LMFDB - Embedded newform 414.2.e.c.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, degree $2$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.1481180578947.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 6x^{8} - 11x^{7} + 22x^{6} - 45x^{5} + 66x^{4} - 99x^{3} + 162x^{2} - 162x + 243 $ x^10 - 2x^9 + 6x^8 - 11x^7 + 22x^6 - 45x^5 + 66x^4 - 99x^3 + 162x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.1
Root			$-1.24278 - 1.20644i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.c.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.66620 - 0.473061i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.274896 - 0.476134i) q^{5} +(0.423416 + 1.67950i) q^{6} +(0.708031 + 1.22635i) q^{7} +1.00000 q^{8} +(2.55243 + 1.57642i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.66620 - 0.473061i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.274896 - 0.476134i) q^{5} +(0.423416 + 1.67950i) q^{6} +(0.708031 + 1.22635i) q^{7} +1.00000 q^{8} +(2.55243 + 1.57642i) q^{9} -0.549792 q^{10} +(-2.68387 - 4.64861i) q^{11} +(1.24278 - 1.20644i) q^{12} +(2.46789 - 4.27450i) q^{13} +(0.708031 - 1.22635i) q^{14} +(-0.683271 + 0.663290i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.10485 q^{17} +(0.0890100 - 2.99868i) q^{18} -5.12850 q^{19} +(0.274896 + 0.476134i) q^{20} +(-0.599583 - 2.37827i) q^{21} +(-2.68387 + 4.64861i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-1.66620 - 0.473061i) q^{24} +(2.34886 + 4.06835i) q^{25} -4.93577 q^{26} +(-3.50710 - 3.83409i) q^{27} -1.41606 q^{28} +(-1.63408 - 2.83031i) q^{29} +(0.916062 + 0.260085i) q^{30} +(-2.64591 + 4.58284i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.27279 + 9.01513i) q^{33} +(2.55243 + 4.42093i) q^{34} +0.778539 q^{35} +(-2.64144 + 1.42225i) q^{36} -7.38719 q^{37} +(2.56425 + 4.44141i) q^{38} +(-6.13408 + 5.95471i) q^{39} +(0.274896 - 0.476134i) q^{40} +(5.82268 - 10.0852i) q^{41} +(-1.75985 + 1.70839i) q^{42} +(-5.67619 - 9.83145i) q^{43} +5.36775 q^{44} +(1.45224 - 0.781944i) q^{45} +1.00000 q^{46} +(-1.98556 - 3.43909i) q^{47} +(0.423416 + 1.67950i) q^{48} +(2.49738 - 4.32560i) q^{49} +(2.34886 - 4.06835i) q^{50} +(8.50570 + 2.41491i) q^{51} +(2.46789 + 4.27450i) q^{52} -9.36654 q^{53} +(-1.56687 + 4.95428i) q^{54} -2.95114 q^{55} +(0.708031 + 1.22635i) q^{56} +(8.54509 + 2.42609i) q^{57} +(-1.63408 + 2.83031i) q^{58} +(5.65562 - 9.79583i) q^{59} +(-0.232791 - 0.923375i) q^{60} +(4.93130 + 8.54127i) q^{61} +5.29181 q^{62} +(-0.126044 + 4.24631i) q^{63} +1.00000 q^{64} +(-1.35682 - 2.35009i) q^{65} +(6.67094 - 6.47586i) q^{66} +(-4.36268 + 7.55638i) q^{67} +(2.55243 - 4.42093i) q^{68} +(1.24278 - 1.20644i) q^{69} +(-0.389269 - 0.674234i) q^{70} -2.81741 q^{71} +(2.55243 + 1.57642i) q^{72} +10.3730 q^{73} +(3.69359 + 6.39749i) q^{74} +(-1.98909 - 7.88983i) q^{75} +(2.56425 - 4.44141i) q^{76} +(3.80053 - 6.58271i) q^{77} +(8.22397 + 2.33492i) q^{78} +(1.72510 + 2.98797i) q^{79} -0.549792 q^{80} +(4.02977 + 8.04742i) q^{81} -11.6454 q^{82} +(2.00735 + 3.47684i) q^{83} +(2.35944 + 0.669883i) q^{84} +(-1.40330 + 2.43059i) q^{85} +(-5.67619 + 9.83145i) q^{86} +(1.38379 + 5.48888i) q^{87} +(-2.68387 - 4.64861i) q^{88} -4.39783 q^{89} +(-1.40330 - 0.866705i) q^{90} +6.98935 q^{91} +(-0.500000 - 0.866025i) q^{92} +(6.57656 - 6.38425i) q^{93} +(-1.98556 + 3.43909i) q^{94} +(-1.40980 + 2.44185i) q^{95} +(1.24278 - 1.20644i) q^{96} +(-7.05014 - 12.2112i) q^{97} -4.99477 q^{98} +(0.477783 - 16.0962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.66620	−	0.473061i	−0.961980	−	0.273122i
$3$	−1.66620	−	0.473061i	−0.961980	−	0.273122i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.274896	−	0.476134i	0.122937	−	0.212933i	−0.797988	−	0.602674i	$-0.794102\pi$
$5$	0.274896	−	0.476134i	0.122937	−	0.212933i	0.920925	+	0.389741i	$0.127435\pi$
$6$	0.423416	+	1.67950i	0.172859	+	0.685653i
$7$	0.708031	+	1.22635i	0.267610	+	0.463515i	0.968244	−	0.250006i	$-0.0804326\pi$
$7$	0.708031	+	1.22635i	0.267610	+	0.463515i	−0.700634	+	0.713521i	$0.747099\pi$
$8$	1.00000			0.353553
$9$	2.55243	+	1.57642i	0.850809	+	0.525475i
$10$	−0.549792			−0.173859
$11$	−2.68387	−	4.64861i	−0.809219	−	1.40161i	−0.913406	−	0.407050i	$-0.866557\pi$
$11$	−2.68387	−	4.64861i	−0.809219	−	1.40161i	0.104187	−	0.994558i	$-0.466776\pi$
$12$	1.24278	−	1.20644i	0.358760	−	0.348269i
$13$	2.46789	−	4.27450i	0.684468	−	1.18553i	−0.289135	−	0.957288i	$-0.593368\pi$
$13$	2.46789	−	4.27450i	0.684468	−	1.18553i	0.973604	−	0.228246i	$-0.0732989\pi$
$14$	0.708031	−	1.22635i	0.189229	−	0.327755i
$15$	−0.683271	+	0.663290i	−0.176420	+	0.171261i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.10485			−1.23811			−0.619055	−	0.785348i	$-0.712484\pi$
$17$	−5.10485			−1.23811			−0.619055	+	0.785348i	$0.712484\pi$
$18$	0.0890100	−	2.99868i	0.0209799	−	0.706795i
$19$	−5.12850			−1.17656			−0.588279	−	0.808658i	$-0.700194\pi$
$19$	−5.12850			−1.17656			−0.588279	+	0.808658i	$0.700194\pi$
$20$	0.274896	+	0.476134i	0.0614686	+	0.106467i
$21$	−0.599583	−	2.37827i	−0.130840	−	0.518982i
$22$	−2.68387	+	4.64861i	−0.572204	+	0.991086i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−1.66620	−	0.473061i	−0.340111	−	0.0965631i
$25$	2.34886	+	4.06835i	0.469773	+	0.813671i
$26$	−4.93577			−0.967984
$27$	−3.50710	−	3.83409i	−0.674942	−	0.737870i
$28$	−1.41606			−0.267610
$29$	−1.63408	−	2.83031i	−0.303442	−	0.525576i	0.673472	−	0.739213i	$-0.264802\pi$
$29$	−1.63408	−	2.83031i	−0.303442	−	0.525576i	−0.976913	+	0.213637i	$0.931469\pi$
$30$	0.916062	+	0.260085i	0.167249	+	0.0474848i
$31$	−2.64591	+	4.58284i	−0.475219	+	0.823103i	−0.999597	−	0.0283825i	$-0.990964\pi$
$31$	−2.64591	+	4.58284i	−0.475219	+	0.823103i	0.524379	+	0.851485i	$0.324298\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.27279	+	9.01513i	0.395642	+	1.56933i
$34$	2.55243	+	4.42093i	0.437738	+	0.758184i
$35$	0.778539			0.131597
$36$	−2.64144	+	1.42225i	−0.440240	+	0.237042i
$37$	−7.38719			−1.21445			−0.607223	−	0.794531i	$-0.707717\pi$
$37$	−7.38719			−1.21445			−0.607223	+	0.794531i	$0.707717\pi$
$38$	2.56425	+	4.44141i	0.415976	+	0.720492i
$39$	−6.13408	+	5.95471i	−0.982239	+	0.953516i
$40$	0.274896	−	0.476134i	0.0434649	−	0.0752833i
$41$	5.82268	−	10.0852i	0.909349	−	1.57504i	0.0943789	−	0.995536i	$-0.469913\pi$
$41$	5.82268	−	10.0852i	0.909349	−	1.57504i	0.814970	−	0.579503i	$-0.196753\pi$
$42$	−1.75985	+	1.70839i	−0.271551	+	0.263611i
$43$	−5.67619	−	9.83145i	−0.865611	−	1.49928i	−0.866440	−	0.499282i	$-0.833597\pi$
$43$	−5.67619	−	9.83145i	−0.865611	−	1.49928i	0.000829163	−	1.00000i	$-0.499736\pi$
$44$	5.36775			0.809219
$45$	1.45224	−	0.781944i	0.216487	−	0.116565i
$46$	1.00000			0.147442
$47$	−1.98556	−	3.43909i	−0.289624	−	0.501644i	0.684096	−	0.729392i	$-0.260197\pi$
$47$	−1.98556	−	3.43909i	−0.289624	−	0.501644i	−0.973720	+	0.227748i	$0.926864\pi$
$48$	0.423416	+	1.67950i	0.0611149	+	0.242415i
$49$	2.49738	−	4.32560i	0.356769	−	0.617943i
$50$	2.34886	−	4.06835i	0.332180	−	0.575352i
$51$	8.50570	+	2.41491i	1.19104	+	0.338154i
$52$	2.46789	+	4.27450i	0.342234	+	0.592767i
$53$	−9.36654			−1.28659			−0.643297	−	0.765617i	$-0.722434\pi$
$53$	−9.36654			−1.28659			−0.643297	+	0.765617i	$0.722434\pi$
$54$	−1.56687	+	4.95428i	−0.213223	+	0.674193i
$55$	−2.95114			−0.397932
$56$	0.708031	+	1.22635i	0.0946146	+	0.163877i
$57$	8.54509	+	2.42609i	1.13183	+	0.321344i
$58$	−1.63408	+	2.83031i	−0.214566	+	0.371638i
$59$	5.65562	−	9.79583i	0.736300	−	1.27531i	−0.217851	−	0.975982i	$-0.569905\pi$
$59$	5.65562	−	9.79583i	0.736300	−	1.27531i	0.954151	−	0.299326i	$-0.0967619\pi$
$60$	−0.232791	−	0.923375i	−0.0300532	−	0.119207i
$61$	4.93130	+	8.54127i	0.631389	+	1.09360i	0.987268	+	0.159065i	$0.0508480\pi$
$61$	4.93130	+	8.54127i	0.631389	+	1.09360i	−0.355879	+	0.934532i	$0.615819\pi$
$62$	5.29181			0.672061
$63$	−0.126044	+	4.24631i	−0.0158800	+	0.534985i
$64$	1.00000			0.125000
$65$	−1.35682	−	2.35009i	−0.168293	−	0.291492i
$66$	6.67094	−	6.47586i	0.821136	−	0.797123i
$67$	−4.36268	+	7.55638i	−0.532986	+	0.923159i	0.466272	+	0.884641i	$0.345597\pi$
$67$	−4.36268	+	7.55638i	−0.532986	+	0.923159i	−0.999258	+	0.0385172i	$0.987737\pi$
$68$	2.55243	−	4.42093i	0.309527	−	0.536117i
$69$	1.24278	−	1.20644i	0.149613	−	0.145238i
$70$	−0.389269	−	0.674234i	−0.0465266	−	0.0805864i
$71$	−2.81741			−0.334365			−0.167183	−	0.985926i	$-0.553467\pi$
$71$	−2.81741			−0.334365			−0.167183	+	0.985926i	$0.553467\pi$
$72$	2.55243	+	1.57642i	0.300806	+	0.185783i
$73$	10.3730			1.21407			0.607035	−	0.794675i	$-0.292359\pi$
$73$	10.3730			1.21407			0.607035	+	0.794675i	$0.292359\pi$
$74$	3.69359	+	6.39749i	0.429371	+	0.743693i
$75$	−1.98909	−	7.88983i	−0.229681	−	0.911040i
$76$	2.56425	−	4.44141i	0.294140	−	0.509465i
$77$	3.80053	−	6.58271i	0.433111	−	0.750170i
$78$	8.22397	+	2.33492i	0.931181	+	0.264377i
$79$	1.72510	+	2.98797i	0.194089	+	0.336173i	0.946602	−	0.322406i	$-0.104491\pi$
$79$	1.72510	+	2.98797i	0.194089	+	0.336173i	−0.752512	+	0.658578i	$0.771158\pi$
$80$	−0.549792			−0.0614686
$81$	4.02977	+	8.04742i	0.447752	+	0.894158i
$82$	−11.6454			−1.28601
$83$	2.00735	+	3.47684i	0.220336	+	0.381633i	0.954910	−	0.296896i	$-0.0959513\pi$
$83$	2.00735	+	3.47684i	0.220336	+	0.381633i	−0.734574	+	0.678528i	$0.762618\pi$
$84$	2.35944	+	0.669883i	0.257436	+	0.0730902i
$85$	−1.40330	+	2.43059i	−0.152210	+	0.263635i
$86$	−5.67619	+	9.83145i	−0.612079	+	1.06015i
$87$	1.38379	+	5.48888i	0.148358	+	0.588470i
$88$	−2.68387	−	4.64861i	−0.286102	−	0.495543i
$89$	−4.39783			−0.466169			−0.233085	−	0.972456i	$-0.574882\pi$
$89$	−4.39783			−0.466169			−0.233085	+	0.972456i	$0.574882\pi$
$90$	−1.40330	−	0.866705i	−0.147921	−	0.0913587i
$91$	6.98935			0.732683
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	6.57656	−	6.38425i	0.681958	−	0.662016i
$94$	−1.98556	+	3.43909i	−0.204795	+	0.354716i
$95$	−1.40980	+	2.44185i	−0.144643	+	0.250529i
$96$	1.24278	−	1.20644i	0.126841	−	0.123132i
$97$	−7.05014	−	12.2112i	−0.715834	−	1.23986i	−0.962637	−	0.270795i	$-0.912714\pi$
$97$	−7.05014	−	12.2112i	−0.715834	−	1.23986i	0.246803	−	0.969066i	$-0.420620\pi$
$98$	−4.99477			−0.504548
$99$	0.477783	−	16.0962i	0.0480190	−	1.61772i
$100$	−4.69773			−0.469773
$101$	7.43191	+	12.8724i	0.739502	+	1.28086i	0.952720	+	0.303851i	$0.0982724\pi$
$101$	7.43191	+	12.8724i	0.739502	+	1.28086i	−0.213217	+	0.977005i	$0.568394\pi$
$102$	−2.16148	−	8.57360i	−0.214018	−	0.848913i
$103$	6.58009	−	11.3971i	0.648356	−	1.12299i	−0.335159	−	0.942161i	$-0.608790\pi$
$103$	6.58009	−	11.3971i	0.648356	−	1.12299i	0.983515	−	0.180824i	$-0.0578765\pi$
$104$	2.46789	−	4.27450i	0.241996	−	0.419149i
$105$	−1.29720	−	0.368296i	−0.126594	−	0.0359420i
$106$	4.68327	+	8.11166i	0.454879	+	0.787874i
$107$	3.34308			0.323188			0.161594	−	0.986857i	$-0.448337\pi$
$107$	3.34308			0.323188			0.161594	+	0.986857i	$0.448337\pi$
$108$	5.07397	−	1.12020i	0.488243	−	0.107791i
$109$	14.3236			1.37196			0.685978	−	0.727622i	$-0.259375\pi$
$109$	14.3236			1.37196			0.685978	+	0.727622i	$0.259375\pi$
$110$	1.47557	+	2.55577i	0.140690	+	0.243683i
$111$	12.3085	+	3.49459i	1.16827	+	0.331691i
$112$	0.708031	−	1.22635i	0.0669026	−	0.115879i
$113$	2.67067	−	4.62573i	0.251235	−	0.435152i	−0.712631	−	0.701539i	$-0.752497\pi$
$113$	2.67067	−	4.62573i	0.251235	−	0.435152i	0.963866	+	0.266387i	$0.0858300\pi$
$114$	−2.17149	−	8.61331i	−0.203379	−	0.806711i
$115$	0.274896	+	0.476134i	0.0256342	+	0.0443997i
$116$	3.26817			0.303442
$117$	13.0375	−	7.01992i	1.20532	−	0.648992i
$118$	−11.3112			−1.04128
$119$	−3.61439	−	6.26031i	−0.331331	−	0.573882i
$120$	−0.683271	+	0.663290i	−0.0623738	+	0.0605498i
$121$	−8.90636	+	15.4263i	−0.809669	+	1.40239i
$122$	4.93130	−	8.54127i	0.446459	−	0.773290i
$123$	−14.4726	+	14.0494i	−1.30495	+	1.26679i
$124$	−2.64591	−	4.58284i	−0.237609	−	0.411551i
$125$	5.33173			0.476885
$126$	3.74044	−	2.01400i	0.333225	−	0.179421i
$127$	−4.31698			−0.383070			−0.191535	−	0.981486i	$-0.561347\pi$
$127$	−4.31698			−0.383070			−0.191535	+	0.981486i	$0.561347\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	4.80678	+	19.0663i	0.423213	+	1.67869i
$130$	−1.35682	+	2.35009i	−0.119001	+	0.206116i
$131$	−4.92464	+	8.52973i	−0.430268	+	0.745246i	−0.996896	−	0.0787274i	$-0.974914\pi$
$131$	−4.92464	+	8.52973i	−0.430268	+	0.745246i	0.566628	+	0.823974i	$0.308248\pi$
$132$	−8.94373	−	2.53927i	−0.778452	−	0.221015i
$133$	−3.63114	−	6.28931i	−0.314859	−	0.545352i
$134$	8.72535			0.753756
$135$	−2.78963	+	0.615875i	−0.240093	+	0.0530061i
$136$	−5.10485			−0.437738
$137$	4.74366	+	8.21625i	0.405278	+	0.701962i	0.994354	−	0.106116i	$-0.0338414\pi$
$137$	4.74366	+	8.21625i	0.405278	+	0.701962i	−0.589076	+	0.808078i	$0.700508\pi$
$138$	−1.66620	−	0.473061i	−0.141836	−	0.0402696i
$139$	4.29267	−	7.43511i	0.364099	−	0.630638i	−0.624532	−	0.780999i	$-0.714710\pi$
$139$	4.29267	−	7.43511i	0.364099	−	0.630638i	0.988631	+	0.150361i	$0.0480436\pi$
$140$	−0.389269	+	0.674234i	−0.0328993	+	0.0569832i
$141$	1.68144	+	6.66950i	0.141603	+	0.561673i
$142$	1.40871	+	2.43995i	0.118216	+	0.204756i
$143$	−26.4940			−2.21554
$144$	0.0890100	−	2.99868i	0.00741750	−	0.249890i
$145$	−1.79681			−0.149217
$146$	−5.18651	−	8.98330i	−0.429239	−	0.743463i
$147$	−6.20741	+	6.02588i	−0.511978	+	0.497007i
$148$	3.69359	−	6.39749i	0.303611	−	0.525871i
$149$	1.67802	−	2.90642i	0.137469	−	0.238103i	−0.789069	−	0.614304i	$-0.789437\pi$
$149$	1.67802	−	2.90642i	0.137469	−	0.238103i	0.926538	+	0.376202i	$0.122770\pi$
$150$	−5.83825	+	5.66752i	−0.476691	+	0.462751i
$151$	5.15710	+	8.93236i	0.419679	+	0.726905i	0.995907	−	0.0903835i	$-0.0288093\pi$
$151$	5.15710	+	8.93236i	0.419679	+	0.726905i	−0.576228	+	0.817289i	$0.695476\pi$
$152$	−5.12850			−0.415976
$153$	−13.0298	−	8.04742i	−1.05339	−	0.650595i
$154$	−7.60106			−0.612511
$155$	1.45470	+	2.51961i	0.116844	+	0.202380i
$156$	−2.08989	−	8.28962i	−0.167325	−	0.663701i
$157$	5.83267	−	10.1025i	0.465497	−	0.806265i	−0.533726	−	0.845657i	$-0.679209\pi$
$157$	5.83267	−	10.1025i	0.465497	−	0.806265i	0.999224	+	0.0393920i	$0.0125421\pi$
$158$	1.72510	−	2.98797i	0.137242	−	0.237710i
$159$	15.6065	+	4.43094i	1.23768	+	0.351397i
$160$	0.274896	+	0.476134i	0.0217324	+	0.0376417i
$161$	−1.41606			−0.111601
$162$	4.95438	−	7.51359i	0.389253	−	0.590324i
$163$	−7.68813			−0.602181			−0.301090	−	0.953596i	$-0.597351\pi$
$163$	−7.68813			−0.602181			−0.301090	+	0.953596i	$0.597351\pi$
$164$	5.82268	+	10.0852i	0.454675	+	0.787520i
$165$	4.91719	+	1.39607i	0.382803	+	0.108684i
$166$	2.00735	−	3.47684i	0.155801	−	0.269855i
$167$	−9.11755	+	15.7921i	−0.705537	+	1.22203i	0.260960	+	0.965350i	$0.415961\pi$
$167$	−9.11755	+	15.7921i	−0.705537	+	1.22203i	−0.966497	+	0.256677i	$0.917372\pi$
$168$	−0.599583	−	2.37827i	−0.0462589	−	0.183488i
$169$	−5.68092	−	9.83963i	−0.436994	−	0.756895i
$170$	2.80661			0.215257
$171$	−13.0901	−	8.08469i	−1.00103	−	0.618252i
$172$	11.3524			0.865611
$173$	0.964918	+	1.67129i	0.0733613	+	0.127066i	0.900373	−	0.435120i	$-0.143294\pi$
$173$	0.964918	+	1.67129i	0.0733613	+	0.127066i	−0.827011	+	0.562185i	$0.809961\pi$
$174$	4.06161	−	3.94284i	0.307910	−	0.298906i
$175$	−3.32614	+	5.76104i	−0.251432	+	0.435494i
$176$	−2.68387	+	4.64861i	−0.202305	+	0.350402i
$177$	−14.0574	+	13.6463i	−1.05662	+	1.02572i
$178$	2.19892	+	3.80863i	0.164816	+	0.285469i
$179$	3.04992			0.227962			0.113981	−	0.993483i	$-0.463640\pi$
$179$	3.04992			0.227962			0.113981	+	0.993483i	$0.463640\pi$
$180$	−0.0489370	+	1.64865i	−0.00364755	+	0.122883i
$181$	6.36970			0.473456			0.236728	−	0.971576i	$-0.423925\pi$
$181$	6.36970			0.473456			0.236728	+	0.971576i	$0.423925\pi$
$182$	−3.49468	−	6.05296i	−0.259043	−	0.448675i
$183$	−4.17599	−	16.5642i	−0.308698	−	1.22446i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−2.03071	+	3.51729i	−0.149301	+	0.258596i
$186$	−8.81720	−	2.50335i	−0.646509	−	0.183554i
$187$	13.7008	+	23.7305i	1.00190	+	1.73534i
$188$	3.97112			0.289624
$189$	2.21878	−	7.01557i	0.161392	−	0.510308i
$190$	2.81961			0.204556
$191$	3.79415	+	6.57167i	0.274535	+	0.475509i	0.970018	−	0.243034i	$-0.0781426\pi$
$191$	3.79415	+	6.57167i	0.274535	+	0.475509i	−0.695482	+	0.718543i	$0.744809\pi$
$192$	−1.66620	−	0.473061i	−0.120247	−	0.0341402i
$193$	3.79378	−	6.57102i	0.273082	−	0.472992i	−0.696567	−	0.717492i	$-0.745290\pi$
$193$	3.79378	−	6.57102i	0.273082	−	0.472992i	0.969650	+	0.244499i	$0.0786235\pi$
$194$	−7.05014	+	12.2112i	−0.506171	+	0.876714i
$195$	1.14900	+	4.55757i	0.0822817	+	0.326374i
$196$	2.49738	+	4.32560i	0.178385	+	0.308971i
$197$	5.44600			0.388011			0.194006	−	0.981000i	$-0.437852\pi$
$197$	5.44600			0.388011			0.194006	+	0.981000i	$0.437852\pi$
$198$	−14.1786	+	7.63431i	−1.00763	+	0.542547i
$199$	−0.729539			−0.0517156			−0.0258578	−	0.999666i	$-0.508232\pi$
$199$	−0.729539			−0.0517156			−0.0258578	+	0.999666i	$0.508232\pi$
$200$	2.34886	+	4.06835i	0.166090	+	0.287676i
$201$	10.8437	−	10.5266i	0.764856	−	0.742490i
$202$	7.43191	−	12.8724i	0.522907	−	0.905702i
$203$	2.31396	−	4.00790i	0.162408	−	0.281299i
$204$	−6.34422	+	6.15870i	−0.444184	+	0.431195i
$205$	−3.20126	−	5.54474i	−0.223586	−	0.387262i
$206$	−13.1602			−0.916914
$207$	−2.64144	+	1.42225i	−0.183593	+	0.0988535i
$208$	−4.93577			−0.342234
$209$	13.7642	+	23.8404i	0.952093	+	1.64907i
$210$	0.329646	+	1.30756i	0.0227477	+	0.0902299i
$211$	3.63341	−	6.29325i	0.250134	−	0.433245i	−0.713428	−	0.700728i	$-0.752859\pi$
$211$	3.63341	−	6.29325i	0.250134	−	0.433245i	0.963563	+	0.267483i	$0.0861920\pi$
$212$	4.68327	−	8.11166i	0.321648	−	0.557111i
$213$	4.69437	+	1.33281i	0.321653	+	0.0913224i
$214$	−1.67154	−	2.89519i	−0.114264	−	0.197911i
$215$	−6.24144			−0.425663
$216$	−3.50710	−	3.83409i	−0.238628	−	0.260877i
$217$	−7.49353			−0.508694
$218$	−7.16182	−	12.4046i	−0.485060	−	0.840148i
$219$	−17.2835	−	4.90707i	−1.16791	−	0.331589i
$220$	1.47557	−	2.55577i	0.0994830	−	0.172310i
$221$	−12.5982	+	21.8207i	−0.847446	+	1.46782i
$222$	−3.12785	−	12.4068i	−0.209928	−	0.832688i
$223$	1.37490	+	2.38140i	0.0920704	+	0.159471i	0.908382	−	0.418141i	$-0.137318\pi$
$223$	1.37490	+	2.38140i	0.0920704	+	0.159471i	−0.816312	+	0.577612i	$0.803985\pi$
$224$	−1.41606			−0.0946146
$225$	−0.418145	+	14.0870i	−0.0278763	+	0.939132i
$226$	−5.34133			−0.355300
$227$	−0.944805	−	1.63645i	−0.0627089	−	0.108615i	0.832966	−	0.553323i	$-0.186641\pi$
$227$	−0.944805	−	1.63645i	−0.0627089	−	0.108615i	−0.895675	+	0.444708i	$0.853307\pi$
$228$	−6.37360	+	6.18722i	−0.422102	+	0.409759i
$229$	6.01654	−	10.4210i	0.397584	−	0.688636i	−0.595843	−	0.803101i	$-0.703182\pi$
$229$	6.01654	−	10.4210i	0.397584	−	0.688636i	0.993427	+	0.114465i	$0.0365153\pi$
$230$	0.274896	−	0.476134i	0.0181261	−	0.0313953i
$231$	−9.44646	+	9.17022i	−0.621531	+	0.603356i
$232$	−1.63408	−	2.83031i	−0.107283	−	0.185819i
$233$	−20.3919			−1.33592			−0.667959	−	0.744198i	$-0.732832\pi$
$233$	−20.3919			−1.33592			−0.667959	+	0.744198i	$0.732832\pi$
$234$	−12.5982	−	7.78087i	−0.823570	−	0.508651i
$235$	−2.18329			−0.142422
$236$	5.65562	+	9.79583i	0.368150	+	0.637654i
$237$	−1.46087	−	5.79462i	−0.0948940	−	0.376401i
$238$	−3.61439	+	6.26031i	−0.234286	+	0.405796i
$239$	14.5563	−	25.2122i	0.941568	−	1.63084i	0.179087	−	0.983833i	$-0.442686\pi$
$239$	14.5563	−	25.2122i	0.941568	−	1.63084i	0.762481	−	0.647011i	$-0.223981\pi$
$240$	0.916062	+	0.260085i	0.0591315	+	0.0167884i
$241$	−2.61985	−	4.53771i	−0.168759	−	0.292299i	0.769225	−	0.638978i	$-0.220643\pi$
$241$	−2.61985	−	4.53771i	−0.168759	−	0.292299i	−0.937984	+	0.346679i	$0.887309\pi$
$242$	17.8127			1.14505
$243$	−2.90748	−	15.3149i	−0.186515	−	0.982452i
$244$	−9.86261			−0.631389
$245$	−1.37304	−	2.37818i	−0.0877204	−	0.151936i
$246$	19.4035	+	5.50896i	1.23712	+	0.351238i
$247$	−12.6565	+	21.9218i	−0.805317	+	1.39485i
$248$	−2.64591	+	4.58284i	−0.168015	+	0.291011i
$249$	−1.69989	−	6.74270i	−0.107726	−	0.427301i
$250$	−2.66587	−	4.61741i	−0.168604	−	0.292031i
$251$	1.66135			0.104864			0.0524318	−	0.998625i	$-0.483303\pi$
$251$	1.66135			0.104864			0.0524318	+	0.998625i	$0.483303\pi$
$252$	−3.61439	−	2.23231i	−0.227685	−	0.140623i
$253$	5.36775			0.337467
$254$	2.15849	+	3.73861i	0.135436	+	0.234582i
$255$	3.48800	−	3.38600i	0.218427	−	0.212040i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.69010	+	4.65939i	−0.167804	+	0.290645i	−0.937647	−	0.347588i	$-0.887001\pi$
$257$	−2.69010	+	4.65939i	−0.167804	+	0.290645i	0.769843	+	0.638233i	$0.220334\pi$
$258$	14.1085	−	13.6959i	0.878358	−	0.852673i
$259$	−5.23035	−	9.05924i	−0.324998	−	0.562914i
$260$	2.71365			0.168293
$261$	0.290899	−	9.80018i	0.0180062	−	0.606616i
$262$	9.84929			0.608491
$263$	−7.51821	−	13.0219i	−0.463593	−	0.802966i	0.535544	−	0.844507i	$-0.320107\pi$
$263$	−7.51821	−	13.0219i	−0.463593	−	0.802966i	−0.999137	+	0.0415413i	$0.986773\pi$
$264$	2.27279	+	9.01513i	0.139881	+	0.554843i
$265$	−2.57482	+	4.45973i	−0.158170	+	0.273959i
$266$	−3.63114	+	6.28931i	−0.222639	+	0.385622i
$267$	7.32766	+	2.08044i	0.448445	+	0.127321i
$268$	−4.36268	−	7.55638i	−0.266493	−	0.461579i
$269$	−25.3665			−1.54663			−0.773313	−	0.634025i	$-0.781402\pi$
$269$	−25.3665			−1.54663			−0.773313	+	0.634025i	$0.781402\pi$
$270$	1.92818	+	2.10795i	0.117345	+	0.128286i
$271$	16.0835			0.977003			0.488502	−	0.872563i	$-0.337544\pi$
$271$	16.0835			0.977003			0.488502	+	0.872563i	$0.337544\pi$
$272$	2.55243	+	4.42093i	0.154764	+	0.268058i
$273$	−11.6456	−	3.30639i	−0.704826	−	0.200112i
$274$	4.74366	−	8.21625i	0.286575	−	0.496362i
$275$	12.6081	−	21.8379i	0.760298	−	1.31687i
$276$	0.423416	+	1.67950i	0.0254867	+	0.101094i
$277$	−13.1560	−	22.7869i	−0.790469	−	1.36913i	−0.925677	−	0.378315i	$-0.876504\pi$
$277$	−13.1560	−	22.7869i	−0.790469	−	1.36913i	0.135208	−	0.990817i	$-0.456830\pi$
$278$	−8.58533			−0.514914
$279$	−13.9780	+	7.52630i	−0.836840	+	0.450588i
$280$	0.778539			0.0465266
$281$	5.49555	+	9.51858i	0.327837	+	0.567831i	0.982082	−	0.188452i	$-0.0603469\pi$
$281$	5.49555	+	9.51858i	0.327837	+	0.567831i	−0.654245	+	0.756282i	$0.727014\pi$
$282$	4.93524	−	4.79092i	0.293889	−	0.285295i
$283$	7.05278	−	12.2158i	0.419244	−	0.726152i	−0.576619	−	0.817013i	$-0.695628\pi$
$283$	7.05278	−	12.2158i	0.419244	−	0.726152i	0.995864	+	0.0908606i	$0.0289618\pi$
$284$	1.40871	−	2.43995i	0.0835914	−	0.144784i
$285$	3.50415	−	3.40168i	0.207568	−	0.201498i
$286$	13.2470	+	22.9445i	0.783311	+	1.35673i
$287$	16.4905			0.973405
$288$	−2.64144	+	1.42225i	−0.155648	+	0.0838072i
$289$	9.05954			0.532914
$290$	0.898405	+	1.55608i	0.0527562	+	0.0913764i
$291$	5.97029	+	23.6814i	0.349985	+	1.38823i
$292$	−5.18651	+	8.98330i	−0.303518	+	0.525708i
$293$	−13.9980	+	24.2452i	−0.817771	+	1.41642i	0.0895497	+	0.995982i	$0.471457\pi$
$293$	−13.9980	+	24.2452i	−0.817771	+	1.41642i	−0.907321	+	0.420439i	$0.861876\pi$
$294$	8.32227	+	2.36283i	0.485365	+	0.137803i
$295$	−3.10942	−	5.38567i	−0.181037	−	0.313566i
$296$	−7.38719			−0.429371
$297$	−8.41054	+	26.5934i	−0.488029	+	1.54310i
$298$	−3.35604			−0.194410
$299$	2.46789	+	4.27450i	0.142721	+	0.247201i
$300$	7.82734	+	2.22231i	0.451912	+	0.128305i
$301$	8.03783	−	13.9219i	0.463293	−	0.802447i
$302$	5.15710	−	8.93236i	0.296758	−	0.514000i
$303$	−6.29358	−	24.9638i	−0.361557	−	1.43413i
$304$	2.56425	+	4.44141i	0.147070	+	0.254732i
$305$	5.42238			0.310485
$306$	−0.454383	+	15.3078i	−0.0259754	+	0.875090i
$307$	26.9288			1.53691			0.768454	−	0.639906i	$-0.221027\pi$
$307$	26.9288			1.53691			0.768454	+	0.639906i	$0.221027\pi$
$308$	3.80053	+	6.58271i	0.216555	+	0.375085i
$309$	−16.3552	+	15.8770i	−0.930417	+	0.903209i
$310$	1.45470	−	2.51961i	0.0826212	−	0.143104i
$311$	10.3452	−	17.9184i	0.586621	−	1.01606i	−0.408050	−	0.912959i	$-0.633791\pi$
$311$	10.3452	−	17.9184i	0.586621	−	1.01606i	0.994671	−	0.103098i	$-0.0328755\pi$
$312$	−6.13408	+	5.95471i	−0.347274	+	0.337119i
$313$	−9.10081	−	15.7631i	−0.514408	−	0.890981i	−0.999860	−	0.0167179i	$-0.994678\pi$
$313$	−9.10081	−	15.7631i	−0.514408	−	0.890981i	0.485452	−	0.874263i	$-0.338655\pi$
$314$	−11.6653			−0.658313
$315$	1.98716	+	1.22731i	0.111964	+	0.0691510i
$316$	−3.45021			−0.194089
$317$	−9.95354	−	17.2400i	−0.559047	−	0.968297i	−0.997576	−	0.0695803i	$-0.977834\pi$
$317$	−9.95354	−	17.2400i	−0.559047	−	0.968297i	0.438530	−	0.898717i	$-0.355499\pi$
$318$	−3.96595	−	15.7311i	−0.222399	−	0.882156i
$319$	−8.77135	+	15.1924i	−0.491101	+	0.850612i
$320$	0.274896	−	0.476134i	0.0153671	−	0.0266167i
$321$	−5.57023	−	1.58148i	−0.310900	−	0.0882696i
$322$	0.708031	+	1.22635i	0.0394570	+	0.0683415i
$323$	26.1802			1.45671
$324$	−8.98415	−	0.533825i	−0.499120	−	0.0296569i
$325$	23.1869			1.28618
$326$	3.84406	+	6.65812i	0.212903	+	0.368759i
$327$	−23.8660	−	6.77595i	−1.31979	−	0.374711i
$328$	5.82268	−	10.0852i	0.321504	−	0.556860i
$329$	2.81168	−	4.86997i	0.155013	−	0.268490i
$330$	−1.24956	−	4.95644i	−0.0687861	−	0.272843i
$331$	1.75715	+	3.04347i	0.0965815	+	0.167284i	0.910268	−	0.414020i	$-0.135876\pi$
$331$	1.75715	+	3.04347i	0.0965815	+	0.167284i	−0.813686	+	0.581305i	$0.802542\pi$
$332$	−4.01471			−0.220336
$333$	−18.8553	−	11.6453i	−1.03326	−	0.638161i
$334$	18.2351			0.997781
$335$	2.39856	+	4.15443i	0.131048	+	0.226981i
$336$	−1.75985	+	1.70839i	−0.0960079	+	0.0932004i
$337$	−9.85472	+	17.0689i	−0.536821	+	0.929801i	0.462252	+	0.886749i	$0.347042\pi$
$337$	−9.85472	+	17.0689i	−0.536821	+	0.929801i	−0.999073	+	0.0430522i	$0.986292\pi$
$338$	−5.68092	+	9.83963i	−0.309001	+	0.535206i
$339$	−6.63810	+	6.44399i	−0.360532	+	0.349989i
$340$	−1.40330	−	2.43059i	−0.0761048	−	0.131817i
$341$	28.4051			1.53822
$342$	−0.456488	+	15.3787i	−0.0246840	+	0.831586i
$343$	16.9853			0.917122
$344$	−5.67619	−	9.83145i	−0.306040	−	0.530076i
$345$	−0.232791	−	0.923375i	−0.0125330	−	0.0497128i
$346$	0.964918	−	1.67129i	0.0518743	−	0.0898489i
$347$	−15.6595	+	27.1231i	−0.840647	+	1.45604i	0.0487016	+	0.998813i	$0.484492\pi$
$347$	−15.6595	+	27.1231i	−0.840647	+	1.45604i	−0.889349	+	0.457230i	$0.848842\pi$
$348$	−5.44541	−	1.54604i	−0.291905	−	0.0828765i
$349$	14.2677	+	24.7124i	0.763732	+	1.32282i	0.940914	+	0.338645i	$0.109968\pi$
$349$	14.2677	+	24.7124i	0.763732	+	1.32282i	−0.177182	+	0.984178i	$0.556698\pi$
$350$	6.65227			0.355579
$351$	−25.0439	+	5.52904i	−1.33675	+	0.295118i
$352$	5.36775			0.286102
$353$	−3.51180	−	6.08262i	−0.186914	−	0.323745i	0.757306	−	0.653061i	$-0.226515\pi$
$353$	−3.51180	−	6.08262i	−0.186914	−	0.323745i	−0.944220	+	0.329316i	$0.893182\pi$
$354$	18.8468	+	5.35091i	1.00169	+	0.284397i
$355$	−0.774495	+	1.34147i	−0.0411059	+	0.0711976i
$356$	2.19892	−	3.80863i	0.116542	−	0.201857i
$357$	3.06079	+	12.1407i	0.161994	+	0.642556i
$358$	−1.52496	−	2.64131i	−0.0805966	−	0.139597i
$359$	14.7689			0.779472			0.389736	−	0.920927i	$-0.372566\pi$
$359$	14.7689			0.779472			0.389736	+	0.920927i	$0.372566\pi$
$360$	1.45224	−	0.781944i	0.0765398	−	0.0412121i
$361$	7.30151			0.384290
$362$	−3.18485	−	5.51633i	−0.167392	−	0.289932i
$363$	22.1373	−	21.4900i	1.16191	−	1.12793i
$364$	−3.49468	+	6.05296i	−0.183171	+	0.317261i
$365$	2.85150	−	4.93894i	0.149254	−	0.258516i
$366$	−12.2571	+	11.8986i	−0.640687	+	0.621951i
$367$	−4.03118	−	6.98221i	−0.210426	−	0.364468i	0.741422	−	0.671039i	$-0.234152\pi$
$367$	−4.03118	−	6.98221i	−0.210426	−	0.364468i	−0.951848	+	0.306571i	$0.900818\pi$
$368$	1.00000			0.0521286
$369$	30.7605	−	16.5627i	1.60133	−	0.862217i
$370$	4.06141			0.211143
$371$	−6.63180	−	11.4866i	−0.344306	−	0.596355i
$372$	2.24064	+	8.88759i	0.116172	+	0.460800i
$373$	−10.9108	+	18.8981i	−0.564941	+	0.978507i	0.432114	+	0.901819i	$0.357768\pi$
$373$	−10.9108	+	18.8981i	−0.564941	+	0.978507i	−0.997055	+	0.0766881i	$0.975565\pi$
$374$	13.7008	−	23.7305i	0.708451	−	1.22707i
$375$	−8.88372	−	2.52223i	−0.458753	−	0.130247i
$376$	−1.98556	−	3.43909i	−0.102398	−	0.177358i
$377$	−16.1309			−0.830784
$378$	−7.18505	+	1.58627i	−0.369559	+	0.0815888i
$379$	5.63096			0.289243			0.144621	−	0.989487i	$-0.453804\pi$
$379$	5.63096			0.289243			0.144621	+	0.989487i	$0.453804\pi$
$380$	−1.40980	−	2.44185i	−0.0723214	−	0.125264i
$381$	7.19294	+	2.04219i	0.368506	+	0.104625i
$382$	3.79415	−	6.57167i	0.194126	−	0.336236i
$383$	9.61375	−	16.6515i	0.491240	−	0.850852i	−0.508710	−	0.860938i	$-0.669877\pi$
$383$	9.61375	−	16.6515i	0.491240	−	0.850852i	0.999949	+	0.0100863i	$0.00321061\pi$
$384$	0.423416	+	1.67950i	0.0216074	+	0.0857066i
$385$	−2.08950	−	3.61912i	−0.106491	−	0.184447i
$386$	−7.58756			−0.386197
$387$	1.01047	−	34.0421i	0.0513653	−	1.73046i
$388$	14.1003			0.715834
$389$	18.3382	+	31.7627i	0.929783	+	1.61043i	0.783683	+	0.621161i	$0.213339\pi$
$389$	18.3382	+	31.7627i	0.929783	+	1.61043i	0.146100	+	0.989270i	$0.453328\pi$
$390$	3.37247	−	3.27385i	0.170772	−	0.165778i
$391$	2.55243	−	4.42093i	0.129082	−	0.223576i
$392$	2.49738	−	4.32560i	0.126137	−	0.218476i
$393$	12.2405	−	11.8826i	0.617452	−	0.599396i
$394$	−2.72300	−	4.71637i	−0.137183	−	0.237608i
$395$	1.89690			0.0954432
$396$	13.7008	+	8.46185i	0.688491	+	0.425224i
$397$	11.0000			0.552072			0.276036	−	0.961147i	$-0.410979\pi$
$397$	11.0000			0.552072			0.276036	+	0.961147i	$0.410979\pi$
$398$	0.364769	+	0.631799i	0.0182842	+	0.0316692i
$399$	3.07496	+	12.1970i	0.153941	+	0.610613i
$400$	2.34886	−	4.06835i	0.117443	−	0.203418i
$401$	2.12653	−	3.68325i	0.106194	−	0.183933i	−0.808032	−	0.589139i	$-0.799467\pi$
$401$	2.12653	−	3.68325i	0.106194	−	0.183933i	0.914225	+	0.405206i	$0.132800\pi$
$402$	−14.5382	−	4.12762i	−0.725098	−	0.205867i
$403$	13.0596	+	22.6199i	0.650544	+	1.12678i
$404$	−14.8638			−0.739502
$405$	4.93941	+	0.293492i	0.245441	+	0.0145838i
$406$	−4.62792			−0.229680
$407$	19.8263	+	34.3401i	0.982752	+	1.70218i
$408$	8.50570	+	2.41491i	0.421095	+	0.119556i
$409$	16.8214	−	29.1355i	0.831764	−	1.44066i	−0.0648746	−	0.997893i	$-0.520665\pi$
$409$	16.8214	−	29.1355i	0.831764	−	1.44066i	0.896638	−	0.442764i	$-0.146002\pi$
$410$	−3.20126	+	5.54474i	−0.158099	+	0.273835i
$411$	−4.01708	−	15.9339i	−0.198148	−	0.785963i
$412$	6.58009	+	11.3971i	0.324178	+	0.561493i
$413$	16.0174			0.788166
$414$	2.55243	+	1.57642i	0.125445	+	0.0774770i
$415$	2.20725			0.108350
$416$	2.46789	+	4.27450i	0.120998	+	0.209575i
$417$	−10.6697	+	10.3577i	−0.522497	+	0.507218i
$418$	13.7642	−	23.8404i	0.673231	−	1.16607i
$419$	−9.51578	+	16.4818i	−0.464876	+	0.805189i	−0.999196	−	0.0400932i	$-0.987235\pi$
$419$	−9.51578	+	16.4818i	−0.464876	+	0.805189i	0.534320	+	0.845282i	$0.320568\pi$
$420$	0.967553	−	0.939260i	0.0472118	−	0.0458312i
$421$	−15.7450	−	27.2711i	−0.767362	−	1.32911i	−0.938989	−	0.343948i	$-0.888236\pi$
$421$	−15.7450	−	27.2711i	−0.767362	−	1.32911i	0.171626	−	0.985162i	$-0.445098\pi$
$422$	−7.26681			−0.353743
$423$	0.353470	−	11.9081i	0.0171863	−	0.578993i
$424$	−9.36654			−0.454879
$425$	−11.9906	−	20.7683i	−0.581630	−	1.00741i
$426$	−1.19294	−	4.73184i	−0.0577981	−	0.229259i
$427$	−6.98303	+	12.0950i	−0.337932	+	0.585316i
$428$	−1.67154	+	2.89519i	−0.0807970	+	0.139944i
$429$	44.1442	+	12.5333i	2.13130	+	0.605111i
$430$	3.12072	+	5.40525i	0.150495	+	0.260664i
$431$	1.83077			0.0881852			0.0440926	−	0.999027i	$-0.485960\pi$
$431$	1.83077			0.0881852			0.0440926	+	0.999027i	$0.485960\pi$
$432$	−1.56687	+	4.95428i	−0.0753858	+	0.238363i
$433$	13.2975			0.639036			0.319518	−	0.947580i	$-0.396479\pi$
$433$	13.2975			0.639036			0.319518	+	0.947580i	$0.396479\pi$
$434$	3.74676	+	6.48959i	0.179850	+	0.311510i
$435$	2.99384	+	0.850000i	0.143544	+	0.0407544i
$436$	−7.16182	+	12.4046i	−0.342989	+	0.594074i
$437$	2.56425	−	4.44141i	0.122665	−	0.212462i
$438$	4.39211	+	17.4215i	0.209863	+	0.832431i
$439$	−6.97305	−	12.0777i	−0.332805	−	0.576436i	0.650255	−	0.759716i	$-0.274662\pi$
$439$	−6.97305	−	12.0777i	−0.332805	−	0.576436i	−0.983061	+	0.183280i	$0.941329\pi$
$440$	−2.95114			−0.140690
$441$	13.1934	−	7.10383i	0.628256	−	0.338278i
$442$	25.1964			1.19847
$443$	−0.548677	−	0.950336i	−0.0260684	−	0.0451518i	0.852697	−	0.522406i	$-0.174965\pi$
$443$	−0.548677	−	0.950336i	−0.0260684	−	0.0451518i	−0.878765	+	0.477254i	$0.841632\pi$
$444$	−9.18066	+	8.91219i	−0.435695	+	0.422954i
$445$	−1.20895	+	2.09396i	−0.0573095	+	0.0992630i
$446$	1.37490	−	2.38140i	0.0651036	−	0.112763i
$447$	−4.17082	+	4.04886i	−0.197273	+	0.191504i
$448$	0.708031	+	1.22635i	0.0334513	+	0.0579394i
$449$	−23.6244			−1.11491			−0.557453	−	0.830209i	$-0.688221\pi$
$449$	−23.6244			−1.11491			−0.557453	+	0.830209i	$0.688221\pi$
$450$	12.4088	−	6.68137i	0.584954	−	0.314963i
$451$	−62.5093			−2.94345
$452$	2.67067	+	4.62573i	0.125618	+	0.217576i
$453$	−4.36720	−	17.3227i	−0.205189	−	0.813892i
$454$	−0.944805	+	1.63645i	−0.0443419	+	0.0768024i
$455$	1.92134	−	3.32787i	0.0900740	−	0.156013i
$456$	8.54509	+	2.42609i	0.400161	+	0.113612i
$457$	−5.55741	−	9.62571i	−0.259965	−	0.450272i	0.706268	−	0.707945i	$-0.250378\pi$
$457$	−5.55741	−	9.62571i	−0.259965	−	0.450272i	−0.966232	+	0.257673i	$0.917044\pi$
$458$	−12.0331			−0.562269
$459$	17.9033	+	19.5725i	0.835652	+	0.913564i
$460$	−0.549792			−0.0256342
$461$	−9.52023	−	16.4895i	−0.443401	−	0.767993i	0.554538	−	0.832158i	$-0.312895\pi$
$461$	−9.52023	−	16.4895i	−0.443401	−	0.767993i	−0.997939	+	0.0641650i	$0.979562\pi$
$462$	12.6649	+	3.59576i	0.589223	+	0.167290i
$463$	−1.95590	+	3.38771i	−0.0908982	+	0.157440i	−0.907889	−	0.419210i	$-0.862307\pi$
$463$	−1.95590	+	3.38771i	−0.0908982	+	0.157440i	0.816991	+	0.576650i	$0.195640\pi$
$464$	−1.63408	+	2.83031i	−0.0758604	+	0.131394i
$465$	−1.23188	−	4.88633i	−0.0571273	−	0.226598i
$466$	10.1959	+	17.6599i	0.472318	+	0.818079i
$467$	30.5055			1.41163			0.705813	−	0.708398i	$-0.250582\pi$
$467$	30.5055			1.41163			0.705813	+	0.708398i	$0.250582\pi$
$468$	−0.439333	+	14.8008i	−0.0203082	+	0.684167i
$469$	−12.3556			−0.570530
$470$	1.09165	+	1.89079i	0.0503539	+	0.0872154i
$471$	−14.4975	+	14.0735i	−0.668008	+	0.648473i
$472$	5.65562	−	9.79583i	0.260321	−	0.450890i
$473$	−30.4684	+	52.7727i	−1.40094	+	2.42649i
$474$	−4.28785	+	4.16247i	−0.196948	+	0.191188i
$475$	−12.0462	−	20.8645i	−0.552715	−	0.957331i
$476$	7.22879			0.331331
$477$	−23.9074	−	14.7656i	−1.09465	−	0.676072i
$478$	−29.1126			−1.33158
$479$	3.16986	+	5.49036i	0.144835	+	0.250861i	0.929311	−	0.369297i	$-0.120402\pi$
$479$	3.16986	+	5.49036i	0.144835	+	0.250861i	−0.784477	+	0.620158i	$0.787068\pi$
$480$	−0.232791	−	0.923375i	−0.0106254	−	0.0421461i
$481$	−18.2307	+	31.5765i	−0.831250	+	1.43977i
$482$	−2.61985	+	4.53771i	−0.119331	+	0.206687i
$483$	2.35944	+	0.669883i	0.107358	+	0.0304807i
$484$	−8.90636	−	15.4263i	−0.404835	−	0.701194i
$485$	−7.75222			−0.352010
$486$	−11.8094	+	10.1754i	−0.535684	+	0.461566i
$487$	11.3575			0.514658			0.257329	−	0.966324i	$-0.417158\pi$
$487$	11.3575			0.514658			0.257329	+	0.966324i	$0.417158\pi$
$488$	4.93130	+	8.54127i	0.223230	+	0.386645i
$489$	12.8099	+	3.63695i	0.579286	+	0.164469i
$490$	−1.37304	+	2.37818i	−0.0620277	+	0.107435i
$491$	−5.13958	+	8.90202i	−0.231946	+	0.401743i	−0.958381	−	0.285493i	$-0.907843\pi$
$491$	−5.13958	+	8.90202i	−0.231946	+	0.401743i	0.726435	+	0.687236i	$0.241176\pi$
$492$	−4.93083	−	19.5584i	−0.222299	−	0.881759i
$493$	8.34175	+	14.4483i	0.375694	+	0.650721i
$494$	25.3131			1.13889
$495$	−7.53258	−	4.65226i	−0.338564	−	0.209103i
$496$	5.29181			0.237609
$497$	−1.99482	−	3.45512i	−0.0894797	−	0.154983i
$498$	−4.98941	+	4.84350i	−0.223581	+	0.217043i
$499$	−12.7356	+	22.0588i	−0.570126	+	0.987487i	0.426427	+	0.904522i	$0.359772\pi$
$499$	−12.7356	+	22.0588i	−0.570126	+	0.987487i	−0.996552	+	0.0829648i	$0.973561\pi$
$500$	−2.66587	+	4.61741i	−0.119221	+	0.206497i
$501$	22.6622	−	21.9995i	1.01247	−	0.982867i
$502$	−0.830676	−	1.43877i	−0.0370749	−	0.0642156i
$503$	−0.683540			−0.0304775			−0.0152388	−	0.999884i	$-0.504851\pi$
$503$	−0.683540			−0.0304775			−0.0152388	+	0.999884i	$0.504851\pi$
$504$	−0.126044	+	4.24631i	−0.00561443	+	0.189146i
$505$	8.17200			0.363649
$506$	−2.68387	−	4.64861i	−0.119313	−	0.206656i
$507$	4.81078	+	19.0822i	0.213654	+	0.847470i
$508$	2.15849	−	3.73861i	0.0957675	−	0.165874i
$509$	21.4008	−	37.0673i	0.948576	−	1.64298i	0.200147	−	0.979766i	$-0.435858\pi$
$509$	21.4008	−	37.0673i	0.948576	−	1.64298i	0.748429	−	0.663215i	$-0.230809\pi$
$510$	−4.67636	−	1.32770i	−0.207073	−	0.0587913i
$511$	7.34442	+	12.7209i	0.324898	+	0.562740i
$512$	1.00000			0.0441942
$513$	17.9862	+	19.6631i	0.794109	+	0.868148i
$514$	5.38021			0.237311
$515$	−3.61768	−	6.26601i	−0.159414	−	0.276113i
$516$	−18.9153	−	5.37036i	−0.832700	−	0.236417i
$517$	−10.6580	+	18.4602i	−0.468738	+	0.811879i
$518$	−5.23035	+	9.05924i	−0.229809	+	0.398040i
$519$	−0.817124	−	3.24116i	−0.0358677	−	0.142271i
$520$	−1.35682	−	2.35009i	−0.0595006	−	0.103058i
$521$	7.23875			0.317135			0.158568	−	0.987348i	$-0.449312\pi$
$521$	7.23875			0.317135			0.158568	+	0.987348i	$0.449312\pi$
$522$	−8.63265	+	4.64816i	−0.377841	+	0.203445i
$523$	−13.4114			−0.586441			−0.293221	−	0.956045i	$-0.594727\pi$
$523$	−13.4114			−0.586441			−0.293221	+	0.956045i	$0.594727\pi$
$524$	−4.92464	−	8.52973i	−0.215134	−	0.372623i
$525$	8.26732	−	8.02556i	0.360815	−	0.350264i
$526$	−7.51821	+	13.0219i	−0.327809	+	0.567783i
$527$	13.5070	−	23.3947i	0.588373	−	1.01909i
$528$	6.67094	−	6.47586i	0.290315	−	0.281826i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	5.14965			0.223686
$531$	29.8780	−	16.0875i	1.29659	−	0.698137i
$532$	7.26227			0.314859
$533$	−28.7394	−	49.7781i	−1.24484	−	2.15613i
$534$	−1.86211	−	7.38616i	−0.0805815	−	0.319630i
$535$	0.918999	−	1.59175i	0.0397318	−	0.0688175i
$536$	−4.36268	+	7.55638i	−0.188439	+	0.326386i
$537$	−5.08177	−	1.44280i	−0.219294	−	0.0622613i
$538$	12.6833	+	21.9681i	0.546815	+	0.947111i
$539$	−26.8107			−1.15482
$540$	0.861449	−	2.72382i	0.0370709	−	0.117215i
$541$	−17.6474			−0.758721			−0.379361	−	0.925249i	$-0.623856\pi$
$541$	−17.6474			−0.758721			−0.379361	+	0.925249i	$0.623856\pi$
$542$	−8.04175	−	13.9287i	−0.345423	−	0.598290i
$543$	−10.6132	−	3.01326i	−0.455455	−	0.129311i
$544$	2.55243	−	4.42093i	0.109434	−	0.189546i
$545$	3.93751	−	6.81997i	0.168664	−	0.292135i
$546$	2.95941	+	11.7386i	0.126651	+	0.502366i
$547$	1.74115	+	3.01576i	0.0744462	+	0.128945i	0.900845	−	0.434140i	$-0.142948\pi$
$547$	1.74115	+	3.01576i	0.0744462	+	0.128945i	−0.826399	+	0.563085i	$0.809614\pi$
$548$	−9.48731			−0.405278
$549$	−0.877870	+	29.5748i	−0.0374666	+	1.26222i
$550$	−25.2162			−1.07522
$551$	8.38039	+	14.5153i	0.357017	+	0.618371i
$552$	1.24278	−	1.20644i	0.0528963	−	0.0513495i
$553$	−2.44285	+	4.23115i	−0.103881	+	0.179927i
$554$	−13.1560	+	22.7869i	−0.558946	+	0.968123i
$555$	5.04745	−	4.89985i	0.214252	−	0.207987i
$556$	4.29267	+	7.43511i	0.182050	+	0.315319i
$557$	−13.1957			−0.559119			−0.279560	−	0.960128i	$-0.590188\pi$
$557$	−13.1957			−0.559119			−0.279560	+	0.960128i	$0.590188\pi$
$558$	13.5070	+	8.34214i	0.571795	+	0.353151i
$559$	−56.0327			−2.36993
$560$	−0.389269	−	0.674234i	−0.0164496	−	0.0284916i
$561$	−11.6023	−	46.0209i	−0.489848	−	1.94301i
$562$	5.49555	−	9.51858i	0.231816	−	0.401517i
$563$	13.7131	−	23.7518i	0.577939	−	1.00102i	−0.417776	−	0.908550i	$-0.637190\pi$
$563$	13.7131	−	23.7518i	0.577939	−	1.00102i	0.995715	−	0.0924701i	$-0.0294763\pi$
$564$	−6.61668	−	1.87858i	−0.278612	−	0.0791026i
$565$	−1.46831	−	2.54319i	−0.0617722	−	0.106993i
$566$	−14.1056			−0.592901
$567$	−7.01571	+	10.6397i	−0.294632	+	0.446826i
$568$	−2.81741			−0.118216
$569$	5.44205	+	9.42591i	0.228143	+	0.395155i	0.957258	−	0.289237i	$-0.0934014\pi$
$569$	5.44205	+	9.42591i	0.228143	+	0.395155i	−0.729115	+	0.684391i	$0.760068\pi$
$570$	−4.69802	−	1.33384i	−0.196778	−	0.0558686i
$571$	−3.26302	+	5.65172i	−0.136553	+	0.236517i	−0.926190	−	0.377058i	$-0.876936\pi$
$571$	−3.26302	+	5.65172i	−0.136553	+	0.236517i	0.789637	+	0.613575i	$0.210269\pi$
$572$	13.2470	−	22.9445i	0.553884	−	0.959356i
$573$	−3.21301	−	12.7446i	−0.134226	−	0.532412i
$574$	−8.24527	−	14.2812i	−0.344151	−	0.596087i
$575$	−4.69773			−0.195909
$576$	2.55243	+	1.57642i	0.106351	+	0.0656844i
$577$	9.02634			0.375771			0.187886	−	0.982191i	$-0.439837\pi$
$577$	9.02634			0.375771			0.187886	+	0.982191i	$0.439837\pi$
$578$	−4.52977	−	7.84579i	−0.188414	−	0.326342i
$579$	−9.42968	+	9.15393i	−0.391884	+	0.380424i
$580$	0.898405	−	1.55608i	0.0373042	−	0.0646128i
$581$	−2.84254	+	4.92342i	−0.117928	+	0.204258i
$582$	17.5236	−	17.0111i	0.726375	−	0.705134i
$583$	25.1386	+	43.5414i	1.04114	+	1.80330i
$584$	10.3730			0.429239
$585$	0.241542	−	8.13735i	0.00998652	−	0.336438i
$586$	27.9960			1.15650
$587$	3.55840	+	6.16332i	0.146871	+	0.254388i	0.930069	−	0.367384i	$-0.119747\pi$
$587$	3.55840	+	6.16332i	0.146871	+	0.254388i	−0.783199	+	0.621772i	$0.786413\pi$
$588$	−2.11487	−	8.38871i	−0.0872156	−	0.345945i
$589$	13.5695	−	23.5031i	0.559123	−	0.968429i
$590$	−3.10942	+	5.38567i	−0.128013	+	0.221724i
$591$	−9.07411	−	2.57629i	−0.373259	−	0.105974i
$592$	3.69359	+	6.39749i	0.151806	+	0.262935i
$593$	−7.28010			−0.298958			−0.149479	−	0.988765i	$-0.547760\pi$
$593$	−7.28010			−0.298958			−0.149479	+	0.988765i	$0.547760\pi$
$594$	27.2358	−	6.01294i	1.11750	−	0.246714i
$595$	−3.97433			−0.162932
$596$	1.67802	+	2.90642i	0.0687344	+	0.119051i
$597$	1.21556	+	0.345116i	0.0497494	+	0.0141247i
$598$	2.46789	−	4.27450i	0.100919	−	0.174797i
$599$	7.21478	−	12.4964i	0.294788	−	0.510588i	−0.680148	−	0.733075i	$-0.738084\pi$
$599$	7.21478	−	12.4964i	0.294788	−	0.510588i	0.974936	+	0.222487i	$0.0714176\pi$
$600$	−1.98909	−	7.88983i	−0.0812045	−	0.322101i
$601$	−8.74249	−	15.1424i	−0.356614	−	0.617673i	0.630779	−	0.775962i	$-0.282735\pi$
$601$	−8.74249	−	15.1424i	−0.356614	−	0.617673i	−0.987393	+	0.158289i	$0.949402\pi$
$602$	−16.0757			−0.655195
$603$	−23.0475	+	12.4097i	−0.938566	+	0.505361i
$604$	−10.3142			−0.419679
$605$	4.89664	+	8.48124i	0.199077	+	0.344811i
$606$	−18.4725	+	17.9323i	−0.750393	+	0.728449i
$607$	0.836379	−	1.44865i	0.0339476	−	0.0587989i	−0.848552	−	0.529111i	$-0.822525\pi$
$607$	0.836379	−	1.44865i	0.0339476	−	0.0587989i	0.882500	+	0.470312i	$0.155859\pi$
$608$	2.56425	−	4.44141i	0.103994	−	0.180123i
$609$	−5.75150	+	5.58331i	−0.233062	+	0.226247i
$610$	−2.71119	−	4.69592i	−0.109773	−	0.190132i
$611$	−19.6006			−0.792954
$612$	13.4842	−	7.26040i	0.545065	−	0.293484i
$613$	−45.7223			−1.84670			−0.923352	−	0.383954i	$-0.874562\pi$
$613$	−45.7223			−1.84670			−0.923352	+	0.383954i	$0.874562\pi$
$614$	−13.4644	−	23.3210i	−0.543379	−	0.941160i
$615$	2.71093	+	10.7530i	0.109315	+	0.433604i
$616$	3.80053	−	6.58271i	0.153128	−	0.265225i
$617$	−10.7797	+	18.6710i	−0.433976	+	0.751668i	−0.997211	−	0.0746285i	$-0.976223\pi$
$617$	−10.7797	+	18.6710i	−0.433976	+	0.751668i	0.563236	+	0.826296i	$0.309556\pi$
$618$	21.9275	+	6.22557i	0.882052	+	0.250429i
$619$	−14.5783	−	25.2504i	−0.585953	−	1.01490i	−0.994756	−	0.102278i	$-0.967387\pi$
$619$	−14.5783	−	25.2504i	−0.585953	−	1.01490i	0.408803	−	0.912623i	$-0.365946\pi$
$620$	−2.90939			−0.116844
$621$	5.07397	−	1.12020i	0.203611	−	0.0449520i
$622$	−20.6903			−0.829607
$623$	−3.11380	−	5.39326i	−0.124752	−	0.216076i
$624$	8.22397	+	2.33492i	0.329222	+	0.0934715i
$625$	−10.2787	+	17.8031i	−0.411146	+	0.712126i
$626$	−9.10081	+	15.7631i	−0.363742	+	0.630019i
$627$	−11.6560	−	46.2341i	−0.465496	−	1.84641i
$628$	5.83267	+	10.1025i	0.232749	+	0.403133i
$629$	37.7105			1.50362
$630$	0.0692977	−	2.33459i	0.00276089	−	0.0930122i
$631$	30.9270			1.23118			0.615592	−	0.788065i	$-0.288917\pi$
$631$	30.9270			1.23118			0.615592	+	0.788065i	$0.288917\pi$
$632$	1.72510	+	2.98797i	0.0686210	+	0.118855i
$633$	−9.03106	+	8.76697i	−0.358952	+	0.348456i
$634$	−9.95354	+	17.2400i	−0.395306	+	0.684689i
$635$	−1.18672	+	2.05546i	−0.0470935	+	0.0815684i
$636$	−11.6406	+	11.3002i	−0.461578	+	0.448081i
$637$	−12.3265	−	21.3502i	−0.488394	−	0.845924i
$638$	17.5427			0.694522
$639$	−7.19124	−	4.44144i	−0.284481	−	0.175701i
$640$	−0.549792			−0.0217324
$641$	−3.00313	−	5.20157i	−0.118616	−	0.205450i	0.800603	−	0.599195i	$-0.204513\pi$
$641$	−3.00313	−	5.20157i	−0.118616	−	0.205450i	−0.919220	+	0.393745i	$0.871179\pi$
$642$	1.41551	+	5.61470i	0.0558659	+	0.221595i
$643$	2.59784	−	4.49960i	0.102449	−	0.177447i	−0.810244	−	0.586093i	$-0.800666\pi$
$643$	2.59784	−	4.49960i	0.102449	−	0.177447i	0.912693	+	0.408646i	$0.133999\pi$
$644$	0.708031	−	1.22635i	0.0279003	−	0.0483248i
$645$	10.3995	+	2.95258i	0.409479	+	0.116258i
$646$	−13.0901	−	22.6728i	−0.515024	−	0.892048i
$647$	23.9468			0.941445			0.470723	−	0.882281i	$-0.343993\pi$
$647$	23.9468			0.941445			0.470723	+	0.882281i	$0.343993\pi$
$648$	4.02977	+	8.04742i	0.158304	+	0.316132i
$649$	−60.7159			−2.38331
$650$	−11.5935	−	20.0805i	−0.454733	−	0.787620i
$651$	12.4857	+	3.54489i	0.489353	+	0.138935i
$652$	3.84406	−	6.65812i	0.150545	−	0.260752i
$653$	2.28391	−	3.95585i	0.0893763	−	0.154804i	−0.817871	−	0.575401i	$-0.804846\pi$
$653$	2.28391	−	3.95585i	0.0893763	−	0.154804i	0.907248	+	0.420597i	$0.138179\pi$
$654$	6.06486	+	24.0566i	0.237155	+	0.940686i
$655$	2.70753	+	4.68958i	0.105792	+	0.183237i
$656$	−11.6454			−0.454675
$657$	26.4764	+	16.3523i	1.03294	+	0.637963i
$658$	−5.62336			−0.219221
$659$	8.74145	+	15.1406i	0.340518	+	0.589795i	0.984529	−	0.175221i	$-0.0560641\pi$
$659$	8.74145	+	15.1406i	0.340518	+	0.589795i	−0.644011	+	0.765016i	$0.722731\pi$
$660$	−3.66763	+	3.56037i	−0.142762	+	0.138587i
$661$	−5.49645	+	9.52013i	−0.213787	+	0.370290i	−0.952897	−	0.303295i	$-0.901913\pi$
$661$	−5.49645	+	9.52013i	−0.213787	+	0.370290i	0.739110	+	0.673585i	$0.235247\pi$
$662$	1.75715	−	3.04347i	0.0682935	−	0.118288i
$663$	31.3136	−	30.3979i	1.21612	−	1.18056i
$664$	2.00735	+	3.47684i	0.0779005	+	0.134928i
$665$	−3.99274			−0.154832
$666$	−0.657533	+	22.1518i	−0.0254789	+	0.858365i
$667$	3.26817			0.126544
$668$	−9.11755	−	15.7921i	−0.352769	−	0.611013i
$669$	−1.16431	−	4.61830i	−0.0450149	−	0.178554i
$670$	2.39856	−	4.15443i	0.0926646	−	0.160500i
$671$	26.4700	−	45.8474i	1.02186	−	1.76992i
$672$	2.35944	+	0.669883i	0.0910173	+	0.0258413i
$673$	−16.0928	−	27.8735i	−0.620331	−	1.07444i	−0.989424	−	0.145052i	$-0.953665\pi$
$673$	−16.0928	−	27.8735i	−0.620331	−	1.07444i	0.369093	−	0.929392i	$-0.379668\pi$
$674$	19.7094			0.759179
$675$	7.36071	−	23.2739i	0.283314	−	0.895812i
$676$	11.3618			0.436994
$677$	−4.43943	−	7.68933i	−0.170621	−	0.295525i	0.768016	−	0.640431i	$-0.221244\pi$
$677$	−4.43943	−	7.68933i	−0.170621	−	0.295525i	−0.938637	+	0.344906i	$0.887911\pi$
$678$	8.89971	+	2.52677i	0.341791	+	0.0970401i
$679$	9.98344	−	17.2918i	0.383129	−	0.663599i
$680$	−1.40330	+	2.43059i	−0.0538142	+	0.0932090i
$681$	0.800091	+	3.17360i	0.0306596	+	0.121613i
$682$	−14.2026	−	24.5995i	−0.543844	−	0.941965i
$683$	4.08079			0.156147			0.0780736	−	0.996948i	$-0.475123\pi$
$683$	4.08079			0.156147			0.0780736	+	0.996948i	$0.475123\pi$
$684$	13.5466	−	7.29403i	0.517968	−	0.278894i
$685$	5.21605			0.199295
$686$	−8.49267	−	14.7097i	−0.324251	−	0.561620i
$687$	−14.9545	+	14.5172i	−0.570549	+	0.553865i
$688$	−5.67619	+	9.83145i	−0.216403	+	0.374820i
$689$	−23.1156	+	40.0373i	−0.880632	+	1.52530i
$690$	−0.683271	+	0.663290i	−0.0260117	+	0.0252510i
$691$	−6.21731	−	10.7687i	−0.236518	−	0.409660i	0.723195	−	0.690644i	$-0.242673\pi$
$691$	−6.21731	−	10.7687i	−0.236518	−	0.409660i	−0.959713	+	0.280983i	$0.909339\pi$
$692$	−1.92984			−0.0733613
$693$	20.0777	−	10.8106i	0.762690	−	0.410663i
$694$	31.3190			1.18885
$695$	−2.36007	−	4.08776i	−0.0895226	−	0.155058i
$696$	1.38379	+	5.48888i	0.0524526	+	0.208056i
$697$	−29.7239	+	51.4833i	−1.12587	+	1.95007i
$698$	14.2677	−	24.7124i	0.540040	−	0.935377i
$699$	33.9769	+	9.64660i	1.28513	+	0.364868i
$700$	−3.32614	−	5.76104i	−0.125716	−	0.217747i
$701$	−13.5222			−0.510726			−0.255363	−	0.966845i	$-0.582195\pi$
$701$	−13.5222			−0.510726			−0.255363	+	0.966845i	$0.582195\pi$
$702$	17.3103	+	18.9242i	0.653334	+	0.714247i
$703$	37.8852			1.42887
$704$	−2.68387	−	4.64861i	−0.101152	−	0.175201i
$705$	3.63779	+	1.03283i	0.137007	+	0.0388986i
$706$	−3.51180	+	6.08262i	−0.132168	+	0.228922i
$707$	−10.5240	+	18.2282i	−0.395797	+	0.685541i
$708$	−4.78937	−	18.9972i	−0.179995	−	0.713960i
$709$	−24.2326	−	41.9720i	−0.910073	−	1.57629i	−0.813958	−	0.580923i	$-0.802692\pi$
$709$	−24.2326	−	41.9720i	−0.910073	−	1.57629i	−0.0961151	−	0.995370i	$-0.530642\pi$
$710$	1.54899			0.0581326
$711$	−0.307103	+	10.3461i	−0.0115173	+	0.388008i
$712$	−4.39783			−0.164816
$713$	−2.64591	−	4.58284i	−0.0990899	−	0.171629i
$714$	8.98380	−	8.72109i	0.336210	−	0.326379i
$715$	−7.28308	+	12.6147i	−0.272372	+	0.471762i
$716$	−1.52496	+	2.64131i	−0.0569904	+	0.0987103i
$717$	−36.1806	+	35.1226i	−1.35119	+	1.31168i
$718$	−7.38444	−	12.7902i	−0.275585	−	0.477327i
$719$	2.34908			0.0876058			0.0438029	−	0.999040i	$-0.486053\pi$
$719$	2.34908			0.0876058			0.0438029	+	0.999040i	$0.486053\pi$
$720$	−1.40330	−	0.866705i	−0.0522980	−	0.0323002i
$721$	18.6356			0.694027
$722$	−3.65076	−	6.32330i	−0.135867	−	0.235329i
$723$	2.21857	+	8.80006i	0.0825095	+	0.327278i
$724$	−3.18485	+	5.51633i	−0.118364	+	0.205013i
$725$	7.67648	−	13.2960i	0.285097	−	0.493803i
$726$	−29.6795	−	8.42650i	−1.10151	−	0.312737i
$727$	23.3294	+	40.4077i	0.865239	+	1.49864i	0.866809	+	0.498640i	$0.166167\pi$
$727$	23.3294	+	40.4077i	0.865239	+	1.49864i	−0.00156982	+	0.999999i	$0.500500\pi$
$728$	6.98935			0.259043
$729$	−2.40045	+	26.8931i	−0.0889055	+	0.996040i
$730$	−5.70300			−0.211078
$731$	28.9761	+	50.1881i	1.07172	+	1.85627i
$732$	16.4330	+	4.66561i	0.607383	+	0.172446i
$733$	1.40717	−	2.43729i	0.0519749	−	0.0900232i	−0.838867	−	0.544336i	$-0.816782\pi$
$733$	1.40717	−	2.43729i	0.0519749	−	0.0900232i	0.890842	+	0.454313i	$0.150115\pi$
$734$	−4.03118	+	6.98221i	−0.148794	+	0.257718i
$735$	1.16274	+	4.61205i	0.0428882	+	0.170118i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	46.8355			1.72521
$738$	−29.7239	−	18.3580i	−1.09415	−	0.675768i
$739$	−48.1419			−1.77093			−0.885465	−	0.464707i	$-0.846160\pi$
$739$	−48.1419			−1.77093			−0.885465	+	0.464707i	$0.846160\pi$
$740$	−2.03071	−	3.51729i	−0.0746503	−	0.129298i
$741$	31.4586	−	30.5387i	1.15566	−	1.12187i
$742$	−6.63180	+	11.4866i	−0.243461	+	0.421687i
$743$	5.10051	−	8.83434i	0.187120	−	0.324101i	−0.757169	−	0.653219i	$-0.773418\pi$
$743$	5.10051	−	8.83434i	0.187120	−	0.324101i	0.944289	+	0.329118i	$0.106751\pi$
$744$	6.57656	−	6.38425i	0.241108	−	0.234058i
$745$	−0.922561	−	1.59792i	−0.0338000	−	0.0585434i
$746$	21.8217			0.798948
$747$	−0.357349	+	12.0388i	−0.0130747	+	0.440478i
$748$	−27.4016			−1.00190
$749$	2.36700	+	4.09977i	0.0864885	+	0.149802i
$750$	2.25754	+	8.95464i	0.0824338	+	0.326977i
$751$	7.27345	−	12.5980i	0.265412	−	0.459707i	−0.702260	−	0.711921i	$-0.747825\pi$
$751$	7.27345	−	12.5980i	0.265412	−	0.459707i	0.967671	+	0.252214i	$0.0811587\pi$
$752$	−1.98556	+	3.43909i	−0.0724060	+	0.125411i
$753$	−2.76814	−	0.785920i	−0.100877	−	0.0286405i
$754$	8.06546	+	13.9698i	0.293727	+	0.508749i
$755$	5.67066			0.206377
$756$	4.96627	+	5.42930i	0.180622	+	0.197462i
$757$	3.61783			0.131492			0.0657461	−	0.997836i	$-0.479057\pi$
$757$	3.61783			0.131492			0.0657461	+	0.997836i	$0.479057\pi$
$758$	−2.81548	−	4.87655i	−0.102263	−	0.177124i
$759$	−8.94373	−	2.53927i	−0.324637	−	0.0921697i
$760$	−1.40980	+	2.44185i	−0.0511389	+	0.0885752i
$761$	−21.2738	+	36.8474i	−0.771176	+	1.33572i	0.165743	+	0.986169i	$0.446998\pi$
$761$	−21.2738	+	36.8474i	−0.771176	+	1.33572i	−0.936919	+	0.349547i	$0.886336\pi$
$762$	−1.82788	−	7.25037i	−0.0662171	−	0.262653i
$763$	10.1416	+	17.5657i	0.367150	+	0.635922i
$764$	−7.58831			−0.274535
$765$	−7.41348	+	3.99171i	−0.268035	+	0.144321i
$766$	−19.2275			−0.694718
$767$	−27.9149	−	48.3500i	−1.00795	−	1.74582i
$768$	1.24278	−	1.20644i	0.0448450	−	0.0435336i
$769$	−19.1560	+	33.1791i	−0.690783	+	1.19647i	0.280799	+	0.959767i	$0.409400\pi$
$769$	−19.1560	+	33.1791i	−0.690783	+	1.19647i	−0.971582	+	0.236704i	$0.923933\pi$
$770$	−2.08950	+	3.61912i	−0.0753004	+	0.130424i
$771$	6.68642	−	6.49089i	0.240805	−	0.233764i
$772$	3.79378	+	6.57102i	0.136541	+	0.236496i
$773$	32.8903			1.18298			0.591490	−	0.806312i	$-0.298540\pi$
$773$	32.8903			1.18298			0.591490	+	0.806312i	$0.298540\pi$
$774$	−29.9866	+	16.1460i	−1.07785	+	0.580355i
$775$	−24.8595			−0.892979
$776$	−7.05014	−	12.2112i	−0.253085	−	0.438357i
$777$	4.42923	+	17.5688i	0.158898	+	0.630276i
$778$	18.3382	−	31.7627i	0.657456	−	1.13875i
$779$	−29.8616	+	51.7218i	−1.06990	+	1.85313i
$780$	−4.52147	−	1.28372i	−0.161895	−	0.0459645i
$781$	7.56158	+	13.0970i	0.270575	+	0.468649i
$782$	−5.10485			−0.182549
$783$	−5.12077	+	16.1914i	−0.183002	+	0.578634i
$784$	−4.99477			−0.178385
$785$	−3.20675	−	5.55426i	−0.114454	−	0.198240i
$786$	−16.4109	−	4.65931i	−0.585356	−	0.166192i
$787$	2.34738	−	4.06578i	0.0836749	−	0.144929i	−0.821151	−	0.570711i	$-0.806668\pi$
$787$	2.34738	−	4.06578i	0.0836749	−	0.144929i	0.904826	+	0.425782i	$0.140001\pi$
$788$	−2.72300	+	4.71637i	−0.0970029	+	0.168014i
$789$	6.36666	+	25.2537i	0.226659	+	0.899054i
$790$	−0.948448	−	1.64276i	−0.0337443	−	0.0584468i
$791$	7.56365			0.268933
$792$	0.477783	−	16.0962i	0.0169773	−	0.571952i
$793$	48.6796			1.72866
$794$	−5.49998	−	9.52624i	−0.195187	−	0.338074i
$795$	6.39988	−	6.21273i	0.226980	−	0.220343i
$796$	0.364769	−	0.631799i	0.0129289	−	0.0223935i
$797$	11.4946	−	19.9093i	0.407160	−	0.705223i	−0.587410	−	0.809290i	$-0.699852\pi$
$797$	11.4946	−	19.9093i	0.407160	−	0.705223i	0.994570	+	0.104067i	$0.0331857\pi$
$798$	9.02541	−	8.76149i	0.319496	−	0.310153i
$799$	10.1360	+	17.5561i	0.358586	+	0.621089i
$800$	−4.69773			−0.166090
$801$	−11.2251	−	6.93285i	−0.396621	−	0.244960i
$802$	−4.25306			−0.150181
$803$	−27.8399	−	48.2201i	−0.982448	−	1.70165i
$804$	3.69446	+	14.6542i	0.130293	+	0.516815i
$805$	−0.389269	+	0.674234i	−0.0137199	+	0.0237636i
$806$	13.0596	−	22.6199i	0.460004	−	0.796751i
$807$	42.2657	+	11.9999i	1.48782	+	0.422417i
$808$	7.43191	+	12.8724i	0.261454	+	0.452851i
$809$	−4.02015			−0.141341			−0.0706706	−	0.997500i	$-0.522514\pi$
$809$	−4.02015			−0.141341			−0.0706706	+	0.997500i	$0.522514\pi$
$810$	−2.21553	−	4.42440i	−0.0778460	−	0.155458i
$811$	49.0852			1.72362			0.861808	−	0.507235i	$-0.169332\pi$
$811$	49.0852			1.72362			0.861808	+	0.507235i	$0.169332\pi$
$812$	2.31396	+	4.00790i	0.0812041	+	0.140650i
$813$	−26.7983	−	7.60847i	−0.939857	−	0.266841i
$814$	19.8263	−	34.3401i	0.694911	−	1.20362i
$815$	−2.11343	+	3.66058i	−0.0740304	+	0.128224i
$816$	−2.16148	−	8.57360i	−0.0756669	−	0.300136i
$817$	29.1103	+	50.4206i	1.01844	+	1.76399i
$818$	−33.6428			−1.17629
$819$	17.8398	+	11.0182i	0.623374	+	0.385007i
$820$	6.40252			0.223586
$821$	4.10027	+	7.10187i	0.143100	+	0.247857i	0.928663	−	0.370926i	$-0.120960\pi$
$821$	4.10027	+	7.10187i	0.143100	+	0.247857i	−0.785562	+	0.618783i	$0.787626\pi$
$822$	−11.7907	+	11.4459i	−0.411246	+	0.399220i
$823$	−15.5837	+	26.9917i	−0.543212	+	0.940871i	0.455505	+	0.890233i	$0.349459\pi$
$823$	−15.5837	+	26.9917i	−0.543212	+	0.940871i	−0.998717	+	0.0506378i	$0.983875\pi$
$824$	6.58009	−	11.3971i	0.229228	−	0.397035i
$825$	−31.3383	+	30.4218i	−1.09106	+	1.05915i
$826$	−8.00871	−	13.8715i	−0.278659	−	0.482651i
$827$	40.1886			1.39749			0.698747	−	0.715369i	$-0.253741\pi$
$827$	40.1886			1.39749			0.698747	+	0.715369i	$0.253741\pi$
$828$	0.0890100	−	2.99868i	0.00309331	−	0.104211i
$829$	−20.6149			−0.715984			−0.357992	−	0.933725i	$-0.616538\pi$
$829$	−20.6149			−0.715984			−0.357992	+	0.933725i	$0.616538\pi$
$830$	−1.10363	−	1.91154i	−0.0383075	−	0.0663505i
$831$	11.1410	+	44.1911i	0.386475	+	1.53297i
$832$	2.46789	−	4.27450i	0.0855585	−	0.148192i
$833$	−12.7488	+	22.0815i	−0.441719	+	0.765080i
$834$	14.3049	+	4.06138i	0.495337	+	0.140634i
$835$	5.01275	+	8.68235i	0.173474	+	0.300465i
$836$	−27.5285			−0.952093
$837$	26.8505	−	5.92787i	0.928088	−	0.204897i
$838$	19.0316			0.657434
$839$	−28.2739	−	48.9718i	−0.976123	−	1.69069i	−0.676179	−	0.736737i	$-0.736365\pi$
$839$	−28.2739	−	48.9718i	−0.976123	−	1.69069i	−0.299944	−	0.953957i	$-0.596968\pi$
$840$	−1.29720	−	0.368296i	−0.0447576	−	0.0127074i
$841$	9.15955	−	15.8648i	0.315846	−	0.547062i
$842$	−15.7450	+	27.2711i	−0.542607	+	0.939823i
$843$	−4.65381	−	18.4596i	−0.160286	−	0.635781i
$844$	3.63341	+	6.29325i	0.125067	+	0.216622i
$845$	−6.24664			−0.214891
$846$	−10.4895	+	5.64795i	−0.360636	+	0.194181i
$847$	−25.2239			−0.866704
$848$	4.68327	+	8.11166i	0.160824	+	0.278556i
$849$	−17.5301	+	17.0175i	−0.601632	+	0.584039i
$850$	−11.9906	+	20.7683i	−0.411275	+	0.712349i
$851$	3.69359	−	6.39749i	0.126615	−	0.219303i
$852$	−3.50143	+	3.39904i	−0.119957	+	0.116449i
$853$	8.39284	+	14.5368i	0.287365	+	0.497731i	0.973180	−	0.230045i	$-0.0738873\pi$
$853$	8.39284	+	14.5368i	0.287365	+	0.497731i	−0.685815	+	0.727776i	$0.740554\pi$
$854$	13.9661			0.477909
$855$	−7.44781	+	4.01020i	−0.254710	+	0.137146i
$856$	3.34308			0.114264
$857$	4.54949	+	7.87995i	0.155408	+	0.269174i	0.933207	−	0.359338i	$-0.116998\pi$
$857$	4.54949	+	7.87995i	0.155408	+	0.269174i	−0.777800	+	0.628512i	$0.783664\pi$
$858$	−11.2180	−	44.4966i	−0.382976	−	1.51909i
$859$	20.5906	−	35.6639i	0.702542	−	1.21684i	−0.265029	−	0.964240i	$-0.585382\pi$
$859$	20.5906	−	35.6639i	0.702542	−	1.21684i	0.967571	−	0.252598i	$-0.0812850\pi$
$860$	3.12072	−	5.40525i	0.106416	−	0.184317i
$861$	−27.4765	−	7.80102i	−0.936396	−	0.265858i
$862$	−0.915386	−	1.58550i	−0.0311782	−	0.0540022i
$863$	−6.76198			−0.230180			−0.115090	−	0.993355i	$-0.536716\pi$
$863$	−6.76198			−0.230180			−0.115090	+	0.993355i	$0.536716\pi$
$864$	5.07397	−	1.12020i	0.172620	−	0.0381099i
$865$	1.06101			0.0360753
$866$	−6.64874	−	11.5160i	−0.225933	−	0.391328i
$867$	−15.0950	−	4.28571i	−0.512653	−	0.145550i
$868$	3.74676	−	6.48959i	0.127173	−	0.220271i
$869$	9.25993	−	16.0387i	0.314121	−	0.544074i
$870$	−0.760799	−	3.01774i	−0.0257935	−	0.102311i
$871$	21.5332	+	37.2966i	0.729624	+	1.26375i
$872$	14.3236			0.485060
$873$	1.25507	−	42.2822i	0.0424776	−	1.43104i
$874$	−5.12850			−0.173474
$875$	3.77503	+	6.53854i	0.127619	+	0.221043i
$876$	12.8914	−	12.5144i	0.435560	−	0.422823i
$877$	16.4722	−	28.5307i	0.556227	−	0.963413i	−0.441580	−	0.897222i	$-0.645582\pi$
$877$	16.4722	−	28.5307i	0.556227	−	0.963413i	0.997807	−	0.0661915i	$-0.0210848\pi$
$878$	−6.97305	+	12.0777i	−0.235329	+	0.407602i
$879$	34.7929	−	33.7754i	1.17353	−	1.13922i
$880$	1.47557	+	2.55577i	0.0497415	+	0.0861548i
$881$	−36.0763			−1.21544			−0.607721	−	0.794150i	$-0.707916\pi$
$881$	−36.0763			−1.21544			−0.607721	+	0.794150i	$0.707916\pi$
$882$	−12.7488	−	7.87388i	−0.429274	−	0.265127i
$883$	−29.3212			−0.986736			−0.493368	−	0.869821i	$-0.664234\pi$
$883$	−29.3212			−0.986736			−0.493368	+	0.869821i	$0.664234\pi$
$884$	−12.5982	−	21.8207i	−0.423723	−	0.733910i
$885$	2.63315	+	10.4445i	0.0885125	+	0.351089i
$886$	−0.548677	+	0.950336i	−0.0184332	+	0.0319272i
$887$	5.90193	−	10.2224i	0.198167	−	0.343236i	−0.749767	−	0.661702i	$-0.769834\pi$
$887$	5.90193	−	10.2224i	0.198167	−	0.343236i	0.947934	+	0.318466i	$0.103168\pi$
$888$	12.3085	+	3.49459i	0.413047	+	0.117271i
$889$	−3.05655	−	5.29411i	−0.102514	−	0.177559i
$890$	2.41789			0.0810479
$891$	26.5939	−	40.3311i	0.890929	−	1.35114i
$892$	−2.74981			−0.0920704
$893$	10.1830	+	17.6374i	0.340760	+	0.590213i
$894$	5.59182	+	1.58761i	0.187019	+	0.0530976i
$895$	0.838410	−	1.45217i	0.0280250	−	0.0485407i
$896$	0.708031	−	1.22635i	0.0236536	−	0.0409693i
$897$	−2.08989	−	8.28962i	−0.0697792	−	0.276783i
$898$	11.8122	+	20.4593i	0.394179	+	0.682737i
$899$	17.2945			0.576804
$900$	−11.9906	−	7.40562i	−0.399687	−	0.246854i
$901$	47.8148			1.59294
$902$	31.2547	+	54.1347i	1.04067	+	1.80249i
$903$	−19.9785	+	19.3943i	−0.664844	+	0.645402i
$904$	2.67067	−	4.62573i	0.0888250	−	0.153849i
$905$	1.75101	−	3.03283i	0.0582054	−	0.100815i
$906$	−12.8183	+	12.4435i	−0.425860	+	0.413406i
$907$	13.8022	+	23.9061i	0.458295	+	0.793790i	0.998871	−	0.0475051i	$-0.0151270\pi$
$907$	13.8022	+	23.9061i	0.458295	+	0.793790i	−0.540576	+	0.841295i	$0.681794\pi$
$908$	1.88961			0.0627089
$909$	−1.32303	+	44.5718i	−0.0438821	+	1.47835i
$910$	−3.84269			−0.127384
$911$	−2.84615	−	4.92967i	−0.0942971	−	0.163327i	0.815018	−	0.579436i	$-0.196727\pi$
$911$	−2.84615	−	4.92967i	−0.0942971	−	0.163327i	−0.909315	+	0.416108i	$0.863394\pi$
$912$	−2.17149	−	8.61331i	−0.0719052	−	0.285215i
$913$	10.7750	−	18.6628i	0.356600	−	0.617649i
$914$	−5.55741	+	9.62571i	−0.183823	+	0.318390i
$915$	−9.03475	−	2.56511i	−0.298680	−	0.0848000i
$916$	6.01654	+	10.4210i	0.198792	+	0.344318i
$917$	−13.9472			−0.460577
$918$	7.99862	−	25.2909i	0.263994	−	0.834724i
$919$	18.2511			0.602048			0.301024	−	0.953616i	$-0.402671\pi$
$919$	18.2511			0.602048			0.301024	+	0.953616i	$0.402671\pi$
$920$	0.274896	+	0.476134i	0.00906305	+	0.0156977i
$921$	−44.8687	−	12.7389i	−1.47847	−	0.419763i
$922$	−9.52023	+	16.4895i	−0.313532	+	0.543053i
$923$	−6.95305	+	12.0430i	−0.228863	+	0.396402i
$924$	−3.21841	−	12.7660i	−0.105878	−	0.419970i
$925$	−17.3515	−	30.0537i	−0.570514	−	0.988159i
$926$	3.91179			0.128549
$927$	34.7618	−	18.7171i	1.14173	−	0.614752i
$928$	3.26817			0.107283
$929$	−14.0513	−	24.3376i	−0.461010	−	0.798492i	0.538002	−	0.842944i	$-0.319179\pi$
$929$	−14.0513	−	24.3376i	−0.461010	−	0.798492i	−0.999012	+	0.0444516i	$0.985846\pi$
$930$	−3.61574	+	3.51001i	−0.118565	+	0.115098i
$931$	−12.8078	+	22.1838i	−0.419760	+	0.727046i
$932$	10.1959	−	17.6599i	0.333979	−	0.578469i
$933$	−25.7136	+	24.9616i	−0.841825	+	0.817207i
$934$	−15.2528	−	26.4185i	−0.499085	−	0.864441i
$935$	15.0652			0.492683
$936$	13.0375	−	7.01992i	0.426145	−	0.229453i
$937$	−21.0972			−0.689216			−0.344608	−	0.938747i	$-0.611988\pi$
$937$	−21.0972			−0.689216			−0.344608	+	0.938747i	$0.611988\pi$
$938$	6.17782	+	10.7003i	0.201713	+	0.349377i
$939$	7.70686	+	30.5696i	0.251504	+	0.997602i
$940$	1.09165	−	1.89079i	0.0356056	−	0.0616706i
$941$	1.77714	−	3.07810i	0.0579331	−	0.100343i	−0.835604	−	0.549332i	$-0.814882\pi$
$941$	1.77714	−	3.07810i	0.0579331	−	0.100343i	0.893537	+	0.448989i	$0.148216\pi$
$942$	19.4367	+	5.51841i	0.633283	+	0.179799i
$943$	5.82268	+	10.0852i	0.189612	+	0.328418i
$944$	−11.3112			−0.368150
$945$	−2.73042	−	2.98499i	−0.0888205	−	0.0971016i
$946$	60.9367			1.98122
$947$	11.3224	+	19.6110i	0.367929	+	0.637271i	0.989242	−	0.146291i	$-0.0467337\pi$
$947$	11.3224	+	19.6110i	0.367929	+	0.637271i	−0.621313	+	0.783563i	$0.713400\pi$
$948$	5.74873	+	1.63216i	0.186710	+	0.0530100i
$949$	25.5994	−	44.3395i	0.830992	−	1.43932i
$950$	−12.0462	+	20.8645i	−0.390829	+	0.676935i
$951$	8.42898	+	33.4339i	0.273328	+	1.08417i
$952$	−3.61439	−	6.26031i	−0.117143	−	0.202898i
$953$	−11.8690			−0.384474			−0.192237	−	0.981349i	$-0.561574\pi$
$953$	−11.8690			−0.384474			−0.192237	+	0.981349i	$0.561574\pi$
$954$	−0.833716	+	28.0873i	−0.0269925	+	0.909358i
$955$	4.17199			0.135002
$956$	14.5563	+	25.2122i	0.470784	+	0.815422i
$957$	21.8017	−	21.1642i	0.704750	−	0.684141i
$958$	3.16986	−	5.49036i	0.102414	−	0.177385i
$959$	−6.71731	+	11.6347i	−0.216913	+	0.375705i
$960$	−0.683271	+	0.663290i	−0.0220525	+	0.0214076i
$961$	1.49837	+	2.59525i	0.0483345	+	0.0837179i
$962$	36.4615			1.17556
$963$	8.53297	+	5.27012i	0.274971	+	0.169827i
$964$	5.23969			0.168759
$965$	−2.08579	−	3.61269i	−0.0671439	−	0.116297i
$966$	−0.599583	−	2.37827i	−0.0192913	−	0.0765197i
$967$	19.3716	−	33.5526i	0.622948	−	1.07898i	−0.365985	−	0.930621i	$-0.619268\pi$
$967$	19.3716	−	33.5526i	0.622948	−	1.07898i	0.988934	−	0.148358i	$-0.0473987\pi$
$968$	−8.90636	+	15.4263i	−0.286261	+	0.495819i
$969$	−43.6215	−	12.3848i	−1.40132	−	0.397858i
$970$	3.87611	+	6.71362i	0.124454	+	0.215561i
$971$	25.2993			0.811892			0.405946	−	0.913897i	$-0.366942\pi$
$971$	25.2993			0.811892			0.405946	+	0.913897i	$0.366942\pi$
$972$	14.7168	+	5.13951i	0.472043	+	0.164850i
$973$	12.1574			0.389747
$974$	−5.67875	−	9.83589i	−0.181959	−	0.315162i
$975$	−38.6340	−	10.9688i	−1.23728	−	0.351283i
$976$	4.93130	−	8.54127i	0.157847	−	0.273399i
$977$	8.12716	−	14.0767i	0.260011	−	0.450352i	−0.706234	−	0.707979i	$-0.749607\pi$
$977$	8.12716	−	14.0767i	0.260011	−	0.450352i	0.966245	+	0.257627i	$0.0829405\pi$
$978$	−3.25528	−	12.9122i	−0.104092	−	0.412887i
$979$	11.8032	+	20.4438i	0.377233	+	0.653386i
$980$	2.74608			0.0877204
$981$	36.5601	+	22.5801i	1.16727	+	0.720929i
$982$	10.2792			0.328021
$983$	0.971151	+	1.68208i	0.0309749	+	0.0536501i	0.881097	−	0.472935i	$-0.156805\pi$
$983$	0.971151	+	1.68208i	0.0309749	+	0.0536501i	−0.850122	+	0.526585i	$0.823472\pi$
$984$	−14.4726	+	14.0494i	−0.461370	+	0.447879i
$985$	1.49708	−	2.59302i	0.0477010	−	0.0826206i
$986$	8.34175	−	14.4483i	0.265656	−	0.460129i
$987$	−6.98860	+	6.78424i	−0.222450	+	0.215945i
$988$	−12.6565	−	21.9218i	−0.402658	−	0.697425i
$989$	11.3524			0.360985
$990$	−0.262681	+	8.84953i	−0.00834856	+	0.281257i
$991$	−19.4357			−0.617395			−0.308697	−	0.951160i	$-0.599893\pi$
$991$	−19.4357			−0.617395			−0.308697	+	0.951160i	$0.599893\pi$
$992$	−2.64591	−	4.58284i	−0.0840076	−	0.145505i
$993$	−1.48801	−	5.90226i	−0.0472205	−	0.187302i
$994$	−1.99482	+	3.45512i	−0.0632717	+	0.109590i
$995$	−0.200547	+	0.347358i	−0.00635777	+	0.0110120i
$996$	6.68930	+	1.89920i	0.211959	+	0.0601785i
$997$	24.7009	+	42.7833i	0.782286	+	1.35496i	0.930607	+	0.366020i	$0.119280\pi$
$997$	24.7009	+	42.7833i	0.782286	+	1.35496i	−0.148320	+	0.988939i	$0.547387\pi$
$998$	25.4713			0.806280
$999$	25.9076	+	28.3231i	0.819681	+	0.896104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.c.139.1	✓	10
3.2	odd	2		1242.2.e.c.415.3		10
9.2	odd	6		1242.2.e.c.829.3		10
9.4	even	3		3726.2.a.t.1.3		5
9.5	odd	6		3726.2.a.s.1.3		5
9.7	even	3	inner	414.2.e.c.277.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.c.139.1	✓	10	1.1	even	1	trivial
414.2.e.c.277.1	yes	10	9.7	even	3	inner
1242.2.e.c.415.3		10	3.2	odd	2
1242.2.e.c.829.3		10	9.2	odd	6
3726.2.a.s.1.3		5	9.5	odd	6
3726.2.a.t.1.3		5	9.4	even	3

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.66620 - 0.473061i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.274896 - 0.476134i) q^{5} +(0.423416 + 1.67950i) q^{6} +(0.708031 + 1.22635i) q^{7} +1.00000 q^{8} +(2.55243 + 1.57642i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.66620 - 0.473061i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.274896 - 0.476134i) q^{5} +(0.423416 + 1.67950i) q^{6} +(0.708031 + 1.22635i) q^{7} +1.00000 q^{8} +(2.55243 + 1.57642i) q^{9} -0.549792 q^{10} +(-2.68387 - 4.64861i) q^{11} +(1.24278 - 1.20644i) q^{12} +(2.46789 - 4.27450i) q^{13} +(0.708031 - 1.22635i) q^{14} +(-0.683271 + 0.663290i) q^{15} +(-0.500000 - 0.866025i) q^{16} -5.10485 q^{17} +(0.0890100 - 2.99868i) q^{18} -5.12850 q^{19} +(0.274896 + 0.476134i) q^{20} +(-0.599583 - 2.37827i) q^{21} +(-2.68387 + 4.64861i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-1.66620 - 0.473061i) q^{24} +(2.34886 + 4.06835i) q^{25} -4.93577 q^{26} +(-3.50710 - 3.83409i) q^{27} -1.41606 q^{28} +(-1.63408 - 2.83031i) q^{29} +(0.916062 + 0.260085i) q^{30} +(-2.64591 + 4.58284i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.27279 + 9.01513i) q^{33} +(2.55243 + 4.42093i) q^{34} +0.778539 q^{35} +(-2.64144 + 1.42225i) q^{36} -7.38719 q^{37} +(2.56425 + 4.44141i) q^{38} +(-6.13408 + 5.95471i) q^{39} +(0.274896 - 0.476134i) q^{40} +(5.82268 - 10.0852i) q^{41} +(-1.75985 + 1.70839i) q^{42} +(-5.67619 - 9.83145i) q^{43} +5.36775 q^{44} +(1.45224 - 0.781944i) q^{45} +1.00000 q^{46} +(-1.98556 - 3.43909i) q^{47} +(0.423416 + 1.67950i) q^{48} +(2.49738 - 4.32560i) q^{49} +(2.34886 - 4.06835i) q^{50} +(8.50570 + 2.41491i) q^{51} +(2.46789 + 4.27450i) q^{52} -9.36654 q^{53} +(-1.56687 + 4.95428i) q^{54} -2.95114 q^{55} +(0.708031 + 1.22635i) q^{56} +(8.54509 + 2.42609i) q^{57} +(-1.63408 + 2.83031i) q^{58} +(5.65562 - 9.79583i) q^{59} +(-0.232791 - 0.923375i) q^{60} +(4.93130 + 8.54127i) q^{61} +5.29181 q^{62} +(-0.126044 + 4.24631i) q^{63} +1.00000 q^{64} +(-1.35682 - 2.35009i) q^{65} +(6.67094 - 6.47586i) q^{66} +(-4.36268 + 7.55638i) q^{67} +(2.55243 - 4.42093i) q^{68} +(1.24278 - 1.20644i) q^{69} +(-0.389269 - 0.674234i) q^{70} -2.81741 q^{71} +(2.55243 + 1.57642i) q^{72} +10.3730 q^{73} +(3.69359 + 6.39749i) q^{74} +(-1.98909 - 7.88983i) q^{75} +(2.56425 - 4.44141i) q^{76} +(3.80053 - 6.58271i) q^{77} +(8.22397 + 2.33492i) q^{78} +(1.72510 + 2.98797i) q^{79} -0.549792 q^{80} +(4.02977 + 8.04742i) q^{81} -11.6454 q^{82} +(2.00735 + 3.47684i) q^{83} +(2.35944 + 0.669883i) q^{84} +(-1.40330 + 2.43059i) q^{85} +(-5.67619 + 9.83145i) q^{86} +(1.38379 + 5.48888i) q^{87} +(-2.68387 - 4.64861i) q^{88} -4.39783 q^{89} +(-1.40330 - 0.866705i) q^{90} +6.98935 q^{91} +(-0.500000 - 0.866025i) q^{92} +(6.57656 - 6.38425i) q^{93} +(-1.98556 + 3.43909i) q^{94} +(-1.40980 + 2.44185i) q^{95} +(1.24278 - 1.20644i) q^{96} +(-7.05014 - 12.2112i) q^{97} -4.99477 q^{98} +(0.477783 - 16.0962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

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