LMFDB - Embedded newform 539.2.q.c.422.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + \cdots + 625 $ x^16 - x^15 - 5x^14 + 16x^13 + 4x^12 - 29x^11 + 10x^10 - 156x^9 + 251x^8 + 240x^7 + 390x^6 - 1375x^5 - 300x^4 + 500x^3 + 375x^2 + 625x + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			422.1
Root			$-2.41283 - 0.512862i$ of defining polynomial
Character	$\chi$	$=$	539.422
Dual form			539.2.q.c.410.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33993 + 0.596574i) q^{2} +(1.58268 - 0.336408i) q^{3} +(0.101241 - 0.112439i) q^{4} +(-0.0487868 - 0.464175i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(0.837913 - 2.57883i) q^{8} +(-0.348943 + 0.155360i) q^{9} +O(q^{10})$	\(q+(-1.33993 + 0.596574i) q^{2} +(1.58268 - 0.336408i) q^{3} +(0.101241 - 0.112439i) q^{4} +(-0.0487868 - 0.464175i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(0.837913 - 2.57883i) q^{8} +(-0.348943 + 0.155360i) q^{9} +(0.342285 + 0.592855i) q^{10} +(-1.01240 + 3.15833i) q^{11} +(0.122406 - 0.212013i) q^{12} +(1.28012 + 0.930062i) q^{13} +(-0.233366 - 0.718226i) q^{15} +(0.447352 + 4.25627i) q^{16} +(4.77540 + 2.12614i) q^{17} +(0.374875 - 0.416341i) q^{18} +(2.82502 + 3.13750i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} +(-0.527635 - 4.83590i) q^{22} +(0.902527 - 1.56322i) q^{23} +(0.458605 - 4.36334i) q^{24} +(4.67766 - 0.994267i) q^{25} +(-2.27012 - 0.482528i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.840363 + 2.58637i) q^{29} +(0.741168 + 0.823150i) q^{30} +(-0.135245 + 1.28677i) q^{31} +(-0.427051 - 0.739674i) q^{32} +(-0.539813 + 5.33919i) q^{33} -7.66708 q^{34} +(-0.0178588 + 0.0549637i) q^{36} +(1.89977 + 0.403808i) q^{37} +(-5.65706 - 2.51869i) q^{38} +(2.33890 + 1.04134i) q^{39} +(-1.23791 - 0.263126i) q^{40} +(-0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(0.252625 + 0.433586i) q^{44} +(0.0891378 + 0.154391i) q^{45} +(-0.276742 + 2.63303i) q^{46} +(-4.27929 - 4.75263i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-5.67457 + 4.12281i) q^{50} +(8.27316 + 1.75851i) q^{51} +(0.234176 - 0.0497757i) q^{52} +(1.38024 - 13.1321i) q^{53} +(4.01308 - 6.95085i) q^{54} +(1.51541 + 0.315846i) q^{55} +(5.52656 + 4.01528i) q^{57} +(-2.66898 - 2.96421i) q^{58} +(-5.75712 + 6.39393i) q^{59} +(-0.104383 - 0.0464744i) q^{60} +(1.59303 + 15.1567i) q^{61} +(-0.586436 - 1.80486i) q^{62} +(-5.91123 - 4.29476i) q^{64} +(0.369259 - 0.639575i) q^{65} +(-2.46191 - 7.47616i) q^{66} +(2.33791 + 4.04938i) q^{67} +(0.722528 - 0.321690i) q^{68} +(0.902527 - 2.77769i) q^{69} +(-7.88234 + 5.72685i) q^{71} +(0.108262 + 1.03004i) q^{72} +(-8.91283 + 9.89870i) q^{73} +(-2.78645 + 0.592278i) q^{74} +(7.06874 - 3.14721i) q^{75} +0.638786 q^{76} -3.75519 q^{78} +(3.27261 - 1.45706i) q^{79} +(1.95383 - 0.415299i) q^{80} +(-5.15780 + 5.72831i) q^{81} +(-0.159620 - 1.51868i) q^{82} +(13.9627 - 10.1445i) q^{83} +(0.753927 - 2.32035i) q^{85} +(-11.6684 + 5.19508i) q^{86} +(2.20010 + 3.81068i) q^{87} +(7.29650 + 5.25721i) q^{88} +(4.45991 - 7.72479i) q^{89} +(-0.211544 - 0.153696i) q^{90} +(-0.0843952 - 0.259742i) q^{92} +(0.218831 + 2.08204i) q^{93} +(8.56923 + 3.81526i) q^{94} +(1.31852 - 1.46437i) q^{95} +(-0.924716 - 1.02700i) q^{96} +(2.18727 + 1.58915i) q^{97} +(-0.137407 - 1.25936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 2 * q^9	$ 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9} + 28 q^{10} - 5 q^{11} + 14 q^{12} + 10 q^{13} + 12 q^{15} + 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 42 q^{20} - 2 q^{22} + 16 q^{23} - 21 q^{24} - 5 q^{25} - 21 q^{26} - 44 q^{27} - 18 q^{29} - 14 q^{30} + 11 q^{31} + 20 q^{32} - 10 q^{33} - 48 q^{34} - 4 q^{36} - 6 q^{37} - 35 q^{38} + 5 q^{39} + 16 q^{40} - 44 q^{41} + 32 q^{43} - 29 q^{44} - 18 q^{45} - 29 q^{46} - 7 q^{47} + 8 q^{48} - 68 q^{50} - 3 q^{51} - 21 q^{52} - 2 q^{53} - 4 q^{54} + 52 q^{55} - 6 q^{57} + 39 q^{58} - 25 q^{59} + 38 q^{60} - 7 q^{61} - 10 q^{62} + 2 q^{64} - 24 q^{65} - 18 q^{66} + 30 q^{67} - 8 q^{68} + 16 q^{69} - 28 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} - 5 q^{75} - 104 q^{76} - 36 q^{78} + 9 q^{79} + 33 q^{80} + 28 q^{81} - 31 q^{82} + 46 q^{83} - 20 q^{85} + 17 q^{86} - 12 q^{87} + 7 q^{88} + 34 q^{89} + 4 q^{90} - 68 q^{92} - 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 60 q^{97}+O(q^{100}) $ 16 * q + q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 2 * q^9 + 28 * q^10 - 5 * q^11 + 14 * q^12 + 10 * q^13 + 12 * q^15 + 3 * q^16 + 11 * q^17 - 4 * q^18 + 9 * q^19 + 42 * q^20 - 2 * q^22 + 16 * q^23 - 21 * q^24 - 5 * q^25 - 21 * q^26 - 44 * q^27 - 18 * q^29 - 14 * q^30 + 11 * q^31 + 20 * q^32 - 10 * q^33 - 48 * q^34 - 4 * q^36 - 6 * q^37 - 35 * q^38 + 5 * q^39 + 16 * q^40 - 44 * q^41 + 32 * q^43 - 29 * q^44 - 18 * q^45 - 29 * q^46 - 7 * q^47 + 8 * q^48 - 68 * q^50 - 3 * q^51 - 21 * q^52 - 2 * q^53 - 4 * q^54 + 52 * q^55 - 6 * q^57 + 39 * q^58 - 25 * q^59 + 38 * q^60 - 7 * q^61 - 10 * q^62 + 2 * q^64 - 24 * q^65 - 18 * q^66 + 30 * q^67 - 8 * q^68 + 16 * q^69 - 28 * q^71 - 3 * q^72 - 3 * q^73 + 9 * q^74 - 5 * q^75 - 104 * q^76 - 36 * q^78 + 9 * q^79 + 33 * q^80 + 28 * q^81 - 31 * q^82 + 46 * q^83 - 20 * q^85 + 17 * q^86 - 12 * q^87 + 7 * q^88 + 34 * q^89 + 4 * q^90 - 68 * q^92 - 8 * q^93 + 30 * q^94 - 24 * q^95 - 10 * q^96 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.33993	+	0.596574i	−0.947471	+	0.421841i	−0.821510	−	0.570194i	$-0.806868\pi$
$2$	−1.33993	+	0.596574i	−0.947471	+	0.421841i	−0.125961	+	0.992035i	$0.540201\pi$
$3$	1.58268	−	0.336408i	0.913758	−	0.194225i	0.273041	−	0.962002i	$-0.411970\pi$
$3$	1.58268	−	0.336408i	0.913758	−	0.194225i	0.640717	+	0.767777i	$0.278637\pi$
$4$	0.101241	−	0.112439i	0.0506205	−	0.0562197i
$5$	−0.0487868	−	0.464175i	−0.0218181	−	0.207585i	0.978182	−	0.207750i	$-0.0666142\pi$
$5$	−0.0487868	−	0.464175i	−0.0218181	−	0.207585i	−1.00000		0.000164961i	$0.999947\pi$
$6$	−1.91998	+	1.39494i	−0.783827	+	0.569484i
$7$		0			0
$7$		0			0
$8$	0.837913	−	2.57883i	0.296247	−	0.911755i
$9$	−0.348943	+	0.155360i	−0.116314	+	0.0517865i
$10$	0.342285	+	0.592855i	0.108240	+	0.187477i
$11$	−1.01240	+	3.15833i	−0.305250	+	0.952272i
$11$	−1.01240	+	3.15833i	−0.305250	+	0.952272i
$12$	0.122406	−	0.212013i	0.0353356	−	0.0612030i
$13$	1.28012	+	0.930062i	0.355042	+	0.257953i	0.750981	−	0.660324i	$-0.229581\pi$
$13$	1.28012	+	0.930062i	0.355042	+	0.257953i	−0.395939	+	0.918277i	$0.629581\pi$
$14$		0			0
$15$	−0.233366	−	0.718226i	−0.0602548	−	0.185445i
$16$	0.447352	+	4.25627i	0.111838	+	1.06407i
$17$	4.77540	+	2.12614i	1.15820	+	0.515666i	0.893676	−	0.448712i	$-0.148117\pi$
$17$	4.77540	+	2.12614i	1.15820	+	0.515666i	0.264528	+	0.964378i	$0.414784\pi$
$18$	0.374875	−	0.416341i	0.0883589	−	0.0981324i
$19$	2.82502	+	3.13750i	0.648103	+	0.719791i	0.974236	−	0.225533i	$-0.0724122\pi$
$19$	2.82502	+	3.13750i	0.648103	+	0.719791i	−0.326133	+	0.945324i	$0.605746\pi$
$20$	−0.0571308	−	0.0415079i	−0.0127748	−	0.00928146i
$21$		0			0
$22$	−0.527635	−	4.83590i	−0.112492	−	1.03102i
$23$	0.902527	−	1.56322i	0.188190	−	0.325954i	−0.756457	−	0.654044i	$-0.773071\pi$
$23$	0.902527	−	1.56322i	0.188190	−	0.325954i	0.944647	+	0.328089i	$0.106405\pi$
$24$	0.458605	−	4.36334i	0.0936124	−	0.890662i
$25$	4.67766	−	0.994267i	0.935532	−	0.198853i
$26$	−2.27012	−	0.482528i	−0.445207	−	0.0946316i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$		0			0
$29$	0.840363	+	2.58637i	0.156051	+	0.480277i	0.998266	−	0.0588657i	$-0.0187484\pi$
$29$	0.840363	+	2.58637i	0.156051	+	0.480277i	−0.842215	+	0.539143i	$0.818748\pi$
$30$	0.741168	+	0.823150i	0.135318	+	0.150286i
$31$	−0.135245	+	1.28677i	−0.0242908	+	0.231111i	0.975640	+	0.219376i	$0.0704022\pi$
$31$	−0.135245	+	1.28677i	−0.0242908	+	0.231111i	−0.999931	+	0.0117351i	$0.996265\pi$
$32$	−0.427051	−	0.739674i	−0.0754927	−	0.130757i
$33$	−0.539813	+	5.33919i	−0.0939694	+	0.929434i
$34$	−7.66708			−1.31489
$35$		0			0
$36$	−0.0178588	+	0.0549637i	−0.00297647	+	0.00916062i
$37$	1.89977	+	0.403808i	0.312320	+	0.0663856i	0.361405	−	0.932409i	$-0.382297\pi$
$37$	1.89977	+	0.403808i	0.312320	+	0.0663856i	−0.0490852	+	0.998795i	$0.515631\pi$
$38$	−5.65706	−	2.51869i	−0.917696	−	0.408585i
$39$	2.33890	+	1.04134i	0.374523	+	0.166749i
$40$	−1.23791	−	0.263126i	−0.195730	−	0.0416038i
$41$	−0.321724	+	0.990166i	−0.0502449	+	0.154638i	−0.973031	−	0.230675i	$-0.925907\pi$
$41$	−0.321724	+	0.990166i	−0.0502449	+	0.154638i	0.922786	+	0.385313i	$0.125907\pi$
$42$		0			0
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	0.252625	+	0.433586i	0.0380846	+	0.0653655i
$45$	0.0891378	+	0.154391i	0.0132879	+	0.0230153i
$46$	−0.276742	+	2.63303i	−0.0408034	+	0.388219i
$47$	−4.27929	−	4.75263i	−0.624198	−	0.693243i	0.345258	−	0.938508i	$-0.387792\pi$
$47$	−4.27929	−	4.75263i	−0.624198	−	0.693243i	−0.969456	+	0.245265i	$0.921125\pi$
$48$	2.13986	+	6.58580i	0.308862	+	0.950578i
$49$		0			0
$50$	−5.67457	+	4.12281i	−0.802505	+	0.583054i
$51$	8.27316	+	1.75851i	1.15847	+	0.246241i
$52$	0.234176	−	0.0497757i	0.0324744	−	0.00690265i
$53$	1.38024	−	13.1321i	0.189590	−	1.80383i	−0.324277	−	0.945962i	$-0.605121\pi$
$53$	1.38024	−	13.1321i	0.189590	−	1.80383i	0.513867	−	0.857870i	$-0.328212\pi$
$54$	4.01308	−	6.95085i	0.546111	−	0.945892i
$55$	1.51541	+	0.315846i	0.204338	+	0.0425887i
$56$		0			0
$57$	5.52656	+	4.01528i	0.732011	+	0.531837i
$58$	−2.66898	−	2.96421i	−0.350455	−	0.389219i
$59$	−5.75712	+	6.39393i	−0.749514	+	0.832419i	−0.990414	−	0.138131i	$-0.955891\pi$
$59$	−5.75712	+	6.39393i	−0.749514	+	0.832419i	0.240900	+	0.970550i	$0.422557\pi$
$60$	−0.104383	−	0.0464744i	−0.0134758	−	0.00599982i
$61$	1.59303	+	15.1567i	0.203967	+	1.94061i	0.320112	+	0.947380i	$0.396279\pi$
$61$	1.59303	+	15.1567i	0.203967	+	1.94061i	−0.116146	+	0.993232i	$0.537054\pi$
$62$	−0.586436	−	1.80486i	−0.0744774	−	0.229218i
$63$		0			0
$64$	−5.91123	−	4.29476i	−0.738904	−	0.536845i
$65$	0.369259	−	0.639575i	0.0458009	−	0.0793295i
$66$	−2.46191	−	7.47616i	−0.303040	−	0.920252i
$67$	2.33791	+	4.04938i	0.285622	+	0.494711i	0.972760	−	0.231816i	$-0.0744666\pi$
$67$	2.33791	+	4.04938i	0.285622	+	0.494711i	−0.687138	+	0.726527i	$0.741133\pi$
$68$	0.722528	−	0.321690i	0.0876194	−	0.0390107i
$69$	0.902527	−	2.77769i	0.108651	−	0.334395i
$70$		0			0
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	−0.947324	−	0.320277i	$-0.896224\pi$
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	0.0118626	+	0.999930i	$0.496224\pi$
$72$	0.108262	+	1.03004i	0.0127588	+	0.121392i
$73$	−8.91283	+	9.89870i	−1.04317	+	1.15856i	−0.0560717	+	0.998427i	$0.517858\pi$
$73$	−8.91283	+	9.89870i	−1.04317	+	1.15856i	−0.987096	+	0.160129i	$0.948809\pi$
$74$	−2.78645	+	0.592278i	−0.323918	+	0.0688509i
$75$	7.06874	−	3.14721i	0.816228	−	0.363408i
$76$	0.638786			0.0732737
$77$		0			0
$78$	−3.75519			−0.425191
$79$	3.27261	−	1.45706i	0.368197	−	0.163932i	−0.214293	−	0.976769i	$-0.568745\pi$
$79$	3.27261	−	1.45706i	0.368197	−	0.163932i	0.582491	+	0.812837i	$0.302078\pi$
$80$	1.95383	−	0.415299i	0.218445	−	0.0464318i
$81$	−5.15780	+	5.72831i	−0.573088	+	0.636479i
$82$	−0.159620	−	1.51868i	−0.0176271	−	0.167710i
$83$	13.9627	−	10.1445i	1.53261	−	1.11351i	0.577842	−	0.816148i	$-0.303895\pi$
$83$	13.9627	−	10.1445i	1.53261	−	1.11351i	0.954766	−	0.297357i	$-0.0961052\pi$
$84$		0			0
$85$	0.753927	−	2.32035i	0.0817748	−	0.251677i
$86$	−11.6684	+	5.19508i	−1.25823	+	0.560200i
$87$	2.20010	+	3.81068i	0.235875	+	0.408548i
$88$	7.29650	+	5.25721i	0.777809	+	0.560421i
$89$	4.45991	−	7.72479i	0.472750	−	0.818826i	−0.526764	−	0.850012i	$-0.676595\pi$
$89$	4.45991	−	7.72479i	0.472750	−	0.818826i	0.999514	+	0.0311853i	$0.00992820\pi$
$90$	−0.211544	−	0.153696i	−0.0222987	−	0.0162009i
$91$		0			0
$92$	−0.0843952	−	0.259742i	−0.00879881	−	0.0270799i
$93$	0.218831	+	2.08204i	0.0226918	+	0.215898i
$94$	8.56923	+	3.81526i	0.883848	+	0.393515i
$95$	1.31852	−	1.46437i	0.135278	−	0.150241i
$96$	−0.924716	−	1.02700i	−0.0943784	−	0.104818i
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	0.693264	−	0.720684i	$-0.256172\pi$
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	−0.471180	+	0.882037i	$0.656172\pi$
$98$		0			0
$99$	−0.137407	−	1.25936i	−0.0138099	−	0.126571i
$100$	0.361776	−	0.626614i	0.0361776	−	0.0626614i
$101$	−0.0186877	+	0.177802i	−0.00185950	+	0.0176919i	−0.995412	−	0.0956784i	$-0.969498\pi$
$101$	−0.0186877	+	0.177802i	−0.00185950	+	0.0176919i	0.993553	+	0.113370i	$0.0361646\pi$
$102$	−12.1345	+	2.57927i	−1.20150	+	0.255386i
$103$	−16.5084	−	3.50897i	−1.62662	−	0.345749i	−0.697806	−	0.716287i	$-0.745840\pi$
$103$	−16.5084	−	3.50897i	−1.62662	−	0.345749i	−0.928817	+	0.370538i	$0.879173\pi$
$104$	3.47110	−	2.52190i	0.340370	−	0.247293i
$105$		0			0
$106$	5.98484	+	18.4195i	0.581299	+	1.78906i
$107$	−10.3556	−	11.5011i	−1.00111	−	1.11185i	−0.993722	−	0.111878i	$-0.964313\pi$
$107$	−10.3556	−	11.5011i	−1.00111	−	1.11185i	−0.00739268	−	0.999973i	$-0.502353\pi$
$108$	−0.0865439	+	0.823411i	−0.00832769	+	0.0792327i
$109$	−5.51745	−	9.55650i	−0.528476	−	0.915347i	−0.999449	−	0.0331994i	$-0.989430\pi$
$109$	−5.51745	−	9.55650i	−0.528476	−	0.915347i	0.470973	−	0.882148i	$-0.343903\pi$
$110$	−2.21896	+	0.480843i	−0.211570	+	0.0458466i
$111$	3.14256			0.298278
$112$		0			0
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	−0.922027	−	0.387127i	$-0.873468\pi$
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	0.973482	+	0.228762i	$0.0734676\pi$
$114$	−9.80060	−	2.08318i	−0.917910	−	0.195108i
$115$	−0.769640	−	0.342666i	−0.0717693	−	0.0319538i
$116$	0.375889	+	0.167357i	0.0349004	+	0.0155387i
$117$	−0.591184	−	0.125660i	−0.0546550	−	0.0116173i
$118$	3.89967	−	12.0019i	0.358994	−	1.10487i
$119$		0			0
$120$	−2.04773			−0.186931
$121$	−8.95009	−	6.39498i	−0.813645	−	0.581362i
$122$	−11.1766	−	19.3584i	−1.01188	−	1.75263i
$123$	−0.176086	+	1.67534i	−0.0158771	+	0.151061i
$124$	0.130992	+	0.145481i	0.0117634	+	0.0130646i
$125$	−1.41086	−	4.34219i	−0.126191	−	0.388377i
$126$		0			0
$127$	6.90919	−	5.01982i	0.613092	−	0.445437i	−0.237410	−	0.971410i	$-0.576298\pi$
$127$	6.90919	−	5.01982i	0.613092	−	0.445437i	0.850502	+	0.525972i	$0.176298\pi$
$128$	12.1536	+	2.58333i	1.07424	+	0.228337i
$129$	13.7823	−	2.92951i	1.21346	−	0.257929i
$130$	−0.113226	+	1.07727i	−0.00993057	+	0.0944831i
$131$	4.83354	−	8.37194i	0.422308	−	0.731460i	−0.573856	−	0.818956i	$-0.694553\pi$
$131$	4.83354	−	8.37194i	0.422308	−	0.731460i	0.996165	+	0.0874963i	$0.0278866\pi$
$132$	0.545685	+	0.601241i	0.0474957	+	0.0523313i
$133$		0			0
$134$	−5.54839	−	4.03114i	−0.479308	−	0.348237i
$135$	1.70897	+	1.89801i	0.147085	+	0.163354i
$136$	9.48434	−	10.5334i	0.813275	−	0.903234i
$137$	−12.7995	−	5.69871i	−1.09354	−	0.486874i	−0.220926	−	0.975291i	$-0.570908\pi$
$137$	−12.7995	−	5.69871i	−1.09354	−	0.486874i	−0.872610	+	0.488417i	$0.837574\pi$
$138$	0.447778	+	4.26033i	0.0381174	+	0.362663i
$139$	2.95966	+	9.10889i	0.251035	+	0.772606i	0.994585	+	0.103926i	$0.0331404\pi$
$139$	2.95966	+	9.10889i	0.251035	+	0.772606i	−0.743550	+	0.668680i	$0.766860\pi$
$140$		0			0
$141$	−8.37155	−	6.08229i	−0.705012	−	0.512221i
$142$	7.14526	−	12.3760i	0.599617	−	1.03857i
$143$	−4.23344	+	3.10145i	−0.354018	+	0.259356i
$144$	−0.817352	−	1.41570i	−0.0681127	−	0.117975i
$145$	1.15953	−	0.516256i	0.0962937	−	0.0428727i
$146$	6.03723	−	18.5807i	0.499645	−	1.53775i
$147$		0			0
$148$	0.237738	−	0.172727i	0.0195419	−	0.0141980i
$149$	−1.56401	−	14.8805i	−0.128128	−	1.21906i	−0.849905	−	0.526935i	$-0.823341\pi$
$149$	−1.56401	−	14.8805i	−0.128128	−	1.21906i	0.721777	−	0.692126i	$-0.243326\pi$
$150$	−7.59405	+	8.43405i	−0.620052	+	0.688637i
$151$	2.80956	−	0.597191i	0.228639	−	0.0485987i	−0.0921673	−	0.995744i	$-0.529379\pi$
$151$	2.80956	−	0.597191i	0.228639	−	0.0485987i	0.320806	+	0.947145i	$0.396046\pi$
$152$	10.4582	−	4.65629i	0.848272	−	0.377675i
$153$	−1.99666			−0.161420
$154$		0			0
$155$	0.603886			0.0485053
$156$	0.353880	−	0.157558i	0.0283331	−	0.0126147i
$157$	18.4697	−	3.92586i	1.47404	−	0.313317i	0.600327	−	0.799755i	$-0.295037\pi$
$157$	18.4697	−	3.92586i	1.47404	−	0.313317i	0.873715	+	0.486437i	$0.161704\pi$
$158$	−3.51581	+	3.90470i	−0.279703	+	0.310642i
$159$	−2.23327	−	21.2482i	−0.177110	−	1.68509i
$160$	−0.322504	+	0.234313i	−0.0254962	+	0.0185240i
$161$		0			0
$162$	3.49371	−	10.7525i	0.274491	−	0.844798i
$163$	10.5927	−	4.71617i	0.829683	−	0.369399i	0.0524596	−	0.998623i	$-0.483294\pi$
$163$	10.5927	−	4.71617i	0.829683	−	0.369399i	0.777224	+	0.629224i	$0.216627\pi$
$164$	0.0787620	+	0.136420i	0.00615028	+	0.0106526i
$165$	2.50466	−	0.00991418i	0.194987	−	0.000771818i
$166$	−12.6571	+	21.9227i	−0.982380	+	1.70153i
$167$	−5.11696	−	3.71769i	−0.395963	−	0.287684i	0.371932	−	0.928260i	$-0.378695\pi$
$167$	−5.11696	−	3.71769i	−0.395963	−	0.287684i	−0.767894	+	0.640576i	$0.778695\pi$
$168$		0			0
$169$	−3.24353	−	9.98255i	−0.249502	−	0.767889i
$170$	0.374052	+	3.55887i	0.0286885	+	0.272953i
$171$	−1.47321	−	0.655916i	−0.112659	−	0.0501591i
$172$	0.881627	−	0.979146i	0.0672234	−	0.0746591i
$173$	0.896008	+	0.995118i	0.0681222	+	0.0756574i	0.776243	−	0.630434i	$-0.217123\pi$
$173$	0.896008	+	0.995118i	0.0681222	+	0.0756574i	−0.708120	+	0.706092i	$0.750457\pi$
$174$	−5.22132	−	3.79351i	−0.395827	−	0.287585i
$175$		0			0
$176$	−13.8956	−	2.89616i	−1.04742	−	0.218306i
$177$	−6.96069	+	12.0563i	−0.523197	+	0.906205i
$178$	−1.36754	+	13.0113i	−0.102502	+	0.975239i
$179$	−17.4001	+	3.69850i	−1.30054	+	0.276439i	−0.805586	−	0.592478i	$-0.798150\pi$
$179$	−17.4001	+	3.69850i	−1.30054	+	0.276439i	−0.494957	+	0.868917i	$0.664816\pi$
$180$	0.0263841	+	0.00560811i	0.00196655	+	0.000418004i
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	−0.558430	−	0.829551i	$-0.688596\pi$
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	0.616386	+	0.787444i	$0.288596\pi$
$182$		0			0
$183$	7.62007	+	23.4522i	0.563292	+	1.73363i
$184$	−3.27505	−	3.63731i	−0.241440	−	0.268146i
$185$	0.0947540	−	0.901524i	0.00696645	−	0.0662814i
$186$	−1.53531	−	2.65923i	−0.112574	−	0.194984i
$187$	−11.5497	+	12.9298i	−0.844596	+	0.945519i
$188$	−0.967622			−0.0705711
$189$		0			0
$190$	−0.893121	+	2.74874i	−0.0647938	+	0.199415i
$191$	15.7373	+	3.34506i	1.13871	+	0.242040i	0.738415	−	0.674347i	$-0.235575\pi$
$191$	15.7373	+	3.34506i	1.13871	+	0.242040i	0.400294	+	0.916387i	$0.368908\pi$
$192$	−10.8004	−	4.80863i	−0.779449	−	0.347033i
$193$	11.0973	+	4.94082i	0.798798	+	0.355648i	0.765204	−	0.643788i	$-0.222638\pi$
$193$	11.0973	+	4.94082i	0.798798	+	0.355648i	0.0335938	+	0.999436i	$0.489305\pi$
$194$	−3.87883	−	0.824470i	−0.278484	−	0.0591935i
$195$	0.369259	−	1.13646i	0.0264432	−	0.0813837i
$196$		0			0
$197$	−2.30179			−0.163996			−0.0819978	−	0.996633i	$-0.526130\pi$
$197$	−2.30179			−0.163996			−0.0819978	+	0.996633i	$0.526130\pi$
$198$	0.935418	+	1.60548i	0.0664773	+	0.114097i
$199$	−10.1399	−	17.5627i	−0.718795	−	1.24499i	−0.961477	−	0.274884i	$-0.911360\pi$
$199$	−10.1399	−	17.5627i	−0.718795	−	1.24499i	0.242682	−	0.970106i	$-0.421973\pi$
$200$	1.35542	−	12.8960i	0.0958430	−	0.911885i
$201$	5.06241	+	5.62237i	0.357075	+	0.396571i
$202$	−0.0810316	−	0.249390i	−0.00570136	−	0.0175470i
$203$		0			0
$204$	1.03531	−	0.752196i	0.0724861	−	0.0526642i
$205$	0.475306	+	0.101029i	0.0331968	+	0.00705620i
$206$	24.2134	−	5.14672i	1.68703	−	0.358589i
$207$	−0.0720692	+	0.685692i	−0.00500915	+	0.0476589i
$208$	−3.38593	+	5.86460i	−0.234772	+	0.406637i
$209$	−12.7693	+	5.74593i	−0.883271	+	0.397454i
$210$		0			0
$211$	−4.34062	−	3.15364i	−0.298820	−	0.217106i	0.428264	−	0.903654i	$-0.359125\pi$
$211$	−4.34062	−	3.15364i	−0.298820	−	0.217106i	−0.727085	+	0.686548i	$0.759125\pi$
$212$	−1.33683	−	1.48470i	−0.0918138	−	0.101970i
$213$	−10.5486	+	11.7154i	−0.722780	+	0.802728i
$214$	20.7370	+	9.23270i	1.41755	+	0.631135i
$215$	−0.424845	−	4.04213i	−0.0289742	−	0.275671i
$216$	4.58517	+	14.1117i	0.311982	+	0.960181i
$217$		0			0
$218$	13.0941	+	9.51344i	0.886847	+	0.644332i
$219$	−10.7761	+	18.6648i	−0.728183	+	1.26125i
$220$	0.188935	−	0.138415i	0.0127380	−	0.00933195i
$221$	4.13564	+	7.16314i	0.278193	+	0.481845i
$222$	−4.21080	+	1.87477i	−0.282610	+	0.125826i
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	0.236072	+	0.971736i	$0.424140\pi$
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	−0.762158	+	0.647391i	$0.775860\pi$
$224$		0			0
$225$	−1.47777	+	1.07366i	−0.0985179	+	0.0715775i
$226$	0.271380	+	2.58201i	0.0180519	+	0.171753i
$227$	−14.5267	+	16.1335i	−0.964169	+	1.07082i	0.0332810	+	0.999446i	$0.489404\pi$
$227$	−14.5267	+	16.1335i	−0.964169	+	1.07082i	−0.997450	+	0.0713718i	$0.977262\pi$
$228$	1.01099	−	0.214893i	0.0669545	−	0.0142316i
$229$	18.7557	−	8.35058i	1.23941	−	0.551822i	0.320861	−	0.947126i	$-0.396028\pi$
$229$	18.7557	−	8.35058i	1.23941	−	0.551822i	0.918550	+	0.395305i	$0.129361\pi$
$230$	1.23569			0.0814787
$231$		0			0
$232$	7.37396			0.484124
$233$	0.634051	−	0.282298i	0.0415381	−	0.0184939i	−0.385862	−	0.922556i	$-0.626096\pi$
$233$	0.634051	−	0.282298i	0.0415381	−	0.0184939i	0.427401	+	0.904062i	$0.359429\pi$
$234$	0.867108	−	0.184309i	0.0566846	−	0.0120487i
$235$	−1.99728	+	2.21820i	−0.130288	+	0.144700i
$236$	0.136074	+	1.29466i	0.00885765	+	0.0842749i
$237$	4.68931	−	3.40699i	0.304604	−	0.221307i
$238$		0			0
$239$	0.107093	−	0.329599i	0.00692728	−	0.0213200i	−0.947533	−	0.319658i	$-0.896432\pi$
$239$	0.107093	−	0.329599i	0.00692728	−	0.0213200i	0.954460	+	0.298338i	$0.0964321\pi$
$240$	2.95257	−	1.31457i	0.190587	−	0.0848550i
$241$	5.21858	+	9.03885i	0.336158	+	0.582243i	0.983707	−	0.179781i	$-0.0575390\pi$
$241$	5.21858	+	9.03885i	0.336158	+	0.582243i	−0.647548	+	0.762024i	$0.724206\pi$
$242$	15.8075	+	3.22942i	1.01615	+	0.207595i
$243$	1.97214	−	3.41584i	0.126513	−	0.219126i
$244$	1.86549	+	1.35536i	0.119426	+	0.0867677i
$245$		0			0
$246$	−0.763523	−	2.34988i	−0.0486805	−	0.149823i
$247$	0.698293	+	6.64382i	0.0444313	+	0.422736i
$248$	3.20505	+	1.42698i	0.203521	+	0.0906132i
$249$	18.6858	−	20.7527i	1.18416	−	1.31515i
$250$	4.48089	+	4.97653i	0.283396	+	0.314743i
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	0.751883	−	0.659297i	$-0.229146\pi$
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	−0.394684	+	0.918817i	$0.629146\pi$
$252$		0			0
$253$	4.02345	+	4.43308i	0.252952	+	0.278706i
$254$	−6.26311	+	10.8480i	−0.392983	+	0.680666i
$255$	0.412638	−	3.92599i	0.0258404	−	0.245855i
$256$	−3.53209	+	0.750768i	−0.220755	+	0.0469230i
$257$	9.73103	+	2.06839i	0.607005	+	0.129023i	0.501153	−	0.865359i	$-0.332910\pi$
$257$	9.73103	+	2.06839i	0.607005	+	0.129023i	0.105853	+	0.994382i	$0.466243\pi$
$258$	−16.7196	+	12.1475i	−1.04091	+	0.756268i
$259$		0			0
$260$	−0.0345293	−	0.106270i	−0.00214142	−	0.00659061i
$261$	−0.695056	−	0.771938i	−0.0430229	−	0.0477818i
$262$	−1.48211	+	14.1013i	−0.0915651	+	0.871184i
$263$	−7.09017	−	12.2805i	−0.437199	−	0.757250i	0.560274	−	0.828308i	$-0.310696\pi$
$263$	−7.09017	−	12.2805i	−0.437199	−	0.757250i	−0.997472	+	0.0710574i	$0.977363\pi$
$264$	13.3166	+	5.86587i	0.819578	+	0.361019i
$265$	−6.16293			−0.378586
$266$		0			0
$267$	4.45991	−	13.7262i	0.272942	−	0.840029i
$268$	0.692003	+	0.147090i	0.0422708	+	0.00898494i
$269$	−16.8120	−	7.48521i	−1.02505	−	0.456381i	−0.175829	−	0.984421i	$-0.556261\pi$
$269$	−16.8120	−	7.48521i	−1.02505	−	0.456381i	−0.849220	+	0.528040i	$0.822927\pi$
$270$	−3.42220	−	1.52366i	−0.208268	−	0.0927270i
$271$	−0.714626	−	0.151898i	−0.0434104	−	0.00922717i	0.186155	−	0.982520i	$-0.440397\pi$
$271$	−0.714626	−	0.151898i	−0.0434104	−	0.00922717i	−0.229566	+	0.973293i	$0.573731\pi$
$272$	−6.91316	+	21.2765i	−0.419172	+	1.29008i
$273$		0			0
$274$	20.5501			1.24148
$275$	−1.59544	+	15.7802i	−0.0962085	+	0.951581i
$276$	−0.220949	−	0.382696i	−0.0132996	−	0.0230356i
$277$	−1.57466	+	14.9819i	−0.0946120	+	0.900173i	0.839540	+	0.543298i	$0.182825\pi$
$277$	−1.57466	+	14.9819i	−0.0946120	+	0.900173i	−0.934152	+	0.356875i	$0.883842\pi$
$278$	−9.39985	−	10.4396i	−0.563765	−	0.626125i
$279$	−0.152719	−	0.470022i	−0.00914308	−	0.0281395i
$280$		0			0
$281$	8.65334	−	6.28702i	0.516215	−	0.375052i	−0.298961	−	0.954265i	$-0.596640\pi$
$281$	8.65334	−	6.28702i	0.516215	−	0.375052i	0.815176	+	0.579213i	$0.196640\pi$
$282$	14.8458	+	3.15557i	0.884054	+	0.187912i
$283$	−8.90985	+	1.89385i	−0.529636	+	0.112578i	−0.464965	−	0.885329i	$-0.653933\pi$
$283$	−8.90985	+	1.89385i	−0.529636	+	0.112578i	−0.0646708	+	0.997907i	$0.520600\pi$
$284$	−0.154091	+	1.46608i	−0.00914361	+	0.0869957i
$285$	1.59417	−	2.76119i	0.0944306	−	0.163559i
$286$	3.82225	−	6.68127i	0.226014	−	0.395072i
$287$		0			0
$288$	0.263932	+	0.191758i	0.0155523	+	0.0112994i
$289$	6.90872	+	7.67291i	0.406395	+	0.451347i
$290$	−1.24570	+	1.38349i	−0.0731500	+	0.0812413i
$291$	3.99635	+	1.77929i	0.234270	+	0.104304i
$292$	0.210661	+	2.00431i	0.0123280	+	0.117293i
$293$	3.67390	+	11.3071i	0.214632	+	0.660569i	0.999180	+	0.0405002i	$0.0128951\pi$
$293$	3.67390	+	11.3071i	0.214632	+	0.660569i	−0.784548	+	0.620068i	$0.787105\pi$
$294$		0			0
$295$	3.24878	+	2.36037i	0.189151	+	0.137426i
$296$	2.63319	−	4.56082i	0.153051	−	0.265092i
$297$	−5.67663	−	17.2384i	−0.329392	−	1.00027i
$298$	10.9730	+	19.0058i	0.635648	+	1.10097i
$299$	2.60924	−	1.16171i	0.150896	−	0.0671833i
$300$	0.361776	−	1.11343i	0.0208871	−	0.0642840i
$301$		0			0
$302$	−3.40834	+	2.47630i	−0.196128	+	0.142495i
$303$	0.0302373	+	0.287689i	0.00173709	+	0.0165273i
$304$	−12.0903	+	13.4276i	−0.693424	+	0.770125i
$305$	6.95762	−	1.47889i	0.398392	−	0.0846809i
$306$	2.67538	−	1.19115i	0.152941	−	0.0680938i
$307$	2.22072			0.126743			0.0633716	−	0.997990i	$-0.479815\pi$
$307$	2.22072			0.126743			0.0633716	+	0.997990i	$0.479815\pi$
$308$		0			0
$309$	−27.3079			−1.55349
$310$	−0.809162	+	0.360262i	−0.0459573	+	0.0204615i
$311$	20.9446	−	4.45192i	1.18766	−	0.252445i	0.428619	−	0.903485i	$-0.359000\pi$
$311$	20.9446	−	4.45192i	1.18766	−	0.252445i	0.759043	+	0.651040i	$0.225667\pi$
$312$	4.64524	−	5.15907i	0.262985	−	0.292075i
$313$	3.29837	+	31.3819i	0.186435	+	1.77381i	0.543188	+	0.839611i	$0.317217\pi$
$313$	3.29837	+	31.3819i	0.186435	+	1.77381i	−0.356753	+	0.934199i	$0.616116\pi$
$314$	−22.4060	+	16.2789i	−1.26444	+	0.918671i
$315$		0			0
$316$	0.167491	−	0.515484i	0.00942211	−	0.0289983i
$317$	−12.0594	+	5.36919i	−0.677324	+	0.301564i	−0.716418	−	0.697672i	$-0.754219\pi$
$317$	−12.0594	+	5.36919i	−0.677324	+	0.301564i	0.0390940	+	0.999236i	$0.487553\pi$
$318$	15.6685	+	27.1387i	0.878647	+	1.52186i
$319$	−9.01939	+	0.0357015i	−0.504989	+	0.00199890i
$320$	−1.70513	+	2.95337i	−0.0953197	+	0.165099i
$321$	−20.2586	−	14.7188i	−1.13073	−	0.821521i
$322$		0			0
$323$	6.81980	+	20.9892i	0.379464	+	1.16787i
$324$	0.121908	+	1.15988i	0.00677268	+	0.0644377i
$325$	6.91270	+	3.07773i	0.383448	+	0.170722i
$326$	−11.3799	+	12.6386i	−0.630273	+	0.699989i
$327$	−11.9472	−	13.2687i	−0.660683	−	0.733763i
$328$	2.28389	+	1.65935i	0.126107	+	0.0916220i
$329$		0			0
$330$	−3.35014	+	1.50750i	−0.184419	+	0.0829849i
$331$	−4.73826	+	8.20692i	−0.260439	+	0.451093i	−0.966359	−	0.257199i	$-0.917200\pi$
$331$	−4.73826	+	8.20692i	−0.260439	+	0.451093i	0.705920	+	0.708292i	$0.250534\pi$
$332$	0.272956	−	2.59700i	0.0149804	−	0.142529i
$333$	−0.725646	+	0.154241i	−0.0397652	+	0.00845234i
$334$	9.07423	+	1.92879i	0.496520	+	0.105539i
$335$	1.76556	−	1.28276i	0.0964631	−	0.0700845i
$336$		0			0
$337$	−5.93346	−	18.2613i	−0.323216	−	0.994758i	−0.972239	−	0.233989i	$-0.924822\pi$
$337$	−5.93346	−	18.2613i	−0.323216	−	0.994758i	0.649023	−	0.760769i	$-0.275178\pi$
$338$	10.3014	+	11.4409i	0.560323	+	0.622302i
$339$	0.299374	−	2.84836i	0.0162598	−	0.154701i
$340$	−0.184570	−	0.319685i	−0.0100097	−	0.0173374i
$341$	−3.92713	−	1.72988i	−0.212666	−	0.0936781i
$342$	2.36530			0.127901
$343$		0			0
$344$	7.29672	−	22.4570i	0.393413	−	1.21080i
$345$	−1.33337	−	0.283416i	−0.0717860	−	0.0152586i
$346$	−1.79425	−	0.798850i	−0.0964593	−	0.0429464i
$347$	2.78477	+	1.23986i	0.149494	+	0.0665591i	0.480120	−	0.877203i	$-0.340593\pi$
$347$	2.78477	+	1.23986i	0.149494	+	0.0665591i	−0.330626	+	0.943762i	$0.607260\pi$
$348$	0.651211	+	0.138419i	0.0349086	+	0.00742004i
$349$	5.99373	−	18.4468i	0.320837	−	0.987435i	−0.652448	−	0.757834i	$-0.726258\pi$
$349$	5.99373	−	18.4468i	0.320837	−	0.987435i	0.973285	−	0.229601i	$-0.0737421\pi$
$350$		0			0
$351$	−8.65865			−0.462165
$352$	2.76848	−	0.599922i	0.147561	−	0.0319759i
$353$	5.37926	+	9.31716i	0.286309	+	0.495902i	0.972926	−	0.231117i	$-0.0742382\pi$
$353$	5.37926	+	9.31716i	0.286309	+	0.495902i	−0.686617	+	0.727020i	$0.740905\pi$
$354$	2.13436	−	20.3071i	0.113440	−	1.07931i
$355$	3.04282	+	3.37939i	0.161496	+	0.179359i
$356$	−0.417046	−	1.28353i	−0.0221034	−	0.0680272i
$357$		0			0
$358$	21.1084	−	15.3361i	1.11561	−	0.810541i
$359$	−0.593956	−	0.126249i	−0.0313478	−	0.00666318i	0.192211	−	0.981354i	$-0.438434\pi$
$359$	−0.593956	−	0.126249i	−0.0313478	−	0.00666318i	−0.223559	+	0.974690i	$0.571768\pi$
$360$	0.472839	−	0.100505i	0.0249208	−	0.00529708i
$361$	0.122862	−	1.16895i	0.00646643	−	0.0615239i
$362$	−0.706801	+	1.22422i	−0.0371486	+	0.0643433i
$363$	−16.3164	−	7.11030i	−0.856390	−	0.373194i
$364$		0			0
$365$	5.02956	+	3.65419i	0.263259	+	0.191269i
$366$	−24.2013	−	26.8783i	−1.26502	−	1.40495i
$367$	18.5101	−	20.5575i	0.966217	−	1.07309i	−0.0310725	−	0.999517i	$-0.509892\pi$
$367$	18.5101	−	20.5575i	0.966217	−	1.07309i	0.997290	−	0.0735758i	$-0.0234411\pi$
$368$	7.05724	+	3.14209i	0.367884	+	0.163793i
$369$	−0.0415682	−	0.395495i	−0.00216395	−	0.0205886i
$370$	0.410862	+	1.26450i	0.0213597	+	0.0657384i
$371$		0			0
$372$	0.256258	+	0.186183i	0.0132864	+	0.00965311i
$373$	14.7257	−	25.5056i	0.762465	−	1.32063i	−0.179111	−	0.983829i	$-0.557322\pi$
$373$	14.7257	−	25.5056i	0.762465	−	1.32063i	0.941576	−	0.336800i	$-0.109345\pi$
$374$	7.76215	−	24.2152i	0.401371	−	1.25214i
$375$	−3.69369	−	6.39765i	−0.190741	−	0.330373i
$376$	−15.8419	+	7.05327i	−0.816984	+	0.363745i
$377$	−1.32972	+	4.09246i	−0.0684840	+	0.210772i
$378$		0			0
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.972817	−	0.231577i	$-0.925612\pi$
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.0803745	+	0.996765i	$0.525612\pi$
$380$	−0.0311643	−	0.296508i	−0.00159869	−	0.0152106i
$381$	9.24630	−	10.2691i	0.473702	−	0.526100i
$382$	−23.0824	+	4.90630i	−1.18100	+	0.251028i
$383$	−29.1715	+	12.9880i	−1.49059	+	0.663655i	−0.980510	−	0.196469i	$-0.937052\pi$
$383$	−29.1715	+	12.9880i	−1.49059	+	0.663655i	−0.510084	+	0.860124i	$0.670386\pi$
$384$	20.1043			1.02594
$385$		0			0
$386$	−17.8171			−0.906865
$387$	−3.03867	+	1.35290i	−0.154464	+	0.0687719i
$388$	0.400124	−	0.0850490i	0.0203132	−	0.00431771i
$389$	11.8782	−	13.1921i	0.602249	−	0.668865i	−0.362516	−	0.931977i	$-0.618082\pi$
$389$	11.8782	−	13.1921i	0.602249	−	0.668865i	0.964765	+	0.263112i	$0.0847489\pi$
$390$	0.183203	+	1.74306i	0.00927687	+	0.0882635i
$391$	7.63356	−	5.54611i	0.386046	−	0.280479i
$392$		0			0
$393$	4.83354	−	14.8761i	0.243820	−	0.750400i
$394$	3.08422	−	1.37319i	0.155381	−	0.0691801i
$395$	−0.835990	−	1.44798i	−0.0420632	−	0.0728557i
$396$	−0.155513	−	0.112049i	−0.00781484	−	0.00563069i
$397$	6.65233	−	11.5222i	0.333871	−	0.578282i	−0.649396	−	0.760450i	$-0.724978\pi$
$397$	6.65233	−	11.5222i	0.333871	−	0.578282i	0.983267	+	0.182169i	$0.0583116\pi$
$398$	24.0641	+	17.4836i	1.20623	+	0.876374i
$399$		0			0
$400$	6.32443	+	19.4646i	0.316221	+	0.973229i
$401$	0.364765	+	3.47051i	0.0182155	+	0.173309i	0.999847	−	0.0174765i	$-0.00556322\pi$
$401$	0.364765	+	3.47051i	0.0182155	+	0.173309i	−0.981632	+	0.190785i	$0.938897\pi$
$402$	−10.1374	−	4.51346i	−0.505608	−	0.225111i
$403$	−1.36991	+	1.52144i	−0.0682400	+	0.0757882i
$404$	0.0181000	+	0.0201020i	0.000900506	+	0.00100011i
$405$	2.91057	+	2.11465i	0.144627	+	0.105078i
$406$		0			0
$407$	−3.19868	+	5.59127i	−0.158553	+	0.277149i
$408$	11.4671	−	19.8616i	0.567706	−	0.983296i
$409$	3.09671	−	29.4632i	0.153122	−	1.45686i	−0.600537	−	0.799597i	$-0.705047\pi$
$409$	3.09671	−	29.4632i	0.153122	−	1.45686i	0.753659	−	0.657265i	$-0.228287\pi$
$410$	−0.697146	+	0.148183i	−0.0344296	+	0.00731824i
$411$	−22.1746	−	4.71335i	−1.09379	−	0.232492i
$412$	−2.06587	+	1.50095i	−0.101778	+	0.0739463i
$413$		0			0
$414$	−0.312499	−	0.961771i	−0.0153585	−	0.0472685i
$415$	−5.39003	−	5.98623i	−0.264586	−	0.293853i
$416$	0.141266	−	1.34406i	0.00692613	−	0.0658978i
$417$	7.74848	+	13.4208i	0.379445	+	0.657218i
$418$	13.6820	−	15.3169i	0.669211	−	0.749176i
$419$	−11.6452			−0.568907			−0.284454	−	0.958690i	$-0.591812\pi$
$419$	−11.6452			−0.568907			−0.284454	+	0.958690i	$0.591812\pi$
$420$		0			0
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	−0.682204	−	0.731162i	$-0.738978\pi$
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	0.981681	−	0.190533i	$-0.0610217\pi$
$422$	7.69748	+	1.63615i	0.374708	+	0.0796466i
$423$	2.23160	+	0.993571i	0.108504	+	0.0483091i
$424$	−32.7089	−	14.5630i	−1.58849	−	0.707240i
$425$	24.4516	+	5.19736i	1.18608	+	0.252109i
$426$	7.14526	−	21.9908i	0.346189	−	1.06546i
$427$		0			0
$428$	−2.34159			−0.113185
$429$	−5.65681	+	6.33275i	−0.273113	+	0.305748i
$430$	2.98069	+	5.16271i	0.143742	+	0.248968i
$431$	−3.16161	+	30.0807i	−0.152289	+	1.44894i	0.605193	+	0.796079i	$0.293096\pi$
$431$	−3.16161	+	30.0807i	−0.152289	+	1.44894i	−0.757482	+	0.652856i	$0.773571\pi$
$432$	−15.6705	−	17.4038i	−0.753946	−	0.837342i
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	0.899694	−	0.436521i	$-0.143789\pi$
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	−0.984448	+	0.175674i	$0.943789\pi$
$434$		0			0
$435$	1.66149	−	1.20714i	0.0796622	−	0.0578780i
$436$	−1.63312	−	0.347130i	−0.0782122	−	0.0166245i
$437$	7.45426	−	1.58445i	0.356586	−	0.0757946i
$438$	3.30429	−	31.4382i	0.157885	−	1.50217i
$439$	−3.42437	+	5.93119i	−0.163436	+	0.283080i	−0.936099	−	0.351737i	$-0.885591\pi$
$439$	−3.42437	+	5.93119i	−0.163436	+	0.283080i	0.772663	+	0.634817i	$0.218925\pi$
$440$	2.08430	−	3.64333i	0.0993649	−	0.173689i
$441$		0			0
$442$	−9.81479	−	7.13086i	−0.466842	−	0.339181i
$443$	0.0673782	+	0.0748311i	0.00320123	+	0.00355533i	0.744743	−	0.667351i	$-0.232572\pi$
$443$	0.0673782	+	0.0748311i	0.00320123	+	0.00355533i	−0.741542	+	0.670906i	$0.765905\pi$
$444$	0.318155	−	0.353347i	0.0150990	−	0.0167691i
$445$	−3.80324	−	1.69331i	−0.180291	−	0.0802707i
$446$	−3.89773	−	37.0845i	−0.184563	−	1.75600i
$447$	−7.48125	−	23.0249i	−0.353851	−	1.08904i
$448$		0			0
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.991729	−	0.128351i	$-0.0409683\pi$
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.184392	+	0.982853i	$0.440968\pi$
$450$	1.33958	−	2.32023i	0.0631486	−	0.109377i
$451$	−2.80156	−	2.01855i	−0.131920	−	0.0950500i
$452$	−0.133908	−	0.231936i	−0.00629852	−	0.0109093i
$453$	4.24573	−	1.89032i	0.199482	−	0.0888150i
$454$	9.83984	−	30.2839i	0.461807	−	1.42129i
$455$		0			0
$456$	14.9855	−	10.8876i	0.701761	−	0.509859i
$457$	−2.41833	−	23.0088i	−0.113124	−	1.07631i	−0.892902	−	0.450251i	$-0.851335\pi$
$457$	−2.41833	−	23.0088i	−0.113124	−	1.07631i	0.779778	−	0.626057i	$-0.215332\pi$
$458$	−20.1495	+	22.3783i	−0.941525	+	1.04567i
$459$	−27.9795	+	5.94724i	−1.30597	+	0.277593i
$460$	−0.116448	+	0.0518461i	−0.00542943	+	0.00241734i
$461$	−2.77839			−0.129403			−0.0647013	−	0.997905i	$-0.520609\pi$
$461$	−2.77839			−0.129403			−0.0647013	+	0.997905i	$0.520609\pi$
$462$		0			0
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	−10.6323	+	4.73382i	−0.493594	+	0.219762i
$465$	0.955756	−	0.203152i	0.0443221	−	0.00942095i
$466$	−0.681171	+	0.756517i	−0.0315546	+	0.0350450i
$467$	0.277867	+	2.64373i	0.0128582	+	0.122337i	0.999068	−	0.0431620i	$-0.0137432\pi$
$467$	0.277867	+	2.64373i	0.0128582	+	0.122337i	−0.986210	+	0.165499i	$0.947076\pi$
$468$	−0.0739811	+	0.0537504i	−0.00341978	+	0.00248461i
$469$		0			0
$470$	1.35289	−	4.16375i	0.0624040	−	0.192060i
$471$	27.9109	−	12.4267i	1.28606	−	0.572593i
$472$	11.6649	+	20.2042i	0.536921	+	0.929974i
$473$	−8.81618	+	27.5034i	−0.405369	+	1.26461i
$474$	−4.25082	+	7.36263i	−0.195246	+	0.338177i
$475$	16.3340	+	11.8673i	0.749454	+	0.544510i
$476$		0			0
$477$	1.55857	+	4.79679i	0.0713621	+	0.219630i
$478$	0.0531330	+	0.505527i	0.00243025	+	0.0231223i
$479$	−7.56620	−	3.36869i	−0.345708	−	0.153919i	0.226535	−	0.974003i	$-0.427260\pi$
$479$	−7.56620	−	3.36869i	−0.345708	−	0.153919i	−0.572244	+	0.820084i	$0.693927\pi$
$480$	−0.431594	+	0.479334i	−0.0196995	+	0.0218785i
$481$	2.05636	+	2.28382i	0.0937621	+	0.104133i
$482$	−12.3848	−	8.99812i	−0.564114	−	0.409853i
$483$		0			0
$484$	−1.62516	+	0.358909i	−0.0738711	+	0.0163141i
$485$	0.630932	−	1.09281i	0.0286492	−	0.0496218i
$486$	−0.604717	+	5.75350i	−0.0274305	+	0.260984i
$487$	19.1674	−	4.07415i	0.868556	−	0.184617i	0.247981	−	0.968765i	$-0.420233\pi$
$487$	19.1674	−	4.07415i	0.868556	−	0.184617i	0.620575	+	0.784147i	$0.286899\pi$
$488$	40.4213	+	8.59181i	1.82979	+	0.388933i
$489$	15.1782	−	11.0276i	0.686384	−	0.498687i
$490$		0			0
$491$	−8.86312	−	27.2779i	−0.399987	−	1.23103i	−0.925009	−	0.379945i	$-0.875943\pi$
$491$	−8.86312	−	27.2779i	−0.399987	−	1.23103i	0.525022	−	0.851089i	$-0.324057\pi$
$492$	0.170547	+	0.189412i	0.00768887	+	0.00853936i
$493$	−1.48593	+	14.1377i	−0.0669229	+	0.636729i
$494$	−4.89919	−	8.48564i	−0.220425	−	0.381787i
$495$	−0.577862	+	0.125221i	−0.0259730	+	0.00562827i
$496$	−5.53735			−0.248634
$497$		0			0
$498$	−12.6571	+	38.9545i	−0.567177	+	1.74559i
$499$	−27.3391	−	5.81111i	−1.22387	−	0.260141i	−0.449734	−	0.893163i	$-0.648481\pi$
$499$	−27.3391	−	5.81111i	−1.22387	−	0.260141i	−0.774134	+	0.633022i	$0.781814\pi$
$500$	−0.631070	−	0.280970i	−0.0282223	−	0.0125654i
$501$	−9.34916	−	4.16251i	−0.417690	−	0.185967i
$502$	−10.0356	−	2.13314i	−0.447912	−	0.0952066i
$503$	−2.50222	+	7.70104i	−0.111568	+	0.343373i	−0.991216	−	0.132254i	$-0.957779\pi$
$503$	−2.50222	+	7.70104i	−0.111568	+	0.343373i	0.879647	+	0.475626i	$0.157779\pi$
$504$		0			0
$505$	0.0834428			0.00371316
$506$	−8.03579	−	3.53972i	−0.357235	−	0.157360i
$507$	−8.49166	−	14.7080i	−0.377128	−	0.653205i
$508$	0.135067	−	1.28508i	0.00599263	−	0.0570161i
$509$	10.9069	+	12.1134i	0.483441	+	0.536916i	0.934681	−	0.355487i	$-0.115685\pi$
$509$	10.9069	+	12.1134i	0.483441	+	0.536916i	−0.451240	+	0.892403i	$0.649018\pi$
$510$	1.78924	+	5.50670i	0.0792287	+	0.243841i
$511$		0			0
$512$	−15.8195	+	11.4935i	−0.699129	+	0.507947i
$513$	−22.5981	−	4.80337i	−0.997729	−	0.212074i
$514$	−14.2728	+	3.03378i	−0.629547	+	0.133814i
$515$	−0.823385	+	7.83399i	−0.0362827	+	0.345207i
$516$	1.06594	−	1.84626i	0.0469252	−	0.0812769i
$517$	19.3427	−	8.70384i	0.850692	−	0.382795i
$518$		0			0
$519$	1.75286	+	1.27352i	0.0769419	+	0.0559015i
$520$	−1.33995	−	1.48816i	−0.0587606	−	0.0652603i
$521$	5.14297	−	5.71185i	0.225318	−	0.250241i	−0.619877	−	0.784699i	$-0.712818\pi$
$521$	5.14297	−	5.71185i	0.225318	−	0.250241i	0.845195	+	0.534458i	$0.179484\pi$
$522$	1.39184	+	0.619688i	0.0609193	+	0.0271230i
$523$	−2.73059	−	25.9798i	−0.119400	−	1.13602i	−0.876058	−	0.482207i	$-0.839835\pi$
$523$	−2.73059	−	25.9798i	−0.119400	−	1.13602i	0.756657	−	0.653812i	$-0.226831\pi$
$524$	−0.451984	−	1.39106i	−0.0197450	−	0.0607689i
$525$		0			0
$526$	16.8265	+	12.2252i	0.733672	+	0.533044i
$527$	−3.38171	+	5.85730i	−0.147310	+	0.255148i
$528$	−22.9665	+	0.0909084i	−0.999489	+	0.00395628i
$529$	9.87089	+	17.0969i	0.429169	+	0.743343i
$530$	8.25787	−	3.67664i	0.358699	−	0.159703i
$531$	1.01555	−	3.12554i	0.0440712	−	0.135637i
$532$		0			0
$533$	−1.33276	+	0.968308i	−0.0577283	+	0.0419421i
$534$	2.21273	+	21.0527i	0.0957543	+	0.911042i
$535$	−4.83329	+	5.36792i	−0.208961	+	0.232075i
$536$	12.4016	−	2.63605i	0.535670	−	0.113860i
$537$	−26.2945	+	11.7071i	−1.13469	+	0.505197i
$538$	26.9924			1.16372
$539$		0			0
$540$	0.386429			0.0166292
$541$	−23.6404	+	10.5254i	−1.01638	+	0.452522i	−0.846186	−	0.532888i	$-0.821107\pi$
$541$	−23.6404	+	10.5254i	−1.01638	+	0.452522i	−0.170195	+	0.985410i	$0.554440\pi$
$542$	1.04816	−	0.222794i	0.0450225	−	0.00956983i
$543$	1.04346	−	1.15888i	0.0447791	−	0.0497322i
$544$	−0.466685	−	4.44021i	−0.0200089	−	0.190372i
$545$	−4.16671	+	3.02729i	−0.178482	+	0.129675i
$546$		0			0
$547$	−11.7726	+	36.2322i	−0.503359	+	1.54918i	0.300154	+	0.953891i	$0.402962\pi$
$547$	−11.7726	+	36.2322i	−0.503359	+	1.54918i	−0.803513	+	0.595288i	$0.797038\pi$
$548$	−1.93659	+	0.862227i	−0.0827272	+	0.0368325i
$549$	−2.91061	−	5.04132i	−0.124222	−	0.215158i
$550$	−7.27627	−	22.0961i	−0.310261	−	0.942180i
$551$	−5.74069	+	9.94317i	−0.244562	+	0.423593i
$552$	−6.40696	−	4.65493i	−0.272698	−	0.198127i
$553$		0			0
$554$	−6.82786	−	21.0140i	−0.290088	−	0.892799i
$555$	−0.153315	−	1.45870i	−0.00650787	−	0.0619182i
$556$	1.32384	+	0.589410i	0.0561432	+	0.0249966i
$557$	23.1132	−	25.6698i	0.979339	−	1.08767i	−0.0167988	−	0.999859i	$-0.505347\pi$
$557$	23.1132	−	25.6698i	0.979339	−	1.08767i	0.996138	−	0.0878070i	$-0.0279859\pi$
$558$	0.485036	+	0.538687i	0.0205332	+	0.0228044i
$559$	11.1476	+	8.09917i	0.471491	+	0.342558i
$560$		0			0
$561$	−13.9297	+	24.3490i	−0.588113	+	1.02802i
$562$	−7.84417	+	13.5865i	−0.330886	+	0.573112i
$563$	−2.03642	+	19.3752i	−0.0858247	+	0.816568i	0.863938	+	0.503598i	$0.167991\pi$
$563$	−2.03642	+	19.3752i	−0.0858247	+	0.816568i	−0.949763	+	0.312970i	$0.898676\pi$
$564$	−1.53143	+	0.325516i	−0.0644850	+	0.0137067i
$565$	−0.808098	−	0.171767i	−0.0339969	−	0.00722627i
$566$	10.8087	−	7.85300i	0.454325	−	0.330086i
$567$		0			0
$568$	8.16387	+	25.1258i	0.342549	+	1.05426i
$569$	11.4614	+	12.7292i	0.480486	+	0.533634i	0.933837	−	0.357698i	$-0.116438\pi$
$569$	11.4614	+	12.7292i	0.480486	+	0.533634i	−0.453351	+	0.891332i	$0.649772\pi$
$570$	−0.488821	+	4.65083i	−0.0204745	+	0.194802i
$571$	1.92790	+	3.33923i	0.0806802	+	0.139742i	0.903542	−	0.428499i	$-0.140957\pi$
$571$	1.92790	+	3.33923i	0.0806802	+	0.139742i	−0.822862	+	0.568241i	$0.807624\pi$
$572$	−0.0798719	+	0.789999i	−0.00333961	+	0.0330315i
$573$	26.0323			1.08751
$574$		0			0
$575$	2.66745	−	8.20958i	0.111240	−	0.342363i
$576$	2.72992	+	0.580262i	0.113747	+	0.0241776i
$577$	−8.93616	−	3.97864i	−0.372017	−	0.165633i	0.212208	−	0.977225i	$-0.431935\pi$
$577$	−8.93616	−	3.97864i	−0.372017	−	0.165633i	−0.584225	+	0.811592i	$0.698601\pi$
$578$	−13.8346	−	6.15957i	−0.575444	−	0.256204i
$579$	19.2255	+	4.08650i	0.798984	+	0.169829i
$580$	0.0593443	−	0.182643i	0.00246414	−	0.00758384i
$581$		0			0
$582$	−6.41628			−0.265964
$583$	40.0781	+	17.6542i	1.65987	+	0.731161i
$584$	18.0589	+	31.2789i	0.747283	+	1.29433i
$585$	−0.0294863	+	0.280543i	−0.00121911	+	0.0115990i
$586$	−11.6683	−	12.9589i	−0.482012	−	0.535329i
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	0.904599	−	0.426264i	$-0.140170\pi$
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	−0.982387	+	0.186855i	$0.940170\pi$
$588$		0			0
$589$	−4.41932	+	3.21082i	−0.182095	+	0.132300i
$590$	−5.76126	−	1.22459i	−0.237187	−	0.0504157i
$591$	−3.64298	+	0.774340i	−0.149852	+	0.0318521i
$592$	−0.868850	+	8.26656i	−0.0357095	+	0.339753i
$593$	−6.61648	+	11.4601i	−0.271706	+	0.470609i	−0.969299	−	0.245886i	$-0.920921\pi$
$593$	−6.61648	+	11.4601i	−0.271706	+	0.470609i	0.697593	+	0.716495i	$0.254255\pi$
$594$	17.8903	+	19.7117i	0.734046	+	0.808780i
$595$		0			0
$596$	−1.83150	−	1.33066i	−0.0750212	−	0.0545061i
$597$	−21.9564	−	24.3850i	−0.898614	−	0.998012i
$598$	−2.80314	+	3.11320i	−0.114629	+	0.127308i
$599$	−5.41289	−	2.40997i	−0.221165	−	0.0984689i	0.293163	−	0.956062i	$-0.405292\pi$
$599$	−5.41289	−	2.40997i	−0.221165	−	0.0984689i	−0.514328	+	0.857593i	$0.671959\pi$
$600$	−2.19312	−	20.8662i	−0.0895339	−	0.851858i
$601$	3.93712	+	12.1172i	0.160599	+	0.494272i	0.998685	−	0.0512657i	$-0.0163255\pi$
$601$	3.93712	+	12.1172i	0.160599	+	0.494272i	−0.838086	+	0.545538i	$0.816326\pi$
$602$		0			0
$603$	−1.44491	−	1.04979i	−0.0588413	−	0.0427507i
$604$	0.217295	−	0.376366i	0.00884161	−	0.0153141i
$605$	−2.53175	+	4.46640i	−0.102930	+	0.181585i
$606$	−0.212144	−	0.367443i	−0.00861774	−	0.0149264i
$607$	7.63853	−	3.40089i	0.310038	−	0.138038i	−0.245819	−	0.969316i	$-0.579057\pi$
$607$	7.63853	−	3.40089i	0.310038	−	0.138038i	0.555857	+	0.831278i	$0.312390\pi$
$608$	1.11430	−	3.42946i	0.0451908	−	0.139083i
$609$		0			0
$610$	−8.44044	+	6.13234i	−0.341743	+	0.248291i
$611$	−1.05776	−	10.0639i	−0.0427925	−	0.407144i
$612$	−0.202144	+	0.224503i	−0.00817118	+	0.00907501i
$613$	6.53690	−	1.38946i	0.264023	−	0.0561198i	−0.0739981	−	0.997258i	$-0.523576\pi$
$613$	6.53690	−	1.38946i	0.264023	−	0.0561198i	0.338021	+	0.941139i	$0.390243\pi$
$614$	−2.97560	+	1.32482i	−0.120086	+	0.0534655i
$615$	0.786243			0.0317044
$616$		0			0
$617$	11.8669			0.477741			0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669			0.477741			0.238871	+	0.971051i	$0.423223\pi$
$618$	36.5906	−	16.2912i	1.47189	−	0.655328i
$619$	−20.1700	+	4.28727i	−0.810702	+	0.172320i	−0.594570	−	0.804044i	$-0.702678\pi$
$619$	−20.1700	+	4.28727i	−0.810702	+	0.172320i	−0.216132	+	0.976364i	$0.569344\pi$
$620$	0.0611379	−	0.0679006i	0.00245536	−	0.00272695i
$621$	1.03248	+	9.82339i	0.0414320	+	0.394199i
$622$	−25.4084	+	18.4603i	−1.01878	+	0.740189i
$623$		0			0
$624$	−3.38593	+	10.4208i	−0.135546	+	0.417167i
$625$	19.8969	−	8.85867i	0.795876	−	0.354347i
$626$	−23.1412	−	40.0817i	−0.924908	−	1.60199i
$627$	−18.2767	+	13.3896i	−0.729900	+	0.534731i
$628$	1.42847	−	2.47418i	0.0570021	−	0.0987305i
$629$	8.21358	+	5.96752i	0.327497	+	0.237941i
$630$		0			0
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	0.809575	−	0.587017i	$-0.199698\pi$
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	−1.00000		0.000949112i	$0.999698\pi$
$632$	−1.01535	−	9.66040i	−0.0403884	−	0.384270i
$633$	−7.93070	−	3.53097i	−0.315217	−	0.140344i
$634$	12.9556	−	14.3886i	0.514532	−	0.571446i
$635$	−2.66715	−	2.96217i	−0.105843	−	0.117550i
$636$	−2.61523	−	1.90008i	−0.103701	−	0.0753430i
$637$		0			0
$638$	12.0640	−	5.42857i	0.477619	−	0.214919i
$639$	1.86077	−	3.22294i	0.0736108	−	0.127498i
$640$	0.606183	−	5.76744i	0.0239615	−	0.227978i
$641$	23.0632	−	4.90224i	0.910943	−	0.193627i	0.271476	−	0.962445i	$-0.412488\pi$
$641$	23.0632	−	4.90224i	0.910943	−	0.193627i	0.639467	+	0.768819i	$0.279155\pi$
$642$	35.9259	+	7.63628i	1.41788	+	0.301380i
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	−0.942285	−	0.334812i	$-0.891327\pi$
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	0.0272428	+	0.999629i	$0.491327\pi$
$644$		0			0
$645$	−2.03220	−	6.25446i	−0.0800177	−	0.246269i
$646$	−21.6596	−	24.0555i	−0.852187	−	0.946449i
$647$	−0.567342	+	5.39789i	−0.0223045	+	0.212213i	0.977693	+	0.210038i	$0.0673589\pi$
$647$	−0.567342	+	5.39789i	−0.0223045	+	0.212213i	−0.999998	+	0.00217472i	$0.999308\pi$
$648$	10.4506	+	18.1009i	0.410537	+	0.711071i
$649$	−14.3656	−	24.6561i	−0.563901	−	0.967837i
$650$	−11.0986			−0.435323
$651$		0			0
$652$	0.542130	−	1.66851i	0.0212315	−	0.0653437i
$653$	12.0724	+	2.56606i	0.472429	+	0.100418i	0.437973	−	0.898988i	$-0.355697\pi$
$653$	12.0724	+	2.56606i	0.472429	+	0.100418i	0.0344564	+	0.999406i	$0.489030\pi$
$654$	23.9242	+	10.6517i	0.935509	+	0.416516i
$655$	−4.12186	−	1.83517i	−0.161054	−	0.0717060i
$656$	−4.35833	−	0.926392i	−0.170164	−	0.0361695i
$657$	1.57221	−	4.83878i	0.0613379	−	0.188779i
$658$		0			0
$659$	16.2115			0.631512			0.315756	−	0.948840i	$-0.397742\pi$
$659$	16.2115			0.631512			0.315756	+	0.948840i	$0.397742\pi$
$660$	0.252459	−	0.282626i	0.00982695	−	0.0110012i
$661$	−21.8525	−	37.8497i	−0.849964	−	1.47218i	−0.881239	−	0.472670i	$-0.843290\pi$
$661$	−21.8525	−	37.8497i	−0.849964	−	1.47218i	0.0312751	−	0.999511i	$-0.490043\pi$
$662$	1.45290	−	13.8234i	0.0564684	−	0.537261i
$663$	8.95512	+	9.94567i	0.347788	+	0.386258i
$664$	−14.4614	−	44.5078i	−0.561213	−	1.72724i
$665$		0			0
$666$	0.880296	−	0.639573i	0.0341108	−	0.0247829i
$667$	4.80152	+	1.02059i	0.185916	+	0.0395176i
$668$	−0.936061	+	0.198966i	−0.0362173	+	0.00769822i
$669$	−4.29981	+	40.9100i	−0.166240	+	1.58167i
$670$	−1.60047	+	2.77209i	−0.0618314	+	0.107095i
$671$	−49.4825	−	10.3133i	−1.91025	−	0.398140i
$672$		0			0
$673$	4.74166	+	3.44502i	0.182778	+	0.132796i	0.675412	−	0.737441i	$-0.263966\pi$
$673$	4.74166	+	3.44502i	0.182778	+	0.132796i	−0.492634	+	0.870237i	$0.663966\pi$
$674$	18.8446	+	20.9291i	0.725868	+	0.806158i
$675$	−17.5102	+	19.4471i	−0.673969	+	0.748519i
$676$	−1.45081	−	0.645942i	−0.0558004	−	0.0248439i
$677$	2.14575	+	20.4155i	0.0824679	+	0.784630i	0.955106	+	0.296263i	$0.0957405\pi$
$677$	2.14575	+	20.4155i	0.0824679	+	0.784630i	−0.872638	+	0.488367i	$0.837593\pi$
$678$	1.29811	+	3.99519i	0.0498538	+	0.153434i
$679$		0			0
$680$	−5.35206	−	3.88850i	−0.205242	−	0.149117i
$681$	−17.5636	+	30.4210i	−0.673037	+	1.16573i
$682$	6.29406	−	0.0249138i	0.241012	−	0.000953999i
$683$	−19.3528	−	33.5200i	−0.740513	−	1.28261i	−0.952262	−	0.305282i	$-0.901249\pi$
$683$	−19.3528	−	33.5200i	−0.740513	−	1.28261i	0.211749	−	0.977324i	$-0.432084\pi$
$684$	−0.222900	+	0.0992415i	−0.00852279	+	0.00379459i
$685$	−2.02075	+	6.21923i	−0.0772090	+	0.237625i
$686$		0			0
$687$	26.8750	−	19.5258i	1.02535	−	0.744957i
$688$	3.89563	+	37.0644i	0.148520	+	1.41307i
$689$	13.9805	−	15.5270i	0.532616	−	0.591530i
$690$	1.95569	−	0.415695i	0.0744519	−	0.0158252i
$691$	−21.1303	+	9.40783i	−0.803835	+	0.357891i	−0.767175	−	0.641437i	$-0.778338\pi$
$691$	−21.1303	+	9.40783i	−0.803835	+	0.357891i	−0.0366598	+	0.999328i	$0.511672\pi$
$692$	0.202603			0.00770182
$693$		0			0
$694$	−4.47105			−0.169719
$695$	4.08373	−	1.81819i	0.154905	−	0.0689680i
$696$	11.6706	−	2.48066i	0.442373	−	0.0940292i
$697$	−3.64160	+	4.04440i	−0.137935	+	0.153193i
$698$	2.97372	+	28.2931i	0.112557	+	1.07091i
$699$	0.908531	−	0.660086i	0.0343638	−	0.0249668i
$700$		0			0
$701$	10.9734	−	33.7727i	0.414460	−	1.27558i	−0.498273	−	0.867020i	$-0.666032\pi$
$701$	10.9734	−	33.7727i	0.414460	−	1.27558i	0.912733	−	0.408557i	$-0.133968\pi$
$702$	11.6020	−	5.16552i	0.437887	−	0.194960i
$703$	4.09992	+	7.10127i	0.154632	+	0.267830i
$704$	19.5488	−	14.3216i	0.736773	−	0.539766i
$705$	−2.41483	+	4.18260i	−0.0909476	+	0.157526i
$706$	−12.7662	−	9.27518i	−0.480462	−	0.349076i
$707$		0			0
$708$	0.650893	+	2.00324i	0.0244621	+	0.0752865i
$709$	−4.57881	−	43.5645i	−0.171961	−	1.63610i	−0.651550	−	0.758606i	$-0.725881\pi$
$709$	−4.57881	−	43.5645i	−0.171961	−	1.63610i	0.479589	−	0.877493i	$-0.340786\pi$
$710$	−6.09320	−	2.71287i	−0.228674	−	0.101812i
$711$	−0.915587	+	1.01686i	−0.0343372	+	0.0381353i
$712$	−16.1839	−	17.9741i	−0.606518	−	0.673606i
$713$	1.88945	+	1.37277i	0.0707604	+	0.0514105i
$714$		0			0
$715$	1.64615	+	1.81375i	0.0615625	+	0.0678303i
$716$	−1.34574	+	2.33090i	−0.0502928	+	0.0871096i
$717$	0.0586140	−	0.557675i	0.00218898	−	0.0208268i
$718$	0.871175	−	0.185174i	0.0325119	−	0.00691063i
$719$	−15.5139	−	3.29758i	−0.578570	−	0.122979i	−0.0906741	−	0.995881i	$-0.528902\pi$
$719$	−15.5139	−	3.29758i	−0.578570	−	0.122979i	−0.487896	+	0.872902i	$0.662235\pi$
$720$	−0.617255	+	0.448462i	−0.0230037	+	0.0167132i
$721$		0			0
$722$	0.532741	+	1.63961i	0.0198266	+	0.0610199i
$723$	11.3001	+	12.5500i	0.420254	+	0.466739i
$724$	0.0152425	−	0.145023i	0.000566483	−	0.00538973i
$725$	6.50247	+	11.2626i	0.241496	+	0.418283i
$726$	26.1046	−	0.206663i	0.968833	−	0.00766999i
$727$	13.7719			0.510770			0.255385	−	0.966839i	$-0.417798\pi$
$727$	13.7719			0.510770			0.255385	+	0.966839i	$0.417798\pi$
$728$		0			0
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	−8.91923	−	1.89584i	−0.330115	−	0.0701682i
$731$	41.5851	+	18.5149i	1.53808	+	0.684798i
$732$	3.40841	+	1.51752i	0.125979	+	0.0560893i
$733$	19.1401	+	4.06836i	0.706956	+	0.150268i	0.547339	−	0.836911i	$-0.315641\pi$
$733$	19.1401	+	4.06836i	0.706956	+	0.150268i	0.159617	+	0.987179i	$0.448974\pi$
$734$	−12.5380	+	38.5881i	−0.462788	+	1.42431i
$735$		0			0
$736$	−1.54170			−0.0568278
$737$	−15.1562	+	3.28430i	−0.558286	+	0.120979i
$738$	0.291640	+	0.505135i	0.0107354	+	0.0185943i
$739$	1.16593	−	11.0931i	0.0428894	−	0.408066i	−0.951923	−	0.306338i	$-0.900896\pi$
$739$	1.16593	−	11.0931i	0.0428894	−	0.408066i	0.994812	−	0.101728i	$-0.0324371\pi$
$740$	−0.0917739	−	0.101925i	−0.00337368	−	0.00374685i
$741$	3.34021	+	10.2801i	0.122706	+	0.377649i
$742$		0			0
$743$	−16.7102	+	12.1407i	−0.613038	+	0.445398i	−0.850483	−	0.526003i	$-0.823690\pi$
$743$	−16.7102	+	12.1407i	−0.613038	+	0.445398i	0.237445	+	0.971401i	$0.423690\pi$
$744$	5.55260	+	1.18024i	0.203568	+	0.0432697i
$745$	−6.83087	+	1.45195i	−0.250264	+	0.0531952i
$746$	−4.51533	+	42.9605i	−0.165318	+	1.57290i
$747$	−3.29615	+	5.70911i	−0.120600	+	0.208885i
$748$	0.284517	+	2.60766i	0.0104030	+	0.0953455i
$749$		0			0
$750$	8.76593	+	6.36882i	0.320087	+	0.232557i
$751$	17.7983	+	19.7670i	0.649468	+	0.721307i	0.974498	−	0.224397i	$-0.0720412\pi$
$751$	17.7983	+	19.7670i	0.649468	+	0.721307i	−0.325030	+	0.945704i	$0.605374\pi$
$752$	18.3141	−	20.3399i	0.667847	−	0.741720i
$753$	10.3397	+	4.60352i	0.376799	+	0.167762i
$754$	−0.659725	−	6.27686i	−0.0240258	−	0.228590i
$755$	−0.414271	−	1.27499i	−0.0150769	−	0.0464018i
$756$		0			0
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	0.232644	−	0.972562i	$-0.425262\pi$
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	−0.853071	+	0.521796i	$0.825262\pi$
$758$	18.5862	−	32.1922i	0.675080	−	1.16927i
$759$	7.85915	+	5.66261i	0.285269	+	0.205540i
$760$	−2.67155	−	4.62727i	−0.0969075	−	0.167849i
$761$	−7.30602	+	3.25285i	−0.264843	+	0.117916i	−0.534862	−	0.844939i	$-0.679637\pi$
$761$	−7.30602	+	3.25285i	−0.264843	+	0.117916i	0.270019	+	0.962855i	$0.412970\pi$
$762$	−6.26311	+	19.2759i	−0.226889	+	0.698292i
$763$		0			0
$764$	1.96937	−	1.43083i	0.0712494	−	0.0517657i
$765$	0.0974106	+	0.926800i	0.00352189	+	0.0335085i
$766$	31.3394	−	34.8059i	1.13234	−	1.25759i
$767$	−13.3166	+	2.83052i	−0.480833	+	0.102204i
$768$	−5.33758	+	2.37645i	−0.192603	+	0.0857526i
$769$	−52.0476			−1.87689			−0.938443	−	0.345435i	$-0.887731\pi$
$769$	−52.0476			−1.87689			−0.938443	+	0.345435i	$0.887731\pi$
$770$		0			0
$771$	16.0969			0.579716
$772$	1.67904	−	0.747556i	0.0604299	−	0.0269051i
$773$	1.54644	−	0.328707i	0.0556218	−	0.0118228i	−0.180017	−	0.983664i	$-0.557615\pi$
$773$	1.54644	−	0.328707i	0.0556218	−	0.0118228i	0.235639	+	0.971841i	$0.424282\pi$
$774$	3.26449	−	3.62558i	0.117340	−	0.130319i
$775$	0.646765	+	6.15355i	0.0232325	+	0.221042i
$776$	5.93089	−	4.30904i	0.212906	−	0.154686i
$777$		0			0
$778$	−8.04587	+	24.7626i	−0.288458	+	0.887784i
$779$	−4.01552	+	1.78782i	−0.143871	+	0.0640554i
$780$	−0.0903990	−	0.156576i	−0.00323680	−	0.00560631i
$781$	−10.1072	−	30.6929i	−0.361665	−	1.09828i
$782$	−6.91975	+	11.9854i	−0.247450	+	0.428595i
$783$	−12.0392	−	8.74702i	−0.430247	−	0.312593i
$784$		0			0
$785$	−2.72336	−	8.38164i	−0.0972009	−	0.299154i
$786$	2.39811	+	22.8165i	0.0855376	+	0.813836i
$787$	21.3685	+	9.51386i	0.761704	+	0.339132i	0.750557	−	0.660805i	$-0.229785\pi$
$787$	21.3685	+	9.51386i	0.761704	+	0.339132i	0.0111467	+	0.999938i	$0.496452\pi$
$788$	−0.233035	+	0.258812i	−0.00830153	+	0.00921978i
$789$	−15.3527	−	17.0509i	−0.546571	−	0.607029i
$790$	1.98399	+	1.44145i	0.0705872	+	0.0512846i
$791$		0			0
$792$	−3.36282	−	0.700889i	−0.119493	−	0.0249050i
$793$	−12.0574	+	20.8840i	−0.428170	+	0.741612i
$794$	−2.03981	+	19.4075i	−0.0723901	+	0.688746i
$795$	−9.75392	+	2.07326i	−0.345936	+	0.0735309i
$796$	−3.00131	−	0.637949i	−0.106379	−	0.0226115i
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.322669	−	0.946512i	$-0.395420\pi$
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.999896	−	0.0143887i	$-0.00458021\pi$
$798$		0			0
$799$	−10.3305	−	31.7941i	−0.365468	−	1.12479i
$800$	−2.73303	−	3.03534i	−0.0966273	−	0.107315i
$801$	−0.356136	+	3.38840i	−0.0125834	+	0.119723i
$802$	−2.55917	−	4.43261i	−0.0903675	−	0.156521i
$803$	−22.2400	−	38.1711i	−0.784833	−	1.34703i
$804$	1.14470			0.0403704
$805$		0			0
$806$	0.927927	−	2.85587i	0.0326848	−	0.100594i
$807$	−29.1261	−	6.19095i	−1.02529	−	0.217932i
$808$	0.442862	+	0.197175i	0.0155798	+	0.00693658i
$809$	30.8323	+	13.7274i	1.08400	+	0.482630i	0.869419	−	0.494075i	$-0.164493\pi$
$809$	30.8323	+	13.7274i	1.08400	+	0.482630i	0.214586	+	0.976705i	$0.431160\pi$
$810$	−5.16150	−	1.09711i	−0.181357	−	0.0385485i
$811$	−9.50690	+	29.2592i	−0.333833	+	1.02743i	0.633462	+	0.773774i	$0.281633\pi$
$811$	−9.50690	+	29.2592i	−0.333833	+	1.02743i	−0.967294	+	0.253657i	$0.918367\pi$
$812$		0			0
$813$	−1.18212			−0.0414588
$814$	0.950391	−	9.40014i	0.0333112	−	0.329475i
$815$	−2.70591	−	4.68677i	−0.0947839	−	0.164171i
$816$	−3.78370	+	35.9995i	−0.132456	+	1.26023i
$817$	24.6008	+	27.3220i	0.860673	+	0.955875i
$818$	13.4276	+	41.3259i	0.469485	+	1.44493i
$819$		0			0
$820$	0.0594801	−	0.0432148i	0.00207714	−	0.00150913i
$821$	−11.8144	−	2.51123i	−0.412326	−	0.0876426i	−0.00292180	−	0.999996i	$-0.500930\pi$
$821$	−11.8144	−	2.51123i	−0.412326	−	0.0876426i	−0.409404	+	0.912353i	$0.634263\pi$
$822$	32.5241	−	6.91322i	1.13441	−	0.241126i
$823$	2.59426	−	24.6827i	0.0904301	−	0.860385i	−0.851450	−	0.524436i	$-0.824276\pi$
$823$	2.59426	−	24.6827i	0.0904301	−	0.860385i	0.941880	−	0.335949i	$-0.109057\pi$
$824$	−22.8817	+	39.6322i	−0.797121	+	1.38065i
$825$	2.78352	+	25.5116i	0.0969098	+	0.888201i
$826$		0			0
$827$	−4.18529	−	3.04079i	−0.145537	−	0.105739i	0.512634	−	0.858607i	$-0.328670\pi$
$827$	−4.18529	−	3.04079i	−0.145537	−	0.105739i	−0.658171	+	0.752868i	$0.728670\pi$
$828$	0.0698025	+	0.0775235i	0.00242580	+	0.00269413i
$829$	21.1134	−	23.4488i	0.733299	−	0.814412i	−0.254999	−	0.966941i	$-0.582075\pi$
$829$	21.1134	−	23.4488i	0.733299	−	0.814412i	0.988299	+	0.152530i	$0.0487420\pi$
$830$	10.7935	+	4.80556i	0.374647	+	0.166803i
$831$	2.54785	+	24.2412i	0.0883840	+	0.840917i
$832$	−3.57270	−	10.9956i	−0.123861	−	0.381205i
$833$		0			0
$834$	−18.3889	−	13.3603i	−0.636755	−	0.462629i
$835$	−1.47602	+	2.55654i	−0.0510798	+	0.0884727i
$836$	−0.646707	+	2.01750i	−0.0223668	+	0.0697766i
$837$	−3.54009	−	6.13162i	−0.122363	−	0.211940i
$838$	15.6038	−	6.94724i	0.539023	−	0.239989i
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	−0.977350	−	0.211628i	$-0.932124\pi$
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	0.915085	+	0.403262i	$0.132124\pi$
$840$		0			0
$841$	17.4784	−	12.6988i	0.602703	−	0.437889i
$842$	3.04865	+	29.0060i	0.105063	+	0.999611i
$843$	11.5804	−	12.8614i	0.398851	−	0.442969i
$844$	−0.794042	+	0.168779i	−0.0273320	+	0.00580960i
$845$	−4.47541	+	1.99258i	−0.153959	+	0.0685469i
$846$	−3.58291			−0.123183
$847$		0			0
$848$	56.5112			1.94060
$849$	−13.4643	+	5.99470i	−0.462094	+	0.205737i
$850$	−35.8640	+	7.62313i	−1.23013	+	0.261471i
$851$	2.34583	−	2.60531i	0.0804140	−	0.0893088i
$852$	0.249324	+	2.37216i	0.00854171	+	0.0812690i
$853$	16.4604	−	11.9592i	0.563593	−	0.409475i	−0.269179	−	0.963090i	$-0.586752\pi$
$853$	16.4604	−	11.9592i	0.563593	−	0.409475i	0.832772	+	0.553616i	$0.186752\pi$
$854$		0			0
$855$	−0.232586	+	0.715828i	−0.00795429	+	0.0244808i
$856$	−38.3364	+	17.0685i	−1.31031	+	0.583389i
$857$	7.55436	+	13.0845i	0.258052	+	0.446959i	0.965720	−	0.259586i	$-0.0835861\pi$
$857$	7.55436	+	13.0845i	0.258052	+	0.446959i	−0.707668	+	0.706545i	$0.750253\pi$
$858$	3.80175	−	11.8601i	0.129790	−	0.404898i
$859$	16.9821	−	29.4138i	0.579420	−	1.00359i	−0.416126	−	0.909307i	$-0.636612\pi$
$859$	16.9821	−	29.4138i	0.579420	−	1.00359i	0.995546	−	0.0942781i	$-0.0300543\pi$
$860$	−0.497507	−	0.361460i	−0.0169648	−	0.0123257i
$861$		0			0
$862$	−13.7090	−	42.1920i	−0.466931	−	1.43707i
$863$	0.290311	+	2.76212i	0.00988230	+	0.0940238i	0.998351	−	0.0573997i	$-0.0182809\pi$
$863$	0.290311	+	2.76212i	0.00988230	+	0.0940238i	−0.988469	+	0.151424i	$0.951614\pi$
$864$	4.26969	+	1.90099i	0.145258	+	0.0646730i
$865$	0.418196	−	0.464453i	0.0142191	−	0.0157919i
$866$	5.60124	+	6.22081i	0.190338	+	0.211392i
$867$	13.5155	+	9.81958i	0.459010	+	0.333490i
$868$		0			0
$869$	1.28869	+	11.8111i	0.0437156	+	0.400664i
$870$	−1.50612	+	2.60868i	−0.0510623	+	0.0884425i
$871$	−0.773368	+	7.35811i	−0.0262046	+	0.249320i
$872$	−29.2678	+	6.22105i	−0.991131	+	0.210671i
$873$	−1.01012	−	0.214708i	−0.0341875	−	0.00726678i
$874$	−9.04292	+	6.57006i	−0.305881	+	0.222236i
$875$		0			0
$876$	1.00767	+	3.10130i	0.0340461	+	0.104783i
$877$	33.2413	+	36.9182i	1.12248	+	1.24664i	0.965884	+	0.258976i	$0.0833849\pi$
$877$	33.2413	+	36.9182i	1.12248	+	1.24664i	0.156595	+	0.987663i	$0.449948\pi$
$878$	1.05002	−	9.99024i	0.0354364	−	0.337154i
$879$	9.61840	+	16.6596i	0.324421	+	0.561913i
$880$	−0.666404	+	6.59128i	−0.0224645	+	0.222192i
$881$	−27.3064			−0.919975			−0.459988	−	0.887925i	$-0.652146\pi$
$881$	−27.3064			−0.919975			−0.459988	+	0.887925i	$0.652146\pi$
$882$		0			0
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	−0.999952	−	0.00978852i	$-0.996884\pi$
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	0.814732	+	0.579838i	$0.196884\pi$
$884$	1.22412	+	0.260194i	0.0411715	+	0.00875126i
$885$	5.93581	+	2.64279i	0.199530	+	0.0888365i
$886$	−0.134924	−	0.0600721i	−0.00453286	−	0.00201816i
$887$	16.1129	+	3.42490i	0.541018	+	0.114997i	0.470312	−	0.882500i	$-0.344141\pi$
$887$	16.1129	+	3.42490i	0.541018	+	0.114997i	0.0707063	+	0.997497i	$0.477475\pi$
$888$	2.63319	−	8.10413i	0.0883641	−	0.271957i
$889$		0			0
$890$	6.10625			0.204682
$891$	−12.8701	−	22.0894i	−0.431166	−	0.740021i
$892$	1.92328	+	3.33122i	0.0643961	+	0.111537i
$893$	2.82231	−	26.8525i	0.0944451	−	0.898585i
$894$	23.7604	+	26.3886i	0.794666	+	0.882566i
$895$	2.56565	+	7.89625i	0.0857601	+	0.263942i
$896$		0			0
$897$	3.73877	−	2.71638i	0.124834	−	0.0906971i
$898$	−44.1950	−	9.39393i	−1.47480	−	0.313479i
$899$	−3.44172	+	0.731561i	−0.114788	+	0.0243989i
$900$	−0.0288887	+	0.274858i	−0.000962958	+	0.00916194i
$901$	34.5119	−	59.7764i	1.14976	−	1.99144i
$902$	4.95809	+	1.03338i	0.165086	+	0.0344078i
$903$		0			0
$904$	−3.88299	−	2.82116i	−0.129146	−	0.0938304i
$905$	−0.300992	−	0.334285i	−0.0100053	−	0.0111120i
$906$	−4.56125	+	5.06578i	−0.151537	+	0.168299i
$907$	26.0248	+	11.5870i	0.864139	+	0.384739i	0.790439	−	0.612541i	$-0.209853\pi$
$907$	26.0248	+	11.5870i	0.864139	+	0.384739i	0.0737001	+	0.997280i	$0.476519\pi$
$908$	0.343348	+	3.26674i	0.0113944	+	0.108411i
$909$	−0.0211022	−	0.0649460i	−0.000699917	−	0.00215412i
$910$		0			0
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	0.728090	−	0.685482i	$-0.240408\pi$
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	−0.426940	+	0.904280i	$0.640408\pi$
$912$	−14.6178	+	25.3188i	−0.484044	+	0.838389i
$913$	17.9039	+	54.3692i	0.592531	+	1.79936i
$914$	16.9668	+	29.3874i	0.561213	+	0.972049i
$915$	10.5142	−	4.68120i	0.347587	−	0.154756i
$916$	0.959910	−	2.95430i	0.0317163	−	0.0976128i
$917$		0			0
$918$	33.9426	−	24.6607i	1.12027	−	0.813925i
$919$	−0.0815799	−	0.776181i	−0.00269107	−	0.0256039i	0.993094	−	0.117322i	$-0.0374309\pi$
$919$	−0.0815799	−	0.776181i	−0.00269107	−	0.0256039i	−0.995785	+	0.0917179i	$0.970764\pi$
$920$	−1.52857	+	1.69765i	−0.0503954	+	0.0559698i
$921$	3.51468	−	0.747069i	0.115813	−	0.0246167i
$922$	3.72284	−	1.65752i	0.122605	−	0.0545874i
$923$	−15.4167			−0.507446
$924$		0			0
$925$	9.28795			0.305386
$926$	34.9654	−	15.5676i	1.14903	−	0.511583i
$927$	6.30566	−	1.34031i	0.207105	−	0.0440215i
$928$	1.55419	−	1.72611i	0.0510189	−	0.0566622i
$929$	−2.78007	−	26.4506i	−0.0912112	−	0.867817i	−0.940478	−	0.339853i	$-0.889623\pi$
$929$	−2.78007	−	26.4506i	−0.0912112	−	0.867817i	0.849267	−	0.527963i	$-0.177044\pi$
$930$	−1.15945	+	0.842387i	−0.0380198	+	0.0276230i
$931$		0			0
$932$	0.0324505	−	0.0998725i	0.00106295	−	0.00327143i
$933$	31.6509	−	14.0919i	1.03620	−	0.461348i
$934$	−1.94950	−	3.37663i	−0.0637896	−	0.110487i
$935$	6.56515	+	4.73027i	0.214703	+	0.154696i
$936$	−0.819416	+	1.41927i	−0.0267835	+	0.0463903i
$937$	−33.9542	−	24.6691i	−1.10923	−	0.805906i	−0.126691	−	0.991942i	$-0.540436\pi$
$937$	−33.9542	−	24.6691i	−1.10923	−	0.805906i	−0.982543	+	0.186036i	$0.940436\pi$
$938$		0			0
$939$	15.7774	+	48.5578i	0.514875	+	1.58462i
$940$	0.0472072	+	0.449146i	0.00153973	+	0.0146495i
$941$	−44.7938	−	19.9435i	−1.46024	−	0.650140i	−0.485651	−	0.874153i	$-0.661418\pi$
$941$	−44.7938	−	19.9435i	−1.46024	−	0.650140i	−0.974586	+	0.224013i	$0.928084\pi$
$942$	−29.9850	+	33.3018i	−0.976965	+	1.08503i
$943$	1.25748	+	1.39658i	0.0409493	+	0.0454788i
$944$	−29.7897	−	21.6435i	−0.969574	−	0.704437i
$945$		0			0
$946$	−4.59475	−	42.1120i	−0.149388	−	1.36918i
$947$	13.6476	−	23.6384i	0.443489	−	0.768145i	−0.554457	−	0.832213i	$-0.687074\pi$
$947$	13.6476	−	23.6384i	0.443489	−	0.768145i	0.997946	+	0.0640672i	$0.0204072\pi$
$948$	0.0916709	−	0.872190i	0.00297733	−	0.0283274i
$949$	−20.6159	+	4.38205i	−0.669221	+	0.142247i
$950$	−28.9661	−	6.15692i	−0.939783	−	0.199757i
$951$	−17.2799	+	12.5546i	−0.560339	+	0.407110i
$952$		0			0
$953$	6.10023	+	18.7746i	0.197606	+	0.608169i	0.999936	+	0.0112883i	$0.00359326\pi$
$953$	6.10023	+	18.7746i	0.197606	+	0.608169i	−0.802330	+	0.596880i	$0.796407\pi$
$954$	−4.95001	−	5.49754i	−0.160262	−	0.177990i
$955$	0.784923	−	7.46804i	0.0253995	−	0.241660i
$956$	−0.0262177	−	0.0454104i	−0.000847941	−	0.00146868i
$957$	−14.2628	+	3.09070i	−0.461050	+	0.0999082i
$958$	12.1478			0.392478
$959$		0			0
$960$	−1.70513	+	5.24785i	−0.0550329	+	0.169374i
$961$	28.6851	+	6.09720i	0.925325	+	0.196684i
$962$	−4.11784	−	1.83338i	−0.132765	−	0.0591106i
$963$	5.40032	+	2.40438i	0.174023	+	0.0774800i
$964$	1.54466	+	0.328327i	0.0497500	+	0.0105747i
$965$	1.75200	−	5.39211i	0.0563990	−	0.173578i
$966$		0			0
$967$	−12.6734			−0.407551			−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734			−0.407551			−0.203775	+	0.979018i	$0.565321\pi$
$968$	−23.9910	+	17.7223i	−0.771100	+	0.569618i
$969$	17.8545	+	30.9249i	0.573568	+	0.993449i
$970$	−0.193463	+	1.84068i	−0.00621172	+	0.0591006i
$971$	11.1769	+	12.4132i	0.358684	+	0.398359i	0.895297	−	0.445470i	$-0.146963\pi$
$971$	11.1769	+	12.4132i	0.358684	+	0.398359i	−0.536613	+	0.843828i	$0.680297\pi$
$972$	−0.184414	−	0.567569i	−0.00591509	−	0.0182048i
$973$		0			0
$974$	−23.2523	+	16.8938i	−0.745052	+	0.541312i
$975$	11.9759	+	2.54556i	0.383537	+	0.0815233i
$976$	−63.7982	+	13.5607i	−2.04213	+	0.434068i
$977$	−2.85835	+	27.1954i	−0.0914468	+	0.870058i	0.848605	+	0.529027i	$0.177443\pi$
$977$	−2.85835	+	27.1954i	−0.0914468	+	0.870058i	−0.940052	+	0.341031i	$0.889224\pi$
$978$	−13.7589	+	23.8312i	−0.439962	+	0.762036i
$979$	19.8822	+	21.9064i	0.635439	+	0.700133i
$980$		0			0
$981$	3.40997	+	2.47749i	0.108872	+	0.0791001i
$982$	28.1492	+	31.2628i	0.898277	+	0.997637i
$983$	−36.8065	+	40.8778i	−1.17395	+	1.30380i	−0.230194	+	0.973145i	$0.573936\pi$
$983$	−36.8065	+	40.8778i	−1.17395	+	1.30380i	−0.943752	+	0.330654i	$0.892731\pi$
$984$	4.17288	+	1.85789i	0.133027	+	0.0592272i
$985$	0.112297	+	1.06843i	0.00357807	+	0.0340431i
$986$	−6.44313	−	19.8299i	−0.205191	−	0.631513i
$987$		0			0
$988$	0.817723	+	0.594110i	0.0260152	+	0.0189012i
$989$	7.85939	−	13.6129i	0.249914	−	0.432864i
$990$	0.699588	−	0.512524i	0.0222344	−	0.0162891i
$991$	−26.6164	−	46.1009i	−0.845497	−	1.46444i	−0.885189	−	0.465232i	$-0.845971\pi$
$991$	−26.6164	−	46.1009i	−0.845497	−	1.46444i	0.0396921	−	0.999212i	$-0.487362\pi$
$992$	1.00955	−	0.449480i	0.0320532	−	0.0142710i
$993$	−4.73826	+	14.5829i	−0.150364	+	0.462774i
$994$		0			0
$995$	−7.65750	+	5.56350i	−0.242759	+	0.176375i
$996$	−0.441652	−	4.20204i	−0.0139943	−	0.133147i
$997$	21.9171	−	24.3414i	0.694121	−	0.770900i	−0.288307	−	0.957538i	$-0.593092\pi$
$997$	21.9171	−	24.3414i	0.694121	−	0.770900i	0.982429	+	0.186638i	$0.0597592\pi$
$998$	40.0992	−	8.52334i	1.26932	−	0.269802i
$999$	−9.70918	+	4.32281i	−0.307185	+	0.136768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.c.422.1		16
7.2	even	3		77.2.f.a.15.2	✓	8
7.3	odd	6		539.2.q.b.312.2		16
7.4	even	3	inner	539.2.q.c.312.2		16
7.5	odd	6		539.2.f.d.246.2		8
7.6	odd	2		539.2.q.b.422.1		16
11.3	even	5	inner	539.2.q.c.520.2		16
21.2	odd	6		693.2.m.g.631.1		8
77.2	odd	30		847.2.f.s.148.2		8
77.3	odd	30		539.2.q.b.410.1		16
77.5	odd	30		5929.2.a.bi.1.1		4
77.9	even	15		847.2.f.p.148.1		8
77.16	even	15		847.2.a.l.1.1		4
77.25	even	15	inner	539.2.q.c.410.1		16
77.30	odd	30		847.2.f.q.729.1		8
77.37	even	15		847.2.f.p.372.1		8
77.47	odd	30		539.2.f.d.344.2		8
77.51	odd	30		847.2.f.s.372.2		8
77.58	even	15		77.2.f.a.36.2	yes	8
77.61	even	30		5929.2.a.bb.1.4		4
77.65	odd	6		847.2.f.q.323.1		8
77.69	odd	10		539.2.q.b.520.2		16
77.72	odd	30		847.2.a.k.1.4		4
231.149	even	30		7623.2.a.co.1.1		4
231.170	odd	30		7623.2.a.ch.1.4		4
231.212	odd	30		693.2.m.g.190.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	7.2	even	3
77.2.f.a.36.2	yes	8	77.58	even	15
539.2.f.d.246.2		8	7.5	odd	6
539.2.f.d.344.2		8	77.47	odd	30
539.2.q.b.312.2		16	7.3	odd	6
539.2.q.b.410.1		16	77.3	odd	30
539.2.q.b.422.1		16	7.6	odd	2
539.2.q.b.520.2		16	77.69	odd	10
539.2.q.c.312.2		16	7.4	even	3	inner
539.2.q.c.410.1		16	77.25	even	15	inner
539.2.q.c.422.1		16	1.1	even	1	trivial
539.2.q.c.520.2		16	11.3	even	5	inner
693.2.m.g.190.1		8	231.212	odd	30
693.2.m.g.631.1		8	21.2	odd	6
847.2.a.k.1.4		4	77.72	odd	30
847.2.a.l.1.1		4	77.16	even	15
847.2.f.p.148.1		8	77.9	even	15
847.2.f.p.372.1		8	77.37	even	15
847.2.f.q.323.1		8	77.65	odd	6
847.2.f.q.729.1		8	77.30	odd	30
847.2.f.s.148.2		8	77.2	odd	30
847.2.f.s.372.2		8	77.51	odd	30
5929.2.a.bb.1.4		4	77.61	even	30
5929.2.a.bi.1.1		4	77.5	odd	30
7623.2.a.ch.1.4		4	231.170	odd	30
7623.2.a.co.1.1		4	231.149	even	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33993 + 0.596574i) q^{2} +(1.58268 - 0.336408i) q^{3} +(0.101241 - 0.112439i) q^{4} +(-0.0487868 - 0.464175i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(0.837913 - 2.57883i) q^{8} +(-0.348943 + 0.155360i) q^{9} +O(q^{10})\)	\(q+(-1.33993 + 0.596574i) q^{2} +(1.58268 - 0.336408i) q^{3} +(0.101241 - 0.112439i) q^{4} +(-0.0487868 - 0.464175i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(0.837913 - 2.57883i) q^{8} +(-0.348943 + 0.155360i) q^{9} +(0.342285 + 0.592855i) q^{10} +(-1.01240 + 3.15833i) q^{11} +(0.122406 - 0.212013i) q^{12} +(1.28012 + 0.930062i) q^{13} +(-0.233366 - 0.718226i) q^{15} +(0.447352 + 4.25627i) q^{16} +(4.77540 + 2.12614i) q^{17} +(0.374875 - 0.416341i) q^{18} +(2.82502 + 3.13750i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} +(-0.527635 - 4.83590i) q^{22} +(0.902527 - 1.56322i) q^{23} +(0.458605 - 4.36334i) q^{24} +(4.67766 - 0.994267i) q^{25} +(-2.27012 - 0.482528i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.840363 + 2.58637i) q^{29} +(0.741168 + 0.823150i) q^{30} +(-0.135245 + 1.28677i) q^{31} +(-0.427051 - 0.739674i) q^{32} +(-0.539813 + 5.33919i) q^{33} -7.66708 q^{34} +(-0.0178588 + 0.0549637i) q^{36} +(1.89977 + 0.403808i) q^{37} +(-5.65706 - 2.51869i) q^{38} +(2.33890 + 1.04134i) q^{39} +(-1.23791 - 0.263126i) q^{40} +(-0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(0.252625 + 0.433586i) q^{44} +(0.0891378 + 0.154391i) q^{45} +(-0.276742 + 2.63303i) q^{46} +(-4.27929 - 4.75263i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-5.67457 + 4.12281i) q^{50} +(8.27316 + 1.75851i) q^{51} +(0.234176 - 0.0497757i) q^{52} +(1.38024 - 13.1321i) q^{53} +(4.01308 - 6.95085i) q^{54} +(1.51541 + 0.315846i) q^{55} +(5.52656 + 4.01528i) q^{57} +(-2.66898 - 2.96421i) q^{58} +(-5.75712 + 6.39393i) q^{59} +(-0.104383 - 0.0464744i) q^{60} +(1.59303 + 15.1567i) q^{61} +(-0.586436 - 1.80486i) q^{62} +(-5.91123 - 4.29476i) q^{64} +(0.369259 - 0.639575i) q^{65} +(-2.46191 - 7.47616i) q^{66} +(2.33791 + 4.04938i) q^{67} +(0.722528 - 0.321690i) q^{68} +(0.902527 - 2.77769i) q^{69} +(-7.88234 + 5.72685i) q^{71} +(0.108262 + 1.03004i) q^{72} +(-8.91283 + 9.89870i) q^{73} +(-2.78645 + 0.592278i) q^{74} +(7.06874 - 3.14721i) q^{75} +0.638786 q^{76} -3.75519 q^{78} +(3.27261 - 1.45706i) q^{79} +(1.95383 - 0.415299i) q^{80} +(-5.15780 + 5.72831i) q^{81} +(-0.159620 - 1.51868i) q^{82} +(13.9627 - 10.1445i) q^{83} +(0.753927 - 2.32035i) q^{85} +(-11.6684 + 5.19508i) q^{86} +(2.20010 + 3.81068i) q^{87} +(7.29650 + 5.25721i) q^{88} +(4.45991 - 7.72479i) q^{89} +(-0.211544 - 0.153696i) q^{90} +(-0.0843952 - 0.259742i) q^{92} +(0.218831 + 2.08204i) q^{93} +(8.56923 + 3.81526i) q^{94} +(1.31852 - 1.46437i) q^{95} +(-0.924716 - 1.02700i) q^{96} +(2.18727 + 1.58915i) q^{97} +(-0.137407 - 1.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 2 * q^9	\( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9} + 28 q^{10} - 5 q^{11} + 14 q^{12} + 10 q^{13} + 12 q^{15} + 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 42 q^{20} - 2 q^{22} + 16 q^{23} - 21 q^{24} - 5 q^{25} - 21 q^{26} - 44 q^{27} - 18 q^{29} - 14 q^{30} + 11 q^{31} + 20 q^{32} - 10 q^{33} - 48 q^{34} - 4 q^{36} - 6 q^{37} - 35 q^{38} + 5 q^{39} + 16 q^{40} - 44 q^{41} + 32 q^{43} - 29 q^{44} - 18 q^{45} - 29 q^{46} - 7 q^{47} + 8 q^{48} - 68 q^{50} - 3 q^{51} - 21 q^{52} - 2 q^{53} - 4 q^{54} + 52 q^{55} - 6 q^{57} + 39 q^{58} - 25 q^{59} + 38 q^{60} - 7 q^{61} - 10 q^{62} + 2 q^{64} - 24 q^{65} - 18 q^{66} + 30 q^{67} - 8 q^{68} + 16 q^{69} - 28 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} - 5 q^{75} - 104 q^{76} - 36 q^{78} + 9 q^{79} + 33 q^{80} + 28 q^{81} - 31 q^{82} + 46 q^{83} - 20 q^{85} + 17 q^{86} - 12 q^{87} + 7 q^{88} + 34 q^{89} + 4 q^{90} - 68 q^{92} - 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 60 q^{97}+O(q^{100}) \) 16 * q + q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 2 * q^9 + 28 * q^10 - 5 * q^11 + 14 * q^12 + 10 * q^13 + 12 * q^15 + 3 * q^16 + 11 * q^17 - 4 * q^18 + 9 * q^19 + 42 * q^20 - 2 * q^22 + 16 * q^23 - 21 * q^24 - 5 * q^25 - 21 * q^26 - 44 * q^27 - 18 * q^29 - 14 * q^30 + 11 * q^31 + 20 * q^32 - 10 * q^33 - 48 * q^34 - 4 * q^36 - 6 * q^37 - 35 * q^38 + 5 * q^39 + 16 * q^40 - 44 * q^41 + 32 * q^43 - 29 * q^44 - 18 * q^45 - 29 * q^46 - 7 * q^47 + 8 * q^48 - 68 * q^50 - 3 * q^51 - 21 * q^52 - 2 * q^53 - 4 * q^54 + 52 * q^55 - 6 * q^57 + 39 * q^58 - 25 * q^59 + 38 * q^60 - 7 * q^61 - 10 * q^62 + 2 * q^64 - 24 * q^65 - 18 * q^66 + 30 * q^67 - 8 * q^68 + 16 * q^69 - 28 * q^71 - 3 * q^72 - 3 * q^73 + 9 * q^74 - 5 * q^75 - 104 * q^76 - 36 * q^78 + 9 * q^79 + 33 * q^80 + 28 * q^81 - 31 * q^82 + 46 * q^83 - 20 * q^85 + 17 * q^86 - 12 * q^87 + 7 * q^88 + 34 * q^89 + 4 * q^90 - 68 * q^92 - 8 * q^93 + 30 * q^94 - 24 * q^95 - 10 * q^96 + 60 * q^97

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