LMFDB - Embedded newform 539.2.q.b.324.2

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

Embedding invariants

Embedding label			324.2
Root			$-0.185798 - 1.76775i$ of defining polynomial
Character	$\chi$	$=$	539.324
Dual form			539.2.q.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760494 + 0.161648i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(-1.27487 - 0.567608i) q^{4} +(0.148892 + 0.165361i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(2.56082 + 0.544320i) q^{9} +O(q^{10})$	\(q+(0.760494 + 0.161648i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(-1.27487 - 0.567608i) q^{4} +(0.148892 + 0.165361i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(2.56082 + 0.544320i) q^{9} +(0.0865012 + 0.149825i) q^{10} +(2.48448 - 2.19713i) q^{11} +(-0.431239 + 0.746928i) q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(0.494158 + 0.548818i) q^{16} +(-4.23989 + 0.901217i) q^{17} +(1.85950 + 0.827904i) q^{18} +(-2.66299 + 1.18564i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +(1.94898 - 3.37573i) q^{23} +(-1.09174 + 1.21250i) q^{24} +(0.517467 - 4.92337i) q^{25} +(-0.530651 - 5.04881i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(0.0976776 - 0.0434889i) q^{30} +(4.61003 - 5.11996i) q^{31} +(2.92705 + 5.06980i) q^{32} +(-1.18996 - 1.66902i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(0.590953 + 5.62254i) q^{37} +(-2.21685 + 0.471205i) q^{38} +(-3.94730 + 0.839024i) q^{39} +(-0.0614035 - 0.584215i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(-4.41449 + 1.39084i) q^{44} +(0.291277 + 0.504506i) q^{45} +(2.02787 - 2.25218i) q^{46} +(-5.52287 + 2.45894i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(0.280025 + 2.66426i) q^{51} +(-0.952474 + 9.06218i) q^{52} +(-1.14951 + 1.27666i) q^{53} +(1.34977 - 2.33786i) q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(2.68054 - 1.19345i) q^{58} +(8.70887 + 3.87744i) q^{59} +(-0.187721 + 0.0399013i) q^{60} +(6.44334 + 7.15606i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +(0.726463 - 1.25827i) q^{65} +(-0.635163 - 1.46163i) q^{66} +(-0.635774 - 1.10119i) q^{67} +(5.91685 + 1.25766i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(-4.62470 - 5.13625i) q^{72} +(-5.10591 - 2.27330i) q^{73} +(-0.459457 + 4.37144i) q^{74} +(-2.99271 - 0.636120i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(4.43056 + 0.941745i) q^{79} +(-0.0171771 + 0.163429i) q^{80} +(5.21470 + 2.32174i) q^{81} +(0.696136 + 0.773138i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(-3.58056 - 0.761072i) q^{86} +(-1.16623 - 2.01996i) q^{87} +(-8.71563 + 0.837331i) q^{88} +(3.96078 - 6.86028i) q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(-2.84916 - 3.16431i) q^{93} +(-4.59760 + 0.977249i) q^{94} +(-0.592557 - 0.263824i) q^{95} +(3.30524 - 1.47159i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.760494	+	0.161648i	0.537751	+	0.114302i	0.468778	−	0.883316i	$-0.344694\pi$
$2$	0.760494	+	0.161648i	0.537751	+	0.114302i	0.0689729	+	0.997619i	$0.478028\pi$
$3$	0.0646021	−	0.614648i	0.0372981	−	0.354867i	−0.959917	−	0.280285i	$-0.909571\pi$
$3$	0.0646021	−	0.614648i	0.0372981	−	0.354867i	0.997215	−	0.0745823i	$-0.0237623\pi$
$4$	−1.27487	−	0.567608i	−0.637435	−	0.283804i
$5$	0.148892	+	0.165361i	0.0665866	+	0.0739519i	0.775518	−	0.631326i	$-0.217489\pi$
$5$	0.148892	+	0.165361i	0.0665866	+	0.0739519i	−0.708931	+	0.705278i	$0.750822\pi$
$6$	0.148486	−	0.456994i	0.0606193	−	0.186567i
$7$		0			0
$7$		0			0
$8$	−2.13577	−	1.55173i	−0.755110	−	0.548620i
$9$	2.56082	+	0.544320i	0.853608	+	0.181440i
$10$	0.0865012	+	0.149825i	0.0273541	+	0.0473787i
$11$	2.48448	−	2.19713i	0.749098	−	0.662459i
$11$	2.48448	−	2.19713i	0.749098	−	0.662459i
$12$	−0.431239	+	0.746928i	−0.124488	+	0.215619i
$13$	−2.01774	−	6.20997i	−0.559620	−	1.72233i	−0.683418	−	0.730027i	$-0.739507\pi$
$13$	−2.01774	−	6.20997i	−0.559620	−	1.72233i	0.123798	−	0.992307i	$-0.460493\pi$
$14$		0			0
$15$	0.111258	−	0.0808336i	0.0287267	−	0.0208711i
$16$	0.494158	+	0.548818i	0.123540	+	0.137205i
$17$	−4.23989	+	0.901217i	−1.02832	+	0.218577i	−0.691033	−	0.722823i	$-0.742844\pi$
$17$	−4.23989	+	0.901217i	−1.02832	+	0.218577i	−0.337292	+	0.941400i	$0.609511\pi$
$18$	1.85950	+	0.827904i	0.438289	+	0.195139i
$19$	−2.66299	+	1.18564i	−0.610932	+	0.272004i	−0.688791	−	0.724960i	$-0.741858\pi$
$19$	−2.66299	+	1.18564i	−0.610932	+	0.272004i	0.0778590	+	0.996964i	$0.475192\pi$
$20$	−0.0959574	−	0.295327i	−0.0214567	−	0.0660370i
$21$		0			0
$22$	2.24459	−	1.26929i	0.478549	−	0.270614i
$23$	1.94898	−	3.37573i	0.406390	−	0.703888i	−0.588092	−	0.808794i	$-0.700121\pi$
$23$	1.94898	−	3.37573i	0.406390	−	0.703888i	0.994482	+	0.104906i	$0.0334540\pi$
$24$	−1.09174	+	1.21250i	−0.222851	+	0.247502i
$25$	0.517467	−	4.92337i	0.103493	−	0.984673i
$26$	−0.530651	−	5.04881i	−0.104069	−	0.990153i
$27$	1.07295	−	3.30220i	0.206489	−	0.635508i
$28$		0			0
$29$	3.05322	−	2.21829i	0.566969	−	0.411927i	−0.267034	−	0.963687i	$-0.586044\pi$
$29$	3.05322	−	2.21829i	0.566969	−	0.411927i	0.834003	+	0.551760i	$0.186044\pi$
$30$	0.0976776	−	0.0434889i	0.0178334	−	0.00793994i
$31$	4.61003	−	5.11996i	0.827986	−	0.919571i	−0.169840	−	0.985472i	$-0.554325\pi$
$31$	4.61003	−	5.11996i	0.827986	−	0.919571i	0.997826	+	0.0659001i	$0.0209919\pi$
$32$	2.92705	+	5.06980i	0.517434	+	0.896223i
$33$	−1.18996	−	1.66902i	−0.207145	−	0.290539i
$34$	−3.37009			−0.577966
$35$		0			0
$36$	−2.95576	−	2.14748i	−0.492626	−	0.357914i
$37$	0.590953	+	5.62254i	0.0971521	+	0.924340i	0.929185	+	0.369614i	$0.120510\pi$
$37$	0.590953	+	5.62254i	0.0971521	+	0.924340i	−0.832033	+	0.554726i	$0.812823\pi$
$38$	−2.21685	+	0.471205i	−0.359620	+	0.0764396i
$39$	−3.94730	+	0.839024i	−0.632073	+	0.134351i
$40$	−0.0614035	−	0.584215i	−0.00970874	−	0.0923725i
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	0.669101	−	0.743171i	$-0.266679\pi$
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	−0.500035	+	0.866005i	$0.666679\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	−4.41449	+	1.39084i	−0.665510	+	0.209677i
$45$	0.291277	+	0.504506i	0.0434210	+	0.0752074i
$46$	2.02787	−	2.25218i	0.298993	−	0.332065i
$47$	−5.52287	+	2.45894i	−0.805594	+	0.358673i	−0.767863	−	0.640615i	$-0.778680\pi$
$47$	−5.52287	+	2.45894i	−0.805594	+	0.358673i	−0.0377310	+	0.999288i	$0.512013\pi$
$48$	0.369254	−	0.268279i	0.0532972	−	0.0387227i
$49$		0			0
$50$	1.18938	−	3.66055i	0.168204	−	0.517679i
$51$	0.280025	+	2.66426i	0.0392114	+	0.373071i
$52$	−0.952474	+	9.06218i	−0.132084	+	1.25670i
$53$	−1.14951	+	1.27666i	−0.157897	+	0.175363i	−0.816903	−	0.576775i	$-0.804311\pi$
$53$	−1.14951	+	1.27666i	−0.157897	+	0.175363i	0.659005	+	0.752138i	$0.270977\pi$
$54$	1.34977	−	2.33786i	0.183680	−	0.318143i
$55$	0.733239	+	0.0837016i	0.0988700	+	0.0112863i
$56$		0			0
$57$	0.556717	+	1.71340i	0.0737389	+	0.226945i
$58$	2.68054	−	1.19345i	0.351972	−	0.156708i
$59$	8.70887	+	3.87744i	1.13380	+	0.504799i	0.885849	−	0.463974i	$-0.153577\pi$
$59$	8.70887	+	3.87744i	1.13380	+	0.504799i	0.247949	+	0.968773i	$0.420244\pi$
$60$	−0.187721	+	0.0399013i	−0.0242347	+	0.00515124i
$61$	6.44334	+	7.15606i	0.824986	+	0.916239i	0.997634	−	0.0687442i	$-0.0218992\pi$
$61$	6.44334	+	7.15606i	0.824986	+	0.916239i	−0.172649	+	0.984983i	$0.555233\pi$
$62$	4.33353	−	3.14850i	0.550359	−	0.399859i
$63$		0			0
$64$	0.950059	+	2.92398i	0.118757	+	0.365498i
$65$	0.726463	−	1.25827i	0.0901067	−	0.156069i
$66$	−0.635163	−	1.46163i	−0.0781832	−	0.179915i
$67$	−0.635774	−	1.10119i	−0.0776722	−	0.134532i	0.824573	−	0.565756i	$-0.191415\pi$
$67$	−0.635774	−	1.10119i	−0.0776722	−	0.134532i	−0.902245	+	0.431223i	$0.858082\pi$
$68$	5.91685	+	1.25766i	0.717523	+	0.152514i
$69$	−1.94898	−	1.41602i	−0.234629	−	0.170468i
$70$		0			0
$71$	−2.87670	+	8.85357i	−0.341401	+	1.05072i	0.622081	+	0.782953i	$0.286287\pi$
$71$	−2.87670	+	8.85357i	−0.341401	+	1.05072i	−0.963482	+	0.267772i	$0.913713\pi$
$72$	−4.62470	−	5.13625i	−0.545026	−	0.605313i
$73$	−5.10591	−	2.27330i	−0.597601	−	0.266069i	0.0855643	−	0.996333i	$-0.472731\pi$
$73$	−5.10591	−	2.27330i	−0.597601	−	0.266069i	−0.683166	+	0.730263i	$0.739397\pi$
$74$	−0.459457	+	4.37144i	−0.0534108	+	0.508169i
$75$	−2.99271	−	0.636120i	−0.345568	−	0.0734528i
$76$	4.06794			0.466625
$77$		0			0
$78$	−3.13752			−0.355254
$79$	4.43056	+	0.941745i	0.498477	+	0.105955i	0.450288	−	0.892884i	$-0.351321\pi$
$79$	4.43056	+	0.941745i	0.498477	+	0.105955i	0.0481897	+	0.998838i	$0.484655\pi$
$80$	−0.0171771	+	0.163429i	−0.00192046	+	0.0182720i
$81$	5.21470	+	2.32174i	0.579412	+	0.257971i
$82$	0.696136	+	0.773138i	0.0768754	+	0.0853788i
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	0.555376	+	0.831599i	$0.312574\pi$
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	−0.938111	+	0.346336i	$0.887426\pi$
$84$		0			0
$85$	−0.780313	−	0.566931i	−0.0846368	−	0.0614922i
$86$	−3.58056	−	0.761072i	−0.386102	−	0.0820685i
$87$	−1.16623	−	2.01996i	−0.125033	−	0.216563i
$88$	−8.71563	+	0.837331i	−0.929090	+	0.0892598i
$89$	3.96078	−	6.86028i	0.419842	−	0.727188i	−0.576081	−	0.817393i	$-0.695419\pi$
$89$	3.96078	−	6.86028i	0.419842	−	0.727188i	0.995923	+	0.0902046i	$0.0287521\pi$
$90$	0.139962	+	0.430759i	0.0147533	+	0.0454059i
$91$		0			0
$92$	−4.40079	+	3.19736i	−0.458814	+	0.333348i
$93$	−2.84916	−	3.16431i	−0.295444	−	0.328123i
$94$	−4.59760	+	0.977249i	−0.474206	+	0.100796i
$95$	−0.592557	−	0.263824i	−0.0607951	−	0.0270677i
$96$	3.30524	−	1.47159i	0.337339	−	0.150193i
$97$	2.79781	+	8.61078i	0.284075	+	0.874292i	0.986674	+	0.162707i	$0.0520225\pi$
$97$	2.79781	+	8.61078i	0.284075	+	0.874292i	−0.702600	+	0.711585i	$0.747977\pi$
$98$		0			0
$99$	7.55825	−	4.27411i	0.759633	−	0.429564i
$100$	−3.45425	+	5.98293i	−0.345425	+	0.598293i
$101$	12.8541	−	14.2759i	1.27903	−	1.42051i	0.420876	−	0.907118i	$-0.361723\pi$
$101$	12.8541	−	14.2759i	1.27903	−	1.42051i	0.858155	−	0.513390i	$-0.171611\pi$
$102$	−0.217715	+	2.07142i	−0.0215570	+	0.205101i
$103$	1.69737	+	16.1494i	0.167246	+	1.59124i	0.680331	+	0.732905i	$0.261836\pi$
$103$	1.69737	+	16.1494i	0.167246	+	1.59124i	−0.513085	+	0.858338i	$0.671497\pi$
$104$	−5.32676	+	16.3941i	−0.522332	+	1.60757i
$105$		0			0
$106$	−1.08057	+	0.785077i	−0.104954	+	0.0762534i
$107$	−4.92708	+	2.19368i	−0.476319	+	0.212071i	−0.630831	−	0.775920i	$-0.717286\pi$
$107$	−4.92708	+	2.19368i	−0.476319	+	0.212071i	0.154513	+	0.987991i	$0.450619\pi$
$108$	−3.24222	+	3.60086i	−0.311983	+	0.346492i
$109$	−2.69951	−	4.67568i	−0.258566	−	0.447849i	0.707292	−	0.706921i	$-0.249917\pi$
$109$	−2.69951	−	4.67568i	−0.258566	−	0.447849i	−0.965858	+	0.259072i	$0.916583\pi$
$110$	0.544094	+	0.182181i	0.0518773	+	0.0173703i
$111$	3.49406			0.331642
$112$		0			0
$113$	13.3457	+	9.69624i	1.25546	+	0.912145i	0.998526	−	0.0542834i	$-0.0172875\pi$
$113$	13.3457	+	9.69624i	1.25546	+	0.912145i	0.256935	+	0.966429i	$0.417287\pi$
$114$	0.146412	+	1.39302i	0.0137128	+	0.130468i
$115$	0.848403	−	0.180334i	0.0791140	−	0.0168162i
$116$	−5.15158	+	1.09500i	−0.478312	+	0.101668i
$117$	−1.78687	−	17.0009i	−0.165196	−	1.57174i
$118$	5.99626	+	4.35654i	0.552001	+	0.401052i
$119$		0			0
$120$	−0.363054			−0.0331421
$121$	1.34525	−	10.9174i	0.122296	−	0.992494i
$122$	3.74336	+	6.48370i	0.338908	+	0.587006i
$123$	0.553369	−	0.614579i	0.0498956	−	0.0554147i
$124$	−8.78332	+	3.91058i	−0.788765	+	0.351181i
$125$	1.79128	−	1.30144i	0.160217	−	0.116404i
$126$		0			0
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	−0.919931	−	0.392079i	$-0.871756\pi$
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	0.974699	+	0.223523i	$0.0717559\pi$
$128$	−0.973982	−	9.26682i	−0.0860886	−	0.819079i
$129$	−0.304160	+	2.89389i	−0.0267798	+	0.254793i
$130$	0.755868	−	0.839477i	0.0662940	−	0.0736270i
$131$	0.685047	−	1.18654i	0.0598528	−	0.103668i	−0.834546	−	0.550938i	$-0.814270\pi$
$131$	0.685047	−	1.18654i	0.0598528	−	0.103668i	0.894399	+	0.447270i	$0.147604\pi$
$132$	0.569693	+	2.80321i	0.0495854	+	0.243988i
$133$		0			0
$134$	−0.305497	−	0.940223i	−0.0263909	−	0.0812229i
$135$	0.705810	−	0.314247i	0.0607464	−	0.0270461i
$136$	10.4539	+	4.65437i	0.896414	+	0.399109i
$137$	−2.44463	+	0.519621i	−0.208858	+	0.0443942i	−0.311153	−	0.950360i	$-0.600715\pi$
$137$	−2.44463	+	0.519621i	−0.208858	+	0.0443942i	0.102294	+	0.994754i	$0.467382\pi$
$138$	−1.25329	−	1.39192i	−0.106687	−	0.118488i
$139$	−3.85302	+	2.79938i	−0.326809	+	0.237441i	−0.739075	−	0.673623i	$-0.764737\pi$
$139$	−3.85302	+	2.79938i	−0.326809	+	0.237441i	0.412266	+	0.911063i	$0.364737\pi$
$140$		0			0
$141$	1.15459	+	3.55348i	0.0972344	+	0.299257i
$142$	−3.61887	+	6.26807i	−0.303689	+	0.526005i
$143$	−18.6571	−	10.9953i	−1.56019	−	0.919472i
$144$	0.966719	+	1.67441i	0.0805599	+	0.139534i
$145$	0.821421	+	0.174598i	0.0682153	+	0.0144996i
$146$	−3.51554	−	2.55419i	−0.290948	−	0.211386i
$147$		0			0
$148$	2.43801	−	7.50344i	0.200404	−	0.616779i
$149$	−4.83772	−	5.37283i	−0.396321	−	0.440159i	0.511649	−	0.859195i	$-0.329035\pi$
$149$	−4.83772	−	5.37283i	−0.396321	−	0.440159i	−0.907970	+	0.419036i	$0.862368\pi$
$150$	−2.17311	−	0.967532i	−0.177434	−	0.0789986i
$151$	−0.850829	+	8.09509i	−0.0692394	+	0.658769i	0.903772	+	0.428014i	$0.140786\pi$
$151$	−0.850829	+	8.09509i	−0.0692394	+	0.658769i	−0.973012	+	0.230756i	$0.925880\pi$
$152$	7.52734	+	1.59999i	0.610548	+	0.129776i
$153$	−11.3482			−0.917445
$154$		0			0
$155$	1.53304			0.123137
$156$	5.50852	+	1.17087i	0.441035	+	0.0937448i
$157$	2.10640	−	20.0410i	0.168109	−	1.59945i	−0.507144	−	0.861861i	$-0.669299\pi$
$157$	2.10640	−	20.0410i	0.168109	−	1.59945i	0.675253	−	0.737587i	$-0.264035\pi$
$158$	3.21719	+	1.43238i	0.255946	+	0.113954i
$159$	0.710436	+	0.789019i	0.0563412	+	0.0625733i
$160$	−0.402535	+	1.23887i	−0.0318232	+	0.0979416i
$161$		0			0
$162$	3.59045	+	2.60861i	0.282092	+	0.204952i
$163$	−7.27203	−	1.54572i	−0.569590	−	0.121070i	−0.0858908	−	0.996305i	$-0.527374\pi$
$163$	−7.27203	−	1.54572i	−0.569590	−	0.121070i	−0.483699	+	0.875235i	$0.660707\pi$
$164$	−0.933679	−	1.61718i	−0.0729080	−	0.126280i
$165$	0.0988159	−	0.445277i	0.00769280	−	0.0346648i
$166$	−4.38647	+	7.59760i	−0.340456	+	0.589688i
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	0.974006	−	0.226520i	$-0.0727350\pi$
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	−0.921133	+	0.389248i	$0.872735\pi$
$168$		0			0
$169$	−23.9752	+	17.4190i	−1.84424	+	1.33992i
$170$	−0.501780	−	0.557284i	−0.0384848	−	0.0427417i
$171$	−7.46482	+	1.58670i	−0.570849	+	0.121338i
$172$	6.00234	+	2.67242i	0.457675	+	0.203770i
$173$	9.46634	−	4.21469i	0.719712	−	0.320437i	−0.0139950	−	0.999902i	$-0.504455\pi$
$173$	9.46634	−	4.21469i	0.719712	−	0.320437i	0.733708	+	0.679465i	$0.237788\pi$
$174$	−0.560385	−	1.72469i	−0.0424827	−	0.130748i
$175$		0			0
$176$	2.43355	+	0.277797i	0.183436	+	0.0209398i
$177$	2.94587	−	5.10240i	0.221425	−	0.383520i
$178$	4.12110	−	4.57695i	0.308890	−	0.343057i
$179$	2.44695	−	23.2812i	0.182894	−	1.74012i	−0.390292	−	0.920691i	$-0.627626\pi$
$179$	2.44695	−	23.2812i	0.182894	−	1.74012i	0.573186	−	0.819426i	$-0.305707\pi$
$180$	−0.0849779	−	0.808511i	−0.00633388	−	0.0602628i
$181$	4.23851	−	13.0448i	0.315046	−	0.969611i	−0.660690	−	0.750659i	$-0.729736\pi$
$181$	4.23851	−	13.0448i	0.315046	−	0.969611i	0.975736	−	0.218952i	$-0.0702639\pi$
$182$		0			0
$183$	4.81471	−	3.49809i	0.355914	−	0.258587i
$184$	−9.40080	+	4.18551i	−0.693036	+	0.308560i
$185$	−0.841764	+	0.934873i	−0.0618877	+	0.0687332i
$186$	−1.65526	−	2.86700i	−0.121370	−	0.210219i
$187$	−8.55382	+	11.5546i	−0.625518	+	0.844959i
$188$	8.43666			0.615306
$189$		0			0
$190$	−0.407990	−	0.296422i	−0.0295987	−	0.0215047i
$191$	1.25695	+	11.9591i	0.0909496	+	0.865328i	0.940950	+	0.338546i	$0.109935\pi$
$191$	1.25695	+	11.9591i	0.0909496	+	0.865328i	−0.850000	+	0.526782i	$0.823398\pi$
$192$	1.85860	−	0.395057i	0.134133	−	0.0285108i
$193$	−15.5368	+	3.30245i	−1.11836	+	0.237716i	−0.729770	−	0.683693i	$-0.760373\pi$
$193$	−15.5368	+	3.30245i	−1.11836	+	0.237716i	−0.388595	+	0.921409i	$0.627039\pi$
$194$	0.735804	+	7.00071i	0.0528277	+	0.502622i
$195$	−0.726463	−	0.527806i	−0.0520231	−	0.0377970i
$196$		0			0
$197$	12.3035			0.876590			0.438295	−	0.898831i	$-0.355582\pi$
$197$	12.3035			0.876590			0.438295	+	0.898831i	$0.355582\pi$
$198$	6.43891	−	2.02866i	0.457593	−	0.144171i
$199$	7.63075	+	13.2168i	0.540929	+	0.936917i	0.998851	+	0.0479244i	$0.0152607\pi$
$199$	7.63075	+	13.2168i	0.540929	+	0.936917i	−0.457922	+	0.888993i	$0.651406\pi$
$200$	−8.74493	+	9.71223i	−0.618360	+	0.686758i
$201$	−0.717919	+	0.319638i	−0.0506381	+	0.0225455i
$202$	12.0832	−	8.77892i	0.850168	−	0.617683i
$203$		0			0
$204$	1.15526	−	3.55553i	0.0808845	−	0.248937i
$205$	0.0311234	+	0.296119i	0.00217375	+	0.0206819i
$206$	−1.31967	+	12.5559i	−0.0919461	+	0.874809i
$207$	6.82847	−	7.58378i	0.474611	−	0.527109i
$208$	2.41106	−	4.17608i	0.167177	−	0.289559i
$209$	−4.01114	+	8.79663i	−0.277456	+	0.608476i
$210$		0			0
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	0.999999	−	0.00159295i	$-0.000507051\pi$
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	−0.809952	+	0.586496i	$0.800507\pi$
$212$	2.19012	−	0.975103i	0.150418	−	0.0669704i
$213$	5.25599	+	2.34012i	0.360134	+	0.160342i
$214$	−4.10162	+	0.871826i	−0.280381	+	0.0595968i
$215$	−0.701014	−	0.778555i	−0.0478088	−	0.0530970i
$216$	−7.41570	+	5.38782i	−0.504574	+	0.366595i
$217$		0			0
$218$	−1.29714	−	3.99220i	−0.0878537	−	0.270386i
$219$	−1.72713	+	2.99148i	−0.116709	+	0.202145i
$220$	−0.887275	−	0.522901i	−0.0598200	−	0.0352540i
$221$	14.1515	+	24.5112i	0.951935	+	1.64880i
$222$	2.65722	+	0.564809i	0.178341	+	0.0379075i
$223$	0.578645	+	0.420410i	0.0387489	+	0.0281527i	0.606991	−	0.794709i	$-0.292376\pi$
$223$	0.578645	+	0.420410i	0.0387489	+	0.0281527i	−0.568242	+	0.822861i	$0.692376\pi$
$224$		0			0
$225$	4.00503	−	12.3262i	0.267002	−	0.821747i
$226$	8.58197	+	9.53124i	0.570864	+	0.634009i
$227$	4.86154	+	2.16450i	0.322672	+	0.143663i	0.561679	−	0.827355i	$-0.310155\pi$
$227$	4.86154	+	2.16450i	0.322672	+	0.143663i	−0.239008	+	0.971018i	$0.576822\pi$
$228$	0.262798	−	2.50036i	0.0174042	−	0.165590i
$229$	−6.46392	−	1.37395i	−0.427148	−	0.0907930i	−0.0106786	−	0.999943i	$-0.503399\pi$
$229$	−6.46392	−	1.37395i	−0.427148	−	0.0907930i	−0.416469	+	0.909150i	$0.636733\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	9.34828	+	1.98704i	0.612426	+	0.130175i	0.503674	−	0.863894i	$-0.331981\pi$
$233$	9.34828	+	1.98704i	0.612426	+	0.130175i	0.108752	+	0.994069i	$0.465315\pi$
$234$	1.38926	−	13.2179i	0.0908189	−	0.864084i
$235$	−1.22893	−	0.547153i	−0.0801663	−	0.0356923i
$236$	−8.90180	−	9.88645i	−0.579458	−	0.643553i
$237$	0.865066	−	2.66240i	0.0561921	−	0.172941i
$238$		0			0
$239$	−21.7194	−	15.7801i	−1.40491	−	1.02073i	−0.994038	−	0.109034i	$-0.965224\pi$
$239$	−21.7194	−	15.7801i	−1.40491	−	1.02073i	−0.410872	−	0.911693i	$-0.634776\pi$
$240$	0.0993419	+	0.0211158i	0.00641249	+	0.00136302i
$241$	9.43316	+	16.3387i	0.607643	+	1.05247i	0.991628	+	0.129129i	$0.0412183\pi$
$241$	9.43316	+	16.3387i	0.607643	+	1.05247i	−0.383985	+	0.923340i	$0.625448\pi$
$242$	2.78784	−	8.08519i	0.179209	−	0.519736i
$243$	6.97214	−	12.0761i	0.447263	−	0.774682i
$244$	−4.15258	−	12.7803i	−0.265842	−	0.818177i
$245$		0			0
$246$	0.520180	−	0.377933i	0.0331654	−	0.0240961i
$247$	12.7360	+	14.1448i	0.810373	+	0.900010i
$248$	−17.7908	+	3.78155i	−1.12972	+	0.240128i
$249$	6.37084	+	2.83648i	0.403735	+	0.179755i
$250$	1.57263	−	0.700180i	0.0994619	−	0.0442833i
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	−0.643146	−	0.765744i	$-0.722371\pi$
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	0.0702229	−	0.997531i	$-0.477629\pi$
$252$		0			0
$253$	−2.57472	−	12.6691i	−0.161871	−	0.796498i
$254$	0.776427	−	1.34481i	0.0487174	−	0.0843810i
$255$	−0.398873	+	0.442993i	−0.0249784	+	0.0277413i
$256$	1.39999	−	13.3200i	0.0874995	−	0.832502i
$257$	−1.76824	−	16.8237i	−0.110300	−	1.04943i	−0.899985	−	0.435922i	$-0.856422\pi$
$257$	−1.76824	−	16.8237i	−0.110300	−	1.04943i	0.789685	−	0.613513i	$-0.210244\pi$
$258$	−0.699104	+	2.15162i	−0.0435243	+	0.133954i
$259$		0			0
$260$	−1.64035	+	1.19178i	−0.101730	+	0.0739114i
$261$	9.02622	−	4.01873i	0.558709	−	0.248753i
$262$	0.712776	−	0.791617i	0.0440354	−	0.0489063i
$263$	4.09017	+	7.08438i	0.252211	+	0.436842i	0.964134	−	0.265415i	$-0.0855091\pi$
$263$	4.09017	+	7.08438i	0.252211	+	0.436842i	−0.711923	+	0.702257i	$0.752176\pi$
$264$	−0.0483844	+	5.41114i	−0.00297785	+	0.333033i
$265$	−0.382263			−0.0234822
$266$		0			0
$267$	−3.96078	−	2.87768i	−0.242396	−	0.176111i
$268$	0.185482	+	1.76475i	0.0113301	+	0.107799i
$269$	−6.11065	+	1.29886i	−0.372573	+	0.0791928i	−0.390393	−	0.920648i	$-0.627661\pi$
$269$	−6.11065	+	1.29886i	−0.372573	+	0.0791928i	0.0178200	+	0.999841i	$0.494327\pi$
$270$	0.587562	−	0.124890i	0.0357579	−	0.00760057i
$271$	0.822312	+	7.82378i	0.0499519	+	0.475261i	0.990691	+	0.136130i	$0.0434664\pi$
$271$	0.822312	+	7.82378i	0.0499519	+	0.475261i	−0.940739	+	0.339131i	$0.889867\pi$
$272$	−2.58978	−	1.88159i	−0.157029	−	0.114088i
$273$		0			0
$274$	−1.94312			−0.117388
$275$	−9.53164	−	13.3689i	−0.574779	−	0.806177i
$276$	1.68095	+	2.91149i	0.101181	+	0.175251i
$277$	8.06145	−	8.95315i	0.484366	−	0.537943i	−0.450579	−	0.892737i	$-0.648782\pi$
$277$	8.06145	−	8.95315i	0.484366	−	0.537943i	0.934944	+	0.354794i	$0.115449\pi$
$278$	−3.38272	+	1.50608i	−0.202882	+	0.0903288i
$279$	14.5924	−	10.6020i	0.873622	−	0.634724i
$280$		0			0
$281$	6.53723	−	20.1195i	0.389978	−	1.20023i	−0.542826	−	0.839846i	$-0.682646\pi$
$281$	6.53723	−	20.1195i	0.389978	−	1.20023i	0.932804	−	0.360384i	$-0.117354\pi$
$282$	0.303650	+	2.88904i	0.0180821	+	0.172040i
$283$	−2.61356	+	24.8664i	−0.155360	+	1.47815i	0.587782	+	0.809020i	$0.300001\pi$
$283$	−2.61356	+	24.8664i	−0.155360	+	1.47815i	−0.743142	+	0.669134i	$0.766665\pi$
$284$	8.69277	−	9.65430i	0.515821	−	0.572877i
$285$	−0.200439	+	0.347171i	−0.0118730	+	0.0205646i
$286$	−12.4113	−	11.3777i	−0.733894	−	0.672780i
$287$		0			0
$288$	4.73607	+	14.5761i	0.279075	+	0.858906i
$289$	1.63422	−	0.727601i	0.0961305	−	0.0428001i
$290$	0.596462	+	0.265562i	0.0350255	+	0.0155943i
$291$	5.47335	−	1.16340i	0.320853	−	0.0681995i
$292$	5.21902	+	5.79631i	0.305420	+	0.339204i
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	−0.598488	−	0.801132i	$-0.704231\pi$
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	0.576979	+	0.816759i	$0.304231\pi$
$294$		0			0
$295$	0.655503	+	2.01743i	0.0381648	+	0.117459i
$296$	7.46253	−	12.9255i	0.433751	−	0.751278i
$297$	−4.58964	−	10.5616i	−0.266318	−	0.612849i
$298$	−2.81055	−	4.86801i	−0.162811	−	0.281996i
$299$	−24.8957	−	5.29175i	−1.43976	−	0.306030i
$300$	3.45425	+	2.50966i	0.199431	+	0.144895i
$301$		0			0
$302$	−1.95561	+	6.01874i	−0.112533	+	0.346339i
$303$	−7.94428	−	8.82301i	−0.456387	−	0.506869i
$304$	−1.96664	−	0.875604i	−0.112794	−	0.0502193i
$305$	−0.223973	+	2.13096i	−0.0128247	+	0.122018i
$306$	−8.63022	−	1.83441i	−0.493357	−	0.104866i
$307$	8.03578			0.458626			0.229313	−	0.973353i	$-0.426352\pi$
$307$	8.03578			0.458626			0.229313	+	0.973353i	$0.426352\pi$
$308$		0			0
$309$	10.0358			0.570918
$310$	1.16587	+	0.247813i	0.0662169	+	0.0140748i
$311$	0.0143167	−	0.136214i	0.000811827	−	0.00772401i	−0.994108	−	0.108390i	$-0.965431\pi$
$311$	0.0143167	−	0.136214i	0.000811827	−	0.00772401i	0.994920	+	0.100666i	$0.0320972\pi$
$312$	9.73247	+	4.33317i	0.550993	+	0.245318i
$313$	10.2310	+	11.3626i	0.578288	+	0.642254i	0.959324	−	0.282306i	$-0.0910994\pi$
$313$	10.2310	+	11.3626i	0.578288	+	0.642254i	−0.381036	+	0.924560i	$0.624433\pi$
$314$	4.84150	−	14.9006i	0.273221	−	0.840889i
$315$		0			0
$316$	−5.11385	−	3.71543i	−0.287676	−	0.209009i
$317$	32.2716	+	6.85953i	1.81255	+	0.385270i	0.984500	−	0.175383i	$-0.0561163\pi$
$317$	32.2716	+	6.85953i	1.81255	+	0.385270i	0.828051	+	0.560653i	$0.189450\pi$
$318$	0.412739	+	0.714885i	0.0231453	+	0.0400888i
$319$	2.71178	−	12.2196i	0.151830	−	0.684167i
$320$	−0.342058	+	0.592461i	−0.0191216	+	0.0331196i
$321$	1.03004	+	3.17014i	0.0574912	+	0.176940i
$322$		0			0
$323$	10.2223	−	7.42692i	0.568783	−	0.413245i
$324$	−5.33023	−	5.91982i	−0.296124	−	0.328879i
$325$	−31.6181	+	6.72063i	−1.75385	+	0.372793i
$326$	−5.28048	−	2.35102i	−0.292459	−	0.130211i
$327$	−3.04830	+	1.35719i	−0.168571	+	0.0750527i
$328$	−1.09162	−	3.35966i	−0.0602747	−	0.185506i
$329$		0			0
$330$	0.147127	−	0.322657i	0.00809908	−	0.0177617i
$331$	−14.7667	+	25.5767i	−0.811653	+	1.40582i	0.100054	+	0.994982i	$0.468099\pi$
$331$	−14.7667	+	25.5767i	−0.811653	+	1.40582i	−0.911707	+	0.410842i	$0.865235\pi$
$332$	10.5366	−	11.7021i	0.578271	−	0.642235i
$333$	−1.54714	+	14.7200i	−0.0847825	+	0.806652i
$334$	0.179696	+	1.70970i	0.00983255	+	0.0935505i
$335$	0.0874331	−	0.269091i	0.00477698	−	0.0147020i
$336$		0			0
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	−0.704895	−	0.709311i	$-0.749006\pi$
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	0.456770	+	0.889585i	$0.349006\pi$
$338$	−21.0487	+	9.37150i	−1.14490	+	0.509742i
$339$	6.82194	−	7.57653i	0.370517	−	0.411501i
$340$	0.673002	+	1.16567i	0.0364987	+	0.0632176i
$341$	0.204309	−	22.8492i	0.0110640	−	1.23736i
$342$	−5.93344			−0.320844
$343$		0			0
$344$	10.0557	+	7.30586i	0.542165	+	0.393906i
$345$	−0.0560331	−	0.533120i	−0.00301672	−	0.0287022i
$346$	7.88039	−	1.67503i	0.423653	−	0.0900501i
$347$	−8.53983	+	1.81520i	−0.458442	+	0.0974449i	−0.431343	−	0.902188i	$-0.641960\pi$
$347$	−8.53983	+	1.81520i	−0.458442	+	0.0974449i	−0.0270988	+	0.999633i	$0.508627\pi$
$348$	0.340238	+	3.23715i	0.0182387	+	0.173529i
$349$	14.9401	+	10.8546i	0.799724	+	0.581034i	0.910833	−	0.412774i	$-0.135440\pi$
$349$	14.9401	+	10.8546i	0.799724	+	0.581034i	−0.111109	+	0.993808i	$0.535440\pi$
$350$		0			0
$351$	−22.6715			−1.21011
$352$	18.4112	+	6.16470i	0.981320	+	0.328579i
$353$	−11.7428	−	20.3392i	−0.625009	−	1.08255i	−0.988539	−	0.150964i	$-0.951762\pi$
$353$	−11.7428	−	20.3392i	−0.625009	−	1.08255i	0.363531	−	0.931582i	$-0.381571\pi$
$354$	3.06511	−	3.40415i	0.162909	−	0.180929i
$355$	−1.89236	+	0.842531i	−0.100436	+	0.0447169i
$356$	−8.94343	+	6.49778i	−0.474001	+	0.344382i
$357$		0			0
$358$	5.62425	−	17.3097i	0.297251	−	0.914844i
$359$	−1.55551	−	14.7997i	−0.0820967	−	0.781098i	−0.955677	−	0.294417i	$-0.904874\pi$
$359$	−1.55551	−	14.7997i	−0.0820967	−	0.781098i	0.873580	−	0.486680i	$-0.161792\pi$
$360$	0.160756	−	1.52949i	0.00847261	−	0.0806115i
$361$	−7.02770	+	7.80505i	−0.369879	+	0.410792i
$362$	5.33203	−	9.23534i	0.280245	−	0.485399i
$363$	−6.62347	−	1.53215i	−0.347642	−	0.0804168i
$364$		0			0
$365$	−0.384314	−	1.18280i	−0.0201159	−	0.0619104i
$366$	4.22702	−	1.88199i	0.220950	−	0.0983733i
$367$	31.2669	+	13.9209i	1.63212	+	0.726667i	0.998881	−	0.0472889i	$-0.0150581\pi$
$367$	31.2669	+	13.9209i	1.63212	+	0.726667i	0.633240	+	0.773956i	$0.281725\pi$
$368$	2.81577	−	0.598509i	0.146782	−	0.0311995i
$369$	2.34411	+	2.60340i	0.122030	+	0.135527i
$370$	−0.791277	+	0.574896i	−0.0411365	+	0.0298874i
$371$		0			0
$372$	1.83621	+	5.65128i	0.0952032	+	0.293005i
$373$	−1.50870	+	2.61314i	−0.0781173	+	0.135303i	−0.902438	−	0.430820i	$-0.858224\pi$
$373$	−1.50870	+	2.61314i	−0.0781173	+	0.135303i	0.824320	+	0.566124i	$0.191558\pi$
$374$	−8.37292	+	7.40453i	−0.432953	+	0.382879i
$375$	−0.684207	−	1.18508i	−0.0353323	−	0.0611973i
$376$	15.6112	+	3.31827i	0.805087	+	0.171127i
$377$	−19.9361	−	14.4845i	−1.02676	−	0.745987i
$378$		0			0
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	−0.987824	−	0.155576i	$-0.950277\pi$
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	0.890612	+	0.454764i	$0.150277\pi$
$380$	0.605685	+	0.672681i	0.0310710	+	0.0345078i
$381$	−1.12767	−	0.502071i	−0.0577723	−	0.0257219i
$382$	−0.977258	+	9.29799i	−0.0500009	+	0.475726i
$383$	4.29503	+	0.912937i	0.219466	+	0.0466489i	0.316332	−	0.948649i	$-0.397549\pi$
$383$	4.29503	+	0.912937i	0.219466	+	0.0466489i	−0.0968663	+	0.995297i	$0.530882\pi$
$384$	−5.75876			−0.293875
$385$		0			0
$386$	−12.3495			−0.628573
$387$	−12.0569	−	2.56277i	−0.612886	−	0.130273i
$388$	1.32071	−	12.5657i	0.0670487	−	0.637926i
$389$	9.58858	+	4.26911i	0.486160	+	0.216452i	0.635154	−	0.772386i	$-0.280937\pi$
$389$	9.58858	+	4.26911i	0.486160	+	0.216452i	−0.148994	+	0.988838i	$0.547603\pi$
$390$	−0.467152	−	0.518825i	−0.0236552	−	0.0262717i
$391$	−5.22119	+	16.0692i	−0.264047	+	0.812654i
$392$		0			0
$393$	−0.685047	−	0.497716i	−0.0345560	−	0.0251064i
$394$	9.35677	+	1.98884i	0.471387	+	0.100196i
$395$	0.503947	+	0.872863i	0.0253563	+	0.0439185i
$396$	−12.0618	+	1.15881i	−0.606128	+	0.0582321i
$397$	5.69441	−	9.86301i	0.285794	−	0.495010i	−0.687007	−	0.726651i	$-0.741076\pi$
$397$	5.69441	−	9.86301i	0.285794	−	0.495010i	0.972801	+	0.231640i	$0.0744093\pi$
$398$	3.66666	+	11.2848i	0.183793	+	0.565657i
$399$		0			0
$400$	2.95774	−	2.14893i	0.147887	−	0.107446i
$401$	−3.16161	−	3.51133i	−0.157883	−	0.175347i	0.659013	−	0.752131i	$-0.270974\pi$
$401$	−3.16161	−	3.51133i	−0.157883	−	0.175347i	−0.816897	+	0.576784i	$0.804307\pi$
$402$	−0.597642	+	0.127033i	−0.0298077	+	0.00633582i
$403$	−41.0966	−	18.2974i	−2.04717	−	0.911458i
$404$	−24.4904	+	10.9038i	−1.21845	+	0.542487i
$405$	0.392503	+	1.20800i	0.0195036	+	0.0600260i
$406$		0			0
$407$	13.8217	+	12.6707i	0.685114	+	0.628062i
$408$	3.53615	−	6.12479i	0.175065	−	0.303222i
$409$	−1.64970	+	1.83218i	−0.0815725	+	0.0905954i	−0.782549	−	0.622589i	$-0.786081\pi$
$409$	−1.64970	+	1.83218i	−0.0815725	+	0.0905954i	0.700977	+	0.713184i	$0.252748\pi$
$410$	−0.0241980	+	0.230228i	−0.00119505	+	0.0113702i
$411$	0.161456	+	1.53615i	0.00796405	+	0.0757729i
$412$	7.00259	−	21.5518i	0.344993	−	1.06178i
$413$		0			0
$414$	6.41892	−	4.66362i	0.315472	−	0.229204i
$415$	−2.29374	+	1.02124i	−0.112595	+	0.0501307i
$416$	25.5773	−	28.4064i	1.25403	−	1.39274i
$417$	1.47172	+	2.54910i	0.0720706	+	0.124830i
$418$	−4.47240	+	6.04139i	−0.218752	+	0.295494i
$419$	14.3399			0.700548			0.350274	−	0.936647i	$-0.386088\pi$
$419$	14.3399			0.700548			0.350274	+	0.936647i	$0.386088\pi$
$420$		0			0
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	0.874267	−	0.485446i	$-0.161343\pi$
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	−0.191523	+	0.981488i	$0.561343\pi$
$422$	0.726014	+	6.90756i	0.0353418	+	0.336255i
$423$	−15.4816	+	3.29071i	−0.752739	+	0.160000i
$424$	4.43613	−	0.942927i	0.215437	−	0.0457926i
$425$	2.24302	+	21.3409i	0.108802	+	1.03519i
$426$	3.61887	+	2.62927i	0.175335	+	0.127388i
$427$		0			0
$428$	7.52653			0.363808
$429$	−7.96352	+	10.7573i	−0.384482	+	0.519365i
$430$	−0.407266	−	0.705405i	−0.0196401	−	0.0340176i
$431$	18.6636	−	20.7280i	0.898994	−	0.998434i	−0.101000	−	0.994886i	$-0.532204\pi$
$431$	18.6636	−	20.7280i	0.898994	−	0.998434i	0.999994	−	0.00354712i	$-0.00112909\pi$
$432$	2.34251	−	1.04295i	0.112704	−	0.0501791i
$433$	−23.9040	+	17.3673i	−1.14875	+	0.834619i	−0.988315	−	0.152426i	$-0.951291\pi$
$433$	−23.9040	+	17.3673i	−1.14875	+	0.834619i	−0.160440	+	0.987046i	$0.551291\pi$
$434$		0			0
$435$	0.160382	−	0.493605i	0.00768973	−	0.0236666i
$436$	0.787562	+	7.49315i	0.0377174	+	0.358857i
$437$	−1.18771	+	11.3003i	−0.0568160	+	0.540568i
$438$	−1.79704	+	1.99582i	−0.0858659	+	0.0953637i
$439$	−16.8328	+	29.1552i	−0.803384	+	1.39150i	0.113992	+	0.993482i	$0.463636\pi$
$439$	−16.8328	+	29.1552i	−0.803384	+	1.39150i	−0.917376	+	0.398021i	$0.869697\pi$
$440$	−1.43615	−	1.31656i	−0.0684658	−	0.0627644i
$441$		0			0
$442$	6.79997	+	20.9282i	0.323442	+	0.995451i
$443$	9.43393	−	4.20025i	0.448219	−	0.199560i	−0.170198	−	0.985410i	$-0.554441\pi$
$443$	9.43393	−	4.20025i	0.448219	−	0.199560i	0.618417	+	0.785850i	$0.287774\pi$
$444$	−4.45447	−	1.98326i	−0.211400	−	0.0941214i
$445$	1.72415	−	0.366480i	0.0817328	−	0.0173728i
$446$	0.372098	+	0.413256i	0.0176193	+	0.0195682i
$447$	−3.61493	+	2.62640i	−0.170980	+	0.124224i
$448$		0			0
$449$	−0.852224	−	2.62287i	−0.0402189	−	0.123781i	0.928931	−	0.370253i	$-0.120729\pi$
$449$	−0.852224	−	2.62287i	−0.0402189	−	0.123781i	−0.969150	+	0.246471i	$0.920729\pi$
$450$	5.03831	−	8.72661i	0.237508	−	0.411376i
$451$	4.41767	−	0.424416i	0.208020	−	0.0199850i
$452$	−11.5104	−	19.9366i	−0.541403	−	0.937738i
$453$	4.92067	+	1.04592i	0.231193	+	0.0491416i
$454$	3.34729	+	2.43195i	0.157096	+	0.114137i
$455$		0			0
$456$	1.46971	−	4.52331i	0.0688255	−	0.211823i
$457$	−26.9864	−	29.9714i	−1.26237	−	1.40200i	−0.877885	−	0.478872i	$-0.841046\pi$
$457$	−26.9864	−	29.9714i	−1.26237	−	1.40200i	−0.384484	−	0.923132i	$-0.625621\pi$
$458$	−4.69367	−	2.08976i	−0.219321	−	0.0976480i
$459$	−1.57319	+	14.9679i	−0.0734303	+	0.698643i
$460$	−1.18396	−	0.251659i	−0.0552025	−	0.0117337i
$461$	34.2251			1.59402			0.797011	−	0.603965i	$-0.206413\pi$
$461$	34.2251			1.59402			0.797011	+	0.603965i	$0.206413\pi$
$462$		0			0
$463$	0.707349			0.0328733			0.0164367	−	0.999865i	$-0.494768\pi$
$463$	0.707349			0.0328733			0.0164367	+	0.999865i	$0.494768\pi$
$464$	2.72621	+	0.579475i	0.126561	+	0.0269014i
$465$	0.0990377	−	0.942281i	0.00459276	−	0.0436972i
$466$	6.78812	+	3.02226i	0.314453	+	0.140004i
$467$	19.1321	+	21.2483i	0.885326	+	0.983255i	0.999948	−	0.0101545i	$-0.00323233\pi$
$467$	19.1321	+	21.2483i	0.885326	+	0.983255i	−0.114622	+	0.993409i	$0.536566\pi$
$468$	−7.37184	+	22.6882i	−0.340764	+	1.04876i
$469$		0			0
$470$	−0.846145	−	0.614760i	−0.0390298	−	0.0283568i
$471$	−12.1821	−	2.58939i	−0.561322	−	0.119313i
$472$	−12.5834	−	21.7951i	−0.579199	−	1.00320i
$473$	−11.6974	+	10.3445i	−0.537848	+	0.475642i
$474$	1.08825	−	1.88490i	0.0499850	−	0.0865765i
$475$	4.45933	+	13.7244i	0.204608	+	0.629719i
$476$		0			0
$477$	−3.63860	+	2.64360i	−0.166600	+	0.121042i
$478$	−13.9666	−	15.5115i	−0.638820	−	0.709481i
$479$	−4.98578	+	1.05976i	−0.227806	+	0.0484217i	−0.320400	−	0.947282i	$-0.603817\pi$
$479$	−4.98578	+	1.05976i	−0.227806	+	0.0484217i	0.0925942	+	0.995704i	$0.470484\pi$
$480$	0.735468	+	0.327451i	0.0335694	+	0.0149460i
$481$	33.7234	−	15.0146i	1.53766	−	0.684608i
$482$	4.53274	+	13.9503i	0.206461	+	0.635421i
$483$		0			0
$484$	−7.91185	+	13.1547i	−0.359629	+	0.597942i
$485$	−1.00732	+	1.74473i	−0.0457400	+	0.0792240i
$486$	7.25435	−	8.05677i	0.329064	−	0.365462i
$487$	−3.05101	+	29.0284i	−0.138254	+	1.31540i	0.676864	+	0.736108i	$0.263338\pi$
$487$	−3.05101	+	29.0284i	−0.138254	+	1.31540i	−0.815119	+	0.579294i	$0.803328\pi$
$488$	−2.65725	−	25.2821i	−0.120288	−	1.14446i
$489$	−1.41986	+	4.36989i	−0.0642084	+	0.197613i
$490$		0			0
$491$	−24.3870	+	17.7182i	−1.10057	+	0.799610i	−0.981153	−	0.193235i	$-0.938102\pi$
$491$	−24.3870	+	17.7182i	−1.10057	+	0.799610i	−0.119416	+	0.992844i	$0.538102\pi$
$492$	−1.05431	+	0.469411i	−0.0475321	+	0.0211627i
$493$	−10.9462	+	12.1569i	−0.492990	+	0.547521i
$494$	7.39919	+	12.8158i	0.332905	+	0.576609i
$495$	1.83214	+	0.613462i	0.0823484	+	0.0275731i
$496$	5.08801			0.228458
$497$		0			0
$498$	4.38647	+	3.18696i	0.196563	+	0.142811i
$499$	−0.622054	−	5.91844i	−0.0278469	−	0.264946i	−0.999583	−	0.0288760i	$-0.990807\pi$
$499$	−0.622054	−	5.91844i	−0.0278469	−	0.264946i	0.971736	−	0.236070i	$-0.0758595\pi$
$500$	−3.02235	+	0.642421i	−0.135164	+	0.0287299i
$501$	1.33669	−	0.284122i	0.0597188	−	0.0126936i
$502$	−2.38713	−	22.7121i	−0.106543	−	1.01369i
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	0.494360	−	0.869257i	$-0.335403\pi$
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	−0.673947	+	0.738779i	$0.735403\pi$
$504$		0			0
$505$	4.27456			0.190216
$506$	0.0898719	−	10.0510i	0.00399529	−	0.446820i
$507$	9.15770	+	15.8616i	0.406708	+	0.704439i
$508$	−1.86503	+	2.07133i	−0.0827473	+	0.0919002i
$509$	19.4846	−	8.67509i	0.863639	−	0.384517i	0.0733902	−	0.997303i	$-0.476618\pi$
$509$	19.4846	−	8.67509i	0.863639	−	0.384517i	0.790248	+	0.612787i	$0.209951\pi$
$510$	−0.374949	+	0.272417i	−0.0166030	+	0.0120628i
$511$		0			0
$512$	−2.54091	+	7.82012i	−0.112293	+	0.345604i
$513$	1.05796	+	10.0659i	0.0467102	+	0.444418i
$514$	1.37478	−	13.0802i	0.0606390	−	0.576942i
$515$	−2.41776	+	2.68519i	−0.106539	+	0.118324i
$516$	2.03036	−	3.51669i	0.0893816	−	0.154814i
$517$	−8.31884	+	18.2436i	−0.365862	+	0.802354i
$518$		0			0
$519$	−1.97900	−	6.09075i	−0.0868686	−	0.267354i
$520$	−3.50406	+	1.56011i	−0.153663	+	0.0684152i
$521$	20.2244	+	9.00448i	0.886046	+	0.394493i	0.798732	−	0.601687i	$-0.205505\pi$
$521$	20.2244	+	9.00448i	0.886046	+	0.394493i	0.0873149	+	0.996181i	$0.472171\pi$
$522$	7.51401	−	1.59715i	0.328879	−	0.0699054i
$523$	−3.28641	−	3.64993i	−0.143705	−	0.159600i	0.666996	−	0.745062i	$-0.267580\pi$
$523$	−3.28641	−	3.64993i	−0.143705	−	0.159600i	−0.810700	+	0.585462i	$0.800913\pi$
$524$	−1.54683	+	1.12384i	−0.0675737	+	0.0490952i
$525$		0			0
$526$	1.96537	+	6.04880i	0.0856944	+	0.263740i
$527$	−14.9318	+	25.8627i	−0.650441	+	1.12660i
$528$	0.327960	−	1.47783i	0.0142726	−	0.0643143i
$529$	3.90296	+	6.76013i	0.169694	+	0.293919i
$530$	−0.290709	−	0.0617921i	−0.0126276	−	0.00268408i
$531$	20.1913	+	14.6698i	0.876228	+	0.636617i
$532$		0			0
$533$	2.69996	−	8.30962i	0.116948	−	0.359929i
$534$	−2.54698	−	2.82871i	−0.110219	−	0.122410i
$535$	−1.09635	−	0.488127i	−0.0473994	−	0.0211036i
$536$	−0.350885	+	3.33845i	−0.0151559	+	0.144199i
$537$	−14.1517	−	3.00803i	−0.610689	−	0.129806i
$538$	−4.85707			−0.209403
$539$		0			0
$540$	−1.07818			−0.0463977
$541$	−18.9609	−	4.03026i	−0.815192	−	0.173274i	−0.218595	−	0.975816i	$-0.570147\pi$
$541$	−18.9609	−	4.03026i	−0.815192	−	0.173274i	−0.596597	+	0.802541i	$0.703481\pi$
$542$	−0.639335	+	6.08287i	−0.0274618	+	0.261281i
$543$	−7.74414	−	3.44791i	−0.332333	−	0.147964i
$544$	−16.9794	−	18.8575i	−0.727984	−	0.808509i
$545$	0.371242	−	1.14257i	0.0159023	−	0.0489422i
$546$		0			0
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	0.309114	−	0.951025i	$-0.399968\pi$
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	−0.808957	+	0.587868i	$0.799968\pi$
$548$	3.41152	+	0.725141i	0.145733	+	0.0309765i
$549$	12.6051	+	21.8326i	0.537972	+	0.931794i
$550$	−5.08769	−	11.7078i	−0.216940	−	0.499221i
$551$	−5.50060	+	9.52732i	−0.234333	+	0.405877i
$552$	1.96530	+	6.04858i	0.0836489	+	0.257445i
$553$		0			0
$554$	7.57795	−	5.50570i	0.321956	−	0.233915i
$555$	0.520239	+	0.577783i	0.0220829	+	0.0245255i
$556$	6.50105	−	1.38184i	0.275706	−	0.0586031i
$557$	16.8739	+	7.51276i	0.714972	+	0.318326i	0.731788	−	0.681533i	$-0.238686\pi$
$557$	16.8739	+	7.51276i	0.714972	+	0.318326i	−0.0168159	+	0.999859i	$0.505353\pi$
$558$	12.8112	−	5.70392i	0.542341	−	0.241466i
$559$	9.49993	+	29.2378i	0.401804	+	1.23663i
$560$		0			0
$561$	6.54945	+	6.00405i	0.276518	+	0.253491i
$562$	8.22381	−	14.2441i	0.346900	−	0.600849i
$563$	−20.9330	+	23.2484i	−0.882220	+	0.979804i	−0.999912	−	0.0132458i	$-0.995784\pi$
$563$	−20.9330	+	23.2484i	−0.882220	+	0.979804i	0.117693	+	0.993050i	$0.462450\pi$
$564$	0.545026	−	5.18558i	0.0229497	−	0.218352i
$565$	0.383689	+	3.65056i	0.0161419	+	0.153580i
$566$	−6.00720	+	18.4883i	−0.252502	+	0.777120i
$567$		0			0
$568$	19.8823	−	14.4454i	0.834244	−	0.606114i
$569$	1.58596	−	0.706115i	0.0664869	−	0.0296019i	−0.373224	−	0.927741i	$-0.621748\pi$
$569$	1.58596	−	0.706115i	0.0664869	−	0.0296019i	0.439711	+	0.898139i	$0.355081\pi$
$570$	−0.208552	+	0.231621i	−0.00873530	+	0.00970153i
$571$	−6.26546	−	10.8521i	−0.262201	−	0.454146i	0.704625	−	0.709580i	$-0.251115\pi$
$571$	−6.26546	−	10.8521i	−0.262201	−	0.454146i	−0.966827	+	0.255433i	$0.917782\pi$
$572$	17.5444	+	24.6075i	0.733567	+	1.02889i
$573$	7.43182			0.310469
$574$		0			0
$575$	−15.6114	−	11.3424i	−0.651042	−	0.473009i
$576$	0.841353	+	8.00494i	0.0350564	+	0.333539i
$577$	19.7484	−	4.19766i	0.822138	−	0.174751i	0.222408	−	0.974954i	$-0.428608\pi$
$577$	19.7484	−	4.19766i	0.822138	−	0.174751i	0.599729	+	0.800203i	$0.295275\pi$
$578$	1.36043	−	0.289168i	0.0565864	−	0.0120278i
$579$	1.02614	+	9.76303i	0.0426447	+	0.405738i
$580$	−0.948101	−	0.688835i	−0.0393677	−	0.0286023i
$581$		0			0
$582$	4.35051			0.180334
$583$	−0.0509445	+	5.69745i	−0.00210990	+	0.235964i
$584$	7.37752	+	12.7782i	0.305284	+	0.528768i
$585$	2.54525	−	2.82678i	0.105233	−	0.116873i
$586$	−0.323234	+	0.143913i	−0.0133527	+	0.00594499i
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	−0.587925	−	0.808915i	$-0.700055\pi$
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	0.587645	+	0.809119i	$0.300055\pi$
$588$		0			0
$589$	−6.20604	+	19.1002i	−0.255716	+	0.787012i
$590$	0.172392	+	1.64021i	0.00709729	+	0.0675262i
$591$	0.794835	−	7.56235i	0.0326951	−	0.311073i
$592$	−2.79373	+	3.10275i	−0.114822	+	0.127522i
$593$	−0.219649	+	0.380443i	−0.00901989	+	0.0156229i	−0.870500	−	0.492168i	$-0.836204\pi$
$593$	−0.219649	+	0.380443i	−0.00901989	+	0.0156229i	0.861480	+	0.507791i	$0.169538\pi$
$594$	−1.78312	−	8.77397i	−0.0731624	−	0.360001i
$595$		0			0
$596$	3.11779	+	9.59558i	0.127710	+	0.393050i
$597$	8.61667	−	3.83639i	0.352657	−	0.157013i
$598$	−18.0776	−	8.04868i	−0.739250	−	0.329135i
$599$	−44.1794	+	9.39061i	−1.80512	+	0.383690i	−0.982702	−	0.185194i	$-0.940709\pi$
$599$	−44.1794	+	9.39061i	−1.80512	+	0.383690i	−0.822418	+	0.568884i	$0.807375\pi$
$600$	5.40467	+	6.00249i	0.220645	+	0.245051i
$601$	9.01541	−	6.55008i	0.367746	−	0.267183i	−0.388529	−	0.921436i	$-0.627017\pi$
$601$	9.01541	−	6.55008i	0.367746	−	0.267183i	0.756276	+	0.654253i	$0.227017\pi$
$602$		0			0
$603$	−1.02870	−	3.16603i	−0.0418921	−	0.128931i
$604$	5.67954	−	9.83725i	0.231097	−	0.400272i
$605$	2.00562	−	1.40307i	0.0815400	−	0.0570428i
$606$	−4.61535	−	7.99403i	−0.187486	−	0.324735i
$607$	−34.9196	−	7.42240i	−1.41734	−	0.301266i	−0.565365	−	0.824841i	$-0.691265\pi$
$607$	−34.9196	−	7.42240i	−1.41734	−	0.301266i	−0.851980	+	0.523575i	$0.824598\pi$
$608$	−13.8057	−	10.0304i	−0.559894	−	0.406787i
$609$		0			0
$610$	−0.514796	+	1.58438i	−0.0208435	+	0.0641496i
$611$	26.4137	+	29.3353i	1.06858	+	1.18678i
$612$	14.4674	+	6.44131i	0.584811	+	0.260375i
$613$	−1.79768	+	17.1038i	−0.0726076	+	0.690815i	0.896309	+	0.443429i	$0.146238\pi$
$613$	−1.79768	+	17.1038i	−0.0726076	+	0.690815i	−0.968917	+	0.247386i	$0.920428\pi$
$614$	6.11116	+	1.29897i	0.246626	+	0.0524221i
$615$	0.184020			0.00742040
$616$		0			0
$617$	−16.8852			−0.679774			−0.339887	−	0.940466i	$-0.610389\pi$
$617$	−16.8852			−0.679774			−0.339887	+	0.940466i	$0.610389\pi$
$618$	7.63219	+	1.62227i	0.307012	+	0.0652573i
$619$	3.24762	−	30.8990i	0.130533	−	1.24194i	−0.711568	−	0.702617i	$-0.752015\pi$
$619$	3.24762	−	30.8990i	0.130533	−	1.24194i	0.842101	−	0.539320i	$-0.181319\pi$
$620$	−1.95443	−	0.870167i	−0.0784917	−	0.0349467i
$621$	−9.05617	−	10.0579i	−0.363412	−	0.403610i
$622$	0.0329066	−	0.101276i	0.00131943	−	0.00406080i
$623$		0			0
$624$	−2.41106	−	1.75174i	−0.0965196	−	0.0701256i
$625$	−23.7296	−	5.04389i	−0.949185	−	0.201755i
$626$	5.94384	+	10.2950i	0.237564	+	0.411472i
$627$	5.14771	+	3.03372i	0.205580	+	0.121155i
$628$	−14.0608	+	24.3541i	−0.561088	+	0.971834i
$629$	−7.57271	−	23.3064i	−0.301944	−	0.929287i
$630$		0			0
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	−0.698434	−	0.715675i	$-0.746119\pi$
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	0.464819	+	0.885406i	$0.346119\pi$
$632$	−8.00135	−	8.88640i	−0.318276	−	0.353482i
$633$	5.40052	−	1.14792i	0.214651	−	0.0456255i
$634$	23.4335	+	10.4333i	0.930664	+	0.414358i
$635$	0.406004	−	0.180765i	0.0161118	−	0.00717342i
$636$	−0.457859	−	1.40915i	−0.0181553	−	0.0558763i
$637$		0			0
$638$	4.03757	−	8.85460i	0.159849	−	0.350557i
$639$	−12.1859	+	21.1066i	−0.482066	+	0.834963i
$640$	1.38736	−	1.54081i	0.0548401	−	0.0609061i
$641$	2.16896	−	20.6362i	0.0856686	−	0.815082i	−0.864350	−	0.502890i	$-0.832270\pi$
$641$	2.16896	−	20.6362i	0.0856686	−	0.815082i	0.950019	−	0.312192i	$-0.101063\pi$
$642$	0.270893	+	2.57737i	0.0106913	+	0.101721i
$643$	−2.19750	+	6.76322i	−0.0866611	+	0.266715i	−0.984991	−	0.172606i	$-0.944781\pi$
$643$	−2.19750	+	6.76322i	−0.0866611	+	0.266715i	0.898330	+	0.439322i	$0.144781\pi$
$644$		0			0
$645$	−0.523825	+	0.380581i	−0.0206256	+	0.0149854i
$646$	8.97453	−	3.99572i	0.353098	−	0.157209i
$647$	−18.4539	+	20.4951i	−0.725496	+	0.805745i	−0.987214	−	0.159399i	$-0.949044\pi$
$647$	−18.4539	+	20.4951i	−0.725496	+	0.805745i	0.261718	+	0.965144i	$0.415711\pi$
$648$	−7.53472	−	13.0505i	−0.295992	−	0.512673i
$649$	30.1562	−	9.50110i	1.18373	−	0.372951i
$650$	−25.1317			−0.985748
$651$		0			0
$652$	8.39353	+	6.09826i	0.328716	+	0.238826i
$653$	−1.68857	−	16.0656i	−0.0660787	−	0.628697i	−0.976575	−	0.215179i	$-0.930966\pi$
$653$	−1.68857	−	16.0656i	−0.0660787	−	0.628697i	0.910496	−	0.413518i	$-0.135700\pi$
$654$	−2.53760	+	0.539383i	−0.0992279	+	0.0210916i
$655$	0.298205	−	0.0633855i	0.0116518	−	0.00247668i
$656$	0.103295	+	0.982791i	0.00403301	+	0.0383715i
$657$	−11.8379	−	8.60076i	−0.461842	−	0.335548i
$658$		0			0
$659$	−13.2085			−0.514531			−0.257266	−	0.966341i	$-0.582822\pi$
$659$	−13.2085			−0.514531			−0.257266	+	0.966341i	$0.582822\pi$
$660$	−0.378720	+	0.511581i	−0.0147417	+	0.0199133i
$661$	−2.45330	−	4.24924i	−0.0954223	−	0.165276i	0.814362	−	0.580357i	$-0.197087\pi$
$661$	−2.45330	−	4.24924i	−0.0954223	−	0.165276i	−0.909785	+	0.415080i	$0.863753\pi$
$662$	−15.3644	+	17.0639i	−0.597156	+	0.663209i
$663$	15.9800	−	7.11474i	0.620610	−	0.276314i
$664$	24.0996	−	17.5094i	0.935245	−	0.679495i
$665$		0			0
$666$	−3.55605	+	10.9444i	−0.137794	+	0.424087i
$667$	−1.53770	−	14.6303i	−0.0595401	−	0.566486i
$668$	0.322540	−	3.06876i	0.0124794	−	0.118734i
$669$	0.295786	−	0.328504i	0.0114357	−	0.0127007i
$670$	0.109991	−	0.190509i	0.00424930	−	0.00736001i
$671$	31.7311	+	3.62221i	1.22497	+	0.139834i
$672$		0			0
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	−0.954723	−	0.297495i	$-0.903849\pi$
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	0.597524	−	0.801851i	$-0.296151\pi$
$674$	−3.99898	+	1.78046i	−0.154035	+	0.0685808i
$675$	−15.7027	−	6.99130i	−0.604398	−	0.269095i
$676$	40.4524	−	8.59842i	1.55586	−	0.330708i
$677$	−8.42364	−	9.35540i	−0.323747	−	0.359557i	0.559198	−	0.829034i	$-0.311109\pi$
$677$	−8.42364	−	9.35540i	−0.323747	−	0.359557i	−0.882945	+	0.469477i	$0.844442\pi$
$678$	6.41278	−	4.65916i	0.246281	−	0.178934i
$679$		0			0
$680$	0.786849	+	2.42167i	0.0301743	+	0.0928668i
$681$	1.64447	−	2.84831i	0.0630163	−	0.109147i
$682$	3.84891	−	17.3437i	0.147382	−	0.664124i
$683$	14.2671	+	24.7114i	0.545916	+	0.945554i	0.998549	+	0.0538567i	$0.0171514\pi$
$683$	14.2671	+	24.7114i	0.545916	+	0.945554i	−0.452633	+	0.891697i	$0.649515\pi$
$684$	10.4173	+	2.21426i	0.398315	+	0.0846645i
$685$	−0.449911	−	0.326879i	−0.0171902	−	0.0124894i
$686$		0			0
$687$	−1.26208	+	3.88427i	−0.0481513	+	0.148194i
$688$	−2.32660	−	2.58395i	−0.0887007	−	0.0985121i
$689$	10.2474	+	4.56245i	0.390396	+	0.173815i
$690$	0.0435649	−	0.414492i	0.00165849	−	0.0157794i
$691$	24.8197	+	5.27560i	0.944188	+	0.200693i	0.654187	−	0.756333i	$-0.273011\pi$
$691$	24.8197	+	5.27560i	0.944188	+	0.200693i	0.290001	+	0.957026i	$0.406344\pi$
$692$	−14.4606			−0.549711
$693$		0			0
$694$	−6.78791			−0.257666
$695$	−1.03659	−	0.220335i	−0.0393203	−	0.00835778i
$696$	−0.643643	+	6.12385i	−0.0243972	+	0.232124i
$697$	−5.29874	−	2.35915i	−0.200704	−	0.0893592i
$698$	9.60722	+	10.6699i	0.363639	+	0.403862i
$699$	1.82525	−	5.61754i	0.0690373	−	0.212475i
$700$		0			0
$701$	36.9738	+	26.8630i	1.39648	+	1.01460i	0.995119	+	0.0986843i	$0.0314634\pi$
$701$	36.9738	+	26.8630i	1.39648	+	1.01460i	0.401363	+	0.915919i	$0.368537\pi$
$702$	−17.2415	−	3.66480i	−0.650739	−	0.138319i
$703$	−8.24002	−	14.2721i	−0.310778	−	0.538283i
$704$	8.78477	+	5.17716i	0.331088	+	0.195122i
$705$	−0.415698	+	0.720010i	−0.0156561	+	0.0271171i
$706$	−5.64257	−	17.3661i	−0.212361	−	0.653580i
$707$		0			0
$708$	−6.65177	+	4.83279i	−0.249989	+	0.181627i
$709$	25.7819	+	28.6337i	0.968258	+	1.07536i	0.997125	+	0.0757766i	$0.0241436\pi$
$709$	25.7819	+	28.6337i	0.968258	+	1.07536i	−0.0288664	+	0.999583i	$0.509190\pi$
$710$	−1.57532	+	0.334844i	−0.0591207	+	0.0125665i
$711$	10.8333	+	4.82329i	0.406280	+	0.180887i
$712$	−19.1046	+	8.50593i	−0.715977	+	0.318773i
$713$	−8.29874	−	25.5409i	−0.310790	−	0.956515i
$714$		0			0
$715$	−0.959703	−	4.72228i	−0.0358908	−	0.176603i
$716$	−16.3341	+	28.2915i	−0.610435	+	1.05730i
$717$	−11.1023	+	12.3304i	−0.414623	+	0.460486i
$718$	1.20938	−	11.5065i	0.0451338	−	0.429420i
$719$	0.596034	+	5.67089i	0.0222283	+	0.211488i	0.999998	+	0.00180831i	$0.000575603\pi$
$719$	0.596034	+	5.67089i	0.0222283	+	0.211488i	−0.977770	+	0.209680i	$0.932758\pi$
$720$	−0.132945	+	0.409164i	−0.00495458	+	0.0152486i
$721$		0			0
$722$	−6.60620	+	4.79969i	−0.245857	+	0.178626i
$723$	10.6520	−	4.74256i	0.396151	−	0.176378i
$724$	−12.8079	+	14.2246i	−0.476001	+	0.528653i
$725$	−9.34154	−	16.1800i	−0.346936	−	0.600911i
$726$	−4.78945	−	2.23586i	−0.177753	−	0.0829806i
$727$	−11.8221			−0.438458			−0.219229	−	0.975673i	$-0.570354\pi$
$727$	−11.8221			−0.438458			−0.219229	+	0.975673i	$0.570354\pi$
$728$		0			0
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	−0.101072	−	0.961634i	−0.00374083	−	0.0355917i
$731$	19.9623	−	4.24311i	0.738331	−	0.156937i
$732$	−8.12368	+	1.72674i	−0.300260	+	0.0638222i
$733$	0.921097	+	8.76365i	0.0340215	+	0.323693i	0.998275	+	0.0587114i	$0.0186992\pi$
$733$	0.921097	+	8.76365i	0.0340215	+	0.323693i	−0.964253	+	0.264981i	$0.914634\pi$
$734$	21.5280	+	15.6410i	0.794614	+	0.577321i
$735$		0			0
$736$	22.8190			0.841121
$737$	−3.99903	−	1.33901i	−0.147306	−	0.0493231i
$738$	1.36185	+	2.35879i	0.0501303	+	0.0868283i
$739$	0.321724	−	0.357311i	0.0118348	−	0.0131439i	−0.737198	−	0.675676i	$-0.763852\pi$
$739$	0.321724	−	0.357311i	0.0118348	−	0.0131439i	0.749033	+	0.662532i	$0.230518\pi$
$740$	1.60378	−	0.714049i	0.0589561	−	0.0262490i
$741$	9.51683	−	6.91438i	0.349610	−	0.254006i
$742$		0			0
$743$	10.2730	−	31.6172i	0.376881	−	1.15992i	−0.565319	−	0.824872i	$-0.691247\pi$
$743$	10.2730	−	31.6172i	0.376881	−	1.15992i	0.942201	−	0.335049i	$-0.108753\pi$
$744$	1.17500	+	11.1794i	0.0430776	+	0.409856i
$745$	0.168161	−	1.59994i	0.00616094	−	0.0586174i
$746$	−1.56976	+	1.74340i	−0.0574731	+	0.0638304i
$747$	−14.7706	+	25.5835i	−0.540429	+	0.936051i
$748$	17.4635	−	9.87543i	0.638530	−	0.361082i
$749$		0			0
$750$	−0.328769	−	1.01185i	−0.0120050	−	0.0369475i
$751$	25.5853	−	11.3913i	0.933622	−	0.415675i	0.117185	−	0.993110i	$-0.462613\pi$
$751$	25.5853	−	11.3913i	0.933622	−	0.415675i	0.816437	+	0.577435i	$0.195946\pi$
$752$	−4.07868	−	1.81595i	−0.148734	−	0.0662208i
$753$	−17.7569	+	3.77435i	−0.647098	+	0.137545i
$754$	−12.8199	−	14.2380i	−0.466875	−	0.518517i
$755$	−1.46530	+	1.06460i	−0.0533276	+	0.0387448i
$756$		0			0
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	−0.994798	−	0.101864i	$-0.967519\pi$
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	0.744935	−	0.667137i	$-0.232481\pi$
$758$	−2.38078	+	4.12363i	−0.0864738	+	0.149777i
$759$	−7.95336	+	0.764098i	−0.288689	+	0.0277350i
$760$	0.856186	+	1.48296i	0.0310571	+	0.0537925i
$761$	−47.1716	−	10.0266i	−1.70997	−	0.363465i	−0.753986	−	0.656891i	$-0.771871\pi$
$761$	−47.1716	−	10.0266i	−1.70997	−	0.363465i	−0.955982	+	0.293426i	$0.905205\pi$
$762$	−0.776427	−	0.564108i	−0.0281270	−	0.0204355i
$763$		0			0
$764$	5.18562	−	15.9597i	0.187609	−	0.577402i
$765$	−1.68965	−	1.87655i	−0.0610895	−	0.0678468i
$766$	3.11877	+	1.38857i	0.112686	+	0.0501709i
$767$	6.50652	−	61.9054i	0.234937	−	2.23528i
$768$	−8.09669	−	1.72101i	−0.292164	−	0.0621014i
$769$	−43.6883			−1.57544			−0.787721	−	0.616032i	$-0.788739\pi$
$769$	−43.6883			−1.57544			−0.787721	+	0.616032i	$0.788739\pi$
$770$		0			0
$771$	−10.4549			−0.376524
$772$	21.6819	+	4.60863i	0.780349	+	0.165868i
$773$	−0.0612087	+	0.582362i	−0.00220152	+	0.0209461i	−0.995568	−	0.0940496i	$-0.970019\pi$
$773$	−0.0612087	+	0.582362i	−0.00220152	+	0.0209461i	0.993366	+	0.114996i	$0.0366854\pi$
$774$	−8.75492	−	3.89794i	−0.314689	−	0.140109i
$775$	−22.8219	−	25.3463i	−0.819787	−	0.910465i
$776$	7.38612	−	22.7321i	0.265146	−	0.816036i
$777$		0			0
$778$	6.60197	+	4.79661i	0.236692	+	0.171967i
$779$	−3.81536	−	0.810980i	−0.136700	−	0.0290564i
$780$	0.626558	+	1.08523i	0.0224344	+	0.0388575i
$781$	12.3053	+	28.3170i	0.440319	+	1.01326i
$782$	−6.56824	+	11.3765i	−0.234880	+	0.406824i
$783$	−4.04930	−	12.4625i	−0.144710	−	0.445372i
$784$		0			0
$785$	3.62764	−	2.63563i	0.129476	−	0.0940698i
$786$	−0.440520	−	0.489247i	−0.0157128	−	0.0174508i
$787$	30.0453	−	6.38634i	1.07100	−	0.227648i	0.361514	−	0.932367i	$-0.382260\pi$
$787$	30.0453	−	6.38634i	1.07100	−	0.227648i	0.709487	+	0.704718i	$0.248927\pi$
$788$	−15.6854	−	6.98359i	−0.558769	−	0.248780i
$789$	4.61864	−	2.05635i	0.164428	−	0.0732080i
$790$	0.242153	+	0.745269i	0.00861540	+	0.0265155i
$791$		0			0
$792$	−22.7750	−	2.59984i	−0.809274	−	0.0923811i
$793$	31.4379	−	54.4520i	1.11639	−	1.93365i
$794$	5.92490	−	6.58027i	0.210267	−	0.233525i
$795$	−0.0246950	+	0.234957i	−0.000875842	+	0.00833308i
$796$	−2.22621	−	21.1810i	−0.0789061	−	0.750741i
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	−0.874096	−	0.485752i	$-0.838546\pi$
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	0.992677	+	0.120799i	$0.0385456\pi$
$798$		0			0
$799$	21.2003	−	15.4029i	0.750014	−	0.544917i
$800$	26.4751	−	11.7875i	0.936038	−	0.416751i
$801$	13.8771	−	15.4120i	0.490322	−	0.544557i
$802$	−1.83679	−	3.18141i	−0.0648593	−	0.112340i
$803$	−17.6802	+	5.57038i	−0.623922	+	0.196575i
$804$	1.09668			0.0386770
$805$		0			0
$806$	−28.2960	−	20.5582i	−0.996684	−	0.724133i
$807$	0.403580	+	3.83981i	0.0142067	+	0.135168i
$808$	−49.6059	+	10.5441i	−1.74513	+	0.370939i
$809$	37.7468	−	8.02332i	1.32711	−	0.282085i	0.510797	−	0.859701i	$-0.329350\pi$
$809$	37.7468	−	8.02332i	1.32711	−	0.282085i	0.816308	+	0.577616i	$0.196017\pi$
$810$	0.103225	+	0.982124i	0.00362697	+	0.0345083i
$811$	−41.1737	−	29.9144i	−1.44580	−	1.05044i	−0.986789	−	0.162010i	$-0.948202\pi$
$811$	−41.1737	−	29.9144i	−1.44580	−	1.05044i	−0.459015	−	0.888428i	$-0.651798\pi$
$812$		0			0
$813$	4.86200			0.170518
$814$	8.46310	+	11.8702i	0.296632	+	0.416051i
$815$	−0.827146	−	1.43266i	−0.0289737	−	0.0501839i
$816$	−1.32382	+	1.47025i	−0.0463429	+	0.0514690i
$817$	12.5379	−	5.58223i	0.438646	−	0.195298i
$818$	−1.55076	+	1.12669i	−0.0542209	+	0.0393938i
$819$		0			0
$820$	0.128402	−	0.395180i	0.00448398	−	0.0138003i
$821$	4.21348	+	40.0886i	0.147052	+	1.39910i	0.780422	+	0.625253i	$0.215004\pi$
$821$	4.21348	+	40.0886i	0.147052	+	1.39910i	−0.633370	+	0.773849i	$0.718329\pi$
$822$	−0.125530	+	1.19434i	−0.00437835	+	0.0416572i
$823$	17.1844	−	19.0853i	0.599012	−	0.665270i	−0.365038	−	0.930993i	$-0.618944\pi$
$823$	17.1844	−	19.0853i	0.599012	−	0.665270i	0.964050	+	0.265723i	$0.0856105\pi$
$824$	21.4343	−	37.1252i	0.746698	−	1.29332i
$825$	−8.83296	+	4.99494i	−0.307524	+	0.173902i
$826$		0			0
$827$	−9.87486	−	30.3917i	−0.343382	−	1.05682i	−0.962444	−	0.271480i	$-0.912487\pi$
$827$	−9.87486	−	30.3917i	−0.343382	−	1.05682i	0.619062	−	0.785342i	$-0.287513\pi$
$828$	−13.0100	+	5.79244i	−0.452130	+	0.201301i
$829$	−44.2158	−	19.6861i	−1.53568	−	0.683728i	−0.547467	−	0.836827i	$-0.684408\pi$
$829$	−44.2158	−	19.6861i	−1.53568	−	0.683728i	−0.988211	+	0.153099i	$0.951075\pi$
$830$	−1.90946	+	0.405868i	−0.0662784	+	0.0140879i
$831$	−4.98225	−	5.53335i	−0.172832	−	0.191950i
$832$	16.2409	−	11.7997i	0.563050	−	0.409080i
$833$		0			0
$834$	0.707180	+	2.17648i	0.0244876	+	0.0753652i
$835$	−0.246005	+	0.426093i	−0.00851335	+	0.0147456i
$836$	10.1067	−	8.93780i	0.349548	−	0.309120i
$837$	−11.9608	−	20.7167i	−0.413425	−	0.716073i
$838$	10.9054	+	2.31801i	0.376720	+	0.0800744i
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.0805734	−	0.996749i	$-0.525675\pi$
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.972863	+	0.231382i	$0.925675\pi$
$840$		0			0
$841$	−4.56017	+	14.0348i	−0.157247	+	0.483957i
$842$	9.00832	+	10.0048i	0.310447	+	0.344787i
$843$	−11.9441	−	5.31786i	−0.411377	−	0.183157i
$844$	1.30313	−	12.3985i	0.0448557	−	0.426773i
$845$	−6.45014	−	1.37102i	−0.221892	−	0.0471645i
$846$	−12.3056			−0.423074
$847$		0			0
$848$	−1.26869			−0.0435671
$849$	15.1152	+	3.21284i	0.518754	+	0.110265i
$850$	−1.74391	+	16.5922i	−0.0598157	+	0.569108i
$851$	20.1319	+	8.96332i	0.690114	+	0.307259i
$852$	−5.37243	−	5.96669i	−0.184056	−	0.204415i
$853$	−2.87035	+	8.83403i	−0.0982789	+	0.302471i	−0.988094	−	0.153849i	$-0.950833\pi$
$853$	−2.87035	+	8.83403i	−0.0982789	+	0.302471i	0.889815	+	0.456321i	$0.150833\pi$
$854$		0			0
$855$	−1.37383	−	0.998146i	−0.0469840	−	0.0341359i
$856$	13.9271	+	2.96030i	0.476019	+	0.101181i
$857$	−14.8822	−	25.7767i	−0.508365	−	0.880515i	−0.999953	−	0.00968670i	$-0.996917\pi$
$857$	−14.8822	−	25.7767i	−0.508365	−	0.880515i	0.491588	−	0.870828i	$-0.336417\pi$
$858$	−7.79510	+	6.89354i	−0.266120	+	0.235342i
$859$	16.6305	−	28.8050i	0.567427	−	0.982812i	−0.429392	−	0.903118i	$-0.641272\pi$
$859$	16.6305	−	28.8050i	0.567427	−	0.982812i	0.996819	−	0.0796943i	$-0.0253944\pi$
$860$	0.451787	+	1.39046i	0.0154058	+	0.0474142i
$861$		0			0
$862$	17.5442	−	12.7466i	0.597558	−	0.434151i
$863$	−12.4242	−	13.7985i	−0.422924	−	0.469705i	0.493597	−	0.869691i	$-0.335682\pi$
$863$	−12.4242	−	13.7985i	−0.422924	−	0.469705i	−0.916521	+	0.399986i	$0.869015\pi$
$864$	19.8821	−	4.22606i	0.676401	−	0.143774i
$865$	2.10641	+	0.937834i	0.0716201	+	0.0318873i
$866$	−20.9863	+	9.34369i	−0.713143	+	0.317512i
$867$	−0.341645	−	1.05147i	−0.0116029	−	0.0357100i
$868$		0			0
$869$	13.0768	−	7.39477i	0.443599	−	0.250850i
$870$	0.201760	−	0.349459i	0.00684031	−	0.0118478i
$871$	−5.55554	+	6.17006i	−0.188242	+	0.209064i
$872$	−1.48986	+	14.1751i	−0.0504532	+	0.480030i
$873$	2.47769	+	23.5736i	0.0838569	+	0.797845i
$874$	−2.72992	+	8.40184i	−0.0923411	+	0.284197i
$875$		0			0
$876$	3.89985	−	2.83341i	0.131764	−	0.0957321i
$877$	−20.5476	+	9.14837i	−0.693842	+	0.308918i	−0.723188	−	0.690651i	$-0.757324\pi$
$877$	−20.5476	+	9.14837i	−0.693842	+	0.308918i	0.0293463	+	0.999569i	$0.490657\pi$
$878$	−17.5141	+	19.4514i	−0.591073	+	0.656453i
$879$	0.140630	+	0.243578i	0.00474332	+	0.00821568i
$880$	0.316399	+	0.443777i	0.0106658	+	0.0149597i
$881$	−7.06565			−0.238048			−0.119024	−	0.992891i	$-0.537977\pi$
$881$	−7.06565			−0.238048			−0.119024	+	0.992891i	$0.537977\pi$
$882$		0			0
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	0.825135	−	0.564936i	$-0.191099\pi$
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	−0.282305	+	0.959325i	$0.591099\pi$
$884$	−4.12861	−	39.2811i	−0.138860	−	1.32116i
$885$	1.28236	−	0.272573i	0.0431060	−	0.00916245i
$886$	7.85341	−	1.66929i	0.263841	−	0.0560810i
$887$	0.726975	+	6.91671i	0.0244094	+	0.232240i	0.999924	+	0.0123067i	$0.00391744\pi$
$887$	0.726975	+	6.91671i	0.0244094	+	0.232240i	−0.975515	+	0.219934i	$0.929416\pi$
$888$	−7.46253	−	5.42185i	−0.250426	−	0.181945i
$889$		0			0
$890$	1.37045			0.0459376
$891$	18.0570	−	5.68908i	0.604931	−	0.190591i
$892$	−0.499068	−	0.864411i	−0.0167100	−	0.0289426i
$893$	11.7919	−	13.0963i	0.394602	−	0.438250i
$894$	−3.17368	+	1.41301i	−0.106144	+	0.0472583i
$895$	4.21414	−	3.06175i	0.140863	−	0.102343i
$896$		0			0
$897$	−4.86088	+	14.9602i	−0.162300	+	0.499508i
$898$	−0.224129	−	2.13244i	−0.00747927	−	0.0711605i
$899$	2.71787	−	25.8588i	0.0906459	−	0.862438i
$900$	−12.1023	+	13.4410i	−0.403412	+	0.448034i
$901$	3.72325	−	6.44886i	0.124039	−	0.214843i
$902$	3.42822	+	0.391342i	0.114147	+	0.0130303i
$903$		0			0
$904$	−13.4575	−	41.4179i	−0.447590	−	1.37754i
$905$	2.78818	−	1.24138i	0.0926824	−	0.0412649i
$906$	3.57307	+	1.59083i	0.118707	+	0.0528519i
$907$	22.9279	−	4.87348i	0.761309	−	0.161821i	0.189132	−	0.981952i	$-0.439432\pi$
$907$	22.9279	−	4.87348i	0.761309	−	0.161821i	0.572177	+	0.820130i	$0.306099\pi$
$908$	−4.96924	−	5.51890i	−0.164910	−	0.183151i
$909$	40.6878	−	29.5614i	1.34953	−	0.980490i
$910$		0			0
$911$	14.4650	+	44.5186i	0.479246	+	1.47497i	0.840145	+	0.542362i	$0.182470\pi$
$911$	14.4650	+	44.5186i	0.479246	+	1.47497i	−0.360899	+	0.932605i	$0.617530\pi$
$912$	−0.665238	+	1.15223i	−0.0220282	+	0.0381540i
$913$	14.9154	+	34.3233i	0.493628	+	1.13593i
$914$	−15.6782	−	27.1554i	−0.518588	−	0.898220i
$915$	1.29532	+	0.275329i	0.0428220	+	0.00910211i
$916$	7.46078	+	5.42058i	0.246511	+	0.179101i
$917$		0			0
$918$	−3.61594	+	11.1287i	−0.119344	+	0.367302i
$919$	7.11106	+	7.89763i	0.234572	+	0.260519i	0.848926	−	0.528512i	$-0.177250\pi$
$919$	7.11106	+	7.89763i	0.234572	+	0.260519i	−0.614354	+	0.789031i	$0.710583\pi$
$920$	−2.09183	−	0.931341i	−0.0689655	−	0.0307054i
$921$	0.519128	−	4.93918i	0.0171059	−	0.162751i
$922$	26.0280	+	5.53242i	0.857186	+	0.182201i
$923$	60.7848			2.00075
$924$		0			0
$925$	27.9876			0.920228
$926$	0.537935	+	0.114342i	0.0176776	+	0.00375750i
$927$	−4.44376	+	42.2795i	−0.145952	+	1.38864i
$928$	20.1832	+	8.98616i	0.662547	+	0.294985i
$929$	24.5377	+	27.2518i	0.805054	+	0.894104i	0.996168	−	0.0874645i	$-0.0278764\pi$
$929$	24.5377	+	27.2518i	0.805054	+	0.894104i	−0.191113	+	0.981568i	$0.561210\pi$
$930$	0.227635	−	0.700590i	0.00746446	−	0.0229733i
$931$		0			0
$932$	−10.7900	−	7.83938i	−0.353438	−	0.256787i
$933$	−0.0827991	−	0.0175995i	−0.00271072	−	0.000576182i
$934$	11.1151	+	19.2519i	0.363697	+	0.629941i
$935$	−3.18429	+	0.305922i	−0.104137	+	0.0100047i
$936$	−22.5645	+	39.0829i	−0.737544	+	1.27746i
$937$	12.4278	+	38.2490i	0.406000	+	1.24954i	0.920057	+	0.391784i	$0.128142\pi$
$937$	12.4278	+	38.2490i	0.406000	+	1.24954i	−0.514057	+	0.857756i	$0.671858\pi$
$938$		0			0
$939$	7.64497	−	5.55439i	0.249484	−	0.181261i
$940$	1.25615	+	1.39510i	0.0409711	+	0.0455031i
$941$	24.3653	−	5.17901i	0.794287	−	0.168831i	0.207140	−	0.978311i	$-0.433584\pi$
$941$	24.3653	−	5.17901i	0.794287	−	0.168831i	0.587147	+	0.809480i	$0.300251\pi$
$942$	−8.84585	−	3.93843i	−0.288213	−	0.128321i
$943$	4.76496	−	2.12150i	0.155168	−	0.0690854i
$944$	2.17555	+	6.69565i	0.0708081	+	0.217925i
$945$		0			0
$946$	−10.5680	+	5.97609i	−0.343595	+	0.194299i
$947$	16.1031	−	27.8913i	0.523279	−	0.906347i	−0.476353	−	0.879254i	$-0.658042\pi$
$947$	16.1031	−	27.8913i	0.523279	−	0.906347i	0.999633	−	0.0270927i	$-0.00862493\pi$
$948$	−2.61405	+	2.90319i	−0.0849003	+	0.0942913i
$949$	−3.81470	+	36.2944i	−0.123830	+	1.17817i
$950$	1.17277	+	11.1582i	0.0380497	+	0.362019i
$951$	6.30101	−	19.3925i	0.204324	−	0.628846i
$952$		0			0
$953$	−36.4552	+	26.4863i	−1.18090	+	0.857975i	−0.992273	−	0.124074i	$-0.960404\pi$
$953$	−36.4552	+	26.4863i	−1.18090	+	0.857975i	−0.188628	+	0.982049i	$0.560404\pi$
$954$	−3.19447	+	1.42227i	−0.103425	+	0.0460477i
$955$	−1.79042	+	1.98846i	−0.0579366	+	0.0643451i
$956$	18.7325	+	32.4456i	0.605852	+	1.04937i
$957$	−7.33558	−	2.45620i	−0.237126	−	0.0793978i
$958$	−3.96296			−0.128038
$959$		0			0
$960$	0.342058	+	0.248519i	0.0110399	+	0.00802093i
$961$	−1.72120	−	16.3761i	−0.0555226	−	0.528263i
$962$	28.0736	−	5.96722i	0.905128	−	0.192391i
$963$	−13.8114	+	2.93571i	−0.445067	+	0.0946020i
$964$	−2.75206	−	26.1841i	−0.0886378	−	0.843332i
$965$	−2.85941	−	2.07748i	−0.0920476	−	0.0668765i
$966$		0			0
$967$	1.81387			0.0583300			0.0291650	−	0.999575i	$-0.490715\pi$
$967$	1.81387			0.0583300			0.0291650	+	0.999575i	$0.490715\pi$
$968$	−19.8141	+	21.2297i	−0.636848	+	0.682348i
$969$	−3.90456	−	6.76290i	−0.125433	−	0.217256i
$970$	−1.04809	+	1.16402i	−0.0336522	+	0.0373746i
$971$	−21.0608	+	9.37687i	−0.675873	+	0.300918i	−0.715821	−	0.698284i	$-0.753947\pi$
$971$	−21.0608	+	9.37687i	−0.675873	+	0.300918i	0.0399480	+	0.999202i	$0.487281\pi$
$972$	−15.7431	+	11.4380i	−0.504959	+	0.366874i
$973$		0			0
$974$	−7.01266	+	21.5827i	−0.224700	+	0.691555i
$975$	2.08823	+	19.8682i	0.0668768	+	0.636290i
$976$	−0.743344	+	7.07245i	−0.0237939	+	0.226384i
$977$	−4.74714	+	5.27223i	−0.151875	+	0.168674i	−0.814281	−	0.580471i	$-0.802869\pi$
$977$	−4.74714	+	5.27223i	−0.151875	+	0.168674i	0.662407	+	0.749145i	$0.269535\pi$
$978$	−1.78618	+	3.09376i	−0.0571158	+	0.0989274i
$979$	−5.23244	−	25.7466i	−0.167229	−	0.822863i
$980$		0			0
$981$	−4.36789	−	13.4430i	−0.139456	−	0.429202i
$982$	−21.4103	+	9.53246i	−0.683229	+	0.304193i
$983$	−35.0347	−	15.5984i	−1.11743	−	0.497513i	−0.236917	−	0.971530i	$-0.576137\pi$
$983$	−35.0347	−	15.5984i	−1.11743	−	0.497513i	−0.880516	+	0.474017i	$0.842804\pi$
$984$	−2.13553	+	0.453922i	−0.0680783	+	0.0144705i
$985$	1.83190	+	2.03453i	0.0583691	+	0.0648255i
$986$	−10.2896	+	7.47586i	−0.327689	+	0.238080i
$987$		0			0
$988$	−8.20806	−	25.2618i	−0.261133	−	0.803685i
$989$	−9.17619	+	15.8936i	−0.291786	+	0.505388i
$990$	1.29416	+	0.762695i	0.0411312	+	0.0242401i
$991$	−10.1361	−	17.5562i	−0.321984	−	0.557692i	0.658914	−	0.752219i	$-0.271016\pi$
$991$	−10.1361	−	17.5562i	−0.321984	−	0.557692i	−0.980897	+	0.194527i	$0.937683\pi$
$992$	39.4510	+	8.38556i	1.25257	+	0.266242i
$993$	14.7667	+	10.7287i	0.468608	+	0.340464i
$994$		0			0
$995$	−1.04940	+	3.22971i	−0.0332681	+	0.102389i
$996$	−6.51198	−	7.23228i	−0.206340	−	0.229164i
$997$	−14.0784	−	6.26810i	−0.445867	−	0.198513i	0.171506	−	0.985183i	$-0.445137\pi$
$997$	−14.0784	−	6.26810i	−0.445867	−	0.198513i	−0.617373	+	0.786670i	$0.711803\pi$
$998$	0.483637	−	4.60150i	0.0153093	−	0.145658i
$999$	19.2008	+	4.08126i	0.607487	+	0.129125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.b.324.2		16
7.2	even	3		539.2.f.d.148.1		8
7.3	odd	6		539.2.q.c.214.1		16
7.4	even	3	inner	539.2.q.b.214.1		16
7.5	odd	6		77.2.f.a.71.1	yes	8
7.6	odd	2		539.2.q.c.324.2		16
11.9	even	5	inner	539.2.q.b.471.1		16
21.5	even	6		693.2.m.g.379.2		8
77.5	odd	30		847.2.f.p.323.2		8
77.9	even	15		539.2.f.d.295.1		8
77.19	even	30		847.2.a.k.1.3		4
77.20	odd	10		539.2.q.c.471.1		16
77.26	odd	30		847.2.f.p.729.2		8
77.30	odd	30		5929.2.a.bb.1.3		4
77.31	odd	30		539.2.q.c.361.2		16
77.40	even	30		847.2.f.s.729.1		8
77.47	odd	30		847.2.a.l.1.2		4
77.53	even	15	inner	539.2.q.b.361.2		16
77.54	even	6		847.2.f.q.148.2		8
77.58	even	15		5929.2.a.bi.1.2		4
77.61	even	30		847.2.f.s.323.1		8
77.68	even	30		847.2.f.q.372.2		8
77.75	odd	30		77.2.f.a.64.1	✓	8
231.47	even	30		7623.2.a.ch.1.3		4
231.152	even	30		693.2.m.g.64.2		8
231.173	odd	30		7623.2.a.co.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	77.75	odd	30
77.2.f.a.71.1	yes	8	7.5	odd	6
539.2.f.d.148.1		8	7.2	even	3
539.2.f.d.295.1		8	77.9	even	15
539.2.q.b.214.1		16	7.4	even	3	inner
539.2.q.b.324.2		16	1.1	even	1	trivial
539.2.q.b.361.2		16	77.53	even	15	inner
539.2.q.b.471.1		16	11.9	even	5	inner
539.2.q.c.214.1		16	7.3	odd	6
539.2.q.c.324.2		16	7.6	odd	2
539.2.q.c.361.2		16	77.31	odd	30
539.2.q.c.471.1		16	77.20	odd	10
693.2.m.g.64.2		8	231.152	even	30
693.2.m.g.379.2		8	21.5	even	6
847.2.a.k.1.3		4	77.19	even	30
847.2.a.l.1.2		4	77.47	odd	30
847.2.f.p.323.2		8	77.5	odd	30
847.2.f.p.729.2		8	77.26	odd	30
847.2.f.q.148.2		8	77.54	even	6
847.2.f.q.372.2		8	77.68	even	30
847.2.f.s.323.1		8	77.61	even	30
847.2.f.s.729.1		8	77.40	even	30
5929.2.a.bb.1.3		4	77.30	odd	30
5929.2.a.bi.1.2		4	77.58	even	15
7623.2.a.ch.1.3		4	231.47	even	30
7623.2.a.co.1.2		4	231.173	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)

\(f(q)\)	\(=\)	\(q+(0.760494 + 0.161648i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(-1.27487 - 0.567608i) q^{4} +(0.148892 + 0.165361i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(2.56082 + 0.544320i) q^{9} +O(q^{10})\)	\(q+(0.760494 + 0.161648i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(-1.27487 - 0.567608i) q^{4} +(0.148892 + 0.165361i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(2.56082 + 0.544320i) q^{9} +(0.0865012 + 0.149825i) q^{10} +(2.48448 - 2.19713i) q^{11} +(-0.431239 + 0.746928i) q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(0.494158 + 0.548818i) q^{16} +(-4.23989 + 0.901217i) q^{17} +(1.85950 + 0.827904i) q^{18} +(-2.66299 + 1.18564i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +(1.94898 - 3.37573i) q^{23} +(-1.09174 + 1.21250i) q^{24} +(0.517467 - 4.92337i) q^{25} +(-0.530651 - 5.04881i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(0.0976776 - 0.0434889i) q^{30} +(4.61003 - 5.11996i) q^{31} +(2.92705 + 5.06980i) q^{32} +(-1.18996 - 1.66902i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(0.590953 + 5.62254i) q^{37} +(-2.21685 + 0.471205i) q^{38} +(-3.94730 + 0.839024i) q^{39} +(-0.0614035 - 0.584215i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(-4.41449 + 1.39084i) q^{44} +(0.291277 + 0.504506i) q^{45} +(2.02787 - 2.25218i) q^{46} +(-5.52287 + 2.45894i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(0.280025 + 2.66426i) q^{51} +(-0.952474 + 9.06218i) q^{52} +(-1.14951 + 1.27666i) q^{53} +(1.34977 - 2.33786i) q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(2.68054 - 1.19345i) q^{58} +(8.70887 + 3.87744i) q^{59} +(-0.187721 + 0.0399013i) q^{60} +(6.44334 + 7.15606i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +(0.726463 - 1.25827i) q^{65} +(-0.635163 - 1.46163i) q^{66} +(-0.635774 - 1.10119i) q^{67} +(5.91685 + 1.25766i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(-4.62470 - 5.13625i) q^{72} +(-5.10591 - 2.27330i) q^{73} +(-0.459457 + 4.37144i) q^{74} +(-2.99271 - 0.636120i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(4.43056 + 0.941745i) q^{79} +(-0.0171771 + 0.163429i) q^{80} +(5.21470 + 2.32174i) q^{81} +(0.696136 + 0.773138i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(-3.58056 - 0.761072i) q^{86} +(-1.16623 - 2.01996i) q^{87} +(-8.71563 + 0.837331i) q^{88} +(3.96078 - 6.86028i) q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(-2.84916 - 3.16431i) q^{93} +(-4.59760 + 0.977249i) q^{94} +(-0.592557 - 0.263824i) q^{95} +(3.30524 - 1.47159i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

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