LMFDB - Embedded newform 1323.2.f.g.883.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.3
Root			$-1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.g.442.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(-1.29589 - 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})$	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(-1.29589 - 2.24456i) q^{5} +0.942820 q^{8} -0.619757 q^{10} +(2.09097 - 3.62167i) q^{11} +(-1.84155 - 3.18966i) q^{13} +(-1.83009 + 3.16982i) q^{16} -1.71107 q^{17} -7.15561 q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 - 4.43818i) q^{23} +(-0.858685 + 1.48729i) q^{25} -0.880716 q^{26} +(-1.06238 + 1.84010i) q^{29} +(3.26793 + 5.66021i) q^{31} +(1.38044 + 2.39099i) q^{32} +(-0.204579 + 0.354341i) q^{34} +1.66019 q^{37} +(-0.855536 + 1.48183i) q^{38} +(-1.22180 - 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +8.12476 q^{44} -1.22545 q^{46} +(4.66912 - 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} +(3.57780 - 6.19694i) q^{52} -10.6465 q^{53} -10.8387 q^{55} +(0.254040 + 0.440011i) q^{58} +(3.03215 + 5.25183i) q^{59} +(3.99298 - 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(-4.77292 + 8.26693i) q^{65} +(-4.13160 - 7.15614i) q^{67} +(-1.66215 - 2.87893i) q^{68} -6.23912 q^{71} +7.15561 q^{73} +(0.198495 - 0.343803i) q^{74} +(-6.95103 - 12.0395i) q^{76} +(4.91423 - 8.51170i) q^{79} +9.48644 q^{80} -2.44359 q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 - 0.343803i) q^{86} +(1.97141 - 3.41458i) q^{88} +5.03538 q^{89} +(4.97825 - 8.62258i) q^{92} +(-1.11650 - 1.93383i) q^{94} +(9.27292 + 16.0612i) q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	−0.820653	−	0.571426i	$-0.806390\pi$
$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	0.905196	+	0.424994i	$0.139724\pi$
$3$		0			0
$3$		0			0
$4$	0.971410	+	1.68253i	0.485705	+	0.841266i
$5$	−1.29589	−	2.24456i	−0.579542	−	1.00380i	−0.995532	−	0.0944264i	$-0.969898\pi$
$5$	−1.29589	−	2.24456i	−0.579542	−	1.00380i	0.415990	−	0.909369i	$-0.363435\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$		0			0
$10$	−0.619757			−0.195984
$11$	2.09097	−	3.62167i	0.630452	−	1.09197i	−0.357008	−	0.934101i	$-0.616203\pi$
$11$	2.09097	−	3.62167i	0.630452	−	1.09197i	0.987459	−	0.157873i	$-0.0504636\pi$
$12$		0			0
$13$	−1.84155	−	3.18966i	−0.510755	−	0.884653i	−0.999922	−	0.0124633i	$-0.996033\pi$
$13$	−1.84155	−	3.18966i	−0.510755	−	0.884653i	0.489168	−	0.872190i	$-0.337301\pi$
$14$		0			0
$15$		0			0
$16$	−1.83009	+	3.16982i	−0.457524	+	0.792454i
$17$	−1.71107			−0.414996			−0.207498	−	0.978235i	$-0.566532\pi$
$17$	−1.71107			−0.414996			−0.207498	+	0.978235i	$0.566532\pi$
$18$		0			0
$19$	−7.15561			−1.64161			−0.820805	−	0.571209i	$-0.806475\pi$
$19$	−7.15561			−1.64161			−0.820805	+	0.571209i	$0.806475\pi$
$20$	2.51769	−	4.36077i	0.562973	−	0.975097i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.56238	−	4.43818i	−0.534294	−	0.925424i	−0.999197	−	0.0400622i	$-0.987244\pi$
$23$	−2.56238	−	4.43818i	−0.534294	−	0.925424i	0.464904	−	0.885361i	$-0.346089\pi$
$24$		0			0
$25$	−0.858685	+	1.48729i	−0.171737	+	0.297457i
$26$	−0.880716			−0.172723
$27$		0			0
$28$		0			0
$29$	−1.06238	+	1.84010i	−0.197279	+	0.341698i	−0.947645	−	0.319325i	$-0.896544\pi$
$29$	−1.06238	+	1.84010i	−0.197279	+	0.341698i	0.750366	+	0.661023i	$0.229877\pi$
$30$		0			0
$31$	3.26793	+	5.66021i	0.586937	+	1.01660i	0.994631	+	0.103486i	$0.0329997\pi$
$31$	3.26793	+	5.66021i	0.586937	+	1.01660i	−0.407694	+	0.913119i	$0.633667\pi$
$32$	1.38044	+	2.39099i	0.244029	+	0.422671i
$33$		0			0
$34$	−0.204579	+	0.354341i	−0.0350850	+	0.0607689i
$35$		0			0
$36$		0			0
$37$	1.66019			0.272934			0.136467	−	0.990645i	$-0.456425\pi$
$37$	1.66019			0.272934			0.136467	+	0.990645i	$0.456425\pi$
$38$	−0.855536	+	1.48183i	−0.138786	+	0.240385i
$39$		0			0
$40$	−1.22180	−	2.11621i	−0.193183	−	0.334602i
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	−0.920938	−	0.389708i	$-0.872576\pi$
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	0.122972	−	0.992410i	$-0.460758\pi$
$42$		0			0
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	−0.795764	−	0.605606i	$-0.792931\pi$
$43$	0.830095	−	1.43777i	0.126588	−	0.219257i	0.922353	+	0.386349i	$0.126264\pi$
$44$	8.12476			1.22485
$45$		0			0
$46$	−1.22545			−0.180683
$47$	4.66912	−	8.08715i	0.681061	−	1.17963i	−0.293596	−	0.955930i	$-0.594852\pi$
$47$	4.66912	−	8.08715i	0.681061	−	1.17963i	0.974657	−	0.223703i	$-0.0718146\pi$
$48$		0			0
$49$		0			0
$50$	0.205332	+	0.355645i	0.0290383	+	0.0502958i
$51$		0			0
$52$	3.57780	−	6.19694i	0.496152	−	0.859361i
$53$	−10.6465			−1.46241			−0.731206	−	0.682157i	$-0.761042\pi$
$53$	−10.6465			−1.46241			−0.731206	+	0.682157i	$0.761042\pi$
$54$		0			0
$55$	−10.8387			−1.46149
$56$		0			0
$57$		0			0
$58$	0.254040	+	0.440011i	0.0333571	+	0.0577762i
$59$	3.03215	+	5.25183i	0.394752	+	0.683730i	0.993069	−	0.117529i	$-0.0374972\pi$
$59$	3.03215	+	5.25183i	0.394752	+	0.683730i	−0.598318	+	0.801259i	$0.704164\pi$
$60$		0			0
$61$	3.99298	−	6.91605i	0.511249	−	0.885509i	−0.488666	−	0.872471i	$-0.662516\pi$
$61$	3.99298	−	6.91605i	0.511249	−	0.885509i	0.999915	−	0.0130384i	$-0.00415038\pi$
$62$	1.56287			0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−4.77292	+	8.26693i	−0.592007	+	1.02539i
$66$		0			0
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	−0.999985	−	0.00549964i	$-0.998249\pi$
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	0.495230	−	0.868762i	$-0.335084\pi$
$68$	−1.66215	−	2.87893i	−0.201566	−	0.349122i
$69$		0			0
$70$		0			0
$71$	−6.23912			−0.740448			−0.370224	−	0.928943i	$-0.620719\pi$
$71$	−6.23912			−0.740448			−0.370224	+	0.928943i	$0.620719\pi$
$72$		0			0
$73$	7.15561			0.837501			0.418750	−	0.908101i	$-0.362468\pi$
$73$	7.15561			0.837501			0.418750	+	0.908101i	$0.362468\pi$
$74$	0.198495	−	0.343803i	0.0230746	−	0.0399663i
$75$		0			0
$76$	−6.95103	−	12.0395i	−0.797338	−	1.38103i
$77$		0			0
$78$		0			0
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	−0.445170	−	0.895446i	$-0.646857\pi$
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	0.998064	−	0.0621945i	$-0.0198099\pi$
$80$	9.48644			1.06062
$81$		0			0
$82$	−2.44359			−0.269849
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	−0.612436	−	0.790521i	$-0.709810\pi$
$83$	3.44733	−	5.97094i	0.378393	−	0.655396i	0.990829	+	0.135124i	$0.0431434\pi$
$84$		0			0
$85$	2.21737	+	3.84060i	0.240508	+	0.416571i
$86$	−0.198495	−	0.343803i	−0.0214043	−	0.0370733i
$87$		0			0
$88$	1.97141	−	3.41458i	0.210153	−	0.363996i
$89$	5.03538			0.533749			0.266875	−	0.963731i	$-0.414009\pi$
$89$	5.03538			0.533749			0.266875	+	0.963731i	$0.414009\pi$
$90$		0			0
$91$		0			0
$92$	4.97825	−	8.62258i	0.519018	−	0.898966i
$93$		0			0
$94$	−1.11650	−	1.93383i	−0.115158	−	0.199459i
$95$	9.27292	+	16.0612i	0.951381	+	1.64784i
$96$		0			0
$97$	−1.53167	+	2.65294i	−0.155518	+	0.269365i	−0.933247	−	0.359234i	$-0.883038\pi$
$97$	−1.53167	+	2.65294i	−0.155518	+	0.269365i	0.777730	+	0.628599i	$0.216371\pi$
$98$		0			0
$99$		0			0
$100$	−3.33654			−0.333654
$101$	−5.54984	+	9.61260i	−0.552229	+	0.956489i	0.445884	+	0.895091i	$0.352889\pi$
$101$	−5.54984	+	9.61260i	−0.552229	+	0.956489i	−0.998113	+	0.0613986i	$0.980444\pi$
$102$		0			0
$103$	−3.99298	−	6.91605i	−0.393440	−	0.681459i	0.599460	−	0.800404i	$-0.295382\pi$
$103$	−3.99298	−	6.91605i	−0.393440	−	0.681459i	−0.992901	+	0.118946i	$0.962049\pi$
$104$	−1.73625	−	3.00728i	−0.170254	−	0.294888i
$105$		0			0
$106$	−1.27292	+	2.20475i	−0.123636	+	0.214145i
$107$	−3.95649			−0.382489			−0.191244	−	0.981542i	$-0.561252\pi$
$107$	−3.95649			−0.382489			−0.191244	+	0.981542i	$0.561252\pi$
$108$		0			0
$109$	7.26320			0.695688			0.347844	−	0.937552i	$-0.386914\pi$
$109$	7.26320			0.695688			0.347844	+	0.937552i	$0.386914\pi$
$110$	−1.29589	+	2.24456i	−0.123559	+	0.214010i
$111$		0			0
$112$		0			0
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	0.981698	−	0.190444i	$-0.0609928\pi$
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	−0.655778	+	0.754953i	$0.727659\pi$
$114$		0			0
$115$	−6.64115	+	11.5028i	−0.619291	+	1.07264i
$116$	−4.12803			−0.383278
$117$		0			0
$118$	1.45011			0.133494
$119$		0			0
$120$		0			0
$121$	−3.24433	−	5.61934i	−0.294939	−	0.510849i
$122$	−0.954815	−	1.65379i	−0.0864449	−	0.149727i
$123$		0			0
$124$	−6.34899	+	10.9968i	−0.570156	+	0.987540i
$125$	−8.50788			−0.760968
$126$		0			0
$127$	9.11109			0.808479			0.404239	−	0.914653i	$-0.367536\pi$
$127$	9.11109			0.808479			0.404239	+	0.914653i	$0.367536\pi$
$128$	−3.55718	+	6.16122i	−0.314413	+	0.544580i
$129$		0			0
$130$	1.14132	+	1.97682i	0.100100	+	0.173378i
$131$	−2.15143	−	3.72639i	−0.187971	−	0.325576i	0.756602	−	0.653875i	$-0.226858\pi$
$131$	−2.15143	−	3.72639i	−0.187971	−	0.325576i	−0.944574	+	0.328299i	$0.893525\pi$
$132$		0			0
$133$		0			0
$134$	−1.97592			−0.170694
$135$		0			0
$136$	−1.61323			−0.138334
$137$	10.2947	−	17.8309i	0.879533	−	1.52340i	0.0276785	−	0.999617i	$-0.491189\pi$
$137$	10.2947	−	17.8309i	0.879533	−	1.52340i	0.851854	−	0.523779i	$-0.175478\pi$
$138$		0			0
$139$	7.88067	+	13.6497i	0.668429	+	1.15775i	0.978343	+	0.206989i	$0.0663665\pi$
$139$	7.88067	+	13.6497i	0.668429	+	1.15775i	−0.309914	+	0.950765i	$0.600300\pi$
$140$		0			0
$141$		0			0
$142$	−0.745960	+	1.29204i	−0.0625996	+	0.108426i
$143$	−15.4025			−1.28802
$144$		0			0
$145$	5.50694			0.457326
$146$	0.855536	−	1.48183i	0.0708047	−	0.122637i
$147$		0			0
$148$	1.61273	+	2.79332i	0.132565	+	0.229610i
$149$	3.03379	+	5.25468i	0.248538	+	0.430480i	0.963120	−	0.269071i	$-0.0867166\pi$
$149$	3.03379	+	5.25468i	0.248538	+	0.430480i	−0.714582	+	0.699551i	$0.753383\pi$
$150$		0			0
$151$	−2.24433	+	3.88728i	−0.182641	+	0.316343i	−0.942779	−	0.333418i	$-0.891798\pi$
$151$	−2.24433	+	3.88728i	−0.182641	+	0.316343i	0.760138	+	0.649761i	$0.225131\pi$
$152$	−6.74645			−0.547210
$153$		0			0
$154$		0			0
$155$	8.46978	−	14.6701i	0.680309	−	1.17833i
$156$		0			0
$157$	−0.514457	−	0.891066i	−0.0410582	−	0.0711148i	0.844766	−	0.535136i	$-0.179740\pi$
$157$	−0.514457	−	0.891066i	−0.0410582	−	0.0711148i	−0.885824	+	0.464021i	$0.846406\pi$
$158$	−1.17511	−	2.03534i	−0.0934865	−	0.161923i
$159$		0			0
$160$	3.57780	−	6.19694i	0.282850	−	0.489911i
$161$		0			0
$162$		0			0
$163$	6.82846			0.534846			0.267423	−	0.963579i	$-0.413828\pi$
$163$	6.82846			0.534846			0.267423	+	0.963579i	$0.413828\pi$
$164$	9.92680	−	17.1937i	0.775153	−	1.34260i
$165$		0			0
$166$	−0.824336	−	1.42779i	−0.0639809	−	0.110818i
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	0.969767	+	0.244032i	$0.0784701\pi$
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	−0.273546	+	0.961859i	$0.588197\pi$
$168$		0			0
$169$	−0.282630	+	0.489530i	−0.0217408	+	0.0376561i
$170$	1.06045			0.0813328
$171$		0			0
$172$	3.22545			0.245938
$173$	−0.415178	+	0.719110i	−0.0315654	+	0.0546729i	−0.881377	−	0.472414i	$-0.843383\pi$
$173$	−0.415178	+	0.719110i	−0.0315654	+	0.0546729i	0.849811	+	0.527087i	$0.176716\pi$
$174$		0			0
$175$		0			0
$176$	7.65335	+	13.2560i	0.576893	+	0.999208i
$177$		0			0
$178$	0.602038	−	1.04276i	0.0451247	−	0.0781582i
$179$	−7.57893			−0.566476			−0.283238	−	0.959050i	$-0.591409\pi$
$179$	−7.57893			−0.566476			−0.283238	+	0.959050i	$0.591409\pi$
$180$		0			0
$181$	0.409157			0.0304124			0.0152062	−	0.999884i	$-0.495160\pi$
$181$	0.409157			0.0304124			0.0152062	+	0.999884i	$0.495160\pi$
$182$		0			0
$183$		0			0
$184$	−2.41586	−	4.18440i	−0.178100	−	0.308478i
$185$	−2.15143	−	3.72639i	−0.158176	−	0.273969i
$186$		0			0
$187$	−3.57780	+	6.19694i	−0.261635	+	0.453165i
$188$	18.1425			1.32318
$189$		0			0
$190$	4.43474			0.321730
$191$	8.01204	−	13.8773i	0.579731	−	1.00412i	−0.415779	−	0.909466i	$-0.636491\pi$
$191$	8.01204	−	13.8773i	0.579731	−	1.00412i	0.995510	−	0.0946575i	$-0.0301756\pi$
$192$		0			0
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	0.998077	−	0.0619822i	$-0.0197422\pi$
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	−0.552717	+	0.833369i	$0.686409\pi$
$194$	0.366259	+	0.634379i	0.0262959	+	0.0455458i
$195$		0			0
$196$		0			0
$197$	−23.1021			−1.64595			−0.822977	−	0.568075i	$-0.807688\pi$
$197$	−23.1021			−1.64595			−0.822977	+	0.568075i	$0.807688\pi$
$198$		0			0
$199$	−6.74645			−0.478243			−0.239122	−	0.970990i	$-0.576859\pi$
$199$	−6.74645			−0.478243			−0.239122	+	0.970990i	$0.576859\pi$
$200$	−0.809585	+	1.40224i	−0.0572463	+	0.0991536i
$201$		0			0
$202$	1.32710	+	2.29860i	0.0933741	+	0.161729i
$203$		0			0
$204$		0			0
$205$	−13.2427	+	22.9370i	−0.924910	+	1.60199i
$206$	−1.90963			−0.133050
$207$		0			0
$208$	13.4809			0.934730
$209$	−14.9622	+	25.9153i	−1.03496	+	1.79260i
$210$		0			0
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	−0.995334	−	0.0964875i	$-0.969239\pi$
$211$	−8.44282	−	14.6234i	−0.581228	−	1.00672i	0.414106	−	0.910228i	$-0.364094\pi$
$212$	−10.3421	−	17.9131i	−0.710301	−	1.23028i
$213$		0			0
$214$	−0.473045	+	0.819338i	−0.0323367	+	0.0560088i
$215$	−4.30286			−0.293453
$216$		0			0
$217$		0			0
$218$	0.868400	−	1.50411i	0.0588155	−	0.101871i
$219$		0			0
$220$	−10.5288	−	18.2365i	−0.709854	−	1.22950i
$221$	3.15103	+	5.45774i	0.211961	+	0.367128i
$222$		0			0
$223$	2.25071	−	3.89834i	0.150719	−	0.261052i	−0.780773	−	0.624815i	$-0.785175\pi$
$223$	2.25071	−	3.89834i	0.150719	−	0.261052i	0.931492	+	0.363762i	$0.118508\pi$
$224$		0			0
$225$		0			0
$226$	1.65692			0.110217
$227$	−3.03215	+	5.25183i	−0.201251	+	0.348576i	−0.948932	−	0.315482i	$-0.897834\pi$
$227$	−3.03215	+	5.25183i	−0.201251	+	0.348576i	0.747681	+	0.664058i	$0.231167\pi$
$228$		0			0
$229$	5.52466	+	9.56899i	0.365080	+	0.632336i	0.988789	−	0.149320i	$-0.0477084\pi$
$229$	5.52466	+	9.56899i	0.365080	+	0.632336i	−0.623709	+	0.781656i	$0.714375\pi$
$230$	1.58805	+	2.75059i	0.104713	+	0.181369i
$231$		0			0
$232$	−1.00163	+	1.73488i	−0.0657605	+	0.113901i
$233$	8.13844			0.533167			0.266583	−	0.963812i	$-0.414105\pi$
$233$	8.13844			0.533167			0.266583	+	0.963812i	$0.414105\pi$
$234$		0			0
$235$	−24.2028			−1.57881
$236$	−5.89092	+	10.2034i	−0.383466	+	0.664183i
$237$		0			0
$238$		0			0
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	0.973611	+	0.228214i	$0.0732886\pi$
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	−0.289166	+	0.957279i	$0.593378\pi$
$240$		0			0
$241$	−6.84573	+	11.8572i	−0.440972	+	0.763786i	−0.997762	−	0.0668671i	$-0.978700\pi$
$241$	−6.84573	+	11.8572i	−0.440972	+	0.763786i	0.556790	+	0.830654i	$0.312033\pi$
$242$	−1.55159			−0.0997398
$243$		0			0
$244$	15.5153			0.993265
$245$		0			0
$246$		0			0
$247$	13.1774	+	22.8240i	0.838460	+	1.45225i
$248$	3.08107	+	5.33656i	0.195648	+	0.338872i
$249$		0			0
$250$	−1.01722	+	1.76187i	−0.0643344	+	0.111430i
$251$	−15.2040			−0.959667			−0.479833	−	0.877360i	$-0.659303\pi$
$251$	−15.2040			−0.959667			−0.479833	+	0.877360i	$0.659303\pi$
$252$		0			0
$253$	−21.4315			−1.34738
$254$	1.08934	−	1.88679i	0.0683511	−	0.118388i
$255$		0			0
$256$	−5.80959	−	10.0625i	−0.363099	−	0.628906i
$257$	12.8107	+	22.1889i	0.799112	+	1.38410i	0.920195	+	0.391461i	$0.128030\pi$
$257$	12.8107	+	22.1889i	0.799112	+	1.38410i	−0.121082	+	0.992642i	$0.538637\pi$
$258$		0			0
$259$		0			0
$260$	−18.5458			−1.15016
$261$		0			0
$262$	−1.02891			−0.0635665
$263$	3.55034	−	6.14938i	0.218924	−	0.379187i	−0.735556	−	0.677464i	$-0.763079\pi$
$263$	3.55034	−	6.14938i	0.218924	−	0.379187i	0.954479	+	0.298278i	$0.0964121\pi$
$264$		0			0
$265$	13.7968	+	23.8967i	0.847528	+	1.46796i
$266$		0			0
$267$		0			0
$268$	8.02696	−	13.9031i	0.490324	−	0.849267i
$269$	16.4314			1.00184			0.500922	−	0.865493i	$-0.332994\pi$
$269$	16.4314			1.00184			0.500922	+	0.865493i	$0.332994\pi$
$270$		0			0
$271$	12.6980			0.771348			0.385674	−	0.922635i	$-0.373969\pi$
$271$	12.6980			0.771348			0.385674	+	0.922635i	$0.373969\pi$
$272$	3.13143	−	5.42379i	0.189871	−	0.328865i
$273$		0			0
$274$	−2.46169	−	4.26378i	−0.148716	−	0.257584i
$275$	3.59097	+	6.21975i	0.216544	+	0.375065i
$276$		0			0
$277$	0.414230	−	0.717468i	0.0248887	−	0.0431084i	−0.853313	−	0.521399i	$-0.825410\pi$
$277$	0.414230	−	0.717468i	0.0248887	−	0.0431084i	0.878201	+	0.478291i	$0.158744\pi$
$278$	3.76890			0.226044
$279$		0			0
$280$		0			0
$281$	2.60985	−	4.52039i	0.155690	−	0.269664i	−0.777620	−	0.628735i	$-0.783573\pi$
$281$	2.60985	−	4.52039i	0.155690	−	0.269664i	0.933310	+	0.359071i	$0.116906\pi$
$282$		0			0
$283$	3.67708	+	6.36890i	0.218580	+	0.378592i	0.954374	−	0.298614i	$-0.0965242\pi$
$283$	3.67708	+	6.36890i	0.218580	+	0.378592i	−0.735794	+	0.677205i	$0.763191\pi$
$284$	−6.06075	−	10.4975i	−0.359639	−	0.622913i
$285$		0			0
$286$	−1.84155	+	3.18966i	−0.108893	+	0.188609i
$287$		0			0
$288$		0			0
$289$	−14.0722			−0.827778
$290$	0.658419	−	1.14041i	0.0386637	−	0.0669674i
$291$		0			0
$292$	6.95103	+	12.0395i	0.406778	+	0.704561i
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	0.957391	−	0.288795i	$-0.0932545\pi$
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	−0.728799	+	0.684728i	$0.759921\pi$
$294$		0			0
$295$	7.85868	−	13.6116i	0.457550	−	0.792500i
$296$	1.56526			0.0909789
$297$		0			0
$298$	1.45090			0.0840484
$299$	−9.43752	+	16.3463i	−0.545786	+	0.945329i
$300$		0			0
$301$		0			0
$302$	0.536670	+	0.929540i	0.0308819	+	0.0534890i
$303$		0			0
$304$	13.0954	−	22.6820i	0.751075	−	1.30090i
$305$	−20.6979			−1.18516
$306$		0			0
$307$	22.6709			1.29390			0.646948	−	0.762534i	$-0.276045\pi$
$307$	22.6709			1.29390			0.646948	+	0.762534i	$0.276045\pi$
$308$		0			0
$309$		0			0
$310$	−2.02532	−	3.50796i	−0.115030	−	0.199239i
$311$	−16.1588	−	27.9879i	−0.916281	−	1.58705i	−0.805015	−	0.593255i	$-0.797843\pi$
$311$	−16.1588	−	27.9879i	−0.916281	−	1.58705i	−0.111266	−	0.993791i	$-0.535491\pi$
$312$		0			0
$313$	12.1598	−	21.0614i	0.687312	−	1.19046i	−0.285392	−	0.958411i	$-0.592124\pi$
$313$	12.1598	−	21.0614i	0.687312	−	1.19046i	0.972704	−	0.232048i	$-0.0745428\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	2.56922	−	4.45002i	0.144302	−	0.249938i	−0.784811	−	0.619736i	$-0.787240\pi$
$317$	2.56922	−	4.45002i	0.144302	−	0.249938i	0.929112	+	0.369798i	$0.120573\pi$
$318$		0			0
$319$	4.44282	+	7.69519i	0.248750	+	0.430848i
$320$	8.63090	+	14.9492i	0.482482	+	0.835684i
$321$		0			0
$322$		0			0
$323$	12.2438			0.681262
$324$		0			0
$325$	6.32525			0.350862
$326$	0.816422	−	1.41408i	0.0452174	−	0.0783189i
$327$		0			0
$328$	−4.81732	−	8.34384i	−0.265992	−	0.460712i
$329$		0			0
$330$		0			0
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	−0.659307	−	0.751874i	$-0.729150\pi$
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	0.980795	+	0.195040i	$0.0624835\pi$
$332$	13.3951			0.735150
$333$		0			0
$334$	4.30286			0.235442
$335$	−10.7082	+	18.5472i	−0.585053	+	1.01334i
$336$		0			0
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.802850	+	0.596181i	$0.203316\pi$
$337$	16.8473	+	29.1804i	0.917733	+	1.58956i	0.114883	+	0.993379i	$0.463351\pi$
$338$	0.0675835	+	0.117058i	0.00367606	+	0.00636711i
$339$		0			0
$340$	−4.30795	+	7.46159i	−0.233631	+	0.404661i
$341$	27.3326			1.48014
$342$		0			0
$343$		0			0
$344$	0.782630	−	1.35556i	0.0421966	−	0.0730866i
$345$		0			0
$346$	0.0992788	+	0.171956i	0.00533726	+	0.00924441i
$347$	13.6557	+	23.6523i	0.733075	+	1.26972i	0.955563	+	0.294788i	$0.0952490\pi$
$347$	13.6557	+	23.6523i	0.733075	+	1.26972i	−0.222488	+	0.974936i	$0.571418\pi$
$348$		0			0
$349$	−11.4585	+	19.8467i	−0.613358	+	1.06237i	0.377312	+	0.926086i	$0.376848\pi$
$349$	−11.4585	+	19.8467i	−0.613358	+	1.06237i	−0.990670	+	0.136281i	$0.956485\pi$
$350$		0			0
$351$		0			0
$352$	11.5458			0.615395
$353$	5.13466	−	8.89349i	0.273290	−	0.473353i	−0.696412	−	0.717642i	$-0.745221\pi$
$353$	5.13466	−	8.89349i	0.273290	−	0.473353i	0.969702	+	0.244289i	$0.0785547\pi$
$354$		0			0
$355$	8.08525	+	14.0041i	0.429120	+	0.743258i
$356$	4.89142	+	8.47218i	0.259245	+	0.449025i
$357$		0			0
$358$	−0.906150	+	1.56950i	−0.0478915	+	0.0829505i
$359$	−10.1007			−0.533094			−0.266547	−	0.963822i	$-0.585883\pi$
$359$	−10.1007			−0.533094			−0.266547	+	0.963822i	$0.585883\pi$
$360$		0			0
$361$	32.2028			1.69488
$362$	0.0489195	−	0.0847311i	0.00257115	−	0.00445337i
$363$		0			0
$364$		0			0
$365$	−9.27292	−	16.0612i	−0.485367	−	0.840680i
$366$		0			0
$367$	3.88768	−	6.73367i	0.202935	−	0.351494i	−0.746538	−	0.665343i	$-0.768285\pi$
$367$	3.88768	−	6.73367i	0.202935	−	0.351494i	0.949473	+	0.313849i	$0.101619\pi$
$368$	18.7576			0.977808
$369$		0			0
$370$	−1.02891			−0.0534907
$371$		0			0
$372$		0			0
$373$	−12.0555	−	20.8808i	−0.624212	−	1.08117i	−0.988693	−	0.149957i	$-0.952087\pi$
$373$	−12.0555	−	20.8808i	−0.624212	−	1.08117i	0.364480	−	0.931211i	$-0.381247\pi$
$374$	0.855536	+	1.48183i	0.0442387	+	0.0766237i
$375$		0			0
$376$	4.40214	−	7.62473i	0.227023	−	0.393215i
$377$	7.82573			0.403045
$378$		0			0
$379$	−13.3581			−0.686161			−0.343081	−	0.939306i	$-0.611470\pi$
$379$	−13.3581			−0.686161			−0.343081	+	0.939306i	$0.611470\pi$
$380$	−18.0156	+	31.2039i	−0.924181	+	1.60073i
$381$		0			0
$382$	−1.91586	−	3.31838i	−0.0980242	−	0.169783i
$383$	−4.62020	−	8.00242i	−0.236081	−	0.408905i	0.723505	−	0.690319i	$-0.242530\pi$
$383$	−4.62020	−	8.00242i	−0.236081	−	0.408905i	−0.959586	+	0.281414i	$0.909196\pi$
$384$		0			0
$385$		0			0
$386$	2.95898			0.150608
$387$		0			0
$388$	−5.95153			−0.302143
$389$	5.22421	−	9.04859i	0.264878	−	0.458782i	−0.702654	−	0.711532i	$-0.748002\pi$
$389$	5.22421	−	9.04859i	0.264878	−	0.458782i	0.967532	+	0.252750i	$0.0813351\pi$
$390$		0			0
$391$	4.38442	+	7.59404i	0.221730	+	0.384047i
$392$		0			0
$393$		0			0
$394$	−2.76212	+	4.78413i	−0.139154	+	0.241021i
$395$	−25.4733			−1.28170
$396$		0			0
$397$	−0.409157			−0.0205350			−0.0102675	−	0.999947i	$-0.503268\pi$
$397$	−0.409157			−0.0205350			−0.0102675	+	0.999947i	$0.503268\pi$
$398$	−0.806617	+	1.39710i	−0.0404321	+	0.0700304i
$399$		0			0
$400$	−3.14295	−	5.44375i	−0.157147	−	0.272187i
$401$	7.62640	+	13.2093i	0.380844	+	0.659641i	0.991183	−	0.132499i	$-0.0423001\pi$
$401$	7.62640	+	13.2093i	0.380844	+	0.659641i	−0.610339	+	0.792140i	$0.708967\pi$
$402$		0			0
$403$	12.0361	−	20.8472i	0.599562	−	1.03847i
$404$	−21.5647			−1.07288
$405$		0			0
$406$		0			0
$407$	3.47141	−	6.01266i	0.172071	−	0.298036i
$408$		0			0
$409$	3.06335	+	5.30587i	0.151473	+	0.262359i	0.931769	−	0.363051i	$-0.118265\pi$
$409$	3.06335	+	5.30587i	0.151473	+	0.262359i	−0.780296	+	0.625410i	$0.784932\pi$
$410$	3.16664	+	5.48477i	0.156389	+	0.270874i
$411$		0			0
$412$	7.75765	−	13.4366i	0.382192	−	0.661976i
$413$		0			0
$414$		0			0
$415$	−17.8695			−0.877178
$416$	5.08430	−	8.80626i	0.249278	−	0.431763i
$417$		0			0
$418$	3.57780	+	6.19694i	0.174996	+	0.303102i
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	0.884482	−	0.466574i	$-0.154512\pi$
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	−0.846306	+	0.532697i	$0.821179\pi$
$420$		0			0
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	0.429982	+	0.902838i	$0.358520\pi$
$421$	−11.6316	+	20.1465i	−0.566889	+	0.981881i	−0.996871	+	0.0790438i	$0.974813\pi$
$422$	−4.03775			−0.196555
$423$		0			0
$424$	−10.0377			−0.487476
$425$	1.46927	−	2.54485i	0.0712702	−	0.123444i
$426$		0			0
$427$		0			0
$428$	−3.84338	−	6.65692i	−0.185777	−	0.321775i
$429$		0			0
$430$	−0.514457	+	0.891066i	−0.0248093	+	0.0429710i
$431$	−1.00576			−0.0484456			−0.0242228	−	0.999707i	$-0.507711\pi$
$431$	−1.00576			−0.0484456			−0.0242228	+	0.999707i	$0.507711\pi$
$432$		0			0
$433$	13.1071			0.629889			0.314945	−	0.949110i	$-0.398014\pi$
$433$	13.1071			0.629889			0.314945	+	0.949110i	$0.398014\pi$
$434$		0			0
$435$		0			0
$436$	7.05555	+	12.2206i	0.337899	+	0.585259i
$437$	18.3354	+	31.7579i	0.877101	+	1.51918i
$438$		0			0
$439$	−9.30704	+	16.1203i	−0.444201	+	0.769378i	−0.997996	−	0.0632744i	$-0.979846\pi$
$439$	−9.30704	+	16.1203i	−0.444201	+	0.769378i	0.553795	+	0.832653i	$0.313179\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	−0.559503	+	0.969088i	−0.0265828	+	0.0460427i	−0.879011	−	0.476802i	$-0.841796\pi$
$443$	−0.559503	+	0.969088i	−0.0265828	+	0.0460427i	0.852428	+	0.522845i	$0.175129\pi$
$444$		0			0
$445$	−6.52532	−	11.3022i	−0.309330	−	0.535775i
$446$	−0.538197	−	0.932185i	−0.0254844	−	0.0441402i
$447$		0			0
$448$		0			0
$449$	39.4419			1.86138			0.930689	−	0.365813i	$-0.119209\pi$
$449$	39.4419			1.86138			0.930689	+	0.365813i	$0.119209\pi$
$450$		0			0
$451$	−42.7351			−2.01232
$452$	−6.73104	+	11.6585i	−0.316602	+	0.548370i
$453$		0			0
$454$	0.725057	+	1.25584i	0.0340286	+	0.0589393i
$455$		0			0
$456$		0			0
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	−0.118205	−	0.992989i	$-0.537714\pi$
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	0.919056	−	0.394126i	$-0.128953\pi$
$458$	2.64215			0.123459
$459$		0			0
$460$	−25.8051			−1.20317
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	−0.524811	−	0.851219i	$-0.675864\pi$
$461$	10.1938	−	17.6561i	0.474772	−	0.822328i	0.999583	+	0.0288903i	$0.00919735\pi$
$462$		0			0
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	0.776006	−	0.630725i	$-0.217243\pi$
$463$	−3.40451	−	5.89679i	−0.158221	−	0.274047i	−0.934227	+	0.356678i	$0.883909\pi$
$464$	−3.88852	−	6.73511i	−0.180520	−	0.312670i
$465$		0			0
$466$	0.973045	−	1.68536i	0.0450754	−	0.0780729i
$467$	−24.7911			−1.14720			−0.573598	−	0.819137i	$-0.694453\pi$
$467$	−24.7911			−1.14720			−0.573598	+	0.819137i	$0.694453\pi$
$468$		0			0
$469$		0			0
$470$	−2.89372	+	5.01207i	−0.133477	+	0.231190i
$471$		0			0
$472$	2.85877	+	4.95153i	0.131586	+	0.227913i
$473$	−3.47141	−	6.01266i	−0.159616	−	0.276462i
$474$		0			0
$475$	6.14441	−	10.6424i	0.281925	−	0.488309i
$476$		0			0
$477$		0			0
$478$	5.06045			0.231460
$479$	−5.54984	+	9.61260i	−0.253579	+	0.439211i	−0.964508	−	0.264052i	$-0.914941\pi$
$479$	−5.54984	+	9.61260i	−0.253579	+	0.439211i	0.710930	+	0.703263i	$0.248274\pi$
$480$		0			0
$481$	−3.05733	−	5.29545i	−0.139402	−	0.241452i
$482$	1.63697	+	2.83532i	0.0745621	+	0.129145i
$483$		0			0
$484$	6.30314	−	10.9174i	0.286506	−	0.496244i
$485$	7.93955			0.360516
$486$		0			0
$487$	−10.0377			−0.454854			−0.227427	−	0.973795i	$-0.573031\pi$
$487$	−10.0377			−0.454854			−0.227427	+	0.973795i	$0.573031\pi$
$488$	3.76466	−	6.52059i	0.170418	−	0.295173i
$489$		0			0
$490$		0			0
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	0.691738	−	0.722149i	$-0.256845\pi$
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	−0.971268	+	0.237988i	$0.923512\pi$
$492$		0			0
$493$	1.81781	−	3.14854i	0.0818702	−	0.141803i
$494$	6.30206			0.283543
$495$		0			0
$496$	−23.9225			−1.07415
$497$		0			0
$498$		0			0
$499$	−5.11109	−	8.85267i	−0.228804	−	0.396300i	0.728650	−	0.684886i	$-0.240148\pi$
$499$	−5.11109	−	8.85267i	−0.228804	−	0.396300i	−0.957454	+	0.288586i	$0.906815\pi$
$500$	−8.26464	−	14.3148i	−0.369606	−	0.640177i
$501$		0			0
$502$	−1.81781	+	3.14854i	−0.0811329	+	0.140526i
$503$	8.45753			0.377102			0.188551	−	0.982063i	$-0.439621\pi$
$503$	8.45753			0.377102			0.188551	+	0.982063i	$0.439621\pi$
$504$		0			0
$505$	28.7680			1.28016
$506$	−2.56238	+	4.43818i	−0.113912	+	0.197301i
$507$		0			0
$508$	8.85060	+	15.3297i	0.392682	+	0.680145i
$509$	−5.28286	−	9.15018i	−0.234159	−	0.405574i	0.724869	−	0.688886i	$-0.241900\pi$
$509$	−5.28286	−	9.15018i	−0.234159	−	0.405574i	−0.959028	+	0.283312i	$0.908567\pi$
$510$		0			0
$511$		0			0
$512$	−17.0071			−0.751616
$513$		0			0
$514$	6.12670			0.270237
$515$	−10.3490	+	17.9249i	−0.456030	+	0.789867i
$516$		0			0
$517$	−19.5260	−	33.8200i	−0.858752	−	1.48740i
$518$		0			0
$519$		0			0
$520$	−4.50000	+	7.79423i	−0.197338	+	0.341800i
$521$	−19.7558			−0.865515			−0.432758	−	0.901510i	$-0.642459\pi$
$521$	−19.7558			−0.865515			−0.432758	+	0.901510i	$0.642459\pi$
$522$		0			0
$523$	−32.5282			−1.42236			−0.711179	−	0.703011i	$-0.751839\pi$
$523$	−32.5282			−1.42236			−0.711179	+	0.703011i	$0.751839\pi$
$524$	4.17984	−	7.23970i	0.182597	−	0.316268i
$525$		0			0
$526$	−0.848970	−	1.47046i	−0.0370168	−	0.0641150i
$527$	−5.59166	−	9.68504i	−0.243577	−	0.421887i
$528$		0			0
$529$	−1.63160	+	2.82601i	−0.0709391	+	0.122870i
$530$	6.59825			0.286610
$531$		0			0
$532$		0			0
$533$	−18.8187	+	32.5950i	−0.815130	+	1.41185i
$534$		0			0
$535$	5.12720	+	8.88057i	0.221668	+	0.383940i
$536$	−3.89536	−	6.74695i	−0.168254	−	0.291424i
$537$		0			0
$538$	1.96457	−	3.40274i	0.0846987	−	0.146702i
$539$		0			0
$540$		0			0
$541$	15.2222			0.654453			0.327226	−	0.944946i	$-0.393886\pi$
$541$	15.2222			0.654453			0.327226	+	0.944946i	$0.393886\pi$
$542$	1.51819	−	2.62959i	0.0652119	−	0.112950i
$543$		0			0
$544$	−2.36203	−	4.09116i	−0.101271	−	0.175407i
$545$	−9.41234	−	16.3027i	−0.403180	−	0.698329i
$546$		0			0
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	−1.00000		0.000339172i	$-0.999892\pi$
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	0.500294	+	0.865856i	$0.333225\pi$
$548$	40.0014			1.70877
$549$		0			0
$550$	1.71737			0.0732289
$551$	7.60199	−	13.1670i	0.323856	−	0.560934i
$552$		0			0
$553$		0			0
$554$	−0.0990521	−	0.171563i	−0.00420832	−	0.00728902i
$555$		0			0
$556$	−15.3107	+	26.5189i	−0.649319	+	1.12465i
$557$	−27.6673			−1.17230			−0.586151	−	0.810202i	$-0.699357\pi$
$557$	−27.6673			−1.17230			−0.586151	+	0.810202i	$0.699357\pi$
$558$		0			0
$559$	−6.11465			−0.258622
$560$		0			0
$561$		0			0
$562$	−0.624075	−	1.08093i	−0.0263250	−	0.0455963i
$563$	−4.27912	−	7.41166i	−0.180343	−	0.312364i	0.761654	−	0.647984i	$-0.224388\pi$
$563$	−4.27912	−	7.41166i	−0.180343	−	0.312364i	−0.941998	+	0.335620i	$0.891054\pi$
$564$		0			0
$565$	8.97944	−	15.5529i	0.377768	−	0.654313i
$566$	1.75855			0.0739175
$567$		0			0
$568$	−5.88237			−0.246819
$569$	6.86389	−	11.8886i	0.287749	−	0.498396i	−0.685523	−	0.728051i	$-0.740426\pi$
$569$	6.86389	−	11.8886i	0.287749	−	0.498396i	0.973272	+	0.229655i	$0.0737597\pi$
$570$		0			0
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	0.731841	−	0.681475i	$-0.238661\pi$
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	−0.956095	+	0.293056i	$0.905328\pi$
$572$	−14.9622	−	25.9153i	−0.625600	−	1.08357i
$573$		0			0
$574$		0			0
$575$	8.80111			0.367032
$576$		0			0
$577$	45.6353			1.89982			0.949912	−	0.312518i	$-0.101173\pi$
$577$	45.6353			1.89982			0.949912	+	0.312518i	$0.101173\pi$
$578$	−1.68250	+	2.91417i	−0.0699827	+	0.121214i
$579$		0			0
$580$	5.34950	+	9.26560i	0.222126	+	0.384733i
$581$		0			0
$582$		0			0
$583$	−22.2616	+	38.5582i	−0.921980	+	1.59692i
$584$	6.74645			0.279170
$585$		0			0
$586$	1.87131			0.0773032
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	−0.741103	−	0.671392i	$-0.765697\pi$
$587$	5.10948	−	8.84988i	0.210891	−	0.365274i	0.951994	+	0.306118i	$0.0990302\pi$
$588$		0			0
$589$	−23.3840	−	40.5023i	−0.963521	−	1.66887i
$590$	−1.87919	−	3.25486i	−0.0773652	−	0.134000i
$591$		0			0
$592$	−3.03831	+	5.26250i	−0.124874	+	0.216287i
$593$	11.3961			0.467981			0.233990	−	0.972239i	$-0.424822\pi$
$593$	11.3961			0.467981			0.233990	+	0.972239i	$0.424822\pi$
$594$		0			0
$595$		0			0
$596$	−5.89411	+	10.2089i	−0.241432	+	0.418173i
$597$		0			0
$598$	2.25673	+	3.90877i	0.0922846	+	0.159842i
$599$	−17.2873	−	29.9424i	−0.706339	−	1.22341i	−0.966206	−	0.257771i	$-0.917012\pi$
$599$	−17.2873	−	29.9424i	−0.706339	−	1.22341i	0.259867	−	0.965644i	$-0.416321\pi$
$600$		0			0
$601$	−19.4207	+	33.6376i	−0.792187	+	1.37211i	0.132423	+	0.991193i	$0.457724\pi$
$601$	−19.4207	+	33.6376i	−0.792187	+	1.37211i	−0.924610	+	0.380915i	$0.875609\pi$
$602$		0			0
$603$		0			0
$604$	−8.72064			−0.354838
$605$	−8.40861	+	14.5641i	−0.341858	+	0.592116i
$606$		0			0
$607$	−20.6662	−	35.7950i	−0.838817	−	1.45287i	−0.890885	−	0.454229i	$-0.849915\pi$
$607$	−20.6662	−	35.7950i	−0.838817	−	1.45287i	0.0520683	−	0.998644i	$-0.483419\pi$
$608$	−9.87788	−	17.1090i	−0.400601	−	0.693861i
$609$		0			0
$610$	−2.47468	+	4.28627i	−0.100197	+	0.173546i
$611$	−34.3937			−1.39142
$612$		0			0
$613$	−28.6569			−1.15744			−0.578721	−	0.815526i	$-0.696448\pi$
$613$	−28.6569			−1.15744			−0.578721	+	0.815526i	$0.696448\pi$
$614$	2.71057	−	4.69485i	0.109390	−	0.189469i
$615$		0			0
$616$		0			0
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	−0.975454	−	0.220205i	$-0.929327\pi$
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	0.297024	−	0.954870i	$-0.404006\pi$
$618$		0			0
$619$	0.719036	−	1.24541i	0.0289005	−	0.0500571i	−0.851213	−	0.524820i	$-0.824133\pi$
$619$	0.719036	−	1.24541i	0.0289005	−	0.0500571i	0.880114	+	0.474763i	$0.157466\pi$
$620$	32.9105			1.32172
$621$		0			0
$622$	−7.72789			−0.309860
$623$		0			0
$624$		0			0
$625$	15.3187	+	26.5328i	0.612750	+	1.06131i
$626$	−2.90769	−	5.03626i	−0.116215	−	0.201290i
$627$		0			0
$628$	0.999498	−	1.73118i	0.0398843	−	0.0690816i
$629$	−2.84071			−0.113266
$630$		0			0
$631$	−30.7680			−1.22486			−0.612428	−	0.790527i	$-0.709807\pi$
$631$	−30.7680			−1.22486			−0.612428	+	0.790527i	$0.709807\pi$
$632$	4.63323	−	8.02500i	0.184300	−	0.319217i
$633$		0			0
$634$	−0.614360	−	1.06410i	−0.0243993	−	0.0422609i
$635$	−11.8070	−	20.4503i	−0.468547	−	0.811547i
$636$		0			0
$637$		0			0
$638$	2.12476			0.0841202
$639$		0			0
$640$	18.4389			0.728862
$641$	4.61956	−	8.00132i	0.182462	−	0.316033i	−0.760257	−	0.649623i	$-0.774927\pi$
$641$	4.61956	−	8.00132i	0.182462	−	0.316033i	0.942718	+	0.333590i	$0.108260\pi$
$642$		0			0
$643$	−12.7795	−	22.1348i	−0.503976	−	0.872912i	−0.999989	−	0.00459728i	$-0.998537\pi$
$643$	−12.7795	−	22.1348i	−0.503976	−	0.872912i	0.496013	−	0.868315i	$-0.334797\pi$
$644$		0			0
$645$		0			0
$646$	1.46389	−	2.53552i	0.0575958	−	0.0997588i
$647$	28.3111			1.11302			0.556512	−	0.830839i	$-0.312139\pi$
$647$	28.3111			1.11302			0.556512	+	0.830839i	$0.312139\pi$
$648$		0			0
$649$	25.3605			0.995488
$650$	0.756258	−	1.30988i	0.0296629	−	0.0513776i
$651$		0			0
$652$	6.63323	+	11.4891i	0.259778	+	0.449948i
$653$	−4.17511	−	7.23150i	−0.163385	−	0.282990i	0.772696	−	0.634776i	$-0.218908\pi$
$653$	−4.17511	−	7.23150i	−0.163385	−	0.282990i	−0.936080	+	0.351786i	$0.885574\pi$
$654$		0			0
$655$	−5.57605	+	9.65801i	−0.217874	+	0.377370i
$656$	37.4033			1.46035
$657$		0			0
$658$		0			0
$659$	−16.7862	+	29.0745i	−0.653897	+	1.13258i	0.328272	+	0.944583i	$0.393534\pi$
$659$	−16.7862	+	29.0745i	−0.653897	+	1.13258i	−0.982169	+	0.188000i	$0.939799\pi$
$660$		0			0
$661$	−8.47668	−	14.6820i	−0.329705	−	0.571065i	0.652748	−	0.757575i	$-0.273616\pi$
$661$	−8.47668	−	14.6820i	−0.329705	−	0.571065i	−0.982453	+	0.186509i	$0.940283\pi$
$662$	−1.39862	−	2.42249i	−0.0543591	−	0.0941527i
$663$		0			0
$664$	3.25021	−	5.62952i	0.126133	−	0.218468i
$665$		0			0
$666$		0			0
$667$	10.8889			0.421620
$668$	−17.4799	+	30.2760i	−0.676316	+	1.17141i
$669$		0			0
$670$	2.56059	+	4.43507i	0.0989242	+	0.171342i
$671$	−16.6984	−	28.9225i	−0.644636	−	1.11654i
$672$		0			0
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	−0.0190299	−	0.999819i	$-0.506058\pi$
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	0.875384	−	0.483429i	$-0.160609\pi$
$674$	8.05718			0.310351
$675$		0			0
$676$	−1.09820			−0.0422384
$677$	7.18681	−	12.4479i	0.276212	−	0.478412i	−0.694229	−	0.719755i	$-0.744254\pi$
$677$	7.18681	−	12.4479i	0.276212	−	0.478412i	0.970440	+	0.241342i	$0.0775876\pi$
$678$		0			0
$679$		0			0
$680$	2.09058	+	3.62099i	0.0801701	+	0.138859i
$681$		0			0
$682$	3.26793	−	5.66021i	0.125135	−	0.216741i
$683$	32.3092			1.23628			0.618138	−	0.786069i	$-0.287887\pi$
$683$	32.3092			1.23628			0.618138	+	0.786069i	$0.287887\pi$
$684$		0			0
$685$	−53.3632			−2.03890
$686$		0			0
$687$		0			0
$688$	3.03831	+	5.26250i	0.115834	+	0.200631i
$689$	19.6061	+	33.9588i	0.746934	+	1.29373i
$690$		0			0
$691$	−14.4981	+	25.1114i	−0.551533	+	0.955283i	0.446631	+	0.894718i	$0.352624\pi$
$691$	−14.4981	+	25.1114i	−0.551533	+	0.955283i	−0.998164	+	0.0605650i	$0.980710\pi$
$692$	−1.61323			−0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	20.4250	−	35.3772i	0.774765	−	1.34193i
$696$		0			0
$697$	8.74269	+	15.1428i	0.331153	+	0.573574i
$698$	2.73999	+	4.74580i	0.103710	+	0.179631i
$699$		0			0
$700$		0			0
$701$	26.3912			0.996783			0.498392	−	0.866952i	$-0.333924\pi$
$701$	26.3912			0.996783			0.498392	+	0.866952i	$0.333924\pi$
$702$		0			0
$703$	−11.8797			−0.448050
$704$	−13.9263	+	24.1210i	−0.524866	+	0.909095i
$705$		0			0
$706$	−1.22782	−	2.12664i	−0.0462095	−	0.0800372i
$707$		0			0
$708$		0			0
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	−0.782441	−	0.622725i	$-0.786025\pi$
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	0.930516	+	0.366251i	$0.119359\pi$
$710$	3.86674			0.145116
$711$		0			0
$712$	4.74746			0.177918
$713$	16.7473	−	29.0073i	0.627193	−	1.08633i
$714$		0			0
$715$	19.9601	+	34.5718i	0.746464	+	1.29291i
$716$	−7.36225	−	12.7518i	−0.275140	−	0.476557i
$717$		0			0
$718$	−1.20765	+	2.09172i	−0.0450693	+	0.0780623i
$719$	−33.1508			−1.23632			−0.618159	−	0.786053i	$-0.712121\pi$
$719$	−33.1508			−1.23632			−0.618159	+	0.786053i	$0.712121\pi$
$720$		0			0
$721$		0			0
$722$	3.85021	−	6.66877i	0.143290	−	0.248186i
$723$		0			0
$724$	0.397460	+	0.688420i	0.0147715	+	0.0255849i
$725$	−1.82450	−	3.16013i	−0.0677603	−	0.117364i
$726$		0			0
$727$	16.5502	−	28.6658i	0.613814	−	1.06316i	−0.376777	−	0.926304i	$-0.622968\pi$
$727$	16.5502	−	28.6658i	0.613814	−	1.06316i	0.990591	−	0.136853i	$-0.0436989\pi$
$728$		0			0
$729$		0			0
$730$	−4.43474			−0.164137
$731$	−1.42035	+	2.46012i	−0.0525337	+	0.0909910i
$732$		0			0
$733$	−22.2795	−	38.5892i	−0.822911	−	1.42532i	−0.903505	−	0.428577i	$-0.859015\pi$
$733$	−22.2795	−	38.5892i	−0.822911	−	1.42532i	0.0805946	−	0.996747i	$-0.474318\pi$
$734$	−0.929636	−	1.61018i	−0.0343135	−	0.0594327i
$735$		0			0
$736$	7.07442	−	12.2533i	0.260767	−	0.451661i
$737$	−34.5562			−1.27290
$738$		0			0
$739$	39.8090			1.46440			0.732199	−	0.681090i	$-0.238494\pi$
$739$	39.8090			1.46440			0.732199	+	0.681090i	$0.238494\pi$
$740$	4.17984	−	7.23970i	0.153654	−	0.266137i
$741$		0			0
$742$		0			0
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	0.947565	−	0.319563i	$-0.103536\pi$
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	−0.750532	+	0.660834i	$0.770203\pi$
$744$		0			0
$745$	7.86295	−	13.6190i	0.288076	−	0.498962i
$746$	−5.76552			−0.211091
$747$		0			0
$748$	−13.9021			−0.508310
$749$		0			0
$750$		0			0
$751$	−9.85705	−	17.0729i	−0.359689	−	0.622999i	0.628220	−	0.778036i	$-0.283784\pi$
$751$	−9.85705	−	17.0729i	−0.359689	−	0.622999i	−0.987909	+	0.155036i	$0.950450\pi$
$752$	17.0899	+	29.6005i	0.623203	+	1.07942i
$753$		0			0
$754$	0.935657	−	1.62060i	0.0340746	−	0.0590189i
$755$	11.6336			0.423391
$756$		0			0
$757$	35.3549			1.28499			0.642497	−	0.766288i	$-0.277898\pi$
$757$	35.3549			1.28499			0.642497	+	0.766288i	$0.277898\pi$
$758$	−1.59712	+	2.76629i	−0.0580100	+	0.100476i
$759$		0			0
$760$	8.74269	+	15.1428i	0.317131	+	0.549286i
$761$	19.5572	+	33.8741i	0.708948	+	1.22793i	0.965248	+	0.261336i	$0.0841632\pi$
$761$	19.5572	+	33.8741i	0.708948	+	1.22793i	−0.256300	+	0.966597i	$0.582503\pi$
$762$		0			0
$763$		0			0
$764$	31.1319			1.12631
$765$		0			0
$766$	−2.20960			−0.0798359
$767$	11.1677	−	19.3430i	0.403243	−	0.698437i
$768$		0			0
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	−0.974242	−	0.225507i	$-0.927596\pi$
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	0.291826	−	0.956471i	$-0.405737\pi$
$770$		0			0
$771$		0			0
$772$	−12.0205	+	20.8201i	−0.432628	+	0.749333i
$773$	29.8265			1.07279			0.536393	−	0.843969i	$-0.319787\pi$
$773$	29.8265			1.07279			0.536393	+	0.843969i	$0.319787\pi$
$774$		0			0
$775$	−11.2245			−0.403195
$776$	−1.44409	+	2.50124i	−0.0518399	+	0.0897894i
$777$		0			0
$778$	−1.24923	−	2.16373i	−0.0447870	−	0.0775734i
$779$	36.5614	+	63.3263i	1.30995	+	2.26890i
$780$		0			0
$781$	−13.0458	+	22.5960i	−0.466817	+	0.808550i
$782$	2.09683			0.0749827
$783$		0			0
$784$		0			0
$785$	−1.33336	+	2.30946i	−0.0475898	+	0.0824280i
$786$		0			0
$787$	8.81030	+	15.2599i	0.314053	+	0.543956i	0.979236	−	0.202724i	$-0.0649796\pi$
$787$	8.81030	+	15.2599i	0.314053	+	0.543956i	−0.665182	+	0.746681i	$0.731646\pi$
$788$	−22.4416	−	38.8700i	−0.799448	−	1.38468i
$789$		0			0
$790$	−3.04563	+	5.27518i	−0.108359	+	0.187683i
$791$		0			0
$792$		0			0
$793$	−29.4132			−1.04449
$794$	−0.0489195	+	0.0847311i	−0.00173609	+	0.00300699i
$795$		0			0
$796$	−6.55357	−	11.3511i	−0.232285	−	0.402330i
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	0.762371	−	0.647140i	$-0.224035\pi$
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	−0.941625	+	0.336663i	$0.890702\pi$
$798$		0			0
$799$	−7.98921	+	13.8377i	−0.282638	+	0.489543i
$800$	−4.74145			−0.167635
$801$		0			0
$802$	3.64730			0.128791
$803$	14.9622	−	25.9153i	0.528004	−	0.914529i
$804$		0			0
$805$		0			0
$806$	−2.87812	−	4.98504i	−0.101377	−	0.175591i
$807$		0			0
$808$	−5.23250	+	9.06295i	−0.184079	+	0.318834i
$809$	47.1469			1.65760			0.828799	−	0.559546i	$-0.189025\pi$
$809$	47.1469			1.65760			0.828799	+	0.559546i	$0.189025\pi$
$810$		0			0
$811$	−21.0577			−0.739435			−0.369717	−	0.929144i	$-0.620546\pi$
$811$	−21.0577			−0.739435			−0.369717	+	0.929144i	$0.620546\pi$
$812$		0			0
$813$		0			0
$814$	−0.830095	−	1.43777i	−0.0290948	−	0.0503937i
$815$	−8.84896	−	15.3269i	−0.309966	−	0.536876i
$816$		0			0
$817$	−5.93984	+	10.2881i	−0.207809	+	0.359935i
$818$	1.46504			0.0512238
$819$		0			0
$820$	−51.4563			−1.79693
$821$	5.58018	−	9.66515i	0.194750	−	0.337316i	−0.752069	−	0.659085i	$-0.770944\pi$
$821$	5.58018	−	9.66515i	0.194750	−	0.337316i	0.946818	+	0.321768i	$0.104277\pi$
$822$		0			0
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	0.772018	−	0.635601i	$-0.219247\pi$
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	−0.936455	+	0.350787i	$0.885914\pi$
$824$	−3.76466	−	6.52059i	−0.131148	−	0.227156i
$825$		0			0
$826$		0			0
$827$	−17.2646			−0.600348			−0.300174	−	0.953884i	$-0.597045\pi$
$827$	−17.2646			−0.600348			−0.300174	+	0.953884i	$0.597045\pi$
$828$		0			0
$829$	48.4526			1.68283			0.841415	−	0.540390i	$-0.181723\pi$
$829$	48.4526			1.68283			0.841415	+	0.540390i	$0.181723\pi$
$830$	−2.13650	+	3.70053i	−0.0741591	+	0.128447i
$831$		0			0
$832$	12.2651	+	21.2438i	0.425215	+	0.736495i
$833$		0			0
$834$		0			0
$835$	23.3187	−	40.3893i	0.806978	−	1.39773i
$836$	−58.1376			−2.01073
$837$		0			0
$838$	0.373720			0.0129099
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	−0.708685	−	0.705525i	$-0.750711\pi$
$839$	7.43429	−	12.8766i	0.256660	−	0.444548i	0.965345	+	0.260977i	$0.0840446\pi$
$840$		0			0
$841$	12.2427	+	21.2050i	0.422162	+	0.731206i
$842$	2.78139	+	4.81750i	0.0958529	+	0.166022i
$843$		0			0
$844$	16.4029	−	28.4106i	0.564610	−	0.977934i
$845$	1.46504			0.0503988
$846$		0			0
$847$		0			0
$848$	19.4841	−	33.7475i	0.669088	−	1.15889i
$849$		0			0
$850$	−0.351337	−	0.608534i	−0.0120508	−	0.0208725i
$851$	−4.25404	−	7.36821i	−0.145827	−	0.252579i
$852$		0			0
$853$	3.99900	−	6.92648i	0.136923	−	0.237158i	−0.789407	−	0.613870i	$-0.789612\pi$
$853$	3.99900	−	6.92648i	0.136923	−	0.237158i	0.926331	+	0.376712i	$0.122945\pi$
$854$		0			0
$855$		0			0
$856$	−3.73026			−0.127498
$857$	21.5661	−	37.3536i	0.736684	−	1.27597i	−0.217296	−	0.976106i	$-0.569724\pi$
$857$	21.5661	−	37.3536i	0.736684	−	1.27597i	0.953980	−	0.299869i	$-0.0969429\pi$
$858$		0			0
$859$	−1.22180	−	2.11621i	−0.0416871	−	0.0722042i	0.844429	−	0.535667i	$-0.179940\pi$
$859$	−1.22180	−	2.11621i	−0.0416871	−	0.0722042i	−0.886116	+	0.463463i	$0.846607\pi$
$860$	−4.17984	−	7.23970i	−0.142531	−	0.246872i
$861$		0			0
$862$	−0.120250	+	0.208279i	−0.00409573	+	0.00709401i
$863$	−25.7187			−0.875476			−0.437738	−	0.899103i	$-0.644220\pi$
$863$	−25.7187			−0.875476			−0.437738	+	0.899103i	$0.644220\pi$
$864$		0			0
$865$	2.15211			0.0731739
$866$	1.56711	−	2.71432i	0.0532526	−	0.0922362i
$867$		0			0
$868$		0			0
$869$	−20.5510	−	35.5954i	−0.697146	−	1.20749i
$870$		0			0
$871$	−15.2171	+	26.3568i	−0.515612	+	0.893067i
$872$	6.84789			0.231899
$873$		0			0
$874$	8.76884			0.296611
$875$		0			0
$876$		0			0
$877$	10.9795	+	19.0170i	0.370751	+	0.642160i	0.989681	−	0.143286i	$-0.0457670\pi$
$877$	10.9795	+	19.0170i	0.370751	+	0.642160i	−0.618930	+	0.785446i	$0.712434\pi$
$878$	2.22553	+	3.85473i	0.0751080	+	0.130091i
$879$		0			0
$880$	19.8359	−	34.3567i	0.668667	−	1.15817i
$881$	−35.0576			−1.18112			−0.590560	−	0.806994i	$-0.701093\pi$
$881$	−35.0576			−1.18112			−0.590560	+	0.806994i	$0.701093\pi$
$882$		0			0
$883$	26.3009			0.885097			0.442549	−	0.896744i	$-0.354074\pi$
$883$	26.3009			0.885097			0.442549	+	0.896744i	$0.354074\pi$
$884$	−6.12188	+	10.6034i	−0.205901	+	0.356631i
$885$		0			0
$886$	0.133790	+	0.231731i	0.00449477	+	0.00778517i
$887$	−23.9090	−	41.4116i	−0.802785	−	1.39046i	−0.917776	−	0.397098i	$-0.870017\pi$
$887$	−23.9090	−	41.4116i	−0.802785	−	1.39046i	0.114991	−	0.993366i	$-0.463316\pi$
$888$		0			0
$889$		0			0
$890$	−3.12071			−0.104607
$891$		0			0
$892$	8.74545			0.292819
$893$	−33.4104	+	57.8685i	−1.11804	+	1.93650i
$894$		0			0
$895$	9.82150	+	17.0113i	0.328296	+	0.568626i
$896$		0			0
$897$		0			0
$898$	4.71574	−	8.16789i	0.157366	−	0.272566i
$899$	−13.8871			−0.463162
$900$		0			0
$901$	18.2170			0.606895
$902$	−5.10948	+	8.84988i	−0.170127	+	0.294669i
$903$		0			0
$904$	3.26647	+	5.65769i	0.108641	+	0.188172i
$905$	−0.530225	−	0.918376i	−0.0176253	−	0.0305279i
$906$		0			0
$907$	9.55718	−	16.5535i	0.317341	−	0.549651i	−0.662591	−	0.748981i	$-0.730543\pi$
$907$	9.55718	−	16.5535i	0.317341	−	0.549651i	0.979932	+	0.199330i	$0.0638767\pi$
$908$	−11.7818			−0.390994
$909$		0			0
$910$		0			0
$911$	−9.02928	+	15.6392i	−0.299153	+	0.518149i	−0.975942	−	0.218028i	$-0.930038\pi$
$911$	−9.02928	+	15.6392i	−0.299153	+	0.518149i	0.676789	+	0.736177i	$0.263371\pi$
$912$		0			0
$913$	−14.4165	−	24.9701i	−0.477117	−	0.826391i
$914$	−4.09385	−	7.09076i	−0.135413	−	0.234541i
$915$		0			0
$916$	−10.7334	+	18.5908i	−0.354642	+	0.614258i
$917$		0			0
$918$		0			0
$919$	16.2093			0.534695			0.267348	−	0.963600i	$-0.413853\pi$
$919$	16.2093			0.534695			0.267348	+	0.963600i	$0.413853\pi$
$920$	−6.26141	+	10.8451i	−0.206433	+	0.357552i
$921$		0			0
$922$	−2.43757	−	4.22199i	−0.0802771	−	0.139044i
$923$	11.4897	+	19.9007i	0.378187	+	0.655039i
$924$		0			0
$925$	−1.42558	+	2.46918i	−0.0468728	+	0.0811860i
$926$	−1.62820			−0.0535059
$927$		0			0
$928$	−5.86621			−0.192568
$929$	−11.3415	+	19.6440i	−0.372102	+	0.644499i	−0.989889	−	0.141846i	$-0.954696\pi$
$929$	−11.3415	+	19.6440i	−0.372102	+	0.644499i	0.617787	+	0.786345i	$0.288029\pi$
$930$		0			0
$931$		0			0
$932$	7.90576	+	13.6932i	0.258962	+	0.448535i
$933$		0			0
$934$	−2.96407	+	5.13392i	−0.0969873	+	0.167987i
$935$	18.5458			0.606513
$936$		0			0
$937$	51.2933			1.67568			0.837840	−	0.545915i	$-0.183818\pi$
$937$	51.2933			1.67568			0.837840	+	0.545915i	$0.183818\pi$
$938$		0			0
$939$		0			0
$940$	−23.5108	−	40.7219i	−0.766838	−	1.32820i
$941$	−15.9659	−	27.6538i	−0.520474	−	0.901487i	−0.999717	−	0.0238048i	$-0.992422\pi$
$941$	−15.9659	−	27.6538i	−0.520474	−	0.901487i	0.479243	−	0.877682i	$-0.340911\pi$
$942$		0			0
$943$	−26.1849	+	45.3535i	−0.852697	+	1.47691i
$944$	−22.1965			−0.722433
$945$		0			0
$946$	−1.66019			−0.0539774
$947$	−2.24665	+	3.89131i	−0.0730063	+	0.126451i	−0.900218	−	0.435440i	$-0.856593\pi$
$947$	−2.24665	+	3.89131i	−0.0730063	+	0.126451i	0.827211	+	0.561891i	$0.189926\pi$
$948$		0			0
$949$	−13.1774	−	22.8240i	−0.427757	−	0.740898i
$950$	−1.46927	−	2.54485i	−0.0476695	−	0.0825660i
$951$		0			0
$952$		0			0
$953$	−1.14635			−0.0371340			−0.0185670	−	0.999828i	$-0.505910\pi$
$953$	−1.14635			−0.0371340			−0.0185670	+	0.999828i	$0.505910\pi$
$954$		0			0
$955$	−41.5310			−1.34391
$956$	−20.5575	+	35.6066i	−0.664876	+	1.15160i
$957$		0			0
$958$	1.32710	+	2.29860i	0.0428765	+	0.0742643i
$959$		0			0
$960$		0			0
$961$	−5.85868	+	10.1475i	−0.188990	+	0.327340i
$962$	−1.46216			−0.0471418
$963$		0			0
$964$	−26.6000			−0.856730
$965$	16.0358	−	27.7748i	0.516210	−	0.894102i
$966$		0			0
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	−0.921065	−	0.389408i	$-0.872680\pi$
$967$	−24.8080	−	42.9686i	−0.797770	−	1.38178i	0.123295	−	0.992370i	$-0.460654\pi$
$968$	−3.05881	−	5.29802i	−0.0983140	−	0.170285i
$969$		0			0
$970$	0.949266	−	1.64418i	0.0304791	−	0.0527913i
$971$	5.13322			0.164733			0.0823664	−	0.996602i	$-0.473752\pi$
$971$	5.13322			0.164733			0.0823664	+	0.996602i	$0.473752\pi$
$972$		0			0
$973$		0			0
$974$	−1.20013	+	2.07869i	−0.0384546	+	0.0666054i
$975$		0			0
$976$	14.6151	+	25.3141i	0.467817	+	0.810283i
$977$	15.5974	+	27.0155i	0.499006	+	0.864303i	0.999999	−	0.00114787i	$-0.000365378\pi$
$977$	15.5974	+	27.0155i	0.499006	+	0.864303i	−0.500994	+	0.865451i	$0.667032\pi$
$978$		0			0
$979$	10.5288	−	18.2365i	0.336503	−	0.582840i
$980$		0			0
$981$		0			0
$982$	−2.96225			−0.0945292
$983$	10.1700	−	17.6150i	0.324374	−	0.561832i	−0.657012	−	0.753880i	$-0.728180\pi$
$983$	10.1700	−	17.6150i	0.324374	−	0.561832i	0.981385	+	0.192049i	$0.0615131\pi$
$984$		0			0
$985$	29.9378	+	51.8539i	0.953899	+	1.65220i
$986$	−0.434681	−	0.752890i	−0.0138431	−	0.0239769i
$987$		0			0
$988$	−25.6014	+	44.3429i	−0.814488	+	1.41074i
$989$	−8.50808			−0.270541
$990$		0			0
$991$	−12.9655			−0.411863			−0.205932	−	0.978566i	$-0.566022\pi$
$991$	−12.9655			−0.411863			−0.205932	+	0.978566i	$0.566022\pi$
$992$	−9.02234	+	15.6272i	−0.286460	+	0.496163i
$993$		0			0
$994$		0			0
$995$	8.74269	+	15.1428i	0.277162	+	0.480059i
$996$		0			0
$997$	24.7408	−	42.8523i	0.783548	−	1.35715i	−0.146314	−	0.989238i	$-0.546741\pi$
$997$	24.7408	−	42.8523i	0.783548	−	1.35715i	0.929863	−	0.367907i	$-0.119926\pi$
$998$	−2.44436			−0.0773749
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.g.883.3		12
3.2	odd	2		441.2.f.g.295.3	yes	12
7.2	even	3		1323.2.h.g.802.3		12
7.3	odd	6		1323.2.g.g.667.3		12
7.4	even	3		1323.2.g.g.667.4		12
7.5	odd	6		1323.2.h.g.802.4		12
7.6	odd	2	inner	1323.2.f.g.883.4		12
9.2	odd	6		3969.2.a.be.1.3		6
9.4	even	3	inner	1323.2.f.g.442.3		12
9.5	odd	6		441.2.f.g.148.3	✓	12
9.7	even	3		3969.2.a.bd.1.4		6
21.2	odd	6		441.2.h.g.214.4		12
21.5	even	6		441.2.h.g.214.3		12
21.11	odd	6		441.2.g.g.79.3		12
21.17	even	6		441.2.g.g.79.4		12
21.20	even	2		441.2.f.g.295.4	yes	12
63.4	even	3		1323.2.h.g.226.3		12
63.5	even	6		441.2.g.g.67.4		12
63.13	odd	6	inner	1323.2.f.g.442.4		12
63.20	even	6		3969.2.a.be.1.4		6
63.23	odd	6		441.2.g.g.67.3		12
63.31	odd	6		1323.2.h.g.226.4		12
63.32	odd	6		441.2.h.g.373.4		12
63.34	odd	6		3969.2.a.bd.1.3		6
63.40	odd	6		1323.2.g.g.361.3		12
63.41	even	6		441.2.f.g.148.4	yes	12
63.58	even	3		1323.2.g.g.361.4		12
63.59	even	6		441.2.h.g.373.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	9.5	odd	6
441.2.f.g.148.4	yes	12	63.41	even	6
441.2.f.g.295.3	yes	12	3.2	odd	2
441.2.f.g.295.4	yes	12	21.20	even	2
441.2.g.g.67.3		12	63.23	odd	6
441.2.g.g.67.4		12	63.5	even	6
441.2.g.g.79.3		12	21.11	odd	6
441.2.g.g.79.4		12	21.17	even	6
441.2.h.g.214.3		12	21.5	even	6
441.2.h.g.214.4		12	21.2	odd	6
441.2.h.g.373.3		12	63.59	even	6
441.2.h.g.373.4		12	63.32	odd	6
1323.2.f.g.442.3		12	9.4	even	3	inner
1323.2.f.g.442.4		12	63.13	odd	6	inner
1323.2.f.g.883.3		12	1.1	even	1	trivial
1323.2.f.g.883.4		12	7.6	odd	2	inner
1323.2.g.g.361.3		12	63.40	odd	6
1323.2.g.g.361.4		12	63.58	even	3
1323.2.g.g.667.3		12	7.3	odd	6
1323.2.g.g.667.4		12	7.4	even	3
1323.2.h.g.226.3		12	63.4	even	3
1323.2.h.g.226.4		12	63.31	odd	6
1323.2.h.g.802.3		12	7.2	even	3
1323.2.h.g.802.4		12	7.5	odd	6
3969.2.a.bd.1.3		6	63.34	odd	6
3969.2.a.bd.1.4		6	9.7	even	3
3969.2.a.be.1.3		6	9.2	odd	6
3969.2.a.be.1.4		6	63.20	even	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(-1.29589 - 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})\)	\(q+(0.119562 - 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(-1.29589 - 2.24456i) q^{5} +0.942820 q^{8} -0.619757 q^{10} +(2.09097 - 3.62167i) q^{11} +(-1.84155 - 3.18966i) q^{13} +(-1.83009 + 3.16982i) q^{16} -1.71107 q^{17} -7.15561 q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 - 4.43818i) q^{23} +(-0.858685 + 1.48729i) q^{25} -0.880716 q^{26} +(-1.06238 + 1.84010i) q^{29} +(3.26793 + 5.66021i) q^{31} +(1.38044 + 2.39099i) q^{32} +(-0.204579 + 0.354341i) q^{34} +1.66019 q^{37} +(-0.855536 + 1.48183i) q^{38} +(-1.22180 - 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +8.12476 q^{44} -1.22545 q^{46} +(4.66912 - 8.08715i) q^{47} +(0.205332 + 0.355645i) q^{50} +(3.57780 - 6.19694i) q^{52} -10.6465 q^{53} -10.8387 q^{55} +(0.254040 + 0.440011i) q^{58} +(3.03215 + 5.25183i) q^{59} +(3.99298 - 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(-4.77292 + 8.26693i) q^{65} +(-4.13160 - 7.15614i) q^{67} +(-1.66215 - 2.87893i) q^{68} -6.23912 q^{71} +7.15561 q^{73} +(0.198495 - 0.343803i) q^{74} +(-6.95103 - 12.0395i) q^{76} +(4.91423 - 8.51170i) q^{79} +9.48644 q^{80} -2.44359 q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 - 0.343803i) q^{86} +(1.97141 - 3.41458i) q^{88} +5.03538 q^{89} +(4.97825 - 8.62258i) q^{92} +(-1.11650 - 1.93383i) q^{94} +(9.27292 + 16.0612i) q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

Modular forms

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