LMFDB - Embedded newform 539.2.f.d.148.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.1
Root			$-0.628998 + 0.456994i$ of defining polynomial
Character	$\chi$	$=$	539.148
Dual form			539.2.f.d.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.240256 - 0.739431i) q^{2} +(0.500000 + 0.363271i) q^{3} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})$	\(q+(-0.240256 - 0.739431i) q^{2} +(0.500000 + 0.363271i) q^{3} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-0.809017 - 2.48990i) q^{9} -0.173002 q^{10} +(0.660531 + 3.25018i) q^{11} +0.862478 q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(0.228211 - 0.702362i) q^{16} +(1.33947 - 4.12246i) q^{17} +(-1.64674 + 1.19643i) q^{18} +(2.35829 + 1.71340i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} -3.89796 q^{23} +(-0.504188 - 1.55173i) q^{24} +(4.00503 + 2.90982i) q^{25} +(-4.10707 + 2.98396i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(-0.0865012 - 0.0628468i) q^{30} +(2.12900 + 6.55238i) q^{31} -5.85410 q^{32} +(-0.850433 + 1.86504i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(4.57379 - 3.32305i) q^{37} +(0.700347 - 2.15545i) q^{38} +(1.24703 - 3.83797i) q^{39} +(-0.475243 + 0.345285i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(3.41175 + 3.12764i) q^{44} -0.582554 q^{45} +(0.936507 + 2.88227i) q^{46} +(4.89094 + 3.55348i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(2.16731 - 1.57464i) q^{51} +(-7.37184 - 5.35596i) q^{52} +(-0.530865 - 1.63383i) q^{53} -2.69953 q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(-2.37383 - 1.72469i) q^{58} +(-7.71239 + 5.60338i) q^{59} +(0.0593050 - 0.182522i) q^{60} +(2.97566 - 9.15813i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} -1.45293 q^{65} +(1.58339 + 0.180749i) q^{66} +1.27155 q^{67} +(-1.86925 - 5.75297i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(-2.13577 + 6.57324i) q^{72} +(4.52169 - 3.28520i) q^{73} +(-3.55605 - 2.58362i) q^{74} +(0.945459 + 2.90982i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-1.39971 - 4.30785i) q^{79} +(-0.132945 - 0.0965905i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(0.321489 - 0.989441i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(1.13117 + 3.48139i) q^{86} +2.33245 q^{87} +(3.63267 - 7.96663i) q^{88} -7.92157 q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(-1.31579 + 4.04959i) q^{93} +(1.45248 - 4.47026i) q^{94} +(0.524757 - 0.381258i) q^{95} +(-2.92705 - 2.12663i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.240256	−	0.739431i	−0.169887	−	0.522857i	0.829477	−	0.558542i	$-0.188639\pi$
$2$	−0.240256	−	0.739431i	−0.169887	−	0.522857i	−0.999363	+	0.0356845i	$0.988639\pi$
$3$	0.500000	+	0.363271i	0.288675	+	0.209735i	0.722692	−	0.691170i	$-0.242904\pi$
$3$	0.500000	+	0.363271i	0.288675	+	0.209735i	−0.434017	+	0.900905i	$0.642904\pi$
$4$	1.12900	−	0.820265i	0.564499	−	0.410133i
$5$	0.0687611	−	0.211625i	0.0307509	−	0.0946416i	−0.934503	−	0.355955i	$-0.884156\pi$
$5$	0.0687611	−	0.211625i	0.0307509	−	0.0946416i	0.965254	+	0.261313i	$0.0841556\pi$
$6$	0.148486	−	0.456994i	0.0606193	−	0.186567i
$7$		0			0
$7$		0			0
$8$	−2.13577	−	1.55173i	−0.755110	−	0.548620i
$9$	−0.809017	−	2.48990i	−0.269672	−	0.829966i
$10$	−0.173002			−0.0547082
$11$	0.660531	+	3.25018i	0.199158	+	0.979967i
$11$	0.660531	+	3.25018i	0.199158	+	0.979967i
$12$	0.862478			0.248976
$13$	−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
$16$	0.228211	−	0.702362i	0.0570529	−	0.175591i
$17$	1.33947	−	4.12246i	0.324869	−	0.999844i	−0.646631	−	0.762803i	$-0.723822\pi$
$17$	1.33947	−	4.12246i	0.324869	−	0.999844i	0.971500	−	0.237041i	$-0.0761775\pi$
$18$	−1.64674	+	1.19643i	−0.388140	+	0.282000i
$19$	2.35829	+	1.71340i	0.541029	+	0.393080i	0.824467	−	0.565910i	$-0.191475\pi$
$19$	2.35829	+	1.71340i	0.541029	+	0.393080i	−0.283438	+	0.958991i	$0.591475\pi$
$20$	−0.0959574	−	0.295327i	−0.0214567	−	0.0660370i
$21$		0			0
$22$	2.24459	−	1.26929i	0.478549	−	0.270614i
$23$	−3.89796			−0.812780			−0.406390	−	0.913700i	$-0.633213\pi$
$23$	−3.89796			−0.812780			−0.406390	+	0.913700i	$0.633213\pi$
$24$	−0.504188	−	1.55173i	−0.102917	−	0.316746i
$25$	4.00503	+	2.90982i	0.801006	+	0.581965i
$26$	−4.10707	+	2.98396i	−0.805463	+	0.585203i
$27$	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	$0.186044\pi$
$30$	−0.0865012	−	0.0628468i	−0.0157929	−	0.0114742i
$31$	2.12900	+	6.55238i	0.382379	+	1.17684i	0.938364	+	0.345650i	$0.112341\pi$
$31$	2.12900	+	6.55238i	0.382379	+	1.17684i	−0.555984	+	0.831193i	$0.687659\pi$
$32$	−5.85410			−1.03487
$33$	−0.850433	+	1.86504i	−0.148041	+	0.324662i
$34$	−3.37009			−0.577966
$35$		0			0
$36$	−2.95576	−	2.14748i	−0.492626	−	0.357914i
$37$	4.57379	−	3.32305i	0.751926	−	0.546306i	−0.144497	−	0.989505i	$-0.546156\pi$
$37$	4.57379	−	3.32305i	0.751926	−	0.546306i	0.896423	+	0.443199i	$0.146156\pi$
$38$	0.700347	−	2.15545i	0.113611	−	0.349660i
$39$	1.24703	−	3.83797i	0.199685	−	0.614567i
$40$	−0.475243	+	0.345285i	−0.0751426	+	0.0545943i
$41$	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	$0.616881\pi$
$44$	3.41175	+	3.12764i	0.514341	+	0.471510i
$45$	−0.582554			−0.0868420
$46$	0.936507	+	2.88227i	0.138080	+	0.424968i
$47$	4.89094	+	3.55348i	0.713417	+	0.518328i	0.884274	−	0.466968i	$-0.154654\pi$
$47$	4.89094	+	3.55348i	0.713417	+	0.518328i	−0.170857	+	0.985296i	$0.554654\pi$
$48$	0.369254	−	0.268279i	0.0532972	−	0.0387227i
$49$		0			0
$50$	1.18938	−	3.66055i	0.168204	−	0.517679i
$51$	2.16731	−	1.57464i	0.303484	−	0.220494i
$52$	−7.37184	−	5.35596i	−1.02229	−	0.742738i
$53$	−0.530865	−	1.63383i	−0.0729199	−	0.224424i	0.907954	−	0.419071i	$-0.137644\pi$
$53$	−0.530865	−	1.63383i	−0.0729199	−	0.224424i	−0.980873	+	0.194646i	$0.937644\pi$
$54$	−2.69953			−0.367360
$55$	0.733239	+	0.0837016i	0.0988700	+	0.0112863i
$56$		0			0
$57$	0.556717	+	1.71340i	0.0737389	+	0.226945i
$58$	−2.37383	−	1.72469i	−0.311699	−	0.226463i
$59$	−7.71239	+	5.60338i	−1.00407	+	0.729498i	−0.962957	−	0.269657i	$-0.913090\pi$
$59$	−7.71239	+	5.60338i	−1.00407	+	0.729498i	−0.0411113	+	0.999155i	$0.513090\pi$
$60$	0.0593050	−	0.182522i	0.00765624	−	0.0235635i
$61$	2.97566	−	9.15813i	0.380994	−	1.17258i	−0.558351	−	0.829605i	$-0.688566\pi$
$61$	2.97566	−	9.15813i	0.380994	−	1.17258i	0.939345	−	0.342974i	$-0.111434\pi$
$62$	4.33353	−	3.14850i	0.550359	−	0.399859i
$63$		0			0
$64$	0.950059	+	2.92398i	0.118757	+	0.365498i
$65$	−1.45293			−0.180213
$66$	1.58339	+	0.180749i	0.194902	+	0.0222487i
$67$	1.27155			0.155344			0.0776722	−	0.996979i	$-0.475251\pi$
$67$	1.27155			0.155344			0.0776722	+	0.996979i	$0.475251\pi$
$68$	−1.86925	−	5.75297i	−0.226680	−	0.697650i
$69$	−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	$0.913713\pi$
$72$	−2.13577	+	6.57324i	−0.251703	+	0.774663i
$73$	4.52169	−	3.28520i	0.529223	−	0.384503i	−0.290844	−	0.956771i	$-0.593936\pi$
$73$	4.52169	−	3.28520i	0.529223	−	0.384503i	0.820067	+	0.572267i	$0.193936\pi$
$74$	−3.55605	−	2.58362i	−0.413382	−	0.300340i
$75$	0.945459	+	2.90982i	0.109172	+	0.335997i
$76$	4.06794			0.466625
$77$		0			0
$78$	−3.13752			−0.355254
$79$	−1.39971	−	4.30785i	−0.157479	−	0.484671i	0.840924	−	0.541153i	$-0.182012\pi$
$79$	−1.39971	−	4.30785i	−0.157479	−	0.484671i	−0.998404	+	0.0564813i	$0.982012\pi$
$80$	−0.132945	−	0.0965905i	−0.0148638	−	0.0107991i
$81$	−4.61803	+	3.35520i	−0.513115	+	0.372800i
$82$	0.321489	−	0.989441i	0.0355025	−	0.109265i
$83$	−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
$86$	1.13117	+	3.48139i	0.121978	+	0.375408i
$87$	2.33245			0.250065
$88$	3.63267	−	7.96663i	0.387244	−	0.849245i
$89$	−7.92157			−0.839684			−0.419842	−	0.907597i	$-0.637915\pi$
$89$	−7.92157			−0.839684			−0.419842	+	0.907597i	$0.637915\pi$
$90$	0.139962	+	0.430759i	0.0147533	+	0.0454059i
$91$		0			0
$92$	−4.40079	+	3.19736i	−0.458814	+	0.333348i
$93$	−1.31579	+	4.04959i	−0.136441	+	0.419923i
$94$	1.45248	−	4.47026i	0.149811	−	0.461072i
$95$	0.524757	−	0.381258i	0.0538389	−	0.0391162i
$96$	−2.92705	−	2.12663i	−0.298741	−	0.217048i
$97$	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
$100$	6.90849			0.690849
$101$	5.93627	+	18.2700i	0.590681	+	1.81793i	0.575149	+	0.818049i	$0.304944\pi$
$101$	5.93627	+	18.2700i	0.590681	+	1.81793i	0.0155316	+	0.999879i	$0.495056\pi$
$102$	−1.68505	−	1.22426i	−0.166845	−	0.121220i
$103$	13.1371	−	9.54464i	1.29443	−	0.940461i	0.294549	−	0.955636i	$-0.404831\pi$
$103$	13.1371	−	9.54464i	1.29443	−	0.940461i	0.999885	+	0.0151755i	$0.00483070\pi$
$104$	−5.32676	+	16.3941i	−0.522332	+	1.60757i
$105$		0			0
$106$	−1.08057	+	0.785077i	−0.104954	+	0.0762534i
$107$	4.36332	+	3.17014i	0.421818	+	0.306469i	0.778369	−	0.627807i	$-0.216047\pi$
$107$	4.36332	+	3.17014i	0.421818	+	0.306469i	−0.356551	+	0.934276i	$0.616047\pi$
$108$	−1.49732	−	4.60828i	−0.144080	−	0.443432i
$109$	5.39901			0.517132			0.258566	−	0.965994i	$-0.416750\pi$
$109$	5.39901			0.517132			0.258566	+	0.965994i	$0.416750\pi$
$110$	−0.114273	−	0.562290i	−0.0108955	−	0.0536122i
$111$	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	$0.417287\pi$
$114$	1.13319	−	0.823308i	0.106133	−	0.0771098i
$115$	−0.268028	+	0.824906i	−0.0249937	+	0.0769228i
$116$	1.62749	−	5.00890i	0.151109	−	0.465065i
$117$	−13.8298	+	10.0479i	−1.27857	+	0.928932i
$118$	5.99626	+	4.35654i	0.552001	+	0.401052i
$119$		0			0
$120$	−0.363054			−0.0331421
$121$	−10.1274	+	4.29369i	−0.920673	+	0.390336i
$122$	−7.48673			−0.677816
$123$	0.255556	+	0.786521i	0.0230427	+	0.0709182i
$124$	7.77832	+	5.65128i	0.698514	+	0.507500i
$125$	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	$0.0717559\pi$
$128$	−7.53831	+	5.47690i	−0.666299	+	0.484094i
$129$	−2.35410	−	1.71036i	−0.207267	−	0.150588i
$130$	0.349074	+	1.07434i	0.0306158	+	0.0942258i
$131$	−1.37009			−0.119706			−0.0598528	−	0.998207i	$-0.519063\pi$
$131$	−1.37009			−0.119706			−0.0598528	+	0.998207i	$0.519063\pi$
$132$	0.569693	+	2.80321i	0.0495854	+	0.243988i
$133$		0			0
$134$	−0.305497	−	0.940223i	−0.0263909	−	0.0812229i
$135$	−0.625051	−	0.454126i	−0.0537958	−	0.0390849i
$136$	−9.25776	+	6.72615i	−0.793846	+	0.576763i
$137$	0.772308	−	2.37692i	0.0659827	−	0.203074i	−0.912629	−	0.408788i	$-0.865952\pi$
$137$	0.772308	−	2.37692i	0.0659827	−	0.203074i	0.978612	+	0.205714i	$0.0659516\pi$
$138$	−0.578793	+	1.78134i	−0.0492702	+	0.151638i
$139$	−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
$142$	7.23775			0.607378
$143$	18.8508	−	10.6599i	1.57638	−	0.891426i
$144$	−1.93344			−0.161120
$145$	−0.259504	−	0.798670i	−0.0215506	−	0.0663260i
$146$	−3.51554	−	2.55419i	−0.290948	−	0.211386i
$147$		0			0
$148$	2.43801	−	7.50344i	0.200404	−	0.616779i
$149$	−2.23415	+	6.87600i	−0.183028	+	0.563304i	−0.999909	−	0.0135034i	$-0.995702\pi$
$149$	−2.23415	+	6.87600i	−0.183028	+	0.563304i	0.816880	+	0.576807i	$0.195702\pi$
$150$	1.92446	−	1.39820i	0.157132	−	0.114163i
$151$	−6.58514	−	4.78439i	−0.535891	−	0.389348i	0.286666	−	0.958031i	$-0.407453\pi$
$151$	−6.58514	−	4.78439i	−0.535891	−	0.389348i	−0.822557	+	0.568683i	$0.807453\pi$
$152$	−2.37804	−	7.31886i	−0.192885	−	0.593638i
$153$	−11.3482			−0.917445
$154$		0			0
$155$	1.53304			0.123137
$156$	−1.74026	−	5.35596i	−0.139332	−	0.428820i
$157$	16.3028	+	11.8447i	1.30111	+	0.945311i	0.999966	−	0.00826862i	$-0.00263201\pi$
$157$	16.3028	+	11.8447i	1.30111	+	0.945311i	0.301143	+	0.953579i	$0.402632\pi$
$158$	−2.84907	+	2.06997i	−0.226660	+	0.164678i
$159$	0.328093	−	1.00977i	0.0260194	−	0.0800796i
$160$	−0.402535	+	1.23887i	−0.0318232	+	0.0979416i
$161$		0			0
$162$	3.59045	+	2.60861i	0.282092	+	0.204952i
$163$	2.29739	+	7.07062i	0.179945	+	0.553814i	0.999825	−	0.0187219i	$-0.00595970\pi$
$163$	2.29739	+	7.07062i	0.179945	+	0.553814i	−0.819880	+	0.572536i	$0.805960\pi$
$164$	1.86736			0.145816
$165$	0.336213	+	0.308216i	0.0261742	+	0.0239945i
$166$	8.77295			0.680913
$167$	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
$170$	−0.231732	+	0.713196i	−0.0177730	+	0.0546997i
$171$	2.35829	−	7.25807i	0.180343	−	0.555038i
$172$	−5.31555	+	3.86198i	−0.405307	+	0.294473i
$173$	−8.38320	−	6.09075i	−0.637363	−	0.463071i	0.221581	−	0.975142i	$-0.428878\pi$
$173$	−8.38320	−	6.09075i	−0.637363	−	0.463071i	−0.858943	+	0.512071i	$0.828878\pi$
$174$	−0.560385	−	1.72469i	−0.0424827	−	0.130748i
$175$		0			0
$176$	2.43355	+	0.277797i	0.183436	+	0.0209398i
$177$	−5.89174			−0.442851
$178$	1.90320	+	5.85746i	0.142651	+	0.439035i
$179$	18.9386	+	13.7597i	1.41554	+	1.02845i	0.992488	+	0.122343i	$0.0390408\pi$
$179$	18.9386	+	13.7597i	1.41554	+	1.02845i	0.423051	+	0.906106i	$0.360959\pi$
$180$	−0.657702	+	0.477849i	−0.0490222	+	0.0356167i
$181$	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
$184$	8.32516	+	6.04858i	0.613739	+	0.445907i
$185$	−0.388742	−	1.19643i	−0.0285809	−	0.0879629i
$186$	3.31052			0.242739
$187$	14.2835	+	1.63051i	1.04451	+	0.119235i
$188$	8.43666			0.615306
$189$		0			0
$190$	−0.407990	−	0.296422i	−0.0295987	−	0.0215047i
$191$	9.72838	−	7.06808i	0.703921	−	0.511429i	−0.177286	−	0.984159i	$-0.556732\pi$
$191$	9.72838	−	7.06808i	0.703921	−	0.511429i	0.881207	+	0.472731i	$0.156732\pi$
$192$	−0.587169	+	1.80712i	−0.0423753	+	0.130418i
$193$	4.90840	−	15.1065i	0.353315	−	1.08739i	−0.603666	−	0.797238i	$-0.706294\pi$
$193$	4.90840	−	15.1065i	0.353315	−	1.08739i	0.956980	−	0.290153i	$-0.0937062\pi$
$194$	5.69489	−	4.13758i	0.408869	−	0.297061i
$195$	−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	$0.355582\pi$
$198$	−4.97632	−	4.56193i	−0.353652	−	0.324202i
$199$	−15.2615			−1.08186			−0.540929	−	0.841068i	$-0.681927\pi$
$199$	−15.2615			−1.08186			−0.540929	+	0.841068i	$0.681927\pi$
$200$	−4.03857	−	12.4294i	−0.285570	−	0.878895i
$201$	0.635774	+	0.461917i	0.0448440	+	0.0325811i
$202$	12.0832	−	8.77892i	0.850168	−	0.617683i
$203$		0			0
$204$	1.15526	−	3.55553i	0.0808845	−	0.248937i
$205$	0.240885	−	0.175013i	0.0168242	−	0.0122235i
$206$	−10.2139	−	7.42080i	−0.711633	−	0.517032i
$207$	3.15351	+	9.70552i	0.219184	+	0.674580i
$208$	−4.82212			−0.334354
$209$	−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	$0.800507\pi$
$212$	−1.93952	−	1.40915i	−0.133207	−	0.0967805i
$213$	−4.65459	+	3.38176i	−0.318928	+	0.231714i
$214$	1.29579	−	3.98802i	0.0885781	−	0.272615i
$215$	−0.323742	+	0.996374i	−0.0220790	+	0.0679521i
$216$	−7.41570	+	5.38782i	−0.504574	+	0.366595i
$217$		0			0
$218$	−1.29714	−	3.99220i	−0.0878537	−	0.270386i
$219$	3.45426			0.233417
$220$	0.896483	−	0.506952i	0.0604409	−	0.0341787i
$221$	−28.3031			−1.90387
$222$	−0.839469	−	2.58362i	−0.0563415	−	0.173401i
$223$	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
$226$	3.96331	−	12.1978i	0.263636	−	0.811387i
$227$	−4.30528	+	3.12797i	−0.285751	+	0.207611i	−0.721422	−	0.692496i	$-0.756511\pi$
$227$	−4.30528	+	3.12797i	−0.285751	+	0.207611i	0.435671	+	0.900106i	$0.356511\pi$
$228$	2.03397	+	1.47777i	0.134703	+	0.0978675i
$229$	2.04208	+	6.28489i	0.134945	+	0.415317i	0.995581	−	0.0939024i	$-0.0299341\pi$
$229$	2.04208	+	6.28489i	0.134945	+	0.415317i	−0.860637	+	0.509219i	$0.829934\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	−2.95332	−	9.08937i	−0.193478	−	0.595464i	−0.999991	−	0.00424788i	$-0.998648\pi$
$233$	−2.95332	−	9.08937i	−0.193478	−	0.595464i	0.806513	−	0.591217i	$-0.201352\pi$
$234$	10.7524	+	7.81211i	0.702910	+	0.510694i
$235$	1.08831	−	0.790705i	0.0709936	−	0.0515799i
$236$	−4.11102	+	12.6524i	−0.267604	+	0.823602i
$237$	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	$-0.634776\pi$
$240$	−0.0313842	−	0.0965905i	−0.00202584	−	0.00623489i
$241$	−18.8663			−1.21529			−0.607643	−	0.794210i	$-0.707885\pi$
$241$	−18.8663			−1.21529			−0.607643	+	0.794210i	$0.707885\pi$
$242$	5.60806	+	6.45693i	0.360500	+	0.415067i
$243$	−13.9443			−0.894525
$244$	−4.15258	−	12.7803i	−0.265842	−	0.818177i
$245$		0			0
$246$	0.520180	−	0.377933i	0.0331654	−	0.0240961i
$247$	5.88173	−	18.1021i	0.374245	−	1.15181i
$248$	5.62047	−	17.2980i	0.356900	−	1.09843i
$249$	−5.64188	+	4.09907i	−0.357540	+	0.259768i
$250$	−1.39269	−	1.01185i	−0.0880814	−	0.0639949i
$251$	−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
$254$	−1.55285			−0.0974348
$255$	−0.184207	−	0.566931i	−0.0115355	−	0.0355026i
$256$	10.8355	+	7.87245i	0.677218	+	0.492028i
$257$	−13.6856	+	9.94320i	−0.853687	+	0.620240i	−0.926160	−	0.377130i	$-0.876911\pi$
$257$	−13.6856	+	9.94320i	−0.853687	+	0.620240i	0.0724730	+	0.997370i	$0.476911\pi$
$258$	−0.699104	+	2.15162i	−0.0435243	+	0.133954i
$259$		0			0
$260$	−1.64035	+	1.19178i	−0.101730	+	0.0739114i
$261$	−7.99343	−	5.80757i	−0.494781	−	0.359480i
$262$	0.329173	+	1.01309i	0.0203364	+	0.0625889i
$263$	−8.18034			−0.504421			−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034			−0.504421			−0.252211	+	0.967672i	$0.581158\pi$
$264$	4.71038	−	2.66367i	0.289904	−	0.163938i
$265$	−0.382263			−0.0234822
$266$		0			0
$267$	−3.96078	−	2.87768i	−0.242396	−	0.176111i
$268$	1.43558	−	1.04301i	0.0876917	−	0.0637118i
$269$	1.93048	−	5.94140i	0.117703	−	0.362254i	−0.874798	−	0.484488i	$-0.839006\pi$
$269$	1.93048	−	5.94140i	0.117703	−	0.362254i	0.992501	+	0.122234i	$0.0390059\pi$
$270$	−0.185623	+	0.571288i	−0.0112966	+	0.0347675i
$271$	6.36444	−	4.62403i	0.386612	−	0.280890i	−0.377454	−	0.926028i	$-0.623200\pi$
$271$	6.36444	−	4.62403i	0.386612	−	0.280890i	0.764066	+	0.645138i	$0.223200\pi$
$272$	−2.58978	−	1.88159i	−0.157029	−	0.114088i
$273$		0			0
$274$	−1.94312			−0.117388
$275$	−6.81202	+	14.9391i	−0.410780	+	0.900862i
$276$	−3.36190			−0.202363
$277$	3.72293	+	11.4580i	0.223689	+	0.688444i	0.998422	+	0.0561556i	$0.0178843\pi$
$277$	3.72293	+	11.4580i	0.223689	+	0.688444i	−0.774733	+	0.632289i	$0.782116\pi$
$278$	2.99566	+	2.17648i	0.179668	+	0.130536i
$279$	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	$-0.117354\pi$
$282$	2.35015	−	1.70749i	0.139950	−	0.101679i
$283$	−20.2281	−	14.6966i	−1.20244	−	0.873623i	−0.207916	−	0.978147i	$-0.566668\pi$
$283$	−20.2281	−	14.6966i	−1.20244	−	0.873623i	−0.994522	+	0.104524i	$0.966668\pi$
$284$	4.01448	+	12.3553i	0.238216	+	0.733153i
$285$	0.400878			0.0237460
$286$	−12.4113	−	11.3777i	−0.733894	−	0.672780i
$287$		0			0
$288$	4.73607	+	14.5761i	0.279075	+	0.858906i
$289$	−1.44723	−	1.05147i	−0.0851312	−	0.0618515i
$290$	−0.528215	+	0.383770i	−0.0310178	+	0.0225358i
$291$	−1.72914	+	5.32176i	−0.101364	+	0.311967i
$292$	2.41024	−	7.41796i	0.141049	−	0.434104i
$293$	−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
$296$	−14.9251			−0.867502
$297$	11.4415	+	1.30608i	0.663901	+	0.0757864i
$298$	5.62110			0.325621
$299$	7.86507	+	24.2062i	0.454849	+	1.39988i
$300$	3.45425	+	2.50966i	0.199431	+	0.144895i
$301$		0			0
$302$	−1.95561	+	6.01874i	−0.112533	+	0.346339i
$303$	−3.66881	+	11.2915i	−0.210768	+	0.648677i
$304$	1.74162	−	1.26536i	0.0998885	−	0.0725732i
$305$	−1.73348	−	1.25945i	−0.0992588	−	0.0721157i
$306$	2.72646	+	8.39119i	0.155862	+	0.479692i
$307$	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
$310$	−0.368322	−	1.13358i	−0.0209193	−	0.0643829i
$311$	0.110807	+	0.0805059i	0.00628328	+	0.00456507i	0.590922	−	0.806728i	$-0.298764\pi$
$311$	0.110807	+	0.0805059i	0.00628328	+	0.00456507i	−0.584639	+	0.811293i	$0.698764\pi$
$312$	−8.61887	+	6.26198i	−0.487948	+	0.354515i
$313$	4.72485	−	14.5416i	0.267064	−	0.821939i	−0.724146	−	0.689646i	$-0.757766\pi$
$313$	4.72485	−	14.5416i	0.267064	−	0.821939i	0.991211	−	0.132293i	$-0.0422340\pi$
$314$	4.84150	−	14.9006i	0.273221	−	0.840889i
$315$		0			0
$316$	−5.11385	−	3.71543i	−0.287676	−	0.209009i
$317$	−10.1953	−	31.3778i	−0.572622	−	1.76235i	−0.644136	−	0.764911i	$-0.722783\pi$
$317$	−10.1953	−	31.3778i	−0.572622	−	1.76235i	0.0715138	−	0.997440i	$-0.477217\pi$
$318$	−0.825478			−0.0462905
$319$	9.22661	+	8.45828i	0.516591	+	0.473573i
$320$	0.684115			0.0382432
$321$	1.03004	+	3.17014i	0.0574912	+	0.176940i
$322$		0			0
$323$	10.2223	−	7.42692i	0.568783	−	0.413245i
$324$	−2.46160	+	7.57602i	−0.136756	+	0.420890i
$325$	9.98880	−	30.7424i	0.554079	−	1.70528i
$326$	4.67628	−	3.39752i	0.258995	−	0.188171i
$327$	2.69951	+	1.96131i	0.149283	+	0.108461i
$328$	−1.09162	−	3.35966i	−0.0602747	−	0.185506i
$329$		0			0
$330$	0.147127	−	0.322657i	0.00809908	−	0.0177617i
$331$	29.5335			1.62331			0.811653	−	0.584140i	$-0.198568\pi$
$331$	29.5335			1.62331			0.811653	+	0.584140i	$0.198568\pi$
$332$	4.86600	+	14.9760i	0.267056	+	0.821915i
$333$	−11.9743	−	8.69986i	−0.656190	−	0.476750i
$334$	1.39079	−	1.01047i	0.0761008	−	0.0552905i
$335$	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	$0.349006\pi$
$338$	18.6403	+	13.5430i	1.01390	+	0.736641i
$339$	3.15050	+	9.69624i	0.171112	+	0.526627i
$340$	−1.34600			−0.0729974
$341$	−19.8902	+	11.2477i	−1.07711	+	0.609096i
$342$	−5.93344			−0.320844
$343$		0			0
$344$	10.0557	+	7.30586i	0.542165	+	0.393906i
$345$	−0.433679	+	0.315086i	−0.0233485	+	0.0169637i
$346$	−2.48958	+	7.66214i	−0.133841	+	0.411919i
$347$	2.69791	−	8.30331i	0.144831	−	0.445745i	−0.852158	−	0.523285i	$-0.824706\pi$
$347$	2.69791	−	8.30331i	0.144831	−	0.445745i	0.996989	+	0.0775398i	$0.0247065\pi$
$348$	2.63333	−	1.91323i	0.141162	−	0.102560i
$349$	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
$352$	−3.86681	−	19.0269i	−0.206102	−	1.01414i
$353$	23.4857			1.25002			0.625009	−	0.780618i	$-0.285095\pi$
$353$	23.4857			1.25002			0.625009	+	0.780618i	$0.285095\pi$
$354$	1.41553	+	4.35654i	0.0752343	+	0.231547i
$355$	1.67583	+	1.21756i	0.0889439	+	0.0646215i
$356$	−8.94343	+	6.49778i	−0.474001	+	0.344382i
$357$		0			0
$358$	5.62425	−	17.3097i	0.297251	−	0.914844i
$359$	−12.0391	+	8.74695i	−0.635402	+	0.461647i	−0.858267	−	0.513203i	$-0.828459\pi$
$359$	−12.0391	+	8.74695i	−0.635402	+	0.461647i	0.222865	+	0.974849i	$0.428459\pi$
$360$	1.24420	+	0.903967i	0.0655753	+	0.0476432i
$361$	−3.24552	−	9.98870i	−0.170817	−	0.525721i
$362$	−10.6641			−0.560490
$363$	−6.62347	−	1.53215i	−0.347642	−	0.0804168i
$364$		0			0
$365$	−0.384314	−	1.18280i	−0.0201159	−	0.0619104i
$366$	−3.74336	−	2.71971i	−0.195669	−	0.142162i
$367$	−27.6894	+	20.1175i	−1.44537	+	1.05012i	−0.458487	+	0.888701i	$0.651609\pi$
$367$	−27.6894	+	20.1175i	−1.44537	+	1.05012i	−0.986885	+	0.161424i	$0.948391\pi$
$368$	−0.889558	+	2.73778i	−0.0463714	+	0.142717i
$369$	1.08255	−	3.33176i	0.0563555	−	0.173444i
$370$	−0.791277	+	0.574896i	−0.0411365	+	0.0298874i
$371$		0			0
$372$	1.83621	+	5.65128i	0.0952032	+	0.293005i
$373$	3.01739			0.156235			0.0781173	−	0.996944i	$-0.475109\pi$
$373$	3.01739			0.156235			0.0781173	+	0.996944i	$0.475109\pi$
$374$	−2.22605	−	10.9534i	−0.115106	−	0.566388i
$375$	1.36841			0.0706646
$376$	−4.93191	−	15.1788i	−0.254344	−	0.782789i
$377$	−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	$0.150277\pi$
$380$	0.279717	−	0.860879i	0.0143492	−	0.0441622i
$381$	0.998641	−	0.725555i	0.0511619	−	0.0371713i
$382$	−7.56367	−	5.49532i	−0.386991	−	0.281165i
$383$	−1.35689	−	4.17607i	−0.0693338	−	0.213387i	0.910386	−	0.413760i	$-0.135785\pi$
$383$	−1.35689	−	4.17607i	−0.0693338	−	0.213387i	−0.979720	+	0.200373i	$0.935785\pi$
$384$	−5.75876			−0.293875
$385$		0			0
$386$	−12.3495			−0.628573
$387$	3.80902	+	11.7229i	0.193623	+	0.595911i
$388$	10.2218	+	7.42661i	0.518936	+	0.377029i
$389$	−8.49145	+	6.16940i	−0.430533	+	0.312801i	−0.781862	−	0.623451i	$-0.785730\pi$
$389$	−8.49145	+	6.16940i	−0.430533	+	0.312801i	0.351329	+	0.936252i	$0.385730\pi$
$390$	−0.215740	+	0.663978i	−0.0109244	+	0.0336218i
$391$	−5.22119	+	16.0692i	−0.264047	+	0.812654i
$392$		0			0
$393$	−0.685047	−	0.497716i	−0.0345560	−	0.0251064i
$394$	−2.95600	−	9.09762i	−0.148921	−	0.458331i
$395$	−1.00789			−0.0507127
$396$	5.02734	−	11.0252i	0.252634	−	0.554038i
$397$	−11.3888			−0.571589			−0.285794	−	0.958291i	$-0.592257\pi$
$397$	−11.3888			−0.571589			−0.285794	+	0.958291i	$0.592257\pi$
$398$	3.66666	+	11.2848i	0.183793	+	0.565657i
$399$		0			0
$400$	2.95774	−	2.14893i	0.147887	−	0.107446i
$401$	−1.46009	+	4.49370i	−0.0729135	+	0.224405i	−0.980871	−	0.194657i	$-0.937641\pi$
$401$	−1.46009	+	4.49370i	−0.0729135	+	0.224405i	0.907958	+	0.419061i	$0.137641\pi$
$402$	0.188807	−	0.581090i	0.00941686	−	0.0289821i
$403$	36.3943	−	26.4420i	1.81293	−	1.31717i
$404$	21.6882	+	15.7574i	1.07903	+	0.783961i
$405$	0.392503	+	1.20800i	0.0195036	+	0.0600260i
$406$		0			0
$407$	13.8217	+	12.6707i	0.685114	+	0.628062i
$408$	−7.07230			−0.350131
$409$	−0.761863	−	2.34477i	−0.0376717	−	0.115942i	0.930452	−	0.366413i	$-0.119414\pi$
$409$	−0.761863	−	2.34477i	−0.0376717	−	0.115942i	−0.968124	+	0.250472i	$0.919414\pi$
$410$	−0.187285	−	0.136070i	−0.00924932	−	0.00672003i
$411$	1.24962	−	0.907902i	0.0616392	−	0.0447835i
$412$	7.00259	−	21.5518i	0.344993	−	1.06178i
$413$		0			0
$414$	6.41892	−	4.66362i	0.315472	−	0.229204i
$415$	2.03129	+	1.47582i	0.0997122	+	0.0724452i
$416$	11.8121	+	36.3538i	0.579134	+	1.78239i
$417$	−2.94345			−0.144141
$418$	7.46820	+	0.852519i	0.365282	+	0.0416981i
$419$	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	$0.561343\pi$
$422$	5.61911	−	4.08253i	0.273534	−	0.198734i
$423$	4.89094	−	15.0528i	0.237806	−	0.731891i
$424$	−1.40146	+	4.31326i	−0.0680611	+	0.209470i
$425$	17.3602	−	12.6130i	0.842096	−	0.611818i
$426$	3.61887	+	2.62927i	0.175335	+	0.127388i
$427$		0			0
$428$	7.52653			0.363808
$429$	13.2978	+	1.51799i	0.642024	+	0.0732891i
$430$	0.814531			0.0392802
$431$	8.61919	+	26.5272i	0.415172	+	1.27777i	0.912097	+	0.409975i	$0.134462\pi$
$431$	8.61919	+	26.5272i	0.415172	+	1.27777i	−0.496925	+	0.867794i	$0.665538\pi$
$432$	−2.07448	−	1.50720i	−0.0998085	−	0.0725151i
$433$	−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
$436$	6.09548	−	4.42862i	0.291920	−	0.212093i
$437$	−9.19251	−	6.67875i	−0.439738	−	0.319488i
$438$	−0.829907	−	2.55419i	−0.0396545	−	0.122044i
$439$	33.6655			1.60677			0.803384	−	0.595461i	$-0.203030\pi$
$439$	33.6655			1.60677			0.803384	+	0.595461i	$0.203030\pi$
$440$	−1.43615	−	1.31656i	−0.0684658	−	0.0627644i
$441$		0			0
$442$	6.79997	+	20.9282i	0.323442	+	0.995451i
$443$	−8.35449	−	6.06989i	−0.396934	−	0.288389i	0.371357	−	0.928490i	$-0.378893\pi$
$443$	−8.35449	−	6.06989i	−0.396934	−	0.288389i	−0.768291	+	0.640101i	$0.778893\pi$
$444$	3.94479	−	2.86606i	0.187211	−	0.136017i
$445$	−0.544696	+	1.67640i	−0.0258211	+	0.0794691i
$446$	0.171842	−	0.528874i	0.00813694	−	0.0250429i
$447$	−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	$0.920729\pi$
$450$	−10.0766			−0.475016
$451$	−1.84128	+	4.03802i	−0.0867025	+	0.190143i
$452$	23.0208			1.08281
$453$	−1.55454	−	4.78439i	−0.0730387	−	0.224790i
$454$	3.34729	+	2.43195i	0.157096	+	0.114137i
$455$		0			0
$456$	1.46971	−	4.52331i	0.0688255	−	0.211823i
$457$	−12.4628	+	38.3566i	−0.582986	+	1.79425i	0.0242276	+	0.999706i	$0.492287\pi$
$457$	−12.4628	+	38.3566i	−0.582986	+	1.79425i	−0.607213	+	0.794539i	$0.707713\pi$
$458$	4.15662	−	3.01996i	0.194226	−	0.141114i
$459$	−12.1760	−	8.84638i	−0.568327	−	0.412914i
$460$	0.374038	+	1.15117i	0.0174396	+	0.0536736i
$461$	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	$0.494768\pi$
$464$	−0.861267	−	2.65071i	−0.0399833	−	0.123056i
$465$	0.766520	+	0.556910i	0.0355465	+	0.0258261i
$466$	−6.01142	+	4.36755i	−0.278473	+	0.202323i
$467$	8.83555	−	27.1930i	0.408860	−	1.25834i	−0.508768	−	0.860904i	$-0.669899\pi$
$467$	8.83555	−	27.1930i	0.408860	−	1.25834i	0.917629	−	0.397439i	$-0.130101\pi$
$468$	−7.37184	+	22.6882i	−0.340764	+	1.04876i
$469$		0			0
$470$	−0.846145	−	0.614760i	−0.0390298	−	0.0283568i
$471$	3.84858	+	11.8447i	0.177333	+	0.545775i
$472$	25.1669			1.15840
$473$	−3.10991	−	15.3025i	−0.142994	−	0.703611i
$474$	−2.17650			−0.0999699
$475$	4.45933	+	13.7244i	0.204608	+	0.629719i
$476$		0			0
$477$	−3.63860	+	2.64360i	−0.166600	+	0.121042i
$478$	−6.45006	+	19.8512i	−0.295019	+	0.907975i
$479$	1.57511	−	4.84769i	0.0719686	−	0.221497i	−0.908602	−	0.417663i	$-0.862849\pi$
$479$	1.57511	−	4.84769i	0.0719686	−	0.221497i	0.980571	+	0.196166i	$0.0628493\pi$
$480$	−0.651315	+	0.473208i	−0.0297283	+	0.0215989i
$481$	−29.8648	−	21.6980i	−1.36172	−	0.989344i
$482$	4.53274	+	13.9503i	0.206461	+	0.635421i
$483$		0			0
$484$	−7.91185	+	13.1547i	−0.359629	+	0.597942i
$485$	2.01464			0.0914800
$486$	3.35019	+	10.3108i	0.151968	+	0.467709i
$487$	−23.6138	−	17.1564i	−1.07004	−	0.777433i	−0.0941240	−	0.995560i	$-0.530005\pi$
$487$	−23.6138	−	17.1564i	−1.07004	−	0.777433i	−0.975920	+	0.218128i	$0.930005\pi$
$488$	−20.5663	+	14.9423i	−0.930992	+	0.676405i
$489$	−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	$0.538102\pi$
$492$	0.933679	+	0.678357i	0.0420935	+	0.0305827i
$493$	−5.05514	−	15.5581i	−0.227672	−	0.700703i
$494$	−14.7984			−0.665810
$495$	−0.384795	−	1.89341i	−0.0172952	−	0.0851023i
$496$	5.08801			0.228458
$497$		0			0
$498$	4.38647	+	3.18696i	0.196563	+	0.142811i
$499$	−4.81450	+	3.49794i	−0.215526	+	0.156589i	−0.690311	−	0.723513i	$-0.742526\pi$
$499$	−4.81450	+	3.49794i	−0.215526	+	0.156589i	0.474784	+	0.880102i	$0.342526\pi$
$500$	0.954823	−	2.93864i	0.0427010	−	0.131420i
$501$	−0.422287	+	1.29967i	−0.0188664	+	0.0580648i
$502$	−18.4757	+	13.4233i	−0.824609	+	0.599113i
$503$	−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
$506$	−8.74933	+	4.94765i	−0.388955	+	0.219950i
$507$	−18.3154			−0.813416
$508$	−0.861305	−	2.65083i	−0.0382142	−	0.117611i
$509$	−17.2551	−	12.5366i	−0.764821	−	0.555675i	0.135565	−	0.990769i	$-0.456715\pi$
$509$	−17.2551	−	12.5366i	−0.764821	−	0.555675i	−0.900385	+	0.435094i	$0.856715\pi$
$510$	−0.374949	+	0.272417i	−0.0166030	+	0.0120628i
$511$		0			0
$512$	−2.54091	+	7.82012i	−0.112293	+	0.345604i
$513$	8.18830	−	5.94915i	0.361522	−	0.262661i
$514$	10.6404	+	7.73068i	0.469327	+	0.340986i
$515$	−1.11656	−	3.43643i	−0.0492017	−	0.151427i
$516$	−4.06072			−0.178763
$517$	−8.31884	+	18.2436i	−0.365862	+	0.802354i
$518$		0			0
$519$	−1.97900	−	6.09075i	−0.0868686	−	0.267354i
$520$	3.10312	+	2.25455i	0.136081	+	0.0988686i
$521$	−17.9103	+	13.0126i	−0.784664	+	0.570092i	−0.906375	−	0.422473i	$-0.861162\pi$
$521$	−17.9103	+	13.0126i	−0.784664	+	0.570092i	0.121711	+	0.992566i	$0.461162\pi$
$522$	−2.37383	+	7.30590i	−0.103900	+	0.319771i
$523$	−1.51773	+	4.67108i	−0.0663655	+	0.204252i	−0.978740	−	0.205104i	$-0.934247\pi$
$523$	−1.51773	+	4.67108i	−0.0663655	+	0.204252i	0.912375	+	0.409356i	$0.134247\pi$
$524$	−1.54683	+	1.12384i	−0.0675737	+	0.0490952i
$525$		0			0
$526$	1.96537	+	6.04880i	0.0856944	+	0.263740i
$527$	29.8637			1.30088
$528$	1.11586	+	1.02294i	0.0485615	+	0.0445176i
$529$	−7.80592			−0.339388
$530$	0.0918410	+	0.282657i	0.00398932	+	0.0122779i
$531$	20.1913	+	14.6698i	0.876228	+	0.636617i
$532$		0			0
$533$	2.69996	−	8.30962i	0.116948	−	0.359929i
$534$	−1.17624	+	3.62011i	−0.0509010	+	0.156657i
$535$	0.970907	−	0.705405i	0.0419760	−	0.0304973i
$536$	−2.71574	−	1.97310i	−0.117302	−	0.0852250i
$537$	4.47080	+	13.7597i	0.192929	+	0.593775i
$538$	−4.85707			−0.209403
$539$		0			0
$540$	−1.07818			−0.0463977
$541$	5.99013	+	18.4357i	0.257536	+	0.792614i	0.993319	+	0.115397i	$0.0368141\pi$
$541$	5.99013	+	18.4357i	0.257536	+	0.792614i	−0.735784	+	0.677217i	$0.763186\pi$
$542$	−4.94825	−	3.59511i	−0.212546	−	0.154423i
$543$	6.85805	−	4.98266i	0.294307	−	0.213827i
$544$	−7.84139	+	24.1333i	−0.336197	+	1.03471i
$545$	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	$0.799968\pi$
$548$	−1.07777	−	3.31703i	−0.0460400	−	0.141697i
$549$	−25.2102			−1.07594
$550$	12.6831	+	1.44781i	0.540808	+	0.0617349i
$551$	11.0012			0.468667
$552$	1.96530	+	6.04858i	0.0836489	+	0.257445i
$553$		0			0
$554$	7.57795	−	5.50570i	0.321956	−	0.233915i
$555$	0.240256	−	0.739431i	0.0101983	−	0.0313871i
$556$	−2.05382	+	6.32100i	−0.0871012	+	0.268070i
$557$	−14.9432	+	10.8569i	−0.633164	+	0.460021i	−0.857495	−	0.514492i	$-0.827980\pi$
$557$	−14.9432	+	10.8569i	−0.633164	+	0.460021i	0.224331	+	0.974513i	$0.427980\pi$
$558$	−11.3453	−	8.24287i	−0.480286	−	0.348949i
$559$	9.49993	+	29.2378i	0.401804	+	1.23663i
$560$		0			0
$561$	6.54945	+	6.00405i	0.276518	+	0.253491i
$562$	−16.4476			−0.693801
$563$	−9.66724	−	29.7527i	−0.407426	−	1.25393i	−0.918853	−	0.394600i	$-0.870883\pi$
$563$	−9.66724	−	29.7527i	−0.407426	−	1.25393i	0.511427	−	0.859327i	$-0.329117\pi$
$564$	4.21833	+	3.06479i	0.177624	+	0.129051i
$565$	2.96963	−	2.15757i	0.124933	−	0.0907695i
$566$	−6.00720	+	18.4883i	−0.252502	+	0.777120i
$567$		0			0
$568$	19.8823	−	14.4454i	0.834244	−	0.606114i
$569$	−1.40449	−	1.02042i	−0.0588794	−	0.0427784i	0.557956	−	0.829870i	$-0.311586\pi$
$569$	−1.40449	−	1.02042i	−0.0588794	−	0.0427784i	−0.616836	+	0.787092i	$0.711586\pi$
$570$	−0.0963134	−	0.296422i	−0.00403412	−	0.0124158i
$571$	12.5309			0.524403			0.262201	−	0.965013i	$-0.415551\pi$
$571$	12.5309			0.524403			0.262201	+	0.965013i	$0.415551\pi$
$572$	12.5385	−	27.4976i	0.524262	−	1.14973i
$573$	7.43182			0.310469
$574$		0			0
$575$	−15.6114	−	11.3424i	−0.651042	−	0.473009i
$576$	6.51180	−	4.73110i	0.271325	−	0.197129i
$577$	−6.23893	+	19.2015i	−0.259730	+	0.799368i	0.733130	+	0.680088i	$0.238058\pi$
$577$	−6.23893	+	19.2015i	−0.259730	+	0.799368i	−0.992861	+	0.119280i	$0.961942\pi$
$578$	−0.429788	+	1.32275i	−0.0178768	+	0.0550192i
$579$	7.94196	−	5.77017i	0.330057	−	0.239800i
$580$	−0.948101	−	0.688835i	−0.0393677	−	0.0286023i
$581$		0			0
$582$	4.35051			0.180334
$583$	4.95961	−	2.80461i	0.205406	−	0.116155i
$584$	−14.7550			−0.610568
$585$	1.17544	+	3.61764i	0.0485986	+	0.149571i
$586$	0.286249	+	0.207972i	0.0118248	+	0.00859125i
$587$	−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
$590$	1.33426	−	0.969399i	0.0549307	−	0.0399095i
$591$	6.15177	+	4.46952i	0.253050	+	0.183851i
$592$	−1.29020	−	3.97082i	−0.0530267	−	0.163200i
$593$	0.439298			0.0180398			0.00901989	−	0.999959i	$-0.497129\pi$
$593$	0.439298			0.0180398			0.00901989	+	0.999959i	$0.497129\pi$
$594$	−1.78312	−	8.77397i	−0.0731624	−	0.360001i
$595$		0			0
$596$	3.11779	+	9.59558i	0.127710	+	0.393050i
$597$	−7.63075	−	5.54406i	−0.312306	−	0.226903i
$598$	16.0092	−	11.6314i	0.654664	−	0.475641i
$599$	13.9572	−	42.9558i	0.570275	−	1.75512i	−0.0814591	−	0.996677i	$-0.525958\pi$
$599$	13.9572	−	42.9558i	0.570275	−	1.75512i	0.651734	−	0.758448i	$-0.274042\pi$
$600$	2.49598	−	7.68182i	0.101898	−	0.313609i
$601$	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
$604$	−11.3591			−0.462194
$605$	0.212282	+	2.43845i	0.00863047	+	0.0991371i
$606$	9.23071			0.374972
$607$	11.0318	+	33.9525i	0.447768	+	1.37809i	0.879419	+	0.476049i	$0.157931\pi$
$607$	11.0318	+	33.9525i	0.447768	+	1.37809i	−0.431651	+	0.902041i	$0.642069\pi$
$608$	−13.8057	−	10.0304i	−0.559894	−	0.406787i
$609$		0			0
$610$	−0.514796	+	1.58438i	−0.0208435	+	0.0641496i
$611$	12.1983	−	37.5426i	0.493491	−	1.51881i
$612$	−12.8121	+	9.30850i	−0.517897	+	0.376274i
$613$	−13.9135	−	10.1087i	−0.561960	−	0.408288i	0.270216	−	0.962800i	$-0.412905\pi$
$613$	−13.9135	−	10.1087i	−0.561960	−	0.408288i	−0.832176	+	0.554512i	$0.812905\pi$
$614$	−1.93064	−	5.94191i	−0.0779144	−	0.239796i
$615$	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	$0.610389\pi$
$618$	−2.41117	−	7.42080i	−0.0969913	−	0.298509i
$619$	25.1355	+	18.2620i	1.01028	+	0.734013i	0.964268	−	0.264928i	$-0.0853481\pi$
$619$	25.1355	+	18.2620i	1.01028	+	0.734013i	0.0460139	+	0.998941i	$0.485348\pi$
$620$	1.73080	−	1.25750i	0.0695106	−	0.0505024i
$621$	−4.18231	+	12.8718i	−0.167830	+	0.516529i
$622$	0.0329066	−	0.101276i	0.00131943	−	0.00406080i
$623$		0			0
$624$	−2.41106	−	1.75174i	−0.0965196	−	0.0701256i
$625$	7.49668	+	23.0724i	0.299867	+	0.922896i
$626$	−11.8877			−0.475127
$627$	−5.20113	+	2.94118i	−0.207713	+	0.117460i
$628$	28.1217			1.12218
$629$	−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	$0.346119\pi$
$632$	−3.69517	+	11.3726i	−0.146986	+	0.452376i
$633$	−1.70613	+	5.25094i	−0.0678128	+	0.208706i
$634$	−20.7522	+	15.0774i	−0.824176	+	0.598799i
$635$	−0.359549	−	0.261227i	−0.0142683	−	0.0103665i
$636$	−0.457859	−	1.40915i	−0.0181553	−	0.0558763i
$637$		0			0
$638$	4.03757	−	8.85460i	0.159849	−	0.350557i
$639$	24.3718			0.964132
$640$	0.640707	+	1.97189i	0.0253262	+	0.0779459i
$641$	16.7870	+	12.1965i	0.663047	+	0.481732i	0.867691	−	0.497104i	$-0.165603\pi$
$641$	16.7870	+	12.1965i	0.663047	+	0.481732i	−0.204643	+	0.978837i	$0.565603\pi$
$642$	2.09663	−	1.52329i	0.0827472	−	0.0601194i
$643$	−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
$646$	−7.94766	−	5.77431i	−0.312696	−	0.227187i
$647$	−8.52234	−	26.2291i	−0.335048	−	1.03117i	−0.966699	−	0.255918i	$-0.917622\pi$
$647$	−8.52234	−	26.2291i	−0.335048	−	1.03117i	0.631651	−	0.775253i	$-0.282378\pi$
$648$	15.0694			0.591984
$649$	−23.3063	−	21.3655i	−0.914852	−	0.838669i
$650$	−25.1317			−0.985748
$651$		0			0
$652$	8.39353	+	6.09826i	0.328716	+	0.238826i
$653$	−13.0690	+	9.49516i	−0.511428	+	0.371574i	−0.813365	−	0.581753i	$-0.802367\pi$
$653$	−13.0690	+	9.49516i	−0.511428	+	0.371574i	0.301937	+	0.953328i	$0.402367\pi$
$654$	0.801680	−	2.46732i	0.0313482	−	0.0964797i
$655$	−0.0942092	+	0.289946i	−0.00368106	+	0.0113291i
$656$	0.799474	−	0.580852i	0.0312142	−	0.0226785i
$657$	−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	$0.582822\pi$
$660$	0.632403	+	0.0721907i	0.0246162	+	0.00281002i
$661$	4.90660			0.190845			0.0954223	−	0.995437i	$-0.469580\pi$
$661$	4.90660			0.190845			0.0954223	+	0.995437i	$0.469580\pi$
$662$	−7.09559	−	21.8380i	−0.275778	−	0.848757i
$663$	−14.1515	−	10.2817i	−0.549600	−	0.399308i
$664$	24.0996	−	17.5094i	0.935245	−	0.679495i
$665$		0			0
$666$	−3.55605	+	10.9444i	−0.137794	+	0.424087i
$667$	−11.9013	+	8.64682i	−0.460821	+	0.334806i
$668$	2.49635	+	1.81371i	0.0965869	+	0.0701745i
$669$	0.136599	+	0.420410i	0.00528124	+	0.0162540i
$670$	−0.219981			−0.00849861
$671$	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	$-0.296151\pi$
$674$	3.54142	+	2.57299i	0.136410	+	0.0991079i
$675$	13.9060	−	10.1033i	0.535242	−	0.388876i
$676$	−12.7797	+	39.3320i	−0.491528	+	1.51277i
$677$	−3.89019	+	11.9728i	−0.149512	+	0.460151i	−0.997564	−	0.0697626i	$-0.977776\pi$
$677$	−3.89019	+	11.9728i	−0.149512	+	0.460151i	0.848051	+	0.529914i	$0.177776\pi$
$678$	6.41278	−	4.65916i	0.246281	−	0.178934i
$679$		0			0
$680$	0.786849	+	2.42167i	0.0301743	+	0.0928668i
$681$	−3.28894			−0.126033
$682$	13.0956	+	12.0051i	0.501457	+	0.459699i
$683$	−28.5342			−1.09183			−0.545916	−	0.837840i	$-0.683818\pi$
$683$	−28.5342			−1.09183			−0.545916	+	0.837840i	$0.683818\pi$
$684$	−3.29104	−	10.1288i	−0.125836	−	0.387283i
$685$	−0.449911	−	0.326879i	−0.0171902	−	0.0124894i
$686$		0			0
$687$	−1.26208	+	3.88427i	−0.0481513	+	0.148194i
$688$	−1.07447	+	3.30687i	−0.0409636	+	0.126073i
$689$	−9.07491	+	6.59331i	−0.345726	+	0.251185i
$690$	0.337178	+	0.244974i	0.0128362	+	0.00932601i
$691$	−7.84107	−	24.1323i	−0.298288	−	0.918037i	−0.982097	−	0.188376i	$-0.939678\pi$
$691$	−7.84107	−	24.1323i	−0.298288	−	0.918037i	0.683809	−	0.729661i	$-0.260322\pi$
$692$	−14.4606			−0.549711
$693$		0			0
$694$	−6.78791			−0.257666
$695$	0.327482	+	1.00788i	0.0124221	+	0.0382312i
$696$	−4.98159	−	3.61934i	−0.188827	−	0.137191i
$697$	4.69245	−	3.40927i	0.177739	−	0.129135i
$698$	4.43679	−	13.6551i	0.167935	−	0.516851i
$699$	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	$0.368537\pi$
$702$	5.44695	+	16.7640i	0.205582	+	0.632716i
$703$	16.4800			0.621556
$704$	−8.87594	+	5.01925i	−0.334525	+	0.189170i
$705$	0.831396			0.0313122
$706$	−5.64257	−	17.3661i	−0.212361	−	0.653580i
$707$		0			0
$708$	−6.65177	+	4.83279i	−0.249989	+	0.181627i
$709$	11.9065	−	36.6446i	0.447160	−	1.37622i	−0.432938	−	0.901424i	$-0.642523\pi$
$709$	11.9065	−	36.6446i	0.447160	−	1.37622i	0.880098	−	0.474793i	$-0.157477\pi$
$710$	0.497676	−	1.53169i	0.0186774	−	0.0574833i
$711$	−9.59373	+	6.97025i	−0.359793	+	0.261405i
$712$	16.9187	+	12.2921i	0.634054	+	0.460667i
$713$	−8.29874	−	25.5409i	−0.310790	−	0.956515i
$714$		0			0
$715$	−0.959703	−	4.72228i	−0.0358908	−	0.176603i
$716$	32.6683			1.22087
$717$	−5.12725	−	15.7801i	−0.191481	−	0.589317i
$718$	9.36025	+	6.80062i	0.349321	+	0.253797i
$719$	4.61312	−	3.35163i	0.172040	−	0.124995i	−0.498433	−	0.866928i	$-0.666091\pi$
$719$	4.61312	−	3.35163i	0.172040	−	0.124995i	0.670473	+	0.741934i	$0.266091\pi$
$720$	−0.132945	+	0.409164i	−0.00495458	+	0.0152486i
$721$		0			0
$722$	−6.60620	+	4.79969i	−0.245857	+	0.178626i
$723$	−9.43316	−	6.85359i	−0.350823	−	0.254888i
$724$	−5.91491	−	18.2042i	−0.219826	−	0.676555i
$725$	18.6831			0.693872
$726$	0.458411	+	5.26571i	0.0170132	+	0.195429i
$727$	−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
$730$	−0.782263	+	0.568347i	−0.0289529	+	0.0210355i
$731$	−6.30649	+	19.4094i	−0.233254	+	0.717882i
$732$	2.56644	−	7.89868i	0.0948582	−	0.291944i
$733$	7.12900	−	5.17952i	0.263316	−	0.191310i	−0.448292	−	0.893887i	$-0.647967\pi$
$733$	7.12900	−	5.17952i	0.263316	−	0.191310i	0.711607	+	0.702577i	$0.247967\pi$
$734$	21.5280	+	15.6410i	0.794614	+	0.577321i
$735$		0			0
$736$	22.8190			0.841121
$737$	0.839897	+	4.13277i	0.0309380	+	0.152232i
$738$	−2.72370			−0.100261
$739$	0.148578	+	0.457276i	0.00546553	+	0.0168212i	0.953752	−	0.300594i	$-0.0971850\pi$
$739$	0.148578	+	0.457276i	0.00546553	+	0.0168212i	−0.948287	+	0.317416i	$0.897185\pi$
$740$	−1.42027	−	1.03189i	−0.0522103	−	0.0379330i
$741$	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	$-0.108753\pi$
$744$	9.09412	−	6.60726i	0.333407	−	0.242234i
$745$	1.30151	+	0.945603i	0.0476837	+	0.0346442i
$746$	−0.724946	−	2.23116i	−0.0265422	−	0.0816884i
$747$	29.5413			1.08086
$748$	17.4635	−	9.87543i	0.638530	−	0.361082i
$749$		0			0
$750$	−0.328769	−	1.01185i	−0.0120050	−	0.0369475i
$751$	−22.6578	−	16.4619i	−0.826796	−	0.600703i	0.0918547	−	0.995772i	$-0.470720\pi$
$751$	−22.6578	−	16.4619i	−0.826796	−	0.600703i	−0.918651	+	0.395070i	$0.870720\pi$
$752$	3.61200	−	2.62427i	0.131716	−	0.0956973i
$753$	5.60977	−	17.2651i	0.204432	−	0.629176i
$754$	−5.92049	+	18.2214i	−0.215611	+	0.663584i
$755$	−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	$-0.232481\pi$
$758$	4.76156			0.172948
$759$	3.31495	−	7.26986i	0.120325	−	0.263879i
$760$	−1.71237			−0.0621142
$761$	14.9025	+	45.8651i	0.540214	+	1.66261i	0.732105	+	0.681192i	$0.238538\pi$
$761$	14.9025	+	45.8651i	0.540214	+	1.66261i	−0.191891	+	0.981416i	$0.561462\pi$
$762$	−0.776427	−	0.564108i	−0.0281270	−	0.0204355i
$763$		0			0
$764$	5.18562	−	15.9597i	0.187609	−	0.577402i
$765$	−0.780313	+	2.40156i	−0.0282123	+	0.0868284i
$766$	−2.76192	+	2.00665i	−0.0997922	+	0.0725033i
$767$	50.3584	+	36.5875i	1.81834	+	1.32110i
$768$	2.55791	+	7.87245i	0.0923007	+	0.284072i
$769$	−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
$772$	−6.84977	−	21.0814i	−0.246528	−	0.758737i
$773$	−0.473736	−	0.344189i	−0.0170391	−	0.0123796i	0.579233	−	0.815162i	$-0.303352\pi$
$773$	−0.473736	−	0.344189i	−0.0170391	−	0.0123796i	−0.596272	+	0.802782i	$0.703352\pi$
$774$	7.75318	−	5.63301i	0.278682	−	0.202475i
$775$	−10.5396	+	32.4375i	−0.378593	+	1.16519i
$776$	7.38612	−	22.7321i	0.265146	−	0.816036i
$777$		0			0
$778$	6.60197	+	4.79661i	0.236692	+	0.171967i
$779$	1.20535	+	3.70969i	0.0431862	+	0.132913i
$780$	−1.25312			−0.0448688
$781$	−30.6759	−	3.50175i	−1.09767	−	0.125302i
$782$	13.1365			0.469760
$783$	−4.04930	−	12.4625i	−0.144710	−	0.445372i
$784$		0			0
$785$	3.62764	−	2.63563i	0.129476	−	0.0940698i
$786$	−0.203440	+	0.626124i	−0.00725647	+	0.0223331i
$787$	−9.49195	+	29.2132i	−0.338351	+	1.04134i	0.626696	+	0.779264i	$0.284407\pi$
$787$	−9.49195	+	29.2132i	−0.338351	+	1.04134i	−0.965048	+	0.262075i	$0.915593\pi$
$788$	13.8907	−	10.0922i	0.494834	−	0.359518i
$789$	−4.09017	−	2.97168i	−0.145614	−	0.105795i
$790$	0.242153	+	0.745269i	0.00861540	+	0.0265155i
$791$		0			0
$792$	−22.7750	−	2.59984i	−0.809274	−	0.0923811i
$793$	−62.8758			−2.23278
$794$	2.73623	+	8.42125i	0.0971052	+	0.298859i
$795$	−0.191132	−	0.138865i	−0.00677874	−	0.00492504i
$796$	−17.2302	+	12.5185i	−0.610708	+	0.443705i
$797$	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
$800$	−23.4458	−	17.0344i	−0.828936	−	0.602257i
$801$	6.40868	+	19.7239i	0.226440	+	0.696910i
$802$	3.67358			0.129719
$803$	13.6642	+	12.5263i	0.482200	+	0.442045i
$804$	1.09668			0.0386770
$805$		0			0
$806$	−28.2960	−	20.5582i	−0.996684	−	0.724133i
$807$	3.12358	−	2.26941i	0.109955	−	0.0798872i
$808$	15.6715	−	48.2320i	0.551322	−	1.69679i
$809$	−11.9250	+	36.7013i	−0.419260	+	1.29035i	0.489125	+	0.872214i	$0.337316\pi$
$809$	−11.9250	+	36.7013i	−0.419260	+	1.29035i	−0.908385	+	0.418136i	$0.862684\pi$
$810$	0.798931	−	0.580458i	0.0280716	−	0.0203952i
$811$	−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
$814$	6.04836	−	13.2644i	0.211995	−	0.464916i
$815$	1.65429			0.0579473
$816$	−0.611364	−	1.88159i	−0.0214020	−	0.0658687i
$817$	−11.1033	−	8.06703i	−0.388456	−	0.282230i
$818$	−1.55076	+	1.12669i	−0.0542209	+	0.0393938i
$819$		0			0
$820$	0.128402	−	0.395180i	0.00448398	−	0.0138003i
$821$	32.6110	−	23.6933i	1.13813	−	0.826901i	0.151274	−	0.988492i	$-0.451662\pi$
$821$	32.6110	−	23.6933i	1.13813	−	0.826901i	0.986858	+	0.161590i	$0.0516623\pi$
$822$	−0.971560	−	0.705880i	−0.0338870	−	0.0246204i
$823$	7.93609	+	24.4248i	0.276635	+	0.851395i	0.988782	+	0.149365i	$0.0477228\pi$
$823$	7.93609	+	24.4248i	0.276635	+	0.851395i	−0.712147	+	0.702030i	$0.752277\pi$
$824$	−42.8685			−1.49340
$825$	−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	$-0.287513\pi$
$828$	11.5214	+	8.37079i	0.400397	+	0.290905i
$829$	39.1566	−	28.4489i	1.35996	−	0.988072i	0.361518	−	0.932365i	$-0.382259\pi$
$829$	39.1566	−	28.4489i	1.35996	−	0.988072i	0.998447	−	0.0557070i	$-0.0177413\pi$
$830$	0.603238	−	1.85658i	0.0209387	−	0.0644427i
$831$	−2.30090	+	7.08143i	−0.0798172	+	0.245652i
$832$	16.2409	−	11.7997i	0.563050	−	0.409080i
$833$		0			0
$834$	0.707180	+	2.17648i	0.0244876	+	0.0753652i
$835$	0.492010			0.0170267
$836$	2.68700	+	13.2216i	0.0929319	+	0.457278i
$837$	23.9216			0.826850
$838$	−3.44524	−	10.6033i	−0.119014	−	0.366287i
$839$	−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
$842$	4.16021	−	12.8038i	0.143370	−	0.441248i
$843$	10.5775	−	7.68497i	0.364307	−	0.264685i
$844$	10.0858	+	7.32779i	0.347169	+	0.252233i
$845$	2.03773	+	6.27150i	0.0701001	+	0.215746i
$846$	−12.3056			−0.423074
$847$		0			0
$848$	−1.26869			−0.0435671
$849$	−4.77522	−	14.6966i	−0.163885	−	0.504386i
$850$	−13.4973	−	9.80638i	−0.462954	−	0.336356i
$851$	−17.8284	+	12.9531i	−0.611151	+	0.444027i
$852$	−2.48109	+	7.63600i	−0.0850007	+	0.261605i
$853$	−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
$856$	−4.39986	−	13.5414i	−0.150384	−	0.462835i
$857$	29.7644			1.01673			0.508365	−	0.861141i	$-0.330250\pi$
$857$	29.7644			1.01673			0.508365	+	0.861141i	$0.330250\pi$
$858$	−2.07243	−	10.1975i	−0.0707516	−	0.348138i
$859$	−33.2611			−1.13485			−0.567427	−	0.823424i	$-0.692061\pi$
$859$	−33.2611			−1.13485			−0.567427	+	0.823424i	$0.692061\pi$
$860$	0.451787	+	1.39046i	0.0154058	+	0.0474142i
$861$		0			0
$862$	17.5442	−	12.7466i	0.597558	−	0.434151i
$863$	−5.73772	+	17.6589i	−0.195314	+	0.601116i	0.804658	+	0.593738i	$0.202348\pi$
$863$	−5.73772	+	17.6589i	−0.195314	+	0.601116i	−0.999973	+	0.00737787i	$0.997652\pi$
$864$	−6.28115	+	19.3314i	−0.213689	+	0.657668i
$865$	−1.86539	+	1.35529i	−0.0634253	+	0.0460812i
$866$	18.5850	+	13.5028i	0.631544	+	0.458844i
$867$	−0.341645	−	1.05147i	−0.0116029	−	0.0357100i
$868$		0			0
$869$	13.0768	−	7.39477i	0.443599	−	0.250850i
$870$	−0.403520			−0.0136806
$871$	−2.56565	−	7.89627i	−0.0869339	−	0.267555i
$872$	−11.5311	−	8.37782i	−0.390491	−	0.283709i
$873$	19.1765	−	13.9325i	0.649026	−	0.471545i
$874$	−2.72992	+	8.40184i	−0.0923411	+	0.284197i
$875$		0			0
$876$	3.89985	−	2.83341i	0.131764	−	0.0957321i
$877$	18.1965	+	13.2205i	0.614452	+	0.446426i	0.850979	−	0.525199i	$-0.176009\pi$
$877$	18.1965	+	13.2205i	0.614452	+	0.446426i	−0.236527	+	0.971625i	$0.576009\pi$
$878$	−8.08834	−	24.8934i	−0.272968	−	0.840110i
$879$	−0.281259			−0.00948664
$880$	0.226122	−	0.495898i	0.00762259	−	0.0167167i
$881$	−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	$0.591099\pi$
$884$	−31.9541	+	23.2160i	−1.07473	+	0.780839i
$885$	−0.405123	+	1.24684i	−0.0136181	+	0.0419121i
$886$	−2.48105	+	7.63590i	−0.0833527	+	0.256533i
$887$	5.62656	−	4.08793i	0.188921	−	0.137259i	−0.489304	−	0.872113i	$-0.662749\pi$
$887$	5.62656	−	4.08793i	0.188921	−	0.137259i	0.678226	+	0.734854i	$0.262749\pi$
$888$	−7.46253	−	5.42185i	−0.250426	−	0.181945i
$889$		0			0
$890$	1.37045			0.0459376
$891$	−13.9554	−	12.7933i	−0.467522	−	0.428590i
$892$	0.998136			0.0334201
$893$	5.44574	+	16.7603i	0.182235	+	0.560861i
$894$	2.81055	+	2.04198i	0.0939988	+	0.0682941i
$895$	4.21414	−	3.06175i	0.140863	−	0.102343i
$896$		0			0
$897$	−4.86088	+	14.9602i	−0.162300	+	0.499508i
$898$	−1.73468	+	1.26032i	−0.0578872	+	0.0420575i
$899$	21.0354	+	15.2831i	0.701570	+	0.509721i
$900$	−5.58909	−	17.2014i	−0.186303	−	0.573382i
$901$	−7.44650			−0.248079
$902$	3.42822	+	0.391342i	0.114147	+	0.0130303i
$903$		0			0
$904$	−13.4575	−	41.4179i	−0.447590	−	1.37754i
$905$	−2.46916	−	1.79395i	−0.0820776	−	0.0596329i
$906$	−3.16424	+	2.29895i	−0.105125	+	0.0763776i
$907$	−7.24340	+	22.2929i	−0.240513	+	0.740224i	0.755829	+	0.654769i	$0.227234\pi$
$907$	−7.24340	+	22.2929i	−0.240513	+	0.740224i	−0.996342	+	0.0854543i	$0.972766\pi$
$908$	−2.29489	+	7.06294i	−0.0761586	+	0.234392i
$909$	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	$0.617530\pi$
$912$	1.33048			0.0440564
$913$	−37.1825	−	4.24450i	−1.23056	−	0.140473i
$914$	31.3563			1.03718
$915$	−0.409219	−	1.25945i	−0.0135284	−	0.0416360i
$916$	7.46078	+	5.42058i	0.246511	+	0.179101i
$917$		0			0
$918$	−3.61594	+	11.1287i	−0.119344	+	0.367302i
$919$	3.28402	−	10.1072i	0.108330	−	0.333405i	−0.882168	−	0.470935i	$-0.843916\pi$
$919$	3.28402	−	10.1072i	0.108330	−	0.333405i	0.990498	+	0.137530i	$0.0439165\pi$
$920$	1.85248	−	1.34590i	0.0610744	−	0.0443732i
$921$	4.01789	+	2.91917i	0.132394	+	0.0961898i
$922$	−8.22278	−	25.3071i	−0.270803	−	0.833445i
$923$	60.7848			2.00075
$924$		0			0
$925$	27.9876			0.920228
$926$	−0.169945	−	0.523036i	−0.00558473	−	0.0171880i
$927$	−34.3933	−	24.9882i	−1.12962	−	0.820720i
$928$	−17.8739	+	12.9861i	−0.586738	+	0.426290i
$929$	11.3319	−	34.8762i	0.371789	−	1.14425i	−0.573830	−	0.818974i	$-0.694543\pi$
$929$	11.3319	−	34.8762i	0.371789	−	1.14425i	0.945619	−	0.325275i	$-0.105457\pi$
$930$	0.227635	−	0.700590i	0.00746446	−	0.0229733i
$931$		0			0
$932$	−10.7900	−	7.83938i	−0.353438	−	0.256787i
$933$	0.0261579	+	0.0805059i	0.000856373	+	0.00263564i
$934$	−22.2302			−0.727393
$935$	1.32721	−	2.91064i	0.0434043	−	0.0951880i
$936$	45.1290			1.47509
$937$	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
$940$	0.580114	−	1.78541i	0.0189212	−	0.0582336i
$941$	−7.69751	+	23.6905i	−0.250932	+	0.772288i	0.743672	+	0.668544i	$0.233082\pi$
$941$	−7.69751	+	23.6905i	−0.250932	+	0.772288i	−0.994604	+	0.103744i	$0.966918\pi$
$942$	7.83371	−	5.69152i	0.255236	−	0.185440i
$943$	−4.21975	−	3.06583i	−0.137414	−	0.0998371i
$944$	2.17555	+	6.69565i	0.0708081	+	0.217925i
$945$		0			0
$946$	−10.5680	+	5.97609i	−0.343595	+	0.194299i
$947$	−32.2061			−1.04656			−0.523279	−	0.852161i	$-0.675292\pi$
$947$	−32.2061			−1.04656			−0.523279	+	0.852161i	$0.675292\pi$
$948$	−1.20722	−	3.71543i	−0.0392085	−	0.120671i
$949$	−29.5246	−	21.4508i	−0.958408	−	0.696324i
$950$	9.07688	−	6.59474i	0.294493	−	0.213962i
$951$	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	$0.560404\pi$
$954$	2.82896	+	2.05536i	0.0915908	+	0.0665446i
$955$	−0.826849	−	2.54478i	−0.0267562	−	0.0823471i
$956$	−37.4650			−1.21170
$957$	1.54066	+	7.58090i	0.0498024	+	0.245056i
$958$	−3.96296			−0.128038
$959$		0			0
$960$	0.342058	+	0.248519i	0.0110399	+	0.00802093i
$961$	−13.3216	+	9.67867i	−0.429727	+	0.312215i
$962$	−8.86901	+	27.2960i	−0.285948	+	0.880059i
$963$	4.36332	−	13.4289i	0.140606	−	0.432741i
$964$	−21.3000	+	15.4754i	−0.686028	+	0.498428i
$965$	−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	$0.490715\pi$
$968$	28.2925	+	6.54464i	0.909355	+	0.210353i
$969$	7.80912			0.250865
$970$	−0.484029	−	1.48969i	−0.0155412	−	0.0478310i
$971$	18.6510	+	13.5507i	0.598539	+	0.434864i	0.845360	−	0.534197i	$-0.179386\pi$
$971$	18.6510	+	13.5507i	0.598539	+	0.434864i	−0.246821	+	0.969061i	$0.579386\pi$
$972$	−15.7431	+	11.4380i	−0.504959	+	0.366874i
$973$		0			0
$974$	−7.01266	+	21.5827i	−0.224700	+	0.691555i
$975$	16.1622	−	11.7425i	0.517605	−	0.376062i
$976$	−5.75325	−	4.17998i	−0.184157	−	0.133798i
$977$	−2.19232	−	6.74726i	−0.0701385	−	0.215864i	0.909843	−	0.414953i	$-0.136202\pi$
$977$	−2.19232	−	6.74726i	−0.0701385	−	0.215864i	−0.979981	+	0.199089i	$0.936202\pi$
$978$	3.57236			0.114232
$979$	−5.23244	−	25.7466i	−0.167229	−	0.822863i
$980$		0			0
$981$	−4.36789	−	13.4430i	−0.139456	−	0.429202i
$982$	18.9605	+	13.7756i	0.605053	+	0.439597i
$983$	31.0260	−	22.5417i	0.989576	−	0.718969i	0.0297474	−	0.999557i	$-0.490530\pi$
$983$	31.0260	−	22.5417i	0.989576	−	0.718969i	0.959828	+	0.280589i	$0.0905297\pi$
$984$	0.674659	−	2.07639i	0.0215073	−	0.0661928i
$985$	0.846005	−	2.60374i	0.0269560	−	0.0829619i
$986$	−10.2896	+	7.47586i	−0.327689	+	0.238080i
$987$		0			0
$988$	−8.20806	−	25.2618i	−0.261133	−	0.803685i
$989$	18.3524			0.583572
$990$	−1.30760	+	0.739431i	−0.0415581	+	0.0235007i
$991$	20.2722			0.643967			0.321984	−	0.946745i	$-0.395650\pi$
$991$	20.2722			0.643967			0.321984	+	0.946745i	$0.395650\pi$
$992$	−12.4634	−	38.3583i	−0.395712	−	1.21788i
$993$	14.7667	+	10.7287i	0.468608	+	0.340464i
$994$		0			0
$995$	−1.04940	+	3.22971i	−0.0332681	+	0.102389i
$996$	−3.00735	+	9.25568i	−0.0952916	+	0.293277i
$997$	12.4675	−	9.05819i	0.394851	−	0.286876i	−0.372590	−	0.927996i	$-0.621530\pi$
$997$	12.4675	−	9.05819i	0.394851	−	0.286876i	0.767440	+	0.641120i	$0.221530\pi$
$998$	3.74319	+	2.71959i	0.118489	+	0.0860871i
$999$	−6.06593	−	18.6690i	−0.191918	−	0.590662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.d.148.1		8
7.2	even	3		539.2.q.b.214.1		16
7.3	odd	6		539.2.q.c.324.2		16
7.4	even	3		539.2.q.b.324.2		16
7.5	odd	6		539.2.q.c.214.1		16
7.6	odd	2		77.2.f.a.71.1	yes	8
11.3	even	5		5929.2.a.bi.1.2		4
11.8	odd	10		5929.2.a.bb.1.3		4
11.9	even	5	inner	539.2.f.d.295.1		8
21.20	even	2		693.2.m.g.379.2		8
77.6	even	10		847.2.f.s.323.1		8
77.9	even	15		539.2.q.b.361.2		16
77.13	even	10		847.2.f.q.372.2		8
77.20	odd	10		77.2.f.a.64.1	✓	8
77.27	odd	10		847.2.f.p.323.2		8
77.31	odd	30		539.2.q.c.471.1		16
77.41	even	10		847.2.a.k.1.3		4
77.48	odd	10		847.2.f.p.729.2		8
77.53	even	15		539.2.q.b.471.1		16
77.62	even	10		847.2.f.s.729.1		8
77.69	odd	10		847.2.a.l.1.2		4
77.75	odd	30		539.2.q.c.361.2		16
77.76	even	2		847.2.f.q.148.2		8
231.20	even	10		693.2.m.g.64.2		8
231.41	odd	10		7623.2.a.co.1.2		4
231.146	even	10		7623.2.a.ch.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	77.20	odd	10
77.2.f.a.71.1	yes	8	7.6	odd	2
539.2.f.d.148.1		8	1.1	even	1	trivial
539.2.f.d.295.1		8	11.9	even	5	inner
539.2.q.b.214.1		16	7.2	even	3
539.2.q.b.324.2		16	7.4	even	3
539.2.q.b.361.2		16	77.9	even	15
539.2.q.b.471.1		16	77.53	even	15
539.2.q.c.214.1		16	7.5	odd	6
539.2.q.c.324.2		16	7.3	odd	6
539.2.q.c.361.2		16	77.75	odd	30
539.2.q.c.471.1		16	77.31	odd	30
693.2.m.g.64.2		8	231.20	even	10
693.2.m.g.379.2		8	21.20	even	2
847.2.a.k.1.3		4	77.41	even	10
847.2.a.l.1.2		4	77.69	odd	10
847.2.f.p.323.2		8	77.27	odd	10
847.2.f.p.729.2		8	77.48	odd	10
847.2.f.q.148.2		8	77.76	even	2
847.2.f.q.372.2		8	77.13	even	10
847.2.f.s.323.1		8	77.6	even	10
847.2.f.s.729.1		8	77.62	even	10
5929.2.a.bb.1.3		4	11.8	odd	10
5929.2.a.bi.1.2		4	11.3	even	5
7623.2.a.ch.1.3		4	231.146	even	10
7623.2.a.co.1.2		4	231.41	odd	10

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.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.240256 - 0.739431i) q^{2} +(0.500000 + 0.363271i) q^{3} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})\)	\(q+(-0.240256 - 0.739431i) q^{2} +(0.500000 + 0.363271i) q^{3} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.148486 - 0.456994i) q^{6} +(-2.13577 - 1.55173i) q^{8} +(-0.809017 - 2.48990i) q^{9} -0.173002 q^{10} +(0.660531 + 3.25018i) q^{11} +0.862478 q^{12} +(-2.01774 - 6.20997i) q^{13} +(0.111258 - 0.0808336i) q^{15} +(0.228211 - 0.702362i) q^{16} +(1.33947 - 4.12246i) q^{17} +(-1.64674 + 1.19643i) q^{18} +(2.35829 + 1.71340i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} -3.89796 q^{23} +(-0.504188 - 1.55173i) q^{24} +(4.00503 + 2.90982i) q^{25} +(-4.10707 + 2.98396i) q^{26} +(1.07295 - 3.30220i) q^{27} +(3.05322 - 2.21829i) q^{29} +(-0.0865012 - 0.0628468i) q^{30} +(2.12900 + 6.55238i) q^{31} -5.85410 q^{32} +(-0.850433 + 1.86504i) q^{33} -3.37009 q^{34} +(-2.95576 - 2.14748i) q^{36} +(4.57379 - 3.32305i) q^{37} +(0.700347 - 2.15545i) q^{38} +(1.24703 - 3.83797i) q^{39} +(-0.475243 + 0.345285i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(3.41175 + 3.12764i) q^{44} -0.582554 q^{45} +(0.936507 + 2.88227i) q^{46} +(4.89094 + 3.55348i) q^{47} +(0.369254 - 0.268279i) q^{48} +(1.18938 - 3.66055i) q^{50} +(2.16731 - 1.57464i) q^{51} +(-7.37184 - 5.35596i) q^{52} +(-0.530865 - 1.63383i) q^{53} -2.69953 q^{54} +(0.733239 + 0.0837016i) q^{55} +(0.556717 + 1.71340i) q^{57} +(-2.37383 - 1.72469i) q^{58} +(-7.71239 + 5.60338i) q^{59} +(0.0593050 - 0.182522i) q^{60} +(2.97566 - 9.15813i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} -1.45293 q^{65} +(1.58339 + 0.180749i) q^{66} +1.27155 q^{67} +(-1.86925 - 5.75297i) q^{68} +(-1.94898 - 1.41602i) q^{69} +(-2.87670 + 8.85357i) q^{71} +(-2.13577 + 6.57324i) q^{72} +(4.52169 - 3.28520i) q^{73} +(-3.55605 - 2.58362i) q^{74} +(0.945459 + 2.90982i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-1.39971 - 4.30785i) q^{79} +(-0.132945 - 0.0965905i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(0.321489 - 0.989441i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(1.13117 + 3.48139i) q^{86} +2.33245 q^{87} +(3.63267 - 7.96663i) q^{88} -7.92157 q^{89} +(0.139962 + 0.430759i) q^{90} +(-4.40079 + 3.19736i) q^{92} +(-1.31579 + 4.04959i) q^{93} +(1.45248 - 4.47026i) q^{94} +(0.524757 - 0.381258i) q^{95} +(-2.92705 - 2.12663i) q^{96} +(2.79781 + 8.61078i) q^{97} +(7.55825 - 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

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