LMFDB - Embedded newform 552.2.j.d.323.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.11
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.975618 - 1.02380i) q^{2} +(1.69183 + 0.371101i) q^{3} +(-0.0963383 + 1.99768i) q^{4} -1.56730 q^{5} +(-1.27065 - 2.09415i) q^{6} -0.668312i q^{7} +(2.13922 - 1.85034i) q^{8} +(2.72457 + 1.25568i) q^{9} +O(q^{10})$	\(q+(-0.975618 - 1.02380i) q^{2} +(1.69183 + 0.371101i) q^{3} +(-0.0963383 + 1.99768i) q^{4} -1.56730 q^{5} +(-1.27065 - 2.09415i) q^{6} -0.668312i q^{7} +(2.13922 - 1.85034i) q^{8} +(2.72457 + 1.25568i) q^{9} +(1.52908 + 1.60460i) q^{10} +4.80506i q^{11} +(-0.904328 + 3.34398i) q^{12} +4.48924i q^{13} +(-0.684219 + 0.652017i) q^{14} +(-2.65160 - 0.581625i) q^{15} +(-3.98144 - 0.384906i) q^{16} -1.05154i q^{17} +(-1.37257 - 4.01448i) q^{18} +1.05324 q^{19} +(0.150991 - 3.13095i) q^{20} +(0.248011 - 1.13067i) q^{21} +(4.91942 - 4.68790i) q^{22} +1.00000 q^{23} +(4.30585 - 2.33659i) q^{24} -2.54358 q^{25} +(4.59609 - 4.37978i) q^{26} +(4.14352 + 3.13548i) q^{27} +(1.33507 + 0.0643840i) q^{28} +7.11293 q^{29} +(1.99148 + 3.28215i) q^{30} +3.88117i q^{31} +(3.49030 + 4.45172i) q^{32} +(-1.78316 + 8.12933i) q^{33} +(-1.07656 + 1.02590i) q^{34} +1.04744i q^{35} +(-2.77092 + 5.32184i) q^{36} -2.44792i q^{37} +(-1.02756 - 1.07831i) q^{38} +(-1.66596 + 7.59502i) q^{39} +(-3.35278 + 2.90003i) q^{40} +2.02989i q^{41} +(-1.39955 + 0.849187i) q^{42} -3.57557 q^{43} +(-9.59896 - 0.462911i) q^{44} +(-4.27021 - 1.96802i) q^{45} +(-0.975618 - 1.02380i) q^{46} +7.09880 q^{47} +(-6.59307 - 2.12871i) q^{48} +6.55336 q^{49} +(2.48156 + 2.60412i) q^{50} +(0.390226 - 1.77902i) q^{51} +(-8.96805 - 0.432485i) q^{52} +0.0884948 q^{53} +(-0.832380 - 7.30117i) q^{54} -7.53095i q^{55} +(-1.23660 - 1.42966i) q^{56} +(1.78191 + 0.390859i) q^{57} +(-6.93951 - 7.28223i) q^{58} +6.15979i q^{59} +(1.41735 - 5.24101i) q^{60} +6.69672i q^{61} +(3.97355 - 3.78654i) q^{62} +(0.839185 - 1.82086i) q^{63} +(1.15248 - 7.91655i) q^{64} -7.03596i q^{65} +(10.0625 - 6.10552i) q^{66} +13.2350 q^{67} +(2.10063 + 0.101303i) q^{68} +(1.69183 + 0.371101i) q^{69} +(1.07237 - 1.02190i) q^{70} -6.95495 q^{71} +(8.15187 - 2.35521i) q^{72} -13.8192 q^{73} +(-2.50618 + 2.38823i) q^{74} +(-4.30330 - 0.943926i) q^{75} +(-0.101468 + 2.10404i) q^{76} +3.21128 q^{77} +(9.40113 - 5.70423i) q^{78} -14.6807i q^{79} +(6.24009 + 0.603261i) q^{80} +(5.84654 + 6.84236i) q^{81} +(2.07820 - 1.98040i) q^{82} -15.1782i q^{83} +(2.23482 + 0.604373i) q^{84} +1.64807i q^{85} +(3.48840 + 3.66068i) q^{86} +(12.0339 + 2.63962i) q^{87} +(8.89099 + 10.2790i) q^{88} +3.28612i q^{89} +(2.15123 + 6.29188i) q^{90} +3.00021 q^{91} +(-0.0963383 + 1.99768i) q^{92} +(-1.44031 + 6.56627i) q^{93} +(-6.92572 - 7.26777i) q^{94} -1.65074 q^{95} +(4.25294 + 8.82680i) q^{96} -14.8592 q^{97} +(-6.39358 - 6.70934i) q^{98} +(-6.03361 + 13.0917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.975618	−	1.02380i	−0.689866	−	0.723937i
$2$	−0.975618	−	1.02380i	−0.689866	−	0.723937i
$3$	1.69183	+	0.371101i	0.976778	+	0.214255i
$3$	1.69183	+	0.371101i	0.976778	+	0.214255i
$4$	−0.0963383	+	1.99768i	−0.0481691	+	0.998839i
$5$	−1.56730			−0.700916			−0.350458	−	0.936578i	$-0.613974\pi$
$5$	−1.56730			−0.700916			−0.350458	+	0.936578i	$0.613974\pi$
$6$	−1.27065	−	2.09415i	−0.518739	−	0.854933i
$7$		−	0.668312i		−	0.252598i	−0.991992	−	0.126299i	$-0.959690\pi$
$7$		−	0.668312i		−	0.252598i	0.991992	−	0.126299i	$-0.0403099\pi$
$8$	2.13922	−	1.85034i	0.756327	−	0.654194i
$9$	2.72457	+	1.25568i	0.908189	+	0.418560i
$10$	1.52908	+	1.60460i	0.483539	+	0.507419i
$11$			4.80506i			1.44878i	0.689391	+	0.724389i	$0.257878\pi$
$11$			4.80506i			1.44878i	−0.689391	+	0.724389i	$0.742122\pi$
$12$	−0.904328	+	3.34398i	−0.261057	+	0.965323i
$13$			4.48924i			1.24509i	0.782584	+	0.622545i	$0.213901\pi$
$13$			4.48924i			1.24509i	−0.782584	+	0.622545i	$0.786099\pi$
$14$	−0.684219	+	0.652017i	−0.182865	+	0.174259i
$15$	−2.65160	−	0.581625i	−0.684639	−	0.150175i
$16$	−3.98144	−	0.384906i	−0.995359	−	0.0962264i
$17$		−	1.05154i		−	0.255035i	−0.991836	−	0.127518i	$-0.959299\pi$
$17$		−	1.05154i		−	0.255035i	0.991836	−	0.127518i	$-0.0407009\pi$
$18$	−1.37257	−	4.01448i	−0.323518	−	0.946222i
$19$	1.05324			0.241630			0.120815	−	0.992675i	$-0.461449\pi$
$19$	1.05324			0.241630			0.120815	+	0.992675i	$0.461449\pi$
$20$	0.150991	−	3.13095i	0.0337625	−	0.700103i
$21$	0.248011	−	1.13067i	0.0541205	−	0.246732i
$22$	4.91942	−	4.68790i	1.04882	−	0.999464i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.30585	−	2.33659i	0.878928	−	0.476955i
$25$	−2.54358			−0.508716
$26$	4.59609	−	4.37978i	0.901367	−	0.858946i
$27$	4.14352	+	3.13548i	0.797421	+	0.603424i
$28$	1.33507	+	0.0643840i	0.252305	+	0.0121674i
$29$	7.11293			1.32084			0.660419	−	0.750897i	$-0.270379\pi$
$29$	7.11293			1.32084			0.660419	+	0.750897i	$0.270379\pi$
$30$	1.99148	+	3.28215i	0.363592	+	0.599236i
$31$			3.88117i			0.697078i	0.937294	+	0.348539i	$0.113322\pi$
$31$			3.88117i			0.697078i	−0.937294	+	0.348539i	$0.886678\pi$
$32$	3.49030	+	4.45172i	0.617003	+	0.786961i
$33$	−1.78316	+	8.12933i	−0.310409	+	1.41514i
$34$	−1.07656	+	1.02590i	−0.184629	+	0.175940i
$35$			1.04744i			0.177050i
$36$	−2.77092	+	5.32184i	−0.461820	+	0.886973i
$37$		−	2.44792i		−	0.402435i	−0.979547	−	0.201218i	$-0.935510\pi$
$37$		−	2.44792i		−	0.402435i	0.979547	−	0.201218i	$-0.0644898\pi$
$38$	−1.02756	−	1.07831i	−0.166693	−	0.174925i
$39$	−1.66596	+	7.59502i	−0.266767	+	1.21618i
$40$	−3.35278	+	2.90003i	−0.530122	+	0.458535i
$41$			2.02989i			0.317015i	0.987358	+	0.158508i	$0.0506683\pi$
$41$			2.02989i			0.317015i	−0.987358	+	0.158508i	$0.949332\pi$
$42$	−1.39955	+	0.849187i	−0.215954	+	0.131032i
$43$	−3.57557			−0.545270			−0.272635	−	0.962118i	$-0.587895\pi$
$43$	−3.57557			−0.545270			−0.272635	+	0.962118i	$0.587895\pi$
$44$	−9.59896	−	0.462911i	−1.44710	−	0.0697864i
$45$	−4.27021	−	1.96802i	−0.636565	−	0.293375i
$46$	−0.975618	−	1.02380i	−0.143847	−	0.150951i
$47$	7.09880			1.03547			0.517734	−	0.855542i	$-0.326776\pi$
$47$	7.09880			1.03547			0.517734	+	0.855542i	$0.326776\pi$
$48$	−6.59307	−	2.12871i	−0.951628	−	0.307253i
$49$	6.55336			0.936194
$50$	2.48156	+	2.60412i	0.350946	+	0.368278i
$51$	0.390226	−	1.77902i	0.0546426	−	0.249113i
$52$	−8.96805	−	0.432485i	−1.24364	−	0.0599749i
$53$	0.0884948			0.0121557			0.00607785	−	0.999982i	$-0.498065\pi$
$53$	0.0884948			0.0121557			0.00607785	+	0.999982i	$0.498065\pi$
$54$	−0.832380	−	7.30117i	−0.113273	−	0.993564i
$55$		−	7.53095i		−	1.01547i
$56$	−1.23660	−	1.42966i	−0.165248	−	0.191047i
$57$	1.78191	+	0.390859i	0.236019	+	0.0517706i
$58$	−6.93951	−	7.28223i	−0.911202	−	0.956204i
$59$			6.15979i			0.801937i	0.916092	+	0.400968i	$0.131326\pi$
$59$			6.15979i			0.801937i	−0.916092	+	0.400968i	$0.868674\pi$
$60$	1.41735	−	5.24101i	0.182979	−	0.676611i
$61$			6.69672i			0.857427i	0.903440	+	0.428714i	$0.141033\pi$
$61$			6.69672i			0.857427i	−0.903440	+	0.428714i	$0.858967\pi$
$62$	3.97355	−	3.78654i	0.504641	−	0.480891i
$63$	0.839185	−	1.82086i	0.105727	−	0.229407i
$64$	1.15248	−	7.91655i	0.144060	−	0.989569i
$65$		−	7.03596i		−	0.872704i
$66$	10.0625	−	6.10552i	1.23861	−	0.751538i
$67$	13.2350			1.61691			0.808457	−	0.588556i	$-0.200303\pi$
$67$	13.2350			1.61691			0.808457	+	0.588556i	$0.200303\pi$
$68$	2.10063	+	0.101303i	0.254739	+	0.0122848i
$69$	1.69183	+	0.371101i	0.203672	+	0.0446753i
$70$	1.07237	−	1.02190i	0.128173	−	0.122141i
$71$	−6.95495			−0.825401			−0.412701	−	0.910867i	$-0.635414\pi$
$71$	−6.95495			−0.825401			−0.412701	+	0.910867i	$0.635414\pi$
$72$	8.15187	−	2.35521i	0.960707	−	0.277564i
$73$	−13.8192			−1.61741			−0.808706	−	0.588213i	$-0.799832\pi$
$73$	−13.8192			−1.61741			−0.808706	+	0.588213i	$0.799832\pi$
$74$	−2.50618	+	2.38823i	−0.291338	+	0.277626i
$75$	−4.30330	−	0.943926i	−0.496903	−	0.108995i
$76$	−0.101468	+	2.10404i	−0.0116391	+	0.241350i
$77$	3.21128			0.365959
$78$	9.40113	−	5.70423i	1.06447	−	0.645876i
$79$		−	14.6807i		−	1.65171i	−0.563885	−	0.825853i	$-0.690694\pi$
$79$		−	14.6807i		−	1.65171i	0.563885	−	0.825853i	$-0.309306\pi$
$80$	6.24009	+	0.603261i	0.697664	+	0.0674467i
$81$	5.84654	+	6.84236i	0.649616	+	0.760263i
$82$	2.07820	−	1.98040i	0.229499	−	0.218698i
$83$		−	15.1782i		−	1.66602i	−0.553256	−	0.833011i	$-0.686615\pi$
$83$		−	15.1782i		−	1.66602i	0.553256	−	0.833011i	$-0.313385\pi$
$84$	2.23482	+	0.604373i	0.243839	+	0.0659425i
$85$			1.64807i			0.178758i
$86$	3.48840	+	3.66068i	0.376163	+	0.394741i
$87$	12.0339	+	2.63962i	1.29017	+	0.282997i
$88$	8.89099	+	10.2790i	0.947783	+	1.09575i
$89$			3.28612i			0.348328i	0.984717	+	0.174164i	$0.0557223\pi$
$89$			3.28612i			0.348328i	−0.984717	+	0.174164i	$0.944278\pi$
$90$	2.15123	+	6.29188i	0.226759	+	0.663222i
$91$	3.00021			0.314507
$92$	−0.0963383	+	1.99768i	−0.0100440	+	0.208272i
$93$	−1.44031	+	6.56627i	−0.149353	+	0.680891i
$94$	−6.92572	−	7.26777i	−0.714334	−	0.749613i
$95$	−1.65074			−0.169363
$96$	4.25294	+	8.82680i	0.434064	+	0.900882i
$97$	−14.8592			−1.50872			−0.754359	−	0.656462i	$-0.772052\pi$
$97$	−14.8592			−1.50872			−0.754359	+	0.656462i	$0.772052\pi$
$98$	−6.39358	−	6.70934i	−0.645849	−	0.677745i
$99$	−6.03361	+	13.0917i	−0.606400	+	1.31577i
$100$	0.245044	−	5.08126i	0.0245044	−	0.508126i
$101$	−9.97023			−0.992075			−0.496037	−	0.868301i	$-0.665212\pi$
$101$	−9.97023			−0.992075			−0.496037	+	0.868301i	$0.665212\pi$
$102$	−2.20208	+	1.33613i	−0.218038	+	0.132297i
$103$		−	10.4993i		−	1.03452i	−0.855827	−	0.517262i	$-0.826951\pi$
$103$		−	10.4993i		−	1.03452i	0.855827	−	0.517262i	$-0.173049\pi$
$104$	8.30661	+	9.60344i	0.814530	+	0.941695i
$105$	−0.388707	+	1.77209i	−0.0379339	+	0.172939i
$106$	−0.0863372	−	0.0906011i	−0.00838581	−	0.00879996i
$107$		−	6.58657i		−	0.636748i	−0.947965	−	0.318374i	$-0.896863\pi$
$107$		−	6.58657i		−	0.636748i	0.947965	−	0.318374i	$-0.103137\pi$
$108$	−6.66287	+	7.97535i	−0.641135	+	0.767428i
$109$		−	0.431361i		−	0.0413169i	−0.999787	−	0.0206584i	$-0.993424\pi$
$109$		−	0.431361i		−	0.0413169i	0.999787	−	0.0206584i	$-0.00657625\pi$
$110$	−7.71019	+	7.34733i	−0.735138	+	0.700540i
$111$	0.908424	−	4.14146i	0.0862238	−	0.393090i
$112$	−0.257237	+	2.66084i	−0.0243066	+	0.251426i
$113$			1.75625i			0.165214i	0.996582	+	0.0826071i	$0.0263247\pi$
$113$			1.75625i			0.165214i	−0.996582	+	0.0826071i	$0.973675\pi$
$114$	−1.33830	−	2.20565i	−0.125343	−	0.206578i
$115$	−1.56730			−0.146151
$116$	−0.685248	+	14.2094i	−0.0636237	+	1.31931i
$117$	−5.63704	+	12.2312i	−0.521144	+	1.13078i
$118$	6.30640	−	6.00961i	0.580552	−	0.553229i
$119$	−0.702755			−0.0644214
$120$	−6.74854	+	3.66213i	−0.616055	+	0.334306i
$121$	−12.0886			−1.09896
$122$	6.85611	−	6.53344i	0.620723	−	0.591510i
$123$	−0.753294	+	3.43422i	−0.0679222	+	0.309654i
$124$	−7.75333	−	0.373905i	−0.696269	−	0.0335777i
$125$	11.8230			1.05748
$126$	−2.68292	+	0.917307i	−0.239014	+	0.0817202i
$127$		−	14.7702i		−	1.31064i	−0.755350	−	0.655322i	$-0.772533\pi$
$127$		−	14.7702i		−	1.31064i	0.755350	−	0.655322i	$-0.227467\pi$
$128$	−9.22936	+	6.54362i	−0.815768	+	0.578380i
$129$	−6.04926	−	1.32690i	−0.532608	−	0.116827i
$130$	−7.20343	+	6.86441i	−0.631783	+	0.602049i
$131$		−	11.9341i		−	1.04268i	−0.853348	−	0.521342i	$-0.825432\pi$
$131$		−	11.9341i		−	1.04268i	0.853348	−	0.521342i	$-0.174568\pi$
$132$	−16.0680	−	4.34535i	−1.39854	−	0.378214i
$133$		−	0.703895i		−	0.0610354i
$134$	−12.9123	−	13.5500i	−1.11545	−	1.17054i
$135$	−6.49412	−	4.91423i	−0.558925	−	0.422950i
$136$	−1.94570	−	2.24946i	−0.166842	−	0.192890i
$137$		−	2.81139i		−	0.240193i	−0.992762	−	0.120096i	$-0.961680\pi$
$137$		−	2.81139i		−	0.240193i	0.992762	−	0.120096i	$-0.0383204\pi$
$138$	−1.27065	−	2.09415i	−0.108164	−	0.178266i
$139$	13.2991			1.12801			0.564007	−	0.825770i	$-0.309259\pi$
$139$	13.2991			1.12801			0.564007	+	0.825770i	$0.309259\pi$
$140$	−2.09245	−	0.100909i	−0.176845	−	0.00852835i
$141$	12.0100	+	2.63437i	1.01142	+	0.221854i
$142$	6.78538	+	7.12049i	0.569416	+	0.597538i
$143$	−21.5710			−1.80386
$144$	−10.3644	−	6.04811i	−0.863698	−	0.504009i
$145$	−11.1481			−0.925798
$146$	13.4822	+	14.1481i	1.11580	+	1.17090i
$147$	11.0872	+	2.43196i	0.914454	+	0.200585i
$148$	4.89015	+	0.235828i	0.401968	+	0.0193849i
$149$	−19.3500			−1.58521			−0.792606	−	0.609735i	$-0.791276\pi$
$149$	−19.3500			−1.58521			−0.792606	+	0.609735i	$0.791276\pi$
$150$	3.23199	+	5.32664i	0.263891	+	0.434918i
$151$			2.97135i			0.241805i	0.992664	+	0.120902i	$0.0385788\pi$
$151$			2.97135i			0.241805i	−0.992664	+	0.120902i	$0.961421\pi$
$152$	2.25311	−	1.94886i	0.182752	−	0.158073i
$153$	1.32039	−	2.86498i	0.106747	−	0.231620i
$154$	−3.13298	−	3.28771i	−0.252463	−	0.264931i
$155$		−	6.08294i		−	0.488594i
$156$	−15.0119	−	4.05974i	−1.20191	−	0.325040i
$157$			2.60654i			0.208025i	0.994576	+	0.104012i	$0.0331682\pi$
$157$			2.60654i			0.208025i	−0.994576	+	0.104012i	$0.966832\pi$
$158$	−15.0301	+	14.3227i	−1.19573	+	1.13946i
$159$	0.149718	+	0.0328405i	0.0118734	+	0.00260442i
$160$	−5.47033	−	6.97717i	−0.432467	−	0.551594i
$161$		−	0.668312i		−	0.0526704i
$162$	1.30123	−	12.6612i	0.102234	−	0.994760i
$163$	−0.285740			−0.0223808			−0.0111904	−	0.999937i	$-0.503562\pi$
$163$	−0.285740			−0.0223808			−0.0111904	+	0.999937i	$0.503562\pi$
$164$	−4.05507	−	0.195556i	−0.316647	−	0.0152704i
$165$	2.79474	−	12.7411i	0.217570	−	0.991891i
$166$	−15.5394	+	14.8081i	−1.20610	+	1.14933i
$167$	2.91498			0.225568			0.112784	−	0.993620i	$-0.464023\pi$
$167$	2.91498			0.225568			0.112784	+	0.993620i	$0.464023\pi$
$168$	−1.56157	−	2.87765i	−0.120478	−	0.222016i
$169$	−7.15324			−0.550249
$170$	1.68730	−	1.60789i	0.129410	−	0.123319i
$171$	2.86963	+	1.32253i	0.219446	+	0.101137i
$172$	0.344465	−	7.14285i	0.0262652	−	0.544637i
$173$	2.97172			0.225935			0.112968	−	0.993599i	$-0.463964\pi$
$173$	2.97172			0.225935			0.112968	+	0.993599i	$0.463964\pi$
$174$	−9.03802	−	14.8955i	−0.685170	−	1.12923i
$175$			1.69991i			0.128501i
$176$	1.84949	−	19.1310i	0.139411	−	1.44206i
$177$	−2.28591	+	10.4213i	−0.171819	+	0.783314i
$178$	3.36434	−	3.20600i	0.252168	−	0.240300i
$179$			6.66837i			0.498417i	0.968450	+	0.249209i	$0.0801705\pi$
$179$			6.66837i			0.498417i	−0.968450	+	0.249209i	$0.919830\pi$
$180$	4.34286	−	8.34090i	0.323697	−	0.621694i
$181$			21.5936i			1.60504i	0.596624	+	0.802521i	$0.296508\pi$
$181$			21.5936i			1.60504i	−0.596624	+	0.802521i	$0.703492\pi$
$182$	−2.92706	−	3.07162i	−0.216968	−	0.227684i
$183$	−2.48516	+	11.3297i	−0.183708	+	0.837516i
$184$	2.13922	−	1.85034i	0.157705	−	0.136409i
$185$			3.83661i			0.282073i
$186$	8.12775	−	4.93159i	0.595955	−	0.361602i
$187$	5.05269			0.369490
$188$	−0.683886	+	14.1811i	−0.0498775	+	1.03427i
$189$	2.09548	−	2.76916i	0.152424	−	0.201427i
$190$	1.61050	+	1.69003i	0.116838	+	0.122608i
$191$	−18.7023			−1.35325			−0.676627	−	0.736326i	$-0.736559\pi$
$191$	−18.7023			−1.35325			−0.676627	+	0.736326i	$0.736559\pi$
$192$	4.88764	−	12.9658i	0.352735	−	0.935723i
$193$	−7.83699			−0.564119			−0.282059	−	0.959397i	$-0.591017\pi$
$193$	−7.83699			−0.564119			−0.282059	+	0.959397i	$0.591017\pi$
$194$	14.4969	+	15.2128i	1.04081	+	1.09222i
$195$	2.61105	−	11.9036i	0.186981	−	0.852438i
$196$	−0.631339	+	13.0915i	−0.0450957	+	0.935107i
$197$	19.7501			1.40714			0.703569	−	0.710627i	$-0.251588\pi$
$197$	19.7501			1.40714			0.703569	+	0.710627i	$0.251588\pi$
$198$	19.2898	−	6.59529i	1.37087	−	0.468707i
$199$		−	25.7268i		−	1.82372i	−0.410498	−	0.911861i	$-0.634645\pi$
$199$		−	25.7268i		−	1.82372i	0.410498	−	0.911861i	$-0.365355\pi$
$200$	−5.44127	+	4.70649i	−0.384756	+	0.332799i
$201$	22.3914	+	4.91152i	1.57936	+	0.346432i
$202$	9.72714	+	10.2075i	0.684399	+	0.718200i
$203$		−	4.75366i		−	0.333641i
$204$	3.51632	+	0.950935i	0.246191	+	0.0665787i
$205$		−	3.18144i		−	0.222201i
$206$	−10.7492	+	10.2433i	−0.748930	+	0.713684i
$207$	2.72457	+	1.25568i	0.189371	+	0.0872757i
$208$	1.72793	−	17.8736i	0.119811	−	1.23931i
$209$			5.06089i			0.350069i
$210$	2.19350	−	1.33093i	0.151366	−	0.0918428i
$211$	8.36042			0.575555			0.287778	−	0.957697i	$-0.407084\pi$
$211$	8.36042			0.575555			0.287778	+	0.957697i	$0.407084\pi$
$212$	−0.00852544	+	0.176784i	−0.000585529	+	0.0121416i
$213$	−11.7666	−	2.58099i	−0.806233	−	0.176847i
$214$	−6.74334	+	6.42598i	−0.460965	+	0.439271i
$215$	5.60399			0.382189
$216$	14.6656	−	0.959446i	0.997867	−	0.0652820i
$217$	2.59383			0.176081
$218$	−0.441628	+	0.420843i	−0.0299108	+	0.0285031i
$219$	−23.3797	−	5.12831i	−1.57985	−	0.346539i
$220$	15.0444	+	0.725518i	1.01429	+	0.0489144i
$221$	4.72060			0.317542
$222$	−5.12630	+	3.11043i	−0.344055	+	0.208759i
$223$			6.61307i			0.442844i	0.975178	+	0.221422i	$0.0710698\pi$
$223$			6.61307i			0.442844i	−0.975178	+	0.221422i	$0.928930\pi$
$224$	2.97514	−	2.33261i	0.198785	−	0.155854i
$225$	−6.93016	−	3.19392i	−0.462011	−	0.212928i
$226$	1.79805	−	1.71343i	0.119605	−	0.113976i
$227$			11.5457i			0.766313i	0.923684	+	0.383156i	$0.125163\pi$
$227$			11.5457i			0.766313i	−0.923684	+	0.383156i	$0.874837\pi$
$228$	−0.952477	+	3.52202i	−0.0630793	+	0.233252i
$229$			14.1282i			0.933618i	0.884358	+	0.466809i	$0.154597\pi$
$229$			14.1282i			0.933618i	−0.884358	+	0.466809i	$0.845403\pi$
$230$	1.52908	+	1.60460i	0.100825	+	0.105804i
$231$	5.43293	+	1.19171i	0.357461	+	0.0784086i
$232$	15.2161	−	13.1613i	0.998986	−	0.864085i
$233$		−	8.39325i		−	0.549860i	−0.961464	−	0.274930i	$-0.911345\pi$
$233$		−	8.39325i		−	0.549860i	0.961464	−	0.274930i	$-0.0886547\pi$
$234$	18.0219	−	6.16180i	1.17813	−	0.402810i
$235$	−11.1259			−0.725776
$236$	−12.3053	−	0.593424i	−0.801006	−	0.0386286i
$237$	5.44802	−	24.8372i	0.353887	−	1.61335i
$238$	0.685620	+	0.719481i	0.0444422	+	0.0466370i
$239$	19.6371			1.27022			0.635109	−	0.772423i	$-0.280955\pi$
$239$	19.6371			1.27022			0.635109	+	0.772423i	$0.280955\pi$
$240$	10.3333	+	3.33632i	0.667012	+	0.215359i
$241$	13.2022			0.850429			0.425214	−	0.905093i	$-0.360199\pi$
$241$	13.2022			0.850429			0.425214	+	0.905093i	$0.360199\pi$
$242$	11.7938	+	12.3763i	0.758136	+	0.795578i
$243$	7.35214	+	13.7458i	0.471640	+	0.881791i
$244$	−13.3779	−	0.645151i	−0.856432	−	0.0413015i
$245$	−10.2711			−0.656194
$246$	4.25089	−	2.57927i	0.271027	−	0.164448i
$247$			4.72826i			0.300852i
$248$	7.18148	+	8.30266i	0.456025	+	0.527219i
$249$	5.63264	−	25.6789i	0.356954	−	1.62733i
$250$	−11.5348	−	12.1044i	−0.729522	−	0.765552i
$251$		−	25.4601i		−	1.60703i	−0.595285	−	0.803515i	$-0.702961\pi$
$251$		−	25.4601i		−	1.60703i	0.595285	−	0.803515i	$-0.297039\pi$
$252$	3.55665	+	1.85184i	0.224048	+	0.116655i
$253$			4.80506i			0.302091i
$254$	−15.1218	+	14.4101i	−0.948823	+	0.904169i
$255$	−0.611601	+	2.78825i	−0.0382999	+	0.174607i
$256$	15.7037	+	3.06496i	0.981481	+	0.191560i
$257$		−	31.0836i		−	1.93894i	−0.245208	−	0.969471i	$-0.578856\pi$
$257$		−	31.0836i		−	1.93894i	0.245208	−	0.969471i	$-0.421144\pi$
$258$	4.54329	+	7.48779i	0.282853	+	0.466169i
$259$	−1.63597			−0.101654
$260$	14.0556	+	0.677833i	0.871691	+	0.0420374i
$261$	19.3797	+	8.93156i	1.19957	+	0.552850i
$262$	−12.2181	+	11.6431i	−0.754837	+	0.719312i
$263$	15.9511			0.983585			0.491793	−	0.870712i	$-0.336342\pi$
$263$	15.9511			0.983585			0.491793	+	0.870712i	$0.336342\pi$
$264$	11.2275	+	20.6898i	0.691003	+	1.27337i
$265$	−0.138698			−0.00852013
$266$	−0.720648	+	0.686733i	−0.0441858	+	0.0421063i
$267$	−1.21948	+	5.55956i	−0.0746312	+	0.340239i
$268$	−1.27504	+	26.4393i	−0.0778853	+	1.61504i
$269$	−1.26899			−0.0773716			−0.0386858	−	0.999251i	$-0.512317\pi$
$269$	−1.26899			−0.0773716			−0.0386858	+	0.999251i	$0.512317\pi$
$270$	1.30459	+	11.4431i	0.0793946	+	0.696405i
$271$			28.0851i			1.70605i	0.521872	+	0.853024i	$0.325234\pi$
$271$			28.0851i			1.70605i	−0.521872	+	0.853024i	$0.674766\pi$
$272$	−0.404743	+	4.18663i	−0.0245411	+	0.253852i
$273$	5.07584	+	1.11338i	0.307204	+	0.0673849i
$274$	−2.87830	+	2.74284i	−0.173884	+	0.165701i
$275$		−	12.2221i		−	0.737018i
$276$	−0.904328	+	3.34398i	−0.0544342	+	0.201284i
$277$			21.5783i			1.29651i	0.761422	+	0.648256i	$0.224502\pi$
$277$			21.5783i			1.29651i	−0.761422	+	0.648256i	$0.775498\pi$
$278$	−12.9748	−	13.6156i	−0.778179	−	0.816611i
$279$	−4.87350	+	10.5745i	−0.291769	+	0.633079i
$280$	1.93813	+	2.24071i	0.115825	+	0.133908i
$281$		−	24.4749i		−	1.46005i	−0.683421	−	0.730024i	$-0.739509\pi$
$281$		−	24.4749i		−	1.46005i	0.683421	−	0.730024i	$-0.260491\pi$
$282$	−9.02006	−	14.8660i	−0.537137	−	0.885255i
$283$	14.9845			0.890739			0.445369	−	0.895347i	$-0.353072\pi$
$283$	14.9845			0.890739			0.445369	+	0.895347i	$0.353072\pi$
$284$	0.670028	−	13.8938i	0.0397589	−	0.824443i
$285$	−2.79278	−	0.612593i	−0.165430	−	0.0362869i
$286$	21.0451	+	22.0845i	1.24442	+	1.30588i
$287$	1.35660			0.0800775
$288$	3.91962	+	16.5117i	0.230966	+	0.972962i
$289$	15.8943			0.934957
$290$	10.8763	+	11.4134i	0.638676	+	0.670219i
$291$	−25.1391	−	5.51425i	−1.47368	−	0.323251i
$292$	1.33132	−	27.6063i	0.0779093	−	1.61553i
$293$	−0.409364			−0.0239153			−0.0119577	−	0.999929i	$-0.503806\pi$
$293$	−0.409364			−0.0239153			−0.0119577	+	0.999929i	$0.503806\pi$
$294$	−8.32699	−	13.7237i	−0.485640	−	0.800383i
$295$		−	9.65422i		−	0.562091i
$296$	−4.52948	−	5.23662i	−0.263271	−	0.304372i
$297$	−15.0662	+	19.9098i	−0.874228	+	1.15529i
$298$	18.8782	+	19.8105i	1.09358	+	1.14759i
$299$			4.48924i			0.259619i
$300$	2.30023	−	8.50568i	0.132804	−	0.491076i
$301$			2.38960i			0.137734i
$302$	3.04207	−	2.89890i	0.175051	−	0.166813i
$303$	−16.8679	−	3.69996i	−0.969037	−	0.212557i
$304$	−4.19342	−	0.405399i	−0.240509	−	0.0232512i
$305$		−	10.4957i		−	0.600985i
$306$	−4.22137	+	1.44331i	−0.241320	+	0.0825086i
$307$	29.7764			1.69943			0.849715	−	0.527243i	$-0.176774\pi$
$307$	29.7764			1.69943			0.849715	+	0.527243i	$0.176774\pi$
$308$	−0.309369	+	6.41510i	−0.0176279	+	0.365534i
$309$	3.89629	−	17.7630i	0.221652	−	1.01050i
$310$	−6.22772	+	5.93463i	−0.353711	+	0.337064i
$311$	24.6431			1.39738			0.698690	−	0.715425i	$-0.253767\pi$
$311$	24.6431			1.39738			0.698690	+	0.715425i	$0.253767\pi$
$312$	10.4895	+	19.3300i	0.593852	+	1.09434i
$313$	27.9670			1.58079			0.790394	−	0.612599i	$-0.209876\pi$
$313$	27.9670			1.58079			0.790394	+	0.612599i	$0.209876\pi$
$314$	2.66858	−	2.54299i	0.150597	−	0.143509i
$315$	−1.31525	+	2.85383i	−0.0741060	+	0.160795i
$316$	29.3273	+	1.41431i	1.64979	+	0.0795613i
$317$	−19.9130			−1.11843			−0.559213	−	0.829024i	$-0.688897\pi$
$317$	−19.9130			−1.11843			−0.559213	+	0.829024i	$0.688897\pi$
$318$	−0.112446	−	0.185321i	−0.00630563	−	0.0103923i
$319$			34.1781i			1.91360i
$320$	−1.80628	+	12.4076i	−0.100974	+	0.693605i
$321$	2.44428	−	11.1434i	0.136427	−	0.621961i
$322$	−0.684219	+	0.652017i	−0.0381300	+	0.0363355i
$323$		−	1.10752i		−	0.0616243i
$324$	−14.2321	+	11.0203i	−0.790672	+	0.612241i
$325$		−	11.4187i		−	0.633398i
$326$	0.278773	+	0.292540i	0.0154398	+	0.0162023i
$327$	0.160078	−	0.729788i	0.00885235	−	0.0403574i
$328$	3.75599	+	4.34237i	0.207390	+	0.239767i
$329$		−	4.74422i		−	0.261557i
$330$	−15.7709	+	9.56916i	−0.868161	+	0.526765i
$331$	−13.6482			−0.750171			−0.375086	−	0.926990i	$-0.622387\pi$
$331$	−13.6482			−0.750171			−0.375086	+	0.926990i	$0.622387\pi$
$332$	30.3211	+	1.46224i	1.66409	+	0.0802509i
$333$	3.07380	−	6.66952i	0.168443	−	0.365487i
$334$	−2.84390	−	2.98436i	−0.155611	−	0.163297i
$335$	−20.7432			−1.13332
$336$	−1.42264	+	4.40623i	−0.0776115	+	0.240379i
$337$	−3.42477			−0.186559			−0.0932796	−	0.995640i	$-0.529735\pi$
$337$	−3.42477			−0.186559			−0.0932796	+	0.995640i	$0.529735\pi$
$338$	6.97883	+	7.32350i	0.379598	+	0.398346i
$339$	−0.651747	+	2.97128i	−0.0353980	+	0.161378i
$340$	−3.29231	−	0.158772i	−0.178551	−	0.00861063i
$341$	−18.6492			−1.00991
$342$	−1.44565	−	4.22822i	−0.0781719	−	0.228636i
$343$		−	9.05787i		−	0.489079i
$344$	−7.64892	+	6.61603i	−0.412402	+	0.356712i
$345$	−2.65160	−	0.581625i	−0.142757	−	0.0313137i
$346$	−2.89926	−	3.04245i	−0.155865	−	0.163563i
$347$		−	17.9791i		−	0.965169i	−0.875849	−	0.482585i	$-0.839698\pi$
$347$		−	17.9791i		−	0.965169i	0.875849	−	0.482585i	$-0.160302\pi$
$348$	−6.43243	+	23.7855i	−0.344814	+	1.27504i
$349$		−	32.6623i		−	1.74837i	−0.485590	−	0.874187i	$-0.661395\pi$
$349$		−	32.6623i		−	1.74837i	0.485590	−	0.874187i	$-0.338605\pi$
$350$	1.74037	−	1.65846i	0.0930265	−	0.0886484i
$351$	−14.0759	+	18.6012i	−0.751317	+	0.992860i
$352$	−21.3908	+	16.7711i	−1.14013	+	0.893901i
$353$		−	7.82574i		−	0.416522i	−0.978073	−	0.208261i	$-0.933220\pi$
$353$		−	7.82574i		−	0.416522i	0.978073	−	0.208261i	$-0.0667804\pi$
$354$	12.8995	−	7.82691i	0.685602	−	0.415996i
$355$	10.9005			0.578537
$356$	−6.56462	−	0.316579i	−0.347924	−	0.0167787i
$357$	−1.18894	−	0.260793i	−0.0629254	−	0.0138026i
$358$	6.82708	−	6.50578i	0.360823	−	0.343841i
$359$	14.3691			0.758370			0.379185	−	0.925321i	$-0.376204\pi$
$359$	14.3691			0.758370			0.379185	+	0.925321i	$0.376204\pi$
$360$	−12.7764	+	3.69131i	−0.673375	+	0.194549i
$361$	−17.8907			−0.941615
$362$	22.1076	−	21.0671i	1.16195	−	1.10726i
$363$	−20.4518	−	4.48608i	−1.07344	−	0.235458i
$364$	−0.289035	+	5.99345i	−0.0151496	+	0.314142i
$365$	21.6587			1.13367
$366$	14.0239	−	8.50916i	0.733043	−	0.444781i
$367$		−	21.9405i		−	1.14529i	−0.819805	−	0.572643i	$-0.805918\pi$
$367$		−	21.9405i		−	1.14529i	0.819805	−	0.572643i	$-0.194082\pi$
$368$	−3.98144	−	0.384906i	−0.207547	−	0.0200646i
$369$	−2.54889	+	5.53057i	−0.132690	+	0.287910i
$370$	3.92793	−	3.74307i	0.204203	−	0.194593i
$371$		−	0.0591421i		−	0.00307051i
$372$	−12.9785	−	3.50985i	−0.672906	−	0.181977i
$373$			11.5427i			0.597660i	0.954306	+	0.298830i	$0.0965963\pi$
$373$			11.5427i			0.597660i	−0.954306	+	0.298830i	$0.903404\pi$
$374$	−4.92950	−	5.17295i	−0.254898	−	0.267487i
$375$	20.0025	+	4.38754i	1.03293	+	0.226571i
$376$	15.1859	−	13.1352i	0.783151	−	0.677396i
$377$			31.9316i			1.64456i
$378$	−4.87946	+	0.556290i	−0.250972	+	0.0286125i
$379$	−23.2230			−1.19288			−0.596442	−	0.802656i	$-0.703419\pi$
$379$	−23.2230			−1.19288			−0.596442	+	0.802656i	$0.703419\pi$
$380$	0.159030	−	3.29766i	0.00815806	−	0.169166i
$381$	5.48124	−	24.9887i	0.280812	−	1.28021i
$382$	18.2463	+	19.1475i	0.933564	+	0.979670i
$383$	−8.37650			−0.428019			−0.214010	−	0.976832i	$-0.568652\pi$
$383$	−8.37650			−0.428019			−0.214010	+	0.976832i	$0.568652\pi$
$384$	−18.0428	+	7.64566i	−0.920745	+	0.390166i
$385$	−5.03302			−0.256507
$386$	7.64591	+	8.02352i	0.389166	+	0.408386i
$387$	−9.74190	−	4.48977i	−0.495208	−	0.228228i
$388$	1.43151	−	29.6838i	0.0726737	−	1.50697i
$389$	−34.5614			−1.75233			−0.876165	−	0.482011i	$-0.839906\pi$
$389$	−34.5614			−1.75233			−0.876165	+	0.482011i	$0.839906\pi$
$390$	−14.7344	+	8.94021i	−0.746103	+	0.452705i
$391$		−	1.05154i		−	0.0531785i
$392$	14.0190	−	12.1259i	0.708069	−	0.612453i
$393$	4.42874	−	20.1904i	0.223401	−	1.01847i
$394$	−19.2686	−	20.2202i	−0.970737	−	1.01868i
$395$			23.0090i			1.15771i
$396$	−25.5717	−	13.3144i	−1.28503	−	0.669076i
$397$			15.3903i			0.772419i	0.922411	+	0.386210i	$0.126216\pi$
$397$			15.3903i			0.772419i	−0.922411	+	0.386210i	$0.873784\pi$
$398$	−26.3391	+	25.0995i	−1.32026	+	1.25812i
$399$	0.261216	−	1.19087i	0.0130772	−	0.0596180i
$400$	10.1271	+	0.979039i	0.506356	+	0.0489520i
$401$			19.6960i			0.983572i	0.870716	+	0.491786i	$0.163656\pi$
$401$			19.6960i			0.983572i	−0.870716	+	0.491786i	$0.836344\pi$
$402$	−16.8170	−	27.7161i	−0.838755	−	1.38235i
$403$	−17.4235			−0.867925
$404$	0.960515	−	19.9173i	0.0477874	−	0.990923i
$405$	−9.16327	−	10.7240i	−0.455326	−	0.532880i
$406$	−4.86680	+	4.63776i	−0.241535	+	0.230168i
$407$	11.7624			0.583039
$408$	−2.45701	−	4.52776i	−0.121640	−	0.224157i
$409$	12.4982			0.617997			0.308999	−	0.951062i	$-0.400006\pi$
$409$	12.4982			0.617997			0.308999	+	0.951062i	$0.400006\pi$
$410$	−3.25716	+	3.10387i	−0.160860	+	0.153289i
$411$	1.04331	−	4.75638i	0.0514626	−	0.234615i
$412$	20.9742	+	1.01148i	1.03332	+	0.0498322i
$413$	4.11666			0.202568
$414$	−1.37257	−	4.01448i	−0.0674583	−	0.197301i
$415$			23.7887i			1.16774i
$416$	−19.9848	+	15.6688i	−0.979837	+	0.768224i
$417$	22.4998	+	4.93531i	1.10182	+	0.241683i
$418$	5.18135	−	4.93750i	0.253428	−	0.241501i
$419$			1.87704i			0.0916996i	0.998948	+	0.0458498i	$0.0145996\pi$
$419$			1.87704i			0.0916996i	−0.998948	+	0.0458498i	$0.985400\pi$
$420$	−3.50263	−	0.947232i	−0.170911	−	0.0462202i
$421$		−	22.8290i		−	1.11262i	−0.830976	−	0.556309i	$-0.812217\pi$
$421$		−	22.8290i		−	1.11262i	0.830976	−	0.556309i	$-0.187783\pi$
$422$	−8.15658	−	8.55941i	−0.397056	−	0.416666i
$423$	19.3412	+	8.91382i	0.940400	+	0.433405i
$424$	0.189309	−	0.163746i	0.00919368	−	0.00795219i
$425$			2.67467i			0.129741i
$426$	8.83728	+	14.5647i	0.428167	+	0.705662i
$427$	4.47550			0.216585
$428$	13.1579	+	0.634539i	0.636009	+	0.0306716i
$429$	−36.4945	−	8.00503i	−1.76197	−	0.386487i
$430$	−5.46735	−	5.73737i	−0.263659	−	0.276680i
$431$	0.774687			0.0373154			0.0186577	−	0.999826i	$-0.494061\pi$
$431$	0.774687			0.0373154			0.0186577	+	0.999826i	$0.494061\pi$
$432$	−15.2903	−	14.0786i	−0.735655	−	0.677357i
$433$	9.61071			0.461861			0.230931	−	0.972970i	$-0.425823\pi$
$433$	9.61071			0.461861			0.230931	+	0.972970i	$0.425823\pi$
$434$	−2.53059	−	2.65557i	−0.121472	−	0.127471i
$435$	−18.8606	−	4.13706i	−0.904298	−	0.198357i
$436$	0.861720	+	0.0415565i	0.0412689	+	0.00199020i
$437$	1.05324			0.0503834
$438$	17.5593	+	28.9394i	0.839014	+	1.38278i
$439$			13.8964i			0.663241i	0.943413	+	0.331620i	$0.107595\pi$
$439$			13.8964i			0.663241i	−0.943413	+	0.331620i	$0.892405\pi$
$440$	−13.9348	−	16.1103i	−0.664316	−	0.768029i
$441$	17.8551	+	8.22891i	0.850242	+	0.391853i
$442$	−4.60550	−	4.83295i	−0.219061	−	0.229880i
$443$		−	5.21277i		−	0.247666i	−0.992303	−	0.123833i	$-0.960481\pi$
$443$		−	5.21277i		−	0.247666i	0.992303	−	0.123833i	$-0.0395187\pi$
$444$	8.18578	+	2.21372i	0.388480	+	0.105059i
$445$		−	5.15033i		−	0.244149i
$446$	6.77046	−	6.45183i	0.320591	−	0.305503i
$447$	−32.7368	−	7.18079i	−1.54840	−	0.339640i
$448$	−5.29073	−	0.770218i	−0.249963	−	0.0363894i
$449$			32.7004i			1.54323i	0.636092	+	0.771614i	$0.280550\pi$
$449$			32.7004i			1.54323i	−0.636092	+	0.771614i	$0.719450\pi$
$450$	3.49125	+	10.2112i	0.164579	+	0.481359i
$451$	−9.75373			−0.459285
$452$	−3.50842	−	0.169194i	−0.165022	−	0.00795822i
$453$	−1.10267	+	5.02701i	−0.0518079	+	0.236189i
$454$	11.8205	−	11.2642i	0.554762	−	0.528653i
$455$	−4.70222			−0.220443
$456$	4.53510	−	2.46100i	0.212376	−	0.115247i
$457$	0.614071			0.0287250			0.0143625	−	0.999897i	$-0.495428\pi$
$457$	0.614071			0.0287250			0.0143625	+	0.999897i	$0.495428\pi$
$458$	14.4645	−	13.7837i	0.675881	−	0.644072i
$459$	3.29708	−	4.35706i	0.153894	−	0.203370i
$460$	0.150991	−	3.13095i	0.00703997	−	0.145982i
$461$	22.4368			1.04498			0.522492	−	0.852644i	$-0.325002\pi$
$461$	22.4368			1.04498			0.522492	+	0.852644i	$0.325002\pi$
$462$	−4.08039	−	6.72489i	−0.189837	−	0.312870i
$463$			5.96498i			0.277216i	0.990347	+	0.138608i	$0.0442629\pi$
$463$			5.96498i			0.277216i	−0.990347	+	0.138608i	$0.955737\pi$
$464$	−28.3197	−	2.73781i	−1.31471	−	0.127100i
$465$	2.25739	−	10.2913i	0.104684	−	0.477247i
$466$	−8.59302	+	8.18861i	−0.398064	+	0.379330i
$467$			27.1219i			1.25505i	0.778596	+	0.627526i	$0.215932\pi$
$467$			27.1219i			1.25505i	−0.778596	+	0.627526i	$0.784068\pi$
$468$	−23.8910	−	12.4393i	−1.10436	−	0.575008i
$469$		−	8.84511i		−	0.408429i
$470$	10.8547	+	11.3907i	0.500688	+	0.525416i
$471$	−0.967291	+	4.40982i	−0.0445704	+	0.203194i
$472$	11.3977	+	13.1771i	0.524622	+	0.606526i
$473$		−	17.1808i		−	0.789976i
$474$	−30.7435	+	18.6539i	−1.41210	+	0.856804i
$475$	−2.67901			−0.122921
$476$	0.0677022	−	1.40388i	0.00310312	−	0.0643466i
$477$	0.241110	+	0.111121i	0.0110397	+	0.00508788i
$478$	−19.1583	−	20.1045i	−0.876280	−	0.919557i
$479$	−36.2434			−1.65600			−0.828002	−	0.560725i	$-0.810522\pi$
$479$	−36.2434			−1.65600			−0.828002	+	0.560725i	$0.810522\pi$
$480$	−6.66562	−	13.8342i	−0.304243	−	0.631443i
$481$	10.9893			0.501068
$482$	−12.8803	−	13.5164i	−0.586682	−	0.615657i
$483$	0.248011	−	1.13067i	0.0112849	−	0.0514472i
$484$	1.16459	−	24.1491i	0.0529360	−	1.09768i
$485$	23.2887			1.05749
$486$	6.90005	−	20.9377i	0.312993	−	0.949756i
$487$		−	0.0454092i		−	0.00205769i	−0.999999	−	0.00102884i	$-0.999673\pi$
$487$		−	0.0454092i		−	0.00205769i	0.999999	−	0.00102884i	$-0.000327491\pi$
$488$	12.3912	+	14.3257i	0.560924	+	0.648495i
$489$	−0.483422	−	0.106038i	−0.0218611	−	0.00479521i
$490$	10.0206	+	10.5155i	0.452686	+	0.475043i
$491$			15.0518i			0.679278i	0.940556	+	0.339639i	$0.110305\pi$
$491$			15.0518i			0.679278i	−0.940556	+	0.339639i	$0.889695\pi$
$492$	−6.78790	−	1.83569i	−0.306022	−	0.0827591i
$493$		−	7.47951i		−	0.336860i
$494$	4.84079	−	4.61297i	0.217798	−	0.207547i
$495$	9.45645	−	20.5186i	0.425036	−	0.922242i
$496$	1.49388	−	15.4526i	0.0670774	−	0.693844i
$497$			4.64808i			0.208495i
$498$	−31.7854	+	19.2861i	−1.42434	+	0.864230i
$499$	−38.3120			−1.71508			−0.857540	−	0.514418i	$-0.828008\pi$
$499$	−38.3120			−1.71508			−0.857540	+	0.514418i	$0.828008\pi$
$500$	−1.13901	+	23.6186i	−0.0509381	+	1.05626i
$501$	4.93164	+	1.08175i	0.220329	+	0.0483290i
$502$	−26.0661	+	24.8394i	−1.16339	+	1.10864i
$503$	26.7772			1.19393			0.596967	−	0.802266i	$-0.296372\pi$
$503$	26.7772			1.19393			0.596967	+	0.802266i	$0.296372\pi$
$504$	−1.57402	−	5.44799i	−0.0701122	−	0.242673i
$505$	15.6263			0.695362
$506$	4.91942	−	4.68790i	0.218695	−	0.208403i
$507$	−12.1021	−	2.65457i	−0.537471	−	0.117894i
$508$	29.5061	+	1.42294i	1.30912	+	0.0631326i
$509$	−16.8618			−0.747385			−0.373692	−	0.927553i	$-0.621908\pi$
$509$	−16.8618			−0.747385			−0.373692	+	0.927553i	$0.621908\pi$
$510$	3.45130	−	2.09411i	0.152826	−	0.0927288i
$511$			9.23552i			0.408555i
$512$	−12.1829	−	19.0677i	−0.538413	−	0.842681i
$513$	4.36413	+	3.30242i	0.192681	+	0.145806i
$514$	−31.8234	+	30.3257i	−1.40367	+	1.33761i
$515$			16.4555i			0.725115i
$516$	3.23349	−	11.9566i	0.142347	−	0.526362i
$517$			34.1102i			1.50016i
$518$	1.59608	+	1.67491i	0.0701279	+	0.0735913i
$519$	5.02763	+	1.10281i	0.220689	+	0.0484079i
$520$	−13.0189	−	15.0514i	−0.570918	−	0.660049i
$521$			23.4366i			1.02678i	0.858156	+	0.513389i	$0.171610\pi$
$521$			23.4366i			1.02678i	−0.858156	+	0.513389i	$0.828390\pi$
$522$	−9.76302	−	28.5547i	−0.427316	−	1.24981i
$523$	18.7934			0.821779			0.410889	−	0.911685i	$-0.365218\pi$
$523$	18.7934			0.821779			0.410889	+	0.911685i	$0.365218\pi$
$524$	23.8404	+	1.14971i	1.04147	+	0.0502252i
$525$	−0.630837	+	2.87595i	−0.0275320	+	0.125517i
$526$	−15.5622	−	16.3307i	−0.678542	−	0.712054i
$527$	4.08119			0.177780
$528$	10.2286	−	31.6801i	0.445141	−	1.37870i
$529$	1.00000			0.0434783
$530$	0.135316	+	0.141999i	0.00587775	+	0.00616803i
$531$	−7.73472	+	16.7828i	−0.335658	+	0.728310i
$532$	1.40616	+	0.0678120i	0.0609646	+	0.00294002i
$533$	−9.11265			−0.394713
$534$	6.88163	−	4.17550i	0.297797	−	0.180691i
$535$			10.3231i			0.446307i
$536$	28.3125	−	24.4893i	1.22291	−	1.05777i
$537$	−2.47464	+	11.2817i	−0.106789	+	0.486843i
$538$	1.23805	+	1.29919i	0.0533761	+	0.0560122i
$539$			31.4893i			1.35634i
$540$	10.4427	−	12.4997i	0.449382	−	0.537903i
$541$		−	40.7585i		−	1.75234i	−0.481999	−	0.876172i	$-0.660089\pi$
$541$		−	40.7585i		−	1.75234i	0.481999	−	0.876172i	$-0.339911\pi$
$542$	28.7535	−	27.4003i	1.23507	−	1.17694i
$543$	−8.01342	+	36.5327i	−0.343889	+	1.56777i
$544$	4.68115	−	3.67018i	0.200703	−	0.157357i
$545$			0.676070i			0.0289597i
$546$	−3.81220	−	6.28289i	−0.163147	−	0.268883i
$547$	3.89430			0.166508			0.0832541	−	0.996528i	$-0.473469\pi$
$547$	3.89430			0.166508			0.0832541	+	0.996528i	$0.473469\pi$
$548$	5.61624	+	0.270844i	0.239914	+	0.0115699i
$549$	−8.40893	+	18.2457i	−0.358884	+	0.778706i
$550$	−12.5130	+	11.9241i	−0.533554	+	0.508444i
$551$	7.49165			0.319155
$552$	4.30585	−	2.33659i	0.183269	−	0.0994520i
$553$	−9.81128			−0.417218
$554$	22.0919	−	21.0522i	0.938594	−	0.894421i
$555$	−1.42377	+	6.49089i	−0.0604357	+	0.275523i
$556$	−1.28121	+	26.5673i	−0.0543355	+	1.12671i
$557$	31.5774			1.33798			0.668988	−	0.743273i	$-0.266728\pi$
$557$	31.5774			1.33798			0.668988	+	0.743273i	$0.266728\pi$
$558$	15.5809	−	5.32719i	0.659591	−	0.225518i
$559$		−	16.0516i		−	0.678910i
$560$	0.403167	−	4.17033i	0.0170369	−	0.176229i
$561$	8.54829	+	1.87506i	0.360909	+	0.0791651i
$562$	−25.0574	+	23.8781i	−1.05698	+	1.00724i
$563$		−	18.8516i		−	0.794502i	−0.917710	−	0.397251i	$-0.869964\pi$
$563$		−	18.8516i		−	0.794502i	0.917710	−	0.397251i	$-0.130036\pi$
$564$	−6.41965	+	23.7382i	−0.270316	+	0.999560i
$565$		−	2.75257i		−	0.115801i
$566$	−14.6192	−	15.3412i	−0.614490	−	0.644838i
$567$	4.57283	−	3.90731i	0.192041	−	0.164092i
$568$	−14.8781	+	12.8690i	−0.624273	+	0.539972i
$569$			7.31968i			0.306857i	0.988160	+	0.153428i	$0.0490314\pi$
$569$			7.31968i			0.306857i	−0.988160	+	0.153428i	$0.950969\pi$
$570$	2.09751	+	3.45690i	0.0878550	+	0.144794i
$571$	9.34744			0.391178			0.195589	−	0.980686i	$-0.437338\pi$
$571$	9.34744			0.391178			0.195589	+	0.980686i	$0.437338\pi$
$572$	2.07812	−	43.0920i	0.0868904	−	1.80177i
$573$	−31.6411	−	6.94046i	−1.32183	−	0.289942i
$574$	−1.32352	−	1.38889i	−0.0552428	−	0.0579711i
$575$	−2.54358			−0.106075
$576$	13.0807	−	20.1220i	0.545028	−	0.838418i
$577$	10.2416			0.426364			0.213182	−	0.977013i	$-0.431617\pi$
$577$	10.2416			0.426364			0.213182	+	0.977013i	$0.431617\pi$
$578$	−15.5067	−	16.2726i	−0.644995	−	0.676850i
$579$	−13.2588	−	2.90831i	−0.551018	−	0.120865i
$580$	1.07399	−	22.2703i	0.0445949	−	0.924723i
$581$	−10.1438			−0.420834
$582$	18.8807	+	31.1173i	0.782631	+	1.28985i
$583$			0.425223i			0.0176109i
$584$	−29.5622	+	25.5702i	−1.22329	+	1.05810i
$585$	8.83491	−	19.1700i	0.365279	−	0.792580i
$586$	0.399383	+	0.419108i	0.0164984	+	0.0173132i
$587$			28.6063i			1.18071i	0.807144	+	0.590354i	$0.201012\pi$
$587$			28.6063i			1.18071i	−0.807144	+	0.590354i	$0.798988\pi$
$588$	−5.92639	+	21.9143i	−0.244400	+	0.903730i
$589$			4.08781i			0.168435i
$590$	−9.88401	+	9.41884i	−0.406918	+	0.387767i
$591$	33.4138	+	7.32929i	1.37446	+	0.301487i
$592$	−0.942217	+	9.74623i	−0.0387249	+	0.400568i
$593$			7.24862i			0.297665i	0.988862	+	0.148833i	$0.0475516\pi$
$593$			7.24862i			0.297665i	−0.988862	+	0.148833i	$0.952448\pi$
$594$	35.0826	−	3.99963i	1.43945	−	0.164107i
$595$	1.10143			0.0451540
$596$	1.86414	−	38.6550i	0.0763582	−	1.58337i
$597$	9.54723	−	43.5253i	0.390742	−	1.78137i
$598$	4.59609	−	4.37978i	0.187948	−	0.179103i
$599$	36.3285			1.48434			0.742172	−	0.670209i	$-0.233796\pi$
$599$	36.3285			1.48434			0.742172	+	0.670209i	$0.233796\pi$
$600$	−10.9523	+	5.94332i	−0.447125	+	0.242635i
$601$	−17.0326			−0.694775			−0.347387	−	0.937722i	$-0.612931\pi$
$601$	−17.0326			−0.694775			−0.347387	+	0.937722i	$0.612931\pi$
$602$	2.44647	−	2.33134i	0.0997109	−	0.0950182i
$603$	36.0597	+	16.6189i	1.46846	+	0.676774i
$604$	−5.93579	−	0.286254i	−0.241524	−	0.0116475i
$605$	18.9464			0.770279
$606$	12.6686	+	20.8792i	0.514628	+	0.848157i
$607$		−	27.9691i		−	1.13523i	−0.823294	−	0.567615i	$-0.807866\pi$
$607$		−	27.9691i		−	1.13523i	0.823294	−	0.567615i	$-0.192134\pi$
$608$	3.67613	+	4.68874i	0.149087	+	0.190154i
$609$	1.76409	−	8.04238i	0.0714845	−	0.325894i
$610$	−10.7456	+	10.2398i	−0.435075	+	0.414599i
$611$			31.8682i			1.28925i
$612$	5.59611	+	2.91373i	0.226209	+	0.117780i
$613$		−	36.4215i		−	1.47105i	−0.677497	−	0.735525i	$-0.736935\pi$
$613$		−	36.4215i		−	1.47105i	0.677497	−	0.735525i	$-0.263065\pi$
$614$	−29.0504	−	30.4851i	−1.17238	−	1.23028i
$615$	1.18063	−	5.38245i	0.0476078	−	0.217041i
$616$	6.86961	−	5.94195i	0.276785	−	0.239408i
$617$			47.4234i			1.90919i	0.297902	+	0.954597i	$0.403713\pi$
$617$			47.4234i			1.90919i	−0.297902	+	0.954597i	$0.596287\pi$
$618$	−21.9871	+	13.3409i	−0.884449	+	0.536648i
$619$	−2.37708			−0.0955429			−0.0477714	−	0.998858i	$-0.515212\pi$
$619$	−2.37708			−0.0955429			−0.0477714	+	0.998858i	$0.515212\pi$
$620$	12.1518	+	0.586020i	0.488027	+	0.0235351i
$621$	4.14352	+	3.13548i	0.166274	+	0.125823i
$622$	−24.0422	−	25.2296i	−0.964005	−	1.01161i
$623$	2.19616			0.0879871
$624$	9.55628	−	29.5979i	0.382557	−	1.18486i
$625$	−5.81228			−0.232491
$626$	−27.2851	−	28.6326i	−1.09053	−	1.14439i
$627$	−1.87810	+	8.56216i	−0.0750042	+	0.341940i
$628$	−5.20704	−	0.251110i	−0.207783	−	0.0100204i
$629$	−2.57407			−0.102635
$630$	4.20494	−	1.43769i	0.167529	−	0.0572790i
$631$		−	20.3545i		−	0.810299i	−0.914251	−	0.405149i	$-0.867220\pi$
$631$		−	20.3545i		−	0.810299i	0.914251	−	0.405149i	$-0.132780\pi$
$632$	−27.1643	−	31.4051i	−1.08054	−	1.24923i
$633$	14.1444	+	3.10256i	0.562189	+	0.123316i
$634$	19.4275	+	20.3870i	0.771564	+	0.809670i
$635$			23.1493i			0.918652i
$636$	−0.0800284	+	0.295925i	−0.00317333	+	0.0117342i
$637$			29.4196i			1.16565i
$638$	34.9915	−	33.3447i	1.38533	−	1.32013i
$639$	−18.9492	−	8.73319i	−0.749620	−	0.345479i
$640$	14.4651	−	10.2558i	0.571785	−	0.405396i
$641$		−	40.4280i		−	1.59681i	−0.602121	−	0.798405i	$-0.705678\pi$
$641$		−	40.4280i		−	1.59681i	0.602121	−	0.798405i	$-0.294322\pi$
$642$	−13.7933	+	8.36920i	−0.544377	+	0.330306i
$643$	4.57967			0.180604			0.0903022	−	0.995914i	$-0.471217\pi$
$643$	4.57967			0.180604			0.0903022	+	0.995914i	$0.471217\pi$
$644$	1.33507	+	0.0643840i	0.0526092	+	0.00253709i
$645$	9.48098	+	2.07964i	0.373313	+	0.0818859i
$646$	−1.13388	+	1.08052i	−0.0446121	+	0.0425125i
$647$	4.41804			0.173691			0.0868456	−	0.996222i	$-0.472321\pi$
$647$	4.41804			0.173691			0.0868456	+	0.996222i	$0.472321\pi$
$648$	25.1677	+	3.81920i	0.988681	+	0.150032i
$649$	−29.5982			−1.16183
$650$	−11.6905	+	11.1403i	−0.458540	+	0.436960i
$651$	4.38832	+	0.962574i	0.171992	+	0.0377262i
$652$	0.0275277	−	0.570816i	0.00107807	−	0.0223549i
$653$	32.2066			1.26034			0.630171	−	0.776456i	$-0.282985\pi$
$653$	32.2066			1.26034			0.630171	+	0.776456i	$0.282985\pi$
$654$	−0.903333	+	0.548106i	−0.0353231	+	0.0214326i
$655$			18.7042i			0.730834i
$656$	0.781316	−	8.08188i	0.0305053	−	0.315544i
$657$	−37.6513	−	17.3524i	−1.46892	−	0.676983i
$658$	−4.85713	+	4.62854i	−0.189351	+	0.180439i
$659$		−	5.23120i		−	0.203779i	−0.994796	−	0.101889i	$-0.967511\pi$
$659$		−	5.23120i		−	0.203779i	0.994796	−	0.101889i	$-0.0324888\pi$
$660$	25.1833	+	6.81045i	0.980260	+	0.265096i
$661$			9.11645i			0.354589i	0.984158	+	0.177294i	$0.0567345\pi$
$661$			9.11645i			0.354589i	−0.984158	+	0.177294i	$0.943266\pi$
$662$	13.3154	+	13.9730i	0.517518	+	0.543077i
$663$	7.98644	+	1.75182i	0.310168	+	0.0680350i
$664$	−28.0848	−	32.4694i	−1.08990	−	1.26006i
$665$			1.10321i			0.0427807i
$666$	−9.82711	+	3.35994i	−0.380793	+	0.130195i
$667$	7.11293			0.275414
$668$	−0.280824	+	5.82318i	−0.0108654	+	0.225306i
$669$	−2.45412	+	11.1882i	−0.0948816	+	0.432560i
$670$	20.2374	+	21.2369i	0.781840	+	0.820453i
$671$	−32.1781			−1.24222
$672$	5.89906	−	2.84229i	0.227561	−	0.109644i
$673$	17.5174			0.675246			0.337623	−	0.941281i	$-0.390377\pi$
$673$	17.5174			0.675246			0.337623	+	0.941281i	$0.390377\pi$
$674$	3.34127	+	3.50628i	0.128701	+	0.135057i
$675$	−10.5394	−	7.97536i	−0.405661	−	0.306972i
$676$	0.689131	−	14.2899i	0.0265050	−	0.549610i
$677$	10.6817			0.410531			0.205265	−	0.978706i	$-0.434194\pi$
$677$	10.6817			0.410531			0.205265	+	0.978706i	$0.434194\pi$
$678$	3.67785	−	2.23157i	0.141247	−	0.0857030i
$679$			9.93055i			0.381100i
$680$	3.04949	+	3.52558i	0.116943	+	0.135200i
$681$	−4.28461	+	19.5333i	−0.164187	+	0.748517i
$682$	18.1945	+	19.0931i	0.696705	+	0.731113i
$683$		−	27.8303i		−	1.06490i	−0.846462	−	0.532449i	$-0.821272\pi$
$683$		−	27.8303i		−	1.06490i	0.846462	−	0.532449i	$-0.178728\pi$
$684$	−2.91845	+	5.60519i	−0.111590	+	0.214320i
$685$			4.40627i			0.168355i
$686$	−9.27346	+	8.83702i	−0.354062	+	0.337399i
$687$	−5.24299	+	23.9025i	−0.200033	+	0.911938i
$688$	14.2359	+	1.37626i	0.542740	+	0.0524694i
$689$			0.397274i			0.0151349i
$690$	1.99148	+	3.28215i	0.0758143	+	0.124949i
$691$	3.28745			0.125060			0.0625302	−	0.998043i	$-0.480083\pi$
$691$	3.28745			0.125060			0.0625302	+	0.998043i	$0.480083\pi$
$692$	−0.286290	+	5.93653i	−0.0108831	+	0.225673i
$693$	8.74934	+	4.03233i	0.332360	+	0.153176i
$694$	−18.4070	+	17.5407i	−0.698722	+	0.665838i
$695$	−20.8436			−0.790644
$696$	30.6272	−	16.6200i	1.16092	−	0.629981i
$697$	2.13450			0.0808501
$698$	−33.4397	+	31.8659i	−1.26571	+	1.20614i
$699$	3.11474	−	14.1999i	0.117810	−	0.537091i
$700$	−3.39587	−	0.163766i	−0.128352	−	0.00618977i
$701$	−24.5409			−0.926897			−0.463448	−	0.886124i	$-0.653388\pi$
$701$	−24.5409			−0.926897			−0.463448	+	0.886124i	$0.653388\pi$
$702$	32.7767	−	3.73675i	1.23708	−	0.141035i
$703$		−	2.57825i		−	0.0972406i
$704$	38.0395	+	5.53774i	1.43367	+	0.208712i
$705$	−18.8232	−	4.12884i	−0.708922	−	0.155501i
$706$	−8.01200	+	7.63494i	−0.301536	+	0.287345i
$707$			6.66322i			0.250596i
$708$	−20.5982	−	5.57048i	−0.774128	−	0.209351i
$709$		−	45.9596i		−	1.72605i	−0.505161	−	0.863025i	$-0.668567\pi$
$709$		−	45.9596i		−	1.72605i	0.505161	−	0.863025i	$-0.331433\pi$
$710$	−10.6347	−	11.1599i	−0.399113	−	0.418824i
$711$	18.4342	−	39.9985i	0.691337	−	1.50006i
$712$	6.08044	+	7.02972i	0.227874	+	0.263450i
$713$			3.88117i			0.145351i
$714$	0.892952	+	1.47167i	0.0334179	+	0.0550760i
$715$	33.8082			1.26436
$716$	−13.3213	−	0.642419i	−0.497839	−	0.0240083i
$717$	33.2226	+	7.28734i	1.24072	+	0.272151i
$718$	−14.0187	−	14.7111i	−0.523174	−	0.549012i
$719$	−49.2136			−1.83536			−0.917679	−	0.397323i	$-0.869939\pi$
$719$	−49.2136			−1.83536			−0.917679	+	0.397323i	$0.869939\pi$
$720$	16.2441	+	9.47918i	0.605380	+	0.353268i
$721$	−7.01679			−0.261319
$722$	17.4545	+	18.3165i	0.649588	+	0.681670i
$723$	22.3359	+	4.89935i	0.830680	+	0.182209i
$724$	−43.1371	−	2.08029i	−1.60318	−	0.0773135i
$725$	−18.0923			−0.671932
$726$	15.3603	+	25.3153i	0.570073	+	0.939537i
$727$		−	11.0106i		−	0.408361i	−0.978933	−	0.204181i	$-0.934547\pi$
$727$		−	11.0106i		−	0.408361i	0.978933	−	0.204181i	$-0.0654530\pi$
$728$	6.41809	−	5.55141i	0.237870	−	0.205749i
$729$	7.33749	+	25.9839i	0.271759	+	0.962365i
$730$	−21.1307	−	22.1743i	−0.782081	−	0.820706i
$731$			3.75985i			0.139063i
$732$	−22.3937	−	6.05604i	−0.827695	−	0.223838i
$733$			11.5660i			0.427202i	0.976921	+	0.213601i	$0.0685192\pi$
$733$			11.5660i			0.427202i	−0.976921	+	0.213601i	$0.931481\pi$
$734$	−22.4627	+	21.4056i	−0.829115	+	0.790094i
$735$	−17.3769	−	3.81160i	−0.640955	−	0.140593i
$736$	3.49030	+	4.45172i	0.128654	+	0.164093i
$737$			63.5949i			2.34255i
$738$	8.14895	−	2.78617i	0.299967	−	0.102560i
$739$	−10.9237			−0.401833			−0.200917	−	0.979608i	$-0.564392\pi$
$739$	−10.9237			−0.401833			−0.200917	+	0.979608i	$0.564392\pi$
$740$	−7.66432	−	0.369612i	−0.281746	−	0.0135872i
$741$	−1.75466	+	7.99940i	−0.0644591	+	0.293865i
$742$	−0.0605498	+	0.0577002i	−0.00222285	+	0.00211824i
$743$	−12.9481			−0.475020			−0.237510	−	0.971385i	$-0.576331\pi$
$743$	−12.9481			−0.475020			−0.237510	+	0.971385i	$0.576331\pi$
$744$	9.06871	+	16.7117i	0.332475	+	0.612682i
$745$	30.3271			1.11110
$746$	11.8175	−	11.2613i	0.432668	−	0.412305i
$747$	19.0589	−	41.3540i	0.697330	−	1.51306i
$748$	−0.486768	+	10.0937i	−0.0177980	+	0.369061i
$749$	−4.40189			−0.160841
$750$	−15.0229	−	24.7592i	−0.548558	−	0.904078i
$751$		−	37.7373i		−	1.37705i	−0.725211	−	0.688527i	$-0.758258\pi$
$751$		−	37.7373i		−	1.37705i	0.725211	−	0.688527i	$-0.241742\pi$
$752$	−28.2634	−	2.73237i	−1.03066	−	0.0996393i
$753$	9.44828	−	43.0742i	0.344314	−	1.56971i
$754$	32.6917	−	31.1531i	1.19056	−	1.13453i
$755$		−	4.65698i		−	0.169485i
$756$	5.33002	+	4.45287i	0.193851	+	0.161949i
$757$			44.6077i			1.62129i	0.585536	+	0.810647i	$0.300884\pi$
$757$			44.6077i			1.62129i	−0.585536	+	0.810647i	$0.699116\pi$
$758$	22.6567	+	23.7757i	0.822930	+	0.863572i
$759$	−1.78316	+	8.12933i	−0.0647247	+	0.295076i
$760$	−3.53130	+	3.05444i	−0.128094	+	0.110796i
$761$			3.93819i			0.142759i	0.997449	+	0.0713796i	$0.0227402\pi$
$761$			3.93819i			0.142759i	−0.997449	+	0.0713796i	$0.977260\pi$
$762$	−30.9310	+	18.7677i	−1.12051	+	0.679882i
$763$	−0.288283			−0.0104366
$764$	1.80175	−	37.3613i	0.0651851	−	1.35168i
$765$	−2.06945	+	4.49028i	−0.0748210	+	0.162346i
$766$	8.17227	+	8.57587i	0.295276	+	0.309859i
$767$	−27.6528			−0.998484
$768$	25.4306	+	11.0130i	0.917646	+	0.397399i
$769$	−25.6413			−0.924649			−0.462324	−	0.886711i	$-0.652984\pi$
$769$	−25.6413			−0.924649			−0.462324	+	0.886711i	$0.652984\pi$
$770$	4.91031	+	5.15282i	0.176955	+	0.185695i
$771$	11.5352	−	52.5881i	0.415428	−	1.89391i
$772$	0.755002	−	15.6558i	0.0271731	−	0.563464i
$773$	−15.7081			−0.564980			−0.282490	−	0.959270i	$-0.591160\pi$
$773$	−15.7081			−0.564980			−0.282490	+	0.959270i	$0.591160\pi$
$774$	4.90774	+	14.3541i	0.176405	+	0.515946i
$775$		−	9.87207i		−	0.354615i
$776$	−31.7869	+	27.4945i	−1.14108	+	0.986995i
$777$	−2.76778	−	0.607111i	−0.0992937	−	0.0217800i
$778$	33.7187	+	35.3840i	1.20887	+	1.26858i
$779$			2.13797i			0.0766006i
$780$	23.5281	+	6.36282i	0.842441	+	0.227826i
$781$		−	33.4189i		−	1.19582i
$782$	−1.07656	+	1.02590i	−0.0384979	+	0.0366861i
$783$	29.4726	+	22.3025i	1.05326	+	0.797026i
$784$	−26.0918	−	2.52243i	−0.931850	−	0.0900866i
$785$		−	4.08523i		−	0.145808i
$786$	−24.9917	+	15.1640i	−0.891425	+	0.540881i
$787$	0.174928			0.00623552			0.00311776	−	0.999995i	$-0.499008\pi$
$787$	0.174928			0.00623552			0.00311776	+	0.999995i	$0.499008\pi$
$788$	−1.90269	+	39.4544i	−0.0677806	+	1.40551i
$789$	26.9865	+	5.91946i	0.960744	+	0.210738i
$790$	23.5566	−	22.4480i	0.838107	−	0.798664i
$791$	1.17372			0.0417328
$792$	11.3169	+	39.1702i	0.402129	+	1.39185i
$793$	−30.0632			−1.06757
$794$	15.7567	−	15.0151i	0.559183	−	0.532866i
$795$	−0.234653	−	0.0514708i	−0.00832227	−	0.00182548i
$796$	51.3938	+	2.47847i	1.82161	+	0.0878472i
$797$	−22.0566			−0.781286			−0.390643	−	0.920542i	$-0.627747\pi$
$797$	−22.0566			−0.781286			−0.390643	+	0.920542i	$0.627747\pi$
$798$	−1.47406	+	0.894400i	−0.0521812	+	0.0316614i
$799$		−	7.46465i		−	0.264081i
$800$	−8.87785	−	11.3233i	−0.313880	−	0.400340i
$801$	−4.12631	+	8.95327i	−0.145796	+	0.316348i
$802$	20.1648	−	19.2158i	0.712044	−	0.678533i
$803$		−	66.4019i		−	2.34327i
$804$	−11.9688	+	44.2576i	−0.422107	+	1.56084i
$805$			1.04744i			0.0369175i
$806$	16.9987	+	17.8382i	0.598752	+	0.628323i
$807$	−2.14691	−	0.470923i	−0.0755749	−	0.0165773i
$808$	−21.3285	+	18.4483i	−0.750333	+	0.649010i
$809$		−	37.0136i		−	1.30133i	−0.759365	−	0.650665i	$-0.774490\pi$
$809$		−	37.0136i		−	1.30133i	0.759365	−	0.650665i	$-0.225510\pi$
$810$	−2.03941	+	19.8439i	−0.0716576	+	0.697244i
$811$	−24.9475			−0.876026			−0.438013	−	0.898969i	$-0.644318\pi$
$811$	−24.9475			−0.876026			−0.438013	+	0.898969i	$0.644318\pi$
$812$	9.49628	+	0.457959i	0.333254	+	0.0160712i
$813$	−10.4224	+	47.5151i	−0.365530	+	1.66643i
$814$	−11.4756	−	12.0423i	−0.402219	−	0.422084i
$815$	0.447839			0.0156871
$816$	−2.23842	+	6.93286i	−0.0783603	+	0.242699i
$817$	−3.76595			−0.131754
$818$	−12.1935	−	12.7957i	−0.426336	−	0.447391i
$819$	8.17428	+	3.76730i	0.285632	+	0.131640i
$820$	6.35549	+	0.306494i	0.221943	+	0.0107032i
$821$	−23.4982			−0.820092			−0.410046	−	0.912065i	$-0.634487\pi$
$821$	−23.4982			−0.820092			−0.410046	+	0.912065i	$0.634487\pi$
$822$	−5.88746	+	3.57227i	−0.205349	+	0.124597i
$823$			2.87299i			0.100146i	0.998746	+	0.0500730i	$0.0159454\pi$
$823$			2.87299i			0.100146i	−0.998746	+	0.0500730i	$0.984055\pi$
$824$	−19.4272	−	22.4602i	−0.676780	−	0.782439i
$825$	4.53562	−	20.6776i	0.157910	−	0.719902i
$826$	−4.01629	−	4.21465i	−0.139745	−	0.146646i
$827$			51.7212i			1.79852i	0.437414	+	0.899260i	$0.355895\pi$
$827$			51.7212i			1.79852i	−0.437414	+	0.899260i	$0.644105\pi$
$828$	−2.77092	+	5.32184i	−0.0962962	+	0.184947i
$829$			38.8057i			1.34778i	0.738833	+	0.673888i	$0.235377\pi$
$829$			38.8057i			1.34778i	−0.738833	+	0.673888i	$0.764623\pi$
$830$	24.3549	−	23.2087i	0.845372	−	0.805586i
$831$	−8.00772	+	36.5067i	−0.277785	+	1.26640i
$832$	35.5393	+	5.17377i	1.23210	+	0.179368i
$833$		−	6.89110i		−	0.238762i
$834$	−16.8984	−	27.8503i	−0.585145	−	0.964377i
$835$	−4.56863			−0.158104
$836$	−10.1100	−	0.487557i	−0.349663	−	0.0168625i
$837$	−12.1693	+	16.0817i	−0.420634	+	0.555865i
$838$	1.92172	−	1.83128i	0.0663847	−	0.0632604i
$839$	−9.48463			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$839$	−9.48463			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$840$	2.44745	+	4.51013i	0.0844450	+	0.155614i
$841$	21.5938			0.744615
$842$	−23.3724	+	22.2724i	−0.805465	+	0.767558i
$843$	9.08265	−	41.4073i	0.312823	−	1.42614i
$844$	−0.805428	+	16.7014i	−0.0277240	+	0.574887i
$845$	11.2112			0.385679
$846$	−9.74363	−	28.4980i	−0.334993	−	0.979782i
$847$			8.07893i			0.277595i
$848$	−0.352337	−	0.0340622i	−0.0120993	−	0.00116970i
$849$	25.3513	+	5.56078i	0.870054	+	0.190845i
$850$	2.73833	−	2.60946i	0.0939240	−	0.0895036i
$851$		−	2.44792i		−	0.0839135i
$852$	6.28956	−	23.2572i	0.215477	−	0.796779i
$853$			23.6973i			0.811380i	0.914011	+	0.405690i	$0.132969\pi$
$853$			23.6973i			0.811380i	−0.914011	+	0.405690i	$0.867031\pi$
$854$	−4.36638	−	4.58202i	−0.149414	−	0.156794i
$855$	−4.49756	−	2.07280i	−0.153813	−	0.0708884i
$856$	−12.1874	−	14.0901i	−0.416557	−	0.481590i
$857$		−	32.7088i		−	1.11731i	−0.829400	−	0.558655i	$-0.811317\pi$
$857$		−	32.7088i		−	1.11731i	0.829400	−	0.558655i	$-0.188683\pi$
$858$	27.4091	+	45.1730i	0.935732	+	1.54218i
$859$	−14.7736			−0.504068			−0.252034	−	0.967718i	$-0.581100\pi$
$859$	−14.7736			−0.504068			−0.252034	+	0.967718i	$0.581100\pi$
$860$	−0.539878	+	11.1950i	−0.0184097	+	0.381745i
$861$	2.29513	+	0.503435i	0.0782179	+	0.0171570i
$862$	−0.755799	−	0.793126i	−0.0257426	−	0.0270140i
$863$	21.4909			0.731558			0.365779	−	0.930702i	$-0.380803\pi$
$863$	21.4909			0.731558			0.365779	+	0.930702i	$0.380803\pi$
$864$	0.503807	+	29.3896i	0.0171399	+	0.999853i
$865$	−4.65756			−0.158362
$866$	−9.37639	−	9.83946i	−0.318623	−	0.334358i
$867$	26.8904	+	5.89838i	0.913245	+	0.200319i
$868$	−0.249885	+	5.18164i	−0.00848166	+	0.175876i
$869$	70.5415			2.39296
$870$	14.1653	+	23.3457i	0.480247	+	0.791495i
$871$			59.4151i			2.01320i
$872$	−0.798164	−	0.922773i	−0.0270292	−	0.0312490i
$873$	−40.4848	−	18.6583i	−1.37020	−	0.631489i
$874$	−1.02756	−	1.07831i	−0.0347578	−	0.0364744i
$875$		−	7.90147i		−	0.267119i
$876$	12.4971	−	46.2110i	0.422237	−	1.56133i
$877$			45.8552i			1.54842i	0.632928	+	0.774211i	$0.281853\pi$
$877$			45.8552i			1.54842i	−0.632928	+	0.774211i	$0.718147\pi$
$878$	14.2272	−	13.5576i	0.480144	−	0.457547i
$879$	−0.692574	−	0.151915i	−0.0233599	−	0.00512398i
$880$	−2.89871	+	29.9840i	−0.0977153	+	1.01076i
$881$			6.52341i			0.219779i	0.993944	+	0.109890i	$0.0350497\pi$
$881$			6.52341i			0.219779i	−0.993944	+	0.109890i	$0.964950\pi$
$882$	−8.99496	−	26.3083i	−0.302876	−	0.885847i
$883$	−34.9822			−1.17724			−0.588622	−	0.808409i	$-0.700329\pi$
$883$	−34.9822			−1.17724			−0.588622	+	0.808409i	$0.700329\pi$
$884$	−0.454774	+	9.43024i	−0.0152957	+	0.317173i
$885$	3.58269	−	16.3333i	0.120431	−	0.549038i
$886$	−5.33684	+	5.08567i	−0.179295	+	0.170856i
$887$	9.28616			0.311799			0.155899	−	0.987773i	$-0.450172\pi$
$887$	9.28616			0.311799			0.155899	+	0.987773i	$0.450172\pi$
$888$	−5.71979	−	10.5404i	−0.191943	−	0.353711i
$889$	−9.87111			−0.331066
$890$	−5.27291	+	5.02475i	−0.176748	+	0.168430i
$891$	−32.8779	+	28.0930i	−1.10145	+	0.941150i
$892$	−13.2108	−	0.637091i	−0.442330	−	0.0213314i
$893$	7.47676			0.250200
$894$	24.5869	+	40.5217i	0.822310	+	1.35525i
$895$		−	10.4513i		−	0.349349i
$896$	4.37318	+	6.16809i	0.146098	+	0.206061i
$897$	−1.66596	+	7.59502i	−0.0556248	+	0.253590i
$898$	33.4787	−	31.9031i	1.11720	−	1.06462i
$899$			27.6065i			0.920728i
$900$	7.04807	−	13.5365i	0.234936	−	0.451218i
$901$		−	0.0930556i		−	0.00310013i
$902$	9.51592	+	9.98588i	0.316845	+	0.332494i
$903$	−0.886783	+	4.04279i	−0.0295103	+	0.134536i
$904$	3.24966	+	3.75700i	0.108082	+	0.124956i
$905$		−	33.8436i		−	1.12500i
$906$	6.22244	−	3.77553i	0.206727	−	0.125433i
$907$	−19.1892			−0.637169			−0.318584	−	0.947895i	$-0.603207\pi$
$907$	−19.1892			−0.637169			−0.318584	+	0.947895i	$0.603207\pi$
$908$	−23.0645	−	1.11229i	−0.765423	−	0.0369126i
$909$	−27.1646	−	12.5194i	−0.900992	−	0.415242i
$910$	4.58757	+	4.81414i	0.152076	+	0.159587i
$911$	44.6786			1.48027			0.740134	−	0.672459i	$-0.234762\pi$
$911$	44.6786			1.48027			0.740134	+	0.672459i	$0.234762\pi$
$912$	−6.94410	−	2.24205i	−0.229942	−	0.0742416i
$913$	72.9321			2.41370
$914$	−0.599099	−	0.628686i	−0.0198164	−	0.0207951i
$915$	3.89498	−	17.7570i	0.128764	−	0.587029i
$916$	−28.2236	−	1.36109i	−0.932535	−	0.0449716i
$917$	−7.97568			−0.263380
$918$	−7.67745	+	0.875279i	−0.253394	+	0.0288885i
$919$		−	17.5667i		−	0.579471i	−0.957107	−	0.289736i	$-0.906433\pi$
$919$		−	17.5667i		−	0.579471i	0.957107	−	0.289736i	$-0.0935674\pi$
$920$	−3.35278	+	2.90003i	−0.110538	+	0.0956112i
$921$	50.3766	+	11.0501i	1.65996	+	0.364112i
$922$	−21.8897	−	22.9708i	−0.720899	−	0.756503i
$923$		−	31.2224i		−	1.02770i
$924$	−2.90405	+	10.7384i	−0.0955362	+	0.353269i
$925$			6.22648i			0.204725i
$926$	6.10696	−	5.81955i	0.200687	−	0.191242i
$927$	13.1837	−	28.6060i	0.433010	−	0.939544i
$928$	24.8263	+	31.6648i	0.814962	+	1.03945i
$929$			31.7804i			1.04268i	0.853348	+	0.521341i	$0.174568\pi$
$929$			31.7804i			1.04268i	−0.853348	+	0.521341i	$0.825432\pi$
$930$	−12.7386	+	7.72926i	−0.417715	+	0.253452i
$931$	6.90228			0.226213
$932$	16.7670	+	0.808591i	0.549222	+	0.0264863i
$933$	41.6918	+	9.14507i	1.36493	+	0.299396i
$934$	27.7674	−	26.4606i	0.908578	−	0.865817i
$935$	−7.91907			−0.258981
$936$	10.5731	+	36.5957i	0.345593	+	1.19617i
$937$	−38.2549			−1.24973			−0.624867	−	0.780731i	$-0.714847\pi$
$937$	−38.2549			−1.24973			−0.624867	+	0.780731i	$0.714847\pi$
$938$	−9.05564	+	8.62945i	−0.295677	+	0.281762i
$939$	47.3153	+	10.3786i	1.54408	+	0.338692i
$940$	1.07185	−	22.2260i	0.0349600	−	0.724933i
$941$	−50.8918			−1.65903			−0.829513	−	0.558487i	$-0.811382\pi$
$941$	−50.8918			−1.65903			−0.829513	+	0.558487i	$0.811382\pi$
$942$	5.45849	−	3.31199i	0.177847	−	0.107911i
$943$			2.02989i			0.0661023i
$944$	2.37094	−	24.5248i	0.0771675	−	0.798215i
$945$	−3.28424	+	4.34010i	−0.106836	+	0.141183i
$946$	−17.5898	+	16.7619i	−0.571892	+	0.544978i
$947$		−	19.4666i		−	0.632579i	−0.948663	−	0.316289i	$-0.897563\pi$
$947$		−	19.4666i		−	0.632579i	0.948663	−	0.316289i	$-0.102437\pi$
$948$	49.0919	+	13.2762i	1.59443	+	0.431190i
$949$		−	62.0375i		−	2.01382i
$950$	2.61369	+	2.74277i	0.0847993	+	0.0889873i
$951$	−33.6894	−	7.38974i	−1.09245	−	0.239629i
$952$	−1.50334	+	1.30034i	−0.0487236	+	0.0421441i
$953$		−	38.8608i		−	1.25882i	−0.777072	−	0.629412i	$-0.783296\pi$
$953$		−	38.8608i		−	1.25882i	0.777072	−	0.629412i	$-0.216704\pi$
$954$	−0.121466	−	0.355261i	−0.00393259	−	0.0115020i
$955$	29.3121			0.948518
$956$	−1.89180	+	39.2286i	−0.0611853	+	1.26874i
$957$	−12.6835	+	57.8234i	−0.410000	+	1.86917i
$958$	35.3597	+	37.1061i	1.14242	+	1.19884i
$959$	−1.87888			−0.0606723
$960$	−7.66039	+	20.3212i	−0.247238	+	0.655864i
$961$	15.9365			0.514082
$962$	−10.7213	−	11.2508i	−0.345670	−	0.362741i
$963$	8.27062	−	17.9456i	0.266517	−	0.578288i
$964$	−1.27188	+	26.3738i	−0.0409644	+	0.849442i
$965$	12.2829			0.395400
$966$	−1.39955	+	0.849187i	−0.0450296	+	0.0273222i
$967$		−	7.74049i		−	0.248917i	−0.992225	−	0.124459i	$-0.960281\pi$
$967$		−	7.74049i		−	0.248917i	0.992225	−	0.124459i	$-0.0397194\pi$
$968$	−25.8600	+	22.3680i	−0.831173	+	0.718933i
$969$	0.411003	−	1.87374i	0.0132033	−	0.0601932i
$970$	−22.7209	−	23.8430i	−0.729524	−	0.765553i
$971$			55.1743i			1.77063i	0.464995	+	0.885313i	$0.346056\pi$
$971$			55.1743i			1.77063i	−0.464995	+	0.885313i	$0.653944\pi$
$972$	−28.1679	+	13.3630i	−0.903486	+	0.428617i
$973$		−	8.88794i		−	0.284934i
$974$	−0.0464900	+	0.0443021i	−0.00148964	+	0.00141953i
$975$	4.23751	−	19.3185i	0.135709	−	0.618689i
$976$	2.57761	−	26.6626i	0.0825072	−	0.853449i
$977$		−	3.29400i		−	0.105384i	−0.998611	−	0.0526921i	$-0.983220\pi$
$977$		−	3.29400i		−	0.105384i	0.998611	−	0.0526921i	$-0.0167802\pi$
$978$	0.363074	+	0.598381i	0.0116098	+	0.0191341i
$979$	−15.7900			−0.504651
$980$	0.989496	−	20.5183i	0.0316083	−	0.655432i
$981$	0.541650	−	1.17527i	0.0172936	−	0.0375235i
$982$	15.4101	−	14.6848i	0.491755	−	0.468611i
$983$	36.9675			1.17908			0.589540	−	0.807739i	$-0.299309\pi$
$983$	36.9675			1.17908			0.589540	+	0.807739i	$0.299309\pi$
$984$	4.74303	+	8.74039i	0.151202	+	0.278634i
$985$	−30.9543			−0.986286
$986$	−7.65754	+	7.29715i	−0.243866	+	0.232389i
$987$	1.76058	−	8.02640i	0.0560400	−	0.255483i
$988$	−9.44553	−	0.455512i	−0.300502	−	0.0144918i
$989$	−3.57557			−0.113697
$990$	−30.2328	+	10.3368i	−0.960863	+	0.328524i
$991$			39.9747i			1.26984i	0.772579	+	0.634918i	$0.218966\pi$
$991$			39.9747i			1.26984i	−0.772579	+	0.634918i	$0.781034\pi$
$992$	−17.2779	+	13.5464i	−0.548573	+	0.430100i
$993$	−23.0904	−	5.06485i	−0.732751	−	0.160728i
$994$	4.75871	−	4.53475i	0.150937	−	0.143834i
$995$			40.3215i			1.27828i
$996$	50.7555	+	13.7261i	1.60825	+	0.434927i
$997$		−	58.0482i		−	1.83841i	−0.393784	−	0.919203i	$-0.628834\pi$
$997$		−	58.0482i		−	1.83841i	0.393784	−	0.919203i	$-0.371166\pi$
$998$	37.3779	+	39.2238i	1.18318	+	1.24161i
$999$	7.67540	−	10.1430i	0.242839	−	0.320910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.11	yes	42
3.2	odd	2		552.2.j.c.323.32	yes	42
4.3	odd	2		2208.2.j.d.47.3		42
8.3	odd	2		552.2.j.c.323.31	✓	42
8.5	even	2		2208.2.j.c.47.3		42
12.11	even	2		2208.2.j.c.47.4		42
24.5	odd	2		2208.2.j.d.47.4		42
24.11	even	2	inner	552.2.j.d.323.12	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.31	✓	42	8.3	odd	2
552.2.j.c.323.32	yes	42	3.2	odd	2
552.2.j.d.323.11	yes	42	1.1	even	1	trivial
552.2.j.d.323.12	yes	42	24.11	even	2	inner
2208.2.j.c.47.3		42	8.5	even	2
2208.2.j.c.47.4		42	12.11	even	2
2208.2.j.d.47.3		42	4.3	odd	2
2208.2.j.d.47.4		42	24.5	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.975618 - 1.02380i) q^{2} +(1.69183 + 0.371101i) q^{3} +(-0.0963383 + 1.99768i) q^{4} -1.56730 q^{5} +(-1.27065 - 2.09415i) q^{6} -0.668312i q^{7} +(2.13922 - 1.85034i) q^{8} +(2.72457 + 1.25568i) q^{9} +O(q^{10})\)	\(q+(-0.975618 - 1.02380i) q^{2} +(1.69183 + 0.371101i) q^{3} +(-0.0963383 + 1.99768i) q^{4} -1.56730 q^{5} +(-1.27065 - 2.09415i) q^{6} -0.668312i q^{7} +(2.13922 - 1.85034i) q^{8} +(2.72457 + 1.25568i) q^{9} +(1.52908 + 1.60460i) q^{10} +4.80506i q^{11} +(-0.904328 + 3.34398i) q^{12} +4.48924i q^{13} +(-0.684219 + 0.652017i) q^{14} +(-2.65160 - 0.581625i) q^{15} +(-3.98144 - 0.384906i) q^{16} -1.05154i q^{17} +(-1.37257 - 4.01448i) q^{18} +1.05324 q^{19} +(0.150991 - 3.13095i) q^{20} +(0.248011 - 1.13067i) q^{21} +(4.91942 - 4.68790i) q^{22} +1.00000 q^{23} +(4.30585 - 2.33659i) q^{24} -2.54358 q^{25} +(4.59609 - 4.37978i) q^{26} +(4.14352 + 3.13548i) q^{27} +(1.33507 + 0.0643840i) q^{28} +7.11293 q^{29} +(1.99148 + 3.28215i) q^{30} +3.88117i q^{31} +(3.49030 + 4.45172i) q^{32} +(-1.78316 + 8.12933i) q^{33} +(-1.07656 + 1.02590i) q^{34} +1.04744i q^{35} +(-2.77092 + 5.32184i) q^{36} -2.44792i q^{37} +(-1.02756 - 1.07831i) q^{38} +(-1.66596 + 7.59502i) q^{39} +(-3.35278 + 2.90003i) q^{40} +2.02989i q^{41} +(-1.39955 + 0.849187i) q^{42} -3.57557 q^{43} +(-9.59896 - 0.462911i) q^{44} +(-4.27021 - 1.96802i) q^{45} +(-0.975618 - 1.02380i) q^{46} +7.09880 q^{47} +(-6.59307 - 2.12871i) q^{48} +6.55336 q^{49} +(2.48156 + 2.60412i) q^{50} +(0.390226 - 1.77902i) q^{51} +(-8.96805 - 0.432485i) q^{52} +0.0884948 q^{53} +(-0.832380 - 7.30117i) q^{54} -7.53095i q^{55} +(-1.23660 - 1.42966i) q^{56} +(1.78191 + 0.390859i) q^{57} +(-6.93951 - 7.28223i) q^{58} +6.15979i q^{59} +(1.41735 - 5.24101i) q^{60} +6.69672i q^{61} +(3.97355 - 3.78654i) q^{62} +(0.839185 - 1.82086i) q^{63} +(1.15248 - 7.91655i) q^{64} -7.03596i q^{65} +(10.0625 - 6.10552i) q^{66} +13.2350 q^{67} +(2.10063 + 0.101303i) q^{68} +(1.69183 + 0.371101i) q^{69} +(1.07237 - 1.02190i) q^{70} -6.95495 q^{71} +(8.15187 - 2.35521i) q^{72} -13.8192 q^{73} +(-2.50618 + 2.38823i) q^{74} +(-4.30330 - 0.943926i) q^{75} +(-0.101468 + 2.10404i) q^{76} +3.21128 q^{77} +(9.40113 - 5.70423i) q^{78} -14.6807i q^{79} +(6.24009 + 0.603261i) q^{80} +(5.84654 + 6.84236i) q^{81} +(2.07820 - 1.98040i) q^{82} -15.1782i q^{83} +(2.23482 + 0.604373i) q^{84} +1.64807i q^{85} +(3.48840 + 3.66068i) q^{86} +(12.0339 + 2.63962i) q^{87} +(8.89099 + 10.2790i) q^{88} +3.28612i q^{89} +(2.15123 + 6.29188i) q^{90} +3.00021 q^{91} +(-0.0963383 + 1.99768i) q^{92} +(-1.44031 + 6.56627i) q^{93} +(-6.92572 - 7.26777i) q^{94} -1.65074 q^{95} +(4.25294 + 8.82680i) q^{96} -14.8592 q^{97} +(-6.39358 - 6.70934i) q^{98} +(-6.03361 + 13.0917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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