LMFDB - Embedded newform 8030.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.97446$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.97446 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.97446 q^{6} -1.89665 q^{7} -1.00000 q^{8} +5.84742 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.97446 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.97446 q^{6} -1.89665 q^{7} -1.00000 q^{8} +5.84742 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.97446 q^{12} -4.17223 q^{13} +1.89665 q^{14} -2.97446 q^{15} +1.00000 q^{16} +0.0330508 q^{17} -5.84742 q^{18} +1.87979 q^{19} +1.00000 q^{20} +5.64152 q^{21} -1.00000 q^{22} -3.17871 q^{23} +2.97446 q^{24} +1.00000 q^{25} +4.17223 q^{26} -8.46956 q^{27} -1.89665 q^{28} +4.44413 q^{29} +2.97446 q^{30} -1.09936 q^{31} -1.00000 q^{32} -2.97446 q^{33} -0.0330508 q^{34} -1.89665 q^{35} +5.84742 q^{36} -2.75775 q^{37} -1.87979 q^{38} +12.4101 q^{39} -1.00000 q^{40} -4.75840 q^{41} -5.64152 q^{42} +8.12442 q^{43} +1.00000 q^{44} +5.84742 q^{45} +3.17871 q^{46} +11.0837 q^{47} -2.97446 q^{48} -3.40270 q^{49} -1.00000 q^{50} -0.0983083 q^{51} -4.17223 q^{52} -9.27441 q^{53} +8.46956 q^{54} +1.00000 q^{55} +1.89665 q^{56} -5.59137 q^{57} -4.44413 q^{58} -7.08133 q^{59} -2.97446 q^{60} -1.29279 q^{61} +1.09936 q^{62} -11.0905 q^{63} +1.00000 q^{64} -4.17223 q^{65} +2.97446 q^{66} +8.20114 q^{67} +0.0330508 q^{68} +9.45495 q^{69} +1.89665 q^{70} +9.05660 q^{71} -5.84742 q^{72} -1.00000 q^{73} +2.75775 q^{74} -2.97446 q^{75} +1.87979 q^{76} -1.89665 q^{77} -12.4101 q^{78} +10.9750 q^{79} +1.00000 q^{80} +7.65010 q^{81} +4.75840 q^{82} -11.4410 q^{83} +5.64152 q^{84} +0.0330508 q^{85} -8.12442 q^{86} -13.2189 q^{87} -1.00000 q^{88} +7.96754 q^{89} -5.84742 q^{90} +7.91327 q^{91} -3.17871 q^{92} +3.27000 q^{93} -11.0837 q^{94} +1.87979 q^{95} +2.97446 q^{96} -18.1500 q^{97} +3.40270 q^{98} +5.84742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * 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
$3$	−2.97446	−1.71731	−0.858653	−	0.512557i	$-0.828698\pi$
$3$	−2.97446	−1.71731	−0.858653	+	0.512557i	$0.828698\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.97446	1.21432
$7$	−1.89665	−0.716868	−0.358434	−	0.933555i	$-0.616689\pi$
$7$	−1.89665	−0.716868	−0.358434	+	0.933555i	$0.616689\pi$
$8$	−1.00000	−0.353553
$9$	5.84742	1.94914
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.97446	−0.858653
$13$	−4.17223	−1.15717	−0.578584	−	0.815623i	$-0.696395\pi$
$13$	−4.17223	−1.15717	−0.578584	+	0.815623i	$0.696395\pi$
$14$	1.89665	0.506902
$15$	−2.97446	−0.768003
$16$	1.00000	0.250000
$17$	0.0330508	0.00801599	0.00400800	−	0.999992i	$-0.498724\pi$
$17$	0.0330508	0.00801599	0.00400800	+	0.999992i	$0.498724\pi$
$18$	−5.84742	−1.37825
$19$	1.87979	0.431254	0.215627	−	0.976476i	$-0.430821\pi$
$19$	1.87979	0.431254	0.215627	+	0.976476i	$0.430821\pi$
$20$	1.00000	0.223607
$21$	5.64152	1.23108
$22$	−1.00000	−0.213201
$23$	−3.17871	−0.662807	−0.331404	−	0.943489i	$-0.607522\pi$
$23$	−3.17871	−0.662807	−0.331404	+	0.943489i	$0.607522\pi$
$24$	2.97446	0.607160
$25$	1.00000	0.200000
$26$	4.17223	0.818241
$27$	−8.46956	−1.62997
$28$	−1.89665	−0.358434
$29$	4.44413	0.825255	0.412627	−	0.910900i	$-0.364611\pi$
$29$	4.44413	0.825255	0.412627	+	0.910900i	$0.364611\pi$
$30$	2.97446	0.543060
$31$	−1.09936	−0.197451	−0.0987253	−	0.995115i	$-0.531477\pi$
$31$	−1.09936	−0.197451	−0.0987253	+	0.995115i	$0.531477\pi$
$32$	−1.00000	−0.176777
$33$	−2.97446	−0.517787
$34$	−0.0330508	−0.00566816
$35$	−1.89665	−0.320593
$36$	5.84742	0.974571
$37$	−2.75775	−0.453372	−0.226686	−	0.973968i	$-0.572789\pi$
$37$	−2.75775	−0.453372	−0.226686	+	0.973968i	$0.572789\pi$
$38$	−1.87979	−0.304942
$39$	12.4101	1.98721
$40$	−1.00000	−0.158114
$41$	−4.75840	−0.743138	−0.371569	−	0.928405i	$-0.621180\pi$
$41$	−4.75840	−0.743138	−0.371569	+	0.928405i	$0.621180\pi$
$42$	−5.64152	−0.870506
$43$	8.12442	1.23896	0.619482	−	0.785011i	$-0.287343\pi$
$43$	8.12442	1.23896	0.619482	+	0.785011i	$0.287343\pi$
$44$	1.00000	0.150756
$45$	5.84742	0.871683
$46$	3.17871	0.468675
$47$	11.0837	1.61672	0.808360	−	0.588688i	$-0.200355\pi$
$47$	11.0837	1.61672	0.808360	+	0.588688i	$0.200355\pi$
$48$	−2.97446	−0.429327
$49$	−3.40270	−0.486101
$50$	−1.00000	−0.141421
$51$	−0.0983083	−0.0137659
$52$	−4.17223	−0.578584
$53$	−9.27441	−1.27394	−0.636969	−	0.770889i	$-0.719812\pi$
$53$	−9.27441	−1.27394	−0.636969	+	0.770889i	$0.719812\pi$
$54$	8.46956	1.15256
$55$	1.00000	0.134840
$56$	1.89665	0.253451
$57$	−5.59137	−0.740595
$58$	−4.44413	−0.583543
$59$	−7.08133	−0.921911	−0.460956	−	0.887423i	$-0.652493\pi$
$59$	−7.08133	−0.921911	−0.460956	+	0.887423i	$0.652493\pi$
$60$	−2.97446	−0.384001
$61$	−1.29279	−0.165525	−0.0827623	−	0.996569i	$-0.526374\pi$
$61$	−1.29279	−0.165525	−0.0827623	+	0.996569i	$0.526374\pi$
$62$	1.09936	0.139619
$63$	−11.0905	−1.39728
$64$	1.00000	0.125000
$65$	−4.17223	−0.517501
$66$	2.97446	0.366131
$67$	8.20114	1.00193	0.500964	−	0.865468i	$-0.332979\pi$
$67$	8.20114	1.00193	0.500964	+	0.865468i	$0.332979\pi$
$68$	0.0330508	0.00400800
$69$	9.45495	1.13824
$70$	1.89665	0.226693
$71$	9.05660	1.07482	0.537410	−	0.843321i	$-0.319403\pi$
$71$	9.05660	1.07482	0.537410	+	0.843321i	$0.319403\pi$
$72$	−5.84742	−0.689126
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	2.75775	0.320582
$75$	−2.97446	−0.343461
$76$	1.87979	0.215627
$77$	−1.89665	−0.216144
$78$	−12.4101	−1.40517
$79$	10.9750	1.23478	0.617392	−	0.786655i	$-0.288189\pi$
$79$	10.9750	1.23478	0.617392	+	0.786655i	$0.288189\pi$
$80$	1.00000	0.111803
$81$	7.65010	0.850011
$82$	4.75840	0.525478
$83$	−11.4410	−1.25581	−0.627907	−	0.778288i	$-0.716088\pi$
$83$	−11.4410	−1.25581	−0.627907	+	0.778288i	$0.716088\pi$
$84$	5.64152	0.615541
$85$	0.0330508	0.00358486
$86$	−8.12442	−0.876079
$87$	−13.2189	−1.41722
$88$	−1.00000	−0.106600
$89$	7.96754	0.844557	0.422279	−	0.906466i	$-0.361230\pi$
$89$	7.96754	0.844557	0.422279	+	0.906466i	$0.361230\pi$
$90$	−5.84742	−0.616373
$91$	7.91327	0.829536
$92$	−3.17871	−0.331404
$93$	3.27000	0.339083
$94$	−11.0837	−1.14319
$95$	1.87979	0.192863
$96$	2.97446	0.303580
$97$	−18.1500	−1.84285	−0.921425	−	0.388556i	$-0.872974\pi$
$97$	−18.1500	−1.84285	−0.921425	+	0.388556i	$0.872974\pi$
$98$	3.40270	0.343725
$99$	5.84742	0.587688
$100$	1.00000	0.100000
$101$	5.42027	0.539337	0.269668	−	0.962953i	$-0.413086\pi$
$101$	5.42027	0.539337	0.269668	+	0.962953i	$0.413086\pi$
$102$	0.0983083	0.00973397
$103$	−2.59335	−0.255530	−0.127765	−	0.991804i	$-0.540780\pi$
$103$	−2.59335	−0.255530	−0.127765	+	0.991804i	$0.540780\pi$
$104$	4.17223	0.409121
$105$	5.64152	0.550556
$106$	9.27441	0.900810
$107$	13.0296	1.25961	0.629807	−	0.776752i	$-0.283134\pi$
$107$	13.0296	1.25961	0.629807	+	0.776752i	$0.283134\pi$
$108$	−8.46956	−0.814983
$109$	0.722833	0.0692348	0.0346174	−	0.999401i	$-0.488979\pi$
$109$	0.722833	0.0692348	0.0346174	+	0.999401i	$0.488979\pi$
$110$	−1.00000	−0.0953463
$111$	8.20283	0.778578
$112$	−1.89665	−0.179217
$113$	−11.9116	−1.12055	−0.560275	−	0.828307i	$-0.689304\pi$
$113$	−11.9116	−1.12055	−0.560275	+	0.828307i	$0.689304\pi$
$114$	5.59137	0.523680
$115$	−3.17871	−0.296416
$116$	4.44413	0.412627
$117$	−24.3968	−2.25548
$118$	7.08133	0.651890
$119$	−0.0626859	−0.00574641
$120$	2.97446	0.271530
$121$	1.00000	0.0909091
$122$	1.29279	0.117044
$123$	14.1537	1.27619
$124$	−1.09936	−0.0987253
$125$	1.00000	0.0894427
$126$	11.0905	0.988024
$127$	6.59772	0.585453	0.292726	−	0.956196i	$-0.405438\pi$
$127$	6.59772	0.585453	0.292726	+	0.956196i	$0.405438\pi$
$128$	−1.00000	−0.0883883
$129$	−24.1658	−2.12768
$130$	4.17223	0.365929
$131$	−22.5624	−1.97129	−0.985644	−	0.168835i	$-0.946000\pi$
$131$	−22.5624	−1.97129	−0.985644	+	0.168835i	$0.946000\pi$
$132$	−2.97446	−0.258894
$133$	−3.56531	−0.309152
$134$	−8.20114	−0.708471
$135$	−8.46956	−0.728943
$136$	−0.0330508	−0.00283408
$137$	8.62933	0.737253	0.368627	−	0.929578i	$-0.379828\pi$
$137$	8.62933	0.737253	0.368627	+	0.929578i	$0.379828\pi$
$138$	−9.45495	−0.804859
$139$	0.157471	0.0133565	0.00667826	−	0.999978i	$-0.497874\pi$
$139$	0.157471	0.0133565	0.00667826	+	0.999978i	$0.497874\pi$
$140$	−1.89665	−0.160297
$141$	−32.9680	−2.77640
$142$	−9.05660	−0.760013
$143$	−4.17223	−0.348899
$144$	5.84742	0.487285
$145$	4.44413	0.369065
$146$	1.00000	0.0827606
$147$	10.1212	0.834784
$148$	−2.75775	−0.226686
$149$	−13.9490	−1.14274	−0.571371	−	0.820692i	$-0.693588\pi$
$149$	−13.9490	−1.14274	−0.571371	+	0.820692i	$0.693588\pi$
$150$	2.97446	0.242864
$151$	7.13342	0.580509	0.290255	−	0.956949i	$-0.406260\pi$
$151$	7.13342	0.580509	0.290255	+	0.956949i	$0.406260\pi$
$152$	−1.87979	−0.152471
$153$	0.193262	0.0156243
$154$	1.89665	0.152837
$155$	−1.09936	−0.0883026
$156$	12.4101	0.993606
$157$	−5.41286	−0.431993	−0.215997	−	0.976394i	$-0.569300\pi$
$157$	−5.41286	−0.431993	−0.215997	+	0.976394i	$0.569300\pi$
$158$	−10.9750	−0.873125
$159$	27.5864	2.18774
$160$	−1.00000	−0.0790569
$161$	6.02891	0.475145
$162$	−7.65010	−0.601048
$163$	24.2400	1.89862	0.949310	−	0.314341i	$-0.101784\pi$
$163$	24.2400	1.89862	0.949310	+	0.314341i	$0.101784\pi$
$164$	−4.75840	−0.371569
$165$	−2.97446	−0.231562
$166$	11.4410	0.887995
$167$	−4.67260	−0.361576	−0.180788	−	0.983522i	$-0.557865\pi$
$167$	−4.67260	−0.361576	−0.180788	+	0.983522i	$0.557865\pi$
$168$	−5.64152	−0.435253
$169$	4.40749	0.339038
$170$	−0.0330508	−0.00253488
$171$	10.9919	0.840575
$172$	8.12442	0.619482
$173$	16.2557	1.23590	0.617950	−	0.786217i	$-0.287963\pi$
$173$	16.2557	1.23590	0.617950	+	0.786217i	$0.287963\pi$
$174$	13.2189	1.00212
$175$	−1.89665	−0.143374
$176$	1.00000	0.0753778
$177$	21.0632	1.58320
$178$	−7.96754	−0.597192
$179$	18.6693	1.39541	0.697704	−	0.716386i	$-0.254205\pi$
$179$	18.6693	1.39541	0.697704	+	0.716386i	$0.254205\pi$
$180$	5.84742	0.435841
$181$	8.92959	0.663731	0.331866	−	0.943327i	$-0.392322\pi$
$181$	8.92959	0.663731	0.331866	+	0.943327i	$0.392322\pi$
$182$	−7.91327	−0.586571
$183$	3.84535	0.284256
$184$	3.17871	0.234338
$185$	−2.75775	−0.202754
$186$	−3.27000	−0.239768
$187$	0.0330508	0.00241691
$188$	11.0837	0.808360
$189$	16.0638	1.16847
$190$	−1.87979	−0.136374
$191$	−3.74327	−0.270854	−0.135427	−	0.990787i	$-0.543241\pi$
$191$	−3.74327	−0.270854	−0.135427	+	0.990787i	$0.543241\pi$
$192$	−2.97446	−0.214663
$193$	2.24199	0.161382	0.0806908	−	0.996739i	$-0.474287\pi$
$193$	2.24199	0.161382	0.0806908	+	0.996739i	$0.474287\pi$
$194$	18.1500	1.30309
$195$	12.4101	0.888708
$196$	−3.40270	−0.243050
$197$	6.27284	0.446922	0.223461	−	0.974713i	$-0.428265\pi$
$197$	6.27284	0.446922	0.223461	+	0.974713i	$0.428265\pi$
$198$	−5.84742	−0.415558
$199$	−6.22995	−0.441630	−0.220815	−	0.975316i	$-0.570872\pi$
$199$	−6.22995	−0.441630	−0.220815	+	0.975316i	$0.570872\pi$
$200$	−1.00000	−0.0707107
$201$	−24.3940	−1.72062
$202$	−5.42027	−0.381369
$203$	−8.42898	−0.591599
$204$	−0.0983083	−0.00688296
$205$	−4.75840	−0.332341
$206$	2.59335	0.180687
$207$	−18.5873	−1.29190
$208$	−4.17223	−0.289292
$209$	1.87979	0.130028
$210$	−5.64152	−0.389302
$211$	26.6630	1.83556	0.917778	−	0.397094i	$-0.129981\pi$
$211$	26.6630	1.83556	0.917778	+	0.397094i	$0.129981\pi$
$212$	−9.27441	−0.636969
$213$	−26.9385	−1.84580
$214$	−13.0296	−0.890682
$215$	8.12442	0.554081
$216$	8.46956	0.576280
$217$	2.08510	0.141546
$218$	−0.722833	−0.0489564
$219$	2.97446	0.200996
$220$	1.00000	0.0674200
$221$	−0.137895	−0.00927585
$222$	−8.20283	−0.550538
$223$	7.36354	0.493099	0.246549	−	0.969130i	$-0.420703\pi$
$223$	7.36354	0.493099	0.246549	+	0.969130i	$0.420703\pi$
$224$	1.89665	0.126726
$225$	5.84742	0.389828
$226$	11.9116	0.792348
$227$	−14.6243	−0.970651	−0.485325	−	0.874334i	$-0.661299\pi$
$227$	−14.6243	−0.970651	−0.485325	+	0.874334i	$0.661299\pi$
$228$	−5.59137	−0.370297
$229$	−0.797458	−0.0526975	−0.0263487	−	0.999653i	$-0.508388\pi$
$229$	−0.797458	−0.0526975	−0.0263487	+	0.999653i	$0.508388\pi$
$230$	3.17871	0.209598
$231$	5.64152	0.371185
$232$	−4.44413	−0.291772
$233$	−6.08566	−0.398685	−0.199342	−	0.979930i	$-0.563881\pi$
$233$	−6.08566	−0.398685	−0.199342	+	0.979930i	$0.563881\pi$
$234$	24.3968	1.59487
$235$	11.0837	0.723019
$236$	−7.08133	−0.460956
$237$	−32.6447	−2.12050
$238$	0.0626859	0.00406332
$239$	12.4954	0.808263	0.404131	−	0.914701i	$-0.367574\pi$
$239$	12.4954	0.808263	0.404131	+	0.914701i	$0.367574\pi$
$240$	−2.97446	−0.192001
$241$	−22.2543	−1.43353	−0.716764	−	0.697316i	$-0.754377\pi$
$241$	−22.2543	−1.43353	−0.716764	+	0.697316i	$0.754377\pi$
$242$	−1.00000	−0.0642824
$243$	2.65374	0.170237
$244$	−1.29279	−0.0827623
$245$	−3.40270	−0.217391
$246$	−14.1537	−0.902406
$247$	−7.84292	−0.499033
$248$	1.09936	0.0698094
$249$	34.0309	2.15662
$250$	−1.00000	−0.0632456
$251$	3.38862	0.213888	0.106944	−	0.994265i	$-0.465893\pi$
$251$	3.38862	0.213888	0.106944	+	0.994265i	$0.465893\pi$
$252$	−11.0905	−0.698638
$253$	−3.17871	−0.199844
$254$	−6.59772	−0.413978
$255$	−0.0983083	−0.00615631
$256$	1.00000	0.0625000
$257$	28.9767	1.80752	0.903760	−	0.428040i	$-0.140796\pi$
$257$	28.9767	1.80752	0.903760	+	0.428040i	$0.140796\pi$
$258$	24.1658	1.50450
$259$	5.23050	0.325007
$260$	−4.17223	−0.258751
$261$	25.9867	1.60854
$262$	22.5624	1.39391
$263$	−31.1258	−1.91930	−0.959649	−	0.281201i	$-0.909267\pi$
$263$	−31.1258	−1.91930	−0.959649	+	0.281201i	$0.909267\pi$
$264$	2.97446	0.183065
$265$	−9.27441	−0.569722
$266$	3.56531	0.218603
$267$	−23.6991	−1.45036
$268$	8.20114	0.500964
$269$	17.7535	1.08245	0.541226	−	0.840877i	$-0.317960\pi$
$269$	17.7535	1.08245	0.541226	+	0.840877i	$0.317960\pi$
$270$	8.46956	0.515441
$271$	10.3504	0.628740	0.314370	−	0.949301i	$-0.398207\pi$
$271$	10.3504	0.628740	0.314370	+	0.949301i	$0.398207\pi$
$272$	0.0330508	0.00200400
$273$	−23.5377	−1.42457
$274$	−8.62933	−0.521317
$275$	1.00000	0.0603023
$276$	9.45495	0.569121
$277$	−10.7718	−0.647214	−0.323607	−	0.946192i	$-0.604896\pi$
$277$	−10.7718	−0.647214	−0.323607	+	0.946192i	$0.604896\pi$
$278$	−0.157471	−0.00944449
$279$	−6.42842	−0.384859
$280$	1.89665	0.113347
$281$	17.2071	1.02649	0.513246	−	0.858242i	$-0.328443\pi$
$281$	17.2071	1.02649	0.513246	+	0.858242i	$0.328443\pi$
$282$	32.9680	1.96321
$283$	−10.8284	−0.643683	−0.321842	−	0.946794i	$-0.604302\pi$
$283$	−10.8284	−0.643683	−0.321842	+	0.946794i	$0.604302\pi$
$284$	9.05660	0.537410
$285$	−5.59137	−0.331204
$286$	4.17223	0.246709
$287$	9.02504	0.532731
$288$	−5.84742	−0.344563
$289$	−16.9989	−0.999936
$290$	−4.44413	−0.260968
$291$	53.9864	3.16474
$292$	−1.00000	−0.0585206
$293$	12.3509	0.721549	0.360775	−	0.932653i	$-0.382512\pi$
$293$	12.3509	0.721549	0.360775	+	0.932653i	$0.382512\pi$
$294$	−10.1212	−0.590281
$295$	−7.08133	−0.412291
$296$	2.75775	0.160291
$297$	−8.46956	−0.491453
$298$	13.9490	0.808041
$299$	13.2623	0.766979
$300$	−2.97446	−0.171731
$301$	−15.4092	−0.888173
$302$	−7.13342	−0.410482
$303$	−16.1224	−0.926207
$304$	1.87979	0.107813
$305$	−1.29279	−0.0740248
$306$	−0.193262	−0.0110481
$307$	27.7793	1.58545	0.792724	−	0.609580i	$-0.208662\pi$
$307$	27.7793	1.58545	0.792724	+	0.609580i	$0.208662\pi$
$308$	−1.89665	−0.108072
$309$	7.71381	0.438823
$310$	1.09936	0.0624394
$311$	−11.2557	−0.638254	−0.319127	−	0.947712i	$-0.603390\pi$
$311$	−11.2557	−0.638254	−0.319127	+	0.947712i	$0.603390\pi$
$312$	−12.4101	−0.702586
$313$	15.2325	0.860992	0.430496	−	0.902593i	$-0.358339\pi$
$313$	15.2325	0.860992	0.430496	+	0.902593i	$0.358339\pi$
$314$	5.41286	0.305465
$315$	−11.0905	−0.624881
$316$	10.9750	0.617392
$317$	7.92225	0.444958	0.222479	−	0.974938i	$-0.428585\pi$
$317$	7.92225	0.444958	0.222479	+	0.974938i	$0.428585\pi$
$318$	−27.5864	−1.54697
$319$	4.44413	0.248824
$320$	1.00000	0.0559017
$321$	−38.7559	−2.16314
$322$	−6.02891	−0.335978
$323$	0.0621286	0.00345693
$324$	7.65010	0.425005
$325$	−4.17223	−0.231434
$326$	−24.2400	−1.34253
$327$	−2.15004	−0.118897
$328$	4.75840	0.262739
$329$	−21.0219	−1.15897
$330$	2.97446	0.163739
$331$	−33.9280	−1.86485	−0.932427	−	0.361358i	$-0.882313\pi$
$331$	−33.9280	−1.86485	−0.932427	+	0.361358i	$0.882313\pi$
$332$	−11.4410	−0.627907
$333$	−16.1257	−0.883685
$334$	4.67260	0.255673
$335$	8.20114	0.448076
$336$	5.64152	0.307770
$337$	12.5914	0.685897	0.342948	−	0.939354i	$-0.388574\pi$
$337$	12.5914	0.685897	0.342948	+	0.939354i	$0.388574\pi$
$338$	−4.40749	−0.239736
$339$	35.4306	1.92433
$340$	0.0330508	0.00179243
$341$	−1.09936	−0.0595336
$342$	−10.9919	−0.594376
$343$	19.7303	1.06534
$344$	−8.12442	−0.438040
$345$	9.45495	0.509038
$346$	−16.2557	−0.873913
$347$	7.69359	0.413014	0.206507	−	0.978445i	$-0.433790\pi$
$347$	7.69359	0.413014	0.206507	+	0.978445i	$0.433790\pi$
$348$	−13.2189	−0.708608
$349$	−0.853212	−0.0456714	−0.0228357	−	0.999739i	$-0.507269\pi$
$349$	−0.853212	−0.0456714	−0.0228357	+	0.999739i	$0.507269\pi$
$350$	1.89665	0.101380
$351$	35.3369	1.88615
$352$	−1.00000	−0.0533002
$353$	−27.4086	−1.45882	−0.729408	−	0.684079i	$-0.760204\pi$
$353$	−27.4086	−1.45882	−0.729408	+	0.684079i	$0.760204\pi$
$354$	−21.0632	−1.11949
$355$	9.05660	0.480674
$356$	7.96754	0.422279
$357$	0.186457	0.00986834
$358$	−18.6693	−0.986702
$359$	9.00667	0.475354	0.237677	−	0.971344i	$-0.423614\pi$
$359$	9.00667	0.475354	0.237677	+	0.971344i	$0.423614\pi$
$360$	−5.84742	−0.308186
$361$	−15.4664	−0.814020
$362$	−8.92959	−0.469329
$363$	−2.97446	−0.156119
$364$	7.91327	0.414768
$365$	−1.00000	−0.0523424
$366$	−3.84535	−0.201000
$367$	−1.01137	−0.0527931	−0.0263965	−	0.999652i	$-0.508403\pi$
$367$	−1.01137	−0.0527931	−0.0263965	+	0.999652i	$0.508403\pi$
$368$	−3.17871	−0.165702
$369$	−27.8244	−1.44848
$370$	2.75775	0.143369
$371$	17.5903	0.913245
$372$	3.27000	0.169542
$373$	6.06209	0.313883	0.156942	−	0.987608i	$-0.449837\pi$
$373$	6.06209	0.313883	0.156942	+	0.987608i	$0.449837\pi$
$374$	−0.0330508	−0.00170902
$375$	−2.97446	−0.153601
$376$	−11.0837	−0.571597
$377$	−18.5419	−0.954959
$378$	−16.0638	−0.826233
$379$	18.6008	0.955457	0.477728	−	0.878508i	$-0.341460\pi$
$379$	18.6008	0.955457	0.477728	+	0.878508i	$0.341460\pi$
$380$	1.87979	0.0964313
$381$	−19.6247	−1.00540
$382$	3.74327	0.191523
$383$	−1.42422	−0.0727743	−0.0363872	−	0.999338i	$-0.511585\pi$
$383$	−1.42422	−0.0727743	−0.0363872	+	0.999338i	$0.511585\pi$
$384$	2.97446	0.151790
$385$	−1.89665	−0.0966624
$386$	−2.24199	−0.114114
$387$	47.5070	2.41491
$388$	−18.1500	−0.921425
$389$	−28.2708	−1.43339	−0.716693	−	0.697389i	$-0.754345\pi$
$389$	−28.2708	−1.43339	−0.716693	+	0.697389i	$0.754345\pi$
$390$	−12.4101	−0.628412
$391$	−0.105059	−0.00531306
$392$	3.40270	0.171863
$393$	67.1111	3.38531
$394$	−6.27284	−0.316021
$395$	10.9750	0.552212
$396$	5.84742	0.293844
$397$	−25.6892	−1.28930	−0.644651	−	0.764477i	$-0.722997\pi$
$397$	−25.6892	−1.28930	−0.644651	+	0.764477i	$0.722997\pi$
$398$	6.22995	0.312279
$399$	10.6049	0.530909
$400$	1.00000	0.0500000
$401$	3.54258	0.176908	0.0884540	−	0.996080i	$-0.471807\pi$
$401$	3.54258	0.176908	0.0884540	+	0.996080i	$0.471807\pi$
$402$	24.3940	1.21666
$403$	4.58678	0.228484
$404$	5.42027	0.269668
$405$	7.65010	0.380136
$406$	8.42898	0.418323
$407$	−2.75775	−0.136697
$408$	0.0983083	0.00486699
$409$	17.7481	0.877587	0.438794	−	0.898588i	$-0.355406\pi$
$409$	17.7481	0.877587	0.438794	+	0.898588i	$0.355406\pi$
$410$	4.75840	0.235001
$411$	−25.6676	−1.26609
$412$	−2.59335	−0.127765
$413$	13.4308	0.660888
$414$	18.5873	0.913515
$415$	−11.4410	−0.561618
$416$	4.17223	0.204560
$417$	−0.468392	−0.0229373
$418$	−1.87979	−0.0919436
$419$	−20.1484	−0.984315	−0.492158	−	0.870506i	$-0.663792\pi$
$419$	−20.1484	−0.984315	−0.492158	+	0.870506i	$0.663792\pi$
$420$	5.64152	0.275278
$421$	−23.1286	−1.12722	−0.563608	−	0.826042i	$-0.690587\pi$
$421$	−23.1286	−1.12722	−0.563608	+	0.826042i	$0.690587\pi$
$422$	−26.6630	−1.29793
$423$	64.8110	3.15122
$424$	9.27441	0.450405
$425$	0.0330508	0.00160320
$426$	26.9385	1.30518
$427$	2.45197	0.118659
$428$	13.0296	0.629807
$429$	12.4101	0.599167
$430$	−8.12442	−0.391795
$431$	−14.1995	−0.683967	−0.341983	−	0.939706i	$-0.611099\pi$
$431$	−14.1995	−0.683967	−0.341983	+	0.939706i	$0.611099\pi$
$432$	−8.46956	−0.407492
$433$	4.56076	0.219176	0.109588	−	0.993977i	$-0.465047\pi$
$433$	4.56076	0.219176	0.109588	+	0.993977i	$0.465047\pi$
$434$	−2.08510	−0.100088
$435$	−13.2189	−0.633798
$436$	0.722833	0.0346174
$437$	−5.97531	−0.285838
$438$	−2.97446	−0.142125
$439$	−27.0957	−1.29321	−0.646603	−	0.762826i	$-0.723811\pi$
$439$	−27.0957	−1.29321	−0.646603	+	0.762826i	$0.723811\pi$
$440$	−1.00000	−0.0476731
$441$	−19.8971	−0.947479
$442$	0.137895	0.00655902
$443$	5.03115	0.239037	0.119519	−	0.992832i	$-0.461865\pi$
$443$	5.03115	0.239037	0.119519	+	0.992832i	$0.461865\pi$
$444$	8.20283	0.389289
$445$	7.96754	0.377697
$446$	−7.36354	−0.348673
$447$	41.4906	1.96244
$448$	−1.89665	−0.0896085
$449$	−11.4325	−0.539535	−0.269767	−	0.962926i	$-0.586947\pi$
$449$	−11.4325	−0.539535	−0.269767	+	0.962926i	$0.586947\pi$
$450$	−5.84742	−0.275650
$451$	−4.75840	−0.224064
$452$	−11.9116	−0.560275
$453$	−21.2181	−0.996913
$454$	14.6243	0.686354
$455$	7.91327	0.370980
$456$	5.59137	0.261840
$457$	23.6982	1.10856	0.554279	−	0.832331i	$-0.312994\pi$
$457$	23.6982	1.10856	0.554279	+	0.832331i	$0.312994\pi$
$458$	0.797458	0.0372627
$459$	−0.279926	−0.0130658
$460$	−3.17871	−0.148208
$461$	−26.9275	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$461$	−26.9275	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$462$	−5.64152	−0.262467
$463$	−22.0951	−1.02685	−0.513423	−	0.858136i	$-0.671623\pi$
$463$	−22.0951	−1.02685	−0.513423	+	0.858136i	$0.671623\pi$
$464$	4.44413	0.206314
$465$	3.27000	0.151643
$466$	6.08566	0.281913
$467$	−11.2602	−0.521059	−0.260529	−	0.965466i	$-0.583897\pi$
$467$	−11.2602	−0.521059	−0.260529	+	0.965466i	$0.583897\pi$
$468$	−24.3968	−1.12774
$469$	−15.5547	−0.718250
$470$	−11.0837	−0.511252
$471$	16.1004	0.741865
$472$	7.08133	0.325945
$473$	8.12442	0.373561
$474$	32.6447	1.49942
$475$	1.87979	0.0862508
$476$	−0.0626859	−0.00287320
$477$	−54.2314	−2.48309
$478$	−12.4954	−0.571528
$479$	6.74366	0.308126	0.154063	−	0.988061i	$-0.450764\pi$
$479$	6.74366	0.308126	0.154063	+	0.988061i	$0.450764\pi$
$480$	2.97446	0.135765
$481$	11.5060	0.524627
$482$	22.2543	1.01366
$483$	−17.9328	−0.815970
$484$	1.00000	0.0454545
$485$	−18.1500	−0.824148
$486$	−2.65374	−0.120376
$487$	−19.7129	−0.893276	−0.446638	−	0.894715i	$-0.647379\pi$
$487$	−19.7129	−0.893276	−0.446638	+	0.894715i	$0.647379\pi$
$488$	1.29279	0.0585218
$489$	−72.1008	−3.26051
$490$	3.40270	0.153719
$491$	−32.9950	−1.48905	−0.744523	−	0.667597i	$-0.767323\pi$
$491$	−32.9950	−1.48905	−0.744523	+	0.667597i	$0.767323\pi$
$492$	14.1537	0.638097
$493$	0.146882	0.00661524
$494$	7.84292	0.352870
$495$	5.84742	0.262822
$496$	−1.09936	−0.0493627
$497$	−17.1772	−0.770504
$498$	−34.0309	−1.52496
$499$	−24.1348	−1.08042	−0.540211	−	0.841529i	$-0.681656\pi$
$499$	−24.1348	−1.08042	−0.540211	+	0.841529i	$0.681656\pi$
$500$	1.00000	0.0447214
$501$	13.8985	0.620938
$502$	−3.38862	−0.151242
$503$	16.5291	0.736996	0.368498	−	0.929628i	$-0.379872\pi$
$503$	16.5291	0.736996	0.368498	+	0.929628i	$0.379872\pi$
$504$	11.0905	0.494012
$505$	5.42027	0.241199
$506$	3.17871	0.141311
$507$	−13.1099	−0.582232
$508$	6.59772	0.292726
$509$	−18.9093	−0.838140	−0.419070	−	0.907954i	$-0.637644\pi$
$509$	−18.9093	−0.838140	−0.419070	+	0.907954i	$0.637644\pi$
$510$	0.0983083	0.00435317
$511$	1.89665	0.0839030
$512$	−1.00000	−0.0441942
$513$	−15.9210	−0.702929
$514$	−28.9767	−1.27811
$515$	−2.59335	−0.114276
$516$	−24.1658	−1.06384
$517$	11.0837	0.487460
$518$	−5.23050	−0.229815
$519$	−48.3520	−2.12242
$520$	4.17223	0.182964
$521$	−10.9649	−0.480381	−0.240190	−	0.970726i	$-0.577210\pi$
$521$	−10.9649	−0.480381	−0.240190	+	0.970726i	$0.577210\pi$
$522$	−25.9867	−1.13741
$523$	−14.1944	−0.620677	−0.310338	−	0.950626i	$-0.600442\pi$
$523$	−14.1944	−0.620677	−0.310338	+	0.950626i	$0.600442\pi$
$524$	−22.5624	−0.985644
$525$	5.64152	0.246216
$526$	31.1258	1.35715
$527$	−0.0363347	−0.00158276
$528$	−2.97446	−0.129447
$529$	−12.8958	−0.560687
$530$	9.27441	0.402855
$531$	−41.4076	−1.79694
$532$	−3.56531	−0.154576
$533$	19.8531	0.859935
$534$	23.6991	1.02556
$535$	13.0296	0.563317
$536$	−8.20114	−0.354235
$537$	−55.5311	−2.39634
$538$	−17.7535	−0.765409
$539$	−3.40270	−0.146565
$540$	−8.46956	−0.364472
$541$	17.2247	0.740546	0.370273	−	0.928923i	$-0.379264\pi$
$541$	17.2247	0.740546	0.370273	+	0.928923i	$0.379264\pi$
$542$	−10.3504	−0.444586
$543$	−26.5607	−1.13983
$544$	−0.0330508	−0.00141704
$545$	0.722833	0.0309628
$546$	23.5377	1.00732
$547$	−33.4988	−1.43231	−0.716153	−	0.697944i	$-0.754099\pi$
$547$	−33.4988	−1.43231	−0.716153	+	0.697944i	$0.754099\pi$
$548$	8.62933	0.368627
$549$	−7.55948	−0.322631
$550$	−1.00000	−0.0426401
$551$	8.35405	0.355894
$552$	−9.45495	−0.402430
$553$	−20.8158	−0.885177
$554$	10.7718	0.457650
$555$	8.20283	0.348191
$556$	0.157471	0.00667826
$557$	−9.06495	−0.384094	−0.192047	−	0.981386i	$-0.561513\pi$
$557$	−9.06495	−0.384094	−0.192047	+	0.981386i	$0.561513\pi$
$558$	6.42842	0.272137
$559$	−33.8970	−1.43369
$560$	−1.89665	−0.0801483
$561$	−0.0983083	−0.00415058
$562$	−17.2071	−0.725839
$563$	41.7592	1.75994	0.879969	−	0.475031i	$-0.157563\pi$
$563$	41.7592	1.75994	0.879969	+	0.475031i	$0.157563\pi$
$564$	−32.9680	−1.38820
$565$	−11.9116	−0.501125
$566$	10.8284	0.455153
$567$	−14.5096	−0.609345
$568$	−9.05660	−0.380006
$569$	29.4266	1.23363	0.616813	−	0.787110i	$-0.288424\pi$
$569$	29.4266	1.23363	0.616813	+	0.787110i	$0.288424\pi$
$570$	5.59137	0.234197
$571$	−0.545329	−0.0228213	−0.0114107	−	0.999935i	$-0.503632\pi$
$571$	−0.545329	−0.0228213	−0.0114107	+	0.999935i	$0.503632\pi$
$572$	−4.17223	−0.174450
$573$	11.1342	0.465139
$574$	−9.02504	−0.376698
$575$	−3.17871	−0.132561
$576$	5.84742	0.243643
$577$	−10.7959	−0.449439	−0.224720	−	0.974423i	$-0.572147\pi$
$577$	−10.7959	−0.449439	−0.224720	+	0.974423i	$0.572147\pi$
$578$	16.9989	0.707061
$579$	−6.66870	−0.277142
$580$	4.44413	0.184533
$581$	21.6997	0.900253
$582$	−53.9864	−2.23781
$583$	−9.27441	−0.384107
$584$	1.00000	0.0413803
$585$	−24.3968	−1.00868
$586$	−12.3509	−0.510212
$587$	8.56290	0.353429	0.176714	−	0.984262i	$-0.443453\pi$
$587$	8.56290	0.353429	0.176714	+	0.984262i	$0.443453\pi$
$588$	10.1212	0.417392
$589$	−2.06657	−0.0851514
$590$	7.08133	0.291534
$591$	−18.6583	−0.767501
$592$	−2.75775	−0.113343
$593$	1.66135	0.0682233	0.0341117	−	0.999418i	$-0.489140\pi$
$593$	1.66135	0.0682233	0.0341117	+	0.999418i	$0.489140\pi$
$594$	8.46956	0.347510
$595$	−0.0626859	−0.00256987
$596$	−13.9490	−0.571371
$597$	18.5308	0.758414
$598$	−13.2623	−0.542336
$599$	−13.6565	−0.557989	−0.278994	−	0.960293i	$-0.590001\pi$
$599$	−13.6565	−0.557989	−0.278994	+	0.960293i	$0.590001\pi$
$600$	2.97446	0.121432
$601$	−25.1165	−1.02452	−0.512262	−	0.858829i	$-0.671192\pi$
$601$	−25.1165	−1.02452	−0.512262	+	0.858829i	$0.671192\pi$
$602$	15.4092	0.628033
$603$	47.9555	1.95290
$604$	7.13342	0.290255
$605$	1.00000	0.0406558
$606$	16.1224	0.654927
$607$	−38.0117	−1.54285	−0.771423	−	0.636323i	$-0.780455\pi$
$607$	−38.0117	−1.54285	−0.771423	+	0.636323i	$0.780455\pi$
$608$	−1.87979	−0.0762356
$609$	25.0717	1.01596
$610$	1.29279	0.0523434
$611$	−46.2436	−1.87082
$612$	0.193262	0.00781215
$613$	−37.7334	−1.52404	−0.762019	−	0.647555i	$-0.775792\pi$
$613$	−37.7334	−1.52404	−0.762019	+	0.647555i	$0.775792\pi$
$614$	−27.7793	−1.12108
$615$	14.1537	0.570732
$616$	1.89665	0.0764184
$617$	−23.7018	−0.954200	−0.477100	−	0.878849i	$-0.658312\pi$
$617$	−23.7018	−0.954200	−0.477100	+	0.878849i	$0.658312\pi$
$618$	−7.71381	−0.310295
$619$	29.8567	1.20004	0.600021	−	0.799984i	$-0.295159\pi$
$619$	29.8567	1.20004	0.600021	+	0.799984i	$0.295159\pi$
$620$	−1.09936	−0.0441513
$621$	26.9223	1.08035
$622$	11.2557	0.451314
$623$	−15.1117	−0.605436
$624$	12.4101	0.496803
$625$	1.00000	0.0400000
$626$	−15.2325	−0.608813
$627$	−5.59137	−0.223298
$628$	−5.41286	−0.215997
$629$	−0.0911459	−0.00363422
$630$	11.0905	0.441858
$631$	−3.21167	−0.127855	−0.0639274	−	0.997955i	$-0.520363\pi$
$631$	−3.21167	−0.127855	−0.0639274	+	0.997955i	$0.520363\pi$
$632$	−10.9750	−0.436562
$633$	−79.3081	−3.15221
$634$	−7.92225	−0.314633
$635$	6.59772	0.261822
$636$	27.5864	1.09387
$637$	14.1969	0.562500
$638$	−4.44413	−0.175945
$639$	52.9578	2.09498
$640$	−1.00000	−0.0395285
$641$	20.1188	0.794644	0.397322	−	0.917679i	$-0.369940\pi$
$641$	20.1188	0.794644	0.397322	+	0.917679i	$0.369940\pi$
$642$	38.7559	1.52957
$643$	−24.2719	−0.957192	−0.478596	−	0.878035i	$-0.658854\pi$
$643$	−24.2719	−0.957192	−0.478596	+	0.878035i	$0.658854\pi$
$644$	6.02891	0.237572
$645$	−24.1658	−0.951527
$646$	−0.0621286	−0.00244442
$647$	−43.6306	−1.71529	−0.857647	−	0.514239i	$-0.828075\pi$
$647$	−43.6306	−1.71529	−0.857647	+	0.514239i	$0.828075\pi$
$648$	−7.65010	−0.300524
$649$	−7.08133	−0.277967
$650$	4.17223	0.163648
$651$	−6.20206	−0.243078
$652$	24.2400	0.949310
$653$	−29.0895	−1.13836	−0.569180	−	0.822213i	$-0.692739\pi$
$653$	−29.0895	−1.13836	−0.569180	+	0.822213i	$0.692739\pi$
$654$	2.15004	0.0840732
$655$	−22.5624	−0.881587
$656$	−4.75840	−0.185784
$657$	−5.84742	−0.228130
$658$	21.0219	0.819519
$659$	−5.67234	−0.220963	−0.110481	−	0.993878i	$-0.535239\pi$
$659$	−5.67234	−0.220963	−0.110481	+	0.993878i	$0.535239\pi$
$660$	−2.97446	−0.115781
$661$	−5.87020	−0.228324	−0.114162	−	0.993462i	$-0.536418\pi$
$661$	−5.87020	−0.228324	−0.114162	+	0.993462i	$0.536418\pi$
$662$	33.9280	1.31865
$663$	0.410165	0.0159295
$664$	11.4410	0.443998
$665$	−3.56531	−0.138257
$666$	16.1257	0.624860
$667$	−14.1266	−0.546985
$668$	−4.67260	−0.180788
$669$	−21.9026	−0.846802
$670$	−8.20114	−0.316838
$671$	−1.29279	−0.0499075
$672$	−5.64152	−0.217627
$673$	19.9629	0.769512	0.384756	−	0.923018i	$-0.374286\pi$
$673$	19.9629	0.769512	0.384756	+	0.923018i	$0.374286\pi$
$674$	−12.5914	−0.485002
$675$	−8.46956	−0.325993
$676$	4.40749	0.169519
$677$	43.6197	1.67644	0.838221	−	0.545330i	$-0.183596\pi$
$677$	43.6197	1.67644	0.838221	+	0.545330i	$0.183596\pi$
$678$	−35.4306	−1.36070
$679$	34.4242	1.32108
$680$	−0.0330508	−0.00126744
$681$	43.4995	1.66690
$682$	1.09936	0.0420966
$683$	6.38356	0.244260	0.122130	−	0.992514i	$-0.461027\pi$
$683$	6.38356	0.244260	0.122130	+	0.992514i	$0.461027\pi$
$684$	10.9919	0.420287
$685$	8.62933	0.329710
$686$	−19.7303	−0.753307
$687$	2.37201	0.0904977
$688$	8.12442	0.309741
$689$	38.6950	1.47416
$690$	−9.45495	−0.359944
$691$	−37.9406	−1.44333	−0.721664	−	0.692243i	$-0.756622\pi$
$691$	−37.9406	−1.44333	−0.721664	+	0.692243i	$0.756622\pi$
$692$	16.2557	0.617950
$693$	−11.0905	−0.421295
$694$	−7.69359	−0.292045
$695$	0.157471	0.00597322
$696$	13.2189	0.501061
$697$	−0.157269	−0.00595699
$698$	0.853212	0.0322946
$699$	18.1016	0.684664
$700$	−1.89665	−0.0716868
$701$	−12.4178	−0.469013	−0.234507	−	0.972115i	$-0.575347\pi$
$701$	−12.4178	−0.469013	−0.234507	+	0.972115i	$0.575347\pi$
$702$	−35.3369	−1.33371
$703$	−5.18400	−0.195518
$704$	1.00000	0.0376889
$705$	−32.9680	−1.24165
$706$	27.4086	1.03154
$707$	−10.2804	−0.386633
$708$	21.0632	0.791602
$709$	−4.05614	−0.152332	−0.0761658	−	0.997095i	$-0.524268\pi$
$709$	−4.05614	−0.152332	−0.0761658	+	0.997095i	$0.524268\pi$
$710$	−9.05660	−0.339888
$711$	64.1755	2.40677
$712$	−7.96754	−0.298596
$713$	3.49454	0.130872
$714$	−0.186457	−0.00697797
$715$	−4.17223	−0.156033
$716$	18.6693	0.697704
$717$	−37.1672	−1.38804
$718$	−9.00667	−0.336126
$719$	17.2380	0.642870	0.321435	−	0.946932i	$-0.395835\pi$
$719$	17.2380	0.642870	0.321435	+	0.946932i	$0.395835\pi$
$720$	5.84742	0.217921
$721$	4.91868	0.183181
$722$	15.4664	0.575599
$723$	66.1947	2.46181
$724$	8.92959	0.331866
$725$	4.44413	0.165051
$726$	2.97446	0.110393
$727$	−50.1636	−1.86046	−0.930232	−	0.366972i	$-0.880395\pi$
$727$	−50.1636	−1.86046	−0.930232	+	0.366972i	$0.880395\pi$
$728$	−7.91327	−0.293285
$729$	−30.8437	−1.14236
$730$	1.00000	0.0370117
$731$	0.268519	0.00993152
$732$	3.84535	0.142128
$733$	44.5209	1.64442	0.822208	−	0.569187i	$-0.192742\pi$
$733$	44.5209	1.64442	0.822208	+	0.569187i	$0.192742\pi$
$734$	1.01137	0.0373304
$735$	10.1212	0.373327
$736$	3.17871	0.117169
$737$	8.20114	0.302093
$738$	27.8244	1.02423
$739$	−31.6244	−1.16332	−0.581662	−	0.813431i	$-0.697597\pi$
$739$	−31.6244	−1.16332	−0.581662	+	0.813431i	$0.697597\pi$
$740$	−2.75775	−0.101377
$741$	23.3285	0.856993
$742$	−17.5903	−0.645762
$743$	27.9538	1.02552	0.512762	−	0.858531i	$-0.328622\pi$
$743$	27.9538	1.02552	0.512762	+	0.858531i	$0.328622\pi$
$744$	−3.27000	−0.119884
$745$	−13.9490	−0.511050
$746$	−6.06209	−0.221949
$747$	−66.9005	−2.44776
$748$	0.0330508	0.00120846
$749$	−24.7125	−0.902977
$750$	2.97446	0.108612
$751$	−27.6429	−1.00871	−0.504353	−	0.863498i	$-0.668269\pi$
$751$	−27.6429	−1.00871	−0.504353	+	0.863498i	$0.668269\pi$
$752$	11.0837	0.404180
$753$	−10.0793	−0.367311
$754$	18.5419	0.675258
$755$	7.13342	0.259612
$756$	16.0638	0.584235
$757$	−19.7097	−0.716361	−0.358180	−	0.933652i	$-0.616603\pi$
$757$	−19.7097	−0.716361	−0.358180	+	0.933652i	$0.616603\pi$
$758$	−18.6008	−0.675610
$759$	9.45495	0.343193
$760$	−1.87979	−0.0681872
$761$	−1.52791	−0.0553867	−0.0276934	−	0.999616i	$-0.508816\pi$
$761$	−1.52791	−0.0553867	−0.0276934	+	0.999616i	$0.508816\pi$
$762$	19.6247	0.710926
$763$	−1.37096	−0.0496322
$764$	−3.74327	−0.135427
$765$	0.193262	0.00698740
$766$	1.42422	0.0514592
$767$	29.5449	1.06681
$768$	−2.97446	−0.107332
$769$	−40.1756	−1.44877	−0.724384	−	0.689397i	$-0.757876\pi$
$769$	−40.1756	−1.44877	−0.724384	+	0.689397i	$0.757876\pi$
$770$	1.89665	0.0683507
$771$	−86.1902	−3.10406
$772$	2.24199	0.0806908
$773$	20.5851	0.740395	0.370198	−	0.928953i	$-0.379290\pi$
$773$	20.5851	0.740395	0.370198	+	0.928953i	$0.379290\pi$
$774$	−47.5070	−1.70760
$775$	−1.09936	−0.0394901
$776$	18.1500	0.651546
$777$	−15.5579	−0.558137
$778$	28.2708	1.01356
$779$	−8.94481	−0.320481
$780$	12.4101	0.444354
$781$	9.05660	0.324071
$782$	0.105059	0.00375690
$783$	−37.6398	−1.34514
$784$	−3.40270	−0.121525
$785$	−5.41286	−0.193193
$786$	−67.1111	−2.39377
$787$	−46.1092	−1.64362	−0.821808	−	0.569765i	$-0.807034\pi$
$787$	−46.1092	−1.64362	−0.821808	+	0.569765i	$0.807034\pi$
$788$	6.27284	0.223461
$789$	92.5824	3.29602
$790$	−10.9750	−0.390473
$791$	22.5922	0.803286
$792$	−5.84742	−0.207779
$793$	5.39381	0.191540
$794$	25.6892	0.911674
$795$	27.5864	0.978388
$796$	−6.22995	−0.220815
$797$	38.3497	1.35842	0.679208	−	0.733946i	$-0.262324\pi$
$797$	38.3497	1.35842	0.679208	+	0.733946i	$0.262324\pi$
$798$	−10.6049	−0.375409
$799$	0.366324	0.0129596
$800$	−1.00000	−0.0353553
$801$	46.5896	1.64616
$802$	−3.54258	−0.125093
$803$	−1.00000	−0.0352892
$804$	−24.3940	−0.860309
$805$	6.02891	0.212491
$806$	−4.58678	−0.161562
$807$	−52.8072	−1.85890
$808$	−5.42027	−0.190684
$809$	30.6788	1.07861	0.539305	−	0.842111i	$-0.318687\pi$
$809$	30.6788	1.07861	0.539305	+	0.842111i	$0.318687\pi$
$810$	−7.65010	−0.268797
$811$	23.5177	0.825820	0.412910	−	0.910772i	$-0.364512\pi$
$811$	23.5177	0.825820	0.412910	+	0.910772i	$0.364512\pi$
$812$	−8.42898	−0.295799
$813$	−30.7868	−1.07974
$814$	2.75775	0.0966591
$815$	24.2400	0.849089
$816$	−0.0983083	−0.00344148
$817$	15.2722	0.534308
$818$	−17.7481	−0.620548
$819$	46.2723	1.61688
$820$	−4.75840	−0.166171
$821$	−37.8356	−1.32047	−0.660237	−	0.751058i	$-0.729544\pi$
$821$	−37.8356	−1.32047	−0.660237	+	0.751058i	$0.729544\pi$
$822$	25.6676	0.895261
$823$	−20.0317	−0.698260	−0.349130	−	0.937074i	$-0.613523\pi$
$823$	−20.0317	−0.698260	−0.349130	+	0.937074i	$0.613523\pi$
$824$	2.59335	0.0903435
$825$	−2.97446	−0.103557
$826$	−13.4308	−0.467319
$827$	−23.2614	−0.808878	−0.404439	−	0.914565i	$-0.632533\pi$
$827$	−23.2614	−0.808878	−0.404439	+	0.914565i	$0.632533\pi$
$828$	−18.5873	−0.645952
$829$	−19.8655	−0.689958	−0.344979	−	0.938610i	$-0.612114\pi$
$829$	−19.8655	−0.689958	−0.344979	+	0.938610i	$0.612114\pi$
$830$	11.4410	0.397124
$831$	32.0403	1.11147
$832$	−4.17223	−0.144646
$833$	−0.112462	−0.00389658
$834$	0.468392	0.0162191
$835$	−4.67260	−0.161702
$836$	1.87979	0.0650140
$837$	9.31108	0.321838
$838$	20.1484	0.696016
$839$	41.5051	1.43292	0.716458	−	0.697630i	$-0.245762\pi$
$839$	41.5051	1.43292	0.716458	+	0.697630i	$0.245762\pi$
$840$	−5.64152	−0.194651
$841$	−9.24968	−0.318954
$842$	23.1286	0.797063
$843$	−51.1820	−1.76280
$844$	26.6630	0.917778
$845$	4.40749	0.151622
$846$	−64.8110	−2.22825
$847$	−1.89665	−0.0651698
$848$	−9.27441	−0.318485
$849$	32.2087	1.10540
$850$	−0.0330508	−0.00113363
$851$	8.76609	0.300498
$852$	−26.9385	−0.922898
$853$	−6.88650	−0.235789	−0.117895	−	0.993026i	$-0.537615\pi$
$853$	−6.88650	−0.235789	−0.117895	+	0.993026i	$0.537615\pi$
$854$	−2.45197	−0.0839047
$855$	10.9919	0.375916
$856$	−13.0296	−0.445341
$857$	−30.2781	−1.03428	−0.517140	−	0.855901i	$-0.673003\pi$
$857$	−30.2781	−1.03428	−0.517140	+	0.855901i	$0.673003\pi$
$858$	−12.4101	−0.423675
$859$	20.7585	0.708270	0.354135	−	0.935194i	$-0.384775\pi$
$859$	20.7585	0.708270	0.354135	+	0.935194i	$0.384775\pi$
$860$	8.12442	0.277041
$861$	−26.8446	−0.914863
$862$	14.1995	0.483637
$863$	−2.81245	−0.0957368	−0.0478684	−	0.998854i	$-0.515243\pi$
$863$	−2.81245	−0.0957368	−0.0478684	+	0.998854i	$0.515243\pi$
$864$	8.46956	0.288140
$865$	16.2557	0.552711
$866$	−4.56076	−0.154981
$867$	50.5626	1.71720
$868$	2.08510	0.0707730
$869$	10.9750	0.372302
$870$	13.2189	0.448163
$871$	−34.2170	−1.15940
$872$	−0.722833	−0.0244782
$873$	−106.131	−3.59198
$874$	5.97531	0.202118
$875$	−1.89665	−0.0641186
$876$	2.97446	0.100498
$877$	−0.933202	−0.0315120	−0.0157560	−	0.999876i	$-0.505015\pi$
$877$	−0.933202	−0.0315120	−0.0157560	+	0.999876i	$0.505015\pi$
$878$	27.0957	0.914435
$879$	−36.7374	−1.23912
$880$	1.00000	0.0337100
$881$	−10.2278	−0.344585	−0.172292	−	0.985046i	$-0.555117\pi$
$881$	−10.2278	−0.344585	−0.172292	+	0.985046i	$0.555117\pi$
$882$	19.8971	0.669969
$883$	37.6491	1.26699	0.633497	−	0.773745i	$-0.281619\pi$
$883$	37.6491	1.26699	0.633497	+	0.773745i	$0.281619\pi$
$884$	−0.137895	−0.00463793
$885$	21.0632	0.708030
$886$	−5.03115	−0.169025
$887$	−20.5107	−0.688681	−0.344341	−	0.938845i	$-0.611898\pi$
$887$	−20.5107	−0.688681	−0.344341	+	0.938845i	$0.611898\pi$
$888$	−8.20283	−0.275269
$889$	−12.5136	−0.419692
$890$	−7.96754	−0.267072
$891$	7.65010	0.256288
$892$	7.36354	0.246549
$893$	20.8350	0.697217
$894$	−41.4906	−1.38765
$895$	18.6693	0.624045
$896$	1.89665	0.0633628
$897$	−39.4482	−1.31714
$898$	11.4325	0.381509
$899$	−4.88570	−0.162947
$900$	5.84742	0.194914
$901$	−0.306527	−0.0102119
$902$	4.75840	0.158437
$903$	45.8341	1.52526
$904$	11.9116	0.396174
$905$	8.92959	0.296830
$906$	21.2181	0.704924
$907$	11.7648	0.390644	0.195322	−	0.980739i	$-0.437425\pi$
$907$	11.7648	0.390644	0.195322	+	0.980739i	$0.437425\pi$
$908$	−14.6243	−0.485325
$909$	31.6946	1.05124
$910$	−7.91327	−0.262322
$911$	−34.7908	−1.15267	−0.576335	−	0.817213i	$-0.695518\pi$
$911$	−34.7908	−1.15267	−0.576335	+	0.817213i	$0.695518\pi$
$912$	−5.59137	−0.185149
$913$	−11.4410	−0.378642
$914$	−23.6982	−0.783868
$915$	3.84535	0.127123
$916$	−0.797458	−0.0263487
$917$	42.7931	1.41315
$918$	0.279926	0.00923892
$919$	24.1502	0.796640	0.398320	−	0.917246i	$-0.369593\pi$
$919$	24.1502	0.796640	0.398320	+	0.917246i	$0.369593\pi$
$920$	3.17871	0.104799
$921$	−82.6285	−2.72270
$922$	26.9275	0.886811
$923$	−37.7862	−1.24375
$924$	5.64152	0.185593
$925$	−2.75775	−0.0906743
$926$	22.0951	0.726090
$927$	−15.1644	−0.498064
$928$	−4.44413	−0.145886
$929$	−12.0539	−0.395475	−0.197738	−	0.980255i	$-0.563359\pi$
$929$	−12.0539	−0.395475	−0.197738	+	0.980255i	$0.563359\pi$
$930$	−3.27000	−0.107228
$931$	−6.39638	−0.209633
$932$	−6.08566	−0.199342
$933$	33.4798	1.09608
$934$	11.2602	0.368444
$935$	0.0330508	0.00108088
$936$	24.3968	0.797434
$937$	−21.7734	−0.711307	−0.355653	−	0.934618i	$-0.615742\pi$
$937$	−21.7734	−0.711307	−0.355653	+	0.934618i	$0.615742\pi$
$938$	15.5547	0.507880
$939$	−45.3085	−1.47859
$940$	11.0837	0.361510
$941$	47.3864	1.54475	0.772376	−	0.635166i	$-0.219068\pi$
$941$	47.3864	1.54475	0.772376	+	0.635166i	$0.219068\pi$
$942$	−16.1004	−0.524578
$943$	15.1256	0.492557
$944$	−7.08133	−0.230478
$945$	16.0638	0.522556
$946$	−8.12442	−0.264148
$947$	−26.5147	−0.861612	−0.430806	−	0.902444i	$-0.641771\pi$
$947$	−26.5147	−0.861612	−0.430806	+	0.902444i	$0.641771\pi$
$948$	−32.6447	−1.06025
$949$	4.17223	0.135436
$950$	−1.87979	−0.0609885
$951$	−23.5644	−0.764129
$952$	0.0626859	0.00203166
$953$	−22.6307	−0.733081	−0.366541	−	0.930402i	$-0.619458\pi$
$953$	−22.6307	−0.733081	−0.366541	+	0.930402i	$0.619458\pi$
$954$	54.2314	1.75581
$955$	−3.74327	−0.121129
$956$	12.4954	0.404131
$957$	−13.2189	−0.427307
$958$	−6.74366	−0.217878
$959$	−16.3669	−0.528513
$960$	−2.97446	−0.0960003
$961$	−29.7914	−0.961013
$962$	−11.5060	−0.370967
$963$	76.1893	2.45517
$964$	−22.2543	−0.716764
$965$	2.24199	0.0721721
$966$	17.9328	0.576978
$967$	−33.9574	−1.09200	−0.545998	−	0.837787i	$-0.683849\pi$
$967$	−33.9574	−1.09200	−0.545998	+	0.837787i	$0.683849\pi$
$968$	−1.00000	−0.0321412
$969$	−0.184799	−0.00593661
$970$	18.1500	0.582760
$971$	17.9072	0.574669	0.287334	−	0.957830i	$-0.407231\pi$
$971$	17.9072	0.574669	0.287334	+	0.957830i	$0.407231\pi$
$972$	2.65374	0.0851187
$973$	−0.298668	−0.00957486
$974$	19.7129	0.631642
$975$	12.4101	0.397442
$976$	−1.29279	−0.0413811
$977$	−18.0109	−0.576218	−0.288109	−	0.957598i	$-0.593027\pi$
$977$	−18.0109	−0.576218	−0.288109	+	0.957598i	$0.593027\pi$
$978$	72.1008	2.30553
$979$	7.96754	0.254644
$980$	−3.40270	−0.108695
$981$	4.22671	0.134948
$982$	32.9950	1.05291
$983$	−44.3216	−1.41364	−0.706820	−	0.707393i	$-0.749871\pi$
$983$	−44.3216	−1.41364	−0.706820	+	0.707393i	$0.749871\pi$
$984$	−14.1537	−0.451203
$985$	6.27284	0.199869
$986$	−0.146882	−0.00467768
$987$	62.5288	1.99032
$988$	−7.84292	−0.249517
$989$	−25.8252	−0.821193
$990$	−5.84742	−0.185843
$991$	−18.2654	−0.580221	−0.290111	−	0.956993i	$-0.593692\pi$
$991$	−18.2654	−0.580221	−0.290111	+	0.956993i	$0.593692\pi$
$992$	1.09936	0.0349047
$993$	100.918	3.20253
$994$	17.1772	0.544829
$995$	−6.22995	−0.197503
$996$	34.0309	1.07831
$997$	51.5079	1.63127	0.815635	−	0.578566i	$-0.196388\pi$
$997$	51.5079	1.63127	0.815635	+	0.578566i	$0.196388\pi$
$998$	24.1348	0.763974
$999$	23.3569	0.738981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.2	✓	11	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.97446 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.97446 q^{6} -1.89665 q^{7} -1.00000 q^{8} +5.84742 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.97446 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.97446 q^{6} -1.89665 q^{7} -1.00000 q^{8} +5.84742 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.97446 q^{12} -4.17223 q^{13} +1.89665 q^{14} -2.97446 q^{15} +1.00000 q^{16} +0.0330508 q^{17} -5.84742 q^{18} +1.87979 q^{19} +1.00000 q^{20} +5.64152 q^{21} -1.00000 q^{22} -3.17871 q^{23} +2.97446 q^{24} +1.00000 q^{25} +4.17223 q^{26} -8.46956 q^{27} -1.89665 q^{28} +4.44413 q^{29} +2.97446 q^{30} -1.09936 q^{31} -1.00000 q^{32} -2.97446 q^{33} -0.0330508 q^{34} -1.89665 q^{35} +5.84742 q^{36} -2.75775 q^{37} -1.87979 q^{38} +12.4101 q^{39} -1.00000 q^{40} -4.75840 q^{41} -5.64152 q^{42} +8.12442 q^{43} +1.00000 q^{44} +5.84742 q^{45} +3.17871 q^{46} +11.0837 q^{47} -2.97446 q^{48} -3.40270 q^{49} -1.00000 q^{50} -0.0983083 q^{51} -4.17223 q^{52} -9.27441 q^{53} +8.46956 q^{54} +1.00000 q^{55} +1.89665 q^{56} -5.59137 q^{57} -4.44413 q^{58} -7.08133 q^{59} -2.97446 q^{60} -1.29279 q^{61} +1.09936 q^{62} -11.0905 q^{63} +1.00000 q^{64} -4.17223 q^{65} +2.97446 q^{66} +8.20114 q^{67} +0.0330508 q^{68} +9.45495 q^{69} +1.89665 q^{70} +9.05660 q^{71} -5.84742 q^{72} -1.00000 q^{73} +2.75775 q^{74} -2.97446 q^{75} +1.87979 q^{76} -1.89665 q^{77} -12.4101 q^{78} +10.9750 q^{79} +1.00000 q^{80} +7.65010 q^{81} +4.75840 q^{82} -11.4410 q^{83} +5.64152 q^{84} +0.0330508 q^{85} -8.12442 q^{86} -13.2189 q^{87} -1.00000 q^{88} +7.96754 q^{89} -5.84742 q^{90} +7.91327 q^{91} -3.17871 q^{92} +3.27000 q^{93} -11.0837 q^{94} +1.87979 q^{95} +2.97446 q^{96} -18.1500 q^{97} +3.40270 q^{98} +5.84742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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