LMFDB - Embedded newform 414.2.e.c.277.1

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			277.1
Root			$-1.24278 + 1.20644i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.c.139.1

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.920925	−	0.389741i	$-0.127435\pi$
$5$	0.274896	+	0.476134i	0.122937	+	0.212933i	−0.797988	+	0.602674i	$0.794102\pi$
$6$	0.423416	−	1.67950i	0.172859	−	0.685653i
$7$	0.708031	−	1.22635i	0.267610	−	0.463515i	−0.700634	−	0.713521i	$-0.747099\pi$
$7$	0.708031	−	1.22635i	0.267610	−	0.463515i	0.968244	+	0.250006i	$0.0804326\pi$
$8$	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	0.104187	+	0.994558i	$0.466776\pi$
$11$	−2.68387	+	4.64861i	−0.809219	+	1.40161i	−0.913406	+	0.407050i	$0.866557\pi$
$12$	1.24278	+	1.20644i	0.358760	+	0.348269i
$13$	2.46789	+	4.27450i	0.684468	+	1.18553i	0.973604	+	0.228246i	$0.0732989\pi$
$13$	2.46789	+	4.27450i	0.684468	+	1.18553i	−0.289135	+	0.957288i	$0.593368\pi$
$14$	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	−0.976913	−	0.213637i	$-0.931469\pi$
$29$	−1.63408	+	2.83031i	−0.303442	+	0.525576i	0.673472	+	0.739213i	$0.264802\pi$
$30$	0.916062	−	0.260085i	0.167249	−	0.0474848i
$31$	−2.64591	−	4.58284i	−0.475219	−	0.823103i	0.524379	−	0.851485i	$-0.324298\pi$
$31$	−2.64591	−	4.58284i	−0.475219	−	0.823103i	−0.999597	+	0.0283825i	$0.990964\pi$
$32$	−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	0.814970	+	0.579503i	$0.196753\pi$
$41$	5.82268	+	10.0852i	0.909349	+	1.57504i	0.0943789	+	0.995536i	$0.469913\pi$
$42$	−1.75985	−	1.70839i	−0.271551	−	0.263611i
$43$	−5.67619	+	9.83145i	−0.865611	+	1.49928i	0.000829163		1.00000i	$0.499736\pi$
$43$	−5.67619	+	9.83145i	−0.865611	+	1.49928i	−0.866440	+	0.499282i	$0.833597\pi$
$44$	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	−0.973720	−	0.227748i	$-0.926864\pi$
$47$	−1.98556	+	3.43909i	−0.289624	+	0.501644i	0.684096	+	0.729392i	$0.260197\pi$
$48$	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	0.954151	+	0.299326i	$0.0967619\pi$
$59$	5.65562	+	9.79583i	0.736300	+	1.27531i	−0.217851	+	0.975982i	$0.569905\pi$
$60$	−0.232791	+	0.923375i	−0.0300532	+	0.119207i
$61$	4.93130	−	8.54127i	0.631389	−	1.09360i	−0.355879	−	0.934532i	$-0.615819\pi$
$61$	4.93130	−	8.54127i	0.631389	−	1.09360i	0.987268	−	0.159065i	$-0.0508480\pi$
$62$	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	−0.999258	−	0.0385172i	$-0.987737\pi$
$67$	−4.36268	−	7.55638i	−0.532986	−	0.923159i	0.466272	−	0.884641i	$-0.345597\pi$
$68$	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	−0.752512	−	0.658578i	$-0.771158\pi$
$79$	1.72510	−	2.98797i	0.194089	−	0.336173i	0.946602	+	0.322406i	$0.104491\pi$
$80$	−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	−0.734574	−	0.678528i	$-0.762618\pi$
$83$	2.00735	−	3.47684i	0.220336	−	0.381633i	0.954910	+	0.296896i	$0.0959513\pi$
$84$	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	0.246803	+	0.969066i	$0.420620\pi$
$97$	−7.05014	+	12.2112i	−0.715834	+	1.23986i	−0.962637	+	0.270795i	$0.912714\pi$
$98$	−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	−0.213217	−	0.977005i	$-0.568394\pi$
$101$	7.43191	−	12.8724i	0.739502	−	1.28086i	0.952720	−	0.303851i	$-0.0982724\pi$
$102$	−2.16148	+	8.57360i	−0.214018	+	0.848913i
$103$	6.58009	+	11.3971i	0.648356	+	1.12299i	0.983515	+	0.180824i	$0.0578765\pi$
$103$	6.58009	+	11.3971i	0.648356	+	1.12299i	−0.335159	+	0.942161i	$0.608790\pi$
$104$	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	0.963866	−	0.266387i	$-0.0858300\pi$
$113$	2.67067	+	4.62573i	0.251235	+	0.435152i	−0.712631	+	0.701539i	$0.752497\pi$
$114$	−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	0.566628	−	0.823974i	$-0.308248\pi$
$131$	−4.92464	−	8.52973i	−0.430268	−	0.745246i	−0.996896	+	0.0787274i	$0.974914\pi$
$132$	−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	−0.589076	−	0.808078i	$-0.700508\pi$
$137$	4.74366	−	8.21625i	0.405278	−	0.701962i	0.994354	+	0.106116i	$0.0338414\pi$
$138$	−1.66620	+	0.473061i	−0.141836	+	0.0402696i
$139$	4.29267	+	7.43511i	0.364099	+	0.630638i	0.988631	−	0.150361i	$-0.0480436\pi$
$139$	4.29267	+	7.43511i	0.364099	+	0.630638i	−0.624532	+	0.780999i	$0.714710\pi$
$140$	−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	0.926538	−	0.376202i	$-0.122770\pi$
$149$	1.67802	+	2.90642i	0.137469	+	0.238103i	−0.789069	+	0.614304i	$0.789437\pi$
$150$	−5.83825	−	5.66752i	−0.476691	−	0.462751i
$151$	5.15710	−	8.93236i	0.419679	−	0.726905i	−0.576228	−	0.817289i	$-0.695476\pi$
$151$	5.15710	−	8.93236i	0.419679	−	0.726905i	0.995907	+	0.0903835i	$0.0288093\pi$
$152$	−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	0.999224	−	0.0393920i	$-0.0125421\pi$
$157$	5.83267	+	10.1025i	0.465497	+	0.806265i	−0.533726	+	0.845657i	$0.679209\pi$
$158$	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	−0.966497	−	0.256677i	$-0.917372\pi$
$167$	−9.11755	−	15.7921i	−0.705537	−	1.22203i	0.260960	−	0.965350i	$-0.415961\pi$
$168$	−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	−0.827011	−	0.562185i	$-0.809961\pi$
$173$	0.964918	−	1.67129i	0.0733613	−	0.127066i	0.900373	+	0.435120i	$0.143294\pi$
$174$	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	−0.695482	−	0.718543i	$-0.744809\pi$
$191$	3.79415	−	6.57167i	0.274535	−	0.475509i	0.970018	+	0.243034i	$0.0781426\pi$
$192$	−1.66620	+	0.473061i	−0.120247	+	0.0341402i
$193$	3.79378	+	6.57102i	0.273082	+	0.472992i	0.969650	−	0.244499i	$-0.0786235\pi$
$193$	3.79378	+	6.57102i	0.273082	+	0.472992i	−0.696567	+	0.717492i	$0.745290\pi$
$194$	−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	0.963563	−	0.267483i	$-0.0861920\pi$
$211$	3.63341	+	6.29325i	0.250134	+	0.433245i	−0.713428	+	0.700728i	$0.752859\pi$
$212$	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	−0.816312	−	0.577612i	$-0.803985\pi$
$223$	1.37490	−	2.38140i	0.0920704	−	0.159471i	0.908382	+	0.418141i	$0.137318\pi$
$224$	−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	−0.895675	−	0.444708i	$-0.853307\pi$
$227$	−0.944805	+	1.63645i	−0.0627089	+	0.108615i	0.832966	+	0.553323i	$0.186641\pi$
$228$	−6.37360	−	6.18722i	−0.422102	−	0.409759i
$229$	6.01654	+	10.4210i	0.397584	+	0.688636i	0.993427	−	0.114465i	$-0.0365153\pi$
$229$	6.01654	+	10.4210i	0.397584	+	0.688636i	−0.595843	+	0.803101i	$0.703182\pi$
$230$	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	0.762481	+	0.647011i	$0.223981\pi$
$239$	14.5563	+	25.2122i	0.941568	+	1.63084i	0.179087	+	0.983833i	$0.442686\pi$
$240$	0.916062	−	0.260085i	0.0591315	−	0.0167884i
$241$	−2.61985	+	4.53771i	−0.168759	+	0.292299i	−0.937984	−	0.346679i	$-0.887309\pi$
$241$	−2.61985	+	4.53771i	−0.168759	+	0.292299i	0.769225	+	0.638978i	$0.220643\pi$
$242$	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	0.769843	−	0.638233i	$-0.220334\pi$
$257$	−2.69010	−	4.65939i	−0.167804	−	0.290645i	−0.937647	+	0.347588i	$0.887001\pi$
$258$	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	−0.999137	−	0.0415413i	$-0.986773\pi$
$263$	−7.51821	+	13.0219i	−0.463593	+	0.802966i	0.535544	+	0.844507i	$0.320107\pi$
$264$	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	0.135208	+	0.990817i	$0.456830\pi$
$277$	−13.1560	+	22.7869i	−0.790469	+	1.36913i	−0.925677	+	0.378315i	$0.876504\pi$
$278$	−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	−0.654245	−	0.756282i	$-0.727014\pi$
$281$	5.49555	−	9.51858i	0.327837	−	0.567831i	0.982082	+	0.188452i	$0.0603469\pi$
$282$	4.93524	+	4.79092i	0.293889	+	0.285295i
$283$	7.05278	+	12.2158i	0.419244	+	0.726152i	0.995864	−	0.0908606i	$-0.0289618\pi$
$283$	7.05278	+	12.2158i	0.419244	+	0.726152i	−0.576619	+	0.817013i	$0.695628\pi$
$284$	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	−0.907321	−	0.420439i	$-0.861876\pi$
$293$	−13.9980	−	24.2452i	−0.817771	−	1.41642i	0.0895497	−	0.995982i	$-0.471457\pi$
$294$	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	0.994671	+	0.103098i	$0.0328755\pi$
$311$	10.3452	+	17.9184i	0.586621	+	1.01606i	−0.408050	+	0.912959i	$0.633791\pi$
$312$	−6.13408	−	5.95471i	−0.347274	−	0.337119i
$313$	−9.10081	+	15.7631i	−0.514408	+	0.890981i	0.485452	+	0.874263i	$0.338655\pi$
$313$	−9.10081	+	15.7631i	−0.514408	+	0.890981i	−0.999860	+	0.0167179i	$0.994678\pi$
$314$	−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	0.438530	+	0.898717i	$0.355499\pi$
$317$	−9.95354	+	17.2400i	−0.559047	+	0.968297i	−0.997576	+	0.0695803i	$0.977834\pi$
$318$	−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	−0.813686	−	0.581305i	$-0.802542\pi$
$331$	1.75715	−	3.04347i	0.0965815	−	0.167284i	0.910268	+	0.414020i	$0.135876\pi$
$332$	−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	−0.999073	−	0.0430522i	$-0.986292\pi$
$337$	−9.85472	−	17.0689i	−0.536821	−	0.929801i	0.462252	−	0.886749i	$-0.347042\pi$
$338$	−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	−0.889349	−	0.457230i	$-0.848842\pi$
$347$	−15.6595	−	27.1231i	−0.840647	−	1.45604i	0.0487016	−	0.998813i	$-0.484492\pi$
$348$	−5.44541	+	1.54604i	−0.291905	+	0.0828765i
$349$	14.2677	−	24.7124i	0.763732	−	1.32282i	−0.177182	−	0.984178i	$-0.556698\pi$
$349$	14.2677	−	24.7124i	0.763732	−	1.32282i	0.940914	−	0.338645i	$-0.109968\pi$
$350$	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	−0.944220	−	0.329316i	$-0.893182\pi$
$353$	−3.51180	+	6.08262i	−0.186914	+	0.323745i	0.757306	+	0.653061i	$0.226515\pi$
$354$	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	−0.951848	−	0.306571i	$-0.900818\pi$
$367$	−4.03118	+	6.98221i	−0.210426	+	0.364468i	0.741422	+	0.671039i	$0.234152\pi$
$368$	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	−0.997055	−	0.0766881i	$-0.975565\pi$
$373$	−10.9108	−	18.8981i	−0.564941	−	0.978507i	0.432114	−	0.901819i	$-0.357768\pi$
$374$	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	0.999949	−	0.0100863i	$-0.00321061\pi$
$383$	9.61375	+	16.6515i	0.491240	+	0.850852i	−0.508710	+	0.860938i	$0.669877\pi$
$384$	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	0.146100	−	0.989270i	$-0.453328\pi$
$389$	18.3382	−	31.7627i	0.929783	−	1.61043i	0.783683	−	0.621161i	$-0.213339\pi$
$390$	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	0.914225	−	0.405206i	$-0.132800\pi$
$401$	2.12653	+	3.68325i	0.106194	+	0.183933i	−0.808032	+	0.589139i	$0.799467\pi$
$402$	−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	0.896638	+	0.442764i	$0.146002\pi$
$409$	16.8214	+	29.1355i	0.831764	+	1.44066i	−0.0648746	+	0.997893i	$0.520665\pi$
$410$	−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	0.534320	−	0.845282i	$-0.320568\pi$
$419$	−9.51578	−	16.4818i	−0.464876	−	0.805189i	−0.999196	+	0.0400932i	$0.987235\pi$
$420$	0.967553	+	0.939260i	0.0472118	+	0.0458312i
$421$	−15.7450	+	27.2711i	−0.767362	+	1.32911i	0.171626	+	0.985162i	$0.445098\pi$
$421$	−15.7450	+	27.2711i	−0.767362	+	1.32911i	−0.938989	+	0.343948i	$0.888236\pi$
$422$	−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	−0.983061	−	0.183280i	$-0.941329\pi$
$439$	−6.97305	+	12.0777i	−0.332805	+	0.576436i	0.650255	+	0.759716i	$0.274662\pi$
$440$	−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	−0.878765	−	0.477254i	$-0.841632\pi$
$443$	−0.548677	+	0.950336i	−0.0260684	+	0.0451518i	0.852697	+	0.522406i	$0.174965\pi$
$444$	−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	−0.966232	−	0.257673i	$-0.917044\pi$
$457$	−5.55741	+	9.62571i	−0.259965	+	0.450272i	0.706268	+	0.707945i	$0.250378\pi$
$458$	−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	−0.997939	−	0.0641650i	$-0.979562\pi$
$461$	−9.52023	+	16.4895i	−0.443401	+	0.767993i	0.554538	+	0.832158i	$0.312895\pi$
$462$	12.6649	−	3.59576i	0.589223	−	0.167290i
$463$	−1.95590	−	3.38771i	−0.0908982	−	0.157440i	0.816991	−	0.576650i	$-0.195640\pi$
$463$	−1.95590	−	3.38771i	−0.0908982	−	0.157440i	−0.907889	+	0.419210i	$0.862307\pi$
$464$	−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	−0.784477	−	0.620158i	$-0.787068\pi$
$479$	3.16986	−	5.49036i	0.144835	−	0.250861i	0.929311	+	0.369297i	$0.120402\pi$
$480$	−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	0.726435	−	0.687236i	$-0.241176\pi$
$491$	−5.13958	−	8.90202i	−0.231946	−	0.401743i	−0.958381	+	0.285493i	$0.907843\pi$
$492$	−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	−0.996552	−	0.0829648i	$-0.973561\pi$
$499$	−12.7356	−	22.0588i	−0.570126	−	0.987487i	0.426427	−	0.904522i	$-0.359772\pi$
$500$	−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	0.748429	+	0.663215i	$0.230809\pi$
$509$	21.4008	+	37.0673i	0.948576	+	1.64298i	0.200147	+	0.979766i	$0.435858\pi$
$510$	−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	−0.826399	−	0.563085i	$-0.809614\pi$
$547$	1.74115	−	3.01576i	0.0744462	−	0.128945i	0.900845	+	0.434140i	$0.142948\pi$
$548$	−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	0.995715	+	0.0924701i	$0.0294763\pi$
$563$	13.7131	+	23.7518i	0.577939	+	1.00102i	−0.417776	+	0.908550i	$0.637190\pi$
$564$	−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	−0.729115	−	0.684391i	$-0.760068\pi$
$569$	5.44205	−	9.42591i	0.228143	−	0.395155i	0.957258	+	0.289237i	$0.0934014\pi$
$570$	−4.69802	+	1.33384i	−0.196778	+	0.0558686i
$571$	−3.26302	−	5.65172i	−0.136553	−	0.236517i	0.789637	−	0.613575i	$-0.210269\pi$
$571$	−3.26302	−	5.65172i	−0.136553	−	0.236517i	−0.926190	+	0.377058i	$0.876936\pi$
$572$	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	−0.783199	−	0.621772i	$-0.786413\pi$
$587$	3.55840	−	6.16332i	0.146871	−	0.254388i	0.930069	+	0.367384i	$0.119747\pi$
$588$	−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	0.974936	−	0.222487i	$-0.0714176\pi$
$599$	7.21478	+	12.4964i	0.294788	+	0.510588i	−0.680148	+	0.733075i	$0.738084\pi$
$600$	−1.98909	+	7.88983i	−0.0812045	+	0.322101i
$601$	−8.74249	+	15.1424i	−0.356614	+	0.617673i	−0.987393	−	0.158289i	$-0.949402\pi$
$601$	−8.74249	+	15.1424i	−0.356614	+	0.617673i	0.630779	+	0.775962i	$0.282735\pi$
$602$	−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	0.882500	−	0.470312i	$-0.155859\pi$
$607$	0.836379	+	1.44865i	0.0339476	+	0.0587989i	−0.848552	+	0.529111i	$0.822525\pi$
$608$	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	0.563236	−	0.826296i	$-0.309556\pi$
$617$	−10.7797	−	18.6710i	−0.433976	−	0.751668i	−0.997211	+	0.0746285i	$0.976223\pi$
$618$	21.9275	−	6.22557i	0.882052	−	0.250429i
$619$	−14.5783	+	25.2504i	−0.585953	+	1.01490i	0.408803	+	0.912623i	$0.365946\pi$
$619$	−14.5783	+	25.2504i	−0.585953	+	1.01490i	−0.994756	+	0.102278i	$0.967387\pi$
$620$	−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	−0.919220	−	0.393745i	$-0.871179\pi$
$641$	−3.00313	+	5.20157i	−0.118616	+	0.205450i	0.800603	+	0.599195i	$0.204513\pi$
$642$	1.41551	−	5.61470i	0.0558659	−	0.221595i
$643$	2.59784	+	4.49960i	0.102449	+	0.177447i	0.912693	−	0.408646i	$-0.133999\pi$
$643$	2.59784	+	4.49960i	0.102449	+	0.177447i	−0.810244	+	0.586093i	$0.800666\pi$
$644$	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	0.907248	−	0.420597i	$-0.138179\pi$
$653$	2.28391	+	3.95585i	0.0893763	+	0.154804i	−0.817871	+	0.575401i	$0.804846\pi$
$654$	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	−0.644011	−	0.765016i	$-0.722731\pi$
$659$	8.74145	−	15.1406i	0.340518	−	0.589795i	0.984529	+	0.175221i	$0.0560641\pi$
$660$	−3.66763	−	3.56037i	−0.142762	−	0.138587i
$661$	−5.49645	−	9.52013i	−0.213787	−	0.370290i	0.739110	−	0.673585i	$-0.235247\pi$
$661$	−5.49645	−	9.52013i	−0.213787	−	0.370290i	−0.952897	+	0.303295i	$0.901913\pi$
$662$	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	0.369093	+	0.929392i	$0.379668\pi$
$673$	−16.0928	+	27.8735i	−0.620331	+	1.07444i	−0.989424	+	0.145052i	$0.953665\pi$
$674$	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	−0.938637	−	0.344906i	$-0.887911\pi$
$677$	−4.43943	+	7.68933i	−0.170621	+	0.295525i	0.768016	+	0.640431i	$0.221244\pi$
$678$	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	−0.959713	−	0.280983i	$-0.909339\pi$
$691$	−6.21731	+	10.7687i	−0.236518	+	0.409660i	0.723195	+	0.690644i	$0.242673\pi$
$692$	−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	−0.0961151	+	0.995370i	$0.530642\pi$
$709$	−24.2326	+	41.9720i	−0.910073	+	1.57629i	−0.813958	+	0.580923i	$0.802692\pi$
$710$	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	−0.00156982	−	0.999999i	$-0.500500\pi$
$727$	23.3294	−	40.4077i	0.865239	−	1.49864i	0.866809	−	0.498640i	$-0.166167\pi$
$728$	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	0.890842	−	0.454313i	$-0.150115\pi$
$733$	1.40717	+	2.43729i	0.0519749	+	0.0900232i	−0.838867	+	0.544336i	$0.816782\pi$
$734$	−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	0.944289	−	0.329118i	$-0.106751\pi$
$743$	5.10051	+	8.83434i	0.187120	+	0.324101i	−0.757169	+	0.653219i	$0.773418\pi$
$744$	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	0.967671	−	0.252214i	$-0.0811587\pi$
$751$	7.27345	+	12.5980i	0.265412	+	0.459707i	−0.702260	+	0.711921i	$0.747825\pi$
$752$	−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	−0.936919	−	0.349547i	$-0.886336\pi$
$761$	−21.2738	−	36.8474i	−0.771176	−	1.33572i	0.165743	−	0.986169i	$-0.446998\pi$
$762$	−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	−0.971582	−	0.236704i	$-0.923933\pi$
$769$	−19.1560	−	33.1791i	−0.690783	−	1.19647i	0.280799	−	0.959767i	$-0.409400\pi$
$770$	−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	0.904826	−	0.425782i	$-0.140001\pi$
$787$	2.34738	+	4.06578i	0.0836749	+	0.144929i	−0.821151	+	0.570711i	$0.806668\pi$
$788$	−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	0.994570	−	0.104067i	$-0.0331857\pi$
$797$	11.4946	+	19.9093i	0.407160	+	0.705223i	−0.587410	+	0.809290i	$0.699852\pi$
$798$	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	−0.785562	−	0.618783i	$-0.787626\pi$
$821$	4.10027	−	7.10187i	0.143100	−	0.247857i	0.928663	+	0.370926i	$0.120960\pi$
$822$	−11.7907	−	11.4459i	−0.411246	−	0.399220i
$823$	−15.5837	−	26.9917i	−0.543212	−	0.940871i	−0.998717	−	0.0506378i	$-0.983875\pi$
$823$	−15.5837	−	26.9917i	−0.543212	−	0.940871i	0.455505	−	0.890233i	$-0.349459\pi$
$824$	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	−0.299944	+	0.953957i	$0.596968\pi$
$839$	−28.2739	+	48.9718i	−0.976123	+	1.69069i	−0.676179	+	0.736737i	$0.736365\pi$
$840$	−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	−0.685815	−	0.727776i	$-0.740554\pi$
$853$	8.39284	−	14.5368i	0.287365	−	0.497731i	0.973180	+	0.230045i	$0.0738873\pi$
$854$	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	−0.777800	−	0.628512i	$-0.783664\pi$
$857$	4.54949	−	7.87995i	0.155408	−	0.269174i	0.933207	+	0.359338i	$0.116998\pi$
$858$	−11.2180	+	44.4966i	−0.382976	+	1.51909i
$859$	20.5906	+	35.6639i	0.702542	+	1.21684i	0.967571	+	0.252598i	$0.0812850\pi$
$859$	20.5906	+	35.6639i	0.702542	+	1.21684i	−0.265029	+	0.964240i	$0.585382\pi$
$860$	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	0.997807	+	0.0661915i	$0.0210848\pi$
$877$	16.4722	+	28.5307i	0.556227	+	0.963413i	−0.441580	+	0.897222i	$0.645582\pi$
$878$	−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	0.947934	−	0.318466i	$-0.103168\pi$
$887$	5.90193	+	10.2224i	0.198167	+	0.343236i	−0.749767	+	0.661702i	$0.769834\pi$
$888$	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	−0.540576	−	0.841295i	$-0.681794\pi$
$907$	13.8022	−	23.9061i	0.458295	−	0.793790i	0.998871	+	0.0475051i	$0.0151270\pi$
$908$	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	−0.909315	−	0.416108i	$-0.863394\pi$
$911$	−2.84615	+	4.92967i	−0.0942971	+	0.163327i	0.815018	+	0.579436i	$0.196727\pi$
$912$	−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	−0.999012	−	0.0444516i	$-0.985846\pi$
$929$	−14.0513	+	24.3376i	−0.461010	+	0.798492i	0.538002	+	0.842944i	$0.319179\pi$
$930$	−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	0.893537	−	0.448989i	$-0.148216\pi$
$941$	1.77714	+	3.07810i	0.0579331	+	0.100343i	−0.835604	+	0.549332i	$0.814882\pi$
$942$	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	−0.621313	−	0.783563i	$-0.713400\pi$
$947$	11.3224	−	19.6110i	0.367929	−	0.637271i	0.989242	+	0.146291i	$0.0467337\pi$
$948$	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	0.988934	+	0.148358i	$0.0473987\pi$
$967$	19.3716	+	33.5526i	0.622948	+	1.07898i	−0.365985	+	0.930621i	$0.619268\pi$
$968$	−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	0.966245	−	0.257627i	$-0.0829405\pi$
$977$	8.12716	+	14.0767i	0.260011	+	0.450352i	−0.706234	+	0.707979i	$0.749607\pi$
$978$	−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	−0.850122	−	0.526585i	$-0.823472\pi$
$983$	0.971151	−	1.68208i	0.0309749	−	0.0536501i	0.881097	+	0.472935i	$0.156805\pi$
$984$	−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	−0.148320	−	0.988939i	$-0.547387\pi$
$997$	24.7009	−	42.7833i	0.782286	−	1.35496i	0.930607	−	0.366020i	$-0.119280\pi$
$998$	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.277.1	yes	10
3.2	odd	2		1242.2.e.c.829.3		10
9.2	odd	6		3726.2.a.s.1.3		5
9.4	even	3	inner	414.2.e.c.139.1	✓	10
9.5	odd	6		1242.2.e.c.415.3		10
9.7	even	3		3726.2.a.t.1.3		5

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