LMFDB - Embedded newform 552.2.j.c.323.18

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

$q$-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	$0.0255502\pi$
$7$			0.424283i			0.160364i	−0.996780	+	0.0801820i	$0.974450\pi$
$8$	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	$0.162295\pi$
$11$			3.23742i			0.976118i	−0.872811	+	0.488059i	$0.837705\pi$
$12$	−0.409442	−	3.43982i	−0.118196	−	0.992990i
$13$			1.55814i			0.432149i	0.976377	+	0.216075i	$0.0693254\pi$
$13$			1.55814i			0.432149i	−0.976377	+	0.216075i	$0.930675\pi$
$14$	−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	$0.0621586\pi$
$17$			1.60008i			0.388076i	−0.980994	+	0.194038i	$0.937841\pi$
$18$	−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	$0.00537738\pi$
$31$			0.188110i			0.0337855i	−0.999857	+	0.0168927i	$0.994623\pi$
$32$	−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	$0.257110\pi$
$37$			8.79231i			1.44545i	−0.691138	+	0.722723i	$0.742890\pi$
$38$	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	$-0.906251\pi$
$41$		−	3.71741i		−	0.580562i	0.956942	−	0.290281i	$-0.0937487\pi$
$42$	−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	$-0.791114\pi$
$59$		−	9.37313i		−	1.22028i	0.792295	−	0.610139i	$-0.208886\pi$
$60$	0.561706	+	4.71903i	0.0725159	+	0.609224i
$61$			7.74409i			0.991529i	0.868457	+	0.495765i	$0.165112\pi$
$61$			7.74409i			0.991529i	−0.868457	+	0.495765i	$0.834888\pi$
$62$	−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	$-0.936491\pi$
$79$		−	3.52326i		−	0.396397i	0.980162	−	0.198199i	$-0.0635091\pi$
$80$	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	$0.159694\pi$
$83$			8.76263i			0.961824i	−0.876769	+	0.480912i	$0.840306\pi$
$84$	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	$-0.964678\pi$
$89$		−	2.08941i		−	0.221477i	0.993850	−	0.110738i	$-0.0353215\pi$
$90$	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	$-0.857757\pi$
$103$		−	8.77157i		−	0.864288i	0.901805	−	0.432144i	$-0.142243\pi$
$104$	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	$-0.990602\pi$
$107$		−	0.610718i		−	0.0590403i	0.999564	−	0.0295201i	$-0.00939792\pi$
$108$	9.22079	−	4.79343i	0.887271	−	0.461248i
$109$			11.0601i			1.05937i	0.848195	+	0.529684i	$0.177690\pi$
$109$			11.0601i			1.05937i	−0.848195	+	0.529684i	$0.822310\pi$
$110$	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	$-0.830889\pi$
$113$		−	10.7712i		−	1.01327i	0.862160	−	0.506635i	$-0.169111\pi$
$114$	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	$-0.686094\pi$
$127$		−	18.7955i		−	1.66783i	0.551891	−	0.833916i	$-0.313906\pi$
$128$	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	$0.0465380\pi$
$131$			3.33484i			0.291366i	−0.989331	+	0.145683i	$0.953462\pi$
$132$	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	$-0.990513\pi$
$137$		−	0.697607i		−	0.0596006i	0.999556	−	0.0298003i	$-0.00948713\pi$
$138$	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	$-0.969105\pi$
$151$		−	2.38161i		−	0.193813i	0.995294	−	0.0969064i	$-0.0308947\pi$
$152$	−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	$0.353975\pi$
$157$			22.4689i			1.79321i	−0.442830	+	0.896606i	$0.646025\pi$
$158$	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	$-0.989141\pi$
$179$		−	0.912682i		−	0.0682171i	0.999418	−	0.0341085i	$-0.0108592\pi$
$180$	−3.84814	+	7.27641i	−0.286823	+	0.542352i
$181$		−	12.6224i		−	0.938212i	−0.883142	−	0.469106i	$-0.844576\pi$
$181$		−	12.6224i		−	0.938212i	0.883142	−	0.469106i	$-0.155424\pi$
$182$	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	$0.0886791\pi$
$199$			7.75881i			0.550007i	−0.961443	+	0.275004i	$0.911321\pi$
$200$	−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	$-0.727337\pi$
$223$		−	22.5676i		−	1.51124i	0.655013	−	0.755618i	$-0.272663\pi$
$224$	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	$-0.752798\pi$
$227$		−	21.1191i		−	1.40173i	0.713295	−	0.700864i	$-0.247202\pi$
$228$	0.100814	+	0.846960i	0.00667654	+	0.0560913i
$229$			25.1844i			1.66423i	0.554600	+	0.832117i	$0.312871\pi$
$229$			25.1844i			1.66423i	−0.554600	+	0.832117i	$0.687129\pi$
$230$	−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	$-0.886008\pi$
$233$		−	10.7007i		−	0.701023i	0.936558	−	0.350511i	$-0.113992\pi$
$234$	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	$0.139863\pi$
$251$			13.4789i			0.850780i	−0.905010	+	0.425390i	$0.860137\pi$
$252$	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	$0.128652\pi$
$257$			12.6088i			0.786514i	−0.919429	+	0.393257i	$0.871348\pi$
$258$	−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	$-0.932475\pi$
$271$		−	6.93217i		−	0.421099i	0.977583	−	0.210550i	$-0.0675253\pi$
$272$	−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	$-0.751527\pi$
$277$		−	23.4240i		−	1.40741i	0.710491	−	0.703707i	$-0.248473\pi$
$278$	−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	$0.219729\pi$
$281$			21.3483i			1.27353i	−0.771057	+	0.636767i	$0.780271\pi$
$282$	−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	$-0.810538\pi$
$347$		−	20.8888i		−	1.12137i	0.828029	−	0.560685i	$-0.189462\pi$
$348$	2.99139	+	25.1314i	0.160355	+	1.34718i
$349$			1.06729i			0.0571305i	0.999592	+	0.0285652i	$0.00909383\pi$
$349$			1.06729i			0.0571305i	−0.999592	+	0.0285652i	$0.990906\pi$
$350$	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	$-0.953313\pi$
$353$		−	5.49169i		−	0.292293i	0.989263	−	0.146147i	$-0.0466871\pi$
$354$	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	$0.0951294\pi$
$367$			11.2809i			0.588858i	−0.955673	+	0.294429i	$0.904871\pi$
$368$	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	$-0.741695\pi$
$373$		−	28.0162i		−	1.45062i	0.688420	−	0.725312i	$-0.258305\pi$
$374$	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	$0.0738146\pi$
$397$			9.15836i			0.459645i	−0.973233	+	0.229823i	$0.926185\pi$
$398$	−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	$0.347366\pi$
$401$			35.5331i			1.77444i	−0.461349	+	0.887219i	$0.652634\pi$
$402$	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	$-0.821626\pi$
$419$		−	21.7593i		−	1.06301i	0.847055	−	0.531506i	$-0.178374\pi$
$420$	−2.00221	+	0.238323i	−0.0976977	+	0.0116290i
$421$		−	12.5414i		−	0.611229i	−0.952155	−	0.305614i	$-0.901138\pi$
$421$		−	12.5414i		−	0.611229i	0.952155	−	0.305614i	$-0.0988618\pi$
$422$	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	$0.168364\pi$
$439$			21.1456i			1.00922i	−0.863346	+	0.504612i	$0.831636\pi$
$440$	−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	$-0.796201\pi$
$443$		−	25.1476i		−	1.19480i	0.801944	−	0.597399i	$-0.203799\pi$
$444$	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	$0.0505550\pi$
$449$			6.70255i			0.316313i	−0.987414	+	0.158156i	$0.949445\pi$
$450$	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	$0.0485683\pi$
$463$			6.54089i			0.303981i	−0.988382	+	0.151990i	$0.951432\pi$
$464$	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	$0.170749\pi$
$467$			22.0884i			1.02213i	−0.859543	+	0.511064i	$0.829251\pi$
$468$	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	$0.180127\pi$
$487$			23.6641i			1.07232i	−0.844115	+	0.536162i	$0.819873\pi$
$488$	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	$-0.967064\pi$
$491$		−	4.57736i		−	0.206573i	0.994652	−	0.103287i	$-0.0329359\pi$
$492$	−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	$0.122864\pi$
$521$			17.1864i			0.752948i	−0.926427	+	0.376474i	$0.877136\pi$
$522$	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	$0.124226\pi$
$541$			17.6974i			0.760871i	−0.924807	+	0.380436i	$0.875774\pi$
$542$	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	$-0.927954\pi$
$563$		−	10.6494i		−	0.448820i	0.974495	−	0.224410i	$-0.0720455\pi$
$564$	−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	$0.127116\pi$
$569$			18.5495i			0.777634i	−0.921315	+	0.388817i	$0.872884\pi$
$570$	−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	$0.213848\pi$
$587$			30.1598i			1.24483i	−0.782688	+	0.622414i	$0.786152\pi$
$588$	−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	$0.173179\pi$
$593$			25.2094i			1.03522i	−0.855615	+	0.517612i	$0.826821\pi$
$594$	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	$-0.661636\pi$
$607$		−	43.0572i		−	1.74764i	0.486250	−	0.873820i	$-0.338364\pi$
$608$	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	$0.155979\pi$
$613$			23.3053i			0.941293i	−0.882322	+	0.470647i	$0.844021\pi$
$614$	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	$-0.866193\pi$
$617$		−	20.2737i		−	0.816189i	0.912940	−	0.408095i	$-0.133807\pi$
$618$	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	$0.107153\pi$
$631$			16.5946i			0.660620i	−0.943873	+	0.330310i	$0.892847\pi$
$632$	−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	$-0.815292\pi$
$641$		−	27.7615i		−	1.09651i	0.836310	−	0.548256i	$-0.184708\pi$
$642$	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	$0.145596\pi$
$659$			22.6737i			0.883241i	−0.897202	+	0.441621i	$0.854404\pi$
$660$	−15.2775	+	1.81848i	−0.594675	+	0.0707841i
$661$		−	28.2857i		−	1.10019i	−0.835103	−	0.550094i	$-0.814592\pi$
$661$		−	28.2857i		−	1.10019i	0.835103	−	0.550094i	$-0.185408\pi$
$662$	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	$-0.998121\pi$
$683$		−	0.308463i		−	0.0118030i	0.999983	−	0.00590151i	$-0.00187852\pi$
$684$	−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	$-0.949414\pi$
$709$		−	8.42757i		−	0.316504i	0.987399	−	0.158252i	$-0.0505859\pi$
$710$	−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	$-0.849980\pi$
$727$		−	24.4848i		−	0.908092i	0.890978	−	0.454046i	$-0.150020\pi$
$728$	−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	$-0.759244\pi$
$733$		−	37.1605i		−	1.37255i	0.727340	−	0.686277i	$-0.240756\pi$
$734$	−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	$0.190390\pi$
$751$			30.8626i			1.12619i	−0.826392	+	0.563095i	$0.809610\pi$
$752$	−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	$0.269445\pi$
$757$			41.2131i			1.49792i	−0.662618	+	0.748958i	$0.730555\pi$
$758$	−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	$0.0249998\pi$
$761$			4.32875i			0.156917i	−0.996917	+	0.0784586i	$0.975000\pi$
$762$	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	$0.0868691\pi$
$809$			15.3326i			0.539065i	−0.962991	+	0.269532i	$0.913131\pi$
$810$	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	$-0.853978\pi$
$823$		−	25.4073i		−	0.885642i	0.896610	−	0.442821i	$-0.146022\pi$
$824$	−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	$0.213300\pi$
$827$			35.7207i			1.24213i	−0.783759	+	0.621065i	$0.786700\pi$
$828$	−2.80500	+	5.30396i	−0.0974806	+	0.184325i
$829$		−	36.3216i		−	1.26150i	−0.775986	−	0.630750i	$-0.782747\pi$
$829$		−	36.3216i		−	1.26150i	0.775986	−	0.630750i	$-0.217253\pi$
$830$	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	$-0.955697\pi$
$853$		−	8.10366i		−	0.277464i	0.990330	−	0.138732i	$-0.0443027\pi$
$854$	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	$0.276996\pi$
$857$			44.7587i			1.52893i	−0.644666	+	0.764464i	$0.723004\pi$
$858$	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	$0.113329\pi$
$877$			20.6446i			0.697120i	−0.937286	+	0.348560i	$0.886671\pi$
$878$	−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	$0.357685\pi$
$881$			53.5282i			1.80341i	−0.432350	+	0.901706i	$0.642315\pi$
$882$	−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	$0.323499\pi$
$919$			51.5456i			1.70033i	−0.526513	+	0.850167i	$0.676501\pi$
$920$	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	$0.164610\pi$
$929$			30.1378i			0.988788i	−0.869238	+	0.494394i	$0.835390\pi$
$930$	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	$-0.757719\pi$
$947$		−	42.4520i		−	1.37951i	0.724045	−	0.689753i	$-0.242281\pi$
$948$	−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	$-0.991421\pi$
$953$		−	1.66386i		−	0.0538978i	0.999637	−	0.0269489i	$-0.00857914\pi$
$954$	−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	$-0.733207\pi$
$967$		−	46.2351i		−	1.48682i	0.668837	−	0.743409i	$-0.266793\pi$
$968$	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	$-0.836089\pi$
$971$		−	30.6925i		−	0.984970i	0.870321	−	0.492485i	$-0.163911\pi$
$972$	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	$-0.689188\pi$
$977$		−	51.7936i		−	1.65702i	0.559971	−	0.828512i	$-0.310812\pi$
$978$	−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	$-0.630389\pi$
$991$		−	57.7515i		−	1.83454i	0.398269	−	0.917269i	$-0.369611\pi$
$992$	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	$0.0439806\pi$
$997$			8.69772i			0.275460i	−0.990470	+	0.137730i	$0.956019\pi$
$998$	−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.323.18	yes	42
3.2	odd	2		552.2.j.d.323.25	yes	42
4.3	odd	2		2208.2.j.c.47.9		42
8.3	odd	2		552.2.j.d.323.26	yes	42
8.5	even	2		2208.2.j.d.47.9		42
12.11	even	2		2208.2.j.d.47.10		42
24.5	odd	2		2208.2.j.c.47.10		42
24.11	even	2	inner	552.2.j.c.323.17	✓	42

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