LMFDB - Embedded newform 539.2.q.g.410.2

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			410.2
Character	$\chi$	$=$	539.410
Dual form			539.2.q.g.422.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.206654 + 0.0920084i) q^{2} +(0.214341 + 0.0455596i) q^{3} +(-1.30402 - 1.44826i) q^{4} +(0.260853 - 2.48185i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(-2.69677 - 1.20068i) q^{9} +(0.282258 - 0.488885i) q^{10} +(3.04162 - 1.32232i) q^{11} +(-0.213523 - 0.369833i) q^{12} +(-4.15429 + 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(-0.386294 + 3.67534i) q^{16} +(-1.31324 + 0.584694i) q^{17} +(-0.446827 - 0.496251i) q^{18} +(-4.06060 + 4.50976i) q^{19} +(-3.93453 + 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +(-3.54146 - 6.13399i) q^{23} +(-0.0204606 - 0.194669i) q^{24} +(-1.20081 - 0.255240i) q^{25} +(-1.13621 + 0.241509i) q^{26} +(-1.05516 - 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(0.0827728 - 0.0919286i) q^{30} +(-0.803714 - 7.64683i) q^{31} +(-1.31126 + 2.27117i) q^{32} +(0.712189 - 0.144853i) q^{33} -0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(3.89726 - 0.828388i) q^{37} +(-1.25408 + 0.558351i) q^{38} +(-1.02795 + 0.457671i) q^{39} +(-2.18046 + 0.463472i) q^{40} +(2.08556 + 6.41868i) q^{41} -0.802299 q^{43} +(-5.88141 - 2.68073i) q^{44} +(-3.68337 + 6.37979i) q^{45} +(-0.167479 - 1.59346i) q^{46} +(4.51812 - 5.01788i) q^{47} +(-0.250246 + 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(-0.308121 + 0.0654930i) q^{51} +(9.78853 + 2.08062i) q^{52} +(-0.687972 - 6.54562i) q^{53} +(-0.147519 - 0.255510i) q^{54} +(-2.48840 - 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(0.986549 - 1.09567i) q^{58} +(1.92459 + 2.13747i) q^{59} +(-0.973568 + 0.433460i) q^{60} +(0.0894075 - 0.850656i) q^{61} +(0.537482 - 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} +(6.40724 + 11.0977i) q^{65} +(0.160505 + 0.0355928i) q^{66} +(0.823340 - 1.42607i) q^{67} +(2.55929 + 1.13947i) q^{68} +(-0.479618 - 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(-0.275633 + 2.62247i) q^{72} +(-9.93521 - 11.0342i) q^{73} +(0.881604 + 0.187391i) q^{74} +(-0.245755 - 0.109417i) q^{75} +11.8264 q^{76} -0.254539 q^{78} +(2.24084 + 0.997687i) q^{79} +(9.02090 + 1.91745i) q^{80} +(5.73455 + 6.36886i) q^{81} +(-0.159584 + 1.51834i) q^{82} +(-1.81851 - 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(-0.165799 - 0.0738183i) q^{86} +(0.714109 - 1.23687i) q^{87} +(-1.96298 - 2.21900i) q^{88} +(-0.867830 - 1.50313i) q^{89} +(-1.34818 + 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(0.176118 - 1.67565i) q^{93} +(1.39538 - 0.621261i) q^{94} +(10.1333 + 11.2542i) q^{95} +(-0.384531 + 0.427065i) q^{96} +(9.77095 - 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Character values

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

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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

)

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

$2$	0.206654	+	0.0920084i	0.146127	+	0.0650598i	0.478497	−	0.878089i	$-0.341182\pi$
$2$	0.206654	+	0.0920084i	0.146127	+	0.0650598i	−0.332370	+	0.943149i	$0.607848\pi$
$3$	0.214341	+	0.0455596i	0.123750	+	0.0263038i	0.269370	−	0.963037i	$-0.413184\pi$
$3$	0.214341	+	0.0455596i	0.123750	+	0.0263038i	−0.145620	+	0.989341i	$0.546518\pi$
$4$	−1.30402	−	1.44826i	−0.652010	−	0.724131i
$5$	0.260853	−	2.48185i	0.116657	−	1.10992i	−0.766956	−	0.641700i	$-0.778229\pi$
$5$	0.260853	−	2.48185i	0.116657	−	1.10992i	0.883613	−	0.468218i	$-0.155104\pi$
$6$	0.0401026	+	0.0291363i	0.0163718	+	0.0118948i
$7$		0			0
$7$		0			0
$8$	−0.276036	−	0.849550i	−0.0975933	−	0.300361i
$9$	−2.69677	−	1.20068i	−0.898923	−	0.400226i
$10$	0.282258	−	0.488885i	0.0892578	−	0.154599i
$11$	3.04162	−	1.32232i	0.917083	−	0.398696i
$11$	3.04162	−	1.32232i	0.917083	−	0.398696i
$12$	−0.213523	−	0.369833i	−0.0616388	−	0.106761i
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.988771	−	0.149439i	$-0.952253\pi$
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.163422	+	0.986556i	$0.552253\pi$
$14$		0			0
$15$	0.168984	−	0.520079i	0.0436314	−	0.134284i
$16$	−0.386294	+	3.67534i	−0.0965736	+	0.918836i
$17$	−1.31324	+	0.584694i	−0.318508	+	0.141809i	−0.559763	−	0.828653i	$-0.689108\pi$
$17$	−1.31324	+	0.584694i	−0.318508	+	0.141809i	0.241254	+	0.970462i	$0.422441\pi$
$18$	−0.446827	−	0.496251i	−0.105318	−	0.116968i
$19$	−4.06060	+	4.50976i	−0.931567	+	1.03461i	0.0677522	+	0.997702i	$0.478417\pi$
$19$	−4.06060	+	4.50976i	−0.931567	+	1.03461i	−0.999319	+	0.0369072i	$0.988249\pi$
$20$	−3.93453	+	2.85860i	−0.879788	+	0.639203i
$21$		0			0
$22$	0.750229	+	0.00659095i	0.159949	+	0.00140520i
$23$	−3.54146	−	6.13399i	−0.738446	−	1.27903i	−0.953195	−	0.302356i	$-0.902227\pi$
$23$	−3.54146	−	6.13399i	−0.738446	−	1.27903i	0.214749	−	0.976669i	$-0.431107\pi$
$24$	−0.0204606	−	0.194669i	−0.00417650	−	0.0397367i
$25$	−1.20081	−	0.255240i	−0.240162	−	0.0510481i
$26$	−1.13621	+	0.241509i	−0.222829	+	0.0473637i
$27$	−1.05516	−	0.766622i	−0.203067	−	0.147536i
$28$		0			0
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	−0.570143	−	0.821545i	$-0.693112\pi$
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	0.944148	−	0.329522i	$-0.106888\pi$
$30$	0.0827728	−	0.0919286i	0.0151122	−	0.0167838i
$31$	−0.803714	−	7.64683i	−0.144351	−	1.37341i	−0.791557	−	0.611096i	$-0.790729\pi$
$31$	−0.803714	−	7.64683i	−0.144351	−	1.37341i	0.647205	−	0.762316i	$-0.275938\pi$
$32$	−1.31126	+	2.27117i	−0.231801	+	0.401490i
$33$	0.712189	−	0.144853i	0.123976	−	0.0252157i
$34$	−0.325184			−0.0557687
$35$		0			0
$36$	1.77775	+	5.47134i	0.296291	+	0.911890i
$37$	3.89726	−	0.828388i	0.640705	−	0.136186i	0.123908	−	0.992294i	$-0.460457\pi$
$37$	3.89726	−	0.828388i	0.640705	−	0.136186i	0.516797	+	0.856108i	$0.327124\pi$
$38$	−1.25408	+	0.558351i	−0.203438	+	0.0905765i
$39$	−1.02795	+	0.457671i	−0.164603	+	0.0732860i
$40$	−2.18046	+	0.463472i	−0.344761	+	0.0732813i
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	0.971120	+	0.238594i	$0.0766864\pi$
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	−0.645410	+	0.763836i	$0.723314\pi$
$42$		0			0
$43$	−0.802299			−0.122349			−0.0611747	−	0.998127i	$-0.519485\pi$
$43$	−0.802299			−0.122349			−0.0611747	+	0.998127i	$0.519485\pi$
$44$	−5.88141	−	2.68073i	−0.886656	−	0.404135i
$45$	−3.68337	+	6.37979i	−0.549085	+	0.951042i
$46$	−0.167479	−	1.59346i	−0.0246935	−	0.234943i
$47$	4.51812	−	5.01788i	0.659035	−	0.731933i	−0.317269	−	0.948336i	$-0.602766\pi$
$47$	4.51812	−	5.01788i	0.659035	−	0.731933i	0.976304	+	0.216403i	$0.0694325\pi$
$48$	−0.250246	+	0.770178i	−0.0361199	+	0.111166i
$49$		0			0
$50$	−0.224669	−	0.163231i	−0.0317729	−	0.0230844i
$51$	−0.308121	+	0.0654930i	−0.0431455	+	0.00917086i
$52$	9.78853	+	2.08062i	1.35742	+	0.288529i
$53$	−0.687972	−	6.54562i	−0.0945002	−	0.899110i	−0.934366	−	0.356315i	$-0.884033\pi$
$53$	−0.687972	−	6.54562i	−0.0945002	−	0.899110i	0.839866	−	0.542795i	$-0.182634\pi$
$54$	−0.147519	−	0.255510i	−0.0200747	−	0.0347705i
$55$	−2.48840	−	7.89379i	−0.335535	−	1.06440i
$56$		0			0
$57$	−1.07582	+	0.781627i	−0.142495	+	0.103529i
$58$	0.986549	−	1.09567i	0.129540	−	0.143869i
$59$	1.92459	+	2.13747i	0.250560	+	0.278275i	0.855283	−	0.518161i	$-0.173383\pi$
$59$	1.92459	+	2.13747i	0.250560	+	0.278275i	−0.604723	+	0.796436i	$0.706716\pi$
$60$	−0.973568	+	0.433460i	−0.125687	+	0.0559595i
$61$	0.0894075	−	0.850656i	0.0114475	−	0.108915i	−0.987306	−	0.158829i	$-0.949228\pi$
$61$	0.0894075	−	0.850656i	0.0114475	−	0.108915i	0.998754	+	0.0499140i	$0.0158947\pi$
$62$	0.537482	−	1.65420i	0.0682603	−	0.210084i
$63$		0			0
$64$	5.49964	−	3.99573i	0.687455	−	0.499466i
$65$	6.40724	+	11.0977i	0.794720	+	1.37650i
$66$	0.160505	+	0.0355928i	0.0197568	+	0.00438118i
$67$	0.823340	−	1.42607i	0.100587	−	0.174222i	−0.811340	−	0.584575i	$-0.801261\pi$
$67$	0.823340	−	1.42607i	0.100587	−	0.174222i	0.911927	+	0.410353i	$0.134595\pi$
$68$	2.55929	+	1.13947i	0.310359	+	0.138181i
$69$	−0.479618	−	1.47611i	−0.0577393	−	0.177703i
$70$		0			0
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	0.349216	−	0.937042i	$-0.386448\pi$
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	−0.783267	+	0.621686i	$0.786448\pi$
$72$	−0.275633	+	2.62247i	−0.0324836	+	0.309061i
$73$	−9.93521	−	11.0342i	−1.16283	−	1.29145i	−0.949249	−	0.314527i	$-0.898154\pi$
$73$	−9.93521	−	11.0342i	−1.16283	−	1.29145i	−0.213580	−	0.976925i	$-0.568513\pi$
$74$	0.881604	+	0.187391i	0.102484	+	0.0217837i
$75$	−0.245755	−	0.109417i	−0.0283773	−	0.0126344i
$76$	11.8264			1.35658
$77$		0			0
$78$	−0.254539			−0.0288209
$79$	2.24084	+	0.997687i	0.252114	+	0.112249i	0.528903	−	0.848682i	$-0.322604\pi$
$79$	2.24084	+	0.997687i	0.252114	+	0.112249i	−0.276789	+	0.960931i	$0.589270\pi$
$80$	9.02090	+	1.91745i	1.00857	+	0.214378i
$81$	5.73455	+	6.36886i	0.637172	+	0.707651i
$82$	−0.159584	+	1.51834i	−0.0176231	+	0.167672i
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	0.483492	−	0.875349i	$-0.339368\pi$
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	−0.683099	+	0.730326i	$0.739368\pi$
$84$		0			0
$85$	1.10856	+	3.41180i	0.120240	+	0.370061i
$86$	−0.165799	−	0.0738183i	−0.0178785	−	0.00796003i
$87$	0.714109	−	1.23687i	0.0765605	−	0.132607i
$88$	−1.96298	−	2.21900i	−0.209254	−	0.236546i
$89$	−0.867830	−	1.50313i	−0.0919898	−	0.159331i	0.816358	−	0.577546i	$-0.195989\pi$
$89$	−0.867830	−	1.50313i	−0.0919898	−	0.159331i	−0.908348	+	0.418214i	$0.862656\pi$
$90$	−1.34818	+	0.979509i	−0.142111	+	0.103249i
$91$		0			0
$92$	−4.26549	+	13.1278i	−0.444708	+	1.36867i
$93$	0.176118	−	1.67565i	0.0182625	−	0.173756i
$94$	1.39538	−	0.621261i	0.143922	−	0.0640782i
$95$	10.1333	+	11.2542i	1.03966	+	1.15466i
$96$	−0.384531	+	0.427065i	−0.0392460	+	0.0435871i
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.0317117	−	0.999497i	$-0.489904\pi$
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.960378	+	0.278702i	$0.0899042\pi$
$98$		0			0
$99$	−9.79024	−	0.0860098i	−0.983956	−	0.00864431i
$100$	1.19623	+	2.07193i	0.119623	+	0.207193i
$101$	0.386063	+	3.67315i	0.0384147	+	0.365492i	0.996795	+	0.0799973i	$0.0254912\pi$
$101$	0.386063	+	3.67315i	0.0384147	+	0.365492i	−0.958380	+	0.285495i	$0.907842\pi$
$102$	−0.0697004	−	0.0148153i	−0.00690136	−	0.00146693i
$103$	1.12640	−	0.239423i	0.110987	−	0.0235911i	−0.152083	−	0.988368i	$-0.548598\pi$
$103$	1.12640	−	0.239423i	0.110987	−	0.0235911i	0.263070	+	0.964777i	$0.415265\pi$
$104$	3.71090	+	2.69613i	0.363884	+	0.264377i
$105$		0			0
$106$	0.460080	−	1.41598i	0.0446869	−	0.137532i
$107$	0.780967	−	0.867351i	0.0754989	−	0.0838500i	−0.704212	−	0.709990i	$-0.748699\pi$
$107$	0.780967	−	0.867351i	0.0754989	−	0.0838500i	0.779711	+	0.626140i	$0.215366\pi$
$108$	0.265687	+	2.52785i	0.0255658	+	0.243242i
$109$	−4.65117	+	8.05606i	−0.445501	+	0.771631i	−0.998087	−	0.0618251i	$-0.980308\pi$
$109$	−4.65117	+	8.05606i	−0.445501	+	0.771631i	0.552586	+	0.833456i	$0.313641\pi$
$110$	0.212058	−	1.86024i	0.0202189	−	0.177367i
$111$	0.873083			0.0828694
$112$		0			0
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	0.987475	−	0.157775i	$-0.0504322\pi$
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	−0.891622	+	0.452780i	$0.850432\pi$
$114$	−0.294238	+	0.0625423i	−0.0275580	+	0.00585762i
$115$	−16.1475	+	7.18931i	−1.50576	+	0.670407i
$116$	−11.6037	+	5.16631i	−1.07738	+	0.479680i
$117$	14.8271	−	3.15161i	1.37077	−	0.291366i
$118$	0.201059	+	0.618796i	0.0185090	+	0.0569648i
$119$		0			0
$120$	−0.488478			−0.0445918
$121$	7.50292	−	8.04401i	0.682084	−	0.731274i
$122$	0.0967440	−	0.167565i	0.00875879	−	0.0151707i
$123$	0.154588	+	1.47080i	0.0139387	+	0.132618i
$124$	−10.0266	+	11.1356i	−0.900411	+	1.00001i
$125$	2.90909	−	8.95326i	0.260197	−	0.800804i
$126$		0			0
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	0.598118	−	0.801408i	$-0.295916\pi$
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	−0.577356	+	0.816492i	$0.695916\pi$
$128$	6.63460	−	1.41023i	0.586421	−	0.124648i
$129$	−0.171966	−	0.0365524i	−0.0151407	−	0.00321826i
$130$	0.303005	+	2.88290i	0.0265753	+	0.252847i
$131$	8.25293	+	14.2945i	0.721062	+	1.24892i	0.960575	+	0.278023i	$0.0896790\pi$
$131$	8.25293	+	14.2945i	0.721062	+	1.24892i	−0.239513	+	0.970893i	$0.576988\pi$
$132$	−1.13849	−	0.842544i	−0.0990932	−	0.0733341i
$133$		0			0
$134$	0.301357	−	0.218949i	0.0260333	−	0.0189143i
$135$	−2.17789	+	2.41879i	−0.187443	+	0.208176i
$136$	0.859229	+	0.954270i	0.0736783	+	0.0818280i
$137$	8.51961	−	3.79318i	0.727880	−	0.324073i	−0.00912708	−	0.999958i	$-0.502905\pi$
$137$	8.51961	−	3.79318i	0.727880	−	0.324073i	0.737007	+	0.675885i	$0.236239\pi$
$138$	0.0366997	−	0.349174i	0.00312408	−	0.0297237i
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	−0.867668	−	0.497145i	$-0.834382\pi$
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	0.994172	+	0.107804i	$0.0343818\pi$
$140$		0			0
$141$	1.19703	−	0.869693i	0.100808	−	0.0732414i
$142$	−0.511325	−	0.885641i	−0.0429094	−	0.0743213i
$143$	−8.64465	+	14.6737i	−0.722902	+	1.22708i
$144$	5.45466	−	9.44774i	0.454555	−	0.787312i
$145$	−14.8589	−	6.61559i	−1.23396	−	0.549395i
$146$	−1.03792	−	3.19438i	−0.0858987	−	0.264369i
$147$		0			0
$148$	−6.28183	−	4.56401i	−0.516363	−	0.375160i
$149$	−0.0963663	+	0.916864i	−0.00789464	+	0.0751125i	−0.997760	−	0.0668977i	$-0.978690\pi$
$149$	−0.0963663	+	0.916864i	−0.00789464	+	0.0751125i	0.989865	+	0.142010i	$0.0453566\pi$
$150$	−0.0407190	−	0.0452230i	−0.00332469	−	0.00369244i
$151$	−17.7010	−	3.76246i	−1.44048	−	0.306184i	−0.579565	−	0.814926i	$-0.696777\pi$
$151$	−17.7010	−	3.76246i	−1.44048	−	0.306184i	−0.860919	+	0.508742i	$0.830111\pi$
$152$	4.95214	+	2.20483i	0.401671	+	0.178836i
$153$	4.24355			0.343070
$154$		0			0
$155$	−19.1880			−1.54121
$156$	2.00329	+	0.891922i	0.160392	+	0.0714109i
$157$	12.0051	+	2.55177i	0.958113	+	0.203653i	0.660326	−	0.750979i	$-0.270418\pi$
$157$	12.0051	+	2.55177i	0.958113	+	0.203653i	0.297787	+	0.954632i	$0.403751\pi$
$158$	0.371284	+	0.412353i	0.0295378	+	0.0328050i
$159$	0.150755	−	1.43434i	0.0119557	−	0.113750i
$160$	5.29467	+	3.84680i	0.418580	+	0.304116i
$161$		0			0
$162$	0.599080	+	1.84378i	0.0470682	+	0.144861i
$163$	7.39892	+	3.29421i	0.579528	+	0.258023i	0.675498	−	0.737362i	$-0.263929\pi$
$163$	7.39892	+	3.29421i	0.579528	+	0.258023i	−0.0959699	+	0.995384i	$0.530595\pi$
$164$	6.57632	−	11.3905i	0.513524	−	0.889450i
$165$	−0.173727	−	1.80533i	−0.0135247	−	0.140545i
$166$	−0.254239	−	0.440355i	−0.0197328	−	0.0341781i
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	−0.0987965	−	0.995108i	$-0.531499\pi$
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	0.915874	+	0.401466i	$0.131499\pi$
$168$		0			0
$169$	4.13096	−	12.7138i	0.317766	−	0.977985i
$170$	−0.0848254	+	0.807060i	−0.00650581	+	0.0618987i
$171$	16.3653	−	7.28630i	1.25148	−	0.557197i
$172$	1.04621	+	1.16194i	0.0797731	+	0.0885970i
$173$	3.95603	−	4.39361i	0.300771	−	0.334040i	−0.573747	−	0.819032i	$-0.694511\pi$
$173$	3.95603	−	4.39361i	0.300771	−	0.334040i	0.874519	+	0.484992i	$0.161178\pi$
$174$	0.261376	−	0.189901i	0.0198149	−	0.0143964i
$175$		0			0
$176$	3.68503	+	11.6898i	0.277770	+	0.881153i
$177$	0.315136	+	0.545831i	0.0236870	+	0.0410272i
$178$	−0.0410406	−	0.390475i	−0.00307612	−	0.0292674i
$179$	−4.24035	−	0.901313i	−0.316938	−	0.0673673i	0.0466958	−	0.998909i	$-0.485131\pi$
$179$	−4.24035	−	0.901313i	−0.316938	−	0.0673673i	−0.363634	+	0.931542i	$0.618464\pi$
$180$	14.0428	−	2.98489i	1.04669	−	0.222480i
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	0.212420	−	0.977179i	$-0.431866\pi$
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	−0.863711	+	0.503988i	$0.831866\pi$
$182$		0			0
$183$	0.0579192	−	0.178257i	0.00428151	−	0.0131771i
$184$	−4.23356	+	4.70185i	−0.312102	+	0.346625i
$185$	−1.03932	−	9.88851i	−0.0764126	−	0.727017i
$186$	0.190569	−	0.330075i	0.0139732	−	0.0242023i
$187$	−3.22124	+	3.51495i	−0.235560	+	0.257039i
$188$	−13.1589			−0.959713
$189$		0			0
$190$	1.05862	+	3.25808i	0.0768000	+	0.236366i
$191$	−11.4009	+	2.42334i	−0.824941	+	0.175347i	−0.600993	−	0.799255i	$-0.705228\pi$
$191$	−11.4009	+	2.42334i	−0.824941	+	0.175347i	−0.223948	+	0.974601i	$0.571895\pi$
$192$	1.36084	−	0.605886i	0.0982104	−	0.0437261i
$193$	20.5049	−	9.12938i	1.47598	−	0.657147i	0.498250	−	0.867033i	$-0.333976\pi$
$193$	20.5049	−	9.12938i	1.47598	−	0.657147i	0.977726	+	0.209886i	$0.0673094\pi$
$194$	2.67238	−	0.568031i	0.191866	−	0.0407823i
$195$	0.867729	+	2.67060i	0.0621394	+	0.191245i
$196$		0			0
$197$	24.1022			1.71721			0.858604	−	0.512639i	$-0.171332\pi$
$197$	24.1022			1.71721			0.858604	+	0.512639i	$0.171332\pi$
$198$	−2.01528	−	0.918559i	−0.143220	−	0.0652791i
$199$	−9.36026	+	16.2125i	−0.663531	+	1.14927i	0.316150	+	0.948709i	$0.397610\pi$
$199$	−9.36026	+	16.2125i	−0.663531	+	1.14927i	−0.979681	+	0.200561i	$0.935724\pi$
$200$	0.114627	+	1.09061i	0.00810537	+	0.0771174i
$201$	0.241447	−	0.268154i	0.0170303	−	0.0189141i
$202$	−0.258179	+	0.794593i	−0.0181654	+	0.0559074i
$203$		0			0
$204$	0.496647	+	0.360835i	0.0347722	+	0.0252635i
$205$	16.4742	−	3.50171i	1.15061	−	0.244570i
$206$	0.254804	+	0.0541603i	0.0177530	+	0.00377353i
$207$	2.18555	+	20.7941i	0.151906	+	1.44529i
$208$	−9.48840	−	16.4344i	−0.657902	−	1.13952i
$209$	−6.38746	+	19.0864i	−0.441830	+	1.32023i
$210$		0			0
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	−0.356796	−	0.934182i	$-0.616131\pi$
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	0.778204	+	0.628011i	$0.216131\pi$
$212$	−8.58264	+	9.53199i	−0.589458	+	0.654659i
$213$	−0.662864	−	0.736185i	−0.0454187	−	0.0504426i
$214$	0.241194	−	0.107386i	0.0164877	−	0.00734078i
$215$	−0.209282	+	1.99119i	−0.0142729	+	0.135798i
$216$	−0.360021	+	1.10803i	−0.0244963	+	0.0753919i
$217$		0			0
$218$	−1.70241	+	1.23687i	−0.115302	+	0.0837717i
$219$	−1.62681	−	2.81772i	−0.109930	−	0.190404i
$220$	−8.18735	+	13.8975i	−0.551991	+	0.936970i
$221$	3.69083	−	6.39271i	0.248272	−	0.430020i
$222$	0.180426	+	0.0803310i	0.0121094	+	0.00539146i
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	0.951447	+	0.307811i	$0.0995966\pi$
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	−0.588810	+	0.808271i	$0.700403\pi$
$224$		0			0
$225$	2.93185	+	2.13011i	0.195457	+	0.142008i
$226$	−0.0779671	+	0.741807i	−0.00518629	+	0.0493443i
$227$	−17.1814	−	19.0819i	−1.14037	−	1.26651i	−0.959096	−	0.283079i	$-0.908644\pi$
$227$	−17.1814	−	19.0819i	−1.14037	−	1.26651i	−0.181276	−	0.983432i	$-0.558023\pi$
$228$	2.53489	+	0.538807i	0.167877	+	0.0356834i
$229$	−18.1219	−	8.06839i	−1.19753	−	0.533174i	−0.291574	−	0.956548i	$-0.594179\pi$
$229$	−18.1219	−	8.06839i	−1.19753	−	0.533174i	−0.905955	+	0.423374i	$0.860846\pi$
$230$	−3.99842			−0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	−18.4669	−	8.22201i	−1.20981	−	0.538642i	−0.300108	−	0.953905i	$-0.597023\pi$
$233$	−18.4669	−	8.22201i	−1.20981	−	0.538642i	−0.909701	+	0.415263i	$0.863689\pi$
$234$	3.35407	+	0.712929i	0.219262	+	0.0466056i
$235$	−11.2751	−	12.5222i	−0.735504	−	0.816860i
$236$	0.585915	−	5.57461i	0.0381398	−	0.362876i
$237$	0.434850	+	0.315937i	0.0282465	+	0.0205223i
$238$		0			0
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	0.963267	+	0.268544i	$0.0865424\pi$
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	−0.621454	+	0.783451i	$0.713458\pi$
$240$	1.84619	+	0.821977i	0.119171	+	0.0530584i
$241$	12.0764	−	20.9170i	0.777912	−	1.34738i	−0.155231	−	0.987878i	$-0.549612\pi$
$241$	12.0764	−	20.9170i	0.777912	−	1.34738i	0.933143	−	0.359505i	$-0.117055\pi$
$242$	2.29063	−	0.971998i	0.147247	−	0.0624824i
$243$	2.89537	+	5.01493i	0.185738	+	0.321708i
$244$	−1.34856	+	0.979787i	−0.0863328	+	0.0627245i
$245$		0			0
$246$	−0.103380	+	0.318171i	−0.00659128	+	0.0202859i
$247$	3.25727	−	30.9908i	0.207255	−	1.97190i
$248$	−6.27451	+	2.79359i	−0.398432	+	0.177393i
$249$	−0.329586	−	0.366043i	−0.0208867	−	0.0231970i
$250$	1.42495	−	1.58257i	0.0901219	−	0.100090i
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	−0.848498	−	0.529198i	$-0.822493\pi$
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	0.241097	+	0.970501i	$0.422493\pi$
$252$		0			0
$253$	−18.8829	−	13.9743i	−1.18716	−	0.878558i
$254$	0.0327107	+	0.0566567i	0.00205245	+	0.00355495i
$255$	0.0821698	+	0.781794i	0.00514568	+	0.0489578i
$256$	−11.7979	−	2.50773i	−0.737371	−	0.156733i
$257$	−22.4591	+	4.77384i	−1.40096	+	0.297784i	−0.845597	−	0.533822i	$-0.820755\pi$
$257$	−22.4591	+	4.77384i	−1.40096	+	0.297784i	−0.555366	+	0.831606i	$0.687422\pi$
$258$	−0.0321743	−	0.0233760i	−0.00200308	−	0.00145533i
$259$		0			0
$260$	7.71715	−	23.7509i	0.478597	−	1.47297i
$261$	−12.8741	+	14.2982i	−0.796889	+	0.885035i
$262$	0.390290	+	3.71336i	0.0241122	+	0.229412i
$263$	−0.968871	+	1.67813i	−0.0597432	+	0.103478i	−0.894350	−	0.447368i	$-0.852362\pi$
$263$	−0.968871	+	1.67813i	−0.0597432	+	0.103478i	0.834607	+	0.550846i	$0.185695\pi$
$264$	−0.319649	−	0.565055i	−0.0196731	−	0.0347768i
$265$	−16.4247			−1.00896
$266$		0			0
$267$	−0.117530	−	0.361720i	−0.00719271	−	0.0221369i
$268$	−3.13897	+	0.667209i	−0.191743	+	0.0407563i
$269$	6.56543	−	2.92312i	0.400301	−	0.178226i	−0.196704	−	0.980463i	$-0.563024\pi$
$269$	6.56543	−	2.92312i	0.400301	−	0.178226i	0.597005	+	0.802237i	$0.296357\pi$
$270$	−0.672618	+	0.299469i	−0.0409343	+	0.0182251i
$271$	−1.16507	+	0.247644i	−0.0707732	+	0.0150433i	−0.243162	−	0.969986i	$-0.578185\pi$
$271$	−1.16507	+	0.247644i	−0.0707732	+	0.0150433i	0.172389	+	0.985029i	$0.444851\pi$
$272$	−1.64165	−	5.05249i	−0.0995398	−	0.306352i
$273$		0			0
$274$	2.10962			0.127447
$275$	−3.98992	+	0.811517i	−0.240602	+	0.0489363i
$276$	−1.51237	+	2.61950i	−0.0910337	+	0.157675i
$277$	−1.08085	−	10.2836i	−0.0649420	−	0.617881i	−0.977791	−	0.209584i	$-0.932789\pi$
$277$	−1.08085	−	10.2836i	−0.0649420	−	0.617881i	0.912849	−	0.408298i	$-0.133878\pi$
$278$	0.730561	−	0.811370i	0.0438161	−	0.0486627i
$279$	−7.01396	+	21.5867i	−0.419915	+	1.29236i
$280$		0			0
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	0.858028	−	0.513603i	$-0.171690\pi$
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	−0.223321	+	0.974745i	$0.571690\pi$
$282$	0.327391	−	0.0695890i	0.0194958	−	0.00414397i
$283$	−0.293474	−	0.0623799i	−0.0174452	−	0.00370810i	0.199181	−	0.979963i	$-0.436172\pi$
$283$	−0.293474	−	0.0623799i	−0.0174452	−	0.00370810i	−0.216626	+	0.976255i	$0.569505\pi$
$284$	0.920917	+	8.76194i	0.0546464	+	0.519926i
$285$	1.65925	+	2.87391i	0.0982856	+	0.170236i
$286$	−3.13656	+	2.23701i	−0.185469	+	0.132277i
$287$		0			0
$288$	6.26312	−	4.55042i	0.369058	−	0.268136i
$289$	−9.99248	+	11.0978i	−0.587793	+	0.652810i
$290$	−2.46196	−	2.73428i	−0.144571	−	0.160562i
$291$	2.41774	−	1.07645i	0.141731	−	0.0631025i
$292$	−3.02465	+	28.7776i	−0.177004	+	1.68408i
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	−0.692942	−	0.720993i	$-0.743686\pi$
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	0.984391	−	0.175994i	$-0.0563140\pi$
$294$		0			0
$295$	5.80692	−	4.21898i	0.338092	−	0.245638i
$296$	−1.77954	−	3.08225i	−0.103434	−	0.179152i
$297$	−4.22313	−	0.936505i	−0.245051	−	0.0543415i
$298$	−0.104274	+	0.180607i	−0.00604042	+	0.0104623i
$299$	33.2263	+	14.7933i	1.92153	+	0.855519i
$300$	0.162005	+	0.498599i	0.00935334	+	0.0287866i
$301$		0			0
$302$	−3.31180	−	2.40617i	−0.190573	−	0.138459i
$303$	−0.0845979	+	0.804895i	−0.00486002	+	0.0462400i
$304$	−15.0063	−	16.6662i	−0.860672	−	0.955873i
$305$	−2.08788	−	0.443793i	−0.119552	−	0.0254115i
$306$	0.876947	+	0.390442i	0.0501318	+	0.0223201i
$307$	−28.6376			−1.63443			−0.817217	−	0.576330i	$-0.804484\pi$
$307$	−28.6376			−1.63443			−0.817217	+	0.576330i	$0.804484\pi$
$308$		0			0
$309$	0.252341			0.0143552
$310$	−3.96528	−	1.76545i	−0.225213	−	0.100271i
$311$	31.1274	+	6.61632i	1.76507	+	0.375177i	0.972189	−	0.234199i	$-0.0752466\pi$
$311$	31.1274	+	6.61632i	1.76507	+	0.375177i	0.792882	+	0.609376i	$0.208580\pi$
$312$	0.672564	+	0.746958i	0.0380764	+	0.0422882i
$313$	−0.00357730	+	0.0340358i	−0.000202201	+	0.00192382i	−0.994623	−	0.103567i	$-0.966975\pi$
$313$	−0.00357730	+	0.0340358i	−0.000202201	+	0.00192382i	0.994420	+	0.105490i	$0.0336412\pi$
$314$	2.24613	+	1.63191i	0.126756	+	0.0920938i
$315$		0			0
$316$	−1.47719	−	4.54633i	−0.0830985	−	0.255751i
$317$	20.4538	+	9.10660i	1.14880	+	0.511478i	0.890678	−	0.454635i	$-0.150230\pi$
$317$	20.4538	+	9.10660i	1.14880	+	0.511478i	0.258120	+	0.966113i	$0.416897\pi$
$318$	0.163125	−	0.282541i	0.00914762	−	0.0158441i
$319$	−2.07061	−	21.5173i	−0.115932	−	1.20474i
$320$	−8.48220	−	14.6916i	−0.474170	−	0.821286i
$321$	0.206909	−	0.150328i	0.0115486	−	0.00839052i
$322$		0			0
$323$	2.69574	−	8.29662i	0.149995	−	0.461636i
$324$	1.74581	−	16.6103i	0.0969893	−	0.922792i
$325$	5.75891	−	2.56403i	0.319447	−	0.142227i
$326$	1.22592	+	1.36153i	0.0678977	+	0.0754080i
$327$	−1.36397	+	1.51484i	−0.0754276	+	0.0837708i
$328$	4.87730	−	3.54357i	0.269304	−	0.195661i
$329$		0			0
$330$	0.130204	−	0.389064i	0.00716751	−	0.0214173i
$331$	−5.37885	−	9.31644i	−0.295648	−	0.512078i	0.679487	−	0.733687i	$-0.262202\pi$
$331$	−5.37885	−	9.31644i	−0.295648	−	0.512078i	−0.975136	+	0.221609i	$0.928869\pi$
$332$	0.457895	+	4.35658i	0.0251302	+	0.239098i
$333$	−11.5046	−	2.44539i	−0.630450	−	0.134006i
$334$	2.88790	−	0.613843i	0.158019	−	0.0335880i
$335$	−3.32452	−	2.41540i	−0.181638	−	0.131968i
$336$		0			0
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	−0.867809	−	0.496897i	$-0.834473\pi$
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	0.994141	+	0.108087i	$0.0344726\pi$
$338$	2.02346	−	2.24728i	0.110062	−	0.122236i
$339$	0.0755262	+	0.718584i	0.00410202	+	0.0390281i
$340$	3.49559	−	6.05454i	0.189575	−	0.328354i
$341$	−12.5562	−	22.1960i	−0.679955	−	1.20198i
$342$	4.05236			0.219126
$343$		0			0
$344$	0.221463	+	0.681593i	0.0119405	+	0.0367490i
$345$	−3.78861	+	0.805293i	−0.203972	+	0.0433555i
$346$	1.22178	−	0.543971i	0.0656833	−	0.0292441i
$347$	−25.2886	+	11.2592i	−1.35756	+	0.604426i	−0.950998	−	0.309197i	$-0.899940\pi$
$347$	−25.2886	+	11.2592i	−1.35756	+	0.604426i	−0.406564	+	0.913622i	$0.633273\pi$
$348$	−2.72253	+	0.578691i	−0.145943	+	0.0310211i
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	0.816952	−	0.576706i	$-0.195662\pi$
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	−0.999907	+	0.0136278i	$0.995662\pi$
$350$		0			0
$351$	6.69733			0.357477
$352$	−0.985138	+	8.64196i	−0.0525080	+	0.460618i
$353$	−15.9601	+	27.6437i	−0.849469	+	1.47132i	0.0322133	+	0.999481i	$0.489744\pi$
$353$	−15.9601	+	27.6437i	−0.849469	+	1.47132i	−0.881683	+	0.471843i	$0.843589\pi$
$354$	0.0149031	+	0.141793i	0.000792091	+	0.00753624i
$355$	−7.54892	+	8.38393i	−0.400655	+	0.444973i
$356$	−1.04525	+	3.21695i	−0.0553982	+	0.170498i
$357$		0			0
$358$	−0.793358	−	0.576408i	−0.0419303	−	0.0304641i
$359$	−3.50007	+	0.743963i	−0.184727	+	0.0392649i	−0.299346	−	0.954145i	$-0.596768\pi$
$359$	−3.50007	+	0.743963i	−0.184727	+	0.0392649i	0.114619	+	0.993409i	$0.463435\pi$
$360$	6.43669	+	1.36816i	0.339243	+	0.0721084i
$361$	−1.86337	−	17.7288i	−0.0980720	−	0.933093i
$362$	−1.22501	−	2.12179i	−0.0643853	−	0.111519i
$363$	1.97467	−	1.38233i	0.103643	−	0.0725536i
$364$		0			0
$365$	−29.9768	+	21.7794i	−1.56906	+	1.13999i
$366$	0.0283704	−	0.0315085i	0.00148295	−	0.00164698i
$367$	1.53496	+	1.70475i	0.0801244	+	0.0889872i	0.781874	−	0.623437i	$-0.214264\pi$
$367$	1.53496	+	1.70475i	0.0801244	+	0.0889872i	−0.701749	+	0.712424i	$0.747597\pi$
$368$	23.9126	−	10.6466i	1.24653	−	0.554990i
$369$	2.08251	−	19.8138i	0.108411	−	1.03146i
$370$	0.695045	−	2.13913i	0.0361337	−	0.111208i
$371$		0			0
$372$	−2.65644	+	1.93001i	−0.137730	+	0.100067i
$373$	−3.98428	−	6.90097i	−0.206298	−	0.357319i	0.744247	−	0.667904i	$-0.232808\pi$
$373$	−3.98428	−	6.90097i	−0.206298	−	0.357319i	−0.950546	+	0.310585i	$0.899475\pi$
$374$	−0.989088	+	0.429999i	−0.0511445	+	0.0222347i
$375$	1.03144	−	1.78651i	0.0532636	−	0.0922552i
$376$	−5.51010	−	2.45325i	−0.284162	−	0.126517i
$377$	10.3423	+	31.8302i	0.532653	+	1.63934i
$378$		0			0
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	0.802461	−	0.596705i	$-0.203524\pi$
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	−0.319526	+	0.947578i	$0.603524\pi$
$380$	3.08496	−	29.3514i	0.158255	−	1.50570i
$381$	0.0424051	+	0.0470956i	0.00217248	+	0.00241278i
$382$	−2.57901	−	0.548187i	−0.131954	−	0.0280477i
$383$	11.4910	+	5.11612i	0.587162	+	0.261421i	0.678743	−	0.734376i	$-0.262525\pi$
$383$	11.4910	+	5.11612i	0.587162	+	0.261421i	−0.0915805	+	0.995798i	$0.529192\pi$
$384$	1.48632			0.0758482
$385$		0			0
$386$	5.07741			0.258433
$387$	2.16361	+	0.963303i	0.109983	+	0.0489675i
$388$	−23.0227	−	4.89363i	−1.16880	−	0.248437i
$389$	−0.293276	−	0.325716i	−0.0148697	−	0.0165144i	0.735664	−	0.677347i	$-0.236870\pi$
$389$	−0.293276	−	0.325716i	−0.0148697	−	0.0165144i	−0.750534	+	0.660832i	$0.770204\pi$
$390$	−0.0663974	+	0.631729i	−0.00336216	+	0.0319888i
$391$	8.23731	+	5.98476i	0.416579	+	0.302662i
$392$		0			0
$393$	1.11769	+	3.43990i	0.0563800	+	0.173520i
$394$	4.98082	+	2.21760i	0.250930	+	0.111721i
$395$	3.06064	−	5.30119i	0.153998	−	0.266732i
$396$	12.6421	+	14.2910i	0.635290	+	0.718149i
$397$	−8.40734	−	14.5619i	−0.421952	−	0.730843i	0.574178	−	0.818730i	$-0.305322\pi$
$397$	−8.40734	−	14.5619i	−0.421952	−	0.730843i	−0.996130	+	0.0878876i	$0.971988\pi$
$398$	−3.42602	+	2.48915i	−0.171731	+	0.124770i
$399$		0			0
$400$	1.40196	−	4.31480i	0.0700981	−	0.215740i
$401$	−3.85301	+	36.6590i	−0.192410	+	1.83066i	0.292696	+	0.956206i	$0.405448\pi$
$401$	−3.85301	+	36.6590i	−0.192410	+	1.83066i	−0.485106	+	0.874455i	$0.661219\pi$
$402$	0.0745684	−	0.0332000i	0.00371913	−	0.00165586i
$403$	26.4191	+	29.3413i	1.31603	+	1.46160i
$404$	4.81624	−	5.34898i	0.239617	−	0.266122i
$405$	17.3024	−	12.5710i	0.859766	−	0.624656i
$406$		0			0
$407$	10.7586	−	7.67308i	0.533283	−	0.380340i
$408$	0.140692	+	0.243685i	0.00696528	+	0.0120642i
$409$	−1.70109	−	16.1847i	−0.0841133	−	0.800284i	−0.952529	−	0.304448i	$-0.901528\pi$
$409$	−1.70109	−	16.1847i	−0.0841133	−	0.800284i	0.868416	−	0.495837i	$-0.165139\pi$
$410$	3.72666	+	0.792126i	0.184047	+	0.0391203i
$411$	1.99892	−	0.424883i	0.0985993	−	0.0209579i
$412$	−1.81559	−	1.31911i	−0.0894479	−	0.0649877i
$413$		0			0
$414$	−1.46158	+	4.49828i	−0.0718328	+	0.221079i
$415$	−3.75344	+	4.16862i	−0.184249	+	0.204630i
$416$	−1.40765	−	13.3929i	−0.0690155	−	0.656639i
$417$	0.528813	−	0.915931i	0.0258961	−	0.0448533i
$418$	−3.07611	+	3.35659i	−0.150457	+	0.164176i
$419$	5.56352			0.271796			0.135898	−	0.990723i	$-0.456608\pi$
$419$	5.56352			0.271796			0.135898	+	0.990723i	$0.456608\pi$
$420$		0			0
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	0.972036	+	0.234831i	$0.0754536\pi$
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$422$	1.67419	−	0.355861i	0.0814985	−	0.0173230i
$423$	−18.2092	+	8.10725i	−0.885361	+	0.394188i
$424$	−5.37093	+	2.39129i	−0.260835	+	0.116131i
$425$	1.72620	−	0.366914i	0.0837328	−	0.0177980i
$426$	−0.0692485	−	0.213125i	−0.00335510	−	0.0103259i
$427$		0			0
$428$	−2.27455			−0.109944
$429$	−2.52143	+	2.75134i	−0.121736	+	0.132836i
$430$	−0.226455	+	0.392232i	−0.0109206	+	0.0189151i
$431$	2.89740	+	27.5669i	0.139563	+	1.32785i	0.810238	+	0.586101i	$0.199338\pi$
$431$	2.89740	+	27.5669i	0.139563	+	1.32785i	−0.670675	+	0.741751i	$0.733996\pi$
$432$	3.22520	−	3.58195i	0.155173	−	0.172337i
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	−0.858102	−	0.513479i	$-0.828356\pi$
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	0.996035	+	0.0889667i	$0.0283565\pi$
$434$		0			0
$435$	−2.88346	−	2.09496i	−0.138251	−	0.100445i
$436$	17.7325	−	3.76916i	0.849233	−	0.180510i
$437$	42.0433	+	8.93658i	2.01120	+	0.427494i
$438$	−0.0769336	−	0.731975i	−0.00367603	−	0.0349751i
$439$	7.35590	+	12.7408i	0.351078	+	0.608085i	0.986439	−	0.164131i	$-0.0524818\pi$
$439$	7.35590	+	12.7408i	0.351078	+	0.608085i	−0.635361	+	0.772216i	$0.719148\pi$
$440$	−6.01928	+	4.29298i	−0.286958	+	0.204660i
$441$		0			0
$442$	1.35091	−	0.981494i	0.0642563	−	0.0466849i
$443$	1.63499	−	1.81584i	0.0776806	−	0.0862730i	−0.703052	−	0.711139i	$-0.748180\pi$
$443$	1.63499	−	1.81584i	0.0776806	−	0.0862730i	0.780732	+	0.624866i	$0.214846\pi$
$444$	−1.13852	−	1.26445i	−0.0540317	−	0.0600083i
$445$	−3.95692	+	1.76173i	−0.187576	+	0.0835141i
$446$	−0.414373	+	3.94250i	−0.0196211	+	0.186683i
$447$	−0.0624272	+	0.192131i	−0.00295271	+	0.00908750i
$448$		0			0
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	−0.675098	−	0.737728i	$-0.735899\pi$
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	0.493005	+	0.870027i	$0.335899\pi$
$450$	0.409891	+	0.709952i	0.0193225	+	0.0334675i
$451$	14.8310	+	16.7654i	0.698367	+	0.789453i
$452$	3.21296	−	5.56502i	0.151125	−	0.261756i
$453$	−3.62263	−	1.61290i	−0.170206	−	0.0757805i
$454$	−1.79492	−	5.52420i	−0.0842398	−	0.259264i
$455$		0			0
$456$	0.960995	+	0.698203i	0.0450027	+	0.0326964i
$457$	−3.24953	+	30.9172i	−0.152007	+	1.44625i	0.606761	+	0.794884i	$0.292468\pi$
$457$	−3.24953	+	30.9172i	−0.152007	+	1.44625i	−0.758768	+	0.651361i	$0.774198\pi$
$458$	−3.00261	−	3.33473i	−0.140303	−	0.155822i
$459$	1.83393	+	0.389813i	0.0856004	+	0.0181949i
$460$	31.4686	+	14.0107i	1.46723	+	0.653254i
$461$	29.7215			1.38427			0.692134	−	0.721769i	$-0.256671\pi$
$461$	29.7215			1.38427			0.692134	+	0.721769i	$0.256671\pi$
$462$		0			0
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	22.0043	+	9.79694i	1.02152	+	0.454812i
$465$	−4.11277	−	0.874196i	−0.190725	−	0.0405399i
$466$	−3.05978	−	3.39823i	−0.141741	−	0.157420i
$467$	0.332914	−	3.16746i	0.0154054	−	0.146573i	−0.984115	−	0.177531i	$-0.943189\pi$
$467$	0.332914	−	3.16746i	0.0154054	−	0.146573i	0.999521	+	0.0309579i	$0.00985577\pi$
$468$	−23.8992	−	17.3638i	−1.10474	−	0.802643i
$469$		0			0
$470$	−1.17789	−	3.62517i	−0.0543320	−	0.167217i
$471$	2.45693	+	1.09390i	0.113209	+	0.0504041i
$472$	1.28463	−	2.22505i	0.0591301	−	0.102416i
$473$	−2.44029	+	1.06090i	−0.112205	+	0.0487802i
$474$	0.0607948	+	0.105300i	0.00279240	+	0.00483657i
$475$	6.02709	−	4.37894i	0.276542	−	0.200920i
$476$		0			0
$477$	−6.00389	+	18.4781i	−0.274899	+	0.846052i
$478$	−0.404348	+	3.84711i	−0.0184944	+	0.175963i
$479$	2.95398	−	1.31520i	0.134971	−	0.0600929i	−0.338140	−	0.941096i	$-0.609798\pi$
$479$	2.95398	−	1.31520i	0.134971	−	0.0600929i	0.473111	+	0.881003i	$0.343131\pi$
$480$	0.959606	+	1.06575i	0.0437998	+	0.0486446i
$481$	−13.6900	+	15.2043i	−0.624212	+	0.693258i
$482$	4.42019	−	3.21146i	0.201334	−	0.146278i
$483$		0			0
$484$	−21.4338	−	0.376632i	−0.974264	−	0.0171196i
$485$	−15.0699	−	26.1019i	−0.684289	−	1.18522i
$486$	0.136925	+	1.30275i	0.00621104	+	0.0590941i
$487$	−9.65526	−	2.05229i	−0.437521	−	0.0929980i	−0.0161154	−	0.999870i	$-0.505130\pi$
$487$	−9.65526	−	2.05229i	−0.437521	−	0.0929980i	−0.421406	+	0.906872i	$0.638463\pi$
$488$	−0.747354	+	0.158855i	−0.0338311	+	0.00719103i
$489$	1.43581	+	1.04318i	0.0649296	+	0.0471741i
$490$		0			0
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	−0.917255	−	0.398300i	$-0.869600\pi$
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	0.976190	+	0.216918i	$0.0696003\pi$
$492$	1.92852	−	2.14184i	0.0869445	−	0.0965617i
$493$	0.979362	+	9.31801i	0.0441083	+	0.419662i
$494$	3.52455	−	6.10470i	0.158577	−	0.274663i
$495$	−2.76728	+	24.2755i	−0.124380	+	1.09110i
$496$	28.4152			1.27588
$497$		0			0
$498$	−0.0344314	−	0.105969i	−0.00154291	−	0.00474859i
$499$	19.9496	−	4.24042i	0.893066	−	0.189827i	0.261550	−	0.965190i	$-0.415766\pi$
$499$	19.9496	−	4.24042i	0.893066	−	0.189827i	0.631516	+	0.775363i	$0.282433\pi$
$500$	−16.7602	+	7.46211i	−0.749538	+	0.333716i
$501$	2.61273	−	1.16326i	0.116728	−	0.0519708i
$502$	−2.63193	+	0.559434i	−0.117469	+	0.0249687i
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	−0.969076	−	0.246762i	$-0.920634\pi$
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	0.638956	−	0.769243i	$-0.279366\pi$
$504$		0			0
$505$	9.21692			0.410147
$506$	−2.61648	−	4.62524i	−0.116317	−	0.205617i
$507$	1.46467	−	2.53688i	0.0650483	−	0.112667i
$508$	−0.0589134	−	0.560524i	−0.00261386	−	0.0248692i
$509$	2.47137	−	2.74474i	0.109542	−	0.121658i	−0.685880	−	0.727714i	$-0.740583\pi$
$509$	2.47137	−	2.74474i	0.109542	−	0.121658i	0.795422	+	0.606056i	$0.207249\pi$
$510$	−0.0549509	+	0.169121i	−0.00243327	+	0.00748882i
$511$		0			0
$512$	−13.1822	−	9.57742i	−0.582576	−	0.423266i
$513$	7.74188	−	1.64559i	0.341813	−	0.0726545i
$514$	−5.08051	−	1.07990i	−0.224092	−	0.0476322i
$515$	−0.300389	−	2.85801i	−0.0132367	−	0.125939i
$516$	0.171309	+	0.296716i	0.00754147	+	0.0130622i
$517$	7.10714	−	21.2369i	0.312572	−	0.933997i
$518$		0			0
$519$	1.04811	−	0.761497i	0.0460069	−	0.0334260i
$520$	7.65940	−	8.50662i	0.335887	−	0.373040i
$521$	−0.159433	−	0.177069i	−0.00698491	−	0.00775753i	0.739642	−	0.673000i	$-0.234995\pi$
$521$	−0.159433	−	0.177069i	−0.00698491	−	0.00775753i	−0.746627	+	0.665243i	$0.768328\pi$
$522$	−3.97605	+	1.77025i	−0.174027	+	0.0774818i
$523$	2.29873	−	21.8710i	0.100516	−	0.956350i	−0.821764	−	0.569828i	$-0.807010\pi$
$523$	2.29873	−	21.8710i	0.100516	−	0.956350i	0.922280	−	0.386522i	$-0.126324\pi$
$524$	9.94018	−	30.5927i	0.434239	−	1.33645i
$525$		0			0
$526$	−0.354624	+	0.257649i	−0.0154623	+	0.0112340i
$527$	5.52653	+	9.57223i	0.240739	+	0.416973i
$528$	0.257271	+	2.67349i	0.0111963	+	0.116349i
$529$	−13.5839	+	23.5280i	−0.590604	+	1.02296i
$530$	−3.39424	−	1.51121i	−0.147436	−	0.0656429i
$531$	−2.62375	−	8.07508i	−0.113861	−	0.350429i
$532$		0			0
$533$	−28.0373	−	20.3703i	−1.21443	−	0.882336i
$534$	0.00899321	−	0.0855647i	0.000389174	−	0.00370275i
$535$	−1.94892	−	2.16450i	−0.0842592	−	0.0935793i
$536$	−1.43879	−	0.305824i	−0.0621461	−	0.0132096i
$537$	−0.867817	−	0.386377i	−0.0374491	−	0.0166734i
$538$	1.62573			0.0700900
$539$		0			0
$540$	6.34305			0.272961
$541$	26.1556	+	11.6452i	1.12452	+	0.500668i	0.882833	−	0.469687i	$-0.155633\pi$
$541$	26.1556	+	11.6452i	1.12452	+	0.500668i	0.241686	+	0.970355i	$0.422300\pi$
$542$	−0.263553	−	0.0560199i	−0.0113206	−	0.00240626i
$543$	−1.58807	−	1.76373i	−0.0681504	−	0.0756887i
$544$	0.394066	−	3.74929i	0.0168955	−	0.160749i
$545$	18.7807	+	13.6450i	0.804477	+	0.584486i
$546$		0			0
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	0.984425	−	0.175805i	$-0.0562529\pi$
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	−0.899752	+	0.436401i	$0.856253\pi$
$548$	−16.6033	−	7.39225i	−0.709256	−	0.315781i
$549$	−1.26248	+	2.18667i	−0.0538812	+	0.0933250i
$550$	−0.899202	−	0.199403i	−0.0383421	−	0.00850259i
$551$	19.7762	+	34.2534i	0.842495	+	1.45924i
$552$	−1.12164	+	0.814919i	−0.0477402	+	0.0346853i
$553$		0			0
$554$	0.722815	−	2.22460i	0.0307095	−	0.0945141i
$555$	0.227747	−	2.16686i	0.00966730	−	0.0919782i
$556$	−8.59280	+	3.82576i	−0.364416	+	0.162248i
$557$	−15.0683	−	16.7351i	−0.638466	−	0.709088i	0.333885	−	0.942614i	$-0.391640\pi$
$557$	−15.0683	−	16.7351i	−0.638466	−	0.709088i	−0.972351	+	0.233526i	$0.924974\pi$
$558$	−3.43563	+	3.81565i	−0.145442	+	0.161529i
$559$	3.33298	−	2.42155i	0.140970	−	0.102421i
$560$		0			0
$561$	−0.850583	+	0.606640i	−0.0359116	+	0.0256124i
$562$	1.48749	+	2.57640i	0.0627459	+	0.108679i
$563$	3.11774	+	29.6633i	0.131397	+	1.25016i	0.839229	+	0.543778i	$0.183007\pi$
$563$	3.11774	+	29.6633i	0.131397	+	1.25016i	−0.707832	+	0.706381i	$0.750327\pi$
$564$	−2.82050	−	0.599515i	−0.118764	−	0.0252441i
$565$	8.04875	−	1.71081i	0.338613	−	0.0719745i
$566$	−0.0549082	−	0.0398932i	−0.00230797	−	0.00167684i
$567$		0			0
$568$	−1.24789	+	3.84062i	−0.0523604	+	0.161149i
$569$	19.5897	−	21.7566i	0.821244	−	0.912084i	−0.176141	−	0.984365i	$-0.556361\pi$
$569$	19.5897	−	21.7566i	0.821244	−	0.912084i	0.997384	+	0.0722815i	$0.0230280\pi$
$570$	0.0784678	+	0.746571i	0.00328665	+	0.0312704i
$571$	−18.9626	+	32.8442i	−0.793559	+	1.37449i	0.130190	+	0.991489i	$0.458441\pi$
$571$	−18.9626	+	32.8442i	−0.793559	+	1.37449i	−0.923750	+	0.382996i	$0.874892\pi$
$572$	32.5242	−	6.61515i	1.35991	−	0.276593i
$573$	−2.55409			−0.106699
$574$		0			0
$575$	2.68699	+	8.26969i	0.112055	+	0.344870i
$576$	−19.6289	+	4.17224i	−0.817869	+	0.173843i
$577$	8.01420	−	3.56815i	0.333635	−	0.148544i	−0.233080	−	0.972458i	$-0.574880\pi$
$577$	8.01420	−	3.56815i	0.333635	−	0.148544i	0.566716	+	0.823913i	$0.308214\pi$
$578$	−3.08608	+	1.37401i	−0.128364	+	0.0571513i
$579$	4.81098	−	1.02260i	0.199937	−	0.0424980i
$580$	9.79515	+	30.1464i	0.406721	+	1.25176i
$581$		0			0
$582$	0.598679			0.0248161
$583$	−10.7480	−	18.9996i	−0.445136	−	0.786882i
$584$	−6.63161	+	11.4863i	−0.274418	+	0.475306i
$585$	−3.95411	−	37.6209i	−0.163483	−	1.55543i
$586$	2.44365	−	2.71395i	0.100946	−	0.112112i
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	−0.875391	−	0.483416i	$-0.839396\pi$
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	0.992351	+	0.123450i	$0.0393958\pi$
$588$		0			0
$589$	37.7489	+	27.4262i	1.55542	+	1.13008i
$590$	1.58821	−	0.337584i	0.0653854	−	0.0138981i
$591$	5.16608	+	1.09809i	0.212504	+	0.0451692i
$592$	1.53912	+	14.6438i	0.0632575	+	0.601855i
$593$	−3.62798	−	6.28385i	−0.148983	−	0.258047i	0.781869	−	0.623443i	$-0.214267\pi$
$593$	−3.62798	−	6.28385i	−0.148983	−	0.258047i	−0.930852	+	0.365396i	$0.880933\pi$
$594$	−0.786562	−	0.582097i	−0.0322730	−	0.0238837i
$595$		0			0
$596$	1.45352	−	1.05605i	0.0595386	−	0.0432573i
$597$	−2.74492	+	3.04854i	−0.112342	+	0.124769i
$598$	5.50525	+	6.11420i	0.225126	+	0.250028i
$599$	−18.2874	+	8.14208i	−0.747203	+	0.332676i	−0.744770	−	0.667321i	$-0.767441\pi$
$599$	−18.2874	+	8.14208i	−0.747203	+	0.332676i	−0.00243264	+	0.999997i	$0.500774\pi$
$600$	−0.0251182	+	0.238984i	−0.00102545	+	0.00975647i
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	−0.996622	−	0.0821246i	$-0.973829\pi$
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	0.854556	+	0.519360i	$0.173829\pi$
$602$		0			0
$603$	−3.93261	+	2.85721i	−0.160148	+	0.116354i
$604$	17.6334	+	30.5419i	0.717493	+	1.24273i
$605$	−18.0069	−	20.7195i	−0.732085	−	0.842366i
$606$	−0.0915397	+	0.158551i	−0.00371854	+	0.00644071i
$607$	−12.3566	−	5.50153i	−0.501541	−	0.223300i	0.140342	−	0.990103i	$-0.455180\pi$
$607$	−12.3566	−	5.50153i	−0.501541	−	0.223300i	−0.641883	+	0.766803i	$0.721846\pi$
$608$	−4.91792	−	15.1358i	−0.199448	−	0.613838i
$609$		0			0
$610$	−0.390637	−	0.283814i	−0.0158164	−	0.0114913i
$611$	−3.62427	+	34.4826i	−0.146622	+	1.39502i
$612$	−5.53367	−	6.14577i	−0.223686	−	0.248428i
$613$	30.1238	+	6.40301i	1.21669	+	0.258615i	0.771154	−	0.636649i	$-0.219680\pi$
$613$	30.1238	+	6.40301i	1.21669	+	0.258615i	0.445535	+	0.895264i	$0.353013\pi$
$614$	−5.91809	−	2.63490i	−0.238834	−	0.106336i
$615$	3.69064			0.148821
$616$		0			0
$617$	23.6896			0.953707			0.476853	−	0.878983i	$-0.341777\pi$
$617$	23.6896			0.953707			0.476853	+	0.878983i	$0.341777\pi$
$618$	0.0521475	+	0.0232175i	0.00209768	+	0.000933947i
$619$	31.7779	+	6.75459i	1.27726	+	0.271490i	0.796112	−	0.605149i	$-0.206887\pi$
$619$	31.7779	+	6.75459i	1.27726	+	0.271490i	0.481148	+	0.876639i	$0.340220\pi$
$620$	25.0215	+	27.7892i	1.00489	+	1.11604i
$621$	−0.965627	+	9.18733i	−0.0387493	+	0.368675i
$622$	5.82385	+	4.23127i	0.233515	+	0.169659i
$623$		0			0
$624$	−1.28501	−	3.95485i	−0.0514415	−	0.158321i
$625$	−27.0694	−	12.0521i	−1.08277	−	0.482082i
$626$	−0.00387084	+	0.00670450i	−0.000154710	+	0.000267966i
$627$	−2.23866	+	3.79999i	−0.0894036	+	0.151757i
$628$	−11.9593	−	20.7141i	−0.477228	−	0.826583i
$629$	−4.63370	+	3.36658i	−0.184758	+	0.134234i
$630$		0			0
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	−0.999967	−	0.00818299i	$-0.997395\pi$
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	0.813800	+	0.581145i	$0.197395\pi$
$632$	0.229033	−	2.17910i	0.00911044	−	0.0866801i
$633$	1.51467	−	0.674374i	0.0602027	−	0.0268040i
$634$	3.38897	+	3.76384i	0.134593	+	0.149481i
$635$	0.482924	−	0.536341i	0.0191642	−	0.0212840i
$636$	−2.27388	+	1.65207i	−0.0901654	+	0.0655090i
$637$		0			0
$638$	1.55187	−	4.63716i	0.0614393	−	0.183587i
$639$	6.67262	+	11.5573i	0.263965	+	0.457200i
$640$	−1.76932	−	16.8340i	−0.0699385	−	0.665420i
$641$	16.1886	+	3.44099i	0.639410	+	0.135911i	0.516198	−	0.856469i	$-0.327347\pi$
$641$	16.1886	+	3.44099i	0.639410	+	0.135911i	0.123213	+	0.992380i	$0.460680\pi$
$642$	0.0565902	−	0.0120286i	0.00223344	−	0.000474732i
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	0.555505	−	0.831513i	$-0.312525\pi$
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	−0.619156	+	0.785268i	$0.712525\pi$
$644$		0			0
$645$	−0.135575	+	0.417258i	−0.00533828	+	0.0164295i
$646$	1.32045	−	1.46650i	0.0519522	−	0.0576988i
$647$	−4.22835	−	40.2301i	−0.166234	−	1.58161i	−0.686194	−	0.727418i	$-0.740720\pi$
$647$	−4.22835	−	40.2301i	−0.166234	−	1.58161i	0.519961	−	0.854190i	$-0.325947\pi$
$648$	3.82773	−	6.62982i	0.150367	−	0.260444i
$649$	8.68029	+	3.95645i	0.340731	+	0.155304i
$650$	1.42602			0.0559329
$651$		0			0
$652$	−4.87747	−	15.0113i	−0.191016	−	0.587888i
$653$	40.5791	−	8.62535i	1.58798	−	0.337536i	0.672563	−	0.740040i	$-0.265193\pi$
$653$	40.5791	−	8.62535i	1.58798	−	0.337536i	0.915418	+	0.402504i	$0.131860\pi$
$654$	−0.421248	+	0.187552i	−0.0164721	+	0.00733385i
$655$	37.6296	−	16.7538i	1.47031	−	0.654625i
$656$	−24.3965	+	5.18564i	−0.952523	+	0.202465i
$657$	13.5445	+	41.6856i	0.528421	+	1.62631i
$658$		0			0
$659$	−51.1359			−1.99197			−0.995985	−	0.0895158i	$-0.971468\pi$
$659$	−51.1359			−1.99197			−0.995985	+	0.0895158i	$0.971468\pi$
$660$	−2.38805	+	2.60579i	−0.0929548	+	0.101430i
$661$	21.4420	−	37.1387i	0.833998	−	1.44453i	−0.0608459	−	0.998147i	$-0.519380\pi$
$661$	21.4420	−	37.1387i	0.833998	−	1.44453i	0.894844	−	0.446380i	$-0.147287\pi$
$662$	−0.254371	−	2.42018i	−0.00988643	−	0.0940631i
$663$	1.08235	−	1.20207i	0.0420349	−	0.0466844i
$664$	−0.620472	+	1.90962i	−0.0240790	+	0.0741075i
$665$		0			0
$666$	−2.15249	−	1.56387i	−0.0834072	−	0.0605988i
$667$	−45.1555	+	9.59809i	−1.74843	+	0.371640i
$668$	−24.8795	−	5.28830i	−0.962617	−	0.204611i
$669$	0.401401	+	3.81907i	0.0155190	+	0.147654i
$670$	−0.464789	−	0.805037i	−0.0179563	−	0.0311013i
$671$	−0.852898	−	2.70560i	−0.0329258	−	0.104448i
$672$		0			0
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	−0.125078	−	0.992147i	$-0.539918\pi$
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	0.904936	+	0.425547i	$0.139918\pi$
$674$	1.13598	−	1.26164i	0.0437564	−	0.0485964i
$675$	1.07138	+	1.18989i	0.0412375	+	0.0457989i
$676$	−23.7998	+	10.5963i	−0.915376	+	0.407552i
$677$	1.03681	−	9.86456i	0.0398477	−	0.379126i	−0.956365	−	0.292175i	$-0.905621\pi$
$677$	1.03681	−	9.86456i	0.0398477	−	0.379126i	0.996213	−	0.0869509i	$-0.0277123\pi$
$678$	−0.0505080	+	0.155448i	−0.00193975	+	0.00596993i
$679$		0			0
$680$	2.59249	−	1.88356i	0.0994175	−	0.0722310i
$681$	−2.81332	−	4.87282i	−0.107807	−	0.186727i
$682$	−0.552570	−	5.74217i	−0.0211590	−	0.219879i
$683$	19.9490	−	34.5527i	0.763328	−	1.32212i	−0.177798	−	0.984067i	$-0.556897\pi$
$683$	19.9490	−	34.5527i	0.763328	−	1.32212i	0.941126	−	0.338056i	$-0.109769\pi$
$684$	−31.8931	−	14.1997i	−1.21946	−	0.542941i
$685$	−7.19174	−	22.1339i	−0.274782	−	0.845692i
$686$		0			0
$687$	−3.51667	−	2.55501i	−0.134169	−	0.0974798i
$688$	0.309923	−	2.94872i	0.0118157	−	0.112419i
$689$	22.6145	+	25.1159i	0.861543	+	0.956840i
$690$	−0.857026	−	0.182166i	−0.0326264	−	0.00693496i
$691$	−6.04220	−	2.69016i	−0.229856	−	0.102338i	0.288577	−	0.957457i	$-0.406818\pi$
$691$	−6.04220	−	2.69016i	−0.229856	−	0.102338i	−0.518433	+	0.855118i	$0.673484\pi$
$692$	−11.5218			−0.437995
$693$		0			0
$694$	−6.26194			−0.237700
$695$	−11.0033	−	4.89899i	−0.417379	−	0.185829i
$696$	−1.24790	−	0.265250i	−0.0473017	−	0.0100543i
$697$	−6.49181	−	7.20988i	−0.245895	−	0.273094i
$698$	0.261531	−	2.48830i	0.00989911	−	0.0941837i
$699$	−3.58363	−	2.60366i	−0.135545	−	0.0984795i
$700$		0			0
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	0.999395	−	0.0347848i	$-0.0110746\pi$
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	−0.828973	+	0.559288i	$0.811075\pi$
$702$	1.38403	+	0.616211i	0.0522369	+	0.0232574i
$703$	−12.0894	+	20.9394i	−0.455960	+	0.789746i
$704$	11.4442	−	19.4258i	0.431319	−	0.732137i
$705$	−1.84620	−	3.19771i	−0.0695320	−	0.120433i
$706$	−5.84167	+	4.24422i	−0.219854	+	0.159733i
$707$		0			0
$708$	0.379563	−	1.16817i	0.0142648	−	0.0439027i
$709$	0.433172	−	4.12136i	0.0162681	−	0.154781i	−0.983372	−	0.181602i	$-0.941872\pi$
$709$	0.433172	−	4.12136i	0.0162681	−	0.154781i	0.999640	+	0.0268211i	$0.00853844\pi$
$710$	−2.33141	+	1.03801i	−0.0874963	+	0.0389559i
$711$	−4.84513	−	5.38106i	−0.181707	−	0.201806i
$712$	−1.03743	+	1.15218i	−0.0388793	+	0.0431798i
$713$	−44.0593	+	32.0109i	−1.65003	+	1.19882i
$714$		0			0
$715$	34.1631	+	25.2824i	1.27763	+	0.945510i
$716$	4.22416	+	7.31646i	0.157864	+	0.273429i
$717$	0.391689	+	3.72667i	0.0146279	+	0.139175i
$718$	−0.791756	−	0.168293i	−0.0295481	−	0.00628063i
$719$	−16.6503	+	3.53913i	−0.620951	+	0.131987i	−0.507636	−	0.861572i	$-0.669480\pi$
$719$	−16.6503	+	3.53913i	−0.620951	+	0.131987i	−0.113315	+	0.993559i	$0.536147\pi$
$720$	−22.0250	−	16.0021i	−0.820825	−	0.596364i
$721$		0			0
$722$	1.24612	−	3.83517i	0.0463759	−	0.142730i
$723$	3.54145	−	3.93318i	0.131708	−	0.146276i
$724$	2.20630	+	20.9916i	0.0819966	+	0.780145i
$725$	−4.00068	+	6.92938i	−0.148582	+	0.257351i
$726$	0.535260	−	0.103979i	0.0198653	−	0.00385902i
$727$	−21.6199			−0.801837			−0.400918	−	0.916114i	$-0.631309\pi$
$727$	−21.6199			−0.801837			−0.400918	+	0.916114i	$0.631309\pi$
$728$		0			0
$729$	−7.55284	−	23.2453i	−0.279735	−	0.860936i
$730$	−8.19873	+	1.74269i	−0.303449	+	0.0645000i
$731$	1.05361	−	0.469099i	0.0389693	−	0.0173503i
$732$	−0.333691	+	0.148569i	−0.0123336	+	0.00549126i
$733$	47.1786	−	10.0281i	1.74258	−	0.370397i	0.776797	−	0.629751i	$-0.216843\pi$
$733$	47.1786	−	10.0281i	1.74258	−	0.370397i	0.965782	+	0.259354i	$0.0835096\pi$
$734$	0.160355	+	0.493523i	0.00591883	+	0.0182163i
$735$		0			0
$736$	18.5751			0.684688
$737$	0.618567	−	5.42628i	0.0227852	−	0.199880i
$738$	2.25340	−	3.90300i	0.0829487	−	0.143671i
$739$	0.853315	+	8.11875i	0.0313897	+	0.298653i	0.998942	+	0.0459831i	$0.0146420\pi$
$739$	0.853315	+	8.11875i	0.0313897	+	0.298653i	−0.967553	+	0.252670i	$0.918691\pi$
$740$	−12.9658	+	14.4000i	−0.476634	+	0.529356i
$741$	2.11010	−	6.49421i	0.0775163	−	0.238571i
$742$		0			0
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	0.258355	−	0.966050i	$-0.416820\pi$
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	−0.838932	+	0.544236i	$0.816820\pi$
$744$	−1.47216	+	0.312917i	−0.0539720	+	0.0114721i
$745$	2.25039	+	0.478334i	0.0824477	+	0.0175248i
$746$	−0.188421	−	1.79270i	−0.00689857	−	0.0656355i
$747$	3.31773	+	5.74648i	0.121389	+	0.210253i
$748$	9.29113	+	0.0816249i	0.339717	+	0.00298450i
$749$		0			0
$750$	0.377527	−	0.274289i	0.0137853	−	0.0100156i
$751$	0.746949	−	0.829571i	0.0272566	−	0.0302715i	−0.729362	−	0.684128i	$-0.760183\pi$
$751$	0.746949	−	0.829571i	0.0272566	−	0.0302715i	0.756619	+	0.653856i	$0.226850\pi$
$752$	16.6971	+	18.5440i	0.608881	+	0.676230i
$753$	−2.38115	+	1.06016i	−0.0867738	+	0.0386342i
$754$	−0.791374	+	7.52942i	−0.0288201	+	0.274205i
$755$	−13.9552	+	42.9497i	−0.507882	+	1.56310i
$756$		0			0
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	−0.123939	−	0.992290i	$-0.539553\pi$
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	0.905424	+	0.424508i	$0.139553\pi$
$758$	1.31442	+	2.27665i	0.0477420	+	0.0826916i
$759$	−3.41072	−	3.85557i	−0.123801	−	0.139948i
$760$	6.76385	−	11.7153i	0.245351	−	0.424960i
$761$	5.75536	+	2.56245i	0.208632	+	0.0928888i	0.508392	−	0.861126i	$-0.330240\pi$
$761$	5.75536	+	2.56245i	0.208632	+	0.0928888i	−0.299760	+	0.954015i	$0.596907\pi$
$762$	0.00443000	+	0.0136341i	0.000160482	+	0.000493913i
$763$		0			0
$764$	18.3766	+	13.3514i	0.664844	+	0.483037i
$765$	1.10694	−	10.5319i	0.0400216	−	0.380780i
$766$	1.90394	+	2.11454i	0.0687920	+	0.0764013i
$767$	−14.4468	−	3.07075i	−0.521642	−	0.110878i
$768$	−2.41453	−	1.07502i	−0.0871269	−	0.0387914i
$769$	13.1916			0.475700			0.237850	−	0.971302i	$-0.423557\pi$
$769$	13.1916			0.475700			0.237850	+	0.971302i	$0.423557\pi$
$770$		0			0
$771$	−5.03141			−0.181202
$772$	−39.9606	−	17.7916i	−1.43821	−	0.640333i
$773$	−44.8166	−	9.52605i	−1.61194	−	0.342628i	−0.688162	−	0.725557i	$-0.741582\pi$
$773$	−44.8166	−	9.52605i	−1.61194	−	0.342628i	−0.923778	+	0.382929i	$0.874915\pi$
$774$	0.358488	+	0.398142i	0.0128856	+	0.0143109i
$775$	−0.986671	+	9.38754i	−0.0354423	+	0.337211i
$776$	−8.72809	−	6.34133i	−0.313320	−	0.227640i
$777$		0			0
$778$	−0.0306381	−	0.0942944i	−0.00109843	−	0.00338062i
$779$	−37.4153	−	16.6584i	−1.34054	−	0.596848i
$780$	2.73619	−	4.73921i	0.0979711	−	0.169691i
$781$	−14.6381	−	3.24609i	−0.523792	−	0.116154i
$782$	1.15163	+	1.99468i	0.0411821	+	0.0713295i
$783$	−6.87723	+	4.99660i	−0.245772	+	0.178564i
$784$		0			0
$785$	9.46469	−	29.1293i	0.337809	−	1.03967i
$786$	−0.0855240	+	0.813707i	−0.00305054	+	0.0290240i
$787$	−17.2184	+	7.66615i	−0.613771	+	0.273269i	−0.689986	−	0.723823i	$-0.742383\pi$
$787$	−17.2184	+	7.66615i	−0.613771	+	0.273269i	0.0762146	+	0.997091i	$0.475717\pi$
$788$	−31.4297	−	34.9063i	−1.11964	−	1.24348i
$789$	−0.284124	+	0.315552i	−0.0101151	+	0.0112339i
$790$	1.12025	−	0.813909i	0.0398567	−	0.0289576i
$791$		0			0
$792$	2.62938	+	8.34104i	0.0934311	+	0.296386i
$793$	2.19608	+	3.80373i	0.0779852	+	0.135074i
$794$	−0.397592	−	3.78283i	−0.0141100	−	0.134248i
$795$	−3.52049	−	0.748304i	−0.124859	−	0.0265396i
$796$	35.6858	−	7.58526i	1.26485	−	0.268852i
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	0.912964	−	0.408040i	$-0.133788\pi$
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	−0.105948	+	0.994372i	$0.533788\pi$
$798$		0			0
$799$	−2.99947	+	9.23141i	−0.106114	+	0.326584i
$800$	2.15427	−	2.39256i	0.0761651	−	0.0845899i
$801$	0.535566	+	5.09557i	0.0189233	+	0.180043i
$802$	−4.16917	+	7.22122i	−0.147219	+	0.254990i
$803$	−44.8099	−	20.4242i	−1.58131	−	0.720755i
$804$	−0.703208			−0.0248002
$805$		0			0
$806$	2.75996	+	8.49429i	0.0972155	+	0.299199i
$807$	1.54042	−	0.327426i	0.0542252	−	0.0115259i
$808$	3.01396	−	1.34190i	0.106031	−	0.0472079i
$809$	−5.97963	+	2.66230i	−0.210233	+	0.0936016i	−0.509151	−	0.860677i	$-0.670041\pi$
$809$	−5.97963	+	2.66230i	−0.210233	+	0.0936016i	0.298919	+	0.954279i	$0.403374\pi$
$810$	4.73226	−	1.00587i	0.166275	−	0.0353428i
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	0.999751	+	0.0223122i	$0.00710279\pi$
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	−0.795701	+	0.605690i	$0.792897\pi$
$812$		0			0
$813$	−0.261006			−0.00915387
$814$	2.92930	−	0.595794i	0.102672	−	0.0208826i
$815$	10.1058	−	17.5037i	0.353990	−	0.613129i
$816$	−0.121684	−	1.15775i	−0.00425980	−	0.0405293i
$817$	3.25782	−	3.61817i	0.113977	−	0.126584i
$818$	1.13760	−	3.50116i	0.0397751	−	0.122415i
$819$		0			0
$820$	−26.5542	−	19.2927i	−0.927311	−	0.673731i
$821$	11.3348	−	2.40928i	0.395586	−	0.0840844i	−0.00582351	−	0.999983i	$-0.501854\pi$
$821$	11.3348	−	2.40928i	0.395586	−	0.0840844i	0.401410	+	0.915899i	$0.368520\pi$
$822$	0.452178	+	0.0961134i	0.0157715	+	0.00335234i
$823$	−1.29055	−	12.2788i	−0.0449857	−	0.428010i	−0.993717	−	0.111925i	$-0.964298\pi$
$823$	−1.29055	−	12.2788i	−0.0449857	−	0.428010i	0.948731	−	0.316085i	$-0.102368\pi$
$824$	−0.514328	−	0.890843i	−0.0179175	−	0.0310340i
$825$	−0.892177	−	0.00783800i	−0.0310616	−	0.000272884i
$826$		0			0
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	−0.522748	−	0.852487i	$-0.675093\pi$
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	0.649225	+	0.760596i	$0.275093\pi$
$828$	27.2653	−	30.2812i	0.947536	−	1.05234i
$829$	−13.2908	−	14.7610i	−0.461610	−	0.512670i	0.466731	−	0.884399i	$-0.345432\pi$
$829$	−13.2908	−	14.7610i	−0.461610	−	0.512670i	−0.928341	+	0.371729i	$0.878765\pi$
$830$	−1.15921	+	0.516115i	−0.0402369	+	0.0179146i
$831$	0.236846	−	2.25344i	0.00821610	−	0.0781710i
$832$	−10.7869	+	33.1988i	−0.373970	+	1.15096i
$833$		0			0
$834$	0.193555	−	0.140626i	0.00670226	−	0.00486947i
$835$	−16.2853	−	28.2069i	−0.563576	−	0.976142i
$836$	35.9715	−	15.6384i	1.24410	−	0.540864i
$837$	−5.01418	+	8.68481i	−0.173315	+	0.300191i
$838$	1.14973	+	0.511891i	0.0397166	+	0.0176830i
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	−0.855373	−	0.518012i	$-0.826672\pi$
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	0.387532	−	0.921856i	$-0.373328\pi$
$840$		0			0
$841$	−10.9057	−	7.92348i	−0.376060	−	0.273224i
$842$	−0.508175	+	4.83496i	−0.0175129	+	0.166624i
$843$	1.92833	+	2.14162i	0.0664151	+	0.0737615i
$844$	−14.4233	−	3.06577i	−0.496471	−	0.105528i
$845$	−30.4762	−	13.5689i	−1.04841	−	0.466784i
$846$	−4.50894			−0.155021
$847$		0			0
$848$	24.3232			0.835261
$849$	−0.0600616	−	0.0267411i	−0.00206131	−	0.000917753i
$850$	0.390485	+	0.0830002i	0.0133935	+	0.00284688i
$851$	−18.8833	−	20.9720i	−0.647311	−	0.718912i
$852$	−0.201800	+	1.92000i	−0.00691356	+	0.0657781i
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.105794	−	0.994388i	$-0.533738\pi$
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.978411	+	0.206667i	$0.933738\pi$
$854$		0			0
$855$	−13.8146	−	42.5169i	−0.472449	−	1.45405i
$856$	−0.952433	−	0.424050i	−0.0325535	−	0.0144937i
$857$	−17.5262	+	30.3563i	−0.598684	+	1.03695i	0.394332	+	0.918968i	$0.370976\pi$
$857$	−17.5262	+	30.3563i	−0.598684	+	1.03695i	−0.993016	+	0.117982i	$0.962357\pi$
$858$	−0.774212	+	0.336583i	−0.0264311	+	0.0114908i
$859$	16.2603	+	28.1636i	0.554794	+	0.960931i	0.997920	+	0.0644717i	$0.0205362\pi$
$859$	16.2603	+	28.1636i	0.554794	+	0.960931i	−0.443126	+	0.896459i	$0.646130\pi$
$860$	3.15667	−	2.29345i	0.107642	−	0.0782061i
$861$		0			0
$862$	−1.93763	+	5.96341i	−0.0659959	+	0.203114i
$863$	−1.32688	+	12.6244i	−0.0451675	+	0.429740i	0.948449	+	0.316930i	$0.102652\pi$
$863$	−1.32688	+	12.6244i	−0.0451675	+	0.429740i	−0.993617	+	0.112811i	$0.964015\pi$
$864$	3.12473	−	1.39122i	0.106305	−	0.0473302i
$865$	−9.87236	−	10.9644i	−0.335670	−	0.372800i
$866$	1.40590	−	1.56140i	0.0477743	−	0.0530587i
$867$	−2.64741	+	1.92345i	−0.0899107	+	0.0653239i
$868$		0			0
$869$	8.13505	+	0.0714685i	0.275963	+	0.00242440i
$870$	−0.403126	−	0.698234i	−0.0136672	−	0.0236724i
$871$	0.883859	+	8.40936i	0.0299484	+	0.284940i
$872$	8.12792	+	1.72764i	0.275246	+	0.0585054i
$873$	−34.8736	+	7.41262i	−1.18029	+	0.250879i
$874$	7.86619	+	5.71512i	0.266078	+	0.193317i
$875$		0			0
$876$	−1.95940	+	6.03041i	−0.0662020	+	0.203749i
$877$	−18.8253	+	20.9076i	−0.635685	+	0.706000i	−0.971796	−	0.235822i	$-0.924222\pi$
$877$	−18.8253	+	20.9076i	−0.635685	+	0.706000i	0.336111	+	0.941822i	$0.390888\pi$
$878$	0.347868	+	3.30975i	0.0117400	+	0.111699i
$879$	1.76882	−	3.06369i	0.0596610	−	0.103336i
$880$	29.9736	−	6.09638i	1.01041	−	0.205509i
$881$	−36.7964			−1.23970			−0.619850	−	0.784720i	$-0.712807\pi$
$881$	−36.7964			−1.23970			−0.619850	+	0.784720i	$0.712807\pi$
$882$		0			0
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	0.938477	−	0.345342i	$-0.112237\pi$
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	−0.962231	+	0.272235i	$0.912237\pi$
$884$	−14.0712	+	2.99094i	−0.473267	+	0.100596i
$885$	1.43688	−	0.639739i	0.0483001	−	0.0215046i
$886$	0.504949	−	0.224818i	0.0169641	−	0.00755291i
$887$	−41.3440	+	8.78794i	−1.38820	+	0.295070i	−0.840592	−	0.541668i	$-0.817793\pi$
$887$	−41.3440	+	8.78794i	−1.38820	+	0.295070i	−0.547603	+	0.836738i	$0.684460\pi$
$888$	−0.241002	−	0.741728i	−0.00808750	−	0.0248908i
$889$		0			0
$890$	−0.979808			−0.0328432
$891$	25.8640	+	11.7887i	0.866477	+	0.394937i
$892$	17.0760	−	29.5765i	0.571747	−	0.990295i
$893$	4.28313	+	40.7512i	0.143329	+	1.36369i
$894$	−0.0305786	+	0.0339609i	−0.00102270	+	0.00113582i
$895$	−3.34304	+	10.2888i	−0.111745	+	0.343917i
$896$		0			0
$897$	6.44778	+	4.68459i	0.215285	+	0.156414i
$898$	−1.05531	+	0.224312i	−0.0352160	+	0.00748539i
$899$	−49.0191	−	10.4193i	−1.63488	−	0.347504i
$900$	−0.738231	−	7.02380i	−0.0246077	−	0.234127i
$901$	4.73066	+	8.19374i	0.157601	+	0.272973i
$902$	1.52234	+	4.82923i	0.0506884	+	0.160796i
$903$		0			0
$904$	2.38288	−	1.73127i	0.0792535	−	0.0575810i
$905$	−18.0855	+	20.0859i	−0.601181	+	0.667679i
$906$	−0.600231	−	0.666624i	−0.0199414	−	0.0221471i
$907$	36.1111	−	16.0777i	1.19905	−	0.533852i	0.292629	−	0.956226i	$-0.405470\pi$
$907$	36.1111	−	16.0777i	1.19905	−	0.533852i	0.906422	+	0.422374i	$0.138803\pi$
$908$	−5.23066	+	49.7664i	−0.173586	+	1.65156i
$909$	3.36915	−	10.3692i	0.111748	−	0.343924i
$910$		0			0
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	−0.00515893	−	0.999987i	$-0.501642\pi$
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	0.949450	+	0.313919i	$0.101642\pi$
$912$	−2.45717	−	4.25593i	−0.0813649	−	0.140928i
$913$	−7.27830	−	1.61401i	−0.240876	−	0.0534158i
$914$	−3.51617	+	6.09019i	−0.116305	+	0.201446i
$915$	−0.427299	−	0.190246i	−0.0141261	−	0.00628934i
$916$	11.9462	+	36.7666i	0.394713	+	1.21480i
$917$		0			0
$918$	0.343123	+	0.249293i	0.0113247	+	0.00822791i
$919$	4.14042	−	39.3935i	0.136580	−	1.29947i	−0.684649	−	0.728873i	$-0.740045\pi$
$919$	4.14042	−	39.3935i	0.136580	−	1.29947i	0.821229	−	0.570598i	$-0.193289\pi$
$920$	10.5650	+	11.7336i	0.348316	+	0.386844i
$921$	−6.13821	−	1.30472i	−0.202261	−	0.0429919i
$922$	6.14208	+	2.73463i	0.202279	+	0.0900602i
$923$	23.2141			0.764101
$924$		0			0
$925$	−4.89131			−0.160825
$926$	−5.26045	−	2.34210i	−0.172869	−	0.0769663i
$927$	−3.32511	−	0.706774i	−0.109211	−	0.0232135i
$928$	11.4373	+	12.7024i	0.375448	+	0.416977i
$929$	−0.273506	+	2.60224i	−0.00897344	+	0.0853766i	−0.998092	−	0.0617438i	$-0.980334\pi$
$929$	−0.273506	+	2.60224i	−0.00897344	+	0.0853766i	0.989119	+	0.147120i	$0.0470005\pi$
$930$	−0.769488	−	0.559066i	−0.0252325	−	0.0183325i
$931$		0			0
$932$	12.1736	+	37.4666i	0.398761	+	1.22726i
$933$	6.37043	+	2.83630i	0.208559	+	0.0928563i
$934$	0.360232	−	0.623939i	0.0117871	−	0.0204159i
$935$	7.88332	+	8.91152i	0.257812	+	0.291438i
$936$	−6.77026	−	11.7264i	−0.221293	−	0.383291i
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.431689	+	0.902022i	$0.642082\pi$
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.991274	+	0.131820i	$0.957918\pi$
$938$		0			0
$939$	−0.00231742	+	0.00713228i	−7.56261e−5	+	0.000232753i
$940$	−3.43255	+	32.6585i	−0.111957	+	1.06520i
$941$	27.0844	−	12.0588i	0.882927	−	0.393105i	0.0853711	−	0.996349i	$-0.472792\pi$
$941$	27.0844	−	12.0588i	0.882927	−	0.393105i	0.797556	+	0.603245i	$0.206126\pi$
$942$	0.407088	+	0.452117i	0.0132636	+	0.0147308i
$943$	31.9862	−	35.5243i	1.04161	−	1.15683i
$944$	−8.59940	+	6.24783i	−0.279887	+	0.203349i
$945$		0			0
$946$	−0.601908	−	0.00528791i	−0.0195697	−	0.000171925i
$947$	7.89306	+	13.6712i	0.256490	+	0.444254i	0.965299	−	0.261146i	$-0.0841006\pi$
$947$	7.89306	+	13.6712i	0.256490	+	0.444254i	−0.708809	+	0.705400i	$0.750767\pi$
$948$	−0.109494	−	1.04176i	−0.00355620	−	0.0338349i
$949$	74.5779	+	15.8520i	2.42090	+	0.514578i
$950$	1.64842	−	0.350383i	0.0534820	−	0.0113679i
$951$	3.96919	+	2.88378i	0.128710	+	0.0935131i
$952$		0			0
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	0.606555	+	0.795041i	$0.292551\pi$
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	−0.958027	+	0.286678i	$0.907449\pi$
$954$	−2.94087	+	3.26616i	−0.0952141	+	0.105746i
$955$	3.04040	+	28.9275i	0.0983852	+	0.936072i
$956$	16.6629	−	28.8609i	0.538916	−	0.933429i
$957$	0.536503	−	4.70638i	0.0173427	−	0.152136i
$958$	0.731463			0.0236325
$959$		0			0
$960$	−1.14874	−	3.53546i	−0.0370754	−	0.114106i
$961$	−27.5055	+	5.84647i	−0.887274	+	0.188596i
$962$	−4.22803	+	1.88244i	−0.136317	+	0.0606924i
$963$	−3.14750	+	1.40136i	−0.101427	+	0.0451581i
$964$	−46.0413	+	9.78637i	−1.48289	+	0.315198i
$965$	−17.3090	−	53.2716i	−0.557196	−	1.71487i
$966$		0			0
$967$	−49.2820			−1.58480			−0.792401	−	0.610001i	$-0.791169\pi$
$967$	−49.2820			−1.58480			−0.792401	+	0.610001i	$0.791169\pi$
$968$	−8.90487	−	4.15367i	−0.286213	−	0.133504i
$969$	0.955798	−	1.65549i	0.0307046	−	0.0531820i
$970$	−0.712672	−	6.78062i	−0.0228825	−	0.217713i
$971$	24.9870	−	27.7508i	0.801870	−	0.890567i	−0.194033	−	0.980995i	$-0.562157\pi$
$971$	24.9870	−	27.7508i	0.801870	−	0.890567i	0.995903	+	0.0904283i	$0.0288236\pi$
$972$	3.48730	−	10.7328i	0.111855	−	0.344255i
$973$		0			0
$974$	−1.80647	−	1.31248i	−0.0578831	−	0.0420545i
$975$	1.35119	−	0.287203i	0.0432726	−	0.00919787i
$976$	3.09192	+	0.657207i	0.0989698	+	0.0210367i
$977$	−4.18620	−	39.8291i	−0.133929	−	1.27425i	−0.830606	−	0.556861i	$-0.812006\pi$
$977$	−4.18620	−	39.8291i	−0.133929	−	1.27425i	0.696677	−	0.717385i	$-0.254661\pi$
$978$	0.200735	+	0.347684i	0.00641881	+	0.0111177i
$979$	−4.62723	−	3.42439i	−0.147887	−	0.109444i
$980$		0			0
$981$	22.2159	−	16.1408i	0.709299	−	0.515336i
$982$	0.639669	−	0.710424i	0.0204127	−	0.0226705i
$983$	−34.8225	−	38.6743i	−1.11067	−	1.23352i	−0.969907	−	0.243476i	$-0.921712\pi$
$983$	−34.8225	−	38.6743i	−1.11067	−	1.23352i	−0.140759	−	0.990044i	$-0.544954\pi$
$984$	1.20685	−	0.537324i	0.0384730	−	0.0171293i
$985$	6.28713	−	59.8180i	0.200325	−	1.90596i
$986$	−0.654946	+	2.01572i	−0.0208577	+	0.0641935i
$987$		0			0
$988$	−49.1304	+	35.6953i	−1.56305	+	1.13562i
$989$	2.84131	+	4.92129i	0.0903484	+	0.156488i
$990$	−2.80542	+	4.76202i	−0.0891621	+	0.151347i
$991$	−22.7414	+	39.3892i	−0.722404	+	1.25124i	0.237630	+	0.971356i	$0.423630\pi$
$991$	−22.7414	+	39.3892i	−0.722404	+	1.25124i	−0.960034	+	0.279885i	$0.909704\pi$
$992$	18.4212	+	8.20162i	0.584872	+	0.260402i
$993$	−0.728455	−	2.24195i	−0.0231168	−	0.0711463i
$994$		0			0
$995$	37.7953	+	27.4599i	1.19819	+	0.870536i
$996$	−0.100338	+	0.954655i	−0.00317934	+	0.0302494i
$997$	18.7085	+	20.7779i	0.592503	+	0.658041i	0.962592	−	0.270955i	$-0.0873395\pi$
$997$	18.7085	+	20.7779i	0.592503	+	0.658041i	−0.370089	+	0.928996i	$0.620673\pi$
$998$	4.51282	+	0.959230i	0.142851	+	0.0303639i
$999$	−4.74731	−	2.11364i	−0.150198	−	0.0668725i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.410.2		32
7.2	even	3	inner	539.2.q.g.520.3		32
7.3	odd	6		539.2.f.e.344.3		16
7.4	even	3		77.2.f.b.36.3	yes	16
7.5	odd	6		539.2.q.f.520.3		32
7.6	odd	2		539.2.q.f.410.2		32
11.4	even	5	inner	539.2.q.g.312.3		32
21.11	odd	6		693.2.m.i.190.2		16
77.4	even	15		77.2.f.b.15.3	✓	16
77.18	odd	30		847.2.f.x.323.2		16
77.24	even	30		5929.2.a.bs.1.5		8
77.25	even	15		847.2.f.w.148.2		16
77.26	odd	30		539.2.q.f.422.2		32
77.31	odd	30		5929.2.a.bt.1.4		8
77.32	odd	6		847.2.f.x.729.2		16
77.37	even	15	inner	539.2.q.g.422.2		32
77.39	odd	30		847.2.f.v.372.3		16
77.46	odd	30		847.2.a.o.1.5		8
77.48	odd	10		539.2.q.f.312.3		32
77.53	even	15		847.2.a.p.1.4		8
77.59	odd	30		539.2.f.e.246.3		16
77.60	even	15		847.2.f.w.372.2		16
77.74	odd	30		847.2.f.v.148.3		16
231.53	odd	30		7623.2.a.ct.1.5		8
231.158	odd	30		693.2.m.i.631.2		16
231.200	even	30		7623.2.a.cw.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	77.4	even	15
77.2.f.b.36.3	yes	16	7.4	even	3
539.2.f.e.246.3		16	77.59	odd	30
539.2.f.e.344.3		16	7.3	odd	6
539.2.q.f.312.3		32	77.48	odd	10
539.2.q.f.410.2		32	7.6	odd	2
539.2.q.f.422.2		32	77.26	odd	30
539.2.q.f.520.3		32	7.5	odd	6
539.2.q.g.312.3		32	11.4	even	5	inner
539.2.q.g.410.2		32	1.1	even	1	trivial
539.2.q.g.422.2		32	77.37	even	15	inner
539.2.q.g.520.3		32	7.2	even	3	inner
693.2.m.i.190.2		16	21.11	odd	6
693.2.m.i.631.2		16	231.158	odd	30
847.2.a.o.1.5		8	77.46	odd	30
847.2.a.p.1.4		8	77.53	even	15
847.2.f.v.148.3		16	77.74	odd	30
847.2.f.v.372.3		16	77.39	odd	30
847.2.f.w.148.2		16	77.25	even	15
847.2.f.w.372.2		16	77.60	even	15
847.2.f.x.323.2		16	77.18	odd	30
847.2.f.x.729.2		16	77.32	odd	6
5929.2.a.bs.1.5		8	77.24	even	30
5929.2.a.bt.1.4		8	77.31	odd	30
7623.2.a.ct.1.5		8	231.53	odd	30
7623.2.a.cw.1.4		8	231.200	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	539.2.q.g.410.2

Level	$539$
Weight	$2$
Character	539.410
Analytic conductor	$4.304$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$