651066	+	0.759021i	$0.725678\pi$
$600$	12.4080	0.506554
$601$	−3.36148	−0.137117	−0.0685587	−	0.997647i	$-0.521840\pi$
$601$	−3.36148	−0.137117	−0.0685587	+	0.997647i	$0.521840\pi$
$602$	−30.1674	−1.22953
$603$	53.0407	2.15999
$604$	5.02039	0.204277
$605$	4.35014	0.176858
$606$	14.9118	0.605749
$607$	−26.3041	−1.06765	−0.533826	−	0.845594i	$-0.679246\pi$
$607$	−26.3041	−1.06765	−0.533826	+	0.845594i	$0.679246\pi$
$608$	0.936792	0.0379919
$609$	22.5965	0.915655
$610$	−2.52161	−0.102097
$611$	−0.297671	−0.0120425
$612$	24.1263	0.975250
$613$	−10.6452	−0.429956	−0.214978	−	0.976619i	$-0.568968\pi$
$613$	−10.6452	−0.429956	−0.214978	+	0.976619i	$0.568968\pi$
$614$	−30.7807	−1.24221
$615$	−7.87399	−0.317510
$616$	−2.96309	−0.119386
$617$	14.5930	0.587493	0.293746	−	0.955883i	$-0.405098\pi$
$617$	14.5930	0.587493	0.293746	+	0.955883i	$0.405098\pi$
$618$	2.92585	0.117695
$619$	8.04386	0.323310	0.161655	−	0.986847i	$-0.448317\pi$
$619$	8.04386	0.323310	0.161655	+	0.986847i	$0.448317\pi$
$620$	4.03675	0.162120
$621$	4.96267	0.199145
$622$	14.9106	0.597861
$623$	8.29761	0.332437
$624$	0.450413	0.0180309
$625$	22.2614	0.890457
$626$	−4.21595	−0.168503
$627$	2.26714	0.0905410
$628$	−15.2459	−0.608376
$629$	−57.7838	−2.30399
$630$	−4.93788	−0.196730
$631$	−14.6628	−0.583718	−0.291859	−	0.956461i	$-0.594274\pi$
$631$	−14.6628	−0.583718	−0.291859	+	0.956461i	$0.594274\pi$
$632$	−7.13386	−0.283770
$633$	−52.7543	−2.09680
$634$	1.42586	0.0566282
$635$	1.69133	0.0671182
$636$	−9.25733	−0.367077
$637$	−0.516350	−0.0204585
$638$	2.61031	0.103343
$639$	6.54362	0.258862
$640$	−0.429942	−0.0169950
$641$	12.0548	0.476137	0.238069	−	0.971248i	$-0.423486\pi$
$641$	12.0548	0.476137	0.238069	+	0.971248i	$0.423486\pi$
$642$	−23.1321	−0.912950
$643$	−18.0296	−0.711017	−0.355508	−	0.934673i	$-0.615692\pi$
$643$	−18.0296	−0.711017	−0.355508	+	0.934673i	$0.615692\pi$
$644$	−9.49048	−0.373977
$645$	−10.5935	−0.417119
$646$	6.20877	0.244281
$647$	35.8770	1.41047	0.705236	−	0.708973i	$-0.250841\pi$
$647$	35.8770	1.41047	0.705236	+	0.708973i	$0.250841\pi$
$648$	−6.66941	−0.261999
$649$	−10.2389	−0.401914
$650$	0.841645	0.0330120
$651$	76.3333	2.99174
$652$	11.5888	0.453854
$653$	24.7106	0.967001	0.483500	−	0.875344i	$-0.339365\pi$
$653$	24.7106	0.967001	0.483500	+	0.875344i	$0.339365\pi$
$654$	−25.7858	−1.00830
$655$	−0.581138	−0.0227069
$656$	−7.10711	−0.277486
$657$	−20.3870	−0.795373
$658$	5.37303	0.209462
$659$	23.0553	0.898108	0.449054	−	0.893505i	$-0.351761\pi$
$659$	23.0553	0.898108	0.449054	+	0.893505i	$0.351761\pi$
$660$	−1.04051	−0.0405018
$661$	−26.2121	−1.01953	−0.509766	−	0.860313i	$-0.670268\pi$
$661$	−26.2121	−1.01953	−0.509766	+	0.860313i	$0.670268\pi$
$662$	−15.9295	−0.619118
$663$	2.98520	0.115935
$664$	−15.7861	−0.612621
$665$	−1.27073	−0.0492769
$666$	−31.7375	−1.22980
$667$	8.36055	0.323722
$668$	−14.4829	−0.560359
$669$	13.1348	0.507822
$670$	−6.26456	−0.242021
$671$	−5.50823	−0.212643
$672$	−8.13004	−0.313623
$673$	−28.5789	−1.10164	−0.550818	−	0.834626i	$-0.685684\pi$
$673$	−28.5789	−1.10164	−0.550818	+	0.834626i	$0.685684\pi$
$674$	27.1463	1.04564
$675$	7.94397	0.305764
$676$	−12.9694	−0.498825
$677$	−26.5917	−1.02200	−0.511000	−	0.859581i	$-0.670725\pi$
$677$	−26.5917	−1.02200	−0.511000	+	0.859581i	$0.670725\pi$
$678$	43.7906	1.68177
$679$	−10.2471	−0.393247
$680$	−2.84953	−0.109274
$681$	58.7850	2.25265
$682$	8.81790	0.337655
$683$	28.3267	1.08389	0.541946	−	0.840413i	$-0.317688\pi$
$683$	28.3267	1.08389	0.541946	+	0.840413i	$0.317688\pi$
$684$	3.41014	0.130390
$685$	−2.00200	−0.0764925
$686$	−12.7649	−0.487365
$687$	25.1114	0.958060
$688$	−9.56175	−0.364538
$689$	−0.627932	−0.0239223
$690$	−3.33264	−0.126872
$691$	−6.46984	−0.246124	−0.123062	−	0.992399i	$-0.539271\pi$
$691$	−6.46984	−0.246124	−0.123062	+	0.992399i	$0.539271\pi$
$692$	−2.25487	−0.0857172
$693$	−10.7863	−0.409739
$694$	−13.6423	−0.517855
$695$	0.0807898	0.00306453
$696$	7.16208	0.271478
$697$	−47.1038	−1.78418
$698$	5.37710	0.203526
$699$	31.3457	1.18560
$700$	−15.1919	−0.574198
$701$	−25.9667	−0.980750	−0.490375	−	0.871511i	$-0.663140\pi$
$701$	−25.9667	−0.980750	−0.490375	+	0.871511i	$0.663140\pi$
$702$	0.288368	0.0108837
$703$	−8.16746	−0.308042
$704$	−0.939170	−0.0353963
$705$	1.88677	0.0710600
$706$	−25.6936	−0.966992
$707$	−18.2574	−0.686640
$708$	−28.0933	−1.05581
$709$	8.53492	0.320536	0.160268	−	0.987074i	$-0.448764\pi$
$709$	8.53492	0.320536	0.160268	+	0.987074i	$0.448764\pi$
$710$	−0.772858	−0.0290048
$711$	−25.9689	−0.973910
$712$	2.62998	0.0985626
$713$	28.2429	1.05770
$714$	−53.8834	−2.01654
$715$	−0.0705786	−0.00263949
$716$	−15.7254	−0.587684
$717$	32.0776	1.19796
$718$	9.76663	0.364487
$719$	−12.0840	−0.450658	−0.225329	−	0.974283i	$-0.572346\pi$
$719$	−12.0840	−0.450658	−0.225329	+	0.974283i	$0.572346\pi$
$720$	−1.56509	−0.0583274
$721$	−3.58229	−0.133412
$722$	−18.1224	−0.674447
$723$	−29.0580	−1.08068
$724$	0.565643	0.0210220
$725$	13.3831	0.497037
$726$	26.0726	0.967645
$727$	13.2435	0.491175	0.245588	−	0.969374i	$-0.421019\pi$
$727$	13.2435	0.491175	0.245588	+	0.969374i	$0.421019\pi$
$728$	−0.551468	−0.0204387
$729$	−37.0320	−1.37156
$730$	2.40788	0.0891196
$731$	−63.3724	−2.34391
$732$	−15.1133	−0.558604
$733$	−6.20841	−0.229313	−0.114656	−	0.993405i	$-0.536577\pi$
$733$	−6.20841	−0.229313	−0.114656	+	0.993405i	$0.536577\pi$
$734$	−6.84402	−0.252617
$735$	3.27286	0.120721
$736$	−3.00807	−0.110879
$737$	−13.6844	−0.504070
$738$	−25.8715	−0.952344
$739$	48.9634	1.80115	0.900574	−	0.434703i	$-0.143146\pi$
$739$	48.9634	1.80115	0.900574	+	0.434703i	$0.143146\pi$
$740$	3.74847	0.137796
$741$	0.421943	0.0155005
$742$	11.3343	0.416096
$743$	33.1504	1.21617	0.608085	−	0.793872i	$-0.291938\pi$
$743$	33.1504	1.21617	0.608085	+	0.793872i	$0.291938\pi$
$744$	24.1943	0.887006
$745$	−2.15112	−0.0788110
$746$	18.5281	0.678363
$747$	−57.4652	−2.10254
$748$	−6.22453	−0.227591
$749$	28.3220	1.03486
$750$	−10.8742	−0.397071
$751$	45.8850	1.67437	0.837183	−	0.546923i	$-0.184201\pi$
$751$	45.8850	1.67437	0.837183	+	0.546923i	$0.184201\pi$
$752$	1.70301	0.0621025
$753$	−44.7379	−1.63034
$754$	0.485810	0.0176922
$755$	−2.15848	−0.0785550
$756$	−5.20510	−0.189308
$757$	−23.9451	−0.870298	−0.435149	−	0.900358i	$-0.643304\pi$
$757$	−23.9451	−0.870298	−0.435149	+	0.900358i	$0.643304\pi$
$758$	33.0383	1.20000
$759$	−7.27986	−0.264242
$760$	−0.402767	−0.0146099
$761$	−12.3998	−0.449492	−0.224746	−	0.974417i	$-0.572155\pi$
$761$	−12.3998	−0.449492	−0.224746	+	0.974417i	$0.572155\pi$
$762$	10.1370	0.367224
$763$	31.5711	1.14295
$764$	12.1006	0.437786
$765$	−10.3729	−0.375034
$766$	−8.82681	−0.318926
$767$	−1.90559	−0.0688069
$768$	−2.57686	−0.0929846
$769$	39.7849	1.43468	0.717341	−	0.696722i	$-0.245359\pi$
$769$	39.7849	1.43468	0.717341	+	0.696722i	$0.245359\pi$
$770$	1.27396	0.0459103
$771$	23.8613	0.859344
$772$	1.09328	0.0393480
$773$	4.66838	0.167910	0.0839550	−	0.996470i	$-0.473245\pi$
$773$	4.66838	0.167910	0.0839550	+	0.996470i	$0.473245\pi$
$774$	−34.8070	−1.25111
$775$	45.2096	1.62398
$776$	−3.24787	−0.116592
$777$	70.8820	2.54288
$778$	−17.6604	−0.633157
$779$	−6.65788	−0.238543
$780$	−0.193651	−0.00693383
$781$	−1.68824	−0.0604099
$782$	−19.9365	−0.712929
$783$	4.58538	0.163868
$784$	2.95410	0.105504
$785$	6.55484	0.233952
$786$	−3.48306	−0.124237
$787$	3.21874	0.114736	0.0573679	−	0.998353i	$-0.481729\pi$
$787$	3.21874	0.114736	0.0573679	+	0.998353i	$0.481729\pi$
$788$	19.9795	0.711741
$789$	24.3073	0.865361
$790$	3.06715	0.109124
$791$	−53.6155	−1.90635
$792$	−3.41879	−0.121482
$793$	−1.02515	−0.0364041
$794$	16.7091	0.592985
$795$	3.98012	0.141160
$796$	12.1436	0.430420
$797$	6.78726	0.240417	0.120209	−	0.992749i	$-0.461644\pi$
$797$	6.78726	0.240417	0.120209	+	0.992749i	$0.461644\pi$
$798$	−7.61616	−0.269609
$799$	11.2871	0.399307
$800$	−4.81515	−0.170241
$801$	9.57372	0.338271
$802$	−21.3786	−0.754904
$803$	5.25979	0.185614
$804$	−37.5467	−1.32417
$805$	4.08036	0.143814
$806$	1.64112	0.0578060
$807$	−18.7403	−0.659689
$808$	−5.78679	−0.203578
$809$	−21.1237	−0.742671	−0.371336	−	0.928499i	$-0.621100\pi$
$809$	−21.1237	−0.742671	−0.371336	+	0.928499i	$0.621100\pi$
$810$	2.86746	0.100752
$811$	13.7126	0.481514	0.240757	−	0.970585i	$-0.422604\pi$
$811$	13.7126	0.481514	0.240757	+	0.970585i	$0.422604\pi$
$812$	−8.76898	−0.307731
$813$	72.6239	2.54703
$814$	8.18819	0.286996
$815$	−4.98253	−0.174530
$816$	−17.0787	−0.597873
$817$	−8.95738	−0.313379
$818$	25.2976	0.884509
$819$	−2.00747	−0.0701466
$820$	3.05565	0.106708
$821$	−5.04464	−0.176059	−0.0880295	−	0.996118i	$-0.528057\pi$
$821$	−5.04464	−0.176059	−0.0880295	+	0.996118i	$0.528057\pi$
$822$	−11.9990	−0.418513
$823$	26.7851	0.933670	0.466835	−	0.884344i	$-0.345394\pi$
$823$	26.7851	0.933670	0.466835	+	0.884344i	$0.345394\pi$
$824$	−1.13543	−0.0395546
$825$	−11.6532	−0.405713
$826$	34.3963	1.19680
$827$	40.2594	1.39996	0.699978	−	0.714165i	$-0.253193\pi$
$827$	40.2594	1.39996	0.699978	+	0.714165i	$0.253193\pi$
$828$	−10.9501	−0.380541
$829$	−32.3136	−1.12230	−0.561149	−	0.827715i	$-0.689641\pi$
$829$	−32.3136	−1.12230	−0.561149	+	0.827715i	$0.689641\pi$
$830$	6.78713	0.235585
$831$	59.6088	2.06781
$832$	−0.174791	−0.00605979
$833$	19.5789	0.678368
$834$	0.484215	0.0167670
$835$	6.22679	0.215487
$836$	−0.879807	−0.0304288
$837$	15.4899	0.535410
$838$	−9.90459	−0.342148
$839$	2.17498	0.0750887	0.0375443	−	0.999295i	$-0.488046\pi$
$839$	2.17498	0.0750887	0.0375443	+	0.999295i	$0.488046\pi$
$840$	3.49545	0.120604
$841$	−21.2751	−0.733622
$842$	−18.0686	−0.622684
$843$	76.6523	2.64005
$844$	20.4723	0.704686
$845$	5.57611	0.191824
$846$	6.19936	0.213138
$847$	−31.9223	−1.09686
$848$	3.59248	0.123366
$849$	−33.4817	−1.14909
$850$	−31.9134	−1.09462
$851$	26.2259	0.899013
$852$	−4.63213	−0.158694
$853$	−14.4019	−0.493110	−0.246555	−	0.969129i	$-0.579299\pi$
$853$	−14.4019	−0.493110	−0.246555	+	0.969129i	$0.579299\pi$
$854$	18.5042	0.633199
$855$	−1.46616	−0.0501417
$856$	8.97683	0.306822
$857$	−13.6780	−0.467232	−0.233616	−	0.972329i	$-0.575056\pi$
$857$	−13.6780	−0.467232	−0.233616	+	0.972329i	$0.575056\pi$
$858$	−0.423014	−0.0144415
$859$	−27.4644	−0.937072	−0.468536	−	0.883444i	$-0.655218\pi$
$859$	−27.4644	−0.937072	−0.468536	+	0.883444i	$0.655218\pi$
$860$	4.11100	0.140184
$861$	57.7811	1.96917
$862$	−12.4829	−0.425170
$863$	−26.4216	−0.899402	−0.449701	−	0.893179i	$-0.648469\pi$
$863$	−26.4216	−0.899402	−0.449701	+	0.893179i	$0.648469\pi$
$864$	−1.64979	−0.0561269
$865$	0.969463	0.0329627
$866$	−0.937072	−0.0318430
$867$	−69.3856	−2.35646
$868$	−29.6225	−1.00545
$869$	6.69991	0.227279
$870$	−3.07928	−0.104397
$871$	−2.54683	−0.0862959
$872$	10.0067	0.338868
$873$	−11.8230	−0.400148
$874$	−2.81793	−0.0953180
$875$	13.3140	0.450095
$876$	14.4317	0.487600
$877$	43.7623	1.47775	0.738874	−	0.673844i	$-0.235358\pi$
$877$	43.7623	1.47775	0.738874	+	0.673844i	$0.235358\pi$
$878$	3.32439	0.112193
$879$	8.93474	0.301361
$880$	0.403789	0.0136117
$881$	−44.8819	−1.51211	−0.756054	−	0.654509i	$-0.772875\pi$
$881$	−44.8819	−1.51211	−0.756054	+	0.654509i	$0.772875\pi$
$882$	10.7536	0.362093
$883$	−40.6244	−1.36712	−0.683560	−	0.729894i	$-0.739569\pi$
$883$	−40.6244	−1.36712	−0.683560	+	0.729894i	$0.739569\pi$
$884$	−1.15846	−0.0389633
$885$	12.0785	0.406014
$886$	4.73887	0.159206
$887$	−41.2970	−1.38662	−0.693310	−	0.720640i	$-0.743848\pi$
$887$	−41.2970	−1.38662	−0.693310	+	0.720640i	$0.743848\pi$
$888$	22.4665	0.753926
$889$	−12.4113	−0.416262
$890$	−1.13074	−0.0379024
$891$	6.26371	0.209842
$892$	−5.09721	−0.170667
$893$	1.59537	0.0533870
$894$	−12.8928	−0.431199
$895$	6.76099	0.225995
$896$	3.15501	0.105402
$897$	−1.35487	−0.0452378
$898$	−8.76916	−0.292631
$899$	26.0957	0.870341
$900$	−17.5283	−0.584275
$901$	23.8098	0.793221
$902$	6.67478	0.222246
$903$	77.7374	2.58694
$904$	−16.9937	−0.565203
$905$	−0.243194	−0.00808404
$906$	−12.9369	−0.429798
$907$	36.2932	1.20510	0.602548	−	0.798082i	$-0.294152\pi$
$907$	36.2932	1.20510	0.602548	+	0.798082i	$0.294152\pi$
$908$	−22.8126	−0.757063
$909$	−21.0652	−0.698690
$910$	0.237099	0.00785976
$911$	−46.9902	−1.55686	−0.778428	−	0.627734i	$-0.783983\pi$
$911$	−46.9902	−1.55686	−0.778428	+	0.627734i	$0.783983\pi$
$912$	−2.41399	−0.0799351
$913$	14.8259	0.490665
$914$	19.5897	0.647969
$915$	6.49785	0.214812
$916$	−9.74494	−0.321982
$917$	4.26452	0.140827
$918$	−10.9343	−0.360885
$919$	−17.1305	−0.565083	−0.282541	−	0.959255i	$-0.591177\pi$
$919$	−17.1305	−0.565083	−0.282541	+	0.959255i	$0.591177\pi$
$920$	1.29329	0.0426387
$921$	79.3176	2.61360
$922$	−0.988261	−0.0325466
$923$	−0.314202	−0.0103421
$924$	7.63549	0.251189
$925$	41.9811	1.38033
$926$	9.08129	0.298430
$927$	−4.13323	−0.135753
$928$	−2.77938	−0.0912376
$929$	7.41814	0.243381	0.121691	−	0.992568i	$-0.461168\pi$
$929$	7.41814	0.243381	0.121691	+	0.992568i	$0.461168\pi$
$930$	−10.4022	−0.341100
$931$	2.76738	0.0906972
$932$	−12.1643	−0.398454
$933$	−38.4226	−1.25790
$934$	−33.4831	−1.09560
$935$	2.67619	0.0875208
$936$	−0.636279	−0.0207974
$937$	21.7232	0.709667	0.354833	−	0.934930i	$-0.384538\pi$
$937$	21.7232	0.709667	0.354833	+	0.934930i	$0.384538\pi$
$938$	45.9707	1.50100
$939$	10.8639	0.354531
$940$	−0.732197	−0.0238816
$941$	−51.2216	−1.66978	−0.834888	−	0.550420i	$-0.814467\pi$
$941$	−51.2216	−1.66978	−0.834888	+	0.550420i	$0.814467\pi$
$942$	39.2865	1.28002
$943$	21.3787	0.696185
$944$	10.9021	0.354834
$945$	2.23789	0.0727986
$946$	8.98011	0.291969
$947$	32.9520	1.07080	0.535398	−	0.844600i	$-0.320162\pi$
$947$	32.9520	1.07080	0.535398	+	0.844600i	$0.320162\pi$
$948$	18.3830	0.597052
$949$	0.978912	0.0317768
$950$	−4.51079	−0.146350
$951$	−3.67425	−0.119146
$952$	20.9105	0.677712
$953$	−1.19925	−0.0388475	−0.0194238	−	0.999811i	$-0.506183\pi$
$953$	−1.19925	−0.0388475	−0.0194238	+	0.999811i	$0.506183\pi$
$954$	13.0774	0.423398
$955$	−5.20258	−0.168351
$956$	−12.4483	−0.402607
$957$	−6.72641	−0.217434
$958$	9.03571	0.291931
$959$	14.6911	0.474401
$960$	1.10790	0.0357574
$961$	57.1541	1.84368
$962$	1.52392	0.0491332
$963$	32.6777	1.05303
$964$	11.2765	0.363191
$965$	−0.470047	−0.0151314
$966$	24.4557	0.786849
$967$	49.2448	1.58361	0.791803	−	0.610776i	$-0.209143\pi$
$967$	49.2448	1.58361	0.791803	+	0.610776i	$0.209143\pi$
$968$	−10.1180	−0.325204
$969$	−15.9992	−0.513967
$970$	1.39640	0.0448356
$971$	−15.8702	−0.509300	−0.254650	−	0.967033i	$-0.581960\pi$
$971$	−15.8702	−0.509300	−0.254650	+	0.967033i	$0.581960\pi$
$972$	22.1355	0.709998
$973$	−0.592853	−0.0190060
$974$	0.0148551	0.000475988 0
$975$	−2.16880	−0.0694573
$976$	5.86500	0.187734
$977$	−42.7687	−1.36829	−0.684146	−	0.729345i	$-0.739825\pi$
$977$	−42.7687	−1.36829	−0.684146	+	0.729345i	$0.739825\pi$
$978$	−29.8629	−0.954909
$979$	−2.46999	−0.0789414
$980$	−1.27009	−0.0405716
$981$	36.4266	1.16301
$982$	1.56381	0.0499033
$983$	0.291638	0.00930180	0.00465090	−	0.999989i	$-0.498520\pi$
$983$	0.291638	0.00930180	0.00465090	+	0.999989i	$0.498520\pi$
$984$	18.3141	0.583831
$985$	−8.59004	−0.273701
$986$	−18.4209	−0.586640
$987$	−13.8456	−0.440709
$988$	−0.163743	−0.00520935
$989$	28.7624	0.914590
$990$	1.46988	0.0467160
$991$	−54.5844	−1.73393	−0.866965	−	0.498370i	$-0.833932\pi$
$991$	−54.5844	−1.73393	−0.866965	+	0.498370i	$0.833932\pi$
$992$	−9.38904	−0.298102
$993$	41.0482	1.30263
$994$	5.67140	0.179886
$995$	−5.22106	−0.165519
$996$	40.6788	1.28896
$997$	23.1076	0.731824	0.365912	−	0.930649i	$-0.380757\pi$
$997$	23.1076	0.731824	0.365912	+	0.930649i	$0.380757\pi$
$998$	27.4848	0.870017
$999$	14.3837	0.455081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.8	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.8	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.57686 q^{3} +1.00000 q^{4} -0.429942 q^{5} -2.57686 q^{6} +3.15501 q^{7} +1.00000 q^{8} +3.64023 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.57686 q^{3} +1.00000 q^{4} -0.429942 q^{5} -2.57686 q^{6} +3.15501 q^{7} +1.00000 q^{8} +3.64023 q^{9} -0.429942 q^{10} -0.939170 q^{11} -2.57686 q^{12} -0.174791 q^{13} +3.15501 q^{14} +1.10790 q^{15} +1.00000 q^{16} +6.62770 q^{17} +3.64023 q^{18} +0.936792 q^{19} -0.429942 q^{20} -8.13004 q^{21} -0.939170 q^{22} -3.00807 q^{23} -2.57686 q^{24} -4.81515 q^{25} -0.174791 q^{26} -1.64979 q^{27} +3.15501 q^{28} -2.77938 q^{29} +1.10790 q^{30} -9.38904 q^{31} +1.00000 q^{32} +2.42011 q^{33} +6.62770 q^{34} -1.35647 q^{35} +3.64023 q^{36} -8.71854 q^{37} +0.936792 q^{38} +0.450413 q^{39} -0.429942 q^{40} -7.10711 q^{41} -8.13004 q^{42} -9.56175 q^{43} -0.939170 q^{44} -1.56509 q^{45} -3.00807 q^{46} +1.70301 q^{47} -2.57686 q^{48} +2.95410 q^{49} -4.81515 q^{50} -17.0787 q^{51} -0.174791 q^{52} +3.59248 q^{53} -1.64979 q^{54} +0.403789 q^{55} +3.15501 q^{56} -2.41399 q^{57} -2.77938 q^{58} +10.9021 q^{59} +1.10790 q^{60} +5.86500 q^{61} -9.38904 q^{62} +11.4850 q^{63} +1.00000 q^{64} +0.0751500 q^{65} +2.42011 q^{66} +14.5707 q^{67} +6.62770 q^{68} +7.75138 q^{69} -1.35647 q^{70} +1.79758 q^{71} +3.64023 q^{72} -5.60047 q^{73} -8.71854 q^{74} +12.4080 q^{75} +0.936792 q^{76} -2.96309 q^{77} +0.450413 q^{78} -7.13386 q^{79} -0.429942 q^{80} -6.66941 q^{81} -7.10711 q^{82} -15.7861 q^{83} -8.13004 q^{84} -2.84953 q^{85} -9.56175 q^{86} +7.16208 q^{87} -0.939170 q^{88} +2.62998 q^{89} -1.56509 q^{90} -0.551468 q^{91} -3.00807 q^{92} +24.1943 q^{93} +1.70301 q^{94} -0.402767 q^{95} -2.57686 q^{96} -3.24787 q^{97} +2.95410 q^{98} -3.41879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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