LMFDB - Embedded newform 936.2.r.f.601.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(601,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.601"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.r (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.16
Character	$\chi$	$=$	936.601
Dual form			936.2.r.f.841.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29506 + 1.15014i) q^{3} +(1.65071 + 2.85912i) q^{5} +(-0.933130 - 1.61623i) q^{7} +(0.354378 + 2.97900i) q^{9} -1.87633 q^{11} +(3.00081 + 1.99878i) q^{13} +(-1.15059 + 5.60128i) q^{15} +(-2.21681 + 3.83963i) q^{17} +(3.24988 - 5.62896i) q^{19} +(0.650419 - 3.16634i) q^{21} +(-1.88173 + 3.25925i) q^{23} +(-2.94970 + 5.10903i) q^{25} +(-2.96731 + 4.26557i) q^{27} +1.33604 q^{29} +(1.73294 + 3.00154i) q^{31} +(-2.42997 - 2.15804i) q^{33} +(3.08066 - 5.33585i) q^{35} +(-0.457982 - 0.793248i) q^{37} +(1.58737 + 6.03989i) q^{39} +(-1.16366 + 2.01552i) q^{41} +(1.87242 + 3.24312i) q^{43} +(-7.93232 + 5.93067i) q^{45} +(5.05850 - 8.76158i) q^{47} +(1.75854 - 3.04588i) q^{49} +(-7.28700 + 2.42293i) q^{51} -9.98182 q^{53} +(-3.09728 - 5.36465i) q^{55} +(10.6829 - 3.55206i) q^{57} +2.93192 q^{59} +(-7.17460 - 12.4268i) q^{61} +(4.48406 - 3.35255i) q^{63} +(-0.761271 + 11.8791i) q^{65} +(-4.48022 + 7.75996i) q^{67} +(-6.18553 + 2.05669i) q^{69} +(-1.03307 + 1.78932i) q^{71} +2.56896 q^{73} +(-9.69611 + 3.22396i) q^{75} +(1.75086 + 3.03258i) q^{77} +(7.05149 - 12.2135i) q^{79} +(-8.74883 + 2.11138i) q^{81} +(1.35281 - 2.34313i) q^{83} -14.6373 q^{85} +(1.73026 + 1.53663i) q^{87} +(4.60157 + 7.97016i) q^{89} +(0.430338 - 6.71512i) q^{91} +(-1.20791 + 5.88030i) q^{93} +21.4585 q^{95} +(5.17758 + 8.96783i) q^{97} +(-0.664931 - 5.58959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.29506	+	1.15014i	0.747705	+	0.664031i
$3$	1.29506	+	1.15014i	0.747705	+	0.664031i
$4$		0			0
$5$	1.65071	+	2.85912i	0.738221	+	1.27864i	0.953296	+	0.302038i	$0.0976670\pi$
$5$	1.65071	+	2.85912i	0.738221	+	1.27864i	−0.215075	+	0.976597i	$0.569000\pi$
$6$		0			0
$7$	−0.933130	−	1.61623i	−0.352690	−	0.610877i	0.634030	−	0.773309i	$-0.281400\pi$
$7$	−0.933130	−	1.61623i	−0.352690	−	0.610877i	−0.986720	+	0.162432i	$0.948066\pi$
$8$		0			0
$9$	0.354378	+	2.97900i	0.118126	+	0.992999i
$10$		0			0
$11$	−1.87633			−0.565736			−0.282868	−	0.959159i	$-0.591286\pi$
$11$	−1.87633			−0.565736			−0.282868	+	0.959159i	$0.591286\pi$
$12$		0			0
$13$	3.00081	+	1.99878i	0.832276	+	0.554362i
$13$	3.00081	+	1.99878i	0.832276	+	0.554362i
$14$		0			0
$15$	−1.15059	+	5.60128i	−0.297082	+	1.44624i
$16$		0			0
$17$	−2.21681	+	3.83963i	−0.537655	+	0.931246i	0.461374	+	0.887206i	$0.347357\pi$
$17$	−2.21681	+	3.83963i	−0.537655	+	0.931246i	−0.999030	+	0.0440408i	$0.985977\pi$
$18$		0			0
$19$	3.24988	−	5.62896i	0.745574	−	1.29137i	−0.204352	−	0.978898i	$-0.565509\pi$
$19$	3.24988	−	5.62896i	0.745574	−	1.29137i	0.949926	−	0.312475i	$-0.101158\pi$
$20$		0			0
$21$	0.650419	−	3.16634i	0.141933	−	0.690953i
$22$		0			0
$23$	−1.88173	+	3.25925i	−0.392367	+	0.679600i	−0.992761	−	0.120104i	$-0.961677\pi$
$23$	−1.88173	+	3.25925i	−0.392367	+	0.679600i	0.600394	+	0.799704i	$0.295011\pi$
$24$		0			0
$25$	−2.94970	+	5.10903i	−0.589939	+	1.02181i
$26$		0			0
$27$	−2.96731	+	4.26557i	−0.571058	+	0.820909i
$28$		0			0
$29$	1.33604			0.248097			0.124048	−	0.992276i	$-0.460412\pi$
$29$	1.33604			0.248097			0.124048	+	0.992276i	$0.460412\pi$
$30$		0			0
$31$	1.73294	+	3.00154i	0.311245	+	0.539093i	0.978632	−	0.205618i	$-0.0659206\pi$
$31$	1.73294	+	3.00154i	0.311245	+	0.539093i	−0.667387	+	0.744711i	$0.732587\pi$
$32$		0			0
$33$	−2.42997	−	2.15804i	−0.423003	−	0.375666i
$34$		0			0
$35$	3.08066	−	5.33585i	0.520726	−	0.901924i
$36$		0			0
$37$	−0.457982	−	0.793248i	−0.0752917	−	0.130409i	0.825921	−	0.563785i	$-0.190655\pi$
$37$	−0.457982	−	0.793248i	−0.0752917	−	0.130409i	−0.901213	+	0.433376i	$0.857322\pi$
$38$		0			0
$39$	1.58737	+	6.03989i	0.254183	+	0.967156i
$40$		0			0
$41$	−1.16366	+	2.01552i	−0.181733	+	0.314771i	−0.942471	−	0.334289i	$-0.891504\pi$
$41$	−1.16366	+	2.01552i	−0.181733	+	0.314771i	0.760738	+	0.649059i	$0.224837\pi$
$42$		0			0
$43$	1.87242	+	3.24312i	0.285541	+	0.494572i	0.972740	−	0.231897i	$-0.0744934\pi$
$43$	1.87242	+	3.24312i	0.285541	+	0.494572i	−0.687199	+	0.726469i	$0.741160\pi$
$44$		0			0
$45$	−7.93232	+	5.93067i	−1.18248	+	0.884092i
$46$		0			0
$47$	5.05850	−	8.76158i	0.737858	−	1.27801i	−0.215600	−	0.976482i	$-0.569171\pi$
$47$	5.05850	−	8.76158i	0.737858	−	1.27801i	0.953458	−	0.301525i	$-0.0974958\pi$
$48$		0			0
$49$	1.75854	−	3.04588i	0.251220	−	0.435125i
$50$		0			0
$51$	−7.28700	+	2.42293i	−1.02038	+	0.339278i
$52$		0			0
$53$	−9.98182			−1.37111			−0.685554	−	0.728022i	$-0.740440\pi$
$53$	−9.98182			−1.37111			−0.685554	+	0.728022i	$0.740440\pi$
$54$		0			0
$55$	−3.09728	−	5.36465i	−0.417638	−	0.723370i
$56$		0			0
$57$	10.6829	−	3.55206i	1.41498	−	0.470482i
$58$		0			0
$59$	2.93192			0.381704			0.190852	−	0.981619i	$-0.438875\pi$
$59$	2.93192			0.381704			0.190852	+	0.981619i	$0.438875\pi$
$60$		0			0
$61$	−7.17460	−	12.4268i	−0.918614	−	1.59109i	−0.801522	−	0.597965i	$-0.795976\pi$
$61$	−7.17460	−	12.4268i	−0.918614	−	1.59109i	−0.117091	−	0.993121i	$-0.537357\pi$
$62$		0			0
$63$	4.48406	−	3.35255i	0.564938	−	0.422381i
$64$		0			0
$65$	−0.761271	+	11.8791i	−0.0944240	+	1.47342i
$66$		0			0
$67$	−4.48022	+	7.75996i	−0.547345	+	0.948030i	0.451110	+	0.892468i	$0.351028\pi$
$67$	−4.48022	+	7.75996i	−0.547345	+	0.948030i	−0.998455	+	0.0555617i	$0.982305\pi$
$68$		0			0
$69$	−6.18553	+	2.05669i	−0.744651	+	0.247597i
$70$		0			0
$71$	−1.03307	+	1.78932i	−0.122602	+	0.212354i	−0.920793	−	0.390051i	$-0.872457\pi$
$71$	−1.03307	+	1.78932i	−0.122602	+	0.212354i	0.798191	+	0.602405i	$0.205791\pi$
$72$		0			0
$73$	2.56896			0.300674			0.150337	−	0.988635i	$-0.451964\pi$
$73$	2.56896			0.300674			0.150337	+	0.988635i	$0.451964\pi$
$74$		0			0
$75$	−9.69611	+	3.22396i	−1.11961	+	0.372271i
$76$		0			0
$77$	1.75086	+	3.03258i	0.199529	+	0.345595i
$78$		0			0
$79$	7.05149	−	12.2135i	0.793355	−	1.37413i	−0.130524	−	0.991445i	$-0.541666\pi$
$79$	7.05149	−	12.2135i	0.793355	−	1.37413i	0.923879	−	0.382685i	$-0.125001\pi$
$80$		0			0
$81$	−8.74883	+	2.11138i	−0.972092	+	0.234598i
$82$		0			0
$83$	1.35281	−	2.34313i	0.148490	−	0.257192i	−0.782179	−	0.623053i	$-0.785892\pi$
$83$	1.35281	−	2.34313i	0.148490	−	0.257192i	0.930670	+	0.365861i	$0.119225\pi$
$84$		0			0
$85$	−14.6373			−1.58763
$86$		0			0
$87$	1.73026	+	1.53663i	0.185503	+	0.164744i
$88$		0			0
$89$	4.60157	+	7.97016i	0.487766	+	0.844835i	0.999901	−	0.0140698i	$-0.00447869\pi$
$89$	4.60157	+	7.97016i	0.487766	+	0.844835i	−0.512135	+	0.858905i	$0.671145\pi$
$90$		0			0
$91$	0.430338	−	6.71512i	0.0451117	−	0.703936i
$92$		0			0
$93$	−1.20791	+	5.88030i	−0.125254	+	0.609759i
$94$		0			0
$95$	21.4585			2.20159
$96$		0			0
$97$	5.17758	+	8.96783i	0.525703	+	0.910545i	0.999552	+	0.0299384i	$0.00953112\pi$
$97$	5.17758	+	8.96783i	0.525703	+	0.910545i	−0.473848	+	0.880606i	$0.657136\pi$
$98$		0			0
$99$	−0.664931	−	5.58959i	−0.0668281	−	0.561775i
$100$		0			0
$101$	14.6652			1.45924			0.729619	−	0.683854i	$-0.239698\pi$
$101$	14.6652			1.45924			0.729619	+	0.683854i	$0.239698\pi$
$102$		0			0
$103$	−3.71350	−	6.43197i	−0.365902	−	0.633760i	0.623019	−	0.782207i	$-0.285906\pi$
$103$	−3.71350	−	6.43197i	−0.365902	−	0.633760i	−0.988920	+	0.148447i	$0.952573\pi$
$104$		0			0
$105$	10.1266	−	3.36710i	0.988255	−	0.328595i
$106$		0			0
$107$	4.77286	+	8.26684i	0.461410	+	0.799185i	0.999031	−	0.0440009i	$-0.0140105\pi$
$107$	4.77286	+	8.26684i	0.461410	+	0.799185i	−0.537622	+	0.843186i	$0.680677\pi$
$108$		0			0
$109$	9.07781			0.869497			0.434748	−	0.900552i	$-0.356837\pi$
$109$	9.07781			0.869497			0.434748	+	0.900552i	$0.356837\pi$
$110$		0			0
$111$	0.319227	−	1.55405i	0.0302997	−	0.147504i
$112$		0			0
$113$	12.8159			1.20562			0.602808	−	0.797886i	$-0.294049\pi$
$113$	12.8159			1.20562			0.602808	+	0.797886i	$0.294049\pi$
$114$		0			0
$115$	−12.4248			−1.15862
$116$		0			0
$117$	−4.89094	+	9.64773i	−0.452167	+	0.891933i
$118$		0			0
$119$	8.27428			0.758502
$120$		0			0
$121$	−7.47938			−0.679943
$122$		0			0
$123$	−3.82513	+	1.27186i	−0.344900	+	0.114679i
$124$		0			0
$125$	−2.96928			−0.265581
$126$		0			0
$127$	−1.84439	−	3.19458i	−0.163663	−	0.283473i	0.772516	−	0.634995i	$-0.218998\pi$
$127$	−1.84439	−	3.19458i	−0.163663	−	0.283473i	−0.936180	+	0.351522i	$0.885664\pi$
$128$		0			0
$129$	−1.30513	+	6.35358i	−0.114910	+	0.559402i
$130$		0			0
$131$	−8.37547	−	14.5067i	−0.731768	−	1.26746i	−0.956127	−	0.292953i	$-0.905362\pi$
$131$	−8.37547	−	14.5067i	−0.731768	−	1.26746i	0.224359	−	0.974507i	$-0.427971\pi$
$132$		0			0
$133$	−12.1302			−1.05183
$134$		0			0
$135$	−17.0939	−	1.44265i	−1.47121	−	0.124163i
$136$		0			0
$137$	1.04969	+	1.81812i	0.0896814	+	0.155333i	0.907376	−	0.420319i	$-0.138082\pi$
$137$	1.04969	+	1.81812i	0.0896814	+	0.155333i	−0.817695	+	0.575652i	$0.804748\pi$
$138$		0			0
$139$	7.84840			0.665693			0.332846	−	0.942981i	$-0.391991\pi$
$139$	7.84840			0.665693			0.332846	+	0.942981i	$0.391991\pi$
$140$		0			0
$141$	16.6281	−	5.52884i	1.40034	−	0.465612i
$142$		0			0
$143$	−5.63052	−	3.75038i	−0.470848	−	0.313622i
$144$		0			0
$145$	2.20542	+	3.81990i	0.183150	+	0.317225i
$146$		0			0
$147$	5.78059	−	1.92205i	0.476775	−	0.158528i
$148$		0			0
$149$	19.0368			1.55956			0.779778	−	0.626057i	$-0.215332\pi$
$149$	19.0368			1.55956			0.779778	+	0.626057i	$0.215332\pi$
$150$		0			0
$151$	−9.78217	+	16.9432i	−0.796062	+	1.37882i	0.126101	+	0.992017i	$0.459754\pi$
$151$	−9.78217	+	16.9432i	−0.796062	+	1.37882i	−0.922163	+	0.386802i	$0.873580\pi$
$152$		0			0
$153$	−12.2238	−	5.24319i	−0.988237	−	0.423887i
$154$		0			0
$155$	−5.72117	+	9.90936i	−0.459536	+	0.795939i
$156$		0			0
$157$	−10.9030	−	18.8845i	−0.870152	−	1.50715i	−0.861839	−	0.507182i	$-0.830687\pi$
$157$	−10.9030	−	18.8845i	−0.870152	−	1.50715i	−0.00831272	−	0.999965i	$-0.502646\pi$
$158$		0			0
$159$	−12.9271	−	11.4804i	−1.02518	−	0.910458i
$160$		0			0
$161$	7.02359			0.553536
$162$		0			0
$163$	5.93328	−	10.2767i	0.464731	−	0.804937i	−0.534459	−	0.845195i	$-0.679484\pi$
$163$	5.93328	−	10.2767i	0.464731	−	0.804937i	0.999189	+	0.0402575i	$0.0128178\pi$
$164$		0			0
$165$	2.15890	−	10.5099i	0.168070	−	0.818192i
$166$		0			0
$167$	7.11118	−	12.3169i	0.550279	−	0.953112i	−0.447975	−	0.894046i	$-0.647855\pi$
$167$	7.11118	−	12.3169i	0.550279	−	0.953112i	0.998254	−	0.0590655i	$-0.0188121\pi$
$168$		0			0
$169$	5.00975	+	11.9959i	0.385365	+	0.922764i
$170$		0			0
$171$	17.9203	+	7.68661i	1.37040	+	0.587810i
$172$		0			0
$173$	8.92649	+	15.4611i	0.678669	+	1.17549i	0.975382	+	0.220522i	$0.0707761\pi$
$173$	8.92649	+	15.4611i	0.678669	+	1.17549i	−0.296713	+	0.954967i	$0.595891\pi$
$174$		0			0
$175$	11.0098			0.832263
$176$		0			0
$177$	3.79702	+	3.37211i	0.285402	+	0.253463i
$178$		0			0
$179$	−3.04421	−	5.27273i	−0.227535	−	0.394102i	0.729542	−	0.683936i	$-0.239733\pi$
$179$	−3.04421	−	5.27273i	−0.227535	−	0.394102i	−0.957077	+	0.289834i	$0.906400\pi$
$180$		0			0
$181$	−5.73434			−0.426230			−0.213115	−	0.977027i	$-0.568361\pi$
$181$	−5.73434			−0.426230			−0.213115	+	0.977027i	$0.568361\pi$
$182$		0			0
$183$	5.00091	−	24.3452i	0.369678	−	1.79965i
$184$		0			0
$185$	1.51199	−	2.61885i	0.111164	−	0.192541i
$186$		0			0
$187$	4.15947	−	7.20442i	0.304171	−	0.526839i
$188$		0			0
$189$	9.66302	+	0.815512i	0.702881	+	0.0593198i
$190$		0			0
$191$	−6.13650	−	10.6287i	−0.444021	−	0.769068i	0.553962	−	0.832542i	$-0.313115\pi$
$191$	−6.13650	−	10.6287i	−0.444021	−	0.769068i	−0.997983	+	0.0634742i	$0.979782\pi$
$192$		0			0
$193$	12.4266	−	21.5236i	0.894490	−	1.54930i	0.0600545	−	0.998195i	$-0.480873\pi$
$193$	12.4266	−	21.5236i	0.894490	−	1.54930i	0.834435	−	0.551106i	$-0.185794\pi$
$194$		0			0
$195$	−14.6484	+	14.5086i	−1.04900	+	1.03898i
$196$		0			0
$197$	−3.80810	−	6.59582i	−0.271316	−	0.469932i	0.697883	−	0.716211i	$-0.254125\pi$
$197$	−3.80810	−	6.59582i	−0.271316	−	0.469932i	−0.969199	+	0.246279i	$0.920792\pi$
$198$		0			0
$199$	11.5276	−	19.9664i	0.817172	−	1.41538i	−0.0905851	−	0.995889i	$-0.528874\pi$
$199$	11.5276	−	19.9664i	0.817172	−	1.41538i	0.907757	−	0.419495i	$-0.137793\pi$
$200$		0			0
$201$	−14.7272	+	4.89679i	−1.03877	+	0.345393i
$202$		0			0
$203$	−1.24670	−	2.15935i	−0.0875011	−	0.151556i
$204$		0			0
$205$	−7.68346			−0.536636
$206$		0			0
$207$	−10.3761	−	4.45065i	−0.721191	−	0.309342i
$208$		0			0
$209$	−6.09786	+	10.5618i	−0.421798	+	0.730575i
$210$		0			0
$211$	−9.88197	+	17.1161i	−0.680303	+	1.17832i	0.294586	+	0.955625i	$0.404818\pi$
$211$	−9.88197	+	17.1161i	−0.680303	+	1.17832i	−0.974888	+	0.222694i	$0.928515\pi$
$212$		0			0
$213$	−3.39585	+	1.12912i	−0.232680	+	0.0773661i
$214$		0			0
$215$	−6.18164	+	10.7069i	−0.421585	+	0.730206i
$216$		0			0
$217$	3.23412	−	5.60166i	0.219546	−	0.380265i
$218$		0			0
$219$	3.32696	+	2.95465i	0.224815	+	0.199657i
$220$		0			0
$221$	−14.3268	+	7.09108i	−0.963725	+	0.476998i
$222$		0			0
$223$	−5.56716			−0.372805			−0.186402	−	0.982473i	$-0.559683\pi$
$223$	−5.56716			−0.372805			−0.186402	+	0.982473i	$0.559683\pi$
$224$		0			0
$225$	−16.2651	−	6.97661i	−1.08434	−	0.465107i
$226$		0			0
$227$	−4.25083	−	7.36265i	−0.282138	−	0.488676i	0.689773	−	0.724025i	$-0.257710\pi$
$227$	−4.25083	−	7.36265i	−0.282138	−	0.488676i	−0.971911	+	0.235349i	$0.924377\pi$
$228$		0			0
$229$	−7.46686	−	12.9330i	−0.493424	−	0.854635i	0.506547	−	0.862212i	$-0.330922\pi$
$229$	−7.46686	−	12.9330i	−0.493424	−	0.854635i	−0.999971	+	0.00757686i	$0.997588\pi$
$230$		0			0
$231$	−1.22040	+	5.94111i	−0.0802966	+	0.390897i
$232$		0			0
$233$	−24.2714			−1.59007			−0.795037	−	0.606561i	$-0.792549\pi$
$233$	−24.2714			−1.59007			−0.795037	+	0.606561i	$0.792549\pi$
$234$		0			0
$235$	33.4005			2.17881
$236$		0			0
$237$	23.1793	−	7.70714i	1.50566	−	0.500633i
$238$		0			0
$239$	−6.45026	−	11.1722i	−0.417232	−	0.722668i	0.578428	−	0.815734i	$-0.303667\pi$
$239$	−6.45026	−	11.1722i	−0.417232	−	0.722668i	−0.995660	+	0.0930660i	$0.970333\pi$
$240$		0			0
$241$	4.80951	+	8.33031i	0.309808	+	0.536603i	0.978320	−	0.207098i	$-0.0664020\pi$
$241$	4.80951	+	8.33031i	0.309808	+	0.536603i	−0.668512	+	0.743701i	$0.733069\pi$
$242$		0			0
$243$	−13.7587	−	7.32797i	−0.882619	−	0.470089i
$244$		0			0
$245$	11.6114			0.741822
$246$		0			0
$247$	21.0033	−	10.3957i	1.33641	−	0.661460i
$248$		0			0
$249$	4.44690	−	1.47859i	0.281811	−	0.0937021i
$250$		0			0
$251$	−6.13449	+	10.6253i	−0.387206	+	0.670660i	−0.992073	−	0.125667i	$-0.959893\pi$
$251$	−6.13449	+	10.6253i	−0.387206	+	0.670660i	0.604867	+	0.796327i	$0.293226\pi$
$252$		0			0
$253$	3.53075	−	6.11544i	0.221976	−	0.384474i
$254$		0			0
$255$	−18.9562	−	16.8348i	−1.18708	−	1.05424i
$256$		0			0
$257$	−9.35628	+	16.2056i	−0.583629	+	1.01087i	0.411416	+	0.911448i	$0.365034\pi$
$257$	−9.35628	+	16.2056i	−0.583629	+	1.01087i	−0.995045	+	0.0994269i	$0.968299\pi$
$258$		0			0
$259$	−0.854713	+	1.48041i	−0.0531093	+	0.0919879i
$260$		0			0
$261$	0.473463	+	3.98006i	0.0293067	+	0.246360i
$262$		0			0
$263$	20.6049			1.27055			0.635277	−	0.772284i	$-0.280886\pi$
$263$	20.6049			1.27055			0.635277	+	0.772284i	$0.280886\pi$
$264$		0			0
$265$	−16.4771	−	28.5392i	−1.01218	−	1.75315i
$266$		0			0
$267$	−3.20743	+	15.6143i	−0.196292	+	0.955579i
$268$		0			0
$269$	8.82631	−	15.2876i	0.538150	−	0.932103i	−0.460854	−	0.887476i	$-0.652457\pi$
$269$	8.82631	−	15.2876i	0.538150	−	0.932103i	0.999004	−	0.0446269i	$-0.0142099\pi$
$270$		0			0
$271$	7.84835	+	13.5937i	0.476753	+	0.825761i	0.999645	−	0.0266382i	$-0.00848020\pi$
$271$	7.84835	+	13.5937i	0.476753	+	0.825761i	−0.522892	+	0.852399i	$0.675147\pi$
$272$		0			0
$273$	8.28061	−	8.20156i	0.501165	−	0.496381i
$274$		0			0
$275$	5.53461	−	9.58623i	0.333750	−	0.578072i
$276$		0			0
$277$	−4.49473	−	7.78510i	−0.270062	−	0.467761i	0.698815	−	0.715302i	$-0.253711\pi$
$277$	−4.49473	−	7.78510i	−0.270062	−	0.467761i	−0.968877	+	0.247541i	$0.920378\pi$
$278$		0			0
$279$	−8.32746	+	6.22610i	−0.498552	+	0.372747i
$280$		0			0
$281$	9.17862	−	15.8978i	0.547551	−	0.948385i	−0.450891	−	0.892579i	$-0.648894\pi$
$281$	9.17862	−	15.8978i	0.547551	−	0.948385i	0.998442	−	0.0558064i	$-0.0177729\pi$
$282$		0			0
$283$	1.51567	−	2.62522i	0.0900974	−	0.156053i	−0.817455	−	0.575993i	$-0.804615\pi$
$283$	1.51567	−	2.62522i	0.0900974	−	0.156053i	0.907552	+	0.419940i	$0.137949\pi$
$284$		0			0
$285$	27.7901	+	24.6801i	1.64614	+	1.46193i
$286$		0			0
$287$	4.34338			0.256381
$288$		0			0
$289$	−1.32849	−	2.30101i	−0.0781465	−	0.135354i
$290$		0			0
$291$	−3.60892	+	17.5688i	−0.211559	+	1.02990i
$292$		0			0
$293$	2.95811			0.172815			0.0864073	−	0.996260i	$-0.472461\pi$
$293$	2.95811			0.172815			0.0864073	+	0.996260i	$0.472461\pi$
$294$		0			0
$295$	4.83976	+	8.38270i	0.281781	+	0.488060i
$296$		0			0
$297$	5.56765	−	8.00363i	0.323068	−	0.464418i
$298$		0			0
$299$	−12.1612	+	6.01923i	−0.703303	+	0.348101i
$300$		0			0
$301$	3.49442	−	6.05251i	0.201415	−	0.348861i
$302$		0			0
$303$	18.9923	+	16.8669i	1.09108	+	0.968978i
$304$		0			0
$305$	23.6864	−	41.0261i	1.35628	−	2.34914i
$306$		0			0
$307$	7.39083			0.421817			0.210909	−	0.977506i	$-0.432358\pi$
$307$	7.39083			0.421817			0.210909	+	0.977506i	$0.432358\pi$
$308$		0			0
$309$	2.58842	−	12.6008i	0.147250	−	0.716836i
$310$		0			0
$311$	−7.06555	−	12.2379i	−0.400651	−	0.693947i	0.593154	−	0.805089i	$-0.297883\pi$
$311$	−7.06555	−	12.2379i	−0.400651	−	0.693947i	−0.993805	+	0.111142i	$0.964549\pi$
$312$		0			0
$313$	5.69278	−	9.86019i	0.321775	−	0.557331i	−0.659079	−	0.752073i	$-0.729054\pi$
$313$	5.69278	−	9.86019i	0.321775	−	0.557331i	0.980854	+	0.194743i	$0.0623872\pi$
$314$		0			0
$315$	16.9872	+	7.28635i	0.957120	+	0.410539i
$316$		0			0
$317$	5.58479	−	9.67314i	0.313673	−	0.543298i	−0.665482	−	0.746414i	$-0.731774\pi$
$317$	5.58479	−	9.67314i	0.313673	−	0.543298i	0.979155	+	0.203117i	$0.0651071\pi$
$318$		0			0
$319$	−2.50686			−0.140357
$320$		0			0
$321$	−3.32682	+	16.1955i	−0.185685	+	0.903945i
$322$		0			0
$323$	14.4087	+	24.9567i	0.801724	+	1.38863i
$324$		0			0
$325$	−19.0633	+	9.43543i	−1.05744	+	0.523383i
$326$		0			0
$327$	11.7563	+	10.4407i	0.650127	+	0.577373i
$328$		0			0
$329$	−18.8809			−1.04094
$330$		0			0
$331$	8.51578	+	14.7498i	0.468069	+	0.810720i	0.999334	−	0.0364858i	$-0.0116164\pi$
$331$	8.51578	+	14.7498i	0.468069	+	0.810720i	−0.531265	+	0.847206i	$0.678283\pi$
$332$		0			0
$333$	2.20078	−	1.64544i	0.120602	−	0.0901693i
$334$		0			0
$335$	−29.5822			−1.61625
$336$		0			0
$337$	15.2871	+	26.4780i	0.832739	+	1.44235i	0.895858	+	0.444340i	$0.146562\pi$
$337$	15.2871	+	26.4780i	0.832739	+	1.44235i	−0.0631194	+	0.998006i	$0.520105\pi$
$338$		0			0
$339$	16.5974	+	14.7400i	0.901445	+	0.800566i
$340$		0			0
$341$	−3.25157	−	5.63189i	−0.176083	−	0.304984i
$342$		0			0
$343$	−19.6276			−1.05979
$344$		0			0
$345$	−16.0909	−	14.2902i	−0.866302	−	0.769356i
$346$		0			0
$347$	−28.8784			−1.55027			−0.775137	−	0.631794i	$-0.782319\pi$
$347$	−28.8784			−1.55027			−0.775137	+	0.631794i	$0.782319\pi$
$348$		0			0
$349$	−26.9396			−1.44204			−0.721022	−	0.692912i	$-0.756327\pi$
$349$	−26.9396			−1.44204			−0.721022	+	0.692912i	$0.756327\pi$
$350$		0			0
$351$	−17.4303	+	6.86918i	−0.930359	+	0.366650i
$352$		0			0
$353$	−28.2964			−1.50606			−0.753032	−	0.657983i	$-0.771410\pi$
$353$	−28.2964			−1.50606			−0.753032	+	0.657983i	$0.771410\pi$
$354$		0			0
$355$	−6.82118			−0.362031
$356$		0			0
$357$	10.7157	+	9.51655i	0.567136	+	0.503669i
$358$		0			0
$359$	18.9967			1.00261			0.501304	−	0.865271i	$-0.332854\pi$
$359$	18.9967			1.00261			0.501304	+	0.865271i	$0.332854\pi$
$360$		0			0
$361$	−11.6235	−	20.1324i	−0.611762	−	1.05960i
$362$		0			0
$363$	−9.68626	−	8.60229i	−0.508397	−	0.451503i
$364$		0			0
$365$	4.24061	+	7.34494i	0.221963	+	0.384452i
$366$		0			0
$367$	25.9910			1.35672			0.678361	−	0.734729i	$-0.262691\pi$
$367$	25.9910			1.35672			0.678361	+	0.734729i	$0.262691\pi$
$368$		0			0
$369$	−6.41659	−	2.75228i	−0.334034	−	0.143278i
$370$		0			0
$371$	9.31433	+	16.1329i	0.483576	+	0.837578i
$372$		0			0
$373$	−31.4505			−1.62844			−0.814222	−	0.580554i	$-0.802836\pi$
$373$	−31.4505			−1.62844			−0.814222	+	0.580554i	$0.802836\pi$
$374$		0			0
$375$	−3.84541	−	3.41507i	−0.198576	−	0.176354i
$376$		0			0
$377$	4.00921	+	2.67045i	0.206485	+	0.137535i
$378$		0			0
$379$	5.08601	+	8.80922i	0.261251	+	0.452499i	0.966575	−	0.256386i	$-0.0825318\pi$
$379$	5.08601	+	8.80922i	0.261251	+	0.452499i	−0.705324	+	0.708885i	$0.749198\pi$
$380$		0			0
$381$	1.28560	−	6.25848i	0.0658630	−	0.320632i
$382$		0			0
$383$	−28.6765			−1.46530			−0.732651	−	0.680604i	$-0.761717\pi$
$383$	−28.6765			−1.46530			−0.732651	+	0.680604i	$0.761717\pi$
$384$		0			0
$385$	−5.78034	+	10.0118i	−0.294593	+	0.510250i
$386$		0			0
$387$	−8.99770	+	6.72722i	−0.457379	+	0.341964i
$388$		0			0
$389$	−7.19376	+	12.4600i	−0.364738	+	0.631745i	−0.988734	−	0.149683i	$-0.952175\pi$
$389$	−7.19376	+	12.4600i	−0.364738	+	0.631745i	0.623996	+	0.781428i	$0.285508\pi$
$390$		0			0
$391$	−8.34287	−	14.4503i	−0.421917	−	0.730782i
$392$		0			0
$393$	5.83795	−	28.4201i	0.294486	−	1.43360i
$394$		0			0
$395$	46.5599			2.34268
$396$		0			0
$397$	−0.0814812	+	0.141130i	−0.00408942	+	0.00708309i	−0.868063	−	0.496454i	$-0.834635\pi$
$397$	−0.0814812	+	0.141130i	−0.00408942	+	0.00708309i	0.863973	+	0.503537i	$0.167968\pi$
$398$		0			0
$399$	−15.7094	−	13.9514i	−0.786456	−	0.698445i
$400$		0			0
$401$	4.82932	−	8.36464i	0.241165	−	0.417710i	−0.719881	−	0.694097i	$-0.755804\pi$
$401$	4.82932	−	8.36464i	0.241165	−	0.417710i	0.961046	+	0.276387i	$0.0891372\pi$
$402$		0			0
$403$	−0.799193	+	12.4708i	−0.0398106	+	0.621216i
$404$		0			0
$405$	−20.4785	−	21.5286i	−1.01758	−	1.06977i
$406$		0			0
$407$	0.859326	+	1.48840i	0.0425952	+	0.0737771i
$408$		0			0
$409$	22.2606			1.10072			0.550358	−	0.834929i	$-0.314491\pi$
$409$	22.2606			1.10072			0.550358	+	0.834929i	$0.314491\pi$
$410$		0			0
$411$	−0.731667	+	3.56187i	−0.0360905	+	0.175694i
$412$		0			0
$413$	−2.73586	−	4.73865i	−0.134623	−	0.233174i
$414$		0			0
$415$	8.93239			0.438474
$416$		0			0
$417$	10.1642	+	9.02673i	0.497742	+	0.442041i
$418$		0			0
$419$	−7.16471	+	12.4097i	−0.350019	+	0.606251i	−0.986252	−	0.165246i	$-0.947158\pi$
$419$	−7.16471	+	12.4097i	−0.350019	+	0.606251i	0.636233	+	0.771497i	$0.280492\pi$
$420$		0			0
$421$	0.334370	−	0.579145i	0.0162962	−	0.0282258i	−0.857762	−	0.514047i	$-0.828146\pi$
$421$	0.334370	−	0.579145i	0.0162962	−	0.0282258i	0.874058	+	0.485821i	$0.161479\pi$
$422$		0			0
$423$	27.8933	+	11.9643i	1.35622	+	0.581726i
$424$		0			0
$425$	−13.0778	−	22.6515i	−0.634368	−	1.09876i
$426$		0			0
$427$	−13.3897	+	23.1916i	−0.647972	+	1.12232i
$428$		0			0
$429$	−2.97844	−	11.3328i	−0.143801	−	0.547155i
$430$		0			0
$431$	−19.1537	−	33.1752i	−0.922601	−	1.59799i	−0.795374	−	0.606119i	$-0.792725\pi$
$431$	−19.1537	−	33.1752i	−0.922601	−	1.59799i	−0.127228	−	0.991874i	$-0.540608\pi$
$432$		0			0
$433$	2.75906	−	4.77883i	0.132592	−	0.229656i	−0.792083	−	0.610413i	$-0.791003\pi$
$433$	2.75906	−	4.77883i	0.132592	−	0.229656i	0.924675	+	0.380757i	$0.124337\pi$
$434$		0			0
$435$	−1.53724	+	7.48354i	−0.0737051	+	0.358808i
$436$		0			0
$437$	12.2308	+	21.1844i	0.585078	+	1.01339i
$438$		0			0
$439$	−30.1821			−1.44051			−0.720257	−	0.693707i	$-0.755976\pi$
$439$	−30.1821			−1.44051			−0.720257	+	0.693707i	$0.755976\pi$
$440$		0			0
$441$	9.69684	+	4.15929i	0.461754	+	0.198061i
$442$		0			0
$443$	−11.2133	+	19.4221i	−0.532762	+	0.922770i	0.466507	+	0.884518i	$0.345512\pi$
$443$	−11.2133	+	19.4221i	−0.532762	+	0.922770i	−0.999268	+	0.0382523i	$0.987821\pi$
$444$		0			0
$445$	−15.1917	+	26.3129i	−0.720157	+	1.24735i
$446$		0			0
$447$	24.6539	+	21.8949i	1.16609	+	1.03559i
$448$		0			0
$449$	−9.68866	+	16.7813i	−0.457236	+	0.791956i	−0.998814	−	0.0486945i	$-0.984494\pi$
$449$	−9.68866	+	16.7813i	−0.457236	+	0.791956i	0.541577	+	0.840651i	$0.317827\pi$
$450$		0			0
$451$	2.18341	−	3.78178i	0.102813	−	0.178077i
$452$		0			0
$453$	−32.1555	+	10.6917i	−1.51080	+	0.502341i
$454$		0			0
$455$	19.9097	−	9.85434i	0.933380	−	0.461978i
$456$		0			0
$457$	38.2374			1.78867			0.894335	−	0.447398i	$-0.147649\pi$
$457$	38.2374			1.78867			0.894335	+	0.447398i	$0.147649\pi$
$458$		0			0
$459$	−9.80025	−	20.8493i	−0.457436	−	0.973162i
$460$		0			0
$461$	20.0579	+	34.7413i	0.934189	+	1.61806i	0.776074	+	0.630641i	$0.217208\pi$
$461$	20.0579	+	34.7413i	0.934189	+	1.61806i	0.158114	+	0.987421i	$0.449459\pi$
$462$		0			0
$463$	8.04452	+	13.9335i	0.373861	+	0.647546i	0.990156	−	0.139970i	$-0.0447005\pi$
$463$	8.04452	+	13.9335i	0.373861	+	0.647546i	−0.616295	+	0.787515i	$0.711367\pi$
$464$		0			0
$465$	−18.8064	+	6.25313i	−0.872125	+	0.289982i
$466$		0			0
$467$	7.11182			0.329096			0.164548	−	0.986369i	$-0.447383\pi$
$467$	7.11182			0.329096			0.164548	+	0.986369i	$0.447383\pi$
$468$		0			0
$469$	16.7225			0.772173
$470$		0			0
$471$	7.59969	−	36.9965i	0.350175	−	1.70471i
$472$		0			0
$473$	−3.51328	−	6.08518i	−0.161541	−	0.279797i
$474$		0			0
$475$	19.1723	+	33.2075i	0.879687	+	1.52366i
$476$		0			0
$477$	−3.53734	−	29.7358i	−0.161964	−	1.36151i
$478$		0			0
$479$	−18.3550			−0.838662			−0.419331	−	0.907833i	$-0.637735\pi$
$479$	−18.3550			−0.838662			−0.419331	+	0.907833i	$0.637735\pi$
$480$		0			0
$481$	0.211211	−	3.29579i	0.00963038	−	0.150275i
$482$		0			0
$483$	9.09599	+	8.07807i	0.413882	+	0.367565i
$484$		0			0
$485$	−17.0934	+	29.6066i	−0.776170	+	1.34437i
$486$		0			0
$487$	−14.3769	+	24.9015i	−0.651479	+	1.12839i	0.331285	+	0.943531i	$0.392518\pi$
$487$	−14.3769	+	24.9015i	−0.651479	+	1.12839i	−0.982764	+	0.184864i	$0.940816\pi$
$488$		0			0
$489$	19.5036	−	6.48496i	0.881985	−	0.293260i
$490$		0			0
$491$	−12.2509	+	21.2193i	−0.552877	+	0.957612i	0.445188	+	0.895437i	$0.353137\pi$
$491$	−12.2509	+	21.2193i	−0.552877	+	0.957612i	−0.998065	+	0.0621744i	$0.980196\pi$
$492$		0			0
$493$	−2.96175	+	5.12990i	−0.133390	+	0.231039i
$494$		0			0
$495$	14.8837	−	11.1279i	0.668971	−	0.500162i
$496$		0			0
$497$	3.85594			0.172963
$498$		0			0
$499$	−16.7052	−	28.9342i	−0.747827	−	1.29527i	−0.948862	−	0.315690i	$-0.897764\pi$
$499$	−16.7052	−	28.9342i	−0.747827	−	1.29527i	0.201036	−	0.979584i	$-0.435569\pi$
$500$		0			0
$501$	23.3755	−	7.77237i	1.04434	−	0.347244i
$502$		0			0
$503$	−9.85083	+	17.0621i	−0.439227	+	0.760763i	−0.997630	−	0.0688067i	$-0.978081\pi$
$503$	−9.85083	+	17.0621i	−0.439227	+	0.760763i	0.558403	+	0.829570i	$0.311414\pi$
$504$		0			0
$505$	24.2079	+	41.9294i	1.07724	+	1.86583i
$506$		0			0
$507$	−7.30900	+	21.2974i	−0.324604	+	0.945850i
$508$		0			0
$509$	3.03285	−	5.25305i	0.134429	−	0.232837i	−0.790950	−	0.611880i	$-0.790413\pi$
$509$	3.03285	−	5.25305i	0.134429	−	0.232837i	0.925379	+	0.379043i	$0.123747\pi$
$510$		0			0
$511$	−2.39717	−	4.15202i	−0.106045	−	0.183674i
$512$		0			0
$513$	14.3673	+	30.5655i	0.634334	+	1.34950i
$514$		0			0
$515$	12.2598	−	21.2346i	0.540232	−	0.935710i
$516$		0			0
$517$	−9.49143	+	16.4396i	−0.417432	+	0.723014i
$518$		0			0
$519$	−6.22203	+	30.2898i	−0.273117	+	1.32958i
$520$		0			0
$521$	20.0607			0.878876			0.439438	−	0.898273i	$-0.355178\pi$
$521$	20.0607			0.878876			0.439438	+	0.898273i	$0.355178\pi$
$522$		0			0
$523$	15.6061	+	27.0306i	0.682408	+	1.18196i	0.974244	+	0.225497i	$0.0724004\pi$
$523$	15.6061	+	27.0306i	0.682408	+	1.18196i	−0.291836	+	0.956468i	$0.594266\pi$
$524$		0			0
$525$	14.2584	+	12.6628i	0.622287	+	0.552648i
$526$		0			0
$527$	−15.3664			−0.669371
$528$		0			0
$529$	4.41820	+	7.65254i	0.192096	+	0.332719i
$530$		0			0
$531$	1.03901	+	8.73418i	0.0450891	+	0.379031i
$532$		0			0
$533$	−7.52049	+	3.72229i	−0.325749	+	0.161230i
$534$		0			0
$535$	−15.7572	+	27.2923i	−0.681245	+	1.17995i
$536$		0			0
$537$	2.12191	−	10.3298i	0.0915670	−	0.445763i
$538$		0			0
$539$	−3.29960	+	5.71508i	−0.142124	+	0.246166i
$540$		0			0
$541$	23.6592			1.01719			0.508594	−	0.861007i	$-0.330166\pi$
$541$	23.6592			1.01719			0.508594	+	0.861007i	$0.330166\pi$
$542$		0			0
$543$	−7.42633	−	6.59526i	−0.318694	−	0.283030i
$544$		0			0
$545$	14.9848	+	25.9545i	0.641880	+	1.11177i
$546$		0			0
$547$	−13.4497	+	23.2955i	−0.575066	+	0.996044i	0.420968	+	0.907075i	$0.361690\pi$
$547$	−13.4497	+	23.2955i	−0.575066	+	0.996044i	−0.996034	+	0.0889686i	$0.971643\pi$
$548$		0			0
$549$	34.4768	−	25.7769i	1.47143	−	1.10013i
$550$		0			0
$551$	4.34198	−	7.52052i	0.184974	−	0.320385i
$552$		0			0
$553$	−26.3198			−1.11923
$554$		0			0
$555$	4.97015	−	1.65258i	0.210971	−	0.0701480i
$556$		0			0
$557$	9.16528	+	15.8747i	0.388346	+	0.672634i	0.992227	−	0.124440i	$-0.0397134\pi$
$557$	9.16528	+	15.8747i	0.388346	+	0.672634i	−0.603882	+	0.797074i	$0.706380\pi$
$558$		0			0
$559$	−0.863517	+	13.4746i	−0.0365229	+	0.569913i
$560$		0			0
$561$	13.6728	−	4.54622i	0.577268	−	0.191942i
$562$		0			0
$563$	11.4336			0.481871			0.240935	−	0.970541i	$-0.422546\pi$
$563$	11.4336			0.481871			0.240935	+	0.970541i	$0.422546\pi$
$564$		0			0
$565$	21.1553	+	36.6421i	0.890010	+	1.54154i
$566$		0			0
$567$	11.5763	+	12.1699i	0.486158	+	0.511088i
$568$		0			0
$569$	−1.40239			−0.0587914			−0.0293957	−	0.999568i	$-0.509358\pi$
$569$	−1.40239			−0.0587914			−0.0293957	+	0.999568i	$0.509358\pi$
$570$		0			0
$571$	−20.3941	−	35.3237i	−0.853468	−	1.47825i	−0.878059	−	0.478552i	$-0.841162\pi$
$571$	−20.3941	−	35.3237i	−0.853468	−	1.47825i	0.0245910	−	0.999698i	$-0.492172\pi$
$572$		0			0
$573$	4.27732	−	20.8227i	0.178688	−	0.869880i
$574$		0			0
$575$	−11.1011	−	19.2276i	−0.462946	−	0.801846i
$576$		0			0
$577$	−11.7497			−0.489146			−0.244573	−	0.969631i	$-0.578648\pi$
$577$	−11.7497			−0.489146			−0.244573	+	0.969631i	$0.578648\pi$
$578$		0			0
$579$	40.8483	−	13.5821i	1.69760	−	0.564452i
$580$		0			0
$581$	−5.04939			−0.209484
$582$		0			0
$583$	18.7292			0.775685
$584$		0			0
$585$	−35.6575	+	1.94186i	−1.47426	+	0.0802861i
$586$		0			0
$587$	−14.2447			−0.587942			−0.293971	−	0.955814i	$-0.594977\pi$
$587$	−14.2447			−0.587942			−0.293971	+	0.955814i	$0.594977\pi$
$588$		0			0
$589$	22.5274			0.928226
$590$		0			0
$591$	2.65435	−	12.9218i	0.109186	−	0.531533i
$592$		0			0
$593$	−26.9551			−1.10691			−0.553457	−	0.832878i	$-0.686692\pi$
$593$	−26.9551			−1.10691			−0.553457	+	0.832878i	$0.686692\pi$
$594$		0			0
$595$	13.6585	+	23.6571i	0.559942	+	0.969848i
$596$		0			0
$597$	37.8931	−	12.5995i	1.55086	−	0.515662i
$598$		0			0
$599$	−14.1367	−	24.4855i	−0.577609	−	1.00045i	−0.995753	−	0.0920675i	$-0.970652\pi$
$599$	−14.1367	−	24.4855i	−0.577609	−	1.00045i	0.418144	−	0.908381i	$-0.362681\pi$
$600$		0			0
$601$	−29.3060			−1.19542			−0.597708	−	0.801714i	$-0.703922\pi$
$601$	−29.3060			−1.19542			−0.597708	+	0.801714i	$0.703922\pi$
$602$		0			0
$603$	−24.7046	−	10.5966i	−1.00605	−	0.431526i
$604$		0			0
$605$	−12.3463	−	21.3844i	−0.501948	−	0.869400i
$606$		0			0
$607$	−30.4950			−1.23775			−0.618877	−	0.785488i	$-0.712412\pi$
$607$	−30.4950			−1.23775			−0.618877	+	0.785488i	$0.712412\pi$
$608$		0			0
$609$	0.868986	−	4.23036i	0.0352131	−	0.171423i
$610$		0			0
$611$	32.6921	−	16.1810i	1.32258	−	0.654614i
$612$		0			0
$613$	−1.13510	−	1.96606i	−0.0458464	−	0.0794083i	0.842192	−	0.539178i	$-0.181265\pi$
$613$	−1.13510	−	1.96606i	−0.0458464	−	0.0794083i	−0.888038	+	0.459770i	$0.847932\pi$
$614$		0			0
$615$	−9.95056	−	8.83701i	−0.401245	−	0.356343i
$616$		0			0
$617$	−4.99497			−0.201090			−0.100545	−	0.994933i	$-0.532059\pi$
$617$	−4.99497			−0.201090			−0.100545	+	0.994933i	$0.532059\pi$
$618$		0			0
$619$	−20.1821	+	34.9564i	−0.811187	+	1.40502i	0.100848	+	0.994902i	$0.467845\pi$
$619$	−20.1821	+	34.9564i	−0.811187	+	1.40502i	−0.912034	+	0.410114i	$0.865489\pi$
$620$		0			0
$621$	−8.31889	−	17.6978i	−0.333826	−	0.710190i
$622$		0			0
$623$	8.58773	−	14.8744i	0.344060	−	0.595930i
$624$		0			0
$625$	9.84706	+	17.0556i	0.393882	+	0.682224i
$626$		0			0
$627$	−20.0446	+	6.66484i	−0.800505	+	0.266168i
$628$		0			0
$629$	4.06103			0.161924
$630$		0			0
$631$	11.3281	−	19.6209i	0.450966	−	0.781096i	−0.547480	−	0.836819i	$-0.684413\pi$
$631$	11.3281	−	19.6209i	0.450966	−	0.781096i	0.998446	+	0.0557225i	$0.0177462\pi$
$632$		0			0
$633$	−32.4836	+	10.8008i	−1.29111	+	0.429293i
$634$		0			0
$635$	6.08912	−	10.5467i	0.241639	−	0.418532i
$636$		0			0
$637$	11.3651	−	5.62517i	0.450301	−	0.222878i
$638$		0			0
$639$	−5.69648	−	2.44340i	−0.225349	−	0.0966596i
$640$		0			0
$641$	−8.21101	−	14.2219i	−0.324315	−	0.561731i	0.657058	−	0.753840i	$-0.271801\pi$
$641$	−8.21101	−	14.2219i	−0.324315	−	0.561731i	−0.981374	+	0.192109i	$0.938467\pi$
$642$		0			0
$643$	1.65374			0.0652172			0.0326086	−	0.999468i	$-0.489619\pi$
$643$	1.65374			0.0652172			0.0326086	+	0.999468i	$0.489619\pi$
$644$		0			0
$645$	−20.3200	+	6.75641i	−0.800100	+	0.266034i
$646$		0			0
$647$	15.5953	+	27.0119i	0.613115	+	1.06195i	0.990712	+	0.135976i	$0.0434171\pi$
$647$	15.5953	+	27.0119i	0.613115	+	1.06195i	−0.377597	+	0.925970i	$0.623250\pi$
$648$		0			0
$649$	−5.50126			−0.215943
$650$		0			0
$651$	10.6310	−	3.53483i	0.416664	−	0.138541i
$652$		0			0
$653$	−11.5210	+	19.9549i	−0.450850	+	0.780896i	−0.998439	−	0.0558518i	$-0.982213\pi$
$653$	−11.5210	+	19.9549i	−0.450850	+	0.780896i	0.547589	+	0.836748i	$0.315546\pi$
$654$		0			0
$655$	27.6510	−	47.8929i	1.08041	−	1.87133i
$656$		0			0
$657$	0.910382	+	7.65291i	0.0355174	+	0.298568i
$658$		0			0
$659$	−19.3490	−	33.5134i	−0.753729	−	1.30550i	−0.946003	−	0.324156i	$-0.894920\pi$
$659$	−19.3490	−	33.5134i	−0.753729	−	1.30550i	0.192274	−	0.981341i	$-0.438414\pi$
$660$		0			0
$661$	1.51740	−	2.62822i	0.0590202	−	0.102226i	−0.835006	−	0.550241i	$-0.814536\pi$
$661$	1.51740	−	2.62822i	0.0590202	−	0.102226i	0.894026	+	0.448015i	$0.147869\pi$
$662$		0			0
$663$	−26.7098	−	7.29436i	−1.03732	−	0.283289i
$664$		0			0
$665$	−20.0235	−	34.6818i	−0.776480	−	1.34490i
$666$		0			0
$667$	−2.51407	+	4.35449i	−0.0973450	+	0.168607i
$668$		0			0
$669$	−7.20983	−	6.40299i	−0.278748	−	0.247554i
$670$		0			0
$671$	13.4619	+	23.3168i	0.519693	+	0.900134i
$672$		0			0
$673$	8.48806			0.327191			0.163595	−	0.986528i	$-0.447691\pi$
$673$	8.48806			0.327191			0.163595	+	0.986528i	$0.447691\pi$
$674$		0			0
$675$	−13.0403	−	27.7422i	−0.501920	−	1.06780i
$676$		0			0
$677$	−9.65503	+	16.7230i	−0.371073	+	0.642717i	−0.989731	−	0.142943i	$-0.954343\pi$
$677$	−9.65503	+	16.7230i	−0.371073	+	0.642717i	0.618658	+	0.785661i	$0.287677\pi$
$678$		0			0
$679$	9.66270	−	16.7363i	0.370820	−	0.642280i
$680$		0			0
$681$	2.96295	−	14.4241i	0.113541	−	0.552734i
$682$		0			0
$683$	12.5757	−	21.7818i	0.481196	−	0.833456i	−0.518571	−	0.855034i	$-0.673536\pi$
$683$	12.5757	−	21.7818i	0.481196	−	0.833456i	0.999767	+	0.0215787i	$0.00686923\pi$
$684$		0			0
$685$	−3.46548	+	6.00239i	−0.132409	+	0.229340i
$686$		0			0
$687$	5.20462	−	25.3369i	0.198569	−	0.966664i
$688$		0			0
$689$	−29.9536	−	19.9515i	−1.14114	−	0.760090i
$690$		0			0
$691$	−48.3376			−1.83885			−0.919425	−	0.393267i	$-0.871345\pi$
$691$	−48.3376			−1.83885			−0.919425	+	0.393267i	$0.871345\pi$
$692$		0			0
$693$	−8.41358	+	6.29049i	−0.319606	+	0.238956i
$694$		0			0
$695$	12.9555	+	22.4395i	0.491428	+	0.851179i
$696$		0			0
$697$	−5.15922	−	8.93603i	−0.195419	−	0.338476i
$698$		0			0
$699$	−31.4330	−	27.9154i	−1.18891	−	1.05586i
$700$		0			0
$701$	−5.76955			−0.217913			−0.108956	−	0.994047i	$-0.534751\pi$
$701$	−5.76955			−0.217913			−0.108956	+	0.994047i	$0.534751\pi$
$702$		0			0
$703$	−5.95355			−0.224542
$704$		0			0
$705$	43.2557	+	38.4151i	1.62911	+	1.44680i
$706$		0			0
$707$	−13.6845	−	23.7022i	−0.514658	−	0.891414i
$708$		0			0
$709$	−13.1418	−	22.7623i	−0.493551	−	0.854855i	0.506422	−	0.862286i	$-0.330968\pi$
$709$	−13.1418	−	22.7623i	−0.493551	−	0.854855i	−0.999972	+	0.00743096i	$0.997635\pi$
$710$		0			0
$711$	38.8830	+	16.6782i	1.45823	+	0.625480i
$712$		0			0
$713$	−13.0437			−0.488490
$714$		0			0
$715$	1.42840	−	22.2891i	0.0534190	−	0.833565i
$716$		0			0
$717$	4.49602	−	21.8873i	0.167907	−	0.817398i
$718$		0			0
$719$	−21.7139	+	37.6096i	−0.809793	+	1.40260i	0.103215	+	0.994659i	$0.467087\pi$
$719$	−21.7139	+	37.6096i	−0.809793	+	1.40260i	−0.913007	+	0.407943i	$0.866246\pi$
$720$		0			0
$721$	−6.93035	+	12.0037i	−0.258100	+	0.447042i
$722$		0			0
$723$	−3.35237	+	16.3199i	−0.124676	+	0.606942i
$724$		0			0
$725$	−3.94092	+	6.82587i	−0.146362	+	0.253506i
$726$		0			0
$727$	14.0746	−	24.3779i	0.521997	−	0.904125i	−0.477675	−	0.878536i	$-0.658521\pi$
$727$	14.0746	−	24.3779i	0.521997	−	0.904125i	0.999673	−	0.0255891i	$-0.00814616\pi$
$728$		0			0
$729$	−9.39019	−	25.3145i	−0.347785	−	0.937574i
$730$		0			0
$731$	−16.6032			−0.614091
$732$		0			0
$733$	−2.35921	−	4.08627i	−0.0871394	−	0.150930i	0.819161	−	0.573563i	$-0.194439\pi$
$733$	−2.35921	−	4.08627i	−0.0871394	−	0.150930i	−0.906301	+	0.422633i	$0.861106\pi$
$734$		0			0
$735$	15.0374	+	13.3546i	0.554664	+	0.492593i
$736$		0			0
$737$	8.40638	−	14.5603i	0.309653	−	0.536334i
$738$		0			0
$739$	−11.0290	−	19.1028i	−0.405709	−	0.702709i	0.588695	−	0.808355i	$-0.299642\pi$
$739$	−11.0290	−	19.1028i	−0.405709	−	0.702709i	−0.994404	+	0.105647i	$0.966309\pi$
$740$		0			0
$741$	39.1571	+	10.6937i	1.43847	+	0.392841i
$742$		0			0
$743$	−12.3469	+	21.3854i	−0.452963	+	0.784556i	−0.998569	−	0.0534867i	$-0.982967\pi$
$743$	−12.3469	+	21.3854i	−0.452963	+	0.784556i	0.545605	+	0.838042i	$0.316300\pi$
$744$		0			0
$745$	31.4243	+	54.4284i	1.15130	+	1.99410i
$746$		0			0
$747$	7.45959	+	3.19966i	0.272932	+	0.117069i
$748$		0			0
$749$	8.90740	−	15.4281i	0.325469	−	0.563729i
$750$		0			0
$751$	4.11594	−	7.12903i	0.150193	−	0.260142i	−0.781105	−	0.624399i	$-0.785344\pi$
$751$	4.11594	−	7.12903i	0.150193	−	0.260142i	0.931298	+	0.364257i	$0.118677\pi$
$752$		0			0
$753$	−20.1650	+	6.70488i	−0.734855	+	0.244339i
$754$		0			0
$755$	−64.5902			−2.35068
$756$		0			0
$757$	3.82380	+	6.62301i	0.138978	+	0.240718i	0.927110	−	0.374789i	$-0.122285\pi$
$757$	3.82380	+	6.62301i	0.138978	+	0.240718i	−0.788132	+	0.615506i	$0.788951\pi$
$758$		0			0
$759$	11.6061	−	3.85904i	0.421275	−	0.140074i
$760$		0			0
$761$	38.9572			1.41220			0.706098	−	0.708114i	$-0.250454\pi$
$761$	38.9572			1.41220			0.706098	+	0.708114i	$0.250454\pi$
$762$		0			0
$763$	−8.47078	−	14.6718i	−0.306663	−	0.531155i
$764$		0			0
$765$	−5.18712	−	43.6043i	−0.187541	−	1.57652i
$766$		0			0
$767$	8.79814	+	5.86027i	0.317683	+	0.211602i
$768$		0			0
$769$	10.4079	−	18.0270i	0.375318	−	0.650070i	−0.615056	−	0.788483i	$-0.710867\pi$
$769$	10.4079	−	18.0270i	0.375318	−	0.650070i	0.990375	+	0.138413i	$0.0442001\pi$
$770$		0			0
$771$	−30.7555	+	10.2262i	−1.10763	+	0.368289i
$772$		0			0
$773$	−12.2723	+	21.2563i	−0.441405	+	0.764537i	−0.997794	−	0.0663855i	$-0.978853\pi$
$773$	−12.2723	+	21.2563i	−0.441405	+	0.764537i	0.556389	+	0.830922i	$0.312187\pi$
$774$		0			0
$775$	−20.4466			−0.734464
$776$		0			0
$777$	−2.80957	+	0.934184i	−0.100793	+	0.0335137i
$778$		0			0
$779$	7.56351	+	13.1004i	0.270991	+	0.469370i
$780$		0			0
$781$	1.93838	−	3.35737i	0.0693606	−	0.120136i
$782$		0			0
$783$	−3.96444	+	5.69898i	−0.141678	+	0.203665i
$784$		0			0
$785$	35.9953	−	62.3457i	1.28473	−	2.22521i
$786$		0			0
$787$	32.5269			1.15946			0.579730	−	0.814809i	$-0.303158\pi$
$787$	32.5269			1.15946			0.579730	+	0.814809i	$0.303158\pi$
$788$		0			0
$789$	26.6847	+	23.6985i	0.950000	+	0.843687i
$790$		0			0
$791$	−11.9589	−	20.7134i	−0.425208	−	0.736483i
$792$		0			0
$793$	3.30876	−	51.6309i	0.117498	−	1.83347i
$794$		0			0
$795$	11.4850	−	55.9109i	0.407332	−	1.98296i
$796$		0			0
$797$	−51.8322			−1.83599			−0.917995	−	0.396591i	$-0.870193\pi$
$797$	−51.8322			−1.83599			−0.917995	+	0.396591i	$0.870193\pi$
$798$		0			0
$799$	22.4275	+	38.8455i	0.793426	+	1.37425i
$800$		0			0
$801$	−22.1124	+	16.5325i	−0.781302	+	0.584148i
$802$		0			0
$803$	−4.82022			−0.170102
$804$		0			0
$805$	11.5939	+	20.0812i	0.408632	+	0.707771i
$806$		0			0
$807$	29.0135	−	9.64699i	1.02132	−	0.339590i
$808$		0			0
$809$	−15.9371	−	27.6039i	−0.560319	−	0.970500i	−0.997468	−	0.0711115i	$-0.977345\pi$
$809$	−15.9371	−	27.6039i	−0.560319	−	0.970500i	0.437150	−	0.899389i	$-0.355988\pi$
$810$		0			0
$811$	−7.14832			−0.251011			−0.125506	−	0.992093i	$-0.540055\pi$
$811$	−7.14832			−0.251011			−0.125506	+	0.992093i	$0.540055\pi$
$812$		0			0
$813$	−5.47053	+	26.6314i	−0.191860	+	0.934004i
$814$		0			0
$815$	39.1766			1.37230
$816$		0			0
$817$	24.3405			0.851568
$818$		0			0
$819$	20.1568	−	1.09771i	0.704336	−	0.0383572i
$820$		0			0
$821$	−10.3484			−0.361160			−0.180580	−	0.983560i	$-0.557797\pi$
$821$	−10.3484			−0.361160			−0.180580	+	0.983560i	$0.557797\pi$
$822$		0			0
$823$	38.9271			1.35691			0.678457	−	0.734640i	$-0.262649\pi$
$823$	38.9271			1.35691			0.678457	+	0.734640i	$0.262649\pi$
$824$		0			0
$825$	18.1931	−	6.04922i	0.633404	−	0.210607i
$826$		0			0
$827$	19.5838			0.680994			0.340497	−	0.940246i	$-0.389405\pi$
$827$	19.5838			0.680994			0.340497	+	0.940246i	$0.389405\pi$
$828$		0			0
$829$	−8.13898	−	14.0971i	−0.282678	−	0.489613i	0.689365	−	0.724414i	$-0.257890\pi$
$829$	−8.13898	−	14.0971i	−0.282678	−	0.489613i	−0.972044	+	0.234801i	$0.924556\pi$
$830$		0			0
$831$	3.13296	−	15.2517i	0.108681	−	0.529077i
$832$		0			0
$833$	7.79669	+	13.5043i	0.270139	+	0.467895i
$834$		0			0
$835$	46.9540			1.62491
$836$		0			0
$837$	−17.9455	−	1.51451i	−0.620286	−	0.0523491i
$838$		0			0
$839$	−25.5149	−	44.1932i	−0.880873	−	1.52572i	−0.850371	−	0.526183i	$-0.823623\pi$
$839$	−25.5149	−	44.1932i	−0.880873	−	1.52572i	−0.0305021	−	0.999535i	$-0.509711\pi$
$840$		0			0
$841$	−27.2150			−0.938448
$842$		0			0
$843$	30.1716	−	10.0320i	1.03916	−	0.345522i
$844$		0			0
$845$	−26.0281	+	34.1253i	−0.895394	+	1.17395i
$846$		0			0
$847$	6.97923	+	12.0884i	0.239809	+	0.415362i
$848$		0			0
$849$	4.98225	−	1.65660i	0.170991	−	0.0568544i
$850$		0			0
$851$	3.44719			0.118168
$852$		0			0
$853$	16.9863	−	29.4212i	0.581601	−	1.00736i	−0.413689	−	0.910418i	$-0.635760\pi$
$853$	16.9863	−	29.4212i	0.581601	−	1.00736i	0.995290	−	0.0969437i	$-0.0309067\pi$
$854$		0			0
$855$	7.60441	+	63.9247i	0.260065	+	2.18618i
$856$		0			0
$857$	7.27876	−	12.6072i	0.248638	−	0.430653i	−0.714510	−	0.699625i	$-0.753350\pi$
$857$	7.27876	−	12.6072i	0.248638	−	0.430653i	0.963148	+	0.268972i	$0.0866838\pi$
$858$		0			0
$859$	−2.44195	−	4.22958i	−0.0833181	−	0.144311i	0.821355	−	0.570417i	$-0.193218\pi$
$859$	−2.44195	−	4.22958i	−0.0833181	−	0.144311i	−0.904673	+	0.426106i	$0.859885\pi$
$860$		0			0
$861$	5.62495	+	4.99547i	0.191698	+	0.170245i
$862$		0			0
$863$	44.0094			1.49810			0.749048	−	0.662515i	$-0.230511\pi$
$863$	44.0094			1.49810			0.749048	+	0.662515i	$0.230511\pi$
$864$		0			0
$865$	−29.4701	+	51.0438i	−1.00201	+	1.73554i
$866$		0			0
$867$	0.925997	−	4.50790i	0.0314485	−	0.153096i
$868$		0			0
$869$	−13.2309	+	22.9167i	−0.448829	+	0.777395i
$870$		0			0
$871$	−28.9547	+	14.3312i	−0.981094	+	0.485595i
$872$		0			0
$873$	−24.8803	+	18.6020i	−0.842071	+	0.629582i
$874$		0			0
$875$	2.77072	+	4.79904i	0.0936676	+	0.162237i
$876$		0			0
$877$	0.888654			0.0300077			0.0150039	−	0.999887i	$-0.495224\pi$
$877$	0.888654			0.0300077			0.0150039	+	0.999887i	$0.495224\pi$
$878$		0			0
$879$	3.83094	+	3.40222i	0.129214	+	0.114754i
$880$		0			0
$881$	−18.0334	−	31.2348i	−0.607561	−	1.05233i	−0.991641	−	0.129027i	$-0.958815\pi$
$881$	−18.0334	−	31.2348i	−0.607561	−	1.05233i	0.384080	−	0.923300i	$-0.374519\pi$
$882$		0			0
$883$	−42.4663			−1.42910			−0.714552	−	0.699582i	$-0.753369\pi$
$883$	−42.4663			−1.42910			−0.714552	+	0.699582i	$0.753369\pi$
$884$		0			0
$885$	−3.37345	+	16.4225i	−0.113397	+	0.552036i
$886$		0			0
$887$	2.01167	−	3.48431i	0.0675453	−	0.116992i	−0.830275	−	0.557354i	$-0.811817\pi$
$887$	2.01167	−	3.48431i	0.0675453	−	0.116992i	0.897820	+	0.440362i	$0.145150\pi$
$888$		0			0
$889$	−3.44211	+	5.96192i	−0.115445	+	0.199956i
$890$		0			0
$891$	16.4157	−	3.96165i	0.549947	−	0.132720i
$892$		0			0
$893$	−32.8790	−	56.9482i	−1.10026	−	1.90570i
$894$		0			0
$895$	10.0502	−	17.4075i	0.335942	−	0.581869i
$896$		0			0
$897$	−22.6725	−	6.19178i	−0.757013	−	0.206738i
$898$		0			0
$899$	2.31528	+	4.01018i	0.0772189	+	0.133747i
$900$		0			0
$901$	22.1278	−	38.3265i	0.737184	−	1.27684i
$902$		0			0
$903$	11.4867	−	3.81933i	0.382253	−	0.127099i
$904$		0			0
$905$	−9.46573	−	16.3951i	−0.314652	−	0.544993i
$906$		0			0
$907$	−27.4963			−0.912999			−0.456500	−	0.889724i	$-0.650897\pi$
$907$	−27.4963			−0.912999			−0.456500	+	0.889724i	$0.650897\pi$
$908$		0			0
$909$	5.19701	+	43.6874i	0.172374	+	1.44902i
$910$		0			0
$911$	−3.01144	+	5.21596i	−0.0997734	+	0.172813i	−0.911591	−	0.411099i	$-0.865145\pi$
$911$	−3.01144	+	5.21596i	−0.0997734	+	0.172813i	0.811817	+	0.583911i	$0.198478\pi$
$912$		0			0
$913$	−2.53832	+	4.39650i	−0.0840062	+	0.145503i
$914$		0			0
$915$	77.8609	−	25.8888i	2.57400	−	0.855856i
$916$		0			0
$917$	−15.6308	+	27.0733i	−0.516175	+	0.894040i
$918$		0			0
$919$	−9.16320	+	15.8711i	−0.302266	+	0.523540i	−0.976649	−	0.214842i	$-0.931076\pi$
$919$	−9.16320	+	15.8711i	−0.302266	+	0.523540i	0.674383	+	0.738382i	$0.264410\pi$
$920$		0			0
$921$	9.57160	+	8.50046i	0.315395	+	0.280100i
$922$		0			0
$923$	−6.67651	+	3.30455i	−0.219760	+	0.108771i
$924$		0			0
$925$	5.40363			0.177670
$926$		0			0
$927$	17.8448	−	13.3418i	0.586101	−	0.438204i
$928$		0			0
$929$	5.58721	+	9.67732i	0.183310	+	0.317503i	0.943006	−	0.332776i	$-0.107985\pi$
$929$	5.58721	+	9.67732i	0.183310	+	0.317503i	−0.759696	+	0.650279i	$0.774652\pi$
$930$		0			0
$931$	−11.4301	−	19.7975i	−0.374606	−	0.648836i
$932$		0			0
$933$	4.92490	−	23.9752i	0.161234	−	0.784912i
$934$		0			0
$935$	27.4644			0.898181
$936$		0			0
$937$	27.5887			0.901285			0.450642	−	0.892705i	$-0.351195\pi$
$937$	27.5887			0.901285			0.450642	+	0.892705i	$0.351195\pi$
$938$		0			0
$939$	18.7131	−	6.22210i	0.610678	−	0.203051i
$940$		0			0
$941$	−16.1229	−	27.9256i	−0.525591	−	0.910350i	−0.999556	−	0.0298061i	$-0.990511\pi$
$941$	−16.1229	−	27.9256i	−0.525591	−	0.910350i	0.473965	−	0.880544i	$-0.342822\pi$
$942$		0			0
$943$	−4.37938	−	7.58530i	−0.142612	−	0.247011i
$944$		0			0
$945$	13.6192	+	28.9739i	0.443033	+	0.942520i
$946$		0			0
$947$	−6.62254			−0.215204			−0.107602	−	0.994194i	$-0.534317\pi$
$947$	−6.62254			−0.215204			−0.107602	+	0.994194i	$0.534317\pi$
$948$		0			0
$949$	7.70896	+	5.13478i	0.250243	+	0.166682i
$950$		0			0
$951$	18.3581	−	6.10406i	0.595301	−	0.197938i
$952$		0			0
$953$	26.5364	−	45.9624i	0.859598	−	1.48887i	−0.0127147	−	0.999919i	$-0.504047\pi$
$953$	26.5364	−	45.9624i	0.859598	−	1.48887i	0.872313	−	0.488948i	$-0.162619\pi$
$954$		0			0
$955$	20.2592	−	35.0899i	0.655572	−	1.13548i
$956$		0			0
$957$	−3.24654	−	2.88322i	−0.104946	−	0.0932014i
$958$		0			0
$959$	1.95900	−	3.39309i	0.0632594	−	0.109569i
$960$		0			0
$961$	9.49383	−	16.4438i	0.306253	−	0.530445i
$962$		0			0
$963$	−22.9355	+	17.1479i	−0.739085	+	0.552584i
$964$		0			0
$965$	82.0512			2.64132
$966$		0			0
$967$	8.71147	+	15.0887i	0.280142	+	0.485220i	0.971419	−	0.237369i	$-0.0762851\pi$
$967$	8.71147	+	15.0887i	0.280142	+	0.485220i	−0.691278	+	0.722589i	$0.742952\pi$
$968$		0			0
$969$	−10.0433	+	48.8925i	−0.322638	+	1.57065i
$970$		0			0
$971$	−8.14921	+	14.1148i	−0.261520	+	0.452967i	−0.966646	−	0.256116i	$-0.917557\pi$
$971$	−8.14921	+	14.1148i	−0.261520	+	0.452967i	0.705126	+	0.709082i	$0.250891\pi$
$972$		0			0
$973$	−7.32358	−	12.6848i	−0.234783	−	0.406656i
$974$		0			0
$975$	−35.5402	−	9.70591i	−1.13820	−	0.310838i
$976$		0			0
$977$	−23.5575	+	40.8028i	−0.753671	+	1.30540i	0.192361	+	0.981324i	$0.438386\pi$
$977$	−23.5575	+	40.8028i	−0.753671	+	1.30540i	−0.946032	+	0.324073i	$0.894948\pi$
$978$		0			0
$979$	−8.63408	−	14.9547i	−0.275946	−	0.477953i
$980$		0			0
$981$	3.21698	+	27.0428i	0.102710	+	0.863409i
$982$		0			0
$983$	3.42744	−	5.93649i	0.109318	−	0.189345i	−0.806176	−	0.591676i	$-0.798467\pi$
$983$	3.42744	−	5.93649i	0.109318	−	0.189345i	0.915494	+	0.402331i	$0.131800\pi$
$984$		0			0
$985$	12.5721	−	21.7756i	0.400582	−	0.693828i
$986$		0			0
$987$	−24.4520	−	21.7156i	−0.778316	−	0.691216i
$988$		0			0
$989$	−14.0935			−0.448148
$990$		0			0
$991$	−0.988777	−	1.71261i	−0.0314095	−	0.0544029i	0.849893	−	0.526955i	$-0.176666\pi$
$991$	−0.988777	−	1.71261i	−0.0314095	−	0.0544029i	−0.881303	+	0.472552i	$0.843333\pi$
$992$		0			0
$993$	−5.93575	+	28.8962i	−0.188365	+	0.916992i
$994$		0			0
$995$	76.1152			2.41301
$996$		0			0
$997$	25.9907	+	45.0171i	0.823132	+	1.42571i	0.903338	+	0.428929i	$0.141109\pi$
$997$	25.9907	+	45.0171i	0.823132	+	1.42571i	−0.0802062	+	0.996778i	$0.525558\pi$
$998$		0			0
$999$	4.74263	+	0.400255i	0.150050	+	0.0126635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.r.f.601.16	✓	40
3.2	odd	2		2808.2.r.f.289.3		40
9.4	even	3		936.2.s.f.913.12	yes	40
9.5	odd	6		2808.2.s.f.1225.3		40
13.9	even	3		936.2.s.f.529.12	yes	40
39.35	odd	6		2808.2.s.f.1153.3		40
117.22	even	3	inner	936.2.r.f.841.16	yes	40
117.113	odd	6		2808.2.r.f.2089.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.16	✓	40	1.1	even	1	trivial
936.2.r.f.841.16	yes	40	117.22	even	3	inner
936.2.s.f.529.12	yes	40	13.9	even	3
936.2.s.f.913.12	yes	40	9.4	even	3
2808.2.r.f.289.3		40	3.2	odd	2
2808.2.r.f.2089.3		40	117.113	odd	6
2808.2.s.f.1153.3		40	39.35	odd	6
2808.2.s.f.1225.3		40	9.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29506 + 1.15014i) q^{3} +(1.65071 + 2.85912i) q^{5} +(-0.933130 - 1.61623i) q^{7} +(0.354378 + 2.97900i) q^{9} -1.87633 q^{11} +(3.00081 + 1.99878i) q^{13} +(-1.15059 + 5.60128i) q^{15} +(-2.21681 + 3.83963i) q^{17} +(3.24988 - 5.62896i) q^{19} +(0.650419 - 3.16634i) q^{21} +(-1.88173 + 3.25925i) q^{23} +(-2.94970 + 5.10903i) q^{25} +(-2.96731 + 4.26557i) q^{27} +1.33604 q^{29} +(1.73294 + 3.00154i) q^{31} +(-2.42997 - 2.15804i) q^{33} +(3.08066 - 5.33585i) q^{35} +(-0.457982 - 0.793248i) q^{37} +(1.58737 + 6.03989i) q^{39} +(-1.16366 + 2.01552i) q^{41} +(1.87242 + 3.24312i) q^{43} +(-7.93232 + 5.93067i) q^{45} +(5.05850 - 8.76158i) q^{47} +(1.75854 - 3.04588i) q^{49} +(-7.28700 + 2.42293i) q^{51} -9.98182 q^{53} +(-3.09728 - 5.36465i) q^{55} +(10.6829 - 3.55206i) q^{57} +2.93192 q^{59} +(-7.17460 - 12.4268i) q^{61} +(4.48406 - 3.35255i) q^{63} +(-0.761271 + 11.8791i) q^{65} +(-4.48022 + 7.75996i) q^{67} +(-6.18553 + 2.05669i) q^{69} +(-1.03307 + 1.78932i) q^{71} +2.56896 q^{73} +(-9.69611 + 3.22396i) q^{75} +(1.75086 + 3.03258i) q^{77} +(7.05149 - 12.2135i) q^{79} +(-8.74883 + 2.11138i) q^{81} +(1.35281 - 2.34313i) q^{83} -14.6373 q^{85} +(1.73026 + 1.53663i) q^{87} +(4.60157 + 7.97016i) q^{89} +(0.430338 - 6.71512i) q^{91} +(-1.20791 + 5.88030i) q^{93} +21.4585 q^{95} +(5.17758 + 8.96783i) q^{97} +(-0.664931 - 5.58959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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