LMFDB - Embedded newform 403.2.k.e.287.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.5
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.471037 + 1.44970i) q^{2} +(0.0410411 + 0.126311i) q^{3} +(-0.261732 - 0.190160i) q^{4} +1.10606 q^{5} -0.202446 q^{6} +(0.346937 + 0.252065i) q^{7} +(-2.06742 + 1.50207i) q^{8} +(2.41278 - 1.75299i) q^{9} +O(q^{10})$	\(q+(-0.471037 + 1.44970i) q^{2} +(0.0410411 + 0.126311i) q^{3} +(-0.261732 - 0.190160i) q^{4} +1.10606 q^{5} -0.202446 q^{6} +(0.346937 + 0.252065i) q^{7} +(-2.06742 + 1.50207i) q^{8} +(2.41278 - 1.75299i) q^{9} +(-0.520995 + 1.60346i) q^{10} +(2.52657 + 1.83566i) q^{11} +(0.0132776 - 0.0408641i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-0.528840 + 0.384225i) q^{14} +(0.0453939 + 0.139708i) q^{15} +(-1.40367 - 4.32005i) q^{16} +(0.591113 - 0.429469i) q^{17} +(1.40480 + 4.32354i) q^{18} +(-2.37130 + 7.29812i) q^{19} +(-0.289492 - 0.210328i) q^{20} +(-0.0176000 + 0.0541672i) q^{21} +(-3.85128 + 2.79812i) q^{22} +(4.52877 - 3.29035i) q^{23} +(-0.274578 - 0.199493i) q^{24} -3.77663 q^{25} -1.52431 q^{26} +(0.642786 + 0.467012i) q^{27} +(-0.0428722 - 0.131947i) q^{28} +(-0.261210 + 0.803923i) q^{29} -0.223917 q^{30} +(5.30572 - 1.68798i) q^{31} +1.81303 q^{32} +(-0.128172 + 0.394473i) q^{33} +(0.344166 + 1.05924i) q^{34} +(0.383733 + 0.278798i) q^{35} -0.964850 q^{36} -7.85694 q^{37} +(-9.46314 - 6.87537i) q^{38} +(-0.107447 + 0.0780648i) q^{39} +(-2.28669 + 1.66138i) q^{40} +(-0.826180 + 2.54272i) q^{41} +(-0.0702361 - 0.0510295i) q^{42} +(-2.99661 + 9.22262i) q^{43} +(-0.312217 - 0.960905i) q^{44} +(2.66868 - 1.93891i) q^{45} +(2.63681 + 8.11526i) q^{46} +(-3.00641 - 9.25277i) q^{47} +(0.488064 - 0.354599i) q^{48} +(-2.10629 - 6.48249i) q^{49} +(1.77894 - 5.47500i) q^{50} +(0.0785067 + 0.0570385i) q^{51} +(0.0999729 - 0.307685i) q^{52} +(-0.0102721 + 0.00746311i) q^{53} +(-0.979805 + 0.711870i) q^{54} +(2.79454 + 2.03035i) q^{55} -1.09589 q^{56} -1.01916 q^{57} +(-1.04241 - 0.757356i) q^{58} +(0.627425 + 1.93102i) q^{59} +(0.0146858 - 0.0451982i) q^{60} +0.398081 q^{61} +(-0.0521209 + 8.48684i) q^{62} +1.27895 q^{63} +(1.95334 - 6.01175i) q^{64} +(0.341791 + 1.05192i) q^{65} +(-0.511495 - 0.371623i) q^{66} +6.84483 q^{67} -0.236381 q^{68} +(0.601474 + 0.436996i) q^{69} +(-0.584928 + 0.424975i) q^{70} +(11.9766 - 8.70154i) q^{71} +(-2.35513 + 7.24834i) q^{72} +(-10.7647 - 7.82100i) q^{73} +(3.70091 - 11.3902i) q^{74} +(-0.154997 - 0.477032i) q^{75} +(2.00845 - 1.45923i) q^{76} +(0.413857 + 1.27372i) q^{77} +(-0.0625593 - 0.192538i) q^{78} +(2.72537 - 1.98010i) q^{79} +(-1.55254 - 4.77824i) q^{80} +(2.73219 - 8.40882i) q^{81} +(-3.29703 - 2.39543i) q^{82} +(3.26155 - 10.0380i) q^{83} +(0.0149069 - 0.0108305i) q^{84} +(0.653806 - 0.475018i) q^{85} +(-11.9586 - 8.68840i) q^{86} -0.112265 q^{87} -7.98079 q^{88} +(14.2343 + 10.3418i) q^{89} +(1.55380 + 4.78209i) q^{90} +(-0.132518 + 0.407849i) q^{91} -1.81102 q^{92} +(0.430964 + 0.600897i) q^{93} +14.8299 q^{94} +(-2.62280 + 8.07215i) q^{95} +(0.0744087 + 0.229007i) q^{96} +(6.29958 + 4.57691i) q^{97} +10.3898 q^{98} +9.31396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.471037	+	1.44970i	−0.333074	+	1.02510i	0.634589	+	0.772850i	$0.281169\pi$
$2$	−0.471037	+	1.44970i	−0.333074	+	1.02510i	−0.967663	+	0.252246i	$0.918831\pi$
$3$	0.0410411	+	0.126311i	0.0236951	+	0.0729259i	0.962205	−	0.272327i	$-0.0877932\pi$
$3$	0.0410411	+	0.126311i	0.0236951	+	0.0729259i	−0.938510	+	0.345253i	$0.887793\pi$
$4$	−0.261732	−	0.190160i	−0.130866	−	0.0950798i
$5$	1.10606			0.494645			0.247322	−	0.968933i	$-0.420449\pi$
$5$	1.10606			0.494645			0.247322	+	0.968933i	$0.420449\pi$
$6$	−0.202446			−0.0826483
$7$	0.346937	+	0.252065i	0.131130	+	0.0952715i	0.651417	−	0.758720i	$-0.274175\pi$
$7$	0.346937	+	0.252065i	0.131130	+	0.0952715i	−0.520287	+	0.853992i	$0.674175\pi$
$8$	−2.06742	+	1.50207i	−0.730944	+	0.531062i
$9$	2.41278	−	1.75299i	0.804260	−	0.584329i
$10$	−0.520995	+	1.60346i	−0.164753	+	0.507058i
$11$	2.52657	+	1.83566i	0.761790	+	0.553473i	0.899459	−	0.437005i	$-0.143961\pi$
$11$	2.52657	+	1.83566i	0.761790	+	0.553473i	−0.137669	+	0.990478i	$0.543961\pi$
$12$	0.0132776	−	0.0408641i	0.00383290	−	0.0117965i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−0.528840	+	0.384225i	−0.141338	+	0.102688i
$15$	0.0453939	+	0.139708i	0.0117206	+	0.0360724i
$16$	−1.40367	−	4.32005i	−0.350918	−	1.08001i
$17$	0.591113	−	0.429469i	0.143366	−	0.104161i	−0.513790	−	0.857916i	$-0.671759\pi$
$17$	0.591113	−	0.429469i	0.143366	−	0.104161i	0.657156	+	0.753754i	$0.271759\pi$
$18$	1.40480	+	4.32354i	0.331115	+	1.01907i
$19$	−2.37130	+	7.29812i	−0.544014	+	1.67430i	0.179309	+	0.983793i	$0.442614\pi$
$19$	−2.37130	+	7.29812i	−0.544014	+	1.67430i	−0.723323	+	0.690510i	$0.757386\pi$
$20$	−0.289492	−	0.210328i	−0.0647323	−	0.0470307i
$21$	−0.0176000	+	0.0541672i	−0.00384063	+	0.0118202i
$22$	−3.85128	+	2.79812i	−0.821095	+	0.596561i
$23$	4.52877	−	3.29035i	0.944314	−	0.686085i	−0.00514096	−	0.999987i	$-0.501636\pi$
$23$	4.52877	−	3.29035i	0.944314	−	0.686085i	0.949455	+	0.313902i	$0.101636\pi$
$24$	−0.274578	−	0.199493i	−0.0560480	−	0.0407213i
$25$	−3.77663			−0.755327
$26$	−1.52431			−0.298942
$27$	0.642786	+	0.467012i	0.123704	+	0.0898764i
$28$	−0.0428722	−	0.131947i	−0.00810208	−	0.0249356i
$29$	−0.261210	+	0.803923i	−0.0485056	+	0.149285i	−0.972376	−	0.233421i	$-0.925008\pi$
$29$	−0.261210	+	0.803923i	−0.0485056	+	0.149285i	0.923870	+	0.382706i	$0.125008\pi$
$30$	−0.223917			−0.0408815
$31$	5.30572	−	1.68798i	0.952936	−	0.303170i
$31$	5.30572	−	1.68798i	0.952936	−	0.303170i
$32$	1.81303			0.320502
$33$	−0.128172	+	0.394473i	−0.0223119	+	0.0686689i
$34$	0.344166	+	1.05924i	0.0590240	+	0.181657i
$35$	0.383733	+	0.278798i	0.0648627	+	0.0471255i
$36$	−0.964850			−0.160808
$37$	−7.85694			−1.29167			−0.645836	−	0.763476i	$-0.723491\pi$
$37$	−7.85694			−1.29167			−0.645836	+	0.763476i	$0.723491\pi$
$38$	−9.46314	−	6.87537i	−1.53512	−	1.11533i
$39$	−0.107447	+	0.0780648i	−0.0172053	+	0.0125004i
$40$	−2.28669	+	1.66138i	−0.361558	+	0.262687i
$41$	−0.826180	+	2.54272i	−0.129028	+	0.397106i	−0.994613	−	0.103655i	$-0.966946\pi$
$41$	−0.826180	+	2.54272i	−0.129028	+	0.397106i	0.865586	+	0.500761i	$0.166946\pi$
$42$	−0.0702361	−	0.0510295i	−0.0108377	−	0.00787403i
$43$	−2.99661	+	9.22262i	−0.456979	+	1.40644i	0.411817	+	0.911266i	$0.364894\pi$
$43$	−2.99661	+	9.22262i	−0.456979	+	1.40644i	−0.868796	+	0.495170i	$0.835106\pi$
$44$	−0.312217	−	0.960905i	−0.0470685	−	0.144862i
$45$	2.66868	−	1.93891i	0.397823	−	0.289035i
$46$	2.63681	+	8.11526i	0.388776	+	1.19653i
$47$	−3.00641	−	9.25277i	−0.438530	−	1.34966i	−0.889426	−	0.457079i	$-0.848896\pi$
$47$	−3.00641	−	9.25277i	−0.438530	−	1.34966i	0.450896	−	0.892576i	$-0.351104\pi$
$48$	0.488064	−	0.354599i	0.0704460	−	0.0511820i
$49$	−2.10629	−	6.48249i	−0.300899	−	0.926071i
$50$	1.77894	−	5.47500i	0.251580	−	0.774282i
$51$	0.0785067	+	0.0570385i	0.0109931	+	0.00798698i
$52$	0.0999729	−	0.307685i	0.0138637	−	0.0426682i
$53$	−0.0102721	+	0.00746311i	−0.00141098	+	0.00102514i	−0.588491	−	0.808504i	$-0.700278\pi$
$53$	−0.0102721	+	0.00746311i	−0.00141098	+	0.00102514i	0.587080	+	0.809529i	$0.300278\pi$
$54$	−0.979805	+	0.711870i	−0.133335	+	0.0968733i
$55$	2.79454	+	2.03035i	0.376816	+	0.273773i
$56$	−1.09589			−0.146444
$57$	−1.01916			−0.134991
$58$	−1.04241	−	0.757356i	−0.136875	−	0.0994457i
$59$	0.627425	+	1.93102i	0.0816838	+	0.251397i	0.983555	−	0.180608i	$-0.0578065\pi$
$59$	0.627425	+	1.93102i	0.0816838	+	0.251397i	−0.901871	+	0.432005i	$0.857806\pi$
$60$	0.0146858	−	0.0451982i	0.00189593	−	0.00583506i
$61$	0.398081			0.0509690			0.0254845	−	0.999675i	$-0.491887\pi$
$61$	0.398081			0.0509690			0.0254845	+	0.999675i	$0.491887\pi$
$62$	−0.0521209	+	8.48684i	−0.00661936	+	1.07783i
$63$	1.27895			0.161133
$64$	1.95334	−	6.01175i	0.244167	−	0.751469i
$65$	0.341791	+	1.05192i	0.0423940	+	0.130475i
$66$	−0.511495	−	0.371623i	−0.0629607	−	0.0457436i
$67$	6.84483			0.836229			0.418114	−	0.908394i	$-0.362691\pi$
$67$	6.84483			0.836229			0.418114	+	0.908394i	$0.362691\pi$
$68$	−0.236381			−0.0286654
$69$	0.601474	+	0.436996i	0.0724090	+	0.0526082i
$70$	−0.584928	+	0.424975i	−0.0699123	+	0.0507942i
$71$	11.9766	−	8.70154i	1.42137	−	1.03268i	0.429822	−	0.902914i	$-0.358576\pi$
$71$	11.9766	−	8.70154i	1.42137	−	1.03268i	0.991544	−	0.129769i	$-0.0414236\pi$
$72$	−2.35513	+	7.24834i	−0.277554	+	0.854225i
$73$	−10.7647	−	7.82100i	−1.25991	−	0.915379i	−0.261157	−	0.965296i	$-0.584104\pi$
$73$	−10.7647	−	7.82100i	−1.25991	−	0.915379i	−0.998753	+	0.0499174i	$0.984104\pi$
$74$	3.70091	−	11.3902i	0.430222	−	1.32409i
$75$	−0.154997	−	0.477032i	−0.0178975	−	0.0550829i
$76$	2.00845	−	1.45923i	0.230386	−	0.167385i
$77$	0.413857	+	1.27372i	0.0471633	+	0.145154i
$78$	−0.0625593	−	0.192538i	−0.00708344	−	0.0218006i
$79$	2.72537	−	1.98010i	0.306629	−	0.222779i	−0.423820	−	0.905746i	$-0.639311\pi$
$79$	2.72537	−	1.98010i	0.306629	−	0.222779i	0.730449	+	0.682968i	$0.239311\pi$
$80$	−1.55254	−	4.77824i	−0.173580	−	0.534223i
$81$	2.73219	−	8.40882i	0.303577	−	0.934314i
$82$	−3.29703	−	2.39543i	−0.364096	−	0.264531i
$83$	3.26155	−	10.0380i	0.358001	−	1.10181i	−0.596247	−	0.802801i	$-0.703342\pi$
$83$	3.26155	−	10.0380i	0.358001	−	1.10181i	0.954249	−	0.299014i	$-0.0966578\pi$
$84$	0.0149069	−	0.0108305i	0.00162648	−	0.00118170i
$85$	0.653806	−	0.475018i	0.0709152	−	0.0515229i
$86$	−11.9586	−	8.68840i	−1.28952	−	0.936894i
$87$	−0.112265			−0.0120361
$88$	−7.98079			−0.850755
$89$	14.2343	+	10.3418i	1.50883	+	1.09623i	0.966692	+	0.255944i	$0.0823863\pi$
$89$	14.2343	+	10.3418i	1.50883	+	1.09623i	0.542142	+	0.840287i	$0.317614\pi$
$90$	1.55380	+	4.78209i	0.163785	+	0.504077i
$91$	−0.132518	+	0.407849i	−0.0138917	+	0.0427542i
$92$	−1.81102			−0.188812
$93$	0.430964	+	0.600897i	0.0446889	+	0.0623101i
$94$	14.8299			1.52959
$95$	−2.62280	+	8.07215i	−0.269094	+	0.828185i
$96$	0.0744087	+	0.229007i	0.00759431	+	0.0233729i
$97$	6.29958	+	4.57691i	0.639625	+	0.464715i	0.859721	−	0.510763i	$-0.170637\pi$
$97$	6.29958	+	4.57691i	0.639625	+	0.464715i	−0.220096	+	0.975478i	$0.570637\pi$
$98$	10.3898			1.04953
$99$	9.31396			0.936088
$100$	0.988467	+	0.718163i	0.0988467	+	0.0718163i
$101$	6.52576	−	4.74124i	0.649337	−	0.471771i	−0.213708	−	0.976898i	$-0.568554\pi$
$101$	6.52576	−	4.74124i	0.649337	−	0.471771i	0.863045	+	0.505126i	$0.168554\pi$
$102$	−0.119669	+	0.0869443i	−0.0118490	+	0.00860877i
$103$	1.17006	−	3.60107i	0.115289	−	0.354824i	−0.876718	−	0.481005i	$-0.840272\pi$
$103$	1.17006	−	3.60107i	0.115289	−	0.354824i	0.992007	+	0.126181i	$0.0402719\pi$
$104$	−2.06742	−	1.50207i	−0.202728	−	0.147290i
$105$	−0.0194666	+	0.0599121i	−0.00189975	+	0.00584682i
$106$	−0.00598076	−	0.0184069i	−0.000580903	−	0.00178783i
$107$	5.06610	−	3.68074i	0.489759	−	0.355830i	−0.315333	−	0.948981i	$-0.602116\pi$
$107$	5.06610	−	3.68074i	0.489759	−	0.355830i	0.805091	+	0.593151i	$0.202116\pi$
$108$	−0.0794312	−	0.244464i	−0.00764327	−	0.0235236i
$109$	3.46784	+	10.6729i	0.332159	+	1.02228i	0.968105	+	0.250546i	$0.0806101\pi$
$109$	3.46784	+	10.6729i	0.332159	+	1.02228i	−0.635946	+	0.771734i	$0.719390\pi$
$110$	−4.25974	+	3.09488i	−0.406150	+	0.295086i
$111$	−0.322457	−	0.992421i	−0.0306063	−	0.0941964i
$112$	0.601947	−	1.85260i	0.0568787	−	0.175055i
$113$	−11.0955	−	8.06135i	−1.04378	−	0.758348i	−0.0727570	−	0.997350i	$-0.523180\pi$
$113$	−11.0955	−	8.06135i	−1.04378	−	0.758348i	−0.971019	+	0.239002i	$0.923180\pi$
$114$	0.480061	−	1.47748i	0.0449618	−	0.138378i
$115$	5.00909	−	3.63932i	0.467100	−	0.339368i
$116$	0.221241	−	0.160741i	0.0205417	−	0.0149244i
$117$	2.41278	+	1.75299i	0.223062	+	0.162064i
$118$	−3.09494			−0.284912
$119$	0.313333			0.0287232
$120$	−0.303700	−	0.220651i	−0.0277238	−	0.0201426i
$121$	−0.385275	−	1.18575i	−0.0350250	−	0.107796i
$122$	−0.187511	+	0.577099i	−0.0169764	+	0.0522481i
$123$	−0.355082			−0.0320167
$124$	−1.70967	−	0.567136i	−0.153533	−	0.0509303i
$125$	−9.70748			−0.868263
$126$	−0.602433	+	1.85410i	−0.0536690	+	0.165176i
$127$	3.03628	+	9.34470i	0.269426	+	0.829208i	0.990641	+	0.136496i	$0.0435842\pi$
$127$	3.03628	+	9.34470i	0.269426	+	0.829208i	−0.721214	+	0.692712i	$0.756416\pi$
$128$	10.7287	+	7.79486i	0.948293	+	0.688975i
$129$	−1.28791			−0.113394
$130$	−1.68598			−0.147870
$131$	−15.1892	−	11.0356i	−1.32709	−	0.964187i	−0.999815	−	0.0192575i	$-0.993870\pi$
$131$	−15.1892	−	11.0356i	−1.32709	−	0.964187i	−0.327275	−	0.944929i	$-0.606130\pi$
$132$	0.108560	−	0.0788731i	0.00944889	−	0.00686502i
$133$	−2.66229	+	1.93427i	−0.230850	+	0.167722i
$134$	−3.22417	+	9.92298i	−0.278526	+	0.857215i
$135$	0.710960	+	0.516542i	0.0611897	+	0.0444569i
$136$	−0.576988	+	1.77579i	−0.0494763	+	0.152273i
$137$	−1.86619	−	5.74353i	−0.159439	−	0.490703i	0.839145	−	0.543909i	$-0.183056\pi$
$137$	−1.86619	−	5.74353i	−0.159439	−	0.490703i	−0.998584	+	0.0532056i	$0.983056\pi$
$138$	−0.916832	+	0.666118i	−0.0780460	+	0.0567037i
$139$	−5.82041	−	17.9134i	−0.493681	−	1.51939i	−0.819003	−	0.573789i	$-0.805473\pi$
$139$	−5.82041	−	17.9134i	−0.493681	−	1.51939i	0.325322	−	0.945603i	$-0.394527\pi$
$140$	−0.0474192	−	0.145941i	−0.00400765	−	0.0123343i
$141$	1.04534	−	0.759487i	0.0880339	−	0.0639604i
$142$	6.97321	+	21.4613i	0.585179	+	1.80100i
$143$	−0.965065	+	2.97016i	−0.0807028	+	0.248378i
$144$	−10.9598	−	7.96273i	−0.913313	−	0.663560i
$145$	−0.288914	+	0.889187i	−0.0239930	+	0.0738429i
$146$	16.4087	−	11.9216i	1.35799	−	0.986641i
$147$	0.732369	−	0.532097i	0.0604048	−	0.0438866i
$148$	2.05641	+	1.49407i	0.169036	+	0.122812i
$149$	6.92836			0.567593			0.283797	−	0.958884i	$-0.408406\pi$
$149$	6.92836			0.567593			0.283797	+	0.958884i	$0.408406\pi$
$150$	0.764565			0.0624264
$151$	−7.40262	−	5.37832i	−0.602416	−	0.437681i	0.244319	−	0.969695i	$-0.421435\pi$
$151$	−7.40262	−	5.37832i	−0.602416	−	0.437681i	−0.846736	+	0.532014i	$0.821435\pi$
$152$	−6.05981	−	18.6502i	−0.491515	−	1.51273i
$153$	0.673373	−	2.07243i	0.0544390	−	0.167546i
$154$	−2.04146			−0.164505
$155$	5.86845	−	1.86701i	0.471365	−	0.149962i
$156$	0.0429671			0.00344012
$157$	−3.29431	+	10.1388i	−0.262914	+	0.809167i	0.729252	+	0.684245i	$0.239868\pi$
$157$	−3.29431	+	10.1388i	−0.262914	+	0.809167i	−0.992167	+	0.124922i	$0.960132\pi$
$158$	1.58681	+	4.88369i	0.126240	+	0.388525i
$159$	−0.00136425		0.000991188i	−0.000108192		7.86063e-5i
$160$	2.00532			0.158534
$161$	2.40058			0.189192
$162$	10.9033	+	7.92174i	0.856648	+	0.622391i
$163$	−9.58851	+	6.96646i	−0.751030	+	0.545655i	−0.896146	−	0.443760i	$-0.853644\pi$
$163$	−9.58851	+	6.96646i	−0.751030	+	0.545655i	0.145116	+	0.989415i	$0.453644\pi$
$164$	0.699761	−	0.508406i	0.0546421	−	0.0396998i
$165$	−0.141766	+	0.436310i	−0.0110364	+	0.0339667i
$166$	13.0158	+	9.45656i	1.01022	+	0.733971i
$167$	−3.49931	+	10.7698i	−0.270785	+	0.833389i	0.719519	+	0.694472i	$0.244362\pi$
$167$	−3.49931	+	10.7698i	−0.270785	+	0.833389i	−0.990304	+	0.138917i	$0.955638\pi$
$168$	−0.0449763	−	0.138423i	−0.00347000	−	0.0106796i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	0.380668	+	1.17158i	0.0291959	+	0.0898558i
$171$	7.07208	+	21.7656i	0.540815	+	1.66446i
$172$	2.53808	−	1.84402i	0.193527	−	0.140605i
$173$	−3.51634	−	10.8222i	−0.267342	−	0.822795i	−0.991145	−	0.132787i	$-0.957607\pi$
$173$	−3.51634	−	10.8222i	−0.267342	−	0.822795i	0.723802	−	0.690007i	$-0.242393\pi$
$174$	0.0528810	−	0.162751i	0.00400890	−	0.0123381i
$175$	−1.31025	−	0.951956i	−0.0990460	−	0.0719611i
$176$	4.38368	−	13.4916i	0.330433	−	1.01697i
$177$	−0.218159	+	0.158502i	−0.0163978	+	0.0119137i
$178$	−21.6975	+	15.7641i	−1.62629	+	1.18157i
$179$	−17.5087	−	12.7208i	−1.30866	−	0.950800i	−0.308665	−	0.951171i	$-0.599882\pi$
$179$	−17.5087	−	12.7208i	−1.30866	−	0.950800i	−1.00000		0.000370549i	$0.999882\pi$
$180$	−1.06718			−0.0795430
$181$	−22.0709			−1.64052			−0.820260	−	0.571991i	$-0.806171\pi$
$181$	−22.0709			−1.64052			−0.820260	+	0.571991i	$0.806171\pi$
$182$	−0.528840	−	0.384225i	−0.0392002	−	0.0284806i
$183$	0.0163377	+	0.0502821i	0.00120771	+	0.00371696i
$184$	−4.42056	+	13.6051i	−0.325888	+	1.00298i
$185$	−8.69024			−0.638919
$186$	−1.07412	+	0.341725i	−0.0787586	+	0.0250565i
$187$	2.28185			0.166865
$188$	−0.972630	+	2.99345i	−0.0709363	+	0.218320i
$189$	0.105289	+	0.324047i	0.00765868	+	0.0235710i
$190$	−10.4668	−	7.60457i	−0.759341	−	0.551694i
$191$	22.2117			1.60718			0.803591	−	0.595183i	$-0.202920\pi$
$191$	22.2117			1.60718			0.803591	+	0.595183i	$0.202920\pi$
$192$	0.839520			0.0605871
$193$	−19.2116	−	13.9580i	−1.38288	−	1.00472i	−0.996604	−	0.0823381i	$-0.973761\pi$
$193$	−19.2116	−	13.9580i	−1.38288	−	1.00472i	−0.386276	−	0.922383i	$-0.626239\pi$
$194$	−9.60251	+	6.97663i	−0.689420	+	0.500893i
$195$	−0.118843	+	0.0863443i	−0.00851050	+	0.00618324i
$196$	−0.681425	+	2.09721i	−0.0486732	+	0.149801i
$197$	−10.8927	−	7.91401i	−0.776073	−	0.563850i	0.127725	−	0.991810i	$-0.459233\pi$
$197$	−10.8927	−	7.91401i	−0.776073	−	0.563850i	−0.903798	+	0.427960i	$0.859233\pi$
$198$	−4.38722	+	13.5025i	−0.311786	+	0.959580i
$199$	4.16997	+	12.8338i	0.295601	+	0.909767i	0.983019	+	0.183504i	$0.0587442\pi$
$199$	4.16997	+	12.8338i	0.295601	+	0.909767i	−0.687418	+	0.726262i	$0.741256\pi$
$200$	7.80790	−	5.67277i	0.552102	−	0.401125i
$201$	0.280919	+	0.864580i	0.0198145	+	0.0609828i
$202$	3.79952	+	11.6937i	0.267333	+	0.822768i
$203$	−0.293264	+	0.213069i	−0.0205831	+	0.0149545i
$204$	−0.00970133	−	0.0298576i	−0.000679229	−	0.00209045i
$205$	−0.913804	+	2.81240i	−0.0638228	+	0.196426i
$206$	4.66935	+	3.39248i	0.325329	+	0.236365i
$207$	5.15900	−	15.8778i	0.358575	−	1.10358i
$208$	3.67486	−	2.66994i	0.254806	−	0.185127i
$209$	−19.3881	+	14.0863i	−1.34111	+	0.974371i
$210$	−0.0776853	−	0.0564417i	−0.00536079	−	0.00389485i
$211$	24.9673			1.71882			0.859411	−	0.511285i	$-0.170830\pi$
$211$	24.9673			1.71882			0.859411	+	0.511285i	$0.170830\pi$
$212$	0.00410772			0.000282119
$213$	1.59064	+	1.15567i	0.108989	+	0.0791849i
$214$	2.94966	+	9.07812i	0.201635	+	0.620567i
$215$	−3.31443	+	10.2008i	−0.226042	+	0.695686i
$216$	−2.03040			−0.138151
$217$	2.26623	+	0.751762i	0.153842	+	0.0510329i
$218$	−17.1061			−1.15857
$219$	0.546088	−	1.68068i	0.0369012	−	0.113570i
$220$	−0.345330	−	1.06282i	−0.0232822	−	0.0716551i
$221$	0.591113	+	0.429469i	0.0397626	+	0.0288892i
$222$	1.59061			0.106754
$223$	−2.13932			−0.143260			−0.0716299	−	0.997431i	$-0.522820\pi$
$223$	−2.13932			−0.143260			−0.0716299	+	0.997431i	$0.522820\pi$
$224$	0.629008	+	0.457001i	0.0420274	+	0.0305347i
$225$	−9.11219	+	6.62039i	−0.607479	+	0.441359i
$226$	16.9130	−	12.2880i	1.12503	−	0.817385i
$227$	−5.21256	+	16.0426i	−0.345970	+	1.06479i	0.615093	+	0.788455i	$0.289119\pi$
$227$	−5.21256	+	16.0426i	−0.345970	+	1.06479i	−0.961063	+	0.276331i	$0.910881\pi$
$228$	0.266746	+	0.193803i	0.0176657	+	0.0128349i
$229$	−6.04215	+	18.5958i	−0.399277	+	1.22885i	0.526304	+	0.850297i	$0.323578\pi$
$229$	−6.04215	+	18.5958i	−0.399277	+	1.22885i	−0.925580	+	0.378551i	$0.876422\pi$
$230$	2.91646	+	8.97596i	0.192306	+	0.591857i
$231$	−0.143900	+	0.104550i	−0.00946794	+	0.00687886i
$232$	−0.667517	−	2.05441i	−0.0438246	−	0.134878i
$233$	−6.50141	−	20.0093i	−0.425922	−	1.31085i	−0.902109	−	0.431508i	$-0.857982\pi$
$233$	−6.50141	−	20.0093i	−0.425922	−	1.31085i	0.476187	−	0.879344i	$-0.342018\pi$
$234$	−3.67782	+	2.67210i	−0.240427	+	0.174680i
$235$	−3.32527	−	10.2341i	−0.216916	−	0.667600i
$236$	0.202984	−	0.624720i	0.0132131	−	0.0406658i
$237$	0.361962	+	0.262981i	0.0235119	+	0.0170824i
$238$	−0.147592	+	0.454240i	−0.00956694	+	0.0294440i
$239$	−10.3802	+	7.54164i	−0.671438	+	0.487828i	−0.870506	−	0.492158i	$-0.836208\pi$
$239$	−10.3802	+	7.54164i	−0.671438	+	0.487828i	0.199069	+	0.979986i	$0.436208\pi$
$240$	0.539828	−	0.392208i	0.0348457	−	0.0253169i
$241$	16.1989	+	11.7692i	1.04346	+	0.758119i	0.970958	−	0.239250i	$-0.0769015\pi$
$241$	16.1989	+	11.7692i	1.04346	+	0.758119i	0.0725025	+	0.997368i	$0.476901\pi$
$242$	1.90047			0.122167
$243$	3.55785			0.228236
$244$	−0.104191	−	0.0756989i	−0.00667012	−	0.00484613i
$245$	−2.32968	−	7.17002i	−0.148838	−	0.458076i
$246$	0.167257	−	0.514764i	0.0106639	−	0.0328201i
$247$	−7.67370			−0.488266
$248$	−8.43371	+	11.4593i	−0.535541	+	0.727669i
$249$	1.40177			0.0888338
$250$	4.57259	−	14.0730i	0.289196	−	0.890053i
$251$	2.60232	+	8.00911i	0.164257	+	0.505531i	0.998981	−	0.0451380i	$-0.0143728\pi$
$251$	2.60232	+	8.00911i	0.164257	+	0.505531i	−0.834724	+	0.550669i	$0.814373\pi$
$252$	−0.334743	−	0.243205i	−0.0210868	−	0.0153205i
$253$	17.4822			1.09910
$254$	−14.9773			−0.939757
$255$	0.0868331	+	0.0630879i	0.00543770	+	0.00395072i
$256$	−6.12607	+	4.45085i	−0.382880	+	0.278178i
$257$	3.21682	−	2.33715i	0.200660	−	0.145788i	−0.482918	−	0.875666i	$-0.660423\pi$
$257$	3.21682	−	2.33715i	0.200660	−	0.145788i	0.683578	+	0.729878i	$0.260423\pi$
$258$	0.606652	−	1.86708i	0.0377685	−	0.116240i
$259$	−2.72586	−	1.98046i	−0.169377	−	0.123060i
$260$	0.110576	−	0.340318i	0.00685763	−	0.0211056i
$261$	0.779024	+	2.39759i	0.0482204	+	0.148407i
$262$	23.1531	−	16.8217i	1.43040	−	1.03925i
$263$	3.77970	+	11.6327i	0.233066	+	0.717305i	0.997372	+	0.0724504i	$0.0230819\pi$
$263$	3.77970	+	11.6327i	0.233066	+	0.717305i	−0.764306	+	0.644854i	$0.776918\pi$
$264$	−0.327540	−	1.00806i	−0.0201587	−	0.0620421i
$265$	−0.0113615	+	0.00825464i	−0.000697933	+	0.000507078i
$266$	−1.55008	−	4.77065i	−0.0950413	−	0.292507i
$267$	−0.722100	+	2.22239i	−0.0441918	+	0.136008i
$268$	−1.79151	−	1.30161i	−0.109434	−	0.0795085i
$269$	−7.84604	+	24.1476i	−0.478382	+	1.47231i	0.362960	+	0.931805i	$0.381766\pi$
$269$	−7.84604	+	24.1476i	−0.478382	+	1.47231i	−0.841342	+	0.540503i	$0.818234\pi$
$270$	−1.08372	+	0.787371i	−0.0659533	+	0.0479178i
$271$	−2.60163	+	1.89020i	−0.158038	+	0.114821i	−0.663994	−	0.747738i	$-0.731140\pi$
$271$	−2.60163	+	1.89020i	−0.158038	+	0.114821i	0.505956	+	0.862559i	$0.331140\pi$
$272$	−2.68506	−	1.95081i	−0.162805	−	0.118285i
$273$	−0.0569547			−0.00344706
$274$	9.20547			0.556122
$275$	−9.54194	−	6.93262i	−0.575400	−	0.418053i
$276$	−0.0743261	−	0.228752i	−0.00447391	−	0.0137693i
$277$	3.82572	−	11.7744i	0.229866	−	0.707453i	−0.767896	−	0.640575i	$-0.778696\pi$
$277$	3.82572	−	11.7744i	0.229866	−	0.707453i	0.997761	−	0.0668783i	$-0.0213039\pi$
$278$	28.7107			1.72195
$279$	9.84254	−	13.3736i	0.589257	−	0.800657i
$280$	−1.21211			−0.0724377
$281$	6.62245	−	20.3818i	0.395062	−	1.21588i	−0.533851	−	0.845579i	$-0.679256\pi$
$281$	6.62245	−	20.3818i	0.395062	−	1.21588i	0.928913	−	0.370298i	$-0.120744\pi$
$282$	0.608636	+	1.87319i	0.0362437	+	0.111547i
$283$	1.80992	+	1.31498i	0.107589	+	0.0781677i	0.640279	−	0.768143i	$-0.278819\pi$
$283$	1.80992	+	1.31498i	0.107589	+	0.0781677i	−0.532690	+	0.846310i	$0.678819\pi$
$284$	−4.78936			−0.284196
$285$	−1.12725			−0.0667724
$286$	−3.85128	−	2.79812i	−0.227731	−	0.165456i
$287$	−0.927563	+	0.673914i	−0.0547523	+	0.0397799i
$288$	4.37445	−	3.17822i	0.257767	−	0.187278i
$289$	−5.08832	+	15.6602i	−0.299313	+	0.921190i
$290$	−1.15297	−	0.837681i	−0.0677046	−	0.0491903i
$291$	−0.319575	+	0.983550i	−0.0187338	+	0.0576567i
$292$	1.33023	+	4.09402i	0.0778456	+	0.239584i
$293$	11.1743	−	8.11860i	0.652809	−	0.474293i	−0.211418	−	0.977396i	$-0.567808\pi$
$293$	11.1743	−	8.11860i	0.652809	−	0.474293i	0.864227	+	0.503102i	$0.167808\pi$
$294$	0.426410	+	1.31236i	0.0248688	+	0.0765381i
$295$	0.693969	+	2.13582i	0.0404044	+	0.124352i
$296$	16.2436	−	11.8017i	0.944141	−	0.685958i
$297$	0.766771	+	2.35988i	0.0444925	+	0.136934i
$298$	−3.26352	+	10.0441i	−0.189050	+	0.581838i
$299$	4.52877	+	3.29035i	0.261906	+	0.190286i
$300$	−0.0501445	+	0.154329i	−0.00289509	+	0.00891018i
$301$	−3.36433	+	2.44433i	−0.193917	+	0.140889i
$302$	11.2839	−	8.19822i	0.649314	−	0.471754i
$303$	0.866697	+	0.629693i	0.0497905	+	0.0361749i
$304$	34.8568			1.99917
$305$	0.440301			0.0252116
$306$	2.68722	+	1.95238i	0.153618	+	0.111610i
$307$	−2.98733	−	9.19404i	−0.170496	−	0.524732i	0.828903	−	0.559392i	$-0.188965\pi$
$307$	−2.98733	−	9.19404i	−0.170496	−	0.524732i	−0.999399	+	0.0346599i	$0.988965\pi$
$308$	0.133890	−	0.412072i	0.00762912	−	0.0234800i
$309$	0.502877			0.0286077
$310$	−0.0576488	+	9.38694i	−0.00327423	+	0.533143i
$311$	−4.22201			−0.239408			−0.119704	−	0.992810i	$-0.538195\pi$
$311$	−4.22201			−0.239408			−0.119704	+	0.992810i	$0.538195\pi$
$312$	0.104879	−	0.322786i	0.00593763	−	0.0182741i
$313$	2.30085	+	7.08128i	0.130052	+	0.400258i	0.994788	−	0.101969i	$-0.0325143\pi$
$313$	2.30085	+	7.08128i	0.130052	+	0.400258i	−0.864736	+	0.502227i	$0.832514\pi$
$314$	−13.1466	−	9.55155i	−0.741904	−	0.539025i
$315$	1.41459			0.0797034
$316$	−1.08985			−0.0613091
$317$	7.35020	+	5.34023i	0.412828	+	0.299937i	0.774746	−	0.632273i	$-0.217878\pi$
$317$	7.35020	+	5.34023i	0.412828	+	0.299937i	−0.361918	+	0.932210i	$0.617878\pi$
$318$	0.00207954	−	0.00151088i	0.000116615	−	8.47258e-5i
$319$	−2.13570	+	1.55168i	−0.119576	+	0.0868772i
$320$	2.16050	−	6.64935i	0.120776	−	0.371710i
$321$	0.672838	+	0.488845i	0.0375541	+	0.0272847i
$322$	−1.13076	+	3.48013i	−0.0630150	+	0.193940i
$323$	1.73261	+	5.33241i	0.0964048	+	0.296703i
$324$	−2.31412	+	1.68131i	−0.128562	+	0.0934060i
$325$	−1.16704	−	3.59179i	−0.0647359	−	0.199237i
$326$	−5.58276	−	17.1820i	−0.309200	−	0.951621i
$327$	−1.20579	+	0.876056i	−0.0666802	+	0.0484460i
$328$	−2.11128	−	6.49786i	−0.116576	−	0.358784i
$329$	1.28926	−	3.96794i	0.0710793	−	0.218760i
$330$	−0.565744	−	0.411037i	−0.0311432	−	0.0226268i
$331$	6.87193	−	21.1496i	0.377715	−	1.16249i	−0.563913	−	0.825834i	$-0.690705\pi$
$331$	6.87193	−	21.1496i	0.377715	−	1.16249i	0.941628	−	0.336654i	$-0.109295\pi$
$332$	−2.76248	+	2.00706i	−0.151611	+	0.110152i
$333$	−18.9571	+	13.7731i	−1.03884	+	0.754762i
$334$	−13.9647	−	10.1459i	−0.764113	−	0.555160i
$335$	7.57078			0.413636
$336$	0.258710			0.0141138
$337$	−7.28573	−	5.29339i	−0.396879	−	0.288349i	0.371390	−	0.928477i	$-0.378881\pi$
$337$	−7.28573	−	5.29339i	−0.396879	−	0.288349i	−0.768268	+	0.640128i	$0.778881\pi$
$338$	−0.471037	−	1.44970i	−0.0256211	−	0.0788535i
$339$	0.562869	−	1.73233i	0.0305709	−	0.0940875i
$340$	−0.261451			−0.0141792
$341$	16.5039	+	5.47471i	0.893734	+	0.296472i
$342$	−34.8849			−1.88636
$343$	1.83089	−	5.63489i	0.0988585	−	0.304255i
$344$	−7.65777	−	23.5682i	−0.412879	−	1.27071i
$345$	0.665266	+	0.483344i	0.0358167	+	0.0260224i
$346$	17.3453			0.932488
$347$	−0.0849528			−0.00456051			−0.00228025	−	0.999997i	$-0.500726\pi$
$347$	−0.0849528			−0.00456051			−0.00228025	+	0.999997i	$0.500726\pi$
$348$	0.0293834	+	0.0213483i	0.00157512	+	0.00114439i
$349$	8.80264	−	6.39550i	0.471195	−	0.342343i	−0.326712	−	0.945124i	$-0.605941\pi$
$349$	8.80264	−	6.39550i	0.471195	−	0.342343i	0.797907	+	0.602781i	$0.205941\pi$
$350$	1.99723	−	1.45108i	0.106757	−	0.0775632i
$351$	−0.245523	+	0.755641i	−0.0131050	+	0.0403331i
$352$	4.58075	+	3.32811i	0.244155	+	0.177389i
$353$	−7.48876	+	23.0480i	−0.398587	+	1.22672i	0.527546	+	0.849526i	$0.323112\pi$
$353$	−7.48876	+	23.0480i	−0.398587	+	1.22672i	−0.926133	+	0.377197i	$0.876888\pi$
$354$	−0.127020	−	0.390927i	−0.00675102	−	0.0207775i
$355$	13.2469	−	9.62442i	0.703071	−	0.510811i
$356$	−1.75898	−	5.41358i	−0.0932257	−	0.286919i
$357$	0.0128595	+	0.0395775i	0.000680598	+	0.00209467i
$358$	26.6887	−	19.3905i	1.41054	−	1.02482i
$359$	7.03258	+	21.6441i	0.371166	+	1.14233i	0.946029	+	0.324081i	$0.105055\pi$
$359$	7.03258	+	21.6441i	0.371166	+	1.14233i	−0.574864	+	0.818249i	$0.694945\pi$
$360$	−2.60491	+	8.01709i	−0.137291	+	0.422538i
$361$	−32.2681	−	23.4442i	−1.69832	−	1.23390i
$362$	10.3962	−	31.9963i	0.546414	−	1.68169i
$363$	0.133962	−	0.0973292i	0.00703119	−	0.00510846i
$364$	0.112241	−	0.0815477i	0.00588302	−	0.00427426i
$365$	−11.9064	−	8.65049i	−0.623208	−	0.452787i
$366$	−0.0805899			−0.00421250
$367$	−8.92455			−0.465858			−0.232929	−	0.972494i	$-0.574831\pi$
$367$	−8.92455			−0.465858			−0.232929	+	0.972494i	$0.574831\pi$
$368$	−20.5714	−	14.9460i	−1.07236	−	0.779113i
$369$	2.46397	+	7.58331i	0.128269	+	0.394771i
$370$	4.09343	−	12.5983i	0.212807	−	0.654953i
$371$	−0.00544495			−0.000282688
$372$	0.00146918	−	0.239226i	7.61735e−5	−	0.0124033i
$373$	9.07619			0.469948			0.234974	−	0.972002i	$-0.424500\pi$
$373$	9.07619			0.469948			0.234974	+	0.972002i	$0.424500\pi$
$374$	−1.07484	+	3.30801i	−0.0555785	+	0.171053i
$375$	−0.398405	−	1.22617i	−0.0205736	−	0.0633189i
$376$	20.1138	+	14.6136i	1.03729	+	0.753637i
$377$	−0.845295			−0.0435349
$378$	−0.519368			−0.0267134
$379$	−9.80998	−	7.12737i	−0.503905	−	0.366108i	0.306602	−	0.951838i	$-0.400808\pi$
$379$	−9.80998	−	7.12737i	−0.503905	−	0.366108i	−0.810507	+	0.585730i	$0.800808\pi$
$380$	2.22147	−	1.61399i	0.113959	−	0.0827961i
$381$	−1.05573	+	0.767033i	−0.0540867	+	0.0392963i
$382$	−10.4625	+	32.2004i	−0.535310	+	1.64751i
$383$	26.6284	+	19.3467i	1.36065	+	0.988569i	0.998403	+	0.0564861i	$0.0179897\pi$
$383$	26.6284	+	19.3467i	1.36065	+	0.988569i	0.362245	+	0.932083i	$0.382010\pi$
$384$	−0.544263	+	1.67507i	−0.0277743	+	0.0854805i
$385$	0.457750	+	1.40881i	0.0233291	+	0.0717996i
$386$	29.2844	−	21.2764i	1.49054	−	1.08294i
$387$	8.93698	+	27.5052i	0.454292	+	1.39817i
$388$	−0.778460	−	2.39585i	−0.0395203	−	0.121631i
$389$	7.98283	−	5.79987i	0.404746	−	0.294065i	−0.366726	−	0.930329i	$-0.619521\pi$
$389$	7.98283	−	5.79987i	0.404746	−	0.294065i	0.771471	+	0.636264i	$0.219521\pi$
$390$	−0.0691943	−	0.212958i	−0.00350379	−	0.0107836i
$391$	1.26392	−	3.88993i	0.0639190	−	0.196722i
$392$	14.0918	+	10.2383i	0.711741	+	0.517110i
$393$	0.770543	−	2.37149i	0.0388687	−	0.119626i
$394$	16.6038	−	12.0634i	0.836490	−	0.607745i
$395$	3.01443	−	2.19011i	0.151672	−	0.110196i
$396$	−2.43776	−	1.77114i	−0.122502	−	0.0890031i
$397$	−9.26761			−0.465128			−0.232564	−	0.972581i	$-0.574711\pi$
$397$	−9.26761			−0.465128			−0.232564	+	0.972581i	$0.574711\pi$
$398$	−20.5695			−1.03105
$399$	−0.353583	−	0.256893i	−0.0177013	−	0.0128608i
$400$	5.30115	+	16.3153i	0.265057	+	0.815763i
$401$	−2.94217	+	9.05508i	−0.146925	+	0.452189i	−0.997254	−	0.0740634i	$-0.976403\pi$
$401$	−2.94217	+	9.05508i	−0.146925	+	0.452189i	0.850328	+	0.526252i	$0.176403\pi$
$402$	−1.38571			−0.0691129
$403$	3.24493	+	4.52443i	0.161641	+	0.225378i
$404$	−2.60960			−0.129832
$405$	3.02197	−	9.30066i	0.150163	−	0.462153i
$406$	−0.170749	−	0.525510i	−0.00847411	−	0.0260806i
$407$	−19.8511	−	14.4227i	−0.983983	−	0.714906i
$408$	−0.247982			−0.0122770
$409$	−3.20698			−0.158575			−0.0792875	−	0.996852i	$-0.525265\pi$
$409$	−3.20698			−0.158575			−0.0792875	+	0.996852i	$0.525265\pi$
$410$	−3.64671	−	2.64949i	−0.180098	−	0.130849i
$411$	0.648883	−	0.471441i	0.0320071	−	0.0232545i
$412$	−0.991021	+	0.720019i	−0.0488241	+	0.0354728i
$413$	−0.269064	+	0.828093i	−0.0132398	+	0.0407478i
$414$	20.5880	+	14.9580i	1.01184	+	0.735148i
$415$	3.60747	−	11.1026i	0.177083	−	0.545007i
$416$	0.560257	+	1.72429i	0.0274689	+	0.0845405i
$417$	2.02379	−	1.47037i	0.0991053	−	0.0720042i
$418$	−11.2884	−	34.7423i	−0.552136	−	1.69930i
$419$	0.168041	+	0.517178i	0.00820936	+	0.0252658i	0.955077	−	0.296357i	$-0.0957718\pi$
$419$	0.168041	+	0.517178i	0.00820936	+	0.0252658i	−0.946868	+	0.321623i	$0.895772\pi$
$420$	0.0164879	−	0.0119792i	0.000804527	−	0.000584523i
$421$	−11.0922	−	34.1384i	−0.540603	−	1.66381i	−0.731221	−	0.682141i	$-0.761049\pi$
$421$	−11.0922	−	34.1384i	−0.540603	−	1.66381i	0.190618	−	0.981664i	$-0.438951\pi$
$422$	−11.7606	+	36.1953i	−0.572495	+	1.76196i
$423$	−23.4738	−	17.0547i	−1.14134	−	0.829229i
$424$	0.0100266	−	0.0308588i	0.000486936	−	0.00149864i
$425$	−2.23242	+	1.62195i	−0.108288	+	0.0786759i
$426$	−2.42462	+	1.76159i	−0.117473	+	0.0853495i
$427$	0.138109	+	0.100342i	0.00668357	+	0.00485589i
$428$	−2.02589			−0.0979251
$429$	−0.414773			−0.0200254
$430$	−13.2269	−	9.60988i	−0.637856	−	0.463430i
$431$	−1.31981	−	4.06197i	−0.0635732	−	0.195658i	0.914225	−	0.405207i	$-0.132801\pi$
$431$	−1.31981	−	4.06197i	−0.0635732	−	0.195658i	−0.977798	+	0.209549i	$0.932801\pi$
$432$	1.11525	−	3.43240i	0.0536577	−	0.165142i
$433$	−9.45085			−0.454179			−0.227090	−	0.973874i	$-0.572921\pi$
$433$	−9.45085			−0.454179			−0.227090	+	0.973874i	$0.572921\pi$
$434$	−2.15731	+	2.93126i	−0.103554	+	0.140705i
$435$	−0.124172			−0.00595358
$436$	1.12191	−	3.45289i	0.0537298	−	0.165363i
$437$	13.2742	+	40.8539i	0.634993	+	1.95431i
$438$	2.17927	+	1.58333i	0.104129	+	0.0756545i
$439$	−3.77467			−0.180155			−0.0900776	−	0.995935i	$-0.528711\pi$
$439$	−3.77467			−0.180155			−0.0900776	+	0.995935i	$0.528711\pi$
$440$	−8.82723			−0.420821
$441$	−16.4457	−	11.9485i	−0.783131	−	0.568978i
$442$	−0.901039	+	0.654643i	−0.0428581	+	0.0311382i
$443$	0.981633	−	0.713198i	0.0466388	−	0.0338851i	−0.564222	−	0.825623i	$-0.690824\pi$
$443$	0.981633	−	0.713198i	0.0466388	−	0.0338851i	0.610860	+	0.791738i	$0.290824\pi$
$444$	−0.104321	+	0.321067i	−0.00495085	+	0.0152372i
$445$	15.7440	+	11.4387i	0.746336	+	0.542245i
$446$	1.00770	−	3.10139i	0.0477161	−	0.146855i
$447$	0.284347	+	0.875131i	0.0134492	+	0.0413923i
$448$	2.19303	−	1.59333i	0.103611	−	0.0752779i
$449$	−7.19533	−	22.1449i	−0.339569	−	1.04508i	−0.964428	−	0.264347i	$-0.914844\pi$
$449$	−7.19533	−	22.1449i	−0.339569	−	1.04508i	0.624859	−	0.780738i	$-0.285156\pi$
$450$	−5.30543	−	16.3284i	−0.250100	−	0.769730i
$451$	−6.75498	+	4.90778i	−0.318080	+	0.231098i
$452$	1.37111	+	4.21983i	0.0644914	+	0.198484i
$453$	0.375531	−	1.15577i	0.0176440	−	0.0543027i
$454$	−20.8017	−	15.1133i	−0.976274	−	0.709304i
$455$	−0.146573	+	0.451105i	−0.00687145	+	0.0211481i
$456$	2.10703	−	1.53085i	0.0986706	−	0.0716884i
$457$	−10.7108	+	7.78186i	−0.501030	+	0.364020i	−0.809410	−	0.587243i	$-0.800213\pi$
$457$	−10.7108	+	7.78186i	−0.501030	+	0.364020i	0.308380	+	0.951263i	$0.400213\pi$
$458$	−24.1124	−	17.5187i	−1.12670	−	0.818594i
$459$	0.580526			0.0270966
$460$	−2.00309			−0.0933947
$461$	−16.2689	−	11.8201i	−0.757720	−	0.550516i	0.140490	−	0.990082i	$-0.455132\pi$
$461$	−16.2689	−	11.8201i	−0.757720	−	0.550516i	−0.898210	+	0.439566i	$0.855132\pi$
$462$	−0.0837836	−	0.257860i	−0.00389797	−	0.0119967i
$463$	−11.2717	+	34.6906i	−0.523839	+	1.61221i	0.242763	+	0.970086i	$0.421946\pi$
$463$	−11.2717	+	34.6906i	−0.523839	+	1.61221i	−0.766601	+	0.642124i	$0.778054\pi$
$464$	3.83964			0.178251
$465$	0.476672	+	0.664628i	0.0221051	+	0.0308214i
$466$	32.0700			1.48561
$467$	−12.3568	+	38.0302i	−0.571803	+	1.75983i	0.0750142	+	0.997182i	$0.476100\pi$
$467$	−12.3568	+	38.0302i	−0.571803	+	1.75983i	−0.646817	+	0.762645i	$0.723900\pi$
$468$	−0.298155	−	0.917627i	−0.0137822	−	0.0424173i
$469$	2.37473	+	1.72534i	0.109655	+	0.0796688i
$470$	16.4028			0.756603
$471$	−1.41585			−0.0652391
$472$	−4.19767	−	3.04979i	−0.193214	−	0.140378i
$473$	−24.5008	+	17.8009i	−1.12655	+	0.818484i
$474$	−0.551741	+	0.400864i	−0.0253423	+	0.0184123i
$475$	8.95554	−	27.5623i	0.410908	−	1.26465i
$476$	−0.0820094	−	0.0595833i	−0.00375889	−	0.00273100i
$477$	−0.0117016	+	0.0360137i	−0.000535777	+	0.00164895i
$478$	−6.04369	−	18.6006i	−0.276432	−	0.850770i
$479$	−8.03313	+	5.83641i	−0.367043	+	0.266672i	−0.755984	−	0.654590i	$-0.772841\pi$
$479$	−8.03313	+	5.83641i	−0.367043	+	0.266672i	0.388941	+	0.921263i	$0.372841\pi$
$480$	0.0823005	+	0.253295i	0.00375649	+	0.0115613i
$481$	−2.42793	−	7.47239i	−0.110704	−	0.340712i
$482$	−24.6921	+	17.9398i	−1.12469	+	0.817138i
$483$	0.0985224	+	0.303221i	0.00448292	+	0.0137970i
$484$	−0.124644	+	0.383614i	−0.00566562	+	0.0174370i
$485$	6.96771	+	5.06234i	0.316387	+	0.229869i
$486$	−1.67588	+	5.15782i	−0.0760194	+	0.233964i
$487$	24.9145	−	18.1014i	1.12898	−	0.820255i	0.143437	−	0.989659i	$-0.454185\pi$
$487$	24.9145	−	18.1014i	1.12898	−	0.820255i	0.985547	+	0.169405i	$0.0541846\pi$
$488$	−0.823001	+	0.597945i	−0.0372555	+	0.0270677i
$489$	−1.27347	−	0.925227i	−0.0575881	−	0.0418402i
$490$	11.4918			0.519146
$491$	25.1650			1.13568			0.567839	−	0.823139i	$-0.307779\pi$
$491$	25.1650			1.13568			0.567839	+	0.823139i	$0.307779\pi$
$492$	0.0929364	+	0.0675223i	0.00418990	+	0.00304414i
$493$	0.190855	+	0.587391i	0.00859568	+	0.0264548i
$494$	3.61460	−	11.1246i	0.162628	−	0.500519i
$495$	10.3018			0.463031
$496$	−14.7397	−	20.5516i	−0.661830	−	0.922796i
$497$	6.34849			0.284769
$498$	−0.660288	+	2.03216i	−0.0295882	+	0.0910631i
$499$	5.57046	+	17.1441i	0.249368	+	0.767476i	0.994887	+	0.100992i	$0.0322016\pi$
$499$	5.57046	+	17.1441i	0.249368	+	0.767476i	−0.745519	+	0.666484i	$0.767798\pi$
$500$	2.54076	+	1.84597i	0.113626	+	0.0825543i
$501$	−1.50396			−0.0671920
$502$	−12.8366			−0.572927
$503$	11.3942	+	8.27839i	0.508044	+	0.369115i	0.812081	−	0.583545i	$-0.198335\pi$
$503$	11.3942	+	8.27839i	0.508044	+	0.369115i	−0.304037	+	0.952660i	$0.598335\pi$
$504$	−2.64413	+	1.92107i	−0.117779	+	0.0855714i
$505$	7.21788	−	5.24410i	0.321191	−	0.233359i
$506$	−8.23479	+	25.3441i	−0.366081	+	1.12668i
$507$	−0.107447	−	0.0780648i	−0.00477189	−	0.00346698i
$508$	0.982294	−	3.02319i	0.0435822	−	0.134132i
$509$	6.77391	+	20.8479i	0.300248	+	0.924069i	0.981408	+	0.191934i	$0.0614760\pi$
$509$	6.77391	+	20.8479i	0.300248	+	0.924069i	−0.681160	+	0.732135i	$0.738524\pi$
$510$	−0.132360	+	0.0961655i	−0.00586102	+	0.00425828i
$511$	−1.76327	−	5.42679i	−0.0780026	−	0.240067i
$512$	4.62919	+	14.2472i	0.204583	+	0.629643i
$513$	−4.93255	+	3.58370i	−0.217777	+	0.158224i
$514$	1.87294	+	5.76432i	0.0826119	+	0.254253i
$515$	1.29416	−	3.98300i	0.0570273	−	0.175512i
$516$	0.337087	+	0.244908i	0.0148394	+	0.0107815i
$517$	9.38906	−	28.8965i	0.412930	−	1.27087i
$518$	4.15506	−	3.01883i	0.182563	−	0.132640i
$519$	1.22265	−	0.888308i	0.0536684	−	0.0389924i
$520$	−2.28669	−	1.66138i	−0.100278	−	0.0728563i
$521$	9.06077			0.396960			0.198480	−	0.980105i	$-0.436400\pi$
$521$	9.06077			0.396960			0.198480	+	0.980105i	$0.436400\pi$
$522$	−3.84274			−0.168192
$523$	36.1764	+	26.2837i	1.58188	+	1.14930i	0.914497	+	0.404592i	$0.132587\pi$
$523$	36.1764	+	26.2837i	1.58188	+	1.14930i	0.667385	+	0.744713i	$0.267413\pi$
$524$	1.87698	+	5.77676i	0.0819964	+	0.252359i
$525$	0.0664686	−	0.204569i	0.00290093	−	0.00892814i
$526$	−18.6444			−0.812934
$527$	2.41135	−	3.27643i	0.105040	−	0.142724i
$528$	1.88405			0.0819929
$529$	2.57601	−	7.92816i	0.112001	−	0.344702i
$530$	−0.00661508	−	0.0203591i	−0.000287340	−	0.000884343i
$531$	4.89888	+	3.55925i	0.212593	+	0.154458i
$532$	1.06463			0.0461575
$533$	−2.67357			−0.115805
$534$	−2.88168	−	2.09366i	−0.124702	−	0.0906016i
$535$	5.60341	−	4.07112i	0.242257	−	0.176010i
$536$	−14.1512	+	10.2814i	−0.611237	+	0.444090i
$537$	0.888210	−	2.73363i	0.0383291	−	0.117965i
$538$	−31.3112	−	22.7489i	−1.34992	−	0.980774i
$539$	6.57798	−	20.2449i	0.283333	−	0.872011i
$540$	−0.0878556	−	0.270392i	−0.00378070	−	0.0116358i
$541$	3.99147	−	2.89997i	0.171607	−	0.124680i	−0.498667	−	0.866794i	$-0.666177\pi$
$541$	3.99147	−	2.89997i	0.171607	−	0.124680i	0.670273	+	0.742114i	$0.266177\pi$
$542$	−1.51476	−	4.66195i	−0.0650645	−	0.200248i
$543$	−0.905815	−	2.78781i	−0.0388722	−	0.119636i
$544$	1.07171	−	0.778640i	0.0459490	−	0.0333839i
$545$	3.83564	+	11.8049i	0.164301	+	0.505665i
$546$	0.0268278	−	0.0825675i	0.00114812	−	0.00353356i
$547$	16.1500	+	11.7337i	0.690526	+	0.501696i	0.876833	−	0.480795i	$-0.159652\pi$
$547$	16.1500	+	11.7337i	0.690526	+	0.501696i	−0.186307	+	0.982492i	$0.559652\pi$
$548$	−0.603747	+	1.85814i	−0.0257908	+	0.0793759i
$549$	0.960482	−	0.697831i	0.0409924	−	0.0297827i
$550$	14.5449	−	10.5675i	0.620195	−	0.450598i
$551$	−5.24772	−	3.81269i	−0.223560	−	0.162426i
$552$	−1.89990			−0.0808652
$553$	1.44465			0.0614327
$554$	15.2673	+	11.0923i	0.648645	+	0.471268i
$555$	−0.356657	−	1.09768i	−0.0151392	−	0.0465938i
$556$	−1.88301	+	5.79532i	−0.0798575	+	0.245776i
$557$	−39.4508			−1.67158			−0.835792	−	0.549046i	$-0.814991\pi$
$557$	−39.4508			−1.67158			−0.835792	+	0.549046i	$0.814991\pi$
$558$	14.7516	+	20.5682i	0.624483	+	0.870723i
$559$	−9.69724			−0.410149
$560$	0.665789	−	2.04909i	0.0281347	−	0.0865898i
$561$	0.0936496	+	0.288224i	0.00395389	+	0.0121688i
$562$	26.4282	+	19.2012i	1.11480	+	0.809953i
$563$	11.4008			0.480486			0.240243	−	0.970713i	$-0.422773\pi$
$563$	11.4008			0.480486			0.240243	+	0.970713i	$0.422773\pi$
$564$	−0.418024			−0.0176020
$565$	−12.2723	−	8.91633i	−0.516298	−	0.375113i
$566$	−2.75888	+	2.00444i	−0.115964	+	0.0842531i
$567$	3.06747	−	2.22865i	0.128822	−	0.0935943i
$568$	−11.6905	+	35.9795i	−0.490521	+	1.50967i
$569$	11.2063	+	8.14185i	0.469792	+	0.341324i	0.797360	−	0.603504i	$-0.206229\pi$
$569$	11.2063	+	8.14185i	0.469792	+	0.341324i	−0.327568	+	0.944828i	$0.606229\pi$
$570$	0.530976	−	1.63418i	0.0222401	−	0.0684481i
$571$	−3.40579	−	10.4820i	−0.142528	−	0.438656i	0.854157	−	0.520016i	$-0.174074\pi$
$571$	−3.40579	−	10.4820i	−0.142528	−	0.438656i	−0.996685	+	0.0813593i	$0.974074\pi$
$572$	0.817394	−	0.593872i	0.0341770	−	0.0248310i
$573$	0.911591	+	2.80559i	0.0380823	+	0.117205i
$574$	−0.540059	−	1.66213i	−0.0225416	−	0.0693760i
$575$	−17.1035	+	12.4264i	−0.713266	+	0.518218i
$576$	−5.82555	−	17.9292i	−0.242731	−	0.747050i
$577$	12.0642	−	37.1298i	0.502240	−	1.54574i	−0.303122	−	0.952952i	$-0.598029\pi$
$577$	12.0642	−	37.1298i	0.502240	−	1.54574i	0.805362	−	0.592784i	$-0.201971\pi$
$578$	−20.3059	−	14.7531i	−0.844615	−	0.613649i
$579$	0.974595	−	2.99950i	0.0405028	−	0.124655i
$580$	0.244706	−	0.177789i	0.0101609	−	0.00738229i
$581$	3.66178	−	2.66044i	0.151916	−	0.110374i
$582$	−1.27533	−	0.926578i	−0.0528639	−	0.0384079i
$583$	−0.0396529			−0.00164226
$584$	34.0029			1.40705
$585$	2.66868	+	1.93891i	0.110336	+	0.0801640i
$586$	6.50606	+	20.0236i	0.268763	+	0.827166i
$587$	−7.90510	+	24.3294i	−0.326279	+	1.00418i	0.644582	+	0.764536i	$0.277032\pi$
$587$	−7.90510	+	24.3294i	−0.326279	+	1.00418i	−0.970860	+	0.239647i	$0.922968\pi$
$588$	−0.292868			−0.0120777
$589$	−0.262388	+	42.7245i	−0.0108115	+	1.76043i
$590$	−3.42319			−0.140930
$591$	0.552582	−	1.70067i	0.0227302	−	0.0699563i
$592$	11.0285	+	33.9424i	0.453271	+	1.39502i
$593$	10.8148	+	7.85742i	0.444111	+	0.322665i	0.787266	−	0.616613i	$-0.211496\pi$
$593$	10.8148	+	7.85742i	0.444111	+	0.322665i	−0.343155	+	0.939279i	$0.611496\pi$
$594$	−3.78230			−0.155190
$595$	0.346565			0.0142078
$596$	−1.81338	−	1.31749i	−0.0742788	−	0.0539667i
$597$	−1.44992	+	1.05343i	−0.0593413	+	0.0431140i
$598$	−6.90325	+	5.01550i	−0.282295	+	0.205099i
$599$	−0.378710	+	1.16555i	−0.0154737	+	0.0476231i	−0.958495	−	0.285109i	$-0.907970\pi$
$599$	−0.378710	+	1.16555i	−0.0154737	+	0.0476231i	0.943022	+	0.332732i	$0.107970\pi$
$600$	1.03698	+	0.753410i	0.0423345	+	0.0307578i
$601$	−14.4942	+	44.6087i	−0.591233	+	1.81963i	−0.0185824	+	0.999827i	$0.505915\pi$
$601$	−14.4942	+	44.6087i	−0.591233	+	1.81963i	−0.572650	+	0.819800i	$0.694085\pi$
$602$	−1.95883	−	6.02866i	−0.0798360	−	0.245710i
$603$	16.5151	−	11.9989i	0.672546	−	0.488633i
$604$	0.914765	+	2.81536i	0.0372213	+	0.114555i
$605$	−0.426137	−	1.31151i	−0.0173249	−	0.0533206i
$606$	−1.32111	+	0.959846i	−0.0536666	+	0.0389911i
$607$	9.05718	+	27.8751i	0.367620	+	1.13142i	0.948324	+	0.317302i	$0.102777\pi$
$607$	9.05718	+	27.8751i	0.367620	+	1.13142i	−0.580705	+	0.814114i	$0.697223\pi$
$608$	−4.29924	+	13.2317i	−0.174357	+	0.536617i
$609$	−0.0389489	−	0.0282981i	−0.00157829	−	0.00114670i
$610$	−0.207398	+	0.638306i	−0.00839731	+	0.0258443i
$611$	7.87088	−	5.71853i	0.318422	−	0.231347i
$612$	−0.570336	+	0.414373i	−0.0230545	+	0.0167500i
$613$	−0.610236	−	0.443363i	−0.0246472	−	0.0179072i	0.575393	−	0.817877i	$-0.304849\pi$
$613$	−0.610236	−	0.443363i	−0.0246472	−	0.0179072i	−0.600041	+	0.799970i	$0.704849\pi$
$614$	14.7358			0.594688
$615$	−0.392742			−0.0158369
$616$	−2.76883	−	2.01168i	−0.111559	−	0.0810527i
$617$	3.91473	+	12.0483i	0.157601	+	0.485046i	0.998415	−	0.0562780i	$-0.0179233\pi$
$617$	3.91473	+	12.0483i	0.157601	+	0.485046i	−0.840814	+	0.541324i	$0.817923\pi$
$618$	−0.236874	+	0.729023i	−0.00952847	+	0.0293256i
$619$	−17.7553			−0.713645			−0.356822	−	0.934172i	$-0.616140\pi$
$619$	−17.7553			−0.713645			−0.356822	+	0.934172i	$0.616140\pi$
$620$	−1.89099	−	0.627286i	−0.0759441	−	0.0251924i
$621$	4.44766			0.178479
$622$	1.98872	−	6.12066i	0.0797405	−	0.245416i
$623$	2.33160	+	7.17593i	0.0934136	+	0.287498i
$624$	0.488064	+	0.354599i	0.0195382	+	0.0141953i
$625$	8.14612			0.325845
$626$	−11.3496			−0.453619
$627$	−2.57497	−	1.87083i	−0.102835	−	0.0747136i
$628$	2.79023	−	2.02722i	0.111342	−	0.0808948i
$629$	−4.64434	+	3.37431i	−0.185182	+	0.134542i
$630$	−0.666327	+	2.05074i	−0.0265471	+	0.0817036i
$631$	−30.6031	−	22.2344i	−1.21829	−	0.885138i	−0.222332	−	0.974971i	$-0.571367\pi$
$631$	−30.6031	−	22.2344i	−1.21829	−	0.885138i	−0.995957	+	0.0898327i	$0.971367\pi$
$632$	−2.66025	+	8.18741i	−0.105819	+	0.325678i
$633$	1.02469	+	3.15366i	0.0407276	+	0.125347i
$634$	−11.2040	+	8.14016i	−0.444967	+	0.323287i
$635$	3.35830	+	10.3358i	0.133270	+	0.410164i
$636$	0.000168585	0	0.000518852i	6.68484e−6	0	2.05738e-5i
$637$	5.51434	−	4.00640i	0.218486	−	0.158739i
$638$	−1.24348	−	3.82703i	−0.0492297	−	0.151514i
$639$	13.6433	−	41.9898i	0.539721	−	1.66109i
$640$	11.8666	+	8.62158i	0.469068	+	0.340798i
$641$	4.21134	−	12.9612i	0.166338	−	0.511935i	−0.832795	−	0.553582i	$-0.813260\pi$
$641$	4.21134	−	12.9612i	0.166338	−	0.511935i	0.999132	+	0.0416470i	$0.0132605\pi$
$642$	−1.02561	+	0.745151i	−0.0404777	+	0.0294088i
$643$	−17.0074	+	12.3566i	−0.670707	+	0.487297i	−0.870262	−	0.492590i	$-0.836050\pi$
$643$	−17.0074	+	12.3566i	−0.670707	+	0.487297i	0.199555	+	0.979887i	$0.436050\pi$
$644$	−0.628310	−	0.456494i	−0.0247589	−	0.0179884i
$645$	−1.42450			−0.0560897
$646$	−8.54654			−0.336259
$647$	11.0461	+	8.02546i	0.434267	+	0.315513i	0.783353	−	0.621577i	$-0.213508\pi$
$647$	11.0461	+	8.02546i	0.434267	+	0.315513i	−0.349086	+	0.937091i	$0.613508\pi$
$648$	6.98205	+	21.4885i	0.274281	+	0.844150i
$649$	−1.95946	+	6.03059i	−0.0769154	+	0.236721i
$650$	5.75676			0.225799
$651$	−0.00194746	+	0.317104i	−7.63270e−5	+	0.0124283i
$652$	3.83436			0.150165
$653$	−0.409437	+	1.26012i	−0.0160225	+	0.0493122i	−0.958748	−	0.284257i	$-0.908253\pi$
$653$	−0.409437	+	1.26012i	−0.0160225	+	0.0493122i	0.942726	+	0.333569i	$0.108253\pi$
$654$	−0.702051	−	2.16069i	−0.0274524	−	0.0844897i
$655$	−16.8002	−	12.2061i	−0.656438	−	0.476930i
$656$	12.1444			0.474158
$657$	−39.6829			−1.54818
$658$	5.14505	+	3.73810i	0.200575	+	0.145726i
$659$	−22.9244	+	16.6555i	−0.893007	+	0.648807i	−0.936660	−	0.350239i	$-0.886100\pi$
$659$	−22.9244	+	16.6555i	−0.893007	+	0.648807i	0.0436536	+	0.999047i	$0.486100\pi$
$660$	0.120073	−	0.0872383i	0.00467385	−	0.00339575i
$661$	−3.18105	+	9.79027i	−0.123729	+	0.380797i	−0.993667	−	0.112363i	$-0.964158\pi$
$661$	−3.18105	+	9.79027i	−0.123729	+	0.380797i	0.869939	+	0.493160i	$0.164158\pi$
$662$	27.4238	+	19.9245i	1.06585	+	0.774389i
$663$	−0.0299869	+	0.0922902i	−0.00116459	+	0.00358425i
$664$	8.33481	+	25.6519i	0.323453	+	0.995487i
$665$	−2.94465	+	2.13941i	−0.114189	+	0.0829629i
$666$	−11.0375	−	33.9698i	−0.427693	−	1.31630i
$667$	1.46222	+	4.50026i	0.0566175	+	0.174251i
$668$	2.96386	−	2.15337i	0.114675	−	0.0833163i
$669$	−0.0878001	−	0.270221i	−0.00339455	−	0.0104473i
$670$	−3.56612	+	10.9754i	−0.137771	+	0.424017i
$671$	1.00578	+	0.730742i	0.0388277	+	0.0282100i
$672$	−0.0319093	+	0.0982067i	−0.00123093	+	0.00378841i
$673$	−4.28962	+	3.11659i	−0.165353	+	0.120136i	−0.667384	−	0.744714i	$-0.732586\pi$
$673$	−4.28962	+	3.11659i	−0.165353	+	0.120136i	0.502032	+	0.864849i	$0.332586\pi$
$674$	11.1057	−	8.06876i	0.427776	−	0.310797i
$675$	−2.42757	−	1.76373i	−0.0934371	−	0.0678860i
$676$	0.323519			0.0124430
$677$	−10.7418			−0.412841			−0.206420	−	0.978463i	$-0.566181\pi$
$677$	−10.7418			−0.412841			−0.206420	+	0.978463i	$0.566181\pi$
$678$	2.24624	+	1.63199i	0.0862663	+	0.0626761i
$679$	1.03188	+	3.17580i	0.0396000	+	0.121876i
$680$	−0.638183	+	1.96413i	−0.0244732	+	0.0753208i
$681$	−2.24029			−0.0858483
$682$	−15.7107	+	21.3469i	−0.601592	+	0.817416i
$683$	−10.4114			−0.398383			−0.199191	−	0.979961i	$-0.563832\pi$
$683$	−10.4114			−0.398383			−0.199191	+	0.979961i	$0.563832\pi$
$684$	2.28795	−	7.04159i	0.0874820	−	0.269242i
$685$	−2.06411	−	6.35269i	−0.0788657	−	0.242724i
$686$	7.30650	+	5.30848i	0.278964	+	0.202679i
$687$	−2.59684			−0.0990758
$688$	44.0485			1.67933
$689$	−0.0102721	−	0.00746311i	−0.000391335	−	0.000284322i
$690$	−1.01407	+	0.736766i	−0.0386050	+	0.0280482i
$691$	17.3970	−	12.6397i	0.661815	−	0.480837i	−0.205461	−	0.978665i	$-0.565869\pi$
$691$	17.3970	−	12.6397i	0.661815	−	0.480837i	0.867275	+	0.497829i	$0.165869\pi$
$692$	−1.13760	+	3.50118i	−0.0432452	+	0.133095i
$693$	3.23136	+	2.34772i	0.122749	+	0.0891825i
$694$	0.0400160	−	0.123156i	0.00151899	−	0.00467496i
$695$	−6.43772	−	19.8133i	−0.244196	−	0.751560i
$696$	0.232099	−	0.168630i	0.00879770	−	0.00639191i
$697$	0.603653	+	1.85785i	0.0228650	+	0.0703712i
$698$	5.12520	+	15.7737i	0.193992	+	0.597045i
$699$	2.26058	−	1.64241i	0.0855029	−	0.0621215i
$700$	0.161912	+	0.498315i	0.00611972	+	0.0188345i
$701$	13.6121	−	41.8937i	0.514122	−	1.58230i	−0.270752	−	0.962649i	$-0.587272\pi$
$701$	13.6121	−	41.8937i	0.514122	−	1.58230i	0.784874	−	0.619656i	$-0.212728\pi$
$702$	−0.979805	−	0.711870i	−0.0369804	−	0.0268678i
$703$	18.6312	−	57.3408i	0.702688	−	2.16265i
$704$	15.9708	−	11.6035i	0.601922	−	0.437322i
$705$	1.15621	−	0.840038i	0.0435455	−	0.0316377i
$706$	−29.8854	−	21.7130i	−1.12475	−	0.817179i
$707$	3.45913			0.130094
$708$	0.0872400			0.00327868
$709$	24.6120	+	17.8816i	0.924321	+	0.671559i	0.944596	−	0.328236i	$-0.106454\pi$
$709$	24.6120	+	17.8816i	0.924321	+	0.671559i	−0.0202746	+	0.999794i	$0.506454\pi$
$710$	7.71279	+	23.7375i	0.289456	+	0.890853i
$711$	3.10464	−	9.55510i	0.116433	−	0.358344i
$712$	−44.9625			−1.68504
$713$	18.4744	−	25.1022i	0.691871	−	0.940083i
$714$	−0.0634331			−0.00237392
$715$	−1.06742	+	3.28518i	−0.0399192	+	0.122859i
$716$	2.16361	+	6.65891i	0.0808580	+	0.248855i
$717$	−1.37861	−	1.00162i	−0.0514851	−	0.0374061i
$718$	−34.6901			−1.29462
$719$	21.5622			0.804136			0.402068	−	0.915610i	$-0.368292\pi$
$719$	21.5622			0.804136			0.402068	+	0.915610i	$0.368292\pi$
$720$	−12.1221	−	8.80725i	−0.451765	−	0.328227i
$721$	1.31364	−	0.954416i	0.0489225	−	0.0355443i
$722$	49.1866	−	35.7362i	1.83054	−	1.32996i
$723$	−0.821761	+	2.52912i	−0.0305616	+	0.0940590i
$724$	5.77668	+	4.19700i	0.214689	+	0.155980i
$725$	0.986496	−	3.03612i	0.0366375	−	0.112759i
$726$	0.0779974	+	0.240051i	0.00289476	+	0.00890914i
$727$	−2.54991	+	1.85262i	−0.0945710	+	0.0687098i	−0.634066	−	0.773279i	$-0.718615\pi$
$727$	−2.54991	+	1.85262i	−0.0945710	+	0.0687098i	0.539495	+	0.841989i	$0.318615\pi$
$728$	−0.338647	−	1.04225i	−0.0125511	−	0.0386283i
$729$	−8.05056	−	24.7771i	−0.298169	−	0.917669i
$730$	18.1490	−	13.1860i	0.671725	−	0.488037i
$731$	2.18949	+	6.73856i	0.0809813	+	0.249235i
$732$	0.00528554	−	0.0162672i	0.000195359	−	0.000601254i
$733$	3.14334	+	2.28377i	0.116102	+	0.0843531i	0.644321	−	0.764755i	$-0.277140\pi$
$733$	3.14334	+	2.28377i	0.116102	+	0.0843531i	−0.528219	+	0.849108i	$0.677140\pi$
$734$	4.20380	−	12.9380i	0.155165	−	0.477549i
$735$	0.810043	−	0.588531i	0.0298789	−	0.0217083i
$736$	8.21081	−	5.96550i	0.302654	−	0.219891i
$737$	17.2940	+	12.5648i	0.637031	+	0.462830i
$738$	−12.1542			−0.447401
$739$	−19.0051			−0.699113			−0.349557	−	0.936915i	$-0.613668\pi$
$739$	−19.0051			−0.699113			−0.349557	+	0.936915i	$0.613668\pi$
$740$	2.27452	+	1.65253i	0.0836129	+	0.0607483i
$741$	−0.314937	−	0.969275i	−0.0115695	−	0.0356072i
$742$	0.00256478	−	0.00789357i	9.41559e−5	−	0.000289782i
$743$	−9.70195			−0.355930			−0.177965	−	0.984037i	$-0.556951\pi$
$743$	−9.70195			−0.355930			−0.177965	+	0.984037i	$0.556951\pi$
$744$	−1.79358	−	0.594970i	−0.0657557	−	0.0218127i
$745$	7.66318			0.280757
$746$	−4.27523	+	13.1578i	−0.156527	+	0.481741i
$747$	−9.72711	−	29.9370i	−0.355896	−	1.09534i
$748$	−0.597234	−	0.433916i	−0.0218370	−	0.0158655i
$749$	2.68540			0.0981225
$750$	1.96524			0.0717605
$751$	24.8628	+	18.0639i	0.907256	+	0.659160i	0.940319	−	0.340293i	$-0.110526\pi$
$751$	24.8628	+	18.0639i	0.907256	+	0.659160i	−0.0330636	+	0.999453i	$0.510526\pi$
$752$	−35.7525	+	25.9757i	−1.30376	+	0.947236i
$753$	−0.904841	+	0.657405i	−0.0329742	+	0.0239572i
$754$	0.398166	−	1.22543i	0.0145003	−	0.0446274i
$755$	−8.18773	−	5.94874i	−0.297982	−	0.216497i
$756$	0.0340631	−	0.104836i	0.00123886	−	0.00381283i
$757$	−3.87346	−	11.9213i	−0.140783	−	0.433286i	0.855662	−	0.517536i	$-0.173151\pi$
$757$	−3.87346	−	11.9213i	−0.140783	−	0.433286i	−0.996445	+	0.0842499i	$0.973151\pi$
$758$	14.9534	−	10.8643i	0.543134	−	0.394610i
$759$	0.717490	+	2.20821i	0.0260432	+	0.0801528i
$760$	−6.70250	−	20.6282i	−0.243125	−	0.748263i
$761$	−23.2979	+	16.9269i	−0.844547	+	0.613599i	−0.923637	−	0.383268i	$-0.874798\pi$
$761$	−23.2979	+	16.9269i	−0.844547	+	0.613599i	0.0790903	+	0.996867i	$0.474798\pi$
$762$	−0.614683	−	1.89180i	−0.0222676	−	0.0685326i
$763$	−1.48714	+	4.57695i	−0.0538381	+	0.165697i
$764$	−5.81352	−	4.22377i	−0.210326	−	0.152811i
$765$	0.744790	−	2.29223i	0.0269279	−	0.0828757i
$766$	−40.5899	+	29.4903i	−1.46657	+	1.06553i
$767$	−1.64262	+	1.19343i	−0.0593116	+	0.0430924i
$768$	−0.813614	−	0.591125i	−0.0293588	−	0.0213304i
$769$	−39.5645			−1.42673			−0.713366	−	0.700791i	$-0.752830\pi$
$769$	−39.5645			−1.42673			−0.713366	+	0.700791i	$0.752830\pi$
$770$	−2.25797			−0.0813717
$771$	0.427231	+	0.310401i	0.0153863	+	0.0111788i
$772$	2.37404	+	7.30654i	0.0854435	+	0.262968i
$773$	−11.9756	+	36.8570i	−0.430731	+	1.32565i	0.466667	+	0.884433i	$0.345455\pi$
$773$	−11.9756	+	36.8570i	−0.430731	+	1.32565i	−0.897398	+	0.441222i	$0.854545\pi$
$774$	−44.0840			−1.58457
$775$	−20.0378	+	6.37489i	−0.719778	+	0.228993i
$776$	−19.8987			−0.714323
$777$	0.138282	−	0.425588i	0.00496083	−	0.0152679i
$778$	4.64788	+	14.3047i	0.166635	+	0.512848i
$779$	−16.5979	−	12.0591i	−0.594683	−	0.432063i
$780$	0.0475242			0.00170164
$781$	46.2329			1.65434
$782$	5.04390	+	3.66461i	0.180370	+	0.131046i
$783$	−0.543344	+	0.394762i	−0.0194175	+	0.0141077i
$784$	−25.0482	+	18.1986i	−0.894578	+	0.649949i
$785$	−3.64370	+	11.2142i	−0.130049	+	0.400250i
$786$	3.07500	+	2.23412i	0.109682	+	0.0796884i
$787$	8.29014	−	25.5144i	0.295512	−	0.909492i	−0.687537	−	0.726149i	$-0.741308\pi$
$787$	8.29014	−	25.5144i	0.295512	−	0.909492i	0.983049	−	0.183343i	$-0.0586917\pi$
$788$	1.34605	+	4.14271i	0.0479509	+	0.147578i
$789$	−1.31422	+	0.954839i	−0.0467876	+	0.0339932i
$790$	1.75510	+	5.40165i	0.0624437	+	0.192182i
$791$	−1.81746	−	5.59356i	−0.0646214	−	0.198884i
$792$	−19.2559	+	13.9902i	−0.684228	+	0.497121i
$793$	0.123014	+	0.378597i	0.00436834	+	0.0134444i
$794$	4.36539	−	13.4353i	0.154922	−	0.476801i
$795$	−0.00150894	−	0.00109631i	−5.35167e−5	−	3.88822e-5i
$796$	1.34906	−	4.15199i	0.0478163	−	0.147163i
$797$	−10.1757	+	7.39308i	−0.360442	+	0.261876i	−0.753236	−	0.657750i	$-0.771508\pi$
$797$	−10.1757	+	7.39308i	−0.360442	+	0.261876i	0.392794	+	0.919626i	$0.371508\pi$
$798$	0.538970	−	0.391585i	0.0190793	−	0.0138620i
$799$	−5.75090	−	4.17828i	−0.203452	−	0.147817i
$800$	−6.84715			−0.242083
$801$	52.4733			1.85405
$802$	−11.7413	−	8.53056i	−0.414600	−	0.301225i
$803$	−12.8410	−	39.5206i	−0.453150	−	1.39465i
$804$	0.0908827	−	0.279708i	0.00320518	−	0.00986454i
$805$	2.65518			0.0935829
$806$	−8.08757	+	2.57301i	−0.284872	+	0.0906303i
$807$	−3.37213			−0.118705
$808$	−6.36983	+	19.6043i	−0.224090	+	0.689677i
$809$	−8.91295	−	27.4312i	−0.313363	−	0.964431i	−0.976423	−	0.215865i	$-0.930743\pi$
$809$	−8.91295	−	27.4312i	−0.313363	−	0.964431i	0.663061	−	0.748566i	$-0.269257\pi$
$810$	12.0597	+	8.76192i	0.423736	+	0.307862i
$811$	−49.5734			−1.74076			−0.870379	−	0.492382i	$-0.836126\pi$
$811$	−49.5734			−1.74076			−0.870379	+	0.492382i	$0.836126\pi$
$812$	0.117274			0.00411551
$813$	−0.345527	−	0.251040i	−0.0121182	−	0.00880437i
$814$	30.2592	−	21.9846i	1.06059	−	0.770561i
$815$	−10.6055	+	7.70531i	−0.371493	+	0.269905i
$816$	0.136212	−	0.419217i	0.00476836	−	0.0146755i
$817$	−60.2019	−	43.7392i	−2.10620	−	1.53024i
$818$	1.51061	−	4.64918i	0.0528172	−	0.162555i
$819$	0.395217	+	1.21635i	0.0138100	+	0.0425028i
$820$	0.773977	−	0.562327i	0.0270285	−	0.0196373i
$821$	2.84084	+	8.74320i	0.0991459	+	0.305140i	0.988312	−	0.152445i	$-0.0487147\pi$
$821$	2.84084	+	8.74320i	0.0991459	+	0.305140i	−0.889166	+	0.457585i	$0.848715\pi$
$822$	0.377802	+	1.16276i	0.0131774	+	0.0405558i
$823$	36.0872	−	26.2189i	1.25792	−	0.913933i	0.259268	−	0.965806i	$-0.416519\pi$
$823$	36.0872	−	26.2189i	1.25792	−	0.913933i	0.998654	+	0.0518722i	$0.0165189\pi$
$824$	2.99006	+	9.20245i	0.104164	+	0.320583i
$825$	0.484058	−	1.48978i	0.0168527	−	0.0518674i
$826$	−1.07375	−	0.780126i	−0.0373606	−	0.0271440i
$827$	−2.82404	+	8.69149i	−0.0982013	+	0.302233i	−0.988075	−	0.153975i	$-0.950793\pi$
$827$	−2.82404	+	8.69149i	−0.0982013	+	0.302233i	0.889873	+	0.456207i	$0.150793\pi$
$828$	−4.36959	+	3.17469i	−0.151854	+	0.110328i
$829$	23.7381	−	17.2467i	0.824457	−	0.599003i	−0.0935284	−	0.995617i	$-0.529815\pi$
$829$	23.7381	−	17.2467i	0.824457	−	0.599003i	0.917986	+	0.396613i	$0.129815\pi$
$830$	14.3963	+	10.4595i	0.499702	+	0.363055i
$831$	1.64425			0.0570384
$832$	6.32113			0.219146
$833$	−4.02908	−	2.92730i	−0.139599	−	0.101425i
$834$	1.17832	+	3.62649i	0.0408019	+	0.125575i
$835$	−3.87044	+	11.9120i	−0.133942	+	0.412232i
$836$	7.75315			0.268148
$837$	4.19875	+	1.39282i	0.145130	+	0.0481430i
$838$	−0.828910			−0.0286342
$839$	9.60726	−	29.5681i	0.331679	−	1.02080i	−0.636655	−	0.771148i	$-0.719683\pi$
$839$	9.60726	−	29.5681i	0.331679	−	1.02080i	0.968335	−	0.249656i	$-0.0803174\pi$
$840$	−0.0497465	−	0.153104i	−0.00171642	−	0.00528259i
$841$	22.8834	+	16.6258i	0.789084	+	0.573303i
$842$	54.7155			1.88562
$843$	2.84625			0.0980299
$844$	−6.53476	−	4.74778i	−0.224936	−	0.163425i
$845$	−0.894821	+	0.650125i	−0.0307828	+	0.0223650i
$846$	35.7813	−	25.9967i	1.23019	−	0.893784i
$847$	0.165221	−	0.508497i	0.00567704	−	0.0174721i
$848$	0.0466596	+	0.0339002i	0.00160230	+	0.00116414i
$849$	−0.0918165	+	0.282582i	−0.00315113	+	0.00969819i
$850$	−1.29979	−	4.00034i	−0.0445824	−	0.137211i
$851$	−35.5823	+	25.8520i	−1.21974	+	0.886196i
$852$	−0.196560	−	0.604951i	−0.00673405	−	0.0207253i
$853$	5.51099	+	16.9611i	0.188693	+	0.580737i	0.999992	−	0.00389383i	$-0.00123945\pi$
$853$	5.51099	+	16.9611i	0.188693	+	0.580737i	−0.811300	+	0.584631i	$0.801239\pi$
$854$	−0.210521	+	0.152952i	−0.00720388	+	0.00523392i
$855$	7.82214	+	24.0741i	0.267512	+	0.823316i
$856$	−4.94505	+	15.2193i	−0.169018	+	0.520185i
$857$	−27.1877	−	19.7530i	−0.928714	−	0.674751i	0.0169633	−	0.999856i	$-0.494600\pi$
$857$	−27.1877	−	19.7530i	−0.928714	−	0.674751i	−0.945678	+	0.325106i	$0.894600\pi$
$858$	0.195374	−	0.601298i	0.00666995	−	0.0205280i
$859$	−27.9448	+	20.3031i	−0.953466	+	0.692733i	−0.951624	−	0.307265i	$-0.900586\pi$
$859$	−27.9448	+	20.3031i	−0.953466	+	0.692733i	−0.00184177	+	0.999998i	$0.500586\pi$
$860$	2.80727	−	2.03960i	0.0957270	−	0.0695498i
$861$	−0.123191	−	0.0895036i	−0.00419834	−	0.00305028i
$862$	6.51034			0.221743
$863$	27.7455			0.944468			0.472234	−	0.881473i	$-0.343448\pi$
$863$	27.7455			0.944468			0.472234	+	0.881473i	$0.343448\pi$
$864$	1.16539	+	0.846706i	0.0396474	+	0.0288055i
$865$	−3.88928	−	11.9700i	−0.132239	−	0.406991i
$866$	4.45171	−	13.7009i	0.151275	−	0.465577i
$867$	−2.18690			−0.0742709
$868$	−0.450192	−	0.627707i	−0.0152805	−	0.0213058i
$869$	10.5207			0.356889
$870$	0.0584896	−	0.180012i	0.00198298	−	0.00610299i
$871$	2.11517	+	6.50982i	0.0716697	+	0.220577i
$872$	−23.2010	−	16.8565i	−0.785684	−	0.570833i
$873$	23.2228			0.785972
$874$	−65.4788			−2.21485
$875$	−3.36789	−	2.44691i	−0.113855	−	0.0827207i
$876$	−0.462527	+	0.336046i	−0.0156273	+	0.0113539i
$877$	20.0468	−	14.5648i	0.676932	−	0.491820i	−0.195407	−	0.980722i	$-0.562603\pi$
$877$	20.0468	−	14.5648i	0.676932	−	0.491820i	0.872338	+	0.488903i	$0.162603\pi$
$878$	1.77801	−	5.47215i	0.0600049	−	0.184676i
$879$	1.48408	+	1.07824i	0.0500567	+	0.0363683i
$880$	4.84862	−	14.9225i	0.163447	−	0.503037i
$881$	−1.16509	−	3.58576i	−0.0392527	−	0.120807i	0.929510	−	0.368797i	$-0.120230\pi$
$881$	−1.16509	−	3.58576i	−0.0392527	−	0.120807i	−0.968763	+	0.247989i	$0.920230\pi$
$882$	25.0684	−	18.2133i	0.844097	−	0.613273i
$883$	−11.5855	−	35.6565i	−0.389883	−	1.19994i	−0.932876	−	0.360199i	$-0.882709\pi$
$883$	−11.5855	−	35.6565i	−0.389883	−	1.19994i	0.542993	−	0.839737i	$-0.317291\pi$
$884$	−0.0730458	−	0.224812i	−0.00245680	−	0.00756124i
$885$	−0.241297	+	0.175312i	−0.00811111	+	0.00589306i
$886$	0.571540	+	1.75902i	0.0192013	+	0.0590954i
$887$	−3.77817	+	11.6280i	−0.126859	+	0.390431i	−0.994235	−	0.107222i	$-0.965805\pi$
$887$	−3.77817	+	11.6280i	−0.126859	+	0.390431i	0.867376	+	0.497653i	$0.165805\pi$
$888$	2.15734	+	1.56740i	0.0723956	+	0.0525985i
$889$	−1.30207	+	4.00736i	−0.0436701	+	0.134403i
$890$	−23.9987	+	17.4361i	−0.804438	+	0.584459i
$891$	22.3388	−	16.2301i	0.748379	−	0.543729i
$892$	0.559930	+	0.406813i	0.0187479	+	0.0136211i
$893$	74.6569			2.49830
$894$	−1.40262			−0.0469106
$895$	−19.3657	−	14.0700i	−0.647324	−	0.470308i
$896$	1.75738	+	5.40866i	0.0587099	+	0.180691i
$897$	−0.229743	+	0.707075i	−0.00767088	+	0.0236085i
$898$	35.4929			1.18441
$899$	−0.0289033	+	4.70631i	−0.000963979	+	0.156964i
$900$	3.64389			0.121463
$901$	−0.00286679	+	0.00882308i	−9.55067e−5	+	0.000293939i
$902$	−3.93298	−	12.1045i	−0.130954	−	0.403035i
$903$	−0.446823	−	0.324636i	−0.0148693	−	0.0108032i
$904$	35.0478			1.16567
$905$	−24.4118			−0.811475
$906$	1.49863	+	1.08882i	0.0497887	+	0.0361736i
$907$	−16.3210	+	11.8579i	−0.541931	+	0.393736i	−0.824802	−	0.565422i	$-0.808713\pi$
$907$	−16.3210	+	11.8579i	−0.541931	+	0.393736i	0.282871	+	0.959158i	$0.408713\pi$
$908$	4.41495	−	3.20765i	0.146515	−	0.106450i
$909$	7.43389	−	22.8792i	0.246567	−	0.758854i
$910$	−0.584928	−	0.424975i	−0.0193902	−	0.0140878i
$911$	−8.52912	+	26.2499i	−0.282582	+	0.869699i	0.704530	+	0.709674i	$0.251158\pi$
$911$	−8.52912	+	26.2499i	−0.282582	+	0.869699i	−0.987113	+	0.160026i	$0.948842\pi$
$912$	1.43056	+	4.40281i	0.0473706	+	0.145792i
$913$	26.6669	−	19.3747i	0.882547	−	0.641208i
$914$	−6.23620	−	19.1930i	−0.206275	−	0.634850i
$915$	0.0180704	+	0.0556150i	0.000597390	+	0.00183858i
$916$	5.11761	−	3.71816i	0.169090	−	0.122851i
$917$	−2.48802	−	7.65734i	−0.0821616	−	0.252868i
$918$	−0.273450	+	0.841591i	−0.00902518	+	0.0277767i
$919$	−9.92294	−	7.20943i	−0.327327	−	0.237817i	0.411968	−	0.911198i	$-0.364841\pi$
$919$	−9.92294	−	7.20943i	−0.327327	−	0.237817i	−0.739296	+	0.673381i	$0.764841\pi$
$920$	−4.88940	+	15.0480i	−0.161199	+	0.496118i
$921$	1.03871	−	0.754667i	0.0342266	−	0.0248671i
$922$	24.7989	−	18.0174i	0.816708	−	0.593373i
$923$	11.9766	+	8.70154i	0.394216	+	0.286415i
$924$	0.0575445			0.00189307
$925$	29.6728			0.975634
$926$	−44.9818	−	32.6812i	−1.47819	−	1.07397i
$927$	−3.48954	−	10.7397i	−0.114612	−	0.352738i
$928$	−0.473583	+	1.45754i	−0.0155461	+	0.0478460i
$929$	3.67399			0.120540			0.0602698	−	0.998182i	$-0.480804\pi$
$929$	3.67399			0.120540			0.0602698	+	0.998182i	$0.480804\pi$
$930$	−1.18804	+	0.377968i	−0.0389575	+	0.0123941i
$931$	52.3047			1.71422
$932$	−2.10333	+	6.47338i	−0.0688969	+	0.212043i
$933$	−0.173276	−	0.533288i	−0.00567279	−	0.0174590i
$934$	−49.3120	−	35.8273i	−1.61354	−	1.17231i
$935$	2.52386			0.0825391
$936$	−7.62135			−0.249112
$937$	−4.75191	−	3.45246i	−0.155238	−	0.112787i	0.507455	−	0.861678i	$-0.330586\pi$
$937$	−4.75191	−	3.45246i	−0.155238	−	0.112787i	−0.662693	+	0.748891i	$0.730586\pi$
$938$	−3.61982	+	2.62995i	−0.118191	+	0.0858709i
$939$	−0.800018	+	0.581247i	−0.0261076	+	0.0189683i
$940$	−1.07579	+	3.31093i	−0.0350883	+	0.107991i
$941$	23.0805	+	16.7689i	0.752402	+	0.546652i	0.896570	−	0.442901i	$-0.146051\pi$
$941$	23.0805	+	16.7689i	0.752402	+	0.546652i	−0.144169	+	0.989553i	$0.546051\pi$
$942$	0.666920	−	2.05257i	0.0217294	−	0.0668763i
$943$	4.62485	+	14.2338i	0.150606	+	0.463517i
$944$	7.46139	−	5.42102i	0.242848	−	0.176439i
$945$	0.116456	+	0.358416i	0.00378832	+	0.0116593i
$946$	−14.2652	−	43.9037i	−0.463801	−	1.42743i
$947$	−0.623733	+	0.453168i	−0.0202686	+	0.0147260i	−0.597873	−	0.801591i	$-0.703987\pi$
$947$	−0.623733	+	0.453168i	−0.0202686	+	0.0147260i	0.577605	+	0.816317i	$0.303987\pi$
$948$	−0.0447288	−	0.137661i	−0.00145272	−	0.00447102i
$949$	4.11174	−	12.6546i	0.133473	−	0.410787i
$950$	35.7388	+	25.9658i	1.15952	+	0.842441i
$951$	−0.372872	+	1.14758i	−0.0120912	+	0.0372129i
$952$	−0.647792	+	0.470648i	−0.0209951	+	0.0152538i
$953$	22.2673	−	16.1782i	0.721310	−	0.524062i	−0.165492	−	0.986211i	$-0.552921\pi$
$953$	22.2673	−	16.1782i	0.721310	−	0.524062i	0.886802	+	0.462149i	$0.152921\pi$
$954$	−0.0466973	−	0.0339276i	−0.00151188	−	0.00109845i
$955$	24.5674			0.794984
$956$	4.15094			0.134251
$957$	−0.283646	−	0.206081i	−0.00916897	−	0.00666164i
$958$	−4.67716	−	14.3948i	−0.151112	−	0.465076i
$959$	0.800292	−	2.46304i	0.0258428	−	0.0795359i
$960$	0.928558			0.0299691
$961$	25.3014	−	17.9119i	0.816175	−	0.577804i
$962$	11.9764			0.386135
$963$	5.77110	−	17.7616i	0.185971	−	0.572361i
$964$	−2.00175	−	6.16074i	−0.0644719	−	0.198424i
$965$	−21.2492	−	15.4384i	−0.684034	−	0.496980i
$966$	−0.485988			−0.0156364
$967$	−33.9203			−1.09080			−0.545402	−	0.838175i	$-0.683623\pi$
$967$	−33.9203			−1.09080			−0.545402	+	0.838175i	$0.683623\pi$
$968$	2.57761	+	1.87275i	0.0828476	+	0.0601923i
$969$	−0.602437	+	0.437696i	−0.0193531	+	0.0140608i
$970$	−10.6209	+	7.71657i	−0.341018	+	0.247764i
$971$	13.0794	−	40.2543i	0.419738	−	1.29182i	−0.488205	−	0.872729i	$-0.662348\pi$
$971$	13.0794	−	40.2543i	0.419738	−	1.29182i	0.907943	−	0.419093i	$-0.137652\pi$
$972$	−0.931203	−	0.676559i	−0.0298684	−	0.0217006i
$973$	2.49601	−	7.68194i	0.0800185	−	0.246272i
$974$	14.5061	+	44.6451i	0.464805	+	1.43052i
$975$	0.405788	−	0.294822i	0.0129956	−	0.00944186i
$976$	−0.558774	−	1.71973i	−0.0178859	−	0.0550472i
$977$	−2.74235	−	8.44008i	−0.0877355	−	0.270022i	0.897557	−	0.440899i	$-0.145340\pi$
$977$	−2.74235	−	8.44008i	−0.0877355	−	0.270022i	−0.985292	+	0.170876i	$0.945340\pi$
$978$	1.94116	−	1.41033i	0.0620713	−	0.0450975i
$979$	16.9799	+	52.2587i	0.542680	+	1.67020i
$980$	−0.753696	+	2.31964i	−0.0240759	+	0.0740981i
$981$	27.0766	+	19.6723i	0.864490	+	0.628089i
$982$	−11.8536	+	36.4818i	−0.378265	+	1.16418i
$983$	15.9839	−	11.6130i	0.509807	−	0.370397i	−0.302943	−	0.953009i	$-0.597969\pi$
$983$	15.9839	−	11.6130i	0.509807	−	0.370397i	0.812750	+	0.582612i	$0.197969\pi$
$984$	0.734105	−	0.533358i	0.0234024	−	0.0170028i
$985$	−12.0480	−	8.75336i	−0.383880	−	0.278905i
$986$	−0.941443			−0.0299817
$987$	0.554109			0.0176375
$988$	2.00845	+	1.45923i	0.0638975	+	0.0464242i
$989$	16.7746	+	51.6270i	0.533403	+	1.64164i
$990$	−4.85253	+	14.9346i	−0.154224	+	0.474651i
$991$	−3.41981			−0.108634			−0.0543170	−	0.998524i	$-0.517298\pi$
$991$	−3.41981			−0.108634			−0.0543170	+	0.998524i	$0.517298\pi$
$992$	9.61944	−	3.06036i	0.305418	−	0.0971666i
$993$	2.95347			0.0937256
$994$	−2.99038	+	9.20344i	−0.0948491	+	0.291915i
$995$	4.61223	+	14.1950i	0.146218	+	0.450011i
$996$	−0.366889	−	0.266561i	−0.0116253	−	0.00844630i
$997$	−11.8260			−0.374533			−0.187266	−	0.982309i	$-0.559963\pi$
$997$	−11.8260			−0.374533			−0.187266	+	0.982309i	$0.559963\pi$
$998$	−27.4778			−0.869794
$999$	−5.05033	−	3.66928i	−0.159785	−	0.116091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.5	yes	68
31.4	even	5	inner	403.2.k.e.66.5	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.5	✓	68	31.4	even	5	inner
403.2.k.e.287.5	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.471037 + 1.44970i) q^{2} +(0.0410411 + 0.126311i) q^{3} +(-0.261732 - 0.190160i) q^{4} +1.10606 q^{5} -0.202446 q^{6} +(0.346937 + 0.252065i) q^{7} +(-2.06742 + 1.50207i) q^{8} +(2.41278 - 1.75299i) q^{9} +O(q^{10})\)	\(q+(-0.471037 + 1.44970i) q^{2} +(0.0410411 + 0.126311i) q^{3} +(-0.261732 - 0.190160i) q^{4} +1.10606 q^{5} -0.202446 q^{6} +(0.346937 + 0.252065i) q^{7} +(-2.06742 + 1.50207i) q^{8} +(2.41278 - 1.75299i) q^{9} +(-0.520995 + 1.60346i) q^{10} +(2.52657 + 1.83566i) q^{11} +(0.0132776 - 0.0408641i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-0.528840 + 0.384225i) q^{14} +(0.0453939 + 0.139708i) q^{15} +(-1.40367 - 4.32005i) q^{16} +(0.591113 - 0.429469i) q^{17} +(1.40480 + 4.32354i) q^{18} +(-2.37130 + 7.29812i) q^{19} +(-0.289492 - 0.210328i) q^{20} +(-0.0176000 + 0.0541672i) q^{21} +(-3.85128 + 2.79812i) q^{22} +(4.52877 - 3.29035i) q^{23} +(-0.274578 - 0.199493i) q^{24} -3.77663 q^{25} -1.52431 q^{26} +(0.642786 + 0.467012i) q^{27} +(-0.0428722 - 0.131947i) q^{28} +(-0.261210 + 0.803923i) q^{29} -0.223917 q^{30} +(5.30572 - 1.68798i) q^{31} +1.81303 q^{32} +(-0.128172 + 0.394473i) q^{33} +(0.344166 + 1.05924i) q^{34} +(0.383733 + 0.278798i) q^{35} -0.964850 q^{36} -7.85694 q^{37} +(-9.46314 - 6.87537i) q^{38} +(-0.107447 + 0.0780648i) q^{39} +(-2.28669 + 1.66138i) q^{40} +(-0.826180 + 2.54272i) q^{41} +(-0.0702361 - 0.0510295i) q^{42} +(-2.99661 + 9.22262i) q^{43} +(-0.312217 - 0.960905i) q^{44} +(2.66868 - 1.93891i) q^{45} +(2.63681 + 8.11526i) q^{46} +(-3.00641 - 9.25277i) q^{47} +(0.488064 - 0.354599i) q^{48} +(-2.10629 - 6.48249i) q^{49} +(1.77894 - 5.47500i) q^{50} +(0.0785067 + 0.0570385i) q^{51} +(0.0999729 - 0.307685i) q^{52} +(-0.0102721 + 0.00746311i) q^{53} +(-0.979805 + 0.711870i) q^{54} +(2.79454 + 2.03035i) q^{55} -1.09589 q^{56} -1.01916 q^{57} +(-1.04241 - 0.757356i) q^{58} +(0.627425 + 1.93102i) q^{59} +(0.0146858 - 0.0451982i) q^{60} +0.398081 q^{61} +(-0.0521209 + 8.48684i) q^{62} +1.27895 q^{63} +(1.95334 - 6.01175i) q^{64} +(0.341791 + 1.05192i) q^{65} +(-0.511495 - 0.371623i) q^{66} +6.84483 q^{67} -0.236381 q^{68} +(0.601474 + 0.436996i) q^{69} +(-0.584928 + 0.424975i) q^{70} +(11.9766 - 8.70154i) q^{71} +(-2.35513 + 7.24834i) q^{72} +(-10.7647 - 7.82100i) q^{73} +(3.70091 - 11.3902i) q^{74} +(-0.154997 - 0.477032i) q^{75} +(2.00845 - 1.45923i) q^{76} +(0.413857 + 1.27372i) q^{77} +(-0.0625593 - 0.192538i) q^{78} +(2.72537 - 1.98010i) q^{79} +(-1.55254 - 4.77824i) q^{80} +(2.73219 - 8.40882i) q^{81} +(-3.29703 - 2.39543i) q^{82} +(3.26155 - 10.0380i) q^{83} +(0.0149069 - 0.0108305i) q^{84} +(0.653806 - 0.475018i) q^{85} +(-11.9586 - 8.68840i) q^{86} -0.112265 q^{87} -7.98079 q^{88} +(14.2343 + 10.3418i) q^{89} +(1.55380 + 4.78209i) q^{90} +(-0.132518 + 0.407849i) q^{91} -1.81102 q^{92} +(0.430964 + 0.600897i) q^{93} +14.8299 q^{94} +(-2.62280 + 8.07215i) q^{95} +(0.0744087 + 0.229007i) q^{96} +(6.29958 + 4.57691i) q^{97} +10.3898 q^{98} +9.31396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Introduction

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