LMFDB - Embedded newform 405.3.l.k.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 36 x^{13} - 109 x^{12} + 482 x^{11} - 98 x^{10} + 3204 x^{9} + \cdots + 2560000 $ x^16 - 2x^15 + 2x^14 - 36x^13 - 109x^12 + 482x^11 - 98x^10 + 3204x^9 + 19069x^8 - 24066x^7 + 130x^6 - 149540x^5 - 149596x^4 + 470880x^3 + 156800x^2 + 896000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.2
Root			$2.05601 - 0.550907i$ of defining polynomial
Character	$\chi$	$=$	405.217
Dual form			405.3.l.k.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05601 + 0.550907i) q^{2} +(0.459586 - 0.265342i) q^{4} +(-2.92464 - 4.05542i) q^{5} +(-6.15409 + 1.64898i) q^{7} +(5.22169 - 5.22169i) q^{8} +O(q^{10})$	\(q+(-2.05601 + 0.550907i) q^{2} +(0.459586 - 0.265342i) q^{4} +(-2.92464 - 4.05542i) q^{5} +(-6.15409 + 1.64898i) q^{7} +(5.22169 - 5.22169i) q^{8} +(8.24726 + 6.72679i) q^{10} +(7.02282 - 12.1639i) q^{11} +(-10.6178 - 2.84504i) q^{13} +(11.7444 - 6.78066i) q^{14} +(-8.92056 + 15.4509i) q^{16} +(15.7268 + 15.7268i) q^{17} -15.5354i q^{19} +(-2.42020 - 1.08778i) q^{20} +(-7.73784 + 28.8780i) q^{22} +(-15.4129 - 4.12988i) q^{23} +(-7.89291 + 23.7213i) q^{25} +23.3977 q^{26} +(-2.39079 + 2.39079i) q^{28} +(-29.8158 - 17.2141i) q^{29} +(24.7090 + 42.7973i) q^{31} +(2.18371 - 8.14971i) q^{32} +(-40.9985 - 23.6705i) q^{34} +(24.6858 + 20.1347i) q^{35} +(22.8392 + 22.8392i) q^{37} +(8.55854 + 31.9409i) q^{38} +(-36.4477 - 5.90457i) q^{40} +(-0.283471 - 0.490987i) q^{41} +(-0.142904 - 0.533325i) q^{43} -7.45379i q^{44} +33.9644 q^{46} +(-31.3977 + 8.41300i) q^{47} +(-7.28159 + 4.20403i) q^{49} +(3.15966 - 53.1196i) q^{50} +(-5.63471 + 1.50982i) q^{52} +(-45.4430 + 45.4430i) q^{53} +(-69.8689 + 7.09452i) q^{55} +(-23.5242 + 40.7452i) q^{56} +(70.7849 + 18.9668i) q^{58} +(39.4795 - 22.7935i) q^{59} +(-6.18147 + 10.7066i) q^{61} +(-74.3794 - 74.3794i) q^{62} -53.4055i q^{64} +(19.5155 + 51.3805i) q^{65} +(-31.4421 + 117.344i) q^{67} +(11.4008 + 3.05483i) q^{68} +(-61.8468 - 27.7977i) q^{70} -48.1581 q^{71} +(-77.4961 + 77.4961i) q^{73} +(-59.5400 - 34.3754i) q^{74} +(-4.12219 - 7.13983i) q^{76} +(-23.1610 + 86.4381i) q^{77} +(114.870 + 66.3203i) q^{79} +(88.7492 - 9.01164i) q^{80} +(0.853308 + 0.853308i) q^{82} +(25.3200 + 94.4956i) q^{83} +(17.7835 - 109.774i) q^{85} +(0.587625 + 1.01780i) q^{86} +(-26.8450 - 100.187i) q^{88} +119.880i q^{89} +70.0345 q^{91} +(-8.17940 + 2.19166i) q^{92} +(59.9193 - 34.5944i) q^{94} +(-63.0025 + 45.4354i) q^{95} +(71.5242 - 19.1648i) q^{97} +(12.6550 - 12.6550i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{5} - 26 q^{7} - 72 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^5 - 26 * q^7 - 72 * q^8	$ 16 q - 2 q^{2} - 2 q^{5} - 26 q^{7} - 72 q^{8} + 52 q^{10} + 20 q^{11} + 28 q^{13} + 76 q^{16} + 76 q^{17} - 12 q^{20} - 10 q^{22} - 68 q^{23} - 128 q^{25} + 248 q^{26} - 280 q^{28} + 116 q^{31} + 232 q^{32} + 28 q^{35} + 100 q^{37} - 66 q^{38} - 228 q^{40} - 316 q^{41} + 34 q^{43} - 16 q^{46} - 302 q^{47} + 22 q^{50} + 28 q^{52} - 236 q^{53} + 332 q^{55} + 420 q^{56} + 318 q^{58} - 112 q^{61} - 580 q^{62} + 112 q^{65} - 8 q^{67} - 76 q^{68} - 168 q^{70} - 496 q^{71} + 148 q^{73} + 48 q^{76} + 50 q^{77} + 1672 q^{80} + 44 q^{82} - 302 q^{83} - 86 q^{85} + 380 q^{86} + 636 q^{88} - 88 q^{91} - 416 q^{92} + 102 q^{95} + 178 q^{97} - 748 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^5 - 26 * q^7 - 72 * q^8 + 52 * q^10 + 20 * q^11 + 28 * q^13 + 76 * q^16 + 76 * q^17 - 12 * q^20 - 10 * q^22 - 68 * q^23 - 128 * q^25 + 248 * q^26 - 280 * q^28 + 116 * q^31 + 232 * q^32 + 28 * q^35 + 100 * q^37 - 66 * q^38 - 228 * q^40 - 316 * q^41 + 34 * q^43 - 16 * q^46 - 302 * q^47 + 22 * q^50 + 28 * q^52 - 236 * q^53 + 332 * q^55 + 420 * q^56 + 318 * q^58 - 112 * q^61 - 580 * q^62 + 112 * q^65 - 8 * q^67 - 76 * q^68 - 168 * q^70 - 496 * q^71 + 148 * q^73 + 48 * q^76 + 50 * q^77 + 1672 * q^80 + 44 * q^82 - 302 * q^83 - 86 * q^85 + 380 * q^86 + 636 * q^88 - 88 * q^91 - 416 * q^92 + 102 * q^95 + 178 * q^97 - 748 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.05601	+	0.550907i	−1.02801	+	0.275453i	−0.733135	−	0.680084i	$-0.761943\pi$
$2$	−2.05601	+	0.550907i	−1.02801	+	0.275453i	−0.294871	+	0.955537i	$0.595277\pi$
$3$		0			0
$3$		0			0
$4$	0.459586	−	0.265342i	0.114896	−	0.0663355i
$5$	−2.92464	−	4.05542i	−0.584929	−	0.811085i
$5$	−2.92464	−	4.05542i	−0.584929	−	0.811085i
$6$		0			0
$7$	−6.15409	+	1.64898i	−0.879155	+	0.235569i	−0.670043	−	0.742323i	$-0.733724\pi$
$7$	−6.15409	+	1.64898i	−0.879155	+	0.235569i	−0.209113	+	0.977892i	$0.567058\pi$
$8$	5.22169	−	5.22169i	0.652711	−	0.652711i
$9$		0			0
$10$	8.24726	+	6.72679i	0.824726	+	0.672679i
$11$	7.02282	−	12.1639i	0.638438	−	1.10581i	−0.347338	−	0.937740i	$-0.612914\pi$
$11$	7.02282	−	12.1639i	0.638438	−	1.10581i	0.985776	−	0.168067i	$-0.0537524\pi$
$12$		0			0
$13$	−10.6178	−	2.84504i	−0.816756	−	0.218849i	−0.173828	−	0.984776i	$-0.555614\pi$
$13$	−10.6178	−	2.84504i	−0.816756	−	0.218849i	−0.642928	+	0.765927i	$0.722280\pi$
$14$	11.7444	−	6.78066i	0.838889	−	0.484333i
$15$		0			0
$16$	−8.92056	+	15.4509i	−0.557535	+	0.965678i
$17$	15.7268	+	15.7268i	0.925105	+	0.925105i	0.997384	−	0.0722791i	$-0.0230272\pi$
$17$	15.7268	+	15.7268i	0.925105	+	0.925105i	−0.0722791	+	0.997384i	$0.523027\pi$
$18$		0			0
$19$		−	15.5354i		−	0.817651i	−0.912613	−	0.408826i	$-0.865938\pi$
$19$		−	15.5354i		−	0.817651i	0.912613	−	0.408826i	$-0.134062\pi$
$20$	−2.42020	−	1.08778i	−0.121010	−	0.0543892i
$21$		0			0
$22$	−7.73784	+	28.8780i	−0.351720	+	1.31264i
$23$	−15.4129	−	4.12988i	−0.670128	−	0.179560i	−0.0923154	−	0.995730i	$-0.529427\pi$
$23$	−15.4129	−	4.12988i	−0.670128	−	0.179560i	−0.577812	+	0.816170i	$0.696093\pi$
$24$		0			0
$25$	−7.89291	+	23.7213i	−0.315716	+	0.948854i
$26$	23.3977			0.899913
$27$		0			0
$28$	−2.39079	+	2.39079i	−0.0853852	+	0.0853852i
$29$	−29.8158	−	17.2141i	−1.02813	−	0.593591i	−0.111681	−	0.993744i	$-0.535624\pi$
$29$	−29.8158	−	17.2141i	−1.02813	−	0.593591i	−0.916448	+	0.400153i	$0.868957\pi$
$30$		0			0
$31$	24.7090	+	42.7973i	0.797065	+	1.38056i	0.921519	+	0.388332i	$0.126949\pi$
$31$	24.7090	+	42.7973i	0.797065	+	1.38056i	−0.124454	+	0.992225i	$0.539718\pi$
$32$	2.18371	−	8.14971i	0.0682409	−	0.254679i
$33$		0			0
$34$	−40.9985	−	23.6705i	−1.20584	−	0.696190i
$35$	24.6858	+	20.1347i	0.705310	+	0.575278i
$36$		0			0
$37$	22.8392	+	22.8392i	0.617276	+	0.617276i	0.944832	−	0.327556i	$-0.106225\pi$
$37$	22.8392	+	22.8392i	0.617276	+	0.617276i	−0.327556	+	0.944832i	$0.606225\pi$
$38$	8.55854	+	31.9409i	0.225225	+	0.840550i
$39$		0			0
$40$	−36.4477	−	5.90457i	−0.911193	−	0.147614i
$41$	−0.283471	−	0.490987i	−0.00691393	−	0.0119753i	0.862548	−	0.505976i	$-0.168867\pi$
$41$	−0.283471	−	0.490987i	−0.00691393	−	0.0119753i	−0.869462	+	0.494000i	$0.835534\pi$
$42$		0			0
$43$	−0.142904	−	0.533325i	−0.00332335	−	0.0124029i	0.964244	−	0.265015i	$-0.0853770\pi$
$43$	−0.142904	−	0.533325i	−0.00332335	−	0.0124029i	−0.967568	+	0.252612i	$0.918710\pi$
$44$		−	7.45379i		−	0.169404i
$45$		0			0
$46$	33.9644			0.738356
$47$	−31.3977	+	8.41300i	−0.668037	+	0.179000i	−0.576870	−	0.816836i	$-0.695726\pi$
$47$	−31.3977	+	8.41300i	−0.668037	+	0.179000i	−0.0911665	+	0.995836i	$0.529060\pi$
$48$		0			0
$49$	−7.28159	+	4.20403i	−0.148604	+	0.0857965i
$50$	3.15966	−	53.1196i	0.0631933	−	1.06239i
$51$		0			0
$52$	−5.63471	+	1.50982i	−0.108360	+	0.0290349i
$53$	−45.4430	+	45.4430i	−0.857415	+	0.857415i	−0.991033	−	0.133618i	$-0.957341\pi$
$53$	−45.4430	+	45.4430i	−0.857415	+	0.857415i	0.133618	+	0.991033i	$0.457341\pi$
$54$		0			0
$55$	−69.8689	+	7.09452i	−1.27034	+	0.128991i
$56$	−23.5242	+	40.7452i	−0.420076	+	0.727593i
$57$		0			0
$58$	70.7849	+	18.9668i	1.22043	+	0.327013i
$59$	39.4795	−	22.7935i	0.669145	−	0.386331i	−0.126608	−	0.991953i	$-0.540409\pi$
$59$	39.4795	−	22.7935i	0.669145	−	0.386331i	0.795753	+	0.605622i	$0.207076\pi$
$60$		0			0
$61$	−6.18147	+	10.7066i	−0.101336	+	0.175518i	−0.912235	−	0.409667i	$-0.865645\pi$
$61$	−6.18147	+	10.7066i	−0.101336	+	0.175518i	0.810900	+	0.585185i	$0.198978\pi$
$62$	−74.3794	−	74.3794i	−1.19967	−	1.19967i
$63$		0			0
$64$		−	53.4055i		−	0.834461i
$65$	19.5155	+	51.3805i	0.300239	+	0.790469i
$66$		0			0
$67$	−31.4421	+	117.344i	−0.469286	+	1.75140i	0.172989	+	0.984924i	$0.444657\pi$
$67$	−31.4421	+	117.344i	−0.469286	+	1.75140i	−0.642275	+	0.766475i	$0.722009\pi$
$68$	11.4008	+	3.05483i	0.167659	+	0.0449240i
$69$		0			0
$70$	−61.8468	−	27.7977i	−0.883525	−	0.397110i
$71$	−48.1581			−0.678282			−0.339141	−	0.940735i	$-0.610136\pi$
$71$	−48.1581			−0.678282			−0.339141	+	0.940735i	$0.610136\pi$
$72$		0			0
$73$	−77.4961	+	77.4961i	−1.06159	+	1.06159i	−0.0636162	+	0.997974i	$0.520263\pi$
$73$	−77.4961	+	77.4961i	−1.06159	+	1.06159i	−0.997974	+	0.0636162i	$0.979737\pi$
$74$	−59.5400	−	34.3754i	−0.804594	−	0.464533i
$75$		0			0
$76$	−4.12219	−	7.13983i	−0.0542393	−	0.0939452i
$77$	−23.1610	+	86.4381i	−0.300792	+	1.12257i
$78$		0			0
$79$	114.870	+	66.3203i	1.45405	+	0.839497i	0.998708	−	0.0508186i	$-0.0161830\pi$
$79$	114.870	+	66.3203i	1.45405	+	0.839497i	0.455344	+	0.890316i	$0.349516\pi$
$80$	88.7492	−	9.01164i	1.10937	−	0.112645i
$81$		0			0
$82$	0.853308	+	0.853308i	0.0104062	+	0.0104062i
$83$	25.3200	+	94.4956i	0.305060	+	1.13850i	0.932893	+	0.360153i	$0.117276\pi$
$83$	25.3200	+	94.4956i	0.305060	+	1.13850i	−0.627833	+	0.778348i	$0.716058\pi$
$84$		0			0
$85$	17.7835	−	109.774i	0.209218	−	1.29146i
$86$	0.587625	+	1.01780i	0.00683285	+	0.0118348i
$87$		0			0
$88$	−26.8450	−	100.187i	−0.305057	−	1.13849i
$89$			119.880i			1.34697i	0.739202	+	0.673484i	$0.235203\pi$
$89$			119.880i			1.34697i	−0.739202	+	0.673484i	$0.764797\pi$
$90$		0			0
$91$	70.0345			0.769610
$92$	−8.17940	+	2.19166i	−0.0889065	+	0.0238224i
$93$		0			0
$94$	59.9193	−	34.5944i	0.637440	−	0.368026i
$95$	−63.0025	+	45.4354i	−0.663184	+	0.478268i
$96$		0			0
$97$	71.5242	−	19.1648i	0.737362	−	0.197576i	0.129457	−	0.991585i	$-0.458677\pi$
$97$	71.5242	−	19.1648i	0.737362	−	0.197576i	0.607906	+	0.794009i	$0.292010\pi$
$98$	12.6550	−	12.6550i	0.129133	−	0.129133i
$99$		0			0
$100$	2.66680	+	12.9963i	0.0266680	+	0.129963i
$101$	90.3436	−	156.480i	0.894491	−	1.54930i	0.0600581	−	0.998195i	$-0.480871\pi$
$101$	90.3436	−	156.480i	0.894491	−	1.54930i	0.834433	−	0.551109i	$-0.185795\pi$
$102$		0			0
$103$	−76.0198	−	20.3694i	−0.738056	−	0.197761i	−0.129842	−	0.991535i	$-0.541447\pi$
$103$	−76.0198	−	20.3694i	−0.738056	−	0.197761i	−0.608214	+	0.793773i	$0.708114\pi$
$104$	−70.2989	+	40.5871i	−0.675951	+	0.390260i
$105$		0			0
$106$	68.3965	−	118.466i	0.645250	−	1.11761i
$107$	−61.3219	−	61.3219i	−0.573102	−	0.573102i	0.359892	−	0.932994i	$-0.382813\pi$
$107$	−61.3219	−	61.3219i	−0.573102	−	0.573102i	−0.932994	+	0.359892i	$0.882813\pi$
$108$		0			0
$109$		−	202.258i		−	1.85557i	−0.373110	−	0.927787i	$-0.621709\pi$
$109$		−	202.258i		−	1.85557i	0.373110	−	0.927787i	$-0.378291\pi$
$110$	139.743	−	53.0777i	1.27039	−	0.482524i
$111$		0			0
$112$	29.4197	−	109.796i	0.262676	−	0.980319i
$113$	108.734	+	29.1353i	0.962252	+	0.257835i	0.705553	−	0.708657i	$-0.250699\pi$
$113$	108.734	+	29.1353i	0.962252	+	0.257835i	0.256699	+	0.966491i	$0.417365\pi$
$114$		0			0
$115$	28.3289	+	74.5844i	0.246339	+	0.648560i
$116$	−18.2705			−0.157505
$117$		0			0
$118$	−68.6133	+	68.6133i	−0.581469	+	0.581469i
$119$	−122.717	−	70.8509i	−1.03124	−	0.595385i
$120$		0			0
$121$	−38.1399	−	66.0603i	−0.315206	−	0.545953i
$122$	6.81083	−	25.4184i	0.0558265	−	0.208347i
$123$		0			0
$124$	22.7118	+	13.1127i	0.183160	+	0.105747i
$125$	119.284	−	37.3674i	0.954272	−	0.298939i
$126$		0			0
$127$	8.86658	+	8.86658i	0.0698156	+	0.0698156i	0.741152	−	0.671337i	$-0.234280\pi$
$127$	8.86658	+	8.86658i	0.0698156	+	0.0698156i	−0.671337	+	0.741152i	$0.734280\pi$
$128$	38.1563	+	142.401i	0.298096	+	1.11251i
$129$		0			0
$130$	−68.4301	−	94.8877i	−0.526385	−	0.729906i
$131$	11.4127	+	19.7674i	0.0871198	+	0.150896i	0.906293	−	0.422651i	$-0.138900\pi$
$131$	11.4127	+	19.7674i	0.0871198	+	0.150896i	−0.819173	+	0.573547i	$0.805567\pi$
$132$		0			0
$133$	25.6176	+	95.6060i	0.192613	+	0.718842i
$134$		−	258.582i		−	1.92971i
$135$		0			0
$136$	164.241			1.20765
$137$	80.6238	−	21.6031i	0.588495	−	0.157687i	0.0477295	−	0.998860i	$-0.484801\pi$
$137$	80.6238	−	21.6031i	0.588495	−	0.157687i	0.540765	+	0.841174i	$0.318135\pi$
$138$		0			0
$139$	101.699	−	58.7157i	0.731644	−	0.422415i	−0.0873791	−	0.996175i	$-0.527849\pi$
$139$	101.699	−	58.7157i	0.731644	−	0.422415i	0.819023	+	0.573760i	$0.194516\pi$
$140$	16.6879	+	2.70345i	0.119199	+	0.0193103i
$141$		0			0
$142$	99.0135	−	26.5306i	0.697278	−	0.186835i
$143$	−109.174	+	109.174i	−0.763453	+	0.763453i
$144$		0			0
$145$	17.3899	+	171.261i	0.119930	+	1.18111i
$146$	116.640	−	202.026i	0.798903	−	1.38374i
$147$		0			0
$148$	16.5568	+	4.43637i	0.111870	+	0.0299755i
$149$	94.4712	−	54.5429i	0.634035	−	0.366060i	−0.148278	−	0.988946i	$-0.547373\pi$
$149$	94.4712	−	54.5429i	0.634035	−	0.366060i	0.782313	+	0.622886i	$0.214040\pi$
$150$		0			0
$151$	−94.5773	+	163.813i	−0.626340	+	1.08485i	0.361940	+	0.932201i	$0.382114\pi$
$151$	−94.5773	+	163.813i	−0.626340	+	1.08485i	−0.988280	+	0.152651i	$0.951219\pi$
$152$	−81.1208	−	81.1208i	−0.533690	−	0.533690i
$153$		0			0
$154$		−	190.477i		−	1.23687i
$155$	101.296	−	225.372i	0.653522	−	1.45402i
$156$		0			0
$157$	31.7599	−	118.529i	0.202292	−	0.754965i	−0.787966	−	0.615719i	$-0.788866\pi$
$157$	31.7599	−	118.529i	0.202292	−	0.754965i	0.990258	−	0.139246i	$-0.0444677\pi$
$158$	−272.711	−	73.0726i	−1.72602	−	0.462485i
$159$		0			0
$160$	−39.4371	+	14.9792i	−0.246482	+	0.0936197i
$161$	101.663			0.631445
$162$		0			0
$163$	−55.2937	+	55.2937i	−0.339225	+	0.339225i	−0.856076	−	0.516851i	$-0.827104\pi$
$163$	−55.2937	+	55.2937i	−0.339225	+	0.339225i	0.516851	+	0.856076i	$0.327104\pi$
$164$	−0.260559	−	0.150434i	−0.00158877	−	0.000917278i
$165$		0			0
$166$	−104.117	−	180.335i	−0.627208	−	1.08636i
$167$	−34.4299	+	128.494i	−0.206167	+	0.769426i	0.782924	+	0.622118i	$0.213728\pi$
$167$	−34.4299	+	128.494i	−0.206167	+	0.769426i	−0.989091	+	0.147308i	$0.952939\pi$
$168$		0			0
$169$	−41.7142	−	24.0837i	−0.246830	−	0.142507i
$170$	23.9122	+	235.494i	0.140660	+	1.38526i
$171$		0			0
$172$	−0.207190	−	0.207190i	−0.00120459	−	0.00120459i
$173$	8.52392	+	31.8117i	0.0492712	+	0.183883i	0.986176	−	0.165703i	$-0.0529892\pi$
$173$	8.52392	+	31.8117i	0.0492712	+	0.183883i	−0.936905	+	0.349585i	$0.886322\pi$
$174$		0			0
$175$	9.45755	−	158.998i	0.0540432	−	0.908563i
$176$	125.295	+	217.017i	0.711903	+	1.23305i
$177$		0			0
$178$	−66.0428	−	246.475i	−0.371027	−	1.38469i
$179$		−	133.416i		−	0.745343i	−0.927963	−	0.372672i	$-0.878442\pi$
$179$		−	133.416i		−	0.745343i	0.927963	−	0.372672i	$-0.121558\pi$
$180$		0			0
$181$	−118.379			−0.654028			−0.327014	−	0.945020i	$-0.606042\pi$
$181$	−118.379			−0.654028			−0.327014	+	0.945020i	$0.606042\pi$
$182$	−143.992	+	38.5825i	−0.791163	+	0.211992i
$183$		0			0
$184$	−102.046	+	58.9166i	−0.554600	+	0.320199i
$185$	25.8261	−	159.419i	0.139600	−	0.861726i
$186$		0			0
$187$	301.745	−	80.8524i	1.61361	−	0.432366i
$188$	−12.1976	+	12.1976i	−0.0648810	+	0.0648810i
$189$		0			0
$190$	104.503	−	128.124i	0.550017	−	0.674339i
$191$	−71.3161	+	123.523i	−0.373383	+	0.646718i	−0.990084	−	0.140480i	$-0.955136\pi$
$191$	−71.3161	+	123.523i	−0.373383	+	0.646718i	0.616701	+	0.787198i	$0.288469\pi$
$192$		0			0
$193$	172.858	+	46.3171i	0.895636	+	0.239985i	0.677141	−	0.735853i	$-0.263219\pi$
$193$	172.858	+	46.3171i	0.895636	+	0.239985i	0.218495	+	0.975838i	$0.429885\pi$
$194$	−136.496	+	78.8063i	−0.703590	+	0.406218i
$195$		0			0
$196$	−2.23101	+	3.86422i	−0.0113827	+	0.0197154i
$197$	−45.6222	−	45.6222i	−0.231585	−	0.231585i	0.581769	−	0.813354i	$-0.302361\pi$
$197$	−45.6222	−	45.6222i	−0.231585	−	0.231585i	−0.813354	+	0.581769i	$0.802361\pi$
$198$		0			0
$199$			328.469i			1.65060i	0.564694	+	0.825300i	$0.308994\pi$
$199$			328.469i			1.65060i	−0.564694	+	0.825300i	$0.691006\pi$
$200$	82.6511	+	165.080i	0.413256	+	0.825398i
$201$		0			0
$202$	−99.5418	+	371.495i	−0.492781	+	1.83908i
$203$	211.875	+	56.7716i	1.04372	+	0.279663i
$204$		0			0
$205$	−1.16211	+	2.58556i	−0.00566881	+	0.0126125i
$206$	167.519			0.813200
$207$		0			0
$208$	138.675	−	138.675i	0.666708	−	0.666708i
$209$	−188.970	−	109.102i	−0.904164	−	0.522019i
$210$		0			0
$211$	146.953	+	254.531i	0.696461	+	1.20631i	0.969686	+	0.244356i	$0.0785764\pi$
$211$	146.953	+	254.531i	0.696461	+	1.20631i	−0.273225	+	0.961950i	$0.588090\pi$
$212$	−8.82702	+	32.9429i	−0.0416369	+	0.155391i
$213$		0			0
$214$	159.861	+	92.2959i	0.747015	+	0.431289i
$215$	−1.74492	+	2.13932i	−0.00811589	+	0.00995034i
$216$		0			0
$217$	−222.634	−	222.634i	−1.02596	−	1.02596i
$218$	111.425	+	415.844i	0.511124	+	1.90754i
$219$		0			0
$220$	−30.2283	+	21.7997i	−0.137401	+	0.0990895i
$221$	−122.241	−	211.728i	−0.553127	−	0.958044i
$222$		0			0
$223$	−45.2387	−	168.833i	−0.202864	−	0.757099i	−0.990090	−	0.140434i	$-0.955150\pi$
$223$	−45.2387	−	168.833i	−0.202864	−	0.757099i	0.787226	−	0.616665i	$-0.211516\pi$
$224$			53.7550i			0.239977i
$225$		0			0
$226$	−239.610			−1.06022
$227$	−174.790	+	46.8349i	−0.770002	+	0.206321i	−0.622372	−	0.782721i	$-0.713831\pi$
$227$	−174.790	+	46.8349i	−0.770002	+	0.206321i	−0.147629	+	0.989043i	$0.547164\pi$
$228$		0			0
$229$	−255.131	+	147.300i	−1.11411	+	0.643232i	−0.939891	−	0.341475i	$-0.889073\pi$
$229$	−255.131	+	147.300i	−1.11411	+	0.643232i	−0.174219	+	0.984707i	$0.555740\pi$
$230$	−99.3337	−	137.740i	−0.431886	−	0.598869i
$231$		0			0
$232$	−245.575	+	65.8017i	−1.05851	+	0.283628i
$233$	−297.567	+	297.567i	−1.27711	+	1.27711i	−0.334832	+	0.942278i	$0.608680\pi$
$233$	−297.567	+	297.567i	−1.27711	+	1.27711i	−0.942278	+	0.334832i	$0.891320\pi$
$234$		0			0
$235$	125.945	+	102.726i	0.535938	+	0.437132i
$236$	12.0962	−	20.9512i	0.0512549	−	0.0887761i
$237$		0			0
$238$	291.340	+	78.0644i	1.22412	+	0.328002i
$239$	7.15486	−	4.13086i	0.0299366	−	0.0172839i	−0.484957	−	0.874538i	$-0.661165\pi$
$239$	7.15486	−	4.13086i	0.0299366	−	0.0172839i	0.514894	+	0.857254i	$0.327831\pi$
$240$		0			0
$241$	−90.0470	+	155.966i	−0.373639	+	0.647162i	−0.990122	−	0.140206i	$-0.955223\pi$
$241$	−90.0470	+	155.966i	−0.373639	+	0.647162i	0.616483	+	0.787368i	$0.288557\pi$
$242$	114.809	+	114.809i	0.474418	+	0.474418i
$243$		0			0
$244$			6.56081i			0.0268886i
$245$	38.3452	+	17.2346i	0.156511	+	0.0703454i
$246$		0			0
$247$	−44.1987	+	164.952i	−0.178942	+	0.667822i
$248$	352.497	+	94.4512i	1.42136	+	0.380852i
$249$		0			0
$250$	−224.663	+	142.542i	−0.898654	+	0.570169i
$251$	−162.440			−0.647170			−0.323585	−	0.946199i	$-0.604888\pi$
$251$	−162.440			−0.647170			−0.323585	+	0.946199i	$0.604888\pi$
$252$		0			0
$253$	−158.478	+	158.478i	−0.626394	+	0.626394i
$254$	−23.1145	−	13.3451i	−0.0910018	−	0.0525399i
$255$		0			0
$256$	−50.0886	−	86.7560i	−0.195659	−	0.338891i
$257$	45.7352	−	170.686i	0.177958	−	0.664148i	−0.818071	−	0.575117i	$-0.804956\pi$
$257$	45.7352	−	170.686i	0.177958	−	0.664148i	0.996029	−	0.0890309i	$-0.0283770\pi$
$258$		0			0
$259$	−178.216	−	102.893i	−0.688093	−	0.397270i
$260$	22.6025	+	18.4355i	0.0869326	+	0.0709056i
$261$		0			0
$262$	−34.3546	−	34.3546i	−0.131124	−	0.131124i
$263$	−23.4884	−	87.6600i	−0.0893096	−	0.333308i	0.906786	−	0.421592i	$-0.138528\pi$
$263$	−23.4884	−	87.6600i	−0.0893096	−	0.333308i	−0.996095	+	0.0882837i	$0.971862\pi$
$264$		0			0
$265$	317.195	+	51.3860i	1.19696	+	0.193909i
$266$	−105.340	−	182.454i	−0.396015	−	0.685918i
$267$		0			0
$268$	16.6858	+	62.2724i	0.0622606	+	0.232360i
$269$		−	415.479i		−	1.54453i	−0.635301	−	0.772265i	$-0.719124\pi$
$269$		−	415.479i		−	1.54453i	0.635301	−	0.772265i	$-0.280876\pi$
$270$		0			0
$271$	164.446			0.606811			0.303405	−	0.952862i	$-0.401876\pi$
$271$	164.446			0.606811			0.303405	+	0.952862i	$0.401876\pi$
$272$	−383.284	+	102.701i	−1.40913	+	0.377576i
$273$		0			0
$274$	−153.862	+	88.8323i	−0.561541	+	0.324206i
$275$	233.113	+	262.599i	0.847684	+	0.954905i
$276$		0			0
$277$	−299.886	+	80.3543i	−1.08262	+	0.290088i	−0.755669	−	0.654953i	$-0.772688\pi$
$277$	−299.886	+	80.3543i	−1.08262	+	0.290088i	−0.326952	+	0.945041i	$0.606022\pi$
$278$	−176.747	+	176.747i	−0.635779	+	0.635779i
$279$		0			0
$280$	234.039	−	23.7644i	0.835854	−	0.0848730i
$281$	−221.587	+	383.800i	−0.788566	+	1.36584i	0.138279	+	0.990393i	$0.455843\pi$
$281$	−221.587	+	383.800i	−0.788566	+	1.36584i	−0.926845	+	0.375443i	$0.877491\pi$
$282$		0			0
$283$	15.2414	+	4.08392i	0.0538565	+	0.0144308i	0.285647	−	0.958335i	$-0.407792\pi$
$283$	15.2414	+	4.08392i	0.0538565	+	0.0144308i	−0.231790	+	0.972766i	$0.574458\pi$
$284$	−22.1328	+	12.7784i	−0.0779322	+	0.0449942i
$285$		0			0
$286$	164.318	−	284.607i	0.574539	−	0.995130i
$287$	2.55414	+	2.55414i	0.00889943	+	0.00889943i
$288$		0			0
$289$			205.664i			0.711640i
$290$	−130.103	−	342.534i	−0.448629	−	1.18115i
$291$		0			0
$292$	−15.0531	+	56.1791i	−0.0515518	+	0.192394i
$293$	−335.831	−	89.9857i	−1.14618	−	0.307119i	−0.364748	−	0.931106i	$-0.618845\pi$
$293$	−335.831	−	89.9857i	−1.14618	−	0.307119i	−0.781434	+	0.623988i	$0.785511\pi$
$294$		0			0
$295$	−207.901	−	93.4433i	−0.704749	−	0.316757i
$296$	238.518			0.805805
$297$		0			0
$298$	−164.186	+	164.186i	−0.550959	+	0.550959i
$299$	151.902	+	87.7008i	0.508034	+	0.293314i
$300$		0			0
$301$	1.75889	+	3.04648i	0.00584348	+	0.0101212i
$302$	104.207	−	388.904i	0.345055	−	1.28776i
$303$		0			0
$304$	240.035	+	138.584i	0.789588	+	0.455869i
$305$	61.4985	−	6.24459i	0.201634	−	0.0204741i
$306$		0			0
$307$	48.6485	+	48.6485i	0.158464	+	0.158464i	0.781886	−	0.623422i	$-0.214258\pi$
$307$	48.6485	+	48.6485i	0.158464	+	0.158464i	−0.623422	+	0.781886i	$0.714258\pi$
$308$	12.2912	+	45.8713i	0.0399064	+	0.148933i
$309$		0			0
$310$	−84.1066	+	519.173i	−0.271311	+	1.67475i
$311$	−155.769	−	269.800i	−0.500866	−	0.867525i	−1.00000		0.000999981i	$-0.999682\pi$
$311$	−155.769	−	269.800i	−0.500866	−	0.867525i	0.499134	−	0.866525i	$-0.333652\pi$
$312$		0			0
$313$	26.8749	+	100.298i	0.0858623	+	0.320442i	0.995476	−	0.0950125i	$-0.0302891\pi$
$313$	26.8749	+	100.298i	0.0858623	+	0.320442i	−0.909614	+	0.415455i	$0.863622\pi$
$314$			261.195i			0.831830i
$315$		0			0
$316$	70.3902			0.222754
$317$	−277.411	+	74.3321i	−0.875114	+	0.234486i	−0.668298	−	0.743894i	$-0.732977\pi$
$317$	−277.411	+	74.3321i	−0.875114	+	0.234486i	−0.206816	+	0.978380i	$0.566310\pi$
$318$		0			0
$319$	−418.781	+	241.783i	−1.31279	+	0.757942i
$320$	−216.582	+	156.192i	−0.676818	+	0.488100i
$321$		0			0
$322$	−209.020	+	56.0067i	−0.649130	+	0.173934i
$323$	244.322	−	244.322i	0.756413	−	0.756413i
$324$		0			0
$325$	151.294	−	229.414i	0.465519	−	0.705888i
$326$	83.2228	−	144.146i	0.255285	−	0.442166i
$327$		0			0
$328$	−4.04398	−	1.08358i	−0.0123292	−	0.00330360i
$329$	179.352	−	103.549i	0.545141	−	0.314738i
$330$		0			0
$331$	−196.224	+	339.870i	−0.592822	+	1.02680i	0.401028	+	0.916066i	$0.368653\pi$
$331$	−196.224	+	339.870i	−0.592822	+	1.02680i	−0.993850	+	0.110732i	$0.964680\pi$
$332$	36.7104	+	36.7104i	0.110573	+	0.110573i
$333$		0			0
$334$		−	283.153i		−	0.847764i
$335$	567.835	−	215.677i	1.69503	−	0.643813i
$336$		0			0
$337$	129.126	−	481.905i	0.383164	−	1.42999i	−0.457878	−	0.889015i	$-0.651390\pi$
$337$	129.126	−	481.905i	0.383164	−	1.42999i	0.841041	−	0.540971i	$-0.181943\pi$
$338$	99.0328	+	26.5358i	0.292997	+	0.0785082i
$339$		0			0
$340$	−20.9546	−	55.1693i	−0.0616312	−	0.162263i
$341$	694.108			2.03551
$342$		0			0
$343$	258.629	−	258.629i	0.754021	−	0.754021i
$344$	−3.53106	−	2.03866i	−0.0102647	−	0.00592633i
$345$		0			0
$346$	−35.0506	−	60.7094i	−0.101302	−	0.175461i
$347$	−10.1941	+	38.0448i	−0.0293777	+	0.109639i	−0.979058	−	0.203582i	$-0.934742\pi$
$347$	−10.1941	+	38.0448i	−0.0293777	+	0.109639i	0.949680	+	0.313221i	$0.101408\pi$
$348$		0			0
$349$	−64.7685	−	37.3941i	−0.185583	−	0.107147i	0.404330	−	0.914613i	$-0.367505\pi$
$349$	−64.7685	−	37.3941i	−0.185583	−	0.107147i	−0.589913	+	0.807467i	$0.700838\pi$
$350$	68.1485	+	332.113i	0.194710	+	0.948894i
$351$		0			0
$352$	−83.7963	−	83.7963i	−0.238058	−	0.238058i
$353$	−10.9753	−	40.9602i	−0.0310914	−	0.116035i	0.948636	−	0.316369i	$-0.102464\pi$
$353$	−10.9753	−	40.9602i	−0.0310914	−	0.116035i	−0.979728	+	0.200334i	$0.935797\pi$
$354$		0			0
$355$	140.845	+	195.301i	0.396747	+	0.550144i
$356$	31.8092	+	55.0952i	0.0893518	+	0.154762i
$357$		0			0
$358$	73.5000	+	274.306i	0.205307	+	0.766217i
$359$			138.605i			0.386086i	0.981190	+	0.193043i	$0.0618357\pi$
$359$			138.605i			0.386086i	−0.981190	+	0.193043i	$0.938164\pi$
$360$		0			0
$361$	119.652			0.331447
$362$	243.389	−	65.2158i	0.672344	−	0.180154i
$363$		0			0
$364$	32.1868	−	18.5831i	0.0884254	−	0.0510524i
$365$	540.928	+	87.6309i	1.48199	+	0.240085i
$366$		0			0
$367$	239.063	−	64.0568i	0.651399	−	0.174542i	0.0820377	−	0.996629i	$-0.473857\pi$
$367$	239.063	−	64.0568i	0.651399	−	0.174542i	0.569361	+	0.822087i	$0.307191\pi$
$368$	201.302	−	201.302i	0.547017	−	0.547017i
$369$		0			0
$370$	34.7264	+	341.996i	0.0938552	+	0.924313i
$371$	204.726	−	354.595i	0.551821	−	0.955782i
$372$		0			0
$373$	−229.403	−	61.4683i	−0.615021	−	0.164794i	−0.0621579	−	0.998066i	$-0.519798\pi$
$373$	−229.403	−	61.4683i	−0.615021	−	0.164794i	−0.552864	+	0.833272i	$0.686465\pi$
$374$	−575.849	+	332.467i	−1.53970	+	0.888949i
$375$		0			0
$376$	−120.019	+	207.879i	−0.319200	+	0.552870i
$377$	267.604	+	267.604i	0.709824	+	0.709824i
$378$		0			0
$379$			589.803i			1.55621i	0.628134	+	0.778105i	$0.283819\pi$
$379$			589.803i			1.55621i	−0.628134	+	0.778105i	$0.716181\pi$
$380$	−16.8991	+	37.5987i	−0.0444714	+	0.0989439i
$381$		0			0
$382$	78.5771	−	293.254i	0.205699	−	0.767680i
$383$	28.3616	+	7.59948i	0.0740513	+	0.0198420i	0.295654	−	0.955295i	$-0.404462\pi$
$383$	28.3616	+	7.59948i	0.0740513	+	0.0198420i	−0.221603	+	0.975137i	$0.571129\pi$
$384$		0			0
$385$	418.281	−	158.873i	1.08644	−	0.412657i
$386$	−380.914			−0.986823
$387$		0			0
$388$	27.7862	−	27.7862i	0.0716140	−	0.0716140i
$389$	−218.171	−	125.961i	−0.560852	−	0.323808i	0.192636	−	0.981270i	$-0.438296\pi$
$389$	−218.171	−	125.961i	−0.560852	−	0.323808i	−0.753487	+	0.657463i	$0.771630\pi$
$390$		0			0
$391$	−177.446	−	307.346i	−0.453827	−	0.786051i
$392$	−16.0701	+	59.9743i	−0.0409950	+	0.152996i
$393$		0			0
$394$	118.933	+	68.6662i	0.301861	+	0.174280i
$395$	−66.9974	−	659.810i	−0.169614	−	1.67040i
$396$		0			0
$397$	−471.289	−	471.289i	−1.18713	−	1.18713i	−0.977858	−	0.209269i	$-0.932892\pi$
$397$	−471.289	−	471.289i	−1.18713	−	1.18713i	−0.209269	−	0.977858i	$-0.567108\pi$
$398$	−180.956	−	675.337i	−0.454663	−	1.69683i
$399$		0			0
$400$	−296.106	−	333.560i	−0.740265	−	0.833899i
$401$	−22.2961	−	38.6179i	−0.0556012	−	0.0963041i	0.836885	−	0.547379i	$-0.184374\pi$
$401$	−22.2961	−	38.6179i	−0.0556012	−	0.0963041i	−0.892486	+	0.451075i	$0.851041\pi$
$402$		0			0
$403$	−140.596	−	524.713i	−0.348874	−	1.30202i
$404$		−	95.8878i		−	0.237346i
$405$		0			0
$406$	−466.893			−1.14998
$407$	438.209	−	117.418i	1.07668	−	0.288496i
$408$		0			0
$409$	−20.0292	+	11.5639i	−0.0489712	+	0.0282735i	−0.524286	−	0.851542i	$-0.675668\pi$
$409$	−20.0292	+	11.5639i	−0.0489712	+	0.0282735i	0.475315	+	0.879816i	$0.342334\pi$
$410$	0.964902	−	5.95615i	0.00235342	−	0.0145272i
$411$		0			0
$412$	−40.3425	+	10.8097i	−0.0979186	+	0.0262372i
$413$	−205.374	+	205.374i	−0.497275	+	0.497275i
$414$		0			0
$415$	309.168	−	379.049i	0.744982	−	0.913372i
$416$	−46.3725	+	80.3195i	−0.111472	+	0.193076i
$417$		0			0
$418$	448.630	+	120.210i	1.07328	+	0.287584i
$419$	−263.471	+	152.115i	−0.628810	+	0.363043i	−0.780291	−	0.625417i	$-0.784929\pi$
$419$	−263.471	+	152.115i	−0.628810	+	0.363043i	0.151481	+	0.988460i	$0.451596\pi$
$420$		0			0
$421$	−124.207	+	215.133i	−0.295029	+	0.511005i	−0.974992	−	0.222242i	$-0.928663\pi$
$421$	−124.207	+	215.133i	−0.295029	+	0.511005i	0.679963	+	0.733246i	$0.261996\pi$
$422$	−442.360	−	442.360i	−1.04825	−	1.04825i
$423$		0			0
$424$			474.578i			1.11929i
$425$	−497.191	+	248.930i	−1.16986	+	0.585719i
$426$		0			0
$427$	20.3863	−	76.0826i	0.0477430	−	0.178179i
$428$	−44.4539	−	11.9114i	−0.103864	−	0.0278304i
$429$		0			0
$430$	2.40900	−	5.35976i	0.00560233	−	0.0124646i
$431$	−553.040			−1.28316			−0.641578	−	0.767058i	$-0.721720\pi$
$431$	−553.040			−1.28316			−0.641578	+	0.767058i	$0.721720\pi$
$432$		0			0
$433$	257.444	−	257.444i	0.594560	−	0.594560i	−0.344300	−	0.938860i	$-0.611884\pi$
$433$	257.444	−	257.444i	0.594560	−	0.594560i	0.938860	+	0.344300i	$0.111884\pi$
$434$	580.388	+	335.087i	1.33730	+	0.772090i
$435$		0			0
$436$	−53.6674	−	92.9547i	−0.123090	−	0.213199i
$437$	−64.1593	+	239.446i	−0.146818	+	0.547931i
$438$		0			0
$439$	12.1098	+	6.99162i	0.0275851	+	0.0159262i	0.513729	−	0.857952i	$-0.328264\pi$
$439$	12.1098	+	6.99162i	0.0275851	+	0.0159262i	−0.486144	+	0.873879i	$0.661597\pi$
$440$	−327.788	+	401.879i	−0.744973	+	0.913361i
$441$		0			0
$442$	367.971	+	367.971i	0.832514	+	0.832514i
$443$	10.8984	+	40.6733i	0.0246013	+	0.0918133i	0.977135	−	0.212620i	$-0.0681996\pi$
$443$	10.8984	+	40.6733i	0.0246013	+	0.0918133i	−0.952534	+	0.304433i	$0.901533\pi$
$444$		0			0
$445$	486.165	−	350.607i	1.09251	−	0.787881i
$446$	186.022	+	322.200i	0.417091	+	0.722422i
$447$		0			0
$448$	88.0648	+	328.662i	0.196573	+	0.733621i
$449$		−	254.042i		−	0.565795i	−0.959150	−	0.282898i	$-0.908704\pi$
$449$		−	254.042i		−	0.565795i	0.959150	−	0.282898i	$-0.0912957\pi$
$450$		0			0
$451$	−7.96307			−0.0176565
$452$	57.7036	−	15.4616i	0.127663	−	0.0342072i
$453$		0			0
$454$	333.569	−	192.586i	0.734734	−	0.424199i
$455$	−204.826	−	284.019i	−0.450167	−	0.624219i
$456$		0			0
$457$	325.593	−	87.2425i	0.712458	−	0.190903i	0.115654	−	0.993290i	$-0.463104\pi$
$457$	325.593	−	87.2425i	0.712458	−	0.190903i	0.596804	+	0.802387i	$0.296437\pi$
$458$	443.404	−	443.404i	0.968131	−	0.968131i
$459$		0			0
$460$	32.8100	+	26.7611i	0.0713260	+	0.0581763i
$461$	−289.085	+	500.709i	−0.627082	+	1.08614i	0.361053	+	0.932545i	$0.382417\pi$
$461$	−289.085	+	500.709i	−0.627082	+	1.08614i	−0.988134	+	0.153592i	$0.950916\pi$
$462$		0			0
$463$	−270.741	−	72.5447i	−0.584753	−	0.156684i	−0.0456989	−	0.998955i	$-0.514551\pi$
$463$	−270.741	−	72.5447i	−0.584753	−	0.156684i	−0.539054	+	0.842271i	$0.681218\pi$
$464$	531.946	−	307.119i	1.14644	−	0.661895i
$465$		0			0
$466$	447.869	−	775.732i	0.961092	−	1.66466i
$467$	377.215	+	377.215i	0.807740	+	0.807740i	0.984291	−	0.176551i	$-0.0564942\pi$
$467$	377.215	+	377.215i	0.807740	+	0.807740i	−0.176551	+	0.984291i	$0.556494\pi$
$468$		0			0
$469$		−	773.991i		−	1.65030i
$470$	−315.538	−	141.822i	−0.671357	−	0.301748i
$471$		0			0
$472$	87.1292	−	325.170i	0.184596	−	0.688920i
$473$	−7.49089	−	2.00718i	−0.0158370	−	0.00424351i
$474$		0			0
$475$	368.520	+	122.619i	0.775831	+	0.258146i
$476$	−75.1988			−0.157981
$477$		0			0
$478$	−12.4348	+	12.4348i	−0.0260141	+	0.0260141i
$479$	603.903	+	348.664i	1.26076	+	0.727899i	0.973221	−	0.229871i	$-0.0738303\pi$
$479$	603.903	+	348.664i	1.26076	+	0.727899i	0.287537	+	0.957770i	$0.407164\pi$
$480$		0			0
$481$	−177.524	−	307.481i	−0.369074	−	0.639254i
$482$	99.2150	−	370.276i	0.205840	−	0.768206i
$483$		0			0
$484$	−35.0571	−	20.2402i	−0.0724321	−	0.0418187i
$485$	−286.904	−	234.010i	−0.591555	−	0.482496i
$486$		0			0
$487$	369.496	+	369.496i	0.758718	+	0.758718i	0.976089	−	0.217371i	$-0.0697481\pi$
$487$	369.496	+	369.496i	0.758718	+	0.758718i	−0.217371	+	0.976089i	$0.569748\pi$
$488$	23.6289	+	88.1843i	0.0484199	+	0.180706i
$489$		0			0
$490$	−88.3328	−	14.3100i	−0.180271	−	0.0292041i
$491$	55.5151	+	96.1550i	0.113065	+	0.195835i	0.917005	−	0.398876i	$-0.130600\pi$
$491$	55.5151	+	96.1550i	0.113065	+	0.195835i	−0.803939	+	0.594711i	$0.797266\pi$
$492$		0			0
$493$	−198.183	−	739.629i	−0.401994	−	1.50026i
$494$		−	363.493i		−	0.735815i
$495$		0			0
$496$	−881.673			−1.77757
$497$	296.369	−	79.4118i	0.596316	−	0.159782i
$498$		0			0
$499$	362.119	−	209.069i	0.725689	−	0.418977i	−0.0911538	−	0.995837i	$-0.529055\pi$
$499$	362.119	−	209.069i	0.725689	−	0.418977i	0.816843	+	0.576860i	$0.195722\pi$
$500$	44.9061	−	48.8246i	0.0898122	−	0.0976492i
$501$		0			0
$502$	333.978	−	89.4891i	0.665295	−	0.178265i
$503$	−496.065	+	496.065i	−0.986213	+	0.986213i	−0.999906	−	0.0136937i	$-0.995641\pi$
$503$	−496.065	+	496.065i	−0.986213	+	0.986213i	0.0136937	+	0.999906i	$0.495641\pi$
$504$		0			0
$505$	−898.814	+	91.2661i	−1.77983	+	0.180725i
$506$	238.526	−	413.138i	0.471394	−	0.816479i
$507$		0			0
$508$	6.42763	+	1.72228i	0.0126528	+	0.00339031i
$509$	−416.912	+	240.704i	−0.819081	+	0.472897i	−0.850099	−	0.526622i	$-0.823458\pi$
$509$	−416.912	+	240.704i	−0.819081	+	0.472897i	0.0310184	+	0.999519i	$0.490125\pi$
$510$		0			0
$511$	349.128	−	604.708i	0.683225	−	1.18338i
$512$	−266.203	−	266.203i	−0.519927	−	0.519927i
$513$		0			0
$514$			376.129i			0.731768i
$515$	139.724	+	367.866i	0.271309	+	0.714302i
$516$		0			0
$517$	−118.166	+	441.001i	−0.228561	+	0.853000i
$518$	423.099	+	113.369i	0.816793	+	0.218859i
$519$		0			0
$520$	370.197	+	166.389i	0.711917	+	0.319979i
$521$	−504.810			−0.968925			−0.484463	−	0.874812i	$-0.660985\pi$
$521$	−504.810			−0.968925			−0.484463	+	0.874812i	$0.660985\pi$
$522$		0			0
$523$	389.397	−	389.397i	0.744545	−	0.744545i	−0.228904	−	0.973449i	$-0.573514\pi$
$523$	389.397	−	389.397i	0.744545	−	0.744545i	0.973449	+	0.228904i	$0.0735143\pi$
$524$	10.4902	+	6.05653i	0.0200195	+	0.0115583i
$525$		0			0
$526$	96.5850	+	167.290i	0.183622	+	0.318042i
$527$	−284.470	+	1061.66i	−0.539792	+	2.01453i
$528$		0			0
$529$	−237.625	−	137.193i	−0.449196	−	0.259343i
$530$	−680.466	+	69.0949i	−1.28390	+	0.130368i
$531$		0			0
$532$	37.1418	+	37.1418i	0.0698153	+	0.0698153i
$533$	1.61297	+	6.01970i	0.00302622	+	0.0112940i
$534$		0			0
$535$	−69.3414	+	428.031i	−0.129610	+	0.800058i
$536$	448.551	+	776.913i	0.836849	+	1.44946i
$537$		0			0
$538$	228.890	+	854.229i	0.425446	+	1.58779i
$539$			118.096i			0.219103i
$540$		0			0
$541$	−110.976			−0.205131			−0.102565	−	0.994726i	$-0.532705\pi$
$541$	−110.976			−0.205131			−0.102565	+	0.994726i	$0.532705\pi$
$542$	−338.102	+	90.5942i	−0.623805	+	0.167148i
$543$		0			0
$544$	162.512	−	93.8261i	0.298735	−	0.172474i
$545$	−820.240	+	591.531i	−1.50503	+	1.08538i
$546$		0			0
$547$	210.140	−	56.3070i	0.384169	−	0.102938i	−0.0615654	−	0.998103i	$-0.519609\pi$
$547$	210.140	−	56.3070i	0.384169	−	0.102938i	0.445734	+	0.895165i	$0.352943\pi$
$548$	31.3213	−	31.3213i	0.0571557	−	0.0571557i
$549$		0			0
$550$	−623.951	−	411.483i	−1.13446	−	0.748151i
$551$	−267.428	+	463.199i	−0.485350	+	0.840651i
$552$		0			0
$553$	−816.282	−	218.722i	−1.47610	−	0.395519i
$554$	572.302	−	330.419i	1.03304	−	0.596424i
$555$		0			0
$556$	31.1595	−	53.9698i	0.0560422	−	0.0970680i
$557$	416.448	+	416.448i	0.747662	+	0.747662i	0.974040	−	0.226378i	$-0.0726884\pi$
$557$	416.448	+	416.448i	0.747662	+	0.747662i	−0.226378	+	0.974040i	$0.572688\pi$
$558$		0			0
$559$			6.06932i			0.0108575i
$560$	−531.310	+	201.804i	−0.948769	+	0.360365i
$561$		0			0
$562$	244.148	−	911.171i	0.434426	−	1.62130i
$563$	−739.834	−	198.238i	−1.31409	−	0.352110i	−0.467331	−	0.884082i	$-0.654784\pi$
$563$	−739.834	−	198.238i	−1.31409	−	0.352110i	−0.846762	+	0.531972i	$0.821451\pi$
$564$		0			0
$565$	−199.854	−	526.175i	−0.353723	−	0.931283i
$566$	−33.5864			−0.0593398
$567$		0			0
$568$	−251.466	+	251.466i	−0.442722	+	0.442722i
$569$	1.55238	+	0.896268i	0.00272826	+	0.00157516i	0.501364	−	0.865237i	$-0.332832\pi$
$569$	1.55238	+	0.896268i	0.00272826	+	0.00157516i	−0.498635	+	0.866812i	$0.666165\pi$
$570$		0			0
$571$	454.163	+	786.634i	0.795382	+	1.37764i	0.922596	+	0.385767i	$0.126063\pi$
$571$	454.163	+	786.634i	0.795382	+	1.37764i	−0.127214	+	0.991875i	$0.540603\pi$
$572$	−21.2063	+	79.1431i	−0.0370740	+	0.138362i
$573$		0			0
$574$	−6.65843	−	3.84424i	−0.0116000	−	0.00669729i
$575$	219.619	−	333.019i	0.381947	−	0.579163i
$576$		0			0
$577$	−518.888	−	518.888i	−0.899286	−	0.899286i	0.0960874	−	0.995373i	$-0.469367\pi$
$577$	−518.888	−	518.888i	−0.899286	−	0.899286i	−0.995373	+	0.0960874i	$0.969367\pi$
$578$	−113.302	−	422.848i	−0.196024	−	0.731570i
$579$		0			0
$580$	53.4348	+	74.0947i	0.0921290	+	0.127749i
$581$	−311.643	−	539.782i	−0.536391	−	0.929057i
$582$		0			0
$583$	233.625	+	871.901i	0.400729	+	1.49554i
$584$			809.321i			1.38582i
$585$		0			0
$586$	740.047			1.26288
$587$	475.752	−	127.477i	0.810481	−	0.217168i	0.170301	−	0.985392i	$-0.445526\pi$
$587$	475.752	−	127.477i	0.810481	−	0.217168i	0.640181	+	0.768224i	$0.278859\pi$
$588$		0			0
$589$	664.872	−	383.864i	1.12881	−	0.651721i
$590$	478.926	+	77.5864i	0.811738	+	0.131502i
$591$		0			0
$592$	−556.624	+	149.147i	−0.940243	+	0.251937i
$593$	528.279	−	528.279i	0.890858	−	0.890858i	−0.103746	−	0.994604i	$-0.533083\pi$
$593$	528.279	−	528.279i	0.890858	−	0.890858i	0.994604	+	0.103746i	$0.0330829\pi$
$594$		0			0
$595$	71.5743	+	704.884i	0.120293	+	1.18468i
$596$	28.9451	−	50.1343i	0.0485655	−	0.0841180i
$597$		0			0
$598$	−360.628	−	96.6300i	−0.603057	−	0.161589i
$599$	448.466	−	258.922i	0.748690	−	0.432257i	−0.0765301	−	0.997067i	$-0.524384\pi$
$599$	448.466	−	258.922i	0.748690	−	0.432257i	0.825221	+	0.564811i	$0.191051\pi$
$600$		0			0
$601$	51.0959	−	88.5006i	0.0850181	−	0.147256i	−0.820381	−	0.571818i	$-0.806239\pi$
$601$	51.0959	−	88.5006i	0.0850181	−	0.147256i	0.905399	+	0.424562i	$0.139572\pi$
$602$	−5.29462	−	5.29462i	−0.00879506	−	0.00879506i
$603$		0			0
$604$			100.381i			0.166194i
$605$	−156.357	+	347.876i	−0.258441	+	0.575002i
$606$		0			0
$607$	−230.837	+	861.496i	−0.380292	+	1.41927i	0.465164	+	0.885224i	$0.345995\pi$
$607$	−230.837	+	861.496i	−0.380292	+	1.41927i	−0.845456	+	0.534044i	$0.820671\pi$
$608$	−126.609	−	33.9247i	−0.208238	−	0.0557973i
$609$		0			0
$610$	−123.001	+	46.7189i	−0.201642	+	0.0765883i
$611$	357.311			0.584797
$612$		0			0
$613$	−91.7462	+	91.7462i	−0.149668	+	0.149668i	−0.777970	−	0.628302i	$-0.783750\pi$
$613$	−91.7462	+	91.7462i	−0.149668	+	0.149668i	0.628302	+	0.777970i	$0.283750\pi$
$614$	−126.823	−	73.2212i	−0.206552	−	0.119253i
$615$		0			0
$616$	330.413	+	572.292i	0.536385	+	0.929045i
$617$	212.585	−	793.378i	0.344546	−	1.28586i	−0.548595	−	0.836088i	$-0.684837\pi$
$617$	212.585	−	793.378i	0.344546	−	1.28586i	0.893142	−	0.449776i	$-0.148496\pi$
$618$		0			0
$619$	−1035.69	−	597.954i	−1.67316	−	0.965999i	−0.965852	−	0.259093i	$-0.916576\pi$
$619$	−1035.69	−	597.954i	−1.67316	−	0.965999i	−0.707308	−	0.706906i	$-0.750090\pi$
$620$	−13.2466	−	130.456i	−0.0213654	−	0.210413i
$621$		0			0
$622$	468.898	+	468.898i	0.753856	+	0.753856i
$623$	−197.680	−	737.753i	−0.317304	−	1.18419i
$624$		0			0
$625$	−500.404	−	374.461i	−0.800646	−	0.599137i
$626$	−110.510	−	191.409i	−0.176534	−	0.305766i
$627$		0			0
$628$	−16.8545	−	62.9017i	−0.0268383	−	0.100162i
$629$			718.375i			1.14209i
$630$		0			0
$631$	1072.92			1.70034			0.850171	−	0.526507i	$-0.176499\pi$
$631$	1072.92			1.70034			0.850171	+	0.526507i	$0.176499\pi$
$632$	946.119	−	253.512i	1.49702	−	0.401126i
$633$		0			0
$634$	529.410	−	305.655i	0.835032	−	0.482106i
$635$	10.0261	−	61.8894i	0.0157892	−	0.0974636i
$636$		0			0
$637$	89.2753	−	23.9212i	0.140150	−	0.0375530i
$638$	727.819	−	727.819i	1.14078	−	1.14078i
$639$		0			0
$640$	465.904	−	571.213i	0.727974	−	0.892520i
$641$	108.538	−	187.994i	0.169327	−	0.293282i	−0.768857	−	0.639421i	$-0.779174\pi$
$641$	108.538	−	187.994i	0.169327	−	0.293282i	0.938183	+	0.346139i	$0.112507\pi$
$642$		0			0
$643$	−384.240	−	102.957i	−0.597573	−	0.160119i	−0.0526611	−	0.998612i	$-0.516770\pi$
$643$	−384.240	−	102.957i	−0.597573	−	0.160119i	−0.544912	+	0.838493i	$0.683437\pi$
$644$	46.7227	−	26.9754i	0.0725508	−	0.0418872i
$645$		0			0
$646$	−367.730	+	636.926i	−0.569241	+	0.985954i
$647$	−308.718	−	308.718i	−0.477154	−	0.477154i	0.427067	−	0.904220i	$-0.359547\pi$
$647$	−308.718	−	308.718i	−0.477154	−	0.477154i	−0.904220	+	0.427067i	$0.859547\pi$
$648$		0			0
$649$		−	640.299i		−	0.986593i
$650$	−184.676	+	555.026i	−0.284117	+	0.853886i
$651$		0			0
$652$	−10.7405	+	40.0839i	−0.0164731	+	0.0614784i
$653$	−337.252	−	90.3665i	−0.516466	−	0.138387i	−0.00883466	−	0.999961i	$-0.502812\pi$
$653$	−337.252	−	90.3665i	−0.516466	−	0.138387i	−0.507632	+	0.861574i	$0.669479\pi$
$654$		0			0
$655$	46.7869	−	104.096i	0.0714304	−	0.158925i
$656$	10.1149			0.0154190
$657$		0			0
$658$	−311.703	+	311.703i	−0.473713	+	0.473713i
$659$	−366.440	−	211.564i	−0.556054	−	0.321038i	0.195506	−	0.980703i	$-0.437365\pi$
$659$	−366.440	−	211.564i	−0.556054	−	0.321038i	−0.751560	+	0.659664i	$0.770698\pi$
$660$		0			0
$661$	−223.082	−	386.390i	−0.337492	−	0.584554i	0.646468	−	0.762941i	$-0.276245\pi$
$661$	−223.082	−	386.390i	−0.337492	−	0.584554i	−0.983960	+	0.178387i	$0.942912\pi$
$662$	216.202	−	806.878i	0.326590	−	1.21885i
$663$		0			0
$664$	625.640	+	361.213i	0.942228	+	0.543996i
$665$	312.801	−	383.504i	0.470377	−	0.576697i
$666$		0			0
$667$	388.456	+	388.456i	0.582393	+	0.582393i
$668$	18.2714	+	68.1897i	0.0273524	+	0.102080i
$669$		0			0
$670$	−1048.66	+	756.260i	−1.56516	+	1.12875i
$671$	86.8227	+	150.381i	0.129393	+	0.224115i
$672$		0			0
$673$	127.705	+	476.600i	0.189754	+	0.708172i	0.993563	+	0.113284i	$0.0361370\pi$
$673$	127.705	+	476.600i	0.189754	+	0.708172i	−0.803808	+	0.594888i	$0.797196\pi$
$674$			1061.94i			1.57558i
$675$		0			0
$676$	−25.5617			−0.0378131
$677$	794.165	−	212.796i	1.17307	−	0.314322i	0.380893	−	0.924619i	$-0.375617\pi$
$677$	794.165	−	212.796i	1.17307	−	0.314322i	0.792172	+	0.610297i	$0.208950\pi$
$678$		0			0
$679$	−408.563	+	235.884i	−0.601714	+	0.347399i
$680$	−480.346	−	666.066i	−0.706391	−	0.979508i
$681$		0			0
$682$	−1427.09	+	382.389i	−2.09251	+	0.560687i
$683$	702.491	−	702.491i	1.02854	−	1.02854i	0.0289564	−	0.999581i	$-0.490782\pi$
$683$	702.491	−	702.491i	1.02854	−	1.02854i	0.999581	−	0.0289564i	$-0.00921838\pi$
$684$		0			0
$685$	−323.405	−	263.782i	−0.472125	−	0.385083i
$686$	−389.264	+	674.226i	−0.567441	+	0.982836i
$687$		0			0
$688$	9.51511	+	2.54957i	0.0138301	+	0.00370577i
$689$	611.793	−	353.219i	0.887944	−	0.512655i
$690$		0			0
$691$	−79.1995	+	137.178i	−0.114616	+	0.198520i	−0.917626	−	0.397445i	$-0.869897\pi$
$691$	−79.1995	+	137.178i	−0.114616	+	0.198520i	0.803010	+	0.595965i	$0.203230\pi$
$692$	12.3585	+	12.3585i	0.0178590	+	0.0178590i
$693$		0			0
$694$		−	83.8365i		−	0.120802i
$695$	−535.549	−	240.708i	−0.770574	−	0.346343i
$696$		0			0
$697$	3.26355	−	12.1797i	0.00468228	−	0.0174745i
$698$	153.766	+	41.2014i	0.220295	+	0.0590277i
$699$		0			0
$700$	−37.8424	−	75.5829i	−0.0540606	−	0.107976i
$701$	−567.989			−0.810255			−0.405128	−	0.914260i	$-0.632773\pi$
$701$	−567.989			−0.810255			−0.405128	+	0.914260i	$0.632773\pi$
$702$		0			0
$703$	354.816	−	354.816i	0.504716	−	0.504716i
$704$	−649.618	−	375.057i	−0.922753	−	0.532752i
$705$		0			0
$706$	45.1305	+	78.1684i	0.0639243	+	0.110720i
$707$	−297.950	+	1111.97i	−0.421429	+	1.57279i
$708$		0			0
$709$	175.177	+	101.139i	0.247077	+	0.142650i	0.618425	−	0.785844i	$-0.287771\pi$
$709$	175.177	+	101.139i	0.247077	+	0.142650i	−0.371348	+	0.928494i	$0.621104\pi$
$710$	−397.172	−	323.949i	−0.559397	−	0.456266i
$711$		0			0
$712$	625.977	+	625.977i	0.879181	+	0.879181i
$713$	−204.091	−	761.677i	−0.286242	−	1.06827i
$714$		0			0
$715$	762.040	+	123.451i	1.06579	+	0.172659i
$716$	−35.4010	−	61.3163i	−0.0494427	−	0.0856373i
$717$		0			0
$718$	−76.3584	−	284.974i	−0.106349	−	0.396899i
$719$			842.936i			1.17237i	0.810176	+	0.586186i	$0.199371\pi$
$719$			842.936i			1.17237i	−0.810176	+	0.586186i	$0.800629\pi$
$720$		0			0
$721$	501.421			0.695452
$722$	−246.006	+	65.9172i	−0.340729	+	0.0912981i
$723$		0			0
$724$	−54.4053	+	31.4109i	−0.0751455	+	0.0433852i
$725$	643.675	−	571.400i	0.887828	−	0.788138i
$726$		0			0
$727$	−638.604	+	171.114i	−0.878410	+	0.235369i	−0.669721	−	0.742613i	$-0.733586\pi$
$727$	−638.604	+	171.114i	−0.878410	+	0.235369i	−0.208689	+	0.977982i	$0.566920\pi$
$728$	365.698	−	365.698i	0.502333	−	0.502333i
$729$		0			0
$730$	−1160.43	+	117.831i	−1.58963	+	0.161412i
$731$	6.14007	−	10.6349i	0.00839955	−	0.0145485i
$732$		0			0
$733$	−211.707	−	56.7266i	−0.288822	−	0.0773896i	0.111499	−	0.993765i	$-0.464435\pi$
$733$	−211.707	−	56.7266i	−0.288822	−	0.0773896i	−0.400321	+	0.916375i	$0.631101\pi$
$734$	−456.228	+	263.403i	−0.621564	+	0.358860i
$735$		0			0
$736$	−67.3148	+	116.593i	−0.0914603	+	0.158414i
$737$	1206.54	+	1206.54i	1.63710	+	1.63710i
$738$		0			0
$739$		−	311.453i		−	0.421451i	−0.977545	−	0.210726i	$-0.932417\pi$
$739$		−	311.453i		−	0.421451i	0.977545	−	0.210726i	$-0.0675827\pi$
$740$	−30.4313	−	80.1195i	−0.0411234	−	0.108270i
$741$		0			0
$742$	−225.569	+	841.836i	−0.304002	+	1.13455i
$743$	44.6785	+	11.9716i	0.0601326	+	0.0161125i	0.288760	−	0.957402i	$-0.406757\pi$
$743$	44.6785	+	11.9716i	0.0601326	+	0.0161125i	−0.228627	+	0.973514i	$0.573424\pi$
$744$		0			0
$745$	−497.489	−	223.602i	−0.667771	−	0.300137i
$746$	505.519			0.677639
$747$		0			0
$748$	117.224	−	117.224i	0.156717	−	0.156717i
$749$	478.499	+	276.262i	0.638851	+	0.368841i
$750$		0			0
$751$	503.153	+	871.487i	0.669978	+	1.16044i	0.977910	+	0.209027i	$0.0670297\pi$
$751$	503.153	+	871.487i	0.669978	+	1.16044i	−0.307932	+	0.951408i	$0.599637\pi$
$752$	150.097	−	560.170i	0.199597	−	0.744907i
$753$		0			0
$754$	−697.621	−	402.772i	−0.925227	−	0.534180i
$755$	940.935	−	95.5430i	1.24627	−	0.126547i
$756$		0			0
$757$	511.251	+	511.251i	0.675364	+	0.675364i	0.958948	−	0.283583i	$-0.0915233\pi$
$757$	511.251	+	511.251i	0.675364	+	0.675364i	−0.283583	+	0.958948i	$0.591523\pi$
$758$	−324.927	−	1212.64i	−0.428663	−	1.59979i
$759$		0			0
$760$	−91.7297	+	566.229i	−0.120697	+	0.745038i
$761$	−268.202	−	464.540i	−0.352434	−	0.610434i	0.634241	−	0.773135i	$-0.281313\pi$
$761$	−268.202	−	464.540i	−0.352434	−	0.610434i	−0.986675	+	0.162701i	$0.947979\pi$
$762$		0			0
$763$	333.519	+	1244.71i	0.437116	+	1.63134i
$764$			75.6926i			0.0990741i
$765$		0			0
$766$	−62.4985			−0.0815907
$767$	−484.036	+	129.697i	−0.631076	+	0.169096i
$768$		0			0
$769$	397.833	−	229.689i	0.517338	−	0.298685i	−0.218507	−	0.975835i	$-0.570119\pi$
$769$	397.833	−	229.689i	0.517338	−	0.298685i	0.735845	+	0.677150i	$0.236785\pi$
$770$	−772.466	+	557.078i	−1.00320	+	0.723478i
$771$		0			0
$772$	91.7328	−	24.5797i	0.118825	−	0.0318390i
$773$	−229.707	+	229.707i	−0.297163	+	0.297163i	−0.839902	−	0.542739i	$-0.817387\pi$
$773$	−229.707	+	229.707i	−0.297163	+	0.297163i	0.542739	+	0.839902i	$0.317387\pi$
$774$		0			0
$775$	−1210.24	+	248.336i	−1.56159	+	0.320434i
$776$	273.404	−	473.549i	0.352325	−	0.610244i
$777$		0			0
$778$	517.956	+	138.786i	0.665753	+	0.178388i
$779$	−7.62766	+	4.40383i	−0.00979161	+	0.00565319i
$780$		0			0
$781$	−338.205	+	585.789i	−0.433041	+	0.750049i
$782$	534.151	+	534.151i	0.683057	+	0.683057i
$783$		0			0
$784$		−	150.009i		−	0.191338i
$785$	−573.573	+	217.857i	−0.730667	+	0.277525i
$786$		0			0
$787$	−111.429	+	415.860i	−0.141587	+	0.528411i	0.858296	+	0.513154i	$0.171523\pi$
$787$	−111.429	+	415.860i	−0.141587	+	0.528411i	−0.999884	+	0.0152567i	$0.995143\pi$
$788$	−33.0728	−	8.86183i	−0.0419705	−	0.0112460i
$789$		0			0
$790$	501.241	+	1319.67i	0.634483	+	1.67047i
$791$	−717.205			−0.906707
$792$		0			0
$793$	96.0946	−	96.0946i	0.121179	−	0.121179i
$794$	1228.61	+	709.340i	1.54737	+	0.893375i
$795$		0			0
$796$	87.1567	+	150.960i	0.109493	+	0.189648i
$797$	16.9281	−	63.1765i	0.0212398	−	0.0792679i	−0.954492	−	0.298235i	$-0.903602\pi$
$797$	16.9281	−	63.1765i	0.0212398	−	0.0792679i	0.975732	+	0.218967i	$0.0702688\pi$
$798$		0			0
$799$	−626.095	−	361.476i	−0.783598	−	0.452411i
$800$	176.086	+	116.125i	0.220108	+	0.145157i
$801$		0			0
$802$	67.1159	+	67.1159i	0.0836856	+	0.0836856i
$803$	398.412	+	1486.89i	0.496155	+	1.85167i
$804$		0			0
$805$	−297.327	−	412.285i	−0.369351	−	0.512156i
$806$	578.135	+	1001.36i	0.717290	+	1.24238i
$807$		0			0
$808$	−345.342	−	1288.83i	−0.427403	−	1.59509i
$809$		−	108.424i		−	0.134022i	−0.997752	−	0.0670111i	$-0.978654\pi$
$809$		−	108.424i		−	0.134022i	0.997752	−	0.0670111i	$-0.0213463\pi$
$810$		0			0
$811$	−182.633			−0.225195			−0.112597	−	0.993641i	$-0.535917\pi$
$811$	−182.633			−0.225195			−0.112597	+	0.993641i	$0.535917\pi$
$812$	112.438	−	30.1278i	0.138471	−	0.0371032i
$813$		0			0
$814$	−836.277	+	482.825i	−1.02737	+	0.593151i
$815$	385.954	+	62.5249i	0.473563	+	0.0767176i
$816$		0			0
$817$	−8.28541	+	2.22007i	−0.0101413	+	0.00271734i
$818$	34.8097	−	34.8097i	0.0425546	−	0.0425546i
$819$		0			0
$820$	0.151970	+	1.49664i	0.000185329	+	0.00182517i
$821$	−307.529	+	532.656i	−0.374579	+	0.648789i	−0.990264	−	0.139203i	$-0.955546\pi$
$821$	−307.529	+	532.656i	−0.374579	+	0.648789i	0.615685	+	0.787992i	$0.288879\pi$
$822$		0			0
$823$	−1036.95	−	277.850i	−1.25996	−	0.337606i	−0.433785	−	0.901016i	$-0.642822\pi$
$823$	−1036.95	−	277.850i	−1.25996	−	0.337606i	−0.826177	+	0.563410i	$0.809489\pi$
$824$	−503.314	+	290.589i	−0.610818	+	0.352656i
$825$		0			0
$826$	309.110	−	535.395i	0.374225	−	0.648177i
$827$	−850.244	−	850.244i	−1.02811	−	1.02811i	−0.999593	−	0.0285125i	$-0.990923\pi$
$827$	−850.244	−	850.244i	−1.02811	−	1.02811i	−0.0285125	−	0.999593i	$-0.509077\pi$
$828$		0			0
$829$			76.6013i			0.0924021i	0.998932	+	0.0462010i	$0.0147115\pi$
$829$			76.6013i			0.0924021i	−0.998932	+	0.0462010i	$0.985289\pi$
$830$	−426.831	+	949.653i	−0.514255	+	1.14416i
$831$		0			0
$832$	−151.941	+	567.051i	−0.182621	+	0.681551i
$833$	−180.632	−	48.4002i	−0.216845	−	0.0581034i
$834$		0			0
$835$	621.793	−	236.172i	0.744662	−	0.282841i
$836$	−115.797			−0.138514
$837$		0			0
$838$	457.899	−	457.899i	0.546419	−	0.546419i
$839$	15.6364	+	9.02767i	0.0186369	+	0.0107600i	0.509290	−	0.860595i	$-0.329908\pi$
$839$	15.6364	+	9.02767i	0.0186369	+	0.0107600i	−0.490653	+	0.871355i	$0.663242\pi$
$840$		0			0
$841$	172.153	+	298.177i	0.204700	+	0.354551i
$842$	136.853	−	510.742i	0.162533	−	0.606582i
$843$		0			0
$844$	135.075	+	77.9857i	0.160042	+	0.0924002i
$845$	24.3296	+	239.605i	0.0287925	+	0.283556i
$846$		0			0
$847$	343.649	+	343.649i	0.405725	+	0.405725i
$848$	−296.756	−	1107.51i	−0.349949	−	1.30603i
$849$		0			0
$850$	885.093	−	785.710i	1.04129	−	0.924364i
$851$	−257.696	−	446.343i	−0.302816	−	0.524492i
$852$		0			0
$853$	−54.1951	−	202.259i	−0.0635347	−	0.237115i	0.926855	−	0.375420i	$-0.122501\pi$
$853$	−54.1951	−	202.259i	−0.0635347	−	0.237115i	−0.990390	+	0.138305i	$0.955835\pi$
$854$			167.658i			0.196321i
$855$		0			0
$856$	−640.407			−0.748139
$857$	−374.050	+	100.226i	−0.436464	+	0.116950i	−0.470359	−	0.882475i	$-0.655876\pi$
$857$	−374.050	+	100.226i	−0.436464	+	0.116950i	0.0338947	+	0.999425i	$0.489209\pi$
$858$		0			0
$859$	330.468	−	190.796i	0.384712	−	0.222114i	−0.295154	−	0.955450i	$-0.595371\pi$
$859$	330.468	−	190.796i	0.384712	−	0.222114i	0.679866	+	0.733336i	$0.262038\pi$
$860$	−0.234286	+	1.44620i	−0.000272426	+	0.00168163i
$861$		0			0
$862$	1137.06	−	304.673i	1.31909	−	0.353449i
$863$	−653.316	+	653.316i	−0.757029	+	0.757029i	−0.975781	−	0.218752i	$-0.929802\pi$
$863$	−653.316	+	653.316i	−0.757029	+	0.757029i	0.218752	+	0.975781i	$0.429802\pi$
$864$		0			0
$865$	104.080	−	127.606i	0.120324	−	0.147521i
$866$	−387.481	+	671.136i	−0.447437	+	0.774984i
$867$		0			0
$868$	−161.393	−	43.2452i	−0.185937	−	0.0498216i
$869$	1613.42	−	931.510i	1.85664	−	1.07193i
$870$		0			0
$871$	667.695	−	1156.48i	0.766584	−	1.32776i
$872$	−1056.13	−	1056.13i	−1.21115	−	1.21115i
$873$		0			0
$874$		−	527.649i		−	0.603717i
$875$	−672.466	+	426.660i	−0.768533	+	0.487611i
$876$		0			0
$877$	32.4798	−	121.216i	0.0370351	−	0.138217i	−0.944933	−	0.327264i	$-0.893873\pi$
$877$	32.4798	−	121.216i	0.0370351	−	0.138217i	0.981968	+	0.189047i	$0.0605400\pi$
$878$	−28.7497	−	7.70346i	−0.0327445	−	0.00877387i
$879$		0			0
$880$	513.653	−	1142.82i	0.583697	−	1.29866i
$881$	−515.743			−0.585406			−0.292703	−	0.956203i	$-0.594555\pi$
$881$	−515.743			−0.585406			−0.292703	+	0.956203i	$0.594555\pi$
$882$		0			0
$883$	61.1931	−	61.1931i	0.0693014	−	0.0693014i	−0.671607	−	0.740908i	$-0.734395\pi$
$883$	61.1931	−	61.1931i	0.0693014	−	0.0693014i	0.740908	+	0.671607i	$0.234395\pi$
$884$	−112.360	−	64.8714i	−0.127105	−	0.0733839i
$885$		0			0
$886$	−44.8144	−	77.6208i	−0.0505806	−	0.0876081i
$887$	−106.220	+	396.418i	−0.119752	+	0.446920i	−0.999598	−	0.0283378i	$-0.990979\pi$
$887$	−106.220	+	396.418i	−0.119752	+	0.446920i	0.879846	+	0.475258i	$0.157645\pi$
$888$		0			0
$889$	−69.1866	−	39.9449i	−0.0778252	−	0.0449324i
$890$	−806.409	+	988.684i	−0.906077	+	1.11088i
$891$		0			0
$892$	−65.5895	−	65.5895i	−0.0735309	−	0.0735309i
$893$	130.699	+	487.775i	0.146360	+	0.546221i
$894$		0			0
$895$	−541.060	+	390.196i	−0.604536	+	0.435973i
$896$	−469.634	−	813.431i	−0.524146	−	0.907847i
$897$		0			0
$898$	139.954	+	522.314i	0.155850	+	0.581641i
$899$		−	1701.38i		−	1.89252i
$900$		0			0
$901$	−1429.35			−1.58640
$902$	16.3722	−	4.38691i	0.0181510	−	0.00486354i
$903$		0			0
$904$	719.913	−	415.642i	0.796364	−	0.459781i
$905$	346.217	+	480.077i	0.382560	+	0.530472i
$906$		0			0
$907$	190.103	−	50.9379i	0.209595	−	0.0561609i	−0.152494	−	0.988304i	$-0.548730\pi$
$907$	190.103	−	50.9379i	0.209595	−	0.0561609i	0.362089	+	0.932144i	$0.382064\pi$
$908$	−67.9039	+	67.9039i	−0.0747840	+	0.0747840i
$909$		0			0
$910$	577.593	+	471.107i	0.634718	+	0.517700i
$911$	439.391	−	761.048i	0.482318	−	0.835399i	−0.517476	−	0.855698i	$-0.673128\pi$
$911$	439.391	−	761.048i	0.482318	−	0.835399i	0.999794	+	0.0202989i	$0.00646178\pi$
$912$		0			0
$913$	1327.25	+	355.636i	1.45372	+	0.389524i
$914$	−621.361	+	358.743i	−0.679826	+	0.392498i
$915$		0			0
$916$	−78.1698	+	135.394i	−0.0853382	+	0.147810i
$917$	−102.831	−	102.831i	−0.112138	−	0.112138i
$918$		0			0
$919$			922.414i			1.00372i	0.864950	+	0.501858i	$0.167350\pi$
$919$			922.414i			1.00372i	−0.864950	+	0.501858i	$0.832650\pi$
$920$	537.381	+	241.532i	0.584110	+	0.262534i
$921$		0			0
$922$	318.517	−	1188.72i	0.345464	−	1.28929i
$923$	511.334	+	137.012i	0.553991	+	0.148442i
$924$		0			0
$925$	−722.045	+	361.509i	−0.780589	+	0.390821i
$926$	596.611			0.644289
$927$		0			0
$928$	−205.399	+	205.399i	−0.221335	+	0.221335i
$929$	64.0110	+	36.9568i	0.0689031	+	0.0397812i	0.534056	−	0.845449i	$-0.320667\pi$
$929$	64.0110	+	36.9568i	0.0689031	+	0.0397812i	−0.465153	+	0.885230i	$0.654001\pi$
$930$		0			0
$931$	65.3111	+	113.122i	0.0701516	+	0.121506i
$932$	−57.8005	+	215.714i	−0.0620177	+	0.231453i
$933$		0			0
$934$	−983.368	−	567.748i	−1.05286	−	0.607867i
$935$	−1210.39	−	987.240i	−1.29453	−	1.05587i
$936$		0			0
$937$	−732.726	−	732.726i	−0.781992	−	0.781992i	0.198175	−	0.980167i	$-0.436499\pi$
$937$	−732.726	−	732.726i	−0.781992	−	0.781992i	−0.980167	+	0.198175i	$0.936499\pi$
$938$	426.397	+	1591.33i	0.454581	+	1.69652i
$939$		0			0
$940$	85.1403	+	13.7928i	0.0905748	+	0.0146732i
$941$	374.739	+	649.067i	0.398235	+	0.689763i	0.993508	−	0.113760i	$-0.0362896\pi$
$941$	374.739	+	649.067i	0.398235	+	0.689763i	−0.595273	+	0.803523i	$0.702956\pi$
$942$		0			0
$943$	2.34141	+	8.73825i	0.00248293	+	0.00926644i
$944$			813.324i			0.861572i
$945$		0			0
$946$	16.5071			0.0174494
$947$	426.171	−	114.192i	0.450022	−	0.120583i	−0.0266874	−	0.999644i	$-0.508496\pi$
$947$	426.171	−	114.192i	0.450022	−	0.120583i	0.476710	+	0.879061i	$0.341829\pi$
$948$		0			0
$949$	1043.32	−	602.361i	1.09939	−	0.634732i
$950$	−825.233	−	49.0865i	−0.868666	−	0.0516700i
$951$		0			0
$952$	−1010.75	+	270.830i	−1.06171	+	0.284485i
$953$	838.669	−	838.669i	0.880030	−	0.880030i	−0.113507	−	0.993537i	$-0.536208\pi$
$953$	838.669	−	838.669i	0.880030	−	0.880030i	0.993537	+	0.113507i	$0.0362084\pi$
$954$		0			0
$955$	709.513	−	72.0443i	0.742946	−	0.0754391i
$956$	2.19218	−	3.79697i	0.00229307	−	0.00397172i
$957$		0			0
$958$	−1433.71	−	384.162i	−1.49657	−	0.401005i
$959$	−460.543	+	265.894i	−0.480232	+	0.277262i
$960$		0			0
$961$	−740.572	+	1282.71i	−0.770627	+	1.33476i
$962$	534.386	+	534.386i	0.555495	+	0.555495i
$963$		0			0
$964$			95.5730i			0.0991421i
$965$	−317.712	−	836.472i	−0.329235	−	0.866810i
$966$		0			0
$967$	356.813	−	1331.65i	0.368990	−	1.37709i	−0.492940	−	0.870063i	$-0.664078\pi$
$967$	356.813	−	1331.65i	0.368990	−	1.37709i	0.861930	−	0.507027i	$-0.169255\pi$
$968$	−544.101	−	145.791i	−0.562088	−	0.150611i
$969$		0			0
$970$	718.797	+	323.071i	0.741027	+	0.333062i
$971$	−1716.72			−1.76800			−0.883998	−	0.467491i	$-0.845158\pi$
$971$	−1716.72			−1.76800			−0.883998	+	0.467491i	$0.845158\pi$
$972$		0			0
$973$	−529.041	+	529.041i	−0.543721	+	0.543721i
$974$	−963.246	−	556.130i	−0.988958	−	0.570975i
$975$		0			0
$976$	−110.284	−	191.018i	−0.112996	−	0.195715i
$977$	−308.607	+	1151.74i	−0.315872	+	1.17885i	0.607303	+	0.794470i	$0.292251\pi$
$977$	−308.607	+	1151.74i	−0.315872	+	1.17885i	−0.923175	+	0.384380i	$0.874415\pi$
$978$		0			0
$979$	1458.21	+	841.897i	1.48949	+	0.859956i
$980$	22.1960	−	2.25379i	0.0226489	−	0.00229978i
$981$		0			0
$982$	−167.112	−	167.112i	−0.170175	−	0.170175i
$983$	−102.104	−	381.057i	−0.103870	−	0.387647i	0.894345	−	0.447378i	$-0.147642\pi$
$983$	−102.104	−	381.057i	−0.103870	−	0.387647i	−0.998214	+	0.0597315i	$0.980976\pi$
$984$		0			0
$985$	−51.5886	+	318.446i	−0.0523742	+	0.323295i
$986$	814.933	+	1411.51i	0.826505	+	1.43155i
$987$		0			0
$988$	23.4556	+	87.5373i	0.0237404	+	0.0886005i
$989$			8.81029i			0.00890828i
$990$		0			0
$991$	567.310			0.572462			0.286231	−	0.958161i	$-0.407598\pi$
$991$	567.310			0.572462			0.286231	+	0.958161i	$0.407598\pi$
$992$	402.743	−	107.915i	0.405991	−	0.108785i
$993$		0			0
$994$	−565.590	+	326.543i	−0.569004	+	0.328514i
$995$	1332.08	−	960.656i	1.33878	−	0.965484i
$996$		0			0
$997$	1648.08	−	441.602i	1.65304	−	0.442931i	0.692579	−	0.721342i	$-0.256475\pi$
$997$	1648.08	−	441.602i	1.65304	−	0.442931i	0.960462	+	0.278411i	$0.0898079\pi$
$998$	−629.343	+	629.343i	−0.630604	+	0.630604i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.k.217.2		16
3.2	odd	2		405.3.l.l.217.3		16
5.3	odd	4	inner	405.3.l.k.298.3		16
9.2	odd	6		405.3.g.c.82.2	✓	8
9.4	even	3	inner	405.3.l.k.352.3		16
9.5	odd	6		405.3.l.l.352.2		16
9.7	even	3		405.3.g.e.82.3	yes	8
15.8	even	4		405.3.l.l.298.2		16
45.13	odd	12	inner	405.3.l.k.28.2		16
45.23	even	12		405.3.l.l.28.3		16
45.38	even	12		405.3.g.c.163.2	yes	8
45.43	odd	12		405.3.g.e.163.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.c.82.2	✓	8	9.2	odd	6
405.3.g.c.163.2	yes	8	45.38	even	12
405.3.g.e.82.3	yes	8	9.7	even	3
405.3.g.e.163.3	yes	8	45.43	odd	12
405.3.l.k.28.2		16	45.13	odd	12	inner
405.3.l.k.217.2		16	1.1	even	1	trivial
405.3.l.k.298.3		16	5.3	odd	4	inner
405.3.l.k.352.3		16	9.4	even	3	inner
405.3.l.l.28.3		16	45.23	even	12
405.3.l.l.217.3		16	3.2	odd	2
405.3.l.l.298.2		16	15.8	even	4
405.3.l.l.352.2		16	9.5	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05601 + 0.550907i) q^{2} +(0.459586 - 0.265342i) q^{4} +(-2.92464 - 4.05542i) q^{5} +(-6.15409 + 1.64898i) q^{7} +(5.22169 - 5.22169i) q^{8} +O(q^{10})\)	\(q+(-2.05601 + 0.550907i) q^{2} +(0.459586 - 0.265342i) q^{4} +(-2.92464 - 4.05542i) q^{5} +(-6.15409 + 1.64898i) q^{7} +(5.22169 - 5.22169i) q^{8} +(8.24726 + 6.72679i) q^{10} +(7.02282 - 12.1639i) q^{11} +(-10.6178 - 2.84504i) q^{13} +(11.7444 - 6.78066i) q^{14} +(-8.92056 + 15.4509i) q^{16} +(15.7268 + 15.7268i) q^{17} -15.5354i q^{19} +(-2.42020 - 1.08778i) q^{20} +(-7.73784 + 28.8780i) q^{22} +(-15.4129 - 4.12988i) q^{23} +(-7.89291 + 23.7213i) q^{25} +23.3977 q^{26} +(-2.39079 + 2.39079i) q^{28} +(-29.8158 - 17.2141i) q^{29} +(24.7090 + 42.7973i) q^{31} +(2.18371 - 8.14971i) q^{32} +(-40.9985 - 23.6705i) q^{34} +(24.6858 + 20.1347i) q^{35} +(22.8392 + 22.8392i) q^{37} +(8.55854 + 31.9409i) q^{38} +(-36.4477 - 5.90457i) q^{40} +(-0.283471 - 0.490987i) q^{41} +(-0.142904 - 0.533325i) q^{43} -7.45379i q^{44} +33.9644 q^{46} +(-31.3977 + 8.41300i) q^{47} +(-7.28159 + 4.20403i) q^{49} +(3.15966 - 53.1196i) q^{50} +(-5.63471 + 1.50982i) q^{52} +(-45.4430 + 45.4430i) q^{53} +(-69.8689 + 7.09452i) q^{55} +(-23.5242 + 40.7452i) q^{56} +(70.7849 + 18.9668i) q^{58} +(39.4795 - 22.7935i) q^{59} +(-6.18147 + 10.7066i) q^{61} +(-74.3794 - 74.3794i) q^{62} -53.4055i q^{64} +(19.5155 + 51.3805i) q^{65} +(-31.4421 + 117.344i) q^{67} +(11.4008 + 3.05483i) q^{68} +(-61.8468 - 27.7977i) q^{70} -48.1581 q^{71} +(-77.4961 + 77.4961i) q^{73} +(-59.5400 - 34.3754i) q^{74} +(-4.12219 - 7.13983i) q^{76} +(-23.1610 + 86.4381i) q^{77} +(114.870 + 66.3203i) q^{79} +(88.7492 - 9.01164i) q^{80} +(0.853308 + 0.853308i) q^{82} +(25.3200 + 94.4956i) q^{83} +(17.7835 - 109.774i) q^{85} +(0.587625 + 1.01780i) q^{86} +(-26.8450 - 100.187i) q^{88} +119.880i q^{89} +70.0345 q^{91} +(-8.17940 + 2.19166i) q^{92} +(59.9193 - 34.5944i) q^{94} +(-63.0025 + 45.4354i) q^{95} +(71.5242 - 19.1648i) q^{97} +(12.6550 - 12.6550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{5} - 26 q^{7} - 72 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^5 - 26 * q^7 - 72 * q^8	\( 16 q - 2 q^{2} - 2 q^{5} - 26 q^{7} - 72 q^{8} + 52 q^{10} + 20 q^{11} + 28 q^{13} + 76 q^{16} + 76 q^{17} - 12 q^{20} - 10 q^{22} - 68 q^{23} - 128 q^{25} + 248 q^{26} - 280 q^{28} + 116 q^{31} + 232 q^{32} + 28 q^{35} + 100 q^{37} - 66 q^{38} - 228 q^{40} - 316 q^{41} + 34 q^{43} - 16 q^{46} - 302 q^{47} + 22 q^{50} + 28 q^{52} - 236 q^{53} + 332 q^{55} + 420 q^{56} + 318 q^{58} - 112 q^{61} - 580 q^{62} + 112 q^{65} - 8 q^{67} - 76 q^{68} - 168 q^{70} - 496 q^{71} + 148 q^{73} + 48 q^{76} + 50 q^{77} + 1672 q^{80} + 44 q^{82} - 302 q^{83} - 86 q^{85} + 380 q^{86} + 636 q^{88} - 88 q^{91} - 416 q^{92} + 102 q^{95} + 178 q^{97} - 748 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^5 - 26 * q^7 - 72 * q^8 + 52 * q^10 + 20 * q^11 + 28 * q^13 + 76 * q^16 + 76 * q^17 - 12 * q^20 - 10 * q^22 - 68 * q^23 - 128 * q^25 + 248 * q^26 - 280 * q^28 + 116 * q^31 + 232 * q^32 + 28 * q^35 + 100 * q^37 - 66 * q^38 - 228 * q^40 - 316 * q^41 + 34 * q^43 - 16 * q^46 - 302 * q^47 + 22 * q^50 + 28 * q^52 - 236 * q^53 + 332 * q^55 + 420 * q^56 + 318 * q^58 - 112 * q^61 - 580 * q^62 + 112 * q^65 - 8 * q^67 - 76 * q^68 - 168 * q^70 - 496 * q^71 + 148 * q^73 + 48 * q^76 + 50 * q^77 + 1672 * q^80 + 44 * q^82 - 302 * q^83 - 86 * q^85 + 380 * q^86 + 636 * q^88 - 88 * q^91 - 416 * q^92 + 102 * q^95 + 178 * q^97 - 748 * q^98

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