LMFDB - Embedded newform 4034.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} -1.11072 q^{10} +3.15031 q^{11} -0.905567 q^{12} -6.12471 q^{13} -1.83235 q^{14} +1.00583 q^{15} +1.00000 q^{16} +1.33116 q^{17} -2.17995 q^{18} +1.55764 q^{19} -1.11072 q^{20} +1.65932 q^{21} +3.15031 q^{22} +5.24174 q^{23} -0.905567 q^{24} -3.76629 q^{25} -6.12471 q^{26} +4.69079 q^{27} -1.83235 q^{28} -1.90586 q^{29} +1.00583 q^{30} +5.13820 q^{31} +1.00000 q^{32} -2.85282 q^{33} +1.33116 q^{34} +2.03524 q^{35} -2.17995 q^{36} -8.79434 q^{37} +1.55764 q^{38} +5.54633 q^{39} -1.11072 q^{40} -1.96990 q^{41} +1.65932 q^{42} -2.51896 q^{43} +3.15031 q^{44} +2.42132 q^{45} +5.24174 q^{46} +7.53212 q^{47} -0.905567 q^{48} -3.64248 q^{49} -3.76629 q^{50} -1.20546 q^{51} -6.12471 q^{52} +2.37305 q^{53} +4.69079 q^{54} -3.49912 q^{55} -1.83235 q^{56} -1.41054 q^{57} -1.90586 q^{58} +13.3052 q^{59} +1.00583 q^{60} -2.35511 q^{61} +5.13820 q^{62} +3.99444 q^{63} +1.00000 q^{64} +6.80285 q^{65} -2.85282 q^{66} +5.23120 q^{67} +1.33116 q^{68} -4.74675 q^{69} +2.03524 q^{70} +2.21953 q^{71} -2.17995 q^{72} +7.62746 q^{73} -8.79434 q^{74} +3.41063 q^{75} +1.55764 q^{76} -5.77249 q^{77} +5.54633 q^{78} +5.41653 q^{79} -1.11072 q^{80} +2.29202 q^{81} -1.96990 q^{82} +13.7768 q^{83} +1.65932 q^{84} -1.47856 q^{85} -2.51896 q^{86} +1.72588 q^{87} +3.15031 q^{88} -3.22130 q^{89} +2.42132 q^{90} +11.2226 q^{91} +5.24174 q^{92} -4.65298 q^{93} +7.53212 q^{94} -1.73010 q^{95} -0.905567 q^{96} -0.906230 q^{97} -3.64248 q^{98} -6.86752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.905567	−0.522829	−0.261415	−	0.965227i	$-0.584189\pi$
$3$	−0.905567	−0.522829	−0.261415	+	0.965227i	$0.584189\pi$
$4$	1.00000	0.500000
$5$	−1.11072	−0.496731	−0.248365	−	0.968666i	$-0.579893\pi$
$5$	−1.11072	−0.496731	−0.248365	+	0.968666i	$0.579893\pi$
$6$	−0.905567	−0.369696
$7$	−1.83235	−0.692565	−0.346282	−	0.938130i	$-0.612556\pi$
$7$	−1.83235	−0.692565	−0.346282	+	0.938130i	$0.612556\pi$
$8$	1.00000	0.353553
$9$	−2.17995	−0.726650
$10$	−1.11072	−0.351242
$11$	3.15031	0.949855	0.474927	−	0.880025i	$-0.342474\pi$
$11$	3.15031	0.949855	0.474927	+	0.880025i	$0.342474\pi$
$12$	−0.905567	−0.261415
$13$	−6.12471	−1.69869	−0.849344	−	0.527840i	$-0.823002\pi$
$13$	−6.12471	−1.69869	−0.849344	+	0.527840i	$0.823002\pi$
$14$	−1.83235	−0.489717
$15$	1.00583	0.259705
$16$	1.00000	0.250000
$17$	1.33116	0.322855	0.161427	−	0.986885i	$-0.448390\pi$
$17$	1.33116	0.322855	0.161427	+	0.986885i	$0.448390\pi$
$18$	−2.17995	−0.513819
$19$	1.55764	0.357346	0.178673	−	0.983909i	$-0.442820\pi$
$19$	1.55764	0.357346	0.178673	+	0.983909i	$0.442820\pi$
$20$	−1.11072	−0.248365
$21$	1.65932	0.362093
$22$	3.15031	0.671649
$23$	5.24174	1.09298	0.546489	−	0.837466i	$-0.315964\pi$
$23$	5.24174	1.09298	0.546489	+	0.837466i	$0.315964\pi$
$24$	−0.905567	−0.184848
$25$	−3.76629	−0.753259
$26$	−6.12471	−1.20115
$27$	4.69079	0.902743
$28$	−1.83235	−0.346282
$29$	−1.90586	−0.353909	−0.176955	−	0.984219i	$-0.556625\pi$
$29$	−1.90586	−0.353909	−0.176955	+	0.984219i	$0.556625\pi$
$30$	1.00583	0.183639
$31$	5.13820	0.922848	0.461424	−	0.887180i	$-0.347339\pi$
$31$	5.13820	0.922848	0.461424	+	0.887180i	$0.347339\pi$
$32$	1.00000	0.176777
$33$	−2.85282	−0.496612
$34$	1.33116	0.228293
$35$	2.03524	0.344018
$36$	−2.17995	−0.363325
$37$	−8.79434	−1.44578	−0.722890	−	0.690963i	$-0.757187\pi$
$37$	−8.79434	−1.44578	−0.722890	+	0.690963i	$0.757187\pi$
$38$	1.55764	0.252682
$39$	5.54633	0.888124
$40$	−1.11072	−0.175621
$41$	−1.96990	−0.307647	−0.153824	−	0.988098i	$-0.549159\pi$
$41$	−1.96990	−0.307647	−0.153824	+	0.988098i	$0.549159\pi$
$42$	1.65932	0.256039
$43$	−2.51896	−0.384138	−0.192069	−	0.981381i	$-0.561520\pi$
$43$	−2.51896	−0.384138	−0.192069	+	0.981381i	$0.561520\pi$
$44$	3.15031	0.474927
$45$	2.42132	0.360949
$46$	5.24174	0.772853
$47$	7.53212	1.09867	0.549336	−	0.835602i	$-0.314881\pi$
$47$	7.53212	1.09867	0.549336	+	0.835602i	$0.314881\pi$
$48$	−0.905567	−0.130707
$49$	−3.64248	−0.520354
$50$	−3.76629	−0.532634
$51$	−1.20546	−0.168798
$52$	−6.12471	−0.849344
$53$	2.37305	0.325963	0.162982	−	0.986629i	$-0.447889\pi$
$53$	2.37305	0.325963	0.162982	+	0.986629i	$0.447889\pi$
$54$	4.69079	0.638336
$55$	−3.49912	−0.471822
$56$	−1.83235	−0.244859
$57$	−1.41054	−0.186831
$58$	−1.90586	−0.250252
$59$	13.3052	1.73218	0.866092	−	0.499885i	$-0.166624\pi$
$59$	13.3052	1.73218	0.866092	+	0.499885i	$0.166624\pi$
$60$	1.00583	0.129853
$61$	−2.35511	−0.301541	−0.150770	−	0.988569i	$-0.548175\pi$
$61$	−2.35511	−0.301541	−0.150770	+	0.988569i	$0.548175\pi$
$62$	5.13820	0.652552
$63$	3.99444	0.503252
$64$	1.00000	0.125000
$65$	6.80285	0.843790
$66$	−2.85282	−0.351158
$67$	5.23120	0.639092	0.319546	−	0.947571i	$-0.396470\pi$
$67$	5.23120	0.639092	0.319546	+	0.947571i	$0.396470\pi$
$68$	1.33116	0.161427
$69$	−4.74675	−0.571441
$70$	2.03524	0.243258
$71$	2.21953	0.263410	0.131705	−	0.991289i	$-0.457955\pi$
$71$	2.21953	0.263410	0.131705	+	0.991289i	$0.457955\pi$
$72$	−2.17995	−0.256909
$73$	7.62746	0.892727	0.446363	−	0.894852i	$-0.352719\pi$
$73$	7.62746	0.892727	0.446363	+	0.894852i	$0.352719\pi$
$74$	−8.79434	−1.02232
$75$	3.41063	0.393826
$76$	1.55764	0.178673
$77$	−5.77249	−0.657836
$78$	5.54633	0.627998
$79$	5.41653	0.609407	0.304703	−	0.952447i	$-0.401443\pi$
$79$	5.41653	0.609407	0.304703	+	0.952447i	$0.401443\pi$
$80$	−1.11072	−0.124183
$81$	2.29202	0.254669
$82$	−1.96990	−0.217540
$83$	13.7768	1.51220	0.756098	−	0.654459i	$-0.227103\pi$
$83$	13.7768	1.51220	0.756098	+	0.654459i	$0.227103\pi$
$84$	1.65932	0.181047
$85$	−1.47856	−0.160372
$86$	−2.51896	−0.271626
$87$	1.72588	0.185034
$88$	3.15031	0.335824
$89$	−3.22130	−0.341457	−0.170728	−	0.985318i	$-0.554612\pi$
$89$	−3.22130	−0.341457	−0.170728	+	0.985318i	$0.554612\pi$
$90$	2.42132	0.255230
$91$	11.2226	1.17645
$92$	5.24174	0.546489
$93$	−4.65298	−0.482492
$94$	7.53212	0.776878
$95$	−1.73010	−0.177505
$96$	−0.905567	−0.0924240
$97$	−0.906230	−0.0920137	−0.0460069	−	0.998941i	$-0.514650\pi$
$97$	−0.906230	−0.0920137	−0.0460069	+	0.998941i	$0.514650\pi$
$98$	−3.64248	−0.367946
$99$	−6.86752	−0.690211
$100$	−3.76629	−0.376629
$101$	15.5762	1.54989	0.774947	−	0.632026i	$-0.217776\pi$
$101$	15.5762	1.54989	0.774947	+	0.632026i	$0.217776\pi$
$102$	−1.20546	−0.119358
$103$	−4.69566	−0.462677	−0.231338	−	0.972873i	$-0.574310\pi$
$103$	−4.69566	−0.462677	−0.231338	+	0.972873i	$0.574310\pi$
$104$	−6.12471	−0.600577
$105$	−1.84305	−0.179863
$106$	2.37305	0.230491
$107$	5.27981	0.510418	0.255209	−	0.966886i	$-0.417856\pi$
$107$	5.27981	0.510418	0.255209	+	0.966886i	$0.417856\pi$
$108$	4.69079	0.451371
$109$	15.1914	1.45507	0.727536	−	0.686069i	$-0.240665\pi$
$109$	15.1914	1.45507	0.727536	+	0.686069i	$0.240665\pi$
$110$	−3.49912	−0.333628
$111$	7.96386	0.755897
$112$	−1.83235	−0.173141
$113$	15.7089	1.47777	0.738884	−	0.673833i	$-0.235353\pi$
$113$	15.7089	1.47777	0.738884	+	0.673833i	$0.235353\pi$
$114$	−1.41054	−0.132109
$115$	−5.82213	−0.542916
$116$	−1.90586	−0.176955
$117$	13.3515	1.23435
$118$	13.3052	1.22484
$119$	−2.43917	−0.223598
$120$	1.00583	0.0918197
$121$	−1.07554	−0.0977763
$122$	−2.35511	−0.213222
$123$	1.78388	0.160847
$124$	5.13820	0.461424
$125$	9.73693	0.870897
$126$	3.99444	0.355853
$127$	−16.9589	−1.50486	−0.752431	−	0.658671i	$-0.771119\pi$
$127$	−16.9589	−1.50486	−0.752431	+	0.658671i	$0.771119\pi$
$128$	1.00000	0.0883883
$129$	2.28109	0.200838
$130$	6.80285	0.596650
$131$	1.09649	0.0958012	0.0479006	−	0.998852i	$-0.484747\pi$
$131$	1.09649	0.0958012	0.0479006	+	0.998852i	$0.484747\pi$
$132$	−2.85282	−0.248306
$133$	−2.85414	−0.247485
$134$	5.23120	0.451907
$135$	−5.21017	−0.448420
$136$	1.33116	0.114146
$137$	3.71597	0.317477	0.158739	−	0.987321i	$-0.449257\pi$
$137$	3.71597	0.317477	0.158739	+	0.987321i	$0.449257\pi$
$138$	−4.74675	−0.404070
$139$	−17.8798	−1.51654	−0.758271	−	0.651940i	$-0.773956\pi$
$139$	−17.8798	−1.51654	−0.758271	+	0.651940i	$0.773956\pi$
$140$	2.03524	0.172009
$141$	−6.82083	−0.574418
$142$	2.21953	0.186259
$143$	−19.2947	−1.61351
$144$	−2.17995	−0.181662
$145$	2.11688	0.175798
$146$	7.62746	0.631253
$147$	3.29851	0.272056
$148$	−8.79434	−0.722890
$149$	3.61186	0.295895	0.147948	−	0.988995i	$-0.452733\pi$
$149$	3.61186	0.295895	0.147948	+	0.988995i	$0.452733\pi$
$150$	3.41063	0.278477
$151$	11.5629	0.940974	0.470487	−	0.882407i	$-0.344078\pi$
$151$	11.5629	0.940974	0.470487	+	0.882407i	$0.344078\pi$
$152$	1.55764	0.126341
$153$	−2.90187	−0.234602
$154$	−5.77249	−0.465160
$155$	−5.70712	−0.458407
$156$	5.54633	0.444062
$157$	−0.651038	−0.0519585	−0.0259793	−	0.999662i	$-0.508270\pi$
$157$	−0.651038	−0.0519585	−0.0259793	+	0.999662i	$0.508270\pi$
$158$	5.41653	0.430916
$159$	−2.14895	−0.170423
$160$	−1.11072	−0.0878104
$161$	−9.60473	−0.756959
$162$	2.29202	0.180078
$163$	13.4358	1.05237	0.526186	−	0.850370i	$-0.323622\pi$
$163$	13.4358	1.05237	0.526186	+	0.850370i	$0.323622\pi$
$164$	−1.96990	−0.153824
$165$	3.16869	0.246682
$166$	13.7768	1.06928
$167$	5.77053	0.446537	0.223268	−	0.974757i	$-0.428327\pi$
$167$	5.77053	0.446537	0.223268	+	0.974757i	$0.428327\pi$
$168$	1.65932	0.128019
$169$	24.5120	1.88554
$170$	−1.47856	−0.113400
$171$	−3.39556	−0.259665
$172$	−2.51896	−0.192069
$173$	−7.86912	−0.598278	−0.299139	−	0.954210i	$-0.596699\pi$
$173$	−7.86912	−0.598278	−0.299139	+	0.954210i	$0.596699\pi$
$174$	1.72588	0.130839
$175$	6.90118	0.521680
$176$	3.15031	0.237464
$177$	−12.0487	−0.905637
$178$	−3.22130	−0.241446
$179$	9.51175	0.710942	0.355471	−	0.934687i	$-0.384321\pi$
$179$	9.51175	0.710942	0.355471	+	0.934687i	$0.384321\pi$
$180$	2.42132	0.180475
$181$	3.98713	0.296361	0.148181	−	0.988960i	$-0.452658\pi$
$181$	3.98713	0.296361	0.148181	+	0.988960i	$0.452658\pi$
$182$	11.2226	0.831877
$183$	2.13271	0.157654
$184$	5.24174	0.386426
$185$	9.76808	0.718164
$186$	−4.65298	−0.341173
$187$	4.19358	0.306665
$188$	7.53212	0.549336
$189$	−8.59519	−0.625208
$190$	−1.73010	−0.125515
$191$	−20.1158	−1.45553	−0.727763	−	0.685829i	$-0.759440\pi$
$191$	−20.1158	−1.45553	−0.727763	+	0.685829i	$0.759440\pi$
$192$	−0.905567	−0.0653537
$193$	−9.29027	−0.668729	−0.334364	−	0.942444i	$-0.608522\pi$
$193$	−9.29027	−0.668729	−0.334364	+	0.942444i	$0.608522\pi$
$194$	−0.906230	−0.0650635
$195$	−6.16044	−0.441158
$196$	−3.64248	−0.260177
$197$	8.76077	0.624179	0.312089	−	0.950053i	$-0.398971\pi$
$197$	8.76077	0.624179	0.312089	+	0.950053i	$0.398971\pi$
$198$	−6.86752	−0.488053
$199$	−18.5188	−1.31276	−0.656382	−	0.754429i	$-0.727914\pi$
$199$	−18.5188	−1.31276	−0.656382	+	0.754429i	$0.727914\pi$
$200$	−3.76629	−0.266317
$201$	−4.73720	−0.334136
$202$	15.5762	1.09594
$203$	3.49221	0.245105
$204$	−1.20546	−0.0843990
$205$	2.18802	0.152818
$206$	−4.69566	−0.327162
$207$	−11.4267	−0.794212
$208$	−6.12471	−0.424672
$209$	4.90704	0.339427
$210$	−1.84305	−0.127182
$211$	−4.14174	−0.285129	−0.142564	−	0.989786i	$-0.545535\pi$
$211$	−4.14174	−0.285129	−0.142564	+	0.989786i	$0.545535\pi$
$212$	2.37305	0.162982
$213$	−2.00993	−0.137718
$214$	5.27981	0.360920
$215$	2.79787	0.190813
$216$	4.69079	0.319168
$217$	−9.41500	−0.639132
$218$	15.1914	1.02889
$219$	−6.90718	−0.466744
$220$	−3.49912	−0.235911
$221$	−8.15299	−0.548430
$222$	7.96386	0.534500
$223$	16.4997	1.10490	0.552452	−	0.833545i	$-0.313692\pi$
$223$	16.4997	1.10490	0.552452	+	0.833545i	$0.313692\pi$
$224$	−1.83235	−0.122429
$225$	8.21033	0.547355
$226$	15.7089	1.04494
$227$	−14.8796	−0.987593	−0.493796	−	0.869577i	$-0.664391\pi$
$227$	−14.8796	−0.987593	−0.493796	+	0.869577i	$0.664391\pi$
$228$	−1.41054	−0.0934155
$229$	−21.2658	−1.40529	−0.702643	−	0.711542i	$-0.747997\pi$
$229$	−21.2658	−1.40529	−0.702643	+	0.711542i	$0.747997\pi$
$230$	−5.82213	−0.383900
$231$	5.22737	0.343936
$232$	−1.90586	−0.125126
$233$	−16.2103	−1.06197	−0.530985	−	0.847381i	$-0.678178\pi$
$233$	−16.2103	−1.06197	−0.530985	+	0.847381i	$0.678178\pi$
$234$	13.3515	0.872818
$235$	−8.36610	−0.545744
$236$	13.3052	0.866092
$237$	−4.90503	−0.318616
$238$	−2.43917	−0.158108
$239$	21.1470	1.36788	0.683942	−	0.729536i	$-0.260264\pi$
$239$	21.1470	1.36788	0.683942	+	0.729536i	$0.260264\pi$
$240$	1.00583	0.0649263
$241$	22.3968	1.44271	0.721353	−	0.692568i	$-0.243521\pi$
$241$	22.3968	1.44271	0.721353	+	0.692568i	$0.243521\pi$
$242$	−1.07554	−0.0691383
$243$	−16.1479	−1.03589
$244$	−2.35511	−0.150770
$245$	4.04579	0.258476
$246$	1.78388	0.113736
$247$	−9.54006	−0.607019
$248$	5.13820	0.326276
$249$	−12.4758	−0.790620
$250$	9.73693	0.615817
$251$	29.5345	1.86420	0.932102	−	0.362196i	$-0.117973\pi$
$251$	29.5345	1.86420	0.932102	+	0.362196i	$0.117973\pi$
$252$	3.99444	0.251626
$253$	16.5131	1.03817
$254$	−16.9589	−1.06410
$255$	1.33893	0.0838472
$256$	1.00000	0.0625000
$257$	−8.15983	−0.508996	−0.254498	−	0.967073i	$-0.581910\pi$
$257$	−8.15983	−0.508996	−0.254498	+	0.967073i	$0.581910\pi$
$258$	2.28109	0.142014
$259$	16.1144	1.00130
$260$	6.80285	0.421895
$261$	4.15468	0.257168
$262$	1.09649	0.0677417
$263$	−6.98993	−0.431018	−0.215509	−	0.976502i	$-0.569141\pi$
$263$	−6.98993	−0.431018	−0.215509	+	0.976502i	$0.569141\pi$
$264$	−2.85282	−0.175579
$265$	−2.63580	−0.161916
$266$	−2.85414	−0.174999
$267$	2.91710	0.178524
$268$	5.23120	0.319546
$269$	18.8231	1.14767	0.573833	−	0.818972i	$-0.305456\pi$
$269$	18.8231	1.14767	0.573833	+	0.818972i	$0.305456\pi$
$270$	−5.21017	−0.317081
$271$	27.9400	1.69724	0.848618	−	0.529006i	$-0.177435\pi$
$271$	27.9400	1.69724	0.848618	+	0.529006i	$0.177435\pi$
$272$	1.33116	0.0807137
$273$	−10.1628	−0.615083
$274$	3.71597	0.224490
$275$	−11.8650	−0.715486
$276$	−4.74675	−0.285721
$277$	−5.83152	−0.350382	−0.175191	−	0.984534i	$-0.556054\pi$
$277$	−5.83152	−0.350382	−0.175191	+	0.984534i	$0.556054\pi$
$278$	−17.8798	−1.07236
$279$	−11.2010	−0.670587
$280$	2.03524	0.121629
$281$	18.3223	1.09302	0.546509	−	0.837453i	$-0.315956\pi$
$281$	18.3223	1.09302	0.546509	+	0.837453i	$0.315956\pi$
$282$	−6.82083	−0.406175
$283$	13.6532	0.811601	0.405801	−	0.913962i	$-0.366993\pi$
$283$	13.6532	0.811601	0.405801	+	0.913962i	$0.366993\pi$
$284$	2.21953	0.131705
$285$	1.56672	0.0928047
$286$	−19.2947	−1.14092
$287$	3.60956	0.213066
$288$	−2.17995	−0.128455
$289$	−15.2280	−0.895765
$290$	2.11688	0.124308
$291$	0.820652	0.0481075
$292$	7.62746	0.446363
$293$	17.3412	1.01309	0.506543	−	0.862215i	$-0.330923\pi$
$293$	17.3412	1.01309	0.506543	+	0.862215i	$0.330923\pi$
$294$	3.29851	0.192373
$295$	−14.7784	−0.860429
$296$	−8.79434	−0.511161
$297$	14.7774	0.857475
$298$	3.61186	0.209230
$299$	−32.1041	−1.85663
$300$	3.41063	0.196913
$301$	4.61563	0.266040
$302$	11.5629	0.665369
$303$	−14.1053	−0.810330
$304$	1.55764	0.0893365
$305$	2.61588	0.149785
$306$	−2.90187	−0.165889
$307$	−14.9562	−0.853598	−0.426799	−	0.904347i	$-0.640359\pi$
$307$	−14.9562	−0.853598	−0.426799	+	0.904347i	$0.640359\pi$
$308$	−5.77249	−0.328918
$309$	4.25223	0.241901
$310$	−5.70712	−0.324143
$311$	14.5546	0.825313	0.412657	−	0.910887i	$-0.364601\pi$
$311$	14.5546	0.825313	0.412657	+	0.910887i	$0.364601\pi$
$312$	5.54633	0.313999
$313$	1.34600	0.0760804	0.0380402	−	0.999276i	$-0.487889\pi$
$313$	1.34600	0.0760804	0.0380402	+	0.999276i	$0.487889\pi$
$314$	−0.651038	−0.0367402
$315$	−4.43672	−0.249981
$316$	5.41653	0.304703
$317$	9.02892	0.507115	0.253557	−	0.967320i	$-0.418399\pi$
$317$	9.02892	0.507115	0.253557	+	0.967320i	$0.418399\pi$
$318$	−2.14895	−0.120507
$319$	−6.00405	−0.336163
$320$	−1.11072	−0.0620913
$321$	−4.78122	−0.266862
$322$	−9.60473	−0.535251
$323$	2.07347	0.115371
$324$	2.29202	0.127335
$325$	23.0674	1.27955
$326$	13.4358	0.744139
$327$	−13.7568	−0.760755
$328$	−1.96990	−0.108770
$329$	−13.8015	−0.760902
$330$	3.16869	0.174431
$331$	17.5993	0.967347	0.483674	−	0.875248i	$-0.339302\pi$
$331$	17.5993	0.967347	0.483674	+	0.875248i	$0.339302\pi$
$332$	13.7768	0.756098
$333$	19.1712	1.05058
$334$	5.77053	0.315749
$335$	−5.81041	−0.317457
$336$	1.65932	0.0905233
$337$	−27.8689	−1.51811	−0.759057	−	0.651025i	$-0.774339\pi$
$337$	−27.8689	−1.51811	−0.759057	+	0.651025i	$0.774339\pi$
$338$	24.5120	1.33328
$339$	−14.2255	−0.772620
$340$	−1.47856	−0.0801860
$341$	16.1869	0.876571
$342$	−3.39556	−0.183611
$343$	19.5008	1.05294
$344$	−2.51896	−0.135813
$345$	5.27232	0.283852
$346$	−7.86912	−0.423047
$347$	9.61696	0.516265	0.258133	−	0.966109i	$-0.416893\pi$
$347$	9.61696	0.516265	0.258133	+	0.966109i	$0.416893\pi$
$348$	1.72588	0.0925171
$349$	−22.0680	−1.18127	−0.590637	−	0.806937i	$-0.701123\pi$
$349$	−22.0680	−1.18127	−0.590637	+	0.806937i	$0.701123\pi$
$350$	6.90118	0.368884
$351$	−28.7297	−1.53348
$352$	3.15031	0.167912
$353$	21.9797	1.16986	0.584930	−	0.811084i	$-0.301122\pi$
$353$	21.9797	1.16986	0.584930	+	0.811084i	$0.301122\pi$
$354$	−12.0487	−0.640382
$355$	−2.46528	−0.130844
$356$	−3.22130	−0.170728
$357$	2.20883	0.116904
$358$	9.51175	0.502712
$359$	−14.5307	−0.766904	−0.383452	−	0.923561i	$-0.625265\pi$
$359$	−14.5307	−0.766904	−0.383452	+	0.923561i	$0.625265\pi$
$360$	2.42132	0.127615
$361$	−16.5738	−0.872304
$362$	3.98713	0.209559
$363$	0.973973	0.0511203
$364$	11.2226	0.588226
$365$	−8.47200	−0.443445
$366$	2.13271	0.111479
$367$	−16.9474	−0.884648	−0.442324	−	0.896855i	$-0.645846\pi$
$367$	−16.9474	−0.884648	−0.442324	+	0.896855i	$0.645846\pi$
$368$	5.24174	0.273245
$369$	4.29429	0.223552
$370$	9.76808	0.507818
$371$	−4.34827	−0.225751
$372$	−4.65298	−0.241246
$373$	−26.1033	−1.35158	−0.675789	−	0.737095i	$-0.736197\pi$
$373$	−26.1033	−1.35158	−0.675789	+	0.737095i	$0.736197\pi$
$374$	4.19358	0.216845
$375$	−8.81744	−0.455331
$376$	7.53212	0.388439
$377$	11.6728	0.601182
$378$	−8.59519	−0.442089
$379$	3.91896	0.201303	0.100652	−	0.994922i	$-0.467907\pi$
$379$	3.91896	0.201303	0.100652	+	0.994922i	$0.467907\pi$
$380$	−1.73010	−0.0887524
$381$	15.3575	0.786786
$382$	−20.1158	−1.02921
$383$	−15.8472	−0.809756	−0.404878	−	0.914371i	$-0.632686\pi$
$383$	−15.8472	−0.809756	−0.404878	+	0.914371i	$0.632686\pi$
$384$	−0.905567	−0.0462120
$385$	6.41164	0.326767
$386$	−9.29027	−0.472862
$387$	5.49120	0.279133
$388$	−0.906230	−0.0460069
$389$	−7.21865	−0.366000	−0.183000	−	0.983113i	$-0.558581\pi$
$389$	−7.21865	−0.366000	−0.183000	+	0.983113i	$0.558581\pi$
$390$	−6.16044	−0.311946
$391$	6.97762	0.352873
$392$	−3.64248	−0.183973
$393$	−0.992950	−0.0500877
$394$	8.76077	0.441361
$395$	−6.01626	−0.302711
$396$	−6.86752	−0.345106
$397$	−15.8773	−0.796859	−0.398430	−	0.917199i	$-0.630445\pi$
$397$	−15.8773	−0.796859	−0.398430	+	0.917199i	$0.630445\pi$
$398$	−18.5188	−0.928264
$399$	2.58461	0.129393
$400$	−3.76629	−0.188315
$401$	1.27789	0.0638149	0.0319075	−	0.999491i	$-0.489842\pi$
$401$	1.27789	0.0638149	0.0319075	+	0.999491i	$0.489842\pi$
$402$	−4.73720	−0.236270
$403$	−31.4700	−1.56763
$404$	15.5762	0.774947
$405$	−2.54580	−0.126502
$406$	3.49221	0.173316
$407$	−27.7049	−1.37328
$408$	−1.20546	−0.0596791
$409$	34.1182	1.68704	0.843519	−	0.537100i	$-0.180480\pi$
$409$	34.1182	1.68704	0.843519	+	0.537100i	$0.180480\pi$
$410$	2.18802	0.108059
$411$	−3.36506	−0.165986
$412$	−4.69566	−0.231338
$413$	−24.3798	−1.19965
$414$	−11.4267	−0.561593
$415$	−15.3022	−0.751154
$416$	−6.12471	−0.300288
$417$	16.1913	0.792893
$418$	4.90704	0.240011
$419$	17.3757	0.848856	0.424428	−	0.905462i	$-0.360475\pi$
$419$	17.3757	0.848856	0.424428	+	0.905462i	$0.360475\pi$
$420$	−1.84305	−0.0899314
$421$	20.8473	1.01603	0.508017	−	0.861347i	$-0.330379\pi$
$421$	20.8473	1.01603	0.508017	+	0.861347i	$0.330379\pi$
$422$	−4.14174	−0.201617
$423$	−16.4196	−0.798350
$424$	2.37305	0.115245
$425$	−5.01356	−0.243193
$426$	−2.00993	−0.0973816
$427$	4.31540	0.208837
$428$	5.27981	0.255209
$429$	17.4727	0.843588
$430$	2.79787	0.134925
$431$	10.5659	0.508940	0.254470	−	0.967081i	$-0.418099\pi$
$431$	10.5659	0.508940	0.254470	+	0.967081i	$0.418099\pi$
$432$	4.69079	0.225686
$433$	−26.6808	−1.28220	−0.641099	−	0.767458i	$-0.721521\pi$
$433$	−26.6808	−1.28220	−0.641099	+	0.767458i	$0.721521\pi$
$434$	−9.41500	−0.451935
$435$	−1.91698	−0.0919122
$436$	15.1914	0.727536
$437$	8.16472	0.390572
$438$	−6.90718	−0.330038
$439$	−11.2927	−0.538973	−0.269487	−	0.963004i	$-0.586854\pi$
$439$	−11.2927	−0.538973	−0.269487	+	0.963004i	$0.586854\pi$
$440$	−3.49912	−0.166814
$441$	7.94041	0.378115
$442$	−8.15299	−0.387798
$443$	−24.0916	−1.14463	−0.572314	−	0.820034i	$-0.693954\pi$
$443$	−24.0916	−1.14463	−0.572314	+	0.820034i	$0.693954\pi$
$444$	7.96386	0.377948
$445$	3.57797	0.169612
$446$	16.4997	0.781285
$447$	−3.27078	−0.154703
$448$	−1.83235	−0.0865706
$449$	−6.74186	−0.318168	−0.159084	−	0.987265i	$-0.550854\pi$
$449$	−6.74186	−0.318168	−0.159084	+	0.987265i	$0.550854\pi$
$450$	8.21033	0.387038
$451$	−6.20581	−0.292220
$452$	15.7089	0.738884
$453$	−10.4710	−0.491969
$454$	−14.8796	−0.698334
$455$	−12.4652	−0.584380
$456$	−1.41054	−0.0660547
$457$	26.9300	1.25973	0.629865	−	0.776704i	$-0.283110\pi$
$457$	26.9300	1.25973	0.629865	+	0.776704i	$0.283110\pi$
$458$	−21.2658	−0.993687
$459$	6.24421	0.291455
$460$	−5.82213	−0.271458
$461$	−34.2071	−1.59318	−0.796591	−	0.604519i	$-0.793365\pi$
$461$	−34.2071	−1.59318	−0.796591	+	0.604519i	$0.793365\pi$
$462$	5.22737	0.243199
$463$	−25.3289	−1.17713	−0.588567	−	0.808449i	$-0.700308\pi$
$463$	−25.3289	−1.17713	−0.588567	+	0.808449i	$0.700308\pi$
$464$	−1.90586	−0.0884774
$465$	5.16818	0.239669
$466$	−16.2103	−0.750926
$467$	41.3175	1.91194	0.955972	−	0.293456i	$-0.0948055\pi$
$467$	41.3175	1.91194	0.955972	+	0.293456i	$0.0948055\pi$
$468$	13.3515	0.617175
$469$	−9.58541	−0.442613
$470$	−8.36610	−0.385899
$471$	0.589559	0.0271654
$472$	13.3052	0.612420
$473$	−7.93551	−0.364875
$474$	−4.90503	−0.225295
$475$	−5.86651	−0.269174
$476$	−2.43917	−0.111799
$477$	−5.17312	−0.236861
$478$	21.1470	0.967240
$479$	14.2931	0.653067	0.326533	−	0.945186i	$-0.394119\pi$
$479$	14.2931	0.653067	0.326533	+	0.945186i	$0.394119\pi$
$480$	1.00583	0.0459099
$481$	53.8628	2.45593
$482$	22.3968	1.02015
$483$	8.69772	0.395760
$484$	−1.07554	−0.0488882
$485$	1.00657	0.0457060
$486$	−16.1479	−0.732486
$487$	−2.49634	−0.113120	−0.0565600	−	0.998399i	$-0.518013\pi$
$487$	−2.49634	−0.113120	−0.0565600	+	0.998399i	$0.518013\pi$
$488$	−2.35511	−0.106611
$489$	−12.1670	−0.550211
$490$	4.04579	0.182770
$491$	0.912369	0.0411747	0.0205873	−	0.999788i	$-0.493446\pi$
$491$	0.912369	0.0411747	0.0205873	+	0.999788i	$0.493446\pi$
$492$	1.78388	0.0804236
$493$	−2.53702	−0.114261
$494$	−9.54006	−0.429227
$495$	7.62791	0.342849
$496$	5.13820	0.230712
$497$	−4.06697	−0.182428
$498$	−12.4758	−0.559053
$499$	−19.7594	−0.884552	−0.442276	−	0.896879i	$-0.645829\pi$
$499$	−19.7594	−0.884552	−0.442276	+	0.896879i	$0.645829\pi$
$500$	9.73693	0.435449
$501$	−5.22560	−0.233463
$502$	29.5345	1.31819
$503$	2.37585	0.105934	0.0529669	−	0.998596i	$-0.483132\pi$
$503$	2.37585	0.105934	0.0529669	+	0.998596i	$0.483132\pi$
$504$	3.99444	0.177926
$505$	−17.3009	−0.769880
$506$	16.5131	0.734098
$507$	−22.1973	−0.985815
$508$	−16.9589	−0.752431
$509$	−31.5294	−1.39751	−0.698757	−	0.715359i	$-0.746263\pi$
$509$	−31.5294	−1.39751	−0.698757	+	0.715359i	$0.746263\pi$
$510$	1.33893	0.0592889
$511$	−13.9762	−0.618271
$512$	1.00000	0.0441942
$513$	7.30654	0.322592
$514$	−8.15983	−0.359915
$515$	5.21558	0.229826
$516$	2.28109	0.100419
$517$	23.7285	1.04358
$518$	16.1144	0.708024
$519$	7.12602	0.312797
$520$	6.80285	0.298325
$521$	5.02777	0.220271	0.110135	−	0.993917i	$-0.464872\pi$
$521$	5.02777	0.220271	0.110135	+	0.993917i	$0.464872\pi$
$522$	4.15468	0.181845
$523$	−10.1924	−0.445684	−0.222842	−	0.974855i	$-0.571533\pi$
$523$	−10.1924	−0.445684	−0.222842	+	0.974855i	$0.571533\pi$
$524$	1.09649	0.0479006
$525$	−6.24948	−0.272750
$526$	−6.98993	−0.304775
$527$	6.83979	0.297946
$528$	−2.85282	−0.124153
$529$	4.47585	0.194602
$530$	−2.63580	−0.114492
$531$	−29.0046	−1.25869
$532$	−2.85414	−0.123743
$533$	12.0651	0.522597
$534$	2.91710	0.126235
$535$	−5.86441	−0.253540
$536$	5.23120	0.225953
$537$	−8.61353	−0.371701
$538$	18.8231	0.811523
$539$	−11.4749	−0.494260
$540$	−5.21017	−0.224210
$541$	−30.4397	−1.30871	−0.654353	−	0.756190i	$-0.727059\pi$
$541$	−30.4397	−1.30871	−0.654353	+	0.756190i	$0.727059\pi$
$542$	27.9400	1.20013
$543$	−3.61061	−0.154946
$544$	1.33116	0.0570732
$545$	−16.8735	−0.722779
$546$	−10.1628	−0.434930
$547$	−17.8855	−0.764730	−0.382365	−	0.924011i	$-0.624890\pi$
$547$	−17.8855	−0.764730	−0.382365	+	0.924011i	$0.624890\pi$
$548$	3.71597	0.158739
$549$	5.13402	0.219115
$550$	−11.8650	−0.505925
$551$	−2.96864	−0.126468
$552$	−4.74675	−0.202035
$553$	−9.92500	−0.422054
$554$	−5.83152	−0.247758
$555$	−8.84565	−0.375477
$556$	−17.8798	−0.758271
$557$	−22.0185	−0.932955	−0.466478	−	0.884533i	$-0.654477\pi$
$557$	−22.0185	−0.932955	−0.466478	+	0.884533i	$0.654477\pi$
$558$	−11.2010	−0.474177
$559$	15.4279	0.652530
$560$	2.03524	0.0860046
$561$	−3.79757	−0.160334
$562$	18.3223	0.772881
$563$	24.2447	1.02179	0.510896	−	0.859642i	$-0.329314\pi$
$563$	24.2447	1.02179	0.510896	+	0.859642i	$0.329314\pi$
$564$	−6.82083	−0.287209
$565$	−17.4482	−0.734053
$566$	13.6532	0.573889
$567$	−4.19980	−0.176375
$568$	2.21953	0.0931294
$569$	−20.0874	−0.842109	−0.421054	−	0.907035i	$-0.638340\pi$
$569$	−20.0874	−0.842109	−0.421054	+	0.907035i	$0.638340\pi$
$570$	1.56672	0.0656228
$571$	34.0325	1.42422	0.712109	−	0.702069i	$-0.247740\pi$
$571$	34.0325	1.42422	0.712109	+	0.702069i	$0.247740\pi$
$572$	−19.2947	−0.806753
$573$	18.2162	0.760992
$574$	3.60956	0.150660
$575$	−19.7419	−0.823296
$576$	−2.17995	−0.0908312
$577$	26.9081	1.12020	0.560100	−	0.828425i	$-0.310763\pi$
$577$	26.9081	1.12020	0.560100	+	0.828425i	$0.310763\pi$
$578$	−15.2280	−0.633401
$579$	8.41296	0.349631
$580$	2.11688	0.0878989
$581$	−25.2439	−1.04729
$582$	0.820652	0.0340171
$583$	7.47584	0.309618
$584$	7.62746	0.315627
$585$	−14.8299	−0.613140
$586$	17.3412	0.716360
$587$	−18.8926	−0.779782	−0.389891	−	0.920861i	$-0.627487\pi$
$587$	−18.8926	−0.779782	−0.389891	+	0.920861i	$0.627487\pi$
$588$	3.29851	0.136028
$589$	8.00344	0.329776
$590$	−14.7784	−0.608415
$591$	−7.93346	−0.326339
$592$	−8.79434	−0.361445
$593$	−8.89094	−0.365107	−0.182554	−	0.983196i	$-0.558436\pi$
$593$	−8.89094	−0.365107	−0.182554	+	0.983196i	$0.558436\pi$
$594$	14.7774	0.606326
$595$	2.70924	0.111068
$596$	3.61186	0.147948
$597$	16.7700	0.686351
$598$	−32.1041	−1.31284
$599$	−5.17748	−0.211546	−0.105773	−	0.994390i	$-0.533732\pi$
$599$	−5.17748	−0.211546	−0.105773	+	0.994390i	$0.533732\pi$
$600$	3.41063	0.139238
$601$	47.0867	1.92071	0.960354	−	0.278784i	$-0.0899315\pi$
$601$	47.0867	1.92071	0.960354	+	0.278784i	$0.0899315\pi$
$602$	4.61563	0.188119
$603$	−11.4037	−0.464396
$604$	11.5629	0.470487
$605$	1.19463	0.0485685
$606$	−14.1053	−0.572990
$607$	42.8514	1.73928	0.869642	−	0.493683i	$-0.164350\pi$
$607$	42.8514	1.73928	0.869642	+	0.493683i	$0.164350\pi$
$608$	1.55764	0.0631705
$609$	−3.16243	−0.128148
$610$	2.61588	0.105914
$611$	−46.1320	−1.86630
$612$	−2.90187	−0.117301
$613$	−3.39865	−0.137270	−0.0686351	−	0.997642i	$-0.521864\pi$
$613$	−3.39865	−0.137270	−0.0686351	+	0.997642i	$0.521864\pi$
$614$	−14.9562	−0.603585
$615$	−1.98140	−0.0798977
$616$	−5.77249	−0.232580
$617$	−12.9012	−0.519382	−0.259691	−	0.965692i	$-0.583621\pi$
$617$	−12.9012	−0.519382	−0.259691	+	0.965692i	$0.583621\pi$
$618$	4.25223	0.171050
$619$	40.9295	1.64510	0.822548	−	0.568695i	$-0.192552\pi$
$619$	40.9295	1.64510	0.822548	+	0.568695i	$0.192552\pi$
$620$	−5.70712	−0.229203
$621$	24.5879	0.986679
$622$	14.5546	0.583584
$623$	5.90256	0.236481
$624$	5.54633	0.222031
$625$	8.01643	0.320657
$626$	1.34600	0.0537969
$627$	−4.44365	−0.177462
$628$	−0.651038	−0.0259793
$629$	−11.7067	−0.466777
$630$	−4.43672	−0.176763
$631$	35.8511	1.42721	0.713606	−	0.700548i	$-0.247061\pi$
$631$	35.8511	1.42721	0.713606	+	0.700548i	$0.247061\pi$
$632$	5.41653	0.215458
$633$	3.75062	0.149074
$634$	9.02892	0.358584
$635$	18.8367	0.747511
$636$	−2.14895	−0.0852116
$637$	22.3091	0.883919
$638$	−6.00405	−0.237703
$639$	−4.83846	−0.191407
$640$	−1.11072	−0.0439052
$641$	−9.10277	−0.359538	−0.179769	−	0.983709i	$-0.557535\pi$
$641$	−9.10277	−0.359538	−0.179769	+	0.983709i	$0.557535\pi$
$642$	−4.78122	−0.188700
$643$	14.3229	0.564842	0.282421	−	0.959291i	$-0.408863\pi$
$643$	14.3229	0.564842	0.282421	+	0.959291i	$0.408863\pi$
$644$	−9.60473	−0.378479
$645$	−2.53366	−0.0997626
$646$	2.07347	0.0815796
$647$	−1.94348	−0.0764062	−0.0382031	−	0.999270i	$-0.512163\pi$
$647$	−1.94348	−0.0764062	−0.0382031	+	0.999270i	$0.512163\pi$
$648$	2.29202	0.0900391
$649$	41.9154	1.64532
$650$	23.0674	0.904779
$651$	8.52592	0.334157
$652$	13.4358	0.526186
$653$	−1.16538	−0.0456047	−0.0228023	−	0.999740i	$-0.507259\pi$
$653$	−1.16538	−0.0456047	−0.0228023	+	0.999740i	$0.507259\pi$
$654$	−13.7568	−0.537935
$655$	−1.21790	−0.0475874
$656$	−1.96990	−0.0769119
$657$	−16.6275	−0.648700
$658$	−13.8015	−0.538039
$659$	1.29591	0.0504816	0.0252408	−	0.999681i	$-0.491965\pi$
$659$	1.29591	0.0504816	0.0252408	+	0.999681i	$0.491965\pi$
$660$	3.16869	0.123341
$661$	−6.48999	−0.252431	−0.126216	−	0.992003i	$-0.540283\pi$
$661$	−6.48999	−0.252431	−0.126216	+	0.992003i	$0.540283\pi$
$662$	17.5993	0.684018
$663$	7.38308	0.286735
$664$	13.7768	0.534642
$665$	3.17016	0.122934
$666$	19.1712	0.742869
$667$	−9.99003	−0.386815
$668$	5.77053	0.223268
$669$	−14.9416	−0.577676
$670$	−5.81041	−0.224476
$671$	−7.41933	−0.286420
$672$	1.65932	0.0640096
$673$	−49.1916	−1.89620	−0.948099	−	0.317976i	$-0.896997\pi$
$673$	−49.1916	−1.89620	−0.948099	+	0.317976i	$0.896997\pi$
$674$	−27.8689	−1.07347
$675$	−17.6669	−0.679999
$676$	24.5120	0.942770
$677$	−26.9734	−1.03667	−0.518337	−	0.855177i	$-0.673449\pi$
$677$	−26.9734	−1.03667	−0.518337	+	0.855177i	$0.673449\pi$
$678$	−14.2255	−0.546325
$679$	1.66053	0.0637255
$680$	−1.47856	−0.0567000
$681$	13.4745	0.516343
$682$	16.1869	0.619830
$683$	−5.23521	−0.200320	−0.100160	−	0.994971i	$-0.531935\pi$
$683$	−5.23521	−0.200320	−0.100160	+	0.994971i	$0.531935\pi$
$684$	−3.39556	−0.129833
$685$	−4.12742	−0.157701
$686$	19.5008	0.744544
$687$	19.2576	0.734725
$688$	−2.51896	−0.0960344
$689$	−14.5342	−0.553710
$690$	5.27232	0.200714
$691$	−1.23484	−0.0469755	−0.0234878	−	0.999724i	$-0.507477\pi$
$691$	−1.23484	−0.0469755	−0.0234878	+	0.999724i	$0.507477\pi$
$692$	−7.86912	−0.299139
$693$	12.5837	0.478016
$694$	9.61696	0.365055
$695$	19.8595	0.753313
$696$	1.72588	0.0654195
$697$	−2.62227	−0.0993255
$698$	−22.0680	−0.835287
$699$	14.6795	0.555229
$700$	6.90118	0.260840
$701$	−10.9735	−0.414463	−0.207232	−	0.978292i	$-0.566445\pi$
$701$	−10.9735	−0.414463	−0.207232	+	0.978292i	$0.566445\pi$
$702$	−28.7297	−1.08433
$703$	−13.6984	−0.516644
$704$	3.15031	0.118732
$705$	7.57606	0.285331
$706$	21.9797	0.827216
$707$	−28.5412	−1.07340
$708$	−12.0487	−0.452818
$709$	13.1590	0.494195	0.247098	−	0.968991i	$-0.420523\pi$
$709$	13.1590	0.494195	0.247098	+	0.968991i	$0.420523\pi$
$710$	−2.46528	−0.0925205
$711$	−11.8078	−0.442825
$712$	−3.22130	−0.120723
$713$	26.9331	1.00865
$714$	2.20883	0.0826633
$715$	21.4311	0.801478
$716$	9.51175	0.355471
$717$	−19.1500	−0.715170
$718$	−14.5307	−0.542283
$719$	−16.5511	−0.617252	−0.308626	−	0.951183i	$-0.599869\pi$
$719$	−16.5511	−0.617252	−0.308626	+	0.951183i	$0.599869\pi$
$720$	2.42132	0.0902373
$721$	8.60411	0.320434
$722$	−16.5738	−0.616812
$723$	−20.2818	−0.754289
$724$	3.98713	0.148181
$725$	7.17803	0.266585
$726$	0.973973	0.0361475
$727$	28.7031	1.06454	0.532269	−	0.846575i	$-0.321339\pi$
$727$	28.7031	1.06454	0.532269	+	0.846575i	$0.321339\pi$
$728$	11.2226	0.415938
$729$	7.74698	0.286925
$730$	−8.47200	−0.313563
$731$	−3.35315	−0.124021
$732$	2.13271	0.0788272
$733$	49.3927	1.82436	0.912181	−	0.409787i	$-0.134397\pi$
$733$	49.3927	1.82436	0.912181	+	0.409787i	$0.134397\pi$
$734$	−16.9474	−0.625541
$735$	−3.66373	−0.135139
$736$	5.24174	0.193213
$737$	16.4799	0.607045
$738$	4.29429	0.158075
$739$	−3.79336	−0.139541	−0.0697705	−	0.997563i	$-0.522227\pi$
$739$	−3.79336	−0.139541	−0.0697705	+	0.997563i	$0.522227\pi$
$740$	9.76808	0.359082
$741$	8.63916	0.317367
$742$	−4.34827	−0.159630
$743$	−39.3661	−1.44420	−0.722100	−	0.691788i	$-0.756823\pi$
$743$	−39.3661	−1.44420	−0.722100	+	0.691788i	$0.756823\pi$
$744$	−4.65298	−0.170587
$745$	−4.01178	−0.146980
$746$	−26.1033	−0.955710
$747$	−30.0326	−1.09884
$748$	4.19358	0.153333
$749$	−9.67448	−0.353498
$750$	−8.81744	−0.321967
$751$	−46.0971	−1.68211	−0.841053	−	0.540952i	$-0.818064\pi$
$751$	−46.0971	−1.68211	−0.841053	+	0.540952i	$0.818064\pi$
$752$	7.53212	0.274668
$753$	−26.7455	−0.974660
$754$	11.6728	0.425100
$755$	−12.8432	−0.467411
$756$	−8.59519	−0.312604
$757$	−38.2945	−1.39184	−0.695919	−	0.718121i	$-0.745003\pi$
$757$	−38.2945	−1.39184	−0.695919	+	0.718121i	$0.745003\pi$
$758$	3.91896	0.142343
$759$	−14.9537	−0.542786
$760$	−1.73010	−0.0627574
$761$	21.0060	0.761465	0.380733	−	0.924685i	$-0.375672\pi$
$761$	21.0060	0.761465	0.380733	+	0.924685i	$0.375672\pi$
$762$	15.3575	0.556342
$763$	−27.8360	−1.00773
$764$	−20.1158	−0.727763
$765$	3.22318	0.116534
$766$	−15.8472	−0.572584
$767$	−81.4902	−2.94244
$768$	−0.905567	−0.0326768
$769$	32.4373	1.16972	0.584859	−	0.811135i	$-0.301150\pi$
$769$	32.4373	1.16972	0.584859	+	0.811135i	$0.301150\pi$
$770$	6.41164	0.231059
$771$	7.38927	0.266118
$772$	−9.29027	−0.334364
$773$	37.2488	1.33974	0.669872	−	0.742476i	$-0.266349\pi$
$773$	37.2488	1.33974	0.669872	+	0.742476i	$0.266349\pi$
$774$	5.49120	0.197377
$775$	−19.3520	−0.695143
$776$	−0.906230	−0.0325318
$777$	−14.5926	−0.523507
$778$	−7.21865	−0.258801
$779$	−3.06839	−0.109937
$780$	−6.16044	−0.220579
$781$	6.99221	0.250201
$782$	6.97762	0.249519
$783$	−8.93999	−0.319489
$784$	−3.64248	−0.130088
$785$	0.723124	0.0258094
$786$	−0.992950	−0.0354173
$787$	−33.9548	−1.21036	−0.605180	−	0.796089i	$-0.706899\pi$
$787$	−33.9548	−1.21036	−0.605180	+	0.796089i	$0.706899\pi$
$788$	8.76077	0.312089
$789$	6.32985	0.225349
$790$	−6.01626	−0.214049
$791$	−28.7843	−1.02345
$792$	−6.86752	−0.244027
$793$	14.4244	0.512224
$794$	−15.8773	−0.563465
$795$	2.38689	0.0846544
$796$	−18.5188	−0.656382
$797$	−6.26895	−0.222058	−0.111029	−	0.993817i	$-0.535415\pi$
$797$	−6.26895	−0.222058	−0.111029	+	0.993817i	$0.535415\pi$
$798$	2.58461	0.0914944
$799$	10.0265	0.354712
$800$	−3.76629	−0.133159
$801$	7.02226	0.248119
$802$	1.27789	0.0451240
$803$	24.0289	0.847961
$804$	−4.73720	−0.167068
$805$	10.6682	0.376005
$806$	−31.4700	−1.10848
$807$	−17.0456	−0.600034
$808$	15.5762	0.547970
$809$	25.6536	0.901934	0.450967	−	0.892541i	$-0.351079\pi$
$809$	25.6536	0.901934	0.450967	+	0.892541i	$0.351079\pi$
$810$	−2.54580	−0.0894504
$811$	27.2425	0.956615	0.478307	−	0.878193i	$-0.341251\pi$
$811$	27.2425	0.956615	0.478307	+	0.878193i	$0.341251\pi$
$812$	3.49221	0.122553
$813$	−25.3016	−0.887365
$814$	−27.7049	−0.971057
$815$	−14.9234	−0.522745
$816$	−1.20546	−0.0421995
$817$	−3.92362	−0.137270
$818$	34.1182	1.19292
$819$	−24.4648	−0.854868
$820$	2.18802	0.0764090
$821$	28.3270	0.988618	0.494309	−	0.869286i	$-0.335421\pi$
$821$	28.3270	0.988618	0.494309	+	0.869286i	$0.335421\pi$
$822$	−3.36506	−0.117370
$823$	−26.6203	−0.927925	−0.463962	−	0.885855i	$-0.653573\pi$
$823$	−26.6203	−0.927925	−0.463962	+	0.885855i	$0.653573\pi$
$824$	−4.69566	−0.163581
$825$	10.7445	0.374077
$826$	−24.3798	−0.848281
$827$	19.5589	0.680129	0.340065	−	0.940402i	$-0.389551\pi$
$827$	19.5589	0.680129	0.340065	+	0.940402i	$0.389551\pi$
$828$	−11.4267	−0.397106
$829$	7.24640	0.251678	0.125839	−	0.992051i	$-0.459838\pi$
$829$	7.24640	0.251678	0.125839	+	0.992051i	$0.459838\pi$
$830$	−15.3022	−0.531146
$831$	5.28084	0.183190
$832$	−6.12471	−0.212336
$833$	−4.84874	−0.167999
$834$	16.1913	0.560660
$835$	−6.40946	−0.221809
$836$	4.90704	0.169713
$837$	24.1022	0.833094
$838$	17.3757	0.600232
$839$	−27.6676	−0.955191	−0.477596	−	0.878580i	$-0.658492\pi$
$839$	−27.6676	−0.955191	−0.477596	+	0.878580i	$0.658492\pi$
$840$	−1.84305	−0.0635911
$841$	−25.3677	−0.874748
$842$	20.8473	0.718444
$843$	−16.5921	−0.571462
$844$	−4.14174	−0.142564
$845$	−27.2261	−0.936606
$846$	−16.4196	−0.564518
$847$	1.97077	0.0677164
$848$	2.37305	0.0814908
$849$	−12.3639	−0.424329
$850$	−5.01356	−0.171964
$851$	−46.0977	−1.58021
$852$	−2.00993	−0.0688592
$853$	−18.0666	−0.618589	−0.309294	−	0.950966i	$-0.600093\pi$
$853$	−18.0666	−0.618589	−0.309294	+	0.950966i	$0.600093\pi$
$854$	4.31540	0.147670
$855$	3.77153	0.128984
$856$	5.27981	0.180460
$857$	−1.24424	−0.0425024	−0.0212512	−	0.999774i	$-0.506765\pi$
$857$	−1.24424	−0.0425024	−0.0212512	+	0.999774i	$0.506765\pi$
$858$	17.4727	0.596507
$859$	45.4253	1.54989	0.774945	−	0.632029i	$-0.217777\pi$
$859$	45.4253	1.54989	0.774945	+	0.632029i	$0.217777\pi$
$860$	2.79787	0.0954065
$861$	−3.26870	−0.111397
$862$	10.5659	0.359875
$863$	56.2099	1.91341	0.956704	−	0.291062i	$-0.0940087\pi$
$863$	56.2099	1.91341	0.956704	+	0.291062i	$0.0940087\pi$
$864$	4.69079	0.159584
$865$	8.74042	0.297183
$866$	−26.6808	−0.906651
$867$	13.7900	0.468332
$868$	−9.41500	−0.319566
$869$	17.0637	0.578848
$870$	−1.91698	−0.0649917
$871$	−32.0395	−1.08562
$872$	15.1914	0.514446
$873$	1.97554	0.0668617
$874$	8.16472	0.276176
$875$	−17.8415	−0.603153
$876$	−6.90718	−0.233372
$877$	−51.0874	−1.72510	−0.862550	−	0.505973i	$-0.831134\pi$
$877$	−51.0874	−1.72510	−0.862550	+	0.505973i	$0.831134\pi$
$878$	−11.2927	−0.381112
$879$	−15.7037	−0.529671
$880$	−3.49912	−0.117955
$881$	30.1872	1.01703	0.508516	−	0.861053i	$-0.330194\pi$
$881$	30.1872	1.01703	0.508516	+	0.861053i	$0.330194\pi$
$882$	7.94041	0.267368
$883$	34.8298	1.17212	0.586058	−	0.810269i	$-0.300679\pi$
$883$	34.8298	1.17212	0.586058	+	0.810269i	$0.300679\pi$
$884$	−8.15299	−0.274215
$885$	13.3828	0.449857
$886$	−24.0916	−0.809374
$887$	−17.4849	−0.587086	−0.293543	−	0.955946i	$-0.594834\pi$
$887$	−17.4849	−0.587086	−0.293543	+	0.955946i	$0.594834\pi$
$888$	7.96386	0.267250
$889$	31.0748	1.04221
$890$	3.57797	0.119934
$891$	7.22058	0.241899
$892$	16.4997	0.552452
$893$	11.7323	0.392606
$894$	−3.27078	−0.109391
$895$	−10.5649	−0.353147
$896$	−1.83235	−0.0612147
$897$	29.0724	0.970700
$898$	−6.74186	−0.224979
$899$	−9.79269	−0.326605
$900$	8.21033	0.273678
$901$	3.15892	0.105239
$902$	−6.20581	−0.206631
$903$	−4.17976	−0.139094
$904$	15.7089	0.522470
$905$	−4.42860	−0.147212
$906$	−10.4710	−0.347875
$907$	22.5762	0.749632	0.374816	−	0.927099i	$-0.377706\pi$
$907$	22.5762	0.749632	0.374816	+	0.927099i	$0.377706\pi$
$908$	−14.8796	−0.493796
$909$	−33.9554	−1.12623
$910$	−12.4652	−0.413219
$911$	−25.2613	−0.836946	−0.418473	−	0.908229i	$-0.637434\pi$
$911$	−25.2613	−0.836946	−0.418473	+	0.908229i	$0.637434\pi$
$912$	−1.41054	−0.0467077
$913$	43.4011	1.43637
$914$	26.9300	0.890764
$915$	−2.36885	−0.0783118
$916$	−21.2658	−0.702643
$917$	−2.00917	−0.0663486
$918$	6.24421	0.206090
$919$	12.5513	0.414028	0.207014	−	0.978338i	$-0.433625\pi$
$919$	12.5513	0.414028	0.207014	+	0.978338i	$0.433625\pi$
$920$	−5.82213	−0.191950
$921$	13.5439	0.446286
$922$	−34.2071	−1.12655
$923$	−13.5940	−0.447451
$924$	5.22737	0.171968
$925$	33.1221	1.08905
$926$	−25.3289	−0.832359
$927$	10.2363	0.336204
$928$	−1.90586	−0.0625629
$929$	−24.3258	−0.798103	−0.399051	−	0.916929i	$-0.630661\pi$
$929$	−24.3258	−0.798103	−0.399051	+	0.916929i	$0.630661\pi$
$930$	5.16818	0.169471
$931$	−5.67365	−0.185946
$932$	−16.2103	−0.530985
$933$	−13.1801	−0.431498
$934$	41.3175	1.35195
$935$	−4.65791	−0.152330
$936$	13.3515	0.436409
$937$	−30.3504	−0.991505	−0.495752	−	0.868464i	$-0.665108\pi$
$937$	−30.3504	−0.991505	−0.495752	+	0.868464i	$0.665108\pi$
$938$	−9.58541	−0.312975
$939$	−1.21889	−0.0397770
$940$	−8.36610	−0.272872
$941$	8.58976	0.280018	0.140009	−	0.990150i	$-0.455287\pi$
$941$	8.58976	0.280018	0.140009	+	0.990150i	$0.455287\pi$
$942$	0.589559	0.0192089
$943$	−10.3257	−0.336252
$944$	13.3052	0.433046
$945$	9.54688	0.310560
$946$	−7.93551	−0.258006
$947$	14.3460	0.466183	0.233091	−	0.972455i	$-0.425116\pi$
$947$	14.3460	0.466183	0.233091	+	0.972455i	$0.425116\pi$
$948$	−4.90503	−0.159308
$949$	−46.7160	−1.51646
$950$	−5.86651	−0.190335
$951$	−8.17630	−0.265135
$952$	−2.43917	−0.0790538
$953$	16.7263	0.541817	0.270909	−	0.962605i	$-0.412676\pi$
$953$	16.7263	0.541817	0.270909	+	0.962605i	$0.412676\pi$
$954$	−5.17312	−0.167486
$955$	22.3431	0.723004
$956$	21.1470	0.683942
$957$	5.43707	0.175756
$958$	14.2931	0.461788
$959$	−6.80898	−0.219873
$960$	1.00583	0.0324632
$961$	−4.59890	−0.148352
$962$	53.8628	1.73660
$963$	−11.5097	−0.370895
$964$	22.3968	0.721353
$965$	10.3189	0.332178
$966$	8.69772	0.279845
$967$	−13.0467	−0.419555	−0.209778	−	0.977749i	$-0.567274\pi$
$967$	−13.0467	−0.419555	−0.209778	+	0.977749i	$0.567274\pi$
$968$	−1.07554	−0.0345691
$969$	−1.87767	−0.0603193
$970$	1.00657	0.0323191
$971$	42.2755	1.35669	0.678343	−	0.734745i	$-0.262698\pi$
$971$	42.2755	1.35669	0.678343	+	0.734745i	$0.262698\pi$
$972$	−16.1479	−0.517946
$973$	32.7621	1.05030
$974$	−2.49634	−0.0799879
$975$	−20.8891	−0.668987
$976$	−2.35511	−0.0753852
$977$	27.9589	0.894484	0.447242	−	0.894413i	$-0.352406\pi$
$977$	27.9589	0.894484	0.447242	+	0.894413i	$0.352406\pi$
$978$	−12.1670	−0.389058
$979$	−10.1481	−0.324334
$980$	4.04579	0.129238
$981$	−33.1165	−1.05733
$982$	0.912369	0.0291149
$983$	38.0913	1.21493	0.607463	−	0.794348i	$-0.292187\pi$
$983$	38.0913	1.21493	0.607463	+	0.794348i	$0.292187\pi$
$984$	1.78388	0.0568680
$985$	−9.73079	−0.310049
$986$	−2.53702	−0.0807950
$987$	12.4982	0.397822
$988$	−9.54006	−0.303510
$989$	−13.2037	−0.419854
$990$	7.62791	0.242431
$991$	−28.9257	−0.918855	−0.459427	−	0.888215i	$-0.651945\pi$
$991$	−28.9257	−0.918855	−0.459427	+	0.888215i	$0.651945\pi$
$992$	5.13820	0.163138
$993$	−15.9374	−0.505757
$994$	−4.06697	−0.128996
$995$	20.5693	0.652090
$996$	−12.4758	−0.395310
$997$	16.4437	0.520777	0.260388	−	0.965504i	$-0.416149\pi$
$997$	16.4437	0.520777	0.260388	+	0.965504i	$0.416149\pi$
$998$	−19.7594	−0.625473
$999$	−41.2524	−1.30517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.18	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.18	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.905567 q^{3} +1.00000 q^{4} -1.11072 q^{5} -0.905567 q^{6} -1.83235 q^{7} +1.00000 q^{8} -2.17995 q^{9} -1.11072 q^{10} +3.15031 q^{11} -0.905567 q^{12} -6.12471 q^{13} -1.83235 q^{14} +1.00583 q^{15} +1.00000 q^{16} +1.33116 q^{17} -2.17995 q^{18} +1.55764 q^{19} -1.11072 q^{20} +1.65932 q^{21} +3.15031 q^{22} +5.24174 q^{23} -0.905567 q^{24} -3.76629 q^{25} -6.12471 q^{26} +4.69079 q^{27} -1.83235 q^{28} -1.90586 q^{29} +1.00583 q^{30} +5.13820 q^{31} +1.00000 q^{32} -2.85282 q^{33} +1.33116 q^{34} +2.03524 q^{35} -2.17995 q^{36} -8.79434 q^{37} +1.55764 q^{38} +5.54633 q^{39} -1.11072 q^{40} -1.96990 q^{41} +1.65932 q^{42} -2.51896 q^{43} +3.15031 q^{44} +2.42132 q^{45} +5.24174 q^{46} +7.53212 q^{47} -0.905567 q^{48} -3.64248 q^{49} -3.76629 q^{50} -1.20546 q^{51} -6.12471 q^{52} +2.37305 q^{53} +4.69079 q^{54} -3.49912 q^{55} -1.83235 q^{56} -1.41054 q^{57} -1.90586 q^{58} +13.3052 q^{59} +1.00583 q^{60} -2.35511 q^{61} +5.13820 q^{62} +3.99444 q^{63} +1.00000 q^{64} +6.80285 q^{65} -2.85282 q^{66} +5.23120 q^{67} +1.33116 q^{68} -4.74675 q^{69} +2.03524 q^{70} +2.21953 q^{71} -2.17995 q^{72} +7.62746 q^{73} -8.79434 q^{74} +3.41063 q^{75} +1.55764 q^{76} -5.77249 q^{77} +5.54633 q^{78} +5.41653 q^{79} -1.11072 q^{80} +2.29202 q^{81} -1.96990 q^{82} +13.7768 q^{83} +1.65932 q^{84} -1.47856 q^{85} -2.51896 q^{86} +1.72588 q^{87} +3.15031 q^{88} -3.22130 q^{89} +2.42132 q^{90} +11.2226 q^{91} +5.24174 q^{92} -4.65298 q^{93} +7.53212 q^{94} -1.73010 q^{95} -0.905567 q^{96} -0.906230 q^{97} -3.64248 q^{98} -6.86752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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