LMFDB - Embedded newform 93.2.e.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(25,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("93.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Root			$1.08504 + 1.87935i$ of defining polynomial
Character	$\chi$	$=$	93.25
Dual form			93.2.e.b.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.539189 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.70928 q^{4} +(1.43968 - 2.49360i) q^{5} +(0.269594 + 0.466951i) q^{6} +(-1.31545 - 2.27842i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-0.539189 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.70928 q^{4} +(1.43968 - 2.49360i) q^{5} +(0.269594 + 0.466951i) q^{6} +(-1.31545 - 2.27842i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.776260 + 1.34452i) q^{10} +(1.90049 - 3.29175i) q^{11} +(0.854638 + 1.48028i) q^{12} +(-2.35464 + 4.07835i) q^{13} +(0.709275 + 1.22850i) q^{14} -2.87936 q^{15} +2.34017 q^{16} +(1.63090 + 2.82480i) q^{17} +(0.269594 - 0.466951i) q^{18} +(-0.354638 - 0.614250i) q^{19} +(-2.46081 + 4.26225i) q^{20} +(-1.31545 + 2.27842i) q^{21} +(-1.02472 + 1.77487i) q^{22} +5.07838 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-1.64536 - 2.84985i) q^{25} +(1.26959 - 2.19900i) q^{26} +1.00000 q^{27} +(2.24846 + 3.89445i) q^{28} -3.95774 q^{29} +1.55252 q^{30} +(5.51026 - 0.798148i) q^{31} -5.26180 q^{32} -3.80098 q^{33} +(-0.879362 - 1.52310i) q^{34} -7.57531 q^{35} +(0.854638 - 1.48028i) q^{36} +(4.60310 + 7.97281i) q^{37} +(0.191217 + 0.331197i) q^{38} +4.70928 q^{39} +(2.87936 - 4.98720i) q^{40} +(4.60977 - 7.98435i) q^{41} +(0.709275 - 1.22850i) q^{42} +(-5.23400 - 9.06555i) q^{43} +(-3.24846 + 5.62651i) q^{44} +(1.43968 + 2.49360i) q^{45} -2.73820 q^{46} +0.695944 q^{47} +(-1.17009 - 2.02665i) q^{48} +(0.0391889 - 0.0678771i) q^{49} +(0.887161 + 1.53661i) q^{50} +(1.63090 - 2.82480i) q^{51} +(4.02472 - 6.97103i) q^{52} +(0.638697 - 1.10626i) q^{53} -0.539189 q^{54} +(-5.47220 - 9.47814i) q^{55} +(-2.63090 - 4.55685i) q^{56} +(-0.354638 + 0.614250i) q^{57} +2.13397 q^{58} +(0.829914 + 1.43745i) q^{59} +4.92162 q^{60} +5.70928 q^{61} +(-2.97107 + 0.430353i) q^{62} +2.63090 q^{63} -1.84324 q^{64} +(6.77985 + 11.7431i) q^{65} +2.04945 q^{66} +(-7.56391 + 13.1011i) q^{67} +(-2.78765 - 4.82836i) q^{68} +(-2.53919 - 4.39800i) q^{69} +4.08452 q^{70} +(-6.24846 + 10.8227i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(-6.01026 + 10.4101i) q^{73} +(-2.48194 - 4.29885i) q^{74} +(-1.64536 + 2.84985i) q^{75} +(0.606173 + 1.04992i) q^{76} -10.0000 q^{77} -2.53919 q^{78} +(1.31545 + 2.27842i) q^{79} +(3.36910 - 5.83546i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.48554 + 4.30507i) q^{82} +(0.560319 - 0.970501i) q^{83} +(2.24846 - 3.89445i) q^{84} +9.39189 q^{85} +(2.82211 + 4.88805i) q^{86} +(1.97887 + 3.42750i) q^{87} +(3.80098 - 6.58350i) q^{88} +14.6381 q^{89} +(-0.776260 - 1.34452i) q^{90} +12.3896 q^{91} -8.68035 q^{92} +(-3.44635 - 4.37295i) q^{93} -0.375245 q^{94} -2.04226 q^{95} +(2.63090 + 4.55685i) q^{96} -10.4186 q^{97} +(-0.0211302 + 0.0365986i) q^{98} +(1.90049 + 3.29175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 7 q^{13} - 10 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} + 5 q^{19} - 18 q^{20} - 4 q^{21} + 12 q^{22} + 24 q^{23} - 6 q^{24} - 17 q^{25} + 6 q^{26} + 6 q^{27} - 4 q^{28} + 8 q^{29} + 8 q^{30} - 16 q^{32} - 4 q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} + 3 q^{37} + 6 q^{38} + 14 q^{39} - 8 q^{40} + 4 q^{41} - 10 q^{42} + q^{43} - 2 q^{44} - 4 q^{45} - 32 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} - 6 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} - 16 q^{55} - 8 q^{56} + 5 q^{57} + 40 q^{58} + 16 q^{59} + 36 q^{60} + 20 q^{61} + 12 q^{62} + 8 q^{63} - 24 q^{64} + 6 q^{65} - 24 q^{66} - 24 q^{67} + 4 q^{68} - 12 q^{69} + 88 q^{70} - 20 q^{71} - 6 q^{72} - 3 q^{73} - 34 q^{74} - 17 q^{75} + 14 q^{76} - 60 q^{77} - 12 q^{78} + 4 q^{79} + 28 q^{80} - 3 q^{81} + 16 q^{83} - 4 q^{84} + 24 q^{85} + 14 q^{86} - 4 q^{87} + 4 q^{88} + 12 q^{89} - 4 q^{90} + 16 q^{91} - 8 q^{92} - 9 q^{93} - 80 q^{94} - 44 q^{95} + 8 q^{96} - 34 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 7 * q^13 - 10 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 + 5 * q^19 - 18 * q^20 - 4 * q^21 + 12 * q^22 + 24 * q^23 - 6 * q^24 - 17 * q^25 + 6 * q^26 + 6 * q^27 - 4 * q^28 + 8 * q^29 + 8 * q^30 - 16 * q^32 - 4 * q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 + 3 * q^37 + 6 * q^38 + 14 * q^39 - 8 * q^40 + 4 * q^41 - 10 * q^42 + q^43 - 2 * q^44 - 4 * q^45 - 32 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 - 6 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 - 16 * q^55 - 8 * q^56 + 5 * q^57 + 40 * q^58 + 16 * q^59 + 36 * q^60 + 20 * q^61 + 12 * q^62 + 8 * q^63 - 24 * q^64 + 6 * q^65 - 24 * q^66 - 24 * q^67 + 4 * q^68 - 12 * q^69 + 88 * q^70 - 20 * q^71 - 6 * q^72 - 3 * q^73 - 34 * q^74 - 17 * q^75 + 14 * q^76 - 60 * q^77 - 12 * q^78 + 4 * q^79 + 28 * q^80 - 3 * q^81 + 16 * q^83 - 4 * q^84 + 24 * q^85 + 14 * q^86 - 4 * q^87 + 4 * q^88 + 12 * q^89 - 4 * q^90 + 16 * q^91 - 8 * q^92 - 9 * q^93 - 80 * q^94 - 44 * q^95 + 8 * q^96 - 34 * q^97 - 16 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.539189			−0.381264			−0.190632	−	0.981662i	$-0.561054\pi$
$2$	−0.539189			−0.381264			−0.190632	+	0.981662i	$0.561054\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.70928			−0.854638
$5$	1.43968	−	2.49360i	0.643845	−	1.11517i	−0.340722	−	0.940164i	$-0.610672\pi$
$5$	1.43968	−	2.49360i	0.643845	−	1.11517i	0.984567	−	0.175008i	$-0.0559951\pi$
$6$	0.269594	+	0.466951i	0.110061	+	0.190632i
$7$	−1.31545	−	2.27842i	−0.497193	−	0.861163i	0.502802	−	0.864402i	$-0.332303\pi$
$7$	−1.31545	−	2.27842i	−0.497193	−	0.861163i	−0.999995	+	0.00323832i	$0.998969\pi$
$8$	2.00000			0.707107
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.776260	+	1.34452i	−0.245475	+	0.425175i
$11$	1.90049	−	3.29175i	0.573020	−	0.992500i	−0.423234	−	0.906021i	$-0.639105\pi$
$11$	1.90049	−	3.29175i	0.573020	−	0.992500i	0.996254	−	0.0864791i	$-0.0275616\pi$
$12$	0.854638	+	1.48028i	0.246713	+	0.427319i
$13$	−2.35464	+	4.07835i	−0.653059	+	1.13113i	0.329318	+	0.944219i	$0.393181\pi$
$13$	−2.35464	+	4.07835i	−0.653059	+	1.13113i	−0.982377	+	0.186912i	$0.940152\pi$
$14$	0.709275	+	1.22850i	0.189562	+	0.328331i
$15$	−2.87936			−0.743448
$16$	2.34017			0.585043
$17$	1.63090	+	2.82480i	0.395551	+	0.685114i	0.993171	−	0.116665i	$-0.0372204\pi$
$17$	1.63090	+	2.82480i	0.395551	+	0.685114i	−0.597621	+	0.801779i	$0.703887\pi$
$18$	0.269594	−	0.466951i	0.0635440	−	0.110061i
$19$	−0.354638	−	0.614250i	−0.0813595	−	0.140919i	0.822475	−	0.568802i	$-0.192593\pi$
$19$	−0.354638	−	0.614250i	−0.0813595	−	0.140919i	−0.903834	+	0.427883i	$0.859260\pi$
$20$	−2.46081	+	4.26225i	−0.550254	+	0.953068i
$21$	−1.31545	+	2.27842i	−0.287054	+	0.497193i
$22$	−1.02472	+	1.77487i	−0.218472	+	0.378404i
$23$	5.07838			1.05891			0.529457	−	0.848336i	$-0.322396\pi$
$23$	5.07838			1.05891			0.529457	+	0.848336i	$0.322396\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$	−1.64536	−	2.84985i	−0.329072	−	0.569970i
$26$	1.26959	−	2.19900i	0.248988	−	0.431260i
$27$	1.00000			0.192450
$28$	2.24846	+	3.89445i	0.424920	+	0.735983i
$29$	−3.95774			−0.734934			−0.367467	−	0.930037i	$-0.619775\pi$
$29$	−3.95774			−0.734934			−0.367467	+	0.930037i	$0.619775\pi$
$30$	1.55252			0.283450
$31$	5.51026	−	0.798148i	0.989672	−	0.143352i
$31$	5.51026	−	0.798148i	0.989672	−	0.143352i
$32$	−5.26180			−0.930163
$33$	−3.80098			−0.661666
$34$	−0.879362	−	1.52310i	−0.150809	−	0.261209i
$35$	−7.57531			−1.28046
$36$	0.854638	−	1.48028i	0.142440	−	0.246713i
$37$	4.60310	+	7.97281i	0.756745	+	1.31072i	0.944502	+	0.328506i	$0.106545\pi$
$37$	4.60310	+	7.97281i	0.756745	+	1.31072i	−0.187757	+	0.982216i	$0.560122\pi$
$38$	0.191217	+	0.331197i	0.0310194	+	0.0537273i
$39$	4.70928			0.754088
$40$	2.87936	−	4.98720i	0.455267	−	0.788546i
$41$	4.60977	−	7.98435i	0.719925	−	1.24695i	−0.241104	−	0.970499i	$-0.577510\pi$
$41$	4.60977	−	7.98435i	0.719925	−	1.24695i	0.961029	−	0.276447i	$-0.0891570\pi$
$42$	0.709275	−	1.22850i	0.109444	−	0.189562i
$43$	−5.23400	−	9.06555i	−0.798177	−	1.38248i	−0.920802	−	0.390031i	$-0.872464\pi$
$43$	−5.23400	−	9.06555i	−0.798177	−	1.38248i	0.122624	−	0.992453i	$-0.460869\pi$
$44$	−3.24846	+	5.62651i	−0.489724	+	0.848228i
$45$	1.43968	+	2.49360i	0.214615	+	0.371724i
$46$	−2.73820			−0.403726
$47$	0.695944			0.101514			0.0507570	−	0.998711i	$-0.483837\pi$
$47$	0.695944			0.101514			0.0507570	+	0.998711i	$0.483837\pi$
$48$	−1.17009	−	2.02665i	−0.168887	−	0.292522i
$49$	0.0391889	−	0.0678771i	0.00559841	−	0.00969673i
$50$	0.887161	+	1.53661i	0.125464	+	0.217309i
$51$	1.63090	−	2.82480i	0.228371	−	0.395551i
$52$	4.02472	−	6.97103i	0.558129	−	0.966707i
$53$	0.638697	−	1.10626i	0.0877318	−	0.151956i	−0.818820	−	0.574050i	$-0.805371\pi$
$53$	0.638697	−	1.10626i	0.0877318	−	0.151956i	0.906552	+	0.422094i	$0.138705\pi$
$54$	−0.539189			−0.0733743
$55$	−5.47220	−	9.47814i	−0.737872	−	1.27803i
$56$	−2.63090	−	4.55685i	−0.351568	−	0.608934i
$57$	−0.354638	+	0.614250i	−0.0469729	+	0.0813595i
$58$	2.13397			0.280204
$59$	0.829914	+	1.43745i	0.108046	+	0.187140i	0.914978	−	0.403503i	$-0.132207\pi$
$59$	0.829914	+	1.43745i	0.108046	+	0.187140i	−0.806933	+	0.590643i	$0.798874\pi$
$60$	4.92162			0.635379
$61$	5.70928			0.730998			0.365499	−	0.930812i	$-0.380898\pi$
$61$	5.70928			0.730998			0.365499	+	0.930812i	$0.380898\pi$
$62$	−2.97107	+	0.430353i	−0.377326	+	0.0546548i
$63$	2.63090			0.331462
$64$	−1.84324			−0.230406
$65$	6.77985	+	11.7431i	0.840937	+	1.45655i
$66$	2.04945			0.252270
$67$	−7.56391	+	13.1011i	−0.924079	+	1.60055i	−0.131043	+	0.991377i	$0.541833\pi$
$67$	−7.56391	+	13.1011i	−0.924079	+	1.60055i	−0.793036	+	0.609175i	$0.791501\pi$
$68$	−2.78765	−	4.82836i	−0.338053	−	0.585524i
$69$	−2.53919	−	4.39800i	−0.305682	−	0.529457i
$70$	4.08452			0.488194
$71$	−6.24846	+	10.8227i	−0.741556	+	1.28441i	0.210230	+	0.977652i	$0.432579\pi$
$71$	−6.24846	+	10.8227i	−0.741556	+	1.28441i	−0.951787	+	0.306761i	$0.900755\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−6.01026	+	10.4101i	−0.703448	+	1.21841i	0.263801	+	0.964577i	$0.415024\pi$
$73$	−6.01026	+	10.4101i	−0.703448	+	1.21841i	−0.967249	+	0.253830i	$0.918310\pi$
$74$	−2.48194	−	4.29885i	−0.288520	−	0.499731i
$75$	−1.64536	+	2.84985i	−0.189990	+	0.329072i
$76$	0.606173	+	1.04992i	0.0695329	+	0.120434i
$77$	−10.0000			−1.13961
$78$	−2.53919			−0.287507
$79$	1.31545	+	2.27842i	0.148000	+	0.256343i	0.930488	−	0.366322i	$-0.119383\pi$
$79$	1.31545	+	2.27842i	0.148000	+	0.256343i	−0.782488	+	0.622665i	$0.786050\pi$
$80$	3.36910	−	5.83546i	0.376677	−	0.652424i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.48554	+	4.30507i	−0.274481	+	0.475416i
$83$	0.560319	−	0.970501i	0.0615030	−	0.106526i	−0.833634	−	0.552317i	$-0.813744\pi$
$83$	0.560319	−	0.970501i	0.0615030	−	0.106526i	0.895137	+	0.445790i	$0.147077\pi$
$84$	2.24846	−	3.89445i	0.245328	−	0.424920i
$85$	9.39189			1.01869
$86$	2.82211	+	4.88805i	0.304316	+	0.527091i
$87$	1.97887	+	3.42750i	0.212157	+	0.367467i
$88$	3.80098	−	6.58350i	0.405186	−	0.701803i
$89$	14.6381			1.55163			0.775817	−	0.630958i	$-0.217338\pi$
$89$	14.6381			1.55163			0.775817	+	0.630958i	$0.217338\pi$
$90$	−0.776260	−	1.34452i	−0.0818250	−	0.141725i
$91$	12.3896			1.29879
$92$	−8.68035			−0.904989
$93$	−3.44635	−	4.37295i	−0.357369	−	0.453454i
$94$	−0.375245			−0.0387036
$95$	−2.04226			−0.209531
$96$	2.63090	+	4.55685i	0.268515	+	0.465081i
$97$	−10.4186			−1.05784			−0.528922	−	0.848671i	$-0.677404\pi$
$97$	−10.4186			−1.05784			−0.528922	+	0.848671i	$0.677404\pi$
$98$	−0.0211302	+	0.0365986i	−0.00213447	+	0.00369702i
$99$	1.90049	+	3.29175i	0.191007	+	0.330833i
$100$	2.81238	+	4.87118i	0.281238	+	0.487118i
$101$	5.95774			0.592817			0.296409	−	0.955061i	$-0.404211\pi$
$101$	5.95774			0.592817			0.296409	+	0.955061i	$0.404211\pi$
$102$	−0.879362	+	1.52310i	−0.0870698	+	0.150809i
$103$	−1.15562	+	2.00160i	−0.113867	+	0.197223i	−0.917326	−	0.398136i	$-0.869657\pi$
$103$	−1.15562	+	2.00160i	−0.113867	+	0.197223i	0.803459	+	0.595360i	$0.202990\pi$
$104$	−4.70928	+	8.15670i	−0.461782	+	0.799831i
$105$	3.78765	+	6.56041i	0.369637	+	0.640230i
$106$	−0.344378	+	0.596481i	−0.0334490	+	0.0579353i
$107$	−6.85823	−	11.8788i	−0.663010	−	1.14837i	−0.979821	−	0.199879i	$-0.935945\pi$
$107$	−6.85823	−	11.8788i	−0.663010	−	1.14837i	0.316810	−	0.948489i	$-0.397388\pi$
$108$	−1.70928			−0.164475
$109$	−10.5174			−1.00739			−0.503694	−	0.863882i	$-0.668026\pi$
$109$	−10.5174			−1.00739			−0.503694	+	0.863882i	$0.668026\pi$
$110$	2.95055	+	5.11051i	0.281324	+	0.487268i
$111$	4.60310	−	7.97281i	0.436907	−	0.756745i
$112$	−3.07838	−	5.33191i	−0.290879	−	0.503818i
$113$	−8.53919	+	14.7903i	−0.803299	+	1.39136i	0.114134	+	0.993465i	$0.463591\pi$
$113$	−8.53919	+	14.7903i	−0.803299	+	1.39136i	−0.917433	+	0.397890i	$0.869743\pi$
$114$	0.191217	−	0.331197i	0.0179091	−	0.0310194i
$115$	7.31124	−	12.6634i	0.681777	−	1.18087i
$116$	6.76487			0.628102
$117$	−2.35464	−	4.07835i	−0.217686	−	0.377044i
$118$	−0.447480	−	0.775058i	−0.0411939	−	0.0713499i
$119$	4.29072	−	7.43175i	0.393330	−	0.681268i
$120$	−5.75872			−0.525697
$121$	−1.72374	−	2.98561i	−0.156704	−	0.271419i
$122$	−3.07838			−0.278703
$123$	−9.21953			−0.831297
$124$	−9.41855	+	1.36426i	−0.845811	+	0.122514i
$125$	4.92162			0.440203
$126$	−1.41855			−0.126375
$127$	1.48667	+	2.57499i	0.131921	+	0.228493i	0.924417	−	0.381384i	$-0.124552\pi$
$127$	1.48667	+	2.57499i	0.131921	+	0.228493i	−0.792496	+	0.609877i	$0.791219\pi$
$128$	11.5174			1.01801
$129$	−5.23400	+	9.06555i	−0.460828	+	0.798177i
$130$	−3.65562	−	6.33172i	−0.320619	−	0.555329i
$131$	−8.07058	−	13.9787i	−0.705130	−	1.22132i	−0.966645	−	0.256121i	$-0.917555\pi$
$131$	−8.07058	−	13.9787i	−0.705130	−	1.22132i	0.261515	−	0.965199i	$-0.415778\pi$
$132$	6.49693			0.565485
$133$	−0.933015	+	1.61603i	−0.0809027	+	0.140128i
$134$	4.07838	−	7.06396i	0.352318	−	0.610233i
$135$	1.43968	−	2.49360i	0.123908	−	0.214615i
$136$	3.26180	+	5.64960i	0.279697	+	0.484449i
$137$	8.77985	−	15.2072i	0.750114	−	1.29923i	−0.197654	−	0.980272i	$-0.563332\pi$
$137$	8.77985	−	15.2072i	0.750114	−	1.29923i	0.947767	−	0.318963i	$-0.103335\pi$
$138$	1.36910	+	2.37135i	0.116546	+	0.201863i
$139$	2.44748			0.207593			0.103796	−	0.994599i	$-0.466901\pi$
$139$	2.44748			0.207593			0.103796	+	0.994599i	$0.466901\pi$
$140$	12.9483			1.09433
$141$	−0.347972	−	0.602705i	−0.0293045	−	0.0507570i
$142$	3.36910	−	5.83546i	0.282729	−	0.489701i
$143$	8.94994	+	15.5018i	0.748432	+	1.29632i
$144$	−1.17009	+	2.02665i	−0.0975072	+	0.168887i
$145$	−5.69788	+	9.86902i	−0.473183	+	0.819578i
$146$	3.24067	−	5.61300i	0.268199	−	0.464535i
$147$	−0.0783777			−0.00646449
$148$	−7.86797	−	13.6277i	−0.646743	−	1.12019i
$149$	−4.70928	−	8.15670i	−0.385799	−	0.668223i	0.606081	−	0.795403i	$-0.292741\pi$
$149$	−4.70928	−	8.15670i	−0.385799	−	0.668223i	−0.991880	+	0.127180i	$0.959407\pi$
$150$	0.887161	−	1.53661i	0.0724364	−	0.125464i
$151$	1.92162			0.156379			0.0781897	−	0.996938i	$-0.475086\pi$
$151$	1.92162			0.156379			0.0781897	+	0.996938i	$0.475086\pi$
$152$	−0.709275	−	1.22850i	−0.0575298	−	0.0996446i
$153$	−3.26180			−0.263701
$154$	5.39189			0.434491
$155$	5.94275	−	14.8895i	0.477333	−	1.19595i
$156$	−8.04945			−0.644472
$157$	3.07611			0.245500			0.122750	−	0.992438i	$-0.460829\pi$
$157$	3.07611			0.245500			0.122750	+	0.992438i	$0.460829\pi$
$158$	−0.709275	−	1.22850i	−0.0564269	−	0.0977343i
$159$	−1.27739			−0.101304
$160$	−7.57531	+	13.1208i	−0.598881	+	1.03729i
$161$	−6.68035	−	11.5707i	−0.526485	−	0.911899i
$162$	0.269594	+	0.466951i	0.0211813	+	0.0366872i
$163$	5.81432			0.455412			0.227706	−	0.973730i	$-0.426877\pi$
$163$	5.81432			0.455412			0.227706	+	0.973730i	$0.426877\pi$
$164$	−7.87936	+	13.6475i	−0.615275	+	1.06569i
$165$	−5.47220	+	9.47814i	−0.426011	+	0.737872i
$166$	−0.302118	+	0.523283i	−0.0234489	+	0.0406147i
$167$	3.34797	+	5.79886i	0.259074	+	0.448729i	0.965994	−	0.258564i	$-0.0832494\pi$
$167$	3.34797	+	5.79886i	0.259074	+	0.448729i	−0.706920	+	0.707293i	$0.749916\pi$
$168$	−2.63090	+	4.55685i	−0.202978	+	0.351568i
$169$	−4.58864	−	7.94775i	−0.352972	−	0.611366i
$170$	−5.06400			−0.388391
$171$	0.709275			0.0542396
$172$	8.94635	+	15.4955i	0.682153	+	1.18152i
$173$	−3.12064	+	5.40510i	−0.237258	+	0.410942i	−0.959926	−	0.280252i	$-0.909582\pi$
$173$	−3.12064	+	5.40510i	−0.237258	+	0.410942i	0.722669	+	0.691195i	$0.242915\pi$
$174$	−1.06698	−	1.84807i	−0.0808879	−	0.140102i
$175$	−4.32878	+	7.49767i	−0.327225	+	0.566770i
$176$	4.44748	−	7.70326i	0.335241	−	0.580655i
$177$	0.829914	−	1.43745i	0.0623801	−	0.108046i
$178$	−7.89269			−0.591582
$179$	1.34797	+	2.33476i	0.100752	+	0.174508i	0.911995	−	0.410202i	$-0.134542\pi$
$179$	1.34797	+	2.33476i	0.100752	+	0.174508i	−0.811243	+	0.584710i	$0.801208\pi$
$180$	−2.46081	−	4.26225i	−0.183418	−	0.317689i
$181$	0.712347	−	1.23382i	0.0529483	−	0.0917092i	−0.838336	−	0.545153i	$-0.816471\pi$
$181$	0.712347	−	1.23382i	0.0529483	−	0.0917092i	0.891285	+	0.453444i	$0.149805\pi$
$182$	−6.68035			−0.495180
$183$	−2.85464	−	4.94438i	−0.211021	−	0.365499i
$184$	10.1568			0.748766
$185$	26.5080			1.94891
$186$	1.85823	+	2.35785i	0.136252	+	0.172886i
$187$	12.3980			0.906634
$188$	−1.18956			−0.0867576
$189$	−1.31545	−	2.27842i	−0.0956848	−	0.165731i
$190$	1.10116			0.0798868
$191$	−10.3324	+	17.8962i	−0.747624	+	1.29492i	0.201334	+	0.979523i	$0.435472\pi$
$191$	−10.3324	+	17.8962i	−0.747624	+	1.29492i	−0.948959	+	0.315401i	$0.897861\pi$
$192$	0.921622	+	1.59630i	0.0665124	+	0.115203i
$193$	−2.47528	−	4.28730i	−0.178174	−	0.308607i	0.763081	−	0.646303i	$-0.223686\pi$
$193$	−2.47528	−	4.28730i	−0.178174	−	0.308607i	−0.941255	+	0.337696i	$0.890352\pi$
$194$	5.61757			0.403318
$195$	6.77985	−	11.7431i	0.485515	−	0.840937i
$196$	−0.0669846	+	0.116021i	−0.00478461	+	0.00828719i
$197$	−6.29791	+	10.9083i	−0.448708	+	0.777185i	−0.998302	−	0.0582470i	$-0.981449\pi$
$197$	−6.29791	+	10.9083i	−0.448708	+	0.777185i	0.549595	+	0.835432i	$0.314782\pi$
$198$	−1.02472	−	1.77487i	−0.0728240	−	0.126135i
$199$	−7.02472	+	12.1672i	−0.497969	+	0.862508i	−0.999997	−	0.00234304i	$-0.999254\pi$
$199$	−7.02472	+	12.1672i	−0.497969	+	0.862508i	0.502028	+	0.864852i	$0.332588\pi$
$200$	−3.29072	−	5.69970i	−0.232689	−	0.403030i
$201$	15.1278			1.06703
$202$	−3.21235			−0.226020
$203$	5.20620	+	9.01741i	0.365404	+	0.632898i
$204$	−2.78765	+	4.82836i	−0.195175	+	0.338053i
$205$	−13.2732	−	22.9898i	−0.927040	−	1.60568i
$206$	0.623098	−	1.07924i	0.0434133	−	0.0751941i
$207$	−2.53919	+	4.39800i	−0.176486	+	0.305682i
$208$	−5.51026	+	9.54405i	−0.382068	+	0.661761i
$209$	−2.69594			−0.186482
$210$	−2.04226	−	3.53730i	−0.140929	−	0.244097i
$211$	−7.23400	−	12.5297i	−0.498009	−	0.862577i	0.501988	−	0.864874i	$-0.332602\pi$
$211$	−7.23400	−	12.5297i	−0.498009	−	0.862577i	−0.999997	+	0.00229741i	$0.999269\pi$
$212$	−1.09171	+	1.89090i	−0.0749789	+	0.129867i
$213$	12.4969			0.856275
$214$	3.69788	+	6.40492i	0.252782	+	0.437831i
$215$	−30.1412			−2.05561
$216$	2.00000			0.136083
$217$	−9.06698	−	11.5048i	−0.615507	−	0.780996i
$218$	5.67089			0.384081
$219$	12.0205			0.812271
$220$	9.35350	+	16.2007i	0.630613	+	1.09225i
$221$	−15.3607			−1.03327
$222$	−2.48194	+	4.29885i	−0.166577	+	0.288520i
$223$	8.54945	+	14.8081i	0.572513	+	0.991622i	0.996307	+	0.0858635i	$0.0273649\pi$
$223$	8.54945	+	14.8081i	0.572513	+	0.991622i	−0.423794	+	0.905759i	$0.639302\pi$
$224$	6.92162	+	11.9886i	0.462470	+	0.801022i
$225$	3.29072			0.219382
$226$	4.60424	−	7.97477i	0.306269	−	0.530474i
$227$	−1.95774	+	3.39090i	−0.129940	+	0.225062i	−0.923653	−	0.383230i	$-0.874812\pi$
$227$	−1.95774	+	3.39090i	−0.129940	+	0.225062i	0.793713	+	0.608292i	$0.208145\pi$
$228$	0.606173	−	1.04992i	0.0401448	−	0.0695329i
$229$	1.97414	+	3.41931i	0.130455	+	0.225955i	0.923852	−	0.382750i	$-0.125023\pi$
$229$	1.97414	+	3.41931i	0.130455	+	0.225955i	−0.793397	+	0.608704i	$0.791690\pi$
$230$	−3.94214	+	6.82799i	−0.259937	+	0.450224i
$231$	5.00000	+	8.66025i	0.328976	+	0.569803i
$232$	−7.91548			−0.519677
$233$	19.7321			1.29269			0.646345	−	0.763045i	$-0.276297\pi$
$233$	19.7321			1.29269			0.646345	+	0.763045i	$0.276297\pi$
$234$	1.26959	+	2.19900i	0.0829960	+	0.143753i
$235$	1.00194	−	1.73541i	0.0653592	−	0.113205i
$236$	−1.41855	−	2.45700i	−0.0923398	−	0.159937i
$237$	1.31545	−	2.27842i	0.0854476	−	0.148000i
$238$	−2.31351	+	4.00712i	−0.149963	+	0.259743i
$239$	−3.89269	+	6.74234i	−0.251797	+	0.436126i	−0.964021	−	0.265827i	$-0.914355\pi$
$239$	−3.89269	+	6.74234i	−0.251797	+	0.436126i	0.712223	+	0.701953i	$0.247688\pi$
$240$	−6.73820			−0.434949
$241$	7.69481	+	13.3278i	0.495666	+	0.858519i	0.999988	−	0.00499689i	$-0.00159056\pi$
$241$	7.69481	+	13.3278i	0.495666	+	0.858519i	−0.504321	+	0.863516i	$0.668257\pi$
$242$	0.929421	+	1.60981i	0.0597455	+	0.103482i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−9.75872			−0.624738
$245$	−0.112839	−	0.195443i	−0.00720902	−	0.0124864i
$246$	4.97107			0.316944
$247$	3.34017			0.212530
$248$	11.0205	−	1.59630i	0.699804	−	0.101365i
$249$	−1.12064			−0.0710176
$250$	−2.65368			−0.167834
$251$	−2.07058	−	3.58635i	−0.130694	−	0.226368i	0.793250	−	0.608896i	$-0.208387\pi$
$251$	−2.07058	−	3.58635i	−0.130694	−	0.226368i	−0.923944	+	0.382527i	$0.875054\pi$
$252$	−4.49693			−0.283280
$253$	9.65142	−	16.7167i	0.606779	−	1.05097i
$254$	−0.801595	−	1.38840i	−0.0502966	−	0.0871162i
$255$	−4.69594	−	8.13361i	−0.294071	−	0.509347i
$256$	−2.52359			−0.157724
$257$	3.97887	−	6.89160i	0.248195	−	0.429886i	−0.714830	−	0.699298i	$-0.753496\pi$
$257$	3.97887	−	6.89160i	0.248195	−	0.429886i	0.963025	+	0.269412i	$0.0868293\pi$
$258$	2.82211	−	4.88805i	0.175697	−	0.304316i
$259$	12.1103	−	20.9756i	0.752497	−	1.30336i
$260$	−11.5886	−	20.0721i	−0.718697	−	1.24482i
$261$	1.97887	−	3.42750i	0.122489	−	0.212157i
$262$	4.35157	+	7.53713i	0.268841	+	0.465646i
$263$	−20.1978			−1.24545			−0.622725	−	0.782441i	$-0.713974\pi$
$263$	−20.1978			−1.24545			−0.622725	+	0.782441i	$0.713974\pi$
$264$	−7.60197			−0.467869
$265$	−1.83904	−	3.18531i	−0.112971	−	0.195672i
$266$	0.503072	−	0.871345i	0.0308453	−	0.0534256i
$267$	−7.31904	−	12.6770i	−0.447918	−	0.775817i
$268$	12.9288	−	22.3934i	0.789753	−	1.36789i
$269$	7.85043	−	13.5973i	0.478649	−	0.829045i	−0.521051	−	0.853526i	$-0.674460\pi$
$269$	7.85043	−	13.5973i	0.478649	−	0.829045i	0.999700	+	0.0244806i	$0.00779320\pi$
$270$	−0.776260	+	1.34452i	−0.0472417	+	0.0818250i
$271$	24.7009			1.50047			0.750235	−	0.661171i	$-0.229940\pi$
$271$	24.7009			1.50047			0.750235	+	0.661171i	$0.229940\pi$
$272$	3.81658	+	6.61051i	0.231414	+	0.400821i
$273$	−6.19481	−	10.7297i	−0.374927	−	0.649393i
$274$	−4.73400	+	8.19953i	−0.285991	+	0.495352i
$275$	−12.5080			−0.754260
$276$	4.34017	+	7.51740i	0.261248	+	0.452494i
$277$	4.05172			0.243444			0.121722	−	0.992564i	$-0.461158\pi$
$277$	4.05172			0.243444			0.121722	+	0.992564i	$0.461158\pi$
$278$	−1.31965			−0.0791476
$279$	−2.06391	+	5.17110i	−0.123563	+	0.309586i
$280$	−15.1506			−0.905422
$281$	−25.8154			−1.54002			−0.770008	−	0.638035i	$-0.779748\pi$
$281$	−25.8154			−1.54002			−0.770008	+	0.638035i	$0.779748\pi$
$282$	0.187623	+	0.324972i	0.0111728	+	0.0193518i
$283$	5.20620			0.309477			0.154738	−	0.987955i	$-0.450547\pi$
$283$	5.20620			0.309477			0.154738	+	0.987955i	$0.450547\pi$
$284$	10.6803	−	18.4989i	0.633762	−	1.09771i
$285$	1.02113	+	1.76865i	0.0604865	+	0.104766i
$286$	−4.82571	−	8.35837i	−0.285350	−	0.494241i
$287$	−24.2557			−1.43177
$288$	2.63090	−	4.55685i	0.155027	−	0.268515i
$289$	3.18035	−	5.50852i	0.187079	−	0.324031i
$290$	3.07223	−	5.32127i	0.180408	−	0.312476i
$291$	5.20928	+	9.02273i	0.305373	+	0.528922i
$292$	10.2732	−	17.7937i	0.601193	−	1.04130i
$293$	0.680346	+	1.17839i	0.0397462	+	0.0688425i	0.885214	−	0.465184i	$-0.154012\pi$
$293$	0.680346	+	1.17839i	0.0397462	+	0.0688425i	−0.845468	+	0.534026i	$0.820678\pi$
$294$	0.0422604			0.00246468
$295$	4.77924			0.278258
$296$	9.20620	+	15.9456i	0.535100	+	0.926820i
$297$	1.90049	−	3.29175i	0.110278	−	0.191007i
$298$	2.53919	+	4.39800i	0.147091	+	0.254770i
$299$	−11.9577	+	20.7114i	−0.691534	+	1.19777i
$300$	2.81238	−	4.87118i	0.162373	−	0.281238i
$301$	−13.7701	+	23.8505i	−0.793696	+	1.37472i
$302$	−1.03612			−0.0596219
$303$	−2.97887	−	5.15955i	−0.171132	−	0.296409i
$304$	−0.829914	−	1.43745i	−0.0475988	−	0.0824435i
$305$	8.21953	−	14.2367i	0.470649	−	0.815188i
$306$	1.75872			0.100540
$307$	−12.8938	−	22.3328i	−0.735890	−	1.27460i	−0.954332	−	0.298748i	$-0.903431\pi$
$307$	−12.8938	−	22.3328i	−0.735890	−	1.27460i	0.218442	−	0.975850i	$-0.429902\pi$
$308$	17.0928			0.973950
$309$	2.31124			0.131482
$310$	−3.20427	+	8.02823i	−0.181990	+	0.455973i
$311$	−5.64423			−0.320055			−0.160027	−	0.987113i	$-0.551158\pi$
$311$	−5.64423			−0.320055			−0.160027	+	0.987113i	$0.551158\pi$
$312$	9.41855			0.533220
$313$	−1.00307	−	1.73737i	−0.0566970	−	0.0982020i	0.836284	−	0.548297i	$-0.184724\pi$
$313$	−1.00307	−	1.73737i	−0.0566970	−	0.0982020i	−0.892981	+	0.450095i	$0.851390\pi$
$314$	−1.65860			−0.0936005
$315$	3.78765	−	6.56041i	0.213410	−	0.369637i
$316$	−2.24846	−	3.89445i	−0.126486	−	0.219080i
$317$	10.8716	+	18.8301i	0.610608	+	1.05760i	0.991138	+	0.132835i	$0.0424081\pi$
$317$	10.8716	+	18.8301i	0.610608	+	1.05760i	−0.380530	+	0.924768i	$0.624259\pi$
$318$	0.688756			0.0386235
$319$	−7.52165	+	13.0279i	−0.421132	+	0.729421i
$320$	−2.65368	+	4.59632i	−0.148345	+	0.256942i
$321$	−6.85823	+	11.8788i	−0.382789	+	0.663010i
$322$	3.60197	+	6.23879i	0.200730	+	0.347674i
$323$	1.15676	−	2.00356i	0.0643636	−	0.111481i
$324$	0.854638	+	1.48028i	0.0474799	+	0.0822375i
$325$	15.4969			0.859615
$326$	−3.13501			−0.173632
$327$	5.25872	+	9.10838i	0.290808	+	0.503694i
$328$	9.21953	−	15.9687i	0.509064	−	0.881724i
$329$	−0.915479	−	1.58566i	−0.0504720	−	0.0874201i
$330$	2.95055	−	5.11051i	0.162423	−	0.281324i
$331$	−9.57417	+	16.5830i	−0.526244	+	0.911482i	0.473288	+	0.880908i	$0.343067\pi$
$331$	−9.57417	+	16.5830i	−0.526244	+	0.911482i	−0.999533	+	0.0305740i	$0.990266\pi$
$332$	−0.957740	+	1.65885i	−0.0525628	+	0.0910414i
$333$	−9.20620			−0.504497
$334$	−1.80519	−	3.12668i	−0.0987756	−	0.171084i
$335$	21.7792	+	37.7228i	1.18993	+	2.06101i
$336$	−3.07838	+	5.33191i	−0.167939	+	0.290879i
$337$	19.6514			1.07048			0.535240	−	0.844700i	$-0.320221\pi$
$337$	19.6514			1.07048			0.535240	+	0.844700i	$0.320221\pi$
$338$	2.47414	+	4.28534i	0.134576	+	0.233092i
$339$	17.0784			0.927570
$340$	−16.0533			−0.870614
$341$	7.84490	−	19.6553i	0.424825	−	1.06439i
$342$	−0.382433			−0.0206796
$343$	−18.6225			−1.00552
$344$	−10.4680	−	18.1311i	−0.564397	−	0.977564i
$345$	−14.6225			−0.787248
$346$	1.68261	−	2.91437i	0.0904579	−	0.156678i
$347$	2.60977	+	4.52025i	0.140100	+	0.242660i	0.927534	−	0.373739i	$-0.121924\pi$
$347$	2.60977	+	4.52025i	0.140100	+	0.242660i	−0.787434	+	0.616399i	$0.788591\pi$
$348$	−3.38243	−	5.85855i	−0.181317	−	0.314051i
$349$	23.1978			1.24175			0.620875	−	0.783910i	$-0.286778\pi$
$349$	23.1978			1.24175			0.620875	+	0.783910i	$0.286778\pi$
$350$	2.33403	−	4.04266i	0.124759	−	0.216089i
$351$	−2.35464	+	4.07835i	−0.125681	+	0.217686i
$352$	−10.0000	+	17.3205i	−0.533002	+	0.923186i
$353$	−4.27739	−	7.40866i	−0.227663	−	0.394323i	0.729452	−	0.684032i	$-0.239775\pi$
$353$	−4.27739	−	7.40866i	−0.227663	−	0.394323i	−0.957115	+	0.289708i	$0.906442\pi$
$354$	−0.447480	+	0.775058i	−0.0237833	+	0.0411939i
$355$	17.9916	+	31.1623i	0.954894	+	1.65393i
$356$	−25.0205			−1.32608
$357$	−8.58145			−0.454178
$358$	−0.726812	−	1.25887i	−0.0384132	−	0.0665336i
$359$	−12.1984	+	21.1283i	−0.643807	+	1.11511i	0.340768	+	0.940147i	$0.389313\pi$
$359$	−12.1984	+	21.1283i	−0.643807	+	1.11511i	−0.984576	+	0.174959i	$0.944021\pi$
$360$	2.87936	+	4.98720i	0.151756	+	0.262849i
$361$	9.24846	−	16.0188i	0.486761	−	0.843095i
$362$	−0.384090	+	0.665263i	−0.0201873	+	0.0349654i
$363$	−1.72374	+	2.98561i	−0.0904729	+	0.156704i
$364$	−21.1773			−1.10999
$365$	17.3057	+	29.9744i	0.905822	+	1.56893i
$366$	1.53919	+	2.66595i	0.0804547	+	0.139352i
$367$	−4.88243	+	8.45662i	−0.254861	+	0.441432i	−0.964858	−	0.262773i	$-0.915363\pi$
$367$	−4.88243	+	8.45662i	−0.254861	+	0.441432i	0.709997	+	0.704205i	$0.248696\pi$
$368$	11.8843			0.619511
$369$	4.60977	+	7.98435i	0.239975	+	0.415649i
$370$	−14.2928			−0.743048
$371$	−3.36069			−0.174478
$372$	5.89076	+	7.47458i	0.305421	+	0.387539i
$373$	−14.5441			−0.753065			−0.376533	−	0.926403i	$-0.622884\pi$
$373$	−14.5441			−0.753065			−0.376533	+	0.926403i	$0.622884\pi$
$374$	−6.68488			−0.345667
$375$	−2.46081	−	4.26225i	−0.127076	−	0.220102i
$376$	1.39189			0.0717812
$377$	9.31904	−	16.1411i	0.479955	−	0.831307i
$378$	0.709275	+	1.22850i	0.0364812	+	0.0631873i
$379$	−12.8607	−	22.2754i	−0.660609	−	1.14421i	−0.980456	−	0.196740i	$-0.936965\pi$
$379$	−12.8607	−	22.2754i	−0.660609	−	1.14421i	0.319846	−	0.947469i	$-0.396369\pi$
$380$	3.49079			0.179074
$381$	1.48667	−	2.57499i	0.0761644	−	0.131921i
$382$	5.57110	−	9.64943i	0.285042	−	0.493708i
$383$	11.6098	−	20.1087i	0.593231	−	1.02751i	−0.400562	−	0.916269i	$-0.631185\pi$
$383$	11.6098	−	20.1087i	0.593231	−	1.02751i	0.993794	−	0.111237i	$-0.0354814\pi$
$384$	−5.75872	−	9.97440i	−0.293874	−	0.509004i
$385$	−14.3968	+	24.9360i	−0.733729	+	1.27086i
$386$	1.33464	+	2.31167i	0.0679314	+	0.117661i
$387$	10.4680			0.532118
$388$	17.8082			0.904073
$389$	−15.7031	−	27.1986i	−0.796180	−	1.37902i	−0.922087	−	0.386983i	$-0.873517\pi$
$389$	−15.7031	−	27.1986i	−0.796180	−	1.37902i	0.125907	−	0.992042i	$-0.459816\pi$
$390$	−3.65562	+	6.33172i	−0.185110	+	0.320619i
$391$	8.28231	+	14.3454i	0.418855	+	0.725478i
$392$	0.0783777	−	0.135754i	0.00395867	−	0.00685662i
$393$	−8.07058	+	13.9787i	−0.407107	+	0.705130i
$394$	3.39576	−	5.88164i	0.171076	−	0.296313i
$395$	7.57531			0.381155
$396$	−3.24846	−	5.62651i	−0.163241	−	0.282743i
$397$	1.81852	+	3.14977i	0.0912689	+	0.158082i	0.908045	−	0.418872i	$-0.137574\pi$
$397$	1.81852	+	3.14977i	0.0912689	+	0.158082i	−0.816776	+	0.576954i	$0.804241\pi$
$398$	3.78765	−	6.56041i	0.189858	−	0.328844i
$399$	1.86603			0.0934184
$400$	−3.85043	−	6.66914i	−0.192522	−	0.333457i
$401$	−7.47641			−0.373354			−0.186677	−	0.982421i	$-0.559772\pi$
$401$	−7.47641			−0.373354			−0.186677	+	0.982421i	$0.559772\pi$
$402$	−8.15676			−0.406822
$403$	−9.71953	+	24.3521i	−0.484165	+	1.21307i
$404$	−10.1834			−0.506644
$405$	−2.87936			−0.143077
$406$	−2.80713	−	4.86209i	−0.139315	−	0.241301i
$407$	34.9926			1.73452
$408$	3.26180	−	5.64960i	0.161483	−	0.279697i
$409$	1.31658	+	2.28039i	0.0651008	+	0.112758i	0.896739	−	0.442560i	$-0.145930\pi$
$409$	1.31658	+	2.28039i	0.0651008	+	0.112758i	−0.831638	+	0.555318i	$0.812596\pi$
$410$	7.15676	+	12.3959i	0.353447	+	0.612188i
$411$	−17.5597			−0.866157
$412$	1.97528	−	3.42128i	0.0973149	−	0.168554i
$413$	2.18342	−	3.78179i	0.107439	−	0.186090i
$414$	1.36910	−	2.37135i	0.0672877	−	0.116546i
$415$	−1.61336	−	2.79442i	−0.0791968	−	0.137173i
$416$	12.3896	−	21.4595i	0.607451	−	1.05214i
$417$	−1.22374	−	2.11958i	−0.0599268	−	0.103796i
$418$	1.45362			0.0710990
$419$	10.7792			0.526600			0.263300	−	0.964714i	$-0.415189\pi$
$419$	10.7792			0.526600			0.263300	+	0.964714i	$0.415189\pi$
$420$	−6.47414	−	11.2135i	−0.315906	−	0.547165i
$421$	−18.8010	+	32.5643i	−0.916304	+	1.58708i	−0.111323	+	0.993784i	$0.535509\pi$
$421$	−18.8010	+	32.5643i	−0.916304	+	1.58708i	−0.804981	+	0.593301i	$0.797825\pi$
$422$	3.90049	+	6.75585i	0.189873	+	0.328870i
$423$	−0.347972	+	0.602705i	−0.0169190	+	0.0293045i
$424$	1.27739	−	2.21251i	0.0620357	−	0.107449i
$425$	5.36683	−	9.29563i	0.260330	−	0.450904i
$426$	−6.73820			−0.326467
$427$	−7.51026	−	13.0082i	−0.363447	−	0.629509i
$428$	11.7226	+	20.3041i	0.566634	+	0.981438i
$429$	8.94994	−	15.5018i	0.432107	−	0.748432i
$430$	16.2518			0.783730
$431$	10.7587	+	18.6347i	0.518229	+	0.897600i	0.999776	+	0.0211791i	$0.00674202\pi$
$431$	10.7587	+	18.6347i	0.518229	+	0.897600i	−0.481546	+	0.876421i	$0.659925\pi$
$432$	2.34017			0.112592
$433$	−17.6947			−0.850354			−0.425177	−	0.905110i	$-0.639788\pi$
$433$	−17.6947			−0.850354			−0.425177	+	0.905110i	$0.639788\pi$
$434$	4.88882	+	6.20325i	0.234671	+	0.297766i
$435$	11.3958			0.546385
$436$	17.9772			0.860952
$437$	−1.80098	−	3.11940i	−0.0861528	−	0.149221i
$438$	−6.48133			−0.309690
$439$	−2.68342	+	4.64782i	−0.128073	+	0.221828i	−0.922930	−	0.384968i	$-0.874212\pi$
$439$	−2.68342	+	4.64782i	−0.128073	+	0.221828i	0.794857	+	0.606796i	$0.207546\pi$
$440$	−10.9444	−	18.9563i	−0.521754	−	0.903705i
$441$	0.0391889	+	0.0678771i	0.00186614	+	0.00323224i
$442$	8.28231			0.393950
$443$	6.85043	−	11.8653i	0.325474	−	0.563737i	−0.656134	−	0.754644i	$-0.727810\pi$
$443$	6.85043	−	11.8653i	0.325474	−	0.563737i	0.981608	+	0.190907i	$0.0611429\pi$
$444$	−7.86797	+	13.6277i	−0.373397	+	0.646743i
$445$	21.0742	−	36.5015i	0.999012	−	1.73034i
$446$	−4.60977	−	7.98435i	−0.218279	−	0.378070i
$447$	−4.70928	+	8.15670i	−0.222741	+	0.385799i
$448$	2.42469	+	4.19969i	0.114556	+	0.198417i
$449$	18.5958			0.877591			0.438796	−	0.898587i	$-0.355405\pi$
$449$	18.5958			0.877591			0.438796	+	0.898587i	$0.355405\pi$
$450$	−1.77432			−0.0836423
$451$	−17.5217	−	30.3484i	−0.825062	−	1.42905i
$452$	14.5958	−	25.2807i	0.686530	−	1.18910i
$453$	−0.960811	−	1.66417i	−0.0451428	−	0.0781897i
$454$	1.05559	−	1.82834i	0.0495414	−	0.0858082i
$455$	17.8371	−	30.8948i	0.836216	−	1.44837i
$456$	−0.709275	+	1.22850i	−0.0332149	+	0.0575298i
$457$	−33.3773			−1.56133			−0.780663	−	0.624952i	$-0.785118\pi$
$457$	−33.3773			−1.56133			−0.780663	+	0.624952i	$0.785118\pi$
$458$	−1.06444	−	1.84366i	−0.0497378	−	0.0861484i
$459$	1.63090	+	2.82480i	0.0761238	+	0.131850i
$460$	−12.4969	+	21.6453i	−0.582672	+	1.00922i
$461$	−36.6525			−1.70708			−0.853538	−	0.521031i	$-0.825548\pi$
$461$	−36.6525			−1.70708			−0.853538	+	0.521031i	$0.825548\pi$
$462$	−2.69594	−	4.66951i	−0.125427	−	0.217245i
$463$	−4.82046			−0.224026			−0.112013	−	0.993707i	$-0.535730\pi$
$463$	−4.82046			−0.224026			−0.112013	+	0.993707i	$0.535730\pi$
$464$	−9.26180			−0.429968
$465$	−15.8660	+	2.29816i	−0.735770	+	0.106575i
$466$	−10.6393			−0.492856
$467$	30.4657			1.40979			0.704893	−	0.709314i	$-0.250995\pi$
$467$	30.4657			1.40979			0.704893	+	0.709314i	$0.250995\pi$
$468$	4.02472	+	6.97103i	0.186043	+	0.322236i
$469$	39.7998			1.83778
$470$	−0.540234	+	0.935712i	−0.0249191	+	0.0431612i
$471$	−1.53806	−	2.66399i	−0.0708698	−	0.122750i
$472$	1.65983	+	2.87490i	0.0763997	+	0.132328i
$473$	−39.7887			−1.82949
$474$	−0.709275	+	1.22850i	−0.0325781	+	0.0564269i
$475$	−1.16701	+	2.02133i	−0.0535463	+	0.0927449i
$476$	−7.33403	+	12.7029i	−0.336155	+	0.582237i
$477$	0.638697	+	1.10626i	0.0292439	+	0.0506520i
$478$	2.09890	−	3.63540i	0.0960013	−	0.166279i
$479$	−16.1412	−	27.9573i	−0.737508	−	1.27740i	−0.953614	−	0.301032i	$-0.902669\pi$
$479$	−16.1412	−	27.9573i	−0.737508	−	1.27740i	0.216106	−	0.976370i	$-0.430664\pi$
$480$	15.1506			0.691528
$481$	−43.3545			−1.97680
$482$	−4.14896	−	7.18620i	−0.188980	−	0.327323i
$483$	−6.68035	+	11.5707i	−0.303966	+	0.526485i
$484$	2.94635	+	5.10322i	0.133925	+	0.231965i
$485$	−14.9994	+	25.9797i	−0.681087	+	1.17968i
$486$	0.269594	−	0.466951i	0.0122291	−	0.0211813i
$487$	10.4825	−	18.1562i	0.475006	−	0.822734i	−0.524584	−	0.851358i	$-0.675779\pi$
$487$	10.4825	−	18.1562i	0.475006	−	0.822734i	0.999590	+	0.0286243i	$0.00911263\pi$
$488$	11.4186			0.516894
$489$	−2.90716	−	5.03534i	−0.131466	−	0.227706i
$490$	0.0608415	+	0.105381i	0.00274854	+	0.00476061i
$491$	−3.53919	+	6.13005i	−0.159721	+	0.276646i	−0.934768	−	0.355258i	$-0.884393\pi$
$491$	−3.53919	+	6.13005i	−0.159721	+	0.276646i	0.775047	+	0.631904i	$0.217726\pi$
$492$	15.7587			0.710458
$493$	−6.45467	−	11.1798i	−0.290704	−	0.503513i
$494$	−1.80098			−0.0810301
$495$	10.9444			0.491915
$496$	12.8950	−	1.86781i	0.579001	−	0.0838669i
$497$	32.8781			1.47479
$498$	0.604236			0.0270764
$499$	3.11643	+	5.39782i	0.139511	+	0.241640i	0.927312	−	0.374290i	$-0.122114\pi$
$499$	3.11643	+	5.39782i	0.139511	+	0.241640i	−0.787801	+	0.615930i	$0.788780\pi$
$500$	−8.41241			−0.376214
$501$	3.34797	−	5.79886i	0.149576	−	0.259074i
$502$	1.11643	+	1.93372i	0.0498288	+	0.0863061i
$503$	4.55252	+	7.88520i	0.202987	+	0.351583i	0.949489	−	0.313799i	$-0.101602\pi$
$503$	4.55252	+	7.88520i	0.202987	+	0.351583i	−0.746503	+	0.665382i	$0.768268\pi$
$504$	5.26180			0.234379
$505$	8.57724	−	14.8562i	0.381682	−	0.661093i
$506$	−5.20394	+	9.01348i	−0.231343	+	0.400698i
$507$	−4.58864	+	7.94775i	−0.203789	+	0.352972i
$508$	−2.54113	−	4.40136i	−0.112744	−	0.195279i
$509$	16.5464	−	28.6592i	0.733405	−	1.27030i	−0.222014	−	0.975043i	$-0.571263\pi$
$509$	16.5464	−	28.6592i	0.733405	−	1.27030i	0.955419	−	0.295252i	$-0.0954035\pi$
$510$	2.53200	+	4.38555i	0.112119	+	0.194196i
$511$	31.6248			1.39900
$512$	−21.6742			−0.957873
$513$	−0.354638	−	0.614250i	−0.0156576	−	0.0271198i
$514$	−2.14536	+	3.71588i	−0.0946279	+	0.163900i
$515$	3.32745	+	5.76332i	0.146625	+	0.253962i
$516$	8.94635	−	15.4955i	0.393841	−	0.682153i
$517$	1.32264	−	2.29087i	0.0581695	−	0.100753i
$518$	−6.52973	+	11.3098i	−0.286900	+	0.496925i
$519$	6.24128			0.273962
$520$	13.5597	+	23.4861i	0.594633	+	1.02993i
$521$	−17.3818	−	30.1062i	−0.761511	−	1.31898i	−0.942071	−	0.335413i	$-0.891124\pi$
$521$	−17.3818	−	30.1062i	−0.761511	−	1.31898i	0.180560	−	0.983564i	$-0.442209\pi$
$522$	−1.06698	+	1.84807i	−0.0467006	+	0.0808879i
$523$	−21.7815			−0.952439			−0.476219	−	0.879326i	$-0.657993\pi$
$523$	−21.7815			−0.952439			−0.476219	+	0.879326i	$0.657993\pi$
$524$	13.7948	+	23.8934i	0.602630	+	1.04379i
$525$	8.65756			0.377847
$526$	10.8904			0.474845
$527$	11.2413	+	14.2637i	0.489678	+	0.621335i
$528$	−8.89496			−0.387103
$529$	2.78992			0.121301
$530$	0.991590	+	1.71748i	0.0430719	+	0.0746027i
$531$	−1.65983			−0.0720304
$532$	1.59478	−	2.76224i	0.0691425	−	0.119758i
$533$	21.7087	+	37.6005i	0.940307	+	1.62866i
$534$	3.94635	+	6.83527i	0.170775	+	0.295791i
$535$	−39.4947			−1.70750
$536$	−15.1278	+	26.2022i	−0.653423	+	1.13176i
$537$	1.34797	−	2.33476i	0.0581693	−	0.100752i
$538$	−4.23287	+	7.33154i	−0.182492	+	0.316085i
$539$	−0.148956	−	0.258000i	−0.00641600	−	0.0111128i
$540$	−2.46081	+	4.26225i	−0.105896	+	0.183418i
$541$	−7.40602	−	12.8276i	−0.318410	−	0.551502i	0.661747	−	0.749728i	$-0.269815\pi$
$541$	−7.40602	−	12.8276i	−0.318410	−	0.551502i	−0.980156	+	0.198226i	$0.936482\pi$
$542$	−13.3184			−0.572076
$543$	−1.42469			−0.0611395
$544$	−8.58145	−	14.8635i	−0.367927	−	0.637268i
$545$	−15.1418	+	26.2263i	−0.648602	+	1.12341i
$546$	3.34017	+	5.78535i	0.142946	+	0.247590i
$547$	6.54945	−	11.3440i	0.280034	−	0.485033i	−0.691359	−	0.722512i	$-0.742988\pi$
$547$	6.54945	−	11.3440i	0.280034	−	0.485033i	0.971393	+	0.237478i	$0.0763209\pi$
$548$	−15.0072	+	25.9932i	−0.641075	+	1.11037i
$549$	−2.85464	+	4.94438i	−0.121833	+	0.211021i
$550$	6.74417			0.287572
$551$	1.40356	+	2.43104i	0.0597938	+	0.103566i
$552$	−5.07838	−	8.79601i	−0.216150	−	0.374383i
$553$	3.46081	−	5.99430i	0.147169	−	0.254904i
$554$	−2.18464			−0.0928165
$555$	−13.2540	−	22.9566i	−0.562601	−	0.974453i
$556$	−4.18342			−0.177416
$557$	−7.86991			−0.333459			−0.166729	−	0.986003i	$-0.553321\pi$
$557$	−7.86991			−0.333459			−0.166729	+	0.986003i	$0.553321\pi$
$558$	1.11284	−	2.78820i	0.0471102	−	0.118034i
$559$	49.2967			2.08503
$560$	−17.7275			−0.749125
$561$	−6.19902	−	10.7370i	−0.261723	−	0.453317i
$562$	13.9194			0.587153
$563$	−1.77985	+	3.08280i	−0.0750119	+	0.129924i	−0.901091	−	0.433629i	$-0.857233\pi$
$563$	−1.77985	+	3.08280i	−0.0750119	+	0.129924i	0.826080	+	0.563554i	$0.190566\pi$
$564$	0.594780	+	1.03019i	0.0250448	+	0.0433788i
$565$	24.5874	+	42.5867i	1.03440	+	1.79163i
$566$	−2.80713			−0.117992
$567$	−1.31545	+	2.27842i	−0.0552437	+	0.0956848i
$568$	−12.4969	+	21.6453i	−0.524359	+	0.908217i
$569$	9.58864	−	16.6080i	0.401977	−	0.696244i	−0.591988	−	0.805947i	$-0.701657\pi$
$569$	9.58864	−	16.6080i	0.401977	−	0.696244i	0.993964	+	0.109703i	$0.0349900\pi$
$570$	−0.550582	−	0.953636i	−0.0230613	−	0.0399434i
$571$	−5.08145	+	8.80133i	−0.212652	+	0.368324i	−0.952544	−	0.304402i	$-0.901543\pi$
$571$	−5.08145	+	8.80133i	−0.212652	+	0.368324i	0.739892	+	0.672726i	$0.234877\pi$
$572$	−15.2979	−	26.4968i	−0.639638	−	1.10789i
$573$	20.6647			0.863282
$574$	13.0784			0.545881
$575$	−8.35577	−	14.4726i	−0.348460	−	0.603550i
$576$	0.921622	−	1.59630i	0.0384009	−	0.0665124i
$577$	13.2599	+	22.9667i	0.552015	+	0.956118i	0.998129	+	0.0611420i	$0.0194743\pi$
$577$	13.2599	+	22.9667i	0.552015	+	0.956118i	−0.446114	+	0.894976i	$0.647192\pi$
$578$	−1.71481	+	2.97013i	−0.0713266	+	0.123541i
$579$	−2.47528	+	4.28730i	−0.102869	+	0.178174i
$580$	9.73925	−	16.8689i	0.404400	−	0.700442i
$581$	−2.94828			−0.122315
$582$	−2.80878	−	4.86496i	−0.116428	−	0.201659i
$583$	−2.42768	−	4.20486i	−0.100544	−	0.174147i
$584$	−12.0205	+	20.8201i	−0.497413	+	0.861544i
$585$	−13.5597			−0.560625
$586$	−0.366835	−	0.635377i	−0.0151538	−	0.0262472i
$587$	−32.7382			−1.35125			−0.675625	−	0.737245i	$-0.736126\pi$
$587$	−32.7382			−1.35125			−0.675625	+	0.737245i	$0.736126\pi$
$588$	0.133969			0.00552479
$589$	−2.44441	−	3.10163i	−0.100720	−	0.127800i
$590$	−2.57691			−0.106090
$591$	12.5958			0.518123
$592$	10.7721	+	18.6577i	0.442729	+	0.766829i
$593$	36.4124			1.49528			0.747639	−	0.664105i	$-0.231187\pi$
$593$	36.4124			1.49528			0.747639	+	0.664105i	$0.231187\pi$
$594$	−1.02472	+	1.77487i	−0.0420449	+	0.0728240i
$595$	−12.3545	−	21.3987i	−0.506487	−	0.877261i
$596$	8.04945	+	13.9421i	0.329718	+	0.571089i
$597$	14.0494			0.575006
$598$	6.44748	−	11.1674i	0.263657	−	0.456667i
$599$	11.4530	−	19.8372i	0.467957	−	0.810526i	−0.531372	−	0.847138i	$-0.678323\pi$
$599$	11.4530	−	19.8372i	0.467957	−	0.810526i	0.999330	+	0.0366125i	$0.0116567\pi$
$600$	−3.29072	+	5.69970i	−0.134343	+	0.232689i
$601$	19.2134	+	33.2786i	0.783731	+	1.35746i	0.929754	+	0.368180i	$0.120019\pi$
$601$	19.2134	+	33.2786i	0.783731	+	1.35746i	−0.146024	+	0.989281i	$0.546648\pi$
$602$	7.42469	−	12.8599i	0.302608	−	0.524132i
$603$	−7.56391	−	13.1011i	−0.308026	−	0.533517i
$604$	−3.28458			−0.133648
$605$	−9.92654			−0.403571
$606$	1.60617	+	2.78197i	0.0652463	+	0.113010i
$607$	−1.13809	+	1.97122i	−0.0461935	+	0.0800094i	−0.888198	−	0.459462i	$-0.848042\pi$
$607$	−1.13809	+	1.97122i	−0.0461935	+	0.0800094i	0.842004	+	0.539471i	$0.181376\pi$
$608$	1.86603	+	3.23206i	0.0756775	+	0.131077i
$609$	5.20620	−	9.01741i	0.210966	−	0.365404i
$610$	−4.43188	+	7.67624i	−0.179442	+	0.310802i
$611$	−1.63870	+	2.83831i	−0.0662946	+	0.114826i
$612$	5.57531			0.225368
$613$	−12.1495	−	21.0435i	−0.490713	−	0.849940i	0.509230	−	0.860630i	$-0.329930\pi$
$613$	−12.1495	−	21.0435i	−0.490713	−	0.849940i	−0.999943	+	0.0106909i	$0.996597\pi$
$614$	6.95221	+	12.0416i	0.280568	+	0.485959i
$615$	−13.2732	+	22.9898i	−0.535227	+	0.927040i
$616$	−20.0000			−0.805823
$617$	−9.71707	−	16.8305i	−0.391195	−	0.677569i	0.601413	−	0.798939i	$-0.294605\pi$
$617$	−9.71707	−	16.8305i	−0.391195	−	0.677569i	−0.992607	+	0.121369i	$0.961271\pi$
$618$	−1.24620			−0.0501294
$619$	2.31512			0.0930525			0.0465262	−	0.998917i	$-0.485185\pi$
$619$	2.31512			0.0930525			0.0465262	+	0.998917i	$0.485185\pi$
$620$	−10.1578	+	25.4502i	−0.407947	+	1.02210i
$621$	5.07838			0.203788
$622$	3.04331			0.122025
$623$	−19.2557	−	33.3518i	−0.771461	−	1.33621i
$624$	11.0205			0.441174
$625$	15.3124	−	26.5218i	0.612495	−	1.06087i
$626$	0.540845	+	0.936771i	0.0216165	+	0.0374409i
$627$	1.34797	+	2.33476i	0.0538328	+	0.0932412i
$628$	−5.25792			−0.209814
$629$	−15.0144	+	26.0057i	−0.598662	+	1.03691i
$630$	−2.04226	+	3.53730i	−0.0813656	+	0.140929i
$631$	−11.4794	+	19.8829i	−0.456987	+	0.791525i	−0.998800	−	0.0489739i	$-0.984405\pi$
$631$	−11.4794	+	19.8829i	−0.456987	+	0.791525i	0.541813	+	0.840499i	$0.317738\pi$
$632$	2.63090	+	4.55685i	0.104651	+	0.181262i
$633$	−7.23400	+	12.5297i	−0.287526	+	0.498009i
$634$	−5.86183	−	10.1530i	−0.232803	−	0.403226i
$635$	8.56132			0.339745
$636$	2.18342			0.0865781
$637$	0.184551	+	0.319652i	0.00731218	+	0.0126651i
$638$	4.05559	−	7.02449i	0.160562	−	0.278102i
$639$	−6.24846	−	10.8227i	−0.247185	−	0.428138i
$640$	16.5814	−	28.7199i	0.655439	−	1.13525i
$641$	−6.94994	+	12.0376i	−0.274506	+	0.475459i	−0.970010	−	0.243063i	$-0.921848\pi$
$641$	−6.94994	+	12.0376i	−0.274506	+	0.475459i	0.695504	+	0.718522i	$0.255181\pi$
$642$	3.69788	−	6.40492i	0.145944	−	0.252782i
$643$	12.3568			0.487305			0.243653	−	0.969863i	$-0.421654\pi$
$643$	12.3568			0.487305			0.243653	+	0.969863i	$0.421654\pi$
$644$	11.4186	+	19.7775i	0.449954	+	0.779343i
$645$	15.0706	+	26.1030i	0.593403	+	1.02780i
$646$	−0.623710	+	1.08030i	−0.0245395	+	0.0425037i
$647$	5.70209			0.224172			0.112086	−	0.993698i	$-0.464247\pi$
$647$	5.70209			0.224172			0.112086	+	0.993698i	$0.464247\pi$
$648$	−1.00000	−	1.73205i	−0.0392837	−	0.0680414i
$649$	6.30898			0.247649
$650$	−8.35577			−0.327740
$651$	−5.42994	+	13.6046i	−0.212816	+	0.533208i
$652$	−9.93827			−0.389213
$653$	9.25073			0.362009			0.181005	−	0.983482i	$-0.442065\pi$
$653$	9.25073			0.362009			0.181005	+	0.983482i	$0.442065\pi$
$654$	−2.83545	−	4.91114i	−0.110875	−	0.192041i
$655$	−46.4762			−1.81598
$656$	10.7877	−	18.6848i	0.421187	−	0.729517i
$657$	−6.01026	−	10.4101i	−0.234483	−	0.406136i
$658$	0.493616	+	0.854968i	0.0192432	+	0.0333301i
$659$	−8.59705			−0.334893			−0.167447	−	0.985881i	$-0.553552\pi$
$659$	−8.59705			−0.334893			−0.167447	+	0.985881i	$0.553552\pi$
$660$	9.35350	−	16.2007i	0.364085	−	0.630613i
$661$	−7.14423	+	12.3742i	−0.277878	+	0.481299i	−0.970857	−	0.239658i	$-0.922965\pi$
$661$	−7.14423	+	12.3742i	−0.277878	+	0.481299i	0.692979	+	0.720958i	$0.256298\pi$
$662$	5.16229	−	8.94134i	0.200638	−	0.347515i
$663$	7.68035	+	13.3027i	0.298280	+	0.516636i
$664$	1.12064	−	1.94100i	0.0434892	−	0.0753255i
$665$	2.68649	+	4.65314i	0.104178	+	0.180441i
$666$	4.96388			0.192347
$667$	−20.0989			−0.778232
$668$	−5.72261	−	9.91184i	−0.221414	−	0.383501i
$669$	8.54945	−	14.8081i	0.330541	−	0.572513i
$670$	−11.7431	−	20.3397i	−0.453677	−	0.785791i
$671$	10.8504	−	18.7935i	0.418876	−	0.725515i
$672$	6.92162	−	11.9886i	0.267007	−	0.462470i
$673$	−0.433820	+	0.751397i	−0.0167225	+	0.0289642i	−0.874266	−	0.485448i	$-0.838657\pi$
$673$	−0.433820	+	0.751397i	−0.0167225	+	0.0289642i	0.857543	+	0.514412i	$0.171990\pi$
$674$	−10.5958			−0.408136
$675$	−1.64536	−	2.84985i	−0.0633300	−	0.109691i
$676$	7.84324	+	13.5849i	0.301663	+	0.522496i
$677$	−11.4819	+	19.8873i	−0.441287	+	0.764331i	−0.997785	−	0.0665174i	$-0.978811\pi$
$677$	−11.4819	+	19.8873i	−0.441287	+	0.764331i	0.556498	+	0.830849i	$0.312145\pi$
$678$	−9.20847			−0.353649
$679$	13.7051	+	23.7379i	0.525952	+	0.910976i
$680$	18.7838			0.720325
$681$	3.91548			0.150041
$682$	−4.22988	+	10.5979i	−0.161971	+	0.405815i
$683$	−4.90934			−0.187851			−0.0939253	−	0.995579i	$-0.529941\pi$
$683$	−4.90934			−0.187851			−0.0939253	+	0.995579i	$0.529941\pi$
$684$	−1.21235			−0.0463552
$685$	−25.2804	−	43.7869i	−0.965914	−	1.67301i
$686$	10.0410			0.383369
$687$	1.97414	−	3.41931i	0.0753182	−	0.130455i
$688$	−12.2485	−	21.2150i	−0.466968	−	0.808813i
$689$	3.00780	+	5.20966i	0.114588	+	0.198472i
$690$	7.88428			0.300149
$691$	−5.18148	+	8.97459i	−0.197113	+	0.341409i	−0.947591	−	0.319486i	$-0.896490\pi$
$691$	−5.18148	+	8.97459i	−0.197113	+	0.341409i	0.750478	+	0.660895i	$0.229823\pi$
$692$	5.33403	−	9.23881i	0.202769	−	0.351207i
$693$	5.00000	−	8.66025i	0.189934	−	0.328976i
$694$	−1.40716	−	2.43727i	−0.0534150	−	0.0925174i
$695$	3.52359	−	6.10304i	0.133657	−	0.231501i
$696$	3.95774	+	6.85501i	0.150018	+	0.259838i
$697$	30.0722			1.13907
$698$	−12.5080			−0.473434
$699$	−9.86603	−	17.0885i	−0.373168	−	0.646345i
$700$	7.39908	−	12.8156i	0.279659	−	0.484383i
$701$	−4.70209	−	8.14425i	−0.177595	−	0.307604i	0.763461	−	0.645854i	$-0.223498\pi$
$701$	−4.70209	−	8.14425i	−0.177595	−	0.307604i	−0.941056	+	0.338250i	$0.890165\pi$
$702$	1.26959	−	2.19900i	0.0479178	−	0.0829960i
$703$	3.26487	−	5.65492i	0.123137	−	0.213279i
$704$	−3.50307	+	6.06750i	−0.132027	+	0.228677i
$705$	−2.00388			−0.0754703
$706$	2.30632	+	3.99467i	0.0867996	+	0.150341i
$707$	−7.83710	−	13.5743i	−0.294745	−	0.510513i
$708$	−1.41855	+	2.45700i	−0.0533124	+	0.0923398i
$709$	−5.55479			−0.208614			−0.104307	−	0.994545i	$-0.533263\pi$
$709$	−5.55479			−0.208614			−0.104307	+	0.994545i	$0.533263\pi$
$710$	−9.70086	−	16.8024i	−0.364067	−	0.630582i
$711$	−2.63090			−0.0986664
$712$	29.2762			1.09717
$713$	27.9832	−	4.05330i	1.04798	−	0.151797i
$714$	4.62702			0.173162
$715$	51.5402			1.92750
$716$	−2.30406	−	3.99074i	−0.0861066	−	0.149141i
$717$	7.78539			0.290751
$718$	6.57724	−	11.3921i	0.245461	−	0.425150i
$719$	−17.8710	−	30.9534i	−0.666474	−	1.15437i	−0.978883	−	0.204419i	$-0.934469\pi$
$719$	−17.8710	−	30.9534i	−0.666474	−	1.15437i	0.312409	−	0.949948i	$-0.398864\pi$
$720$	3.36910	+	5.83546i	0.125559	+	0.217475i
$721$	6.08065			0.226455
$722$	−4.98667	+	8.63716i	−0.185585	+	0.321442i
$723$	7.69481	−	13.3278i	0.286173	−	0.495666i
$724$	−1.21760	+	2.10894i	−0.0452516	+	0.0783781i
$725$	6.51192	+	11.2790i	0.241846	+	0.418890i
$726$	0.929421	−	1.60981i	0.0344941	−	0.0597455i
$727$	−11.4174	−	19.7755i	−0.423449	−	0.733434i	0.572826	−	0.819677i	$-0.305847\pi$
$727$	−11.4174	−	19.7755i	−0.423449	−	0.733434i	−0.996274	+	0.0862429i	$0.972514\pi$
$728$	24.7792			0.918380
$729$	1.00000			0.0370370
$730$	−9.33105	−	16.1618i	−0.345358	−	0.598177i
$731$	17.0722	−	29.5700i	0.631439	−	1.09369i
$732$	4.87936	+	8.45130i	0.180346	+	0.312369i
$733$	−4.98554	+	8.63520i	−0.184145	+	0.318948i	−0.943288	−	0.331975i	$-0.892285\pi$
$733$	−4.98554	+	8.63520i	−0.184145	+	0.318948i	0.759143	+	0.650924i	$0.225618\pi$
$734$	2.63255	−	4.55972i	0.0971693	−	0.168302i
$735$	−0.112839	+	0.195443i	−0.00416213	+	0.00720902i
$736$	−26.7214			−0.984963
$737$	28.7503	+	49.7970i	1.05903	+	1.83430i
$738$	−2.48554	−	4.30507i	−0.0914938	−	0.158472i
$739$	−4.24733	+	7.35659i	−0.156241	+	0.270617i	−0.933510	−	0.358551i	$-0.883271\pi$
$739$	−4.24733	+	7.35659i	−0.156241	+	0.270617i	0.777269	+	0.629168i	$0.216604\pi$
$740$	−45.3095			−1.66561
$741$	−1.67009	−	2.89267i	−0.0613522	−	0.106265i
$742$	1.81205			0.0665224
$743$	−19.7854			−0.725855			−0.362928	−	0.931817i	$-0.618223\pi$
$743$	−19.7854			−0.725855			−0.362928	+	0.931817i	$0.618223\pi$
$744$	−6.89269	−	8.74590i	−0.252698	−	0.320640i
$745$	−27.1194			−0.993579
$746$	7.84202			0.287117
$747$	0.560319	+	0.970501i	0.0205010	+	0.0355088i
$748$	−21.1917			−0.774843
$749$	−18.0433	+	31.2519i	−0.659288	+	1.14192i
$750$	1.32684	+	2.29816i	0.0484494	+	0.0839169i
$751$	−12.7576	−	22.0968i	−0.465531	−	0.806323i	0.533694	−	0.845678i	$-0.320803\pi$
$751$	−12.7576	−	22.0968i	−0.465531	−	0.806323i	−0.999225	+	0.0393540i	$0.987470\pi$
$752$	1.62863			0.0593900
$753$	−2.07058	+	3.58635i	−0.0754561	+	0.130694i
$754$	−5.02472	+	8.70308i	−0.182990	+	0.316947i
$755$	2.76652	−	4.79176i	0.100684	−	0.174390i
$756$	2.24846	+	3.89445i	0.0817759	+	0.141640i
$757$	11.4433	−	19.8203i	0.415913	−	0.720382i	−0.579611	−	0.814893i	$-0.696795\pi$
$757$	11.4433	−	19.8203i	0.415913	−	0.720382i	0.995524	+	0.0945111i	$0.0301288\pi$
$758$	6.93434	+	12.0106i	0.251867	+	0.436246i
$759$	−19.3028			−0.700648
$760$	−4.08452			−0.148161
$761$	11.6098	+	20.1087i	0.420854	+	0.728940i	0.996023	−	0.0890942i	$-0.0283972\pi$
$761$	11.6098	+	20.1087i	0.420854	+	0.728940i	−0.575169	+	0.818034i	$0.695064\pi$
$762$	−0.801595	+	1.38840i	−0.0290387	+	0.0502966i
$763$	13.8352	+	23.9632i	0.500867	+	0.867526i
$764$	17.6609	−	30.5895i	0.638948	−	1.10669i
$765$	−4.69594	+	8.13361i	−0.169782	+	0.294071i
$766$	−6.25986	+	10.8424i	−0.226178	+	0.391752i
$767$	−7.81658			−0.282240
$768$	1.26180	+	2.18549i	0.0455311	+	0.0788622i
$769$	17.0452	+	29.5232i	0.614667	+	1.06463i	0.990443	+	0.137924i	$0.0440430\pi$
$769$	17.0452	+	29.5232i	0.614667	+	1.06463i	−0.375776	+	0.926711i	$0.622624\pi$
$770$	7.76260	−	13.4452i	0.279745	−	0.484532i
$771$	−7.95774			−0.286591
$772$	4.23093	+	7.32818i	0.152274	+	0.263747i
$773$	−32.5113			−1.16935			−0.584675	−	0.811267i	$-0.698778\pi$
$773$	−32.5113			−1.16935			−0.584675	+	0.811267i	$0.698778\pi$
$774$	−5.64423			−0.202878
$775$	−11.3410	−	14.3902i	−0.407380	−	0.516910i
$776$	−20.8371			−0.748008
$777$	−24.2206			−0.868908
$778$	8.46695	+	14.6652i	0.303555	+	0.525773i
$779$	−6.53919			−0.234291
$780$	−11.5886	+	20.0721i	−0.414940	+	0.718697i
$781$	23.7503	+	41.1367i	0.849853	+	1.47199i
$782$	−4.46573	−	7.73487i	−0.159694	−	0.276599i
$783$	−3.95774			−0.141438
$784$	0.0917087	−	0.158844i	0.00327531	−	0.00567301i
$785$	4.42862	−	7.67059i	0.158064	−	0.273775i
$786$	4.35157	−	7.53713i	0.155215	−	0.268841i
$787$	16.0392	+	27.7807i	0.571735	+	0.990275i	0.996388	+	0.0849183i	$0.0270629\pi$
$787$	16.0392	+	27.7807i	0.571735	+	0.990275i	−0.424653	+	0.905356i	$0.639604\pi$
$788$	10.7649	−	18.6453i	0.383483	−	0.664211i
$789$	10.0989	+	17.4918i	0.359530	+	0.622725i
$790$	−4.08452			−0.145321
$791$	44.9315			1.59758
$792$	3.80098	+	6.58350i	0.135062	+	0.233934i
$793$	−13.4433	+	23.2844i	−0.477385	+	0.826855i
$794$	−0.980526	−	1.69832i	−0.0347976	−	0.0602711i
$795$	−1.83904	+	3.18531i	−0.0652240	+	0.112971i
$796$	12.0072	−	20.7971i	0.425583	−	0.737132i
$797$	11.6598	−	20.1954i	0.413012	−	0.715358i	−0.582205	−	0.813042i	$-0.697810\pi$
$797$	11.6598	−	20.1954i	0.413012	−	0.715358i	0.995218	+	0.0976836i	$0.0311433\pi$
$798$	−1.00614			−0.0356171
$799$	1.13501	+	1.96590i	0.0401539	+	0.0695486i
$800$	8.65756	+	14.9953i	0.306091	+	0.530165i
$801$	−7.31904	+	12.6770i	−0.258606	+	0.447918i
$802$	4.03120			0.142347
$803$	22.8449	+	39.5685i	0.806179	+	1.39634i
$804$	−25.8576			−0.911928
$805$	−38.4703			−1.35590
$806$	5.24067	−	13.1304i	0.184595	−	0.462498i
$807$	−15.7009			−0.552697
$808$	11.9155			0.419185
$809$	8.77985	+	15.2072i	0.308683	+	0.534655i	0.978075	−	0.208255i	$-0.0667784\pi$
$809$	8.77985	+	15.2072i	0.308683	+	0.534655i	−0.669391	+	0.742910i	$0.733445\pi$
$810$	1.55252			0.0545500
$811$	14.8154	−	25.6611i	0.520241	−	0.901083i	−0.479482	−	0.877552i	$-0.659176\pi$
$811$	14.8154	−	25.6611i	0.520241	−	0.901083i	0.999723	−	0.0235319i	$-0.00749113\pi$
$812$	−8.89884	−	15.4132i	−0.312288	−	0.540899i
$813$	−12.3504	−	21.3916i	−0.433149	−	0.750235i
$814$	−18.8676			−0.661310
$815$	8.37076	−	14.4986i	0.293215	−	0.507863i
$816$	3.81658	−	6.61051i	0.133607	−	0.231414i
$817$	−3.71235	+	6.42997i	−0.129879	+	0.224956i
$818$	−0.709887	−	1.22956i	−0.0248206	−	0.0429905i
$819$	−6.19481	+	10.7297i	−0.216464	+	0.374927i
$820$	22.6875	+	39.2960i	0.792283	+	1.37227i
$821$	−37.8531			−1.32108			−0.660541	−	0.750790i	$-0.729673\pi$
$821$	−37.8531			−1.32108			−0.660541	+	0.750790i	$0.729673\pi$
$822$	9.46800			0.330234
$823$	8.19481	+	14.1938i	0.285653	+	0.494766i	0.972767	−	0.231784i	$-0.0744561\pi$
$823$	8.19481	+	14.1938i	0.285653	+	0.494766i	−0.687114	+	0.726549i	$0.741123\pi$
$824$	−2.31124	+	4.00319i	−0.0805160	+	0.139458i
$825$	6.25400	+	10.8322i	0.217736	+	0.377130i
$826$	−1.17727	+	2.03910i	−0.0409626	+	0.0709493i
$827$	1.61203	−	2.79213i	0.0560559	−	0.0970917i	−0.836636	−	0.547760i	$-0.815481\pi$
$827$	1.61203	−	2.79213i	0.0560559	−	0.0970917i	0.892692	+	0.450668i	$0.148814\pi$
$828$	4.34017	−	7.51740i	0.150831	−	0.261248i
$829$	−40.3074			−1.39993			−0.699966	−	0.714176i	$-0.746802\pi$
$829$	−40.3074			−1.39993			−0.699966	+	0.714176i	$0.746802\pi$
$830$	0.869906	+	1.50672i	0.0301949	+	0.0522991i
$831$	−2.02586	−	3.50889i	−0.0702762	−	0.121722i
$832$	4.34017	−	7.51740i	0.150468	−	0.260619i
$833$	0.255652			0.00885782
$834$	0.659827	+	1.14285i	0.0228479	+	0.0395738i
$835$	19.2800			0.667214
$836$	4.60811			0.159375
$837$	5.51026	−	0.798148i	0.190462	−	0.0275880i
$838$	−5.81205			−0.200774
$839$	44.5958			1.53962			0.769809	−	0.638274i	$-0.220351\pi$
$839$	44.5958			1.53962			0.769809	+	0.638274i	$0.220351\pi$
$840$	7.57531	+	13.1208i	0.261373	+	0.452711i
$841$	−13.3363			−0.459872
$842$	10.1373	−	17.5583i	0.349354	−	0.605099i
$843$	12.9077	+	22.3568i	0.444564	+	0.770008i
$844$	12.3649	+	21.4166i	0.425617	+	0.737191i
$845$	−26.4247			−0.909037
$846$	0.187623	−	0.324972i	0.00645060	−	0.0111728i
$847$	−4.53498	+	7.85482i	−0.155824	+	0.269895i
$848$	1.49466	−	2.58883i	0.0513269	−	0.0889007i
$849$	−2.60310	−	4.50870i	−0.0893382	−	0.154738i
$850$	−2.89374	+	5.01210i	−0.0992544	+	0.171914i
$851$	23.3763	+	40.4889i	0.801329	+	1.38794i
$852$	−21.3607			−0.731805
$853$	29.9360			1.02499			0.512495	−	0.858690i	$-0.328721\pi$
$853$	29.9360			1.02499			0.512495	+	0.858690i	$0.328721\pi$
$854$	4.04945	+	7.01385i	0.138569	+	0.240009i
$855$	1.02113	−	1.76865i	0.0349219	−	0.0604865i
$856$	−13.7165	−	23.7576i	−0.468819	−	0.812018i
$857$	17.5308	−	30.3642i	0.598840	−	1.03722i	−0.394153	−	0.919045i	$-0.628962\pi$
$857$	17.5308	−	30.3642i	0.598840	−	1.03722i	0.992993	−	0.118176i	$-0.0377048\pi$
$858$	−4.82571	+	8.35837i	−0.164747	+	0.285350i
$859$	−15.3752	+	26.6306i	−0.524594	+	0.908623i	0.474996	+	0.879988i	$0.342449\pi$
$859$	−15.3752	+	26.6306i	−0.524594	+	0.908623i	−0.999590	+	0.0286350i	$0.990884\pi$
$860$	51.5195			1.75680
$861$	12.1278	+	21.0060i	0.413315	+	0.715883i
$862$	−5.80098	−	10.0476i	−0.197582	−	0.342223i
$863$	1.78600	−	3.09344i	0.0607960	−	0.105302i	−0.834025	−	0.551726i	$-0.813969\pi$
$863$	1.78600	−	3.09344i	0.0607960	−	0.105302i	0.894821	+	0.446424i	$0.147303\pi$
$864$	−5.26180			−0.179010
$865$	8.98545	+	15.5632i	0.305514	+	0.529166i
$866$	9.54080			0.324209
$867$	−6.36069			−0.216020
$868$	15.4980	+	19.6648i	0.526035	+	0.667468i
$869$	10.0000			0.339227
$870$	−6.14447			−0.208317
$871$	−35.6205	−	61.6966i	−1.20696	−	2.09051i
$872$	−21.0349			−0.712331
$873$	5.20928	−	9.02273i	0.176307	−	0.305373i
$874$	0.971071	+	1.68194i	0.0328470	+	0.0568926i
$875$	−6.47414	−	11.2135i	−0.218866	−	0.379087i
$876$	−20.5464			−0.694198
$877$	4.79791	−	8.31023i	0.162014	−	0.280616i	−0.773577	−	0.633702i	$-0.781534\pi$
$877$	4.79791	−	8.31023i	0.162014	−	0.280616i	0.935591	+	0.353086i	$0.114868\pi$
$878$	1.44687	−	2.50605i	0.0488295	−	0.0845751i
$879$	0.680346	−	1.17839i	0.0229475	−	0.0397462i
$880$	−12.8059	−	22.1805i	−0.431687	−	0.747704i
$881$	−22.0928	+	38.2658i	−0.744324	+	1.28921i	0.206186	+	0.978513i	$0.433895\pi$
$881$	−22.0928	+	38.2658i	−0.744324	+	1.28921i	−0.950510	+	0.310694i	$0.899439\pi$
$882$	−0.0211302	−	0.0365986i	−0.000711491	−	0.00123234i
$883$	−17.2907			−0.581879			−0.290940	−	0.956741i	$-0.593968\pi$
$883$	−17.2907			−0.581879			−0.290940	+	0.956741i	$0.593968\pi$
$884$	26.2557			0.883073
$885$	−2.38962	−	4.13895i	−0.0803262	−	0.139129i
$886$	−3.69368	+	6.39764i	−0.124092	+	0.214933i
$887$	21.5025	+	37.2434i	0.721982	+	1.25051i	0.960204	+	0.279299i	$0.0901020\pi$
$887$	21.5025	+	37.2434i	0.721982	+	1.25051i	−0.238222	+	0.971211i	$0.576565\pi$
$888$	9.20620	−	15.9456i	0.308940	−	0.535100i
$889$	3.91127	−	6.77453i	0.131180	−	0.227210i
$890$	−11.3630	+	19.6812i	−0.380887	+	0.659716i
$891$	−3.80098			−0.127338
$892$	−14.6134	−	25.3111i	−0.489292	−	0.847478i
$893$	−0.246808	−	0.427484i	−0.00825912	−	0.0143052i
$894$	2.53919	−	4.39800i	0.0849232	−	0.147091i
$895$	7.76260			0.259475
$896$	−15.1506	−	26.2416i	−0.506146	−	0.876671i
$897$	23.9155			0.798515
$898$	−10.0267			−0.334594
$899$	−21.8082	+	3.15886i	−0.727343	+	0.105354i
$900$	−5.62475			−0.187492
$901$	4.16660			0.138809
$902$	9.44748	+	16.3635i	0.314567	+	0.544845i
$903$	27.5402			0.916482
$904$	−17.0784	+	29.5806i	−0.568018	+	0.983837i
$905$	−2.05110	−	3.55262i	−0.0681810	−	0.118093i
$906$	0.518059	+	0.897304i	0.0172113	+	0.0298109i
$907$	−42.0326			−1.39567			−0.697835	−	0.716258i	$-0.745853\pi$
$907$	−42.0326			−1.39567			−0.697835	+	0.716258i	$0.745853\pi$
$908$	3.34632	−	5.79599i	0.111051	−	0.192347i
$909$	−2.97887	+	5.15955i	−0.0988029	+	0.171132i
$910$	−9.61757	+	16.6581i	−0.318819	+	0.552211i
$911$	10.4114	+	18.0330i	0.344944	+	0.597460i	0.985344	−	0.170582i	$-0.0545646\pi$
$911$	10.4114	+	18.0330i	0.344944	+	0.597460i	−0.640400	+	0.768042i	$0.721231\pi$
$912$	−0.829914	+	1.43745i	−0.0274812	+	0.0475988i
$913$	−2.12976	−	3.68886i	−0.0704849	−	0.122083i
$914$	17.9967			0.595278
$915$	−16.4391			−0.543459
$916$	−3.37435	−	5.84455i	−0.111492	−	0.193109i
$917$	−21.2329	+	36.7764i	−0.701171	+	1.21446i
$918$	−0.879362	−	1.52310i	−0.0290233	−	0.0502698i
$919$	−3.06812	+	5.31414i	−0.101208	+	0.175297i	−0.912183	−	0.409784i	$-0.865604\pi$
$919$	−3.06812	+	5.31414i	−0.101208	+	0.175297i	0.810975	+	0.585081i	$0.198937\pi$
$920$	14.6225	−	25.3269i	0.482089	−	0.835003i
$921$	−12.8938	+	22.3328i	−0.424866	+	0.735890i
$922$	19.7626			0.650847
$923$	−29.4257	−	50.9669i	−0.968560	−	1.67760i
$924$	−8.54638	−	14.8028i	−0.281155	−	0.486975i
$925$	15.1475	−	26.2363i	0.498048	−	0.862645i
$926$	2.59914			0.0854130
$927$	−1.15562	−	2.00160i	−0.0379556	−	0.0657410i
$928$	20.8248			0.683608
$929$	34.9672			1.14724			0.573618	−	0.819123i	$-0.305539\pi$
$929$	34.9672			1.14724			0.573618	+	0.819123i	$0.305539\pi$
$930$	8.55479	−	1.23914i	0.280523	−	0.0406330i
$931$	−0.0555914			−0.00182193
$932$	−33.7275			−1.10478
$933$	2.82211	+	4.88805i	0.0923919	+	0.160027i
$934$	−16.4268			−0.537501
$935$	17.8492	−	30.9157i	0.583732	−	1.01105i
$936$	−4.70928	−	8.15670i	−0.153927	−	0.266610i
$937$	−6.66588	−	11.5456i	−0.217765	−	0.377180i	0.736359	−	0.676591i	$-0.236543\pi$
$937$	−6.66588	−	11.5456i	−0.217765	−	0.377180i	−0.954124	+	0.299411i	$0.903210\pi$
$938$	−21.4596			−0.700680
$939$	−1.00307	+	1.73737i	−0.0327340	+	0.0566970i
$940$	−1.71259	+	2.96629i	−0.0558584	+	0.0967497i
$941$	−3.54638	+	6.14250i	−0.115609	+	0.200240i	−0.918023	−	0.396527i	$-0.870215\pi$
$941$	−3.54638	+	6.14250i	−0.115609	+	0.200240i	0.802414	+	0.596767i	$0.203548\pi$
$942$	0.829302	+	1.43639i	0.0270201	+	0.0468002i
$943$	23.4101	−	40.5476i	0.762339	−	1.32041i
$944$	1.94214	+	3.36389i	0.0632113	+	0.109485i
$945$	−7.57531			−0.246425
$946$	21.4536			0.697517
$947$	−26.6309	−	46.1261i	−0.865388	−	1.49890i	−0.866662	−	0.498897i	$-0.833739\pi$
$947$	−26.6309	−	46.1261i	−0.865388	−	1.49890i	0.00127362	−	0.999999i	$-0.499595\pi$
$948$	−2.24846	+	3.89445i	−0.0730267	+	0.126486i
$949$	−28.3040	−	49.0239i	−0.918786	−	1.59138i
$950$	0.629241	−	1.08988i	0.0204153	−	0.0353603i
$951$	10.8716	−	18.8301i	0.352535	−	0.610608i
$952$	8.58145	−	14.8635i	0.278126	−	0.481729i
$953$	−18.9639			−0.614300			−0.307150	−	0.951661i	$-0.599375\pi$
$953$	−18.9639			−0.614300			−0.307150	+	0.951661i	$0.599375\pi$
$954$	−0.344378	−	0.596481i	−0.0111497	−	0.0193118i
$955$	29.7506	+	51.5296i	0.962708	+	1.66746i
$956$	6.65368	−	11.5245i	0.215196	−	0.372730i
$957$	15.0433			0.486281
$958$	8.70313	+	15.0743i	0.281185	+	0.487027i
$959$	−46.1978			−1.49180
$960$	5.30737			0.171295
$961$	29.7259	−	8.79601i	0.958901	−	0.283742i
$962$	23.3763			0.753682
$963$	13.7165			0.442007
$964$	−13.1526	−	22.7809i	−0.423615	−	0.733723i
$965$	−14.2544			−0.458866
$966$	3.60197	−	6.23879i	0.115891	−	0.200730i
$967$	−2.05365	−	3.55703i	−0.0660410	−	0.114386i	0.831114	−	0.556102i	$-0.187703\pi$
$967$	−2.05365	−	3.55703i	−0.0660410	−	0.114386i	−0.897155	+	0.441715i	$0.854370\pi$
$968$	−3.44748	−	5.97121i	−0.110806	−	0.191922i
$969$	−2.31351			−0.0743207
$970$	8.08750	−	14.0080i	0.259674	−	0.449769i
$971$	22.2628	−	38.5604i	0.714449	−	1.23746i	−0.248723	−	0.968575i	$-0.580011\pi$
$971$	22.2628	−	38.5604i	0.714449	−	1.23746i	0.963172	−	0.268887i	$-0.0866557\pi$
$972$	0.854638	−	1.48028i	0.0274125	−	0.0474799i
$973$	−3.21953	−	5.57640i	−0.103214	−	0.178771i
$974$	−5.65203	+	9.78960i	−0.181103	+	0.313679i
$975$	−7.74846	−	13.4207i	−0.248149	−	0.429807i
$976$	13.3607			0.427665
$977$	−37.6209			−1.20360			−0.601799	−	0.798647i	$-0.705549\pi$
$977$	−37.6209			−1.20360			−0.601799	+	0.798647i	$0.705549\pi$
$978$	1.56751	+	2.71500i	0.0501233	+	0.0868162i
$979$	27.8196	−	48.1849i	0.889117	−	1.54000i
$980$	0.192873	+	0.334066i	0.00616110	+	0.0106713i
$981$	5.25872	−	9.10838i	0.167898	−	0.290808i
$982$	1.90829	−	3.30526i	0.0608960	−	0.105475i
$983$	−4.20620	+	7.28536i	−0.134157	+	0.232367i	−0.925275	−	0.379297i	$-0.876166\pi$
$983$	−4.20620	+	7.28536i	−0.134157	+	0.232367i	0.791118	+	0.611663i	$0.209499\pi$
$984$	−18.4391			−0.587816
$985$	18.1340	+	31.4090i	0.577796	+	1.00077i
$986$	3.48029	+	6.02803i	0.110835	+	0.191972i
$987$	−0.915479	+	1.58566i	−0.0291400	+	0.0504720i
$988$	−5.70928			−0.181636
$989$	−26.5802	−	46.0383i	−0.845202	−	1.46393i
$990$	−5.90110			−0.187549
$991$	48.1955			1.53098			0.765491	−	0.643447i	$-0.222496\pi$
$991$	48.1955			1.53098			0.765491	+	0.643447i	$0.222496\pi$
$992$	−28.9939	+	4.19969i	−0.920556	+	0.133340i
$993$	19.1483			0.607654
$994$	−17.7275			−0.562283
$995$	20.2267	+	35.0337i	0.641230	+	1.11064i
$996$	1.91548			0.0606943
$997$	−16.3070	+	28.2446i	−0.516449	+	0.894516i	0.483369	+	0.875417i	$0.339413\pi$
$997$	−16.3070	+	28.2446i	−0.516449	+	0.894516i	−0.999818	+	0.0190991i	$0.993920\pi$
$998$	−1.68035	−	2.91044i	−0.0531904	−	0.0921285i
$999$	4.60310	+	7.97281i	0.145636	+	0.252248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.e.b.25.2	✓	6
3.2	odd	2		279.2.h.d.118.2		6
4.3	odd	2		1488.2.q.m.769.3		6
31.5	even	3	inner	93.2.e.b.67.2	yes	6
31.6	odd	6		2883.2.a.g.1.2		3
31.25	even	3		2883.2.a.h.1.2		3
93.5	odd	6		279.2.h.d.253.2		6
93.56	odd	6		8649.2.a.o.1.2		3
93.68	even	6		8649.2.a.n.1.2		3
124.67	odd	6		1488.2.q.m.625.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.e.b.25.2	✓	6	1.1	even	1	trivial
93.2.e.b.67.2	yes	6	31.5	even	3	inner
279.2.h.d.118.2		6	3.2	odd	2
279.2.h.d.253.2		6	93.5	odd	6
1488.2.q.m.625.3		6	124.67	odd	6
1488.2.q.m.769.3		6	4.3	odd	2
2883.2.a.g.1.2		3	31.6	odd	6
2883.2.a.h.1.2		3	31.25	even	3
8649.2.a.n.1.2		3	93.68	even	6
8649.2.a.o.1.2		3	93.56	odd	6

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.539189 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.70928 q^{4} +(1.43968 - 2.49360i) q^{5} +(0.269594 + 0.466951i) q^{6} +(-1.31545 - 2.27842i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-0.539189 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.70928 q^{4} +(1.43968 - 2.49360i) q^{5} +(0.269594 + 0.466951i) q^{6} +(-1.31545 - 2.27842i) q^{7} +2.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.776260 + 1.34452i) q^{10} +(1.90049 - 3.29175i) q^{11} +(0.854638 + 1.48028i) q^{12} +(-2.35464 + 4.07835i) q^{13} +(0.709275 + 1.22850i) q^{14} -2.87936 q^{15} +2.34017 q^{16} +(1.63090 + 2.82480i) q^{17} +(0.269594 - 0.466951i) q^{18} +(-0.354638 - 0.614250i) q^{19} +(-2.46081 + 4.26225i) q^{20} +(-1.31545 + 2.27842i) q^{21} +(-1.02472 + 1.77487i) q^{22} +5.07838 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-1.64536 - 2.84985i) q^{25} +(1.26959 - 2.19900i) q^{26} +1.00000 q^{27} +(2.24846 + 3.89445i) q^{28} -3.95774 q^{29} +1.55252 q^{30} +(5.51026 - 0.798148i) q^{31} -5.26180 q^{32} -3.80098 q^{33} +(-0.879362 - 1.52310i) q^{34} -7.57531 q^{35} +(0.854638 - 1.48028i) q^{36} +(4.60310 + 7.97281i) q^{37} +(0.191217 + 0.331197i) q^{38} +4.70928 q^{39} +(2.87936 - 4.98720i) q^{40} +(4.60977 - 7.98435i) q^{41} +(0.709275 - 1.22850i) q^{42} +(-5.23400 - 9.06555i) q^{43} +(-3.24846 + 5.62651i) q^{44} +(1.43968 + 2.49360i) q^{45} -2.73820 q^{46} +0.695944 q^{47} +(-1.17009 - 2.02665i) q^{48} +(0.0391889 - 0.0678771i) q^{49} +(0.887161 + 1.53661i) q^{50} +(1.63090 - 2.82480i) q^{51} +(4.02472 - 6.97103i) q^{52} +(0.638697 - 1.10626i) q^{53} -0.539189 q^{54} +(-5.47220 - 9.47814i) q^{55} +(-2.63090 - 4.55685i) q^{56} +(-0.354638 + 0.614250i) q^{57} +2.13397 q^{58} +(0.829914 + 1.43745i) q^{59} +4.92162 q^{60} +5.70928 q^{61} +(-2.97107 + 0.430353i) q^{62} +2.63090 q^{63} -1.84324 q^{64} +(6.77985 + 11.7431i) q^{65} +2.04945 q^{66} +(-7.56391 + 13.1011i) q^{67} +(-2.78765 - 4.82836i) q^{68} +(-2.53919 - 4.39800i) q^{69} +4.08452 q^{70} +(-6.24846 + 10.8227i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(-6.01026 + 10.4101i) q^{73} +(-2.48194 - 4.29885i) q^{74} +(-1.64536 + 2.84985i) q^{75} +(0.606173 + 1.04992i) q^{76} -10.0000 q^{77} -2.53919 q^{78} +(1.31545 + 2.27842i) q^{79} +(3.36910 - 5.83546i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.48554 + 4.30507i) q^{82} +(0.560319 - 0.970501i) q^{83} +(2.24846 - 3.89445i) q^{84} +9.39189 q^{85} +(2.82211 + 4.88805i) q^{86} +(1.97887 + 3.42750i) q^{87} +(3.80098 - 6.58350i) q^{88} +14.6381 q^{89} +(-0.776260 - 1.34452i) q^{90} +12.3896 q^{91} -8.68035 q^{92} +(-3.44635 - 4.37295i) q^{93} -0.375245 q^{94} -2.04226 q^{95} +(2.63090 + 4.55685i) q^{96} -10.4186 q^{97} +(-0.0211302 + 0.0365986i) q^{98} +(1.90049 + 3.29175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 3 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 7 q^{13} - 10 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} + 5 q^{19} - 18 q^{20} - 4 q^{21} + 12 q^{22} + 24 q^{23} - 6 q^{24} - 17 q^{25} + 6 q^{26} + 6 q^{27} - 4 q^{28} + 8 q^{29} + 8 q^{30} - 16 q^{32} - 4 q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} + 3 q^{37} + 6 q^{38} + 14 q^{39} - 8 q^{40} + 4 q^{41} - 10 q^{42} + q^{43} - 2 q^{44} - 4 q^{45} - 32 q^{46} - 12 q^{47} + 4 q^{48} - 3 q^{49} - 6 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} - 16 q^{55} - 8 q^{56} + 5 q^{57} + 40 q^{58} + 16 q^{59} + 36 q^{60} + 20 q^{61} + 12 q^{62} + 8 q^{63} - 24 q^{64} + 6 q^{65} - 24 q^{66} - 24 q^{67} + 4 q^{68} - 12 q^{69} + 88 q^{70} - 20 q^{71} - 6 q^{72} - 3 q^{73} - 34 q^{74} - 17 q^{75} + 14 q^{76} - 60 q^{77} - 12 q^{78} + 4 q^{79} + 28 q^{80} - 3 q^{81} + 16 q^{83} - 4 q^{84} + 24 q^{85} + 14 q^{86} - 4 q^{87} + 4 q^{88} + 12 q^{89} - 4 q^{90} + 16 q^{91} - 8 q^{92} - 9 q^{93} - 80 q^{94} - 44 q^{95} + 8 q^{96} - 34 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 3 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 7 * q^13 - 10 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 + 5 * q^19 - 18 * q^20 - 4 * q^21 + 12 * q^22 + 24 * q^23 - 6 * q^24 - 17 * q^25 + 6 * q^26 + 6 * q^27 - 4 * q^28 + 8 * q^29 + 8 * q^30 - 16 * q^32 - 4 * q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 + 3 * q^37 + 6 * q^38 + 14 * q^39 - 8 * q^40 + 4 * q^41 - 10 * q^42 + q^43 - 2 * q^44 - 4 * q^45 - 32 * q^46 - 12 * q^47 + 4 * q^48 - 3 * q^49 - 6 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 - 16 * q^55 - 8 * q^56 + 5 * q^57 + 40 * q^58 + 16 * q^59 + 36 * q^60 + 20 * q^61 + 12 * q^62 + 8 * q^63 - 24 * q^64 + 6 * q^65 - 24 * q^66 - 24 * q^67 + 4 * q^68 - 12 * q^69 + 88 * q^70 - 20 * q^71 - 6 * q^72 - 3 * q^73 - 34 * q^74 - 17 * q^75 + 14 * q^76 - 60 * q^77 - 12 * q^78 + 4 * q^79 + 28 * q^80 - 3 * q^81 + 16 * q^83 - 4 * q^84 + 24 * q^85 + 14 * q^86 - 4 * q^87 + 4 * q^88 + 12 * q^89 - 4 * q^90 + 16 * q^91 - 8 * q^92 - 9 * q^93 - 80 * q^94 - 44 * q^95 + 8 * q^96 - 34 * q^97 - 16 * q^98 + 2 * q^99

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