LMFDB - Embedded newform 1183.2.a.q.1.5

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			1.5
Root			$0.983820$ 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)

$f(q)$	$=$	$q-0.983820 q^{2} -1.57171 q^{3} -1.03210 q^{4} -0.398447 q^{5} +1.54628 q^{6} -1.00000 q^{7} +2.98304 q^{8} -0.529731 q^{9} +O(q^{10})$	\(q-0.983820 q^{2} -1.57171 q^{3} -1.03210 q^{4} -0.398447 q^{5} +1.54628 q^{6} -1.00000 q^{7} +2.98304 q^{8} -0.529731 q^{9} +0.392000 q^{10} -4.24206 q^{11} +1.62216 q^{12} +0.983820 q^{14} +0.626242 q^{15} -0.870575 q^{16} -5.10528 q^{17} +0.521160 q^{18} -2.12698 q^{19} +0.411236 q^{20} +1.57171 q^{21} +4.17342 q^{22} +2.19449 q^{23} -4.68847 q^{24} -4.84124 q^{25} +5.54771 q^{27} +1.03210 q^{28} +2.90902 q^{29} -0.616110 q^{30} -2.20466 q^{31} -5.10959 q^{32} +6.66728 q^{33} +5.02268 q^{34} +0.398447 q^{35} +0.546734 q^{36} -11.4227 q^{37} +2.09256 q^{38} -1.18858 q^{40} -5.07633 q^{41} -1.54628 q^{42} -0.328195 q^{43} +4.37822 q^{44} +0.211070 q^{45} -2.15899 q^{46} -6.62722 q^{47} +1.36829 q^{48} +1.00000 q^{49} +4.76291 q^{50} +8.02401 q^{51} +10.9423 q^{53} -5.45795 q^{54} +1.69024 q^{55} -2.98304 q^{56} +3.34299 q^{57} -2.86195 q^{58} +7.70620 q^{59} -0.646344 q^{60} +14.6039 q^{61} +2.16899 q^{62} +0.529731 q^{63} +6.76806 q^{64} -6.55941 q^{66} -1.22074 q^{67} +5.26915 q^{68} -3.44910 q^{69} -0.392000 q^{70} +1.75019 q^{71} -1.58021 q^{72} +6.11791 q^{73} +11.2379 q^{74} +7.60902 q^{75} +2.19525 q^{76} +4.24206 q^{77} +4.20871 q^{79} +0.346878 q^{80} -7.13019 q^{81} +4.99419 q^{82} -10.8154 q^{83} -1.62216 q^{84} +2.03418 q^{85} +0.322884 q^{86} -4.57213 q^{87} -12.6542 q^{88} +15.6973 q^{89} -0.207654 q^{90} -2.26493 q^{92} +3.46508 q^{93} +6.51999 q^{94} +0.847488 q^{95} +8.03079 q^{96} +14.4763 q^{97} -0.983820 q^{98} +2.24715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.983820	−0.695666	−0.347833	−	0.937557i	$-0.613082\pi$
$2$	−0.983820	−0.695666	−0.347833	+	0.937557i	$0.613082\pi$
$3$	−1.57171	−0.907427	−0.453713	−	0.891148i	$-0.649901\pi$
$3$	−1.57171	−0.907427	−0.453713	+	0.891148i	$0.649901\pi$
$4$	−1.03210	−0.516049
$5$	−0.398447	−0.178191	−0.0890954	−	0.996023i	$-0.528398\pi$
$5$	−0.398447	−0.178191	−0.0890954	+	0.996023i	$0.528398\pi$
$6$	1.54628	0.631265
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.98304	1.05466
$9$	−0.529731	−0.176577
$10$	0.392000	0.123961
$11$	−4.24206	−1.27903	−0.639515	−	0.768779i	$-0.720865\pi$
$11$	−4.24206	−1.27903	−0.639515	+	0.768779i	$0.720865\pi$
$12$	1.62216	0.468277
$13$	0	0
$13$	0	0
$14$	0.983820	0.262937
$15$	0.626242	0.161695
$16$	−0.870575	−0.217644
$17$	−5.10528	−1.23821	−0.619106	−	0.785307i	$-0.712505\pi$
$17$	−5.10528	−1.23821	−0.619106	+	0.785307i	$0.712505\pi$
$18$	0.521160	0.122838
$19$	−2.12698	−0.487962	−0.243981	−	0.969780i	$-0.578454\pi$
$19$	−2.12698	−0.487962	−0.243981	+	0.969780i	$0.578454\pi$
$20$	0.411236	0.0919553
$21$	1.57171	0.342975
$22$	4.17342	0.889777
$23$	2.19449	0.457583	0.228792	−	0.973475i	$-0.426523\pi$
$23$	2.19449	0.457583	0.228792	+	0.973475i	$0.426523\pi$
$24$	−4.68847	−0.957030
$25$	−4.84124	−0.968248
$26$	0	0
$27$	5.54771	1.06766
$28$	1.03210	0.195048
$29$	2.90902	0.540191	0.270095	−	0.962834i	$-0.412945\pi$
$29$	2.90902	0.540191	0.270095	+	0.962834i	$0.412945\pi$
$30$	−0.616110	−0.112486
$31$	−2.20466	−0.395968	−0.197984	−	0.980205i	$-0.563439\pi$
$31$	−2.20466	−0.395968	−0.197984	+	0.980205i	$0.563439\pi$
$32$	−5.10959	−0.903256
$33$	6.66728	1.16063
$34$	5.02268	0.861382
$35$	0.398447	0.0673498
$36$	0.546734	0.0911224
$37$	−11.4227	−1.87788	−0.938941	−	0.344077i	$-0.888192\pi$
$37$	−11.4227	−1.87788	−0.938941	+	0.344077i	$0.888192\pi$
$38$	2.09256	0.339459
$39$	0	0
$40$	−1.18858	−0.187931
$41$	−5.07633	−0.792790	−0.396395	−	0.918080i	$-0.629739\pi$
$41$	−5.07633	−0.792790	−0.396395	+	0.918080i	$0.629739\pi$
$42$	−1.54628	−0.238596
$43$	−0.328195	−0.0500492	−0.0250246	−	0.999687i	$-0.507966\pi$
$43$	−0.328195	−0.0500492	−0.0250246	+	0.999687i	$0.507966\pi$
$44$	4.37822	0.660042
$45$	0.211070	0.0314644
$46$	−2.15899	−0.318325
$47$	−6.62722	−0.966679	−0.483340	−	0.875433i	$-0.660576\pi$
$47$	−6.62722	−0.966679	−0.483340	+	0.875433i	$0.660576\pi$
$48$	1.36829	0.197496
$49$	1.00000	0.142857
$50$	4.76291	0.673577
$51$	8.02401	1.12359
$52$	0	0
$53$	10.9423	1.50304	0.751518	−	0.659712i	$-0.229322\pi$
$53$	10.9423	1.50304	0.751518	+	0.659712i	$0.229322\pi$
$54$	−5.45795	−0.742732
$55$	1.69024	0.227911
$56$	−2.98304	−0.398625
$57$	3.34299	0.442790
$58$	−2.86195	−0.375792
$59$	7.70620	1.00326	0.501631	−	0.865082i	$-0.332734\pi$
$59$	7.70620	1.00326	0.501631	+	0.865082i	$0.332734\pi$
$60$	−0.646344	−0.0834427
$61$	14.6039	1.86984	0.934921	−	0.354857i	$-0.115470\pi$
$61$	14.6039	1.86984	0.934921	+	0.354857i	$0.115470\pi$
$62$	2.16899	0.275462
$63$	0.529731	0.0667398
$64$	6.76806	0.846008
$65$	0	0
$66$	−6.55941	−0.807407
$67$	−1.22074	−0.149137	−0.0745685	−	0.997216i	$-0.523758\pi$
$67$	−1.22074	−0.149137	−0.0745685	+	0.997216i	$0.523758\pi$
$68$	5.26915	0.638979
$69$	−3.44910	−0.415223
$70$	−0.392000	−0.0468529
$71$	1.75019	0.207709	0.103854	−	0.994593i	$-0.466882\pi$
$71$	1.75019	0.207709	0.103854	+	0.994593i	$0.466882\pi$
$72$	−1.58021	−0.186229
$73$	6.11791	0.716047	0.358023	−	0.933713i	$-0.383451\pi$
$73$	6.11791	0.716047	0.358023	+	0.933713i	$0.383451\pi$
$74$	11.2379	1.30638
$75$	7.60902	0.878614
$76$	2.19525	0.251813
$77$	4.24206	0.483428
$78$	0	0
$79$	4.20871	0.473517	0.236759	−	0.971569i	$-0.423915\pi$
$79$	4.20871	0.473517	0.236759	+	0.971569i	$0.423915\pi$
$80$	0.346878	0.0387821
$81$	−7.13019	−0.792244
$82$	4.99419	0.551517
$83$	−10.8154	−1.18714	−0.593571	−	0.804782i	$-0.702282\pi$
$83$	−10.8154	−1.18714	−0.593571	+	0.804782i	$0.702282\pi$
$84$	−1.62216	−0.176992
$85$	2.03418	0.220638
$86$	0.322884	0.0348175
$87$	−4.57213	−0.490183
$88$	−12.6542	−1.34895
$89$	15.6973	1.66392	0.831958	−	0.554839i	$-0.187220\pi$
$89$	15.6973	1.66392	0.831958	+	0.554839i	$0.187220\pi$
$90$	−0.207654	−0.0218887
$91$	0	0
$92$	−2.26493	−0.236136
$93$	3.46508	0.359312
$94$	6.51999	0.672485
$95$	0.847488	0.0869504
$96$	8.03079	0.819639
$97$	14.4763	1.46985	0.734924	−	0.678149i	$-0.237218\pi$
$97$	14.4763	1.46985	0.734924	+	0.678149i	$0.237218\pi$
$98$	−0.983820	−0.0993808
$99$	2.24715	0.225847
$100$	4.99664	0.499664
$101$	7.31830	0.728198	0.364099	−	0.931360i	$-0.381377\pi$
$101$	7.31830	0.728198	0.364099	+	0.931360i	$0.381377\pi$
$102$	−7.89418	−0.781641
$103$	−12.7643	−1.25770	−0.628851	−	0.777526i	$-0.716474\pi$
$103$	−12.7643	−1.25770	−0.628851	+	0.777526i	$0.716474\pi$
$104$	0	0
$105$	−0.626242	−0.0611150
$106$	−10.7652	−1.04561
$107$	9.06986	0.876816	0.438408	−	0.898776i	$-0.355542\pi$
$107$	9.06986	0.876816	0.438408	+	0.898776i	$0.355542\pi$
$108$	−5.72578	−0.550964
$109$	4.95091	0.474211	0.237106	−	0.971484i	$-0.423801\pi$
$109$	4.95091	0.474211	0.237106	+	0.971484i	$0.423801\pi$
$110$	−1.66289	−0.158550
$111$	17.9532	1.70404
$112$	0.870575	0.0822616
$113$	2.39270	0.225086	0.112543	−	0.993647i	$-0.464100\pi$
$113$	2.39270	0.225086	0.112543	+	0.993647i	$0.464100\pi$
$114$	−3.28890	−0.308034
$115$	−0.874389	−0.0815372
$116$	−3.00239	−0.278765
$117$	0	0
$118$	−7.58151	−0.697935
$119$	5.10528	0.468000
$120$	1.86811	0.170534
$121$	6.99507	0.635915
$122$	−14.3676	−1.30078
$123$	7.97852	0.719398
$124$	2.27543	0.204339
$125$	3.92121	0.350724
$126$	−0.521160	−0.0464286
$127$	15.0587	1.33625	0.668123	−	0.744051i	$-0.267098\pi$
$127$	15.0587	1.33625	0.668123	+	0.744051i	$0.267098\pi$
$128$	3.56062	0.314718
$129$	0.515826	0.0454160
$130$	0	0
$131$	−11.6011	−1.01359	−0.506796	−	0.862066i	$-0.669170\pi$
$131$	−11.6011	−1.01359	−0.506796	+	0.862066i	$0.669170\pi$
$132$	−6.88129	−0.598940
$133$	2.12698	0.184432
$134$	1.20099	0.103750
$135$	−2.21047	−0.190247
$136$	−15.2292	−1.30590
$137$	−0.410279	−0.0350525	−0.0175263	−	0.999846i	$-0.505579\pi$
$137$	−0.410279	−0.0350525	−0.0175263	+	0.999846i	$0.505579\pi$
$138$	3.39330	0.288857
$139$	−18.1715	−1.54129	−0.770644	−	0.637266i	$-0.780065\pi$
$139$	−18.1715	−1.54129	−0.770644	+	0.637266i	$0.780065\pi$
$140$	−0.411236	−0.0347558
$141$	10.4161	0.877190
$142$	−1.72187	−0.144496
$143$	0	0
$144$	0.461170	0.0384309
$145$	−1.15909	−0.0962570
$146$	−6.01892	−0.498129
$147$	−1.57171	−0.129632
$148$	11.7894	0.969080
$149$	−10.9195	−0.894561	−0.447280	−	0.894394i	$-0.647607\pi$
$149$	−10.9195	−0.894561	−0.447280	+	0.894394i	$0.647607\pi$
$150$	−7.48590	−0.611222
$151$	−20.3174	−1.65341	−0.826703	−	0.562639i	$-0.809786\pi$
$151$	−20.3174	−1.65341	−0.826703	+	0.562639i	$0.809786\pi$
$152$	−6.34486	−0.514636
$153$	2.70442	0.218640
$154$	−4.17342	−0.336304
$155$	0.878439	0.0705579
$156$	0	0
$157$	23.4474	1.87131	0.935653	−	0.352922i	$-0.114812\pi$
$157$	23.4474	1.87131	0.935653	+	0.352922i	$0.114812\pi$
$158$	−4.14062	−0.329410
$159$	−17.1981	−1.36390
$160$	2.03590	0.160952
$161$	−2.19449	−0.172950
$162$	7.01482	0.551137
$163$	−12.7006	−0.994791	−0.497396	−	0.867524i	$-0.665710\pi$
$163$	−12.7006	−0.994791	−0.497396	+	0.867524i	$0.665710\pi$
$164$	5.23927	0.409119
$165$	−2.65656	−0.206813
$166$	10.6404	0.825853
$167$	10.0996	0.781531	0.390765	−	0.920490i	$-0.372210\pi$
$167$	10.0996	0.781531	0.390765	+	0.920490i	$0.372210\pi$
$168$	4.68847	0.361723
$169$	0	0
$170$	−2.00127	−0.153490
$171$	1.12673	0.0861629
$172$	0.338729	0.0258279
$173$	16.5810	1.26063	0.630316	−	0.776339i	$-0.282925\pi$
$173$	16.5810	1.26063	0.630316	+	0.776339i	$0.282925\pi$
$174$	4.49815	0.341004
$175$	4.84124	0.365963
$176$	3.69303	0.278373
$177$	−12.1119	−0.910386
$178$	−15.4434	−1.15753
$179$	−23.5863	−1.76292	−0.881461	−	0.472257i	$-0.843439\pi$
$179$	−23.5863	−1.76292	−0.881461	+	0.472257i	$0.843439\pi$
$180$	−0.217845	−0.0162372
$181$	−23.7219	−1.76324	−0.881619	−	0.471962i	$-0.843546\pi$
$181$	−23.7219	−1.76324	−0.881619	+	0.471962i	$0.843546\pi$
$182$	0	0
$183$	−22.9531	−1.69674
$184$	6.54626	0.482596
$185$	4.55134	0.334621
$186$	−3.40902	−0.249961
$187$	21.6569	1.58371
$188$	6.83994	0.498854
$189$	−5.54771	−0.403537
$190$	−0.833775	−0.0604884
$191$	2.18467	0.158077	0.0790385	−	0.996872i	$-0.474815\pi$
$191$	2.18467	0.158077	0.0790385	+	0.996872i	$0.474815\pi$
$192$	−10.6374	−0.767690
$193$	−18.6395	−1.34170	−0.670851	−	0.741592i	$-0.734071\pi$
$193$	−18.6395	−1.34170	−0.670851	+	0.741592i	$0.734071\pi$
$194$	−14.2421	−1.02252
$195$	0	0
$196$	−1.03210	−0.0737213
$197$	14.9820	1.06743	0.533713	−	0.845666i	$-0.320796\pi$
$197$	14.9820	1.06743	0.533713	+	0.845666i	$0.320796\pi$
$198$	−2.21079	−0.157114
$199$	8.58624	0.608662	0.304331	−	0.952566i	$-0.401567\pi$
$199$	8.58624	0.608662	0.304331	+	0.952566i	$0.401567\pi$
$200$	−14.4416	−1.02118
$201$	1.91865	0.135331
$202$	−7.19989	−0.506583
$203$	−2.90902	−0.204173
$204$	−8.28157	−0.579826
$205$	2.02265	0.141268
$206$	12.5578	0.874940
$207$	−1.16249	−0.0807987
$208$	0	0
$209$	9.02277	0.624118
$210$	0.616110	0.0425156
$211$	−28.3478	−1.95155	−0.975773	−	0.218785i	$-0.929791\pi$
$211$	−28.3478	−1.95155	−0.975773	+	0.218785i	$0.929791\pi$
$212$	−11.2935	−0.775641
$213$	−2.75078	−0.188481
$214$	−8.92310	−0.609971
$215$	0.130768	0.00891831
$216$	16.5490	1.12602
$217$	2.20466	0.149662
$218$	−4.87080	−0.329892
$219$	−9.61557	−0.649760
$220$	−1.74449	−0.117613
$221$	0	0
$222$	−17.6627	−1.18544
$223$	14.1295	0.946181	0.473091	−	0.881014i	$-0.343138\pi$
$223$	14.1295	0.946181	0.473091	+	0.881014i	$0.343138\pi$
$224$	5.10959	0.341399
$225$	2.56455	0.170970
$226$	−2.35399	−0.156585
$227$	18.7325	1.24332	0.621661	−	0.783286i	$-0.286458\pi$
$227$	18.7325	1.24332	0.621661	+	0.783286i	$0.286458\pi$
$228$	−3.45030	−0.228502
$229$	3.24595	0.214499	0.107249	−	0.994232i	$-0.465796\pi$
$229$	3.24595	0.214499	0.107249	+	0.994232i	$0.465796\pi$
$230$	0.860241	0.0567226
$231$	−6.66728	−0.438675
$232$	8.67771	0.569719
$233$	17.4275	1.14171	0.570856	−	0.821050i	$-0.306612\pi$
$233$	17.4275	1.14171	0.570856	+	0.821050i	$0.306612\pi$
$234$	0	0
$235$	2.64059	0.172253
$236$	−7.95356	−0.517732
$237$	−6.61487	−0.429682
$238$	−5.02268	−0.325572
$239$	3.89803	0.252142	0.126071	−	0.992021i	$-0.459763\pi$
$239$	3.89803	0.252142	0.126071	+	0.992021i	$0.459763\pi$
$240$	−0.545191	−0.0351919
$241$	−17.6973	−1.13998	−0.569990	−	0.821652i	$-0.693053\pi$
$241$	−17.6973	−1.13998	−0.569990	+	0.821652i	$0.693053\pi$
$242$	−6.88189	−0.442385
$243$	−5.43654	−0.348754
$244$	−15.0727	−0.964930
$245$	−0.398447	−0.0254558
$246$	−7.84942	−0.500461
$247$	0	0
$248$	−6.57658	−0.417613
$249$	16.9986	1.07724
$250$	−3.85776	−0.243986
$251$	−1.70708	−0.107750	−0.0538750	−	0.998548i	$-0.517157\pi$
$251$	−1.70708	−0.107750	−0.0538750	+	0.998548i	$0.517157\pi$
$252$	−0.546734	−0.0344410
$253$	−9.30917	−0.585262
$254$	−14.8151	−0.929581
$255$	−3.19714	−0.200213
$256$	−17.0391	−1.06495
$257$	23.2726	1.45171	0.725853	−	0.687849i	$-0.241445\pi$
$257$	23.2726	1.45171	0.725853	+	0.687849i	$0.241445\pi$
$258$	−0.507480	−0.0315943
$259$	11.4227	0.709773
$260$	0	0
$261$	−1.54100	−0.0953852
$262$	11.4134	0.705121
$263$	14.0596	0.866949	0.433475	−	0.901166i	$-0.357287\pi$
$263$	14.0596	0.866949	0.433475	+	0.901166i	$0.357287\pi$
$264$	19.8888	1.22407
$265$	−4.35991	−0.267827
$266$	−2.09256	−0.128303
$267$	−24.6717	−1.50988
$268$	1.25992	0.0769621
$269$	3.44689	0.210161	0.105080	−	0.994464i	$-0.466490\pi$
$269$	3.44689	0.210161	0.105080	+	0.994464i	$0.466490\pi$
$270$	2.17470	0.132348
$271$	21.2277	1.28949	0.644744	−	0.764399i	$-0.276964\pi$
$271$	21.2277	1.28949	0.644744	+	0.764399i	$0.276964\pi$
$272$	4.44453	0.269489
$273$	0	0
$274$	0.403641	0.0243848
$275$	20.5368	1.23842
$276$	3.55982	0.214276
$277$	7.06655	0.424588	0.212294	−	0.977206i	$-0.431907\pi$
$277$	7.06655	0.424588	0.212294	+	0.977206i	$0.431907\pi$
$278$	17.8775	1.07222
$279$	1.16788	0.0699189
$280$	1.18858	0.0710314
$281$	−2.37834	−0.141880	−0.0709398	−	0.997481i	$-0.522600\pi$
$281$	−2.37834	−0.141880	−0.0709398	+	0.997481i	$0.522600\pi$
$282$	−10.2475	−0.610231
$283$	−14.2529	−0.847248	−0.423624	−	0.905838i	$-0.639242\pi$
$283$	−14.2529	−0.847248	−0.423624	+	0.905838i	$0.639242\pi$
$284$	−1.80636	−0.107188
$285$	−1.33200	−0.0789011
$286$	0	0
$287$	5.07633	0.299646
$288$	2.70671	0.159494
$289$	9.06388	0.533169
$290$	1.14033	0.0669627
$291$	−22.7526	−1.33378
$292$	−6.31428	−0.369515
$293$	7.15874	0.418218	0.209109	−	0.977892i	$-0.432944\pi$
$293$	7.15874	0.418218	0.209109	+	0.977892i	$0.432944\pi$
$294$	1.54628	0.0901808
$295$	−3.07051	−0.178772
$296$	−34.0744	−1.98053
$297$	−23.5337	−1.36556
$298$	10.7428	0.622315
$299$	0	0
$300$	−7.85326	−0.453408
$301$	0.328195	0.0189168
$302$	19.9887	1.15022
$303$	−11.5022	−0.660787
$304$	1.85169	0.106202
$305$	−5.81889	−0.333189
$306$	−2.66067	−0.152100
$307$	−24.4217	−1.39382	−0.696910	−	0.717159i	$-0.745442\pi$
$307$	−24.4217	−1.39382	−0.696910	+	0.717159i	$0.745442\pi$
$308$	−4.37822	−0.249472
$309$	20.0617	1.14127
$310$	−0.864226	−0.0490847
$311$	23.7212	1.34510	0.672552	−	0.740050i	$-0.265198\pi$
$311$	23.7212	1.34510	0.672552	+	0.740050i	$0.265198\pi$
$312$	0	0
$313$	−15.0876	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$313$	−15.0876	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$314$	−23.0680	−1.30180
$315$	−0.211070	−0.0118924
$316$	−4.34381	−0.244358
$317$	−31.5913	−1.77434	−0.887172	−	0.461440i	$-0.847333\pi$
$317$	−31.5913	−1.77434	−0.887172	+	0.461440i	$0.847333\pi$
$318$	16.9198	0.948815
$319$	−12.3402	−0.690920
$320$	−2.69671	−0.150751
$321$	−14.2552	−0.795646
$322$	2.15899	0.120316
$323$	10.8588	0.604201
$324$	7.35906	0.408837
$325$	0	0
$326$	12.4951	0.692042
$327$	−7.78139	−0.430312
$328$	−15.1429	−0.836126
$329$	6.62722	0.365370
$330$	2.61357	0.143873
$331$	−19.8976	−1.09367	−0.546835	−	0.837240i	$-0.684168\pi$
$331$	−19.8976	−1.09367	−0.546835	+	0.837240i	$0.684168\pi$
$332$	11.1625	0.612623
$333$	6.05096	0.331591
$334$	−9.93619	−0.543684
$335$	0.486400	0.0265749
$336$	−1.36829	−0.0746464
$337$	−2.71943	−0.148137	−0.0740685	−	0.997253i	$-0.523598\pi$
$337$	−2.71943	−0.148137	−0.0740685	+	0.997253i	$0.523598\pi$
$338$	0	0
$339$	−3.76063	−0.204249
$340$	−2.09948	−0.113860
$341$	9.35229	0.506455
$342$	−1.10850	−0.0599406
$343$	−1.00000	−0.0539949
$344$	−0.979017	−0.0527851
$345$	1.37428	0.0739890
$346$	−16.3127	−0.876978
$347$	−12.8135	−0.687865	−0.343932	−	0.938994i	$-0.611759\pi$
$347$	−12.8135	−0.687865	−0.343932	+	0.938994i	$0.611759\pi$
$348$	4.71889	0.252959
$349$	9.05354	0.484625	0.242312	−	0.970198i	$-0.422094\pi$
$349$	9.05354	0.484625	0.242312	+	0.970198i	$0.422094\pi$
$350$	−4.76291	−0.254588
$351$	0	0
$352$	21.6752	1.15529
$353$	9.43537	0.502194	0.251097	−	0.967962i	$-0.419209\pi$
$353$	9.43537	0.502194	0.251097	+	0.967962i	$0.419209\pi$
$354$	11.9159	0.633324
$355$	−0.697356	−0.0370118
$356$	−16.2012	−0.858662
$357$	−8.02401	−0.424676
$358$	23.2047	1.22640
$359$	−9.68118	−0.510953	−0.255477	−	0.966815i	$-0.582232\pi$
$359$	−9.68118	−0.510953	−0.255477	+	0.966815i	$0.582232\pi$
$360$	0.629629	0.0331843
$361$	−14.4760	−0.761893
$362$	23.3381	1.22662
$363$	−10.9942	−0.577047
$364$	0	0
$365$	−2.43766	−0.127593
$366$	22.5817	1.18037
$367$	−15.3650	−0.802047	−0.401023	−	0.916068i	$-0.631345\pi$
$367$	−15.3650	−0.802047	−0.401023	+	0.916068i	$0.631345\pi$
$368$	−1.91047	−0.0995901
$369$	2.68909	0.139988
$370$	−4.47770	−0.232785
$371$	−10.9423	−0.568094
$372$	−3.57631	−0.185423
$373$	12.6878	0.656948	0.328474	−	0.944513i	$-0.393466\pi$
$373$	12.6878	0.656948	0.328474	+	0.944513i	$0.393466\pi$
$374$	−21.3065	−1.10173
$375$	−6.16300	−0.318256
$376$	−19.7692	−1.01952
$377$	0	0
$378$	5.45795	0.280726
$379$	−6.59026	−0.338519	−0.169259	−	0.985572i	$-0.554138\pi$
$379$	−6.59026	−0.338519	−0.169259	+	0.985572i	$0.554138\pi$
$380$	−0.874691	−0.0448707
$381$	−23.6679	−1.21255
$382$	−2.14932	−0.109969
$383$	31.3776	1.60332	0.801660	−	0.597781i	$-0.203951\pi$
$383$	31.3776	1.60332	0.801660	+	0.597781i	$0.203951\pi$
$384$	−5.59626	−0.285583
$385$	−1.69024	−0.0861424
$386$	18.3379	0.933376
$387$	0.173855	0.00883754
$388$	−14.9410	−0.758514
$389$	16.4265	0.832857	0.416428	−	0.909169i	$-0.363282\pi$
$389$	16.4265	0.832857	0.416428	+	0.909169i	$0.363282\pi$
$390$	0	0
$391$	−11.2035	−0.566585
$392$	2.98304	0.150666
$393$	18.2335	0.919760
$394$	−14.7396	−0.742572
$395$	−1.67695	−0.0843764
$396$	−2.31928	−0.116548
$397$	6.94037	0.348327	0.174163	−	0.984717i	$-0.444278\pi$
$397$	6.94037	0.348327	0.174163	+	0.984717i	$0.444278\pi$
$398$	−8.44731	−0.423425
$399$	−3.34299	−0.167359
$400$	4.21466	0.210733
$401$	0.890125	0.0444507	0.0222254	−	0.999753i	$-0.492925\pi$
$401$	0.890125	0.0444507	0.0222254	+	0.999753i	$0.492925\pi$
$402$	−1.88760	−0.0941451
$403$	0	0
$404$	−7.55321	−0.375786
$405$	2.84100	0.141171
$406$	2.86195	0.142036
$407$	48.4558	2.40187
$408$	23.9359	1.18501
$409$	−2.00173	−0.0989793	−0.0494897	−	0.998775i	$-0.515759\pi$
$409$	−2.00173	−0.0989793	−0.0494897	+	0.998775i	$0.515759\pi$
$410$	−1.98992	−0.0982752
$411$	0.644840	0.0318076
$412$	13.1740	0.649036
$413$	−7.70620	−0.379197
$414$	1.14368	0.0562088
$415$	4.30935	0.211538
$416$	0	0
$417$	28.5603	1.39861
$418$	−8.87678	−0.434178
$419$	32.3340	1.57962	0.789809	−	0.613353i	$-0.210180\pi$
$419$	32.3340	1.57962	0.789809	+	0.613353i	$0.210180\pi$
$420$	0.646344	0.0315384
$421$	−9.10353	−0.443679	−0.221839	−	0.975083i	$-0.571206\pi$
$421$	−9.10353	−0.443679	−0.221839	+	0.975083i	$0.571206\pi$
$422$	27.8892	1.35762
$423$	3.51064	0.170693
$424$	32.6412	1.58520
$425$	24.7159	1.19890
$426$	2.70627	0.131119
$427$	−14.6039	−0.706734
$428$	−9.36099	−0.452480
$429$	0	0
$430$	−0.128652	−0.00620416
$431$	15.8655	0.764216	0.382108	−	0.924118i	$-0.375198\pi$
$431$	15.8655	0.764216	0.382108	+	0.924118i	$0.375198\pi$
$432$	−4.82970	−0.232369
$433$	15.8736	0.762835	0.381418	−	0.924403i	$-0.375436\pi$
$433$	15.8736	0.762835	0.381418	+	0.924403i	$0.375436\pi$
$434$	−2.16899	−0.104115
$435$	1.82175	0.0873462
$436$	−5.10983	−0.244716
$437$	−4.66764	−0.223283
$438$	9.45999	0.452016
$439$	5.37687	0.256624	0.128312	−	0.991734i	$-0.459044\pi$
$439$	5.37687	0.256624	0.128312	+	0.991734i	$0.459044\pi$
$440$	5.04204	0.240370
$441$	−0.529731	−0.0252253
$442$	0	0
$443$	−25.4188	−1.20768	−0.603841	−	0.797105i	$-0.706364\pi$
$443$	−25.4188	−1.20768	−0.603841	+	0.797105i	$0.706364\pi$
$444$	−18.5295	−0.879369
$445$	−6.25456	−0.296494
$446$	−13.9009	−0.658226
$447$	17.1623	0.811748
$448$	−6.76806	−0.319761
$449$	15.4369	0.728512	0.364256	−	0.931299i	$-0.381323\pi$
$449$	15.4369	0.728512	0.364256	+	0.931299i	$0.381323\pi$
$450$	−2.52306	−0.118938
$451$	21.5341	1.01400
$452$	−2.46950	−0.116156
$453$	31.9330	1.50034
$454$	−18.4294	−0.864936
$455$	0	0
$456$	9.97227	0.466995
$457$	−30.2784	−1.41636	−0.708181	−	0.706031i	$-0.750484\pi$
$457$	−30.2784	−1.41636	−0.708181	+	0.706031i	$0.750484\pi$
$458$	−3.19343	−0.149219
$459$	−28.3226	−1.32199
$460$	0.902455	0.0420772
$461$	−25.3431	−1.18035	−0.590173	−	0.807276i	$-0.700941\pi$
$461$	−25.3431	−1.18035	−0.590173	+	0.807276i	$0.700941\pi$
$462$	6.55941	0.305171
$463$	2.93975	0.136622	0.0683109	−	0.997664i	$-0.478239\pi$
$463$	2.93975	0.136622	0.0683109	+	0.997664i	$0.478239\pi$
$464$	−2.53252	−0.117569
$465$	−1.38065	−0.0640262
$466$	−17.1455	−0.794250
$467$	24.0967	1.11506	0.557531	−	0.830156i	$-0.311749\pi$
$467$	24.0967	1.11506	0.557531	+	0.830156i	$0.311749\pi$
$468$	0	0
$469$	1.22074	0.0563685
$470$	−2.59787	−0.119831
$471$	−36.8525	−1.69807
$472$	22.9879	1.05810
$473$	1.39222	0.0640144
$474$	6.50784	0.298915
$475$	10.2972	0.472469
$476$	−5.26915	−0.241511
$477$	−5.79646	−0.265402
$478$	−3.83495	−0.175407
$479$	−11.1069	−0.507488	−0.253744	−	0.967271i	$-0.581662\pi$
$479$	−11.1069	−0.507488	−0.253744	+	0.967271i	$0.581662\pi$
$480$	−3.19984	−0.146052
$481$	0	0
$482$	17.4109	0.793045
$483$	3.44910	0.156940
$484$	−7.21960	−0.328164
$485$	−5.76805	−0.261913
$486$	5.34858	0.242616
$487$	29.1520	1.32100	0.660501	−	0.750825i	$-0.270344\pi$
$487$	29.1520	1.32100	0.660501	+	0.750825i	$0.270344\pi$
$488$	43.5641	1.97205
$489$	19.9617	0.902700
$490$	0.392000	0.0177087
$491$	0.374507	0.0169013	0.00845063	−	0.999964i	$-0.497310\pi$
$491$	0.374507	0.0169013	0.00845063	+	0.999964i	$0.497310\pi$
$492$	−8.23462	−0.371245
$493$	−14.8513	−0.668871
$494$	0	0
$495$	−0.895370	−0.0402439
$496$	1.91932	0.0861800
$497$	−1.75019	−0.0785066
$498$	−16.7236	−0.749401
$499$	0.402490	0.0180179	0.00900896	−	0.999959i	$-0.497132\pi$
$499$	0.402490	0.0180179	0.00900896	+	0.999959i	$0.497132\pi$
$500$	−4.04708	−0.180991
$501$	−15.8736	−0.709182
$502$	1.67946	0.0749580
$503$	14.1098	0.629124	0.314562	−	0.949237i	$-0.398142\pi$
$503$	14.1098	0.629124	0.314562	+	0.949237i	$0.398142\pi$
$504$	1.58021	0.0703880
$505$	−2.91596	−0.129758
$506$	9.15854	0.407147
$507$	0	0
$508$	−15.5421	−0.689569
$509$	−37.0510	−1.64225	−0.821127	−	0.570745i	$-0.806655\pi$
$509$	−37.0510	−1.64225	−0.821127	+	0.570745i	$0.806655\pi$
$510$	3.14541	0.139281
$511$	−6.11791	−0.270640
$512$	9.64220	0.426129
$513$	−11.7999	−0.520977
$514$	−22.8961	−1.00990
$515$	5.08589	0.224111
$516$	−0.532384	−0.0234369
$517$	28.1131	1.23641
$518$	−11.2379	−0.493765
$519$	−26.0605	−1.14393
$520$	0	0
$521$	28.5515	1.25086	0.625432	−	0.780279i	$-0.284923\pi$
$521$	28.5515	1.25086	0.625432	+	0.780279i	$0.284923\pi$
$522$	1.51606	0.0663562
$523$	−7.85498	−0.343474	−0.171737	−	0.985143i	$-0.554938\pi$
$523$	−7.85498	−0.343474	−0.171737	+	0.985143i	$0.554938\pi$
$524$	11.9735	0.523063
$525$	−7.60902	−0.332085
$526$	−13.8321	−0.603107
$527$	11.2554	0.490293
$528$	−5.80437	−0.252603
$529$	−18.1842	−0.790617
$530$	4.28937	0.186318
$531$	−4.08221	−0.177153
$532$	−2.19525	−0.0951763
$533$	0	0
$534$	24.2725	1.05037
$535$	−3.61386	−0.156241
$536$	−3.64151	−0.157289
$537$	37.0708	1.59972
$538$	−3.39112	−0.146202
$539$	−4.24206	−0.182718
$540$	2.28142	0.0981767
$541$	36.0835	1.55135	0.775676	−	0.631131i	$-0.217409\pi$
$541$	36.0835	1.55135	0.775676	+	0.631131i	$0.217409\pi$
$542$	−20.8842	−0.897052
$543$	37.2840	1.60001
$544$	26.0859	1.11842
$545$	−1.97267	−0.0845001
$546$	0	0
$547$	−30.0255	−1.28380	−0.641899	−	0.766789i	$-0.721853\pi$
$547$	−30.0255	−1.28380	−0.641899	+	0.766789i	$0.721853\pi$
$548$	0.423449	0.0180888
$549$	−7.73615	−0.330171
$550$	−20.2045	−0.861524
$551$	−6.18742	−0.263593
$552$	−10.2888	−0.437921
$553$	−4.20871	−0.178973
$554$	−6.95221	−0.295371
$555$	−7.15339	−0.303644
$556$	18.7548	0.795380
$557$	11.6919	0.495400	0.247700	−	0.968837i	$-0.420325\pi$
$557$	11.6919	0.495400	0.247700	+	0.968837i	$0.420325\pi$
$558$	−1.14898	−0.0486402
$559$	0	0
$560$	−0.346878	−0.0146583
$561$	−34.0383	−1.43710
$562$	2.33985	0.0987008
$563$	−24.4062	−1.02860	−0.514300	−	0.857610i	$-0.671948\pi$
$563$	−24.4062	−1.02860	−0.514300	+	0.857610i	$0.671948\pi$
$564$	−10.7504	−0.452674
$565$	−0.953364	−0.0401083
$566$	14.0223	0.589401
$567$	7.13019	0.299440
$568$	5.22087	0.219063
$569$	21.2322	0.890099	0.445050	−	0.895506i	$-0.353186\pi$
$569$	21.2322	0.890099	0.445050	+	0.895506i	$0.353186\pi$
$570$	1.31045	0.0548888
$571$	29.0906	1.21741	0.608703	−	0.793398i	$-0.291690\pi$
$571$	29.0906	1.21741	0.608703	+	0.793398i	$0.291690\pi$
$572$	0	0
$573$	−3.43366	−0.143443
$574$	−4.99419	−0.208454
$575$	−10.6241	−0.443054
$576$	−3.58525	−0.149385
$577$	25.1627	1.04754	0.523768	−	0.851861i	$-0.324526\pi$
$577$	25.1627	1.04754	0.523768	+	0.851861i	$0.324526\pi$
$578$	−8.91723	−0.370908
$579$	29.2959	1.21750
$580$	1.19629	0.0496734
$581$	10.8154	0.448697
$582$	22.3844	0.927864
$583$	−46.4178	−1.92243
$584$	18.2499	0.755188
$585$	0	0
$586$	−7.04291	−0.290940
$587$	−21.7327	−0.897006	−0.448503	−	0.893781i	$-0.648043\pi$
$587$	−21.7327	−0.897006	−0.448503	+	0.893781i	$0.648043\pi$
$588$	1.62216	0.0668967
$589$	4.68926	0.193218
$590$	3.02083	0.124366
$591$	−23.5474	−0.968611
$592$	9.94433	0.408709
$593$	30.7678	1.26348	0.631741	−	0.775180i	$-0.282341\pi$
$593$	30.7678	1.26348	0.631741	+	0.775180i	$0.282341\pi$
$594$	23.1529	0.949976
$595$	−2.03418	−0.0833934
$596$	11.2700	0.461637
$597$	−13.4951	−0.552316
$598$	0	0
$599$	−17.7791	−0.726436	−0.363218	−	0.931704i	$-0.618322\pi$
$599$	−17.7791	−0.726436	−0.363218	+	0.931704i	$0.618322\pi$
$600$	22.6980	0.926642
$601$	−7.17744	−0.292774	−0.146387	−	0.989227i	$-0.546764\pi$
$601$	−7.17744	−0.292774	−0.146387	+	0.989227i	$0.546764\pi$
$602$	−0.322884	−0.0131598
$603$	0.646663	0.0263342
$604$	20.9696	0.853239
$605$	−2.78716	−0.113314
$606$	11.3161	0.459687
$607$	27.2937	1.10782	0.553908	−	0.832578i	$-0.313136\pi$
$607$	27.2937	1.10782	0.553908	+	0.832578i	$0.313136\pi$
$608$	10.8680	0.440755
$609$	4.57213	0.185272
$610$	5.72474	0.231788
$611$	0	0
$612$	−2.79123	−0.112829
$613$	19.4824	0.786888	0.393444	−	0.919349i	$-0.371284\pi$
$613$	19.4824	0.786888	0.393444	+	0.919349i	$0.371284\pi$
$614$	24.0265	0.969632
$615$	−3.17901	−0.128190
$616$	12.6542	0.509853
$617$	−7.14474	−0.287636	−0.143818	−	0.989604i	$-0.545938\pi$
$617$	−7.14474	−0.287636	−0.143818	+	0.989604i	$0.545938\pi$
$618$	−19.7371	−0.793944
$619$	22.9703	0.923255	0.461628	−	0.887074i	$-0.347266\pi$
$619$	22.9703	0.923255	0.461628	+	0.887074i	$0.347266\pi$
$620$	−0.906636	−0.0364114
$621$	12.1744	0.488542
$622$	−23.3374	−0.935743
$623$	−15.6973	−0.628901
$624$	0	0
$625$	22.6438	0.905752
$626$	14.8435	0.593266
$627$	−14.1812	−0.566341
$628$	−24.2000	−0.965686
$629$	58.3161	2.32522
$630$	0.207654	0.00827315
$631$	30.1524	1.20035	0.600173	−	0.799870i	$-0.295098\pi$
$631$	30.1524	1.20035	0.600173	+	0.799870i	$0.295098\pi$
$632$	12.5548	0.499401
$633$	44.5546	1.77089
$634$	31.0801	1.23435
$635$	−6.00010	−0.238107
$636$	17.7501	0.703837
$637$	0	0
$638$	12.1406	0.480649
$639$	−0.927127	−0.0366766
$640$	−1.41872	−0.0560798
$641$	−40.2705	−1.59059	−0.795295	−	0.606223i	$-0.792684\pi$
$641$	−40.2705	−1.59059	−0.795295	+	0.606223i	$0.792684\pi$
$642$	14.0245	0.553504
$643$	13.6321	0.537598	0.268799	−	0.963196i	$-0.413373\pi$
$643$	13.6321	0.537598	0.268799	+	0.963196i	$0.413373\pi$
$644$	2.26493	0.0892509
$645$	−0.205529	−0.00809271
$646$	−10.6831	−0.420322
$647$	−2.57274	−0.101145	−0.0505724	−	0.998720i	$-0.516105\pi$
$647$	−2.57274	−0.101145	−0.0505724	+	0.998720i	$0.516105\pi$
$648$	−21.2696	−0.835550
$649$	−32.6902	−1.28320
$650$	0	0
$651$	−3.46508	−0.135807
$652$	13.1083	0.513361
$653$	38.5454	1.50840	0.754198	−	0.656647i	$-0.228026\pi$
$653$	38.5454	1.50840	0.754198	+	0.656647i	$0.228026\pi$
$654$	7.65548	0.299353
$655$	4.62241	0.180613
$656$	4.41933	0.172546
$657$	−3.24084	−0.126437
$658$	−6.51999	−0.254176
$659$	15.1716	0.591000	0.295500	−	0.955343i	$-0.404514\pi$
$659$	15.1716	0.591000	0.295500	+	0.955343i	$0.404514\pi$
$660$	2.74183	0.106726
$661$	3.88736	0.151201	0.0756003	−	0.997138i	$-0.475913\pi$
$661$	3.88736	0.151201	0.0756003	+	0.997138i	$0.475913\pi$
$662$	19.5756	0.760829
$663$	0	0
$664$	−32.2627	−1.25203
$665$	−0.847488	−0.0328642
$666$	−5.95306	−0.230676
$667$	6.38381	0.247182
$668$	−10.4238	−0.403308
$669$	−22.2075	−0.858590
$670$	−0.478530	−0.0184872
$671$	−61.9507	−2.39158
$672$	−8.03079	−0.309794
$673$	−31.7515	−1.22393	−0.611965	−	0.790885i	$-0.709621\pi$
$673$	−31.7515	−1.22393	−0.611965	+	0.790885i	$0.709621\pi$
$674$	2.67543	0.103054
$675$	−26.8578	−1.03376
$676$	0	0
$677$	−11.8303	−0.454677	−0.227338	−	0.973816i	$-0.573002\pi$
$677$	−11.8303	−0.454677	−0.227338	+	0.973816i	$0.573002\pi$
$678$	3.69978	0.142089
$679$	−14.4763	−0.555550
$680$	6.06804	0.232699
$681$	−29.4421	−1.12822
$682$	−9.20097	−0.352323
$683$	12.6451	0.483852	0.241926	−	0.970295i	$-0.422221\pi$
$683$	12.6451	0.483852	0.241926	+	0.970295i	$0.422221\pi$
$684$	−1.16289	−0.0444643
$685$	0.163474	0.00624604
$686$	0.983820	0.0375624
$687$	−5.10169	−0.194642
$688$	0.285718	0.0108929
$689$	0	0
$690$	−1.35205	−0.0514716
$691$	−14.6468	−0.557190	−0.278595	−	0.960409i	$-0.589869\pi$
$691$	−14.6468	−0.557190	−0.278595	+	0.960409i	$0.589869\pi$
$692$	−17.1132	−0.650548
$693$	−2.24715	−0.0853622
$694$	12.6062	0.478524
$695$	7.24038	0.274643
$696$	−13.6388	−0.516979
$697$	25.9161	0.981642
$698$	−8.90705	−0.337137
$699$	−27.3909	−1.03602
$700$	−4.99664	−0.188855
$701$	7.16794	0.270729	0.135365	−	0.990796i	$-0.456779\pi$
$701$	7.16794	0.270729	0.135365	+	0.990796i	$0.456779\pi$
$702$	0	0
$703$	24.2959	0.916336
$704$	−28.7105	−1.08207
$705$	−4.15025	−0.156307
$706$	−9.28271	−0.349359
$707$	−7.31830	−0.275233
$708$	12.5007	0.469804
$709$	−2.14832	−0.0806817	−0.0403409	−	0.999186i	$-0.512844\pi$
$709$	−2.14832	−0.0806817	−0.0403409	+	0.999186i	$0.512844\pi$
$710$	0.686073	0.0257478
$711$	−2.22948	−0.0836122
$712$	46.8258	1.75487
$713$	−4.83811	−0.181189
$714$	7.89418	0.295432
$715$	0	0
$716$	24.3434	0.909755
$717$	−6.12656	−0.228801
$718$	9.52454	0.355453
$719$	9.34269	0.348424	0.174212	−	0.984708i	$-0.444262\pi$
$719$	9.34269	0.348424	0.174212	+	0.984708i	$0.444262\pi$
$720$	−0.183752	−0.00684803
$721$	12.7643	0.475367
$722$	14.2417	0.530023
$723$	27.8149	1.03445
$724$	24.4834	0.909918
$725$	−14.0832	−0.523039
$726$	10.8163	0.401432
$727$	41.2539	1.53002	0.765011	−	0.644017i	$-0.222733\pi$
$727$	41.2539	1.53002	0.765011	+	0.644017i	$0.222733\pi$
$728$	0	0
$729$	29.9352	1.10871
$730$	2.39822	0.0887620
$731$	1.67553	0.0619715
$732$	23.6899	0.875604
$733$	−11.6062	−0.428686	−0.214343	−	0.976758i	$-0.568761\pi$
$733$	−11.6062	−0.428686	−0.214343	+	0.976758i	$0.568761\pi$
$734$	15.1164	0.557956
$735$	0.626242	0.0230993
$736$	−11.2130	−0.413315
$737$	5.17845	0.190751
$738$	−2.64558	−0.0973851
$739$	7.80551	0.287130	0.143565	−	0.989641i	$-0.454143\pi$
$739$	7.80551	0.287130	0.143565	+	0.989641i	$0.454143\pi$
$740$	−4.69744	−0.172681
$741$	0	0
$742$	10.7652	0.395204
$743$	−41.5158	−1.52307	−0.761533	−	0.648126i	$-0.775553\pi$
$743$	−41.5158	−1.52307	−0.761533	+	0.648126i	$0.775553\pi$
$744$	10.3365	0.378954
$745$	4.35084	0.159402
$746$	−12.4825	−0.457016
$747$	5.72924	0.209622
$748$	−22.3521	−0.817272
$749$	−9.06986	−0.331405
$750$	6.06328	0.221400
$751$	−22.7184	−0.829005	−0.414503	−	0.910048i	$-0.636044\pi$
$751$	−22.7184	−0.829005	−0.414503	+	0.910048i	$0.636044\pi$
$752$	5.76949	0.210392
$753$	2.68304	0.0977753
$754$	0	0
$755$	8.09540	0.294622
$756$	5.72578	0.208245
$757$	−4.60782	−0.167474	−0.0837370	−	0.996488i	$-0.526686\pi$
$757$	−4.60782	−0.167474	−0.0837370	+	0.996488i	$0.526686\pi$
$758$	6.48362	0.235496
$759$	14.6313	0.531083
$760$	2.52809	0.0917034
$761$	−21.2169	−0.769112	−0.384556	−	0.923102i	$-0.625645\pi$
$761$	−21.2169	−0.769112	−0.384556	+	0.923102i	$0.625645\pi$
$762$	23.2850	0.843526
$763$	−4.95091	−0.179235
$764$	−2.25479	−0.0815755
$765$	−1.07757	−0.0389596
$766$	−30.8699	−1.11537
$767$	0	0
$768$	26.7806	0.966360
$769$	15.0781	0.543731	0.271865	−	0.962335i	$-0.412359\pi$
$769$	15.0781	0.543731	0.271865	+	0.962335i	$0.412359\pi$
$770$	1.66289	0.0599263
$771$	−36.5778	−1.31732
$772$	19.2378	0.692385
$773$	−4.39415	−0.158047	−0.0790233	−	0.996873i	$-0.525180\pi$
$773$	−4.39415	−0.158047	−0.0790233	+	0.996873i	$0.525180\pi$
$774$	−0.171042	−0.00614797
$775$	10.6733	0.383396
$776$	43.1834	1.55020
$777$	−17.9532	−0.644067
$778$	−16.1607	−0.579390
$779$	10.7972	0.386852
$780$	0	0
$781$	−7.42439	−0.265666
$782$	11.0222	0.394154
$783$	16.1384	0.576739
$784$	−0.870575	−0.0310920
$785$	−9.34254	−0.333449
$786$	−17.9385	−0.639845
$787$	28.1360	1.00294	0.501470	−	0.865175i	$-0.332793\pi$
$787$	28.1360	1.00294	0.501470	+	0.865175i	$0.332793\pi$
$788$	−15.4629	−0.550845
$789$	−22.0975	−0.786693
$790$	1.64982	0.0586978
$791$	−2.39270	−0.0850746
$792$	6.70333	0.238193
$793$	0	0
$794$	−6.82807	−0.242319
$795$	6.85251	0.243034
$796$	−8.86185	−0.314100
$797$	14.7844	0.523692	0.261846	−	0.965110i	$-0.415669\pi$
$797$	14.7844	0.523692	0.261846	+	0.965110i	$0.415669\pi$
$798$	3.28890	0.116426
$799$	33.8338	1.19695
$800$	24.7367	0.874576
$801$	−8.31537	−0.293809
$802$	−0.875723	−0.0309229
$803$	−25.9525	−0.915845
$804$	−1.98023	−0.0698375
$805$	0.874389	0.0308181
$806$	0	0
$807$	−5.41751	−0.190705
$808$	21.8308	0.768004
$809$	23.3097	0.819525	0.409763	−	0.912192i	$-0.365612\pi$
$809$	23.3097	0.819525	0.409763	+	0.912192i	$0.365612\pi$
$810$	−2.79503	−0.0982075
$811$	13.6662	0.479886	0.239943	−	0.970787i	$-0.422871\pi$
$811$	13.6662	0.479886	0.239943	+	0.970787i	$0.422871\pi$
$812$	3.00239	0.105363
$813$	−33.3637	−1.17012
$814$	−47.6718	−1.67090
$815$	5.06053	0.177263
$816$	−6.98550	−0.244542
$817$	0.698063	0.0244221
$818$	1.96934	0.0688565
$819$	0	0
$820$	−2.08757	−0.0729012
$821$	−11.8254	−0.412708	−0.206354	−	0.978477i	$-0.566160\pi$
$821$	−11.8254	−0.412708	−0.206354	+	0.978477i	$0.566160\pi$
$822$	−0.634406	−0.0221274
$823$	−12.6805	−0.442015	−0.221007	−	0.975272i	$-0.570935\pi$
$823$	−12.6805	−0.442015	−0.221007	+	0.975272i	$0.570935\pi$
$824$	−38.0763	−1.32645
$825$	−32.2779	−1.12377
$826$	7.58151	0.263794
$827$	−19.7897	−0.688156	−0.344078	−	0.938941i	$-0.611809\pi$
$827$	−19.7897	−0.688156	−0.344078	+	0.938941i	$0.611809\pi$
$828$	1.19980	0.0416961
$829$	−15.7027	−0.545378	−0.272689	−	0.962102i	$-0.587913\pi$
$829$	−15.7027	−0.545378	−0.272689	+	0.962102i	$0.587913\pi$
$830$	−4.23962	−0.147160
$831$	−11.1066	−0.385282
$832$	0	0
$833$	−5.10528	−0.176887
$834$	−28.0982	−0.972962
$835$	−4.02416	−0.139262
$836$	−9.31239	−0.322076
$837$	−12.2308	−0.422759
$838$	−31.8108	−1.09889
$839$	−18.8485	−0.650722	−0.325361	−	0.945590i	$-0.605486\pi$
$839$	−18.8485	−0.650722	−0.325361	+	0.945590i	$0.605486\pi$
$840$	−1.86811	−0.0644558
$841$	−20.5376	−0.708194
$842$	8.95623	0.308652
$843$	3.73805	0.128745
$844$	29.2578	1.00709
$845$	0	0
$846$	−3.45384	−0.118745
$847$	−6.99507	−0.240353
$848$	−9.52606	−0.327126
$849$	22.4014	0.768815
$850$	−24.3160	−0.834031
$851$	−25.0671	−0.859288
$852$	2.83908	0.0972653
$853$	2.42144	0.0829084	0.0414542	−	0.999140i	$-0.486801\pi$
$853$	2.42144	0.0829084	0.0414542	+	0.999140i	$0.486801\pi$
$854$	14.3676	0.491650
$855$	−0.448940	−0.0153534
$856$	27.0557	0.924746
$857$	39.9800	1.36569	0.682845	−	0.730564i	$-0.260743\pi$
$857$	39.9800	1.36569	0.682845	+	0.730564i	$0.260743\pi$
$858$	0	0
$859$	−2.31038	−0.0788292	−0.0394146	−	0.999223i	$-0.512549\pi$
$859$	−2.31038	−0.0788292	−0.0394146	+	0.999223i	$0.512549\pi$
$860$	−0.134966	−0.00460229
$861$	−7.97852	−0.271907
$862$	−15.6088	−0.531639
$863$	−46.1232	−1.57005	−0.785027	−	0.619462i	$-0.787351\pi$
$863$	−46.1232	−1.57005	−0.785027	+	0.619462i	$0.787351\pi$
$864$	−28.3465	−0.964368
$865$	−6.60665	−0.224633
$866$	−15.6167	−0.530678
$867$	−14.2458	−0.483812
$868$	−2.27543	−0.0772330
$869$	−17.8536	−0.605642
$870$	−1.79227	−0.0607637
$871$	0	0
$872$	14.7688	0.500133
$873$	−7.66856	−0.259541
$874$	4.59212	0.155331
$875$	−3.92121	−0.132561
$876$	9.92421	0.335308
$877$	22.7695	0.768870	0.384435	−	0.923152i	$-0.374396\pi$
$877$	22.7695	0.768870	0.384435	+	0.923152i	$0.374396\pi$
$878$	−5.28987	−0.178524
$879$	−11.2515	−0.379502
$880$	−1.47148	−0.0496035
$881$	20.0984	0.677131	0.338566	−	0.940943i	$-0.390058\pi$
$881$	20.0984	0.677131	0.338566	+	0.940943i	$0.390058\pi$
$882$	0.521160	0.0175484
$883$	−22.1650	−0.745911	−0.372956	−	0.927849i	$-0.621656\pi$
$883$	−22.1650	−0.745911	−0.372956	+	0.927849i	$0.621656\pi$
$884$	0	0
$885$	4.82595	0.162222
$886$	25.0075	0.840143
$887$	6.35544	0.213395	0.106697	−	0.994292i	$-0.465972\pi$
$887$	6.35544	0.213395	0.106697	+	0.994292i	$0.465972\pi$
$888$	53.5550	1.79719
$889$	−15.0587	−0.505054
$890$	6.15336	0.206261
$891$	30.2467	1.01330
$892$	−14.5830	−0.488276
$893$	14.0960	0.471703
$894$	−16.8846	−0.564705
$895$	9.39788	0.314136
$896$	−3.56062	−0.118952
$897$	0	0
$898$	−15.1871	−0.506801
$899$	−6.41339	−0.213898
$900$	−2.64687	−0.0882291
$901$	−55.8633	−1.86108
$902$	−21.1857	−0.705406
$903$	−0.515826	−0.0171656
$904$	7.13752	0.237390
$905$	9.45193	0.314193
$906$	−31.4163	−1.04374
$907$	−29.7539	−0.987964	−0.493982	−	0.869472i	$-0.664459\pi$
$907$	−29.7539	−0.987964	−0.493982	+	0.869472i	$0.664459\pi$
$908$	−19.3338	−0.641615
$909$	−3.87673	−0.128583
$910$	0	0
$911$	−34.3649	−1.13856	−0.569279	−	0.822144i	$-0.692778\pi$
$911$	−34.3649	−1.13856	−0.569279	+	0.822144i	$0.692778\pi$
$912$	−2.91032	−0.0963705
$913$	45.8795	1.51839
$914$	29.7884	0.985314
$915$	9.14560	0.302344
$916$	−3.35014	−0.110692
$917$	11.6011	0.383101
$918$	27.8643	0.919660
$919$	−44.0300	−1.45241	−0.726207	−	0.687476i	$-0.758719\pi$
$919$	−44.0300	−1.45241	−0.726207	+	0.687476i	$0.758719\pi$
$920$	−2.60833	−0.0859943
$921$	38.3838	1.26479
$922$	24.9331	0.821127
$923$	0	0
$924$	6.88129	0.226378
$925$	55.3001	1.81826
$926$	−2.89218	−0.0950430
$927$	6.76163	0.222081
$928$	−14.8639	−0.487931
$929$	33.8451	1.11042	0.555210	−	0.831710i	$-0.312638\pi$
$929$	33.8451	1.11042	0.555210	+	0.831710i	$0.312638\pi$
$930$	1.35831	0.0445408
$931$	−2.12698	−0.0697089
$932$	−17.9869	−0.589180
$933$	−37.2828	−1.22058
$934$	−23.7068	−0.775710
$935$	−8.62912	−0.282203
$936$	0	0
$937$	24.0910	0.787017	0.393509	−	0.919321i	$-0.371261\pi$
$937$	24.0910	0.787017	0.393509	+	0.919321i	$0.371261\pi$
$938$	−1.20099	−0.0392136
$939$	23.7134	0.773856
$940$	−2.72535	−0.0888912
$941$	−29.5369	−0.962874	−0.481437	−	0.876481i	$-0.659885\pi$
$941$	−29.5369	−0.962874	−0.481437	+	0.876481i	$0.659885\pi$
$942$	36.2562	1.18129
$943$	−11.1400	−0.362767
$944$	−6.70882	−0.218354
$945$	2.21047	0.0719065
$946$	−1.36969	−0.0445326
$947$	−22.6950	−0.737490	−0.368745	−	0.929531i	$-0.620212\pi$
$947$	−22.6950	−0.737490	−0.368745	+	0.929531i	$0.620212\pi$
$948$	6.82720	0.221737
$949$	0	0
$950$	−10.1306	−0.328680
$951$	49.6523	1.61009
$952$	15.2292	0.493583
$953$	49.0720	1.58960	0.794799	−	0.606872i	$-0.207576\pi$
$953$	49.0720	1.58960	0.794799	+	0.606872i	$0.207576\pi$
$954$	5.70267	0.184631
$955$	−0.870474	−0.0281679
$956$	−4.02315	−0.130118
$957$	19.3952	0.626959
$958$	10.9272	0.353042
$959$	0.410279	0.0132486
$960$	4.23845	0.136795
$961$	−26.1395	−0.843209
$962$	0	0
$963$	−4.80458	−0.154825
$964$	18.2653	0.588286
$965$	7.42686	0.239079
$966$	−3.39330	−0.109178
$967$	−23.1018	−0.742905	−0.371452	−	0.928452i	$-0.621140\pi$
$967$	−23.1018	−0.742905	−0.371452	+	0.928452i	$0.621140\pi$
$968$	20.8666	0.670677
$969$	−17.0669	−0.548268
$970$	5.67472	0.182204
$971$	−30.3111	−0.972729	−0.486365	−	0.873756i	$-0.661677\pi$
$971$	−30.3111	−0.972729	−0.486365	+	0.873756i	$0.661677\pi$
$972$	5.61105	0.179974
$973$	18.1715	0.582552
$974$	−28.6803	−0.918976
$975$	0	0
$976$	−12.7138	−0.406959
$977$	2.18246	0.0698230	0.0349115	−	0.999390i	$-0.488885\pi$
$977$	2.18246	0.0698230	0.0349115	+	0.999390i	$0.488885\pi$
$978$	−19.6387	−0.627977
$979$	−66.5891	−2.12820
$980$	0.411236	0.0131365
$981$	−2.62265	−0.0837347
$982$	−0.368447	−0.0117576
$983$	−2.60962	−0.0832339	−0.0416170	−	0.999134i	$-0.513251\pi$
$983$	−2.60962	−0.0832339	−0.0416170	+	0.999134i	$0.513251\pi$
$984$	23.8002	0.758723
$985$	−5.96955	−0.190206
$986$	14.6110	0.465310
$987$	−10.4161	−0.331547
$988$	0	0
$989$	−0.720221	−0.0229017
$990$	0.880882	0.0279963
$991$	12.5621	0.399048	0.199524	−	0.979893i	$-0.436060\pi$
$991$	12.5621	0.399048	0.199524	+	0.979893i	$0.436060\pi$
$992$	11.2649	0.357661
$993$	31.2732	0.992426
$994$	1.72187	0.0546143
$995$	−3.42116	−0.108458
$996$	−17.5443	−0.555911
$997$	−32.9839	−1.04461	−0.522305	−	0.852759i	$-0.674928\pi$
$997$	−32.9839	−1.04461	−0.522305	+	0.852759i	$0.674928\pi$
$998$	−0.395978	−0.0125345
$999$	−63.3699	−2.00493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.q.1.5	✓	12
7.6	odd	2		8281.2.a.cn.1.5		12
13.5	odd	4		1183.2.c.j.337.16		24
13.8	odd	4		1183.2.c.j.337.9		24
13.12	even	2		1183.2.a.r.1.8	yes	12
91.90	odd	2		8281.2.a.cq.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.5	✓	12	1.1	even	1	trivial
1183.2.a.r.1.8	yes	12	13.12	even	2
1183.2.c.j.337.9		24	13.8	odd	4
1183.2.c.j.337.16		24	13.5	odd	4
8281.2.a.cn.1.5		12	7.6	odd	2
8281.2.a.cq.1.8		12	91.90	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)

\(f(q)\)	\(=\)	\(q-0.983820 q^{2} -1.57171 q^{3} -1.03210 q^{4} -0.398447 q^{5} +1.54628 q^{6} -1.00000 q^{7} +2.98304 q^{8} -0.529731 q^{9} +O(q^{10})\)	\(q-0.983820 q^{2} -1.57171 q^{3} -1.03210 q^{4} -0.398447 q^{5} +1.54628 q^{6} -1.00000 q^{7} +2.98304 q^{8} -0.529731 q^{9} +0.392000 q^{10} -4.24206 q^{11} +1.62216 q^{12} +0.983820 q^{14} +0.626242 q^{15} -0.870575 q^{16} -5.10528 q^{17} +0.521160 q^{18} -2.12698 q^{19} +0.411236 q^{20} +1.57171 q^{21} +4.17342 q^{22} +2.19449 q^{23} -4.68847 q^{24} -4.84124 q^{25} +5.54771 q^{27} +1.03210 q^{28} +2.90902 q^{29} -0.616110 q^{30} -2.20466 q^{31} -5.10959 q^{32} +6.66728 q^{33} +5.02268 q^{34} +0.398447 q^{35} +0.546734 q^{36} -11.4227 q^{37} +2.09256 q^{38} -1.18858 q^{40} -5.07633 q^{41} -1.54628 q^{42} -0.328195 q^{43} +4.37822 q^{44} +0.211070 q^{45} -2.15899 q^{46} -6.62722 q^{47} +1.36829 q^{48} +1.00000 q^{49} +4.76291 q^{50} +8.02401 q^{51} +10.9423 q^{53} -5.45795 q^{54} +1.69024 q^{55} -2.98304 q^{56} +3.34299 q^{57} -2.86195 q^{58} +7.70620 q^{59} -0.646344 q^{60} +14.6039 q^{61} +2.16899 q^{62} +0.529731 q^{63} +6.76806 q^{64} -6.55941 q^{66} -1.22074 q^{67} +5.26915 q^{68} -3.44910 q^{69} -0.392000 q^{70} +1.75019 q^{71} -1.58021 q^{72} +6.11791 q^{73} +11.2379 q^{74} +7.60902 q^{75} +2.19525 q^{76} +4.24206 q^{77} +4.20871 q^{79} +0.346878 q^{80} -7.13019 q^{81} +4.99419 q^{82} -10.8154 q^{83} -1.62216 q^{84} +2.03418 q^{85} +0.322884 q^{86} -4.57213 q^{87} -12.6542 q^{88} +15.6973 q^{89} -0.207654 q^{90} -2.26493 q^{92} +3.46508 q^{93} +6.51999 q^{94} +0.847488 q^{95} +8.03079 q^{96} +14.4763 q^{97} -0.983820 q^{98} +2.24715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 8 q^{3} + 15 q^{4} + 4 q^{5} - 2 q^{6} - 12 q^{7} - 12 q^{8} + 26 q^{9}+O(q^{10}) \) 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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