LMFDB - Embedded newform 539.2.q.h.214.5

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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			214.5
Character	$\chi$	$=$	539.214
Dual form			539.2.q.h.471.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76087 - 1.95564i) q^{2} +(2.02209 - 0.900292i) q^{3} +(-0.514820 - 4.89819i) q^{4} +(-1.15065 + 0.244578i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(1.27093 - 1.41151i) q^{9} +O(q^{10})$	\(q+(1.76087 - 1.95564i) q^{2} +(2.02209 - 0.900292i) q^{3} +(-0.514820 - 4.89819i) q^{4} +(-1.15065 + 0.244578i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(1.27093 - 1.41151i) q^{9} +(-1.54783 + 2.68093i) q^{10} +(1.11001 + 3.12536i) q^{11} +(-5.45081 - 9.44109i) q^{12} +(-0.0112624 - 0.0346622i) q^{13} +(-2.10653 + 1.53048i) q^{15} +(-10.1795 + 2.16373i) q^{16} +(4.07409 + 4.52474i) q^{17} +(-0.522468 - 4.97095i) q^{18} +(0.201336 - 1.91558i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(-1.02155 - 1.76938i) q^{23} +(-16.6664 - 3.54254i) q^{24} +(-3.30355 + 1.47083i) q^{25} +(-0.0876184 - 0.0390102i) q^{26} +(-0.752823 + 2.31695i) q^{27} +(4.02767 - 2.92628i) q^{29} +(-0.716241 + 6.81458i) q^{30} +(2.77028 + 0.588842i) q^{31} +(-5.99553 + 10.3846i) q^{32} +(5.05828 + 5.32042i) q^{33} +16.0227 q^{34} +(-7.56813 - 5.49857i) q^{36} +(-2.43221 - 1.08289i) q^{37} +(-3.39167 - 3.76683i) q^{38} +(-0.0539798 - 0.0599506i) q^{39} +(8.27247 + 3.68314i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(14.7371 - 7.04605i) q^{44} +(-1.11717 + 1.93499i) q^{45} +(-5.25907 - 1.11785i) q^{46} +(0.333862 - 3.17649i) q^{47} +(-18.6359 + 13.5398i) q^{48} +(-2.94068 + 9.05049i) q^{50} +(12.3118 + 5.48155i) q^{51} +(-0.163984 + 0.0730103i) q^{52} +(9.69717 + 2.06120i) q^{53} +(3.20550 + 5.55209i) q^{54} +(-2.04163 - 3.32471i) q^{55} +(-1.31747 - 4.05475i) q^{57} +(1.36945 - 13.0295i) q^{58} +(0.424357 + 4.03749i) q^{59} +(8.58107 + 9.53024i) q^{60} +(-8.48892 + 1.80438i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(0.0214368 + 0.0371295i) q^{65} +(19.3118 - 0.523635i) q^{66} +(-1.12669 + 1.95148i) q^{67} +(20.0656 - 22.2851i) q^{68} +(-3.65862 - 2.65815i) q^{69} +(1.31384 - 4.04359i) q^{71} +(-14.3015 + 3.03987i) q^{72} +(0.448694 + 4.26904i) q^{73} +(-6.40054 + 2.84970i) q^{74} +(-5.35589 + 5.94832i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(-2.07712 + 2.30688i) q^{79} +(11.1839 - 4.97939i) q^{80} +(1.15927 + 11.0297i) q^{81} +(-21.0471 + 4.47369i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(-5.22687 + 5.80502i) q^{86} +(5.50981 - 9.54328i) q^{87} +(7.22838 - 24.4860i) q^{88} +(2.16161 + 3.74402i) q^{89} +(1.81697 + 5.59204i) q^{90} +(-8.14083 + 5.91466i) q^{92} +(6.13189 - 1.30337i) q^{93} +(-5.62417 - 6.24628i) q^{94} +(0.236843 + 2.25341i) q^{95} +(-2.77436 + 26.3962i) q^{96} +(-1.43258 - 4.40904i) q^{97} +(5.82222 + 2.40531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.76087	−	1.95564i	1.24512	−	1.38285i	0.350165	−	0.936688i	$-0.386125\pi$
$2$	1.76087	−	1.95564i	1.24512	−	1.38285i	0.894954	−	0.446157i	$-0.147208\pi$
$3$	2.02209	−	0.900292i	1.16745	−	0.519784i	0.270852	−	0.962621i	$-0.412695\pi$
$3$	2.02209	−	0.900292i	1.16745	−	0.519784i	0.896602	+	0.442837i	$0.146028\pi$
$4$	−0.514820	−	4.89819i	−0.257410	−	2.44909i
$5$	−1.15065	+	0.244578i	−0.514587	+	0.109379i	−0.457883	−	0.889012i	$-0.651392\pi$
$5$	−1.15065	+	0.244578i	−0.514587	+	0.109379i	−0.0567033	+	0.998391i	$0.518059\pi$
$6$	1.79998	−	5.53977i	0.734839	−	2.26160i
$7$		0			0
$7$		0			0
$8$	−6.22764	−	4.52465i	−2.20180	−	1.59970i
$9$	1.27093	−	1.41151i	0.423643	−	0.470503i
$10$	−1.54783	+	2.68093i	−0.489468	+	0.847783i
$11$	1.11001	+	3.12536i	0.334682	+	0.942331i
$11$	1.11001	+	3.12536i	0.334682	+	0.942331i
$12$	−5.45081	−	9.44109i	−1.57351	−	2.72541i
$13$	−0.0112624	−	0.0346622i	−0.00312364	−	0.00961357i	0.949483	−	0.313820i	$-0.101609\pi$
$13$	−0.0112624	−	0.0346622i	−0.00312364	−	0.00961357i	−0.952606	+	0.304206i	$0.901609\pi$
$14$		0			0
$15$	−2.10653	+	1.53048i	−0.543903	+	0.395169i
$16$	−10.1795	+	2.16373i	−2.54488	+	0.540932i
$17$	4.07409	+	4.52474i	0.988113	+	1.09741i	0.995242	+	0.0974360i	$0.0310641\pi$
$17$	4.07409	+	4.52474i	0.988113	+	1.09741i	−0.00712889	+	0.999975i	$0.502269\pi$
$18$	−0.522468	−	4.97095i	−0.123147	−	1.17166i
$19$	0.201336	−	1.91558i	0.0461897	−	0.439465i	−0.946849	−	0.321678i	$-0.895753\pi$
$19$	0.201336	−	1.91558i	0.0461897	−	0.439465i	0.993039	−	0.117787i	$-0.0375801\pi$
$20$	1.79037	+	5.51019i	0.400339	+	1.23212i
$21$		0			0
$22$	8.06666	+	3.33255i	1.71982	+	0.710502i
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	0.739647	−	0.672996i	$-0.234993\pi$
$23$	−1.02155	−	1.76938i	−0.213008	−	0.368941i	−0.952655	+	0.304055i	$0.901659\pi$
$24$	−16.6664	−	3.54254i	−3.40201	−	0.723119i
$25$	−3.30355	+	1.47083i	−0.660710	+	0.294167i
$26$	−0.0876184	−	0.0390102i	−0.0171834	−	0.00765053i
$27$	−0.752823	+	2.31695i	−0.144881	+	0.445898i
$28$		0			0
$29$	4.02767	−	2.92628i	0.747920	−	0.543396i	−0.147261	−	0.989098i	$-0.547046\pi$
$29$	4.02767	−	2.92628i	0.747920	−	0.543396i	0.895182	+	0.445702i	$0.147046\pi$
$30$	−0.716241	+	6.81458i	−0.130767	+	1.24417i
$31$	2.77028	+	0.588842i	0.497558	+	0.105759i	0.449854	−	0.893102i	$-0.351476\pi$
$31$	2.77028	+	0.588842i	0.497558	+	0.105759i	0.0477042	+	0.998862i	$0.484810\pi$
$32$	−5.99553	+	10.3846i	−1.05987	+	1.83575i
$33$	5.05828	+	5.32042i	0.880534	+	0.926166i
$34$	16.0227			2.74787
$35$		0			0
$36$	−7.56813	−	5.49857i	−1.26136	−	0.916429i
$37$	−2.43221	−	1.08289i	−0.399853	−	0.178026i	0.196950	−	0.980413i	$-0.436896\pi$
$37$	−2.43221	−	1.08289i	−0.399853	−	0.178026i	−0.596804	+	0.802387i	$0.703563\pi$
$38$	−3.39167	−	3.76683i	−0.550201	−	0.611060i
$39$	−0.0539798	−	0.0599506i	−0.00864368	−	0.00959978i
$40$	8.27247	+	3.68314i	1.30799	+	0.582356i
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.0641641	−	0.997939i	$-0.520438\pi$
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.968925	+	0.247357i	$0.920438\pi$
$42$		0			0
$43$	−2.96835			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$43$	−2.96835			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$44$	14.7371	−	7.04605i	2.22171	−	1.06223i
$45$	−1.11717	+	1.93499i	−0.166538	+	0.288452i
$46$	−5.25907	−	1.11785i	−0.775408	−	0.164818i
$47$	0.333862	−	3.17649i	0.0486988	−	0.463338i	−0.942813	−	0.333322i	$-0.891830\pi$
$47$	0.333862	−	3.17649i	0.0486988	−	0.463338i	0.991512	−	0.130016i	$-0.0415029\pi$
$48$	−18.6359	+	13.5398i	−2.68987	+	1.95430i
$49$		0			0
$50$	−2.94068	+	9.05049i	−0.415875	+	1.27993i
$51$	12.3118	+	5.48155i	1.72399	+	0.767571i
$52$	−0.163984	+	0.0730103i	−0.0227405	+	0.0101247i
$53$	9.69717	+	2.06120i	1.33201	+	0.283127i	0.818277	−	0.574824i	$-0.194929\pi$
$53$	9.69717	+	2.06120i	1.33201	+	0.283127i	0.513732	+	0.857951i	$0.328263\pi$
$54$	3.20550	+	5.55209i	0.436213	+	0.755544i
$55$	−2.04163	−	3.32471i	−0.275294	−	0.448304i
$56$		0			0
$57$	−1.31747	−	4.05475i	−0.174503	−	0.537064i
$58$	1.36945	−	13.0295i	0.179818	−	1.71085i
$59$	0.424357	+	4.03749i	0.0552466	+	0.525636i	0.986790	+	0.162006i	$0.0517962\pi$
$59$	0.424357	+	4.03749i	0.0552466	+	0.525636i	−0.931543	+	0.363630i	$0.881537\pi$
$60$	8.58107	+	9.53024i	1.10781	+	1.23035i
$61$	−8.48892	+	1.80438i	−1.08689	+	0.231027i	−0.716317	−	0.697775i	$-0.754174\pi$
$61$	−8.48892	+	1.80438i	−1.08689	+	0.231027i	−0.370578	+	0.928801i	$0.620840\pi$
$62$	6.02966	−	4.38080i	0.765767	−	0.556363i
$63$		0			0
$64$	3.31928	+	10.2157i	0.414910	+	1.27696i
$65$	0.0214368	+	0.0371295i	0.00265890	+	0.00460535i
$66$	19.3118	−	0.523635i	2.37711	−	0.0644550i
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	−0.926605	−	0.376035i	$-0.877287\pi$
$67$	−1.12669	+	1.95148i	−0.137647	+	0.238411i	0.788959	+	0.614446i	$0.210621\pi$
$68$	20.0656	−	22.2851i	2.43331	−	2.70247i
$69$	−3.65862	−	2.65815i	−0.440446	−	0.320003i
$70$		0			0
$71$	1.31384	−	4.04359i	0.155924	−	0.479885i	−0.842329	−	0.538963i	$-0.818816\pi$
$71$	1.31384	−	4.04359i	0.155924	−	0.479885i	0.998253	+	0.0590780i	$0.0188161\pi$
$72$	−14.3015	+	3.03987i	−1.68544	+	0.358252i
$73$	0.448694	+	4.26904i	0.0525157	+	0.499653i	0.988890	+	0.148650i	$0.0474928\pi$
$73$	0.448694	+	4.26904i	0.0525157	+	0.499653i	−0.936374	+	0.351003i	$0.885841\pi$
$74$	−6.40054	+	2.84970i	−0.744048	+	0.331271i
$75$	−5.35589	+	5.94832i	−0.618445	+	0.686853i
$76$	−9.48655			−1.08818
$77$		0			0
$78$	−0.212293			−0.0240374
$79$	−2.07712	+	2.30688i	−0.233694	+	0.259544i	−0.848574	−	0.529077i	$-0.822538\pi$
$79$	−2.07712	+	2.30688i	−0.233694	+	0.259544i	0.614879	+	0.788621i	$0.289205\pi$
$80$	11.1839	−	4.97939i	1.25040	−	0.556712i
$81$	1.15927	+	11.0297i	0.128808	+	1.22553i
$82$	−21.0471	+	4.47369i	−2.32426	+	0.494036i
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	0.793779	+	0.608206i	$0.208111\pi$
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	−0.999675	+	0.0254778i	$0.991889\pi$
$84$		0			0
$85$	−5.79451	−	4.20996i	−0.628503	−	0.456634i
$86$	−5.22687	+	5.80502i	−0.563628	+	0.625972i
$87$	5.50981	−	9.54328i	0.590714	−	1.02315i
$88$	7.22838	−	24.4860i	0.770548	−	2.61022i
$89$	2.16161	+	3.74402i	0.229130	+	0.396866i	0.957551	−	0.288265i	$-0.0930784\pi$
$89$	2.16161	+	3.74402i	0.229130	+	0.396866i	−0.728420	+	0.685131i	$0.759745\pi$
$90$	1.81697	+	5.59204i	0.191525	+	0.589453i
$91$		0			0
$92$	−8.14083	+	5.91466i	−0.848740	+	0.616646i
$93$	6.13189	−	1.30337i	0.635848	−	0.135154i
$94$	−5.62417	−	6.24628i	−0.580089	−	0.644254i
$95$	0.236843	+	2.25341i	0.0242996	+	0.231195i
$96$	−2.77436	+	26.3962i	−0.283156	+	2.69405i
$97$	−1.43258	−	4.40904i	−0.145457	−	0.447670i	0.851613	−	0.524172i	$-0.175625\pi$
$97$	−1.43258	−	4.40904i	−0.145457	−	0.447670i	−0.997069	+	0.0765015i	$0.975625\pi$
$98$		0			0
$99$	5.82222	+	2.40531i	0.585155	+	0.241743i
$100$	8.90516	+	15.4242i	0.890516	+	1.54242i
$101$	−16.6397	−	3.53688i	−1.65571	−	0.351933i	−0.717117	−	0.696952i	$-0.754539\pi$
$101$	−16.6397	−	3.53688i	−1.65571	−	0.351933i	−0.938595	+	0.345020i	$0.887872\pi$
$102$	32.3993	−	14.4251i	3.20801	−	1.42830i
$103$	15.3949	+	6.85426i	1.51691	+	0.675371i	0.985177	−	0.171543i	$-0.0548751\pi$
$103$	15.3949	+	6.85426i	1.51691	+	0.675371i	0.531731	+	0.846913i	$0.321542\pi$
$104$	−0.0866959	+	0.266822i	−0.00850123	+	0.0261641i
$105$		0			0
$106$	21.1064	−	15.3347i	2.05003	−	1.48944i
$107$	0.0974866	−	0.927523i	0.00942438	−	0.0896670i	−0.988799	−	0.149256i	$-0.952312\pi$
$107$	0.0974866	−	0.927523i	0.00942438	−	0.0896670i	0.998223	+	0.0595887i	$0.0189789\pi$
$108$	11.7364	+	2.49466i	1.12934	+	0.240048i
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	−0.902281	−	0.431148i	$-0.858109\pi$
$109$	−0.811795	+	1.40607i	−0.0777558	+	0.134677i	0.824526	+	0.565825i	$0.191442\pi$
$110$	−10.0970	−	1.86167i	−0.962709	−	0.177503i
$111$	−5.89307			−0.559345
$112$		0			0
$113$	−2.86311	−	2.08017i	−0.269338	−	0.195686i	0.444915	−	0.895573i	$-0.353234\pi$
$113$	−2.86311	−	2.08017i	−0.269338	−	0.195686i	−0.714254	+	0.699887i	$0.753234\pi$
$114$	−10.2495	−	4.56337i	−0.959953	−	0.427399i
$115$	1.60820	+	1.78609i	0.149965	+	0.166553i
$116$	−16.4070	−	18.2218i	−1.52335	−	1.69185i
$117$	−0.0632398	−	0.0281562i	−0.00584652	−	0.00260304i
$118$	8.64310	+	6.27958i	0.795662	+	0.578082i
$119$		0			0
$120$	20.0436			1.82972
$121$	−8.53574	+	6.93838i	−0.775976	+	0.630762i
$122$	−11.4191	+	19.7785i	−1.03384	+	1.79066i
$123$	−17.7030	−	3.76289i	−1.59622	−	0.339288i
$124$	1.45806	−	13.8725i	0.130938	−	1.24579i
$125$	8.19996	−	5.95762i	0.733427	−	0.532866i
$126$		0			0
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	0.190903	+	0.981609i	$0.438858\pi$
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	−0.731419	+	0.681928i	$0.761142\pi$
$128$	3.91425	+	1.74274i	0.345975	+	0.154038i
$129$	−6.00227	+	2.67238i	−0.528471	+	0.235290i
$130$	0.110359	+	0.0234576i	0.00967914	+	0.00205737i
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	−0.965969	−	0.258659i	$-0.916719\pi$
$131$	−8.09187	−	14.0155i	−0.706990	−	1.22454i	0.258979	−	0.965883i	$-0.416614\pi$
$132$	23.4563	−	27.5155i	2.04161	−	2.39492i
$133$		0			0
$134$	1.83244	+	5.63968i	0.158299	+	0.487194i
$135$	0.299560	−	2.85013i	0.0257821	−	0.245300i
$136$	−4.89915	−	46.6123i	−0.420099	−	3.99697i
$137$	−11.3594	−	12.6159i	−0.970499	−	1.07785i	−0.996938	−	0.0781984i	$-0.975083\pi$
$137$	−11.3594	−	12.6159i	−0.970499	−	1.07785i	0.0264383	−	0.999650i	$-0.491583\pi$
$138$	−11.6407	+	2.47431i	−0.990923	+	0.210627i
$139$	−5.94380	+	4.31842i	−0.504146	+	0.366284i	−0.810598	−	0.585602i	$-0.800858\pi$
$139$	−5.94380	+	4.31842i	−0.504146	+	0.366284i	0.306452	+	0.951886i	$0.400858\pi$
$140$		0			0
$141$	−2.18467	−	6.72371i	−0.183982	−	0.566239i
$142$	−5.59430	−	9.68961i	−0.469463	−	0.813134i
$143$	0.0958304	−	0.0736747i	0.00801374	−	0.00616099i
$144$	−9.88334	+	17.1184i	−0.823611	+	1.42654i
$145$	−3.91874	+	4.35220i	−0.325434	+	0.361431i
$146$	9.13879	+	6.63972i	0.756332	+	0.549507i
$147$		0			0
$148$	−4.05205	+	12.4709i	−0.333076	+	1.02510i
$149$	4.91122	−	1.04391i	0.402342	−	0.0855205i	−0.00229578	−	0.999997i	$-0.500731\pi$
$149$	4.91122	−	1.04391i	0.402342	−	0.0855205i	0.404638	+	0.914477i	$0.367397\pi$
$150$	2.20176	+	20.9484i	0.179773	+	1.71043i
$151$	7.67189	−	3.41575i	0.624330	−	0.277969i	−0.0700890	−	0.997541i	$-0.522328\pi$
$151$	7.67189	−	3.41575i	0.624330	−	0.277969i	0.694419	+	0.719571i	$0.255662\pi$
$152$	−9.92120	+	11.0186i	−0.804715	+	0.893727i
$153$	11.5646			0.934942
$154$		0			0
$155$	−3.33165			−0.267604
$156$	−0.265859	+	0.295267i	−0.0212858	+	0.0236403i
$157$	13.6545	−	6.07938i	1.08975	−	0.485187i	0.218403	−	0.975859i	$-0.429915\pi$
$157$	13.6545	−	6.07938i	1.08975	−	0.485187i	0.871345	+	0.490671i	$0.163248\pi$
$158$	0.853888	+	8.12420i	0.0679317	+	0.646327i
$159$	21.4642	−	4.56236i	1.70222	−	0.361819i
$160$	4.35892	−	13.4154i	0.344603	−	1.06058i
$161$		0			0
$162$	23.6115	+	17.1548i	1.85510	+	1.34781i
$163$	1.66521	−	1.84941i	0.130430	−	0.144857i	−0.674392	−	0.738373i	$-0.735594\pi$
$163$	1.66521	−	1.84941i	0.130430	−	0.144857i	0.804822	+	0.593517i	$0.202261\pi$
$164$	−20.1355	+	34.8758i	−1.57232	+	2.72334i
$165$	−7.12158	−	4.88480i	−0.554414	−	0.380281i
$166$	7.98713	+	13.8341i	0.619921	+	1.07374i
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	0.983471	+	0.181068i	$0.0579553\pi$
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	−0.689216	+	0.724556i	$0.742045\pi$
$168$		0			0
$169$	10.5161	−	7.64043i	0.808934	−	0.587725i
$170$	−18.4365	+	3.91880i	−1.41402	+	0.300558i
$171$	−2.44798	−	2.71876i	−0.187202	−	0.207909i
$172$	1.52817	+	14.5395i	0.116522	+	1.10863i
$173$	1.27577	−	12.1382i	0.0969953	−	0.922848i	−0.832503	−	0.554021i	$-0.813093\pi$
$173$	1.27577	−	12.1382i	0.0969953	−	0.922848i	0.929498	−	0.368827i	$-0.120241\pi$
$174$	−8.96116	−	27.5796i	−0.679344	−	2.09081i
$175$		0			0
$176$	−18.0618	−	29.4129i	−1.36146	−	2.21708i
$177$	4.49301	+	7.78211i	0.337715	+	0.584940i
$178$	11.1283	+	2.36539i	0.834098	+	0.177293i
$179$	3.48419	−	1.55126i	0.260421	−	0.115947i	−0.272373	−	0.962192i	$-0.587809\pi$
$179$	3.48419	−	1.55126i	0.260421	−	0.115947i	0.532794	+	0.846245i	$0.321142\pi$
$180$	10.0531	+	4.47593i	0.749315	+	0.333616i
$181$	−2.17667	+	6.69911i	−0.161791	+	0.497941i	−0.998785	−	0.0492703i	$-0.984310\pi$
$181$	−2.17667	+	6.69911i	−0.161791	+	0.497941i	0.836995	+	0.547211i	$0.184310\pi$
$182$		0			0
$183$	−15.5409	+	11.2911i	−1.14882	+	0.834664i
$184$	−1.64396	+	15.6412i	−0.121194	+	1.15309i
$185$	3.06348	+	0.651162i	0.225231	+	0.0478744i
$186$	8.24851	−	14.2868i	0.604810	−	1.04756i
$187$	−9.61914	+	17.7555i	−0.703421	+	1.29841i
$188$	−15.7309			−1.14729
$189$		0			0
$190$	4.82391	+	3.50477i	0.349963	+	0.254263i
$191$	−14.5491	−	6.47769i	−1.05274	−	0.468710i	−0.193935	−	0.981014i	$-0.562125\pi$
$191$	−14.5491	−	6.47769i	−1.05274	−	0.468710i	−0.858804	+	0.512305i	$0.828792\pi$
$192$	15.9090	+	17.6687i	1.14813	+	1.27513i
$193$	9.90162	+	10.9969i	0.712734	+	0.791572i	0.985349	−	0.170552i	$-0.0545550\pi$
$193$	9.90162	+	10.9969i	0.712734	+	0.791572i	−0.272614	+	0.962123i	$0.587888\pi$
$194$	−11.1451	−	4.96211i	−0.800170	−	0.356259i
$195$	0.0767745	+	0.0557799i	0.00549793	+	0.00399448i
$196$		0			0
$197$	8.28808			0.590501			0.295251	−	0.955420i	$-0.404597\pi$
$197$	8.28808			0.590501			0.295251	+	0.955420i	$0.404597\pi$
$198$	14.9561	−	7.15073i	1.06288	−	0.508180i
$199$	9.14220	−	15.8348i	0.648073	−	1.12250i	−0.335509	−	0.942037i	$-0.608908\pi$
$199$	9.14220	−	15.8348i	0.648073	−	1.12250i	0.983582	−	0.180459i	$-0.0577583\pi$
$200$	27.2283	+	5.78756i	1.92533	+	0.409242i
$201$	−0.521360	+	4.96041i	−0.0367739	+	0.349880i
$202$	−36.2171	+	26.3133i	−2.54823	+	1.85140i
$203$		0			0
$204$	20.5113	−	63.1274i	1.43608	−	4.41980i
$205$	8.78701	+	3.91223i	0.613711	+	0.273242i
$206$	40.5129	−	18.0375i	2.82266	−	1.25673i
$207$	−3.79581	−	0.806824i	−0.263827	−	0.0560781i
$208$	0.189646	+	0.328476i	0.0131496	+	0.0227757i
$209$	6.21038	−	1.49708i	0.429581	−	0.103555i
$210$		0			0
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	0.805516	+	0.592573i	$0.201888\pi$
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	−0.303370	+	0.952873i	$0.598112\pi$
$212$	5.10383	−	48.5597i	0.350533	−	3.33510i
$213$	−0.983706	−	9.35934i	−0.0674024	−	0.641291i
$214$	−1.64224	−	1.82389i	−0.112261	−	0.124679i
$215$	3.41554	−	0.725995i	0.232938	−	0.0495124i
$216$	15.1717	−	11.0229i	1.03230	−	0.750013i
$217$		0			0
$218$	1.32030	+	4.06348i	0.0894222	+	0.275213i
$219$	4.75068	+	8.22842i	0.321021	+	0.556025i
$220$	−15.2340	+	11.7119i	−1.02708	+	0.789618i
$221$	0.110953	−	0.192177i	0.00746352	−	0.0129272i
$222$	−10.3769	+	11.5247i	−0.696452	+	0.773488i
$223$	−9.76962	−	7.09804i	−0.654222	−	0.475320i	0.210485	−	0.977597i	$-0.432496\pi$
$223$	−9.76962	−	7.09804i	−0.654222	−	0.475320i	−0.864707	+	0.502277i	$0.832496\pi$
$224$		0			0
$225$	−2.12248	+	6.53231i	−0.141498	+	0.435488i
$226$	−9.10960	+	1.93631i	−0.605962	+	0.128801i
$227$	−1.07950	−	10.2707i	−0.0716488	−	0.681693i	−0.970114	−	0.242649i	$-0.921984\pi$
$227$	−1.07950	−	10.2707i	−0.0716488	−	0.681693i	0.898465	−	0.439044i	$-0.144683\pi$
$228$	−19.1826	+	8.54066i	−1.27040	+	0.565619i
$229$	18.4416	−	20.4814i	1.21865	−	1.35345i	0.302233	−	0.953234i	$-0.402268\pi$
$229$	18.4416	−	20.4814i	1.21865	−	1.35345i	0.916420	−	0.400218i	$-0.131065\pi$
$230$	6.32476			0.417042
$231$		0			0
$232$	−38.3233			−2.51605
$233$	2.67665	−	2.97272i	0.175353	−	0.194750i	−0.649061	−	0.760736i	$-0.724838\pi$
$233$	2.67665	−	2.97272i	0.175353	−	0.194750i	0.824414	+	0.565987i	$0.191505\pi$
$234$	−0.166420	+	0.0740949i	−0.0108792	+	0.00484374i
$235$	0.392741	+	3.73668i	0.0256196	+	0.243754i
$236$	19.5579	−	4.15716i	1.27311	−	0.270608i
$237$	−2.12326	+	6.53473i	−0.137921	+	0.424476i
$238$		0			0
$239$	−17.1705	−	12.4751i	−1.11067	−	0.806946i	−0.127897	−	0.991787i	$-0.540823\pi$
$239$	−17.1705	−	12.4751i	−1.11067	−	0.806946i	−0.982768	+	0.184842i	$0.940823\pi$
$240$	18.1319	−	20.1375i	1.17041	−	1.29987i
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	−0.997554	−	0.0699056i	$-0.977730\pi$
$241$	−6.80326	+	11.7836i	−0.438237	+	0.759048i	0.559317	+	0.828954i	$0.311064\pi$
$242$	−1.46132	+	28.9104i	−0.0939369	+	1.85843i
$243$	8.61987	+	14.9301i	0.552965	+	0.957763i
$244$	13.2084	+	40.6514i	0.845584	+	2.60244i
$245$		0			0
$246$	−38.5314	+	27.9947i	−2.45667	+	1.78488i
$247$	−0.0686659	+	0.0145954i	−0.00436911	+	0.000928683i
$248$	−14.5880	−	16.2017i	−0.926341	−	1.02881i
$249$	1.40446	+	13.3626i	0.0890042	+	0.846819i
$250$	2.78807	−	26.5267i	0.176333	−	1.67770i
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	0.972731	+	0.231937i	$0.0745062\pi$
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	−0.650627	+	0.759398i	$0.725494\pi$
$252$		0			0
$253$	4.39600	−	5.15674i	0.276374	−	0.324202i
$254$	25.9366	+	44.9235i	1.62741	+	2.81875i
$255$	−15.5072	−	3.29616i	−0.971099	−	0.206414i
$256$	−9.32489	+	4.15171i	−0.582806	+	0.259482i
$257$	−26.7243	−	11.8984i	−1.66702	−	0.742203i	−0.667020	−	0.745040i	$-0.732430\pi$
$257$	−26.7243	−	11.8984i	−1.66702	−	0.742203i	−0.999996	+	0.00283638i	$0.999097\pi$
$258$	−5.34298	+	16.4440i	−0.332639	+	1.02376i
$259$		0			0
$260$	0.170831	−	0.124116i	0.0105945	−	0.00769737i
$261$	0.988420	−	9.40418i	0.0611816	−	0.582104i
$262$	−41.6580	−	8.85468i	−2.57364	−	0.547044i
$263$	9.96601	−	17.2616i	0.614530	−	1.06440i	−0.375936	−	0.926646i	$-0.622679\pi$
$263$	9.96601	−	17.2616i	0.614530	−	1.06440i	0.990467	−	0.137752i	$-0.0439878\pi$
$264$	−7.42816	−	56.0206i	−0.457172	−	3.44783i
$265$	−11.6622			−0.716402
$266$		0			0
$267$	7.74169	+	5.62466i	0.473784	+	0.344224i
$268$	10.1387	+	4.51406i	0.619323	+	0.275740i
$269$	−0.413989	−	0.459782i	−0.0252414	−	0.0280334i	0.730392	−	0.683028i	$-0.239337\pi$
$269$	−0.413989	−	0.459782i	−0.0252414	−	0.0280334i	−0.755633	+	0.654995i	$0.772671\pi$
$270$	−5.04633	−	5.60452i	−0.307110	−	0.341080i
$271$	0.105794	+	0.0471026i	0.00642654	+	0.00286128i	0.409947	−	0.912109i	$-0.365547\pi$
$271$	0.105794	+	0.0471026i	0.00642654	+	0.00286128i	−0.403521	+	0.914970i	$0.632214\pi$
$272$	−51.2627	−	37.2445i	−3.10826	−	2.25828i
$273$		0			0
$274$	−44.6745			−2.69889
$275$	−8.26387	−	8.69213i	−0.498330	−	0.524155i
$276$	−11.1366	+	19.2891i	−0.670342	+	1.16107i
$277$	−9.45250	−	2.00919i	−0.567946	−	0.120721i	−0.0850158	−	0.996380i	$-0.527094\pi$
$277$	−9.45250	−	2.00919i	−0.567946	−	0.120721i	−0.482930	+	0.875659i	$0.660427\pi$
$278$	−2.02095	+	19.2281i	−0.121209	+	1.15322i
$279$	4.35199	−	3.16190i	0.260547	−	0.189298i
$280$		0			0
$281$	−1.07026	+	3.29393i	−0.0638466	+	0.196500i	−0.977891	−	0.209114i	$-0.932942\pi$
$281$	−1.07026	+	3.29393i	−0.0638466	+	0.196500i	0.914045	+	0.405613i	$0.132942\pi$
$282$	−16.9961	−	7.56713i	−1.01210	−	0.450616i
$283$	−24.0623	+	10.7132i	−1.43036	+	0.636835i	−0.968249	−	0.249989i	$-0.919573\pi$
$283$	−24.0623	+	10.7132i	−1.43036	+	0.636835i	−0.462107	+	0.886824i	$0.652906\pi$
$284$	−20.4826	−	4.35372i	−1.21542	−	0.258346i
$285$	2.50765	+	4.34337i	0.148540	+	0.257279i
$286$	0.0246633	−	0.317141i	0.00145837	−	0.0187529i
$287$		0			0
$288$	7.03801	+	21.6608i	0.414719	+	1.27637i
$289$	−2.09804	+	19.9616i	−0.123414	+	1.17421i
$290$	1.61096	+	15.3273i	0.0945990	+	0.900049i
$291$	−6.86624	−	7.62573i	−0.402506	−	0.447028i
$292$	20.6796	−	4.39558i	1.21018	−	0.257232i
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	−0.164570	−	0.986365i	$-0.552624\pi$
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	0.887234	+	0.461319i	$0.152624\pi$
$294$		0			0
$295$	−1.47577	−	4.54195i	−0.0859226	−	0.264442i
$296$	10.2473	+	17.7488i	0.595609	+	1.03163i
$297$	−8.07695	+	0.219005i	−0.468672	+	0.0127080i
$298$	6.60648	−	11.4428i	0.382703	−	0.662861i
$299$	−0.0498254	+	0.0553367i	−0.00288148	+	0.00320020i
$300$	31.8933	+	23.1718i	1.84136	+	1.33783i
$301$		0			0
$302$	6.82920	−	21.0181i	0.392976	−	1.20946i
$303$	−36.8312	+	7.82871i	−2.11590	+	0.449748i
$304$	2.09529	+	19.9354i	0.120173	+	1.14337i
$305$	9.32647	−	4.15241i	0.534032	−	0.237766i
$306$	20.3637	−	22.6162i	1.16411	−	1.29288i
$307$	−32.1611			−1.83553			−0.917766	−	0.397123i	$-0.870009\pi$
$307$	−32.1611			−1.83553			−0.917766	+	0.397123i	$0.870009\pi$
$308$		0			0
$309$	37.3008			2.12197
$310$	−5.86658	+	6.51550i	−0.333199	+	0.370055i
$311$	−1.93513	+	0.861574i	−0.109731	+	0.0488554i	−0.460868	−	0.887469i	$-0.652462\pi$
$311$	−1.93513	+	0.861574i	−0.109731	+	0.0488554i	0.351137	+	0.936324i	$0.385795\pi$
$312$	0.0649114	+	0.617591i	0.00367488	+	0.0349642i
$313$	−6.00431	+	1.27626i	−0.339384	+	0.0721383i	−0.374451	−	0.927247i	$-0.622169\pi$
$313$	−6.00431	+	1.27626i	−0.339384	+	0.0721383i	0.0350672	+	0.999385i	$0.488835\pi$
$314$	12.1547	−	37.4082i	0.685928	−	2.11107i
$315$		0			0
$316$	12.3689	+	8.98651i	0.695803	+	0.505530i
$317$	−11.8931	+	13.2086i	−0.667981	+	0.741868i	−0.977941	−	0.208881i	$-0.933018\pi$
$317$	−11.8931	+	13.2086i	−0.667981	+	0.741868i	0.309960	+	0.950750i	$0.399684\pi$
$318$	28.8733	−	50.0100i	1.61913	−	2.80442i
$319$	13.6164	+	9.33972i	0.762374	+	0.522924i
$320$	−6.31787	−	10.9429i	−0.353179	−	0.611725i
$321$	−0.637915	−	1.96330i	−0.0356050	−	0.109581i
$322$		0			0
$323$	9.48778	−	6.89328i	0.527914	−	0.383552i
$324$	53.4290	−	11.3567i	2.96828	−	0.630926i
$325$	0.0881884	+	0.0979431i	0.00489181	+	0.00543291i
$326$	−0.684556	−	6.51312i	−0.0379141	−	0.360728i
$327$	−0.375648	+	3.57405i	−0.0207734	+	0.197645i
$328$	19.4500	+	59.8610i	1.07395	+	3.30527i
$329$		0			0
$330$	−22.0930	+	5.32576i	−1.21618	+	0.293174i
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	−0.999027	−	0.0441108i	$-0.985955\pi$
$331$	−9.78286	−	16.9444i	−0.537714	−	0.931349i	0.461312	−	0.887238i	$-0.347379\pi$
$332$	29.2436	+	6.21592i	1.60495	+	0.341143i
$333$	−4.61968	+	2.05681i	−0.253157	+	0.112713i
$334$	29.5832	+	13.1713i	1.61872	+	0.720701i
$335$	0.819133	−	2.52103i	0.0447540	−	0.137739i
$336$		0			0
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.965551	−	0.260215i	$-0.916207\pi$
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.0508925	+	0.998704i	$0.516207\pi$
$338$	3.57560	−	34.0195i	0.194487	−	1.85042i
$339$	−7.66222	−	1.62865i	−0.416155	−	0.0884564i
$340$	−17.6380	+	30.5500i	−0.956557	+	1.65681i
$341$	1.23471	+	9.31176i	0.0668633	+	0.504260i
$342$	−9.62747			−0.520594
$343$		0			0
$344$	18.4858	+	13.4307i	0.996690	+	0.724137i
$345$	4.85992	+	2.16378i	0.261649	+	0.116494i
$346$	−21.4914	−	23.8686i	−1.15539	−	1.28319i
$347$	−16.7559	−	18.6093i	−0.899504	−	0.999000i	−0.999992	−	0.00406186i	$-0.998707\pi$
$347$	−16.7559	−	18.6093i	−0.899504	−	0.999000i	0.100488	−	0.994938i	$-0.467960\pi$
$348$	−49.5813	−	22.0750i	−2.65784	−	1.18335i
$349$	15.8320	+	11.5026i	0.847467	+	0.615721i	0.924446	−	0.381312i	$-0.124528\pi$
$349$	15.8320	+	11.5026i	0.847467	+	0.615721i	−0.0769797	+	0.997033i	$0.524528\pi$
$350$		0			0
$351$	0.0887893			0.00473922
$352$	−39.1106	−	7.21117i	−2.08460	−	0.384357i
$353$	10.1136	−	17.5172i	0.538292	−	0.932349i	−0.460704	−	0.887554i	$-0.652403\pi$
$353$	10.1136	−	17.5172i	0.538292	−	0.932349i	0.998996	−	0.0447952i	$-0.0142635\pi$
$354$	23.1306	+	4.91656i	1.22938	+	0.261312i
$355$	−0.522798	+	4.97409i	−0.0277472	+	0.263997i
$356$	17.2261	−	12.5155i	0.912981	−	0.663319i
$357$		0			0
$358$	3.10148	−	9.54539i	0.163919	−	0.504489i
$359$	−22.7685	−	10.1372i	−1.20168	−	0.535021i	−0.294452	−	0.955666i	$-0.595137\pi$
$359$	−22.7685	−	10.1372i	−1.20168	−	0.535021i	−0.907225	+	0.420645i	$0.861804\pi$
$360$	15.7125	−	6.99566i	0.828122	−	0.368704i
$361$	14.9559	+	3.17897i	0.787151	+	0.167314i
$362$	9.26821	+	16.0530i	0.487126	+	0.843727i
$363$	−11.0135	+	21.7147i	−0.578057	+	1.13973i
$364$		0			0
$365$	−1.56040	−	4.80243i	−0.0816753	−	0.251371i
$366$	−5.28406	+	50.2745i	−0.276202	+	2.62789i
$367$	0.782866	+	7.44847i	0.0408653	+	0.388807i	0.995769	+	0.0918915i	$0.0292913\pi$
$367$	0.782866	+	7.44847i	0.0408653	+	0.388807i	−0.954904	+	0.296915i	$0.904042\pi$
$368$	14.2274	+	15.8011i	0.741652	+	0.823688i
$369$	−15.1910	+	3.22895i	−0.790812	+	0.168092i
$370$	6.66781	−	4.84445i	0.346643	−	0.251851i
$371$		0			0
$372$	−9.54099	−	29.3642i	−0.494678	−	1.52246i
$373$	0.802488	+	1.38995i	0.0415513	+	0.0719689i	0.886053	−	0.463584i	$-0.153437\pi$
$373$	0.802488	+	1.38995i	0.0415513	+	0.0719689i	−0.844502	+	0.535553i	$0.820103\pi$
$374$	17.7854	+	50.0766i	0.919661	+	2.58940i
$375$	11.2175	−	19.4292i	0.579267	−	1.00332i
$376$	−16.4517	+	18.2714i	−0.848429	+	0.942276i
$377$	−0.146793	−	0.106651i	−0.00756021	−	0.00549281i
$378$		0			0
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	−0.719779	−	0.694204i	$-0.755757\pi$
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	0.990356	−	0.138547i	$-0.0442433\pi$
$380$	10.9157	−	2.32020i	0.559964	−	0.119024i
$381$	4.56071	+	43.3923i	0.233652	+	2.22305i
$382$	−38.2871	+	17.0465i	−1.95894	+	0.872176i
$383$	11.6576	−	12.9471i	0.595678	−	0.661567i	−0.367628	−	0.929973i	$-0.619830\pi$
$383$	11.6576	−	12.9471i	0.595678	−	0.661567i	0.963306	+	0.268406i	$0.0864967\pi$
$384$	9.48395			0.483976
$385$		0			0
$386$	38.9413			1.98206
$387$	−3.77256	+	4.18985i	−0.191770	+	0.212982i
$388$	−20.8588	+	9.28693i	−1.05894	+	0.471472i
$389$	1.17444	+	11.1740i	0.0595465	+	0.566547i	0.983099	+	0.183075i	$0.0586050\pi$
$389$	1.17444	+	11.1740i	0.0595465	+	0.566547i	−0.923553	+	0.383472i	$0.874728\pi$
$390$	0.244275	−	0.0519222i	0.0123693	−	0.00262918i
$391$	3.84408	−	11.8309i	0.194403	−	0.598312i
$392$		0			0
$393$	−28.9805	−	21.0556i	−1.46188	−	1.06211i
$394$	14.5942	−	16.2085i	0.735245	−	0.816572i
$395$	1.82583	−	3.16243i	0.0918674	−	0.159119i
$396$	8.78428	−	29.7566i	0.441427	−	1.49533i
$397$	9.85421	+	17.0680i	0.494568	+	0.856618i	0.999980	−	0.00626047i	$-0.00199278\pi$
$397$	9.85421	+	17.0680i	0.494568	+	0.856618i	−0.505412	+	0.862878i	$0.668659\pi$
$398$	−14.8689	−	45.7617i	−0.745310	−	2.29383i
$399$		0			0
$400$	30.4461	−	22.1204i	1.52231	−	1.10602i
$401$	12.2643	−	2.60685i	0.612448	−	0.130180i	0.108764	−	0.994068i	$-0.465311\pi$
$401$	12.2643	−	2.60685i	0.612448	−	0.130180i	0.503684	+	0.863888i	$0.331977\pi$
$402$	8.78273	+	9.75421i	0.438043	+	0.486496i
$403$	−0.0107896	−	0.102656i	−0.000537467	−	0.00511366i
$404$	−8.75784	+	83.3253i	−0.435719	+	4.14559i
$405$	−4.03156	−	12.4079i	−0.200330	−	0.616551i
$406$		0			0
$407$	0.684633	−	8.80356i	0.0339360	−	0.436376i
$408$	−51.8712	−	89.8436i	−2.56801	−	4.44792i
$409$	15.2647	+	3.24461i	0.754791	+	0.160436i	0.569209	−	0.822193i	$-0.307250\pi$
$409$	15.2647	+	3.24461i	0.754791	+	0.160436i	0.185582	+	0.982629i	$0.440583\pi$
$410$	23.1236	−	10.2953i	1.14200	−	0.508449i
$411$	−34.3277	−	15.2837i	−1.69326	−	0.753889i
$412$	25.6479	−	78.9360i	1.26358	−	3.88890i
$413$		0			0
$414$	−8.26176	+	6.00252i	−0.406043	+	0.295008i
$415$	0.746413	−	7.10165i	0.0366400	−	0.348606i
$416$	0.427476	+	0.0908628i	0.0209587	+	0.00445492i
$417$	−8.13105	+	14.0834i	−0.398179	+	0.689666i
$418$	8.00789	−	14.7814i	0.391679	−	0.722982i
$419$	31.8183			1.55443			0.777213	−	0.629238i	$-0.216633\pi$
$419$	31.8183			1.55443			0.777213	+	0.629238i	$0.216633\pi$
$420$		0			0
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	0.00719220	−	0.999974i	$-0.497711\pi$
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	−0.948809	+	0.315849i	$0.897711\pi$
$422$	56.7459	+	25.2649i	2.76234	+	1.22988i
$423$	−4.05932	−	4.50833i	−0.197371	−	0.219203i
$424$	−51.0643	−	56.7127i	−2.47990	−	2.75421i
$425$	−20.1141	−	8.95538i	−0.975678	−	0.434400i
$426$	−20.0357	−	14.5568i	−0.970731	−	0.705277i
$427$		0			0
$428$	−4.59337			−0.222029
$429$	0.127449	−	0.235252i	0.00615329	−	0.0113581i
$430$	4.59452	−	7.95793i	0.221567	−	0.383766i
$431$	8.16153	+	1.73479i	0.393127	+	0.0835618i	0.400234	−	0.916413i	$-0.368929\pi$
$431$	8.16153	+	1.73479i	0.393127	+	0.0835618i	−0.00710679	+	0.999975i	$0.502262\pi$
$432$	2.65014	−	25.2144i	0.127505	−	1.21313i
$433$	10.3850	−	7.54511i	0.499069	−	0.362595i	−0.309592	−	0.950869i	$-0.600193\pi$
$433$	10.3850	−	7.54511i	0.499069	−	0.362595i	0.808661	+	0.588275i	$0.200193\pi$
$434$		0			0
$435$	−4.00579	+	12.3286i	−0.192063	+	0.591109i
$436$	7.30512	+	3.25245i	0.349852	+	0.155764i
$437$	−3.59507	+	1.60063i	−0.171975	+	0.0765684i
$438$	24.4571	+	5.19852i	1.16861	+	0.248395i
$439$	−12.2991	−	21.3026i	−0.587002	−	1.01672i	−0.994623	−	0.103566i	$-0.966975\pi$
$439$	−12.2991	−	21.3026i	−0.587002	−	1.01672i	0.407620	−	0.913151i	$-0.366359\pi$
$440$	−2.32858	+	29.9428i	−0.111011	+	1.42747i
$441$		0			0
$442$	−0.180454	−	0.555382i	−0.00858334	−	0.0264168i
$443$	1.68573	−	16.0387i	0.0800916	−	0.762021i	−0.878597	−	0.477564i	$-0.841520\pi$
$443$	1.68573	−	16.0387i	0.0800916	−	0.762021i	0.958689	−	0.284457i	$-0.0918133\pi$
$444$	3.03387	+	28.8654i	0.143981	+	1.36989i
$445$	−3.40297	−	3.77938i	−0.161316	−	0.179160i
$446$	−31.0842	+	6.60715i	−1.47188	+	0.312858i
$447$	8.99109	−	6.53241i	0.425264	−	0.308972i
$448$		0			0
$449$	10.6496	+	32.7763i	0.502588	+	1.54681i	0.804788	+	0.593562i	$0.202279\pi$
$449$	10.6496	+	32.7763i	0.502588	+	1.54681i	−0.302200	+	0.953245i	$0.597721\pi$
$450$	9.03745	+	15.6533i	0.426029	+	0.737905i
$451$	7.67798	−	26.0090i	0.361542	−	1.22472i
$452$	−8.71507	+	15.0950i	−0.409923	+	0.710007i
$453$	12.4381	−	13.8139i	0.584392	−	0.649033i
$454$	−21.9867	−	15.9743i	−1.03189	−	0.749710i
$455$		0			0
$456$	−10.1416	+	31.2126i	−0.474923	+	1.46166i
$457$	31.7391	−	6.74634i	1.48469	−	0.315581i	0.606959	−	0.794733i	$-0.292389\pi$
$457$	31.7391	−	6.74634i	1.48469	−	0.315581i	0.877732	+	0.479153i	$0.159056\pi$
$458$	−7.58118	−	72.1301i	−0.354245	−	3.37042i
$459$	−13.5507	+	6.03315i	−0.632491	+	0.281603i
$460$	7.92065	−	8.79677i	0.369302	−	0.410152i
$461$	29.4973			1.37383			0.686914	−	0.726739i	$-0.258965\pi$
$461$	29.4973			1.37383			0.686914	+	0.726739i	$0.258965\pi$
$462$		0			0
$463$	22.2588			1.03445			0.517227	−	0.855848i	$-0.326964\pi$
$463$	22.2588			1.03445			0.517227	+	0.855848i	$0.326964\pi$
$464$	−34.6682	+	38.5029i	−1.60943	+	1.78745i
$465$	−6.73689	+	2.99946i	−0.312416	+	0.139096i
$466$	−1.10035	−	10.4691i	−0.0509727	−	0.484973i
$467$	23.1410	−	4.91878i	1.07084	−	0.227614i	0.361422	−	0.932402i	$-0.382292\pi$
$467$	23.1410	−	4.91878i	1.07084	−	0.227614i	0.709417	+	0.704789i	$0.248958\pi$
$468$	−0.105357	+	0.324256i	−0.00487013	+	0.0149887i
$469$		0			0
$470$	7.99916	+	5.81173i	0.368974	+	0.268075i
$471$	22.1374	−	24.5861i	1.02004	−	1.13287i
$472$	15.6255	−	27.0641i	0.719220	−	1.24573i
$473$	−3.29491	−	9.27717i	−0.151500	−	0.426565i
$474$	9.04079	+	15.6591i	0.415257	+	0.719247i
$475$	2.15239	+	6.62436i	0.0987582	+	0.303946i
$476$		0			0
$477$	15.2338	−	11.0680i	0.697508	−	0.506769i
$478$	−54.6316	+	11.6123i	−2.49879	+	0.531135i
$479$	7.73143	+	8.58662i	0.353258	+	0.392333i	0.893416	−	0.449231i	$-0.148302\pi$
$479$	7.73143	+	8.58662i	0.353258	+	0.392333i	−0.540158	+	0.841564i	$0.681635\pi$
$480$	−3.26363	−	31.0514i	−0.148964	−	1.41730i
$481$	−0.0101428	+	0.0965018i	−0.000462470	+	0.00440010i
$482$	11.0648	+	34.0541i	0.503989	+	1.55112i
$483$		0			0
$484$	38.3799	+	38.2376i	1.74454	+	1.73807i
$485$	2.72676	+	4.72289i	0.123816	+	0.214455i
$486$	44.3762	+	9.43245i	2.01295	+	0.427865i
$487$	0.120369	−	0.0535917i	0.00545444	−	0.00242847i	−0.404008	−	0.914756i	$-0.632383\pi$
$487$	0.120369	−	0.0535917i	0.00545444	−	0.00242847i	0.409462	+	0.912327i	$0.365716\pi$
$488$	61.0301	+	27.1724i	2.76270	+	1.23004i
$489$	1.70221	−	5.23885i	0.0769764	−	0.236909i
$490$		0			0
$491$	0.0180456	−	0.0131109i	0.000814388	−	0.000591687i	−0.587378	−	0.809313i	$-0.699840\pi$
$491$	0.0180456	−	0.0131109i	0.000814388	−	0.000591687i	0.588192	+	0.808721i	$0.299840\pi$
$492$	−9.31746	+	88.6498i	−0.420064	+	3.99664i
$493$	29.6498	+	6.30225i	1.33536	+	0.283839i
$494$	−0.0923681	+	0.159986i	−0.00415584	+	0.00719812i
$495$	−7.28763	−	1.34369i	−0.327554	−	0.0603942i
$496$	−29.4743			−1.32343
$497$		0			0
$498$	28.6054	+	20.7831i	1.28184	+	0.931312i
$499$	−6.33006	−	2.81832i	−0.283372	−	0.126166i	0.260129	−	0.965574i	$-0.416235\pi$
$499$	−6.33006	−	2.81832i	−0.283372	−	0.126166i	−0.543501	+	0.839408i	$0.682902\pi$
$500$	−33.4030	−	37.0978i	−1.49383	−	1.65907i
$501$	18.2256	+	20.2415i	0.814258	+	0.904325i
$502$	39.7005	+	17.6758i	1.77192	+	0.788910i
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	0.425978	−	0.904734i	$-0.359930\pi$
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	−0.728818	+	0.684707i	$0.759930\pi$
$504$		0			0
$505$	20.0115			0.890502
$506$	−2.34396	−	17.6773i	−0.104202	−	0.785853i
$507$	14.3860	−	24.9172i	0.638903	−	1.10661i
$508$	94.9628	+	20.1850i	4.21329	+	0.895563i
$509$	−0.129599	+	1.23305i	−0.00574439	+	0.0546542i	−0.997019	−	0.0771619i	$-0.975414\pi$
$509$	−0.129599	+	1.23305i	−0.00574439	+	0.0546542i	0.991274	+	0.131816i	$0.0420808\pi$
$510$	−33.7522	+	24.5224i	−1.49457	+	1.08587i
$511$		0			0
$512$	−10.9487	+	33.6967i	−0.483869	+	1.48920i
$513$	4.28675	+	1.90858i	0.189265	+	0.0842660i
$514$	−70.3269	+	31.3116i	−3.10199	+	1.38109i
$515$	−19.3906	−	4.12160i	−0.854451	−	0.181619i
$516$	16.1799	+	28.0245i	0.712282	+	1.23371i
$517$	10.2983	−	2.48250i	0.452917	−	0.109180i
$518$		0			0
$519$	−8.34818	−	25.6930i	−0.366444	−	1.12780i
$520$	0.0344977	−	0.328223i	0.00151282	−	0.0143935i
$521$	4.57272	+	43.5065i	0.200334	+	1.90605i	0.384444	+	0.923148i	$0.374393\pi$
$521$	4.57272	+	43.5065i	0.200334	+	1.90605i	−0.184110	+	0.982906i	$0.558940\pi$
$522$	−16.6507	−	18.4925i	−0.728782	−	0.809394i
$523$	−29.8442	+	6.34358i	−1.30500	+	0.277385i	−0.807390	−	0.590018i	$-0.799121\pi$
$523$	−29.8442	+	6.34358i	−1.30500	+	0.277385i	−0.497606	+	0.867403i	$0.665787\pi$
$524$	−64.4848	+	46.8510i	−2.81703	+	2.04669i
$525$		0			0
$526$	−16.2087	−	49.8853i	−0.706734	−	2.17510i
$527$	8.62204	+	14.9338i	0.375582	+	0.650527i
$528$	−63.0029	−	43.2146i	−2.74185	−	1.88068i
$529$	9.41287	−	16.3036i	0.409255	−	0.708851i
$530$	−20.5355	+	22.8070i	−0.892006	+	0.990674i
$531$	6.23827	+	4.53237i	0.270718	+	0.196688i
$532$		0			0
$533$	−0.0920882	+	0.283418i	−0.00398878	+	0.0122762i
$534$	24.6319	−	5.23567i	1.06593	−	0.226569i
$535$	0.114679	+	1.09110i	0.00495801	+	0.0471723i
$536$	15.8464	−	7.05525i	0.684458	−	0.304740i
$537$	5.64876	−	6.27358i	0.243762	−	0.270725i
$538$	−1.62815			−0.0701944
$539$		0			0
$540$	−14.1147			−0.607399
$541$	0.189956	−	0.210968i	0.00816685	−	0.00907020i	−0.739048	−	0.673653i	$-0.764724\pi$
$541$	0.189956	−	0.210968i	0.00816685	−	0.00907020i	0.747214	+	0.664583i	$0.231391\pi$
$542$	0.278405	−	0.123954i	0.0119585	−	0.00532427i
$543$	1.62973	+	15.5058i	0.0699383	+	0.665419i
$544$	−71.4137	+	15.1795i	−3.06184	+	0.650814i
$545$	0.590198	−	1.81644i	0.0252813	−	0.0778078i
$546$		0			0
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	0.385733	−	0.922610i	$-0.373948\pi$
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	−0.758256	+	0.651957i	$0.773948\pi$
$548$	−55.9470	+	62.1354i	−2.38994	+	2.65429i
$549$	−8.24192	+	14.2754i	−0.351756	+	0.609260i
$550$	−31.5502	+	0.855479i	−1.34531	+	0.0364777i
$551$	−4.79461	−	8.30452i	−0.204257	−	0.353784i
$552$	10.7574	+	33.1080i	0.457867	+	1.40917i
$553$		0			0
$554$	−20.5738	+	14.9478i	−0.874098	+	0.635070i
$555$	6.78086	−	1.44132i	0.287832	−	0.0611805i
$556$	24.2124	+	26.8906i	1.02684	+	1.14042i
$557$	−4.17612	−	39.7331i	−0.176948	−	1.68355i	−0.618088	−	0.786109i	$-0.712092\pi$
$557$	−4.17612	−	39.7331i	−0.176948	−	1.68355i	0.441140	−	0.897438i	$-0.354574\pi$
$558$	1.47972	−	14.0786i	0.0626416	−	0.595995i
$559$	0.0334309	+	0.102890i	0.00141398	+	0.00435177i
$560$		0			0
$561$	−3.46559	+	44.5633i	−0.146317	+	1.88146i
$562$	4.55716	+	7.89323i	0.192232	+	0.332956i
$563$	−11.6820	−	2.48308i	−0.492336	−	0.104649i	−0.0449482	−	0.998989i	$-0.514312\pi$
$563$	−11.6820	−	2.48308i	−0.492336	−	0.104649i	−0.447388	+	0.894340i	$0.647646\pi$
$564$	−31.8093	+	14.1624i	−1.33941	+	0.596345i
$565$	3.80320	+	1.69329i	0.160002	+	0.0712374i
$566$	−21.4193	+	65.9217i	−0.900319	+	2.77090i
$567$		0			0
$568$	−26.4779	+	19.2374i	−1.11099	+	0.807181i
$569$	1.14725	−	10.9154i	0.0480953	−	0.457596i	−0.943798	−	0.330523i	$-0.892775\pi$
$569$	1.14725	−	10.9154i	0.0480953	−	0.457596i	0.991893	−	0.127073i	$-0.0405584\pi$
$570$	12.9097	+	2.74404i	0.540727	+	0.114935i
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	−0.933705	−	0.358044i	$-0.883444\pi$
$571$	−3.74628	+	6.48874i	−0.156777	+	0.271545i	0.776928	+	0.629590i	$0.216777\pi$
$572$	−0.410208	−	0.431466i	−0.0171517	−	0.0180405i
$573$	−35.2515			−1.47265
$574$		0			0
$575$	5.97720	+	4.34269i	0.249267	+	0.181103i
$576$	18.6381	+	8.29821i	0.776587	+	0.345759i
$577$	23.9838	+	26.6367i	0.998457	+	1.10890i	0.994052	+	0.108909i	$0.0347356\pi$
$577$	23.9838	+	26.6367i	0.998457	+	1.10890i	0.00440519	+	0.999990i	$0.498598\pi$
$578$	35.3432	+	39.2526i	1.47008	+	1.63269i
$579$	29.9224	+	13.3223i	1.24353	+	0.553656i
$580$	23.3354	+	16.9541i	0.968948	+	0.703982i
$581$		0			0
$582$	−27.0037			−1.11934
$583$	4.32201	+	32.5951i	0.178999	+	1.34995i
$584$	16.5216	−	28.6162i	0.683668	−	1.18415i
$585$	0.0796532	+	0.0169308i	0.00329326	+	0.000700003i
$586$	4.20593	−	40.0168i	0.173746	−	1.65308i
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	−0.407551	−	0.913182i	$-0.633617\pi$
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	0.742548	+	0.669793i	$0.233617\pi$
$588$		0			0
$589$	1.68574	−	5.18816i	0.0694595	−	0.213774i
$590$	−11.4810	−	5.11169i	−0.472667	−	0.210445i
$591$	16.7592	−	7.46170i	0.689383	−	0.306933i
$592$	27.1019	+	5.76068i	1.11388	+	0.236762i
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	0.995248	+	0.0973765i	$0.0310451\pi$
$593$	14.1715	+	24.5458i	0.581954	+	1.00797i	−0.413293	+	0.910598i	$0.635622\pi$
$594$	−13.7941	+	16.1812i	−0.565980	+	0.663924i
$595$		0			0
$596$	−7.64167	−	23.5186i	−0.313015	−	0.963361i
$597$	4.23044	−	40.2499i	0.173140	−	1.64732i
$598$	0.0204828	+	0.194881i	0.000837604	+	0.00796927i
$599$	22.3396	+	24.8106i	0.912769	+	1.01373i	0.999846	+	0.0175315i	$0.00558074\pi$
$599$	22.3396	+	24.8106i	0.912769	+	1.01373i	−0.0870769	+	0.996202i	$0.527753\pi$
$600$	60.2686	−	12.8105i	2.46046	−	0.522986i
$601$	−1.42697	+	1.03676i	−0.0582074	+	0.0422901i	−0.616508	−	0.787348i	$-0.711453\pi$
$601$	−1.42697	+	1.03676i	−0.0582074	+	0.0422901i	0.558301	+	0.829638i	$0.311453\pi$
$602$		0			0
$603$	1.32259	+	4.07052i	0.0538601	+	0.165764i
$604$	−20.6806	−	35.8199i	−0.841482	−	1.45749i
$605$	8.12468	−	10.0713i	0.330315	−	0.409457i
$606$	−49.5446	+	85.8138i	−2.01261	+	3.48595i
$607$	9.57278	−	10.6316i	0.388547	−	0.431525i	−0.516860	−	0.856070i	$-0.672899\pi$
$607$	9.57278	−	10.6316i	0.388547	−	0.431525i	0.905407	+	0.424545i	$0.139566\pi$
$608$	18.6854	+	13.5757i	0.757792	+	0.550568i
$609$		0			0
$610$	8.30204	−	25.5510i	0.336140	−	1.03453i
$611$	−0.113864	+	0.0242026i	−0.00460645	+	0.000979131i
$612$	−5.95369	−	56.6455i	−0.240663	−	2.28976i
$613$	−5.20695	+	2.31828i	−0.210307	+	0.0936346i	−0.509187	−	0.860656i	$-0.670054\pi$
$613$	−5.20695	+	2.31828i	−0.210307	+	0.0936346i	0.298880	+	0.954291i	$0.403387\pi$
$614$	−56.6314	+	62.8955i	−2.28546	+	2.53826i
$615$	21.2903			0.858506
$616$		0			0
$617$	17.9653			0.723257			0.361628	−	0.932322i	$-0.382221\pi$
$617$	17.9653			0.723257			0.361628	+	0.932322i	$0.382221\pi$
$618$	65.6816	−	72.9468i	2.64210	−	2.93435i
$619$	−5.56618	+	2.47822i	−0.223723	+	0.0996081i	−0.515538	−	0.856867i	$-0.672408\pi$
$619$	−5.56618	+	2.47822i	−0.223723	+	0.0996081i	0.291814	+	0.956475i	$0.405741\pi$
$620$	1.71520	+	16.3190i	0.0688841	+	0.655388i
$621$	4.86861	−	1.03485i	0.195371	−	0.0415273i
$622$	−1.72257	+	5.30152i	−0.0690688	+	0.212572i
$623$		0			0
$624$	0.679206	+	0.493472i	0.0271900	+	0.0197547i
$625$	4.12032	−	4.57607i	0.164813	−	0.183043i
$626$	−8.07689	+	13.9896i	−0.322817	+	0.559136i
$627$	11.2101	−	8.61838i	0.447689	−	0.344185i
$628$	−36.8076	−	63.7526i	−1.46878	−	2.54400i
$629$	−5.00926	−	15.4169i	−0.199732	−	0.614713i
$630$		0			0
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.435522	+	0.900178i	$0.643436\pi$
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.990704	+	0.136036i	$0.956564\pi$
$632$	23.3734	−	4.96817i	0.929743	−	0.197623i
$633$	34.9599	+	38.8269i	1.38953	+	1.54323i
$634$	4.88914	+	46.5171i	0.194173	+	1.84743i
$635$	2.42383	−	23.0612i	0.0961867	−	0.915155i
$636$	−33.3975	−	102.787i	−1.32430	−	4.07577i
$637$		0			0
$638$	42.2418	−	10.1828i	1.67237	−	0.403143i
$639$	−4.03776	−	6.99361i	−0.159731	−	0.276663i
$640$	−4.93018	−	1.04794i	−0.194882	−	0.0414235i
$641$	34.9905	−	15.5788i	1.38204	−	0.615324i	0.424977	−	0.905204i	$-0.360282\pi$
$641$	34.9905	−	15.5788i	1.38204	−	0.615324i	0.957063	+	0.289880i	$0.0936154\pi$
$642$	−4.96279	−	2.20958i	−0.195866	−	0.0872050i
$643$	8.87538	−	27.3156i	0.350011	−	1.07722i	−0.608835	−	0.793297i	$-0.708363\pi$
$643$	8.87538	−	27.3156i	0.350011	−	1.07722i	0.958846	−	0.283926i	$-0.0916371\pi$
$644$		0			0
$645$	6.25291	−	4.54301i	0.246208	−	0.178881i
$646$	3.22594	−	30.6928i	0.126923	−	1.20759i
$647$	−20.0193	−	4.25524i	−0.787042	−	0.167291i	−0.203177	−	0.979142i	$-0.565127\pi$
$647$	−20.0193	−	4.25524i	−0.787042	−	0.167291i	−0.583864	+	0.811851i	$0.698460\pi$
$648$	42.6862	−	73.9346i	1.67687	−	2.90443i
$649$	−12.1476	+	5.80793i	−0.476833	+	0.227981i
$650$	0.346829			0.0136038
$651$		0			0
$652$	−9.91604	−	7.20442i	−0.388342	−	0.282147i
$653$	25.8153	+	11.4937i	1.01023	+	0.449784i	0.844023	−	0.536306i	$-0.180181\pi$
$653$	25.8153	+	11.4937i	1.01023	+	0.449784i	0.166209	+	0.986091i	$0.446847\pi$
$654$	6.32809	+	7.02805i	0.247448	+	0.274819i
$655$	12.7388	+	14.1479i	0.497746	+	0.552803i
$656$	77.7366	+	34.6106i	3.03510	+	1.35132i
$657$	6.59604	+	4.79231i	0.257336	+	0.186966i
$658$		0			0
$659$	25.1666			0.980350			0.490175	−	0.871624i	$-0.336933\pi$
$659$	25.1666			0.980350			0.490175	+	0.871624i	$0.336933\pi$
$660$	−20.2603	+	37.3976i	−0.788632	+	1.45570i
$661$	10.3561	−	17.9373i	0.402805	−	0.697679i	−0.591258	−	0.806483i	$-0.701368\pi$
$661$	10.3561	−	17.9373i	0.402805	−	0.697679i	0.994063	+	0.108803i	$0.0347018\pi$
$662$	−50.3634	−	10.7051i	−1.95743	−	0.416065i
$663$	0.0513422	−	0.488489i	0.00199397	−	0.0189713i
$664$	37.8033	−	27.4657i	1.46705	−	1.06588i
$665$		0			0
$666$	−4.11224	+	12.6562i	−0.159346	+	0.490417i
$667$	−9.29216	−	4.13714i	−0.359794	−	0.160191i
$668$	55.3670	−	24.6510i	2.14221	−	0.953775i
$669$	−26.1454	−	5.55737i	−1.01084	−	0.214860i
$670$	−3.48785	−	6.04113i	−0.134747	−	0.233389i
$671$	−15.0621	−	24.5280i	−0.581467	−	0.946895i
$672$		0			0
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	−0.997284	−	0.0736535i	$-0.976534\pi$
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	0.763527	−	0.645776i	$-0.223466\pi$
$674$	−6.34439	+	60.3629i	−0.244377	+	2.32509i
$675$	−0.920865	−	8.76144i	−0.0354441	−	0.337228i
$676$	−42.8382	−	47.5766i	−1.64762	−	1.82987i
$677$	22.2973	−	4.73944i	0.856956	−	0.182152i	0.241575	−	0.970382i	$-0.422336\pi$
$677$	22.2973	−	4.73944i	0.856956	−	0.182152i	0.615380	+	0.788231i	$0.289003\pi$
$678$	−16.6772	+	12.1167i	−0.640484	+	0.465339i
$679$		0			0
$680$	17.0376	+	52.4363i	0.653361	+	2.01084i
$681$	−11.4295	−	19.7965i	−0.437980	−	0.758603i
$682$	20.3846	+	13.9821i	0.780566	+	0.535402i
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	−0.540645	−	0.841251i	$-0.681820\pi$
$683$	11.9753	−	20.7418i	0.458222	−	0.793664i	0.998867	+	0.0475871i	$0.0151532\pi$
$684$	−12.0567	+	13.3903i	−0.461000	+	0.511993i
$685$	16.1563	+	11.7382i	0.617300	+	0.448495i
$686$		0			0
$687$	18.8512	−	58.0181i	0.719219	−	2.21353i
$688$	30.2164	−	6.42270i	1.15199	−	0.244863i
$689$	−0.0377681	−	0.359340i	−0.00143885	−	0.0136897i
$690$	12.7892	−	5.69413i	0.486878	−	0.216772i
$691$	−27.3931	+	30.4231i	−1.04208	+	1.15735i	−0.0547807	+	0.998498i	$0.517446\pi$
$691$	−27.3931	+	30.4231i	−1.04208	+	1.15735i	−0.987302	+	0.158852i	$0.949221\pi$
$692$	−60.1119			−2.28511
$693$		0			0
$694$	−65.8980			−2.50145
$695$	5.78304	−	6.42272i	0.219363	−	0.243628i
$696$	−77.4931	+	34.5022i	−2.93737	+	1.30780i
$697$	−5.20387	−	49.5115i	−0.197111	−	1.87538i
$698$	50.3729	−	10.7071i	1.90664	−	0.405270i
$699$	2.73611	−	8.42088i	0.103489	−	0.318507i
$700$		0			0
$701$	−8.05784	−	5.85436i	−0.304340	−	0.221116i	0.425124	−	0.905135i	$-0.360231\pi$
$701$	−8.05784	−	5.85436i	−0.304340	−	0.221116i	−0.729464	+	0.684019i	$0.760231\pi$
$702$	0.156346	−	0.173640i	0.00590090	−	0.00655361i
$703$	−2.56406	+	4.44108i	−0.0967054	+	0.167499i
$704$	−28.2432	+	21.7135i	−1.06446	+	0.818358i
$705$	4.15826	+	7.20232i	0.156609	+	0.271255i
$706$	−16.4487	−	50.6240i	−0.619057	−	1.90526i
$707$		0			0
$708$	35.8052	−	26.0140i	1.34564	−	0.977665i
$709$	46.4802	−	9.87966i	1.74560	−	0.371039i	0.778939	−	0.627100i	$-0.215758\pi$
$709$	46.4802	−	9.87966i	1.74560	−	0.371039i	0.966660	+	0.256062i	$0.0824250\pi$
$710$	8.80695	+	9.78111i	0.330519	+	0.367079i
$711$	0.616305	+	5.86375i	0.0231132	+	0.219908i
$712$	3.47863	−	33.0970i	0.130367	−	1.24036i
$713$	−1.78810	−	5.50321i	−0.0669649	−	0.206097i
$714$		0			0
$715$	−0.0922481	+	0.108212i	−0.00344988	+	0.00404689i
$716$	−9.39211	−	16.2676i	−0.351000	−	0.607949i
$717$	−45.9515	−	9.76728i	−1.71609	−	0.364766i
$718$	−59.9170	+	26.6768i	−2.23608	+	0.995568i
$719$	−18.0374	−	8.03076i	−0.672681	−	0.299497i	0.0418262	−	0.999125i	$-0.486682\pi$
$719$	−18.0374	−	8.03076i	−0.672681	−	0.299497i	−0.714507	+	0.699628i	$0.753349\pi$
$720$	7.18547	−	22.1146i	0.267787	−	0.824162i
$721$		0			0
$722$	32.5522	−	23.6506i	1.21147	−	0.880182i
$723$	−3.14813	+	29.9524i	−0.117080	+	1.11394i
$724$	33.9341	+	7.21291i	1.26115	+	0.268066i
$725$	−9.00155	+	15.5911i	−0.334309	+	0.579040i
$726$	23.0729	+	59.7750i	0.856315	+	2.21846i
$727$	−38.0241			−1.41024			−0.705118	−	0.709090i	$-0.749106\pi$
$727$	−38.0241			−1.41024			−0.705118	+	0.709090i	$0.749106\pi$
$728$		0			0
$729$	3.95434	+	2.87300i	0.146457	+	0.106407i
$730$	−12.1395	−	5.40485i	−0.449302	−	0.200042i
$731$	−12.0933	−	13.4310i	−0.447289	−	0.496764i
$732$	63.3068	+	70.3093i	2.33989	+	2.59871i
$733$	−26.1399	−	11.6382i	−0.965499	−	0.429868i	−0.137441	−	0.990510i	$-0.543888\pi$
$733$	−26.1399	−	11.6382i	−0.965499	−	0.429868i	−0.828058	+	0.560642i	$0.810554\pi$
$734$	15.9450	+	11.5847i	0.588542	+	0.427601i
$735$		0			0
$736$	24.4989			0.903042
$737$	−7.34971	−	1.35513i	−0.270730	−	0.0499169i
$738$	−20.4346	+	35.3938i	−0.752210	+	1.30287i
$739$	−8.86002	−	1.88325i	−0.325921	−	0.0692766i	0.0420455	−	0.999116i	$-0.486613\pi$
$739$	−8.86002	−	1.88325i	−0.325921	−	0.0692766i	−0.367966	+	0.929839i	$0.619946\pi$
$740$	1.61237	−	15.3407i	0.0592721	−	0.563936i
$741$	−0.125709	+	0.0913326i	−0.00461802	+	0.00335519i
$742$		0			0
$743$	2.57977	−	7.93973i	0.0946427	−	0.291280i	−0.892518	−	0.451012i	$-0.851063\pi$
$743$	2.57977	−	7.93973i	0.0946427	−	0.291280i	0.987160	+	0.159732i	$0.0510630\pi$
$744$	−44.0846	−	19.6277i	−1.61622	−	0.719587i
$745$	−5.39578	+	2.40235i	−0.197686	+	0.0880154i
$746$	4.13131	+	0.878138i	0.151258	+	0.0321509i
$747$	5.76482	+	9.98496i	0.210924	+	0.365331i
$748$	91.9221	+	37.9754i	3.36100	+	1.38852i
$749$		0			0
$750$	−18.2441	−	56.1495i	−0.666179	−	2.05029i
$751$	−5.14447	+	48.9464i	−0.187725	+	1.78608i	0.343806	+	0.939041i	$0.388284\pi$
$751$	−5.14447	+	48.9464i	−0.187725	+	1.78608i	−0.531531	+	0.847039i	$0.678383\pi$
$752$	3.47449	+	33.0575i	0.126701	+	1.20548i
$753$	24.4586	+	27.1640i	0.891321	+	0.989913i
$754$	−0.467053	+	0.0992752i	−0.0170091	+	0.00361539i
$755$	−7.99225	+	5.80671i	−0.290868	+	0.211328i
$756$		0			0
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	0.994482	+	0.104907i	$0.0334545\pi$
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	−0.742890	+	0.669413i	$0.766546\pi$
$758$	−22.4292	−	38.8485i	−0.814665	−	1.41104i
$759$	4.24654	−	14.3851i	0.154140	−	0.522146i
$760$	8.72092	−	15.1051i	0.316341	−	0.547919i
$761$	16.9867	−	18.8656i	0.615767	−	0.683878i	−0.351921	−	0.936030i	$-0.614471\pi$
$761$	16.9867	−	18.8656i	0.615767	−	0.683878i	0.967688	+	0.252151i	$0.0811381\pi$
$762$	92.8905	+	67.4889i	3.36507	+	2.44486i
$763$		0			0
$764$	−24.2388	+	74.5993i	−0.876928	+	2.69891i
$765$	−13.3068	+	2.82845i	−0.481108	+	0.102263i
$766$	−4.79236	−	45.5963i	−0.173155	−	1.64746i
$767$	0.135169	−	0.0601811i	0.00488067	−	0.00217301i
$768$	−15.1180	+	16.7903i	−0.545524	+	0.605866i
$769$	44.5582			1.60681			0.803406	−	0.595432i	$-0.203019\pi$
$769$	44.5582			1.60681			0.803406	+	0.595432i	$0.203019\pi$
$770$		0			0
$771$	−64.7510			−2.33195
$772$	48.7672	−	54.1614i	1.75517	−	1.94931i
$773$	−30.1833	+	13.4385i	−1.08562	+	0.483349i	−0.869961	−	0.493120i	$-0.835856\pi$
$773$	−30.1833	+	13.4385i	−1.08562	+	0.483349i	−0.215658	+	0.976469i	$0.569190\pi$
$774$	1.55087	+	14.7555i	0.0557449	+	0.530377i
$775$	−10.0179	+	2.12936i	−0.359852	+	0.0764889i
$776$	−11.0277	+	33.9399i	−0.395873	+	1.21837i
$777$		0			0
$778$	23.9204	+	17.3792i	0.857589	+	0.623075i
$779$	−10.5383	+	11.7039i	−0.377573	+	0.419337i
$780$	0.233696	−	0.404772i	0.00836764	−	0.0144932i
$781$	14.0960	−	0.382212i	0.504396	−	0.0136766i
$782$	−16.3680	−	28.3502i	−0.585318	−	1.01380i
$783$	3.74792	+	11.5349i	0.133940	+	0.412224i
$784$		0			0
$785$	−14.2247	+	10.3348i	−0.507701	+	0.368866i
$786$	−92.2080	+	19.5994i	−3.28895	+	0.699088i
$787$	−28.8917	−	32.0875i	−1.02988	−	1.14379i	−0.989489	−	0.144610i	$-0.953807\pi$
$787$	−28.8917	−	32.0875i	−1.02988	−	1.14379i	−0.0403883	−	0.999184i	$-0.512860\pi$
$788$	−4.26687	−	40.5966i	−0.152001	−	1.44619i
$789$	4.61165	−	43.8769i	0.164179	−	1.56206i
$790$	−2.96953	−	9.13927i	−0.105651	−	0.325161i
$791$		0			0
$792$	−25.3755	−	41.3229i	−0.901679	−	1.46835i
$793$	0.158150	+	0.273923i	0.00561606	+	0.00972729i
$794$	50.7307	+	10.7832i	1.80037	+	0.382680i
$795$	−23.5820	+	10.4994i	−0.836367	+	0.372374i
$796$	−82.2682	−	36.6282i	−2.91592	−	1.29825i
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	−0.875066	−	0.484003i	$-0.839182\pi$
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	0.992433	+	0.122785i	$0.0391825\pi$
$798$		0			0
$799$	15.7330	−	11.4307i	0.556592	−	0.404388i
$800$	4.53255	−	43.1243i	0.160250	−	1.52467i
$801$	8.03197	+	1.70725i	0.283796	+	0.0603227i
$802$	16.4977	−	28.5748i	0.582553	−	1.00901i
$803$	−12.8442	+	6.14102i	−0.453263	+	0.216712i
$804$	24.5654			0.866356
$805$		0			0
$806$	−0.219757	−	0.159663i	−0.00774061	−	0.00562388i
$807$	−1.25106	−	0.557009i	−0.0440395	−	0.0196076i
$808$	87.6230	+	97.3152i	3.08257	+	3.42354i
$809$	−0.769904	−	0.855064i	−0.0270684	−	0.0300625i	0.729459	−	0.684025i	$-0.239772\pi$
$809$	−0.769904	−	0.855064i	−0.0270684	−	0.0300625i	−0.756527	+	0.653962i	$0.773105\pi$
$810$	−31.3643	−	13.9643i	−1.10203	−	0.490655i
$811$	−28.6938	−	20.8473i	−1.00758	−	0.732047i	−0.0438772	−	0.999037i	$-0.513971\pi$
$811$	−28.6938	−	20.8473i	−1.00758	−	0.732047i	−0.963699	+	0.266990i	$0.913971\pi$
$812$		0			0
$813$	0.256331			0.00898993
$814$	−16.0110	−	16.8408i	−0.561186	−	0.590269i
$815$	−1.46375	+	2.53530i	−0.0512731	+	0.0888076i
$816$	−137.189	−	29.1603i	−4.80256	−	1.02082i
$817$	−0.597636	+	5.68613i	−0.0209086	+	0.198933i
$818$	33.2244	−	24.1389i	1.16166	−	0.843997i
$819$		0			0
$820$	14.6391	−	45.0545i	0.511220	−	1.57337i
$821$	18.0170	+	8.02169i	0.628798	+	0.279959i	0.696290	−	0.717761i	$-0.254833\pi$
$821$	18.0170	+	8.02169i	0.628798	+	0.279959i	−0.0674914	+	0.997720i	$0.521500\pi$
$822$	−90.3359	+	40.2201i	−3.15083	+	1.40284i
$823$	−39.9340	−	8.48824i	−1.39201	−	0.295882i	−0.549922	−	0.835216i	$-0.685342\pi$
$823$	−39.9340	−	8.48824i	−1.39201	−	0.295882i	−0.842092	+	0.539335i	$0.818676\pi$
$824$	−64.8610	−	112.343i	−2.25954	−	3.91364i
$825$	−24.5357	−	10.1364i	−0.854225	−	0.352903i
$826$		0			0
$827$	−0.289657	−	0.891474i	−0.0100724	−	0.0309996i	0.945894	−	0.324476i	$-0.105188\pi$
$827$	−0.289657	−	0.891474i	−0.0100724	−	0.0309996i	−0.955966	+	0.293476i	$0.905188\pi$
$828$	−1.99782	+	19.0080i	−0.0694289	+	0.660572i
$829$	−1.59882	−	15.2118i	−0.0555295	−	0.528328i	−0.986562	−	0.163390i	$-0.947757\pi$
$829$	−1.59882	−	15.2118i	−0.0555295	−	0.528328i	0.931032	−	0.364937i	$-0.118910\pi$
$830$	−12.5739	−	13.9648i	−0.436447	−	0.484724i
$831$	−20.9227	+	4.44725i	−0.725799	+	0.154273i
$832$	0.316715	−	0.230107i	0.0109801	−	0.00797753i
$833$		0			0
$834$	13.2243	+	40.7003i	0.457921	+	1.40934i
$835$	−7.23784	−	12.5363i	−0.250476	−	0.433837i
$836$	−10.5302	−	29.6489i	−0.364194	−	1.02543i
$837$	−3.44985	+	5.97532i	−0.119244	+	0.206537i
$838$	56.0277	−	62.2251i	1.93545	−	2.14953i
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	0.766350	−	0.642423i	$-0.222071\pi$
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	−0.374166	+	0.927362i	$0.622071\pi$
$840$		0			0
$841$	−1.30243	+	4.00846i	−0.0449113	+	0.138223i
$842$	−61.4720	+	13.0663i	−2.11847	+	0.450294i
$843$	0.801334	+	7.62418i	0.0275994	+	0.262591i
$844$	106.204	−	47.2850i	3.65569	−	1.62762i
$845$	−10.2317	+	11.3635i	−0.351982	+	0.390916i
$846$	−15.9646			−0.548874
$847$		0			0
$848$	−103.173			−3.54296
$849$	−39.0111	+	43.3262i	−1.33886	+	1.48695i
$850$	−52.9317	+	23.5667i	−1.81554	+	0.808332i
$851$	0.568585	+	5.40973i	0.0194909	+	0.185443i
$852$	−45.3374	+	9.63675i	−1.55323	+	0.330150i
$853$	−1.13225	+	3.48472i	−0.0387677	+	0.119315i	−0.968567	−	0.248751i	$-0.919980\pi$
$853$	−1.13225	+	3.48472i	−0.0387677	+	0.119315i	0.929800	+	0.368066i	$0.119980\pi$
$854$		0			0
$855$	3.48172	+	2.52962i	0.119072	+	0.0865111i
$856$	−4.80383	+	5.33519i	−0.164191	+	0.182353i
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	−0.819752	−	0.572718i	$-0.805889\pi$
$857$	2.52090	−	4.36633i	0.0861124	−	0.149151i	0.905865	+	0.423567i	$0.139222\pi$
$858$	−0.235648	−	0.663491i	−0.00804489	−	0.0226512i
$859$	26.8888	+	46.5728i	0.917434	+	1.58904i	0.803298	+	0.595578i	$0.203077\pi$
$859$	26.8888	+	46.5728i	0.917434	+	1.58904i	0.114137	+	0.993465i	$0.463590\pi$
$860$	−5.31445	−	16.3562i	−0.181221	−	0.557741i
$861$		0			0
$862$	17.7640	−	12.9063i	0.605043	−	0.439590i
$863$	32.5472	−	6.91812i	1.10792	−	0.235495i	0.382604	−	0.923913i	$-0.375027\pi$
$863$	32.5472	−	6.91812i	1.10792	−	0.235495i	0.725315	+	0.688417i	$0.241694\pi$
$864$	−19.5469	−	21.7091i	−0.665001	−	0.738558i
$865$	1.50076	+	14.2788i	0.0510275	+	0.485495i
$866$	3.53099	−	33.5951i	0.119988	−	1.14161i
$867$	13.7288	+	42.2529i	0.466255	+	1.43498i
$868$		0			0
$869$	−9.51545	−	3.93109i	−0.322790	−	0.133353i
$870$	17.0565	+	29.5428i	0.578271	+	1.00160i
$871$	0.0803318	+	0.0170750i	0.00272194	+	0.000578566i
$872$	11.4175	−	5.08341i	0.386647	−	0.172146i
$873$	−8.04411	−	3.58147i	−0.272252	−	0.121214i
$874$	−3.20018	+	9.84914i	−0.108248	+	0.333152i
$875$		0			0
$876$	37.8586	−	27.5059i	1.27912	−	0.929338i
$877$	1.37629	−	13.0945i	0.0464741	−	0.442171i	−0.946399	−	0.322998i	$-0.895309\pi$
$877$	1.37629	−	13.0945i	0.0464741	−	0.442171i	0.992874	−	0.119173i	$-0.0380242\pi$
$878$	−63.3172	−	13.4585i	−2.13685	−	0.454202i
$879$	16.9220	−	29.3098i	0.570766	−	0.988596i
$880$	27.9766	+	29.4265i	0.943092	+	0.991966i
$881$	33.1960			1.11840			0.559201	−	0.829032i	$-0.311108\pi$
$881$	33.1960			1.11840			0.559201	+	0.829032i	$0.311108\pi$
$882$		0			0
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	0.924633	−	0.380859i	$-0.124372\pi$
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	−0.0764906	+	0.997070i	$0.524372\pi$
$884$	−0.998439	−	0.444534i	−0.0335811	−	0.0149513i
$885$	−7.07322	−	7.85560i	−0.237764	−	0.264063i
$886$	−28.3975	−	31.5386i	−0.954033	−	1.05956i
$887$	30.2685	+	13.4764i	1.01632	+	0.452493i	0.846163	−	0.532924i	$-0.178907\pi$
$887$	30.2685	+	13.4764i	1.01632	+	0.452493i	0.170153	+	0.985418i	$0.445574\pi$
$888$	36.6999	+	26.6641i	1.23157	+	0.894787i
$889$		0			0
$890$	−13.3833			−0.448608
$891$	−33.1851	+	15.8663i	−1.11174	+	0.531542i
$892$	−29.7380	+	51.5076i	−0.995700	+	1.72460i
$893$	−6.01761	−	1.27908i	−0.201372	−	0.0428029i
$894$	3.05706	−	29.0860i	0.102244	−	0.972782i
$895$	−3.62968	+	2.63712i	−0.121327	+	0.0881492i
$896$		0			0
$897$	−0.0509322	+	0.156753i	−0.00170058	+	0.00523384i
$898$	82.8511	+	36.8877i	2.76478	+	1.23096i
$899$	12.8809	−	5.73495i	0.429603	−	0.191271i
$900$	33.0892	+	7.03333i	1.10297	+	0.234444i
$901$	30.1808	+	52.2747i	1.00547	+	1.74152i
$902$	−37.3444	−	60.8138i	−1.24343	−	2.02488i
$903$		0			0
$904$	8.41838	+	25.9091i	0.279991	+	0.861724i
$905$	0.866132	−	8.24070i	0.0287912	−	0.273930i
$906$	−5.11319	−	48.6488i	−0.169874	−	1.61625i
$907$	7.58896	+	8.42840i	0.251987	+	0.279860i	0.855846	−	0.517231i	$-0.173037\pi$
$907$	7.58896	+	8.42840i	0.251987	+	0.279860i	−0.603858	+	0.797092i	$0.706371\pi$
$908$	−49.7523	+	10.5752i	−1.65109	+	0.350949i
$909$	−26.1402	+	18.9920i	−0.867016	+	0.629924i
$910$		0			0
$911$	−9.02202	−	27.7669i	−0.298913	−	0.919959i	−0.981879	−	0.189509i	$-0.939310\pi$
$911$	−9.02202	−	27.7669i	−0.298913	−	0.919959i	0.682966	−	0.730450i	$-0.260690\pi$
$912$	22.1846	+	38.4248i	0.734604	+	1.27237i
$913$	−20.1253	+	0.545694i	−0.666050	+	0.0180598i
$914$	42.6948	−	73.9495i	1.41222	−	2.44603i
$915$	15.1206	−	16.7931i	0.499871	−	0.555163i
$916$	−109.816	−	79.7860i	−3.62842	−	2.63620i
$917$		0			0
$918$	−12.0623	+	37.1238i	−0.398114	+	1.22527i
$919$	−14.2369	+	3.02615i	−0.469633	+	0.0998236i	−0.436648	−	0.899632i	$-0.643835\pi$
$919$	−14.2369	+	3.02615i	−0.469633	+	0.0998236i	−0.0329848	+	0.999456i	$0.510501\pi$
$920$	−1.93388	−	18.3996i	−0.0637581	−	0.606618i
$921$	−65.0326	+	28.9544i	−2.14290	+	0.954080i
$922$	51.9408	−	57.6861i	1.71058	−	1.89979i
$923$	−0.154957			−0.00510046
$924$		0			0
$925$	9.62768			0.316556
$926$	39.1948	−	43.5302i	1.28802	−	1.43049i
$927$	29.2407	−	13.0188i	0.960391	−	0.427593i
$928$	6.24006	+	59.3702i	0.204840	+	1.94892i
$929$	−6.43399	+	1.36759i	−0.211092	+	0.0448691i	−0.312244	−	0.950002i	$-0.601081\pi$
$929$	−6.43399	+	1.36759i	−0.211092	+	0.0448691i	0.101152	+	0.994871i	$0.467747\pi$
$930$	−5.99690	+	18.4566i	−0.196646	+	0.605214i
$931$		0			0
$932$	−15.9389	−	11.5803i	−0.522098	−	0.379326i
$933$	−3.13733	+	3.48436i	−0.102712	+	0.114073i
$934$	31.1289	−	53.9168i	1.01857	−	1.76421i
$935$	6.72565	−	22.7830i	0.219952	−	0.745085i
$936$	0.266438	+	0.461484i	0.00870880	+	0.0150841i
$937$	9.37722	+	28.8601i	0.306340	+	0.942818i	0.979174	+	0.203024i	$0.0650771\pi$
$937$	9.37722	+	28.8601i	0.306340	+	0.942818i	−0.672833	+	0.739794i	$0.734923\pi$
$938$		0			0
$939$	−10.9923	+	7.98634i	−0.358719	+	0.260624i
$940$	18.1008	−	3.84744i	0.590382	−	0.125490i
$941$	10.2017	+	11.3301i	0.332565	+	0.369351i	0.886115	−	0.463465i	$-0.153394\pi$
$941$	10.2017	+	11.3301i	0.332565	+	0.369351i	−0.553550	+	0.832816i	$0.686727\pi$
$942$	−9.10051	−	86.5856i	−0.296511	−	2.82111i
$943$	−1.74621	+	16.6141i	−0.0568644	+	0.541028i
$944$	−13.0558	−	40.1815i	−0.424929	−	1.30780i
$945$		0			0
$946$	−23.9447	−	9.89218i	−0.778509	−	0.321623i
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	−0.999966	−	0.00818941i	$-0.997393\pi$
$947$	−15.6044	−	27.0276i	−0.507075	−	0.878280i	0.492891	−	0.870091i	$-0.335940\pi$
$948$	33.1014	+	7.03593i	1.07508	+	0.228516i
$949$	0.142921	−	0.0636325i	0.00463941	−	0.00206560i
$950$	16.7449	+	7.45532i	0.543277	+	0.241882i
$951$	−12.1573	+	37.4162i	−0.394226	+	1.21330i
$952$		0			0
$953$	−17.4834	+	12.7024i	−0.566342	+	0.411471i	−0.833774	−	0.552105i	$-0.813825\pi$
$953$	−17.4834	+	12.7024i	−0.566342	+	0.411471i	0.267433	+	0.963577i	$0.413825\pi$
$954$	5.17965	−	49.2811i	0.167697	−	1.59553i
$955$	18.3253	+	3.89516i	0.592992	+	0.126044i
$956$	−52.2656	+	90.5266i	−1.69039	+	2.92784i
$957$	35.9421	+	6.62698i	1.16184	+	0.214220i
$958$	30.4063			0.982384
$959$		0			0
$960$	−22.6271	−	16.4395i	−0.730285	−	0.530583i
$961$	−20.9922	−	9.34632i	−0.677167	−	0.301494i
$962$	0.170863	+	0.189762i	0.00550883	+	0.00611818i
$963$	−1.18531	−	1.31642i	−0.0381960	−	0.0424210i
$964$	61.2207	+	27.2572i	1.97179	+	0.877896i
$965$	−14.0829	−	10.2318i	−0.453345	−	0.329374i
$966$		0			0
$967$	5.74025			0.184594			0.0922970	−	0.995732i	$-0.470579\pi$
$967$	5.74025			0.184594			0.0922970	+	0.995732i	$0.470579\pi$
$968$	84.5513	−	4.58856i	2.71758	−	0.147482i
$969$	12.9792	−	22.4806i	0.416951	−	0.722181i
$970$	14.0377	+	2.98381i	0.450724	+	0.0958043i
$971$	−0.717256	+	6.82424i	−0.0230178	+	0.219000i	0.976966	+	0.213393i	$0.0684515\pi$
$971$	−0.717256	+	6.82424i	−0.0230178	+	0.219000i	−0.999984	+	0.00560712i	$0.998215\pi$
$972$	68.6925	−	49.9080i	2.20331	−	1.60080i
$973$		0			0
$974$	0.107148	−	0.329766i	0.00343323	−	0.0105664i
$975$	0.266502	+	0.118654i	0.00853490	+	0.00379998i
$976$	82.5091	−	36.7354i	2.64105	−	1.17587i
$977$	10.1873	+	2.16538i	0.325920	+	0.0692765i	0.367966	−	0.929839i	$-0.380054\pi$
$977$	10.1873	+	2.16538i	0.325920	+	0.0692765i	−0.0420458	+	0.999116i	$0.513388\pi$
$978$	−7.24794	−	12.5538i	−0.231764	−	0.401426i
$979$	−9.30199	+	10.9117i	−0.297293	+	0.348740i
$980$		0			0
$981$	0.952947	+	2.93287i	0.0304252	+	0.0936393i
$982$	0.00613570	−	0.0583773i	0.000195798	−	0.00186289i
$983$	1.64651	+	15.6655i	0.0525155	+	0.499651i	0.988890	+	0.148649i	$0.0474924\pi$
$983$	1.64651	+	15.6655i	0.0525155	+	0.499651i	−0.936375	+	0.351002i	$0.885841\pi$
$984$	93.2221	+	103.534i	2.97181	+	3.30053i
$985$	−9.53669	+	2.02709i	−0.303864	+	0.0645883i
$986$	64.5342	−	46.8868i	2.05519	−	1.49318i
$987$		0			0
$988$	0.106842	+	0.328825i	0.00339908	+	0.0104613i
$989$	3.03232	+	5.25213i	0.0964222	+	0.167008i
$990$	−15.4603	+	11.8859i	−0.491360	+	0.377759i
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	−0.923264	−	0.384167i	$-0.874489\pi$
$991$	−4.05884	+	7.03011i	−0.128933	+	0.223319i	0.794330	+	0.607486i	$0.207822\pi$
$992$	−22.7242	+	25.2378i	−0.721493	+	0.801299i
$993$	−35.0367	−	25.4557i	−1.11186	−	0.807811i
$994$		0			0
$995$	−6.64664	+	20.4563i	−0.210713	+	0.648507i
$996$	64.7294	−	13.7586i	2.05103	−	0.435959i
$997$	−4.31228	−	41.0286i	−0.136571	−	1.29939i	−0.821261	−	0.570553i	$-0.806729\pi$
$997$	−4.31228	−	41.0286i	−0.136571	−	1.29939i	0.684690	−	0.728835i	$-0.259938\pi$
$998$	−16.6580	+	7.41662i	−0.527300	+	0.234769i
$999$	4.34003	−	4.82009i	0.137313	−	0.152501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.h.214.5		40
7.2	even	3	inner	539.2.q.h.324.1		40
7.3	odd	6		539.2.f.h.148.5		20
7.4	even	3		539.2.f.g.148.5		20
7.5	odd	6		77.2.m.b.16.1	yes	40
7.6	odd	2		77.2.m.b.60.5	yes	40
11.9	even	5	inner	539.2.q.h.361.1		40
21.5	even	6		693.2.by.b.478.5		40
21.20	even	2		693.2.by.b.676.1		40
77.3	odd	30		5929.2.a.bw.1.10		10
77.5	odd	30		847.2.n.i.807.5		40
77.6	even	10		847.2.n.h.81.5		40
77.9	even	15	inner	539.2.q.h.471.5		40
77.13	even	10		847.2.n.j.130.5		40
77.19	even	30		847.2.e.h.485.10		20
77.20	odd	10		77.2.m.b.53.1	yes	40
77.25	even	15		5929.2.a.bx.1.10		10
77.26	odd	30		847.2.n.i.366.1		40
77.27	odd	10		847.2.n.i.81.1		40
77.31	odd	30		539.2.f.h.295.5		20
77.40	even	30		847.2.n.h.366.5		40
77.41	even	10		847.2.e.h.606.10		20
77.47	odd	30		847.2.e.i.485.1		20
77.48	odd	10		847.2.n.i.487.5		40
77.52	even	30		5929.2.a.by.1.1		10
77.53	even	15		539.2.f.g.295.5		20
77.54	even	6		847.2.n.j.632.5		40
77.61	even	30		847.2.n.h.807.1		40
77.62	even	10		847.2.n.h.487.1		40
77.68	even	30		847.2.n.j.9.1		40
77.69	odd	10		847.2.e.i.606.1		20
77.74	odd	30		5929.2.a.bz.1.1		10
77.75	odd	30		77.2.m.b.9.5	✓	40
77.76	even	2		847.2.n.j.753.1		40
231.20	even	10		693.2.by.b.361.5		40
231.152	even	30		693.2.by.b.163.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	77.75	odd	30
77.2.m.b.16.1	yes	40	7.5	odd	6
77.2.m.b.53.1	yes	40	77.20	odd	10
77.2.m.b.60.5	yes	40	7.6	odd	2
539.2.f.g.148.5		20	7.4	even	3
539.2.f.g.295.5		20	77.53	even	15
539.2.f.h.148.5		20	7.3	odd	6
539.2.f.h.295.5		20	77.31	odd	30
539.2.q.h.214.5		40	1.1	even	1	trivial
539.2.q.h.324.1		40	7.2	even	3	inner
539.2.q.h.361.1		40	11.9	even	5	inner
539.2.q.h.471.5		40	77.9	even	15	inner
693.2.by.b.163.1		40	231.152	even	30
693.2.by.b.361.5		40	231.20	even	10
693.2.by.b.478.5		40	21.5	even	6
693.2.by.b.676.1		40	21.20	even	2
847.2.e.h.485.10		20	77.19	even	30
847.2.e.h.606.10		20	77.41	even	10
847.2.e.i.485.1		20	77.47	odd	30
847.2.e.i.606.1		20	77.69	odd	10
847.2.n.h.81.5		40	77.6	even	10
847.2.n.h.366.5		40	77.40	even	30
847.2.n.h.487.1		40	77.62	even	10
847.2.n.h.807.1		40	77.61	even	30
847.2.n.i.81.1		40	77.27	odd	10
847.2.n.i.366.1		40	77.26	odd	30
847.2.n.i.487.5		40	77.48	odd	10
847.2.n.i.807.5		40	77.5	odd	30
847.2.n.j.9.1		40	77.68	even	30
847.2.n.j.130.5		40	77.13	even	10
847.2.n.j.632.5		40	77.54	even	6
847.2.n.j.753.1		40	77.76	even	2
5929.2.a.bw.1.10		10	77.3	odd	30
5929.2.a.bx.1.10		10	77.25	even	15
5929.2.a.by.1.1		10	77.52	even	30
5929.2.a.bz.1.1		10	77.74	odd	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)

\(f(q)\)	\(=\)	\(q+(1.76087 - 1.95564i) q^{2} +(2.02209 - 0.900292i) q^{3} +(-0.514820 - 4.89819i) q^{4} +(-1.15065 + 0.244578i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(1.27093 - 1.41151i) q^{9} +O(q^{10})\)	\(q+(1.76087 - 1.95564i) q^{2} +(2.02209 - 0.900292i) q^{3} +(-0.514820 - 4.89819i) q^{4} +(-1.15065 + 0.244578i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(1.27093 - 1.41151i) q^{9} +(-1.54783 + 2.68093i) q^{10} +(1.11001 + 3.12536i) q^{11} +(-5.45081 - 9.44109i) q^{12} +(-0.0112624 - 0.0346622i) q^{13} +(-2.10653 + 1.53048i) q^{15} +(-10.1795 + 2.16373i) q^{16} +(4.07409 + 4.52474i) q^{17} +(-0.522468 - 4.97095i) q^{18} +(0.201336 - 1.91558i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(-1.02155 - 1.76938i) q^{23} +(-16.6664 - 3.54254i) q^{24} +(-3.30355 + 1.47083i) q^{25} +(-0.0876184 - 0.0390102i) q^{26} +(-0.752823 + 2.31695i) q^{27} +(4.02767 - 2.92628i) q^{29} +(-0.716241 + 6.81458i) q^{30} +(2.77028 + 0.588842i) q^{31} +(-5.99553 + 10.3846i) q^{32} +(5.05828 + 5.32042i) q^{33} +16.0227 q^{34} +(-7.56813 - 5.49857i) q^{36} +(-2.43221 - 1.08289i) q^{37} +(-3.39167 - 3.76683i) q^{38} +(-0.0539798 - 0.0599506i) q^{39} +(8.27247 + 3.68314i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(14.7371 - 7.04605i) q^{44} +(-1.11717 + 1.93499i) q^{45} +(-5.25907 - 1.11785i) q^{46} +(0.333862 - 3.17649i) q^{47} +(-18.6359 + 13.5398i) q^{48} +(-2.94068 + 9.05049i) q^{50} +(12.3118 + 5.48155i) q^{51} +(-0.163984 + 0.0730103i) q^{52} +(9.69717 + 2.06120i) q^{53} +(3.20550 + 5.55209i) q^{54} +(-2.04163 - 3.32471i) q^{55} +(-1.31747 - 4.05475i) q^{57} +(1.36945 - 13.0295i) q^{58} +(0.424357 + 4.03749i) q^{59} +(8.58107 + 9.53024i) q^{60} +(-8.48892 + 1.80438i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(0.0214368 + 0.0371295i) q^{65} +(19.3118 - 0.523635i) q^{66} +(-1.12669 + 1.95148i) q^{67} +(20.0656 - 22.2851i) q^{68} +(-3.65862 - 2.65815i) q^{69} +(1.31384 - 4.04359i) q^{71} +(-14.3015 + 3.03987i) q^{72} +(0.448694 + 4.26904i) q^{73} +(-6.40054 + 2.84970i) q^{74} +(-5.35589 + 5.94832i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(-2.07712 + 2.30688i) q^{79} +(11.1839 - 4.97939i) q^{80} +(1.15927 + 11.0297i) q^{81} +(-21.0471 + 4.47369i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(-5.22687 + 5.80502i) q^{86} +(5.50981 - 9.54328i) q^{87} +(7.22838 - 24.4860i) q^{88} +(2.16161 + 3.74402i) q^{89} +(1.81697 + 5.59204i) q^{90} +(-8.14083 + 5.91466i) q^{92} +(6.13189 - 1.30337i) q^{93} +(-5.62417 - 6.24628i) q^{94} +(0.236843 + 2.25341i) q^{95} +(-2.77436 + 26.3962i) q^{96} +(-1.43258 - 4.40904i) q^{97} +(5.82222 + 2.40531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more