LMFDB - Embedded newform 784.2.bb.b.111.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.6
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.977383 - 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(1.48039 + 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +O(q^{10})$	\(q+(-0.977383 - 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(1.48039 + 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +(-5.53257 + 1.26277i) q^{11} +(0.517931 - 0.118214i) q^{13} +(0.918900 + 0.209733i) q^{15} +(0.00663338 - 0.0137744i) q^{17} -4.54052 q^{19} +(1.24060 - 3.95759i) q^{21} +(0.102508 + 0.212861i) q^{23} +(-1.03216 + 4.52219i) q^{25} +(-5.00346 + 2.40954i) q^{27} +(-3.07949 - 1.48300i) q^{29} -5.84992 q^{31} +(6.95509 + 5.54650i) q^{33} +(-1.51794 - 0.475836i) q^{35} +(5.35144 + 2.57712i) q^{37} +(-0.651100 - 0.519235i) q^{39} +(1.23297 - 0.983262i) q^{41} +(5.47172 + 4.36355i) q^{43} +(0.141559 + 0.293950i) q^{45} +(-0.699308 - 3.06387i) q^{47} +(-2.61688 + 6.49245i) q^{49} +(-0.0233652 + 0.00533296i) q^{51} +(-10.7318 + 5.16818i) q^{53} +(2.12738 - 2.66764i) q^{55} +(4.43782 + 5.56486i) q^{57} +(-6.17584 + 7.74426i) q^{59} +(-3.48363 + 7.23382i) q^{61} +(1.33881 - 0.518390i) q^{63} +(-0.199154 + 0.249731i) q^{65} +5.76147i q^{67} +(0.160692 - 0.333681i) q^{69} +(1.23326 + 2.56090i) q^{71} +(3.26962 + 0.746269i) q^{73} +(6.55121 - 3.15490i) q^{75} +(-10.9594 - 10.2625i) q^{77} +7.84700i q^{79} +(6.37675 + 3.07088i) q^{81} +(3.22440 - 14.1270i) q^{83} +(0.00204547 + 0.00896179i) q^{85} +(1.19227 + 5.22368i) q^{87} +(-4.67524 - 1.06709i) q^{89} +(1.02596 + 0.960723i) q^{91} +(5.71761 + 7.16966i) q^{93} +(2.13442 - 1.70214i) q^{95} -13.2524i q^{97} +3.07934i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

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
$3$	−0.977383	−	1.22560i	−0.564292	−	0.707600i	0.415053	−	0.909797i	$-0.363763\pi$
$3$	−0.977383	−	1.22560i	−0.564292	−	0.707600i	−0.979345	+	0.202197i	$0.935192\pi$
$4$		0			0
$5$	−0.470082	+	0.374878i	−0.210227	+	0.167650i	−0.722943	−	0.690908i	$-0.757211\pi$
$5$	−0.470082	+	0.374878i	−0.210227	+	0.167650i	0.512716	+	0.858558i	$0.328640\pi$
$6$		0			0
$7$	1.48039	+	2.19281i	0.559536	+	0.828806i
$7$	1.48039	+	2.19281i	0.559536	+	0.828806i
$8$		0			0
$9$	0.120747	−	0.529025i	0.0402488	−	0.176342i
$10$		0			0
$11$	−5.53257	+	1.26277i	−1.66813	+	0.380740i	−0.949282	−	0.314425i	$-0.898188\pi$
$11$	−5.53257	+	1.26277i	−1.66813	+	0.380740i	−0.718850	+	0.695165i	$0.755331\pi$
$12$		0			0
$13$	0.517931	−	0.118214i	0.143648	−	0.0327868i	−0.150092	−	0.988672i	$-0.547957\pi$
$13$	0.517931	−	0.118214i	0.143648	−	0.0327868i	0.293740	+	0.955885i	$0.405100\pi$
$14$		0			0
$15$	0.918900	+	0.209733i	0.237259	+	0.0541528i
$16$		0			0
$17$	0.00663338	−	0.0137744i	0.00160883	−	0.00334077i	−0.900163	−	0.435553i	$-0.856553\pi$
$17$	0.00663338	−	0.0137744i	0.00160883	−	0.00334077i	0.901772	+	0.432213i	$0.142267\pi$
$18$		0			0
$19$	−4.54052			−1.04167			−0.520833	−	0.853658i	$-0.674379\pi$
$19$	−4.54052			−1.04167			−0.520833	+	0.853658i	$0.674379\pi$
$20$		0			0
$21$	1.24060	−	3.95759i	0.270722	−	0.863616i
$22$		0			0
$23$	0.102508	+	0.212861i	0.0213745	+	0.0443846i	0.911383	−	0.411560i	$-0.135016\pi$
$23$	0.102508	+	0.212861i	0.0213745	+	0.0443846i	−0.890008	+	0.455944i	$0.849302\pi$
$24$		0			0
$25$	−1.03216	+	4.52219i	−0.206432	+	0.904439i
$26$		0			0
$27$	−5.00346	+	2.40954i	−0.962917	+	0.463717i
$28$		0			0
$29$	−3.07949	−	1.48300i	−0.571846	−	0.275387i	0.125532	−	0.992090i	$-0.459936\pi$
$29$	−3.07949	−	1.48300i	−0.571846	−	0.275387i	−0.697379	+	0.716703i	$0.745650\pi$
$30$		0			0
$31$	−5.84992			−1.05068			−0.525338	−	0.850893i	$-0.676061\pi$
$31$	−5.84992			−1.05068			−0.525338	+	0.850893i	$0.676061\pi$
$32$		0			0
$33$	6.95509	+	5.54650i	1.21073	+	0.965522i
$34$		0			0
$35$	−1.51794	−	0.475836i	−0.256579	−	0.0804310i
$36$		0			0
$37$	5.35144	+	2.57712i	0.879772	+	0.423676i	0.818541	−	0.574448i	$-0.194783\pi$
$37$	5.35144	+	2.57712i	0.879772	+	0.423676i	0.0612307	+	0.998124i	$0.480497\pi$
$38$		0			0
$39$	−0.651100	−	0.519235i	−0.104259	−	0.0831442i
$40$		0			0
$41$	1.23297	−	0.983262i	0.192558	−	0.153560i	−0.522465	−	0.852661i	$-0.674988\pi$
$41$	1.23297	−	0.983262i	0.192558	−	0.153560i	0.715023	+	0.699101i	$0.246416\pi$
$42$		0			0
$43$	5.47172	+	4.36355i	0.834429	+	0.665435i	0.944508	−	0.328488i	$-0.106539\pi$
$43$	5.47172	+	4.36355i	0.834429	+	0.665435i	−0.110079	+	0.993923i	$0.535110\pi$
$44$		0			0
$45$	0.141559	+	0.293950i	0.0211024	+	0.0438195i
$46$		0			0
$47$	−0.699308	−	3.06387i	−0.102005	−	0.446911i	−0.999976	−	0.00685856i	$-0.997817\pi$
$47$	−0.699308	−	3.06387i	−0.102005	−	0.446911i	0.897972	−	0.440053i	$-0.145040\pi$
$48$		0			0
$49$	−2.61688	+	6.49245i	−0.373839	+	0.927493i
$50$		0			0
$51$	−0.0233652	+	0.00533296i	−0.00327178	+	0.000746763i
$52$		0			0
$53$	−10.7318	+	5.16818i	−1.47413	+	0.709904i	−0.986593	−	0.163198i	$-0.947819\pi$
$53$	−10.7318	+	5.16818i	−1.47413	+	0.709904i	−0.487537	+	0.873102i	$0.662105\pi$
$54$		0			0
$55$	2.12738	−	2.66764i	0.286855	−	0.359705i
$56$		0			0
$57$	4.43782	+	5.56486i	0.587804	+	0.737083i
$58$		0			0
$59$	−6.17584	+	7.74426i	−0.804026	+	1.00822i	0.195595	+	0.980685i	$0.437336\pi$
$59$	−6.17584	+	7.74426i	−0.804026	+	1.00822i	−0.999621	+	0.0275323i	$0.991235\pi$
$60$		0			0
$61$	−3.48363	+	7.23382i	−0.446033	+	0.926196i	0.549826	+	0.835279i	$0.314694\pi$
$61$	−3.48363	+	7.23382i	−0.446033	+	0.926196i	−0.995858	+	0.0909169i	$0.971020\pi$
$62$		0			0
$63$	1.33881	−	0.518390i	0.168674	−	0.0653110i
$64$		0			0
$65$	−0.199154	+	0.249731i	−0.0247020	+	0.0309754i
$66$		0			0
$67$			5.76147i			0.703875i	0.936024	+	0.351937i	$0.114477\pi$
$67$			5.76147i			0.703875i	−0.936024	+	0.351937i	$0.885523\pi$
$68$		0			0
$69$	0.160692	−	0.333681i	0.0193451	−	0.0401705i
$70$		0			0
$71$	1.23326	+	2.56090i	0.146362	+	0.303923i	0.961242	−	0.275706i	$-0.0889117\pi$
$71$	1.23326	+	2.56090i	0.146362	+	0.303923i	−0.814880	+	0.579629i	$0.803197\pi$
$72$		0			0
$73$	3.26962	+	0.746269i	0.382680	+	0.0873442i	0.409533	−	0.912295i	$-0.365692\pi$
$73$	3.26962	+	0.746269i	0.382680	+	0.0873442i	−0.0268533	+	0.999639i	$0.508549\pi$
$74$		0			0
$75$	6.55121	−	3.15490i	0.756469	−	0.364296i
$76$		0			0
$77$	−10.9594	−	10.2625i	−1.24894	−	1.16952i
$78$		0			0
$79$			7.84700i			0.882856i	0.897297	+	0.441428i	$0.145528\pi$
$79$			7.84700i			0.882856i	−0.897297	+	0.441428i	$0.854472\pi$
$80$		0			0
$81$	6.37675	+	3.07088i	0.708528	+	0.341209i
$82$		0			0
$83$	3.22440	−	14.1270i	0.353924	−	1.55064i	−0.414106	−	0.910229i	$-0.635906\pi$
$83$	3.22440	−	14.1270i	0.353924	−	1.55064i	0.768030	−	0.640414i	$-0.221237\pi$
$84$		0			0
$85$	0.00204547	+	0.00896179i	0.000221862	+	0.000972043i
$86$		0			0
$87$	1.19227	+	5.22368i	0.127825	+	0.560037i
$88$		0			0
$89$	−4.67524	−	1.06709i	−0.495575	−	0.113112i	−0.0325735	−	0.999469i	$-0.510370\pi$
$89$	−4.67524	−	1.06709i	−0.495575	−	0.113112i	−0.463001	+	0.886358i	$0.653227\pi$
$90$		0			0
$91$	1.02596	+	0.960723i	0.107550	+	0.100711i
$92$		0			0
$93$	5.71761	+	7.16966i	0.592889	+	0.743459i
$94$		0			0
$95$	2.13442	−	1.70214i	0.218986	−	0.174636i
$96$		0			0
$97$		−	13.2524i		−	1.34558i	−0.739833	−	0.672791i	$-0.765095\pi$
$97$		−	13.2524i		−	1.34558i	0.739833	−	0.672791i	$-0.234905\pi$
$98$		0			0
$99$			3.07934i			0.309486i
$100$		0			0
$101$	10.2089	−	8.14136i	1.01583	−	0.810095i	0.0339137	−	0.999425i	$-0.489203\pi$
$101$	10.2089	−	8.14136i	1.01583	−	0.810095i	0.981914	+	0.189330i	$0.0606314\pi$
$102$		0			0
$103$	−5.97069	−	7.48701i	−0.588310	−	0.737717i	0.395195	−	0.918597i	$-0.370677\pi$
$103$	−5.97069	−	7.48701i	−0.588310	−	0.737717i	−0.983505	+	0.180880i	$0.942105\pi$
$104$		0			0
$105$	0.900427	+	2.32546i	0.0878727	+	0.226942i
$106$		0			0
$107$	−4.83564	−	1.10370i	−0.467479	−	0.106699i	−0.0177083	−	0.999843i	$-0.505637\pi$
$107$	−4.83564	−	1.10370i	−0.467479	−	0.106699i	−0.449770	+	0.893144i	$0.648494\pi$
$108$		0			0
$109$	−4.07697	−	17.8624i	−0.390503	−	1.71090i	−0.662891	−	0.748716i	$-0.730671\pi$
$109$	−4.07697	−	17.8624i	−0.390503	−	1.71090i	0.272388	−	0.962187i	$-0.412187\pi$
$110$		0			0
$111$	−2.07189	−	9.07756i	−0.196655	−	0.861604i
$112$		0			0
$113$	−1.48222	+	6.49402i	−0.139435	+	0.610906i	0.856124	+	0.516770i	$0.172866\pi$
$113$	−1.48222	+	6.49402i	−0.139435	+	0.610906i	−0.995559	+	0.0941358i	$0.969991\pi$
$114$		0			0
$115$	−0.127984	−	0.0616340i	−0.0119346	−	0.00574740i
$116$		0			0
$117$		−	0.288272i		−	0.0266508i
$118$		0			0
$119$	0.0400246	−	0.00584568i	0.00366905	−	0.000535873i
$120$		0			0
$121$	19.1041	−	9.20003i	1.73673	−	0.836367i
$122$		0			0
$123$	−2.41017	−	0.550105i	−0.217318	−	0.0496013i
$124$		0			0
$125$	−2.51445	−	5.22131i	−0.224899	−	0.467008i
$126$		0			0
$127$	0.726717	−	1.50904i	0.0644857	−	0.133906i	−0.866235	−	0.499637i	$-0.833467\pi$
$127$	0.726717	−	1.50904i	0.0644857	−	0.133906i	0.930721	+	0.365731i	$0.119181\pi$
$128$		0			0
$129$		−	10.9710i		−	0.965942i
$130$		0			0
$131$	11.1098	−	13.9313i	0.970669	−	1.21718i	−0.00545948	−	0.999985i	$-0.501738\pi$
$131$	11.1098	−	13.9313i	0.970669	−	1.21718i	0.976128	−	0.217195i	$-0.0696908\pi$
$132$		0			0
$133$	−6.72175	−	9.95652i	−0.582850	−	0.863340i
$134$		0			0
$135$	1.44875	−	3.00837i	0.124689	−	0.258919i
$136$		0			0
$137$	−11.5875	+	14.5302i	−0.989983	+	1.24140i	−0.0196056	+	0.999808i	$0.506241\pi$
$137$	−11.5875	+	14.5302i	−0.989983	+	1.24140i	−0.970378	+	0.241592i	$0.922330\pi$
$138$		0			0
$139$	0.243306	+	0.305096i	0.0206370	+	0.0258779i	0.792043	−	0.610465i	$-0.209018\pi$
$139$	0.243306	+	0.305096i	0.0206370	+	0.0258779i	−0.771406	+	0.636343i	$0.780446\pi$
$140$		0			0
$141$	−3.07158	+	3.85165i	−0.258674	+	0.324367i
$142$		0			0
$143$	−2.71621	+	1.30806i	−0.227141	+	0.109385i
$144$		0			0
$145$	2.00356	−	0.457299i	0.166386	−	0.0379766i
$146$		0			0
$147$	10.5148	−	3.13837i	0.867249	−	0.258849i
$148$		0			0
$149$	−0.0316917	−	0.138850i	−0.00259629	−	0.0113751i	0.973613	−	0.228205i	$-0.0732855\pi$
$149$	−0.0316917	−	0.138850i	−0.00259629	−	0.0113751i	−0.976209	+	0.216830i	$0.930428\pi$
$150$		0			0
$151$	8.20129	+	17.0302i	0.667412	+	1.38589i	0.909526	+	0.415647i	$0.136445\pi$
$151$	8.20129	+	17.0302i	0.667412	+	1.38589i	−0.242114	+	0.970248i	$0.577841\pi$
$152$		0			0
$153$	−0.00648603	−	0.00517243i	−0.000524364	−	0.000418166i
$154$		0			0
$155$	2.74994	−	2.19301i	0.220881	−	0.176146i
$156$		0			0
$157$	−17.4714	−	13.9330i	−1.39437	−	1.11198i	−0.979352	−	0.202164i	$-0.935203\pi$
$157$	−17.4714	−	13.9330i	−1.39437	−	1.11198i	−0.415022	−	0.909812i	$-0.636226\pi$
$158$		0			0
$159$	16.8232	+	8.10164i	1.33417	+	0.642502i
$160$		0			0
$161$	−0.315012	+	0.539900i	−0.0248264	+	0.0425501i
$162$		0			0
$163$	3.05602	+	2.43709i	0.239366	+	0.190888i	0.735824	−	0.677173i	$-0.236795\pi$
$163$	3.05602	+	2.43709i	0.239366	+	0.190888i	−0.496458	+	0.868061i	$0.665366\pi$
$164$		0			0
$165$	−5.34872			−0.416397
$166$		0			0
$167$	−8.61377	−	4.14817i	−0.666554	−	0.320995i	0.0698306	−	0.997559i	$-0.477754\pi$
$167$	−8.61377	−	4.14817i	−0.666554	−	0.320995i	−0.736384	+	0.676564i	$0.763468\pi$
$168$		0			0
$169$	−11.4583	+	5.51803i	−0.881409	+	0.424464i
$170$		0			0
$171$	−0.548252	+	2.40205i	−0.0419259	+	0.183689i
$172$		0			0
$173$	4.07147	+	8.45450i	0.309548	+	0.642784i	0.996470	−	0.0839475i	$-0.0267528\pi$
$173$	4.07147	+	8.45450i	0.309548	+	0.642784i	−0.686922	+	0.726731i	$0.741039\pi$
$174$		0			0
$175$	−11.4443	+	4.43128i	−0.865110	+	0.334974i
$176$		0			0
$177$	15.5275			1.16712
$178$		0			0
$179$	3.27697	−	6.80471i	0.244933	−	0.508608i	−0.741868	−	0.670545i	$-0.766060\pi$
$179$	3.27697	−	6.80471i	0.244933	−	0.508608i	0.986801	+	0.161938i	$0.0517744\pi$
$180$		0			0
$181$	1.86582	+	0.425860i	0.138685	+	0.0316539i	0.291300	−	0.956632i	$-0.405912\pi$
$181$	1.86582	+	0.425860i	0.138685	+	0.0316539i	−0.152615	+	0.988286i	$0.548769\pi$
$182$		0			0
$183$	12.2706	−	2.80069i	0.907069	−	0.207033i
$184$		0			0
$185$	−3.48172	+	0.794680i	−0.255981	+	0.0584261i
$186$		0			0
$187$	−0.0193058	+	0.0845841i	−0.00141178	+	0.00618540i
$188$		0			0
$189$	−12.6908	−	7.40460i	−0.923118	−	0.538606i
$190$		0			0
$191$	20.6249	−	16.4478i	1.49237	−	1.19012i	0.560063	−	0.828450i	$-0.310777\pi$
$191$	20.6249	−	16.4478i	1.49237	−	1.19012i	0.932305	−	0.361673i	$-0.117794\pi$
$192$		0			0
$193$	3.82962	+	4.80219i	0.275662	+	0.345669i	0.900319	−	0.435230i	$-0.143333\pi$
$193$	3.82962	+	4.80219i	0.275662	+	0.345669i	−0.624658	+	0.780899i	$0.714761\pi$
$194$		0			0
$195$	0.500720			0.0358573
$196$		0			0
$197$	0.465162			0.0331414			0.0165707	−	0.999863i	$-0.494725\pi$
$197$	0.465162			0.0331414			0.0165707	+	0.999863i	$0.494725\pi$
$198$		0			0
$199$	−11.6098	−	14.5582i	−0.822995	−	1.03200i	−0.998867	−	0.0475898i	$-0.984846\pi$
$199$	−11.6098	−	14.5582i	−0.822995	−	1.03200i	0.175872	−	0.984413i	$-0.443725\pi$
$200$		0			0
$201$	7.06125	−	5.63116i	0.498062	−	0.397191i
$202$		0			0
$203$	−1.30690	−	8.94817i	−0.0917263	−	0.628039i
$204$		0			0
$205$	−0.210994	+	0.924427i	−0.0147365	+	0.0645648i
$206$		0			0
$207$	0.124986	−	0.0285273i	0.00868715	−	0.00198279i
$208$		0			0
$209$	25.1207	−	5.73364i	1.73764	−	0.396604i
$210$		0			0
$211$	20.9566	+	4.78320i	1.44271	+	0.329289i	0.871047	−	0.491199i	$-0.163441\pi$
$211$	20.9566	+	4.78320i	1.44271	+	0.329289i	0.571663	+	0.820489i	$0.306298\pi$
$212$		0			0
$213$	1.93327	−	4.01447i	0.132465	−	0.275067i
$214$		0			0
$215$	−4.20795			−0.286980
$216$		0			0
$217$	−8.66018	−	12.8278i	−0.587891	−	0.870808i
$218$		0			0
$219$	−2.28104	−	4.73663i	−0.154139	−	0.320072i
$220$		0			0
$221$	0.00180731	−	0.00791833i	0.000121573	−	0.000532645i
$222$		0			0
$223$	9.57519	−	4.61117i	0.641202	−	0.308787i	−0.0848835	−	0.996391i	$-0.527052\pi$
$223$	9.57519	−	4.61117i	0.641202	−	0.308787i	0.726086	+	0.687604i	$0.241338\pi$
$224$		0			0
$225$	2.26772	+	1.09208i	0.151182	+	0.0728052i
$226$		0			0
$227$	10.0968			0.670150			0.335075	−	0.942192i	$-0.391238\pi$
$227$	10.0968			0.670150			0.335075	+	0.942192i	$0.391238\pi$
$228$		0			0
$229$	16.1208	+	12.8559i	1.06529	+	0.849542i	0.989055	−	0.147548i	$-0.0471380\pi$
$229$	16.1208	+	12.8559i	1.06529	+	0.849542i	0.0762369	+	0.997090i	$0.475709\pi$
$230$		0			0
$231$	−1.86618	+	23.4622i	−0.122786	+	1.54370i
$232$		0			0
$233$	−18.6175	−	8.96571i	−1.21967	−	0.587363i	−0.290452	−	0.956890i	$-0.593806\pi$
$233$	−18.6175	−	8.96571i	−1.21967	−	0.587363i	−0.929220	+	0.369527i	$0.879520\pi$
$234$		0			0
$235$	1.47731	+	1.17812i	0.0963690	+	0.0768518i
$236$		0			0
$237$	9.61727	−	7.66952i	0.624709	−	0.498189i
$238$		0			0
$239$	−1.90732	−	1.52104i	−0.123374	−	0.0983876i	0.559859	−	0.828588i	$-0.310855\pi$
$239$	−1.90732	−	1.52104i	−0.123374	−	0.0983876i	−0.683233	+	0.730200i	$0.739427\pi$
$240$		0			0
$241$	5.37926	+	11.1701i	0.346508	+	0.719532i	0.999277	−	0.0380255i	$-0.0121068\pi$
$241$	5.37926	+	11.1701i	0.346508	+	0.719532i	−0.652768	+	0.757558i	$0.726393\pi$
$242$		0			0
$243$	1.23840	+	5.42580i	0.0794436	+	0.348065i
$244$		0			0
$245$	−1.20373	−	4.03299i	−0.0769036	−	0.257659i
$246$		0			0
$247$	−2.35168	+	0.536755i	−0.149634	+	0.0341529i
$248$		0			0
$249$	−20.4656	+	9.85569i	−1.29695	+	0.624579i
$250$		0			0
$251$	−6.62267	+	8.30457i	−0.418019	+	0.524180i	−0.945603	−	0.325323i	$-0.894527\pi$
$251$	−6.62267	+	8.30457i	−0.418019	+	0.524180i	0.527583	+	0.849503i	$0.323098\pi$
$252$		0			0
$253$	−0.835930	−	1.04822i	−0.0525545	−	0.0659012i
$254$		0			0
$255$	0.00898435	−	0.0112660i	0.000562622	−	0.000705506i
$256$		0			0
$257$	−11.0392	+	22.9231i	−0.688604	+	1.42990i	0.203959	+	0.978979i	$0.434619\pi$
$257$	−11.0392	+	22.9231i	−0.688604	+	1.42990i	−0.892563	+	0.450922i	$0.851095\pi$
$258$		0			0
$259$	2.27109	+	15.5499i	0.141119	+	0.966222i
$260$		0			0
$261$	−1.15638	+	1.45006i	−0.0715783	+	0.0897563i
$262$		0			0
$263$		−	15.3223i		−	0.944812i	−0.881381	−	0.472406i	$-0.843386\pi$
$263$		−	15.3223i		−	0.944812i	0.881381	−	0.472406i	$-0.156614\pi$
$264$		0			0
$265$	3.10741	−	6.45259i	0.190886	−	0.396380i
$266$		0			0
$267$	3.26167	+	6.77293i	0.199611	+	0.414497i
$268$		0			0
$269$	−31.4742	−	7.18379i	−1.91902	−	0.438003i	−0.998928	−	0.0462989i	$-0.985257\pi$
$269$	−31.4742	−	7.18379i	−1.91902	−	0.438003i	−0.920091	−	0.391705i	$-0.871886\pi$
$270$		0			0
$271$	2.89788	−	1.39555i	0.176034	−	0.0847734i	−0.343792	−	0.939046i	$-0.611711\pi$
$271$	2.89788	−	1.39555i	0.176034	−	0.0847734i	0.519825	+	0.854273i	$0.325997\pi$
$272$		0			0
$273$	0.174703	−	2.19641i	0.0105735	−	0.132933i
$274$		0			0
$275$		−	26.3227i		−	1.58732i
$276$		0			0
$277$	−11.9688	−	5.76386i	−0.719134	−	0.346317i	0.0382663	−	0.999268i	$-0.487816\pi$
$277$	−11.9688	−	5.76386i	−0.719134	−	0.346317i	−0.757400	+	0.652951i	$0.773531\pi$
$278$		0			0
$279$	−0.706358	+	3.09475i	−0.0422885	+	0.185278i
$280$		0			0
$281$	4.33185	+	18.9791i	0.258417	+	1.13220i	0.922944	+	0.384934i	$0.125776\pi$
$281$	4.33185	+	18.9791i	0.258417	+	1.13220i	−0.664527	+	0.747264i	$0.731367\pi$
$282$		0			0
$283$	−0.177804	−	0.779009i	−0.0105693	−	0.0463073i	0.969368	−	0.245612i	$-0.0789888\pi$
$283$	−0.177804	−	0.779009i	−0.0105693	−	0.0463073i	−0.979938	+	0.199305i	$0.936132\pi$
$284$		0			0
$285$	−4.17228	−	0.952296i	−0.247145	−	0.0564092i
$286$		0			0
$287$	3.98139	+	1.24806i	0.235014	+	0.0736709i
$288$		0			0
$289$	10.5992	+	13.2910i	0.623481	+	0.781821i
$290$		0			0
$291$	−16.2422	+	12.9527i	−0.952134	+	0.759301i
$292$		0			0
$293$			0.330751i			0.0193227i	0.999953	+	0.00966134i	$0.00307535\pi$
$293$			0.330751i			0.0193227i	−0.999953	+	0.00966134i	$0.996925\pi$
$294$		0			0
$295$		−	5.95563i		−	0.346750i
$296$		0			0
$297$	24.6393	−	19.6492i	1.42972	−	1.14016i
$298$		0			0
$299$	0.0782556	+	0.0981294i	0.00452564	+	0.00567497i
$300$		0			0
$301$	−1.46816	+	18.4582i	−0.0846236	+	1.06391i
$302$		0			0
$303$	−19.9561	−	4.55484i	−1.14645	−	0.261669i
$304$		0			0
$305$	−1.07421	−	4.70642i	−0.0615091	−	0.269489i
$306$		0			0
$307$	6.19856	+	27.1577i	0.353770	+	1.54997i	0.768395	+	0.639976i	$0.221056\pi$
$307$	6.19856	+	27.1577i	0.353770	+	1.54997i	−0.414624	+	0.909993i	$0.636087\pi$
$308$		0			0
$309$	−3.34042	+	14.6353i	−0.190030	+	0.832576i
$310$		0			0
$311$	−18.7589	−	9.03380i	−1.06372	−	0.512260i	−0.181642	−	0.983365i	$-0.558141\pi$
$311$	−18.7589	−	9.03380i	−1.06372	−	0.512260i	−0.882077	+	0.471105i	$0.843855\pi$
$312$		0			0
$313$			8.00551i			0.452498i	0.974069	+	0.226249i	$0.0726464\pi$
$313$			8.00551i			0.452498i	−0.974069	+	0.226249i	$0.927354\pi$
$314$		0			0
$315$	−0.435016	+	0.745575i	−0.0245104	+	0.0420084i
$316$		0			0
$317$	12.4573	−	5.99912i	0.699671	−	0.336944i	−0.0500047	−	0.998749i	$-0.515924\pi$
$317$	12.4573	−	5.99912i	0.699671	−	0.336944i	0.749676	+	0.661805i	$0.230209\pi$
$318$		0			0
$319$	18.9102	+	4.31612i	1.05877	+	0.241656i
$320$		0			0
$321$	3.37357	+	7.00529i	0.188294	+	0.390997i
$322$		0			0
$323$	−0.0301190	+	0.0625428i	−0.00167587	+	0.00347997i
$324$		0			0
$325$			2.46420i			0.136689i
$326$		0			0
$327$	−17.9073	+	22.4551i	−0.990278	+	1.24177i
$328$		0			0
$329$	5.68325	−	6.06919i	0.313328	−	0.334605i
$330$		0			0
$331$	7.92697	−	16.4605i	0.435706	−	0.904752i	−0.561314	−	0.827603i	$-0.689704\pi$
$331$	7.92697	−	16.4605i	0.435706	−	0.904752i	0.997020	−	0.0771491i	$-0.0245817\pi$
$332$		0			0
$333$	2.00953	−	2.51987i	0.110121	−	0.138088i
$334$		0			0
$335$	−2.15985	−	2.70836i	−0.118005	−	0.147974i
$336$		0			0
$337$	−9.72562	+	12.1955i	−0.529788	+	0.664333i	−0.972655	−	0.232254i	$-0.925390\pi$
$337$	−9.72562	+	12.1955i	−0.529788	+	0.664333i	0.442867	+	0.896587i	$0.353961\pi$
$338$		0			0
$339$	9.40776	−	4.53054i	0.510960	−	0.246065i
$340$		0			0
$341$	32.3651	−	7.38712i	1.75267	−	0.400035i
$342$		0			0
$343$	−18.1108	+	3.87306i	−0.977889	+	0.209126i
$344$		0			0
$345$	0.0495511	+	0.217097i	0.00266774	+	0.0116881i
$346$		0			0
$347$	6.93676	+	14.4043i	0.372385	+	0.773265i	0.999986	−	0.00527002i	$-0.00167751\pi$
$347$	6.93676	+	14.4043i	0.372385	+	0.773265i	−0.627601	+	0.778535i	$0.715963\pi$
$348$		0			0
$349$	7.39975	+	5.90111i	0.396100	+	0.315879i	0.801204	−	0.598392i	$-0.204193\pi$
$349$	7.39975	+	5.90111i	0.396100	+	0.315879i	−0.405104	+	0.914271i	$0.632765\pi$
$350$		0			0
$351$	−2.30661	+	1.83946i	−0.123118	+	0.0981830i
$352$		0			0
$353$	−10.1340	−	8.08158i	−0.539377	−	0.430139i	0.315533	−	0.948915i	$-0.397817\pi$
$353$	−10.1340	−	8.08158i	−0.539377	−	0.430139i	−0.854911	+	0.518775i	$0.826388\pi$
$354$		0			0
$355$	−1.53976	−	0.741510i	−0.0817220	−	0.0393552i
$356$		0			0
$357$	−0.0462839	−	0.0433407i	−0.00244960	−	0.00229383i
$358$		0			0
$359$	−2.16713	−	1.72823i	−0.114377	−	0.0912123i	0.564631	−	0.825343i	$-0.309018\pi$
$359$	−2.16713	−	1.72823i	−0.114377	−	0.0912123i	−0.679008	+	0.734131i	$0.737590\pi$
$360$		0			0
$361$	1.61631			0.0850690
$362$		0			0
$363$	−29.9475	−	14.4220i	−1.57184	−	0.756957i
$364$		0			0
$365$	−1.81675	+	0.874900i	−0.0950930	+	0.0457944i
$366$		0			0
$367$	−2.28986	+	10.0325i	−0.119530	+	0.523693i	0.879342	+	0.476191i	$0.157983\pi$
$367$	−2.28986	+	10.0325i	−0.119530	+	0.523693i	−0.998871	+	0.0475016i	$0.984874\pi$
$368$		0			0
$369$	−0.371293	−	0.770998i	−0.0193287	−	0.0401365i
$370$		0			0
$371$	−27.2202	−	15.8820i	−1.41320	−	0.824552i
$372$		0			0
$373$	11.9550			0.619005			0.309502	−	0.950899i	$-0.399838\pi$
$373$	11.9550			0.619005			0.309502	+	0.950899i	$0.399838\pi$
$374$		0			0
$375$	−3.94165	+	8.18492i	−0.203546	+	0.422668i
$376$		0			0
$377$	−1.77027	−	0.404054i	−0.0911738	−	0.0208098i
$378$		0			0
$379$	−10.9222	+	2.49293i	−0.561038	+	0.128053i	−0.493629	−	0.869672i	$-0.664330\pi$
$379$	−10.9222	+	2.49293i	−0.561038	+	0.128053i	−0.0674081	+	0.997725i	$0.521473\pi$
$380$		0			0
$381$	−2.55976	+	0.584249i	−0.131141	+	0.0299320i
$382$		0			0
$383$	3.70012	−	16.2113i	0.189067	−	0.828357i	−0.788043	−	0.615621i	$-0.788905\pi$
$383$	3.70012	−	16.2113i	0.189067	−	0.828357i	0.977110	−	0.212736i	$-0.0682375\pi$
$384$		0			0
$385$	8.99900	+	0.715779i	0.458632	+	0.0364795i
$386$		0			0
$387$	2.96912	−	2.36779i	0.150929	−	0.120362i
$388$		0			0
$389$	7.77214	+	9.74595i	0.394063	+	0.494139i	0.938798	−	0.344469i	$-0.111941\pi$
$389$	7.77214	+	9.74595i	0.394063	+	0.494139i	−0.544735	+	0.838608i	$0.683370\pi$
$390$		0			0
$391$	0.00361200			0.000182667
$392$		0			0
$393$	−27.9327			−1.40902
$394$		0			0
$395$	−2.94167	−	3.68873i	−0.148011	−	0.185600i
$396$		0			0
$397$	−2.53902	+	2.02480i	−0.127430	+	0.101622i	−0.685131	−	0.728420i	$-0.740255\pi$
$397$	−2.53902	+	2.02480i	−0.127430	+	0.101622i	0.557701	+	0.830042i	$0.311684\pi$
$398$		0			0
$399$	−5.63298	+	17.9695i	−0.282002	+	0.899600i
$400$		0			0
$401$	0.282584	−	1.23808i	0.0141116	−	0.0618269i	−0.967382	−	0.253322i	$-0.918477\pi$
$401$	0.282584	−	1.23808i	0.0141116	−	0.0618269i	0.981493	+	0.191496i	$0.0613338\pi$
$402$		0			0
$403$	−3.02986	+	0.691545i	−0.150928	+	0.0344483i
$404$		0			0
$405$	−4.14880	+	0.946937i	−0.206156	+	0.0470537i
$406$		0			0
$407$	−32.8615	−	7.50043i	−1.62889	−	0.371783i
$408$		0			0
$409$	12.4653	−	25.8844i	0.616369	−	1.27990i	−0.326014	−	0.945365i	$-0.605706\pi$
$409$	12.4653	−	25.8844i	0.616369	−	1.27990i	0.942382	−	0.334538i	$-0.108580\pi$
$410$		0			0
$411$	29.1336			1.43705
$412$		0			0
$413$	−26.1244	−	2.07793i	−1.28550	−	0.102248i
$414$		0			0
$415$	3.78018	+	7.84962i	0.185562	+	0.385323i
$416$		0			0
$417$	0.136122	−	0.596391i	0.00666595	−	0.0292054i
$418$		0			0
$419$	−31.6865	+	15.2594i	−1.54799	+	0.745471i	−0.996082	−	0.0884361i	$-0.971813\pi$
$419$	−31.6865	+	15.2594i	−1.54799	+	0.745471i	−0.551905	+	0.833907i	$0.686099\pi$
$420$		0			0
$421$	23.4369	+	11.2866i	1.14225	+	0.550077i	0.906696	−	0.421785i	$-0.138596\pi$
$421$	23.4369	+	11.2866i	1.14225	+	0.550077i	0.235551	+	0.971862i	$0.424311\pi$
$422$		0			0
$423$	−1.70530			−0.0829147
$424$		0			0
$425$	0.0554436	+	0.0442148i	0.00268941	+	0.00214473i
$426$		0			0
$427$	−21.0196	+	3.06995i	−1.01721	+	0.148565i
$428$		0			0
$429$	4.25793	+	2.05051i	0.205575	+	0.0989997i
$430$		0			0
$431$	17.5563	+	14.0007i	0.845659	+	0.674390i	0.947271	−	0.320434i	$-0.103829\pi$
$431$	17.5563	+	14.0007i	0.845659	+	0.674390i	−0.101612	+	0.994824i	$0.532400\pi$
$432$		0			0
$433$	23.3517	−	18.6224i	1.12221	−	0.894935i	0.126927	−	0.991912i	$-0.459489\pi$
$433$	23.3517	−	18.6224i	1.12221	−	0.894935i	0.995287	+	0.0969770i	$0.0309173\pi$
$434$		0			0
$435$	−2.51871	−	2.00860i	−0.120763	−	0.0963050i
$436$		0			0
$437$	−0.465442	−	0.966500i	−0.0222651	−	0.0462339i
$438$		0			0
$439$	4.30520	+	18.8623i	0.205476	+	0.900249i	0.967534	+	0.252740i	$0.0813319\pi$
$439$	4.30520	+	18.8623i	0.205476	+	0.900249i	−0.762058	+	0.647509i	$0.775811\pi$
$440$		0			0
$441$	3.11869	+	2.16833i	0.148509	+	0.103254i
$442$		0			0
$443$	−26.9869	+	6.15958i	−1.28218	+	0.292650i	−0.808736	−	0.588171i	$-0.799848\pi$
$443$	−26.9869	+	6.15958i	−1.28218	+	0.292650i	−0.473448	+	0.880822i	$0.656991\pi$
$444$		0			0
$445$	2.59778	−	1.25102i	0.123146	−	0.0593042i
$446$		0			0
$447$	−0.139200	+	0.174551i	−0.00658394	+	0.00825600i
$448$		0			0
$449$	1.34377	+	1.68504i	0.0634166	+	0.0795219i	0.812528	−	0.582922i	$-0.198091\pi$
$449$	1.34377	+	1.68504i	0.0634166	+	0.0795219i	−0.749111	+	0.662444i	$0.769519\pi$
$450$		0			0
$451$	−5.57986	+	6.99692i	−0.262745	+	0.329472i
$452$		0			0
$453$	12.8563	−	26.6965i	0.604044	−	1.25431i
$454$		0			0
$455$	−0.842441	−	0.0670076i	−0.0394942	−	0.00314137i
$456$		0			0
$457$	−17.0661	+	21.4002i	−0.798319	+	1.00106i	0.201448	+	0.979499i	$0.435435\pi$
$457$	−17.0661	+	21.4002i	−0.798319	+	1.00106i	−0.999768	+	0.0215614i	$0.993136\pi$
$458$		0			0
$459$			0.0849030i			0.00396293i
$460$		0			0
$461$	−0.184354	+	0.382815i	−0.00858622	+	0.0178295i	−0.905218	−	0.424948i	$-0.860292\pi$
$461$	−0.184354	+	0.382815i	−0.00858622	+	0.0178295i	0.896632	+	0.442777i	$0.146007\pi$
$462$		0			0
$463$	−10.7832	−	22.3916i	−0.501139	−	1.04063i	−0.986110	−	0.166096i	$-0.946884\pi$
$463$	−10.7832	−	22.3916i	−0.501139	−	1.04063i	0.484971	−	0.874530i	$-0.338830\pi$
$464$		0			0
$465$	−5.37549	−	1.22692i	−0.249283	−	0.0568971i
$466$		0			0
$467$	15.1510	−	7.29634i	0.701105	−	0.337634i	−0.0491422	−	0.998792i	$-0.515649\pi$
$467$	15.1510	−	7.29634i	0.701105	−	0.337634i	0.750247	+	0.661157i	$0.229934\pi$
$468$		0			0
$469$	−12.6338	+	8.52923i	−0.583376	+	0.393843i
$470$		0			0
$471$			35.0309i			1.61414i
$472$		0			0
$473$	−35.7828	−	17.2321i	−1.64530	−	0.792333i
$474$		0			0
$475$	4.68655	−	20.5331i	0.215034	−	0.942123i
$476$		0			0
$477$	1.43826	+	6.30145i	0.0658536	+	0.288523i
$478$		0			0
$479$	−1.99233	−	8.72898i	−0.0910320	−	0.398837i	0.908799	−	0.417235i	$-0.137001\pi$
$479$	−1.99233	−	8.72898i	−0.0910320	−	0.398837i	−0.999831	+	0.0183974i	$0.994144\pi$
$480$		0			0
$481$	3.07633	+	0.702153i	0.140269	+	0.0320154i
$482$		0			0
$483$	0.969588	−	0.141610i	0.0441178	−	0.00644350i
$484$		0			0
$485$	4.96805	+	6.22974i	0.225587	+	0.282878i
$486$		0			0
$487$	18.2801	−	14.5779i	0.828350	−	0.660587i	−0.114640	−	0.993407i	$-0.536572\pi$
$487$	18.2801	−	14.5779i	0.828350	−	0.660587i	0.942990	+	0.332820i	$0.108000\pi$
$488$		0			0
$489$		−	6.12743i		−	0.277092i
$490$		0			0
$491$			23.0316i			1.03940i	0.854348	+	0.519701i	$0.173957\pi$
$491$			23.0316i			1.03940i	−0.854348	+	0.519701i	$0.826043\pi$
$492$		0			0
$493$	−0.0408548	+	0.0325806i	−0.00184001	+	0.00146736i
$494$		0			0
$495$	−1.15438	−	1.44754i	−0.0518854	−	0.0650622i
$496$		0			0
$497$	−3.78987	+	6.49546i	−0.169999	+	0.291361i
$498$		0			0
$499$	−25.2438	−	5.76173i	−1.13007	−	0.257930i	−0.383695	−	0.923460i	$-0.625349\pi$
$499$	−25.2438	−	5.76173i	−1.13007	−	0.257930i	−0.746372	+	0.665529i	$0.768206\pi$
$500$		0			0
$501$	3.33495	+	14.6114i	0.148995	+	0.652788i
$502$		0			0
$503$	−1.46034	−	6.39816i	−0.0651133	−	0.285280i	0.931880	−	0.362766i	$-0.118168\pi$
$503$	−1.46034	−	6.39816i	−0.0651133	−	0.285280i	−0.996993	+	0.0774865i	$0.975311\pi$
$504$		0			0
$505$	−1.74702	+	7.65421i	−0.0777415	+	0.340608i
$506$		0			0
$507$	17.9621	+	8.65007i	0.797723	+	0.384163i
$508$		0			0
$509$			28.9425i			1.28286i	0.767183	+	0.641428i	$0.221658\pi$
$509$			28.9425i			1.28286i	−0.767183	+	0.641428i	$0.778342\pi$
$510$		0			0
$511$	3.20389	+	8.27444i	0.141732	+	0.366040i
$512$		0			0
$513$	22.7183	−	10.9406i	1.00304	−	0.483038i
$514$		0			0
$515$	5.61343	+	1.28123i	0.247357	+	0.0564577i
$516$		0			0
$517$	7.73794	+	16.0680i	0.340314	+	0.706670i
$518$		0			0
$519$	6.38244	−	13.2533i	0.280158	−	0.581754i
$520$		0			0
$521$			28.1910i			1.23507i	0.786543	+	0.617536i	$0.211869\pi$
$521$			28.1910i			1.23507i	−0.786543	+	0.617536i	$0.788131\pi$
$522$		0			0
$523$	3.51846	−	4.41201i	0.153852	−	0.192924i	−0.698932	−	0.715188i	$-0.746341\pi$
$523$	3.51846	−	4.41201i	0.153852	−	0.192924i	0.852784	+	0.522264i	$0.174912\pi$
$524$		0			0
$525$	16.6165	+	9.69511i	0.725202	+	0.423129i
$526$		0			0
$527$	−0.0388048	+	0.0805790i	−0.00169036	+	0.00351007i
$528$		0			0
$529$	14.3055	−	17.9385i	0.621977	−	0.779934i
$530$		0			0
$531$	3.35120	+	4.20227i	0.145430	+	0.182363i
$532$		0			0
$533$	0.522358	−	0.655017i	0.0226259	−	0.0283719i
$534$		0			0
$535$	2.68690	−	1.29394i	0.116165	−	0.0559420i
$536$		0			0
$537$	−11.5427	+	2.63455i	−0.498104	+	0.113689i
$538$		0			0
$539$	6.27955	−	39.2245i	0.270479	−	1.68952i
$540$		0			0
$541$	−2.16996	−	9.50722i	−0.0932939	−	0.408747i	0.906619	−	0.421950i	$-0.138654\pi$
$541$	−2.16996	−	9.50722i	−0.0932939	−	0.408747i	−0.999913	+	0.0132031i	$0.995797\pi$
$542$		0			0
$543$	−1.30168	−	2.70297i	−0.0558605	−	0.115996i
$544$		0			0
$545$	8.61271	+	6.86841i	0.368928	+	0.294210i
$546$		0			0
$547$	−20.8866	+	16.6565i	−0.893045	+	0.712179i	−0.958323	−	0.285688i	$-0.907778\pi$
$547$	−20.8866	+	16.6565i	−0.893045	+	0.712179i	0.0652781	+	0.997867i	$0.479207\pi$
$548$		0			0
$549$	3.40624	+	2.71638i	0.145375	+	0.115932i
$550$		0			0
$551$	13.9825	+	6.73360i	0.595673	+	0.286861i
$552$		0			0
$553$	−17.2070	+	11.6166i	−0.731716	+	0.493990i
$554$		0			0
$555$	4.37693	+	3.49049i	0.185791	+	0.148163i
$556$		0			0
$557$	16.1878			0.685900			0.342950	−	0.939354i	$-0.388574\pi$
$557$	16.1878			0.685900			0.342950	+	0.939354i	$0.388574\pi$
$558$		0			0
$559$	3.34981	+	1.61318i	0.141682	+	0.0682303i
$560$		0			0
$561$	0.122535	−	0.0590099i	0.00517344	−	0.00249140i
$562$		0			0
$563$	−2.82099	+	12.3596i	−0.118891	+	0.520894i	0.880050	+	0.474881i	$0.157509\pi$
$563$	−2.82099	+	12.3596i	−0.118891	+	0.520894i	−0.998941	+	0.0460134i	$0.985348\pi$
$564$		0			0
$565$	−1.73770	−	3.60837i	−0.0731056	−	0.151805i
$566$		0			0
$567$	2.70622	+	18.5292i	0.113651	+	0.778151i
$568$		0			0
$569$	−15.3269			−0.642535			−0.321268	−	0.946988i	$-0.604109\pi$
$569$	−15.3269			−0.642535			−0.321268	+	0.946988i	$0.604109\pi$
$570$		0			0
$571$	−12.4813	+	25.9177i	−0.522327	+	1.08462i	0.458311	+	0.888792i	$0.348455\pi$
$571$	−12.4813	+	25.9177i	−0.522327	+	1.08462i	−0.980638	+	0.195831i	$0.937260\pi$
$572$		0			0
$573$	−40.3169	−	9.20207i	−1.68426	−	0.384422i
$574$		0			0
$575$	−1.06840	+	0.243856i	−0.0445555	+	0.0101695i
$576$		0			0
$577$	18.9234	−	4.31915i	0.787793	−	0.179809i	0.190346	−	0.981717i	$-0.439039\pi$
$577$	18.9234	−	4.31915i	0.787793	−	0.179809i	0.597447	+	0.801908i	$0.296182\pi$
$578$		0			0
$579$	2.14256	−	9.38715i	0.0890415	−	0.390117i
$580$		0			0
$581$	35.7513	−	13.8430i	1.48322	−	0.574306i
$582$		0			0
$583$	52.8484	−	42.1452i	2.18876	−	1.74547i
$584$		0			0
$585$	0.108067	+	0.135512i	0.00446802	+	0.00560272i
$586$		0			0
$587$	46.2068			1.90716			0.953580	−	0.301141i	$-0.0973674\pi$
$587$	46.2068			1.90716			0.953580	+	0.301141i	$0.0973674\pi$
$588$		0			0
$589$	26.5617			1.09445
$590$		0			0
$591$	−0.454641	−	0.570102i	−0.0187015	−	0.0234509i
$592$		0			0
$593$	−26.5710	+	21.1896i	−1.09114	+	0.870154i	−0.992165	−	0.124936i	$-0.960127\pi$
$593$	−26.5710	+	21.1896i	−1.09114	+	0.870154i	−0.0989739	+	0.995090i	$0.531556\pi$
$594$		0			0
$595$	−0.0166234	+	0.0177523i	−0.000681495	+	0.000727774i
$596$		0			0
$597$	−6.49532	+	28.4578i	−0.265836	+	1.16470i
$598$		0			0
$599$	20.6554	−	4.71446i	0.843957	−	0.192628i	0.221382	−	0.975187i	$-0.428943\pi$
$599$	20.6554	−	4.71446i	0.843957	−	0.192628i	0.622576	+	0.782560i	$0.286086\pi$
$600$		0			0
$601$	−16.2174	+	3.70152i	−0.661521	+	0.150988i	−0.540084	−	0.841611i	$-0.681608\pi$
$601$	−16.2174	+	3.70152i	−0.661521	+	0.150988i	−0.121437	+	0.992599i	$0.538750\pi$
$602$		0			0
$603$	3.04796	+	0.695677i	0.124122	+	0.0283301i
$604$		0			0
$605$	−5.53159	+	11.4865i	−0.224891	+	0.466991i
$606$		0			0
$607$	−39.8869			−1.61896			−0.809479	−	0.587149i	$-0.800250\pi$
$607$	−39.8869			−1.61896			−0.809479	+	0.587149i	$0.800250\pi$
$608$		0			0
$609$	−9.68953	+	10.3475i	−0.392640	+	0.419303i
$610$		0			0
$611$	−0.724387	−	1.50421i	−0.0293056	−	0.0608536i
$612$		0			0
$613$	−3.58047	+	15.6871i	−0.144614	+	0.633594i	0.849715	+	0.527243i	$0.176774\pi$
$613$	−3.58047	+	15.6871i	−0.144614	+	0.633594i	−0.994329	+	0.106352i	$0.966083\pi$
$614$		0			0
$615$	1.33920	−	0.644924i	0.0540017	−	0.0260059i
$616$		0			0
$617$	−40.1516	−	19.3360i	−1.61644	−	0.778437i	−0.616481	−	0.787370i	$-0.711442\pi$
$617$	−40.1516	−	19.3360i	−1.61644	−	0.778437i	−0.999960	+	0.00893318i	$0.997156\pi$
$618$		0			0
$619$	21.5643			0.866743			0.433371	−	0.901215i	$-0.357324\pi$
$619$	21.5643			0.866743			0.433371	+	0.901215i	$0.357324\pi$
$620$		0			0
$621$	−1.02580	−	0.818044i	−0.0411637	−	0.0328270i
$622$		0			0
$623$	−4.58126	−	11.8317i	−0.183544	−	0.474025i
$624$		0			0
$625$	−17.7563	−	8.55099i	−0.710253	−	0.342040i
$626$		0			0
$627$	−31.5797	−	25.1840i	−1.26117	−	1.00575i
$628$		0			0
$629$	0.0709964	−	0.0566177i	0.00283081	−	0.00225750i
$630$		0			0
$631$	27.6690	+	22.0653i	1.10148	+	0.878405i	0.993281	−	0.115724i	$-0.0369188\pi$
$631$	27.6690	+	22.0653i	1.10148	+	0.878405i	0.108203	+	0.994129i	$0.465490\pi$
$632$		0			0
$633$	−14.6203	−	30.3594i	−0.581105	−	1.20668i
$634$		0			0
$635$	0.224090	+	0.981804i	0.00889275	+	0.0389617i
$636$		0			0
$637$	−0.587859	+	3.67200i	−0.0232918	+	0.145490i
$638$		0			0
$639$	1.50369	−	0.343208i	0.0594852	−	0.0135771i
$640$		0			0
$641$	0.149827	−	0.0721528i	0.00591781	−	0.00284987i	−0.430922	−	0.902389i	$-0.641812\pi$
$641$	0.149827	−	0.0721528i	0.00591781	−	0.00284987i	0.436840	+	0.899539i	$0.356097\pi$
$642$		0			0
$643$	−26.6992	+	33.4797i	−1.05291	+	1.32031i	−0.107582	+	0.994196i	$0.534311\pi$
$643$	−26.6992	+	33.4797i	−1.05291	+	1.32031i	−0.945331	+	0.326114i	$0.894261\pi$
$644$		0			0
$645$	4.11278	+	5.15726i	0.161941	+	0.203067i
$646$		0			0
$647$	3.44553	−	4.32055i	0.135458	−	0.169858i	−0.709476	−	0.704729i	$-0.751068\pi$
$647$	3.44553	−	4.32055i	0.135458	−	0.169858i	0.844934	+	0.534871i	$0.179640\pi$
$648$		0			0
$649$	24.3890	−	50.6444i	0.957353	−	1.98796i
$650$		0			0
$651$	−7.25742	+	23.1516i	−0.284441	+	0.907382i
$652$		0			0
$653$	−15.9289	+	19.9742i	−0.623344	+	0.781649i	−0.988811	−	0.149175i	$-0.952338\pi$
$653$	−15.9289	+	19.9742i	−0.623344	+	0.781649i	0.365466	+	0.930825i	$0.380910\pi$
$654$		0			0
$655$			10.7137i			0.418617i
$656$		0			0
$657$	0.789590	−	1.63960i	0.0308048	−	0.0639669i
$658$		0			0
$659$	3.91741	+	8.13459i	0.152601	+	0.316878i	0.963229	−	0.268683i	$-0.0865884\pi$
$659$	3.91741	+	8.13459i	0.152601	+	0.316878i	−0.810628	+	0.585561i	$0.800874\pi$
$660$		0			0
$661$	−3.38856	−	0.773416i	−0.131800	−	0.0300824i	0.156112	−	0.987739i	$-0.450104\pi$
$661$	−3.38856	−	0.773416i	−0.131800	−	0.0300824i	−0.287912	+	0.957657i	$0.592961\pi$
$662$		0			0
$663$	−0.0114711	+	0.00552421i	−0.000445502	+	0.000214542i
$664$		0			0
$665$	6.89225	+	2.16054i	0.267270	+	0.0837823i
$666$		0			0
$667$		−	0.807523i		−	0.0312674i
$668$		0			0
$669$	−15.0101	−	7.22847i	−0.580323	−	0.279469i
$670$		0			0
$671$	10.1387	−	44.4207i	0.391401	−	1.71484i
$672$		0			0
$673$	−3.03339	−	13.2901i	−0.116929	−	0.512297i	−0.999141	−	0.0414454i	$-0.986804\pi$
$673$	−3.03339	−	13.2901i	−0.116929	−	0.512297i	0.882212	−	0.470852i	$-0.156053\pi$
$674$		0			0
$675$	−5.73203	−	25.1137i	−0.220626	−	0.966626i
$676$		0			0
$677$	30.4123	+	6.94141i	1.16884	+	0.266780i	0.762528	−	0.646955i	$-0.223958\pi$
$677$	30.4123	+	6.94141i	1.16884	+	0.266780i	0.406311	+	0.913735i	$0.366815\pi$
$678$		0			0
$679$	29.0602	−	19.6188i	1.11523	−	0.752901i
$680$		0			0
$681$	−9.86846	−	12.3747i	−0.378160	−	0.474198i
$682$		0			0
$683$	15.6111	−	12.4495i	0.597343	−	0.476365i	−0.277530	−	0.960717i	$-0.589516\pi$
$683$	15.6111	−	12.4495i	0.597343	−	0.476365i	0.874874	+	0.484351i	$0.160944\pi$
$684$		0			0
$685$		−	11.1743i		−	0.426947i
$686$		0			0
$687$		−	32.3228i		−	1.23319i
$688$		0			0
$689$	−4.94740	+	3.94542i	−0.188481	+	0.150308i
$690$		0			0
$691$	0.808127	+	1.01336i	0.0307426	+	0.0385500i	0.796965	−	0.604025i	$-0.206437\pi$
$691$	0.808127	+	1.01336i	0.0307426	+	0.0385500i	−0.766223	+	0.642575i	$0.777866\pi$
$692$		0			0
$693$	−6.75243	+	4.55864i	−0.256504	+	0.173168i
$694$		0			0
$695$	−0.228748	−	0.0522101i	−0.00867689	−	0.00198044i
$696$		0			0
$697$	−0.00536503	−	0.0235057i	−0.000203215	−	0.000890344i
$698$		0			0
$699$	7.20804	+	31.5805i	0.272633	+	1.19448i
$700$		0			0
$701$	8.19084	−	35.8864i	0.309364	−	1.35541i	−0.546175	−	0.837671i	$-0.683916\pi$
$701$	8.19084	−	35.8864i	0.309364	−	1.35541i	0.855538	−	0.517740i	$-0.173226\pi$
$702$		0			0
$703$	−24.2983	−	11.7015i	−0.916429	−	0.441329i
$704$		0			0
$705$		−	2.96206i		−	0.111558i
$706$		0			0
$707$	32.9657	+	10.3339i	1.23980	+	0.388647i
$708$		0			0
$709$	36.8366	−	17.7396i	1.38343	−	0.666223i	0.413699	−	0.910414i	$-0.364237\pi$
$709$	36.8366	−	17.7396i	1.38343	−	0.666223i	0.969727	+	0.244191i	$0.0785223\pi$
$710$		0			0
$711$	4.15126	+	0.947497i	0.155684	+	0.0355339i
$712$		0			0
$713$	−0.599667	−	1.24522i	−0.0224577	−	0.0466339i
$714$		0			0
$715$	0.786480	−	1.63314i	0.0294127	−	0.0610761i
$716$		0			0
$717$			3.82424i			0.142819i
$718$		0			0
$719$	−20.5798	+	25.8063i	−0.767497	+	0.962411i	−0.999948	−	0.0101970i	$-0.996754\pi$
$719$	−20.5798	+	25.8063i	−0.767497	+	0.962411i	0.232451	+	0.972608i	$0.425326\pi$
$720$		0			0
$721$	7.57866	−	24.1763i	0.282244	−	0.900374i
$722$		0			0
$723$	8.43252	−	17.5103i	0.313609	−	0.651216i
$724$		0			0
$725$	9.88495	−	12.3953i	0.367118	−	0.460351i
$726$		0			0
$727$	13.8787	+	17.4034i	0.514734	+	0.645456i	0.969482	−	0.245164i	$-0.0788419\pi$
$727$	13.8787	+	17.4034i	0.514734	+	0.645456i	−0.454747	+	0.890620i	$0.650270\pi$
$728$		0			0
$729$	18.6780	−	23.4215i	0.691778	−	0.867463i
$730$		0			0
$731$	0.0964011	−	0.0464243i	0.00356552	−	0.00171707i
$732$		0			0
$733$	−26.8704	+	6.13299i	−0.992480	+	0.226527i	−0.687778	−	0.725921i	$-0.741414\pi$
$733$	−26.8704	+	6.13299i	−0.992480	+	0.226527i	−0.304702	+	0.952448i	$0.598557\pi$
$734$		0			0
$735$	−3.76633	+	5.41707i	−0.138923	+	0.199812i
$736$		0			0
$737$	−7.27542	−	31.8757i	−0.267994	−	1.17416i
$738$		0			0
$739$	−15.7143	−	32.6310i	−0.578058	−	1.20035i	−0.960992	−	0.276575i	$-0.910801\pi$
$739$	−15.7143	−	32.6310i	−0.578058	−	1.20035i	0.382934	−	0.923776i	$-0.374914\pi$
$740$		0			0
$741$	2.95633	+	2.35760i	0.108604	+	0.0866085i
$742$		0			0
$743$	29.2699	−	23.3419i	1.07381	−	0.856333i	0.0836785	−	0.996493i	$-0.473333\pi$
$743$	29.2699	−	23.3419i	1.07381	−	0.856333i	0.990129	+	0.140160i	$0.0447617\pi$
$744$		0			0
$745$	0.0669497	+	0.0533906i	0.00245285	+	0.00195608i
$746$		0			0
$747$	−7.08422	−	3.41158i	−0.259198	−	0.124823i
$748$		0			0
$749$	−4.73843	−	12.2376i	−0.173138	−	0.447151i
$750$		0			0
$751$	1.87218	+	1.49302i	0.0683169	+	0.0544809i	0.657053	−	0.753844i	$-0.271803\pi$
$751$	1.87218	+	1.49302i	0.0683169	+	0.0544809i	−0.588736	+	0.808325i	$0.700374\pi$
$752$		0			0
$753$	16.6510			0.606795
$754$		0			0
$755$	−10.2395	−	4.93109i	−0.372654	−	0.179461i
$756$		0			0
$757$	5.80434	−	2.79522i	0.210962	−	0.101594i	−0.325419	−	0.945570i	$-0.605505\pi$
$757$	5.80434	−	2.79522i	0.210962	−	0.101594i	0.536381	+	0.843976i	$0.319791\pi$
$758$		0			0
$759$	−0.467678	+	2.04903i	−0.0169756	+	0.0743751i
$760$		0			0
$761$	−4.63303	−	9.62059i	−0.167947	−	0.348746i	0.799960	−	0.600053i	$-0.204854\pi$
$761$	−4.63303	−	9.62059i	−0.167947	−	0.348746i	−0.967907	+	0.251307i	$0.919140\pi$
$762$		0			0
$763$	33.1333	−	35.3833i	1.19951	−	1.28096i
$764$		0			0
$765$	0.00498799			0.000180341
$766$		0			0
$767$	−2.28318	+	4.74107i	−0.0824408	+	0.171190i
$768$		0			0
$769$	−6.17361	−	1.40909i	−0.222626	−	0.0508129i	0.109753	−	0.993959i	$-0.464994\pi$
$769$	−6.17361	−	1.40909i	−0.222626	−	0.0508129i	−0.332379	+	0.943146i	$0.607851\pi$
$770$		0			0
$771$	38.8840	−	8.87501i	1.40037	−	0.319626i
$772$		0			0
$773$	14.0641	−	3.21005i	0.505852	−	0.115457i	0.0380238	−	0.999277i	$-0.487894\pi$
$773$	14.0641	−	3.21005i	0.505852	−	0.115457i	0.467828	+	0.883819i	$0.345037\pi$
$774$		0			0
$775$	6.03806	−	26.4545i	0.216894	−	0.950273i
$776$		0			0
$777$	16.8382	−	17.9816i	0.604067	−	0.645087i
$778$		0			0
$779$	−5.59833	+	4.46452i	−0.200581	+	0.159958i
$780$		0			0
$781$	−10.0570	−	12.6110i	−0.359866	−	0.451258i
$782$		0			0
$783$	18.9815			0.678342
$784$		0			0
$785$	13.4362			0.479558
$786$		0			0
$787$	13.3793	+	16.7771i	0.476920	+	0.598039i	0.960850	−	0.277068i	$-0.0893627\pi$
$787$	13.3793	+	16.7771i	0.476920	+	0.598039i	−0.483930	+	0.875106i	$0.660791\pi$
$788$		0			0
$789$	−18.7790	+	14.9757i	−0.668549	+	0.533150i
$790$		0			0
$791$	−16.4345	+	6.36347i	−0.584342	+	0.226259i
$792$		0			0
$793$	−0.949136	+	4.15844i	−0.0337048	+	0.147670i
$794$		0			0
$795$	−10.9454	+	2.49822i	−0.388194	+	0.0886028i
$796$		0			0
$797$	50.4157	−	11.5070i	1.78581	−	0.407601i	0.803571	−	0.595209i	$-0.202931\pi$
$797$	50.4157	−	11.5070i	1.78581	−	0.407601i	0.982244	+	0.187609i	$0.0600737\pi$
$798$		0			0
$799$	−0.0468416	−	0.0106913i	−0.00165714	−	0.000378231i
$800$		0			0
$801$	−1.12904	+	2.34447i	−0.0398926	+	0.0828379i
$802$		0			0
$803$	−19.0318			−0.671616
$804$		0			0
$805$	−0.0543151	−	0.371888i	−0.00191435	−	0.0131073i
$806$		0			0
$807$	21.9579	+	45.5961i	0.772956	+	1.60506i
$808$		0			0
$809$	−9.86145	+	43.2058i	−0.346710	+	1.51904i	0.437887	+	0.899030i	$0.355727\pi$
$809$	−9.86145	+	43.2058i	−0.346710	+	1.51904i	−0.784597	+	0.620006i	$0.787130\pi$
$810$		0			0
$811$	−17.7628	+	8.55413i	−0.623737	+	0.300376i	−0.718930	−	0.695083i	$-0.755368\pi$
$811$	−17.7628	+	8.55413i	−0.623737	+	0.300376i	0.0951925	+	0.995459i	$0.469653\pi$
$812$		0			0
$813$	−4.54272	−	2.18766i	−0.159320	−	0.0767245i
$814$		0			0
$815$	−2.35019			−0.0823236
$816$		0			0
$817$	−24.8444	−	19.8128i	−0.869197	−	0.693161i
$818$		0			0
$819$	0.632128	−	0.426756i	0.0220883	−	0.0149121i
$820$		0			0
$821$	−41.2010	−	19.8413i	−1.43792	−	0.692468i	−0.457471	−	0.889224i	$-0.651245\pi$
$821$	−41.2010	−	19.8413i	−1.43792	−	0.692468i	−0.980452	+	0.196757i	$0.936959\pi$
$822$		0			0
$823$	−35.5899	−	28.3820i	−1.24059	−	0.989334i	−0.999824	−	0.0187491i	$-0.994032\pi$
$823$	−35.5899	−	28.3820i	−1.24059	−	0.989334i	−0.240761	−	0.970584i	$-0.577397\pi$
$824$		0			0
$825$	−32.2611	+	25.7274i	−1.12319	+	0.895712i
$826$		0			0
$827$	−11.3608	−	9.05991i	−0.395052	−	0.315044i	0.405737	−	0.913990i	$-0.367015\pi$
$827$	−11.3608	−	9.05991i	−0.395052	−	0.315044i	−0.800789	+	0.598946i	$0.795586\pi$
$828$		0			0
$829$	23.5540	+	48.9105i	0.818065	+	1.69873i	0.709572	+	0.704633i	$0.248889\pi$
$829$	23.5540	+	48.9105i	0.818065	+	1.69873i	0.108494	+	0.994097i	$0.465397\pi$
$830$		0			0
$831$	4.63389	+	20.3024i	0.160748	+	0.704283i
$832$		0			0
$833$	0.0720707	+	0.0791127i	0.00249710	+	0.00274109i
$834$		0			0
$835$	5.60424	−	1.27913i	0.193943	−	0.0442661i
$836$		0			0
$837$	29.2699	−	14.0956i	1.01171	−	0.487216i
$838$		0			0
$839$	10.0997	−	12.6647i	0.348682	−	0.437233i	−0.576304	−	0.817236i	$-0.695505\pi$
$839$	10.0997	−	12.6647i	0.348682	−	0.437233i	0.924985	+	0.380002i	$0.124077\pi$
$840$		0			0
$841$	−10.7973	−	13.5393i	−0.372319	−	0.466874i
$842$		0			0
$843$	19.0269	−	23.8590i	0.655321	−	0.821746i
$844$		0			0
$845$	3.31776	−	6.88940i	0.114134	−	0.237003i
$846$		0			0
$847$	48.4555	+	28.2720i	1.66495	+	0.971438i
$848$		0			0
$849$	−0.780970	+	0.979306i	−0.0268028	+	0.0336097i
$850$		0			0
$851$			1.40329i			0.0481042i
$852$		0			0
$853$	−23.0511	+	47.8660i	−0.789253	+	1.63890i	−0.0201333	+	0.999797i	$0.506409\pi$
$853$	−23.0511	+	47.8660i	−0.789253	+	1.63890i	−0.769120	+	0.639104i	$0.779305\pi$
$854$		0			0
$855$	−0.642751	−	1.33469i	−0.0219816	−	0.0456453i
$856$		0			0
$857$	−44.9322	−	10.2555i	−1.53486	−	0.350321i	−0.630190	−	0.776441i	$-0.717023\pi$
$857$	−44.9322	−	10.2555i	−1.53486	−	0.350321i	−0.904667	+	0.426120i	$0.859880\pi$
$858$		0			0
$859$	33.1725	−	15.9750i	1.13183	−	0.545061i	0.228302	−	0.973590i	$-0.426683\pi$
$859$	33.1725	−	15.9750i	1.13183	−	0.545061i	0.903528	+	0.428530i	$0.140968\pi$
$860$		0			0
$861$	−2.36172	−	6.09943i	−0.0804871	−	0.207868i
$862$		0			0
$863$			58.1443i			1.97925i	0.143659	+	0.989627i	$0.454113\pi$
$863$			58.1443i			1.97925i	−0.143659	+	0.989627i	$0.545887\pi$
$864$		0			0
$865$	−5.08333	−	2.44800i	−0.172838	−	0.0832346i
$866$		0			0
$867$	5.92992	−	25.9807i	0.201391	−	0.882351i
$868$		0			0
$869$	−9.90897	−	43.4140i	−0.336139	−	1.47272i
$870$		0			0
$871$	0.681088	+	2.98404i	0.0230778	+	0.101110i
$872$		0			0
$873$	−7.01088	−	1.60019i	−0.237282	−	0.0541581i
$874$		0			0
$875$	7.72699	−	13.2433i	0.261220	−	0.447705i
$876$		0			0
$877$	−13.5741	−	17.0213i	−0.458364	−	0.574770i	0.497915	−	0.867226i	$-0.334099\pi$
$877$	−13.5741	−	17.0213i	−0.458364	−	0.574770i	−0.956279	+	0.292456i	$0.905528\pi$
$878$		0			0
$879$	0.405368	−	0.323270i	0.0136727	−	0.0109036i
$880$		0			0
$881$		−	17.8583i		−	0.601660i	−0.953678	−	0.300830i	$-0.902736\pi$
$881$		−	17.8583i		−	0.601660i	0.953678	−	0.300830i	$-0.0972636\pi$
$882$		0			0
$883$			26.5907i			0.894847i	0.894322	+	0.447423i	$0.147658\pi$
$883$			26.5907i			0.894847i	−0.894322	+	0.447423i	$0.852342\pi$
$884$		0			0
$885$	−7.29921	+	5.82093i	−0.245360	+	0.195668i
$886$		0			0
$887$	−24.2089	−	30.3570i	−0.812855	−	1.01929i	−0.999322	−	0.0368271i	$-0.988275\pi$
$887$	−24.2089	−	30.3570i	−0.812855	−	1.01929i	0.186466	−	0.982461i	$-0.440297\pi$
$888$		0			0
$889$	4.38488	−	0.640421i	0.147064	−	0.0214790i
$890$		0			0
$891$	−39.1577	−	8.93748i	−1.31183	−	0.299417i
$892$		0			0
$893$	3.17522	+	13.9116i	0.106255	+	0.465533i
$894$		0			0
$895$	1.01049	+	4.42723i	0.0337769	+	0.147986i
$896$		0			0
$897$	0.0437816	−	0.191820i	0.00146183	−	0.00640468i
$898$		0			0
$899$	18.0148	+	8.67545i	0.600826	+	0.289342i
$900$		0			0
$901$			0.182107i			0.00606685i
$902$		0			0
$903$	24.0573	−	16.2414i	0.800578	−	0.540479i
$904$		0			0
$905$	−1.03673	+	0.499264i	−0.0344621	+	0.0165961i
$906$		0			0
$907$	−19.6798	−	4.49179i	−0.653458	−	0.149148i	−0.117076	−	0.993123i	$-0.537352\pi$
$907$	−19.6798	−	4.49179i	−0.653458	−	0.149148i	−0.536382	+	0.843975i	$0.680209\pi$
$908$		0			0
$909$	−3.07429	−	6.38382i	−0.101968	−	0.211738i
$910$		0			0
$911$	−16.9113	+	35.1167i	−0.560296	+	1.16347i	0.407842	+	0.913052i	$0.366281\pi$
$911$	−16.9113	+	35.1167i	−0.560296	+	1.16347i	−0.968139	+	0.250415i	$0.919433\pi$
$912$		0			0
$913$			82.2305i			2.72143i
$914$		0			0
$915$	−4.71827	+	5.91653i	−0.155981	+	0.195594i
$916$		0			0
$917$	46.9956	+	3.73802i	1.55193	+	0.123440i
$918$		0			0
$919$	−5.39717	+	11.2073i	−0.178036	+	0.369696i	−0.970821	−	0.239806i	$-0.922916\pi$
$919$	−5.39717	+	11.2073i	−0.178036	+	0.369696i	0.792785	+	0.609502i	$0.208631\pi$
$920$		0			0
$921$	27.2260	−	34.1404i	0.897128	−	1.12496i
$922$		0			0
$923$	0.941482	+	1.18058i	0.0309892	+	0.0388593i
$924$		0			0
$925$	−17.1778	+	21.5403i	−0.564802	+	0.708239i
$926$		0			0
$927$	−4.68176	+	2.25461i	−0.153769	+	0.0740513i
$928$		0			0
$929$	0.982385	−	0.224223i	0.0322310	−	0.00735651i	−0.206375	−	0.978473i	$-0.566167\pi$
$929$	0.982385	−	0.224223i	0.0322310	−	0.00735651i	0.238606	+	0.971116i	$0.423310\pi$
$930$		0			0
$931$	11.8820	−	29.4791i	0.389416	−	0.966139i
$932$		0			0
$933$	7.26279	+	31.8204i	0.237773	+	1.04175i
$934$		0			0
$935$	−0.0226334	−	0.0469988i	−0.000740192	−	0.00153702i
$936$		0			0
$937$	−26.7844	−	21.3598i	−0.875007	−	0.697795i	0.0792267	−	0.996857i	$-0.474755\pi$
$937$	−26.7844	−	21.3598i	−0.875007	−	0.697795i	−0.954234	+	0.299062i	$0.903326\pi$
$938$		0			0
$939$	9.81155	−	7.82445i	0.320188	−	0.255341i
$940$		0			0
$941$	34.1990	+	27.2728i	1.11485	+	0.889067i	0.994611	−	0.103677i	$-0.0330609\pi$
$941$	34.1990	+	27.2728i	1.11485	+	0.889067i	0.120244	+	0.992744i	$0.461632\pi$
$942$		0			0
$943$	0.335688	+	0.161659i	0.0109315	+	0.00526434i
$944$		0			0
$945$	8.74153	−	1.27672i	0.284362	−	0.0415316i
$946$		0			0
$947$	22.6938	+	18.0977i	0.737450	+	0.588097i	0.918521	−	0.395373i	$-0.129385\pi$
$947$	22.6938	+	18.0977i	0.737450	+	0.588097i	−0.181070	+	0.983470i	$0.557956\pi$
$948$		0			0
$949$	1.78166			0.0578350
$950$		0			0
$951$	−19.5281	−	9.40422i	−0.633241	−	0.304953i
$952$		0			0
$953$	35.9750	−	17.3246i	1.16534	−	0.561200i	0.251736	−	0.967796i	$-0.418998\pi$
$953$	35.9750	−	17.3246i	1.16534	−	0.561200i	0.913608	+	0.406596i	$0.133284\pi$
$954$		0			0
$955$	−3.52948	+	15.4637i	−0.114211	+	0.500392i
$956$		0			0
$957$	−13.1926	−	27.3948i	−0.426457	−	0.885548i
$958$		0			0
$959$	−49.0161	−	3.89873i	−1.58281	−	0.125897i
$960$		0			0
$961$	3.22159			0.103922
$962$		0			0
$963$	−1.16777	+	2.42490i	−0.0376309	+	0.0781414i
$964$		0			0
$965$	−3.60047	−	0.821783i	−0.115903	−	0.0264541i
$966$		0			0
$967$	−37.1536	+	8.48006i	−1.19478	+	0.272700i	−0.773242	−	0.634111i	$-0.781366\pi$
$967$	−37.1536	+	8.48006i	−1.19478	+	0.272700i	−0.421536	+	0.906812i	$0.638509\pi$
$968$		0			0
$969$	0.106090	−	0.0242144i	0.00340811	−	0.000777878i
$970$		0			0
$971$	4.23374	−	18.5492i	0.135867	−	0.595273i	−0.860451	−	0.509534i	$-0.829818\pi$
$971$	4.23374	−	18.5492i	0.135867	−	0.595273i	0.996318	−	0.0857387i	$-0.0273250\pi$
$972$		0			0
$973$	−0.308831	+	0.985187i	−0.00990066	+	0.0315837i
$974$		0			0
$975$	3.02012	−	2.40847i	0.0967213	−	0.0771327i
$976$		0			0
$977$	28.7015	+	35.9906i	0.918244	+	1.15144i	0.988089	+	0.153883i	$0.0491780\pi$
$977$	28.7015	+	35.9906i	0.918244	+	1.15144i	−0.0698454	+	0.997558i	$0.522251\pi$
$978$		0			0
$979$	27.2136			0.869750
$980$		0			0
$981$	−9.94191			−0.317421
$982$		0			0
$983$	−18.2035	−	22.8264i	−0.580600	−	0.728049i	0.401615	−	0.915809i	$-0.368449\pi$
$983$	−18.2035	−	22.8264i	−0.580600	−	0.728049i	−0.982215	+	0.187759i	$0.939878\pi$
$984$		0			0
$985$	−0.218664	+	0.174379i	−0.00696723	+	0.00555618i
$986$		0			0
$987$	−12.9931	−	1.03347i	−0.413575	−	0.0328957i
$988$		0			0
$989$	−0.367932	+	1.61202i	−0.0116996	+	0.0512591i
$990$		0			0
$991$	1.95126	−	0.445363i	0.0619839	−	0.0141474i	−0.191417	−	0.981509i	$-0.561308\pi$
$991$	1.95126	−	0.445363i	0.0619839	−	0.0141474i	0.253400	+	0.967361i	$0.418451\pi$
$992$		0			0
$993$	−27.9217	+	6.37294i	−0.886068	+	0.202239i
$994$		0			0
$995$	10.9151	+	2.49130i	0.346032	+	0.0789794i
$996$		0			0
$997$	23.5121	−	48.8233i	0.744635	−	1.54625i	−0.0903080	−	0.995914i	$-0.528785\pi$
$997$	23.5121	−	48.8233i	0.744635	−	1.54625i	0.834943	−	0.550336i	$-0.185501\pi$
$998$		0			0
$999$	−32.9854			−1.04361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.6	✓	120
4.3	odd	2	inner	784.2.bb.b.111.15	yes	120
49.34	odd	14	inner	784.2.bb.b.671.15	yes	120
196.83	even	14	inner	784.2.bb.b.671.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.6	✓	120	1.1	even	1	trivial
784.2.bb.b.111.15	yes	120	4.3	odd	2	inner
784.2.bb.b.671.6	yes	120	196.83	even	14	inner
784.2.bb.b.671.15	yes	120	49.34	odd	14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.977383 - 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(1.48039 + 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +O(q^{10})\)	\(q+(-0.977383 - 1.22560i) q^{3} +(-0.470082 + 0.374878i) q^{5} +(1.48039 + 2.19281i) q^{7} +(0.120747 - 0.529025i) q^{9} +(-5.53257 + 1.26277i) q^{11} +(0.517931 - 0.118214i) q^{13} +(0.918900 + 0.209733i) q^{15} +(0.00663338 - 0.0137744i) q^{17} -4.54052 q^{19} +(1.24060 - 3.95759i) q^{21} +(0.102508 + 0.212861i) q^{23} +(-1.03216 + 4.52219i) q^{25} +(-5.00346 + 2.40954i) q^{27} +(-3.07949 - 1.48300i) q^{29} -5.84992 q^{31} +(6.95509 + 5.54650i) q^{33} +(-1.51794 - 0.475836i) q^{35} +(5.35144 + 2.57712i) q^{37} +(-0.651100 - 0.519235i) q^{39} +(1.23297 - 0.983262i) q^{41} +(5.47172 + 4.36355i) q^{43} +(0.141559 + 0.293950i) q^{45} +(-0.699308 - 3.06387i) q^{47} +(-2.61688 + 6.49245i) q^{49} +(-0.0233652 + 0.00533296i) q^{51} +(-10.7318 + 5.16818i) q^{53} +(2.12738 - 2.66764i) q^{55} +(4.43782 + 5.56486i) q^{57} +(-6.17584 + 7.74426i) q^{59} +(-3.48363 + 7.23382i) q^{61} +(1.33881 - 0.518390i) q^{63} +(-0.199154 + 0.249731i) q^{65} +5.76147i q^{67} +(0.160692 - 0.333681i) q^{69} +(1.23326 + 2.56090i) q^{71} +(3.26962 + 0.746269i) q^{73} +(6.55121 - 3.15490i) q^{75} +(-10.9594 - 10.2625i) q^{77} +7.84700i q^{79} +(6.37675 + 3.07088i) q^{81} +(3.22440 - 14.1270i) q^{83} +(0.00204547 + 0.00896179i) q^{85} +(1.19227 + 5.22368i) q^{87} +(-4.67524 - 1.06709i) q^{89} +(1.02596 + 0.960723i) q^{91} +(5.71761 + 7.16966i) q^{93} +(2.13442 - 1.70214i) q^{95} -13.2524i q^{97} +3.07934i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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