LMFDB - Embedded newform 1338.2.e.j.1075.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1338,2,Mod(931,1338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1338.931");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.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:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 23 x^{16} + 4 x^{15} + 377 x^{14} + 11 x^{13} + 2342 x^{12} + 157 x^{11} + 10694 x^{10} + \cdots + 64 $ x^18 - x^17 + 23x^16 + 4x^15 + 377x^14 + 11x^13 + 2342x^12 + 157x^11 + 10694x^10 - 113x^9 + 14446x^8 + 5345x^7 + 13369x^6 + 3928x^5 + 5491x^4 + 1793x^3 + 1593x^2 + 312x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1075.3
Root			$-0.355961 - 0.616542i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.j.931.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.355961 + 0.616542i) q^{5} +(-0.500000 - 0.866025i) q^{6} -0.0500871 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.355961 + 0.616542i) q^{5} +(-0.500000 - 0.866025i) q^{6} -0.0500871 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.355961 + 0.616542i) q^{10} +(-0.119016 + 0.206142i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.08940 q^{13} -0.0500871 q^{14} +0.711921 q^{15} +1.00000 q^{16} -2.89113 q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.64073 + 4.57387i) q^{19} +(-0.355961 + 0.616542i) q^{20} +(0.0250435 + 0.0433767i) q^{21} +(-0.119016 + 0.206142i) q^{22} +(-1.63887 - 2.83860i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.24658 + 3.89120i) q^{25} +6.08940 q^{26} +1.00000 q^{27} -0.0500871 q^{28} +(4.04185 - 7.00069i) q^{29} +0.711921 q^{30} +(1.00721 + 1.74455i) q^{31} +1.00000 q^{32} +0.238032 q^{33} -2.89113 q^{34} +(0.0178290 - 0.0308808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.18358 - 3.78207i) q^{37} +(2.64073 + 4.57387i) q^{38} +(-3.04470 - 5.27358i) q^{39} +(-0.355961 + 0.616542i) q^{40} +10.3734 q^{41} +(0.0250435 + 0.0433767i) q^{42} +(0.543104 + 0.940683i) q^{43} +(-0.119016 + 0.206142i) q^{44} +(-0.355961 - 0.616542i) q^{45} +(-1.63887 - 2.83860i) q^{46} +(-1.00392 + 1.73883i) q^{47} +(-0.500000 - 0.866025i) q^{48} -6.99749 q^{49} +(2.24658 + 3.89120i) q^{50} +(1.44557 + 2.50380i) q^{51} +6.08940 q^{52} +(2.23284 - 3.86739i) q^{53} +1.00000 q^{54} +(-0.0847301 - 0.146757i) q^{55} -0.0500871 q^{56} +(2.64073 - 4.57387i) q^{57} +(4.04185 - 7.00069i) q^{58} +9.30639 q^{59} +0.711921 q^{60} +(0.798509 + 1.38306i) q^{61} +(1.00721 + 1.74455i) q^{62} +(0.0250435 - 0.0433767i) q^{63} +1.00000 q^{64} +(-2.16759 + 3.75437i) q^{65} +0.238032 q^{66} +(2.18092 + 3.77746i) q^{67} -2.89113 q^{68} +(-1.63887 + 2.83860i) q^{69} +(0.0178290 - 0.0308808i) q^{70} +(1.74602 + 3.02420i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.369119 + 0.639334i) q^{73} +(2.18358 - 3.78207i) q^{74} +(2.24658 - 3.89120i) q^{75} +(2.64073 + 4.57387i) q^{76} +(0.00596117 - 0.0103250i) q^{77} +(-3.04470 - 5.27358i) q^{78} +(4.02459 - 6.97079i) q^{79} +(-0.355961 + 0.616542i) q^{80} +(-0.500000 - 0.866025i) q^{81} +10.3734 q^{82} +(-4.53232 + 7.85020i) q^{83} +(0.0250435 + 0.0433767i) q^{84} +(1.02913 - 1.78250i) q^{85} +(0.543104 + 0.940683i) q^{86} -8.08370 q^{87} +(-0.119016 + 0.206142i) q^{88} +(-4.61528 - 7.99390i) q^{89} +(-0.355961 - 0.616542i) q^{90} -0.305000 q^{91} +(-1.63887 - 2.83860i) q^{92} +(1.00721 - 1.74455i) q^{93} +(-1.00392 + 1.73883i) q^{94} -3.75998 q^{95} +(-0.500000 - 0.866025i) q^{96} +(1.07175 - 1.85633i) q^{97} -6.99749 q^{98} +(-0.119016 - 0.206142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} - 9 q^{3} + 18 q^{4} + q^{5} - 9 q^{6} + 4 q^{7} + 18 q^{8} - 9 q^{9}+O(q^{10}) $ 18 * q + 18 * q^2 - 9 * q^3 + 18 * q^4 + q^5 - 9 * q^6 + 4 * q^7 + 18 * q^8 - 9 * q^9	\( 18 q + 18 q^{2} - 9 q^{3} + 18 q^{4} + q^{5} - 9 q^{6} + 4 q^{7} + 18 q^{8} - 9 q^{9} + q^{10} + 6 q^{11} - 9 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + 18 q^{16} + 12 q^{17} - 9 q^{18} - q^{19} + q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 9 q^{24} + 4 q^{26} + 18 q^{27} + 4 q^{28} - 2 q^{29} - 2 q^{30} + 13 q^{31} + 18 q^{32} - 12 q^{33} + 12 q^{34} + 3 q^{35} - 9 q^{36} + 9 q^{37} - q^{38} - 2 q^{39} + q^{40} - 4 q^{41} - 2 q^{42} + 5 q^{43} + 6 q^{44} + q^{45} + 10 q^{46} + 5 q^{47} - 9 q^{48} + 14 q^{49} - 6 q^{51} + 4 q^{52} - 5 q^{53} + 18 q^{54} + 11 q^{55} + 4 q^{56} - q^{57} - 2 q^{58} - 24 q^{59} - 2 q^{60} - 22 q^{61} + 13 q^{62} - 2 q^{63} + 18 q^{64} + 15 q^{65} - 12 q^{66} - 10 q^{67} + 12 q^{68} + 10 q^{69} + 3 q^{70} - 6 q^{71} - 9 q^{72} + 17 q^{73} + 9 q^{74} - q^{76} + 37 q^{77} - 2 q^{78} - 32 q^{79} + q^{80} - 9 q^{81} - 4 q^{82} + 13 q^{83} - 2 q^{84} + 14 q^{85} + 5 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + q^{90} - 26 q^{91} + 10 q^{92} + 13 q^{93} + 5 q^{94} - 22 q^{95} - 9 q^{96} - 6 q^{97} + 14 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 18 * q^2 - 9 * q^3 + 18 * q^4 + q^5 - 9 * q^6 + 4 * q^7 + 18 * q^8 - 9 * q^9 + q^10 + 6 * q^11 - 9 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^15 + 18 * q^16 + 12 * q^17 - 9 * q^18 - q^19 + q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 9 * q^24 + 4 * q^26 + 18 * q^27 + 4 * q^28 - 2 * q^29 - 2 * q^30 + 13 * q^31 + 18 * q^32 - 12 * q^33 + 12 * q^34 + 3 * q^35 - 9 * q^36 + 9 * q^37 - q^38 - 2 * q^39 + q^40 - 4 * q^41 - 2 * q^42 + 5 * q^43 + 6 * q^44 + q^45 + 10 * q^46 + 5 * q^47 - 9 * q^48 + 14 * q^49 - 6 * q^51 + 4 * q^52 - 5 * q^53 + 18 * q^54 + 11 * q^55 + 4 * q^56 - q^57 - 2 * q^58 - 24 * q^59 - 2 * q^60 - 22 * q^61 + 13 * q^62 - 2 * q^63 + 18 * q^64 + 15 * q^65 - 12 * q^66 - 10 * q^67 + 12 * q^68 + 10 * q^69 + 3 * q^70 - 6 * q^71 - 9 * q^72 + 17 * q^73 + 9 * q^74 - q^76 + 37 * q^77 - 2 * q^78 - 32 * q^79 + q^80 - 9 * q^81 - 4 * q^82 + 13 * q^83 - 2 * q^84 + 14 * q^85 + 5 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + q^90 - 26 * q^91 + 10 * q^92 + 13 * q^93 + 5 * q^94 - 22 * q^95 - 9 * q^96 - 6 * q^97 + 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	−0.355961	+	0.616542i	−0.159190	+	0.275726i	−0.934577	−	0.355761i	$-0.884222\pi$
$5$	−0.355961	+	0.616542i	−0.159190	+	0.275726i	0.775387	+	0.631487i	$0.217555\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.0500871			−0.0189311			−0.00946556	−	0.999955i	$-0.503013\pi$
$7$	−0.0500871			−0.0189311			−0.00946556	+	0.999955i	$0.503013\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.355961	+	0.616542i	−0.112565	+	0.194968i
$11$	−0.119016	+	0.206142i	−0.0358847	+	0.0621541i	−0.883410	−	0.468601i	$-0.844758\pi$
$11$	−0.119016	+	0.206142i	−0.0358847	+	0.0621541i	0.847525	+	0.530755i	$0.178092\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	6.08940			1.68890			0.844449	−	0.535637i	$-0.179928\pi$
$13$	6.08940			1.68890			0.844449	+	0.535637i	$0.179928\pi$
$14$	−0.0500871			−0.0133863
$15$	0.711921			0.183817
$16$	1.00000			0.250000
$17$	−2.89113			−0.701203			−0.350602	−	0.936525i	$-0.614023\pi$
$17$	−2.89113			−0.701203			−0.350602	+	0.936525i	$0.614023\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.64073	+	4.57387i	0.605824	+	1.04932i	0.991921	+	0.126860i	$0.0404899\pi$
$19$	2.64073	+	4.57387i	0.605824	+	1.04932i	−0.386096	+	0.922458i	$0.626177\pi$
$20$	−0.355961	+	0.616542i	−0.0795952	+	0.137863i
$21$	0.0250435	+	0.0433767i	0.00546495	+	0.00946556i
$22$	−0.119016	+	0.206142i	−0.0253743	+	0.0439496i
$23$	−1.63887	−	2.83860i	−0.341728	−	0.591890i	0.643026	−	0.765844i	$-0.277679\pi$
$23$	−1.63887	−	2.83860i	−0.341728	−	0.591890i	−0.984754	+	0.173955i	$0.944345\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.24658	+	3.89120i	0.449317	+	0.778240i
$26$	6.08940			1.19423
$27$	1.00000			0.192450
$28$	−0.0500871			−0.00946556
$29$	4.04185	−	7.00069i	0.750553	−	1.30000i	−0.197003	−	0.980403i	$-0.563121\pi$
$29$	4.04185	−	7.00069i	0.750553	−	1.30000i	0.947555	−	0.319592i	$-0.103546\pi$
$30$	0.711921			0.129978
$31$	1.00721	+	1.74455i	0.180901	+	0.313330i	0.942188	−	0.335086i	$-0.108765\pi$
$31$	1.00721	+	1.74455i	0.180901	+	0.313330i	−0.761287	+	0.648416i	$0.775432\pi$
$32$	1.00000			0.176777
$33$	0.238032			0.0414361
$34$	−2.89113			−0.495825
$35$	0.0178290	−	0.0308808i	0.00301365	−	0.00521980i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.18358	−	3.78207i	0.358978	−	0.621769i	−0.628812	−	0.777557i	$-0.716459\pi$
$37$	2.18358	−	3.78207i	0.358978	−	0.621769i	0.987790	+	0.155789i	$0.0497919\pi$
$38$	2.64073	+	4.57387i	0.428382	+	0.741980i
$39$	−3.04470	−	5.27358i	−0.487543	−	0.844449i
$40$	−0.355961	+	0.616542i	−0.0562823	+	0.0974838i
$41$	10.3734			1.62005			0.810026	−	0.586393i	$-0.199453\pi$
$41$	10.3734			1.62005			0.810026	+	0.586393i	$0.199453\pi$
$42$	0.0250435	+	0.0433767i	0.00386430	+	0.00669317i
$43$	0.543104	+	0.940683i	0.0828225	+	0.143453i	0.904461	−	0.426556i	$-0.140273\pi$
$43$	0.543104	+	0.940683i	0.0828225	+	0.143453i	−0.821639	+	0.570009i	$0.806940\pi$
$44$	−0.119016	+	0.206142i	−0.0179424	+	0.0310771i
$45$	−0.355961	−	0.616542i	−0.0530635	−	0.0919086i
$46$	−1.63887	−	2.83860i	−0.241638	−	0.418529i
$47$	−1.00392	+	1.73883i	−0.146436	+	0.253635i	−0.929908	−	0.367793i	$-0.880114\pi$
$47$	−1.00392	+	1.73883i	−0.146436	+	0.253635i	0.783472	+	0.621428i	$0.213447\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−6.99749			−0.999642
$50$	2.24658	+	3.89120i	0.317715	+	0.550299i
$51$	1.44557	+	2.50380i	0.202420	+	0.350602i
$52$	6.08940			0.844449
$53$	2.23284	−	3.86739i	0.306704	−	0.531228i	−0.670935	−	0.741516i	$-0.734107\pi$
$53$	2.23284	−	3.86739i	0.306704	−	0.531228i	0.977639	+	0.210289i	$0.0674404\pi$
$54$	1.00000			0.136083
$55$	−0.0847301	−	0.146757i	−0.0114250	−	0.0197887i
$56$	−0.0500871			−0.00669317
$57$	2.64073	−	4.57387i	0.349773	−	0.605824i
$58$	4.04185	−	7.00069i	0.530721	−	0.919235i
$59$	9.30639			1.21159			0.605794	−	0.795621i	$-0.292855\pi$
$59$	9.30639			1.21159			0.605794	+	0.795621i	$0.292855\pi$
$60$	0.711921			0.0919086
$61$	0.798509	+	1.38306i	0.102239	+	0.177083i	0.912607	−	0.408839i	$-0.134066\pi$
$61$	0.798509	+	1.38306i	0.102239	+	0.177083i	−0.810368	+	0.585921i	$0.800733\pi$
$62$	1.00721	+	1.74455i	0.127916	+	0.221558i
$63$	0.0250435	−	0.0433767i	0.00315519	−	0.00546495i
$64$	1.00000			0.125000
$65$	−2.16759	+	3.75437i	−0.268856	+	0.465673i
$66$	0.238032			0.0292997
$67$	2.18092	+	3.77746i	0.266441	+	0.461490i	0.967940	−	0.251181i	$-0.0808188\pi$
$67$	2.18092	+	3.77746i	0.266441	+	0.461490i	−0.701499	+	0.712671i	$0.747485\pi$
$68$	−2.89113			−0.350602
$69$	−1.63887	+	2.83860i	−0.197297	+	0.341728i
$70$	0.0178290	−	0.0308808i	0.00213097	−	0.00369096i
$71$	1.74602	+	3.02420i	0.207215	+	0.358907i	0.950836	−	0.309694i	$-0.100227\pi$
$71$	1.74602	+	3.02420i	0.207215	+	0.358907i	−0.743621	+	0.668601i	$0.766893\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−0.369119	+	0.639334i	−0.0432022	+	0.0748283i	−0.886818	−	0.462119i	$-0.847089\pi$
$73$	−0.369119	+	0.639334i	−0.0432022	+	0.0748283i	0.843616	+	0.536947i	$0.180423\pi$
$74$	2.18358	−	3.78207i	0.253836	−	0.439657i
$75$	2.24658	−	3.89120i	0.259413	−	0.449317i
$76$	2.64073	+	4.57387i	0.302912	+	0.524659i
$77$	0.00596117	−	0.0103250i	0.000679338	−	0.00117665i
$78$	−3.04470	−	5.27358i	−0.344745	−	0.597115i
$79$	4.02459	−	6.97079i	0.452801	−	0.784275i	−0.545757	−	0.837943i	$-0.683758\pi$
$79$	4.02459	−	6.97079i	0.452801	−	0.784275i	0.998559	+	0.0536681i	$0.0170913\pi$
$80$	−0.355961	+	0.616542i	−0.0397976	+	0.0689315i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.3734			1.14555
$83$	−4.53232	+	7.85020i	−0.497486	+	0.861672i	−0.999996	−	0.00289998i	$-0.999077\pi$
$83$	−4.53232	+	7.85020i	−0.497486	+	0.861672i	0.502509	+	0.864572i	$0.332410\pi$
$84$	0.0250435	+	0.0433767i	0.00273247	+	0.00473278i
$85$	1.02913	−	1.78250i	0.111625	−	0.193340i
$86$	0.543104	+	0.940683i	0.0585644	+	0.101436i
$87$	−8.08370			−0.866663
$88$	−0.119016	+	0.206142i	−0.0126872	+	0.0219748i
$89$	−4.61528	−	7.99390i	−0.489219	−	0.847351i	0.510704	−	0.859756i	$-0.329385\pi$
$89$	−4.61528	−	7.99390i	−0.489219	−	0.847351i	−0.999923	+	0.0124049i	$0.996051\pi$
$90$	−0.355961	−	0.616542i	−0.0375215	−	0.0649892i
$91$	−0.305000			−0.0319727
$92$	−1.63887	−	2.83860i	−0.170864	−	0.295945i
$93$	1.00721	−	1.74455i	0.104443	−	0.180901i
$94$	−1.00392	+	1.73883i	−0.103546	+	0.179347i
$95$	−3.75998			−0.385766
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	1.07175	−	1.85633i	0.108820	−	0.188482i	−0.806472	−	0.591272i	$-0.798626\pi$
$97$	1.07175	−	1.85633i	0.108820	−	0.188482i	0.915293	+	0.402790i	$0.131959\pi$
$98$	−6.99749			−0.706853
$99$	−0.119016	−	0.206142i	−0.0119616	−	0.0207180i
$100$	2.24658	+	3.89120i	0.224658	+	0.389120i
$101$	−7.67946	−	13.3012i	−0.764134	−	1.32352i	−0.940703	−	0.339231i	$-0.889833\pi$
$101$	−7.67946	−	13.3012i	−0.764134	−	1.32352i	0.176568	−	0.984288i	$-0.443500\pi$
$102$	1.44557	+	2.50380i	0.143132	+	0.247913i
$103$	−13.9141			−1.37100			−0.685499	−	0.728073i	$-0.740416\pi$
$103$	−13.9141			−1.37100			−0.685499	+	0.728073i	$0.740416\pi$
$104$	6.08940			0.597115
$105$	−0.0356580			−0.00347987
$106$	2.23284	−	3.86739i	0.216873	−	0.375635i
$107$	−3.45333	+	5.98134i	−0.333846	+	0.578238i	−0.983262	−	0.182195i	$-0.941680\pi$
$107$	−3.45333	+	5.98134i	−0.333846	+	0.578238i	0.649417	+	0.760433i	$0.275013\pi$
$108$	1.00000			0.0962250
$109$	−1.91519	+	3.31720i	−0.183442	+	0.317730i	−0.943050	−	0.332650i	$-0.892057\pi$
$109$	−1.91519	+	3.31720i	−0.183442	+	0.317730i	0.759609	+	0.650380i	$0.225391\pi$
$110$	−0.0847301	−	0.146757i	−0.00807870	−	0.0139927i
$111$	−4.36716			−0.414512
$112$	−0.0500871			−0.00473278
$113$	2.03896	+	3.53159i	0.191810	+	0.332224i	0.945850	−	0.324604i	$-0.105231\pi$
$113$	2.03896	+	3.53159i	0.191810	+	0.332224i	−0.754040	+	0.656828i	$0.771898\pi$
$114$	2.64073	−	4.57387i	0.247327	−	0.428382i
$115$	2.33349			0.217599
$116$	4.04185	−	7.00069i	0.375276	−	0.649998i
$117$	−3.04470	+	5.27358i	−0.281483	+	0.487543i
$118$	9.30639			0.856723
$119$	0.144808			0.0132746
$120$	0.711921			0.0649892
$121$	5.47167	+	9.47721i	0.497425	+	0.861565i
$122$	0.798509	+	1.38306i	0.0722936	+	0.125216i
$123$	−5.18670	−	8.98363i	−0.467669	−	0.810026i
$124$	1.00721	+	1.74455i	0.0904505	+	0.156665i
$125$	−6.75839			−0.604488
$126$	0.0250435	−	0.0433767i	0.00223106	−	0.00386430i
$127$	2.66370	+	4.61366i	0.236365	+	0.409396i	0.959669	−	0.281134i	$-0.0907106\pi$
$127$	2.66370	+	4.61366i	0.236365	+	0.409396i	−0.723303	+	0.690530i	$0.757377\pi$
$128$	1.00000			0.0883883
$129$	0.543104	−	0.940683i	0.0478176	−	0.0828225i
$130$	−2.16759	+	3.75437i	−0.190110	+	0.329280i
$131$	−1.75869	−	3.04614i	−0.153657	−	0.266142i	0.778912	−	0.627133i	$-0.215772\pi$
$131$	−1.75869	−	3.04614i	−0.153657	−	0.266142i	−0.932569	+	0.360991i	$0.882438\pi$
$132$	0.238032			0.0207180
$133$	−0.132266	−	0.229092i	−0.0114689	−	0.0198648i
$134$	2.18092	+	3.77746i	0.188402	+	0.326323i
$135$	−0.355961	+	0.616542i	−0.0306362	+	0.0530635i
$136$	−2.89113			−0.247913
$137$	−6.77141	−	11.7284i	−0.578520	−	1.00203i	−0.995649	−	0.0931793i	$-0.970297\pi$
$137$	−6.77141	−	11.7284i	−0.578520	−	1.00203i	0.417129	−	0.908847i	$-0.363036\pi$
$138$	−1.63887	+	2.83860i	−0.139510	+	0.241638i
$139$	−1.31959	−	2.28560i	−0.111926	−	0.193862i	0.804621	−	0.593789i	$-0.202369\pi$
$139$	−1.31959	−	2.28560i	−0.111926	−	0.193862i	−0.916547	+	0.399927i	$0.869035\pi$
$140$	0.0178290	−	0.0308808i	0.00150683	−	0.00260990i
$141$	2.00783			0.169090
$142$	1.74602	+	3.02420i	0.146523	+	0.253785i
$143$	−0.724737	+	1.25528i	−0.0606056	+	0.104972i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.87748	+	4.98394i	0.238962	+	0.413893i
$146$	−0.369119	+	0.639334i	−0.0305485	+	0.0529116i
$147$	3.49875	+	6.06001i	0.288572	+	0.499821i
$148$	2.18358	−	3.78207i	0.179489	−	0.310884i
$149$	3.80880	−	6.59703i	0.312029	−	0.540450i	−0.666773	−	0.745261i	$-0.732325\pi$
$149$	3.80880	−	6.59703i	0.312029	−	0.540450i	0.978801	+	0.204811i	$0.0656581\pi$
$150$	2.24658	−	3.89120i	0.183433	−	0.317715i
$151$	−9.54177	+	16.5268i	−0.776498	+	1.34493i	0.157451	+	0.987527i	$0.449672\pi$
$151$	−9.54177	+	16.5268i	−0.776498	+	1.34493i	−0.933949	+	0.357407i	$0.883661\pi$
$152$	2.64073	+	4.57387i	0.214191	+	0.370990i
$153$	1.44557	−	2.50380i	0.116867	−	0.202420i
$154$	0.00596117	−	0.0103250i	0.000480365	−	0.000832016i
$155$	−1.43411			−0.115191
$156$	−3.04470	−	5.27358i	−0.243771	−	0.422224i
$157$	6.48492			0.517553			0.258776	−	0.965937i	$-0.416681\pi$
$157$	6.48492			0.517553			0.258776	+	0.965937i	$0.416681\pi$
$158$	4.02459	−	6.97079i	0.320179	−	0.554566i
$159$	−4.46568			−0.354152
$160$	−0.355961	+	0.616542i	−0.0281411	+	0.0487419i
$161$	0.0820861	+	0.142177i	0.00646929	+	0.0112051i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−5.53504			−0.433538			−0.216769	−	0.976223i	$-0.569552\pi$
$163$	−5.53504			−0.433538			−0.216769	+	0.976223i	$0.569552\pi$
$164$	10.3734			0.810026
$165$	−0.0847301	+	0.146757i	−0.00659623	+	0.0114250i
$166$	−4.53232	+	7.85020i	−0.351776	+	0.609294i
$167$	3.84736			0.297717			0.148859	−	0.988858i	$-0.452440\pi$
$167$	3.84736			0.297717			0.148859	+	0.988858i	$0.452440\pi$
$168$	0.0250435	+	0.0433767i	0.00193215	+	0.00334658i
$169$	24.0809			1.85237
$170$	1.02913	−	1.78250i	0.0789306	−	0.136712i
$171$	−5.28145			−0.403883
$172$	0.543104	+	0.940683i	0.0414113	+	0.0717264i
$173$	0.646627	+	1.11999i	0.0491621	+	0.0851513i	0.889559	−	0.456820i	$-0.151012\pi$
$173$	0.646627	+	1.11999i	0.0491621	+	0.0851513i	−0.840397	+	0.541971i	$0.817678\pi$
$174$	−8.08370			−0.612824
$175$	−0.112525	−	0.194899i	−0.00850608	−	0.0147330i
$176$	−0.119016	+	0.206142i	−0.00897118	+	0.0155385i
$177$	−4.65320	−	8.05957i	−0.349756	−	0.605794i
$178$	−4.61528	−	7.99390i	−0.345930	−	0.599168i
$179$	−10.4033	+	18.0190i	−0.777579	+	1.34681i	0.155754	+	0.987796i	$0.450219\pi$
$179$	−10.4033	+	18.0190i	−0.777579	+	1.34681i	−0.933333	+	0.359011i	$0.883114\pi$
$180$	−0.355961	−	0.616542i	−0.0265317	−	0.0459543i
$181$	10.6949	+	18.5241i	0.794944	+	1.37688i	0.922875	+	0.385100i	$0.125833\pi$
$181$	10.6949	+	18.5241i	0.794944	+	1.37688i	−0.127932	+	0.991783i	$0.540834\pi$
$182$	−0.305000			−0.0226081
$183$	0.798509	−	1.38306i	0.0590275	−	0.102239i
$184$	−1.63887	−	2.83860i	−0.120819	−	0.209265i
$185$	1.55454	+	2.69254i	0.114292	+	0.197959i
$186$	1.00721	−	1.74455i	0.0738526	−	0.127916i
$187$	0.344092	−	0.595984i	0.0251625	−	0.0435827i
$188$	−1.00392	+	1.73883i	−0.0732181	+	0.126818i
$189$	−0.0500871			−0.00364330
$190$	−3.75998			−0.272777
$191$	−21.0306			−1.52172			−0.760862	−	0.648914i	$-0.775224\pi$
$191$	−21.0306			−1.52172			−0.760862	+	0.648914i	$0.775224\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−22.9321			−1.65069			−0.825344	−	0.564630i	$-0.809019\pi$
$193$	−22.9321			−1.65069			−0.825344	+	0.564630i	$0.809019\pi$
$194$	1.07175	−	1.85633i	0.0769474	−	0.133277i
$195$	4.33518			0.310448
$196$	−6.99749			−0.499821
$197$	−7.87651			−0.561178			−0.280589	−	0.959828i	$-0.590530\pi$
$197$	−7.87651			−0.561178			−0.280589	+	0.959828i	$0.590530\pi$
$198$	−0.119016	−	0.206142i	−0.00845811	−	0.0146499i
$199$	−11.8545	−	20.5326i	−0.840342	−	1.45551i	−0.889606	−	0.456728i	$-0.849021\pi$
$199$	−11.8545	−	20.5326i	−0.840342	−	1.45551i	0.0492647	−	0.998786i	$-0.484312\pi$
$200$	2.24658	+	3.89120i	0.158857	+	0.275149i
$201$	2.18092	−	3.77746i	0.153830	−	0.266441i
$202$	−7.67946	−	13.3012i	−0.540325	−	0.935870i
$203$	−0.202444	+	0.350644i	−0.0142088	+	0.0246104i
$204$	1.44557	+	2.50380i	0.101210	+	0.175301i
$205$	−3.69252	+	6.39563i	−0.257897	+	0.446690i
$206$	−13.9141			−0.969442
$207$	3.27774			0.227819
$208$	6.08940			0.422224
$209$	−1.25716			−0.0869593
$210$	−0.0356580			−0.00246064
$211$	−5.37153	−	9.30377i	−0.369792	−	0.640498i	0.619741	−	0.784806i	$-0.287238\pi$
$211$	−5.37153	−	9.30377i	−0.369792	−	0.640498i	−0.989533	+	0.144308i	$0.953904\pi$
$212$	2.23284	−	3.86739i	0.153352	−	0.265614i
$213$	1.74602	−	3.02420i	0.119636	−	0.207215i
$214$	−3.45333	+	5.98134i	−0.236065	+	0.408876i
$215$	−0.773294			−0.0527382
$216$	1.00000			0.0680414
$217$	−0.0504484	−	0.0873792i	−0.00342466	−	0.00593169i
$218$	−1.91519	+	3.31720i	−0.129713	+	0.224669i
$219$	0.738239			0.0498856
$220$	−0.0847301	−	0.146757i	−0.00571250	−	0.00989434i
$221$	−17.6053			−1.18426
$222$	−4.36716			−0.293104
$223$	3.73581	+	14.4583i	0.250168	+	0.968202i
$223$	3.73581	+	14.4583i	0.250168	+	0.968202i
$224$	−0.0500871			−0.00334658
$225$	−4.49317			−0.299545
$226$	2.03896	+	3.53159i	0.135630	+	0.234918i
$227$	−9.78329			−0.649339			−0.324670	−	0.945827i	$-0.605253\pi$
$227$	−9.78329			−0.649339			−0.324670	+	0.945827i	$0.605253\pi$
$228$	2.64073	−	4.57387i	0.174886	−	0.302912i
$229$	2.54981	+	4.41641i	0.168496	+	0.291844i	0.937891	−	0.346929i	$-0.112775\pi$
$229$	2.54981	+	4.41641i	0.168496	+	0.291844i	−0.769395	+	0.638773i	$0.779442\pi$
$230$	2.33349			0.153866
$231$	−0.0119223			−0.000784432
$232$	4.04185	−	7.00069i	0.265360	−	0.459618i
$233$	−4.65509	+	8.06286i	−0.304965	+	0.528215i	−0.977254	−	0.212074i	$-0.931978\pi$
$233$	−4.65509	+	8.06286i	−0.304965	+	0.528215i	0.672288	+	0.740289i	$0.265312\pi$
$234$	−3.04470	+	5.27358i	−0.199038	+	0.344745i
$235$	−0.714709	−	1.23791i	−0.0466225	−	0.0807525i
$236$	9.30639			0.605794
$237$	−8.04918			−0.522850
$238$	0.144808			0.00938654
$239$	13.6826			0.885056			0.442528	−	0.896755i	$-0.354082\pi$
$239$	13.6826			0.885056			0.442528	+	0.896755i	$0.354082\pi$
$240$	0.711921			0.0459543
$241$	8.23257	−	14.2592i	0.530306	−	0.918518i	−0.469068	−	0.883162i	$-0.655410\pi$
$241$	8.23257	−	14.2592i	0.530306	−	0.918518i	0.999375	−	0.0353559i	$-0.0112565\pi$
$242$	5.47167	+	9.47721i	0.351732	+	0.609218i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.798509	+	1.38306i	0.0511193	+	0.0885413i
$245$	2.49083	−	4.31425i	0.159133	−	0.275627i
$246$	−5.18670	−	8.98363i	−0.330692	−	0.572775i
$247$	16.0805	+	27.8522i	1.02317	+	1.77219i
$248$	1.00721	+	1.74455i	0.0639582	+	0.110779i
$249$	9.06463			0.574448
$250$	−6.75839			−0.427438
$251$	11.6521			0.735474			0.367737	−	0.929930i	$-0.380133\pi$
$251$	11.6521			0.735474			0.367737	+	0.929930i	$0.380133\pi$
$252$	0.0250435	−	0.0433767i	0.00157759	−	0.00273247i
$253$	0.780207			0.0490512
$254$	2.66370	+	4.61366i	0.167135	+	0.289487i
$255$	−2.05826			−0.128893
$256$	1.00000			0.0625000
$257$	−11.2746			−0.703292			−0.351646	−	0.936133i	$-0.614378\pi$
$257$	−11.2746			−0.703292			−0.351646	+	0.936133i	$0.614378\pi$
$258$	0.543104	−	0.940683i	0.0338122	−	0.0585644i
$259$	−0.109369	+	0.189433i	−0.00679586	+	0.0117708i
$260$	−2.16759	+	3.75437i	−0.134428	+	0.232836i
$261$	4.04185	+	7.00069i	0.250184	+	0.433332i
$262$	−1.75869	−	3.04614i	−0.108652	−	0.188191i
$263$	−6.15272	+	10.6568i	−0.379393	+	0.657128i	−0.990974	−	0.134054i	$-0.957201\pi$
$263$	−6.15272	+	10.6568i	−0.379393	+	0.657128i	0.611581	+	0.791182i	$0.290534\pi$
$264$	0.238032			0.0146499
$265$	1.58961	+	2.75328i	0.0976488	+	0.169133i
$266$	−0.132266	−	0.229092i	−0.00810976	−	0.0140465i
$267$	−4.61528	+	7.99390i	−0.282450	+	0.489219i
$268$	2.18092	+	3.77746i	0.133221	+	0.230745i
$269$	−5.20507	−	9.01544i	−0.317359	−	0.549681i	0.662577	−	0.748993i	$-0.269463\pi$
$269$	−5.20507	−	9.01544i	−0.317359	−	0.549681i	−0.979936	+	0.199312i	$0.936129\pi$
$270$	−0.355961	+	0.616542i	−0.0216631	+	0.0375215i
$271$	−8.72371	−	15.1099i	−0.529927	−	0.917861i	−0.999390	−	0.0349092i	$-0.988886\pi$
$271$	−8.72371	−	15.1099i	−0.529927	−	0.917861i	0.469463	−	0.882952i	$-0.344448\pi$
$272$	−2.89113			−0.175301
$273$	0.152500	+	0.264138i	0.00922973	+	0.0159864i
$274$	−6.77141	−	11.7284i	−0.409076	−	0.708540i
$275$	−1.06952			−0.0644944
$276$	−1.63887	+	2.83860i	−0.0986483	+	0.170864i
$277$	−21.5632			−1.29561			−0.647804	−	0.761807i	$-0.724312\pi$
$277$	−21.5632			−1.29561			−0.647804	+	0.761807i	$0.724312\pi$
$278$	−1.31959	−	2.28560i	−0.0791438	−	0.137081i
$279$	−2.01443			−0.120601
$280$	0.0178290	−	0.0308808i	0.00106549	−	0.00184548i
$281$	2.83723	−	4.91422i	0.169255	−	0.293158i	−0.768903	−	0.639365i	$-0.779197\pi$
$281$	2.83723	−	4.91422i	0.169255	−	0.293158i	0.938158	+	0.346207i	$0.112531\pi$
$282$	2.00783			0.119565
$283$	0.879276			0.0522676			0.0261338	−	0.999658i	$-0.491680\pi$
$283$	0.879276			0.0522676			0.0261338	+	0.999658i	$0.491680\pi$
$284$	1.74602	+	3.02420i	0.103607	+	0.179453i
$285$	1.87999	+	3.25624i	0.111361	+	0.192883i
$286$	−0.724737	+	1.25528i	−0.0428546	+	0.0742264i
$287$	−0.519573			−0.0306694
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−8.64134			−0.508314
$290$	2.87748	+	4.98394i	0.168971	+	0.292667i
$291$	−2.14351			−0.125655
$292$	−0.369119	+	0.639334i	−0.0216011	+	0.0374142i
$293$	−0.695703	+	1.20499i	−0.0406434	+	0.0703964i	−0.885632	−	0.464389i	$-0.846274\pi$
$293$	−0.695703	+	1.20499i	−0.0406434	+	0.0703964i	0.844988	+	0.534785i	$0.179607\pi$
$294$	3.49875	+	6.06001i	0.204051	+	0.353427i
$295$	−3.31271	+	5.73778i	−0.192873	+	0.334066i
$296$	2.18358	−	3.78207i	0.126918	−	0.219828i
$297$	−0.119016	+	0.206142i	−0.00690602	+	0.0119616i
$298$	3.80880	−	6.59703i	0.220638	−	0.382156i
$299$	−9.97974	−	17.2854i	−0.577143	−	0.999641i
$300$	2.24658	−	3.89120i	0.129707	−	0.224658i
$301$	−0.0272025	−	0.0471161i	−0.00156792	−	0.00271572i
$302$	−9.54177	+	16.5268i	−0.549067	+	0.951012i
$303$	−7.67946	+	13.3012i	−0.441173	+	0.764134i
$304$	2.64073	+	4.57387i	0.151456	+	0.262330i
$305$	−1.13695			−0.0651016
$306$	1.44557	−	2.50380i	0.0826376	−	0.143132i
$307$	0.860812	+	1.49097i	0.0491292	+	0.0850942i	0.889544	−	0.456849i	$-0.151022\pi$
$307$	0.860812	+	1.49097i	0.0491292	+	0.0850942i	−0.840415	+	0.541943i	$0.817689\pi$
$308$	0.00596117	−	0.0103250i	0.000339669	−	0.000588324i
$309$	6.95706	+	12.0500i	0.395773	+	0.685499i
$310$	−1.43411			−0.0814522
$311$	−0.323617	+	0.560522i	−0.0183507	+	0.0317843i	−0.875055	−	0.484024i	$-0.839175\pi$
$311$	−0.323617	+	0.560522i	−0.0183507	+	0.0317843i	0.856704	+	0.515808i	$0.172508\pi$
$312$	−3.04470	−	5.27358i	−0.172372	−	0.298558i
$313$	14.0059	+	24.2589i	0.791661	+	1.37120i	0.924938	+	0.380118i	$0.124117\pi$
$313$	14.0059	+	24.2589i	0.791661	+	1.37120i	−0.133277	+	0.991079i	$0.542550\pi$
$314$	6.48492			0.365965
$315$	0.0178290	+	0.0308808i	0.00100455	+	0.00173993i
$316$	4.02459	−	6.97079i	0.226401	−	0.392138i
$317$	6.48625	−	11.2345i	0.364304	−	0.630993i	−0.624360	−	0.781137i	$-0.714640\pi$
$317$	6.48625	−	11.2345i	0.364304	−	0.630993i	0.988664	+	0.150144i	$0.0479736\pi$
$318$	−4.46568			−0.250423
$319$	0.962091	+	1.66639i	0.0538667	+	0.0932999i
$320$	−0.355961	+	0.616542i	−0.0198988	+	0.0344657i
$321$	6.90666			0.385492
$322$	0.0820861	+	0.142177i	0.00457448	+	0.00792323i
$323$	−7.63470	−	13.2237i	−0.424806	−	0.735785i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	13.6804	+	23.6951i	0.758850	+	1.31437i
$326$	−5.53504			−0.306557
$327$	3.83038			0.211820
$328$	10.3734			0.572775
$329$	0.0502832	−	0.0870931i	0.00277220	−	0.00480160i
$330$	−0.0847301	+	0.146757i	−0.00466424	+	0.00807870i
$331$	−19.4415			−1.06860			−0.534301	−	0.845294i	$-0.679425\pi$
$331$	−19.4415			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$332$	−4.53232	+	7.85020i	−0.248743	+	0.430836i
$333$	2.18358	+	3.78207i	0.119659	+	0.207256i
$334$	3.84736			0.210518
$335$	−3.10528			−0.169660
$336$	0.0250435	+	0.0433767i	0.00136624	+	0.00236639i
$337$	−7.49038	+	12.9737i	−0.408027	+	0.706723i	−0.994669	−	0.103123i	$-0.967116\pi$
$337$	−7.49038	+	12.9737i	−0.408027	+	0.706723i	0.586642	+	0.809847i	$0.300450\pi$
$338$	24.0809			1.30983
$339$	2.03896	−	3.53159i	0.110741	−	0.191810i
$340$	1.02913	−	1.78250i	0.0558124	−	0.0966699i
$341$	−0.479499			−0.0259663
$342$	−5.28145			−0.285588
$343$	0.701093			0.0378555
$344$	0.543104	+	0.940683i	0.0292822	+	0.0507182i
$345$	−1.16675	−	2.02086i	−0.0628154	−	0.108800i
$346$	0.646627	+	1.11999i	0.0347629	+	0.0602111i
$347$	−16.2473	−	28.1412i	−0.872201	−	1.51070i	−0.859715	−	0.510775i	$-0.829359\pi$
$347$	−16.2473	−	28.1412i	−0.872201	−	1.51070i	−0.0124867	−	0.999922i	$-0.503975\pi$
$348$	−8.08370			−0.433332
$349$	16.7922	−	29.0849i	0.898864	−	1.55688i	0.0699153	−	0.997553i	$-0.477727\pi$
$349$	16.7922	−	29.0849i	0.898864	−	1.55688i	0.828949	−	0.559325i	$-0.188940\pi$
$350$	−0.112525	−	0.194899i	−0.00601470	−	0.0104178i
$351$	6.08940			0.325028
$352$	−0.119016	+	0.206142i	−0.00634358	+	0.0109874i
$353$	7.62705	−	13.2104i	0.405947	−	0.703120i	−0.588484	−	0.808509i	$-0.700275\pi$
$353$	7.62705	−	13.2104i	0.405947	−	0.703120i	0.994431	+	0.105388i	$0.0336085\pi$
$354$	−4.65320	−	8.05957i	−0.247315	−	0.428361i
$355$	−2.48606			−0.131946
$356$	−4.61528	−	7.99390i	−0.244609	−	0.423676i
$357$	−0.0724042	−	0.125408i	−0.00383204	−	0.00663728i
$358$	−10.4033	+	18.0190i	−0.549831	+	0.952336i
$359$	−27.3141			−1.44159			−0.720793	−	0.693151i	$-0.756222\pi$
$359$	−27.3141			−1.44159			−0.720793	+	0.693151i	$0.756222\pi$
$360$	−0.355961	−	0.616542i	−0.0187608	−	0.0324946i
$361$	−4.44688	+	7.70222i	−0.234046	+	0.405380i
$362$	10.6949	+	18.5241i	0.562110	+	0.973603i
$363$	5.47167	−	9.47721i	0.287188	−	0.497425i
$364$	−0.305000			−0.0159864
$365$	−0.262784	−	0.455155i	−0.0137547	−	0.0238239i
$366$	0.798509	−	1.38306i	0.0417387	−	0.0722936i
$367$	3.19056	−	5.52621i	0.166546	−	0.288466i	−0.770657	−	0.637250i	$-0.780072\pi$
$367$	3.19056	−	5.52621i	0.166546	−	0.288466i	0.937203	+	0.348784i	$0.113405\pi$
$368$	−1.63887	−	2.83860i	−0.0854319	−	0.147972i
$369$	−5.18670	+	8.98363i	−0.270009	+	0.467669i
$370$	1.55454	+	2.69254i	0.0808165	+	0.139978i
$371$	−0.111836	+	0.193706i	−0.00580626	+	0.0100567i
$372$	1.00721	−	1.74455i	0.0522216	−	0.0904505i
$373$	2.70078	−	4.67788i	0.139841	−	0.242211i	−0.787595	−	0.616193i	$-0.788674\pi$
$373$	2.70078	−	4.67788i	0.139841	−	0.242211i	0.927436	+	0.373981i	$0.122008\pi$
$374$	0.344092	−	0.595984i	0.0177926	−	0.0308176i
$375$	3.37919	+	5.85293i	0.174501	+	0.302244i
$376$	−1.00392	+	1.73883i	−0.0517730	+	0.0896735i
$377$	24.6125	−	42.6300i	1.26761	−	2.19556i
$378$	−0.0500871			−0.00257620
$379$	−2.14889	−	3.72199i	−0.110381	−	0.191186i	0.805543	−	0.592538i	$-0.201874\pi$
$379$	−2.14889	−	3.72199i	−0.110381	−	0.191186i	−0.915924	+	0.401352i	$0.868541\pi$
$380$	−3.75998			−0.192883
$381$	2.66370	−	4.61366i	0.136465	−	0.236365i
$382$	−21.0306			−1.07602
$383$	4.19654	−	7.26862i	0.214433	−	0.371409i	−0.738664	−	0.674074i	$-0.764543\pi$
$383$	4.19654	−	7.26862i	0.214433	−	0.371409i	0.953097	+	0.302665i	$0.0978763\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	0.00424388	+	0.00735062i	0.000216288	+	0.000374622i
$386$	−22.9321			−1.16721
$387$	−1.08621			−0.0552150
$388$	1.07175	−	1.85633i	0.0544101	−	0.0942410i
$389$	−17.4688	+	30.2568i	−0.885703	+	1.53408i	−0.0407968	+	0.999167i	$0.512990\pi$
$389$	−17.4688	+	30.2568i	−0.885703	+	1.53408i	−0.844906	+	0.534915i	$0.820344\pi$
$390$	4.33518			0.219520
$391$	4.73819	+	8.20679i	0.239621	+	0.415035i
$392$	−6.99749			−0.353427
$393$	−1.75869	+	3.04614i	−0.0887140	+	0.153657i
$394$	−7.87651			−0.396813
$395$	2.86519	+	4.96265i	0.144163	+	0.249698i
$396$	−0.119016	−	0.206142i	−0.00598079	−	0.0103590i
$397$	−10.0967			−0.506740			−0.253370	−	0.967369i	$-0.581539\pi$
$397$	−10.0967			−0.506740			−0.253370	+	0.967369i	$0.581539\pi$
$398$	−11.8545	−	20.5326i	−0.594211	−	1.02920i
$399$	−0.132266	+	0.229092i	−0.00662159	+	0.0114689i
$400$	2.24658	+	3.89120i	0.112329	+	0.194560i
$401$	3.37268	+	5.84166i	0.168424	+	0.291719i	0.937866	−	0.346998i	$-0.112799\pi$
$401$	3.37268	+	5.84166i	0.168424	+	0.291719i	−0.769442	+	0.638717i	$0.779466\pi$
$402$	2.18092	−	3.77746i	0.108774	−	0.188402i
$403$	6.13334	+	10.6233i	0.305523	+	0.529182i
$404$	−7.67946	−	13.3012i	−0.382067	−	0.661760i
$405$	0.711921			0.0353756
$406$	−0.202444	+	0.350644i	−0.0100471	+	0.0174022i
$407$	0.519762	+	0.900255i	0.0257637	+	0.0446240i
$408$	1.44557	+	2.50380i	0.0715662	+	0.123956i
$409$	16.4609	−	28.5112i	0.813940	−	1.40979i	−0.0961459	−	0.995367i	$-0.530652\pi$
$409$	16.4609	−	28.5112i	0.813940	−	1.40979i	0.910086	−	0.414419i	$-0.136015\pi$
$410$	−3.69252	+	6.39563i	−0.182361	+	0.315858i
$411$	−6.77141	+	11.7284i	−0.334009	+	0.578520i
$412$	−13.9141			−0.685499
$413$	−0.466130			−0.0229367
$414$	3.27774			0.161092
$415$	−3.22665	−	5.58872i	−0.158390	−	0.274340i
$416$	6.08940			0.298558
$417$	−1.31959	+	2.28560i	−0.0646207	+	0.111926i
$418$	−1.25716			−0.0614895
$419$	−21.4045			−1.04568			−0.522839	−	0.852431i	$-0.675127\pi$
$419$	−21.4045			−1.04568			−0.522839	+	0.852431i	$0.675127\pi$
$420$	−0.0356580			−0.00173993
$421$	10.2834	+	17.8114i	0.501183	+	0.868074i	0.999999	+	0.00136603i	$0.000434822\pi$
$421$	10.2834	+	17.8114i	0.501183	+	0.868074i	−0.498817	+	0.866708i	$0.666232\pi$
$422$	−5.37153	−	9.30377i	−0.261482	−	0.452900i
$423$	−1.00392	−	1.73883i	−0.0488121	−	0.0845450i
$424$	2.23284	−	3.86739i	0.108436	−	0.187817i
$425$	−6.49518	−	11.2500i	−0.315062	−	0.545704i
$426$	1.74602	−	3.02420i	0.0845951	−	0.146523i
$427$	−0.0399950	−	0.0692733i	−0.00193549	−	0.00335237i
$428$	−3.45333	+	5.98134i	−0.166923	+	0.289119i
$429$	1.44947			0.0699813
$430$	−0.773294			−0.0372915
$431$	−3.62208			−0.174470			−0.0872348	−	0.996188i	$-0.527803\pi$
$431$	−3.62208			−0.174470			−0.0872348	+	0.996188i	$0.527803\pi$
$432$	1.00000			0.0481125
$433$	23.5556			1.13201			0.566005	−	0.824402i	$-0.308488\pi$
$433$	23.5556			1.13201			0.566005	+	0.824402i	$0.308488\pi$
$434$	−0.0504484	−	0.0873792i	−0.00242160	−	0.00419434i
$435$	2.87748	−	4.98394i	0.137964	−	0.238962i
$436$	−1.91519	+	3.31720i	−0.0917208	+	0.158865i
$437$	8.65561	−	14.9920i	0.414054	−	0.717163i
$438$	0.738239			0.0352744
$439$	16.0295			0.765047			0.382523	−	0.923946i	$-0.375055\pi$
$439$	16.0295			0.765047			0.382523	+	0.923946i	$0.375055\pi$
$440$	−0.0847301	−	0.146757i	−0.00403935	−	0.00699636i
$441$	3.49875	−	6.06001i	0.166607	−	0.288572i
$442$	−17.6053			−0.837398
$443$	7.41778	+	12.8480i	0.352429	+	0.610426i	0.986675	−	0.162706i	$-0.0520223\pi$
$443$	7.41778	+	12.8480i	0.352429	+	0.610426i	−0.634245	+	0.773132i	$0.718689\pi$
$444$	−4.36716			−0.207256
$445$	6.57143			0.311516
$446$	3.73581	+	14.4583i	0.176896	+	0.684622i
$447$	−7.61759			−0.360300
$448$	−0.0500871			−0.00236639
$449$	−0.0524197	−	0.0907936i	−0.00247384	−	0.00428482i	0.864786	−	0.502141i	$-0.167454\pi$
$449$	−0.0524197	−	0.0907936i	−0.00247384	−	0.00428482i	−0.867260	+	0.497856i	$0.834121\pi$
$450$	−4.49317			−0.211810
$451$	−1.23460	+	2.13839i	−0.0581351	+	0.100693i
$452$	2.03896	+	3.53159i	0.0959048	+	0.166112i
$453$	19.0835			0.896623
$454$	−9.78329			−0.459152
$455$	0.108568	−	0.188045i	0.00508975	−	0.00881571i
$456$	2.64073	−	4.57387i	0.123663	−	0.214191i
$457$	15.2865	−	26.4770i	0.715073	−	1.23854i	−0.247858	−	0.968796i	$-0.579727\pi$
$457$	15.2865	−	26.4770i	0.715073	−	1.23854i	0.962931	−	0.269747i	$-0.0869400\pi$
$458$	2.54981	+	4.41641i	0.119145	+	0.206365i
$459$	−2.89113			−0.134947
$460$	2.33349			0.108800
$461$	27.9212			1.30042			0.650209	−	0.759755i	$-0.274681\pi$
$461$	27.9212			1.30042			0.650209	+	0.759755i	$0.274681\pi$
$462$	−0.0119223			−0.000554677
$463$	−3.93371			−0.182815			−0.0914076	−	0.995814i	$-0.529137\pi$
$463$	−3.93371			−0.182815			−0.0914076	+	0.995814i	$0.529137\pi$
$464$	4.04185	−	7.00069i	0.187638	−	0.324999i
$465$	0.717057	+	1.24198i	0.0332527	+	0.0575954i
$466$	−4.65509	+	8.06286i	−0.215643	+	0.373505i
$467$	−8.19816	−	14.1996i	−0.379365	−	0.657080i	0.611605	−	0.791164i	$-0.290524\pi$
$467$	−8.19816	−	14.1996i	−0.379365	−	0.657080i	−0.990970	+	0.134083i	$0.957191\pi$
$468$	−3.04470	+	5.27358i	−0.140741	+	0.243771i
$469$	−0.109236	−	0.189202i	−0.00504404	−	0.00873653i
$470$	−0.714709	−	1.23791i	−0.0329671	−	0.0571006i
$471$	−3.24246	−	5.61610i	−0.149405	−	0.258776i
$472$	9.30639			0.428361
$473$	−0.258552			−0.0118883
$474$	−8.04918			−0.369711
$475$	−11.8652	+	20.5512i	−0.544414	+	0.942953i
$476$	0.144808			0.00663728
$477$	2.23284	+	3.86739i	0.102235	+	0.177076i
$478$	13.6826			0.625829
$479$	30.4075			1.38936			0.694678	−	0.719321i	$-0.255547\pi$
$479$	30.4075			1.38936			0.694678	+	0.719321i	$0.255547\pi$
$480$	0.711921			0.0324946
$481$	13.2967	−	23.0306i	0.606277	−	1.05010i
$482$	8.23257	−	14.2592i	0.374983	−	0.649490i
$483$	0.0820861	−	0.142177i	0.00373505	−	0.00646929i
$484$	5.47167	+	9.47721i	0.248712	+	0.430782i
$485$	0.763004	+	1.32156i	0.0346462	+	0.0600090i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	39.0435			1.76923			0.884615	−	0.466321i	$-0.154421\pi$
$487$	39.0435			1.76923			0.884615	+	0.466321i	$0.154421\pi$
$488$	0.798509	+	1.38306i	0.0361468	+	0.0626081i
$489$	2.76752	+	4.79348i	0.125152	+	0.216769i
$490$	2.49083	−	4.31425i	0.112524	−	0.194898i
$491$	−16.1006	−	27.8871i	−0.726611	−	1.25853i	−0.958307	−	0.285740i	$-0.907761\pi$
$491$	−16.1006	−	27.8871i	−0.726611	−	1.25853i	0.231696	−	0.972788i	$-0.425573\pi$
$492$	−5.18670	−	8.98363i	−0.233834	−	0.405013i
$493$	−11.6855	+	20.2399i	−0.526290	+	0.911561i
$494$	16.0805	+	27.8522i	0.723494	+	1.25313i
$495$	0.169460			0.00761667
$496$	1.00721	+	1.74455i	0.0452253	+	0.0783325i
$497$	−0.0874532	−	0.151473i	−0.00392281	−	0.00679451i
$498$	9.06463			0.406196
$499$	−8.88900	+	15.3962i	−0.397926	+	0.689229i	−0.993470	−	0.114094i	$-0.963603\pi$
$499$	−8.88900	+	15.3962i	−0.397926	+	0.689229i	0.595544	+	0.803323i	$0.296937\pi$
$500$	−6.75839			−0.302244
$501$	−1.92368	−	3.33191i	−0.0859436	−	0.148859i
$502$	11.6521			0.520059
$503$	10.2168	−	17.6960i	0.455544	−	0.789025i	−0.543175	−	0.839619i	$-0.682778\pi$
$503$	10.2168	−	17.6960i	0.455544	−	0.789025i	0.998719	+	0.0505941i	$0.0161115\pi$
$504$	0.0250435	−	0.0433767i	0.00111553	−	0.00193215i
$505$	10.9343			0.486571
$506$	0.780207			0.0346844
$507$	−12.0404	−	20.8546i	−0.534734	−	0.926187i
$508$	2.66370	+	4.61366i	0.118183	+	0.204698i
$509$	2.19511	−	3.80203i	0.0972963	−	0.168522i	−0.813268	−	0.581889i	$-0.802314\pi$
$509$	2.19511	−	3.80203i	0.0972963	−	0.168522i	0.910565	+	0.413367i	$0.135647\pi$
$510$	−2.05826			−0.0911413
$511$	0.0184881	−	0.0320223i	0.000817866	−	0.00141658i
$512$	1.00000			0.0441942
$513$	2.64073	+	4.57387i	0.116591	+	0.201941i
$514$	−11.2746			−0.497303
$515$	4.95288	−	8.57863i	0.218250	−	0.378020i
$516$	0.543104	−	0.940683i	0.0239088	−	0.0414113i
$517$	−0.238964	−	0.413899i	−0.0105096	−	0.0182032i
$518$	−0.109369	+	0.189433i	−0.00480540	+	0.00832320i
$519$	0.646627	−	1.11999i	0.0283838	−	0.0491621i
$520$	−2.16759	+	3.75437i	−0.0950550	+	0.164640i
$521$	−6.80779	+	11.7914i	−0.298255	+	0.516592i	−0.975737	−	0.218947i	$-0.929738\pi$
$521$	−6.80779	+	11.7914i	−0.298255	+	0.516592i	0.677482	+	0.735539i	$0.263071\pi$
$522$	4.04185	+	7.00069i	0.176907	+	0.306412i
$523$	−4.91739	+	8.51717i	−0.215022	+	0.372430i	−0.953280	−	0.302090i	$-0.902316\pi$
$523$	−4.91739	+	8.51717i	−0.215022	+	0.372430i	0.738257	+	0.674519i	$0.235649\pi$
$524$	−1.75869	−	3.04614i	−0.0768286	−	0.133071i
$525$	−0.112525	+	0.194899i	−0.00491098	+	0.00850608i
$526$	−6.15272	+	10.6568i	−0.268271	+	0.464660i
$527$	−2.91199	−	5.04372i	−0.126848	−	0.219708i
$528$	0.238032			0.0103590
$529$	6.12822	−	10.6144i	0.266444	−	0.461495i
$530$	1.58961	+	2.75328i	0.0690481	+	0.119595i
$531$	−4.65320	+	8.05957i	−0.201931	+	0.349756i
$532$	−0.132266	−	0.229092i	−0.00573447	−	0.00993239i
$533$	63.1678			2.73610
$534$	−4.61528	+	7.99390i	−0.199723	+	0.345930i
$535$	−2.45850	−	4.25824i	−0.106290	−	0.184100i
$536$	2.18092	+	3.77746i	0.0942012	+	0.163161i
$537$	20.8066			0.897871
$538$	−5.20507	−	9.01544i	−0.224406	−	0.388683i
$539$	0.832814	−	1.44248i	0.0358719	−	0.0621319i
$540$	−0.355961	+	0.616542i	−0.0153181	+	0.0265317i
$541$	27.2969			1.17359			0.586794	−	0.809736i	$-0.300390\pi$
$541$	27.2969			1.17359			0.586794	+	0.809736i	$0.300390\pi$
$542$	−8.72371	−	15.1099i	−0.374715	−	0.649026i
$543$	10.6949	−	18.5241i	0.458961	−	0.794944i
$544$	−2.89113			−0.123956
$545$	−1.36346	−	2.36159i	−0.0584043	−	0.101159i
$546$	0.152500	+	0.264138i	0.00652641	+	0.0113041i
$547$	−20.8949	−	36.1911i	−0.893403	−	1.54742i	−0.835769	−	0.549081i	$-0.814978\pi$
$547$	−20.8949	−	36.1911i	−0.893403	−	1.54742i	−0.0576332	−	0.998338i	$-0.518355\pi$
$548$	−6.77141	−	11.7284i	−0.289260	−	0.501013i
$549$	−1.59702			−0.0681591
$550$	−1.06952			−0.0456044
$551$	42.6937			1.81881
$552$	−1.63887	+	2.83860i	−0.0697549	+	0.120819i
$553$	−0.201580	+	0.349146i	−0.00857204	+	0.0148472i
$554$	−21.5632			−0.916133
$555$	1.55454	−	2.69254i	0.0659864	−	0.114292i
$556$	−1.31959	−	2.28560i	−0.0559631	−	0.0969310i
$557$	−41.7961			−1.77096			−0.885478	−	0.464681i	$-0.846169\pi$
$557$	−41.7961			−1.77096			−0.885478	+	0.464681i	$0.846169\pi$
$558$	−2.01443			−0.0852776
$559$	3.30718	+	5.72820i	0.139879	+	0.242277i
$560$	0.0178290	−	0.0308808i	0.000753413	−	0.00130495i
$561$	−0.688183			−0.0290551
$562$	2.83723	−	4.91422i	0.119681	−	0.207294i
$563$	−15.7610	+	27.2989i	−0.664249	+	1.15051i	0.315240	+	0.949012i	$0.397915\pi$
$563$	−15.7610	+	27.2989i	−0.664249	+	1.15051i	−0.979488	+	0.201501i	$0.935418\pi$
$564$	2.00783			0.0845450
$565$	−2.90316			−0.122137
$566$	0.879276			0.0369587
$567$	0.0250435	+	0.0433767i	0.00105173	+	0.00182165i
$568$	1.74602	+	3.02420i	0.0732615	+	0.126893i
$569$	9.51908	+	16.4875i	0.399061	+	0.691194i	0.993610	−	0.112865i	$-0.0360029\pi$
$569$	9.51908	+	16.4875i	0.399061	+	0.691194i	−0.594550	+	0.804059i	$0.702670\pi$
$570$	1.87999	+	3.25624i	0.0787441	+	0.136389i
$571$	2.31163			0.0967388			0.0483694	−	0.998830i	$-0.484598\pi$
$571$	2.31163			0.0967388			0.0483694	+	0.998830i	$0.484598\pi$
$572$	−0.724737	+	1.25528i	−0.0303028	+	0.0524860i
$573$	10.5153	+	18.2131i	0.439284	+	0.760862i
$574$	−0.519573			−0.0216866
$575$	7.36371	−	12.7543i	0.307088	−	0.531892i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.54212	−	2.67103i	−0.0641992	−	0.111196i	0.832139	−	0.554567i	$-0.187116\pi$
$577$	−1.54212	−	2.67103i	−0.0641992	−	0.111196i	−0.896338	+	0.443370i	$0.853783\pi$
$578$	−8.64134			−0.359432
$579$	11.4660	+	19.8598i	0.476513	+	0.825344i
$580$	2.87748	+	4.98394i	0.119481	+	0.206947i
$581$	0.227010	−	0.393194i	0.00941798	−	0.0163124i
$582$	−2.14351			−0.0888512
$583$	0.531488	+	0.920565i	0.0220120	+	0.0381259i
$584$	−0.369119	+	0.639334i	−0.0152743	+	0.0264558i
$585$	−2.16759	−	3.75437i	−0.0896187	−	0.155224i
$586$	−0.695703	+	1.20499i	−0.0287392	+	0.0497778i
$587$	−26.0777			−1.07634			−0.538170	−	0.842836i	$-0.680884\pi$
$587$	−26.0777			−1.07634			−0.538170	+	0.842836i	$0.680884\pi$
$588$	3.49875	+	6.06001i	0.144286	+	0.249910i
$589$	−5.31956	+	9.21374i	−0.219189	+	0.379646i
$590$	−3.31271	+	5.73778i	−0.136382	+	0.236221i
$591$	3.93825	+	6.82125i	0.161998	+	0.280589i
$592$	2.18358	−	3.78207i	0.0897446	−	0.155442i
$593$	−8.68051	−	15.0351i	−0.356466	−	0.617417i	0.630902	−	0.775863i	$-0.282685\pi$
$593$	−8.68051	−	15.0351i	−0.356466	−	0.617417i	−0.987368	+	0.158446i	$0.949352\pi$
$594$	−0.119016	+	0.206142i	−0.00488329	+	0.00845811i
$595$	−0.0515461	+	0.0892804i	−0.00211318	+	0.00366014i
$596$	3.80880	−	6.59703i	0.156014	−	0.270225i
$597$	−11.8545	+	20.5326i	−0.485171	+	0.840342i
$598$	−9.97974	−	17.2854i	−0.408102	−	0.706853i
$599$	−2.13484	+	3.69765i	−0.0872271	+	0.151082i	−0.906338	−	0.422553i	$-0.861134\pi$
$599$	−2.13484	+	3.69765i	−0.0872271	+	0.151082i	0.819111	+	0.573635i	$0.194467\pi$
$600$	2.24658	−	3.89120i	0.0917164	−	0.158857i
$601$	23.9511			0.976984			0.488492	−	0.872568i	$-0.337547\pi$
$601$	23.9511			0.976984			0.488492	+	0.872568i	$0.337547\pi$
$602$	−0.0272025	−	0.0471161i	−0.00110869	−	0.00192031i
$603$	−4.36183			−0.177628
$604$	−9.54177	+	16.5268i	−0.388249	+	0.672467i
$605$	−7.79079			−0.316741
$606$	−7.67946	+	13.3012i	−0.311957	+	0.540325i
$607$	−16.4245	−	28.4481i	−0.666651	−	1.15467i	−0.978835	−	0.204652i	$-0.934394\pi$
$607$	−16.4245	−	28.4481i	−0.666651	−	1.15467i	0.312184	−	0.950022i	$-0.398939\pi$
$608$	2.64073	+	4.57387i	0.107096	+	0.185495i
$609$	0.404889			0.0164069
$610$	−1.13695			−0.0460338
$611$	−6.11325	+	10.5885i	−0.247316	+	0.428363i
$612$	1.44557	−	2.50380i	0.0584336	−	0.101210i
$613$	14.7764			0.596811			0.298406	−	0.954439i	$-0.403545\pi$
$613$	14.7764			0.596811			0.298406	+	0.954439i	$0.403545\pi$
$614$	0.860812	+	1.49097i	0.0347396	+	0.0601707i
$615$	7.38504			0.297794
$616$	0.00596117	−	0.0103250i	0.000240182	−	0.000416008i
$617$	−19.3305			−0.778217			−0.389108	−	0.921192i	$-0.627217\pi$
$617$	−19.3305			−0.778217			−0.389108	+	0.921192i	$0.627217\pi$
$618$	6.95706	+	12.0500i	0.279854	+	0.484721i
$619$	21.9517	+	38.0215i	0.882313	+	1.52821i	0.848762	+	0.528775i	$0.177348\pi$
$619$	21.9517	+	38.0215i	0.882313	+	1.52821i	0.0335510	+	0.999437i	$0.489318\pi$
$620$	−1.43411			−0.0575954
$621$	−1.63887	−	2.83860i	−0.0657655	−	0.113909i
$622$	−0.323617	+	0.560522i	−0.0129759	+	0.0224749i
$623$	0.231166	+	0.400391i	0.00926146	+	0.0160413i
$624$	−3.04470	−	5.27358i	−0.121886	−	0.211112i
$625$	−8.82720	+	15.2892i	−0.353088	+	0.611567i
$626$	14.0059	+	24.2589i	0.559789	+	0.969582i
$627$	0.628578	+	1.08873i	0.0251030	+	0.0434797i
$628$	6.48492			0.258776
$629$	−6.31302	+	10.9345i	−0.251717	+	0.435986i
$630$	0.0178290	+	0.0308808i	0.000710325	+	0.00123032i
$631$	−8.09263	−	14.0169i	−0.322163	−	0.558002i	0.658771	−	0.752343i	$-0.271076\pi$
$631$	−8.09263	−	14.0169i	−0.322163	−	0.558002i	−0.980934	+	0.194341i	$0.937743\pi$
$632$	4.02459	−	6.97079i	0.160089	−	0.277283i
$633$	−5.37153	+	9.30377i	−0.213499	+	0.369792i
$634$	6.48625	−	11.2345i	0.257602	−	0.446179i
$635$	−3.79269			−0.150508
$636$	−4.46568			−0.177076
$637$	−42.6106			−1.68829
$638$	0.962091	+	1.66639i	0.0380895	+	0.0659730i
$639$	−3.49205			−0.138143
$640$	−0.355961	+	0.616542i	−0.0140706	+	0.0243710i
$641$	4.86958			0.192337			0.0961685	−	0.995365i	$-0.469341\pi$
$641$	4.86958			0.192337			0.0961685	+	0.995365i	$0.469341\pi$
$642$	6.90666			0.272584
$643$	−30.1091			−1.18739			−0.593693	−	0.804691i	$-0.702331\pi$
$643$	−30.1091			−1.18739			−0.593693	+	0.804691i	$0.702331\pi$
$644$	0.0820861	+	0.142177i	0.00323465	+	0.00560257i
$645$	0.386647	+	0.669692i	0.0152242	+	0.0263691i
$646$	−7.63470	−	13.2237i	−0.300383	−	0.520279i
$647$	−12.0345	+	20.8443i	−0.473123	+	0.819473i	−0.999527	−	0.0307615i	$-0.990207\pi$
$647$	−12.0345	+	20.8443i	−0.473123	+	0.819473i	0.526404	+	0.850235i	$0.323540\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.10761	+	1.91844i	−0.0434775	+	0.0753053i
$650$	13.6804	+	23.6951i	0.536588	+	0.929397i
$651$	−0.0504484	+	0.0873792i	−0.00197723	+	0.00342466i
$652$	−5.53504			−0.216769
$653$	19.1985			0.751294			0.375647	−	0.926763i	$-0.377421\pi$
$653$	19.1985			0.751294			0.375647	+	0.926763i	$0.377421\pi$
$654$	3.83038			0.149780
$655$	2.50409			0.0978430
$656$	10.3734			0.405013
$657$	−0.369119	−	0.639334i	−0.0144007	−	0.0249428i
$658$	0.0502832	−	0.0870931i	0.00196024	−	0.00339524i
$659$	−19.0439	+	32.9849i	−0.741843	+	1.28491i	0.209812	+	0.977742i	$0.432715\pi$
$659$	−19.0439	+	32.9849i	−0.741843	+	1.28491i	−0.951655	+	0.307169i	$0.900618\pi$
$660$	−0.0847301	+	0.146757i	−0.00329811	+	0.00571250i
$661$	−24.0288			−0.934614			−0.467307	−	0.884095i	$-0.654776\pi$
$661$	−24.0288			−0.934614			−0.467307	+	0.884095i	$0.654776\pi$
$662$	−19.4415			−0.755616
$663$	8.80264	+	15.2466i	0.341866	+	0.592130i
$664$	−4.53232	+	7.85020i	−0.175888	+	0.304647i
$665$	0.188326			0.00730298
$666$	2.18358	+	3.78207i	0.0846120	+	0.146552i
$667$	−26.4962			−1.02594
$668$	3.84736			0.148859
$669$	10.6534	−	10.4645i	0.411884	−	0.404580i
$670$	−3.10528			−0.119967
$671$	−0.380142			−0.0146752
$672$	0.0250435	+	0.0433767i	0.000966075	+	0.00167329i
$673$	10.8852			0.419592			0.209796	−	0.977745i	$-0.432720\pi$
$673$	10.8852			0.419592			0.209796	+	0.977745i	$0.432720\pi$
$674$	−7.49038	+	12.9737i	−0.288519	+	0.499729i
$675$	2.24658	+	3.89120i	0.0864711	+	0.149772i
$676$	24.0809			0.926187
$677$	30.3616			1.16689			0.583445	−	0.812152i	$-0.301704\pi$
$677$	30.3616			1.16689			0.583445	+	0.812152i	$0.301704\pi$
$678$	2.03896	−	3.53159i	0.0783059	−	0.135630i
$679$	−0.0536810	+	0.0929782i	−0.00206009	+	0.00356818i
$680$	1.02913	−	1.78250i	0.0394653	−	0.0683559i
$681$	4.89164	+	8.47257i	0.187448	+	0.324670i
$682$	−0.479499			−0.0183610
$683$	21.3729			0.817812			0.408906	−	0.912577i	$-0.365910\pi$
$683$	21.3729			0.817812			0.408906	+	0.912577i	$0.365910\pi$
$684$	−5.28145			−0.201941
$685$	9.64141			0.368379
$686$	0.701093			0.0267679
$687$	2.54981	−	4.41641i	0.0972815	−	0.168496i
$688$	0.543104	+	0.940683i	0.0207056	+	0.0358632i
$689$	13.5967	−	23.5501i	0.517992	−	0.897189i
$690$	−1.16675	−	2.02086i	−0.0444172	−	0.0769329i
$691$	13.3532	−	23.1284i	0.507979	−	0.879846i	−0.491978	−	0.870608i	$-0.663726\pi$
$691$	13.3532	−	23.1284i	0.507979	−	0.879846i	0.999957	−	0.00923827i	$-0.00294067\pi$
$692$	0.646627	+	1.11999i	0.0245811	+	0.0425756i
$693$	0.00596117	+	0.0103250i	0.000226446	+	0.000392216i
$694$	−16.2473	−	28.1412i	−0.616739	−	1.06822i
$695$	1.87889			0.0712704
$696$	−8.08370			−0.306412
$697$	−29.9909			−1.13599
$698$	16.7922	−	29.0849i	0.635593	−	1.10088i
$699$	9.31019			0.352144
$700$	−0.112525	−	0.194899i	−0.00425304	−	0.00736648i
$701$	−40.3493			−1.52397			−0.761986	−	0.647594i	$-0.775775\pi$
$701$	−40.3493			−1.52397			−0.761986	+	0.647594i	$0.775775\pi$
$702$	6.08940			0.229830
$703$	23.0649			0.869911
$704$	−0.119016	+	0.206142i	−0.00448559	+	0.00776927i
$705$	−0.714709	+	1.23791i	−0.0269175	+	0.0466225i
$706$	7.62705	−	13.2104i	0.287048	−	0.497181i
$707$	0.384641	+	0.666218i	0.0144659	+	0.0250557i
$708$	−4.65320	−	8.05957i	−0.174878	−	0.302897i
$709$	25.0533	−	43.3937i	0.940898	−	1.62968i	0.177135	−	0.984187i	$-0.443317\pi$
$709$	25.0533	−	43.3937i	0.940898	−	1.62968i	0.763763	−	0.645496i	$-0.223349\pi$
$710$	−2.48606			−0.0933002
$711$	4.02459	+	6.97079i	0.150934	+	0.261425i
$712$	−4.61528	−	7.99390i	−0.172965	−	0.299584i
$713$	3.30138	−	5.71817i	0.123638	−	0.214147i
$714$	−0.0724042	−	0.125408i	−0.00270966	−	0.00469327i
$715$	−0.515956	−	0.893662i	−0.0192957	−	0.0334211i
$716$	−10.4033	+	18.0190i	−0.388790	+	0.673403i
$717$	−6.84131	−	11.8495i	−0.255494	−	0.442528i
$718$	−27.3141			−1.01935
$719$	26.0177	+	45.0639i	0.970296	+	1.68060i	0.694659	+	0.719339i	$0.255555\pi$
$719$	26.0177	+	45.0639i	0.970296	+	1.68060i	0.275637	+	0.961262i	$0.411111\pi$
$720$	−0.355961	−	0.616542i	−0.0132659	−	0.0229772i
$721$	0.696917			0.0259545
$722$	−4.44688	+	7.70222i	−0.165496	+	0.286647i
$723$	−16.4651			−0.612345
$724$	10.6949	+	18.5241i	0.397472	+	0.688441i
$725$	36.3214			1.34894
$726$	5.47167	−	9.47721i	0.203073	−	0.351732i
$727$	21.4731	−	37.1925i	0.796393	−	1.37939i	−0.125557	−	0.992086i	$-0.540072\pi$
$727$	21.4731	−	37.1925i	0.796393	−	1.37939i	0.921951	−	0.387307i	$-0.126595\pi$
$728$	−0.305000			−0.0113041
$729$	1.00000			0.0370370
$730$	−0.262784	−	0.455155i	−0.00972607	−	0.0168460i
$731$	−1.57019	−	2.71964i	−0.0580754	−	0.100590i
$732$	0.798509	−	1.38306i	0.0295138	−	0.0511193i
$733$	−2.15962			−0.0797672			−0.0398836	−	0.999204i	$-0.512699\pi$
$733$	−2.15962			−0.0797672			−0.0398836	+	0.999204i	$0.512699\pi$
$734$	3.19056	−	5.52621i	0.117766	−	0.203976i
$735$	−4.98166			−0.183751
$736$	−1.63887	−	2.83860i	−0.0604095	−	0.104632i
$737$	−1.03826			−0.0382447
$738$	−5.18670	+	8.98363i	−0.190925	+	0.330692i
$739$	9.95834	−	17.2484i	0.366324	−	0.634491i	−0.622664	−	0.782489i	$-0.713950\pi$
$739$	9.95834	−	17.2484i	0.366324	−	0.634491i	0.988988	+	0.147998i	$0.0472830\pi$
$740$	1.55454	+	2.69254i	0.0571459	+	0.0989796i
$741$	16.0805	−	27.8522i	0.590730	−	1.02317i
$742$	−0.111836	+	0.193706i	−0.00410565	+	0.00711119i
$743$	9.20375	−	15.9414i	0.337653	−	0.584832i	−0.646338	−	0.763051i	$-0.723700\pi$
$743$	9.20375	−	15.9414i	0.337653	−	0.584832i	0.983991	+	0.178220i	$0.0570337\pi$
$744$	1.00721	−	1.74455i	0.0369263	−	0.0639582i
$745$	2.71156	+	4.69656i	0.0993440	+	0.172069i
$746$	2.70078	−	4.67788i	0.0988824	−	0.171269i
$747$	−4.53232	−	7.85020i	−0.165829	−	0.287224i
$748$	0.344092	−	0.595984i	0.0125812	−	0.0217913i
$749$	0.172967	−	0.299588i	0.00632008	−	0.0109467i
$750$	3.37919	+	5.85293i	0.123391	+	0.213719i
$751$	−14.4658			−0.527866			−0.263933	−	0.964541i	$-0.585020\pi$
$751$	−14.4658			−0.527866			−0.263933	+	0.964541i	$0.585020\pi$
$752$	−1.00392	+	1.73883i	−0.0366091	+	0.0634088i
$753$	−5.82605	−	10.0910i	−0.212313	−	0.367737i
$754$	24.6125	−	42.6300i	0.896333	−	1.55249i
$755$	−6.79298	−	11.7658i	−0.247222	−	0.428201i
$756$	−0.0500871			−0.00182165
$757$	1.17056	−	2.02747i	0.0425448	−	0.0736898i	−0.843969	−	0.536392i	$-0.819787\pi$
$757$	1.17056	−	2.02747i	0.0425448	−	0.0736898i	0.886514	+	0.462702i	$0.153120\pi$
$758$	−2.14889	−	3.72199i	−0.0780513	−	0.135189i
$759$	−0.390104	−	0.675679i	−0.0141599	−	0.0245256i
$760$	−3.75998			−0.136389
$761$	16.6798	+	28.8903i	0.604643	+	1.04727i	0.992108	+	0.125388i	$0.0400175\pi$
$761$	16.6798	+	28.8903i	0.604643	+	1.04727i	−0.387465	+	0.921884i	$0.626649\pi$
$762$	2.66370	−	4.61366i	0.0964956	−	0.167135i
$763$	0.0959261	−	0.166149i	0.00347276	−	0.00601499i
$764$	−21.0306			−0.760862
$765$	1.02913	+	1.78250i	0.0372083	+	0.0644466i
$766$	4.19654	−	7.26862i	0.151627	−	0.262626i
$767$	56.6704			2.04625
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	16.9215	+	29.3089i	0.610206	+	1.05691i	0.991205	+	0.132332i	$0.0422466\pi$
$769$	16.9215	+	29.3089i	0.610206	+	1.05691i	−0.381000	+	0.924575i	$0.624420\pi$
$770$	0.00424388	+	0.00735062i	0.000152939	+	0.000264898i
$771$	5.63732	+	9.76412i	0.203023	+	0.351646i
$772$	−22.9321			−0.825344
$773$	−2.06534			−0.0742852			−0.0371426	−	0.999310i	$-0.511826\pi$
$773$	−2.06534			−0.0742852			−0.0371426	+	0.999310i	$0.511826\pi$
$774$	−1.08621			−0.0390429
$775$	−4.52558	+	7.83854i	−0.162564	+	0.281569i
$776$	1.07175	−	1.85633i	0.0384737	−	0.0666384i
$777$	0.218738			0.00784719
$778$	−17.4688	+	30.2568i	−0.626286	+	1.08476i
$779$	27.3933	+	47.4466i	0.981467	+	1.69995i
$780$	4.33518			0.155224
$781$	−0.831220			−0.0297434
$782$	4.73819	+	8.20679i	0.169437	+	0.293474i
$783$	4.04185	−	7.00069i	0.144444	−	0.250184i
$784$	−6.99749			−0.249910
$785$	−2.30837	+	3.99822i	−0.0823894	+	0.142703i
$786$	−1.75869	+	3.04614i	−0.0627303	+	0.108652i
$787$	−44.3100			−1.57948			−0.789740	−	0.613442i	$-0.789785\pi$
$787$	−44.3100			−1.57948			−0.789740	+	0.613442i	$0.789785\pi$
$788$	−7.87651			−0.280589
$789$	12.3054			0.438085
$790$	2.86519	+	4.96265i	0.101939	+	0.176563i
$791$	−0.102126	−	0.176887i	−0.00363117	−	0.00628937i
$792$	−0.119016	−	0.206142i	−0.00422905	−	0.00732494i
$793$	4.86245	+	8.42200i	0.172671	+	0.299074i
$794$	−10.0967			−0.358319
$795$	1.58961	−	2.75328i	0.0563775	−	0.0976488i
$796$	−11.8545	−	20.5326i	−0.420171	−	0.727757i
$797$	−47.5531			−1.68442			−0.842209	−	0.539151i	$-0.818745\pi$
$797$	−47.5531			−1.68442			−0.842209	+	0.539151i	$0.818745\pi$
$798$	−0.132266	+	0.229092i	−0.00468217	+	0.00810976i
$799$	2.90246	−	5.02720i	0.102682	−	0.177850i
$800$	2.24658	+	3.89120i	0.0794287	+	0.137575i
$801$	9.23056			0.326146
$802$	3.37268	+	5.84166i	0.119094	+	0.206276i
$803$	−0.0878623	−	0.152182i	−0.00310059	−	0.00537039i
$804$	2.18092	−	3.77746i	0.0769150	−	0.133221i
$805$	−0.116878			−0.00411940
$806$	6.13334	+	10.6233i	0.216038	+	0.374188i
$807$	−5.20507	+	9.01544i	−0.183227	+	0.317359i
$808$	−7.67946	−	13.3012i	−0.270162	−	0.467935i
$809$	−3.83432	+	6.64124i	−0.134808	+	0.233494i	−0.925524	−	0.378689i	$-0.876375\pi$
$809$	−3.83432	+	6.64124i	−0.134808	+	0.233494i	0.790716	+	0.612183i	$0.209708\pi$
$810$	0.711921			0.0250144
$811$	6.22974	+	10.7902i	0.218756	+	0.378896i	0.954428	−	0.298442i	$-0.0964668\pi$
$811$	6.22974	+	10.7902i	0.218756	+	0.378896i	−0.735672	+	0.677338i	$0.763134\pi$
$812$	−0.202444	+	0.350644i	−0.00710440	+	0.0123052i
$813$	−8.72371	+	15.1099i	−0.305954	+	0.529927i
$814$	0.519762	+	0.900255i	0.0182177	+	0.0315539i
$815$	1.97025	−	3.41258i	0.0690150	−	0.119538i
$816$	1.44557	+	2.50380i	0.0506050	+	0.0876504i
$817$	−2.86838	+	4.96818i	−0.100352	+	0.173814i
$818$	16.4609	−	28.5112i	0.575543	−	0.996869i
$819$	0.152500	−	0.264138i	0.00532879	−	0.00922973i
$820$	−3.69252	+	6.39563i	−0.128948	+	0.223345i
$821$	24.1305	+	41.7952i	0.842160	+	1.45866i	0.888065	+	0.459718i	$0.152050\pi$
$821$	24.1305	+	41.7952i	0.842160	+	1.45866i	−0.0459049	+	0.998946i	$0.514617\pi$
$822$	−6.77141	+	11.7284i	−0.236180	+	0.409076i
$823$	13.4462	−	23.2895i	0.468705	−	0.811822i	−0.530655	−	0.847588i	$-0.678054\pi$
$823$	13.4462	−	23.2895i	0.468705	−	0.811822i	0.999360	+	0.0357664i	$0.0113872\pi$
$824$	−13.9141			−0.484721
$825$	0.534760	+	0.926231i	0.0186179	+	0.0322472i
$826$	−0.466130			−0.0162187
$827$	7.28594	−	12.6196i	0.253357	−	0.438827i	−0.711091	−	0.703100i	$-0.751799\pi$
$827$	7.28594	−	12.6196i	0.253357	−	0.438827i	0.964448	+	0.264273i	$0.0851319\pi$
$828$	3.27774			0.113909
$829$	4.27916	−	7.41173i	0.148621	−	0.257420i	−0.782097	−	0.623157i	$-0.785850\pi$
$829$	4.27916	−	7.41173i	0.148621	−	0.257420i	0.930718	+	0.365737i	$0.119183\pi$
$830$	−3.22665	−	5.58872i	−0.111999	−	0.193987i
$831$	10.7816	+	18.6743i	0.374010	+	0.647804i
$832$	6.08940			0.211112
$833$	20.2307			0.700952
$834$	−1.31959	+	2.28560i	−0.0456937	+	0.0791438i
$835$	−1.36951	+	2.37206i	−0.0473937	+	0.0820884i
$836$	−1.25716			−0.0434797
$837$	1.00721	+	1.74455i	0.0348144	+	0.0603004i
$838$	−21.4045			−0.739406
$839$	26.4520	−	45.8162i	0.913224	−	1.58175i	0.103743	−	0.994604i	$-0.466918\pi$
$839$	26.4520	−	45.8162i	0.913224	−	1.58175i	0.809481	−	0.587146i	$-0.199749\pi$
$840$	−0.0356580			−0.00123032
$841$	−18.1731	−	31.4767i	−0.626658	−	1.08540i
$842$	10.2834	+	17.8114i	0.354390	+	0.613821i
$843$	−5.67445			−0.195439
$844$	−5.37153	−	9.30377i	−0.184896	−	0.320249i
$845$	−8.57183	+	14.8468i	−0.294880	+	0.510747i
$846$	−1.00392	−	1.73883i	−0.0345154	−	0.0597823i
$847$	−0.274060	−	0.474686i	−0.00941681	−	0.0163104i
$848$	2.23284	−	3.86739i	0.0766761	−	0.132807i
$849$	−0.439638	−	0.761476i	−0.0150883	−	0.0261338i
$850$	−6.49518	−	11.2500i	−0.222783	−	0.385871i
$851$	−14.3144			−0.490691
$852$	1.74602	−	3.02420i	0.0598178	−	0.103607i
$853$	17.0838	+	29.5900i	0.584938	+	1.01314i	0.994883	+	0.101033i	$0.0322146\pi$
$853$	17.0838	+	29.5900i	0.584938	+	1.01314i	−0.409945	+	0.912110i	$0.634452\pi$
$854$	−0.0399950	−	0.0692733i	−0.00136860	−	0.00237049i
$855$	1.87999	−	3.25624i	0.0642943	−	0.111361i
$856$	−3.45333	+	5.98134i	−0.118032	+	0.204438i
$857$	22.5276	−	39.0190i	0.769529	−	1.33286i	−0.168290	−	0.985738i	$-0.553824\pi$
$857$	22.5276	−	39.0190i	0.769529	−	1.33286i	0.937819	−	0.347126i	$-0.112842\pi$
$858$	1.44947			0.0494843
$859$	35.3463			1.20600			0.602999	−	0.797742i	$-0.293972\pi$
$859$	35.3463			1.20600			0.602999	+	0.797742i	$0.293972\pi$
$860$	−0.773294			−0.0263691
$861$	0.259787	+	0.449963i	0.00885350	+	0.0153347i
$862$	−3.62208			−0.123369
$863$	−14.0683	+	24.3669i	−0.478889	+	0.829460i	−0.999707	−	0.0242075i	$-0.992294\pi$
$863$	−14.0683	+	24.3669i	−0.478889	+	0.829460i	0.520818	+	0.853668i	$0.325627\pi$
$864$	1.00000			0.0340207
$865$	−0.920694			−0.0313045
$866$	23.5556			0.800452
$867$	4.32067	+	7.48362i	0.146738	+	0.254157i
$868$	−0.0504484	−	0.0873792i	−0.00171233	−	0.00296584i
$869$	0.957982	+	1.65927i	0.0324973	+	0.0562870i
$870$	2.87748	−	4.98394i	0.0975556	−	0.168971i
$871$	13.2805	+	23.0025i	0.449992	+	0.779409i
$872$	−1.91519	+	3.31720i	−0.0648564	+	0.112335i
$873$	1.07175	+	1.85633i	0.0362734	+	0.0628273i
$874$	8.65561	−	14.9920i	0.292780	−	0.507110i
$875$	0.338508			0.0114436
$876$	0.738239			0.0249428
$877$	−35.0531			−1.18366			−0.591829	−	0.806064i	$-0.701594\pi$
$877$	−35.0531			−1.18366			−0.591829	+	0.806064i	$0.701594\pi$
$878$	16.0295			0.540970
$879$	1.39141			0.0469309
$880$	−0.0847301	−	0.146757i	−0.00285625	−	0.00494717i
$881$	12.0494	−	20.8702i	0.405955	−	0.703134i	−0.588477	−	0.808514i	$-0.700272\pi$
$881$	12.0494	−	20.8702i	0.405955	−	0.703134i	0.994432	+	0.105380i	$0.0336057\pi$
$882$	3.49875	−	6.06001i	0.117809	−	0.204051i
$883$	12.8255	−	22.2144i	0.431612	−	0.747573i	−0.565401	−	0.824816i	$-0.691278\pi$
$883$	12.8255	−	22.2144i	0.431612	−	0.747573i	0.997012	+	0.0772431i	$0.0246117\pi$
$884$	−17.6053			−0.592130
$885$	6.62542			0.222711
$886$	7.41778	+	12.8480i	0.249205	+	0.431636i
$887$	3.49064	−	6.04597i	0.117204	−	0.203004i	−0.801454	−	0.598056i	$-0.795940\pi$
$887$	3.49064	−	6.04597i	0.117204	−	0.203004i	0.918659	+	0.395052i	$0.129273\pi$
$888$	−4.36716			−0.146552
$889$	−0.133417	−	0.231085i	−0.00447466	−	0.00775033i
$890$	6.57143			0.220275
$891$	0.238032			0.00797438
$892$	3.73581	+	14.4583i	0.125084	+	0.484101i
$893$	−10.6043			−0.354859
$894$	−7.61759			−0.254770
$895$	−7.40633	−	12.8281i	−0.247566	−	0.428797i
$896$	−0.0500871			−0.00167329
$897$	−9.97974	+	17.2854i	−0.333214	+	0.577143i
$898$	−0.0524197	−	0.0907936i	−0.00174927	−	0.00302982i
$899$	16.2840			0.543103
$900$	−4.49317			−0.149772
$901$	−6.45544	+	11.1812i	−0.215062	+	0.372498i
$902$	−1.23460	+	2.13839i	−0.0411077	+	0.0712007i
$903$	−0.0272025	+	0.0471161i	−0.000905242	+	0.00156792i
$904$	2.03896	+	3.53159i	0.0678149	+	0.117459i
$905$	−15.2278			−0.506189
$906$	19.0835			0.634008
$907$	−51.4319			−1.70777			−0.853885	−	0.520462i	$-0.825760\pi$
$907$	−51.4319			−1.70777			−0.853885	+	0.520462i	$0.825760\pi$
$908$	−9.78329			−0.324670
$909$	15.3589			0.509423
$910$	0.108568	−	0.188045i	0.00359900	−	0.00623365i
$911$	2.90709	+	5.03522i	0.0963161	+	0.166824i	0.910157	−	0.414263i	$-0.135961\pi$
$911$	2.90709	+	5.03522i	0.0963161	+	0.166824i	−0.813841	+	0.581088i	$0.802627\pi$
$912$	2.64073	−	4.57387i	0.0874432	−	0.151456i
$913$	−1.07884	−	1.86860i	−0.0357043	−	0.0618417i
$914$	15.2865	−	26.4770i	0.505633	−	0.875782i
$915$	0.568476	+	0.984629i	0.0187932	+	0.0325508i
$916$	2.54981	+	4.41641i	0.0842482	+	0.145922i
$917$	0.0880875	+	0.152572i	0.00290890	+	0.00503837i
$918$	−2.89113			−0.0954217
$919$	9.40255			0.310162			0.155081	−	0.987902i	$-0.450436\pi$
$919$	9.40255			0.310162			0.155081	+	0.987902i	$0.450436\pi$
$920$	2.33349			0.0769329
$921$	0.860812	−	1.49097i	0.0283647	−	0.0491292i
$922$	27.9212			0.919535
$923$	10.6322	+	18.4156i	0.349965	+	0.606156i
$924$	−0.0119223			−0.000392216
$925$	19.6224			0.645180
$926$	−3.93371			−0.129270
$927$	6.95706	−	12.0500i	0.228500	−	0.395773i
$928$	4.04185	−	7.00069i	0.132680	−	0.229809i
$929$	10.4614	−	18.1197i	0.343228	−	0.594489i	−0.641802	−	0.766870i	$-0.721813\pi$
$929$	10.4614	−	18.1197i	0.343228	−	0.594489i	0.985030	+	0.172382i	$0.0551462\pi$
$930$	0.717057	+	1.24198i	0.0235132	+	0.0407261i
$931$	−18.4785	−	32.0056i	−0.605607	−	1.04894i
$932$	−4.65509	+	8.06286i	−0.152483	+	0.264108i
$933$	0.647235			0.0211895
$934$	−8.19816	−	14.1996i	−0.268252	−	0.464626i
$935$	0.244966	+	0.424294i	0.00801125	+	0.0138759i
$936$	−3.04470	+	5.27358i	−0.0995192	+	0.172372i
$937$	−0.499929	−	0.865903i	−0.0163320	−	0.0282878i	0.857744	−	0.514077i	$-0.171866\pi$
$937$	−0.499929	−	0.865903i	−0.0163320	−	0.0282878i	−0.874076	+	0.485789i	$0.838532\pi$
$938$	−0.109236	−	0.189202i	−0.00356667	−	0.00617766i
$939$	14.0059	−	24.2589i	0.457066	−	0.791661i
$940$	−0.714709	−	1.23791i	−0.0233112	−	0.0403763i
$941$	−31.9629			−1.04196			−0.520980	−	0.853569i	$-0.674433\pi$
$941$	−31.9629			−1.04196			−0.520980	+	0.853569i	$0.674433\pi$
$942$	−3.24246	−	5.61610i	−0.105645	−	0.182983i
$943$	−17.0006	−	29.4460i	−0.553617	−	0.958893i
$944$	9.30639			0.302897
$945$	0.0178290	−	0.0308808i	0.000579978	−	0.00100455i
$946$	−0.258552			−0.00840626
$947$	−1.48187	−	2.56668i	−0.0481544	−	0.0834058i	0.840944	−	0.541123i	$-0.182001\pi$
$947$	−1.48187	−	2.56668i	−0.0481544	−	0.0834058i	−0.889098	+	0.457717i	$0.848667\pi$
$948$	−8.04918			−0.261425
$949$	−2.24772	+	3.89316i	−0.0729640	+	0.126377i
$950$	−11.8652	+	20.5512i	−0.384959	+	0.666768i
$951$	−12.9725			−0.420662
$952$	0.144808			0.00469327
$953$	−7.57833	−	13.1261i	−0.245486	−	0.425195i	0.716782	−	0.697297i	$-0.245614\pi$
$953$	−7.57833	−	13.1261i	−0.245486	−	0.425195i	−0.962268	+	0.272103i	$0.912281\pi$
$954$	2.23284	+	3.86739i	0.0722909	+	0.125212i
$955$	7.48608	−	12.9663i	0.242244	−	0.419579i
$956$	13.6826			0.442528
$957$	0.962091	−	1.66639i	0.0311000	−	0.0538667i
$958$	30.4075			0.982423
$959$	0.339160	+	0.587442i	0.0109520	+	0.0189695i
$960$	0.711921			0.0229772
$961$	13.4710	−	23.3325i	0.434550	−	0.752662i
$962$	13.2967	−	23.0306i	0.428703	−	0.742535i
$963$	−3.45333	−	5.98134i	−0.111282	−	0.192746i
$964$	8.23257	−	14.2592i	0.265153	−	0.459259i
$965$	8.16292	−	14.1386i	0.262774	−	0.455137i
$966$	0.0820861	−	0.142177i	0.00264108	−	0.00457448i
$967$	15.1835	−	26.2987i	0.488270	−	0.845708i	−0.511639	−	0.859200i	$-0.670962\pi$
$967$	15.1835	−	26.2987i	0.488270	−	0.845708i	0.999909	+	0.0134925i	$0.00429492\pi$
$968$	5.47167	+	9.47721i	0.175866	+	0.304609i
$969$	−7.63470	+	13.2237i	−0.245262	+	0.424806i
$970$	0.763004	+	1.32156i	0.0244986	+	0.0424328i
$971$	−21.6894	+	37.5671i	−0.696045	+	1.20559i	0.273782	+	0.961792i	$0.411725\pi$
$971$	−21.6894	+	37.5671i	−0.696045	+	1.20559i	−0.969827	+	0.243794i	$0.921608\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	0.0660945	+	0.114479i	0.00211889	+	0.00367003i
$974$	39.0435			1.25104
$975$	13.6804	−	23.6951i	0.438122	−	0.758850i
$976$	0.798509	+	1.38306i	0.0255597	+	0.0442706i
$977$	−12.9093	+	22.3595i	−0.413004	+	0.715343i	−0.995217	−	0.0976932i	$-0.968854\pi$
$977$	−12.9093	+	22.3595i	−0.413004	+	0.715343i	0.582213	+	0.813036i	$0.302187\pi$
$978$	2.76752	+	4.79348i	0.0884955	+	0.153279i
$979$	2.19717			0.0702219
$980$	2.49083	−	4.31425i	0.0795667	−	0.137814i
$981$	−1.91519	−	3.31720i	−0.0611472	−	0.105910i
$982$	−16.1006	−	27.8871i	−0.513792	−	0.889914i
$983$	17.3761			0.554211			0.277106	−	0.960839i	$-0.410625\pi$
$983$	17.3761			0.554211			0.277106	+	0.960839i	$0.410625\pi$
$984$	−5.18670	−	8.98363i	−0.165346	−	0.286388i
$985$	2.80373	−	4.85619i	0.0893341	−	0.154731i
$986$	−11.6855	+	20.2399i	−0.372143	+	0.644571i
$987$	−0.100566			−0.00320107
$988$	16.0805	+	27.8522i	0.511587	+	0.886095i
$989$	1.78015	−	3.08331i	0.0566055	−	0.0980436i
$990$	0.169460			0.00538580
$991$	2.59261	+	4.49053i	0.0823569	+	0.142646i	0.904262	−	0.426978i	$-0.140422\pi$
$991$	2.59261	+	4.49053i	0.0823569	+	0.142646i	−0.821905	+	0.569625i	$0.807089\pi$
$992$	1.00721	+	1.74455i	0.0319791	+	0.0553894i
$993$	9.72076	+	16.8369i	0.308479	+	0.534301i
$994$	−0.0874532	−	0.151473i	−0.00277385	−	0.00480444i
$995$	16.8789			0.535097
$996$	9.06463			0.287224
$997$	−13.7049			−0.434038			−0.217019	−	0.976167i	$-0.569633\pi$
$997$	−13.7049			−0.434038			−0.217019	+	0.976167i	$0.569633\pi$
$998$	−8.88900	+	15.3962i	−0.281376	+	0.487358i
$999$	2.18358	−	3.78207i	0.0690854	−	0.119659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.j.1075.3	yes	18
223.39	even	3	inner	1338.2.e.j.931.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.j.931.3	✓	18	223.39	even	3	inner
1338.2.e.j.1075.3	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.355961 + 0.616542i) q^{5} +(-0.500000 - 0.866025i) q^{6} -0.0500871 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.355961 + 0.616542i) q^{5} +(-0.500000 - 0.866025i) q^{6} -0.0500871 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.355961 + 0.616542i) q^{10} +(-0.119016 + 0.206142i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.08940 q^{13} -0.0500871 q^{14} +0.711921 q^{15} +1.00000 q^{16} -2.89113 q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.64073 + 4.57387i) q^{19} +(-0.355961 + 0.616542i) q^{20} +(0.0250435 + 0.0433767i) q^{21} +(-0.119016 + 0.206142i) q^{22} +(-1.63887 - 2.83860i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.24658 + 3.89120i) q^{25} +6.08940 q^{26} +1.00000 q^{27} -0.0500871 q^{28} +(4.04185 - 7.00069i) q^{29} +0.711921 q^{30} +(1.00721 + 1.74455i) q^{31} +1.00000 q^{32} +0.238032 q^{33} -2.89113 q^{34} +(0.0178290 - 0.0308808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.18358 - 3.78207i) q^{37} +(2.64073 + 4.57387i) q^{38} +(-3.04470 - 5.27358i) q^{39} +(-0.355961 + 0.616542i) q^{40} +10.3734 q^{41} +(0.0250435 + 0.0433767i) q^{42} +(0.543104 + 0.940683i) q^{43} +(-0.119016 + 0.206142i) q^{44} +(-0.355961 - 0.616542i) q^{45} +(-1.63887 - 2.83860i) q^{46} +(-1.00392 + 1.73883i) q^{47} +(-0.500000 - 0.866025i) q^{48} -6.99749 q^{49} +(2.24658 + 3.89120i) q^{50} +(1.44557 + 2.50380i) q^{51} +6.08940 q^{52} +(2.23284 - 3.86739i) q^{53} +1.00000 q^{54} +(-0.0847301 - 0.146757i) q^{55} -0.0500871 q^{56} +(2.64073 - 4.57387i) q^{57} +(4.04185 - 7.00069i) q^{58} +9.30639 q^{59} +0.711921 q^{60} +(0.798509 + 1.38306i) q^{61} +(1.00721 + 1.74455i) q^{62} +(0.0250435 - 0.0433767i) q^{63} +1.00000 q^{64} +(-2.16759 + 3.75437i) q^{65} +0.238032 q^{66} +(2.18092 + 3.77746i) q^{67} -2.89113 q^{68} +(-1.63887 + 2.83860i) q^{69} +(0.0178290 - 0.0308808i) q^{70} +(1.74602 + 3.02420i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.369119 + 0.639334i) q^{73} +(2.18358 - 3.78207i) q^{74} +(2.24658 - 3.89120i) q^{75} +(2.64073 + 4.57387i) q^{76} +(0.00596117 - 0.0103250i) q^{77} +(-3.04470 - 5.27358i) q^{78} +(4.02459 - 6.97079i) q^{79} +(-0.355961 + 0.616542i) q^{80} +(-0.500000 - 0.866025i) q^{81} +10.3734 q^{82} +(-4.53232 + 7.85020i) q^{83} +(0.0250435 + 0.0433767i) q^{84} +(1.02913 - 1.78250i) q^{85} +(0.543104 + 0.940683i) q^{86} -8.08370 q^{87} +(-0.119016 + 0.206142i) q^{88} +(-4.61528 - 7.99390i) q^{89} +(-0.355961 - 0.616542i) q^{90} -0.305000 q^{91} +(-1.63887 - 2.83860i) q^{92} +(1.00721 - 1.74455i) q^{93} +(-1.00392 + 1.73883i) q^{94} -3.75998 q^{95} +(-0.500000 - 0.866025i) q^{96} +(1.07175 - 1.85633i) q^{97} -6.99749 q^{98} +(-0.119016 - 0.206142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} - 9 q^{3} + 18 q^{4} + q^{5} - 9 q^{6} + 4 q^{7} + 18 q^{8} - 9 q^{9}+O(q^{10}) \) 18 * q + 18 * q^2 - 9 * q^3 + 18 * q^4 + q^5 - 9 * q^6 + 4 * q^7 + 18 * q^8 - 9 * q^9	\( 18 q + 18 q^{2} - 9 q^{3} + 18 q^{4} + q^{5} - 9 q^{6} + 4 q^{7} + 18 q^{8} - 9 q^{9} + q^{10} + 6 q^{11} - 9 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + 18 q^{16} + 12 q^{17} - 9 q^{18} - q^{19} + q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 9 q^{24} + 4 q^{26} + 18 q^{27} + 4 q^{28} - 2 q^{29} - 2 q^{30} + 13 q^{31} + 18 q^{32} - 12 q^{33} + 12 q^{34} + 3 q^{35} - 9 q^{36} + 9 q^{37} - q^{38} - 2 q^{39} + q^{40} - 4 q^{41} - 2 q^{42} + 5 q^{43} + 6 q^{44} + q^{45} + 10 q^{46} + 5 q^{47} - 9 q^{48} + 14 q^{49} - 6 q^{51} + 4 q^{52} - 5 q^{53} + 18 q^{54} + 11 q^{55} + 4 q^{56} - q^{57} - 2 q^{58} - 24 q^{59} - 2 q^{60} - 22 q^{61} + 13 q^{62} - 2 q^{63} + 18 q^{64} + 15 q^{65} - 12 q^{66} - 10 q^{67} + 12 q^{68} + 10 q^{69} + 3 q^{70} - 6 q^{71} - 9 q^{72} + 17 q^{73} + 9 q^{74} - q^{76} + 37 q^{77} - 2 q^{78} - 32 q^{79} + q^{80} - 9 q^{81} - 4 q^{82} + 13 q^{83} - 2 q^{84} + 14 q^{85} + 5 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + q^{90} - 26 q^{91} + 10 q^{92} + 13 q^{93} + 5 q^{94} - 22 q^{95} - 9 q^{96} - 6 q^{97} + 14 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 18 * q^2 - 9 * q^3 + 18 * q^4 + q^5 - 9 * q^6 + 4 * q^7 + 18 * q^8 - 9 * q^9 + q^10 + 6 * q^11 - 9 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^15 + 18 * q^16 + 12 * q^17 - 9 * q^18 - q^19 + q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 9 * q^24 + 4 * q^26 + 18 * q^27 + 4 * q^28 - 2 * q^29 - 2 * q^30 + 13 * q^31 + 18 * q^32 - 12 * q^33 + 12 * q^34 + 3 * q^35 - 9 * q^36 + 9 * q^37 - q^38 - 2 * q^39 + q^40 - 4 * q^41 - 2 * q^42 + 5 * q^43 + 6 * q^44 + q^45 + 10 * q^46 + 5 * q^47 - 9 * q^48 + 14 * q^49 - 6 * q^51 + 4 * q^52 - 5 * q^53 + 18 * q^54 + 11 * q^55 + 4 * q^56 - q^57 - 2 * q^58 - 24 * q^59 - 2 * q^60 - 22 * q^61 + 13 * q^62 - 2 * q^63 + 18 * q^64 + 15 * q^65 - 12 * q^66 - 10 * q^67 + 12 * q^68 + 10 * q^69 + 3 * q^70 - 6 * q^71 - 9 * q^72 + 17 * q^73 + 9 * q^74 - q^76 + 37 * q^77 - 2 * q^78 - 32 * q^79 + q^80 - 9 * q^81 - 4 * q^82 + 13 * q^83 - 2 * q^84 + 14 * q^85 + 5 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + q^90 - 26 * q^91 + 10 * q^92 + 13 * q^93 + 5 * q^94 - 22 * q^95 - 9 * q^96 - 6 * q^97 + 14 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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