LMFDB - Embedded newform 320.2.j.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(47,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.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:	$2.55521286468$
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			47.3
Root			$0.482716 + 1.32928i$ of defining polynomial
Character	$\chi$	$=$	320.47
Dual form			320.2.j.b.143.7

$q$-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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		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	0.984135	−	0.177421i	$-0.0567754\pi$
$7$	2.13436	+	2.13436i	0.806714	+	0.806714i	−0.177421	+	0.984135i	$0.556775\pi$
$8$		0			0
$9$	1.05903			0.353011
$10$		0			0
$11$	−2.17074	−	2.17074i	−0.654501	−	0.654501i	0.299572	−	0.954074i	$-0.403156\pi$
$11$	−2.17074	−	2.17074i	−0.654501	−	0.654501i	−0.954074	+	0.299572i	$0.903156\pi$
$12$		0			0
$13$	1.54663			0.428958			0.214479	−	0.976729i	$-0.431195\pi$
$13$	1.54663			0.428958			0.214479	+	0.976729i	$0.431195\pi$
$14$		0			0
$15$	−3.02466	−	0.745827i	−0.780964	−	0.192572i
$16$		0			0
$17$	−3.86386	−	3.86386i	−0.937125	−	0.937125i	0.0610123	−	0.998137i	$-0.480567\pi$
$17$	−3.86386	−	3.86386i	−0.937125	−	0.937125i	−0.998137	+	0.0610123i	$0.980567\pi$
$18$		0			0
$19$	0.0136865	+	0.0136865i	0.00313991	+	0.00313991i	0.708675	−	0.705535i	$-0.249293\pi$
$19$	0.0136865	+	0.0136865i	0.00313991	+	0.00313991i	−0.705535	+	0.708675i	$0.749293\pi$
$20$		0			0
$21$	2.97357	−	2.97357i	0.648886	−	0.648886i
$22$		0			0
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	−0.297425	−	0.954745i	$-0.596128\pi$
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	0.954745	+	0.297425i	$0.0961279\pi$
$24$		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	$-0.894413\pi$
$29$	−3.33787	+	3.33787i	−0.619826	+	0.619826i	0.325660	+	0.945487i	$0.394413\pi$
$30$		0			0
$31$			8.92639i			1.60323i	0.597843	+	0.801613i	$0.296025\pi$
$31$			8.92639i			1.60323i	−0.597843	+	0.801613i	$0.703975\pi$
$32$		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	$-0.296863\pi$
$37$	7.24737			1.19146			0.595730	+	0.803184i	$0.296863\pi$
$38$		0			0
$39$		−	2.15475i		−	0.345035i
$40$		0			0
$41$			10.3771i			1.62063i	0.585996	+	0.810314i	$0.300704\pi$
$41$			10.3771i			1.62063i	−0.585996	+	0.810314i	$0.699296\pi$
$42$		0			0
$43$	2.02975			0.309534			0.154767	−	0.987951i	$-0.450537\pi$
$43$	2.02975			0.309534			0.154767	+	0.987951i	$0.450537\pi$
$44$		0			0
$45$	0.566942	−	2.29920i	0.0845147	−	0.342745i
$46$		0			0
$47$	3.34313	−	3.34313i	0.487646	−	0.487646i	−0.419917	−	0.907563i	$-0.637941\pi$
$47$	3.34313	−	3.34313i	0.487646	−	0.487646i	0.907563	+	0.419917i	$0.137941\pi$
$48$		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	$-0.855269\pi$
$59$	−3.52732	+	3.52732i	−0.459218	+	0.459218i	0.439181	+	0.898399i	$0.355269\pi$
$60$		0			0
$61$	1.41629	+	1.41629i	0.181338	+	0.181338i	0.791939	−	0.610601i	$-0.209072\pi$
$61$	1.41629	+	1.41629i	0.181338	+	0.181338i	−0.610601	+	0.791939i	$0.709072\pi$
$62$		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	$-0.514553\pi$
$67$	−0.748197			−0.0914068			−0.0457034	+	0.998955i	$0.514553\pi$
$68$		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	0.657998	−	0.753020i	$-0.271404\pi$
$73$	−0.811870	−	0.811870i	−0.0950222	−	0.0950222i	−0.753020	+	0.657998i	$0.771404\pi$
$74$		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	0.951338	−	0.308151i	$-0.0997101\pi$
$97$	6.33466	+	6.33466i	0.643187	+	0.643187i	−0.308151	+	0.951338i	$0.599710\pi$
$98$		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	$-0.835719\pi$
$101$	−3.78129	+	3.78129i	−0.376252	+	0.376252i	0.493496	+	0.869748i	$0.335719\pi$
$102$		0			0
$103$	−10.7199	+	10.7199i	−1.05626	+	1.05626i	−0.0579430	+	0.998320i	$0.518454\pi$
$103$	−10.7199	+	10.7199i	−1.05626	+	1.05626i	−0.998320	+	0.0579430i	$0.981546\pi$
$104$		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	$-0.961967\pi$
$109$	−9.12139	+	9.12139i	−0.873670	+	0.873670i	0.119200	+	0.992870i	$0.461967\pi$
$110$		0			0
$111$		−	10.0969i		−	0.958359i
$112$		0			0
$113$	4.88810	−	4.88810i	0.459834	−	0.459834i	−0.438767	−	0.898601i	$-0.644585\pi$
$113$	4.88810	−	4.88810i	0.459834	−	0.459834i	0.898601	+	0.438767i	$0.144585\pi$
$114$		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	−0.642941	−	0.765916i	$-0.722286\pi$
$127$	1.38586	−	1.38586i	0.122975	−	0.122975i	0.765916	+	0.642941i	$0.222286\pi$
$128$		0			0
$129$		−	2.82782i		−	0.248976i
$130$		0			0
$131$	3.52096	−	3.52096i	0.307627	−	0.307627i	−0.536361	−	0.843989i	$-0.680202\pi$
$131$	3.52096	−	3.52096i	0.307627	−	0.307627i	0.843989	+	0.536361i	$0.180202\pi$
$132$		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	−0.424732	−	0.905319i	$-0.639632\pi$
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	0.905319	+	0.424732i	$0.139632\pi$
$138$		0			0
$139$	−12.1022	+	12.1022i	−1.02650	+	1.02650i	−0.0268584	+	0.999639i	$0.508550\pi$
$139$	−12.1022	+	12.1022i	−1.02650	+	1.02650i	−0.999639	+	0.0268584i	$0.991450\pi$
$140$		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	−0.993042	−	0.117757i	$-0.962430\pi$
$149$	−13.5590	−	13.5590i	−1.11080	−	1.11080i	−0.117757	−	0.993042i	$-0.537570\pi$
$150$		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	0.608281	−	0.793722i	$-0.291859\pi$
$167$	−2.39642	−	2.39642i	−0.185441	−	0.185441i	−0.793722	+	0.608281i	$0.791859\pi$
$168$		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	$-0.616989\pi$
$173$	−9.45205			−0.718626			−0.359313	+	0.933217i	$0.616989\pi$
$174$		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	$-0.0356691\pi$
$179$	11.7991	+	11.7991i	0.881905	+	0.881905i	−0.111824	+	0.993728i	$0.535669\pi$
$180$		0			0
$181$	2.54155	−	2.54155i	0.188912	−	0.188912i	−0.606314	−	0.795225i	$-0.707352\pi$
$181$	2.54155	−	2.54155i	0.188912	−	0.188912i	0.795225	+	0.606314i	$0.207352\pi$
$182$		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	$-0.936657\pi$
$191$		−	5.46421i		−	0.395376i	0.980265	−	0.197688i	$-0.0633433\pi$
$192$		0			0
$193$	4.82485	−	4.82485i	0.347300	−	0.347300i	−0.511803	−	0.859103i	$-0.671022\pi$
$193$	4.82485	−	4.82485i	0.347300	−	0.347300i	0.859103	+	0.511803i	$0.171022\pi$
$194$		0			0
$195$	−4.67804	−	1.15352i	−0.335001	−	0.0826053i
$196$		0			0
$197$	2.94582			0.209881			0.104941	−	0.994478i	$-0.466535\pi$
$197$	2.94582			0.209881			0.104941	+	0.994478i	$0.466535\pi$
$198$		0			0
$199$		−	2.14620i		−	0.152140i	−0.997102	−	0.0760700i	$-0.975763\pi$
$199$		−	2.14620i		−	0.152140i	0.997102	−	0.0760700i	$-0.0242372\pi$
$200$		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	$-0.836988\pi$
$211$	−5.54427	+	5.54427i	−0.381684	+	0.381684i	0.490025	+	0.871708i	$0.336988\pi$
$212$		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	0.744930	−	0.667142i	$-0.232483\pi$
$223$	1.16163	+	1.16163i	0.0777882	+	0.0777882i	−0.667142	+	0.744930i	$0.732483\pi$
$224$		0			0
$225$	−4.68815	−	2.46171i	−0.312543	−	0.164114i
$226$		0			0
$227$	−12.8161			−0.850632			−0.425316	−	0.905045i	$-0.639837\pi$
$227$	−12.8161			−0.850632			−0.425316	+	0.905045i	$0.639837\pi$
$228$		0			0
$229$	−0.976882	−	0.976882i	−0.0645542	−	0.0645542i	0.674093	−	0.738647i	$-0.264535\pi$
$229$	−0.976882	−	0.976882i	−0.0645542	−	0.0645542i	−0.738647	+	0.674093i	$0.764535\pi$
$230$		0			0
$231$	−12.9097			−0.849393
$232$		0			0
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	0.716990	−	0.697083i	$-0.245519\pi$
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	−0.697083	+	0.716990i	$0.745519\pi$
$234$		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	$-0.324229\pi$
$251$	−5.17763	−	5.17763i	−0.326809	−	0.326809i	−0.851372	+	0.524563i	$0.824229\pi$
$252$		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	0.0741183	−	0.997249i	$-0.476386\pi$
$257$	−14.7989	−	14.7989i	−0.923131	−	0.923131i	−0.997249	+	0.0741183i	$0.976386\pi$
$258$		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	−0.970029	−	0.242991i	$-0.921871\pi$
$263$	−11.7906	+	11.7906i	−0.727038	+	0.727038i	0.242991	+	0.970029i	$0.421871\pi$
$264$		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	$-0.778875\pi$
$269$	−2.10121	+	2.10121i	−0.128113	+	0.128113i	0.640143	+	0.768256i	$0.278875\pi$
$270$		0			0
$271$			18.8596i			1.14564i	0.819683	+	0.572818i	$0.194150\pi$
$271$			18.8596i			1.14564i	−0.819683	+	0.572818i	$0.805850\pi$
$272$		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	$-0.403684\pi$
$277$	9.91909			0.595980			0.297990	+	0.954569i	$0.403684\pi$
$278$		0			0
$279$			9.45334i			0.565956i
$280$		0			0
$281$			9.31434i			0.555647i	0.960632	+	0.277823i	$0.0896130\pi$
$281$			9.31434i			0.555647i	−0.960632	+	0.277823i	$0.910387\pi$
$282$		0			0
$283$	3.42364			0.203514			0.101757	−	0.994809i	$-0.467554\pi$
$283$	3.42364			0.203514			0.101757	+	0.994809i	$0.467554\pi$
$284$		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	$-0.597392\pi$
$307$	−10.5554			−0.602430			−0.301215	+	0.953556i	$0.597392\pi$
$308$		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	0.782397	−	0.622780i	$-0.213997\pi$
$313$	2.82393	+	2.82393i	0.159618	+	0.159618i	−0.622780	+	0.782397i	$0.713997\pi$
$314$		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	−0.997244	−	0.0741908i	$-0.976363\pi$
$331$	−19.4930	−	19.4930i	−1.07143	−	1.07143i	−0.0741908	−	0.997244i	$-0.523637\pi$
$332$		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	0.528093	−	0.849186i	$-0.322907\pi$
$337$	−5.89449	−	5.89449i	−0.321093	−	0.321093i	−0.849186	+	0.528093i	$0.822907\pi$
$338$		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	$-0.753830\pi$
$349$	−0.317872	+	0.317872i	−0.0170153	+	0.0170153i	0.698548	+	0.715563i	$0.253830\pi$
$350$		0			0
$351$		−	8.74618i		−	0.466837i
$352$		0			0
$353$	−18.4551	+	18.4551i	−0.982266	+	0.982266i	−0.999845	−	0.0175800i	$-0.994404\pi$
$353$	−18.4551	+	18.4551i	−0.982266	+	0.982266i	0.0175800	+	0.999845i	$0.494404\pi$
$354$		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	$-0.865129\pi$
$359$		−	15.5802i		−	0.822292i	0.911569	−	0.411146i	$-0.134871\pi$
$360$		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	−0.833335	−	0.552768i	$-0.813572\pi$
$367$	−5.37489	+	5.37489i	−0.280567	+	0.280567i	0.552768	+	0.833335i	$0.313572\pi$
$368$		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	0.412882	−	0.910785i	$-0.364522\pi$
$379$	25.7690	−	25.7690i	1.32367	−	1.32367i	0.910785	−	0.412882i	$-0.135478\pi$
$380$		0			0
$381$	−1.93076	−	1.93076i	−0.0989160	−	0.0989160i
$382$		0			0
$383$	−0.418091	−	0.418091i	−0.0213634	−	0.0213634i	0.696344	−	0.717708i	$-0.254809\pi$
$383$	−0.418091	−	0.418091i	−0.0213634	−	0.0213634i	−0.717708	+	0.696344i	$0.754809\pi$
$384$		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	$-0.0909737\pi$
$389$	13.3626	+	13.3626i	0.677508	+	0.677508i	−0.281927	+	0.959436i	$0.590974\pi$
$390$		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	$-0.454144\pi$
$419$	−17.3188	−	17.3188i	−0.846079	−	0.846079i	−0.989641	+	0.143563i	$0.954144\pi$
$420$		0			0
$421$	11.5457	−	11.5457i	0.562703	−	0.562703i	−0.367372	−	0.930074i	$-0.619742\pi$
$421$	11.5457	−	11.5457i	0.562703	−	0.562703i	0.930074	+	0.367372i	$0.119742\pi$
$422$		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	$-0.874514\pi$
$431$		−	15.9479i		−	0.768185i	0.923295	−	0.384093i	$-0.125486\pi$
$432$		0			0
$433$	3.52109	−	3.52109i	0.169213	−	0.169213i	−0.617420	−	0.786633i	$-0.711822\pi$
$433$	3.52109	−	3.52109i	0.169213	−	0.169213i	0.786633	+	0.617420i	$0.211822\pi$
$434$		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	$0.0492546\pi$
$439$			6.45840i			0.308242i	−0.988052	+	0.154121i	$0.950745\pi$
$440$		0			0
$441$			2.23565i			0.106459i
$442$		0			0
$443$	−27.0992			−1.28752			−0.643761	−	0.765226i	$-0.722627\pi$
$443$	−27.0992			−1.28752			−0.643761	+	0.765226i	$0.722627\pi$
$444$		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	$-0.578780\pi$
$449$		−	41.0879i		−	1.93906i	0.244976	−	0.969529i	$-0.421220\pi$
$450$		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	−0.137096	−	0.990558i	$-0.543777\pi$
$457$	18.2449	−	18.2449i	0.853462	−	0.853462i	0.990558	+	0.137096i	$0.0437769\pi$
$458$		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	$-0.179310\pi$
$461$	6.68802	+	6.68802i	0.311492	+	0.311492i	−0.533995	+	0.845488i	$0.679310\pi$
$462$		0			0
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.902254	−	0.431205i	$-0.858089\pi$
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.431205	−	0.902254i	$-0.641911\pi$
$464$		0			0
$465$	6.65754	−	26.9993i	0.308736	−	1.25206i
$466$		0			0
$467$	32.4161			1.50004			0.750018	−	0.661417i	$-0.230045\pi$
$467$	32.4161			1.50004			0.750018	+	0.661417i	$0.230045\pi$
$468$		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	0.921666	−	0.387985i	$-0.126829\pi$
$487$	11.7773	+	11.7773i	0.533681	+	0.533681i	−0.387985	+	0.921666i	$0.626829\pi$
$488$		0			0
$489$	−25.0634			−1.13341
$490$		0			0
$491$	27.3556	+	27.3556i	1.23454	+	1.23454i	0.962200	+	0.272343i	$0.0877985\pi$
$491$	27.3556	+	27.3556i	1.23454	+	1.23454i	0.272343	+	0.962200i	$0.412202\pi$
$492$		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	$-0.375802\pi$
$499$	−12.1629	−	12.1629i	−0.544488	−	0.544488i	−0.924841	+	0.380353i	$0.875802\pi$
$500$		0			0
$501$	−3.33866	+	3.33866i	−0.149160	+	0.149160i
$502$		0			0
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	−0.346250	−	0.938142i	$-0.612545\pi$
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	0.938142	+	0.346250i	$0.112545\pi$
$504$		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	$-0.655853\pi$
$509$	9.29995	−	9.29995i	0.412213	−	0.412213i	0.882509	+	0.470296i	$0.155853\pi$
$510$		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	$-0.737444\pi$
$521$		−	33.5279i		−	1.46888i	0.678671	−	0.734442i	$-0.262556\pi$
$522$		0			0
$523$	25.9463			1.13455			0.567276	−	0.823528i	$-0.307997\pi$
$523$	25.9463			1.13455			0.567276	+	0.823528i	$0.307997\pi$
$524$		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	$-0.206598\pi$
$541$	4.47122	+	4.47122i	0.192233	+	0.192233i	−0.604428	+	0.796660i	$0.706598\pi$
$542$		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	$-0.608205\pi$
$547$	−15.5964			−0.666853			−0.333426	+	0.942776i	$0.608205\pi$
$548$		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	$-0.163489\pi$
$571$	9.07187	+	9.07187i	0.379646	+	0.379646i	−0.491328	+	0.870974i	$0.663489\pi$
$572$		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	0.674401	−	0.738365i	$-0.264402\pi$
$577$	−1.53648	−	1.53648i	−0.0639645	−	0.0639645i	−0.738365	+	0.674401i	$0.764402\pi$
$578$		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	−0.990747	−	0.135718i	$-0.956666\pi$
$593$	−20.8213	+	20.8213i	−0.855029	+	0.855029i	0.135718	+	0.990747i	$0.456666\pi$
$594$		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	$0.192944\pi$
$599$			27.8866i			1.13942i	−0.821847	+	0.569709i	$0.807056\pi$
$600$		0			0
$601$		−	4.70260i		−	0.191823i	−0.995390	−	0.0959115i	$-0.969423\pi$
$601$		−	4.70260i		−	0.191823i	0.995390	−	0.0959115i	$-0.0305766\pi$
$602$		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	0.187975	−	0.982174i	$-0.439807\pi$
$607$	28.8294	−	28.8294i	1.17015	−	1.17015i	0.982174	−	0.187975i	$-0.0601925\pi$
$608$		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	−0.834907	−	0.550391i	$-0.814479\pi$
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	0.550391	+	0.834907i	$0.314479\pi$
$618$		0			0
$619$	28.1001	−	28.1001i	1.12944	−	1.12944i	0.139172	−	0.990268i	$-0.455556\pi$
$619$	28.1001	−	28.1001i	1.12944	−	1.12944i	0.990268	−	0.139172i	$-0.0444440\pi$
$620$		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	0.511624	−	0.859209i	$-0.329044\pi$
$647$	−8.84125	−	8.84125i	−0.347585	−	0.347585i	−0.859209	+	0.511624i	$0.829044\pi$
$648$		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	$-0.633320\pi$
$653$	−20.7854			−0.813396			−0.406698	+	0.913563i	$0.633320\pi$
$654$		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	$-0.369703\pi$
$659$	−13.3330	−	13.3330i	−0.519382	−	0.519382i	−0.917384	+	0.398003i	$0.869703\pi$
$660$		0			0
$661$	−30.5831	+	30.5831i	−1.18954	+	1.18954i	−0.212350	+	0.977194i	$0.568112\pi$
$661$	−30.5831	+	30.5831i	−1.18954	+	1.18954i	−0.977194	+	0.212350i	$0.931888\pi$
$662$		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	0.170652	−	0.985331i	$-0.445413\pi$
$673$	29.9888	−	29.9888i	1.15598	−	1.15598i	0.985331	−	0.170652i	$-0.0545873\pi$
$674$		0			0
$675$	−13.1449	+	25.0336i	−0.505949	+	0.963545i
$676$		0			0
$677$	−33.4274			−1.28472			−0.642360	−	0.766403i	$-0.722044\pi$
$677$	−33.4274			−1.28472			−0.642360	+	0.766403i	$0.722044\pi$
$678$		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	$-0.475153\pi$
$683$	4.07583			0.155957			0.0779787	+	0.996955i	$0.475153\pi$
$684$		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	$-0.674830\pi$
$691$	8.69768	−	8.69768i	0.330875	−	0.330875i	0.852919	+	0.522044i	$0.174830\pi$
$692$		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	$-0.147656\pi$
$701$	11.8325	+	11.8325i	0.446908	+	0.446908i	−0.447418	+	0.894325i	$0.647656\pi$
$702$		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	0.968872	+	0.247563i	$0.0796297\pi$
$709$	32.3901	+	32.3901i	1.21643	+	1.21643i	0.247563	+	0.968872i	$0.420370\pi$
$710$		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	−0.998030	−	0.0627368i	$-0.980017\pi$
$727$	−28.6014	−	28.6014i	−1.06077	−	1.06077i	−0.0627368	−	0.998030i	$-0.519983\pi$
$728$		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	$-0.387717\pi$
$733$	18.7069			0.690956			0.345478	+	0.938427i	$0.387717\pi$
$734$		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	0.942808	+	0.333337i	$0.108175\pi$
$739$	34.6914	+	34.6914i	1.27614	+	1.27614i	0.333337	+	0.942808i	$0.391825\pi$
$740$		0			0
$741$	0.0294910	−	0.0294910i	0.00108338	−	0.00108338i
$742$		0			0
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	−0.996157	−	0.0875803i	$-0.972087\pi$
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	0.0875803	+	0.996157i	$0.472087\pi$
$744$		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	$0.309028\pi$
$751$			45.2370i			1.65072i	−0.564606	+	0.825361i	$0.690972\pi$
$752$		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	$-0.462658\pi$
$757$	6.44058			0.234087			0.117044	+	0.993127i	$0.462658\pi$
$758$		0			0
$759$			19.0672i			0.692095i
$760$		0			0
$761$			9.50571i			0.344582i	0.985046	+	0.172291i	$0.0551169\pi$
$761$			9.50571i			0.344582i	−0.985046	+	0.172291i	$0.944883\pi$
$762$		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	$-0.679748\pi$
$769$		−	46.8513i		−	1.68950i	0.535159	−	0.844751i	$-0.320252\pi$
$770$		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	$-0.349701\pi$
$787$	25.5190			0.909653			0.454826	+	0.890580i	$0.349701\pi$
$788$		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	$-0.262444\pi$
$811$	−1.57411	−	1.57411i	−0.0552745	−	0.0552745i	−0.734204	+	0.678929i	$0.762444\pi$
$812$		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	$-0.969410\pi$
$821$	−25.7715	+	25.7715i	−0.899431	+	0.899431i	0.0959548	+	0.995386i	$0.469410\pi$
$822$		0			0
$823$	17.5565	−	17.5565i	0.611982	−	0.611982i	−0.331480	−	0.943462i	$-0.607548\pi$
$823$	17.5565	−	17.5565i	0.611982	−	0.611982i	0.943462	+	0.331480i	$0.107548\pi$
$824$		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	$-0.826680\pi$
$829$	−9.71444	+	9.71444i	−0.337397	+	0.337397i	0.517990	+	0.855387i	$0.326680\pi$
$830$		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	$0.0249979\pi$
$839$			4.54484i			0.156905i	−0.996918	+	0.0784527i	$0.975002\pi$
$840$		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	−0.929893	−	0.367831i	$-0.880101\pi$
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$858$		0			0
$859$	−15.7662	+	15.7662i	−0.537935	+	0.537935i	−0.922922	−	0.384987i	$-0.874206\pi$
$859$	−15.7662	+	15.7662i	−0.537935	+	0.537935i	0.384987	+	0.922922i	$0.374206\pi$
$860$		0			0
$861$	30.8570	+	30.8570i	1.05160	+	1.05160i
$862$		0			0
$863$	−22.6395	−	22.6395i	−0.770659	−	0.770659i	0.207563	−	0.978222i	$-0.433447\pi$
$863$	−22.6395	−	22.6395i	−0.770659	−	0.770659i	−0.978222	+	0.207563i	$0.933447\pi$
$864$		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	0.454863	−	0.890561i	$-0.349688\pi$
$887$	−12.9762	−	12.9762i	−0.435699	−	0.435699i	−0.890561	+	0.454863i	$0.849688\pi$
$888$		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	$0.230843\pi$
$911$			40.0402i			1.32659i	−0.748358	+	0.663295i	$0.769157\pi$
$912$		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	$-0.953558\pi$
$919$		−	8.81475i		−	0.290772i	0.989375	−	0.145386i	$-0.0464423\pi$
$920$		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	$0.288304\pi$
$929$			47.9673i			1.57376i	−0.617109	+	0.786878i	$0.711696\pi$
$930$		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	−0.895953	−	0.444150i	$-0.853506\pi$
$937$	−13.8299	+	13.8299i	−0.451803	+	0.451803i	0.444150	+	0.895953i	$0.353506\pi$
$938$		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	$-0.288180\pi$
$941$	−5.19108	−	5.19108i	−0.169224	−	0.169224i	−0.786638	+	0.617414i	$0.788180\pi$
$942$		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	$-0.371739\pi$
$947$	24.1342			0.784255			0.392128	+	0.919911i	$0.371739\pi$
$948$		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	0.232430	−	0.972613i	$-0.425332\pi$
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	−0.972613	+	0.232430i	$0.925332\pi$
$954$		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	0.961979	−	0.273124i	$-0.0880569\pi$
$967$	21.4211	+	21.4211i	0.688855	+	0.688855i	−0.273124	+	0.961979i	$0.588057\pi$
$968$		0			0
$969$	−0.147351			−0.00473361
$970$		0			0
$971$	11.7978	+	11.7978i	0.378609	+	0.378609i	0.870600	−	0.491991i	$-0.163731\pi$
$971$	11.7978	+	11.7978i	0.378609	+	0.378609i	−0.491991	+	0.870600i	$0.663731\pi$
$972$		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	0.740769	−	0.671760i	$-0.234461\pi$
$977$	2.15703	+	2.15703i	0.0690096	+	0.0690096i	−0.671760	+	0.740769i	$0.734461\pi$
$978$		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	−0.949810	−	0.312827i	$-0.898724\pi$
$983$	−19.9712	+	19.9712i	−0.636983	+	0.636983i	0.312827	+	0.949810i	$0.398724\pi$
$984$		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	$-0.901215\pi$
$991$		−	19.2270i		−	0.610767i	0.952230	−	0.305383i	$-0.0987846\pi$
$992$		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	$-0.510168\pi$
$997$	−2.01694			−0.0638771			−0.0319385	+	0.999490i	$0.510168\pi$
$998$		0			0
$999$		−	40.9838i		−	1.29667i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	80.53	odd	4
80.2.j.b.67.8	yes	18	4.3	odd	2
80.2.s.b.3.8	yes	18	20.3	even	4
80.2.s.b.27.8	yes	18	16.5	even	4
320.2.j.b.47.3		18	1.1	even	1	trivial
320.2.j.b.143.7		18	80.43	even	4	inner
320.2.s.b.207.7		18	16.11	odd	4
320.2.s.b.303.7		18	5.3	odd	4
400.2.j.d.43.2		18	80.37	odd	4
400.2.j.d.307.2		18	20.19	odd	2
400.2.s.d.107.2		18	80.69	even	4
400.2.s.d.243.2		18	20.7	even	4
640.2.j.c.543.3		18	80.3	even	4
640.2.j.c.607.7		18	8.5	even	2
640.2.j.d.543.7		18	80.13	odd	4
640.2.j.d.607.3		18	8.3	odd	2
640.2.s.c.223.3		18	40.13	odd	4
640.2.s.c.287.3		18	16.3	odd	4
640.2.s.d.223.7		18	40.3	even	4
640.2.s.d.287.7		18	16.13	even	4
720.2.z.g.163.2		18	60.23	odd	4
720.2.z.g.667.2		18	48.5	odd	4
720.2.bd.g.307.2		18	12.11	even	2
720.2.bd.g.523.2		18	240.53	even	4
1600.2.j.d.143.3		18	80.27	even	4
1600.2.j.d.1007.7		18	5.4	even	2
1600.2.s.d.207.3		18	80.59	odd	4
1600.2.s.d.943.3		18	5.2	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.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

Introduction

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