LMFDB - Embedded newform 1334.2.a.k.1.10

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.27355$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.27355 q^{3} +1.00000 q^{4} -3.29757 q^{5} +3.27355 q^{6} +1.59623 q^{7} +1.00000 q^{8} +7.71610 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.27355 q^{3} +1.00000 q^{4} -3.29757 q^{5} +3.27355 q^{6} +1.59623 q^{7} +1.00000 q^{8} +7.71610 q^{9} -3.29757 q^{10} -0.552280 q^{11} +3.27355 q^{12} +4.95703 q^{13} +1.59623 q^{14} -10.7948 q^{15} +1.00000 q^{16} -6.15426 q^{17} +7.71610 q^{18} +3.34715 q^{19} -3.29757 q^{20} +5.22533 q^{21} -0.552280 q^{22} +1.00000 q^{23} +3.27355 q^{24} +5.87400 q^{25} +4.95703 q^{26} +15.4384 q^{27} +1.59623 q^{28} +1.00000 q^{29} -10.7948 q^{30} -7.43456 q^{31} +1.00000 q^{32} -1.80791 q^{33} -6.15426 q^{34} -5.26368 q^{35} +7.71610 q^{36} -1.25503 q^{37} +3.34715 q^{38} +16.2271 q^{39} -3.29757 q^{40} -8.64391 q^{41} +5.22533 q^{42} +9.52529 q^{43} -0.552280 q^{44} -25.4444 q^{45} +1.00000 q^{46} -0.00901703 q^{47} +3.27355 q^{48} -4.45205 q^{49} +5.87400 q^{50} -20.1462 q^{51} +4.95703 q^{52} -0.871657 q^{53} +15.4384 q^{54} +1.82118 q^{55} +1.59623 q^{56} +10.9570 q^{57} +1.00000 q^{58} +5.17777 q^{59} -10.7948 q^{60} -3.51216 q^{61} -7.43456 q^{62} +12.3167 q^{63} +1.00000 q^{64} -16.3462 q^{65} -1.80791 q^{66} +3.01199 q^{67} -6.15426 q^{68} +3.27355 q^{69} -5.26368 q^{70} -11.6173 q^{71} +7.71610 q^{72} +16.3319 q^{73} -1.25503 q^{74} +19.2288 q^{75} +3.34715 q^{76} -0.881566 q^{77} +16.2271 q^{78} -15.3275 q^{79} -3.29757 q^{80} +27.3899 q^{81} -8.64391 q^{82} +3.61068 q^{83} +5.22533 q^{84} +20.2941 q^{85} +9.52529 q^{86} +3.27355 q^{87} -0.552280 q^{88} +12.8119 q^{89} -25.4444 q^{90} +7.91256 q^{91} +1.00000 q^{92} -24.3374 q^{93} -0.00901703 q^{94} -11.0375 q^{95} +3.27355 q^{96} +3.40031 q^{97} -4.45205 q^{98} -4.26145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.27355	1.88998	0.944991	−	0.327096i	$-0.106070\pi$
$3$	3.27355	1.88998	0.944991	+	0.327096i	$0.106070\pi$
$4$	1.00000	0.500000
$5$	−3.29757	−1.47472	−0.737360	−	0.675500i	$-0.763928\pi$
$5$	−3.29757	−1.47472	−0.737360	+	0.675500i	$0.763928\pi$
$6$	3.27355	1.33642
$7$	1.59623	0.603318	0.301659	−	0.953416i	$-0.402460\pi$
$7$	1.59623	0.603318	0.301659	+	0.953416i	$0.402460\pi$
$8$	1.00000	0.353553
$9$	7.71610	2.57203
$10$	−3.29757	−1.04278
$11$	−0.552280	−0.166519	−0.0832594	−	0.996528i	$-0.526533\pi$
$11$	−0.552280	−0.166519	−0.0832594	+	0.996528i	$0.526533\pi$
$12$	3.27355	0.944991
$13$	4.95703	1.37483	0.687417	−	0.726263i	$-0.258745\pi$
$13$	4.95703	1.37483	0.687417	+	0.726263i	$0.258745\pi$
$14$	1.59623	0.426610
$15$	−10.7948	−2.78719
$16$	1.00000	0.250000
$17$	−6.15426	−1.49263	−0.746313	−	0.665595i	$-0.768178\pi$
$17$	−6.15426	−1.49263	−0.746313	+	0.665595i	$0.768178\pi$
$18$	7.71610	1.81870
$19$	3.34715	0.767889	0.383944	−	0.923356i	$-0.374565\pi$
$19$	3.34715	0.767889	0.383944	+	0.923356i	$0.374565\pi$
$20$	−3.29757	−0.737360
$21$	5.22533	1.14026
$22$	−0.552280	−0.117747
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.27355	0.668210
$25$	5.87400	1.17480
$26$	4.95703	0.972154
$27$	15.4384	2.97112
$28$	1.59623	0.301659
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−10.7948	−1.97084
$31$	−7.43456	−1.33529	−0.667643	−	0.744482i	$-0.732697\pi$
$31$	−7.43456	−1.33529	−0.667643	+	0.744482i	$0.732697\pi$
$32$	1.00000	0.176777
$33$	−1.80791	−0.314717
$34$	−6.15426	−1.05545
$35$	−5.26368	−0.889725
$36$	7.71610	1.28602
$37$	−1.25503	−0.206326	−0.103163	−	0.994664i	$-0.532896\pi$
$37$	−1.25503	−0.206326	−0.103163	+	0.994664i	$0.532896\pi$
$38$	3.34715	0.542979
$39$	16.2271	2.59841
$40$	−3.29757	−0.521392
$41$	−8.64391	−1.34995	−0.674976	−	0.737840i	$-0.735846\pi$
$41$	−8.64391	−1.34995	−0.674976	+	0.737840i	$0.735846\pi$
$42$	5.22533	0.806286
$43$	9.52529	1.45259	0.726296	−	0.687382i	$-0.241240\pi$
$43$	9.52529	1.45259	0.726296	+	0.687382i	$0.241240\pi$
$44$	−0.552280	−0.0832594
$45$	−25.4444	−3.79303
$46$	1.00000	0.147442
$47$	−0.00901703	−0.00131527	−0.000657634	−	1.00000i	$-0.500209\pi$
$47$	−0.00901703	−0.00131527	−0.000657634		1.00000i	$0.500209\pi$
$48$	3.27355	0.472496
$49$	−4.45205	−0.636008
$50$	5.87400	0.830708
$51$	−20.1462	−2.82104
$52$	4.95703	0.687417
$53$	−0.871657	−0.119731	−0.0598657	−	0.998206i	$-0.519067\pi$
$53$	−0.871657	−0.119731	−0.0598657	+	0.998206i	$0.519067\pi$
$54$	15.4384	2.10090
$55$	1.82118	0.245569
$56$	1.59623	0.213305
$57$	10.9570	1.45130
$58$	1.00000	0.131306
$59$	5.17777	0.674088	0.337044	−	0.941489i	$-0.390573\pi$
$59$	5.17777	0.674088	0.337044	+	0.941489i	$0.390573\pi$
$60$	−10.7948	−1.39360
$61$	−3.51216	−0.449686	−0.224843	−	0.974395i	$-0.572187\pi$
$61$	−3.51216	−0.449686	−0.224843	+	0.974395i	$0.572187\pi$
$62$	−7.43456	−0.944189
$63$	12.3167	1.55175
$64$	1.00000	0.125000
$65$	−16.3462	−2.02749
$66$	−1.80791	−0.222539
$67$	3.01199	0.367973	0.183987	−	0.982929i	$-0.441100\pi$
$67$	3.01199	0.367973	0.183987	+	0.982929i	$0.441100\pi$
$68$	−6.15426	−0.746313
$69$	3.27355	0.394089
$70$	−5.26368	−0.629130
$71$	−11.6173	−1.37872	−0.689359	−	0.724420i	$-0.742108\pi$
$71$	−11.6173	−1.37872	−0.689359	+	0.724420i	$0.742108\pi$
$72$	7.71610	0.909351
$73$	16.3319	1.91150	0.955749	−	0.294183i	$-0.0950474\pi$
$73$	16.3319	1.91150	0.955749	+	0.294183i	$0.0950474\pi$
$74$	−1.25503	−0.145894
$75$	19.2288	2.22035
$76$	3.34715	0.383944
$77$	−0.881566	−0.100464
$78$	16.2271	1.83735
$79$	−15.3275	−1.72448	−0.862239	−	0.506501i	$-0.830939\pi$
$79$	−15.3275	−1.72448	−0.862239	+	0.506501i	$0.830939\pi$
$80$	−3.29757	−0.368680
$81$	27.3899	3.04332
$82$	−8.64391	−0.954560
$83$	3.61068	0.396323	0.198162	−	0.980169i	$-0.436503\pi$
$83$	3.61068	0.396323	0.198162	+	0.980169i	$0.436503\pi$
$84$	5.22533	0.570130
$85$	20.2941	2.20121
$86$	9.52529	1.02714
$87$	3.27355	0.350961
$88$	−0.552280	−0.0588733
$89$	12.8119	1.35806	0.679029	−	0.734111i	$-0.262401\pi$
$89$	12.8119	1.35806	0.679029	+	0.734111i	$0.262401\pi$
$90$	−25.4444	−2.68208
$91$	7.91256	0.829461
$92$	1.00000	0.104257
$93$	−24.3374	−2.52367
$94$	−0.00901703	−0.000930036 0
$95$	−11.0375	−1.13242
$96$	3.27355	0.334105
$97$	3.40031	0.345249	0.172624	−	0.984988i	$-0.444775\pi$
$97$	3.40031	0.345249	0.172624	+	0.984988i	$0.444775\pi$
$98$	−4.45205	−0.449725
$99$	−4.26145	−0.428292
$100$	5.87400	0.587400
$101$	−5.06984	−0.504468	−0.252234	−	0.967666i	$-0.581165\pi$
$101$	−5.06984	−0.504468	−0.252234	+	0.967666i	$0.581165\pi$
$102$	−20.1462	−1.99478
$103$	−1.24154	−0.122332	−0.0611662	−	0.998128i	$-0.519482\pi$
$103$	−1.24154	−0.122332	−0.0611662	+	0.998128i	$0.519482\pi$
$104$	4.95703	0.486077
$105$	−17.2309	−1.68156
$106$	−0.871657	−0.0846628
$107$	−13.3065	−1.28639	−0.643193	−	0.765704i	$-0.722391\pi$
$107$	−13.3065	−1.28639	−0.643193	+	0.765704i	$0.722391\pi$
$108$	15.4384	1.48556
$109$	−5.40597	−0.517798	−0.258899	−	0.965904i	$-0.583360\pi$
$109$	−5.40597	−0.517798	−0.258899	+	0.965904i	$0.583360\pi$
$110$	1.82118	0.173643
$111$	−4.10840	−0.389952
$112$	1.59623	0.150829
$113$	−17.5166	−1.64782	−0.823910	−	0.566721i	$-0.808212\pi$
$113$	−17.5166	−1.64782	−0.823910	+	0.566721i	$0.808212\pi$
$114$	10.9570	1.02622
$115$	−3.29757	−0.307500
$116$	1.00000	0.0928477
$117$	38.2490	3.53612
$118$	5.17777	0.476652
$119$	−9.82360	−0.900528
$120$	−10.7948	−0.985422
$121$	−10.6950	−0.972272
$122$	−3.51216	−0.317976
$123$	−28.2962	−2.55138
$124$	−7.43456	−0.667643
$125$	−2.88206	−0.257780
$126$	12.3167	1.09726
$127$	−20.8758	−1.85243	−0.926215	−	0.376995i	$-0.876957\pi$
$127$	−20.8758	−1.85243	−0.926215	+	0.376995i	$0.876957\pi$
$128$	1.00000	0.0883883
$129$	31.1815	2.74537
$130$	−16.3462	−1.43365
$131$	2.41945	0.211389	0.105694	−	0.994399i	$-0.466293\pi$
$131$	2.41945	0.211389	0.105694	+	0.994399i	$0.466293\pi$
$132$	−1.80791	−0.157359
$133$	5.34282	0.463281
$134$	3.01199	0.260196
$135$	−50.9092	−4.38156
$136$	−6.15426	−0.527723
$137$	−6.20469	−0.530102	−0.265051	−	0.964234i	$-0.585389\pi$
$137$	−6.20469	−0.530102	−0.265051	+	0.964234i	$0.585389\pi$
$138$	3.27355	0.278663
$139$	−16.3177	−1.38405	−0.692024	−	0.721874i	$-0.743281\pi$
$139$	−16.3177	−1.38405	−0.692024	+	0.721874i	$0.743281\pi$
$140$	−5.26368	−0.444862
$141$	−0.0295177	−0.00248584
$142$	−11.6173	−0.974901
$143$	−2.73767	−0.228936
$144$	7.71610	0.643008
$145$	−3.29757	−0.273849
$146$	16.3319	1.35163
$147$	−14.5740	−1.20204
$148$	−1.25503	−0.103163
$149$	6.64874	0.544686	0.272343	−	0.962200i	$-0.412202\pi$
$149$	6.64874	0.544686	0.272343	+	0.962200i	$0.412202\pi$
$150$	19.2288	1.57002
$151$	−7.65474	−0.622934	−0.311467	−	0.950257i	$-0.600820\pi$
$151$	−7.65474	−0.622934	−0.311467	+	0.950257i	$0.600820\pi$
$152$	3.34715	0.271490
$153$	−47.4869	−3.83909
$154$	−0.881566	−0.0710386
$155$	24.5160	1.96917
$156$	16.2271	1.29921
$157$	0.0321937	0.00256933	0.00128467	−	0.999999i	$-0.499591\pi$
$157$	0.0321937	0.00256933	0.00128467	+	0.999999i	$0.499591\pi$
$158$	−15.3275	−1.21939
$159$	−2.85341	−0.226290
$160$	−3.29757	−0.260696
$161$	1.59623	0.125800
$162$	27.3899	2.15195
$163$	16.3434	1.28011	0.640056	−	0.768328i	$-0.278911\pi$
$163$	16.3434	1.28011	0.640056	+	0.768328i	$0.278911\pi$
$164$	−8.64391	−0.674976
$165$	5.96173	0.464120
$166$	3.61068	0.280243
$167$	0.683279	0.0528737	0.0264368	−	0.999650i	$-0.491584\pi$
$167$	0.683279	0.0528737	0.0264368	+	0.999650i	$0.491584\pi$
$168$	5.22533	0.403143
$169$	11.5722	0.890167
$170$	20.2941	1.55649
$171$	25.8269	1.97504
$172$	9.52529	0.726296
$173$	−17.2121	−1.30861	−0.654306	−	0.756230i	$-0.727039\pi$
$173$	−17.2121	−1.30861	−0.654306	+	0.756230i	$0.727039\pi$
$174$	3.27355	0.248167
$175$	9.37624	0.708777
$176$	−0.552280	−0.0416297
$177$	16.9497	1.27401
$178$	12.8119	0.960292
$179$	−3.66007	−0.273566	−0.136783	−	0.990601i	$-0.543676\pi$
$179$	−3.66007	−0.273566	−0.136783	+	0.990601i	$0.543676\pi$
$180$	−25.4444	−1.89651
$181$	9.97909	0.741740	0.370870	−	0.928685i	$-0.379060\pi$
$181$	9.97909	0.741740	0.370870	+	0.928685i	$0.379060\pi$
$182$	7.91256	0.586518
$183$	−11.4972	−0.849899
$184$	1.00000	0.0737210
$185$	4.13856	0.304273
$186$	−24.3374	−1.78450
$187$	3.39887	0.248550
$188$	−0.00901703	−0.000657634 0
$189$	24.6432	1.79253
$190$	−11.0375	−0.800742
$191$	−25.9285	−1.87612	−0.938060	−	0.346473i	$-0.887379\pi$
$191$	−25.9285	−1.87612	−0.938060	+	0.346473i	$0.887379\pi$
$192$	3.27355	0.236248
$193$	−2.13136	−0.153418	−0.0767091	−	0.997054i	$-0.524441\pi$
$193$	−2.13136	−0.153418	−0.0767091	+	0.997054i	$0.524441\pi$
$194$	3.40031	0.244128
$195$	−53.5100	−3.83193
$196$	−4.45205	−0.318004
$197$	22.1869	1.58075	0.790375	−	0.612624i	$-0.209886\pi$
$197$	22.1869	1.58075	0.790375	+	0.612624i	$0.209886\pi$
$198$	−4.26145	−0.302848
$199$	−1.47716	−0.104713	−0.0523564	−	0.998628i	$-0.516673\pi$
$199$	−1.47716	−0.104713	−0.0523564	+	0.998628i	$0.516673\pi$
$200$	5.87400	0.415354
$201$	9.85989	0.695463
$202$	−5.06984	−0.356712
$203$	1.59623	0.112033
$204$	−20.1462	−1.41052
$205$	28.5039	1.99080
$206$	−1.24154	−0.0865020
$207$	7.71610	0.536306
$208$	4.95703	0.343708
$209$	−1.84856	−0.127868
$210$	−17.2309	−1.18905
$211$	−27.7870	−1.91294	−0.956469	−	0.291835i	$-0.905734\pi$
$211$	−27.7870	−1.91294	−0.956469	+	0.291835i	$0.905734\pi$
$212$	−0.871657	−0.0598657
$213$	−38.0297	−2.60575
$214$	−13.3065	−0.909612
$215$	−31.4103	−2.14217
$216$	15.4384	1.05045
$217$	−11.8673	−0.805602
$218$	−5.40597	−0.366139
$219$	53.4631	3.61270
$220$	1.82118	0.122784
$221$	−30.5069	−2.05211
$222$	−4.10840	−0.275738
$223$	13.9207	0.932197	0.466099	−	0.884733i	$-0.345659\pi$
$223$	13.9207	0.932197	0.466099	+	0.884733i	$0.345659\pi$
$224$	1.59623	0.106653
$225$	45.3243	3.02162
$226$	−17.5166	−1.16518
$227$	12.1810	0.808482	0.404241	−	0.914653i	$-0.367536\pi$
$227$	12.1810	0.808482	0.404241	+	0.914653i	$0.367536\pi$
$228$	10.9570	0.725648
$229$	3.05844	0.202107	0.101054	−	0.994881i	$-0.467779\pi$
$229$	3.05844	0.202107	0.101054	+	0.994881i	$0.467779\pi$
$230$	−3.29757	−0.217436
$231$	−2.88585	−0.189875
$232$	1.00000	0.0656532
$233$	27.9095	1.82841	0.914207	−	0.405249i	$-0.132815\pi$
$233$	27.9095	1.82841	0.914207	+	0.405249i	$0.132815\pi$
$234$	38.2490	2.50041
$235$	0.0297343	0.00193965
$236$	5.17777	0.337044
$237$	−50.1753	−3.25923
$238$	−9.82360	−0.636770
$239$	13.4148	0.867733	0.433867	−	0.900977i	$-0.357149\pi$
$239$	13.4148	0.867733	0.433867	+	0.900977i	$0.357149\pi$
$240$	−10.7948	−0.696799
$241$	1.46376	0.0942894	0.0471447	−	0.998888i	$-0.484988\pi$
$241$	1.46376	0.0942894	0.0471447	+	0.998888i	$0.484988\pi$
$242$	−10.6950	−0.687500
$243$	43.3470	2.78071
$244$	−3.51216	−0.224843
$245$	14.6810	0.937933
$246$	−28.2962	−1.80410
$247$	16.5919	1.05572
$248$	−7.43456	−0.472095
$249$	11.8197	0.749044
$250$	−2.88206	−0.182278
$251$	18.3994	1.16136	0.580681	−	0.814131i	$-0.302786\pi$
$251$	18.3994	1.16136	0.580681	+	0.814131i	$0.302786\pi$
$252$	12.3167	0.775877
$253$	−0.552280	−0.0347216
$254$	−20.8758	−1.30987
$255$	66.4337	4.16024
$256$	1.00000	0.0625000
$257$	4.55642	0.284221	0.142111	−	0.989851i	$-0.454611\pi$
$257$	4.55642	0.284221	0.142111	+	0.989851i	$0.454611\pi$
$258$	31.1815	1.94127
$259$	−2.00332	−0.124480
$260$	−16.3462	−1.01375
$261$	7.71610	0.477615
$262$	2.41945	0.149474
$263$	20.8784	1.28742	0.643710	−	0.765270i	$-0.277394\pi$
$263$	20.8784	1.28742	0.643710	+	0.765270i	$0.277394\pi$
$264$	−1.80791	−0.111269
$265$	2.87435	0.176570
$266$	5.34282	0.327589
$267$	41.9403	2.56671
$268$	3.01199	0.183987
$269$	−5.29823	−0.323039	−0.161520	−	0.986870i	$-0.551639\pi$
$269$	−5.29823	−0.323039	−0.161520	+	0.986870i	$0.551639\pi$
$270$	−50.9092	−3.09823
$271$	16.4222	0.997575	0.498788	−	0.866724i	$-0.333779\pi$
$271$	16.4222	0.997575	0.498788	+	0.866724i	$0.333779\pi$
$272$	−6.15426	−0.373157
$273$	25.9021	1.56767
$274$	−6.20469	−0.374839
$275$	−3.24409	−0.195626
$276$	3.27355	0.197044
$277$	−17.6762	−1.06206	−0.531031	−	0.847352i	$-0.678195\pi$
$277$	−17.6762	−1.06206	−0.531031	+	0.847352i	$0.678195\pi$
$278$	−16.3177	−0.978670
$279$	−57.3658	−3.43440
$280$	−5.26368	−0.314565
$281$	30.4811	1.81835	0.909175	−	0.416414i	$-0.136713\pi$
$281$	30.4811	1.81835	0.909175	+	0.416414i	$0.136713\pi$
$282$	−0.0295177	−0.00175775
$283$	−9.32659	−0.554408	−0.277204	−	0.960811i	$-0.589408\pi$
$283$	−9.32659	−0.554408	−0.277204	+	0.960811i	$0.589408\pi$
$284$	−11.6173	−0.689359
$285$	−36.1317	−2.14026
$286$	−2.73767	−0.161882
$287$	−13.7977	−0.814450
$288$	7.71610	0.454676
$289$	20.8749	1.22793
$290$	−3.29757	−0.193640
$291$	11.1311	0.652514
$292$	16.3319	0.955749
$293$	−18.8304	−1.10008	−0.550042	−	0.835137i	$-0.685388\pi$
$293$	−18.8304	−1.10008	−0.550042	+	0.835137i	$0.685388\pi$
$294$	−14.5740	−0.849973
$295$	−17.0741	−0.994091
$296$	−1.25503	−0.0729472
$297$	−8.52631	−0.494746
$298$	6.64874	0.385151
$299$	4.95703	0.286673
$300$	19.2288	1.11017
$301$	15.2045	0.876375
$302$	−7.65474	−0.440481
$303$	−16.5963	−0.953435
$304$	3.34715	0.191972
$305$	11.5816	0.663161
$306$	−47.4869	−2.71464
$307$	0.0366673	0.00209271	0.00104636	−	0.999999i	$-0.499667\pi$
$307$	0.0366673	0.00209271	0.00104636	+	0.999999i	$0.499667\pi$
$308$	−0.881566	−0.0502319
$309$	−4.06423	−0.231206
$310$	24.5160	1.39242
$311$	2.77546	0.157382	0.0786909	−	0.996899i	$-0.474926\pi$
$311$	2.77546	0.157382	0.0786909	+	0.996899i	$0.474926\pi$
$312$	16.2271	0.918677
$313$	26.1120	1.47594	0.737970	−	0.674834i	$-0.235785\pi$
$313$	26.1120	1.47594	0.737970	+	0.674834i	$0.235785\pi$
$314$	0.0321937	0.00181679
$315$	−40.6151	−2.28840
$316$	−15.3275	−0.862239
$317$	−13.4149	−0.753458	−0.376729	−	0.926323i	$-0.622951\pi$
$317$	−13.4149	−0.753458	−0.376729	+	0.926323i	$0.622951\pi$
$318$	−2.85341	−0.160011
$319$	−0.552280	−0.0309218
$320$	−3.29757	−0.184340
$321$	−43.5594	−2.43125
$322$	1.59623	0.0889544
$323$	−20.5992	−1.14617
$324$	27.3899	1.52166
$325$	29.1176	1.61515
$326$	16.3434	0.905176
$327$	−17.6967	−0.978630
$328$	−8.64391	−0.477280
$329$	−0.0143932	−0.000793525 0
$330$	5.96173	0.328183
$331$	11.4673	0.630299	0.315150	−	0.949042i	$-0.397945\pi$
$331$	11.4673	0.630299	0.315150	+	0.949042i	$0.397945\pi$
$332$	3.61068	0.198162
$333$	−9.68394	−0.530677
$334$	0.683279	0.0373873
$335$	−9.93226	−0.542657
$336$	5.22533	0.285065
$337$	26.1503	1.42450	0.712250	−	0.701926i	$-0.247676\pi$
$337$	26.1503	1.42450	0.712250	+	0.701926i	$0.247676\pi$
$338$	11.5722	0.629443
$339$	−57.3413	−3.11435
$340$	20.2941	1.10060
$341$	4.10596	0.222350
$342$	25.8269	1.39656
$343$	−18.2801	−0.987033
$344$	9.52529	0.513569
$345$	−10.7948	−0.581170
$346$	−17.2121	−0.925328
$347$	−23.2027	−1.24559	−0.622793	−	0.782386i	$-0.714002\pi$
$347$	−23.2027	−1.24559	−0.622793	+	0.782386i	$0.714002\pi$
$348$	3.27355	0.175480
$349$	21.1885	1.13419	0.567096	−	0.823651i	$-0.308067\pi$
$349$	21.1885	1.13419	0.567096	+	0.823651i	$0.308067\pi$
$350$	9.37624	0.501181
$351$	76.5285	4.08479
$352$	−0.552280	−0.0294366
$353$	32.9951	1.75615	0.878077	−	0.478519i	$-0.158826\pi$
$353$	32.9951	1.75615	0.878077	+	0.478519i	$0.158826\pi$
$354$	16.9497	0.900864
$355$	38.3089	2.03322
$356$	12.8119	0.679029
$357$	−32.1580	−1.70198
$358$	−3.66007	−0.193441
$359$	12.1987	0.643824	0.321912	−	0.946770i	$-0.395674\pi$
$359$	12.1987	0.643824	0.321912	+	0.946770i	$0.395674\pi$
$360$	−25.4444	−1.34104
$361$	−7.79659	−0.410347
$362$	9.97909	0.524489
$363$	−35.0105	−1.83758
$364$	7.91256	0.414731
$365$	−53.8555	−2.81893
$366$	−11.4972	−0.600969
$367$	19.6501	1.02573	0.512863	−	0.858471i	$-0.328585\pi$
$367$	19.6501	1.02573	0.512863	+	0.858471i	$0.328585\pi$
$368$	1.00000	0.0521286
$369$	−66.6973	−3.47212
$370$	4.13856	0.215153
$371$	−1.39136	−0.0722361
$372$	−24.3374	−1.26183
$373$	38.3586	1.98613	0.993066	−	0.117561i	$-0.0375076\pi$
$373$	38.3586	1.98613	0.993066	+	0.117561i	$0.0375076\pi$
$374$	3.39887	0.175752
$375$	−9.43457	−0.487199
$376$	−0.00901703	−0.000465018 0
$377$	4.95703	0.255300
$378$	24.6432	1.26751
$379$	−18.0070	−0.924959	−0.462480	−	0.886630i	$-0.653040\pi$
$379$	−18.0070	−0.924959	−0.462480	+	0.886630i	$0.653040\pi$
$380$	−11.0375	−0.566210
$381$	−68.3380	−3.50106
$382$	−25.9285	−1.32662
$383$	10.6468	0.544026	0.272013	−	0.962294i	$-0.412311\pi$
$383$	10.6468	0.544026	0.272013	+	0.962294i	$0.412311\pi$
$384$	3.27355	0.167052
$385$	2.90703	0.148156
$386$	−2.13136	−0.108483
$387$	73.4981	3.73612
$388$	3.40031	0.172624
$389$	−4.61219	−0.233847	−0.116924	−	0.993141i	$-0.537303\pi$
$389$	−4.61219	−0.233847	−0.116924	+	0.993141i	$0.537303\pi$
$390$	−53.5100	−2.70958
$391$	−6.15426	−0.311234
$392$	−4.45205	−0.224863
$393$	7.92020	0.399521
$394$	22.1869	1.11776
$395$	50.5436	2.54312
$396$	−4.26145	−0.214146
$397$	−18.9016	−0.948642	−0.474321	−	0.880352i	$-0.657306\pi$
$397$	−18.9016	−0.948642	−0.474321	+	0.880352i	$0.657306\pi$
$398$	−1.47716	−0.0740431
$399$	17.4900	0.875593
$400$	5.87400	0.293700
$401$	−14.0922	−0.703728	−0.351864	−	0.936051i	$-0.614452\pi$
$401$	−14.0922	−0.703728	−0.351864	+	0.936051i	$0.614452\pi$
$402$	9.85989	0.491766
$403$	−36.8533	−1.83580
$404$	−5.06984	−0.252234
$405$	−90.3203	−4.48805
$406$	1.59623	0.0792195
$407$	0.693129	0.0343571
$408$	−20.1462	−0.997388
$409$	−2.63865	−0.130473	−0.0652363	−	0.997870i	$-0.520780\pi$
$409$	−2.63865	−0.130473	−0.0652363	+	0.997870i	$0.520780\pi$
$410$	28.5039	1.40771
$411$	−20.3113	−1.00188
$412$	−1.24154	−0.0611662
$413$	8.26490	0.406689
$414$	7.71610	0.379226
$415$	−11.9065	−0.584466
$416$	4.95703	0.243038
$417$	−53.4167	−2.61583
$418$	−1.84856	−0.0904162
$419$	29.4474	1.43860	0.719300	−	0.694699i	$-0.244462\pi$
$419$	29.4474	1.43860	0.719300	+	0.694699i	$0.244462\pi$
$420$	−17.2309	−0.840782
$421$	13.7508	0.670175	0.335088	−	0.942187i	$-0.391234\pi$
$421$	13.7508	0.670175	0.335088	+	0.942187i	$0.391234\pi$
$422$	−27.7870	−1.35265
$423$	−0.0695763	−0.00338292
$424$	−0.871657	−0.0423314
$425$	−36.1501	−1.75354
$426$	−38.0297	−1.84255
$427$	−5.60621	−0.271304
$428$	−13.3065	−0.643193
$429$	−8.96189	−0.432684
$430$	−31.4103	−1.51474
$431$	14.5369	0.700220	0.350110	−	0.936709i	$-0.386144\pi$
$431$	14.5369	0.700220	0.350110	+	0.936709i	$0.386144\pi$
$432$	15.4384	0.742779
$433$	−12.7243	−0.611492	−0.305746	−	0.952113i	$-0.598906\pi$
$433$	−12.7243	−0.611492	−0.305746	+	0.952113i	$0.598906\pi$
$434$	−11.8673	−0.569646
$435$	−10.7948	−0.517569
$436$	−5.40597	−0.258899
$437$	3.34715	0.160116
$438$	53.4631	2.55456
$439$	31.9579	1.52527	0.762634	−	0.646830i	$-0.223906\pi$
$439$	31.9579	1.52527	0.762634	+	0.646830i	$0.223906\pi$
$440$	1.82118	0.0868216
$441$	−34.3525	−1.63583
$442$	−30.5069	−1.45106
$443$	0.992296	0.0471454	0.0235727	−	0.999722i	$-0.492496\pi$
$443$	0.992296	0.0471454	0.0235727	+	0.999722i	$0.492496\pi$
$444$	−4.10840	−0.194976
$445$	−42.2482	−2.00276
$446$	13.9207	0.659163
$447$	21.7649	1.02945
$448$	1.59623	0.0754147
$449$	11.7431	0.554189	0.277095	−	0.960843i	$-0.410628\pi$
$449$	11.7431	0.554189	0.277095	+	0.960843i	$0.410628\pi$
$450$	45.3243	2.13661
$451$	4.77386	0.224792
$452$	−17.5166	−0.823910
$453$	−25.0581	−1.17733
$454$	12.1810	0.571683
$455$	−26.0922	−1.22322
$456$	10.9570	0.513111
$457$	−27.2244	−1.27351	−0.636753	−	0.771068i	$-0.719723\pi$
$457$	−27.2244	−1.27351	−0.636753	+	0.771068i	$0.719723\pi$
$458$	3.05844	0.142911
$459$	−95.0117	−4.43477
$460$	−3.29757	−0.153750
$461$	−5.21010	−0.242659	−0.121329	−	0.992612i	$-0.538716\pi$
$461$	−5.21010	−0.242659	−0.121329	+	0.992612i	$0.538716\pi$
$462$	−2.88585	−0.134262
$463$	−22.5031	−1.04581	−0.522905	−	0.852391i	$-0.675152\pi$
$463$	−22.5031	−1.04581	−0.522905	+	0.852391i	$0.675152\pi$
$464$	1.00000	0.0464238
$465$	80.2542	3.72170
$466$	27.9095	1.29288
$467$	13.6048	0.629554	0.314777	−	0.949166i	$-0.398070\pi$
$467$	13.6048	0.629554	0.314777	+	0.949166i	$0.398070\pi$
$468$	38.2490	1.76806
$469$	4.80783	0.222005
$470$	0.0297343	0.00137154
$471$	0.105387	0.00485600
$472$	5.17777	0.238326
$473$	−5.26063	−0.241884
$474$	−50.1753	−2.30463
$475$	19.6611	0.902115
$476$	−9.82360	−0.450264
$477$	−6.72580	−0.307953
$478$	13.4148	0.613580
$479$	−23.5814	−1.07746	−0.538732	−	0.842477i	$-0.681096\pi$
$479$	−23.5814	−1.07746	−0.538732	+	0.842477i	$0.681096\pi$
$480$	−10.7948	−0.492711
$481$	−6.22123	−0.283664
$482$	1.46376	0.0666727
$483$	5.22533	0.237761
$484$	−10.6950	−0.486136
$485$	−11.2128	−0.509145
$486$	43.3470	1.96626
$487$	23.6863	1.07333	0.536665	−	0.843796i	$-0.319684\pi$
$487$	23.6863	1.07333	0.536665	+	0.843796i	$0.319684\pi$
$488$	−3.51216	−0.158988
$489$	53.5008	2.41939
$490$	14.6810	0.663219
$491$	19.9716	0.901306	0.450653	−	0.892699i	$-0.351191\pi$
$491$	19.9716	0.901306	0.450653	+	0.892699i	$0.351191\pi$
$492$	−28.2962	−1.27569
$493$	−6.15426	−0.277174
$494$	16.5919	0.746506
$495$	14.0524	0.631610
$496$	−7.43456	−0.333821
$497$	−18.5438	−0.831805
$498$	11.8197	0.529654
$499$	−34.0407	−1.52387	−0.761935	−	0.647653i	$-0.775750\pi$
$499$	−34.0407	−1.52387	−0.761935	+	0.647653i	$0.775750\pi$
$500$	−2.88206	−0.128890
$501$	2.23674	0.0999304
$502$	18.3994	0.821207
$503$	22.4631	1.00158	0.500789	−	0.865569i	$-0.333043\pi$
$503$	22.4631	1.00158	0.500789	+	0.865569i	$0.333043\pi$
$504$	12.3167	0.548628
$505$	16.7182	0.743948
$506$	−0.552280	−0.0245518
$507$	37.8820	1.68240
$508$	−20.8758	−0.926215
$509$	−0.202425	−0.00897233	−0.00448617	−	0.999990i	$-0.501428\pi$
$509$	−0.202425	−0.00897233	−0.00448617	+	0.999990i	$0.501428\pi$
$510$	66.4337	2.94173
$511$	26.0694	1.15324
$512$	1.00000	0.0441942
$513$	51.6745	2.28149
$514$	4.55642	0.200975
$515$	4.09406	0.180406
$516$	31.1815	1.37269
$517$	0.00497993	0.000219017 0
$518$	−2.00332	−0.0880207
$519$	−56.3446	−2.47325
$520$	−16.3462	−0.716827
$521$	14.5379	0.636916	0.318458	−	0.947937i	$-0.396835\pi$
$521$	14.5379	0.636916	0.318458	+	0.947937i	$0.396835\pi$
$522$	7.71610	0.337725
$523$	−15.9611	−0.697931	−0.348966	−	0.937136i	$-0.613467\pi$
$523$	−15.9611	−0.697931	−0.348966	+	0.937136i	$0.613467\pi$
$524$	2.41945	0.105694
$525$	30.6936	1.33958
$526$	20.8784	0.910343
$527$	45.7542	1.99308
$528$	−1.80791	−0.0786794
$529$	1.00000	0.0434783
$530$	2.87435	0.124854
$531$	39.9522	1.73378
$532$	5.34282	0.231640
$533$	−42.8481	−1.85596
$534$	41.9403	1.81494
$535$	43.8791	1.89706
$536$	3.01199	0.130098
$537$	−11.9814	−0.517036
$538$	−5.29823	−0.228423
$539$	2.45878	0.105907
$540$	−50.9092	−2.19078
$541$	−24.4733	−1.05219	−0.526095	−	0.850425i	$-0.676345\pi$
$541$	−24.4733	−1.05219	−0.526095	+	0.850425i	$0.676345\pi$
$542$	16.4222	0.705392
$543$	32.6670	1.40188
$544$	−6.15426	−0.263862
$545$	17.8266	0.763607
$546$	25.9021	1.10851
$547$	30.8182	1.31769	0.658846	−	0.752278i	$-0.271045\pi$
$547$	30.8182	1.31769	0.658846	+	0.752278i	$0.271045\pi$
$548$	−6.20469	−0.265051
$549$	−27.1002	−1.15661
$550$	−3.24409	−0.138329
$551$	3.34715	0.142593
$552$	3.27355	0.139331
$553$	−24.4662	−1.04041
$554$	−17.6762	−0.750991
$555$	13.5478	0.575070
$556$	−16.3177	−0.692024
$557$	24.8700	1.05377	0.526887	−	0.849935i	$-0.323359\pi$
$557$	24.8700	1.05377	0.526887	+	0.849935i	$0.323359\pi$
$558$	−57.3658	−2.42849
$559$	47.2172	1.99707
$560$	−5.26368	−0.222431
$561$	11.1264	0.469756
$562$	30.4811	1.28577
$563$	23.1366	0.975093	0.487546	−	0.873097i	$-0.337892\pi$
$563$	23.1366	0.975093	0.487546	+	0.873097i	$0.337892\pi$
$564$	−0.0295177	−0.00124292
$565$	57.7622	2.43007
$566$	−9.32659	−0.392026
$567$	43.7206	1.83609
$568$	−11.6173	−0.487450
$569$	−25.1902	−1.05603	−0.528015	−	0.849235i	$-0.677063\pi$
$569$	−25.1902	−1.05603	−0.528015	+	0.849235i	$0.677063\pi$
$570$	−36.1317	−1.51339
$571$	−32.4847	−1.35944	−0.679721	−	0.733471i	$-0.737899\pi$
$571$	−32.4847	−1.35944	−0.679721	+	0.733471i	$0.737899\pi$
$572$	−2.73767	−0.114468
$573$	−84.8781	−3.54583
$574$	−13.7977	−0.575903
$575$	5.87400	0.244963
$576$	7.71610	0.321504
$577$	20.5133	0.853978	0.426989	−	0.904257i	$-0.359574\pi$
$577$	20.5133	0.853978	0.426989	+	0.904257i	$0.359574\pi$
$578$	20.8749	0.868281
$579$	−6.97709	−0.289958
$580$	−3.29757	−0.136924
$581$	5.76347	0.239109
$582$	11.1311	0.461397
$583$	0.481399	0.0199375
$584$	16.3319	0.675817
$585$	−126.129	−5.21478
$586$	−18.8304	−0.777876
$587$	−7.13799	−0.294616	−0.147308	−	0.989091i	$-0.547061\pi$
$587$	−7.13799	−0.294616	−0.147308	+	0.989091i	$0.547061\pi$
$588$	−14.5740	−0.601022
$589$	−24.8846	−1.02535
$590$	−17.0741	−0.702928
$591$	72.6298	2.98759
$592$	−1.25503	−0.0515814
$593$	−15.5287	−0.637688	−0.318844	−	0.947807i	$-0.603295\pi$
$593$	−15.5287	−0.637688	−0.318844	+	0.947807i	$0.603295\pi$
$594$	−8.52631	−0.349839
$595$	32.3941	1.32803
$596$	6.64874	0.272343
$597$	−4.83554	−0.197905
$598$	4.95703	0.202708
$599$	4.77510	0.195105	0.0975526	−	0.995230i	$-0.468899\pi$
$599$	4.77510	0.195105	0.0975526	+	0.995230i	$0.468899\pi$
$600$	19.2288	0.785012
$601$	20.3673	0.830800	0.415400	−	0.909639i	$-0.363642\pi$
$601$	20.3673	0.830800	0.415400	+	0.909639i	$0.363642\pi$
$602$	15.2045	0.619691
$603$	23.2408	0.946439
$604$	−7.65474	−0.311467
$605$	35.2675	1.43383
$606$	−16.5963	−0.674180
$607$	−13.3907	−0.543512	−0.271756	−	0.962366i	$-0.587604\pi$
$607$	−13.3907	−0.543512	−0.271756	+	0.962366i	$0.587604\pi$
$608$	3.34715	0.135745
$609$	5.22533	0.211741
$610$	11.5816	0.468926
$611$	−0.0446977	−0.00180828
$612$	−47.4869	−1.91954
$613$	−35.5871	−1.43735	−0.718674	−	0.695347i	$-0.755251\pi$
$613$	−35.5871	−1.43735	−0.718674	+	0.695347i	$0.755251\pi$
$614$	0.0366673	0.00147977
$615$	93.3089	3.76258
$616$	−0.881566	−0.0355193
$617$	38.1407	1.53549	0.767744	−	0.640757i	$-0.221379\pi$
$617$	38.1407	1.53549	0.767744	+	0.640757i	$0.221379\pi$
$618$	−4.06423	−0.163487
$619$	−33.4208	−1.34329	−0.671647	−	0.740871i	$-0.734413\pi$
$619$	−33.4208	−1.34329	−0.671647	+	0.740871i	$0.734413\pi$
$620$	24.5160	0.984586
$621$	15.4384	0.619521
$622$	2.77546	0.111286
$623$	20.4507	0.819341
$624$	16.2271	0.649603
$625$	−19.8662	−0.794646
$626$	26.1120	1.04365
$627$	−6.05136	−0.241668
$628$	0.0321937	0.00128467
$629$	7.72378	0.307967
$630$	−40.6151	−1.61814
$631$	21.5288	0.857047	0.428524	−	0.903531i	$-0.359034\pi$
$631$	21.5288	0.857047	0.428524	+	0.903531i	$0.359034\pi$
$632$	−15.3275	−0.609695
$633$	−90.9621	−3.61542
$634$	−13.4149	−0.532775
$635$	68.8396	2.73182
$636$	−2.85341	−0.113145
$637$	−22.0690	−0.874404
$638$	−0.552280	−0.0218650
$639$	−89.6401	−3.54611
$640$	−3.29757	−0.130348
$641$	18.8597	0.744914	0.372457	−	0.928049i	$-0.378515\pi$
$641$	18.8597	0.744914	0.372457	+	0.928049i	$0.378515\pi$
$642$	−43.5594	−1.71915
$643$	12.2608	0.483517	0.241758	−	0.970336i	$-0.422276\pi$
$643$	12.2608	0.483517	0.241758	+	0.970336i	$0.422276\pi$
$644$	1.59623	0.0629002
$645$	−102.823	−4.04866
$646$	−20.5992	−0.810465
$647$	19.9660	0.784944	0.392472	−	0.919764i	$-0.371620\pi$
$647$	19.9660	0.784944	0.392472	+	0.919764i	$0.371620\pi$
$648$	27.3899	1.07598
$649$	−2.85958	−0.112248
$650$	29.1176	1.14209
$651$	−38.8480	−1.52257
$652$	16.3434	0.640056
$653$	8.26476	0.323425	0.161713	−	0.986838i	$-0.448298\pi$
$653$	8.26476	0.323425	0.161713	+	0.986838i	$0.448298\pi$
$654$	−17.6967	−0.691996
$655$	−7.97833	−0.311739
$656$	−8.64391	−0.337488
$657$	126.018	4.91644
$658$	−0.0143932	−0.000561107 0
$659$	−22.5618	−0.878883	−0.439441	−	0.898271i	$-0.644824\pi$
$659$	−22.5618	−0.878883	−0.439441	+	0.898271i	$0.644824\pi$
$660$	5.96173	0.232060
$661$	−26.5795	−1.03382	−0.516911	−	0.856039i	$-0.672918\pi$
$661$	−26.5795	−1.03382	−0.516911	+	0.856039i	$0.672918\pi$
$662$	11.4673	0.445689
$663$	−99.8656	−3.87846
$664$	3.61068	0.140121
$665$	−17.6183	−0.683210
$666$	−9.68394	−0.375245
$667$	1.00000	0.0387202
$668$	0.683279	0.0264368
$669$	45.5699	1.76184
$670$	−9.93226	−0.383717
$671$	1.93970	0.0748811
$672$	5.22533	0.201571
$673$	25.5212	0.983771	0.491885	−	0.870660i	$-0.336308\pi$
$673$	25.5212	0.983771	0.491885	+	0.870660i	$0.336308\pi$
$674$	26.1503	1.00727
$675$	90.6849	3.49046
$676$	11.5722	0.445083
$677$	−32.7230	−1.25765	−0.628824	−	0.777548i	$-0.716463\pi$
$677$	−32.7230	−1.25765	−0.628824	+	0.777548i	$0.716463\pi$
$678$	−57.3413	−2.20218
$679$	5.42767	0.208295
$680$	20.2941	0.778244
$681$	39.8751	1.52802
$682$	4.10596	0.157225
$683$	29.0725	1.11243	0.556214	−	0.831039i	$-0.312254\pi$
$683$	29.0725	1.11243	0.556214	+	0.831039i	$0.312254\pi$
$684$	25.8269	0.987518
$685$	20.4604	0.781752
$686$	−18.2801	−0.697937
$687$	10.0119	0.381979
$688$	9.52529	0.363148
$689$	−4.32083	−0.164611
$690$	−10.7948	−0.410949
$691$	−21.9244	−0.834042	−0.417021	−	0.908897i	$-0.636926\pi$
$691$	−21.9244	−0.834042	−0.417021	+	0.908897i	$0.636926\pi$
$692$	−17.2121	−0.654306
$693$	−6.80225	−0.258396
$694$	−23.2027	−0.880763
$695$	53.8088	2.04108
$696$	3.27355	0.124083
$697$	53.1968	2.01497
$698$	21.1885	0.801995
$699$	91.3631	3.45567
$700$	9.37624	0.354389
$701$	32.4982	1.22744	0.613720	−	0.789524i	$-0.289672\pi$
$701$	32.4982	1.22744	0.613720	+	0.789524i	$0.289672\pi$
$702$	76.5285	2.88838
$703$	−4.20077	−0.158435
$704$	−0.552280	−0.0208148
$705$	0.0973367	0.00366591
$706$	32.9951	1.24179
$707$	−8.09262	−0.304354
$708$	16.9497	0.637007
$709$	−12.0648	−0.453102	−0.226551	−	0.973999i	$-0.572745\pi$
$709$	−12.0648	−0.453102	−0.226551	+	0.973999i	$0.572745\pi$
$710$	38.3089	1.43771
$711$	−118.269	−4.43542
$712$	12.8119	0.480146
$713$	−7.43456	−0.278426
$714$	−32.1580	−1.20348
$715$	9.02767	0.337616
$716$	−3.66007	−0.136783
$717$	43.9141	1.64000
$718$	12.1987	0.455253
$719$	−13.4055	−0.499940	−0.249970	−	0.968254i	$-0.580421\pi$
$719$	−13.4055	−0.499940	−0.249970	+	0.968254i	$0.580421\pi$
$720$	−25.4444	−0.948257
$721$	−1.98178	−0.0738053
$722$	−7.79659	−0.290159
$723$	4.79170	0.178205
$724$	9.97909	0.370870
$725$	5.87400	0.218155
$726$	−35.0105	−1.29936
$727$	−16.6857	−0.618839	−0.309419	−	0.950926i	$-0.600135\pi$
$727$	−16.6857	−0.618839	−0.309419	+	0.950926i	$0.600135\pi$
$728$	7.91256	0.293259
$729$	59.7287	2.21217
$730$	−53.8555	−1.99328
$731$	−58.6211	−2.16818
$732$	−11.4972	−0.424949
$733$	10.5836	0.390915	0.195457	−	0.980712i	$-0.437381\pi$
$733$	10.5836	0.390915	0.195457	+	0.980712i	$0.437381\pi$
$734$	19.6501	0.725297
$735$	48.0588	1.77268
$736$	1.00000	0.0368605
$737$	−1.66346	−0.0612744
$738$	−66.6973	−2.45516
$739$	26.6985	0.982119	0.491059	−	0.871126i	$-0.336610\pi$
$739$	26.6985	0.982119	0.491059	+	0.871126i	$0.336610\pi$
$740$	4.13856	0.152136
$741$	54.3144	1.99529
$742$	−1.39136	−0.0510786
$743$	−22.9133	−0.840607	−0.420303	−	0.907384i	$-0.638076\pi$
$743$	−22.9133	−0.840607	−0.420303	+	0.907384i	$0.638076\pi$
$744$	−24.3374	−0.892251
$745$	−21.9247	−0.803259
$746$	38.3586	1.40441
$747$	27.8604	1.01936
$748$	3.39887	0.124275
$749$	−21.2402	−0.776100
$750$	−9.43457	−0.344502
$751$	21.2835	0.776647	0.388323	−	0.921523i	$-0.373054\pi$
$751$	21.2835	0.776647	0.388323	+	0.921523i	$0.373054\pi$
$752$	−0.00901703	−0.000328817 0
$753$	60.2314	2.19495
$754$	4.95703	0.180524
$755$	25.2421	0.918653
$756$	24.6432	0.896264
$757$	−17.2500	−0.626962	−0.313481	−	0.949594i	$-0.601495\pi$
$757$	−17.2500	−0.626962	−0.313481	+	0.949594i	$0.601495\pi$
$758$	−18.0070	−0.654045
$759$	−1.80791	−0.0656231
$760$	−11.0375	−0.400371
$761$	−50.4848	−1.83007	−0.915037	−	0.403370i	$-0.867839\pi$
$761$	−50.4848	−1.83007	−0.915037	+	0.403370i	$0.867839\pi$
$762$	−68.3380	−2.47562
$763$	−8.62917	−0.312397
$764$	−25.9285	−0.938060
$765$	156.591	5.66158
$766$	10.6468	0.384685
$767$	25.6664	0.926758
$768$	3.27355	0.118124
$769$	−6.85030	−0.247028	−0.123514	−	0.992343i	$-0.539416\pi$
$769$	−6.85030	−0.247028	−0.123514	+	0.992343i	$0.539416\pi$
$770$	2.90703	0.104762
$771$	14.9156	0.537173
$772$	−2.13136	−0.0767091
$773$	−23.8265	−0.856980	−0.428490	−	0.903547i	$-0.640954\pi$
$773$	−23.8265	−0.856980	−0.428490	+	0.903547i	$0.640954\pi$
$774$	73.4981	2.64183
$775$	−43.6705	−1.56869
$776$	3.40031	0.122064
$777$	−6.55795	−0.235265
$778$	−4.61219	−0.165355
$779$	−28.9324	−1.03661
$780$	−53.5100	−1.91596
$781$	6.41600	0.229582
$782$	−6.15426	−0.220076
$783$	15.4384	0.551722
$784$	−4.45205	−0.159002
$785$	−0.106161	−0.00378905
$786$	7.92020	0.282504
$787$	20.0996	0.716473	0.358237	−	0.933631i	$-0.383378\pi$
$787$	20.0996	0.716473	0.358237	+	0.933631i	$0.383378\pi$
$788$	22.1869	0.790375
$789$	68.3465	2.43320
$790$	50.5436	1.79826
$791$	−27.9604	−0.994159
$792$	−4.26145	−0.151424
$793$	−17.4099	−0.618243
$794$	−18.9016	−0.670791
$795$	9.40933	0.333715
$796$	−1.47716	−0.0523564
$797$	−13.8681	−0.491232	−0.245616	−	0.969367i	$-0.578990\pi$
$797$	−13.8681	−0.491232	−0.245616	+	0.969367i	$0.578990\pi$
$798$	17.4900	0.619138
$799$	0.0554931	0.00196321
$800$	5.87400	0.207677
$801$	98.8579	3.49297
$802$	−14.0922	−0.497611
$803$	−9.01976	−0.318300
$804$	9.85989	0.347731
$805$	−5.26368	−0.185520
$806$	−36.8533	−1.29810
$807$	−17.3440	−0.610538
$808$	−5.06984	−0.178356
$809$	2.26839	0.0797524	0.0398762	−	0.999205i	$-0.487304\pi$
$809$	2.26839	0.0797524	0.0398762	+	0.999205i	$0.487304\pi$
$810$	−90.3203	−3.17353
$811$	10.7716	0.378244	0.189122	−	0.981954i	$-0.439436\pi$
$811$	10.7716	0.378244	0.189122	+	0.981954i	$0.439436\pi$
$812$	1.59623	0.0560167
$813$	53.7587	1.88540
$814$	0.693129	0.0242941
$815$	−53.8935	−1.88781
$816$	−20.1462	−0.705260
$817$	31.8826	1.11543
$818$	−2.63865	−0.0922581
$819$	61.0541	2.13340
$820$	28.5039	0.995400
$821$	−37.6894	−1.31537	−0.657684	−	0.753294i	$-0.728464\pi$
$821$	−37.6894	−1.31537	−0.657684	+	0.753294i	$0.728464\pi$
$822$	−20.3113	−0.708439
$823$	13.0001	0.453155	0.226577	−	0.973993i	$-0.427246\pi$
$823$	13.0001	0.453155	0.226577	+	0.973993i	$0.427246\pi$
$824$	−1.24154	−0.0432510
$825$	−10.6197	−0.369730
$826$	8.26490	0.287573
$827$	36.7808	1.27899	0.639496	−	0.768794i	$-0.279143\pi$
$827$	36.7808	1.27899	0.639496	+	0.768794i	$0.279143\pi$
$828$	7.71610	0.268153
$829$	−5.81034	−0.201801	−0.100901	−	0.994897i	$-0.532172\pi$
$829$	−5.81034	−0.201801	−0.100901	+	0.994897i	$0.532172\pi$
$830$	−11.9065	−0.413280
$831$	−57.8640	−2.00728
$832$	4.95703	0.171854
$833$	27.3991	0.949322
$834$	−53.4167	−1.84967
$835$	−2.25316	−0.0779739
$836$	−1.84856	−0.0639339
$837$	−114.777	−3.96729
$838$	29.4474	1.01724
$839$	−7.13166	−0.246212	−0.123106	−	0.992394i	$-0.539286\pi$
$839$	−7.13166	−0.246212	−0.123106	+	0.992394i	$0.539286\pi$
$840$	−17.2309	−0.594523
$841$	1.00000	0.0344828
$842$	13.7508	0.473886
$843$	99.7813	3.43665
$844$	−27.7870	−0.956469
$845$	−38.1601	−1.31275
$846$	−0.0695763	−0.00239208
$847$	−17.0716	−0.586589
$848$	−0.871657	−0.0299328
$849$	−30.5310	−1.04782
$850$	−36.1501	−1.23994
$851$	−1.25503	−0.0430219
$852$	−38.0297	−1.30288
$853$	5.60453	0.191895	0.0959477	−	0.995386i	$-0.469412\pi$
$853$	5.60453	0.191895	0.0959477	+	0.995386i	$0.469412\pi$
$854$	−5.60621	−0.191841
$855$	−85.1662	−2.91262
$856$	−13.3065	−0.454806
$857$	−7.57654	−0.258810	−0.129405	−	0.991592i	$-0.541307\pi$
$857$	−7.57654	−0.258810	−0.129405	+	0.991592i	$0.541307\pi$
$858$	−8.96189	−0.305954
$859$	−48.9430	−1.66991	−0.834956	−	0.550316i	$-0.814507\pi$
$859$	−48.9430	−1.66991	−0.834956	+	0.550316i	$0.814507\pi$
$860$	−31.4103	−1.07108
$861$	−45.1673	−1.53930
$862$	14.5369	0.495130
$863$	−33.9415	−1.15538	−0.577690	−	0.816256i	$-0.696046\pi$
$863$	−33.9415	−1.15538	−0.577690	+	0.816256i	$0.696046\pi$
$864$	15.4384	0.525224
$865$	56.7582	1.92984
$866$	−12.7243	−0.432390
$867$	68.3349	2.32077
$868$	−11.8673	−0.402801
$869$	8.46507	0.287158
$870$	−10.7948	−0.365977
$871$	14.9305	0.505902
$872$	−5.40597	−0.183069
$873$	26.2371	0.887992
$874$	3.34715	0.113219
$875$	−4.60044	−0.155523
$876$	53.4631	1.80635
$877$	56.3014	1.90116	0.950581	−	0.310477i	$-0.100489\pi$
$877$	56.3014	1.90116	0.950581	+	0.310477i	$0.100489\pi$
$878$	31.9579	1.07853
$879$	−61.6422	−2.07914
$880$	1.82118	0.0613921
$881$	−16.9990	−0.572710	−0.286355	−	0.958124i	$-0.592444\pi$
$881$	−16.9990	−0.572710	−0.286355	+	0.958124i	$0.592444\pi$
$882$	−34.3525	−1.15671
$883$	−28.6063	−0.962678	−0.481339	−	0.876534i	$-0.659849\pi$
$883$	−28.6063	−0.962678	−0.481339	+	0.876534i	$0.659849\pi$
$884$	−30.5069	−1.02606
$885$	−55.8928	−1.87881
$886$	0.992296	0.0333368
$887$	33.6503	1.12987	0.564934	−	0.825136i	$-0.308902\pi$
$887$	33.6503	1.12987	0.564934	+	0.825136i	$0.308902\pi$
$888$	−4.10840	−0.137869
$889$	−33.3226	−1.11760
$890$	−42.2482	−1.41616
$891$	−15.1269	−0.506770
$892$	13.9207	0.466099
$893$	−0.0301813	−0.00100998
$894$	21.7649	0.727929
$895$	12.0694	0.403434
$896$	1.59623	0.0533263
$897$	16.2271	0.541806
$898$	11.7431	0.391871
$899$	−7.43456	−0.247956
$900$	45.3243	1.51081
$901$	5.36440	0.178714
$902$	4.77386	0.158952
$903$	49.7728	1.65633
$904$	−17.5166	−0.582592
$905$	−32.9068	−1.09386
$906$	−25.0581	−0.832501
$907$	36.6732	1.21771	0.608857	−	0.793280i	$-0.291628\pi$
$907$	36.6732	1.21771	0.608857	+	0.793280i	$0.291628\pi$
$908$	12.1810	0.404241
$909$	−39.1194	−1.29751
$910$	−26.0922	−0.864950
$911$	−37.8826	−1.25511	−0.627553	−	0.778574i	$-0.715944\pi$
$911$	−37.8826	−1.25511	−0.627553	+	0.778574i	$0.715944\pi$
$912$	10.9570	0.362824
$913$	−1.99411	−0.0659953
$914$	−27.2244	−0.900505
$915$	37.9129	1.25336
$916$	3.05844	0.101054
$917$	3.86200	0.127535
$918$	−95.0117	−3.13585
$919$	−2.25943	−0.0745319	−0.0372659	−	0.999305i	$-0.511865\pi$
$919$	−2.25943	−0.0745319	−0.0372659	+	0.999305i	$0.511865\pi$
$920$	−3.29757	−0.108718
$921$	0.120032	0.00395519
$922$	−5.21010	−0.171586
$923$	−57.5872	−1.89551
$924$	−2.88585	−0.0949373
$925$	−7.37204	−0.242391
$926$	−22.5031	−0.739499
$927$	−9.57983	−0.314643
$928$	1.00000	0.0328266
$929$	1.33661	0.0438526	0.0219263	−	0.999760i	$-0.493020\pi$
$929$	1.33661	0.0438526	0.0219263	+	0.999760i	$0.493020\pi$
$930$	80.2542	2.63164
$931$	−14.9017	−0.488383
$932$	27.9095	0.914207
$933$	9.08559	0.297449
$934$	13.6048	0.445162
$935$	−11.2080	−0.366542
$936$	38.2490	1.25021
$937$	−22.4359	−0.732950	−0.366475	−	0.930428i	$-0.619435\pi$
$937$	−22.4359	−0.732950	−0.366475	+	0.930428i	$0.619435\pi$
$938$	4.80783	0.156981
$939$	85.4789	2.78950
$940$	0.0297343	0.000969827 0
$941$	5.94381	0.193763	0.0968813	−	0.995296i	$-0.469113\pi$
$941$	5.94381	0.193763	0.0968813	+	0.995296i	$0.469113\pi$
$942$	0.105387	0.00343371
$943$	−8.64391	−0.281484
$944$	5.17777	0.168522
$945$	−81.2627	−2.64348
$946$	−5.26063	−0.171038
$947$	−24.2576	−0.788267	−0.394134	−	0.919053i	$-0.628955\pi$
$947$	−24.2576	−0.788267	−0.394134	+	0.919053i	$0.628955\pi$
$948$	−50.1753	−1.62962
$949$	80.9575	2.62799
$950$	19.6611	0.637892
$951$	−43.9144	−1.42402
$952$	−9.82360	−0.318385
$953$	1.54227	0.0499591	0.0249795	−	0.999688i	$-0.492048\pi$
$953$	1.54227	0.0499591	0.0249795	+	0.999688i	$0.492048\pi$
$954$	−6.72580	−0.217756
$955$	85.5011	2.76675
$956$	13.4148	0.433867
$957$	−1.80791	−0.0584416
$958$	−23.5814	−0.761881
$959$	−9.90410	−0.319820
$960$	−10.7948	−0.348399
$961$	24.2726	0.782988
$962$	−6.22123	−0.200580
$963$	−102.674	−3.30863
$964$	1.46376	0.0471447
$965$	7.02830	0.226249
$966$	5.22533	0.168122
$967$	39.4228	1.26775	0.633876	−	0.773435i	$-0.281463\pi$
$967$	39.4228	1.26775	0.633876	+	0.773435i	$0.281463\pi$
$968$	−10.6950	−0.343750
$969$	−67.4325	−2.16624
$970$	−11.2128	−0.360020
$971$	−13.6854	−0.439185	−0.219593	−	0.975592i	$-0.570473\pi$
$971$	−13.6854	−0.439185	−0.219593	+	0.975592i	$0.570473\pi$
$972$	43.3470	1.39036
$973$	−26.0468	−0.835021
$974$	23.6863	0.758959
$975$	95.3177	3.05261
$976$	−3.51216	−0.112421
$977$	−49.8315	−1.59425	−0.797126	−	0.603813i	$-0.793647\pi$
$977$	−49.8315	−1.59425	−0.797126	+	0.603813i	$0.793647\pi$
$978$	53.5008	1.71077
$979$	−7.07576	−0.226142
$980$	14.6810	0.468967
$981$	−41.7130	−1.33179
$982$	19.9716	0.637320
$983$	−22.6672	−0.722970	−0.361485	−	0.932378i	$-0.617730\pi$
$983$	−22.6672	−0.722970	−0.361485	+	0.932378i	$0.617730\pi$
$984$	−28.2962	−0.902051
$985$	−73.1629	−2.33116
$986$	−6.15426	−0.195991
$987$	−0.0471169	−0.00149975
$988$	16.5919	0.527859
$989$	9.52529	0.302887
$990$	14.0524	0.446616
$991$	−49.2307	−1.56386	−0.781932	−	0.623364i	$-0.785766\pi$
$991$	−49.2307	−1.56386	−0.781932	+	0.623364i	$0.785766\pi$
$992$	−7.43456	−0.236047
$993$	37.5387	1.19125
$994$	−18.5438	−0.588175
$995$	4.87103	0.154422
$996$	11.8197	0.374522
$997$	30.6175	0.969665	0.484832	−	0.874607i	$-0.338881\pi$
$997$	30.6175	0.969665	0.484832	+	0.874607i	$0.338881\pi$
$998$	−34.0407	−1.07754
$999$	−19.3756	−0.613018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.10	✓	10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.27355 q^{3} +1.00000 q^{4} -3.29757 q^{5} +3.27355 q^{6} +1.59623 q^{7} +1.00000 q^{8} +7.71610 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.27355 q^{3} +1.00000 q^{4} -3.29757 q^{5} +3.27355 q^{6} +1.59623 q^{7} +1.00000 q^{8} +7.71610 q^{9} -3.29757 q^{10} -0.552280 q^{11} +3.27355 q^{12} +4.95703 q^{13} +1.59623 q^{14} -10.7948 q^{15} +1.00000 q^{16} -6.15426 q^{17} +7.71610 q^{18} +3.34715 q^{19} -3.29757 q^{20} +5.22533 q^{21} -0.552280 q^{22} +1.00000 q^{23} +3.27355 q^{24} +5.87400 q^{25} +4.95703 q^{26} +15.4384 q^{27} +1.59623 q^{28} +1.00000 q^{29} -10.7948 q^{30} -7.43456 q^{31} +1.00000 q^{32} -1.80791 q^{33} -6.15426 q^{34} -5.26368 q^{35} +7.71610 q^{36} -1.25503 q^{37} +3.34715 q^{38} +16.2271 q^{39} -3.29757 q^{40} -8.64391 q^{41} +5.22533 q^{42} +9.52529 q^{43} -0.552280 q^{44} -25.4444 q^{45} +1.00000 q^{46} -0.00901703 q^{47} +3.27355 q^{48} -4.45205 q^{49} +5.87400 q^{50} -20.1462 q^{51} +4.95703 q^{52} -0.871657 q^{53} +15.4384 q^{54} +1.82118 q^{55} +1.59623 q^{56} +10.9570 q^{57} +1.00000 q^{58} +5.17777 q^{59} -10.7948 q^{60} -3.51216 q^{61} -7.43456 q^{62} +12.3167 q^{63} +1.00000 q^{64} -16.3462 q^{65} -1.80791 q^{66} +3.01199 q^{67} -6.15426 q^{68} +3.27355 q^{69} -5.26368 q^{70} -11.6173 q^{71} +7.71610 q^{72} +16.3319 q^{73} -1.25503 q^{74} +19.2288 q^{75} +3.34715 q^{76} -0.881566 q^{77} +16.2271 q^{78} -15.3275 q^{79} -3.29757 q^{80} +27.3899 q^{81} -8.64391 q^{82} +3.61068 q^{83} +5.22533 q^{84} +20.2941 q^{85} +9.52529 q^{86} +3.27355 q^{87} -0.552280 q^{88} +12.8119 q^{89} -25.4444 q^{90} +7.91256 q^{91} +1.00000 q^{92} -24.3374 q^{93} -0.00901703 q^{94} -11.0375 q^{95} +3.27355 q^{96} +3.40031 q^{97} -4.45205 q^{98} -4.26145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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