LMFDB - Embedded newform 405.3.g.c.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(82,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("405.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 16x^{5} + 145x^{4} - 130x^{3} + 98x^{2} + 560x + 1600 $ x^8 - 2x^7 + 2x^6 + 16x^5 + 145x^4 - 130x^3 + 98x^2 + 560*x + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.2
Root			$1.50511 + 1.50511i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.c.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50511 + 1.50511i) q^{2} -0.530684i q^{4} +(-4.97442 - 0.505105i) q^{5} +(4.50511 - 4.50511i) q^{7} +(-5.22169 - 5.22169i) q^{8} +O(q^{10})$	\(q+(-1.50511 + 1.50511i) q^{2} -0.530684i q^{4} +(-4.97442 - 0.505105i) q^{5} +(4.50511 - 4.50511i) q^{7} +(-5.22169 - 5.22169i) q^{8} +(8.24726 - 6.72679i) q^{10} +14.0456 q^{11} +(7.77279 + 7.77279i) q^{13} +13.5613i q^{14} +17.8411 q^{16} +(-15.7268 + 15.7268i) q^{17} +15.5354i q^{19} +(-0.268051 + 2.63985i) q^{20} +(-21.1402 + 21.1402i) q^{22} +(-11.2831 - 11.2831i) q^{23} +(24.4897 + 5.02521i) q^{25} -23.3977 q^{26} +(-2.39079 - 2.39079i) q^{28} +34.4283i q^{29} -49.4181 q^{31} +(-5.96600 + 5.96600i) q^{32} -47.3410i q^{34} +(-24.6858 + 20.1347i) q^{35} +(22.8392 - 22.8392i) q^{37} +(-23.3824 - 23.3824i) q^{38} +(23.3374 + 28.6124i) q^{40} -0.566943 q^{41} +(-0.390421 - 0.390421i) q^{43} -7.45379i q^{44} +33.9644 q^{46} +(-22.9847 + 22.9847i) q^{47} +8.40805i q^{49} +(-44.4231 + 29.2962i) q^{50} +(4.12489 - 4.12489i) q^{52} +(45.4430 + 45.4430i) q^{53} +(-69.8689 - 7.09452i) q^{55} -47.0485 q^{56} +(-51.8182 - 51.8182i) q^{58} +45.5871i q^{59} +12.3629 q^{61} +(74.3794 - 74.3794i) q^{62} +53.4055i q^{64} +(-34.7391 - 42.5912i) q^{65} +(-85.9015 + 85.9015i) q^{67} +(8.34595 + 8.34595i) q^{68} +(6.84989 - 67.4597i) q^{70} +48.1581 q^{71} +(-77.4961 - 77.4961i) q^{73} +68.7508i q^{74} +8.24437 q^{76} +(63.2771 - 63.2771i) q^{77} +132.641i q^{79} +(-88.7492 - 9.01164i) q^{80} +(0.853308 - 0.853308i) q^{82} +(-69.1756 - 69.1756i) q^{83} +(86.1754 - 70.2880i) q^{85} +1.17525 q^{86} +(-73.3419 - 73.3419i) q^{88} +119.880i q^{89} +70.0345 q^{91} +(-5.98773 + 5.98773i) q^{92} -69.1889i q^{94} +(7.84700 - 77.2795i) q^{95} +(-52.3593 + 52.3593i) q^{97} +(-12.6550 - 12.6550i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{5} + 26 q^{7} + 36 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^5 + 26 * q^7 + 36 * q^8	$ 8 q - 2 q^{2} - 2 q^{5} + 26 q^{7} + 36 q^{8} + 26 q^{10} + 20 q^{11} - 28 q^{13} - 76 q^{16} - 38 q^{17} - 12 q^{20} + 10 q^{22} - 68 q^{23} + 128 q^{25} - 124 q^{26} - 140 q^{28} - 116 q^{31} + 232 q^{32} - 14 q^{35} + 50 q^{37} - 66 q^{38} + 228 q^{40} - 316 q^{41} - 34 q^{43} - 8 q^{46} - 302 q^{47} + 22 q^{50} - 28 q^{52} + 118 q^{53} + 166 q^{55} + 420 q^{56} - 318 q^{58} + 112 q^{61} + 290 q^{62} + 112 q^{65} + 8 q^{67} - 76 q^{68} + 168 q^{70} + 248 q^{71} + 74 q^{73} - 48 q^{76} + 50 q^{77} - 836 q^{80} + 22 q^{82} - 302 q^{83} + 86 q^{85} + 380 q^{86} - 636 q^{88} - 44 q^{91} - 416 q^{92} + 102 q^{95} - 178 q^{97} + 374 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^5 + 26 * q^7 + 36 * q^8 + 26 * q^10 + 20 * q^11 - 28 * q^13 - 76 * q^16 - 38 * q^17 - 12 * q^20 + 10 * q^22 - 68 * q^23 + 128 * q^25 - 124 * q^26 - 140 * q^28 - 116 * q^31 + 232 * q^32 - 14 * q^35 + 50 * q^37 - 66 * q^38 + 228 * q^40 - 316 * q^41 - 34 * q^43 - 8 * q^46 - 302 * q^47 + 22 * q^50 - 28 * q^52 + 118 * q^53 + 166 * q^55 + 420 * q^56 - 318 * q^58 + 112 * q^61 + 290 * q^62 + 112 * q^65 + 8 * q^67 - 76 * q^68 + 168 * q^70 + 248 * q^71 + 74 * q^73 - 48 * q^76 + 50 * q^77 - 836 * q^80 + 22 * q^82 - 302 * q^83 + 86 * q^85 + 380 * q^86 - 636 * q^88 - 44 * q^91 - 416 * q^92 + 102 * q^95 - 178 * q^97 + 374 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.50511	+	1.50511i	−0.752553	+	0.752553i	−0.974955	−	0.222402i	$-0.928610\pi$
$2$	−1.50511	+	1.50511i	−0.752553	+	0.752553i	0.222402	+	0.974955i	$0.428610\pi$
$3$		0			0
$3$		0			0
$4$		−	0.530684i		−	0.132671i
$5$	−4.97442	−	0.505105i	−0.994884	−	0.101021i
$5$	−4.97442	−	0.505105i	−0.994884	−	0.101021i
$6$		0			0
$7$	4.50511	−	4.50511i	0.643586	−	0.643586i	−0.307849	−	0.951435i	$-0.599609\pi$
$7$	4.50511	−	4.50511i	0.643586	−	0.643586i	0.951435	+	0.307849i	$0.0996091\pi$
$8$	−5.22169	−	5.22169i	−0.652711	−	0.652711i
$9$		0			0
$10$	8.24726	−	6.72679i	0.824726	−	0.672679i
$11$	14.0456			1.27688			0.638438	−	0.769673i	$-0.279581\pi$
$11$	14.0456			1.27688			0.638438	+	0.769673i	$0.279581\pi$
$12$		0			0
$13$	7.77279	+	7.77279i	0.597907	+	0.597907i	0.939755	−	0.341848i	$-0.111053\pi$
$13$	7.77279	+	7.77279i	0.597907	+	0.597907i	−0.341848	+	0.939755i	$0.611053\pi$
$14$			13.5613i			0.968665i
$15$		0			0
$16$	17.8411			1.11507
$17$	−15.7268	+	15.7268i	−0.925105	+	0.925105i	−0.997384	−	0.0722791i	$-0.976973\pi$
$17$	−15.7268	+	15.7268i	−0.925105	+	0.925105i	0.0722791	+	0.997384i	$0.476973\pi$
$18$		0			0
$19$			15.5354i			0.817651i	0.912613	+	0.408826i	$0.134062\pi$
$19$			15.5354i			0.817651i	−0.912613	+	0.408826i	$0.865938\pi$
$20$	−0.268051	+	2.63985i	−0.0134026	+	0.131992i
$21$		0			0
$22$	−21.1402	+	21.1402i	−0.960916	+	0.960916i
$23$	−11.2831	−	11.2831i	−0.490568	−	0.490568i	0.417917	−	0.908485i	$-0.362760\pi$
$23$	−11.2831	−	11.2831i	−0.490568	−	0.490568i	−0.908485	+	0.417917i	$0.862760\pi$
$24$		0			0
$25$	24.4897	+	5.02521i	0.979589	+	0.201009i
$26$	−23.3977			−0.899913
$27$		0			0
$28$	−2.39079	−	2.39079i	−0.0853852	−	0.0853852i
$29$			34.4283i			1.18718i	0.804767	+	0.593591i	$0.202290\pi$
$29$			34.4283i			1.18718i	−0.804767	+	0.593591i	$0.797710\pi$
$30$		0			0
$31$	−49.4181			−1.59413			−0.797065	−	0.603893i	$-0.793615\pi$
$31$	−49.4181			−1.59413			−0.797065	+	0.603893i	$0.793615\pi$
$32$	−5.96600	+	5.96600i	−0.186438	+	0.186438i
$33$		0			0
$34$		−	47.3410i		−	1.39238i
$35$	−24.6858	+	20.1347i	−0.705310	+	0.575278i
$36$		0			0
$37$	22.8392	−	22.8392i	0.617276	−	0.617276i	−0.327556	−	0.944832i	$-0.606225\pi$
$37$	22.8392	−	22.8392i	0.617276	−	0.617276i	0.944832	+	0.327556i	$0.106225\pi$
$38$	−23.3824	−	23.3824i	−0.615326	−	0.615326i
$39$		0			0
$40$	23.3374	+	28.6124i	0.583434	+	0.715309i
$41$	−0.566943			−0.0138279			−0.00691393	−	0.999976i	$-0.502201\pi$
$41$	−0.566943			−0.0138279			−0.00691393	+	0.999976i	$0.502201\pi$
$42$		0			0
$43$	−0.390421	−	0.390421i	−0.00907956	−	0.00907956i	0.702552	−	0.711632i	$-0.252044\pi$
$43$	−0.390421	−	0.390421i	−0.00907956	−	0.00907956i	−0.711632	+	0.702552i	$0.752044\pi$
$44$		−	7.45379i		−	0.169404i
$45$		0			0
$46$	33.9644			0.738356
$47$	−22.9847	+	22.9847i	−0.489037	+	0.489037i	−0.908002	−	0.418965i	$-0.862393\pi$
$47$	−22.9847	+	22.9847i	−0.489037	+	0.489037i	0.418965	+	0.908002i	$0.362393\pi$
$48$		0			0
$49$			8.40805i			0.171593i
$50$	−44.4231	+	29.2962i	−0.888462	+	0.585923i
$51$		0			0
$52$	4.12489	−	4.12489i	0.0793249	−	0.0793249i
$53$	45.4430	+	45.4430i	0.857415	+	0.857415i	0.991033	−	0.133618i	$-0.0426594\pi$
$53$	45.4430	+	45.4430i	0.857415	+	0.857415i	−0.133618	+	0.991033i	$0.542659\pi$
$54$		0			0
$55$	−69.8689	−	7.09452i	−1.27034	−	0.128991i
$56$	−47.0485			−0.840152
$57$		0			0
$58$	−51.8182	−	51.8182i	−0.893417	−	0.893417i
$59$			45.5871i			0.772662i	0.922360	+	0.386331i	$0.126258\pi$
$59$			45.5871i			0.772662i	−0.922360	+	0.386331i	$0.873742\pi$
$60$		0			0
$61$	12.3629			0.202671			0.101336	−	0.994852i	$-0.467688\pi$
$61$	12.3629			0.202671			0.101336	+	0.994852i	$0.467688\pi$
$62$	74.3794	−	74.3794i	1.19967	−	1.19967i
$63$		0			0
$64$			53.4055i			0.834461i
$65$	−34.7391	−	42.5912i	−0.534447	−	0.655249i
$66$		0			0
$67$	−85.9015	+	85.9015i	−1.28211	+	1.28211i	−0.342649	+	0.939463i	$0.611324\pi$
$67$	−85.9015	+	85.9015i	−1.28211	+	1.28211i	−0.939463	+	0.342649i	$0.888676\pi$
$68$	8.34595	+	8.34595i	0.122735	+	0.122735i
$69$		0			0
$70$	6.84989	−	67.4597i	0.0978556	−	0.963710i
$71$	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	−0.997974	−	0.0636162i	$-0.979737\pi$
$73$	−77.4961	−	77.4961i	−1.06159	−	1.06159i	−0.0636162	−	0.997974i	$-0.520263\pi$
$74$			68.7508i			0.929065i
$75$		0			0
$76$	8.24437			0.108479
$77$	63.2771	−	63.2771i	0.821780	−	0.821780i
$78$		0			0
$79$			132.641i			1.67899i	0.543364	+	0.839497i	$0.317150\pi$
$79$			132.641i			1.67899i	−0.543364	+	0.839497i	$0.682850\pi$
$80$	−88.7492	−	9.01164i	−1.10937	−	0.112645i
$81$		0			0
$82$	0.853308	−	0.853308i	0.0104062	−	0.0104062i
$83$	−69.1756	−	69.1756i	−0.833441	−	0.833441i	0.154545	−	0.987986i	$-0.450609\pi$
$83$	−69.1756	−	69.1756i	−0.833441	−	0.833441i	−0.987986	+	0.154545i	$0.950609\pi$
$84$		0			0
$85$	86.1754	−	70.2880i	1.01383	−	0.826918i
$86$	1.17525			0.0136657
$87$		0			0
$88$	−73.3419	−	73.3419i	−0.833431	−	0.833431i
$89$			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
$92$	−5.98773	+	5.98773i	−0.0650841	+	0.0650841i
$93$		0			0
$94$		−	69.1889i		−	0.736052i
$95$	7.84700	−	77.2795i	0.0826000	−	0.813468i
$96$		0			0
$97$	−52.3593	+	52.3593i	−0.539787	+	0.539787i	−0.923466	−	0.383680i	$-0.874657\pi$
$97$	−52.3593	+	52.3593i	−0.539787	+	0.539787i	0.383680	+	0.923466i	$0.374657\pi$
$98$	−12.6550	−	12.6550i	−0.129133	−	0.129133i
$99$		0			0
$100$	2.66680	−	12.9963i	0.0266680	−	0.129963i
$101$	180.687			1.78898			0.894491	−	0.447086i	$-0.147538\pi$
$101$	180.687			1.78898			0.894491	+	0.447086i	$0.147538\pi$
$102$		0			0
$103$	55.6503	+	55.6503i	0.540294	+	0.540294i	0.923615	−	0.383321i	$-0.125220\pi$
$103$	55.6503	+	55.6503i	0.540294	+	0.540294i	−0.383321	+	0.923615i	$0.625220\pi$
$104$		−	81.1741i		−	0.780521i
$105$		0			0
$106$	−136.793			−1.29050
$107$	61.3219	−	61.3219i	0.573102	−	0.573102i	−0.359892	−	0.932994i	$-0.617187\pi$
$107$	61.3219	−	61.3219i	0.573102	−	0.573102i	0.932994	+	0.359892i	$0.117187\pi$
$108$		0			0
$109$			202.258i			1.85557i	0.373110	+	0.927787i	$0.378291\pi$
$109$			202.258i			1.85557i	−0.373110	+	0.927787i	$0.621709\pi$
$110$	115.838	−	94.4821i	1.05307	−	0.858928i
$111$		0			0
$112$	80.3761	−	80.3761i	0.717644	−	0.717644i
$113$	79.5992	+	79.5992i	0.704417	+	0.704417i	0.965356	−	0.260938i	$-0.0840319\pi$
$113$	79.5992	+	79.5992i	0.704417	+	0.704417i	−0.260938	+	0.965356i	$0.584032\pi$
$114$		0			0
$115$	50.4275	+	61.8258i	0.438500	+	0.537616i
$116$	18.2705			0.157505
$117$		0			0
$118$	−68.6133	−	68.6133i	−0.581469	−	0.581469i
$119$			141.702i			1.19077i
$120$		0			0
$121$	76.2798			0.630412
$122$	−18.6075	+	18.6075i	−0.152521	+	0.152521i
$123$		0			0
$124$			26.2254i			0.211495i
$125$	−119.284	−	37.3674i	−0.954272	−	0.298939i
$126$		0			0
$127$	8.86658	−	8.86658i	0.0698156	−	0.0698156i	−0.671337	−	0.741152i	$-0.734280\pi$
$127$	8.86658	−	8.86658i	0.0698156	−	0.0698156i	0.741152	+	0.671337i	$0.234280\pi$
$128$	−104.245	−	104.245i	−0.814414	−	0.814414i
$129$		0			0
$130$	116.390	+	11.8183i	0.895309	+	0.0909102i
$131$	22.8254			0.174240			0.0871198	−	0.996198i	$-0.472234\pi$
$131$	22.8254			0.174240			0.0871198	+	0.996198i	$0.472234\pi$
$132$		0			0
$133$	69.9885	+	69.9885i	0.526229	+	0.526229i
$134$		−	258.582i		−	1.92971i
$135$		0			0
$136$	164.241			1.20765
$137$	59.0207	−	59.0207i	0.430808	−	0.430808i	−0.458095	−	0.888903i	$-0.651468\pi$
$137$	59.0207	−	59.0207i	0.430808	−	0.430808i	0.888903	+	0.458095i	$0.151468\pi$
$138$		0			0
$139$		−	117.431i		−	0.844830i	−0.906403	−	0.422415i	$-0.861182\pi$
$139$		−	117.431i		−	0.844830i	0.906403	−	0.422415i	$-0.138818\pi$
$140$	10.6852	+	13.1004i	0.0763227	+	0.0935741i
$141$		0			0
$142$	−72.4829	+	72.4829i	−0.510443	+	0.510443i
$143$	109.174	+	109.174i	0.763453	+	0.763453i
$144$		0			0
$145$	17.3899	−	171.261i	0.119930	−	1.18111i
$146$	233.280			1.59781
$147$		0			0
$148$	−12.1204	−	12.1204i	−0.0818946	−	0.0818946i
$149$			109.086i			0.732120i	0.930591	+	0.366060i	$0.119294\pi$
$149$			109.086i			0.732120i	−0.930591	+	0.366060i	$0.880706\pi$
$150$		0			0
$151$	189.155			1.25268			0.626340	−	0.779550i	$-0.284552\pi$
$151$	189.155			1.25268			0.626340	+	0.779550i	$0.284552\pi$
$152$	81.1208	−	81.1208i	0.533690	−	0.533690i
$153$		0			0
$154$			190.477i			1.23687i
$155$	245.826	+	24.9613i	1.58598	+	0.161041i
$156$		0			0
$157$	86.7696	−	86.7696i	0.552673	−	0.552673i	−0.374539	−	0.927211i	$-0.622199\pi$
$157$	86.7696	−	86.7696i	0.552673	−	0.552673i	0.927211	+	0.374539i	$0.122199\pi$
$158$	−199.638	−	199.638i	−1.26353	−	1.26353i
$159$		0			0
$160$	32.6909	−	26.6640i	0.204318	−	0.166650i
$161$	−101.663			−0.631445
$162$		0			0
$163$	−55.2937	−	55.2937i	−0.339225	−	0.339225i	0.516851	−	0.856076i	$-0.327104\pi$
$163$	−55.2937	−	55.2937i	−0.339225	−	0.339225i	−0.856076	+	0.516851i	$0.827104\pi$
$164$			0.300867i			0.00183456i
$165$		0			0
$166$	208.233			1.25442
$167$	94.0642	−	94.0642i	0.563259	−	0.563259i	−0.366973	−	0.930232i	$-0.619606\pi$
$167$	94.0642	−	94.0642i	0.563259	−	0.563259i	0.930232	+	0.366973i	$0.119606\pi$
$168$		0			0
$169$		−	48.1674i		−	0.285014i
$170$	−23.9122	+	235.494i	−0.140660	+	1.38526i
$171$		0			0
$172$	−0.207190	+	0.207190i	−0.00120459	+	0.00120459i
$173$	−23.2878	−	23.2878i	−0.134611	−	0.134611i	0.636591	−	0.771202i	$-0.280344\pi$
$173$	−23.2878	−	23.2878i	−0.134611	−	0.134611i	−0.771202	+	0.636591i	$0.780344\pi$
$174$		0			0
$175$	132.968	−	87.6897i	0.759817	−	0.501084i
$176$	250.590			1.42381
$177$		0			0
$178$	−180.432	−	180.432i	−1.01366	−	1.01366i
$179$		−	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	$0.606042\pi$
$182$	−105.409	+	105.409i	−0.579172	+	0.579172i
$183$		0			0
$184$			117.833i			0.640397i
$185$	−125.148	+	102.076i	−0.676476	+	0.551760i
$186$		0			0
$187$	−220.893	+	220.893i	−1.18124	+	1.18124i
$188$	12.1976	+	12.1976i	0.0648810	+	0.0648810i
$189$		0			0
$190$	104.503	+	128.124i	0.550017	+	0.674339i
$191$	−142.632			−0.746766			−0.373383	−	0.927677i	$-0.621802\pi$
$191$	−142.632			−0.746766			−0.373383	+	0.927677i	$0.621802\pi$
$192$		0			0
$193$	−126.541	−	126.541i	−0.655651	−	0.655651i	0.298697	−	0.954348i	$-0.403448\pi$
$193$	−126.541	−	126.541i	−0.655651	−	0.655651i	−0.954348	+	0.298697i	$0.903448\pi$
$194$		−	157.613i		−	0.812436i
$195$		0			0
$196$	4.46202			0.0227654
$197$	45.6222	−	45.6222i	0.231585	−	0.231585i	−0.581769	−	0.813354i	$-0.697639\pi$
$197$	45.6222	−	45.6222i	0.231585	−	0.231585i	0.813354	+	0.581769i	$0.197639\pi$
$198$		0			0
$199$		−	328.469i		−	1.65060i	−0.564694	−	0.825300i	$-0.691006\pi$
$199$		−	328.469i		−	1.65060i	0.564694	−	0.825300i	$-0.308994\pi$
$200$	−101.638	−	154.118i	−0.508188	−	0.770589i
$201$		0			0
$202$	−271.953	+	271.953i	−1.34630	+	1.34630i
$203$	155.103	+	155.103i	0.764054	+	0.764054i
$204$		0			0
$205$	2.82021	+	0.286366i	0.0137571	+	0.00139691i
$206$	−167.519			−0.813200
$207$		0			0
$208$	138.675	+	138.675i	0.666708	+	0.666708i
$209$			218.204i			1.04404i
$210$		0			0
$211$	−293.907			−1.39292			−0.696461	−	0.717595i	$-0.745243\pi$
$211$	−293.907			−1.39292			−0.696461	+	0.717595i	$0.745243\pi$
$212$	24.1159	−	24.1159i	0.113754	−	0.113754i
$213$		0			0
$214$			184.592i			0.862579i
$215$	1.74492	+	2.13932i	0.00811589	+	0.00995034i
$216$		0			0
$217$	−222.634	+	222.634i	−1.02596	+	1.02596i
$218$	−304.419	−	304.419i	−1.39642	−	1.39642i
$219$		0			0
$220$	−3.76495	+	37.0783i	−0.0171134	+	0.168538i
$221$	−244.482			−1.10625
$222$		0			0
$223$	−123.594	−	123.594i	−0.554235	−	0.554235i	0.373425	−	0.927660i	$-0.378183\pi$
$223$	−123.594	−	123.594i	−0.554235	−	0.554235i	−0.927660	+	0.373425i	$0.878183\pi$
$224$			53.7550i			0.239977i
$225$		0			0
$226$	−239.610			−1.06022
$227$	−127.955	+	127.955i	−0.563680	+	0.563680i	−0.930351	−	0.366671i	$-0.880498\pi$
$227$	−127.955	+	127.955i	−0.563680	+	0.563680i	0.366671	+	0.930351i	$0.380498\pi$
$228$		0			0
$229$			294.600i			1.28646i	0.765672	+	0.643232i	$0.222407\pi$
$229$			294.600i			1.28646i	−0.765672	+	0.643232i	$0.777593\pi$
$230$	−168.953	−	17.1556i	−0.734579	−	0.0745895i
$231$		0			0
$232$	179.774	−	179.774i	0.774886	−	0.774886i
$233$	297.567	+	297.567i	1.27711	+	1.27711i	0.942278	+	0.334832i	$0.108680\pi$
$233$	297.567	+	297.567i	1.27711	+	1.27711i	0.334832	+	0.942278i	$0.391320\pi$
$234$		0			0
$235$	125.945	−	102.726i	0.535938	−	0.437132i
$236$	24.1923			0.102510
$237$		0			0
$238$	−213.276	−	213.276i	−0.896118	−	0.896118i
$239$			8.26172i			0.0345678i	0.999851	+	0.0172839i	$0.00550192\pi$
$239$			8.26172i			0.0345678i	−0.999851	+	0.0172839i	$0.994498\pi$
$240$		0			0
$241$	180.094			0.747278			0.373639	−	0.927574i	$-0.378110\pi$
$241$	180.094			0.747278			0.373639	+	0.927574i	$0.378110\pi$
$242$	−114.809	+	114.809i	−0.474418	+	0.474418i
$243$		0			0
$244$		−	6.56081i		−	0.0268886i
$245$	4.24695	−	41.8252i	0.0173345	−	0.170715i
$246$		0			0
$247$	−120.753	+	120.753i	−0.488879	+	0.488879i
$248$	258.046	+	258.046i	1.04051	+	1.04051i
$249$		0			0
$250$	235.777	−	123.293i	0.943108	−	0.493172i
$251$	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
$254$			26.6903i			0.105080i
$255$		0			0
$256$	100.177			0.391317
$257$	−124.951	+	124.951i	−0.486190	+	0.486190i	−0.907102	−	0.420911i	$-0.861710\pi$
$257$	−124.951	+	124.951i	−0.486190	+	0.486190i	0.420911	+	0.907102i	$0.361710\pi$
$258$		0			0
$259$		−	205.786i		−	0.794541i
$260$	−22.6025	+	18.4355i	−0.0869326	+	0.0709056i
$261$		0			0
$262$	−34.3546	+	34.3546i	−0.131124	+	0.131124i
$263$	64.1716	+	64.1716i	0.243998	+	0.243998i	0.818502	−	0.574504i	$-0.194805\pi$
$263$	64.1716	+	64.1716i	0.243998	+	0.243998i	−0.574504	+	0.818502i	$0.694805\pi$
$264$		0			0
$265$	−203.099	−	249.006i	−0.766412	−	0.939646i
$266$	−210.680			−0.792030
$267$		0			0
$268$	45.5866	+	45.5866i	0.170099	+	0.170099i
$269$		−	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	$0.401876\pi$
$272$	−280.583	+	280.583i	−1.03156	+	1.03156i
$273$		0			0
$274$			177.665i			0.648411i
$275$	343.974	+	70.5823i	1.25081	+	0.256663i
$276$		0			0
$277$	219.532	−	219.532i	0.792534	−	0.792534i	−0.189371	−	0.981906i	$-0.560645\pi$
$277$	219.532	−	219.532i	0.792534	−	0.792534i	0.981906	+	0.189371i	$0.0606450\pi$
$278$	176.747	+	176.747i	0.635779	+	0.635779i
$279$		0			0
$280$	234.039	+	23.7644i	0.835854	+	0.0848730i
$281$	−443.174			−1.57713			−0.788566	−	0.614950i	$-0.789176\pi$
$281$	−443.174			−1.57713			−0.788566	+	0.614950i	$0.789176\pi$
$282$		0			0
$283$	−11.1575	−	11.1575i	−0.0394257	−	0.0394257i	0.687119	−	0.726545i	$-0.258875\pi$
$283$	−11.1575	−	11.1575i	−0.0394257	−	0.0394257i	−0.726545	+	0.687119i	$0.758875\pi$
$284$		−	25.5567i		−	0.0899884i
$285$		0			0
$286$	−328.636			−1.14908
$287$	−2.55414	+	2.55414i	−0.00889943	+	0.00889943i
$288$		0			0
$289$		−	205.664i		−	0.711640i
$290$	231.592	+	283.939i	0.798592	+	0.979100i
$291$		0			0
$292$	−41.1259	+	41.1259i	−0.140842	+	0.140842i
$293$	−245.846	−	245.846i	−0.839063	−	0.839063i	0.149672	−	0.988736i	$-0.452178\pi$
$293$	−245.846	−	245.846i	−0.839063	−	0.839063i	−0.988736	+	0.149672i	$0.952178\pi$
$294$		0			0
$295$	23.0263	−	226.769i	0.0780551	−	0.768709i
$296$	−238.518			−0.805805
$297$		0			0
$298$	−164.186	−	164.186i	−0.550959	−	0.550959i
$299$		−	175.402i		−	0.586628i
$300$		0			0
$301$	−3.51778			−0.0116870
$302$	−284.698	+	284.698i	−0.942707	+	0.942707i
$303$		0			0
$304$			277.168i			0.911738i
$305$	−61.4985	−	6.24459i	−0.201634	−	0.0204741i
$306$		0			0
$307$	48.6485	−	48.6485i	0.158464	−	0.158464i	−0.623422	−	0.781886i	$-0.714258\pi$
$307$	48.6485	−	48.6485i	0.158464	−	0.158464i	0.781886	+	0.623422i	$0.214258\pi$
$308$	−33.5801	−	33.5801i	−0.109026	−	0.109026i
$309$		0			0
$310$	−407.564	+	332.425i	−1.31472	+	1.07234i
$311$	−311.539			−1.00173			−0.500866	−	0.865525i	$-0.666985\pi$
$311$	−311.539			−1.00173			−0.500866	+	0.865525i	$0.666985\pi$
$312$		0			0
$313$	73.4236	+	73.4236i	0.234580	+	0.234580i	0.814601	−	0.580021i	$-0.196956\pi$
$313$	73.4236	+	73.4236i	0.234580	+	0.234580i	−0.580021	+	0.814601i	$0.696956\pi$
$314$			261.195i			0.831830i
$315$		0			0
$316$	70.3902			0.222754
$317$	−203.079	+	203.079i	−0.640628	+	0.640628i	−0.950710	−	0.310082i	$-0.899643\pi$
$317$	−203.079	+	203.079i	−0.640628	+	0.640628i	0.310082	+	0.950710i	$0.399643\pi$
$318$		0			0
$319$			483.567i			1.51588i
$320$	26.9754	−	265.662i	0.0842981	−	0.830192i
$321$		0			0
$322$	153.013	−	153.013i	0.475196	−	0.475196i
$323$	−244.322	−	244.322i	−0.756413	−	0.756413i
$324$		0			0
$325$	151.294	+	229.414i	0.465519	+	0.705888i
$326$	166.446			0.510569
$327$		0			0
$328$	2.96040	+	2.96040i	0.00902560	+	0.00902560i
$329$			207.097i			0.629475i
$330$		0			0
$331$	392.448			1.18564			0.592822	−	0.805334i	$-0.298014\pi$
$331$	392.448			1.18564			0.592822	+	0.805334i	$0.298014\pi$
$332$	−36.7104	+	36.7104i	−0.110573	+	0.110573i
$333$		0			0
$334$			283.153i			0.847764i
$335$	470.700	−	383.921i	1.40507	−	1.14603i
$336$		0			0
$337$	352.779	−	352.779i	1.04682	−	1.04682i	0.0479739	−	0.998849i	$-0.484724\pi$
$337$	352.779	−	352.779i	1.04682	−	1.04682i	0.998849	−	0.0479739i	$-0.0152764\pi$
$338$	72.4971	+	72.4971i	0.214488	+	0.214488i
$339$		0			0
$340$	−37.3007	−	45.7319i	−0.109708	−	0.134506i
$341$	−694.108			−2.03551
$342$		0			0
$343$	258.629	+	258.629i	0.754021	+	0.754021i
$344$			4.07731i			0.0118527i
$345$		0			0
$346$	70.1011			0.202604
$347$	27.8507	−	27.8507i	0.0802614	−	0.0802614i	−0.665836	−	0.746098i	$-0.731925\pi$
$347$	27.8507	−	27.8507i	0.0802614	−	0.0802614i	0.746098	+	0.665836i	$0.231925\pi$
$348$		0			0
$349$		−	74.7883i		−	0.214293i	−0.994243	−	0.107147i	$-0.965829\pi$
$349$		−	74.7883i		−	0.214293i	0.994243	−	0.107147i	$-0.0341714\pi$
$350$	−68.1485	+	332.113i	−0.194710	+	0.948894i
$351$		0			0
$352$	−83.7963	+	83.7963i	−0.238058	+	0.238058i
$353$	29.9850	+	29.9850i	0.0849433	+	0.0849433i	0.748302	−	0.663358i	$-0.230870\pi$
$353$	29.9850	+	29.9850i	0.0849433	+	0.0849433i	−0.663358	+	0.748302i	$0.730870\pi$
$354$		0			0
$355$	−239.558	−	24.3249i	−0.674813	−	0.0685208i
$356$	63.6185			0.178704
$357$		0			0
$358$	200.806	+	200.806i	0.560910	+	0.560910i
$359$			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
$362$	178.173	−	178.173i	0.492190	−	0.492190i
$363$		0			0
$364$		−	37.1662i		−	0.102105i
$365$	346.355	+	424.642i	0.948917	+	1.16340i
$366$		0			0
$367$	−175.007	+	175.007i	−0.476857	+	0.476857i	−0.904125	−	0.427268i	$-0.859476\pi$
$367$	−175.007	+	175.007i	−0.476857	+	0.476857i	0.427268	+	0.904125i	$0.359476\pi$
$368$	−201.302	−	201.302i	−0.547017	−	0.547017i
$369$		0			0
$370$	34.7264	−	341.996i	0.0938552	−	0.924313i
$371$	409.451			1.10364
$372$		0			0
$373$	167.935	+	167.935i	0.450227	+	0.450227i	0.895430	−	0.445203i	$-0.146868\pi$
$373$	167.935	+	167.935i	0.450227	+	0.450227i	−0.445203	+	0.895430i	$0.646868\pi$
$374$		−	664.934i		−	1.77790i
$375$		0			0
$376$	240.038			0.638399
$377$	−267.604	+	267.604i	−0.709824	+	0.709824i
$378$		0			0
$379$		−	589.803i		−	1.55621i	−0.628134	−	0.778105i	$-0.716181\pi$
$379$		−	589.803i		−	1.55621i	0.628134	−	0.778105i	$-0.283819\pi$
$380$	−41.0110	−	4.16428i	−0.107924	−	0.0109586i
$381$		0			0
$382$	214.677	−	214.677i	0.561981	−	0.561981i
$383$	20.7622	+	20.7622i	0.0542093	+	0.0542093i	0.733692	−	0.679482i	$-0.237796\pi$
$383$	20.7622	+	20.7622i	0.0542093	+	0.0542093i	−0.679482	+	0.733692i	$0.737796\pi$
$384$		0			0
$385$	−346.728	+	282.805i	−0.900593	+	0.734559i
$386$	380.914			0.986823
$387$		0			0
$388$	27.7862	+	27.7862i	0.0716140	+	0.0716140i
$389$			251.922i			0.647616i	0.946123	+	0.323808i	$0.104963\pi$
$389$			251.922i			0.647616i	−0.946123	+	0.323808i	$0.895037\pi$
$390$		0			0
$391$	354.892			0.907653
$392$	43.9042	−	43.9042i	0.112001	−	0.112001i
$393$		0			0
$394$			137.332i			0.348559i
$395$	66.9974	−	659.810i	0.169614	−	1.67040i
$396$		0			0
$397$	−471.289	+	471.289i	−1.18713	+	1.18713i	−0.209269	+	0.977858i	$0.567108\pi$
$397$	−471.289	+	471.289i	−1.18713	+	1.18713i	−0.977858	+	0.209269i	$0.932892\pi$
$398$	494.381	+	494.381i	1.24216	+	1.24216i
$399$		0			0
$400$	436.924	+	89.6554i	1.09231	+	0.224138i
$401$	−44.5921			−0.111202			−0.0556012	−	0.998453i	$-0.517708\pi$
$401$	−44.5921			−0.111202			−0.0556012	+	0.998453i	$0.517708\pi$
$402$		0			0
$403$	−384.116	−	384.116i	−0.953142	−	0.953142i
$404$		−	95.8878i		−	0.237346i
$405$		0			0
$406$	−466.893			−1.14998
$407$	320.791	−	320.791i	0.788185	−	0.788185i
$408$		0			0
$409$			23.1278i			0.0565471i	0.999600	+	0.0282735i	$0.00900094\pi$
$409$			23.1278i			0.0565471i	−0.999600	+	0.0282735i	$0.990999\pi$
$410$	−4.67573	+	3.81371i	−0.0114042	+	0.00930172i
$411$		0			0
$412$	29.5327	−	29.5327i	0.0716814	−	0.0716814i
$413$	205.374	+	205.374i	0.497275	+	0.497275i
$414$		0			0
$415$	309.168	+	379.049i	0.744982	+	0.913372i
$416$	−92.7450			−0.222945
$417$		0			0
$418$	−328.420	−	328.420i	−0.785694	−	0.785694i
$419$		−	304.230i		−	0.726087i	−0.931772	−	0.363043i	$-0.881738\pi$
$419$		−	304.230i		−	0.726087i	0.931772	−	0.363043i	$-0.118262\pi$
$420$		0			0
$421$	248.414			0.590057			0.295029	−	0.955488i	$-0.404671\pi$
$421$	248.414			0.590057			0.295029	+	0.955488i	$0.404671\pi$
$422$	442.360	−	442.360i	1.04825	−	1.04825i
$423$		0			0
$424$		−	474.578i		−	1.11929i
$425$	−464.175	+	306.115i	−1.09218	+	0.720269i
$426$		0			0
$427$	55.6963	−	55.6963i	0.130436	−	0.130436i
$428$	−32.5425	−	32.5425i	−0.0760340	−	0.0760340i
$429$		0			0
$430$	−5.84619	−	0.593625i	−0.0135958	−	0.00138052i
$431$	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	0.938860	−	0.344300i	$-0.111884\pi$
$433$	257.444	+	257.444i	0.594560	+	0.594560i	−0.344300	+	0.938860i	$0.611884\pi$
$434$		−	670.174i		−	1.54418i
$435$		0			0
$436$	107.335			0.246181
$437$	175.286	−	175.286i	0.401113	−	0.401113i
$438$		0			0
$439$			13.9832i			0.0318525i	0.999873	+	0.0159262i	$0.00506969\pi$
$439$			13.9832i			0.0318525i	−0.999873	+	0.0159262i	$0.994930\pi$
$440$	327.788	+	401.879i	0.744973	+	0.913361i
$441$		0			0
$442$	367.971	−	367.971i	0.832514	−	0.832514i
$443$	−29.7749	−	29.7749i	−0.0672120	−	0.0672120i	0.672702	−	0.739914i	$-0.265134\pi$
$443$	−29.7749	−	29.7749i	−0.0672120	−	0.0672120i	−0.739914	+	0.672702i	$0.765134\pi$
$444$		0			0
$445$	60.5521	−	596.335i	0.136072	−	1.34008i
$446$	372.045			0.834182
$447$		0			0
$448$	240.597	+	240.597i	0.537048	+	0.537048i
$449$		−	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
$452$	42.2420	−	42.2420i	0.0934557	−	0.0934557i
$453$		0			0
$454$		−	385.173i		−	0.848398i
$455$	−348.381	−	35.3748i	−0.765673	−	0.0777468i
$456$		0			0
$457$	−238.351	+	238.351i	−0.521555	+	0.521555i	−0.918041	−	0.396486i	$-0.870230\pi$
$457$	−238.351	+	238.351i	−0.521555	+	0.521555i	0.396486	+	0.918041i	$0.370230\pi$
$458$	−443.404	−	443.404i	−0.968131	−	0.968131i
$459$		0			0
$460$	32.8100	−	26.7611i	0.0713260	−	0.0581763i
$461$	−578.169			−1.25416			−0.627082	−	0.778954i	$-0.715751\pi$
$461$	−578.169			−1.25416			−0.627082	+	0.778954i	$0.715751\pi$
$462$		0			0
$463$	198.196	+	198.196i	0.428069	+	0.428069i	0.887970	−	0.459901i	$-0.152115\pi$
$463$	198.196	+	198.196i	0.428069	+	0.428069i	−0.459901	+	0.887970i	$0.652115\pi$
$464$			614.238i			1.32379i
$465$		0			0
$466$	−895.738			−1.92218
$467$	−377.215	+	377.215i	−0.807740	+	0.807740i	−0.984291	−	0.176551i	$-0.943506\pi$
$467$	−377.215	+	377.215i	−0.807740	+	0.807740i	0.176551	+	0.984291i	$0.443506\pi$
$468$		0			0
$469$			773.991i			1.65030i
$470$	−34.9477	+	344.175i	−0.0743568	+	0.732287i
$471$		0			0
$472$	238.041	−	238.041i	0.504325	−	0.504325i
$473$	−5.48371	−	5.48371i	−0.0115935	−	0.0115935i
$474$		0			0
$475$	−78.0686	+	380.457i	−0.164355	+	0.800962i
$476$	75.1988			0.157981
$477$		0			0
$478$	−12.4348	−	12.4348i	−0.0260141	−	0.0260141i
$479$		−	697.327i		−	1.45580i	−0.685684	−	0.727899i	$-0.740497\pi$
$479$		−	697.327i		−	1.45580i	0.685684	−	0.727899i	$-0.259503\pi$
$480$		0			0
$481$	355.049			0.738147
$482$	−271.060	+	271.060i	−0.562366	+	0.562366i
$483$		0			0
$484$		−	40.4805i		−	0.0836374i
$485$	286.904	−	234.010i	0.591555	−	0.482496i
$486$		0			0
$487$	369.496	−	369.496i	0.758718	−	0.758718i	−0.217371	−	0.976089i	$-0.569748\pi$
$487$	369.496	−	369.496i	0.758718	−	0.758718i	0.976089	+	0.217371i	$0.0697481\pi$
$488$	−64.5554	−	64.5554i	−0.132286	−	0.132286i
$489$		0			0
$490$	56.5592	+	69.3434i	0.115427	+	0.141517i
$491$	111.030			0.226131			0.113065	−	0.993588i	$-0.463933\pi$
$491$	111.030			0.226131			0.113065	+	0.993588i	$0.463933\pi$
$492$		0			0
$493$	−541.446	−	541.446i	−1.09827	−	1.09827i
$494$		−	363.493i		−	0.735815i
$495$		0			0
$496$	−881.673			−1.77757
$497$	216.957	−	216.957i	0.436533	−	0.436533i
$498$		0			0
$499$		−	418.139i		−	0.837954i	−0.907997	−	0.418977i	$-0.862389\pi$
$499$		−	418.139i		−	0.837954i	0.907997	−	0.418977i	$-0.137611\pi$
$500$	−19.8303	+	63.3021i	−0.0396606	+	0.126604i
$501$		0			0
$502$	−244.489	+	244.489i	−0.487029	+	0.487029i
$503$	496.065	+	496.065i	0.986213	+	0.986213i	0.999906	−	0.0136937i	$-0.00435898\pi$
$503$	496.065	+	496.065i	0.986213	+	0.986213i	−0.0136937	+	0.999906i	$0.504359\pi$
$504$		0			0
$505$	−898.814	−	91.2661i	−1.77983	−	0.180725i
$506$	477.051			0.942789
$507$		0			0
$508$	−4.70535	−	4.70535i	−0.00926251	−	0.00926251i
$509$		−	481.409i		−	0.945793i	−0.881118	−	0.472897i	$-0.843208\pi$
$509$		−	481.409i		−	0.945793i	0.881118	−	0.472897i	$-0.156792\pi$
$510$		0			0
$511$	−698.256			−1.36645
$512$	266.203	−	266.203i	0.519927	−	0.519927i
$513$		0			0
$514$		−	376.129i		−	0.731768i
$515$	−248.719	−	304.937i	−0.482949	−	0.592111i
$516$		0			0
$517$	−322.835	+	322.835i	−0.624439	+	0.624439i
$518$	309.730	+	309.730i	0.597934	+	0.597934i
$519$		0			0
$520$	−41.0015	+	403.794i	−0.0788490	+	0.776528i
$521$	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	0.973449	−	0.228904i	$-0.0735143\pi$
$523$	389.397	+	389.397i	0.744545	+	0.744545i	−0.228904	+	0.973449i	$0.573514\pi$
$524$		−	12.1131i		−	0.0231165i
$525$		0			0
$526$	−193.170			−0.367243
$527$	777.187	−	777.187i	1.47474	−	1.47474i
$528$		0			0
$529$		−	274.385i		−	0.518687i
$530$	680.466	+	69.0949i	1.28390	+	0.130368i
$531$		0			0
$532$	37.1418	−	37.1418i	0.0698153	−	0.0698153i
$533$	−4.40673	−	4.40673i	−0.00826778	−	0.00826778i
$534$		0			0
$535$	−336.015	+	274.067i	−0.628065	+	0.512275i
$536$	897.102			1.67370
$537$		0			0
$538$	625.339	+	625.339i	1.16234	+	1.16234i
$539$			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	$0.532705\pi$
$542$	−247.508	+	247.508i	−0.456657	+	0.456657i
$543$		0			0
$544$		−	187.652i		−	0.344949i
$545$	102.161	−	1006.11i	0.187452	−	1.84608i
$546$		0			0
$547$	−153.833	+	153.833i	−0.281231	+	0.281231i	−0.833600	−	0.552369i	$-0.813724\pi$
$547$	−153.833	+	153.833i	−0.281231	+	0.281231i	0.552369	+	0.833600i	$0.313724\pi$
$548$	−31.3213	−	31.3213i	−0.0571557	−	0.0571557i
$549$		0			0
$550$	−623.951	+	411.483i	−1.13446	+	0.748151i
$551$	−534.856			−0.970700
$552$		0			0
$553$	597.560	+	597.560i	1.08058	+	1.08058i
$554$			660.837i			1.19285i
$555$		0			0
$556$	−62.3189			−0.112084
$557$	−416.448	+	416.448i	−0.747662	+	0.747662i	−0.974040	−	0.226378i	$-0.927312\pi$
$557$	−416.448	+	416.448i	−0.747662	+	0.747662i	0.226378	+	0.974040i	$0.427312\pi$
$558$		0			0
$559$		−	6.06932i		−	0.0108575i
$560$	−440.423	+	359.226i	−0.786469	+	0.641475i
$561$		0			0
$562$	667.024	−	667.024i	1.18687	−	1.18687i
$563$	−541.596	−	541.596i	−0.961983	−	0.961983i	0.0373204	−	0.999303i	$-0.488118\pi$
$563$	−541.596	−	541.596i	−0.961983	−	0.961983i	−0.999303	+	0.0373204i	$0.988118\pi$
$564$		0			0
$565$	−355.754	−	436.166i	−0.629653	−	0.771975i
$566$	33.5864			0.0593398
$567$		0			0
$568$	−251.466	−	251.466i	−0.442722	−	0.442722i
$569$		−	1.79254i		−	0.00315033i	−0.999999	−	0.00157516i	$-0.999499\pi$
$569$		−	1.79254i		−	0.00315033i	0.999999	−	0.00157516i	$-0.000501390\pi$
$570$		0			0
$571$	−908.327			−1.59076			−0.795382	−	0.606108i	$-0.792730\pi$
$571$	−908.327			−1.59076			−0.795382	+	0.606108i	$0.792730\pi$
$572$	57.9368	−	57.9368i	0.101288	−	0.101288i
$573$		0			0
$574$		−	7.68849i		−	0.0133946i
$575$	−219.619	−	333.019i	−0.381947	−	0.579163i
$576$		0			0
$577$	−518.888	+	518.888i	−0.899286	+	0.899286i	−0.995373	−	0.0960874i	$-0.969367\pi$
$577$	−518.888	+	518.888i	−0.899286	+	0.899286i	0.0960874	+	0.995373i	$0.469367\pi$
$578$	309.546	+	309.546i	0.535546	+	0.535546i
$579$		0			0
$580$	−90.8853	−	9.22854i	−0.156699	−	0.0159113i
$581$	−623.287			−1.07278
$582$		0			0
$583$	638.276	+	638.276i	1.09481	+	1.09481i
$584$			809.321i			1.38582i
$585$		0			0
$586$	740.047			1.26288
$587$	348.275	−	348.275i	0.593313	−	0.593313i	−0.345211	−	0.938525i	$-0.612193\pi$
$587$	348.275	−	348.275i	0.593313	−	0.593313i	0.938525	+	0.345211i	$0.112193\pi$
$588$		0			0
$589$		−	767.728i		−	1.30344i
$590$	306.655	+	375.968i	0.519754	+	0.637235i
$591$		0			0
$592$	407.477	−	407.477i	0.688306	−	0.688306i
$593$	−528.279	−	528.279i	−0.890858	−	0.890858i	0.103746	−	0.994604i	$-0.466917\pi$
$593$	−528.279	−	528.279i	−0.890858	−	0.890858i	−0.994604	+	0.103746i	$0.966917\pi$
$594$		0			0
$595$	71.5743	−	704.884i	0.120293	−	1.18468i
$596$	57.8901			0.0971311
$597$		0			0
$598$	263.998	+	263.998i	0.441468	+	0.441468i
$599$			517.843i			0.864513i	0.901751	+	0.432257i	$0.142283\pi$
$599$			517.843i			0.864513i	−0.901751	+	0.432257i	$0.857717\pi$
$600$		0			0
$601$	−102.192			−0.170036			−0.0850181	−	0.996379i	$-0.527095\pi$
$601$	−102.192			−0.170036			−0.0850181	+	0.996379i	$0.527095\pi$
$602$	5.29462	−	5.29462i	0.00879506	−	0.00879506i
$603$		0			0
$604$		−	100.381i		−	0.166194i
$605$	−379.448	−	38.5294i	−0.627187	−	0.0636849i
$606$		0			0
$607$	−630.659	+	630.659i	−1.03898	+	1.03898i	−0.0397679	+	0.999209i	$0.512662\pi$
$607$	−630.659	+	630.659i	−1.03898	+	1.03898i	−0.999209	+	0.0397679i	$0.987338\pi$
$608$	−92.6841	−	92.6841i	−0.152441	−	0.152441i
$609$		0			0
$610$	101.960	−	83.1629i	0.167148	−	0.136333i
$611$	−357.311			−0.584797
$612$		0			0
$613$	−91.7462	−	91.7462i	−0.149668	−	0.149668i	0.628302	−	0.777970i	$-0.283750\pi$
$613$	−91.7462	−	91.7462i	−0.149668	−	0.149668i	−0.777970	+	0.628302i	$0.783750\pi$
$614$			146.442i			0.238505i
$615$		0			0
$616$	−660.826			−1.07277
$617$	−580.793	+	580.793i	−0.941317	+	0.941317i	−0.998371	−	0.0570537i	$-0.981829\pi$
$617$	−580.793	+	580.793i	−0.941317	+	0.941317i	0.0570537	+	0.998371i	$0.481829\pi$
$618$		0			0
$619$		−	1195.91i		−	1.93200i	−0.258545	−	0.965999i	$-0.583243\pi$
$619$		−	1195.91i		−	1.93200i	0.258545	−	0.965999i	$-0.416757\pi$
$620$	13.2466	−	130.456i	0.0213654	−	0.210413i
$621$		0			0
$622$	468.898	−	468.898i	0.753856	−	0.753856i
$623$	540.073	+	540.073i	0.866891	+	0.866891i
$624$		0			0
$625$	574.494	+	246.132i	0.919191	+	0.393812i
$626$	−221.020			−0.353068
$627$		0			0
$628$	−46.0472	−	46.0472i	−0.0733236	−	0.0733236i
$629$			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	$0.176499\pi$
$632$	692.607	−	692.607i	1.09590	−	1.09590i
$633$		0			0
$634$		−	611.310i		−	0.964212i
$635$	−48.5847	+	39.6276i	−0.0765113	+	0.0624056i
$636$		0			0
$637$	−65.3540	+	65.3540i	−0.102597	+	0.102597i
$638$	−727.819	−	727.819i	−1.14078	−	1.14078i
$639$		0			0
$640$	465.904	+	571.213i	0.727974	+	0.892520i
$641$	217.077			0.338653			0.169327	−	0.985560i	$-0.445841\pi$
$641$	217.077			0.338653			0.169327	+	0.985560i	$0.445841\pi$
$642$		0			0
$643$	281.283	+	281.283i	0.437454	+	0.437454i	0.891154	−	0.453700i	$-0.149896\pi$
$643$	281.283	+	281.283i	0.437454	+	0.437454i	−0.453700	+	0.891154i	$0.649896\pi$
$644$			53.9507i			0.0837745i
$645$		0			0
$646$	735.459			1.13848
$647$	308.718	−	308.718i	0.477154	−	0.477154i	−0.427067	−	0.904220i	$-0.640453\pi$
$647$	308.718	−	308.718i	0.477154	−	0.477154i	0.904220	+	0.427067i	$0.140453\pi$
$648$		0			0
$649$			640.299i			0.986593i
$650$	−573.004	−	117.579i	−0.881545	−	0.180890i
$651$		0			0
$652$	−29.3435	+	29.3435i	−0.0450053	+	0.0450053i
$653$	−246.886	−	246.886i	−0.378079	−	0.378079i	0.492329	−	0.870409i	$-0.336146\pi$
$653$	−246.886	−	246.886i	−0.378079	−	0.378079i	−0.870409	+	0.492329i	$0.836146\pi$
$654$		0			0
$655$	−113.543	−	11.5292i	−0.173348	−	0.0176019i
$656$	−10.1149			−0.0154190
$657$		0			0
$658$	−311.703	−	311.703i	−0.473713	−	0.473713i
$659$			423.128i			0.642076i	0.947066	+	0.321038i	$0.104032\pi$
$659$			423.128i			0.642076i	−0.947066	+	0.321038i	$0.895968\pi$
$660$		0			0
$661$	446.165			0.674985			0.337492	−	0.941328i	$-0.390421\pi$
$661$	446.165			0.674985			0.337492	+	0.941328i	$0.390421\pi$
$662$	−590.676	+	590.676i	−0.892260	+	0.892260i
$663$		0			0
$664$			722.426i			1.08799i
$665$	−312.801	−	383.504i	−0.470377	−	0.576697i
$666$		0			0
$667$	388.456	−	388.456i	0.582393	−	0.582393i
$668$	−49.9184	−	49.9184i	−0.0747281	−	0.0747281i
$669$		0			0
$670$	−130.611	+	1286.29i	−0.194942	+	1.91984i
$671$	173.645			0.258786
$672$		0			0
$673$	348.895	+	348.895i	0.518418	+	0.518418i	0.917093	−	0.398674i	$-0.130530\pi$
$673$	348.895	+	348.895i	0.518418	+	0.518418i	−0.398674	+	0.917093i	$0.630530\pi$
$674$			1061.94i			1.57558i
$675$		0			0
$676$	−25.5617			−0.0378131
$677$	581.369	−	581.369i	0.858743	−	0.858743i	−0.132447	−	0.991190i	$-0.542283\pi$
$677$	581.369	−	581.369i	0.858743	−	0.858743i	0.991190	+	0.132447i	$0.0422833\pi$
$678$		0			0
$679$			471.768i			0.694799i
$680$	−817.003	−	82.9589i	−1.20147	−	0.121998i
$681$		0			0
$682$	1044.71	−	1044.71i	1.53183	−	1.53183i
$683$	−702.491	−	702.491i	−1.02854	−	1.02854i	−0.999581	−	0.0289564i	$-0.990782\pi$
$683$	−702.491	−	702.491i	−1.02854	−	1.02854i	−0.0289564	−	0.999581i	$-0.509218\pi$
$684$		0			0
$685$	−323.405	+	263.782i	−0.472125	+	0.385083i
$686$	−778.529			−1.13488
$687$		0			0
$688$	−6.96555	−	6.96555i	−0.0101243	−	0.0101243i
$689$			706.438i			1.02531i
$690$		0			0
$691$	158.399			0.229232			0.114616	−	0.993410i	$-0.463436\pi$
$691$	158.399			0.229232			0.114616	+	0.993410i	$0.463436\pi$
$692$	−12.3585	+	12.3585i	−0.0178590	+	0.0178590i
$693$		0			0
$694$			83.8365i			0.120802i
$695$	−59.3152	+	584.153i	−0.0853456	+	0.840508i
$696$		0			0
$697$	8.91619	−	8.91619i	0.0127922	−	0.0127922i
$698$	112.564	+	112.564i	0.161267	+	0.161267i
$699$		0			0
$700$	−46.5355	−	70.5639i	−0.0664793	−	0.100806i
$701$	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
$704$			750.114i			1.06550i
$705$		0			0
$706$	−90.2611			−0.127849
$707$	814.015	−	814.015i	1.15136	−	1.15136i
$708$		0			0
$709$			202.277i			0.285300i	0.989773	+	0.142650i	$0.0455623\pi$
$709$			202.277i			0.285300i	−0.989773	+	0.142650i	$0.954438\pi$
$710$	397.172	−	323.949i	0.559397	−	0.456266i
$711$		0			0
$712$	625.977	−	625.977i	0.879181	−	0.879181i
$713$	557.587	+	557.587i	0.782029	+	0.782029i
$714$		0			0
$715$	−487.932	−	598.221i	−0.682423	−	0.836672i
$716$	−70.8019			−0.0988854
$717$		0			0
$718$	−208.615	−	208.615i	−0.290550	−	0.290550i
$719$			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
$722$	−180.089	+	180.089i	−0.249431	+	0.249431i
$723$		0			0
$724$			62.8218i			0.0867705i
$725$	−173.009	+	843.139i	−0.238634	+	1.16295i
$726$		0			0
$727$	467.491	−	467.491i	0.643041	−	0.643041i	−0.308261	−	0.951302i	$-0.599747\pi$
$727$	467.491	−	467.491i	0.643041	−	0.643041i	0.951302	+	0.308261i	$0.0997470\pi$
$728$	−365.698	−	365.698i	−0.502333	−	0.502333i
$729$		0			0
$730$	−1160.43	−	117.831i	−1.58963	−	0.161412i
$731$	12.2801			0.0167991
$732$		0			0
$733$	154.980	+	154.980i	0.211432	+	0.211432i	0.804876	−	0.593443i	$-0.202232\pi$
$733$	154.980	+	154.980i	0.211432	+	0.211432i	−0.593443	+	0.804876i	$0.702232\pi$
$734$		−	526.807i		−	0.717720i
$735$		0			0
$736$	134.630			0.182921
$737$	−1206.54	+	1206.54i	−1.63710	+	1.63710i
$738$		0			0
$739$			311.453i			0.421451i	0.977545	+	0.210726i	$0.0675827\pi$
$739$			311.453i			0.421451i	−0.977545	+	0.210726i	$0.932417\pi$
$740$	54.1699	+	66.4141i	0.0732026	+	0.0897487i
$741$		0			0
$742$	−616.267	+	616.267i	−0.830548	+	0.830548i
$743$	32.7069	+	32.7069i	0.0440201	+	0.0440201i	0.728774	−	0.684754i	$-0.240090\pi$
$743$	32.7069	+	32.7069i	0.0440201	+	0.0440201i	−0.684754	+	0.728774i	$0.740090\pi$
$744$		0			0
$745$	55.0999	−	542.639i	0.0739595	−	0.728375i
$746$	−505.519			−0.677639
$747$		0			0
$748$	117.224	+	117.224i	0.156717	+	0.156717i
$749$		−	552.523i		−	0.737681i
$750$		0			0
$751$	−1006.31			−1.33996			−0.669978	−	0.742381i	$-0.733696\pi$
$751$	−1006.31			−1.33996			−0.669978	+	0.742381i	$0.733696\pi$
$752$	−410.073	+	410.073i	−0.545310	+	0.545310i
$753$		0			0
$754$		−	805.544i		−	1.06836i
$755$	−940.935	−	95.5430i	−1.24627	−	0.126547i
$756$		0			0
$757$	511.251	−	511.251i	0.675364	−	0.675364i	−0.283583	−	0.958948i	$-0.591523\pi$
$757$	511.251	−	511.251i	0.675364	−	0.675364i	0.958948	+	0.283583i	$0.0915233\pi$
$758$	887.716	+	887.716i	1.17113	+	1.17113i
$759$		0			0
$760$	−444.504	+	362.555i	−0.584873	+	0.477046i
$761$	−536.405			−0.704868			−0.352434	−	0.935837i	$-0.614646\pi$
$761$	−536.405			−0.704868			−0.352434	+	0.935837i	$0.614646\pi$
$762$		0			0
$763$	911.192	+	911.192i	1.19422	+	1.19422i
$764$			75.6926i			0.0990741i
$765$		0			0
$766$	−62.4985			−0.0815907
$767$	−354.339	+	354.339i	−0.461980	+	0.461980i
$768$		0			0
$769$		−	459.378i		−	0.597370i	−0.954352	−	0.298685i	$-0.903452\pi$
$769$		−	459.378i		−	0.597370i	0.954352	−	0.298685i	$-0.0965481\pi$
$770$	96.2111	−	947.514i	0.124949	−	1.23054i
$771$		0			0
$772$	−67.1531	+	67.1531i	−0.0869858	+	0.0869858i
$773$	229.707	+	229.707i	0.297163	+	0.297163i	0.839902	−	0.542739i	$-0.182613\pi$
$773$	229.707	+	229.707i	0.297163	+	0.297163i	−0.542739	+	0.839902i	$0.682613\pi$
$774$		0			0
$775$	−1210.24	−	248.336i	−1.56159	−	0.320434i
$776$	546.808			0.704649
$777$		0			0
$778$	−379.170	−	379.170i	−0.487365	−	0.487365i
$779$		−	8.80766i		−	0.0113064i
$780$		0			0
$781$	676.410			0.866082
$782$	−534.151	+	534.151i	−0.683057	+	0.683057i
$783$		0			0
$784$			150.009i			0.191338i
$785$	−475.456	+	387.801i	−0.605677	+	0.494014i
$786$		0			0
$787$	−304.430	+	304.430i	−0.386824	+	0.386824i	−0.873553	−	0.486729i	$-0.838190\pi$
$787$	−304.430	+	304.430i	−0.386824	+	0.386824i	0.486729	+	0.873553i	$0.338190\pi$
$788$	−24.2110	−	24.2110i	−0.0307246	−	0.0307246i
$789$		0			0
$790$	892.245	+	1093.92i	1.12942	+	1.38471i
$791$	717.205			0.906707
$792$		0			0
$793$	96.0946	+	96.0946i	0.121179	+	0.121179i
$794$		−	1418.68i		−	1.78675i
$795$		0			0
$796$	−174.313			−0.218987
$797$	−46.2484	+	46.2484i	−0.0580281	+	0.0580281i	−0.735525	−	0.677497i	$-0.763065\pi$
$797$	−46.2484	+	46.2484i	−0.0580281	+	0.0580281i	0.677497	+	0.735525i	$0.263065\pi$
$798$		0			0
$799$		−	722.952i		−	0.904821i
$800$	−176.086	+	116.125i	−0.220108	+	0.145157i
$801$		0			0
$802$	67.1159	−	67.1159i	0.0836856	−	0.0836856i
$803$	−1088.48	−	1088.48i	−1.35552	−	1.35552i
$804$		0			0
$805$	505.713	+	51.3504i	0.628215	+	0.0637893i
$806$	1156.27			1.43458
$807$		0			0
$808$	−943.492	−	943.492i	−1.16769	−	1.16769i
$809$		−	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	$0.535917\pi$
$812$	82.3106	−	82.3106i	0.101368	−	0.101368i
$813$		0			0
$814$			965.649i			1.18630i
$815$	247.125	+	302.983i	0.303221	+	0.371759i
$816$		0			0
$817$	6.06534	−	6.06534i	0.00742391	−	0.00742391i
$818$	−34.8097	−	34.8097i	−0.0425546	−	0.0425546i
$819$		0			0
$820$	0.151970	−	1.49664i	0.000185329	−	0.00182517i
$821$	−615.058			−0.749157			−0.374579	−	0.927195i	$-0.622213\pi$
$821$	−615.058			−0.749157			−0.374579	+	0.927195i	$0.622213\pi$
$822$		0			0
$823$	759.099	+	759.099i	0.922356	+	0.922356i	0.997196	−	0.0748391i	$-0.0238443\pi$
$823$	759.099	+	759.099i	0.922356	+	0.922356i	−0.0748391	+	0.997196i	$0.523844\pi$
$824$		−	581.177i		−	0.705312i
$825$		0			0
$826$	−618.220			−0.748451
$827$	850.244	−	850.244i	1.02811	−	1.02811i	0.0285125	−	0.999593i	$-0.490923\pi$
$827$	850.244	−	850.244i	1.02811	−	1.02811i	0.999593	−	0.0285125i	$-0.00907704\pi$
$828$		0			0
$829$		−	76.6013i		−	0.0924021i	−0.998932	−	0.0462010i	$-0.985289\pi$
$829$		−	76.6013i		−	0.0924021i	0.998932	−	0.0462010i	$-0.0147115\pi$
$830$	−1035.84	−	105.180i	−1.24800	−	0.126722i
$831$		0			0
$832$	−415.110	+	415.110i	−0.498930	+	0.498930i
$833$	−132.232	−	132.232i	−0.158742	−	0.158742i
$834$		0			0
$835$	−515.427	+	420.403i	−0.617278	+	0.503476i
$836$	115.797			0.138514
$837$		0			0
$838$	457.899	+	457.899i	0.546419	+	0.546419i
$839$		−	18.0553i		−	0.0215201i	−0.999942	−	0.0107600i	$-0.996575\pi$
$839$		−	18.0553i		−	0.0215201i	0.999942	−	0.0107600i	$-0.00342509\pi$
$840$		0			0
$841$	−344.305			−0.409400
$842$	−373.889	+	373.889i	−0.444049	+	0.444049i
$843$		0			0
$844$			155.971i			0.184800i
$845$	−24.3296	+	239.605i	−0.0287925	+	0.283556i
$846$		0			0
$847$	343.649	−	343.649i	0.405725	−	0.405725i
$848$	810.754	+	810.754i	0.956077	+	0.956077i
$849$		0			0
$850$	237.898	−	1159.37i	0.279880	−	1.36396i
$851$	−515.392			−0.605631
$852$		0			0
$853$	−148.064	−	148.064i	−0.173580	−	0.173580i	0.614970	−	0.788550i	$-0.289168\pi$
$853$	−148.064	−	148.064i	−0.173580	−	0.173580i	−0.788550	+	0.614970i	$0.789168\pi$
$854$			167.658i			0.196321i
$855$		0			0
$856$	−640.407			−0.748139
$857$	−273.824	+	273.824i	−0.319514	+	0.319514i	−0.848580	−	0.529066i	$-0.822542\pi$
$857$	−273.824	+	273.824i	−0.319514	+	0.319514i	0.529066	+	0.848580i	$0.322542\pi$
$858$		0			0
$859$		−	381.591i		−	0.444227i	−0.975021	−	0.222114i	$-0.928704\pi$
$859$		−	381.591i		−	0.444227i	0.975021	−	0.222114i	$-0.0712956\pi$
$860$	1.13530	−	0.925999i	0.00132012	−	0.00107674i
$861$		0			0
$862$	−832.383	+	832.383i	−0.965642	+	0.965642i
$863$	653.316	+	653.316i	0.757029	+	0.757029i	0.975781	−	0.218752i	$-0.0701984\pi$
$863$	653.316	+	653.316i	0.757029	+	0.757029i	−0.218752	+	0.975781i	$0.570198\pi$
$864$		0			0
$865$	104.080	+	127.606i	0.120324	+	0.147521i
$866$	−774.962			−0.894875
$867$		0			0
$868$	118.148	+	118.148i	0.136115	+	0.136115i
$869$			1863.02i			2.14387i
$870$		0			0
$871$	−1335.39			−1.53317
$872$	1056.13	−	1056.13i	1.21115	−	1.21115i
$873$		0			0
$874$			527.649i			0.603717i
$875$	−705.731	+	369.043i	−0.806550	+	0.421763i
$876$		0			0
$877$	88.7364	−	88.7364i	0.101182	−	0.101182i	−0.654704	−	0.755886i	$-0.727207\pi$
$877$	88.7364	−	88.7364i	0.101182	−	0.101182i	0.755886	+	0.654704i	$0.227207\pi$
$878$	−21.0462	−	21.0462i	−0.0239707	−	0.0239707i
$879$		0			0
$880$	−1246.54	−	126.574i	−1.41652	−	0.143834i
$881$	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	0.740908	−	0.671607i	$-0.234395\pi$
$883$	61.1931	+	61.1931i	0.0693014	+	0.0693014i	−0.671607	+	0.740908i	$0.734395\pi$
$884$			129.743i			0.146768i
$885$		0			0
$886$	89.6288			0.101161
$887$	290.198	−	290.198i	0.327168	−	0.327168i	−0.524340	−	0.851509i	$-0.675688\pi$
$887$	290.198	−	290.198i	0.327168	−	0.327168i	0.851509	+	0.524340i	$0.175688\pi$
$888$		0			0
$889$		−	79.8898i		−	0.0898648i
$890$	806.409	+	988.684i	0.906077	+	1.11088i
$891$		0			0
$892$	−65.5895	+	65.5895i	−0.0735309	+	0.0735309i
$893$	−357.076	−	357.076i	−0.399862	−	0.399862i
$894$		0			0
$895$	−67.3893	+	663.670i	−0.0752954	+	0.741530i
$896$	−939.269			−1.04829
$897$		0			0
$898$	382.360	+	382.360i	0.425791	+	0.425791i
$899$		−	1701.38i		−	1.89252i
$900$		0			0
$901$	−1429.35			−1.58640
$902$	11.9853	−	11.9853i	0.0132874	−	0.0132874i
$903$		0			0
$904$		−	831.284i		−	0.919562i
$905$	588.867	+	59.7939i	0.650682	+	0.0660706i
$906$		0			0
$907$	−139.165	+	139.165i	−0.153434	+	0.153434i	−0.779650	−	0.626216i	$-0.784603\pi$
$907$	−139.165	+	139.165i	−0.153434	+	0.153434i	0.626216	+	0.779650i	$0.284603\pi$
$908$	67.9039	+	67.9039i	0.0747840	+	0.0747840i
$909$		0			0
$910$	577.593	−	471.107i	0.634718	−	0.517700i
$911$	878.783			0.964635			0.482318	−	0.875996i	$-0.339795\pi$
$911$	878.783			0.964635			0.482318	+	0.875996i	$0.339795\pi$
$912$		0			0
$913$	−971.615	−	971.615i	−1.06420	−	1.06420i
$914$		−	717.486i		−	0.784996i
$915$		0			0
$916$	156.340			0.170676
$917$	102.831	−	102.831i	0.112138	−	0.112138i
$918$		0			0
$919$		−	922.414i		−	1.00372i	−0.864950	−	0.501858i	$-0.832650\pi$
$919$		−	922.414i		−	1.00372i	0.864950	−	0.501858i	$-0.167350\pi$
$920$	59.5181	−	586.152i	0.0646936	−	0.637121i
$921$		0			0
$922$	870.206	−	870.206i	0.943824	−	0.943824i
$923$	374.322	+	374.322i	0.405550	+	0.405550i
$924$		0			0
$925$	674.098	−	444.554i	0.728755	−	0.480599i
$926$	−596.611			−0.644289
$927$		0			0
$928$	−205.399	−	205.399i	−0.221335	−	0.221335i
$929$		−	73.9135i		−	0.0795625i	−0.999208	−	0.0397812i	$-0.987334\pi$
$929$		−	73.9135i		−	0.0795625i	0.999208	−	0.0397812i	$-0.0126661\pi$
$930$		0			0
$931$	−130.622			−0.140303
$932$	157.914	−	157.914i	0.169435	−	0.169435i
$933$		0			0
$934$		−	1135.50i		−	1.21573i
$935$	1210.39	−	987.240i	1.29453	−	1.05587i
$936$		0			0
$937$	−732.726	+	732.726i	−0.781992	+	0.781992i	−0.980167	−	0.198175i	$-0.936499\pi$
$937$	−732.726	+	732.726i	−0.781992	+	0.781992i	0.198175	+	0.980167i	$0.436499\pi$
$938$	−1164.94	−	1164.94i	−1.24194	−	1.24194i
$939$		0			0
$940$	−54.5151	−	66.8372i	−0.0579947	−	0.0711034i
$941$	749.478			0.796470			0.398235	−	0.917284i	$-0.369623\pi$
$941$	749.478			0.796470			0.398235	+	0.917284i	$0.369623\pi$
$942$		0			0
$943$	6.39684	+	6.39684i	0.00678350	+	0.00678350i
$944$			813.324i			0.861572i
$945$		0			0
$946$	16.5071			0.0174494
$947$	311.979	−	311.979i	0.329439	−	0.329439i	−0.522934	−	0.852373i	$-0.675163\pi$
$947$	311.979	−	311.979i	0.329439	−	0.329439i	0.852373	+	0.522934i	$0.175163\pi$
$948$		0			0
$949$		−	1204.72i		−	1.26946i
$950$	−455.127	−	690.129i	−0.479081	−	0.726452i
$951$		0			0
$952$	739.922	−	739.922i	0.777229	−	0.777229i
$953$	−838.669	−	838.669i	−0.880030	−	0.880030i	0.113507	−	0.993537i	$-0.463792\pi$
$953$	−838.669	−	838.669i	−0.880030	−	0.880030i	−0.993537	+	0.113507i	$0.963792\pi$
$954$		0			0
$955$	709.513	+	72.0443i	0.742946	+	0.0754391i
$956$	4.38436			0.00458615
$957$		0			0
$958$	1049.55	+	1049.55i	1.09556	+	1.09556i
$959$		−	531.789i		−	0.554524i
$960$		0			0
$961$	1481.14			1.54125
$962$	−534.386	+	534.386i	−0.555495	+	0.555495i
$963$		0			0
$964$		−	95.5730i		−	0.0991421i
$965$	565.550	+	693.383i	0.586062	+	0.718531i
$966$		0			0
$967$	974.832	−	974.832i	1.00810	−	1.00810i	0.00813285	−	0.999967i	$-0.497411\pi$
$967$	974.832	−	974.832i	1.00810	−	1.00810i	0.999967	−	0.00813285i	$-0.00258879\pi$
$968$	−398.309	−	398.309i	−0.411477	−	0.411477i
$969$		0			0
$970$	−79.6109	+	784.031i	−0.0820731	+	0.808280i
$971$	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
$974$			1112.26i			1.14195i
$975$		0			0
$976$	220.569			0.225992
$977$	843.129	−	843.129i	0.862978	−	0.862978i	−0.128705	−	0.991683i	$-0.541082\pi$
$977$	843.129	−	843.129i	0.862978	−	0.862978i	0.991683	+	0.128705i	$0.0410820\pi$
$978$		0			0
$979$			1683.79i			1.71991i
$980$	−22.1960	−	2.25379i	−0.0226489	−	0.00229978i
$981$		0			0
$982$	−167.112	+	167.112i	−0.170175	+	0.170175i
$983$	278.953	+	278.953i	0.283777	+	0.283777i	0.834613	−	0.550836i	$-0.185691\pi$
$983$	278.953	+	278.953i	0.283777	+	0.283777i	−0.550836	+	0.834613i	$0.685691\pi$
$984$		0			0
$985$	−249.988	+	203.900i	−0.253795	+	0.207005i
$986$	1629.87			1.65301
$987$		0			0
$988$	64.0818	+	64.0818i	0.0648601	+	0.0648601i
$989$			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	$0.407598\pi$
$992$	294.828	−	294.828i	0.297206	−	0.297206i
$993$		0			0
$994$			653.087i			0.657029i
$995$	−165.912	+	1633.95i	−0.166745	+	1.64216i
$996$		0			0
$997$	−1206.48	+	1206.48i	−1.21011	+	1.21011i	−0.239120	+	0.970990i	$0.576859\pi$
$997$	−1206.48	+	1206.48i	−1.21011	+	1.21011i	−0.970990	+	0.239120i	$0.923141\pi$
$998$	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.g.c.163.2	yes	8
3.2	odd	2		405.3.g.e.163.3	yes	8
5.2	odd	4	inner	405.3.g.c.82.2	✓	8
9.2	odd	6		405.3.l.k.28.2		16
9.4	even	3		405.3.l.l.298.2		16
9.5	odd	6		405.3.l.k.298.3		16
9.7	even	3		405.3.l.l.28.3		16
15.2	even	4		405.3.g.e.82.3	yes	8
45.2	even	12		405.3.l.k.352.3		16
45.7	odd	12		405.3.l.l.352.2		16
45.22	odd	12		405.3.l.l.217.3		16
45.32	even	12		405.3.l.k.217.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.c.82.2	✓	8	5.2	odd	4	inner
405.3.g.c.163.2	yes	8	1.1	even	1	trivial
405.3.g.e.82.3	yes	8	15.2	even	4
405.3.g.e.163.3	yes	8	3.2	odd	2
405.3.l.k.28.2		16	9.2	odd	6
405.3.l.k.217.2		16	45.32	even	12
405.3.l.k.298.3		16	9.5	odd	6
405.3.l.k.352.3		16	45.2	even	12
405.3.l.l.28.3		16	9.7	even	3
405.3.l.l.217.3		16	45.22	odd	12
405.3.l.l.298.2		16	9.4	even	3
405.3.l.l.352.2		16	45.7	odd	12

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.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50511 + 1.50511i) q^{2} -0.530684i q^{4} +(-4.97442 - 0.505105i) q^{5} +(4.50511 - 4.50511i) q^{7} +(-5.22169 - 5.22169i) q^{8} +O(q^{10})\)	\(q+(-1.50511 + 1.50511i) q^{2} -0.530684i q^{4} +(-4.97442 - 0.505105i) q^{5} +(4.50511 - 4.50511i) q^{7} +(-5.22169 - 5.22169i) q^{8} +(8.24726 - 6.72679i) q^{10} +14.0456 q^{11} +(7.77279 + 7.77279i) q^{13} +13.5613i q^{14} +17.8411 q^{16} +(-15.7268 + 15.7268i) q^{17} +15.5354i q^{19} +(-0.268051 + 2.63985i) q^{20} +(-21.1402 + 21.1402i) q^{22} +(-11.2831 - 11.2831i) q^{23} +(24.4897 + 5.02521i) q^{25} -23.3977 q^{26} +(-2.39079 - 2.39079i) q^{28} +34.4283i q^{29} -49.4181 q^{31} +(-5.96600 + 5.96600i) q^{32} -47.3410i q^{34} +(-24.6858 + 20.1347i) q^{35} +(22.8392 - 22.8392i) q^{37} +(-23.3824 - 23.3824i) q^{38} +(23.3374 + 28.6124i) q^{40} -0.566943 q^{41} +(-0.390421 - 0.390421i) q^{43} -7.45379i q^{44} +33.9644 q^{46} +(-22.9847 + 22.9847i) q^{47} +8.40805i q^{49} +(-44.4231 + 29.2962i) q^{50} +(4.12489 - 4.12489i) q^{52} +(45.4430 + 45.4430i) q^{53} +(-69.8689 - 7.09452i) q^{55} -47.0485 q^{56} +(-51.8182 - 51.8182i) q^{58} +45.5871i q^{59} +12.3629 q^{61} +(74.3794 - 74.3794i) q^{62} +53.4055i q^{64} +(-34.7391 - 42.5912i) q^{65} +(-85.9015 + 85.9015i) q^{67} +(8.34595 + 8.34595i) q^{68} +(6.84989 - 67.4597i) q^{70} +48.1581 q^{71} +(-77.4961 - 77.4961i) q^{73} +68.7508i q^{74} +8.24437 q^{76} +(63.2771 - 63.2771i) q^{77} +132.641i q^{79} +(-88.7492 - 9.01164i) q^{80} +(0.853308 - 0.853308i) q^{82} +(-69.1756 - 69.1756i) q^{83} +(86.1754 - 70.2880i) q^{85} +1.17525 q^{86} +(-73.3419 - 73.3419i) q^{88} +119.880i q^{89} +70.0345 q^{91} +(-5.98773 + 5.98773i) q^{92} -69.1889i q^{94} +(7.84700 - 77.2795i) q^{95} +(-52.3593 + 52.3593i) q^{97} +(-12.6550 - 12.6550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{5} + 26 q^{7} + 36 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^5 + 26 * q^7 + 36 * q^8	\( 8 q - 2 q^{2} - 2 q^{5} + 26 q^{7} + 36 q^{8} + 26 q^{10} + 20 q^{11} - 28 q^{13} - 76 q^{16} - 38 q^{17} - 12 q^{20} + 10 q^{22} - 68 q^{23} + 128 q^{25} - 124 q^{26} - 140 q^{28} - 116 q^{31} + 232 q^{32} - 14 q^{35} + 50 q^{37} - 66 q^{38} + 228 q^{40} - 316 q^{41} - 34 q^{43} - 8 q^{46} - 302 q^{47} + 22 q^{50} - 28 q^{52} + 118 q^{53} + 166 q^{55} + 420 q^{56} - 318 q^{58} + 112 q^{61} + 290 q^{62} + 112 q^{65} + 8 q^{67} - 76 q^{68} + 168 q^{70} + 248 q^{71} + 74 q^{73} - 48 q^{76} + 50 q^{77} - 836 q^{80} + 22 q^{82} - 302 q^{83} + 86 q^{85} + 380 q^{86} - 636 q^{88} - 44 q^{91} - 416 q^{92} + 102 q^{95} - 178 q^{97} + 374 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^5 + 26 * q^7 + 36 * q^8 + 26 * q^10 + 20 * q^11 - 28 * q^13 - 76 * q^16 - 38 * q^17 - 12 * q^20 + 10 * q^22 - 68 * q^23 + 128 * q^25 - 124 * q^26 - 140 * q^28 - 116 * q^31 + 232 * q^32 - 14 * q^35 + 50 * q^37 - 66 * q^38 + 228 * q^40 - 316 * q^41 - 34 * q^43 - 8 * q^46 - 302 * q^47 + 22 * q^50 - 28 * q^52 + 118 * q^53 + 166 * q^55 + 420 * q^56 - 318 * q^58 + 112 * q^61 + 290 * q^62 + 112 * q^65 + 8 * q^67 - 76 * q^68 + 168 * q^70 + 248 * q^71 + 74 * q^73 - 48 * q^76 + 50 * q^77 - 836 * q^80 + 22 * q^82 - 302 * q^83 + 86 * q^85 + 380 * q^86 - 636 * q^88 - 44 * q^91 - 416 * q^92 + 102 * q^95 - 178 * q^97 + 374 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more