LMFDB - Embedded newform 640.2.j.c.543.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(543,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("640.543");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.j (of order $4$, degree $2$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			543.3
Root			$0.482716 + 1.32928i$ of defining polynomial
Character	$\chi$	$=$	640.543
Dual form			640.2.j.c.607.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.39319i q^{3} +(-0.535339 - 2.17104i) q^{5} +(2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +O(q^{10})$	\(q-1.39319i q^{3} +(-0.535339 - 2.17104i) q^{5} +(2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +(2.17074 - 2.17074i) q^{11} -1.54663 q^{13} +(-3.02466 + 0.745827i) q^{15} +(-3.86386 + 3.86386i) q^{17} +(-0.0136865 + 0.0136865i) q^{19} +(-2.97357 - 2.97357i) q^{21} +(3.15240 + 3.15240i) q^{23} +(-4.42682 + 2.32449i) q^{25} -5.65499i q^{27} +(3.33787 + 3.33787i) q^{29} -8.92639i q^{31} +(-3.02424 - 3.02424i) q^{33} +(-5.77640 - 3.49118i) q^{35} -7.24737 q^{37} +2.15475i q^{39} -10.3771i q^{41} -2.02975 q^{43} +(-0.566942 - 2.29920i) q^{45} +(3.34313 + 3.34313i) q^{47} -2.11103i q^{49} +(5.38308 + 5.38308i) q^{51} +7.30702i q^{53} +(-5.87483 - 3.55067i) q^{55} +(0.0190679 + 0.0190679i) q^{57} +(3.52732 + 3.52732i) q^{59} +(-1.41629 + 1.41629i) q^{61} +(2.26036 - 2.26036i) q^{63} +(0.827973 + 3.35780i) q^{65} +0.748197 q^{67} +(4.39187 - 4.39187i) q^{69} +0.269603 q^{71} +(-0.811870 + 0.811870i) q^{73} +(3.23844 + 6.16739i) q^{75} -9.26628i q^{77} -2.80567 q^{79} -4.70135 q^{81} +12.8279i q^{83} +(10.4571 + 6.32012i) q^{85} +(4.65027 - 4.65027i) q^{87} +13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} -12.4361 q^{93} +(0.0370409 + 0.0223871i) q^{95} +(6.33466 - 6.33466i) q^{97} +(2.29888 - 2.29888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9	$ 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9} - 2 q^{11} - 20 q^{15} - 6 q^{17} + 2 q^{19} + 16 q^{21} + 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} - 6 q^{35} - 8 q^{37} - 44 q^{43} + 4 q^{45} + 38 q^{47} + 8 q^{51} + 6 q^{55} + 24 q^{57} - 10 q^{59} - 14 q^{61} - 6 q^{63} + 12 q^{67} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 64 q^{75} - 16 q^{79} + 2 q^{81} + 10 q^{85} - 24 q^{87} - 12 q^{89} - 16 q^{93} + 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9 - 2 * q^11 - 20 * q^15 - 6 * q^17 + 2 * q^19 + 16 * q^21 + 2 * q^23 + 6 * q^25 + 14 * q^29 - 8 * q^33 - 6 * q^35 - 8 * q^37 - 44 * q^43 + 4 * q^45 + 38 * q^47 + 8 * q^51 + 6 * q^55 + 24 * q^57 - 10 * q^59 - 14 * q^61 - 6 * q^63 + 12 * q^67 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 64 * q^75 - 16 * q^79 + 2 * q^81 + 10 * q^85 - 24 * q^87 - 12 * q^89 - 16 * q^93 + 34 * q^95 + 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		−	1.39319i		−	0.804356i	−0.915561	−	0.402178i	$-0.868253\pi$
$3$		−	1.39319i		−	0.804356i	0.915561	−	0.402178i	$-0.131747\pi$
$4$		0			0
$5$	−0.535339	−	2.17104i	−0.239411	−	0.970918i
$5$	−0.535339	−	2.17104i	−0.239411	−	0.970918i
$6$		0			0
$7$	2.13436	−	2.13436i	0.806714	−	0.806714i	−0.177421	−	0.984135i	$-0.556775\pi$
$7$	2.13436	−	2.13436i	0.806714	−	0.806714i	0.984135	+	0.177421i	$0.0567754\pi$
$8$		0			0
$9$	1.05903			0.353011
$10$		0			0
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	−0.299572	−	0.954074i	$-0.596844\pi$
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	0.954074	+	0.299572i	$0.0968440\pi$
$12$		0			0
$13$	−1.54663			−0.428958			−0.214479	−	0.976729i	$-0.568805\pi$
$13$	−1.54663			−0.428958			−0.214479	+	0.976729i	$0.568805\pi$
$14$		0			0
$15$	−3.02466	+	0.745827i	−0.780964	+	0.192572i
$16$		0			0
$17$	−3.86386	+	3.86386i	−0.937125	+	0.937125i	−0.998137	−	0.0610123i	$-0.980567\pi$
$17$	−3.86386	+	3.86386i	−0.937125	+	0.937125i	0.0610123	+	0.998137i	$0.480567\pi$
$18$		0			0
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	−0.708675	−	0.705535i	$-0.750707\pi$
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	0.705535	+	0.708675i	$0.250707\pi$
$20$		0			0
$21$	−2.97357	−	2.97357i	−0.648886	−	0.648886i
$22$		0			0
$23$	3.15240	+	3.15240i	0.657320	+	0.657320i	0.954745	−	0.297425i	$-0.0961279\pi$
$23$	3.15240	+	3.15240i	0.657320	+	0.657320i	−0.297425	+	0.954745i	$0.596128\pi$
$24$		0			0
$25$	−4.42682	+	2.32449i	−0.885365	+	0.464897i
$26$		0			0
$27$		−	5.65499i		−	1.08830i
$28$		0			0
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	0.945487	−	0.325660i	$-0.105587\pi$
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	−0.325660	+	0.945487i	$0.605587\pi$
$30$		0			0
$31$		−	8.92639i		−	1.60323i	−0.597843	−	0.801613i	$-0.703975\pi$
$31$		−	8.92639i		−	1.60323i	0.597843	−	0.801613i	$-0.296025\pi$
$32$		0			0
$33$	−3.02424	−	3.02424i	−0.526452	−	0.526452i
$34$		0			0
$35$	−5.77640	−	3.49118i	−0.976390	−	0.590117i
$36$		0			0
$37$	−7.24737			−1.19146			−0.595730	−	0.803184i	$-0.703137\pi$
$37$	−7.24737			−1.19146			−0.595730	+	0.803184i	$0.703137\pi$
$38$		0			0
$39$			2.15475i			0.345035i
$40$		0			0
$41$		−	10.3771i		−	1.62063i	−0.585996	−	0.810314i	$-0.699296\pi$
$41$		−	10.3771i		−	1.62063i	0.585996	−	0.810314i	$-0.300704\pi$
$42$		0			0
$43$	−2.02975			−0.309534			−0.154767	−	0.987951i	$-0.549463\pi$
$43$	−2.02975			−0.309534			−0.154767	+	0.987951i	$0.549463\pi$
$44$		0			0
$45$	−0.566942	−	2.29920i	−0.0845147	−	0.342745i
$46$		0			0
$47$	3.34313	+	3.34313i	0.487646	+	0.487646i	0.907563	−	0.419917i	$-0.137941\pi$
$47$	3.34313	+	3.34313i	0.487646	+	0.487646i	−0.419917	+	0.907563i	$0.637941\pi$
$48$		0			0
$49$		−	2.11103i		−	0.301575i
$50$		0			0
$51$	5.38308	+	5.38308i	0.753782	+	0.753782i
$52$		0			0
$53$			7.30702i			1.00370i	0.864956	+	0.501848i	$0.167346\pi$
$53$			7.30702i			1.00370i	−0.864956	+	0.501848i	$0.832654\pi$
$54$		0			0
$55$	−5.87483	−	3.55067i	−0.792162	−	0.478772i
$56$		0			0
$57$	0.0190679	+	0.0190679i	0.00252560	+	0.00252560i
$58$		0			0
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	0.898399	−	0.439181i	$-0.144731\pi$
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	−0.439181	+	0.898399i	$0.644731\pi$
$60$		0			0
$61$	−1.41629	+	1.41629i	−0.181338	+	0.181338i	−0.791939	−	0.610601i	$-0.790928\pi$
$61$	−1.41629	+	1.41629i	−0.181338	+	0.181338i	0.610601	+	0.791939i	$0.290928\pi$
$62$		0			0
$63$	2.26036	−	2.26036i	0.284779	−	0.284779i
$64$		0			0
$65$	0.827973	+	3.35780i	0.102697	+	0.416484i
$66$		0			0
$67$	0.748197			0.0914068			0.0457034	−	0.998955i	$-0.485447\pi$
$67$	0.748197			0.0914068			0.0457034	+	0.998955i	$0.485447\pi$
$68$		0			0
$69$	4.39187	−	4.39187i	0.528719	−	0.528719i
$70$		0			0
$71$	0.269603			0.0319960			0.0159980	−	0.999872i	$-0.494907\pi$
$71$	0.269603			0.0319960			0.0159980	+	0.999872i	$0.494907\pi$
$72$		0			0
$73$	−0.811870	+	0.811870i	−0.0950222	+	0.0950222i	−0.753020	−	0.657998i	$-0.771404\pi$
$73$	−0.811870	+	0.811870i	−0.0950222	+	0.0950222i	0.657998	+	0.753020i	$0.271404\pi$
$74$		0			0
$75$	3.23844	+	6.16739i	0.373943	+	0.712149i
$76$		0			0
$77$		−	9.26628i		−	1.05599i
$78$		0			0
$79$	−2.80567			−0.315662			−0.157831	−	0.987466i	$-0.550450\pi$
$79$	−2.80567			−0.315662			−0.157831	+	0.987466i	$0.550450\pi$
$80$		0			0
$81$	−4.70135			−0.522372
$82$		0			0
$83$			12.8279i			1.40804i	0.710178	+	0.704022i	$0.248614\pi$
$83$			12.8279i			1.40804i	−0.710178	+	0.704022i	$0.751386\pi$
$84$		0			0
$85$	10.4571	+	6.32012i	1.13423	+	0.685514i
$86$		0			0
$87$	4.65027	−	4.65027i	0.498561	−	0.498561i
$88$		0			0
$89$	13.3732			1.41755			0.708777	−	0.705432i	$-0.249247\pi$
$89$	13.3732			1.41755			0.708777	+	0.705432i	$0.249247\pi$
$90$		0			0
$91$	−3.30108	+	3.30108i	−0.346047	+	0.346047i
$92$		0			0
$93$	−12.4361			−1.28957
$94$		0			0
$95$	0.0370409	+	0.0223871i	0.00380032	+	0.00229686i
$96$		0			0
$97$	6.33466	−	6.33466i	0.643187	−	0.643187i	−0.308151	−	0.951338i	$-0.599710\pi$
$97$	6.33466	−	6.33466i	0.643187	−	0.643187i	0.951338	+	0.308151i	$0.0997101\pi$
$98$		0			0
$99$	2.29888	−	2.29888i	0.231046	−	0.231046i
$100$		0			0
$101$	3.78129	+	3.78129i	0.376252	+	0.376252i	0.869748	−	0.493496i	$-0.164281\pi$
$101$	3.78129	+	3.78129i	0.376252	+	0.376252i	−0.493496	+	0.869748i	$0.664281\pi$
$102$		0			0
$103$	−10.7199	−	10.7199i	−1.05626	−	1.05626i	−0.998320	−	0.0579430i	$-0.981546\pi$
$103$	−10.7199	−	10.7199i	−1.05626	−	1.05626i	−0.0579430	−	0.998320i	$-0.518454\pi$
$104$		0			0
$105$	−4.86386	+	8.04760i	−0.474665	+	0.785365i
$106$		0			0
$107$		−	10.9109i		−	1.05479i	−0.849619	−	0.527397i	$-0.823168\pi$
$107$		−	10.9109i		−	1.05479i	0.849619	−	0.527397i	$-0.176832\pi$
$108$		0			0
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	0.992870	−	0.119200i	$-0.0380329\pi$
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	−0.119200	+	0.992870i	$0.538033\pi$
$110$		0			0
$111$			10.0969i			0.958359i
$112$		0			0
$113$	4.88810	+	4.88810i	0.459834	+	0.459834i	0.898601	−	0.438767i	$-0.144585\pi$
$113$	4.88810	+	4.88810i	0.459834	+	0.459834i	−0.438767	+	0.898601i	$0.644585\pi$
$114$		0			0
$115$	5.15637	−	8.53157i	0.480834	−	0.795573i
$116$		0			0
$117$	−1.63793			−0.151427
$118$		0			0
$119$			16.4938i			1.51198i
$120$		0			0
$121$			1.57582i			0.143256i
$122$		0			0
$123$	−14.4572			−1.30356
$124$		0			0
$125$	7.41640	+	8.36642i	0.663343	+	0.748315i
$126$		0			0
$127$	1.38586	+	1.38586i	0.122975	+	0.122975i	0.765916	−	0.642941i	$-0.222286\pi$
$127$	1.38586	+	1.38586i	0.122975	+	0.122975i	−0.642941	+	0.765916i	$0.722286\pi$
$128$		0			0
$129$			2.82782i			0.248976i
$130$		0			0
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	0.536361	−	0.843989i	$-0.319798\pi$
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	−0.843989	+	0.536361i	$0.819798\pi$
$132$		0			0
$133$			0.0584241i			0.00506601i
$134$		0			0
$135$	−12.2772	+	3.02734i	−1.05665	+	0.260552i
$136$		0			0
$137$	5.62512	+	5.62512i	0.480587	+	0.480587i	0.905319	−	0.424732i	$-0.139632\pi$
$137$	5.62512	+	5.62512i	0.480587	+	0.480587i	−0.424732	+	0.905319i	$0.639632\pi$
$138$		0			0
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.999639	+	0.0268584i	$0.00855031\pi$
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.0268584	+	0.999639i	$0.491450\pi$
$140$		0			0
$141$	4.65760	−	4.65760i	0.392241	−	0.392241i
$142$		0			0
$143$	−3.35733	+	3.35733i	−0.280754	+	0.280754i
$144$		0			0
$145$	5.45975	−	9.03353i	0.453408	−	0.750194i
$146$		0			0
$147$	−2.94105			−0.242574
$148$		0			0
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.117757	−	0.993042i	$-0.462430\pi$
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.993042	−	0.117757i	$-0.0375702\pi$
$150$		0			0
$151$	20.7185			1.68605			0.843025	−	0.537874i	$-0.180772\pi$
$151$	20.7185			1.68605			0.843025	+	0.537874i	$0.180772\pi$
$152$		0			0
$153$	−4.09196	+	4.09196i	−0.330815	+	0.330815i
$154$		0			0
$155$	−19.3795	+	4.77865i	−1.55660	+	0.383830i
$156$		0			0
$157$		−	5.72312i		−	0.456755i	−0.973573	−	0.228377i	$-0.926658\pi$
$157$		−	5.72312i		−	0.456755i	0.973573	−	0.228377i	$-0.0733420\pi$
$158$		0			0
$159$	10.1800			0.807329
$160$		0			0
$161$	13.4567			1.06054
$162$		0			0
$163$		−	17.9900i		−	1.40909i	−0.709662	−	0.704543i	$-0.751152\pi$
$163$		−	17.9900i		−	1.40909i	0.709662	−	0.704543i	$-0.248848\pi$
$164$		0			0
$165$	−4.94675	+	8.18473i	−0.385104	+	0.637181i
$166$		0			0
$167$	−2.39642	+	2.39642i	−0.185441	+	0.185441i	−0.793722	−	0.608281i	$-0.791859\pi$
$167$	−2.39642	+	2.39642i	−0.185441	+	0.185441i	0.608281	+	0.793722i	$0.291859\pi$
$168$		0			0
$169$	−10.6079			−0.815995
$170$		0			0
$171$	−0.0144945	+	0.0144945i	−0.00110842	+	0.00110842i
$172$		0			0
$173$	9.45205			0.718626			0.359313	−	0.933217i	$-0.383011\pi$
$173$	9.45205			0.718626			0.359313	+	0.933217i	$0.383011\pi$
$174$		0			0
$175$	−4.48716	+	14.4098i	−0.339197	+	1.08928i
$176$		0			0
$177$	4.91421	−	4.91421i	0.369375	−	0.369375i
$178$		0			0
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	−0.993728	−	0.111824i	$-0.964331\pi$
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	0.111824	+	0.993728i	$0.464331\pi$
$180$		0			0
$181$	−2.54155	−	2.54155i	−0.188912	−	0.188912i	0.606314	−	0.795225i	$-0.292648\pi$
$181$	−2.54155	−	2.54155i	−0.188912	−	0.188912i	−0.795225	+	0.606314i	$0.792648\pi$
$182$		0			0
$183$	1.97316	+	1.97316i	0.145860	+	0.145860i
$184$		0			0
$185$	3.87980	+	15.7343i	0.285249	+	1.15681i
$186$		0			0
$187$			16.7748i			1.22670i
$188$		0			0
$189$	−12.0698	−	12.0698i	−0.877949	−	0.877949i
$190$		0			0
$191$			5.46421i			0.395376i	0.980265	+	0.197688i	$0.0633433\pi$
$191$			5.46421i			0.395376i	−0.980265	+	0.197688i	$0.936657\pi$
$192$		0			0
$193$	4.82485	+	4.82485i	0.347300	+	0.347300i	0.859103	−	0.511803i	$-0.171022\pi$
$193$	4.82485	+	4.82485i	0.347300	+	0.347300i	−0.511803	+	0.859103i	$0.671022\pi$
$194$		0			0
$195$	4.67804	−	1.15352i	0.335001	−	0.0826053i
$196$		0			0
$197$	−2.94582			−0.209881			−0.104941	−	0.994478i	$-0.533465\pi$
$197$	−2.94582			−0.209881			−0.104941	+	0.994478i	$0.533465\pi$
$198$		0			0
$199$			2.14620i			0.152140i	0.997102	+	0.0760700i	$0.0242372\pi$
$199$			2.14620i			0.152140i	−0.997102	+	0.0760700i	$0.975763\pi$
$200$		0			0
$201$		−	1.04238i		−	0.0735236i
$202$		0			0
$203$	14.2485			1.00005
$204$		0			0
$205$	−22.5291	+	5.55526i	−1.57350	+	0.387996i
$206$		0			0
$207$	3.33849	+	3.33849i	0.232041	+	0.232041i
$208$		0			0
$209$			0.0594197i			0.00411014i
$210$		0			0
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	0.871708	−	0.490025i	$-0.163012\pi$
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	−0.490025	+	0.871708i	$0.663012\pi$
$212$		0			0
$213$		−	0.375608i		−	0.0257362i
$214$		0			0
$215$	1.08661	+	4.40667i	0.0741059	+	0.300532i
$216$		0			0
$217$	−19.0522	−	19.0522i	−1.29335	−	1.29335i
$218$		0			0
$219$	1.13109	+	1.13109i	0.0764317	+	0.0764317i
$220$		0			0
$221$	5.97597	−	5.97597i	0.401988	−	0.401988i
$222$		0			0
$223$	1.16163	−	1.16163i	0.0777882	−	0.0777882i	−0.667142	−	0.744930i	$-0.732483\pi$
$223$	1.16163	−	1.16163i	0.0777882	−	0.0777882i	0.744930	+	0.667142i	$0.232483\pi$
$224$		0			0
$225$	−4.68815	+	2.46171i	−0.312543	+	0.164114i
$226$		0			0
$227$	12.8161			0.850632			0.425316	−	0.905045i	$-0.360163\pi$
$227$	12.8161			0.850632			0.425316	+	0.905045i	$0.360163\pi$
$228$		0			0
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	−0.674093	−	0.738647i	$-0.735465\pi$
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	0.738647	+	0.674093i	$0.235465\pi$
$230$		0			0
$231$	−12.9097			−0.849393
$232$		0			0
$233$	0.303870	−	0.303870i	0.0199072	−	0.0199072i	−0.697083	−	0.716990i	$-0.745519\pi$
$233$	0.303870	−	0.303870i	0.0199072	−	0.0199072i	0.716990	+	0.697083i	$0.245519\pi$
$234$		0			0
$235$	5.46836	−	9.04777i	0.356716	−	0.590212i
$236$		0			0
$237$			3.90881i			0.253905i
$238$		0			0
$239$	−12.5096			−0.809178			−0.404589	−	0.914499i	$-0.632585\pi$
$239$	−12.5096			−0.809178			−0.404589	+	0.914499i	$0.632585\pi$
$240$		0			0
$241$	−19.5775			−1.26110			−0.630548	−	0.776150i	$-0.717170\pi$
$241$	−19.5775			−1.26110			−0.630548	+	0.776150i	$0.717170\pi$
$242$		0			0
$243$		−	10.4151i		−	0.668129i
$244$		0			0
$245$	−4.58312	+	1.13012i	−0.292805	+	0.0722004i
$246$		0			0
$247$	0.0211680	−	0.0211680i	0.00134689	−	0.00134689i
$248$		0			0
$249$	17.8716			1.13257
$250$		0			0
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	−0.524563	−	0.851372i	$-0.675771\pi$
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	0.851372	+	0.524563i	$0.175771\pi$
$252$		0			0
$253$	13.6860			0.860433
$254$		0			0
$255$	8.80511	−	14.5687i	0.551397	−	0.912325i
$256$		0			0
$257$	−14.7989	+	14.7989i	−0.923131	+	0.923131i	−0.997249	−	0.0741183i	$-0.976386\pi$
$257$	−14.7989	+	14.7989i	−0.923131	+	0.923131i	0.0741183	+	0.997249i	$0.476386\pi$
$258$		0			0
$259$	−15.4685	+	15.4685i	−0.961168	+	0.961168i
$260$		0			0
$261$	3.53491	+	3.53491i	0.218805	+	0.218805i
$262$		0			0
$263$	−11.7906	−	11.7906i	−0.727038	−	0.727038i	0.242991	−	0.970029i	$-0.421871\pi$
$263$	−11.7906	−	11.7906i	−0.727038	−	0.727038i	−0.970029	+	0.242991i	$0.921871\pi$
$264$		0			0
$265$	15.8638	−	3.91173i	0.974507	−	0.240296i
$266$		0			0
$267$		−	18.6313i		−	1.14022i
$268$		0			0
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	0.768256	−	0.640143i	$-0.221125\pi$
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	−0.640143	+	0.768256i	$0.721125\pi$
$270$		0			0
$271$		−	18.8596i		−	1.14564i	−0.819683	−	0.572818i	$-0.805850\pi$
$271$		−	18.8596i		−	1.14564i	0.819683	−	0.572818i	$-0.194150\pi$
$272$		0			0
$273$	4.59901	+	4.59901i	0.278345	+	0.278345i
$274$		0			0
$275$	−4.56362	+	14.6553i	−0.275197	+	0.883748i
$276$		0			0
$277$	−9.91909			−0.595980			−0.297990	−	0.954569i	$-0.596316\pi$
$277$	−9.91909			−0.595980			−0.297990	+	0.954569i	$0.596316\pi$
$278$		0			0
$279$		−	9.45334i		−	0.565956i
$280$		0			0
$281$		−	9.31434i		−	0.555647i	−0.960632	−	0.277823i	$-0.910387\pi$
$281$		−	9.31434i		−	0.555647i	0.960632	−	0.277823i	$-0.0896130\pi$
$282$		0			0
$283$	−3.42364			−0.203514			−0.101757	−	0.994809i	$-0.532446\pi$
$283$	−3.42364			−0.203514			−0.101757	+	0.994809i	$0.532446\pi$
$284$		0			0
$285$	0.0311893	−	0.0516049i	0.00184750	−	0.00305681i
$286$		0			0
$287$	−22.1485	−	22.1485i	−1.30738	−	1.30738i
$288$		0			0
$289$		−	12.8589i		−	0.756405i
$290$		0			0
$291$	−8.82535	−	8.82535i	−0.517351	−	0.517351i
$292$		0			0
$293$		−	2.66471i		−	0.155674i	−0.996966	−	0.0778369i	$-0.975199\pi$
$293$		−	2.66471i		−	0.155674i	0.996966	−	0.0778369i	$-0.0248013\pi$
$294$		0			0
$295$	5.76963	−	9.54626i	0.335921	−	0.555804i
$296$		0			0
$297$	−12.2755	−	12.2755i	−0.712296	−	0.712296i
$298$		0			0
$299$	−4.87559	−	4.87559i	−0.281963	−	0.281963i
$300$		0			0
$301$	−4.33223	+	4.33223i	−0.249706	+	0.249706i
$302$		0			0
$303$	5.26804	−	5.26804i	0.302641	−	0.302641i
$304$		0			0
$305$	3.83303	+	2.31663i	0.219478	+	0.132650i
$306$		0			0
$307$	10.5554			0.602430			0.301215	−	0.953556i	$-0.402608\pi$
$307$	10.5554			0.602430			0.301215	+	0.953556i	$0.402608\pi$
$308$		0			0
$309$	−14.9348	+	14.9348i	−0.849612	+	0.849612i
$310$		0			0
$311$	20.4762			1.16110			0.580550	−	0.814225i	$-0.302838\pi$
$311$	20.4762			1.16110			0.580550	+	0.814225i	$0.302838\pi$
$312$		0			0
$313$	2.82393	−	2.82393i	0.159618	−	0.159618i	−0.622780	−	0.782397i	$-0.713997\pi$
$313$	2.82393	−	2.82393i	0.159618	−	0.159618i	0.782397	+	0.622780i	$0.213997\pi$
$314$		0			0
$315$	−6.11740	−	3.69727i	−0.344676	−	0.208318i
$316$		0			0
$317$			20.2533i			1.13754i	0.822497	+	0.568769i	$0.192580\pi$
$317$			20.2533i			1.13754i	−0.822497	+	0.568769i	$0.807420\pi$
$318$		0			0
$319$	14.4913			0.811354
$320$		0			0
$321$	−15.2009			−0.848430
$322$		0			0
$323$		−	0.105766i		−	0.00588497i
$324$		0			0
$325$	6.84667	−	3.59512i	0.379785	−	0.199422i
$326$		0			0
$327$	12.7078	−	12.7078i	0.702742	−	0.702742i
$328$		0			0
$329$	14.2709			0.786781
$330$		0			0
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.0741908	−	0.997244i	$-0.476363\pi$
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.997244	−	0.0741908i	$-0.0236374\pi$
$332$		0			0
$333$	−7.67521			−0.420599
$334$		0			0
$335$	−0.400539	−	1.62437i	−0.0218838	−	0.0887485i
$336$		0			0
$337$	−5.89449	+	5.89449i	−0.321093	+	0.321093i	−0.849186	−	0.528093i	$-0.822907\pi$
$337$	−5.89449	+	5.89449i	−0.321093	+	0.321093i	0.528093	+	0.849186i	$0.322907\pi$
$338$		0			0
$339$	6.81003	−	6.81003i	0.369870	−	0.369870i
$340$		0			0
$341$	−19.3768	−	19.3768i	−1.04931	−	1.04931i
$342$		0			0
$343$	10.4349	+	10.4349i	0.563429	+	0.563429i
$344$		0			0
$345$	−11.8861	−	7.18379i	−0.639925	−	0.386762i
$346$		0			0
$347$			11.4626i			0.615346i	0.951492	+	0.307673i	$0.0995502\pi$
$347$			11.4626i			0.615346i	−0.951492	+	0.307673i	$0.900450\pi$
$348$		0			0
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	0.715563	−	0.698548i	$-0.246170\pi$
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	−0.698548	+	0.715563i	$0.746170\pi$
$350$		0			0
$351$			8.74618i			0.466837i
$352$		0			0
$353$	−18.4551	−	18.4551i	−0.982266	−	0.982266i	0.0175800	−	0.999845i	$-0.494404\pi$
$353$	−18.4551	−	18.4551i	−0.982266	−	0.982266i	−0.999845	+	0.0175800i	$0.994404\pi$
$354$		0			0
$355$	−0.144329	−	0.585320i	−0.00766020	−	0.0310655i
$356$		0			0
$357$	22.9789			1.21617
$358$		0			0
$359$			15.5802i			0.822292i	0.911569	+	0.411146i	$0.134871\pi$
$359$			15.5802i			0.822292i	−0.911569	+	0.411146i	$0.865129\pi$
$360$		0			0
$361$			18.9996i			0.999980i
$362$		0			0
$363$	2.19541			0.115229
$364$		0			0
$365$	2.19723	+	1.32798i	0.115008	+	0.0695095i
$366$		0			0
$367$	−5.37489	−	5.37489i	−0.280567	−	0.280567i	0.552768	−	0.833335i	$-0.313572\pi$
$367$	−5.37489	−	5.37489i	−0.280567	−	0.280567i	−0.833335	+	0.552768i	$0.813572\pi$
$368$		0			0
$369$		−	10.9897i		−	0.572100i
$370$		0			0
$371$	15.5958	+	15.5958i	0.809696	+	0.809696i
$372$		0			0
$373$		−	3.24424i		−	0.167980i	−0.996467	−	0.0839902i	$-0.973234\pi$
$373$		−	3.24424i		−	0.167980i	0.996467	−	0.0839902i	$-0.0267664\pi$
$374$		0			0
$375$	11.6560	−	10.3324i	0.601912	−	0.533564i
$376$		0			0
$377$	−5.16245	−	5.16245i	−0.265880	−	0.265880i
$378$		0			0
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.910785	−	0.412882i	$-0.864522\pi$
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.412882	−	0.910785i	$-0.635478\pi$
$380$		0			0
$381$	1.93076	−	1.93076i	0.0989160	−	0.0989160i
$382$		0			0
$383$	−0.418091	+	0.418091i	−0.0213634	+	0.0213634i	−0.717708	−	0.696344i	$-0.754809\pi$
$383$	−0.418091	+	0.418091i	−0.0213634	+	0.0213634i	0.696344	+	0.717708i	$0.254809\pi$
$384$		0			0
$385$	−20.1175	+	4.96060i	−1.02528	+	0.252816i
$386$		0			0
$387$	−2.14957			−0.109269
$388$		0			0
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	−0.959436	−	0.281927i	$-0.909026\pi$
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	0.281927	+	0.959436i	$0.409026\pi$
$390$		0			0
$391$	−24.3609			−1.23198
$392$		0			0
$393$	−4.90535	+	4.90535i	−0.247442	+	0.247442i
$394$		0			0
$395$	1.50198	+	6.09121i	0.0755730	+	0.306482i
$396$		0			0
$397$		−	13.8391i		−	0.694564i	−0.937761	−	0.347282i	$-0.887105\pi$
$397$		−	13.8391i		−	0.694564i	0.937761	−	0.347282i	$-0.112895\pi$
$398$		0			0
$399$	0.0813957			0.00407488
$400$		0			0
$401$	20.3112			1.01430			0.507148	−	0.861859i	$-0.330700\pi$
$401$	20.3112			1.01430			0.507148	+	0.861859i	$0.330700\pi$
$402$		0			0
$403$			13.8058i			0.687718i
$404$		0			0
$405$	2.51682	+	10.2068i	0.125062	+	0.507181i
$406$		0			0
$407$	−15.7321	+	15.7321i	−0.779813	+	0.779813i
$408$		0			0
$409$	−18.2875			−0.904259			−0.452130	−	0.891952i	$-0.649336\pi$
$409$	−18.2875			−0.904259			−0.452130	+	0.891952i	$0.649336\pi$
$410$		0			0
$411$	7.83684	−	7.83684i	0.386563	−	0.386563i
$412$		0			0
$413$	15.0572			0.740915
$414$		0			0
$415$	27.8499	−	6.86728i	1.36710	−	0.337101i
$416$		0			0
$417$	16.8607	−	16.8607i	0.825670	−	0.825670i
$418$		0			0
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	−0.143563	−	0.989641i	$-0.545856\pi$
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	0.989641	+	0.143563i	$0.0458558\pi$
$420$		0			0
$421$	−11.5457	−	11.5457i	−0.562703	−	0.562703i	0.367372	−	0.930074i	$-0.380258\pi$
$421$	−11.5457	−	11.5457i	−0.562703	−	0.562703i	−0.930074	+	0.367372i	$0.880258\pi$
$422$		0			0
$423$	3.54048	+	3.54048i	0.172144	+	0.172144i
$424$		0			0
$425$	8.12315	−	26.0861i	0.394031	−	1.26536i
$426$		0			0
$427$			6.04577i			0.292576i
$428$		0			0
$429$	4.67738	+	4.67738i	0.225826	+	0.225826i
$430$		0			0
$431$			15.9479i			0.768185i	0.923295	+	0.384093i	$0.125486\pi$
$431$			15.9479i			0.768185i	−0.923295	+	0.384093i	$0.874514\pi$
$432$		0			0
$433$	3.52109	+	3.52109i	0.169213	+	0.169213i	0.786633	−	0.617420i	$-0.211822\pi$
$433$	3.52109	+	3.52109i	0.169213	+	0.169213i	−0.617420	+	0.786633i	$0.711822\pi$
$434$		0			0
$435$	−12.5854	−	7.60645i	−0.603423	−	0.364701i
$436$		0			0
$437$	−0.0862907			−0.00412784
$438$		0			0
$439$		−	6.45840i		−	0.308242i	−0.988052	−	0.154121i	$-0.950745\pi$
$439$		−	6.45840i		−	0.308242i	0.988052	−	0.154121i	$-0.0492546\pi$
$440$		0			0
$441$		−	2.23565i		−	0.106459i
$442$		0			0
$443$	27.0992			1.28752			0.643761	−	0.765226i	$-0.277373\pi$
$443$	27.0992			1.28752			0.643761	+	0.765226i	$0.277373\pi$
$444$		0			0
$445$	−7.15919	−	29.0337i	−0.339378	−	1.37633i
$446$		0			0
$447$	−18.8903	−	18.8903i	−0.893478	−	0.893478i
$448$		0			0
$449$			41.0879i			1.93906i	0.244976	+	0.969529i	$0.421220\pi$
$449$			41.0879i			1.93906i	−0.244976	+	0.969529i	$0.578780\pi$
$450$		0			0
$451$	−22.5259	−	22.5259i	−1.06070	−	1.06070i
$452$		0			0
$453$		−	28.8648i		−	1.35619i
$454$		0			0
$455$	8.93396	+	5.39957i	0.418831	+	0.253136i
$456$		0			0
$457$	18.2449	+	18.2449i	0.853462	+	0.853462i	0.990558	−	0.137096i	$-0.0437769\pi$
$457$	18.2449	+	18.2449i	0.853462	+	0.853462i	−0.137096	+	0.990558i	$0.543777\pi$
$458$		0			0
$459$	21.8501	+	21.8501i	1.01988	+	1.01988i
$460$		0			0
$461$	−6.68802	+	6.68802i	−0.311492	+	0.311492i	−0.845488	−	0.533995i	$-0.820690\pi$
$461$	−6.68802	+	6.68802i	−0.311492	+	0.311492i	0.533995	+	0.845488i	$0.320690\pi$
$462$		0			0
$463$	−28.6926	+	28.6926i	−1.33346	+	1.33346i	−0.431205	+	0.902254i	$0.641911\pi$
$463$	−28.6926	+	28.6926i	−1.33346	+	1.33346i	−0.902254	+	0.431205i	$0.858089\pi$
$464$		0			0
$465$	6.65754	+	26.9993i	0.308736	+	1.25206i
$466$		0			0
$467$	−32.4161			−1.50004			−0.750018	−	0.661417i	$-0.769955\pi$
$467$	−32.4161			−1.50004			−0.750018	+	0.661417i	$0.769955\pi$
$468$		0			0
$469$	1.59693	−	1.59693i	0.0737392	−	0.0737392i
$470$		0			0
$471$	−7.97337			−0.367394
$472$		0			0
$473$	−4.40605	+	4.40605i	−0.202591	+	0.202591i
$474$		0			0
$475$	0.0287737	−	0.0924020i	0.00132023	−	0.00423970i
$476$		0			0
$477$			7.73837i			0.354316i
$478$		0			0
$479$	−7.33117			−0.334970			−0.167485	−	0.985875i	$-0.553565\pi$
$479$	−7.33117			−0.334970			−0.167485	+	0.985875i	$0.553565\pi$
$480$		0			0
$481$	11.2090			0.511087
$482$		0			0
$483$		−	18.7477i		−	0.853051i
$484$		0			0
$485$	−17.1440	−	10.3616i	−0.778468	−	0.470496i
$486$		0			0
$487$	11.7773	−	11.7773i	0.533681	−	0.533681i	−0.387985	−	0.921666i	$-0.626829\pi$
$487$	11.7773	−	11.7773i	0.533681	−	0.533681i	0.921666	+	0.387985i	$0.126829\pi$
$488$		0			0
$489$	−25.0634			−1.13341
$490$		0			0
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.272343	+	0.962200i	$0.587798\pi$
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.962200	+	0.272343i	$0.912202\pi$
$492$		0			0
$493$	−25.7941			−1.16171
$494$		0			0
$495$	−6.22164	−	3.76028i	−0.279642	−	0.169012i
$496$		0			0
$497$	0.575432	−	0.575432i	0.0258117	−	0.0258117i
$498$		0			0
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	−0.380353	−	0.924841i	$-0.624198\pi$
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	0.924841	+	0.380353i	$0.124198\pi$
$500$		0			0
$501$	3.33866	+	3.33866i	0.149160	+	0.149160i
$502$		0			0
$503$	13.2748	+	13.2748i	0.591892	+	0.591892i	0.938142	−	0.346250i	$-0.112545\pi$
$503$	13.2748	+	13.2748i	0.591892	+	0.591892i	−0.346250	+	0.938142i	$0.612545\pi$
$504$		0			0
$505$	6.18505	−	10.2336i	0.275231	−	0.455389i
$506$		0			0
$507$			14.7788i			0.656350i
$508$		0			0
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	0.470296	−	0.882509i	$-0.344147\pi$
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	−0.882509	+	0.470296i	$0.844147\pi$
$510$		0			0
$511$			3.46565i			0.153312i
$512$		0			0
$513$	0.0773972	+	0.0773972i	0.00341717	+	0.00341717i
$514$		0			0
$515$	−17.5345	+	29.0121i	−0.772664	+	1.27843i
$516$		0			0
$517$	14.5141			0.638329
$518$		0			0
$519$		−	13.1685i		−	0.578031i
$520$		0			0
$521$			33.5279i			1.46888i	0.678671	+	0.734442i	$0.262556\pi$
$521$			33.5279i			1.46888i	−0.678671	+	0.734442i	$0.737444\pi$
$522$		0			0
$523$	−25.9463			−1.13455			−0.567276	−	0.823528i	$-0.692003\pi$
$523$	−25.9463			−1.13455			−0.567276	+	0.823528i	$0.692003\pi$
$524$		0			0
$525$	20.0755	+	6.25144i	0.876165	+	0.272835i
$526$		0			0
$527$	34.4903	+	34.4903i	1.50242	+	1.50242i
$528$		0			0
$529$		−	3.12481i		−	0.135861i
$530$		0			0
$531$	3.73554	+	3.73554i	0.162109	+	0.162109i
$532$		0			0
$533$			16.0495i			0.695182i
$534$		0			0
$535$	−23.6879	+	5.84102i	−1.02412	+	0.252529i
$536$		0			0
$537$	16.4383	+	16.4383i	0.709365	+	0.709365i
$538$		0			0
$539$	−4.58248	−	4.58248i	−0.197381	−	0.197381i
$540$		0			0
$541$	−4.47122	+	4.47122i	−0.192233	+	0.192233i	−0.796660	−	0.604428i	$-0.793402\pi$
$541$	−4.47122	+	4.47122i	−0.192233	+	0.192233i	0.604428	+	0.796660i	$0.293402\pi$
$542$		0			0
$543$	−3.54085	+	3.54085i	−0.151952	+	0.151952i
$544$		0			0
$545$	14.9199	−	24.6859i	0.639096	−	1.05743i
$546$		0			0
$547$	15.5964			0.666853			0.333426	−	0.942776i	$-0.391795\pi$
$547$	15.5964			0.666853			0.333426	+	0.942776i	$0.391795\pi$
$548$		0			0
$549$	−1.49990	+	1.49990i	−0.0640142	+	0.0640142i
$550$		0			0
$551$	−0.0913677			−0.00389239
$552$		0			0
$553$	−5.98831	+	5.98831i	−0.254649	+	0.254649i
$554$		0			0
$555$	21.9209	−	5.40529i	0.930488	−	0.229442i
$556$		0			0
$557$			15.5348i			0.658231i	0.944290	+	0.329116i	$0.106751\pi$
$557$			15.5348i			0.658231i	−0.944290	+	0.329116i	$0.893249\pi$
$558$		0			0
$559$	3.13928			0.132777
$560$		0			0
$561$	23.3705			0.986703
$562$		0			0
$563$			24.3087i			1.02449i	0.858839	+	0.512245i	$0.171186\pi$
$563$			24.3087i			1.02449i	−0.858839	+	0.512245i	$0.828814\pi$
$564$		0			0
$565$	7.99547	−	13.2291i	0.336372	−	0.556550i
$566$		0			0
$567$	−10.0344	+	10.0344i	−0.421405	+	0.421405i
$568$		0			0
$569$	0.187259			0.00785029			0.00392515	−	0.999992i	$-0.498751\pi$
$569$	0.187259			0.00785029			0.00392515	+	0.999992i	$0.498751\pi$
$570$		0			0
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	−0.870974	−	0.491328i	$-0.836511\pi$
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	0.491328	+	0.870974i	$0.336511\pi$
$572$		0			0
$573$	7.61266			0.318023
$574$		0			0
$575$	−21.2828	−	6.62740i	−0.887554	−	0.276382i
$576$		0			0
$577$	−1.53648	+	1.53648i	−0.0639645	+	0.0639645i	−0.738365	−	0.674401i	$-0.764402\pi$
$577$	−1.53648	+	1.53648i	−0.0639645	+	0.0639645i	0.674401	+	0.738365i	$0.264402\pi$
$578$		0			0
$579$	6.72191	−	6.72191i	0.279353	−	0.279353i
$580$		0			0
$581$	27.3794	+	27.3794i	1.13589	+	1.13589i
$582$		0			0
$583$	15.8616	+	15.8616i	0.656920	+	0.656920i
$584$		0			0
$585$	0.876850	+	3.55602i	0.0362533	+	0.147023i
$586$		0			0
$587$			3.06150i			0.126362i	0.998002	+	0.0631808i	$0.0201245\pi$
$587$			3.06150i			0.126362i	−0.998002	+	0.0631808i	$0.979876\pi$
$588$		0			0
$589$	0.122171	+	0.122171i	0.00503398	+	0.00503398i
$590$		0			0
$591$			4.10408i			0.168819i
$592$		0			0
$593$	−20.8213	−	20.8213i	−0.855029	−	0.855029i	0.135718	−	0.990747i	$-0.456666\pi$
$593$	−20.8213	−	20.8213i	−0.855029	−	0.855029i	−0.990747	+	0.135718i	$0.956666\pi$
$594$		0			0
$595$	35.8087	−	8.82977i	1.46801	−	0.361985i
$596$		0			0
$597$	2.99005			0.122375
$598$		0			0
$599$		−	27.8866i		−	1.13942i	−0.821847	−	0.569709i	$-0.807056\pi$
$599$		−	27.8866i		−	1.13942i	0.821847	−	0.569709i	$-0.192944\pi$
$600$		0			0
$601$			4.70260i			0.191823i	0.995390	+	0.0959115i	$0.0305766\pi$
$601$			4.70260i			0.191823i	−0.995390	+	0.0959115i	$0.969423\pi$
$602$		0			0
$603$	0.792365			0.0322676
$604$		0			0
$605$	3.42116	−	0.843598i	0.139090	−	0.0342971i
$606$		0			0
$607$	28.8294	+	28.8294i	1.17015	+	1.17015i	0.982174	+	0.187975i	$0.0601925\pi$
$607$	28.8294	+	28.8294i	1.17015	+	1.17015i	0.187975	+	0.982174i	$0.439807\pi$
$608$		0			0
$609$		−	19.8507i		−	0.804393i
$610$		0			0
$611$	−5.17059	−	5.17059i	−0.209180	−	0.209180i
$612$		0			0
$613$			38.7980i			1.56704i	0.621369	+	0.783518i	$0.286577\pi$
$613$			38.7980i			1.56704i	−0.621369	+	0.783518i	$0.713423\pi$
$614$		0			0
$615$	7.73951	+	31.3872i	0.312087	+	1.26565i
$616$		0			0
$617$	−7.06723	−	7.06723i	−0.284516	−	0.284516i	0.550391	−	0.834907i	$-0.314479\pi$
$617$	−7.06723	−	7.06723i	−0.284516	−	0.284516i	−0.834907	+	0.550391i	$0.814479\pi$
$618$		0			0
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.990268	−	0.139172i	$-0.955556\pi$
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.139172	−	0.990268i	$-0.544444\pi$
$620$		0			0
$621$	17.8268	−	17.8268i	0.715363	−	0.715363i
$622$		0			0
$623$	28.5432	−	28.5432i	1.14356	−	1.14356i
$624$		0			0
$625$	14.1935	−	20.5802i	0.567741	−	0.823207i
$626$		0			0
$627$	0.0827827			0.00330602
$628$		0			0
$629$	28.0029	−	28.0029i	1.11655	−	1.11655i
$630$		0			0
$631$	−38.2613			−1.52316			−0.761580	−	0.648071i	$-0.775576\pi$
$631$	−38.2613			−1.52316			−0.761580	+	0.648071i	$0.775576\pi$
$632$		0			0
$633$	7.72420	−	7.72420i	0.307010	−	0.307010i
$634$		0			0
$635$	2.26685	−	3.75067i	0.0899574	−	0.148841i
$636$		0			0
$637$			3.26498i			0.129363i
$638$		0			0
$639$	0.285519			0.0112950
$640$		0			0
$641$	7.15922			0.282772			0.141386	−	0.989955i	$-0.454844\pi$
$641$	7.15922			0.282772			0.141386	+	0.989955i	$0.454844\pi$
$642$		0			0
$643$			8.74864i			0.345013i	0.985008	+	0.172506i	$0.0551866\pi$
$643$			8.74864i			0.345013i	−0.985008	+	0.172506i	$0.944813\pi$
$644$		0			0
$645$	6.13931	−	1.51384i	0.241735	−	0.0596076i
$646$		0			0
$647$	−8.84125	+	8.84125i	−0.347585	+	0.347585i	−0.859209	−	0.511624i	$-0.829044\pi$
$647$	−8.84125	+	8.84125i	−0.347585	+	0.347585i	0.511624	+	0.859209i	$0.329044\pi$
$648$		0			0
$649$	15.3137			0.601117
$650$		0			0
$651$	−26.5432	+	26.5432i	−1.04031	+	1.04031i
$652$		0			0
$653$	20.7854			0.813396			0.406698	−	0.913563i	$-0.366680\pi$
$653$	20.7854			0.813396			0.406698	+	0.913563i	$0.366680\pi$
$654$		0			0
$655$	−5.75923	+	9.52904i	−0.225032	+	0.372330i
$656$		0			0
$657$	−0.859797	+	0.859797i	−0.0335439	+	0.0335439i
$658$		0			0
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	−0.398003	−	0.917384i	$-0.630297\pi$
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	0.917384	+	0.398003i	$0.130297\pi$
$660$		0			0
$661$	30.5831	+	30.5831i	1.18954	+	1.18954i	0.977194	+	0.212350i	$0.0681116\pi$
$661$	30.5831	+	30.5831i	1.18954	+	1.18954i	0.212350	+	0.977194i	$0.431888\pi$
$662$		0			0
$663$	−8.32564	−	8.32564i	−0.323341	−	0.323341i
$664$		0			0
$665$	0.126841	−	0.0312767i	0.00491868	−	0.00121286i
$666$		0			0
$667$			21.0446i			0.814848i
$668$		0			0
$669$	−1.61836	−	1.61836i	−0.0625695	−	0.0625695i
$670$		0			0
$671$			6.14880i			0.237372i
$672$		0			0
$673$	29.9888	+	29.9888i	1.15598	+	1.15598i	0.985331	+	0.170652i	$0.0545873\pi$
$673$	29.9888	+	29.9888i	1.15598	+	1.15598i	0.170652	+	0.985331i	$0.445413\pi$
$674$		0			0
$675$	13.1449	+	25.0336i	0.505949	+	0.963545i
$676$		0			0
$677$	33.4274			1.28472			0.642360	−	0.766403i	$-0.277956\pi$
$677$	33.4274			1.28472			0.642360	+	0.766403i	$0.277956\pi$
$678$		0			0
$679$		−	27.0409i		−	1.03774i
$680$		0			0
$681$		−	17.8551i		−	0.684211i
$682$		0			0
$683$	−4.07583			−0.155957			−0.0779787	−	0.996955i	$-0.524847\pi$
$683$	−4.07583			−0.155957			−0.0779787	+	0.996955i	$0.524847\pi$
$684$		0			0
$685$	9.20102	−	15.2237i	0.351553	−	0.581668i
$686$		0			0
$687$	−1.36098	−	1.36098i	−0.0519246	−	0.0519246i
$688$		0			0
$689$		−	11.3013i		−	0.430544i
$690$		0			0
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	0.522044	−	0.852919i	$-0.325170\pi$
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	−0.852919	+	0.522044i	$0.825170\pi$
$692$		0			0
$693$		−	9.81330i		−	0.372776i
$694$		0			0
$695$	19.7956	−	32.7532i	0.750890	−	1.24240i
$696$		0			0
$697$	40.0956	+	40.0956i	1.51873	+	1.51873i
$698$		0			0
$699$	−0.423347	−	0.423347i	−0.0160125	−	0.0160125i
$700$		0			0
$701$	−11.8325	+	11.8325i	−0.446908	+	0.446908i	−0.894325	−	0.447418i	$-0.852344\pi$
$701$	−11.8325	+	11.8325i	−0.446908	+	0.446908i	0.447418	+	0.894325i	$0.352344\pi$
$702$		0			0
$703$	0.0991914	−	0.0991914i	0.00374108	−	0.00374108i
$704$		0			0
$705$	−12.6052	−	7.61844i	−0.474740	−	0.286927i
$706$		0			0
$707$	16.1413			0.607056
$708$		0			0
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.247563	+	0.968872i	$0.579630\pi$
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.968872	+	0.247563i	$0.920370\pi$
$710$		0			0
$711$	−2.97129			−0.111432
$712$		0			0
$713$	28.1395	−	28.1395i	1.05383	−	1.05383i
$714$		0			0
$715$	9.08620	+	5.49158i	0.339805	+	0.205373i
$716$		0			0
$717$			17.4282i			0.650868i
$718$		0			0
$719$	4.16893			0.155475			0.0777374	−	0.996974i	$-0.475230\pi$
$719$	4.16893			0.155475			0.0777374	+	0.996974i	$0.475230\pi$
$720$		0			0
$721$	−45.7603			−1.70420
$722$		0			0
$723$			27.2751i			1.01437i
$724$		0			0
$725$	−22.5350	−	7.01733i	−0.836928	−	0.260617i
$726$		0			0
$727$	−28.6014	+	28.6014i	−1.06077	+	1.06077i	−0.0627368	+	0.998030i	$0.519983\pi$
$727$	−28.6014	+	28.6014i	−1.06077	+	1.06077i	−0.998030	+	0.0627368i	$0.980017\pi$
$728$		0			0
$729$	−28.6142			−1.05979
$730$		0			0
$731$	7.84269	−	7.84269i	0.290072	−	0.290072i
$732$		0			0
$733$	−18.7069			−0.690956			−0.345478	−	0.938427i	$-0.612283\pi$
$733$	−18.7069			−0.690956			−0.345478	+	0.938427i	$0.612283\pi$
$734$		0			0
$735$	1.57446	+	6.38514i	0.0580749	+	0.235519i
$736$		0			0
$737$	1.62414	−	1.62414i	0.0598259	−	0.0598259i
$738$		0			0
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.333337	+	0.942808i	$0.608175\pi$
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.942808	+	0.333337i	$0.891825\pi$
$740$		0			0
$741$	−0.0294910	−	0.0294910i	−0.00108338	−	0.00108338i
$742$		0			0
$743$	−24.7660	−	24.7660i	−0.908577	−	0.908577i	0.0875803	−	0.996157i	$-0.472087\pi$
$743$	−24.7660	−	24.7660i	−0.908577	−	0.908577i	−0.996157	+	0.0875803i	$0.972087\pi$
$744$		0			0
$745$	−36.6959	−	22.1785i	−1.34443	−	0.812558i
$746$		0			0
$747$			13.5852i			0.497055i
$748$		0			0
$749$	−23.2878	−	23.2878i	−0.850917	−	0.850917i
$750$		0			0
$751$		−	45.2370i		−	1.65072i	−0.564606	−	0.825361i	$-0.690972\pi$
$751$		−	45.2370i		−	1.65072i	0.564606	−	0.825361i	$-0.309028\pi$
$752$		0			0
$753$	−7.21340	−	7.21340i	−0.262871	−	0.262871i
$754$		0			0
$755$	−11.0914	−	44.9808i	−0.403659	−	1.63702i
$756$		0			0
$757$	−6.44058			−0.234087			−0.117044	−	0.993127i	$-0.537342\pi$
$757$	−6.44058			−0.234087			−0.117044	+	0.993127i	$0.537342\pi$
$758$		0			0
$759$		−	19.0672i		−	0.692095i
$760$		0			0
$761$		−	9.50571i		−	0.344582i	−0.985046	−	0.172291i	$-0.944883\pi$
$761$		−	9.50571i		−	0.344582i	0.985046	−	0.172291i	$-0.0551169\pi$
$762$		0			0
$763$	38.9367			1.40960
$764$		0			0
$765$	11.0744	+	6.69322i	0.400395	+	0.241994i
$766$		0			0
$767$	−5.45546	−	5.45546i	−0.196985	−	0.196985i
$768$		0			0
$769$			46.8513i			1.68950i	0.535159	+	0.844751i	$0.320252\pi$
$769$			46.8513i			1.68950i	−0.535159	+	0.844751i	$0.679748\pi$
$770$		0			0
$771$	20.6176	+	20.6176i	0.742526	+	0.742526i
$772$		0			0
$773$		−	10.9964i		−	0.395513i	−0.980251	−	0.197756i	$-0.936635\pi$
$773$		−	10.9964i		−	0.395513i	0.980251	−	0.197756i	$-0.0633655\pi$
$774$		0			0
$775$	20.7493	+	39.5155i	0.745335	+	1.41944i
$776$		0			0
$777$	21.5506	+	21.5506i	0.773122	+	0.773122i
$778$		0			0
$779$	0.142026	+	0.142026i	0.00508862	+	0.00508862i
$780$		0			0
$781$	0.585238	−	0.585238i	0.0209414	−	0.0209414i
$782$		0			0
$783$	18.8756	−	18.8756i	0.674559	−	0.674559i
$784$		0			0
$785$	−12.4251	+	3.06381i	−0.443472	+	0.109352i
$786$		0			0
$787$	−25.5190			−0.909653			−0.454826	−	0.890580i	$-0.650299\pi$
$787$	−25.5190			−0.909653			−0.454826	+	0.890580i	$0.650299\pi$
$788$		0			0
$789$	−16.4265	+	16.4265i	−0.584797	+	0.584797i
$790$		0			0
$791$	20.8660			0.741909
$792$		0			0
$793$	2.19048	−	2.19048i	0.0777864	−	0.0777864i
$794$		0			0
$795$	−5.44977	−	22.1013i	−0.193283	−	0.783851i
$796$		0			0
$797$		−	13.3808i		−	0.473972i	−0.971513	−	0.236986i	$-0.923840\pi$
$797$		−	13.3808i		−	0.473972i	0.971513	−	0.236986i	$-0.0761595\pi$
$798$		0			0
$799$	−25.8348			−0.913969
$800$		0			0
$801$	14.1626			0.500412
$802$		0			0
$803$			3.52471i			0.124384i
$804$		0			0
$805$	−7.20391	−	29.2151i	−0.253905	−	1.02970i
$806$		0			0
$807$	2.92738	−	2.92738i	0.103049	−	0.103049i
$808$		0			0
$809$	−52.7958			−1.85620			−0.928102	−	0.372327i	$-0.878560\pi$
$809$	−52.7958			−1.85620			−0.928102	+	0.372327i	$0.878560\pi$
$810$		0			0
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	−0.678929	−	0.734204i	$-0.737556\pi$
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	0.734204	+	0.678929i	$0.237556\pi$
$812$		0			0
$813$	−26.2749			−0.921500
$814$		0			0
$815$	−39.0570	+	9.63075i	−1.36811	+	0.337351i
$816$		0			0
$817$	0.0277803	−	0.0277803i	0.000971909	−	0.000971909i
$818$		0			0
$819$	−3.49595	+	3.49595i	−0.122158	+	0.122158i
$820$		0			0
$821$	25.7715	+	25.7715i	0.899431	+	0.899431i	0.995386	−	0.0959548i	$-0.0305904\pi$
$821$	25.7715	+	25.7715i	0.899431	+	0.899431i	−0.0959548	+	0.995386i	$0.530590\pi$
$822$		0			0
$823$	17.5565	+	17.5565i	0.611982	+	0.611982i	0.943462	−	0.331480i	$-0.107548\pi$
$823$	17.5565	+	17.5565i	0.611982	+	0.611982i	−0.331480	+	0.943462i	$0.607548\pi$
$824$		0			0
$825$	20.4176	+	6.35797i	0.710848	+	0.221356i
$826$		0			0
$827$		−	14.8548i		−	0.516551i	−0.966071	−	0.258276i	$-0.916846\pi$
$827$		−	14.8548i		−	0.516551i	0.966071	−	0.258276i	$-0.0831543\pi$
$828$		0			0
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	0.855387	−	0.517990i	$-0.173320\pi$
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	−0.517990	+	0.855387i	$0.673320\pi$
$830$		0			0
$831$			13.8191i			0.479380i
$832$		0			0
$833$	8.15672	+	8.15672i	0.282614	+	0.282614i
$834$		0			0
$835$	6.48563	+	3.91983i	0.224444	+	0.135651i
$836$		0			0
$837$	−50.4786			−1.74480
$838$		0			0
$839$		−	4.54484i		−	0.156905i	−0.996918	−	0.0784527i	$-0.975002\pi$
$839$		−	4.54484i		−	0.156905i	0.996918	−	0.0784527i	$-0.0249979\pi$
$840$		0			0
$841$		−	6.71729i		−	0.231631i
$842$		0			0
$843$	−12.9766			−0.446938
$844$		0			0
$845$	5.67884	+	23.0302i	0.195358	+	0.792264i
$846$		0			0
$847$	3.36337	+	3.36337i	0.115567	+	0.115567i
$848$		0			0
$849$			4.76977i			0.163698i
$850$		0			0
$851$	−22.8466	−	22.8466i	−0.783171	−	0.783171i
$852$		0			0
$853$		−	37.3745i		−	1.27968i	−0.768509	−	0.639839i	$-0.779001\pi$
$853$		−	37.3745i		−	1.27968i	0.768509	−	0.639839i	$-0.220999\pi$
$854$		0			0
$855$	0.0392276	+	0.0237086i	0.00134155	+	0.000810818i
$856$		0			0
$857$	−16.4541	−	16.4541i	−0.562062	−	0.562062i	0.367831	−	0.929893i	$-0.380101\pi$
$857$	−16.4541	−	16.4541i	−0.562062	−	0.562062i	−0.929893	+	0.367831i	$0.880101\pi$
$858$		0			0
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	0.922922	−	0.384987i	$-0.125794\pi$
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	−0.384987	+	0.922922i	$0.625794\pi$
$860$		0			0
$861$	−30.8570	+	30.8570i	−1.05160	+	1.05160i
$862$		0			0
$863$	−22.6395	+	22.6395i	−0.770659	+	0.770659i	−0.978222	−	0.207563i	$-0.933447\pi$
$863$	−22.6395	+	22.6395i	−0.770659	+	0.770659i	0.207563	+	0.978222i	$0.433447\pi$
$864$		0			0
$865$	−5.06005	−	20.5208i	−0.172047	−	0.697727i
$866$		0			0
$867$	−17.9148			−0.608419
$868$		0			0
$869$	−6.09036	+	6.09036i	−0.206601	+	0.206601i
$870$		0			0
$871$	−1.15719			−0.0392097
$872$		0			0
$873$	6.70861	−	6.70861i	0.227052	−	0.227052i
$874$		0			0
$875$	33.6863	+	2.02769i	1.13880	+	0.0685483i
$876$		0			0
$877$		−	30.0542i		−	1.01486i	−0.861694	−	0.507429i	$-0.830596\pi$
$877$		−	30.0542i		−	1.01486i	0.861694	−	0.507429i	$-0.169404\pi$
$878$		0			0
$879$	−3.71243			−0.125217
$880$		0			0
$881$	−3.86747			−0.130298			−0.0651492	−	0.997876i	$-0.520752\pi$
$881$	−3.86747			−0.130298			−0.0651492	+	0.997876i	$0.520752\pi$
$882$		0			0
$883$		−	0.485919i		−	0.0163525i	−0.999967	−	0.00817624i	$-0.997397\pi$
$883$		−	0.485919i		−	0.0163525i	0.999967	−	0.00817624i	$-0.00260261\pi$
$884$		0			0
$885$	−13.2997	−	8.03817i	−0.447065	−	0.270200i
$886$		0			0
$887$	−12.9762	+	12.9762i	−0.435699	+	0.435699i	−0.890561	−	0.454863i	$-0.849688\pi$
$887$	−12.9762	+	12.9762i	−0.435699	+	0.435699i	0.454863	+	0.890561i	$0.349688\pi$
$888$		0			0
$889$	5.91587			0.198412
$890$		0			0
$891$	−10.2054	+	10.2054i	−0.341893	+	0.341893i
$892$		0			0
$893$	−0.0915117			−0.00306232
$894$		0			0
$895$	31.9328	+	19.2998i	1.06739	+	0.645120i
$896$		0			0
$897$	−6.79261	+	6.79261i	−0.226799	+	0.226799i
$898$		0			0
$899$	29.7951	−	29.7951i	0.993722	−	0.993722i
$900$		0			0
$901$	−28.2333	−	28.2333i	−0.940588	−	0.940588i
$902$		0			0
$903$	6.03560	+	6.03560i	0.200852	+	0.200852i
$904$		0			0
$905$	−4.15721	+	6.87839i	−0.138190	+	0.228645i
$906$		0			0
$907$		−	54.3645i		−	1.80514i	−0.430540	−	0.902571i	$-0.641677\pi$
$907$		−	54.3645i		−	1.80514i	0.430540	−	0.902571i	$-0.358323\pi$
$908$		0			0
$909$	4.00451	+	4.00451i	0.132821	+	0.132821i
$910$		0			0
$911$		−	40.0402i		−	1.32659i	−0.748358	−	0.663295i	$-0.769157\pi$
$911$		−	40.0402i		−	1.32659i	0.748358	−	0.663295i	$-0.230843\pi$
$912$		0			0
$913$	27.8460	+	27.8460i	0.921567	+	0.921567i
$914$		0			0
$915$	3.22750	−	5.34012i	0.106698	−	0.176539i
$916$		0			0
$917$	−15.0300			−0.496335
$918$		0			0
$919$			8.81475i			0.290772i	0.989375	+	0.145386i	$0.0464423\pi$
$919$			8.81475i			0.290772i	−0.989375	+	0.145386i	$0.953558\pi$
$920$		0			0
$921$		−	14.7057i		−	0.484568i
$922$		0			0
$923$	−0.416977			−0.0137250
$924$		0			0
$925$	32.0828	−	16.8464i	1.05488	−	0.553907i
$926$		0			0
$927$	−11.3527	−	11.3527i	−0.372872	−	0.372872i
$928$		0			0
$929$		−	47.9673i		−	1.57376i	−0.617109	−	0.786878i	$-0.711696\pi$
$929$		−	47.9673i		−	1.57376i	0.617109	−	0.786878i	$-0.288304\pi$
$930$		0			0
$931$	0.0288926	+	0.0288926i	0.000946918	+	0.000946918i
$932$		0			0
$933$		−	28.5272i		−	0.933938i
$934$		0			0
$935$	36.4189	−	8.98024i	1.19102	−	0.293685i
$936$		0			0
$937$	−13.8299	−	13.8299i	−0.451803	−	0.451803i	0.444150	−	0.895953i	$-0.353506\pi$
$937$	−13.8299	−	13.8299i	−0.451803	−	0.451803i	−0.895953	+	0.444150i	$0.853506\pi$
$938$		0			0
$939$	−3.93426	−	3.93426i	−0.128390	−	0.128390i
$940$		0			0
$941$	5.19108	−	5.19108i	0.169224	−	0.169224i	−0.617414	−	0.786638i	$-0.711820\pi$
$941$	5.19108	−	5.19108i	0.169224	−	0.169224i	0.786638	+	0.617414i	$0.211820\pi$
$942$		0			0
$943$	32.7127	−	32.7127i	1.06527	−	1.06527i
$944$		0			0
$945$	−19.7426	+	32.6655i	−0.642226	+	1.06261i
$946$		0			0
$947$	−24.1342			−0.784255			−0.392128	−	0.919911i	$-0.628261\pi$
$947$	−24.1342			−0.784255			−0.392128	+	0.919911i	$0.628261\pi$
$948$		0			0
$949$	1.25566	−	1.25566i	0.0407606	−	0.0407606i
$950$		0			0
$951$	28.2166			0.914986
$952$		0			0
$953$	−22.8500	+	22.8500i	−0.740183	+	0.740183i	−0.972613	−	0.232430i	$-0.925332\pi$
$953$	−22.8500	+	22.8500i	−0.740183	+	0.740183i	0.232430	+	0.972613i	$0.425332\pi$
$954$		0			0
$955$	11.8630	−	2.92521i	0.383878	−	0.0946574i
$956$		0			0
$957$		−	20.1890i		−	0.652618i
$958$		0			0
$959$	24.0121			0.775392
$960$		0			0
$961$	−48.6804			−1.57034
$962$		0			0
$963$		−	11.5550i		−	0.372354i
$964$		0			0
$965$	7.89200	−	13.0579i	0.254052	−	0.420347i
$966$		0			0
$967$	21.4211	−	21.4211i	0.688855	−	0.688855i	−0.273124	−	0.961979i	$-0.588057\pi$
$967$	21.4211	−	21.4211i	0.688855	−	0.688855i	0.961979	+	0.273124i	$0.0880569\pi$
$968$		0			0
$969$	−0.147351			−0.00473361
$970$		0			0
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	−0.870600	−	0.491991i	$-0.836269\pi$
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	0.491991	+	0.870600i	$0.336269\pi$
$972$		0			0
$973$	51.6611			1.65618
$974$		0			0
$975$	−5.00867	−	9.53868i	−0.160406	−	0.305482i
$976$		0			0
$977$	2.15703	−	2.15703i	0.0690096	−	0.0690096i	−0.671760	−	0.740769i	$-0.734461\pi$
$977$	2.15703	−	2.15703i	0.0690096	−	0.0690096i	0.740769	+	0.671760i	$0.234461\pi$
$978$		0			0
$979$	29.0296	−	29.0296i	0.927791	−	0.927791i
$980$		0			0
$981$	9.65985	+	9.65985i	0.308415	+	0.308415i
$982$		0			0
$983$	−19.9712	−	19.9712i	−0.636983	−	0.636983i	0.312827	−	0.949810i	$-0.398724\pi$
$983$	−19.9712	−	19.9712i	−0.636983	−	0.636983i	−0.949810	+	0.312827i	$0.898724\pi$
$984$		0			0
$985$	1.57702	+	6.39550i	0.0502479	+	0.203778i
$986$		0			0
$987$		−	19.8820i		−	0.632852i
$988$		0			0
$989$	−6.39858	−	6.39858i	−0.203463	−	0.203463i
$990$		0			0
$991$			19.2270i			0.610767i	0.952230	+	0.305383i	$0.0987846\pi$
$991$			19.2270i			0.610767i	−0.952230	+	0.305383i	$0.901215\pi$
$992$		0			0
$993$	−27.1574	−	27.1574i	−0.861815	−	0.861815i
$994$		0			0
$995$	4.65948	−	1.14894i	0.147715	−	0.0364240i
$996$		0			0
$997$	2.01694			0.0638771			0.0319385	−	0.999490i	$-0.489832\pi$
$997$	2.01694			0.0638771			0.0319385	+	0.999490i	$0.489832\pi$
$998$		0			0
$999$			40.9838i			1.29667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.j.c.543.3		18
4.3	odd	2		640.2.j.d.543.7		18
5.2	odd	4		640.2.s.c.287.3		18
8.3	odd	2		80.2.j.b.43.8	✓	18
8.5	even	2		320.2.j.b.143.7		18
16.3	odd	4		640.2.s.c.223.3		18
16.5	even	4		80.2.s.b.3.8	yes	18
16.11	odd	4		320.2.s.b.303.7		18
16.13	even	4		640.2.s.d.223.7		18
20.7	even	4		640.2.s.d.287.7		18
24.11	even	2		720.2.bd.g.523.2		18
40.3	even	4		400.2.s.d.107.2		18
40.13	odd	4		1600.2.s.d.207.3		18
40.19	odd	2		400.2.j.d.43.2		18
40.27	even	4		80.2.s.b.27.8	yes	18
40.29	even	2		1600.2.j.d.143.3		18
40.37	odd	4		320.2.s.b.207.7		18
48.5	odd	4		720.2.z.g.163.2		18
80.27	even	4		320.2.j.b.47.3		18
80.37	odd	4		80.2.j.b.67.8	yes	18
80.43	even	4		1600.2.j.d.1007.7		18
80.53	odd	4		400.2.j.d.307.2		18
80.59	odd	4		1600.2.s.d.943.3		18
80.67	even	4	inner	640.2.j.c.607.7		18
80.69	even	4		400.2.s.d.243.2		18
80.77	odd	4		640.2.j.d.607.3		18
120.107	odd	4		720.2.z.g.667.2		18
240.197	even	4		720.2.bd.g.307.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	8.3	odd	2
80.2.j.b.67.8	yes	18	80.37	odd	4
80.2.s.b.3.8	yes	18	16.5	even	4
80.2.s.b.27.8	yes	18	40.27	even	4
320.2.j.b.47.3		18	80.27	even	4
320.2.j.b.143.7		18	8.5	even	2
320.2.s.b.207.7		18	40.37	odd	4
320.2.s.b.303.7		18	16.11	odd	4
400.2.j.d.43.2		18	40.19	odd	2
400.2.j.d.307.2		18	80.53	odd	4
400.2.s.d.107.2		18	40.3	even	4
400.2.s.d.243.2		18	80.69	even	4
640.2.j.c.543.3		18	1.1	even	1	trivial
640.2.j.c.607.7		18	80.67	even	4	inner
640.2.j.d.543.7		18	4.3	odd	2
640.2.j.d.607.3		18	80.77	odd	4
640.2.s.c.223.3		18	16.3	odd	4
640.2.s.c.287.3		18	5.2	odd	4
640.2.s.d.223.7		18	16.13	even	4
640.2.s.d.287.7		18	20.7	even	4
720.2.z.g.163.2		18	48.5	odd	4
720.2.z.g.667.2		18	120.107	odd	4
720.2.bd.g.307.2		18	240.197	even	4
720.2.bd.g.523.2		18	24.11	even	2
1600.2.j.d.143.3		18	40.29	even	2
1600.2.j.d.1007.7		18	80.43	even	4
1600.2.s.d.207.3		18	40.13	odd	4
1600.2.s.d.943.3		18	80.59	odd	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.39319i q^{3} +(-0.535339 - 2.17104i) q^{5} +(2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +O(q^{10})\)	\(q-1.39319i q^{3} +(-0.535339 - 2.17104i) q^{5} +(2.13436 - 2.13436i) q^{7} +1.05903 q^{9} +(2.17074 - 2.17074i) q^{11} -1.54663 q^{13} +(-3.02466 + 0.745827i) q^{15} +(-3.86386 + 3.86386i) q^{17} +(-0.0136865 + 0.0136865i) q^{19} +(-2.97357 - 2.97357i) q^{21} +(3.15240 + 3.15240i) q^{23} +(-4.42682 + 2.32449i) q^{25} -5.65499i q^{27} +(3.33787 + 3.33787i) q^{29} -8.92639i q^{31} +(-3.02424 - 3.02424i) q^{33} +(-5.77640 - 3.49118i) q^{35} -7.24737 q^{37} +2.15475i q^{39} -10.3771i q^{41} -2.02975 q^{43} +(-0.566942 - 2.29920i) q^{45} +(3.34313 + 3.34313i) q^{47} -2.11103i q^{49} +(5.38308 + 5.38308i) q^{51} +7.30702i q^{53} +(-5.87483 - 3.55067i) q^{55} +(0.0190679 + 0.0190679i) q^{57} +(3.52732 + 3.52732i) q^{59} +(-1.41629 + 1.41629i) q^{61} +(2.26036 - 2.26036i) q^{63} +(0.827973 + 3.35780i) q^{65} +0.748197 q^{67} +(4.39187 - 4.39187i) q^{69} +0.269603 q^{71} +(-0.811870 + 0.811870i) q^{73} +(3.23844 + 6.16739i) q^{75} -9.26628i q^{77} -2.80567 q^{79} -4.70135 q^{81} +12.8279i q^{83} +(10.4571 + 6.32012i) q^{85} +(4.65027 - 4.65027i) q^{87} +13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} -12.4361 q^{93} +(0.0370409 + 0.0223871i) q^{95} +(6.33466 - 6.33466i) q^{97} +(2.29888 - 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9} - 2 q^{11} - 20 q^{15} - 6 q^{17} + 2 q^{19} + 16 q^{21} + 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} - 6 q^{35} - 8 q^{37} - 44 q^{43} + 4 q^{45} + 38 q^{47} + 8 q^{51} + 6 q^{55} + 24 q^{57} - 10 q^{59} - 14 q^{61} - 6 q^{63} + 12 q^{67} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 64 q^{75} - 16 q^{79} + 2 q^{81} + 10 q^{85} - 24 q^{87} - 12 q^{89} - 16 q^{93} + 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9 - 2 * q^11 - 20 * q^15 - 6 * q^17 + 2 * q^19 + 16 * q^21 + 2 * q^23 + 6 * q^25 + 14 * q^29 - 8 * q^33 - 6 * q^35 - 8 * q^37 - 44 * q^43 + 4 * q^45 + 38 * q^47 + 8 * q^51 + 6 * q^55 + 24 * q^57 - 10 * q^59 - 14 * q^61 - 6 * q^63 + 12 * q^67 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 64 * q^75 - 16 * q^79 + 2 * q^81 + 10 * q^85 - 24 * q^87 - 12 * q^89 - 16 * q^93 + 34 * q^95 + 18 * q^97 - 22 * q^99

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