LMFDB - Embedded newform 405.3.l.l.217.3

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			217.3
Root			$2.05601 - 0.550907i$ of defining polynomial
Character	$\chi$	$=$	405.217
Dual form			405.3.l.l.28.3

$q$-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	0.294871	−	0.955537i	$-0.404723\pi$
$2$	2.05601	−	0.550907i	1.02801	−	0.275453i	0.733135	+	0.680084i	$0.238057\pi$
$3$		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	$0.387086\pi$
$11$	−7.02282	+	12.1639i	−0.638438	+	1.10581i	−0.985776	+	0.168067i	$0.946248\pi$
$12$		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	0.0722791	−	0.997384i	$-0.476973\pi$
$17$	−15.7268	−	15.7268i	−0.925105	−	0.925105i	−0.997384	+	0.0722791i	$0.976973\pi$
$18$		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	0.577812	−	0.816170i	$-0.303907\pi$
$23$	15.4129	+	4.12988i	0.670128	+	0.179560i	0.0923154	+	0.995730i	$0.470573\pi$
$24$		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	0.916448	−	0.400153i	$-0.131043\pi$
$29$	29.8158	+	17.2141i	1.02813	+	0.593591i	0.111681	+	0.993744i	$0.464376\pi$
$30$		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	0.869462	−	0.494000i	$-0.164466\pi$
$41$	0.283471	+	0.490987i	0.00691393	+	0.0119753i	−0.862548	+	0.505976i	$0.831133\pi$
$42$		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	0.0911665	−	0.995836i	$-0.470940\pi$
$47$	31.3977	−	8.41300i	0.668037	−	0.179000i	0.576870	+	0.816836i	$0.304274\pi$
$48$		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	−0.133618	−	0.991033i	$-0.542659\pi$
$53$	45.4430	−	45.4430i	0.857415	−	0.857415i	0.991033	+	0.133618i	$0.0426594\pi$
$54$		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	−0.795753	−	0.605622i	$-0.792924\pi$
$59$	−39.4795	+	22.7935i	−0.669145	+	0.386331i	0.126608	+	0.991953i	$0.459591\pi$
$60$		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	$-0.389864\pi$
$71$	48.1581			0.678282			0.339141	+	0.940735i	$0.389864\pi$
$72$		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	$-0.882724\pi$
$83$	−25.3200	−	94.4956i	−0.305060	−	1.13850i	0.627833	−	0.778348i	$-0.283942\pi$
$84$		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	$-0.764797\pi$
$89$		−	119.880i		−	1.34697i	0.739202	−	0.673484i	$-0.235203\pi$
$90$		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	$0.519129\pi$
$101$	−90.3436	+	156.480i	−0.894491	+	1.54930i	−0.834433	+	0.551109i	$0.814205\pi$
$102$		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	0.932994	−	0.359892i	$-0.117187\pi$
$107$	61.3219	+	61.3219i	0.573102	+	0.573102i	−0.359892	+	0.932994i	$0.617187\pi$
$108$		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	−0.256699	−	0.966491i	$-0.582635\pi$
$113$	−108.734	−	29.1353i	−0.962252	−	0.257835i	−0.705553	+	0.708657i	$0.749301\pi$
$114$		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	0.819173	−	0.573547i	$-0.194433\pi$
$131$	−11.4127	−	19.7674i	−0.0871198	−	0.150896i	−0.906293	+	0.422651i	$0.861100\pi$
$132$		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	−0.540765	−	0.841174i	$-0.681865\pi$
$137$	−80.6238	+	21.6031i	−0.588495	+	0.157687i	−0.0477295	+	0.998860i	$0.515199\pi$
$138$		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	−0.782313	−	0.622886i	$-0.785960\pi$
$149$	−94.4712	+	54.5429i	−0.634035	+	0.366060i	0.148278	+	0.988946i	$0.452627\pi$
$150$		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	$-0.786272\pi$
$167$	34.4299	−	128.494i	0.206167	−	0.769426i	0.989091	−	0.147308i	$-0.0470608\pi$
$168$		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	0.936905	−	0.349585i	$-0.113678\pi$
$173$	−8.52392	−	31.8117i	−0.0492712	−	0.183883i	−0.986176	+	0.165703i	$0.947011\pi$
$174$		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	$0.121558\pi$
$179$			133.416i			0.745343i	−0.927963	+	0.372672i	$0.878442\pi$
$180$		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	−0.616701	−	0.787198i	$-0.711531\pi$
$191$	71.3161	−	123.523i	0.373383	−	0.646718i	0.990084	+	0.140480i	$0.0448644\pi$
$192$		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	0.813354	−	0.581769i	$-0.197639\pi$
$197$	45.6222	+	45.6222i	0.231585	+	0.231585i	−0.581769	+	0.813354i	$0.697639\pi$
$198$		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	0.147629	−	0.989043i	$-0.452836\pi$
$227$	174.790	−	46.8349i	0.770002	−	0.206321i	0.622372	+	0.782721i	$0.286169\pi$
$228$		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	$-0.391320\pi$
$233$	297.567	−	297.567i	1.27711	−	1.27711i	0.942278	−	0.334832i	$-0.108680\pi$
$234$		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	−0.514894	−	0.857254i	$-0.672169\pi$
$239$	−7.15486	+	4.13086i	−0.0299366	+	0.0172839i	0.484957	+	0.874538i	$0.338835\pi$
$240$		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	$-0.395112\pi$
$251$	162.440			0.647170			0.323585	+	0.946199i	$0.395112\pi$
$252$		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	$0.195044\pi$
$257$	−45.7352	+	170.686i	−0.177958	+	0.664148i	−0.996029	+	0.0890309i	$0.971623\pi$
$258$		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	0.996095	−	0.0882837i	$-0.0281382\pi$
$263$	23.4884	+	87.6600i	0.0893096	+	0.333308i	−0.906786	+	0.421592i	$0.861472\pi$
$264$		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	$0.280876\pi$
$269$			415.479i			1.54453i	−0.635301	+	0.772265i	$0.719124\pi$
$270$		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	$-0.544157\pi$
$281$	221.587	−	383.800i	0.788566	−	1.36584i	0.926845	−	0.375443i	$-0.122509\pi$
$282$		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	0.781434	−	0.623988i	$-0.214489\pi$
$293$	335.831	+	89.9857i	1.14618	+	0.307119i	0.364748	+	0.931106i	$0.381155\pi$
$294$		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	$0.000318304\pi$
$311$	155.769	+	269.800i	0.500866	+	0.867525i	−0.499134	+	0.866525i	$0.666348\pi$
$312$		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	0.206816	−	0.978380i	$-0.433690\pi$
$317$	277.411	−	74.3321i	0.875114	−	0.234486i	0.668298	+	0.743894i	$0.267023\pi$
$318$		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	−0.949680	−	0.313221i	$-0.898592\pi$
$347$	10.1941	−	38.0448i	0.0293777	−	0.109639i	0.979058	+	0.203582i	$0.0652584\pi$
$348$		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	0.979728	−	0.200334i	$-0.0642029\pi$
$353$	10.9753	+	40.9602i	0.0310914	+	0.116035i	−0.948636	+	0.316369i	$0.897536\pi$
$354$		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	$-0.938164\pi$
$359$		−	138.605i		−	0.386086i	0.981190	−	0.193043i	$-0.0618357\pi$
$360$		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	0.221603	−	0.975137i	$-0.428871\pi$
$383$	−28.3616	−	7.59948i	−0.0740513	−	0.0198420i	−0.295654	+	0.955295i	$0.595538\pi$
$384$		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	0.753487	−	0.657463i	$-0.228370\pi$
$389$	218.171	+	125.961i	0.560852	+	0.323808i	−0.192636	+	0.981270i	$0.561704\pi$
$390$		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	0.892486	−	0.451075i	$-0.148959\pi$
$401$	22.2961	+	38.6179i	0.0556012	+	0.0963041i	−0.836885	+	0.547379i	$0.815626\pi$
$402$		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	−0.151481	−	0.988460i	$-0.548404\pi$
$419$	263.471	−	152.115i	0.628810	−	0.363043i	0.780291	+	0.625417i	$0.215071\pi$
$420$		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	$-0.278280\pi$
$431$	553.040			1.28316			0.641578	+	0.767058i	$0.278280\pi$
$432$		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	0.952534	−	0.304433i	$-0.0984671\pi$
$443$	−10.8984	−	40.6733i	−0.0246013	−	0.0918133i	−0.977135	+	0.212620i	$0.931800\pi$
$444$		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	$0.0912957\pi$
$449$			254.042i			0.565795i	−0.959150	+	0.282898i	$0.908704\pi$
$450$		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	$-0.617583\pi$
$461$	289.085	−	500.709i	0.627082	−	1.08614i	0.988134	−	0.153592i	$-0.0490841\pi$
$462$		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	0.176551	−	0.984291i	$-0.443506\pi$
$467$	−377.215	−	377.215i	−0.807740	−	0.807740i	−0.984291	+	0.176551i	$0.943506\pi$
$468$		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	−0.287537	−	0.957770i	$-0.592836\pi$
$479$	−603.903	−	348.664i	−1.26076	−	0.727899i	−0.973221	+	0.229871i	$0.926170\pi$
$480$		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	0.803939	−	0.594711i	$-0.202734\pi$
$491$	−55.5151	−	96.1550i	−0.113065	−	0.195835i	−0.917005	+	0.398876i	$0.869400\pi$
$492$		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	−0.0136937	−	0.999906i	$-0.504359\pi$
$503$	496.065	−	496.065i	0.986213	−	0.986213i	0.999906	+	0.0136937i	$0.00435898\pi$
$504$		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	−0.0310184	−	0.999519i	$-0.509875\pi$
$509$	416.912	−	240.704i	0.819081	−	0.472897i	0.850099	+	0.526622i	$0.176542\pi$
$510$		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	$-0.339015\pi$
$521$	504.810			0.968925			0.484463	+	0.874812i	$0.339015\pi$
$522$		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	0.226378	−	0.974040i	$-0.427312\pi$
$557$	−416.448	−	416.448i	−0.747662	−	0.747662i	−0.974040	+	0.226378i	$0.927312\pi$
$558$		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	0.846762	−	0.531972i	$-0.178549\pi$
$563$	739.834	+	198.238i	1.31409	+	0.352110i	0.467331	+	0.884082i	$0.345216\pi$
$564$		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	0.498635	−	0.866812i	$-0.333835\pi$
$569$	−1.55238	−	0.896268i	−0.00272826	−	0.00157516i	−0.501364	+	0.865237i	$0.667168\pi$
$570$		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	−0.640181	−	0.768224i	$-0.721141\pi$
$587$	−475.752	+	127.477i	−0.810481	+	0.217168i	−0.170301	+	0.985392i	$0.554474\pi$
$588$		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	−0.994604	−	0.103746i	$-0.966917\pi$
$593$	−528.279	+	528.279i	−0.890858	+	0.890858i	0.103746	+	0.994604i	$0.466917\pi$
$594$		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	−0.825221	−	0.564811i	$-0.808949\pi$
$599$	−448.466	+	258.922i	−0.748690	+	0.432257i	0.0765301	+	0.997067i	$0.475616\pi$
$600$		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	$0.315163\pi$
$617$	−212.585	+	793.378i	−0.344546	+	1.28586i	−0.893142	+	0.449776i	$0.851504\pi$
$618$		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	−0.938183	−	0.346139i	$-0.887493\pi$
$641$	−108.538	+	187.994i	−0.169327	+	0.293282i	0.768857	+	0.639421i	$0.220826\pi$
$642$		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	0.904220	−	0.427067i	$-0.140453\pi$
$647$	308.718	+	308.718i	0.477154	+	0.477154i	−0.427067	+	0.904220i	$0.640453\pi$
$648$		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	0.507632	−	0.861574i	$-0.330521\pi$
$653$	337.252	+	90.3665i	0.516466	+	0.138387i	0.00883466	+	0.999961i	$0.497188\pi$
$654$		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	0.751560	−	0.659664i	$-0.229302\pi$
$659$	366.440	+	211.564i	0.556054	+	0.321038i	−0.195506	+	0.980703i	$0.562635\pi$
$660$		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	−0.792172	−	0.610297i	$-0.791050\pi$
$677$	−794.165	+	212.796i	−1.17307	+	0.314322i	−0.380893	+	0.924619i	$0.624383\pi$
$678$		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	$0.509218\pi$
$683$	−702.491	+	702.491i	−1.02854	+	1.02854i	−0.999581	+	0.0289564i	$0.990782\pi$
$684$		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	$-0.367227\pi$
$701$	567.989			0.810255			0.405128	+	0.914260i	$0.367227\pi$
$702$		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	$-0.800629\pi$
$719$		−	842.936i		−	1.17237i	0.810176	−	0.586186i	$-0.199371\pi$
$720$		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	0.228627	−	0.973514i	$-0.426576\pi$
$743$	−44.6785	−	11.9716i	−0.0601326	−	0.0161125i	−0.288760	+	0.957402i	$0.593243\pi$
$744$		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	0.986675	−	0.162701i	$-0.0520207\pi$
$761$	268.202	+	464.540i	0.352434	+	0.610434i	−0.634241	+	0.773135i	$0.718687\pi$
$762$		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	−0.542739	−	0.839902i	$-0.682613\pi$
$773$	229.707	−	229.707i	0.297163	−	0.297163i	0.839902	+	0.542739i	$0.182613\pi$
$774$		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	−0.975732	−	0.218967i	$-0.929731\pi$
$797$	−16.9281	+	63.1765i	−0.0212398	+	0.0792679i	0.954492	+	0.298235i	$0.0963979\pi$
$798$		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	$0.0213463\pi$
$809$			108.424i			0.134022i	−0.997752	+	0.0670111i	$0.978654\pi$
$810$		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	−0.615685	−	0.787992i	$-0.711121\pi$
$821$	307.529	−	532.656i	0.374579	−	0.648789i	0.990264	+	0.139203i	$0.0444541\pi$
$822$		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	$0.00907704\pi$
$827$	850.244	+	850.244i	1.02811	+	1.02811i	0.0285125	+	0.999593i	$0.490923\pi$
$828$		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	0.490653	−	0.871355i	$-0.336758\pi$
$839$	−15.6364	−	9.02767i	−0.0186369	−	0.0107600i	−0.509290	+	0.860595i	$0.670092\pi$
$840$		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	−0.0338947	−	0.999425i	$-0.510791\pi$
$857$	374.050	−	100.226i	0.436464	−	0.116950i	0.470359	+	0.882475i	$0.344124\pi$
$858$		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	−0.218752	−	0.975781i	$-0.570198\pi$
$863$	653.316	−	653.316i	0.757029	−	0.757029i	0.975781	+	0.218752i	$0.0701984\pi$
$864$		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	$-0.405445\pi$
$881$	515.743			0.585406			0.292703	+	0.956203i	$0.405445\pi$
$882$		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	−0.879846	−	0.475258i	$-0.842355\pi$
$887$	106.220	−	396.418i	0.119752	−	0.446920i	0.999598	+	0.0283378i	$0.00902139\pi$
$888$		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	−0.999794	−	0.0202989i	$-0.993538\pi$
$911$	−439.391	+	761.048i	−0.482318	+	0.835399i	0.517476	+	0.855698i	$0.326872\pi$
$912$		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	0.465153	−	0.885230i	$-0.345999\pi$
$929$	−64.0110	−	36.9568i	−0.0689031	−	0.0397812i	−0.534056	+	0.845449i	$0.679333\pi$
$930$		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	0.595273	−	0.803523i	$-0.297044\pi$
$941$	−374.739	−	649.067i	−0.398235	−	0.689763i	−0.993508	+	0.113760i	$0.963710\pi$
$942$		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	−0.476710	−	0.879061i	$-0.658171\pi$
$947$	−426.171	+	114.192i	−0.450022	+	0.120583i	0.0266874	+	0.999644i	$0.491504\pi$
$948$		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	−0.993537	−	0.113507i	$-0.963792\pi$
$953$	−838.669	+	838.669i	−0.880030	+	0.880030i	0.113507	+	0.993537i	$0.463792\pi$
$954$		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	$-0.154842\pi$
$971$	1716.72			1.76800			0.883998	+	0.467491i	$0.154842\pi$
$972$		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	$-0.707749\pi$
$977$	308.607	−	1151.74i	0.315872	−	1.17885i	0.923175	−	0.384380i	$-0.125585\pi$
$978$		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	0.998214	−	0.0597315i	$-0.0190245\pi$
$983$	102.104	+	381.057i	0.103870	+	0.387647i	−0.894345	+	0.447378i	$0.852358\pi$
$984$		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.l.217.3		16
3.2	odd	2		405.3.l.k.217.2		16
5.3	odd	4	inner	405.3.l.l.298.2		16
9.2	odd	6		405.3.g.e.82.3	yes	8
9.4	even	3	inner	405.3.l.l.352.2		16
9.5	odd	6		405.3.l.k.352.3		16
9.7	even	3		405.3.g.c.82.2	✓	8
15.8	even	4		405.3.l.k.298.3		16
45.13	odd	12	inner	405.3.l.l.28.3		16
45.23	even	12		405.3.l.k.28.2		16
45.38	even	12		405.3.g.e.163.3	yes	8
45.43	odd	12		405.3.g.c.163.2	yes	8

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

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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