LMFDB - Embedded newform 1334.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.978400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 6x^{2} + 14x + 2 $ x^5 - 2x^4 - 7x^3 + 6x^2 + 14x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.32108$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.38739 q^{3} +1.00000 q^{4} -2.84168 q^{5} +1.38739 q^{6} +2.52061 q^{7} -1.00000 q^{8} -1.07515 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.38739 q^{3} +1.00000 q^{4} -2.84168 q^{5} +1.38739 q^{6} +2.52061 q^{7} -1.00000 q^{8} -1.07515 q^{9} +2.84168 q^{10} +0.734155 q^{11} -1.38739 q^{12} -3.90800 q^{13} -2.52061 q^{14} +3.94252 q^{15} +1.00000 q^{16} -6.26359 q^{17} +1.07515 q^{18} +4.68776 q^{19} -2.84168 q^{20} -3.49706 q^{21} -0.734155 q^{22} +1.00000 q^{23} +1.38739 q^{24} +3.07515 q^{25} +3.90800 q^{26} +5.65382 q^{27} +2.52061 q^{28} -1.00000 q^{29} -3.94252 q^{30} +1.26585 q^{31} -1.00000 q^{32} -1.01856 q^{33} +6.26359 q^{34} -7.16276 q^{35} -1.07515 q^{36} -5.36443 q^{37} -4.68776 q^{38} +5.42191 q^{39} +2.84168 q^{40} -8.40564 q^{41} +3.49706 q^{42} +2.10967 q^{43} +0.734155 q^{44} +3.05523 q^{45} -1.00000 q^{46} -5.57369 q^{47} -1.38739 q^{48} -0.646548 q^{49} -3.07515 q^{50} +8.69005 q^{51} -3.90800 q^{52} +2.53384 q^{53} -5.65382 q^{54} -2.08623 q^{55} -2.52061 q^{56} -6.50375 q^{57} +1.00000 q^{58} +7.55073 q^{59} +3.94252 q^{60} +15.4971 q^{61} -1.26585 q^{62} -2.71003 q^{63} +1.00000 q^{64} +11.1053 q^{65} +1.01856 q^{66} +2.37856 q^{67} -6.26359 q^{68} -1.38739 q^{69} +7.16276 q^{70} +10.4581 q^{71} +1.07515 q^{72} +2.50294 q^{73} +5.36443 q^{74} -4.26643 q^{75} +4.68776 q^{76} +1.85051 q^{77} -5.42191 q^{78} -0.332160 q^{79} -2.84168 q^{80} -4.61861 q^{81} +8.40564 q^{82} +8.04506 q^{83} -3.49706 q^{84} +17.7991 q^{85} -2.10967 q^{86} +1.38739 q^{87} -0.734155 q^{88} +13.9458 q^{89} -3.05523 q^{90} -9.85051 q^{91} +1.00000 q^{92} -1.75622 q^{93} +5.57369 q^{94} -13.3211 q^{95} +1.38739 q^{96} +14.8198 q^{97} +0.646548 q^{98} -0.789326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - 3 q^{13} - 4 q^{14} + q^{15} + 5 q^{16} - 4 q^{17} - 12 q^{18} + 14 q^{19} + 3 q^{20} + 10 q^{21} - 3 q^{22} + 5 q^{23} - q^{24} - 2 q^{25} + 3 q^{26} + 19 q^{27} + 4 q^{28} - 5 q^{29} - q^{30} + 7 q^{31} - 5 q^{32} - q^{33} + 4 q^{34} - 10 q^{35} + 12 q^{36} + 2 q^{37} - 14 q^{38} + 17 q^{39} - 3 q^{40} + 4 q^{41} - 10 q^{42} - 9 q^{43} + 3 q^{44} + 6 q^{45} - 5 q^{46} - 13 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 11 q^{53} - 19 q^{54} - 3 q^{55} - 4 q^{56} + 10 q^{57} + 5 q^{58} + 2 q^{59} + q^{60} + 50 q^{61} - 7 q^{62} + 4 q^{63} + 5 q^{64} + 11 q^{65} + q^{66} + 22 q^{67} - 4 q^{68} + q^{69} + 10 q^{70} + 2 q^{71} - 12 q^{72} + 40 q^{73} - 2 q^{74} - 20 q^{75} + 14 q^{76} - 26 q^{77} - 17 q^{78} - 3 q^{79} + 3 q^{80} + 13 q^{81} - 4 q^{82} - 18 q^{83} + 10 q^{84} + 22 q^{85} + 9 q^{86} - q^{87} - 3 q^{88} + 12 q^{89} - 6 q^{90} - 14 q^{91} + 5 q^{92} + 3 q^{93} + 13 q^{94} + 10 q^{95} - q^{96} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - 3 * q^13 - 4 * q^14 + q^15 + 5 * q^16 - 4 * q^17 - 12 * q^18 + 14 * q^19 + 3 * q^20 + 10 * q^21 - 3 * q^22 + 5 * q^23 - q^24 - 2 * q^25 + 3 * q^26 + 19 * q^27 + 4 * q^28 - 5 * q^29 - q^30 + 7 * q^31 - 5 * q^32 - q^33 + 4 * q^34 - 10 * q^35 + 12 * q^36 + 2 * q^37 - 14 * q^38 + 17 * q^39 - 3 * q^40 + 4 * q^41 - 10 * q^42 - 9 * q^43 + 3 * q^44 + 6 * q^45 - 5 * q^46 - 13 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 11 * q^53 - 19 * q^54 - 3 * q^55 - 4 * q^56 + 10 * q^57 + 5 * q^58 + 2 * q^59 + q^60 + 50 * q^61 - 7 * q^62 + 4 * q^63 + 5 * q^64 + 11 * q^65 + q^66 + 22 * q^67 - 4 * q^68 + q^69 + 10 * q^70 + 2 * q^71 - 12 * q^72 + 40 * q^73 - 2 * q^74 - 20 * q^75 + 14 * q^76 - 26 * q^77 - 17 * q^78 - 3 * q^79 + 3 * q^80 + 13 * q^81 - 4 * q^82 - 18 * q^83 + 10 * q^84 + 22 * q^85 + 9 * q^86 - q^87 - 3 * q^88 + 12 * q^89 - 6 * q^90 - 14 * q^91 + 5 * q^92 + 3 * q^93 + 13 * q^94 + 10 * q^95 - q^96 + 11 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.38739	−0.801010	−0.400505	−	0.916295i	$-0.631165\pi$
$3$	−1.38739	−0.801010	−0.400505	+	0.916295i	$0.631165\pi$
$4$	1.00000	0.500000
$5$	−2.84168	−1.27084	−0.635419	−	0.772167i	$-0.719173\pi$
$5$	−2.84168	−1.27084	−0.635419	+	0.772167i	$0.719173\pi$
$6$	1.38739	0.566400
$7$	2.52061	0.952699	0.476350	−	0.879256i	$-0.341960\pi$
$7$	2.52061	0.952699	0.476350	+	0.879256i	$0.341960\pi$
$8$	−1.00000	−0.353553
$9$	−1.07515	−0.358383
$10$	2.84168	0.898618
$11$	0.734155	0.221356	0.110678	−	0.993856i	$-0.464698\pi$
$11$	0.734155	0.221356	0.110678	+	0.993856i	$0.464698\pi$
$12$	−1.38739	−0.400505
$13$	−3.90800	−1.08388	−0.541941	−	0.840416i	$-0.682311\pi$
$13$	−3.90800	−1.08388	−0.541941	+	0.840416i	$0.682311\pi$
$14$	−2.52061	−0.673660
$15$	3.94252	1.01795
$16$	1.00000	0.250000
$17$	−6.26359	−1.51914	−0.759572	−	0.650423i	$-0.774592\pi$
$17$	−6.26359	−1.51914	−0.759572	+	0.650423i	$0.774592\pi$
$18$	1.07515	0.253415
$19$	4.68776	1.07545	0.537723	−	0.843122i	$-0.319285\pi$
$19$	4.68776	1.07545	0.537723	+	0.843122i	$0.319285\pi$
$20$	−2.84168	−0.635419
$21$	−3.49706	−0.763122
$22$	−0.734155	−0.156522
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.38739	0.283200
$25$	3.07515	0.615030
$26$	3.90800	0.766421
$27$	5.65382	1.08808
$28$	2.52061	0.476350
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.94252	−0.719802
$31$	1.26585	0.227352	0.113676	−	0.993518i	$-0.463737\pi$
$31$	1.26585	0.227352	0.113676	+	0.993518i	$0.463737\pi$
$32$	−1.00000	−0.176777
$33$	−1.01856	−0.177308
$34$	6.26359	1.07420
$35$	−7.16276	−1.21073
$36$	−1.07515	−0.179191
$37$	−5.36443	−0.881907	−0.440954	−	0.897530i	$-0.645360\pi$
$37$	−5.36443	−0.881907	−0.440954	+	0.897530i	$0.645360\pi$
$38$	−4.68776	−0.760455
$39$	5.42191	0.868201
$40$	2.84168	0.449309
$41$	−8.40564	−1.31274	−0.656371	−	0.754439i	$-0.727909\pi$
$41$	−8.40564	−1.31274	−0.656371	+	0.754439i	$0.727909\pi$
$42$	3.49706	0.539609
$43$	2.10967	0.321722	0.160861	−	0.986977i	$-0.448573\pi$
$43$	2.10967	0.321722	0.160861	+	0.986977i	$0.448573\pi$
$44$	0.734155	0.110678
$45$	3.05523	0.455447
$46$	−1.00000	−0.147442
$47$	−5.57369	−0.813006	−0.406503	−	0.913649i	$-0.633252\pi$
$47$	−5.57369	−0.813006	−0.406503	+	0.913649i	$0.633252\pi$
$48$	−1.38739	−0.200252
$49$	−0.646548	−0.0923640
$50$	−3.07515	−0.434892
$51$	8.69005	1.21685
$52$	−3.90800	−0.541941
$53$	2.53384	0.348049	0.174025	−	0.984741i	$-0.444323\pi$
$53$	2.53384	0.348049	0.174025	+	0.984741i	$0.444323\pi$
$54$	−5.65382	−0.769388
$55$	−2.08623	−0.281308
$56$	−2.52061	−0.336830
$57$	−6.50375	−0.861443
$58$	1.00000	0.131306
$59$	7.55073	0.983022	0.491511	−	0.870871i	$-0.336445\pi$
$59$	7.55073	0.983022	0.491511	+	0.870871i	$0.336445\pi$
$60$	3.94252	0.508977
$61$	15.4971	1.98420	0.992098	−	0.125467i	$-0.0400429\pi$
$61$	15.4971	1.98420	0.992098	+	0.125467i	$0.0400429\pi$
$62$	−1.26585	−0.160762
$63$	−2.71003	−0.341431
$64$	1.00000	0.125000
$65$	11.1053	1.37744
$66$	1.01856	0.125376
$67$	2.37856	0.290587	0.145293	−	0.989389i	$-0.453587\pi$
$67$	2.37856	0.290587	0.145293	+	0.989389i	$0.453587\pi$
$68$	−6.26359	−0.759572
$69$	−1.38739	−0.167022
$70$	7.16276	0.856113
$71$	10.4581	1.24115	0.620577	−	0.784146i	$-0.286899\pi$
$71$	10.4581	1.24115	0.620577	+	0.784146i	$0.286899\pi$
$72$	1.07515	0.126708
$73$	2.50294	0.292947	0.146473	−	0.989215i	$-0.453208\pi$
$73$	2.50294	0.292947	0.146473	+	0.989215i	$0.453208\pi$
$74$	5.36443	0.623603
$75$	−4.26643	−0.492645
$76$	4.68776	0.537723
$77$	1.85051	0.210886
$78$	−5.42191	−0.613911
$79$	−0.332160	−0.0373709	−0.0186855	−	0.999825i	$-0.505948\pi$
$79$	−0.332160	−0.0373709	−0.0186855	+	0.999825i	$0.505948\pi$
$80$	−2.84168	−0.317710
$81$	−4.61861	−0.513179
$82$	8.40564	0.928248
$83$	8.04506	0.883060	0.441530	−	0.897246i	$-0.354436\pi$
$83$	8.04506	0.883060	0.441530	+	0.897246i	$0.354436\pi$
$84$	−3.49706	−0.381561
$85$	17.7991	1.93059
$86$	−2.10967	−0.227492
$87$	1.38739	0.148744
$88$	−0.734155	−0.0782612
$89$	13.9458	1.47825	0.739125	−	0.673568i	$-0.235239\pi$
$89$	13.9458	1.47825	0.739125	+	0.673568i	$0.235239\pi$
$90$	−3.05523	−0.322050
$91$	−9.85051	−1.03261
$92$	1.00000	0.104257
$93$	−1.75622	−0.182112
$94$	5.57369	0.574882
$95$	−13.3211	−1.36672
$96$	1.38739	0.141600
$97$	14.8198	1.50473	0.752363	−	0.658748i	$-0.228914\pi$
$97$	14.8198	1.50473	0.752363	+	0.658748i	$0.228914\pi$
$98$	0.646548	0.0653112
$99$	−0.789326	−0.0793302
$100$	3.07515	0.307515
$101$	9.76809	0.971962	0.485981	−	0.873969i	$-0.338462\pi$
$101$	9.76809	0.971962	0.485981	+	0.873969i	$0.338462\pi$
$102$	−8.69005	−0.860443
$103$	12.1238	1.19460	0.597298	−	0.802019i	$-0.296241\pi$
$103$	12.1238	1.19460	0.597298	+	0.802019i	$0.296241\pi$
$104$	3.90800	0.383210
$105$	9.93754	0.969804
$106$	−2.53384	−0.246108
$107$	−4.41308	−0.426629	−0.213314	−	0.976984i	$-0.568426\pi$
$107$	−4.41308	−0.426629	−0.213314	+	0.976984i	$0.568426\pi$
$108$	5.65382	0.544039
$109$	−14.6945	−1.40748	−0.703738	−	0.710459i	$-0.748487\pi$
$109$	−14.6945	−1.40748	−0.703738	+	0.710459i	$0.748487\pi$
$110$	2.08623	0.198915
$111$	7.44256	0.706417
$112$	2.52061	0.238175
$113$	−16.8210	−1.58239	−0.791194	−	0.611565i	$-0.790540\pi$
$113$	−16.8210	−1.58239	−0.791194	+	0.611565i	$0.790540\pi$
$114$	6.50375	0.609132
$115$	−2.84168	−0.264988
$116$	−1.00000	−0.0928477
$117$	4.20168	0.388445
$118$	−7.55073	−0.695101
$119$	−15.7881	−1.44729
$120$	−3.94252	−0.359901
$121$	−10.4610	−0.951002
$122$	−15.4971	−1.40304
$123$	11.6619	1.05152
$124$	1.26585	0.113676
$125$	5.46981	0.489235
$126$	2.71003	0.241428
$127$	13.9912	1.24152	0.620759	−	0.784001i	$-0.286824\pi$
$127$	13.9912	1.24152	0.620759	+	0.784001i	$0.286824\pi$
$128$	−1.00000	−0.0883883
$129$	−2.92694	−0.257703
$130$	−11.1053	−0.973997
$131$	16.6790	1.45725	0.728624	−	0.684914i	$-0.240160\pi$
$131$	16.6790	1.45725	0.728624	+	0.684914i	$0.240160\pi$
$132$	−1.01856	−0.0886542
$133$	11.8160	1.02458
$134$	−2.37856	−0.205476
$135$	−16.0664	−1.38277
$136$	6.26359	0.537099
$137$	9.10742	0.778100	0.389050	−	0.921217i	$-0.372803\pi$
$137$	9.10742	0.778100	0.389050	+	0.921217i	$0.372803\pi$
$138$	1.38739	0.118102
$139$	14.6061	1.23888	0.619439	−	0.785045i	$-0.287360\pi$
$139$	14.6061	1.23888	0.619439	+	0.785045i	$0.287360\pi$
$140$	−7.16276	−0.605363
$141$	7.73288	0.651226
$142$	−10.4581	−0.877628
$143$	−2.86907	−0.239924
$144$	−1.07515	−0.0895957
$145$	2.84168	0.235989
$146$	−2.50294	−0.207145
$147$	0.897014	0.0739845
$148$	−5.36443	−0.440954
$149$	0.640003	0.0524311	0.0262156	−	0.999656i	$-0.491654\pi$
$149$	0.640003	0.0524311	0.0262156	+	0.999656i	$0.491654\pi$
$150$	4.26643	0.348353
$151$	3.73474	0.303929	0.151964	−	0.988386i	$-0.451440\pi$
$151$	3.73474	0.303929	0.151964	+	0.988386i	$0.451440\pi$
$152$	−4.68776	−0.380227
$153$	6.73430	0.544436
$154$	−1.85051	−0.149119
$155$	−3.59713	−0.288928
$156$	5.42191	0.434101
$157$	12.4428	0.993041	0.496520	−	0.868025i	$-0.334611\pi$
$157$	12.4428	0.993041	0.496520	+	0.868025i	$0.334611\pi$
$158$	0.332160	0.0264252
$159$	−3.51542	−0.278791
$160$	2.84168	0.224655
$161$	2.52061	0.198652
$162$	4.61861	0.362872
$163$	−10.0472	−0.786958	−0.393479	−	0.919334i	$-0.628729\pi$
$163$	−10.0472	−0.786958	−0.393479	+	0.919334i	$0.628729\pi$
$164$	−8.40564	−0.656371
$165$	2.89442	0.225330
$166$	−8.04506	−0.624418
$167$	−4.26526	−0.330056	−0.165028	−	0.986289i	$-0.552771\pi$
$167$	−4.26526	−0.330056	−0.165028	+	0.986289i	$0.552771\pi$
$168$	3.49706	0.269804
$169$	2.27243	0.174802
$170$	−17.7991	−1.36513
$171$	−5.04004	−0.385421
$172$	2.10967	0.160861
$173$	12.1105	0.920741	0.460371	−	0.887727i	$-0.347717\pi$
$173$	12.1105	0.920741	0.460371	+	0.887727i	$0.347717\pi$
$174$	−1.38739	−0.105178
$175$	7.75124	0.585938
$176$	0.734155	0.0553390
$177$	−10.4758	−0.787410
$178$	−13.9458	−1.04528
$179$	−21.3998	−1.59949	−0.799747	−	0.600337i	$-0.795033\pi$
$179$	−21.3998	−1.59949	−0.799747	+	0.600337i	$0.795033\pi$
$180$	3.05523	0.227723
$181$	15.3221	1.13888	0.569441	−	0.822032i	$-0.307160\pi$
$181$	15.3221	1.13888	0.569441	+	0.822032i	$0.307160\pi$
$182$	9.85051	0.730169
$183$	−21.5005	−1.58936
$184$	−1.00000	−0.0737210
$185$	15.2440	1.12076
$186$	1.75622	0.128772
$187$	−4.59845	−0.336272
$188$	−5.57369	−0.406503
$189$	14.2511	1.03661
$190$	13.3211	0.966415
$191$	−24.5087	−1.77339	−0.886693	−	0.462360i	$-0.847003\pi$
$191$	−24.5087	−1.77339	−0.886693	+	0.462360i	$0.847003\pi$
$192$	−1.38739	−0.100126
$193$	−8.19171	−0.589652	−0.294826	−	0.955551i	$-0.595262\pi$
$193$	−8.19171	−0.589652	−0.294826	+	0.955551i	$0.595262\pi$
$194$	−14.8198	−1.06400
$195$	−15.4073	−1.10334
$196$	−0.646548	−0.0461820
$197$	−14.1929	−1.01120	−0.505600	−	0.862768i	$-0.668729\pi$
$197$	−14.1929	−1.01120	−0.505600	+	0.862768i	$0.668729\pi$
$198$	0.789326	0.0560949
$199$	−5.63315	−0.399324	−0.199662	−	0.979865i	$-0.563984\pi$
$199$	−5.63315	−0.399324	−0.199662	+	0.979865i	$0.563984\pi$
$200$	−3.07515	−0.217446
$201$	−3.29998	−0.232763
$202$	−9.76809	−0.687281
$203$	−2.52061	−0.176912
$204$	8.69005	0.608425
$205$	23.8862	1.66828
$206$	−12.1238	−0.844708
$207$	−1.07515	−0.0747280
$208$	−3.90800	−0.270971
$209$	3.44154	0.238056
$210$	−9.93754	−0.685755
$211$	21.8865	1.50673	0.753366	−	0.657602i	$-0.228429\pi$
$211$	21.8865	1.50673	0.753366	+	0.657602i	$0.228429\pi$
$212$	2.53384	0.174025
$213$	−14.5095	−0.994176
$214$	4.41308	0.301672
$215$	−5.99502	−0.408857
$216$	−5.65382	−0.384694
$217$	3.19070	0.216599
$218$	14.6945	0.995236
$219$	−3.47255	−0.234653
$220$	−2.08623	−0.140654
$221$	24.4781	1.64658
$222$	−7.44256	−0.499512
$223$	−2.57310	−0.172308	−0.0861538	−	0.996282i	$-0.527458\pi$
$223$	−2.57310	−0.172308	−0.0861538	+	0.996282i	$0.527458\pi$
$224$	−2.52061	−0.168415
$225$	−3.30624	−0.220416
$226$	16.8210	1.11892
$227$	26.7528	1.77564	0.887822	−	0.460187i	$-0.152218\pi$
$227$	26.7528	1.77564	0.887822	+	0.460187i	$0.152218\pi$
$228$	−6.50375	−0.430721
$229$	−14.8228	−0.979517	−0.489758	−	0.871858i	$-0.662915\pi$
$229$	−14.8228	−0.979517	−0.489758	+	0.871858i	$0.662915\pi$
$230$	2.84168	0.187375
$231$	−2.56739	−0.168922
$232$	1.00000	0.0656532
$233$	−26.9324	−1.76440	−0.882198	−	0.470878i	$-0.843937\pi$
$233$	−26.9324	−1.76440	−0.882198	+	0.470878i	$0.843937\pi$
$234$	−4.20168	−0.274672
$235$	15.8386	1.03320
$236$	7.55073	0.491511
$237$	0.460835	0.0299345
$238$	15.7881	1.02339
$239$	11.4660	0.741674	0.370837	−	0.928698i	$-0.379071\pi$
$239$	11.4660	0.741674	0.370837	+	0.928698i	$0.379071\pi$
$240$	3.94252	0.254489
$241$	−9.96395	−0.641835	−0.320917	−	0.947107i	$-0.603991\pi$
$241$	−9.96395	−0.641835	−0.320917	+	0.947107i	$0.603991\pi$
$242$	10.4610	0.672460
$243$	−10.5537	−0.677017
$244$	15.4971	0.992098
$245$	1.83728	0.117380
$246$	−11.6619	−0.743536
$247$	−18.3197	−1.16566
$248$	−1.26585	−0.0803812
$249$	−11.1616	−0.707340
$250$	−5.46981	−0.345941
$251$	24.4662	1.54429	0.772147	−	0.635444i	$-0.219183\pi$
$251$	24.4662	1.54429	0.772147	+	0.635444i	$0.219183\pi$
$252$	−2.71003	−0.170716
$253$	0.734155	0.0461559
$254$	−13.9912	−0.877886
$255$	−24.6943	−1.54642
$256$	1.00000	0.0625000
$257$	−5.67757	−0.354157	−0.177078	−	0.984197i	$-0.556665\pi$
$257$	−5.67757	−0.354157	−0.177078	+	0.984197i	$0.556665\pi$
$258$	2.92694	0.182223
$259$	−13.5216	−0.840193
$260$	11.1053	0.688720
$261$	1.07515	0.0665501
$262$	−16.6790	−1.03043
$263$	2.99198	0.184493	0.0922467	−	0.995736i	$-0.470595\pi$
$263$	2.99198	0.184493	0.0922467	+	0.995736i	$0.470595\pi$
$264$	1.01856	0.0626880
$265$	−7.20036	−0.442314
$266$	−11.8160	−0.724485
$267$	−19.3482	−1.18409
$268$	2.37856	0.145293
$269$	−8.07436	−0.492303	−0.246151	−	0.969231i	$-0.579166\pi$
$269$	−8.07436	−0.492303	−0.246151	+	0.969231i	$0.579166\pi$
$270$	16.0664	0.977767
$271$	10.6092	0.644465	0.322232	−	0.946661i	$-0.395567\pi$
$271$	10.6092	0.644465	0.322232	+	0.946661i	$0.395567\pi$
$272$	−6.26359	−0.379786
$273$	13.6665	0.827135
$274$	−9.10742	−0.550199
$275$	2.25764	0.136141
$276$	−1.38739	−0.0835111
$277$	11.6423	0.699515	0.349758	−	0.936840i	$-0.386264\pi$
$277$	11.6423	0.699515	0.349758	+	0.936840i	$0.386264\pi$
$278$	−14.6061	−0.876019
$279$	−1.36097	−0.0814793
$280$	7.16276	0.428057
$281$	20.2733	1.20941	0.604703	−	0.796451i	$-0.293292\pi$
$281$	20.2733	1.20941	0.604703	+	0.796451i	$0.293292\pi$
$282$	−7.73288	−0.460486
$283$	−3.76862	−0.224021	−0.112011	−	0.993707i	$-0.535729\pi$
$283$	−3.76862	−0.224021	−0.112011	+	0.993707i	$0.535729\pi$
$284$	10.4581	0.620577
$285$	18.4816	1.09475
$286$	2.86907	0.169652
$287$	−21.1873	−1.25065
$288$	1.07515	0.0633538
$289$	22.2326	1.30780
$290$	−2.84168	−0.166869
$291$	−20.5609	−1.20530
$292$	2.50294	0.146473
$293$	−17.7800	−1.03872	−0.519359	−	0.854556i	$-0.673829\pi$
$293$	−17.7800	−1.03872	−0.519359	+	0.854556i	$0.673829\pi$
$294$	−0.897014	−0.0523149
$295$	−21.4568	−1.24926
$296$	5.36443	0.311801
$297$	4.15078	0.240853
$298$	−0.640003	−0.0370744
$299$	−3.90800	−0.226005
$300$	−4.26643	−0.246323
$301$	5.31765	0.306504
$302$	−3.73474	−0.214910
$303$	−13.5522	−0.778551
$304$	4.68776	0.268861
$305$	−44.0377	−2.52159
$306$	−6.73430	−0.384974
$307$	−12.2591	−0.699666	−0.349833	−	0.936812i	$-0.613762\pi$
$307$	−12.2591	−0.699666	−0.349833	+	0.936812i	$0.613762\pi$
$308$	1.85051	0.105443
$309$	−16.8205	−0.956884
$310$	3.59713	0.204303
$311$	28.7366	1.62950	0.814751	−	0.579812i	$-0.196874\pi$
$311$	28.7366	1.62950	0.814751	+	0.579812i	$0.196874\pi$
$312$	−5.42191	−0.306955
$313$	−25.3261	−1.43152	−0.715758	−	0.698349i	$-0.753919\pi$
$313$	−25.3261	−1.43152	−0.715758	+	0.698349i	$0.753919\pi$
$314$	−12.4428	−0.702186
$315$	7.70103	0.433904
$316$	−0.332160	−0.0186855
$317$	7.56759	0.425038	0.212519	−	0.977157i	$-0.431833\pi$
$317$	7.56759	0.425038	0.212519	+	0.977157i	$0.431833\pi$
$318$	3.51542	0.197135
$319$	−0.734155	−0.0411048
$320$	−2.84168	−0.158855
$321$	6.12266	0.341734
$322$	−2.52061	−0.140468
$323$	−29.3622	−1.63376
$324$	−4.61861	−0.256589
$325$	−12.0177	−0.666620
$326$	10.0472	0.556463
$327$	20.3870	1.12740
$328$	8.40564	0.464124
$329$	−14.0491	−0.774550
$330$	−2.89442	−0.159333
$331$	−16.9557	−0.931969	−0.465985	−	0.884793i	$-0.654300\pi$
$331$	−16.9557	−0.931969	−0.465985	+	0.884793i	$0.654300\pi$
$332$	8.04506	0.441530
$333$	5.76756	0.316061
$334$	4.26526	0.233385
$335$	−6.75910	−0.369289
$336$	−3.49706	−0.190780
$337$	24.3457	1.32619	0.663096	−	0.748534i	$-0.269242\pi$
$337$	24.3457	1.32619	0.663096	+	0.748534i	$0.269242\pi$
$338$	−2.27243	−0.123604
$339$	23.3373	1.26751
$340$	17.7991	0.965294
$341$	0.929326	0.0503258
$342$	5.04004	0.272534
$343$	−19.2739	−1.04069
$344$	−2.10967	−0.113746
$345$	3.94252	0.212258
$346$	−12.1105	−0.651062
$347$	−8.26193	−0.443524	−0.221762	−	0.975101i	$-0.571181\pi$
$347$	−8.26193	−0.443524	−0.221762	+	0.975101i	$0.571181\pi$
$348$	1.38739	0.0743719
$349$	−31.5428	−1.68845	−0.844224	−	0.535991i	$-0.819938\pi$
$349$	−31.5428	−1.68845	−0.844224	+	0.535991i	$0.819938\pi$
$350$	−7.75124	−0.414321
$351$	−22.0951	−1.17935
$352$	−0.734155	−0.0391306
$353$	−2.83348	−0.150811	−0.0754054	−	0.997153i	$-0.524025\pi$
$353$	−2.83348	−0.150811	−0.0754054	+	0.997153i	$0.524025\pi$
$354$	10.4758	0.556783
$355$	−29.7187	−1.57730
$356$	13.9458	0.739125
$357$	21.9042	1.15929
$358$	21.3998	1.13101
$359$	15.6284	0.824833	0.412417	−	0.910995i	$-0.364685\pi$
$359$	15.6284	0.824833	0.412417	+	0.910995i	$0.364685\pi$
$360$	−3.05523	−0.161025
$361$	2.97508	0.156583
$362$	−15.3221	−0.805311
$363$	14.5135	0.761762
$364$	−9.85051	−0.516307
$365$	−7.11255	−0.372288
$366$	21.5005	1.12385
$367$	−8.98158	−0.468835	−0.234417	−	0.972136i	$-0.575318\pi$
$367$	−8.98158	−0.468835	−0.234417	+	0.972136i	$0.575318\pi$
$368$	1.00000	0.0521286
$369$	9.03732	0.470464
$370$	−15.2440	−0.792498
$371$	6.38680	0.331586
$372$	−1.75622	−0.0910558
$373$	−20.3675	−1.05459	−0.527294	−	0.849683i	$-0.676794\pi$
$373$	−20.3675	−1.05459	−0.527294	+	0.849683i	$0.676794\pi$
$374$	4.59845	0.237780
$375$	−7.58876	−0.391882
$376$	5.57369	0.287441
$377$	3.90800	0.201272
$378$	−14.2511	−0.732995
$379$	33.1444	1.70251	0.851257	−	0.524748i	$-0.175841\pi$
$379$	33.1444	1.70251	0.851257	+	0.524748i	$0.175841\pi$
$380$	−13.3211	−0.683359
$381$	−19.4113	−0.994469
$382$	24.5087	1.25397
$383$	−20.3378	−1.03921	−0.519606	−	0.854406i	$-0.673921\pi$
$383$	−20.3378	−1.03921	−0.519606	+	0.854406i	$0.673921\pi$
$384$	1.38739	0.0707999
$385$	−5.25857	−0.268002
$386$	8.19171	0.416947
$387$	−2.26821	−0.115300
$388$	14.8198	0.752363
$389$	25.4009	1.28788	0.643938	−	0.765078i	$-0.277299\pi$
$389$	25.4009	1.28788	0.643938	+	0.765078i	$0.277299\pi$
$390$	15.4073	0.780181
$391$	−6.26359	−0.316764
$392$	0.646548	0.0326556
$393$	−23.1402	−1.16727
$394$	14.1929	0.715027
$395$	0.943892	0.0474924
$396$	−0.789326	−0.0396651
$397$	−10.9891	−0.551529	−0.275765	−	0.961225i	$-0.588931\pi$
$397$	−10.9891	−0.551529	−0.275765	+	0.961225i	$0.588931\pi$
$398$	5.63315	0.282364
$399$	−16.3934	−0.820696
$400$	3.07515	0.153757
$401$	2.33050	0.116379	0.0581897	−	0.998306i	$-0.481467\pi$
$401$	2.33050	0.116379	0.0581897	+	0.998306i	$0.481467\pi$
$402$	3.29998	0.164588
$403$	−4.94692	−0.246423
$404$	9.76809	0.485981
$405$	13.1246	0.652167
$406$	2.52061	0.125096
$407$	−3.93832	−0.195216
$408$	−8.69005	−0.430222
$409$	14.6030	0.722073	0.361037	−	0.932552i	$-0.382423\pi$
$409$	14.6030	0.722073	0.361037	+	0.932552i	$0.382423\pi$
$410$	−23.8862	−1.17965
$411$	−12.6355	−0.623266
$412$	12.1238	0.597298
$413$	19.0324	0.936524
$414$	1.07515	0.0528407
$415$	−22.8615	−1.12223
$416$	3.90800	0.191605
$417$	−20.2644	−0.992353
$418$	−3.44154	−0.168331
$419$	−3.14297	−0.153544	−0.0767720	−	0.997049i	$-0.524461\pi$
$419$	−3.14297	−0.153544	−0.0767720	+	0.997049i	$0.524461\pi$
$420$	9.93754	0.484902
$421$	36.5863	1.78311	0.891553	−	0.452917i	$-0.149617\pi$
$421$	36.5863	1.78311	0.891553	+	0.452917i	$0.149617\pi$
$422$	−21.8865	−1.06542
$423$	5.99255	0.291368
$424$	−2.53384	−0.123054
$425$	−19.2615	−0.934319
$426$	14.5095	0.702989
$427$	39.0620	1.89034
$428$	−4.41308	−0.213314
$429$	3.98052	0.192182
$430$	5.99502	0.289105
$431$	−23.0513	−1.11034	−0.555170	−	0.831737i	$-0.687347\pi$
$431$	−23.0513	−1.11034	−0.555170	+	0.831737i	$0.687347\pi$
$432$	5.65382	0.272020
$433$	10.7172	0.515034	0.257517	−	0.966274i	$-0.417096\pi$
$433$	10.7172	0.515034	0.257517	+	0.966274i	$0.417096\pi$
$434$	−3.19070	−0.153158
$435$	−3.94252	−0.189029
$436$	−14.6945	−0.703738
$437$	4.68776	0.224246
$438$	3.47255	0.165925
$439$	3.07573	0.146797	0.0733984	−	0.997303i	$-0.476616\pi$
$439$	3.07573	0.146797	0.0733984	+	0.997303i	$0.476616\pi$
$440$	2.08623	0.0994573
$441$	0.695135	0.0331017
$442$	−24.4781	−1.16430
$443$	16.1752	0.768507	0.384253	−	0.923228i	$-0.374459\pi$
$443$	16.1752	0.768507	0.384253	+	0.923228i	$0.374459\pi$
$444$	7.44256	0.353208
$445$	−39.6295	−1.87862
$446$	2.57310	0.121840
$447$	−0.887934	−0.0419978
$448$	2.52061	0.119087
$449$	−19.0110	−0.897183	−0.448591	−	0.893737i	$-0.648074\pi$
$449$	−19.0110	−0.897183	−0.448591	+	0.893737i	$0.648074\pi$
$450$	3.30624	0.155858
$451$	−6.17104	−0.290583
$452$	−16.8210	−0.791194
$453$	−5.18154	−0.243450
$454$	−26.7528	−1.25557
$455$	27.9920	1.31229
$456$	6.50375	0.304566
$457$	−16.3420	−0.764447	−0.382223	−	0.924070i	$-0.624842\pi$
$457$	−16.3420	−0.764447	−0.382223	+	0.924070i	$0.624842\pi$
$458$	14.8228	0.692623
$459$	−35.4132	−1.65295
$460$	−2.84168	−0.132494
$461$	12.4470	0.579713	0.289856	−	0.957070i	$-0.406392\pi$
$461$	12.4470	0.579713	0.289856	+	0.957070i	$0.406392\pi$
$462$	2.56739	0.119446
$463$	25.9867	1.20770	0.603852	−	0.797096i	$-0.293632\pi$
$463$	25.9867	1.20770	0.603852	+	0.797096i	$0.293632\pi$
$464$	−1.00000	−0.0464238
$465$	4.99062	0.231434
$466$	26.9324	1.24762
$467$	−17.3411	−0.802451	−0.401226	−	0.915979i	$-0.631416\pi$
$467$	−17.3411	−0.802451	−0.401226	+	0.915979i	$0.631416\pi$
$468$	4.20168	0.194223
$469$	5.99540	0.276842
$470$	−15.8386	−0.730582
$471$	−17.2630	−0.795435
$472$	−7.55073	−0.347551
$473$	1.54883	0.0712151
$474$	−0.460835	−0.0211669
$475$	14.4156	0.661431
$476$	−15.7881	−0.723644
$477$	−2.72425	−0.124735
$478$	−11.4660	−0.524443
$479$	−5.50912	−0.251718	−0.125859	−	0.992048i	$-0.540169\pi$
$479$	−5.50912	−0.251718	−0.125859	+	0.992048i	$0.540169\pi$
$480$	−3.94252	−0.179951
$481$	20.9642	0.955884
$482$	9.96395	0.453846
$483$	−3.49706	−0.159122
$484$	−10.4610	−0.475501
$485$	−42.1133	−1.91226
$486$	10.5537	0.478723
$487$	−0.239608	−0.0108577	−0.00542885	−	0.999985i	$-0.501728\pi$
$487$	−0.239608	−0.0108577	−0.00542885	+	0.999985i	$0.501728\pi$
$488$	−15.4971	−0.701519
$489$	13.9394	0.630361
$490$	−1.83728	−0.0830000
$491$	−11.6301	−0.524858	−0.262429	−	0.964951i	$-0.584524\pi$
$491$	−11.6301	−0.524858	−0.262429	+	0.964951i	$0.584524\pi$
$492$	11.6619	0.525759
$493$	6.26359	0.282098
$494$	18.3197	0.824244
$495$	2.24301	0.100816
$496$	1.26585	0.0568381
$497$	26.3608	1.18245
$498$	11.1616	0.500165
$499$	16.1813	0.724376	0.362188	−	0.932105i	$-0.382030\pi$
$499$	16.1813	0.724376	0.362188	+	0.932105i	$0.382030\pi$
$500$	5.46981	0.244617
$501$	5.91758	0.264378
$502$	−24.4662	−1.09198
$503$	40.3514	1.79918	0.899590	−	0.436736i	$-0.143866\pi$
$503$	40.3514	1.79918	0.899590	+	0.436736i	$0.143866\pi$
$504$	2.71003	0.120714
$505$	−27.7578	−1.23521
$506$	−0.734155	−0.0326372
$507$	−3.15274	−0.140018
$508$	13.9912	0.620759
$509$	20.4157	0.904912	0.452456	−	0.891787i	$-0.350548\pi$
$509$	20.4157	0.904912	0.452456	+	0.891787i	$0.350548\pi$
$510$	24.6943	1.09348
$511$	6.30892	0.279090
$512$	−1.00000	−0.0441942
$513$	26.5037	1.17017
$514$	5.67757	0.250427
$515$	−34.4521	−1.51814
$516$	−2.92694	−0.128851
$517$	−4.09195	−0.179964
$518$	13.5216	0.594106
$519$	−16.8019	−0.737523
$520$	−11.1053	−0.486999
$521$	−6.28939	−0.275543	−0.137772	−	0.990464i	$-0.543994\pi$
$521$	−6.28939	−0.275543	−0.137772	+	0.990464i	$0.543994\pi$
$522$	−1.07515	−0.0470580
$523$	−32.7708	−1.43297	−0.716484	−	0.697604i	$-0.754250\pi$
$523$	−32.7708	−1.43297	−0.716484	+	0.697604i	$0.754250\pi$
$524$	16.6790	0.728624
$525$	−10.7540	−0.469343
$526$	−2.99198	−0.130456
$527$	−7.92874	−0.345381
$528$	−1.01856	−0.0443271
$529$	1.00000	0.0434783
$530$	7.20036	0.312763
$531$	−8.11816	−0.352298
$532$	11.8160	0.512288
$533$	32.8492	1.42286
$534$	19.3482	0.837280
$535$	12.5406	0.542176
$536$	−2.37856	−0.102738
$537$	29.6898	1.28121
$538$	8.07436	0.348110
$539$	−0.474666	−0.0204453
$540$	−16.0664	−0.691386
$541$	25.6853	1.10430	0.552150	−	0.833745i	$-0.313808\pi$
$541$	25.6853	1.10430	0.552150	+	0.833745i	$0.313808\pi$
$542$	−10.6092	−0.455705
$543$	−21.2577	−0.912256
$544$	6.26359	0.268549
$545$	41.7570	1.78867
$546$	−13.6665	−0.584872
$547$	22.3692	0.956439	0.478219	−	0.878240i	$-0.341282\pi$
$547$	22.3692	0.956439	0.478219	+	0.878240i	$0.341282\pi$
$548$	9.10742	0.389050
$549$	−16.6617	−0.711102
$550$	−2.25764	−0.0962659
$551$	−4.68776	−0.199705
$552$	1.38739	0.0590512
$553$	−0.837244	−0.0356032
$554$	−11.6423	−0.494632
$555$	−21.1494	−0.897741
$556$	14.6061	0.619439
$557$	15.9773	0.676979	0.338490	−	0.940970i	$-0.390084\pi$
$557$	15.9773	0.676979	0.338490	+	0.940970i	$0.390084\pi$
$558$	1.36097	0.0576145
$559$	−8.24459	−0.348709
$560$	−7.16276	−0.302682
$561$	6.37984	0.269357
$562$	−20.2733	−0.855179
$563$	9.58411	0.403922	0.201961	−	0.979394i	$-0.435269\pi$
$563$	9.58411	0.403922	0.201961	+	0.979394i	$0.435269\pi$
$564$	7.73288	0.325613
$565$	47.7999	2.01096
$566$	3.76862	0.158407
$567$	−11.6417	−0.488905
$568$	−10.4581	−0.438814
$569$	18.5834	0.779056	0.389528	−	0.921015i	$-0.372638\pi$
$569$	18.5834	0.779056	0.389528	+	0.921015i	$0.372638\pi$
$570$	−18.4816	−0.774108
$571$	−15.9827	−0.668853	−0.334427	−	0.942422i	$-0.608543\pi$
$571$	−15.9827	−0.668853	−0.334427	+	0.942422i	$0.608543\pi$
$572$	−2.86907	−0.119962
$573$	34.0031	1.42050
$574$	21.1873	0.884341
$575$	3.07515	0.128243
$576$	−1.07515	−0.0447979
$577$	9.19809	0.382922	0.191461	−	0.981500i	$-0.438678\pi$
$577$	9.19809	0.382922	0.191461	+	0.981500i	$0.438678\pi$
$578$	−22.2326	−0.924755
$579$	11.3651	0.472317
$580$	2.84168	0.117994
$581$	20.2784	0.841291
$582$	20.5609	0.852277
$583$	1.86023	0.0770428
$584$	−2.50294	−0.103572
$585$	−11.9398	−0.493651
$586$	17.7800	0.734485
$587$	4.11201	0.169721	0.0848604	−	0.996393i	$-0.472956\pi$
$587$	4.11201	0.169721	0.0848604	+	0.996393i	$0.472956\pi$
$588$	0.897014	0.0369922
$589$	5.93398	0.244505
$590$	21.4568	0.883361
$591$	19.6911	0.809982
$592$	−5.36443	−0.220477
$593$	6.27830	0.257819	0.128910	−	0.991656i	$-0.458852\pi$
$593$	6.27830	0.257819	0.128910	+	0.991656i	$0.458852\pi$
$594$	−4.15078	−0.170309
$595$	44.8646	1.83927
$596$	0.640003	0.0262156
$597$	7.81538	0.319862
$598$	3.90800	0.159810
$599$	3.33039	0.136076	0.0680381	−	0.997683i	$-0.478326\pi$
$599$	3.33039	0.136076	0.0680381	+	0.997683i	$0.478326\pi$
$600$	4.26643	0.174176
$601$	−25.2877	−1.03151	−0.515754	−	0.856737i	$-0.672488\pi$
$601$	−25.2877	−1.03151	−0.515754	+	0.856737i	$0.672488\pi$
$602$	−5.31765	−0.216731
$603$	−2.55730	−0.104141
$604$	3.73474	0.151964
$605$	29.7269	1.20857
$606$	13.5522	0.550519
$607$	−7.12841	−0.289333	−0.144667	−	0.989480i	$-0.546211\pi$
$607$	−7.12841	−0.289333	−0.144667	+	0.989480i	$0.546211\pi$
$608$	−4.68776	−0.190114
$609$	3.49706	0.141708
$610$	44.0377	1.78303
$611$	21.7819	0.881203
$612$	6.73430	0.272218
$613$	−28.3495	−1.14503	−0.572513	−	0.819895i	$-0.694031\pi$
$613$	−28.3495	−1.14503	−0.572513	+	0.819895i	$0.694031\pi$
$614$	12.2591	0.494739
$615$	−33.1394	−1.33631
$616$	−1.85051	−0.0745594
$617$	−7.65439	−0.308154	−0.154077	−	0.988059i	$-0.549240\pi$
$617$	−7.65439	−0.308154	−0.154077	+	0.988059i	$0.549240\pi$
$618$	16.8205	0.676619
$619$	16.6712	0.670071	0.335035	−	0.942206i	$-0.391252\pi$
$619$	16.6712	0.670071	0.335035	+	0.942206i	$0.391252\pi$
$620$	−3.59713	−0.144464
$621$	5.65382	0.226880
$622$	−28.7366	−1.15223
$623$	35.1518	1.40833
$624$	5.42191	0.217050
$625$	−30.9192	−1.23677
$626$	25.3261	1.01223
$627$	−4.77476	−0.190686
$628$	12.4428	0.496520
$629$	33.6006	1.33975
$630$	−7.70103	−0.306816
$631$	10.4224	0.414909	0.207455	−	0.978245i	$-0.433482\pi$
$631$	10.4224	0.414909	0.207455	+	0.978245i	$0.433482\pi$
$632$	0.332160	0.0132126
$633$	−30.3652	−1.20691
$634$	−7.56759	−0.300547
$635$	−39.7585	−1.57777
$636$	−3.51542	−0.139395
$637$	2.52671	0.100112
$638$	0.734155	0.0290655
$639$	−11.2441	−0.444808
$640$	2.84168	0.112327
$641$	−23.4547	−0.926407	−0.463203	−	0.886252i	$-0.653300\pi$
$641$	−23.4547	−0.926407	−0.463203	+	0.886252i	$0.653300\pi$
$642$	−6.12266	−0.241642
$643$	22.0383	0.869104	0.434552	−	0.900647i	$-0.356907\pi$
$643$	22.0383	0.869104	0.434552	+	0.900647i	$0.356907\pi$
$644$	2.52061	0.0993258
$645$	8.31743	0.327498
$646$	29.3622	1.15524
$647$	−16.2174	−0.637570	−0.318785	−	0.947827i	$-0.603275\pi$
$647$	−16.2174	−0.637570	−0.318785	+	0.947827i	$0.603275\pi$
$648$	4.61861	0.181436
$649$	5.54341	0.217598
$650$	12.0177	0.471372
$651$	−4.42674	−0.173498
$652$	−10.0472	−0.393479
$653$	11.9039	0.465835	0.232917	−	0.972497i	$-0.425173\pi$
$653$	11.9039	0.465835	0.232917	+	0.972497i	$0.425173\pi$
$654$	−20.3870	−0.797194
$655$	−47.3963	−1.85193
$656$	−8.40564	−0.328185
$657$	−2.69103	−0.104987
$658$	14.0491	0.547690
$659$	34.9511	1.36150	0.680751	−	0.732514i	$-0.261653\pi$
$659$	34.9511	1.36150	0.680751	+	0.732514i	$0.261653\pi$
$660$	2.89442	0.112665
$661$	−11.2201	−0.436410	−0.218205	−	0.975903i	$-0.570020\pi$
$661$	−11.2201	−0.436410	−0.218205	+	0.975903i	$0.570020\pi$
$662$	16.9557	0.659002
$663$	−33.9607	−1.31892
$664$	−8.04506	−0.312209
$665$	−33.5773	−1.30207
$666$	−5.76756	−0.223489
$667$	−1.00000	−0.0387202
$668$	−4.26526	−0.165028
$669$	3.56990	0.138020
$670$	6.75910	0.261127
$671$	11.3772	0.439214
$672$	3.49706	0.134902
$673$	17.8131	0.686644	0.343322	−	0.939218i	$-0.388448\pi$
$673$	17.8131	0.686644	0.343322	+	0.939218i	$0.388448\pi$
$674$	−24.3457	−0.937760
$675$	17.3863	0.669201
$676$	2.27243	0.0874011
$677$	43.1495	1.65837	0.829184	−	0.558975i	$-0.188805\pi$
$677$	43.1495	1.65837	0.829184	+	0.558975i	$0.188805\pi$
$678$	−23.3373	−0.896264
$679$	37.3550	1.43355
$680$	−17.7991	−0.682566
$681$	−37.1165	−1.42231
$682$	−0.929326	−0.0355857
$683$	37.5158	1.43550	0.717752	−	0.696299i	$-0.245171\pi$
$683$	37.5158	1.43550	0.717752	+	0.696299i	$0.245171\pi$
$684$	−5.04004	−0.192711
$685$	−25.8804	−0.988839
$686$	19.2739	0.735882
$687$	20.5650	0.784603
$688$	2.10967	0.0804305
$689$	−9.90222	−0.377245
$690$	−3.94252	−0.150089
$691$	39.4528	1.50085	0.750427	−	0.660953i	$-0.229848\pi$
$691$	39.4528	1.50085	0.750427	+	0.660953i	$0.229848\pi$
$692$	12.1105	0.460371
$693$	−1.98958	−0.0755779
$694$	8.26193	0.313619
$695$	−41.5060	−1.57441
$696$	−1.38739	−0.0525889
$697$	52.6495	1.99424
$698$	31.5428	1.19391
$699$	37.3657	1.41330
$700$	7.75124	0.292969
$701$	35.6694	1.34721	0.673607	−	0.739090i	$-0.264744\pi$
$701$	35.6694	1.34721	0.673607	+	0.739090i	$0.264744\pi$
$702$	22.0951	0.833926
$703$	−25.1472	−0.948443
$704$	0.734155	0.0276695
$705$	−21.9744	−0.827603
$706$	2.83348	0.106639
$707$	24.6215	0.925987
$708$	−10.4758	−0.393705
$709$	−8.35453	−0.313761	−0.156880	−	0.987618i	$-0.550144\pi$
$709$	−8.35453	−0.313761	−0.156880	+	0.987618i	$0.550144\pi$
$710$	29.7187	1.11532
$711$	0.357121	0.0133931
$712$	−13.9458	−0.522640
$713$	1.26585	0.0474063
$714$	−21.9042	−0.819743
$715$	8.15299	0.304905
$716$	−21.3998	−0.799747
$717$	−15.9078	−0.594088
$718$	−15.6284	−0.583245
$719$	14.4444	0.538684	0.269342	−	0.963045i	$-0.413194\pi$
$719$	14.4444	0.538684	0.269342	+	0.963045i	$0.413194\pi$
$720$	3.05523	0.113862
$721$	30.5594	1.13809
$722$	−2.97508	−0.110721
$723$	13.8239	0.514116
$724$	15.3221	0.569441
$725$	−3.07515	−0.114208
$726$	−14.5135	−0.538647
$727$	−20.9724	−0.777823	−0.388911	−	0.921275i	$-0.627149\pi$
$727$	−20.9724	−0.777823	−0.388911	+	0.921275i	$0.627149\pi$
$728$	9.85051	0.365084
$729$	28.4979	1.05548
$730$	7.11255	0.263247
$731$	−13.2141	−0.488742
$732$	−21.5005	−0.794680
$733$	−41.3075	−1.52573	−0.762863	−	0.646560i	$-0.776207\pi$
$733$	−41.3075	−1.52573	−0.762863	+	0.646560i	$0.776207\pi$
$734$	8.98158	0.331516
$735$	−2.54903	−0.0940223
$736$	−1.00000	−0.0368605
$737$	1.74623	0.0643231
$738$	−9.03732	−0.332668
$739$	−1.03551	−0.0380919	−0.0190460	−	0.999819i	$-0.506063\pi$
$739$	−1.03551	−0.0380919	−0.0190460	+	0.999819i	$0.506063\pi$
$740$	15.2440	0.560381
$741$	25.4166	0.933703
$742$	−6.38680	−0.234467
$743$	16.0699	0.589547	0.294773	−	0.955567i	$-0.404756\pi$
$743$	16.0699	0.589547	0.294773	+	0.955567i	$0.404756\pi$
$744$	1.75622	0.0643862
$745$	−1.81869	−0.0666315
$746$	20.3675	0.745707
$747$	−8.64964	−0.316474
$748$	−4.59845	−0.168136
$749$	−11.1236	−0.406449
$750$	7.58876	0.277102
$751$	−10.4177	−0.380146	−0.190073	−	0.981770i	$-0.560872\pi$
$751$	−10.4177	−0.380146	−0.190073	+	0.981770i	$0.560872\pi$
$752$	−5.57369	−0.203252
$753$	−33.9442	−1.23700
$754$	−3.90800	−0.142321
$755$	−10.6129	−0.386244
$756$	14.2511	0.518306
$757$	−16.8208	−0.611361	−0.305681	−	0.952134i	$-0.598884\pi$
$757$	−16.8208	−0.611361	−0.305681	+	0.952134i	$0.598884\pi$
$758$	−33.1444	−1.20386
$759$	−1.01856	−0.0369714
$760$	13.3211	0.483208
$761$	−38.4700	−1.39454	−0.697269	−	0.716810i	$-0.745602\pi$
$761$	−38.4700	−1.39454	−0.697269	+	0.716810i	$0.745602\pi$
$762$	19.4113	0.703196
$763$	−37.0390	−1.34090
$764$	−24.5087	−0.886693
$765$	−19.1367	−0.691890
$766$	20.3378	0.734833
$767$	−29.5082	−1.06548
$768$	−1.38739	−0.0500631
$769$	−47.3222	−1.70648	−0.853241	−	0.521517i	$-0.825366\pi$
$769$	−47.3222	−1.70648	−0.853241	+	0.521517i	$0.825366\pi$
$770$	5.25857	0.189506
$771$	7.87700	0.283683
$772$	−8.19171	−0.294826
$773$	−46.8158	−1.68385	−0.841924	−	0.539596i	$-0.818577\pi$
$773$	−46.8158	−1.68385	−0.841924	+	0.539596i	$0.818577\pi$
$774$	2.26821	0.0815292
$775$	3.89266	0.139829
$776$	−14.8198	−0.532001
$777$	18.7598	0.673003
$778$	−25.4009	−0.910666
$779$	−39.4036	−1.41178
$780$	−15.4073	−0.551672
$781$	7.67790	0.274737
$782$	6.26359	0.223986
$783$	−5.65382	−0.202051
$784$	−0.646548	−0.0230910
$785$	−35.3584	−1.26199
$786$	23.1402	0.825385
$787$	−15.4372	−0.550278	−0.275139	−	0.961404i	$-0.588724\pi$
$787$	−15.4372	−0.550278	−0.275139	+	0.961404i	$0.588724\pi$
$788$	−14.1929	−0.505600
$789$	−4.15104	−0.147781
$790$	−0.943892	−0.0335822
$791$	−42.3991	−1.50754
$792$	0.789326	0.0280475
$793$	−60.5625	−2.15064
$794$	10.9891	0.389990
$795$	9.98970	0.354298
$796$	−5.63315	−0.199662
$797$	47.1992	1.67188	0.835941	−	0.548819i	$-0.184923\pi$
$797$	47.1992	1.67188	0.835941	+	0.548819i	$0.184923\pi$
$798$	16.3934	0.580320
$799$	34.9113	1.23507
$800$	−3.07515	−0.108723
$801$	−14.9938	−0.529780
$802$	−2.33050	−0.0822926
$803$	1.83754	0.0648455
$804$	−3.29998	−0.116381
$805$	−7.16276	−0.252454
$806$	4.94692	0.174248
$807$	11.2023	0.394339
$808$	−9.76809	−0.343640
$809$	−20.2662	−0.712521	−0.356260	−	0.934387i	$-0.615948\pi$
$809$	−20.2662	−0.712521	−0.356260	+	0.934387i	$0.615948\pi$
$810$	−13.1246	−0.461152
$811$	5.35630	0.188085	0.0940426	−	0.995568i	$-0.470021\pi$
$811$	5.35630	0.188085	0.0940426	+	0.995568i	$0.470021\pi$
$812$	−2.52061	−0.0884559
$813$	−14.7191	−0.516223
$814$	3.93832	0.138038
$815$	28.5510	1.00010
$816$	8.69005	0.304213
$817$	9.88964	0.345995
$818$	−14.6030	−0.510583
$819$	10.5908	0.370071
$820$	23.8862	0.834141
$821$	2.78973	0.0973623	0.0486811	−	0.998814i	$-0.484498\pi$
$821$	2.78973	0.0973623	0.0486811	+	0.998814i	$0.484498\pi$
$822$	12.6355	0.440715
$823$	−23.2050	−0.808875	−0.404437	−	0.914566i	$-0.632533\pi$
$823$	−23.2050	−0.808875	−0.404437	+	0.914566i	$0.632533\pi$
$824$	−12.1238	−0.422354
$825$	−3.13222	−0.109050
$826$	−19.0324	−0.662222
$827$	−53.4999	−1.86037	−0.930187	−	0.367086i	$-0.880356\pi$
$827$	−53.4999	−1.86037	−0.930187	+	0.367086i	$0.880356\pi$
$828$	−1.07515	−0.0373640
$829$	49.2081	1.70907	0.854534	−	0.519396i	$-0.173843\pi$
$829$	49.2081	1.70907	0.854534	+	0.519396i	$0.173843\pi$
$830$	22.8615	0.793534
$831$	−16.1523	−0.560319
$832$	−3.90800	−0.135485
$833$	4.04971	0.140314
$834$	20.2644	0.701700
$835$	12.1205	0.419447
$836$	3.44154	0.119028
$837$	7.15686	0.247377
$838$	3.14297	0.108572
$839$	−16.4962	−0.569513	−0.284757	−	0.958600i	$-0.591913\pi$
$839$	−16.4962	−0.569513	−0.284757	+	0.958600i	$0.591913\pi$
$840$	−9.93754	−0.342878
$841$	1.00000	0.0344828
$842$	−36.5863	−1.26085
$843$	−28.1270	−0.968747
$844$	21.8865	0.753366
$845$	−6.45752	−0.222145
$846$	−5.99255	−0.206028
$847$	−26.3681	−0.906018
$848$	2.53384	0.0870123
$849$	5.22855	0.179443
$850$	19.2615	0.660664
$851$	−5.36443	−0.183890
$852$	−14.5095	−0.497088
$853$	32.3693	1.10830	0.554151	−	0.832416i	$-0.313043\pi$
$853$	32.3693	1.10830	0.554151	+	0.832416i	$0.313043\pi$
$854$	−39.0620	−1.33667
$855$	14.3222	0.489808
$856$	4.41308	0.150836
$857$	11.1485	0.380825	0.190413	−	0.981704i	$-0.439017\pi$
$857$	11.1485	0.380825	0.190413	+	0.981704i	$0.439017\pi$
$858$	−3.98052	−0.135893
$859$	33.7436	1.15132	0.575659	−	0.817690i	$-0.304746\pi$
$859$	33.7436	1.15132	0.575659	+	0.817690i	$0.304746\pi$
$860$	−5.99502	−0.204428
$861$	29.3951	1.00178
$862$	23.0513	0.785129
$863$	4.66055	0.158647	0.0793235	−	0.996849i	$-0.474724\pi$
$863$	4.66055	0.158647	0.0793235	+	0.996849i	$0.474724\pi$
$864$	−5.65382	−0.192347
$865$	−34.4141	−1.17011
$866$	−10.7172	−0.364184
$867$	−30.8453	−1.04756
$868$	3.19070	0.108299
$869$	−0.243857	−0.00827228
$870$	3.94252	0.133664
$871$	−9.29539	−0.314962
$872$	14.6945	0.497618
$873$	−15.9335	−0.539269
$874$	−4.68776	−0.158566
$875$	13.7872	0.466094
$876$	−3.47255	−0.117327
$877$	−10.5927	−0.357688	−0.178844	−	0.983877i	$-0.557236\pi$
$877$	−10.5927	−0.357688	−0.178844	+	0.983877i	$0.557236\pi$
$878$	−3.07573	−0.103801
$879$	24.6678	0.832024
$880$	−2.08623	−0.0703269
$881$	23.2833	0.784434	0.392217	−	0.919873i	$-0.371708\pi$
$881$	23.2833	0.784434	0.392217	+	0.919873i	$0.371708\pi$
$882$	−0.695135	−0.0234064
$883$	−33.3081	−1.12091	−0.560453	−	0.828186i	$-0.689373\pi$
$883$	−33.3081	−1.12091	−0.560453	+	0.828186i	$0.689373\pi$
$884$	24.4781	0.823288
$885$	29.7689	1.00067
$886$	−16.1752	−0.543416
$887$	23.9552	0.804336	0.402168	−	0.915566i	$-0.368257\pi$
$887$	23.9552	0.804336	0.402168	+	0.915566i	$0.368257\pi$
$888$	−7.44256	−0.249756
$889$	35.2663	1.18279
$890$	39.6295	1.32838
$891$	−3.39077	−0.113595
$892$	−2.57310	−0.0861538
$893$	−26.1281	−0.874344
$894$	0.887934	0.0296970
$895$	60.8113	2.03270
$896$	−2.52061	−0.0842075
$897$	5.42191	0.181032
$898$	19.0110	0.634404
$899$	−1.26585	−0.0422183
$900$	−3.30624	−0.110208
$901$	−15.8709	−0.528737
$902$	6.17104	0.205473
$903$	−7.37766	−0.245513
$904$	16.8210	0.559459
$905$	−43.5405	−1.44733
$906$	5.18154	0.172145
$907$	36.7450	1.22010	0.610049	−	0.792363i	$-0.291150\pi$
$907$	36.7450	1.22010	0.610049	+	0.792363i	$0.291150\pi$
$908$	26.7528	0.887822
$909$	−10.5022	−0.348334
$910$	−27.9920	−0.927926
$911$	49.8370	1.65117	0.825586	−	0.564276i	$-0.190845\pi$
$911$	49.8370	1.65117	0.825586	+	0.564276i	$0.190845\pi$
$912$	−6.50375	−0.215361
$913$	5.90632	0.195471
$914$	16.3420	0.540546
$915$	61.0975	2.01982
$916$	−14.8228	−0.489758
$917$	42.0411	1.38832
$918$	35.4132	1.16881
$919$	54.5727	1.80019	0.900094	−	0.435696i	$-0.143498\pi$
$919$	54.5727	1.80019	0.900094	+	0.435696i	$0.143498\pi$
$920$	2.84168	0.0936874
$921$	17.0082	0.560439
$922$	−12.4470	−0.409919
$923$	−40.8704	−1.34526
$924$	−2.56739	−0.0844608
$925$	−16.4964	−0.542399
$926$	−25.9867	−0.853976
$927$	−13.0349	−0.428123
$928$	1.00000	0.0328266
$929$	−23.4390	−0.769008	−0.384504	−	0.923123i	$-0.625628\pi$
$929$	−23.4390	−0.769008	−0.384504	+	0.923123i	$0.625628\pi$
$930$	−4.99062	−0.163649
$931$	−3.03086	−0.0993325
$932$	−26.9324	−0.882198
$933$	−39.8688	−1.30525
$934$	17.3411	0.567419
$935$	13.0673	0.427347
$936$	−4.20168	−0.137336
$937$	25.7724	0.841948	0.420974	−	0.907073i	$-0.361688\pi$
$937$	25.7724	0.841948	0.420974	+	0.907073i	$0.361688\pi$
$938$	−5.99540	−0.195757
$939$	35.1372	1.14666
$940$	15.8386	0.516600
$941$	−51.4863	−1.67841	−0.839203	−	0.543818i	$-0.816978\pi$
$941$	−51.4863	−1.67841	−0.839203	+	0.543818i	$0.816978\pi$
$942$	17.2630	0.562458
$943$	−8.40564	−0.273725
$944$	7.55073	0.245755
$945$	−40.4969	−1.31737
$946$	−1.54883	−0.0503567
$947$	−33.1302	−1.07659	−0.538293	−	0.842758i	$-0.680931\pi$
$947$	−33.1302	−1.07659	−0.538293	+	0.842758i	$0.680931\pi$
$948$	0.460835	0.0149672
$949$	−9.78147	−0.317520
$950$	−14.4156	−0.467702
$951$	−10.4992	−0.340460
$952$	15.7881	0.511694
$953$	6.48217	0.209978	0.104989	−	0.994473i	$-0.466519\pi$
$953$	6.48217	0.209978	0.104989	+	0.994473i	$0.466519\pi$
$954$	2.72425	0.0882009
$955$	69.6458	2.25369
$956$	11.4660	0.370837
$957$	1.01856	0.0329253
$958$	5.50912	0.177992
$959$	22.9562	0.741295
$960$	3.94252	0.127244
$961$	−29.3976	−0.948311
$962$	−20.9642	−0.675912
$963$	4.74472	0.152896
$964$	−9.96395	−0.320917
$965$	23.2782	0.749353
$966$	3.49706	0.112516
$967$	58.5688	1.88344	0.941722	−	0.336392i	$-0.109207\pi$
$967$	58.5688	1.88344	0.941722	+	0.336392i	$0.109207\pi$
$968$	10.4610	0.336230
$969$	40.7369	1.30866
$970$	42.1133	1.35218
$971$	−4.44319	−0.142589	−0.0712944	−	0.997455i	$-0.522713\pi$
$971$	−4.44319	−0.142589	−0.0712944	+	0.997455i	$0.522713\pi$
$972$	−10.5537	−0.338509
$973$	36.8163	1.18028
$974$	0.239608	0.00767755
$975$	16.6732	0.533970
$976$	15.4971	0.496049
$977$	17.7915	0.569200	0.284600	−	0.958646i	$-0.408139\pi$
$977$	17.7915	0.569200	0.284600	+	0.958646i	$0.408139\pi$
$978$	−13.9394	−0.445733
$979$	10.2384	0.327220
$980$	1.83728	0.0586899
$981$	15.7988	0.504416
$982$	11.6301	0.371131
$983$	−21.2726	−0.678490	−0.339245	−	0.940698i	$-0.610172\pi$
$983$	−21.2726	−0.678490	−0.339245	+	0.940698i	$0.610172\pi$
$984$	−11.6619	−0.371768
$985$	40.3316	1.28507
$986$	−6.26359	−0.199473
$987$	19.4915	0.620423
$988$	−18.3197	−0.582829
$989$	2.10967	0.0670837
$990$	−2.24301	−0.0712876
$991$	59.2974	1.88364	0.941822	−	0.336112i	$-0.109112\pi$
$991$	59.2974	1.88364	0.941822	+	0.336112i	$0.109112\pi$
$992$	−1.26585	−0.0401906
$993$	23.5242	0.746517
$994$	−26.3608	−0.836115
$995$	16.0076	0.507476
$996$	−11.1616	−0.353670
$997$	−19.6045	−0.620880	−0.310440	−	0.950593i	$-0.600476\pi$
$997$	−19.6045	−0.620880	−0.310440	+	0.950593i	$0.600476\pi$
$998$	−16.1813	−0.512211
$999$	−30.3295	−0.959584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.g.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.g.1.2	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.38739 q^{3} +1.00000 q^{4} -2.84168 q^{5} +1.38739 q^{6} +2.52061 q^{7} -1.00000 q^{8} -1.07515 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.38739 q^{3} +1.00000 q^{4} -2.84168 q^{5} +1.38739 q^{6} +2.52061 q^{7} -1.00000 q^{8} -1.07515 q^{9} +2.84168 q^{10} +0.734155 q^{11} -1.38739 q^{12} -3.90800 q^{13} -2.52061 q^{14} +3.94252 q^{15} +1.00000 q^{16} -6.26359 q^{17} +1.07515 q^{18} +4.68776 q^{19} -2.84168 q^{20} -3.49706 q^{21} -0.734155 q^{22} +1.00000 q^{23} +1.38739 q^{24} +3.07515 q^{25} +3.90800 q^{26} +5.65382 q^{27} +2.52061 q^{28} -1.00000 q^{29} -3.94252 q^{30} +1.26585 q^{31} -1.00000 q^{32} -1.01856 q^{33} +6.26359 q^{34} -7.16276 q^{35} -1.07515 q^{36} -5.36443 q^{37} -4.68776 q^{38} +5.42191 q^{39} +2.84168 q^{40} -8.40564 q^{41} +3.49706 q^{42} +2.10967 q^{43} +0.734155 q^{44} +3.05523 q^{45} -1.00000 q^{46} -5.57369 q^{47} -1.38739 q^{48} -0.646548 q^{49} -3.07515 q^{50} +8.69005 q^{51} -3.90800 q^{52} +2.53384 q^{53} -5.65382 q^{54} -2.08623 q^{55} -2.52061 q^{56} -6.50375 q^{57} +1.00000 q^{58} +7.55073 q^{59} +3.94252 q^{60} +15.4971 q^{61} -1.26585 q^{62} -2.71003 q^{63} +1.00000 q^{64} +11.1053 q^{65} +1.01856 q^{66} +2.37856 q^{67} -6.26359 q^{68} -1.38739 q^{69} +7.16276 q^{70} +10.4581 q^{71} +1.07515 q^{72} +2.50294 q^{73} +5.36443 q^{74} -4.26643 q^{75} +4.68776 q^{76} +1.85051 q^{77} -5.42191 q^{78} -0.332160 q^{79} -2.84168 q^{80} -4.61861 q^{81} +8.40564 q^{82} +8.04506 q^{83} -3.49706 q^{84} +17.7991 q^{85} -2.10967 q^{86} +1.38739 q^{87} -0.734155 q^{88} +13.9458 q^{89} -3.05523 q^{90} -9.85051 q^{91} +1.00000 q^{92} -1.75622 q^{93} +5.57369 q^{94} -13.3211 q^{95} +1.38739 q^{96} +14.8198 q^{97} +0.646548 q^{98} -0.789326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - 5 q^{8} + 12 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - 3 q^{13} - 4 q^{14} + q^{15} + 5 q^{16} - 4 q^{17} - 12 q^{18} + 14 q^{19} + 3 q^{20} + 10 q^{21} - 3 q^{22} + 5 q^{23} - q^{24} - 2 q^{25} + 3 q^{26} + 19 q^{27} + 4 q^{28} - 5 q^{29} - q^{30} + 7 q^{31} - 5 q^{32} - q^{33} + 4 q^{34} - 10 q^{35} + 12 q^{36} + 2 q^{37} - 14 q^{38} + 17 q^{39} - 3 q^{40} + 4 q^{41} - 10 q^{42} - 9 q^{43} + 3 q^{44} + 6 q^{45} - 5 q^{46} - 13 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 11 q^{53} - 19 q^{54} - 3 q^{55} - 4 q^{56} + 10 q^{57} + 5 q^{58} + 2 q^{59} + q^{60} + 50 q^{61} - 7 q^{62} + 4 q^{63} + 5 q^{64} + 11 q^{65} + q^{66} + 22 q^{67} - 4 q^{68} + q^{69} + 10 q^{70} + 2 q^{71} - 12 q^{72} + 40 q^{73} - 2 q^{74} - 20 q^{75} + 14 q^{76} - 26 q^{77} - 17 q^{78} - 3 q^{79} + 3 q^{80} + 13 q^{81} - 4 q^{82} - 18 q^{83} + 10 q^{84} + 22 q^{85} + 9 q^{86} - q^{87} - 3 q^{88} + 12 q^{89} - 6 q^{90} - 14 q^{91} + 5 q^{92} + 3 q^{93} + 13 q^{94} + 10 q^{95} - q^{96} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 + 3 * q^5 - q^6 + 4 * q^7 - 5 * q^8 + 12 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - 3 * q^13 - 4 * q^14 + q^15 + 5 * q^16 - 4 * q^17 - 12 * q^18 + 14 * q^19 + 3 * q^20 + 10 * q^21 - 3 * q^22 + 5 * q^23 - q^24 - 2 * q^25 + 3 * q^26 + 19 * q^27 + 4 * q^28 - 5 * q^29 - q^30 + 7 * q^31 - 5 * q^32 - q^33 + 4 * q^34 - 10 * q^35 + 12 * q^36 + 2 * q^37 - 14 * q^38 + 17 * q^39 - 3 * q^40 + 4 * q^41 - 10 * q^42 - 9 * q^43 + 3 * q^44 + 6 * q^45 - 5 * q^46 - 13 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 11 * q^53 - 19 * q^54 - 3 * q^55 - 4 * q^56 + 10 * q^57 + 5 * q^58 + 2 * q^59 + q^60 + 50 * q^61 - 7 * q^62 + 4 * q^63 + 5 * q^64 + 11 * q^65 + q^66 + 22 * q^67 - 4 * q^68 + q^69 + 10 * q^70 + 2 * q^71 - 12 * q^72 + 40 * q^73 - 2 * q^74 - 20 * q^75 + 14 * q^76 - 26 * q^77 - 17 * q^78 - 3 * q^79 + 3 * q^80 + 13 * q^81 - 4 * q^82 - 18 * q^83 + 10 * q^84 + 22 * q^85 + 9 * q^86 - q^87 - 3 * q^88 + 12 * q^89 - 6 * q^90 - 14 * q^91 + 5 * q^92 + 3 * q^93 + 13 * q^94 + 10 * q^95 - q^96 + 11 * q^98 + 46 * q^99

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