LMFDB - Embedded newform 672.2.bb.a.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.83809 - 4.91572i) q^{11} +5.31228 q^{13} -2.50301i q^{15} +(-0.393919 + 0.227429i) q^{17} +(3.19938 + 1.84716i) q^{19} +(-0.0468128 + 2.64534i) q^{21} +(4.43443 + 2.56022i) q^{23} +(-0.632521 - 1.09556i) q^{25} +1.00000i q^{27} -2.57962i q^{29} +(3.00333 + 5.20192i) q^{31} +(4.91572 + 2.83809i) q^{33} +(3.20917 + 5.79280i) q^{35} +(7.80778 + 4.50782i) q^{37} +(-4.60057 + 2.65614i) q^{39} -4.65692i q^{41} -3.66703 q^{43} +(1.25150 + 2.16767i) q^{45} +(-0.478841 + 0.829377i) q^{47} +(-3.28332 - 6.18222i) q^{49} +(0.227429 - 0.393919i) q^{51} +(5.41124 - 3.12418i) q^{53} +14.2075 q^{55} -3.69433 q^{57} +(8.76604 - 5.06108i) q^{59} +(2.50184 - 4.33331i) q^{61} +(-1.28213 - 2.31434i) q^{63} +(-6.64834 + 11.5153i) q^{65} +(-4.65133 - 8.05634i) q^{67} -5.12043 q^{69} +7.35240i q^{71} +(5.93541 - 3.42681i) q^{73} +(1.09556 + 0.632521i) q^{75} +(-15.0154 - 0.265718i) q^{77} +(-7.71882 - 4.45646i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.96259i q^{83} -1.13851i q^{85} +(1.28981 + 2.23402i) q^{87} +(5.91361 + 3.41423i) q^{89} +(7.24175 - 12.0457i) q^{91} +(-5.20192 - 3.00333i) q^{93} +(-8.00807 + 4.62346i) q^{95} -3.71270i q^{97} -5.67619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	−1.25150	+	2.16767i	−0.559689	+	0.969410i	0.437833	+	0.899056i	$0.355746\pi$
$5$	−1.25150	+	2.16767i	−0.559689	+	0.969410i	−0.997522	+	0.0703538i	$0.977587\pi$
$6$		0			0
$7$	1.36321	−	2.26752i	0.515245	−	0.857043i
$7$	1.36321	−	2.26752i	0.515245	−	0.857043i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.83809	−	4.91572i	−0.855717	−	1.48215i	−0.875978	−	0.482351i	$-0.839783\pi$
$11$	−2.83809	−	4.91572i	−0.855717	−	1.48215i	0.0202603	−	0.999795i	$-0.493550\pi$
$12$		0			0
$13$	5.31228			1.47336			0.736681	−	0.676241i	$-0.236392\pi$
$13$	5.31228			1.47336			0.736681	+	0.676241i	$0.236392\pi$
$14$		0			0
$15$		−	2.50301i		−	0.646273i
$16$		0			0
$17$	−0.393919	+	0.227429i	−0.0955393	+	0.0551596i	−0.547008	−	0.837127i	$-0.684233\pi$
$17$	−0.393919	+	0.227429i	−0.0955393	+	0.0551596i	0.451469	+	0.892287i	$0.350900\pi$
$18$		0			0
$19$	3.19938	+	1.84716i	0.733988	+	0.423768i	0.819879	−	0.572536i	$-0.194040\pi$
$19$	3.19938	+	1.84716i	0.733988	+	0.423768i	−0.0858912	+	0.996305i	$0.527374\pi$
$20$		0			0
$21$	−0.0468128	+	2.64534i	−0.0102154	+	0.577260i
$22$		0			0
$23$	4.43443	+	2.56022i	0.924642	+	0.533842i	0.885113	−	0.465376i	$-0.154081\pi$
$23$	4.43443	+	2.56022i	0.924642	+	0.533842i	0.0395287	+	0.999218i	$0.487414\pi$
$24$		0			0
$25$	−0.632521	−	1.09556i	−0.126504	−	0.219112i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	2.57962i		−	0.479024i	−0.970893	−	0.239512i	$-0.923013\pi$
$29$		−	2.57962i		−	0.479024i	0.970893	−	0.239512i	$-0.0769874\pi$
$30$		0			0
$31$	3.00333	+	5.20192i	0.539414	+	0.934293i	0.998936	+	0.0461260i	$0.0146876\pi$
$31$	3.00333	+	5.20192i	0.539414	+	0.934293i	−0.459521	+	0.888167i	$0.651979\pi$
$32$		0			0
$33$	4.91572	+	2.83809i	0.855717	+	0.494049i
$34$		0			0
$35$	3.20917	+	5.79280i	0.542449	+	0.979161i
$36$		0			0
$37$	7.80778	+	4.50782i	1.28359	+	0.741082i	0.977503	−	0.210922i	$-0.0676465\pi$
$37$	7.80778	+	4.50782i	1.28359	+	0.741082i	0.306088	+	0.952003i	$0.400980\pi$
$38$		0			0
$39$	−4.60057	+	2.65614i	−0.736681	+	0.425323i
$40$		0			0
$41$		−	4.65692i		−	0.727289i	−0.931538	−	0.363644i	$-0.881532\pi$
$41$		−	4.65692i		−	0.727289i	0.931538	−	0.363644i	$-0.118468\pi$
$42$		0			0
$43$	−3.66703			−0.559217			−0.279608	−	0.960114i	$-0.590205\pi$
$43$	−3.66703			−0.559217			−0.279608	+	0.960114i	$0.590205\pi$
$44$		0			0
$45$	1.25150	+	2.16767i	0.186563	+	0.323137i
$46$		0			0
$47$	−0.478841	+	0.829377i	−0.0698461	+	0.120977i	−0.898833	−	0.438290i	$-0.855584\pi$
$47$	−0.478841	+	0.829377i	−0.0698461	+	0.120977i	0.828987	+	0.559267i	$0.188918\pi$
$48$		0			0
$49$	−3.28332	−	6.18222i	−0.469046	−	0.883174i
$50$		0			0
$51$	0.227429	−	0.393919i	0.0318464	−	0.0551596i
$52$		0			0
$53$	5.41124	−	3.12418i	0.743290	−	0.429139i	−0.0799741	−	0.996797i	$-0.525484\pi$
$53$	5.41124	−	3.12418i	0.743290	−	0.429139i	0.823264	+	0.567658i	$0.192150\pi$
$54$		0			0
$55$	14.2075			1.91574
$56$		0			0
$57$	−3.69433			−0.489326
$58$		0			0
$59$	8.76604	−	5.06108i	1.14124	−	0.658896i	0.194503	−	0.980902i	$-0.437690\pi$
$59$	8.76604	−	5.06108i	1.14124	−	0.658896i	0.946738	+	0.322006i	$0.104357\pi$
$60$		0			0
$61$	2.50184	−	4.33331i	0.320327	−	0.554823i	−0.660228	−	0.751065i	$-0.729540\pi$
$61$	2.50184	−	4.33331i	0.320327	−	0.554823i	0.980555	+	0.196242i	$0.0628738\pi$
$62$		0			0
$63$	−1.28213	−	2.31434i	−0.161533	−	0.291579i
$64$		0			0
$65$	−6.64834	+	11.5153i	−0.824625	+	1.42829i
$66$		0			0
$67$	−4.65133	−	8.05634i	−0.568251	−	0.984239i	−0.996739	−	0.0806916i	$-0.974287\pi$
$67$	−4.65133	−	8.05634i	−0.568251	−	0.984239i	0.428489	−	0.903547i	$-0.359046\pi$
$68$		0			0
$69$	−5.12043			−0.616428
$70$		0			0
$71$			7.35240i			0.872569i	0.899809	+	0.436285i	$0.143706\pi$
$71$			7.35240i			0.872569i	−0.899809	+	0.436285i	$0.856294\pi$
$72$		0			0
$73$	5.93541	−	3.42681i	0.694687	−	0.401078i	−0.110678	−	0.993856i	$-0.535302\pi$
$73$	5.93541	−	3.42681i	0.694687	−	0.401078i	0.805366	+	0.592779i	$0.201969\pi$
$74$		0			0
$75$	1.09556	+	0.632521i	0.126504	+	0.0730372i
$76$		0			0
$77$	−15.0154	−	0.265718i	−1.71117	−	0.0302814i
$78$		0			0
$79$	−7.71882	−	4.45646i	−0.868435	−	0.501391i	−0.00160740	−	0.999999i	$-0.500512\pi$
$79$	−7.71882	−	4.45646i	−0.868435	−	0.501391i	−0.866828	+	0.498607i	$0.833845\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			1.96259i			0.215423i	0.994182	+	0.107711i	$0.0343522\pi$
$83$			1.96259i			0.215423i	−0.994182	+	0.107711i	$0.965648\pi$
$84$		0			0
$85$		−	1.13851i		−	0.123489i
$86$		0			0
$87$	1.28981	+	2.23402i	0.138282	+	0.239512i
$88$		0			0
$89$	5.91361	+	3.41423i	0.626842	+	0.361907i	0.779528	−	0.626367i	$-0.215459\pi$
$89$	5.91361	+	3.41423i	0.626842	+	0.361907i	−0.152686	+	0.988275i	$0.548792\pi$
$90$		0			0
$91$	7.24175	−	12.0457i	0.759142	−	1.26273i
$92$		0			0
$93$	−5.20192	−	3.00333i	−0.539414	−	0.311431i
$94$		0			0
$95$	−8.00807	+	4.62346i	−0.821611	+	0.474357i
$96$		0			0
$97$		−	3.71270i		−	0.376967i	−0.982076	−	0.188484i	$-0.939643\pi$
$97$		−	3.71270i		−	0.376967i	0.982076	−	0.188484i	$-0.0603573\pi$
$98$		0			0
$99$	−5.67619			−0.570478
$100$		0			0
$101$	−2.84077	−	4.92036i	−0.282667	−	0.489594i	0.689373	−	0.724406i	$-0.257886\pi$
$101$	−2.84077	−	4.92036i	−0.282667	−	0.489594i	−0.972041	+	0.234812i	$0.924553\pi$
$102$		0			0
$103$	2.95345	−	5.11553i	0.291013	−	0.504049i	−0.683037	−	0.730384i	$-0.739341\pi$
$103$	2.95345	−	5.11553i	0.291013	−	0.504049i	0.974049	+	0.226335i	$0.0726745\pi$
$104$		0			0
$105$	−5.67562	−	3.41212i	−0.553884	−	0.332989i
$106$		0			0
$107$	−5.33045	+	9.23261i	−0.515314	+	0.892550i	0.484528	+	0.874776i	$0.338991\pi$
$107$	−5.33045	+	9.23261i	−0.515314	+	0.892550i	−0.999842	+	0.0177741i	$0.994342\pi$
$108$		0			0
$109$	−2.75319	+	1.58956i	−0.263708	+	0.152252i	−0.626025	−	0.779803i	$-0.715319\pi$
$109$	−2.75319	+	1.58956i	−0.263708	+	0.152252i	0.362317	+	0.932055i	$0.381986\pi$
$110$		0			0
$111$	−9.01565			−0.855727
$112$		0			0
$113$	−0.302446			−0.0284518			−0.0142259	−	0.999899i	$-0.504528\pi$
$113$	−0.302446			−0.0284518			−0.0142259	+	0.999899i	$0.504528\pi$
$114$		0			0
$115$	−11.0994	+	6.40824i	−1.03502	+	0.597571i
$116$		0			0
$117$	2.65614	−	4.60057i	0.245560	−	0.425323i
$118$		0			0
$119$	−0.0212932	+	1.20325i	−0.00195194	+	0.110302i
$120$		0			0
$121$	−10.6096	+	18.3763i	−0.964505	+	1.67057i
$122$		0			0
$123$	2.32846	+	4.03301i	0.209950	+	0.363644i
$124$		0			0
$125$	−9.34863			−0.836167
$126$		0			0
$127$		−	6.39751i		−	0.567687i	−0.958871	−	0.283843i	$-0.908390\pi$
$127$		−	6.39751i		−	0.567687i	0.958871	−	0.283843i	$-0.0916096\pi$
$128$		0			0
$129$	3.17574	−	1.83351i	0.279608	−	0.161432i
$130$		0			0
$131$	12.5596	+	7.25130i	1.09734	+	0.633549i	0.935521	−	0.353272i	$-0.114931\pi$
$131$	12.5596	+	7.25130i	1.09734	+	0.633549i	0.161818	+	0.986821i	$0.448264\pi$
$132$		0			0
$133$	8.54991	−	4.73660i	0.741371	−	0.410715i
$134$		0			0
$135$	−2.16767	−	1.25150i	−0.186563	−	0.107712i
$136$		0			0
$137$	−0.615559	−	1.06618i	−0.0525908	−	0.0910899i	0.838532	−	0.544853i	$-0.183415\pi$
$137$	−0.615559	−	1.06618i	−0.0525908	−	0.0910899i	−0.891122	+	0.453763i	$0.850081\pi$
$138$		0			0
$139$			15.7788i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$139$			15.7788i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$140$		0			0
$141$		−	0.957682i		−	0.0806514i
$142$		0			0
$143$	−15.0768	−	26.1137i	−1.26078	−	2.18374i
$144$		0			0
$145$	5.59176	+	3.22841i	0.464371	+	0.268104i
$146$		0			0
$147$	5.93455	+	3.71230i	0.489473	+	0.306185i
$148$		0			0
$149$	5.15767	+	2.97778i	0.422532	+	0.243949i	0.696160	−	0.717886i	$-0.254890\pi$
$149$	5.15767	+	2.97778i	0.422532	+	0.243949i	−0.273628	+	0.961836i	$0.588224\pi$
$150$		0			0
$151$	3.11126	−	1.79629i	0.253191	−	0.146180i	−0.368034	−	0.929812i	$-0.619969\pi$
$151$	3.11126	−	1.79629i	0.253191	−	0.146180i	0.621224	+	0.783633i	$0.286636\pi$
$152$		0			0
$153$			0.454858i			0.0367731i
$154$		0			0
$155$	−15.0347			−1.20762
$156$		0			0
$157$	0.491762	+	0.851757i	0.0392469	+	0.0679776i	0.884982	−	0.465626i	$-0.154171\pi$
$157$	0.491762	+	0.851757i	0.0392469	+	0.0679776i	−0.845735	+	0.533604i	$0.820837\pi$
$158$		0			0
$159$	−3.12418	+	5.41124i	−0.247763	+	0.429139i
$160$		0			0
$161$	11.8504	−	6.56505i	0.933942	−	0.517398i
$162$		0			0
$163$	1.26083	−	2.18383i	0.0987562	−	0.171051i	−0.812414	−	0.583081i	$-0.801847\pi$
$163$	1.26083	−	2.18383i	0.0987562	−	0.171051i	0.911170	+	0.412030i	$0.135180\pi$
$164$		0			0
$165$	−12.3041	+	7.10377i	−0.957872	+	0.553028i
$166$		0			0
$167$	−5.26232			−0.407211			−0.203605	−	0.979053i	$-0.565266\pi$
$167$	−5.26232			−0.407211			−0.203605	+	0.979053i	$0.565266\pi$
$168$		0			0
$169$	15.2203			1.17079
$170$		0			0
$171$	3.19938	−	1.84716i	0.244663	−	0.141256i
$172$		0			0
$173$	0.0718117	−	0.124381i	0.00545974	−	0.00945654i	−0.863283	−	0.504721i	$-0.831595\pi$
$173$	0.0718117	−	0.124381i	0.00545974	−	0.00945654i	0.868742	+	0.495264i	$0.164929\pi$
$174$		0			0
$175$	−3.34646	−	0.0592202i	−0.252969	−	0.00447662i
$176$		0			0
$177$	−5.06108	+	8.76604i	−0.380414	+	0.658896i
$178$		0			0
$179$	−9.46239	−	16.3893i	−0.707252	−	1.22500i	−0.965873	−	0.259018i	$-0.916601\pi$
$179$	−9.46239	−	16.3893i	−0.707252	−	1.22500i	0.258621	−	0.965979i	$-0.416732\pi$
$180$		0			0
$181$	−22.2260			−1.65204			−0.826022	−	0.563637i	$-0.809402\pi$
$181$	−22.2260			−1.65204			−0.826022	+	0.563637i	$0.809402\pi$
$182$		0			0
$183$			5.00367i			0.369882i
$184$		0			0
$185$	−19.5429	+	11.2831i	−1.43682	+	0.829551i
$186$		0			0
$187$	2.23596	+	1.29093i	0.163509	+	0.0944021i
$188$		0			0
$189$	2.26752	+	1.36321i	0.164938	+	0.0991589i
$190$		0			0
$191$	−10.2112	−	5.89547i	−0.738860	−	0.426581i	0.0827947	−	0.996567i	$-0.473615\pi$
$191$	−10.2112	−	5.89547i	−0.738860	−	0.426581i	−0.821655	+	0.569986i	$0.806949\pi$
$192$		0			0
$193$	−13.4112	−	23.2289i	−0.965361	−	1.67205i	−0.708642	−	0.705568i	$-0.750692\pi$
$193$	−13.4112	−	23.2289i	−0.965361	−	1.67205i	−0.256719	−	0.966486i	$-0.582641\pi$
$194$		0			0
$195$		−	13.2967i		−	0.952195i
$196$		0			0
$197$			16.5842i			1.18157i	0.806828	+	0.590786i	$0.201182\pi$
$197$			16.5842i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$198$		0			0
$199$	5.70420	+	9.87996i	0.404360	+	0.700372i	0.994247	−	0.107114i	$-0.0341610\pi$
$199$	5.70420	+	9.87996i	0.404360	+	0.700372i	−0.589887	+	0.807486i	$0.700828\pi$
$200$		0			0
$201$	8.05634	+	4.65133i	0.568251	+	0.328080i
$202$		0			0
$203$	−5.84935	−	3.51657i	−0.410544	−	0.246815i
$204$		0			0
$205$	10.0947	+	5.82815i	0.705041	+	0.407056i
$206$		0			0
$207$	4.43443	−	2.56022i	0.308214	−	0.177947i
$208$		0			0
$209$		−	20.9697i		−	1.45050i
$210$		0			0
$211$	4.13300			0.284527			0.142264	−	0.989829i	$-0.454562\pi$
$211$	4.13300			0.284527			0.142264	+	0.989829i	$0.454562\pi$
$212$		0			0
$213$	−3.67620	−	6.36736i	−0.251889	−	0.436285i
$214$		0			0
$215$	4.58930	−	7.94890i	0.312988	−	0.542110i
$216$		0			0
$217$	15.8896	+	0.281189i	1.07866	+	0.0190883i
$218$		0			0
$219$	−3.42681	+	5.93541i	−0.231562	+	0.401078i
$220$		0			0
$221$	−2.09261	+	1.20817i	−0.140764	+	0.0812701i
$222$		0			0
$223$	−18.1063			−1.21249			−0.606245	−	0.795278i	$-0.707325\pi$
$223$	−18.1063			−1.21249			−0.606245	+	0.795278i	$0.707325\pi$
$224$		0			0
$225$	−1.26504			−0.0843361
$226$		0			0
$227$	−6.86343	+	3.96260i	−0.455542	+	0.263007i	−0.710168	−	0.704032i	$-0.751381\pi$
$227$	−6.86343	+	3.96260i	−0.455542	+	0.263007i	0.254626	+	0.967040i	$0.418048\pi$
$228$		0			0
$229$	−1.07787	+	1.86692i	−0.0712274	+	0.123370i	−0.899440	−	0.437045i	$-0.856025\pi$
$229$	−1.07787	+	1.86692i	−0.0712274	+	0.123370i	0.828212	+	0.560415i	$0.189358\pi$
$230$		0			0
$231$	13.1366	−	7.27760i	0.864325	−	0.478831i
$232$		0			0
$233$	10.0072	−	17.3330i	0.655594	−	1.13552i	−0.326151	−	0.945318i	$-0.605752\pi$
$233$	10.0072	−	17.3330i	0.655594	−	1.13552i	0.981745	−	0.190204i	$-0.0609149\pi$
$234$		0			0
$235$	−1.19854	−	2.07594i	−0.0781843	−	0.135419i
$236$		0			0
$237$	8.91293			0.578957
$238$		0			0
$239$			18.8923i			1.22204i	0.791614	+	0.611021i	$0.209241\pi$
$239$			18.8923i			1.22204i	−0.791614	+	0.611021i	$0.790759\pi$
$240$		0			0
$241$	−15.8555	+	9.15417i	−1.02134	+	0.589672i	−0.914492	−	0.404603i	$-0.867410\pi$
$241$	−15.8555	+	9.15417i	−1.02134	+	0.589672i	−0.106849	+	0.994275i	$0.534076\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	17.5101	+	0.619923i	1.11868	+	0.0396054i
$246$		0			0
$247$	16.9960	+	9.81265i	1.08143	+	0.624364i
$248$		0			0
$249$	−0.981297	−	1.69966i	−0.0621872	−	0.107711i
$250$		0			0
$251$			3.43251i			0.216658i	0.994115	+	0.108329i	$0.0345500\pi$
$251$			3.43251i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$252$		0			0
$253$		−	29.0645i		−	1.82727i
$254$		0			0
$255$	0.569256	+	0.985981i	0.0356482	+	0.0617445i
$256$		0			0
$257$	21.7104	+	12.5345i	1.35426	+	0.781882i	0.988843	−	0.148962i	$-0.0475932\pi$
$257$	21.7104	+	12.5345i	1.35426	+	0.781882i	0.365417	+	0.930844i	$0.380927\pi$
$258$		0			0
$259$	20.8652	−	11.5592i	1.29650	−	0.718254i
$260$		0			0
$261$	−2.23402	−	1.28981i	−0.138282	−	0.0798373i
$262$		0			0
$263$	13.4314	−	7.75460i	0.828214	−	0.478169i	−0.0250270	−	0.999687i	$-0.507967\pi$
$263$	13.4314	−	7.75460i	0.828214	−	0.478169i	0.853241	+	0.521517i	$0.174634\pi$
$264$		0			0
$265$			15.6397i			0.960738i
$266$		0			0
$267$	−6.82845			−0.417894
$268$		0			0
$269$	11.8667	+	20.5537i	0.723523	+	1.25318i	0.959579	+	0.281440i	$0.0908120\pi$
$269$	11.8667	+	20.5537i	0.723523	+	1.25318i	−0.236055	+	0.971740i	$0.575855\pi$
$270$		0			0
$271$	7.35684	−	12.7424i	0.446896	−	0.774047i	−0.551286	−	0.834316i	$-0.685863\pi$
$271$	7.35684	−	12.7424i	0.446896	−	0.774047i	0.998182	+	0.0602693i	$0.0191959\pi$
$272$		0			0
$273$	−0.248683	+	14.0528i	−0.0150510	+	0.850513i
$274$		0			0
$275$	−3.59031	+	6.21859i	−0.216504	+	0.374995i
$276$		0			0
$277$	−6.16822	+	3.56123i	−0.370613	+	0.213973i	−0.673726	−	0.738981i	$-0.735307\pi$
$277$	−6.16822	+	3.56123i	−0.370613	+	0.213973i	0.303113	+	0.952954i	$0.401974\pi$
$278$		0			0
$279$	6.00666			0.359609
$280$		0			0
$281$	−13.0561			−0.778861			−0.389430	−	0.921056i	$-0.627328\pi$
$281$	−13.0561			−0.778861			−0.389430	+	0.921056i	$0.627328\pi$
$282$		0			0
$283$	1.83051	−	1.05685i	0.108813	−	0.0628230i	−0.444606	−	0.895726i	$-0.646656\pi$
$283$	1.83051	−	1.05685i	0.108813	−	0.0628230i	0.553419	+	0.832903i	$0.313323\pi$
$284$		0			0
$285$	4.62346	−	8.00807i	0.273870	−	0.474357i
$286$		0			0
$287$	−10.5597	−	6.34836i	−0.623318	−	0.374732i
$288$		0			0
$289$	−8.39655	+	14.5433i	−0.493915	+	0.855486i
$290$		0			0
$291$	1.85635	+	3.21529i	0.108821	+	0.188484i
$292$		0			0
$293$	−0.334002			−0.0195126			−0.00975630	−	0.999952i	$-0.503106\pi$
$293$	−0.334002			−0.0195126			−0.00975630	+	0.999952i	$0.503106\pi$
$294$		0			0
$295$			25.3358i			1.47511i
$296$		0			0
$297$	4.91572	−	2.83809i	0.285239	−	0.164683i
$298$		0			0
$299$	23.5569	+	13.6006i	1.36233	+	0.786542i
$300$		0			0
$301$	−4.99893	+	8.31507i	−0.288134	+	0.479273i
$302$		0			0
$303$	4.92036	+	2.84077i	0.282667	+	0.163198i
$304$		0			0
$305$	6.26211	+	10.8463i	0.358567	+	0.621057i
$306$		0			0
$307$		−	9.39141i		−	0.535996i	−0.963419	−	0.267998i	$-0.913638\pi$
$307$		−	9.39141i		−	0.535996i	0.963419	−	0.267998i	$-0.0863621\pi$
$308$		0			0
$309$			5.90691i			0.336032i
$310$		0			0
$311$	7.93750	+	13.7482i	0.450095	+	0.779587i	0.998391	−	0.0566971i	$-0.0180569\pi$
$311$	7.93750	+	13.7482i	0.450095	+	0.779587i	−0.548297	+	0.836284i	$0.684724\pi$
$312$		0			0
$313$	−27.8562	−	16.0828i	−1.57453	−	0.909054i	−0.995603	−	0.0936727i	$-0.970139\pi$
$313$	−27.8562	−	16.0828i	−1.57453	−	0.909054i	−0.578924	−	0.815381i	$-0.696527\pi$
$314$		0			0
$315$	6.62130	+	0.117173i	0.373068	+	0.00660194i
$316$		0			0
$317$	−13.2252	−	7.63558i	−0.742802	−	0.428857i	0.0802854	−	0.996772i	$-0.474417\pi$
$317$	−13.2252	−	7.63558i	−0.742802	−	0.428857i	−0.823087	+	0.567915i	$0.807750\pi$
$318$		0			0
$319$	−12.6807	+	7.32121i	−0.709983	+	0.409909i
$320$		0			0
$321$		−	10.6609i		−	0.595033i
$322$		0			0
$323$	−1.68039			−0.0934996
$324$		0			0
$325$	−3.36013	−	5.81991i	−0.186386	−	0.322831i
$326$		0			0
$327$	1.58956	−	2.75319i	0.0879027	−	0.152252i
$328$		0			0
$329$	1.22787	+	2.21640i	0.0676947	+	0.122194i
$330$		0			0
$331$	−10.5189	+	18.2193i	−0.578174	+	1.00143i	0.417515	+	0.908670i	$0.362901\pi$
$331$	−10.5189	+	18.2193i	−0.578174	+	1.00143i	−0.995689	+	0.0927561i	$0.970432\pi$
$332$		0			0
$333$	7.80778	−	4.50782i	0.427864	−	0.247027i
$334$		0			0
$335$	23.2846			1.27217
$336$		0			0
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$		0			0
$339$	0.261926	−	0.151223i	0.0142259	−	0.00821332i
$340$		0			0
$341$	17.0475	−	29.5271i	0.923172	−	1.59898i
$342$		0			0
$343$	−18.4942	−	0.982659i	−0.998591	−	0.0530586i
$344$		0			0
$345$	6.40824	−	11.0994i	0.345008	−	0.597571i
$346$		0			0
$347$	−2.40670	−	4.16854i	−0.129199	−	0.223779i	0.794168	−	0.607699i	$-0.207907\pi$
$347$	−2.40670	−	4.16854i	−0.129199	−	0.223779i	−0.923366	+	0.383920i	$0.874574\pi$
$348$		0			0
$349$	35.4792			1.89916			0.949578	−	0.313530i	$-0.101512\pi$
$349$	35.4792			1.89916			0.949578	+	0.313530i	$0.101512\pi$
$350$		0			0
$351$			5.31228i			0.283549i
$352$		0			0
$353$	−4.13712	+	2.38857i	−0.220197	+	0.127131i	−0.606041	−	0.795433i	$-0.707243\pi$
$353$	−4.13712	+	2.38857i	−0.220197	+	0.127131i	0.385845	+	0.922564i	$0.373910\pi$
$354$		0			0
$355$	−15.9375	−	9.20155i	−0.845877	−	0.488367i
$356$		0			0
$357$	−0.583186	−	1.05269i	−0.0308655	−	0.0557145i
$358$		0			0
$359$	31.9690	+	18.4573i	1.68726	+	0.974140i	0.956603	+	0.291394i	$0.0941192\pi$
$359$	31.9690	+	18.4573i	1.68726	+	0.974140i	0.730656	+	0.682745i	$0.239214\pi$
$360$		0			0
$361$	−2.67598	−	4.63493i	−0.140841	−	0.243943i
$362$		0			0
$363$		−	21.2191i		−	1.11371i
$364$		0			0
$365$			17.1547i			0.897916i
$366$		0			0
$367$	0.284416	+	0.492623i	0.0148464	+	0.0257147i	0.873353	−	0.487088i	$-0.161941\pi$
$367$	0.284416	+	0.492623i	0.0148464	+	0.0257147i	−0.858507	+	0.512802i	$0.828607\pi$
$368$		0			0
$369$	−4.03301	−	2.32846i	−0.209950	−	0.121215i
$370$		0			0
$371$	0.292503	−	16.5290i	0.0151860	−	0.858143i
$372$		0			0
$373$	−20.2929	−	11.7161i	−1.05073	−	0.606638i	−0.127874	−	0.991790i	$-0.540815\pi$
$373$	−20.2929	−	11.7161i	−1.05073	−	0.606638i	−0.922853	+	0.385153i	$0.874149\pi$
$374$		0			0
$375$	8.09615	−	4.67431i	0.418083	−	0.241380i
$376$		0			0
$377$		−	13.7037i		−	0.705775i
$378$		0			0
$379$	14.7240			0.756320			0.378160	−	0.925740i	$-0.376557\pi$
$379$	14.7240			0.756320			0.378160	+	0.925740i	$0.376557\pi$
$380$		0			0
$381$	3.19875	+	5.54040i	0.163877	+	0.283843i
$382$		0			0
$383$	−2.49754	+	4.32587i	−0.127618	+	0.221042i	−0.922753	−	0.385391i	$-0.874067\pi$
$383$	−2.49754	+	4.32587i	−0.127618	+	0.221042i	0.795135	+	0.606432i	$0.207400\pi$
$384$		0			0
$385$	19.3678	−	32.2159i	0.987077	−	1.64187i
$386$		0			0
$387$	−1.83351	+	3.17574i	−0.0932028	+	0.161432i
$388$		0			0
$389$	27.6098	−	15.9405i	1.39987	−	0.808216i	0.405492	−	0.914099i	$-0.367100\pi$
$389$	27.6098	−	15.9405i	1.39987	−	0.808216i	0.994379	+	0.105883i	$0.0337668\pi$
$390$		0			0
$391$	−2.32907			−0.117786
$392$		0			0
$393$	−14.5026			−0.731559
$394$		0			0
$395$	19.3203	−	11.1546i	0.972108	−	0.561247i
$396$		0			0
$397$	−16.4530	+	28.4975i	−0.825753	+	1.43025i	0.0755896	+	0.997139i	$0.475916\pi$
$397$	−16.4530	+	28.4975i	−0.825753	+	1.43025i	−0.901343	+	0.433107i	$0.857417\pi$
$398$		0			0
$399$	−5.03614	+	8.37697i	−0.252122	+	0.419373i
$400$		0			0
$401$	−0.106236	+	0.184006i	−0.00530517	+	0.00918883i	−0.868666	−	0.495399i	$-0.835022\pi$
$401$	−0.106236	+	0.184006i	−0.00530517	+	0.00918883i	0.863361	+	0.504587i	$0.168355\pi$
$402$		0			0
$403$	15.9545	+	27.6341i	0.794752	+	1.37655i
$404$		0			0
$405$	2.50301			0.124375
$406$		0			0
$407$		−	51.1745i		−	2.53663i
$408$		0			0
$409$	17.7288	−	10.2357i	0.876633	−	0.506124i	0.00708628	−	0.999975i	$-0.497744\pi$
$409$	17.7288	−	10.2357i	0.876633	−	0.506124i	0.869547	+	0.493851i	$0.164411\pi$
$410$		0			0
$411$	1.06618	+	0.615559i	0.0525908	+	0.0303633i
$412$		0			0
$413$	0.473847	−	26.7765i	0.0233165	−	1.31759i
$414$		0			0
$415$	−4.25425	−	2.45619i	−0.208833	−	0.120570i
$416$		0			0
$417$	−7.88942	−	13.6649i	−0.386347	−	0.669172i
$418$		0			0
$419$		−	11.8439i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$419$		−	11.8439i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$420$		0			0
$421$			21.7928i			1.06211i	0.847336	+	0.531057i	$0.178205\pi$
$421$			21.7928i			1.06211i	−0.847336	+	0.531057i	$0.821795\pi$
$422$		0			0
$423$	0.478841	+	0.829377i	0.0232820	+	0.0403257i
$424$		0			0
$425$	0.498323	+	0.287707i	0.0241722	+	0.0139558i
$426$		0			0
$427$	−6.41534	−	11.5802i	−0.310460	−	0.560404i
$428$		0			0
$429$	26.1137	+	15.0768i	1.26078	+	0.727912i
$430$		0			0
$431$	−14.3234	+	8.26964i	−0.689936	+	0.398335i	−0.803588	−	0.595186i	$-0.797078\pi$
$431$	−14.3234	+	8.26964i	−0.689936	+	0.398335i	0.113652	+	0.993521i	$0.463745\pi$
$432$		0			0
$433$			39.2724i			1.88731i	0.330929	+	0.943656i	$0.392638\pi$
$433$			39.2724i			1.88731i	−0.330929	+	0.943656i	$0.607362\pi$
$434$		0			0
$435$	−6.45681			−0.309580
$436$		0			0
$437$	9.45828	+	16.3822i	0.452451	+	0.783668i
$438$		0			0
$439$	−15.5165	+	26.8754i	−0.740564	+	1.28269i	0.211674	+	0.977340i	$0.432108\pi$
$439$	−15.5165	+	26.8754i	−0.740564	+	1.28269i	−0.952239	+	0.305355i	$0.901225\pi$
$440$		0			0
$441$	−6.99562	−	0.247671i	−0.333125	−	0.0117939i
$442$		0			0
$443$	−0.422464	+	0.731729i	−0.0200719	+	0.0347655i	−0.875887	−	0.482517i	$-0.839723\pi$
$443$	−0.422464	+	0.731729i	−0.0200719	+	0.0347655i	0.855815	+	0.517282i	$0.173056\pi$
$444$		0			0
$445$	−14.8018	+	8.54583i	−0.701673	+	0.405111i
$446$		0			0
$447$	−5.95556			−0.281688
$448$		0			0
$449$	−41.7433			−1.96999			−0.984995	−	0.172585i	$-0.944788\pi$
$449$	−41.7433			−1.96999			−0.984995	+	0.172585i	$0.944788\pi$
$450$		0			0
$451$	−22.8921	+	13.2168i	−1.07795	+	0.622354i
$452$		0			0
$453$	−1.79629	+	3.11126i	−0.0843968	+	0.146180i
$454$		0			0
$455$	17.0480	+	30.7730i	0.799224	+	1.44266i
$456$		0			0
$457$	3.74286	−	6.48282i	0.175083	−	0.303254i	−0.765107	−	0.643904i	$-0.777314\pi$
$457$	3.74286	−	6.48282i	0.175083	−	0.303254i	0.940190	+	0.340650i	$0.110647\pi$
$458$		0			0
$459$	−0.227429	−	0.393919i	−0.0106155	−	0.0183865i
$460$		0			0
$461$	−4.33499			−0.201901			−0.100950	−	0.994891i	$-0.532188\pi$
$461$	−4.33499			−0.201901			−0.100950	+	0.994891i	$0.532188\pi$
$462$		0			0
$463$		−	35.3200i		−	1.64146i	−0.571316	−	0.820730i	$-0.693567\pi$
$463$		−	35.3200i		−	1.64146i	0.571316	−	0.820730i	$-0.306433\pi$
$464$		0			0
$465$	13.0204	−	7.51736i	0.603809	−	0.348609i
$466$		0			0
$467$	−9.09213	−	5.24934i	−0.420733	−	0.242911i	0.274658	−	0.961542i	$-0.411435\pi$
$467$	−9.09213	−	5.24934i	−0.420733	−	0.242911i	−0.695391	+	0.718632i	$0.744769\pi$
$468$		0			0
$469$	−24.6087	−	0.435484i	−1.13632	−	0.0201088i
$470$		0			0
$471$	−0.851757	−	0.491762i	−0.0392469	−	0.0226592i
$472$		0			0
$473$	10.4074	+	18.0261i	0.478532	+	0.828841i
$474$		0			0
$475$		−	4.67348i		−	0.214434i
$476$		0			0
$477$		−	6.24836i		−	0.286093i
$478$		0			0
$479$	8.46375	+	14.6596i	0.386719	+	0.669816i	0.992006	−	0.126191i	$-0.0402752\pi$
$479$	8.46375	+	14.6596i	0.386719	+	0.669816i	−0.605287	+	0.796007i	$0.706942\pi$
$480$		0			0
$481$	41.4771	+	23.9468i	1.89119	+	1.09188i
$482$		0			0
$483$	−6.98022	+	11.6107i	−0.317611	+	0.528305i
$484$		0			0
$485$	8.04790	+	4.64645i	0.365436	+	0.210985i
$486$		0			0
$487$	20.5482	−	11.8635i	0.931127	−	0.537586i	0.0439591	−	0.999033i	$-0.486003\pi$
$487$	20.5482	−	11.8635i	0.931127	−	0.537586i	0.887168	+	0.461447i	$0.152670\pi$
$488$		0			0
$489$			2.52167i			0.114034i
$490$		0			0
$491$	3.41198			0.153980			0.0769901	−	0.997032i	$-0.475469\pi$
$491$	3.41198			0.153980			0.0769901	+	0.997032i	$0.475469\pi$
$492$		0			0
$493$	0.586681	+	1.01616i	0.0264228	+	0.0457656i
$494$		0			0
$495$	7.10377	−	12.3041i	0.319291	−	0.553028i
$496$		0			0
$497$	16.6717	+	10.0229i	0.747829	+	0.449587i
$498$		0			0
$499$	−8.72998	+	15.1208i	−0.390808	+	0.676899i	−0.992556	−	0.121787i	$-0.961138\pi$
$499$	−8.72998	+	15.1208i	−0.390808	+	0.676899i	0.601749	+	0.798686i	$0.294471\pi$
$500$		0			0
$501$	4.55730	−	2.63116i	0.203605	−	0.117552i
$502$		0			0
$503$	7.08646			0.315970			0.157985	−	0.987442i	$-0.449500\pi$
$503$	7.08646			0.315970			0.157985	+	0.987442i	$0.449500\pi$
$504$		0			0
$505$	14.2209			0.632824
$506$		0			0
$507$	−13.1812	+	7.61017i	−0.585397	+	0.337979i
$508$		0			0
$509$	−18.9653	+	32.8488i	−0.840622	+	1.45600i	0.0487485	+	0.998811i	$0.484477\pi$
$509$	−18.9653	+	32.8488i	−0.840622	+	1.45600i	−0.889370	+	0.457188i	$0.848857\pi$
$510$		0			0
$511$	0.320837	−	18.1301i	0.0141930	−	0.802030i
$512$		0			0
$513$	−1.84716	+	3.19938i	−0.0815543	+	0.141256i
$514$		0			0
$515$	7.39252	+	12.8042i	0.325753	+	0.564221i
$516$		0			0
$517$	5.43598			0.239074
$518$		0			0
$519$			0.143623i			0.00630436i
$520$		0			0
$521$	6.91166	−	3.99045i	0.302805	−	0.174825i	−0.340897	−	0.940101i	$-0.610731\pi$
$521$	6.91166	−	3.99045i	0.302805	−	0.174825i	0.643702	+	0.765276i	$0.277397\pi$
$522$		0			0
$523$	−12.3267	−	7.11681i	−0.539008	−	0.311196i	0.205669	−	0.978622i	$-0.434063\pi$
$523$	−12.3267	−	7.11681i	−0.539008	−	0.311196i	−0.744677	+	0.667425i	$0.767396\pi$
$524$		0			0
$525$	2.92773	−	1.62194i	0.127777	−	0.0707874i
$526$		0			0
$527$	−2.36614	−	1.36609i	−0.103071	−	0.0595078i
$528$		0			0
$529$	1.60942	+	2.78759i	0.0699747	+	0.121200i
$530$		0			0
$531$		−	10.1222i		−	0.439264i
$532$		0			0
$533$		−	24.7389i		−	1.07156i
$534$		0			0
$535$	−13.3421	−	23.1093i	−0.576831	−	0.999101i
$536$		0			0
$537$	16.3893	+	9.46239i	0.707252	+	0.408332i
$538$		0			0
$539$	−21.0717	+	33.6856i	−0.907622	+	1.45094i
$540$		0			0
$541$	6.43282	+	3.71399i	0.276569	+	0.159677i	0.631869	−	0.775075i	$-0.282288\pi$
$541$	6.43282	+	3.71399i	0.276569	+	0.159677i	−0.355300	+	0.934752i	$0.615621\pi$
$542$		0			0
$543$	19.2483	−	11.1130i	0.826022	−	0.476904i
$544$		0			0
$545$		−	7.95734i		−	0.340855i
$546$		0			0
$547$	28.2287			1.20697			0.603485	−	0.797374i	$-0.293778\pi$
$547$	28.2287			1.20697			0.603485	+	0.797374i	$0.293778\pi$
$548$		0			0
$549$	−2.50184	−	4.33331i	−0.106776	−	0.184941i
$550$		0			0
$551$	4.76498	−	8.25319i	0.202995	−	0.351598i
$552$		0			0
$553$	−20.6275	+	11.4275i	−0.877171	+	0.485947i
$554$		0			0
$555$	11.2831	−	19.5429i	0.478941	−	0.829551i
$556$		0			0
$557$	−29.9378	+	17.2846i	−1.26850	+	0.732371i	−0.974705	−	0.223496i	$-0.928253\pi$
$557$	−29.9378	+	17.2846i	−1.26850	+	0.732371i	−0.293799	+	0.955867i	$0.594920\pi$
$558$		0			0
$559$	−19.4803			−0.823929
$560$		0			0
$561$	−2.58186			−0.109006
$562$		0			0
$563$	10.1504	−	5.86033i	0.427788	−	0.246983i	−0.270616	−	0.962687i	$-0.587227\pi$
$563$	10.1504	−	5.86033i	0.427788	−	0.246983i	0.698404	+	0.715704i	$0.253894\pi$
$564$		0			0
$565$	0.378513	−	0.655603i	0.0159242	−	0.0275814i
$566$		0			0
$567$	−2.64534	−	0.0468128i	−0.111094	−	0.00196595i
$568$		0			0
$569$	5.55324	−	9.61849i	0.232804	−	0.403228i	−0.725828	−	0.687876i	$-0.758543\pi$
$569$	5.55324	−	9.61849i	0.232804	−	0.403228i	0.958632	+	0.284648i	$0.0918766\pi$
$570$		0			0
$571$	−17.7557	−	30.7537i	−0.743052	−	1.28700i	−0.951099	−	0.308885i	$-0.900044\pi$
$571$	−17.7557	−	30.7537i	−0.743052	−	1.28700i	0.208047	−	0.978119i	$-0.433289\pi$
$572$		0			0
$573$	11.7909			0.492573
$574$		0			0
$575$		−	6.47756i		−	0.270133i
$576$		0			0
$577$	−23.4304	+	13.5276i	−0.975421	+	0.563159i	−0.900885	−	0.434059i	$-0.857081\pi$
$577$	−23.4304	+	13.5276i	−0.975421	+	0.563159i	−0.0745363	+	0.997218i	$0.523748\pi$
$578$		0			0
$579$	23.2289	+	13.4112i	0.965361	+	0.557351i
$580$		0			0
$581$	4.45023	+	2.67543i	0.184627	+	0.110995i
$582$		0			0
$583$	−30.7152	−	17.7334i	−1.27209	−	0.734443i
$584$		0			0
$585$	6.64834	+	11.5153i	0.274875	+	0.476097i
$586$		0			0
$587$		−	35.3797i		−	1.46027i	−0.683300	−	0.730137i	$-0.739456\pi$
$587$		−	35.3797i		−	1.46027i	0.683300	−	0.730137i	$-0.260544\pi$
$588$		0			0
$589$			22.1906i			0.914347i
$590$		0			0
$591$	−8.29208	−	14.3623i	−0.341091	−	0.590786i
$592$		0			0
$593$	−33.9659	−	19.6102i	−1.39481	−	0.805294i	−0.400968	−	0.916092i	$-0.631326\pi$
$593$	−33.9659	−	19.6102i	−1.39481	−	0.805294i	−0.993843	+	0.110798i	$0.964659\pi$
$594$		0			0
$595$	−2.58160	−	1.55203i	−0.105835	−	0.0636271i
$596$		0			0
$597$	−9.87996	−	5.70420i	−0.404360	−	0.233457i
$598$		0			0
$599$	−41.2853	+	23.8361i	−1.68687	+	0.973916i	−0.729982	+	0.683466i	$0.760472\pi$
$599$	−41.2853	+	23.8361i	−1.68687	+	0.973916i	−0.956890	+	0.290450i	$0.906195\pi$
$600$		0			0
$601$			13.4207i			0.547442i	0.961809	+	0.273721i	$0.0882544\pi$
$601$			13.4207i			0.547442i	−0.961809	+	0.273721i	$0.911746\pi$
$602$		0			0
$603$	−9.30266			−0.378834
$604$		0			0
$605$	−26.5558	−	45.9960i	−1.07965	−	1.87000i
$606$		0			0
$607$	−19.1391	+	33.1498i	−0.776831	+	1.34551i	0.156929	+	0.987610i	$0.449841\pi$
$607$	−19.1391	+	33.1498i	−0.776831	+	1.34551i	−0.933760	+	0.357901i	$0.883493\pi$
$608$		0			0
$609$	6.82397	+	0.120759i	0.276521	+	0.00489342i
$610$		0			0
$611$	−2.54374	+	4.40588i	−0.102909	+	0.178243i
$612$		0			0
$613$	−16.9225	+	9.77021i	−0.683493	+	0.394615i	−0.801170	−	0.598437i	$-0.795789\pi$
$613$	−16.9225	+	9.77021i	−0.683493	+	0.394615i	0.117677	+	0.993052i	$0.462455\pi$
$614$		0			0
$615$	−11.6563			−0.470028
$616$		0			0
$617$	−1.16195			−0.0467785			−0.0233892	−	0.999726i	$-0.507446\pi$
$617$	−1.16195			−0.0467785			−0.0233892	+	0.999726i	$0.507446\pi$
$618$		0			0
$619$	−31.0842	+	17.9465i	−1.24938	+	0.721330i	−0.970986	−	0.239137i	$-0.923136\pi$
$619$	−31.0842	+	17.9465i	−1.24938	+	0.721330i	−0.278394	+	0.960467i	$0.589802\pi$
$620$		0			0
$621$	−2.56022	+	4.43443i	−0.102738	+	0.177947i
$622$		0			0
$623$	15.8033	−	8.75495i	0.633147	−	0.350759i
$624$		0			0
$625$	14.8624	−	25.7425i	0.594498	−	1.02970i
$626$		0			0
$627$	10.4848	+	18.1603i	0.418724	+	0.725252i
$628$		0			0
$629$	−4.10084			−0.163511
$630$		0			0
$631$		−	8.26460i		−	0.329008i	−0.986376	−	0.164504i	$-0.947398\pi$
$631$		−	8.26460i		−	0.329008i	0.986376	−	0.164504i	$-0.0526024\pi$
$632$		0			0
$633$	−3.57928	+	2.06650i	−0.142264	+	0.0821360i
$634$		0			0
$635$	13.8677	+	8.00650i	0.550322	+	0.317728i
$636$		0			0
$637$	−17.4419	−	32.8417i	−0.691074	−	1.30123i
$638$		0			0
$639$	6.36736	+	3.67620i	0.251889	+	0.145428i
$640$		0			0
$641$	−14.4955	−	25.1070i	−0.572539	−	0.991666i	−0.996304	−	0.0858940i	$-0.972625\pi$
$641$	−14.4955	−	25.1070i	−0.572539	−	0.991666i	0.423766	−	0.905772i	$-0.360708\pi$
$642$		0			0
$643$			39.1239i			1.54289i	0.636293	+	0.771447i	$0.280467\pi$
$643$			39.1239i			1.54289i	−0.636293	+	0.771447i	$0.719533\pi$
$644$		0			0
$645$			9.17860i			0.361407i
$646$		0			0
$647$	6.09491	+	10.5567i	0.239616	+	0.415027i	0.960604	−	0.277921i	$-0.0896452\pi$
$647$	6.09491	+	10.5567i	0.239616	+	0.415027i	−0.720988	+	0.692947i	$0.756312\pi$
$648$		0			0
$649$	−49.7577	−	28.7276i	−1.95316	−	1.12766i
$650$		0			0
$651$	−13.9014	+	7.70131i	−0.544840	+	0.301838i
$652$		0			0
$653$	−8.80194	−	5.08180i	−0.344446	−	0.198866i	0.317790	−	0.948161i	$-0.397059\pi$
$653$	−8.80194	−	5.08180i	−0.344446	−	0.198866i	−0.662237	+	0.749295i	$0.730393\pi$
$654$		0			0
$655$	−31.4368	+	18.1500i	−1.22834	+	0.709181i
$656$		0			0
$657$		−	6.85362i		−	0.267385i
$658$		0			0
$659$	8.28558			0.322760			0.161380	−	0.986892i	$-0.448405\pi$
$659$	8.28558			0.322760			0.161380	+	0.986892i	$0.448405\pi$
$660$		0			0
$661$	−8.30890	−	14.3914i	−0.323179	−	0.559762i	0.657963	−	0.753050i	$-0.271418\pi$
$661$	−8.30890	−	14.3914i	−0.323179	−	0.559762i	−0.981142	+	0.193288i	$0.938085\pi$
$662$		0			0
$663$	1.20817	−	2.09261i	0.0469213	−	0.0812701i
$664$		0			0
$665$	−0.432875	+	24.4612i	−0.0167862	+	0.948566i
$666$		0			0
$667$	6.60439	−	11.4391i	0.255723	−	0.442925i
$668$		0			0
$669$	15.6805	−	9.05316i	0.606245	−	0.350016i
$670$		0			0
$671$	−28.4018			−1.09644
$672$		0			0
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$		0			0
$675$	1.09556	−	0.632521i	0.0421680	−	0.0243457i
$676$		0			0
$677$	10.2201	−	17.7017i	0.392790	−	0.680332i	−0.600026	−	0.799980i	$-0.704843\pi$
$677$	10.2201	−	17.7017i	0.392790	−	0.680332i	0.992816	+	0.119648i	$0.0381766\pi$
$678$		0			0
$679$	−8.41863	−	5.06119i	−0.323077	−	0.194231i
$680$		0			0
$681$	3.96260	−	6.86343i	0.151847	−	0.263007i
$682$		0			0
$683$	−7.87273	−	13.6360i	−0.301242	−	0.521766i	0.675176	−	0.737657i	$-0.264068\pi$
$683$	−7.87273	−	13.6360i	−0.301242	−	0.521766i	−0.976418	+	0.215891i	$0.930734\pi$
$684$		0			0
$685$	3.08150			0.117738
$686$		0			0
$687$		−	2.15573i		−	0.0822464i
$688$		0			0
$689$	28.7460	−	16.5965i	1.09514	−	0.632277i
$690$		0			0
$691$	−2.76346	−	1.59549i	−0.105127	−	0.0606952i	0.446515	−	0.894776i	$-0.352665\pi$
$691$	−2.76346	−	1.59549i	−0.105127	−	0.0606952i	−0.551642	+	0.834081i	$0.685998\pi$
$692$		0			0
$693$	−7.73783	+	12.8709i	−0.293936	+	0.488924i
$694$		0			0
$695$	−34.2033	−	19.7473i	−1.29740	−	0.749057i
$696$		0			0
$697$	1.05912	+	1.83445i	0.0401170	+	0.0694847i
$698$		0			0
$699$			20.0144i			0.757015i
$700$		0			0
$701$		−	39.2121i		−	1.48102i	−0.672045	−	0.740511i	$-0.734584\pi$
$701$		−	39.2121i		−	1.48102i	0.672045	−	0.740511i	$-0.265416\pi$
$702$		0			0
$703$	16.6534	+	28.8445i	0.628094	+	1.08789i
$704$		0			0
$705$	2.07594	+	1.19854i	0.0781843	+	0.0451397i
$706$		0			0
$707$	−15.0296	−	0.265969i	−0.565246	−	0.0100028i
$708$		0			0
$709$	−33.3653	−	19.2635i	−1.25306	−	0.723454i	−0.281343	−	0.959607i	$-0.590780\pi$
$709$	−33.3653	−	19.2635i	−1.25306	−	0.723454i	−0.971716	+	0.236153i	$0.924113\pi$
$710$		0			0
$711$	−7.71882	+	4.45646i	−0.289478	+	0.167130i
$712$		0			0
$713$			30.7567i			1.15185i
$714$		0			0
$715$	75.4744			2.82258
$716$		0			0
$717$	−9.44616	−	16.3612i	−0.352773	−	0.611021i
$718$		0			0
$719$	11.5009	−	19.9202i	0.428912	−	0.742897i	−0.567865	−	0.823122i	$-0.692230\pi$
$719$	11.5009	−	19.9202i	0.428912	−	0.742897i	0.996777	+	0.0802246i	$0.0255637\pi$
$720$		0			0
$721$	−7.57341	−	13.6706i	−0.282049	−	0.509119i
$722$		0			0
$723$	9.15417	−	15.8555i	0.340447	−	0.589672i
$724$		0			0
$725$	−2.82613	+	1.63166i	−0.104960	+	0.0605985i
$726$		0			0
$727$	21.8433			0.810125			0.405062	−	0.914289i	$-0.367250\pi$
$727$	21.8433			0.810125			0.405062	+	0.914289i	$0.367250\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.44451	−	0.833989i	0.0534272	−	0.0308462i
$732$		0			0
$733$	24.0681	−	41.6871i	0.888974	−	1.53975i	0.0478850	−	0.998853i	$-0.484752\pi$
$733$	24.0681	−	41.6871i	0.888974	−	1.53975i	0.841089	−	0.540896i	$-0.181915\pi$
$734$		0			0
$735$	−15.4741	+	8.21817i	−0.570772	+	0.303132i
$736$		0			0
$737$	−26.4018	+	45.7293i	−0.972524	+	1.68446i
$738$		0			0
$739$	−3.23455	−	5.60241i	−0.118985	−	0.206088i	0.800381	−	0.599492i	$-0.204631\pi$
$739$	−3.23455	−	5.60241i	−0.118985	−	0.206088i	−0.919366	+	0.393404i	$0.871297\pi$
$740$		0			0
$741$	−19.6253			−0.720953
$742$		0			0
$743$			16.6709i			0.611597i	0.952096	+	0.305798i	$0.0989234\pi$
$743$			16.6709i			0.611597i	−0.952096	+	0.305798i	$0.901077\pi$
$744$		0			0
$745$	−12.9097	+	7.45340i	−0.472974	+	0.273072i
$746$		0			0
$747$	1.69966	+	0.981297i	0.0621872	+	0.0359038i
$748$		0			0
$749$	13.6686	+	24.6729i	0.499441	+	0.901528i
$750$		0			0
$751$	21.2698	+	12.2801i	0.776145	+	0.448108i	0.835062	−	0.550155i	$-0.185431\pi$
$751$	21.2698	+	12.2801i	0.776145	+	0.448108i	−0.0589171	+	0.998263i	$0.518765\pi$
$752$		0			0
$753$	−1.71626	−	2.97264i	−0.0625439	−	0.108329i
$754$		0			0
$755$			8.99223i			0.327261i
$756$		0			0
$757$			2.80888i			0.102091i	0.998696	+	0.0510453i	$0.0162553\pi$
$757$			2.80888i			0.102091i	−0.998696	+	0.0510453i	$0.983745\pi$
$758$		0			0
$759$	14.5323	+	25.1706i	0.527488	+	0.913636i
$760$		0			0
$761$	−17.4708	−	10.0868i	−0.633317	−	0.365646i	0.148718	−	0.988880i	$-0.452485\pi$
$761$	−17.4708	−	10.0868i	−0.633317	−	0.365646i	−0.782036	+	0.623234i	$0.785819\pi$
$762$		0			0
$763$	−0.148823	+	8.40982i	−0.00538776	+	0.304456i
$764$		0			0
$765$	−0.985981	−	0.569256i	−0.0356482	−	0.0205815i
$766$		0			0
$767$	46.5677	−	26.8859i	1.68146	−	0.970792i
$768$		0			0
$769$			32.1388i			1.15895i	0.814988	+	0.579477i	$0.196743\pi$
$769$			32.1388i			1.15895i	−0.814988	+	0.579477i	$0.803257\pi$
$770$		0			0
$771$	−25.0690			−0.902840
$772$		0			0
$773$	11.2931	+	19.5603i	0.406186	+	0.703534i	0.994459	−	0.105128i	$-0.0335253\pi$
$773$	11.2931	+	19.5603i	0.406186	+	0.703534i	−0.588273	+	0.808662i	$0.700192\pi$
$774$		0			0
$775$	3.79934	−	6.58065i	0.136476	−	0.236384i
$776$		0			0
$777$	−12.2902	+	20.4432i	−0.440909	+	0.733395i
$778$		0			0
$779$	8.60209	−	14.8993i	0.308202	−	0.533822i
$780$		0			0
$781$	36.1423	−	20.8668i	1.29327	−	0.746673i
$782$		0			0
$783$	2.57962			0.0921882
$784$		0			0
$785$	−2.46177			−0.0878642
$786$		0			0
$787$	29.2593	−	16.8929i	1.04298	−	0.602166i	0.122306	−	0.992492i	$-0.460971\pi$
$787$	29.2593	−	16.8929i	1.04298	−	0.602166i	0.920677	+	0.390326i	$0.127638\pi$
$788$		0			0
$789$	−7.75460	+	13.4314i	−0.276071	+	0.478169i
$790$		0			0
$791$	−0.412298	+	0.685804i	−0.0146596	+	0.0243844i
$792$		0			0
$793$	13.2905	−	23.0197i	0.471958	−	0.817455i
$794$		0			0
$795$	−7.81984	−	13.5444i	−0.277341	−	0.480369i
$796$		0			0
$797$	−27.0472			−0.958061			−0.479030	−	0.877798i	$-0.659012\pi$
$797$	−27.0472			−0.958061			−0.479030	+	0.877798i	$0.659012\pi$
$798$		0			0
$799$		−	0.435609i		−	0.0154108i
$800$		0			0
$801$	5.91361	−	3.41423i	0.208947	−	0.120636i
$802$		0			0
$803$	−33.6905	−	19.4512i	−1.18891	−	0.686418i
$804$		0			0
$805$	−0.599976	+	33.9039i	−0.0211464	+	1.19496i
$806$		0			0
$807$	−20.5537	−	11.8667i	−0.723523	−	0.417726i
$808$		0			0
$809$	24.9224	+	43.1669i	0.876226	+	1.51767i	0.855451	+	0.517884i	$0.173280\pi$
$809$	24.9224	+	43.1669i	0.876226	+	1.51767i	0.0207751	+	0.999784i	$0.493387\pi$
$810$		0			0
$811$			36.5330i			1.28285i	0.767188	+	0.641423i	$0.221655\pi$
$811$			36.5330i			1.28285i	−0.767188	+	0.641423i	$0.778345\pi$
$812$		0			0
$813$			14.7137i			0.516031i
$814$		0			0
$815$	3.15588	+	5.46614i	0.110546	+	0.191470i
$816$		0			0
$817$	−11.7322	−	6.77360i	−0.410459	−	0.236978i
$818$		0			0
$819$	−6.81102	−	12.2944i	−0.237996	−	0.429601i
$820$		0			0
$821$	2.59911	+	1.50060i	0.0907095	+	0.0523711i	0.544669	−	0.838651i	$-0.316655\pi$
$821$	2.59911	+	1.50060i	0.0907095	+	0.0523711i	−0.453959	+	0.891023i	$0.649989\pi$
$822$		0			0
$823$	13.8543	−	7.99877i	0.482930	−	0.278820i	−0.238707	−	0.971092i	$-0.576723\pi$
$823$	13.8543	−	7.99877i	0.482930	−	0.278820i	0.721637	+	0.692272i	$0.243390\pi$
$824$		0			0
$825$		−	7.18061i		−	0.249997i
$826$		0			0
$827$	−4.57856			−0.159212			−0.0796060	−	0.996826i	$-0.525366\pi$
$827$	−4.57856			−0.159212			−0.0796060	+	0.996826i	$0.525366\pi$
$828$		0			0
$829$	1.53077	+	2.65136i	0.0531657	+	0.0920857i	0.891383	−	0.453250i	$-0.149736\pi$
$829$	1.53077	+	2.65136i	0.0531657	+	0.0920857i	−0.838218	+	0.545336i	$0.816402\pi$
$830$		0			0
$831$	3.56123	−	6.16822i	0.123538	−	0.213973i
$832$		0			0
$833$	2.69938	+	1.68857i	0.0935279	+	0.0585054i
$834$		0			0
$835$	6.58581	−	11.4070i	0.227911	−	0.394754i
$836$		0			0
$837$	−5.20192	+	3.00333i	−0.179805	+	0.103810i
$838$		0			0
$839$	−39.0864			−1.34941			−0.674706	−	0.738087i	$-0.735730\pi$
$839$	−39.0864			−1.34941			−0.674706	+	0.738087i	$0.735730\pi$
$840$		0			0
$841$	22.3456			0.770536
$842$		0			0
$843$	11.3069	−	6.52804i	0.389430	−	0.224838i
$844$		0			0
$845$	−19.0483	+	32.9926i	−0.655281	+	1.13498i
$846$		0			0
$847$	27.2056	+	49.1081i	0.934795	+	1.68738i
$848$		0			0
$849$	−1.05685	+	1.83051i	−0.0362709	+	0.0628230i
$850$		0			0
$851$	23.0820	+	39.9792i	0.791241	+	1.37047i
$852$		0			0
$853$	26.4897			0.906989			0.453495	−	0.891259i	$-0.350177\pi$
$853$	26.4897			0.906989			0.453495	+	0.891259i	$0.350177\pi$
$854$		0			0
$855$			9.24692i			0.316238i
$856$		0			0
$857$	38.9066	−	22.4627i	1.32902	−	0.767312i	0.343875	−	0.939015i	$-0.388260\pi$
$857$	38.9066	−	22.4627i	1.32902	−	0.767312i	0.985149	+	0.171703i	$0.0549269\pi$
$858$		0			0
$859$	−30.6621	−	17.7028i	−1.04618	−	0.604011i	−0.124601	−	0.992207i	$-0.539765\pi$
$859$	−30.6621	−	17.7028i	−1.04618	−	0.604011i	−0.921577	+	0.388196i	$0.873098\pi$
$860$		0			0
$861$	12.3191	+	0.218004i	0.419835	+	0.00742955i
$862$		0			0
$863$	2.40437	+	1.38816i	0.0818456	+	0.0472536i	0.540364	−	0.841431i	$-0.318286\pi$
$863$	2.40437	+	1.38816i	0.0818456	+	0.0472536i	−0.458519	+	0.888685i	$0.651620\pi$
$864$		0			0
$865$	0.179745	+	0.311328i	0.00611151	+	0.0105855i
$866$		0			0
$867$		−	16.7931i		−	0.570324i
$868$		0			0
$869$			50.5915i			1.71620i
$870$		0			0
$871$	−24.7092	−	42.7976i	−0.837239	−	1.45014i
$872$		0			0
$873$	−3.21529	−	1.85635i	−0.108821	−	0.0628279i
$874$		0			0
$875$	−12.7441	+	21.1982i	−0.430830	+	0.716631i
$876$		0			0
$877$	14.3264	+	8.27135i	0.483768	+	0.279304i	0.721986	−	0.691908i	$-0.243230\pi$
$877$	14.3264	+	8.27135i	0.483768	+	0.279304i	−0.238217	+	0.971212i	$0.576563\pi$
$878$		0			0
$879$	0.289254	−	0.167001i	0.00975630	−	0.00563280i
$880$		0			0
$881$		−	24.6158i		−	0.829327i	−0.909975	−	0.414664i	$-0.863899\pi$
$881$		−	24.6158i		−	0.829327i	0.909975	−	0.414664i	$-0.136101\pi$
$882$		0			0
$883$	−40.4623			−1.36167			−0.680833	−	0.732439i	$-0.738382\pi$
$883$	−40.4623			−1.36167			−0.680833	+	0.732439i	$0.738382\pi$
$884$		0			0
$885$	−12.6679	−	21.9415i	−0.425827	−	0.737554i
$886$		0			0
$887$	4.64231	−	8.04072i	0.155873	−	0.269981i	−0.777503	−	0.628879i	$-0.783514\pi$
$887$	4.64231	−	8.04072i	0.155873	−	0.269981i	0.933377	+	0.358898i	$0.116847\pi$
$888$		0			0
$889$	−14.5065	−	8.72114i	−0.486532	−	0.292498i
$890$		0			0
$891$	−2.83809	+	4.91572i	−0.0950797	+	0.164683i
$892$		0			0
$893$	−3.06399	+	1.76900i	−0.102533	+	0.0591972i
$894$		0			0
$895$	47.3688			1.58337
$896$		0			0
$897$	−27.2012			−0.908221
$898$		0			0
$899$	13.4190	−	7.74746i	0.447548	−	0.258392i
$900$		0			0
$901$	−1.42106	+	2.46134i	−0.0473423	+	0.0819993i
$902$		0			0
$903$	0.171664	−	9.70053i	0.00571262	−	0.322813i
$904$		0			0
$905$	27.8159	−	48.1786i	0.924632	−	1.60151i
$906$		0			0
$907$	2.55327	+	4.42240i	0.0847800	+	0.146843i	0.905297	−	0.424778i	$-0.139648\pi$
$907$	2.55327	+	4.42240i	0.0847800	+	0.146843i	−0.820517	+	0.571621i	$0.806315\pi$
$908$		0			0
$909$	−5.68155			−0.188445
$910$		0			0
$911$			36.3702i			1.20500i	0.798119	+	0.602500i	$0.205829\pi$
$911$			36.3702i			1.20500i	−0.798119	+	0.602500i	$0.794171\pi$
$912$		0			0
$913$	9.64757	−	5.57003i	0.319288	−	0.184341i
$914$		0			0
$915$	−10.8463	−	6.26211i	−0.358567	−	0.207019i
$916$		0			0
$917$	33.5639	−	18.5942i	1.10838	−	0.614034i
$918$		0			0
$919$	40.4248	+	23.3393i	1.33349	+	0.769892i	0.985833	−	0.167729i	$-0.0536433\pi$
$919$	40.4248	+	23.3393i	1.33349	+	0.769892i	0.347659	+	0.937621i	$0.386977\pi$
$920$		0			0
$921$	4.69571	+	8.13320i	0.154729	+	0.267998i
$922$		0			0
$923$			39.0580i			1.28561i
$924$		0			0
$925$		−	11.4052i		−	0.375000i
$926$		0			0
$927$	−2.95345	−	5.11553i	−0.0970042	−	0.168016i
$928$		0			0
$929$	33.8671	+	19.5532i	1.11114	+	0.641518i	0.939125	−	0.343576i	$-0.111638\pi$
$929$	33.8671	+	19.5532i	1.11114	+	0.641518i	0.172017	+	0.985094i	$0.444972\pi$
$930$		0			0
$931$	0.914979	−	25.8441i	0.0299872	−	0.847006i
$932$		0			0
$933$	−13.7482	−	7.93750i	−0.450095	−	0.259862i
$934$		0			0
$935$	−5.59661	+	3.23121i	−0.183029	+	0.105672i
$936$		0			0
$937$			14.4038i			0.470551i	0.971929	+	0.235275i	$0.0755992\pi$
$937$			14.4038i			0.470551i	−0.971929	+	0.235275i	$0.924401\pi$
$938$		0			0
$939$	32.1656			1.04969
$940$		0			0
$941$	13.1269	+	22.7364i	0.427924	+	0.741186i	0.996688	−	0.0813146i	$-0.0259118\pi$
$941$	13.1269	+	22.7364i	0.427924	+	0.741186i	−0.568765	+	0.822500i	$0.692579\pi$
$942$		0			0
$943$	11.9227	−	20.6508i	0.388257	−	0.672482i
$944$		0			0
$945$	−5.79280	+	3.20917i	−0.188440	+	0.104394i
$946$		0			0
$947$	7.85354	−	13.6027i	0.255206	−	0.442030i	−0.709746	−	0.704458i	$-0.751190\pi$
$947$	7.85354	−	13.6027i	0.255206	−	0.442030i	0.964951	+	0.262429i	$0.0845234\pi$
$948$		0			0
$949$	31.5306	−	18.2042i	1.02353	−	0.590933i
$950$		0			0
$951$	15.2712			0.495201
$952$		0			0
$953$	42.8466			1.38794			0.693968	−	0.720006i	$-0.255861\pi$
$953$	42.8466			1.38794			0.693968	+	0.720006i	$0.255861\pi$
$954$		0			0
$955$	25.5588	−	14.7564i	0.827064	−	0.477506i
$956$		0			0
$957$	7.32121	−	12.6807i	0.236661	−	0.409909i
$958$		0			0
$959$	−3.25672	−	0.0576322i	−0.105165	−	0.00186104i
$960$		0			0
$961$	−2.53999	+	4.39939i	−0.0819352	+	0.141916i
$962$		0			0
$963$	5.33045	+	9.23261i	0.171771	+	0.297517i
$964$		0			0
$965$	67.1368			2.16121
$966$		0			0
$967$			0.672082i			0.0216127i	0.999942	+	0.0108063i	$0.00343983\pi$
$967$			0.672082i			0.0216127i	−0.999942	+	0.0108063i	$0.996560\pi$
$968$		0			0
$969$	1.45526	−	0.840197i	0.0467498	−	0.0269910i
$970$		0			0
$971$	6.45838	+	3.72875i	0.207259	+	0.119661i	0.600037	−	0.799972i	$-0.295153\pi$
$971$	6.45838	+	3.72875i	0.207259	+	0.119661i	−0.392778	+	0.919633i	$0.628486\pi$
$972$		0			0
$973$	35.7789	+	21.5099i	1.14702	+	0.689575i
$974$		0			0
$975$	5.81991	+	3.36013i	0.186386	+	0.107610i
$976$		0			0
$977$	−8.78701	−	15.2195i	−0.281121	−	0.486916i	0.690540	−	0.723294i	$-0.257373\pi$
$977$	−8.78701	−	15.2195i	−0.281121	−	0.486916i	−0.971661	+	0.236378i	$0.924040\pi$
$978$		0			0
$979$		−	38.7596i		−	1.23876i
$980$		0			0
$981$			3.17911i			0.101501i
$982$		0			0
$983$	−21.3661	−	37.0072i	−0.681472	−	1.18034i	−0.974532	−	0.224250i	$-0.928007\pi$
$983$	−21.3661	−	37.0072i	−0.681472	−	1.18034i	0.293059	−	0.956094i	$-0.405327\pi$
$984$		0			0
$985$	−35.9489	−	20.7551i	−1.14543	−	0.661313i
$986$		0			0
$987$	−2.17157	−	1.30552i	−0.0691217	−	0.0415552i
$988$		0			0
$989$	−16.2612	−	9.38839i	−0.517075	−	0.298533i
$990$		0			0
$991$	39.3373	−	22.7114i	1.24959	−	0.721451i	0.278563	−	0.960418i	$-0.410142\pi$
$991$	39.3373	−	22.7114i	1.24959	−	0.721451i	0.971028	+	0.238967i	$0.0768087\pi$
$992$		0			0
$993$		−	21.0379i		−	0.667617i
$994$		0			0
$995$	−28.5553			−0.905264
$996$		0			0
$997$	21.8718	+	37.8831i	0.692687	+	1.19977i	0.970954	+	0.239265i	$0.0769065\pi$
$997$	21.8718	+	37.8831i	0.692687	+	1.19977i	−0.278268	+	0.960504i	$0.589760\pi$
$998$		0			0
$999$	−4.50782	+	7.80778i	−0.142621	+	0.247027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.271.2		32
3.2	odd	2		2016.2.bs.c.271.13		32
4.3	odd	2		168.2.t.a.19.4	✓	32
7.2	even	3		4704.2.p.a.3919.1		32
7.3	odd	6	inner	672.2.bb.a.367.7		32
7.5	odd	6		4704.2.p.a.3919.16		32
8.3	odd	2	inner	672.2.bb.a.271.7		32
8.5	even	2		168.2.t.a.19.8	yes	32
12.11	even	2		504.2.bk.c.19.13		32
21.17	even	6		2016.2.bs.c.1711.4		32
24.5	odd	2		504.2.bk.c.19.9		32
24.11	even	2		2016.2.bs.c.271.4		32
28.3	even	6		168.2.t.a.115.8	yes	32
28.19	even	6		1176.2.p.a.979.28		32
28.23	odd	6		1176.2.p.a.979.27		32
56.3	even	6	inner	672.2.bb.a.367.2		32
56.5	odd	6		1176.2.p.a.979.25		32
56.19	even	6		4704.2.p.a.3919.2		32
56.37	even	6		1176.2.p.a.979.26		32
56.45	odd	6		168.2.t.a.115.4	yes	32
56.51	odd	6		4704.2.p.a.3919.15		32
84.59	odd	6		504.2.bk.c.451.9		32
168.59	odd	6		2016.2.bs.c.1711.13		32
168.101	even	6		504.2.bk.c.451.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	4.3	odd	2
168.2.t.a.19.8	yes	32	8.5	even	2
168.2.t.a.115.4	yes	32	56.45	odd	6
168.2.t.a.115.8	yes	32	28.3	even	6
504.2.bk.c.19.9		32	24.5	odd	2
504.2.bk.c.19.13		32	12.11	even	2
504.2.bk.c.451.9		32	84.59	odd	6
504.2.bk.c.451.13		32	168.101	even	6
672.2.bb.a.271.2		32	1.1	even	1	trivial
672.2.bb.a.271.7		32	8.3	odd	2	inner
672.2.bb.a.367.2		32	56.3	even	6	inner
672.2.bb.a.367.7		32	7.3	odd	6	inner
1176.2.p.a.979.25		32	56.5	odd	6
1176.2.p.a.979.26		32	56.37	even	6
1176.2.p.a.979.27		32	28.23	odd	6
1176.2.p.a.979.28		32	28.19	even	6
2016.2.bs.c.271.4		32	24.11	even	2
2016.2.bs.c.271.13		32	3.2	odd	2
2016.2.bs.c.1711.4		32	21.17	even	6
2016.2.bs.c.1711.13		32	168.59	odd	6
4704.2.p.a.3919.1		32	7.2	even	3
4704.2.p.a.3919.2		32	56.19	even	6
4704.2.p.a.3919.15		32	56.51	odd	6
4704.2.p.a.3919.16		32	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.83809 - 4.91572i) q^{11} +5.31228 q^{13} -2.50301i q^{15} +(-0.393919 + 0.227429i) q^{17} +(3.19938 + 1.84716i) q^{19} +(-0.0468128 + 2.64534i) q^{21} +(4.43443 + 2.56022i) q^{23} +(-0.632521 - 1.09556i) q^{25} +1.00000i q^{27} -2.57962i q^{29} +(3.00333 + 5.20192i) q^{31} +(4.91572 + 2.83809i) q^{33} +(3.20917 + 5.79280i) q^{35} +(7.80778 + 4.50782i) q^{37} +(-4.60057 + 2.65614i) q^{39} -4.65692i q^{41} -3.66703 q^{43} +(1.25150 + 2.16767i) q^{45} +(-0.478841 + 0.829377i) q^{47} +(-3.28332 - 6.18222i) q^{49} +(0.227429 - 0.393919i) q^{51} +(5.41124 - 3.12418i) q^{53} +14.2075 q^{55} -3.69433 q^{57} +(8.76604 - 5.06108i) q^{59} +(2.50184 - 4.33331i) q^{61} +(-1.28213 - 2.31434i) q^{63} +(-6.64834 + 11.5153i) q^{65} +(-4.65133 - 8.05634i) q^{67} -5.12043 q^{69} +7.35240i q^{71} +(5.93541 - 3.42681i) q^{73} +(1.09556 + 0.632521i) q^{75} +(-15.0154 - 0.265718i) q^{77} +(-7.71882 - 4.45646i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.96259i q^{83} -1.13851i q^{85} +(1.28981 + 2.23402i) q^{87} +(5.91361 + 3.41423i) q^{89} +(7.24175 - 12.0457i) q^{91} +(-5.20192 - 3.00333i) q^{93} +(-8.00807 + 4.62346i) q^{95} -3.71270i q^{97} -5.67619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

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