LMFDB - Embedded newform 546.2.k.e.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$0.769836 + 1.33339i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.e.445.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.769836 + 1.33339i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.131875 - 2.64246i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.769836 + 1.33339i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.131875 - 2.64246i) q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.53967 q^{10} -6.38352 q^{11} +(0.500000 - 0.866025i) q^{12} +(0.520213 - 3.56783i) q^{13} +(2.22250 - 1.43544i) q^{14} +(0.769836 - 1.33339i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.19176 + 3.79624i) q^{17} +(0.500000 + 0.866025i) q^{18} +0.101912 q^{19} +(-0.769836 - 1.33339i) q^{20} +(0.131875 + 2.64246i) q^{21} +(-3.19176 - 5.52829i) q^{22} +(-4.54614 - 7.87414i) q^{23} +1.00000 q^{24} +(1.31471 + 2.27714i) q^{25} +(3.34993 - 1.33339i) q^{26} -1.00000 q^{27} +(2.35438 + 1.20702i) q^{28} +(3.51255 - 6.08392i) q^{29} +1.53967 q^{30} +(-0.611662 - 1.05943i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.38352 q^{33} -4.38352 q^{34} +(3.62497 + 1.85842i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.92192 - 3.32887i) q^{37} +(0.0509558 + 0.0882581i) q^{38} +(-0.520213 + 3.56783i) q^{39} +(0.769836 - 1.33339i) q^{40} +(-2.42192 + 4.19490i) q^{41} +(-2.22250 + 1.43544i) q^{42} +(-0.877054 - 1.51910i) q^{43} +(3.19176 - 5.52829i) q^{44} +(-0.769836 + 1.33339i) q^{45} +(4.54614 - 7.87414i) q^{46} +(-2.07041 + 3.58606i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.96522 + 0.696949i) q^{49} +(-1.31471 + 2.27714i) q^{50} +(2.19176 - 3.79624i) q^{51} +(2.82972 + 2.23443i) q^{52} +(-4.11084 - 7.12019i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.91426 - 8.51175i) q^{55} +(0.131875 + 2.64246i) q^{56} -0.101912 q^{57} +7.02510 q^{58} +(-3.56881 + 6.18137i) q^{59} +(0.769836 + 1.33339i) q^{60} -6.16908 q^{61} +(0.611662 - 1.05943i) q^{62} +(-0.131875 - 2.64246i) q^{63} +1.00000 q^{64} +(4.35684 + 3.44029i) q^{65} +(3.19176 + 5.52829i) q^{66} -1.71519 q^{67} +(-2.19176 - 3.79624i) q^{68} +(4.54614 + 7.87414i) q^{69} +(0.203044 + 4.06852i) q^{70} +(4.57326 + 7.92111i) q^{71} -1.00000 q^{72} +(4.82528 + 8.35763i) q^{73} +(1.92192 - 3.32887i) q^{74} +(-1.31471 - 2.27714i) q^{75} +(-0.0509558 + 0.0882581i) q^{76} +(0.841826 + 16.8682i) q^{77} +(-3.34993 + 1.33339i) q^{78} +(-2.03359 + 3.52227i) q^{79} +1.53967 q^{80} +1.00000 q^{81} -4.84385 q^{82} -7.02510 q^{83} +(-2.35438 - 1.20702i) q^{84} +(-3.37459 - 5.84496i) q^{85} +(0.877054 - 1.51910i) q^{86} +(-3.51255 + 6.08392i) q^{87} +6.38352 q^{88} +(7.77395 + 13.4649i) q^{89} -1.53967 q^{90} +(-9.49645 - 0.904138i) q^{91} +9.09227 q^{92} +(0.611662 + 1.05943i) q^{93} -4.14083 q^{94} +(-0.0784553 + 0.135889i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(0.996781 + 1.72648i) q^{97} +(-4.08618 - 5.68358i) q^{98} -6.38352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.769836	+	1.33339i	−0.344281	+	0.596312i	−0.985223	−	0.171277i	$-0.945211\pi$
$5$	−0.769836	+	1.33339i	−0.344281	+	0.596312i	0.640942	+	0.767589i	$0.278544\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.131875	−	2.64246i	−0.0498440	−	0.998757i
$7$	−0.131875	−	2.64246i	−0.0498440	−	0.998757i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	−1.53967			−0.486887
$11$	−6.38352			−1.92470			−0.962352	−	0.271807i	$-0.912379\pi$
$11$	−6.38352			−1.92470			−0.962352	+	0.271807i	$0.912379\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.520213	−	3.56783i	0.144281	−	0.989537i
$13$	0.520213	−	3.56783i	0.144281	−	0.989537i
$14$	2.22250	−	1.43544i	0.593989	−	0.383637i
$15$	0.769836	−	1.33339i	0.198771	−	0.344281i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.19176	+	3.79624i	−0.531580	+	0.920723i	0.467741	+	0.883866i	$0.345068\pi$
$17$	−2.19176	+	3.79624i	−0.531580	+	0.920723i	−0.999321	+	0.0368575i	$0.988265\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	0.101912			0.0233801			0.0116901	−	0.999932i	$-0.496279\pi$
$19$	0.101912			0.0233801			0.0116901	+	0.999932i	$0.496279\pi$
$20$	−0.769836	−	1.33339i	−0.172141	−	0.298156i
$21$	0.131875	+	2.64246i	0.0287775	+	0.576633i
$22$	−3.19176	−	5.52829i	−0.680485	−	1.17864i
$23$	−4.54614	−	7.87414i	−0.947935	−	1.64187i	−0.749765	−	0.661704i	$-0.769834\pi$
$23$	−4.54614	−	7.87414i	−0.947935	−	1.64187i	−0.198170	−	0.980168i	$-0.563500\pi$
$24$	1.00000			0.204124
$25$	1.31471	+	2.27714i	0.262941	+	0.455427i
$26$	3.34993	−	1.33339i	0.656976	−	0.261500i
$27$	−1.00000			−0.192450
$28$	2.35438	+	1.20702i	0.444935	+	0.228106i
$29$	3.51255	−	6.08392i	0.652264	−	1.12976i	−0.330308	−	0.943873i	$-0.607153\pi$
$29$	3.51255	−	6.08392i	0.652264	−	1.12976i	0.982572	−	0.185882i	$-0.0595142\pi$
$30$	1.53967			0.281104
$31$	−0.611662	−	1.05943i	−0.109858	−	0.190279i	0.805855	−	0.592113i	$-0.201706\pi$
$31$	−0.611662	−	1.05943i	−0.109858	−	0.190279i	−0.915712	+	0.401834i	$0.868373\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	6.38352			1.11123
$34$	−4.38352			−0.751767
$35$	3.62497	+	1.85842i	0.612731	+	0.314131i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.92192	−	3.32887i	−0.315962	−	0.547263i	0.663679	−	0.748017i	$-0.268994\pi$
$37$	−1.92192	−	3.32887i	−0.315962	−	0.547263i	−0.979642	+	0.200754i	$0.935661\pi$
$38$	0.0509558	+	0.0882581i	0.00826613	+	0.0143174i
$39$	−0.520213	+	3.56783i	−0.0833008	+	0.571309i
$40$	0.769836	−	1.33339i	0.121722	−	0.210828i
$41$	−2.42192	+	4.19490i	−0.378241	+	0.655133i	−0.990806	−	0.135287i	$-0.956804\pi$
$41$	−2.42192	+	4.19490i	−0.378241	+	0.655133i	0.612565	+	0.790420i	$0.290138\pi$
$42$	−2.22250	+	1.43544i	−0.342940	+	0.221493i
$43$	−0.877054	−	1.51910i	−0.133750	−	0.231661i	0.791370	−	0.611338i	$-0.209368\pi$
$43$	−0.877054	−	1.51910i	−0.133750	−	0.231661i	−0.925119	+	0.379677i	$0.876035\pi$
$44$	3.19176	−	5.52829i	0.481176	−	0.833421i
$45$	−0.769836	+	1.33339i	−0.114760	+	0.198771i
$46$	4.54614	−	7.87414i	0.670291	−	1.16098i
$47$	−2.07041	+	3.58606i	−0.302001	+	0.523081i	−0.976589	−	0.215113i	$-0.930988\pi$
$47$	−2.07041	+	3.58606i	−0.302001	+	0.523081i	0.674588	+	0.738194i	$0.264321\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.96522	+	0.696949i	−0.995031	+	0.0995641i
$50$	−1.31471	+	2.27714i	−0.185927	+	0.322036i
$51$	2.19176	−	3.79624i	0.306908	−	0.531580i
$52$	2.82972	+	2.23443i	0.392412	+	0.309860i
$53$	−4.11084	−	7.12019i	−0.564667	−	0.978033i	−0.997081	−	0.0763570i	$-0.975671\pi$
$53$	−4.11084	−	7.12019i	−0.564667	−	0.978033i	0.432413	−	0.901676i	$-0.357662\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	4.91426	−	8.51175i	0.662639	−	1.14772i
$56$	0.131875	+	2.64246i	0.0176225	+	0.353114i
$57$	−0.101912			−0.0134985
$58$	7.02510			0.922441
$59$	−3.56881	+	6.18137i	−0.464620	+	0.804745i	−0.999184	−	0.0403823i	$-0.987142\pi$
$59$	−3.56881	+	6.18137i	−0.464620	+	0.804745i	0.534564	+	0.845128i	$0.320476\pi$
$60$	0.769836	+	1.33339i	0.0993854	+	0.172141i
$61$	−6.16908			−0.789870			−0.394935	−	0.918709i	$-0.629233\pi$
$61$	−6.16908			−0.789870			−0.394935	+	0.918709i	$0.629233\pi$
$62$	0.611662	−	1.05943i	0.0776811	−	0.134548i
$63$	−0.131875	−	2.64246i	−0.0166147	−	0.332919i
$64$	1.00000			0.125000
$65$	4.35684	+	3.44029i	0.540400	+	0.426715i
$66$	3.19176	+	5.52829i	0.392878	+	0.680485i
$67$	−1.71519			−0.209544			−0.104772	−	0.994496i	$-0.533411\pi$
$67$	−1.71519			−0.209544			−0.104772	+	0.994496i	$0.533411\pi$
$68$	−2.19176	−	3.79624i	−0.265790	−	0.460362i
$69$	4.54614	+	7.87414i	0.547291	+	0.947935i
$70$	0.203044	+	4.06852i	0.0242684	+	0.486282i
$71$	4.57326	+	7.92111i	0.542746	+	0.940063i	0.998745	+	0.0500831i	$0.0159486\pi$
$71$	4.57326	+	7.92111i	0.542746	+	0.940063i	−0.455999	+	0.889980i	$0.650718\pi$
$72$	−1.00000			−0.117851
$73$	4.82528	+	8.35763i	0.564756	+	0.978186i	0.997072	+	0.0764641i	$0.0243631\pi$
$73$	4.82528	+	8.35763i	0.564756	+	0.978186i	−0.432316	+	0.901722i	$0.642304\pi$
$74$	1.92192	−	3.32887i	0.223419	−	0.386973i
$75$	−1.31471	−	2.27714i	−0.151809	−	0.262941i
$76$	−0.0509558	+	0.0882581i	−0.00584504	+	0.0101239i
$77$	0.841826	+	16.8682i	0.0959349	+	1.92231i
$78$	−3.34993	+	1.33339i	−0.379305	+	0.150977i
$79$	−2.03359	+	3.52227i	−0.228796	+	0.396287i	−0.957452	−	0.288594i	$-0.906812\pi$
$79$	−2.03359	+	3.52227i	−0.228796	+	0.396287i	0.728655	+	0.684881i	$0.240146\pi$
$80$	1.53967			0.172141
$81$	1.00000			0.111111
$82$	−4.84385			−0.534914
$83$	−7.02510			−0.771105			−0.385553	−	0.922686i	$-0.625989\pi$
$83$	−7.02510			−0.771105			−0.385553	+	0.922686i	$0.625989\pi$
$84$	−2.35438	−	1.20702i	−0.256884	−	0.131697i
$85$	−3.37459	−	5.84496i	−0.366026	−	0.633975i
$86$	0.877054	−	1.51910i	0.0945752	−	0.163809i
$87$	−3.51255	+	6.08392i	−0.376585	+	0.652264i
$88$	6.38352			0.680485
$89$	7.77395	+	13.4649i	0.824037	+	1.42727i	0.902653	+	0.430368i	$0.141616\pi$
$89$	7.77395	+	13.4649i	0.824037	+	1.42727i	−0.0786167	+	0.996905i	$0.525050\pi$
$90$	−1.53967			−0.162296
$91$	−9.49645	−	0.904138i	−0.995498	−	0.0947794i
$92$	9.09227			0.947935
$93$	0.611662	+	1.05943i	0.0634264	+	0.109858i
$94$	−4.14083			−0.427094
$95$	−0.0784553	+	0.135889i	−0.00804934	+	0.0139419i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	0.996781	+	1.72648i	0.101208	+	0.175297i	0.912183	−	0.409784i	$-0.134396\pi$
$97$	0.996781	+	1.72648i	0.101208	+	0.175297i	−0.810975	+	0.585081i	$0.801063\pi$
$98$	−4.08618	−	5.68358i	−0.412767	−	0.574128i
$99$	−6.38352			−0.641568
$100$	−2.62941			−0.262941
$101$	−0.741985			−0.0738303			−0.0369151	−	0.999318i	$-0.511753\pi$
$101$	−0.741985			−0.0738303			−0.0369151	+	0.999318i	$0.511753\pi$
$102$	4.38352			0.434033
$103$	2.87705	−	4.98320i	0.283485	−	0.491010i	−0.688756	−	0.724993i	$-0.741843\pi$
$103$	2.87705	−	4.98320i	0.283485	−	0.491010i	0.972241	+	0.233984i	$0.0751762\pi$
$104$	−0.520213	+	3.56783i	−0.0510111	+	0.349854i
$105$	−3.62497	−	1.85842i	−0.353761	−	0.181363i
$106$	4.11084	−	7.12019i	0.399280	−	0.691574i
$107$	1.43530	+	2.48601i	0.138755	+	0.240331i	0.927026	−	0.374998i	$-0.122357\pi$
$107$	1.43530	+	2.48601i	0.138755	+	0.240331i	−0.788270	+	0.615329i	$0.789023\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−4.52510	−	7.83771i	−0.433426	−	0.750716i	0.563739	−	0.825953i	$-0.309362\pi$
$109$	−4.52510	−	7.83771i	−0.433426	−	0.750716i	−0.997166	+	0.0752364i	$0.976029\pi$
$110$	9.82852			0.937113
$111$	1.92192	+	3.32887i	0.182421	+	0.315962i
$112$	−2.22250	+	1.43544i	−0.210007	+	0.135636i
$113$	−0.302154	−	0.523346i	−0.0284243	−	0.0492323i	0.851463	−	0.524414i	$-0.175716\pi$
$113$	−0.302154	−	0.523346i	−0.0284243	−	0.0492323i	−0.879888	+	0.475182i	$0.842382\pi$
$114$	−0.0509558	−	0.0882581i	−0.00477245	−	0.00826613i
$115$	13.9991			1.30542
$116$	3.51255	+	6.08392i	0.326132	+	0.564878i
$117$	0.520213	−	3.56783i	0.0480937	−	0.329846i
$118$	−7.13763			−0.657072
$119$	10.3205	+	5.29102i	0.946075	+	0.485027i
$120$	−0.769836	+	1.33339i	−0.0702761	+	0.121722i
$121$	29.7493			2.70448
$122$	−3.08454	−	5.34258i	−0.279261	−	0.483695i
$123$	2.42192	−	4.19490i	0.218378	−	0.378241i
$124$	1.22332			0.109858
$125$	−11.7468			−1.05066
$126$	2.22250	−	1.43544i	0.197996	−	0.127879i
$127$	−3.18892	+	5.52337i	−0.282971	+	0.490119i	−0.972115	−	0.234505i	$-0.924653\pi$
$127$	−3.18892	+	5.52337i	−0.282971	+	0.490119i	0.689144	+	0.724624i	$0.257987\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.877054	+	1.51910i	0.0772203	+	0.133750i
$130$	−0.800958	+	5.49328i	−0.0702486	+	0.481793i
$131$	5.42681	−	9.39952i	0.474143	−	0.821240i	−0.525419	−	0.850844i	$-0.676091\pi$
$131$	5.42681	−	9.39952i	0.474143	−	0.821240i	0.999562	+	0.0296041i	$0.00942467\pi$
$132$	−3.19176	+	5.52829i	−0.277807	+	0.481176i
$133$	−0.0134396	−	0.269298i	−0.00116536	−	0.0233511i
$134$	−0.857596	−	1.48540i	−0.0740850	−	0.128319i
$135$	0.769836	−	1.33339i	0.0662569	−	0.114760i
$136$	2.19176	−	3.79624i	0.187942	−	0.325525i
$137$	3.97052	−	6.87715i	0.339225	−	0.587555i	−0.645062	−	0.764130i	$-0.723169\pi$
$137$	3.97052	−	6.87715i	0.339225	−	0.587555i	0.984287	+	0.176575i	$0.0565019\pi$
$138$	−4.54614	+	7.87414i	−0.386993	+	0.670291i
$139$	−5.72452	−	9.91517i	−0.485548	−	0.840994i	0.514314	−	0.857602i	$-0.328047\pi$
$139$	−5.72452	−	9.91517i	−0.485548	−	0.840994i	−0.999862	+	0.0166083i	$0.994713\pi$
$140$	−3.42192	+	2.21010i	−0.289205	+	0.186788i
$141$	2.07041	−	3.58606i	0.174360	−	0.302001i
$142$	−4.57326	+	7.92111i	−0.383779	+	0.664725i
$143$	−3.32079	+	22.7753i	−0.277699	+	1.90456i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.40818	+	9.36724i	0.449125	+	0.777907i
$146$	−4.82528	+	8.35763i	−0.399343	+	0.691682i
$147$	6.96522	−	0.696949i	0.574482	−	0.0574834i
$148$	3.84385			0.315962
$149$	−21.2136			−1.73788			−0.868941	−	0.494916i	$-0.835199\pi$
$149$	−21.2136			−1.73788			−0.868941	+	0.494916i	$0.835199\pi$
$150$	1.31471	−	2.27714i	0.107345	−	0.185927i
$151$	−8.72661	−	15.1149i	−0.710162	−	1.23004i	−0.964796	−	0.262999i	$-0.915288\pi$
$151$	−8.72661	−	15.1149i	−0.710162	−	1.23004i	0.254635	−	0.967037i	$-0.418045\pi$
$152$	−0.101912			−0.00826613
$153$	−2.19176	+	3.79624i	−0.177193	+	0.306908i
$154$	−14.1874	+	9.16315i	−1.14325	+	0.738388i
$155$	1.88352			0.151288
$156$	−2.82972	−	2.23443i	−0.226559	−	0.178898i
$157$	10.6720	+	18.4844i	0.851718	+	1.47522i	0.879657	+	0.475609i	$0.157772\pi$
$157$	10.6720	+	18.4844i	0.851718	+	1.47522i	−0.0279391	+	0.999610i	$0.508894\pi$
$158$	−4.06717			−0.323567
$159$	4.11084	+	7.12019i	0.326011	+	0.564667i
$160$	0.769836	+	1.33339i	0.0608609	+	0.105414i
$161$	−20.2076	+	13.0514i	−1.59258	+	1.02859i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−16.7477			−1.31178			−0.655889	−	0.754857i	$-0.727706\pi$
$163$	−16.7477			−1.31178			−0.655889	+	0.754857i	$0.727706\pi$
$164$	−2.42192	−	4.19490i	−0.189120	−	0.327566i
$165$	−4.91426	+	8.51175i	−0.382575	+	0.662639i
$166$	−3.51255	−	6.08392i	−0.272627	−	0.472204i
$167$	12.4467	−	21.5582i	0.963151	−	1.66823i	0.248648	−	0.968594i	$-0.420014\pi$
$167$	12.4467	−	21.5582i	0.963151	−	1.66823i	0.714503	−	0.699632i	$-0.246653\pi$
$168$	−0.131875	−	2.64246i	−0.0101744	−	0.203870i
$169$	−12.4588	−	3.71206i	−0.958366	−	0.285543i
$170$	3.37459	−	5.84496i	0.258819	−	0.448288i
$171$	0.101912			0.00779338
$172$	1.75411			0.133750
$173$	18.8998			1.43692			0.718462	−	0.695566i	$-0.244846\pi$
$173$	18.8998			1.43692			0.718462	+	0.695566i	$0.244846\pi$
$174$	−7.02510			−0.532572
$175$	5.84387	−	3.77436i	0.441755	−	0.285315i
$176$	3.19176	+	5.52829i	0.240588	+	0.416711i
$177$	3.56881	−	6.18137i	0.268248	−	0.464620i
$178$	−7.77395	+	13.4649i	−0.582682	+	1.00923i
$179$	−1.58583			−0.118531			−0.0592654	−	0.998242i	$-0.518876\pi$
$179$	−1.58583			−0.118531			−0.0592654	+	0.998242i	$0.518876\pi$
$180$	−0.769836	−	1.33339i	−0.0573802	−	0.0993854i
$181$	−13.1480			−0.977285			−0.488642	−	0.872484i	$-0.662508\pi$
$181$	−13.1480			−0.977285			−0.488642	+	0.872484i	$0.662508\pi$
$182$	−3.96522	−	8.67623i	−0.293922	−	0.643125i
$183$	6.16908			0.456032
$184$	4.54614	+	7.87414i	0.335146	+	0.580489i
$185$	5.91826			0.435119
$186$	−0.611662	+	1.05943i	−0.0448492	+	0.0776811i
$187$	13.9911	−	24.2334i	1.02313	−	1.77212i
$188$	−2.07041	−	3.58606i	−0.151000	−	0.261541i
$189$	0.131875	+	2.64246i	0.00959248	+	0.192211i
$190$	−0.156911			−0.0113835
$191$	12.7038			0.919217			0.459608	−	0.888122i	$-0.347990\pi$
$191$	12.7038			0.919217			0.459608	+	0.888122i	$0.347990\pi$
$192$	−1.00000			−0.0721688
$193$	−8.18276			−0.589008			−0.294504	−	0.955650i	$-0.595154\pi$
$193$	−8.18276			−0.589008			−0.294504	+	0.955650i	$0.595154\pi$
$194$	−0.996781	+	1.72648i	−0.0715647	+	0.123954i
$195$	−4.35684	−	3.44029i	−0.312000	−	0.246364i
$196$	2.87903	−	6.38053i	0.205645	−	0.455752i
$197$	−2.09350	+	3.62604i	−0.149155	+	0.258345i	−0.930916	−	0.365235i	$-0.880989\pi$
$197$	−2.09350	+	3.62604i	−0.149155	+	0.258345i	0.781760	+	0.623579i	$0.214322\pi$
$198$	−3.19176	−	5.52829i	−0.226828	−	0.392878i
$199$	−1.95797	+	3.39131i	−0.138797	+	0.240404i	−0.927042	−	0.374959i	$-0.877657\pi$
$199$	−1.95797	+	3.39131i	−0.138797	+	0.240404i	0.788244	+	0.615362i	$0.210990\pi$
$200$	−1.31471	−	2.27714i	−0.0929637	−	0.161018i
$201$	1.71519			0.120980
$202$	−0.370993	−	0.642578i	−0.0261030	−	0.0452116i
$203$	−16.5397	−	8.47947i	−1.16086	−	0.595142i
$204$	2.19176	+	3.79624i	0.153454	+	0.265790i
$205$	−3.72897	−	6.45876i	−0.260442	−	0.451099i
$206$	5.75411			0.400908
$207$	−4.54614	−	7.87414i	−0.315978	−	0.547291i
$208$	−3.34993	+	1.33339i	−0.232276	+	0.0924543i
$209$	−0.650555			−0.0449998
$210$	−0.203044	−	4.06852i	−0.0140114	−	0.280755i
$211$	7.24076	−	12.5414i	0.498475	−	0.863384i	−0.501524	−	0.865144i	$-0.667227\pi$
$211$	7.24076	−	12.5414i	0.498475	−	0.863384i	0.999998	+	0.00176028i	$0.000560315\pi$
$212$	8.22168			0.564667
$213$	−4.57326	−	7.92111i	−0.313354	−	0.542746i
$214$	−1.43530	+	2.48601i	−0.0981148	+	0.169940i
$215$	2.70075			0.184190
$216$	1.00000			0.0680414
$217$	−2.71884	+	1.75600i	−0.184567	+	0.119205i
$218$	4.52510	−	7.83771i	0.306479	−	0.530837i
$219$	−4.82528	−	8.35763i	−0.326062	−	0.564756i
$220$	4.91426	+	8.51175i	0.331319	+	0.573862i
$221$	12.4041	+	9.79467i	0.834393	+	0.658861i
$222$	−1.92192	+	3.32887i	−0.128991	+	0.223419i
$223$	5.98916	−	10.3735i	0.401064	−	0.694663i	−0.592791	−	0.805357i	$-0.701974\pi$
$223$	5.98916	−	10.3735i	0.401064	−	0.694663i	0.993855	+	0.110693i	$0.0353072\pi$
$224$	−2.35438	−	1.20702i	−0.157308	−	0.0806477i
$225$	1.31471	+	2.27714i	0.0876470	+	0.151809i
$226$	0.302154	−	0.523346i	0.0200990	−	0.0348125i
$227$	2.14976	−	3.72349i	0.142684	−	0.247137i	−0.785822	−	0.618452i	$-0.787760\pi$
$227$	2.14976	−	3.72349i	0.142684	−	0.247137i	0.928507	+	0.371316i	$0.121093\pi$
$228$	0.0509558	−	0.0882581i	0.00337463	−	0.00584504i
$229$	−11.1486	+	19.3099i	−0.736718	+	1.27603i	0.217248	+	0.976116i	$0.430292\pi$
$229$	−11.1486	+	19.3099i	−0.736718	+	1.27603i	−0.953966	+	0.299916i	$0.903041\pi$
$230$	6.99956	+	12.1236i	0.461537	+	0.799406i
$231$	−0.841826	−	16.8682i	−0.0553881	−	1.10985i
$232$	−3.51255	+	6.08392i	−0.230610	+	0.399429i
$233$	−1.90691	+	3.30286i	−0.124926	+	0.216378i	−0.921704	−	0.387894i	$-0.873203\pi$
$233$	−1.90691	+	3.30286i	−0.124926	+	0.216378i	0.796778	+	0.604272i	$0.206536\pi$
$234$	3.34993	−	1.33339i	0.218992	−	0.0871667i
$235$	−3.18776	−	5.52136i	−0.207946	−	0.360174i
$236$	−3.56881	−	6.18137i	−0.232310	−	0.402373i
$237$	2.03359	−	3.52227i	0.132096	−	0.228796i
$238$	0.578076	+	11.5833i	0.0374711	+	0.750833i
$239$	12.9555			0.838021			0.419010	−	0.907981i	$-0.362377\pi$
$239$	12.9555			0.838021			0.419010	+	0.907981i	$0.362377\pi$
$240$	−1.53967			−0.0993854
$241$	−0.486277	+	0.842256i	−0.0313238	+	0.0542545i	−0.881262	−	0.472627i	$-0.843306\pi$
$241$	−0.486277	+	0.842256i	−0.0313238	+	0.0542545i	0.849939	+	0.526882i	$0.176639\pi$
$242$	14.8747	+	25.7637i	0.956179	+	1.65615i
$243$	−1.00000			−0.0641500
$244$	3.08454	−	5.34258i	0.197468	−	0.342024i
$245$	4.43277	−	9.82392i	0.283199	−	0.627627i
$246$	4.84385			0.308832
$247$	0.0530158	−	0.363603i	0.00337332	−	0.0231355i
$248$	0.611662	+	1.05943i	0.0388405	+	0.0672738i
$249$	7.02510			0.445198
$250$	−5.87339	−	10.1730i	−0.371466	−	0.643398i
$251$	4.83297	+	8.37095i	0.305054	+	0.528369i	0.977273	−	0.211983i	$-0.0679921\pi$
$251$	4.83297	+	8.37095i	0.305054	+	0.528369i	−0.672219	+	0.740352i	$0.734659\pi$
$252$	2.35438	+	1.20702i	0.148312	+	0.0760354i
$253$	29.0204	+	50.2647i	1.82449	+	3.16012i
$254$	−6.37783			−0.400181
$255$	3.37459	+	5.84496i	0.211325	+	0.366026i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.5595	−	23.4858i	−0.845819	−	1.46500i	−0.884908	−	0.465766i	$-0.845779\pi$
$257$	−13.5595	−	23.4858i	−0.845819	−	1.46500i	0.0390891	−	0.999236i	$-0.487554\pi$
$258$	−0.877054	+	1.51910i	−0.0546030	+	0.0945752i
$259$	−8.54296	+	5.51761i	−0.530834	+	0.342847i
$260$	−5.15780	+	2.05299i	−0.319873	+	0.127321i
$261$	3.51255	−	6.08392i	0.217421	−	0.376585i
$262$	10.8536			0.670539
$263$	4.72830			0.291560			0.145780	−	0.989317i	$-0.453431\pi$
$263$	4.72830			0.291560			0.145780	+	0.989317i	$0.453431\pi$
$264$	−6.38352			−0.392878
$265$	12.6587			0.777617
$266$	0.226499	−	0.146288i	0.0138875	−	0.00896949i
$267$	−7.77395	−	13.4649i	−0.475758	−	0.824037i
$268$	0.857596	−	1.48540i	0.0523860	−	0.0907352i
$269$	13.3480	−	23.1194i	0.813841	−	1.40961i	−0.0963164	−	0.995351i	$-0.530706\pi$
$269$	13.3480	−	23.1194i	0.813841	−	1.40961i	0.910157	−	0.414263i	$-0.135961\pi$
$270$	1.53967			0.0937014
$271$	−2.40455	−	4.16481i	−0.146066	−	0.252994i	0.783704	−	0.621134i	$-0.213328\pi$
$271$	−2.40455	−	4.16481i	−0.146066	−	0.252994i	−0.929770	+	0.368140i	$0.879995\pi$
$272$	4.38352			0.265790
$273$	9.49645	+	0.904138i	0.574751	+	0.0547209i
$274$	7.94105			0.479736
$275$	−8.39245	−	14.5361i	−0.506084	−	0.876563i
$276$	−9.09227			−0.547291
$277$	12.6133	−	21.8469i	0.757862	−	1.31265i	−0.186077	−	0.982535i	$-0.559577\pi$
$277$	12.6133	−	21.8469i	0.757862	−	1.31265i	0.943939	−	0.330120i	$-0.107089\pi$
$278$	5.72452	−	9.91517i	0.343334	−	0.594672i
$279$	−0.611662	−	1.05943i	−0.0366192	−	0.0634264i
$280$	−3.62497	−	1.85842i	−0.216633	−	0.111062i
$281$	−3.38912			−0.202178			−0.101089	−	0.994877i	$-0.532233\pi$
$281$	−3.38912			−0.202178			−0.101089	+	0.994877i	$0.532233\pi$
$282$	4.14083			0.246583
$283$	−10.5072			−0.624591			−0.312296	−	0.949985i	$-0.601098\pi$
$283$	−10.5072			−0.624591			−0.312296	+	0.949985i	$0.601098\pi$
$284$	−9.14651			−0.542746
$285$	0.0784553	−	0.135889i	0.00464729	−	0.00804934i
$286$	−21.3844	+	8.51175i	−1.26448	+	0.503310i
$287$	11.4042	+	5.84664i	0.673171	+	0.345116i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−1.10762	−	1.91846i	−0.0651542	−	0.112850i
$290$	−5.40818	+	9.36724i	−0.317579	+	0.550063i
$291$	−0.996781	−	1.72648i	−0.0584324	−	0.101208i
$292$	−9.65056			−0.564756
$293$	−6.47179	−	11.2095i	−0.378086	−	0.654864i	0.612698	−	0.790317i	$-0.290084\pi$
$293$	−6.47179	−	11.2095i	−0.378086	−	0.654864i	−0.990784	+	0.135453i	$0.956751\pi$
$294$	4.08618	+	5.68358i	0.238311	+	0.331473i
$295$	−5.49480	−	9.51728i	−0.319920	−	0.554117i
$296$	1.92192	+	3.32887i	0.111710	+	0.193487i
$297$	6.38352			0.370409
$298$	−10.6068	−	18.3715i	−0.614434	−	1.06423i
$299$	−30.4585	+	12.1236i	−1.76146	+	0.701125i
$300$	2.62941			0.151809
$301$	−3.89851	+	2.51791i	−0.224706	+	0.145130i
$302$	8.72661	−	15.1149i	0.502160	−	0.869767i
$303$	0.741985			0.0426259
$304$	−0.0509558	−	0.0882581i	−0.00292252	−	0.00506195i
$305$	4.74918	−	8.22582i	0.271937	−	0.471009i
$306$	−4.38352			−0.250589
$307$	28.9573			1.65268			0.826339	−	0.563173i	$-0.190419\pi$
$307$	28.9573			1.65268			0.826339	+	0.563173i	$0.190419\pi$
$308$	−15.0292	−	7.70506i	−0.856369	−	0.439037i
$309$	−2.87705	+	4.98320i	−0.163670	+	0.283485i
$310$	0.941758	+	1.63117i	0.0534883	+	0.0926444i
$311$	−15.8321	−	27.4220i	−0.897757	−	1.55496i	−0.830355	−	0.557235i	$-0.811862\pi$
$311$	−15.8321	−	27.4220i	−0.897757	−	1.55496i	−0.0674027	−	0.997726i	$-0.521471\pi$
$312$	0.520213	−	3.56783i	0.0294513	−	0.201988i
$313$	1.35811	−	2.35231i	0.0767648	−	0.132961i	−0.825088	−	0.565005i	$-0.808874\pi$
$313$	1.35811	−	2.35231i	0.0767648	−	0.132961i	0.901852	+	0.432044i	$0.142208\pi$
$314$	−10.6720	+	18.4844i	−0.602255	+	1.04314i
$315$	3.62497	+	1.85842i	0.204244	+	0.104710i
$316$	−2.03359	−	3.52227i	−0.114398	−	0.198143i
$317$	15.3346	−	26.5603i	0.861278	−	1.49178i	−0.00941891	−	0.999956i	$-0.502998\pi$
$317$	15.3346	−	26.5603i	0.861278	−	1.49178i	0.870696	−	0.491821i	$-0.163668\pi$
$318$	−4.11084	+	7.12019i	−0.230525	+	0.399280i
$319$	−22.4224	+	38.8368i	−1.25542	+	2.17444i
$320$	−0.769836	+	1.33339i	−0.0430351	+	0.0745390i
$321$	−1.43530	−	2.48601i	−0.0801104	−	0.138755i
$322$	−21.4066	−	10.9746i	−1.19295	−	0.611590i
$323$	−0.223366	+	0.386881i	−0.0124284	+	0.0215266i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	8.80835	−	3.50604i	0.488600	−	0.194480i
$326$	−8.37384	−	14.5039i	−0.463784	−	0.803297i
$327$	4.52510	+	7.83771i	0.250239	+	0.433426i
$328$	2.42192	−	4.19490i	0.133728	−	0.231624i
$329$	9.74907	+	4.99808i	0.537484	+	0.275553i
$330$	−9.82852			−0.541042
$331$	20.0753			1.10344			0.551719	−	0.834030i	$-0.313972\pi$
$331$	20.0753			1.10344			0.551719	+	0.834030i	$0.313972\pi$
$332$	3.51255	−	6.08392i	0.192776	−	0.333898i
$333$	−1.92192	−	3.32887i	−0.105321	−	0.182421i
$334$	24.8933			1.36210
$335$	1.32042	−	2.28703i	0.0721420	−	0.124954i
$336$	2.22250	−	1.43544i	0.121247	−	0.0783096i
$337$	29.0567			1.58282			0.791408	−	0.611288i	$-0.209348\pi$
$337$	29.0567			1.58282			0.791408	+	0.611288i	$0.209348\pi$
$338$	−3.01464	−	12.6456i	−0.163975	−	0.687832i
$339$	0.302154	+	0.523346i	0.0164108	+	0.0284243i
$340$	6.74918			0.366026
$341$	3.90455	+	6.76289i	0.211443	+	0.366231i
$342$	0.0509558	+	0.0882581i	0.00275538	+	0.00477245i
$343$	2.76020	+	18.3134i	0.149037	+	0.988832i
$344$	0.877054	+	1.51910i	0.0472876	+	0.0819045i
$345$	−13.9991			−0.753687
$346$	9.44989	+	16.3677i	0.508029	+	0.879933i
$347$	4.65985	−	8.07109i	0.250154	−	0.433279i	−0.713414	−	0.700742i	$-0.752852\pi$
$347$	4.65985	−	8.07109i	0.250154	−	0.433279i	0.963568	+	0.267464i	$0.0861855\pi$
$348$	−3.51255	−	6.08392i	−0.188293	−	0.326132i
$349$	−12.0769	+	20.9178i	−0.646461	+	1.11970i	0.337501	+	0.941325i	$0.390418\pi$
$349$	−12.0769	+	20.9178i	−0.646461	+	1.11970i	−0.983962	+	0.178378i	$0.942915\pi$
$350$	6.19063	+	3.17376i	0.330903	+	0.169645i
$351$	−0.520213	+	3.56783i	−0.0277669	+	0.190436i
$352$	−3.19176	+	5.52829i	−0.170121	+	0.294659i
$353$	−5.17326			−0.275345			−0.137672	−	0.990478i	$-0.543962\pi$
$353$	−5.17326			−0.275345			−0.137672	+	0.990478i	$0.543962\pi$
$354$	7.13763			0.379361
$355$	−14.0826			−0.747428
$356$	−15.5479			−0.824037
$357$	−10.3205	−	5.29102i	−0.546217	−	0.280030i
$358$	−0.792917	−	1.37337i	−0.0419069	−	0.0725850i
$359$	−16.7226	+	28.9643i	−0.882584	+	1.52868i	−0.0341253	+	0.999418i	$0.510865\pi$
$359$	−16.7226	+	28.9643i	−0.882584	+	1.52868i	−0.848458	+	0.529262i	$0.822469\pi$
$360$	0.769836	−	1.33339i	0.0405739	−	0.0702761i
$361$	−18.9896			−0.999453
$362$	−6.57401	−	11.3865i	−0.345522	−	0.598462i
$363$	−29.7493			−1.56143
$364$	5.53123	−	7.77210i	0.289915	−	0.407369i
$365$	−14.8587			−0.777739
$366$	3.08454	+	5.34258i	0.161232	+	0.279261i
$367$	−7.96108			−0.415565			−0.207783	−	0.978175i	$-0.566625\pi$
$367$	−7.96108			−0.415565			−0.207783	+	0.978175i	$0.566625\pi$
$368$	−4.54614	+	7.87414i	−0.236984	+	0.410468i
$369$	−2.42192	+	4.19490i	−0.126080	+	0.218378i
$370$	2.95913	+	5.12537i	0.153838	+	0.266455i
$371$	−18.2727	+	11.8017i	−0.948672	+	0.612715i
$372$	−1.22332			−0.0634264
$373$	35.5973			1.84316			0.921579	−	0.388191i	$-0.126900\pi$
$373$	35.5973			1.84316			0.921579	+	0.388191i	$0.126900\pi$
$374$	27.9823			1.44693
$375$	11.7468			0.606602
$376$	2.07041	−	3.58606i	0.106773	−	0.184937i
$377$	−19.8791	−	15.6971i	−1.02382	−	0.808442i
$378$	−2.22250	+	1.43544i	−0.114313	+	0.0738310i
$379$	2.29603	−	3.97683i	0.117939	−	0.204276i	−0.801012	−	0.598649i	$-0.795705\pi$
$379$	2.29603	−	3.97683i	0.117939	−	0.204276i	0.918951	+	0.394372i	$0.129038\pi$
$380$	−0.0784553	−	0.135889i	−0.00402467	−	0.00697093i
$381$	3.18892	−	5.52337i	0.163373	−	0.282971i
$382$	6.35191	+	11.0018i	0.324992	+	0.562903i
$383$	10.4181			0.532341			0.266171	−	0.963926i	$-0.414242\pi$
$383$	10.4181			0.532341			0.266171	+	0.963926i	$0.414242\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−23.1401	−	11.8633i	−1.17933	−	0.604608i
$386$	−4.09138	−	7.08648i	−0.208246	−	0.360692i
$387$	−0.877054	−	1.51910i	−0.0445832	−	0.0772203i
$388$	−1.99356			−0.101208
$389$	−6.19665	−	10.7329i	−0.314183	−	0.544180i	0.665081	−	0.746771i	$-0.268397\pi$
$389$	−6.19665	−	10.7329i	−0.314183	−	0.544180i	−0.979263	+	0.202591i	$0.935064\pi$
$390$	0.800958	−	5.49328i	0.0405581	−	0.278163i
$391$	39.8562			2.01561
$392$	6.96522	−	0.696949i	0.351797	−	0.0352012i
$393$	−5.42681	+	9.39952i	−0.273747	+	0.474143i
$394$	−4.18699			−0.210938
$395$	−3.13105	−	5.42314i	−0.157540	−	0.272868i
$396$	3.19176	−	5.52829i	0.160392	−	0.277807i
$397$	0.824424			0.0413766			0.0206883	−	0.999786i	$-0.493414\pi$
$397$	0.824424			0.0413766			0.0206883	+	0.999786i	$0.493414\pi$
$398$	−3.91595			−0.196289
$399$	0.0134396	+	0.269298i	0.000672821	+	0.0134818i
$400$	1.31471	−	2.27714i	0.0657353	−	0.113857i
$401$	−13.4698	−	23.3303i	−0.672648	−	1.16506i	−0.977150	−	0.212550i	$-0.931823\pi$
$401$	−13.4698	−	23.3303i	−0.672648	−	1.16506i	0.304502	−	0.952512i	$-0.401510\pi$
$402$	0.857596	+	1.48540i	0.0427730	+	0.0740850i
$403$	−4.09805	+	1.63117i	−0.204139	+	0.0812545i
$404$	0.370993	−	0.642578i	0.0184576	−	0.0319695i
$405$	−0.769836	+	1.33339i	−0.0382535	+	0.0662569i
$406$	−0.926434	−	18.5636i	−0.0459782	−	0.921295i
$407$	12.2686	+	21.2499i	0.608134	+	1.05332i
$408$	−2.19176	+	3.79624i	−0.108508	+	0.187942i
$409$	5.57528	−	9.65666i	0.275680	−	0.477491i	−0.694627	−	0.719370i	$-0.744430\pi$
$409$	5.57528	−	9.65666i	0.275680	−	0.477491i	0.970306	+	0.241879i	$0.0777638\pi$
$410$	3.72897	−	6.45876i	0.184161	−	0.318976i
$411$	−3.97052	+	6.87715i	−0.195852	+	0.339225i
$412$	2.87705	+	4.98320i	0.141742	+	0.245505i
$413$	16.8047	+	8.61529i	0.826904	+	0.423931i
$414$	4.54614	−	7.87414i	0.223430	−	0.386993i
$415$	5.40818	−	9.36724i	0.265477	−	0.459820i
$416$	−2.82972	−	2.23443i	−0.138738	−	0.109552i
$417$	5.72452	+	9.91517i	0.280331	+	0.485548i
$418$	−0.325278	−	0.563397i	−0.0159098	−	0.0275567i
$419$	−13.2788	+	22.9995i	−0.648710	+	1.12360i	0.334721	+	0.942317i	$0.391358\pi$
$419$	−13.2788	+	22.9995i	−0.648710	+	1.12360i	−0.983431	+	0.181282i	$0.941975\pi$
$420$	3.42192	−	2.21010i	0.166973	−	0.107842i
$421$	−13.7766			−0.671432			−0.335716	−	0.941963i	$-0.608978\pi$
$421$	−13.7766			−0.671432			−0.335716	+	0.941963i	$0.608978\pi$
$422$	14.4815			0.704950
$423$	−2.07041	+	3.58606i	−0.100667	+	0.174360i
$424$	4.11084	+	7.12019i	0.199640	+	0.345787i
$425$	−11.5261			−0.559097
$426$	4.57326	−	7.92111i	0.221575	−	0.383779i
$427$	0.813547	+	16.3016i	0.0393703	+	0.788888i
$428$	−2.87059			−0.138755
$429$	3.32079	−	22.7753i	0.160329	−	1.09960i
$430$	1.35038	+	2.33892i	0.0651209	+	0.112793i
$431$	−10.7549			−0.518046			−0.259023	−	0.965871i	$-0.583401\pi$
$431$	−10.7549			−0.518046			−0.259023	+	0.965871i	$0.583401\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−16.7913	−	29.0833i	−0.806937	−	1.39766i	−0.914975	−	0.403509i	$-0.867790\pi$
$433$	−16.7913	−	29.0833i	−0.806937	−	1.39766i	0.108038	−	0.994147i	$-0.465543\pi$
$434$	−2.88016	−	1.47658i	−0.138252	−	0.0708781i
$435$	−5.40818	−	9.36724i	−0.259302	−	0.449125i
$436$	9.05021			0.433426
$437$	−0.463305	−	0.802467i	−0.0221629	−	0.0383872i
$438$	4.82528	−	8.35763i	0.230561	−	0.399343i
$439$	0.605618	+	1.04896i	0.0289046	+	0.0500642i	0.880116	−	0.474759i	$-0.157465\pi$
$439$	0.605618	+	1.04896i	0.0289046	+	0.0500642i	−0.851211	+	0.524823i	$0.824131\pi$
$440$	−4.91426	+	8.51175i	−0.234278	+	0.405782i
$441$	−6.96522	+	0.696949i	−0.331677	+	0.0331880i
$442$	−2.28037	+	15.6396i	−0.108466	+	0.743901i
$443$	−4.92357	+	8.52787i	−0.233926	+	0.405171i	−0.958960	−	0.283542i	$-0.908491\pi$
$443$	−4.92357	+	8.52787i	−0.233926	+	0.405171i	0.725034	+	0.688713i	$0.241824\pi$
$444$	−3.84385			−0.182421
$445$	−23.9386			−1.13480
$446$	11.9783			0.567190
$447$	21.2136			1.00337
$448$	−0.131875	−	2.64246i	−0.00623050	−	0.124845i
$449$	17.5968	+	30.4786i	0.830446	+	1.43837i	0.897685	+	0.440637i	$0.145247\pi$
$449$	17.5968	+	30.4786i	0.830446	+	1.43837i	−0.0672397	+	0.997737i	$0.521419\pi$
$450$	−1.31471	+	2.27714i	−0.0619758	+	0.107345i
$451$	15.4604	−	26.7782i	0.728002	−	1.26094i
$452$	0.604308			0.0284243
$453$	8.72661	+	15.1149i	0.410012	+	0.710162i
$454$	4.29952			0.201786
$455$	8.51628	−	11.9665i	0.399249	−	0.560997i
$456$	0.101912			0.00477245
$457$	17.8946	+	30.9943i	0.837073	+	1.44985i	0.892332	+	0.451380i	$0.149068\pi$
$457$	17.8946	+	30.9943i	0.837073	+	1.44985i	−0.0552593	+	0.998472i	$0.517599\pi$
$458$	−22.2971			−1.04188
$459$	2.19176	−	3.79624i	0.102303	−	0.177193i
$460$	−6.99956	+	12.1236i	−0.326356	+	0.565265i
$461$	−16.5830	−	28.7225i	−0.772346	−	1.33774i	−0.936274	−	0.351270i	$-0.885750\pi$
$461$	−16.5830	−	28.7225i	−0.772346	−	1.33774i	0.163929	−	0.986472i	$-0.447583\pi$
$462$	14.1874	−	9.16315i	0.660057	−	0.426308i
$463$	−23.6423			−1.09875			−0.549374	−	0.835576i	$-0.685134\pi$
$463$	−23.6423			−1.09875			−0.549374	+	0.835576i	$0.685134\pi$
$464$	−7.02510			−0.326132
$465$	−1.88352			−0.0873460
$466$	−3.81382			−0.176672
$467$	−14.1464	+	24.5024i	−0.654620	+	1.13383i	0.327369	+	0.944896i	$0.393838\pi$
$467$	−14.1464	+	24.5024i	−0.654620	+	1.13383i	−0.981989	+	0.188938i	$0.939495\pi$
$468$	2.82972	+	2.23443i	0.130804	+	0.103287i
$469$	0.226191	+	4.53233i	0.0104445	+	0.209284i
$470$	3.18776	−	5.52136i	0.147040	−	0.254681i
$471$	−10.6720	−	18.4844i	−0.491739	−	0.851718i
$472$	3.56881	−	6.18137i	0.164268	−	0.284520i
$473$	5.59869	+	9.69722i	0.257428	+	0.445879i
$474$	4.06717			0.186811
$475$	0.133984	+	0.232067i	0.00614760	+	0.0106480i
$476$	−9.74238	+	6.29227i	−0.446541	+	0.288406i
$477$	−4.11084	−	7.12019i	−0.188222	−	0.326011i
$478$	6.47775	+	11.2198i	0.296285	+	0.513181i
$479$	−18.5825			−0.849056			−0.424528	−	0.905415i	$-0.639560\pi$
$479$	−18.5825			−0.849056			−0.424528	+	0.905415i	$0.639560\pi$
$480$	−0.769836	−	1.33339i	−0.0351380	−	0.0608609i
$481$	−12.8766	+	5.12537i	−0.587124	+	0.233697i
$482$	−0.972553			−0.0442986
$483$	20.2076	−	13.0514i	0.919478	−	0.593859i
$484$	−14.8747	+	25.7637i	−0.676121	+	1.17108i
$485$	−3.06943			−0.139376
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−14.3184	+	24.8002i	−0.648827	+	1.12380i	0.334576	+	0.942369i	$0.391407\pi$
$487$	−14.3184	+	24.8002i	−0.648827	+	1.12380i	−0.983403	+	0.181433i	$0.941926\pi$
$488$	6.16908			0.279261
$489$	16.7477			0.757356
$490$	10.7241	−	1.07307i	0.484468	−	0.0484765i
$491$	−4.18769	+	7.25330i	−0.188988	+	0.327337i	−0.944913	−	0.327321i	$-0.893854\pi$
$491$	−4.18769	+	7.25330i	−0.188988	+	0.327337i	0.755925	+	0.654658i	$0.227187\pi$
$492$	2.42192	+	4.19490i	0.109189	+	0.189120i
$493$	15.3973	+	26.6690i	0.693461	+	1.20111i
$494$	0.341397	−	0.135889i	0.0153602	−	0.00611391i
$495$	4.91426	−	8.51175i	0.220880	−	0.382575i
$496$	−0.611662	+	1.05943i	−0.0274644	+	0.0475698i
$497$	20.3282	−	13.1293i	0.911842	−	0.588928i
$498$	3.51255	+	6.08392i	0.157401	+	0.272627i
$499$	0.333676	−	0.577944i	0.0149374	−	0.0258723i	−0.858460	−	0.512880i	$-0.828578\pi$
$499$	0.333676	−	0.577944i	0.0149374	−	0.0258723i	0.873397	+	0.487008i	$0.161912\pi$
$500$	5.87339	−	10.1730i	0.262666	−	0.454951i
$501$	−12.4467	+	21.5582i	−0.556075	+	0.963151i
$502$	−4.83297	+	8.37095i	−0.215706	+	0.373614i
$503$	6.58181	+	11.4000i	0.293468	+	0.508302i	0.974627	−	0.223833i	$-0.0718571\pi$
$503$	6.58181	+	11.4000i	0.293468	+	0.508302i	−0.681159	+	0.732136i	$0.738524\pi$
$504$	0.131875	+	2.64246i	0.00587417	+	0.117705i
$505$	0.571207	−	0.989359i	0.0254184	−	0.0440259i
$506$	−29.0204	+	50.2647i	−1.29011	+	2.23454i
$507$	12.4588	+	3.71206i	0.553313	+	0.164858i
$508$	−3.18892	−	5.52337i	−0.141485	−	0.245060i
$509$	−1.30380	−	2.25825i	−0.0577899	−	0.100095i	0.835683	−	0.549212i	$-0.185072\pi$
$509$	−1.30380	−	2.25825i	−0.0577899	−	0.100095i	−0.893473	+	0.449117i	$0.851739\pi$
$510$	−3.37459	+	5.84496i	−0.149429	+	0.258819i
$511$	21.4484	−	13.8528i	0.948821	−	0.612811i
$512$	−1.00000			−0.0441942
$513$	−0.101912			−0.00449951
$514$	13.5595	−	23.4858i	0.598084	−	1.03591i
$515$	4.42972	+	7.67250i	0.195197	+	0.338091i
$516$	−1.75411			−0.0772203
$517$	13.2165	−	22.8917i	0.581262	−	1.00678i
$518$	−9.04987	−	4.63962i	−0.397628	−	0.203853i
$519$	−18.8998			−0.829609
$520$	−4.35684	−	3.44029i	−0.191060	−	0.150867i
$521$	4.42237	+	7.65976i	0.193747	+	0.335580i	0.946489	−	0.322736i	$-0.104602\pi$
$521$	4.42237	+	7.65976i	0.193747	+	0.335580i	−0.752742	+	0.658316i	$0.771269\pi$
$522$	7.02510			0.307480
$523$	12.1996	+	21.1303i	0.533449	+	0.923962i	0.999237	+	0.0390648i	$0.0124379\pi$
$523$	12.1996	+	21.1303i	0.533449	+	0.923962i	−0.465787	+	0.884897i	$0.654229\pi$
$524$	5.42681	+	9.39952i	0.237071	+	0.410620i
$525$	−5.84387	+	3.77436i	−0.255048	+	0.164726i
$526$	2.36415	+	4.09483i	0.103082	+	0.178543i
$527$	5.36246			0.233592
$528$	−3.19176	−	5.52829i	−0.138904	−	0.240588i
$529$	−29.8347	+	51.6753i	−1.29716	+	2.24675i
$530$	6.32935	+	10.9627i	0.274929	+	0.476191i
$531$	−3.56881	+	6.18137i	−0.154873	+	0.268248i
$532$	0.239939	+	0.123010i	0.0104027	+	0.00533316i
$533$	13.7067	+	10.8232i	0.593705	+	0.468807i
$534$	7.77395	−	13.4649i	0.336412	−	0.582682i
$535$	−4.41977			−0.191083
$536$	1.71519			0.0740850
$537$	1.58583			0.0684338
$538$	26.6960			1.15094
$539$	44.4626	−	4.44899i	1.91514	−	0.191631i
$540$	0.769836	+	1.33339i	0.0331285	+	0.0573802i
$541$	−17.5725	+	30.4365i	−0.755501	+	1.30857i	0.189624	+	0.981857i	$0.439273\pi$
$541$	−17.5725	+	30.4365i	−0.755501	+	1.30857i	−0.945125	+	0.326709i	$0.894060\pi$
$542$	2.40455	−	4.16481i	0.103284	−	0.178894i
$543$	13.1480			0.564236
$544$	2.19176	+	3.79624i	0.0939709	+	0.162762i
$545$	13.9343			0.596882
$546$	3.96522	+	8.67623i	0.169696	+	0.371309i
$547$	−20.9144			−0.894237			−0.447119	−	0.894475i	$-0.647550\pi$
$547$	−20.9144			−0.894237			−0.447119	+	0.894475i	$0.647550\pi$
$548$	3.97052	+	6.87715i	0.169612	+	0.293777i
$549$	−6.16908			−0.263290
$550$	8.39245	−	14.5361i	0.357855	−	0.619823i
$551$	0.357970	−	0.620022i	0.0152500	−	0.0264138i
$552$	−4.54614	−	7.87414i	−0.193496	−	0.335146i
$553$	9.57566	+	4.90917i	0.407198	+	0.208759i
$554$	25.2267			1.07178
$555$	−5.91826			−0.251216
$556$	11.4490			0.485548
$557$	16.3149			0.691286			0.345643	−	0.938366i	$-0.387661\pi$
$557$	16.3149			0.691286			0.345643	+	0.938366i	$0.387661\pi$
$558$	0.611662	−	1.05943i	0.0258937	−	0.0448492i
$559$	−5.87615	+	2.33892i	−0.248535	+	0.0989257i
$560$	−0.203044	−	4.06852i	−0.00858017	−	0.171927i
$561$	−13.9911	+	24.2334i	−0.590706	+	1.02313i
$562$	−1.69456	−	2.93506i	−0.0714807	−	0.123808i
$563$	−3.26864	+	5.66145i	−0.137757	+	0.238602i	−0.926647	−	0.375932i	$-0.877323\pi$
$563$	−3.26864	+	5.66145i	−0.137757	+	0.238602i	0.788890	+	0.614534i	$0.210656\pi$
$564$	2.07041	+	3.58606i	0.0871802	+	0.151000i
$565$	0.930436			0.0391437
$566$	−5.25362	−	9.09954i	−0.220826	−	0.382482i
$567$	−0.131875	−	2.64246i	−0.00553822	−	0.110973i
$568$	−4.57326	−	7.92111i	−0.191890	−	0.332363i
$569$	−16.3751	−	28.3625i	−0.686480	−	1.18902i	−0.972969	−	0.230935i	$-0.925821\pi$
$569$	−16.3751	−	28.3625i	−0.686480	−	1.18902i	0.286489	−	0.958084i	$-0.407512\pi$
$570$	0.156911			0.00657226
$571$	6.42470	+	11.1279i	0.268865	+	0.465688i	0.968569	−	0.248745i	$-0.0800180\pi$
$571$	6.42470	+	11.1279i	0.268865	+	0.465688i	−0.699704	+	0.714433i	$0.746685\pi$
$572$	−18.0636	−	14.2635i	−0.755276	−	0.596388i
$573$	−12.7038			−0.530710
$574$	0.638782	+	12.7997i	0.0266622	+	0.534249i
$575$	11.9537	−	20.7044i	0.498502	−	0.863431i
$576$	1.00000			0.0416667
$577$	5.71122	+	9.89213i	0.237761	+	0.411815i	0.960072	−	0.279755i	$-0.0902531\pi$
$577$	5.71122	+	9.89213i	0.237761	+	0.411815i	−0.722310	+	0.691569i	$0.756920\pi$
$578$	1.10762	−	1.91846i	0.0460710	−	0.0797973i
$579$	8.18276			0.340064
$580$	−10.8164			−0.449125
$581$	0.926434	+	18.5636i	0.0384350	+	0.770147i
$582$	0.996781	−	1.72648i	0.0413179	−	0.0715647i
$583$	26.2416	+	45.4518i	1.08682	+	1.88242i
$584$	−4.82528	−	8.35763i	−0.199671	−	0.345841i
$585$	4.35684	+	3.44029i	0.180133	+	0.142238i
$586$	6.47179	−	11.2095i	0.267347	−	0.463059i
$587$	−19.3637	+	33.5389i	−0.799226	+	1.38430i	0.120895	+	0.992665i	$0.461424\pi$
$587$	−19.3637	+	33.5389i	−0.799226	+	1.38430i	−0.920121	+	0.391634i	$0.871910\pi$
$588$	−2.87903	+	6.38053i	−0.118729	+	0.263129i
$589$	−0.0623355	−	0.107968i	−0.00256849	−	0.00444875i
$590$	5.49480	−	9.51728i	0.226217	−	0.391820i
$591$	2.09350	−	3.62604i	0.0861149	−	0.149155i
$592$	−1.92192	+	3.32887i	−0.0789906	+	0.136816i
$593$	7.35202	−	12.7341i	0.301911	−	0.522926i	−0.674658	−	0.738131i	$-0.735709\pi$
$593$	7.35202	−	12.7341i	0.301911	−	0.522926i	0.976569	+	0.215205i	$0.0690420\pi$
$594$	3.19176	+	5.52829i	0.130959	+	0.226828i
$595$	−15.0001	+	9.68803i	−0.614943	+	0.397171i
$596$	10.6068	−	18.3715i	0.434471	−	0.752525i
$597$	1.95797	−	3.39131i	0.0801345	−	0.138797i
$598$	−25.7286	−	20.3161i	−1.05212	−	0.830785i
$599$	−17.4915	−	30.2961i	−0.714681	−	1.23786i	−0.963082	−	0.269207i	$-0.913238\pi$
$599$	−17.4915	−	30.2961i	−0.714681	−	1.23786i	0.248401	−	0.968657i	$-0.420095\pi$
$600$	1.31471	+	2.27714i	0.0536726	+	0.0929637i
$601$	18.1926	−	31.5105i	0.742091	−	1.28534i	−0.209451	−	0.977819i	$-0.567168\pi$
$601$	18.1926	−	31.5105i	0.742091	−	1.28534i	0.951542	−	0.307520i	$-0.0994991\pi$
$602$	−4.12983	−	2.11725i	−0.168319	−	0.0862927i
$603$	−1.71519			−0.0698480
$604$	17.4532			0.710162
$605$	−22.9021	+	39.6676i	−0.931103	+	1.61272i
$606$	0.370993	+	0.642578i	0.0150705	+	0.0261030i
$607$	−21.7987			−0.884782			−0.442391	−	0.896822i	$-0.645870\pi$
$607$	−21.7987			−0.884782			−0.442391	+	0.896822i	$0.645870\pi$
$608$	0.0509558	−	0.0882581i	0.00206653	−	0.00357934i
$609$	16.5397	+	8.47947i	0.670224	+	0.343605i
$610$	9.49836			0.384577
$611$	11.7174	+	9.25239i	0.474035	+	0.374312i
$612$	−2.19176	−	3.79624i	−0.0885966	−	0.153454i
$613$	13.6141			0.549868			0.274934	−	0.961463i	$-0.411344\pi$
$613$	13.6141			0.549868			0.274934	+	0.961463i	$0.411344\pi$
$614$	14.4786	+	25.0777i	0.584310	+	1.01205i
$615$	3.72897	+	6.45876i	0.150366	+	0.260442i
$616$	−0.841826	−	16.8682i	−0.0339181	−	0.679640i
$617$	−9.03652	−	15.6517i	−0.363797	−	0.630114i	0.624786	−	0.780796i	$-0.285186\pi$
$617$	−9.03652	−	15.6517i	−0.363797	−	0.630114i	−0.988582	+	0.150682i	$0.951853\pi$
$618$	−5.75411			−0.231464
$619$	−17.8683	−	30.9488i	−0.718188	−	1.24394i	−0.961717	−	0.274045i	$-0.911638\pi$
$619$	−17.8683	−	30.9488i	−0.718188	−	1.24394i	0.243529	−	0.969894i	$-0.421695\pi$
$620$	−0.941758	+	1.63117i	−0.0378219	+	0.0655095i
$621$	4.54614	+	7.87414i	0.182430	+	0.315978i
$622$	15.8321	−	27.4220i	0.634810	−	1.09952i
$623$	34.5552	−	22.3180i	1.38443	−	0.894153i
$624$	3.34993	−	1.33339i	0.134105	−	0.0533785i
$625$	2.46957	−	4.27742i	0.0987828	−	0.171097i
$626$	2.71622			0.108562
$627$	0.650555			0.0259807
$628$	−21.3440			−0.851718
$629$	16.8496			0.671837
$630$	0.203044	+	4.06852i	0.00808947	+	0.162094i
$631$	−8.96088	−	15.5207i	−0.356727	−	0.617870i	0.630685	−	0.776039i	$-0.282774\pi$
$631$	−8.96088	−	15.5207i	−0.356727	−	0.617870i	−0.987412	+	0.158170i	$0.949441\pi$
$632$	2.03359	−	3.52227i	0.0808917	−	0.140109i
$633$	−7.24076	+	12.5414i	−0.287795	+	0.498475i
$634$	30.6692			1.21803
$635$	−4.90988	−	8.50417i	−0.194843	−	0.337478i
$636$	−8.22168			−0.326011
$637$	−1.13681	+	25.2132i	−0.0450419	+	0.998985i
$638$	−44.8449			−1.77543
$639$	4.57326	+	7.92111i	0.180915	+	0.313354i
$640$	−1.53967			−0.0608609
$641$	16.1541	−	27.9798i	0.638050	−	1.10513i	−0.347810	−	0.937565i	$-0.613075\pi$
$641$	16.1541	−	27.9798i	0.638050	−	1.10513i	0.985860	−	0.167570i	$-0.0535920\pi$
$642$	1.43530	−	2.48601i	0.0566466	−	0.0981148i
$643$	7.45605	+	12.9143i	0.294038	+	0.509288i	0.974761	−	0.223253i	$-0.0716675\pi$
$643$	7.45605	+	12.9143i	0.294038	+	0.509288i	−0.680723	+	0.732541i	$0.738334\pi$
$644$	−1.19904	−	24.0260i	−0.0472489	−	0.946757i
$645$	−2.70075			−0.106342
$646$	−0.446732			−0.0175764
$647$	3.18530			0.125227			0.0626135	−	0.998038i	$-0.480056\pi$
$647$	3.18530			0.125227			0.0626135	+	0.998038i	$0.480056\pi$
$648$	−1.00000			−0.0392837
$649$	22.7816	−	39.4589i	0.894256	−	1.54890i
$650$	7.44050	+	5.87524i	0.291840	+	0.230446i
$651$	2.71884	−	1.75600i	0.106560	−	0.0688233i
$652$	8.37384	−	14.5039i	0.327945	−	0.568017i
$653$	−4.09680	−	7.09586i	−0.160320	−	0.277683i	0.774663	−	0.632374i	$-0.217919\pi$
$653$	−4.09680	−	7.09586i	−0.160320	−	0.277683i	−0.934983	+	0.354691i	$0.884586\pi$
$654$	−4.52510	+	7.83771i	−0.176946	+	0.306479i
$655$	8.35551	+	14.4722i	0.326477	+	0.565474i
$656$	4.84385			0.189120
$657$	4.82528	+	8.35763i	0.188252	+	0.326062i
$658$	0.546071	+	10.9420i	0.0212881	+	0.426563i
$659$	5.27966	+	9.14463i	0.205666	+	0.356224i	0.950345	−	0.311199i	$-0.100731\pi$
$659$	5.27966	+	9.14463i	0.205666	+	0.356224i	−0.744679	+	0.667423i	$0.767397\pi$
$660$	−4.91426	−	8.51175i	−0.191287	−	0.331319i
$661$	−36.6166			−1.42422			−0.712111	−	0.702067i	$-0.752261\pi$
$661$	−36.6166			−1.42422			−0.712111	+	0.702067i	$0.752261\pi$
$662$	10.0377	+	17.3857i	0.390125	+	0.675715i
$663$	−12.4041	−	9.79467i	−0.481737	−	0.380393i
$664$	7.02510			0.272627
$665$	0.369427	+	0.189395i	0.0143257	+	0.00734442i
$666$	1.92192	−	3.32887i	0.0744730	−	0.128991i
$667$	−63.8742			−2.47322
$668$	12.4467	+	21.5582i	0.481575	+	0.834113i
$669$	−5.98916	+	10.3735i	−0.231554	+	0.401064i
$670$	2.64083			0.102024
$671$	39.3805			1.52027
$672$	2.35438	+	1.20702i	0.0908221	+	0.0465620i
$673$	16.0264	−	27.7585i	0.617771	−	1.07001i	−0.372120	−	0.928184i	$-0.621369\pi$
$673$	16.0264	−	27.7585i	0.617771	−	1.07001i	0.989892	−	0.141827i	$-0.0452975\pi$
$674$	14.5283	+	25.1638i	0.559610	+	0.969273i
$675$	−1.31471	−	2.27714i	−0.0506030	−	0.0876470i
$676$	9.44412	−	8.93357i	0.363235	−	0.343599i
$677$	−21.7427	+	37.6595i	−0.835641	+	1.44737i	0.0578671	+	0.998324i	$0.481570\pi$
$677$	−21.7427	+	37.6595i	−0.835641	+	1.44737i	−0.893508	+	0.449048i	$0.851763\pi$
$678$	−0.302154	+	0.523346i	−0.0116042	+	0.0200990i
$679$	4.43070	−	2.86164i	0.170035	−	0.109820i
$680$	3.37459	+	5.84496i	0.129410	+	0.224144i
$681$	−2.14976	+	3.72349i	−0.0823789	+	0.142684i
$682$	−3.90455	+	6.76289i	−0.149513	+	0.258964i
$683$	15.4733	−	26.8005i	0.592069	−	1.02549i	−0.401884	−	0.915691i	$-0.631644\pi$
$683$	15.4733	−	26.8005i	0.592069	−	1.02549i	0.993953	−	0.109804i	$-0.0350222\pi$
$684$	−0.0509558	+	0.0882581i	−0.00194835	+	0.00337463i
$685$	6.11330	+	10.5886i	0.233577	+	0.404568i
$686$	−14.4798	+	11.5471i	−0.552841	+	0.440871i
$687$	11.1486	−	19.3099i	0.425344	−	0.736718i
$688$	−0.877054	+	1.51910i	−0.0334374	+	0.0579152i
$689$	−27.5421	+	10.9627i	−1.04927	+	0.417647i
$690$	−6.99956	−	12.1236i	−0.266469	−	0.461537i
$691$	7.75728	+	13.4360i	0.295101	+	0.511130i	0.975008	−	0.222168i	$-0.0713134\pi$
$691$	7.75728	+	13.4360i	0.295101	+	0.511130i	−0.679907	+	0.733298i	$0.737980\pi$
$692$	−9.44989	+	16.3677i	−0.359231	+	0.622206i
$693$	0.841826	+	16.8682i	0.0319783	+	0.640770i
$694$	9.31969			0.353771
$695$	17.6278			0.668660
$696$	3.51255	−	6.08392i	0.133143	−	0.230610i
$697$	−10.6166	−	18.3884i	−0.402131	−	0.696511i
$698$	−24.1538			−0.914234
$699$	1.90691	−	3.30286i	0.0721259	−	0.124926i
$700$	0.346753	+	6.94812i	0.0131060	+	0.262614i
$701$	−12.7687			−0.482267			−0.241133	−	0.970492i	$-0.577519\pi$
$701$	−12.7687			−0.482267			−0.241133	+	0.970492i	$0.577519\pi$
$702$	−3.34993	+	1.33339i	−0.126435	+	0.0503257i
$703$	−0.195867	−	0.339251i	−0.00738725	−	0.0127951i
$704$	−6.38352			−0.240588
$705$	3.18776	+	5.52136i	0.120058	+	0.207946i
$706$	−2.58663	−	4.48017i	−0.0973491	−	0.168614i
$707$	0.0978492	+	1.96067i	0.00368000	+	0.0737385i
$708$	3.56881	+	6.18137i	0.134124	+	0.232310i
$709$	−40.4217			−1.51807			−0.759034	−	0.651051i	$-0.774328\pi$
$709$	−40.4217			−1.51807			−0.759034	+	0.651051i	$0.774328\pi$
$710$	−7.04131	−	12.1959i	−0.264256	−	0.457705i
$711$	−2.03359	+	3.52227i	−0.0762654	+	0.132096i
$712$	−7.77395	−	13.4649i	−0.291341	−	0.504617i
$713$	−5.56139	+	9.63262i	−0.208276	+	0.360744i
$714$	−0.578076	−	11.5833i	−0.0216340	−	0.433494i
$715$	−27.8120	−	21.9612i	−1.04011	−	0.821301i
$716$	0.792917	−	1.37337i	0.0296327	−	0.0513253i
$717$	−12.9555			−0.483832
$718$	−33.4451			−1.24816
$719$	−17.4466			−0.650647			−0.325324	−	0.945603i	$-0.605473\pi$
$719$	−17.4466			−0.650647			−0.325324	+	0.945603i	$0.605473\pi$
$720$	1.53967			0.0573802
$721$	−13.5473	−	6.94535i	−0.504529	−	0.258658i
$722$	−9.49481	−	16.4455i	−0.353360	−	0.612038i
$723$	0.486277	−	0.842256i	0.0180848	−	0.0313238i
$724$	6.57401	−	11.3865i	0.244321	−	0.423177i
$725$	18.4719			0.686029
$726$	−14.8747	−	25.7637i	−0.552050	−	0.956179i
$727$	24.4378			0.906347			0.453173	−	0.891422i	$-0.350292\pi$
$727$	24.4378			0.906347			0.453173	+	0.891422i	$0.350292\pi$
$728$	9.49645	+	0.904138i	0.351962	+	0.0335096i
$729$	1.00000			0.0370370
$730$	−7.42934	−	12.8680i	−0.274972	−	0.476266i
$731$	7.68917			0.284394
$732$	−3.08454	+	5.34258i	−0.114008	+	0.197468i
$733$	17.1113	−	29.6376i	0.632020	−	1.09469i	−0.355118	−	0.934821i	$-0.615559\pi$
$733$	17.1113	−	29.6376i	0.632020	−	1.09469i	0.987138	−	0.159869i	$-0.0511072\pi$
$734$	−3.98054	−	6.89450i	−0.146924	−	0.254481i
$735$	−4.43277	+	9.82392i	−0.163505	+	0.362361i
$736$	−9.09227			−0.335146
$737$	10.9490			0.403310
$738$	−4.84385			−0.178305
$739$	−23.5714			−0.867086			−0.433543	−	0.901133i	$-0.642737\pi$
$739$	−23.5714			−0.867086			−0.433543	+	0.901133i	$0.642737\pi$
$740$	−2.95913	+	5.12537i	−0.108780	+	0.188412i
$741$	−0.0530158	+	0.363603i	−0.00194758	+	0.0133573i
$742$	−19.3569	−	9.92377i	−0.710616	−	0.364313i
$743$	−13.4988	+	23.3807i	−0.495225	+	0.857754i	−0.999985	−	0.00550536i	$-0.998248\pi$
$743$	−13.4988	+	23.3807i	−0.495225	+	0.857754i	0.504760	+	0.863260i	$0.331581\pi$
$744$	−0.611662	−	1.05943i	−0.0224246	−	0.0388405i
$745$	16.3310	−	28.2860i	0.598320	−	1.03632i
$746$	17.7986	+	30.8282i	0.651655	+	1.12870i
$747$	−7.02510			−0.257035
$748$	13.9911	+	24.2334i	0.511567	+	0.886060i
$749$	6.37990	−	4.12056i	0.233116	−	0.150562i
$750$	5.87339	+	10.1730i	0.214466	+	0.371466i
$751$	14.6335	+	25.3460i	0.533985	+	0.924889i	0.999212	+	0.0396974i	$0.0126394\pi$
$751$	14.6335	+	25.3460i	0.533985	+	0.924889i	−0.465227	+	0.885191i	$0.654027\pi$
$752$	4.14083			0.151000
$753$	−4.83297	−	8.37095i	−0.176123	−	0.305054i
$754$	3.65455	−	25.0643i	0.133091	−	0.912789i
$755$	26.8722			0.977981
$756$	−2.35438	−	1.20702i	−0.0856279	−	0.0438991i
$757$	10.2367	−	17.7305i	0.372059	−	0.644425i	−0.617823	−	0.786317i	$-0.711985\pi$
$757$	10.2367	−	17.7305i	0.372059	−	0.644425i	0.989882	+	0.141892i	$0.0453185\pi$
$758$	4.59205			0.166791
$759$	−29.0204	−	50.2647i	−1.05337	−	1.82449i
$760$	0.0784553	−	0.135889i	0.00284587	−	0.00492919i
$761$	12.1860			0.441741			0.220870	−	0.975303i	$-0.429110\pi$
$761$	12.1860			0.441741			0.220870	+	0.975303i	$0.429110\pi$
$762$	6.37783			0.231045
$763$	−20.1141	+	12.9910i	−0.728179	+	0.470306i
$764$	−6.35191	+	11.0018i	−0.229804	+	0.398032i
$765$	−3.37459	−	5.84496i	−0.122009	−	0.211325i
$766$	5.20906	+	9.02236i	0.188211	+	0.325991i
$767$	20.1975	+	15.9485i	0.729289	+	0.575868i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−6.71153	+	11.6247i	−0.242024	+	0.419198i	−0.961291	−	0.275536i	$-0.911145\pi$
$769$	−6.71153	+	11.6247i	−0.242024	+	0.419198i	0.719267	+	0.694734i	$0.244478\pi$
$770$	−1.29614	−	25.9715i	−0.0467095	−	0.935948i
$771$	13.5595	+	23.4858i	0.488334	+	0.845819i
$772$	4.09138	−	7.08648i	0.147252	−	0.255048i
$773$	14.9034	−	25.8134i	0.536037	−	0.928443i	−0.463076	−	0.886319i	$-0.653254\pi$
$773$	14.9034	−	25.8134i	0.536037	−	0.928443i	0.999112	−	0.0421240i	$-0.0134124\pi$
$774$	0.877054	−	1.51910i	0.0315251	−	0.0546030i
$775$	1.60831	−	2.78567i	0.0577722	−	0.100064i
$776$	−0.996781	−	1.72648i	−0.0357824	−	0.0619769i
$777$	8.54296	−	5.51761i	0.306477	−	0.197943i
$778$	6.19665	−	10.7329i	0.222161	−	0.384794i
$779$	−0.246822	+	0.427509i	−0.00884333	+	0.0153171i
$780$	5.15780	−	2.05299i	0.184679	−	0.0735088i
$781$	−29.1935	−	50.5646i	−1.04462	−	1.80934i
$782$	19.9281	+	34.5164i	0.712627	+	1.23431i
$783$	−3.51255	+	6.08392i	−0.125528	+	0.217421i
$784$	4.08618	+	5.68358i	0.145935	+	0.202985i
$785$	−32.8627			−1.17292
$786$	−10.8536			−0.387136
$787$	13.5975	−	23.5516i	0.484700	−	0.839525i	−0.515146	−	0.857103i	$-0.672262\pi$
$787$	13.5975	−	23.5516i	0.484700	−	0.839525i	0.999845	+	0.0175778i	$0.00559547\pi$
$788$	−2.09350	−	3.62604i	−0.0745777	−	0.129172i
$789$	−4.72830			−0.168332
$790$	3.13105	−	5.42314i	0.111398	−	0.192947i
$791$	−1.34308	+	0.867447i	−0.0477543	+	0.0308429i
$792$	6.38352			0.226828
$793$	−3.20924	+	22.0102i	−0.113963	+	0.781605i
$794$	0.412212	+	0.713972i	0.0146289	+	0.0253379i
$795$	−12.6587			−0.448957
$796$	−1.95797	−	3.39131i	−0.0693985	−	0.120202i
$797$	−13.7060	−	23.7395i	−0.485492	−	0.840897i	0.514369	−	0.857569i	$-0.328026\pi$
$797$	−13.7060	−	23.7395i	−0.485492	−	0.840897i	−0.999861	+	0.0166718i	$0.994693\pi$
$798$	−0.226499	+	0.146288i	−0.00801798	+	0.00517854i
$799$	−9.07570	−	15.7196i	−0.321075	−	0.556119i
$800$	2.62941			0.0929637
$801$	7.77395	+	13.4649i	0.274679	+	0.475758i
$802$	13.4698	−	23.3303i	0.475634	−	0.823823i
$803$	−30.8023	−	53.3511i	−1.08699	−	1.88272i
$804$	−0.857596	+	1.48540i	−0.0302451	+	0.0523860i
$805$	−1.84613	−	36.9921i	−0.0650676	−	1.30380i
$806$	−3.46166	−	2.73343i	−0.121932	−	0.0962810i
$807$	−13.3480	+	23.1194i	−0.469871	+	0.813841i
$808$	0.741985			0.0261030
$809$	−0.983915			−0.0345926			−0.0172963	−	0.999850i	$-0.505506\pi$
$809$	−0.983915			−0.0345926			−0.0172963	+	0.999850i	$0.505506\pi$
$810$	−1.53967			−0.0540985
$811$	1.17290			0.0411862			0.0205931	−	0.999788i	$-0.493445\pi$
$811$	1.17290			0.0411862			0.0205931	+	0.999788i	$0.493445\pi$
$812$	15.6133	−	10.0841i	0.547920	−	0.353883i
$813$	2.40455	+	4.16481i	0.0843314	+	0.146066i
$814$	−12.2686	+	21.2499i	−0.430016	+	0.744809i
$815$	12.8930	−	22.3313i	0.451621	−	0.782230i
$816$	−4.38352			−0.153454
$817$	−0.0893821	−	0.154814i	−0.00312708	−	0.00541627i
$818$	11.1506			0.389870
$819$	−9.49645	−	0.904138i	−0.331833	−	0.0315931i
$820$	7.45794			0.260442
$821$	−18.8293	−	32.6132i	−0.657146	−	1.13821i	−0.981351	−	0.192223i	$-0.938430\pi$
$821$	−18.8293	−	32.6132i	−0.657146	−	1.13821i	0.324206	−	0.945987i	$-0.394903\pi$
$822$	−7.94105			−0.276976
$823$	17.1529	−	29.7098i	0.597914	−	1.03562i	−0.395215	−	0.918589i	$-0.629330\pi$
$823$	17.1529	−	29.7098i	0.597914	−	1.03562i	0.993129	−	0.117028i	$-0.0373368\pi$
$824$	−2.87705	+	4.98320i	−0.100227	+	0.173598i
$825$	8.39245	+	14.5361i	0.292188	+	0.506084i
$826$	0.941274	+	18.8609i	0.0327511	+	0.656255i
$827$	−21.7508			−0.756349			−0.378174	−	0.925734i	$-0.623448\pi$
$827$	−21.7508			−0.756349			−0.378174	+	0.925734i	$0.623448\pi$
$828$	9.09227			0.315978
$829$	−31.3732			−1.08964			−0.544818	−	0.838554i	$-0.683401\pi$
$829$	−31.3732			−1.08964			−0.544818	+	0.838554i	$0.683401\pi$
$830$	10.8164			0.375441
$831$	−12.6133	+	21.8469i	−0.437552	+	0.757862i
$832$	0.520213	−	3.56783i	0.0180352	−	0.123692i
$833$	12.6203	−	27.9692i	0.437268	−	0.969075i
$834$	−5.72452	+	9.91517i	−0.198224	+	0.343334i
$835$	19.1638	+	33.1926i	0.663189	+	1.14868i
$836$	0.325278	−	0.563397i	0.0112500	−	0.0194855i
$837$	0.611662	+	1.05943i	0.0211421	+	0.0366192i
$838$	−26.5575			−0.917415
$839$	5.76946	+	9.99300i	0.199184	+	0.344997i	0.948264	−	0.317483i	$-0.102838\pi$
$839$	5.76946	+	9.99300i	0.199184	+	0.344997i	−0.749080	+	0.662479i	$0.769504\pi$
$840$	3.62497	+	1.85842i	0.125073	+	0.0641216i
$841$	−10.1760	−	17.6254i	−0.350898	−	0.607773i
$842$	−6.88831	−	11.9309i	−0.237387	−	0.411166i
$843$	3.38912			0.116727
$844$	7.24076	+	12.5414i	0.249237	+	0.431692i
$845$	14.5408	−	13.7548i	0.500220	−	0.473178i
$846$	−4.14083			−0.142365
$847$	−3.92319	−	78.6115i	−0.134802	−	2.70112i
$848$	−4.11084	+	7.12019i	−0.141167	+	0.244508i
$849$	10.5072			0.360608
$850$	−5.76304	−	9.98187i	−0.197671	−	0.342375i
$851$	−17.4747	+	30.2670i	−0.599024	+	1.03754i
$852$	9.14651			0.313354
$853$	−12.7275			−0.435781			−0.217891	−	0.975973i	$-0.569918\pi$
$853$	−12.7275			−0.435781			−0.217891	+	0.975973i	$0.569918\pi$
$854$	−13.7108	+	8.85534i	−0.469174	+	0.303023i
$855$	−0.0784553	+	0.135889i	−0.00268311	+	0.00464729i
$856$	−1.43530	−	2.48601i	−0.0490574	−	0.0849699i
$857$	−21.7384	−	37.6520i	−0.742570	−	1.28617i	−0.951322	−	0.308200i	$-0.900273\pi$
$857$	−21.7384	−	37.6520i	−0.742570	−	1.28617i	0.208752	−	0.977969i	$-0.433060\pi$
$858$	21.3844	−	8.51175i	0.730050	−	0.290586i
$859$	−26.5599	+	46.0032i	−0.906213	+	1.56961i	−0.0869327	+	0.996214i	$0.527707\pi$
$859$	−26.5599	+	46.0032i	−0.906213	+	1.56961i	−0.819280	+	0.573393i	$0.805627\pi$
$860$	−1.35038	+	2.33892i	−0.0460474	+	0.0797565i
$861$	−11.4042	−	5.84664i	−0.388656	−	0.199253i
$862$	−5.37746	−	9.31403i	−0.183157	−	0.317237i
$863$	−3.19247	+	5.52953i	−0.108673	+	0.188227i	−0.915233	−	0.402925i	$-0.867993\pi$
$863$	−3.19247	+	5.52953i	−0.108673	+	0.188227i	0.806560	+	0.591152i	$0.201327\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−14.5497	+	25.2009i	−0.494706	+	0.856856i
$866$	16.7913	−	29.0833i	0.570591	−	0.988292i
$867$	1.10762	+	1.91846i	0.0376168	+	0.0651542i
$868$	−0.161326	−	3.23259i	−0.00547575	−	0.109721i
$869$	12.9814	−	22.4845i	0.440365	−	0.762734i
$870$	5.40818	−	9.36724i	0.183354	−	0.317579i
$871$	−0.892266	+	6.11950i	−0.0302333	+	0.207352i
$872$	4.52510	+	7.83771i	0.153239	+	0.265418i
$873$	0.996781	+	1.72648i	0.0337359	+	0.0584324i
$874$	0.463305	−	0.802467i	0.0156715	−	0.0271438i
$875$	1.54911	+	31.0404i	0.0523693	+	1.04936i
$876$	9.65056			0.326062
$877$	−44.2027			−1.49262			−0.746309	−	0.665599i	$-0.768176\pi$
$877$	−44.2027			−1.49262			−0.746309	+	0.665599i	$0.768176\pi$
$878$	−0.605618	+	1.04896i	−0.0204386	+	0.0354007i
$879$	6.47179	+	11.2095i	0.218288	+	0.378086i
$880$	−9.82852			−0.331319
$881$	−13.3933	+	23.1979i	−0.451233	+	0.781558i	−0.998463	−	0.0554239i	$-0.982349\pi$
$881$	−13.3933	+	23.1979i	−0.451233	+	0.781558i	0.547230	+	0.836982i	$0.315682\pi$
$882$	−4.08618	−	5.68358i	−0.137589	−	0.191376i
$883$	−48.6765			−1.63809			−0.819047	−	0.573726i	$-0.805498\pi$
$883$	−48.6765			−1.63809			−0.819047	+	0.573726i	$0.805498\pi$
$884$	−14.6845	+	5.84496i	−0.493893	+	0.196587i
$885$	5.49480	+	9.51728i	0.184706	+	0.319920i
$886$	−9.84713			−0.330821
$887$	18.9600	+	32.8397i	0.636614	+	1.10265i	0.986171	+	0.165732i	$0.0529988\pi$
$887$	18.9600	+	32.8397i	0.636614	+	1.10265i	−0.349557	+	0.936915i	$0.613668\pi$
$888$	−1.92192	−	3.32887i	−0.0644955	−	0.111710i
$889$	15.0158	+	7.69820i	0.503615	+	0.258189i
$890$	−11.9693	−	20.7315i	−0.401213	−	0.694921i
$891$	−6.38352			−0.213856
$892$	5.98916	+	10.3735i	0.200532	+	0.347332i
$893$	−0.210999	+	0.365462i	−0.00706083	+	0.0122297i
$894$	10.6068	+	18.3715i	0.354744	+	0.614434i
$895$	1.22083	−	2.11454i	0.0408079	−	0.0706813i
$896$	2.22250	−	1.43544i	0.0742486	−	0.0479546i
$897$	30.4585	−	12.1236i	1.01698	−	0.404795i
$898$	−17.5968	+	30.4786i	−0.587214	+	1.01708i
$899$	−8.59397			−0.286625
$900$	−2.62941			−0.0876470
$901$	36.0399			1.20066
$902$	30.9208			1.02955
$903$	3.89851	−	2.51791i	0.129734	−	0.0837910i
$904$	0.302154	+	0.523346i	0.0100495	+	0.0174062i
$905$	10.1218	−	17.5315i	0.336461	−	0.582767i
$906$	−8.72661	+	15.1149i	−0.289922	+	0.502160i
$907$	20.1692			0.669706			0.334853	−	0.942270i	$-0.391313\pi$
$907$	20.1692			0.669706			0.334853	+	0.942270i	$0.391313\pi$
$908$	2.14976	+	3.72349i	0.0713422	+	0.123568i
$909$	−0.741985			−0.0246101
$910$	14.6214	+	1.39208i	0.484695	+	0.0461468i
$911$	23.6361			0.783098			0.391549	−	0.920157i	$-0.371939\pi$
$911$	23.6361			0.783098			0.391549	+	0.920157i	$0.371939\pi$
$912$	0.0509558	+	0.0882581i	0.00168732	+	0.00292252i
$913$	44.8449			1.48415
$914$	−17.8946	+	30.9943i	−0.591900	+	1.02520i
$915$	−4.74918	+	8.22582i	−0.157003	+	0.271937i
$916$	−11.1486	−	19.3099i	−0.368359	−	0.638016i
$917$	−25.5535	−	13.1006i	−0.843852	−	0.432620i
$918$	4.38352			0.144678
$919$	8.21825			0.271095			0.135548	−	0.990771i	$-0.456721\pi$
$919$	8.21825			0.271095			0.135548	+	0.990771i	$0.456721\pi$
$920$	−13.9991			−0.461537
$921$	−28.9573			−0.954174
$922$	16.5830	−	28.7225i	0.546131	−	0.945926i
$923$	30.6402	−	12.1959i	1.00854	−	0.401433i
$924$	15.0292	+	7.70506i	0.494425	+	0.253478i
$925$	5.05353	−	8.75297i	0.166159	−	0.287796i
$926$	−11.8211	−	20.4748i	−0.388466	−	0.672844i
$927$	2.87705	−	4.98320i	0.0944949	−	0.163670i
$928$	−3.51255	−	6.08392i	−0.115305	−	0.199714i
$929$	−35.1178			−1.15218			−0.576089	−	0.817387i	$-0.695422\pi$
$929$	−35.1178			−1.15218			−0.576089	+	0.817387i	$0.695422\pi$
$930$	−0.941758	−	1.63117i	−0.0308815	−	0.0534883i
$931$	−0.709837	+	0.0710272i	−0.0232640	+	0.00232782i
$932$	−1.90691	−	3.30286i	−0.0624629	−	0.108189i
$933$	15.8321	+	27.4220i	0.518320	+	0.897757i
$934$	−28.2929			−0.925772
$935$	21.5418	+	37.3114i	0.704491	+	1.22021i
$936$	−0.520213	+	3.56783i	−0.0170037	+	0.116618i
$937$	10.3940			0.339557			0.169779	−	0.985482i	$-0.445695\pi$
$937$	10.3940			0.339557			0.169779	+	0.985482i	$0.445695\pi$
$938$	−3.81202	+	2.46205i	−0.124467	+	0.0803888i
$939$	−1.35811	+	2.35231i	−0.0443202	+	0.0767648i
$940$	6.37552			0.207946
$941$	29.6148	+	51.2943i	0.965413	+	1.67215i	0.708500	+	0.705711i	$0.249372\pi$
$941$	29.6148	+	51.2943i	0.965413	+	1.67215i	0.256913	+	0.966434i	$0.417294\pi$
$942$	10.6720	−	18.4844i	0.347712	−	0.602255i
$943$	44.0416			1.43419
$944$	7.13763			0.232310
$945$	−3.62497	−	1.85842i	−0.117920	−	0.0604544i
$946$	−5.59869	+	9.69722i	−0.182029	+	0.315284i
$947$	14.4009	+	24.9431i	0.467967	+	0.810542i	0.999330	−	0.0366021i	$-0.0116534\pi$
$947$	14.4009	+	24.9431i	0.467967	+	0.810542i	−0.531363	+	0.847144i	$0.678320\pi$
$948$	2.03359	+	3.52227i	0.0660478	+	0.114398i
$949$	32.3287	−	12.8680i	1.04943	−	0.417713i
$950$	−0.133984	+	0.232067i	−0.00434701	+	0.00752924i
$951$	−15.3346	+	26.5603i	−0.497259	+	0.861278i
$952$	−10.3205	−	5.29102i	−0.334488	−	0.171483i
$953$	13.6541	+	23.6496i	0.442300	+	0.766086i	0.997860	−	0.0653905i	$-0.0208293\pi$
$953$	13.6541	+	23.6496i	0.442300	+	0.766086i	−0.555560	+	0.831477i	$0.687496\pi$
$954$	4.11084	−	7.12019i	0.133093	−	0.230525i
$955$	−9.77986	+	16.9392i	−0.316469	+	0.548140i
$956$	−6.47775	+	11.2198i	−0.209505	+	0.362874i
$957$	22.4224	−	38.8368i	0.724815	−	1.25542i
$958$	−9.29125	−	16.0929i	−0.300187	−	0.519939i
$959$	−18.6962	−	9.58504i	−0.603733	−	0.309517i
$960$	0.769836	−	1.33339i	0.0248463	−	0.0430351i
$961$	14.7517	−	25.5508i	0.475863	−	0.824218i
$962$	−10.8770	−	8.58881i	−0.350689	−	0.276914i
$963$	1.43530	+	2.48601i	0.0462518	+	0.0801104i
$964$	−0.486277	−	0.842256i	−0.0156619	−	0.0271272i
$965$	6.29939	−	10.9109i	0.202784	−	0.351233i
$966$	21.4066	+	10.9746i	0.688747	+	0.353102i
$967$	34.9687			1.12452			0.562259	−	0.826961i	$-0.309932\pi$
$967$	34.9687			1.12452			0.562259	+	0.826961i	$0.309932\pi$
$968$	−29.7493			−0.956179
$969$	0.223366	−	0.386881i	0.00717555	−	0.0124284i
$970$	−1.53472	−	2.65821i	−0.0492768	−	0.0853499i
$971$	58.6185			1.88116			0.940579	−	0.339574i	$-0.110283\pi$
$971$	58.6185			1.88116			0.940579	+	0.339574i	$0.110283\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−25.4455	+	16.4344i	−0.815747	+	0.526863i
$974$	−28.6367			−0.917581
$975$	−8.80835	+	3.50604i	−0.282093	+	0.112283i
$976$	3.08454	+	5.34258i	0.0987338	+	0.171012i
$977$	−26.3631			−0.843431			−0.421716	−	0.906728i	$-0.638572\pi$
$977$	−26.3631			−0.843431			−0.421716	+	0.906728i	$0.638572\pi$
$978$	8.37384	+	14.5039i	0.267766	+	0.463784i
$979$	−49.6251	−	85.9533i	−1.58603	−	2.74708i
$980$	6.29138	+	8.75085i	0.200971	+	0.279536i
$981$	−4.52510	−	7.83771i	−0.144475	−	0.250239i
$982$	−8.37538			−0.267269
$983$	−16.4337	−	28.4640i	−0.524153	−	0.907860i	−0.999605	−	0.0281179i	$-0.991049\pi$
$983$	−16.4337	−	28.4640i	−0.524153	−	0.907860i	0.475452	−	0.879742i	$-0.342285\pi$
$984$	−2.42192	+	4.19490i	−0.0772081	+	0.133728i
$985$	−3.22330	−	5.58291i	−0.102703	−	0.177886i
$986$	−15.3973	+	26.6690i	−0.490351	+	0.849313i
$987$	−9.74907	−	4.99808i	−0.310316	−	0.159091i
$988$	0.288382	+	0.227715i	0.00917464	+	0.00724457i
$989$	−7.97442	+	13.8121i	−0.253572	+	0.439199i
$990$	9.82852			0.312371
$991$	23.3619			0.742115			0.371058	−	0.928610i	$-0.378995\pi$
$991$	23.3619			0.742115			0.371058	+	0.928610i	$0.378995\pi$
$992$	−1.22332			−0.0388405
$993$	−20.0753			−0.637071
$994$	21.5343	+	11.0401i	0.683028	+	0.350170i
$995$	−3.01464	−	5.22150i	−0.0955704	−	0.165533i
$996$	−3.51255	+	6.08392i	−0.111299	+	0.192776i
$997$	8.70760	−	15.0820i	0.275772	−	0.477652i	−0.694557	−	0.719437i	$-0.744400\pi$
$997$	8.70760	−	15.0820i	0.275772	−	0.477652i	0.970330	+	0.241786i	$0.0777331\pi$
$998$	0.667352			0.0211247
$999$	1.92192	+	3.32887i	0.0608070	+	0.105321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.e.373.2	yes	10
3.2	odd	2		1638.2.p.j.919.4		10
7.4	even	3		546.2.j.e.529.2	yes	10
13.3	even	3		546.2.j.e.289.2	✓	10
21.11	odd	6		1638.2.m.k.1621.4		10
39.29	odd	6		1638.2.m.k.289.4		10
91.81	even	3	inner	546.2.k.e.445.2	yes	10
273.263	odd	6		1638.2.p.j.991.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.2	✓	10	13.3	even	3
546.2.j.e.529.2	yes	10	7.4	even	3
546.2.k.e.373.2	yes	10	1.1	even	1	trivial
546.2.k.e.445.2	yes	10	91.81	even	3	inner
1638.2.m.k.289.4		10	39.29	odd	6
1638.2.m.k.1621.4		10	21.11	odd	6
1638.2.p.j.919.4		10	3.2	odd	2
1638.2.p.j.991.4		10	273.263	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.769836 + 1.33339i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.131875 - 2.64246i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.769836 + 1.33339i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.131875 - 2.64246i) q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.53967 q^{10} -6.38352 q^{11} +(0.500000 - 0.866025i) q^{12} +(0.520213 - 3.56783i) q^{13} +(2.22250 - 1.43544i) q^{14} +(0.769836 - 1.33339i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.19176 + 3.79624i) q^{17} +(0.500000 + 0.866025i) q^{18} +0.101912 q^{19} +(-0.769836 - 1.33339i) q^{20} +(0.131875 + 2.64246i) q^{21} +(-3.19176 - 5.52829i) q^{22} +(-4.54614 - 7.87414i) q^{23} +1.00000 q^{24} +(1.31471 + 2.27714i) q^{25} +(3.34993 - 1.33339i) q^{26} -1.00000 q^{27} +(2.35438 + 1.20702i) q^{28} +(3.51255 - 6.08392i) q^{29} +1.53967 q^{30} +(-0.611662 - 1.05943i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.38352 q^{33} -4.38352 q^{34} +(3.62497 + 1.85842i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.92192 - 3.32887i) q^{37} +(0.0509558 + 0.0882581i) q^{38} +(-0.520213 + 3.56783i) q^{39} +(0.769836 - 1.33339i) q^{40} +(-2.42192 + 4.19490i) q^{41} +(-2.22250 + 1.43544i) q^{42} +(-0.877054 - 1.51910i) q^{43} +(3.19176 - 5.52829i) q^{44} +(-0.769836 + 1.33339i) q^{45} +(4.54614 - 7.87414i) q^{46} +(-2.07041 + 3.58606i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.96522 + 0.696949i) q^{49} +(-1.31471 + 2.27714i) q^{50} +(2.19176 - 3.79624i) q^{51} +(2.82972 + 2.23443i) q^{52} +(-4.11084 - 7.12019i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.91426 - 8.51175i) q^{55} +(0.131875 + 2.64246i) q^{56} -0.101912 q^{57} +7.02510 q^{58} +(-3.56881 + 6.18137i) q^{59} +(0.769836 + 1.33339i) q^{60} -6.16908 q^{61} +(0.611662 - 1.05943i) q^{62} +(-0.131875 - 2.64246i) q^{63} +1.00000 q^{64} +(4.35684 + 3.44029i) q^{65} +(3.19176 + 5.52829i) q^{66} -1.71519 q^{67} +(-2.19176 - 3.79624i) q^{68} +(4.54614 + 7.87414i) q^{69} +(0.203044 + 4.06852i) q^{70} +(4.57326 + 7.92111i) q^{71} -1.00000 q^{72} +(4.82528 + 8.35763i) q^{73} +(1.92192 - 3.32887i) q^{74} +(-1.31471 - 2.27714i) q^{75} +(-0.0509558 + 0.0882581i) q^{76} +(0.841826 + 16.8682i) q^{77} +(-3.34993 + 1.33339i) q^{78} +(-2.03359 + 3.52227i) q^{79} +1.53967 q^{80} +1.00000 q^{81} -4.84385 q^{82} -7.02510 q^{83} +(-2.35438 - 1.20702i) q^{84} +(-3.37459 - 5.84496i) q^{85} +(0.877054 - 1.51910i) q^{86} +(-3.51255 + 6.08392i) q^{87} +6.38352 q^{88} +(7.77395 + 13.4649i) q^{89} -1.53967 q^{90} +(-9.49645 - 0.904138i) q^{91} +9.09227 q^{92} +(0.611662 + 1.05943i) q^{93} -4.14083 q^{94} +(-0.0784553 + 0.135889i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(0.996781 + 1.72648i) q^{97} +(-4.08618 - 5.68358i) q^{98} -6.38352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

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