LMFDB - Embedded newform 504.2.bk.c.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725478 + 1.21395i) q^{2} +(-0.947364 + 1.76139i) q^{4} +(-1.14053 + 1.97545i) q^{5} +(-1.95181 - 1.78618i) q^{7} +(-2.82554 + 0.127796i) q^{8} +O(q^{10})$	\(q+(0.725478 + 1.21395i) q^{2} +(-0.947364 + 1.76139i) q^{4} +(-1.14053 + 1.97545i) q^{5} +(-1.95181 - 1.78618i) q^{7} +(-2.82554 + 0.127796i) q^{8} +(-3.22553 + 0.0485996i) q^{10} +(2.60093 + 4.50494i) q^{11} -1.44266 q^{13} +(0.752336 - 3.66524i) q^{14} +(-2.20500 - 3.33736i) q^{16} +(-1.71846 + 0.992153i) q^{17} +(-4.27974 - 2.47091i) q^{19} +(-2.39905 - 3.88039i) q^{20} +(-3.58187 + 6.42563i) q^{22} +(-6.02437 - 3.47817i) q^{23} +(-0.101603 - 0.175982i) q^{25} +(-1.04662 - 1.75133i) q^{26} +(4.99523 - 1.74575i) q^{28} +5.21252i q^{29} +(1.69622 + 2.93794i) q^{31} +(2.45171 - 5.09795i) q^{32} +(-2.45113 - 1.36634i) q^{34} +(5.75460 - 1.81853i) q^{35} +(2.53971 + 1.46630i) q^{37} +(-0.105289 - 6.98799i) q^{38} +(2.97015 - 5.72747i) q^{40} +6.20691i q^{41} +12.2362 q^{43} +(-10.3990 + 0.313438i) q^{44} +(-0.148210 - 9.83665i) q^{46} +(1.25342 - 2.17098i) q^{47} +(0.619151 + 6.97256i) q^{49} +(0.139923 - 0.251012i) q^{50} +(1.36673 - 2.54110i) q^{52} +(-3.15993 + 1.82438i) q^{53} -11.8657 q^{55} +(5.74319 + 4.79748i) q^{56} +(-6.32775 + 3.78157i) q^{58} +(8.59616 - 4.96300i) q^{59} +(-3.57405 + 6.19044i) q^{61} +(-2.33595 + 4.19054i) q^{62} +(7.96734 - 0.722185i) q^{64} +(1.64540 - 2.84991i) q^{65} +(2.73520 + 4.73750i) q^{67} +(-0.119564 - 3.96681i) q^{68} +(6.38244 + 5.66651i) q^{70} +12.6367i q^{71} +(-9.13118 + 5.27189i) q^{73} +(0.0624814 + 4.14685i) q^{74} +(8.40670 - 5.19745i) q^{76} +(2.97009 - 13.4385i) q^{77} +(4.38431 + 2.53128i) q^{79} +(9.10765 - 0.549530i) q^{80} +(-7.53490 + 4.50298i) q^{82} +0.265100i q^{83} -4.52631i q^{85} +(8.87708 + 14.8542i) q^{86} +(-7.92473 - 12.3965i) q^{88} +(-8.23469 - 4.75430i) q^{89} +(2.81581 + 2.57685i) q^{91} +(11.8337 - 7.31619i) q^{92} +(3.54480 - 0.0534101i) q^{94} +(9.76231 - 5.63627i) q^{95} -10.7267i q^{97} +(-8.01519 + 5.81006i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.725478	+	1.21395i	0.512990	+	0.858394i
$2$	0.725478	+	1.21395i	0.512990	+	0.858394i
$3$		0			0
$3$		0			0
$4$	−0.947364	+	1.76139i	−0.473682	+	0.880696i
$5$	−1.14053	+	1.97545i	−0.510059	+	0.883448i	0.489873	+	0.871794i	$0.337043\pi$
$5$	−1.14053	+	1.97545i	−0.510059	+	0.883448i	−0.999932	+	0.0116545i	$0.996290\pi$
$6$		0			0
$7$	−1.95181	−	1.78618i	−0.737716	−	0.675111i
$7$	−1.95181	−	1.78618i	−0.737716	−	0.675111i
$8$	−2.82554	+	0.127796i	−0.998979	+	0.0451827i
$9$		0			0
$10$	−3.22553	+	0.0485996i	−1.02000	+	0.0153686i
$11$	2.60093	+	4.50494i	0.784209	+	1.35829i	0.929471	+	0.368896i	$0.120264\pi$
$11$	2.60093	+	4.50494i	0.784209	+	1.35829i	−0.145262	+	0.989393i	$0.546403\pi$
$12$		0			0
$13$	−1.44266			−0.400123			−0.200061	−	0.979783i	$-0.564114\pi$
$13$	−1.44266			−0.400123			−0.200061	+	0.979783i	$0.564114\pi$
$14$	0.752336	−	3.66524i	0.201070	−	0.979577i
$15$		0			0
$16$	−2.20500	−	3.33736i	−0.551251	−	0.834339i
$17$	−1.71846	+	0.992153i	−0.416788	+	0.240632i	−0.693702	−	0.720262i	$-0.744022\pi$
$17$	−1.71846	+	0.992153i	−0.416788	+	0.240632i	0.276914	+	0.960895i	$0.410688\pi$
$18$		0			0
$19$	−4.27974	−	2.47091i	−0.981839	−	0.566865i	−0.0790140	−	0.996874i	$-0.525177\pi$
$19$	−4.27974	−	2.47091i	−0.981839	−	0.566865i	−0.902825	+	0.430009i	$0.858511\pi$
$20$	−2.39905	−	3.88039i	−0.536444	−	0.867680i
$21$		0			0
$22$	−3.58187	+	6.42563i	−0.763656	+	1.36995i
$23$	−6.02437	−	3.47817i	−1.25617	−	0.725249i	−0.283841	−	0.958871i	$-0.591609\pi$
$23$	−6.02437	−	3.47817i	−1.25617	−	0.725249i	−0.972328	+	0.233622i	$0.924942\pi$
$24$		0			0
$25$	−0.101603	−	0.175982i	−0.0203206	−	0.0351964i
$26$	−1.04662	−	1.75133i	−0.205259	−	0.343463i
$27$		0			0
$28$	4.99523	−	1.74575i	0.944010	−	0.329916i
$29$			5.21252i			0.967941i	0.875084	+	0.483970i	$0.160806\pi$
$29$			5.21252i			0.967941i	−0.875084	+	0.483970i	$0.839194\pi$
$30$		0			0
$31$	1.69622	+	2.93794i	0.304650	+	0.527670i	0.977183	−	0.212397i	$-0.0681271\pi$
$31$	1.69622	+	2.93794i	0.304650	+	0.527670i	−0.672533	+	0.740067i	$0.734794\pi$
$32$	2.45171	−	5.09795i	0.433406	−	0.901199i
$33$		0			0
$34$	−2.45113	−	1.36634i	−0.420366	−	0.234326i
$35$	5.75460	−	1.81853i	0.972705	−	0.307387i
$36$		0			0
$37$	2.53971	+	1.46630i	0.417525	+	0.241058i	0.694018	−	0.719958i	$-0.255839\pi$
$37$	2.53971	+	1.46630i	0.417525	+	0.241058i	−0.276493	+	0.961016i	$0.589172\pi$
$38$	−0.105289	−	6.98799i	−0.0170802	−	1.13360i
$39$		0			0
$40$	2.97015	−	5.72747i	0.469622	−	0.905592i
$41$			6.20691i			0.969357i	0.874692	+	0.484679i	$0.161063\pi$
$41$			6.20691i			0.969357i	−0.874692	+	0.484679i	$0.838937\pi$
$42$		0			0
$43$	12.2362			1.86600			0.933000	−	0.359876i	$-0.117181\pi$
$43$	12.2362			1.86600			0.933000	+	0.359876i	$0.117181\pi$
$44$	−10.3990	+	0.313438i	−1.56771	+	0.0472525i
$45$		0			0
$46$	−0.148210	−	9.83665i	−0.0218524	−	1.45033i
$47$	1.25342	−	2.17098i	0.182830	−	0.316670i	−0.760013	−	0.649907i	$-0.774808\pi$
$47$	1.25342	−	2.17098i	0.182830	−	0.316670i	0.942843	+	0.333237i	$0.108141\pi$
$48$		0			0
$49$	0.619151	+	6.97256i	0.0884501	+	0.996081i
$50$	0.139923	−	0.251012i	0.0197881	−	0.0354985i
$51$		0			0
$52$	1.36673	−	2.54110i	0.189531	−	0.352387i
$53$	−3.15993	+	1.82438i	−0.434049	+	0.250598i	−0.701070	−	0.713092i	$-0.747294\pi$
$53$	−3.15993	+	1.82438i	−0.434049	+	0.250598i	0.267021	+	0.963691i	$0.413961\pi$
$54$		0			0
$55$	−11.8657			−1.59997
$56$	5.74319	+	4.79748i	0.767466	+	0.641090i
$57$		0			0
$58$	−6.32775	+	3.78157i	−0.830875	+	0.496544i
$59$	8.59616	−	4.96300i	1.11912	−	0.646127i	0.177947	−	0.984040i	$-0.443054\pi$
$59$	8.59616	−	4.96300i	1.11912	−	0.646127i	0.941177	+	0.337913i	$0.109721\pi$
$60$		0			0
$61$	−3.57405	+	6.19044i	−0.457611	+	0.792605i	−0.998834	−	0.0482738i	$-0.984628\pi$
$61$	−3.57405	+	6.19044i	−0.457611	+	0.792605i	0.541223	+	0.840879i	$0.317961\pi$
$62$	−2.33595	+	4.19054i	−0.296666	+	0.532200i
$63$		0			0
$64$	7.96734	−	0.722185i	0.995917	−	0.0902731i
$65$	1.64540	−	2.84991i	0.204086	−	0.353488i
$66$		0			0
$67$	2.73520	+	4.73750i	0.334158	+	0.578778i	0.983323	−	0.181870i	$-0.0582149\pi$
$67$	2.73520	+	4.73750i	0.334158	+	0.578778i	−0.649165	+	0.760648i	$0.724882\pi$
$68$	−0.119564	−	3.96681i	−0.0144993	−	0.481046i
$69$		0			0
$70$	6.38244	+	5.66651i	0.762848	+	0.677277i
$71$			12.6367i			1.49970i	0.661606	+	0.749852i	$0.269875\pi$
$71$			12.6367i			1.49970i	−0.661606	+	0.749852i	$0.730125\pi$
$72$		0			0
$73$	−9.13118	+	5.27189i	−1.06872	+	0.617028i	−0.927832	−	0.372997i	$-0.878330\pi$
$73$	−9.13118	+	5.27189i	−1.06872	+	0.617028i	−0.140891	+	0.990025i	$0.544997\pi$
$74$	0.0624814	+	4.14685i	0.00726331	+	0.482062i
$75$		0			0
$76$	8.40670	−	5.19745i	0.964315	−	0.596188i
$77$	2.97009	−	13.4385i	0.338473	−	1.53146i
$78$		0			0
$79$	4.38431	+	2.53128i	0.493274	+	0.284792i	0.725932	−	0.687767i	$-0.241409\pi$
$79$	4.38431	+	2.53128i	0.493274	+	0.284792i	−0.232658	+	0.972559i	$0.574742\pi$
$80$	9.10765	−	0.549530i	1.01827	−	0.0614393i
$81$		0			0
$82$	−7.53490	+	4.50298i	−0.832091	+	0.497271i
$83$			0.265100i			0.0290986i	0.999894	+	0.0145493i	$0.00463134\pi$
$83$			0.265100i			0.0290986i	−0.999894	+	0.0145493i	$0.995369\pi$
$84$		0			0
$85$		−	4.52631i		−	0.490947i
$86$	8.87708	+	14.8542i	0.957240	+	1.60176i
$87$		0			0
$88$	−7.92473	−	12.3965i	−0.844779	−	1.32147i
$89$	−8.23469	−	4.75430i	−0.872875	−	0.503955i	−0.00457273	−	0.999990i	$-0.501456\pi$
$89$	−8.23469	−	4.75430i	−0.872875	−	0.503955i	−0.868303	+	0.496035i	$0.834789\pi$
$90$		0			0
$91$	2.81581	+	2.57685i	0.295177	+	0.270127i
$92$	11.8337	−	7.31619i	1.23375	−	0.762765i
$93$		0			0
$94$	3.54480	−	0.0534101i	0.365618	−	0.00550883i
$95$	9.76231	−	5.63627i	1.00159	−	0.578269i
$96$		0			0
$97$		−	10.7267i		−	1.08914i	−0.838717	−	0.544568i	$-0.816694\pi$
$97$		−	10.7267i		−	1.08914i	0.838717	−	0.544568i	$-0.183306\pi$
$98$	−8.01519	+	5.81006i	−0.809656	+	0.586905i
$99$		0			0
$100$	0.406228	−	0.0122442i	0.0406228	−	0.00122442i
$101$	6.31858	+	10.9441i	0.628722	+	1.08898i	0.987808	+	0.155675i	$0.0497551\pi$
$101$	6.31858	+	10.9441i	0.628722	+	1.08898i	−0.359086	+	0.933304i	$0.616912\pi$
$102$		0			0
$103$	9.86612	−	17.0886i	0.972138	−	1.68379i	0.283065	−	0.959101i	$-0.408649\pi$
$103$	9.86612	−	17.0886i	0.972138	−	1.68379i	0.689073	−	0.724692i	$-0.258018\pi$
$104$	4.07630	−	0.184367i	0.399714	−	0.0180786i
$105$		0			0
$106$	−4.50717	−	2.51245i	−0.437775	−	0.244031i
$107$	−3.61692	+	6.26468i	−0.349661	+	0.605630i	−0.986189	−	0.165623i	$-0.947036\pi$
$107$	−3.61692	+	6.26468i	−0.349661	+	0.605630i	0.636529	+	0.771253i	$0.280370\pi$
$108$		0			0
$109$	5.24653	−	3.02908i	0.502526	−	0.290134i	−0.227230	−	0.973841i	$-0.572967\pi$
$109$	5.24653	−	3.02908i	0.502526	−	0.290134i	0.729756	+	0.683707i	$0.239634\pi$
$110$	−8.60831	−	14.4044i	−0.820770	−	1.37341i
$111$		0			0
$112$	−1.65735	+	10.4524i	−0.156605	+	0.987661i
$113$	1.46831			0.138127			0.0690633	−	0.997612i	$-0.477999\pi$
$113$	1.46831			0.138127			0.0690633	+	0.997612i	$0.477999\pi$
$114$		0			0
$115$	13.7419	−	7.93390i	1.28144	−	0.739840i
$116$	−9.18129	−	4.93815i	−0.852462	−	0.458496i
$117$		0			0
$118$	12.2612	+	6.83479i	1.12873	+	0.629194i
$119$	5.12627	+	1.13297i	0.469925	+	0.103860i
$120$		0			0
$121$	−8.02963	+	13.9077i	−0.729966	+	1.26434i
$122$	−10.1078	+	0.152296i	−0.915118	+	0.0137882i
$123$		0			0
$124$	−6.78181	+	0.204412i	−0.609024	+	0.0183567i
$125$	−10.9417			−0.978659
$126$		0			0
$127$			6.55533i			0.581691i	0.956770	+	0.290846i	$0.0939366\pi$
$127$			6.55533i			0.581691i	−0.956770	+	0.290846i	$0.906063\pi$
$128$	6.65682	+	9.14804i	0.588386	+	0.808580i
$129$		0			0
$130$	4.65336	−	0.0701129i	0.408126	−	0.00614931i
$131$	−9.22508	−	5.32610i	−0.805999	−	0.465344i	0.0395654	−	0.999217i	$-0.487403\pi$
$131$	−9.22508	−	5.32610i	−0.805999	−	0.465344i	−0.845565	+	0.533873i	$0.820736\pi$
$132$		0			0
$133$	3.93977	+	12.4671i	0.341622	+	1.08104i
$134$	−3.76678	+	6.75735i	−0.325400	+	0.583746i
$135$		0			0
$136$	4.72878	−	3.02298i	0.405490	−	0.259218i
$137$	2.65614	+	4.60057i	0.226929	+	0.393053i	0.956897	−	0.290429i	$-0.0937980\pi$
$137$	2.65614	+	4.60057i	0.226929	+	0.393053i	−0.729967	+	0.683482i	$0.760465\pi$
$138$		0			0
$139$		−	7.08794i		−	0.601191i	−0.953752	−	0.300596i	$-0.902815\pi$
$139$		−	7.08794i		−	0.601191i	0.953752	−	0.300596i	$-0.0971854\pi$
$140$	−2.24855	+	11.8589i	−0.190038	+	1.00226i
$141$		0			0
$142$	−15.3404	+	9.16767i	−1.28734	+	0.769334i
$143$	−3.75226	−	6.49911i	−0.313780	−	0.543483i
$144$		0			0
$145$	−10.2971	−	5.94502i	−0.855126	−	0.493707i
$146$	−13.0243	−	7.26018i	−1.07790	−	0.600857i
$147$		0			0
$148$	−4.98876	+	3.08430i	−0.410073	+	0.253528i
$149$	7.19693	+	4.15515i	0.589596	+	0.340403i	0.764938	−	0.644104i	$-0.222770\pi$
$149$	7.19693	+	4.15515i	0.589596	+	0.340403i	−0.175342	+	0.984508i	$0.556103\pi$
$150$		0			0
$151$	11.6286	−	6.71378i	0.946323	−	0.546360i	0.0543864	−	0.998520i	$-0.482680\pi$
$151$	11.6286	−	6.71378i	0.946323	−	0.546360i	0.891937	+	0.452160i	$0.149346\pi$
$152$	12.4083	+	6.43471i	1.00645	+	0.521924i
$153$		0			0
$154$	18.4684	−	6.14379i	1.48823	−	0.495081i
$155$	−7.73834			−0.621559
$156$		0			0
$157$	8.55081	+	14.8104i	0.682429	+	1.18200i	0.974237	+	0.225525i	$0.0724098\pi$
$157$	8.55081	+	14.8104i	0.682429	+	1.18200i	−0.291808	+	0.956477i	$0.594257\pi$
$158$	0.107862	+	7.15874i	0.00858103	+	0.569519i
$159$		0			0
$160$	7.27450	+	10.6576i	0.575100	+	0.842556i
$161$	5.54582	+	17.5493i	0.437072	+	1.38308i
$162$		0			0
$163$	−0.807425	+	1.39850i	−0.0632424	+	0.109539i	−0.895913	−	0.444230i	$-0.853477\pi$
$163$	−0.807425	+	1.39850i	−0.0632424	+	0.109539i	0.832671	+	0.553769i	$0.186811\pi$
$164$	−10.9328	−	5.88020i	−0.853709	−	0.459167i
$165$		0			0
$166$	−0.321819	+	0.192324i	−0.0249780	+	0.0149273i
$167$	−4.11126			−0.318139			−0.159069	−	0.987267i	$-0.550849\pi$
$167$	−4.11126			−0.318139			−0.159069	+	0.987267i	$0.550849\pi$
$168$		0			0
$169$	−10.9187			−0.839902
$170$	5.49473	−	3.28374i	0.421426	−	0.251851i
$171$		0			0
$172$	−11.5921	+	21.5527i	−0.883891	+	1.64338i
$173$	8.16562	−	14.1433i	0.620821	−	1.07529i	−0.368512	−	0.929623i	$-0.620133\pi$
$173$	8.16562	−	14.1433i	0.620821	−	1.07529i	0.989333	−	0.145670i	$-0.0465339\pi$
$174$		0			0
$175$	−0.116024	+	0.524965i	−0.00877060	+	0.0396836i
$176$	9.29953	−	18.6136i	0.700978	−	1.40305i
$177$		0			0
$178$	−0.202588	−	13.4457i	−0.0151846	−	1.00780i
$179$	−3.19876	−	5.54042i	−0.239087	−	0.414110i	0.721366	−	0.692554i	$-0.243515\pi$
$179$	−3.19876	−	5.54042i	−0.239087	−	0.414110i	−0.960452	+	0.278444i	$0.910181\pi$
$180$		0			0
$181$	4.79758			0.356601			0.178301	−	0.983976i	$-0.442940\pi$
$181$	4.79758			0.356601			0.178301	+	0.983976i	$0.442940\pi$
$182$	−1.08537	+	5.28771i	−0.0804528	+	0.391951i
$183$		0			0
$184$	17.4666	+	9.05782i	1.28765	+	0.667752i
$185$	−5.79321	+	3.34471i	−0.425925	+	0.245908i
$186$		0			0
$187$	−8.93917	−	5.16103i	−0.653697	−	0.377412i
$188$	2.63651	+	4.26447i	0.192287	+	0.311018i
$189$		0			0
$190$	13.9245	+	7.76199i	1.01019	+	0.563114i
$191$	−11.1694	−	6.44863i	−0.808186	−	0.466607i	0.0381392	−	0.999272i	$-0.487857\pi$
$191$	−11.1694	−	6.44863i	−0.808186	−	0.466607i	−0.846326	+	0.532666i	$0.821190\pi$
$192$		0			0
$193$	−3.67943	−	6.37295i	−0.264851	−	0.458735i	0.702674	−	0.711512i	$-0.251989\pi$
$193$	−3.67943	−	6.37295i	−0.264851	−	0.458735i	−0.967525	+	0.252777i	$0.918656\pi$
$194$	13.0218	−	7.78201i	0.934908	−	0.558716i
$195$		0			0
$196$	−12.8680	−	5.51499i	−0.919141	−	0.393928i
$197$			3.22473i			0.229753i	0.993380	+	0.114876i	$0.0366472\pi$
$197$			3.22473i			0.229753i	−0.993380	+	0.114876i	$0.963353\pi$
$198$		0			0
$199$	−8.05878	−	13.9582i	−0.571272	−	0.989471i	−0.996436	−	0.0843551i	$-0.973117\pi$
$199$	−8.05878	−	13.9582i	−0.571272	−	0.989471i	0.425164	−	0.905116i	$-0.360216\pi$
$200$	0.309573	+	0.484259i	0.0218901	+	0.0342423i
$201$		0			0
$202$	−8.70164	+	15.6102i	−0.612245	+	1.09833i
$203$	9.31048	−	10.1739i	0.653468	−	0.714065i
$204$		0			0
$205$	−12.2615	−	7.07915i	−0.856377	−	0.494429i
$206$	27.9024	−	0.420411i	1.94406	−	0.0292914i
$207$		0			0
$208$	3.18108	+	4.81468i	0.220568	+	0.333838i
$209$		−	25.7066i		−	1.77816i
$210$		0			0
$211$	1.31181			0.0903089			0.0451544	−	0.998980i	$-0.485622\pi$
$211$	1.31181			0.0903089			0.0451544	+	0.998980i	$0.485622\pi$
$212$	−0.219857	−	7.29423i	−0.0150998	−	0.500969i
$213$		0			0
$214$	−10.2290	+	0.154122i	−0.699242	+	0.0105356i
$215$	−13.9557	+	24.1720i	−0.951771	+	1.64852i
$216$		0			0
$217$	1.93697	−	8.76406i	0.131490	−	0.594943i
$218$	7.48341	+	4.17151i	0.506840	+	0.282530i
$219$		0			0
$220$	11.2411	−	20.9002i	0.757877	−	1.40909i
$221$	2.47916	−	1.43134i	0.166766	−	0.0962826i
$222$		0			0
$223$	−20.4329			−1.36829			−0.684143	−	0.729348i	$-0.739824\pi$
$223$	−20.4329			−1.36829			−0.684143	+	0.729348i	$0.739824\pi$
$224$	−13.8911	+	5.57106i	−0.928140	+	0.372232i
$225$		0			0
$226$	1.06522	+	1.78246i	0.0708577	+	0.118567i
$227$	−18.5734	+	10.7233i	−1.23276	+	0.711733i	−0.967604	−	0.252473i	$-0.918756\pi$
$227$	−18.5734	+	10.7233i	−1.23276	+	0.711733i	−0.265154	+	0.964206i	$0.585423\pi$
$228$		0			0
$229$	−8.24413	+	14.2792i	−0.544787	+	0.943599i	0.453833	+	0.891087i	$0.350056\pi$
$229$	−8.24413	+	14.2792i	−0.544787	+	0.943599i	−0.998620	+	0.0525125i	$0.983277\pi$
$230$	19.6008	+	10.9262i	1.29244	+	0.720451i
$231$		0			0
$232$	−0.666139	−	14.7282i	−0.0437342	−	0.966952i
$233$	6.14007	−	10.6349i	0.402249	−	0.696716i	−0.591748	−	0.806123i	$-0.701562\pi$
$233$	6.14007	−	10.6349i	0.402249	−	0.696716i	0.993997	+	0.109407i	$0.0348952\pi$
$234$		0			0
$235$	2.85911	+	4.95213i	0.186508	+	0.323041i
$236$	0.598091	+	19.8430i	0.0389324	+	1.29167i
$237$		0			0
$238$	2.34362	+	7.04500i	0.151914	+	0.456660i
$239$		−	16.7654i		−	1.08447i	−0.840228	−	0.542233i	$-0.817579\pi$
$239$		−	16.7654i		−	1.08447i	0.840228	−	0.542233i	$-0.182421\pi$
$240$		0			0
$241$	17.7711	−	10.2601i	1.14474	−	0.660914i	0.197138	−	0.980376i	$-0.436835\pi$
$241$	17.7711	−	10.2601i	1.14474	−	0.660914i	0.947599	+	0.319462i	$0.103502\pi$
$242$	−22.7086	+	0.342155i	−1.45977	+	0.0219946i
$243$		0			0
$244$	−7.51787	−	12.1599i	−0.481282	−	0.778459i
$245$	−14.4801	−	6.72930i	−0.925101	−	0.429919i
$246$		0			0
$247$	6.17422	+	3.56469i	0.392856	+	0.226816i
$248$	−5.16820	−	8.08450i	−0.328181	−	0.513366i
$249$		0			0
$250$	−7.93799	−	13.2828i	−0.502043	−	0.840076i
$251$		−	3.32849i		−	0.210092i	−0.994467	−	0.105046i	$-0.966501\pi$
$251$		−	3.32849i		−	0.210092i	0.994467	−	0.105046i	$-0.0334990\pi$
$252$		0			0
$253$		−	36.1859i		−	2.27499i
$254$	−7.95786	+	4.75574i	−0.499320	+	0.298402i
$255$		0			0
$256$	−6.27591	+	14.7178i	−0.392245	+	0.919861i
$257$	−3.19537	−	1.84485i	−0.199322	−	0.115078i	0.397017	−	0.917811i	$-0.370045\pi$
$257$	−3.19537	−	1.84485i	−0.199322	−	0.115078i	−0.596339	+	0.802733i	$0.703379\pi$
$258$		0			0
$259$	−2.33796	−	7.39831i	−0.145274	−	0.459709i
$260$	3.46102	+	5.59809i	0.214643	+	0.347179i
$261$		0			0
$262$	−0.226954	−	15.0628i	−0.0140212	−	0.930582i
$263$	23.6724	−	13.6673i	1.45970	−	0.842759i	0.460705	−	0.887553i	$-0.347597\pi$
$263$	23.6724	−	13.6673i	1.45970	−	0.842759i	0.998996	+	0.0447943i	$0.0142633\pi$
$264$		0			0
$265$		−	8.32304i		−	0.511280i
$266$	−12.2763	+	13.8273i	−0.752706	+	0.847807i
$267$		0			0
$268$	−10.9358	+	0.329619i	−0.668012	+	0.0201347i
$269$	3.25085	+	5.63064i	0.198208	+	0.343306i	0.947947	−	0.318427i	$-0.103155\pi$
$269$	3.25085	+	5.63064i	0.198208	+	0.343306i	−0.749740	+	0.661733i	$0.769821\pi$
$270$		0			0
$271$	0.880710	−	1.52543i	0.0534993	−	0.0926636i	−0.838035	−	0.545616i	$-0.816296\pi$
$271$	0.880710	−	1.52543i	0.0534993	−	0.0926636i	0.891535	+	0.452952i	$0.149629\pi$
$272$	7.10038	+	3.54741i	0.430524	+	0.215094i
$273$		0			0
$274$	−3.65790	+	6.56204i	−0.220982	+	0.396427i
$275$	0.528525	−	0.915431i	0.0318712	−	0.0552026i
$276$		0			0
$277$	6.52030	−	3.76450i	0.391767	−	0.226187i	−0.291159	−	0.956675i	$-0.594041\pi$
$277$	6.52030	−	3.76450i	0.391767	−	0.226187i	0.682925	+	0.730488i	$0.260707\pi$
$278$	8.60442	−	5.14214i	0.516059	−	0.308405i
$279$		0			0
$280$	−16.0274	+	5.87374i	−0.957823	+	0.351023i
$281$	−6.57050			−0.391963			−0.195981	−	0.980608i	$-0.562789\pi$
$281$	−6.57050			−0.391963			−0.195981	+	0.980608i	$0.562789\pi$
$282$		0			0
$283$	−12.6420	+	7.29886i	−0.751489	+	0.433872i	−0.826232	−	0.563330i	$-0.809520\pi$
$283$	−12.6420	+	7.29886i	−0.751489	+	0.433872i	0.0747426	+	0.997203i	$0.476186\pi$
$284$	−22.2582	−	11.9716i	−1.32078	−	0.710382i
$285$		0			0
$286$	5.16743	−	9.27003i	0.305556	−	0.548148i
$287$	11.0866	−	12.1147i	0.654424	−	0.715110i
$288$		0			0
$289$	−6.53126	+	11.3125i	−0.384192	+	0.665440i
$290$	−0.253327	−	16.8131i	−0.0148758	−	0.987302i
$291$		0			0
$292$	−0.635315	−	21.0780i	−0.0371790	−	1.23350i
$293$	24.3253			1.42110			0.710551	−	0.703646i	$-0.248446\pi$
$293$	24.3253			1.42110			0.710551	+	0.703646i	$0.248446\pi$
$294$		0			0
$295$			22.6417i			1.31825i
$296$	−7.36343	−	3.81853i	−0.427991	−	0.221947i
$297$		0			0
$298$	0.177057	+	11.7512i	0.0102567	+	0.680729i
$299$	8.69115	+	5.01784i	0.502622	+	0.290189i
$300$		0			0
$301$	−23.8827	−	21.8560i	−1.37658	−	1.25976i
$302$	16.5865	+	9.24589i	0.954447	+	0.532041i
$303$		0			0
$304$	1.19054	+	19.7314i	0.0682819	+	1.13167i
$305$	−8.15261	−	14.1207i	−0.466817	−	0.808551i
$306$		0			0
$307$			17.1823i			0.980645i	0.871541	+	0.490323i	$0.163121\pi$
$307$			17.1823i			0.980645i	−0.871541	+	0.490323i	$0.836879\pi$
$308$	20.8567	+	17.9626i	1.18842	+	1.02352i
$309$		0			0
$310$	−5.61400	−	9.39399i	−0.318854	−	0.533543i
$311$	6.71170	+	11.6250i	0.380586	+	0.659194i	0.991146	−	0.132776i	$-0.0423891\pi$
$311$	6.71170	+	11.6250i	0.380586	+	0.659194i	−0.610560	+	0.791970i	$0.709056\pi$
$312$		0			0
$313$	29.9258	+	17.2777i	1.69151	+	0.976593i	0.953302	+	0.302019i	$0.0976606\pi$
$313$	29.9258	+	17.2777i	1.69151	+	0.976593i	0.738207	+	0.674574i	$0.235673\pi$
$314$	−11.7758	+	21.1249i	−0.664544	+	1.19215i
$315$		0			0
$316$	−8.61212	+	5.32445i	−0.484470	+	0.299523i
$317$	−12.9883	−	7.49878i	−0.729493	−	0.421173i	0.0887434	−	0.996055i	$-0.471715\pi$
$317$	−12.9883	−	7.49878i	−0.729493	−	0.421173i	−0.818237	+	0.574881i	$0.805048\pi$
$318$		0			0
$319$	−23.4821	+	13.5574i	−1.31474	+	0.759068i
$320$	−7.66032	+	16.5628i	−0.428225	+	0.925886i
$321$		0			0
$322$	−17.2807	+	19.4640i	−0.963016	+	1.08469i
$323$	9.80607			0.545624
$324$		0			0
$325$	0.146579	+	0.253883i	0.00813075	+	0.0140829i
$326$	−2.28348	+	0.0344057i	−0.126471	+	0.00190555i
$327$		0			0
$328$	−0.793219	−	17.5379i	−0.0437982	−	0.968367i
$329$	−6.32419	+	1.99853i	−0.348664	+	0.110182i
$330$		0			0
$331$	−4.53217	+	7.84994i	−0.249110	+	0.431472i	−0.963279	−	0.268502i	$-0.913472\pi$
$331$	−4.53217	+	7.84994i	−0.249110	+	0.431472i	0.714169	+	0.699974i	$0.246805\pi$
$332$	−0.466946	−	0.251147i	−0.0256270	−	0.0137835i
$333$		0			0
$334$	−2.98263	−	4.99088i	−0.163202	−	0.273089i
$335$	−12.4783			−0.681760
$336$		0			0
$337$	8.05752			0.438921			0.219460	−	0.975621i	$-0.429570\pi$
$337$	8.05752			0.438921			0.219460	+	0.975621i	$0.429570\pi$
$338$	−7.92129	−	13.2548i	−0.430861	−	0.720967i
$339$		0			0
$340$	7.97261	+	4.28806i	0.432375	+	0.232553i
$341$	−8.82349	+	15.2827i	−0.477819	+	0.827607i
$342$		0			0
$343$	11.2458	−	14.7151i	0.607214	−	0.794538i
$344$	−34.5738	+	1.56374i	−1.86409	+	0.0843110i
$345$		0			0
$346$	23.0932	−	0.347950i	1.24150	−	0.0187059i
$347$	−4.84620	−	8.39387i	−0.260158	−	0.450607i	0.706126	−	0.708086i	$-0.250441\pi$
$347$	−4.84620	−	8.39387i	−0.260158	−	0.450607i	−0.966284	+	0.257480i	$0.917108\pi$
$348$		0			0
$349$	27.5070			1.47242			0.736208	−	0.676755i	$-0.236614\pi$
$349$	27.5070			1.47242			0.736208	+	0.676755i	$0.236614\pi$
$350$	−0.721456	+	0.240003i	−0.0385634	+	0.0128287i
$351$		0			0
$352$	29.3427	−	2.21458i	1.56397	−	0.118037i
$353$	−4.47937	+	2.58616i	−0.238413	+	0.137648i	−0.614447	−	0.788958i	$-0.710621\pi$
$353$	−4.47937	+	2.58616i	−0.238413	+	0.137648i	0.376034	+	0.926606i	$0.377287\pi$
$354$		0			0
$355$	−24.9632	−	14.4125i	−1.32491	−	0.764938i
$356$	16.1754	−	10.0005i	0.857296	−	0.530024i
$357$		0			0
$358$	4.40518	−	7.90260i	0.232821	−	0.417665i
$359$	3.43494	+	1.98316i	0.181289	+	0.104667i	0.587898	−	0.808935i	$-0.299956\pi$
$359$	3.43494	+	1.98316i	0.181289	+	0.104667i	−0.406609	+	0.913602i	$0.633289\pi$
$360$		0			0
$361$	2.71076	+	4.69517i	0.142672	+	0.247114i
$362$	3.48054	+	5.82404i	0.182933	+	0.306105i
$363$		0			0
$364$	−7.20644	+	2.51853i	−0.377720	+	0.132007i
$365$		−	24.0509i		−	1.25888i
$366$		0			0
$367$	15.8584	+	27.4675i	0.827801	+	1.43379i	0.899760	+	0.436386i	$0.143742\pi$
$367$	15.8584	+	27.4675i	0.827801	+	1.43379i	−0.0719586	+	0.997408i	$0.522925\pi$
$368$	1.67586	+	27.7749i	0.0873601	+	1.44787i
$369$		0			0
$370$	−8.26317	−	4.60617i	−0.429582	−	0.239463i
$371$	9.42626	+	2.08333i	0.489387	+	0.108161i
$372$		0			0
$373$	−14.3298	−	8.27329i	−0.741966	−	0.428374i	0.0808175	−	0.996729i	$-0.474247\pi$
$373$	−14.3298	−	8.27329i	−0.741966	−	0.428374i	−0.822784	+	0.568354i	$0.807580\pi$
$374$	−0.219920	−	14.5959i	−0.0113718	−	0.754739i
$375$		0			0
$376$	−3.26414	+	6.29438i	−0.168335	+	0.324608i
$377$		−	7.51991i		−	0.387295i
$378$		0			0
$379$	−28.7422			−1.47639			−0.738195	−	0.674588i	$-0.764321\pi$
$379$	−28.7422			−1.47639			−0.738195	+	0.674588i	$0.764321\pi$
$380$	0.679227	+	22.5348i	0.0348436	+	1.15601i
$381$		0			0
$382$	−0.274786	−	18.2374i	−0.0140593	−	0.933107i
$383$	−2.52741	+	4.37760i	−0.129144	+	0.223685i	−0.923345	−	0.383971i	$-0.874556\pi$
$383$	−2.52741	+	4.37760i	−0.129144	+	0.223685i	0.794201	+	0.607655i	$0.207890\pi$
$384$		0			0
$385$	23.1596	+	21.1942i	1.18032	+	1.08016i
$386$	5.06712	−	9.09009i	0.257910	−	0.462673i
$387$		0			0
$388$	18.8940	+	10.1621i	0.959197	+	0.515904i
$389$	−2.81257	+	1.62384i	−0.142603	+	0.0823318i	−0.569604	−	0.821919i	$-0.692903\pi$
$389$	−2.81257	+	1.62384i	−0.142603	+	0.0823318i	0.427001	+	0.904251i	$0.359570\pi$
$390$		0			0
$391$	13.8035			0.698074
$392$	−2.64050	−	19.6221i	−0.133365	−	0.991067i
$393$		0			0
$394$	−3.91467	+	2.33947i	−0.197218	+	0.117861i
$395$	−10.0009	+	5.77399i	−0.503197	+	0.290521i
$396$		0			0
$397$	−15.2933	+	26.4888i	−0.767550	+	1.32944i	0.171338	+	0.985212i	$0.445191\pi$
$397$	−15.2933	+	26.4888i	−0.767550	+	1.32944i	−0.938888	+	0.344223i	$0.888142\pi$
$398$	11.0981	−	19.9093i	0.556300	−	0.997966i
$399$		0			0
$400$	−0.363279	+	0.727127i	−0.0181640	+	0.0363563i
$401$	−13.0004	+	22.5173i	−0.649209	+	1.12446i	0.334103	+	0.942536i	$0.391567\pi$
$401$	−13.0004	+	22.5173i	−0.649209	+	1.12446i	−0.983312	+	0.181926i	$0.941767\pi$
$402$		0			0
$403$	−2.44708	−	4.23846i	−0.121898	−	0.211133i
$404$	−25.2629	+	0.761452i	−1.25687	+	0.0378837i
$405$		0			0
$406$	19.1051	+	3.92157i	0.948172	+	0.194624i
$407$			15.2550i			0.756160i
$408$		0			0
$409$	10.0633	−	5.81005i	0.497598	−	0.287289i	−0.230123	−	0.973162i	$-0.573913\pi$
$409$	10.0633	−	5.81005i	0.497598	−	0.287289i	0.727721	+	0.685873i	$0.240579\pi$
$410$	−0.301654	−	20.0206i	−0.0148976	−	0.988747i
$411$		0			0
$412$	20.7530	+	33.5673i	1.02243	+	1.65374i
$413$	−25.6429	−	5.66741i	−1.26180	−	0.278875i
$414$		0			0
$415$	−0.523693	−	0.302354i	−0.0257071	−	0.0148420i
$416$	−3.53700	+	7.35463i	−0.173416	+	0.360590i
$417$		0			0
$418$	31.2066	−	18.6496i	1.52636	−	0.912180i
$419$		−	12.0074i		−	0.586601i	−0.956020	−	0.293300i	$-0.905246\pi$
$419$		−	12.0074i		−	0.586601i	0.956020	−	0.293300i	$-0.0947536\pi$
$420$		0			0
$421$			16.4501i			0.801728i	0.916138	+	0.400864i	$0.131290\pi$
$421$			16.4501i			0.801728i	−0.916138	+	0.400864i	$0.868710\pi$
$422$	0.951690	+	1.59248i	0.0463276	+	0.0775206i
$423$		0			0
$424$	8.69535	−	5.55869i	0.422283	−	0.269954i
$425$	0.349202	+	0.201612i	0.0169388	+	0.00977961i
$426$		0			0
$427$	18.0331	−	5.69870i	0.872683	−	0.275779i
$428$	−7.60803	−	12.3057i	−0.367748	−	0.594821i
$429$		0			0
$430$	−39.4682	+	0.594674i	−1.90333	+	0.0286777i
$431$	10.8768	−	6.27975i	0.523919	−	0.302485i	−0.214617	−	0.976698i	$-0.568850\pi$
$431$	10.8768	−	6.27975i	0.523919	−	0.302485i	0.738537	+	0.674213i	$0.235517\pi$
$432$		0			0
$433$		−	16.0148i		−	0.769621i	−0.922996	−	0.384810i	$-0.874267\pi$
$433$		−	16.0148i		−	0.769621i	0.922996	−	0.384810i	$-0.125733\pi$
$434$	12.0444	−	4.00674i	0.578149	−	0.192330i
$435$		0			0
$436$	0.365035	+	12.1108i	0.0174820	+	0.580004i
$437$	17.1885	+	29.7713i	0.822237	+	1.42416i
$438$		0			0
$439$	−2.73079	+	4.72986i	−0.130333	+	0.225744i	−0.923805	−	0.382863i	$-0.874938\pi$
$439$	−2.73079	+	4.72986i	−0.130333	+	0.225744i	0.793472	+	0.608607i	$0.208271\pi$
$440$	33.5270	−	1.51639i	1.59834	−	0.0722910i
$441$		0			0
$442$	3.53616	+	1.97117i	0.168198	+	0.0937592i
$443$	−3.94594	+	6.83457i	−0.187477	+	0.324720i	−0.944409	−	0.328774i	$-0.893364\pi$
$443$	−3.94594	+	6.83457i	−0.187477	+	0.324720i	0.756931	+	0.653495i	$0.226698\pi$
$444$		0			0
$445$	18.7838	−	10.8448i	0.890436	−	0.514094i
$446$	−14.8236	−	24.8046i	−0.701918	−	1.17453i
$447$		0			0
$448$	−16.8407	−	12.8215i	−0.795648	−	0.605759i
$449$	10.4903			0.495068			0.247534	−	0.968879i	$-0.420380\pi$
$449$	10.4903			0.495068			0.247534	+	0.968879i	$0.420380\pi$
$450$		0			0
$451$	−27.9617	+	16.1437i	−1.31667	+	0.760178i
$452$	−1.39102	+	2.58626i	−0.0654281	+	0.121648i
$453$		0			0
$454$	−26.4922	−	14.7676i	−1.24334	−	0.693080i
$455$	−8.30195	+	2.62353i	−0.389201	+	0.122993i
$456$		0			0
$457$	20.2117	−	35.0077i	0.945463	−	1.63759i	0.190641	−	0.981660i	$-0.438943\pi$
$457$	20.2117	−	35.0077i	0.945463	−	1.63759i	0.754822	−	0.655930i	$-0.227723\pi$
$458$	−23.3153	+	0.351295i	−1.08945	+	0.0164149i
$459$		0			0
$460$	0.956115	+	31.7212i	0.0445791	+	1.47901i
$461$	−23.0641			−1.07420			−0.537102	−	0.843517i	$-0.680481\pi$
$461$	−23.0641			−1.07420			−0.537102	+	0.843517i	$0.680481\pi$
$462$		0			0
$463$			14.7738i			0.686595i	0.939227	+	0.343298i	$0.111544\pi$
$463$			14.7738i			0.686595i	−0.939227	+	0.343298i	$0.888456\pi$
$464$	17.3960	−	11.4936i	0.807591	−	0.533578i
$465$		0			0
$466$	17.3648	−	0.261638i	0.804407	−	0.0121201i
$467$	10.6190	+	6.13089i	0.491389	+	0.283704i	0.725151	−	0.688590i	$-0.241770\pi$
$467$	10.6190	+	6.13089i	0.491389	+	0.283704i	−0.233761	+	0.972294i	$0.575103\pi$
$468$		0			0
$469$	3.12342	−	14.1323i	0.144226	−	0.652567i
$470$	−3.93743	+	7.06349i	−0.181620	+	0.325814i
$471$		0			0
$472$	−23.6545	+	15.1217i	−1.08879	+	0.696032i
$473$	31.8254	+	55.1232i	1.46333	+	2.53457i
$474$		0			0
$475$			1.00421i			0.0460762i
$476$	−6.85206	+	7.95604i	−0.314063	+	0.364664i
$477$		0			0
$478$	20.3525	−	12.1630i	0.930899	−	0.556321i
$479$	18.5847	+	32.1897i	0.849159	+	1.47079i	0.881960	+	0.471324i	$0.156224\pi$
$479$	18.5847	+	32.1897i	0.849159	+	1.47079i	−0.0328017	+	0.999462i	$0.510443\pi$
$480$		0			0
$481$	−3.66394	−	2.11538i	−0.167061	−	0.0964530i
$482$	25.3479	+	14.1298i	1.15456	+	0.643593i
$483$		0			0
$484$	−16.8900	−	27.3190i	−0.767726	−	1.24177i
$485$	21.1901	+	12.2341i	0.962195	+	0.555524i
$486$		0			0
$487$	16.5990	−	9.58345i	0.752174	−	0.434268i	−0.0743051	−	0.997236i	$-0.523674\pi$
$487$	16.5990	−	9.58345i	0.752174	−	0.434268i	0.826479	+	0.562968i	$0.190341\pi$
$488$	9.30751	−	17.9481i	0.421331	−	0.812472i
$489$		0			0
$490$	−2.33595	−	22.4601i	−0.105528	−	1.01465i
$491$	−3.45295			−0.155830			−0.0779148	−	0.996960i	$-0.524826\pi$
$491$	−3.45295			−0.155830			−0.0779148	+	0.996960i	$0.524826\pi$
$492$		0			0
$493$	−5.17162	−	8.95751i	−0.232918	−	0.403426i
$494$	0.151897	+	10.0813i	0.00683416	+	0.453580i
$495$		0			0
$496$	6.06479	−	12.1391i	0.272317	−	0.545060i
$497$	22.5714	−	24.6645i	1.01247	−	1.10636i
$498$		0			0
$499$	0.159728	−	0.276658i	0.00715042	−	0.0123849i	−0.862428	−	0.506180i	$-0.831057\pi$
$499$	0.159728	−	0.276658i	0.00715042	−	0.0123849i	0.869578	+	0.493795i	$0.164391\pi$
$500$	10.3658	−	19.2727i	0.463573	−	0.861901i
$501$		0			0
$502$	4.04063	−	2.41474i	0.180342	−	0.107775i
$503$	−25.3573			−1.13063			−0.565314	−	0.824876i	$-0.691245\pi$
$503$	−25.3573			−1.13063			−0.565314	+	0.824876i	$0.691245\pi$
$504$		0			0
$505$	−28.8260			−1.28274
$506$	43.9280	−	26.2521i	1.95284	−	1.16705i
$507$		0			0
$508$	−11.5465	−	6.21028i	−0.512293	−	0.275536i
$509$	−5.33380	+	9.23841i	−0.236416	+	0.409485i	−0.959683	−	0.281083i	$-0.909306\pi$
$509$	−5.33380	+	9.23841i	−0.236416	+	0.409485i	0.723267	+	0.690569i	$0.242640\pi$
$510$		0			0
$511$	27.2389	+	6.02015i	1.20498	+	0.266316i
$512$	−22.4197	+	3.05876i	−0.990821	+	0.135179i
$513$		0			0
$514$	−0.0786119	−	5.21743i	−0.00346742	−	0.230131i
$515$	22.5052	+	38.9801i	0.991696	+	1.71767i
$516$		0			0
$517$	13.0402			0.573507
$518$	7.28506	−	8.20549i	0.320087	−	0.360528i
$519$		0			0
$520$	−4.28492	+	8.26281i	−0.187906	+	0.362348i
$521$	21.3366	−	12.3187i	0.934774	−	0.539692i	0.0464560	−	0.998920i	$-0.485207\pi$
$521$	21.3366	−	12.3187i	0.934774	−	0.539692i	0.888318	+	0.459228i	$0.151874\pi$
$522$		0			0
$523$	4.11510	+	2.37586i	0.179941	+	0.103889i	0.587265	−	0.809395i	$-0.300205\pi$
$523$	4.11510	+	2.37586i	0.179941	+	0.103889i	−0.407324	+	0.913284i	$0.633538\pi$
$524$	18.1209	−	11.2032i	0.791614	−	0.489415i
$525$		0			0
$526$	33.7652	+	18.8219i	1.47223	+	0.820672i
$527$	−5.82978	−	3.36582i	−0.253949	−	0.146618i
$528$		0			0
$529$	12.6954	+	21.9891i	0.551974	+	0.956046i
$530$	10.1038	−	6.03818i	0.438880	−	0.262282i
$531$		0			0
$532$	−25.6919	−	4.87141i	−1.11388	−	0.211202i
$533$		−	8.95449i		−	0.387862i
$534$		0			0
$535$	−8.25038	−	14.2901i	−0.356695	−	0.617814i
$536$	−8.33384	−	13.0364i	−0.359967	−	0.563089i
$537$		0			0
$538$	−4.47691	+	8.03128i	−0.193013	+	0.346253i
$539$	−29.8006	+	20.9244i	−1.28360	+	0.901276i
$540$		0			0
$541$	1.31933	+	0.761716i	0.0567224	+	0.0327487i	0.528093	−	0.849187i	$-0.322907\pi$
$541$	1.31933	+	0.761716i	0.0567224	+	0.0327487i	−0.471371	+	0.881935i	$0.656241\pi$
$542$	2.49074	−	0.0375284i	0.106987	−	0.00161198i
$543$		0			0
$544$	0.844776	+	11.1931i	0.0362195	+	0.479900i
$545$			13.8190i			0.591941i
$546$		0			0
$547$	42.5128			1.81772			0.908858	−	0.417106i	$-0.136956\pi$
$547$	42.5128			1.81772			0.908858	+	0.417106i	$0.136956\pi$
$548$	−10.6197	+	0.320091i	−0.453653	+	0.0136736i
$549$		0			0
$550$	1.49472	−	0.0225213i	0.0637352	−	0.000960310i
$551$	12.8797	−	22.3082i	0.548692	−	0.950362i
$552$		0			0
$553$	−4.03604	−	12.7717i	−0.171630	−	0.543110i
$554$	9.30026	+	5.18428i	0.395130	+	0.220259i
$555$		0			0
$556$	12.4846	+	6.71486i	0.529467	+	0.284773i
$557$	27.4340	−	15.8390i	1.16242	−	0.671121i	0.210535	−	0.977586i	$-0.432480\pi$
$557$	27.4340	−	15.8390i	1.16242	−	0.671121i	0.951882	+	0.306465i	$0.0991462\pi$
$558$		0			0
$559$	−17.6527			−0.746630
$560$	−18.7580	−	15.1953i	−0.792670	−	0.642118i
$561$		0			0
$562$	−4.76675	−	7.97627i	−0.201073	−	0.336459i
$563$	2.81241	−	1.62374i	0.118529	−	0.0684327i	−0.439563	−	0.898212i	$-0.644867\pi$
$563$	2.81241	−	1.62374i	0.118529	−	0.0684327i	0.558092	+	0.829779i	$0.311534\pi$
$564$		0			0
$565$	−1.67464	+	2.90057i	−0.0704528	+	0.122028i
$566$	−18.0320	−	10.0516i	−0.757940	−	0.422502i
$567$		0			0
$568$	−1.61492	−	35.7056i	−0.0677607	−	1.49817i
$569$	22.7654	−	39.4309i	0.954377	−	1.65303i	0.218589	−	0.975817i	$-0.429855\pi$
$569$	22.7654	−	39.4309i	0.954377	−	1.65303i	0.735788	−	0.677212i	$-0.236812\pi$
$570$		0			0
$571$	−0.356697	−	0.617818i	−0.0149273	−	0.0258549i	0.858465	−	0.512872i	$-0.171418\pi$
$571$	−0.356697	−	0.617818i	−0.0149273	−	0.0258549i	−0.873393	+	0.487017i	$0.838085\pi$
$572$	15.0022	−	0.452185i	0.627275	−	0.0189068i
$573$		0			0
$574$	22.7498	+	4.66969i	0.949560	+	0.194909i
$575$			1.41357i			0.0589501i
$576$		0			0
$577$	−5.50982	+	3.18110i	−0.229377	+	0.132431i	−0.610285	−	0.792182i	$-0.708945\pi$
$577$	−5.50982	+	3.18110i	−0.229377	+	0.132431i	0.380908	+	0.924613i	$0.375612\pi$
$578$	−18.4711	+	0.278307i	−0.768297	+	0.0115761i
$579$		0			0
$580$	20.2266	−	12.5051i	0.839863	−	0.519246i
$581$	0.473516	−	0.517427i	0.0196448	−	0.0214665i
$582$		0			0
$583$	−16.4375	−	9.49018i	−0.680770	−	0.393043i
$584$	25.1268	−	16.0629i	1.03975	−	0.664686i
$585$		0			0
$586$	17.6475	+	29.5298i	0.729011	+	1.21987i
$587$		−	0.534646i		−	0.0220672i	−0.999939	−	0.0110336i	$-0.996488\pi$
$587$		−	0.534646i		−	0.0220672i	0.999939	−	0.0110336i	$-0.00351218\pi$
$588$		0			0
$589$		−	16.7648i		−	0.690782i
$590$	−27.4860	+	16.4261i	−1.13158	+	0.676250i
$591$		0			0
$592$	−0.706495	−	11.7091i	−0.0290368	−	0.481242i
$593$	26.0980	+	15.0677i	1.07172	+	0.618756i	0.928650	−	0.370957i	$-0.120970\pi$
$593$	26.0980	+	15.0677i	1.07172	+	0.618756i	0.143067	+	0.989713i	$0.454304\pi$
$594$		0			0
$595$	−8.08478	+	8.83451i	−0.331444	+	0.362180i
$596$	−14.1370	+	8.74018i	−0.579072	+	0.358012i
$597$		0			0
$598$	0.213818	+	14.1910i	0.00874366	+	0.580312i
$599$	−23.7748	+	13.7264i	−0.971411	+	0.560844i	−0.899666	−	0.436579i	$-0.856190\pi$
$599$	−23.7748	+	13.7264i	−0.971411	+	0.560844i	−0.0717449	+	0.997423i	$0.522857\pi$
$600$		0			0
$601$		−	2.94649i		−	0.120190i	−0.998193	−	0.0600948i	$-0.980860\pi$
$601$		−	2.94649i		−	0.120190i	0.998193	−	0.0600948i	$-0.0191403\pi$
$602$	9.20573	−	44.8486i	0.375197	−	1.82789i
$603$		0			0
$604$	0.809078	+	26.8429i	0.0329209	+	1.09222i
$605$	−18.3160	−	31.7243i	−0.744652	−	1.28978i
$606$		0			0
$607$	10.5832	−	18.3307i	0.429560	−	0.744021i	−0.567274	−	0.823529i	$-0.692002\pi$
$607$	10.5832	−	18.3307i	0.429560	−	0.744021i	0.996834	+	0.0795088i	$0.0253352\pi$
$608$	−23.0892	+	15.7599i	−0.936393	+	0.639149i
$609$		0			0
$610$	11.2274	−	20.1412i	0.454583	−	0.815492i
$611$	−1.80826	+	3.13200i	−0.0731544	+	0.126707i
$612$		0			0
$613$	−25.0083	+	14.4385i	−1.01008	+	0.583167i	−0.911214	−	0.411934i	$-0.864853\pi$
$613$	−25.0083	+	14.4385i	−1.01008	+	0.583167i	−0.0988618	+	0.995101i	$0.531520\pi$
$614$	−20.8585	+	12.4654i	−0.841780	+	0.503062i
$615$		0			0
$616$	−6.67471	+	38.3506i	−0.268932	+	1.54519i
$617$	−12.1395			−0.488717			−0.244359	−	0.969685i	$-0.578577\pi$
$617$	−12.1395			−0.488717			−0.244359	+	0.969685i	$0.578577\pi$
$618$		0			0
$619$	−14.0233	+	8.09635i	−0.563643	+	0.325420i	−0.754607	−	0.656178i	$-0.772172\pi$
$619$	−14.0233	+	8.09635i	−0.563643	+	0.325420i	0.190963	+	0.981597i	$0.438839\pi$
$620$	7.33103	−	13.6303i	0.294421	−	0.547404i
$621$		0			0
$622$	−9.24302	+	16.5814i	−0.370611	+	0.664853i
$623$	7.58056	+	23.9881i	0.303709	+	0.961063i
$624$		0			0
$625$	12.9874	−	22.4948i	0.519495	−	0.899791i
$626$	0.736230	+	48.8632i	0.0294257	+	1.95296i
$627$		0			0
$628$	−34.1877	+	1.03046i	−1.36424	+	0.0411198i
$629$	−5.81918			−0.232026
$630$		0			0
$631$			35.2865i			1.40473i	0.711815	+	0.702367i	$0.247873\pi$
$631$			35.2865i			1.40473i	−0.711815	+	0.702367i	$0.752127\pi$
$632$	−12.7115	−	6.59194i	−0.505637	−	0.262213i
$633$		0			0
$634$	−0.319535	−	21.2073i	−0.0126903	−	0.842251i
$635$	−12.9497	−	7.47652i	−0.513894	−	0.296697i
$636$		0			0
$637$	−0.893226	−	10.0591i	−0.0353909	−	0.398555i
$638$	−33.4937	−	18.6706i	−1.32603	−	0.739174i
$639$		0			0
$640$	−25.6638	+	2.71664i	−1.01445	+	0.107385i
$641$	10.8251	+	18.7496i	0.427566	+	0.740565i	0.996656	−	0.0817094i	$-0.0260379\pi$
$641$	10.8251	+	18.7496i	0.427566	+	0.740565i	−0.569091	+	0.822275i	$0.692705\pi$
$642$		0			0
$643$			36.8664i			1.45387i	0.686708	+	0.726934i	$0.259055\pi$
$643$			36.8664i			1.45387i	−0.686708	+	0.726934i	$0.740945\pi$
$644$	−36.1652	−	6.85724i	−1.42511	−	0.270213i
$645$		0			0
$646$	7.11409	+	11.9041i	0.279900	+	0.468361i
$647$	−6.03892	−	10.4597i	−0.237414	−	0.411214i	0.722557	−	0.691311i	$-0.242967\pi$
$647$	−6.03892	−	10.4597i	−0.237414	−	0.411214i	−0.959972	+	0.280097i	$0.909633\pi$
$648$		0			0
$649$	44.7160	+	25.8168i	1.75525	+	1.01340i
$650$	−0.201862	+	0.362126i	−0.00791766	+	0.0142038i
$651$		0			0
$652$	−1.69838	−	2.74708i	−0.0665139	−	0.107584i
$653$	10.4008	+	6.00493i	0.407017	+	0.234991i	0.689507	−	0.724279i	$-0.257827\pi$
$653$	10.4008	+	6.00493i	0.407017	+	0.234991i	−0.282490	+	0.959270i	$0.591161\pi$
$654$		0			0
$655$	21.0429	−	12.1491i	0.822215	−	0.474706i
$656$	20.7147	−	13.6863i	0.808773	−	0.534359i
$657$		0			0
$658$	−7.01418	−	6.22739i	−0.273441	−	0.242769i
$659$	10.7760			0.419775			0.209887	−	0.977726i	$-0.432690\pi$
$659$	10.7760			0.419775			0.209887	+	0.977726i	$0.432690\pi$
$660$		0			0
$661$	18.3606	+	31.8014i	0.714143	+	1.23693i	0.963289	+	0.268466i	$0.0865167\pi$
$661$	18.3606	+	31.8014i	0.714143	+	1.23693i	−0.249146	+	0.968466i	$0.580150\pi$
$662$	−12.8174	+	0.193123i	−0.498164	+	0.00750593i
$663$		0			0
$664$	−0.0338788	−	0.749051i	−0.00131475	−	0.0290688i
$665$	−29.1216	−	6.43625i	−1.12929	−	0.249587i
$666$		0			0
$667$	18.1301	−	31.4022i	0.701999	−	1.21590i
$668$	3.89486	−	7.24154i	0.150697	−	0.280184i
$669$		0			0
$670$	−9.05271	−	15.1480i	−0.349737	−	0.585219i
$671$	−37.1834			−1.43545
$672$		0			0
$673$	−19.8549			−0.765349			−0.382675	−	0.923883i	$-0.624997\pi$
$673$	−19.8549			−0.765349			−0.382675	+	0.923883i	$0.624997\pi$
$674$	5.84555	+	9.78145i	0.225162	+	0.376767i
$675$		0			0
$676$	10.3440	−	19.2321i	0.397846	−	0.739698i
$677$	−19.7262	+	34.1668i	−0.758140	+	1.31314i	0.185658	+	0.982615i	$0.440558\pi$
$677$	−19.7262	+	34.1668i	−0.758140	+	1.31314i	−0.943798	+	0.330523i	$0.892775\pi$
$678$		0			0
$679$	−19.1598	+	20.9366i	−0.735287	+	0.803473i
$680$	0.578444	+	12.7893i	0.0221823	+	0.490446i
$681$		0			0
$682$	−24.9538	+	0.375983i	−0.955529	+	0.0143971i
$683$	−15.7567	−	27.2914i	−0.602913	−	1.04428i	−0.992378	−	0.123234i	$-0.960673\pi$
$683$	−15.7567	−	27.2914i	−0.602913	−	1.04428i	0.389465	−	0.921041i	$-0.372660\pi$
$684$		0			0
$685$	−12.1176			−0.462989
$686$	26.0219	+	2.97638i	0.993522	+	0.113639i
$687$		0			0
$688$	−26.9808	−	40.8365i	−1.02863	−	1.55688i
$689$	4.55871	−	2.63197i	0.173673	−	0.100270i
$690$		0			0
$691$	37.6139	+	21.7164i	1.43090	+	0.826130i	0.997189	−	0.0749234i	$-0.0238712\pi$
$691$	37.6139	+	21.7164i	1.43090	+	0.826130i	0.433709	+	0.901053i	$0.357205\pi$
$692$	17.1760	+	27.7817i	0.652935	+	1.05610i
$693$		0			0
$694$	6.67395	−	11.9726i	0.253340	−	0.454475i
$695$	14.0019	+	8.08399i	0.531121	+	0.306643i
$696$		0			0
$697$	−6.15821	−	10.6663i	−0.233259	−	0.404016i
$698$	19.9557	+	33.3922i	0.755335	+	1.26391i
$699$		0			0
$700$	−0.814752	−	0.701697i	−0.0307947	−	0.0265216i
$701$		−	22.3655i		−	0.844733i	−0.906425	−	0.422366i	$-0.861200\pi$
$701$		−	22.3655i		−	0.844733i	0.906425	−	0.422366i	$-0.138800\pi$
$702$		0			0
$703$	−7.24619	−	12.5508i	−0.273295	−	0.473361i
$704$	23.9758	+	34.0140i	0.903624	+	1.28195i
$705$		0			0
$706$	−6.38917	−	3.56154i	−0.240459	−	0.134040i
$707$	7.21540	−	32.6469i	0.271363	−	1.22781i
$708$		0			0
$709$	26.8480	+	15.5007i	1.00830	+	0.582142i	0.910693	−	0.413084i	$-0.135548\pi$
$709$	26.8480	+	15.5007i	1.00830	+	0.582142i	0.0976057	+	0.995225i	$0.468882\pi$
$710$	−0.614140	−	40.7602i	−0.0230483	−	1.52970i
$711$		0			0
$712$	23.8750	+	12.3811i	0.894754	+	0.464001i
$713$		−	23.5990i		−	0.883790i
$714$		0			0
$715$	17.1182			0.640185
$716$	12.7892	−	0.385483i	0.477956	−	0.0144062i
$717$		0			0
$718$	0.0845056	+	5.60859i	0.00315372	+	0.209311i
$719$	17.2451	−	29.8693i	0.643133	−	1.11394i	−0.341597	−	0.939847i	$-0.610968\pi$
$719$	17.2451	−	29.8693i	0.643133	−	1.11394i	0.984729	−	0.174092i	$-0.0556990\pi$
$720$		0			0
$721$	−49.7801	+	15.7312i	−1.85391	+	0.585860i
$722$	−3.73312	+	6.69698i	−0.138932	+	0.249236i
$723$		0			0
$724$	−4.54505	+	8.45042i	−0.168916	+	0.314057i
$725$	0.917309	−	0.529609i	0.0340680	−	0.0196692i
$726$		0			0
$727$	−38.6780			−1.43449			−0.717243	−	0.696823i	$-0.754596\pi$
$727$	−38.6780			−1.43449			−0.717243	+	0.696823i	$0.754596\pi$
$728$	−8.28549	−	6.92114i	−0.307081	−	0.256515i
$729$		0			0
$730$	29.1967	−	17.4484i	1.08062	−	0.645795i
$731$	−21.0274	+	12.1402i	−0.777726	+	0.449020i
$732$		0			0
$733$	7.05716	−	12.2234i	0.260662	−	0.451480i	−0.705756	−	0.708455i	$-0.749392\pi$
$733$	7.05716	−	12.2234i	0.260662	−	0.451480i	0.966418	+	0.256975i	$0.0827258\pi$
$734$	−21.8394	+	39.1784i	−0.806106	+	1.44610i
$735$		0			0
$736$	−32.5016	+	22.1845i	−1.19802	+	0.817731i
$737$	−14.2281	+	24.6438i	−0.524099	+	0.907765i
$738$		0			0
$739$	−21.7301	−	37.6376i	−0.799353	−	1.38452i	−0.920038	−	0.391830i	$-0.871842\pi$
$739$	−21.7301	−	37.6376i	−0.799353	−	1.38452i	0.120684	−	0.992691i	$-0.461491\pi$
$740$	−0.403071	−	13.3728i	−0.0148172	−	0.491593i
$741$		0			0
$742$	4.30948	+	12.9544i	0.158206	+	0.475573i
$743$			4.88557i			0.179234i	0.995976	+	0.0896170i	$0.0285643\pi$
$743$			4.88557i			0.179234i	−0.995976	+	0.0896170i	$0.971436\pi$
$744$		0			0
$745$	−16.4166	+	9.47812i	−0.601457	+	0.347251i
$746$	−0.352538	−	23.3977i	−0.0129073	−	0.856652i
$747$		0			0
$748$	17.5593	−	10.8560i	0.642030	−	0.396935i
$749$	18.2494	−	5.76704i	0.666818	−	0.210723i
$750$		0			0
$751$	−34.7208	−	20.0461i	−1.26698	−	0.731492i	−0.292566	−	0.956245i	$-0.594509\pi$
$751$	−34.7208	−	20.0461i	−1.26698	−	0.731492i	−0.974416	+	0.224754i	$0.927842\pi$
$752$	−10.0091	+	0.603923i	−0.364996	+	0.0220228i
$753$		0			0
$754$	9.12882	−	5.45553i	0.332452	−	0.198679i
$755$			30.6290i			1.11470i
$756$		0			0
$757$		−	1.51805i		−	0.0551745i	−0.999619	−	0.0275872i	$-0.991218\pi$
$757$		−	1.51805i		−	0.0551745i	0.999619	−	0.0275872i	$-0.00878240\pi$
$758$	−20.8519	−	34.8917i	−0.757374	−	1.26732i
$759$		0			0
$760$	−26.8635	+	17.1731i	−0.974441	+	0.622933i
$761$	11.7084	+	6.75982i	0.424427	+	0.245043i	0.696970	−	0.717101i	$-0.254531\pi$
$761$	11.7084	+	6.75982i	0.424427	+	0.245043i	−0.272542	+	0.962144i	$0.587864\pi$
$762$		0			0
$763$	−15.6507	−	3.45902i	−0.566594	−	0.125225i
$764$	21.9400	−	13.5644i	0.793762	−	0.490744i
$765$		0			0
$766$	−7.14777	+	0.107697i	−0.258260	+	0.00389124i
$767$	−12.4014	+	7.15993i	−0.447787	+	0.258530i
$768$		0			0
$769$			35.6272i			1.28475i	0.766391	+	0.642374i	$0.222050\pi$
$769$			35.6272i			1.28475i	−0.766391	+	0.642374i	$0.777950\pi$
$770$	−8.92700	+	43.4907i	−0.321707	+	1.56729i
$771$		0			0
$772$	14.7110	−	0.443408i	0.529461	−	0.0159586i
$773$	2.79215	+	4.83615i	0.100427	+	0.173944i	0.911861	−	0.410500i	$-0.134646\pi$
$773$	2.79215	+	4.83615i	0.100427	+	0.173944i	−0.811434	+	0.584444i	$0.801313\pi$
$774$		0			0
$775$	0.344683	−	0.597008i	0.0123814	−	0.0214452i
$776$	1.37083	+	30.3088i	0.0492101	+	1.08802i
$777$		0			0
$778$	−4.01172	−	2.23627i	−0.143827	−	0.0801741i
$779$	15.3367	−	26.5640i	0.549494	−	0.951752i
$780$		0			0
$781$	−56.9276	+	32.8672i	−2.03703	+	1.17608i
$782$	10.0142	+	16.7568i	0.358105	+	0.599223i
$783$		0			0
$784$	21.9047	−	17.4409i	0.782311	−	0.622888i
$785$	−39.0097			−1.39232
$786$		0			0
$787$	−3.54682	+	2.04776i	−0.126431	+	0.0729947i	−0.561881	−	0.827218i	$-0.689922\pi$
$787$	−3.54682	+	2.04776i	−0.126431	+	0.0729947i	0.435451	+	0.900212i	$0.356589\pi$
$788$	−5.68001	−	3.05499i	−0.202342	−	0.108830i
$789$		0			0
$790$	−14.2648	−	7.95166i	−0.507517	−	0.282907i
$791$	−2.86586	−	2.62265i	−0.101898	−	0.0932509i
$792$		0			0
$793$	5.15616	−	8.93073i	0.183101	−	0.317139i
$794$	−43.2511	+	0.651672i	−1.53493	+	0.0231270i
$795$		0			0
$796$	32.2205	−	0.971163i	1.14202	−	0.0344220i
$797$	−2.62717			−0.0930592			−0.0465296	−	0.998917i	$-0.514816\pi$
$797$	−2.62717			−0.0930592			−0.0465296	+	0.998917i	$0.514816\pi$
$798$		0			0
$799$			4.97433i			0.175979i
$800$	−1.14625	+	0.0865108i	−0.0405260	+	0.00305862i
$801$		0			0
$802$	−36.7665	+	0.553967i	−1.29827	+	0.0195613i
$803$	−47.4990	−	27.4236i	−1.67620	−	0.967757i
$804$		0			0
$805$	−40.9930	−	9.05999i	−1.44481	−	0.319323i
$806$	3.36999	−	6.04555i	0.118703	−	0.212945i
$807$		0			0
$808$	−19.2520	−	30.1155i	−0.677283	−	1.05946i
$809$	−16.3253	−	28.2763i	−0.573968	−	0.994142i	−0.996153	−	0.0876324i	$-0.972070\pi$
$809$	−16.3253	−	28.2763i	−0.573968	−	0.994142i	0.422185	−	0.906510i	$-0.361263\pi$
$810$		0			0
$811$			12.6334i			0.443617i	0.975090	+	0.221809i	$0.0711960\pi$
$811$			12.6334i			0.443617i	−0.975090	+	0.221809i	$0.928804\pi$
$812$	9.09976	+	26.0378i	0.319339	+	0.913746i
$813$		0			0
$814$	−18.5188	+	11.0671i	−0.649084	+	0.387903i
$815$	−1.84178	−	3.19006i	−0.0645148	−	0.111743i
$816$		0			0
$817$	−52.3676	−	30.2345i	−1.83211	−	1.05777i
$818$	14.3538	+	8.00132i	0.501870	+	0.279759i
$819$		0			0
$820$	24.0852	−	14.8907i	0.841092	−	0.520005i
$821$	5.10901	+	2.94969i	0.178306	+	0.102945i	0.586496	−	0.809952i	$-0.300507\pi$
$821$	5.10901	+	2.94969i	0.178306	+	0.102945i	−0.408191	+	0.912897i	$0.633840\pi$
$822$		0			0
$823$	2.88967	−	1.66835i	0.100728	−	0.0581551i	−0.448790	−	0.893637i	$-0.648145\pi$
$823$	2.88967	−	1.66835i	0.100728	−	0.0581551i	0.549518	+	0.835482i	$0.314812\pi$
$824$	−25.6933	+	49.5454i	−0.895067	+	1.72600i
$825$		0			0
$826$	−11.7234	−	35.2408i	−0.407908	−	1.22619i
$827$	30.1464			1.04829			0.524147	−	0.851628i	$-0.324384\pi$
$827$	30.1464			1.04829			0.524147	+	0.851628i	$0.324384\pi$
$828$		0			0
$829$	−18.5173	−	32.0728i	−0.643131	−	1.11394i	−0.984730	−	0.174090i	$-0.944302\pi$
$829$	−18.5173	−	32.0728i	−0.643131	−	1.11394i	0.341599	−	0.939846i	$-0.389032\pi$
$830$	−0.0128838	−	0.855090i	−0.000447203	−	0.0296806i
$831$		0			0
$832$	−11.4942	+	1.04187i	−0.398489	+	0.0361203i
$833$	−7.98184	−	11.3678i	−0.276554	−	0.393870i
$834$		0			0
$835$	4.68900	−	8.12159i	0.162270	−	0.281059i
$836$	45.2794	+	24.3535i	1.56602	+	0.842283i
$837$		0			0
$838$	14.5764	−	8.71111i	0.503535	−	0.300920i
$839$	31.7898			1.09751			0.548753	−	0.835985i	$-0.315103\pi$
$839$	31.7898			1.09751			0.548753	+	0.835985i	$0.315103\pi$
$840$		0			0
$841$	1.82963			0.0630907
$842$	−19.9696	+	11.9342i	−0.688199	+	0.411279i
$843$		0			0
$844$	−1.24276	+	2.31061i	−0.0427777	+	0.0795346i
$845$	12.4531	−	21.5694i	0.428400	−	0.742010i
$846$		0			0
$847$	40.5140	−	12.8030i	1.39208	−	0.439915i
$848$	13.0563	+	6.52303i	0.448354	+	0.224002i
$849$		0			0
$850$	0.00859099	+	0.570180i	0.000294669	+	0.0195570i
$851$	−10.2001	−	17.6671i	−0.349655	−	0.605620i
$852$		0			0
$853$	23.7173			0.812063			0.406032	−	0.913859i	$-0.366912\pi$
$853$	23.7173			0.812063			0.406032	+	0.913859i	$0.366912\pi$
$854$	20.0006	+	17.7571i	0.684406	+	0.607634i
$855$		0			0
$856$	9.41914	−	18.1633i	0.321939	−	0.620810i
$857$	−11.6340	+	6.71692i	−0.397411	+	0.229445i	−0.685366	−	0.728198i	$-0.740358\pi$
$857$	−11.6340	+	6.71692i	−0.397411	+	0.229445i	0.287955	+	0.957644i	$0.407025\pi$
$858$		0			0
$859$	−9.92452	−	5.72992i	−0.338620	−	0.195502i	0.321041	−	0.947065i	$-0.395967\pi$
$859$	−9.92452	−	5.72992i	−0.338620	−	0.195502i	−0.659662	+	0.751563i	$0.729300\pi$
$860$	−29.3552	−	47.4811i	−1.00100	−	1.61909i
$861$		0			0
$862$	15.5142	+	8.64816i	0.528417	+	0.294558i
$863$	20.7525	+	11.9815i	0.706425	+	0.407855i	0.809736	−	0.586794i	$-0.199610\pi$
$863$	20.7525	+	11.9815i	0.706425	+	0.407855i	−0.103311	+	0.994649i	$0.532944\pi$
$864$		0			0
$865$	18.6262	+	32.2616i	0.633311	+	1.09693i
$866$	19.4412	−	11.6184i	0.660638	−	0.394808i
$867$		0			0
$868$	13.6019	+	11.7145i	0.461680	+	0.397617i
$869$			26.3347i			0.893344i
$870$		0			0
$871$	−3.94597	−	6.83462i	−0.133704	−	0.231582i
$872$	−14.4372	+	9.22928i	−0.488904	+	0.312543i
$873$		0			0
$874$	−23.6711	+	42.4645i	−0.800688	+	1.43638i
$875$	21.3562	+	19.5439i	0.721973	+	0.660704i
$876$		0			0
$877$	22.5651	+	13.0279i	0.761968	+	0.439922i	0.830002	−	0.557761i	$-0.188339\pi$
$877$	22.5651	+	13.0279i	0.761968	+	0.439922i	−0.0680341	+	0.997683i	$0.521673\pi$
$878$	−7.72296	+	0.116363i	−0.260637	+	0.00392707i
$879$		0			0
$880$	26.1639	+	39.6001i	0.881986	+	1.33492i
$881$			12.4856i			0.420651i	0.977631	+	0.210325i	$0.0674523\pi$
$881$			12.4856i			0.420651i	−0.977631	+	0.210325i	$0.932548\pi$
$882$		0			0
$883$	−7.70463			−0.259281			−0.129641	−	0.991561i	$-0.541382\pi$
$883$	−7.70463			−0.259281			−0.129641	+	0.991561i	$0.541382\pi$
$884$	0.172491	+	5.72277i	0.00580151	+	0.192478i
$885$		0			0
$886$	−11.1595	+	0.168143i	−0.374912	+	0.00564886i
$887$	15.5727	−	26.9728i	0.522881	−	0.905657i	−0.476764	−	0.879031i	$-0.658190\pi$
$887$	15.5727	−	26.9728i	0.522881	−	0.905657i	0.999645	−	0.0266255i	$-0.00847617\pi$
$888$		0			0
$889$	11.7090	−	12.7948i	0.392706	−	0.429123i
$890$	26.7923	+	14.9349i	0.898080	+	0.500620i
$891$		0			0
$892$	19.3574	−	35.9903i	0.648133	−	1.20504i
$893$	−10.7286	+	6.19415i	−0.359019	+	0.207279i
$894$		0			0
$895$	14.5931			0.487793
$896$	3.34713	−	29.7455i	0.111820	−	0.993728i
$897$		0			0
$898$	7.61048	+	12.7347i	0.253965	+	0.424963i
$899$	−15.3141	+	8.84159i	−0.510753	+	0.294883i
$900$		0			0
$901$	3.62014	−	6.27026i	0.120604	−	0.208893i
$902$	−39.8833	−	22.2323i	−1.32797	−	0.740256i
$903$		0			0
$904$	−4.14876	+	0.187644i	−0.137986	+	0.00624094i
$905$	−5.47177	+	9.47738i	−0.181888	+	0.315039i
$906$		0			0
$907$	11.9178	+	20.6423i	0.395725	+	0.685416i	0.993193	−	0.116477i	$-0.0371601\pi$
$907$	11.9178	+	20.6423i	0.395725	+	0.685416i	−0.597469	+	0.801892i	$0.703827\pi$
$908$	−1.29227	−	42.8739i	−0.0428855	−	1.42282i
$909$		0			0
$910$	−9.20772	−	8.17487i	−0.305233	−	0.270994i
$911$			21.2488i			0.704006i	0.935999	+	0.352003i	$0.114499\pi$
$911$			21.2488i			0.704006i	−0.935999	+	0.352003i	$0.885501\pi$
$912$		0			0
$913$	−1.19426	+	0.689507i	−0.0395242	+	0.0228193i
$914$	57.1608	−	0.861251i	1.89071	−	0.0284877i
$915$		0			0
$916$	−17.3412	−	28.0488i	−0.572968	−	0.926758i
$917$	8.49228	+	26.8732i	0.280440	+	0.887431i
$918$		0			0
$919$	10.2220	+	5.90166i	0.337192	+	0.194678i	0.659030	−	0.752117i	$-0.270967\pi$
$919$	10.2220	+	5.90166i	0.337192	+	0.194678i	−0.321838	+	0.946795i	$0.604301\pi$
$920$	−37.8144	+	24.1737i	−1.24670	+	0.796984i
$921$		0			0
$922$	−16.7325	−	27.9988i	−0.551056	−	0.922091i
$923$		−	18.2305i		−	0.600066i
$924$		0			0
$925$		−	0.595923i		−	0.0195938i
$926$	−17.9347	+	10.7180i	−0.589369	+	0.352217i
$927$		0			0
$928$	26.5732	+	12.7796i	0.872307	+	0.419511i
$929$	−10.2519	−	5.91892i	−0.336353	−	0.194193i	0.322305	−	0.946636i	$-0.395542\pi$
$929$	−10.2519	−	5.91892i	−0.336353	−	0.194193i	−0.658658	+	0.752442i	$0.728876\pi$
$930$		0			0
$931$	14.5788	−	31.3706i	0.477799	−	1.02813i
$932$	12.9154	+	20.8902i	0.423057	+	0.684281i
$933$		0			0
$934$	0.261247	+	17.3388i	0.00854826	+	0.567343i
$935$	20.3907	−	11.7726i	0.666848	−	0.385005i
$936$		0			0
$937$		−	8.94738i		−	0.292298i	−0.989263	−	0.146149i	$-0.953312\pi$
$937$		−	8.94738i		−	0.292298i	0.989263	−	0.146149i	$-0.0466879\pi$
$938$	19.4219	−	6.46096i	0.634147	−	0.210958i
$939$		0			0
$940$	−11.4313	+	0.344552i	−0.372847	+	0.0112380i
$941$	−12.9899	−	22.4991i	−0.423458	−	0.733451i	0.572817	−	0.819683i	$-0.305851\pi$
$941$	−12.9899	−	22.4991i	−0.423458	−	0.733451i	−0.996275	+	0.0862325i	$0.972517\pi$
$942$		0			0
$943$	21.5887	−	37.3928i	0.703026	−	1.21768i
$944$	−35.5179	−	17.7450i	−1.15601	−	0.577552i
$945$		0			0
$946$	−43.8284	+	78.6252i	−1.42498	+	2.55633i
$947$	3.36911	−	5.83547i	0.109481	−	0.189627i	−0.806079	−	0.591808i	$-0.798414\pi$
$947$	3.36911	−	5.83547i	0.109481	−	0.189627i	0.915560	+	0.402181i	$0.131748\pi$
$948$		0			0
$949$	13.1732	−	7.60556i	0.427621	−	0.246887i
$950$	−1.21906	+	0.728531i	−0.0395516	+	0.0236367i
$951$		0			0
$952$	−14.6293	−	2.54614i	−0.474137	−	0.0825210i
$953$	11.4172			0.369841			0.184920	−	0.982754i	$-0.440797\pi$
$953$	11.4172			0.369841			0.184920	+	0.982754i	$0.440797\pi$
$954$		0			0
$955$	25.4779	−	14.7097i	0.824446	−	0.475994i
$956$	29.5305	+	15.8830i	0.955085	+	0.513692i
$957$		0			0
$958$	−25.5940	+	45.9139i	−0.826904	+	1.48341i
$959$	3.03314	−	13.7238i	0.0979451	−	0.443164i
$960$		0			0
$961$	9.74567	−	16.8800i	0.314376	−	0.544516i
$962$	−0.0901396	−	5.98252i	−0.00290622	−	0.192884i
$963$		0			0
$964$	1.23645	+	41.0220i	0.0398234	+	1.32123i
$965$	16.7859			0.540358
$966$		0			0
$967$		−	17.1228i		−	0.550633i	−0.961354	−	0.275317i	$-0.911217\pi$
$967$		−	17.1228i		−	0.550633i	0.961354	−	0.275317i	$-0.0887827\pi$
$968$	20.9107	−	40.3230i	0.672095	−	1.29603i
$969$		0			0
$970$	0.521316	+	34.5994i	0.0167384	+	1.11092i
$971$	38.4985	+	22.2271i	1.23548	+	0.713303i	0.968166	−	0.250308i	$-0.0805318\pi$
$971$	38.4985	+	22.2271i	1.23548	+	0.713303i	0.267310	+	0.963611i	$0.413865\pi$
$972$		0			0
$973$	−12.6603	+	13.8343i	−0.405871	+	0.443508i
$974$	23.6761	+	13.1979i	0.758631	+	0.422887i
$975$		0			0
$976$	28.5405	−	1.72206i	0.913560	−	0.0551216i
$977$	−28.2632	−	48.9533i	−0.904220	−	1.56616i	−0.821961	−	0.569544i	$-0.807120\pi$
$977$	−28.2632	−	48.9533i	−0.904220	−	1.56616i	−0.0822595	−	0.996611i	$-0.526214\pi$
$978$		0			0
$979$		−	49.4623i		−	1.58082i
$980$	25.5709	−	19.1301i	0.816831	−	0.611088i
$981$		0			0
$982$	−2.50504	−	4.19172i	−0.0799391	−	0.133763i
$983$	−26.5315	−	45.9539i	−0.846224	−	1.46570i	−0.884554	−	0.466438i	$-0.845537\pi$
$983$	−26.5315	−	45.9539i	−0.846224	−	1.46570i	0.0383296	−	0.999265i	$-0.487796\pi$
$984$		0			0
$985$	−6.37029	−	3.67789i	−0.202974	−	0.117187i
$986$	7.12210	−	12.7766i	0.226814	−	0.406889i
$987$		0			0
$988$	−12.1280	+	7.49817i	−0.385844	+	0.238548i
$989$	−73.7154	−	42.5596i	−2.34401	−	1.35332i
$990$		0			0
$991$	−7.29353	+	4.21092i	−0.231687	+	0.133764i	−0.611350	−	0.791360i	$-0.709373\pi$
$991$	−7.29353	+	4.21092i	−0.231687	+	0.133764i	0.379663	+	0.925125i	$0.376040\pi$
$992$	19.1361	−	1.44426i	0.607573	−	0.0458553i
$993$		0			0
$994$	46.3167	+	9.50707i	1.46907	+	0.301546i
$995$	36.7650			1.16553
$996$		0			0
$997$	5.24827	+	9.09027i	0.166214	+	0.287892i	0.937086	−	0.349099i	$-0.113512\pi$
$997$	5.24827	+	9.09027i	0.166214	+	0.287892i	−0.770871	+	0.636991i	$0.780179\pi$
$998$	0.451729	−	0.00680627i	0.0142992	−	0.000215449i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.11		32
3.2	odd	2		168.2.t.a.19.6	✓	32
4.3	odd	2		2016.2.bs.c.271.5		32
7.3	odd	6	inner	504.2.bk.c.451.1		32
8.3	odd	2	inner	504.2.bk.c.19.1		32
8.5	even	2		2016.2.bs.c.271.12		32
12.11	even	2		672.2.bb.a.271.14		32
21.2	odd	6		1176.2.p.a.979.12		32
21.5	even	6		1176.2.p.a.979.11		32
21.17	even	6		168.2.t.a.115.16	yes	32
24.5	odd	2		672.2.bb.a.271.11		32
24.11	even	2		168.2.t.a.19.16	yes	32
28.3	even	6		2016.2.bs.c.1711.12		32
56.3	even	6	inner	504.2.bk.c.451.11		32
56.45	odd	6		2016.2.bs.c.1711.5		32
84.23	even	6		4704.2.p.a.3919.4		32
84.47	odd	6		4704.2.p.a.3919.17		32
84.59	odd	6		672.2.bb.a.367.11		32
168.5	even	6		4704.2.p.a.3919.3		32
168.59	odd	6		168.2.t.a.115.6	yes	32
168.101	even	6		672.2.bb.a.367.14		32
168.107	even	6		1176.2.p.a.979.9		32
168.131	odd	6		1176.2.p.a.979.10		32
168.149	odd	6		4704.2.p.a.3919.18		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.6	✓	32	3.2	odd	2
168.2.t.a.19.16	yes	32	24.11	even	2
168.2.t.a.115.6	yes	32	168.59	odd	6
168.2.t.a.115.16	yes	32	21.17	even	6
504.2.bk.c.19.1		32	8.3	odd	2	inner
504.2.bk.c.19.11		32	1.1	even	1	trivial
504.2.bk.c.451.1		32	7.3	odd	6	inner
504.2.bk.c.451.11		32	56.3	even	6	inner
672.2.bb.a.271.11		32	24.5	odd	2
672.2.bb.a.271.14		32	12.11	even	2
672.2.bb.a.367.11		32	84.59	odd	6
672.2.bb.a.367.14		32	168.101	even	6
1176.2.p.a.979.9		32	168.107	even	6
1176.2.p.a.979.10		32	168.131	odd	6
1176.2.p.a.979.11		32	21.5	even	6
1176.2.p.a.979.12		32	21.2	odd	6
2016.2.bs.c.271.5		32	4.3	odd	2
2016.2.bs.c.271.12		32	8.5	even	2
2016.2.bs.c.1711.5		32	56.45	odd	6
2016.2.bs.c.1711.12		32	28.3	even	6
4704.2.p.a.3919.3		32	168.5	even	6
4704.2.p.a.3919.4		32	84.23	even	6
4704.2.p.a.3919.17		32	84.47	odd	6
4704.2.p.a.3919.18		32	168.149	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.725478 + 1.21395i) q^{2} +(-0.947364 + 1.76139i) q^{4} +(-1.14053 + 1.97545i) q^{5} +(-1.95181 - 1.78618i) q^{7} +(-2.82554 + 0.127796i) q^{8} +O(q^{10})\)	\(q+(0.725478 + 1.21395i) q^{2} +(-0.947364 + 1.76139i) q^{4} +(-1.14053 + 1.97545i) q^{5} +(-1.95181 - 1.78618i) q^{7} +(-2.82554 + 0.127796i) q^{8} +(-3.22553 + 0.0485996i) q^{10} +(2.60093 + 4.50494i) q^{11} -1.44266 q^{13} +(0.752336 - 3.66524i) q^{14} +(-2.20500 - 3.33736i) q^{16} +(-1.71846 + 0.992153i) q^{17} +(-4.27974 - 2.47091i) q^{19} +(-2.39905 - 3.88039i) q^{20} +(-3.58187 + 6.42563i) q^{22} +(-6.02437 - 3.47817i) q^{23} +(-0.101603 - 0.175982i) q^{25} +(-1.04662 - 1.75133i) q^{26} +(4.99523 - 1.74575i) q^{28} +5.21252i q^{29} +(1.69622 + 2.93794i) q^{31} +(2.45171 - 5.09795i) q^{32} +(-2.45113 - 1.36634i) q^{34} +(5.75460 - 1.81853i) q^{35} +(2.53971 + 1.46630i) q^{37} +(-0.105289 - 6.98799i) q^{38} +(2.97015 - 5.72747i) q^{40} +6.20691i q^{41} +12.2362 q^{43} +(-10.3990 + 0.313438i) q^{44} +(-0.148210 - 9.83665i) q^{46} +(1.25342 - 2.17098i) q^{47} +(0.619151 + 6.97256i) q^{49} +(0.139923 - 0.251012i) q^{50} +(1.36673 - 2.54110i) q^{52} +(-3.15993 + 1.82438i) q^{53} -11.8657 q^{55} +(5.74319 + 4.79748i) q^{56} +(-6.32775 + 3.78157i) q^{58} +(8.59616 - 4.96300i) q^{59} +(-3.57405 + 6.19044i) q^{61} +(-2.33595 + 4.19054i) q^{62} +(7.96734 - 0.722185i) q^{64} +(1.64540 - 2.84991i) q^{65} +(2.73520 + 4.73750i) q^{67} +(-0.119564 - 3.96681i) q^{68} +(6.38244 + 5.66651i) q^{70} +12.6367i q^{71} +(-9.13118 + 5.27189i) q^{73} +(0.0624814 + 4.14685i) q^{74} +(8.40670 - 5.19745i) q^{76} +(2.97009 - 13.4385i) q^{77} +(4.38431 + 2.53128i) q^{79} +(9.10765 - 0.549530i) q^{80} +(-7.53490 + 4.50298i) q^{82} +0.265100i q^{83} -4.52631i q^{85} +(8.87708 + 14.8542i) q^{86} +(-7.92473 - 12.3965i) q^{88} +(-8.23469 - 4.75430i) q^{89} +(2.81581 + 2.57685i) q^{91} +(11.8337 - 7.31619i) q^{92} +(3.54480 - 0.0534101i) q^{94} +(9.76231 - 5.63627i) q^{95} -10.7267i q^{97} +(-8.01519 + 5.81006i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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