LMFDB - Embedded newform 243.4.e.b.28.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,4,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, 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:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.8
Character	$\chi$	$=$	243.28
Dual form			243.4.e.b.217.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.751659 + 4.26287i) q^{2} +(-10.0895 + 3.67228i) q^{4} +(3.28965 + 2.76034i) q^{5} +(19.2025 + 6.98913i) q^{7} +(-5.92381 - 10.2603i) q^{8} +O(q^{10})$	\(q+(0.751659 + 4.26287i) q^{2} +(-10.0895 + 3.67228i) q^{4} +(3.28965 + 2.76034i) q^{5} +(19.2025 + 6.98913i) q^{7} +(-5.92381 - 10.2603i) q^{8} +(-9.29428 + 16.0982i) q^{10} +(21.3219 - 17.8912i) q^{11} +(-15.7039 + 89.0610i) q^{13} +(-15.3600 + 87.1111i) q^{14} +(-26.5146 + 22.2484i) q^{16} +(37.8692 - 65.5913i) q^{17} +(32.9713 + 57.1079i) q^{19} +(-43.3277 - 15.7700i) q^{20} +(92.2948 + 77.4446i) q^{22} +(-134.579 + 48.9827i) q^{23} +(-18.5037 - 104.940i) q^{25} -391.459 q^{26} -219.410 q^{28} +(3.27079 + 18.5496i) q^{29} +(32.2613 - 11.7422i) q^{31} +(-187.378 - 157.229i) q^{32} +(308.072 + 112.129i) q^{34} +(43.8770 + 75.9972i) q^{35} +(-62.6156 + 108.453i) q^{37} +(-218.660 + 183.478i) q^{38} +(8.83481 - 50.1047i) q^{40} +(10.0543 - 57.0207i) q^{41} +(-74.2022 + 62.2630i) q^{43} +(-149.426 + 258.814i) q^{44} +(-309.964 - 536.874i) q^{46} +(-99.0627 - 36.0559i) q^{47} +(57.1340 + 47.9411i) q^{49} +(433.436 - 157.758i) q^{50} +(-168.613 - 956.251i) q^{52} +603.869 q^{53} +119.528 q^{55} +(-42.0410 - 238.426i) q^{56} +(-76.6159 + 27.8859i) q^{58} +(-318.985 - 267.660i) q^{59} +(507.666 + 184.775i) q^{61} +(74.3048 + 128.700i) q^{62} +(390.953 - 677.150i) q^{64} +(-297.499 + 249.631i) q^{65} +(-10.5922 + 60.0715i) q^{67} +(-141.212 + 800.851i) q^{68} +(-290.986 + 244.166i) q^{70} +(50.1993 - 86.9478i) q^{71} +(277.621 + 480.854i) q^{73} +(-509.388 - 185.402i) q^{74} +(-542.381 - 455.112i) q^{76} +(534.478 - 194.534i) q^{77} +(-54.9931 - 311.881i) q^{79} -148.637 q^{80} +250.629 q^{82} +(67.1108 + 380.604i) q^{83} +(305.631 - 111.240i) q^{85} +(-321.194 - 269.514i) q^{86} +(-309.878 - 112.786i) q^{88} +(-566.411 - 981.053i) q^{89} +(-924.012 + 1600.44i) q^{91} +(1177.96 - 988.423i) q^{92} +(79.2401 - 449.393i) q^{94} +(-49.1735 + 278.877i) q^{95} +(-858.296 + 720.196i) q^{97} +(-161.421 + 279.590i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8	$ 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8} - 3 q^{10} + 159 q^{11} + 3 q^{13} + 336 q^{14} - 45 q^{16} + 207 q^{17} - 3 q^{19} - 681 q^{20} + 111 q^{22} - 33 q^{23} + 435 q^{25} - 1914 q^{26} - 12 q^{28} + 51 q^{29} + 111 q^{31} - 1647 q^{32} - 513 q^{34} + 1257 q^{35} - 3 q^{37} + 525 q^{38} - 6 q^{40} - 447 q^{41} + 516 q^{43} + 2211 q^{44} - 3 q^{46} - 2109 q^{47} - 591 q^{49} + 4938 q^{50} - 1350 q^{52} - 2736 q^{53} - 12 q^{55} + 7773 q^{56} - 888 q^{58} - 3048 q^{59} + 57 q^{61} + 2118 q^{62} - 195 q^{64} - 3297 q^{65} + 2082 q^{67} - 3573 q^{68} + 1524 q^{70} + 3105 q^{71} - 219 q^{73} - 9006 q^{74} - 1425 q^{76} + 8985 q^{77} - 1401 q^{79} - 9870 q^{80} - 12 q^{82} + 8511 q^{83} - 1827 q^{85} - 12507 q^{86} - 3693 q^{88} + 5202 q^{89} + 267 q^{91} - 5118 q^{92} - 2211 q^{94} - 5178 q^{95} + 1569 q^{97} + 4392 q^{98}+O(q^{100}) $ 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8 - 3 * q^10 + 159 * q^11 + 3 * q^13 + 336 * q^14 - 45 * q^16 + 207 * q^17 - 3 * q^19 - 681 * q^20 + 111 * q^22 - 33 * q^23 + 435 * q^25 - 1914 * q^26 - 12 * q^28 + 51 * q^29 + 111 * q^31 - 1647 * q^32 - 513 * q^34 + 1257 * q^35 - 3 * q^37 + 525 * q^38 - 6 * q^40 - 447 * q^41 + 516 * q^43 + 2211 * q^44 - 3 * q^46 - 2109 * q^47 - 591 * q^49 + 4938 * q^50 - 1350 * q^52 - 2736 * q^53 - 12 * q^55 + 7773 * q^56 - 888 * q^58 - 3048 * q^59 + 57 * q^61 + 2118 * q^62 - 195 * q^64 - 3297 * q^65 + 2082 * q^67 - 3573 * q^68 + 1524 * q^70 + 3105 * q^71 - 219 * q^73 - 9006 * q^74 - 1425 * q^76 + 8985 * q^77 - 1401 * q^79 - 9870 * q^80 - 12 * q^82 + 8511 * q^83 - 1827 * q^85 - 12507 * q^86 - 3693 * q^88 + 5202 * q^89 + 267 * q^91 - 5118 * q^92 - 2211 * q^94 - 5178 * q^95 + 1569 * q^97 + 4392 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.751659	+	4.26287i	0.265751	+	1.50715i	0.766887	+	0.641783i	$0.221805\pi$
$2$	0.751659	+	4.26287i	0.265751	+	1.50715i	−0.501135	+	0.865369i	$0.667084\pi$
$3$		0			0
$3$		0			0
$4$	−10.0895	+	3.67228i	−1.26119	+	0.459035i
$5$	3.28965	+	2.76034i	0.294235	+	0.246893i	0.777940	−	0.628339i	$-0.216265\pi$
$5$	3.28965	+	2.76034i	0.294235	+	0.246893i	−0.483705	+	0.875231i	$0.660709\pi$
$6$		0			0
$7$	19.2025	+	6.98913i	1.03684	+	0.377378i	0.803680	−	0.595062i	$-0.202872\pi$
$7$	19.2025	+	6.98913i	1.03684	+	0.377378i	0.233156	+	0.972439i	$0.425095\pi$
$8$	−5.92381	−	10.2603i	−0.261798	−	0.453447i
$9$		0			0
$10$	−9.29428	+	16.0982i	−0.293911	+	0.509069i
$11$	21.3219	−	17.8912i	0.584437	−	0.490401i	−0.301964	−	0.953319i	$-0.597642\pi$
$11$	21.3219	−	17.8912i	0.584437	−	0.490401i	0.886401	+	0.462918i	$0.153198\pi$
$12$		0			0
$13$	−15.7039	+	89.0610i	−0.335036	+	1.90008i	0.0918417	+	0.995774i	$0.470725\pi$
$13$	−15.7039	+	89.0610i	−0.335036	+	1.90008i	−0.426878	+	0.904309i	$0.640386\pi$
$14$	−15.3600	+	87.1111i	−0.293224	+	1.66296i
$15$		0			0
$16$	−26.5146	+	22.2484i	−0.414290	+	0.347631i
$17$	37.8692	−	65.5913i	0.540272	−	0.935778i	−0.458616	−	0.888634i	$-0.651655\pi$
$17$	37.8692	−	65.5913i	0.540272	−	0.935778i	0.998888	−	0.0471436i	$-0.0150118\pi$
$18$		0			0
$19$	32.9713	+	57.1079i	0.398112	+	0.689551i	0.993493	−	0.113893i	$-0.0363321\pi$
$19$	32.9713	+	57.1079i	0.398112	+	0.689551i	−0.595381	+	0.803444i	$0.702999\pi$
$20$	−43.3277	−	15.7700i	−0.484419	−	0.176314i
$21$		0			0
$22$	92.2948	+	77.4446i	0.894424	+	0.750511i
$23$	−134.579	+	48.9827i	−1.22007	+	0.444069i	−0.870186	−	0.492723i	$-0.836001\pi$
$23$	−134.579	+	48.9827i	−1.22007	+	0.444069i	−0.349885	+	0.936793i	$0.613779\pi$
$24$		0			0
$25$	−18.5037	−	104.940i	−0.148030	−	0.839519i
$26$	−391.459			−2.95275
$27$		0			0
$28$	−219.410			−1.48088
$29$	3.27079	+	18.5496i	0.0209438	+	0.118778i	0.993487	−	0.113943i	$-0.0363481\pi$
$29$	3.27079	+	18.5496i	0.0209438	+	0.118778i	−0.972543	+	0.232721i	$0.925237\pi$
$30$		0			0
$31$	32.2613	−	11.7422i	0.186913	−	0.0680308i	−0.246868	−	0.969049i	$-0.579401\pi$
$31$	32.2613	−	11.7422i	0.186913	−	0.0680308i	0.433781	+	0.901018i	$0.357179\pi$
$32$	−187.378	−	157.229i	−1.03513	−	0.868576i
$33$		0			0
$34$	308.072	+	112.129i	1.55394	+	0.565587i
$35$	43.8770	+	75.9972i	0.211902	+	0.367025i
$36$		0			0
$37$	−62.6156	+	108.453i	−0.278215	+	0.481882i	−0.970941	−	0.239319i	$-0.923076\pi$
$37$	−62.6156	+	108.453i	−0.278215	+	0.481882i	0.692727	+	0.721200i	$0.256409\pi$
$38$	−218.660	+	183.478i	−0.933458	+	0.783264i
$39$		0			0
$40$	8.83481	−	50.1047i	0.0349226	−	0.198056i
$41$	10.0543	−	57.0207i	0.0382980	−	0.217199i	−0.959653	−	0.281188i	$-0.909271\pi$
$41$	10.0543	−	57.0207i	0.0382980	−	0.217199i	0.997951	+	0.0639898i	$0.0203825\pi$
$42$		0			0
$43$	−74.2022	+	62.2630i	−0.263156	+	0.220814i	−0.764813	−	0.644252i	$-0.777169\pi$
$43$	−74.2022	+	62.2630i	−0.263156	+	0.220814i	0.501656	+	0.865067i	$0.332724\pi$
$44$	−149.426	+	258.814i	−0.511975	+	0.886766i
$45$		0			0
$46$	−309.964	−	536.874i	−0.993515	−	1.72082i
$47$	−99.0627	−	36.0559i	−0.307442	−	0.111900i	0.183692	−	0.982984i	$-0.441195\pi$
$47$	−99.0627	−	36.0559i	−0.307442	−	0.111900i	−0.491134	+	0.871084i	$0.663417\pi$
$48$		0			0
$49$	57.1340	+	47.9411i	0.166571	+	0.139770i
$50$	433.436	−	157.758i	1.22594	−	0.446207i
$51$		0			0
$52$	−168.613	−	956.251i	−0.449662	−	2.55016i
$53$	603.869			1.56505			0.782527	−	0.622617i	$-0.213931\pi$
$53$	603.869			1.56505			0.782527	+	0.622617i	$0.213931\pi$
$54$		0			0
$55$	119.528			0.293038
$56$	−42.0410	−	238.426i	−0.100321	−	0.568948i
$57$		0			0
$58$	−76.6159	+	27.8859i	−0.173451	+	0.0631310i
$59$	−318.985	−	267.660i	−0.703870	−	0.590617i	0.219002	−	0.975724i	$-0.429720\pi$
$59$	−318.985	−	267.660i	−0.703870	−	0.590617i	−0.922872	+	0.385108i	$0.874164\pi$
$60$		0			0
$61$	507.666	+	184.775i	1.06557	+	0.387837i	0.814519	−	0.580136i	$-0.197001\pi$
$61$	507.666	+	184.775i	1.06557	+	0.387837i	0.251054	+	0.967973i	$0.419223\pi$
$62$	74.3048	+	128.700i	0.152205	+	0.263627i
$63$		0			0
$64$	390.953	−	677.150i	0.763580	−	1.32256i
$65$	−297.499	+	249.631i	−0.567696	+	0.476353i
$66$		0			0
$67$	−10.5922	+	60.0715i	−0.0193141	+	0.109536i	−0.992941	−	0.118612i	$-0.962156\pi$
$67$	−10.5922	+	60.0715i	−0.0193141	+	0.109536i	0.973627	+	0.228147i	$0.0732668\pi$
$68$	−141.212	+	800.851i	−0.251830	+	1.42820i
$69$		0			0
$70$	−290.986	+	244.166i	−0.496849	+	0.416906i
$71$	50.1993	−	86.9478i	0.0839094	−	0.145335i	−0.821017	−	0.570904i	$-0.806593\pi$
$71$	50.1993	−	86.9478i	0.0839094	−	0.145335i	0.904926	+	0.425569i	$0.139926\pi$
$72$		0			0
$73$	277.621	+	480.854i	0.445111	+	0.770955i	0.998060	−	0.0622601i	$-0.0198308\pi$
$73$	277.621	+	480.854i	0.445111	+	0.770955i	−0.552949	+	0.833215i	$0.686497\pi$
$74$	−509.388	−	185.402i	−0.800205	−	0.291251i
$75$		0			0
$76$	−542.381	−	455.112i	−0.818623	−	0.686906i
$77$	534.478	−	194.534i	0.791032	−	0.287912i
$78$		0			0
$79$	−54.9931	−	311.881i	−0.0783190	−	0.444169i	−0.998599	−	0.0529095i	$-0.983151\pi$
$79$	−54.9931	−	311.881i	−0.0783190	−	0.444169i	0.920280	−	0.391260i	$-0.127961\pi$
$80$	−148.637			−0.207726
$81$		0			0
$82$	250.629			0.337529
$83$	67.1108	+	380.604i	0.0887514	+	0.503334i	0.996484	+	0.0837847i	$0.0267008\pi$
$83$	67.1108	+	380.604i	0.0887514	+	0.503334i	−0.907732	+	0.419549i	$0.862188\pi$
$84$		0			0
$85$	305.631	−	111.240i	0.390003	−	0.141950i
$86$	−321.194	−	269.514i	−0.402735	−	0.337935i
$87$		0			0
$88$	−309.878	−	112.786i	−0.375376	−	0.136626i
$89$	−566.411	−	981.053i	−0.674601	−	1.16844i	−0.976585	−	0.215130i	$-0.930982\pi$
$89$	−566.411	−	981.053i	−0.674601	−	1.16844i	0.301984	−	0.953313i	$-0.402351\pi$
$90$		0			0
$91$	−924.012	+	1600.44i	−1.06443	+	1.84364i
$92$	1177.96	−	988.423i	1.33490	−	1.12011i
$93$		0			0
$94$	79.2401	−	449.393i	0.0869467	−	0.493099i
$95$	−49.1735	+	278.877i	−0.0531063	+	0.301181i
$96$		0			0
$97$	−858.296	+	720.196i	−0.898420	+	0.753864i	−0.969881	−	0.243579i	$-0.921678\pi$
$97$	−858.296	+	720.196i	−0.898420	+	0.753864i	0.0714607	+	0.997443i	$0.477234\pi$
$98$	−161.421	+	279.590i	−0.166388	+	0.288193i
$99$		0			0
$100$	572.063	+	990.841i	0.572063	+	0.990841i
$101$	1490.93	+	542.654i	1.46884	+	0.534615i	0.947786	−	0.318908i	$-0.103316\pi$
$101$	1490.93	+	542.654i	1.46884	+	0.534615i	0.521056	+	0.853522i	$0.325538\pi$
$102$		0			0
$103$	782.178	+	656.325i	0.748255	+	0.627861i	0.935041	−	0.354540i	$-0.115363\pi$
$103$	782.178	+	656.325i	0.748255	+	0.627861i	−0.186786	+	0.982401i	$0.559807\pi$
$104$	1006.82	−	366.454i	0.949300	−	0.345517i
$105$		0			0
$106$	453.904	+	2574.22i	0.415915	+	2.35877i
$107$	1325.51			1.19759			0.598796	−	0.800902i	$-0.295646\pi$
$107$	1325.51			1.19759			0.598796	+	0.800902i	$0.295646\pi$
$108$		0			0
$109$	860.346			0.756020			0.378010	−	0.925801i	$-0.376608\pi$
$109$	860.346			0.756020			0.378010	+	0.925801i	$0.376608\pi$
$110$	89.8440	+	509.531i	0.0778754	+	0.441653i
$111$		0			0
$112$	−664.642	+	241.910i	−0.560739	+	0.204092i
$113$	−107.129	−	89.8918i	−0.0891844	−	0.0748346i	0.597105	−	0.802163i	$-0.296317\pi$
$113$	−107.129	−	89.8918i	−0.0891844	−	0.0748346i	−0.686290	+	0.727328i	$0.740762\pi$
$114$		0			0
$115$	−577.926	−	210.348i	−0.468625	−	0.170566i
$116$	−101.120	−	175.145i	−0.0809375	−	0.140188i
$117$		0			0
$118$	901.232	−	1560.98i	0.703094	−	1.21780i
$119$	1185.61	−	994.843i	0.913315	−	0.766362i
$120$		0			0
$121$	−96.5967	+	547.827i	−0.0725745	+	0.411590i
$122$	−406.081	+	2303.00i	−0.301351	+	1.70905i
$123$		0			0
$124$	−282.380	+	236.945i	−0.204504	+	0.171599i
$125$	497.195	−	861.167i	0.355764	−	0.616201i
$126$		0			0
$127$	−588.559	−	1019.41i	−0.411229	−	0.712270i	0.583795	−	0.811901i	$-0.301567\pi$
$127$	−588.559	−	1019.41i	−0.411229	−	0.712270i	−0.995024	+	0.0996308i	$0.968234\pi$
$128$	1341.64	+	488.316i	0.926446	+	0.337199i
$129$		0			0
$130$	−1287.76	−	1080.56i	−0.868802	−	0.729012i
$131$	1596.99	−	581.258i	1.06511	−	0.387670i	0.250766	−	0.968048i	$-0.419317\pi$
$131$	1596.99	−	581.258i	1.06511	−	0.387670i	0.814347	+	0.580378i	$0.197095\pi$
$132$		0			0
$133$	233.996	+	1327.05i	0.152556	+	0.865190i
$134$	−264.038			−0.170220
$135$		0			0
$136$	−897.319			−0.565768
$137$	−234.862	−	1331.97i	−0.146465	−	0.830642i	−0.966180	−	0.257870i	$-0.916979\pi$
$137$	−234.862	−	1331.97i	−0.146465	−	0.830642i	0.819715	−	0.572772i	$-0.194132\pi$
$138$		0			0
$139$	686.677	−	249.930i	0.419016	−	0.152509i	−0.123903	−	0.992294i	$-0.539541\pi$
$139$	686.677	−	249.930i	0.419016	−	0.152509i	0.542919	+	0.839785i	$0.317319\pi$
$140$	−721.781	−	605.646i	−0.435726	−	0.365617i
$141$		0			0
$142$	408.380	+	148.638i	0.241341	+	0.0878411i
$143$	1258.57	+	2179.92i	0.735995	+	1.27478i
$144$		0			0
$145$	−40.4434	+	70.0501i	−0.0231631	+	0.0401196i
$146$	−1841.14	+	1544.90i	−1.04366	+	0.875732i
$147$		0			0
$148$	233.489	−	1324.18i	0.129680	−	0.735455i
$149$	258.108	−	1463.80i	0.141913	−	0.804829i	−0.827881	−	0.560904i	$-0.810454\pi$
$149$	258.108	−	1463.80i	0.141913	−	0.804829i	0.969794	−	0.243925i	$-0.0784351\pi$
$150$		0			0
$151$	2400.11	−	2013.93i	1.29350	−	1.08537i	0.302269	−	0.953223i	$-0.402256\pi$
$151$	2400.11	−	2013.93i	1.29350	−	1.08537i	0.991230	−	0.132151i	$-0.0421885\pi$
$152$	390.631	−	676.594i	0.208450	−	0.361046i
$153$		0			0
$154$	1231.02	+	2132.19i	0.644145	+	1.11569i
$155$	138.541	+	50.4247i	0.0717926	+	0.0261304i
$156$		0			0
$157$	135.081	+	113.347i	0.0686666	+	0.0576181i	0.676475	−	0.736466i	$-0.263507\pi$
$157$	135.081	+	113.347i	0.0686666	+	0.0576181i	−0.607808	+	0.794084i	$0.707951\pi$
$158$	1288.17	−	468.856i	0.648617	−	0.236077i
$159$		0			0
$160$	−182.403	−	1034.46i	−0.0901262	−	0.511131i
$161$	−2926.59			−1.43260
$162$		0			0
$163$	751.835			0.361278			0.180639	−	0.983549i	$-0.442183\pi$
$163$	751.835			0.361278			0.180639	+	0.983549i	$0.442183\pi$
$164$	107.953	+	612.234i	0.0514009	+	0.291509i
$165$		0			0
$166$	−1572.02	+	572.169i	−0.735015	+	0.267524i
$167$	−418.150	−	350.870i	−0.193757	−	0.162582i	0.540748	−	0.841185i	$-0.318141\pi$
$167$	−418.150	−	350.870i	−0.193757	−	0.162582i	−0.734505	+	0.678603i	$0.762586\pi$
$168$		0			0
$169$	−5620.75	−	2045.78i	−2.55837	−	0.931172i
$170$	703.933	+	1219.25i	0.317584	+	0.550071i
$171$		0			0
$172$	520.017	−	900.695i	0.230528	−	0.399287i
$173$	−1645.54	+	1380.77i	−0.723167	+	0.606809i	−0.928259	−	0.371934i	$-0.878695\pi$
$173$	−1645.54	+	1380.77i	−0.723167	+	0.606809i	0.205093	+	0.978743i	$0.434250\pi$
$174$		0			0
$175$	378.121	−	2144.43i	0.163333	−	0.926307i
$176$	−167.291	+	948.757i	−0.0716481	+	0.406337i
$177$		0			0
$178$	3756.35	−	3151.96i	1.58175	−	1.32724i
$179$	1061.43	−	1838.46i	0.443213	−	0.767668i	−0.554712	−	0.832042i	$-0.687172\pi$
$179$	1061.43	−	1838.46i	0.443213	−	0.767668i	0.997926	+	0.0643740i	$0.0205050\pi$
$180$		0			0
$181$	−1739.32	−	3012.59i	−0.714269	−	1.23715i	−0.963241	−	0.268639i	$-0.913426\pi$
$181$	−1739.32	−	3012.59i	−0.714269	−	1.23715i	0.248972	−	0.968511i	$-0.419907\pi$
$182$	−7516.99	−	2735.96i	−3.06152	−	1.11430i
$183$		0			0
$184$	1299.80	+	1090.66i	0.520774	+	0.436981i
$185$	−505.352	+	183.933i	−0.200834	+	0.0730974i
$186$		0			0
$187$	−366.065	−	2076.06i	−0.143152	−	0.811853i
$188$	1131.90			0.439109
$189$		0			0
$190$	−1225.78			−0.468038
$191$	−340.279	−	1929.82i	−0.128910	−	0.731083i	−0.978909	−	0.204298i	$-0.934509\pi$
$191$	−340.279	−	1929.82i	−0.128910	−	0.731083i	0.849999	−	0.526784i	$-0.176602\pi$
$192$		0			0
$193$	3797.15	−	1382.05i	1.41619	−	0.515451i	0.483250	−	0.875483i	$-0.339456\pi$
$193$	3797.15	−	1382.05i	1.41619	−	0.515451i	0.932940	+	0.360032i	$0.117234\pi$
$194$	−3715.25	−	3117.46i	−1.37494	−	1.15372i
$195$		0			0
$196$	−752.508	−	273.891i	−0.274238	−	0.0998143i
$197$	432.661	+	749.391i	0.156476	+	0.271025i	0.933596	−	0.358328i	$-0.116653\pi$
$197$	432.661	+	749.391i	0.156476	+	0.271025i	−0.777119	+	0.629353i	$0.783320\pi$
$198$		0			0
$199$	−1079.38	+	1869.54i	−0.384499	+	0.665971i	−0.991700	−	0.128577i	$-0.958959\pi$
$199$	−1079.38	+	1869.54i	−0.384499	+	0.665971i	0.607201	+	0.794548i	$0.292292\pi$
$200$	−967.107	+	811.499i	−0.341924	+	0.286908i
$201$		0			0
$202$	−1192.59	+	6763.53i	−0.415399	+	2.35584i
$203$	−66.8381	+	379.058i	−0.0231089	+	0.131057i
$204$		0			0
$205$	190.472	−	159.825i	0.0648933	−	0.0544520i
$206$	−2209.90	+	3827.65i	−0.747431	+	1.29459i
$207$		0			0
$208$	−1565.08	−	2710.80i	−0.521725	−	0.903655i
$209$	1724.74	+	627.755i	0.570828	+	0.207764i
$210$		0			0
$211$	−2195.32	−	1842.09i	−0.716266	−	0.601019i	0.210083	−	0.977684i	$-0.432627\pi$
$211$	−2195.32	−	1842.09i	−0.716266	−	0.601019i	−0.926350	+	0.376665i	$0.877071\pi$
$212$	−6092.75	+	2217.58i	−1.97383	+	0.718415i
$213$		0			0
$214$	996.334	+	5650.49i	0.318262	+	1.80495i
$215$	−415.966			−0.131947
$216$		0			0
$217$	701.565			0.219471
$218$	646.687	+	3667.54i	0.200913	+	1.13944i
$219$		0			0
$220$	−1205.98	+	438.939i	−0.369577	+	0.134515i
$221$	5246.93	+	4402.70i	1.59705	+	1.34008i
$222$		0			0
$223$	4712.99	+	1715.39i	1.41527	+	0.515116i	0.932672	−	0.360727i	$-0.117471\pi$
$223$	4712.99	+	1715.39i	1.41527	+	0.515116i	0.482597	+	0.875842i	$0.339694\pi$
$224$	−2499.23	−	4328.80i	−0.745478	−	1.29121i
$225$		0			0
$226$	302.672	−	524.244i	0.0890862	−	0.154302i
$227$	1861.97	−	1562.38i	0.544420	−	0.456822i	−0.328626	−	0.944460i	$-0.606586\pi$
$227$	1861.97	−	1562.38i	0.544420	−	0.456822i	0.873046	+	0.487638i	$0.162141\pi$
$228$		0			0
$229$	211.811	−	1201.24i	0.0611217	−	0.346639i	−0.938875	−	0.344257i	$-0.888131\pi$
$229$	211.811	−	1201.24i	0.0611217	−	0.346639i	0.999997	−	0.00238155i	$-0.000758071\pi$
$230$	462.282	−	2621.73i	0.132530	−	0.751617i
$231$		0			0
$232$	170.949	−	143.444i	0.0483766	−	0.0405928i
$233$	−2692.95	+	4664.33i	−0.757173	+	1.31146i	0.187114	+	0.982338i	$0.440087\pi$
$233$	−2692.95	+	4664.33i	−0.757173	+	1.31146i	−0.944287	+	0.329124i	$0.893247\pi$
$234$		0			0
$235$	−226.355	−	392.058i	−0.0628330	−	0.108830i
$236$	4201.33	+	1529.16i	1.15883	+	0.421778i
$237$		0			0
$238$	5132.06	+	4306.31i	1.39774	+	1.17284i
$239$	2612.35	−	950.816i	0.707024	−	0.257336i	0.0366169	−	0.999329i	$-0.488342\pi$
$239$	2612.35	−	950.816i	0.707024	−	0.257336i	0.670407	+	0.741994i	$0.266120\pi$
$240$		0			0
$241$	−476.900	−	2704.63i	−0.127468	−	0.722908i	−0.979811	−	0.199925i	$-0.935930\pi$
$241$	−476.900	−	2704.63i	−0.127468	−	0.722908i	0.852343	−	0.522983i	$-0.175181\pi$
$242$	−2407.92			−0.639616
$243$		0			0
$244$	−5800.65			−1.52192
$245$	55.6169	+	315.419i	0.0145030	+	0.0822505i
$246$		0			0
$247$	−5603.87	+	2039.64i	−1.44359	+	0.525422i
$248$	−311.589	−	261.454i	−0.0797818	−	0.0669449i
$249$		0			0
$250$	4044.76	+	1472.17i	1.02325	+	0.372433i
$251$	−3302.16	−	5719.51i	−0.830401	−	1.43830i	−0.897721	−	0.440565i	$-0.854778\pi$
$251$	−3302.16	−	5719.51i	−0.830401	−	1.43830i	0.0673196	−	0.997731i	$-0.478555\pi$
$252$		0			0
$253$	−1993.12	+	3452.19i	−0.495283	+	0.857855i
$254$	3903.23	−	3275.20i	0.964214	−	0.809072i
$255$		0			0
$256$	13.0379	−	73.9417i	0.00318308	−	0.0180522i
$257$	−41.4298	+	234.960i	−0.0100557	+	0.0570288i	−0.989423	−	0.145061i	$-0.953662\pi$
$257$	−41.4298	+	234.960i	−0.0100557	+	0.0570288i	0.979367	+	0.202090i	$0.0647733\pi$
$258$		0			0
$259$	−1960.37	+	1644.95i	−0.470314	+	0.394641i
$260$	2084.90	−	3611.16i	0.497309	−	0.861364i
$261$		0			0
$262$	3678.22	+	6370.86i	0.867332	+	1.50226i
$263$	243.207	+	88.5199i	0.0570219	+	0.0207543i	0.370374	−	0.928883i	$-0.379230\pi$
$263$	243.207	+	88.5199i	0.0570219	+	0.0207543i	−0.313352	+	0.949637i	$0.601452\pi$
$264$		0			0
$265$	1986.52	+	1666.89i	0.460494	+	0.386400i
$266$	−5481.17	+	1994.98i	−1.26343	+	0.459851i
$267$		0			0
$268$	−113.729	−	644.990i	−0.0259220	−	0.147011i
$269$	1093.35			0.247816			0.123908	−	0.992294i	$-0.460457\pi$
$269$	1093.35			0.247816			0.123908	+	0.992294i	$0.460457\pi$
$270$		0			0
$271$	−948.590			−0.212630			−0.106315	−	0.994332i	$-0.533905\pi$
$271$	−948.590			−0.212630			−0.106315	+	0.994332i	$0.533905\pi$
$272$	455.215	+	2581.65i	0.101476	+	0.575499i
$273$		0			0
$274$	5501.48	−	2002.38i	1.21298	−	0.441489i
$275$	−2272.04	−	1906.47i	−0.498215	−	0.418052i
$276$		0			0
$277$	695.785	+	253.245i	0.150923	+	0.0549315i	0.416377	−	0.909192i	$-0.363300\pi$
$277$	695.785	+	253.245i	0.150923	+	0.0549315i	−0.265454	+	0.964124i	$0.585522\pi$
$278$	1581.56	+	2739.35i	0.341208	+	0.590990i
$279$		0			0
$280$	519.838	−	900.386i	0.110951	−	0.192173i
$281$	−2485.15	+	2085.29i	−0.527585	+	0.442697i	−0.867267	−	0.497844i	$-0.834125\pi$
$281$	−2485.15	+	2085.29i	−0.527585	+	0.442697i	0.339681	+	0.940541i	$0.389681\pi$
$282$		0			0
$283$	−283.508	+	1607.85i	−0.0595506	+	0.337728i	−0.999998	−	0.00221230i	$-0.999296\pi$
$283$	−283.508	+	1607.85i	−0.0595506	+	0.337728i	0.940447	+	0.339940i	$0.110407\pi$
$284$	−187.190	+	1061.61i	−0.0391116	+	0.221813i
$285$		0			0
$286$	−8346.68	+	7003.69i	−1.72570	+	1.44803i
$287$	591.593	−	1024.67i	0.121675	−	0.210747i
$288$		0			0
$289$	−411.645	−	712.990i	−0.0837869	−	0.145123i
$290$	−329.014	−	119.751i	−0.0666219	−	0.0242484i
$291$		0			0
$292$	−4566.90	−	3832.08i	−0.915265	−	0.767999i
$293$	−5024.97	+	1828.94i	−1.00192	+	0.364668i	−0.790324	−	0.612689i	$-0.790088\pi$
$293$	−5024.97	+	1828.94i	−1.00192	+	0.364668i	−0.211594	+	0.977358i	$0.567865\pi$
$294$		0			0
$295$	−310.514	−	1761.02i	−0.0612842	−	0.347560i
$296$	1483.69			0.291344
$297$		0			0
$298$	6434.01			1.25071
$299$	−2249.04	−	12754.9i	−0.435001	−	2.46701i
$300$		0			0
$301$	−1860.03	+	676.996i	−0.356181	+	0.129639i
$302$	10389.2	+	8717.57i	1.97957	+	1.66106i
$303$		0			0
$304$	−2144.78	−	780.635i	−0.404643	−	0.147278i
$305$	1160.00	+	2009.18i	0.217775	+	0.377197i
$306$		0			0
$307$	943.563	−	1634.30i	0.175414	−	0.303825i	−0.764891	−	0.644160i	$-0.777207\pi$
$307$	943.563	−	1634.30i	0.175414	−	0.303825i	0.940304	+	0.340335i	$0.110540\pi$
$308$	−4678.24	+	3925.51i	−0.865480	+	0.726224i
$309$		0			0
$310$	−110.819	+	628.483i	−0.0203034	+	0.115147i
$311$	−333.818	+	1893.18i	−0.0608652	+	0.345184i	0.939133	+	0.343553i	$0.111630\pi$
$311$	−333.818	+	1893.18i	−0.0608652	+	0.345184i	−0.999999	+	0.00163122i	$0.999481\pi$
$312$		0			0
$313$	−62.2893	+	52.2669i	−0.0112486	+	0.00943866i	−0.648395	−	0.761304i	$-0.724559\pi$
$313$	−62.2893	+	52.2669i	−0.0112486	+	0.00943866i	0.637146	+	0.770743i	$0.280115\pi$
$314$	−381.647	+	661.032i	−0.0685910	+	0.118803i
$315$		0			0
$316$	1700.17	+	2944.78i	0.302665	+	0.524230i
$317$	−2230.91	−	811.983i	−0.395269	−	0.143866i	0.136736	−	0.990608i	$-0.456339\pi$
$317$	−2230.91	−	811.983i	−0.395269	−	0.143866i	−0.532005	+	0.846742i	$0.678561\pi$
$318$		0			0
$319$	401.614	+	336.995i	0.0704893	+	0.0591476i
$320$	3155.26	−	1148.42i	0.551202	−	0.200621i
$321$		0			0
$322$	−2199.80	−	12475.7i	−0.380714	−	2.15914i
$323$	4994.38			0.860355
$324$		0			0
$325$	9636.63			1.64475
$326$	565.123	+	3204.97i	0.0960101	+	0.544500i
$327$		0			0
$328$	−644.612	+	234.620i	−0.108515	+	0.0394960i
$329$	−1650.25	−	1384.72i	−0.276539	−	0.232043i
$330$		0			0
$331$	985.865	+	358.825i	0.163710	+	0.0595856i	0.422575	−	0.906328i	$-0.361126\pi$
$331$	985.865	+	358.825i	0.163710	+	0.0595856i	−0.258865	+	0.965913i	$0.583348\pi$
$332$	−2074.80	−	3593.66i	−0.342981	−	0.594060i
$333$		0			0
$334$	1181.41	−	2046.25i	0.193544	−	0.335228i
$335$	−200.662	+	168.376i	−0.0327265	+	0.0274608i
$336$		0			0
$337$	819.354	−	4646.79i	0.132442	−	0.751117i	−0.844165	−	0.536084i	$-0.819903\pi$
$337$	819.354	−	4646.79i	0.132442	−	0.751117i	0.976607	−	0.215033i	$-0.0689859\pi$
$338$	4496.03	−	25498.2i	0.723526	−	4.10332i
$339$		0			0
$340$	−2675.16	+	2244.72i	−0.426708	+	0.358051i
$341$	477.792	−	827.561i	0.0758765	−	0.131422i
$342$		0			0
$343$	−2742.53	−	4750.20i	−0.431728	−	0.747775i
$344$	1078.40	+	392.505i	0.169022	+	0.0615188i
$345$		0			0
$346$	−7122.92	−	5976.84i	−1.10674	−	0.928661i
$347$	576.065	−	209.671i	0.0891205	−	0.0324372i	−0.297075	−	0.954854i	$-0.596011\pi$
$347$	576.065	−	209.671i	0.0891205	−	0.0324372i	0.386196	+	0.922417i	$0.373789\pi$
$348$		0			0
$349$	231.325	+	1311.91i	0.0354801	+	0.201218i	0.997395	−	0.0721308i	$-0.0229799\pi$
$349$	231.325	+	1311.91i	0.0354801	+	0.201218i	−0.961915	+	0.273348i	$0.911869\pi$
$350$	9425.64			1.43949
$351$		0			0
$352$	−6808.29			−1.03092
$353$	1542.91	+	8750.28i	0.232637	+	1.31935i	0.847533	+	0.530742i	$0.178087\pi$
$353$	1542.91	+	8750.28i	0.232637	+	1.31935i	−0.614896	+	0.788608i	$0.710802\pi$
$354$		0			0
$355$	405.144	−	147.460i	0.0605713	−	0.0220461i
$356$	9317.52	+	7818.33i	1.38716	+	1.16396i
$357$		0			0
$358$	8634.93	+	3142.86i	1.27478	+	0.463981i
$359$	5829.25	+	10096.6i	0.856980	+	1.48433i	0.874796	+	0.484492i	$0.160995\pi$
$359$	5829.25	+	10096.6i	0.856980	+	1.48433i	−0.0178157	+	0.999841i	$0.505671\pi$
$360$		0			0
$361$	1255.29	−	2174.22i	0.183013	−	0.316988i
$362$	11534.9	−	9678.94i	1.67475	−	1.40529i
$363$		0			0
$364$	3445.58	−	19540.9i	0.496147	−	2.81379i
$365$	−414.046	+	2348.17i	−0.0593758	+	0.336737i
$366$		0			0
$367$	743.037	−	623.482i	0.105685	−	0.0886799i	−0.588414	−	0.808560i	$-0.700248\pi$
$367$	743.037	−	623.482i	0.105685	−	0.0886799i	0.694099	+	0.719880i	$0.255803\pi$
$368$	2478.51	−	4292.91i	0.351091	−	0.608108i
$369$		0			0
$370$	−1163.93	−	2015.99i	−0.163541	−	0.283261i
$371$	11595.8	+	4220.52i	1.62270	+	0.590616i
$372$		0			0
$373$	−5344.41	−	4484.49i	−0.741885	−	0.622515i	0.191458	−	0.981501i	$-0.438678\pi$
$373$	−5344.41	−	4484.49i	−0.741885	−	0.622515i	−0.933343	+	0.358985i	$0.883123\pi$
$374$	8574.82	−	3120.98i	1.18554	−	0.431502i
$375$		0			0
$376$	216.883	+	1230.01i	0.0297471	+	0.168704i
$377$	−1703.41			−0.232705
$378$		0			0
$379$	−328.370			−0.0445045			−0.0222523	−	0.999752i	$-0.507084\pi$
$379$	−328.370			−0.0445045			−0.0222523	+	0.999752i	$0.507084\pi$
$380$	−527.978	−	2994.31i	−0.0712756	−	0.404224i
$381$		0			0
$382$	7970.79	−	2901.13i	1.06759	−	0.388573i
$383$	−395.050	−	331.486i	−0.0527052	−	0.0442249i	0.616055	−	0.787703i	$-0.288730\pi$
$383$	−395.050	−	331.486i	−0.0527052	−	0.0442249i	−0.668760	+	0.743479i	$0.733175\pi$
$384$		0			0
$385$	2295.23	+	835.394i	0.303833	+	0.110586i
$386$	8745.65	+	15147.9i	1.15322	+	1.99743i
$387$		0			0
$388$	6015.03	−	10418.3i	0.787028	−	1.36317i
$389$	−10011.7	+	8400.85i	−1.30492	+	1.09496i	−0.315652	+	0.948875i	$0.602223\pi$
$389$	−10011.7	+	8400.85i	−1.30492	+	1.09496i	−0.989272	+	0.146086i	$0.953332\pi$
$390$		0			0
$391$	−1883.55	+	10682.1i	−0.243619	+	1.38163i
$392$	153.441	−	870.209i	0.0197703	−	0.112123i
$393$		0			0
$394$	−2869.34	+	2407.66i	−0.366892	+	0.307859i
$395$	679.991	−	1177.78i	0.0866179	−	0.150027i
$396$		0			0
$397$	3450.77	+	5976.90i	0.436244	+	0.755597i	0.997396	−	0.0721155i	$-0.0229750\pi$
$397$	3450.77	+	5976.90i	0.436244	+	0.755597i	−0.561152	+	0.827713i	$0.689642\pi$
$398$	−8780.94	−	3196.00i	−1.10590	−	0.402515i
$399$		0			0
$400$	2825.36	+	2370.76i	0.353170	+	0.296345i
$401$	−4069.03	+	1481.01i	−0.506727	+	0.184434i	−0.582717	−	0.812675i	$-0.698011\pi$
$401$	−4069.03	+	1481.01i	−0.506727	+	0.184434i	0.0759899	+	0.997109i	$0.475788\pi$
$402$		0			0
$403$	539.141	+	3057.62i	0.0666415	+	0.377943i
$404$	−17035.5			−2.09790
$405$		0			0
$406$	−1666.11			−0.203664
$407$	605.279	+	3432.71i	0.0737164	+	0.418066i
$408$		0			0
$409$	−3487.94	+	1269.51i	−0.421682	+	0.153480i	−0.544141	−	0.838994i	$-0.683144\pi$
$409$	−3487.94	+	1269.51i	−0.421682	+	0.153480i	0.122459	+	0.992474i	$0.460922\pi$
$410$	824.482	+	691.823i	0.0993129	+	0.0833334i
$411$		0			0
$412$	−10302.0	−	3749.62i	−1.23190	−	0.448376i
$413$	−4254.59	−	7369.17i	−0.506912	−	0.877997i
$414$		0			0
$415$	−829.827	+	1437.30i	−0.0981557	+	0.170011i
$416$	16945.5	−	14219.0i	1.99717	−	1.67583i
$417$		0			0
$418$	−1379.62	+	7824.21i	−0.161434	+	0.915538i
$419$	1567.70	−	8890.86i	0.182785	−	1.03663i	−0.745982	−	0.665966i	$-0.768020\pi$
$419$	1567.70	−	8890.86i	0.182785	−	1.03663i	0.928768	−	0.370662i	$-0.120869\pi$
$420$		0			0
$421$	−9736.77	+	8170.12i	−1.12718	+	0.945813i	−0.998945	−	0.0459309i	$-0.985375\pi$
$421$	−9736.77	+	8170.12i	−1.12718	+	0.945813i	−0.128232	+	0.991744i	$0.540930\pi$
$422$	6202.47	−	10743.0i	0.715478	−	1.23924i
$423$		0			0
$424$	−3577.21	−	6195.91i	−0.409728	−	0.709670i
$425$	−7583.86	−	2760.30i	−0.865580	−	0.315045i
$426$		0			0
$427$	8457.02	+	7096.29i	0.958464	+	0.804247i
$428$	−13373.8	+	4867.66i	−1.51039	+	0.549737i
$429$		0			0
$430$	−312.665	−	1773.21i	−0.0350652	−	0.198865i
$431$	−5967.69			−0.666945			−0.333473	−	0.942760i	$-0.608220\pi$
$431$	−5967.69			−0.666945			−0.333473	+	0.942760i	$0.608220\pi$
$432$		0			0
$433$	4953.29			0.549746			0.274873	−	0.961481i	$-0.411364\pi$
$433$	4953.29			0.549746			0.274873	+	0.961481i	$0.411364\pi$
$434$	527.337	+	2990.68i	0.0583249	+	0.330777i
$435$		0			0
$436$	−8680.47	+	3159.43i	−0.953485	+	0.347040i
$437$	−7234.54	−	6070.50i	−0.791933	−	0.664511i
$438$		0			0
$439$	9489.51	+	3453.90i	1.03168	+	0.375502i	0.801722	−	0.597697i	$-0.203917\pi$
$439$	9489.51	+	3453.90i	1.03168	+	0.375502i	0.229962	+	0.973200i	$0.426140\pi$
$440$	−708.059	−	1226.39i	−0.0767168	−	0.132877i
$441$		0			0
$442$	−14824.2	+	25676.3i	−1.59529	+	2.76312i
$443$	−13951.0	+	11706.3i	−1.49624	+	1.25549i	−0.609878	+	0.792495i	$0.708781\pi$
$443$	−13951.0	+	11706.3i	−1.49624	+	1.25549i	−0.886360	+	0.462997i	$0.846774\pi$
$444$		0			0
$445$	844.749	−	4790.81i	0.0899886	−	0.510351i
$446$	−3769.91	+	21380.2i	−0.400248	+	2.26992i
$447$		0			0
$448$	12240.0	−	10270.5i	1.29081	−	1.08312i
$449$	−4502.96	+	7799.36i	−0.473292	+	0.819766i	−0.999533	−	0.0305701i	$-0.990268\pi$
$449$	−4502.96	+	7799.36i	−0.473292	+	0.819766i	0.526241	+	0.850336i	$0.323601\pi$
$450$		0			0
$451$	−805.795	−	1395.68i	−0.0841317	−	0.145720i
$452$	1410.99	+	513.557i	0.146830	+	0.0534418i
$453$		0			0
$454$	8059.78	+	6762.96i	0.833181	+	0.699122i
$455$	−7457.42	+	2714.28i	−0.768372	+	0.279665i
$456$		0			0
$457$	3155.52	+	17895.8i	0.322996	+	1.83180i	0.523401	+	0.852086i	$0.324663\pi$
$457$	3155.52	+	17895.8i	0.322996	+	1.83180i	−0.200406	+	0.979713i	$0.564226\pi$
$458$	5279.94			0.538680
$459$		0			0
$460$	6603.45			0.669320
$461$	−1377.38	−	7811.49i	−0.139156	−	0.789192i	−0.971875	−	0.235497i	$-0.924328\pi$
$461$	−1377.38	−	7811.49i	−0.139156	−	0.789192i	0.832719	−	0.553695i	$-0.186783\pi$
$462$		0			0
$463$	6768.40	−	2463.50i	0.679383	−	0.247275i	0.0208003	−	0.999784i	$-0.493379\pi$
$463$	6768.40	−	2463.50i	0.679383	−	0.247275i	0.658582	+	0.752509i	$0.271156\pi$
$464$	−499.421	−	419.064i	−0.0499678	−	0.0419279i
$465$		0			0
$466$	−21907.6	−	7973.72i	−2.17779	−	0.792652i
$467$	−8196.21	−	14196.3i	−0.812153	−	1.40669i	−0.911354	−	0.411622i	$-0.864962\pi$
$467$	−8196.21	−	14196.3i	−0.812153	−	1.40669i	0.0992017	−	0.995067i	$-0.468371\pi$
$468$		0			0
$469$	−623.244	+	1079.49i	−0.0613619	+	0.106282i
$470$	1501.15	−	1259.61i	0.147325	−	0.123621i
$471$		0			0
$472$	−856.678	+	4858.46i	−0.0835420	+	0.473790i
$473$	−468.172	+	2655.14i	−0.0455108	+	0.258104i
$474$		0			0
$475$	5382.81	−	4516.71i	0.519958	−	0.436297i
$476$	−8308.86	+	14391.4i	−0.800076	+	1.38577i
$477$		0			0
$478$	6016.80	+	10421.4i	0.575736	+	0.997205i
$479$	17492.0	+	6366.58i	1.66854	+	0.607299i	0.991670	−	0.128802i	$-0.0411132\pi$
$479$	17492.0	+	6366.58i	1.66854	+	0.607299i	0.676871	+	0.736102i	$0.263335\pi$
$480$		0			0
$481$	−8675.66	−	7279.74i	−0.822404	−	0.690079i
$482$	11171.0	−	4065.92i	1.05566	−	0.384228i
$483$		0			0
$484$	−1037.16	−	5882.04i	−0.0974044	−	0.552408i
$485$	−4811.48			−0.450470
$486$		0			0
$487$	−16907.0			−1.57317			−0.786583	−	0.617485i	$-0.788152\pi$
$487$	−16907.0			−1.57317			−0.786583	+	0.617485i	$0.788152\pi$
$488$	−1111.46	−	6303.40i	−0.103101	−	0.584716i
$489$		0			0
$490$	−1302.78	+	474.175i	−0.120110	+	0.0437164i
$491$	5453.75	+	4576.24i	0.501271	+	0.420617i	0.858045	−	0.513574i	$-0.171679\pi$
$491$	5453.75	+	4576.24i	0.501271	+	0.420617i	−0.356774	+	0.934191i	$0.616123\pi$
$492$		0			0
$493$	1340.55	+	487.921i	0.122465	+	0.0445738i
$494$	−12906.9	−	22355.4i	−1.17553	−	2.03607i
$495$		0			0
$496$	−594.151	+	1029.10i	−0.0537866	+	0.0931612i
$497$	1571.64	−	1318.76i	0.141847	−	0.119023i
$498$		0			0
$499$	−3780.61	+	21440.9i	−0.339165	+	1.92350i	0.0422691	+	0.999106i	$0.486541\pi$
$499$	−3780.61	+	21440.9i	−0.339165	+	1.92350i	−0.381434	+	0.924396i	$0.624570\pi$
$500$	−1854.01	+	10514.6i	−0.165827	+	0.940454i
$501$		0			0
$502$	21899.4	−	18375.8i	1.94705	−	1.63377i
$503$	5865.29	−	10159.0i	0.519921	−	0.900530i	−0.479811	−	0.877372i	$-0.659295\pi$
$503$	5865.29	−	10159.0i	0.519921	−	0.900530i	0.999732	−	0.0231576i	$-0.00737195\pi$
$504$		0			0
$505$	3406.72	+	5900.62i	0.300192	+	0.519948i
$506$	−16214.4	−	5901.55i	−1.42454	−	0.518490i
$507$		0			0
$508$	9681.85	+	8124.03i	0.845595	+	0.709539i
$509$	−12707.2	+	4625.05i	−1.10656	+	0.402754i	−0.829729	−	0.558166i	$-0.811505\pi$
$509$	−12707.2	+	4625.05i	−1.10656	+	0.402754i	−0.276827	+	0.960920i	$0.589283\pi$
$510$		0			0
$511$	1970.26	+	11173.9i	0.170566	+	0.967329i
$512$	11746.9			1.01396
$513$		0			0
$514$	−1032.75			−0.0886234
$515$	761.408	+	4318.16i	0.0651488	+	0.369477i
$516$		0			0
$517$	−2757.29	+	1003.57i	−0.234556	+	0.0853715i
$518$	−8485.71	−	7120.36i	−0.719770	−	0.603959i
$519$		0			0
$520$	4323.63	+	1573.67i	0.364623	+	0.132712i
$521$	2309.59	+	4000.32i	0.194213	+	0.336386i	0.946642	−	0.322287i	$-0.104451\pi$
$521$	2309.59	+	4000.32i	0.194213	+	0.336386i	−0.752429	+	0.658673i	$0.771118\pi$
$522$		0			0
$523$	7043.69	−	12200.0i	0.588909	−	1.02002i	−0.405467	−	0.914110i	$-0.632891\pi$
$523$	7043.69	−	12200.0i	0.588909	−	1.02002i	0.994376	−	0.105910i	$-0.0337756\pi$
$524$	−13978.3	+	11729.2i	−1.16536	+	0.977850i
$525$		0			0
$526$	−194.541	+	1103.29i	−0.0161262	+	0.0914561i
$527$	451.525	−	2560.73i	0.0373221	−	0.211664i
$528$		0			0
$529$	6391.69	−	5363.27i	0.525330	−	0.440804i
$530$	−5612.53	+	9721.19i	−0.459987	+	0.796720i
$531$		0			0
$532$	−7234.22	−	12530.0i	−0.589555	−	1.02114i
$533$	4920.43	+	1790.89i	0.399864	+	0.145539i
$534$		0			0
$535$	4360.48	+	3658.87i	0.352373	+	0.295676i
$536$	679.100	−	247.172i	0.0547251	−	0.0199183i
$537$		0			0
$538$	821.823	+	4660.79i	0.0658574	+	0.373496i
$539$	2075.93			0.165894
$540$		0			0
$541$	−9754.66			−0.775205			−0.387602	−	0.921827i	$-0.626697\pi$
$541$	−9754.66			−0.775205			−0.387602	+	0.921827i	$0.626697\pi$
$542$	−713.016	−	4043.71i	−0.0565068	−	0.320466i
$543$		0			0
$544$	−17408.7	+	6336.25i	−1.37204	+	0.499383i
$545$	2830.24	+	2374.85i	0.222448	+	0.186656i
$546$		0			0
$547$	−12838.2	−	4672.74i	−1.00352	−	0.365250i	−0.212577	−	0.977144i	$-0.568186\pi$
$547$	−12838.2	−	4672.74i	−1.00352	−	0.365250i	−0.790940	+	0.611894i	$0.790408\pi$
$548$	7261.02	+	12576.5i	0.566014	+	0.980364i
$549$		0			0
$550$	6419.22	−	11118.4i	0.497666	−	0.861984i
$551$	−951.486	+	798.391i	−0.0735656	+	0.0617289i
$552$		0			0
$553$	1123.78	−	6373.25i	0.0864155	−	0.490087i
$554$	−556.557	+	3156.39i	−0.0426820	+	0.242062i
$555$		0			0
$556$	−6010.42	+	5043.34i	−0.458451	+	0.384686i
$557$	−10118.4	+	17525.6i	−0.769714	+	1.33318i	0.168004	+	0.985786i	$0.446268\pi$
$557$	−10118.4	+	17525.6i	−0.769714	+	1.33318i	−0.937718	+	0.347397i	$0.887066\pi$
$558$		0			0
$559$	−4379.95	−	7586.29i	−0.331399	−	0.574000i
$560$	−2854.19	−	1038.84i	−0.215378	−	0.0783912i
$561$		0			0
$562$	−10757.3	−	9026.43i	−0.807417	−	0.677504i
$563$	21402.2	−	7789.78i	1.60213	−	0.583126i	0.622265	−	0.782807i	$-0.286213\pi$
$563$	21402.2	−	7789.78i	1.60213	−	0.583126i	0.979861	+	0.199681i	$0.0639905\pi$
$564$		0			0
$565$	−104.284	−	591.425i	−0.00776507	−	0.0440379i
$566$	−7067.18			−0.524833
$567$		0			0
$568$	−1189.49			−0.0878692
$569$	81.6479	+	463.048i	0.00601557	+	0.0341160i	0.987668	−	0.156564i	$-0.0500418\pi$
$569$	81.6479	+	463.048i	0.00601557	+	0.0341160i	−0.981652	+	0.190680i	$0.938931\pi$
$570$		0			0
$571$	696.582	−	253.535i	0.0510526	−	0.0185816i	−0.316368	−	0.948637i	$-0.602463\pi$
$571$	696.582	−	253.535i	0.0510526	−	0.0185816i	0.367420	+	0.930055i	$0.380241\pi$
$572$	−20703.7	−	17372.5i	−1.51340	−	1.26989i
$573$		0			0
$574$	4812.70	+	1751.68i	0.349962	+	0.127376i
$575$	7630.45	+	13216.3i	0.553411	+	0.958537i
$576$		0			0
$577$	9077.41	−	15722.5i	0.654935	−	1.13438i	−0.326975	−	0.945033i	$-0.606029\pi$
$577$	9077.41	−	15722.5i	0.654935	−	1.13438i	0.981910	−	0.189348i	$-0.0606374\pi$
$578$	2729.97	−	2290.71i	0.196456	−	0.164846i
$579$		0			0
$580$	150.811	−	855.291i	0.0107967	−	0.0612311i
$581$	−1371.40	+	7777.59i	−0.0979264	+	0.555368i
$582$		0			0
$583$	12875.7	−	10804.0i	0.914676	−	0.767504i
$584$	3289.15	−	5696.98i	0.233058	−	0.403669i
$585$		0			0
$586$	−11573.6	−	20046.0i	−0.815871	−	1.41313i
$587$	−24782.9	−	9020.24i	−1.74259	−	0.634251i	−0.743197	−	0.669073i	$-0.766691\pi$
$587$	−24782.9	−	9020.24i	−1.74259	−	0.634251i	−0.999394	+	0.0348221i	$0.988914\pi$
$588$		0			0
$589$	1734.27	+	1455.22i	0.121323	+	0.101802i
$590$	7273.58	−	2647.36i	0.507540	−	0.184729i
$591$		0			0
$592$	−752.685	−	4268.69i	−0.0522554	−	0.296355i
$593$	13727.4			0.950620			0.475310	−	0.879818i	$-0.342336\pi$
$593$	13727.4			0.950620			0.475310	+	0.879818i	$0.342336\pi$
$594$		0			0
$595$	6646.34			0.457938
$596$	2771.32	+	15716.9i	0.190466	+	1.08018i
$597$		0			0
$598$	52682.1	−	19174.7i	3.60256	−	1.31123i
$599$	−9685.25	−	8126.89i	−0.660649	−	0.554350i	0.249632	−	0.968341i	$-0.419690\pi$
$599$	−9685.25	−	8126.89i	−0.660649	−	0.554350i	−0.910281	+	0.413990i	$0.864135\pi$
$600$		0			0
$601$	−11469.1	−	4174.40i	−0.778424	−	0.283323i	−0.0779089	−	0.996960i	$-0.524824\pi$
$601$	−11469.1	−	4174.40i	−0.778424	−	0.283323i	−0.700516	+	0.713637i	$0.747047\pi$
$602$	−4284.05	−	7420.19i	−0.290041	−	0.502366i
$603$		0			0
$604$	−16820.2	+	29133.5i	−1.13312	+	1.96262i
$605$	−1829.96	+	1535.52i	−0.122973	+	0.103186i
$606$		0			0
$607$	3373.82	−	19133.9i	0.225600	−	1.27944i	−0.635935	−	0.771743i	$-0.719385\pi$
$607$	3373.82	−	19133.9i	0.225600	−	1.27944i	0.861535	−	0.507698i	$-0.169503\pi$
$608$	2800.92	−	15884.8i	0.186830	−	1.05956i
$609$		0			0
$610$	−7692.93	+	6455.14i	−0.510619	+	0.428460i
$611$	4766.84	−	8256.40i	0.315623	−	0.546675i
$612$		0			0
$613$	10897.5	+	18875.0i	0.718019	+	1.24364i	0.961784	+	0.273810i	$0.0882841\pi$
$613$	10897.5	+	18875.0i	0.718019	+	1.24364i	−0.243765	+	0.969834i	$0.578383\pi$
$614$	7676.04	+	2793.85i	0.504527	+	0.183633i
$615$		0			0
$616$	−5162.14	−	4331.55i	−0.337644	−	0.283317i
$617$	−184.007	+	66.9731i	−0.0120062	+	0.00436991i	−0.348016	−	0.937488i	$-0.613145\pi$
$617$	−184.007	+	66.9731i	−0.0120062	+	0.00436991i	0.336010	+	0.941858i	$0.390922\pi$
$618$		0			0
$619$	−3834.83	−	21748.4i	−0.249006	−	1.41219i	−0.811001	−	0.585045i	$-0.801077\pi$
$619$	−3834.83	−	21748.4i	−0.249006	−	1.41219i	0.561995	−	0.827141i	$-0.310034\pi$
$620$	−1582.98			−0.102539
$621$		0			0
$622$	−8321.28			−0.536419
$623$	−4019.79	−	22797.4i	−0.258507	−	1.46606i
$624$		0			0
$625$	−8503.85	+	3095.15i	−0.544246	+	0.198089i
$626$	−269.627	−	226.244i	−0.0172148	−	0.0144449i
$627$		0			0
$628$	−1779.15	−	647.556i	−0.113050	−	0.0411470i
$629$	4742.40	+	8214.08i	0.300623	+	0.520694i
$630$		0			0
$631$	−557.064	+	964.862i	−0.0351448	+	0.0608725i	−0.883063	−	0.469255i	$-0.844523\pi$
$631$	−557.064	+	964.862i	−0.0351448	+	0.0608725i	0.847918	+	0.530127i	$0.177856\pi$
$632$	−2874.24	+	2411.77i	−0.180904	+	0.151796i
$633$		0			0
$634$	1784.50	−	10120.4i	0.111785	−	0.633962i
$635$	877.779	−	4978.13i	0.0548561	−	0.311104i
$636$		0			0
$637$	−5166.91	+	4335.55i	−0.321382	+	0.269672i
$638$	−1134.69	+	1965.33i	−0.0704117	+	0.121957i
$639$		0			0
$640$	3065.60	+	5309.77i	0.189341	+	0.327948i
$641$	4696.93	+	1709.54i	0.289419	+	0.105340i	0.482650	−	0.875813i	$-0.339674\pi$
$641$	4696.93	+	1709.54i	0.289419	+	0.105340i	−0.193231	+	0.981153i	$0.561897\pi$
$642$		0			0
$643$	−6141.15	−	5153.04i	−0.376646	−	0.316044i	0.434738	−	0.900557i	$-0.356841\pi$
$643$	−6141.15	−	5153.04i	−0.376646	−	0.316044i	−0.811384	+	0.584513i	$0.801285\pi$
$644$	29527.9	−	10747.3i	1.80677	−	0.657612i
$645$		0			0
$646$	3754.07	+	21290.4i	0.228641	+	1.29669i
$647$	−29929.6			−1.81863			−0.909315	−	0.416109i	$-0.863393\pi$
$647$	−29929.6			−1.81863			−0.909315	+	0.416109i	$0.863393\pi$
$648$		0			0
$649$	−11590.2			−0.701007
$650$	7243.46	+	41079.7i	0.437095	+	2.47889i
$651$		0			0
$652$	−7585.65	+	2760.95i	−0.455640	+	0.165839i
$653$	−11638.6	−	9765.98i	−0.697481	−	0.585256i	0.223575	−	0.974687i	$-0.428227\pi$
$653$	−11638.6	−	9765.98i	−0.697481	−	0.585256i	−0.921056	+	0.389431i	$0.872672\pi$
$654$		0			0
$655$	6858.01	+	2496.11i	0.409106	+	0.148903i
$656$	1002.03	+	1735.57i	0.0596384	+	0.103297i
$657$		0			0
$658$	4662.47	−	8075.64i	0.276234	−	0.478452i
$659$	9607.55	−	8061.69i	0.567917	−	0.476539i	−0.313037	−	0.949741i	$-0.601346\pi$
$659$	9607.55	−	8061.69i	0.567917	−	0.476539i	0.880954	+	0.473202i	$0.156902\pi$
$660$		0			0
$661$	1676.01	−	9505.13i	0.0986222	−	0.559314i	−0.894955	−	0.446157i	$-0.852792\pi$
$661$	1676.01	−	9505.13i	0.0986222	−	0.559314i	0.993577	−	0.113158i	$-0.0360965\pi$
$662$	−788.592	+	4472.33i	−0.0462983	+	0.262571i
$663$		0			0
$664$	3507.58	−	2943.21i	0.205001	−	0.172016i
$665$	−2893.36	+	5011.45i	−0.168721	+	0.292234i
$666$		0			0
$667$	−1348.79	−	2336.17i	−0.0782987	−	0.135617i
$668$	5507.43	+	2004.54i	0.318995	+	0.116105i
$669$		0			0
$670$	−868.594	−	728.837i	−0.0500846	−	0.0420260i
$671$	14130.3	−	5143.00i	0.812956	−	0.295892i
$672$		0			0
$673$	−2479.89	−	14064.1i	−0.142040	−	0.805546i	−0.969697	−	0.244312i	$-0.921438\pi$
$673$	−2479.89	−	14064.1i	−0.142040	−	0.805546i	0.827657	−	0.561234i	$-0.189673\pi$
$674$	20424.5			1.16724
$675$		0			0
$676$	64223.3			3.65403
$677$	−2968.37	−	16834.5i	−0.168514	−	0.955689i	−0.945367	−	0.326008i	$-0.894296\pi$
$677$	−2968.37	−	16834.5i	−0.168514	−	0.955689i	0.776853	−	0.629682i	$-0.216815\pi$
$678$		0			0
$679$	−21515.0	+	7830.80i	−1.21601	+	0.442590i
$680$	−2951.86	−	2476.91i	−0.166469	−	0.139684i
$681$		0			0
$682$	3886.92	+	1414.72i	0.218237	+	0.0794319i
$683$	−1510.44	−	2616.16i	−0.0846198	−	0.146566i	0.820609	−	0.571490i	$-0.193634\pi$
$683$	−1510.44	−	2616.16i	−0.0846198	−	0.146566i	−0.905229	+	0.424924i	$0.860301\pi$
$684$		0			0
$685$	2904.08	−	5030.02i	0.161984	−	0.280565i
$686$	18188.0	−	15261.6i	1.01228	−	0.849402i
$687$		0			0
$688$	582.188	−	3301.75i	0.0322612	−	0.182962i
$689$	−9483.08	+	53781.2i	−0.524349	+	2.97373i
$690$		0			0
$691$	−15237.9	+	12786.1i	−0.838894	+	0.703916i	−0.957315	−	0.289048i	$-0.906661\pi$
$691$	−15237.9	+	12786.1i	−0.838894	+	0.703916i	0.118421	+	0.992964i	$0.462217\pi$
$692$	11532.1	−	19974.2i	0.633503	−	1.09726i
$693$		0			0
$694$	1326.80	+	2298.09i	0.0725717	+	0.125698i
$695$	2948.82	+	1073.28i	0.160942	+	0.0585783i
$696$		0			0
$697$	−3359.32	−	2818.80i	−0.182558	−	0.153185i
$698$	−5418.62	+	1972.22i	−0.293837	+	0.106948i
$699$		0			0
$700$	4059.90	+	23024.8i	0.219214	+	1.24322i
$701$	800.939			0.0431541			0.0215771	−	0.999767i	$-0.493131\pi$
$701$	800.939			0.0431541			0.0215771	+	0.999767i	$0.493131\pi$
$702$		0			0
$703$	−8258.07			−0.443042
$704$	−3779.18	−	21432.8i	−0.202320	−	1.14741i
$705$		0			0
$706$	−36141.6	+	13154.5i	−1.92664	+	0.701239i
$707$	24836.9	+	20840.6i	1.32120	+	1.10862i
$708$		0			0
$709$	−3810.45	−	1386.89i	−0.201840	−	0.0734638i	0.239122	−	0.970990i	$-0.423140\pi$
$709$	−3810.45	−	1386.89i	−0.201840	−	0.0734638i	−0.440962	+	0.897526i	$0.645363\pi$
$710$	933.134	+	1616.24i	0.0493238	+	0.0854313i
$711$		0			0
$712$	−6710.63	+	11623.2i	−0.353218	+	0.611792i
$713$	−3766.53	+	3160.49i	−0.197837	+	0.166005i
$714$		0			0
$715$	−1877.05	+	10645.3i	−0.0981783	+	0.556797i
$716$	−3958.01	+	22447.0i	−0.206589	+	1.17163i
$717$		0			0
$718$	−38658.7	+	32438.5i	−2.00937	+	1.68606i
$719$	15633.9	−	27078.6i	0.810910	−	1.40454i	−0.101317	−	0.994854i	$-0.532306\pi$
$719$	15633.9	−	27078.6i	0.810910	−	1.40454i	0.912228	−	0.409684i	$-0.134361\pi$
$720$		0			0
$721$	10432.6	+	18069.8i	0.538878	+	0.933363i
$722$	10212.0	+	3716.86i	0.526386	+	0.191589i
$723$		0			0
$724$	28612.0	+	24008.3i	1.46872	+	1.23241i
$725$	1886.07	−	686.472i	0.0966163	−	0.0351654i
$726$		0			0
$727$	−2540.64	−	14408.7i	−0.129611	−	0.735060i	−0.978462	−	0.206427i	$-0.933816\pi$
$727$	−2540.64	−	14408.7i	−0.129611	−	0.735060i	0.848851	−	0.528632i	$-0.177295\pi$
$728$	21894.7			1.11466
$729$		0			0
$730$	−10321.2			−0.523292
$731$	1273.94	+	7224.86i	0.0644573	+	0.365556i
$732$		0			0
$733$	28396.3	−	10335.4i	1.43089	−	0.520801i	0.493703	−	0.869631i	$-0.335643\pi$
$733$	28396.3	−	10335.4i	1.43089	−	0.520801i	0.937186	+	0.348830i	$0.113421\pi$
$734$	3216.33	+	2698.82i	0.161740	+	0.135716i
$735$		0			0
$736$	32918.6	+	11981.4i	1.64864	+	0.600055i
$737$	848.906	+	1470.35i	0.0424286	+	0.0734884i
$738$		0			0
$739$	11968.5	−	20730.1i	0.595763	−	1.03189i	−0.397675	−	0.917526i	$-0.630183\pi$
$739$	11968.5	−	20730.1i	0.595763	−	1.03189i	0.993439	−	0.114366i	$-0.0364838\pi$
$740$	4423.30	−	3711.59i	0.219735	−	0.184379i
$741$		0			0
$742$	−9275.45	+	52603.7i	−0.458912	+	2.60262i
$743$	3628.76	−	20579.7i	0.179174	−	1.01615i	−0.754041	−	0.656828i	$-0.771898\pi$
$743$	3628.76	−	20579.7i	0.179174	−	1.01615i	0.933215	−	0.359319i	$-0.116991\pi$
$744$		0			0
$745$	4889.69	−	4102.93i	0.240462	−	0.201772i
$746$	15099.6	−	26153.3i	0.741068	−	1.28357i
$747$		0			0
$748$	11317.3	+	19602.1i	0.553211	+	0.958189i
$749$	25453.2	+	9264.19i	1.24171	+	0.451944i
$750$		0			0
$751$	−9243.41	−	7756.14i	−0.449130	−	0.376865i	0.389983	−	0.920822i	$-0.372481\pi$
$751$	−9243.41	−	7756.14i	−0.449130	−	0.376865i	−0.839113	+	0.543957i	$0.816925\pi$
$752$	3428.79	−	1247.98i	0.166270	−	0.0605173i
$753$		0			0
$754$	−1280.38	−	7261.40i	−0.0618418	−	0.350722i
$755$	13454.7			0.648563
$756$		0			0
$757$	15978.5			0.767172			0.383586	−	0.923505i	$-0.374689\pi$
$757$	15978.5			0.767172			0.383586	+	0.923505i	$0.374689\pi$
$758$	−246.822	−	1399.80i	−0.0118271	−	0.0670750i
$759$		0			0
$760$	3152.67	−	1147.48i	0.150473	−	0.0547676i
$761$	9048.54	+	7592.63i	0.431024	+	0.361672i	0.832338	−	0.554268i	$-0.187002\pi$
$761$	9048.54	+	7592.63i	0.431024	+	0.361672i	−0.401314	+	0.915941i	$0.631446\pi$
$762$		0			0
$763$	16520.8	+	6013.07i	0.783869	+	0.285305i
$764$	10520.1	+	18221.3i	0.498172	+	0.862860i
$765$		0			0
$766$	1116.14	−	1933.21i	0.0526472	−	0.0911875i
$767$	28847.4	−	24205.8i	1.35804	−	1.13953i
$768$		0			0
$769$	2488.04	−	14110.4i	0.116672	−	0.661682i	−0.869236	−	0.494397i	$-0.835389\pi$
$769$	2488.04	−	14110.4i	0.116672	−	0.661682i	0.985909	−	0.167285i	$-0.0534999\pi$
$770$	−1835.95	+	10412.2i	−0.0859260	+	0.487310i
$771$		0			0
$772$	−33236.1	+	27888.4i	−1.54947	+	1.30016i
$773$	−2301.12	+	3985.65i	−0.107070	+	0.185452i	−0.914582	−	0.404400i	$-0.867480\pi$
$773$	−2301.12	+	3985.65i	−0.107070	+	0.185452i	0.807512	+	0.589851i	$0.200814\pi$
$774$		0			0
$775$	−1829.17	−	3168.22i	−0.0847818	−	0.146846i
$776$	12473.8	+	4540.11i	0.577042	+	0.210026i
$777$		0			0
$778$	−43337.1	−	36364.2i	−1.99706	−	1.67573i
$779$	3587.84	−	1305.87i	0.165016	−	0.0600610i
$780$		0			0
$781$	−485.256	−	2752.03i	−0.0222328	−	0.126089i
$782$	−46952.3			−2.14707
$783$		0			0
$784$	−2581.50			−0.117597
$785$	131.494	+	745.741i	0.00597864	+	0.0339065i
$786$		0			0
$787$	14878.2	−	5415.23i	0.673891	−	0.245276i	0.0176684	−	0.999844i	$-0.494376\pi$
$787$	14878.2	−	5415.23i	0.673891	−	0.245276i	0.656222	+	0.754568i	$0.272153\pi$
$788$	−7117.32	−	5972.14i	−0.321756	−	0.269986i
$789$		0			0
$790$	5531.84	+	2013.42i	0.249132	+	0.0906765i
$791$	−1428.87	−	2474.88i	−0.0642287	−	0.111247i
$792$		0			0
$793$	−24428.6	+	42311.5i	−1.09393	+	1.89474i
$794$	−22884.9	+	19202.8i	−1.02287	+	0.858287i
$795$		0			0
$796$	4024.94	−	22826.6i	0.179221	−	1.01641i
$797$	5271.31	−	29895.1i	0.234278	−	1.32866i	−0.609851	−	0.792516i	$-0.708771\pi$
$797$	5271.31	−	29895.1i	0.234278	−	1.32866i	0.844129	−	0.536140i	$-0.180118\pi$
$798$		0			0
$799$	−6116.37	+	5132.24i	−0.270816	+	0.227241i
$800$	−13032.4	+	22572.8i	−0.575956	+	0.997585i
$801$		0			0
$802$	−9371.86	−	16232.5i	−0.412633	−	0.714702i
$803$	14522.5	+	5285.76i	0.638217	+	0.232292i
$804$		0			0
$805$	−9627.46	−	8078.40i	−0.421520	−	0.353697i
$806$	−12629.0	+	4596.58i	−0.551907	+	0.200878i
$807$		0			0
$808$	−3264.17	−	18512.0i	−0.142120	−	0.806004i
$809$	−12492.6			−0.542913			−0.271457	−	0.962451i	$-0.587505\pi$
$809$	−12492.6			−0.542913			−0.271457	+	0.962451i	$0.587505\pi$
$810$		0			0
$811$	−37598.6			−1.62795			−0.813974	−	0.580902i	$-0.802700\pi$
$811$	−37598.6			−1.62795			−0.813974	+	0.580902i	$0.802700\pi$
$812$	−717.643	−	4069.96i	−0.0310152	−	0.175896i
$813$		0			0
$814$	−14178.2	+	5160.45i	−0.610499	+	0.222204i
$815$	2473.27	+	2075.32i	0.106301	+	0.0891968i
$816$		0			0
$817$	−6002.25	−	2184.64i	−0.257028	−	0.0935507i
$818$	−8033.49	−	13914.4i	−0.343379	−	0.594751i
$819$		0			0
$820$	−1334.85	+	2312.02i	−0.0568474	+	0.0984626i
$821$	−23150.6	+	19425.6i	−0.984118	+	0.825773i	−0.984706	−	0.174227i	$-0.944257\pi$
$821$	−23150.6	+	19425.6i	−0.984118	+	0.825773i	0.000587385		1.00000i	$0.499813\pi$
$822$		0			0
$823$	−858.797	+	4870.48i	−0.0363740	+	0.206287i	−0.997578	−	0.0695496i	$-0.977844\pi$
$823$	−858.797	+	4870.48i	−0.0363740	+	0.206287i	0.961205	+	0.275837i	$0.0889549\pi$
$824$	2100.65	−	11913.4i	0.0888101	−	0.503667i
$825$		0			0
$826$	28215.8	−	23675.9i	1.18856	−	0.997322i
$827$	−1750.28	+	3031.58i	−0.0735953	+	0.127471i	−0.900475	−	0.434909i	$-0.856781\pi$
$827$	−1750.28	+	3031.58i	−0.0735953	+	0.127471i	0.826879	+	0.562380i	$0.190114\pi$
$828$		0			0
$829$	−1059.09	−	1834.40i	−0.0443712	−	0.0768532i	0.842987	−	0.537934i	$-0.180795\pi$
$829$	−1059.09	−	1834.40i	−0.0443712	−	0.0768532i	−0.887358	+	0.461081i	$0.847462\pi$
$830$	−6750.78	−	2457.08i	−0.282317	−	0.102755i
$831$		0			0
$832$	54168.2	+	45452.5i	2.25715	+	1.89397i
$833$	5308.14	−	1932.00i	0.220788	−	0.0803601i
$834$		0			0
$835$	−407.047	−	2308.48i	−0.0168700	−	0.0956744i
$836$	−19707.1			−0.815293
$837$		0			0
$838$	39078.9			1.61093
$839$	−1108.92	−	6289.02i	−0.0456308	−	0.258785i	0.953455	−	0.301536i	$-0.0974992\pi$
$839$	−1108.92	−	6289.02i	−0.0456308	−	0.258785i	−0.999086	+	0.0427501i	$0.986388\pi$
$840$		0			0
$841$	22584.8	−	8220.19i	0.926023	−	0.337045i
$842$	−42146.9	−	35365.4i	−1.72503	−	1.44747i
$843$		0			0
$844$	28914.4	+	10524.0i	1.17924	+	0.429207i
$845$	−12843.2	−	22245.1i	−0.522864	−	0.905627i
$846$		0			0
$847$	−5683.73	+	9844.51i	−0.230573	+	0.399364i
$848$	−16011.3	+	13435.1i	−0.648386	+	0.544061i
$849$		0			0
$850$	6066.32	−	34403.8i	0.244792	−	1.38828i
$851$	3114.39	−	17662.6i	0.125452	−	0.711476i
$852$		0			0
$853$	−13176.9	+	11056.7i	−0.528918	+	0.443815i	−0.867728	−	0.497040i	$-0.834420\pi$
$853$	−13176.9	+	11056.7i	−0.528918	+	0.443815i	0.338810	+	0.940855i	$0.389976\pi$
$854$	−23893.7	+	41385.2i	−0.957409	+	1.65828i
$855$		0			0
$856$	−7852.10	−	13600.2i	−0.313527	−	0.543045i
$857$	−33675.4	−	12256.8i	−1.34227	−	0.488548i	−0.431746	−	0.901995i	$-0.642102\pi$
$857$	−33675.4	−	12256.8i	−1.34227	−	0.488548i	−0.910528	+	0.413448i	$0.864324\pi$
$858$		0			0
$859$	32362.9	+	27155.7i	1.28546	+	1.07863i	0.992467	+	0.122509i	$0.0390941\pi$
$859$	32362.9	+	27155.7i	1.28546	+	1.07863i	0.292988	+	0.956116i	$0.405350\pi$
$860$	4196.90	−	1527.55i	0.166410	−	0.0605685i
$861$		0			0
$862$	−4485.66	−	25439.5i	−0.177242	−	1.00519i
$863$	42613.9			1.68088			0.840438	−	0.541908i	$-0.182298\pi$
$863$	42613.9			1.68088			0.840438	+	0.541908i	$0.182298\pi$
$864$		0			0
$865$	−9224.63			−0.362597
$866$	3723.18	+	21115.2i	0.146096	+	0.828550i
$867$		0			0
$868$	−7078.45	+	2576.34i	−0.276795	+	0.100745i
$869$	−6752.50	−	5666.02i	−0.263594	−	0.221181i
$870$		0			0
$871$	−5183.69	−	1886.71i	−0.201656	−	0.0733968i
$872$	−5096.53	−	8827.45i	−0.197925	−	0.342815i
$873$		0			0
$874$	20439.8	−	35402.8i	0.791061	−	1.37016i
$875$	15566.2	−	13061.6i	0.601409	−	0.504642i
$876$		0			0
$877$	212.665	−	1206.08i	0.00818836	−	0.0464385i	−0.980440	−	0.196819i	$-0.936939\pi$
$877$	212.665	−	1206.08i	0.00818836	−	0.0464385i	0.988628	+	0.150381i	$0.0480499\pi$
$878$	−7590.64	+	43048.7i	−0.291767	+	1.65469i
$879$		0			0
$880$	−3169.22	+	2659.29i	−0.121403	+	0.101869i
$881$	−18786.4	+	32539.1i	−0.718424	+	1.24435i	0.243200	+	0.969976i	$0.421803\pi$
$881$	−18786.4	+	32539.1i	−0.718424	+	1.24435i	−0.961624	+	0.274370i	$0.911531\pi$
$882$		0			0
$883$	−4042.46	−	7001.74i	−0.154065	−	0.266849i	0.778653	−	0.627455i	$-0.215903\pi$
$883$	−4042.46	−	7001.74i	−0.154065	−	0.266849i	−0.932718	+	0.360606i	$0.882570\pi$
$884$	−69107.0	−	25152.9i	−2.62932	−	0.956995i
$885$		0			0
$886$	−60388.8	−	50672.2i	−2.28984	−	1.92141i
$887$	−9898.62	+	3602.80i	−0.374705	+	0.136381i	−0.522506	−	0.852636i	$-0.675003\pi$
$887$	−9898.62	+	3602.80i	−0.374705	+	0.136381i	0.147801	+	0.989017i	$0.452780\pi$
$888$		0			0
$889$	−4176.97	−	23688.8i	−0.157583	−	0.893696i
$890$	21057.6			0.793091
$891$		0			0
$892$	−53851.1			−2.02138
$893$	−1207.15	−	6846.07i	−0.0452359	−	0.256545i
$894$		0			0
$895$	8566.51	−	3117.95i	0.319940	−	0.116449i
$896$	22349.9	+	18753.8i	0.833322	+	0.699240i
$897$		0			0
$898$	−36632.4	−	13333.1i	−1.36129	−	0.495469i
$899$	323.332	+	560.027i	0.0119952	+	0.0207764i
$900$		0			0
$901$	22868.0	−	39608.6i	0.845554	−	1.46454i
$902$	5343.91	−	4484.07i	0.197265	−	0.165525i
$903$		0			0
$904$	−287.709	+	1631.68i	−0.0105853	+	0.0600320i
$905$	2594.03	−	14711.5i	0.0952802	−	0.540361i
$906$		0			0
$907$	33345.1	−	27979.8i	1.22073	−	1.02432i	0.221948	−	0.975059i	$-0.428759\pi$
$907$	33345.1	−	27979.8i	1.22073	−	1.02432i	0.998786	−	0.0492585i	$-0.0156858\pi$
$908$	−13048.9	+	22601.3i	−0.476919	+	0.826048i
$909$		0			0
$910$	−17176.1	−	29749.8i	−0.625693	−	1.08373i
$911$	511.270	+	186.087i	0.0185940	+	0.00676766i	0.351300	−	0.936263i	$-0.385740\pi$
$911$	511.270	+	186.087i	0.0185940	+	0.00676766i	−0.332706	+	0.943030i	$0.607962\pi$
$912$		0			0
$913$	8240.41	+	6914.53i	0.298705	+	0.250643i
$914$	−73915.8	+	26903.1i	−2.67496	+	0.973607i
$915$		0			0
$916$	2274.23	+	12897.8i	0.0820333	+	0.465234i
$917$	34728.7			1.25065
$918$		0			0
$919$	−2288.18			−0.0821328			−0.0410664	−	0.999156i	$-0.513076\pi$
$919$	−2288.18			−0.0821328			−0.0410664	+	0.999156i	$0.513076\pi$
$920$	1265.28	+	7175.78i	0.0453426	+	0.257151i
$921$		0			0
$922$	32264.1	−	11743.2i	1.15245	−	0.419458i
$923$	6955.34	+	5836.22i	0.248037	+	0.208127i
$924$		0			0
$925$	12539.7	+	4564.08i	0.445733	+	0.162234i
$926$	15589.1	+	27001.1i	0.553228	+	0.958219i
$927$		0			0
$928$	2303.66	−	3990.05i	0.0814884	−	0.141142i
$929$	−11324.8	+	9502.66i	−0.399952	+	0.335600i	−0.820475	−	0.571682i	$-0.806291\pi$
$929$	−11324.8	+	9502.66i	−0.399952	+	0.335600i	0.420523	+	0.907282i	$0.361847\pi$
$930$		0			0
$931$	−854.037	+	4843.49i	−0.0300644	+	0.170504i
$932$	10041.9	−	56950.2i	0.352931	−	2.00157i
$933$		0			0
$934$	54356.0	−	45610.1i	1.90426	−	1.59787i
$935$	4526.41	−	7839.97i	0.158320	−	0.274219i
$936$		0			0
$937$	−2235.23	−	3871.53i	−0.0779313	−	0.134981i	0.824426	−	0.565970i	$-0.191498\pi$
$937$	−2235.23	−	3871.53i	−0.0779313	−	0.134981i	−0.902357	+	0.430989i	$0.858165\pi$
$938$	−5070.19	−	1845.40i	−0.176490	−	0.0642371i
$939$		0			0
$940$	3723.56	+	3124.44i	0.129201	+	0.108413i
$941$	25956.5	−	9447.39i	0.899211	−	0.327286i	0.149275	−	0.988796i	$-0.452306\pi$
$941$	25956.5	−	9447.39i	0.899211	−	0.327286i	0.749937	+	0.661510i	$0.230084\pi$
$942$		0			0
$943$	1439.93	+	8166.27i	0.0497250	+	0.282005i
$944$	14412.7			0.496923
$945$		0			0
$946$	−11670.4			−0.401097
$947$	5998.82	+	34021.0i	0.205845	+	1.16741i	0.896104	+	0.443843i	$0.146385\pi$
$947$	5998.82	+	34021.0i	0.205845	+	1.16741i	−0.690259	+	0.723562i	$0.742504\pi$
$948$		0			0
$949$	−47185.1	+	17174.0i	−1.61401	+	0.587450i
$950$	23300.2	+	19551.2i	0.795745	+	0.667709i
$951$		0			0
$952$	−17230.8	−	6271.48i	−0.586609	−	0.213508i
$953$	−14761.2	−	25567.2i	−0.501745	−	0.869047i	−0.999998	−	0.00201555i	$-0.999358\pi$
$953$	−14761.2	−	25567.2i	−0.501745	−	0.869047i	0.498253	−	0.867031i	$-0.333975\pi$
$954$		0			0
$955$	4207.56	−	7287.71i	0.142569	−	0.246937i
$956$	−22865.6	+	19186.6i	−0.773565	+	0.649098i
$957$		0			0
$958$	−13991.9	+	79351.7i	−0.471875	+	2.67614i
$959$	4799.38	−	27218.6i	0.161606	−	0.916512i
$960$		0			0
$961$	−21918.3	+	18391.7i	−0.735736	+	0.617356i
$962$	24511.5	−	42455.1i	0.821498	−	1.42288i
$963$		0			0
$964$	14743.9	+	25537.1i	0.492602	+	0.853211i
$965$	16306.2	+	5934.97i	0.543954	+	0.197983i
$966$		0			0
$967$	24256.8	+	20353.9i	0.806667	+	0.676874i	0.949810	−	0.312828i	$-0.101276\pi$
$967$	24256.8	+	20353.9i	0.806667	+	0.676874i	−0.143143	+	0.989702i	$0.545721\pi$
$968$	6193.11	−	2254.11i	0.205635	−	0.0748449i
$969$		0			0
$970$	−3616.59	−	20510.7i	−0.119713	−	0.678927i
$971$	−13353.2			−0.441324			−0.220662	−	0.975350i	$-0.570822\pi$
$971$	−13353.2			−0.441324			−0.220662	+	0.975350i	$0.570822\pi$
$972$		0			0
$973$	14932.7			0.492004
$974$	−12708.3	−	72072.5i	−0.418071	−	2.37100i
$975$		0			0
$976$	−17571.5	+	6395.50i	−0.576280	+	0.209749i
$977$	−3487.32	−	2926.21i	−0.114196	−	0.0958215i	0.583902	−	0.811824i	$-0.301525\pi$
$977$	−3487.32	−	2926.21i	−0.114196	−	0.0958215i	−0.698097	+	0.716003i	$0.745970\pi$
$978$		0			0
$979$	−29629.3	−	10784.2i	−0.967268	−	0.352057i
$980$	−1719.45	−	2978.18i	−0.0560469	−	0.0970761i
$981$		0			0
$982$	−15408.5	+	26688.4i	−0.500719	+	0.867272i
$983$	10118.2	−	8490.21i	0.328303	−	0.275479i	−0.463705	−	0.885990i	$-0.653480\pi$
$983$	10118.2	−	8490.21i	0.328303	−	0.275479i	0.792008	+	0.610511i	$0.209036\pi$
$984$		0			0
$985$	−645.273	+	3659.53i	−0.0208732	+	0.118378i
$986$	−1072.31	+	6081.35i	−0.0346340	+	0.196419i
$987$		0			0
$988$	49050.2	−	41158.0i	1.57945	−	1.32531i
$989$	6936.23	−	12013.9i	0.223012	−	0.386269i
$990$		0			0
$991$	21023.0	+	36413.0i	0.673884	+	1.16720i	0.976794	+	0.214182i	$0.0687086\pi$
$991$	21023.0	+	36413.0i	0.673884	+	1.16720i	−0.302910	+	0.953019i	$0.597958\pi$
$992$	−7891.28	−	2872.19i	−0.252569	−	0.0919275i
$993$		0			0
$994$	6803.05	+	5708.44i	0.217082	+	0.182154i
$995$	−8711.36	+	3170.67i	−0.277556	+	0.101022i
$996$		0			0
$997$	4666.65	+	26465.9i	0.148239	+	0.840706i	0.964709	+	0.263318i	$0.0848168\pi$
$997$	4666.65	+	26465.9i	0.148239	+	0.840706i	−0.816470	+	0.577388i	$0.804072\pi$
$998$	−94241.6			−2.98914
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.b.28.8		48
3.2	odd	2		243.4.e.c.28.1		48
9.2	odd	6		243.4.e.d.109.1		48
9.4	even	3		81.4.e.a.64.1		48
9.5	odd	6		27.4.e.a.4.8	✓	48
9.7	even	3		243.4.e.a.109.8		48
27.2	odd	18		243.4.e.c.217.1		48
27.5	odd	18		729.4.a.d.1.3		24
27.7	even	9		243.4.e.a.136.8		48
27.11	odd	18		27.4.e.a.7.8	yes	48
27.16	even	9		81.4.e.a.19.1		48
27.20	odd	18		243.4.e.d.136.1		48
27.22	even	9		729.4.a.c.1.22		24
27.25	even	9	inner	243.4.e.b.217.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.8	✓	48	9.5	odd	6
27.4.e.a.7.8	yes	48	27.11	odd	18
81.4.e.a.19.1		48	27.16	even	9
81.4.e.a.64.1		48	9.4	even	3
243.4.e.a.109.8		48	9.7	even	3
243.4.e.a.136.8		48	27.7	even	9
243.4.e.b.28.8		48	1.1	even	1	trivial
243.4.e.b.217.8		48	27.25	even	9	inner
243.4.e.c.28.1		48	3.2	odd	2
243.4.e.c.217.1		48	27.2	odd	18
243.4.e.d.109.1		48	9.2	odd	6
243.4.e.d.136.1		48	27.20	odd	18
729.4.a.c.1.22		24	27.22	even	9
729.4.a.d.1.3		24	27.5	odd	18

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.751659 + 4.26287i) q^{2} +(-10.0895 + 3.67228i) q^{4} +(3.28965 + 2.76034i) q^{5} +(19.2025 + 6.98913i) q^{7} +(-5.92381 - 10.2603i) q^{8} +O(q^{10})\)	\(q+(0.751659 + 4.26287i) q^{2} +(-10.0895 + 3.67228i) q^{4} +(3.28965 + 2.76034i) q^{5} +(19.2025 + 6.98913i) q^{7} +(-5.92381 - 10.2603i) q^{8} +(-9.29428 + 16.0982i) q^{10} +(21.3219 - 17.8912i) q^{11} +(-15.7039 + 89.0610i) q^{13} +(-15.3600 + 87.1111i) q^{14} +(-26.5146 + 22.2484i) q^{16} +(37.8692 - 65.5913i) q^{17} +(32.9713 + 57.1079i) q^{19} +(-43.3277 - 15.7700i) q^{20} +(92.2948 + 77.4446i) q^{22} +(-134.579 + 48.9827i) q^{23} +(-18.5037 - 104.940i) q^{25} -391.459 q^{26} -219.410 q^{28} +(3.27079 + 18.5496i) q^{29} +(32.2613 - 11.7422i) q^{31} +(-187.378 - 157.229i) q^{32} +(308.072 + 112.129i) q^{34} +(43.8770 + 75.9972i) q^{35} +(-62.6156 + 108.453i) q^{37} +(-218.660 + 183.478i) q^{38} +(8.83481 - 50.1047i) q^{40} +(10.0543 - 57.0207i) q^{41} +(-74.2022 + 62.2630i) q^{43} +(-149.426 + 258.814i) q^{44} +(-309.964 - 536.874i) q^{46} +(-99.0627 - 36.0559i) q^{47} +(57.1340 + 47.9411i) q^{49} +(433.436 - 157.758i) q^{50} +(-168.613 - 956.251i) q^{52} +603.869 q^{53} +119.528 q^{55} +(-42.0410 - 238.426i) q^{56} +(-76.6159 + 27.8859i) q^{58} +(-318.985 - 267.660i) q^{59} +(507.666 + 184.775i) q^{61} +(74.3048 + 128.700i) q^{62} +(390.953 - 677.150i) q^{64} +(-297.499 + 249.631i) q^{65} +(-10.5922 + 60.0715i) q^{67} +(-141.212 + 800.851i) q^{68} +(-290.986 + 244.166i) q^{70} +(50.1993 - 86.9478i) q^{71} +(277.621 + 480.854i) q^{73} +(-509.388 - 185.402i) q^{74} +(-542.381 - 455.112i) q^{76} +(534.478 - 194.534i) q^{77} +(-54.9931 - 311.881i) q^{79} -148.637 q^{80} +250.629 q^{82} +(67.1108 + 380.604i) q^{83} +(305.631 - 111.240i) q^{85} +(-321.194 - 269.514i) q^{86} +(-309.878 - 112.786i) q^{88} +(-566.411 - 981.053i) q^{89} +(-924.012 + 1600.44i) q^{91} +(1177.96 - 988.423i) q^{92} +(79.2401 - 449.393i) q^{94} +(-49.1735 + 278.877i) q^{95} +(-858.296 + 720.196i) q^{97} +(-161.421 + 279.590i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8	\( 48 q - 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} + 75 q^{8} - 3 q^{10} + 159 q^{11} + 3 q^{13} + 336 q^{14} - 45 q^{16} + 207 q^{17} - 3 q^{19} - 681 q^{20} + 111 q^{22} - 33 q^{23} + 435 q^{25} - 1914 q^{26} - 12 q^{28} + 51 q^{29} + 111 q^{31} - 1647 q^{32} - 513 q^{34} + 1257 q^{35} - 3 q^{37} + 525 q^{38} - 6 q^{40} - 447 q^{41} + 516 q^{43} + 2211 q^{44} - 3 q^{46} - 2109 q^{47} - 591 q^{49} + 4938 q^{50} - 1350 q^{52} - 2736 q^{53} - 12 q^{55} + 7773 q^{56} - 888 q^{58} - 3048 q^{59} + 57 q^{61} + 2118 q^{62} - 195 q^{64} - 3297 q^{65} + 2082 q^{67} - 3573 q^{68} + 1524 q^{70} + 3105 q^{71} - 219 q^{73} - 9006 q^{74} - 1425 q^{76} + 8985 q^{77} - 1401 q^{79} - 9870 q^{80} - 12 q^{82} + 8511 q^{83} - 1827 q^{85} - 12507 q^{86} - 3693 q^{88} + 5202 q^{89} + 267 q^{91} - 5118 q^{92} - 2211 q^{94} - 5178 q^{95} + 1569 q^{97} + 4392 q^{98}+O(q^{100}) \) 48 * q - 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 + 75 * q^8 - 3 * q^10 + 159 * q^11 + 3 * q^13 + 336 * q^14 - 45 * q^16 + 207 * q^17 - 3 * q^19 - 681 * q^20 + 111 * q^22 - 33 * q^23 + 435 * q^25 - 1914 * q^26 - 12 * q^28 + 51 * q^29 + 111 * q^31 - 1647 * q^32 - 513 * q^34 + 1257 * q^35 - 3 * q^37 + 525 * q^38 - 6 * q^40 - 447 * q^41 + 516 * q^43 + 2211 * q^44 - 3 * q^46 - 2109 * q^47 - 591 * q^49 + 4938 * q^50 - 1350 * q^52 - 2736 * q^53 - 12 * q^55 + 7773 * q^56 - 888 * q^58 - 3048 * q^59 + 57 * q^61 + 2118 * q^62 - 195 * q^64 - 3297 * q^65 + 2082 * q^67 - 3573 * q^68 + 1524 * q^70 + 3105 * q^71 - 219 * q^73 - 9006 * q^74 - 1425 * q^76 + 8985 * q^77 - 1401 * q^79 - 9870 * q^80 - 12 * q^82 + 8511 * q^83 - 1827 * q^85 - 12507 * q^86 - 3693 * q^88 + 5202 * q^89 + 267 * q^91 - 5118 * q^92 - 2211 * q^94 - 5178 * q^95 + 1569 * q^97 + 4392 * q^98

Introduction

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