LMFDB - Embedded newform 6026.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.25480 q^{3} +1.00000 q^{4} +3.43025 q^{5} -3.25480 q^{6} +2.34297 q^{7} +1.00000 q^{8} +7.59373 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.25480 q^{3} +1.00000 q^{4} +3.43025 q^{5} -3.25480 q^{6} +2.34297 q^{7} +1.00000 q^{8} +7.59373 q^{9} +3.43025 q^{10} +4.43053 q^{11} -3.25480 q^{12} -7.18545 q^{13} +2.34297 q^{14} -11.1648 q^{15} +1.00000 q^{16} -5.19562 q^{17} +7.59373 q^{18} +2.28786 q^{19} +3.43025 q^{20} -7.62590 q^{21} +4.43053 q^{22} +1.00000 q^{23} -3.25480 q^{24} +6.76659 q^{25} -7.18545 q^{26} -14.9517 q^{27} +2.34297 q^{28} +6.34711 q^{29} -11.1648 q^{30} -4.21714 q^{31} +1.00000 q^{32} -14.4205 q^{33} -5.19562 q^{34} +8.03696 q^{35} +7.59373 q^{36} +4.13634 q^{37} +2.28786 q^{38} +23.3872 q^{39} +3.43025 q^{40} +5.21322 q^{41} -7.62590 q^{42} +4.75055 q^{43} +4.43053 q^{44} +26.0484 q^{45} +1.00000 q^{46} +10.2740 q^{47} -3.25480 q^{48} -1.51049 q^{49} +6.76659 q^{50} +16.9107 q^{51} -7.18545 q^{52} +2.24465 q^{53} -14.9517 q^{54} +15.1978 q^{55} +2.34297 q^{56} -7.44651 q^{57} +6.34711 q^{58} -12.7867 q^{59} -11.1648 q^{60} +13.0865 q^{61} -4.21714 q^{62} +17.7919 q^{63} +1.00000 q^{64} -24.6479 q^{65} -14.4205 q^{66} -14.6034 q^{67} -5.19562 q^{68} -3.25480 q^{69} +8.03696 q^{70} +14.6374 q^{71} +7.59373 q^{72} +1.57445 q^{73} +4.13634 q^{74} -22.0239 q^{75} +2.28786 q^{76} +10.3806 q^{77} +23.3872 q^{78} -8.12653 q^{79} +3.43025 q^{80} +25.8835 q^{81} +5.21322 q^{82} -0.119214 q^{83} -7.62590 q^{84} -17.8222 q^{85} +4.75055 q^{86} -20.6586 q^{87} +4.43053 q^{88} +17.3240 q^{89} +26.0484 q^{90} -16.8353 q^{91} +1.00000 q^{92} +13.7259 q^{93} +10.2740 q^{94} +7.84791 q^{95} -3.25480 q^{96} +6.80022 q^{97} -1.51049 q^{98} +33.6443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−3.25480	−1.87916	−0.939580	−	0.342329i	$-0.888784\pi$
$3$	−3.25480	−1.87916	−0.939580	+	0.342329i	$0.888784\pi$
$4$	1.00000	0.500000
$5$	3.43025	1.53405	0.767026	−	0.641616i	$-0.221736\pi$
$5$	3.43025	1.53405	0.767026	+	0.641616i	$0.221736\pi$
$6$	−3.25480	−1.32877
$7$	2.34297	0.885559	0.442780	−	0.896630i	$-0.353992\pi$
$7$	2.34297	0.885559	0.442780	+	0.896630i	$0.353992\pi$
$8$	1.00000	0.353553
$9$	7.59373	2.53124
$10$	3.43025	1.08474
$11$	4.43053	1.33586	0.667928	−	0.744226i	$-0.267181\pi$
$11$	4.43053	1.33586	0.667928	+	0.744226i	$0.267181\pi$
$12$	−3.25480	−0.939580
$13$	−7.18545	−1.99289	−0.996443	−	0.0842697i	$-0.973144\pi$
$13$	−7.18545	−1.99289	−0.996443	+	0.0842697i	$0.973144\pi$
$14$	2.34297	0.626185
$15$	−11.1648	−2.88273
$16$	1.00000	0.250000
$17$	−5.19562	−1.26012	−0.630061	−	0.776546i	$-0.716970\pi$
$17$	−5.19562	−1.26012	−0.630061	+	0.776546i	$0.716970\pi$
$18$	7.59373	1.78986
$19$	2.28786	0.524870	0.262435	−	0.964950i	$-0.415474\pi$
$19$	2.28786	0.524870	0.262435	+	0.964950i	$0.415474\pi$
$20$	3.43025	0.767026
$21$	−7.62590	−1.66411
$22$	4.43053	0.944593
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.25480	−0.664383
$25$	6.76659	1.35332
$26$	−7.18545	−1.40918
$27$	−14.9517	−2.87745
$28$	2.34297	0.442780
$29$	6.34711	1.17863	0.589314	−	0.807904i	$-0.299398\pi$
$29$	6.34711	1.17863	0.589314	+	0.807904i	$0.299398\pi$
$30$	−11.1648	−2.03840
$31$	−4.21714	−0.757420	−0.378710	−	0.925515i	$-0.623632\pi$
$31$	−4.21714	−0.757420	−0.378710	+	0.925515i	$0.623632\pi$
$32$	1.00000	0.176777
$33$	−14.4205	−2.51029
$34$	−5.19562	−0.891041
$35$	8.03696	1.35849
$36$	7.59373	1.26562
$37$	4.13634	0.680009	0.340005	−	0.940424i	$-0.389571\pi$
$37$	4.13634	0.680009	0.340005	+	0.940424i	$0.389571\pi$
$38$	2.28786	0.371139
$39$	23.3872	3.74495
$40$	3.43025	0.542370
$41$	5.21322	0.814168	0.407084	−	0.913391i	$-0.366546\pi$
$41$	5.21322	0.814168	0.407084	+	0.913391i	$0.366546\pi$
$42$	−7.62590	−1.17670
$43$	4.75055	0.724452	0.362226	−	0.932090i	$-0.382017\pi$
$43$	4.75055	0.724452	0.362226	+	0.932090i	$0.382017\pi$
$44$	4.43053	0.667928
$45$	26.0484	3.88306
$46$	1.00000	0.147442
$47$	10.2740	1.49862	0.749312	−	0.662218i	$-0.230385\pi$
$47$	10.2740	1.49862	0.749312	+	0.662218i	$0.230385\pi$
$48$	−3.25480	−0.469790
$49$	−1.51049	−0.215784
$50$	6.76659	0.956940
$51$	16.9107	2.36797
$52$	−7.18545	−0.996443
$53$	2.24465	0.308327	0.154163	−	0.988045i	$-0.450732\pi$
$53$	2.24465	0.308327	0.154163	+	0.988045i	$0.450732\pi$
$54$	−14.9517	−2.03467
$55$	15.1978	2.04927
$56$	2.34297	0.313093
$57$	−7.44651	−0.986315
$58$	6.34711	0.833416
$59$	−12.7867	−1.66468	−0.832341	−	0.554264i	$-0.813000\pi$
$59$	−12.7867	−1.66468	−0.832341	+	0.554264i	$0.813000\pi$
$60$	−11.1648	−1.44137
$61$	13.0865	1.67555	0.837777	−	0.546013i	$-0.183855\pi$
$61$	13.0865	1.67555	0.837777	+	0.546013i	$0.183855\pi$
$62$	−4.21714	−0.535577
$63$	17.7919	2.24157
$64$	1.00000	0.125000
$65$	−24.6479	−3.05719
$66$	−14.4205	−1.77504
$67$	−14.6034	−1.78409	−0.892046	−	0.451944i	$-0.850731\pi$
$67$	−14.6034	−1.78409	−0.892046	+	0.451944i	$0.850731\pi$
$68$	−5.19562	−0.630061
$69$	−3.25480	−0.391832
$70$	8.03696	0.960601
$71$	14.6374	1.73714	0.868571	−	0.495565i	$-0.165039\pi$
$71$	14.6374	1.73714	0.868571	+	0.495565i	$0.165039\pi$
$72$	7.59373	0.894930
$73$	1.57445	0.184275	0.0921375	−	0.995746i	$-0.470630\pi$
$73$	1.57445	0.184275	0.0921375	+	0.995746i	$0.470630\pi$
$74$	4.13634	0.480839
$75$	−22.0239	−2.54310
$76$	2.28786	0.262435
$77$	10.3806	1.18298
$78$	23.3872	2.64808
$79$	−8.12653	−0.914306	−0.457153	−	0.889388i	$-0.651131\pi$
$79$	−8.12653	−0.914306	−0.457153	+	0.889388i	$0.651131\pi$
$80$	3.43025	0.383513
$81$	25.8835	2.87595
$82$	5.21322	0.575704
$83$	−0.119214	−0.0130855	−0.00654273	−	0.999979i	$-0.502083\pi$
$83$	−0.119214	−0.0130855	−0.00654273	+	0.999979i	$0.502083\pi$
$84$	−7.62590	−0.832054
$85$	−17.8222	−1.93309
$86$	4.75055	0.512265
$87$	−20.6586	−2.21483
$88$	4.43053	0.472296
$89$	17.3240	1.83634	0.918169	−	0.396189i	$-0.129667\pi$
$89$	17.3240	1.83634	0.918169	+	0.396189i	$0.129667\pi$
$90$	26.0484	2.74574
$91$	−16.8353	−1.76482
$92$	1.00000	0.104257
$93$	13.7259	1.42331
$94$	10.2740	1.05969
$95$	7.84791	0.805178
$96$	−3.25480	−0.332192
$97$	6.80022	0.690458	0.345229	−	0.938518i	$-0.387801\pi$
$97$	6.80022	0.690458	0.345229	+	0.938518i	$0.387801\pi$
$98$	−1.51049	−0.152583
$99$	33.6443	3.38138
$100$	6.76659	0.676659
$101$	5.49563	0.546836	0.273418	−	0.961895i	$-0.411846\pi$
$101$	5.49563	0.546836	0.273418	+	0.961895i	$0.411846\pi$
$102$	16.9107	1.67441
$103$	−6.74159	−0.664268	−0.332134	−	0.943232i	$-0.607769\pi$
$103$	−6.74159	−0.664268	−0.332134	+	0.943232i	$0.607769\pi$
$104$	−7.18545	−0.704592
$105$	−26.1587	−2.55283
$106$	2.24465	0.218020
$107$	−7.79663	−0.753728	−0.376864	−	0.926269i	$-0.622998\pi$
$107$	−7.79663	−0.753728	−0.376864	+	0.926269i	$0.622998\pi$
$108$	−14.9517	−1.43873
$109$	−14.0335	−1.34416	−0.672080	−	0.740478i	$-0.734599\pi$
$109$	−14.0335	−1.34416	−0.672080	+	0.740478i	$0.734599\pi$
$110$	15.1978	1.44906
$111$	−13.4630	−1.27785
$112$	2.34297	0.221390
$113$	16.5659	1.55839	0.779196	−	0.626781i	$-0.215628\pi$
$113$	16.5659	1.55839	0.779196	+	0.626781i	$0.215628\pi$
$114$	−7.44651	−0.697430
$115$	3.43025	0.319872
$116$	6.34711	0.589314
$117$	−54.5644	−5.04448
$118$	−12.7867	−1.17711
$119$	−12.1732	−1.11591
$120$	−11.1648	−1.01920
$121$	8.62963	0.784512
$122$	13.0865	1.18480
$123$	−16.9680	−1.52995
$124$	−4.21714	−0.378710
$125$	6.05984	0.542008
$126$	17.7919	1.58503
$127$	−4.03695	−0.358221	−0.179111	−	0.983829i	$-0.557322\pi$
$127$	−4.03695	−0.358221	−0.179111	+	0.983829i	$0.557322\pi$
$128$	1.00000	0.0883883
$129$	−15.4621	−1.36136
$130$	−24.6479	−2.16176
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−14.4205	−1.25514
$133$	5.36038	0.464804
$134$	−14.6034	−1.26154
$135$	−51.2879	−4.41416
$136$	−5.19562	−0.445521
$137$	−11.7533	−1.00415	−0.502076	−	0.864824i	$-0.667430\pi$
$137$	−11.7533	−1.00415	−0.502076	+	0.864824i	$0.667430\pi$
$138$	−3.25480	−0.277067
$139$	−9.53312	−0.808589	−0.404294	−	0.914629i	$-0.632483\pi$
$139$	−9.53312	−0.808589	−0.404294	+	0.914629i	$0.632483\pi$
$140$	8.03696	0.679247
$141$	−33.4400	−2.81615
$142$	14.6374	1.22834
$143$	−31.8354	−2.66221
$144$	7.59373	0.632811
$145$	21.7721	1.80808
$146$	1.57445	0.130302
$147$	4.91635	0.405494
$148$	4.13634	0.340005
$149$	−4.12882	−0.338246	−0.169123	−	0.985595i	$-0.554094\pi$
$149$	−4.12882	−0.338246	−0.169123	+	0.985595i	$0.554094\pi$
$150$	−22.0239	−1.79824
$151$	19.9257	1.62153	0.810766	−	0.585371i	$-0.199051\pi$
$151$	19.9257	1.62153	0.810766	+	0.585371i	$0.199051\pi$
$152$	2.28786	0.185570
$153$	−39.4541	−3.18968
$154$	10.3806	0.836493
$155$	−14.4658	−1.16192
$156$	23.3872	1.87248
$157$	10.7681	0.859387	0.429693	−	0.902975i	$-0.358622\pi$
$157$	10.7681	0.859387	0.429693	+	0.902975i	$0.358622\pi$
$158$	−8.12653	−0.646512
$159$	−7.30590	−0.579396
$160$	3.43025	0.271185
$161$	2.34297	0.184652
$162$	25.8835	2.03360
$163$	20.1567	1.57880	0.789398	−	0.613882i	$-0.210393\pi$
$163$	20.1567	1.57880	0.789398	+	0.613882i	$0.210393\pi$
$164$	5.21322	0.407084
$165$	−49.4659	−3.85091
$166$	−0.119214	−0.00925281
$167$	−12.2624	−0.948895	−0.474447	−	0.880284i	$-0.657352\pi$
$167$	−12.2624	−0.948895	−0.474447	+	0.880284i	$0.657352\pi$
$168$	−7.62590	−0.588351
$169$	38.6307	2.97159
$170$	−17.8222	−1.36690
$171$	17.3734	1.32857
$172$	4.75055	0.362226
$173$	12.6496	0.961728	0.480864	−	0.876795i	$-0.340323\pi$
$173$	12.6496	0.961728	0.480864	+	0.876795i	$0.340323\pi$
$174$	−20.6586	−1.56612
$175$	15.8539	1.19844
$176$	4.43053	0.333964
$177$	41.6180	3.12820
$178$	17.3240	1.29849
$179$	6.50914	0.486516	0.243258	−	0.969962i	$-0.421784\pi$
$179$	6.50914	0.486516	0.243258	+	0.969962i	$0.421784\pi$
$180$	26.0484	1.94153
$181$	−5.71579	−0.424851	−0.212426	−	0.977177i	$-0.568136\pi$
$181$	−5.71579	−0.424851	−0.212426	+	0.977177i	$0.568136\pi$
$182$	−16.8353	−1.24792
$183$	−42.5939	−3.14863
$184$	1.00000	0.0737210
$185$	14.1887	1.04317
$186$	13.7259	1.00644
$187$	−23.0194	−1.68334
$188$	10.2740	0.749312
$189$	−35.0313	−2.54815
$190$	7.84791	0.569347
$191$	15.3441	1.11026	0.555131	−	0.831763i	$-0.312668\pi$
$191$	15.3441	1.11026	0.555131	+	0.831763i	$0.312668\pi$
$192$	−3.25480	−0.234895
$193$	−10.5556	−0.759812	−0.379906	−	0.925025i	$-0.624044\pi$
$193$	−10.5556	−0.759812	−0.379906	+	0.925025i	$0.624044\pi$
$194$	6.80022	0.488228
$195$	80.2239	5.74495
$196$	−1.51049	−0.107892
$197$	10.0025	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$197$	10.0025	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$198$	33.6443	2.39099
$199$	−25.7471	−1.82517	−0.912583	−	0.408891i	$-0.865916\pi$
$199$	−25.7471	−1.82517	−0.912583	+	0.408891i	$0.865916\pi$
$200$	6.76659	0.478470
$201$	47.5313	3.35260
$202$	5.49563	0.386671
$203$	14.8711	1.04375
$204$	16.9107	1.18399
$205$	17.8826	1.24898
$206$	−6.74159	−0.469709
$207$	7.59373	0.527801
$208$	−7.18545	−0.498221
$209$	10.1364	0.701151
$210$	−26.1587	−1.80512
$211$	−14.1344	−0.973050	−0.486525	−	0.873667i	$-0.661736\pi$
$211$	−14.1344	−0.973050	−0.486525	+	0.873667i	$0.661736\pi$
$212$	2.24465	0.154163
$213$	−47.6419	−3.26437
$214$	−7.79663	−0.532966
$215$	16.2956	1.11135
$216$	−14.9517	−1.01733
$217$	−9.88063	−0.670741
$218$	−14.0335	−0.950465
$219$	−5.12451	−0.346282
$220$	15.1978	1.02464
$221$	37.3329	2.51128
$222$	−13.4630	−0.903574
$223$	−6.12566	−0.410205	−0.205102	−	0.978741i	$-0.565753\pi$
$223$	−6.12566	−0.410205	−0.205102	+	0.978741i	$0.565753\pi$
$224$	2.34297	0.156546
$225$	51.3836	3.42558
$226$	16.5659	1.10195
$227$	10.3943	0.689893	0.344947	−	0.938622i	$-0.387897\pi$
$227$	10.3943	0.689893	0.344947	+	0.938622i	$0.387897\pi$
$228$	−7.44651	−0.493157
$229$	4.64907	0.307219	0.153610	−	0.988132i	$-0.450910\pi$
$229$	4.64907	0.307219	0.153610	+	0.988132i	$0.450910\pi$
$230$	3.43025	0.226184
$231$	−33.7868	−2.22301
$232$	6.34711	0.416708
$233$	9.14425	0.599059	0.299530	−	0.954087i	$-0.403170\pi$
$233$	9.14425	0.599059	0.299530	+	0.954087i	$0.403170\pi$
$234$	−54.5644	−3.56699
$235$	35.2425	2.29897
$236$	−12.7867	−0.832341
$237$	26.4502	1.71813
$238$	−12.1732	−0.789070
$239$	−0.536308	−0.0346909	−0.0173455	−	0.999850i	$-0.505522\pi$
$239$	−0.536308	−0.0346909	−0.0173455	+	0.999850i	$0.505522\pi$
$240$	−11.1648	−0.720683
$241$	−13.4572	−0.866855	−0.433427	−	0.901188i	$-0.642696\pi$
$241$	−13.4572	−0.866855	−0.433427	+	0.901188i	$0.642696\pi$
$242$	8.62963	0.554734
$243$	−39.3907	−2.52692
$244$	13.0865	0.837777
$245$	−5.18136	−0.331025
$246$	−16.9680	−1.08184
$247$	−16.4393	−1.04601
$248$	−4.21714	−0.267789
$249$	0.388018	0.0245897
$250$	6.05984	0.383258
$251$	−14.6327	−0.923605	−0.461802	−	0.886983i	$-0.652797\pi$
$251$	−14.6327	−0.923605	−0.461802	+	0.886983i	$0.652797\pi$
$252$	17.7919	1.12078
$253$	4.43053	0.278545
$254$	−4.03695	−0.253301
$255$	58.0079	3.63259
$256$	1.00000	0.0625000
$257$	13.7750	0.859259	0.429630	−	0.903005i	$-0.358644\pi$
$257$	13.7750	0.859259	0.429630	+	0.903005i	$0.358644\pi$
$258$	−15.4621	−0.962628
$259$	9.69131	0.602189
$260$	−24.6479	−1.52860
$261$	48.1982	2.98340
$262$	1.00000	0.0617802
$263$	−28.6462	−1.76640	−0.883201	−	0.468995i	$-0.844616\pi$
$263$	−28.6462	−1.76640	−0.883201	+	0.468995i	$0.844616\pi$
$264$	−14.4205	−0.887521
$265$	7.69972	0.472990
$266$	5.36038	0.328666
$267$	−56.3861	−3.45077
$268$	−14.6034	−0.892046
$269$	23.3596	1.42426	0.712129	−	0.702049i	$-0.247731\pi$
$269$	23.3596	1.42426	0.712129	+	0.702049i	$0.247731\pi$
$270$	−51.2879	−3.12128
$271$	−11.2294	−0.682139	−0.341069	−	0.940038i	$-0.610789\pi$
$271$	−11.2294	−0.682139	−0.341069	+	0.940038i	$0.610789\pi$
$272$	−5.19562	−0.315031
$273$	54.7956	3.31638
$274$	−11.7533	−0.710043
$275$	29.9796	1.80784
$276$	−3.25480	−0.195916
$277$	20.0900	1.20709	0.603547	−	0.797328i	$-0.293754\pi$
$277$	20.0900	1.20709	0.603547	+	0.797328i	$0.293754\pi$
$278$	−9.53312	−0.571758
$279$	−32.0238	−1.91721
$280$	8.03696	0.480300
$281$	−0.623658	−0.0372043	−0.0186022	−	0.999827i	$-0.505922\pi$
$281$	−0.623658	−0.0372043	−0.0186022	+	0.999827i	$0.505922\pi$
$282$	−33.4400	−1.99132
$283$	20.1432	1.19739	0.598694	−	0.800978i	$-0.295687\pi$
$283$	20.1432	1.19739	0.598694	+	0.800978i	$0.295687\pi$
$284$	14.6374	0.868571
$285$	−25.5434	−1.51306
$286$	−31.8354	−1.88247
$287$	12.2144	0.720994
$288$	7.59373	0.447465
$289$	9.99444	0.587908
$290$	21.7721	1.27850
$291$	−22.1334	−1.29748
$292$	1.57445	0.0921375
$293$	3.28024	0.191634	0.0958169	−	0.995399i	$-0.469454\pi$
$293$	3.28024	0.191634	0.0958169	+	0.995399i	$0.469454\pi$
$294$	4.91635	0.286727
$295$	−43.8614	−2.55371
$296$	4.13634	0.240420
$297$	−66.2439	−3.84386
$298$	−4.12882	−0.239176
$299$	−7.18545	−0.415545
$300$	−22.0239	−1.27155
$301$	11.1304	0.641545
$302$	19.9257	1.14660
$303$	−17.8872	−1.02759
$304$	2.28786	0.131217
$305$	44.8899	2.57039
$306$	−39.4541	−2.25544
$307$	−10.9637	−0.625733	−0.312866	−	0.949797i	$-0.601289\pi$
$307$	−10.9637	−0.625733	−0.312866	+	0.949797i	$0.601289\pi$
$308$	10.3806	0.591490
$309$	21.9425	1.24827
$310$	−14.4658	−0.821603
$311$	20.6437	1.17060	0.585299	−	0.810818i	$-0.300977\pi$
$311$	20.6437	1.17060	0.585299	+	0.810818i	$0.300977\pi$
$312$	23.3872	1.32404
$313$	−7.54678	−0.426569	−0.213285	−	0.976990i	$-0.568416\pi$
$313$	−7.54678	−0.426569	−0.213285	+	0.976990i	$0.568416\pi$
$314$	10.7681	0.607678
$315$	61.0305	3.43868
$316$	−8.12653	−0.457153
$317$	8.11996	0.456062	0.228031	−	0.973654i	$-0.426771\pi$
$317$	8.11996	0.456062	0.228031	+	0.973654i	$0.426771\pi$
$318$	−7.30590	−0.409695
$319$	28.1211	1.57448
$320$	3.43025	0.191757
$321$	25.3765	1.41638
$322$	2.34297	0.130569
$323$	−11.8868	−0.661400
$324$	25.8835	1.43797
$325$	−48.6210	−2.69701
$326$	20.1567	1.11638
$327$	45.6761	2.52589
$328$	5.21322	0.287852
$329$	24.0718	1.32712
$330$	−49.4659	−2.72301
$331$	−3.05741	−0.168051	−0.0840253	−	0.996464i	$-0.526778\pi$
$331$	−3.05741	−0.168051	−0.0840253	+	0.996464i	$0.526778\pi$
$332$	−0.119214	−0.00654273
$333$	31.4102	1.72127
$334$	−12.2624	−0.670970
$335$	−50.0934	−2.73689
$336$	−7.62590	−0.416027
$337$	9.89832	0.539196	0.269598	−	0.962973i	$-0.413109\pi$
$337$	9.89832	0.539196	0.269598	+	0.962973i	$0.413109\pi$
$338$	38.6307	2.10123
$339$	−53.9188	−2.92847
$340$	−17.8222	−0.966547
$341$	−18.6842	−1.01180
$342$	17.3734	0.939443
$343$	−19.9398	−1.07665
$344$	4.75055	0.256133
$345$	−11.1648	−0.601091
$346$	12.6496	0.680045
$347$	17.3697	0.932454	0.466227	−	0.884665i	$-0.345613\pi$
$347$	17.3697	0.932454	0.466227	+	0.884665i	$0.345613\pi$
$348$	−20.6586	−1.10742
$349$	−23.2708	−1.24566	−0.622828	−	0.782358i	$-0.714017\pi$
$349$	−23.2708	−1.24566	−0.622828	+	0.782358i	$0.714017\pi$
$350$	15.8539	0.847427
$351$	107.435	5.73443
$352$	4.43053	0.236148
$353$	−4.55658	−0.242522	−0.121261	−	0.992621i	$-0.538694\pi$
$353$	−4.55658	−0.242522	−0.121261	+	0.992621i	$0.538694\pi$
$354$	41.6180	2.21197
$355$	50.2099	2.66487
$356$	17.3240	0.918169
$357$	39.6213	2.09698
$358$	6.50914	0.344019
$359$	6.32428	0.333783	0.166891	−	0.985975i	$-0.446627\pi$
$359$	6.32428	0.333783	0.166891	+	0.985975i	$0.446627\pi$
$360$	26.0484	1.37287
$361$	−13.7657	−0.724512
$362$	−5.71579	−0.300415
$363$	−28.0877	−1.47422
$364$	−16.8353	−0.882410
$365$	5.40074	0.282688
$366$	−42.5939	−2.22642
$367$	−23.9131	−1.24825	−0.624127	−	0.781323i	$-0.714545\pi$
$367$	−23.9131	−1.24825	−0.624127	+	0.781323i	$0.714545\pi$
$368$	1.00000	0.0521286
$369$	39.5878	2.06086
$370$	14.1887	0.737633
$371$	5.25916	0.273042
$372$	13.7259	0.711657
$373$	8.33473	0.431556	0.215778	−	0.976442i	$-0.430771\pi$
$373$	8.33473	0.431556	0.215778	+	0.976442i	$0.430771\pi$
$374$	−23.0194	−1.19030
$375$	−19.7236	−1.01852
$376$	10.2740	0.529843
$377$	−45.6069	−2.34887
$378$	−35.0313	−1.80182
$379$	2.35090	0.120758	0.0603788	−	0.998176i	$-0.480769\pi$
$379$	2.35090	0.120758	0.0603788	+	0.998176i	$0.480769\pi$
$380$	7.84791	0.402589
$381$	13.1395	0.673156
$382$	15.3441	0.785074
$383$	−22.8976	−1.17001	−0.585006	−	0.811029i	$-0.698908\pi$
$383$	−22.8976	−1.17001	−0.585006	+	0.811029i	$0.698908\pi$
$384$	−3.25480	−0.166096
$385$	35.6080	1.81475
$386$	−10.5556	−0.537268
$387$	36.0744	1.83376
$388$	6.80022	0.345229
$389$	3.96743	0.201157	0.100578	−	0.994929i	$-0.467931\pi$
$389$	3.96743	0.201157	0.100578	+	0.994929i	$0.467931\pi$
$390$	80.2239	4.06230
$391$	−5.19562	−0.262754
$392$	−1.51049	−0.0762913
$393$	−3.25480	−0.164183
$394$	10.0025	0.503920
$395$	−27.8760	−1.40259
$396$	33.6443	1.69069
$397$	−7.97774	−0.400391	−0.200196	−	0.979756i	$-0.564158\pi$
$397$	−7.97774	−0.400391	−0.200196	+	0.979756i	$0.564158\pi$
$398$	−25.7471	−1.29059
$399$	−17.4470	−0.873440
$400$	6.76659	0.338329
$401$	27.8837	1.39245	0.696224	−	0.717825i	$-0.254862\pi$
$401$	27.8837	1.39245	0.696224	+	0.717825i	$0.254862\pi$
$402$	47.5313	2.37064
$403$	30.3020	1.50945
$404$	5.49563	0.273418
$405$	88.7869	4.41186
$406$	14.8711	0.738040
$407$	18.3262	0.908395
$408$	16.9107	0.837204
$409$	27.9520	1.38214	0.691070	−	0.722788i	$-0.257140\pi$
$409$	27.9520	1.38214	0.691070	+	0.722788i	$0.257140\pi$
$410$	17.8826	0.883160
$411$	38.2546	1.88696
$412$	−6.74159	−0.332134
$413$	−29.9588	−1.47417
$414$	7.59373	0.373211
$415$	−0.408934	−0.0200738
$416$	−7.18545	−0.352296
$417$	31.0284	1.51947
$418$	10.1364	0.495788
$419$	27.8530	1.36071	0.680355	−	0.732883i	$-0.261826\pi$
$419$	27.8530	1.36071	0.680355	+	0.732883i	$0.261826\pi$
$420$	−26.1587	−1.27641
$421$	−33.8281	−1.64868	−0.824342	−	0.566093i	$-0.808454\pi$
$421$	−33.8281	−1.64868	−0.824342	+	0.566093i	$0.808454\pi$
$422$	−14.1344	−0.688050
$423$	78.0183	3.79338
$424$	2.24465	0.109010
$425$	−35.1566	−1.70535
$426$	−47.6419	−2.30826
$427$	30.6613	1.48380
$428$	−7.79663	−0.376864
$429$	103.618	5.00272
$430$	16.2956	0.785842
$431$	27.7823	1.33823	0.669114	−	0.743160i	$-0.266674\pi$
$431$	27.7823	1.33823	0.669114	+	0.743160i	$0.266674\pi$
$432$	−14.9517	−0.719363
$433$	−34.1307	−1.64022	−0.820108	−	0.572209i	$-0.806087\pi$
$433$	−34.1307	−1.64022	−0.820108	+	0.572209i	$0.806087\pi$
$434$	−9.88063	−0.474285
$435$	−70.8640	−3.39767
$436$	−14.0335	−0.672080
$437$	2.28786	0.109443
$438$	−5.12451	−0.244859
$439$	1.78285	0.0850907	0.0425454	−	0.999095i	$-0.486453\pi$
$439$	1.78285	0.0850907	0.0425454	+	0.999095i	$0.486453\pi$
$440$	15.1978	0.724528
$441$	−11.4703	−0.546203
$442$	37.3329	1.77574
$443$	−41.5548	−1.97433	−0.987165	−	0.159706i	$-0.948945\pi$
$443$	−41.5548	−1.97433	−0.987165	+	0.159706i	$0.948945\pi$
$444$	−13.4630	−0.638923
$445$	59.4255	2.81704
$446$	−6.12566	−0.290058
$447$	13.4385	0.635618
$448$	2.34297	0.110695
$449$	−3.39352	−0.160150	−0.0800751	−	0.996789i	$-0.525516\pi$
$449$	−3.39352	−0.160150	−0.0800751	+	0.996789i	$0.525516\pi$
$450$	51.3836	2.42225
$451$	23.0973	1.08761
$452$	16.5659	0.779196
$453$	−64.8542	−3.04712
$454$	10.3943	0.487828
$455$	−57.7492	−2.70733
$456$	−7.44651	−0.348715
$457$	−4.72748	−0.221142	−0.110571	−	0.993868i	$-0.535268\pi$
$457$	−4.72748	−0.221142	−0.110571	+	0.993868i	$0.535268\pi$
$458$	4.64907	0.217237
$459$	77.6832	3.62594
$460$	3.43025	0.159936
$461$	−20.2023	−0.940916	−0.470458	−	0.882422i	$-0.655911\pi$
$461$	−20.2023	−0.940916	−0.470458	+	0.882422i	$0.655911\pi$
$462$	−33.7868	−1.57190
$463$	−1.24720	−0.0579624	−0.0289812	−	0.999580i	$-0.509226\pi$
$463$	−1.24720	−0.0579624	−0.0289812	+	0.999580i	$0.509226\pi$
$464$	6.34711	0.294657
$465$	47.0834	2.18344
$466$	9.14425	0.423599
$467$	12.4654	0.576831	0.288415	−	0.957505i	$-0.406872\pi$
$467$	12.4654	0.576831	0.288415	+	0.957505i	$0.406872\pi$
$468$	−54.5644	−2.52224
$469$	−34.2154	−1.57992
$470$	35.2425	1.62562
$471$	−35.0480	−1.61492
$472$	−12.7867	−0.588554
$473$	21.0475	0.967764
$474$	26.4502	1.21490
$475$	15.4810	0.710316
$476$	−12.1732	−0.557957
$477$	17.0453	0.780450
$478$	−0.536308	−0.0245302
$479$	30.2180	1.38070	0.690349	−	0.723477i	$-0.257457\pi$
$479$	30.2180	1.38070	0.690349	+	0.723477i	$0.257457\pi$
$480$	−11.1648	−0.509600
$481$	−29.7214	−1.35518
$482$	−13.4572	−0.612959
$483$	−7.62590	−0.346991
$484$	8.62963	0.392256
$485$	23.3264	1.05920
$486$	−39.3907	−1.78680
$487$	−13.3792	−0.606268	−0.303134	−	0.952948i	$-0.598033\pi$
$487$	−13.3792	−0.606268	−0.303134	+	0.952948i	$0.598033\pi$
$488$	13.0865	0.592398
$489$	−65.6061	−2.96681
$490$	−5.18136	−0.234070
$491$	15.5792	0.703079	0.351539	−	0.936173i	$-0.385658\pi$
$491$	15.5792	0.703079	0.351539	+	0.936173i	$0.385658\pi$
$492$	−16.9680	−0.764976
$493$	−32.9772	−1.48522
$494$	−16.4393	−0.739638
$495$	115.408	5.18721
$496$	−4.21714	−0.189355
$497$	34.2950	1.53834
$498$	0.388018	0.0173875
$499$	33.9158	1.51828	0.759140	−	0.650927i	$-0.225620\pi$
$499$	33.9158	1.51828	0.759140	+	0.650927i	$0.225620\pi$
$500$	6.05984	0.271004
$501$	39.9117	1.78313
$502$	−14.6327	−0.653087
$503$	30.4241	1.35654	0.678272	−	0.734811i	$-0.262729\pi$
$503$	30.4241	1.35654	0.678272	+	0.734811i	$0.262729\pi$
$504$	17.7919	0.792513
$505$	18.8514	0.838875
$506$	4.43053	0.196961
$507$	−125.735	−5.58410
$508$	−4.03695	−0.179111
$509$	−31.7408	−1.40689	−0.703443	−	0.710751i	$-0.748355\pi$
$509$	−31.7408	−1.40689	−0.703443	+	0.710751i	$0.748355\pi$
$510$	58.0079	2.56863
$511$	3.68888	0.163187
$512$	1.00000	0.0441942
$513$	−34.2073	−1.51029
$514$	13.7750	0.607588
$515$	−23.1253	−1.01902
$516$	−15.4621	−0.680681
$517$	45.5195	2.00195
$518$	9.69131	0.425812
$519$	−41.1718	−1.80724
$520$	−24.6479	−1.08088
$521$	37.8525	1.65835	0.829173	−	0.558992i	$-0.188812\pi$
$521$	37.8525	1.65835	0.829173	+	0.558992i	$0.188812\pi$
$522$	48.1982	2.10958
$523$	0.837177	0.0366072	0.0183036	−	0.999832i	$-0.494173\pi$
$523$	0.837177	0.0366072	0.0183036	+	0.999832i	$0.494173\pi$
$524$	1.00000	0.0436852
$525$	−51.6013	−2.25207
$526$	−28.6462	−1.24903
$527$	21.9106	0.954442
$528$	−14.4205	−0.627572
$529$	1.00000	0.0434783
$530$	7.69972	0.334454
$531$	−97.0985	−4.21371
$532$	5.36038	0.232402
$533$	−37.4593	−1.62254
$534$	−56.3861	−2.44007
$535$	−26.7443	−1.15626
$536$	−14.6034	−0.630772
$537$	−21.1859	−0.914241
$538$	23.3596	1.00710
$539$	−6.69228	−0.288257
$540$	−51.2879	−2.20708
$541$	−5.11284	−0.219818	−0.109909	−	0.993942i	$-0.535056\pi$
$541$	−5.11284	−0.219818	−0.109909	+	0.993942i	$0.535056\pi$
$542$	−11.2294	−0.482345
$543$	18.6038	0.798364
$544$	−5.19562	−0.222760
$545$	−48.1382	−2.06201
$546$	54.7956	2.34503
$547$	−1.06585	−0.0455723	−0.0227861	−	0.999740i	$-0.507254\pi$
$547$	−1.06585	−0.0455723	−0.0227861	+	0.999740i	$0.507254\pi$
$548$	−11.7533	−0.502076
$549$	99.3753	4.24123
$550$	29.9796	1.27833
$551$	14.5213	0.618627
$552$	−3.25480	−0.138534
$553$	−19.0402	−0.809673
$554$	20.0900	0.853544
$555$	−46.1812	−1.96028
$556$	−9.53312	−0.404294
$557$	6.50318	0.275548	0.137774	−	0.990464i	$-0.456005\pi$
$557$	6.50318	0.275548	0.137774	+	0.990464i	$0.456005\pi$
$558$	−32.0238	−1.35568
$559$	−34.1349	−1.44375
$560$	8.03696	0.339624
$561$	74.9234	3.16327
$562$	−0.623658	−0.0263074
$563$	−27.2194	−1.14716	−0.573581	−	0.819149i	$-0.694446\pi$
$563$	−27.2194	−1.14716	−0.573581	+	0.819149i	$0.694446\pi$
$564$	−33.4400	−1.40808
$565$	56.8252	2.39065
$566$	20.1432	0.846681
$567$	60.6444	2.54682
$568$	14.6374	0.614172
$569$	0.987303	0.0413899	0.0206949	−	0.999786i	$-0.493412\pi$
$569$	0.987303	0.0413899	0.0206949	+	0.999786i	$0.493412\pi$
$570$	−25.5434	−1.06989
$571$	6.31527	0.264286	0.132143	−	0.991231i	$-0.457814\pi$
$571$	6.31527	0.264286	0.132143	+	0.991231i	$0.457814\pi$
$572$	−31.8354	−1.33110
$573$	−49.9421	−2.08636
$574$	12.2144	0.509820
$575$	6.76659	0.282186
$576$	7.59373	0.316405
$577$	−35.7034	−1.48635	−0.743177	−	0.669095i	$-0.766682\pi$
$577$	−35.7034	−1.48635	−0.743177	+	0.669095i	$0.766682\pi$
$578$	9.99444	0.415714
$579$	34.3565	1.42781
$580$	21.7721	0.904039
$581$	−0.279315	−0.0115879
$582$	−22.1334	−0.917458
$583$	9.94501	0.411880
$584$	1.57445	0.0651511
$585$	−187.169	−7.73850
$586$	3.28024	0.135506
$587$	−17.0204	−0.702508	−0.351254	−	0.936280i	$-0.614245\pi$
$587$	−17.0204	−0.702508	−0.351254	+	0.936280i	$0.614245\pi$
$588$	4.91635	0.202747
$589$	−9.64820	−0.397547
$590$	−43.8614	−1.80575
$591$	−32.5562	−1.33918
$592$	4.13634	0.170002
$593$	3.12464	0.128314	0.0641568	−	0.997940i	$-0.479564\pi$
$593$	3.12464	0.128314	0.0641568	+	0.997940i	$0.479564\pi$
$594$	−66.2439	−2.71802
$595$	−41.7570	−1.71187
$596$	−4.12882	−0.169123
$597$	83.8018	3.42978
$598$	−7.18545	−0.293835
$599$	−2.08138	−0.0850429	−0.0425214	−	0.999096i	$-0.513539\pi$
$599$	−2.08138	−0.0850429	−0.0425214	+	0.999096i	$0.513539\pi$
$600$	−22.0239	−0.899122
$601$	45.8168	1.86891	0.934453	−	0.356085i	$-0.115889\pi$
$601$	45.8168	1.86891	0.934453	+	0.356085i	$0.115889\pi$
$602$	11.1304	0.453641
$603$	−110.894	−4.51597
$604$	19.9257	0.810766
$605$	29.6018	1.20348
$606$	−17.8872	−0.726618
$607$	−2.74600	−0.111457	−0.0557283	−	0.998446i	$-0.517748\pi$
$607$	−2.74600	−0.111457	−0.0557283	+	0.998446i	$0.517748\pi$
$608$	2.28786	0.0927848
$609$	−48.4024	−1.96137
$610$	44.8899	1.81754
$611$	−73.8236	−2.98659
$612$	−39.4541	−1.59484
$613$	−23.7535	−0.959395	−0.479697	−	0.877434i	$-0.659254\pi$
$613$	−23.7535	−0.959395	−0.479697	+	0.877434i	$0.659254\pi$
$614$	−10.9637	−0.442460
$615$	−58.2044	−2.34703
$616$	10.3806	0.418247
$617$	5.19674	0.209213	0.104606	−	0.994514i	$-0.466642\pi$
$617$	5.19674	0.209213	0.104606	+	0.994514i	$0.466642\pi$
$618$	21.9425	0.882658
$619$	−8.01411	−0.322114	−0.161057	−	0.986945i	$-0.551490\pi$
$619$	−8.01411	−0.322114	−0.161057	+	0.986945i	$0.551490\pi$
$620$	−14.4658	−0.580961
$621$	−14.9517	−0.599990
$622$	20.6437	0.827738
$623$	40.5896	1.62619
$624$	23.3872	0.936238
$625$	−13.0462	−0.521849
$626$	−7.54678	−0.301630
$627$	−32.9920	−1.31757
$628$	10.7681	0.429693
$629$	−21.4908	−0.856895
$630$	61.0305	2.43151
$631$	−0.342993	−0.0136543	−0.00682717	−	0.999977i	$-0.502173\pi$
$631$	−0.342993	−0.0136543	−0.00682717	+	0.999977i	$0.502173\pi$
$632$	−8.12653	−0.323256
$633$	46.0046	1.82852
$634$	8.11996	0.322485
$635$	−13.8477	−0.549531
$636$	−7.30590	−0.289698
$637$	10.8536	0.430034
$638$	28.1211	1.11332
$639$	111.153	4.39713
$640$	3.43025	0.135592
$641$	1.77411	0.0700732	0.0350366	−	0.999386i	$-0.488845\pi$
$641$	1.77411	0.0700732	0.0350366	+	0.999386i	$0.488845\pi$
$642$	25.3765	1.00153
$643$	−22.0759	−0.870589	−0.435294	−	0.900288i	$-0.643356\pi$
$643$	−22.0759	−0.870589	−0.435294	+	0.900288i	$0.643356\pi$
$644$	2.34297	0.0923260
$645$	−53.0388	−2.08840
$646$	−11.8868	−0.467681
$647$	8.30174	0.326375	0.163187	−	0.986595i	$-0.447822\pi$
$647$	8.30174	0.326375	0.163187	+	0.986595i	$0.447822\pi$
$648$	25.8835	1.01680
$649$	−56.6517	−2.22378
$650$	−48.6210	−1.90707
$651$	32.1595	1.26043
$652$	20.1567	0.789398
$653$	−35.6204	−1.39393	−0.696966	−	0.717104i	$-0.745467\pi$
$653$	−35.6204	−1.39393	−0.696966	+	0.717104i	$0.745467\pi$
$654$	45.6761	1.78608
$655$	3.43025	0.134031
$656$	5.21322	0.203542
$657$	11.9559	0.466445
$658$	24.0718	0.938416
$659$	−5.73662	−0.223467	−0.111733	−	0.993738i	$-0.535640\pi$
$659$	−5.73662	−0.223467	−0.111733	+	0.993738i	$0.535640\pi$
$660$	−49.4659	−1.92546
$661$	27.4933	1.06937	0.534684	−	0.845052i	$-0.320431\pi$
$661$	27.4933	1.06937	0.534684	+	0.845052i	$0.320431\pi$
$662$	−3.05741	−0.118830
$663$	−121.511	−4.71910
$664$	−0.119214	−0.00462641
$665$	18.3874	0.713033
$666$	31.4102	1.21712
$667$	6.34711	0.245761
$668$	−12.2624	−0.474447
$669$	19.9378	0.770840
$670$	−50.0934	−1.93528
$671$	57.9801	2.23830
$672$	−7.62590	−0.294176
$673$	−30.8640	−1.18972	−0.594861	−	0.803829i	$-0.702793\pi$
$673$	−30.8640	−1.18972	−0.594861	+	0.803829i	$0.702793\pi$
$674$	9.89832	0.381269
$675$	−101.172	−3.89411
$676$	38.6307	1.48580
$677$	35.3815	1.35982	0.679911	−	0.733294i	$-0.262018\pi$
$677$	35.3815	1.35982	0.679911	+	0.733294i	$0.262018\pi$
$678$	−53.9188	−2.07074
$679$	15.9327	0.611442
$680$	−17.8222	−0.683452
$681$	−33.8313	−1.29642
$682$	−18.6842	−0.715454
$683$	29.3802	1.12420	0.562102	−	0.827068i	$-0.309993\pi$
$683$	29.3802	1.12420	0.562102	+	0.827068i	$0.309993\pi$
$684$	17.3734	0.664287
$685$	−40.3167	−1.54042
$686$	−19.9398	−0.761306
$687$	−15.1318	−0.577315
$688$	4.75055	0.181113
$689$	−16.1289	−0.614460
$690$	−11.1648	−0.425035
$691$	24.4886	0.931589	0.465794	−	0.884893i	$-0.345769\pi$
$691$	24.4886	0.931589	0.465794	+	0.884893i	$0.345769\pi$
$692$	12.6496	0.480864
$693$	78.8275	2.99441
$694$	17.3697	0.659345
$695$	−32.7009	−1.24042
$696$	−20.6586	−0.783061
$697$	−27.0859	−1.02595
$698$	−23.2708	−0.880812
$699$	−29.7627	−1.12573
$700$	15.8539	0.599222
$701$	9.05964	0.342178	0.171089	−	0.985256i	$-0.445271\pi$
$701$	9.05964	0.342178	0.171089	+	0.985256i	$0.445271\pi$
$702$	107.435	4.05486
$703$	9.46334	0.356917
$704$	4.43053	0.166982
$705$	−114.707	−4.32013
$706$	−4.55658	−0.171489
$707$	12.8761	0.484256
$708$	41.6180	1.56410
$709$	−18.4622	−0.693361	−0.346681	−	0.937983i	$-0.612691\pi$
$709$	−18.4622	−0.693361	−0.346681	+	0.937983i	$0.612691\pi$
$710$	50.2099	1.88435
$711$	−61.7107	−2.31433
$712$	17.3240	0.649244
$713$	−4.21714	−0.157933
$714$	39.6213	1.48279
$715$	−109.203	−4.08397
$716$	6.50914	0.243258
$717$	1.74558	0.0651898
$718$	6.32428	0.236020
$719$	−12.0984	−0.451194	−0.225597	−	0.974221i	$-0.572433\pi$
$719$	−12.0984	−0.451194	−0.225597	+	0.974221i	$0.572433\pi$
$720$	26.0484	0.970765
$721$	−15.7953	−0.588249
$722$	−13.7657	−0.512307
$723$	43.8005	1.62896
$724$	−5.71579	−0.212426
$725$	42.9483	1.59506
$726$	−28.0877	−1.04243
$727$	10.9794	0.407203	0.203601	−	0.979054i	$-0.434735\pi$
$727$	10.9794	0.407203	0.203601	+	0.979054i	$0.434735\pi$
$728$	−16.8353	−0.623958
$729$	50.5584	1.87253
$730$	5.40074	0.199890
$731$	−24.6820	−0.912898
$732$	−42.5939	−1.57432
$733$	0.299273	0.0110539	0.00552695	−	0.999985i	$-0.498241\pi$
$733$	0.299273	0.0110539	0.00552695	+	0.999985i	$0.498241\pi$
$734$	−23.9131	−0.882649
$735$	16.8643	0.622048
$736$	1.00000	0.0368605
$737$	−64.7010	−2.38329
$738$	39.5878	1.45725
$739$	−24.0331	−0.884072	−0.442036	−	0.896997i	$-0.645744\pi$
$739$	−24.0331	−0.884072	−0.442036	+	0.896997i	$0.645744\pi$
$740$	14.1887	0.521585
$741$	53.5066	1.96561
$742$	5.25916	0.193070
$743$	29.3676	1.07739	0.538697	−	0.842500i	$-0.318917\pi$
$743$	29.3676	1.07739	0.538697	+	0.842500i	$0.318917\pi$
$744$	13.7259	0.503218
$745$	−14.1629	−0.518887
$746$	8.33473	0.305156
$747$	−0.905280	−0.0331225
$748$	−23.0194	−0.841671
$749$	−18.2673	−0.667471
$750$	−19.7236	−0.720202
$751$	1.37237	0.0500784	0.0250392	−	0.999686i	$-0.492029\pi$
$751$	1.37237	0.0500784	0.0250392	+	0.999686i	$0.492029\pi$
$752$	10.2740	0.374656
$753$	47.6264	1.73560
$754$	−45.6069	−1.66090
$755$	68.3501	2.48751
$756$	−35.0313	−1.27408
$757$	−0.0226100	−0.000821775 0	−0.000410887	−	1.00000i	$-0.500131\pi$
$757$	−0.0226100	−0.000821775 0	−0.000410887		1.00000i	$0.500131\pi$
$758$	2.35090	0.0853886
$759$	−14.4205	−0.523431
$760$	7.84791	0.284673
$761$	−48.0170	−1.74061	−0.870307	−	0.492510i	$-0.836079\pi$
$761$	−48.0170	−1.74061	−0.870307	+	0.492510i	$0.836079\pi$
$762$	13.1395	0.475993
$763$	−32.8800	−1.19033
$764$	15.3441	0.555131
$765$	−135.337	−4.89313
$766$	−22.8976	−0.827324
$767$	91.8780	3.31752
$768$	−3.25480	−0.117448
$769$	7.09637	0.255902	0.127951	−	0.991781i	$-0.459160\pi$
$769$	7.09637	0.255902	0.127951	+	0.991781i	$0.459160\pi$
$770$	35.6080	1.28322
$771$	−44.8348	−1.61469
$772$	−10.5556	−0.379906
$773$	−42.6003	−1.53223	−0.766113	−	0.642706i	$-0.777812\pi$
$773$	−42.6003	−1.53223	−0.766113	+	0.642706i	$0.777812\pi$
$774$	36.0744	1.29667
$775$	−28.5356	−1.02503
$776$	6.80022	0.244114
$777$	−31.5433	−1.13161
$778$	3.96743	0.142239
$779$	11.9271	0.427332
$780$	80.2239	2.87248
$781$	64.8516	2.32057
$782$	−5.19562	−0.185795
$783$	−94.8999	−3.39145
$784$	−1.51049	−0.0539461
$785$	36.9372	1.31834
$786$	−3.25480	−0.116095
$787$	−25.4516	−0.907253	−0.453627	−	0.891192i	$-0.649870\pi$
$787$	−25.4516	−0.907253	−0.453627	+	0.891192i	$0.649870\pi$
$788$	10.0025	0.356325
$789$	93.2377	3.31935
$790$	−27.8760	−0.991784
$791$	38.8135	1.38005
$792$	33.6443	1.19550
$793$	−94.0324	−3.33919
$794$	−7.97774	−0.283119
$795$	−25.0610	−0.888824
$796$	−25.7471	−0.912583
$797$	3.57613	0.126673	0.0633365	−	0.997992i	$-0.479826\pi$
$797$	3.57613	0.126673	0.0633365	+	0.997992i	$0.479826\pi$
$798$	−17.4470	−0.617616
$799$	−53.3800	−1.88845
$800$	6.76659	0.239235
$801$	131.554	4.64822
$802$	27.8837	0.984609
$803$	6.97564	0.246165
$804$	47.5313	1.67630
$805$	8.03696	0.283266
$806$	30.3020	1.06734
$807$	−76.0308	−2.67641
$808$	5.49563	0.193336
$809$	0.134623	0.00473308	0.00236654	−	0.999997i	$-0.499247\pi$
$809$	0.134623	0.00473308	0.00236654	+	0.999997i	$0.499247\pi$
$810$	88.7869	3.11965
$811$	50.3112	1.76667	0.883333	−	0.468745i	$-0.155294\pi$
$811$	50.3112	1.76667	0.883333	+	0.468745i	$0.155294\pi$
$812$	14.8711	0.521873
$813$	36.5495	1.28185
$814$	18.3262	0.642332
$815$	69.1425	2.42195
$816$	16.9107	0.591993
$817$	10.8686	0.380243
$818$	27.9520	0.977320
$819$	−127.843	−4.46719
$820$	17.8826	0.624488
$821$	−2.08996	−0.0729403	−0.0364701	−	0.999335i	$-0.511611\pi$
$821$	−2.08996	−0.0729403	−0.0364701	+	0.999335i	$0.511611\pi$
$822$	38.2546	1.33428
$823$	23.4274	0.816627	0.408313	−	0.912842i	$-0.366117\pi$
$823$	23.4274	0.816627	0.408313	+	0.912842i	$0.366117\pi$
$824$	−6.74159	−0.234854
$825$	−97.5776	−3.39722
$826$	−29.9588	−1.04240
$827$	−8.63743	−0.300353	−0.150176	−	0.988659i	$-0.547984\pi$
$827$	−8.63743	−0.300353	−0.150176	+	0.988659i	$0.547984\pi$
$828$	7.59373	0.263900
$829$	−42.0079	−1.45899	−0.729497	−	0.683984i	$-0.760246\pi$
$829$	−42.0079	−1.45899	−0.729497	+	0.683984i	$0.760246\pi$
$830$	−0.408934	−0.0141943
$831$	−65.3891	−2.26832
$832$	−7.18545	−0.249111
$833$	7.84793	0.271915
$834$	31.0284	1.07443
$835$	−42.0631	−1.45565
$836$	10.1364	0.350575
$837$	63.0533	2.17944
$838$	27.8530	0.962167
$839$	−24.9899	−0.862748	−0.431374	−	0.902173i	$-0.641971\pi$
$839$	−24.9899	−0.862748	−0.431374	+	0.902173i	$0.641971\pi$
$840$	−26.1587	−0.902562
$841$	11.2858	0.389166
$842$	−33.8281	−1.16579
$843$	2.02988	0.0699129
$844$	−14.1344	−0.486525
$845$	132.513	4.55858
$846$	78.0183	2.68232
$847$	20.2190	0.694732
$848$	2.24465	0.0770817
$849$	−65.5621	−2.25008
$850$	−35.1566	−1.20586
$851$	4.13634	0.141792
$852$	−47.6419	−1.63218
$853$	−16.9855	−0.581573	−0.290787	−	0.956788i	$-0.593917\pi$
$853$	−16.9855	−0.581573	−0.290787	+	0.956788i	$0.593917\pi$
$854$	30.6613	1.04921
$855$	59.5949	2.03810
$856$	−7.79663	−0.266483
$857$	43.8220	1.49693	0.748465	−	0.663175i	$-0.230791\pi$
$857$	43.8220	1.49693	0.748465	+	0.663175i	$0.230791\pi$
$858$	103.618	3.53746
$859$	−25.5915	−0.873172	−0.436586	−	0.899663i	$-0.643812\pi$
$859$	−25.5915	−0.873172	−0.436586	+	0.899663i	$0.643812\pi$
$860$	16.2956	0.555674
$861$	−39.7555	−1.35486
$862$	27.7823	0.946270
$863$	2.07047	0.0704798	0.0352399	−	0.999379i	$-0.488780\pi$
$863$	2.07047	0.0704798	0.0352399	+	0.999379i	$0.488780\pi$
$864$	−14.9517	−0.508666
$865$	43.3911	1.47534
$866$	−34.1307	−1.15981
$867$	−32.5299	−1.10477
$868$	−9.88063	−0.335370
$869$	−36.0049	−1.22138
$870$	−70.8640	−2.40252
$871$	104.932	3.55549
$872$	−14.0335	−0.475233
$873$	51.6391	1.74772
$874$	2.28786	0.0773879
$875$	14.1980	0.479980
$876$	−5.12451	−0.173141
$877$	8.98665	0.303458	0.151729	−	0.988422i	$-0.451516\pi$
$877$	8.98665	0.303458	0.151729	+	0.988422i	$0.451516\pi$
$878$	1.78285	0.0601682
$879$	−10.6765	−0.360110
$880$	15.1978	0.512318
$881$	34.2932	1.15537	0.577684	−	0.816261i	$-0.303957\pi$
$881$	34.2932	1.15537	0.577684	+	0.816261i	$0.303957\pi$
$882$	−11.4703	−0.386224
$883$	−49.1133	−1.65279	−0.826397	−	0.563088i	$-0.809613\pi$
$883$	−49.1133	−1.65279	−0.826397	+	0.563088i	$0.809613\pi$
$884$	37.3329	1.25564
$885$	142.760	4.79883
$886$	−41.5548	−1.39606
$887$	40.2317	1.35085	0.675425	−	0.737429i	$-0.263960\pi$
$887$	40.2317	1.35085	0.675425	+	0.737429i	$0.263960\pi$
$888$	−13.4630	−0.451787
$889$	−9.45846	−0.317226
$890$	59.4255	1.99195
$891$	114.678	3.84185
$892$	−6.12566	−0.205102
$893$	23.5055	0.786582
$894$	13.4385	0.449450
$895$	22.3279	0.746341
$896$	2.34297	0.0782731
$897$	23.3872	0.780876
$898$	−3.39352	−0.113243
$899$	−26.7666	−0.892717
$900$	51.3836	1.71279
$901$	−11.6624	−0.388530
$902$	23.0973	0.769057
$903$	−36.2272	−1.20557
$904$	16.5659	0.550975
$905$	−19.6066	−0.651744
$906$	−64.8542	−2.15464
$907$	−12.1521	−0.403503	−0.201752	−	0.979437i	$-0.564663\pi$
$907$	−12.1521	−0.403503	−0.201752	+	0.979437i	$0.564663\pi$
$908$	10.3943	0.344947
$909$	41.7324	1.38417
$910$	−57.7492	−1.91437
$911$	−43.8135	−1.45160	−0.725802	−	0.687903i	$-0.758531\pi$
$911$	−43.8135	−1.45160	−0.725802	+	0.687903i	$0.758531\pi$
$912$	−7.44651	−0.246579
$913$	−0.528182	−0.0174803
$914$	−4.72748	−0.156371
$915$	−146.108	−4.83017
$916$	4.64907	0.153610
$917$	2.34297	0.0773717
$918$	77.6832	2.56393
$919$	−33.2258	−1.09602	−0.548009	−	0.836472i	$-0.684614\pi$
$919$	−33.2258	−1.09602	−0.548009	+	0.836472i	$0.684614\pi$
$920$	3.43025	0.113092
$921$	35.6847	1.17585
$922$	−20.2023	−0.665328
$923$	−105.176	−3.46193
$924$	−33.7868	−1.11150
$925$	27.9889	0.920269
$926$	−1.24720	−0.0409856
$927$	−51.1938	−1.68142
$928$	6.34711	0.208354
$929$	57.2799	1.87929	0.939646	−	0.342147i	$-0.111154\pi$
$929$	57.2799	1.87929	0.939646	+	0.342147i	$0.111154\pi$
$930$	47.0834	1.54392
$931$	−3.45578	−0.113259
$932$	9.14425	0.299530
$933$	−67.1912	−2.19974
$934$	12.4654	0.407881
$935$	−78.9621	−2.58234
$936$	−54.5644	−1.78349
$937$	34.0069	1.11096	0.555478	−	0.831531i	$-0.312535\pi$
$937$	34.0069	1.11096	0.555478	+	0.831531i	$0.312535\pi$
$938$	−34.2154	−1.11717
$939$	24.5633	0.801592
$940$	35.2425	1.14948
$941$	8.11698	0.264606	0.132303	−	0.991209i	$-0.457763\pi$
$941$	8.11698	0.264606	0.132303	+	0.991209i	$0.457763\pi$
$942$	−35.0480	−1.14192
$943$	5.21322	0.169766
$944$	−12.7867	−0.416170
$945$	−120.166	−3.90900
$946$	21.0475	0.684312
$947$	−46.2352	−1.50244	−0.751222	−	0.660050i	$-0.770535\pi$
$947$	−46.2352	−1.50244	−0.751222	+	0.660050i	$0.770535\pi$
$948$	26.4502	0.859064
$949$	−11.3131	−0.367239
$950$	15.4810	0.502269
$951$	−26.4288	−0.857014
$952$	−12.1732	−0.394535
$953$	55.4249	1.79539	0.897694	−	0.440620i	$-0.145241\pi$
$953$	55.4249	1.79539	0.897694	+	0.440620i	$0.145241\pi$
$954$	17.0453	0.551862
$955$	52.6341	1.70320
$956$	−0.536308	−0.0173455
$957$	−91.5285	−2.95870
$958$	30.2180	0.976301
$959$	−27.5376	−0.889236
$960$	−11.1648	−0.360341
$961$	−13.2157	−0.426314
$962$	−29.7214	−0.958258
$963$	−59.2055	−1.90787
$964$	−13.4572	−0.433427
$965$	−36.2085	−1.16559
$966$	−7.62590	−0.245359
$967$	−34.8312	−1.12010	−0.560049	−	0.828460i	$-0.689218\pi$
$967$	−34.8312	−1.12010	−0.560049	+	0.828460i	$0.689218\pi$
$968$	8.62963	0.277367
$969$	38.6892	1.24288
$970$	23.3264	0.748967
$971$	−32.8843	−1.05531	−0.527654	−	0.849459i	$-0.676928\pi$
$971$	−32.8843	−1.05531	−0.527654	+	0.849459i	$0.676928\pi$
$972$	−39.3907	−1.26346
$973$	−22.3358	−0.716053
$974$	−13.3792	−0.428696
$975$	158.252	5.06811
$976$	13.0865	0.418888
$977$	6.96029	0.222680	0.111340	−	0.993782i	$-0.464486\pi$
$977$	6.96029	0.222680	0.111340	+	0.993782i	$0.464486\pi$
$978$	−65.6061	−2.09785
$979$	76.7545	2.45308
$980$	−5.18136	−0.165512
$981$	−106.566	−3.40240
$982$	15.5792	0.497152
$983$	−53.9734	−1.72149	−0.860743	−	0.509040i	$-0.830000\pi$
$983$	−53.9734	−1.72149	−0.860743	+	0.509040i	$0.830000\pi$
$984$	−16.9680	−0.540920
$985$	34.3111	1.09324
$986$	−32.9772	−1.05021
$987$	−78.3488	−2.49387
$988$	−16.4393	−0.523003
$989$	4.75055	0.151059
$990$	115.408	3.66791
$991$	−27.4896	−0.873235	−0.436617	−	0.899647i	$-0.643824\pi$
$991$	−27.4896	−0.873235	−0.436617	+	0.899647i	$0.643824\pi$
$992$	−4.21714	−0.133894
$993$	9.95127	0.315794
$994$	34.2950	1.08777
$995$	−88.3190	−2.79990
$996$	0.388018	0.0122948
$997$	25.3553	0.803010	0.401505	−	0.915857i	$-0.368487\pi$
$997$	25.3553	0.803010	0.401505	+	0.915857i	$0.368487\pi$
$998$	33.9158	1.07359
$999$	−61.8452	−1.95669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.2	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.2	✓	41	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.25480 q^{3} +1.00000 q^{4} +3.43025 q^{5} -3.25480 q^{6} +2.34297 q^{7} +1.00000 q^{8} +7.59373 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.25480 q^{3} +1.00000 q^{4} +3.43025 q^{5} -3.25480 q^{6} +2.34297 q^{7} +1.00000 q^{8} +7.59373 q^{9} +3.43025 q^{10} +4.43053 q^{11} -3.25480 q^{12} -7.18545 q^{13} +2.34297 q^{14} -11.1648 q^{15} +1.00000 q^{16} -5.19562 q^{17} +7.59373 q^{18} +2.28786 q^{19} +3.43025 q^{20} -7.62590 q^{21} +4.43053 q^{22} +1.00000 q^{23} -3.25480 q^{24} +6.76659 q^{25} -7.18545 q^{26} -14.9517 q^{27} +2.34297 q^{28} +6.34711 q^{29} -11.1648 q^{30} -4.21714 q^{31} +1.00000 q^{32} -14.4205 q^{33} -5.19562 q^{34} +8.03696 q^{35} +7.59373 q^{36} +4.13634 q^{37} +2.28786 q^{38} +23.3872 q^{39} +3.43025 q^{40} +5.21322 q^{41} -7.62590 q^{42} +4.75055 q^{43} +4.43053 q^{44} +26.0484 q^{45} +1.00000 q^{46} +10.2740 q^{47} -3.25480 q^{48} -1.51049 q^{49} +6.76659 q^{50} +16.9107 q^{51} -7.18545 q^{52} +2.24465 q^{53} -14.9517 q^{54} +15.1978 q^{55} +2.34297 q^{56} -7.44651 q^{57} +6.34711 q^{58} -12.7867 q^{59} -11.1648 q^{60} +13.0865 q^{61} -4.21714 q^{62} +17.7919 q^{63} +1.00000 q^{64} -24.6479 q^{65} -14.4205 q^{66} -14.6034 q^{67} -5.19562 q^{68} -3.25480 q^{69} +8.03696 q^{70} +14.6374 q^{71} +7.59373 q^{72} +1.57445 q^{73} +4.13634 q^{74} -22.0239 q^{75} +2.28786 q^{76} +10.3806 q^{77} +23.3872 q^{78} -8.12653 q^{79} +3.43025 q^{80} +25.8835 q^{81} +5.21322 q^{82} -0.119214 q^{83} -7.62590 q^{84} -17.8222 q^{85} +4.75055 q^{86} -20.6586 q^{87} +4.43053 q^{88} +17.3240 q^{89} +26.0484 q^{90} -16.8353 q^{91} +1.00000 q^{92} +13.7259 q^{93} +10.2740 q^{94} +7.84791 q^{95} -3.25480 q^{96} +6.80022 q^{97} -1.51049 q^{98} +33.6443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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