LMFDB - Embedded newform 280.2.q.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(81,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("280.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	280.121
Dual form			280.2.q.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.62132 + 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.62132 + 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(2.41421 + 4.18154i) q^{11} +2.00000 q^{13} -2.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(-2.82843 + 4.89898i) q^{19} +(-3.91421 - 5.04757i) q^{21} +(4.20711 - 7.28692i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.414214 q^{27} -2.17157 q^{29} +(2.41421 + 4.18154i) q^{31} +(-5.82843 + 10.0951i) q^{33} +(1.00000 - 2.44949i) q^{35} +(2.82843 - 4.89898i) q^{37} +(2.41421 + 4.18154i) q^{39} +0.171573 q^{41} +12.8995 q^{43} +(-1.41421 - 2.44949i) q^{45} +(-0.171573 + 0.297173i) q^{47} +(6.74264 - 1.88064i) q^{49} +(4.41421 - 7.64564i) q^{51} +(-2.82843 - 4.89898i) q^{53} -4.82843 q^{55} -13.6569 q^{57} +(2.00000 + 3.46410i) q^{59} +(2.32843 - 4.03295i) q^{61} +(2.82843 - 6.92820i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(-3.44975 - 5.97514i) q^{67} +20.3137 q^{69} -12.0000 q^{71} +(3.82843 + 6.63103i) q^{73} +(1.20711 - 2.09077i) q^{75} +(-7.82843 - 10.0951i) q^{77} +(2.00000 - 3.46410i) q^{79} +(4.74264 + 8.21449i) q^{81} -13.2426 q^{83} +3.65685 q^{85} +(-2.62132 - 4.54026i) q^{87} +(8.32843 - 14.4253i) q^{89} +(-5.24264 + 0.717439i) q^{91} +(-5.82843 + 10.0951i) q^{93} +(-2.82843 - 4.89898i) q^{95} +6.00000 q^{97} -13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} + 8 q^{13} - 4 q^{15} + 4 q^{17} - 10 q^{21} + 14 q^{23} - 2 q^{25} - 4 q^{27} - 20 q^{29} + 4 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} + 12 q^{41} + 12 q^{43} - 12 q^{47} + 10 q^{49} + 12 q^{51} - 8 q^{55} - 32 q^{57} + 8 q^{59} - 2 q^{61} - 4 q^{65} + 6 q^{67} + 36 q^{69} - 48 q^{71} + 4 q^{73} + 2 q^{75} - 20 q^{77} + 8 q^{79} + 2 q^{81} - 36 q^{83} - 8 q^{85} - 2 q^{87} + 22 q^{89} - 4 q^{91} - 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 + 8 * q^13 - 4 * q^15 + 4 * q^17 - 10 * q^21 + 14 * q^23 - 2 * q^25 - 4 * q^27 - 20 * q^29 + 4 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 + 12 * q^41 + 12 * q^43 - 12 * q^47 + 10 * q^49 + 12 * q^51 - 8 * q^55 - 32 * q^57 + 8 * q^59 - 2 * q^61 - 4 * q^65 + 6 * q^67 + 36 * q^69 - 48 * q^71 + 4 * q^73 + 2 * q^75 - 20 * q^77 + 8 * q^79 + 2 * q^81 - 36 * q^83 - 8 * q^85 - 2 * q^87 + 22 * q^89 - 4 * q^91 - 12 * q^93 + 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	0.969528	+	0.244981i	$0.0787816\pi$
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	−0.272605	+	0.962126i	$0.587885\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$		0			0
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	0.957764	+	0.287556i	$0.0928428\pi$
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	−0.229851	+	0.973226i	$0.573824\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−2.41421			−0.623347
$16$		0			0
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	0.554485	−	0.832194i	$-0.312915\pi$
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	−0.997943	+	0.0641009i	$0.979582\pi$
$18$		0			0
$19$	−2.82843	+	4.89898i	−0.648886	+	1.12390i	0.334504	+	0.942394i	$0.391431\pi$
$19$	−2.82843	+	4.89898i	−0.648886	+	1.12390i	−0.983389	+	0.181509i	$0.941902\pi$
$20$		0			0
$21$	−3.91421	−	5.04757i	−0.854151	−	1.10147i
$22$		0			0
$23$	4.20711	−	7.28692i	0.877242	−	1.51943i	0.0228877	−	0.999738i	$-0.492714\pi$
$23$	4.20711	−	7.28692i	0.877242	−	1.51943i	0.854355	−	0.519690i	$-0.173953\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	0.414214			0.0797154
$28$		0			0
$29$	−2.17157			−0.403251			−0.201625	−	0.979463i	$-0.564622\pi$
$29$	−2.17157			−0.403251			−0.201625	+	0.979463i	$0.564622\pi$
$30$		0			0
$31$	2.41421	+	4.18154i	0.433606	+	0.751027i	0.997181	−	0.0750380i	$-0.0239078\pi$
$31$	2.41421	+	4.18154i	0.433606	+	0.751027i	−0.563575	+	0.826065i	$0.690574\pi$
$32$		0			0
$33$	−5.82843	+	10.0951i	−1.01460	+	1.75734i
$34$		0			0
$35$	1.00000	−	2.44949i	0.169031	−	0.414039i
$36$		0			0
$37$	2.82843	−	4.89898i	0.464991	−	0.805387i	−0.534211	−	0.845351i	$-0.679391\pi$
$37$	2.82843	−	4.89898i	0.464991	−	0.805387i	0.999201	+	0.0399642i	$0.0127244\pi$
$38$		0			0
$39$	2.41421	+	4.18154i	0.386584	+	0.669582i
$40$		0			0
$41$	0.171573			0.0267952			0.0133976	−	0.999910i	$-0.495735\pi$
$41$	0.171573			0.0267952			0.0133976	+	0.999910i	$0.495735\pi$
$42$		0			0
$43$	12.8995			1.96715			0.983577	−	0.180488i	$-0.0577676\pi$
$43$	12.8995			1.96715			0.983577	+	0.180488i	$0.0577676\pi$
$44$		0			0
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$		0			0
$47$	−0.171573	+	0.297173i	−0.0250265	+	0.0433471i	−0.878267	−	0.478170i	$-0.841300\pi$
$47$	−0.171573	+	0.297173i	−0.0250265	+	0.0433471i	0.853241	+	0.521517i	$0.174634\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$	4.41421	−	7.64564i	0.618114	−	1.07060i
$52$		0			0
$53$	−2.82843	−	4.89898i	−0.388514	−	0.672927i	0.603736	−	0.797185i	$-0.293678\pi$
$53$	−2.82843	−	4.89898i	−0.388514	−	0.672927i	−0.992250	+	0.124258i	$0.960345\pi$
$54$		0			0
$55$	−4.82843			−0.651065
$56$		0			0
$57$	−13.6569			−1.80889
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	2.32843	−	4.03295i	0.298125	−	0.516367i	−0.677582	−	0.735447i	$-0.736972\pi$
$61$	2.32843	−	4.03295i	0.298125	−	0.516367i	0.975707	+	0.219080i	$0.0703056\pi$
$62$		0			0
$63$	2.82843	−	6.92820i	0.356348	−	0.872872i
$64$		0			0
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	−3.44975	−	5.97514i	−0.421454	−	0.729979i	0.574628	−	0.818415i	$-0.305147\pi$
$67$	−3.44975	−	5.97514i	−0.421454	−	0.729979i	−0.996082	+	0.0884353i	$0.971813\pi$
$68$		0			0
$69$	20.3137			2.44548
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	3.82843	+	6.63103i	0.448084	+	0.776103i	0.998261	−	0.0589442i	$-0.0187734\pi$
$73$	3.82843	+	6.63103i	0.448084	+	0.776103i	−0.550178	+	0.835048i	$0.685440\pi$
$74$		0			0
$75$	1.20711	−	2.09077i	0.139385	−	0.241421i
$76$		0			0
$77$	−7.82843	−	10.0951i	−0.892132	−	1.15045i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	−13.2426			−1.45357			−0.726784	−	0.686866i	$-0.758986\pi$
$83$	−13.2426			−1.45357			−0.726784	+	0.686866i	$0.758986\pi$
$84$		0			0
$85$	3.65685			0.396642
$86$		0			0
$87$	−2.62132	−	4.54026i	−0.281035	−	0.486767i
$88$		0			0
$89$	8.32843	−	14.4253i	0.882812	−	1.52907i	0.0346099	−	0.999401i	$-0.488981\pi$
$89$	8.32843	−	14.4253i	0.882812	−	1.52907i	0.848202	−	0.529673i	$-0.177686\pi$
$90$		0			0
$91$	−5.24264	+	0.717439i	−0.549578	+	0.0752080i
$92$		0			0
$93$	−5.82843	+	10.0951i	−0.604380	+	1.04682i
$94$		0			0
$95$	−2.82843	−	4.89898i	−0.290191	−	0.502625i
$96$		0			0
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	−13.6569			−1.37257
$100$		0			0
$101$	−2.74264	−	4.75039i	−0.272903	−	0.472682i	0.696701	−	0.717362i	$-0.254650\pi$
$101$	−2.74264	−	4.75039i	−0.272903	−	0.472682i	−0.969604	+	0.244680i	$0.921317\pi$
$102$		0			0
$103$	−5.20711	+	9.01897i	−0.513071	+	0.888666i	0.486814	+	0.873506i	$0.338159\pi$
$103$	−5.20711	+	9.01897i	−0.513071	+	0.888666i	−0.999885	+	0.0151600i	$0.995174\pi$
$104$		0			0
$105$	6.32843	−	0.866025i	0.617591	−	0.0845154i
$106$		0			0
$107$	4.20711	−	7.28692i	0.406716	−	0.704453i	−0.587803	−	0.809004i	$-0.700007\pi$
$107$	4.20711	−	7.28692i	0.406716	−	0.704453i	0.994520	+	0.104551i	$0.0333404\pi$
$108$		0			0
$109$	2.15685	+	3.73578i	0.206589	+	0.357823i	0.950638	−	0.310302i	$-0.100430\pi$
$109$	2.15685	+	3.73578i	0.206589	+	0.357823i	−0.744049	+	0.668125i	$0.767097\pi$
$110$		0			0
$111$	13.6569			1.29625
$112$		0			0
$113$	−11.3137			−1.06430			−0.532152	−	0.846649i	$-0.678617\pi$
$113$	−11.3137			−1.06430			−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$	4.20711	+	7.28692i	0.392315	+	0.679509i
$116$		0			0
$117$	−2.82843	+	4.89898i	−0.261488	+	0.452911i
$118$		0			0
$119$	5.92893	+	7.64564i	0.543504	+	0.700875i
$120$		0			0
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$		0			0
$123$	0.207107	+	0.358719i	0.0186742	+	0.0323446i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−15.6569			−1.38932			−0.694661	−	0.719338i	$-0.744445\pi$
$127$	−15.6569			−1.38932			−0.694661	+	0.719338i	$0.744445\pi$
$128$		0			0
$129$	15.5711	+	26.9699i	1.37096	+	2.37457i
$130$		0			0
$131$	−1.17157	+	2.02922i	−0.102361	+	0.177294i	−0.912657	−	0.408727i	$-0.865973\pi$
$131$	−1.17157	+	2.02922i	−0.102361	+	0.177294i	0.810296	+	0.586021i	$0.199306\pi$
$132$		0			0
$133$	5.65685	−	13.8564i	0.490511	−	1.20150i
$134$		0			0
$135$	−0.207107	+	0.358719i	−0.0178249	+	0.0308737i
$136$		0			0
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−14.4853			−1.22863			−0.614313	−	0.789063i	$-0.710567\pi$
$139$	−14.4853			−1.22863			−0.614313	+	0.789063i	$0.710567\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$		0			0
$143$	4.82843	+	8.36308i	0.403773	+	0.699356i
$144$		0			0
$145$	1.08579	−	1.88064i	0.0901697	−	0.156178i
$146$		0			0
$147$	12.0711	+	11.8272i	0.995605	+	0.975490i
$148$		0			0
$149$	3.32843	−	5.76500i	0.272675	−	0.472288i	−0.696871	−	0.717197i	$-0.745425\pi$
$149$	3.32843	−	5.76500i	0.272675	−	0.472288i	0.969546	+	0.244909i	$0.0787582\pi$
$150$		0			0
$151$	8.41421	+	14.5738i	0.684739	+	1.18600i	0.973519	+	0.228607i	$0.0734171\pi$
$151$	8.41421	+	14.5738i	0.684739	+	1.18600i	−0.288780	+	0.957396i	$0.593250\pi$
$152$		0			0
$153$	10.3431			0.836194
$154$		0			0
$155$	−4.82843			−0.387829
$156$		0			0
$157$	10.6569	+	18.4582i	0.850510	+	1.47313i	0.880749	+	0.473583i	$0.157040\pi$
$157$	10.6569	+	18.4582i	0.850510	+	1.47313i	−0.0302396	+	0.999543i	$0.509627\pi$
$158$		0			0
$159$	6.82843	−	11.8272i	0.541529	−	0.937957i
$160$		0			0
$161$	−8.41421	+	20.6105i	−0.663133	+	1.62434i
$162$		0			0
$163$	2.17157	−	3.76127i	0.170091	−	0.294606i	−0.768361	−	0.640017i	$-0.778927\pi$
$163$	2.17157	−	3.76127i	0.170091	−	0.294606i	0.938451	+	0.345411i	$0.112261\pi$
$164$		0			0
$165$	−5.82843	−	10.0951i	−0.453742	−	0.785905i
$166$		0			0
$167$	−12.0711			−0.934087			−0.467044	−	0.884234i	$-0.654681\pi$
$167$	−12.0711			−0.934087			−0.467044	+	0.884234i	$0.654681\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−8.00000	−	13.8564i	−0.611775	−	1.05963i
$172$		0			0
$173$	−10.8284	+	18.7554i	−0.823270	+	1.42595i	0.0799642	+	0.996798i	$0.474519\pi$
$173$	−10.8284	+	18.7554i	−0.823270	+	1.42595i	−0.903234	+	0.429148i	$0.858814\pi$
$174$		0			0
$175$	1.62132	+	2.09077i	0.122560	+	0.158047i
$176$		0			0
$177$	−4.82843	+	8.36308i	−0.362927	+	0.628608i
$178$		0			0
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	0.600841	−	0.799369i	$-0.294833\pi$
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	−0.992694	+	0.120659i	$0.961499\pi$
$180$		0			0
$181$	−9.82843			−0.730541			−0.365271	−	0.930901i	$-0.619024\pi$
$181$	−9.82843			−0.730541			−0.365271	+	0.930901i	$0.619024\pi$
$182$		0			0
$183$	11.2426			0.831080
$184$		0			0
$185$	2.82843	+	4.89898i	0.207950	+	0.360180i
$186$		0			0
$187$	8.82843	−	15.2913i	0.645599	−	1.11821i
$188$		0			0
$189$	−1.08579	+	0.148586i	−0.0789793	+	0.0108081i
$190$		0			0
$191$	11.2426	−	19.4728i	0.813489	−	1.40900i	−0.0969189	−	0.995292i	$-0.530899\pi$
$191$	11.2426	−	19.4728i	0.813489	−	1.40900i	0.910408	−	0.413712i	$-0.135768\pi$
$192$		0			0
$193$	−8.65685	−	14.9941i	−0.623134	−	1.07930i	−0.988899	−	0.148592i	$-0.952526\pi$
$193$	−8.65685	−	14.9941i	−0.623134	−	1.07930i	0.365765	−	0.930707i	$-0.380808\pi$
$194$		0			0
$195$	−4.82843			−0.345771
$196$		0			0
$197$	11.6569			0.830516			0.415258	−	0.909704i	$-0.363691\pi$
$197$	11.6569			0.830516			0.415258	+	0.909704i	$0.363691\pi$
$198$		0			0
$199$	0.343146	+	0.594346i	0.0243250	+	0.0421321i	0.877932	−	0.478786i	$-0.158923\pi$
$199$	0.343146	+	0.594346i	0.0243250	+	0.0421321i	−0.853607	+	0.520918i	$0.825590\pi$
$200$		0			0
$201$	8.32843	−	14.4253i	0.587442	−	1.01748i
$202$		0			0
$203$	5.69239	−	0.778985i	0.399527	−	0.0546741i
$204$		0			0
$205$	−0.0857864	+	0.148586i	−0.00599158	+	0.0103777i
$206$		0			0
$207$	11.8995	+	20.6105i	0.827072	+	1.43253i
$208$		0			0
$209$	−27.3137			−1.88933
$210$		0			0
$211$	−18.6274			−1.28236			−0.641182	−	0.767389i	$-0.721556\pi$
$211$	−18.6274			−1.28236			−0.641182	+	0.767389i	$0.721556\pi$
$212$		0			0
$213$	−14.4853	−	25.0892i	−0.992515	−	1.71909i
$214$		0			0
$215$	−6.44975	+	11.1713i	−0.439869	+	0.761876i
$216$		0			0
$217$	−7.82843	−	10.0951i	−0.531428	−	0.685302i
$218$		0			0
$219$	−9.24264	+	16.0087i	−0.624560	+	1.08177i
$220$		0			0
$221$	−3.65685	−	6.33386i	−0.245987	−	0.426061i
$222$		0			0
$223$	18.9706			1.27036			0.635181	−	0.772363i	$-0.280925\pi$
$223$	18.9706			1.27036			0.635181	+	0.772363i	$0.280925\pi$
$224$		0			0
$225$	2.82843			0.188562
$226$		0			0
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$	11.6569	−	28.5533i	0.766965	−	1.87867i
$232$		0			0
$233$	−0.171573	+	0.297173i	−0.0112401	+	0.0194684i	−0.871591	−	0.490234i	$-0.836911\pi$
$233$	−0.171573	+	0.297173i	−0.0112401	+	0.0194684i	0.860351	+	0.509703i	$0.170245\pi$
$234$		0			0
$235$	−0.171573	−	0.297173i	−0.0111922	−	0.0193854i
$236$		0			0
$237$	9.65685			0.627280
$238$		0			0
$239$	−13.5147			−0.874194			−0.437097	−	0.899414i	$-0.643993\pi$
$239$	−13.5147			−0.874194			−0.437097	+	0.899414i	$0.643993\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$		0			0
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$		0			0
$245$	−1.74264	+	6.77962i	−0.111333	+	0.433134i
$246$		0			0
$247$	−5.65685	+	9.79796i	−0.359937	+	0.623429i
$248$		0			0
$249$	−15.9853	−	27.6873i	−1.01303	−	1.75461i
$250$		0			0
$251$	23.4558			1.48052			0.740260	−	0.672321i	$-0.234702\pi$
$251$	23.4558			1.48052			0.740260	+	0.672321i	$0.234702\pi$
$252$		0			0
$253$	40.6274			2.55422
$254$		0			0
$255$	4.41421	+	7.64564i	0.276429	+	0.478789i
$256$		0			0
$257$	3.65685	−	6.33386i	0.228108	−	0.395095i	−0.729139	−	0.684365i	$-0.760079\pi$
$257$	3.65685	−	6.33386i	0.228108	−	0.395095i	0.957247	+	0.289270i	$0.0934126\pi$
$258$		0			0
$259$	−5.65685	+	13.8564i	−0.351500	+	0.860995i
$260$		0			0
$261$	3.07107	−	5.31925i	0.190094	−	0.329253i
$262$		0			0
$263$	−4.86396	−	8.42463i	−0.299925	−	0.519485i	0.676194	−	0.736724i	$-0.263628\pi$
$263$	−4.86396	−	8.42463i	−0.299925	−	0.519485i	−0.976118	+	0.217239i	$0.930295\pi$
$264$		0			0
$265$	5.65685			0.347498
$266$		0			0
$267$	40.2132			2.46101
$268$		0			0
$269$	−2.32843	−	4.03295i	−0.141967	−	0.245894i	0.786270	−	0.617882i	$-0.212009\pi$
$269$	−2.32843	−	4.03295i	−0.141967	−	0.245894i	−0.928237	+	0.371989i	$0.878676\pi$
$270$		0			0
$271$	−9.65685	+	16.7262i	−0.586612	+	1.01604i	0.408060	+	0.912955i	$0.366205\pi$
$271$	−9.65685	+	16.7262i	−0.586612	+	1.01604i	−0.994672	+	0.103087i	$0.967128\pi$
$272$		0			0
$273$	−7.82843	−	10.0951i	−0.473798	−	0.610985i
$274$		0			0
$275$	2.41421	−	4.18154i	0.145583	−	0.252156i
$276$		0			0
$277$	8.31371	+	14.3998i	0.499522	+	0.865198i	1.00000		0.000551476i	$-0.000175540\pi$
$277$	8.31371	+	14.3998i	0.499522	+	0.865198i	−0.500478	+	0.865750i	$0.666842\pi$
$278$		0			0
$279$	−13.6569			−0.817614
$280$		0			0
$281$	25.3137			1.51009			0.755045	−	0.655673i	$-0.227615\pi$
$281$	25.3137			1.51009			0.755045	+	0.655673i	$0.227615\pi$
$282$		0			0
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	−0.999164	−	0.0408910i	$-0.986980\pi$
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	0.464169	−	0.885747i	$-0.346353\pi$
$284$		0			0
$285$	6.82843	−	11.8272i	0.404481	−	0.700582i
$286$		0			0
$287$	−0.449747	+	0.0615465i	−0.0265478	+	0.00363298i
$288$		0			0
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$		0			0
$291$	7.24264	+	12.5446i	0.424571	+	0.735379i
$292$		0			0
$293$	−16.9706			−0.991431			−0.495715	−	0.868485i	$-0.665094\pi$
$293$	−16.9706			−0.991431			−0.495715	+	0.868485i	$0.665094\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$		0			0
$299$	8.41421	−	14.5738i	0.486607	−	0.842827i
$300$		0			0
$301$	−33.8137	+	4.62730i	−1.94899	+	0.266713i
$302$		0			0
$303$	6.62132	−	11.4685i	0.380385	−	0.658846i
$304$		0			0
$305$	2.32843	+	4.03295i	0.133325	+	0.230926i
$306$		0			0
$307$	13.2426			0.755797			0.377899	−	0.925847i	$-0.376647\pi$
$307$	13.2426			0.755797			0.377899	+	0.925847i	$0.376647\pi$
$308$		0			0
$309$	−25.1421			−1.43029
$310$		0			0
$311$	−5.17157	−	8.95743i	−0.293253	−	0.507929i	0.681324	−	0.731982i	$-0.261404\pi$
$311$	−5.17157	−	8.95743i	−0.293253	−	0.507929i	−0.974577	+	0.224053i	$0.928071\pi$
$312$		0			0
$313$	6.48528	−	11.2328i	0.366570	−	0.634917i	−0.622457	−	0.782654i	$-0.713865\pi$
$313$	6.48528	−	11.2328i	0.366570	−	0.634917i	0.989027	+	0.147737i	$0.0471988\pi$
$314$		0			0
$315$	4.58579	+	5.91359i	0.258380	+	0.333193i
$316$		0			0
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$		0			0
$319$	−5.24264	−	9.08052i	−0.293532	−	0.508412i
$320$		0			0
$321$	20.3137			1.13380
$322$		0			0
$323$	20.6863			1.15102
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$		0			0
$327$	−5.20711	+	9.01897i	−0.287954	+	0.498750i
$328$		0			0
$329$	0.343146	−	0.840532i	0.0189182	−	0.0463400i
$330$		0			0
$331$	−4.75736	+	8.23999i	−0.261488	+	0.452911i	−0.966638	−	0.256148i	$-0.917547\pi$
$331$	−4.75736	+	8.23999i	−0.261488	+	0.452911i	0.705149	+	0.709059i	$0.250880\pi$
$332$		0			0
$333$	8.00000	+	13.8564i	0.438397	+	0.759326i
$334$		0			0
$335$	6.89949			0.376960
$336$		0			0
$337$	−8.97056			−0.488658			−0.244329	−	0.969692i	$-0.578568\pi$
$337$	−8.97056			−0.488658			−0.244329	+	0.969692i	$0.578568\pi$
$338$		0			0
$339$	−13.6569	−	23.6544i	−0.741739	−	1.28473i
$340$		0			0
$341$	−11.6569	+	20.1903i	−0.631254	+	1.09336i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$	−10.1569	+	17.5922i	−0.546827	+	0.947132i
$346$		0			0
$347$	12.6924	+	21.9839i	0.681363	+	1.18016i	0.974565	+	0.224105i	$0.0719458\pi$
$347$	12.6924	+	21.9839i	0.681363	+	1.18016i	−0.293202	+	0.956051i	$0.594721\pi$
$348$		0			0
$349$	4.17157			0.223299			0.111650	−	0.993748i	$-0.464387\pi$
$349$	4.17157			0.223299			0.111650	+	0.993748i	$0.464387\pi$
$350$		0			0
$351$	0.828427			0.0442182
$352$		0			0
$353$	−11.1716	−	19.3497i	−0.594603	−	1.02988i	−0.993603	−	0.112931i	$-0.963976\pi$
$353$	−11.1716	−	19.3497i	−0.594603	−	1.02988i	0.399000	−	0.916951i	$-0.369357\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$		0			0
$357$	−8.82843	+	21.6251i	−0.467250	+	1.14452i
$358$		0			0
$359$	−5.24264	+	9.08052i	−0.276696	+	0.479252i	−0.970562	−	0.240853i	$-0.922573\pi$
$359$	−5.24264	+	9.08052i	−0.276696	+	0.479252i	0.693866	+	0.720105i	$0.255906\pi$
$360$		0			0
$361$	−6.50000	−	11.2583i	−0.342105	−	0.592544i
$362$		0			0
$363$	−29.7279			−1.56031
$364$		0			0
$365$	−7.65685			−0.400778
$366$		0			0
$367$	−12.2071	−	21.1433i	−0.637206	−	1.10367i	−0.986043	−	0.166490i	$-0.946757\pi$
$367$	−12.2071	−	21.1433i	−0.637206	−	1.10367i	0.348837	−	0.937183i	$-0.386577\pi$
$368$		0			0
$369$	−0.242641	+	0.420266i	−0.0126314	+	0.0218782i
$370$		0			0
$371$	9.17157	+	11.8272i	0.476164	+	0.614037i
$372$		0			0
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	−0.978507	−	0.206213i	$-0.933886\pi$
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	0.667839	+	0.744306i	$0.267219\pi$
$374$		0			0
$375$	1.20711	+	2.09077i	0.0623347	+	0.107967i
$376$		0			0
$377$	−4.34315			−0.223683
$378$		0			0
$379$	27.3137			1.40301			0.701505	−	0.712664i	$-0.252512\pi$
$379$	27.3137			1.40301			0.701505	+	0.712664i	$0.252512\pi$
$380$		0			0
$381$	−18.8995	−	32.7349i	−0.968250	−	1.67706i
$382$		0			0
$383$	−9.44975	+	16.3674i	−0.482860	+	0.836337i	−0.999806	−	0.0196803i	$-0.993735\pi$
$383$	−9.44975	+	16.3674i	−0.482860	+	0.836337i	0.516947	+	0.856018i	$0.327069\pi$
$384$		0			0
$385$	12.6569	−	1.73205i	0.645053	−	0.0882735i
$386$		0			0
$387$	−18.2426	+	31.5972i	−0.927326	+	1.60617i
$388$		0			0
$389$	8.65685	+	14.9941i	0.438920	+	0.760232i	0.997606	−	0.0691473i	$-0.0220278\pi$
$389$	8.65685	+	14.9941i	0.438920	+	0.760232i	−0.558687	+	0.829379i	$0.688695\pi$
$390$		0			0
$391$	−30.7696			−1.55608
$392$		0			0
$393$	−5.65685			−0.285351
$394$		0			0
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$		0			0
$397$	−10.3137	+	17.8639i	−0.517630	+	0.896562i	0.482160	+	0.876083i	$0.339852\pi$
$397$	−10.3137	+	17.8639i	−0.517630	+	0.896562i	−0.999790	+	0.0204787i	$0.993481\pi$
$398$		0			0
$399$	35.7990	−	4.89898i	1.79219	−	0.245256i
$400$		0			0
$401$	4.84315	−	8.38857i	0.241855	−	0.418905i	−0.719388	−	0.694609i	$-0.755577\pi$
$401$	4.84315	−	8.38857i	0.241855	−	0.418905i	0.961243	+	0.275703i	$0.0889108\pi$
$402$		0			0
$403$	4.82843	+	8.36308i	0.240521	+	0.416595i
$404$		0			0
$405$	−9.48528			−0.471327
$406$		0			0
$407$	27.3137			1.35389
$408$		0			0
$409$	−1.57107	−	2.72117i	−0.0776843	−	0.134553i	0.824566	−	0.565766i	$-0.191419\pi$
$409$	−1.57107	−	2.72117i	−0.0776843	−	0.134553i	−0.902250	+	0.431212i	$0.858086\pi$
$410$		0			0
$411$	−4.82843	+	8.36308i	−0.238169	+	0.412520i
$412$		0			0
$413$	−6.48528	−	8.36308i	−0.319120	−	0.411520i
$414$		0			0
$415$	6.62132	−	11.4685i	0.325028	−	0.562965i
$416$		0			0
$417$	−17.4853	−	30.2854i	−0.856258	−	1.48308i
$418$		0			0
$419$	7.31371			0.357298			0.178649	−	0.983913i	$-0.442827\pi$
$419$	7.31371			0.357298			0.178649	+	0.983913i	$0.442827\pi$
$420$		0			0
$421$	38.6569			1.88402			0.942010	−	0.335585i	$-0.108934\pi$
$421$	38.6569			1.88402			0.942010	+	0.335585i	$0.108934\pi$
$422$		0			0
$423$	−0.485281	−	0.840532i	−0.0235952	−	0.0408681i
$424$		0			0
$425$	−1.82843	+	3.16693i	−0.0886917	+	0.153619i
$426$		0			0
$427$	−4.65685	+	11.4069i	−0.225361	+	0.552019i
$428$		0			0
$429$	−11.6569	+	20.1903i	−0.562798	+	0.974795i
$430$		0			0
$431$	−2.41421	−	4.18154i	−0.116289	−	0.201418i	0.802006	−	0.597317i	$-0.203766\pi$
$431$	−2.41421	−	4.18154i	−0.116289	−	0.201418i	−0.918294	+	0.395899i	$0.870433\pi$
$432$		0			0
$433$	3.31371			0.159247			0.0796233	−	0.996825i	$-0.474628\pi$
$433$	3.31371			0.159247			0.0796233	+	0.996825i	$0.474628\pi$
$434$		0			0
$435$	5.24264			0.251365
$436$		0			0
$437$	23.7990	+	41.2211i	1.13846	+	1.97187i
$438$		0			0
$439$	14.8284	−	25.6836i	0.707722	−	1.22581i	−0.257978	−	0.966151i	$-0.583056\pi$
$439$	14.8284	−	25.6836i	0.707722	−	1.22581i	0.965700	−	0.259660i	$-0.0836105\pi$
$440$		0			0
$441$	−4.92893	+	19.1757i	−0.234711	+	0.913126i
$442$		0			0
$443$	9.20711	−	15.9472i	0.437443	−	0.757673i	−0.560049	−	0.828460i	$-0.689218\pi$
$443$	9.20711	−	15.9472i	0.437443	−	0.757673i	0.997491	+	0.0707865i	$0.0225509\pi$
$444$		0			0
$445$	8.32843	+	14.4253i	0.394805	+	0.683823i
$446$		0			0
$447$	16.0711			0.760135
$448$		0			0
$449$	9.48528			0.447638			0.223819	−	0.974631i	$-0.428148\pi$
$449$	9.48528			0.447638			0.223819	+	0.974631i	$0.428148\pi$
$450$		0			0
$451$	0.414214	+	0.717439i	0.0195046	+	0.0337829i
$452$		0			0
$453$	−20.3137	+	35.1844i	−0.954421	+	1.65311i
$454$		0			0
$455$	2.00000	−	4.89898i	0.0937614	−	0.229668i
$456$		0			0
$457$	2.48528	−	4.30463i	0.116257	−	0.201362i	−0.802025	−	0.597291i	$-0.796244\pi$
$457$	2.48528	−	4.30463i	0.116257	−	0.201362i	0.918281	+	0.395928i	$0.129577\pi$
$458$		0			0
$459$	−0.757359	−	1.31178i	−0.0353505	−	0.0612289i
$460$		0			0
$461$	−21.3137			−0.992678			−0.496339	−	0.868129i	$-0.665323\pi$
$461$	−21.3137			−0.992678			−0.496339	+	0.868129i	$0.665323\pi$
$462$		0			0
$463$	−4.89949			−0.227699			−0.113849	−	0.993498i	$-0.536318\pi$
$463$	−4.89949			−0.227699			−0.113849	+	0.993498i	$0.536318\pi$
$464$		0			0
$465$	−5.82843	−	10.0951i	−0.270287	−	0.468151i
$466$		0			0
$467$	−7.93503	+	13.7439i	−0.367189	+	0.635991i	−0.989125	−	0.147078i	$-0.953013\pi$
$467$	−7.93503	+	13.7439i	−0.367189	+	0.635991i	0.621936	+	0.783068i	$0.286347\pi$
$468$		0			0
$469$	11.1863	+	14.4253i	0.516535	+	0.666097i
$470$		0			0
$471$	−25.7279	+	44.5621i	−1.18548	+	2.05331i
$472$		0			0
$473$	31.1421	+	53.9398i	1.43192	+	2.48015i
$474$		0			0
$475$	5.65685			0.259554
$476$		0			0
$477$	16.0000			0.732590
$478$		0			0
$479$	9.24264	+	16.0087i	0.422307	+	0.731457i	0.996165	−	0.0874978i	$-0.0278871\pi$
$479$	9.24264	+	16.0087i	0.422307	+	0.731457i	−0.573858	+	0.818955i	$0.694554\pi$
$480$		0			0
$481$	5.65685	−	9.79796i	0.257930	−	0.446748i
$482$		0			0
$483$	−53.2487	+	7.28692i	−2.42290	+	0.331566i
$484$		0			0
$485$	−3.00000	+	5.19615i	−0.136223	+	0.235945i
$486$		0			0
$487$	−9.14214	−	15.8346i	−0.414270	−	0.717536i	0.581082	−	0.813845i	$-0.302630\pi$
$487$	−9.14214	−	15.8346i	−0.414270	−	0.717536i	−0.995351	+	0.0963090i	$0.969296\pi$
$488$		0			0
$489$	10.4853			0.474161
$490$		0			0
$491$	18.4853			0.834229			0.417115	−	0.908854i	$-0.363041\pi$
$491$	18.4853			0.834229			0.417115	+	0.908854i	$0.363041\pi$
$492$		0			0
$493$	3.97056	+	6.87722i	0.178825	+	0.309734i
$494$		0			0
$495$	6.82843	−	11.8272i	0.306915	−	0.531592i
$496$		0			0
$497$	31.4558	−	4.30463i	1.41099	−	0.193089i
$498$		0			0
$499$	−7.92893	+	13.7333i	−0.354948	+	0.614788i	−0.987109	−	0.160049i	$-0.948835\pi$
$499$	−7.92893	+	13.7333i	−0.354948	+	0.614788i	0.632161	+	0.774837i	$0.282168\pi$
$500$		0			0
$501$	−14.5711	−	25.2378i	−0.650987	−	1.12754i
$502$		0			0
$503$	−18.0711			−0.805749			−0.402875	−	0.915255i	$-0.631989\pi$
$503$	−18.0711			−0.805749			−0.402875	+	0.915255i	$0.631989\pi$
$504$		0			0
$505$	5.48528			0.244092
$506$		0			0
$507$	−10.8640	−	18.8169i	−0.482485	−	0.835689i
$508$		0			0
$509$	8.25736	−	14.3022i	0.366001	−	0.633932i	−0.622935	−	0.782273i	$-0.714060\pi$
$509$	8.25736	−	14.3022i	0.366001	−	0.633932i	0.988936	+	0.148341i	$0.0473933\pi$
$510$		0			0
$511$	−12.4142	−	16.0087i	−0.549172	−	0.708184i
$512$		0			0
$513$	−1.17157	+	2.02922i	−0.0517262	+	0.0895924i
$514$		0			0
$515$	−5.20711	−	9.01897i	−0.229453	−	0.397423i
$516$		0			0
$517$	−1.65685			−0.0728684
$518$		0			0
$519$	−52.2843			−2.29502
$520$		0			0
$521$	4.31371	+	7.47156i	0.188987	+	0.327335i	0.944913	−	0.327322i	$-0.106146\pi$
$521$	4.31371	+	7.47156i	0.188987	+	0.327335i	−0.755926	+	0.654657i	$0.772813\pi$
$522$		0			0
$523$	19.9706	−	34.5900i	0.873252	−	1.51252i	0.0146382	−	0.999893i	$-0.495340\pi$
$523$	19.9706	−	34.5900i	0.873252	−	1.51252i	0.858613	−	0.512624i	$-0.171326\pi$
$524$		0			0
$525$	−2.41421	+	5.91359i	−0.105365	+	0.258090i
$526$		0			0
$527$	8.82843	−	15.2913i	0.384572	−	0.666099i
$528$		0			0
$529$	−23.8995	−	41.3951i	−1.03911	−	1.79979i
$530$		0			0
$531$	−11.3137			−0.490973
$532$		0			0
$533$	0.343146			0.0148633
$534$		0			0
$535$	4.20711	+	7.28692i	0.181889	+	0.315041i
$536$		0			0
$537$	12.6569	−	21.9223i	0.546184	−	0.946018i
$538$		0			0
$539$	24.1421	+	23.6544i	1.03988	+	1.01887i
$540$		0			0
$541$	3.25736	−	5.64191i	0.140045	−	0.242565i	−0.787468	−	0.616355i	$-0.788609\pi$
$541$	3.25736	−	5.64191i	0.140045	−	0.242565i	0.927513	+	0.373790i	$0.121942\pi$
$542$		0			0
$543$	−11.8640	−	20.5490i	−0.509131	−	0.881841i
$544$		0			0
$545$	−4.31371			−0.184779
$546$		0			0
$547$	−27.7279			−1.18556			−0.592780	−	0.805364i	$-0.701970\pi$
$547$	−27.7279			−1.18556			−0.592780	+	0.805364i	$0.701970\pi$
$548$		0			0
$549$	6.58579	+	11.4069i	0.281075	+	0.486835i
$550$		0			0
$551$	6.14214	−	10.6385i	0.261664	−	0.453215i
$552$		0			0
$553$	−4.00000	+	9.79796i	−0.170097	+	0.416652i
$554$		0			0
$555$	−6.82843	+	11.8272i	−0.289851	+	0.502036i
$556$		0			0
$557$	−2.65685	−	4.60181i	−0.112575	−	0.194985i	0.804233	−	0.594314i	$-0.202576\pi$
$557$	−2.65685	−	4.60181i	−0.112575	−	0.194985i	−0.916808	+	0.399329i	$0.869243\pi$
$558$		0			0
$559$	25.7990			1.09118
$560$		0			0
$561$	42.6274			1.79973
$562$		0			0
$563$	−5.03553	−	8.72180i	−0.212222	−	0.367580i	0.740187	−	0.672401i	$-0.234737\pi$
$563$	−5.03553	−	8.72180i	−0.212222	−	0.367580i	−0.952410	+	0.304821i	$0.901403\pi$
$564$		0			0
$565$	5.65685	−	9.79796i	0.237986	−	0.412203i
$566$		0			0
$567$	−15.3787	−	19.8315i	−0.645844	−	0.832847i
$568$		0			0
$569$	−4.31371	+	7.47156i	−0.180840	+	0.313224i	−0.942167	−	0.335144i	$-0.891215\pi$
$569$	−4.31371	+	7.47156i	−0.180840	+	0.313224i	0.761327	+	0.648368i	$0.224548\pi$
$570$		0			0
$571$	−6.48528	−	11.2328i	−0.271401	−	0.470080i	0.697820	−	0.716273i	$-0.254153\pi$
$571$	−6.48528	−	11.2328i	−0.271401	−	0.470080i	−0.969221	+	0.246193i	$0.920820\pi$
$572$		0			0
$573$	54.2843			2.26776
$574$		0			0
$575$	−8.41421			−0.350897
$576$		0			0
$577$	−17.1421	−	29.6910i	−0.713636	−	1.23605i	−0.963483	−	0.267769i	$-0.913714\pi$
$577$	−17.1421	−	29.6910i	−0.713636	−	1.23605i	0.249847	−	0.968285i	$-0.419620\pi$
$578$		0			0
$579$	20.8995	−	36.1990i	0.868553	−	1.50438i
$580$		0			0
$581$	34.7132	−	4.75039i	1.44015	−	0.197080i
$582$		0			0
$583$	13.6569	−	23.6544i	0.565609	−	0.979664i
$584$		0			0
$585$	−2.82843	−	4.89898i	−0.116941	−	0.202548i
$586$		0			0
$587$	−45.3137			−1.87030			−0.935148	−	0.354256i	$-0.884734\pi$
$587$	−45.3137			−1.87030			−0.935148	+	0.354256i	$0.884734\pi$
$588$		0			0
$589$	−27.3137			−1.12544
$590$		0			0
$591$	14.0711	+	24.3718i	0.578806	+	1.00252i
$592$		0			0
$593$	18.9706	−	32.8580i	0.779028	−	1.34932i	−0.153475	−	0.988153i	$-0.549046\pi$
$593$	18.9706	−	32.8580i	0.779028	−	1.34932i	0.932503	−	0.361163i	$-0.117620\pi$
$594$		0			0
$595$	−9.58579	+	1.31178i	−0.392979	+	0.0537779i
$596$		0			0
$597$	−0.828427	+	1.43488i	−0.0339053	+	0.0587256i
$598$		0			0
$599$	1.31371	+	2.27541i	0.0536767	+	0.0929707i	0.891615	−	0.452794i	$-0.149573\pi$
$599$	1.31371	+	2.27541i	0.0536767	+	0.0929707i	−0.837939	+	0.545765i	$0.816239\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$	19.5147			0.794701
$604$		0			0
$605$	−6.15685	−	10.6640i	−0.250312	−	0.433553i
$606$		0			0
$607$	−9.37868	+	16.2443i	−0.380669	+	0.659338i	−0.991158	−	0.132687i	$-0.957640\pi$
$607$	−9.37868	+	16.2443i	−0.380669	+	0.659338i	0.610489	+	0.792025i	$0.290973\pi$
$608$		0			0
$609$	8.50000	+	10.9612i	0.344437	+	0.444169i
$610$		0			0
$611$	−0.343146	+	0.594346i	−0.0138822	+	0.0240447i
$612$		0			0
$613$	−2.51472	−	4.35562i	−0.101569	−	0.175922i	0.810763	−	0.585375i	$-0.199053\pi$
$613$	−2.51472	−	4.35562i	−0.101569	−	0.175922i	−0.912331	+	0.409453i	$0.865719\pi$
$614$		0			0
$615$	−0.414214			−0.0167027
$616$		0			0
$617$	−35.3137			−1.42168			−0.710838	−	0.703356i	$-0.751684\pi$
$617$	−35.3137			−1.42168			−0.710838	+	0.703356i	$0.751684\pi$
$618$		0			0
$619$	5.72792	+	9.92105i	0.230225	+	0.398761i	0.957874	−	0.287188i	$-0.0927206\pi$
$619$	5.72792	+	9.92105i	0.230225	+	0.398761i	−0.727649	+	0.685949i	$0.759387\pi$
$620$		0			0
$621$	1.74264	−	3.01834i	0.0699298	−	0.121122i
$622$		0			0
$623$	−16.6569	+	40.8008i	−0.667343	+	1.63465i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−32.9706	−	57.1067i	−1.31672	−	2.28062i
$628$		0			0
$629$	−20.6863			−0.824816
$630$		0			0
$631$	−18.4853			−0.735887			−0.367944	−	0.929848i	$-0.619938\pi$
$631$	−18.4853			−0.735887			−0.367944	+	0.929848i	$0.619938\pi$
$632$		0			0
$633$	−22.4853	−	38.9456i	−0.893710	−	1.54795i
$634$		0			0
$635$	7.82843	−	13.5592i	0.310662	−	0.538082i
$636$		0			0
$637$	13.4853	−	3.76127i	0.534306	−	0.149027i
$638$		0			0
$639$	16.9706	−	29.3939i	0.671345	−	1.16280i
$640$		0			0
$641$	24.0563	+	41.6668i	0.950169	+	1.64574i	0.745056	+	0.667002i	$0.232423\pi$
$641$	24.0563	+	41.6668i	0.950169	+	1.64574i	0.205113	+	0.978738i	$0.434244\pi$
$642$		0			0
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$		0			0
$645$	−31.1421			−1.22622
$646$		0			0
$647$	14.6213	+	25.3249i	0.574823	+	0.995623i	0.996061	+	0.0886729i	$0.0282626\pi$
$647$	14.6213	+	25.3249i	0.574823	+	0.995623i	−0.421237	+	0.906950i	$0.638404\pi$
$648$		0			0
$649$	−9.65685	+	16.7262i	−0.379065	+	0.656559i
$650$		0			0
$651$	11.6569	−	28.5533i	0.456868	−	1.11909i
$652$		0			0
$653$	2.17157	−	3.76127i	0.0849802	−	0.147190i	−0.820403	−	0.571786i	$-0.806251\pi$
$653$	2.17157	−	3.76127i	0.0849802	−	0.147190i	0.905383	+	0.424596i	$0.139584\pi$
$654$		0			0
$655$	−1.17157	−	2.02922i	−0.0457771	−	0.0792883i
$656$		0			0
$657$	−21.6569			−0.844914
$658$		0			0
$659$	35.3137			1.37563			0.687813	−	0.725888i	$-0.258571\pi$
$659$	35.3137			1.37563			0.687813	+	0.725888i	$0.258571\pi$
$660$		0			0
$661$	13.8431	+	23.9770i	0.538436	+	0.932598i	0.998989	+	0.0449660i	$0.0143180\pi$
$661$	13.8431	+	23.9770i	0.538436	+	0.932598i	−0.460553	+	0.887632i	$0.652349\pi$
$662$		0			0
$663$	8.82843	−	15.2913i	0.342868	−	0.593864i
$664$		0			0
$665$	9.17157	+	11.8272i	0.355658	+	0.458638i
$666$		0			0
$667$	−9.13604	+	15.8241i	−0.353749	+	0.612711i
$668$		0			0
$669$	22.8995	+	39.6631i	0.885346	+	1.53346i
$670$		0			0
$671$	22.4853			0.868035
$672$		0			0
$673$	5.65685			0.218056			0.109028	−	0.994039i	$-0.465226\pi$
$673$	5.65685			0.218056			0.109028	+	0.994039i	$0.465226\pi$
$674$		0			0
$675$	−0.207107	−	0.358719i	−0.00797154	−	0.0138071i
$676$		0			0
$677$	5.48528	−	9.50079i	0.210816	−	0.365145i	−0.741154	−	0.671335i	$-0.765721\pi$
$677$	5.48528	−	9.50079i	0.210816	−	0.365145i	0.951970	+	0.306190i	$0.0990544\pi$
$678$		0			0
$679$	−15.7279	+	2.15232i	−0.603582	+	0.0825983i
$680$		0			0
$681$	16.8995	−	29.2708i	0.647590	−	1.12166i
$682$		0			0
$683$	8.03553	+	13.9180i	0.307471	+	0.532556i	0.977808	−	0.209501i	$-0.0671839\pi$
$683$	8.03553	+	13.9180i	0.307471	+	0.532556i	−0.670337	+	0.742057i	$0.733851\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$		0			0
$687$	33.7990			1.28951
$688$		0			0
$689$	−5.65685	−	9.79796i	−0.215509	−	0.373273i
$690$		0			0
$691$	−15.3848	+	26.6472i	−0.585264	+	1.01371i	0.409578	+	0.912275i	$0.365676\pi$
$691$	−15.3848	+	26.6472i	−0.585264	+	1.01371i	−0.994842	+	0.101433i	$0.967657\pi$
$692$		0			0
$693$	35.7990	−	4.89898i	1.35989	−	0.186097i
$694$		0			0
$695$	7.24264	−	12.5446i	0.274729	−	0.475845i
$696$		0			0
$697$	−0.313708	−	0.543359i	−0.0118826	−	0.0205812i
$698$		0			0
$699$	−0.828427			−0.0313340
$700$		0			0
$701$	−11.0000			−0.415464			−0.207732	−	0.978186i	$-0.566608\pi$
$701$	−11.0000			−0.415464			−0.207732	+	0.978186i	$0.566608\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$		0			0
$705$	0.414214	−	0.717439i	0.0156002	−	0.0270203i
$706$		0			0
$707$	8.89340	+	11.4685i	0.334471	+	0.431316i
$708$		0			0
$709$	−24.7132	+	42.8045i	−0.928124	+	1.60756i	−0.141665	+	0.989915i	$0.545246\pi$
$709$	−24.7132	+	42.8045i	−0.928124	+	1.60756i	−0.786459	+	0.617643i	$0.788088\pi$
$710$		0			0
$711$	5.65685	+	9.79796i	0.212149	+	0.367452i
$712$		0			0
$713$	40.6274			1.52151
$714$		0			0
$715$	−9.65685			−0.361146
$716$		0			0
$717$	−16.3137	−	28.2562i	−0.609247	−	1.05525i
$718$		0			0
$719$	−6.89949	+	11.9503i	−0.257308	+	0.445670i	−0.965520	−	0.260330i	$-0.916169\pi$
$719$	−6.89949	+	11.9503i	−0.257308	+	0.445670i	0.708212	+	0.706000i	$0.249502\pi$
$720$		0			0
$721$	10.4142	−	25.5095i	0.387846	−	0.950024i
$722$		0			0
$723$	−12.0711	+	20.9077i	−0.448928	+	0.777566i
$724$		0			0
$725$	1.08579	+	1.88064i	0.0403251	+	0.0698451i
$726$		0			0
$727$	23.9289			0.887475			0.443737	−	0.896157i	$-0.353652\pi$
$727$	23.9289			0.887475			0.443737	+	0.896157i	$0.353652\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−23.5858	−	40.8518i	−0.872352	−	1.51096i
$732$		0			0
$733$	1.82843	−	3.16693i	0.0675345	−	0.116973i	−0.830281	−	0.557345i	$-0.811820\pi$
$733$	1.82843	−	3.16693i	0.0675345	−	0.116973i	0.897815	+	0.440372i	$0.145153\pi$
$734$		0			0
$735$	−16.2782	+	4.54026i	−0.600430	+	0.167470i
$736$		0			0
$737$	16.6569	−	28.8505i	0.613563	−	1.06272i
$738$		0			0
$739$	−5.58579	−	9.67487i	−0.205476	−	0.355896i	0.744808	−	0.667279i	$-0.232541\pi$
$739$	−5.58579	−	9.67487i	−0.205476	−	0.355896i	−0.950284	+	0.311383i	$0.899208\pi$
$740$		0			0
$741$	−27.3137			−1.00339
$742$		0			0
$743$	−19.2426			−0.705944			−0.352972	−	0.935634i	$-0.614829\pi$
$743$	−19.2426			−0.705944			−0.352972	+	0.935634i	$0.614829\pi$
$744$		0			0
$745$	3.32843	+	5.76500i	0.121944	+	0.211213i
$746$		0			0
$747$	18.7279	−	32.4377i	0.685219	−	1.18683i
$748$		0			0
$749$	−8.41421	+	20.6105i	−0.307449	+	0.753092i
$750$		0			0
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$		0			0
$753$	28.3137	+	49.0408i	1.03181	+	1.78715i
$754$		0			0
$755$	−16.8284			−0.612449
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$		0			0
$759$	49.0416	+	84.9426i	1.78010	+	3.08322i
$760$		0			0
$761$	−11.9706	+	20.7336i	−0.433933	+	0.751593i	−0.997208	−	0.0746761i	$-0.976208\pi$
$761$	−11.9706	+	20.7336i	−0.433933	+	0.751593i	0.563275	+	0.826269i	$0.309541\pi$
$762$		0			0
$763$	−6.99390	−	9.01897i	−0.253196	−	0.326509i
$764$		0			0
$765$	−5.17157	+	8.95743i	−0.186979	+	0.323856i
$766$		0			0
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−47.2548			−1.70405			−0.852026	−	0.523499i	$-0.824626\pi$
$769$	−47.2548			−1.70405			−0.852026	+	0.523499i	$0.824626\pi$
$770$		0			0
$771$	17.6569			0.635896
$772$		0			0
$773$	−17.8284	−	30.8797i	−0.641244	−	1.11067i	−0.985155	−	0.171665i	$-0.945085\pi$
$773$	−17.8284	−	30.8797i	−0.641244	−	1.11067i	0.343911	−	0.939002i	$-0.388248\pi$
$774$		0			0
$775$	2.41421	−	4.18154i	0.0867211	−	0.150205i
$776$		0			0
$777$	−35.7990	+	4.89898i	−1.28428	+	0.175750i
$778$		0			0
$779$	−0.485281	+	0.840532i	−0.0173870	+	0.0301152i
$780$		0			0
$781$	−28.9706	−	50.1785i	−1.03665	−	1.79553i
$782$		0			0
$783$	−0.899495			−0.0321453
$784$		0			0
$785$	−21.3137			−0.760719
$786$		0			0
$787$	2.20711	+	3.82282i	0.0786749	+	0.136269i	0.902678	−	0.430316i	$-0.141598\pi$
$787$	2.20711	+	3.82282i	0.0786749	+	0.136269i	−0.824004	+	0.566585i	$0.808264\pi$
$788$		0			0
$789$	11.7426	−	20.3389i	0.418049	−	0.724082i
$790$		0			0
$791$	29.6569	−	4.05845i	1.05448	−	0.144302i
$792$		0			0
$793$	4.65685	−	8.06591i	0.165370	−	0.286429i
$794$		0			0
$795$	6.82843	+	11.8272i	0.242179	+	0.419467i
$796$		0			0
$797$	−12.6863			−0.449372			−0.224686	−	0.974431i	$-0.572136\pi$
$797$	−12.6863			−0.449372			−0.224686	+	0.974431i	$0.572136\pi$
$798$		0			0
$799$	1.25483			0.0443928
$800$		0			0
$801$	23.5563	+	40.8008i	0.832323	+	1.44163i
$802$		0			0
$803$	−18.4853	+	32.0174i	−0.652331	+	1.12987i
$804$		0			0
$805$	−13.6421	−	17.5922i	−0.480822	−	0.620043i
$806$		0			0
$807$	5.62132	−	9.73641i	0.197880	−	0.342738i
$808$		0			0
$809$	1.01472	+	1.75754i	0.0356756	+	0.0617920i	0.883312	−	0.468786i	$-0.155308\pi$
$809$	1.01472	+	1.75754i	0.0356756	+	0.0617920i	−0.847636	+	0.530578i	$0.821975\pi$
$810$		0			0
$811$	23.8579			0.837763			0.418881	−	0.908041i	$-0.362422\pi$
$811$	23.8579			0.837763			0.418881	+	0.908041i	$0.362422\pi$
$812$		0			0
$813$	−46.6274			−1.63529
$814$		0			0
$815$	2.17157	+	3.76127i	0.0760669	+	0.131752i
$816$		0			0
$817$	−36.4853	+	63.1944i	−1.27646	+	2.21089i
$818$		0			0
$819$	5.65685	−	13.8564i	0.197666	−	0.484182i
$820$		0			0
$821$	−6.31371	+	10.9357i	−0.220350	+	0.381657i	−0.954914	−	0.296882i	$-0.904053\pi$
$821$	−6.31371	+	10.9357i	−0.220350	+	0.381657i	0.734564	+	0.678539i	$0.237387\pi$
$822$		0			0
$823$	26.0061	+	45.0439i	0.906516	+	1.57013i	0.818870	+	0.573979i	$0.194601\pi$
$823$	26.0061	+	45.0439i	0.906516	+	1.57013i	0.0876457	+	0.996152i	$0.472066\pi$
$824$		0			0
$825$	11.6569			0.405840
$826$		0			0
$827$	−51.5269			−1.79177			−0.895883	−	0.444290i	$-0.853456\pi$
$827$	−51.5269			−1.79177			−0.895883	+	0.444290i	$0.853456\pi$
$828$		0			0
$829$	8.65685	+	14.9941i	0.300665	+	0.520767i	0.976287	−	0.216481i	$-0.0694581\pi$
$829$	8.65685	+	14.9941i	0.300665	+	0.520767i	−0.675622	+	0.737248i	$0.736125\pi$
$830$		0			0
$831$	−20.0711	+	34.7641i	−0.696258	+	1.20595i
$832$		0			0
$833$	−18.2843	−	17.9149i	−0.633512	−	0.620713i
$834$		0			0
$835$	6.03553	−	10.4539i	0.208868	−	0.361770i
$836$		0			0
$837$	1.00000	+	1.73205i	0.0345651	+	0.0598684i
$838$		0			0
$839$	−8.14214			−0.281098			−0.140549	−	0.990074i	$-0.544887\pi$
$839$	−8.14214			−0.281098			−0.140549	+	0.990074i	$0.544887\pi$
$840$		0			0
$841$	−24.2843			−0.837389
$842$		0			0
$843$	30.5563	+	52.9251i	1.05242	+	1.82284i
$844$		0			0
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	12.3137	−	30.1623i	0.423104	−	1.03639i
$848$		0			0
$849$	21.7279	−	37.6339i	0.745700	−	1.29159i
$850$		0			0
$851$	−23.7990	−	41.2211i	−0.815819	−	1.41304i
$852$		0			0
$853$	35.3137			1.20912			0.604559	−	0.796560i	$-0.293349\pi$
$853$	35.3137			1.20912			0.604559	+	0.796560i	$0.293349\pi$
$854$		0			0
$855$	16.0000			0.547188
$856$		0			0
$857$	−7.48528	−	12.9649i	−0.255692	−	0.442872i	0.709391	−	0.704815i	$-0.248970\pi$
$857$	−7.48528	−	12.9649i	−0.255692	−	0.442872i	−0.965083	+	0.261943i	$0.915637\pi$
$858$		0			0
$859$	−7.31371	+	12.6677i	−0.249541	+	0.432217i	−0.963398	−	0.268074i	$-0.913613\pi$
$859$	−7.31371	+	12.6677i	−0.249541	+	0.432217i	0.713858	+	0.700291i	$0.246946\pi$
$860$		0			0
$861$	−0.671573	−	0.866025i	−0.0228871	−	0.0295141i
$862$		0			0
$863$	−13.0061	+	22.5272i	−0.442733	+	0.766835i	−0.997891	−	0.0649091i	$-0.979324\pi$
$863$	−13.0061	+	22.5272i	−0.442733	+	0.766835i	0.555159	+	0.831745i	$0.312658\pi$
$864$		0			0
$865$	−10.8284	−	18.7554i	−0.368178	−	0.637702i
$866$		0			0
$867$	8.75736			0.297416
$868$		0			0
$869$	19.3137			0.655173
$870$		0			0
$871$	−6.89949	−	11.9503i	−0.233780	−	0.404920i
$872$		0			0
$873$	−8.48528	+	14.6969i	−0.287183	+	0.497416i
$874$		0			0
$875$	−2.62132	+	0.358719i	−0.0886168	+	0.0121269i
$876$		0			0
$877$	−14.1421	+	24.4949i	−0.477546	+	0.827134i	−0.999669	−	0.0257364i	$-0.991807\pi$
$877$	−14.1421	+	24.4949i	−0.477546	+	0.827134i	0.522123	+	0.852870i	$0.325140\pi$
$878$		0			0
$879$	−20.4853	−	35.4815i	−0.690951	−	1.19676i
$880$		0			0
$881$	24.4558			0.823938			0.411969	−	0.911198i	$-0.364841\pi$
$881$	24.4558			0.823938			0.411969	+	0.911198i	$0.364841\pi$
$882$		0			0
$883$	29.3137			0.986485			0.493242	−	0.869892i	$-0.335812\pi$
$883$	29.3137			0.986485			0.493242	+	0.869892i	$0.335812\pi$
$884$		0			0
$885$	−4.82843	−	8.36308i	−0.162306	−	0.281122i
$886$		0			0
$887$	−10.2071	+	17.6792i	−0.342721	+	0.593610i	−0.984937	−	0.172913i	$-0.944682\pi$
$887$	−10.2071	+	17.6792i	−0.342721	+	0.593610i	0.642216	+	0.766524i	$0.278015\pi$
$888$		0			0
$889$	41.0416	−	5.61642i	1.37649	−	0.188369i
$890$		0			0
$891$	−22.8995	+	39.6631i	−0.767162	+	1.32876i
$892$		0			0
$893$	−0.970563	−	1.68106i	−0.0324786	−	0.0562547i
$894$		0			0
$895$	10.4853			0.350484
$896$		0			0
$897$	40.6274			1.35651
$898$		0			0
$899$	−5.24264	−	9.08052i	−0.174852	−	0.302852i
$900$		0			0
$901$	−10.3431	+	17.9149i	−0.344580	+	0.596830i
$902$		0			0
$903$	−50.4914	−	65.1111i	−1.68025	−	2.16676i
$904$		0			0
$905$	4.91421	−	8.51167i	0.163354	−	0.282937i
$906$		0			0
$907$	−1.89340	−	3.27946i	−0.0628693	−	0.108893i	0.832878	−	0.553457i	$-0.186692\pi$
$907$	−1.89340	−	3.27946i	−0.0628693	−	0.108893i	−0.895747	+	0.444565i	$0.853358\pi$
$908$		0			0
$909$	15.5147			0.514591
$910$		0			0
$911$	−1.51472			−0.0501849			−0.0250924	−	0.999685i	$-0.507988\pi$
$911$	−1.51472			−0.0501849			−0.0250924	+	0.999685i	$0.507988\pi$
$912$		0			0
$913$	−31.9706	−	55.3746i	−1.05807	−	1.83263i
$914$		0			0
$915$	−5.62132	+	9.73641i	−0.185835	+	0.321876i
$916$		0			0
$917$	2.34315	−	5.73951i	0.0773775	−	0.189535i
$918$		0			0
$919$	−28.6274	+	49.5841i	−0.944331	+	1.63563i	−0.187247	+	0.982313i	$0.559956\pi$
$919$	−28.6274	+	49.5841i	−0.944331	+	1.63563i	−0.757084	+	0.653317i	$0.773377\pi$
$920$		0			0
$921$	15.9853	+	27.6873i	0.526733	+	0.912328i
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−5.65685			−0.185996
$926$		0			0
$927$	−14.7279	−	25.5095i	−0.483728	−	0.837842i
$928$		0			0
$929$	−24.3995	+	42.2612i	−0.800521	+	1.38654i	0.118752	+	0.992924i	$0.462111\pi$
$929$	−24.3995	+	42.2612i	−0.800521	+	1.38654i	−0.919273	+	0.393620i	$0.871223\pi$
$930$		0			0
$931$	−9.85786	+	38.3513i	−0.323078	+	1.25691i
$932$		0			0
$933$	12.4853	−	21.6251i	0.408750	−	0.707975i
$934$		0			0
$935$	8.82843	+	15.2913i	0.288720	+	0.500078i
$936$		0			0
$937$	−26.6274			−0.869880			−0.434940	−	0.900459i	$-0.643230\pi$
$937$	−26.6274			−0.869880			−0.434940	+	0.900459i	$0.643230\pi$
$938$		0			0
$939$	31.3137			1.02188
$940$		0			0
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	0.935942	−	0.352155i	$-0.114551\pi$
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	−0.772946	+	0.634472i	$0.781218\pi$
$942$		0			0
$943$	0.721825	−	1.25024i	0.0235059	−	0.0407134i
$944$		0			0
$945$	0.414214	−	1.01461i	0.0134744	−	0.0330053i
$946$		0			0
$947$	−15.4497	+	26.7597i	−0.502049	+	0.869575i	0.497948	+	0.867207i	$0.334087\pi$
$947$	−15.4497	+	26.7597i	−0.502049	+	0.869575i	−0.999997	+	0.00236799i	$0.999246\pi$
$948$		0			0
$949$	7.65685	+	13.2621i	0.248552	+	0.430505i
$950$		0			0
$951$	53.1127			1.72230
$952$		0			0
$953$	−9.37258			−0.303608			−0.151804	−	0.988411i	$-0.548508\pi$
$953$	−9.37258			−0.303608			−0.151804	+	0.988411i	$0.548508\pi$
$954$		0			0
$955$	11.2426	+	19.4728i	0.363803	+	0.630126i
$956$		0			0
$957$	12.6569	−	21.9223i	0.409138	−	0.708648i
$958$		0			0
$959$	−6.48528	−	8.36308i	−0.209421	−	0.270058i
$960$		0			0
$961$	3.84315	−	6.65652i	0.123972	−	0.214727i
$962$		0			0
$963$	11.8995	+	20.6105i	0.383456	+	0.664165i
$964$		0			0
$965$	17.3137			0.557348
$966$		0			0
$967$	−33.2426			−1.06901			−0.534506	−	0.845165i	$-0.679502\pi$
$967$	−33.2426			−1.06901			−0.534506	+	0.845165i	$0.679502\pi$
$968$		0			0
$969$	24.9706	+	43.2503i	0.802170	+	1.38940i
$970$		0			0
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	−0.923044	−	0.384695i	$-0.874307\pi$
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	0.794678	+	0.607032i	$0.207640\pi$
$972$		0			0
$973$	37.9706	−	5.19615i	1.21728	−	0.166581i
$974$		0			0
$975$	2.41421	−	4.18154i	0.0773167	−	0.133916i
$976$		0			0
$977$	13.1421	+	22.7628i	0.420454	+	0.728248i	0.995984	−	0.0895329i	$-0.0285374\pi$
$977$	13.1421	+	22.7628i	0.420454	+	0.728248i	−0.575530	+	0.817781i	$0.695204\pi$
$978$		0			0
$979$	80.4264			2.57044
$980$		0			0
$981$	−12.2010			−0.389548
$982$		0			0
$983$	2.30761	+	3.99690i	0.0736014	+	0.127481i	0.900477	−	0.434903i	$-0.143217\pi$
$983$	2.30761	+	3.99690i	0.0736014	+	0.127481i	−0.826876	+	0.562385i	$0.809884\pi$
$984$		0			0
$985$	−5.82843	+	10.0951i	−0.185709	+	0.321658i
$986$		0			0
$987$	2.17157	−	0.297173i	0.0691219	−	0.00945912i
$988$		0			0
$989$	54.2696	−	93.9976i	1.72567	−	2.98895i
$990$		0			0
$991$	0.414214	+	0.717439i	0.0131579	+	0.0227902i	0.872529	−	0.488562i	$-0.162478\pi$
$991$	0.414214	+	0.717439i	0.0131579	+	0.0227902i	−0.859371	+	0.511352i	$0.829145\pi$
$992$		0			0
$993$	−22.9706			−0.728949
$994$		0			0
$995$	−0.686292			−0.0217569
$996$		0			0
$997$	12.8284	+	22.2195i	0.406280	+	0.703698i	0.994470	−	0.105025i	$-0.0334923\pi$
$997$	12.8284	+	22.2195i	0.406280	+	0.703698i	−0.588189	+	0.808723i	$0.700159\pi$
$998$		0			0
$999$	1.17157	−	2.02922i	0.0370669	−	0.0642018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.q.d.121.2	yes	4
3.2	odd	2		2520.2.bi.k.1801.1		4
4.3	odd	2		560.2.q.j.401.1		4
5.2	odd	4		1400.2.bh.g.849.4		8
5.3	odd	4		1400.2.bh.g.849.1		8
5.4	even	2		1400.2.q.h.401.1		4
7.2	even	3		1960.2.a.p.1.1		2
7.3	odd	6		1960.2.q.q.361.1		4
7.4	even	3	inner	280.2.q.d.81.2	✓	4
7.5	odd	6		1960.2.a.t.1.2		2
7.6	odd	2		1960.2.q.q.961.1		4
21.11	odd	6		2520.2.bi.k.361.1		4
28.11	odd	6		560.2.q.j.81.1		4
28.19	even	6		3920.2.a.bp.1.1		2
28.23	odd	6		3920.2.a.bz.1.2		2
35.4	even	6		1400.2.q.h.1201.1		4
35.9	even	6		9800.2.a.bz.1.2		2
35.18	odd	12		1400.2.bh.g.249.4		8
35.19	odd	6		9800.2.a.br.1.1		2
35.32	odd	12		1400.2.bh.g.249.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.d.81.2	✓	4	7.4	even	3	inner
280.2.q.d.121.2	yes	4	1.1	even	1	trivial
560.2.q.j.81.1		4	28.11	odd	6
560.2.q.j.401.1		4	4.3	odd	2
1400.2.q.h.401.1		4	5.4	even	2
1400.2.q.h.1201.1		4	35.4	even	6
1400.2.bh.g.249.1		8	35.32	odd	12
1400.2.bh.g.249.4		8	35.18	odd	12
1400.2.bh.g.849.1		8	5.3	odd	4
1400.2.bh.g.849.4		8	5.2	odd	4
1960.2.a.p.1.1		2	7.2	even	3
1960.2.a.t.1.2		2	7.5	odd	6
1960.2.q.q.361.1		4	7.3	odd	6
1960.2.q.q.961.1		4	7.6	odd	2
2520.2.bi.k.361.1		4	21.11	odd	6
2520.2.bi.k.1801.1		4	3.2	odd	2
3920.2.a.bp.1.1		2	28.19	even	6
3920.2.a.bz.1.2		2	28.23	odd	6
9800.2.a.br.1.1		2	35.19	odd	6
9800.2.a.bz.1.2		2	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.62132 + 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.62132 + 0.358719i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(2.41421 + 4.18154i) q^{11} +2.00000 q^{13} -2.41421 q^{15} +(-1.82843 - 3.16693i) q^{17} +(-2.82843 + 4.89898i) q^{19} +(-3.91421 - 5.04757i) q^{21} +(4.20711 - 7.28692i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.414214 q^{27} -2.17157 q^{29} +(2.41421 + 4.18154i) q^{31} +(-5.82843 + 10.0951i) q^{33} +(1.00000 - 2.44949i) q^{35} +(2.82843 - 4.89898i) q^{37} +(2.41421 + 4.18154i) q^{39} +0.171573 q^{41} +12.8995 q^{43} +(-1.41421 - 2.44949i) q^{45} +(-0.171573 + 0.297173i) q^{47} +(6.74264 - 1.88064i) q^{49} +(4.41421 - 7.64564i) q^{51} +(-2.82843 - 4.89898i) q^{53} -4.82843 q^{55} -13.6569 q^{57} +(2.00000 + 3.46410i) q^{59} +(2.32843 - 4.03295i) q^{61} +(2.82843 - 6.92820i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(-3.44975 - 5.97514i) q^{67} +20.3137 q^{69} -12.0000 q^{71} +(3.82843 + 6.63103i) q^{73} +(1.20711 - 2.09077i) q^{75} +(-7.82843 - 10.0951i) q^{77} +(2.00000 - 3.46410i) q^{79} +(4.74264 + 8.21449i) q^{81} -13.2426 q^{83} +3.65685 q^{85} +(-2.62132 - 4.54026i) q^{87} +(8.32843 - 14.4253i) q^{89} +(-5.24264 + 0.717439i) q^{91} +(-5.82843 + 10.0951i) q^{93} +(-2.82843 - 4.89898i) q^{95} +6.00000 q^{97} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 4 q^{11} + 8 q^{13} - 4 q^{15} + 4 q^{17} - 10 q^{21} + 14 q^{23} - 2 q^{25} - 4 q^{27} - 20 q^{29} + 4 q^{31} - 12 q^{33} + 4 q^{35} + 4 q^{39} + 12 q^{41} + 12 q^{43} - 12 q^{47} + 10 q^{49} + 12 q^{51} - 8 q^{55} - 32 q^{57} + 8 q^{59} - 2 q^{61} - 4 q^{65} + 6 q^{67} + 36 q^{69} - 48 q^{71} + 4 q^{73} + 2 q^{75} - 20 q^{77} + 8 q^{79} + 2 q^{81} - 36 q^{83} - 8 q^{85} - 2 q^{87} + 22 q^{89} - 4 q^{91} - 12 q^{93} + 24 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^5 - 2 * q^7 + 4 * q^11 + 8 * q^13 - 4 * q^15 + 4 * q^17 - 10 * q^21 + 14 * q^23 - 2 * q^25 - 4 * q^27 - 20 * q^29 + 4 * q^31 - 12 * q^33 + 4 * q^35 + 4 * q^39 + 12 * q^41 + 12 * q^43 - 12 * q^47 + 10 * q^49 + 12 * q^51 - 8 * q^55 - 32 * q^57 + 8 * q^59 - 2 * q^61 - 4 * q^65 + 6 * q^67 + 36 * q^69 - 48 * q^71 + 4 * q^73 + 2 * q^75 - 20 * q^77 + 8 * q^79 + 2 * q^81 - 36 * q^83 - 8 * q^85 - 2 * q^87 + 22 * q^89 - 4 * q^91 - 12 * q^93 + 24 * q^97 - 32 * q^99

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