LMFDB - Embedded newform 4334.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.16186$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +1.61035 q^{10} +1.00000 q^{11} -3.16186 q^{12} +0.481640 q^{13} -0.0905305 q^{14} +5.09170 q^{15} +1.00000 q^{16} +0.419983 q^{17} -6.99733 q^{18} -1.64931 q^{19} -1.61035 q^{20} -0.286244 q^{21} -1.00000 q^{22} +0.827258 q^{23} +3.16186 q^{24} -2.40677 q^{25} -0.481640 q^{26} -12.6390 q^{27} +0.0905305 q^{28} -0.561896 q^{29} -5.09170 q^{30} -8.42633 q^{31} -1.00000 q^{32} -3.16186 q^{33} -0.419983 q^{34} -0.145786 q^{35} +6.99733 q^{36} +1.21121 q^{37} +1.64931 q^{38} -1.52288 q^{39} +1.61035 q^{40} -7.62488 q^{41} +0.286244 q^{42} +7.99759 q^{43} +1.00000 q^{44} -11.2682 q^{45} -0.827258 q^{46} +12.0094 q^{47} -3.16186 q^{48} -6.99180 q^{49} +2.40677 q^{50} -1.32793 q^{51} +0.481640 q^{52} +1.16240 q^{53} +12.6390 q^{54} -1.61035 q^{55} -0.0905305 q^{56} +5.21489 q^{57} +0.561896 q^{58} +6.82384 q^{59} +5.09170 q^{60} -2.12051 q^{61} +8.42633 q^{62} +0.633472 q^{63} +1.00000 q^{64} -0.775610 q^{65} +3.16186 q^{66} +8.17063 q^{67} +0.419983 q^{68} -2.61567 q^{69} +0.145786 q^{70} +3.26805 q^{71} -6.99733 q^{72} -0.788272 q^{73} -1.21121 q^{74} +7.60986 q^{75} -1.64931 q^{76} +0.0905305 q^{77} +1.52288 q^{78} +11.1043 q^{79} -1.61035 q^{80} +18.9707 q^{81} +7.62488 q^{82} -7.46511 q^{83} -0.286244 q^{84} -0.676320 q^{85} -7.99759 q^{86} +1.77663 q^{87} -1.00000 q^{88} -8.38001 q^{89} +11.2682 q^{90} +0.0436031 q^{91} +0.827258 q^{92} +26.6428 q^{93} -12.0094 q^{94} +2.65597 q^{95} +3.16186 q^{96} +14.5344 q^{97} +6.99180 q^{98} +6.99733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * 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
$3$	−3.16186	−1.82550	−0.912749	−	0.408520i	$-0.866045\pi$
$3$	−3.16186	−1.82550	−0.912749	+	0.408520i	$0.866045\pi$
$4$	1.00000	0.500000
$5$	−1.61035	−0.720171	−0.360085	−	0.932919i	$-0.617252\pi$
$5$	−1.61035	−0.720171	−0.360085	+	0.932919i	$0.617252\pi$
$6$	3.16186	1.29082
$7$	0.0905305	0.0342173	0.0171087	−	0.999854i	$-0.494554\pi$
$7$	0.0905305	0.0342173	0.0171087	+	0.999854i	$0.494554\pi$
$8$	−1.00000	−0.353553
$9$	6.99733	2.33244
$10$	1.61035	0.509238
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.16186	−0.912749
$13$	0.481640	0.133583	0.0667915	−	0.997767i	$-0.478724\pi$
$13$	0.481640	0.133583	0.0667915	+	0.997767i	$0.478724\pi$
$14$	−0.0905305	−0.0241953
$15$	5.09170	1.31467
$16$	1.00000	0.250000
$17$	0.419983	0.101861	0.0509305	−	0.998702i	$-0.483781\pi$
$17$	0.419983	0.101861	0.0509305	+	0.998702i	$0.483781\pi$
$18$	−6.99733	−1.64929
$19$	−1.64931	−0.378379	−0.189189	−	0.981941i	$-0.560586\pi$
$19$	−1.64931	−0.378379	−0.189189	+	0.981941i	$0.560586\pi$
$20$	−1.61035	−0.360085
$21$	−0.286244	−0.0624637
$22$	−1.00000	−0.213201
$23$	0.827258	0.172495	0.0862476	−	0.996274i	$-0.472512\pi$
$23$	0.827258	0.172495	0.0862476	+	0.996274i	$0.472512\pi$
$24$	3.16186	0.645411
$25$	−2.40677	−0.481354
$26$	−0.481640	−0.0944574
$27$	−12.6390	−2.43238
$28$	0.0905305	0.0171087
$29$	−0.561896	−0.104341	−0.0521707	−	0.998638i	$-0.516614\pi$
$29$	−0.561896	−0.104341	−0.0521707	+	0.998638i	$0.516614\pi$
$30$	−5.09170	−0.929612
$31$	−8.42633	−1.51341	−0.756707	−	0.653754i	$-0.773193\pi$
$31$	−8.42633	−1.51341	−0.756707	+	0.653754i	$0.773193\pi$
$32$	−1.00000	−0.176777
$33$	−3.16186	−0.550408
$34$	−0.419983	−0.0720265
$35$	−0.145786	−0.0246423
$36$	6.99733	1.16622
$37$	1.21121	0.199121	0.0995605	−	0.995032i	$-0.468256\pi$
$37$	1.21121	0.199121	0.0995605	+	0.995032i	$0.468256\pi$
$38$	1.64931	0.267554
$39$	−1.52288	−0.243855
$40$	1.61035	0.254619
$41$	−7.62488	−1.19081	−0.595403	−	0.803427i	$-0.703008\pi$
$41$	−7.62488	−1.19081	−0.595403	+	0.803427i	$0.703008\pi$
$42$	0.286244	0.0441685
$43$	7.99759	1.21962	0.609811	−	0.792547i	$-0.291245\pi$
$43$	7.99759	1.21962	0.609811	+	0.792547i	$0.291245\pi$
$44$	1.00000	0.150756
$45$	−11.2682	−1.67976
$46$	−0.827258	−0.121972
$47$	12.0094	1.75175	0.875873	−	0.482542i	$-0.160286\pi$
$47$	12.0094	1.75175	0.875873	+	0.482542i	$0.160286\pi$
$48$	−3.16186	−0.456375
$49$	−6.99180	−0.998829
$50$	2.40677	0.340369
$51$	−1.32793	−0.185947
$52$	0.481640	0.0667915
$53$	1.16240	0.159667	0.0798337	−	0.996808i	$-0.474561\pi$
$53$	1.16240	0.159667	0.0798337	+	0.996808i	$0.474561\pi$
$54$	12.6390	1.71995
$55$	−1.61035	−0.217140
$56$	−0.0905305	−0.0120976
$57$	5.21489	0.690730
$58$	0.561896	0.0737805
$59$	6.82384	0.888389	0.444194	−	0.895930i	$-0.353490\pi$
$59$	6.82384	0.888389	0.444194	+	0.895930i	$0.353490\pi$
$60$	5.09170	0.657335
$61$	−2.12051	−0.271503	−0.135752	−	0.990743i	$-0.543345\pi$
$61$	−2.12051	−0.271503	−0.135752	+	0.990743i	$0.543345\pi$
$62$	8.42633	1.07015
$63$	0.633472	0.0798100
$64$	1.00000	0.125000
$65$	−0.775610	−0.0962025
$66$	3.16186	0.389198
$67$	8.17063	0.998201	0.499101	−	0.866544i	$-0.333664\pi$
$67$	8.17063	0.998201	0.499101	+	0.866544i	$0.333664\pi$
$68$	0.419983	0.0509305
$69$	−2.61567	−0.314890
$70$	0.145786	0.0174247
$71$	3.26805	0.387846	0.193923	−	0.981017i	$-0.437879\pi$
$71$	3.26805	0.387846	0.193923	+	0.981017i	$0.437879\pi$
$72$	−6.99733	−0.824644
$73$	−0.788272	−0.0922602	−0.0461301	−	0.998935i	$-0.514689\pi$
$73$	−0.788272	−0.0922602	−0.0461301	+	0.998935i	$0.514689\pi$
$74$	−1.21121	−0.140800
$75$	7.60986	0.878711
$76$	−1.64931	−0.189189
$77$	0.0905305	0.0103169
$78$	1.52288	0.172432
$79$	11.1043	1.24933	0.624665	−	0.780893i	$-0.285236\pi$
$79$	11.1043	1.24933	0.624665	+	0.780893i	$0.285236\pi$
$80$	−1.61035	−0.180043
$81$	18.9707	2.10785
$82$	7.62488	0.842027
$83$	−7.46511	−0.819403	−0.409701	−	0.912220i	$-0.634367\pi$
$83$	−7.46511	−0.819403	−0.409701	+	0.912220i	$0.634367\pi$
$84$	−0.286244	−0.0312318
$85$	−0.676320	−0.0733572
$86$	−7.99759	−0.862403
$87$	1.77663	0.190475
$88$	−1.00000	−0.106600
$89$	−8.38001	−0.888280	−0.444140	−	0.895958i	$-0.646491\pi$
$89$	−8.38001	−0.888280	−0.444140	+	0.895958i	$0.646491\pi$
$90$	11.2682	1.18777
$91$	0.0436031	0.00457085
$92$	0.827258	0.0862476
$93$	26.6428	2.76273
$94$	−12.0094	−1.23867
$95$	2.65597	0.272497
$96$	3.16186	0.322706
$97$	14.5344	1.47574	0.737872	−	0.674940i	$-0.235831\pi$
$97$	14.5344	1.47574	0.737872	+	0.674940i	$0.235831\pi$
$98$	6.99180	0.706279
$99$	6.99733	0.703259
$100$	−2.40677	−0.240677
$101$	−2.15350	−0.214282	−0.107141	−	0.994244i	$-0.534170\pi$
$101$	−2.15350	−0.214282	−0.107141	+	0.994244i	$0.534170\pi$
$102$	1.32793	0.131484
$103$	−14.1960	−1.39877	−0.699387	−	0.714743i	$-0.746544\pi$
$103$	−14.1960	−1.39877	−0.699387	+	0.714743i	$0.746544\pi$
$104$	−0.481640	−0.0472287
$105$	0.460954	0.0449845
$106$	−1.16240	−0.112902
$107$	14.9970	1.44982	0.724909	−	0.688845i	$-0.241882\pi$
$107$	14.9970	1.44982	0.724909	+	0.688845i	$0.241882\pi$
$108$	−12.6390	−1.21619
$109$	12.6556	1.21219	0.606095	−	0.795392i	$-0.292735\pi$
$109$	12.6556	1.21219	0.606095	+	0.795392i	$0.292735\pi$
$110$	1.61035	0.153541
$111$	−3.82966	−0.363495
$112$	0.0905305	0.00855433
$113$	−3.43974	−0.323583	−0.161792	−	0.986825i	$-0.551727\pi$
$113$	−3.43974	−0.323583	−0.161792	+	0.986825i	$0.551727\pi$
$114$	−5.21489	−0.488420
$115$	−1.33218	−0.124226
$116$	−0.561896	−0.0521707
$117$	3.37020	0.311575
$118$	−6.82384	−0.628186
$119$	0.0380213	0.00348541
$120$	−5.09170	−0.464806
$121$	1.00000	0.0909091
$122$	2.12051	0.191982
$123$	24.1088	2.17381
$124$	−8.42633	−0.756707
$125$	11.9275	1.06683
$126$	−0.633472	−0.0564342
$127$	−10.0677	−0.893364	−0.446682	−	0.894693i	$-0.647394\pi$
$127$	−10.0677	−0.893364	−0.446682	+	0.894693i	$0.647394\pi$
$128$	−1.00000	−0.0883883
$129$	−25.2872	−2.22642
$130$	0.775610	0.0680255
$131$	3.84049	0.335545	0.167773	−	0.985826i	$-0.446343\pi$
$131$	3.84049	0.335545	0.167773	+	0.985826i	$0.446343\pi$
$132$	−3.16186	−0.275204
$133$	−0.149313	−0.0129471
$134$	−8.17063	−0.705835
$135$	20.3532	1.75173
$136$	−0.419983	−0.0360133
$137$	−2.88628	−0.246591	−0.123296	−	0.992370i	$-0.539346\pi$
$137$	−2.88628	−0.246591	−0.123296	+	0.992370i	$0.539346\pi$
$138$	2.61567	0.222661
$139$	−10.3432	−0.877296	−0.438648	−	0.898659i	$-0.644543\pi$
$139$	−10.3432	−0.877296	−0.438648	+	0.898659i	$0.644543\pi$
$140$	−0.145786	−0.0123212
$141$	−37.9719	−3.19781
$142$	−3.26805	−0.274248
$143$	0.481640	0.0402768
$144$	6.99733	0.583111
$145$	0.904849	0.0751436
$146$	0.788272	0.0652378
$147$	22.1071	1.82336
$148$	1.21121	0.0995605
$149$	−10.9026	−0.893175	−0.446587	−	0.894740i	$-0.647361\pi$
$149$	−10.9026	−0.893175	−0.446587	+	0.894740i	$0.647361\pi$
$150$	−7.60986	−0.621343
$151$	1.16138	0.0945119	0.0472560	−	0.998883i	$-0.484952\pi$
$151$	1.16138	0.0945119	0.0472560	+	0.998883i	$0.484952\pi$
$152$	1.64931	0.133777
$153$	2.93876	0.237585
$154$	−0.0905305	−0.00729516
$155$	13.5693	1.08992
$156$	−1.52288	−0.121928
$157$	12.4185	0.991105	0.495553	−	0.868578i	$-0.334966\pi$
$157$	12.4185	0.991105	0.495553	+	0.868578i	$0.334966\pi$
$158$	−11.1043	−0.883409
$159$	−3.67533	−0.291473
$160$	1.61035	0.127309
$161$	0.0748921	0.00590232
$162$	−18.9707	−1.49048
$163$	−1.80088	−0.141056	−0.0705278	−	0.997510i	$-0.522468\pi$
$163$	−1.80088	−0.141056	−0.0705278	+	0.997510i	$0.522468\pi$
$164$	−7.62488	−0.595403
$165$	5.09170	0.396388
$166$	7.46511	0.579405
$167$	14.4726	1.11992	0.559962	−	0.828518i	$-0.310816\pi$
$167$	14.4726	1.11992	0.559962	+	0.828518i	$0.310816\pi$
$168$	0.286244	0.0220842
$169$	−12.7680	−0.982156
$170$	0.676320	0.0518714
$171$	−11.5408	−0.882547
$172$	7.99759	0.609811
$173$	16.6108	1.26289	0.631447	−	0.775419i	$-0.282461\pi$
$173$	16.6108	1.26289	0.631447	+	0.775419i	$0.282461\pi$
$174$	−1.77663	−0.134686
$175$	−0.217886	−0.0164706
$176$	1.00000	0.0753778
$177$	−21.5760	−1.62175
$178$	8.38001	0.628108
$179$	14.6241	1.09306	0.546529	−	0.837440i	$-0.315949\pi$
$179$	14.6241	1.09306	0.546529	+	0.837440i	$0.315949\pi$
$180$	−11.2682	−0.839879
$181$	−22.8349	−1.69731	−0.848653	−	0.528950i	$-0.822586\pi$
$181$	−22.8349	−1.69731	−0.848653	+	0.528950i	$0.822586\pi$
$182$	−0.0436031	−0.00323208
$183$	6.70475	0.495629
$184$	−0.827258	−0.0609862
$185$	−1.95047	−0.143401
$186$	−26.6428	−1.95355
$187$	0.419983	0.0307122
$188$	12.0094	0.875873
$189$	−1.14421	−0.0832294
$190$	−2.65597	−0.192685
$191$	20.0238	1.44887	0.724435	−	0.689343i	$-0.242101\pi$
$191$	20.0238	1.44887	0.724435	+	0.689343i	$0.242101\pi$
$192$	−3.16186	−0.228187
$193$	−12.5215	−0.901316	−0.450658	−	0.892697i	$-0.648811\pi$
$193$	−12.5215	−0.901316	−0.450658	+	0.892697i	$0.648811\pi$
$194$	−14.5344	−1.04351
$195$	2.45237	0.175618
$196$	−6.99180	−0.499415
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−6.99733	−0.497279
$199$	−6.27326	−0.444699	−0.222350	−	0.974967i	$-0.571373\pi$
$199$	−6.27326	−0.444699	−0.222350	+	0.974967i	$0.571373\pi$
$200$	2.40677	0.170184
$201$	−25.8344	−1.82222
$202$	2.15350	0.151520
$203$	−0.0508687	−0.00357028
$204$	−1.32793	−0.0929735
$205$	12.2787	0.857583
$206$	14.1960	0.989083
$207$	5.78860	0.402335
$208$	0.481640	0.0333957
$209$	−1.64931	−0.114085
$210$	−0.460954	−0.0318088
$211$	5.76182	0.396660	0.198330	−	0.980135i	$-0.436448\pi$
$211$	5.76182	0.396660	0.198330	+	0.980135i	$0.436448\pi$
$212$	1.16240	0.0798337
$213$	−10.3331	−0.708012
$214$	−14.9970	−1.02518
$215$	−12.8789	−0.878336
$216$	12.6390	0.859975
$217$	−0.762840	−0.0517850
$218$	−12.6556	−0.857148
$219$	2.49240	0.168421
$220$	−1.61035	−0.108570
$221$	0.202281	0.0136069
$222$	3.82966	0.257030
$223$	−6.56179	−0.439410	−0.219705	−	0.975566i	$-0.570509\pi$
$223$	−6.56179	−0.439410	−0.219705	+	0.975566i	$0.570509\pi$
$224$	−0.0905305	−0.00604882
$225$	−16.8410	−1.12273
$226$	3.43974	0.228808
$227$	23.2625	1.54399	0.771995	−	0.635629i	$-0.219259\pi$
$227$	23.2625	1.54399	0.771995	+	0.635629i	$0.219259\pi$
$228$	5.21489	0.345365
$229$	−26.6070	−1.75824	−0.879120	−	0.476600i	$-0.841869\pi$
$229$	−26.6070	−1.75824	−0.879120	+	0.476600i	$0.841869\pi$
$230$	1.33218	0.0878410
$231$	−0.286244	−0.0188335
$232$	0.561896	0.0368903
$233$	−3.84104	−0.251635	−0.125817	−	0.992053i	$-0.540155\pi$
$233$	−3.84104	−0.251635	−0.125817	+	0.992053i	$0.540155\pi$
$234$	−3.37020	−0.220317
$235$	−19.3393	−1.26156
$236$	6.82384	0.444194
$237$	−35.1101	−2.28065
$238$	−0.0380213	−0.00246456
$239$	−22.6659	−1.46613	−0.733067	−	0.680156i	$-0.761912\pi$
$239$	−22.6659	−1.46613	−0.733067	+	0.680156i	$0.761912\pi$
$240$	5.09170	0.328668
$241$	8.64726	0.557019	0.278510	−	0.960433i	$-0.410160\pi$
$241$	8.64726	0.557019	0.278510	+	0.960433i	$0.410160\pi$
$242$	−1.00000	−0.0642824
$243$	−22.0656	−1.41551
$244$	−2.12051	−0.135752
$245$	11.2593	0.719328
$246$	−24.1088	−1.53712
$247$	−0.794376	−0.0505449
$248$	8.42633	0.535073
$249$	23.6036	1.49582
$250$	−11.9275	−0.754361
$251$	9.71156	0.612988	0.306494	−	0.951873i	$-0.400844\pi$
$251$	9.71156	0.612988	0.306494	+	0.951873i	$0.400844\pi$
$252$	0.633472	0.0399050
$253$	0.827258	0.0520092
$254$	10.0677	0.631703
$255$	2.13843	0.133914
$256$	1.00000	0.0625000
$257$	7.38542	0.460690	0.230345	−	0.973109i	$-0.426015\pi$
$257$	7.38542	0.460690	0.230345	+	0.973109i	$0.426015\pi$
$258$	25.2872	1.57431
$259$	0.109651	0.00681339
$260$	−0.775610	−0.0481013
$261$	−3.93177	−0.243371
$262$	−3.84049	−0.237266
$263$	−7.42250	−0.457691	−0.228845	−	0.973463i	$-0.573495\pi$
$263$	−7.42250	−0.457691	−0.228845	+	0.973463i	$0.573495\pi$
$264$	3.16186	0.194599
$265$	−1.87187	−0.114988
$266$	0.149313	0.00915498
$267$	26.4964	1.62155
$268$	8.17063	0.499101
$269$	−20.6674	−1.26011	−0.630056	−	0.776550i	$-0.716968\pi$
$269$	−20.6674	−1.26011	−0.630056	+	0.776550i	$0.716968\pi$
$270$	−20.3532	−1.23866
$271$	−20.5331	−1.24730	−0.623649	−	0.781704i	$-0.714351\pi$
$271$	−20.5331	−1.24730	−0.623649	+	0.781704i	$0.714351\pi$
$272$	0.419983	0.0254652
$273$	−0.137867	−0.00834408
$274$	2.88628	0.174366
$275$	−2.40677	−0.145134
$276$	−2.61567	−0.157445
$277$	13.5361	0.813307	0.406653	−	0.913583i	$-0.366696\pi$
$277$	13.5361	0.813307	0.406653	+	0.913583i	$0.366696\pi$
$278$	10.3432	0.620342
$279$	−58.9619	−3.52995
$280$	0.145786	0.00871237
$281$	−9.89976	−0.590570	−0.295285	−	0.955409i	$-0.595415\pi$
$281$	−9.89976	−0.590570	−0.295285	+	0.955409i	$0.595415\pi$
$282$	37.9719	2.26119
$283$	1.91549	0.113864	0.0569320	−	0.998378i	$-0.481868\pi$
$283$	1.91549	0.113864	0.0569320	+	0.998378i	$0.481868\pi$
$284$	3.26805	0.193923
$285$	−8.39781	−0.497443
$286$	−0.481640	−0.0284800
$287$	−0.690284	−0.0407462
$288$	−6.99733	−0.412322
$289$	−16.8236	−0.989624
$290$	−0.904849	−0.0531346
$291$	−45.9557	−2.69397
$292$	−0.788272	−0.0461301
$293$	8.73898	0.510537	0.255268	−	0.966870i	$-0.417836\pi$
$293$	8.73898	0.510537	0.255268	+	0.966870i	$0.417836\pi$
$294$	−22.1071	−1.28931
$295$	−10.9888	−0.639791
$296$	−1.21121	−0.0703999
$297$	−12.6390	−0.733389
$298$	10.9026	0.631570
$299$	0.398441	0.0230424
$300$	7.60986	0.439356
$301$	0.724026	0.0417322
$302$	−1.16138	−0.0668300
$303$	6.80907	0.391171
$304$	−1.64931	−0.0945947
$305$	3.41476	0.195529
$306$	−2.93876	−0.167998
$307$	−29.4724	−1.68208	−0.841040	−	0.540972i	$-0.818056\pi$
$307$	−29.4724	−1.68208	−0.841040	+	0.540972i	$0.818056\pi$
$308$	0.0905305	0.00515846
$309$	44.8857	2.55346
$310$	−13.5693	−0.770687
$311$	15.7060	0.890607	0.445303	−	0.895380i	$-0.353096\pi$
$311$	15.7060	0.890607	0.445303	+	0.895380i	$0.353096\pi$
$312$	1.52288	0.0862159
$313$	−9.38008	−0.530194	−0.265097	−	0.964222i	$-0.585404\pi$
$313$	−9.38008	−0.530194	−0.265097	+	0.964222i	$0.585404\pi$
$314$	−12.4185	−0.700817
$315$	−1.02011	−0.0574768
$316$	11.1043	0.624665
$317$	0.406226	0.0228159	0.0114080	−	0.999935i	$-0.496369\pi$
$317$	0.406226	0.0228159	0.0114080	+	0.999935i	$0.496369\pi$
$318$	3.67533	0.206102
$319$	−0.561896	−0.0314601
$320$	−1.61035	−0.0900213
$321$	−47.4185	−2.64664
$322$	−0.0748921	−0.00417357
$323$	−0.692684	−0.0385420
$324$	18.9707	1.05393
$325$	−1.15920	−0.0643007
$326$	1.80088	0.0997414
$327$	−40.0153	−2.21285
$328$	7.62488	0.421013
$329$	1.08721	0.0599400
$330$	−5.09170	−0.280289
$331$	32.8525	1.80573	0.902867	−	0.429919i	$-0.141458\pi$
$331$	32.8525	1.80573	0.902867	+	0.429919i	$0.141458\pi$
$332$	−7.46511	−0.409701
$333$	8.47521	0.464439
$334$	−14.4726	−0.791906
$335$	−13.1576	−0.718875
$336$	−0.286244	−0.0156159
$337$	−1.57192	−0.0856279	−0.0428139	−	0.999083i	$-0.513632\pi$
$337$	−1.57192	−0.0856279	−0.0428139	+	0.999083i	$0.513632\pi$
$338$	12.7680	0.694489
$339$	10.8760	0.590701
$340$	−0.676320	−0.0366786
$341$	−8.42633	−0.456311
$342$	11.5408	0.624055
$343$	−1.26669	−0.0683946
$344$	−7.99759	−0.431201
$345$	4.21215	0.226774
$346$	−16.6108	−0.893001
$347$	−33.0672	−1.77514	−0.887571	−	0.460671i	$-0.847609\pi$
$347$	−33.0672	−1.77514	−0.887571	+	0.460671i	$0.847609\pi$
$348$	1.77663	0.0952376
$349$	−17.8947	−0.957879	−0.478939	−	0.877848i	$-0.658979\pi$
$349$	−17.8947	−0.957879	−0.478939	+	0.877848i	$0.658979\pi$
$350$	0.217886	0.0116465
$351$	−6.08745	−0.324924
$352$	−1.00000	−0.0533002
$353$	0.965407	0.0513834	0.0256917	−	0.999670i	$-0.491821\pi$
$353$	0.965407	0.0513834	0.0256917	+	0.999670i	$0.491821\pi$
$354$	21.5760	1.14675
$355$	−5.26270	−0.279315
$356$	−8.38001	−0.444140
$357$	−0.120218	−0.00636261
$358$	−14.6241	−0.772909
$359$	4.14233	0.218624	0.109312	−	0.994008i	$-0.465135\pi$
$359$	4.14233	0.218624	0.109312	+	0.994008i	$0.465135\pi$
$360$	11.2682	0.593884
$361$	−16.2798	−0.856830
$362$	22.8349	1.20018
$363$	−3.16186	−0.165954
$364$	0.0436031	0.00228543
$365$	1.26939	0.0664431
$366$	−6.70475	−0.350463
$367$	−34.2662	−1.78868	−0.894340	−	0.447388i	$-0.852354\pi$
$367$	−34.2662	−1.78868	−0.894340	+	0.447388i	$0.852354\pi$
$368$	0.827258	0.0431238
$369$	−53.3538	−2.77749
$370$	1.95047	0.101400
$371$	0.105232	0.00546339
$372$	26.6428	1.38137
$373$	−22.9046	−1.18596	−0.592979	−	0.805218i	$-0.702048\pi$
$373$	−22.9046	−1.18596	−0.592979	+	0.805218i	$0.702048\pi$
$374$	−0.419983	−0.0217168
$375$	−37.7130	−1.94749
$376$	−12.0094	−0.619336
$377$	−0.270632	−0.0139382
$378$	1.14421	0.0588521
$379$	0.208774	0.0107240	0.00536200	−	0.999986i	$-0.498293\pi$
$379$	0.208774	0.0107240	0.00536200	+	0.999986i	$0.498293\pi$
$380$	2.65597	0.136249
$381$	31.8326	1.63083
$382$	−20.0238	−1.02451
$383$	−24.4168	−1.24764	−0.623819	−	0.781569i	$-0.714420\pi$
$383$	−24.4168	−1.24764	−0.623819	+	0.781569i	$0.714420\pi$
$384$	3.16186	0.161353
$385$	−0.145786	−0.00742994
$386$	12.5215	0.637327
$387$	55.9618	2.84470
$388$	14.5344	0.737872
$389$	2.00470	0.101642	0.0508211	−	0.998708i	$-0.483816\pi$
$389$	2.00470	0.101642	0.0508211	+	0.998708i	$0.483816\pi$
$390$	−2.45237	−0.124180
$391$	0.347434	0.0175705
$392$	6.99180	0.353139
$393$	−12.1431	−0.612537
$394$	−1.00000	−0.0503793
$395$	−17.8818	−0.899730
$396$	6.99733	0.351629
$397$	4.97318	0.249597	0.124798	−	0.992182i	$-0.460172\pi$
$397$	4.97318	0.249597	0.124798	+	0.992182i	$0.460172\pi$
$398$	6.27326	0.314450
$399$	0.472107	0.0236349
$400$	−2.40677	−0.120339
$401$	−5.06123	−0.252746	−0.126373	−	0.991983i	$-0.540334\pi$
$401$	−5.06123	−0.252746	−0.126373	+	0.991983i	$0.540334\pi$
$402$	25.8344	1.28850
$403$	−4.05846	−0.202166
$404$	−2.15350	−0.107141
$405$	−30.5494	−1.51801
$406$	0.0508687	0.00252457
$407$	1.21121	0.0600372
$408$	1.32793	0.0657422
$409$	13.7553	0.680158	0.340079	−	0.940397i	$-0.389546\pi$
$409$	13.7553	0.680158	0.340079	+	0.940397i	$0.389546\pi$
$410$	−12.2787	−0.606403
$411$	9.12599	0.450152
$412$	−14.1960	−0.699387
$413$	0.617766	0.0303983
$414$	−5.78860	−0.284494
$415$	12.0215	0.590110
$416$	−0.481640	−0.0236144
$417$	32.7036	1.60150
$418$	1.64931	0.0806706
$419$	−1.85667	−0.0907042	−0.0453521	−	0.998971i	$-0.514441\pi$
$419$	−1.85667	−0.0907042	−0.0453521	+	0.998971i	$0.514441\pi$
$420$	0.460954	0.0224923
$421$	6.84016	0.333369	0.166684	−	0.986010i	$-0.446694\pi$
$421$	6.84016	0.333369	0.166684	+	0.986010i	$0.446694\pi$
$422$	−5.76182	−0.280481
$423$	84.0335	4.08585
$424$	−1.16240	−0.0564509
$425$	−1.01080	−0.0490312
$426$	10.3331	0.500640
$427$	−0.191971	−0.00929012
$428$	14.9970	0.724909
$429$	−1.52288	−0.0735252
$430$	12.8789	0.621077
$431$	−5.73620	−0.276303	−0.138152	−	0.990411i	$-0.544116\pi$
$431$	−5.73620	−0.276303	−0.138152	+	0.990411i	$0.544116\pi$
$432$	−12.6390	−0.608094
$433$	16.0484	0.771236	0.385618	−	0.922659i	$-0.373988\pi$
$433$	16.0484	0.771236	0.385618	+	0.922659i	$0.373988\pi$
$434$	0.762840	0.0366175
$435$	−2.86100	−0.137175
$436$	12.6556	0.606095
$437$	−1.36441	−0.0652685
$438$	−2.49240	−0.119092
$439$	−14.8135	−0.707012	−0.353506	−	0.935432i	$-0.615011\pi$
$439$	−14.8135	−0.707012	−0.353506	+	0.935432i	$0.615011\pi$
$440$	1.61035	0.0767705
$441$	−48.9240	−2.32971
$442$	−0.202281	−0.00962152
$443$	−15.7001	−0.745933	−0.372966	−	0.927845i	$-0.621659\pi$
$443$	−15.7001	−0.745933	−0.372966	+	0.927845i	$0.621659\pi$
$444$	−3.82966	−0.181748
$445$	13.4948	0.639713
$446$	6.56179	0.310710
$447$	34.4724	1.63049
$448$	0.0905305	0.00427717
$449$	12.0150	0.567021	0.283511	−	0.958969i	$-0.408501\pi$
$449$	12.0150	0.567021	0.283511	+	0.958969i	$0.408501\pi$
$450$	16.8410	0.793891
$451$	−7.62488	−0.359041
$452$	−3.43974	−0.161792
$453$	−3.67212	−0.172531
$454$	−23.2625	−1.09177
$455$	−0.0702163	−0.00329179
$456$	−5.21489	−0.244210
$457$	1.13638	0.0531574	0.0265787	−	0.999647i	$-0.491539\pi$
$457$	1.13638	0.0531574	0.0265787	+	0.999647i	$0.491539\pi$
$458$	26.6070	1.24326
$459$	−5.30817	−0.247764
$460$	−1.33218	−0.0621130
$461$	16.5049	0.768710	0.384355	−	0.923185i	$-0.374424\pi$
$461$	16.5049	0.768710	0.384355	+	0.923185i	$0.374424\pi$
$462$	0.286244	0.0133173
$463$	−37.7903	−1.75626	−0.878131	−	0.478420i	$-0.841210\pi$
$463$	−37.7903	−1.75626	−0.878131	+	0.478420i	$0.841210\pi$
$464$	−0.561896	−0.0260854
$465$	−42.9043	−1.98964
$466$	3.84104	0.177933
$467$	1.47313	0.0681685	0.0340843	−	0.999419i	$-0.489149\pi$
$467$	1.47313	0.0681685	0.0340843	+	0.999419i	$0.489149\pi$
$468$	3.37020	0.155787
$469$	0.739691	0.0341558
$470$	19.3393	0.892055
$471$	−39.2656	−1.80926
$472$	−6.82384	−0.314093
$473$	7.99759	0.367730
$474$	35.1101	1.61266
$475$	3.96952	0.182134
$476$	0.0380213	0.00174270
$477$	8.13367	0.372415
$478$	22.6659	1.03671
$479$	8.78124	0.401225	0.200612	−	0.979671i	$-0.435707\pi$
$479$	8.78124	0.401225	0.200612	+	0.979671i	$0.435707\pi$
$480$	−5.09170	−0.232403
$481$	0.583365	0.0265992
$482$	−8.64726	−0.393872
$483$	−0.236798	−0.0107747
$484$	1.00000	0.0454545
$485$	−23.4055	−1.06279
$486$	22.0656	1.00091
$487$	38.7747	1.75705	0.878525	−	0.477697i	$-0.158528\pi$
$487$	38.7747	1.75705	0.878525	+	0.477697i	$0.158528\pi$
$488$	2.12051	0.0959910
$489$	5.69412	0.257497
$490$	−11.2593	−0.508641
$491$	−12.6103	−0.569094	−0.284547	−	0.958662i	$-0.591843\pi$
$491$	−12.6103	−0.569094	−0.284547	+	0.958662i	$0.591843\pi$
$492$	24.1088	1.08691
$493$	−0.235987	−0.0106283
$494$	0.794376	0.0357407
$495$	−11.2682	−0.506466
$496$	−8.42633	−0.378353
$497$	0.295858	0.0132710
$498$	−23.6036	−1.05770
$499$	40.8293	1.82777	0.913885	−	0.405974i	$-0.133068\pi$
$499$	40.8293	1.82777	0.913885	+	0.405974i	$0.133068\pi$
$500$	11.9275	0.533414
$501$	−45.7603	−2.04442
$502$	−9.71156	−0.433448
$503$	0.743243	0.0331396	0.0165698	−	0.999863i	$-0.494725\pi$
$503$	0.743243	0.0331396	0.0165698	+	0.999863i	$0.494725\pi$
$504$	−0.633472	−0.0282171
$505$	3.46790	0.154319
$506$	−0.827258	−0.0367761
$507$	40.3707	1.79292
$508$	−10.0677	−0.446682
$509$	9.84334	0.436298	0.218149	−	0.975915i	$-0.429998\pi$
$509$	9.84334	0.436298	0.218149	+	0.975915i	$0.429998\pi$
$510$	−2.13843	−0.0946912
$511$	−0.0713627	−0.00315690
$512$	−1.00000	−0.0441942
$513$	20.8457	0.920359
$514$	−7.38542	−0.325757
$515$	22.8606	1.00736
$516$	−25.2872	−1.11321
$517$	12.0094	0.528171
$518$	−0.109651	−0.00481779
$519$	−52.5209	−2.30541
$520$	0.775610	0.0340127
$521$	3.77380	0.165333	0.0826667	−	0.996577i	$-0.473656\pi$
$521$	3.77380	0.165333	0.0826667	+	0.996577i	$0.473656\pi$
$522$	3.93177	0.172089
$523$	8.14264	0.356053	0.178026	−	0.984026i	$-0.443029\pi$
$523$	8.14264	0.356053	0.178026	+	0.984026i	$0.443029\pi$
$524$	3.84049	0.167773
$525$	0.688925	0.0300671
$526$	7.42250	0.323636
$527$	−3.53892	−0.154158
$528$	−3.16186	−0.137602
$529$	−22.3156	−0.970245
$530$	1.87187	0.0813086
$531$	47.7487	2.07212
$532$	−0.149313	−0.00647355
$533$	−3.67245	−0.159071
$534$	−26.4964	−1.14661
$535$	−24.1505	−1.04412
$536$	−8.17063	−0.352917
$537$	−46.2394	−1.99538
$538$	20.6674	0.891033
$539$	−6.99180	−0.301158
$540$	20.3532	0.875863
$541$	−31.8864	−1.37090	−0.685452	−	0.728118i	$-0.740395\pi$
$541$	−31.8864	−1.37090	−0.685452	+	0.728118i	$0.740395\pi$
$542$	20.5331	0.881973
$543$	72.2007	3.09843
$544$	−0.419983	−0.0180066
$545$	−20.3800	−0.872984
$546$	0.137867	0.00590016
$547$	−29.2911	−1.25240	−0.626198	−	0.779664i	$-0.715390\pi$
$547$	−29.2911	−1.25240	−0.626198	+	0.779664i	$0.715390\pi$
$548$	−2.88628	−0.123296
$549$	−14.8379	−0.633267
$550$	2.40677	0.102625
$551$	0.926743	0.0394806
$552$	2.61567	0.111330
$553$	1.00528	0.0427487
$554$	−13.5361	−0.575095
$555$	6.16709	0.261779
$556$	−10.3432	−0.438648
$557$	−18.4722	−0.782691	−0.391346	−	0.920244i	$-0.627990\pi$
$557$	−18.4722	−0.782691	−0.391346	+	0.920244i	$0.627990\pi$
$558$	58.9619	2.49605
$559$	3.85196	0.162921
$560$	−0.145786	−0.00616058
$561$	−1.32793	−0.0560651
$562$	9.89976	0.417596
$563$	−15.1463	−0.638338	−0.319169	−	0.947698i	$-0.603404\pi$
$563$	−15.1463	−0.638338	−0.319169	+	0.947698i	$0.603404\pi$
$564$	−37.9719	−1.59890
$565$	5.53918	0.233035
$566$	−1.91549	−0.0805140
$567$	1.71743	0.0721251
$568$	−3.26805	−0.137124
$569$	−39.5200	−1.65677	−0.828383	−	0.560162i	$-0.810739\pi$
$569$	−39.5200	−1.65677	−0.828383	+	0.560162i	$0.810739\pi$
$570$	8.39781	0.351745
$571$	−2.41783	−0.101183	−0.0505916	−	0.998719i	$-0.516111\pi$
$571$	−2.41783	−0.101183	−0.0505916	+	0.998719i	$0.516111\pi$
$572$	0.481640	0.0201384
$573$	−63.3123	−2.64491
$574$	0.690284	0.0288119
$575$	−1.99102	−0.0830313
$576$	6.99733	0.291556
$577$	−20.2179	−0.841683	−0.420841	−	0.907134i	$-0.638265\pi$
$577$	−20.2179	−0.841683	−0.420841	+	0.907134i	$0.638265\pi$
$578$	16.8236	0.699770
$579$	39.5911	1.64535
$580$	0.904849	0.0375718
$581$	−0.675821	−0.0280378
$582$	45.9557	1.90492
$583$	1.16240	0.0481415
$584$	0.788272	0.0326189
$585$	−5.42720	−0.224387
$586$	−8.73898	−0.361004
$587$	−37.3524	−1.54170	−0.770848	−	0.637019i	$-0.780167\pi$
$587$	−37.3524	−1.54170	−0.770848	+	0.637019i	$0.780167\pi$
$588$	22.1071	0.911681
$589$	13.8977	0.572643
$590$	10.9888	0.452401
$591$	−3.16186	−0.130061
$592$	1.21121	0.0497803
$593$	22.3854	0.919260	0.459630	−	0.888110i	$-0.347982\pi$
$593$	22.3854	0.919260	0.459630	+	0.888110i	$0.347982\pi$
$594$	12.6390	0.518584
$595$	−0.0612276	−0.00251009
$596$	−10.9026	−0.446587
$597$	19.8351	0.811798
$598$	−0.398441	−0.0162934
$599$	25.0022	1.02156	0.510781	−	0.859711i	$-0.329356\pi$
$599$	25.0022	1.02156	0.510781	+	0.859711i	$0.329356\pi$
$600$	−7.60986	−0.310671
$601$	−11.6416	−0.474869	−0.237435	−	0.971404i	$-0.576307\pi$
$601$	−11.6416	−0.474869	−0.237435	+	0.971404i	$0.576307\pi$
$602$	−0.724026	−0.0295091
$603$	57.1726	2.32825
$604$	1.16138	0.0472560
$605$	−1.61035	−0.0654701
$606$	−6.80907	−0.276599
$607$	16.5455	0.671561	0.335780	−	0.941940i	$-0.391000\pi$
$607$	16.5455	0.671561	0.335780	+	0.941940i	$0.391000\pi$
$608$	1.64931	0.0668885
$609$	0.160840	0.00651755
$610$	−3.41476	−0.138260
$611$	5.78419	0.234003
$612$	2.93876	0.118792
$613$	−39.2445	−1.58507	−0.792536	−	0.609825i	$-0.791240\pi$
$613$	−39.2445	−1.58507	−0.792536	+	0.609825i	$0.791240\pi$
$614$	29.4724	1.18941
$615$	−38.8236	−1.56552
$616$	−0.0905305	−0.00364758
$617$	4.59232	0.184880	0.0924400	−	0.995718i	$-0.470533\pi$
$617$	4.59232	0.184880	0.0924400	+	0.995718i	$0.470533\pi$
$618$	−44.8857	−1.80557
$619$	−16.0564	−0.645363	−0.322681	−	0.946508i	$-0.604584\pi$
$619$	−16.0564	−0.645363	−0.322681	+	0.946508i	$0.604584\pi$
$620$	13.5693	0.544958
$621$	−10.4557	−0.419573
$622$	−15.7060	−0.629754
$623$	−0.758647	−0.0303945
$624$	−1.52288	−0.0609639
$625$	−7.17360	−0.286944
$626$	9.38008	0.374903
$627$	5.21489	0.208263
$628$	12.4185	0.495553
$629$	0.508686	0.0202826
$630$	1.02011	0.0406423
$631$	−5.86225	−0.233372	−0.116686	−	0.993169i	$-0.537227\pi$
$631$	−5.86225	−0.233372	−0.116686	+	0.993169i	$0.537227\pi$
$632$	−11.1043	−0.441705
$633$	−18.2180	−0.724102
$634$	−0.406226	−0.0161333
$635$	16.2125	0.643374
$636$	−3.67533	−0.145736
$637$	−3.36753	−0.133427
$638$	0.561896	0.0222457
$639$	22.8676	0.904629
$640$	1.61035	0.0636547
$641$	19.5228	0.771103	0.385551	−	0.922686i	$-0.374011\pi$
$641$	19.5228	0.771103	0.385551	+	0.922686i	$0.374011\pi$
$642$	47.4185	1.87146
$643$	0.210958	0.00831936	0.00415968	−	0.999991i	$-0.498676\pi$
$643$	0.210958	0.00831936	0.00415968	+	0.999991i	$0.498676\pi$
$644$	0.0748921	0.00295116
$645$	40.7213	1.60340
$646$	0.692684	0.0272533
$647$	2.15038	0.0845402	0.0422701	−	0.999106i	$-0.486541\pi$
$647$	2.15038	0.0845402	0.0422701	+	0.999106i	$0.486541\pi$
$648$	−18.9707	−0.745239
$649$	6.82384	0.267859
$650$	1.15920	0.0454675
$651$	2.41199	0.0945334
$652$	−1.80088	−0.0705278
$653$	13.3050	0.520664	0.260332	−	0.965519i	$-0.416168\pi$
$653$	13.3050	0.520664	0.260332	+	0.965519i	$0.416168\pi$
$654$	40.0153	1.56472
$655$	−6.18453	−0.241650
$656$	−7.62488	−0.297701
$657$	−5.51580	−0.215192
$658$	−1.08721	−0.0423840
$659$	6.26635	0.244102	0.122051	−	0.992524i	$-0.461053\pi$
$659$	6.26635	0.244102	0.122051	+	0.992524i	$0.461053\pi$
$660$	5.09170	0.198194
$661$	−26.6034	−1.03475	−0.517376	−	0.855758i	$-0.673091\pi$
$661$	−26.6034	−1.03475	−0.517376	+	0.855758i	$0.673091\pi$
$662$	−32.8525	−1.27685
$663$	−0.639583	−0.0248393
$664$	7.46511	0.289703
$665$	0.240447	0.00932412
$666$	−8.47521	−0.328408
$667$	−0.464833	−0.0179984
$668$	14.4726	0.559962
$669$	20.7474	0.802142
$670$	13.1576	0.508322
$671$	−2.12051	−0.0818614
$672$	0.286244	0.0110421
$673$	16.9958	0.655139	0.327570	−	0.944827i	$-0.393770\pi$
$673$	16.9958	0.655139	0.327570	+	0.944827i	$0.393770\pi$
$674$	1.57192	0.0605481
$675$	30.4192	1.17083
$676$	−12.7680	−0.491078
$677$	8.01111	0.307892	0.153946	−	0.988079i	$-0.450802\pi$
$677$	8.01111	0.307892	0.153946	+	0.988079i	$0.450802\pi$
$678$	−10.8760	−0.417689
$679$	1.31581	0.0504960
$680$	0.676320	0.0259357
$681$	−73.5528	−2.81855
$682$	8.42633	0.322661
$683$	39.8758	1.52581	0.762903	−	0.646513i	$-0.223773\pi$
$683$	39.8758	1.52581	0.762903	+	0.646513i	$0.223773\pi$
$684$	−11.5408	−0.441274
$685$	4.64792	0.177588
$686$	1.26669	0.0483623
$687$	84.1275	3.20967
$688$	7.99759	0.304905
$689$	0.559857	0.0213288
$690$	−4.21215	−0.160354
$691$	−27.8331	−1.05882	−0.529411	−	0.848366i	$-0.677587\pi$
$691$	−27.8331	−1.05882	−0.529411	+	0.848366i	$0.677587\pi$
$692$	16.6108	0.631447
$693$	0.633472	0.0240636
$694$	33.0672	1.25521
$695$	16.6561	0.631803
$696$	−1.77663	−0.0673431
$697$	−3.20232	−0.121297
$698$	17.8947	0.677323
$699$	12.1448	0.459359
$700$	−0.217886	−0.00823532
$701$	−5.61712	−0.212156	−0.106078	−	0.994358i	$-0.533829\pi$
$701$	−5.61712	−0.212156	−0.106078	+	0.994358i	$0.533829\pi$
$702$	6.08745	0.229756
$703$	−1.99766	−0.0753431
$704$	1.00000	0.0376889
$705$	61.1480	2.30297
$706$	−0.965407	−0.0363336
$707$	−0.194958	−0.00733214
$708$	−21.5760	−0.810876
$709$	−16.9164	−0.635308	−0.317654	−	0.948207i	$-0.602895\pi$
$709$	−16.9164	−0.635308	−0.317654	+	0.948207i	$0.602895\pi$
$710$	5.26270	0.197506
$711$	77.7004	2.91399
$712$	8.38001	0.314054
$713$	−6.97075	−0.261057
$714$	0.120218	0.00449904
$715$	−0.775610	−0.0290062
$716$	14.6241	0.546529
$717$	71.6663	2.67643
$718$	−4.14233	−0.154590
$719$	0.492657	0.0183730	0.00918650	−	0.999958i	$-0.497076\pi$
$719$	0.492657	0.0183730	0.00918650	+	0.999958i	$0.497076\pi$
$720$	−11.2682	−0.419940
$721$	−1.28517	−0.0478623
$722$	16.2798	0.605870
$723$	−27.3414	−1.01684
$724$	−22.8349	−0.848653
$725$	1.35235	0.0502252
$726$	3.16186	0.117347
$727$	−21.0884	−0.782125	−0.391062	−	0.920364i	$-0.627892\pi$
$727$	−21.0884	−0.782125	−0.391062	+	0.920364i	$0.627892\pi$
$728$	−0.0436031	−0.00161604
$729$	12.8561	0.476153
$730$	−1.26939	−0.0469824
$731$	3.35886	0.124232
$732$	6.70475	0.247815
$733$	24.5006	0.904951	0.452476	−	0.891777i	$-0.350541\pi$
$733$	24.5006	0.904951	0.452476	+	0.891777i	$0.350541\pi$
$734$	34.2662	1.26479
$735$	−35.6001	−1.31313
$736$	−0.827258	−0.0304931
$737$	8.17063	0.300969
$738$	53.3538	1.96398
$739$	3.13925	0.115479	0.0577397	−	0.998332i	$-0.481611\pi$
$739$	3.13925	0.115479	0.0577397	+	0.998332i	$0.481611\pi$
$740$	−1.95047	−0.0717006
$741$	2.51170	0.0922697
$742$	−0.105232	−0.00386320
$743$	24.7621	0.908434	0.454217	−	0.890891i	$-0.349919\pi$
$743$	24.7621	0.908434	0.454217	+	0.890891i	$0.349919\pi$
$744$	−26.6428	−0.976774
$745$	17.5570	0.643238
$746$	22.9046	0.838599
$747$	−52.2359	−1.91121
$748$	0.419983	0.0153561
$749$	1.35769	0.0496089
$750$	37.7130	1.37709
$751$	−42.8569	−1.56387	−0.781935	−	0.623360i	$-0.785767\pi$
$751$	−42.8569	−1.56387	−0.781935	+	0.623360i	$0.785767\pi$
$752$	12.0094	0.437936
$753$	−30.7066	−1.11901
$754$	0.270632	0.00985582
$755$	−1.87023	−0.0680647
$756$	−1.14421	−0.0416147
$757$	−12.8451	−0.466863	−0.233431	−	0.972373i	$-0.574995\pi$
$757$	−12.8451	−0.466863	−0.233431	+	0.972373i	$0.574995\pi$
$758$	−0.208774	−0.00758301
$759$	−2.61567	−0.0949428
$760$	−2.65597	−0.0963423
$761$	−41.1022	−1.48995	−0.744977	−	0.667090i	$-0.767540\pi$
$761$	−41.1022	−1.48995	−0.744977	+	0.667090i	$0.767540\pi$
$762$	−31.8326	−1.15317
$763$	1.14572	0.0414779
$764$	20.0238	0.724435
$765$	−4.73244	−0.171102
$766$	24.4168	0.882214
$767$	3.28664	0.118674
$768$	−3.16186	−0.114094
$769$	−14.1741	−0.511132	−0.255566	−	0.966792i	$-0.582262\pi$
$769$	−14.1741	−0.511132	−0.255566	+	0.966792i	$0.582262\pi$
$770$	0.145786	0.00525376
$771$	−23.3516	−0.840989
$772$	−12.5215	−0.450658
$773$	16.3094	0.586607	0.293304	−	0.956019i	$-0.405245\pi$
$773$	16.3094	0.586607	0.293304	+	0.956019i	$0.405245\pi$
$774$	−55.9618	−2.01151
$775$	20.2802	0.728488
$776$	−14.5344	−0.521755
$777$	−0.346701	−0.0124378
$778$	−2.00470	−0.0718719
$779$	12.5758	0.450575
$780$	2.45237	0.0878088
$781$	3.26805	0.116940
$782$	−0.347434	−0.0124242
$783$	7.10180	0.253798
$784$	−6.99180	−0.249707
$785$	−19.9982	−0.713765
$786$	12.1431	0.433129
$787$	−5.25108	−0.187181	−0.0935904	−	0.995611i	$-0.529834\pi$
$787$	−5.25108	−0.187181	−0.0935904	+	0.995611i	$0.529834\pi$
$788$	1.00000	0.0356235
$789$	23.4689	0.835514
$790$	17.8818	0.636205
$791$	−0.311401	−0.0110722
$792$	−6.99733	−0.248639
$793$	−1.02132	−0.0362682
$794$	−4.97318	−0.176492
$795$	5.91857	0.209910
$796$	−6.27326	−0.222350
$797$	41.2924	1.46265	0.731325	−	0.682029i	$-0.238902\pi$
$797$	41.2924	1.46265	0.731325	+	0.682029i	$0.238902\pi$
$798$	−0.472107	−0.0167124
$799$	5.04373	0.178434
$800$	2.40677	0.0850922
$801$	−58.6377	−2.07186
$802$	5.06123	0.178718
$803$	−0.788272	−0.0278175
$804$	−25.8344	−0.911108
$805$	−0.120602	−0.00425068
$806$	4.05846	0.142953
$807$	65.3472	2.30033
$808$	2.15350	0.0757600
$809$	−15.5840	−0.547903	−0.273952	−	0.961743i	$-0.588331\pi$
$809$	−15.5840	−0.547903	−0.273952	+	0.961743i	$0.588331\pi$
$810$	30.5494	1.07340
$811$	5.66060	0.198771	0.0993853	−	0.995049i	$-0.468312\pi$
$811$	5.66060	0.198771	0.0993853	+	0.995049i	$0.468312\pi$
$812$	−0.0508687	−0.00178514
$813$	64.9228	2.27694
$814$	−1.21121	−0.0424527
$815$	2.90004	0.101584
$816$	−1.32793	−0.0464867
$817$	−13.1905	−0.461479
$818$	−13.7553	−0.480944
$819$	0.305106	0.0106613
$820$	12.2787	0.428792
$821$	−39.8262	−1.38994	−0.694972	−	0.719037i	$-0.744583\pi$
$821$	−39.8262	−1.38994	−0.694972	+	0.719037i	$0.744583\pi$
$822$	−9.12599	−0.318305
$823$	−3.71062	−0.129344	−0.0646720	−	0.997907i	$-0.520600\pi$
$823$	−3.71062	−0.129344	−0.0646720	+	0.997907i	$0.520600\pi$
$824$	14.1960	0.494541
$825$	7.60986	0.264941
$826$	−0.617766	−0.0214948
$827$	3.26348	0.113482	0.0567411	−	0.998389i	$-0.481929\pi$
$827$	3.26348	0.113482	0.0567411	+	0.998389i	$0.481929\pi$
$828$	5.78860	0.201168
$829$	6.39376	0.222064	0.111032	−	0.993817i	$-0.464584\pi$
$829$	6.39376	0.222064	0.111032	+	0.993817i	$0.464584\pi$
$830$	−12.0215	−0.417271
$831$	−42.7993	−1.48469
$832$	0.481640	0.0166979
$833$	−2.93644	−0.101742
$834$	−32.7036	−1.13243
$835$	−23.3060	−0.806537
$836$	−1.64931	−0.0570427
$837$	106.500	3.68119
$838$	1.85667	0.0641375
$839$	11.5824	0.399869	0.199934	−	0.979809i	$-0.435927\pi$
$839$	11.5824	0.399869	0.199934	+	0.979809i	$0.435927\pi$
$840$	−0.460954	−0.0159044
$841$	−28.6843	−0.989113
$842$	−6.84016	−0.235727
$843$	31.3016	1.07808
$844$	5.76182	0.198330
$845$	20.5610	0.707320
$846$	−84.0335	−2.88913
$847$	0.0905305	0.00311067
$848$	1.16240	0.0399168
$849$	−6.05650	−0.207859
$850$	1.01080	0.0346703
$851$	1.00198	0.0343474
$852$	−10.3331	−0.354006
$853$	−11.7851	−0.403513	−0.201757	−	0.979436i	$-0.564665\pi$
$853$	−11.7851	−0.403513	−0.201757	+	0.979436i	$0.564665\pi$
$854$	0.191971	0.00656911
$855$	18.5847	0.635585
$856$	−14.9970	−0.512588
$857$	−20.3899	−0.696507	−0.348253	−	0.937400i	$-0.613225\pi$
$857$	−20.3899	−0.696507	−0.348253	+	0.937400i	$0.613225\pi$
$858$	1.52288	0.0519902
$859$	26.7342	0.912159	0.456079	−	0.889939i	$-0.349253\pi$
$859$	26.7342	0.912159	0.456079	+	0.889939i	$0.349253\pi$
$860$	−12.8789	−0.439168
$861$	2.18258	0.0743821
$862$	5.73620	0.195376
$863$	−50.8908	−1.73234	−0.866171	−	0.499748i	$-0.833426\pi$
$863$	−50.8908	−1.73234	−0.866171	+	0.499748i	$0.833426\pi$
$864$	12.6390	0.429987
$865$	−26.7492	−0.909500
$866$	−16.0484	−0.545346
$867$	53.1938	1.80656
$868$	−0.762840	−0.0258925
$869$	11.1043	0.376687
$870$	2.86100	0.0969971
$871$	3.93530	0.133343
$872$	−12.6556	−0.428574
$873$	101.702	3.44209
$874$	1.36441	0.0461518
$875$	1.07980	0.0365040
$876$	2.49240	0.0842105
$877$	2.08367	0.0703604	0.0351802	−	0.999381i	$-0.488799\pi$
$877$	2.08367	0.0703604	0.0351802	+	0.999381i	$0.488799\pi$
$878$	14.8135	0.499933
$879$	−27.6314	−0.931984
$880$	−1.61035	−0.0542849
$881$	−18.6018	−0.626712	−0.313356	−	0.949636i	$-0.601453\pi$
$881$	−18.6018	−0.626712	−0.313356	+	0.949636i	$0.601453\pi$
$882$	48.9240	1.64736
$883$	12.2050	0.410732	0.205366	−	0.978685i	$-0.434161\pi$
$883$	12.2050	0.410732	0.205366	+	0.978685i	$0.434161\pi$
$884$	0.202281	0.00680344
$885$	34.7449	1.16794
$886$	15.7001	0.527454
$887$	6.67456	0.224110	0.112055	−	0.993702i	$-0.464257\pi$
$887$	6.67456	0.224110	0.112055	+	0.993702i	$0.464257\pi$
$888$	3.82966	0.128515
$889$	−0.911434	−0.0305685
$890$	−13.4948	−0.452345
$891$	18.9707	0.635542
$892$	−6.56179	−0.219705
$893$	−19.8072	−0.662823
$894$	−34.4724	−1.15293
$895$	−23.5500	−0.787188
$896$	−0.0905305	−0.00302441
$897$	−1.25981	−0.0420639
$898$	−12.0150	−0.400945
$899$	4.73472	0.157912
$900$	−16.8410	−0.561366
$901$	0.488187	0.0162639
$902$	7.62488	0.253881
$903$	−2.28927	−0.0761820
$904$	3.43974	0.114404
$905$	36.7722	1.22235
$906$	3.67212	0.121998
$907$	2.05244	0.0681501	0.0340750	−	0.999419i	$-0.489151\pi$
$907$	2.05244	0.0681501	0.0340750	+	0.999419i	$0.489151\pi$
$908$	23.2625	0.771995
$909$	−15.0688	−0.499800
$910$	0.0702163	0.00232765
$911$	0.884430	0.0293025	0.0146512	−	0.999893i	$-0.495336\pi$
$911$	0.884430	0.0293025	0.0146512	+	0.999893i	$0.495336\pi$
$912$	5.21489	0.172682
$913$	−7.46511	−0.247059
$914$	−1.13638	−0.0375880
$915$	−10.7970	−0.356938
$916$	−26.6070	−0.879120
$917$	0.347681	0.0114815
$918$	5.30817	0.175196
$919$	48.9391	1.61435	0.807176	−	0.590311i	$-0.200995\pi$
$919$	48.9391	1.61435	0.807176	+	0.590311i	$0.200995\pi$
$920$	1.33218	0.0439205
$921$	93.1876	3.07064
$922$	−16.5049	−0.543560
$923$	1.57402	0.0518096
$924$	−0.286244	−0.00941675
$925$	−2.91509	−0.0958477
$926$	37.7903	1.24186
$927$	−99.3342	−3.26256
$928$	0.561896	0.0184451
$929$	−13.6229	−0.446954	−0.223477	−	0.974709i	$-0.571741\pi$
$929$	−13.6229	−0.446954	−0.223477	+	0.974709i	$0.571741\pi$
$930$	42.9043	1.40689
$931$	11.5317	0.377936
$932$	−3.84104	−0.125817
$933$	−49.6602	−1.62580
$934$	−1.47313	−0.0482024
$935$	−0.676320	−0.0221180
$936$	−3.37020	−0.110158
$937$	−18.8355	−0.615327	−0.307664	−	0.951495i	$-0.599547\pi$
$937$	−18.8355	−0.615327	−0.307664	+	0.951495i	$0.599547\pi$
$938$	−0.739691	−0.0241518
$939$	29.6585	0.967868
$940$	−19.3393	−0.630778
$941$	−56.7175	−1.84894	−0.924469	−	0.381257i	$-0.875491\pi$
$941$	−56.7175	−1.84894	−0.924469	+	0.381257i	$0.875491\pi$
$942$	39.2656	1.27934
$943$	−6.30774	−0.205408
$944$	6.82384	0.222097
$945$	1.84259	0.0599394
$946$	−7.99759	−0.260024
$947$	30.7764	1.00010	0.500049	−	0.865997i	$-0.333315\pi$
$947$	30.7764	1.00010	0.500049	+	0.865997i	$0.333315\pi$
$948$	−35.1101	−1.14032
$949$	−0.379663	−0.0123244
$950$	−3.96952	−0.128788
$951$	−1.28443	−0.0416505
$952$	−0.0380213	−0.00123228
$953$	−32.8697	−1.06475	−0.532377	−	0.846507i	$-0.678701\pi$
$953$	−32.8697	−1.06475	−0.532377	+	0.846507i	$0.678701\pi$
$954$	−8.13367	−0.263337
$955$	−32.2453	−1.04343
$956$	−22.6659	−0.733067
$957$	1.77663	0.0574304
$958$	−8.78124	−0.283709
$959$	−0.261296	−0.00843769
$960$	5.09170	0.164334
$961$	40.0031	1.29042
$962$	−0.583365	−0.0188085
$963$	104.939	3.38162
$964$	8.64726	0.278510
$965$	20.1640	0.649102
$966$	0.236798	0.00761885
$967$	15.2791	0.491341	0.245671	−	0.969353i	$-0.420992\pi$
$967$	15.2791	0.491341	0.245671	+	0.969353i	$0.420992\pi$
$968$	−1.00000	−0.0321412
$969$	2.19017	0.0703583
$970$	23.4055	0.751505
$971$	−35.4425	−1.13741	−0.568703	−	0.822543i	$-0.692555\pi$
$971$	−35.4425	−1.13741	−0.568703	+	0.822543i	$0.692555\pi$
$972$	−22.0656	−0.707754
$973$	−0.936372	−0.0300187
$974$	−38.7747	−1.24242
$975$	3.66522	0.117381
$976$	−2.12051	−0.0678759
$977$	−54.1371	−1.73200	−0.866000	−	0.500043i	$-0.833317\pi$
$977$	−54.1371	−1.73200	−0.866000	+	0.500043i	$0.833317\pi$
$978$	−5.69412	−0.182078
$979$	−8.38001	−0.267826
$980$	11.2593	0.359664
$981$	88.5557	2.82737
$982$	12.6103	0.402410
$983$	5.14061	0.163960	0.0819800	−	0.996634i	$-0.473876\pi$
$983$	5.14061	0.163960	0.0819800	+	0.996634i	$0.473876\pi$
$984$	−24.1088	−0.768559
$985$	−1.61035	−0.0513100
$986$	0.235987	0.00751535
$987$	−3.43761	−0.109420
$988$	−0.794376	−0.0252725
$989$	6.61607	0.210379
$990$	11.2682	0.358126
$991$	49.4147	1.56971	0.784855	−	0.619679i	$-0.212737\pi$
$991$	49.4147	1.56971	0.784855	+	0.619679i	$0.212737\pi$
$992$	8.42633	0.267536
$993$	−103.875	−3.29637
$994$	−0.295858	−0.00938405
$995$	10.1021	0.320259
$996$	23.6036	0.747909
$997$	60.0884	1.90302	0.951509	−	0.307621i	$-0.0995328\pi$
$997$	60.0884	1.90302	0.951509	+	0.307621i	$0.0995328\pi$
$998$	−40.8293	−1.29243
$999$	−15.3084	−0.484337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.1	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.1	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.16186 q^{3} +1.00000 q^{4} -1.61035 q^{5} +3.16186 q^{6} +0.0905305 q^{7} -1.00000 q^{8} +6.99733 q^{9} +1.61035 q^{10} +1.00000 q^{11} -3.16186 q^{12} +0.481640 q^{13} -0.0905305 q^{14} +5.09170 q^{15} +1.00000 q^{16} +0.419983 q^{17} -6.99733 q^{18} -1.64931 q^{19} -1.61035 q^{20} -0.286244 q^{21} -1.00000 q^{22} +0.827258 q^{23} +3.16186 q^{24} -2.40677 q^{25} -0.481640 q^{26} -12.6390 q^{27} +0.0905305 q^{28} -0.561896 q^{29} -5.09170 q^{30} -8.42633 q^{31} -1.00000 q^{32} -3.16186 q^{33} -0.419983 q^{34} -0.145786 q^{35} +6.99733 q^{36} +1.21121 q^{37} +1.64931 q^{38} -1.52288 q^{39} +1.61035 q^{40} -7.62488 q^{41} +0.286244 q^{42} +7.99759 q^{43} +1.00000 q^{44} -11.2682 q^{45} -0.827258 q^{46} +12.0094 q^{47} -3.16186 q^{48} -6.99180 q^{49} +2.40677 q^{50} -1.32793 q^{51} +0.481640 q^{52} +1.16240 q^{53} +12.6390 q^{54} -1.61035 q^{55} -0.0905305 q^{56} +5.21489 q^{57} +0.561896 q^{58} +6.82384 q^{59} +5.09170 q^{60} -2.12051 q^{61} +8.42633 q^{62} +0.633472 q^{63} +1.00000 q^{64} -0.775610 q^{65} +3.16186 q^{66} +8.17063 q^{67} +0.419983 q^{68} -2.61567 q^{69} +0.145786 q^{70} +3.26805 q^{71} -6.99733 q^{72} -0.788272 q^{73} -1.21121 q^{74} +7.60986 q^{75} -1.64931 q^{76} +0.0905305 q^{77} +1.52288 q^{78} +11.1043 q^{79} -1.61035 q^{80} +18.9707 q^{81} +7.62488 q^{82} -7.46511 q^{83} -0.286244 q^{84} -0.676320 q^{85} -7.99759 q^{86} +1.77663 q^{87} -1.00000 q^{88} -8.38001 q^{89} +11.2682 q^{90} +0.0436031 q^{91} +0.827258 q^{92} +26.6428 q^{93} -12.0094 q^{94} +2.65597 q^{95} +3.16186 q^{96} +14.5344 q^{97} +6.99180 q^{98} +6.99733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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