LMFDB - Embedded newform 552.2.j.c.323.15

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			323.15
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.610595 - 1.27561i) q^{2} +(0.0769352 + 1.73034i) q^{3} +(-1.25435 + 1.55776i) q^{4} +2.14134 q^{5} +(2.16026 - 1.15468i) q^{6} +2.49021i q^{7} +(2.75299 + 0.648892i) q^{8} +(-2.98816 + 0.266248i) q^{9} +O(q^{10})$	\(q+(-0.610595 - 1.27561i) q^{2} +(0.0769352 + 1.73034i) q^{3} +(-1.25435 + 1.55776i) q^{4} +2.14134 q^{5} +(2.16026 - 1.15468i) q^{6} +2.49021i q^{7} +(2.75299 + 0.648892i) q^{8} +(-2.98816 + 0.266248i) q^{9} +(-1.30749 - 2.73151i) q^{10} +5.52646i q^{11} +(-2.79196 - 2.05060i) q^{12} -4.17941i q^{13} +(3.17654 - 1.52051i) q^{14} +(0.164745 + 3.70525i) q^{15} +(-0.853230 - 3.90794i) q^{16} +1.36569i q^{17} +(2.16419 + 3.64915i) q^{18} -5.17716 q^{19} +(-2.68598 + 3.33570i) q^{20} +(-4.30892 + 0.191585i) q^{21} +(7.04960 - 3.37443i) q^{22} -1.00000 q^{23} +(-0.911003 + 4.81353i) q^{24} -0.414655 q^{25} +(-5.33128 + 2.55193i) q^{26} +(-0.690595 - 5.15006i) q^{27} +(-3.87916 - 3.12359i) q^{28} +3.61529 q^{29} +(4.62585 - 2.47256i) q^{30} +2.18490i q^{31} +(-4.46402 + 3.47456i) q^{32} +(-9.56267 + 0.425180i) q^{33} +(1.74208 - 0.833883i) q^{34} +5.33240i q^{35} +(3.33344 - 4.98881i) q^{36} +2.97461i q^{37} +(3.16115 + 6.60402i) q^{38} +(7.23180 - 0.321543i) q^{39} +(5.89509 + 1.38950i) q^{40} +8.18249i q^{41} +(2.87540 + 5.37951i) q^{42} +0.482816 q^{43} +(-8.60890 - 6.93210i) q^{44} +(-6.39868 + 0.570129i) q^{45} +(0.610595 + 1.27561i) q^{46} +12.8074 q^{47} +(6.69643 - 1.77704i) q^{48} +0.798829 q^{49} +(0.253186 + 0.528936i) q^{50} +(-2.36311 + 0.105069i) q^{51} +(6.51051 + 5.24242i) q^{52} -7.36333 q^{53} +(-6.14777 + 4.02553i) q^{54} +11.8340i q^{55} +(-1.61588 + 6.85553i) q^{56} +(-0.398306 - 8.95825i) q^{57} +(-2.20748 - 4.61169i) q^{58} +2.97621i q^{59} +(-5.97854 - 4.39104i) q^{60} +6.75457i q^{61} +(2.78707 - 1.33409i) q^{62} +(-0.663015 - 7.44117i) q^{63} +(7.15788 + 3.57278i) q^{64} -8.94954i q^{65} +(6.38128 + 11.9386i) q^{66} -5.95258 q^{67} +(-2.12741 - 1.71305i) q^{68} +(-0.0769352 - 1.73034i) q^{69} +(6.80205 - 3.25594i) q^{70} +5.75602 q^{71} +(-8.39914 - 1.20602i) q^{72} +12.9577 q^{73} +(3.79443 - 1.81628i) q^{74} +(-0.0319015 - 0.717494i) q^{75} +(6.49395 - 8.06477i) q^{76} -13.7621 q^{77} +(-4.82587 - 9.02860i) q^{78} -7.69927i q^{79} +(-1.82706 - 8.36824i) q^{80} +(8.85822 - 1.59119i) q^{81} +(10.4376 - 4.99619i) q^{82} -9.34193i q^{83} +(5.10644 - 6.95258i) q^{84} +2.92440i q^{85} +(-0.294805 - 0.615883i) q^{86} +(0.278143 + 6.25569i) q^{87} +(-3.58608 + 15.2143i) q^{88} -16.2647i q^{89} +(4.63426 + 7.81408i) q^{90} +10.4076 q^{91} +(1.25435 - 1.55776i) q^{92} +(-3.78062 + 0.168096i) q^{93} +(-7.82012 - 16.3372i) q^{94} -11.0861 q^{95} +(-6.35561 - 7.45696i) q^{96} +6.05323 q^{97} +(-0.487762 - 1.01899i) q^{98} +(-1.47141 - 16.5140i) 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 $

$2$	−0.610595	−	1.27561i	−0.431756	−	0.901990i
$2$	−0.610595	−	1.27561i	−0.431756	−	0.901990i
$3$	0.0769352	+	1.73034i	0.0444186	+	0.999013i
$3$	0.0769352	+	1.73034i	0.0444186	+	0.999013i
$4$	−1.25435	+	1.55776i	−0.627173	+	0.778880i
$5$	2.14134			0.957637			0.478819	−	0.877914i	$-0.341065\pi$
$5$	2.14134			0.957637			0.478819	+	0.877914i	$0.341065\pi$
$6$	2.16026	−	1.15468i	0.881922	−	0.471395i
$7$			2.49021i			0.941213i	0.882343	+	0.470606i	$0.155965\pi$
$7$			2.49021i			0.941213i	−0.882343	+	0.470606i	$0.844035\pi$
$8$	2.75299	+	0.648892i	0.973328	+	0.229418i
$9$	−2.98816	+	0.266248i	−0.996054	+	0.0887494i
$10$	−1.30749	−	2.73151i	−0.413466	−	0.863780i
$11$			5.52646i			1.66629i	0.553054	+	0.833146i	$0.313463\pi$
$11$			5.52646i			1.66629i	−0.553054	+	0.833146i	$0.686537\pi$
$12$	−2.79196	−	2.05060i	−0.805969	−	0.591958i
$13$		−	4.17941i		−	1.15916i	−0.814916	−	0.579579i	$-0.803217\pi$
$13$		−	4.17941i		−	1.15916i	0.814916	−	0.579579i	$-0.196783\pi$
$14$	3.17654	−	1.52051i	0.848965	−	0.406374i
$15$	0.164745	+	3.70525i	0.0425369	+	0.956692i
$16$	−0.853230	−	3.90794i	−0.213307	−	0.976985i
$17$			1.36569i			0.331228i	0.986191	+	0.165614i	$0.0529606\pi$
$17$			1.36569i			0.331228i	−0.986191	+	0.165614i	$0.947039\pi$
$18$	2.16419	+	3.64915i	0.510104	+	0.860113i
$19$	−5.17716			−1.18772			−0.593861	−	0.804568i	$-0.702397\pi$
$19$	−5.17716			−1.18772			−0.593861	+	0.804568i	$0.702397\pi$
$20$	−2.68598	+	3.33570i	−0.600604	+	0.745884i
$21$	−4.30892	+	0.191585i	−0.940284	+	0.0418073i
$22$	7.04960	−	3.37443i	1.50298	−	0.719432i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−0.911003	+	4.81353i	−0.185958	+	0.982558i
$25$	−0.414655			−0.0829309
$26$	−5.33128	+	2.55193i	−1.04555	+	0.500474i
$27$	−0.690595	−	5.15006i	−0.132905	−	0.991129i
$28$	−3.87916	−	3.12359i	−0.733092	−	0.590303i
$29$	3.61529			0.671343			0.335672	−	0.941979i	$-0.391037\pi$
$29$	3.61529			0.671343			0.335672	+	0.941979i	$0.391037\pi$
$30$	4.62585	−	2.47256i	0.844561	−	0.451426i
$31$			2.18490i			0.392420i	0.980562	+	0.196210i	$0.0628634\pi$
$31$			2.18490i			0.392420i	−0.980562	+	0.196210i	$0.937137\pi$
$32$	−4.46402	+	3.47456i	−0.789134	+	0.614221i
$33$	−9.56267	+	0.425180i	−1.66465	+	0.0740143i
$34$	1.74208	−	0.833883i	0.298764	−	0.143010i
$35$			5.33240i			0.901340i
$36$	3.33344	−	4.98881i	0.555573	−	0.831468i
$37$			2.97461i			0.489023i	0.969646	+	0.244511i	$0.0786275\pi$
$37$			2.97461i			0.489023i	−0.969646	+	0.244511i	$0.921372\pi$
$38$	3.16115	+	6.60402i	0.512806	+	1.07131i
$39$	7.23180	−	0.321543i	1.15801	−	0.0514882i
$40$	5.89509	+	1.38950i	0.932095	+	0.219699i
$41$			8.18249i			1.27789i	0.769253	+	0.638945i	$0.220629\pi$
$41$			8.18249i			1.27789i	−0.769253	+	0.638945i	$0.779371\pi$
$42$	2.87540	+	5.37951i	0.443683	+	0.830076i
$43$	0.482816			0.0736287			0.0368143	−	0.999322i	$-0.488279\pi$
$43$	0.482816			0.0736287			0.0368143	+	0.999322i	$0.488279\pi$
$44$	−8.60890	−	6.93210i	−1.29784	−	1.04505i
$45$	−6.39868	+	0.570129i	−0.953858	+	0.0849898i
$46$	0.610595	+	1.27561i	0.0900274	+	0.188078i
$47$	12.8074			1.86815			0.934073	−	0.357081i	$-0.116228\pi$
$47$	12.8074			1.86815			0.934073	+	0.357081i	$0.116228\pi$
$48$	6.69643	−	1.77704i	0.966546	−	0.256493i
$49$	0.798829			0.114118
$50$	0.253186	+	0.528936i	0.0358059	+	0.0748029i
$51$	−2.36311	+	0.105069i	−0.330901	+	0.0147127i
$52$	6.51051	+	5.24242i	0.902845	+	0.726993i
$53$	−7.36333			−1.01143			−0.505716	−	0.862700i	$-0.668772\pi$
$53$	−7.36333			−1.01143			−0.505716	+	0.862700i	$0.668772\pi$
$54$	−6.14777	+	4.02553i	−0.836606	+	0.547805i
$55$			11.8340i			1.59570i
$56$	−1.61588	+	6.85553i	−0.215931	+	0.916109i
$57$	−0.398306	−	8.95825i	−0.0527569	−	1.18655i
$58$	−2.20748	−	4.61169i	−0.289856	−	0.605545i
$59$			2.97621i			0.387469i	0.981054	+	0.193735i	$0.0620601\pi$
$59$			2.97621i			0.387469i	−0.981054	+	0.193735i	$0.937940\pi$
$60$	−5.97854	−	4.39104i	−0.771826	−	0.566881i
$61$			6.75457i			0.864834i	0.901674	+	0.432417i	$0.142339\pi$
$61$			6.75457i			0.864834i	−0.901674	+	0.432417i	$0.857661\pi$
$62$	2.78707	−	1.33409i	0.353959	−	0.169430i
$63$	−0.663015	−	7.44117i	−0.0835321	−	0.937499i
$64$	7.15788	+	3.57278i	0.894735	+	0.446598i
$65$		−	8.94954i		−	1.11005i
$66$	6.38128	+	11.9386i	0.785482	+	1.46954i
$67$	−5.95258			−0.727224			−0.363612	−	0.931551i	$-0.618457\pi$
$67$	−5.95258			−0.727224			−0.363612	+	0.931551i	$0.618457\pi$
$68$	−2.12741	−	1.71305i	−0.257987	−	0.207737i
$69$	−0.0769352	−	1.73034i	−0.00926191	−	0.208309i
$70$	6.80205	−	3.25594i	0.813000	−	0.389159i
$71$	5.75602			0.683114			0.341557	−	0.939861i	$-0.389046\pi$
$71$	5.75602			0.683114			0.341557	+	0.939861i	$0.389046\pi$
$72$	−8.39914	−	1.20602i	−0.989848	−	0.142130i
$73$	12.9577			1.51658			0.758292	−	0.651915i	$-0.226034\pi$
$73$	12.9577			1.51658			0.758292	+	0.651915i	$0.226034\pi$
$74$	3.79443	−	1.81628i	0.441094	−	0.211139i
$75$	−0.0319015	−	0.717494i	−0.00368367	−	0.0828491i
$76$	6.49395	−	8.06477i	0.744907	−	0.925092i
$77$	−13.7621			−1.56833
$78$	−4.82587	−	9.02860i	−0.546422	−	1.02229i
$79$		−	7.69927i		−	0.866236i	−0.901337	−	0.433118i	$-0.857413\pi$
$79$		−	7.69927i		−	0.866236i	0.901337	−	0.433118i	$-0.142587\pi$
$80$	−1.82706	−	8.36824i	−0.204271	−	0.935597i
$81$	8.85822	−	1.59119i	0.984247	−	0.176798i
$82$	10.4376	−	4.99619i	1.15264	−	0.551737i
$83$		−	9.34193i		−	1.02541i	−0.858565	−	0.512705i	$-0.828643\pi$
$83$		−	9.34193i		−	1.02541i	0.858565	−	0.512705i	$-0.171357\pi$
$84$	5.10644	−	6.95258i	0.557158	−	0.758589i
$85$			2.92440i			0.317196i
$86$	−0.294805	−	0.615883i	−0.0317896	−	0.0664124i
$87$	0.278143	+	6.25569i	0.0298201	+	0.670680i
$88$	−3.58608	+	15.2143i	−0.382277	+	1.62185i
$89$		−	16.2647i		−	1.72405i	−0.506864	−	0.862026i	$-0.669195\pi$
$89$		−	16.2647i		−	1.72405i	0.506864	−	0.862026i	$-0.330805\pi$
$90$	4.63426	+	7.81408i	0.488494	+	0.823676i
$91$	10.4076			1.09102
$92$	1.25435	−	1.55776i	0.130775	−	0.162408i
$93$	−3.78062	+	0.168096i	−0.392032	+	0.0174307i
$94$	−7.82012	−	16.3372i	−0.806584	−	1.68505i
$95$	−11.0861			−1.13741
$96$	−6.35561	−	7.45696i	−0.648667	−	0.761073i
$97$	6.05323			0.614613			0.307306	−	0.951611i	$-0.400572\pi$
$97$	6.05323			0.614613			0.307306	+	0.951611i	$0.400572\pi$
$98$	−0.487762	−	1.01899i	−0.0492714	−	0.102934i
$99$	−1.47141	−	16.5140i	−0.147882	−	1.65972i
$100$	0.520121	−	0.645932i	0.0520121	−	0.0645932i
$101$	5.24485			0.521882			0.260941	−	0.965355i	$-0.415967\pi$
$101$	5.24485			0.521882			0.260941	+	0.965355i	$0.415967\pi$
$102$	1.57693	+	2.95024i	0.156139	+	0.292117i
$103$			16.1613i			1.59242i	0.605020	+	0.796210i	$0.293165\pi$
$103$			16.1613i			1.59242i	−0.605020	+	0.796210i	$0.706835\pi$
$104$	2.71198	−	11.5059i	0.265932	−	1.12824i
$105$	−9.22688	+	0.410249i	−0.900451	+	0.0400362i
$106$	4.49602	+	9.39272i	0.436692	+	0.912302i
$107$			15.8005i			1.52749i	0.645517	+	0.763746i	$0.276642\pi$
$107$			15.8005i			1.52749i	−0.645517	+	0.763746i	$0.723358\pi$
$108$	8.88880	+	5.38417i	0.855325	+	0.518092i
$109$		−	15.2171i		−	1.45753i	−0.684763	−	0.728766i	$-0.740094\pi$
$109$		−	15.2171i		−	1.45753i	0.684763	−	0.728766i	$-0.259906\pi$
$110$	15.0956	−	7.22582i	1.43931	−	0.688954i
$111$	−5.14709	+	0.228852i	−0.488540	+	0.0217217i
$112$	9.73161	−	2.12473i	0.919551	−	0.200768i
$113$			2.00565i			0.188676i	0.995540	+	0.0943378i	$0.0300734\pi$
$113$			2.00565i			0.188676i	−0.995540	+	0.0943378i	$0.969927\pi$
$114$	−11.1840	+	5.97795i	−1.04748	+	0.559886i
$115$	−2.14134			−0.199681
$116$	−4.53483	+	5.63176i	−0.421048	+	0.522896i
$117$	1.11276	+	12.4887i	0.102875	+	1.15458i
$118$	3.79647	−	1.81726i	0.349493	−	0.167292i
$119$	−3.40086			−0.311756
$120$	−1.95077	+	10.3074i	−0.178080	+	0.940934i
$121$	−19.5418			−1.77653
$122$	8.61617	−	4.12431i	0.780072	−	0.373397i
$123$	−14.1585	+	0.629521i	−1.27663	+	0.0567620i
$124$	−3.40355	−	2.74062i	−0.305648	−	0.246115i
$125$	−11.5946			−1.03705
$126$	−9.08717	+	5.38929i	−0.809549	+	0.480116i
$127$		−	16.7607i		−	1.48727i	−0.668586	−	0.743635i	$-0.733100\pi$
$127$		−	16.7607i		−	1.48727i	0.668586	−	0.743635i	$-0.266900\pi$
$128$	0.186901	−	11.3122i	0.0165199	−	0.999864i
$129$	0.0371455	+	0.835436i	0.00327048	+	0.0735560i
$130$	−11.4161	+	5.46455i	−1.00126	+	0.479273i
$131$			5.88161i			0.513878i	0.966428	+	0.256939i	$0.0827140\pi$
$131$			5.88161i			0.513878i	−0.966428	+	0.256939i	$0.917286\pi$
$132$	11.3326	−	15.4297i	0.986374	−	1.34298i
$133$		−	12.8922i		−	1.11790i
$134$	3.63462	+	7.59315i	0.313983	+	0.655949i
$135$	−1.47880	−	11.0280i	−0.127275	−	0.949142i
$136$	−0.886184	+	3.75972i	−0.0759897	+	0.322393i
$137$			10.7609i			0.919368i	0.888082	+	0.459684i	$0.152037\pi$
$137$			10.7609i			0.919368i	−0.888082	+	0.459684i	$0.847963\pi$
$138$	−2.16026	+	1.15468i	−0.183893	+	0.0982927i
$139$	−9.41032			−0.798173			−0.399087	−	0.916913i	$-0.630673\pi$
$139$	−9.41032			−0.798173			−0.399087	+	0.916913i	$0.630673\pi$
$140$	−8.30660	−	6.68868i	−0.702036	−	0.565297i
$141$	0.985337	+	22.1611i	0.0829804	+	1.86630i
$142$	−3.51460	−	7.34242i	−0.294939	−	0.616162i
$143$	23.0973			1.93150
$144$	3.59007	+	11.4504i	0.299173	+	0.954199i
$145$	7.74158			0.642903
$146$	−7.91191	−	16.5289i	−0.654795	−	1.36794i
$147$	0.0614581	+	1.38225i	0.00506898	+	0.114006i
$148$	−4.63373	−	3.73119i	−0.380890	−	0.306702i
$149$	−2.65775			−0.217731			−0.108866	−	0.994056i	$-0.534722\pi$
$149$	−2.65775			−0.217731			−0.108866	+	0.994056i	$0.534722\pi$
$150$	−0.895761	+	0.478792i	−0.0731386	+	0.0390932i
$151$		−	12.2361i		−	0.995763i	−0.867245	−	0.497882i	$-0.834111\pi$
$151$		−	12.2361i		−	0.995763i	0.867245	−	0.497882i	$-0.165889\pi$
$152$	−14.2527	−	3.35942i	−1.15604	−	0.272485i
$153$	−0.363612	−	4.08090i	−0.0293963	−	0.329921i
$154$	8.40306	+	17.5550i	0.677138	+	1.41462i
$155$			4.67862i			0.375796i
$156$	−8.57030	+	11.6687i	−0.686173	+	0.934246i
$157$		−	2.78283i		−	0.222094i	−0.993815	−	0.111047i	$-0.964580\pi$
$157$		−	2.78283i		−	0.222094i	0.993815	−	0.111047i	$-0.0354204\pi$
$158$	−9.82125	+	4.70114i	−0.781336	+	0.374003i
$159$	−0.566500	−	12.7411i	−0.0449263	−	1.01043i
$160$	−9.55899	+	7.44021i	−0.755704	+	0.588201i
$161$		−	2.49021i		−	0.196256i
$162$	−7.43852	−	10.3280i	−0.584425	−	0.811448i
$163$	11.3682			0.890429			0.445214	−	0.895424i	$-0.353127\pi$
$163$	11.3682			0.890429			0.445214	+	0.895424i	$0.353127\pi$
$164$	−12.7463	−	10.2637i	−0.995322	−	0.801458i
$165$	−20.4769	+	0.910455i	−1.59413	+	0.0708788i
$166$	−11.9166	+	5.70414i	−0.924910	+	0.442727i
$167$	18.3881			1.42291			0.711456	−	0.702731i	$-0.248036\pi$
$167$	18.3881			1.42291			0.711456	+	0.702731i	$0.248036\pi$
$168$	−11.9867	−	2.26859i	−0.924796	−	0.175026i
$169$	−4.46744			−0.343649
$170$	3.73039	−	1.78563i	0.286108	−	0.136951i
$171$	15.4702	−	1.37841i	1.18303	−	0.105410i
$172$	−0.605618	+	0.752111i	−0.0461779	+	0.0573479i
$173$	18.1052			1.37651			0.688255	−	0.725469i	$-0.258377\pi$
$173$	18.1052			1.37651			0.688255	+	0.725469i	$0.258377\pi$
$174$	7.80997	−	4.17450i	0.592072	−	0.316468i
$175$		−	1.03258i		−	0.0780556i
$176$	21.5971	−	4.71534i	1.62794	−	0.355432i
$177$	−5.14985	+	0.228975i	−0.387087	+	0.0172108i
$178$	−20.7473	+	9.93114i	−1.55508	+	0.744370i
$179$		−	6.18721i		−	0.462454i	−0.972900	−	0.231227i	$-0.925726\pi$
$179$		−	6.18721i		−	0.462454i	0.972900	−	0.231227i	$-0.0742740\pi$
$180$	7.13803	−	10.6827i	0.532038	−	0.796244i
$181$		−	4.08820i		−	0.303874i	−0.988390	−	0.151937i	$-0.951449\pi$
$181$		−	4.08820i		−	0.303874i	0.988390	−	0.151937i	$-0.0485510\pi$
$182$	−6.35485	−	13.2760i	−0.471053	−	0.984085i
$183$	−11.6877	+	0.519664i	−0.863980	+	0.0384147i
$184$	−2.75299	−	0.648892i	−0.202953	−	0.0478370i
$185$			6.36966i			0.468306i
$186$	2.52285	+	4.71995i	0.184985	+	0.346084i
$187$	−7.54742			−0.551922
$188$	−16.0649	+	19.9508i	−1.17165	+	1.45506i
$189$	12.8247	−	1.71973i	0.932863	−	0.125092i
$190$	6.76910	+	14.1415i	0.491082	+	1.02593i
$191$	6.20967			0.449316			0.224658	−	0.974438i	$-0.427873\pi$
$191$	6.20967			0.449316			0.224658	+	0.974438i	$0.427873\pi$
$192$	−5.63144	+	12.6604i	−0.406414	+	0.913689i
$193$	3.42228			0.246341			0.123171	−	0.992386i	$-0.460694\pi$
$193$	3.42228			0.246341			0.123171	+	0.992386i	$0.460694\pi$
$194$	−3.69608	−	7.72155i	−0.265363	−	0.554375i
$195$	15.4858	−	0.688535i	1.10896	−	0.0493070i
$196$	−1.00201	+	1.24438i	−0.0715721	+	0.0888846i
$197$	−6.84131			−0.487423			−0.243712	−	0.969848i	$-0.578365\pi$
$197$	−6.84131			−0.487423			−0.243712	+	0.969848i	$0.578365\pi$
$198$	−20.1669	+	11.9603i	−1.43320	+	0.849981i
$199$			21.3626i			1.51436i	0.653208	+	0.757178i	$0.273423\pi$
$199$			21.3626i			1.51436i	−0.653208	+	0.757178i	$0.726577\pi$
$200$	−1.14154	−	0.269066i	−0.0807190	−	0.0190259i
$201$	−0.457963	−	10.3000i	−0.0323022	−	0.726506i
$202$	−3.20248	−	6.69036i	−0.225326	−	0.470732i
$203$			9.00286i			0.631877i
$204$	2.80048	−	3.81294i	0.196073	−	0.266960i
$205$			17.5215i			1.22375i
$206$	20.6155	−	9.86802i	1.43635	−	0.687537i
$207$	2.98816	−	0.266248i	0.207692	−	0.0185055i
$208$	−16.3329	+	3.56599i	−1.13248	+	0.247257i
$209$		−	28.6114i		−	1.97909i
$210$	6.15720	+	11.5194i	0.424887	+	0.794912i
$211$	15.3446			1.05637			0.528183	−	0.849130i	$-0.322873\pi$
$211$	15.3446			1.05637			0.528183	+	0.849130i	$0.322873\pi$
$212$	9.23617	−	11.4703i	0.634343	−	0.787784i
$213$	0.442840	+	9.95988i	0.0303429	+	0.682440i
$214$	20.1552	−	9.64771i	1.37778	−	0.659504i
$215$	1.03387			0.0705096
$216$	1.44063	−	14.6262i	0.0980226	−	0.995184i
$217$	−5.44087			−0.369350
$218$	−19.4110	+	9.29148i	−1.31468	+	0.629299i
$219$	0.996903	+	22.4212i	0.0673645	+	1.51509i
$220$	−18.4346	−	14.8440i	−1.24286	−	1.00078i
$221$	5.70776			0.383946
$222$	3.43471	+	6.42593i	0.230523	+	0.431280i
$223$		−	20.0468i		−	1.34243i	−0.741261	−	0.671217i	$-0.765772\pi$
$223$		−	20.0468i		−	1.34243i	0.741261	−	0.671217i	$-0.234228\pi$
$224$	−8.65239	−	11.1164i	−0.578112	−	0.742743i
$225$	1.23906	−	0.110401i	0.0826037	−	0.00736007i
$226$	2.55842	−	1.22464i	0.170184	−	0.0814618i
$227$		−	16.0730i		−	1.06680i	−0.845862	−	0.533401i	$-0.820914\pi$
$227$		−	16.0730i		−	1.06680i	0.845862	−	0.533401i	$-0.179086\pi$
$228$	14.4544	+	10.6163i	0.957267	+	0.703081i
$229$		−	22.5643i		−	1.49109i	−0.666454	−	0.745547i	$-0.732189\pi$
$229$		−	22.5643i		−	1.49109i	0.666454	−	0.745547i	$-0.267811\pi$
$230$	1.30749	+	2.73151i	0.0862136	+	0.180110i
$231$	−1.05879	−	23.8131i	−0.0696632	−	1.56679i
$232$	9.95286	+	2.34594i	0.653437	+	0.154018i
$233$			3.46125i			0.226754i	0.993552	+	0.113377i	$0.0361668\pi$
$233$			3.46125i			0.226754i	−0.993552	+	0.113377i	$0.963833\pi$
$234$	15.2513	−	9.04501i	0.997008	−	0.591291i
$235$	27.4250			1.78901
$236$	−4.63622	−	3.73320i	−0.301792	−	0.243010i
$237$	13.3224	−	0.592345i	0.865381	−	0.0384769i
$238$	2.07655	+	4.33816i	0.134603	+	0.281201i
$239$	17.4104			1.12618			0.563092	−	0.826394i	$-0.309612\pi$
$239$	17.4104			1.12618			0.563092	+	0.826394i	$0.309612\pi$
$240$	14.3393	−	3.80524i	0.925600	−	0.245627i
$241$	11.5993			0.747178			0.373589	−	0.927594i	$-0.378127\pi$
$241$	11.5993			0.747178			0.373589	+	0.927594i	$0.378127\pi$
$242$	11.9321	+	24.9277i	0.767027	+	1.60241i
$243$	3.43480	+	15.2053i	0.220343	+	0.975423i
$244$	−10.5220	−	8.47257i	−0.673602	−	0.542401i
$245$	1.71057			0.109284
$246$	9.44813	+	17.6763i	0.602391	+	1.12700i
$247$			21.6375i			1.37676i
$248$	−1.41776	+	6.01500i	−0.0900281	+	0.381953i
$249$	16.1647	−	0.718723i	1.02440	−	0.0455472i
$250$	7.07963	+	14.7902i	0.447755	+	0.935414i
$251$			1.87874i			0.118585i	0.998241	+	0.0592924i	$0.0188844\pi$
$251$			1.87874i			0.118585i	−0.998241	+	0.0592924i	$0.981116\pi$
$252$	12.4232	+	8.30098i	0.782588	+	0.522913i
$253$		−	5.52646i		−	0.347446i
$254$	−21.3800	+	10.2340i	−1.34150	+	0.642138i
$255$	−5.06022	+	0.224990i	−0.316883	+	0.0140894i
$256$	−14.5440	+	6.66874i	−0.909000	+	0.416796i
$257$			31.5286i			1.96670i	0.181718	+	0.983351i	$0.441834\pi$
$257$			31.5286i			1.96670i	−0.181718	+	0.983351i	$0.558166\pi$
$258$	1.04301	−	0.557496i	0.0649348	−	0.0347082i
$259$	−7.40742			−0.460274
$260$	13.9412	+	11.2258i	0.864598	+	0.696196i
$261$	−10.8031	+	0.962566i	−0.668694	+	0.0595813i
$262$	7.50262	−	3.59128i	0.463513	−	0.221870i
$263$	1.06864			0.0658953			0.0329476	−	0.999457i	$-0.489511\pi$
$263$	1.06864			0.0658953			0.0329476	+	0.999457i	$0.489511\pi$
$264$	−26.6018	−	5.03463i	−1.63723	−	0.309860i
$265$	−15.7674			−0.968585
$266$	−16.4454	+	7.87194i	−1.00833	+	0.482660i
$267$	28.1434	−	1.25133i	1.72235	−	0.0765799i
$268$	7.46660	−	9.27269i	0.456095	−	0.566420i
$269$	9.58145			0.584191			0.292096	−	0.956389i	$-0.405647\pi$
$269$	9.58145			0.584191			0.292096	+	0.956389i	$0.405647\pi$
$270$	−13.1645	+	8.62003i	−0.801165	+	0.524599i
$271$			6.38538i			0.387884i	0.981013	+	0.193942i	$0.0621274\pi$
$271$			6.38538i			0.387884i	−0.981013	+	0.193942i	$0.937873\pi$
$272$	5.33703	−	1.16525i	0.323605	−	0.0706534i
$273$	0.800712	+	18.0087i	0.0484613	+	1.08994i
$274$	13.7267	−	6.57057i	0.829261	−	0.396943i
$275$		−	2.29157i		−	0.138187i
$276$	2.79196	+	2.05060i	0.168056	+	0.123432i
$277$		−	23.8172i		−	1.43104i	−0.698593	−	0.715519i	$-0.746190\pi$
$277$		−	23.8172i		−	1.43104i	0.698593	−	0.715519i	$-0.253810\pi$
$278$	5.74590	+	12.0039i	0.344616	+	0.719945i
$279$	−0.581726	−	6.52883i	−0.0348270	−	0.390871i
$280$	−3.46015	+	14.6800i	−0.206784	+	0.877300i
$281$			4.53416i			0.270486i	0.990812	+	0.135243i	$0.0431814\pi$
$281$			4.53416i			0.270486i	−0.990812	+	0.135243i	$0.956819\pi$
$282$	27.6672	−	14.7884i	1.64756	−	0.880635i
$283$	−28.0159			−1.66537			−0.832687	−	0.553744i	$-0.813198\pi$
$283$	−28.0159			−1.66537			−0.832687	+	0.553744i	$0.813198\pi$
$284$	−7.22004	+	8.96649i	−0.428431	+	0.532064i
$285$	−0.852909	−	19.1827i	−0.0505220	−	1.13628i
$286$	−14.1031	−	29.4631i	−0.833936	−	1.74219i
$287$	−20.3761			−1.20277
$288$	12.4141	−	11.5711i	0.731509	−	0.681832i
$289$	15.1349			0.890288
$290$	−4.72697	−	9.87521i	−0.277577	−	0.579892i
$291$	0.465707	+	10.4742i	0.0273002	+	0.614006i
$292$	−16.2534	+	20.1850i	−0.951161	+	1.18124i
$293$	−10.4263			−0.609110			−0.304555	−	0.952495i	$-0.598508\pi$
$293$	−10.4263			−0.609110			−0.304555	+	0.952495i	$0.598508\pi$
$294$	1.72568	−	0.922390i	0.100644	−	0.0537949i
$295$			6.37308i			0.371055i
$296$	−1.93020	+	8.18906i	−0.112191	+	0.475980i
$297$	28.4616	−	3.81655i	1.65151	−	0.221459i
$298$	1.62281	+	3.39025i	0.0940069	+	0.196392i
$299$			4.17941i			0.241701i
$300$	1.15770	+	0.850291i	0.0668398	+	0.0490916i
$301$			1.20231i			0.0693003i
$302$	−15.6085	+	7.47133i	−0.898169	+	0.429927i
$303$	0.403513	+	9.07538i	0.0231812	+	0.521367i
$304$	4.41731	+	20.2320i	0.253350	+	1.16039i
$305$			14.4638i			0.828197i
$306$	−4.98360	+	2.95560i	−0.284893	+	0.168961i
$307$	2.48737			0.141962			0.0709809	−	0.997478i	$-0.477387\pi$
$307$	2.48737			0.141962			0.0709809	+	0.997478i	$0.477387\pi$
$308$	17.2624	−	21.4380i	0.983618	−	1.22154i
$309$	−27.9646	+	1.24337i	−1.59085	+	0.0707330i
$310$	5.96808	−	2.85674i	0.338964	−	0.162252i
$311$	−34.8679			−1.97718			−0.988590	−	0.150634i	$-0.951869\pi$
$311$	−34.8679			−1.97718			−0.988590	+	0.150634i	$0.951869\pi$
$312$	20.1177	+	3.80745i	1.13894	+	0.215555i
$313$	14.3096			0.808826			0.404413	−	0.914577i	$-0.367476\pi$
$313$	14.3096			0.808826			0.404413	+	0.914577i	$0.367476\pi$
$314$	−3.54980	+	1.69918i	−0.200327	+	0.0958905i
$315$	−1.41974	−	15.9341i	−0.0799934	−	0.897784i
$316$	11.9936	+	9.65755i	0.674694	+	0.543280i
$317$	32.7414			1.83894			0.919469	−	0.393161i	$-0.128619\pi$
$317$	32.7414			1.83894			0.919469	+	0.393161i	$0.128619\pi$
$318$	−15.9067	+	8.50228i	−0.892004	+	0.476784i
$319$			19.9798i			1.11865i
$320$	15.3275	+	7.65055i	0.856831	+	0.427679i
$321$	−27.3403	+	1.21561i	−1.52598	+	0.0678490i
$322$	−3.17654	+	1.52051i	−0.177021	+	0.0847349i
$323$		−	7.07038i		−	0.393407i
$324$	−8.63260	+	15.7949i	−0.479589	+	0.877493i
$325$			1.73301i			0.0961301i
$326$	−6.94139	−	14.5014i	−0.384448	−	0.803158i
$327$	26.3308	−	1.17073i	1.45609	−	0.0647415i
$328$	−5.30955	+	22.5263i	−0.293171	+	1.24381i
$329$			31.8931i			1.75832i
$330$	13.6645	+	25.5646i	0.752207	+	1.40729i
$331$	−23.4573			−1.28933			−0.644666	−	0.764465i	$-0.723003\pi$
$331$	−23.4573			−1.28933			−0.644666	+	0.764465i	$0.723003\pi$
$332$	14.5525	+	11.7180i	0.798671	+	0.643110i
$333$	−0.791985	−	8.88861i	−0.0434005	−	0.487093i
$334$	−11.2277	−	23.4559i	−0.614351	−	1.28345i
$335$	−12.7465			−0.696416
$336$	4.42520	+	16.6755i	0.241415	+	0.909725i
$337$	28.0962			1.53050			0.765248	−	0.643736i	$-0.222617\pi$
$337$	28.0962			1.53050			0.765248	+	0.643736i	$0.222617\pi$
$338$	2.72780	+	5.69870i	0.148373	+	0.309968i
$339$	−3.47046	+	0.154305i	−0.188489	+	0.00838070i
$340$	−4.55552	−	3.66822i	−0.247058	−	0.198937i
$341$	−12.0748			−0.653885
$342$	−11.2043	−	18.8922i	−0.605861	−	1.02157i
$343$			19.4208i			1.04862i
$344$	1.32919	+	0.313295i	0.0716649	+	0.0168918i
$345$	−0.164745	−	3.70525i	−0.00886955	−	0.199484i
$346$	−11.0549	−	23.0951i	−0.594317	−	1.24160i
$347$			4.70683i			0.252676i	0.991987	+	0.126338i	$0.0403223\pi$
$347$			4.70683i			0.252676i	−0.991987	+	0.126338i	$0.959678\pi$
$348$	−10.0937	−	7.41352i	−0.541082	−	0.397407i
$349$		−	10.5632i		−	0.565434i	−0.959203	−	0.282717i	$-0.908764\pi$
$349$		−	10.5632i		−	0.565434i	0.959203	−	0.282717i	$-0.0912357\pi$
$350$	−1.31717	+	0.630488i	−0.0704054	+	0.0337010i
$351$	−21.5242	+	2.88628i	−1.14888	+	0.154058i
$352$	−19.2020	−	24.6702i	−1.02347	−	1.31493i
$353$			27.7632i			1.47769i	0.673877	+	0.738843i	$0.264628\pi$
$353$			27.7632i			1.47769i	−0.673877	+	0.738843i	$0.735372\pi$
$354$	3.43656	+	6.42938i	0.182651	+	0.341718i
$355$	12.3256			0.654175
$356$	25.3365	+	20.4015i	1.34283	+	1.08128i
$357$	−0.261646	−	5.88464i	−0.0138478	−	0.311448i
$358$	−7.89245	+	3.77788i	−0.417129	+	0.199667i
$359$	−5.48103			−0.289278			−0.144639	−	0.989485i	$-0.546202\pi$
$359$	−5.48103			−0.289278			−0.144639	+	0.989485i	$0.546202\pi$
$360$	−17.9854	−	2.58249i	−0.947915	−	0.136109i
$361$	7.80297			0.410683
$362$	−5.21494	+	2.49624i	−0.274091	+	0.131199i
$363$	−1.50345	−	33.8140i	−0.0789108	−	1.77477i
$364$	−13.0548	+	16.2126i	−0.684256	+	0.849770i
$365$	27.7469			1.45234
$366$	7.79935	+	14.5916i	0.407678	+	0.762716i
$367$		−	18.5731i		−	0.969506i	−0.874651	−	0.484753i	$-0.838909\pi$
$367$		−	18.5731i		−	0.969506i	0.874651	−	0.484753i	$-0.161091\pi$
$368$	0.853230	+	3.90794i	0.0444777	+	0.203715i
$369$	−2.17857	−	24.4506i	−0.113412	−	1.27285i
$370$	8.12518	−	3.88928i	0.422408	−	0.202194i
$371$		−	18.3363i		−	0.951972i
$372$	4.48036	−	6.10015i	0.232296	−	0.316278i
$373$			14.6276i			0.757389i	0.925522	+	0.378694i	$0.123627\pi$
$373$			14.6276i			0.757389i	−0.925522	+	0.378694i	$0.876373\pi$
$374$	4.60842	+	9.62755i	0.238296	+	0.497829i
$375$	−0.892035	−	20.0627i	−0.0460645	−	1.03603i
$376$	35.2585	+	8.31060i	1.81832	+	0.428587i
$377$		−	15.1098i		−	0.778193i
$378$	−10.0244	−	15.3093i	−0.515601	−	0.787424i
$379$	−16.1428			−0.829201			−0.414600	−	0.910004i	$-0.636079\pi$
$379$	−16.1428			−0.829201			−0.414600	+	0.910004i	$0.636079\pi$
$380$	13.9058	−	17.2694i	0.713351	−	0.885903i
$381$	29.0017	−	1.28949i	1.48580	−	0.0660624i
$382$	−3.79160	−	7.92110i	−0.193995	−	0.405279i
$383$	4.53571			0.231764			0.115882	−	0.993263i	$-0.463031\pi$
$383$	4.53571			0.231764			0.115882	+	0.993263i	$0.463031\pi$
$384$	19.5883	−	0.546900i	0.999610	−	0.0279089i
$385$	−29.4693			−1.50190
$386$	−2.08963	−	4.36549i	−0.106359	−	0.222197i
$387$	−1.44273	+	0.128549i	−0.0733382	+	0.00653451i
$388$	−7.59285	+	9.42948i	−0.385469	+	0.478710i
$389$	−27.2762			−1.38296			−0.691478	−	0.722397i	$-0.743040\pi$
$389$	−27.2762			−1.38296			−0.691478	+	0.722397i	$0.743040\pi$
$390$	−10.3338	−	19.3333i	−0.523274	−	0.978981i
$391$		−	1.36569i		−	0.0690658i
$392$	2.19917	+	0.518354i	0.111075	+	0.0261808i
$393$	−10.1772	+	0.452503i	−0.513371	+	0.0228257i
$394$	4.17727	+	8.72682i	0.210448	+	0.439651i
$395$		−	16.4868i		−	0.829540i
$396$	27.5705	+	18.4221i	1.38547	+	0.925747i
$397$			13.5840i			0.681763i	0.940106	+	0.340882i	$0.110726\pi$
$397$			13.5840i			0.681763i	−0.940106	+	0.340882i	$0.889274\pi$
$398$	27.2503	−	13.0439i	1.36594	−	0.653833i
$399$	22.3080	−	0.991867i	1.11680	−	0.0496554i
$400$	0.353796	+	1.62045i	0.0176898	+	0.0810223i
$401$		−	13.3388i		−	0.666109i	−0.942908	−	0.333055i	$-0.891921\pi$
$401$		−	13.3388i		−	0.666109i	0.942908	−	0.333055i	$-0.108079\pi$
$402$	−12.8591	+	6.87331i	−0.641355	+	0.342810i
$403$	9.13158			0.454877
$404$	−6.57886	+	8.17021i	−0.327310	+	0.406483i
$405$	18.9685	−	3.40727i	0.942552	−	0.169309i
$406$	11.4841	−	5.49710i	0.569947	−	0.272817i
$407$	−16.4391			−0.814854
$408$	−6.57378	−	1.24415i	−0.325451	−	0.0615944i
$409$	−12.6081			−0.623432			−0.311716	−	0.950175i	$-0.600904\pi$
$409$	−12.6081			−0.623432			−0.311716	+	0.950175i	$0.600904\pi$
$410$	22.3505	−	10.6985i	1.10381	−	0.528364i
$411$	−18.6201	+	0.827894i	−0.918461	+	0.0408370i
$412$	−25.1754	−	20.2719i	−1.24030	−	0.998723i
$413$	−7.41140			−0.364691
$414$	−2.16419	−	3.64915i	−0.106364	−	0.179346i
$415$		−	20.0043i		−	0.981971i
$416$	14.5216	+	18.6569i	0.711979	+	0.914732i
$417$	−0.723985	−	16.2831i	−0.0354537	−	0.797386i
$418$	−36.4969	+	17.4700i	−1.78512	+	0.854484i
$419$		−	6.37490i		−	0.311434i	−0.987802	−	0.155717i	$-0.950231\pi$
$419$		−	6.37490i		−	0.311434i	0.987802	−	0.155717i	$-0.0497688\pi$
$420$	10.9346	−	14.8878i	0.533555	−	0.726453i
$421$			0.723414i			0.0352570i	0.999845	+	0.0176285i	$0.00561162\pi$
$421$			0.723414i			0.0352570i	−0.999845	+	0.0176285i	$0.994388\pi$
$422$	−9.36935	−	19.5737i	−0.456093	−	0.952832i
$423$	−38.2705	+	3.40994i	−1.86077	+	0.165797i
$424$	−20.2712	−	4.77801i	−0.984455	−	0.232041i
$425$		−	0.566289i		−	0.0274690i
$426$	12.4345	−	6.64635i	0.602453	−	0.322017i
$427$	−16.8203			−0.813993
$428$	−24.6134	−	19.8193i	−1.18973	−	0.958002i
$429$	1.77700	+	39.9663i	0.0857943	+	1.92959i
$430$	−0.631278	−	1.31882i	−0.0304429	−	0.0635990i
$431$	−34.4423			−1.65903			−0.829514	−	0.558485i	$-0.811383\pi$
$431$	−34.4423			−1.65903			−0.829514	+	0.558485i	$0.811383\pi$
$432$	−19.5369	+	7.09299i	−0.939968	+	0.341261i
$433$	−4.28986			−0.206158			−0.103079	−	0.994673i	$-0.532869\pi$
$433$	−4.28986			−0.206158			−0.103079	+	0.994673i	$0.532869\pi$
$434$	3.32217	+	6.94041i	0.159469	+	0.333150i
$435$	0.595600	+	13.3956i	0.0285568	+	0.642269i
$436$	23.7046	+	19.0875i	1.13524	+	0.914125i
$437$	5.17716			0.247657
$438$	27.9920	−	14.9620i	1.33751	−	0.714911i
$439$			11.9341i			0.569586i	0.958589	+	0.284793i	$0.0919248\pi$
$439$			11.9341i			0.569586i	−0.958589	+	0.284793i	$0.908075\pi$
$440$	−7.67902	+	32.5790i	−0.366083	+	1.55314i
$441$	−2.38703	+	0.212687i	−0.113668	+	0.0101279i
$442$	−3.48514	−	7.28086i	−0.165771	−	0.346315i
$443$		−	4.62576i		−	0.219777i	−0.993944	−	0.109888i	$-0.964951\pi$
$443$		−	4.62576i		−	0.219777i	0.993944	−	0.109888i	$-0.0350493\pi$
$444$	6.09974	−	8.30499i	0.289481	−	0.394137i
$445$		−	34.8282i		−	1.65102i
$446$	−25.5719	+	12.2405i	−1.21086	+	0.579604i
$447$	−0.204475	−	4.59882i	−0.00967132	−	0.217517i
$448$	−8.89700	+	17.8247i	−0.420344	+	0.842136i
$449$		−	22.9288i		−	1.08208i	−0.840998	−	0.541038i	$-0.818032\pi$
$449$		−	22.9288i		−	1.08208i	0.840998	−	0.541038i	$-0.181968\pi$
$450$	−0.897390	−	1.51314i	−0.0423034	−	0.0713300i
$451$	−45.2202			−2.12934
$452$	−3.12432	−	2.51578i	−0.146956	−	0.118332i
$453$	21.1727	−	0.941390i	0.994780	−	0.0442304i
$454$	−20.5028	+	9.81410i	−0.962245	+	0.460598i
$455$	22.2863			1.04480
$456$	4.71641	−	24.9204i	0.220866	−	1.16701i
$457$	−4.17030			−0.195079			−0.0975393	−	0.995232i	$-0.531097\pi$
$457$	−4.17030			−0.195079			−0.0975393	+	0.995232i	$0.531097\pi$
$458$	−28.7832	+	13.7777i	−1.34495	+	0.643789i
$459$	7.03337	−	0.943138i	0.328290	−	0.0440219i
$460$	2.68598	−	3.33570i	0.125235	−	0.155528i
$461$	21.3350			0.993672			0.496836	−	0.867845i	$-0.334495\pi$
$461$	21.3350			0.993672			0.496836	+	0.867845i	$0.334495\pi$
$462$	−29.7297	+	15.8908i	−1.38315	+	0.739305i
$463$		−	5.45991i		−	0.253744i	−0.991919	−	0.126872i	$-0.959506\pi$
$463$		−	5.45991i		−	0.253744i	0.991919	−	0.126872i	$-0.0404937\pi$
$464$	−3.08468	−	14.1283i	−0.143202	−	0.655892i
$465$	−8.09560	+	0.359950i	−0.375425	+	0.0166923i
$466$	4.41519	−	2.11342i	0.204530	−	0.0979023i
$467$			22.5006i			1.04121i	0.853799	+	0.520603i	$0.174293\pi$
$467$			22.5006i			1.04121i	−0.853799	+	0.520603i	$0.825707\pi$
$468$	−20.8502	−	13.9318i	−0.963803	−	0.643998i
$469$		−	14.8232i		−	0.684472i
$470$	−16.7456	−	34.9835i	−0.772415	−	1.61367i
$471$	4.81525	−	0.214098i	0.221875	−	0.00986510i
$472$	−1.93124	+	8.19346i	−0.0888924	+	0.377135i
$473$			2.66826i			0.122687i
$474$	−8.89018	−	16.6324i	−0.408339	−	0.763953i
$475$	2.14673			0.0984989
$476$	4.26585	−	5.29772i	0.195525	−	0.242820i
$477$	22.0028	−	1.96048i	1.00744	−	0.0897640i
$478$	−10.6307	−	22.2088i	−0.486237	−	1.01581i
$479$	−29.4670			−1.34638			−0.673191	−	0.739469i	$-0.735077\pi$
$479$	−29.4670			−1.34638			−0.673191	+	0.739469i	$0.735077\pi$
$480$	−13.6095	−	15.9679i	−0.621187	−	0.728832i
$481$	12.4321			0.566855
$482$	−7.08250	−	14.7962i	−0.322599	−	0.673948i
$483$	4.30892	−	0.191585i	0.196063	−	0.00871743i
$484$	24.5122	−	30.4414i	1.11419	−	1.38370i
$485$	12.9620			0.588576
$486$	17.2988	−	13.6658i	0.784687	−	0.619892i
$487$			39.6032i			1.79459i	0.441427	+	0.897297i	$0.354472\pi$
$487$			39.6032i			1.79459i	−0.441427	+	0.897297i	$0.645528\pi$
$488$	−4.38299	+	18.5952i	−0.198409	+	0.841767i
$489$	0.874617	+	19.6709i	0.0395516	+	0.889550i
$490$	−1.04446	−	2.18201i	−0.0471841	−	0.0985732i
$491$		−	21.0974i		−	0.952112i	−0.879415	−	0.476056i	$-0.842066\pi$
$491$		−	21.0974i		−	0.952112i	0.879415	−	0.476056i	$-0.157934\pi$
$492$	16.7790	−	22.8452i	0.756456	−	1.02994i
$493$			4.93736i			0.222368i
$494$	27.6009	−	13.2117i	1.24182	−	0.594424i
$495$	−3.15080	−	35.3621i	−0.141618	−	1.58941i
$496$	8.53846	−	1.86422i	0.383388	−	0.0837060i
$497$			14.3337i			0.642955i
$498$	−10.7869	−	20.1810i	−0.483373	−	0.904332i
$499$	−33.1697			−1.48488			−0.742439	−	0.669913i	$-0.766331\pi$
$499$	−33.1697			−1.48488			−0.742439	+	0.669913i	$0.766331\pi$
$500$	14.5437	−	18.0616i	0.650413	−	0.807741i
$501$	1.41469	+	31.8176i	0.0632037	+	1.42151i
$502$	2.39653	−	1.14715i	0.106962	−	0.0511998i
$503$	18.3467			0.818040			0.409020	−	0.912525i	$-0.365871\pi$
$503$	18.3467			0.818040			0.409020	+	0.912525i	$0.365871\pi$
$504$	3.00324	−	20.9157i	0.133775	−	0.931658i
$505$	11.2310			0.499774
$506$	−7.04960	+	3.37443i	−0.313393	+	0.150012i
$507$	−0.343703	−	7.73020i	−0.0152644	−	0.343310i
$508$	26.1091	+	21.0237i	1.15840	+	0.932776i
$509$	−13.4870			−0.597801			−0.298901	−	0.954284i	$-0.596620\pi$
$509$	−13.4870			−0.597801			−0.298901	+	0.954284i	$0.596620\pi$
$510$	3.37674	+	6.31747i	0.149525	+	0.279742i
$511$			32.2675i			1.42743i
$512$	17.3872	+	14.4805i	0.768413	+	0.639955i
$513$	3.57532	+	26.6627i	0.157854	+	1.17719i
$514$	40.2181	−	19.2512i	1.77395	−	0.849135i
$515$			34.6069i			1.52496i
$516$	−1.34800	−	0.990062i	−0.0593425	−	0.0435851i
$517$			70.7795i			3.11288i
$518$	4.52293	+	9.44895i	0.198726	+	0.415163i
$519$	1.39292	+	31.3281i	0.0611426	+	1.37515i
$520$	5.80729	−	24.6380i	0.254666	−	1.08045i
$521$		−	30.9591i		−	1.35634i	−0.734904	−	0.678171i	$-0.762773\pi$
$521$		−	30.9591i		−	1.35634i	0.734904	−	0.678171i	$-0.237227\pi$
$522$	7.82417	+	13.1927i	0.342454	+	0.577431i
$523$	34.8401			1.52345			0.761725	−	0.647900i	$-0.224353\pi$
$523$	34.8401			1.52345			0.761725	+	0.647900i	$0.224353\pi$
$524$	−9.16213	−	7.37757i	−0.400250	−	0.322291i
$525$	1.78671	−	0.0794417i	0.0779786	−	0.00346712i
$526$	−0.652508	−	1.36317i	−0.0284507	−	0.0594369i
$527$	−2.98389			−0.129980
$528$	9.82073	+	37.0076i	0.427392	+	1.61055i
$529$	1.00000			0.0434783
$530$	9.62751	+	20.1130i	0.418192	+	0.873654i
$531$	−0.792410	−	8.89339i	−0.0343877	−	0.385940i
$532$	20.0830	+	16.1713i	0.870709	+	0.701116i
$533$	34.1979			1.48128
$534$	−18.7805	−	35.1359i	−0.812710	−	1.52048i
$535$			33.8343i			1.46278i
$536$	−16.3874	−	3.86258i	−0.707827	−	0.166838i
$537$	10.7060	−	0.476014i	0.461998	−	0.0205415i
$538$	−5.85039	−	12.2222i	−0.252228	−	0.526935i
$539$			4.41470i			0.190155i
$540$	19.0339	+	11.5294i	0.819091	+	0.496145i
$541$		−	19.0031i		−	0.817005i	−0.912757	−	0.408503i	$-0.866051\pi$
$541$		−	19.0031i		−	0.817005i	0.912757	−	0.408503i	$-0.133949\pi$
$542$	8.14523	−	3.89888i	0.349868	−	0.167471i
$543$	7.07399	−	0.314527i	0.303574	−	0.0134976i
$544$	−4.74516	−	6.09646i	−0.203447	−	0.261383i
$545$		−	32.5850i		−	1.39579i
$546$	22.4832	−	12.0174i	0.962190	−	0.514299i
$547$	29.1003			1.24424			0.622120	−	0.782922i	$-0.286272\pi$
$547$	29.1003			1.24424			0.622120	+	0.782922i	$0.286272\pi$
$548$	−16.7629	−	13.4979i	−0.716077	−	0.576603i
$549$	−1.79839	−	20.1837i	−0.0767535	−	0.861421i
$550$	−2.92315	+	1.39922i	−0.124643	+	0.0596631i
$551$	−18.7169			−0.797369
$552$	0.911003	−	4.81353i	0.0387749	−	0.204877i
$553$	19.1728			0.815312
$554$	−30.3814	+	14.5427i	−1.29078	+	0.617860i
$555$	−11.0217	+	0.490051i	−0.467844	+	0.0208015i
$556$	11.8038	−	14.6590i	0.500593	−	0.621681i
$557$	−26.7504			−1.13345			−0.566726	−	0.823907i	$-0.691790\pi$
$557$	−26.7504			−1.13345			−0.566726	+	0.823907i	$0.691790\pi$
$558$	−7.97303	+	4.72853i	−0.337525	+	0.200175i
$559$		−	2.01788i		−	0.0853474i
$560$	20.8387	−	4.54976i	0.880596	−	0.192263i
$561$	−0.580663	−	13.0596i	−0.0245156	−	0.551378i
$562$	5.78381	−	2.76854i	0.243975	−	0.116784i
$563$		−	2.06048i		−	0.0868387i	−0.999057	−	0.0434194i	$-0.986175\pi$
$563$		−	2.06048i		−	0.0868387i	0.999057	−	0.0434194i	$-0.0138252\pi$
$564$	−35.7576	−	26.2628i	−1.50567	−	1.10586i
$565$			4.29478i			0.180683i
$566$	17.1064	+	35.7373i	0.719035	+	1.50215i
$567$	3.96240	+	22.0589i	0.166405	+	0.926386i
$568$	15.8462	+	3.73504i	0.664894	+	0.156719i
$569$		−	8.59511i		−	0.360326i	−0.983637	−	0.180163i	$-0.942338\pi$
$569$		−	8.59511i		−	0.360326i	0.983637	−	0.180163i	$-0.0576625\pi$
$570$	−23.9488	+	12.8008i	−1.00310	+	0.536168i
$571$	12.7478			0.533480			0.266740	−	0.963769i	$-0.414054\pi$
$571$	12.7478			0.533480			0.266740	+	0.963769i	$0.414054\pi$
$572$	−28.9721	+	35.9801i	−1.21138	+	1.50440i
$573$	0.477743	+	10.7449i	0.0199580	+	0.448873i
$574$	12.4416	+	25.9920i	0.519302	+	1.08488i
$575$	0.414655			0.0172923
$576$	−22.3401	−	8.77029i	−0.930839	−	0.365429i
$577$	−38.2443			−1.59213			−0.796066	−	0.605209i	$-0.793089\pi$
$577$	−38.2443			−1.59213			−0.796066	+	0.605209i	$0.793089\pi$
$578$	−9.24130	−	19.3062i	−0.384387	−	0.803031i
$579$	0.263294	+	5.92172i	0.0109421	+	0.246098i
$580$	−9.71062	+	12.0595i	−0.403212	+	0.500744i
$581$	23.2634			0.965129
$582$	13.0766	−	6.98953i	0.542041	−	0.289726i
$583$		−	40.6932i		−	1.68534i
$584$	35.6724	+	8.40815i	1.47613	+	0.347932i
$585$	2.38280	+	26.7427i	0.0985166	+	1.10567i
$586$	6.36624	+	13.2998i	0.262987	+	0.549411i
$587$			13.0666i			0.539317i	0.962956	+	0.269659i	$0.0869108\pi$
$587$			13.0666i			0.539317i	−0.962956	+	0.269659i	$0.913089\pi$
$588$	−2.23030	−	1.63808i	−0.0919760	−	0.0675533i
$589$		−	11.3116i		−	0.466085i
$590$	8.12954	−	3.89137i	0.334688	−	0.160205i
$591$	−0.526338	−	11.8378i	−0.0216506	−	0.486942i
$592$	11.6246	−	2.53803i	0.477768	−	0.104312i
$593$		−	0.526422i		−	0.0216176i	−0.999942	−	0.0108088i	$-0.996559\pi$
$593$		−	0.526422i		−	0.0216176i	0.999942	−	0.0108088i	$-0.00344061\pi$
$594$	−22.2469	−	33.9754i	−0.912803	−	1.39403i
$595$	−7.28240			−0.298549
$596$	3.33374	−	4.14014i	0.136555	−	0.169587i
$597$	−36.9646	+	1.64354i	−1.51286	+	0.0672656i
$598$	5.33128	−	2.55193i	0.218012	−	0.104356i
$599$	34.6829			1.41710			0.708551	−	0.705659i	$-0.249349\pi$
$599$	34.6829			1.41710			0.708551	+	0.705659i	$0.249349\pi$
$600$	0.377752	−	1.99595i	0.0154217	−	0.0814844i
$601$	1.57784			0.0643616			0.0321808	−	0.999482i	$-0.489755\pi$
$601$	1.57784			0.0643616			0.0321808	+	0.999482i	$0.489755\pi$
$602$	1.53368	−	0.734128i	0.0625082	−	0.0299208i
$603$	17.7873	−	1.58486i	0.724354	−	0.0645407i
$604$	19.0610	+	15.3484i	0.775580	+	0.624516i
$605$	−41.8457			−1.70127
$606$	11.3302	−	6.05611i	0.460259	−	0.246013i
$607$		−	40.5141i		−	1.64442i	−0.569186	−	0.822209i	$-0.692742\pi$
$607$		−	40.5141i		−	1.64442i	0.569186	−	0.822209i	$-0.307258\pi$
$608$	23.1109	−	17.9883i	0.937272	−	0.729523i
$609$	−15.5780	+	0.692637i	−0.631253	+	0.0280670i
$610$	18.4502	−	8.83155i	0.747026	−	0.357579i
$611$		−	53.5272i		−	2.16548i
$612$	6.81315	+	4.55244i	0.275405	+	0.184021i
$613$		−	33.6058i		−	1.35733i	−0.734450	−	0.678663i	$-0.762560\pi$
$613$		−	33.6058i		−	1.35733i	0.734450	−	0.678663i	$-0.237440\pi$
$614$	−1.51878	−	3.17291i	−0.0612929	−	0.128048i
$615$	−30.3182	+	1.34802i	−1.22255	+	0.0543574i
$616$	−37.8868	−	8.93011i	−1.52650	−	0.359804i
$617$			28.9542i			1.16565i	0.812597	+	0.582826i	$0.198053\pi$
$617$			28.9542i			1.16565i	−0.812597	+	0.582826i	$0.801947\pi$
$618$	18.6611	+	34.9126i	0.750659	+	1.40439i
$619$	−19.8168			−0.796504			−0.398252	−	0.917276i	$-0.630383\pi$
$619$	−19.8168			−0.796504			−0.398252	+	0.917276i	$0.630383\pi$
$620$	−7.28816	−	5.86861i	−0.292700	−	0.235689i
$621$	0.690595	+	5.15006i	0.0277126	+	0.206665i
$622$	21.2902	+	44.4778i	0.853659	+	1.78340i
$623$	40.5025			1.62270
$624$	−7.42696	−	27.9871i	−0.297316	−	1.12038i
$625$	−22.7548			−0.910192
$626$	−8.73737	−	18.2534i	−0.349216	−	0.729553i
$627$	49.5074	−	2.20122i	1.97714	−	0.0879083i
$628$	4.33498	+	3.49064i	0.172985	+	0.139292i
$629$	−4.06239			−0.161978
$630$	−19.4587	+	11.5403i	−0.775255	+	0.459777i
$631$			0.270243i			0.0107582i	0.999986	+	0.00537911i	$0.00171223\pi$
$631$			0.270243i			0.0107582i	−0.999986	+	0.00537911i	$0.998288\pi$
$632$	4.99600	−	21.1960i	0.198730	−	0.843132i
$633$	1.18054	+	26.5514i	0.0469223	+	1.05532i
$634$	−19.9917	−	41.7651i	−0.793973	−	1.65871i
$635$		−	35.8903i		−	1.42426i
$636$	20.5581	+	15.0993i	0.815183	+	0.598725i
$637$		−	3.33863i		−	0.132281i
$638$	25.4864	−	12.1996i	1.00901	−	0.482985i
$639$	−17.1999	+	1.53253i	−0.680418	+	0.0606260i
$640$	0.400220	−	24.2232i	0.0158201	−	0.957507i
$641$			10.6165i			0.419326i	0.977774	+	0.209663i	$0.0672366\pi$
$641$			10.6165i			0.419326i	−0.977774	+	0.209663i	$0.932763\pi$
$642$	18.2445	+	34.1332i	0.720052	+	1.34713i
$643$	−45.5485			−1.79626			−0.898129	−	0.439732i	$-0.855073\pi$
$643$	−45.5485			−1.79626			−0.898129	+	0.439732i	$0.855073\pi$
$644$	3.87916	+	3.12359i	0.152860	+	0.123087i
$645$	0.0795413	+	1.78895i	0.00313193	+	0.0704400i
$646$	−9.01903	+	4.31714i	−0.354849	+	0.169856i
$647$	−24.1544			−0.949609			−0.474804	−	0.880091i	$-0.657481\pi$
$647$	−24.1544			−0.949609			−0.474804	+	0.880091i	$0.657481\pi$
$648$	25.4191	+	1.36752i	0.998556	+	0.0537212i
$649$	−16.4479			−0.645637
$650$	2.21064	−	1.05817i	0.0867084	−	0.0415048i
$651$	−0.418594	−	9.41456i	−0.0164060	−	0.368986i
$652$	−14.2597	+	17.7090i	−0.558453	+	0.693537i
$653$	−14.4404			−0.565098			−0.282549	−	0.959253i	$-0.591180\pi$
$653$	−14.4404			−0.565098			−0.282549	+	0.959253i	$0.591180\pi$
$654$	−17.5708	−	32.8728i	−0.687074	−	1.28543i
$655$			12.5945i			0.492109i
$656$	31.9767	−	6.98154i	1.24848	−	0.272583i
$657$	−38.7197	+	3.44997i	−1.51060	+	0.134596i
$658$	40.6831	−	19.4738i	1.58599	−	0.759167i
$659$		−	26.8601i		−	1.04632i	−0.852235	−	0.523160i	$-0.824753\pi$
$659$		−	26.8601i		−	1.04632i	0.852235	−	0.523160i	$-0.175247\pi$
$660$	24.2669	−	33.0402i	0.944588	−	1.28609i
$661$		−	27.4456i		−	1.06751i	−0.845639	−	0.533755i	$-0.820780\pi$
$661$		−	27.4456i		−	1.06751i	0.845639	−	0.533755i	$-0.179220\pi$
$662$	14.3229	+	29.9223i	0.556677	+	1.16296i
$663$	0.439128	+	9.87638i	0.0170543	+	0.383567i
$664$	6.06191	−	25.7182i	0.235248	−	0.998060i
$665$		−	27.6067i		−	1.07054i
$666$	−10.8548	+	6.43761i	−0.420615	+	0.249452i
$667$	−3.61529			−0.139985
$668$	−23.0650	+	28.6442i	−0.892412	+	1.10828i
$669$	34.6878	−	1.54231i	1.34111	−	0.0596290i
$670$	7.78296	+	16.2595i	0.300682	+	0.628161i
$671$	−37.3289			−1.44107
$672$	18.5694	−	15.8268i	0.716331	−	0.610533i
$673$	6.61048			0.254815			0.127408	−	0.991850i	$-0.459334\pi$
$673$	6.61048			0.254815			0.127408	+	0.991850i	$0.459334\pi$
$674$	−17.1554	−	35.8397i	−0.660801	−	1.38049i
$675$	0.286359	+	2.13549i	0.0110219	+	0.0821952i
$676$	5.60372	−	6.95920i	0.215528	−	0.267661i
$677$	19.4686			0.748241			0.374120	−	0.927380i	$-0.377945\pi$
$677$	19.4686			0.748241			0.374120	+	0.927380i	$0.377945\pi$
$678$	2.31588	+	4.33272i	0.0889407	+	0.166397i
$679$			15.0739i			0.578481i
$680$	−1.89762	+	8.05085i	−0.0727705	+	0.308736i
$681$	27.8118	−	1.23658i	1.06575	−	0.0473858i
$682$	7.37280	+	15.4027i	0.282319	+	0.589798i
$683$			41.6436i			1.59345i	0.604343	+	0.796724i	$0.293435\pi$
$683$			41.6436i			1.59345i	−0.604343	+	0.796724i	$0.706565\pi$
$684$	−17.2577	+	25.8278i	−0.659866	+	0.987552i
$685$			23.0428i			0.880421i
$686$	24.7733	−	11.8582i	0.945847	−	0.452749i
$687$	39.0440	−	1.73599i	1.48962	−	0.0662322i
$688$	−0.411953	−	1.88681i	−0.0157056	−	0.0719341i
$689$			30.7744i			1.17241i
$690$	−4.62585	+	2.47256i	−0.176103	+	0.0941287i
$691$	−31.6587			−1.20436			−0.602178	−	0.798362i	$-0.705700\pi$
$691$	−31.6587			−1.20436			−0.602178	+	0.798362i	$0.705700\pi$
$692$	−22.7102	+	28.2035i	−0.863311	+	1.07214i
$693$	41.1233	−	3.66413i	1.56215	−	0.139189i
$694$	6.00406	−	2.87397i	0.227911	−	0.109094i
$695$	−20.1507			−0.764360
$696$	−3.29354	+	17.4023i	−0.124841	+	0.659633i
$697$	−11.1747			−0.423273
$698$	−13.4745	+	6.44983i	−0.510016	+	0.244130i
$699$	−5.98914	+	0.266292i	−0.226530	+	0.0100721i
$700$	1.60851	+	1.29521i	0.0607960	+	0.0489544i
$701$	28.0180			1.05822			0.529112	−	0.848552i	$-0.322525\pi$
$701$	28.0180			1.05822			0.529112	+	0.848552i	$0.322525\pi$
$702$	16.8243	+	25.6940i	0.634993	+	0.969759i
$703$		−	15.4000i		−	0.580823i
$704$	−19.7449	+	39.5578i	−0.744163	+	1.49089i
$705$	2.10994	+	47.4545i	0.0794651	+	1.78724i
$706$	35.4149	−	16.9521i	1.33286	−	0.638000i
$707$			13.0608i			0.491202i
$708$	6.10301	−	8.30945i	0.229365	−	0.312288i
$709$			46.9593i			1.76359i	0.471631	+	0.881796i	$0.343665\pi$
$709$			46.9593i			1.76359i	−0.471631	+	0.881796i	$0.656335\pi$
$710$	−7.52596	−	15.7226i	−0.282444	−	0.590060i
$711$	2.04992	+	23.0067i	0.0768779	+	0.862818i
$712$	10.5540	−	44.7764i	0.395529	−	1.67807i
$713$		−	2.18490i		−	0.0818251i
$714$	−7.34673	+	3.92689i	−0.274944	+	0.146960i
$715$	49.4593			1.84967
$716$	9.63819	+	7.76091i	0.360196	+	0.290039i
$717$	1.33947	+	30.1259i	0.0500235	+	1.12507i
$718$	3.34669	+	6.99164i	0.124898	+	0.260926i
$719$	−21.2135			−0.791131			−0.395566	−	0.918438i	$-0.629451\pi$
$719$	−21.2135			−0.791131			−0.395566	+	0.918438i	$0.629451\pi$
$720$	7.68757	+	24.5192i	0.286499	+	0.913776i
$721$	−40.2451			−1.49881
$722$	−4.76446	−	9.95352i	−0.177315	−	0.370432i
$723$	0.892397	+	20.0708i	0.0331886	+	0.746441i
$724$	6.36844	+	5.12802i	0.236681	+	0.190581i
$725$	−1.49910			−0.0556751
$726$	−42.2154	+	22.5645i	−1.56676	+	0.837446i
$727$		−	31.9371i		−	1.18448i	−0.805761	−	0.592241i	$-0.798243\pi$
$727$		−	31.9371i		−	1.18448i	0.805761	−	0.592241i	$-0.201757\pi$
$728$	28.6520	+	6.75343i	1.06192	+	0.250299i
$729$	−26.0462	+	7.11321i	−0.964672	+	0.263452i
$730$	−16.9421	−	35.3941i	−0.627056	−	1.30999i
$731$			0.659375i			0.0243879i
$732$	13.8509	−	18.8585i	0.511945	−	0.697029i
$733$			11.5042i			0.424919i	0.977170	+	0.212459i	$0.0681473\pi$
$733$			11.5042i			0.424919i	−0.977170	+	0.212459i	$0.931853\pi$
$734$	−23.6919	+	11.3406i	−0.874485	+	0.418590i
$735$	0.131603	+	2.95986i	0.00485424	+	0.109176i
$736$	4.46402	−	3.47456i	0.164546	−	0.128074i
$737$		−	32.8967i		−	1.21177i
$738$	−29.8591	+	17.7084i	−1.09913	+	0.651856i
$739$	44.7930			1.64774			0.823868	−	0.566782i	$-0.191812\pi$
$739$	44.7930			1.64774			0.823868	+	0.566782i	$0.191812\pi$
$740$	−9.92239	−	7.98975i	−0.364754	−	0.293709i
$741$	−37.4402	+	1.66468i	−1.37540	+	0.0611536i
$742$	−23.3899	+	11.1961i	−0.858670	+	0.411020i
$743$	−32.7874			−1.20285			−0.601426	−	0.798929i	$-0.705400\pi$
$743$	−32.7874			−1.20285			−0.601426	+	0.798929i	$0.705400\pi$
$744$	−10.5171	−	1.99045i	−0.385575	−	0.0729735i
$745$	−5.69115			−0.208508
$746$	18.6591	−	8.93155i	0.683157	−	0.327007i
$747$	2.48727	+	27.9152i	0.0910045	+	1.02136i
$748$	9.46708	−	11.7571i	0.346151	−	0.429881i
$749$	−39.3466			−1.43769
$750$	−25.0474	+	13.3881i	−0.914602	+	0.488863i
$751$		−	9.60918i		−	0.350644i	−0.984511	−	0.175322i	$-0.943903\pi$
$751$		−	9.60918i		−	0.350644i	0.984511	−	0.175322i	$-0.0560966\pi$
$752$	−10.9276	−	50.0504i	−0.398490	−	1.82515i
$753$	−3.25086	+	0.144541i	−0.118468	+	0.00526737i
$754$	−19.2741	+	9.22596i	−0.701923	+	0.335990i
$755$		−	26.2018i		−	0.953580i
$756$	−13.4077	+	22.1350i	−0.487635	+	0.805043i
$757$			32.2804i			1.17325i	0.809858	+	0.586626i	$0.199544\pi$
$757$			32.2804i			1.17325i	−0.809858	+	0.586626i	$0.800456\pi$
$758$	9.85673	+	20.5919i	0.358013	+	0.747931i
$759$	9.56267	−	0.425180i	0.347103	−	0.0154330i
$760$	−30.5198	−	7.19366i	−1.10707	−	0.260942i
$761$		−	14.8126i		−	0.536955i	−0.963286	−	0.268477i	$-0.913480\pi$
$761$		−	14.8126i		−	0.536955i	0.963286	−	0.268477i	$-0.0865204\pi$
$762$	−19.3532	−	36.2074i	−0.701092	−	1.31166i
$763$	37.8938			1.37185
$764$	−7.78908	+	9.67318i	−0.281799	+	0.349963i
$765$	−0.778618	−	8.73859i	−0.0281510	−	0.315945i
$766$	−2.76948	−	5.78578i	−0.100065	−	0.209049i
$767$	12.4388			0.449138
$768$	−12.6581	−	24.6530i	−0.456762	−	0.889589i
$769$	1.65980			0.0598538			0.0299269	−	0.999552i	$-0.490473\pi$
$769$	1.65980			0.0598538			0.0299269	+	0.999552i	$0.490473\pi$
$770$	17.9938	+	37.5913i	0.648453	+	1.35470i
$771$	−54.5553	+	2.42566i	−1.96476	+	0.0873580i
$772$	−4.29273	+	5.33109i	−0.154499	+	0.191870i
$773$	41.2677			1.48430			0.742148	−	0.670236i	$-0.233807\pi$
$773$	41.2677			1.48430			0.742148	+	0.670236i	$0.233807\pi$
$774$	1.04490	+	1.76187i	0.0375583	+	0.0633290i
$775$		−	0.905979i		−	0.0325437i
$776$	16.6645	+	3.92790i	0.598220	+	0.141003i
$777$	−0.569891	−	12.8174i	−0.0204447	−	0.459820i
$778$	16.6547	+	34.7937i	0.597100	+	1.24741i
$779$		−	42.3620i		−	1.51778i
$780$	−18.3519	+	24.9867i	−0.657105	+	0.894669i
$781$			31.8104i			1.13827i
$782$	−1.74208	+	0.833883i	−0.0622967	+	0.0298196i
$783$	−2.49670	−	18.6190i	−0.0892249	−	0.665387i
$784$	−0.681585	−	3.12178i	−0.0243423	−	0.111492i
$785$		−	5.95900i		−	0.212686i
$786$	6.79136	+	12.7058i	0.242240	+	0.453201i
$787$	−24.1766			−0.861804			−0.430902	−	0.902399i	$-0.641805\pi$
$787$	−24.1766			−0.861804			−0.430902	+	0.902399i	$0.641805\pi$
$788$	8.58137	−	10.6571i	0.305699	−	0.379644i
$789$	0.0822161	+	1.84911i	0.00292697	+	0.0658302i
$790$	−21.0306	+	10.0667i	−0.748237	+	0.358159i
$791$	−4.99450			−0.177584
$792$	6.66501	−	46.4175i	0.236831	−	1.64938i
$793$	28.2301			1.00248
$794$	17.3279	−	8.29435i	0.614944	−	0.294355i
$795$	−1.21307	−	27.2830i	−0.0430231	−	0.967629i
$796$	−33.2778	−	26.7961i	−1.17950	−	0.949764i
$797$	−41.4292			−1.46750			−0.733748	−	0.679421i	$-0.762231\pi$
$797$	−41.4292			−1.46750			−0.733748	+	0.679421i	$0.762231\pi$
$798$	−14.8864	−	27.8506i	−0.526972	−	0.985900i
$799$			17.4909i			0.618782i
$800$	1.85103	−	1.44074i	0.0654436	−	0.0509379i
$801$	4.33044	+	48.6015i	0.153009	+	1.71725i
$802$	−17.0151	+	8.14463i	−0.600824	+	0.287597i
$803$			71.6103i			2.52707i
$804$	16.6194	+	12.2064i	0.586120	+	0.430485i
$805$		−	5.33240i		−	0.187942i
$806$	−5.57570	−	11.6483i	−0.196396	−	0.410294i
$807$	0.737151	+	16.5792i	0.0259489	+	0.583615i
$808$	14.4390	+	3.40334i	0.507962	+	0.119729i
$809$		−	19.9176i		−	0.700264i	−0.936700	−	0.350132i	$-0.886137\pi$
$809$		−	19.9176i		−	0.700264i	0.936700	−	0.350132i	$-0.113863\pi$
$810$	−15.9284	−	22.1159i	−0.559667	−	0.777072i
$811$	−13.5044			−0.474205			−0.237102	−	0.971485i	$-0.576198\pi$
$811$	−13.5044			−0.474205			−0.237102	+	0.971485i	$0.576198\pi$
$812$	−14.0243	−	11.2927i	−0.492156	−	0.396296i
$813$	−11.0489	+	0.491260i	−0.387501	+	0.0172293i
$814$	10.0376	+	20.9698i	0.351818	+	0.734991i
$815$	24.3433			0.852708
$816$	2.42688	+	9.14523i	0.0849577	+	0.320147i
$817$	−2.49961			−0.0874504
$818$	7.69846	+	16.0830i	0.269170	+	0.562329i
$819$	−31.0997	+	2.77101i	−1.08671	+	0.0968270i
$820$	−27.2943	−	21.9780i	−0.953158	−	0.767506i
$821$	4.66451			0.162792			0.0813962	−	0.996682i	$-0.474062\pi$
$821$	4.66451			0.162792			0.0813962	+	0.996682i	$0.474062\pi$
$822$	12.4254	+	23.2464i	0.433386	+	0.810811i
$823$		−	29.5387i		−	1.02965i	−0.857294	−	0.514827i	$-0.827856\pi$
$823$		−	29.5387i		−	1.02965i	0.857294	−	0.514827i	$-0.172144\pi$
$824$	−10.4869	+	44.4919i	−0.365330	+	1.54995i
$825$	3.96520	−	0.176303i	0.138051	−	0.00613807i
$826$	4.52536	+	9.45403i	0.157458	+	0.328948i
$827$			9.20874i			0.320219i	0.987099	+	0.160110i	$0.0511848\pi$
$827$			9.20874i			0.320219i	−0.987099	+	0.160110i	$0.948815\pi$
$828$	−3.33344	+	4.98881i	−0.115845	+	0.173373i
$829$			13.6138i			0.472828i	0.971652	+	0.236414i	$0.0759721\pi$
$829$			13.6138i			0.472828i	−0.971652	+	0.236414i	$0.924028\pi$
$830$	−25.5176	+	12.2145i	−0.885728	+	0.423972i
$831$	41.2119	−	1.83238i	1.42963	−	0.0635647i
$832$	14.9321	−	29.9157i	0.517678	−	1.03714i
$833$			1.09095i			0.0377992i
$834$	−20.3287	+	10.8659i	−0.703927	+	0.376255i
$835$	39.3751			1.36263
$836$	44.5696	+	35.8886i	1.54147	+	1.24123i
$837$	11.2524	−	1.50888i	0.388938	−	0.0521546i
$838$	−8.13187	+	3.89249i	−0.280911	+	0.134464i
$839$	21.6772			0.748379			0.374189	−	0.927352i	$-0.377921\pi$
$839$	21.6772			0.748379			0.374189	+	0.927352i	$0.377921\pi$
$840$	−25.6677	−	4.85784i	−0.885619	−	0.167611i
$841$	−15.9297			−0.549299
$842$	0.922792	−	0.441713i	0.0318015	−	0.0152224i
$843$	−7.84565	+	0.348837i	−0.270219	+	0.0120146i
$844$	−19.2475	+	23.9032i	−0.662525	+	0.822782i
$845$	−9.56632			−0.329091
$846$	27.7175	+	46.7360i	0.952948	+	1.60682i
$847$		−	48.6633i		−	1.67209i
$848$	6.28262	+	28.7755i	0.215746	+	0.988154i
$849$	−2.15541	−	48.4771i	−0.0739735	−	1.66373i
$850$	−0.722362	+	0.345773i	−0.0247768	+	0.0118599i
$851$		−	2.97461i		−	0.101968i
$852$	−16.0706	−	11.8033i	−0.550569	−	0.404374i
$853$		−	24.9638i		−	0.854745i	−0.904076	−	0.427373i	$-0.859439\pi$
$853$		−	24.9638i		−	0.854745i	0.904076	−	0.427373i	$-0.140561\pi$
$854$	10.2704	+	21.4561i	0.351446	+	0.734214i
$855$	33.1270	−	2.95165i	1.13292	−	0.100944i
$856$	−10.2528	+	43.4986i	−0.350434	+	1.48675i
$857$		−	44.6218i		−	1.52425i	−0.647429	−	0.762126i	$-0.724156\pi$
$857$		−	44.6218i		−	1.52425i	0.647429	−	0.762126i	$-0.275844\pi$
$858$	49.8962	−	26.6700i	1.70343	−	0.910498i
$859$	−6.20591			−0.211743			−0.105871	−	0.994380i	$-0.533763\pi$
$859$	−6.20591			−0.211743			−0.105871	+	0.994380i	$0.533763\pi$
$860$	−1.29684	+	1.61053i	−0.0442217	+	0.0549185i
$861$	−1.56764	−	35.2577i	−0.0534251	−	1.20158i
$862$	21.0303	+	43.9349i	0.716296	+	1.49643i
$863$	−28.9792			−0.986464			−0.493232	−	0.869898i	$-0.664185\pi$
$863$	−28.9792			−0.986464			−0.493232	+	0.869898i	$0.664185\pi$
$864$	20.9770	+	20.5904i	0.713652	+	0.700501i
$865$	38.7694			1.31820
$866$	2.61937	+	5.47218i	0.0890098	+	0.185952i
$867$	1.16441	+	26.1885i	0.0395453	+	0.889409i
$868$	6.82474	−	8.47557i	0.231647	−	0.287680i
$869$	42.5497			1.44340
$870$	16.7238	−	8.93903i	0.566990	−	0.303061i
$871$			24.8783i			0.842968i
$872$	9.87425	−	41.8924i	0.334384	−	1.41866i
$873$	−18.0880	+	1.61166i	−0.612188	+	0.0545465i
$874$	−3.16115	−	6.60402i	−0.106927	−	0.223384i
$875$		−	28.8731i		−	0.976089i
$876$	−36.1774	−	26.5711i	−1.22232	−	0.897754i
$877$		−	12.3171i		−	0.415920i	−0.978137	−	0.207960i	$-0.933318\pi$
$877$		−	12.3171i		−	0.415920i	0.978137	−	0.207960i	$-0.0666824\pi$
$878$	15.2233	−	7.28694i	0.513761	−	0.245922i
$879$	−0.802148	−	18.0410i	−0.0270558	−	0.608508i
$880$	46.2468	−	10.0972i	1.55898	−	0.340375i
$881$			12.6586i			0.426478i	0.977000	+	0.213239i	$0.0684013\pi$
$881$			12.6586i			0.426478i	−0.977000	+	0.213239i	$0.931599\pi$
$882$	1.72882	+	2.91505i	0.0582122	+	0.0981548i
$883$	46.7189			1.57222			0.786108	−	0.618090i	$-0.212093\pi$
$883$	46.7189			1.57222			0.786108	+	0.618090i	$0.212093\pi$
$884$	−7.15951	+	8.89133i	−0.240801	+	0.299048i
$885$	−11.0276	+	0.490314i	−0.370689	+	0.0164817i
$886$	−5.90066	+	2.82447i	−0.198236	+	0.0948899i
$887$	15.6784			0.526428			0.263214	−	0.964737i	$-0.415217\pi$
$887$	15.6784			0.526428			0.263214	+	0.964737i	$0.415217\pi$
$888$	−14.3184	−	2.70988i	−0.480493	−	0.0909376i
$889$	41.7377			1.39984
$890$	−44.4271	+	21.2660i	−1.48920	+	0.712837i
$891$	8.79363	+	48.9547i	0.294598	+	1.64004i
$892$	31.2281	+	25.1456i	1.04559	+	0.841938i
$893$	−66.3058			−2.21884
$894$	−5.74143	+	3.06885i	−0.192022	+	0.102638i
$895$		−	13.2489i		−	0.442863i
$896$	28.1697	+	0.465425i	0.941084	+	0.0155487i
$897$	−7.23180	+	0.321543i	−0.241463	+	0.0107360i
$898$	−29.2481	+	14.0002i	−0.976022	+	0.467193i
$899$			7.89905i			0.263448i
$900$	−1.38223	+	2.06863i	−0.0460742	+	0.0689544i
$901$		−	10.0560i		−	0.335014i
$902$	27.6113	+	57.6832i	0.919354	+	1.92064i
$903$	−2.08041	+	0.0925003i	−0.0692319	+	0.00307822i
$904$	−1.30145	+	5.52153i	−0.0432856	+	0.183643i
$905$		−	8.75424i		−	0.291001i
$906$	−14.1288	−	26.4332i	−0.469398	−	0.878186i
$907$	−22.5175			−0.747681			−0.373841	−	0.927493i	$-0.621959\pi$
$907$	−22.5175			−0.747681			−0.373841	+	0.927493i	$0.621959\pi$
$908$	25.0379	+	20.1611i	0.830911	+	0.669070i
$909$	−15.6725	+	1.39643i	−0.519823	+	0.0463167i
$910$	−13.6079	−	28.4285i	−0.451097	−	0.942397i
$911$	−2.59414			−0.0859477			−0.0429738	−	0.999076i	$-0.513683\pi$
$911$	−2.59414			−0.0859477			−0.0429738	+	0.999076i	$0.513683\pi$
$912$	−34.6685	+	9.20000i	−1.14799	+	0.304643i
$913$	51.6278			1.70863
$914$	2.54637	+	5.31967i	0.0842263	+	0.175959i
$915$	−25.0274	+	1.11278i	−0.827380	+	0.0367873i
$916$	35.1498	+	28.3035i	1.16138	+	0.935174i
$917$	−14.6465			−0.483669
$918$	−5.49762	−	8.39594i	−0.181448	−	0.277107i
$919$			21.4741i			0.708365i	0.935176	+	0.354183i	$0.115241\pi$
$919$			21.4741i			0.708365i	−0.935176	+	0.354183i	$0.884759\pi$
$920$	−5.89509	−	1.38950i	−0.194355	−	0.0458105i
$921$	0.191366	+	4.30400i	0.00630574	+	0.141822i
$922$	−13.0271	−	27.2151i	−0.429024	−	0.896282i
$923$		−	24.0567i		−	0.791837i
$924$	38.4232	+	28.2205i	1.26403	+	0.928388i
$925$		−	1.23344i		−	0.0405551i
$926$	−6.96470	+	3.33380i	−0.228874	+	0.109555i
$927$	−4.30292	−	48.2926i	−0.141326	−	1.58614i
$928$	−16.1387	+	12.5615i	−0.529780	+	0.412353i
$929$		−	21.0384i		−	0.690249i	−0.938557	−	0.345124i	$-0.887837\pi$
$929$		−	21.0384i		−	0.690249i	0.938557	−	0.345124i	$-0.112163\pi$
$930$	5.40229	+	10.1070i	0.177148	+	0.331422i
$931$	−4.13567			−0.135541
$932$	−5.39179	−	4.34160i	−0.176614	−	0.142214i
$933$	−2.68257	−	60.3334i	−0.0878234	−	1.97523i
$934$	28.7020	−	13.7388i	0.939157	−	0.449547i
$935$	−16.1616			−0.528541
$936$	−5.04044	+	35.1034i	−0.164752	+	1.14739i
$937$	−21.4368			−0.700311			−0.350156	−	0.936692i	$-0.613871\pi$
$937$	−21.4368			−0.700311			−0.350156	+	0.936692i	$0.613871\pi$
$938$	−18.9086	+	9.05098i	−0.617387	+	0.295525i
$939$	1.10091	+	24.7605i	0.0359269	+	0.808027i
$940$	−34.4004	+	42.7215i	−1.12202	+	1.39342i
$941$	38.2581			1.24718			0.623589	−	0.781752i	$-0.285674\pi$
$941$	38.2581			1.24718			0.623589	+	0.781752i	$0.285674\pi$
$942$	−3.21327	−	6.01164i	−0.104694	−	0.195870i
$943$		−	8.18249i		−	0.266458i
$944$	11.6308	−	2.53939i	0.378552	−	0.0826501i
$945$	27.4622	−	3.68253i	0.893344	−	0.119793i
$946$	3.40366	−	1.62923i	0.110662	−	0.0529708i
$947$			45.0385i			1.46355i	0.681544	+	0.731777i	$0.261309\pi$
$947$			45.0385i			1.46355i	−0.681544	+	0.731777i	$0.738691\pi$
$948$	−15.7881	+	21.4961i	−0.512775	+	0.698159i
$949$		−	54.1555i		−	1.75796i
$950$	−1.31079	−	2.73839i	−0.0425275	−	0.0888450i
$951$	2.51896	+	56.6538i	0.0816830	+	1.83712i
$952$	−9.36251	−	2.20679i	−0.303441	−	0.0715225i
$953$			49.2969i			1.59688i	0.602072	+	0.798442i	$0.294342\pi$
$953$			49.2969i			1.59688i	−0.602072	+	0.798442i	$0.705658\pi$
$954$	−15.9356	−	26.8699i	−0.515935	−	0.869946i
$955$	13.2970			0.430282
$956$	−21.8387	+	27.1212i	−0.706313	+	0.877162i
$957$	−34.5718	+	1.53715i	−1.11755	+	0.0496890i
$958$	17.9924	+	37.5883i	0.581309	+	1.21442i
$959$	−26.7970			−0.865321
$960$	−12.0588	+	27.1103i	−0.389198	+	0.874982i
$961$	26.2262			0.846007
$962$	−7.59098	−	15.8585i	−0.244743	−	0.511298i
$963$	−4.20686	−	47.2144i	−0.135564	−	1.52146i
$964$	−14.5496	+	18.0690i	−0.468610	+	0.581962i
$965$	7.32828			0.235906
$966$	−2.87540	−	5.37951i	−0.0925143	−	0.173083i
$967$			0.632369i			0.0203356i	0.999948	+	0.0101678i	$0.00323657\pi$
$967$			0.632369i			0.0203356i	−0.999948	+	0.0101678i	$0.996763\pi$
$968$	−53.7983	−	12.6805i	−1.72914	−	0.407567i
$969$	12.2342	−	0.543961i	0.393018	−	0.0174746i
$970$	−7.91457	−	16.5345i	−0.254121	−	0.530890i
$971$		−	21.9488i		−	0.704369i	−0.935931	−	0.352184i	$-0.885439\pi$
$971$		−	21.9488i		−	0.704369i	0.935931	−	0.352184i	$-0.114561\pi$
$972$	−27.9947	−	13.7222i	−0.897930	−	0.440138i
$973$		−	23.4337i		−	0.751251i
$974$	50.5182	−	24.1816i	1.61871	−	0.774827i
$975$	−2.99870	+	0.133329i	−0.0960352	+	0.00426996i
$976$	26.3965	−	5.76320i	0.844930	−	0.184476i
$977$		−	5.06944i		−	0.162186i	−0.996707	−	0.0810929i	$-0.974159\pi$
$977$		−	5.06944i		−	0.162186i	0.996707	−	0.0810929i	$-0.0258411\pi$
$978$	24.5583	−	13.1266i	0.785289	−	0.419744i
$979$	89.8861			2.87277
$980$	−2.14564	+	2.66465i	−0.0685401	+	0.0851192i
$981$	4.05152	+	45.4711i	0.129355	+	1.45178i
$982$	−26.9120	+	12.8820i	−0.858796	+	0.411080i
$983$	59.3291			1.89230			0.946152	−	0.323724i	$-0.104935\pi$
$983$	59.3291			1.89230			0.946152	+	0.323724i	$0.104935\pi$
$984$	−39.3866	−	7.45427i	−1.25560	−	0.237634i
$985$	−14.6496			−0.466775
$986$	6.29813	−	3.01473i	0.200573	−	0.0960086i
$987$	−55.1859	+	2.45370i	−1.75659	+	0.0781022i
$988$	−33.7059	−	27.1409i	−1.07233	−	0.863466i
$989$	−0.482816			−0.0153526
$990$	−43.1842	+	25.6111i	−1.37248	+	0.813974i
$991$			6.16294i			0.195772i	0.995198	+	0.0978861i	$0.0312081\pi$
$991$			6.16294i			0.195772i	−0.995198	+	0.0978861i	$0.968792\pi$
$992$	−7.59156	−	9.75343i	−0.241032	−	0.309672i
$993$	−1.80469	−	40.5892i	−0.0572702	−	1.28806i
$994$	18.2842	−	8.75211i	0.579940	−	0.277600i
$995$			45.7447i			1.45020i
$996$	−19.1566	+	26.0823i	−0.606999	+	0.826449i
$997$			29.0677i			0.920583i	0.887768	+	0.460292i	$0.152255\pi$
$997$			29.0677i			0.920583i	−0.887768	+	0.460292i	$0.847745\pi$
$998$	20.2532	+	42.3115i	0.641105	+	1.33935i
$999$	15.3194	−	2.05425i	0.484684	−	0.0649936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.15	✓	42
3.2	odd	2		552.2.j.d.323.28	yes	42
4.3	odd	2		2208.2.j.c.47.23		42
8.3	odd	2		552.2.j.d.323.27	yes	42
8.5	even	2		2208.2.j.d.47.23		42
12.11	even	2		2208.2.j.d.47.24		42
24.5	odd	2		2208.2.j.c.47.24		42
24.11	even	2	inner	552.2.j.c.323.16	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.15	✓	42	1.1	even	1	trivial
552.2.j.c.323.16	yes	42	24.11	even	2	inner
552.2.j.d.323.27	yes	42	8.3	odd	2
552.2.j.d.323.28	yes	42	3.2	odd	2
2208.2.j.c.47.23		42	4.3	odd	2
2208.2.j.c.47.24		42	24.5	odd	2
2208.2.j.d.47.23		42	8.5	even	2
2208.2.j.d.47.24		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)

\(f(q)\)	\(=\)	\(q+(-0.610595 - 1.27561i) q^{2} +(0.0769352 + 1.73034i) q^{3} +(-1.25435 + 1.55776i) q^{4} +2.14134 q^{5} +(2.16026 - 1.15468i) q^{6} +2.49021i q^{7} +(2.75299 + 0.648892i) q^{8} +(-2.98816 + 0.266248i) q^{9} +O(q^{10})\)	\(q+(-0.610595 - 1.27561i) q^{2} +(0.0769352 + 1.73034i) q^{3} +(-1.25435 + 1.55776i) q^{4} +2.14134 q^{5} +(2.16026 - 1.15468i) q^{6} +2.49021i q^{7} +(2.75299 + 0.648892i) q^{8} +(-2.98816 + 0.266248i) q^{9} +(-1.30749 - 2.73151i) q^{10} +5.52646i q^{11} +(-2.79196 - 2.05060i) q^{12} -4.17941i q^{13} +(3.17654 - 1.52051i) q^{14} +(0.164745 + 3.70525i) q^{15} +(-0.853230 - 3.90794i) q^{16} +1.36569i q^{17} +(2.16419 + 3.64915i) q^{18} -5.17716 q^{19} +(-2.68598 + 3.33570i) q^{20} +(-4.30892 + 0.191585i) q^{21} +(7.04960 - 3.37443i) q^{22} -1.00000 q^{23} +(-0.911003 + 4.81353i) q^{24} -0.414655 q^{25} +(-5.33128 + 2.55193i) q^{26} +(-0.690595 - 5.15006i) q^{27} +(-3.87916 - 3.12359i) q^{28} +3.61529 q^{29} +(4.62585 - 2.47256i) q^{30} +2.18490i q^{31} +(-4.46402 + 3.47456i) q^{32} +(-9.56267 + 0.425180i) q^{33} +(1.74208 - 0.833883i) q^{34} +5.33240i q^{35} +(3.33344 - 4.98881i) q^{36} +2.97461i q^{37} +(3.16115 + 6.60402i) q^{38} +(7.23180 - 0.321543i) q^{39} +(5.89509 + 1.38950i) q^{40} +8.18249i q^{41} +(2.87540 + 5.37951i) q^{42} +0.482816 q^{43} +(-8.60890 - 6.93210i) q^{44} +(-6.39868 + 0.570129i) q^{45} +(0.610595 + 1.27561i) q^{46} +12.8074 q^{47} +(6.69643 - 1.77704i) q^{48} +0.798829 q^{49} +(0.253186 + 0.528936i) q^{50} +(-2.36311 + 0.105069i) q^{51} +(6.51051 + 5.24242i) q^{52} -7.36333 q^{53} +(-6.14777 + 4.02553i) q^{54} +11.8340i q^{55} +(-1.61588 + 6.85553i) q^{56} +(-0.398306 - 8.95825i) q^{57} +(-2.20748 - 4.61169i) q^{58} +2.97621i q^{59} +(-5.97854 - 4.39104i) q^{60} +6.75457i q^{61} +(2.78707 - 1.33409i) q^{62} +(-0.663015 - 7.44117i) q^{63} +(7.15788 + 3.57278i) q^{64} -8.94954i q^{65} +(6.38128 + 11.9386i) q^{66} -5.95258 q^{67} +(-2.12741 - 1.71305i) q^{68} +(-0.0769352 - 1.73034i) q^{69} +(6.80205 - 3.25594i) q^{70} +5.75602 q^{71} +(-8.39914 - 1.20602i) q^{72} +12.9577 q^{73} +(3.79443 - 1.81628i) q^{74} +(-0.0319015 - 0.717494i) q^{75} +(6.49395 - 8.06477i) q^{76} -13.7621 q^{77} +(-4.82587 - 9.02860i) q^{78} -7.69927i q^{79} +(-1.82706 - 8.36824i) q^{80} +(8.85822 - 1.59119i) q^{81} +(10.4376 - 4.99619i) q^{82} -9.34193i q^{83} +(5.10644 - 6.95258i) q^{84} +2.92440i q^{85} +(-0.294805 - 0.615883i) q^{86} +(0.278143 + 6.25569i) q^{87} +(-3.58608 + 15.2143i) q^{88} -16.2647i q^{89} +(4.63426 + 7.81408i) q^{90} +10.4076 q^{91} +(1.25435 - 1.55776i) q^{92} +(-3.78062 + 0.168096i) q^{93} +(-7.82012 - 16.3372i) q^{94} -11.0861 q^{95} +(-6.35561 - 7.45696i) q^{96} +6.05323 q^{97} +(-0.487762 - 1.01899i) q^{98} +(-1.47141 - 16.5140i) 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

L-functions

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