LMFDB - Embedded newform 552.2.j.c.323.17

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			323.17
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.581428 - 1.28916i) q^{2} +(1.42468 - 0.985030i) q^{3} +(-1.32388 + 1.49911i) q^{4} -1.37188 q^{5} +(-2.09821 - 1.26392i) q^{6} -0.424283i q^{7} +(2.70234 + 0.835077i) q^{8} +(1.05943 - 2.80671i) q^{9} +O(q^{10})$	\(q+(-0.581428 - 1.28916i) q^{2} +(1.42468 - 0.985030i) q^{3} +(-1.32388 + 1.49911i) q^{4} -1.37188 q^{5} +(-2.09821 - 1.26392i) q^{6} -0.424283i q^{7} +(2.70234 + 0.835077i) q^{8} +(1.05943 - 2.80671i) q^{9} +(0.797651 + 1.76858i) q^{10} -3.23742i q^{11} +(-0.409442 + 3.43982i) q^{12} -1.55814i q^{13} +(-0.546971 + 0.246690i) q^{14} +(-1.95450 + 1.35135i) q^{15} +(-0.494666 - 3.96930i) q^{16} -1.60008i q^{17} +(-4.23429 + 0.266119i) q^{18} -0.246222 q^{19} +(1.81621 - 2.05661i) q^{20} +(-0.417932 - 0.604468i) q^{21} +(-4.17356 + 1.88233i) q^{22} -1.00000 q^{23} +(4.67255 - 1.47217i) q^{24} -3.11794 q^{25} +(-2.00869 + 0.905943i) q^{26} +(-1.25534 - 5.04223i) q^{27} +(0.636048 + 0.561702i) q^{28} -7.30601 q^{29} +(2.87850 + 1.73395i) q^{30} -0.188110i q^{31} +(-4.82946 + 2.94556i) q^{32} +(-3.18896 - 4.61229i) q^{33} +(-2.06276 + 0.930331i) q^{34} +0.582067i q^{35} +(2.80500 + 5.30396i) q^{36} -8.79231i q^{37} +(0.143160 + 0.317421i) q^{38} +(-1.53481 - 2.21985i) q^{39} +(-3.70730 - 1.14563i) q^{40} +3.71741i q^{41} +(-0.536261 + 0.890237i) q^{42} +3.26934 q^{43} +(4.85325 + 4.28596i) q^{44} +(-1.45342 + 3.85048i) q^{45} +(0.581428 + 1.28916i) q^{46} +4.69268 q^{47} +(-4.61462 - 5.16772i) q^{48} +6.81998 q^{49} +(1.81285 + 4.01953i) q^{50} +(-1.57613 - 2.27960i) q^{51} +(2.33582 + 2.06279i) q^{52} +8.35640 q^{53} +(-5.77037 + 4.55004i) q^{54} +4.44136i q^{55} +(0.354309 - 1.14656i) q^{56} +(-0.350788 + 0.242536i) q^{57} +(4.24792 + 9.41865i) q^{58} +9.37313i q^{59} +(0.561706 - 4.71903i) q^{60} -7.74409i q^{61} +(-0.242504 + 0.109372i) q^{62} +(-1.19084 - 0.449499i) q^{63} +(6.60529 + 4.51332i) q^{64} +2.13758i q^{65} +(-4.09184 + 6.79280i) q^{66} -4.22242 q^{67} +(2.39870 + 2.11832i) q^{68} +(-1.42468 + 0.985030i) q^{69} +(0.750380 - 0.338430i) q^{70} -5.51211 q^{71} +(5.20676 - 6.69997i) q^{72} +12.6874 q^{73} +(-11.3347 + 5.11209i) q^{74} +(-4.44206 + 3.07126i) q^{75} +(0.325969 - 0.369114i) q^{76} -1.37358 q^{77} +(-1.96936 + 3.26930i) q^{78} +3.52326i q^{79} +(0.678624 + 5.44541i) q^{80} +(-6.75521 - 5.94702i) q^{81} +(4.79234 - 2.16140i) q^{82} -8.76263i q^{83} +(1.45946 + 0.173719i) q^{84} +2.19512i q^{85} +(-1.90088 - 4.21471i) q^{86} +(-10.4087 + 7.19665i) q^{87} +(2.70349 - 8.74861i) q^{88} +2.08941i q^{89} +(5.80895 - 0.365084i) q^{90} -0.661091 q^{91} +(1.32388 - 1.49911i) q^{92} +(-0.185294 - 0.267996i) q^{93} +(-2.72846 - 6.04963i) q^{94} +0.337788 q^{95} +(-3.97896 + 8.95365i) q^{96} +6.32684 q^{97} +(-3.96533 - 8.79207i) q^{98} +(-9.08649 - 3.42982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * 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 $

$2$	−0.581428	−	1.28916i	−0.411132	−	0.911576i
$2$	−0.581428	−	1.28916i	−0.411132	−	0.911576i
$3$	1.42468	−	0.985030i	0.822540	−	0.568708i
$3$	1.42468	−	0.985030i	0.822540	−	0.568708i
$4$	−1.32388	+	1.49911i	−0.661942	+	0.749555i
$5$	−1.37188			−0.613525			−0.306762	−	0.951786i	$-0.599246\pi$
$5$	−1.37188			−0.613525			−0.306762	+	0.951786i	$0.599246\pi$
$6$	−2.09821	−	1.26392i	−0.856592	−	0.515994i
$7$		−	0.424283i		−	0.160364i	−0.996780	−	0.0801820i	$-0.974450\pi$
$7$		−	0.424283i		−	0.160364i	0.996780	−	0.0801820i	$-0.0255502\pi$
$8$	2.70234	+	0.835077i	0.955422	+	0.295244i
$9$	1.05943	−	2.80671i	0.353144	−	0.935569i
$10$	0.797651	+	1.76858i	0.252239	+	0.559275i
$11$		−	3.23742i		−	0.976118i	−0.872811	−	0.488059i	$-0.837705\pi$
$11$		−	3.23742i		−	0.976118i	0.872811	−	0.488059i	$-0.162295\pi$
$12$	−0.409442	+	3.43982i	−0.118196	+	0.992990i
$13$		−	1.55814i		−	0.432149i	−0.976377	−	0.216075i	$-0.930675\pi$
$13$		−	1.55814i		−	0.432149i	0.976377	−	0.216075i	$-0.0693254\pi$
$14$	−0.546971	+	0.246690i	−0.146184	+	0.0659307i
$15$	−1.95450	+	1.35135i	−0.504649	+	0.348916i
$16$	−0.494666	−	3.96930i	−0.123667	−	0.992324i
$17$		−	1.60008i		−	0.388076i	−0.980994	−	0.194038i	$-0.937841\pi$
$17$		−	1.60008i		−	0.388076i	0.980994	−	0.194038i	$-0.0621586\pi$
$18$	−4.23429	+	0.266119i	−0.998031	+	0.0627249i
$19$	−0.246222			−0.0564872			−0.0282436	−	0.999601i	$-0.508991\pi$
$19$	−0.246222			−0.0564872			−0.0282436	+	0.999601i	$0.508991\pi$
$20$	1.81621	−	2.05661i	0.406118	−	0.459871i
$21$	−0.417932	−	0.604468i	−0.0912003	−	0.131906i
$22$	−4.17356	+	1.88233i	−0.889806	+	0.401313i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	4.67255	−	1.47217i	0.953780	−	0.300505i
$25$	−3.11794			−0.623587
$26$	−2.00869	+	0.905943i	−0.393937	+	0.177670i
$27$	−1.25534	−	5.04223i	−0.241591	−	0.970378i
$28$	0.636048	+	0.561702i	0.120202	+	0.106152i
$29$	−7.30601			−1.35669			−0.678346	−	0.734742i	$-0.737303\pi$
$29$	−7.30601			−1.35669			−0.678346	+	0.734742i	$0.737303\pi$
$30$	2.87850	+	1.73395i	0.525541	+	0.316575i
$31$		−	0.188110i		−	0.0337855i	−0.999857	−	0.0168927i	$-0.994623\pi$
$31$		−	0.188110i		−	0.0337855i	0.999857	−	0.0168927i	$-0.00537738\pi$
$32$	−4.82946	+	2.94556i	−0.853735	+	0.520707i
$33$	−3.18896	−	4.61229i	−0.555126	−	0.802896i
$34$	−2.06276	+	0.930331i	−0.353761	+	0.159550i
$35$			0.582067i			0.0983873i
$36$	2.80500	+	5.30396i	0.467500	+	0.883993i
$37$		−	8.79231i		−	1.44545i	−0.691138	−	0.722723i	$-0.742890\pi$
$37$		−	8.79231i		−	1.44545i	0.691138	−	0.722723i	$-0.257110\pi$
$38$	0.143160	+	0.317421i	0.0232237	+	0.0514924i
$39$	−1.53481	−	2.21985i	−0.245766	−	0.355460i
$40$	−3.70730	−	1.14563i	−0.586175	−	0.181140i
$41$			3.71741i			0.580562i	0.956942	+	0.290281i	$0.0937487\pi$
$41$			3.71741i			0.580562i	−0.956942	+	0.290281i	$0.906251\pi$
$42$	−0.536261	+	0.890237i	−0.0827469	+	0.137367i
$43$	3.26934			0.498569			0.249285	−	0.968430i	$-0.419805\pi$
$43$	3.26934			0.498569			0.249285	+	0.968430i	$0.419805\pi$
$44$	4.85325	+	4.28596i	0.731655	+	0.646133i
$45$	−1.45342	+	3.85048i	−0.216662	+	0.573995i
$46$	0.581428	+	1.28916i	0.0857269	+	0.190077i
$47$	4.69268			0.684498			0.342249	−	0.939609i	$-0.388811\pi$
$47$	4.69268			0.684498			0.342249	+	0.939609i	$0.388811\pi$
$48$	−4.61462	−	5.16772i	−0.666063	−	0.745896i
$49$	6.81998			0.974283
$50$	1.81285	+	4.01953i	0.256376	+	0.568447i
$51$	−1.57613	−	2.27960i	−0.220702	−	0.319208i
$52$	2.33582	+	2.06279i	0.323920	+	0.286057i
$53$	8.35640			1.14784			0.573920	−	0.818911i	$-0.305422\pi$
$53$	8.35640			1.14784			0.573920	+	0.818911i	$0.305422\pi$
$54$	−5.77037	+	4.55004i	−0.785248	+	0.619181i
$55$			4.44136i			0.598873i
$56$	0.354309	−	1.14656i	0.0473466	−	0.153215i
$57$	−0.350788	+	0.242536i	−0.0464630	+	0.0321247i
$58$	4.24792	+	9.41865i	0.557779	+	1.23673i
$59$			9.37313i			1.22028i	0.792295	+	0.610139i	$0.208886\pi$
$59$			9.37313i			1.22028i	−0.792295	+	0.610139i	$0.791114\pi$
$60$	0.561706	−	4.71903i	0.0725159	−	0.609224i
$61$		−	7.74409i		−	0.991529i	−0.868457	−	0.495765i	$-0.834888\pi$
$61$		−	7.74409i		−	0.991529i	0.868457	−	0.495765i	$-0.165112\pi$
$62$	−0.242504	+	0.109372i	−0.0307980	+	0.0138903i
$63$	−1.19084	−	0.449499i	−0.150032	−	0.0566315i
$64$	6.60529	+	4.51332i	0.825662	+	0.564166i
$65$			2.13758i			0.265134i
$66$	−4.09184	+	6.79280i	−0.503671	+	0.836135i
$67$	−4.22242			−0.515850			−0.257925	−	0.966165i	$-0.583039\pi$
$67$	−4.22242			−0.515850			−0.257925	+	0.966165i	$0.583039\pi$
$68$	2.39870	+	2.11832i	0.290885	+	0.256884i
$69$	−1.42468	+	0.985030i	−0.171511	+	0.118584i
$70$	0.750380	−	0.338430i	0.0896875	−	0.0404501i
$71$	−5.51211			−0.654168			−0.327084	−	0.944995i	$-0.606066\pi$
$71$	−5.51211			−0.654168			−0.327084	+	0.944995i	$0.606066\pi$
$72$	5.20676	−	6.69997i	0.613622	−	0.789600i
$73$	12.6874			1.48495			0.742477	−	0.669872i	$-0.233651\pi$
$73$	12.6874			1.48495			0.742477	+	0.669872i	$0.233651\pi$
$74$	−11.3347	+	5.11209i	−1.31763	+	0.594269i
$75$	−4.44206	+	3.07126i	−0.512925	+	0.354639i
$76$	0.325969	−	0.369114i	0.0373913	−	0.0423403i
$77$	−1.37358			−0.156534
$78$	−1.96936	+	3.26930i	−0.222986	+	0.370176i
$79$			3.52326i			0.396397i	0.980162	+	0.198199i	$0.0635091\pi$
$79$			3.52326i			0.396397i	−0.980162	+	0.198199i	$0.936491\pi$
$80$	0.678624	+	5.44541i	0.0758725	+	0.608815i
$81$	−6.75521	−	5.94702i	−0.750579	−	0.660780i
$82$	4.79234	−	2.16140i	0.529226	−	0.238687i
$83$		−	8.76263i		−	0.961824i	−0.876769	−	0.480912i	$-0.840306\pi$
$83$		−	8.76263i		−	0.961824i	0.876769	−	0.480912i	$-0.159694\pi$
$84$	1.45946	+	0.173719i	0.159240	+	0.0189543i
$85$			2.19512i			0.238095i
$86$	−1.90088	−	4.21471i	−0.204977	−	0.454484i
$87$	−10.4087	+	7.19665i	−1.11593	+	0.771561i
$88$	2.70349	−	8.74861i	0.288193	−	0.932605i
$89$			2.08941i			0.221477i	0.993850	+	0.110738i	$0.0353215\pi$
$89$			2.08941i			0.221477i	−0.993850	+	0.110738i	$0.964678\pi$
$90$	5.80895	−	0.365084i	0.612317	−	0.0384833i
$91$	−0.661091			−0.0693012
$92$	1.32388	−	1.49911i	0.138024	−	0.156293i
$93$	−0.185294	−	0.267996i	−0.0192141	−	0.0277899i
$94$	−2.72846	−	6.04963i	−0.281419	−	0.623972i
$95$	0.337788			0.0346563
$96$	−3.97896	+	8.95365i	−0.406101	+	0.913828i
$97$	6.32684			0.642393			0.321196	−	0.947013i	$-0.395915\pi$
$97$	6.32684			0.642393			0.321196	+	0.947013i	$0.395915\pi$
$98$	−3.96533	−	8.79207i	−0.400559	−	0.888133i
$99$	−9.08649	−	3.42982i	−0.913226	−	0.344710i
$100$	4.12778	−	4.67413i	0.412778	−	0.467413i
$101$	8.72407			0.868077			0.434039	−	0.900894i	$-0.357088\pi$
$101$	8.72407			0.868077			0.434039	+	0.900894i	$0.357088\pi$
$102$	−2.02238	+	3.35731i	−0.200245	+	0.332423i
$103$			8.77157i			0.864288i	0.901805	+	0.432144i	$0.142243\pi$
$103$			8.77157i			0.864288i	−0.901805	+	0.432144i	$0.857757\pi$
$104$	1.30116	−	4.21061i	0.127590	−	0.412885i
$105$	0.573354	+	0.829260i	0.0559536	+	0.0809275i
$106$	−4.85864	−	10.7728i	−0.471913	−	1.04634i
$107$			0.610718i			0.0590403i	0.999564	+	0.0295201i	$0.00939792\pi$
$107$			0.610718i			0.0590403i	−0.999564	+	0.0295201i	$0.990602\pi$
$108$	9.22079	+	4.79343i	0.887271	+	0.461248i
$109$		−	11.0601i		−	1.05937i	−0.848195	−	0.529684i	$-0.822310\pi$
$109$		−	11.0601i		−	1.05937i	0.848195	−	0.529684i	$-0.177690\pi$
$110$	5.72564	−	2.58233i	0.545918	−	0.246216i
$111$	−8.66069	−	12.5262i	−0.822036	−	1.18894i
$112$	−1.68411	+	0.209879i	−0.159133	+	0.0198317i
$113$			10.7712i			1.01327i	0.862160	+	0.506635i	$0.169111\pi$
$113$			10.7712i			1.01327i	−0.862160	+	0.506635i	$0.830889\pi$
$114$	0.516627	+	0.311206i	0.0483865	+	0.0291471i
$115$	1.37188			0.127929
$116$	9.67231	−	10.9525i	0.898052	−	1.01692i
$117$	−4.37323	−	1.65074i	−0.404305	−	0.152611i
$118$	12.0835	−	5.44980i	1.11238	−	0.501695i
$119$	−0.678888			−0.0622335
$120$	−6.41019	+	2.01965i	−0.585168	+	0.184368i
$121$	0.519122			0.0471929
$122$	−9.98340	+	4.50263i	−0.903854	+	0.407649i
$123$	3.66176	+	5.29612i	0.330170	+	0.477535i
$124$	0.281997	+	0.249035i	0.0253241	+	0.0223640i
$125$	11.1369			0.996111
$126$	0.112910	+	1.79654i	0.0100588	+	0.160048i
$127$			18.7955i			1.66783i	0.551891	+	0.833916i	$0.313906\pi$
$127$			18.7955i			1.66783i	−0.551891	+	0.833916i	$0.686094\pi$
$128$	1.97791	−	11.1395i	0.174824	−	0.984600i
$129$	4.65776	−	3.22039i	0.410093	−	0.283540i
$130$	2.75569	−	1.24285i	0.241690	−	0.109005i
$131$		−	3.33484i		−	0.291366i	−0.989331	−	0.145683i	$-0.953462\pi$
$131$		−	3.33484i		−	0.291366i	0.989331	−	0.145683i	$-0.0465380\pi$
$132$	11.1361	+	1.32553i	0.969276	+	0.115373i
$133$			0.104468i			0.00905852i
$134$	2.45503	+	5.44339i	0.212082	+	0.470237i
$135$	1.72218	+	6.91736i	0.148222	+	0.595351i
$136$	1.33619	−	4.32396i	0.114577	−	0.370777i
$137$			0.697607i			0.0596006i	0.999556	+	0.0298003i	$0.00948713\pi$
$137$			0.697607i			0.0596006i	−0.999556	+	0.0298003i	$0.990513\pi$
$138$	2.09821	+	1.26392i	0.178612	+	0.107592i
$139$	9.59377			0.813733			0.406866	−	0.913488i	$-0.366621\pi$
$139$	9.59377			0.813733			0.406866	+	0.913488i	$0.366621\pi$
$140$	−0.872584	−	0.770589i	−0.0737468	−	0.0651267i
$141$	6.68557	−	4.62243i	0.563027	−	0.389279i
$142$	3.20490	+	7.10601i	0.268949	+	0.596323i
$143$	−5.04434			−0.421829
$144$	−11.6647	−	2.81681i	−0.972060	−	0.234734i
$145$	10.0230			0.832365
$146$	−7.37683	−	16.3562i	−0.610511	−	1.35365i
$147$	9.71630	−	6.71789i	0.801387	−	0.554082i
$148$	13.1806	+	11.6400i	1.08344	+	0.956801i
$149$	16.4514			1.34775			0.673877	−	0.738843i	$-0.264628\pi$
$149$	16.4514			1.34775			0.673877	+	0.738843i	$0.264628\pi$
$150$	6.54210	+	3.94083i	0.534160	+	0.321767i
$151$			2.38161i			0.193813i	0.995294	+	0.0969064i	$0.0308947\pi$
$151$			2.38161i			0.193813i	−0.995294	+	0.0969064i	$0.969105\pi$
$152$	−0.665376	−	0.205614i	−0.0539691	−	0.0166775i
$153$	−4.49096	−	1.69517i	−0.363072	−	0.137047i
$154$	0.798639	+	1.77077i	0.0643562	+	0.142693i
$155$			0.258065i			0.0207282i
$156$	5.35970	+	0.637965i	0.429120	+	0.0510781i
$157$		−	22.4689i		−	1.79321i	−0.442830	−	0.896606i	$-0.646025\pi$
$157$		−	22.4689i		−	1.79321i	0.442830	−	0.896606i	$-0.353975\pi$
$158$	4.54205	−	2.04852i	0.361346	−	0.162971i
$159$	11.9052	−	8.23131i	0.944144	−	0.652785i
$160$	6.62545	−	4.04097i	0.523788	−	0.319467i
$161$			0.424283i			0.0334382i
$162$	−3.73901	+	12.1663i	−0.293765	+	0.955878i
$163$	1.61022			0.126122			0.0630612	−	0.998010i	$-0.479914\pi$
$163$	1.61022			0.126122			0.0630612	+	0.998010i	$0.479914\pi$
$164$	−5.57281	−	4.92141i	−0.435163	−	0.384298i
$165$	4.37487	+	6.32752i	0.340584	+	0.492597i
$166$	−11.2965	+	5.09484i	−0.876775	+	0.395436i
$167$	−18.6708			−1.44479			−0.722394	−	0.691482i	$-0.756958\pi$
$167$	−18.6708			−1.44479			−0.722394	+	0.691482i	$0.756958\pi$
$168$	−0.624617	−	1.98249i	−0.0481903	−	0.152952i
$169$	10.5722			0.813247
$170$	2.82987	−	1.27631i	0.217041	−	0.0978882i
$171$	−0.260855	+	0.691074i	−0.0199481	+	0.0528477i
$172$	−4.32822	+	4.90110i	−0.330024	+	0.373705i
$173$	12.7423			0.968782			0.484391	−	0.874852i	$-0.339041\pi$
$173$	12.7423			0.968782			0.484391	+	0.874852i	$0.339041\pi$
$174$	15.3296	+	9.23423i	1.16213	+	0.700045i
$175$			1.32289i			0.100001i
$176$	−12.8503	+	1.60144i	−0.968626	+	0.120713i
$177$	9.23282	+	13.3537i	0.693981	+	1.00373i
$178$	2.69358	−	1.21484i	0.201893	−	0.0910560i
$179$			0.912682i			0.0682171i	0.999418	+	0.0341085i	$0.0108592\pi$
$179$			0.912682i			0.0682171i	−0.999418	+	0.0341085i	$0.989141\pi$
$180$	−3.84814	−	7.27641i	−0.286823	−	0.542352i
$181$			12.6224i			0.938212i	0.883142	+	0.469106i	$0.155424\pi$
$181$			12.6224i			0.938212i	−0.883142	+	0.469106i	$0.844576\pi$
$182$	0.384377	+	0.852254i	0.0284919	+	0.0631733i
$183$	−7.62816	−	11.0329i	−0.563890	−	0.815572i
$184$	−2.70234	−	0.835077i	−0.199219	−	0.0615627i
$185$			12.0620i			0.886817i
$186$	−0.237756	+	0.394694i	−0.0174331	+	0.0289404i
$187$	−5.18013			−0.378809
$188$	−6.21256	+	7.03485i	−0.453098	+	0.513069i
$189$	−2.13934	+	0.532621i	−0.155614	+	0.0387425i
$190$	−0.196399	−	0.435464i	−0.0142483	−	0.0315919i
$191$	5.82206			0.421270			0.210635	−	0.977565i	$-0.432447\pi$
$191$	5.82206			0.421270			0.210635	+	0.977565i	$0.432447\pi$
$192$	13.8562	−	0.0763675i	0.999985	−	0.00551135i
$193$	−14.2300			−1.02430			−0.512151	−	0.858896i	$-0.671151\pi$
$193$	−14.2300			−1.02430			−0.512151	+	0.858896i	$0.671151\pi$
$194$	−3.67860	−	8.15633i	−0.264108	−	0.585590i
$195$	2.10558	+	3.04537i	0.150784	+	0.218083i
$196$	−9.02886	+	10.2239i	−0.644919	+	0.730279i
$197$	7.50895			0.534991			0.267495	−	0.963559i	$-0.413804\pi$
$197$	7.50895			0.534991			0.267495	+	0.963559i	$0.413804\pi$
$198$	0.861539	+	13.7082i	0.0612269	+	0.974196i
$199$		−	7.75881i		−	0.550007i	−0.961443	−	0.275004i	$-0.911321\pi$
$199$		−	7.75881i		−	0.550007i	0.961443	−	0.275004i	$-0.0886791\pi$
$200$	−8.42573	−	2.60372i	−0.595789	−	0.184111i
$201$	−6.01560	+	4.15921i	−0.424308	+	0.293368i
$202$	−5.07242	−	11.2467i	−0.356894	−	0.791318i
$203$			3.09982i			0.217565i
$204$	5.50399	+	0.655139i	0.385356	+	0.0458689i
$205$		−	5.09985i		−	0.356189i
$206$	11.3080	−	5.10003i	0.787864	−	0.355336i
$207$	−1.05943	+	2.80671i	−0.0736355	+	0.195080i
$208$	−6.18470	+	0.770757i	−0.428832	+	0.0534424i
$209$			0.797124i			0.0551382i
$210$	0.735688	−	1.22130i	0.0507673	−	0.0842778i
$211$	−21.7986			−1.50068			−0.750338	−	0.661054i	$-0.770109\pi$
$211$	−21.7986			−1.50068			−0.750338	+	0.661054i	$0.770109\pi$
$212$	−11.0629	+	12.5272i	−0.759803	+	0.860369i
$213$	−7.85300	+	5.42960i	−0.538079	+	0.372030i
$214$	0.787315	−	0.355088i	0.0538197	−	0.0242733i
$215$	−4.48515			−0.305885
$216$	0.818291	−	14.6741i	0.0556777	−	0.998449i
$217$	−0.0798118			−0.00541798
$218$	−14.2583	+	6.43067i	−0.965695	+	0.435540i
$219$	18.0756	−	12.4975i	1.22143	−	0.844504i
$220$	−6.65809	−	5.87984i	−0.448888	−	0.396419i
$221$	−2.49314			−0.167707
$222$	−11.1128	+	18.4481i	−0.745841	+	1.23816i
$223$			22.5676i			1.51124i	0.655013	+	0.755618i	$0.272663\pi$
$223$			22.5676i			1.51124i	−0.655013	+	0.755618i	$0.727337\pi$
$224$	1.24975	+	2.04906i	0.0835027	+	0.136908i
$225$	−3.30324	+	8.75113i	−0.220216	+	0.583409i
$226$	13.8859	−	6.26268i	0.923673	−	0.416588i
$227$			21.1191i			1.40173i	0.713295	+	0.700864i	$0.247202\pi$
$227$			21.1191i			1.40173i	−0.713295	+	0.700864i	$0.752798\pi$
$228$	0.100814	−	0.846960i	0.00667654	−	0.0560913i
$229$		−	25.1844i		−	1.66423i	−0.554600	−	0.832117i	$-0.687129\pi$
$229$		−	25.1844i		−	1.66423i	0.554600	−	0.832117i	$-0.312871\pi$
$230$	−0.797651	−	1.76858i	−0.0525956	−	0.116617i
$231$	−1.95692	+	1.35302i	−0.128756	+	0.0890222i
$232$	−19.7433	−	6.10108i	−1.29621	−	0.400556i
$233$			10.7007i			0.701023i	0.936558	+	0.350511i	$0.113992\pi$
$233$			10.7007i			0.701023i	−0.936558	+	0.350511i	$0.886008\pi$
$234$	0.414650	+	6.59759i	0.0271065	+	0.431298i
$235$	−6.43781			−0.419956
$236$	−14.0514	−	12.4089i	−0.914666	−	0.807753i
$237$	3.47051	+	5.01952i	0.225434	+	0.326053i
$238$	0.394724	+	0.875197i	0.0255862	+	0.0567306i
$239$	21.8458			1.41308			0.706542	−	0.707671i	$-0.250254\pi$
$239$	21.8458			1.41308			0.706542	+	0.707671i	$0.250254\pi$
$240$	6.33072	+	7.08951i	0.408646	+	0.457626i
$241$	−17.5958			−1.13345			−0.566723	−	0.823908i	$-0.691789\pi$
$241$	−17.5958			−1.13345			−0.566723	+	0.823908i	$0.691789\pi$
$242$	−0.301832	−	0.669233i	−0.0194025	−	0.0430199i
$243$	−15.4820	−	1.81852i	−0.993172	−	0.116658i
$244$	11.6093	+	10.2523i	0.743206	+	0.656335i
$245$	−9.35622			−0.597747
$246$	4.69851	−	7.79992i	0.299566	−	0.497304i
$247$			0.383647i			0.0244109i
$248$	0.157086	−	0.508336i	0.00997497	−	0.0322794i
$249$	−8.63146	−	12.4840i	−0.546996	−	0.791138i
$250$	−6.47528	−	14.3572i	−0.409533	−	0.908031i
$251$		−	13.4789i		−	0.850780i	−0.905010	−	0.425390i	$-0.860137\pi$
$251$		−	13.4789i		−	0.850780i	0.905010	−	0.425390i	$-0.139863\pi$
$252$	2.25038	−	1.19012i	0.141761	−	0.0749703i
$253$			3.23742i			0.203535i
$254$	24.2305	−	10.9282i	1.52036	−	0.685698i
$255$	2.16226	+	3.12735i	0.135406	+	0.195842i
$256$	−15.5106	+	3.92695i	−0.969413	+	0.245434i
$257$		−	12.6088i		−	0.786514i	−0.919429	−	0.393257i	$-0.871348\pi$
$257$		−	12.6088i		−	0.786514i	0.919429	−	0.393257i	$-0.128652\pi$
$258$	−6.85977	−	4.13219i	−0.427070	−	0.257259i
$259$	−3.73043			−0.231798
$260$	−3.20447	−	2.82991i	−0.198733	−	0.175503i
$261$	−7.74022	+	20.5058i	−0.479107	+	1.26928i
$262$	−4.29915	+	1.93897i	−0.265602	+	0.119790i
$263$	26.1589			1.61303			0.806514	−	0.591215i	$-0.201351\pi$
$263$	26.1589			1.61303			0.806514	+	0.591215i	$0.201351\pi$
$264$	−4.76603	−	15.1270i	−0.293329	−	0.931002i
$265$	−11.4640			−0.704228
$266$	0.134676	−	0.0607406i	0.00825753	−	0.00372424i
$267$	2.05813	+	2.97674i	0.125955	+	0.182173i
$268$	5.58999	−	6.32987i	0.341463	−	0.386658i
$269$	−28.6261			−1.74537			−0.872683	−	0.488287i	$-0.837622\pi$
$269$	−28.6261			−1.74537			−0.872683	+	0.488287i	$0.837622\pi$
$270$	7.91628	−	6.24212i	0.481769	−	0.379883i
$271$			6.93217i			0.421099i	0.977583	+	0.210550i	$0.0675253\pi$
$271$			6.93217i			0.421099i	−0.977583	+	0.210550i	$0.932475\pi$
$272$	−6.35119	+	0.791505i	−0.385098	+	0.0479921i
$273$	−0.941844	+	0.651195i	−0.0570030	+	0.0394121i
$274$	0.899329	−	0.405608i	0.0543305	−	0.0245037i
$275$			10.0941i			0.608695i
$276$	0.409442	−	3.43982i	0.0246455	−	0.207053i
$277$			23.4240i			1.40741i	0.710491	+	0.703707i	$0.248473\pi$
$277$			23.4240i			1.40741i	−0.710491	+	0.703707i	$0.751527\pi$
$278$	−5.57808	−	12.3679i	−0.334551	−	0.741779i
$279$	−0.527969	−	0.199289i	−0.0316087	−	0.0119311i
$280$	−0.486071	+	1.57294i	−0.0290483	+	0.0940014i
$281$		−	21.3483i		−	1.27353i	−0.771057	−	0.636767i	$-0.780271\pi$
$281$		−	21.3483i		−	1.27353i	0.771057	−	0.636767i	$-0.219729\pi$
$282$	−9.84625	−	5.93118i	−0.586336	−	0.353197i
$283$	−32.0324			−1.90413			−0.952065	−	0.305896i	$-0.901044\pi$
$283$	−32.0324			−1.90413			−0.952065	+	0.305896i	$0.901044\pi$
$284$	7.29740	−	8.26327i	0.433021	−	0.490335i
$285$	0.481240	−	0.332731i	0.0285062	−	0.0197093i
$286$	2.93292	+	6.50297i	0.173427	+	0.384529i
$287$	1.57723			0.0931012
$288$	3.15086	+	16.6755i	0.185666	+	0.982613i
$289$	14.4397			0.849397
$290$	−5.82765	−	12.9213i	−0.342211	−	0.758764i
$291$	9.01372	−	6.23213i	0.528394	−	0.365334i
$292$	−16.7967	+	19.0199i	−0.982952	+	1.11305i
$293$	11.8269			0.690937			0.345468	−	0.938430i	$-0.387720\pi$
$293$	11.8269			0.690937			0.345468	+	0.938430i	$0.387720\pi$
$294$	−14.3098	−	8.61993i	−0.834564	−	0.502724i
$295$		−	12.8588i		−	0.748671i
$296$	7.34225	−	23.7598i	0.426760	−	1.38101i
$297$	−16.3238	+	4.06407i	−0.947204	+	0.235821i
$298$	−9.56533	−	21.2086i	−0.554104	−	1.22858i
$299$			1.55814i			0.0901093i
$300$	1.27661	−	10.7251i	0.0737053	−	0.619216i
$301$		−	1.38713i		−	0.0799526i
$302$	3.07028	−	1.38473i	0.176675	−	0.0796825i
$303$	12.4290	−	8.59347i	0.714028	−	0.493682i
$304$	0.121798	+	0.977328i	0.00698558	+	0.0560536i
$305$			10.6240i			0.608328i
$306$	0.425812	+	6.77520i	0.0243420	+	0.387312i
$307$	−15.0472			−0.858787			−0.429393	−	0.903118i	$-0.641273\pi$
$307$	−15.0472			−0.858787			−0.429393	+	0.903118i	$0.641273\pi$
$308$	1.81846	−	2.05915i	0.103617	−	0.117331i
$309$	8.64026	+	12.4967i	0.491527	+	0.710912i
$310$	0.332687	−	0.150046i	0.0188954	−	0.00852203i
$311$	6.39161			0.362435			0.181217	−	0.983443i	$-0.441996\pi$
$311$	6.39161			0.362435			0.181217	+	0.983443i	$0.441996\pi$
$312$	−2.29384	−	7.28046i	−0.129863	−	0.412175i
$313$	1.37009			0.0774422			0.0387211	−	0.999250i	$-0.487672\pi$
$313$	1.37009			0.0774422			0.0387211	+	0.999250i	$0.487672\pi$
$314$	−28.9660	+	13.0640i	−1.63465	+	0.737246i
$315$	1.63369	+	0.616660i	0.0920482	+	0.0347449i
$316$	−5.28175	−	4.66438i	−0.297122	−	0.262392i
$317$	14.2598			0.800909			0.400455	−	0.916317i	$-0.368852\pi$
$317$	14.2598			0.800909			0.400455	+	0.916317i	$0.368852\pi$
$318$	−17.5335	−	10.5618i	−0.983231	−	0.592278i
$319$			23.6526i			1.32429i
$320$	−9.06169	−	6.19176i	−0.506564	−	0.346130i
$321$	0.601575	+	0.870078i	0.0335767	+	0.0485630i
$322$	0.546971	−	0.246690i	0.0304815	−	0.0137475i
$323$			0.393975i			0.0219214i
$324$	17.8584	−	2.25365i	0.992131	−	0.125203i
$325$			4.85817i			0.269483i
$326$	−0.936229	−	2.07584i	−0.0518529	−	0.114970i
$327$	−10.8946	−	15.7572i	−0.602471	−	0.871373i
$328$	−3.10432	+	10.0457i	−0.171407	+	0.554681i
$329$		−	1.99103i		−	0.109769i
$330$	5.61353	−	9.31892i	0.309015	−	0.512990i
$331$	−0.606247			−0.0333223			−0.0166612	−	0.999861i	$-0.505304\pi$
$331$	−0.606247			−0.0333223			−0.0166612	+	0.999861i	$0.505304\pi$
$332$	13.1362	+	11.6007i	0.720940	+	0.636671i
$333$	−24.6774	−	9.31484i	−1.35231	−	0.510450i
$334$	10.8557	+	24.0697i	0.593998	+	1.31703i
$335$	5.79267			0.316487
$336$	−2.19258	+	1.95791i	−0.119615	+	0.106813i
$337$	−36.3548			−1.98037			−0.990186	−	0.139754i	$-0.955369\pi$
$337$	−36.3548			−1.98037			−0.990186	+	0.139754i	$0.955369\pi$
$338$	−6.14698	−	13.6293i	−0.334352	−	0.741337i
$339$	10.6100	+	15.3455i	0.576255	+	0.833455i
$340$	−3.29073	−	2.90609i	−0.178465	−	0.157605i
$341$	−0.608990			−0.0329786
$342$	1.04258	−	0.0655244i	0.0563760	−	0.00354315i
$343$		−	5.86359i		−	0.316604i
$344$	8.83486	+	2.73015i	0.476344	+	0.147200i
$345$	1.95450	−	1.35135i	0.105227	−	0.0727541i
$346$	−7.40875	−	16.4270i	−0.398297	−	0.883118i
$347$			20.8888i			1.12137i	0.828029	+	0.560685i	$0.189462\pi$
$347$			20.8888i			1.12137i	−0.828029	+	0.560685i	$0.810538\pi$
$348$	2.99139	−	25.1314i	0.160355	−	1.34718i
$349$		−	1.06729i		−	0.0571305i	−0.999592	−	0.0285652i	$-0.990906\pi$
$349$		−	1.06729i		−	0.0571305i	0.999592	−	0.0285652i	$-0.00909383\pi$
$350$	1.70542	−	0.769164i	0.0911585	−	0.0411136i
$351$	−7.85648	+	1.95599i	−0.419348	+	0.104403i
$352$	9.53602	+	15.6350i	0.508272	+	0.833347i
$353$			5.49169i			0.292293i	0.989263	+	0.146147i	$0.0466871\pi$
$353$			5.49169i			0.292293i	−0.989263	+	0.146147i	$0.953313\pi$
$354$	11.8469	−	19.6668i	0.629656	−	1.04528i
$355$	7.56198			0.401348
$356$	−3.13225	−	2.76613i	−0.166009	−	0.146605i
$357$	−0.967198	+	0.668725i	−0.0511896	+	0.0353927i
$358$	1.17660	−	0.530659i	0.0621851	−	0.0280462i
$359$	2.20137			0.116184			0.0580920	−	0.998311i	$-0.481498\pi$
$359$	2.20137			0.116184			0.0580920	+	0.998311i	$0.481498\pi$
$360$	−7.14307	+	9.19158i	−0.376473	+	0.484439i
$361$	−18.9394			−0.996809
$362$	16.2723	−	7.33899i	0.855252	−	0.385729i
$363$	0.739583	−	0.511351i	0.0388180	−	0.0268390i
$364$	0.875207	−	0.991049i	0.0458733	−	0.0519451i
$365$	−17.4057			−0.911056
$366$	−9.78793	+	16.2488i	−0.511623	+	0.849336i
$367$		−	11.2809i		−	0.588858i	−0.955673	−	0.294429i	$-0.904871\pi$
$367$		−	11.2809i		−	0.588858i	0.955673	−	0.294429i	$-0.0951294\pi$
$368$	0.494666	+	3.96930i	0.0257863	+	0.206914i
$369$	10.4337	+	3.93834i	0.543155	+	0.205022i
$370$	15.5499	−	7.01319i	0.808401	−	0.364599i
$371$		−	3.54548i		−	0.184072i
$372$	0.647063	+	0.0770199i	0.0335487	+	0.00399330i
$373$			28.0162i			1.45062i	0.688420	+	0.725312i	$0.258305\pi$
$373$			28.0162i			1.45062i	−0.688420	+	0.725312i	$0.741695\pi$
$374$	3.01187	+	6.67803i	0.155740	+	0.345313i
$375$	15.8665	−	10.9701i	0.819341	−	0.566496i
$376$	12.6812	+	3.91875i	0.653984	+	0.202094i
$377$			11.3838i			0.586294i
$378$	1.93050	+	2.44827i	0.0992944	+	0.125926i
$379$	27.6278			1.41914			0.709572	−	0.704633i	$-0.248888\pi$
$379$	27.6278			1.41914			0.709572	+	0.704633i	$0.248888\pi$
$380$	−0.447192	+	0.506382i	−0.0229405	+	0.0259768i
$381$	18.5141	+	26.7776i	0.948509	+	1.37186i
$382$	−3.38511	−	7.50559i	−0.173197	−	0.384019i
$383$	13.8817			0.709320			0.354660	−	0.934995i	$-0.384597\pi$
$383$	13.8817			0.709320			0.354660	+	0.934995i	$0.384597\pi$
$384$	−8.15483	−	17.8185i	−0.416149	−	0.909296i
$385$	1.88440			0.0960377
$386$	8.27375	+	18.3449i	0.421123	+	0.933729i
$387$	3.46363	−	9.17607i	0.176066	−	0.466446i
$388$	−8.37599	+	9.48463i	−0.425227	+	0.481509i
$389$	−30.3407			−1.53833			−0.769166	−	0.639049i	$-0.779328\pi$
$389$	−30.3407			−1.53833			−0.769166	+	0.639049i	$0.779328\pi$
$390$	2.70173	−	4.48510i	0.136808	−	0.227112i
$391$			1.60008i			0.0809195i
$392$	18.4299	+	5.69521i	0.930852	+	0.287652i
$393$	−3.28492	−	4.75108i	−0.165702	−	0.239660i
$394$	−4.36591	−	9.68026i	−0.219952	−	0.487685i
$395$		−	4.83350i		−	0.243200i
$396$	17.1711	−	9.08097i	0.862882	−	0.456336i
$397$		−	9.15836i		−	0.459645i	−0.973233	−	0.229823i	$-0.926185\pi$
$397$		−	9.15836i		−	0.459645i	0.973233	−	0.229823i	$-0.0738146\pi$
$398$	−10.0024	+	4.51119i	−0.501374	+	0.226125i
$399$	0.102904	+	0.148834i	0.00515165	+	0.00745100i
$400$	1.54234	+	12.3760i	0.0771169	+	0.618800i
$401$		−	35.5331i		−	1.77444i	−0.461349	−	0.887219i	$-0.652634\pi$
$401$		−	35.5331i		−	1.77444i	0.461349	−	0.887219i	$-0.347366\pi$
$402$	8.85954	+	5.33681i	0.441874	+	0.266176i
$403$	−0.293100			−0.0146004
$404$	−11.5496	+	13.0783i	−0.574616	+	0.650672i
$405$	9.26737	+	8.15862i	0.460499	+	0.405405i
$406$	3.99618	−	1.80232i	0.198327	−	0.0894478i
$407$	−28.4644			−1.41093
$408$	−2.35559	−	7.47645i	−0.116619	−	0.370140i
$409$	21.4324			1.05976			0.529882	−	0.848071i	$-0.322236\pi$
$409$	21.4324			1.05976			0.529882	+	0.848071i	$0.322236\pi$
$410$	−6.57454	+	2.96519i	−0.324693	+	0.146441i
$411$	0.687164	+	0.993867i	0.0338953	+	0.0490239i
$412$	−13.1496	−	11.6125i	−0.647832	−	0.572108i
$413$	3.97686			0.195689
$414$	4.23429	−	0.266119i	0.208104	−	0.0130790i
$415$			12.0213i			0.590103i
$416$	4.58959	+	7.52495i	0.225023	+	0.368941i
$417$	13.6681	−	9.45015i	0.669328	−	0.462776i
$418$	1.02762	−	0.463470i	0.0502627	−	0.0226691i
$419$			21.7593i			1.06301i	0.847055	+	0.531506i	$0.178374\pi$
$419$			21.7593i			1.06301i	−0.847055	+	0.531506i	$0.821626\pi$
$420$	−2.00221	−	0.238323i	−0.0976977	−	0.0116290i
$421$			12.5414i			0.611229i	0.952155	+	0.305614i	$0.0988618\pi$
$421$			12.5414i			0.611229i	−0.952155	+	0.305614i	$0.901138\pi$
$422$	12.6743	+	28.1019i	0.616976	+	1.36798i
$423$	4.97157	−	13.1710i	0.241726	−	0.640395i
$424$	22.5818	+	6.97824i	1.09667	+	0.338893i
$425$			4.98895i			0.242000i
$426$	11.5656	+	6.96688i	0.560355	+	0.337547i
$427$	−3.28569			−0.159006
$428$	−0.915533	−	0.808519i	−0.0442540	−	0.0390812i
$429$	−7.18657	+	4.96882i	−0.346971	+	0.239897i
$430$	2.60779	+	5.78209i	0.125759	+	0.278837i
$431$	15.7627			0.759261			0.379631	−	0.925138i	$-0.376051\pi$
$431$	15.7627			0.759261			0.379631	+	0.925138i	$0.376051\pi$
$432$	−19.3931	+	7.47704i	−0.933053	+	0.359739i
$433$	0.635216			0.0305265			0.0152633	−	0.999884i	$-0.495141\pi$
$433$	0.635216			0.0305265			0.0152633	+	0.999884i	$0.495141\pi$
$434$	0.0464048	+	0.102890i	0.00222750	+	0.00493890i
$435$	14.2796	−	9.87296i	0.684653	−	0.473372i
$436$	16.5804	+	14.6423i	0.794055	+	0.701240i
$437$	0.246222			0.0117784
$438$	−26.6210	−	16.0359i	−1.27200	−	0.766227i
$439$		−	21.1456i		−	1.00922i	−0.863346	−	0.504612i	$-0.831636\pi$
$439$		−	21.1456i		−	1.00922i	0.863346	−	0.504612i	$-0.168364\pi$
$440$	−3.70888	+	12.0021i	−0.176814	+	0.572176i
$441$	7.22530	−	19.1417i	0.344062	−	0.911509i
$442$	1.44958	+	3.21407i	0.0689496	+	0.152878i
$443$			25.1476i			1.19480i	0.801944	+	0.597399i	$0.203799\pi$
$443$			25.1476i			1.19480i	−0.801944	+	0.597399i	$0.796201\pi$
$444$	30.2439	+	3.59993i	1.43531	+	0.170845i
$445$		−	2.86642i		−	0.135881i
$446$	29.0933	−	13.1214i	1.37761	−	0.621317i
$447$	23.4381	−	16.2052i	1.10858	−	0.766478i
$448$	1.91493	−	2.80252i	0.0904719	−	0.132406i
$449$		−	6.70255i		−	0.316313i	−0.987414	−	0.158156i	$-0.949445\pi$
$449$		−	6.70255i		−	0.316313i	0.987414	−	0.158156i	$-0.0505550\pi$
$450$	13.2022	−	0.829742i	0.622359	−	0.0391144i
$451$	12.0348			0.566697
$452$	−16.1472	−	14.2598i	−0.759502	−	0.670726i
$453$	2.34596	+	3.39303i	0.110223	+	0.159419i
$454$	27.2260	−	12.2793i	1.27778	−	0.576294i
$455$	0.906940			0.0425180
$456$	−1.15049	+	0.362481i	−0.0538764	+	0.0169747i
$457$	33.3516			1.56012			0.780061	−	0.625704i	$-0.215188\pi$
$457$	33.3516			1.56012			0.780061	+	0.625704i	$0.215188\pi$
$458$	−32.4669	+	14.6429i	−1.51708	+	0.684219i
$459$	−8.06798	+	2.00865i	−0.376581	+	0.0937556i
$460$	−1.81621	+	2.05661i	−0.0846814	+	0.0958897i
$461$	−13.9143			−0.648054			−0.324027	−	0.946048i	$-0.605037\pi$
$461$	−13.9143			−0.648054			−0.324027	+	0.946048i	$0.605037\pi$
$462$	2.88207	+	1.73610i	0.134086	+	0.0807708i
$463$		−	6.54089i		−	0.303981i	−0.988382	−	0.151990i	$-0.951432\pi$
$463$		−	6.54089i		−	0.303981i	0.988382	−	0.151990i	$-0.0485683\pi$
$464$	3.61404	+	28.9997i	0.167777	+	1.34628i
$465$	0.254201	+	0.367660i	0.0117883	+	0.0170498i
$466$	13.7949	−	6.22166i	0.639036	−	0.288213i
$467$		−	22.0884i		−	1.02213i	−0.859543	−	0.511064i	$-0.829251\pi$
$467$		−	22.0884i		−	1.02213i	0.859543	−	0.511064i	$-0.170749\pi$
$468$	8.26428	−	4.37057i	0.382017	−	0.202030i
$469$			1.79150i			0.0827239i
$470$	3.74312	+	8.29939i	0.172657	+	0.382822i
$471$	−22.1325	−	32.0110i	−1.01981	−	1.47499i
$472$	−7.82728	+	25.3294i	−0.360280	+	1.16588i
$473$		−	10.5842i		−	0.486662i
$474$	4.45312	−	7.39255i	0.204539	−	0.339551i
$475$	0.767705			0.0352247
$476$	0.898768	−	1.01773i	0.0411950	−	0.0466475i
$477$	8.85302	−	23.4540i	0.405352	−	1.07388i
$478$	−12.7017	−	28.1628i	−0.580964	−	1.28813i
$479$	18.9070			0.863883			0.431942	−	0.901902i	$-0.357829\pi$
$479$	18.9070			0.863883			0.431942	+	0.901902i	$0.357829\pi$
$480$	5.45867	−	12.2834i	0.249153	−	0.560656i
$481$	−13.6996			−0.624648
$482$	10.2307	+	22.6839i	0.465996	+	1.03322i
$483$	0.417932	+	0.604468i	0.0190166	+	0.0275043i
$484$	−0.687257	+	0.778221i	−0.0312390	+	0.0353737i
$485$	−8.67968			−0.394124
$486$	6.65731	+	21.0162i	0.301982	+	0.953314i
$487$		−	23.6641i		−	1.07232i	−0.844115	−	0.536162i	$-0.819873\pi$
$487$		−	23.6641i		−	1.07232i	0.844115	−	0.536162i	$-0.180127\pi$
$488$	6.46691	−	20.9272i	0.292743	−	0.947329i
$489$	2.29405	−	1.58612i	0.103741	−	0.0717268i
$490$	5.43997	+	12.0617i	0.245753	+	0.544892i
$491$			4.57736i			0.206573i	0.994652	+	0.103287i	$0.0329359\pi$
$491$			4.57736i			0.206573i	−0.994652	+	0.103287i	$0.967064\pi$
$492$	−12.7872	−	1.52206i	−0.576492	−	0.0686198i
$493$			11.6902i			0.526501i
$494$	0.494584	−	0.223063i	0.0222524	−	0.0100361i
$495$	12.4656	+	4.70531i	0.560287	+	0.211488i
$496$	−0.746663	+	0.0930515i	−0.0335261	+	0.00417813i
$497$			2.33870i			0.104905i
$498$	−11.0753	+	18.3859i	−0.496295	+	0.823891i
$499$	17.0710			0.764202			0.382101	−	0.924121i	$-0.375201\pi$
$499$	17.0710			0.764202			0.382101	+	0.924121i	$0.375201\pi$
$500$	−14.7439	+	16.6954i	−0.659367	+	0.746640i
$501$	−26.5999	+	18.3913i	−1.18839	+	0.821661i
$502$	−17.3765	+	7.83700i	−0.775551	+	0.349783i
$503$	−43.2545			−1.92862			−0.964311	−	0.264770i	$-0.914704\pi$
$503$	−43.2545			−1.92862			−0.964311	+	0.264770i	$0.914704\pi$
$504$	−2.84269	−	2.20914i	−0.126623	−	0.0984030i
$505$	−11.9684			−0.532587
$506$	4.17356	−	1.88233i	0.185537	−	0.0836796i
$507$	15.0620	−	10.4140i	0.668928	−	0.462500i
$508$	−28.1766	−	24.8831i	−1.25013	−	1.10401i
$509$	−9.40840			−0.417020			−0.208510	−	0.978020i	$-0.566861\pi$
$509$	−9.40840			−0.417020			−0.208510	+	0.978020i	$0.566861\pi$
$510$	2.77446	−	4.60584i	0.122855	−	0.203950i
$511$		−	5.38307i		−	0.238133i
$512$	14.0808	+	17.7125i	0.622289	+	0.782788i
$513$	0.309093	+	1.24151i	0.0136468	+	0.0548140i
$514$	−16.2548	+	7.33109i	−0.716967	+	0.323361i
$515$		−	12.0336i		−	0.530262i
$516$	−1.33860	+	11.2459i	−0.0589287	+	0.495074i
$517$		−	15.1922i		−	0.668151i
$518$	2.16898	+	4.80913i	0.0952993	+	0.211301i
$519$	18.1538	−	12.5516i	0.796862	−	0.550954i
$520$	−1.78504	+	5.77647i	−0.0782793	+	0.253315i
$521$		−	17.1864i		−	0.752948i	−0.926427	−	0.376474i	$-0.877136\pi$
$521$		−	17.1864i		−	0.752948i	0.926427	−	0.376474i	$-0.122864\pi$
$522$	30.9358	−	1.94427i	1.35402	−	0.0850984i
$523$	2.64611			0.115706			0.0578532	−	0.998325i	$-0.481574\pi$
$523$	2.64611			0.115706			0.0578532	+	0.998325i	$0.481574\pi$
$524$	4.99929	+	4.41494i	0.218395	+	0.192867i
$525$	1.30309	+	1.88469i	0.0568713	+	0.0822548i
$526$	−15.2095	−	33.7231i	−0.663167	−	1.47040i
$527$	−0.300991			−0.0131114
$528$	−16.7301	+	14.9394i	−0.728083	+	0.650156i
$529$	1.00000			0.0434783
$530$	6.66549	+	14.7790i	0.289530	+	0.641958i
$531$	26.3076	+	9.93018i	1.14165	+	0.430933i
$532$	−0.156609	−	0.138303i	−0.00678986	−	0.00599621i
$533$	5.79222			0.250889
$534$	2.64085	−	4.38402i	0.114281	−	0.189715i
$535$		−	0.837833i		−	0.0362227i
$536$	−11.4104	−	3.52604i	−0.492855	−	0.152302i
$537$	0.899020	+	1.30028i	0.0387956	+	0.0561113i
$538$	16.6440	+	36.9038i	0.717575	+	1.59103i
$539$		−	22.0791i		−	0.951016i
$540$	−12.6499	−	6.57603i	−0.544363	−	0.282987i
$541$		−	17.6974i		−	0.760871i	−0.924807	−	0.380436i	$-0.875774\pi$
$541$		−	17.6974i		−	0.760871i	0.924807	−	0.380436i	$-0.124226\pi$
$542$	8.93669	−	4.03055i	0.383864	−	0.173127i
$543$	12.4334	+	17.9828i	0.533568	+	0.771717i
$544$	4.71314	+	7.72752i	0.202074	+	0.331315i
$545$			15.1732i			0.649949i
$546$	1.38711	+	0.835568i	0.0593629	+	0.0357590i
$547$	8.13620			0.347879			0.173939	−	0.984756i	$-0.444350\pi$
$547$	8.13620			0.347879			0.173939	+	0.984756i	$0.444350\pi$
$548$	−1.04579	−	0.923550i	−0.0446739	−	0.0394521i
$549$	−21.7354	−	8.20433i	−0.927644	−	0.350152i
$550$	13.0129	−	5.86897i	0.554872	−	0.250254i
$551$	1.79890			0.0766358
$552$	−4.67255	+	1.47217i	−0.198877	+	0.0626597i
$553$	1.49486			0.0635679
$554$	30.1974	−	13.6194i	1.28296	−	0.578632i
$555$	11.8815	+	17.1845i	0.504340	+	0.729442i
$556$	−12.7010	+	14.3821i	−0.538644	+	0.609938i
$557$	−28.6521			−1.21403			−0.607015	−	0.794690i	$-0.707633\pi$
$557$	−28.6521			−1.21403			−0.607015	+	0.794690i	$0.707633\pi$
$558$	0.0500596	+	0.796510i	0.00211919	+	0.0337190i
$559$		−	5.09407i		−	0.215456i
$560$	2.31040	−	0.287929i	0.0976321	−	0.0121672i
$561$	−7.38003	+	5.10258i	−0.311585	+	0.215431i
$562$	−27.5215	+	12.4125i	−1.16092	+	0.523590i
$563$			10.6494i			0.448820i	0.974495	+	0.224410i	$0.0720455\pi$
$563$			10.6494i			0.448820i	−0.974495	+	0.224410i	$0.927954\pi$
$564$	−1.92138	+	16.1420i	−0.0809046	+	0.679700i
$565$		−	14.7769i		−	0.621667i
$566$	18.6245	+	41.2950i	0.782848	+	1.73576i
$567$	−2.52322	+	2.86613i	−0.105965	+	0.120366i
$568$	−14.8956	−	4.60304i	−0.625006	−	0.193139i
$569$		−	18.5495i		−	0.777634i	−0.921315	−	0.388817i	$-0.872884\pi$
$569$		−	18.5495i		−	0.777634i	0.921315	−	0.388817i	$-0.127116\pi$
$570$	−0.708752	−	0.426938i	−0.0296863	−	0.0178825i
$571$	−26.3697			−1.10354			−0.551768	−	0.833998i	$-0.686047\pi$
$571$	−26.3697			−1.10354			−0.551768	+	0.833998i	$0.686047\pi$
$572$	6.67811	−	7.56202i	0.279226	−	0.316184i
$573$	8.29458	−	5.73491i	0.346511	−	0.239579i
$574$	−0.917048	−	2.03331i	−0.0382768	−	0.0848688i
$575$	3.11794			0.130027
$576$	19.6654	−	13.7576i	0.819393	−	0.573232i
$577$	24.6833			1.02758			0.513789	−	0.857917i	$-0.328241\pi$
$577$	24.6833			1.02758			0.513789	+	0.857917i	$0.328241\pi$
$578$	−8.39567	−	18.6152i	−0.349214	−	0.774290i
$579$	−20.2733	+	14.0170i	−0.842529	+	0.582528i
$580$	−13.2693	+	15.0256i	−0.550977	+	0.623904i
$581$	−3.71784			−0.154242
$582$	−13.2751	−	7.99663i	−0.550269	−	0.331471i
$583$		−	27.0532i		−	1.12043i
$584$	34.2858	+	10.5950i	1.41876	+	0.438424i
$585$	5.99956	+	2.26462i	0.248051	+	0.0936304i
$586$	−6.87651	−	15.2468i	−0.284066	−	0.629841i
$587$		−	30.1598i		−	1.24483i	−0.782688	−	0.622414i	$-0.786152\pi$
$587$		−	30.1598i		−	1.24483i	0.782688	−	0.622414i	$-0.213848\pi$
$588$	−2.79238	+	23.4595i	−0.115156	+	0.967454i
$589$			0.0463168i			0.00190845i
$590$	−16.5771	+	7.47649i	−0.682470	+	0.307802i
$591$	10.6979	−	7.39654i	0.440051	−	0.304253i
$592$	−34.8993	+	4.34925i	−1.43435	+	0.178753i
$593$		−	25.2094i		−	1.03522i	−0.855615	−	0.517612i	$-0.826821\pi$
$593$		−	25.2094i		−	1.03522i	0.855615	−	0.517612i	$-0.173179\pi$
$594$	14.7304	+	18.6811i	0.604394	+	0.766495i
$595$	0.931355			0.0381818
$596$	−21.7798	+	24.6625i	−0.892135	+	1.01022i
$597$	−7.64266	−	11.0538i	−0.312793	−	0.452403i
$598$	2.00869	−	0.905943i	0.0821415	−	0.0370468i
$599$	6.85614			0.280134			0.140067	−	0.990142i	$-0.455268\pi$
$599$	6.85614			0.280134			0.140067	+	0.990142i	$0.455268\pi$
$600$	−14.5687	+	4.59013i	−0.594765	+	0.187391i
$601$	−12.0365			−0.490979			−0.245489	−	0.969399i	$-0.578949\pi$
$601$	−12.0365			−0.490979			−0.245489	+	0.969399i	$0.578949\pi$
$602$	−1.78823	+	0.806513i	−0.0728828	+	0.0328710i
$603$	−4.47336	+	11.8511i	−0.182169	+	0.482614i
$604$	−3.57030	−	3.15297i	−0.145273	−	0.128293i
$605$	−0.712175			−0.0289540
$606$	−18.3050	−	11.0265i	−0.743588	−	0.447923i
$607$			43.0572i			1.74764i	0.486250	+	0.873820i	$0.338364\pi$
$607$			43.0572i			1.74764i	−0.486250	+	0.873820i	$0.661636\pi$
$608$	1.18912	−	0.725263i	0.0482252	−	0.0294133i
$609$	3.05342	+	4.41626i	0.123731	+	0.178956i
$610$	13.6961	−	6.17708i	0.554537	−	0.250103i
$611$		−	7.31183i		−	0.295805i
$612$	8.48676	−	4.48823i	0.343057	−	0.181426i
$613$		−	23.3053i		−	0.941293i	−0.882322	−	0.470647i	$-0.844021\pi$
$613$		−	23.3053i		−	0.941293i	0.882322	−	0.470647i	$-0.155979\pi$
$614$	8.74884	+	19.3982i	0.353074	+	0.782849i
$615$	−5.02351	−	7.26566i	−0.202567	−	0.292980i
$616$	−3.71189	−	1.14705i	−0.149556	−	0.0462159i
$617$			20.2737i			0.816189i	0.912940	+	0.408095i	$0.133807\pi$
$617$			20.2737i			0.816189i	−0.912940	+	0.408095i	$0.866193\pi$
$618$	11.0866	−	18.4046i	0.445968	−	0.740343i
$619$	48.5363			1.95084			0.975419	−	0.220356i	$-0.0707220\pi$
$619$	48.5363			1.95084			0.975419	+	0.220356i	$0.0707220\pi$
$620$	−0.386867	−	0.341647i	−0.0155370	−	0.0137209i
$621$	1.25534	+	5.04223i	0.0503751	+	0.202338i
$622$	−3.71626	−	8.23983i	−0.149008	−	0.330387i
$623$	0.886500			0.0355169
$624$	−8.05200	+	7.19020i	−0.322338	+	0.287838i
$625$	0.311205			0.0124482
$626$	−0.796610	−	1.76627i	−0.0318389	−	0.0705944i
$627$	0.785191	+	1.13565i	0.0313575	+	0.0453534i
$628$	33.6833	+	29.7462i	1.34411	+	1.18700i
$629$	−14.0684			−0.560944
$630$	−0.154899	−	2.46464i	−0.00617133	−	0.0981936i
$631$		−	16.5946i		−	0.660620i	−0.943873	−	0.330310i	$-0.892847\pi$
$631$		−	16.5946i		−	0.660620i	0.943873	−	0.330310i	$-0.107153\pi$
$632$	−2.94219	+	9.52104i	−0.117034	+	0.378727i
$633$	−31.0560	+	21.4723i	−1.23437	+	0.853446i
$634$	−8.29104	−	18.3832i	−0.329279	−	0.730090i
$635$		−	25.7852i		−	1.02326i
$636$	−3.42146	+	28.7445i	−0.135670	+	1.13979i
$637$		−	10.6265i		−	0.421036i
$638$	30.4921	−	13.7523i	1.20719	−	0.544459i
$639$	−5.83970	+	15.4709i	−0.231015	+	0.612019i
$640$	−2.71346	+	15.2821i	−0.107259	+	0.604076i
$641$			27.7615i			1.09651i	0.836310	+	0.548256i	$0.184708\pi$
$641$			27.7615i			1.09651i	−0.836310	+	0.548256i	$0.815292\pi$
$642$	0.771899	−	1.28142i	0.0304644	−	0.0505735i
$643$	−9.81955			−0.387245			−0.193623	−	0.981076i	$-0.562024\pi$
$643$	−9.81955			−0.387245			−0.193623	+	0.981076i	$0.562024\pi$
$644$	−0.636048	−	0.561702i	−0.0250638	−	0.0221342i
$645$	−6.38990	+	4.41801i	−0.251602	+	0.173959i
$646$	0.507898	−	0.229068i	0.0199830	−	0.00901257i
$647$	−31.5143			−1.23896			−0.619478	−	0.785014i	$-0.712656\pi$
$647$	−31.5143			−1.23896			−0.619478	+	0.785014i	$0.712656\pi$
$648$	−13.2887	−	21.7120i	−0.522028	−	0.852928i
$649$	30.3447			1.19114
$650$	6.26297	−	2.82467i	0.245654	−	0.110793i
$651$	−0.113706	+	0.0786171i	−0.00445650	+	0.00308125i
$652$	−2.13175	+	2.41390i	−0.0834857	+	0.0945358i
$653$	3.75735			0.147036			0.0735182	−	0.997294i	$-0.476577\pi$
$653$	3.75735			0.147036			0.0735182	+	0.997294i	$0.476577\pi$
$654$	−13.9791	+	23.2065i	−0.546628	+	0.907447i
$655$			4.57501i			0.178760i
$656$	14.7555	−	1.83888i	0.576105	−	0.0717960i
$657$	13.4415	−	35.6099i	0.524402	−	1.38928i
$658$	−2.56676	+	1.15764i	−0.100063	+	0.0451294i
$659$		−	22.6737i		−	0.883241i	−0.897202	−	0.441621i	$-0.854404\pi$
$659$		−	22.6737i		−	0.883241i	0.897202	−	0.441621i	$-0.145596\pi$
$660$	−15.2775	−	1.81848i	−0.594675	−	0.0707841i
$661$			28.2857i			1.10019i	0.835103	+	0.550094i	$0.185408\pi$
$661$			28.2857i			1.10019i	−0.835103	+	0.550094i	$0.814592\pi$
$662$	0.352489	+	0.781551i	0.0136999	+	0.0303758i
$663$	−3.55193	+	2.45582i	−0.137946	+	0.0953762i
$664$	7.31747	−	23.6796i	0.283973	−	0.918947i
$665$		−	0.143318i		−	0.00555763i
$666$	2.33980	+	37.2291i	0.0906654	+	1.44260i
$667$	7.30601			0.282890
$668$	24.7179	−	27.9895i	0.956365	−	1.08295i
$669$	22.2297	+	32.1516i	0.859451	+	1.24305i
$670$	−3.36802	−	7.46769i	−0.130118	−	0.288502i
$671$	−25.0709			−0.967850
$672$	3.79889	+	1.68821i	0.146545	+	0.0651241i
$673$	0.656771			0.0253167			0.0126583	−	0.999920i	$-0.495971\pi$
$673$	0.656771			0.0253167			0.0126583	+	0.999920i	$0.495971\pi$
$674$	21.1377	+	46.8673i	0.814194	+	1.80526i
$675$	3.91407	+	15.7214i	0.150653	+	0.605115i
$676$	−13.9964	+	15.8489i	−0.538322	+	0.609574i
$677$	43.3340			1.66546			0.832730	−	0.553680i	$-0.186777\pi$
$677$	43.3340			1.66546			0.832730	+	0.553680i	$0.186777\pi$
$678$	13.6140	−	22.6003i	0.522842	−	0.867960i
$679$		−	2.68437i		−	0.103017i
$680$	−1.83310	+	5.93197i	−0.0702961	+	0.227481i
$681$	20.8030	+	30.0880i	0.797173	+	1.15298i
$682$	0.354084	+	0.785087i	0.0135586	+	0.0300625i
$683$			0.308463i			0.0118030i	0.999983	+	0.00590151i	$0.00187852\pi$
$683$			0.308463i			0.0118030i	−0.999983	+	0.00590151i	$0.998121\pi$
$684$	−0.690654	−	1.30595i	−0.0264078	−	0.0499343i
$685$		−	0.957036i		−	0.0365664i
$686$	−7.55912	+	3.40925i	−0.288609	+	0.130166i
$687$	−24.8074	−	35.8798i	−0.946463	−	1.36890i
$688$	−1.61723	−	12.9770i	−0.0616563	−	0.494742i
$689$		−	13.0204i		−	0.496038i
$690$	−2.87850	−	1.73395i	−0.109583	−	0.0660105i
$691$	38.5518			1.46658			0.733289	−	0.679917i	$-0.237984\pi$
$691$	38.5518			1.46658			0.733289	+	0.679917i	$0.237984\pi$
$692$	−16.8694	+	19.1022i	−0.641277	+	0.726156i
$693$	−1.45522	+	3.85525i	−0.0552791	+	0.146449i
$694$	26.9291	−	12.1453i	1.02221	−	0.461030i
$695$	−13.1615			−0.499245
$696$	−34.1377	+	10.7557i	−1.29399	+	0.407694i
$697$	5.94815			0.225302
$698$	−1.37590	+	0.620549i	−0.0520788	+	0.0234881i
$699$	10.5405	+	15.2450i	0.398677	+	0.576619i
$700$	−1.98316	−	1.75135i	−0.0749563	−	0.0661948i
$701$	−45.9731			−1.73638			−0.868190	−	0.496233i	$-0.834716\pi$
$701$	−45.9731			−1.73638			−0.868190	+	0.496233i	$0.834716\pi$
$702$	7.08957	+	8.99102i	0.267579	+	0.339344i
$703$			2.16486i			0.0816493i
$704$	14.6115	−	21.3841i	0.550692	−	0.805944i
$705$	−9.17183	+	6.34144i	−0.345431	+	0.238832i
$706$	7.07969	−	3.19302i	0.266448	−	0.120171i
$707$		−	3.70148i		−	0.139208i
$708$	−32.2419	−	3.83775i	−1.21172	−	0.144231i
$709$			8.42757i			0.316504i	0.987399	+	0.158252i	$0.0505859\pi$
$709$			8.42757i			0.316504i	−0.987399	+	0.158252i	$0.949414\pi$
$710$	−4.39674	−	9.74862i	−0.165007	−	0.365859i
$711$	9.88875	+	3.73265i	0.370857	+	0.139985i
$712$	−1.74481	+	5.64629i	−0.0653897	+	0.211604i
$713$			0.188110i			0.00704476i
$714$	1.42445	+	0.858061i	0.0533088	+	0.0321121i
$715$	6.92024			0.258802
$716$	−1.36821	−	1.20828i	−0.0511325	−	0.0451557i
$717$	31.1232	−	21.5187i	1.16232	−	0.803632i
$718$	−1.27994	−	2.83793i	−0.0477669	−	0.105911i
$719$	−19.5740			−0.729985			−0.364993	−	0.931010i	$-0.618928\pi$
$719$	−19.5740			−0.729985			−0.364993	+	0.931010i	$0.618928\pi$
$720$	16.0026	+	3.86433i	0.596383	+	0.144015i
$721$	3.72163			0.138601
$722$	11.0119	+	24.4159i	0.409820	+	0.908667i
$723$	−25.0684	+	17.3324i	−0.932305	+	0.644600i
$724$	−18.9223	−	16.7105i	−0.703242	−	0.621042i
$725$	22.7797			0.846016
$726$	−1.08923	−	0.656130i	−0.0404251	−	0.0243513i
$727$			24.4848i			0.908092i	0.890978	+	0.454046i	$0.150020\pi$
$727$			24.4848i			0.908092i	−0.890978	+	0.454046i	$0.849980\pi$
$728$	−1.78649	−	0.552062i	−0.0662119	−	0.0204608i
$729$	−23.8482	+	12.6595i	−0.883268	+	0.468869i
$730$	10.1202	+	22.4388i	0.374564	+	0.830496i
$731$		−	5.23120i		−	0.193483i
$732$	26.6383	+	3.17075i	0.984579	+	0.117194i
$733$			37.1605i			1.37255i	0.727340	+	0.686277i	$0.240756\pi$
$733$			37.1605i			1.37255i	−0.727340	+	0.686277i	$0.759244\pi$
$734$	−14.5429	+	6.55903i	−0.536789	+	0.242098i
$735$	−13.3296	+	9.21616i	−0.491671	+	0.339943i
$736$	4.82946	−	2.94556i	0.178016	−	0.108575i
$737$			13.6697i			0.503531i
$738$	−0.989273	−	15.7406i	−0.0364156	−	0.579418i
$739$	−16.2945			−0.599402			−0.299701	−	0.954033i	$-0.596887\pi$
$739$	−16.2945			−0.599402			−0.299701	+	0.954033i	$0.596887\pi$
$740$	−18.0823	−	15.9687i	−0.664719	−	0.587021i
$741$	0.377904	+	0.546575i	0.0138827	+	0.0200789i
$742$	−4.57070	+	2.06144i	−0.167796	+	0.0756779i
$743$	1.68794			0.0619246			0.0309623	−	0.999521i	$-0.490143\pi$
$743$	1.68794			0.0619246			0.0309623	+	0.999521i	$0.490143\pi$
$744$	−0.276929	−	0.878952i	−0.0101527	−	0.0322239i
$745$	−22.5695			−0.826881
$746$	36.1175	−	16.2894i	1.32235	−	0.596397i
$747$	−24.5941	−	9.28340i	−0.899853	−	0.339662i
$748$	6.85789	−	7.76559i	0.250749	−	0.283938i
$749$	0.259117			0.00946794
$750$	−23.3675	−	14.0761i	−0.853261	−	0.513987i
$751$		−	30.8626i		−	1.12619i	−0.826392	−	0.563095i	$-0.809610\pi$
$751$		−	30.8626i		−	1.12619i	0.826392	−	0.563095i	$-0.190390\pi$
$752$	−2.32131	−	18.6266i	−0.0846495	−	0.679244i
$753$	−13.2771	−	19.2031i	−0.483845	−	0.699801i
$754$	14.6755	−	6.61884i	0.534451	−	0.241044i
$755$		−	3.26729i		−	0.118909i
$756$	2.03377	−	3.91223i	0.0739676	−	0.142286i
$757$		−	41.2131i		−	1.49792i	−0.662618	−	0.748958i	$-0.730555\pi$
$757$		−	41.2131i		−	1.49792i	0.662618	−	0.748958i	$-0.269445\pi$
$758$	−16.0636	−	35.6167i	−0.583455	−	1.29366i
$759$	3.18896	+	4.61229i	0.115752	+	0.167415i
$760$	0.912819	+	0.282079i	0.0331114	+	0.0102321i
$761$		−	4.32875i		−	0.156917i	−0.996917	−	0.0784586i	$-0.975000\pi$
$761$		−	4.32875i		−	0.156917i	0.996917	−	0.0784586i	$-0.0249998\pi$
$762$	23.7561	−	39.4370i	0.860591	−	1.42865i
$763$	−4.69263			−0.169885
$764$	−7.70773	+	8.72792i	−0.278856	+	0.315765i
$765$	6.16107	+	2.32558i	0.222754	+	0.0840816i
$766$	−8.07119	−	17.8957i	−0.291624	−	0.646599i
$767$	14.6046			0.527342
$768$	−18.2295	+	20.8731i	−0.657801	+	0.753192i
$769$	−6.66540			−0.240361			−0.120180	−	0.992752i	$-0.538347\pi$
$769$	−6.66540			−0.240361			−0.120180	+	0.992752i	$0.538347\pi$
$770$	−1.09564	−	2.42929i	−0.0394841	−	0.0875457i
$771$	−12.4200	−	17.9635i	−0.447296	−	0.646939i
$772$	18.8389	−	21.3324i	0.678028	−	0.767771i
$773$	−1.15246			−0.0414512			−0.0207256	−	0.999785i	$-0.506598\pi$
$773$	−1.15246			−0.0414512			−0.0207256	+	0.999785i	$0.506598\pi$
$774$	−13.8433	+	0.870033i	−0.497587	+	0.0312727i
$775$			0.586514i			0.0210682i
$776$	17.0973	+	5.28339i	0.613756	+	0.189663i
$777$	−5.31467	+	3.67459i	−0.190663	+	0.131825i
$778$	17.6409	+	39.1141i	0.632457	+	1.40231i
$779$		−	0.915308i		−	0.0327943i
$780$	−7.35289	−	0.875214i	−0.263276	−	0.0313377i
$781$			17.8450i			0.638545i
$782$	2.06276	−	0.930331i	0.0737643	−	0.0332686i
$783$	9.17154	+	36.8386i	0.327764	+	1.31651i
$784$	−3.37361	−	27.0705i	−0.120486	−	0.966805i
$785$			30.8247i			1.10018i
$786$	−4.21498	+	6.99721i	−0.150343	+	0.249582i
$787$	−33.5493			−1.19590			−0.597952	−	0.801532i	$-0.704019\pi$
$787$	−33.5493			−1.19590			−0.597952	+	0.801532i	$0.704019\pi$
$788$	−9.94097	+	11.2567i	−0.354133	+	0.401005i
$789$	37.2681	−	25.7673i	1.32678	−	0.917341i
$790$	−6.23117	+	2.81033i	−0.221695	+	0.0999870i
$791$	4.57005			0.162492
$792$	−21.6906	−	16.8565i	−0.770743	−	0.598968i
$793$	−12.0663			−0.428488
$794$	−11.8066	+	5.32493i	−0.419001	+	0.188975i
$795$	−16.3325	+	11.2924i	−0.579256	+	0.400500i
$796$	11.6313	+	10.2718i	0.412261	+	0.364073i
$797$	25.9102			0.917787			0.458894	−	0.888491i	$-0.348246\pi$
$797$	25.9102			0.917787			0.458894	+	0.888491i	$0.348246\pi$
$798$	0.132039	−	0.219196i	0.00467414	−	0.00775946i
$799$		−	7.50867i		−	0.265638i
$800$	15.0579	−	9.18408i	0.532378	−	0.324706i
$801$	5.86435	+	2.21358i	0.207207	+	0.0782130i
$802$	−45.8080	+	20.6599i	−1.61754	+	0.729527i
$803$		−	41.0746i		−	1.44949i
$804$	1.72883	−	14.5244i	0.0609713	−	0.512235i
$805$		−	0.582067i		−	0.0205152i
$806$	0.170417	+	0.377854i	0.00600267	+	0.0133093i
$807$	−40.7831	+	28.1976i	−1.43563	+	0.992603i
$808$	23.5754	+	7.28527i	0.829380	+	0.256295i
$809$		−	15.3326i		−	0.539065i	−0.962991	−	0.269532i	$-0.913131\pi$
$809$		−	15.3326i		−	0.539065i	0.962991	−	0.269532i	$-0.0868691\pi$
$810$	5.12949	−	16.6908i	0.180232	−	0.586455i
$811$	−27.7423			−0.974163			−0.487081	−	0.873357i	$-0.661939\pi$
$811$	−27.7423			−0.974163			−0.487081	+	0.873357i	$0.661939\pi$
$812$	−4.64698	−	4.10380i	−0.163077	−	0.144015i
$813$	6.82839	+	9.87612i	0.239482	+	0.346371i
$814$	16.5500	+	36.6952i	0.580076	+	1.28617i
$815$	−2.20904			−0.0773793
$816$	−8.26876	+	7.38376i	−0.289465	+	0.258483i
$817$	−0.804983			−0.0281628
$818$	−12.4614	−	27.6299i	−0.435702	−	0.966055i
$819$	−0.700380	+	1.85549i	−0.0244733	+	0.0648360i
$820$	7.64524	+	6.75161i	0.266983	+	0.235776i
$821$	−0.539947			−0.0188443			−0.00942214	−	0.999956i	$-0.502999\pi$
$821$	−0.539947			−0.0188443			−0.00942214	+	0.999956i	$0.502999\pi$
$822$	0.881721	−	1.46373i	0.0307535	−	0.0510534i
$823$			25.4073i			0.885642i	0.896610	+	0.442821i	$0.146022\pi$
$823$			25.4073i			0.885642i	−0.896610	+	0.442821i	$0.853978\pi$
$824$	−7.32493	+	23.7038i	−0.255176	+	0.825760i
$825$	9.94296	+	14.3808i	0.346169	+	0.500676i
$826$	−2.31226	−	5.12683i	−0.0804538	−	0.178385i
$827$		−	35.7207i		−	1.24213i	−0.783759	−	0.621065i	$-0.786700\pi$
$827$		−	35.7207i		−	1.24213i	0.783759	−	0.621065i	$-0.213300\pi$
$828$	−2.80500	−	5.30396i	−0.0974806	−	0.184325i
$829$			36.3216i			1.26150i	0.775986	+	0.630750i	$0.217253\pi$
$829$			36.3216i			1.26150i	−0.775986	+	0.630750i	$0.782747\pi$
$830$	15.4974	−	6.98952i	0.537924	−	0.242610i
$831$	23.0734	+	33.3718i	0.800407	+	1.15765i
$832$	7.03237	−	10.2919i	0.243804	−	0.356809i
$833$		−	10.9125i		−	0.378096i
$834$	−20.1298	−	12.1258i	−0.697037	−	0.419881i
$835$	25.6141			0.886413
$836$	−1.19498	−	1.05530i	−0.0413292	−	0.0364983i
$837$	−0.948493	+	0.236142i	−0.0327847	+	0.00816226i
$838$	28.0513	−	12.6515i	0.969016	−	0.437038i
$839$	−2.79230			−0.0964009			−0.0482004	−	0.998838i	$-0.515349\pi$
$839$	−2.79230			−0.0964009			−0.0482004	+	0.998838i	$0.515349\pi$
$840$	0.856902	+	2.71974i	0.0295659	+	0.0938399i
$841$	24.3779			0.840616
$842$	16.1679	−	7.29190i	0.557181	−	0.251295i
$843$	−21.0287	−	30.4145i	−0.724268	−	1.04753i
$844$	28.8588	−	32.6785i	0.993360	−	1.12484i
$845$	−14.5038			−0.498947
$846$	−19.8702	+	1.24881i	−0.683150	+	0.0429350i
$847$		−	0.220255i		−	0.00756805i
$848$	−4.13363	−	33.1690i	−0.141949	−	1.13903i
$849$	−45.6360	+	31.5529i	−1.56622	+	1.08289i
$850$	6.43157	−	2.90071i	0.220601	−	0.0994936i
$851$			8.79231i			0.301396i
$852$	2.25689	−	18.9607i	0.0773197	−	0.649582i
$853$			8.10366i			0.277464i	0.990330	+	0.138732i	$0.0443027\pi$
$853$			8.10366i			0.277464i	−0.990330	+	0.138732i	$0.955697\pi$
$854$	1.91039	+	4.23579i	0.0653723	+	0.144946i
$855$	0.357863	−	0.948072i	0.0122387	−	0.0324234i
$856$	−0.509996	+	1.65037i	−0.0174313	+	0.0564084i
$857$		−	44.7587i		−	1.52893i	−0.644666	−	0.764464i	$-0.723004\pi$
$857$		−	44.7587i		−	1.52893i	0.644666	−	0.764464i	$-0.276996\pi$
$858$	10.5841	+	6.37565i	0.361335	+	0.217661i
$859$	−41.5998			−1.41937			−0.709684	−	0.704520i	$-0.751162\pi$
$859$	−41.5998			−1.41937			−0.709684	+	0.704520i	$0.751162\pi$
$860$	5.93781	−	6.72373i	0.202478	−	0.229277i
$861$	2.24706	−	1.55362i	0.0765794	−	0.0529474i
$862$	−9.16486	−	20.3207i	−0.312156	−	0.692124i
$863$	41.3467			1.40746			0.703728	−	0.710469i	$-0.251517\pi$
$863$	41.3467			1.40746			0.703728	+	0.710469i	$0.251517\pi$
$864$	20.9148	+	20.6536i	0.711537	+	0.702648i
$865$	−17.4810			−0.594372
$866$	−0.369332	−	0.818897i	−0.0125504	−	0.0278273i
$867$	20.5720	−	14.2236i	0.698663	−	0.483058i
$868$	0.105662	−	0.119647i	0.00358639	−	0.00406108i
$869$	11.4063			0.386931
$870$	−21.0304	−	12.6683i	−0.712997	−	0.429495i
$871$			6.57910i			0.222924i
$872$	9.23606	−	29.8882i	0.312772	−	1.01214i
$873$	6.70284	−	17.7576i	0.226857	−	0.601003i
$874$	−0.143160	−	0.317421i	−0.00484247	−	0.0107369i
$875$		−	4.72519i		−	0.159740i
$876$	−5.19477	+	43.6425i	−0.175515	+	1.47454i
$877$		−	20.6446i		−	0.697120i	−0.937286	−	0.348560i	$-0.886671\pi$
$877$		−	20.6446i		−	0.697120i	0.937286	−	0.348560i	$-0.113329\pi$
$878$	−27.2601	+	12.2946i	−0.919984	+	0.414924i
$879$	16.8496	−	11.6499i	0.568323	−	0.392941i
$880$	17.6291	−	2.19699i	0.594276	−	0.0740605i
$881$		−	53.5282i		−	1.80341i	−0.432350	−	0.901706i	$-0.642315\pi$
$881$		−	53.5282i		−	1.80341i	0.432350	−	0.901706i	$-0.357685\pi$
$882$	−28.8778	+	1.81493i	−0.972365	+	0.0611118i
$883$	32.6308			1.09811			0.549057	−	0.835785i	$-0.314987\pi$
$883$	32.6308			1.09811			0.549057	+	0.835785i	$0.314987\pi$
$884$	3.30063	−	3.73750i	0.111012	−	0.125706i
$885$	−12.6663	−	18.3197i	−0.425775	−	0.615811i
$886$	32.4194	−	14.6215i	1.08915	−	0.491219i
$887$	−45.5513			−1.52946			−0.764732	−	0.644348i	$-0.777129\pi$
$887$	−45.5513			−1.52946			−0.764732	+	0.644348i	$0.777129\pi$
$888$	−12.9438	−	41.0825i	−0.434364	−	1.37864i
$889$	7.97462			0.267460
$890$	−3.69528	+	1.66662i	−0.123866	+	0.0558651i
$891$	−19.2530	+	21.8695i	−0.645000	+	0.732654i
$892$	−33.8313	−	29.8768i	−1.13276	−	1.00035i
$893$	−1.15544			−0.0386654
$894$	−34.5186	−	20.7933i	−1.15448	−	0.695433i
$895$		−	1.25209i		−	0.0418529i
$896$	−4.72629	−	0.839195i	−0.157894	−	0.0280355i
$897$	1.53481	+	2.21985i	0.0512458	+	0.0741185i
$898$	−8.64068	+	3.89705i	−0.288343	+	0.130046i
$899$			1.37433i			0.0458365i
$900$	−8.74582	−	16.5374i	−0.291527	−	0.551247i
$901$		−	13.3709i		−	0.445450i
$902$	−6.99737	−	15.5148i	−0.232987	−	0.516587i
$903$	−1.36636	−	1.97621i	−0.0454696	−	0.0657642i
$904$	−8.99479	+	29.1075i	−0.299162	+	0.968101i
$905$		−	17.3164i		−	0.575617i
$906$	3.01017	−	4.99713i	0.100006	−	0.166018i
$907$	−40.5011			−1.34482			−0.672408	−	0.740180i	$-0.734740\pi$
$907$	−40.5011			−1.34482			−0.672408	+	0.740180i	$0.734740\pi$
$908$	−31.6599	−	27.9593i	−1.05067	−	0.927862i
$909$	9.24254	−	24.4859i	0.306556	−	0.812146i
$910$	−0.527320	−	1.16919i	−0.0174805	−	0.0387584i
$911$	17.6200			0.583775			0.291888	−	0.956453i	$-0.405717\pi$
$911$	17.6200			0.583775			0.291888	+	0.956453i	$0.405717\pi$
$912$	1.13622	+	1.27241i	0.0376240	+	0.0421336i
$913$	−28.3683			−0.938854
$914$	−19.3915	−	42.9956i	−0.641415	−	1.42217i
$915$	10.4650	+	15.1358i	0.345961	+	0.500374i
$916$	37.7543	+	33.3413i	1.24744	+	1.10163i
$917$	−1.41492			−0.0467247
$918$	7.28042	+	9.23306i	0.240290	+	0.304736i
$919$		−	51.5456i		−	1.70033i	−0.526513	−	0.850167i	$-0.676501\pi$
$919$		−	51.5456i		−	1.70033i	0.526513	−	0.850167i	$-0.323499\pi$
$920$	3.70730	+	1.14563i	0.122226	+	0.0377702i
$921$	−21.4374	+	14.8219i	−0.706386	+	0.488398i
$922$	8.09016	+	17.9378i	0.266435	+	0.590750i
$923$			8.58862i			0.282698i
$924$	0.562402	−	4.72488i	0.0185017	−	0.155437i
$925$			27.4138i			0.901362i
$926$	−8.43227	+	3.80305i	−0.277102	+	0.124976i
$927$	24.6192	+	9.29287i	0.808601	+	0.305218i
$928$	35.2841	−	21.5203i	1.15826	−	0.706440i
$929$		−	30.1378i		−	0.988788i	−0.869238	−	0.494394i	$-0.835390\pi$
$929$		−	30.1378i		−	0.988788i	0.869238	−	0.494394i	$-0.164610\pi$
$930$	0.326173	−	0.541475i	0.0106956	−	0.0177556i
$931$	−1.67923			−0.0550346
$932$	−16.0415	−	14.1664i	−0.525456	−	0.464036i
$933$	9.10600	−	6.29593i	0.298117	−	0.206119i
$934$	−28.4755	+	12.8428i	−0.931748	+	0.420229i
$935$	7.10653			0.232408
$936$	−10.4395	−	8.11284i	−0.341225	−	0.265176i
$937$	14.3837			0.469896			0.234948	−	0.972008i	$-0.424508\pi$
$937$	14.3837			0.469896			0.234948	+	0.972008i	$0.424508\pi$
$938$	2.30954	−	1.04163i	0.0754091	−	0.0340104i
$939$	1.95194	−	1.34958i	0.0636993	−	0.0440420i
$940$	8.52291	−	9.65099i	0.277987	−	0.314781i
$941$	−30.7702			−1.00308			−0.501541	−	0.865134i	$-0.667233\pi$
$941$	−30.7702			−1.00308			−0.501541	+	0.865134i	$0.667233\pi$
$942$	−28.3989	+	47.1445i	−0.925286	+	1.53605i
$943$		−	3.71741i		−	0.121055i
$944$	37.2047	−	4.63657i	1.21091	−	0.150907i
$945$	2.93492	−	0.730693i	0.0954729	−	0.0237695i
$946$	−13.6448	+	6.15395i	−0.443630	+	0.200082i
$947$			42.4520i			1.37951i	0.724045	+	0.689753i	$0.242281\pi$
$947$			42.4520i			1.37951i	−0.724045	+	0.689753i	$0.757719\pi$
$948$	−12.1194	−	1.44257i	−0.393619	−	0.0468524i
$949$		−	19.7688i		−	0.641721i
$950$	−0.446365	−	0.989697i	−0.0144820	−	0.0321100i
$951$	20.3156	−	14.0463i	0.658780	−	0.455483i
$952$	−1.83459	−	0.566923i	−0.0594593	−	0.0183741i
$953$			1.66386i			0.0538978i	0.999637	+	0.0269489i	$0.00857914\pi$
$953$			1.66386i			0.0538978i	−0.999637	+	0.0269489i	$0.991421\pi$
$954$	−35.3834	+	2.22380i	−1.14558	+	0.0719981i
$955$	−7.98719			−0.258459
$956$	−28.9212	+	32.7492i	−0.935380	+	1.05919i
$957$	23.2986	+	33.6974i	0.753135	+	1.08928i
$958$	−10.9931	−	24.3742i	−0.355170	−	0.787495i
$959$	0.295983			0.00955779
$960$	−19.0091	+	0.104767i	−0.613516	+	0.00338135i
$961$	30.9646			0.998859
$962$	7.96533	+	17.6610i	0.256813	+	0.569414i
$963$	1.71411	+	0.647013i	0.0552363	+	0.0208497i
$964$	23.2948	−	26.3781i	0.750276	−	0.849581i
$965$	19.5220			0.628434
$966$	0.536261	−	0.890237i	0.0172539	−	0.0286429i
$967$			46.2351i			1.48682i	0.668837	+	0.743409i	$0.266793\pi$
$967$			46.2351i			1.48682i	−0.668837	+	0.743409i	$0.733207\pi$
$968$	1.40284	+	0.433507i	0.0450891	+	0.0139334i
$969$	0.388078	+	0.561289i	0.0124668	+	0.0180312i
$970$	5.04661	+	11.1895i	0.162037	+	0.359274i
$971$			30.6925i			0.984970i	0.870321	+	0.492485i	$0.163911\pi$
$971$			30.6925i			0.984970i	−0.870321	+	0.492485i	$0.836089\pi$
$972$	23.2226	−	20.8018i	0.744864	−	0.667217i
$973$		−	4.07048i		−	0.130494i
$974$	−30.5069	+	13.7590i	−0.977506	+	0.440867i
$975$	4.78544	+	6.92134i	0.153257	+	0.221660i
$976$	−30.7386	+	3.83074i	−0.983918	+	0.122619i
$977$			51.7936i			1.65702i	0.559971	+	0.828512i	$0.310812\pi$
$977$			51.7936i			1.65702i	−0.559971	+	0.828512i	$0.689188\pi$
$978$	−3.37859	−	2.03520i	−0.108036	−	0.0650784i
$979$	6.76428			0.216187
$980$	12.3865	−	14.0260i	0.395674	−	0.448045i
$981$	−31.0425	−	11.7174i	−0.991112	−	0.374109i
$982$	5.90096	−	2.66140i	0.188307	−	0.0849288i
$983$	−19.4666			−0.620889			−0.310444	−	0.950592i	$-0.600478\pi$
$983$	−19.4666			−0.620889			−0.310444	+	0.950592i	$0.600478\pi$
$984$	5.47266	+	17.3698i	0.174462	+	0.553728i
$985$	−10.3014			−0.328230
$986$	15.0706	−	6.79701i	0.479945	−	0.216461i
$987$	−1.96122	−	2.83658i	−0.0624264	−	0.0902893i
$988$	−0.575130	−	0.507904i	−0.0182973	−	0.0161586i
$989$	−3.26934			−0.103959
$990$	−1.18193	−	18.8060i	−0.0375642	−	0.597694i
$991$			57.7515i			1.83454i	0.398269	+	0.917269i	$0.369611\pi$
$991$			57.7515i			1.83454i	−0.398269	+	0.917269i	$0.630389\pi$
$992$	0.554089	+	0.908467i	0.0175923	+	0.0288439i
$993$	−0.863708	+	0.597171i	−0.0274089	+	0.0189507i
$994$	3.01496	−	1.35978i	0.0956289	−	0.0431297i
$995$			10.6442i			0.337443i
$996$	30.1419	+	3.58779i	0.955082	+	0.113683i
$997$		−	8.69772i		−	0.275460i	−0.990470	−	0.137730i	$-0.956019\pi$
$997$		−	8.69772i		−	0.275460i	0.990470	−	0.137730i	$-0.0439806\pi$
$998$	−9.92554	−	22.0073i	−0.314187	−	0.696628i
$999$	−44.3329	+	11.0373i	−1.40263	+	0.349206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.17	✓	42
3.2	odd	2		552.2.j.d.323.26	yes	42
4.3	odd	2		2208.2.j.c.47.10		42
8.3	odd	2		552.2.j.d.323.25	yes	42
8.5	even	2		2208.2.j.d.47.10		42
12.11	even	2		2208.2.j.d.47.9		42
24.5	odd	2		2208.2.j.c.47.9		42
24.11	even	2	inner	552.2.j.c.323.18	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.17	✓	42	1.1	even	1	trivial
552.2.j.c.323.18	yes	42	24.11	even	2	inner
552.2.j.d.323.25	yes	42	8.3	odd	2
552.2.j.d.323.26	yes	42	3.2	odd	2
2208.2.j.c.47.9		42	24.5	odd	2
2208.2.j.c.47.10		42	4.3	odd	2
2208.2.j.d.47.9		42	12.11	even	2
2208.2.j.d.47.10		42	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(-0.581428 - 1.28916i) q^{2} +(1.42468 - 0.985030i) q^{3} +(-1.32388 + 1.49911i) q^{4} -1.37188 q^{5} +(-2.09821 - 1.26392i) q^{6} -0.424283i q^{7} +(2.70234 + 0.835077i) q^{8} +(1.05943 - 2.80671i) q^{9} +O(q^{10})\)	\(q+(-0.581428 - 1.28916i) q^{2} +(1.42468 - 0.985030i) q^{3} +(-1.32388 + 1.49911i) q^{4} -1.37188 q^{5} +(-2.09821 - 1.26392i) q^{6} -0.424283i q^{7} +(2.70234 + 0.835077i) q^{8} +(1.05943 - 2.80671i) q^{9} +(0.797651 + 1.76858i) q^{10} -3.23742i q^{11} +(-0.409442 + 3.43982i) q^{12} -1.55814i q^{13} +(-0.546971 + 0.246690i) q^{14} +(-1.95450 + 1.35135i) q^{15} +(-0.494666 - 3.96930i) q^{16} -1.60008i q^{17} +(-4.23429 + 0.266119i) q^{18} -0.246222 q^{19} +(1.81621 - 2.05661i) q^{20} +(-0.417932 - 0.604468i) q^{21} +(-4.17356 + 1.88233i) q^{22} -1.00000 q^{23} +(4.67255 - 1.47217i) q^{24} -3.11794 q^{25} +(-2.00869 + 0.905943i) q^{26} +(-1.25534 - 5.04223i) q^{27} +(0.636048 + 0.561702i) q^{28} -7.30601 q^{29} +(2.87850 + 1.73395i) q^{30} -0.188110i q^{31} +(-4.82946 + 2.94556i) q^{32} +(-3.18896 - 4.61229i) q^{33} +(-2.06276 + 0.930331i) q^{34} +0.582067i q^{35} +(2.80500 + 5.30396i) q^{36} -8.79231i q^{37} +(0.143160 + 0.317421i) q^{38} +(-1.53481 - 2.21985i) q^{39} +(-3.70730 - 1.14563i) q^{40} +3.71741i q^{41} +(-0.536261 + 0.890237i) q^{42} +3.26934 q^{43} +(4.85325 + 4.28596i) q^{44} +(-1.45342 + 3.85048i) q^{45} +(0.581428 + 1.28916i) q^{46} +4.69268 q^{47} +(-4.61462 - 5.16772i) q^{48} +6.81998 q^{49} +(1.81285 + 4.01953i) q^{50} +(-1.57613 - 2.27960i) q^{51} +(2.33582 + 2.06279i) q^{52} +8.35640 q^{53} +(-5.77037 + 4.55004i) q^{54} +4.44136i q^{55} +(0.354309 - 1.14656i) q^{56} +(-0.350788 + 0.242536i) q^{57} +(4.24792 + 9.41865i) q^{58} +9.37313i q^{59} +(0.561706 - 4.71903i) q^{60} -7.74409i q^{61} +(-0.242504 + 0.109372i) q^{62} +(-1.19084 - 0.449499i) q^{63} +(6.60529 + 4.51332i) q^{64} +2.13758i q^{65} +(-4.09184 + 6.79280i) q^{66} -4.22242 q^{67} +(2.39870 + 2.11832i) q^{68} +(-1.42468 + 0.985030i) q^{69} +(0.750380 - 0.338430i) q^{70} -5.51211 q^{71} +(5.20676 - 6.69997i) q^{72} +12.6874 q^{73} +(-11.3347 + 5.11209i) q^{74} +(-4.44206 + 3.07126i) q^{75} +(0.325969 - 0.369114i) q^{76} -1.37358 q^{77} +(-1.96936 + 3.26930i) q^{78} +3.52326i q^{79} +(0.678624 + 5.44541i) q^{80} +(-6.75521 - 5.94702i) q^{81} +(4.79234 - 2.16140i) q^{82} -8.76263i q^{83} +(1.45946 + 0.173719i) q^{84} +2.19512i q^{85} +(-1.90088 - 4.21471i) q^{86} +(-10.4087 + 7.19665i) q^{87} +(2.70349 - 8.74861i) q^{88} +2.08941i q^{89} +(5.80895 - 0.365084i) q^{90} -0.661091 q^{91} +(1.32388 - 1.49911i) q^{92} +(-0.185294 - 0.267996i) q^{93} +(-2.72846 - 6.04963i) q^{94} +0.337788 q^{95} +(-3.97896 + 8.95365i) q^{96} +6.32684 q^{97} +(-3.96533 - 8.79207i) q^{98} +(-9.08649 - 3.42982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

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