LMFDB - Embedded newform 560.2.cc.c.159.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(159,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 5]))

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

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

chi := DirichletCharacter("560.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cc (of order $6$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	560.159
Dual form			560.2.cc.c.479.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686141 + 0.396143i) q^{3} +(-1.50000 - 1.65831i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.18614 + 2.05446i) q^{9} +O(q^{10})$	\(q+(-0.686141 + 0.396143i) q^{3} +(-1.50000 - 1.65831i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.18614 + 2.05446i) q^{9} +(1.50000 - 0.866025i) q^{11} -4.37228 q^{13} +(1.68614 + 0.543620i) q^{15} +(-3.68614 - 6.38458i) q^{17} +(-2.87228 + 4.97494i) q^{19} +(-0.686141 + 1.98072i) q^{21} +(2.87228 - 4.97494i) q^{23} +(-0.500000 + 4.97494i) q^{25} -4.25639i q^{27} -2.74456 q^{29} +(-5.05842 - 8.76144i) q^{31} +(-0.686141 + 1.18843i) q^{33} +(-5.87228 - 0.718549i) q^{35} +(-7.50000 - 4.33013i) q^{37} +(3.00000 - 1.73205i) q^{39} +0.939764i q^{41} -4.00000 q^{43} +(5.18614 - 1.11469i) q^{45} +(10.2446 + 5.91470i) q^{47} +(1.00000 - 6.92820i) q^{49} +(5.05842 + 2.92048i) q^{51} +(5.61684 - 3.24289i) q^{53} +(-3.68614 - 1.18843i) q^{55} -4.55134i q^{57} +(-2.31386 - 4.00772i) q^{59} +(-0.941578 - 0.543620i) q^{61} +(1.18614 + 6.16337i) q^{63} +(6.55842 + 7.25061i) q^{65} +(-4.05842 - 7.02939i) q^{67} +4.55134i q^{69} +10.3923i q^{71} +(2.31386 + 4.00772i) q^{73} +(-1.62772 - 3.61158i) q^{75} +(1.50000 - 4.33013i) q^{77} +(8.05842 + 4.65253i) q^{79} +(-1.87228 - 3.24289i) q^{81} +8.51278i q^{83} +(-5.05842 + 15.6896i) q^{85} +(1.88316 - 1.08724i) q^{87} +(-3.68614 - 2.12819i) q^{89} +(-8.74456 + 7.57301i) q^{91} +(6.94158 + 4.00772i) q^{93} +(12.5584 - 2.69927i) q^{95} -6.00000 q^{97} +4.10891i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} - 6 q^{5} + 8 q^{7} + q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 - 6 * q^5 + 8 * q^7 + q^9	$ 4 q + 3 q^{3} - 6 q^{5} + 8 q^{7} + q^{9} + 6 q^{11} - 6 q^{13} + q^{15} - 9 q^{17} + 3 q^{21} - 2 q^{25} + 12 q^{29} - 3 q^{31} + 3 q^{33} - 12 q^{35} - 30 q^{37} + 12 q^{39} - 16 q^{43} + 15 q^{45} + 18 q^{47} + 4 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} - 15 q^{59} - 21 q^{61} - q^{63} + 9 q^{65} + q^{67} + 15 q^{73} - 18 q^{75} + 6 q^{77} + 15 q^{79} + 4 q^{81} - 3 q^{85} + 42 q^{87} - 9 q^{89} - 12 q^{91} + 45 q^{93} + 33 q^{95} - 24 q^{97}+O(q^{100}) $ 4 * q + 3 * q^3 - 6 * q^5 + 8 * q^7 + q^9 + 6 * q^11 - 6 * q^13 + q^15 - 9 * q^17 + 3 * q^21 - 2 * q^25 + 12 * q^29 - 3 * q^31 + 3 * q^33 - 12 * q^35 - 30 * q^37 + 12 * q^39 - 16 * q^43 + 15 * q^45 + 18 * q^47 + 4 * q^49 + 3 * q^51 - 12 * q^53 - 9 * q^55 - 15 * q^59 - 21 * q^61 - q^63 + 9 * q^65 + q^67 + 15 * q^73 - 18 * q^75 + 6 * q^77 + 15 * q^79 + 4 * q^81 - 3 * q^85 + 42 * q^87 - 9 * q^89 - 12 * q^91 + 45 * q^93 + 33 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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
$3$	−0.686141	+	0.396143i	−0.396143	+	0.228714i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	−0.686141	+	0.396143i	−0.396143	+	0.228714i	0.288675	+	0.957427i	$0.406785\pi$
$4$		0			0
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$	−1.18614	+	2.05446i	−0.395380	+	0.684819i
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		0			0
$13$	−4.37228			−1.21265			−0.606326	−	0.795216i	$-0.707357\pi$
$13$	−4.37228			−1.21265			−0.606326	+	0.795216i	$0.707357\pi$
$14$		0			0
$15$	1.68614	+	0.543620i	0.435360	+	0.140362i
$16$		0			0
$17$	−3.68614	−	6.38458i	−0.894020	−	1.54849i	−0.835012	−	0.550231i	$-0.814540\pi$
$17$	−3.68614	−	6.38458i	−0.894020	−	1.54849i	−0.0590081	−	0.998258i	$-0.518794\pi$
$18$		0			0
$19$	−2.87228	+	4.97494i	−0.658947	+	1.14133i	0.321942	+	0.946759i	$0.395664\pi$
$19$	−2.87228	+	4.97494i	−0.658947	+	1.14133i	−0.980889	+	0.194570i	$0.937669\pi$
$20$		0			0
$21$	−0.686141	+	1.98072i	−0.149728	+	0.432228i
$22$		0			0
$23$	2.87228	−	4.97494i	0.598912	−	1.03735i	−0.394070	−	0.919080i	$-0.628933\pi$
$23$	2.87228	−	4.97494i	0.598912	−	1.03735i	0.992982	−	0.118266i	$-0.0377334\pi$
$24$		0			0
$25$	−0.500000	+	4.97494i	−0.100000	+	0.994987i
$26$		0			0
$27$		−	4.25639i		−	0.819142i
$28$		0			0
$29$	−2.74456			−0.509652			−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456			−0.509652			−0.254826	+	0.966987i	$0.582018\pi$
$30$		0			0
$31$	−5.05842	−	8.76144i	−0.908519	−	1.57360i	−0.816122	−	0.577880i	$-0.803880\pi$
$31$	−5.05842	−	8.76144i	−0.908519	−	1.57360i	−0.0923973	−	0.995722i	$-0.529453\pi$
$32$		0			0
$33$	−0.686141	+	1.18843i	−0.119442	+	0.206879i
$34$		0			0
$35$	−5.87228	−	0.718549i	−0.992597	−	0.121457i
$36$		0			0
$37$	−7.50000	−	4.33013i	−1.23299	−	0.711868i	−0.265340	−	0.964155i	$-0.585484\pi$
$37$	−7.50000	−	4.33013i	−1.23299	−	0.711868i	−0.967653	+	0.252286i	$0.918817\pi$
$38$		0			0
$39$	3.00000	−	1.73205i	0.480384	−	0.277350i
$40$		0			0
$41$			0.939764i			0.146766i	0.997304	+	0.0733832i	$0.0233796\pi$
$41$			0.939764i			0.146766i	−0.997304	+	0.0733832i	$0.976620\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	5.18614	−	1.11469i	0.773104	−	0.166168i
$46$		0			0
$47$	10.2446	+	5.91470i	1.49432	+	0.862748i	0.999979	−	0.00651839i	$-0.00207488\pi$
$47$	10.2446	+	5.91470i	1.49432	+	0.862748i	0.494344	+	0.869266i	$0.335408\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	5.05842	+	2.92048i	0.708321	+	0.408949i
$52$		0			0
$53$	5.61684	−	3.24289i	0.771533	−	0.445445i	−0.0618883	−	0.998083i	$-0.519712\pi$
$53$	5.61684	−	3.24289i	0.771533	−	0.445445i	0.833421	+	0.552638i	$0.186379\pi$
$54$		0			0
$55$	−3.68614	−	1.18843i	−0.497039	−	0.160248i
$56$		0			0
$57$		−	4.55134i		−	0.602840i
$58$		0			0
$59$	−2.31386	−	4.00772i	−0.301239	−	0.521761i	0.675178	−	0.737655i	$-0.264067\pi$
$59$	−2.31386	−	4.00772i	−0.301239	−	0.521761i	−0.976417	+	0.215894i	$0.930733\pi$
$60$		0			0
$61$	−0.941578	−	0.543620i	−0.120557	−	0.0696034i	0.438509	−	0.898727i	$-0.355507\pi$
$61$	−0.941578	−	0.543620i	−0.120557	−	0.0696034i	−0.559066	+	0.829123i	$0.688840\pi$
$62$		0			0
$63$	1.18614	+	6.16337i	0.149440	+	0.776511i
$64$		0			0
$65$	6.55842	+	7.25061i	0.813472	+	0.899327i
$66$		0			0
$67$	−4.05842	−	7.02939i	−0.495815	−	0.858777i	0.504173	−	0.863603i	$-0.331797\pi$
$67$	−4.05842	−	7.02939i	−0.495815	−	0.858777i	−0.999988	+	0.00482552i	$0.998464\pi$
$68$		0			0
$69$			4.55134i			0.547917i
$70$		0			0
$71$			10.3923i			1.23334i	0.787222	+	0.616670i	$0.211519\pi$
$71$			10.3923i			1.23334i	−0.787222	+	0.616670i	$0.788481\pi$
$72$		0			0
$73$	2.31386	+	4.00772i	0.270817	+	0.469068i	0.969071	−	0.246781i	$-0.0793729\pi$
$73$	2.31386	+	4.00772i	0.270817	+	0.469068i	−0.698254	+	0.715850i	$0.746040\pi$
$74$		0			0
$75$	−1.62772	−	3.61158i	−0.187953	−	0.417029i
$76$		0			0
$77$	1.50000	−	4.33013i	0.170941	−	0.493464i
$78$		0			0
$79$	8.05842	+	4.65253i	0.906643	+	0.523451i	0.879350	−	0.476177i	$-0.157978\pi$
$79$	8.05842	+	4.65253i	0.906643	+	0.523451i	0.0272937	+	0.999627i	$0.491311\pi$
$80$		0			0
$81$	−1.87228	−	3.24289i	−0.208031	−	0.360321i
$82$		0			0
$83$			8.51278i			0.934399i	0.884152	+	0.467199i	$0.154737\pi$
$83$			8.51278i			0.934399i	−0.884152	+	0.467199i	$0.845263\pi$
$84$		0			0
$85$	−5.05842	+	15.6896i	−0.548663	+	1.70178i
$86$		0			0
$87$	1.88316	−	1.08724i	0.201896	−	0.116564i
$88$		0			0
$89$	−3.68614	−	2.12819i	−0.390730	−	0.225588i	0.291746	−	0.956496i	$-0.405764\pi$
$89$	−3.68614	−	2.12819i	−0.390730	−	0.225588i	−0.682476	+	0.730908i	$0.739097\pi$
$90$		0			0
$91$	−8.74456	+	7.57301i	−0.916679	+	0.793868i
$92$		0			0
$93$	6.94158	+	4.00772i	0.719808	+	0.415581i
$94$		0			0
$95$	12.5584	−	2.69927i	1.28847	−	0.276939i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$			4.10891i			0.412961i
$100$		0			0
$101$	9.43070	−	5.44482i	0.938390	−	0.541780i	0.0489348	−	0.998802i	$-0.484417\pi$
$101$	9.43070	−	5.44482i	0.938390	−	0.541780i	0.889455	+	0.457022i	$0.151084\pi$
$102$		0			0
$103$	−8.05842	−	4.65253i	−0.794020	−	0.458428i	0.0473559	−	0.998878i	$-0.484921\pi$
$103$	−8.05842	−	4.65253i	−0.794020	−	0.458428i	−0.841376	+	0.540450i	$0.818254\pi$
$104$		0			0
$105$	4.31386	−	1.83324i	0.420990	−	0.178906i
$106$		0			0
$107$	−0.686141	+	1.18843i	−0.0663317	+	0.114890i	−0.897284	−	0.441454i	$-0.854463\pi$
$107$	−0.686141	+	1.18843i	−0.0663317	+	0.114890i	0.830952	+	0.556344i	$0.187796\pi$
$108$		0			0
$109$	6.05842	+	10.4935i	0.580292	+	1.00509i	0.995444	+	0.0953429i	$0.0303947\pi$
$109$	6.05842	+	10.4935i	0.580292	+	1.00509i	−0.415153	+	0.909752i	$0.636272\pi$
$110$		0			0
$111$	6.86141			0.651256
$112$		0			0
$113$			6.92820i			0.651751i	0.945413	+	0.325875i	$0.105659\pi$
$113$			6.92820i			0.651751i	−0.945413	+	0.325875i	$0.894341\pi$
$114$		0			0
$115$	−12.5584	+	2.69927i	−1.17108	+	0.251708i
$116$		0			0
$117$	5.18614	−	8.98266i	0.479459	−	0.830447i
$118$		0			0
$119$	−18.4307	−	6.38458i	−1.68954	−	0.585274i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		0			0
$123$	−0.372281	−	0.644810i	−0.0335675	−	0.0581406i
$124$		0			0
$125$	9.00000	−	6.63325i	0.804984	−	0.593296i
$126$		0			0
$127$	15.1168			1.34140			0.670701	−	0.741727i	$-0.265993\pi$
$127$	15.1168			1.34140			0.670701	+	0.741727i	$0.265993\pi$
$128$		0			0
$129$	2.74456	−	1.58457i	0.241645	−	0.139514i
$130$		0			0
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$		0			0
$133$	2.87228	+	14.9248i	0.249058	+	1.29415i
$134$		0			0
$135$	−7.05842	+	6.38458i	−0.607492	+	0.549497i
$136$		0			0
$137$	8.05842	−	4.65253i	0.688477	−	0.397493i	−0.114564	−	0.993416i	$-0.536547\pi$
$137$	8.05842	−	4.65253i	0.688477	−	0.397493i	0.803041	+	0.595923i	$0.203214\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−9.37228			−0.789288
$142$		0			0
$143$	−6.55842	+	3.78651i	−0.548443	+	0.316644i
$144$		0			0
$145$	4.11684	+	4.55134i	0.341885	+	0.377968i
$146$		0			0
$147$	2.05842	+	5.14987i	0.169776	+	0.424754i
$148$		0			0
$149$	6.43070	−	11.1383i	0.526824	−	0.912485i	−0.472688	−	0.881230i	$-0.656716\pi$
$149$	6.43070	−	11.1383i	0.526824	−	0.912485i	0.999511	−	0.0312555i	$-0.00995054\pi$
$150$		0			0
$151$	9.94158	−	5.73977i	0.809034	−	0.467096i	−0.0375862	−	0.999293i	$-0.511967\pi$
$151$	9.94158	−	5.73977i	0.809034	−	0.467096i	0.846620	+	0.532197i	$0.178634\pi$
$152$		0			0
$153$	17.4891			1.41391
$154$		0			0
$155$	−6.94158	+	21.5306i	−0.557561	+	1.72938i
$156$		0			0
$157$	−4.50000	−	7.79423i	−0.359139	−	0.622047i	0.628678	−	0.777666i	$-0.283596\pi$
$157$	−4.50000	−	7.79423i	−0.359139	−	0.622047i	−0.987817	+	0.155618i	$0.950263\pi$
$158$		0			0
$159$	−2.56930	+	4.45015i	−0.203758	+	0.352920i
$160$		0			0
$161$	−2.87228	−	14.9248i	−0.226367	−	1.17624i
$162$		0			0
$163$	−1.94158	+	3.36291i	−0.152076	+	0.263404i	−0.931991	−	0.362483i	$-0.881929\pi$
$163$	−1.94158	+	3.36291i	−0.152076	+	0.263404i	0.779914	+	0.625886i	$0.215263\pi$
$164$		0			0
$165$	3.00000	−	0.644810i	0.233550	−	0.0501984i
$166$		0			0
$167$		−	5.69349i		−	0.440575i	−0.975435	−	0.220288i	$-0.929300\pi$
$167$		−	5.69349i		−	0.440575i	0.975435	−	0.220288i	$-0.0706996\pi$
$168$		0			0
$169$	6.11684			0.470526
$170$		0			0
$171$	−6.81386	−	11.8020i	−0.521069	−	0.902518i
$172$		0			0
$173$	−5.61684	+	9.72866i	−0.427041	+	0.739656i	−0.996609	−	0.0822881i	$-0.973777\pi$
$173$	−5.61684	+	9.72866i	−0.427041	+	0.739656i	0.569568	+	0.821944i	$0.307111\pi$
$174$		0			0
$175$	7.61684	+	10.8159i	0.575779	+	0.817605i
$176$		0			0
$177$	3.17527	+	1.83324i	0.238668	+	0.137795i
$178$		0			0
$179$	15.7337	−	9.08385i	1.17599	−	0.678959i	0.220907	−	0.975295i	$-0.429098\pi$
$179$	15.7337	−	9.08385i	1.17599	−	0.678959i	0.955084	+	0.296336i	$0.0957648\pi$
$180$		0			0
$181$			1.28962i			0.0958567i	0.998851	+	0.0479284i	$0.0152619\pi$
$181$			1.28962i			0.0958567i	−0.998851	+	0.0479284i	$0.984738\pi$
$182$		0			0
$183$	0.861407			0.0636770
$184$		0			0
$185$	4.06930	+	18.9325i	0.299181	+	1.39195i
$186$		0			0
$187$	−11.0584	−	6.38458i	−0.808672	−	0.466887i
$188$		0			0
$189$	−7.37228	−	8.51278i	−0.536255	−	0.619213i
$190$		0			0
$191$	−5.05842	−	2.92048i	−0.366015	−	0.211319i	0.305701	−	0.952127i	$-0.401109\pi$
$191$	−5.05842	−	2.92048i	−0.366015	−	0.211319i	−0.671716	+	0.740809i	$0.734442\pi$
$192$		0			0
$193$	−3.94158	+	2.27567i	−0.283721	+	0.163806i	−0.635107	−	0.772424i	$-0.719044\pi$
$193$	−3.94158	+	2.27567i	−0.283721	+	0.163806i	0.351386	+	0.936231i	$0.385711\pi$
$194$		0			0
$195$	−7.37228	−	2.37686i	−0.527940	−	0.170211i
$196$		0			0
$197$		−	9.74749i		−	0.694480i	−0.937776	−	0.347240i	$-0.887119\pi$
$197$		−	9.74749i		−	0.694480i	0.937776	−	0.347240i	$-0.112881\pi$
$198$		0			0
$199$	−3.43070	−	5.94215i	−0.243196	−	0.421228i	0.718427	−	0.695603i	$-0.244863\pi$
$199$	−3.43070	−	5.94215i	−0.243196	−	0.421228i	−0.961623	+	0.274375i	$0.911529\pi$
$200$		0			0
$201$	5.56930	+	3.21543i	0.392828	+	0.226799i
$202$		0			0
$203$	−5.48913	+	4.75372i	−0.385261	+	0.333646i
$204$		0			0
$205$	1.55842	−	1.40965i	0.108845	−	0.0984539i
$206$		0			0
$207$	6.81386	+	11.8020i	0.473596	+	0.820292i
$208$		0			0
$209$			9.94987i			0.688247i
$210$		0			0
$211$			7.57301i			0.521348i	0.965427	+	0.260674i	$0.0839447\pi$
$211$			7.57301i			0.521348i	−0.965427	+	0.260674i	$0.916055\pi$
$212$		0			0
$213$	−4.11684	−	7.13058i	−0.282082	−	0.488579i
$214$		0			0
$215$	6.00000	+	6.63325i	0.409197	+	0.452384i
$216$		0			0
$217$	−25.2921	−	8.76144i	−1.71694	−	0.594766i
$218$		0			0
$219$	−3.17527	−	1.83324i	−0.214565	−	0.123879i
$220$		0			0
$221$	16.1168	+	27.9152i	1.08414	+	1.87778i
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$		0			0
$225$	−9.62772	−	6.92820i	−0.641848	−	0.461880i
$226$		0			0
$227$	5.31386	−	3.06796i	0.352693	−	0.203628i	−0.313178	−	0.949695i	$-0.601394\pi$
$227$	5.31386	−	3.06796i	0.352693	−	0.203628i	0.665871	+	0.746067i	$0.268060\pi$
$228$		0			0
$229$	−6.94158	−	4.00772i	−0.458712	−	0.264838i	0.252790	−	0.967521i	$-0.418652\pi$
$229$	−6.94158	−	4.00772i	−0.458712	−	0.264838i	−0.711503	+	0.702683i	$0.751985\pi$
$230$		0			0
$231$	0.686141	+	3.56529i	0.0451447	+	0.234579i
$232$		0			0
$233$	−18.1753	−	10.4935i	−1.19070	−	0.687452i	−0.232236	−	0.972660i	$-0.574604\pi$
$233$	−18.1753	−	10.4935i	−1.19070	−	0.687452i	−0.958466	+	0.285208i	$0.907937\pi$
$234$		0			0
$235$	−5.55842	−	25.8607i	−0.362591	−	1.68697i
$236$		0			0
$237$	−7.37228			−0.478881
$238$		0			0
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.00239235	−	0.999997i	$-0.499238\pi$
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.867219	+	0.497927i	$0.165905\pi$
$242$		0			0
$243$	13.6277	+	7.86797i	0.874219	+	0.504730i
$244$		0			0
$245$	−12.9891	+	8.73399i	−0.829845	+	0.557994i
$246$		0			0
$247$	12.5584	−	21.7518i	0.799073	−	1.38404i
$248$		0			0
$249$	−3.37228	−	5.84096i	−0.213710	−	0.370156i
$250$		0			0
$251$	−3.86141			−0.243730			−0.121865	−	0.992547i	$-0.538887\pi$
$251$	−3.86141			−0.243730			−0.121865	+	0.992547i	$0.538887\pi$
$252$		0			0
$253$		−	9.94987i		−	0.625543i
$254$		0			0
$255$	−2.74456	−	12.7692i	−0.171871	−	0.799636i
$256$		0			0
$257$	5.05842	−	8.76144i	0.315536	−	0.546524i	−0.664016	−	0.747719i	$-0.731149\pi$
$257$	5.05842	−	8.76144i	0.315536	−	0.546524i	0.979551	+	0.201195i	$0.0644825\pi$
$258$		0			0
$259$	−22.5000	+	4.33013i	−1.39808	+	0.269061i
$260$		0			0
$261$	3.25544	−	5.63858i	0.201507	−	0.349020i
$262$		0			0
$263$	−9.68614	−	16.7769i	−0.597273	−	1.03451i	−0.993222	−	0.116235i	$-0.962918\pi$
$263$	−9.68614	−	16.7769i	−0.597273	−	1.03451i	0.395949	−	0.918273i	$-0.370416\pi$
$264$		0			0
$265$	−13.8030	−	4.45015i	−0.847911	−	0.273371i
$266$		0			0
$267$	3.37228			0.206380
$268$		0			0
$269$	1.19702	−	0.691097i	0.0729833	−	0.0421369i	−0.463064	−	0.886325i	$-0.653250\pi$
$269$	1.19702	−	0.691097i	0.0729833	−	0.0421369i	0.536048	+	0.844188i	$0.319917\pi$
$270$		0			0
$271$	0.686141	−	1.18843i	0.0416801	−	0.0721920i	−0.844433	−	0.535662i	$-0.820062\pi$
$271$	0.686141	−	1.18843i	0.0416801	−	0.0721920i	0.886113	+	0.463469i	$0.153396\pi$
$272$		0			0
$273$	3.00000	−	8.66025i	0.181568	−	0.524142i
$274$		0			0
$275$	3.55842	+	7.89542i	0.214581	+	0.476112i
$276$		0			0
$277$	−17.0584	+	9.84868i	−1.02494	+	0.591750i	−0.915531	−	0.402247i	$-0.868229\pi$
$277$	−17.0584	+	9.84868i	−1.02494	+	0.591750i	−0.109410	+	0.993997i	$0.534896\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	−25.1168			−1.49835			−0.749173	−	0.662375i	$-0.769549\pi$
$281$	−25.1168			−1.49835			−0.749173	+	0.662375i	$0.769549\pi$
$282$		0			0
$283$	6.94158	−	4.00772i	0.412634	−	0.238234i	−0.279287	−	0.960208i	$-0.590098\pi$
$283$	6.94158	−	4.00772i	0.412634	−	0.238234i	0.691921	+	0.721973i	$0.256765\pi$
$284$		0			0
$285$	−7.54755	+	6.82701i	−0.447078	+	0.404397i
$286$		0			0
$287$	1.62772	+	1.87953i	0.0960812	+	0.110945i
$288$		0			0
$289$	−18.6753	+	32.3465i	−1.09855	+	1.90274i
$290$		0			0
$291$	4.11684	−	2.37686i	0.241334	−	0.139334i
$292$		0			0
$293$	−2.13859			−0.124938			−0.0624690	−	0.998047i	$-0.519897\pi$
$293$	−2.13859			−0.124938			−0.0624690	+	0.998047i	$0.519897\pi$
$294$		0			0
$295$	−3.17527	+	9.84868i	−0.184871	+	0.573413i
$296$		0			0
$297$	−3.68614	−	6.38458i	−0.213892	−	0.370471i
$298$		0			0
$299$	−12.5584	+	21.7518i	−0.726272	+	1.25794i
$300$		0			0
$301$	−8.00000	+	6.92820i	−0.461112	+	0.399335i
$302$		0			0
$303$	−4.31386	+	7.47182i	−0.247825	+	0.429245i
$304$		0			0
$305$	0.510875	+	2.37686i	0.0292526	+	0.136099i
$306$		0			0
$307$			12.9715i			0.740325i	0.928967	+	0.370163i	$0.120698\pi$
$307$			12.9715i			0.740325i	−0.928967	+	0.370163i	$0.879302\pi$
$308$		0			0
$309$	7.37228			0.419394
$310$		0			0
$311$	−0.686141	−	1.18843i	−0.0389075	−	0.0673897i	0.845916	−	0.533316i	$-0.179054\pi$
$311$	−0.686141	−	1.18843i	−0.0389075	−	0.0673897i	−0.884823	+	0.465927i	$0.845721\pi$
$312$		0			0
$313$	−6.43070	+	11.1383i	−0.363485	+	0.629574i	−0.988532	−	0.151013i	$-0.951746\pi$
$313$	−6.43070	+	11.1383i	−0.363485	+	0.629574i	0.625047	+	0.780587i	$0.285080\pi$
$314$		0			0
$315$	8.44158	−	11.2120i	0.475629	−	0.631727i
$316$		0			0
$317$	0.941578	+	0.543620i	0.0528843	+	0.0305328i	0.526209	−	0.850355i	$-0.323613\pi$
$317$	0.941578	+	0.543620i	0.0528843	+	0.0305328i	−0.473325	+	0.880888i	$0.656946\pi$
$318$		0			0
$319$	−4.11684	+	2.37686i	−0.230499	+	0.133079i
$320$		0			0
$321$		−	1.08724i		−	0.0606839i
$322$		0			0
$323$	42.3505			2.35645
$324$		0			0
$325$	2.18614	−	21.7518i	0.121265	−	1.20657i
$326$		0			0
$327$	−8.31386	−	4.80001i	−0.459757	−	0.265441i
$328$		0			0
$329$	30.7337	−	5.91470i	1.69440	−	0.326088i
$330$		0			0
$331$	10.5000	+	6.06218i	0.577132	+	0.333207i	0.759993	−	0.649931i	$-0.225202\pi$
$331$	10.5000	+	6.06218i	0.577132	+	0.333207i	−0.182861	+	0.983139i	$0.558536\pi$
$332$		0			0
$333$	17.7921	−	10.2723i	0.975002	−	0.562917i
$334$		0			0
$335$	−5.56930	+	17.2742i	−0.304283	+	0.943792i
$336$		0			0
$337$			6.92820i			0.377403i	0.982034	+	0.188702i	$0.0604279\pi$
$337$			6.92820i			0.377403i	−0.982034	+	0.188702i	$0.939572\pi$
$338$		0			0
$339$	−2.74456	−	4.75372i	−0.149064	−	0.258187i
$340$		0			0
$341$	−15.1753	−	8.76144i	−0.821787	−	0.474459i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	7.54755	−	6.82701i	0.406346	−	0.367554i
$346$		0			0
$347$	−6.43070	−	11.1383i	−0.345218	−	0.597936i	0.640175	−	0.768229i	$-0.278862\pi$
$347$	−6.43070	−	11.1383i	−0.345218	−	0.597936i	−0.985393	+	0.170293i	$0.945528\pi$
$348$		0			0
$349$			8.21782i			0.439890i	0.975512	+	0.219945i	$0.0705878\pi$
$349$			8.21782i			0.439890i	−0.975512	+	0.219945i	$0.929412\pi$
$350$		0			0
$351$			18.6101i			0.993335i
$352$		0			0
$353$	−5.31386	−	9.20387i	−0.282828	−	0.489873i	0.689252	−	0.724522i	$-0.257939\pi$
$353$	−5.31386	−	9.20387i	−0.282828	−	0.489873i	−0.972080	+	0.234649i	$0.924606\pi$
$354$		0			0
$355$	17.2337	−	15.5885i	0.914669	−	0.827349i
$356$		0			0
$357$	15.1753	−	2.92048i	0.803160	−	0.154568i
$358$		0			0
$359$	9.17527	+	5.29734i	0.484252	+	0.279583i	0.722187	−	0.691698i	$-0.243137\pi$
$359$	9.17527	+	5.29734i	0.484252	+	0.279583i	−0.237935	+	0.971281i	$0.576470\pi$
$360$		0			0
$361$	−7.00000	−	12.1244i	−0.368421	−	0.638124i
$362$		0			0
$363$		−	6.33830i		−	0.332674i
$364$		0			0
$365$	3.17527	−	9.84868i	0.166201	−	0.515504i
$366$		0			0
$367$	−14.6168	+	8.43904i	−0.762993	+	0.440514i	−0.830369	−	0.557213i	$-0.811871\pi$
$367$	−14.6168	+	8.43904i	−0.762993	+	0.440514i	0.0673763	+	0.997728i	$0.478537\pi$
$368$		0			0
$369$	−1.93070	−	1.11469i	−0.100508	−	0.0580286i
$370$		0			0
$371$	5.61684	−	16.2144i	0.291612	−	0.841811i
$372$		0			0
$373$	−13.2921	−	7.67420i	−0.688239	−	0.397355i	0.114713	−	0.993399i	$-0.463405\pi$
$373$	−13.2921	−	7.67420i	−0.688239	−	0.397355i	−0.802952	+	0.596044i	$0.796739\pi$
$374$		0			0
$375$	−3.54755	+	8.11663i	−0.183195	+	0.419141i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$		−	35.2858i		−	1.81251i	−0.422730	−	0.906256i	$-0.638928\pi$
$379$		−	35.2858i		−	1.81251i	0.422730	−	0.906256i	$-0.361072\pi$
$380$		0			0
$381$	−10.3723	+	5.98844i	−0.531388	+	0.306797i
$382$		0			0
$383$	−19.2446	−	11.1109i	−0.983351	−	0.567738i	−0.0800710	−	0.996789i	$-0.525515\pi$
$383$	−19.2446	−	11.1109i	−0.983351	−	0.567738i	−0.903280	+	0.429051i	$0.858848\pi$
$384$		0			0
$385$	−9.43070	+	4.00772i	−0.480633	+	0.204252i
$386$		0			0
$387$	4.74456	−	8.21782i	0.241180	−	0.417735i
$388$		0			0
$389$	−5.05842	−	8.76144i	−0.256472	−	0.444223i	0.708822	−	0.705387i	$-0.249227\pi$
$389$	−5.05842	−	8.76144i	−0.256472	−	0.444223i	−0.965294	+	0.261164i	$0.915894\pi$
$390$		0			0
$391$	−42.3505			−2.14176
$392$		0			0
$393$			2.37686i			0.119897i
$394$		0			0
$395$	−4.37228	−	20.3422i	−0.219993	−	1.02353i
$396$		0			0
$397$	−8.05842	+	13.9576i	−0.404441	+	0.700512i	−0.994256	−	0.107026i	$-0.965867\pi$
$397$	−8.05842	+	13.9576i	−0.404441	+	0.700512i	0.589816	+	0.807538i	$0.299200\pi$
$398$		0			0
$399$	−7.88316	−	9.10268i	−0.394651	−	0.455704i
$400$		0			0
$401$	−3.12772	+	5.41737i	−0.156191	+	0.270530i	−0.933492	−	0.358598i	$-0.883255\pi$
$401$	−3.12772	+	5.41737i	−0.156191	+	0.270530i	0.777301	+	0.629129i	$0.216588\pi$
$402$		0			0
$403$	22.1168	+	38.3075i	1.10172	+	1.90823i
$404$		0			0
$405$	−2.56930	+	7.96916i	−0.127669	+	0.395991i
$406$		0			0
$407$	−15.0000			−0.743522
$408$		0			0
$409$	−0.941578	+	0.543620i	−0.0465580	+	0.0268803i	−0.523098	−	0.852272i	$-0.675224\pi$
$409$	−0.941578	+	0.543620i	−0.0465580	+	0.0268803i	0.476540	+	0.879153i	$0.341891\pi$
$410$		0			0
$411$	−3.68614	+	6.38458i	−0.181824	+	0.314928i
$412$		0			0
$413$	−11.5693	−	4.00772i	−0.569288	−	0.197207i
$414$		0			0
$415$	14.1168	−	12.7692i	0.692969	−	0.626814i
$416$		0			0
$417$	−8.23369	+	4.75372i	−0.403205	+	0.232791i
$418$		0			0
$419$	25.6277			1.25200			0.625998	−	0.779825i	$-0.284692\pi$
$419$	25.6277			1.25200			0.625998	+	0.779825i	$0.284692\pi$
$420$		0			0
$421$	16.2337			0.791182			0.395591	−	0.918427i	$-0.370540\pi$
$421$	16.2337			0.791182			0.395591	+	0.918427i	$0.370540\pi$
$422$		0			0
$423$	−24.3030	+	14.0313i	−1.18165	+	0.682227i
$424$		0			0
$425$	33.6060	−	15.1460i	1.63013	−	0.734690i
$426$		0			0
$427$	−2.82473	+	0.543620i	−0.136698	+	0.0263076i
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$		0			0
$431$	12.1753	−	7.02939i	0.586462	−	0.338594i	−0.177235	−	0.984169i	$-0.556715\pi$
$431$	12.1753	−	7.02939i	0.586462	−	0.338594i	0.763697	+	0.645575i	$0.223382\pi$
$432$		0			0
$433$	0.510875			0.0245511			0.0122755	−	0.999925i	$-0.496092\pi$
$433$	0.510875			0.0245511			0.0122755	+	0.999925i	$0.496092\pi$
$434$		0			0
$435$	−4.62772	−	1.49200i	−0.221882	−	0.0715359i
$436$		0			0
$437$	16.5000	+	28.5788i	0.789302	+	1.36711i
$438$		0			0
$439$	−10.8030	+	18.7113i	−0.515598	+	0.893042i	0.484238	+	0.874936i	$0.339097\pi$
$439$	−10.8030	+	18.7113i	−0.515598	+	0.893042i	−0.999836	+	0.0181060i	$0.994236\pi$
$440$		0			0
$441$	13.0475	+	10.2723i	0.621312	+	0.489156i
$442$		0			0
$443$	9.68614	−	16.7769i	0.460202	−	0.797094i	−0.538768	−	0.842454i	$-0.681110\pi$
$443$	9.68614	−	16.7769i	0.460202	−	0.797094i	0.998971	+	0.0453600i	$0.0144435\pi$
$444$		0			0
$445$	2.00000	+	9.30506i	0.0948091	+	0.441102i
$446$		0			0
$447$			10.1899i			0.481967i
$448$		0			0
$449$	2.13859			0.100926			0.0504632	−	0.998726i	$-0.483930\pi$
$449$	2.13859			0.100926			0.0504632	+	0.998726i	$0.483930\pi$
$450$		0			0
$451$	0.813859	+	1.40965i	0.0383231	+	0.0663776i
$452$		0			0
$453$	−4.54755	+	7.87658i	−0.213662	+	0.370074i
$454$		0			0
$455$	25.6753	+	3.14170i	1.20368	+	0.147285i
$456$		0			0
$457$	28.2921	+	16.3345i	1.32345	+	0.764094i	0.984277	−	0.176631i	$-0.0565198\pi$
$457$	28.2921	+	16.3345i	1.32345	+	0.764094i	0.339172	+	0.940724i	$0.389853\pi$
$458$		0			0
$459$	−27.1753	+	15.6896i	−1.26843	+	0.732330i
$460$		0			0
$461$		−	28.4125i		−	1.32330i	−0.749811	−	0.661652i	$-0.769856\pi$
$461$		−	28.4125i		−	1.32330i	0.749811	−	0.661652i	$-0.230144\pi$
$462$		0			0
$463$	−37.3505			−1.73583			−0.867913	−	0.496716i	$-0.834539\pi$
$463$	−37.3505			−1.73583			−0.867913	+	0.496716i	$0.834539\pi$
$464$		0			0
$465$	−3.76631	−	17.5229i	−0.174659	−	0.812604i
$466$		0			0
$467$	20.9198	+	12.0781i	0.968054	+	0.558906i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	20.9198	+	12.0781i	0.968054	+	0.558906i	0.0694117	+	0.997588i	$0.477888\pi$
$468$		0			0
$469$	−20.2921	−	7.02939i	−0.937003	−	0.324587i
$470$		0			0
$471$	6.17527	+	3.56529i	0.284541	+	0.164280i
$472$		0			0
$473$	−6.00000	+	3.46410i	−0.275880	+	0.159280i
$474$		0			0
$475$	−23.3139	−	16.7769i	−1.06971	−	0.769776i
$476$		0			0
$477$			15.3861i			0.704480i
$478$		0			0
$479$	16.8030	+	29.1036i	0.767748	+	1.32978i	0.938781	+	0.344513i	$0.111956\pi$
$479$	16.8030	+	29.1036i	0.767748	+	1.32978i	−0.171033	+	0.985265i	$0.554711\pi$
$480$		0			0
$481$	32.7921	+	18.9325i	1.49519	+	0.863249i
$482$		0			0
$483$	7.88316	+	9.10268i	0.358696	+	0.414186i
$484$		0			0
$485$	9.00000	+	9.94987i	0.408669	+	0.451801i
$486$		0			0
$487$	−4.94158	−	8.55906i	−0.223924	−	0.387848i	0.732072	−	0.681227i	$-0.238553\pi$
$487$	−4.94158	−	8.55906i	−0.223924	−	0.387848i	−0.955996	+	0.293379i	$0.905220\pi$
$488$		0			0
$489$		−	3.07657i		−	0.139127i
$490$		0			0
$491$			10.3923i			0.468998i	0.972116	+	0.234499i	$0.0753450\pi$
$491$			10.3923i			0.468998i	−0.972116	+	0.234499i	$0.924655\pi$
$492$		0			0
$493$	10.1168	+	17.5229i	0.455640	+	0.789191i
$494$		0			0
$495$	6.81386	−	6.16337i	0.306260	−	0.277023i
$496$		0			0
$497$	18.0000	+	20.7846i	0.807410	+	0.932317i
$498$		0			0
$499$	16.2921	+	9.40625i	0.729335	+	0.421082i	0.818179	−	0.574964i	$-0.194984\pi$
$499$	16.2921	+	9.40625i	0.729335	+	0.421082i	−0.0888438	+	0.996046i	$0.528317\pi$
$500$		0			0
$501$	2.25544	+	3.90653i	0.100766	+	0.174531i
$502$		0			0
$503$		−	14.1514i		−	0.630978i	−0.948929	−	0.315489i	$-0.897831\pi$
$503$		−	14.1514i		−	0.630978i	0.948929	−	0.315489i	$-0.102169\pi$
$504$		0			0
$505$	−23.1753	−	7.47182i	−1.03129	−	0.332492i
$506$		0			0
$507$	−4.19702	+	2.42315i	−0.186396	+	0.107616i
$508$		0			0
$509$	−36.4307	−	21.0333i	−1.61476	−	0.932284i	−0.988245	−	0.152876i	$-0.951147\pi$
$509$	−36.4307	−	21.0333i	−1.61476	−	0.932284i	−0.626517	−	0.779408i	$-0.715520\pi$
$510$		0			0
$511$	11.5693	+	4.00772i	0.511796	+	0.177291i
$512$		0			0
$513$	21.1753	+	12.2255i	0.934911	+	0.539771i
$514$		0			0
$515$	4.37228	+	20.3422i	0.192666	+	0.896384i
$516$		0			0
$517$	20.4891			0.901111
$518$		0			0
$519$		−	8.90030i		−	0.390680i
$520$		0			0
$521$	−14.3614	+	8.29156i	−0.629185	+	0.363260i	−0.780436	−	0.625235i	$-0.785003\pi$
$521$	−14.3614	+	8.29156i	−0.629185	+	0.363260i	0.151252	+	0.988495i	$0.451670\pi$
$522$		0			0
$523$	15.9416	+	9.20387i	0.697077	+	0.402457i	0.806258	−	0.591565i	$-0.201490\pi$
$523$	15.9416	+	9.20387i	0.697077	+	0.402457i	−0.109181	+	0.994022i	$0.534823\pi$
$524$		0			0
$525$	−9.51087	−	4.40387i	−0.415089	−	0.192200i
$526$		0			0
$527$	−37.2921	+	64.5918i	−1.62447	+	2.81366i
$528$		0			0
$529$	−5.00000	−	8.66025i	−0.217391	−	0.376533i
$530$		0			0
$531$	10.9783			0.476415
$532$		0			0
$533$		−	4.10891i		−	0.177977i
$534$		0			0
$535$	3.00000	−	0.644810i	0.129701	−	0.0278776i
$536$		0			0
$537$	−7.19702	+	12.4656i	−0.310574	+	0.537930i
$538$		0			0
$539$	−4.50000	−	11.2583i	−0.193829	−	0.484931i
$540$		0			0
$541$	11.1753	−	19.3561i	0.480462	−	0.832185i	−0.519287	−	0.854600i	$-0.673802\pi$
$541$	11.1753	−	19.3561i	0.480462	−	0.832185i	0.999749	+	0.0224152i	$0.00713559\pi$
$542$		0			0
$543$	−0.510875	−	0.884861i	−0.0219237	−	0.0379730i
$544$		0			0
$545$	8.31386	−	25.7870i	0.356127	−	1.10459i
$546$		0			0
$547$	−36.4674			−1.55923			−0.779616	−	0.626258i	$-0.784586\pi$
$547$	−36.4674			−1.55923			−0.779616	+	0.626258i	$0.784586\pi$
$548$		0			0
$549$	2.23369	−	1.28962i	0.0953315	−	0.0550397i
$550$		0			0
$551$	7.88316	−	13.6540i	0.335834	−	0.581681i
$552$		0			0
$553$	24.1753	−	4.65253i	1.02804	−	0.197846i
$554$		0			0
$555$	−10.2921	−	11.3784i	−0.436876	−	0.482984i
$556$		0			0
$557$	30.7337	−	17.7441i	1.30223	−	0.751842i	0.321442	−	0.946929i	$-0.395832\pi$
$557$	30.7337	−	17.7441i	1.30223	−	0.751842i	0.980786	+	0.195087i	$0.0624991\pi$
$558$		0			0
$559$	17.4891			0.739711
$560$		0			0
$561$	10.1168			0.427133
$562$		0			0
$563$	16.8030	−	9.70121i	0.708161	−	0.408857i	−0.102219	−	0.994762i	$-0.532594\pi$
$563$	16.8030	−	9.70121i	0.708161	−	0.408857i	0.810380	+	0.585905i	$0.199261\pi$
$564$		0			0
$565$	11.4891	−	10.3923i	0.483351	−	0.437208i
$566$		0			0
$567$	−9.36141	−	3.24289i	−0.393142	−	0.136188i
$568$		0			0
$569$	−0.383156	+	0.663646i	−0.0160627	+	0.0278215i	−0.873945	−	0.486025i	$-0.838446\pi$
$569$	−0.383156	+	0.663646i	−0.0160627	+	0.0278215i	0.857882	+	0.513846i	$0.171780\pi$
$570$		0			0
$571$	12.1753	−	7.02939i	0.509519	−	0.294171i	−0.223117	−	0.974792i	$-0.571623\pi$
$571$	12.1753	−	7.02939i	0.509519	−	0.294171i	0.732636	+	0.680621i	$0.238290\pi$
$572$		0			0
$573$	4.62772			0.193326
$574$		0			0
$575$	23.3139	+	16.7769i	0.972255	+	0.699645i
$576$		0			0
$577$	12.6861	+	21.9730i	0.528131	+	0.914750i	0.999462	+	0.0327933i	$0.0104403\pi$
$577$	12.6861	+	21.9730i	0.528131	+	0.914750i	−0.471331	+	0.881956i	$0.656226\pi$
$578$		0			0
$579$	1.80298	−	3.12286i	0.0749295	−	0.129782i
$580$		0			0
$581$	14.7446	+	17.0256i	0.611708	+	0.706339i
$582$		0			0
$583$	5.61684	−	9.72866i	0.232626	−	0.402920i
$584$		0			0
$585$	−22.6753	+	4.87375i	−0.937507	+	0.201505i
$586$		0			0
$587$			6.63325i			0.273784i	0.990586	+	0.136892i	$0.0437113\pi$
$587$			6.63325i			0.273784i	−0.990586	+	0.136892i	$0.956289\pi$
$588$		0			0
$589$	58.1168			2.39466
$590$		0			0
$591$	3.86141	+	6.68815i	0.158837	+	0.275114i
$592$		0			0
$593$	10.5475	−	18.2689i	0.433136	−	0.750213i	−0.564006	−	0.825771i	$-0.690740\pi$
$593$	10.5475	−	18.2689i	0.433136	−	0.750213i	0.997141	+	0.0755577i	$0.0240737\pi$
$594$		0			0
$595$	17.0584	+	40.1407i	0.699327	+	1.64561i
$596$		0			0
$597$	4.70789	+	2.71810i	0.192681	+	0.111244i
$598$		0			0
$599$	−27.1753	+	15.6896i	−1.11035	+	0.641062i	−0.938920	−	0.344135i	$-0.888172\pi$
$599$	−27.1753	+	15.6896i	−1.11035	+	0.641062i	−0.171431	+	0.985196i	$0.554839\pi$
$600$		0			0
$601$		−	9.50744i		−	0.387817i	−0.981020	−	0.193908i	$-0.937884\pi$
$601$		−	9.50744i		−	0.387817i	0.981020	−	0.193908i	$-0.0621164\pi$
$602$		0			0
$603$	19.2554			0.784142
$604$		0			0
$605$	17.4891	−	3.75906i	0.711034	−	0.152827i
$606$		0			0
$607$	6.38316	+	3.68532i	0.259084	+	0.149582i	0.623917	−	0.781491i	$-0.285540\pi$
$607$	6.38316	+	3.68532i	0.259084	+	0.149582i	−0.364832	+	0.931073i	$0.618874\pi$
$608$		0			0
$609$	1.88316	−	5.43620i	0.0763093	−	0.220286i
$610$		0			0
$611$	−44.7921	−	25.8607i	−1.81209	−	1.04621i
$612$		0			0
$613$	4.50000	−	2.59808i	0.181753	−	0.104935i	−0.406363	−	0.913712i	$-0.633203\pi$
$613$	4.50000	−	2.59808i	0.181753	−	0.104935i	0.588116	+	0.808776i	$0.299870\pi$
$614$		0			0
$615$	−0.510875	+	1.58457i	−0.0206005	+	0.0638962i
$616$		0			0
$617$			45.4381i			1.82927i	0.404283	+	0.914634i	$0.367521\pi$
$617$			45.4381i			1.82927i	−0.404283	+	0.914634i	$0.632479\pi$
$618$		0			0
$619$	21.9891	+	38.0863i	0.883818	+	1.53082i	0.847063	+	0.531493i	$0.178369\pi$
$619$	21.9891	+	38.0863i	0.883818	+	1.53082i	0.0367546	+	0.999324i	$0.488298\pi$
$620$		0			0
$621$	−21.1753	−	12.2255i	−0.849734	−	0.490594i
$622$		0			0
$623$	−11.0584	+	2.12819i	−0.443046	+	0.0852643i
$624$		0			0
$625$	−24.5000	−	4.97494i	−0.980000	−	0.198997i
$626$		0			0
$627$	−3.94158	−	6.82701i	−0.157411	−	0.272645i
$628$		0			0
$629$			63.8458i			2.54570i
$630$		0			0
$631$		−	28.1176i		−	1.11934i	−0.828715	−	0.559671i	$-0.810927\pi$
$631$		−	28.1176i		−	1.11934i	0.828715	−	0.559671i	$-0.189073\pi$
$632$		0			0
$633$	−3.00000	−	5.19615i	−0.119239	−	0.206529i
$634$		0			0
$635$	−22.6753	−	25.0684i	−0.899840	−	0.994811i
$636$		0			0
$637$	−4.37228	+	30.2921i	−0.173236	+	1.20021i
$638$		0			0
$639$	−21.3505	−	12.3267i	−0.844614	−	0.487638i
$640$		0			0
$641$	−17.8723	−	30.9557i	−0.705913	−	1.22268i	−0.966361	−	0.257189i	$-0.917204\pi$
$641$	−17.8723	−	30.9557i	−0.705913	−	1.22268i	0.260448	−	0.965488i	$-0.416130\pi$
$642$		0			0
$643$			40.6844i			1.60443i	0.597032	+	0.802217i	$0.296346\pi$
$643$			40.6844i			1.60443i	−0.597032	+	0.802217i	$0.703654\pi$
$644$		0			0
$645$	−6.74456	−	2.17448i	−0.265567	−	0.0856201i
$646$		0			0
$647$	−3.63859	+	2.10074i	−0.143048	+	0.0825887i	−0.569816	−	0.821772i	$-0.692985\pi$
$647$	−3.63859	+	2.10074i	−0.143048	+	0.0825887i	0.426768	+	0.904361i	$0.359652\pi$
$648$		0			0
$649$	−6.94158	−	4.00772i	−0.272481	−	0.157317i
$650$		0			0
$651$	20.8247	−	4.00772i	0.816186	−	0.157075i
$652$		0			0
$653$	−26.6168	−	15.3672i	−1.04160	−	0.601367i	−0.121312	−	0.992614i	$-0.538710\pi$
$653$	−26.6168	−	15.3672i	−1.04160	−	0.601367i	−0.920285	+	0.391248i	$0.872044\pi$
$654$		0			0
$655$	−6.55842	+	1.40965i	−0.256259	+	0.0550794i
$656$		0			0
$657$	−10.9783			−0.428302
$658$		0			0
$659$		−	40.6844i		−	1.58484i	−0.609977	−	0.792419i	$-0.708822\pi$
$659$		−	40.6844i		−	1.58484i	0.609977	−	0.792419i	$-0.291178\pi$
$660$		0			0
$661$	−21.1753	+	12.2255i	−0.823622	+	0.475519i	−0.851664	−	0.524088i	$-0.824406\pi$
$661$	−21.1753	+	12.2255i	−0.823622	+	0.475519i	0.0280416	+	0.999607i	$0.491073\pi$
$662$		0			0
$663$	−22.1168	−	12.7692i	−0.858947	−	0.495913i
$664$		0			0
$665$	20.4416	−	27.1504i	0.792690	−	1.05285i
$666$		0			0
$667$	−7.88316	+	13.6540i	−0.305237	+	0.528686i
$668$		0			0
$669$	4.11684	+	7.13058i	0.159166	+	0.275684i
$670$		0			0
$671$	−1.88316			−0.0726984
$672$		0			0
$673$		−	15.1460i		−	0.583836i	−0.956443	−	0.291918i	$-0.905706\pi$
$673$		−	15.1460i		−	0.583836i	0.956443	−	0.291918i	$-0.0942935\pi$
$674$		0			0
$675$	21.1753	+	2.12819i	0.815036	+	0.0819142i
$676$		0			0
$677$	−11.6168	+	20.1210i	−0.446472	+	0.773311i	−0.998153	−	0.0607432i	$-0.980653\pi$
$677$	−11.6168	+	20.1210i	−0.446472	+	0.773311i	0.551682	+	0.834055i	$0.313986\pi$
$678$		0			0
$679$	−12.0000	+	10.3923i	−0.460518	+	0.398820i
$680$		0			0
$681$	−2.43070	+	4.21010i	−0.0931448	+	0.161331i
$682$		0			0
$683$	−5.31386	−	9.20387i	−0.203329	−	0.352176i	0.746270	−	0.665643i	$-0.231843\pi$
$683$	−5.31386	−	9.20387i	−0.203329	−	0.352176i	−0.949599	+	0.313467i	$0.898509\pi$
$684$		0			0
$685$	−19.8030	−	6.38458i	−0.756633	−	0.243942i
$686$		0			0
$687$	6.35053			0.242288
$688$		0			0
$689$	−24.5584	+	14.1788i	−0.935601	+	0.540170i
$690$		0			0
$691$	8.31386	−	14.4000i	0.316274	−	0.547803i	−0.663433	−	0.748235i	$-0.730901\pi$
$691$	8.31386	−	14.4000i	0.316274	−	0.547803i	0.979708	+	0.200433i	$0.0642347\pi$
$692$		0			0
$693$	7.11684	+	8.21782i	0.270347	+	0.312169i
$694$		0			0
$695$	−18.0000	−	19.8997i	−0.682779	−	0.754840i
$696$		0			0
$697$	6.00000	−	3.46410i	0.227266	−	0.131212i
$698$		0			0
$699$	16.6277			0.628918
$700$		0			0
$701$	9.25544			0.349573			0.174787	−	0.984606i	$-0.444076\pi$
$701$	9.25544			0.349573			0.174787	+	0.984606i	$0.444076\pi$
$702$		0			0
$703$	43.0842	−	24.8747i	1.62495	−	0.938167i
$704$		0			0
$705$	14.0584	+	15.5422i	0.529471	+	0.585352i
$706$		0			0
$707$	9.43070	−	27.2241i	0.354678	−	1.02387i
$708$		0			0
$709$	17.1753	−	29.7484i	0.645031	−	1.11723i	−0.339264	−	0.940691i	$-0.610178\pi$
$709$	17.1753	−	29.7484i	0.645031	−	1.11723i	0.984294	−	0.176535i	$-0.0564887\pi$
$710$		0			0
$711$	−19.1168	+	11.0371i	−0.716938	+	0.413924i
$712$		0			0
$713$	−58.1168			−2.17649
$714$		0			0
$715$	16.1168	+	5.19615i	0.602736	+	0.194325i
$716$		0			0
$717$	4.11684	+	7.13058i	0.153746	+	0.266296i
$718$		0			0
$719$	−11.3139	+	19.5962i	−0.421936	+	0.730814i	−0.996129	−	0.0879058i	$-0.971983\pi$
$719$	−11.3139	+	19.5962i	−0.421936	+	0.730814i	0.574193	+	0.818720i	$0.305316\pi$
$720$		0			0
$721$	−24.1753	+	4.65253i	−0.900334	+	0.173269i
$722$		0			0
$723$	−6.17527	+	10.6959i	−0.229661	+	0.397784i
$724$		0			0
$725$	1.37228	−	13.6540i	0.0509652	−	0.507098i
$726$		0			0
$727$		−	36.5754i		−	1.35651i	−0.734827	−	0.678254i	$-0.762737\pi$
$727$		−	36.5754i		−	1.35651i	0.734827	−	0.678254i	$-0.237263\pi$
$728$		0			0
$729$	−1.23369			−0.0456921
$730$		0			0
$731$	14.7446	+	25.5383i	0.545347	+	0.944569i
$732$		0			0
$733$	18.9891	−	32.8901i	0.701379	−	1.21482i	−0.266603	−	0.963806i	$-0.585901\pi$
$733$	18.9891	−	32.8901i	0.701379	−	1.21482i	0.967982	−	0.251018i	$-0.0807654\pi$
$734$		0			0
$735$	5.45245	−	11.1383i	0.201117	−	0.410843i
$736$		0			0
$737$	−12.1753	−	7.02939i	−0.448482	−	0.258931i
$738$		0			0
$739$	−17.6168	+	10.1711i	−0.648046	+	0.374150i	−0.787707	−	0.616050i	$-0.788732\pi$
$739$	−17.6168	+	10.1711i	−0.648046	+	0.374150i	0.139661	+	0.990199i	$0.455399\pi$
$740$		0			0
$741$			19.8997i			0.731036i
$742$		0			0
$743$	−27.8614			−1.02214			−0.511068	−	0.859540i	$-0.670750\pi$
$743$	−27.8614			−1.02214			−0.511068	+	0.859540i	$0.670750\pi$
$744$		0			0
$745$	−28.1168	+	6.04334i	−1.03012	+	0.221411i
$746$		0			0
$747$	−17.4891	−	10.0974i	−0.639894	−	0.369443i
$748$		0			0
$749$	0.686141	+	3.56529i	0.0250710	+	0.130273i
$750$		0			0
$751$	6.94158	+	4.00772i	0.253302	+	0.146244i	0.621275	−	0.783592i	$-0.286615\pi$
$751$	6.94158	+	4.00772i	0.253302	+	0.146244i	−0.367973	+	0.929836i	$0.619948\pi$
$752$		0			0
$753$	2.64947	−	1.52967i	0.0965520	−	0.0557443i
$754$		0			0
$755$	−24.4307	−	7.87658i	−0.889124	−	0.286658i
$756$		0			0
$757$		−	16.4356i		−	0.597364i	−0.954353	−	0.298682i	$-0.903453\pi$
$757$		−	16.4356i		−	0.597364i	0.954353	−	0.298682i	$-0.0965469\pi$
$758$		0			0
$759$	3.94158	+	6.82701i	0.143070	+	0.247805i
$760$		0			0
$761$	46.3397	+	26.7542i	1.67981	+	0.969839i	0.961778	+	0.273831i	$0.0882908\pi$
$761$	46.3397	+	26.7542i	1.67981	+	0.969839i	0.718033	+	0.696009i	$0.245042\pi$
$762$		0			0
$763$	30.2921	+	10.4935i	1.09665	+	0.379890i
$764$		0			0
$765$	−26.2337	−	29.0024i	−0.948481	−	1.04859i
$766$		0			0
$767$	10.1168	+	17.5229i	0.365298	+	0.632715i
$768$		0			0
$769$		−	27.4728i		−	0.990693i	−0.868695	−	0.495347i	$-0.835041\pi$
$769$		−	27.4728i		−	0.990693i	0.868695	−	0.495347i	$-0.164959\pi$
$770$		0			0
$771$			8.01544i			0.288669i
$772$		0			0
$773$	−20.8723	−	36.1519i	−0.750724	−	1.30029i	−0.947472	−	0.319838i	$-0.896372\pi$
$773$	−20.8723	−	36.1519i	−0.750724	−	1.30029i	0.196749	−	0.980454i	$-0.436962\pi$
$774$		0			0
$775$	46.1168	−	20.7846i	1.65657	−	0.746605i
$776$		0			0
$777$	13.7228	−	11.8843i	0.492303	−	0.426347i
$778$		0			0
$779$	−4.67527	−	2.69927i	−0.167509	−	0.0967112i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$			11.6819i			0.417478i
$784$		0			0
$785$	−6.17527	+	19.1537i	−0.220405	+	0.683627i
$786$		0			0
$787$	−8.82473	+	5.09496i	−0.314568	+	0.181616i	−0.648969	−	0.760815i	$-0.724799\pi$
$787$	−8.82473	+	5.09496i	−0.314568	+	0.181616i	0.334401	+	0.942431i	$0.391466\pi$
$788$		0			0
$789$	13.2921	+	7.67420i	0.473212	+	0.273209i
$790$		0			0
$791$	12.0000	+	13.8564i	0.426671	+	0.492677i
$792$		0			0
$793$	4.11684	+	2.37686i	0.146193	+	0.0844048i
$794$		0			0
$795$	11.2337	−	2.41453i	0.398418	−	0.0856346i
$796$		0			0
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$		−	87.2097i		−	3.08526i
$800$		0			0
$801$	8.74456	−	5.04868i	0.308974	−	0.178386i
$802$		0			0
$803$	6.94158	+	4.00772i	0.244963	+	0.141429i
$804$		0			0
$805$	−20.4416	+	27.1504i	−0.720471	+	0.956924i
$806$		0			0
$807$	−0.547547	+	0.948380i	−0.0192746	+	0.0333845i
$808$		0			0
$809$	−17.8723	−	30.9557i	−0.628356	−	1.08834i	−0.987882	−	0.155209i	$-0.950395\pi$
$809$	−17.8723	−	30.9557i	−0.628356	−	1.08834i	0.359526	−	0.933135i	$-0.382939\pi$
$810$		0			0
$811$	−46.3723			−1.62835			−0.814176	−	0.580619i	$-0.802811\pi$
$811$	−46.3723			−1.62835			−0.814176	+	0.580619i	$0.802811\pi$
$812$		0			0
$813$			1.08724i			0.0381312i
$814$		0			0
$815$	8.48913	−	1.82462i	0.297361	−	0.0639138i
$816$		0			0
$817$	11.4891	−	19.8997i	0.401954	−	0.696204i
$818$		0			0
$819$	−5.18614	−	26.9480i	−0.181218	−	0.941639i
$820$		0			0
$821$	20.0584	−	34.7422i	0.700044	−	1.21251i	−0.268407	−	0.963306i	$-0.586497\pi$
$821$	20.0584	−	34.7422i	0.700044	−	1.21251i	0.968451	−	0.249206i	$-0.0801695\pi$
$822$		0			0
$823$	−7.17527	−	12.4279i	−0.250114	−	0.433210i	0.713443	−	0.700713i	$-0.247135\pi$
$823$	−7.17527	−	12.4279i	−0.250114	−	0.433210i	−0.963557	+	0.267503i	$0.913801\pi$
$824$		0			0
$825$	−5.56930	−	4.00772i	−0.193898	−	0.139531i
$826$		0			0
$827$	−19.7228			−0.685829			−0.342915	−	0.939367i	$-0.611414\pi$
$827$	−19.7228			−0.685829			−0.342915	+	0.939367i	$0.611414\pi$
$828$		0			0
$829$	−41.4090	+	23.9075i	−1.43819	+	0.830341i	−0.997724	−	0.0674274i	$-0.978521\pi$
$829$	−41.4090	+	23.9075i	−1.43819	+	0.830341i	−0.440468	+	0.897768i	$0.645188\pi$
$830$		0			0
$831$	7.80298	−	13.5152i	0.270683	−	0.468836i
$832$		0			0
$833$	−47.9198	+	19.1537i	−1.66032	+	0.663638i
$834$		0			0
$835$	−9.44158	+	8.54023i	−0.326739	+	0.295547i
$836$		0			0
$837$	−37.2921	+	21.5306i	−1.28900	+	0.744207i
$838$		0			0
$839$	44.7446			1.54475			0.772377	−	0.635164i	$-0.219068\pi$
$839$	44.7446			1.54475			0.772377	+	0.635164i	$0.219068\pi$
$840$		0			0
$841$	−21.4674			−0.740254
$842$		0			0
$843$	17.2337	−	9.94987i	0.593560	−	0.342692i
$844$		0			0
$845$	−9.17527	−	10.1436i	−0.315639	−	0.348952i
$846$		0			0
$847$	4.00000	+	20.7846i	0.137442	+	0.714168i
$848$		0			0
$849$	−3.17527	+	5.49972i	−0.108975	+	0.188750i
$850$		0			0
$851$	−43.0842	+	24.8747i	−1.47691	+	0.852693i
$852$		0			0
$853$	37.1168			1.27086			0.635428	−	0.772160i	$-0.280824\pi$
$853$	37.1168			1.27086			0.635428	+	0.772160i	$0.280824\pi$
$854$		0			0
$855$	−9.35053	+	29.0024i	−0.319781	+	0.991862i
$856$		0			0
$857$	0.686141	+	1.18843i	0.0234381	+	0.0405960i	0.877507	−	0.479565i	$-0.159205\pi$
$857$	0.686141	+	1.18843i	0.0234381	+	0.0405960i	−0.854068	+	0.520161i	$0.825872\pi$
$858$		0			0
$859$	4.54755	−	7.87658i	0.155160	−	0.268746i	−0.777957	−	0.628317i	$-0.783744\pi$
$859$	4.54755	−	7.87658i	0.155160	−	0.268746i	0.933117	+	0.359572i	$0.117077\pi$
$860$		0			0
$861$	−1.86141	−	0.644810i	−0.0634366	−	0.0219751i
$862$		0			0
$863$	18.1277	−	31.3981i	0.617075	−	1.06880i	−0.372942	−	0.927855i	$-0.621651\pi$
$863$	18.1277	−	31.3981i	0.617075	−	1.06880i	0.990017	−	0.140950i	$-0.0450157\pi$
$864$		0			0
$865$	24.5584	−	5.27851i	0.835011	−	0.179475i
$866$		0			0
$867$		−	29.5923i		−	1.00501i
$868$		0			0
$869$	16.1168			0.546726
$870$		0			0
$871$	17.7446	+	30.7345i	0.601252	+	1.04140i
$872$		0			0
$873$	7.11684	−	12.3267i	0.240869	−	0.417197i
$874$		0			0
$875$	6.51087	−	28.8550i	0.220108	−	0.975476i
$876$		0			0
$877$	−1.50000	−	0.866025i	−0.0506514	−	0.0292436i	0.474460	−	0.880277i	$-0.342643\pi$
$877$	−1.50000	−	0.866025i	−0.0506514	−	0.0292436i	−0.525112	+	0.851033i	$0.675977\pi$
$878$		0			0
$879$	1.46738	−	0.847190i	0.0494934	−	0.0285750i
$880$		0			0
$881$			8.56768i			0.288652i	0.989530	+	0.144326i	$0.0461015\pi$
$881$			8.56768i			0.288652i	−0.989530	+	0.144326i	$0.953899\pi$
$882$		0			0
$883$	−24.4674			−0.823393			−0.411696	−	0.911321i	$-0.635064\pi$
$883$	−24.4674			−0.823393			−0.411696	+	0.911321i	$0.635064\pi$
$884$		0			0
$885$	−1.72281	−	8.01544i	−0.0579117	−	0.269436i
$886$		0			0
$887$	−5.31386	−	3.06796i	−0.178422	−	0.103012i	0.408129	−	0.912924i	$-0.366181\pi$
$887$	−5.31386	−	3.06796i	−0.178422	−	0.103012i	−0.586551	+	0.809912i	$0.699515\pi$
$888$		0			0
$889$	30.2337	−	26.1831i	1.01401	−	0.878154i
$890$		0			0
$891$	−5.61684	−	3.24289i	−0.188171	−	0.108641i
$892$		0			0
$893$	−58.8505	+	33.9774i	−1.96936	+	1.13701i
$894$		0			0
$895$	−38.6644	−	12.4656i	−1.29241	−	0.416679i
$896$		0			0
$897$		−	19.8997i		−	0.664433i
$898$		0			0
$899$	13.8832	+	24.0463i	0.463029	+	0.801990i
$900$		0			0
$901$	−41.4090	−	23.9075i	−1.37953	−	0.796473i
$902$		0			0
$903$	2.74456	−	7.92287i	0.0913333	−	0.263657i
$904$		0			0
$905$	2.13859	−	1.93443i	0.0710892	−	0.0643026i
$906$		0			0
$907$	22.1753	+	38.4087i	0.736318	+	1.27534i	0.954143	+	0.299352i	$0.0967704\pi$
$907$	22.1753	+	38.4087i	0.736318	+	1.27534i	−0.217825	+	0.975988i	$0.569896\pi$
$908$		0			0
$909$			25.8333i			0.856836i
$910$		0			0
$911$			26.8280i			0.888850i	0.895816	+	0.444425i	$0.146592\pi$
$911$			26.8280i			0.888850i	−0.895816	+	0.444425i	$0.853408\pi$
$912$		0			0
$913$	7.37228	+	12.7692i	0.243987	+	0.422598i
$914$		0			0
$915$	−1.29211	−	1.42848i	−0.0427158	−	0.0472241i
$916$		0			0
$917$	−1.50000	−	7.79423i	−0.0495344	−	0.257388i
$918$		0			0
$919$	−7.29211	−	4.21010i	−0.240545	−	0.138878i	0.374882	−	0.927072i	$-0.377683\pi$
$919$	−7.29211	−	4.21010i	−0.240545	−	0.138878i	−0.615427	+	0.788194i	$0.711016\pi$
$920$		0			0
$921$	−5.13859	−	8.90030i	−0.169322	−	0.293275i
$922$		0			0
$923$		−	45.4381i		−	1.49561i
$924$		0			0
$925$	25.2921	−	35.1470i	0.831599	−	1.15563i
$926$		0			0
$927$	19.1168	−	11.0371i	0.627880	−	0.362506i
$928$		0			0
$929$	33.2228	+	19.1812i	1.09001	+	0.629315i	0.933578	−	0.358375i	$-0.116669\pi$
$929$	33.2228	+	19.1812i	1.09001	+	0.629315i	0.156427	+	0.987689i	$0.450002\pi$
$930$		0			0
$931$	31.5951	+	24.8747i	1.03549	+	0.815235i
$932$		0			0
$933$	0.941578	+	0.543620i	0.0308259	+	0.0177973i
$934$		0			0
$935$	6.00000	+	27.9152i	0.196221	+	0.912924i
$936$		0			0
$937$	−14.7446			−0.481684			−0.240842	−	0.970564i	$-0.577424\pi$
$937$	−14.7446			−0.481684			−0.240842	+	0.970564i	$0.577424\pi$
$938$		0			0
$939$		−	10.1899i		−	0.332536i
$940$		0			0
$941$	−10.1970	+	5.88725i	−0.332413	+	0.191919i	−0.656912	−	0.753967i	$-0.728138\pi$
$941$	−10.1970	+	5.88725i	−0.332413	+	0.191919i	0.324499	+	0.945886i	$0.394804\pi$
$942$		0			0
$943$	4.67527	+	2.69927i	0.152248	+	0.0879002i
$944$		0			0
$945$	−3.05842	+	24.9947i	−0.0994905	+	0.813078i
$946$		0			0
$947$	22.8030	−	39.4959i	0.740997	−	1.28345i	−0.211044	−	0.977477i	$-0.567686\pi$
$947$	22.8030	−	39.4959i	0.740997	−	1.28345i	0.952042	−	0.305969i	$-0.0989803\pi$
$948$		0			0
$949$	−10.1168	−	17.5229i	−0.328407	−	0.568817i
$950$		0			0
$951$	−0.861407			−0.0279330
$952$		0			0
$953$		−	26.4232i		−	0.855931i	−0.903795	−	0.427966i	$-0.859230\pi$
$953$		−	26.4232i		−	0.855931i	0.903795	−	0.427966i	$-0.140770\pi$
$954$		0			0
$955$	2.74456	+	12.7692i	0.0888120	+	0.413201i
$956$		0			0
$957$	1.88316	−	3.26172i	0.0608738	−	0.105436i
$958$		0			0
$959$	8.05842	−	23.2627i	0.260220	−	0.751190i
$960$		0			0
$961$	−35.6753	+	61.7914i	−1.15082	+	1.99327i
$962$		0			0
$963$	−1.62772	−	2.81929i	−0.0524525	−	0.0908504i
$964$		0			0
$965$	9.68614	+	3.12286i	0.311808	+	0.100528i
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$		0			0
$969$	−29.0584	+	16.7769i	−0.933491	+	0.538951i
$970$		0			0
$971$	18.9891	−	32.8901i	0.609390	−	1.05549i	−0.381951	−	0.924183i	$-0.624748\pi$
$971$	18.9891	−	32.8901i	0.609390	−	1.05549i	0.991341	−	0.131312i	$-0.0419190\pi$
$972$		0			0
$973$	24.0000	−	20.7846i	0.769405	−	0.666324i
$974$		0			0
$975$	7.11684	+	15.7908i	0.227921	+	0.505712i
$976$		0			0
$977$	−30.1753	+	17.4217i	−0.965392	+	0.557369i	−0.897828	−	0.440345i	$-0.854856\pi$
$977$	−30.1753	+	17.4217i	−0.965392	+	0.557369i	−0.0675639	+	0.997715i	$0.521523\pi$
$978$		0			0
$979$	−7.37228			−0.235619
$980$		0			0
$981$	−28.7446			−0.917743
$982$		0			0
$983$	−5.36141	+	3.09541i	−0.171002	+	0.0987282i	−0.583058	−	0.812430i	$-0.698144\pi$
$983$	−5.36141	+	3.09541i	−0.171002	+	0.0987282i	0.412056	+	0.911158i	$0.364811\pi$
$984$		0			0
$985$	−16.1644	+	14.6212i	−0.515040	+	0.465872i
$986$		0			0
$987$	−18.7446	+	16.2333i	−0.596646	+	0.516711i
$988$		0			0
$989$	−11.4891	+	19.8997i	−0.365333	+	0.632775i
$990$		0			0
$991$	−34.2921	+	19.7986i	−1.08932	+	0.628922i	−0.933397	−	0.358846i	$-0.883170\pi$
$991$	−34.2921	+	19.7986i	−1.08932	+	0.628922i	−0.155928	+	0.987768i	$0.549837\pi$
$992$		0			0
$993$	−9.60597			−0.304836
$994$		0			0
$995$	−4.70789	+	14.6024i	−0.149250	+	0.462927i
$996$		0			0
$997$	−8.05842	−	13.9576i	−0.255213	−	0.442042i	0.709741	−	0.704463i	$-0.248812\pi$
$997$	−8.05842	−	13.9576i	−0.255213	−	0.442042i	−0.964953	+	0.262422i	$0.915479\pi$
$998$		0			0
$999$	−18.4307	+	31.9229i	−0.583122	+	1.01000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cc.c.159.1	yes	4
4.3	odd	2		560.2.cc.a.159.2	✓	4
5.4	even	2		560.2.cc.b.159.2	yes	4
7.3	odd	6		560.2.cc.d.479.1	yes	4
20.19	odd	2		560.2.cc.d.159.1	yes	4
28.3	even	6		560.2.cc.b.479.2	yes	4
35.24	odd	6		560.2.cc.a.479.2	yes	4
140.59	even	6	inner	560.2.cc.c.479.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cc.a.159.2	✓	4	4.3	odd	2
560.2.cc.a.479.2	yes	4	35.24	odd	6
560.2.cc.b.159.2	yes	4	5.4	even	2
560.2.cc.b.479.2	yes	4	28.3	even	6
560.2.cc.c.159.1	yes	4	1.1	even	1	trivial
560.2.cc.c.479.1	yes	4	140.59	even	6	inner
560.2.cc.d.159.1	yes	4	20.19	odd	2
560.2.cc.d.479.1	yes	4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686141 + 0.396143i) q^{3} +(-1.50000 - 1.65831i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.18614 + 2.05446i) q^{9} +O(q^{10})\)	\(q+(-0.686141 + 0.396143i) q^{3} +(-1.50000 - 1.65831i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-1.18614 + 2.05446i) q^{9} +(1.50000 - 0.866025i) q^{11} -4.37228 q^{13} +(1.68614 + 0.543620i) q^{15} +(-3.68614 - 6.38458i) q^{17} +(-2.87228 + 4.97494i) q^{19} +(-0.686141 + 1.98072i) q^{21} +(2.87228 - 4.97494i) q^{23} +(-0.500000 + 4.97494i) q^{25} -4.25639i q^{27} -2.74456 q^{29} +(-5.05842 - 8.76144i) q^{31} +(-0.686141 + 1.18843i) q^{33} +(-5.87228 - 0.718549i) q^{35} +(-7.50000 - 4.33013i) q^{37} +(3.00000 - 1.73205i) q^{39} +0.939764i q^{41} -4.00000 q^{43} +(5.18614 - 1.11469i) q^{45} +(10.2446 + 5.91470i) q^{47} +(1.00000 - 6.92820i) q^{49} +(5.05842 + 2.92048i) q^{51} +(5.61684 - 3.24289i) q^{53} +(-3.68614 - 1.18843i) q^{55} -4.55134i q^{57} +(-2.31386 - 4.00772i) q^{59} +(-0.941578 - 0.543620i) q^{61} +(1.18614 + 6.16337i) q^{63} +(6.55842 + 7.25061i) q^{65} +(-4.05842 - 7.02939i) q^{67} +4.55134i q^{69} +10.3923i q^{71} +(2.31386 + 4.00772i) q^{73} +(-1.62772 - 3.61158i) q^{75} +(1.50000 - 4.33013i) q^{77} +(8.05842 + 4.65253i) q^{79} +(-1.87228 - 3.24289i) q^{81} +8.51278i q^{83} +(-5.05842 + 15.6896i) q^{85} +(1.88316 - 1.08724i) q^{87} +(-3.68614 - 2.12819i) q^{89} +(-8.74456 + 7.57301i) q^{91} +(6.94158 + 4.00772i) q^{93} +(12.5584 - 2.69927i) q^{95} -6.00000 q^{97} +4.10891i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} - 6 q^{5} + 8 q^{7} + q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 - 6 * q^5 + 8 * q^7 + q^9	\( 4 q + 3 q^{3} - 6 q^{5} + 8 q^{7} + q^{9} + 6 q^{11} - 6 q^{13} + q^{15} - 9 q^{17} + 3 q^{21} - 2 q^{25} + 12 q^{29} - 3 q^{31} + 3 q^{33} - 12 q^{35} - 30 q^{37} + 12 q^{39} - 16 q^{43} + 15 q^{45} + 18 q^{47} + 4 q^{49} + 3 q^{51} - 12 q^{53} - 9 q^{55} - 15 q^{59} - 21 q^{61} - q^{63} + 9 q^{65} + q^{67} + 15 q^{73} - 18 q^{75} + 6 q^{77} + 15 q^{79} + 4 q^{81} - 3 q^{85} + 42 q^{87} - 9 q^{89} - 12 q^{91} + 45 q^{93} + 33 q^{95} - 24 q^{97}+O(q^{100}) \) 4 * q + 3 * q^3 - 6 * q^5 + 8 * q^7 + q^9 + 6 * q^11 - 6 * q^13 + q^15 - 9 * q^17 + 3 * q^21 - 2 * q^25 + 12 * q^29 - 3 * q^31 + 3 * q^33 - 12 * q^35 - 30 * q^37 + 12 * q^39 - 16 * q^43 + 15 * q^45 + 18 * q^47 + 4 * q^49 + 3 * q^51 - 12 * q^53 - 9 * q^55 - 15 * q^59 - 21 * q^61 - q^63 + 9 * q^65 + q^67 + 15 * q^73 - 18 * q^75 + 6 * q^77 + 15 * q^79 + 4 * q^81 - 3 * q^85 + 42 * q^87 - 9 * q^89 - 12 * q^91 + 45 * q^93 + 33 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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