LMFDB - Embedded newform 888.2.br.a.569.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.22
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.567654 - 1.63639i) q^{3} +(0.0585783 - 0.218617i) q^{5} +(1.23175 + 2.13345i) q^{7} +(-2.35554 - 1.85780i) q^{9} +4.45126 q^{11} +(1.45800 + 0.390671i) q^{13} +(-0.324490 - 0.219956i) q^{15} +(-1.17157 + 0.313921i) q^{17} +(4.74490 + 1.27139i) q^{19} +(4.19035 - 0.804556i) q^{21} +(-3.28903 - 3.28903i) q^{23} +(4.28577 + 2.47439i) q^{25} +(-4.37722 + 2.79999i) q^{27} +(5.98185 - 5.98185i) q^{29} +(-7.24947 - 7.24947i) q^{31} +(2.52677 - 7.28399i) q^{33} +(0.538561 - 0.144307i) q^{35} +(5.17282 + 3.20030i) q^{37} +(1.46693 - 2.16410i) q^{39} +(5.48131 + 9.49391i) q^{41} +(-1.65145 + 1.65145i) q^{43} +(-0.544131 + 0.406134i) q^{45} -1.96589i q^{47} +(0.465605 - 0.806452i) q^{49} +(-0.151349 + 2.09534i) q^{51} +(-9.27137 - 5.35283i) q^{53} +(0.260747 - 0.973120i) q^{55} +(4.77395 - 7.04279i) q^{57} +(-6.54296 + 1.75318i) q^{59} +(3.26812 - 12.1968i) q^{61} +(1.06210 - 7.31376i) q^{63} +(0.170815 - 0.295860i) q^{65} +(-12.3822 + 7.14887i) q^{67} +(-7.24917 + 3.51510i) q^{69} +(3.52135 - 2.03305i) q^{71} -8.68620i q^{73} +(6.48189 - 5.60858i) q^{75} +(5.48281 + 9.49651i) q^{77} +(-2.07721 - 0.556587i) q^{79} +(2.09712 + 8.75226i) q^{81} +(1.03984 + 0.600350i) q^{83} +0.274514i q^{85} +(-6.39301 - 13.1843i) q^{87} +(3.33227 + 12.4362i) q^{89} +(0.962415 + 3.59178i) q^{91} +(-15.9781 + 7.74777i) q^{93} +(0.555896 - 0.962840i) q^{95} +(7.22624 - 7.22624i) q^{97} +(-10.4851 - 8.26956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.567654	−	1.63639i	0.327735	−	0.944770i
$3$	0.567654	−	1.63639i	0.327735	−	0.944770i
$4$		0			0
$5$	0.0585783	−	0.218617i	0.0261970	−	0.0977685i	−0.951590	−	0.307372i	$-0.900551\pi$
$5$	0.0585783	−	0.218617i	0.0261970	−	0.0977685i	0.977787	+	0.209603i	$0.0672172\pi$
$6$		0			0
$7$	1.23175	+	2.13345i	0.465556	+	0.806367i	0.999226	−	0.0393258i	$-0.0125210\pi$
$7$	1.23175	+	2.13345i	0.465556	+	0.806367i	−0.533670	+	0.845693i	$0.679188\pi$
$8$		0			0
$9$	−2.35554	−	1.85780i	−0.785179	−	0.619268i
$10$		0			0
$11$	4.45126			1.34210			0.671052	−	0.741410i	$-0.265843\pi$
$11$	4.45126			1.34210			0.671052	+	0.741410i	$0.265843\pi$
$12$		0			0
$13$	1.45800	+	0.390671i	0.404378	+	0.108353i	0.455274	−	0.890351i	$-0.349541\pi$
$13$	1.45800	+	0.390671i	0.404378	+	0.108353i	−0.0508965	+	0.998704i	$0.516208\pi$
$14$		0			0
$15$	−0.324490	−	0.219956i	−0.0837830	−	0.0567923i
$16$		0			0
$17$	−1.17157	+	0.313921i	−0.284147	+	0.0761370i	−0.398078	−	0.917352i	$-0.630323\pi$
$17$	−1.17157	+	0.313921i	−0.284147	+	0.0761370i	0.113931	+	0.993489i	$0.463656\pi$
$18$		0			0
$19$	4.74490	+	1.27139i	1.08856	+	0.291677i	0.758096	−	0.652143i	$-0.226130\pi$
$19$	4.74490	+	1.27139i	1.08856	+	0.291677i	0.330459	+	0.943820i	$0.392796\pi$
$20$		0			0
$21$	4.19035	−	0.804556i	0.914410	−	0.175569i
$22$		0			0
$23$	−3.28903	−	3.28903i	−0.685810	−	0.685810i	0.275493	−	0.961303i	$-0.411159\pi$
$23$	−3.28903	−	3.28903i	−0.685810	−	0.685810i	−0.961303	+	0.275493i	$0.911159\pi$
$24$		0			0
$25$	4.28577	+	2.47439i	0.857153	+	0.494878i
$26$		0			0
$27$	−4.37722	+	2.79999i	−0.842397	+	0.538858i
$28$		0			0
$29$	5.98185	−	5.98185i	1.11080	−	1.11080i	0.117759	−	0.993042i	$-0.462429\pi$
$29$	5.98185	−	5.98185i	1.11080	−	1.11080i	0.993042	−	0.117759i	$-0.0375712\pi$
$30$		0			0
$31$	−7.24947	−	7.24947i	−1.30204	−	1.30204i	−0.927012	−	0.375032i	$-0.877632\pi$
$31$	−7.24947	−	7.24947i	−1.30204	−	1.30204i	−0.375032	−	0.927012i	$-0.622368\pi$
$32$		0			0
$33$	2.52677	−	7.28399i	0.439855	−	1.26798i
$34$		0			0
$35$	0.538561	−	0.144307i	0.0910334	−	0.0243923i
$36$		0			0
$37$	5.17282	+	3.20030i	0.850407	+	0.526126i
$37$	5.17282	+	3.20030i	0.850407	+	0.526126i
$38$		0			0
$39$	1.46693	−	2.16410i	0.234897	−	0.346533i
$40$		0			0
$41$	5.48131	+	9.49391i	0.856037	+	1.48270i	0.875680	+	0.482892i	$0.160414\pi$
$41$	5.48131	+	9.49391i	0.856037	+	1.48270i	−0.0196432	+	0.999807i	$0.506253\pi$
$42$		0			0
$43$	−1.65145	+	1.65145i	−0.251843	+	0.251843i	−0.821726	−	0.569883i	$-0.806989\pi$
$43$	−1.65145	+	1.65145i	−0.251843	+	0.251843i	0.569883	+	0.821726i	$0.306989\pi$
$44$		0			0
$45$	−0.544131	+	0.406134i	−0.0811143	+	0.0605429i
$46$		0			0
$47$		−	1.96589i		−	0.286755i	−0.989668	−	0.143377i	$-0.954204\pi$
$47$		−	1.96589i		−	0.286755i	0.989668	−	0.143377i	$-0.0457963\pi$
$48$		0			0
$49$	0.465605	−	0.806452i	0.0665150	−	0.115207i
$50$		0			0
$51$	−0.151349	+	2.09534i	−0.0211930	+	0.293406i
$52$		0			0
$53$	−9.27137	−	5.35283i	−1.27352	−	0.735267i	−0.297872	−	0.954606i	$-0.596277\pi$
$53$	−9.27137	−	5.35283i	−1.27352	−	0.735267i	−0.975649	+	0.219339i	$0.929610\pi$
$54$		0			0
$55$	0.260747	−	0.973120i	0.0351591	−	0.131215i
$56$		0			0
$57$	4.77395	−	7.04279i	0.632326	−	0.932841i
$58$		0			0
$59$	−6.54296	+	1.75318i	−0.851820	+	0.228245i	−0.658210	−	0.752834i	$-0.728686\pi$
$59$	−6.54296	+	1.75318i	−0.851820	+	0.228245i	−0.193610	+	0.981079i	$0.562020\pi$
$60$		0			0
$61$	3.26812	−	12.1968i	0.418440	−	1.56164i	−0.359403	−	0.933182i	$-0.617020\pi$
$61$	3.26812	−	12.1968i	0.418440	−	1.56164i	0.777844	−	0.628458i	$-0.216314\pi$
$62$		0			0
$63$	1.06210	−	7.31376i	0.133812	−	0.921447i
$64$		0			0
$65$	0.170815	−	0.295860i	0.0211870	−	0.0366969i
$66$		0			0
$67$	−12.3822	+	7.14887i	−1.51273	+	0.873374i	−0.512838	+	0.858485i	$0.671406\pi$
$67$	−12.3822	+	7.14887i	−1.51273	+	0.873374i	−0.999889	+	0.0148885i	$0.995261\pi$
$68$		0			0
$69$	−7.24917	+	3.51510i	−0.872697	+	0.423169i
$70$		0			0
$71$	3.52135	−	2.03305i	0.417907	−	0.241279i	−0.276274	−	0.961079i	$-0.589100\pi$
$71$	3.52135	−	2.03305i	0.417907	−	0.241279i	0.694181	+	0.719800i	$0.255767\pi$
$72$		0			0
$73$		−	8.68620i		−	1.01664i	−0.861168	−	0.508321i	$-0.830266\pi$
$73$		−	8.68620i		−	1.01664i	0.861168	−	0.508321i	$-0.169734\pi$
$74$		0			0
$75$	6.48189	−	5.60858i	0.748464	−	0.647623i
$76$		0			0
$77$	5.48281	+	9.49651i	0.624825	+	1.08223i
$78$		0			0
$79$	−2.07721	−	0.556587i	−0.233705	−	0.0626210i	0.140066	−	0.990142i	$-0.455269\pi$
$79$	−2.07721	−	0.556587i	−0.233705	−	0.0626210i	−0.373770	+	0.927521i	$0.621935\pi$
$80$		0			0
$81$	2.09712	+	8.75226i	0.233014	+	0.972473i
$82$		0			0
$83$	1.03984	+	0.600350i	0.114137	+	0.0658970i	0.555982	−	0.831195i	$-0.312342\pi$
$83$	1.03984	+	0.600350i	0.114137	+	0.0658970i	−0.441845	+	0.897092i	$0.645676\pi$
$84$		0			0
$85$			0.274514i			0.0297752i
$86$		0			0
$87$	−6.39301	−	13.1843i	−0.685403	−	1.41350i
$88$		0			0
$89$	3.33227	+	12.4362i	0.353220	+	1.31824i	0.882709	+	0.469919i	$0.155717\pi$
$89$	3.33227	+	12.4362i	0.353220	+	1.31824i	−0.529489	+	0.848317i	$0.677616\pi$
$90$		0			0
$91$	0.962415	+	3.59178i	0.100889	+	0.376521i
$92$		0			0
$93$	−15.9781	+	7.74777i	−1.65686	+	0.803406i
$94$		0			0
$95$	0.555896	−	0.962840i	0.0570337	−	0.0987853i
$96$		0			0
$97$	7.22624	−	7.22624i	0.733713	−	0.733713i	−0.237640	−	0.971353i	$-0.576374\pi$
$97$	7.22624	−	7.22624i	0.733713	−	0.733713i	0.971353	+	0.237640i	$0.0763738\pi$
$98$		0			0
$99$	−10.4851	−	8.26956i	−1.05379	−	0.831122i
$100$		0			0
$101$	0.0671349			0.00668017			0.00334008	−	0.999994i	$-0.498937\pi$
$101$	0.0671349			0.00668017			0.00334008	+	0.999994i	$0.498937\pi$
$102$		0			0
$103$	3.59033	+	3.59033i	0.353766	+	0.353766i	0.861509	−	0.507743i	$-0.169520\pi$
$103$	3.59033	+	3.59033i	0.353766	+	0.353766i	−0.507743	+	0.861509i	$0.669520\pi$
$104$		0			0
$105$	0.0695738	−	0.963212i	0.00678971	−	0.0939999i
$106$		0			0
$107$	1.23880	−	0.715223i	0.119760	−	0.0691432i	−0.438924	−	0.898524i	$-0.644640\pi$
$107$	1.23880	−	0.715223i	0.119760	−	0.0691432i	0.558683	+	0.829381i	$0.311307\pi$
$108$		0			0
$109$	1.39660	+	5.21219i	0.133770	+	0.499237i	1.00000		0.000408725i	$-0.000130101\pi$
$109$	1.39660	+	5.21219i	0.133770	+	0.499237i	−0.866230	+	0.499646i	$0.833463\pi$
$110$		0			0
$111$	8.17331	−	6.64809i	0.775776	−	0.631008i
$112$		0			0
$113$	−0.172540	−	0.643927i	−0.0162312	−	0.0605756i	0.957335	−	0.288980i	$-0.0933160\pi$
$113$	−0.172540	−	0.643927i	−0.0162312	−	0.0605756i	−0.973566	+	0.228404i	$0.926649\pi$
$114$		0			0
$115$	−0.911704	+	0.526372i	−0.0850168	+	0.0490845i
$116$		0			0
$117$	−2.70860	−	3.62893i	−0.250410	−	0.335495i
$118$		0			0
$119$	−2.11281	−	2.11281i	−0.193681	−	0.193681i
$120$		0			0
$121$	8.81367			0.801243
$122$		0			0
$123$	18.6472	−	3.58030i	1.68136	−	0.322825i
$124$		0			0
$125$	1.59219	−	1.59219i	0.142410	−	0.142410i
$126$		0			0
$127$	−7.31452	+	12.6691i	−0.649059	+	1.12420i	0.334290	+	0.942470i	$0.391504\pi$
$127$	−7.31452	+	12.6691i	−0.649059	+	1.12420i	−0.983348	+	0.181732i	$0.941830\pi$
$128$		0			0
$129$	1.76496	+	3.63986i	0.155396	+	0.320472i
$130$		0			0
$131$	3.39004	+	12.6518i	0.296189	+	1.10539i	0.940269	+	0.340434i	$0.110574\pi$
$131$	3.39004	+	12.6518i	0.296189	+	1.10539i	−0.644080	+	0.764958i	$0.722759\pi$
$132$		0			0
$133$	3.13206	+	11.6890i	0.271584	+	1.01357i
$134$		0			0
$135$	0.355715	+	1.12095i	0.0306151	+	0.0964763i
$136$		0			0
$137$			23.1334i			1.97642i	0.153117	+	0.988208i	$0.451069\pi$
$137$			23.1334i			1.97642i	−0.153117	+	0.988208i	$0.548931\pi$
$138$		0			0
$139$	−9.94218	−	5.74012i	−0.843284	−	0.486870i	0.0150949	−	0.999886i	$-0.495195\pi$
$139$	−9.94218	−	5.74012i	−0.843284	−	0.486870i	−0.858379	+	0.513016i	$0.828528\pi$
$140$		0			0
$141$	−3.21696	−	1.11595i	−0.270917	−	0.0939796i
$142$		0			0
$143$	6.48995	+	1.73898i	0.542717	+	0.145421i
$144$		0			0
$145$	−0.957328	−	1.65814i	−0.0795017	−	0.137701i
$146$		0			0
$147$	−1.05537	−	1.21970i	−0.0870452	−	0.100599i
$148$		0			0
$149$			5.83665i			0.478157i	0.971000	+	0.239078i	$0.0768453\pi$
$149$			5.83665i			0.478157i	−0.971000	+	0.239078i	$0.923155\pi$
$150$		0			0
$151$	4.70939	−	2.71897i	0.383245	−	0.221267i	−0.295984	−	0.955193i	$-0.595648\pi$
$151$	4.70939	−	2.71897i	0.383245	−	0.221267i	0.679229	+	0.733926i	$0.262314\pi$
$152$		0			0
$153$	3.34288	+	1.43709i	0.270256	+	0.116182i
$154$		0			0
$155$	−2.00952	+	1.16020i	−0.161408	+	0.0931892i
$156$		0			0
$157$	−10.2984	+	17.8374i	−0.821902	+	1.42358i	0.0823617	+	0.996603i	$0.473754\pi$
$157$	−10.2984	+	17.8374i	−0.821902	+	1.42358i	−0.904264	+	0.426974i	$0.859580\pi$
$158$		0			0
$159$	−14.0222	+	12.1330i	−1.11204	+	0.962211i
$160$		0			0
$161$	2.96572	−	11.0682i	0.233732	−	0.872298i
$162$		0			0
$163$	7.33801	−	1.96621i	0.574757	−	0.154006i	0.0402796	−	0.999188i	$-0.487175\pi$
$163$	7.33801	−	1.96621i	0.574757	−	0.154006i	0.534477	+	0.845183i	$0.320508\pi$
$164$		0			0
$165$	−1.44439	−	0.979079i	−0.112446	−	0.0762212i
$166$		0			0
$167$	2.79944	−	10.4476i	0.216627	−	0.808462i	−0.768961	−	0.639296i	$-0.779226\pi$
$167$	2.79944	−	10.4476i	0.216627	−	0.808462i	0.985588	−	0.169166i	$-0.0541075\pi$
$168$		0			0
$169$	−9.28518	−	5.36080i	−0.714244	−	0.412369i
$170$		0			0
$171$	−8.81480	−	11.8099i	−0.674085	−	0.903127i
$172$		0			0
$173$	−8.63122	+	14.9497i	−0.656220	+	1.13661i	0.325367	+	0.945588i	$0.394512\pi$
$173$	−8.63122	+	14.9497i	−0.656220	+	1.13661i	−0.981587	+	0.191018i	$0.938821\pi$
$174$		0			0
$175$			12.1913i			0.921573i
$176$		0			0
$177$	−0.845249	+	11.7020i	−0.0635328	+	0.879578i
$178$		0			0
$179$	−11.4532	+	11.4532i	−0.856050	+	0.856050i	−0.990870	−	0.134820i	$-0.956954\pi$
$179$	−11.4532	+	11.4532i	−0.856050	+	0.856050i	0.134820	+	0.990870i	$0.456954\pi$
$180$		0			0
$181$	1.12019	+	1.94023i	0.0832634	+	0.144216i	0.904650	−	0.426156i	$-0.140132\pi$
$181$	1.12019	+	1.94023i	0.0832634	+	0.144216i	−0.821386	+	0.570372i	$0.806799\pi$
$182$		0			0
$183$	−18.1035	−	12.2715i	−1.33825	−	0.907134i
$184$		0			0
$185$	1.00265	−	0.943399i	0.0737167	−	0.0693601i
$186$		0			0
$187$	−5.21495	+	1.39734i	−0.381355	+	0.102184i
$188$		0			0
$189$	−11.3652	−	5.88969i	−0.826700	−	0.428412i
$190$		0			0
$191$	9.50724	+	9.50724i	0.687920	+	0.687920i	0.961772	−	0.273852i	$-0.0882979\pi$
$191$	9.50724	+	9.50724i	0.687920	+	0.687920i	−0.273852	+	0.961772i	$0.588298\pi$
$192$		0			0
$193$	17.9607	−	17.9607i	1.29284	−	1.29284i	0.359815	−	0.933024i	$-0.382840\pi$
$193$	17.9607	−	17.9607i	1.29284	−	1.29284i	0.933024	−	0.359815i	$-0.117160\pi$
$194$		0			0
$195$	−0.387178	−	0.447465i	−0.0277264	−	0.0320437i
$196$		0			0
$197$	−0.506502	−	0.292429i	−0.0360868	−	0.0208347i	0.481848	−	0.876255i	$-0.339966\pi$
$197$	−0.506502	−	0.292429i	−0.0360868	−	0.0208347i	−0.517935	+	0.855420i	$0.673299\pi$
$198$		0			0
$199$	−9.17777	−	9.17777i	−0.650595	−	0.650595i	0.302541	−	0.953136i	$-0.402165\pi$
$199$	−9.17777	−	9.17777i	−0.650595	−	0.650595i	−0.953136	+	0.302541i	$0.902165\pi$
$200$		0			0
$201$	4.66953	+	24.3202i	0.329363	+	1.71541i
$202$		0			0
$203$	20.1301	+	5.39384i	1.41285	+	0.378573i
$204$		0			0
$205$	2.39662	−	0.642171i	0.167387	−	0.0448512i
$206$		0			0
$207$	1.63706	+	13.8578i	0.113784	+	0.963185i
$208$		0			0
$209$	21.1208	+	5.65929i	1.46095	+	0.391461i
$210$		0			0
$211$	−9.11565			−0.627547			−0.313774	−	0.949498i	$-0.601593\pi$
$211$	−9.11565			−0.627547			−0.313774	+	0.949498i	$0.601593\pi$
$212$		0			0
$213$	−1.32796	−	6.91636i	−0.0909900	−	0.473901i
$214$		0			0
$215$	0.264295	+	0.457773i	0.0180248	+	0.0312199i
$216$		0			0
$217$	6.53685	−	24.3959i	0.443750	−	1.65610i
$218$		0			0
$219$	−14.2140	−	4.93075i	−0.960493	−	0.333189i
$220$		0			0
$221$	−1.83079			−0.123152
$222$		0			0
$223$	−19.6194			−1.31381			−0.656907	−	0.753971i	$-0.728136\pi$
$223$	−19.6194			−1.31381			−0.656907	+	0.753971i	$0.728136\pi$
$224$		0			0
$225$	−5.49835	−	13.7906i	−0.366557	−	0.919375i
$226$		0			0
$227$	−2.22664	+	8.30994i	−0.147787	+	0.551550i	0.851828	+	0.523821i	$0.175494\pi$
$227$	−2.22664	+	8.30994i	−0.147787	+	0.551550i	−0.999615	+	0.0277286i	$0.991173\pi$
$228$		0			0
$229$	−8.10744	−	14.0425i	−0.535755	−	0.927954i	−0.999126	−	0.0417901i	$-0.986694\pi$
$229$	−8.10744	−	14.0425i	−0.535755	−	0.927954i	0.463372	−	0.886164i	$-0.346639\pi$
$230$		0			0
$231$	18.6523	−	3.58129i	1.22723	−	0.235631i
$232$		0			0
$233$	−0.377103			−0.0247049			−0.0123524	−	0.999924i	$-0.503932\pi$
$233$	−0.377103			−0.0247049			−0.0123524	+	0.999924i	$0.503932\pi$
$234$		0			0
$235$	−0.429777	−	0.115158i	−0.0280356	−	0.00751211i
$236$		0			0
$237$	−2.08993	+	3.08318i	−0.135756	+	0.200274i
$238$		0			0
$239$	−12.8354	+	3.43923i	−0.830251	+	0.222465i	−0.648823	−	0.760939i	$-0.724739\pi$
$239$	−12.8354	+	3.43923i	−0.830251	+	0.222465i	−0.181428	+	0.983404i	$0.558072\pi$
$240$		0			0
$241$	−12.9634	−	3.47352i	−0.835044	−	0.223749i	−0.184131	−	0.982902i	$-0.558947\pi$
$241$	−12.9634	−	3.47352i	−0.835044	−	0.223749i	−0.650913	+	0.759152i	$0.725614\pi$
$242$		0			0
$243$	15.5125	+	1.53655i	0.995130	+	0.0985695i
$244$		0			0
$245$	−0.149030	−	0.149030i	−0.00952116	−	0.00952116i
$246$		0			0
$247$	6.42139	+	3.70739i	0.408583	+	0.235896i
$248$		0			0
$249$	1.57267	−	1.36079i	0.0996641	−	0.0862363i
$250$		0			0
$251$	5.07555	−	5.07555i	0.320366	−	0.320366i	−0.528542	−	0.848907i	$-0.677261\pi$
$251$	5.07555	−	5.07555i	0.320366	−	0.320366i	0.848907	+	0.528542i	$0.177261\pi$
$252$		0			0
$253$	−14.6403	−	14.6403i	−0.920429	−	0.920429i
$254$		0			0
$255$	0.449211	+	0.155829i	0.0281307	+	0.00975837i
$256$		0			0
$257$	−15.1582	+	4.06162i	−0.945541	+	0.253357i	−0.698469	−	0.715640i	$-0.746135\pi$
$257$	−15.1582	+	4.06162i	−0.945541	+	0.253357i	−0.247072	+	0.968997i	$0.579468\pi$
$258$		0			0
$259$	−0.456068	+	14.9779i	−0.0283387	+	0.930681i
$260$		0			0
$261$	−25.2036	+	2.97737i	−1.56006	+	0.184294i
$262$		0			0
$263$	−8.53905	−	14.7901i	−0.526541	−	0.911995i	−0.999522	−	0.0309225i	$-0.990156\pi$
$263$	−8.53905	−	14.7901i	−0.526541	−	0.911995i	0.472981	−	0.881072i	$-0.343178\pi$
$264$		0			0
$265$	−1.71332	+	1.71332i	−0.105248	+	0.105248i
$266$		0			0
$267$	22.2421	+	1.60657i	1.36119	+	0.0983203i
$268$		0			0
$269$			1.45662i			0.0888118i	0.999014	+	0.0444059i	$0.0141395\pi$
$269$			1.45662i			0.0888118i	−0.999014	+	0.0444059i	$0.985861\pi$
$270$		0			0
$271$	−3.79443	+	6.57214i	−0.230495	+	0.399229i	−0.957954	−	0.286922i	$-0.907368\pi$
$271$	−3.79443	+	6.57214i	−0.230495	+	0.399229i	0.727459	+	0.686151i	$0.240701\pi$
$272$		0			0
$273$	6.42387	+	0.464003i	0.388790	+	0.0280827i
$274$		0			0
$275$	19.0770	+	11.0141i	1.15039	+	0.664177i
$276$		0			0
$277$	−2.23675	+	8.34768i	−0.134393	+	0.501563i	0.865606	+	0.500725i	$0.166933\pi$
$277$	−2.23675	+	8.34768i	−0.134393	+	0.501563i	−1.00000		0.000837887i	$0.999733\pi$
$278$		0			0
$279$	3.60830	+	30.5445i	0.216024	+	1.82865i
$280$		0			0
$281$	3.23004	−	0.865487i	0.192688	−	0.0516307i	−0.161184	−	0.986924i	$-0.551531\pi$
$281$	3.23004	−	0.865487i	0.192688	−	0.0516307i	0.353872	+	0.935294i	$0.384865\pi$
$282$		0			0
$283$	−4.34988	+	16.2340i	−0.258574	+	0.965010i	0.707494	+	0.706720i	$0.249826\pi$
$283$	−4.34988	+	16.2340i	−0.258574	+	0.965010i	−0.966067	+	0.258291i	$0.916841\pi$
$284$		0			0
$285$	−1.26002	−	1.45622i	−0.0746374	−	0.0862592i
$286$		0			0
$287$	−13.5032	+	23.3882i	−0.797066	+	1.38056i
$288$		0			0
$289$	−13.4484	+	7.76444i	−0.791083	+	0.456732i
$290$		0			0
$291$	−7.72294	−	15.9269i	−0.452727	−	0.933654i
$292$		0			0
$293$	−3.69152	+	2.13130i	−0.215661	+	0.124512i	−0.603939	−	0.797030i	$-0.706403\pi$
$293$	−3.69152	+	2.13130i	−0.215661	+	0.124512i	0.388279	+	0.921542i	$0.373070\pi$
$294$		0			0
$295$			1.53310i			0.0892605i
$296$		0			0
$297$	−19.4841	+	12.4635i	−1.13058	+	0.723203i
$298$		0			0
$299$	−3.51049	−	6.08035i	−0.203017	−	0.351636i
$300$		0			0
$301$	−5.55743	−	1.48911i	−0.320325	−	0.0858308i
$302$		0			0
$303$	0.0381094	−	0.109859i	0.00218933	−	0.00631122i
$304$		0			0
$305$	−2.47499	−	1.42893i	−0.141717	−	0.0818205i
$306$		0			0
$307$			2.48057i			0.141574i	0.997491	+	0.0707869i	$0.0225510\pi$
$307$			2.48057i			0.141574i	−0.997491	+	0.0707869i	$0.977449\pi$
$308$		0			0
$309$	7.91324	−	3.83711i	0.450168	−	0.218286i
$310$		0			0
$311$	1.33321	+	4.97559i	0.0755992	+	0.282140i	0.993369	−	0.114974i	$-0.0366785\pi$
$311$	1.33321	+	4.97559i	0.0755992	+	0.282140i	−0.917769	+	0.397114i	$0.870012\pi$
$312$		0			0
$313$	5.40623	+	20.1763i	0.305578	+	1.14043i	0.932447	+	0.361308i	$0.117670\pi$
$313$	5.40623	+	20.1763i	0.305578	+	1.14043i	−0.626869	+	0.779125i	$0.715664\pi$
$314$		0			0
$315$	−1.53670	−	0.660621i	−0.0865830	−	0.0372218i
$316$		0			0
$317$	11.8164	−	20.4666i	0.663676	−	1.14952i	−0.315967	−	0.948770i	$-0.602329\pi$
$317$	11.8164	−	20.4666i	0.663676	−	1.14952i	0.979643	−	0.200750i	$-0.0643378\pi$
$318$		0			0
$319$	26.6267	−	26.6267i	1.49081	−	1.49081i
$320$		0			0
$321$	−0.467172	−	2.43316i	−0.0260750	−	0.135806i
$322$		0			0
$323$	−5.95809			−0.331517
$324$		0			0
$325$	5.28199	+	5.28199i	0.292992	+	0.292992i
$326$		0			0
$327$	9.32196	+	0.673335i	0.515505	+	0.0372355i
$328$		0			0
$329$	4.19412	−	2.42148i	0.231229	−	0.133500i
$330$		0			0
$331$	−0.552844	−	2.06324i	−0.0303871	−	0.113406i	0.949067	−	0.315076i	$-0.102030\pi$
$331$	−0.552844	−	2.06324i	−0.0303871	−	0.113406i	−0.979454	+	0.201670i	$0.935363\pi$
$332$		0			0
$333$	−6.23925	−	17.1485i	−0.341909	−	0.939733i
$334$		0			0
$335$	0.837537	+	3.12573i	0.0457595	+	0.170777i
$336$		0			0
$337$	12.4013	−	7.15988i	0.675540	−	0.390023i	−0.122632	−	0.992452i	$-0.539134\pi$
$337$	12.4013	−	7.15988i	0.675540	−	0.390023i	0.798173	+	0.602429i	$0.205800\pi$
$338$		0			0
$339$	−1.15166	−	0.0831855i	−0.0625495	−	0.00451802i
$340$		0			0
$341$	−32.2693	−	32.2693i	−1.74748	−	1.74748i
$342$		0			0
$343$	19.5385			1.05498
$344$		0			0
$345$	0.343818	+	1.79070i	0.0185105	+	0.0964080i
$346$		0			0
$347$	−0.460002	+	0.460002i	−0.0246942	+	0.0246942i	−0.719346	−	0.694652i	$-0.755558\pi$
$347$	−0.460002	+	0.460002i	−0.0246942	+	0.0246942i	0.694652	+	0.719346i	$0.255558\pi$
$348$		0			0
$349$	5.36611	−	9.29437i	0.287241	−	0.497516i	−0.685909	−	0.727687i	$-0.740595\pi$
$349$	5.36611	−	9.29437i	0.287241	−	0.497516i	0.973150	+	0.230171i	$0.0739285\pi$
$350$		0			0
$351$	−7.47588	+	2.37234i	−0.399033	+	0.126626i
$352$		0			0
$353$	−4.60846	−	17.1990i	−0.245283	−	0.915410i	−0.973241	−	0.229788i	$-0.926197\pi$
$353$	−4.60846	−	17.1990i	−0.245283	−	0.915410i	0.727957	−	0.685622i	$-0.240470\pi$
$354$		0			0
$355$	−0.238185	−	0.888919i	−0.0126416	−	0.0471789i
$356$		0			0
$357$	−4.65672	+	2.25803i	−0.246460	+	0.119508i
$358$		0			0
$359$			19.1592i			1.01118i	0.862773	+	0.505592i	$0.168726\pi$
$359$			19.1592i			1.01118i	−0.862773	+	0.505592i	$0.831274\pi$
$360$		0			0
$361$	4.44317	+	2.56527i	0.233851	+	0.135014i
$362$		0			0
$363$	5.00312	−	14.4226i	0.262595	−	0.756990i
$364$		0			0
$365$	−1.89895	−	0.508822i	−0.0993956	−	0.0266330i
$366$		0			0
$367$	−12.0629	−	20.8936i	−0.629681	−	1.09064i	−0.987616	−	0.156893i	$-0.949852\pi$
$367$	−12.0629	−	20.8936i	−0.629681	−	1.09064i	0.357935	−	0.933747i	$-0.383481\pi$
$368$		0			0
$369$	4.72639	−	32.5465i	0.246046	−	1.69430i
$370$		0			0
$371$		−	26.3733i		−	1.36923i
$372$		0			0
$373$	−18.6091	+	10.7439i	−0.963541	+	0.556300i	−0.897261	−	0.441501i	$-0.854446\pi$
$373$	−18.6091	+	10.7439i	−0.963541	+	0.556300i	−0.0662798	+	0.997801i	$0.521113\pi$
$374$		0			0
$375$	−1.70163	−	3.50925i	−0.0878718	−	0.181217i
$376$		0			0
$377$	11.0585	−	6.38463i	0.569542	−	0.328825i
$378$		0			0
$379$	−1.12950	+	1.95636i	−0.0580187	+	0.100491i	−0.893576	−	0.448912i	$-0.851812\pi$
$379$	−1.12950	+	1.95636i	−0.0580187	+	0.100491i	0.835557	+	0.549403i	$0.185145\pi$
$380$		0			0
$381$	16.5795	+	19.1611i	0.849393	+	0.981651i
$382$		0			0
$383$	−1.52675	+	5.69790i	−0.0780131	+	0.291149i	−0.993900	−	0.110288i	$-0.964823\pi$
$383$	−1.52675	+	5.69790i	−0.0780131	+	0.291149i	0.915887	+	0.401437i	$0.131489\pi$
$384$		0			0
$385$	2.39727	−	0.642347i	0.122176	−	0.0327371i
$386$		0			0
$387$	6.95811	−	0.821980i	0.353700	−	0.0417836i
$388$		0			0
$389$	4.33825	−	16.1906i	0.219958	−	0.820894i	−0.764404	−	0.644737i	$-0.776967\pi$
$389$	4.33825	−	16.1906i	0.219958	−	0.820894i	0.984362	−	0.176157i	$-0.0563665\pi$
$390$		0			0
$391$	4.88582	+	2.82083i	0.247086	+	0.142655i
$392$		0			0
$393$	22.6276	+	1.63442i	1.14141	+	0.0824455i
$394$		0			0
$395$	−0.243359	+	0.421510i	−0.0122447	+	0.0212085i
$396$		0			0
$397$			21.7296i			1.09058i	0.838249	+	0.545288i	$0.183580\pi$
$397$			21.7296i			1.09058i	−0.838249	+	0.545288i	$0.816420\pi$
$398$		0			0
$399$	20.9057	+	1.51004i	1.04660	+	0.0755967i
$400$		0			0
$401$	11.1869	−	11.1869i	0.558649	−	0.558649i	−0.370274	−	0.928923i	$-0.620736\pi$
$401$	11.1869	−	11.1869i	0.558649	−	0.558649i	0.928923	+	0.370274i	$0.120736\pi$
$402$		0			0
$403$	−7.73760	−	13.4019i	−0.385438	−	0.667597i
$404$		0			0
$405$	2.03624	+	0.0542257i	0.101182	+	0.00269449i
$406$		0			0
$407$	23.0255	+	14.2454i	1.14133	+	0.706116i
$408$		0			0
$409$	24.2104	−	6.48715i	1.19713	−	0.320769i	0.395427	−	0.918498i	$-0.370597\pi$
$409$	24.2104	−	6.48715i	1.19713	−	0.320769i	0.801698	+	0.597729i	$0.203930\pi$
$410$		0			0
$411$	37.8552	+	13.1317i	1.86726	+	0.647741i
$412$		0			0
$413$	−11.7996	−	11.7996i	−0.580619	−	0.580619i
$414$		0			0
$415$	0.192158	−	0.192158i	0.00943269	−	0.00943269i
$416$		0			0
$417$	−15.0368	+	13.0109i	−0.736354	+	0.637145i
$418$		0			0
$419$	−26.5640	−	15.3367i	−1.29774	−	0.749249i	−0.317724	−	0.948183i	$-0.602918\pi$
$419$	−26.5640	−	15.3367i	−1.29774	−	0.749249i	−0.980013	+	0.198935i	$0.936252\pi$
$420$		0			0
$421$	26.0674	+	26.0674i	1.27045	+	1.27045i	0.945854	+	0.324591i	$0.105227\pi$
$421$	26.0674	+	26.0674i	1.27045	+	1.27045i	0.324591	+	0.945854i	$0.394773\pi$
$422$		0			0
$423$	−3.65224	+	4.63073i	−0.177578	+	0.225154i
$424$		0			0
$425$	−5.79783	−	1.55352i	−0.281236	−	0.0753569i
$426$		0			0
$427$	30.0467	−	8.05099i	1.45406	−	0.389615i
$428$		0			0
$429$	6.52969	−	9.63295i	0.315256	−	0.465083i
$430$		0			0
$431$	−36.5952	−	9.80565i	−1.76273	−	0.472321i	−0.775461	−	0.631396i	$-0.782482\pi$
$431$	−36.5952	−	9.80565i	−1.76273	−	0.472321i	−0.987267	+	0.159074i	$0.949149\pi$
$432$		0			0
$433$	−18.1410			−0.871802			−0.435901	−	0.899995i	$-0.643570\pi$
$433$	−18.1410			−0.871802			−0.435901	+	0.899995i	$0.643570\pi$
$434$		0			0
$435$	−3.25679	+	0.625311i	−0.156151	+	0.0299814i
$436$		0			0
$437$	−11.4245	−	19.7878i	−0.546507	−	0.946578i
$438$		0			0
$439$	7.02768	−	26.2276i	0.335413	−	1.25178i	−0.568009	−	0.823023i	$-0.692286\pi$
$439$	7.02768	−	26.2276i	0.335413	−	1.25178i	0.903421	−	0.428754i	$-0.141047\pi$
$440$		0			0
$441$	−2.59498	+	1.03462i	−0.123571	+	0.0492678i
$442$		0			0
$443$	20.1006			0.955006			0.477503	−	0.878630i	$-0.341542\pi$
$443$	20.1006			0.955006			0.477503	+	0.878630i	$0.341542\pi$
$444$		0			0
$445$	2.91397			0.138135
$446$		0			0
$447$	9.55103	+	3.31320i	0.451748	+	0.156709i
$448$		0			0
$449$	1.70335	−	6.35701i	0.0803863	−	0.300006i	−0.914014	−	0.405682i	$-0.867034\pi$
$449$	1.70335	−	6.35701i	0.0803863	−	0.300006i	0.994401	+	0.105676i	$0.0337007\pi$
$450$		0			0
$451$	24.3987	+	42.2598i	1.14889	+	1.98994i
$452$		0			0
$453$	−1.77599	−	9.24984i	−0.0834432	−	0.434595i
$454$		0			0
$455$	0.841601			0.0394549
$456$		0			0
$457$	22.9313	+	6.14442i	1.07268	+	0.287424i	0.751594	−	0.659626i	$-0.229285\pi$
$457$	22.9313	+	6.14442i	1.07268	+	0.287424i	0.321086	+	0.947050i	$0.395952\pi$
$458$		0			0
$459$	4.24924	−	4.65448i	0.198338	−	0.217252i
$460$		0			0
$461$	2.41743	−	0.647749i	0.112591	−	0.0301687i	−0.202084	−	0.979368i	$-0.564771\pi$
$461$	2.41743	−	0.647749i	0.112591	−	0.0301687i	0.314675	+	0.949200i	$0.398105\pi$
$462$		0			0
$463$	7.65932	+	2.05231i	0.355959	+	0.0953789i	0.432367	−	0.901698i	$-0.357679\pi$
$463$	7.65932	+	2.05231i	0.355959	+	0.0953789i	−0.0764081	+	0.997077i	$0.524345\pi$
$464$		0			0
$465$	0.757822	+	3.94695i	0.0351431	+	0.183035i
$466$		0			0
$467$	−21.6777	−	21.6777i	−1.00312	−	1.00312i	−0.999995	−	0.00312870i	$-0.999004\pi$
$467$	−21.6777	−	21.6777i	−1.00312	−	1.00312i	−0.00312870	−	0.999995i	$-0.500996\pi$
$468$		0			0
$469$	−30.5035	−	17.6112i	−1.40852	−	0.813209i
$470$		0			0
$471$	23.3429	+	26.9776i	1.07559	+	1.24306i
$472$		0			0
$473$	−7.35101	+	7.35101i	−0.338000	+	0.338000i
$474$		0			0
$475$	17.1896	+	17.1896i	0.788714	+	0.788714i
$476$		0			0
$477$	11.8946	+	29.8332i	0.544614	+	1.36597i
$478$		0			0
$479$	32.7324	−	8.77062i	1.49558	−	0.400740i	0.583963	−	0.811780i	$-0.301501\pi$
$479$	32.7324	−	8.77062i	1.49558	−	0.400740i	0.911617	+	0.411040i	$0.134834\pi$
$480$		0			0
$481$	6.29173	+	6.68692i	0.286878	+	0.304898i
$482$		0			0
$483$	−16.4284	−	11.1360i	−0.747519	−	0.506705i
$484$		0			0
$485$	−1.15648	−	2.00308i	−0.0525130	−	0.0909551i
$486$		0			0
$487$	10.5292	−	10.5292i	0.477123	−	0.477123i	−0.427087	−	0.904210i	$-0.640460\pi$
$487$	10.5292	−	10.5292i	0.477123	−	0.477123i	0.904210	+	0.427087i	$0.140460\pi$
$488$		0			0
$489$	0.947958	−	13.1240i	0.0428681	−	0.593486i
$490$		0			0
$491$		−	31.0545i		−	1.40147i	−0.713421	−	0.700735i	$-0.752855\pi$
$491$		−	31.0545i		−	1.40147i	0.713421	−	0.700735i	$-0.247145\pi$
$492$		0			0
$493$	−5.13032	+	8.88597i	−0.231058	+	0.400204i
$494$		0			0
$495$	−2.42207	+	1.80781i	−0.108864	+	0.0812548i
$496$		0			0
$497$	8.67481	+	5.00840i	0.389118	+	0.224658i
$498$		0			0
$499$	−8.68332	+	32.4066i	−0.388719	+	1.45072i	0.443501	+	0.896274i	$0.353736\pi$
$499$	−8.68332	+	32.4066i	−0.388719	+	1.45072i	−0.832220	+	0.554445i	$0.812931\pi$
$500$		0			0
$501$	−15.5073	−	10.5116i	−0.692814	−	0.469624i
$502$		0			0
$503$	−11.6298	+	3.11619i	−0.518547	+	0.138944i	−0.508594	−	0.861006i	$-0.669835\pi$
$503$	−11.6298	+	3.11619i	−0.518547	+	0.138944i	−0.00995261	+	0.999950i	$0.503168\pi$
$504$		0			0
$505$	0.00393264	−	0.0146768i	0.000175000	−	0.000653110i
$506$		0			0
$507$	−14.0431	+	12.1511i	−0.623677	+	0.539649i
$508$		0			0
$509$	0.107609	−	0.186384i	0.00476967	−	0.00826130i	−0.863631	−	0.504125i	$-0.831815\pi$
$509$	0.107609	−	0.186384i	0.00476967	−	0.00826130i	0.868400	+	0.495864i	$0.165148\pi$
$510$		0			0
$511$	18.5315	−	10.6992i	0.819787	−	0.473304i
$512$		0			0
$513$	−24.3294	+	7.72050i	−1.07417	+	0.340868i
$514$		0			0
$515$	0.995222	−	0.574592i	0.0438547	−	0.0253195i
$516$		0			0
$517$		−	8.75068i		−	0.384855i
$518$		0			0
$519$	19.5640	+	22.6103i	0.858765	+	0.992482i
$520$		0			0
$521$	−7.89146	−	13.6684i	−0.345731	−	0.598824i	0.639755	−	0.768579i	$-0.279036\pi$
$521$	−7.89146	−	13.6684i	−0.345731	−	0.598824i	−0.985486	+	0.169755i	$0.945702\pi$
$522$		0			0
$523$	−21.7748	−	5.83454i	−0.952146	−	0.255127i	−0.250873	−	0.968020i	$-0.580718\pi$
$523$	−21.7748	−	5.83454i	−0.952146	−	0.255127i	−0.701273	+	0.712893i	$0.747384\pi$
$524$		0			0
$525$	19.9497	+	6.92042i	0.870674	+	0.302032i
$526$		0			0
$527$	10.7690	+	6.21749i	0.469105	+	0.270838i
$528$		0			0
$529$		−	1.36455i		−	0.0593282i
$530$		0			0
$531$	18.6692	+	8.02585i	0.810176	+	0.348292i
$532$		0			0
$533$	4.28278	+	15.9835i	0.185508	+	0.692324i
$534$		0			0
$535$	−0.0837930	−	0.312720i	−0.00362269	−	0.0135201i
$536$		0			0
$537$	12.2404	+	25.2433i	0.528213	+	1.08933i
$538$		0			0
$539$	2.07253	−	3.58972i	0.0892701	−	0.154620i
$540$		0			0
$541$	14.4643	−	14.4643i	0.621867	−	0.621867i	−0.324141	−	0.946009i	$-0.605075\pi$
$541$	14.4643	−	14.4643i	0.621867	−	0.621867i	0.946009	+	0.324141i	$0.105075\pi$
$542$		0			0
$543$	3.81086	−	0.731693i	0.163540	−	0.0314000i
$544$		0			0
$545$	1.22128			0.0523141
$546$		0			0
$547$	−0.426209	−	0.426209i	−0.0182234	−	0.0182234i	0.697936	−	0.716160i	$-0.254102\pi$
$547$	−0.426209	−	0.426209i	−0.0182234	−	0.0182234i	−0.716160	+	0.697936i	$0.754102\pi$
$548$		0			0
$549$	−30.3575	+	22.6585i	−1.29562	+	0.967041i
$550$		0			0
$551$	35.9886	−	20.7780i	1.53316	−	0.885173i
$552$		0			0
$553$	−1.37115	−	5.11719i	−0.0583071	−	0.217605i
$554$		0			0
$555$	−0.974607	−	2.17626i	−0.0413697	−	0.0923770i
$556$		0			0
$557$	0.394978	+	1.47408i	0.0167358	+	0.0624587i	0.973789	−	0.227454i	$-0.0730403\pi$
$557$	0.394978	+	1.47408i	0.0167358	+	0.0624587i	−0.957053	+	0.289913i	$0.906374\pi$
$558$		0			0
$559$	−3.05299	+	1.76264i	−0.129128	+	0.0745519i
$560$		0			0
$561$	−0.673691	+	9.32689i	−0.0284433	+	0.393782i
$562$		0			0
$563$	−5.46656	−	5.46656i	−0.230388	−	0.230388i	0.582467	−	0.812855i	$-0.302088\pi$
$563$	−5.46656	−	5.46656i	−0.230388	−	0.230388i	−0.812855	+	0.582467i	$0.802088\pi$
$564$		0			0
$565$	−0.150881			−0.00634759
$566$		0			0
$567$	−16.0894	+	15.2547i	−0.675689	+	0.640635i
$568$		0			0
$569$	19.3464	−	19.3464i	0.811041	−	0.811041i	−0.173749	−	0.984790i	$-0.555588\pi$
$569$	19.3464	−	19.3464i	0.811041	−	0.811041i	0.984790	+	0.173749i	$0.0555881\pi$
$570$		0			0
$571$	−3.95833	+	6.85602i	−0.165651	+	0.286916i	−0.936886	−	0.349634i	$-0.886306\pi$
$571$	−3.95833	+	6.85602i	−0.165651	+	0.286916i	0.771235	+	0.636550i	$0.219639\pi$
$572$		0			0
$573$	20.9544	−	10.1607i	0.875381	−	0.424470i
$574$		0			0
$575$	−5.95768	−	22.2344i	−0.248452	−	0.927237i
$576$		0			0
$577$	−7.45957	−	27.8395i	−0.310546	−	1.15897i	−0.928065	−	0.372417i	$-0.878529\pi$
$577$	−7.45957	−	27.8395i	−0.310546	−	1.15897i	0.617520	−	0.786556i	$-0.288138\pi$
$578$		0			0
$579$	−19.1952	−	39.5861i	−0.797726	−	1.64514i
$580$		0			0
$581$			2.95791i			0.122715i
$582$		0			0
$583$	−41.2692	−	23.8268i	−1.70920	−	0.986805i
$584$		0			0
$585$	−0.952010	+	0.379569i	−0.0393608	+	0.0156932i
$586$		0			0
$587$	−46.6306	−	12.4946i	−1.92465	−	0.515709i	−0.984652	−	0.174531i	$-0.944159\pi$
$587$	−46.6306	−	12.4946i	−1.92465	−	0.515709i	−0.939999	−	0.341177i	$-0.889174\pi$
$588$		0			0
$589$	−25.1811	−	43.6150i	−1.03757	−	1.79712i
$590$		0			0
$591$	−0.766046	+	0.662836i	−0.0315109	+	0.0272654i
$592$		0			0
$593$			46.7556i			1.92002i	0.279964	+	0.960011i	$0.409677\pi$
$593$			46.7556i			1.92002i	−0.279964	+	0.960011i	$0.590323\pi$
$594$		0			0
$595$	−0.585660	+	0.338131i	−0.0240097	+	0.0138620i
$596$		0			0
$597$	−20.2282	+	9.80861i	−0.827885	+	0.401440i
$598$		0			0
$599$	16.1108	−	9.30155i	0.658267	−	0.380051i	−0.133349	−	0.991069i	$-0.542573\pi$
$599$	16.1108	−	9.30155i	0.658267	−	0.380051i	0.791617	+	0.611018i	$0.209240\pi$
$600$		0			0
$601$	7.42846	−	12.8665i	0.303013	−	0.524835i	−0.673804	−	0.738910i	$-0.735341\pi$
$601$	7.42846	−	12.8665i	0.303013	−	0.524835i	0.976817	+	0.214076i	$0.0686740\pi$
$602$		0			0
$603$	42.4480	+	6.16429i	1.72862	+	0.251029i
$604$		0			0
$605$	0.516290	−	1.92682i	0.0209902	−	0.0783363i
$606$		0			0
$607$	−34.4637	+	9.23452i	−1.39884	+	0.374817i	−0.877927	−	0.478794i	$-0.841074\pi$
$607$	−34.4637	+	9.23452i	−1.39884	+	0.374817i	−0.520910	+	0.853611i	$0.674407\pi$
$608$		0			0
$609$	20.2533	−	29.8788i	0.820706	−	1.21075i
$610$		0			0
$611$	0.768017	−	2.86628i	0.0310706	−	0.115957i
$612$		0			0
$613$	15.9482	+	9.20773i	0.644144	+	0.371897i	0.786209	−	0.617961i	$-0.212041\pi$
$613$	15.9482	+	9.20773i	0.644144	+	0.371897i	−0.142065	+	0.989857i	$0.545374\pi$
$614$		0			0
$615$	0.309606	−	4.28633i	0.0124845	−	0.172841i
$616$		0			0
$617$	17.5649	−	30.4233i	0.707137	−	1.22480i	−0.258777	−	0.965937i	$-0.583320\pi$
$617$	17.5649	−	30.4233i	0.707137	−	1.22480i	0.965915	−	0.258861i	$-0.0833471\pi$
$618$		0			0
$619$		−	31.7751i		−	1.27715i	−0.769560	−	0.638574i	$-0.779525\pi$
$619$		−	31.7751i		−	1.27715i	0.769560	−	0.638574i	$-0.220475\pi$
$620$		0			0
$621$	23.6061	+	5.18757i	0.947279	+	0.208170i
$622$		0			0
$623$	−22.4275	+	22.4275i	−0.898538	+	0.898538i
$624$		0			0
$625$	12.1171	+	20.9875i	0.484685	+	0.839499i
$626$		0			0
$627$	21.2501	−	31.3493i	0.848647	−	1.25197i
$628$		0			0
$629$	−7.06495	−	2.12551i	−0.281698	−	0.0847498i
$630$		0			0
$631$	27.3099	−	7.31765i	1.08719	−	0.291311i	0.329651	−	0.944103i	$-0.393069\pi$
$631$	27.3099	−	7.31765i	1.08719	−	0.291311i	0.757537	+	0.652792i	$0.226402\pi$
$632$		0			0
$633$	−5.17453	+	14.9168i	−0.205669	+	0.592888i
$634$		0			0
$635$	2.34121	+	2.34121i	0.0929082	+	0.0929082i
$636$		0			0
$637$	0.993912	−	0.993912i	0.0393802	−	0.0393802i
$638$		0			0
$639$	−12.0717	−	1.75305i	−0.477548	−	0.0693495i
$640$		0			0
$641$	−25.0815	−	14.4808i	−0.990659	−	0.571957i	−0.0851877	−	0.996365i	$-0.527149\pi$
$641$	−25.0815	−	14.4808i	−0.990659	−	0.571957i	−0.905471	+	0.424408i	$0.860482\pi$
$642$		0			0
$643$	18.1755	+	18.1755i	0.716774	+	0.716774i	0.967943	−	0.251170i	$-0.0808152\pi$
$643$	18.1755	+	18.1755i	0.716774	+	0.716774i	−0.251170	+	0.967943i	$0.580815\pi$
$644$		0			0
$645$	0.899123	−	0.172633i	0.0354029	−	0.00679743i
$646$		0			0
$647$	−36.1138	−	9.67667i	−1.41978	−	0.380429i	−0.534375	−	0.845248i	$-0.679453\pi$
$647$	−36.1138	−	9.67667i	−1.41978	−	0.380429i	−0.885406	+	0.464818i	$0.846120\pi$
$648$		0			0
$649$	−29.1244	+	7.80385i	−1.14323	+	0.306328i
$650$		0			0
$651$	−36.2105	−	24.5452i	−1.41920	−	0.962004i
$652$		0			0
$653$	−5.03318	−	1.34864i	−0.196964	−	0.0527762i	0.158989	−	0.987280i	$-0.449177\pi$
$653$	−5.03318	−	1.34864i	−0.196964	−	0.0527762i	−0.355952	+	0.934504i	$0.615843\pi$
$654$		0			0
$655$	2.96448			0.115832
$656$		0			0
$657$	−16.1373	+	20.4607i	−0.629574	+	0.798247i
$658$		0			0
$659$	22.7117	+	39.3379i	0.884724	+	1.53239i	0.846030	+	0.533136i	$0.178986\pi$
$659$	22.7117	+	39.3379i	0.884724	+	1.53239i	0.0386941	+	0.999251i	$0.487680\pi$
$660$		0			0
$661$	2.16031	−	8.06239i	0.0840264	−	0.313591i	−0.911102	−	0.412182i	$-0.864767\pi$
$661$	2.16031	−	8.06239i	0.0840264	−	0.313591i	0.995128	+	0.0985910i	$0.0314336\pi$
$662$		0			0
$663$	−1.03926	+	2.99589i	−0.0403614	+	0.116351i
$664$		0			0
$665$	2.73889			0.106210
$666$		0			0
$667$	−39.3490			−1.52360
$668$		0			0
$669$	−11.1370	+	32.1050i	−0.430583	+	1.24125i
$670$		0			0
$671$	14.5472	−	54.2911i	0.561590	−	2.09588i
$672$		0			0
$673$	14.5856	+	25.2629i	0.562232	+	0.973814i	0.997301	+	0.0734172i	$0.0233905\pi$
$673$	14.5856	+	25.2629i	0.562232	+	0.973814i	−0.435069	+	0.900397i	$0.643276\pi$
$674$		0			0
$675$	−25.6880	+	1.16914i	−0.988732	+	0.0450004i
$676$		0			0
$677$	2.45041			0.0941769			0.0470885	−	0.998891i	$-0.485006\pi$
$677$	2.45041			0.0941769			0.0470885	+	0.998891i	$0.485006\pi$
$678$		0			0
$679$	24.3177	+	6.51590i	0.933227	+	0.250057i
$680$		0			0
$681$	12.3343	+	8.36082i	0.472653	+	0.320387i
$682$		0			0
$683$	−1.09874	+	0.294408i	−0.0420423	+	0.0112652i	−0.279779	−	0.960064i	$-0.590261\pi$
$683$	−1.09874	+	0.294408i	−0.0420423	+	0.0112652i	0.237737	+	0.971330i	$0.423594\pi$
$684$		0			0
$685$	5.05735	+	1.35511i	0.193231	+	0.0517762i
$686$		0			0
$687$	−27.5812	+	5.29565i	−1.05229	+	0.202042i
$688$		0			0
$689$	−11.4265	−	11.4265i	−0.435315	−	0.435315i
$690$		0			0
$691$	−21.2531	−	12.2705i	−0.808505	−	0.466791i	0.0379311	−	0.999280i	$-0.487923\pi$
$691$	−21.2531	−	12.2705i	−0.808505	−	0.466791i	−0.846437	+	0.532489i	$0.821257\pi$
$692$		0			0
$693$	4.72769	−	32.5554i	0.179590	−	1.23668i
$694$		0			0
$695$	−1.83728	+	1.83728i	−0.0696921	+	0.0696921i
$696$		0			0
$697$	−9.40206	−	9.40206i	−0.356128	−	0.356128i
$698$		0			0
$699$	−0.214064	+	0.617088i	−0.00809665	+	0.0233404i
$700$		0			0
$701$	−39.4724	+	10.5766i	−1.49085	+	0.399472i	−0.910024	−	0.414555i	$-0.863937\pi$
$701$	−39.4724	+	10.5766i	−1.49085	+	0.399472i	−0.580827	+	0.814027i	$0.697271\pi$
$702$		0			0
$703$	20.4757	+	21.7618i	0.772255	+	0.820762i
$704$		0			0
$705$	−0.432409	+	0.637913i	−0.0162855	+	0.0240252i
$706$		0			0
$707$	0.0826931	+	0.143229i	0.00310999	+	0.00538667i
$708$		0			0
$709$	−28.2172	+	28.2172i	−1.05972	+	1.05972i	−0.0616179	+	0.998100i	$0.519626\pi$
$709$	−28.2172	+	28.2172i	−1.05972	+	1.05972i	−0.998100	+	0.0616179i	$0.980374\pi$
$710$		0			0
$711$	3.85892	+	5.17012i	0.144721	+	0.193895i
$712$		0			0
$713$			47.6875i			1.78591i
$714$		0			0
$715$	0.760340	−	1.31695i	0.0284351	−	0.0492510i
$716$		0			0
$717$	−1.65813	+	22.9559i	−0.0619241	+	0.857306i
$718$		0			0
$719$	12.4163	+	7.16857i	0.463051	+	0.267342i	0.713326	−	0.700832i	$-0.247188\pi$
$719$	12.4163	+	7.16857i	0.463051	+	0.267342i	−0.250275	+	0.968175i	$0.580521\pi$
$720$		0			0
$721$	−3.23740	+	12.0821i	−0.120567	+	0.449962i
$722$		0			0
$723$	−13.0427	+	19.2414i	−0.485065	+	0.715594i
$724$		0			0
$725$	40.4382	−	10.8354i	1.50184	−	0.402416i
$726$		0			0
$727$	0.397199	−	1.48237i	0.0147313	−	0.0549779i	−0.958169	−	0.286203i	$-0.907607\pi$
$727$	0.397199	−	1.48237i	0.0147313	−	0.0549779i	0.972900	+	0.231225i	$0.0742734\pi$
$728$		0			0
$729$	11.3201	−	24.5123i	0.419265	−	0.907864i
$730$		0			0
$731$	1.41636	−	2.45320i	0.0523859	−	0.0907350i
$732$		0			0
$733$	−20.1897	+	11.6565i	−0.745724	+	0.430544i	−0.824147	−	0.566376i	$-0.808345\pi$
$733$	−20.1897	+	11.6565i	−0.745724	+	0.430544i	0.0784226	+	0.996920i	$0.475012\pi$
$734$		0			0
$735$	−0.328468	+	0.159273i	−0.0121157	+	0.00587489i
$736$		0			0
$737$	−55.1164	+	31.8215i	−2.03024	+	1.17216i
$738$		0			0
$739$			24.0696i			0.885413i	0.896667	+	0.442706i	$0.145982\pi$
$739$			24.0696i			0.885413i	−0.896667	+	0.442706i	$0.854018\pi$
$740$		0			0
$741$	9.71186	−	8.40338i	0.356774	−	0.308706i
$742$		0			0
$743$	17.3243	+	30.0065i	0.635566	+	1.10083i	0.986395	+	0.164393i	$0.0525664\pi$
$743$	17.3243	+	30.0065i	0.635566	+	1.10083i	−0.350829	+	0.936439i	$0.614100\pi$
$744$		0			0
$745$	1.27599	+	0.341901i	0.0467487	+	0.0125263i
$746$		0			0
$747$	−1.33404	−	3.34596i	−0.0488100	−	0.122422i
$748$		0			0
$749$	3.05178	+	1.76195i	0.111510	+	0.0643801i
$750$		0			0
$751$			37.0885i			1.35338i	0.736269	+	0.676689i	$0.236586\pi$
$751$			37.0885i			1.35338i	−0.736269	+	0.676689i	$0.763414\pi$
$752$		0			0
$753$	−5.42442	−	11.1867i	−0.197677	−	0.407667i
$754$		0			0
$755$	−0.318545	−	1.18883i	−0.0115930	−	0.0432658i
$756$		0			0
$757$	−0.237085	−	0.884814i	−0.00861700	−	0.0321591i	0.961483	−	0.274863i	$-0.0886324\pi$
$757$	−0.237085	−	0.884814i	−0.00861700	−	0.0321591i	−0.970100	+	0.242704i	$0.921966\pi$
$758$		0			0
$759$	−32.2679	+	15.6466i	−1.17125	+	0.567936i
$760$		0			0
$761$	24.6401	−	42.6779i	0.893203	−	1.54707i	0.0571905	−	0.998363i	$-0.481786\pi$
$761$	24.6401	−	42.6779i	0.893203	−	1.54707i	0.836013	−	0.548710i	$-0.184881\pi$
$762$		0			0
$763$	−9.39967	+	9.39967i	−0.340291	+	0.340291i
$764$		0			0
$765$	0.509993	−	0.646627i	0.0184388	−	0.0233789i
$766$		0			0
$767$	−10.2246			−0.369188
$768$		0			0
$769$	18.2063	+	18.2063i	0.656535	+	0.656535i	0.954559	−	0.298023i	$-0.0963273\pi$
$769$	18.2063	+	18.2063i	0.656535	+	0.656535i	−0.298023	+	0.954559i	$0.596327\pi$
$770$		0			0
$771$	−1.95820	+	27.1103i	−0.0705230	+	0.976352i
$772$		0			0
$773$	−26.6079	+	15.3621i	−0.957019	+	0.552535i	−0.895254	−	0.445556i	$-0.853006\pi$
$773$	−26.6079	+	15.3621i	−0.957019	+	0.552535i	−0.0617647	+	0.998091i	$0.519673\pi$
$774$		0			0
$775$	−13.1315	−	49.0075i	−0.471698	−	1.76040i
$776$		0			0
$777$	24.2508	+	9.24856i	0.869991	+	0.331790i
$778$		0			0
$779$	13.9378	+	52.0165i	0.499373	+	1.86369i
$780$		0			0
$781$	15.6744	−	9.04963i	0.560875	−	0.323821i
$782$		0			0
$783$	−9.43478	+	42.9330i	−0.337172	+	1.53430i
$784$		0			0
$785$	3.29629	+	3.29629i	0.117650	+	0.117650i
$786$		0			0
$787$	−31.3695			−1.11820			−0.559101	−	0.829099i	$-0.688854\pi$
$787$	−31.3695			−1.11820			−0.559101	+	0.829099i	$0.688854\pi$
$788$		0			0
$789$	−29.0495	+	5.57757i	−1.03419	+	0.198567i
$790$		0			0
$791$	1.16126	−	1.16126i	0.0412896	−	0.0412896i
$792$		0			0
$793$	9.52988	−	16.5062i	0.338416	−	0.586153i
$794$		0			0
$795$	1.83109	+	3.77623i	0.0649419	+	0.133929i
$796$		0			0
$797$	9.28165	+	34.6396i	0.328773	+	1.22700i	0.910464	+	0.413588i	$0.135725\pi$
$797$	9.28165	+	34.6396i	0.328773	+	1.22700i	−0.581691	+	0.813410i	$0.697609\pi$
$798$		0			0
$799$	0.617134	+	2.30318i	0.0218326	+	0.0814805i
$800$		0			0
$801$	15.2548	−	35.4847i	0.539000	−	1.25379i
$802$		0			0
$803$		−	38.6645i		−	1.36444i
$804$		0			0
$805$	−2.24597	−	1.29671i	−0.0791602	−	0.0457032i
$806$		0			0
$807$	2.38360	+	0.826857i	0.0839067	+	0.0291067i
$808$		0			0
$809$	−0.633818	−	0.169831i	−0.0222839	−	0.00597094i	0.247660	−	0.968847i	$-0.420338\pi$
$809$	−0.633818	−	0.169831i	−0.0222839	−	0.00597094i	−0.269944	+	0.962876i	$0.587005\pi$
$810$		0			0
$811$	−5.99623	−	10.3858i	−0.210556	−	0.364694i	0.741332	−	0.671138i	$-0.234194\pi$
$811$	−5.99623	−	10.3858i	−0.210556	−	0.364694i	−0.951889	+	0.306444i	$0.900861\pi$
$812$		0			0
$813$	8.60066	+	9.93986i	0.301638	+	0.348606i
$814$		0			0
$815$		−	1.71939i		−	0.0602276i
$816$		0			0
$817$	−9.93558	+	5.73631i	−0.347602	+	0.200688i
$818$		0			0
$819$	4.40582	−	10.2486i	0.153952	−	0.358114i
$820$		0			0
$821$	13.5599	−	7.82883i	0.473245	−	0.273228i	−0.244352	−	0.969687i	$-0.578575\pi$
$821$	13.5599	−	7.82883i	0.473245	−	0.273228i	0.717597	+	0.696458i	$0.245242\pi$
$822$		0			0
$823$	13.2593	−	22.9659i	0.462192	−	0.800539i	−0.536878	−	0.843660i	$-0.680397\pi$
$823$	13.2593	−	22.9659i	0.462192	−	0.800539i	0.999070	+	0.0431204i	$0.0137299\pi$
$824$		0			0
$825$	28.8526	−	24.9652i	1.00452	−	0.869178i
$826$		0			0
$827$	5.59905	−	20.8959i	0.194698	−	0.726623i	−0.797647	−	0.603125i	$-0.793922\pi$
$827$	5.59905	−	20.8959i	0.194698	−	0.726623i	0.992345	−	0.123498i	$-0.0394112\pi$
$828$		0			0
$829$	−1.37988	+	0.369737i	−0.0479251	+	0.0128415i	−0.282702	−	0.959208i	$-0.591231\pi$
$829$	−1.37988	+	0.369737i	−0.0479251	+	0.0128415i	0.234777	+	0.972049i	$0.424564\pi$
$830$		0			0
$831$	12.3903	+	8.39879i	0.429816	+	0.291351i
$832$		0			0
$833$	−0.292326	+	1.09098i	−0.0101285	+	0.0378001i
$834$		0			0
$835$	−2.12004	−	1.22401i	−0.0733672	−	0.0423586i
$836$		0			0
$837$	52.0310	+	11.4341i	1.79845	+	0.395221i
$838$		0			0
$839$	−22.8111	+	39.5099i	−0.787525	+	1.36403i	0.139953	+	0.990158i	$0.455305\pi$
$839$	−22.8111	+	39.5099i	−0.787525	+	1.36403i	−0.927479	+	0.373876i	$0.878029\pi$
$840$		0			0
$841$		−	42.5650i		−	1.46776i
$842$		0			0
$843$	0.417272	−	5.77690i	0.0143716	−	0.198967i
$844$		0			0
$845$	−1.71587	+	1.71587i	−0.0590278	+	0.0590278i
$846$		0			0
$847$	10.8562	+	18.8035i	0.373024	+	0.646096i
$848$		0			0
$849$	24.0959	+	16.3334i	0.826969	+	0.560560i
$850$		0			0
$851$	−6.48768	−	27.5395i	−0.222395	−	0.944040i
$852$		0			0
$853$	−32.0094	+	8.57690i	−1.09598	+	0.293668i	−0.761128	−	0.648602i	$-0.775354\pi$
$853$	−32.0094	+	8.57690i	−1.09598	+	0.293668i	−0.334855	+	0.942270i	$0.608687\pi$
$854$		0			0
$855$	−3.09820	+	1.23526i	−0.105956	+	0.0422450i
$856$		0			0
$857$	22.2267	+	22.2267i	0.759250	+	0.759250i	0.976186	−	0.216936i	$-0.0696063\pi$
$857$	22.2267	+	22.2267i	0.759250	+	0.759250i	−0.216936	+	0.976186i	$0.569606\pi$
$858$		0			0
$859$	14.3461	−	14.3461i	0.489482	−	0.489482i	−0.418660	−	0.908143i	$-0.637500\pi$
$859$	14.3461	−	14.3461i	0.489482	−	0.489482i	0.908143	+	0.418660i	$0.137500\pi$
$860$		0			0
$861$	30.6070	+	35.3728i	1.04308	+	1.20550i
$862$		0			0
$863$	−4.58633	−	2.64792i	−0.156120	−	0.0901362i	0.419905	−	0.907568i	$-0.362064\pi$
$863$	−4.58633	−	2.64792i	−0.156120	−	0.0901362i	−0.576025	+	0.817432i	$0.695397\pi$
$864$		0			0
$865$	2.76266	+	2.76266i	0.0939333	+	0.0939333i
$866$		0			0
$867$	5.07161	+	26.4143i	0.172241	+	0.897078i
$868$		0			0
$869$	−9.24620	−	2.47751i	−0.313656	−	0.0840438i
$870$		0			0
$871$	−20.8462	+	5.58572i	−0.706346	+	0.189265i
$872$		0			0
$873$	−30.4466	+	3.59674i	−1.03046	+	0.121731i
$874$		0			0
$875$	5.35802	+	1.43568i	0.181134	+	0.0485348i
$876$		0			0
$877$	11.0306			0.372478			0.186239	−	0.982504i	$-0.440370\pi$
$877$	11.0306			0.372478			0.186239	+	0.982504i	$0.440370\pi$
$878$		0			0
$879$	1.39213	+	7.25060i	0.0469554	+	0.244557i
$880$		0			0
$881$	−5.69886	−	9.87071i	−0.191999	−	0.332553i	0.753913	−	0.656974i	$-0.228164\pi$
$881$	−5.69886	−	9.87071i	−0.191999	−	0.332553i	−0.945913	+	0.324421i	$0.894830\pi$
$882$		0			0
$883$	2.09452	−	7.81687i	0.0704863	−	0.263058i	−0.921686	−	0.387938i	$-0.873188\pi$
$883$	2.09452	−	7.81687i	0.0704863	−	0.263058i	0.992172	+	0.124879i	$0.0398543\pi$
$884$		0			0
$885$	2.50875	+	0.870270i	0.0843306	+	0.0292538i
$886$		0			0
$887$	20.8997			0.701744			0.350872	−	0.936423i	$-0.385885\pi$
$887$	20.8997			0.701744			0.350872	+	0.936423i	$0.385885\pi$
$888$		0			0
$889$	−36.0385			−1.20869
$890$		0			0
$891$	9.33483	+	38.9586i	0.312728	+	1.30516i
$892$		0			0
$893$	2.49942	−	9.32796i	0.0836399	−	0.312148i
$894$		0			0
$895$	1.83295	+	3.17476i	0.0612688	+	0.106121i
$896$		0			0
$897$	−11.9426	+	2.29300i	−0.398751	+	0.0765610i
$898$		0			0
$899$	−86.7305			−2.89262
$900$		0			0
$901$	12.5424	+	3.36073i	0.417848	+	0.111962i
$902$		0			0
$903$	−5.59146	+	8.24882i	−0.186072	+	0.274504i
$904$		0			0
$905$	0.489787	−	0.131238i	0.0162811	−	0.00436250i
$906$		0			0
$907$	6.39589	+	1.71377i	0.212372	+	0.0569049i	0.363436	−	0.931619i	$-0.381603\pi$
$907$	6.39589	+	1.71377i	0.212372	+	0.0569049i	−0.151064	+	0.988524i	$0.548270\pi$
$908$		0			0
$909$	−0.158139	−	0.124723i	−0.00524513	−	0.00413682i
$910$		0			0
$911$	−9.09846	−	9.09846i	−0.301445	−	0.301445i	0.540134	−	0.841579i	$-0.318374\pi$
$911$	−9.09846	−	9.09846i	−0.301445	−	0.301445i	−0.841579	+	0.540134i	$0.818374\pi$
$912$		0			0
$913$	4.62858	+	2.67231i	0.153184	+	0.0884406i
$914$		0			0
$915$	−3.74323	+	3.23890i	−0.123747	+	0.107075i
$916$		0			0
$917$	−22.8163	+	22.8163i	−0.753459	+	0.753459i
$918$		0			0
$919$	−9.52431	−	9.52431i	−0.314178	−	0.314178i	0.532348	−	0.846526i	$-0.321310\pi$
$919$	−9.52431	−	9.52431i	−0.314178	−	0.314178i	−0.846526	+	0.532348i	$0.821310\pi$
$920$		0			0
$921$	4.05918	+	1.40811i	0.133755	+	0.0463987i
$922$		0			0
$923$	5.92839	−	1.58851i	0.195135	−	0.0522864i
$924$		0			0
$925$	14.2507	+	26.5153i	0.468561	+	0.871818i
$926$		0			0
$927$	−1.78703	−	15.1273i	−0.0586936	−	0.496845i
$928$		0			0
$929$	−24.4271	−	42.3091i	−0.801429	−	1.38812i	−0.918676	−	0.395012i	$-0.870740\pi$
$929$	−24.4271	−	42.3091i	−0.801429	−	1.38812i	0.117247	−	0.993103i	$-0.462593\pi$
$930$		0			0
$931$	3.23457	−	3.23457i	0.106009	−	0.106009i
$932$		0			0
$933$	8.89880	+	0.642770i	0.291334	+	0.0210433i
$934$		0			0
$935$			1.22193i			0.0399614i
$936$		0			0
$937$	−7.40825	+	12.8315i	−0.242017	+	0.419186i	−0.961289	−	0.275543i	$-0.911142\pi$
$937$	−7.40825	+	12.8315i	−0.242017	+	0.419186i	0.719272	+	0.694729i	$0.244476\pi$
$938$		0			0
$939$	36.0852	+	2.60647i	1.17759	+	0.0850589i
$940$		0			0
$941$	49.0237	+	28.3039i	1.59813	+	0.922679i	0.991848	+	0.127428i	$0.0406721\pi$
$941$	49.0237	+	28.3039i	1.59813	+	0.922679i	0.606280	+	0.795251i	$0.292661\pi$
$942$		0			0
$943$	13.1976	−	49.2540i	0.429772	−	1.60393i
$944$		0			0
$945$	−1.95334	+	2.13963i	−0.0635423	+	0.0696021i
$946$		0			0
$947$	11.2784	−	3.02204i	0.366499	−	0.0982031i	−0.0708693	−	0.997486i	$-0.522577\pi$
$947$	11.2784	−	3.02204i	0.366499	−	0.0982031i	0.437368	+	0.899283i	$0.355911\pi$
$948$		0			0
$949$	3.39345	−	12.6645i	0.110156	−	0.411108i
$950$		0			0
$951$	−26.7837	−	30.9542i	−0.868522	−	1.00376i
$952$		0			0
$953$	0.551659	−	0.955501i	0.0178700	−	0.0309517i	−0.856952	−	0.515396i	$-0.827645\pi$
$953$	0.551659	−	0.955501i	0.0178700	−	0.0309517i	0.874822	+	0.484444i	$0.160978\pi$
$954$		0			0
$955$	2.63536	−	1.52153i	0.0852783	−	0.0492355i
$956$		0			0
$957$	−28.4569	−	58.6865i	−0.919882	−	1.89706i
$958$		0			0
$959$	−49.3538	+	28.4944i	−1.59372	+	0.920133i
$960$		0			0
$961$			74.1097i			2.39064i
$962$		0			0
$963$	−4.24679	−	0.616718i	−0.136851	−	0.0198735i
$964$		0			0
$965$	−2.87441	−	4.97862i	−0.0925304	−	0.160267i
$966$		0			0
$967$	−35.4927	−	9.51023i	−1.14137	−	0.305828i	−0.361867	−	0.932230i	$-0.617860\pi$
$967$	−35.4927	−	9.51023i	−1.14137	−	0.305828i	−0.779501	+	0.626402i	$0.784527\pi$
$968$		0			0
$969$	−3.38213	+	9.74976i	−0.108650	+	0.313207i
$970$		0			0
$971$	41.6117	+	24.0245i	1.33538	+	0.770983i	0.986119	−	0.166042i	$-0.0530986\pi$
$971$	41.6117	+	24.0245i	1.33538	+	0.770983i	0.349263	+	0.937025i	$0.386432\pi$
$972$		0			0
$973$		−	28.2815i		−	0.906662i
$974$		0			0
$975$	11.6417	−	5.64505i	0.372834	−	0.180786i
$976$		0			0
$977$	1.90353	+	7.10405i	0.0608992	+	0.227279i	0.989667	−	0.143382i	$-0.0457978\pi$
$977$	1.90353	+	7.10405i	0.0608992	+	0.227279i	−0.928768	+	0.370661i	$0.879131\pi$
$978$		0			0
$979$	14.8328	+	55.3567i	0.474058	+	1.76921i
$980$		0			0
$981$	6.39348	−	14.8721i	0.204128	−	0.474831i
$982$		0			0
$983$	−10.1160	+	17.5214i	−0.322649	+	0.558844i	−0.981034	−	0.193837i	$-0.937907\pi$
$983$	−10.1160	+	17.5214i	−0.322649	+	0.558844i	0.658385	+	0.752682i	$0.271240\pi$
$984$		0			0
$985$	−0.0936000	+	0.0936000i	−0.00298234	+	0.00298234i
$986$		0			0
$987$	−1.58167	−	8.23778i	−0.0503451	−	0.262211i
$988$		0			0
$989$	10.8633			0.345433
$990$		0			0
$991$	2.69940	+	2.69940i	0.0857491	+	0.0857491i	0.748680	−	0.662931i	$-0.230688\pi$
$991$	2.69940	+	2.69940i	0.0857491	+	0.0857491i	−0.662931	+	0.748680i	$0.730688\pi$
$992$		0			0
$993$	−3.69009	−	0.266539i	−0.117102	−	0.00845837i
$994$		0			0
$995$	−2.54403	+	1.46880i	−0.0806513	+	0.0465641i
$996$		0			0
$997$	−9.90893	−	36.9806i	−0.313819	−	1.17119i	−0.925084	−	0.379763i	$-0.876006\pi$
$997$	−9.90893	−	36.9806i	−0.313819	−	1.17119i	0.611265	−	0.791426i	$-0.290661\pi$
$998$		0			0
$999$	−31.6034	+	0.475409i	−0.999887	+	0.0150413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.22	✓	152
3.2	odd	2	inner	888.2.br.a.569.34	yes	152
37.8	odd	12	inner	888.2.br.a.785.34	yes	152
111.8	even	12	inner	888.2.br.a.785.22	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.22	✓	152	1.1	even	1	trivial
888.2.br.a.569.34	yes	152	3.2	odd	2	inner
888.2.br.a.785.22	yes	152	111.8	even	12	inner
888.2.br.a.785.34	yes	152	37.8	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567654 - 1.63639i) q^{3} +(0.0585783 - 0.218617i) q^{5} +(1.23175 + 2.13345i) q^{7} +(-2.35554 - 1.85780i) q^{9} +4.45126 q^{11} +(1.45800 + 0.390671i) q^{13} +(-0.324490 - 0.219956i) q^{15} +(-1.17157 + 0.313921i) q^{17} +(4.74490 + 1.27139i) q^{19} +(4.19035 - 0.804556i) q^{21} +(-3.28903 - 3.28903i) q^{23} +(4.28577 + 2.47439i) q^{25} +(-4.37722 + 2.79999i) q^{27} +(5.98185 - 5.98185i) q^{29} +(-7.24947 - 7.24947i) q^{31} +(2.52677 - 7.28399i) q^{33} +(0.538561 - 0.144307i) q^{35} +(5.17282 + 3.20030i) q^{37} +(1.46693 - 2.16410i) q^{39} +(5.48131 + 9.49391i) q^{41} +(-1.65145 + 1.65145i) q^{43} +(-0.544131 + 0.406134i) q^{45} -1.96589i q^{47} +(0.465605 - 0.806452i) q^{49} +(-0.151349 + 2.09534i) q^{51} +(-9.27137 - 5.35283i) q^{53} +(0.260747 - 0.973120i) q^{55} +(4.77395 - 7.04279i) q^{57} +(-6.54296 + 1.75318i) q^{59} +(3.26812 - 12.1968i) q^{61} +(1.06210 - 7.31376i) q^{63} +(0.170815 - 0.295860i) q^{65} +(-12.3822 + 7.14887i) q^{67} +(-7.24917 + 3.51510i) q^{69} +(3.52135 - 2.03305i) q^{71} -8.68620i q^{73} +(6.48189 - 5.60858i) q^{75} +(5.48281 + 9.49651i) q^{77} +(-2.07721 - 0.556587i) q^{79} +(2.09712 + 8.75226i) q^{81} +(1.03984 + 0.600350i) q^{83} +0.274514i q^{85} +(-6.39301 - 13.1843i) q^{87} +(3.33227 + 12.4362i) q^{89} +(0.962415 + 3.59178i) q^{91} +(-15.9781 + 7.74777i) q^{93} +(0.555896 - 0.962840i) q^{95} +(7.22624 - 7.22624i) q^{97} +(-10.4851 - 8.26956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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