LMFDB - Embedded newform 320.2.s.b.303.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(207,320)]

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, 1, 1]))

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

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

chi := DirichletCharacter("320.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.s (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			303.7
Root			$0.482716 - 1.32928i$ of defining polynomial
Character	$\chi$	$=$	320.303
Dual form			320.2.s.b.207.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +O(q^{10})$	\(q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +(-2.17074 - 2.17074i) q^{11} +1.54663i q^{13} +(3.02466 - 0.745827i) q^{15} +(-3.86386 + 3.86386i) q^{17} +(-0.0136865 - 0.0136865i) q^{19} +(2.97357 - 2.97357i) q^{21} +(3.15240 + 3.15240i) q^{23} +(4.42682 - 2.32449i) q^{25} -5.65499 q^{27} +(3.33787 - 3.33787i) q^{29} +8.92639i q^{31} +(-3.02424 - 3.02424i) q^{33} +(3.49118 - 5.77640i) q^{35} -7.24737i q^{37} +2.15475i q^{39} +10.3771i q^{41} +2.02975i q^{43} +(-2.29920 + 0.566942i) q^{45} +(-3.34313 - 3.34313i) q^{47} -2.11103i q^{49} +(-5.38308 + 5.38308i) q^{51} -7.30702 q^{53} +(-5.87483 - 3.55067i) q^{55} +(-0.0190679 - 0.0190679i) q^{57} +(3.52732 - 3.52732i) q^{59} +(1.41629 + 1.41629i) q^{61} +(-2.26036 + 2.26036i) q^{63} +(0.827973 + 3.35780i) q^{65} +0.748197i q^{67} +(4.39187 + 4.39187i) q^{69} +0.269603 q^{71} +(0.811870 - 0.811870i) q^{73} +(6.16739 - 3.23844i) q^{75} -9.26628 q^{77} +2.80567 q^{79} -4.70135 q^{81} -12.8279 q^{83} +(-6.32012 + 10.4571i) q^{85} +(4.65027 - 4.65027i) q^{87} -13.3732 q^{89} +(3.30108 + 3.30108i) q^{91} +12.4361i q^{93} +(-0.0370409 - 0.0223871i) q^{95} +(6.33466 - 6.33466i) q^{97} +(2.29888 + 2.29888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q + 2 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} + 24 q^{27} + 14 q^{29} - 8 q^{33} - 2 q^{35} - 14 q^{45} - 38 q^{47} - 8 q^{51} + 12 q^{53} + 6 q^{55} - 24 q^{57} - 10 q^{59} + 14 q^{61} + 6 q^{63} - 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{75} - 44 q^{77} + 16 q^{79} + 2 q^{81} - 40 q^{83} + 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * 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 + 24 * q^27 + 14 * q^29 - 8 * q^33 - 2 * q^35 - 14 * q^45 - 38 * q^47 - 8 * q^51 + 12 * q^53 + 6 * q^55 - 24 * q^57 - 10 * q^59 + 14 * q^61 + 6 * q^63 - 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^75 - 44 * q^77 + 16 * q^79 + 2 * q^81 - 40 * q^83 + 14 * q^85 - 24 * q^87 + 12 * q^89 - 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$	1.39319			0.804356			0.402178	−	0.915561i	$-0.368253\pi$
$3$	1.39319			0.804356			0.402178	+	0.915561i	$0.368253\pi$
$4$		0			0
$5$	2.17104	−	0.535339i	0.970918	−	0.239411i
$5$	2.17104	−	0.535339i	0.970918	−	0.239411i
$6$		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	$-0.403156\pi$
$11$	−2.17074	−	2.17074i	−0.654501	−	0.654501i	−0.954074	+	0.299572i	$0.903156\pi$
$12$		0			0
$13$			1.54663i			0.428958i	0.976729	+	0.214479i	$0.0688054\pi$
$13$			1.54663i			0.428958i	−0.976729	+	0.214479i	$0.931195\pi$
$14$		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	0.705535	−	0.708675i	$-0.250707\pi$
$19$	−0.0136865	−	0.0136865i	−0.00313991	−	0.00313991i	−0.708675	+	0.705535i	$0.750707\pi$
$20$		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
$27$	−5.65499			−1.08830
$28$		0			0
$29$	3.33787	−	3.33787i	0.619826	−	0.619826i	−0.325660	−	0.945487i	$-0.605587\pi$
$29$	3.33787	−	3.33787i	0.619826	−	0.619826i	0.945487	+	0.325660i	$0.105587\pi$
$30$		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
$35$	3.49118	−	5.77640i	0.590117	−	0.976390i
$36$		0			0
$37$		−	7.24737i		−	1.19146i	−0.803184	−	0.595730i	$-0.796863\pi$
$37$		−	7.24737i		−	1.19146i	0.803184	−	0.595730i	$-0.203137\pi$
$38$		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
$43$			2.02975i			0.309534i	0.987951	+	0.154767i	$0.0494627\pi$
$43$			2.02975i			0.309534i	−0.987951	+	0.154767i	$0.950537\pi$
$44$		0			0
$45$	−2.29920	+	0.566942i	−0.342745	+	0.0845147i
$46$		0			0
$47$	−3.34313	−	3.34313i	−0.487646	−	0.487646i	0.419917	−	0.907563i	$-0.362059\pi$
$47$	−3.34313	−	3.34313i	−0.487646	−	0.487646i	−0.907563	+	0.419917i	$0.862059\pi$
$48$		0			0
$49$		−	2.11103i		−	0.301575i
$50$		0			0
$51$	−5.38308	+	5.38308i	−0.753782	+	0.753782i
$52$		0			0
$53$	−7.30702			−1.00370			−0.501848	−	0.864956i	$-0.667346\pi$
$53$	−7.30702			−1.00370			−0.501848	+	0.864956i	$0.667346\pi$
$54$		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	−0.439181	−	0.898399i	$-0.644731\pi$
$59$	3.52732	−	3.52732i	0.459218	−	0.459218i	0.898399	+	0.439181i	$0.144731\pi$
$60$		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
$67$			0.748197i			0.0914068i	0.998955	+	0.0457034i	$0.0145529\pi$
$67$			0.748197i			0.0914068i	−0.998955	+	0.0457034i	$0.985447\pi$
$68$		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	$-0.728596\pi$
$73$	0.811870	−	0.811870i	0.0950222	−	0.0950222i	0.753020	+	0.657998i	$0.228596\pi$
$74$		0			0
$75$	6.16739	−	3.23844i	0.712149	−	0.373943i
$76$		0			0
$77$	−9.26628			−1.05599
$78$		0			0
$79$	2.80567			0.315662			0.157831	−	0.987466i	$-0.449550\pi$
$79$	2.80567			0.315662			0.157831	+	0.987466i	$0.449550\pi$
$80$		0			0
$81$	−4.70135			−0.522372
$82$		0			0
$83$	−12.8279			−1.40804			−0.704022	−	0.710178i	$-0.748614\pi$
$83$	−12.8279			−1.40804			−0.704022	+	0.710178i	$0.748614\pi$
$84$		0			0
$85$	−6.32012	+	10.4571i	−0.685514	+	1.13423i
$86$		0			0
$87$	4.65027	−	4.65027i	0.498561	−	0.498561i
$88$		0			0
$89$	−13.3732			−1.41755			−0.708777	−	0.705432i	$-0.750753\pi$
$89$	−13.3732			−1.41755			−0.708777	+	0.705432i	$0.750753\pi$
$90$		0			0
$91$	3.30108	+	3.30108i	0.346047	+	0.346047i
$92$		0			0
$93$			12.4361i			1.28957i
$94$		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	$-0.835719\pi$
$101$	−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	−0.998320	−	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
$107$	−10.9109			−1.05479			−0.527397	−	0.849619i	$-0.676832\pi$
$107$	−10.9109			−1.05479			−0.527397	+	0.849619i	$0.676832\pi$
$108$		0			0
$109$	9.12139	−	9.12139i	0.873670	−	0.873670i	−0.119200	−	0.992870i	$-0.538033\pi$
$109$	9.12139	−	9.12139i	0.873670	−	0.873670i	0.992870	+	0.119200i	$0.0380329\pi$
$110$		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
$115$	8.53157	+	5.15637i	0.795573	+	0.480834i
$116$		0			0
$117$		−	1.63793i		−	0.151427i
$118$		0			0
$119$			16.4938i			1.51198i
$120$		0			0
$121$		−	1.57582i		−	0.143256i
$122$		0			0
$123$			14.4572i			1.30356i
$124$		0			0
$125$	8.36642	−	7.41640i	0.748315	−	0.663343i
$126$		0			0
$127$	−1.38586	−	1.38586i	−0.122975	−	0.122975i	0.642941	−	0.765916i	$-0.277714\pi$
$127$	−1.38586	−	1.38586i	−0.122975	−	0.122975i	−0.765916	+	0.642941i	$0.777714\pi$
$128$		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
$133$	−0.0584241			−0.00506601
$134$		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	$-0.360368\pi$
$137$	−5.62512	−	5.62512i	−0.480587	−	0.480587i	−0.905319	+	0.424732i	$0.860368\pi$
$138$		0			0
$139$	12.1022	−	12.1022i	1.02650	−	1.02650i	0.0268584	−	0.999639i	$-0.491450\pi$
$139$	12.1022	−	12.1022i	1.02650	−	1.02650i	0.999639	−	0.0268584i	$-0.00855031\pi$
$140$		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
$147$		−	2.94105i		−	0.242574i
$148$		0			0
$149$	13.5590	+	13.5590i	1.11080	+	1.11080i	0.993042	+	0.117757i	$0.0375702\pi$
$149$	13.5590	+	13.5590i	1.11080	+	1.11080i	0.117757	+	0.993042i	$0.462430\pi$
$150$		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
$155$	4.77865	+	19.3795i	0.383830	+	1.55660i
$156$		0			0
$157$	−5.72312			−0.456755			−0.228377	−	0.973573i	$-0.573342\pi$
$157$	−5.72312			−0.456755			−0.228377	+	0.973573i	$0.573342\pi$
$158$		0			0
$159$	−10.1800			−0.807329
$160$		0			0
$161$	13.4567			1.06054
$162$		0			0
$163$	17.9900			1.40909			0.704543	−	0.709662i	$-0.251152\pi$
$163$	17.9900			1.40909			0.704543	+	0.709662i	$0.251152\pi$
$164$		0			0
$165$	−8.18473	−	4.94675i	−0.637181	−	0.385104i
$166$		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
$173$		−	9.45205i		−	0.718626i	−0.933217	−	0.359313i	$-0.883011\pi$
$173$		−	9.45205i		−	0.718626i	0.933217	−	0.359313i	$-0.116989\pi$
$174$		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	0.111824	−	0.993728i	$-0.464331\pi$
$179$	−11.7991	−	11.7991i	−0.881905	−	0.881905i	−0.993728	+	0.111824i	$0.964331\pi$
$180$		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
$187$	16.7748			1.22670
$188$		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	0.859103	−	0.511803i	$-0.171022\pi$
$193$	4.82485	+	4.82485i	0.347300	+	0.347300i	−0.511803	+	0.859103i	$0.671022\pi$
$194$		0			0
$195$	1.15352	+	4.67804i	0.0826053	+	0.335001i
$196$		0			0
$197$		−	2.94582i		−	0.209881i	−0.994478	−	0.104941i	$-0.966535\pi$
$197$		−	2.94582i		−	0.209881i	0.994478	−	0.104941i	$-0.0334653\pi$
$198$		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
$203$		−	14.2485i		−	1.00005i
$204$		0			0
$205$	5.55526	+	22.5291i	0.387996	+	1.57350i
$206$		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
$213$	0.375608			0.0257362
$214$		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	$-0.767517\pi$
$223$	−1.16163	+	1.16163i	−0.0777882	+	0.0777882i	0.667142	+	0.744930i	$0.267517\pi$
$224$		0			0
$225$	−4.68815	+	2.46171i	−0.312543	+	0.164114i
$226$		0			0
$227$			12.8161i			0.850632i	0.905045	+	0.425316i	$0.139837\pi$
$227$			12.8161i			0.850632i	−0.905045	+	0.425316i	$0.860163\pi$
$228$		0			0
$229$	0.976882	+	0.976882i	0.0645542	+	0.0645542i	0.738647	−	0.674093i	$-0.235465\pi$
$229$	0.976882	+	0.976882i	0.0645542	+	0.0645542i	−0.674093	+	0.738647i	$0.735465\pi$
$230$		0			0
$231$	−12.9097			−0.849393
$232$		0			0
$233$	−0.303870	+	0.303870i	−0.0199072	+	0.0199072i	−0.716990	−	0.697083i	$-0.754481\pi$
$233$	−0.303870	+	0.303870i	−0.0199072	+	0.0199072i	0.697083	+	0.716990i	$0.254481\pi$
$234$		0			0
$235$	−9.04777	−	5.46836i	−0.590212	−	0.356716i
$236$		0			0
$237$	3.90881			0.253905
$238$		0			0
$239$	12.5096			0.809178			0.404589	−	0.914499i	$-0.367415\pi$
$239$	12.5096			0.809178			0.404589	+	0.914499i	$0.367415\pi$
$240$		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
$243$	10.4151			0.668129
$244$		0			0
$245$	−1.13012	−	4.58312i	−0.0722004	−	0.292805i
$246$		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
$253$		−	13.6860i		−	0.860433i
$254$		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
$267$	−18.6313			−1.14022
$268$		0			0
$269$	2.10121	−	2.10121i	0.128113	−	0.128113i	−0.640143	−	0.768256i	$-0.721125\pi$
$269$	2.10121	−	2.10121i	0.128113	−	0.128113i	0.768256	+	0.640143i	$0.221125\pi$
$270$		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
$275$	−14.6553	−	4.56362i	−0.883748	−	0.275197i
$276$		0			0
$277$		−	9.91909i		−	0.595980i	−0.954569	−	0.297990i	$-0.903684\pi$
$277$		−	9.91909i		−	0.595980i	0.954569	−	0.297990i	$-0.0963162\pi$
$278$		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
$283$			3.42364i			0.203514i	0.994809	+	0.101757i	$0.0324465\pi$
$283$			3.42364i			0.203514i	−0.994809	+	0.101757i	$0.967554\pi$
$284$		0			0
$285$	−0.0516049	−	0.0311893i	−0.00305681	−	0.00184750i
$286$		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
$293$	2.66471			0.155674			0.0778369	−	0.996966i	$-0.475199\pi$
$293$	2.66471			0.155674			0.0778369	+	0.996966i	$0.475199\pi$
$294$		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
$307$			10.5554i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$307$			10.5554i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$308$		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	$-0.786003\pi$
$313$	−2.82393	+	2.82393i	−0.159618	+	0.159618i	0.622780	+	0.782397i	$0.286003\pi$
$314$		0			0
$315$	−3.69727	+	6.11740i	−0.208318	+	0.344676i
$316$		0			0
$317$	20.2533			1.13754			0.568769	−	0.822497i	$-0.307420\pi$
$317$	20.2533			1.13754			0.568769	+	0.822497i	$0.307420\pi$
$318$		0			0
$319$	−14.4913			−0.811354
$320$		0			0
$321$	−15.2009			−0.848430
$322$		0			0
$323$	0.105766			0.00588497
$324$		0			0
$325$	3.59512	+	6.84667i	0.199422	+	0.379785i
$326$		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
$333$			7.67521i			0.420599i
$334$		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
$347$	11.4626			0.615346			0.307673	−	0.951492i	$-0.400450\pi$
$347$	11.4626			0.615346			0.307673	+	0.951492i	$0.400450\pi$
$348$		0			0
$349$	0.317872	−	0.317872i	0.0170153	−	0.0170153i	−0.698548	−	0.715563i	$-0.746170\pi$
$349$	0.317872	−	0.317872i	0.0170153	−	0.0170153i	0.715563	+	0.698548i	$0.246170\pi$
$350$		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
$355$	0.585320	−	0.144329i	0.0310655	−	0.00766020i
$356$		0			0
$357$			22.9789i			1.21617i
$358$		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
$363$		−	2.19541i		−	0.115229i
$364$		0			0
$365$	1.32798	−	2.19723i	0.0695095	−	0.115008i
$366$		0			0
$367$	5.37489	+	5.37489i	0.280567	+	0.280567i	0.833335	−	0.552768i	$-0.186428\pi$
$367$	5.37489	+	5.37489i	0.280567	+	0.280567i	−0.552768	+	0.833335i	$0.686428\pi$
$368$		0			0
$369$		−	10.9897i		−	0.572100i
$370$		0			0
$371$	−15.5958	+	15.5958i	−0.809696	+	0.809696i
$372$		0			0
$373$	3.24424			0.167980			0.0839902	−	0.996467i	$-0.473234\pi$
$373$	3.24424			0.167980			0.0839902	+	0.996467i	$0.473234\pi$
$374$		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	$0.635478\pi$
$379$	−25.7690	+	25.7690i	−1.32367	+	1.32367i	−0.910785	+	0.412882i	$0.864522\pi$
$380$		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	$-0.745191\pi$
$383$	0.418091	−	0.418091i	0.0213634	−	0.0213634i	0.717708	+	0.696344i	$0.245191\pi$
$384$		0			0
$385$	−20.1175	+	4.96060i	−1.02528	+	0.252816i
$386$		0			0
$387$		−	2.14957i		−	0.109269i
$388$		0			0
$389$	−13.3626	−	13.3626i	−0.677508	−	0.677508i	0.281927	−	0.959436i	$-0.409026\pi$
$389$	−13.3626	−	13.3626i	−0.677508	−	0.677508i	−0.959436	+	0.281927i	$0.909026\pi$
$390$		0			0
$391$	−24.3609			−1.23198
$392$		0			0
$393$	4.90535	−	4.90535i	0.247442	−	0.247442i
$394$		0			0
$395$	6.09121	−	1.50198i	0.306482	−	0.0755730i
$396$		0			0
$397$	−13.8391			−0.694564			−0.347282	−	0.937761i	$-0.612895\pi$
$397$	−13.8391			−0.694564			−0.347282	+	0.937761i	$0.612895\pi$
$398$		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
$403$	−13.8058			−0.687718
$404$		0			0
$405$	−10.2068	+	2.51682i	−0.507181	+	0.125062i
$406$		0			0
$407$	−15.7321	+	15.7321i	−0.779813	+	0.779813i
$408$		0			0
$409$	18.2875			0.904259			0.452130	−	0.891952i	$-0.350664\pi$
$409$	18.2875			0.904259			0.452130	+	0.891952i	$0.350664\pi$
$410$		0			0
$411$	−7.83684	−	7.83684i	−0.386563	−	0.386563i
$412$		0			0
$413$		−	15.0572i		−	0.740915i
$414$		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	0.989641	−	0.143563i	$-0.0458558\pi$
$419$	17.3188	+	17.3188i	0.846079	+	0.846079i	−0.143563	+	0.989641i	$0.545856\pi$
$420$		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
$427$	6.04577			0.292576
$428$		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	0.786633	−	0.617420i	$-0.211822\pi$
$433$	3.52109	+	3.52109i	0.169213	+	0.169213i	−0.617420	+	0.786633i	$0.711822\pi$
$434$		0			0
$435$	7.60645	−	12.5854i	0.364701	−	0.603423i
$436$		0			0
$437$		−	0.0862907i		−	0.00412784i
$438$		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
$443$		−	27.0992i		−	1.28752i	−0.765226	−	0.643761i	$-0.777373\pi$
$443$		−	27.0992i		−	1.28752i	0.765226	−	0.643761i	$-0.222627\pi$
$444$		0			0
$445$	−29.0337	+	7.15919i	−1.37633	+	0.339378i
$446$		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
$453$	28.8648			1.35619
$454$		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	$-0.456223\pi$
$457$	−18.2449	−	18.2449i	−0.853462	−	0.853462i	−0.990558	+	0.137096i	$0.956223\pi$
$458$		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	0.431205	−	0.902254i	$-0.358089\pi$
$463$	28.6926	−	28.6926i	1.33346	−	1.33346i	0.902254	−	0.431205i	$-0.141911\pi$
$464$		0			0
$465$	6.65754	+	26.9993i	0.308736	+	1.25206i
$466$		0			0
$467$		−	32.4161i		−	1.50004i	−0.661417	−	0.750018i	$-0.730045\pi$
$467$		−	32.4161i		−	1.50004i	0.661417	−	0.750018i	$-0.269955\pi$
$468$		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
$475$	−0.0924020	−	0.0287737i	−0.00423970	−	0.00132023i
$476$		0			0
$477$	7.73837			0.354316
$478$		0			0
$479$	7.33117			0.334970			0.167485	−	0.985875i	$-0.446435\pi$
$479$	7.33117			0.334970			0.167485	+	0.985875i	$0.446435\pi$
$480$		0			0
$481$	11.2090			0.511087
$482$		0			0
$483$	18.7477			0.853051
$484$		0			0
$485$	10.3616	−	17.1440i	0.470496	−	0.778468i
$486$		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	0.962200	+	0.272343i	$0.0877985\pi$
$491$	27.3556	+	27.3556i	1.23454	+	1.23454i	0.272343	+	0.962200i	$0.412202\pi$
$492$		0			0
$493$			25.7941i			1.16171i
$494$		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	0.924841	−	0.380353i	$-0.124198\pi$
$499$	12.1629	+	12.1629i	0.544488	+	0.544488i	−0.380353	+	0.924841i	$0.624198\pi$
$500$		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
$507$	14.7788			0.656350
$508$		0			0
$509$	−9.29995	+	9.29995i	−0.412213	+	0.412213i	−0.882509	−	0.470296i	$-0.844147\pi$
$509$	−9.29995	+	9.29995i	−0.412213	+	0.412213i	0.470296	+	0.882509i	$0.344147\pi$
$510$		0			0
$511$		−	3.46565i		−	0.153312i
$512$		0			0
$513$	0.0773972	+	0.0773972i	0.00341717	+	0.00341717i
$514$		0			0
$515$	−29.0121	−	17.5345i	−1.27843	−	0.772664i
$516$		0			0
$517$			14.5141i			0.638329i
$518$		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
$523$			25.9463i			1.13455i	0.823528	+	0.567276i	$0.192003\pi$
$523$			25.9463i			1.13455i	−0.823528	+	0.567276i	$0.807997\pi$
$524$		0			0
$525$	6.25144	−	20.0755i	0.272835	−	0.876165i
$526$		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
$533$	−16.0495			−0.695182
$534$		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
$547$			15.5964i			0.666853i	0.942776	+	0.333426i	$0.108205\pi$
$547$			15.5964i			0.666853i	−0.942776	+	0.333426i	$0.891795\pi$
$548$		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
$555$	−5.40529	−	21.9209i	−0.229442	−	0.930488i
$556$		0			0
$557$	15.5348			0.658231			0.329116	−	0.944290i	$-0.393249\pi$
$557$	15.5348			0.658231			0.329116	+	0.944290i	$0.393249\pi$
$558$		0			0
$559$	−3.13928			−0.132777
$560$		0			0
$561$	23.3705			0.986703
$562$		0			0
$563$	−24.3087			−1.02449			−0.512245	−	0.858839i	$-0.671186\pi$
$563$	−24.3087			−1.02449			−0.512245	+	0.858839i	$0.671186\pi$
$564$		0			0
$565$	13.2291	+	7.99547i	0.556550	+	0.336372i
$566$		0			0
$567$	−10.0344	+	10.0344i	−0.421405	+	0.421405i
$568$		0			0
$569$	−0.187259			−0.00785029			−0.00392515	−	0.999992i	$-0.501249\pi$
$569$	−0.187259			−0.00785029			−0.00392515	+	0.999992i	$0.501249\pi$
$570$		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
$573$		−	7.61266i		−	0.318023i
$574$		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
$587$	3.06150			0.126362			0.0631808	−	0.998002i	$-0.479876\pi$
$587$	3.06150			0.126362			0.0631808	+	0.998002i	$0.479876\pi$
$588$		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
$595$	8.82977	+	35.8087i	0.361985	+	1.46801i
$596$		0			0
$597$			2.99005i			0.122375i
$598$		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	$-0.969423\pi$
$601$		−	4.70260i		−	0.191823i	0.995390	−	0.0959115i	$-0.0305766\pi$
$602$		0			0
$603$		−	0.792365i		−	0.0322676i
$604$		0			0
$605$	−0.843598	−	3.42116i	−0.0342971	−	0.139090i
$606$		0			0
$607$	−28.8294	−	28.8294i	−1.17015	−	1.17015i	−0.982174	−	0.187975i	$-0.939807\pi$
$607$	−28.8294	−	28.8294i	−1.17015	−	1.17015i	−0.187975	−	0.982174i	$-0.560193\pi$
$608$		0			0
$609$		−	19.8507i		−	0.804393i
$610$		0			0
$611$	5.17059	−	5.17059i	0.209180	−	0.209180i
$612$		0			0
$613$	−38.7980			−1.56704			−0.783518	−	0.621369i	$-0.786577\pi$
$613$	−38.7980			−1.56704			−0.783518	+	0.621369i	$0.786577\pi$
$614$		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	$-0.185521\pi$
$617$	7.06723	+	7.06723i	0.284516	+	0.284516i	−0.550391	+	0.834907i	$0.685521\pi$
$618$		0			0
$619$	−28.1001	+	28.1001i	−1.12944	+	1.12944i	−0.139172	+	0.990268i	$0.544444\pi$
$619$	−28.1001	+	28.1001i	−1.12944	+	1.12944i	−0.990268	+	0.139172i	$0.955556\pi$
$620$		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
$627$			0.0827827i			0.00330602i
$628$		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
$635$	−3.75067	−	2.26685i	−0.148841	−	0.0899574i
$636$		0			0
$637$	3.26498			0.129363
$638$		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
$643$	−8.74864			−0.345013			−0.172506	−	0.985008i	$-0.555187\pi$
$643$	−8.74864			−0.345013			−0.172506	+	0.985008i	$0.555187\pi$
$644$		0			0
$645$	1.51384	+	6.13931i	0.0596076	+	0.241735i
$646$		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
$653$		−	20.7854i		−	0.813396i	−0.913563	−	0.406698i	$-0.866680\pi$
$653$		−	20.7854i		−	0.813396i	0.913563	−	0.406698i	$-0.133320\pi$
$654$		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	0.917384	−	0.398003i	$-0.130297\pi$
$659$	13.3330	+	13.3330i	0.519382	+	0.519382i	−0.398003	+	0.917384i	$0.630297\pi$
$660$		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
$667$	21.0446			0.814848
$668$		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
$675$	−25.0336	+	13.1449i	−0.963545	+	0.505949i
$676$		0			0
$677$			33.4274i			1.28472i	0.766403	+	0.642360i	$0.222044\pi$
$677$			33.4274i			1.28472i	−0.766403	+	0.642360i	$0.777956\pi$
$678$		0			0
$679$		−	27.0409i		−	1.03774i
$680$		0			0
$681$			17.8551i			0.684211i
$682$		0			0
$683$			4.07583i			0.155957i	0.996955	+	0.0779787i	$0.0248466\pi$
$683$			4.07583i			0.155957i	−0.996955	+	0.0779787i	$0.975153\pi$
$684$		0			0
$685$	−15.2237	−	9.20102i	−0.581668	−	0.351553i
$686$		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
$693$	9.81330			0.372776
$694$		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
$707$			16.1413i			0.607056i
$708$		0			0
$709$	−32.3901	−	32.3901i	−1.21643	−	1.21643i	−0.968872	−	0.247563i	$-0.920370\pi$
$709$	−32.3901	−	32.3901i	−1.21643	−	1.21643i	−0.247563	−	0.968872i	$-0.579630\pi$
$710$		0			0
$711$	−2.97129			−0.111432
$712$		0			0
$713$	−28.1395	+	28.1395i	−1.05383	+	1.05383i
$714$		0			0
$715$	5.49158	−	9.08620i	0.205373	−	0.339805i
$716$		0			0
$717$	17.4282			0.650868
$718$		0			0
$719$	−4.16893			−0.155475			−0.0777374	−	0.996974i	$-0.524770\pi$
$719$	−4.16893			−0.155475			−0.0777374	+	0.996974i	$0.524770\pi$
$720$		0			0
$721$	−45.7603			−1.70420
$722$		0			0
$723$	−27.2751			−1.01437
$724$		0			0
$725$	7.01733	−	22.5350i	0.260617	−	0.836928i
$726$		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
$733$			18.7069i			0.690956i	0.938427	+	0.345478i	$0.112283\pi$
$733$			18.7069i			0.690956i	−0.938427	+	0.345478i	$0.887717\pi$
$734$		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	$-0.891825\pi$
$739$	−34.6914	−	34.6914i	−1.27614	−	1.27614i	−0.333337	−	0.942808i	$-0.608175\pi$
$740$		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
$747$	13.5852			0.497055
$748$		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
$755$	44.9808	−	11.0914i	1.63702	−	0.403659i
$756$		0			0
$757$		−	6.44058i		−	0.234087i	−0.993127	−	0.117044i	$-0.962658\pi$
$757$		−	6.44058i		−	0.234087i	0.993127	−	0.117044i	$-0.0373417\pi$
$758$		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
$763$		−	38.9367i		−	1.40960i
$764$		0			0
$765$	6.69322	−	11.0744i	0.241994	−	0.400395i
$766$		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
$773$	10.9964			0.395513			0.197756	−	0.980251i	$-0.436635\pi$
$773$	10.9964			0.395513			0.197756	+	0.980251i	$0.436635\pi$
$774$		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
$787$		−	25.5190i		−	0.909653i	−0.890580	−	0.454826i	$-0.849701\pi$
$787$		−	25.5190i		−	0.909653i	0.890580	−	0.454826i	$-0.150299\pi$
$788$		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
$795$	−22.1013	+	5.44977i	−0.783851	+	0.193283i
$796$		0			0
$797$	−13.3808			−0.473972			−0.236986	−	0.971513i	$-0.576160\pi$
$797$	−13.3808			−0.473972			−0.236986	+	0.971513i	$0.576160\pi$
$798$		0			0
$799$	25.8348			0.913969
$800$		0			0
$801$	14.1626			0.500412
$802$		0			0
$803$	−3.52471			−0.124384
$804$		0			0
$805$	29.2151	−	7.20391i	1.02970	−	0.253905i
$806$		0			0
$807$	2.92738	−	2.92738i	0.103049	−	0.103049i
$808$		0			0
$809$	52.7958			1.85620			0.928102	−	0.372327i	$-0.121440\pi$
$809$	52.7958			1.85620			0.928102	+	0.372327i	$0.121440\pi$
$810$		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
$813$			26.2749i			0.921500i
$814$		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	0.943462	−	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
$827$	−14.8548			−0.516551			−0.258276	−	0.966071i	$-0.583154\pi$
$827$	−14.8548			−0.516551			−0.258276	+	0.966071i	$0.583154\pi$
$828$		0			0
$829$	9.71444	−	9.71444i	0.337397	−	0.337397i	−0.517990	−	0.855387i	$-0.673320\pi$
$829$	9.71444	−	9.71444i	0.337397	−	0.337397i	0.855387	+	0.517990i	$0.173320\pi$
$830$		0			0
$831$		−	13.8191i		−	0.479380i
$832$		0			0
$833$	8.15672	+	8.15672i	0.282614	+	0.282614i
$834$		0			0
$835$	−3.91983	+	6.48563i	−0.135651	+	0.224444i
$836$		0			0
$837$		−	50.4786i		−	1.74480i
$838$		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
$843$			12.9766i			0.446938i
$844$		0			0
$845$	23.0302	−	5.67884i	0.792264	−	0.195358i
$846$		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
$853$	37.3745			1.27968			0.639839	−	0.768509i	$-0.279001\pi$
$853$	37.3745			1.27968			0.639839	+	0.768509i	$0.279001\pi$
$854$		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	$-0.119899\pi$
$857$	16.4541	+	16.4541i	0.562062	+	0.562062i	−0.367831	+	0.929893i	$0.619899\pi$
$858$		0			0
$859$	15.7662	−	15.7662i	0.537935	−	0.537935i	−0.384987	−	0.922922i	$-0.625794\pi$
$859$	15.7662	−	15.7662i	0.537935	−	0.537935i	0.922922	+	0.384987i	$0.125794\pi$
$860$		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	$-0.566553\pi$
$863$	22.6395	−	22.6395i	0.770659	−	0.770659i	0.978222	+	0.207563i	$0.0665532\pi$
$864$		0			0
$865$	−5.06005	−	20.5208i	−0.172047	−	0.697727i
$866$		0			0
$867$		−	17.9148i		−	0.608419i
$868$		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
$875$	2.02769	−	33.6863i	0.0685483	−	1.13880i
$876$		0			0
$877$	−30.0542			−1.01486			−0.507429	−	0.861694i	$-0.669404\pi$
$877$	−30.0542			−1.01486			−0.507429	+	0.861694i	$0.669404\pi$
$878$		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
$883$	0.485919			0.0163525			0.00817624	−	0.999967i	$-0.497397\pi$
$883$	0.485919			0.0163525			0.00817624	+	0.999967i	$0.497397\pi$
$884$		0			0
$885$	8.03817	−	13.2997i	0.270200	−	0.447065i
$886$		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
$893$			0.0915117i			0.00306232i
$894$		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
$907$	−54.3645			−1.80514			−0.902571	−	0.430540i	$-0.858323\pi$
$907$	−54.3645			−1.80514			−0.902571	+	0.430540i	$0.858323\pi$
$908$		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
$915$	5.34012	+	3.22750i	0.176539	+	0.106698i
$916$		0			0
$917$		−	15.0300i		−	0.496335i
$918$		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
$923$			0.416977i			0.0137250i
$924$		0			0
$925$	−16.8464	−	32.0828i	−0.553907	−	1.05488i
$926$		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
$933$	28.5272			0.933938
$934$		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	$-0.146494\pi$
$937$	13.8299	+	13.8299i	0.451803	+	0.451803i	−0.444150	+	0.895953i	$0.646494\pi$
$938$		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
$947$		−	24.1342i		−	0.784255i	−0.919911	−	0.392128i	$-0.871739\pi$
$947$		−	24.1342i		−	0.784255i	0.919911	−	0.392128i	$-0.128261\pi$
$948$		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	$-0.574668\pi$
$953$	22.8500	−	22.8500i	0.740183	−	0.740183i	0.972613	+	0.232430i	$0.0746678\pi$
$954$		0			0
$955$	−2.92521	−	11.8630i	−0.0946574	−	0.383878i
$956$		0			0
$957$	−20.1890			−0.652618
$958$		0			0
$959$	−24.0121			−0.775392
$960$		0			0
$961$	−48.6804			−1.57034
$962$		0			0
$963$	11.5550			0.372354
$964$		0			0
$965$	13.0579	+	7.89200i	0.420347	+	0.254052i
$966$		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	$-0.163731\pi$
$971$	11.7978	+	11.7978i	0.378609	+	0.378609i	−0.491991	+	0.870600i	$0.663731\pi$
$972$		0			0
$973$		−	51.6611i		−	1.65618i
$974$		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
$987$	−19.8820			−0.632852
$988$		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
$995$	1.14894	+	4.65948i	0.0364240	+	0.147715i
$996$		0			0
$997$			2.01694i			0.0638771i	0.999490	+	0.0319385i	$0.0101681\pi$
$997$			2.01694i			0.0638771i	−0.999490	+	0.0319385i	$0.989832\pi$
$998$		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.s.b.303.7		18
4.3	odd	2		80.2.s.b.3.8	yes	18
5.2	odd	4		320.2.j.b.47.3		18
5.3	odd	4		1600.2.j.d.1007.7		18
5.4	even	2		1600.2.s.d.943.3		18
8.3	odd	2		640.2.s.d.223.7		18
8.5	even	2		640.2.s.c.223.3		18
12.11	even	2		720.2.z.g.163.2		18
16.3	odd	4		640.2.j.c.543.3		18
16.5	even	4		80.2.j.b.43.8	✓	18
16.11	odd	4		320.2.j.b.143.7		18
16.13	even	4		640.2.j.d.543.7		18
20.3	even	4		400.2.j.d.307.2		18
20.7	even	4		80.2.j.b.67.8	yes	18
20.19	odd	2		400.2.s.d.243.2		18
40.27	even	4		640.2.j.d.607.3		18
40.37	odd	4		640.2.j.c.607.7		18
48.5	odd	4		720.2.bd.g.523.2		18
60.47	odd	4		720.2.bd.g.307.2		18
80.27	even	4	inner	320.2.s.b.207.7		18
80.37	odd	4		80.2.s.b.27.8	yes	18
80.43	even	4		1600.2.s.d.207.3		18
80.53	odd	4		400.2.s.d.107.2		18
80.59	odd	4		1600.2.j.d.143.3		18
80.67	even	4		640.2.s.c.287.3		18
80.69	even	4		400.2.j.d.43.2		18
80.77	odd	4		640.2.s.d.287.7		18
240.197	even	4		720.2.z.g.667.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	16.5	even	4
80.2.j.b.67.8	yes	18	20.7	even	4
80.2.s.b.3.8	yes	18	4.3	odd	2
80.2.s.b.27.8	yes	18	80.37	odd	4
320.2.j.b.47.3		18	5.2	odd	4
320.2.j.b.143.7		18	16.11	odd	4
320.2.s.b.207.7		18	80.27	even	4	inner
320.2.s.b.303.7		18	1.1	even	1	trivial
400.2.j.d.43.2		18	80.69	even	4
400.2.j.d.307.2		18	20.3	even	4
400.2.s.d.107.2		18	80.53	odd	4
400.2.s.d.243.2		18	20.19	odd	2
640.2.j.c.543.3		18	16.3	odd	4
640.2.j.c.607.7		18	40.37	odd	4
640.2.j.d.543.7		18	16.13	even	4
640.2.j.d.607.3		18	40.27	even	4
640.2.s.c.223.3		18	8.5	even	2
640.2.s.c.287.3		18	80.67	even	4
640.2.s.d.223.7		18	8.3	odd	2
640.2.s.d.287.7		18	80.77	odd	4
720.2.z.g.163.2		18	12.11	even	2
720.2.z.g.667.2		18	240.197	even	4
720.2.bd.g.307.2		18	60.47	odd	4
720.2.bd.g.523.2		18	48.5	odd	4
1600.2.j.d.143.3		18	80.59	odd	4
1600.2.j.d.1007.7		18	5.3	odd	4
1600.2.s.d.207.3		18	80.43	even	4
1600.2.s.d.943.3		18	5.4	even	2

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.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +O(q^{10})\)	\(q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +(-2.17074 - 2.17074i) q^{11} +1.54663i q^{13} +(3.02466 - 0.745827i) q^{15} +(-3.86386 + 3.86386i) q^{17} +(-0.0136865 - 0.0136865i) q^{19} +(2.97357 - 2.97357i) q^{21} +(3.15240 + 3.15240i) q^{23} +(4.42682 - 2.32449i) q^{25} -5.65499 q^{27} +(3.33787 - 3.33787i) q^{29} +8.92639i q^{31} +(-3.02424 - 3.02424i) q^{33} +(3.49118 - 5.77640i) q^{35} -7.24737i q^{37} +2.15475i q^{39} +10.3771i q^{41} +2.02975i q^{43} +(-2.29920 + 0.566942i) q^{45} +(-3.34313 - 3.34313i) q^{47} -2.11103i q^{49} +(-5.38308 + 5.38308i) q^{51} -7.30702 q^{53} +(-5.87483 - 3.55067i) q^{55} +(-0.0190679 - 0.0190679i) q^{57} +(3.52732 - 3.52732i) q^{59} +(1.41629 + 1.41629i) q^{61} +(-2.26036 + 2.26036i) q^{63} +(0.827973 + 3.35780i) q^{65} +0.748197i q^{67} +(4.39187 + 4.39187i) q^{69} +0.269603 q^{71} +(0.811870 - 0.811870i) q^{73} +(6.16739 - 3.23844i) q^{75} -9.26628 q^{77} +2.80567 q^{79} -4.70135 q^{81} -12.8279 q^{83} +(-6.32012 + 10.4571i) q^{85} +(4.65027 - 4.65027i) q^{87} -13.3732 q^{89} +(3.30108 + 3.30108i) q^{91} +12.4361i q^{93} +(-0.0370409 - 0.0223871i) q^{95} +(6.33466 - 6.33466i) q^{97} +(2.29888 + 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} + 2 q^{19} - 16 q^{21} + 2 q^{23} - 6 q^{25} + 24 q^{27} + 14 q^{29} - 8 q^{33} - 2 q^{35} - 14 q^{45} - 38 q^{47} - 8 q^{51} + 12 q^{53} + 6 q^{55} - 24 q^{57} - 10 q^{59} + 14 q^{61} + 6 q^{63} - 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{75} - 44 q^{77} + 16 q^{79} + 2 q^{81} - 40 q^{83} + 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * 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 + 24 * q^27 + 14 * q^29 - 8 * q^33 - 2 * q^35 - 14 * q^45 - 38 * q^47 - 8 * q^51 + 12 * q^53 + 6 * q^55 - 24 * q^57 - 10 * q^59 + 14 * q^61 + 6 * q^63 - 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^75 - 44 * q^77 + 16 * q^79 + 2 * q^81 - 40 * q^83 + 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more