LMFDB - Embedded newform 403.2.k.e.66.5

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			66.5
Character	$\chi$	$=$	403.66
Dual form			403.2.k.e.287.5

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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	−0.967663	−	0.252246i	$-0.918831\pi$
$2$	−0.471037	−	1.44970i	−0.333074	−	1.02510i	0.634589	−	0.772850i	$-0.281169\pi$
$3$	0.0410411	−	0.126311i	0.0236951	−	0.0729259i	−0.938510	−	0.345253i	$-0.887793\pi$
$3$	0.0410411	−	0.126311i	0.0236951	−	0.0729259i	0.962205	+	0.272327i	$0.0877932\pi$
$4$	−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	−0.520287	−	0.853992i	$-0.674175\pi$
$7$	0.346937	−	0.252065i	0.131130	−	0.0952715i	0.651417	+	0.758720i	$0.274175\pi$
$8$	−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	−0.137669	−	0.990478i	$-0.543961\pi$
$11$	2.52657	−	1.83566i	0.761790	−	0.553473i	0.899459	+	0.437005i	$0.143961\pi$
$12$	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	0.657156	−	0.753754i	$-0.271759\pi$
$17$	0.591113	+	0.429469i	0.143366	+	0.104161i	−0.513790	+	0.857916i	$0.671759\pi$
$18$	1.40480	−	4.32354i	0.331115	−	1.01907i
$19$	−2.37130	−	7.29812i	−0.544014	−	1.67430i	−0.723323	−	0.690510i	$-0.757386\pi$
$19$	−2.37130	−	7.29812i	−0.544014	−	1.67430i	0.179309	−	0.983793i	$-0.442614\pi$
$20$	−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	0.949455	−	0.313902i	$-0.101636\pi$
$23$	4.52877	+	3.29035i	0.944314	+	0.686085i	−0.00514096	+	0.999987i	$0.501636\pi$
$24$	−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	0.923870	−	0.382706i	$-0.125008\pi$
$29$	−0.261210	−	0.803923i	−0.0485056	−	0.149285i	−0.972376	+	0.233421i	$0.925008\pi$
$30$	−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	0.865586	−	0.500761i	$-0.166946\pi$
$41$	−0.826180	−	2.54272i	−0.129028	−	0.397106i	−0.994613	+	0.103655i	$0.966946\pi$
$42$	−0.0702361	+	0.0510295i	−0.0108377	+	0.00787403i
$43$	−2.99661	−	9.22262i	−0.456979	−	1.40644i	−0.868796	−	0.495170i	$-0.835106\pi$
$43$	−2.99661	−	9.22262i	−0.456979	−	1.40644i	0.411817	−	0.911266i	$-0.364894\pi$
$44$	−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	0.450896	+	0.892576i	$0.351104\pi$
$47$	−3.00641	+	9.25277i	−0.438530	+	1.34966i	−0.889426	+	0.457079i	$0.848896\pi$
$48$	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	0.587080	−	0.809529i	$-0.300278\pi$
$53$	−0.0102721	−	0.00746311i	−0.00141098	−	0.00102514i	−0.588491	+	0.808504i	$0.700278\pi$
$54$	−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	−0.901871	−	0.432005i	$-0.857806\pi$
$59$	0.627425	−	1.93102i	0.0816838	−	0.251397i	0.983555	+	0.180608i	$0.0578065\pi$
$60$	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	0.991544	+	0.129769i	$0.0414236\pi$
$71$	11.9766	+	8.70154i	1.42137	+	1.03268i	0.429822	+	0.902914i	$0.358576\pi$
$72$	−2.35513	−	7.24834i	−0.277554	−	0.854225i
$73$	−10.7647	+	7.82100i	−1.25991	+	0.915379i	−0.998753	−	0.0499174i	$-0.984104\pi$
$73$	−10.7647	+	7.82100i	−1.25991	+	0.915379i	−0.261157	+	0.965296i	$0.584104\pi$
$74$	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	0.730449	−	0.682968i	$-0.239311\pi$
$79$	2.72537	+	1.98010i	0.306629	+	0.222779i	−0.423820	+	0.905746i	$0.639311\pi$
$80$	−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	0.954249	+	0.299014i	$0.0966578\pi$
$83$	3.26155	+	10.0380i	0.358001	+	1.10181i	−0.596247	+	0.802801i	$0.703342\pi$
$84$	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	0.542142	−	0.840287i	$-0.317614\pi$
$89$	14.2343	−	10.3418i	1.50883	−	1.09623i	0.966692	−	0.255944i	$-0.0823863\pi$
$90$	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	−0.220096	−	0.975478i	$-0.570637\pi$
$97$	6.29958	−	4.57691i	0.639625	−	0.464715i	0.859721	+	0.510763i	$0.170637\pi$
$98$	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	0.863045	−	0.505126i	$-0.168554\pi$
$101$	6.52576	+	4.74124i	0.649337	+	0.471771i	−0.213708	+	0.976898i	$0.568554\pi$
$102$	−0.119669	−	0.0869443i	−0.0118490	−	0.00860877i
$103$	1.17006	+	3.60107i	0.115289	+	0.354824i	0.992007	−	0.126181i	$-0.0402719\pi$
$103$	1.17006	+	3.60107i	0.115289	+	0.354824i	−0.876718	+	0.481005i	$0.840272\pi$
$104$	−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	0.805091	−	0.593151i	$-0.202116\pi$
$107$	5.06610	+	3.68074i	0.489759	+	0.355830i	−0.315333	+	0.948981i	$0.602116\pi$
$108$	−0.0794312	+	0.244464i	−0.00764327	+	0.0235236i
$109$	3.46784	−	10.6729i	0.332159	−	1.02228i	−0.635946	−	0.771734i	$-0.719390\pi$
$109$	3.46784	−	10.6729i	0.332159	−	1.02228i	0.968105	−	0.250546i	$-0.0806101\pi$
$110$	−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	−0.971019	−	0.239002i	$-0.923180\pi$
$113$	−11.0955	+	8.06135i	−1.04378	+	0.758348i	−0.0727570	+	0.997350i	$0.523180\pi$
$114$	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	−0.721214	−	0.692712i	$-0.756416\pi$
$127$	3.03628	−	9.34470i	0.269426	−	0.829208i	0.990641	−	0.136496i	$-0.0435842\pi$
$128$	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	−0.327275	+	0.944929i	$0.606130\pi$
$131$	−15.1892	+	11.0356i	−1.32709	+	0.964187i	−0.999815	+	0.0192575i	$0.993870\pi$
$132$	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	−0.998584	−	0.0532056i	$-0.983056\pi$
$137$	−1.86619	+	5.74353i	−0.159439	+	0.490703i	0.839145	+	0.543909i	$0.183056\pi$
$138$	−0.916832	−	0.666118i	−0.0780460	−	0.0567037i
$139$	−5.82041	+	17.9134i	−0.493681	+	1.51939i	0.325322	+	0.945603i	$0.394527\pi$
$139$	−5.82041	+	17.9134i	−0.493681	+	1.51939i	−0.819003	+	0.573789i	$0.805473\pi$
$140$	−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	−0.846736	−	0.532014i	$-0.821435\pi$
$151$	−7.40262	+	5.37832i	−0.602416	+	0.437681i	0.244319	+	0.969695i	$0.421435\pi$
$152$	−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	−0.992167	−	0.124922i	$-0.960132\pi$
$157$	−3.29431	−	10.1388i	−0.262914	−	0.809167i	0.729252	−	0.684245i	$-0.239868\pi$
$158$	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	0.145116	−	0.989415i	$-0.453644\pi$
$163$	−9.58851	−	6.96646i	−0.751030	−	0.545655i	−0.896146	+	0.443760i	$0.853644\pi$
$164$	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	−0.990304	−	0.138917i	$-0.955638\pi$
$167$	−3.49931	−	10.7698i	−0.270785	−	0.833389i	0.719519	−	0.694472i	$-0.244362\pi$
$168$	−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	0.723802	+	0.690007i	$0.242393\pi$
$173$	−3.51634	+	10.8222i	−0.267342	+	0.822795i	−0.991145	+	0.132787i	$0.957607\pi$
$174$	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	−1.00000		0.000370549i	$-0.999882\pi$
$179$	−17.5087	+	12.7208i	−1.30866	+	0.950800i	−0.308665	+	0.951171i	$0.599882\pi$
$180$	−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	−0.386276	+	0.922383i	$0.626239\pi$
$193$	−19.2116	+	13.9580i	−1.38288	+	1.00472i	−0.996604	+	0.0823381i	$0.973761\pi$
$194$	−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	−0.903798	−	0.427960i	$-0.859233\pi$
$197$	−10.8927	+	7.91401i	−0.776073	+	0.563850i	0.127725	+	0.991810i	$0.459233\pi$
$198$	−4.38722	−	13.5025i	−0.311786	−	0.959580i
$199$	4.16997	−	12.8338i	0.295601	−	0.909767i	−0.687418	−	0.726262i	$-0.741256\pi$
$199$	4.16997	−	12.8338i	0.295601	−	0.909767i	0.983019	−	0.183504i	$-0.0587442\pi$
$200$	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	−0.961063	−	0.276331i	$-0.910881\pi$
$227$	−5.21256	−	16.0426i	−0.345970	−	1.06479i	0.615093	−	0.788455i	$-0.289119\pi$
$228$	0.266746	−	0.193803i	0.0176657	−	0.0128349i
$229$	−6.04215	−	18.5958i	−0.399277	−	1.22885i	−0.925580	−	0.378551i	$-0.876422\pi$
$229$	−6.04215	−	18.5958i	−0.399277	−	1.22885i	0.526304	−	0.850297i	$-0.323578\pi$
$230$	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	0.476187	+	0.879344i	$0.342018\pi$
$233$	−6.50141	+	20.0093i	−0.425922	+	1.31085i	−0.902109	+	0.431508i	$0.857982\pi$
$234$	−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	0.199069	−	0.979986i	$-0.436208\pi$
$239$	−10.3802	−	7.54164i	−0.671438	−	0.487828i	−0.870506	+	0.492158i	$0.836208\pi$
$240$	0.539828	+	0.392208i	0.0348457	+	0.0253169i
$241$	16.1989	−	11.7692i	1.04346	−	0.758119i	0.0725025	−	0.997368i	$-0.476901\pi$
$241$	16.1989	−	11.7692i	1.04346	−	0.758119i	0.970958	+	0.239250i	$0.0769015\pi$
$242$	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	−0.834724	−	0.550669i	$-0.814373\pi$
$251$	2.60232	−	8.00911i	0.164257	−	0.505531i	0.998981	+	0.0451380i	$0.0143728\pi$
$252$	−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	0.683578	−	0.729878i	$-0.260423\pi$
$257$	3.21682	+	2.33715i	0.200660	+	0.145788i	−0.482918	+	0.875666i	$0.660423\pi$
$258$	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	−0.764306	−	0.644854i	$-0.776918\pi$
$263$	3.77970	−	11.6327i	0.233066	−	0.717305i	0.997372	−	0.0724504i	$-0.0230819\pi$
$264$	−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	−0.841342	−	0.540503i	$-0.818234\pi$
$269$	−7.84604	−	24.1476i	−0.478382	−	1.47231i	0.362960	−	0.931805i	$-0.381766\pi$
$270$	−1.08372	−	0.787371i	−0.0659533	−	0.0479178i
$271$	−2.60163	−	1.89020i	−0.158038	−	0.114821i	0.505956	−	0.862559i	$-0.331140\pi$
$271$	−2.60163	−	1.89020i	−0.158038	−	0.114821i	−0.663994	+	0.747738i	$0.731140\pi$
$272$	−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	0.997761	+	0.0668783i	$0.0213039\pi$
$277$	3.82572	+	11.7744i	0.229866	+	0.707453i	−0.767896	+	0.640575i	$0.778696\pi$
$278$	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	0.928913	+	0.370298i	$0.120744\pi$
$281$	6.62245	+	20.3818i	0.395062	+	1.21588i	−0.533851	+	0.845579i	$0.679256\pi$
$282$	0.608636	−	1.87319i	0.0362437	−	0.111547i
$283$	1.80992	−	1.31498i	0.107589	−	0.0781677i	−0.532690	−	0.846310i	$-0.678819\pi$
$283$	1.80992	−	1.31498i	0.107589	−	0.0781677i	0.640279	+	0.768143i	$0.278819\pi$
$284$	−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	0.864227	−	0.503102i	$-0.167808\pi$
$293$	11.1743	+	8.11860i	0.652809	+	0.474293i	−0.211418	+	0.977396i	$0.567808\pi$
$294$	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	−0.999399	−	0.0346599i	$-0.988965\pi$
$307$	−2.98733	+	9.19404i	−0.170496	+	0.524732i	0.828903	+	0.559392i	$0.188965\pi$
$308$	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	−0.864736	−	0.502227i	$-0.832514\pi$
$313$	2.30085	−	7.08128i	0.130052	−	0.400258i	0.994788	+	0.101969i	$0.0325143\pi$
$314$	−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	−0.361918	−	0.932210i	$-0.617878\pi$
$317$	7.35020	−	5.34023i	0.412828	−	0.299937i	0.774746	+	0.632273i	$0.217878\pi$
$318$	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	0.941628	+	0.336654i	$0.109295\pi$
$331$	6.87193	+	21.1496i	0.377715	+	1.16249i	−0.563913	+	0.825834i	$0.690705\pi$
$332$	−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	−0.768268	−	0.640128i	$-0.778881\pi$
$337$	−7.28573	+	5.29339i	−0.396879	+	0.288349i	0.371390	+	0.928477i	$0.378881\pi$
$338$	−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	0.797907	−	0.602781i	$-0.205941\pi$
$349$	8.80264	+	6.39550i	0.471195	+	0.342343i	−0.326712	+	0.945124i	$0.605941\pi$
$350$	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	−0.926133	−	0.377197i	$-0.876888\pi$
$353$	−7.48876	−	23.0480i	−0.398587	−	1.22672i	0.527546	−	0.849526i	$-0.323112\pi$
$354$	−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	−0.574864	−	0.818249i	$-0.694945\pi$
$359$	7.03258	−	21.6441i	0.371166	−	1.14233i	0.946029	−	0.324081i	$-0.105055\pi$
$360$	−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	−0.810507	−	0.585730i	$-0.800808\pi$
$379$	−9.80998	+	7.12737i	−0.503905	+	0.366108i	0.306602	+	0.951838i	$0.400808\pi$
$380$	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	0.362245	−	0.932083i	$-0.382010\pi$
$383$	26.6284	−	19.3467i	1.36065	−	0.988569i	0.998403	−	0.0564861i	$-0.0179897\pi$
$384$	−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	0.771471	−	0.636264i	$-0.219521\pi$
$389$	7.98283	+	5.79987i	0.404746	+	0.294065i	−0.366726	+	0.930329i	$0.619521\pi$
$390$	−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	0.850328	−	0.526252i	$-0.176403\pi$
$401$	−2.94217	−	9.05508i	−0.146925	−	0.452189i	−0.997254	+	0.0740634i	$0.976403\pi$
$402$	−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	−0.946868	−	0.321623i	$-0.895772\pi$
$419$	0.168041	−	0.517178i	0.00820936	−	0.0252658i	0.955077	+	0.296357i	$0.0957718\pi$
$420$	0.0164879	+	0.0119792i	0.000804527	+	0.000584523i
$421$	−11.0922	+	34.1384i	−0.540603	+	1.66381i	0.190618	+	0.981664i	$0.438951\pi$
$421$	−11.0922	+	34.1384i	−0.540603	+	1.66381i	−0.731221	+	0.682141i	$0.761049\pi$
$422$	−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	−0.977798	−	0.209549i	$-0.932801\pi$
$431$	−1.31981	+	4.06197i	−0.0635732	+	0.195658i	0.914225	+	0.405207i	$0.132801\pi$
$432$	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	0.610860	−	0.791738i	$-0.290824\pi$
$443$	0.981633	+	0.713198i	0.0466388	+	0.0338851i	−0.564222	+	0.825623i	$0.690824\pi$
$444$	−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	0.624859	+	0.780738i	$0.285156\pi$
$449$	−7.19533	+	22.1449i	−0.339569	+	1.04508i	−0.964428	+	0.264347i	$0.914844\pi$
$450$	−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	0.308380	−	0.951263i	$-0.400213\pi$
$457$	−10.7108	−	7.78186i	−0.501030	−	0.364020i	−0.809410	+	0.587243i	$0.800213\pi$
$458$	−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	−0.898210	−	0.439566i	$-0.855132\pi$
$461$	−16.2689	+	11.8201i	−0.757720	+	0.550516i	0.140490	+	0.990082i	$0.455132\pi$
$462$	−0.0837836	+	0.257860i	−0.00389797	+	0.0119967i
$463$	−11.2717	−	34.6906i	−0.523839	−	1.61221i	−0.766601	−	0.642124i	$-0.778054\pi$
$463$	−11.2717	−	34.6906i	−0.523839	−	1.61221i	0.242763	−	0.970086i	$-0.421946\pi$
$464$	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	−0.646817	−	0.762645i	$-0.723900\pi$
$467$	−12.3568	−	38.0302i	−0.571803	−	1.75983i	0.0750142	−	0.997182i	$-0.476100\pi$
$468$	−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	0.388941	−	0.921263i	$-0.372841\pi$
$479$	−8.03313	−	5.83641i	−0.367043	−	0.266672i	−0.755984	+	0.654590i	$0.772841\pi$
$480$	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	0.985547	−	0.169405i	$-0.0541846\pi$
$487$	24.9145	+	18.1014i	1.12898	+	0.820255i	0.143437	+	0.989659i	$0.454185\pi$
$488$	−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	−0.745519	−	0.666484i	$-0.767798\pi$
$499$	5.57046	−	17.1441i	0.249368	−	0.767476i	0.994887	−	0.100992i	$-0.0322016\pi$
$500$	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	−0.304037	−	0.952660i	$-0.598335\pi$
$503$	11.3942	−	8.27839i	0.508044	−	0.369115i	0.812081	+	0.583545i	$0.198335\pi$
$504$	−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	−0.681160	−	0.732135i	$-0.738524\pi$
$509$	6.77391	−	20.8479i	0.300248	−	0.924069i	0.981408	−	0.191934i	$-0.0614760\pi$
$510$	−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	0.667385	−	0.744713i	$-0.267413\pi$
$523$	36.1764	−	26.2837i	1.58188	−	1.14930i	0.914497	−	0.404592i	$-0.132587\pi$
$524$	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	0.670273	−	0.742114i	$-0.266177\pi$
$541$	3.99147	+	2.89997i	0.171607	+	0.124680i	−0.498667	+	0.866794i	$0.666177\pi$
$542$	−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	−0.186307	−	0.982492i	$-0.559652\pi$
$547$	16.1500	−	11.7337i	0.690526	−	0.501696i	0.876833	+	0.480795i	$0.159652\pi$
$548$	−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	−0.327568	−	0.944828i	$-0.606229\pi$
$569$	11.2063	−	8.14185i	0.469792	−	0.341324i	0.797360	+	0.603504i	$0.206229\pi$
$570$	0.530976	+	1.63418i	0.0222401	+	0.0684481i
$571$	−3.40579	+	10.4820i	−0.142528	+	0.438656i	−0.996685	−	0.0813593i	$-0.974074\pi$
$571$	−3.40579	+	10.4820i	−0.142528	+	0.438656i	0.854157	+	0.520016i	$0.174074\pi$
$572$	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	0.805362	+	0.592784i	$0.201971\pi$
$577$	12.0642	+	37.1298i	0.502240	+	1.54574i	−0.303122	+	0.952952i	$0.598029\pi$
$578$	−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	−0.970860	−	0.239647i	$-0.922968\pi$
$587$	−7.90510	−	24.3294i	−0.326279	−	1.00418i	0.644582	−	0.764536i	$-0.277032\pi$
$588$	−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	−0.343155	−	0.939279i	$-0.611496\pi$
$593$	10.8148	−	7.85742i	0.444111	−	0.322665i	0.787266	+	0.616613i	$0.211496\pi$
$594$	−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	0.943022	−	0.332732i	$-0.107970\pi$
$599$	−0.378710	−	1.16555i	−0.0154737	−	0.0476231i	−0.958495	+	0.285109i	$0.907970\pi$
$600$	1.03698	−	0.753410i	0.0423345	−	0.0307578i
$601$	−14.4942	−	44.6087i	−0.591233	−	1.81963i	−0.572650	−	0.819800i	$-0.694085\pi$
$601$	−14.4942	−	44.6087i	−0.591233	−	1.81963i	−0.0185824	−	0.999827i	$-0.505915\pi$
$602$	−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	−0.580705	−	0.814114i	$-0.697223\pi$
$607$	9.05718	−	27.8751i	0.367620	−	1.13142i	0.948324	−	0.317302i	$-0.102777\pi$
$608$	−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	−0.600041	−	0.799970i	$-0.704849\pi$
$613$	−0.610236	+	0.443363i	−0.0246472	+	0.0179072i	0.575393	+	0.817877i	$0.304849\pi$
$614$	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	−0.840814	−	0.541324i	$-0.817923\pi$
$617$	3.91473	−	12.0483i	0.157601	−	0.485046i	0.998415	+	0.0562780i	$0.0179233\pi$
$618$	−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	−0.995957	−	0.0898327i	$-0.971367\pi$
$631$	−30.6031	+	22.2344i	−1.21829	+	0.885138i	−0.222332	+	0.974971i	$0.571367\pi$
$632$	−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	0.999132	−	0.0416470i	$-0.0132605\pi$
$641$	4.21134	+	12.9612i	0.166338	+	0.511935i	−0.832795	+	0.553582i	$0.813260\pi$
$642$	−1.02561	−	0.745151i	−0.0404777	−	0.0294088i
$643$	−17.0074	−	12.3566i	−0.670707	−	0.487297i	0.199555	−	0.979887i	$-0.436050\pi$
$643$	−17.0074	−	12.3566i	−0.670707	−	0.487297i	−0.870262	+	0.492590i	$0.836050\pi$
$644$	−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	−0.349086	−	0.937091i	$-0.613508\pi$
$647$	11.0461	−	8.02546i	0.434267	−	0.315513i	0.783353	+	0.621577i	$0.213508\pi$
$648$	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	0.942726	−	0.333569i	$-0.108253\pi$
$653$	−0.409437	−	1.26012i	−0.0160225	−	0.0493122i	−0.958748	+	0.284257i	$0.908253\pi$
$654$	−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	0.0436536	−	0.999047i	$-0.486100\pi$
$659$	−22.9244	−	16.6555i	−0.893007	−	0.648807i	−0.936660	+	0.350239i	$0.886100\pi$
$660$	0.120073	+	0.0872383i	0.00467385	+	0.00339575i
$661$	−3.18105	−	9.79027i	−0.123729	−	0.380797i	0.869939	−	0.493160i	$-0.164158\pi$
$661$	−3.18105	−	9.79027i	−0.123729	−	0.380797i	−0.993667	+	0.112363i	$0.964158\pi$
$662$	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	0.502032	−	0.864849i	$-0.332586\pi$
$673$	−4.28962	−	3.11659i	−0.165353	−	0.120136i	−0.667384	+	0.744714i	$0.732586\pi$
$674$	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	0.867275	−	0.497829i	$-0.165869\pi$
$691$	17.3970	+	12.6397i	0.661815	+	0.480837i	−0.205461	+	0.978665i	$0.565869\pi$
$692$	−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	0.784874	+	0.619656i	$0.212728\pi$
$701$	13.6121	+	41.8937i	0.514122	+	1.58230i	−0.270752	+	0.962649i	$0.587272\pi$
$702$	−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	−0.0202746	−	0.999794i	$-0.506454\pi$
$709$	24.6120	−	17.8816i	0.924321	−	0.671559i	0.944596	+	0.328236i	$0.106454\pi$
$710$	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	0.539495	−	0.841989i	$-0.318615\pi$
$727$	−2.54991	−	1.85262i	−0.0945710	−	0.0687098i	−0.634066	+	0.773279i	$0.718615\pi$
$728$	−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	−0.528219	−	0.849108i	$-0.677140\pi$
$733$	3.14334	−	2.28377i	0.116102	−	0.0843531i	0.644321	+	0.764755i	$0.277140\pi$
$734$	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	−0.0330636	−	0.999453i	$-0.510526\pi$
$751$	24.8628	−	18.0639i	0.907256	−	0.659160i	0.940319	+	0.340293i	$0.110526\pi$
$752$	−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	−0.996445	−	0.0842499i	$-0.973151\pi$
$757$	−3.87346	+	11.9213i	−0.140783	+	0.433286i	0.855662	+	0.517536i	$0.173151\pi$
$758$	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	0.0790903	−	0.996867i	$-0.474798\pi$
$761$	−23.2979	−	16.9269i	−0.844547	−	0.613599i	−0.923637	+	0.383268i	$0.874798\pi$
$762$	−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	−0.897398	−	0.441222i	$-0.854545\pi$
$773$	−11.9756	−	36.8570i	−0.430731	−	1.32565i	0.466667	−	0.884433i	$-0.345455\pi$
$774$	−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	0.983049	+	0.183343i	$0.0586917\pi$
$787$	8.29014	+	25.5144i	0.295512	+	0.909492i	−0.687537	+	0.726149i	$0.741308\pi$
$788$	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	0.392794	−	0.919626i	$-0.371508\pi$
$797$	−10.1757	−	7.39308i	−0.360442	−	0.261876i	−0.753236	+	0.657750i	$0.771508\pi$
$798$	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	0.663061	+	0.748566i	$0.269257\pi$
$809$	−8.91295	+	27.4312i	−0.313363	+	0.964431i	−0.976423	+	0.215865i	$0.930743\pi$
$810$	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	−0.889166	−	0.457585i	$-0.848715\pi$
$821$	2.84084	−	8.74320i	0.0991459	−	0.305140i	0.988312	+	0.152445i	$0.0487147\pi$
$822$	0.377802	−	1.16276i	0.0131774	−	0.0405558i
$823$	36.0872	+	26.2189i	1.25792	+	0.913933i	0.998654	−	0.0518722i	$-0.0165189\pi$
$823$	36.0872	+	26.2189i	1.25792	+	0.913933i	0.259268	+	0.965806i	$0.416519\pi$
$824$	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	0.889873	−	0.456207i	$-0.150793\pi$
$827$	−2.82404	−	8.69149i	−0.0982013	−	0.302233i	−0.988075	+	0.153975i	$0.950793\pi$
$828$	−4.36959	−	3.17469i	−0.151854	−	0.110328i
$829$	23.7381	+	17.2467i	0.824457	+	0.599003i	0.917986	−	0.396613i	$-0.129815\pi$
$829$	23.7381	+	17.2467i	0.824457	+	0.599003i	−0.0935284	+	0.995617i	$0.529815\pi$
$830$	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	0.968335	+	0.249656i	$0.0803174\pi$
$839$	9.60726	+	29.5681i	0.331679	+	1.02080i	−0.636655	+	0.771148i	$0.719683\pi$
$840$	−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	−0.811300	−	0.584631i	$-0.801239\pi$
$853$	5.51099	−	16.9611i	0.188693	−	0.580737i	0.999992	+	0.00389383i	$0.00123945\pi$
$854$	−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	−0.945678	−	0.325106i	$-0.894600\pi$
$857$	−27.1877	+	19.7530i	−0.928714	+	0.674751i	0.0169633	+	0.999856i	$0.494600\pi$
$858$	0.195374	+	0.601298i	0.00666995	+	0.0205280i
$859$	−27.9448	−	20.3031i	−0.953466	−	0.692733i	−0.00184177	−	0.999998i	$-0.500586\pi$
$859$	−27.9448	−	20.3031i	−0.953466	−	0.692733i	−0.951624	+	0.307265i	$0.900586\pi$
$860$	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	0.872338	−	0.488903i	$-0.162603\pi$
$877$	20.0468	+	14.5648i	0.676932	+	0.491820i	−0.195407	+	0.980722i	$0.562603\pi$
$878$	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	−0.968763	−	0.247989i	$-0.920230\pi$
$881$	−1.16509	+	3.58576i	−0.0392527	+	0.120807i	0.929510	+	0.368797i	$0.120230\pi$
$882$	25.0684	+	18.2133i	0.844097	+	0.613273i
$883$	−11.5855	+	35.6565i	−0.389883	+	1.19994i	0.542993	+	0.839737i	$0.317291\pi$
$883$	−11.5855	+	35.6565i	−0.389883	+	1.19994i	−0.932876	+	0.360199i	$0.882709\pi$
$884$	−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	0.867376	−	0.497653i	$-0.165805\pi$
$887$	−3.77817	−	11.6280i	−0.126859	−	0.390431i	−0.994235	+	0.107222i	$0.965805\pi$
$888$	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	0.282871	−	0.959158i	$-0.408713\pi$
$907$	−16.3210	−	11.8579i	−0.541931	−	0.393736i	−0.824802	+	0.565422i	$0.808713\pi$
$908$	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	−0.987113	−	0.160026i	$-0.948842\pi$
$911$	−8.52912	−	26.2499i	−0.282582	−	0.869699i	0.704530	−	0.709674i	$-0.251158\pi$
$912$	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	−0.739296	−	0.673381i	$-0.764841\pi$
$919$	−9.92294	+	7.20943i	−0.327327	+	0.237817i	0.411968	+	0.911198i	$0.364841\pi$
$920$	−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	−0.662693	−	0.748891i	$-0.730586\pi$
$937$	−4.75191	+	3.45246i	−0.155238	+	0.112787i	0.507455	+	0.861678i	$0.330586\pi$
$938$	−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	−0.144169	−	0.989553i	$-0.546051\pi$
$941$	23.0805	−	16.7689i	0.752402	−	0.546652i	0.896570	+	0.442901i	$0.146051\pi$
$942$	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	0.577605	−	0.816317i	$-0.303987\pi$
$947$	−0.623733	−	0.453168i	−0.0202686	−	0.0147260i	−0.597873	+	0.801591i	$0.703987\pi$
$948$	−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	0.886802	−	0.462149i	$-0.152921\pi$
$953$	22.2673	+	16.1782i	0.721310	+	0.524062i	−0.165492	+	0.986211i	$0.552921\pi$
$954$	−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	0.907943	+	0.419093i	$0.137652\pi$
$971$	13.0794	+	40.2543i	0.419738	+	1.29182i	−0.488205	+	0.872729i	$0.662348\pi$
$972$	−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	−0.985292	−	0.170876i	$-0.945340\pi$
$977$	−2.74235	+	8.44008i	−0.0877355	+	0.270022i	0.897557	+	0.440899i	$0.145340\pi$
$978$	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	0.812750	−	0.582612i	$-0.197969\pi$
$983$	15.9839	+	11.6130i	0.509807	+	0.370397i	−0.302943	+	0.953009i	$0.597969\pi$
$984$	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.66.5	✓	68
31.8	even	5	inner	403.2.k.e.287.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.5	✓	68	1.1	even	1	trivial
403.2.k.e.287.5	yes	68	31.8	even	5	inner

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

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