LMFDB - Embedded newform 1110.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1110.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.339102$ of defining polynomial
Character	$\chi$	$=$	1110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.832640 q^{11} +1.00000 q^{12} +3.21973 q^{13} +1.84556 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.95030 q^{17} +1.00000 q^{18} +4.20681 q^{19} +1.00000 q^{20} +1.84556 q^{21} +0.832640 q^{22} -6.57614 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.21973 q^{26} +1.00000 q^{27} +1.84556 q^{28} +3.03945 q^{29} +1.00000 q^{30} -4.73057 q^{31} +1.00000 q^{32} +0.832640 q^{33} -7.95030 q^{34} +1.84556 q^{35} +1.00000 q^{36} -1.00000 q^{37} +4.20681 q^{38} +3.21973 q^{39} +1.00000 q^{40} +2.73057 q^{41} +1.84556 q^{42} -5.03945 q^{43} +0.832640 q^{44} +1.00000 q^{45} -6.57614 q^{46} +9.11766 q^{47} +1.00000 q^{48} -3.59390 q^{49} +1.00000 q^{50} -7.95030 q^{51} +3.21973 q^{52} +3.95030 q^{53} +1.00000 q^{54} +0.832640 q^{55} +1.84556 q^{56} +4.20681 q^{57} +3.03945 q^{58} -3.69113 q^{59} +1.00000 q^{60} +5.40878 q^{61} -4.73057 q^{62} +1.84556 q^{63} +1.00000 q^{64} +3.21973 q^{65} +0.832640 q^{66} +11.7959 q^{67} -7.95030 q^{68} -6.57614 q^{69} +1.84556 q^{70} -13.7700 q^{71} +1.00000 q^{72} -3.52860 q^{73} -1.00000 q^{74} +1.00000 q^{75} +4.20681 q^{76} +1.53669 q^{77} +3.21973 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.73057 q^{82} -3.55445 q^{83} +1.84556 q^{84} -7.95030 q^{85} -5.03945 q^{86} +3.03945 q^{87} +0.832640 q^{88} -6.55029 q^{89} +1.00000 q^{90} +5.94222 q^{91} -6.57614 q^{92} -4.73057 q^{93} +9.11766 q^{94} +4.20681 q^{95} +1.00000 q^{96} -10.4918 q^{97} -3.59390 q^{98} +0.832640 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} + 3 q^{19} + 4 q^{20} + 4 q^{21} + 2 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} + 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 3 q^{38} - 3 q^{39} + 4 q^{40} - 11 q^{41} + 4 q^{42} - 5 q^{43} + 2 q^{44} + 4 q^{45} - q^{46} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 6 q^{51} - 3 q^{52} - 22 q^{53} + 4 q^{54} + 2 q^{55} + 4 q^{56} + 3 q^{57} - 3 q^{58} - 8 q^{59} + 4 q^{60} - 5 q^{61} + 3 q^{62} + 4 q^{63} + 4 q^{64} - 3 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - q^{69} + 4 q^{70} - 18 q^{71} + 4 q^{72} - 5 q^{73} - 4 q^{74} + 4 q^{75} + 3 q^{76} - 4 q^{77} - 3 q^{78} + 16 q^{79} + 4 q^{80} + 4 q^{81} - 11 q^{82} - q^{83} + 4 q^{84} + 6 q^{85} - 5 q^{86} - 3 q^{87} + 2 q^{88} - 5 q^{89} + 4 q^{90} - 13 q^{91} - q^{92} + 3 q^{93} + 3 q^{95} + 4 q^{96} + 7 q^{97} + 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 + 3 * q^19 + 4 * q^20 + 4 * q^21 + 2 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 + 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 3 * q^38 - 3 * q^39 + 4 * q^40 - 11 * q^41 + 4 * q^42 - 5 * q^43 + 2 * q^44 + 4 * q^45 - q^46 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 6 * q^51 - 3 * q^52 - 22 * q^53 + 4 * q^54 + 2 * q^55 + 4 * q^56 + 3 * q^57 - 3 * q^58 - 8 * q^59 + 4 * q^60 - 5 * q^61 + 3 * q^62 + 4 * q^63 + 4 * q^64 - 3 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - q^69 + 4 * q^70 - 18 * q^71 + 4 * q^72 - 5 * q^73 - 4 * q^74 + 4 * q^75 + 3 * q^76 - 4 * q^77 - 3 * q^78 + 16 * q^79 + 4 * q^80 + 4 * q^81 - 11 * q^82 - q^83 + 4 * q^84 + 6 * q^85 - 5 * q^86 - 3 * q^87 + 2 * q^88 - 5 * q^89 + 4 * q^90 - 13 * q^91 - q^92 + 3 * q^93 + 3 * q^95 + 4 * q^96 + 7 * q^97 + 14 * q^98 + 2 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	1.84556	0.697557	0.348779	−	0.937205i	$-0.386596\pi$
$7$	1.84556	0.697557	0.348779	+	0.937205i	$0.386596\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0.832640	0.251050	0.125525	−	0.992090i	$-0.459938\pi$
$11$	0.832640	0.251050	0.125525	+	0.992090i	$0.459938\pi$
$12$	1.00000	0.288675
$13$	3.21973	0.892992	0.446496	−	0.894786i	$-0.352672\pi$
$13$	3.21973	0.892992	0.446496	+	0.894786i	$0.352672\pi$
$14$	1.84556	0.493248
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−7.95030	−1.92823	−0.964116	−	0.265482i	$-0.914469\pi$
$17$	−7.95030	−1.92823	−0.964116	+	0.265482i	$0.914469\pi$
$18$	1.00000	0.235702
$19$	4.20681	0.965108	0.482554	−	0.875866i	$-0.339709\pi$
$19$	4.20681	0.965108	0.482554	+	0.875866i	$0.339709\pi$
$20$	1.00000	0.223607
$21$	1.84556	0.402735
$22$	0.832640	0.177519
$23$	−6.57614	−1.37122	−0.685610	−	0.727969i	$-0.740464\pi$
$23$	−6.57614	−1.37122	−0.685610	+	0.727969i	$0.740464\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	3.21973	0.631441
$27$	1.00000	0.192450
$28$	1.84556	0.348779
$29$	3.03945	0.564411	0.282206	−	0.959354i	$-0.408934\pi$
$29$	3.03945	0.564411	0.282206	+	0.959354i	$0.408934\pi$
$30$	1.00000	0.182574
$31$	−4.73057	−0.849636	−0.424818	−	0.905279i	$-0.639662\pi$
$31$	−4.73057	−0.849636	−0.424818	+	0.905279i	$0.639662\pi$
$32$	1.00000	0.176777
$33$	0.832640	0.144944
$34$	−7.95030	−1.36347
$35$	1.84556	0.311957
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.20681	0.682434
$39$	3.21973	0.515569
$40$	1.00000	0.158114
$41$	2.73057	0.426444	0.213222	−	0.977004i	$-0.431604\pi$
$41$	2.73057	0.426444	0.213222	+	0.977004i	$0.431604\pi$
$42$	1.84556	0.284777
$43$	−5.03945	−0.768508	−0.384254	−	0.923227i	$-0.625541\pi$
$43$	−5.03945	−0.768508	−0.384254	+	0.923227i	$0.625541\pi$
$44$	0.832640	0.125525
$45$	1.00000	0.149071
$46$	−6.57614	−0.969598
$47$	9.11766	1.32995	0.664974	−	0.746867i	$-0.268443\pi$
$47$	9.11766	1.32995	0.664974	+	0.746867i	$0.268443\pi$
$48$	1.00000	0.144338
$49$	−3.59390	−0.513414
$50$	1.00000	0.141421
$51$	−7.95030	−1.11327
$52$	3.21973	0.446496
$53$	3.95030	0.542616	0.271308	−	0.962493i	$-0.412544\pi$
$53$	3.95030	0.542616	0.271308	+	0.962493i	$0.412544\pi$
$54$	1.00000	0.136083
$55$	0.832640	0.112273
$56$	1.84556	0.246624
$57$	4.20681	0.557205
$58$	3.03945	0.399099
$59$	−3.69113	−0.480544	−0.240272	−	0.970706i	$-0.577237\pi$
$59$	−3.69113	−0.480544	−0.240272	+	0.970706i	$0.577237\pi$
$60$	1.00000	0.129099
$61$	5.40878	0.692523	0.346261	−	0.938138i	$-0.387451\pi$
$61$	5.40878	0.692523	0.346261	+	0.938138i	$0.387451\pi$
$62$	−4.73057	−0.600783
$63$	1.84556	0.232519
$64$	1.00000	0.125000
$65$	3.21973	0.399358
$66$	0.832640	0.102491
$67$	11.7959	1.44109	0.720547	−	0.693406i	$-0.243891\pi$
$67$	11.7959	1.44109	0.720547	+	0.693406i	$0.243891\pi$
$68$	−7.95030	−0.964116
$69$	−6.57614	−0.791674
$70$	1.84556	0.220587
$71$	−13.7700	−1.63420	−0.817100	−	0.576495i	$-0.804420\pi$
$71$	−13.7700	−1.63420	−0.817100	+	0.576495i	$0.804420\pi$
$72$	1.00000	0.117851
$73$	−3.52860	−0.412992	−0.206496	−	0.978447i	$-0.566206\pi$
$73$	−3.52860	−0.412992	−0.206496	+	0.978447i	$0.566206\pi$
$74$	−1.00000	−0.116248
$75$	1.00000	0.115470
$76$	4.20681	0.482554
$77$	1.53669	0.175122
$78$	3.21973	0.364563
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.73057	0.301541
$83$	−3.55445	−0.390151	−0.195076	−	0.980788i	$-0.562495\pi$
$83$	−3.55445	−0.390151	−0.195076	+	0.980788i	$0.562495\pi$
$84$	1.84556	0.201367
$85$	−7.95030	−0.862331
$86$	−5.03945	−0.543417
$87$	3.03945	0.325863
$88$	0.832640	0.0887597
$89$	−6.55029	−0.694329	−0.347165	−	0.937804i	$-0.612856\pi$
$89$	−6.55029	−0.694329	−0.347165	+	0.937804i	$0.612856\pi$
$90$	1.00000	0.105409
$91$	5.94222	0.622913
$92$	−6.57614	−0.685610
$93$	−4.73057	−0.490538
$94$	9.11766	0.940415
$95$	4.20681	0.431609
$96$	1.00000	0.102062
$97$	−10.4918	−1.06528	−0.532642	−	0.846341i	$-0.678801\pi$
$97$	−10.4918	−1.06528	−0.532642	+	0.846341i	$0.678801\pi$
$98$	−3.59390	−0.363038
$99$	0.832640	0.0836835
$100$	1.00000	0.100000
$101$	−3.63067	−0.361265	−0.180633	−	0.983551i	$-0.557814\pi$
$101$	−3.63067	−0.361265	−0.180633	+	0.983551i	$0.557814\pi$
$102$	−7.95030	−0.787197
$103$	−9.11766	−0.898390	−0.449195	−	0.893434i	$-0.648289\pi$
$103$	−9.11766	−0.898390	−0.449195	+	0.893434i	$0.648289\pi$
$104$	3.21973	0.315720
$105$	1.84556	0.180109
$106$	3.95030	0.383687
$107$	8.91086	0.861445	0.430723	−	0.902484i	$-0.358259\pi$
$107$	8.91086	0.861445	0.430723	+	0.902484i	$0.358259\pi$
$108$	1.00000	0.0962250
$109$	11.2979	1.08215	0.541073	−	0.840975i	$-0.318018\pi$
$109$	11.2979	1.08215	0.541073	+	0.840975i	$0.318018\pi$
$110$	0.832640	0.0793891
$111$	−1.00000	−0.0949158
$112$	1.84556	0.174389
$113$	−11.0394	−1.03850	−0.519252	−	0.854621i	$-0.673789\pi$
$113$	−11.0394	−1.03850	−0.519252	+	0.854621i	$0.673789\pi$
$114$	4.20681	0.394004
$115$	−6.57614	−0.613228
$116$	3.03945	0.282206
$117$	3.21973	0.297664
$118$	−3.69113	−0.339796
$119$	−14.6728	−1.34505
$120$	1.00000	0.0912871
$121$	−10.3067	−0.936974
$122$	5.40878	0.489688
$123$	2.73057	0.246208
$124$	−4.73057	−0.424818
$125$	1.00000	0.0894427
$126$	1.84556	0.164416
$127$	−0.136678	−0.0121282	−0.00606410	−	0.999982i	$-0.501930\pi$
$127$	−0.136678	−0.0121282	−0.00606410	+	0.999982i	$0.501930\pi$
$128$	1.00000	0.0883883
$129$	−5.03945	−0.443699
$130$	3.21973	0.282389
$131$	2.07889	0.181634	0.0908169	−	0.995868i	$-0.471052\pi$
$131$	2.07889	0.181634	0.0908169	+	0.995868i	$0.471052\pi$
$132$	0.832640	0.0724720
$133$	7.76393	0.673218
$134$	11.7959	1.01901
$135$	1.00000	0.0860663
$136$	−7.95030	−0.681733
$137$	3.06597	0.261943	0.130972	−	0.991386i	$-0.458190\pi$
$137$	3.06597	0.261943	0.130972	+	0.991386i	$0.458190\pi$
$138$	−6.57614	−0.559798
$139$	22.1917	1.88228	0.941139	−	0.338021i	$-0.109757\pi$
$139$	22.1917	1.88228	0.941139	+	0.338021i	$0.109757\pi$
$140$	1.84556	0.155979
$141$	9.11766	0.767846
$142$	−13.7700	−1.15555
$143$	2.68088	0.224186
$144$	1.00000	0.0833333
$145$	3.03945	0.252412
$146$	−3.52860	−0.292029
$147$	−3.59390	−0.296420
$148$	−1.00000	−0.0821995
$149$	−14.4999	−1.18788	−0.593940	−	0.804510i	$-0.702428\pi$
$149$	−14.4999	−1.18788	−0.593940	+	0.804510i	$0.702428\pi$
$150$	1.00000	0.0816497
$151$	8.24142	0.670677	0.335339	−	0.942098i	$-0.391149\pi$
$151$	8.24142	0.670677	0.335339	+	0.942098i	$0.391149\pi$
$152$	4.20681	0.341217
$153$	−7.95030	−0.642744
$154$	1.53669	0.123830
$155$	−4.73057	−0.379969
$156$	3.21973	0.257785
$157$	−6.11283	−0.487857	−0.243928	−	0.969793i	$-0.578436\pi$
$157$	−6.11283	−0.487857	−0.243928	+	0.969793i	$0.578436\pi$
$158$	4.00000	0.318223
$159$	3.95030	0.313279
$160$	1.00000	0.0790569
$161$	−12.1367	−0.956504
$162$	1.00000	0.0785674
$163$	−21.4373	−1.67910	−0.839549	−	0.543283i	$-0.817181\pi$
$163$	−21.4373	−1.67910	−0.839549	+	0.543283i	$0.817181\pi$
$164$	2.73057	0.213222
$165$	0.832640	0.0648210
$166$	−3.55445	−0.275879
$167$	−22.5815	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$167$	−22.5815	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$168$	1.84556	0.142388
$169$	−2.63334	−0.202565
$170$	−7.95030	−0.609760
$171$	4.20681	0.321703
$172$	−5.03945	−0.384254
$173$	−6.48916	−0.493361	−0.246681	−	0.969097i	$-0.579340\pi$
$173$	−6.48916	−0.493361	−0.246681	+	0.969097i	$0.579340\pi$
$174$	3.03945	0.230420
$175$	1.84556	0.139511
$176$	0.832640	0.0627626
$177$	−3.69113	−0.277442
$178$	−6.55029	−0.490965
$179$	16.2095	1.21155	0.605777	−	0.795635i	$-0.292862\pi$
$179$	16.2095	1.21155	0.605777	+	0.795635i	$0.292862\pi$
$180$	1.00000	0.0745356
$181$	5.38225	0.400060	0.200030	−	0.979790i	$-0.435896\pi$
$181$	5.38225	0.400060	0.200030	+	0.979790i	$0.435896\pi$
$182$	5.94222	0.440466
$183$	5.40878	0.399828
$184$	−6.57614	−0.484799
$185$	−1.00000	−0.0735215
$186$	−4.73057	−0.346862
$187$	−6.61974	−0.484083
$188$	9.11766	0.664974
$189$	1.84556	0.134245
$190$	4.20681	0.305194
$191$	−10.5680	−0.764677	−0.382339	−	0.924022i	$-0.624881\pi$
$191$	−10.5680	−0.764677	−0.382339	+	0.924022i	$0.624881\pi$
$192$	1.00000	0.0721688
$193$	3.11766	0.224414	0.112207	−	0.993685i	$-0.464208\pi$
$193$	3.11766	0.224414	0.112207	+	0.993685i	$0.464208\pi$
$194$	−10.4918	−0.753269
$195$	3.21973	0.230570
$196$	−3.59390	−0.256707
$197$	0.576137	0.0410481	0.0205240	−	0.999789i	$-0.493467\pi$
$197$	0.576137	0.0410481	0.0205240	+	0.999789i	$0.493467\pi$
$198$	0.832640	0.0591732
$199$	6.64359	0.470952	0.235476	−	0.971880i	$-0.424335\pi$
$199$	6.64359	0.470952	0.235476	+	0.971880i	$0.424335\pi$
$200$	1.00000	0.0707107
$201$	11.7959	0.832016
$202$	−3.63067	−0.255453
$203$	5.60949	0.393709
$204$	−7.95030	−0.556633
$205$	2.73057	0.190712
$206$	−9.11766	−0.635258
$207$	−6.57614	−0.457073
$208$	3.21973	0.223248
$209$	3.50276	0.242291
$210$	1.84556	0.127356
$211$	−8.83531	−0.608248	−0.304124	−	0.952632i	$-0.598364\pi$
$211$	−8.83531	−0.608248	−0.304124	+	0.952632i	$0.598364\pi$
$212$	3.95030	0.271308
$213$	−13.7700	−0.943506
$214$	8.91086	0.609134
$215$	−5.03945	−0.343687
$216$	1.00000	0.0680414
$217$	−8.73057	−0.592670
$218$	11.2979	0.765193
$219$	−3.52860	−0.238441
$220$	0.832640	0.0561366
$221$	−25.5978	−1.72190
$222$	−1.00000	−0.0671156
$223$	17.8828	1.19752	0.598762	−	0.800927i	$-0.295660\pi$
$223$	17.8828	1.19752	0.598762	+	0.800927i	$0.295660\pi$
$224$	1.84556	0.123312
$225$	1.00000	0.0666667
$226$	−11.0394	−0.734333
$227$	25.1959	1.67231	0.836155	−	0.548494i	$-0.184799\pi$
$227$	25.1959	1.67231	0.836155	+	0.548494i	$0.184799\pi$
$228$	4.20681	0.278603
$229$	−5.48699	−0.362591	−0.181295	−	0.983429i	$-0.558029\pi$
$229$	−5.48699	−0.362591	−0.181295	+	0.983429i	$0.558029\pi$
$230$	−6.57614	−0.433618
$231$	1.53669	0.101107
$232$	3.03945	0.199549
$233$	−28.5788	−1.87226	−0.936130	−	0.351654i	$-0.885619\pi$
$233$	−28.5788	−1.87226	−0.936130	+	0.351654i	$0.885619\pi$
$234$	3.21973	0.210480
$235$	9.11766	0.594771
$236$	−3.69113	−0.240272
$237$	4.00000	0.259828
$238$	−14.6728	−0.951096
$239$	1.77811	0.115016	0.0575081	−	0.998345i	$-0.481684\pi$
$239$	1.77811	0.115016	0.0575081	+	0.998345i	$0.481684\pi$
$240$	1.00000	0.0645497
$241$	22.2612	1.43397	0.716984	−	0.697090i	$-0.245522\pi$
$241$	22.2612	1.43397	0.716984	+	0.697090i	$0.245522\pi$
$242$	−10.3067	−0.662540
$243$	1.00000	0.0641500
$244$	5.40878	0.346261
$245$	−3.59390	−0.229606
$246$	2.73057	0.174095
$247$	13.5448	0.861834
$248$	−4.73057	−0.300392
$249$	−3.55445	−0.225254
$250$	1.00000	0.0632456
$251$	−28.6748	−1.80994	−0.904968	−	0.425479i	$-0.860106\pi$
$251$	−28.6748	−1.80994	−0.904968	+	0.425479i	$0.860106\pi$
$252$	1.84556	0.116260
$253$	−5.47556	−0.344245
$254$	−0.136678	−0.00857593
$255$	−7.95030	−0.497867
$256$	1.00000	0.0625000
$257$	9.19388	0.573499	0.286749	−	0.958006i	$-0.407425\pi$
$257$	9.19388	0.573499	0.286749	+	0.958006i	$0.407425\pi$
$258$	−5.03945	−0.313742
$259$	−1.84556	−0.114678
$260$	3.21973	0.199679
$261$	3.03945	0.188137
$262$	2.07889	0.128434
$263$	−8.02652	−0.494937	−0.247468	−	0.968896i	$-0.579599\pi$
$263$	−8.02652	−0.494937	−0.247468	+	0.968896i	$0.579599\pi$
$264$	0.832640	0.0512455
$265$	3.95030	0.242665
$266$	7.76393	0.476037
$267$	−6.55029	−0.400871
$268$	11.7959	0.720547
$269$	21.3849	1.30386	0.651931	−	0.758278i	$-0.273959\pi$
$269$	21.3849	1.30386	0.651931	+	0.758278i	$0.273959\pi$
$270$	1.00000	0.0608581
$271$	2.64359	0.160587	0.0802934	−	0.996771i	$-0.474414\pi$
$271$	2.64359	0.160587	0.0802934	+	0.996771i	$0.474414\pi$
$272$	−7.95030	−0.482058
$273$	5.94222	0.359639
$274$	3.06597	0.185222
$275$	0.832640	0.0502101
$276$	−6.57614	−0.395837
$277$	−14.4456	−0.867949	−0.433975	−	0.900925i	$-0.642889\pi$
$277$	−14.4456	−0.867949	−0.433975	+	0.900925i	$0.642889\pi$
$278$	22.1917	1.33097
$279$	−4.73057	−0.283212
$280$	1.84556	0.110294
$281$	−11.2197	−0.669313	−0.334656	−	0.942340i	$-0.608620\pi$
$281$	−11.2197	−0.669313	−0.334656	+	0.942340i	$0.608620\pi$
$282$	9.11766	0.542949
$283$	3.86332	0.229651	0.114825	−	0.993386i	$-0.463369\pi$
$283$	3.86332	0.229651	0.114825	+	0.993386i	$0.463369\pi$
$284$	−13.7700	−0.817100
$285$	4.20681	0.249190
$286$	2.68088	0.158524
$287$	5.03945	0.297469
$288$	1.00000	0.0589256
$289$	46.2073	2.71808
$290$	3.03945	0.178482
$291$	−10.4918	−0.615042
$292$	−3.52860	−0.206496
$293$	−16.1544	−0.943752	−0.471876	−	0.881665i	$-0.656423\pi$
$293$	−16.1544	−0.943752	−0.471876	+	0.881665i	$0.656423\pi$
$294$	−3.59390	−0.209600
$295$	−3.69113	−0.214906
$296$	−1.00000	−0.0581238
$297$	0.832640	0.0483147
$298$	−14.4999	−0.839958
$299$	−21.1734	−1.22449
$300$	1.00000	0.0577350
$301$	−9.30062	−0.536079
$302$	8.24142	0.474240
$303$	−3.63067	−0.208577
$304$	4.20681	0.241277
$305$	5.40878	0.309706
$306$	−7.95030	−0.454489
$307$	6.28303	0.358591	0.179296	−	0.983795i	$-0.442618\pi$
$307$	6.28303	0.358591	0.179296	+	0.983795i	$0.442618\pi$
$308$	1.53669	0.0875611
$309$	−9.11766	−0.518686
$310$	−4.73057	−0.268679
$311$	20.6312	1.16989	0.584943	−	0.811074i	$-0.301117\pi$
$311$	20.6312	1.16989	0.584943	+	0.811074i	$0.301117\pi$
$312$	3.21973	0.182281
$313$	−7.32180	−0.413852	−0.206926	−	0.978357i	$-0.566346\pi$
$313$	−7.32180	−0.413852	−0.206926	+	0.978357i	$0.566346\pi$
$314$	−6.11283	−0.344967
$315$	1.84556	0.103986
$316$	4.00000	0.225018
$317$	19.1442	1.07524	0.537622	−	0.843186i	$-0.319323\pi$
$317$	19.1442	1.07524	0.537622	+	0.843186i	$0.319323\pi$
$318$	3.95030	0.221522
$319$	2.53077	0.141696
$320$	1.00000	0.0559017
$321$	8.91086	0.497356
$322$	−12.1367	−0.676351
$323$	−33.4454	−1.86095
$324$	1.00000	0.0555556
$325$	3.21973	0.178598
$326$	−21.4373	−1.18730
$327$	11.2979	0.624778
$328$	2.73057	0.150771
$329$	16.8272	0.927715
$330$	0.832640	0.0458353
$331$	0.908184	0.0499183	0.0249591	−	0.999688i	$-0.492054\pi$
$331$	0.908184	0.0499183	0.0249591	+	0.999688i	$0.492054\pi$
$332$	−3.55445	−0.195076
$333$	−1.00000	−0.0547997
$334$	−22.5815	−1.23560
$335$	11.7959	0.644477
$336$	1.84556	0.100684
$337$	−8.11083	−0.441825	−0.220913	−	0.975294i	$-0.570904\pi$
$337$	−8.11083	−0.441825	−0.220913	+	0.975294i	$0.570904\pi$
$338$	−2.63334	−0.143235
$339$	−11.0394	−0.599580
$340$	−7.95030	−0.431166
$341$	−3.93887	−0.213302
$342$	4.20681	0.227478
$343$	−19.5517	−1.05569
$344$	−5.03945	−0.271709
$345$	−6.57614	−0.354047
$346$	−6.48916	−0.348859
$347$	9.35641	0.502278	0.251139	−	0.967951i	$-0.419195\pi$
$347$	9.35641	0.502278	0.251139	+	0.967951i	$0.419195\pi$
$348$	3.03945	0.162931
$349$	−35.4665	−1.89848	−0.949239	−	0.314556i	$-0.898144\pi$
$349$	−35.4665	−1.89848	−0.949239	+	0.314556i	$0.898144\pi$
$350$	1.84556	0.0986495
$351$	3.21973	0.171856
$352$	0.832640	0.0443799
$353$	−36.0923	−1.92100	−0.960500	−	0.278279i	$-0.910236\pi$
$353$	−36.0923	−1.92100	−0.960500	+	0.278279i	$0.910236\pi$
$354$	−3.69113	−0.196181
$355$	−13.7700	−0.730837
$356$	−6.55029	−0.347165
$357$	−14.6728	−0.776566
$358$	16.2095	0.856698
$359$	2.07889	0.109720	0.0548599	−	0.998494i	$-0.482529\pi$
$359$	2.07889	0.109720	0.0548599	+	0.998494i	$0.482529\pi$
$360$	1.00000	0.0527046
$361$	−1.30278	−0.0685674
$362$	5.38225	0.282885
$363$	−10.3067	−0.540962
$364$	5.94222	0.311457
$365$	−3.52860	−0.184696
$366$	5.40878	0.282721
$367$	34.2645	1.78859	0.894297	−	0.447474i	$-0.147676\pi$
$367$	34.2645	1.78859	0.894297	+	0.447474i	$0.147676\pi$
$368$	−6.57614	−0.342805
$369$	2.73057	0.142148
$370$	−1.00000	−0.0519875
$371$	7.29053	0.378506
$372$	−4.73057	−0.245269
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−6.61974	−0.342299
$375$	1.00000	0.0516398
$376$	9.11766	0.470208
$377$	9.78620	0.504015
$378$	1.84556	0.0949255
$379$	29.8217	1.53184	0.765919	−	0.642937i	$-0.222284\pi$
$379$	29.8217	1.53184	0.765919	+	0.642937i	$0.222284\pi$
$380$	4.20681	0.215805
$381$	−0.136678	−0.00700222
$382$	−10.5680	−0.540708
$383$	−6.78027	−0.346456	−0.173228	−	0.984882i	$-0.555420\pi$
$383$	−6.78027	−0.346456	−0.173228	+	0.984882i	$0.555420\pi$
$384$	1.00000	0.0510310
$385$	1.53669	0.0783170
$386$	3.11766	0.158685
$387$	−5.03945	−0.256169
$388$	−10.4918	−0.532642
$389$	35.1959	1.78450	0.892251	−	0.451540i	$-0.149125\pi$
$389$	35.1959	1.78450	0.892251	+	0.451540i	$0.149125\pi$
$390$	3.21973	0.163037
$391$	52.2823	2.64403
$392$	−3.59390	−0.181519
$393$	2.07889	0.104866
$394$	0.576137	0.0290254
$395$	4.00000	0.201262
$396$	0.832640	0.0418417
$397$	−3.56054	−0.178698	−0.0893492	−	0.996000i	$-0.528479\pi$
$397$	−3.56054	−0.178698	−0.0893492	+	0.996000i	$0.528479\pi$
$398$	6.64359	0.333013
$399$	7.76393	0.388683
$400$	1.00000	0.0500000
$401$	1.44971	0.0723950	0.0361975	−	0.999345i	$-0.488475\pi$
$401$	1.44971	0.0723950	0.0361975	+	0.999345i	$0.488475\pi$
$402$	11.7959	0.588324
$403$	−15.2312	−0.758718
$404$	−3.63067	−0.180633
$405$	1.00000	0.0496904
$406$	5.60949	0.278394
$407$	−0.832640	−0.0412724
$408$	−7.95030	−0.393599
$409$	25.1781	1.24498	0.622489	−	0.782629i	$-0.286122\pi$
$409$	25.1781	1.24498	0.622489	+	0.782629i	$0.286122\pi$
$410$	2.73057	0.134853
$411$	3.06597	0.151233
$412$	−9.11766	−0.449195
$413$	−6.81221	−0.335207
$414$	−6.57614	−0.323199
$415$	−3.55445	−0.174481
$416$	3.21973	0.157860
$417$	22.1917	1.08673
$418$	3.50276	0.171325
$419$	31.6938	1.54834	0.774172	−	0.632976i	$-0.218167\pi$
$419$	31.6938	1.54834	0.774172	+	0.632976i	$0.218167\pi$
$420$	1.84556	0.0900543
$421$	−5.14351	−0.250679	−0.125340	−	0.992114i	$-0.540002\pi$
$421$	−5.14351	−0.250679	−0.125340	+	0.992114i	$0.540002\pi$
$422$	−8.83531	−0.430096
$423$	9.11766	0.443316
$424$	3.95030	0.191844
$425$	−7.95030	−0.385646
$426$	−13.7700	−0.667160
$427$	9.98224	0.483075
$428$	8.91086	0.430723
$429$	2.68088	0.129434
$430$	−5.03945	−0.243024
$431$	2.72448	0.131234	0.0656168	−	0.997845i	$-0.479098\pi$
$431$	2.72448	0.131234	0.0656168	+	0.997845i	$0.479098\pi$
$432$	1.00000	0.0481125
$433$	−8.68088	−0.417176	−0.208588	−	0.978004i	$-0.566887\pi$
$433$	−8.68088	−0.417176	−0.208588	+	0.978004i	$0.566887\pi$
$434$	−8.73057	−0.419081
$435$	3.03945	0.145730
$436$	11.2979	0.541073
$437$	−27.6645	−1.32337
$438$	−3.52860	−0.168603
$439$	7.64752	0.364996	0.182498	−	0.983206i	$-0.441582\pi$
$439$	7.64752	0.364996	0.182498	+	0.983206i	$0.441582\pi$
$440$	0.832640	0.0396946
$441$	−3.59390	−0.171138
$442$	−25.5978	−1.21756
$443$	16.7917	0.797798	0.398899	−	0.916995i	$-0.369392\pi$
$443$	16.7917	0.797798	0.398899	+	0.916995i	$0.369392\pi$
$444$	−1.00000	−0.0474579
$445$	−6.55029	−0.310514
$446$	17.8828	0.846777
$447$	−14.4999	−0.685823
$448$	1.84556	0.0871947
$449$	26.1047	1.23196	0.615979	−	0.787762i	$-0.288760\pi$
$449$	26.1047	1.23196	0.615979	+	0.787762i	$0.288760\pi$
$450$	1.00000	0.0471405
$451$	2.27359	0.107059
$452$	−11.0394	−0.519252
$453$	8.24142	0.387216
$454$	25.1959	1.18250
$455$	5.94222	0.278575
$456$	4.20681	0.197002
$457$	−17.6646	−0.826315	−0.413158	−	0.910660i	$-0.635574\pi$
$457$	−17.6646	−0.826315	−0.413158	+	0.910660i	$0.635574\pi$
$458$	−5.48699	−0.256390
$459$	−7.95030	−0.371088
$460$	−6.57614	−0.306614
$461$	−21.2231	−0.988457	−0.494229	−	0.869332i	$-0.664549\pi$
$461$	−21.2231	−0.988457	−0.494229	+	0.869332i	$0.664549\pi$
$462$	1.53669	0.0714933
$463$	32.5530	1.51286	0.756432	−	0.654072i	$-0.226941\pi$
$463$	32.5530	1.51286	0.756432	+	0.654072i	$0.226941\pi$
$464$	3.03945	0.141103
$465$	−4.73057	−0.219375
$466$	−28.5788	−1.32389
$467$	15.1170	0.699531	0.349765	−	0.936837i	$-0.386261\pi$
$467$	15.1170	0.699531	0.349765	+	0.936837i	$0.386261\pi$
$468$	3.21973	0.148832
$469$	21.7700	1.00525
$470$	9.11766	0.420566
$471$	−6.11283	−0.281664
$472$	−3.69113	−0.169898
$473$	−4.19605	−0.192934
$474$	4.00000	0.183726
$475$	4.20681	0.193022
$476$	−14.6728	−0.672526
$477$	3.95030	0.180872
$478$	1.77811	0.0813288
$479$	3.44971	0.157621	0.0788106	−	0.996890i	$-0.474888\pi$
$479$	3.44971	0.157621	0.0788106	+	0.996890i	$0.474888\pi$
$480$	1.00000	0.0456435
$481$	−3.21973	−0.146807
$482$	22.2612	1.01397
$483$	−12.1367	−0.552238
$484$	−10.3067	−0.468487
$485$	−10.4918	−0.476409
$486$	1.00000	0.0453609
$487$	−15.6619	−0.709707	−0.354853	−	0.934922i	$-0.615469\pi$
$487$	−15.6619	−0.709707	−0.354853	+	0.934922i	$0.615469\pi$
$488$	5.40878	0.244844
$489$	−21.4373	−0.969428
$490$	−3.59390	−0.162356
$491$	7.89793	0.356429	0.178214	−	0.983992i	$-0.442968\pi$
$491$	7.89793	0.356429	0.178214	+	0.983992i	$0.442968\pi$
$492$	2.73057	0.123104
$493$	−24.1645	−1.08832
$494$	13.5448	0.609408
$495$	0.832640	0.0374244
$496$	−4.73057	−0.212409
$497$	−25.4134	−1.13995
$498$	−3.55445	−0.159279
$499$	5.87209	0.262871	0.131435	−	0.991325i	$-0.458041\pi$
$499$	5.87209	0.262871	0.131435	+	0.991325i	$0.458041\pi$
$500$	1.00000	0.0447214
$501$	−22.5815	−1.00887
$502$	−28.6748	−1.27982
$503$	3.33056	0.148502	0.0742512	−	0.997240i	$-0.476343\pi$
$503$	3.33056	0.148502	0.0742512	+	0.997240i	$0.476343\pi$
$504$	1.84556	0.0822079
$505$	−3.63067	−0.161563
$506$	−5.47556	−0.243418
$507$	−2.63334	−0.116951
$508$	−0.136678	−0.00606410
$509$	−30.9508	−1.37187	−0.685935	−	0.727663i	$-0.740607\pi$
$509$	−30.9508	−1.37187	−0.685935	+	0.727663i	$0.740607\pi$
$510$	−7.95030	−0.352045
$511$	−6.51226	−0.288085
$512$	1.00000	0.0441942
$513$	4.20681	0.185735
$514$	9.19388	0.405525
$515$	−9.11766	−0.401772
$516$	−5.03945	−0.221849
$517$	7.59173	0.333884
$518$	−1.84556	−0.0810894
$519$	−6.48916	−0.284842
$520$	3.21973	0.141194
$521$	7.45306	0.326524	0.163262	−	0.986583i	$-0.447798\pi$
$521$	7.45306	0.326524	0.163262	+	0.986583i	$0.447798\pi$
$522$	3.03945	0.133033
$523$	31.5917	1.38141	0.690705	−	0.723137i	$-0.257300\pi$
$523$	31.5917	1.38141	0.690705	+	0.723137i	$0.257300\pi$
$524$	2.07889	0.0908169
$525$	1.84556	0.0805470
$526$	−8.02652	−0.349973
$527$	37.6095	1.63830
$528$	0.832640	0.0362360
$529$	20.2456	0.880242
$530$	3.95030	0.171590
$531$	−3.69113	−0.160181
$532$	7.76393	0.336609
$533$	8.79171	0.380811
$534$	−6.55029	−0.283459
$535$	8.91086	0.385250
$536$	11.7959	0.509504
$537$	16.2095	0.699491
$538$	21.3849	0.921970
$539$	−2.99242	−0.128893
$540$	1.00000	0.0430331
$541$	36.0816	1.55127	0.775634	−	0.631183i	$-0.217430\pi$
$541$	36.0816	1.55127	0.775634	+	0.631183i	$0.217430\pi$
$542$	2.64359	0.113552
$543$	5.38225	0.230975
$544$	−7.95030	−0.340866
$545$	11.2979	0.483951
$546$	5.94222	0.254303
$547$	−38.7420	−1.65649	−0.828244	−	0.560367i	$-0.810660\pi$
$547$	−38.7420	−1.65649	−0.828244	+	0.560367i	$0.810660\pi$
$548$	3.06597	0.130972
$549$	5.40878	0.230841
$550$	0.832640	0.0355039
$551$	12.7864	0.544717
$552$	−6.57614	−0.279899
$553$	7.38225	0.313925
$554$	−14.4456	−0.613733
$555$	−1.00000	−0.0424476
$556$	22.1917	0.941139
$557$	−23.3618	−0.989869	−0.494935	−	0.868930i	$-0.664808\pi$
$557$	−23.3618	−0.989869	−0.494935	+	0.868930i	$0.664808\pi$
$558$	−4.73057	−0.200261
$559$	−16.2257	−0.686272
$560$	1.84556	0.0779893
$561$	−6.61974	−0.279486
$562$	−11.2197	−0.473276
$563$	39.0351	1.64513	0.822567	−	0.568668i	$-0.192541\pi$
$563$	39.0351	1.64513	0.822567	+	0.568668i	$0.192541\pi$
$564$	9.11766	0.383923
$565$	−11.0394	−0.464433
$566$	3.86332	0.162388
$567$	1.84556	0.0775064
$568$	−13.7700	−0.577777
$569$	35.4809	1.48744	0.743718	−	0.668493i	$-0.233060\pi$
$569$	35.4809	1.48744	0.743718	+	0.668493i	$0.233060\pi$
$570$	4.20681	0.176204
$571$	37.0093	1.54879	0.774395	−	0.632702i	$-0.218054\pi$
$571$	37.0093	1.54879	0.774395	+	0.632702i	$0.218054\pi$
$572$	2.68088	0.112093
$573$	−10.5680	−0.441487
$574$	5.03945	0.210342
$575$	−6.57614	−0.274244
$576$	1.00000	0.0416667
$577$	−15.7354	−0.655074	−0.327537	−	0.944838i	$-0.606219\pi$
$577$	−15.7354	−0.655074	−0.327537	+	0.944838i	$0.606219\pi$
$578$	46.2073	1.92197
$579$	3.11766	0.129566
$580$	3.03945	0.126206
$581$	−6.55996	−0.272153
$582$	−10.4918	−0.434900
$583$	3.28918	0.136224
$584$	−3.52860	−0.146015
$585$	3.21973	0.133119
$586$	−16.1544	−0.667334
$587$	37.3006	1.53956	0.769781	−	0.638309i	$-0.220366\pi$
$587$	37.3006	1.53956	0.769781	+	0.638309i	$0.220366\pi$
$588$	−3.59390	−0.148210
$589$	−19.9006	−0.819990
$590$	−3.69113	−0.151961
$591$	0.576137	0.0236991
$592$	−1.00000	−0.0410997
$593$	−17.9829	−0.738470	−0.369235	−	0.929336i	$-0.620380\pi$
$593$	−17.9829	−0.738470	−0.369235	+	0.929336i	$0.620380\pi$
$594$	0.832640	0.0341636
$595$	−14.6728	−0.601526
$596$	−14.4999	−0.593940
$597$	6.64359	0.271904
$598$	−21.1734	−0.865844
$599$	−32.9998	−1.34834	−0.674168	−	0.738578i	$-0.735498\pi$
$599$	−32.9998	−1.34834	−0.674168	+	0.738578i	$0.735498\pi$
$600$	1.00000	0.0408248
$601$	33.0334	1.34746	0.673729	−	0.738978i	$-0.264691\pi$
$601$	33.0334	1.34746	0.673729	+	0.738978i	$0.264691\pi$
$602$	−9.30062	−0.379065
$603$	11.7959	0.480365
$604$	8.24142	0.335339
$605$	−10.3067	−0.419027
$606$	−3.63067	−0.147486
$607$	27.6102	1.12066	0.560331	−	0.828269i	$-0.310674\pi$
$607$	27.6102	1.12066	0.560331	+	0.828269i	$0.310674\pi$
$608$	4.20681	0.170609
$609$	5.60949	0.227308
$610$	5.40878	0.218995
$611$	29.3564	1.18763
$612$	−7.95030	−0.321372
$613$	1.62999	0.0658348	0.0329174	−	0.999458i	$-0.489520\pi$
$613$	1.62999	0.0658348	0.0329174	+	0.999458i	$0.489520\pi$
$614$	6.28303	0.253562
$615$	2.73057	0.110107
$616$	1.53669	0.0619150
$617$	28.6143	1.15197	0.575985	−	0.817460i	$-0.304619\pi$
$617$	28.6143	1.15197	0.575985	+	0.817460i	$0.304619\pi$
$618$	−9.11766	−0.366766
$619$	19.6830	0.791128	0.395564	−	0.918438i	$-0.370549\pi$
$619$	19.6830	0.791128	0.395564	+	0.918438i	$0.370549\pi$
$620$	−4.73057	−0.189984
$621$	−6.57614	−0.263891
$622$	20.6312	0.827235
$623$	−12.0890	−0.484335
$624$	3.21973	0.128892
$625$	1.00000	0.0400000
$626$	−7.32180	−0.292638
$627$	3.50276	0.139887
$628$	−6.11283	−0.243928
$629$	7.95030	0.316999
$630$	1.84556	0.0735290
$631$	−5.76193	−0.229379	−0.114689	−	0.993401i	$-0.536587\pi$
$631$	−5.76193	−0.229379	−0.114689	+	0.993401i	$0.536587\pi$
$632$	4.00000	0.159111
$633$	−8.83531	−0.351172
$634$	19.1442	0.760313
$635$	−0.136678	−0.00542390
$636$	3.95030	0.156640
$637$	−11.5714	−0.458474
$638$	2.53077	0.100194
$639$	−13.7700	−0.544734
$640$	1.00000	0.0395285
$641$	20.8967	0.825369	0.412685	−	0.910874i	$-0.364591\pi$
$641$	20.8967	0.825369	0.412685	+	0.910874i	$0.364591\pi$
$642$	8.91086	0.351683
$643$	30.6197	1.20752	0.603762	−	0.797164i	$-0.293668\pi$
$643$	30.6197	1.20752	0.603762	+	0.797164i	$0.293668\pi$
$644$	−12.1367	−0.478252
$645$	−5.03945	−0.198428
$646$	−33.4454	−1.31589
$647$	−10.6278	−0.417823	−0.208912	−	0.977935i	$-0.566992\pi$
$647$	−10.6278	−0.417823	−0.208912	+	0.977935i	$0.566992\pi$
$648$	1.00000	0.0392837
$649$	−3.07338	−0.120641
$650$	3.21973	0.126288
$651$	−8.73057	−0.342178
$652$	−21.4373	−0.839549
$653$	−5.90061	−0.230909	−0.115454	−	0.993313i	$-0.536832\pi$
$653$	−5.90061	−0.230909	−0.115454	+	0.993313i	$0.536832\pi$
$654$	11.2979	0.441785
$655$	2.07889	0.0812291
$656$	2.73057	0.106611
$657$	−3.52860	−0.137664
$658$	16.8272	0.655994
$659$	19.8305	0.772486	0.386243	−	0.922397i	$-0.373773\pi$
$659$	19.8305	0.772486	0.386243	+	0.922397i	$0.373773\pi$
$660$	0.832640	0.0324105
$661$	−9.32379	−0.362653	−0.181327	−	0.983423i	$-0.558039\pi$
$661$	−9.32379	−0.362653	−0.181327	+	0.983423i	$0.558039\pi$
$662$	0.908184	0.0352976
$663$	−25.5978	−0.994137
$664$	−3.55445	−0.137939
$665$	7.76393	0.301072
$666$	−1.00000	−0.0387492
$667$	−19.9878	−0.773931
$668$	−22.5815	−0.873704
$669$	17.8828	0.691391
$670$	11.7959	0.455714
$671$	4.50357	0.173858
$672$	1.84556	0.0711942
$673$	33.0113	1.27249	0.636245	−	0.771487i	$-0.280487\pi$
$673$	33.0113	1.27249	0.636245	+	0.771487i	$0.280487\pi$
$674$	−8.11083	−0.312418
$675$	1.00000	0.0384900
$676$	−2.63334	−0.101282
$677$	26.1245	1.00405	0.502023	−	0.864854i	$-0.332589\pi$
$677$	26.1245	1.00405	0.502023	+	0.864854i	$0.332589\pi$
$678$	−11.0394	−0.423967
$679$	−19.3633	−0.743097
$680$	−7.95030	−0.304880
$681$	25.1959	0.965508
$682$	−3.93887	−0.150827
$683$	−39.3957	−1.50743	−0.753717	−	0.657199i	$-0.771741\pi$
$683$	−39.3957	−1.50743	−0.753717	+	0.657199i	$0.771741\pi$
$684$	4.20681	0.160851
$685$	3.06597	0.117145
$686$	−19.5517	−0.746488
$687$	−5.48699	−0.209342
$688$	−5.03945	−0.192127
$689$	12.7189	0.484552
$690$	−6.57614	−0.250349
$691$	−9.45306	−0.359611	−0.179806	−	0.983702i	$-0.557547\pi$
$691$	−9.45306	−0.359611	−0.179806	+	0.983702i	$0.557547\pi$
$692$	−6.48916	−0.246681
$693$	1.53669	0.0583740
$694$	9.35641	0.355164
$695$	22.1917	0.841780
$696$	3.03945	0.115210
$697$	−21.7089	−0.822283
$698$	−35.4665	−1.34243
$699$	−28.5788	−1.08095
$700$	1.84556	0.0697557
$701$	37.2842	1.40821	0.704103	−	0.710098i	$-0.251349\pi$
$701$	37.2842	1.40821	0.704103	+	0.710098i	$0.251349\pi$
$702$	3.21973	0.121521
$703$	−4.20681	−0.158663
$704$	0.832640	0.0313813
$705$	9.11766	0.343391
$706$	−36.0923	−1.35835
$707$	−6.70063	−0.252003
$708$	−3.69113	−0.138721
$709$	−19.8110	−0.744016	−0.372008	−	0.928230i	$-0.621331\pi$
$709$	−19.8110	−0.744016	−0.372008	+	0.928230i	$0.621331\pi$
$710$	−13.7700	−0.516780
$711$	4.00000	0.150012
$712$	−6.55029	−0.245483
$713$	31.1089	1.16504
$714$	−14.6728	−0.549115
$715$	2.68088	0.100259
$716$	16.2095	0.605777
$717$	1.77811	0.0664046
$718$	2.07889	0.0775836
$719$	−19.2136	−0.716548	−0.358274	−	0.933617i	$-0.616635\pi$
$719$	−19.2136	−0.716548	−0.358274	+	0.933617i	$0.616635\pi$
$720$	1.00000	0.0372678
$721$	−16.8272	−0.626679
$722$	−1.30278	−0.0484845
$723$	22.2612	0.827902
$724$	5.38225	0.200030
$725$	3.03945	0.112882
$726$	−10.3067	−0.382518
$727$	−45.0183	−1.66964	−0.834818	−	0.550527i	$-0.814427\pi$
$727$	−45.0183	−1.66964	−0.834818	+	0.550527i	$0.814427\pi$
$728$	5.94222	0.220233
$729$	1.00000	0.0370370
$730$	−3.52860	−0.130599
$731$	40.0651	1.48186
$732$	5.40878	0.199914
$733$	−20.7262	−0.765541	−0.382771	−	0.923843i	$-0.625030\pi$
$733$	−20.7262	−0.765541	−0.382771	+	0.923843i	$0.625030\pi$
$734$	34.2645	1.26473
$735$	−3.59390	−0.132563
$736$	−6.57614	−0.242400
$737$	9.82171	0.361787
$738$	2.73057	0.100514
$739$	24.2176	0.890858	0.445429	−	0.895317i	$-0.353051\pi$
$739$	24.2176	0.890858	0.445429	+	0.895317i	$0.353051\pi$
$740$	−1.00000	−0.0367607
$741$	13.5448	0.497580
$742$	7.29053	0.267644
$743$	13.9530	0.511885	0.255943	−	0.966692i	$-0.417614\pi$
$743$	13.9530	0.511885	0.255943	+	0.966692i	$0.417614\pi$
$744$	−4.73057	−0.173431
$745$	−14.4999	−0.531236
$746$	−6.00000	−0.219676
$747$	−3.55445	−0.130050
$748$	−6.61974	−0.242042
$749$	16.4456	0.600907
$750$	1.00000	0.0365148
$751$	41.6176	1.51865	0.759324	−	0.650713i	$-0.225530\pi$
$751$	41.6176	1.51865	0.759324	+	0.650713i	$0.225530\pi$
$752$	9.11766	0.332487
$753$	−28.6748	−1.04497
$754$	9.78620	0.356392
$755$	8.24142	0.299936
$756$	1.84556	0.0671225
$757$	−45.4034	−1.65021	−0.825107	−	0.564977i	$-0.808885\pi$
$757$	−45.4034	−1.65021	−0.825107	+	0.564977i	$0.808885\pi$
$758$	29.8217	1.08317
$759$	−5.47556	−0.198750
$760$	4.20681	0.152597
$761$	18.9347	0.686383	0.343191	−	0.939266i	$-0.388492\pi$
$761$	18.9347	0.686383	0.343191	+	0.939266i	$0.388492\pi$
$762$	−0.136678	−0.00495132
$763$	20.8511	0.754860
$764$	−10.5680	−0.382339
$765$	−7.95030	−0.287444
$766$	−6.78027	−0.244981
$767$	−11.8844	−0.429122
$768$	1.00000	0.0360844
$769$	31.0884	1.12108	0.560538	−	0.828129i	$-0.310594\pi$
$769$	31.0884	1.12108	0.560538	+	0.828129i	$0.310594\pi$
$770$	1.53669	0.0553785
$771$	9.19388	0.331110
$772$	3.11766	0.112207
$773$	34.3542	1.23564	0.617818	−	0.786321i	$-0.288017\pi$
$773$	34.3542	1.23564	0.617818	+	0.786321i	$0.288017\pi$
$774$	−5.03945	−0.181139
$775$	−4.73057	−0.169927
$776$	−10.4918	−0.376635
$777$	−1.84556	−0.0662092
$778$	35.1959	1.26183
$779$	11.4870	0.411564
$780$	3.21973	0.115285
$781$	−11.4655	−0.410267
$782$	52.2823	1.86961
$783$	3.03945	0.108621
$784$	−3.59390	−0.128353
$785$	−6.11283	−0.218176
$786$	2.07889	0.0741517
$787$	36.0053	1.28345	0.641726	−	0.766934i	$-0.278219\pi$
$787$	36.0053	1.28345	0.641726	+	0.766934i	$0.278219\pi$
$788$	0.576137	0.0205240
$789$	−8.02652	−0.285752
$790$	4.00000	0.142314
$791$	−20.3740	−0.724416
$792$	0.832640	0.0295866
$793$	17.4148	0.618418
$794$	−3.56054	−0.126359
$795$	3.95030	0.140103
$796$	6.64359	0.235476
$797$	43.2107	1.53060	0.765300	−	0.643674i	$-0.222591\pi$
$797$	43.2107	1.53060	0.765300	+	0.643674i	$0.222591\pi$
$798$	7.76393	0.274840
$799$	−72.4882	−2.56445
$800$	1.00000	0.0353553
$801$	−6.55029	−0.231443
$802$	1.44971	0.0511910
$803$	−2.93806	−0.103682
$804$	11.7959	0.416008
$805$	−12.1367	−0.427762
$806$	−15.2312	−0.536495
$807$	21.3849	0.752785
$808$	−3.63067	−0.127727
$809$	−32.2209	−1.13283	−0.566414	−	0.824121i	$-0.691669\pi$
$809$	−32.2209	−1.13283	−0.566414	+	0.824121i	$0.691669\pi$
$810$	1.00000	0.0351364
$811$	8.87892	0.311781	0.155890	−	0.987774i	$-0.450175\pi$
$811$	8.87892	0.311781	0.155890	+	0.987774i	$0.450175\pi$
$812$	5.60949	0.196855
$813$	2.64359	0.0927148
$814$	−0.832640	−0.0291840
$815$	−21.4373	−0.750916
$816$	−7.95030	−0.278316
$817$	−21.2000	−0.741693
$818$	25.1781	0.880332
$819$	5.94222	0.207638
$820$	2.73057	0.0953558
$821$	2.31155	0.0806735	0.0403368	−	0.999186i	$-0.487157\pi$
$821$	2.31155	0.0806735	0.0403368	+	0.999186i	$0.487157\pi$
$822$	3.06597	0.106938
$823$	13.6280	0.475042	0.237521	−	0.971382i	$-0.423665\pi$
$823$	13.6280	0.475042	0.237521	+	0.971382i	$0.423665\pi$
$824$	−9.11766	−0.317629
$825$	0.832640	0.0289888
$826$	−6.81221	−0.237027
$827$	−17.8298	−0.620003	−0.310001	−	0.950736i	$-0.600330\pi$
$827$	−17.8298	−0.620003	−0.310001	+	0.950736i	$0.600330\pi$
$828$	−6.57614	−0.228537
$829$	−29.7388	−1.03287	−0.516435	−	0.856326i	$-0.672741\pi$
$829$	−29.7388	−1.03287	−0.516435	+	0.856326i	$0.672741\pi$
$830$	−3.55445	−0.123377
$831$	−14.4456	−0.501111
$832$	3.21973	0.111624
$833$	28.5726	0.989980
$834$	22.1917	0.768436
$835$	−22.5815	−0.781464
$836$	3.50276	0.121145
$837$	−4.73057	−0.163513
$838$	31.6938	1.09484
$839$	−10.4556	−0.360969	−0.180484	−	0.983578i	$-0.557766\pi$
$839$	−10.4556	−0.360969	−0.180484	+	0.983578i	$0.557766\pi$
$840$	1.84556	0.0636780
$841$	−19.7618	−0.681440
$842$	−5.14351	−0.177257
$843$	−11.2197	−0.386428
$844$	−8.83531	−0.304124
$845$	−2.63334	−0.0905897
$846$	9.11766	0.313472
$847$	−19.0217	−0.653593
$848$	3.95030	0.135654
$849$	3.86332	0.132589
$850$	−7.95030	−0.272693
$851$	6.57614	0.225427
$852$	−13.7700	−0.471753
$853$	−15.6333	−0.535275	−0.267638	−	0.963520i	$-0.586243\pi$
$853$	−15.6333	−0.535275	−0.267638	+	0.963520i	$0.586243\pi$
$854$	9.98224	0.341585
$855$	4.20681	0.143870
$856$	8.91086	0.304567
$857$	−14.4945	−0.495123	−0.247561	−	0.968872i	$-0.579629\pi$
$857$	−14.4945	−0.495123	−0.247561	+	0.968872i	$0.579629\pi$
$858$	2.68088	0.0915236
$859$	3.38493	0.115492	0.0577461	−	0.998331i	$-0.481609\pi$
$859$	3.38493	0.115492	0.0577461	+	0.998331i	$0.481609\pi$
$860$	−5.03945	−0.171844
$861$	5.03945	0.171744
$862$	2.72448	0.0927962
$863$	−56.3924	−1.91962	−0.959810	−	0.280649i	$-0.909450\pi$
$863$	−56.3924	−1.91962	−0.959810	+	0.280649i	$0.909450\pi$
$864$	1.00000	0.0340207
$865$	−6.48916	−0.220638
$866$	−8.68088	−0.294988
$867$	46.2073	1.56928
$868$	−8.73057	−0.296335
$869$	3.33056	0.112982
$870$	3.03945	0.103047
$871$	37.9795	1.28689
$872$	11.2979	0.382597
$873$	−10.4918	−0.355095
$874$	−27.6645	−0.935767
$875$	1.84556	0.0623914
$876$	−3.52860	−0.119220
$877$	−32.1755	−1.08649	−0.543245	−	0.839574i	$-0.682805\pi$
$877$	−32.1755	−1.08649	−0.543245	+	0.839574i	$0.682805\pi$
$878$	7.64752	0.258091
$879$	−16.1544	−0.544876
$880$	0.832640	0.0280683
$881$	14.6097	0.492212	0.246106	−	0.969243i	$-0.420849\pi$
$881$	14.6097	0.492212	0.246106	+	0.969243i	$0.420849\pi$
$882$	−3.59390	−0.121013
$883$	18.5203	0.623259	0.311630	−	0.950204i	$-0.399125\pi$
$883$	18.5203	0.623259	0.311630	+	0.950204i	$0.399125\pi$
$884$	−25.5978	−0.860948
$885$	−3.69113	−0.124076
$886$	16.7917	0.564128
$887$	−28.5611	−0.958986	−0.479493	−	0.877546i	$-0.659179\pi$
$887$	−28.5611	−0.958986	−0.479493	+	0.877546i	$0.659179\pi$
$888$	−1.00000	−0.0335578
$889$	−0.252248	−0.00846012
$890$	−6.55029	−0.219566
$891$	0.832640	0.0278945
$892$	17.8828	0.598762
$893$	38.3562	1.28354
$894$	−14.4999	−0.484950
$895$	16.2095	0.541823
$896$	1.84556	0.0616559
$897$	−21.1734	−0.706959
$898$	26.1047	0.871126
$899$	−14.3783	−0.479544
$900$	1.00000	0.0333333
$901$	−31.4061	−1.04629
$902$	2.27359	0.0757021
$903$	−9.30062	−0.309505
$904$	−11.0394	−0.367167
$905$	5.38225	0.178912
$906$	8.24142	0.273803
$907$	−25.8428	−0.858097	−0.429048	−	0.903282i	$-0.641151\pi$
$907$	−25.8428	−0.858097	−0.429048	+	0.903282i	$0.641151\pi$
$908$	25.1959	0.836155
$909$	−3.63067	−0.120422
$910$	5.94222	0.196983
$911$	24.9998	0.828281	0.414141	−	0.910213i	$-0.364082\pi$
$911$	24.9998	0.828281	0.414141	+	0.910213i	$0.364082\pi$
$912$	4.20681	0.139301
$913$	−2.95958	−0.0979477
$914$	−17.6646	−0.584293
$915$	5.40878	0.178809
$916$	−5.48699	−0.181295
$917$	3.83673	0.126700
$918$	−7.95030	−0.262399
$919$	−34.3931	−1.13452	−0.567262	−	0.823537i	$-0.691997\pi$
$919$	−34.3931	−1.13452	−0.567262	+	0.823537i	$0.691997\pi$
$920$	−6.57614	−0.216809
$921$	6.28303	0.207033
$922$	−21.2231	−0.698945
$923$	−44.3357	−1.45933
$924$	1.53669	0.0505534
$925$	−1.00000	−0.0328798
$926$	32.5530	1.06976
$927$	−9.11766	−0.299463
$928$	3.03945	0.0997747
$929$	55.6310	1.82519	0.912597	−	0.408860i	$-0.134074\pi$
$929$	55.6310	1.82519	0.912597	+	0.408860i	$0.134074\pi$
$930$	−4.73057	−0.155122
$931$	−15.1188	−0.495499
$932$	−28.5788	−0.936130
$933$	20.6312	0.675434
$934$	15.1170	0.494643
$935$	−6.61974	−0.216489
$936$	3.21973	0.105240
$937$	−53.9576	−1.76272	−0.881360	−	0.472446i	$-0.843371\pi$
$937$	−53.9576	−1.76272	−0.881360	+	0.472446i	$0.843371\pi$
$938$	21.7700	0.710816
$939$	−7.32180	−0.238938
$940$	9.11766	0.297385
$941$	−50.1092	−1.63351	−0.816756	−	0.576983i	$-0.804230\pi$
$941$	−50.1092	−1.63351	−0.816756	+	0.576983i	$0.804230\pi$
$942$	−6.11283	−0.199167
$943$	−17.9566	−0.584748
$944$	−3.69113	−0.120136
$945$	1.84556	0.0600362
$946$	−4.19605	−0.136425
$947$	39.3795	1.27966	0.639831	−	0.768516i	$-0.279004\pi$
$947$	39.3795	1.27966	0.639831	+	0.768516i	$0.279004\pi$
$948$	4.00000	0.129914
$949$	−11.3611	−0.368798
$950$	4.20681	0.136487
$951$	19.1442	0.620793
$952$	−14.6728	−0.475548
$953$	−20.5096	−0.664371	−0.332185	−	0.943214i	$-0.607786\pi$
$953$	−20.5096	−0.664371	−0.332185	+	0.943214i	$0.607786\pi$
$954$	3.95030	0.127896
$955$	−10.5680	−0.341974
$956$	1.77811	0.0575081
$957$	2.53077	0.0818080
$958$	3.44971	0.111455
$959$	5.65844	0.182721
$960$	1.00000	0.0322749
$961$	−8.62168	−0.278119
$962$	−3.21973	−0.103808
$963$	8.91086	0.287148
$964$	22.2612	0.716984
$965$	3.11766	0.100361
$966$	−12.1367	−0.390491
$967$	18.6265	0.598988	0.299494	−	0.954098i	$-0.403182\pi$
$967$	18.6265	0.598988	0.299494	+	0.954098i	$0.403182\pi$
$968$	−10.3067	−0.331270
$969$	−33.4454	−1.07442
$970$	−10.4918	−0.336872
$971$	−3.56656	−0.114456	−0.0572282	−	0.998361i	$-0.518226\pi$
$971$	−3.56656	−0.114456	−0.0572282	+	0.998361i	$0.518226\pi$
$972$	1.00000	0.0320750
$973$	40.9562	1.31300
$974$	−15.6619	−0.501838
$975$	3.21973	0.103114
$976$	5.40878	0.173131
$977$	−43.6998	−1.39808	−0.699041	−	0.715082i	$-0.746389\pi$
$977$	−43.6998	−1.39808	−0.699041	+	0.715082i	$0.746389\pi$
$978$	−21.4373	−0.685489
$979$	−5.45404	−0.174312
$980$	−3.59390	−0.114803
$981$	11.2979	0.360716
$982$	7.89793	0.252033
$983$	53.1096	1.69393	0.846966	−	0.531647i	$-0.178427\pi$
$983$	53.1096	1.69393	0.846966	+	0.531647i	$0.178427\pi$
$984$	2.73057	0.0870475
$985$	0.576137	0.0183572
$986$	−24.1645	−0.769555
$987$	16.8272	0.535616
$988$	13.5448	0.430917
$989$	33.1401	1.05379
$990$	0.832640	0.0264630
$991$	−9.14283	−0.290432	−0.145216	−	0.989400i	$-0.546388\pi$
$991$	−9.14283	−0.290432	−0.145216	+	0.989400i	$0.546388\pi$
$992$	−4.73057	−0.150196
$993$	0.908184	0.0288203
$994$	−25.4134	−0.806066
$995$	6.64359	0.210616
$996$	−3.55445	−0.112627
$997$	−15.6280	−0.494944	−0.247472	−	0.968895i	$-0.579600\pi$
$997$	−15.6280	−0.494944	−0.247472	+	0.968895i	$0.579600\pi$
$998$	5.87209	0.185878
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.a.s.1.3	✓	4
3.2	odd	2		3330.2.a.bj.1.3		4
4.3	odd	2		8880.2.a.cg.1.2		4
5.4	even	2		5550.2.a.cj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.s.1.3	✓	4	1.1	even	1	trivial
3330.2.a.bj.1.3		4	3.2	odd	2
5550.2.a.cj.1.2		4	5.4	even	2
8880.2.a.cg.1.2		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.832640 q^{11} +1.00000 q^{12} +3.21973 q^{13} +1.84556 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.95030 q^{17} +1.00000 q^{18} +4.20681 q^{19} +1.00000 q^{20} +1.84556 q^{21} +0.832640 q^{22} -6.57614 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.21973 q^{26} +1.00000 q^{27} +1.84556 q^{28} +3.03945 q^{29} +1.00000 q^{30} -4.73057 q^{31} +1.00000 q^{32} +0.832640 q^{33} -7.95030 q^{34} +1.84556 q^{35} +1.00000 q^{36} -1.00000 q^{37} +4.20681 q^{38} +3.21973 q^{39} +1.00000 q^{40} +2.73057 q^{41} +1.84556 q^{42} -5.03945 q^{43} +0.832640 q^{44} +1.00000 q^{45} -6.57614 q^{46} +9.11766 q^{47} +1.00000 q^{48} -3.59390 q^{49} +1.00000 q^{50} -7.95030 q^{51} +3.21973 q^{52} +3.95030 q^{53} +1.00000 q^{54} +0.832640 q^{55} +1.84556 q^{56} +4.20681 q^{57} +3.03945 q^{58} -3.69113 q^{59} +1.00000 q^{60} +5.40878 q^{61} -4.73057 q^{62} +1.84556 q^{63} +1.00000 q^{64} +3.21973 q^{65} +0.832640 q^{66} +11.7959 q^{67} -7.95030 q^{68} -6.57614 q^{69} +1.84556 q^{70} -13.7700 q^{71} +1.00000 q^{72} -3.52860 q^{73} -1.00000 q^{74} +1.00000 q^{75} +4.20681 q^{76} +1.53669 q^{77} +3.21973 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.73057 q^{82} -3.55445 q^{83} +1.84556 q^{84} -7.95030 q^{85} -5.03945 q^{86} +3.03945 q^{87} +0.832640 q^{88} -6.55029 q^{89} +1.00000 q^{90} +5.94222 q^{91} -6.57614 q^{92} -4.73057 q^{93} +9.11766 q^{94} +4.20681 q^{95} +1.00000 q^{96} -10.4918 q^{97} -3.59390 q^{98} +0.832640 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} + 3 q^{19} + 4 q^{20} + 4 q^{21} + 2 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} + 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} + 3 q^{31} + 4 q^{32} + 2 q^{33} + 6 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 3 q^{38} - 3 q^{39} + 4 q^{40} - 11 q^{41} + 4 q^{42} - 5 q^{43} + 2 q^{44} + 4 q^{45} - q^{46} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 6 q^{51} - 3 q^{52} - 22 q^{53} + 4 q^{54} + 2 q^{55} + 4 q^{56} + 3 q^{57} - 3 q^{58} - 8 q^{59} + 4 q^{60} - 5 q^{61} + 3 q^{62} + 4 q^{63} + 4 q^{64} - 3 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - q^{69} + 4 q^{70} - 18 q^{71} + 4 q^{72} - 5 q^{73} - 4 q^{74} + 4 q^{75} + 3 q^{76} - 4 q^{77} - 3 q^{78} + 16 q^{79} + 4 q^{80} + 4 q^{81} - 11 q^{82} - q^{83} + 4 q^{84} + 6 q^{85} - 5 q^{86} - 3 q^{87} + 2 q^{88} - 5 q^{89} + 4 q^{90} - 13 q^{91} - q^{92} + 3 q^{93} + 3 q^{95} + 4 q^{96} + 7 q^{97} + 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 + 3 * q^19 + 4 * q^20 + 4 * q^21 + 2 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 + 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 + 3 * q^31 + 4 * q^32 + 2 * q^33 + 6 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 3 * q^38 - 3 * q^39 + 4 * q^40 - 11 * q^41 + 4 * q^42 - 5 * q^43 + 2 * q^44 + 4 * q^45 - q^46 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 6 * q^51 - 3 * q^52 - 22 * q^53 + 4 * q^54 + 2 * q^55 + 4 * q^56 + 3 * q^57 - 3 * q^58 - 8 * q^59 + 4 * q^60 - 5 * q^61 + 3 * q^62 + 4 * q^63 + 4 * q^64 - 3 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - q^69 + 4 * q^70 - 18 * q^71 + 4 * q^72 - 5 * q^73 - 4 * q^74 + 4 * q^75 + 3 * q^76 - 4 * q^77 - 3 * q^78 + 16 * q^79 + 4 * q^80 + 4 * q^81 - 11 * q^82 - q^83 + 4 * q^84 + 6 * q^85 - 5 * q^86 - 3 * q^87 + 2 * q^88 - 5 * q^89 + 4 * q^90 - 13 * q^91 - q^92 + 3 * q^93 + 3 * q^95 + 4 * q^96 + 7 * q^97 + 14 * q^98 + 2 * q^99

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