LMFDB - Embedded newform 1456.2.s.q.1121.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(113,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.113"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,1,0,-14] 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.59066497296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1121.2
Root			$-1.11000 + 1.92258i$ of defining polynomial
Character	$\chi$	$=$	1456.1121
Dual form			1456.2.s.q.113.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.274776 + 0.475925i) q^{3} -4.22001 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.34900 - 2.33653i) q^{9} +(-0.274776 - 0.475925i) q^{11} +(-2.95900 - 2.06017i) q^{13} +(-1.15956 - 2.00841i) q^{15} +(1.18944 - 2.06017i) q^{17} +(-1.80534 + 3.12694i) q^{19} -0.549551 q^{21} +(2.90945 + 5.03931i) q^{23} +12.8085 q^{25} +3.13134 q^{27} +(1.79945 + 3.11673i) q^{29} +5.14844 q^{31} +(0.151003 - 0.261545i) q^{33} +(2.11000 - 3.65463i) q^{35} +(0.164772 + 0.285393i) q^{37} +(0.167428 - 1.97435i) q^{39} +(3.14579 + 5.44866i) q^{41} +(1.61000 - 2.78861i) q^{43} +(-5.69278 + 9.86018i) q^{45} -8.20957 q^{47} +(-0.500000 - 0.866025i) q^{49} +1.30732 q^{51} +2.65866 q^{53} +(1.15956 + 2.00841i) q^{55} -1.98426 q^{57} +(-0.903765 + 1.56537i) q^{59} +(-0.304662 + 0.527691i) q^{61} +(1.34900 + 2.33653i) q^{63} +(12.4870 + 8.69395i) q^{65} +(5.18490 + 8.98052i) q^{67} +(-1.59889 + 2.76936i) q^{69} +(-5.59889 + 9.69756i) q^{71} +4.90621 q^{73} +(3.51945 + 6.09587i) q^{75} +0.549551 q^{77} +14.0171 q^{79} +(-3.18657 - 5.51931i) q^{81} +5.73159 q^{83} +(-5.01945 + 8.69395i) q^{85} +(-0.988887 + 1.71280i) q^{87} +(3.73378 + 6.46709i) q^{89} +(3.26366 - 1.53248i) q^{91} +(1.41467 + 2.45027i) q^{93} +(7.61856 - 13.1957i) q^{95} +(3.42035 - 5.92422i) q^{97} -1.48269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 14 q^{5} - 4 q^{7} - 7 q^{9} - q^{11} + 4 q^{13} + 3 q^{15} + 4 q^{17} + q^{19} - 2 q^{21} - 2 q^{23} + 10 q^{25} + 52 q^{27} - q^{29} + 8 q^{31} + 19 q^{33} + 7 q^{35} + 10 q^{37} - 20 q^{39}+ \cdots - 46 q^{99}+O(q^{100}) $ 8 * q + q^3 - 14 * q^5 - 4 * q^7 - 7 * q^9 - q^11 + 4 * q^13 + 3 * q^15 + 4 * q^17 + q^19 - 2 * q^21 - 2 * q^23 + 10 * q^25 + 52 * q^27 - q^29 + 8 * q^31 + 19 * q^33 + 7 * q^35 + 10 * q^37 - 20 * q^39 + 22 * q^41 + 3 * q^43 + 11 * q^45 - 4 * q^47 - 4 * q^49 - 14 * q^51 + 4 * q^53 - 3 * q^55 - 34 * q^57 - 8 * q^59 - 8 * q^61 - 7 * q^63 + 7 * q^65 - 6 * q^67 + 18 * q^69 - 14 * q^71 - 16 * q^73 - 7 * q^75 + 2 * q^77 + 52 * q^79 - 24 * q^81 - 5 * q^85 + 13 * q^87 + q^89 + 4 * q^91 + 7 * q^93 + 21 * q^95 - 3 * q^97 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$3$	0.274776	+	0.475925i	0.158642	+	0.274776i	0.934379	−	0.356280i	$-0.115955\pi$
$3$	0.274776	+	0.475925i	0.158642	+	0.274776i	−0.775737	+	0.631056i	$0.782622\pi$
$4$		0			0
$5$	−4.22001			−1.88724			−0.943622	−	0.331024i	$-0.892606\pi$
$5$	−4.22001			−1.88724			−0.943622	+	0.331024i	$0.892606\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	1.34900	−	2.33653i	0.449666	−	0.778844i
$10$		0			0
$11$	−0.274776	−	0.475925i	−0.0828480	−	0.143497i	0.821624	−	0.570030i	$-0.193068\pi$
$11$	−0.274776	−	0.475925i	−0.0828480	−	0.143497i	−0.904472	+	0.426533i	$0.859735\pi$
$12$		0			0
$13$	−2.95900	−	2.06017i	−0.820679	−	0.571389i
$13$	−2.95900	−	2.06017i	−0.820679	−	0.571389i
$14$		0			0
$15$	−1.15956	−	2.00841i	−0.299396	−	0.518569i
$16$		0			0
$17$	1.18944	−	2.06017i	0.288482	−	0.499665i	−0.684966	−	0.728575i	$-0.740183\pi$
$17$	1.18944	−	2.06017i	0.288482	−	0.499665i	0.973448	+	0.228910i	$0.0735161\pi$
$18$		0			0
$19$	−1.80534	+	3.12694i	−0.414174	+	0.717370i	−0.995341	−	0.0964139i	$-0.969263\pi$
$19$	−1.80534	+	3.12694i	−0.414174	+	0.717370i	0.581168	+	0.813784i	$0.302596\pi$
$20$		0			0
$21$	−0.549551			−0.119922
$22$		0			0
$23$	2.90945	+	5.03931i	0.606662	+	1.05077i	0.991786	+	0.127905i	$0.0408253\pi$
$23$	2.90945	+	5.03931i	0.606662	+	1.05077i	−0.385124	+	0.922865i	$0.625841\pi$
$24$		0			0
$25$	12.8085			2.56169
$26$		0			0
$27$	3.13134			0.602626
$28$		0			0
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	0.983321	−	0.181879i	$-0.0582179\pi$
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	−0.649172	+	0.760641i	$0.724885\pi$
$30$		0			0
$31$	5.14844			0.924688			0.462344	−	0.886701i	$-0.347009\pi$
$31$	5.14844			0.924688			0.462344	+	0.886701i	$0.347009\pi$
$32$		0			0
$33$	0.151003	−	0.261545i	0.0262863	−	0.0455292i
$34$		0			0
$35$	2.11000	−	3.65463i	0.356656	−	0.617746i
$36$		0			0
$37$	0.164772	+	0.285393i	0.0270883	+	0.0469183i	0.879252	−	0.476357i	$-0.158043\pi$
$37$	0.164772	+	0.285393i	0.0270883	+	0.0469183i	−0.852163	+	0.523276i	$0.824710\pi$
$38$		0			0
$39$	0.167428	−	1.97435i	0.0268099	−	0.316149i
$40$		0			0
$41$	3.14579	+	5.44866i	0.491289	+	0.850938i	0.999950	−	0.0100292i	$-0.00319244\pi$
$41$	3.14579	+	5.44866i	0.491289	+	0.850938i	−0.508660	+	0.860967i	$0.669859\pi$
$42$		0			0
$43$	1.61000	−	2.78861i	0.245523	−	0.425259i	−0.716755	−	0.697325i	$-0.754374\pi$
$43$	1.61000	−	2.78861i	0.245523	−	0.425259i	0.962279	+	0.272066i	$0.0877069\pi$
$44$		0			0
$45$	−5.69278	+	9.86018i	−0.848629	+	1.46987i
$46$		0			0
$47$	−8.20957			−1.19749			−0.598745	−	0.800940i	$-0.704334\pi$
$47$	−8.20957			−1.19749			−0.598745	+	0.800940i	$0.704334\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	1.30732			0.183061
$52$		0			0
$53$	2.65866			0.365196			0.182598	−	0.983188i	$-0.441549\pi$
$53$	2.65866			0.365196			0.182598	+	0.983188i	$0.441549\pi$
$54$		0			0
$55$	1.15956	+	2.00841i	0.156354	+	0.270814i
$56$		0			0
$57$	−1.98426			−0.262821
$58$		0			0
$59$	−0.903765	+	1.56537i	−0.117660	+	0.203793i	−0.918840	−	0.394630i	$-0.870873\pi$
$59$	−0.903765	+	1.56537i	−0.117660	+	0.203793i	0.801180	+	0.598424i	$0.204206\pi$
$60$		0			0
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	−0.884870	−	0.465838i	$-0.845753\pi$
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	0.845862	+	0.533401i	$0.179086\pi$
$62$		0			0
$63$	1.34900	+	2.33653i	0.169958	+	0.294375i
$64$		0			0
$65$	12.4870	+	8.69395i	1.54882	+	1.07835i
$66$		0			0
$67$	5.18490	+	8.98052i	0.633437	+	1.09714i	0.986844	+	0.161675i	$0.0516897\pi$
$67$	5.18490	+	8.98052i	0.633437	+	1.09714i	−0.353407	+	0.935470i	$0.614977\pi$
$68$		0			0
$69$	−1.59889	+	2.76936i	−0.192484	+	0.333392i
$70$		0			0
$71$	−5.59889	+	9.69756i	−0.664466	+	1.15089i	0.314964	+	0.949104i	$0.398008\pi$
$71$	−5.59889	+	9.69756i	−0.664466	+	1.15089i	−0.979430	+	0.201785i	$0.935326\pi$
$72$		0			0
$73$	4.90621			0.574228			0.287114	−	0.957896i	$-0.407304\pi$
$73$	4.90621			0.574228			0.287114	+	0.957896i	$0.407304\pi$
$74$		0			0
$75$	3.51945	+	6.09587i	0.406391	+	0.703891i
$76$		0			0
$77$	0.549551			0.0626272
$78$		0			0
$79$	14.0171			1.57705			0.788524	−	0.615004i	$-0.210846\pi$
$79$	14.0171			1.57705			0.788524	+	0.615004i	$0.210846\pi$
$80$		0			0
$81$	−3.18657	−	5.51931i	−0.354064	−	0.613257i
$82$		0			0
$83$	5.73159			0.629124			0.314562	−	0.949237i	$-0.398142\pi$
$83$	5.73159			0.629124			0.314562	+	0.949237i	$0.398142\pi$
$84$		0			0
$85$	−5.01945	+	8.69395i	−0.544436	+	0.942991i
$86$		0			0
$87$	−0.988887	+	1.71280i	−0.106020	+	0.183632i
$88$		0			0
$89$	3.73378	+	6.46709i	0.395779	+	0.685510i	0.993200	−	0.116418i	$-0.0371411\pi$
$89$	3.73378	+	6.46709i	0.395779	+	0.685510i	−0.597421	+	0.801928i	$0.703808\pi$
$90$		0			0
$91$	3.26366	−	1.53248i	0.342125	−	0.160648i
$92$		0			0
$93$	1.41467	+	2.45027i	0.146694	+	0.254082i
$94$		0			0
$95$	7.61856	−	13.1957i	0.781647	−	1.35385i
$96$		0			0
$97$	3.42035	−	5.92422i	0.347284	−	0.601514i	−0.638482	−	0.769637i	$-0.720437\pi$
$97$	3.42035	−	5.92422i	0.347284	−	0.601514i	0.985766	+	0.168123i	$0.0537706\pi$
$98$		0			0
$99$	−1.48269			−0.149015
$100$		0			0
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	0.686451	−	0.727176i	$-0.259168\pi$
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	−0.972978	+	0.230896i	$0.925834\pi$
$102$		0			0
$103$	−0.571776			−0.0563388			−0.0281694	−	0.999603i	$-0.508968\pi$
$103$	−0.571776			−0.0563388			−0.0281694	+	0.999603i	$0.508968\pi$
$104$		0			0
$105$	2.31911			0.226322
$106$		0			0
$107$	2.03578	+	3.52608i	0.196807	+	0.340879i	0.947491	−	0.319782i	$-0.103610\pi$
$107$	2.03578	+	3.52608i	0.196807	+	0.340879i	−0.750685	+	0.660661i	$0.770276\pi$
$108$		0			0
$109$	15.3087			1.46631			0.733153	−	0.680064i	$-0.238048\pi$
$109$	15.3087			1.46631			0.733153	+	0.680064i	$0.238048\pi$
$110$		0			0
$111$	−0.0905505	+	0.156838i	−0.00859467	+	0.0148864i
$112$		0			0
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	0.423528	+	0.905883i	$0.360792\pi$
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	−0.996282	+	0.0861558i	$0.972542\pi$
$114$		0			0
$115$	−12.2779	−	21.2659i	−1.14492	−	1.98306i
$116$		0			0
$117$	−8.80534	+	4.13463i	−0.814054	+	0.382247i
$118$		0			0
$119$	1.18944	+	2.06017i	0.109036	+	0.188856i
$120$		0			0
$121$	5.34900	−	9.26473i	0.486272	−	0.842249i
$122$		0			0
$123$	−1.72877	+	2.99432i	−0.155878	+	0.269989i
$124$		0			0
$125$	−32.9518			−2.94730
$126$		0			0
$127$	0.980336	+	1.69799i	0.0869907	+	0.150672i	0.906238	−	0.422768i	$-0.138942\pi$
$127$	0.980336	+	1.69799i	0.0869907	+	0.150672i	−0.819247	+	0.573441i	$0.805608\pi$
$128$		0			0
$129$	1.76956			0.155801
$130$		0			0
$131$	6.50021			0.567926			0.283963	−	0.958835i	$-0.408351\pi$
$131$	6.50021			0.567926			0.283963	+	0.958835i	$0.408351\pi$
$132$		0			0
$133$	−1.80534	−	3.12694i	−0.156543	−	0.271140i
$134$		0			0
$135$	−13.2143			−1.13730
$136$		0			0
$137$	7.62878	−	13.2134i	0.651770	−	1.12890i	−0.330923	−	0.943658i	$-0.607360\pi$
$137$	7.62878	−	13.2134i	0.651770	−	1.12890i	0.982693	−	0.185242i	$-0.0593068\pi$
$138$		0			0
$139$	−8.74801	+	15.1520i	−0.741997	+	1.28518i	0.209588	+	0.977790i	$0.432788\pi$
$139$	−8.74801	+	15.1520i	−0.741997	+	1.28518i	−0.951585	+	0.307386i	$0.900546\pi$
$140$		0			0
$141$	−2.25579	−	3.90714i	−0.189972	−	0.329041i
$142$		0			0
$143$	−0.167428	+	1.97435i	−0.0140010	+	0.165103i
$144$		0			0
$145$	−7.59367	−	13.1526i	−0.630620	−	1.09227i
$146$		0			0
$147$	0.274776	−	0.475925i	0.0226631	−	0.0392537i
$148$		0			0
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	−0.944106	−	0.329642i	$-0.893072\pi$
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	0.757531	+	0.652799i	$0.226405\pi$
$150$		0			0
$151$	6.32912			0.515057			0.257528	−	0.966271i	$-0.417092\pi$
$151$	6.32912			0.515057			0.257528	+	0.966271i	$0.417092\pi$
$152$		0			0
$153$	−3.20911	−	5.55833i	−0.259441	−	0.449365i
$154$		0			0
$155$	−21.7265			−1.74511
$156$		0			0
$157$	16.3100			1.30168			0.650841	−	0.759214i	$-0.274416\pi$
$157$	16.3100			1.30168			0.650841	+	0.759214i	$0.274416\pi$
$158$		0			0
$159$	0.730536	+	1.26533i	0.0579353	+	0.100347i
$160$		0			0
$161$	−5.81890			−0.458593
$162$		0			0
$163$	11.7999	−	20.4381i	0.924241	−	1.60083i	0.131463	−	0.991321i	$-0.458033\pi$
$163$	11.7999	−	20.4381i	0.924241	−	1.60083i	0.792778	−	0.609511i	$-0.208634\pi$
$164$		0			0
$165$	−0.637235	+	1.10372i	−0.0496087	+	0.0859247i
$166$		0			0
$167$	−8.91513	−	15.4415i	−0.689874	−	1.19490i	−0.971878	−	0.235483i	$-0.924333\pi$
$167$	−8.91513	−	15.4415i	−0.689874	−	1.19490i	0.282005	−	0.959413i	$-0.409001\pi$
$168$		0			0
$169$	4.51137	+	12.1921i	0.347028	+	0.937855i
$170$		0			0
$171$	4.87080	+	8.43647i	0.372479	+	0.645153i
$172$		0			0
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	−0.685469	−	0.728101i	$-0.740403\pi$
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	0.973289	+	0.229583i	$0.0737363\pi$
$174$		0			0
$175$	−6.40423	+	11.0925i	−0.484115	+	0.838511i
$176$		0			0
$177$	−0.993330			−0.0746632
$178$		0			0
$179$	−11.4017	−	19.7483i	−0.852201	−	1.47606i	−0.879218	−	0.476420i	$-0.841934\pi$
$179$	−11.4017	−	19.7483i	−0.852201	−	1.47606i	0.0270166	−	0.999635i	$-0.491399\pi$
$180$		0			0
$181$	13.9294			1.03536			0.517681	−	0.855574i	$-0.326795\pi$
$181$	13.9294			1.03536			0.517681	+	0.855574i	$0.326795\pi$
$182$		0			0
$183$	−0.334855			−0.0247532
$184$		0			0
$185$	−0.695338	−	1.20436i	−0.0511222	−	0.0885463i
$186$		0			0
$187$	−1.30732			−0.0956006
$188$		0			0
$189$	−1.56567	+	2.71182i	−0.113886	+	0.197256i
$190$		0			0
$191$	−6.33591	+	10.9741i	−0.458450	+	0.794059i	−0.998879	−	0.0473305i	$-0.984929\pi$
$191$	−6.33591	+	10.9741i	−0.458450	+	0.794059i	0.540429	+	0.841390i	$0.318262\pi$
$192$		0			0
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	0.931057	−	0.364873i	$-0.118888\pi$
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	−0.781518	+	0.623882i	$0.785554\pi$
$194$		0			0
$195$	−0.706545	+	8.33177i	−0.0505968	+	0.596650i
$196$		0			0
$197$	3.42510	+	5.93245i	0.244028	+	0.422669i	0.961858	−	0.273549i	$-0.0881977\pi$
$197$	3.42510	+	5.93245i	0.244028	+	0.422669i	−0.717830	+	0.696219i	$0.754864\pi$
$198$		0			0
$199$	−0.406794	+	0.704587i	−0.0288368	+	0.0499469i	−0.880084	−	0.474819i	$-0.842514\pi$
$199$	−0.406794	+	0.704587i	−0.0288368	+	0.0499469i	0.851247	+	0.524766i	$0.175847\pi$
$200$		0			0
$201$	−2.84937	+	4.93525i	−0.200979	+	0.348106i
$202$		0			0
$203$	−3.59889			−0.252593
$204$		0			0
$205$	−13.2752	−	22.9934i	−0.927183	−	1.60593i
$206$		0			0
$207$	15.6994			1.09118
$208$		0			0
$209$	1.98426			0.137254
$210$		0			0
$211$	−6.98670	−	12.1013i	−0.480984	−	0.833089i	0.518778	−	0.854909i	$-0.326387\pi$
$211$	−6.98670	−	12.1013i	−0.480984	−	0.833089i	−0.999762	+	0.0218200i	$0.993054\pi$
$212$		0			0
$213$	−6.15375			−0.421648
$214$		0			0
$215$	−6.79423	+	11.7679i	−0.463363	+	0.802568i
$216$		0			0
$217$	−2.57422	+	4.45868i	−0.174750	+	0.302675i
$218$		0			0
$219$	1.34811	+	2.33499i	0.0910966	+	0.157784i
$220$		0			0
$221$	−7.76387	+	3.64560i	−0.522255	+	0.245229i
$222$		0			0
$223$	−6.76700	−	11.7208i	−0.453152	−	0.784882i	0.545428	−	0.838158i	$-0.316367\pi$
$223$	−6.76700	−	11.7208i	−0.453152	−	0.784882i	−0.998580	+	0.0532758i	$0.983034\pi$
$224$		0			0
$225$	17.2786	−	29.9274i	1.15191	−	1.99516i
$226$		0			0
$227$	−2.68376	+	4.64840i	−0.178127	+	0.308525i	−0.941239	−	0.337741i	$-0.890337\pi$
$227$	−2.68376	+	4.64840i	−0.178127	+	0.308525i	0.763112	+	0.646266i	$0.223671\pi$
$228$		0			0
$229$	3.09910			0.204794			0.102397	−	0.994744i	$-0.467349\pi$
$229$	3.09910			0.204794			0.102397	+	0.994744i	$0.467349\pi$
$230$		0			0
$231$	0.151003	+	0.261545i	0.00993528	+	0.0172084i
$232$		0			0
$233$	−20.3712			−1.33456			−0.667280	−	0.744807i	$-0.732541\pi$
$233$	−20.3712			−1.33456			−0.667280	+	0.744807i	$0.732541\pi$
$234$		0			0
$235$	34.6445			2.25996
$236$		0			0
$237$	3.85156	+	6.67109i	0.250186	+	0.433334i
$238$		0			0
$239$	1.29157			0.0835449			0.0417725	−	0.999127i	$-0.486700\pi$
$239$	1.29157			0.0835449			0.0417725	+	0.999127i	$0.486700\pi$
$240$		0			0
$241$	−1.06635	+	1.84697i	−0.0686896	+	0.118974i	−0.898325	−	0.439332i	$-0.855215\pi$
$241$	−1.06635	+	1.84697i	−0.0686896	+	0.118974i	0.829635	+	0.558306i	$0.188548\pi$
$242$		0			0
$243$	6.44819	−	11.1686i	0.413652	−	0.716466i
$244$		0			0
$245$	2.11000	+	3.65463i	0.134803	+	0.233486i
$246$		0			0
$247$	11.7841	−	5.53331i	0.749801	−	0.352076i
$248$		0			0
$249$	1.57490	+	2.72781i	0.0998053	+	0.172868i
$250$		0			0
$251$	−15.3856	+	26.6486i	−0.971128	+	1.68204i	−0.278964	+	0.960302i	$0.589991\pi$
$251$	−15.3856	+	26.6486i	−0.971128	+	1.68204i	−0.692164	+	0.721741i	$0.743342\pi$
$252$		0			0
$253$	1.59889	−	2.76936i	0.100521	−	0.174108i
$254$		0			0
$255$	−5.51689			−0.345481
$256$		0			0
$257$	0.736805	+	1.27618i	0.0459607	+	0.0796062i	0.888091	−	0.459669i	$-0.152032\pi$
$257$	0.736805	+	1.27618i	0.0459607	+	0.0796062i	−0.842130	+	0.539275i	$0.818698\pi$
$258$		0			0
$259$	−0.329543			−0.0204768
$260$		0			0
$261$	9.70979			0.601021
$262$		0			0
$263$	3.33847	+	5.78240i	0.205859	+	0.356558i	0.950406	−	0.311012i	$-0.100668\pi$
$263$	3.33847	+	5.78240i	0.205859	+	0.356558i	−0.744547	+	0.667570i	$0.767335\pi$
$264$		0			0
$265$	−11.2196			−0.689214
$266$		0			0
$267$	−2.05190	+	3.55400i	−0.125574	+	0.217501i
$268$		0			0
$269$	−3.78786	+	6.56077i	−0.230950	+	0.400017i	−0.958088	−	0.286474i	$-0.907517\pi$
$269$	−3.78786	+	6.56077i	−0.230950	+	0.400017i	0.727138	+	0.686492i	$0.240850\pi$
$270$		0			0
$271$	10.2840	+	17.8124i	0.624709	+	1.08203i	0.988597	+	0.150585i	$0.0481157\pi$
$271$	10.2840	+	17.8124i	0.624709	+	1.08203i	−0.363888	+	0.931443i	$0.618551\pi$
$272$		0			0
$273$	1.62612	+	1.13217i	0.0984174	+	0.0685221i
$274$		0			0
$275$	−3.51945	−	6.09587i	−0.212231	−	0.367595i
$276$		0			0
$277$	−2.85271	+	4.94103i	−0.171402	+	0.296878i	−0.938910	−	0.344162i	$-0.888163\pi$
$277$	−2.85271	+	4.94103i	−0.171402	+	0.296878i	0.767508	+	0.641039i	$0.221497\pi$
$278$		0			0
$279$	6.94523	−	12.0295i	0.415800	−	0.720187i
$280$		0			0
$281$	−6.37315			−0.380190			−0.190095	−	0.981766i	$-0.560880\pi$
$281$	−6.37315			−0.380190			−0.190095	+	0.981766i	$0.560880\pi$
$282$		0			0
$283$	13.5097	+	23.3995i	0.803068	+	1.39096i	0.917587	+	0.397534i	$0.130134\pi$
$283$	13.5097	+	23.3995i	0.803068	+	1.39096i	−0.114519	+	0.993421i	$0.536533\pi$
$284$		0			0
$285$	8.37357			0.496008
$286$		0			0
$287$	−6.29157			−0.371380
$288$		0			0
$289$	5.67046	+	9.82152i	0.333556	+	0.577736i
$290$		0			0
$291$	3.75932			0.220375
$292$		0			0
$293$	2.43736	−	4.22163i	0.142392	−	0.246630i	−0.786005	−	0.618220i	$-0.787854\pi$
$293$	2.43736	−	4.22163i	0.142392	−	0.246630i	0.928397	+	0.371590i	$0.121187\pi$
$294$		0			0
$295$	3.81389	−	6.60586i	0.222053	−	0.384608i
$296$		0			0
$297$	−0.860415	−	1.49028i	−0.0499264	−	0.0864750i
$298$		0			0
$299$	1.77280	−	20.9053i	0.102524	−	1.20899i
$300$		0			0
$301$	1.61000	+	2.78861i	0.0927991	+	0.160733i
$302$		0			0
$303$	1.58247	−	2.74091i	0.0909104	−	0.157461i
$304$		0			0
$305$	1.28568	−	2.22686i	0.0736177	−	0.127510i
$306$		0			0
$307$	−16.1760			−0.923212			−0.461606	−	0.887085i	$-0.652727\pi$
$307$	−16.1760			−0.923212			−0.461606	+	0.887085i	$0.652727\pi$
$308$		0			0
$309$	−0.157110	−	0.272123i	−0.00893769	−	0.0154805i
$310$		0			0
$311$	1.30806			0.0741735			0.0370868	−	0.999312i	$-0.488192\pi$
$311$	1.30806			0.0741735			0.0370868	+	0.999312i	$0.488192\pi$
$312$		0			0
$313$	13.1978			0.745983			0.372991	−	0.927835i	$-0.378332\pi$
$313$	13.1978			0.745983			0.372991	+	0.927835i	$0.378332\pi$
$314$		0			0
$315$	−5.69278	−	9.86018i	−0.320752	−	0.555558i
$316$		0			0
$317$	−8.07552			−0.453566			−0.226783	−	0.973945i	$-0.572821\pi$
$317$	−8.07552			−0.453566			−0.226783	+	0.973945i	$0.572821\pi$
$318$		0			0
$319$	0.988887	−	1.71280i	0.0553671	−	0.0958986i
$320$		0			0
$321$	−1.11877	+	1.93776i	−0.0624435	+	0.108155i
$322$		0			0
$323$	4.29470	+	7.43863i	0.238963	+	0.413897i
$324$		0			0
$325$	−37.9003	−	26.3877i	−2.10233	−	1.46372i
$326$		0			0
$327$	4.20645	+	7.28579i	0.232617	+	0.402905i
$328$		0			0
$329$	4.10479	−	7.10970i	0.226304	−	0.391970i
$330$		0			0
$331$	−7.47256	+	12.9429i	−0.410729	+	0.711403i	−0.994970	−	0.100177i	$-0.968059\pi$
$331$	−7.47256	+	12.9429i	−0.410729	+	0.711403i	0.584241	+	0.811580i	$0.301392\pi$
$332$		0			0
$333$	0.889106			0.0487227
$334$		0			0
$335$	−21.8803	−	37.8979i	−1.19545	−	2.07058i
$336$		0			0
$337$	−17.1695			−0.935282			−0.467641	−	0.883918i	$-0.654896\pi$
$337$	−17.1695			−0.935282			−0.467641	+	0.883918i	$0.654896\pi$
$338$		0			0
$339$	−6.69184			−0.363451
$340$		0			0
$341$	−1.41467	−	2.45027i	−0.0766085	−	0.132690i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	6.74733	−	11.6867i	0.363264	−	0.629192i
$346$		0			0
$347$	−1.96922	+	3.41079i	−0.105713	+	0.183101i	−0.914029	−	0.405648i	$-0.867046\pi$
$347$	−1.96922	+	3.41079i	−0.105713	+	0.183101i	0.808316	+	0.588749i	$0.200379\pi$
$348$		0			0
$349$	−8.58883	−	14.8763i	−0.459750	−	0.796310i	0.539198	−	0.842179i	$-0.318728\pi$
$349$	−8.58883	−	14.8763i	−0.459750	−	0.796310i	−0.998947	+	0.0458695i	$0.985394\pi$
$350$		0			0
$351$	−9.26563	−	6.45110i	−0.494563	−	0.344334i
$352$		0			0
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	0.999836	−	0.0180932i	$-0.00575957\pi$
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	−0.515587	+	0.856837i	$0.672426\pi$
$354$		0			0
$355$	23.6274	−	40.9238i	1.25401	−	2.17201i
$356$		0			0
$357$	−0.653659	+	1.13217i	−0.0345953	+	0.0599208i
$358$		0			0
$359$	−16.3126			−0.860948			−0.430474	−	0.902603i	$-0.641654\pi$
$359$	−16.3126			−0.860948			−0.430474	+	0.902603i	$0.641654\pi$
$360$		0			0
$361$	2.98148	+	5.16408i	0.156920	+	0.271794i
$362$		0			0
$363$	5.87909			0.308572
$364$		0			0
$365$	−20.7042			−1.08371
$366$		0			0
$367$	−18.0982	−	31.3469i	−0.944716	−	1.63630i	−0.756319	−	0.654203i	$-0.773004\pi$
$367$	−18.0982	−	31.3469i	−0.944716	−	1.63630i	−0.188398	−	0.982093i	$-0.560329\pi$
$368$		0			0
$369$	16.9746			0.883664
$370$		0			0
$371$	−1.32933	+	2.30247i	−0.0690155	+	0.119538i
$372$		0			0
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	−0.964530	−	0.263974i	$-0.914967\pi$
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	0.710873	+	0.703320i	$0.248300\pi$
$374$		0			0
$375$	−9.05435	−	15.6826i	−0.467564	−	0.809845i
$376$		0			0
$377$	1.09645	−	12.9296i	0.0564699	−	0.665907i
$378$		0			0
$379$	6.53275	+	11.3151i	0.335565	+	0.581216i	0.983593	−	0.180401i	$-0.0577394\pi$
$379$	6.53275	+	11.3151i	0.335565	+	0.581216i	−0.648028	+	0.761616i	$0.724406\pi$
$380$		0			0
$381$	−0.538745	+	0.933133i	−0.0276007	+	0.0478058i
$382$		0			0
$383$	13.8965	−	24.0694i	0.710076	−	1.22989i	−0.254753	−	0.967006i	$-0.581994\pi$
$383$	13.8965	−	24.0694i	0.710076	−	1.22989i	0.964828	−	0.262881i	$-0.0846726\pi$
$384$		0			0
$385$	−2.31911			−0.118193
$386$		0			0
$387$	−4.34378	−	7.52365i	−0.220807	−	0.382449i
$388$		0			0
$389$	13.7047			0.694854			0.347427	−	0.937707i	$-0.387055\pi$
$389$	13.7047			0.694854			0.347427	+	0.937707i	$0.387055\pi$
$390$		0			0
$391$	13.8425			0.700044
$392$		0			0
$393$	1.78610	+	3.09361i	0.0900968	+	0.156052i
$394$		0			0
$395$	−59.1523			−2.97627
$396$		0			0
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	−0.948057	−	0.318101i	$-0.896955\pi$
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	0.749512	+	0.661991i	$0.230288\pi$
$398$		0			0
$399$	0.992128	−	1.71842i	0.0496685	−	0.0860284i
$400$		0			0
$401$	8.27212	+	14.3277i	0.413090	+	0.715493i	0.995226	−	0.0975987i	$-0.0311162\pi$
$401$	8.27212	+	14.3277i	0.413090	+	0.715493i	−0.582136	+	0.813092i	$0.697783\pi$
$402$		0			0
$403$	−15.2342	−	10.6067i	−0.758872	−	0.528357i
$404$		0			0
$405$	13.4474	+	23.2915i	0.668205	+	1.15737i
$406$		0			0
$407$	0.0905505	−	0.156838i	0.00448842	−	0.00777417i
$408$		0			0
$409$	−12.8909	+	22.3278i	−0.637416	+	1.10404i	0.348582	+	0.937278i	$0.386663\pi$
$409$	−12.8909	+	22.3278i	−0.637416	+	1.10404i	−0.985998	+	0.166758i	$0.946670\pi$
$410$		0			0
$411$	8.38481			0.413592
$412$		0			0
$413$	−0.903765	−	1.56537i	−0.0444713	−	0.0770266i
$414$		0			0
$415$	−24.1873			−1.18731
$416$		0			0
$417$	−9.61496			−0.470847
$418$		0			0
$419$	11.8436	+	20.5137i	0.578596	+	1.00216i	0.995641	+	0.0932720i	$0.0297326\pi$
$419$	11.8436	+	20.5137i	0.578596	+	1.00216i	−0.417044	+	0.908886i	$0.636934\pi$
$420$		0			0
$421$	−20.8246			−1.01493			−0.507465	−	0.861672i	$-0.669417\pi$
$421$	−20.8246			−1.01493			−0.507465	+	0.861672i	$0.669417\pi$
$422$		0			0
$423$	−11.0747	+	19.1819i	−0.538470	+	0.932657i
$424$		0			0
$425$	15.2349	−	26.3877i	0.739002	−	1.27999i
$426$		0			0
$427$	−0.304662	−	0.527691i	−0.0147436	−	0.0255367i
$428$		0			0
$429$	−0.985647	+	0.462820i	−0.0475875	+	0.0223451i
$430$		0			0
$431$	9.97521	+	17.2776i	0.480489	+	0.832232i	0.999749	−	0.0223845i	$-0.00712581\pi$
$431$	9.97521	+	17.2776i	0.480489	+	0.832232i	−0.519260	+	0.854616i	$0.673792\pi$
$432$		0			0
$433$	−0.00834083	+	0.0144467i	−0.000400835	+	0.000694266i	−0.866226	−	0.499653i	$-0.833461\pi$
$433$	−0.00834083	+	0.0144467i	−0.000400835	+	0.000694266i	0.865825	+	0.500347i	$0.166794\pi$
$434$		0			0
$435$	4.17311	−	7.22804i	0.200085	−	0.346558i
$436$		0			0
$437$	−21.0102			−1.00505
$438$		0			0
$439$	6.74801	+	11.6879i	0.322065	+	0.557833i	0.980914	−	0.194442i	$-0.0622897\pi$
$439$	6.74801	+	11.6879i	0.322065	+	0.557833i	−0.658849	+	0.752275i	$0.728956\pi$
$440$		0			0
$441$	−2.69799			−0.128476
$442$		0			0
$443$	15.0110			0.713196			0.356598	−	0.934258i	$-0.383937\pi$
$443$	15.0110			0.713196			0.356598	+	0.934258i	$0.383937\pi$
$444$		0			0
$445$	−15.7566	−	27.2912i	−0.746933	−	1.29373i
$446$		0			0
$447$	−2.50313			−0.118394
$448$		0			0
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	−0.436181	−	0.899859i	$-0.643669\pi$
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	0.997391	−	0.0721852i	$-0.0229973\pi$
$450$		0			0
$451$	1.72877	−	2.99432i	0.0814046	−	0.140997i
$452$		0			0
$453$	1.73909	+	3.01219i	0.0817095	+	0.141525i
$454$		0			0
$455$	−13.7727	+	6.46709i	−0.645673	+	0.303182i
$456$		0			0
$457$	−9.06567	−	15.7022i	−0.424074	−	0.734518i	0.572259	−	0.820073i	$-0.306067\pi$
$457$	−9.06567	−	15.7022i	−0.424074	−	0.734518i	−0.996333	+	0.0855548i	$0.972734\pi$
$458$		0			0
$459$	3.72455	−	6.45110i	0.173847	−	0.301112i
$460$		0			0
$461$	3.03980	−	5.26508i	0.141577	−	0.245219i	−0.786513	−	0.617573i	$-0.788116\pi$
$461$	3.03980	−	5.26508i	0.141577	−	0.245219i	0.928091	+	0.372354i	$0.121449\pi$
$462$		0			0
$463$	−5.19289			−0.241334			−0.120667	−	0.992693i	$-0.538503\pi$
$463$	−5.19289			−0.241334			−0.120667	+	0.992693i	$0.538503\pi$
$464$		0			0
$465$	−5.96990	−	10.3402i	−0.276848	−	0.479514i
$466$		0			0
$467$	8.69968			0.402573			0.201287	−	0.979532i	$-0.435488\pi$
$467$	8.69968			0.402573			0.201287	+	0.979532i	$0.435488\pi$
$468$		0			0
$469$	−10.3698			−0.478833
$470$		0			0
$471$	4.48160	+	7.76236i	0.206501	+	0.357671i
$472$		0			0
$473$	−1.76956			−0.0813644
$474$		0			0
$475$	−23.1237	+	40.0513i	−1.06099	+	1.83768i
$476$		0			0
$477$	3.58653	−	6.21205i	0.164216	−	0.284430i
$478$		0			0
$479$	12.1094	+	20.9741i	0.553294	+	0.958332i	0.998034	+	0.0626730i	$0.0199625\pi$
$479$	12.1094	+	20.9741i	0.553294	+	0.958332i	−0.444741	+	0.895659i	$0.646704\pi$
$480$		0			0
$481$	0.100399	−	1.18394i	0.00457782	−	0.0539828i
$482$		0			0
$483$	−1.59889	−	2.76936i	−0.0727521	−	0.126010i
$484$		0			0
$485$	−14.4339	+	25.0003i	−0.655410	+	1.13520i
$486$		0			0
$487$	0.886967	−	1.53627i	0.0401923	−	0.0696151i	−0.845229	−	0.534404i	$-0.820536\pi$
$487$	0.886967	−	1.53627i	0.0401923	−	0.0696151i	0.885422	+	0.464788i	$0.153870\pi$
$488$		0			0
$489$	12.9693			0.586493
$490$		0			0
$491$	−3.34483	−	5.79342i	−0.150950	−	0.261453i	0.780627	−	0.624997i	$-0.214900\pi$
$491$	−3.34483	−	5.79342i	−0.150950	−	0.261453i	−0.931577	+	0.363544i	$0.881567\pi$
$492$		0			0
$493$	8.56134			0.385584
$494$		0			0
$495$	6.25694			0.281229
$496$		0			0
$497$	−5.59889	−	9.69756i	−0.251145	−	0.434995i
$498$		0			0
$499$	−24.6387			−1.10298			−0.551491	−	0.834181i	$-0.685941\pi$
$499$	−24.6387			−1.10298			−0.551491	+	0.834181i	$0.685941\pi$
$500$		0			0
$501$	4.89932	−	8.48588i	0.218886	−	0.379121i
$502$		0			0
$503$	16.5726	−	28.7046i	0.738936	−	1.27987i	−0.214039	−	0.976825i	$-0.568662\pi$
$503$	16.5726	−	28.7046i	0.738936	−	1.27987i	0.952975	−	0.303049i	$-0.0980046\pi$
$504$		0			0
$505$	12.1518	+	21.0475i	0.540747	+	0.936601i
$506$		0			0
$507$	−4.56292	+	5.49717i	−0.202646	+	0.244138i
$508$		0			0
$509$	13.8290	+	23.9526i	0.612961	+	1.06168i	0.990739	+	0.135783i	$0.0433549\pi$
$509$	13.8290	+	23.9526i	0.612961	+	1.06168i	−0.377778	+	0.925896i	$0.623312\pi$
$510$		0			0
$511$	−2.45310	+	4.24890i	−0.108519	+	0.187960i
$512$		0			0
$513$	−5.65314	+	9.79152i	−0.249592	+	0.432306i
$514$		0			0
$515$	2.41290			0.106325
$516$		0			0
$517$	2.25579	+	3.90714i	0.0992096	+	0.171836i
$518$		0			0
$519$	4.16085			0.182641
$520$		0			0
$521$	1.42217			0.0623062			0.0311531	−	0.999515i	$-0.490082\pi$
$521$	1.42217			0.0623062			0.0311531	+	0.999515i	$0.490082\pi$
$522$		0			0
$523$	−1.68089	−	2.91139i	−0.0735002	−	0.127306i	0.826933	−	0.562301i	$-0.190084\pi$
$523$	−1.68089	−	2.91139i	−0.0735002	−	0.127306i	−0.900433	+	0.434995i	$0.856750\pi$
$524$		0			0
$525$	−7.03891			−0.307203
$526$		0			0
$527$	6.12377	−	10.6067i	0.266756	−	0.462034i
$528$		0			0
$529$	−5.42979	+	9.40468i	−0.236078	+	0.408899i
$530$		0			0
$531$	2.43835	+	4.22335i	0.105815	+	0.183278i
$532$		0			0
$533$	1.91681	−	22.6035i	0.0830260	−	0.979065i
$534$		0			0
$535$	−8.59102	−	14.8801i	−0.371422	−	0.643322i
$536$		0			0
$537$	6.26580	−	10.8527i	0.270389	−	0.468328i
$538$		0			0
$539$	−0.274776	+	0.475925i	−0.0118354	+	0.0204996i
$540$		0			0
$541$	7.76289			0.333753			0.166876	−	0.985978i	$-0.446632\pi$
$541$	7.76289			0.333753			0.166876	+	0.985978i	$0.446632\pi$
$542$		0			0
$543$	3.82745	+	6.62934i	0.164252	+	0.284492i
$544$		0			0
$545$	−64.6027			−2.76728
$546$		0			0
$547$	6.19247			0.264771			0.132385	−	0.991198i	$-0.457736\pi$
$547$	6.19247			0.264771			0.132385	+	0.991198i	$0.457736\pi$
$548$		0			0
$549$	0.821977	+	1.42371i	0.0350811	+	0.0607623i
$550$		0			0
$551$	−12.9945			−0.553582
$552$		0			0
$553$	−7.00855	+	12.1392i	−0.298034	+	0.516210i
$554$		0			0
$555$	0.382124	−	0.661858i	0.0162202	−	0.0280943i
$556$		0			0
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	−0.988357	−	0.152154i	$-0.951379\pi$
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	0.362409	−	0.932019i	$-0.381954\pi$
$558$		0			0
$559$	−10.5090	+	4.93461i	−0.444484	+	0.208712i
$560$		0			0
$561$	−0.359219	−	0.622186i	−0.0151662	−	0.0262687i
$562$		0			0
$563$	3.23368	−	5.60090i	0.136283	−	0.236050i	−0.789804	−	0.613360i	$-0.789818\pi$
$563$	3.23368	−	5.60090i	0.136283	−	0.236050i	0.926087	+	0.377310i	$0.123151\pi$
$564$		0			0
$565$	25.6933	−	44.5022i	1.08093	−	1.87222i
$566$		0			0
$567$	6.37315			0.267647
$568$		0			0
$569$	−10.8478	−	18.7889i	−0.454763	−	0.787673i	0.543911	−	0.839143i	$-0.316943\pi$
$569$	−10.8478	−	18.7889i	−0.454763	−	0.787673i	−0.998675	+	0.0514697i	$0.983609\pi$
$570$		0			0
$571$	16.6418			0.696436			0.348218	−	0.937414i	$-0.386787\pi$
$571$	16.6418			0.696436			0.348218	+	0.937414i	$0.386787\pi$
$572$		0			0
$573$	−6.96381			−0.290917
$574$		0			0
$575$	37.2656	+	64.5459i	1.55408	+	2.69175i
$576$		0			0
$577$	−2.64240			−0.110005			−0.0550024	−	0.998486i	$-0.517517\pi$
$577$	−2.64240			−0.110005			−0.0550024	+	0.998486i	$0.517517\pi$
$578$		0			0
$579$	−1.14167	+	1.97743i	−0.0474462	+	0.0821793i
$580$		0			0
$581$	−2.86579	+	4.96370i	−0.118893	+	0.205929i
$582$		0			0
$583$	−0.730536	−	1.26533i	−0.0302557	−	0.0524044i
$584$		0			0
$585$	37.1586	−	17.4482i	1.53632	−	0.721393i
$586$		0			0
$587$	3.69407	+	6.39832i	0.152471	+	0.264087i	0.932135	−	0.362110i	$-0.117944\pi$
$587$	3.69407	+	6.39832i	0.152471	+	0.264087i	−0.779664	+	0.626198i	$0.784610\pi$
$588$		0			0
$589$	−9.29470	+	16.0989i	−0.382981	+	0.663343i
$590$		0			0
$591$	−1.88227	+	3.26018i	−0.0774261	+	0.134106i
$592$		0			0
$593$	46.9030			1.92607			0.963037	−	0.269370i	$-0.0868153\pi$
$593$	46.9030			1.92607			0.963037	+	0.269370i	$0.0868153\pi$
$594$		0			0
$595$	−5.01945	−	8.69395i	−0.205778	−	0.356417i
$596$		0			0
$597$	−0.447108			−0.0182989
$598$		0			0
$599$	−1.62290			−0.0663098			−0.0331549	−	0.999450i	$-0.510555\pi$
$599$	−1.62290			−0.0663098			−0.0331549	+	0.999450i	$0.510555\pi$
$600$		0			0
$601$	23.5174	+	40.7333i	0.959293	+	1.66154i	0.724223	+	0.689566i	$0.242199\pi$
$601$	23.5174	+	40.7333i	0.959293	+	1.66154i	0.235070	+	0.971978i	$0.424468\pi$
$602$		0			0
$603$	27.9777			1.13934
$604$		0			0
$605$	−22.5728	+	39.0973i	−0.917715	+	1.58953i
$606$		0			0
$607$	−14.1935	+	24.5838i	−0.576095	+	0.997825i	0.419827	+	0.907604i	$0.362091\pi$
$607$	−14.1935	+	24.5838i	−0.576095	+	0.997825i	−0.995922	+	0.0902211i	$0.971243\pi$
$608$		0			0
$609$	−0.988887	−	1.71280i	−0.0400717	−	0.0694063i
$610$		0			0
$611$	24.2921	+	16.9131i	0.982755	+	0.684233i
$612$		0			0
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.721514	+	0.692399i	$0.243446\pi$
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.238878	+	0.971050i	$0.423220\pi$
$614$		0			0
$615$	7.29543	−	12.6360i	0.294180	−	0.509535i
$616$		0			0
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	−0.651012	−	0.759068i	$-0.725655\pi$
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	0.982878	+	0.184259i	$0.0589885\pi$
$618$		0			0
$619$	31.9412			1.28382			0.641912	−	0.766778i	$-0.278141\pi$
$619$	31.9412			1.28382			0.641912	+	0.766778i	$0.278141\pi$
$620$		0			0
$621$	9.11047	+	15.7798i	0.365591	+	0.633222i
$622$		0			0
$623$	−7.46755			−0.299181
$624$		0			0
$625$	75.0145			3.00058
$626$		0			0
$627$	0.545225	+	0.944357i	0.0217742	+	0.0377140i
$628$		0			0
$629$	0.783945			0.0312579
$630$		0			0
$631$	6.59577	−	11.4242i	0.262573	−	0.454790i	−0.704352	−	0.709851i	$-0.748762\pi$
$631$	6.59577	−	11.4242i	0.262573	−	0.454790i	0.966925	+	0.255061i	$0.0820955\pi$
$632$		0			0
$633$	3.83955	−	6.65029i	0.152608	−	0.264325i
$634$		0			0
$635$	−4.13702	−	7.16554i	−0.164173	−	0.284356i
$636$		0			0
$637$	−0.304662	+	3.59266i	−0.0120712	+	0.142346i
$638$		0			0
$639$	15.1058	+	26.1640i	0.597575	+	1.03503i
$640$		0			0
$641$	23.5814	−	40.8441i	0.931408	−	1.61325i	0.150490	−	0.988612i	$-0.451915\pi$
$641$	23.5814	−	40.8441i	0.931408	−	1.61325i	0.780918	−	0.624634i	$-0.214752\pi$
$642$		0			0
$643$	−1.40679	+	2.43664i	−0.0554785	+	0.0960916i	−0.892431	−	0.451184i	$-0.851002\pi$
$643$	−1.40679	+	2.43664i	−0.0554785	+	0.0960916i	0.836952	+	0.547276i	$0.184335\pi$
$644$		0			0
$645$	−7.46755			−0.294035
$646$		0			0
$647$	12.9891	+	22.4979i	0.510656	+	0.884482i	0.999924	+	0.0123485i	$0.00393074\pi$
$647$	12.9891	+	22.4979i	0.510656	+	0.884482i	−0.489268	+	0.872134i	$0.662736\pi$
$648$		0			0
$649$	0.993330			0.0389916
$650$		0			0
$651$	−2.82933			−0.110890
$652$		0			0
$653$	13.4213	+	23.2464i	0.525216	+	0.909700i	0.999569	+	0.0293654i	$0.00934865\pi$
$653$	13.4213	+	23.2464i	0.525216	+	0.909700i	−0.474353	+	0.880335i	$0.657318\pi$
$654$		0			0
$655$	−27.4309			−1.07182
$656$		0			0
$657$	6.61846	−	11.4635i	0.258211	−	0.447234i
$658$		0			0
$659$	7.78666	−	13.4869i	0.303325	−	0.525375i	−0.673562	−	0.739131i	$-0.735236\pi$
$659$	7.78666	−	13.4869i	0.303325	−	0.525375i	0.976887	+	0.213756i	$0.0685698\pi$
$660$		0			0
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	−0.983320	−	0.181881i	$-0.941781\pi$
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	0.334146	−	0.942521i	$-0.391552\pi$
$662$		0			0
$663$	−3.86836	−	2.69330i	−0.150234	−	0.104599i
$664$		0			0
$665$	7.61856	+	13.1957i	0.295435	+	0.511708i
$666$		0			0
$667$	−10.4708	+	18.1359i	−0.405431	+	0.702227i
$668$		0			0
$669$	3.71881	−	6.44117i	0.143778	−	0.249030i
$670$		0			0
$671$	0.334855			0.0129269
$672$		0			0
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	0.857677	−	0.514189i	$-0.171907\pi$
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	−0.874139	+	0.485675i	$0.838574\pi$
$674$		0			0
$675$	40.1076			1.54374
$676$		0			0
$677$	−24.5449			−0.943339			−0.471669	−	0.881775i	$-0.656348\pi$
$677$	−24.5449			−0.943339			−0.471669	+	0.881775i	$0.656348\pi$
$678$		0			0
$679$	3.42035	+	5.92422i	0.131261	+	0.227351i
$680$		0			0
$681$	−2.94972			−0.113034
$682$		0			0
$683$	−21.5186	+	37.2714i	−0.823387	+	1.42615i	0.0797583	+	0.996814i	$0.474585\pi$
$683$	−21.5186	+	37.2714i	−0.823387	+	1.42615i	−0.903146	+	0.429334i	$0.858748\pi$
$684$		0			0
$685$	−32.1935	+	55.7608i	−1.23005	+	2.13051i
$686$		0			0
$687$	0.851558	+	1.47494i	0.0324889	+	0.0562725i
$688$		0			0
$689$	−7.86699	−	5.47731i	−0.299708	−	0.208669i
$690$		0			0
$691$	−12.9098	−	22.3604i	−0.491110	−	0.850628i	0.508837	−	0.860863i	$-0.330075\pi$
$691$	−12.9098	−	22.3604i	−0.491110	−	0.850628i	−0.999948	+	0.0102348i	$0.996742\pi$
$692$		0			0
$693$	0.741343	−	1.28404i	0.0281613	−	0.0487768i
$694$		0			0
$695$	36.9167	−	63.9416i	1.40033	−	2.42544i
$696$		0			0
$697$	14.9669			0.566913
$698$		0			0
$699$	−5.59750	−	9.69515i	−0.211717	−	0.366704i
$700$		0			0
$701$	16.3178			0.616313			0.308156	−	0.951336i	$-0.400288\pi$
$701$	16.3178			0.616313			0.308156	+	0.951336i	$0.400288\pi$
$702$		0			0
$703$	−1.18988			−0.0448770
$704$		0			0
$705$	9.51945	+	16.4882i	0.358523	+	0.620981i
$706$		0			0
$707$	5.75913			0.216594
$708$		0			0
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	−0.575725	−	0.817644i	$-0.695280\pi$
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	0.995963	+	0.0897702i	$0.0286133\pi$
$710$		0			0
$711$	18.9090	−	32.7514i	0.709144	−	1.22827i
$712$		0			0
$713$	14.9791	+	25.9446i	0.560973	+	0.971634i
$714$		0			0
$715$	0.706545	−	8.33177i	0.0264233	−	0.311590i
$716$		0			0
$717$	0.354893	+	0.614692i	0.0132537	+	0.0229561i
$718$		0			0
$719$	−11.3723	+	19.6973i	−0.424113	+	0.734586i	−0.996337	−	0.0855115i	$-0.972748\pi$
$719$	−11.3723	+	19.6973i	−0.424113	+	0.734586i	0.572224	+	0.820098i	$0.306081\pi$
$720$		0			0
$721$	0.285888	−	0.495173i	0.0106470	−	0.0184412i
$722$		0			0
$723$	−1.17203			−0.0435881
$724$		0			0
$725$	23.0481	+	39.9205i	0.855986	+	1.48261i
$726$		0			0
$727$	−18.7274			−0.694561			−0.347280	−	0.937761i	$-0.612895\pi$
$727$	−18.7274			−0.694561			−0.347280	+	0.937761i	$0.612895\pi$
$728$		0			0
$729$	−12.0322			−0.445638
$730$		0			0
$731$	−3.83001	−	6.63377i	−0.141658	−	0.245359i
$732$		0			0
$733$	−1.69268			−0.0625206			−0.0312603	−	0.999511i	$-0.509952\pi$
$733$	−1.69268			−0.0625206			−0.0312603	+	0.999511i	$0.509952\pi$
$734$		0			0
$735$	−1.15956	+	2.00841i	−0.0427708	+	0.0740813i
$736$		0			0
$737$	2.84937	−	4.93525i	0.104958	−	0.181792i
$738$		0			0
$739$	23.4581	+	40.6305i	0.862919	+	1.49462i	0.869099	+	0.494638i	$0.164699\pi$
$739$	23.4581	+	40.6305i	0.862919	+	1.49462i	−0.00618065	+	0.999981i	$0.501967\pi$
$740$		0			0
$741$	5.87141	+	4.08791i	0.215692	+	0.150173i
$742$		0			0
$743$	6.44831	+	11.1688i	0.236566	+	0.409744i	0.959727	−	0.280936i	$-0.0906449\pi$
$743$	6.44831	+	11.1688i	0.236566	+	0.409744i	−0.723161	+	0.690680i	$0.757312\pi$
$744$		0			0
$745$	9.61078	−	16.6464i	0.352112	−	0.609875i
$746$		0			0
$747$	7.73189	−	13.3920i	0.282895	−	0.489989i
$748$		0			0
$749$	−4.07157			−0.148772
$750$		0			0
$751$	−22.8166	−	39.5196i	−0.832591	−	1.44209i	−0.895977	−	0.444101i	$-0.853523\pi$
$751$	−22.8166	−	39.5196i	−0.832591	−	1.44209i	0.0633855	−	0.997989i	$-0.479810\pi$
$752$		0			0
$753$	−16.9103			−0.616245
$754$		0			0
$755$	−26.7089			−0.972038
$756$		0			0
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	0.970714	+	0.240239i	$0.0772260\pi$
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	−0.277303	+	0.960782i	$0.589441\pi$
$758$		0			0
$759$	1.75735			0.0637876
$760$		0			0
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	0.160478	+	0.987039i	$0.448696\pi$
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	−0.935040	+	0.354542i	$0.884637\pi$
$762$		0			0
$763$	−7.65434	+	13.2577i	−0.277106	+	0.479961i
$764$		0			0
$765$	13.5425	+	23.4562i	0.489628	+	0.848061i
$766$		0			0
$767$	5.89917	−	2.77001i	0.213007	−	0.100019i
$768$		0			0
$769$	−10.8088	−	18.7215i	−0.389777	−	0.675113i	0.602643	−	0.798011i	$-0.294114\pi$
$769$	−10.8088	−	18.7215i	−0.389777	−	0.675113i	−0.992419	+	0.122898i	$0.960781\pi$
$770$		0			0
$771$	−0.404912	+	0.701329i	−0.0145826	+	0.0252577i
$772$		0			0
$773$	−5.00056	+	8.66123i	−0.179858	+	0.311523i	−0.941832	−	0.336085i	$-0.890897\pi$
$773$	−5.00056	+	8.66123i	−0.179858	+	0.311523i	0.761974	+	0.647608i	$0.224230\pi$
$774$		0			0
$775$	65.9436			2.36877
$776$		0			0
$777$	−0.0905505	−	0.156838i	−0.00324848	−	0.00562653i
$778$		0			0
$779$	−22.7169			−0.813917
$780$		0			0
$781$	6.15375			0.220199
$782$		0			0
$783$	5.63467	+	9.75954i	0.201367	+	0.348778i
$784$		0			0
$785$	−68.8285			−2.45659
$786$		0			0
$787$	20.8939	−	36.1893i	0.744787	−	1.29001i	−0.205507	−	0.978656i	$-0.565884\pi$
$787$	20.8939	−	36.1893i	0.744787	−	1.29001i	0.950294	−	0.311353i	$-0.100782\pi$
$788$		0			0
$789$	−1.83466	+	3.17772i	−0.0653156	+	0.113130i
$790$		0			0
$791$	−6.08846	−	10.5455i	−0.216481	−	0.374955i
$792$		0			0
$793$	1.98863	−	0.933780i	0.0706183	−	0.0331595i
$794$		0			0
$795$	−3.08287	−	5.33968i	−0.109338	−	0.189379i
$796$		0			0
$797$	11.3856	−	19.7204i	0.403297	−	0.698531i	−0.590825	−	0.806800i	$-0.701197\pi$
$797$	11.3856	−	19.7204i	0.403297	−	0.698531i	0.994122	+	0.108269i	$0.0345308\pi$
$798$		0			0
$799$	−9.76481	+	16.9131i	−0.345454	+	0.598344i
$800$		0			0
$801$	20.1474			0.711874
$802$		0			0
$803$	−1.34811	−	2.33499i	−0.0475736	−	0.0824000i
$804$		0			0
$805$	24.5558			0.865478
$806$		0			0
$807$	−4.16325			−0.146553
$808$		0			0
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	0.980498	+	0.196530i	$0.0629672\pi$
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	−0.320049	+	0.947401i	$0.603699\pi$
$810$		0			0
$811$	−11.5936			−0.407106			−0.203553	−	0.979064i	$-0.565249\pi$
$811$	−11.5936			−0.407106			−0.203553	+	0.979064i	$0.565249\pi$
$812$		0			0
$813$	−5.65159	+	9.78884i	−0.198210	+	0.343309i
$814$		0			0
$815$	−49.7957	+	86.2487i	−1.74427	+	3.02116i
$816$		0			0
$817$	5.81321	+	10.0688i	0.203379	+	0.352262i
$818$		0			0
$819$	0.821977	−	9.69296i	0.0287222	−	0.338700i
$820$		0			0
$821$	−15.5121	−	26.8678i	−0.541378	−	0.937693i	−0.998825	−	0.0484569i	$-0.984570\pi$
$821$	−15.5121	−	26.8678i	−0.541378	−	0.937693i	0.457448	−	0.889237i	$-0.348764\pi$
$822$		0			0
$823$	14.5387	−	25.1818i	0.506789	−	0.877784i	−0.493180	−	0.869927i	$-0.664166\pi$
$823$	14.5387	−	25.1818i	0.506789	−	0.877784i	0.999969	−	0.00785682i	$-0.00250093\pi$
$824$		0			0
$825$	1.93412	−	3.34999i	0.0673374	−	0.116632i
$826$		0			0
$827$	−14.8920			−0.517846			−0.258923	−	0.965898i	$-0.583368\pi$
$827$	−14.8920			−0.517846			−0.258923	+	0.965898i	$0.583368\pi$
$828$		0			0
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	0.901486	−	0.432807i	$-0.142477\pi$
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	−0.825565	+	0.564306i	$0.809144\pi$
$830$		0			0
$831$	−3.13541			−0.108766
$832$		0			0
$833$	−2.37888			−0.0824234
$834$		0			0
$835$	37.6219	+	65.1631i	1.30196	+	2.25506i
$836$		0			0
$837$	16.1215			0.557241
$838$		0			0
$839$	11.4109	−	19.7643i	0.393948	−	0.682338i	−0.599018	−	0.800735i	$-0.704442\pi$
$839$	11.4109	−	19.7643i	0.393948	−	0.682338i	0.992966	+	0.118397i	$0.0377756\pi$
$840$		0			0
$841$	8.02399	−	13.8980i	0.276689	−	0.479240i
$842$		0			0
$843$	−1.75119	−	3.03314i	−0.0603140	−	0.104467i
$844$		0			0
$845$	−19.0380	−	51.4508i	−0.654928	−	1.76996i
$846$		0			0
$847$	5.34900	+	9.26473i	0.183794	+	0.318340i
$848$		0			0
$849$	−7.42427	+	12.8592i	−0.254800	+	0.441327i
$850$		0			0
$851$	−0.958790	+	1.66067i	−0.0328669	+	0.0569271i
$852$		0			0
$853$	23.3549			0.799656			0.399828	−	0.916590i	$-0.369070\pi$
$853$	23.3549			0.799656			0.399828	+	0.916590i	$0.369070\pi$
$854$		0			0
$855$	−20.5548	−	35.6020i	−0.702960	−	1.21756i
$856$		0			0
$857$	−43.5306			−1.48698			−0.743488	−	0.668750i	$-0.766830\pi$
$857$	−43.5306			−1.48698			−0.743488	+	0.668750i	$0.766830\pi$
$858$		0			0
$859$	−20.5113			−0.699838			−0.349919	−	0.936780i	$-0.613791\pi$
$859$	−20.5113			−0.699838			−0.349919	+	0.936780i	$0.613791\pi$
$860$		0			0
$861$	−1.72877	−	2.99432i	−0.0589163	−	0.102046i
$862$		0			0
$863$	50.6678			1.72475			0.862376	−	0.506268i	$-0.168975\pi$
$863$	50.6678			1.72475			0.862376	+	0.506268i	$0.168975\pi$
$864$		0			0
$865$	−15.9756	+	27.6705i	−0.543186	+	0.940826i
$866$		0			0
$867$	−3.11621	+	5.39743i	−0.105832	+	0.183306i
$868$		0			0
$869$	−3.85156	−	6.67109i	−0.130655	−	0.226301i
$870$		0			0
$871$	3.15929	−	37.2552i	0.107048	−	1.26234i
$872$		0			0
$873$	−9.22809	−	15.9835i	−0.312323	−	0.540960i
$874$		0			0
$875$	16.4759	−	28.5371i	0.556987	−	0.964730i
$876$		0			0
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	−0.129231	−	0.991615i	$-0.541251\pi$
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	0.923379	−	0.383890i	$-0.125416\pi$
$878$		0			0
$879$	2.67891			0.0903573
$880$		0			0
$881$	8.05674	+	13.9547i	0.271439	+	0.470145i	0.969230	−	0.246155i	$-0.0791673\pi$
$881$	8.05674	+	13.9547i	0.271439	+	0.470145i	−0.697792	+	0.716301i	$0.745834\pi$
$882$		0			0
$883$	−42.0733			−1.41588			−0.707940	−	0.706273i	$-0.750375\pi$
$883$	−42.0733			−1.41588			−0.707940	+	0.706273i	$0.750375\pi$
$884$		0			0
$885$	4.19186			0.140908
$886$		0			0
$887$	−20.8814	−	36.1676i	−0.701128	−	1.21439i	−0.968071	−	0.250678i	$-0.919347\pi$
$887$	−20.8814	−	36.1676i	−0.701128	−	1.21439i	0.266942	−	0.963713i	$-0.413987\pi$
$888$		0			0
$889$	−1.96067			−0.0657588
$890$		0			0
$891$	−1.75119	+	3.03314i	−0.0586669	+	0.101614i
$892$		0			0
$893$	14.8211	−	25.6709i	0.495969	−	0.859043i
$894$		0			0
$895$	48.1151	+	83.3379i	1.60831	+	2.78568i
$896$		0			0
$897$	10.4365	−	4.90055i	0.348464	−	0.163625i
$898$		0			0
$899$	9.26434	+	16.0463i	0.308983	+	0.535174i
$900$		0			0
$901$	3.16233	−	5.47731i	0.105352	−	0.182476i
$902$		0			0
$903$	−0.884779	+	1.53248i	−0.0294436	+	0.0509978i
$904$		0			0
$905$	−58.7821			−1.95398
$906$		0			0
$907$	−7.71125	−	13.3563i	−0.256048	−	0.443488i	0.709132	−	0.705076i	$-0.249087\pi$
$907$	−7.71125	−	13.3563i	−0.256048	−	0.443488i	−0.965180	+	0.261588i	$0.915754\pi$
$908$		0			0
$909$	−15.5381			−0.515366
$910$		0			0
$911$	−37.5462			−1.24396			−0.621981	−	0.783033i	$-0.713672\pi$
$911$	−37.5462			−1.24396			−0.621981	+	0.783033i	$0.713672\pi$
$912$		0			0
$913$	−1.57490	−	2.72781i	−0.0521216	−	0.0902773i
$914$		0			0
$915$	1.41309			0.0467153
$916$		0			0
$917$	−3.25011	+	5.62935i	−0.107328	+	0.185897i
$918$		0			0
$919$	−4.73732	+	8.20528i	−0.156270	+	0.270667i	−0.933521	−	0.358524i	$-0.883280\pi$
$919$	−4.73732	+	8.20528i	−0.156270	+	0.270667i	0.777251	+	0.629191i	$0.216614\pi$
$920$		0			0
$921$	−4.44476	−	7.69856i	−0.146460	−	0.253676i
$922$		0			0
$923$	36.5458	−	17.1604i	1.20292	−	0.564842i
$924$		0			0
$925$	2.11047	+	3.65545i	0.0693919	+	0.120190i
$926$		0			0
$927$	−0.771324	+	1.33597i	−0.0253336	+	0.0438791i
$928$		0			0
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	0.406493	+	0.913654i	$0.366751\pi$
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	−0.994494	+	0.104793i	$0.966582\pi$
$930$		0			0
$931$	3.61068			0.118335
$932$		0			0
$933$	0.359424	+	0.622541i	0.0117670	+	0.0203811i
$934$		0			0
$935$	5.51689			0.180422
$936$		0			0
$937$	−31.3709			−1.02484			−0.512422	−	0.858734i	$-0.671252\pi$
$937$	−31.3709			−1.02484			−0.512422	+	0.858734i	$0.671252\pi$
$938$		0			0
$939$	3.62643	+	6.28116i	0.118344	+	0.204978i
$940$		0			0
$941$	44.7844			1.45993			0.729964	−	0.683486i	$-0.239537\pi$
$941$	44.7844			1.45993			0.729964	+	0.683486i	$0.239537\pi$
$942$		0			0
$943$	−18.3050	+	31.7052i	−0.596093	+	1.03246i
$944$		0			0
$945$	6.60714	−	11.4439i	0.214930	−	0.372270i
$946$		0			0
$947$	−17.5337	−	30.3692i	−0.569768	−	0.986868i	−0.996588	−	0.0825312i	$-0.973700\pi$
$947$	−17.5337	−	30.3692i	−0.569768	−	0.986868i	0.426820	−	0.904337i	$-0.359634\pi$
$948$		0			0
$949$	−14.5175	−	10.1076i	−0.471257	−	0.328108i
$950$		0			0
$951$	−2.21896	−	3.84334i	−0.0719546	−	0.124629i
$952$		0			0
$953$	−29.4852	+	51.0699i	−0.955120	+	1.65432i	−0.221027	+	0.975268i	$0.570941\pi$
$953$	−29.4852	+	51.0699i	−0.955120	+	1.65432i	−0.734093	+	0.679048i	$0.762393\pi$
$954$		0			0
$955$	26.7376	−	46.3108i	0.865208	−	1.49858i
$956$		0			0
$957$	1.08689			0.0351341
$958$		0			0
$959$	7.62878	+	13.2134i	0.246346	+	0.426684i
$960$		0			0
$961$	−4.49354			−0.144953
$962$		0			0
$963$	10.9851			0.353989
$964$		0			0
$965$	−8.76690	−	15.1847i	−0.282217	−	0.488813i
$966$		0			0
$967$	−30.3671			−0.976540			−0.488270	−	0.872693i	$-0.662372\pi$
$967$	−30.3671			−0.976540			−0.488270	+	0.872693i	$0.662372\pi$
$968$		0			0
$969$	−2.36016	+	4.08791i	−0.0758191	+	0.131323i
$970$		0			0
$971$	−24.7588	+	42.8834i	−0.794546	+	1.37619i	0.128581	+	0.991699i	$0.458958\pi$
$971$	−24.7588	+	42.8834i	−0.794546	+	1.37619i	−0.923127	+	0.384495i	$0.874375\pi$
$972$		0			0
$973$	−8.74801	−	15.1520i	−0.280448	−	0.485751i
$974$		0			0
$975$	2.14449	−	25.2884i	0.0686786	−	0.809876i
$976$		0			0
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	0.939757	−	0.341842i	$-0.111051\pi$
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	−0.765923	+	0.642933i	$0.777717\pi$
$978$		0			0
$979$	2.05190	−	3.55400i	0.0655790	−	0.113586i
$980$		0			0
$981$	20.6514	−	35.7692i	0.659347	−	1.14202i
$982$		0			0
$983$	−2.34833			−0.0749001			−0.0374501	−	0.999299i	$-0.511924\pi$
$983$	−2.34833			−0.0749001			−0.0374501	+	0.999299i	$0.511924\pi$
$984$		0			0
$985$	−14.4539	−	25.0350i	−0.460541	−	0.797680i
$986$		0			0
$987$	4.51158			0.143605
$988$		0			0
$989$	18.7369			0.595799
$990$		0			0
$991$	12.2408	+	21.2016i	0.388841	+	0.673492i	0.992294	−	0.123907i	$-0.0395424\pi$
$991$	12.2408	+	21.2016i	0.388841	+	0.673492i	−0.603453	+	0.797398i	$0.706209\pi$
$992$		0			0
$993$	−8.21311			−0.260635
$994$		0			0
$995$	1.71667	−	2.97336i	0.0544222	−	0.0942620i
$996$		0			0
$997$	3.31171	−	5.73604i	0.104883	−	0.181662i	−0.808808	−	0.588073i	$-0.799887\pi$
$997$	3.31171	−	5.73604i	0.104883	−	0.181662i	0.913690	+	0.406411i	$0.133220\pi$
$998$		0			0
$999$	0.515956	+	0.893662i	0.0163241	+	0.0282742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.q.1121.2		8
4.3	odd	2		91.2.f.c.29.1	yes	8
12.11	even	2		819.2.o.h.757.4		8
13.9	even	3	inner	1456.2.s.q.113.2		8
28.3	even	6		637.2.h.i.471.4		8
28.11	odd	6		637.2.h.h.471.4		8
28.19	even	6		637.2.g.j.263.1		8
28.23	odd	6		637.2.g.k.263.1		8
28.27	even	2		637.2.f.i.393.1		8
52.3	odd	6		1183.2.a.k.1.4		4
52.11	even	12		1183.2.c.g.337.7		8
52.15	even	12		1183.2.c.g.337.2		8
52.23	odd	6		1183.2.a.l.1.1		4
52.35	odd	6		91.2.f.c.22.1	✓	8
156.35	even	6		819.2.o.h.568.4		8
364.55	even	6		8281.2.a.bp.1.4		4
364.87	even	6		637.2.g.j.373.1		8
364.139	even	6		637.2.f.i.295.1		8
364.191	odd	6		637.2.h.h.165.4		8
364.243	even	6		637.2.h.i.165.4		8
364.335	even	6		8281.2.a.bt.1.1		4
364.347	odd	6		637.2.g.k.373.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	52.35	odd	6
91.2.f.c.29.1	yes	8	4.3	odd	2
637.2.f.i.295.1		8	364.139	even	6
637.2.f.i.393.1		8	28.27	even	2
637.2.g.j.263.1		8	28.19	even	6
637.2.g.j.373.1		8	364.87	even	6
637.2.g.k.263.1		8	28.23	odd	6
637.2.g.k.373.1		8	364.347	odd	6
637.2.h.h.165.4		8	364.191	odd	6
637.2.h.h.471.4		8	28.11	odd	6
637.2.h.i.165.4		8	364.243	even	6
637.2.h.i.471.4		8	28.3	even	6
819.2.o.h.568.4		8	156.35	even	6
819.2.o.h.757.4		8	12.11	even	2
1183.2.a.k.1.4		4	52.3	odd	6
1183.2.a.l.1.1		4	52.23	odd	6
1183.2.c.g.337.2		8	52.15	even	12
1183.2.c.g.337.7		8	52.11	even	12
1456.2.s.q.113.2		8	13.9	even	3	inner
1456.2.s.q.1121.2		8	1.1	even	1	trivial
8281.2.a.bp.1.4		4	364.55	even	6
8281.2.a.bt.1.1		4	364.335	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.274776 + 0.475925i) q^{3} -4.22001 q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.34900 - 2.33653i) q^{9} +(-0.274776 - 0.475925i) q^{11} +(-2.95900 - 2.06017i) q^{13} +(-1.15956 - 2.00841i) q^{15} +(1.18944 - 2.06017i) q^{17} +(-1.80534 + 3.12694i) q^{19} -0.549551 q^{21} +(2.90945 + 5.03931i) q^{23} +12.8085 q^{25} +3.13134 q^{27} +(1.79945 + 3.11673i) q^{29} +5.14844 q^{31} +(0.151003 - 0.261545i) q^{33} +(2.11000 - 3.65463i) q^{35} +(0.164772 + 0.285393i) q^{37} +(0.167428 - 1.97435i) q^{39} +(3.14579 + 5.44866i) q^{41} +(1.61000 - 2.78861i) q^{43} +(-5.69278 + 9.86018i) q^{45} -8.20957 q^{47} +(-0.500000 - 0.866025i) q^{49} +1.30732 q^{51} +2.65866 q^{53} +(1.15956 + 2.00841i) q^{55} -1.98426 q^{57} +(-0.903765 + 1.56537i) q^{59} +(-0.304662 + 0.527691i) q^{61} +(1.34900 + 2.33653i) q^{63} +(12.4870 + 8.69395i) q^{65} +(5.18490 + 8.98052i) q^{67} +(-1.59889 + 2.76936i) q^{69} +(-5.59889 + 9.69756i) q^{71} +4.90621 q^{73} +(3.51945 + 6.09587i) q^{75} +0.549551 q^{77} +14.0171 q^{79} +(-3.18657 - 5.51931i) q^{81} +5.73159 q^{83} +(-5.01945 + 8.69395i) q^{85} +(-0.988887 + 1.71280i) q^{87} +(3.73378 + 6.46709i) q^{89} +(3.26366 - 1.53248i) q^{91} +(1.41467 + 2.45027i) q^{93} +(7.61856 - 13.1957i) q^{95} +(3.42035 - 5.92422i) q^{97} -1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 14 q^{5} - 4 q^{7} - 7 q^{9} - q^{11} + 4 q^{13} + 3 q^{15} + 4 q^{17} + q^{19} - 2 q^{21} - 2 q^{23} + 10 q^{25} + 52 q^{27} - q^{29} + 8 q^{31} + 19 q^{33} + 7 q^{35} + 10 q^{37} - 20 q^{39}+ \cdots - 46 q^{99}+O(q^{100}) \) 8 * q + q^3 - 14 * q^5 - 4 * q^7 - 7 * q^9 - q^11 + 4 * q^13 + 3 * q^15 + 4 * q^17 + q^19 - 2 * q^21 - 2 * q^23 + 10 * q^25 + 52 * q^27 - q^29 + 8 * q^31 + 19 * q^33 + 7 * q^35 + 10 * q^37 - 20 * q^39 + 22 * q^41 + 3 * q^43 + 11 * q^45 - 4 * q^47 - 4 * q^49 - 14 * q^51 + 4 * q^53 - 3 * q^55 - 34 * q^57 - 8 * q^59 - 8 * q^61 - 7 * q^63 + 7 * q^65 - 6 * q^67 + 18 * q^69 - 14 * q^71 - 16 * q^73 - 7 * q^75 + 2 * q^77 + 52 * q^79 - 24 * q^81 - 5 * q^85 + 13 * q^87 + q^89 + 4 * q^91 + 7 * q^93 + 21 * q^95 - 3 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

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Database

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