LMFDB - Embedded newform 1183.2.c.j.337.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.9
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.983820i q^{2} -1.57171 q^{3} +1.03210 q^{4} -0.398447i q^{5} +1.54628i q^{6} +1.00000i q^{7} -2.98304i q^{8} -0.529731 q^{9} +O(q^{10})$	\(q-0.983820i q^{2} -1.57171 q^{3} +1.03210 q^{4} -0.398447i q^{5} +1.54628i q^{6} +1.00000i q^{7} -2.98304i q^{8} -0.529731 q^{9} -0.392000 q^{10} +4.24206i q^{11} -1.62216 q^{12} +0.983820 q^{14} +0.626242i q^{15} -0.870575 q^{16} +5.10528 q^{17} +0.521160i q^{18} -2.12698i q^{19} -0.411236i q^{20} -1.57171i q^{21} +4.17342 q^{22} -2.19449 q^{23} +4.68847i q^{24} +4.84124 q^{25} +5.54771 q^{27} +1.03210i q^{28} +2.90902 q^{29} +0.616110 q^{30} -2.20466i q^{31} -5.10959i q^{32} -6.66728i q^{33} -5.02268i q^{34} +0.398447 q^{35} -0.546734 q^{36} +11.4227i q^{37} -2.09256 q^{38} -1.18858 q^{40} -5.07633i q^{41} -1.54628 q^{42} +0.328195 q^{43} +4.37822i q^{44} +0.211070i q^{45} +2.15899i q^{46} +6.62722i q^{47} +1.36829 q^{48} -1.00000 q^{49} -4.76291i q^{50} -8.02401 q^{51} +10.9423 q^{53} -5.45795i q^{54} +1.69024 q^{55} +2.98304 q^{56} +3.34299i q^{57} -2.86195i q^{58} -7.70620i q^{59} +0.646344i q^{60} +14.6039 q^{61} -2.16899 q^{62} -0.529731i q^{63} -6.76806 q^{64} -6.55941 q^{66} -1.22074i q^{67} +5.26915 q^{68} +3.44910 q^{69} -0.392000i q^{70} +1.75019i q^{71} +1.58021i q^{72} -6.11791i q^{73} +11.2379 q^{74} -7.60902 q^{75} -2.19525i q^{76} -4.24206 q^{77} +4.20871 q^{79} +0.346878i q^{80} -7.13019 q^{81} -4.99419 q^{82} -10.8154i q^{83} -1.62216i q^{84} -2.03418i q^{85} -0.322884i q^{86} -4.57213 q^{87} +12.6542 q^{88} -15.6973i q^{89} +0.207654 q^{90} -2.26493 q^{92} +3.46508i q^{93} +6.51999 q^{94} -0.847488 q^{95} +8.03079i q^{96} +14.4763i q^{97} +0.983820i q^{98} -2.24715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 0.983820i	− 0.695666i	−0.937557	−	0.347833i	$-0.886918\pi$
$2$	− 0.983820i	− 0.695666i	0.937557	−	0.347833i	$-0.113082\pi$
$3$	−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
$5$	− 0.398447i	− 0.178191i	−0.996023	−	0.0890954i	$-0.971602\pi$
$5$	− 0.398447i	− 0.178191i	0.996023	−	0.0890954i	$-0.0283976\pi$
$6$	1.54628i	0.631265i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 2.98304i	− 1.05466i
$9$	−0.529731	−0.176577
$10$	−0.392000	−0.123961
$11$	4.24206i	1.27903i	0.768779	+	0.639515i	$0.220865\pi$
$11$	4.24206i	1.27903i	−0.768779	+	0.639515i	$0.779135\pi$
$12$	−1.62216	−0.468277
$13$	0	0
$13$	0	0
$14$	0.983820	0.262937
$15$	0.626242i	0.161695i
$16$	−0.870575	−0.217644
$17$	5.10528	1.23821	0.619106	−	0.785307i	$-0.287495\pi$
$17$	5.10528	1.23821	0.619106	+	0.785307i	$0.287495\pi$
$18$	0.521160i	0.122838i
$19$	− 2.12698i	− 0.487962i	−0.969780	−	0.243981i	$-0.921546\pi$
$19$	− 2.12698i	− 0.487962i	0.969780	−	0.243981i	$-0.0784535\pi$
$20$	− 0.411236i	− 0.0919553i
$21$	− 1.57171i	− 0.342975i
$22$	4.17342	0.889777
$23$	−2.19449	−0.457583	−0.228792	−	0.973475i	$-0.573477\pi$
$23$	−2.19449	−0.457583	−0.228792	+	0.973475i	$0.573477\pi$
$24$	4.68847i	0.957030i
$25$	4.84124	0.968248
$26$	0	0
$27$	5.54771	1.06766
$28$	1.03210i	0.195048i
$29$	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
$31$	− 2.20466i	− 0.395968i	−0.980205	−	0.197984i	$-0.936561\pi$
$31$	− 2.20466i	− 0.395968i	0.980205	−	0.197984i	$-0.0634395\pi$
$32$	− 5.10959i	− 0.903256i
$33$	− 6.66728i	− 1.16063i
$34$	− 5.02268i	− 0.861382i
$35$	0.398447	0.0673498
$36$	−0.546734	−0.0911224
$37$	11.4227i	1.87788i	0.344077	+	0.938941i	$0.388192\pi$
$37$	11.4227i	1.87788i	−0.344077	+	0.938941i	$0.611808\pi$
$38$	−2.09256	−0.339459
$39$	0	0
$40$	−1.18858	−0.187931
$41$	− 5.07633i	− 0.792790i	−0.918080	−	0.396395i	$-0.870261\pi$
$41$	− 5.07633i	− 0.792790i	0.918080	−	0.396395i	$-0.129739\pi$
$42$	−1.54628	−0.238596
$43$	0.328195	0.0500492	0.0250246	−	0.999687i	$-0.492034\pi$
$43$	0.328195	0.0500492	0.0250246	+	0.999687i	$0.492034\pi$
$44$	4.37822i	0.660042i
$45$	0.211070i	0.0314644i
$46$	2.15899i	0.318325i
$47$	6.62722i	0.966679i	0.875433	+	0.483340i	$0.160576\pi$
$47$	6.62722i	0.966679i	−0.875433	+	0.483340i	$0.839424\pi$
$48$	1.36829	0.197496
$49$	−1.00000	−0.142857
$50$	− 4.76291i	− 0.673577i
$51$	−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	$0.229322\pi$
$54$	− 5.45795i	− 0.742732i
$55$	1.69024	0.227911
$56$	2.98304	0.398625
$57$	3.34299i	0.442790i
$58$	− 2.86195i	− 0.375792i
$59$	− 7.70620i	− 1.00326i	−0.865082	−	0.501631i	$-0.832734\pi$
$59$	− 7.70620i	− 1.00326i	0.865082	−	0.501631i	$-0.167266\pi$
$60$	0.646344i	0.0834427i
$61$	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
$63$	− 0.529731i	− 0.0667398i
$64$	−6.76806	−0.846008
$65$	0	0
$66$	−6.55941	−0.807407
$67$	− 1.22074i	− 0.149137i	−0.997216	−	0.0745685i	$-0.976242\pi$
$67$	− 1.22074i	− 0.149137i	0.997216	−	0.0745685i	$-0.0237580\pi$
$68$	5.26915	0.638979
$69$	3.44910	0.415223
$70$	− 0.392000i	− 0.0468529i
$71$	1.75019i	0.207709i	0.994593	+	0.103854i	$0.0331176\pi$
$71$	1.75019i	0.207709i	−0.994593	+	0.103854i	$0.966882\pi$
$72$	1.58021i	0.186229i
$73$	− 6.11791i	− 0.716047i	−0.933713	−	0.358023i	$-0.883451\pi$
$73$	− 6.11791i	− 0.716047i	0.933713	−	0.358023i	$-0.116549\pi$
$74$	11.2379	1.30638
$75$	−7.60902	−0.878614
$76$	− 2.19525i	− 0.251813i
$77$	−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	$0.423915\pi$
$80$	0.346878i	0.0387821i
$81$	−7.13019	−0.792244
$82$	−4.99419	−0.551517
$83$	− 10.8154i	− 1.18714i	−0.804782	−	0.593571i	$-0.797718\pi$
$83$	− 10.8154i	− 1.18714i	0.804782	−	0.593571i	$-0.202282\pi$
$84$	− 1.62216i	− 0.176992i
$85$	− 2.03418i	− 0.220638i
$86$	− 0.322884i	− 0.0348175i
$87$	−4.57213	−0.490183
$88$	12.6542	1.34895
$89$	− 15.6973i	− 1.66392i	−0.554839	−	0.831958i	$-0.687220\pi$
$89$	− 15.6973i	− 1.66392i	0.554839	−	0.831958i	$-0.312780\pi$
$90$	0.207654	0.0218887
$91$	0	0
$92$	−2.26493	−0.236136
$93$	3.46508i	0.359312i
$94$	6.51999	0.672485
$95$	−0.847488	−0.0869504
$96$	8.03079i	0.819639i
$97$	14.4763i	1.46985i	0.678149	+	0.734924i	$0.262782\pi$
$97$	14.4763i	1.46985i	−0.678149	+	0.734924i	$0.737218\pi$
$98$	0.983820i	0.0993808i
$99$	− 2.24715i	− 0.225847i
$100$	4.99664	0.499664
$101$	−7.31830	−0.728198	−0.364099	−	0.931360i	$-0.618623\pi$
$101$	−7.31830	−0.728198	−0.364099	+	0.931360i	$0.618623\pi$
$102$	7.89418i	0.781641i
$103$	12.7643	1.25770	0.628851	−	0.777526i	$-0.283526\pi$
$103$	12.7643	1.25770	0.628851	+	0.777526i	$0.283526\pi$
$104$	0	0
$105$	−0.626242	−0.0611150
$106$	− 10.7652i	− 1.04561i
$107$	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
$109$	4.95091i	0.474211i	0.971484	+	0.237106i	$0.0761987\pi$
$109$	4.95091i	0.474211i	−0.971484	+	0.237106i	$0.923801\pi$
$110$	− 1.66289i	− 0.158550i
$111$	− 17.9532i	− 1.70404i
$112$	− 0.870575i	− 0.0822616i
$113$	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
$115$	0.874389i	0.0815372i
$116$	3.00239	0.278765
$117$	0	0
$118$	−7.58151	−0.697935
$119$	5.10528i	0.468000i
$120$	1.86811	0.170534
$121$	−6.99507	−0.635915
$122$	− 14.3676i	− 1.30078i
$123$	7.97852i	0.719398i
$124$	− 2.27543i	− 0.204339i
$125$	− 3.92121i	− 0.350724i
$126$	−0.521160	−0.0464286
$127$	−15.0587	−1.33625	−0.668123	−	0.744051i	$-0.732902\pi$
$127$	−15.0587	−1.33625	−0.668123	+	0.744051i	$0.732902\pi$
$128$	− 3.56062i	− 0.314718i
$129$	−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	$0.669170\pi$
$132$	− 6.88129i	− 0.598940i
$133$	2.12698	0.184432
$134$	−1.20099	−0.103750
$135$	− 2.21047i	− 0.190247i
$136$	− 15.2292i	− 1.30590i
$137$	0.410279i	0.0350525i	0.999846	+	0.0175263i	$0.00557907\pi$
$137$	0.410279i	0.0350525i	−0.999846	+	0.0175263i	$0.994421\pi$
$138$	− 3.39330i	− 0.288857i
$139$	−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
$141$	− 10.4161i	− 0.877190i
$142$	1.72187	0.144496
$143$	0	0
$144$	0.461170	0.0384309
$145$	− 1.15909i	− 0.0962570i
$146$	−6.01892	−0.498129
$147$	1.57171	0.129632
$148$	11.7894i	0.969080i
$149$	− 10.9195i	− 0.894561i	−0.894394	−	0.447280i	$-0.852393\pi$
$149$	− 10.9195i	− 0.894561i	0.894394	−	0.447280i	$-0.147607\pi$
$150$	7.48590i	0.611222i
$151$	20.3174i	1.65341i	0.562639	+	0.826703i	$0.309786\pi$
$151$	20.3174i	1.65341i	−0.562639	+	0.826703i	$0.690214\pi$
$152$	−6.34486	−0.514636
$153$	−2.70442	−0.218640
$154$	4.17342i	0.336304i
$155$	−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	$0.114812\pi$
$158$	− 4.14062i	− 0.329410i
$159$	−17.1981	−1.36390
$160$	−2.03590	−0.160952
$161$	− 2.19449i	− 0.172950i
$162$	7.01482i	0.551137i
$163$	12.7006i	0.994791i	0.867524	+	0.497396i	$0.165710\pi$
$163$	12.7006i	0.994791i	−0.867524	+	0.497396i	$0.834290\pi$
$164$	− 5.23927i	− 0.409119i
$165$	−2.65656	−0.206813
$166$	−10.6404	−0.825853
$167$	− 10.0996i	− 0.781531i	−0.920490	−	0.390765i	$-0.872210\pi$
$167$	− 10.0996i	− 0.781531i	0.920490	−	0.390765i	$-0.127790\pi$
$168$	−4.68847	−0.361723
$169$	0	0
$170$	−2.00127	−0.153490
$171$	1.12673i	0.0861629i
$172$	0.338729	0.0258279
$173$	−16.5810	−1.26063	−0.630316	−	0.776339i	$-0.717075\pi$
$173$	−16.5810	−1.26063	−0.630316	+	0.776339i	$0.717075\pi$
$174$	4.49815i	0.341004i
$175$	4.84124i	0.365963i
$176$	− 3.69303i	− 0.278373i
$177$	12.1119i	0.910386i
$178$	−15.4434	−1.15753
$179$	23.5863	1.76292	0.881461	−	0.472257i	$-0.156561\pi$
$179$	23.5863	1.76292	0.881461	+	0.472257i	$0.156561\pi$
$180$	0.217845i	0.0162372i
$181$	23.7219	1.76324	0.881619	−	0.471962i	$-0.156454\pi$
$181$	23.7219	1.76324	0.881619	+	0.471962i	$0.156454\pi$
$182$	0	0
$183$	−22.9531	−1.69674
$184$	6.54626i	0.482596i
$185$	4.55134	0.334621
$186$	3.40902	0.249961
$187$	21.6569i	1.58371i
$188$	6.83994i	0.498854i
$189$	5.54771i	0.403537i
$190$	0.833775i	0.0604884i
$191$	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
$193$	18.6395i	1.34170i	0.741592	+	0.670851i	$0.234071\pi$
$193$	18.6395i	1.34170i	−0.741592	+	0.670851i	$0.765929\pi$
$194$	14.2421	1.02252
$195$	0	0
$196$	−1.03210	−0.0737213
$197$	14.9820i	1.06743i	0.845666	+	0.533713i	$0.179204\pi$
$197$	14.9820i	1.06743i	−0.845666	+	0.533713i	$0.820796\pi$
$198$	−2.21079	−0.157114
$199$	−8.58624	−0.608662	−0.304331	−	0.952566i	$-0.598433\pi$
$199$	−8.58624	−0.608662	−0.304331	+	0.952566i	$0.598433\pi$
$200$	− 14.4416i	− 1.02118i
$201$	1.91865i	0.135331i
$202$	7.19989i	0.506583i
$203$	2.90902i	0.204173i
$204$	−8.28157	−0.579826
$205$	−2.02265	−0.141268
$206$	− 12.5578i	− 0.874940i
$207$	1.16249	0.0807987
$208$	0	0
$209$	9.02277	0.624118
$210$	0.616110i	0.0425156i
$211$	−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
$213$	− 2.75078i	− 0.188481i
$214$	− 8.92310i	− 0.609971i
$215$	− 0.130768i	− 0.00891831i
$216$	− 16.5490i	− 1.12602i
$217$	2.20466	0.149662
$218$	4.87080	0.329892
$219$	9.61557i	0.649760i
$220$	1.74449	0.117613
$221$	0	0
$222$	−17.6627	−1.18544
$223$	14.1295i	0.946181i	0.881014	+	0.473091i	$0.156862\pi$
$223$	14.1295i	0.946181i	−0.881014	+	0.473091i	$0.843138\pi$
$224$	5.10959	0.341399
$225$	−2.56455	−0.170970
$226$	− 2.35399i	− 0.156585i
$227$	18.7325i	1.24332i	0.783286	+	0.621661i	$0.213542\pi$
$227$	18.7325i	1.24332i	−0.783286	+	0.621661i	$0.786458\pi$
$228$	3.45030i	0.228502i
$229$	− 3.24595i	− 0.214499i	−0.994232	−	0.107249i	$-0.965796\pi$
$229$	− 3.24595i	− 0.214499i	0.994232	−	0.107249i	$-0.0342043\pi$
$230$	0.860241	0.0567226
$231$	6.66728	0.438675
$232$	− 8.67771i	− 0.569719i
$233$	−17.4275	−1.14171	−0.570856	−	0.821050i	$-0.693388\pi$
$233$	−17.4275	−1.14171	−0.570856	+	0.821050i	$0.693388\pi$
$234$	0	0
$235$	2.64059	0.172253
$236$	− 7.95356i	− 0.517732i
$237$	−6.61487	−0.429682
$238$	5.02268	0.325572
$239$	3.89803i	0.252142i	0.992021	+	0.126071i	$0.0402368\pi$
$239$	3.89803i	0.252142i	−0.992021	+	0.126071i	$0.959763\pi$
$240$	− 0.545191i	− 0.0351919i
$241$	17.6973i	1.13998i	0.821652	+	0.569990i	$0.193053\pi$
$241$	17.6973i	1.13998i	−0.821652	+	0.569990i	$0.806947\pi$
$242$	6.88189i	0.442385i
$243$	−5.43654	−0.348754
$244$	15.0727	0.964930
$245$	0.398447i	0.0254558i
$246$	7.84942	0.500461
$247$	0	0
$248$	−6.57658	−0.417613
$249$	16.9986i	1.07724i
$250$	−3.85776	−0.243986
$251$	1.70708	0.107750	0.0538750	−	0.998548i	$-0.482843\pi$
$251$	1.70708	0.107750	0.0538750	+	0.998548i	$0.482843\pi$
$252$	− 0.546734i	− 0.0344410i
$253$	− 9.30917i	− 0.585262i
$254$	14.8151i	0.929581i
$255$	3.19714i	0.200213i
$256$	−17.0391	−1.06495
$257$	−23.2726	−1.45171	−0.725853	−	0.687849i	$-0.758555\pi$
$257$	−23.2726	−1.45171	−0.725853	+	0.687849i	$0.758555\pi$
$258$	0.507480i	0.0315943i
$259$	−11.4227	−0.709773
$260$	0	0
$261$	−1.54100	−0.0953852
$262$	11.4134i	0.705121i
$263$	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
$265$	− 4.35991i	− 0.267827i
$266$	− 2.09256i	− 0.128303i
$267$	24.6717i	1.50988i
$268$	− 1.25992i	− 0.0769621i
$269$	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
$271$	− 21.2277i	− 1.28949i	−0.764399	−	0.644744i	$-0.776964\pi$
$271$	− 21.2277i	− 1.28949i	0.764399	−	0.644744i	$-0.223036\pi$
$272$	−4.44453	−0.269489
$273$	0	0
$274$	0.403641	0.0243848
$275$	20.5368i	1.23842i
$276$	3.55982	0.214276
$277$	−7.06655	−0.424588	−0.212294	−	0.977206i	$-0.568093\pi$
$277$	−7.06655	−0.424588	−0.212294	+	0.977206i	$0.568093\pi$
$278$	17.8775i	1.07222i
$279$	1.16788i	0.0699189i
$280$	− 1.18858i	− 0.0710314i
$281$	2.37834i	0.141880i	0.997481	+	0.0709398i	$0.0225998\pi$
$281$	2.37834i	0.141880i	−0.997481	+	0.0709398i	$0.977400\pi$
$282$	−10.2475	−0.610231
$283$	14.2529	0.847248	0.423624	−	0.905838i	$-0.360758\pi$
$283$	14.2529	0.847248	0.423624	+	0.905838i	$0.360758\pi$
$284$	1.80636i	0.107188i
$285$	1.33200	0.0789011
$286$	0	0
$287$	5.07633	0.299646
$288$	2.70671i	0.159494i
$289$	9.06388	0.533169
$290$	−1.14033	−0.0669627
$291$	− 22.7526i	− 1.33378i
$292$	− 6.31428i	− 0.369515i
$293$	− 7.15874i	− 0.418218i	−0.977892	−	0.209109i	$-0.932944\pi$
$293$	− 7.15874i	− 0.418218i	0.977892	−	0.209109i	$-0.0670564\pi$
$294$	− 1.54628i	− 0.0901808i
$295$	−3.07051	−0.178772
$296$	34.0744	1.98053
$297$	23.5337i	1.36556i
$298$	−10.7428	−0.622315
$299$	0	0
$300$	−7.85326	−0.453408
$301$	0.328195i	0.0189168i
$302$	19.9887	1.15022
$303$	11.5022	0.660787
$304$	1.85169i	0.106202i
$305$	− 5.81889i	− 0.333189i
$306$	2.66067i	0.152100i
$307$	24.4217i	1.39382i	0.717159	+	0.696910i	$0.245442\pi$
$307$	24.4217i	1.39382i	−0.717159	+	0.696910i	$0.754558\pi$
$308$	−4.37822	−0.249472
$309$	−20.0617	−1.14127
$310$	0.864226i	0.0490847i
$311$	−23.7212	−1.34510	−0.672552	−	0.740050i	$-0.734802\pi$
$311$	−23.7212	−1.34510	−0.672552	+	0.740050i	$0.734802\pi$
$312$	0	0
$313$	−15.0876	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$313$	−15.0876	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$314$	− 23.0680i	− 1.30180i
$315$	−0.211070	−0.0118924
$316$	4.34381	0.244358
$317$	− 31.5913i	− 1.77434i	−0.461440	−	0.887172i	$-0.652667\pi$
$317$	− 31.5913i	− 1.77434i	0.461440	−	0.887172i	$-0.347333\pi$
$318$	16.9198i	0.948815i
$319$	12.3402i	0.690920i
$320$	2.69671i	0.150751i
$321$	−14.2552	−0.795646
$322$	−2.15899	−0.120316
$323$	− 10.8588i	− 0.604201i
$324$	−7.35906	−0.408837
$325$	0	0
$326$	12.4951	0.692042
$327$	− 7.78139i	− 0.430312i
$328$	−15.1429	−0.836126
$329$	−6.62722	−0.365370
$330$	2.61357i	0.143873i
$331$	− 19.8976i	− 1.09367i	−0.837240	−	0.546835i	$-0.815832\pi$
$331$	− 19.8976i	− 1.09367i	0.837240	−	0.546835i	$-0.184168\pi$
$332$	− 11.1625i	− 0.612623i
$333$	− 6.05096i	− 0.331591i
$334$	−9.93619	−0.543684
$335$	−0.486400	−0.0265749
$336$	1.36829i	0.0746464i
$337$	2.71943	0.148137	0.0740685	−	0.997253i	$-0.476402\pi$
$337$	2.71943	0.148137	0.0740685	+	0.997253i	$0.476402\pi$
$338$	0	0
$339$	−3.76063	−0.204249
$340$	− 2.09948i	− 0.113860i
$341$	9.35229	0.506455
$342$	1.10850	0.0599406
$343$	− 1.00000i	− 0.0539949i
$344$	− 0.979017i	− 0.0527851i
$345$	− 1.37428i	− 0.0739890i
$346$	16.3127i	0.876978i
$347$	−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
$349$	− 9.05354i	− 0.484625i	−0.970198	−	0.242312i	$-0.922094\pi$
$349$	− 9.05354i	− 0.484625i	0.970198	−	0.242312i	$-0.0779059\pi$
$350$	4.76291	0.254588
$351$	0	0
$352$	21.6752	1.15529
$353$	9.43537i	0.502194i	0.967962	+	0.251097i	$0.0807914\pi$
$353$	9.43537i	0.502194i	−0.967962	+	0.251097i	$0.919209\pi$
$354$	11.9159	0.633324
$355$	0.697356	0.0370118
$356$	− 16.2012i	− 0.858662i
$357$	− 8.02401i	− 0.424676i
$358$	− 23.2047i	− 1.22640i
$359$	9.68118i	0.510953i	0.966815	+	0.255477i	$0.0822324\pi$
$359$	9.68118i	0.510953i	−0.966815	+	0.255477i	$0.917768\pi$
$360$	0.629629	0.0331843
$361$	14.4760	0.761893
$362$	− 23.3381i	− 1.22662i
$363$	10.9942	0.577047
$364$	0	0
$365$	−2.43766	−0.127593
$366$	22.5817i	1.18037i
$367$	−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
$369$	2.68909i	0.139988i
$370$	− 4.47770i	− 0.232785i
$371$	10.9423i	0.568094i
$372$	3.57631i	0.185423i
$373$	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
$375$	6.16300i	0.318256i
$376$	19.7692	1.01952
$377$	0	0
$378$	5.45795	0.280726
$379$	− 6.59026i	− 0.338519i	−0.985572	−	0.169259i	$-0.945862\pi$
$379$	− 6.59026i	− 0.338519i	0.985572	−	0.169259i	$-0.0541375\pi$
$380$	−0.874691	−0.0448707
$381$	23.6679	1.21255
$382$	− 2.14932i	− 0.109969i
$383$	31.3776i	1.60332i	0.597781	+	0.801660i	$0.296049\pi$
$383$	31.3776i	1.60332i	−0.597781	+	0.801660i	$0.703951\pi$
$384$	5.59626i	0.285583i
$385$	1.69024i	0.0861424i
$386$	18.3379	0.933376
$387$	−0.173855	−0.00883754
$388$	14.9410i	0.758514i
$389$	−16.4265	−0.832857	−0.416428	−	0.909169i	$-0.636718\pi$
$389$	−16.4265	−0.832857	−0.416428	+	0.909169i	$0.636718\pi$
$390$	0	0
$391$	−11.2035	−0.566585
$392$	2.98304i	0.150666i
$393$	18.2335	0.919760
$394$	14.7396	0.742572
$395$	− 1.67695i	− 0.0843764i
$396$	− 2.31928i	− 0.116548i
$397$	− 6.94037i	− 0.348327i	−0.984717	−	0.174163i	$-0.944278\pi$
$397$	− 6.94037i	− 0.348327i	0.984717	−	0.174163i	$-0.0557221\pi$
$398$	8.44731i	0.423425i
$399$	−3.34299	−0.167359
$400$	−4.21466	−0.210733
$401$	− 0.890125i	− 0.0444507i	−0.999753	−	0.0222254i	$-0.992925\pi$
$401$	− 0.890125i	− 0.0444507i	0.999753	−	0.0222254i	$-0.00707514\pi$
$402$	1.88760	0.0941451
$403$	0	0
$404$	−7.55321	−0.375786
$405$	2.84100i	0.141171i
$406$	2.86195	0.142036
$407$	−48.4558	−2.40187
$408$	23.9359i	1.18501i
$409$	− 2.00173i	− 0.0989793i	−0.998775	−	0.0494897i	$-0.984241\pi$
$409$	− 2.00173i	− 0.0989793i	0.998775	−	0.0494897i	$-0.0157595\pi$
$410$	1.98992i	0.0982752i
$411$	− 0.644840i	− 0.0318076i
$412$	13.1740	0.649036
$413$	7.70620	0.379197
$414$	− 1.14368i	− 0.0562088i
$415$	−4.30935	−0.211538
$416$	0	0
$417$	28.5603	1.39861
$418$	− 8.87678i	− 0.434178i
$419$	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
$421$	− 9.10353i	− 0.443679i	−0.975083	−	0.221839i	$-0.928794\pi$
$421$	− 9.10353i	− 0.443679i	0.975083	−	0.221839i	$-0.0712061\pi$
$422$	27.8892i	1.35762i
$423$	− 3.51064i	− 0.170693i
$424$	− 32.6412i	− 1.58520i
$425$	24.7159	1.19890
$426$	−2.70627	−0.131119
$427$	14.6039i	0.706734i
$428$	9.36099	0.452480
$429$	0	0
$430$	−0.128652	−0.00620416
$431$	15.8655i	0.764216i	0.924118	+	0.382108i	$0.124802\pi$
$431$	15.8655i	0.764216i	−0.924118	+	0.382108i	$0.875198\pi$
$432$	−4.82970	−0.232369
$433$	−15.8736	−0.762835	−0.381418	−	0.924403i	$-0.624564\pi$
$433$	−15.8736	−0.762835	−0.381418	+	0.924403i	$0.624564\pi$
$434$	− 2.16899i	− 0.104115i
$435$	1.82175i	0.0873462i
$436$	5.10983i	0.244716i
$437$	4.66764i	0.223283i
$438$	9.45999	0.452016
$439$	−5.37687	−0.256624	−0.128312	−	0.991734i	$-0.540956\pi$
$439$	−5.37687	−0.256624	−0.128312	+	0.991734i	$0.540956\pi$
$440$	− 5.04204i	− 0.240370i
$441$	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	$0.706364\pi$
$444$	− 18.5295i	− 0.879369i
$445$	−6.25456	−0.296494
$446$	13.9009	0.658226
$447$	17.1623i	0.811748i
$448$	− 6.76806i	− 0.319761i
$449$	− 15.4369i	− 0.728512i	−0.931299	−	0.364256i	$-0.881323\pi$
$449$	− 15.4369i	− 0.728512i	0.931299	−	0.364256i	$-0.118677\pi$
$450$	2.52306i	0.118938i
$451$	21.5341	1.01400
$452$	2.46950	0.116156
$453$	− 31.9330i	− 1.50034i
$454$	18.4294	0.864936
$455$	0	0
$456$	9.97227	0.466995
$457$	− 30.2784i	− 1.41636i	−0.706031	−	0.708181i	$-0.749516\pi$
$457$	− 30.2784i	− 1.41636i	0.706031	−	0.708181i	$-0.250484\pi$
$458$	−3.19343	−0.149219
$459$	28.3226	1.32199
$460$	0.902455i	0.0420772i
$461$	− 25.3431i	− 1.18035i	−0.807276	−	0.590173i	$-0.799059\pi$
$461$	− 25.3431i	− 1.18035i	0.807276	−	0.590173i	$-0.200941\pi$
$462$	− 6.55941i	− 0.305171i
$463$	− 2.93975i	− 0.136622i	−0.997664	−	0.0683109i	$-0.978239\pi$
$463$	− 2.93975i	− 0.136622i	0.997664	−	0.0683109i	$-0.0217610\pi$
$464$	−2.53252	−0.117569
$465$	1.38065	0.0640262
$466$	17.1455i	0.794250i
$467$	−24.0967	−1.11506	−0.557531	−	0.830156i	$-0.688251\pi$
$467$	−24.0967	−1.11506	−0.557531	+	0.830156i	$0.688251\pi$
$468$	0	0
$469$	1.22074	0.0563685
$470$	− 2.59787i	− 0.119831i
$471$	−36.8525	−1.69807
$472$	−22.9879	−1.05810
$473$	1.39222i	0.0640144i
$474$	6.50784i	0.298915i
$475$	− 10.2972i	− 0.472469i
$476$	5.26915i	0.241511i
$477$	−5.79646	−0.265402
$478$	3.83495	0.175407
$479$	11.1069i	0.507488i	0.967271	+	0.253744i	$0.0816620\pi$
$479$	11.1069i	0.507488i	−0.967271	+	0.253744i	$0.918338\pi$
$480$	3.19984	0.146052
$481$	0	0
$482$	17.4109	0.793045
$483$	3.44910i	0.156940i
$484$	−7.21960	−0.328164
$485$	5.76805	0.261913
$486$	5.34858i	0.242616i
$487$	29.1520i	1.32100i	0.750825	+	0.660501i	$0.229656\pi$
$487$	29.1520i	1.32100i	−0.750825	+	0.660501i	$0.770344\pi$
$488$	− 43.5641i	− 1.97205i
$489$	− 19.9617i	− 0.902700i
$490$	0.392000	0.0177087
$491$	−0.374507	−0.0169013	−0.00845063	−	0.999964i	$-0.502690\pi$
$491$	−0.374507	−0.0169013	−0.00845063	+	0.999964i	$0.502690\pi$
$492$	8.23462i	0.371245i
$493$	14.8513	0.668871
$494$	0	0
$495$	−0.895370	−0.0402439
$496$	1.91932i	0.0861800i
$497$	−1.75019	−0.0785066
$498$	16.7236	0.749401
$499$	0.402490i	0.0180179i	0.999959	+	0.00900896i	$0.00286768\pi$
$499$	0.402490i	0.0180179i	−0.999959	+	0.00900896i	$0.997132\pi$
$500$	− 4.04708i	− 0.180991i
$501$	15.8736i	0.709182i
$502$	− 1.67946i	− 0.0749580i
$503$	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
$505$	2.91596i	0.129758i
$506$	−9.15854	−0.407147
$507$	0	0
$508$	−15.5421	−0.689569
$509$	− 37.0510i	− 1.64225i	−0.570745	−	0.821127i	$-0.693345\pi$
$509$	− 37.0510i	− 1.64225i	0.570745	−	0.821127i	$-0.306655\pi$
$510$	3.14541	0.139281
$511$	6.11791	0.270640
$512$	9.64220i	0.426129i
$513$	− 11.7999i	− 0.520977i
$514$	22.8961i	1.00990i
$515$	− 5.08589i	− 0.224111i
$516$	−0.532384	−0.0234369
$517$	−28.1131	−1.23641
$518$	11.2379i	0.493765i
$519$	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	$0.284923\pi$
$522$	1.51606i	0.0663562i
$523$	−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
$525$	− 7.60902i	− 0.332085i
$526$	− 13.8321i	− 0.603107i
$527$	− 11.2554i	− 0.490293i
$528$	5.80437i	0.252603i
$529$	−18.1842	−0.790617
$530$	−4.28937	−0.186318
$531$	4.08221i	0.177153i
$532$	2.19525	0.0951763
$533$	0	0
$534$	24.2725	1.05037
$535$	− 3.61386i	− 0.156241i
$536$	−3.64151	−0.157289
$537$	−37.0708	−1.59972
$538$	− 3.39112i	− 0.146202i
$539$	− 4.24206i	− 0.182718i
$540$	− 2.28142i	− 0.0981767i
$541$	− 36.0835i	− 1.55135i	−0.631131	−	0.775676i	$-0.717409\pi$
$541$	− 36.0835i	− 1.55135i	0.631131	−	0.775676i	$-0.282591\pi$
$542$	−20.8842	−0.897052
$543$	−37.2840	−1.60001
$544$	− 26.0859i	− 1.11842i
$545$	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	$0.721853\pi$
$548$	0.423449i	0.0180888i
$549$	−7.73615	−0.330171
$550$	20.2045	0.861524
$551$	− 6.18742i	− 0.263593i
$552$	− 10.2888i	− 0.437921i
$553$	4.20871i	0.178973i
$554$	6.95221i	0.295371i
$555$	−7.15339	−0.303644
$556$	−18.7548	−0.795380
$557$	− 11.6919i	− 0.495400i	−0.968837	−	0.247700i	$-0.920325\pi$
$557$	− 11.6919i	− 0.495400i	0.968837	−	0.247700i	$-0.0796748\pi$
$558$	1.14898	0.0486402
$559$	0	0
$560$	−0.346878	−0.0146583
$561$	− 34.0383i	− 1.43710i
$562$	2.33985	0.0987008
$563$	24.4062	1.02860	0.514300	−	0.857610i	$-0.328052\pi$
$563$	24.4062	1.02860	0.514300	+	0.857610i	$0.328052\pi$
$564$	− 10.7504i	− 0.452674i
$565$	− 0.953364i	− 0.0401083i
$566$	− 14.0223i	− 0.589401i
$567$	− 7.13019i	− 0.299440i
$568$	5.22087	0.219063
$569$	−21.2322	−0.890099	−0.445050	−	0.895506i	$-0.646814\pi$
$569$	−21.2322	−0.890099	−0.445050	+	0.895506i	$0.646814\pi$
$570$	− 1.31045i	− 0.0548888i
$571$	−29.0906	−1.21741	−0.608703	−	0.793398i	$-0.708310\pi$
$571$	−29.0906	−1.21741	−0.608703	+	0.793398i	$0.708310\pi$
$572$	0	0
$573$	−3.43366	−0.143443
$574$	− 4.99419i	− 0.208454i
$575$	−10.6241	−0.443054
$576$	3.58525	0.149385
$577$	25.1627i	1.04754i	0.851861	+	0.523768i	$0.175474\pi$
$577$	25.1627i	1.04754i	−0.851861	+	0.523768i	$0.824526\pi$
$578$	− 8.91723i	− 0.370908i
$579$	− 29.2959i	− 1.21750i
$580$	− 1.19629i	− 0.0496734i
$581$	10.8154	0.448697
$582$	−22.3844	−0.927864
$583$	46.4178i	1.92243i
$584$	−18.2499	−0.755188
$585$	0	0
$586$	−7.04291	−0.290940
$587$	− 21.7327i	− 0.897006i	−0.893781	−	0.448503i	$-0.851957\pi$
$587$	− 21.7327i	− 0.897006i	0.893781	−	0.448503i	$-0.148043\pi$
$588$	1.62216	0.0668967
$589$	−4.68926	−0.193218
$590$	3.02083i	0.124366i
$591$	− 23.5474i	− 0.968611i
$592$	− 9.94433i	− 0.408709i
$593$	− 30.7678i	− 1.26348i	−0.775180	−	0.631741i	$-0.782341\pi$
$593$	− 30.7678i	− 1.26348i	0.775180	−	0.631741i	$-0.217659\pi$
$594$	23.1529	0.949976
$595$	2.03418	0.0833934
$596$	− 11.2700i	− 0.461637i
$597$	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	$0.618322\pi$
$600$	22.6980i	0.926642i
$601$	−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
$603$	0.646663i	0.0263342i
$604$	20.9696i	0.853239i
$605$	2.78716i	0.113314i
$606$	− 11.3161i	− 0.459687i
$607$	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
$609$	− 4.57213i	− 0.185272i
$610$	−5.72474	−0.231788
$611$	0	0
$612$	−2.79123	−0.112829
$613$	19.4824i	0.786888i	0.919349	+	0.393444i	$0.128716\pi$
$613$	19.4824i	0.786888i	−0.919349	+	0.393444i	$0.871284\pi$
$614$	24.0265	0.969632
$615$	3.17901	0.128190
$616$	12.6542i	0.509853i
$617$	− 7.14474i	− 0.287636i	−0.989604	−	0.143818i	$-0.954062\pi$
$617$	− 7.14474i	− 0.287636i	0.989604	−	0.143818i	$-0.0459381\pi$
$618$	19.7371i	0.793944i
$619$	− 22.9703i	− 0.923255i	−0.887074	−	0.461628i	$-0.847266\pi$
$619$	− 22.9703i	− 0.923255i	0.887074	−	0.461628i	$-0.152734\pi$
$620$	−0.906636	−0.0364114
$621$	−12.1744	−0.488542
$622$	23.3374i	0.935743i
$623$	15.6973	0.628901
$624$	0	0
$625$	22.6438	0.905752
$626$	14.8435i	0.593266i
$627$	−14.1812	−0.566341
$628$	24.2000	0.965686
$629$	58.3161i	2.32522i
$630$	0.207654i	0.00827315i
$631$	− 30.1524i	− 1.20035i	−0.799870	−	0.600173i	$-0.795098\pi$
$631$	− 30.1524i	− 1.20035i	0.799870	−	0.600173i	$-0.204902\pi$
$632$	− 12.5548i	− 0.499401i
$633$	44.5546	1.77089
$634$	−31.0801	−1.23435
$635$	6.00010i	0.238107i
$636$	−17.7501	−0.703837
$637$	0	0
$638$	12.1406	0.480649
$639$	− 0.927127i	− 0.0366766i
$640$	−1.41872	−0.0560798
$641$	40.2705	1.59059	0.795295	−	0.606223i	$-0.207316\pi$
$641$	40.2705	1.59059	0.795295	+	0.606223i	$0.207316\pi$
$642$	14.0245i	0.553504i
$643$	13.6321i	0.537598i	0.963196	+	0.268799i	$0.0866268\pi$
$643$	13.6321i	0.537598i	−0.963196	+	0.268799i	$0.913373\pi$
$644$	− 2.26493i	− 0.0892509i
$645$	0.205529i	0.00809271i
$646$	−10.6831	−0.420322
$647$	2.57274	0.101145	0.0505724	−	0.998720i	$-0.483895\pi$
$647$	2.57274	0.101145	0.0505724	+	0.998720i	$0.483895\pi$
$648$	21.2696i	0.835550i
$649$	32.6902	1.28320
$650$	0	0
$651$	−3.46508	−0.135807
$652$	13.1083i	0.513361i
$653$	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
$655$	4.62241i	0.180613i
$656$	4.41933i	0.172546i
$657$	3.24084i	0.126437i
$658$	6.51999i	0.254176i
$659$	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
$661$	− 3.88736i	− 0.151201i	−0.997138	−	0.0756003i	$-0.975913\pi$
$661$	− 3.88736i	− 0.151201i	0.997138	−	0.0756003i	$-0.0240873\pi$
$662$	−19.5756	−0.760829
$663$	0	0
$664$	−32.2627	−1.25203
$665$	− 0.847488i	− 0.0328642i
$666$	−5.95306	−0.230676
$667$	−6.38381	−0.247182
$668$	− 10.4238i	− 0.403308i
$669$	− 22.2075i	− 0.858590i
$670$	0.478530i	0.0184872i
$671$	61.9507i	2.39158i
$672$	−8.03079	−0.309794
$673$	31.7515	1.22393	0.611965	−	0.790885i	$-0.290379\pi$
$673$	31.7515	1.22393	0.611965	+	0.790885i	$0.290379\pi$
$674$	− 2.67543i	− 0.103054i
$675$	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	$0.573002\pi$
$678$	3.69978i	0.142089i
$679$	−14.4763	−0.555550
$680$	−6.06804	−0.232699
$681$	− 29.4421i	− 1.12822i
$682$	− 9.20097i	− 0.352323i
$683$	− 12.6451i	− 0.483852i	−0.970295	−	0.241926i	$-0.922221\pi$
$683$	− 12.6451i	− 0.483852i	0.970295	−	0.241926i	$-0.0777792\pi$
$684$	1.16289i	0.0444643i
$685$	0.163474	0.00624604
$686$	−0.983820	−0.0375624
$687$	5.10169i	0.194642i
$688$	−0.285718	−0.0108929
$689$	0	0
$690$	−1.35205	−0.0514716
$691$	− 14.6468i	− 0.557190i	−0.960409	−	0.278595i	$-0.910131\pi$
$691$	− 14.6468i	− 0.557190i	0.960409	−	0.278595i	$-0.0898687\pi$
$692$	−17.1132	−0.650548
$693$	2.24715	0.0853622
$694$	12.6062i	0.478524i
$695$	7.24038i	0.274643i
$696$	13.6388i	0.516979i
$697$	− 25.9161i	− 0.981642i
$698$	−8.90705	−0.337137
$699$	27.3909	1.03602
$700$	4.99664i	0.188855i
$701$	−7.16794	−0.270729	−0.135365	−	0.990796i	$-0.543221\pi$
$701$	−7.16794	−0.270729	−0.135365	+	0.990796i	$0.543221\pi$
$702$	0	0
$703$	24.2959	0.916336
$704$	− 28.7105i	− 1.08207i
$705$	−4.15025	−0.156307
$706$	9.28271	0.349359
$707$	− 7.31830i	− 0.275233i
$708$	12.5007i	0.469804i
$709$	2.14832i	0.0806817i	0.999186	+	0.0403409i	$0.0128444\pi$
$709$	2.14832i	0.0806817i	−0.999186	+	0.0403409i	$0.987156\pi$
$710$	− 0.686073i	− 0.0257478i
$711$	−2.22948	−0.0836122
$712$	−46.8258	−1.75487
$713$	4.83811i	0.181189i
$714$	−7.89418	−0.295432
$715$	0	0
$716$	24.3434	0.909755
$717$	− 6.12656i	− 0.228801i
$718$	9.52454	0.355453
$719$	−9.34269	−0.348424	−0.174212	−	0.984708i	$-0.555738\pi$
$719$	−9.34269	−0.348424	−0.174212	+	0.984708i	$0.555738\pi$
$720$	− 0.183752i	− 0.00684803i
$721$	12.7643i	0.475367i
$722$	− 14.2417i	− 0.530023i
$723$	− 27.8149i	− 1.03445i
$724$	24.4834	0.909918
$725$	14.0832	0.523039
$726$	− 10.8163i	− 0.401432i
$727$	−41.2539	−1.53002	−0.765011	−	0.644017i	$-0.777267\pi$
$727$	−41.2539	−1.53002	−0.765011	+	0.644017i	$0.777267\pi$
$728$	0	0
$729$	29.9352	1.10871
$730$	2.39822i	0.0887620i
$731$	1.67553	0.0619715
$732$	−23.6899	−0.875604
$733$	− 11.6062i	− 0.428686i	−0.976758	−	0.214343i	$-0.931239\pi$
$733$	− 11.6062i	− 0.428686i	0.976758	−	0.214343i	$-0.0687610\pi$
$734$	15.1164i	0.557956i
$735$	− 0.626242i	− 0.0230993i
$736$	11.2130i	0.413315i
$737$	5.17845	0.190751
$738$	2.64558	0.0973851
$739$	− 7.80551i	− 0.287130i	−0.989641	−	0.143565i	$-0.954143\pi$
$739$	− 7.80551i	− 0.287130i	0.989641	−	0.143565i	$-0.0458567\pi$
$740$	4.69744	0.172681
$741$	0	0
$742$	10.7652	0.395204
$743$	− 41.5158i	− 1.52307i	−0.648126	−	0.761533i	$-0.724447\pi$
$743$	− 41.5158i	− 1.52307i	0.648126	−	0.761533i	$-0.275553\pi$
$744$	10.3365	0.378954
$745$	−4.35084	−0.159402
$746$	− 12.4825i	− 0.457016i
$747$	5.72924i	0.209622i
$748$	22.3521i	0.817272i
$749$	9.06986i	0.331405i
$750$	6.06328	0.221400
$751$	22.7184	0.829005	0.414503	−	0.910048i	$-0.363956\pi$
$751$	22.7184	0.829005	0.414503	+	0.910048i	$0.363956\pi$
$752$	− 5.76949i	− 0.210392i
$753$	−2.68304	−0.0977753
$754$	0	0
$755$	8.09540	0.294622
$756$	5.72578i	0.208245i
$757$	−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
$759$	14.6313i	0.531083i
$760$	2.52809i	0.0917034i
$761$	21.2169i	0.769112i	0.923102	+	0.384556i	$0.125645\pi$
$761$	21.2169i	0.769112i	−0.923102	+	0.384556i	$0.874355\pi$
$762$	− 23.2850i	− 0.843526i
$763$	−4.95091	−0.179235
$764$	2.25479	0.0815755
$765$	1.07757i	0.0389596i
$766$	30.8699	1.11537
$767$	0	0
$768$	26.7806	0.966360
$769$	15.0781i	0.543731i	0.962335	+	0.271865i	$0.0876406\pi$
$769$	15.0781i	0.543731i	−0.962335	+	0.271865i	$0.912359\pi$
$770$	1.66289	0.0599263
$771$	36.5778	1.31732
$772$	19.2378i	0.692385i
$773$	− 4.39415i	− 0.158047i	−0.996873	−	0.0790233i	$-0.974820\pi$
$773$	− 4.39415i	− 0.158047i	0.996873	−	0.0790233i	$-0.0251801\pi$
$774$	0.171042i	0.00614797i
$775$	− 10.6733i	− 0.383396i
$776$	43.1834	1.55020
$777$	17.9532	0.644067
$778$	16.1607i	0.579390i
$779$	−10.7972	−0.386852
$780$	0	0
$781$	−7.42439	−0.265666
$782$	11.0222i	0.394154i
$783$	16.1384	0.576739
$784$	0.870575	0.0310920
$785$	− 9.34254i	− 0.333449i
$786$	− 17.9385i	− 0.639845i
$787$	− 28.1360i	− 1.00294i	−0.865175	−	0.501470i	$-0.832793\pi$
$787$	− 28.1360i	− 1.00294i	0.865175	−	0.501470i	$-0.167207\pi$
$788$	15.4629i	0.550845i
$789$	−22.0975	−0.786693
$790$	−1.64982	−0.0586978
$791$	2.39270i	0.0850746i
$792$	−6.70333	−0.238193
$793$	0	0
$794$	−6.82807	−0.242319
$795$	6.85251i	0.243034i
$796$	−8.86185	−0.314100
$797$	−14.7844	−0.523692	−0.261846	−	0.965110i	$-0.584331\pi$
$797$	−14.7844	−0.523692	−0.261846	+	0.965110i	$0.584331\pi$
$798$	3.28890i	0.116426i
$799$	33.8338i	1.19695i
$800$	− 24.7367i	− 0.874576i
$801$	8.31537i	0.293809i
$802$	−0.875723	−0.0309229
$803$	25.9525	0.915845
$804$	1.98023i	0.0698375i
$805$	−0.874389	−0.0308181
$806$	0	0
$807$	−5.41751	−0.190705
$808$	21.8308i	0.768004i
$809$	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
$811$	13.6662i	0.479886i	0.970787	+	0.239943i	$0.0771287\pi$
$811$	13.6662i	0.479886i	−0.970787	+	0.239943i	$0.922871\pi$
$812$	3.00239i	0.105363i
$813$	33.3637i	1.17012i
$814$	47.6718i	1.67090i
$815$	5.06053	0.177263
$816$	6.98550	0.244542
$817$	− 0.698063i	− 0.0244221i
$818$	−1.96934	−0.0688565
$819$	0	0
$820$	−2.08757	−0.0729012
$821$	− 11.8254i	− 0.412708i	−0.978477	−	0.206354i	$-0.933840\pi$
$821$	− 11.8254i	− 0.412708i	0.978477	−	0.206354i	$-0.0661598\pi$
$822$	−0.634406	−0.0221274
$823$	12.6805	0.442015	0.221007	−	0.975272i	$-0.429065\pi$
$823$	12.6805	0.442015	0.221007	+	0.975272i	$0.429065\pi$
$824$	− 38.0763i	− 1.32645i
$825$	− 32.2779i	− 1.12377i
$826$	− 7.58151i	− 0.263794i
$827$	19.7897i	0.688156i	0.938941	+	0.344078i	$0.111809\pi$
$827$	19.7897i	0.688156i	−0.938941	+	0.344078i	$0.888191\pi$
$828$	1.19980	0.0416961
$829$	15.7027	0.545378	0.272689	−	0.962102i	$-0.412087\pi$
$829$	15.7027	0.545378	0.272689	+	0.962102i	$0.412087\pi$
$830$	4.23962i	0.147160i
$831$	11.1066	0.385282
$832$	0	0
$833$	−5.10528	−0.176887
$834$	− 28.0982i	− 0.972962i
$835$	−4.02416	−0.139262
$836$	9.31239	0.322076
$837$	− 12.2308i	− 0.422759i
$838$	− 31.8108i	− 1.09889i
$839$	18.8485i	0.650722i	0.945590	+	0.325361i	$0.105486\pi$
$839$	18.8485i	0.650722i	−0.945590	+	0.325361i	$0.894514\pi$
$840$	1.86811i	0.0644558i
$841$	−20.5376	−0.708194
$842$	−8.95623	−0.308652
$843$	− 3.73805i	− 0.128745i
$844$	−29.2578	−1.00709
$845$	0	0
$846$	−3.45384	−0.118745
$847$	− 6.99507i	− 0.240353i
$848$	−9.52606	−0.327126
$849$	−22.4014	−0.768815
$850$	− 24.3160i	− 0.834031i
$851$	− 25.0671i	− 0.859288i
$852$	− 2.83908i	− 0.0972653i
$853$	− 2.42144i	− 0.0829084i	−0.999140	−	0.0414542i	$-0.986801\pi$
$853$	− 2.42144i	− 0.0829084i	0.999140	−	0.0414542i	$-0.0131991\pi$
$854$	14.3676	0.491650
$855$	0.448940	0.0153534
$856$	− 27.0557i	− 0.924746i
$857$	−39.9800	−1.36569	−0.682845	−	0.730564i	$-0.739257\pi$
$857$	−39.9800	−1.36569	−0.682845	+	0.730564i	$0.739257\pi$
$858$	0	0
$859$	−2.31038	−0.0788292	−0.0394146	−	0.999223i	$-0.512549\pi$
$859$	−2.31038	−0.0788292	−0.0394146	+	0.999223i	$0.512549\pi$
$860$	− 0.134966i	− 0.00460229i
$861$	−7.97852	−0.271907
$862$	15.6088	0.531639
$863$	− 46.1232i	− 1.57005i	−0.619462	−	0.785027i	$-0.712649\pi$
$863$	− 46.1232i	− 1.57005i	0.619462	−	0.785027i	$-0.287351\pi$
$864$	− 28.3465i	− 0.964368i
$865$	6.60665i	0.224633i
$866$	15.6167i	0.530678i
$867$	−14.2458	−0.483812
$868$	2.27543	0.0772330
$869$	17.8536i	0.605642i
$870$	1.79227	0.0607637
$871$	0	0
$872$	14.7688	0.500133
$873$	− 7.66856i	− 0.259541i
$874$	4.59212	0.155331
$875$	3.92121	0.132561
$876$	9.92421i	0.335308i
$877$	22.7695i	0.768870i	0.923152	+	0.384435i	$0.125604\pi$
$877$	22.7695i	0.768870i	−0.923152	+	0.384435i	$0.874396\pi$
$878$	5.28987i	0.178524i
$879$	11.2515i	0.379502i
$880$	−1.47148	−0.0496035
$881$	−20.0984	−0.677131	−0.338566	−	0.940943i	$-0.609942\pi$
$881$	−20.0984	−0.677131	−0.338566	+	0.940943i	$0.609942\pi$
$882$	− 0.521160i	− 0.0175484i
$883$	22.1650	0.745911	0.372956	−	0.927849i	$-0.378344\pi$
$883$	22.1650	0.745911	0.372956	+	0.927849i	$0.378344\pi$
$884$	0	0
$885$	4.82595	0.162222
$886$	25.0075i	0.840143i
$887$	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
$889$	− 15.0587i	− 0.505054i
$890$	6.15336i	0.206261i
$891$	− 30.2467i	− 1.01330i
$892$	14.5830i	0.488276i
$893$	14.0960	0.471703
$894$	16.8846	0.564705
$895$	− 9.39788i	− 0.314136i
$896$	3.56062	0.118952
$897$	0	0
$898$	−15.1871	−0.506801
$899$	− 6.41339i	− 0.213898i
$900$	−2.64687	−0.0882291
$901$	55.8633	1.86108
$902$	− 21.1857i	− 0.705406i
$903$	− 0.515826i	− 0.0171656i
$904$	− 7.13752i	− 0.237390i
$905$	− 9.45193i	− 0.314193i
$906$	−31.4163	−1.04374
$907$	29.7539	0.987964	0.493982	−	0.869472i	$-0.335541\pi$
$907$	29.7539	0.987964	0.493982	+	0.869472i	$0.335541\pi$
$908$	19.3338i	0.641615i
$909$	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	$0.692778\pi$
$912$	− 2.91032i	− 0.0963705i
$913$	45.8795	1.51839
$914$	−29.7884	−0.985314
$915$	9.14560i	0.302344i
$916$	− 3.35014i	− 0.110692i
$917$	− 11.6011i	− 0.383101i
$918$	− 27.8643i	− 0.919660i
$919$	−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
$921$	− 38.3838i	− 1.26479i
$922$	−24.9331	−0.821127
$923$	0	0
$924$	6.88129	0.226378
$925$	55.3001i	1.81826i
$926$	−2.89218	−0.0950430
$927$	−6.76163	−0.222081
$928$	− 14.8639i	− 0.487931i
$929$	33.8451i	1.11042i	0.831710	+	0.555210i	$0.187362\pi$
$929$	33.8451i	1.11042i	−0.831710	+	0.555210i	$0.812638\pi$
$930$	− 1.35831i	− 0.0445408i
$931$	2.12698i	0.0697089i
$932$	−17.9869	−0.589180
$933$	37.2828	1.22058
$934$	23.7068i	0.775710i
$935$	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	$0.371261\pi$
$938$	− 1.20099i	− 0.0392136i
$939$	23.7134	0.773856
$940$	2.72535	0.0888912
$941$	− 29.5369i	− 0.962874i	−0.876481	−	0.481437i	$-0.840115\pi$
$941$	− 29.5369i	− 0.962874i	0.876481	−	0.481437i	$-0.159885\pi$
$942$	36.2562i	1.18129i
$943$	11.1400i	0.362767i
$944$	6.70882i	0.218354i
$945$	2.21047	0.0719065
$946$	1.36969	0.0445326
$947$	22.6950i	0.737490i	0.929531	+	0.368745i	$0.120212\pi$
$947$	22.6950i	0.737490i	−0.929531	+	0.368745i	$0.879788\pi$
$948$	−6.82720	−0.221737
$949$	0	0
$950$	−10.1306	−0.328680
$951$	49.6523i	1.61009i
$952$	15.2292	0.493583
$953$	−49.0720	−1.58960	−0.794799	−	0.606872i	$-0.792424\pi$
$953$	−49.0720	−1.58960	−0.794799	+	0.606872i	$0.792424\pi$
$954$	5.70267i	0.184631i
$955$	− 0.870474i	− 0.0281679i
$956$	4.02315i	0.130118i
$957$	− 19.3952i	− 0.626959i
$958$	10.9272	0.353042
$959$	−0.410279	−0.0132486
$960$	− 4.23845i	− 0.136795i
$961$	26.1395	0.843209
$962$	0	0
$963$	−4.80458	−0.154825
$964$	18.2653i	0.588286i
$965$	7.42686	0.239079
$966$	3.39330	0.109178
$967$	− 23.1018i	− 0.742905i	−0.928452	−	0.371452i	$-0.878860\pi$
$967$	− 23.1018i	− 0.742905i	0.928452	−	0.371452i	$-0.121140\pi$
$968$	20.8666i	0.670677i
$969$	17.0669i	0.548268i
$970$	− 5.67472i	− 0.182204i
$971$	−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
$973$	− 18.1715i	− 0.582552i
$974$	28.6803	0.918976
$975$	0	0
$976$	−12.7138	−0.406959
$977$	2.18246i	0.0698230i	0.999390	+	0.0349115i	$0.0111149\pi$
$977$	2.18246i	0.0698230i	−0.999390	+	0.0349115i	$0.988885\pi$
$978$	−19.6387	−0.627977
$979$	66.5891	2.12820
$980$	0.411236i	0.0131365i
$981$	− 2.62265i	− 0.0837347i
$982$	0.368447i	0.0117576i
$983$	2.60962i	0.0832339i	0.999134	+	0.0416170i	$0.0132509\pi$
$983$	2.60962i	0.0832339i	−0.999134	+	0.0416170i	$0.986749\pi$
$984$	23.8002	0.758723
$985$	5.96955	0.190206
$986$	− 14.6110i	− 0.465310i
$987$	10.4161	0.331547
$988$	0	0
$989$	−0.720221	−0.0229017
$990$	0.880882i	0.0279963i
$991$	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
$993$	31.2732i	0.992426i
$994$	1.72187i	0.0546143i
$995$	3.42116i	0.108458i
$996$	17.5443i	0.555911i
$997$	−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
$999$	63.3699i	2.00493i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.5	✓	12	13.5	odd	4
1183.2.a.r.1.8	yes	12	13.8	odd	4
1183.2.c.j.337.9		24	1.1	even	1	trivial
1183.2.c.j.337.16		24	13.12	even	2	inner
8281.2.a.cn.1.5		12	91.83	even	4
8281.2.a.cq.1.8		12	91.34	even	4

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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.983820i q^{2} -1.57171 q^{3} +1.03210 q^{4} -0.398447i q^{5} +1.54628i q^{6} +1.00000i q^{7} -2.98304i q^{8} -0.529731 q^{9} +O(q^{10})\)	\(q-0.983820i q^{2} -1.57171 q^{3} +1.03210 q^{4} -0.398447i q^{5} +1.54628i q^{6} +1.00000i q^{7} -2.98304i q^{8} -0.529731 q^{9} -0.392000 q^{10} +4.24206i q^{11} -1.62216 q^{12} +0.983820 q^{14} +0.626242i q^{15} -0.870575 q^{16} +5.10528 q^{17} +0.521160i q^{18} -2.12698i q^{19} -0.411236i q^{20} -1.57171i q^{21} +4.17342 q^{22} -2.19449 q^{23} +4.68847i q^{24} +4.84124 q^{25} +5.54771 q^{27} +1.03210i q^{28} +2.90902 q^{29} +0.616110 q^{30} -2.20466i q^{31} -5.10959i q^{32} -6.66728i q^{33} -5.02268i q^{34} +0.398447 q^{35} -0.546734 q^{36} +11.4227i q^{37} -2.09256 q^{38} -1.18858 q^{40} -5.07633i q^{41} -1.54628 q^{42} +0.328195 q^{43} +4.37822i q^{44} +0.211070i q^{45} +2.15899i q^{46} +6.62722i q^{47} +1.36829 q^{48} -1.00000 q^{49} -4.76291i q^{50} -8.02401 q^{51} +10.9423 q^{53} -5.45795i q^{54} +1.69024 q^{55} +2.98304 q^{56} +3.34299i q^{57} -2.86195i q^{58} -7.70620i q^{59} +0.646344i q^{60} +14.6039 q^{61} -2.16899 q^{62} -0.529731i q^{63} -6.76806 q^{64} -6.55941 q^{66} -1.22074i q^{67} +5.26915 q^{68} +3.44910 q^{69} -0.392000i q^{70} +1.75019i q^{71} +1.58021i q^{72} -6.11791i q^{73} +11.2379 q^{74} -7.60902 q^{75} -2.19525i q^{76} -4.24206 q^{77} +4.20871 q^{79} +0.346878i q^{80} -7.13019 q^{81} -4.99419 q^{82} -10.8154i q^{83} -1.62216i q^{84} -2.03418i q^{85} -0.322884i q^{86} -4.57213 q^{87} +12.6542 q^{88} -15.6973i q^{89} +0.207654 q^{90} -2.26493 q^{92} +3.46508i q^{93} +6.51999 q^{94} -0.847488 q^{95} +8.03079i q^{96} +14.4763i q^{97} +0.983820i q^{98} -2.24715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

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