LMFDB - Embedded newform 539.2.q.b.361.2

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			361.2
Root			$-0.185798 + 1.76775i$ of defining polynomial
Character	$\chi$	$=$	539.361
Dual form			539.2.q.b.324.2

$q$-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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

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

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	0.0689729	−	0.997619i	$-0.478028\pi$
$2$	0.760494	−	0.161648i	0.537751	−	0.114302i	0.468778	+	0.883316i	$0.344694\pi$
$3$	0.0646021	+	0.614648i	0.0372981	+	0.354867i	0.997215	+	0.0745823i	$0.0237623\pi$
$3$	0.0646021	+	0.614648i	0.0372981	+	0.354867i	−0.959917	+	0.280285i	$0.909571\pi$
$4$	−1.27487	+	0.567608i	−0.637435	+	0.283804i
$5$	0.148892	−	0.165361i	0.0665866	−	0.0739519i	−0.708931	−	0.705278i	$-0.750822\pi$
$5$	0.148892	−	0.165361i	0.0665866	−	0.0739519i	0.775518	+	0.631326i	$0.217489\pi$
$6$	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	0.123798	+	0.992307i	$0.460493\pi$
$13$	−2.01774	+	6.20997i	−0.559620	+	1.72233i	−0.683418	+	0.730027i	$0.739507\pi$
$14$		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	−0.337292	−	0.941400i	$-0.609511\pi$
$17$	−4.23989	−	0.901217i	−1.02832	−	0.218577i	−0.691033	+	0.722823i	$0.742844\pi$
$18$	1.85950	−	0.827904i	0.438289	−	0.195139i
$19$	−2.66299	−	1.18564i	−0.610932	−	0.272004i	0.0778590	−	0.996964i	$-0.475192\pi$
$19$	−2.66299	−	1.18564i	−0.610932	−	0.272004i	−0.688791	+	0.724960i	$0.741858\pi$
$20$	−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	0.994482	−	0.104906i	$-0.0334540\pi$
$23$	1.94898	+	3.37573i	0.406390	+	0.703888i	−0.588092	+	0.808794i	$0.700121\pi$
$24$	−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	0.834003	−	0.551760i	$-0.186044\pi$
$29$	3.05322	+	2.21829i	0.566969	+	0.411927i	−0.267034	+	0.963687i	$0.586044\pi$
$30$	0.0976776	+	0.0434889i	0.0178334	+	0.00793994i
$31$	4.61003	+	5.11996i	0.827986	+	0.919571i	0.997826	−	0.0659001i	$-0.0209919\pi$
$31$	4.61003	+	5.11996i	0.827986	+	0.919571i	−0.169840	+	0.985472i	$0.554325\pi$
$32$	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	−0.832033	−	0.554726i	$-0.812823\pi$
$37$	0.590953	−	5.62254i	0.0971521	−	0.924340i	0.929185	−	0.369614i	$-0.120510\pi$
$38$	−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	−0.500035	−	0.866005i	$-0.666679\pi$
$41$	1.08255	−	0.786521i	0.169066	−	0.122834i	0.669101	+	0.743171i	$0.266679\pi$
$42$		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	−0.0377310	−	0.999288i	$-0.512013\pi$
$47$	−5.52287	−	2.45894i	−0.805594	−	0.358673i	−0.767863	+	0.640615i	$0.778680\pi$
$48$	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	0.659005	−	0.752138i	$-0.270977\pi$
$53$	−1.14951	−	1.27666i	−0.157897	−	0.175363i	−0.816903	+	0.576775i	$0.804311\pi$
$54$	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	0.247949	−	0.968773i	$-0.420244\pi$
$59$	8.70887	−	3.87744i	1.13380	−	0.504799i	0.885849	+	0.463974i	$0.153577\pi$
$60$	−0.187721	−	0.0399013i	−0.0242347	−	0.00515124i
$61$	6.44334	−	7.15606i	0.824986	−	0.916239i	−0.172649	−	0.984983i	$-0.555233\pi$
$61$	6.44334	−	7.15606i	0.824986	−	0.916239i	0.997634	+	0.0687442i	$0.0218992\pi$
$62$	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	−0.902245	−	0.431223i	$-0.858082\pi$
$67$	−0.635774	+	1.10119i	−0.0776722	+	0.134532i	0.824573	+	0.565756i	$0.191415\pi$
$68$	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	−0.963482	−	0.267772i	$-0.913713\pi$
$71$	−2.87670	−	8.85357i	−0.341401	−	1.05072i	0.622081	−	0.782953i	$-0.286287\pi$
$72$	−4.62470	+	5.13625i	−0.545026	+	0.605313i
$73$	−5.10591	+	2.27330i	−0.597601	+	0.266069i	−0.683166	−	0.730263i	$-0.739397\pi$
$73$	−5.10591	+	2.27330i	−0.597601	+	0.266069i	0.0855643	+	0.996333i	$0.472731\pi$
$74$	−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	0.0481897	−	0.998838i	$-0.484655\pi$
$79$	4.43056	−	0.941745i	0.498477	−	0.105955i	0.450288	+	0.892884i	$0.351321\pi$
$80$	−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	−0.938111	−	0.346336i	$-0.887426\pi$
$83$	−3.48688	−	10.7315i	−0.382734	−	1.17793i	0.555376	−	0.831599i	$-0.312574\pi$
$84$		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	0.995923	−	0.0902046i	$-0.0287521\pi$
$89$	3.96078	+	6.86028i	0.419842	+	0.727188i	−0.576081	+	0.817393i	$0.695419\pi$
$90$	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	−0.702600	−	0.711585i	$-0.747977\pi$
$97$	2.79781	−	8.61078i	0.284075	−	0.874292i	0.986674	−	0.162707i	$-0.0520225\pi$
$98$		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	0.858155	+	0.513390i	$0.171611\pi$
$101$	12.8541	+	14.2759i	1.27903	+	1.42051i	0.420876	+	0.907118i	$0.361723\pi$
$102$	−0.217715	−	2.07142i	−0.0215570	−	0.205101i
$103$	1.69737	−	16.1494i	0.167246	−	1.59124i	−0.513085	−	0.858338i	$-0.671497\pi$
$103$	1.69737	−	16.1494i	0.167246	−	1.59124i	0.680331	−	0.732905i	$-0.261836\pi$
$104$	−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	0.154513	−	0.987991i	$-0.450619\pi$
$107$	−4.92708	−	2.19368i	−0.476319	−	0.212071i	−0.630831	+	0.775920i	$0.717286\pi$
$108$	−3.24222	−	3.60086i	−0.311983	−	0.346492i
$109$	−2.69951	+	4.67568i	−0.258566	+	0.447849i	−0.965858	−	0.259072i	$-0.916583\pi$
$109$	−2.69951	+	4.67568i	−0.258566	+	0.447849i	0.707292	+	0.706921i	$0.249917\pi$
$110$	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	0.256935	−	0.966429i	$-0.417287\pi$
$113$	13.3457	−	9.69624i	1.25546	−	0.912145i	0.998526	+	0.0542834i	$0.0172875\pi$
$114$	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	0.974699	−	0.223523i	$-0.0717559\pi$
$127$	0.617194	+	1.89953i	0.0547671	+	0.168556i	−0.919931	+	0.392079i	$0.871756\pi$
$128$	−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	0.894399	−	0.447270i	$-0.147604\pi$
$131$	0.685047	+	1.18654i	0.0598528	+	0.103668i	−0.834546	+	0.550938i	$0.814270\pi$
$132$	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	0.102294	−	0.994754i	$-0.467382\pi$
$137$	−2.44463	−	0.519621i	−0.208858	−	0.0443942i	−0.311153	+	0.950360i	$0.600715\pi$
$138$	−1.25329	+	1.39192i	−0.106687	+	0.118488i
$139$	−3.85302	−	2.79938i	−0.326809	−	0.237441i	0.412266	−	0.911063i	$-0.364737\pi$
$139$	−3.85302	−	2.79938i	−0.326809	−	0.237441i	−0.739075	+	0.673623i	$0.764737\pi$
$140$		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	−0.907970	−	0.419036i	$-0.862368\pi$
$149$	−4.83772	+	5.37283i	−0.396321	+	0.440159i	0.511649	+	0.859195i	$0.329035\pi$
$150$	−2.17311	+	0.967532i	−0.177434	+	0.0789986i
$151$	−0.850829	−	8.09509i	−0.0692394	−	0.658769i	−0.973012	−	0.230756i	$-0.925880\pi$
$151$	−0.850829	−	8.09509i	−0.0692394	−	0.658769i	0.903772	−	0.428014i	$-0.140786\pi$
$152$	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	0.675253	+	0.737587i	$0.264035\pi$
$157$	2.10640	+	20.0410i	0.168109	+	1.59945i	−0.507144	+	0.861861i	$0.669299\pi$
$158$	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	−0.483699	−	0.875235i	$-0.660707\pi$
$163$	−7.27203	+	1.54572i	−0.569590	+	0.121070i	−0.0858908	+	0.996305i	$0.527374\pi$
$164$	−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	−0.921133	−	0.389248i	$-0.872735\pi$
$167$	0.683275	−	2.10290i	0.0528734	−	0.162728i	0.974006	+	0.226520i	$0.0727350\pi$
$168$		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	0.733708	−	0.679465i	$-0.237788\pi$
$173$	9.46634	+	4.21469i	0.719712	+	0.320437i	−0.0139950	+	0.999902i	$0.504455\pi$
$174$	−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	0.573186	+	0.819426i	$0.305707\pi$
$179$	2.44695	+	23.2812i	0.182894	+	1.74012i	−0.390292	+	0.920691i	$0.627626\pi$
$180$	−0.0849779	+	0.808511i	−0.00633388	+	0.0602628i
$181$	4.23851	+	13.0448i	0.315046	+	0.969611i	0.975736	+	0.218952i	$0.0702639\pi$
$181$	4.23851	+	13.0448i	0.315046	+	0.969611i	−0.660690	+	0.750659i	$0.729736\pi$
$182$		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	−0.850000	−	0.526782i	$-0.823398\pi$
$191$	1.25695	−	11.9591i	0.0909496	−	0.865328i	0.940950	−	0.338546i	$-0.109935\pi$
$192$	1.85860	+	0.395057i	0.134133	+	0.0285108i
$193$	−15.5368	−	3.30245i	−1.11836	−	0.237716i	−0.388595	−	0.921409i	$-0.627039\pi$
$193$	−15.5368	−	3.30245i	−1.11836	−	0.237716i	−0.729770	+	0.683693i	$0.760373\pi$
$194$	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	−0.457922	−	0.888993i	$-0.651406\pi$
$199$	7.63075	−	13.2168i	0.540929	−	0.936917i	0.998851	−	0.0479244i	$-0.0152607\pi$
$200$	−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	−0.809952	−	0.586496i	$-0.800507\pi$
$211$	2.76058	−	8.49620i	0.190046	−	0.584903i	0.999999	+	0.00159295i	$0.000507051\pi$
$212$	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	−0.568242	−	0.822861i	$-0.692376\pi$
$223$	0.578645	−	0.420410i	0.0387489	−	0.0281527i	0.606991	+	0.794709i	$0.292376\pi$
$224$		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	−0.239008	−	0.971018i	$-0.576822\pi$
$227$	4.86154	−	2.16450i	0.322672	−	0.143663i	0.561679	+	0.827355i	$0.310155\pi$
$228$	0.262798	+	2.50036i	0.0174042	+	0.165590i
$229$	−6.46392	+	1.37395i	−0.427148	+	0.0907930i	−0.416469	−	0.909150i	$-0.636733\pi$
$229$	−6.46392	+	1.37395i	−0.427148	+	0.0907930i	−0.0106786	+	0.999943i	$0.503399\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	9.34828	−	1.98704i	0.612426	−	0.130175i	0.108752	−	0.994069i	$-0.465315\pi$
$233$	9.34828	−	1.98704i	0.612426	−	0.130175i	0.503674	+	0.863894i	$0.331981\pi$
$234$	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	−0.410872	+	0.911693i	$0.634776\pi$
$239$	−21.7194	+	15.7801i	−1.40491	+	1.02073i	−0.994038	+	0.109034i	$0.965224\pi$
$240$	0.0993419	−	0.0211158i	0.00641249	−	0.00136302i
$241$	9.43316	−	16.3387i	0.607643	−	1.05247i	−0.383985	−	0.923340i	$-0.625448\pi$
$241$	9.43316	−	16.3387i	0.607643	−	1.05247i	0.991628	−	0.129129i	$-0.0412183\pi$
$242$	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	0.0702229	+	0.997531i	$0.477629\pi$
$251$	−9.07680	+	27.9355i	−0.572923	+	1.76328i	−0.643146	+	0.765744i	$0.722371\pi$
$252$		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	0.789685	+	0.613513i	$0.210244\pi$
$257$	−1.76824	+	16.8237i	−0.110300	+	1.04943i	−0.899985	+	0.435922i	$0.856422\pi$
$258$	−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	−0.711923	−	0.702257i	$-0.752176\pi$
$263$	4.09017	−	7.08438i	0.252211	−	0.436842i	0.964134	+	0.265415i	$0.0855091\pi$
$264$	−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	0.0178200	−	0.999841i	$-0.494327\pi$
$269$	−6.11065	−	1.29886i	−0.372573	−	0.0791928i	−0.390393	+	0.920648i	$0.627661\pi$
$270$	0.587562	+	0.124890i	0.0357579	+	0.00760057i
$271$	0.822312	−	7.82378i	0.0499519	−	0.475261i	−0.940739	−	0.339131i	$-0.889867\pi$
$271$	0.822312	−	7.82378i	0.0499519	−	0.475261i	0.990691	−	0.136130i	$-0.0434664\pi$
$272$	−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	0.934944	−	0.354794i	$-0.115449\pi$
$277$	8.06145	+	8.95315i	0.484366	+	0.537943i	−0.450579	+	0.892737i	$0.648782\pi$
$278$	−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	0.932804	+	0.360384i	$0.117354\pi$
$281$	6.53723	+	20.1195i	0.389978	+	1.20023i	−0.542826	+	0.839846i	$0.682646\pi$
$282$	0.303650	−	2.88904i	0.0180821	−	0.172040i
$283$	−2.61356	−	24.8664i	−0.155360	−	1.47815i	−0.743142	−	0.669134i	$-0.766665\pi$
$283$	−2.61356	−	24.8664i	−0.155360	−	1.47815i	0.587782	−	0.809020i	$-0.300001\pi$
$284$	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	0.576979	−	0.816759i	$-0.304231\pi$
$293$	−0.368173	−	0.267494i	−0.0215089	−	0.0156271i	−0.598488	+	0.801132i	$0.704231\pi$
$294$		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	0.994920	−	0.100666i	$-0.0320972\pi$
$311$	0.0143167	+	0.136214i	0.000811827	+	0.00772401i	−0.994108	+	0.108390i	$0.965431\pi$
$312$	9.73247	−	4.33317i	0.550993	−	0.245318i
$313$	10.2310	−	11.3626i	0.578288	−	0.642254i	−0.381036	−	0.924560i	$-0.624433\pi$
$313$	10.2310	−	11.3626i	0.578288	−	0.642254i	0.959324	+	0.282306i	$0.0910994\pi$
$314$	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	0.828051	−	0.560653i	$-0.189450\pi$
$317$	32.2716	−	6.85953i	1.81255	−	0.385270i	0.984500	+	0.175383i	$0.0561163\pi$
$318$	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	−0.911707	−	0.410842i	$-0.865235\pi$
$331$	−14.7667	−	25.5767i	−0.811653	−	1.40582i	0.100054	−	0.994982i	$-0.468099\pi$
$332$	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	0.456770	−	0.889585i	$-0.349006\pi$
$337$	−4.55497	−	3.30938i	−0.248125	−	0.180273i	−0.704895	+	0.709311i	$0.749006\pi$
$338$	−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	−0.0270988	−	0.999633i	$-0.508627\pi$
$347$	−8.53983	−	1.81520i	−0.458442	−	0.0974449i	−0.431343	+	0.902188i	$0.641960\pi$
$348$	0.340238	−	3.23715i	0.0182387	−	0.173529i
$349$	14.9401	−	10.8546i	0.799724	−	0.581034i	−0.111109	−	0.993808i	$-0.535440\pi$
$349$	14.9401	−	10.8546i	0.799724	−	0.581034i	0.910833	+	0.412774i	$0.135440\pi$
$350$		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	0.363531	+	0.931582i	$0.381571\pi$
$353$	−11.7428	+	20.3392i	−0.625009	+	1.08255i	−0.988539	+	0.150964i	$0.951762\pi$
$354$	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	0.873580	+	0.486680i	$0.161792\pi$
$359$	−1.55551	+	14.7997i	−0.0820967	+	0.781098i	−0.955677	+	0.294417i	$0.904874\pi$
$360$	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	0.633240	−	0.773956i	$-0.281725\pi$
$367$	31.2669	−	13.9209i	1.63212	−	0.726667i	0.998881	+	0.0472889i	$0.0150581\pi$
$368$	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	0.824320	−	0.566124i	$-0.191558\pi$
$373$	−1.50870	−	2.61314i	−0.0781173	−	0.135303i	−0.902438	+	0.430820i	$0.858224\pi$
$374$	−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	0.890612	−	0.454764i	$-0.150277\pi$
$379$	−1.89252	−	5.82457i	−0.0972121	−	0.299188i	−0.987824	+	0.155576i	$0.950277\pi$
$380$	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	−0.0968663	−	0.995297i	$-0.530882\pi$
$383$	4.29503	−	0.912937i	0.219466	−	0.0466489i	0.316332	+	0.948649i	$0.397549\pi$
$384$	−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	−0.148994	−	0.988838i	$-0.547603\pi$
$389$	9.58858	−	4.26911i	0.486160	−	0.216452i	0.635154	+	0.772386i	$0.280937\pi$
$390$	−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	0.972801	−	0.231640i	$-0.0744093\pi$
$397$	5.69441	+	9.86301i	0.285794	+	0.495010i	−0.687007	+	0.726651i	$0.741076\pi$
$398$	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	−0.816897	−	0.576784i	$-0.804307\pi$
$401$	−3.16161	+	3.51133i	−0.157883	+	0.175347i	0.659013	+	0.752131i	$0.270974\pi$
$402$	−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	0.700977	−	0.713184i	$-0.252748\pi$
$409$	−1.64970	−	1.83218i	−0.0815725	−	0.0905954i	−0.782549	+	0.622589i	$0.786081\pi$
$410$	−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	−0.191523	−	0.981488i	$-0.561343\pi$
$421$	14.0087	−	10.1779i	0.682744	−	0.496043i	0.874267	+	0.485446i	$0.161343\pi$
$422$	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	0.999994	+	0.00354712i	$0.00112909\pi$
$431$	18.6636	+	20.7280i	0.898994	+	0.998434i	−0.101000	+	0.994886i	$0.532204\pi$
$432$	2.34251	+	1.04295i	0.112704	+	0.0501791i
$433$	−23.9040	−	17.3673i	−1.14875	−	0.834619i	−0.160440	−	0.987046i	$-0.551291\pi$
$433$	−23.9040	−	17.3673i	−1.14875	−	0.834619i	−0.988315	+	0.152426i	$0.951291\pi$
$434$		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	−0.917376	−	0.398021i	$-0.869697\pi$
$439$	−16.8328	−	29.1552i	−0.803384	−	1.39150i	0.113992	−	0.993482i	$-0.463636\pi$
$440$	−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	0.618417	−	0.785850i	$-0.287774\pi$
$443$	9.43393	+	4.20025i	0.448219	+	0.199560i	−0.170198	+	0.985410i	$0.554441\pi$
$444$	−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	−0.969150	−	0.246471i	$-0.920729\pi$
$449$	−0.852224	+	2.62287i	−0.0402189	+	0.123781i	0.928931	+	0.370253i	$0.120729\pi$
$450$	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	−0.384484	+	0.923132i	$0.625621\pi$
$457$	−26.9864	+	29.9714i	−1.26237	+	1.40200i	−0.877885	+	0.478872i	$0.841046\pi$
$458$	−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	−0.114622	−	0.993409i	$-0.536566\pi$
$467$	19.1321	−	21.2483i	0.885326	−	0.983255i	0.999948	+	0.0101545i	$0.00323233\pi$
$468$	−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	0.0925942	−	0.995704i	$-0.470484\pi$
$479$	−4.98578	−	1.05976i	−0.227806	−	0.0484217i	−0.320400	+	0.947282i	$0.603817\pi$
$480$	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	−0.815119	−	0.579294i	$-0.803328\pi$
$487$	−3.05101	−	29.0284i	−0.138254	−	1.31540i	0.676864	−	0.736108i	$-0.263338\pi$
$488$	−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	−0.119416	−	0.992844i	$-0.538102\pi$
$491$	−24.3870	−	17.7182i	−1.10057	−	0.799610i	−0.981153	+	0.193235i	$0.938102\pi$
$492$	−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	0.971736	+	0.236070i	$0.0758595\pi$
$499$	−0.622054	+	5.91844i	−0.0278469	+	0.264946i	−0.999583	+	0.0288760i	$0.990807\pi$
$500$	−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	−0.673947	−	0.738779i	$-0.735403\pi$
$503$	−4.02773	+	2.92632i	−0.179588	+	0.130478i	0.494360	+	0.869257i	$0.335403\pi$
$504$		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	0.790248	−	0.612787i	$-0.209951\pi$
$509$	19.4846	+	8.67509i	0.863639	+	0.384517i	0.0733902	+	0.997303i	$0.476618\pi$
$510$	−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	0.0873149	−	0.996181i	$-0.472171\pi$
$521$	20.2244	−	9.00448i	0.886046	−	0.394493i	0.798732	+	0.601687i	$0.205505\pi$
$522$	7.51401	+	1.59715i	0.328879	+	0.0699054i
$523$	−3.28641	+	3.64993i	−0.143705	+	0.159600i	−0.810700	−	0.585462i	$-0.800913\pi$
$523$	−3.28641	+	3.64993i	−0.143705	+	0.159600i	0.666996	+	0.745062i	$0.267580\pi$
$524$	−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	−0.596597	−	0.802541i	$-0.703481\pi$
$541$	−18.9609	+	4.03026i	−0.815192	+	0.173274i	−0.218595	+	0.975816i	$0.570147\pi$
$542$	−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	−0.808957	−	0.587868i	$-0.799968\pi$
$547$	−11.6904	+	8.49354i	−0.499843	+	0.363158i	0.309114	+	0.951025i	$0.399968\pi$
$548$	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	−0.0168159	−	0.999859i	$-0.505353\pi$
$557$	16.8739	−	7.51276i	0.714972	−	0.318326i	0.731788	+	0.681533i	$0.238686\pi$
$558$	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	0.117693	−	0.993050i	$-0.462450\pi$
$563$	−20.9330	−	23.2484i	−0.882220	−	0.979804i	−0.999912	+	0.0132458i	$0.995784\pi$
$564$	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	0.439711	−	0.898139i	$-0.355081\pi$
$569$	1.58596	+	0.706115i	0.0664869	+	0.0296019i	−0.373224	+	0.927741i	$0.621748\pi$
$570$	−0.208552	−	0.231621i	−0.00873530	−	0.00970153i
$571$	−6.26546	+	10.8521i	−0.262201	+	0.454146i	−0.966827	−	0.255433i	$-0.917782\pi$
$571$	−6.26546	+	10.8521i	−0.262201	+	0.454146i	0.704625	+	0.709580i	$0.251115\pi$
$572$	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	0.599729	−	0.800203i	$-0.295275\pi$
$577$	19.7484	+	4.19766i	0.822138	+	0.174751i	0.222408	+	0.974954i	$0.428608\pi$
$578$	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	0.587645	−	0.809119i	$-0.300055\pi$
$587$	−0.00677611	−	0.00492314i	−0.000279680	−	0.000203200i	−0.587925	+	0.808915i	$0.700055\pi$
$588$		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	0.861480	−	0.507791i	$-0.169538\pi$
$593$	−0.219649	−	0.380443i	−0.00901989	−	0.0156229i	−0.870500	+	0.492168i	$0.836204\pi$
$594$	−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	−0.822418	−	0.568884i	$-0.807375\pi$
$599$	−44.1794	−	9.39061i	−1.80512	−	0.383690i	−0.982702	+	0.185194i	$0.940709\pi$
$600$	5.40467	−	6.00249i	0.220645	−	0.245051i
$601$	9.01541	+	6.55008i	0.367746	+	0.267183i	0.756276	−	0.654253i	$-0.227017\pi$
$601$	9.01541	+	6.55008i	0.367746	+	0.267183i	−0.388529	+	0.921436i	$0.627017\pi$
$602$		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	−0.851980	−	0.523575i	$-0.824598\pi$
$607$	−34.9196	+	7.42240i	−1.41734	+	0.301266i	−0.565365	+	0.824841i	$0.691265\pi$
$608$	−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	−0.968917	−	0.247386i	$-0.920428\pi$
$613$	−1.79768	−	17.1038i	−0.0726076	−	0.690815i	0.896309	−	0.443429i	$-0.146238\pi$
$614$	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	0.842101	+	0.539320i	$0.181319\pi$
$619$	3.24762	+	30.8990i	0.130533	+	1.24194i	−0.711568	+	0.702617i	$0.752015\pi$
$620$	−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	0.464819	−	0.885406i	$-0.346119\pi$
$631$	−5.86832	−	4.26359i	−0.233614	−	0.169731i	−0.698434	+	0.715675i	$0.746119\pi$
$632$	−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	0.950019	+	0.312192i	$0.101063\pi$
$641$	2.16896	+	20.6362i	0.0856686	+	0.815082i	−0.864350	+	0.502890i	$0.832270\pi$
$642$	0.270893	−	2.57737i	0.0106913	−	0.101721i
$643$	−2.19750	−	6.76322i	−0.0866611	−	0.266715i	0.898330	−	0.439322i	$-0.144781\pi$
$643$	−2.19750	−	6.76322i	−0.0866611	−	0.266715i	−0.984991	+	0.172606i	$0.944781\pi$
$644$		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	0.261718	−	0.965144i	$-0.415711\pi$
$647$	−18.4539	−	20.4951i	−0.725496	−	0.805745i	−0.987214	+	0.159399i	$0.949044\pi$
$648$	−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	0.910496	+	0.413518i	$0.135700\pi$
$653$	−1.68857	+	16.0656i	−0.0660787	+	0.628697i	−0.976575	+	0.215179i	$0.930966\pi$
$654$	−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	−0.909785	−	0.415080i	$-0.863753\pi$
$661$	−2.45330	+	4.24924i	−0.0954223	+	0.165276i	0.814362	+	0.580357i	$0.197087\pi$
$662$	−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	0.597524	+	0.801851i	$0.296151\pi$
$673$	−9.26654	+	28.5195i	−0.357199	+	1.09935i	−0.954723	+	0.297495i	$0.903849\pi$
$674$	−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	−0.882945	−	0.469477i	$-0.844442\pi$
$677$	−8.42364	+	9.35540i	−0.323747	+	0.359557i	0.559198	+	0.829034i	$0.311109\pi$
$678$	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	−0.452633	−	0.891697i	$-0.649515\pi$
$683$	14.2671	−	24.7114i	0.545916	−	0.945554i	0.998549	−	0.0538567i	$-0.0171514\pi$
$684$	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	0.290001	−	0.957026i	$-0.406344\pi$
$691$	24.8197	−	5.27560i	0.944188	−	0.200693i	0.654187	+	0.756333i	$0.273011\pi$
$692$	−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	0.401363	−	0.915919i	$-0.368537\pi$
$701$	36.9738	−	26.8630i	1.39648	−	1.01460i	0.995119	−	0.0986843i	$-0.0314634\pi$
$702$	−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	−0.0288664	−	0.999583i	$-0.509190\pi$
$709$	25.7819	−	28.6337i	0.968258	−	1.07536i	0.997125	−	0.0757766i	$-0.0241436\pi$
$710$	−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	−0.977770	−	0.209680i	$-0.932758\pi$
$719$	0.596034	−	5.67089i	0.0222283	−	0.211488i	0.999998	−	0.00180831i	$-0.000575603\pi$
$720$	−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	−0.964253	−	0.264981i	$-0.914634\pi$
$733$	0.921097	−	8.76365i	0.0340215	−	0.323693i	0.998275	−	0.0587114i	$-0.0186992\pi$
$734$	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	0.749033	−	0.662532i	$-0.230518\pi$
$739$	0.321724	+	0.357311i	0.0118348	+	0.0131439i	−0.737198	+	0.675676i	$0.763852\pi$
$740$	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	0.942201	+	0.335049i	$0.108753\pi$
$743$	10.2730	+	31.6172i	0.376881	+	1.15992i	−0.565319	+	0.824872i	$0.691247\pi$
$744$	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	0.816437	−	0.577435i	$-0.195946\pi$
$751$	25.5853	+	11.3913i	0.933622	+	0.415675i	0.117185	+	0.993110i	$0.462613\pi$
$752$	−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	0.744935	+	0.667137i	$0.232481\pi$
$757$	−6.87465	+	21.1580i	−0.249863	+	0.769001i	−0.994798	+	0.101864i	$0.967519\pi$
$758$	−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	−0.955982	−	0.293426i	$-0.905205\pi$
$761$	−47.1716	+	10.0266i	−1.70997	+	0.363465i	−0.753986	+	0.656891i	$0.771871\pi$
$762$	−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	0.993366	−	0.114996i	$-0.0366854\pi$
$773$	−0.0612087	−	0.582362i	−0.00220152	−	0.0209461i	−0.995568	+	0.0940496i	$0.970019\pi$
$774$	−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	0.709487	−	0.704718i	$-0.248927\pi$
$787$	30.0453	+	6.38634i	1.07100	+	0.227648i	0.361514	+	0.932367i	$0.382260\pi$
$788$	−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	0.992677	−	0.120799i	$-0.0385456\pi$
$797$	3.34767	+	10.3031i	0.118581	+	0.364953i	−0.874096	+	0.485752i	$0.838546\pi$
$798$		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	0.816308	−	0.577616i	$-0.196017\pi$
$809$	37.7468	+	8.02332i	1.32711	+	0.282085i	0.510797	+	0.859701i	$0.329350\pi$
$810$	0.103225	−	0.982124i	0.00362697	−	0.0345083i
$811$	−41.1737	+	29.9144i	−1.44580	+	1.05044i	−0.459015	+	0.888428i	$0.651798\pi$
$811$	−41.1737	+	29.9144i	−1.44580	+	1.05044i	−0.986789	+	0.162010i	$0.948202\pi$
$812$		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	−0.633370	−	0.773849i	$-0.718329\pi$
$821$	4.21348	−	40.0886i	0.147052	−	1.39910i	0.780422	−	0.625253i	$-0.215004\pi$
$822$	−0.125530	−	1.19434i	−0.00437835	−	0.0416572i
$823$	17.1844	+	19.0853i	0.599012	+	0.665270i	0.964050	−	0.265723i	$-0.0856105\pi$
$823$	17.1844	+	19.0853i	0.599012	+	0.665270i	−0.365038	+	0.930993i	$0.618944\pi$
$824$	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	0.619062	+	0.785342i	$0.287513\pi$
$827$	−9.87486	+	30.3917i	−0.343382	+	1.05682i	−0.962444	+	0.271480i	$0.912487\pi$
$828$	−13.0100	−	5.79244i	−0.452130	−	0.201301i
$829$	−44.2158	+	19.6861i	−1.53568	+	0.683728i	−0.988211	−	0.153099i	$-0.951075\pi$
$829$	−44.2158	+	19.6861i	−1.53568	+	0.683728i	−0.547467	+	0.836827i	$0.684408\pi$
$830$	−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	−0.972863	−	0.231382i	$-0.925675\pi$
$839$	−30.5133	+	22.1692i	−1.05344	+	0.765366i	−0.0805734	+	0.996749i	$0.525675\pi$
$840$		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	0.889815	−	0.456321i	$-0.150833\pi$
$853$	−2.87035	−	8.83403i	−0.0982789	−	0.302471i	−0.988094	+	0.153849i	$0.950833\pi$
$854$		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	0.491588	+	0.870828i	$0.336417\pi$
$857$	−14.8822	+	25.7767i	−0.508365	+	0.880515i	−0.999953	+	0.00968670i	$0.996917\pi$
$858$	−7.79510	−	6.89354i	−0.266120	−	0.235342i
$859$	16.6305	+	28.8050i	0.567427	+	0.982812i	0.996819	+	0.0796943i	$0.0253944\pi$
$859$	16.6305	+	28.8050i	0.567427	+	0.982812i	−0.429392	+	0.903118i	$0.641272\pi$
$860$	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	−0.916521	−	0.399986i	$-0.869015\pi$
$863$	−12.4242	+	13.7985i	−0.422924	+	0.469705i	0.493597	+	0.869691i	$0.335682\pi$
$864$	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	0.0293463	−	0.999569i	$-0.490657\pi$
$877$	−20.5476	−	9.14837i	−0.693842	−	0.308918i	−0.723188	+	0.690651i	$0.757324\pi$
$878$	−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	−0.282305	−	0.959325i	$-0.591099\pi$
$883$	16.1304	−	11.7194i	0.542830	−	0.394389i	0.825135	+	0.564936i	$0.191099\pi$
$884$	−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	−0.975515	−	0.219934i	$-0.929416\pi$
$887$	0.726975	−	6.91671i	0.0244094	−	0.232240i	0.999924	−	0.0123067i	$-0.00391744\pi$
$888$	−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	0.572177	−	0.820130i	$-0.306099\pi$
$907$	22.9279	+	4.87348i	0.761309	+	0.161821i	0.189132	+	0.981952i	$0.439432\pi$
$908$	−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	−0.360899	−	0.932605i	$-0.617530\pi$
$911$	14.4650	−	44.5186i	0.479246	−	1.47497i	0.840145	−	0.542362i	$-0.182470\pi$
$912$	−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	−0.614354	−	0.789031i	$-0.710583\pi$
$919$	7.11106	−	7.89763i	0.234572	−	0.260519i	0.848926	+	0.528512i	$0.177250\pi$
$920$	−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	−0.191113	−	0.981568i	$-0.561210\pi$
$929$	24.5377	−	27.2518i	0.805054	−	0.894104i	0.996168	+	0.0874645i	$0.0278764\pi$
$930$	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	−0.514057	−	0.857756i	$-0.671858\pi$
$937$	12.4278	−	38.2490i	0.406000	−	1.24954i	0.920057	−	0.391784i	$-0.128142\pi$
$938$		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	0.587147	−	0.809480i	$-0.300251\pi$
$941$	24.3653	+	5.17901i	0.794287	+	0.168831i	0.207140	+	0.978311i	$0.433584\pi$
$942$	−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	0.999633	+	0.0270927i	$0.00862493\pi$
$947$	16.1031	+	27.8913i	0.523279	+	0.906347i	−0.476353	+	0.879254i	$0.658042\pi$
$948$	−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	−0.188628	−	0.982049i	$-0.560404\pi$
$953$	−36.4552	−	26.4863i	−1.18090	−	0.857975i	−0.992273	+	0.124074i	$0.960404\pi$
$954$	−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	0.0399480	−	0.999202i	$-0.487281\pi$
$971$	−21.0608	−	9.37687i	−0.675873	−	0.300918i	−0.715821	+	0.698284i	$0.753947\pi$
$972$	−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	0.662407	−	0.749145i	$-0.269535\pi$
$977$	−4.74714	−	5.27223i	−0.151875	−	0.168674i	−0.814281	+	0.580471i	$0.802869\pi$
$978$	−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	−0.880516	−	0.474017i	$-0.842804\pi$
$983$	−35.0347	+	15.5984i	−1.11743	+	0.497513i	−0.236917	+	0.971530i	$0.576137\pi$
$984$	−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	−0.980897	−	0.194527i	$-0.937683\pi$
$991$	−10.1361	+	17.5562i	−0.321984	+	0.557692i	0.658914	+	0.752219i	$0.271016\pi$
$992$	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	−0.617373	−	0.786670i	$-0.711803\pi$
$997$	−14.0784	+	6.26810i	−0.445867	+	0.198513i	0.171506	+	0.985183i	$0.445137\pi$
$998$	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.361.2		16
7.2	even	3	inner	539.2.q.b.471.1		16
7.3	odd	6		77.2.f.a.64.1	✓	8
7.4	even	3		539.2.f.d.295.1		8
7.5	odd	6		539.2.q.c.471.1		16
7.6	odd	2		539.2.q.c.361.2		16
11.5	even	5	inner	539.2.q.b.214.1		16
21.17	even	6		693.2.m.g.64.2		8
77.3	odd	30		847.2.f.p.323.2		8
77.4	even	15		5929.2.a.bi.1.2		4
77.5	odd	30		539.2.q.c.324.2		16
77.10	even	6		847.2.f.q.372.2		8
77.16	even	15	inner	539.2.q.b.324.2		16
77.17	even	30		847.2.f.q.148.2		8
77.18	odd	30		5929.2.a.bb.1.3		4
77.24	even	30		847.2.f.s.729.1		8
77.27	odd	10		539.2.q.c.214.1		16
77.31	odd	30		847.2.f.p.729.2		8
77.38	odd	30		77.2.f.a.71.1	yes	8
77.52	even	30		847.2.f.s.323.1		8
77.59	odd	30		847.2.a.l.1.2		4
77.60	even	15		539.2.f.d.148.1		8
77.73	even	30		847.2.a.k.1.3		4
231.38	even	30		693.2.m.g.379.2		8
231.59	even	30		7623.2.a.ch.1.3		4
231.227	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	7.3	odd	6
77.2.f.a.71.1	yes	8	77.38	odd	30
539.2.f.d.148.1		8	77.60	even	15
539.2.f.d.295.1		8	7.4	even	3
539.2.q.b.214.1		16	11.5	even	5	inner
539.2.q.b.324.2		16	77.16	even	15	inner
539.2.q.b.361.2		16	1.1	even	1	trivial
539.2.q.b.471.1		16	7.2	even	3	inner
539.2.q.c.214.1		16	77.27	odd	10
539.2.q.c.324.2		16	77.5	odd	30
539.2.q.c.361.2		16	7.6	odd	2
539.2.q.c.471.1		16	7.5	odd	6
693.2.m.g.64.2		8	21.17	even	6
693.2.m.g.379.2		8	231.38	even	30
847.2.a.k.1.3		4	77.73	even	30
847.2.a.l.1.2		4	77.59	odd	30
847.2.f.p.323.2		8	77.3	odd	30
847.2.f.p.729.2		8	77.31	odd	30
847.2.f.q.148.2		8	77.17	even	30
847.2.f.q.372.2		8	77.10	even	6
847.2.f.s.323.1		8	77.52	even	30
847.2.f.s.729.1		8	77.24	even	30
5929.2.a.bb.1.3		4	77.18	odd	30
5929.2.a.bi.1.2		4	77.4	even	15
7623.2.a.ch.1.3		4	231.59	even	30
7623.2.a.co.1.2		4	231.227	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more