LMFDB - Embedded newform 1183.2.a.r.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.62803$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.62803 q^{2} -1.76762 q^{3} +4.90656 q^{4} -2.94291 q^{5} -4.64535 q^{6} +1.00000 q^{7} +7.63852 q^{8} +0.124466 q^{9} +O(q^{10})$	\(q+2.62803 q^{2} -1.76762 q^{3} +4.90656 q^{4} -2.94291 q^{5} -4.64535 q^{6} +1.00000 q^{7} +7.63852 q^{8} +0.124466 q^{9} -7.73406 q^{10} +4.28290 q^{11} -8.67291 q^{12} +2.62803 q^{14} +5.20193 q^{15} +10.2612 q^{16} +2.94049 q^{17} +0.327101 q^{18} +4.98782 q^{19} -14.4396 q^{20} -1.76762 q^{21} +11.2556 q^{22} +7.58085 q^{23} -13.5020 q^{24} +3.66072 q^{25} +5.08284 q^{27} +4.90656 q^{28} -1.82633 q^{29} +13.6709 q^{30} +6.57664 q^{31} +11.6897 q^{32} -7.57053 q^{33} +7.72771 q^{34} -2.94291 q^{35} +0.610701 q^{36} -8.31285 q^{37} +13.1082 q^{38} -22.4795 q^{40} -4.15934 q^{41} -4.64535 q^{42} -8.48158 q^{43} +21.0143 q^{44} -0.366293 q^{45} +19.9227 q^{46} +0.910136 q^{47} -18.1378 q^{48} +1.00000 q^{49} +9.62049 q^{50} -5.19766 q^{51} +4.47393 q^{53} +13.3579 q^{54} -12.6042 q^{55} +7.63852 q^{56} -8.81656 q^{57} -4.79965 q^{58} -9.42007 q^{59} +25.5236 q^{60} -1.75588 q^{61} +17.2836 q^{62} +0.124466 q^{63} +10.1985 q^{64} -19.8956 q^{66} +0.413638 q^{67} +14.4277 q^{68} -13.4000 q^{69} -7.73406 q^{70} -2.95901 q^{71} +0.950738 q^{72} -0.885074 q^{73} -21.8464 q^{74} -6.47075 q^{75} +24.4730 q^{76} +4.28290 q^{77} +10.0505 q^{79} -30.1977 q^{80} -9.35791 q^{81} -10.9309 q^{82} +6.04519 q^{83} -8.67291 q^{84} -8.65360 q^{85} -22.2899 q^{86} +3.22825 q^{87} +32.7151 q^{88} -3.82110 q^{89} -0.962630 q^{90} +37.1958 q^{92} -11.6250 q^{93} +2.39187 q^{94} -14.6787 q^{95} -20.6628 q^{96} -2.37500 q^{97} +2.62803 q^{98} +0.533077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * 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 $

$2$	2.62803	1.85830	0.929150	−	0.369703i	$-0.120541\pi$
$2$	2.62803	1.85830	0.929150	+	0.369703i	$0.120541\pi$
$3$	−1.76762	−1.02053	−0.510267	−	0.860016i	$-0.670453\pi$
$3$	−1.76762	−1.02053	−0.510267	+	0.860016i	$0.670453\pi$
$4$	4.90656	2.45328
$5$	−2.94291	−1.31611	−0.658055	−	0.752970i	$-0.728620\pi$
$5$	−2.94291	−1.31611	−0.658055	+	0.752970i	$0.728620\pi$
$6$	−4.64535	−1.89646
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	7.63852	2.70063
$9$	0.124466	0.0414887
$10$	−7.73406	−2.44573
$11$	4.28290	1.29134	0.645672	−	0.763615i	$-0.276577\pi$
$11$	4.28290	1.29134	0.645672	+	0.763615i	$0.276577\pi$
$12$	−8.67291	−2.50365
$13$	0	0
$13$	0	0
$14$	2.62803	0.702371
$15$	5.20193	1.34313
$16$	10.2612	2.56529
$17$	2.94049	0.713174	0.356587	−	0.934262i	$-0.383940\pi$
$17$	2.94049	0.713174	0.356587	+	0.934262i	$0.383940\pi$
$18$	0.327101	0.0770985
$19$	4.98782	1.14429	0.572143	−	0.820154i	$-0.306112\pi$
$19$	4.98782	1.14429	0.572143	+	0.820154i	$0.306112\pi$
$20$	−14.4396	−3.22878
$21$	−1.76762	−0.385725
$22$	11.2556	2.39970
$23$	7.58085	1.58072	0.790358	−	0.612646i	$-0.209895\pi$
$23$	7.58085	1.58072	0.790358	+	0.612646i	$0.209895\pi$
$24$	−13.5020	−2.75608
$25$	3.66072	0.732144
$26$	0	0
$27$	5.08284	0.978193
$28$	4.90656	0.927252
$29$	−1.82633	−0.339141	−0.169570	−	0.985518i	$-0.554238\pi$
$29$	−1.82633	−0.339141	−0.169570	+	0.985518i	$0.554238\pi$
$30$	13.6709	2.49595
$31$	6.57664	1.18120	0.590600	−	0.806965i	$-0.298891\pi$
$31$	6.57664	1.18120	0.590600	+	0.806965i	$0.298891\pi$
$32$	11.6897	2.06646
$33$	−7.57053	−1.31786
$34$	7.72771	1.32529
$35$	−2.94291	−0.497443
$36$	0.610701	0.101783
$37$	−8.31285	−1.36662	−0.683312	−	0.730126i	$-0.739461\pi$
$37$	−8.31285	−1.36662	−0.683312	+	0.730126i	$0.739461\pi$
$38$	13.1082	2.12643
$39$	0	0
$40$	−22.4795	−3.55432
$41$	−4.15934	−0.649579	−0.324790	−	0.945786i	$-0.605293\pi$
$41$	−4.15934	−0.649579	−0.324790	+	0.945786i	$0.605293\pi$
$42$	−4.64535	−0.716793
$43$	−8.48158	−1.29343	−0.646714	−	0.762733i	$-0.723857\pi$
$43$	−8.48158	−1.29343	−0.646714	+	0.762733i	$0.723857\pi$
$44$	21.0143	3.16803
$45$	−0.366293	−0.0546037
$46$	19.9227	2.93744
$47$	0.910136	0.132757	0.0663785	−	0.997795i	$-0.478856\pi$
$47$	0.910136	0.132757	0.0663785	+	0.997795i	$0.478856\pi$
$48$	−18.1378	−2.61797
$49$	1.00000	0.142857
$50$	9.62049	1.36054
$51$	−5.19766	−0.727818
$52$	0	0
$53$	4.47393	0.614542	0.307271	−	0.951622i	$-0.400584\pi$
$53$	4.47393	0.614542	0.307271	+	0.951622i	$0.400584\pi$
$54$	13.3579	1.81778
$55$	−12.6042	−1.69955
$56$	7.63852	1.02074
$57$	−8.81656	−1.16778
$58$	−4.79965	−0.630225
$59$	−9.42007	−1.22639	−0.613194	−	0.789932i	$-0.710116\pi$
$59$	−9.42007	−1.22639	−0.613194	+	0.789932i	$0.710116\pi$
$60$	25.5236	3.29508
$61$	−1.75588	−0.224817	−0.112409	−	0.993662i	$-0.535857\pi$
$61$	−1.75588	−0.224817	−0.112409	+	0.993662i	$0.535857\pi$
$62$	17.2836	2.19502
$63$	0.124466	0.0156813
$64$	10.1985	1.27481
$65$	0	0
$66$	−19.8956	−2.44898
$67$	0.413638	0.0505340	0.0252670	−	0.999681i	$-0.491956\pi$
$67$	0.413638	0.0505340	0.0252670	+	0.999681i	$0.491956\pi$
$68$	14.4277	1.74961
$69$	−13.4000	−1.61317
$70$	−7.73406	−0.924397
$71$	−2.95901	−0.351170	−0.175585	−	0.984464i	$-0.556182\pi$
$71$	−2.95901	−0.351170	−0.175585	+	0.984464i	$0.556182\pi$
$72$	0.950738	0.112046
$73$	−0.885074	−0.103590	−0.0517951	−	0.998658i	$-0.516494\pi$
$73$	−0.885074	−0.103590	−0.0517951	+	0.998658i	$0.516494\pi$
$74$	−21.8464	−2.53960
$75$	−6.47075	−0.747177
$76$	24.4730	2.80725
$77$	4.28290	0.488082
$78$	0	0
$79$	10.0505	1.13077	0.565384	−	0.824828i	$-0.308728\pi$
$79$	10.0505	1.13077	0.565384	+	0.824828i	$0.308728\pi$
$80$	−30.1977	−3.37621
$81$	−9.35791	−1.03977
$82$	−10.9309	−1.20711
$83$	6.04519	0.663546	0.331773	−	0.943359i	$-0.392353\pi$
$83$	6.04519	0.663546	0.331773	+	0.943359i	$0.392353\pi$
$84$	−8.67291	−0.946292
$85$	−8.65360	−0.938615
$86$	−22.2899	−2.40358
$87$	3.22825	0.346104
$88$	32.7151	3.48744
$89$	−3.82110	−0.405036	−0.202518	−	0.979279i	$-0.564912\pi$
$89$	−3.82110	−0.405036	−0.202518	+	0.979279i	$0.564912\pi$
$90$	−0.962630	−0.101470
$91$	0	0
$92$	37.1958	3.87793
$93$	−11.6250	−1.20545
$94$	2.39187	0.246702
$95$	−14.6787	−1.50600
$96$	−20.6628	−2.10889
$97$	−2.37500	−0.241144	−0.120572	−	0.992705i	$-0.538473\pi$
$97$	−2.37500	−0.241144	−0.120572	+	0.992705i	$0.538473\pi$
$98$	2.62803	0.265471
$99$	0.533077	0.0535762
$100$	17.9615	1.79615
$101$	−1.36229	−0.135553	−0.0677763	−	0.997701i	$-0.521590\pi$
$101$	−1.36229	−0.135553	−0.0677763	+	0.997701i	$0.521590\pi$
$102$	−13.6596	−1.35250
$103$	18.6811	1.84071	0.920354	−	0.391086i	$-0.127900\pi$
$103$	18.6811	1.84071	0.920354	+	0.391086i	$0.127900\pi$
$104$	0	0
$105$	5.20193	0.507657
$106$	11.7576	1.14200
$107$	5.93855	0.574101	0.287051	−	0.957915i	$-0.407325\pi$
$107$	5.93855	0.574101	0.287051	+	0.957915i	$0.407325\pi$
$108$	24.9392	2.39978
$109$	1.63519	0.156623	0.0783115	−	0.996929i	$-0.475047\pi$
$109$	1.63519	0.156623	0.0783115	+	0.996929i	$0.475047\pi$
$110$	−33.1242	−3.15827
$111$	14.6939	1.39469
$112$	10.2612	0.969590
$113$	0.870896	0.0819270	0.0409635	−	0.999161i	$-0.486957\pi$
$113$	0.870896	0.0819270	0.0409635	+	0.999161i	$0.486957\pi$
$114$	−23.1702	−2.17009
$115$	−22.3097	−2.08039
$116$	−8.96098	−0.832006
$117$	0	0
$118$	−24.7562	−2.27900
$119$	2.94049	0.269554
$120$	39.7351	3.62730
$121$	7.34326	0.667569
$122$	−4.61451	−0.417778
$123$	7.35211	0.662917
$124$	32.2686	2.89781
$125$	3.94138	0.352528
$126$	0.327101	0.0291405
$127$	−5.72408	−0.507930	−0.253965	−	0.967213i	$-0.581735\pi$
$127$	−5.72408	−0.507930	−0.253965	+	0.967213i	$0.581735\pi$
$128$	3.42255	0.302514
$129$	14.9922	1.31999
$130$	0	0
$131$	−4.27598	−0.373594	−0.186797	−	0.982398i	$-0.559811\pi$
$131$	−4.27598	−0.373594	−0.186797	+	0.982398i	$0.559811\pi$
$132$	−37.1452	−3.23308
$133$	4.98782	0.432499
$134$	1.08705	0.0939072
$135$	−14.9583	−1.28741
$136$	22.4610	1.92602
$137$	−18.0596	−1.54294	−0.771468	−	0.636269i	$-0.780477\pi$
$137$	−18.0596	−1.54294	−0.771468	+	0.636269i	$0.780477\pi$
$138$	−35.2157	−2.99776
$139$	−0.0934521	−0.00792650	−0.00396325	−	0.999992i	$-0.501262\pi$
$139$	−0.0934521	−0.00792650	−0.00396325	+	0.999992i	$0.501262\pi$
$140$	−14.4396	−1.22036
$141$	−1.60877	−0.135483
$142$	−7.77638	−0.652579
$143$	0	0
$144$	1.27717	0.106431
$145$	5.37472	0.446346
$146$	−2.32600	−0.192502
$147$	−1.76762	−0.145791
$148$	−40.7875	−3.35271
$149$	−16.6989	−1.36802	−0.684012	−	0.729470i	$-0.739767\pi$
$149$	−16.6989	−1.36802	−0.684012	+	0.729470i	$0.739767\pi$
$150$	−17.0053	−1.38848
$151$	−16.4932	−1.34220	−0.671099	−	0.741368i	$-0.734177\pi$
$151$	−16.4932	−1.34220	−0.671099	+	0.741368i	$0.734177\pi$
$152$	38.0996	3.09029
$153$	0.365992	0.0295887
$154$	11.2556	0.907003
$155$	−19.3545	−1.55459
$156$	0	0
$157$	−22.6447	−1.80724	−0.903622	−	0.428331i	$-0.859102\pi$
$157$	−22.6447	−1.80724	−0.903622	+	0.428331i	$0.859102\pi$
$158$	26.4130	2.10131
$159$	−7.90819	−0.627160
$160$	−34.4016	−2.71969
$161$	7.58085	0.597454
$162$	−24.5929	−1.93220
$163$	−4.37249	−0.342480	−0.171240	−	0.985229i	$-0.554777\pi$
$163$	−4.37249	−0.342480	−0.171240	+	0.985229i	$0.554777\pi$
$164$	−20.4080	−1.59360
$165$	22.2794	1.73445
$166$	15.8870	1.23307
$167$	−17.2083	−1.33162	−0.665808	−	0.746123i	$-0.731913\pi$
$167$	−17.2083	−1.33162	−0.665808	+	0.746123i	$0.731913\pi$
$168$	−13.5020	−1.04170
$169$	0	0
$170$	−22.7419	−1.74423
$171$	0.620816	0.0474750
$172$	−41.6153	−3.17314
$173$	22.4082	1.70366	0.851832	−	0.523815i	$-0.175492\pi$
$173$	22.4082	1.70366	0.851832	+	0.523815i	$0.175492\pi$
$174$	8.48394	0.643165
$175$	3.66072	0.276724
$176$	43.9476	3.31268
$177$	16.6511	1.25157
$178$	−10.0420	−0.752678
$179$	−2.75303	−0.205771	−0.102885	−	0.994693i	$-0.532808\pi$
$179$	−2.75303	−0.205771	−0.102885	+	0.994693i	$0.532808\pi$
$180$	−1.79724	−0.133958
$181$	6.26508	0.465680	0.232840	−	0.972515i	$-0.425198\pi$
$181$	6.26508	0.465680	0.232840	+	0.972515i	$0.425198\pi$
$182$	0	0
$183$	3.10372	0.229434
$184$	57.9065	4.26892
$185$	24.4640	1.79863
$186$	−30.5508	−2.24009
$187$	12.5938	0.920953
$188$	4.46563	0.325690
$189$	5.08284	0.369722
$190$	−38.5761	−2.79861
$191$	23.4239	1.69489	0.847445	−	0.530883i	$-0.178140\pi$
$191$	23.4239	1.69489	0.847445	+	0.530883i	$0.178140\pi$
$192$	−18.0270	−1.30098
$193$	16.4710	1.18561	0.592803	−	0.805347i	$-0.298021\pi$
$193$	16.4710	1.18561	0.592803	+	0.805347i	$0.298021\pi$
$194$	−6.24157	−0.448119
$195$	0	0
$196$	4.90656	0.350468
$197$	2.02734	0.144442	0.0722210	−	0.997389i	$-0.476991\pi$
$197$	2.02734	0.144442	0.0722210	+	0.997389i	$0.476991\pi$
$198$	1.40094	0.0995607
$199$	−27.1238	−1.92276	−0.961379	−	0.275229i	$-0.911246\pi$
$199$	−27.1238	−1.92276	−0.961379	+	0.275229i	$0.911246\pi$
$200$	27.9625	1.97725
$201$	−0.731154	−0.0515716
$202$	−3.58014	−0.251898
$203$	−1.82633	−0.128183
$204$	−25.5026	−1.78554
$205$	12.2406	0.854917
$206$	49.0947	3.42059
$207$	0.943559	0.0655819
$208$	0	0
$209$	21.3624	1.47767
$210$	13.6709	0.943379
$211$	−3.11031	−0.214123	−0.107061	−	0.994252i	$-0.534144\pi$
$211$	−3.11031	−0.214123	−0.107061	+	0.994252i	$0.534144\pi$
$212$	21.9516	1.50764
$213$	5.23040	0.358381
$214$	15.6067	1.06685
$215$	24.9605	1.70229
$216$	38.8254	2.64173
$217$	6.57664	0.446451
$218$	4.29734	0.291052
$219$	1.56447	0.105717
$220$	−61.8432	−4.16947
$221$	0	0
$222$	38.6161	2.59174
$223$	−15.7646	−1.05568	−0.527838	−	0.849345i	$-0.676997\pi$
$223$	−15.7646	−1.05568	−0.527838	+	0.849345i	$0.676997\pi$
$224$	11.6897	0.781048
$225$	0.455636	0.0303757
$226$	2.28874	0.152245
$227$	4.65356	0.308868	0.154434	−	0.988003i	$-0.450645\pi$
$227$	4.65356	0.308868	0.154434	+	0.988003i	$0.450645\pi$
$228$	−43.2589	−2.86489
$229$	−16.5125	−1.09118	−0.545589	−	0.838053i	$-0.683694\pi$
$229$	−16.5125	−1.09118	−0.545589	+	0.838053i	$0.683694\pi$
$230$	−58.6307	−3.86600
$231$	−7.57053	−0.498104
$232$	−13.9504	−0.915892
$233$	17.2023	1.12696	0.563481	−	0.826129i	$-0.309462\pi$
$233$	17.2023	1.12696	0.563481	+	0.826129i	$0.309462\pi$
$234$	0	0
$235$	−2.67845	−0.174723
$236$	−46.2201	−3.00867
$237$	−17.7654	−1.15399
$238$	7.72771	0.500913
$239$	4.42647	0.286325	0.143162	−	0.989699i	$-0.454273\pi$
$239$	4.42647	0.286325	0.143162	+	0.989699i	$0.454273\pi$
$240$	53.3780	3.44553
$241$	−18.5421	−1.19440	−0.597202	−	0.802091i	$-0.703721\pi$
$241$	−18.5421	−1.19440	−0.597202	+	0.802091i	$0.703721\pi$
$242$	19.2983	1.24054
$243$	1.29267	0.0829247
$244$	−8.61533	−0.551540
$245$	−2.94291	−0.188016
$246$	19.3216	1.23190
$247$	0	0
$248$	50.2358	3.18998
$249$	−10.6856	−0.677171
$250$	10.3581	0.655102
$251$	9.82212	0.619967	0.309983	−	0.950742i	$-0.399676\pi$
$251$	9.82212	0.619967	0.309983	+	0.950742i	$0.399676\pi$
$252$	0.610701	0.0384705
$253$	32.4680	2.04125
$254$	−15.0431	−0.943887
$255$	15.2962	0.957888
$256$	−11.4023	−0.712645
$257$	19.5729	1.22092	0.610462	−	0.792046i	$-0.290984\pi$
$257$	19.5729	1.22092	0.610462	+	0.792046i	$0.290984\pi$
$258$	39.3999	2.45293
$259$	−8.31285	−0.516535
$260$	0	0
$261$	−0.227316	−0.0140705
$262$	−11.2374	−0.694250
$263$	−6.07215	−0.374425	−0.187212	−	0.982319i	$-0.559945\pi$
$263$	−6.07215	−0.374425	−0.187212	+	0.982319i	$0.559945\pi$
$264$	−57.8277	−3.55905
$265$	−13.1664	−0.808804
$266$	13.1082	0.803713
$267$	6.75424	0.413353
$268$	2.02954	0.123974
$269$	0.134388	0.00819378	0.00409689	−	0.999992i	$-0.498696\pi$
$269$	0.134388	0.00819378	0.00409689	+	0.999992i	$0.498696\pi$
$270$	−39.3110	−2.39239
$271$	−14.9723	−0.909500	−0.454750	−	0.890619i	$-0.650271\pi$
$271$	−14.9723	−0.909500	−0.454750	+	0.890619i	$0.650271\pi$
$272$	30.1729	1.82950
$273$	0	0
$274$	−47.4612	−2.86724
$275$	15.6785	0.945450
$276$	−65.7480	−3.95756
$277$	15.5609	0.934965	0.467483	−	0.884002i	$-0.345161\pi$
$277$	15.5609	0.934965	0.467483	+	0.884002i	$0.345161\pi$
$278$	−0.245595	−0.0147298
$279$	0.818570	0.0490065
$280$	−22.4795	−1.34341
$281$	22.3371	1.33252	0.666261	−	0.745719i	$-0.267894\pi$
$281$	22.3371	1.33252	0.666261	+	0.745719i	$0.267894\pi$
$282$	−4.22790	−0.251768
$283$	3.08431	0.183343	0.0916715	−	0.995789i	$-0.470779\pi$
$283$	3.08431	0.183343	0.0916715	+	0.995789i	$0.470779\pi$
$284$	−14.5186	−0.861518
$285$	25.9463	1.53693
$286$	0	0
$287$	−4.15934	−0.245518
$288$	1.45497	0.0857348
$289$	−8.35351	−0.491383
$290$	14.1249	0.829445
$291$	4.19808	0.246096
$292$	−4.34267	−0.254135
$293$	−25.9733	−1.51737	−0.758687	−	0.651456i	$-0.774159\pi$
$293$	−25.9733	−1.51737	−0.758687	+	0.651456i	$0.774159\pi$
$294$	−4.64535	−0.270922
$295$	27.7224	1.61406
$296$	−63.4979	−3.69074
$297$	21.7693	1.26318
$298$	−43.8852	−2.54220
$299$	0	0
$300$	−31.7491	−1.83303
$301$	−8.48158	−0.488870
$302$	−43.3447	−2.49421
$303$	2.40800	0.138336
$304$	51.1809	2.93543
$305$	5.16740	0.295884
$306$	0.961839	0.0549847
$307$	−15.8008	−0.901800	−0.450900	−	0.892574i	$-0.648897\pi$
$307$	−15.8008	−0.901800	−0.450900	+	0.892574i	$0.648897\pi$
$308$	21.0143	1.19740
$309$	−33.0211	−1.87850
$310$	−50.8641	−2.88889
$311$	14.2953	0.810613	0.405307	−	0.914181i	$-0.367165\pi$
$311$	14.2953	0.810613	0.405307	+	0.914181i	$0.367165\pi$
$312$	0	0
$313$	11.7613	0.664790	0.332395	−	0.943140i	$-0.392143\pi$
$313$	11.7613	0.664790	0.332395	+	0.943140i	$0.392143\pi$
$314$	−59.5110	−3.35840
$315$	−0.366293	−0.0206383
$316$	49.3133	2.77409
$317$	−20.9307	−1.17559	−0.587793	−	0.809011i	$-0.700003\pi$
$317$	−20.9307	−1.17559	−0.587793	+	0.809011i	$0.700003\pi$
$318$	−20.7830	−1.16545
$319$	−7.82198	−0.437947
$320$	−30.0131	−1.67779
$321$	−10.4971	−0.585889
$322$	19.9227	1.11025
$323$	14.6667	0.816074
$324$	−45.9151	−2.55084
$325$	0	0
$326$	−11.4911	−0.636431
$327$	−2.89039	−0.159839
$328$	−31.7712	−1.75427
$329$	0.910136	0.0501774
$330$	58.5509	3.22312
$331$	8.25635	0.453810	0.226905	−	0.973917i	$-0.427139\pi$
$331$	8.25635	0.453810	0.226905	+	0.973917i	$0.427139\pi$
$332$	29.6611	1.62786
$333$	−1.03467	−0.0566995
$334$	−45.2239	−2.47454
$335$	−1.21730	−0.0665082
$336$	−18.1378	−0.989499
$337$	−13.4122	−0.730611	−0.365305	−	0.930888i	$-0.619035\pi$
$337$	−13.4122	−0.730611	−0.365305	+	0.930888i	$0.619035\pi$
$338$	0	0
$339$	−1.53941	−0.0836092
$340$	−42.4594	−2.30268
$341$	28.1671	1.52533
$342$	1.63152	0.0882227
$343$	1.00000	0.0539949
$344$	−64.7867	−3.49307
$345$	39.4351	2.12311
$346$	58.8895	3.16592
$347$	−13.4937	−0.724379	−0.362190	−	0.932104i	$-0.617971\pi$
$347$	−13.4937	−0.724379	−0.362190	+	0.932104i	$0.617971\pi$
$348$	15.8396	0.849090
$349$	−16.1192	−0.862843	−0.431421	−	0.902151i	$-0.641988\pi$
$349$	−16.1192	−0.862843	−0.431421	+	0.902151i	$0.641988\pi$
$350$	9.62049	0.514237
$351$	0	0
$352$	50.0657	2.66851
$353$	37.4141	1.99135	0.995675	−	0.0929089i	$-0.0296165\pi$
$353$	37.4141	1.99135	0.995675	+	0.0929089i	$0.0296165\pi$
$354$	43.7595	2.32579
$355$	8.70811	0.462178
$356$	−18.7484	−0.993665
$357$	−5.19766	−0.275089
$358$	−7.23505	−0.382384
$359$	18.8373	0.994192	0.497096	−	0.867695i	$-0.334400\pi$
$359$	18.8373	0.994192	0.497096	+	0.867695i	$0.334400\pi$
$360$	−2.79794	−0.147464
$361$	5.87839	0.309389
$362$	16.4648	0.865372
$363$	−12.9801	−0.681277
$364$	0	0
$365$	2.60469	0.136336
$366$	8.15669	0.426357
$367$	32.9116	1.71797	0.858987	−	0.511997i	$-0.171094\pi$
$367$	32.9116	1.71797	0.858987	+	0.511997i	$0.171094\pi$
$368$	77.7884	4.05500
$369$	−0.517697	−0.0269502
$370$	64.2921	3.34239
$371$	4.47393	0.232275
$372$	−57.0386	−2.95731
$373$	−28.3543	−1.46813	−0.734065	−	0.679079i	$-0.762379\pi$
$373$	−28.3543	−1.46813	−0.734065	+	0.679079i	$0.762379\pi$
$374$	33.0970	1.71141
$375$	−6.96685	−0.359766
$376$	6.95210	0.358527
$377$	0	0
$378$	13.3579	0.687055
$379$	−3.59222	−0.184520	−0.0922600	−	0.995735i	$-0.529409\pi$
$379$	−3.59222	−0.184520	−0.0922600	+	0.995735i	$0.529409\pi$
$380$	−72.0219	−3.69465
$381$	10.1180	0.518360
$382$	61.5587	3.14961
$383$	18.6107	0.950962	0.475481	−	0.879726i	$-0.342274\pi$
$383$	18.6107	0.950962	0.475481	+	0.879726i	$0.342274\pi$
$384$	−6.04976	−0.308726
$385$	−12.6042	−0.642369
$386$	43.2862	2.20321
$387$	−1.05567	−0.0536627
$388$	−11.6531	−0.591594
$389$	−7.22028	−0.366083	−0.183041	−	0.983105i	$-0.558594\pi$
$389$	−7.22028	−0.366083	−0.183041	+	0.983105i	$0.558594\pi$
$390$	0	0
$391$	22.2914	1.12732
$392$	7.63852	0.385804
$393$	7.55830	0.381266
$394$	5.32791	0.268416
$395$	−29.5777	−1.48822
$396$	2.61557	0.131437
$397$	−3.49931	−0.175626	−0.0878128	−	0.996137i	$-0.527988\pi$
$397$	−3.49931	−0.175626	−0.0878128	+	0.996137i	$0.527988\pi$
$398$	−71.2823	−3.57306
$399$	−8.81656	−0.441380
$400$	37.5633	1.87816
$401$	37.0199	1.84869	0.924344	−	0.381560i	$-0.124613\pi$
$401$	37.0199	1.84869	0.924344	+	0.381560i	$0.124613\pi$
$402$	−1.92150	−0.0958355
$403$	0	0
$404$	−6.68414	−0.332548
$405$	27.5395	1.36845
$406$	−4.79965	−0.238203
$407$	−35.6031	−1.76478
$408$	−39.7024	−1.96556
$409$	−35.4369	−1.75224	−0.876122	−	0.482090i	$-0.839878\pi$
$409$	−35.4369	−1.75224	−0.876122	+	0.482090i	$0.839878\pi$
$410$	32.1686	1.58869
$411$	31.9224	1.57462
$412$	91.6601	4.51577
$413$	−9.42007	−0.463531
$414$	2.47970	0.121871
$415$	−17.7904	−0.873299
$416$	0	0
$417$	0.165187	0.00808926
$418$	56.1410	2.74595
$419$	13.3595	0.652657	0.326328	−	0.945256i	$-0.394189\pi$
$419$	13.3595	0.652657	0.326328	+	0.945256i	$0.394189\pi$
$420$	25.5236	1.24542
$421$	−10.9549	−0.533911	−0.266955	−	0.963709i	$-0.586018\pi$
$421$	−10.9549	−0.533911	−0.266955	+	0.963709i	$0.586018\pi$
$422$	−8.17401	−0.397904
$423$	0.113281	0.00550792
$424$	34.1742	1.65965
$425$	10.7643	0.522146
$426$	13.7457	0.665979
$427$	−1.75588	−0.0849730
$428$	29.1378	1.40843
$429$	0	0
$430$	65.5970	3.16337
$431$	−13.5976	−0.654971	−0.327486	−	0.944856i	$-0.606201\pi$
$431$	−13.5976	−0.654971	−0.327486	+	0.944856i	$0.606201\pi$
$432$	52.1559	2.50935
$433$	−17.8666	−0.858613	−0.429306	−	0.903159i	$-0.641242\pi$
$433$	−17.8666	−0.858613	−0.429306	+	0.903159i	$0.641242\pi$
$434$	17.2836	0.829640
$435$	−9.50044	−0.455511
$436$	8.02316	0.384240
$437$	37.8119	1.80879
$438$	4.11148	0.196454
$439$	−21.6009	−1.03096	−0.515478	−	0.856903i	$-0.672386\pi$
$439$	−21.6009	−1.03096	−0.515478	+	0.856903i	$0.672386\pi$
$440$	−96.2775	−4.58985
$441$	0.124466	0.00592696
$442$	0	0
$443$	29.7875	1.41525	0.707623	−	0.706590i	$-0.249768\pi$
$443$	29.7875	1.41525	0.707623	+	0.706590i	$0.249768\pi$
$444$	72.0966	3.42155
$445$	11.2452	0.533071
$446$	−41.4299	−1.96176
$447$	29.5172	1.39612
$448$	10.1985	0.481832
$449$	17.6072	0.830934	0.415467	−	0.909608i	$-0.363618\pi$
$449$	17.6072	0.830934	0.415467	+	0.909608i	$0.363618\pi$
$450$	1.19743	0.0564472
$451$	−17.8140	−0.838830
$452$	4.27310	0.200990
$453$	29.1537	1.36976
$454$	12.2297	0.573969
$455$	0	0
$456$	−67.3455	−3.15374
$457$	18.0432	0.844024	0.422012	−	0.906590i	$-0.361324\pi$
$457$	18.0432	0.844024	0.422012	+	0.906590i	$0.361324\pi$
$458$	−43.3954	−2.02773
$459$	14.9460	0.697622
$460$	−109.464	−5.10379
$461$	15.1623	0.706180	0.353090	−	0.935589i	$-0.385131\pi$
$461$	15.1623	0.706180	0.353090	+	0.935589i	$0.385131\pi$
$462$	−19.8956	−0.925627
$463$	−26.7145	−1.24153	−0.620765	−	0.783997i	$-0.713178\pi$
$463$	−26.7145	−1.24153	−0.620765	+	0.783997i	$0.713178\pi$
$464$	−18.7403	−0.869995
$465$	34.2113	1.58651
$466$	45.2082	2.09423
$467$	−29.4908	−1.36467	−0.682335	−	0.731039i	$-0.739036\pi$
$467$	−29.4908	−1.36467	−0.682335	+	0.731039i	$0.739036\pi$
$468$	0	0
$469$	0.413638	0.0191000
$470$	−7.03905	−0.324687
$471$	40.0271	1.84435
$472$	−71.9554	−3.31202
$473$	−36.3258	−1.67026
$474$	−46.6881	−2.14445
$475$	18.2590	0.837782
$476$	14.4277	0.661292
$477$	0.556853	0.0254966
$478$	11.6329	0.532077
$479$	−33.4865	−1.53004	−0.765019	−	0.644007i	$-0.777271\pi$
$479$	−33.4865	−1.53004	−0.765019	+	0.644007i	$0.777271\pi$
$480$	60.8089	2.77553
$481$	0	0
$482$	−48.7293	−2.21956
$483$	−13.4000	−0.609722
$484$	36.0301	1.63773
$485$	6.98940	0.317372
$486$	3.39717	0.154099
$487$	11.4592	0.519265	0.259633	−	0.965707i	$-0.416399\pi$
$487$	11.4592	0.519265	0.259633	+	0.965707i	$0.416399\pi$
$488$	−13.4123	−0.607148
$489$	7.72889	0.349513
$490$	−7.73406	−0.349389
$491$	−33.5043	−1.51203	−0.756013	−	0.654557i	$-0.772855\pi$
$491$	−33.5043	−1.51203	−0.756013	+	0.654557i	$0.772855\pi$
$492$	36.0735	1.62632
$493$	−5.37030	−0.241866
$494$	0	0
$495$	−1.56880	−0.0705122
$496$	67.4841	3.03012
$497$	−2.95901	−0.132730
$498$	−28.0820	−1.25839
$499$	26.3516	1.17966	0.589831	−	0.807527i	$-0.299194\pi$
$499$	26.3516	1.17966	0.589831	+	0.807527i	$0.299194\pi$
$500$	19.3386	0.864849
$501$	30.4176	1.35896
$502$	25.8129	1.15208
$503$	−28.4677	−1.26931	−0.634657	−	0.772794i	$-0.718858\pi$
$503$	−28.4677	−1.26931	−0.634657	+	0.772794i	$0.718858\pi$
$504$	0.950738	0.0423492
$505$	4.00909	0.178402
$506$	85.3270	3.79325
$507$	0	0
$508$	−28.0855	−1.24609
$509$	−29.8491	−1.32304	−0.661519	−	0.749929i	$-0.730088\pi$
$509$	−29.8491	−1.32304	−0.661519	+	0.749929i	$0.730088\pi$
$510$	40.1990	1.78004
$511$	−0.885074	−0.0391534
$512$	−36.8108	−1.62682
$513$	25.3523	1.11933
$514$	51.4382	2.26884
$515$	−54.9769	−2.42257
$516$	73.5599	3.23829
$517$	3.89803	0.171435
$518$	−21.8464	−0.959877
$519$	−39.6091	−1.73865
$520$	0	0
$521$	10.9955	0.481724	0.240862	−	0.970559i	$-0.422570\pi$
$521$	10.9955	0.481724	0.240862	+	0.970559i	$0.422570\pi$
$522$	−0.597394	−0.0261472
$523$	4.19652	0.183501	0.0917505	−	0.995782i	$-0.470754\pi$
$523$	4.19652	0.183501	0.0917505	+	0.995782i	$0.470754\pi$
$524$	−20.9804	−0.916531
$525$	−6.47075	−0.282407
$526$	−15.9578	−0.695793
$527$	19.3385	0.842400
$528$	−77.6825	−3.38070
$529$	34.4692	1.49866
$530$	−34.6017	−1.50300
$531$	−1.17248	−0.0508813
$532$	24.4730	1.06104
$533$	0	0
$534$	17.7504	0.768133
$535$	−17.4766	−0.755580
$536$	3.15959	0.136473
$537$	4.86630	0.209996
$538$	0.353176	0.0152265
$539$	4.28290	0.184478
$540$	−73.3939	−3.15837
$541$	7.98767	0.343417	0.171708	−	0.985148i	$-0.445071\pi$
$541$	7.98767	0.343417	0.171708	+	0.985148i	$0.445071\pi$
$542$	−39.3476	−1.69012
$543$	−11.0743	−0.475242
$544$	34.3733	1.47374
$545$	−4.81222	−0.206133
$546$	0	0
$547$	−20.5549	−0.878865	−0.439433	−	0.898276i	$-0.644820\pi$
$547$	−20.5549	−0.878865	−0.439433	+	0.898276i	$0.644820\pi$
$548$	−88.6104	−3.78525
$549$	−0.218548	−0.00932740
$550$	41.2036	1.75693
$551$	−9.10940	−0.388074
$552$	−102.356	−4.35658
$553$	10.0505	0.427390
$554$	40.8946	1.73745
$555$	−43.2429	−1.83556
$556$	−0.458528	−0.0194459
$557$	−8.79065	−0.372472	−0.186236	−	0.982505i	$-0.559629\pi$
$557$	−8.79065	−0.372472	−0.186236	+	0.982505i	$0.559629\pi$
$558$	2.15123	0.0910687
$559$	0	0
$560$	−30.1977	−1.27609
$561$	−22.2611	−0.939863
$562$	58.7027	2.47623
$563$	30.9567	1.30467	0.652335	−	0.757931i	$-0.273790\pi$
$563$	30.9567	1.30467	0.652335	+	0.757931i	$0.273790\pi$
$564$	−7.89353	−0.332377
$565$	−2.56297	−0.107825
$566$	8.10566	0.340706
$567$	−9.35791	−0.392995
$568$	−22.6025	−0.948379
$569$	23.4540	0.983242	0.491621	−	0.870809i	$-0.336405\pi$
$569$	23.4540	0.983242	0.491621	+	0.870809i	$0.336405\pi$
$570$	68.1878	2.85607
$571$	16.6808	0.698071	0.349036	−	0.937109i	$-0.386509\pi$
$571$	16.6808	0.698071	0.349036	+	0.937109i	$0.386509\pi$
$572$	0	0
$573$	−41.4044	−1.72969
$574$	−10.9309	−0.456246
$575$	27.7514	1.15731
$576$	1.26936	0.0528901
$577$	16.8209	0.700263	0.350132	−	0.936701i	$-0.386137\pi$
$577$	16.8209	0.700263	0.350132	+	0.936701i	$0.386137\pi$
$578$	−21.9533	−0.913137
$579$	−29.1143	−1.20995
$580$	26.3714	1.09501
$581$	6.04519	0.250797
$582$	11.0327	0.457320
$583$	19.1614	0.793584
$584$	−6.76066	−0.279758
$585$	0	0
$586$	−68.2585	−2.81973
$587$	25.0653	1.03455	0.517277	−	0.855818i	$-0.326946\pi$
$587$	25.0653	1.03455	0.517277	+	0.855818i	$0.326946\pi$
$588$	−8.67291	−0.357665
$589$	32.8031	1.35163
$590$	72.8554	2.99941
$591$	−3.58356	−0.147408
$592$	−85.2996	−3.50579
$593$	−9.99617	−0.410493	−0.205247	−	0.978710i	$-0.565800\pi$
$593$	−9.99617	−0.410493	−0.205247	+	0.978710i	$0.565800\pi$
$594$	57.2105	2.34737
$595$	−8.65360	−0.354763
$596$	−81.9339	−3.35615
$597$	47.9445	1.96224
$598$	0	0
$599$	−5.51511	−0.225341	−0.112671	−	0.993632i	$-0.535941\pi$
$599$	−5.51511	−0.225341	−0.112671	+	0.993632i	$0.535941\pi$
$600$	−49.4269	−2.01785
$601$	−13.1290	−0.535544	−0.267772	−	0.963482i	$-0.586287\pi$
$601$	−13.1290	−0.535544	−0.267772	+	0.963482i	$0.586287\pi$
$602$	−22.2899	−0.908467
$603$	0.0514840	0.00209659
$604$	−80.9248	−3.29278
$605$	−21.6106	−0.878594
$606$	6.32831	0.257070
$607$	−12.8493	−0.521537	−0.260768	−	0.965401i	$-0.583976\pi$
$607$	−12.8493	−0.521537	−0.260768	+	0.965401i	$0.583976\pi$
$608$	58.3060	2.36462
$609$	3.22825	0.130815
$610$	13.5801	0.549842
$611$	0	0
$612$	1.79576	0.0725893
$613$	−23.9497	−0.967321	−0.483660	−	0.875256i	$-0.660693\pi$
$613$	−23.9497	−0.967321	−0.483660	+	0.875256i	$0.660693\pi$
$614$	−41.5251	−1.67581
$615$	−21.6366	−0.872472
$616$	32.7151	1.31813
$617$	33.6198	1.35348	0.676742	−	0.736221i	$-0.263391\pi$
$617$	33.6198	1.35348	0.676742	+	0.736221i	$0.263391\pi$
$618$	−86.7805	−3.49082
$619$	39.1125	1.57206	0.786031	−	0.618187i	$-0.212132\pi$
$619$	39.1125	1.57206	0.786031	+	0.618187i	$0.212132\pi$
$620$	−94.9637	−3.81384
$621$	38.5322	1.54624
$622$	37.5686	1.50636
$623$	−3.82110	−0.153089
$624$	0	0
$625$	−29.9027	−1.19611
$626$	30.9092	1.23538
$627$	−37.7605	−1.50801
$628$	−111.107	−4.43367
$629$	−24.4439	−0.974640
$630$	−0.962630	−0.0383521
$631$	−22.4517	−0.893788	−0.446894	−	0.894587i	$-0.647470\pi$
$631$	−22.4517	−0.893788	−0.446894	+	0.894587i	$0.647470\pi$
$632$	76.7709	3.05378
$633$	5.49784	0.218520
$634$	−55.0066	−2.18459
$635$	16.8455	0.668492
$636$	−38.8020	−1.53860
$637$	0	0
$638$	−20.5564	−0.813837
$639$	−0.368297	−0.0145696
$640$	−10.0723	−0.398141
$641$	−30.5785	−1.20778	−0.603888	−	0.797069i	$-0.706383\pi$
$641$	−30.5785	−1.20778	−0.603888	+	0.797069i	$0.706383\pi$
$642$	−27.5866	−1.08876
$643$	−43.9241	−1.73220	−0.866098	−	0.499874i	$-0.833380\pi$
$643$	−43.9241	−1.73220	−0.866098	+	0.499874i	$0.833380\pi$
$644$	37.1958	1.46572
$645$	−44.1206	−1.73725
$646$	38.5444	1.51651
$647$	5.07899	0.199676	0.0998379	−	0.995004i	$-0.468168\pi$
$647$	5.07899	0.199676	0.0998379	+	0.995004i	$0.468168\pi$
$648$	−71.4806	−2.80802
$649$	−40.3452	−1.58369
$650$	0	0
$651$	−11.6250	−0.455619
$652$	−21.4539	−0.840199
$653$	−13.6294	−0.533360	−0.266680	−	0.963785i	$-0.585927\pi$
$653$	−13.6294	−0.533360	−0.266680	+	0.963785i	$0.585927\pi$
$654$	−7.59604	−0.297029
$655$	12.5838	0.491691
$656$	−42.6797	−1.66636
$657$	−0.110162	−0.00429782
$658$	2.39187	0.0932447
$659$	−41.6783	−1.62356	−0.811778	−	0.583967i	$-0.801500\pi$
$659$	−41.6783	−1.62356	−0.811778	+	0.583967i	$0.801500\pi$
$660$	109.315	4.25508
$661$	−21.5457	−0.838029	−0.419015	−	0.907979i	$-0.637624\pi$
$661$	−21.5457	−0.838029	−0.419015	+	0.907979i	$0.637624\pi$
$662$	21.6980	0.843315
$663$	0	0
$664$	46.1763	1.79199
$665$	−14.6787	−0.569216
$666$	−2.71914	−0.105365
$667$	−13.8451	−0.536085
$668$	−84.4334	−3.26683
$669$	27.8658	1.07735
$670$	−3.19910	−0.123592
$671$	−7.52027	−0.290317
$672$	−20.6628	−0.797086
$673$	30.4598	1.17414	0.587070	−	0.809536i	$-0.300281\pi$
$673$	30.4598	1.17414	0.587070	+	0.809536i	$0.300281\pi$
$674$	−35.2478	−1.35769
$675$	18.6069	0.716178
$676$	0	0
$677$	−32.1171	−1.23436	−0.617179	−	0.786822i	$-0.711725\pi$
$677$	−32.1171	−1.23436	−0.617179	+	0.786822i	$0.711725\pi$
$678$	−4.04562	−0.155371
$679$	−2.37500	−0.0911440
$680$	−66.1007	−2.53485
$681$	−8.22571	−0.315210
$682$	74.0241	2.83453
$683$	30.4004	1.16324	0.581620	−	0.813460i	$-0.302419\pi$
$683$	30.4004	1.16324	0.581620	+	0.813460i	$0.302419\pi$
$684$	3.04607	0.116469
$685$	53.1478	2.03067
$686$	2.62803	0.100339
$687$	29.1878	1.11358
$688$	−87.0309	−3.31802
$689$	0	0
$690$	103.637	3.94538
$691$	−10.0657	−0.382917	−0.191458	−	0.981501i	$-0.561322\pi$
$691$	−10.0657	−0.382917	−0.191458	+	0.981501i	$0.561322\pi$
$692$	109.947	4.17956
$693$	0.533077	0.0202499
$694$	−35.4619	−1.34611
$695$	0.275021	0.0104321
$696$	24.6590	0.934698
$697$	−12.2305	−0.463263
$698$	−42.3619	−1.60342
$699$	−30.4071	−1.15010
$700$	17.9615	0.678882
$701$	−10.9013	−0.411738	−0.205869	−	0.978580i	$-0.566002\pi$
$701$	−10.9013	−0.411738	−0.205869	+	0.978580i	$0.566002\pi$
$702$	0	0
$703$	−41.4630	−1.56381
$704$	43.6790	1.64621
$705$	4.73447	0.178310
$706$	98.3254	3.70052
$707$	−1.36229	−0.0512341
$708$	81.6994	3.07045
$709$	−21.2250	−0.797122	−0.398561	−	0.917142i	$-0.630490\pi$
$709$	−21.2250	−0.797122	−0.398561	+	0.917142i	$0.630490\pi$
$710$	22.8852	0.858866
$711$	1.25095	0.0469142
$712$	−29.1876	−1.09385
$713$	49.8565	1.86714
$714$	−13.6596	−0.511198
$715$	0	0
$716$	−13.5079	−0.504813
$717$	−7.82430	−0.292204
$718$	49.5049	1.84751
$719$	17.3439	0.646819	0.323409	−	0.946259i	$-0.395171\pi$
$719$	17.3439	0.646819	0.323409	+	0.946259i	$0.395171\pi$
$720$	−3.75860	−0.140075
$721$	18.6811	0.695722
$722$	15.4486	0.574937
$723$	32.7754	1.21893
$724$	30.7400	1.14244
$725$	−6.68567	−0.248300
$726$	−34.1120	−1.26602
$727$	44.4135	1.64720	0.823602	−	0.567168i	$-0.191961\pi$
$727$	44.4135	1.64720	0.823602	+	0.567168i	$0.191961\pi$
$728$	0	0
$729$	25.7888	0.955140
$730$	6.84522	0.253353
$731$	−24.9400	−0.922439
$732$	15.2286	0.562865
$733$	16.4500	0.607594	0.303797	−	0.952737i	$-0.401746\pi$
$733$	16.4500	0.607594	0.303797	+	0.952737i	$0.401746\pi$
$734$	86.4929	3.19251
$735$	5.20193	0.191876
$736$	88.6175	3.26648
$737$	1.77157	0.0652567
$738$	−1.36052	−0.0500816
$739$	−16.2732	−0.598621	−0.299310	−	0.954156i	$-0.596757\pi$
$739$	−16.2732	−0.598621	−0.299310	+	0.954156i	$0.596757\pi$
$740$	120.034	4.41253
$741$	0	0
$742$	11.7576	0.431636
$743$	−1.61345	−0.0591918	−0.0295959	−	0.999562i	$-0.509422\pi$
$743$	−1.61345	−0.0591918	−0.0295959	+	0.999562i	$0.509422\pi$
$744$	−88.7976	−3.25548
$745$	49.1433	1.80047
$746$	−74.5160	−2.72823
$747$	0.752422	0.0275297
$748$	61.7924	2.25935
$749$	5.93855	0.216990
$750$	−18.3091	−0.668554
$751$	−3.02262	−0.110297	−0.0551485	−	0.998478i	$-0.517563\pi$
$751$	−3.02262	−0.110297	−0.0551485	+	0.998478i	$0.517563\pi$
$752$	9.33907	0.340561
$753$	−17.3617	−0.632697
$754$	0	0
$755$	48.5380	1.76648
$756$	24.9392	0.907031
$757$	−30.4752	−1.10764	−0.553821	−	0.832636i	$-0.686831\pi$
$757$	−30.4752	−1.10764	−0.553821	+	0.832636i	$0.686831\pi$
$758$	−9.44047	−0.342893
$759$	−57.3910	−2.08316
$760$	−112.124	−4.06715
$761$	24.4562	0.886538	0.443269	−	0.896389i	$-0.353819\pi$
$761$	24.4562	0.886538	0.443269	+	0.896389i	$0.353819\pi$
$762$	26.5904	0.963268
$763$	1.63519	0.0591979
$764$	114.930	4.15804
$765$	−1.07708	−0.0389420
$766$	48.9095	1.76717
$767$	0	0
$768$	20.1549	0.727279
$769$	−34.3811	−1.23982	−0.619908	−	0.784675i	$-0.712830\pi$
$769$	−34.3811	−1.23982	−0.619908	+	0.784675i	$0.712830\pi$
$770$	−33.1242	−1.19371
$771$	−34.5974	−1.24599
$772$	80.8157	2.90862
$773$	−0.930605	−0.0334715	−0.0167358	−	0.999860i	$-0.505327\pi$
$773$	−0.930605	−0.0334715	−0.0167358	+	0.999860i	$0.505327\pi$
$774$	−2.77433	−0.0997214
$775$	24.0752	0.864808
$776$	−18.1415	−0.651241
$777$	14.6939	0.527142
$778$	−18.9751	−0.680291
$779$	−20.7460	−0.743304
$780$	0	0
$781$	−12.6732	−0.453481
$782$	58.5825	2.09491
$783$	−9.28293	−0.331745
$784$	10.2612	0.366471
$785$	66.6413	2.37853
$786$	19.8635	0.708506
$787$	35.7268	1.27352	0.636762	−	0.771061i	$-0.280274\pi$
$787$	35.7268	1.27352	0.636762	+	0.771061i	$0.280274\pi$
$788$	9.94725	0.354356
$789$	10.7332	0.382113
$790$	−77.7311	−2.76555
$791$	0.870896	0.0309655
$792$	4.07192	0.144689
$793$	0	0
$794$	−9.19631	−0.326365
$795$	23.2731	0.825412
$796$	−133.085	−4.71706
$797$	14.1123	0.499884	0.249942	−	0.968261i	$-0.419588\pi$
$797$	14.1123	0.499884	0.249942	+	0.968261i	$0.419588\pi$
$798$	−23.1702	−0.820216
$799$	2.67625	0.0946788
$800$	42.7926	1.51295
$801$	−0.475598	−0.0168044
$802$	97.2896	3.43542
$803$	−3.79069	−0.133770
$804$	−3.58745	−0.126519
$805$	−22.3097	−0.786315
$806$	0	0
$807$	−0.237546	−0.00836203
$808$	−10.4059	−0.366077
$809$	−26.6217	−0.935970	−0.467985	−	0.883736i	$-0.655020\pi$
$809$	−26.6217	−0.935970	−0.467985	+	0.883736i	$0.655020\pi$
$810$	72.3746	2.54299
$811$	54.9687	1.93021	0.965106	−	0.261861i	$-0.0843362\pi$
$811$	54.9687	1.93021	0.965106	+	0.261861i	$0.0843362\pi$
$812$	−8.96098	−0.314469
$813$	26.4652	0.928176
$814$	−93.5662	−3.27949
$815$	12.8679	0.450741
$816$	−53.3341	−1.86707
$817$	−42.3046	−1.48005
$818$	−93.1294	−3.25619
$819$	0	0
$820$	60.0590	2.09735
$821$	24.9388	0.870370	0.435185	−	0.900341i	$-0.356683\pi$
$821$	24.9388	0.870370	0.435185	+	0.900341i	$0.356683\pi$
$822$	83.8932	2.92611
$823$	−2.81664	−0.0981820	−0.0490910	−	0.998794i	$-0.515632\pi$
$823$	−2.81664	−0.0981820	−0.0490910	+	0.998794i	$0.515632\pi$
$824$	142.696	4.97106
$825$	−27.7136	−0.964863
$826$	−24.7562	−0.861380
$827$	−27.5297	−0.957302	−0.478651	−	0.878005i	$-0.658874\pi$
$827$	−27.5297	−0.957302	−0.478651	+	0.878005i	$0.658874\pi$
$828$	4.62963	0.160891
$829$	22.5946	0.784744	0.392372	−	0.919807i	$-0.371655\pi$
$829$	22.5946	0.784744	0.392372	+	0.919807i	$0.371655\pi$
$830$	−46.7539	−1.62285
$831$	−27.5057	−0.954164
$832$	0	0
$833$	2.94049	0.101882
$834$	0.434118	0.0150323
$835$	50.6424	1.75255
$836$	104.816	3.62512
$837$	33.4280	1.15544
$838$	35.1093	1.21283
$839$	−35.2752	−1.21784	−0.608918	−	0.793233i	$-0.708396\pi$
$839$	−35.2752	−1.21784	−0.608918	+	0.793233i	$0.708396\pi$
$840$	39.7351	1.37099
$841$	−25.6645	−0.884984
$842$	−28.7899	−0.992166
$843$	−39.4835	−1.35988
$844$	−15.2609	−0.525303
$845$	0	0
$846$	0.297707	0.0102354
$847$	7.34326	0.252317
$848$	45.9078	1.57648
$849$	−5.45187	−0.187108
$850$	28.2890	0.970304
$851$	−63.0184	−2.16024
$852$	25.6632	0.879208
$853$	−48.7120	−1.66787	−0.833934	−	0.551864i	$-0.813917\pi$
$853$	−48.7120	−1.66787	−0.833934	+	0.551864i	$0.813917\pi$
$854$	−4.61451	−0.157905
$855$	−1.82700	−0.0624822
$856$	45.3617	1.55043
$857$	−7.16347	−0.244700	−0.122350	−	0.992487i	$-0.539043\pi$
$857$	−7.16347	−0.244700	−0.122350	+	0.992487i	$0.539043\pi$
$858$	0	0
$859$	−36.8202	−1.25629	−0.628144	−	0.778097i	$-0.716185\pi$
$859$	−36.8202	−1.25629	−0.628144	+	0.778097i	$0.716185\pi$
$860$	122.470	4.17620
$861$	7.35211	0.250559
$862$	−35.7348	−1.21713
$863$	11.2697	0.383624	0.191812	−	0.981432i	$-0.438564\pi$
$863$	11.2697	0.383624	0.191812	+	0.981432i	$0.438564\pi$
$864$	59.4167	2.02140
$865$	−65.9453	−2.24221
$866$	−46.9539	−1.59556
$867$	14.7658	0.501473
$868$	32.2686	1.09527
$869$	43.0453	1.46021
$870$	−24.9675	−0.846476
$871$	0	0
$872$	12.4905	0.422980
$873$	−0.295607	−0.0100048
$874$	99.3710	3.36127
$875$	3.94138	0.133243
$876$	7.67617	0.259354
$877$	24.5926	0.830432	0.415216	−	0.909723i	$-0.363706\pi$
$877$	24.5926	0.830432	0.415216	+	0.909723i	$0.363706\pi$
$878$	−56.7679	−1.91582
$879$	45.9107	1.54853
$880$	−129.334	−4.35984
$881$	−25.1057	−0.845832	−0.422916	−	0.906169i	$-0.638993\pi$
$881$	−25.1057	−0.845832	−0.422916	+	0.906169i	$0.638993\pi$
$882$	0.327101	0.0110141
$883$	55.6948	1.87428	0.937140	−	0.348953i	$-0.113463\pi$
$883$	55.6948	1.87428	0.937140	+	0.348953i	$0.113463\pi$
$884$	0	0
$885$	−49.0026	−1.64720
$886$	78.2825	2.62995
$887$	28.0635	0.942281	0.471141	−	0.882058i	$-0.343842\pi$
$887$	28.0635	0.942281	0.471141	+	0.882058i	$0.343842\pi$
$888$	112.240	3.76652
$889$	−5.72408	−0.191980
$890$	29.5526	0.990606
$891$	−40.0790	−1.34270
$892$	−77.3499	−2.58987
$893$	4.53960	0.151912
$894$	77.5722	2.59440
$895$	8.10191	0.270817
$896$	3.42255	0.114340
$897$	0	0
$898$	46.2722	1.54412
$899$	−12.0111	−0.400593
$900$	2.23560	0.0745201
$901$	13.1556	0.438275
$902$	−46.8159	−1.55880
$903$	14.9922	0.498908
$904$	6.65236	0.221254
$905$	−18.4376	−0.612885
$906$	76.6168	2.54542
$907$	−34.1285	−1.13322	−0.566609	−	0.823987i	$-0.691745\pi$
$907$	−34.1285	−1.13322	−0.566609	+	0.823987i	$0.691745\pi$
$908$	22.8330	0.757739
$909$	−0.169559	−0.00562391
$910$	0	0
$911$	32.8842	1.08950	0.544751	−	0.838598i	$-0.316624\pi$
$911$	32.8842	1.08950	0.544751	+	0.838598i	$0.316624\pi$
$912$	−90.4682	−2.99570
$913$	25.8910	0.856866
$914$	47.4180	1.56845
$915$	−9.13398	−0.301960
$916$	−81.0195	−2.67696
$917$	−4.27598	−0.141205
$918$	39.2787	1.29639
$919$	−8.57983	−0.283022	−0.141511	−	0.989937i	$-0.545196\pi$
$919$	−8.57983	−0.283022	−0.141511	+	0.989937i	$0.545196\pi$
$920$	−170.414	−5.61837
$921$	27.9298	0.920317
$922$	39.8471	1.31229
$923$	0	0
$924$	−37.1452	−1.22199
$925$	−30.4310	−1.00057
$926$	−70.2067	−2.30713
$927$	2.32517	0.0763687
$928$	−21.3491	−0.700820
$929$	−31.4204	−1.03087	−0.515435	−	0.856929i	$-0.672370\pi$
$929$	−31.4204	−1.03087	−0.515435	+	0.856929i	$0.672370\pi$
$930$	89.9083	2.94821
$931$	4.98782	0.163469
$932$	84.4041	2.76475
$933$	−25.2686	−0.827258
$934$	−77.5028	−2.53597
$935$	−37.0625	−1.21207
$936$	0	0
$937$	5.52675	0.180551	0.0902755	−	0.995917i	$-0.471225\pi$
$937$	5.52675	0.180551	0.0902755	+	0.995917i	$0.471225\pi$
$938$	1.08705	0.0354936
$939$	−20.7895	−0.678441
$940$	−13.1420	−0.428644
$941$	49.6039	1.61704	0.808521	−	0.588468i	$-0.200269\pi$
$941$	49.6039	1.61704	0.808521	+	0.588468i	$0.200269\pi$
$942$	105.193	3.42736
$943$	−31.5313	−1.02680
$944$	−96.6610	−3.14605
$945$	−14.9583	−0.486595
$946$	−95.4653	−3.10384
$947$	16.3021	0.529748	0.264874	−	0.964283i	$-0.414670\pi$
$947$	16.3021	0.529748	0.264874	+	0.964283i	$0.414670\pi$
$948$	−87.1670	−2.83105
$949$	0	0
$950$	47.9853	1.55685
$951$	36.9975	1.19972
$952$	22.4610	0.727965
$953$	49.6685	1.60892	0.804461	−	0.594006i	$-0.202454\pi$
$953$	49.6685	1.60892	0.804461	+	0.594006i	$0.202454\pi$
$954$	1.46343	0.0473802
$955$	−68.9343	−2.23066
$956$	21.7187	0.702434
$957$	13.8263	0.446940
$958$	−88.0037	−2.84327
$959$	−18.0596	−0.583175
$960$	53.0517	1.71224
$961$	12.2522	0.395232
$962$	0	0
$963$	0.739149	0.0238187
$964$	−90.9780	−2.93020
$965$	−48.4726	−1.56039
$966$	−35.2157	−1.13305
$967$	0.978584	0.0314691	0.0157346	−	0.999876i	$-0.494991\pi$
$967$	0.978584	0.0314691	0.0157346	+	0.999876i	$0.494991\pi$
$968$	56.0917	1.80285
$969$	−25.9250	−0.832831
$970$	18.3684	0.589773
$971$	−8.33615	−0.267520	−0.133760	−	0.991014i	$-0.542705\pi$
$971$	−8.33615	−0.267520	−0.133760	+	0.991014i	$0.542705\pi$
$972$	6.34254	0.203437
$973$	−0.0934521	−0.00299594
$974$	30.1151	0.964951
$975$	0	0
$976$	−18.0174	−0.576723
$977$	46.0001	1.47167	0.735837	−	0.677159i	$-0.236789\pi$
$977$	46.0001	1.47167	0.735837	+	0.677159i	$0.236789\pi$
$978$	20.3118	0.649499
$979$	−16.3654	−0.523040
$980$	−14.4396	−0.461255
$981$	0.203526	0.00649809
$982$	−88.0503	−2.80980
$983$	21.5565	0.687546	0.343773	−	0.939053i	$-0.388295\pi$
$983$	21.5565	0.687546	0.343773	+	0.939053i	$0.388295\pi$
$984$	56.1593	1.79029
$985$	−5.96628	−0.190101
$986$	−14.1133	−0.449460
$987$	−1.60877	−0.0512078
$988$	0	0
$989$	−64.2975	−2.04454
$990$	−4.12285	−0.131033
$991$	−20.8493	−0.662299	−0.331150	−	0.943578i	$-0.607437\pi$
$991$	−20.8493	−0.662299	−0.331150	+	0.943578i	$0.607437\pi$
$992$	76.8787	2.44090
$993$	−14.5941	−0.463128
$994$	−7.77638	−0.246652
$995$	79.8230	2.53056
$996$	−52.4294	−1.66129
$997$	2.72406	0.0862718	0.0431359	−	0.999069i	$-0.486265\pi$
$997$	2.72406	0.0862718	0.0431359	+	0.999069i	$0.486265\pi$
$998$	69.2530	2.19216
$999$	−42.2529	−1.33682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.12	yes	12
7.6	odd	2		8281.2.a.cq.1.12		12
13.5	odd	4		1183.2.c.j.337.1		24
13.8	odd	4		1183.2.c.j.337.24		24
13.12	even	2		1183.2.a.q.1.1	✓	12
91.90	odd	2		8281.2.a.cn.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.1	✓	12	13.12	even	2
1183.2.a.r.1.12	yes	12	1.1	even	1	trivial
1183.2.c.j.337.1		24	13.5	odd	4
1183.2.c.j.337.24		24	13.8	odd	4
8281.2.a.cn.1.1		12	91.90	odd	2
8281.2.a.cq.1.12		12	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+2.62803 q^{2} -1.76762 q^{3} +4.90656 q^{4} -2.94291 q^{5} -4.64535 q^{6} +1.00000 q^{7} +7.63852 q^{8} +0.124466 q^{9} +O(q^{10})\)	\(q+2.62803 q^{2} -1.76762 q^{3} +4.90656 q^{4} -2.94291 q^{5} -4.64535 q^{6} +1.00000 q^{7} +7.63852 q^{8} +0.124466 q^{9} -7.73406 q^{10} +4.28290 q^{11} -8.67291 q^{12} +2.62803 q^{14} +5.20193 q^{15} +10.2612 q^{16} +2.94049 q^{17} +0.327101 q^{18} +4.98782 q^{19} -14.4396 q^{20} -1.76762 q^{21} +11.2556 q^{22} +7.58085 q^{23} -13.5020 q^{24} +3.66072 q^{25} +5.08284 q^{27} +4.90656 q^{28} -1.82633 q^{29} +13.6709 q^{30} +6.57664 q^{31} +11.6897 q^{32} -7.57053 q^{33} +7.72771 q^{34} -2.94291 q^{35} +0.610701 q^{36} -8.31285 q^{37} +13.1082 q^{38} -22.4795 q^{40} -4.15934 q^{41} -4.64535 q^{42} -8.48158 q^{43} +21.0143 q^{44} -0.366293 q^{45} +19.9227 q^{46} +0.910136 q^{47} -18.1378 q^{48} +1.00000 q^{49} +9.62049 q^{50} -5.19766 q^{51} +4.47393 q^{53} +13.3579 q^{54} -12.6042 q^{55} +7.63852 q^{56} -8.81656 q^{57} -4.79965 q^{58} -9.42007 q^{59} +25.5236 q^{60} -1.75588 q^{61} +17.2836 q^{62} +0.124466 q^{63} +10.1985 q^{64} -19.8956 q^{66} +0.413638 q^{67} +14.4277 q^{68} -13.4000 q^{69} -7.73406 q^{70} -2.95901 q^{71} +0.950738 q^{72} -0.885074 q^{73} -21.8464 q^{74} -6.47075 q^{75} +24.4730 q^{76} +4.28290 q^{77} +10.0505 q^{79} -30.1977 q^{80} -9.35791 q^{81} -10.9309 q^{82} +6.04519 q^{83} -8.67291 q^{84} -8.65360 q^{85} -22.2899 q^{86} +3.22825 q^{87} +32.7151 q^{88} -3.82110 q^{89} -0.962630 q^{90} +37.1958 q^{92} -11.6250 q^{93} +2.39187 q^{94} -14.6787 q^{95} -20.6628 q^{96} -2.37500 q^{97} +2.62803 q^{98} +0.533077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

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