LMFDB - Embedded newform 546.2.j.b.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$1.33821 - 2.31784i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.b.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.36323 - 1.18960i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.36323 - 1.18960i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.651388 + 1.12824i) q^{10} +(-1.05939 + 1.83493i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0315412 + 3.60541i) q^{13} +(2.36323 + 1.18960i) q^{14} +(0.651388 + 1.12824i) q^{15} +1.00000 q^{16} -0.486762 q^{17} +(0.500000 + 0.866025i) q^{18} +(3.13815 + 5.43544i) q^{19} +(0.651388 - 1.12824i) q^{20} +(2.21184 - 1.45181i) q^{21} +(1.05939 - 1.83493i) q^{22} -4.78954 q^{23} +(0.500000 - 0.866025i) q^{24} +(1.65139 + 2.86029i) q^{25} +(-0.0315412 - 3.60541i) q^{26} +1.00000 q^{27} +(-2.36323 - 1.18960i) q^{28} +(1.74338 + 3.01962i) q^{29} +(-0.651388 - 1.12824i) q^{30} +(2.24338 + 3.88565i) q^{31} -1.00000 q^{32} +(-1.05939 - 1.83493i) q^{33} +0.486762 q^{34} +(-2.88153 + 1.89139i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.15751 q^{37} +(-3.13815 - 5.43544i) q^{38} +(-3.13815 - 1.77539i) q^{39} +(-0.651388 + 1.12824i) q^{40} +(-6.31845 - 10.9439i) q^{41} +(-2.21184 + 1.45181i) q^{42} +(-4.01356 + 6.95169i) q^{43} +(-1.05939 + 1.83493i) q^{44} -1.30278 q^{45} +4.78954 q^{46} +(-3.98570 + 6.90344i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.16969 + 5.62260i) q^{49} +(-1.65139 - 2.86029i) q^{50} +(0.243381 - 0.421549i) q^{51} +(0.0315412 + 3.60541i) q^{52} +(4.29060 + 7.43153i) q^{53} -1.00000 q^{54} +(1.38015 + 2.39050i) q^{55} +(2.36323 + 1.18960i) q^{56} -6.27630 q^{57} +(-1.74338 - 3.01962i) q^{58} -9.15014 q^{59} +(0.651388 + 1.12824i) q^{60} +(5.09231 + 8.82015i) q^{61} +(-2.24338 - 3.88565i) q^{62} +(0.151388 + 2.64142i) q^{63} +1.00000 q^{64} +(4.08831 + 2.31294i) q^{65} +(1.05939 + 1.83493i) q^{66} +(1.67924 - 2.90853i) q^{67} -0.486762 q^{68} +(2.39477 - 4.14786i) q^{69} +(2.88153 - 1.89139i) q^{70} +(1.46740 - 2.54161i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-8.09337 - 14.0181i) q^{73} +1.15751 q^{74} -3.30278 q^{75} +(3.13815 + 5.43544i) q^{76} +(4.68642 - 3.07609i) q^{77} +(3.13815 + 1.77539i) q^{78} +(-7.16738 + 12.4143i) q^{79} +(0.651388 - 1.12824i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.31845 + 10.9439i) q^{82} +3.48676 q^{83} +(2.21184 - 1.45181i) q^{84} +(-0.317071 + 0.549183i) q^{85} +(4.01356 - 6.95169i) q^{86} -3.48676 q^{87} +(1.05939 - 1.83493i) q^{88} +9.39720 q^{89} +1.30278 q^{90} +(4.21447 - 8.55793i) q^{91} -4.78954 q^{92} -4.48676 q^{93} +(3.98570 - 6.90344i) q^{94} +8.17661 q^{95} +(0.500000 - 0.866025i) q^{96} +(0.698602 - 1.21001i) q^{97} +(-4.16969 - 5.62260i) q^{98} +2.11879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	−0.682810	−	0.730596i	$-0.739242\pi$
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	0.974120	+	0.226033i	$0.0725757\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.36323	−	1.18960i	−0.893216	−	0.449628i
$7$	−2.36323	−	1.18960i	−0.893216	−	0.449628i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.651388	+	1.12824i	−0.205987	+	0.356780i
$11$	−1.05939	+	1.83493i	−0.319419	+	0.553251i	−0.980367	−	0.197181i	$-0.936821\pi$
$11$	−1.05939	+	1.83493i	−0.319419	+	0.553251i	0.660948	+	0.750432i	$0.270155\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.0315412	+	3.60541i	0.00874794	+	0.999962i
$13$	0.0315412	+	3.60541i	0.00874794	+	0.999962i
$14$	2.36323	+	1.18960i	0.631599	+	0.317935i
$15$	0.651388	+	1.12824i	0.168188	+	0.291309i
$16$	1.00000			0.250000
$17$	−0.486762			−0.118057			−0.0590286	−	0.998256i	$-0.518800\pi$
$17$	−0.486762			−0.118057			−0.0590286	+	0.998256i	$0.518800\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.13815	+	5.43544i	0.719941	+	1.24697i	0.961023	+	0.276470i	$0.0891645\pi$
$19$	3.13815	+	5.43544i	0.719941	+	1.24697i	−0.241082	+	0.970505i	$0.577502\pi$
$20$	0.651388	−	1.12824i	0.145655	−	0.252281i
$21$	2.21184	−	1.45181i	0.482663	−	0.316812i
$22$	1.05939	−	1.83493i	0.225864	−	0.391207i
$23$	−4.78954			−0.998688			−0.499344	−	0.866404i	$-0.666426\pi$
$23$	−4.78954			−0.998688			−0.499344	+	0.866404i	$0.666426\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.65139	+	2.86029i	0.330278	+	0.572058i
$26$	−0.0315412	−	3.60541i	−0.00618573	−	0.707080i
$27$	1.00000			0.192450
$28$	−2.36323	−	1.18960i	−0.446608	−	0.224814i
$29$	1.74338	+	3.01962i	0.323738	+	0.560730i	0.981256	−	0.192708i	$-0.0617271\pi$
$29$	1.74338	+	3.01962i	0.323738	+	0.560730i	−0.657518	+	0.753439i	$0.728394\pi$
$30$	−0.651388	−	1.12824i	−0.118927	−	0.205987i
$31$	2.24338	+	3.88565i	0.402923	+	0.697883i	0.994077	−	0.108675i	$-0.0346609\pi$
$31$	2.24338	+	3.88565i	0.402923	+	0.697883i	−0.591154	+	0.806559i	$0.701328\pi$
$32$	−1.00000			−0.176777
$33$	−1.05939	−	1.83493i	−0.184417	−	0.319419i
$34$	0.486762			0.0834790
$35$	−2.88153	+	1.89139i	−0.487068	+	0.319703i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.15751			−0.190294			−0.0951468	−	0.995463i	$-0.530332\pi$
$37$	−1.15751			−0.190294			−0.0951468	+	0.995463i	$0.530332\pi$
$38$	−3.13815	−	5.43544i	−0.509075	−	0.881744i
$39$	−3.13815	−	1.77539i	−0.502506	−	0.284290i
$40$	−0.651388	+	1.12824i	−0.102993	+	0.178390i
$41$	−6.31845	−	10.9439i	−0.986776	−	1.70915i	−0.633762	−	0.773528i	$-0.718490\pi$
$41$	−6.31845	−	10.9439i	−0.986776	−	1.70915i	−0.353014	−	0.935618i	$-0.614843\pi$
$42$	−2.21184	+	1.45181i	−0.341294	+	0.224020i
$43$	−4.01356	+	6.95169i	−0.612062	+	1.06012i	0.378831	+	0.925466i	$0.376326\pi$
$43$	−4.01356	+	6.95169i	−0.612062	+	1.06012i	−0.990892	+	0.134656i	$0.957007\pi$
$44$	−1.05939	+	1.83493i	−0.159710	+	0.276625i
$45$	−1.30278			−0.194206
$46$	4.78954			0.706179
$47$	−3.98570	+	6.90344i	−0.581375	+	1.00697i	0.413942	+	0.910303i	$0.364152\pi$
$47$	−3.98570	+	6.90344i	−0.581375	+	1.00697i	−0.995317	+	0.0966674i	$0.969182\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	4.16969	+	5.62260i	0.595670	+	0.803229i
$50$	−1.65139	−	2.86029i	−0.233542	−	0.404506i
$51$	0.243381	−	0.421549i	0.0340802	−	0.0590286i
$52$	0.0315412	+	3.60541i	0.00437397	+	0.499981i
$53$	4.29060	+	7.43153i	0.589359	+	1.02080i	0.994317	+	0.106464i	$0.0339528\pi$
$53$	4.29060	+	7.43153i	0.589359	+	1.02080i	−0.404958	+	0.914335i	$0.632714\pi$
$54$	−1.00000			−0.136083
$55$	1.38015	+	2.39050i	0.186100	+	0.322334i
$56$	2.36323	+	1.18960i	0.315800	+	0.158967i
$57$	−6.27630			−0.831316
$58$	−1.74338	−	3.01962i	−0.228917	−	0.396496i
$59$	−9.15014			−1.19125			−0.595623	−	0.803264i	$-0.703095\pi$
$59$	−9.15014			−1.19125			−0.595623	+	0.803264i	$0.703095\pi$
$60$	0.651388	+	1.12824i	0.0840938	+	0.145655i
$61$	5.09231	+	8.82015i	0.652004	+	1.12930i	0.982636	+	0.185544i	$0.0594048\pi$
$61$	5.09231	+	8.82015i	0.652004	+	1.12930i	−0.330632	+	0.943760i	$0.607262\pi$
$62$	−2.24338	−	3.88565i	−0.284910	−	0.493478i
$63$	0.151388	+	2.64142i	0.0190731	+	0.332787i
$64$	1.00000			0.125000
$65$	4.08831	+	2.31294i	0.507092	+	0.286884i
$66$	1.05939	+	1.83493i	0.130402	+	0.225864i
$67$	1.67924	−	2.90853i	0.205152	−	0.355334i	−0.745029	−	0.667032i	$-0.767564\pi$
$67$	1.67924	−	2.90853i	0.205152	−	0.355334i	0.950181	+	0.311698i	$0.100898\pi$
$68$	−0.486762			−0.0590286
$69$	2.39477	−	4.14786i	0.288296	−	0.499344i
$70$	2.88153	−	1.89139i	0.344409	−	0.226064i
$71$	1.46740	−	2.54161i	0.174148	−	0.301634i	−0.765718	−	0.643177i	$-0.777616\pi$
$71$	1.46740	−	2.54161i	0.174148	−	0.301634i	0.939866	+	0.341543i	$0.110949\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−8.09337	−	14.0181i	−0.947257	−	1.64070i	−0.751167	−	0.660112i	$-0.770509\pi$
$73$	−8.09337	−	14.0181i	−0.947257	−	1.64070i	−0.196090	−	0.980586i	$-0.562825\pi$
$74$	1.15751			0.134558
$75$	−3.30278			−0.381372
$76$	3.13815	+	5.43544i	0.359971	+	0.623487i
$77$	4.68642	−	3.07609i	0.534067	−	0.350553i
$78$	3.13815	+	1.77539i	0.355326	+	0.201023i
$79$	−7.16738	+	12.4143i	−0.806393	+	1.39671i	0.108953	+	0.994047i	$0.465250\pi$
$79$	−7.16738	+	12.4143i	−0.806393	+	1.39671i	−0.915346	+	0.402667i	$0.868083\pi$
$80$	0.651388	−	1.12824i	0.0728274	−	0.126141i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.31845	+	10.9439i	0.697756	+	1.20855i
$83$	3.48676			0.382722			0.191361	−	0.981520i	$-0.438710\pi$
$83$	3.48676			0.382722			0.191361	+	0.981520i	$0.438710\pi$
$84$	2.21184	−	1.45181i	0.241332	−	0.158406i
$85$	−0.317071	+	0.549183i	−0.0343912	+	0.0595673i
$86$	4.01356	−	6.95169i	0.432793	−	0.749620i
$87$	−3.48676			−0.373820
$88$	1.05939	−	1.83493i	0.112932	−	0.195604i
$89$	9.39720			0.996102			0.498051	−	0.867148i	$-0.334049\pi$
$89$	9.39720			0.996102			0.498051	+	0.867148i	$0.334049\pi$
$90$	1.30278			0.137325
$91$	4.21447	−	8.55793i	0.441797	−	0.897115i
$92$	−4.78954			−0.499344
$93$	−4.48676			−0.465256
$94$	3.98570	−	6.90344i	0.411094	−	0.712036i
$95$	8.17661			0.838903
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	0.698602	−	1.21001i	0.0709323	−	0.122858i	−0.828378	−	0.560170i	$-0.810736\pi$
$97$	0.698602	−	1.21001i	0.0709323	−	0.122858i	0.899310	+	0.437311i	$0.144069\pi$
$98$	−4.16969	−	5.62260i	−0.421202	−	0.567969i
$99$	2.11879			0.212946
$100$	1.65139	+	2.86029i	0.165139	+	0.286029i
$101$	3.01725	−	5.22602i	0.300227	−	0.520009i	−0.675960	−	0.736938i	$-0.736271\pi$
$101$	3.01725	−	5.22602i	0.300227	−	0.520009i	0.976187	+	0.216930i	$0.0696042\pi$
$102$	−0.243381	+	0.421549i	−0.0240983	+	0.0417395i
$103$	5.64770	−	9.78210i	0.556484	−	0.963859i	−0.441302	−	0.897359i	$-0.645483\pi$
$103$	5.64770	−	9.78210i	0.556484	−	0.963859i	0.997786	−	0.0665006i	$-0.0211834\pi$
$104$	−0.0315412	−	3.60541i	−0.00309287	−	0.353540i
$105$	−0.197224	−	3.44117i	−0.0192471	−	0.335824i
$106$	−4.29060	−	7.43153i	−0.416739	−	0.721814i
$107$	−14.0292			−1.35626			−0.678128	−	0.734943i	$-0.737209\pi$
$107$	−14.0292			−1.35626			−0.678128	+	0.734943i	$0.737209\pi$
$108$	1.00000			0.0962250
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	−1.38015	−	2.39050i	−0.131592	−	0.227925i
$111$	0.578756	−	1.00243i	0.0549331	−	0.0951468i
$112$	−2.36323	−	1.18960i	−0.223304	−	0.112407i
$113$	3.56552	−	6.17566i	0.335416	−	0.580957i	−0.648149	−	0.761514i	$-0.724457\pi$
$113$	3.56552	−	6.17566i	0.335416	−	0.580957i	0.983565	+	0.180557i	$0.0577899\pi$
$114$	6.27630			0.587829
$115$	−3.11985	+	5.40373i	−0.290927	+	0.503901i
$116$	1.74338	+	3.01962i	0.161869	+	0.280365i
$117$	3.10661	−	1.83002i	0.287206	−	0.169186i
$118$	9.15014			0.842338
$119$	1.15033	+	0.579054i	0.105451	+	0.0530818i
$120$	−0.651388	−	1.12824i	−0.0594633	−	0.102993i
$121$	3.25537	+	5.63846i	0.295942	+	0.512587i
$122$	−5.09231	−	8.82015i	−0.461036	−	0.798538i
$123$	12.6369			1.13943
$124$	2.24338	+	3.88565i	0.201462	+	0.348942i
$125$	10.8167			0.967471
$126$	−0.151388	−	2.64142i	−0.0134867	−	0.235316i
$127$	2.59305	+	4.49130i	0.230096	+	0.398538i	0.957836	−	0.287315i	$-0.0927626\pi$
$127$	2.59305	+	4.49130i	0.230096	+	0.398538i	−0.727740	+	0.685853i	$0.759429\pi$
$128$	−1.00000			−0.0883883
$129$	−4.01356	−	6.95169i	−0.353374	−	0.612062i
$130$	−4.08831	−	2.31294i	−0.358568	−	0.202858i
$131$	4.03186	−	6.98339i	0.352265	−	0.610142i	−0.634381	−	0.773021i	$-0.718745\pi$
$131$	4.03186	−	6.98339i	0.352265	−	0.610142i	0.986646	+	0.162879i	$0.0520781\pi$
$132$	−1.05939	−	1.83493i	−0.0922085	−	0.159710i
$133$	−0.950155	−	16.5783i	−0.0823889	−	1.43752i
$134$	−1.67924	+	2.90853i	−0.145064	+	0.251259i
$135$	0.651388	−	1.12824i	0.0560625	−	0.0971032i
$136$	0.486762			0.0417395
$137$	−6.79165			−0.580250			−0.290125	−	0.956989i	$-0.593697\pi$
$137$	−6.79165			−0.580250			−0.290125	+	0.956989i	$0.593697\pi$
$138$	−2.39477	+	4.14786i	−0.203856	+	0.353089i
$139$	6.45522	−	11.1808i	0.547525	−	0.948341i	−0.450919	−	0.892565i	$-0.648904\pi$
$139$	6.45522	−	11.1808i	0.547525	−	0.948341i	0.998443	−	0.0557755i	$-0.0177631\pi$
$140$	−2.88153	+	1.89139i	−0.243534	+	0.159851i
$141$	−3.98570	−	6.90344i	−0.335657	−	0.581375i
$142$	−1.46740	+	2.54161i	−0.123142	+	0.213287i
$143$	−6.64908	−	3.76168i	−0.556024	−	0.314567i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.54247			0.377232
$146$	8.09337	+	14.0181i	0.669812	+	1.16015i
$147$	−6.95416	+	0.799757i	−0.573570	+	0.0659628i
$148$	−1.15751			−0.0951468
$149$	11.6820	+	20.2338i	0.957026	+	1.65762i	0.729661	+	0.683809i	$0.239678\pi$
$149$	11.6820	+	20.2338i	0.957026	+	1.65762i	0.227365	+	0.973810i	$0.426989\pi$
$150$	3.30278			0.269671
$151$	−2.93692	−	5.08689i	−0.239003	−	0.413965i	0.721425	−	0.692492i	$-0.243487\pi$
$151$	−2.93692	−	5.08689i	−0.239003	−	0.413965i	−0.960428	+	0.278527i	$0.910154\pi$
$152$	−3.13815	−	5.43544i	−0.254538	−	0.440872i
$153$	0.243381	+	0.421549i	0.0196762	+	0.0340802i
$154$	−4.68642	+	3.07609i	−0.377643	+	0.247878i
$155$	5.84524			0.469501
$156$	−3.13815	−	1.77539i	−0.251253	−	0.142145i
$157$	−3.12248	−	5.40829i	−0.249201	−	0.431628i	0.714104	−	0.700040i	$-0.246835\pi$
$157$	−3.12248	−	5.40829i	−0.249201	−	0.431628i	−0.963304	+	0.268412i	$0.913501\pi$
$158$	7.16738	−	12.4143i	0.570206	−	0.987626i
$159$	−8.58119			−0.680533
$160$	−0.651388	+	1.12824i	−0.0514967	+	0.0891950i
$161$	11.3188	+	5.69765i	0.892044	+	0.449037i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	1.30383	+	2.25831i	0.102124	+	0.176884i	0.912560	−	0.408944i	$-0.134103\pi$
$163$	1.30383	+	2.25831i	0.102124	+	0.176884i	−0.810435	+	0.585828i	$0.800769\pi$
$164$	−6.31845	−	10.9439i	−0.493388	−	0.854573i
$165$	−2.76031			−0.214890
$166$	−3.48676			−0.270625
$167$	−3.45416	−	5.98279i	−0.267291	−	0.462962i	0.700870	−	0.713289i	$-0.252795\pi$
$167$	−3.45416	−	5.98279i	−0.267291	−	0.462962i	−0.968161	+	0.250327i	$0.919462\pi$
$168$	−2.21184	+	1.45181i	−0.170647	+	0.112010i
$169$	−12.9980	+	0.227438i	−0.999847	+	0.0174952i
$170$	0.317071	−	0.549183i	0.0243182	−	0.0421204i
$171$	3.13815	−	5.43544i	0.239980	−	0.415658i
$172$	−4.01356	+	6.95169i	−0.306031	+	0.530061i
$173$	3.86355	+	6.69186i	0.293740	+	0.508773i	0.974691	−	0.223556i	$-0.0717666\pi$
$173$	3.86355	+	6.69186i	0.293740	+	0.508773i	−0.680951	+	0.732329i	$0.738433\pi$
$174$	3.48676			0.264331
$175$	−0.500000	−	8.72401i	−0.0377964	−	0.659473i
$176$	−1.05939	+	1.83493i	−0.0798549	+	0.138313i
$177$	4.57507	−	7.92425i	0.343883	−	0.595623i
$178$	−9.39720			−0.704350
$179$	−9.57539	+	16.5851i	−0.715698	+	1.23963i	0.246992	+	0.969018i	$0.420558\pi$
$179$	−9.57539	+	16.5851i	−0.715698	+	1.23963i	−0.962690	+	0.270608i	$0.912775\pi$
$180$	−1.30278			−0.0971032
$181$	13.0972			0.973506			0.486753	−	0.873540i	$-0.338181\pi$
$181$	13.0972			0.973506			0.486753	+	0.873540i	$0.338181\pi$
$182$	−4.21447	+	8.55793i	−0.312397	+	0.634356i
$183$	−10.1846			−0.752869
$184$	4.78954			0.353089
$185$	−0.753989	+	1.30595i	−0.0554344	+	0.0960151i
$186$	4.48676			0.328985
$187$	0.515673	−	0.893172i	0.0377098	−	0.0653152i
$188$	−3.98570	+	6.90344i	−0.290687	+	0.503485i
$189$	−2.36323	−	1.18960i	−0.171900	−	0.0865309i
$190$	−8.17661			−0.593194
$191$	5.74444	+	9.94966i	0.415653	+	0.719932i	0.995497	−	0.0947956i	$-0.0302197\pi$
$191$	5.74444	+	9.94966i	0.415653	+	0.719932i	−0.579844	+	0.814728i	$0.696886\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	0.138150	−	0.239283i	0.00994426	−	0.0172240i	−0.861010	−	0.508587i	$-0.830168\pi$
$193$	0.138150	−	0.239283i	0.00994426	−	0.0172240i	0.870955	+	0.491363i	$0.163501\pi$
$194$	−0.698602	+	1.21001i	−0.0501567	+	0.0868740i
$195$	−4.04721	+	2.38411i	−0.289827	+	0.170730i
$196$	4.16969	+	5.62260i	0.297835	+	0.401615i
$197$	−6.63552	−	11.4931i	−0.472761	−	0.818846i	0.526753	−	0.850019i	$-0.323409\pi$
$197$	−6.63552	−	11.4931i	−0.472761	−	0.818846i	−0.999514	+	0.0311721i	$0.990076\pi$
$198$	−2.11879			−0.150576
$199$	19.0219			1.34842			0.674212	−	0.738538i	$-0.264483\pi$
$199$	19.0219			1.34842			0.674212	+	0.738538i	$0.264483\pi$
$200$	−1.65139	−	2.86029i	−0.116771	−	0.202253i
$201$	1.67924	+	2.90853i	0.118445	+	0.205152i
$202$	−3.01725	+	5.22602i	−0.212293	+	0.367702i
$203$	−0.527853	−	9.20999i	−0.0370480	−	0.646415i
$204$	0.243381	−	0.421549i	0.0170401	−	0.0295143i
$205$	−16.4630			−1.14983
$206$	−5.64770	+	9.78210i	−0.393494	+	0.681551i
$207$	2.39477	+	4.14786i	0.166448	+	0.288296i
$208$	0.0315412	+	3.60541i	0.00218699	+	0.249990i
$209$	−13.2982			−0.919853
$210$	0.197224	+	3.44117i	0.0136098	+	0.237464i
$211$	−1.98750	−	3.44245i	−0.136825	−	0.236988i	0.789468	−	0.613792i	$-0.210357\pi$
$211$	−1.98750	−	3.44245i	−0.136825	−	0.236988i	−0.926293	+	0.376804i	$0.877023\pi$
$212$	4.29060	+	7.43153i	0.294679	+	0.510400i
$213$	1.46740	+	2.54161i	0.100545	+	0.174148i
$214$	14.0292			0.959019
$215$	5.22877	+	9.05649i	0.356599	+	0.617647i
$216$	−1.00000			−0.0680414
$217$	−0.679241	−	11.8514i	−0.0461099	−	0.804526i
$218$	5.50000	+	9.52628i	0.372507	+	0.645201i
$219$	16.1867			1.09380
$220$	1.38015	+	2.39050i	0.0930499	+	0.161167i
$221$	−0.0153530	−	1.75498i	−0.00103276	−	0.118053i
$222$	−0.578756	+	1.00243i	−0.0388435	+	0.0672790i
$223$	9.58013	+	16.5933i	0.641533	+	1.11117i	0.985091	+	0.172036i	$0.0550347\pi$
$223$	9.58013	+	16.5933i	0.641533	+	1.11117i	−0.343557	+	0.939132i	$0.611632\pi$
$224$	2.36323	+	1.18960i	0.157900	+	0.0794837i
$225$	1.65139	−	2.86029i	0.110093	−	0.190686i
$226$	−3.56552	+	6.17566i	−0.237175	+	0.410799i
$227$	−1.18251			−0.0784861			−0.0392430	−	0.999230i	$-0.512495\pi$
$227$	−1.18251			−0.0784861			−0.0392430	+	0.999230i	$0.512495\pi$
$228$	−6.27630			−0.415658
$229$	7.51599	−	13.0181i	0.496671	−	0.860259i	−0.503322	−	0.864099i	$-0.667889\pi$
$229$	7.51599	−	13.0181i	0.496671	−	0.860259i	0.999993	+	0.00383994i	$0.00122229\pi$
$230$	3.11985	−	5.40373i	0.205717	−	0.356312i
$231$	0.320759	+	5.59660i	0.0211044	+	0.368230i
$232$	−1.74338	−	3.01962i	−0.114459	−	0.198248i
$233$	−2.59706	+	4.49824i	−0.170139	+	0.294689i	−0.938468	−	0.345365i	$-0.887755\pi$
$233$	−2.59706	+	4.49824i	−0.170139	+	0.294689i	0.768329	+	0.640055i	$0.221088\pi$
$234$	−3.10661	+	1.83002i	−0.203085	+	0.119632i
$235$	5.19248	+	8.99364i	0.338720	+	0.586680i
$236$	−9.15014			−0.595623
$237$	−7.16738	−	12.4143i	−0.465571	−	0.806393i
$238$	−1.15033	−	0.579054i	−0.0745648	−	0.0375345i
$239$	25.3978			1.64285			0.821425	−	0.570317i	$-0.193179\pi$
$239$	25.3978			1.64285			0.821425	+	0.570317i	$0.193179\pi$
$240$	0.651388	+	1.12824i	0.0420469	+	0.0728274i
$241$	−11.8575			−0.763808			−0.381904	−	0.924202i	$-0.624732\pi$
$241$	−11.8575			−0.763808			−0.381904	+	0.924202i	$0.624732\pi$
$242$	−3.25537	−	5.63846i	−0.209263	−	0.362454i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	5.09231	+	8.82015i	0.326002	+	0.564652i
$245$	9.05971	−	1.04190i	0.578804	−	0.0665648i
$246$	−12.6369			−0.805699
$247$	−19.4980	+	11.4858i	−1.24063	+	0.730822i
$248$	−2.24338	−	3.88565i	−0.142455	−	0.246739i
$249$	−1.74338	+	3.01962i	−0.110482	+	0.191361i
$250$	−10.8167			−0.684105
$251$	10.7397	−	18.6017i	0.677883	−	1.17413i	−0.297734	−	0.954649i	$-0.596231\pi$
$251$	10.7397	−	18.6017i	0.677883	−	1.17413i	0.975617	−	0.219480i	$-0.0704359\pi$
$252$	0.151388	+	2.64142i	0.00953654	+	0.166394i
$253$	5.07401	−	8.78844i	0.319000	−	0.552525i
$254$	−2.59305	−	4.49130i	−0.162702	−	0.281809i
$255$	−0.317071	−	0.549183i	−0.0198558	−	0.0343912i
$256$	1.00000			0.0625000
$257$	−6.84589			−0.427035			−0.213517	−	0.976939i	$-0.568492\pi$
$257$	−6.84589			−0.427035			−0.213517	+	0.976939i	$0.568492\pi$
$258$	4.01356	+	6.95169i	0.249873	+	0.432793i
$259$	2.73546	+	1.37698i	0.169973	+	0.0855613i
$260$	4.08831	+	2.31294i	0.253546	+	0.143442i
$261$	1.74338	−	3.01962i	0.107913	−	0.186910i
$262$	−4.03186	+	6.98339i	−0.249089	+	0.431435i
$263$	−7.69998	+	13.3368i	−0.474801	+	0.822380i	−0.999584	−	0.0288567i	$-0.990813\pi$
$263$	−7.69998	+	13.3368i	−0.474801	+	0.822380i	0.524782	+	0.851236i	$0.324147\pi$
$264$	1.05939	+	1.83493i	0.0652012	+	0.112932i
$265$	11.1794			0.686743
$266$	0.950155	+	16.5783i	0.0582578	+	1.01648i
$267$	−4.69860	+	8.13822i	−0.287550	+	0.498051i
$268$	1.67924	−	2.90853i	0.102576	−	0.177667i
$269$	−11.7313			−0.715272			−0.357636	−	0.933861i	$-0.616417\pi$
$269$	−11.7313			−0.715272			−0.357636	+	0.933861i	$0.616417\pi$
$270$	−0.651388	+	1.12824i	−0.0396422	+	0.0686623i
$271$	−26.0856			−1.58459			−0.792293	−	0.610141i	$-0.791113\pi$
$271$	−26.0856			−1.58459			−0.792293	+	0.610141i	$0.791113\pi$
$272$	−0.486762			−0.0295143
$273$	5.30415	+	7.92881i	0.321022	+	0.479873i
$274$	6.79165			0.410299
$275$	−6.99788			−0.421988
$276$	2.39477	−	4.14786i	0.144148	−	0.249672i
$277$	23.4307			1.40781			0.703906	−	0.710293i	$-0.251438\pi$
$277$	23.4307			1.40781			0.703906	+	0.710293i	$0.251438\pi$
$278$	−6.45522	+	11.1808i	−0.387158	+	0.670578i
$279$	2.24338	−	3.88565i	0.134308	−	0.232628i
$280$	2.88153	−	1.89139i	0.172204	−	0.113032i
$281$	6.15751			0.367326			0.183663	−	0.982989i	$-0.441204\pi$
$281$	6.15751			0.367326			0.183663	+	0.982989i	$0.441204\pi$
$282$	3.98570	+	6.90344i	0.237345	+	0.411094i
$283$	−10.9661	+	18.9939i	−0.651870	+	1.12907i	0.330799	+	0.943701i	$0.392682\pi$
$283$	−10.9661	+	18.9939i	−0.651870	+	1.12907i	−0.982669	+	0.185370i	$0.940651\pi$
$284$	1.46740	−	2.54161i	0.0870742	−	0.150817i
$285$	−4.08831	+	7.08115i	−0.242170	+	0.419451i
$286$	6.64908	+	3.76168i	0.393168	+	0.222433i
$287$	1.91307	+	33.3793i	0.112925	+	1.97032i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−16.7631			−0.986062
$290$	−4.54247			−0.266743
$291$	0.698602	+	1.21001i	0.0409528	+	0.0709323i
$292$	−8.09337	−	14.0181i	−0.473629	−	0.820349i
$293$	−8.74075	+	15.1394i	−0.510640	+	0.884455i	0.489284	+	0.872125i	$0.337258\pi$
$293$	−8.74075	+	15.1394i	−0.510640	+	0.884455i	−0.999924	+	0.0123300i	$0.996075\pi$
$294$	6.95416	−	0.799757i	0.405575	−	0.0466428i
$295$	−5.96029	+	10.3235i	−0.347021	+	0.601059i
$296$	1.15751			0.0672790
$297$	−1.05939	+	1.83493i	−0.0614723	+	0.106473i
$298$	−11.6820	−	20.2338i	−0.676720	−	1.17211i
$299$	−0.151068	−	17.2683i	−0.00873646	−	0.998649i
$300$	−3.30278			−0.190686
$301$	17.7547	−	11.6539i	1.02336	−	0.671718i
$302$	2.93692	+	5.08689i	0.169001	+	0.292718i
$303$	3.01725	+	5.22602i	0.173336	+	0.300227i
$304$	3.13815	+	5.43544i	0.179985	+	0.311744i
$305$	13.2683			0.759740
$306$	−0.243381	−	0.421549i	−0.0139132	−	0.0240983i
$307$	−12.0673			−0.688718			−0.344359	−	0.938838i	$-0.611904\pi$
$307$	−12.0673			−0.688718			−0.344359	+	0.938838i	$0.611904\pi$
$308$	4.68642	−	3.07609i	0.267034	−	0.175276i
$309$	5.64770	+	9.78210i	0.321286	+	0.556484i
$310$	−5.84524			−0.331988
$311$	0.755881	+	1.30923i	0.0428621	+	0.0742393i	0.886661	−	0.462421i	$-0.153019\pi$
$311$	0.755881	+	1.30923i	0.0428621	+	0.0742393i	−0.843798	+	0.536660i	$0.819686\pi$
$312$	3.13815	+	1.77539i	0.177663	+	0.100512i
$313$	−0.862908	+	1.49460i	−0.0487744	+	0.0844798i	−0.889382	−	0.457165i	$-0.848865\pi$
$313$	−0.862908	+	1.49460i	−0.0487744	+	0.0844798i	0.840607	+	0.541645i	$0.182198\pi$
$314$	3.12248	+	5.40829i	0.176212	+	0.305207i
$315$	3.07876	+	1.54979i	0.173468	+	0.0873205i
$316$	−7.16738	+	12.4143i	−0.403197	+	0.698357i
$317$	−10.6520	+	18.4499i	−0.598278	+	1.03625i	0.394798	+	0.918768i	$0.370815\pi$
$317$	−10.6520	+	18.4499i	−0.598278	+	1.03625i	−0.993075	+	0.117479i	$0.962519\pi$
$318$	8.58119			0.481209
$319$	−7.38771			−0.413633
$320$	0.651388	−	1.12824i	0.0364137	−	0.0630704i
$321$	7.01462	−	12.1497i	0.391518	−	0.678128i
$322$	−11.3188	−	5.69765i	−0.630770	−	0.317517i
$323$	−1.52753	−	2.64576i	−0.0849942	−	0.147214i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−10.2604	+	6.04415i	−0.569146	+	0.335269i
$326$	−1.30383	−	2.25831i	−0.0722126	−	0.125076i
$327$	11.0000			0.608301
$328$	6.31845	+	10.9439i	0.348878	+	0.604274i
$329$	17.6315	−	11.5730i	0.972055	−	0.638040i
$330$	2.76031			0.151950
$331$	−8.21691	−	14.2321i	−0.451642	−	0.782267i	0.546846	−	0.837233i	$-0.315828\pi$
$331$	−8.21691	−	14.2321i	−0.451642	−	0.782267i	−0.998488	+	0.0549662i	$0.982495\pi$
$332$	3.48676			0.191361
$333$	0.578756	+	1.00243i	0.0317156	+	0.0549331i
$334$	3.45416	+	5.98279i	0.189003	+	0.327364i
$335$	−2.18767	−	3.78916i	−0.119525	−	0.207024i
$336$	2.21184	−	1.45181i	0.120666	−	0.0792029i
$337$	−12.9178			−0.703678			−0.351839	−	0.936060i	$-0.614444\pi$
$337$	−12.9178			−0.703678			−0.351839	+	0.936060i	$0.614444\pi$
$338$	12.9980	−	0.227438i	0.706999	−	0.0123710i
$339$	3.56552	+	6.17566i	0.193652	+	0.335416i
$340$	−0.317071	+	0.549183i	−0.0171956	+	0.0297836i
$341$	−9.50650			−0.514806
$342$	−3.13815	+	5.43544i	−0.169692	+	0.293915i
$343$	−3.16527	−	18.2478i	−0.170908	−	0.985287i
$344$	4.01356	−	6.95169i	0.216397	−	0.374810i
$345$	−3.11985	−	5.40373i	−0.167967	−	0.290927i
$346$	−3.86355	−	6.69186i	−0.207706	−	0.359757i
$347$	−16.0387			−0.861004			−0.430502	−	0.902590i	$-0.641663\pi$
$347$	−16.0387			−0.861004			−0.430502	+	0.902590i	$0.641663\pi$
$348$	−3.48676			−0.186910
$349$	−3.81951	−	6.61558i	−0.204453	−	0.354124i	0.745505	−	0.666500i	$-0.232208\pi$
$349$	−3.81951	−	6.61558i	−0.204453	−	0.354124i	−0.949958	+	0.312376i	$0.898875\pi$
$350$	0.500000	+	8.72401i	0.0267261	+	0.466318i
$351$	0.0315412	+	3.60541i	0.00168354	+	0.192443i
$352$	1.05939	−	1.83493i	0.0564659	−	0.0978018i
$353$	16.1956	−	28.0515i	0.862002	−	1.49303i	−0.00799069	−	0.999968i	$-0.502544\pi$
$353$	16.1956	−	28.0515i	0.862002	−	1.49303i	0.869993	−	0.493064i	$-0.164123\pi$
$354$	−4.57507	+	7.92425i	−0.243162	+	0.421169i
$355$	−1.91169	−	3.31115i	−0.101462	−	0.175738i
$356$	9.39720			0.498051
$357$	−1.07664	+	0.706688i	−0.0569818	+	0.0374019i
$358$	9.57539	−	16.5851i	0.506075	−	0.876548i
$359$	1.57507	−	2.72810i	0.0831289	−	0.143983i	−0.821463	−	0.570261i	$-0.806842\pi$
$359$	1.57507	−	2.72810i	0.0831289	−	0.143983i	0.904592	+	0.426278i	$0.140175\pi$
$360$	1.30278			0.0686623
$361$	−10.1960	+	17.6599i	−0.536630	+	0.929471i
$362$	−13.0972			−0.688373
$363$	−6.51073			−0.341725
$364$	4.21447	−	8.55793i	0.220898	−	0.448558i
$365$	−21.0877			−1.10378
$366$	10.1846			0.532359
$367$	2.23463	−	3.87049i	0.116647	−	0.202038i	−0.801790	−	0.597606i	$-0.796119\pi$
$367$	2.23463	−	3.87049i	0.116647	−	0.202038i	0.918437	+	0.395568i	$0.129452\pi$
$368$	−4.78954			−0.249672
$369$	−6.31845	+	10.9439i	−0.328925	+	0.569715i
$370$	0.753989	−	1.30595i	0.0391980	−	0.0678929i
$371$	−1.29909	−	22.6665i	−0.0674453	−	1.17679i
$372$	−4.48676			−0.232628
$373$	−2.47615	−	4.28883i	−0.128210	−	0.222067i	0.794773	−	0.606907i	$-0.207590\pi$
$373$	−2.47615	−	4.28883i	−0.128210	−	0.222067i	−0.922983	+	0.384840i	$0.874257\pi$
$374$	−0.515673	+	0.893172i	−0.0266648	+	0.0461848i
$375$	−5.40833	+	9.36750i	−0.279285	+	0.483735i
$376$	3.98570	−	6.90344i	0.205547	−	0.356018i
$377$	−10.8320	+	6.38085i	−0.557877	+	0.328631i
$378$	2.36323	+	1.18960i	0.121551	+	0.0611866i
$379$	6.55920	+	11.3609i	0.336923	+	0.583569i	0.983852	−	0.178982i	$-0.0572803\pi$
$379$	6.55920	+	11.3609i	0.336923	+	0.583569i	−0.646929	+	0.762550i	$0.723947\pi$
$380$	8.17661			0.419451
$381$	−5.18610			−0.265692
$382$	−5.74444	−	9.94966i	−0.293911	−	0.509069i
$383$	6.09000	+	10.5482i	0.311185	+	0.538988i	0.978619	−	0.205681i	$-0.0659409\pi$
$383$	6.09000	+	10.5482i	0.311185	+	0.538988i	−0.667434	+	0.744669i	$0.732608\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−0.417877	−	7.29112i	−0.0212970	−	0.371590i
$386$	−0.138150	+	0.239283i	−0.00703165	+	0.0121792i
$387$	8.02712			0.408041
$388$	0.698602	−	1.21001i	0.0354662	−	0.0614292i
$389$	3.34598	+	5.79541i	0.169648	+	0.293839i	0.938296	−	0.345833i	$-0.112404\pi$
$389$	3.34598	+	5.79541i	0.169648	+	0.293839i	−0.768648	+	0.639672i	$0.779070\pi$
$390$	4.04721	−	2.38411i	0.204939	−	0.120724i
$391$	2.33137			0.117902
$392$	−4.16969	−	5.62260i	−0.210601	−	0.283984i
$393$	4.03186	+	6.98339i	0.203381	+	0.352265i
$394$	6.63552	+	11.4931i	0.334293	+	0.579012i
$395$	9.33749	+	16.1730i	0.469820	+	0.813752i
$396$	2.11879			0.106473
$397$	−12.2912	−	21.2890i	−0.616879	−	1.06847i	−0.990052	−	0.140704i	$-0.955063\pi$
$397$	−12.2912	−	21.2890i	−0.616879	−	1.06847i	0.373172	−	0.927762i	$-0.378270\pi$
$398$	−19.0219			−0.953479
$399$	14.8323	+	7.46630i	0.742545	+	0.373783i
$400$	1.65139	+	2.86029i	0.0825694	+	0.143014i
$401$	34.6545			1.73056			0.865282	−	0.501285i	$-0.167139\pi$
$401$	34.6545			1.73056			0.865282	+	0.501285i	$0.167139\pi$
$402$	−1.67924	−	2.90853i	−0.0837529	−	0.145064i
$403$	−13.9386	+	8.21087i	−0.694332	+	0.409013i
$404$	3.01725	−	5.22602i	0.150114	−	0.260004i
$405$	0.651388	+	1.12824i	0.0323677	+	0.0560625i
$406$	0.527853	+	9.20999i	0.0261969	+	0.457084i
$407$	1.22626	−	2.12395i	0.0607835	−	0.105280i
$408$	−0.243381	+	0.421549i	−0.0120492	+	0.0208698i
$409$	−23.9090			−1.18222			−0.591111	−	0.806590i	$-0.701311\pi$
$409$	−23.9090			−1.18222			−0.591111	+	0.806590i	$0.701311\pi$
$410$	16.4630			0.813052
$411$	3.39583	−	5.88174i	0.167504	−	0.290125i
$412$	5.64770	−	9.78210i	0.278242	−	0.481930i
$413$	21.6239	+	10.8850i	1.06404	+	0.535617i
$414$	−2.39477	−	4.14786i	−0.117696	−	0.203856i
$415$	2.27123	−	3.93389i	0.111491	−	0.193107i
$416$	−0.0315412	−	3.60541i	−0.00154643	−	0.176770i
$417$	6.45522	+	11.1808i	0.316114	+	0.547525i
$418$	13.2982			0.650434
$419$	−6.09738	−	10.5610i	−0.297876	−	0.515937i	0.677773	−	0.735271i	$-0.262945\pi$
$419$	−6.09738	−	10.5610i	−0.297876	−	0.515937i	−0.975650	+	0.219334i	$0.929612\pi$
$420$	−0.197224	−	3.44117i	−0.00962356	−	0.167912i
$421$	14.0504			0.684777			0.342388	−	0.939558i	$-0.388764\pi$
$421$	14.0504			0.684777			0.342388	+	0.939558i	$0.388764\pi$
$422$	1.98750	+	3.44245i	0.0967500	+	0.167576i
$423$	7.97141			0.387583
$424$	−4.29060	−	7.43153i	−0.208370	−	0.360907i
$425$	−0.803833	−	1.39228i	−0.0389916	−	0.0675355i
$426$	−1.46740	−	2.54161i	−0.0710958	−	0.123142i
$427$	−1.54183	−	26.9018i	−0.0746143	−	1.30187i
$428$	−14.0292			−0.678128
$429$	6.58225	−	3.87743i	0.317794	−	0.187204i
$430$	−5.22877	−	9.05649i	−0.252153	−	0.436743i
$431$	−8.65171	+	14.9852i	−0.416738	+	0.721812i	−0.995609	−	0.0936075i	$-0.970160\pi$
$431$	−8.65171	+	14.9852i	−0.416738	+	0.721812i	0.578871	+	0.815419i	$0.303493\pi$
$432$	1.00000			0.0481125
$433$	10.1803	−	17.6328i	0.489234	−	0.847378i	−0.510689	−	0.859765i	$-0.670610\pi$
$433$	10.1803	−	17.6328i	0.489234	−	0.847378i	0.999923	+	0.0123873i	$0.00394309\pi$
$434$	0.679241	+	11.8514i	0.0326046	+	0.568886i
$435$	−2.27123	+	3.93389i	−0.108897	+	0.188616i
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	−15.0303	−	26.0332i	−0.718996	−	1.24534i
$438$	−16.1867			−0.773432
$439$	4.04398			0.193009			0.0965044	−	0.995333i	$-0.469234\pi$
$439$	4.04398			0.193009			0.0965044	+	0.995333i	$0.469234\pi$
$440$	−1.38015	−	2.39050i	−0.0657962	−	0.113962i
$441$	2.78447	−	6.42236i	0.132594	−	0.305827i
$442$	0.0153530	+	1.75498i	0.000730270	+	0.0834758i
$443$	10.1092	−	17.5097i	0.480304	−	0.831912i	−0.519440	−	0.854507i	$-0.673860\pi$
$443$	10.1092	−	17.5097i	0.480304	−	0.831912i	0.999745	+	0.0225951i	$0.00719285\pi$
$444$	0.578756	−	1.00243i	0.0274665	−	0.0475734i
$445$	6.12122	−	10.6023i	0.290174	−	0.502596i
$446$	−9.58013	−	16.5933i	−0.453632	−	0.785714i
$447$	−23.3640			−1.10508
$448$	−2.36323	−	1.18960i	−0.111652	−	0.0562034i
$449$	−19.8059	+	34.3047i	−0.934696	+	1.61894i	−0.159521	+	0.987195i	$0.550995\pi$
$449$	−19.8059	+	34.3047i	−0.934696	+	1.61894i	−0.775175	+	0.631746i	$0.782338\pi$
$450$	−1.65139	+	2.86029i	−0.0778472	+	0.134835i
$451$	26.7749			1.26078
$452$	3.56552	−	6.17566i	0.167708	−	0.290479i
$453$	5.87384			0.275977
$454$	1.18251			0.0554980
$455$	−6.91012	−	10.3295i	−0.323952	−	0.484252i
$456$	6.27630			0.293915
$457$	−6.64742			−0.310953			−0.155477	−	0.987840i	$-0.549691\pi$
$457$	−6.64742			−0.310953			−0.155477	+	0.987840i	$0.549691\pi$
$458$	−7.51599	+	13.0181i	−0.351199	+	0.608295i
$459$	−0.486762			−0.0227201
$460$	−3.11985	+	5.40373i	−0.145464	+	0.251950i
$461$	−10.2371	+	17.7311i	−0.476788	+	0.825820i	−0.999646	−	0.0265991i	$-0.991532\pi$
$461$	−10.2371	+	17.7311i	−0.476788	+	0.825820i	0.522859	+	0.852419i	$0.324866\pi$
$462$	−0.320759	−	5.59660i	−0.0149231	−	0.260378i
$463$	17.2668			0.802457			0.401228	−	0.915978i	$-0.368583\pi$
$463$	17.2668			0.802457			0.401228	+	0.915978i	$0.368583\pi$
$464$	1.74338	+	3.01962i	0.0809344	+	0.140183i
$465$	−2.92262	+	5.06213i	−0.135533	+	0.234751i
$466$	2.59706	−	4.49824i	0.120306	−	0.208377i
$467$	4.37922	−	7.58503i	0.202646	−	0.350994i	−0.746734	−	0.665123i	$-0.768379\pi$
$467$	4.37922	−	7.58503i	0.202646	−	0.350994i	0.949380	+	0.314129i	$0.101713\pi$
$468$	3.10661	−	1.83002i	0.143603	−	0.0845928i
$469$	−7.42843	+	4.87589i	−0.343013	+	0.225148i
$470$	−5.19248	−	8.99364i	−0.239511	−	0.414846i
$471$	6.24495			0.287752
$472$	9.15014			0.421169
$473$	−8.50388	−	14.7292i	−0.391009	−	0.677247i
$474$	7.16738	+	12.4143i	0.329209	+	0.570206i
$475$	−10.3646	+	17.9520i	−0.475561	+	0.823695i
$476$	1.15033	+	0.579054i	0.0527253	+	0.0265409i
$477$	4.29060	−	7.43153i	0.196453	−	0.340266i
$478$	−25.3978			−1.16167
$479$	13.5126	−	23.4046i	0.617408	−	1.06938i	−0.372549	−	0.928012i	$-0.621516\pi$
$479$	13.5126	−	23.4046i	0.617408	−	1.06938i	0.989957	−	0.141369i	$-0.0451504\pi$
$480$	−0.651388	−	1.12824i	−0.0297317	−	0.0514967i
$481$	−0.0365092	−	4.17331i	−0.00166468	−	0.190286i
$482$	11.8575			0.540094
$483$	−10.5937	+	6.95352i	−0.482030	+	0.316396i
$484$	3.25537	+	5.63846i	0.147971	+	0.256294i
$485$	−0.910122	−	1.57638i	−0.0413265	−	0.0715796i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	21.9435			0.994353			0.497177	−	0.867649i	$-0.334370\pi$
$487$	21.9435			0.994353			0.497177	+	0.867649i	$0.334370\pi$
$488$	−5.09231	−	8.82015i	−0.230518	−	0.399269i
$489$	−2.60767			−0.117923
$490$	−9.05971	+	1.04190i	−0.409276	+	0.0470684i
$491$	−7.09020	−	12.2806i	−0.319976	−	0.554215i	0.660507	−	0.750820i	$-0.270342\pi$
$491$	−7.09020	−	12.2806i	−0.319976	−	0.554215i	−0.980483	+	0.196605i	$0.937008\pi$
$492$	12.6369			0.569715
$493$	−0.848612	−	1.46984i	−0.0382196	−	0.0661982i
$494$	19.4980	−	11.4858i	0.877257	−	0.516769i
$495$	1.38015	−	2.39050i	0.0620333	−	0.107445i
$496$	2.24338	+	3.88565i	0.100731	+	0.174471i
$497$	−6.49131	+	4.26079i	−0.291175	+	0.191122i
$498$	1.74338	−	3.01962i	0.0781228	−	0.135313i
$499$	14.7488	−	25.5456i	0.660245	−	1.14358i	−0.320306	−	0.947314i	$-0.603786\pi$
$499$	14.7488	−	25.5456i	0.660245	−	1.14358i	0.980551	−	0.196264i	$-0.0628811\pi$
$500$	10.8167			0.483735
$501$	6.90833			0.308641
$502$	−10.7397	+	18.6017i	−0.479336	+	0.830234i
$503$	−7.49400	+	12.9800i	−0.334141	+	0.578749i	−0.983319	−	0.181887i	$-0.941780\pi$
$503$	−7.49400	+	12.9800i	−0.334141	+	0.578749i	0.649178	+	0.760636i	$0.275113\pi$
$504$	−0.151388	−	2.64142i	−0.00674335	−	0.117658i
$505$	−3.93079	−	6.80834i	−0.174918	−	0.302967i
$506$	−5.07401	+	8.78844i	−0.225567	+	0.390694i
$507$	6.30204	−	11.3703i	0.279883	−	0.504974i
$508$	2.59305	+	4.49130i	0.115048	+	0.199269i
$509$	41.9674			1.86017			0.930087	−	0.367340i	$-0.119731\pi$
$509$	41.9674			1.86017			0.930087	+	0.367340i	$0.119731\pi$
$510$	0.317071	+	0.549183i	0.0140401	+	0.0243182i
$511$	2.45048	+	42.7559i	0.108403	+	1.89141i
$512$	−1.00000			−0.0441942
$513$	3.13815	+	5.43544i	0.138553	+	0.239980i
$514$	6.84589			0.301959
$515$	−7.35769	−	12.7439i	−0.324218	−	0.561563i
$516$	−4.01356	−	6.95169i	−0.176687	−	0.306031i
$517$	−8.44487	−	14.6269i	−0.371405	−	0.643292i
$518$	−2.73546	−	1.37698i	−0.120189	−	0.0605010i
$519$	−7.72710			−0.339182
$520$	−4.08831	−	2.31294i	−0.179284	−	0.101429i
$521$	−8.68748	−	15.0472i	−0.380605	−	0.659228i	0.610544	−	0.791983i	$-0.290951\pi$
$521$	−8.68748	−	15.0472i	−0.380605	−	0.659228i	−0.991149	+	0.132755i	$0.957618\pi$
$522$	−1.74338	+	3.01962i	−0.0763057	+	0.132165i
$523$	33.0034			1.44314			0.721569	−	0.692343i	$-0.243421\pi$
$523$	33.0034			1.44314			0.721569	+	0.692343i	$0.243421\pi$
$524$	4.03186	−	6.98339i	0.176133	−	0.305071i
$525$	7.80521	+	3.92899i	0.340647	+	0.171475i
$526$	7.69998	−	13.3368i	0.335735	−	0.581510i
$527$	−1.09199	−	1.89139i	−0.0475680	−	0.0823902i
$528$	−1.05939	−	1.83493i	−0.0461042	−	0.0798549i
$529$	−0.0603265			−0.00262289
$530$	−11.1794			−0.485601
$531$	4.57507	+	7.92425i	0.198541	+	0.343883i
$532$	−0.950155	−	16.5783i	−0.0411945	−	0.718761i
$533$	39.2579	−	23.1258i	1.70045	−	1.00169i
$534$	4.69860	−	8.13822i	0.203328	−	0.352175i
$535$	−9.13847	+	15.8283i	−0.395091	+	0.684317i
$536$	−1.67924	+	2.90853i	−0.0725322	+	0.125629i
$537$	−9.57539	−	16.5851i	−0.413208	−	0.715698i
$538$	11.7313			0.505773
$539$	−14.7344	+	1.69452i	−0.634656	+	0.0729879i
$540$	0.651388	−	1.12824i	0.0280313	−	0.0485516i
$541$	−8.93967	+	15.4840i	−0.384347	+	0.665708i	−0.991678	−	0.128741i	$-0.958907\pi$
$541$	−8.93967	+	15.4840i	−0.384347	+	0.665708i	0.607332	+	0.794448i	$0.292240\pi$
$542$	26.0856			1.12047
$543$	−6.54859	+	11.3425i	−0.281027	+	0.486753i
$544$	0.486762			0.0208698
$545$	−14.3305			−0.613853
$546$	−5.30415	−	7.92881i	−0.226997	−	0.339322i
$547$	11.4550			0.489782			0.244891	−	0.969551i	$-0.421248\pi$
$547$	11.4550			0.489782			0.244891	+	0.969551i	$0.421248\pi$
$548$	−6.79165			−0.290125
$549$	5.09231	−	8.82015i	0.217335	−	0.376435i
$550$	6.99788			0.298391
$551$	−10.9420	+	18.9521i	−0.466144	+	0.807385i
$552$	−2.39477	+	4.14786i	−0.101928	+	0.176545i
$553$	31.7062	−	20.8114i	1.34828	−	0.884991i
$554$	−23.4307			−0.995474
$555$	−0.753989	−	1.30595i	−0.0320050	−	0.0554344i
$556$	6.45522	−	11.1808i	0.273762	−	0.474170i
$557$	−20.3122	+	35.1817i	−0.860654	+	1.49070i	0.0106442	+	0.999943i	$0.496612\pi$
$557$	−20.3122	+	35.1817i	−0.860654	+	1.49070i	−0.871298	+	0.490754i	$0.836722\pi$
$558$	−2.24338	+	3.88565i	−0.0949699	+	0.164493i
$559$	−25.1903	−	14.2513i	−1.06544	−	0.602765i
$560$	−2.88153	+	1.89139i	−0.121767	+	0.0799257i
$561$	0.515673	+	0.893172i	0.0217717	+	0.0377098i
$562$	−6.15751			−0.259739
$563$	33.1855			1.39860			0.699301	−	0.714827i	$-0.253495\pi$
$563$	33.1855			1.39860			0.699301	+	0.714827i	$0.253495\pi$
$564$	−3.98570	−	6.90344i	−0.167828	−	0.290687i
$565$	−4.64507	−	8.04550i	−0.195420	−	0.338477i
$566$	10.9661	−	18.9939i	0.460942	−	0.798374i
$567$	2.21184	−	1.45181i	0.0928885	−	0.0609705i
$568$	−1.46740	+	2.54161i	−0.0615708	+	0.106644i
$569$	0.0679534			0.00284876			0.00142438	−	0.999999i	$-0.499547\pi$
$569$	0.0679534			0.00284876			0.00142438	+	0.999999i	$0.499547\pi$
$570$	4.08831	−	7.08115i	0.171240	−	0.296597i
$571$	−10.2822	−	17.8092i	−0.430295	−	0.745293i	0.566603	−	0.823991i	$-0.308257\pi$
$571$	−10.2822	−	17.8092i	−0.430295	−	0.745293i	−0.996899	+	0.0786977i	$0.974924\pi$
$572$	−6.64908	−	3.76168i	−0.278012	−	0.157284i
$573$	−11.4889			−0.479955
$574$	−1.91307	−	33.3793i	−0.0798501	−	1.39323i
$575$	−7.90938	−	13.6995i	−0.329844	−	0.571307i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	22.7814	+	39.4586i	0.948403	+	1.64268i	0.748790	+	0.662808i	$0.230635\pi$
$577$	22.7814	+	39.4586i	0.948403	+	1.64268i	0.199613	+	0.979875i	$0.436031\pi$
$578$	16.7631			0.697251
$579$	0.138150	+	0.239283i	0.00574132	+	0.00994426i
$580$	4.54247			0.188616
$581$	−8.24001	−	4.14786i	−0.341853	−	0.172082i
$582$	−0.698602	−	1.21001i	−0.0289580	−	0.0501567i
$583$	−18.1817			−0.753010
$584$	8.09337	+	14.0181i	0.334906	+	0.580074i
$585$	−0.0410911	−	4.69704i	−0.00169891	−	0.194199i
$586$	8.74075	−	15.1394i	0.361077	−	0.625404i
$587$	2.71527	+	4.70298i	0.112071	+	0.194113i	0.916605	−	0.399794i	$-0.130918\pi$
$587$	2.71527	+	4.70298i	0.112071	+	0.194113i	−0.804534	+	0.593906i	$0.797585\pi$
$588$	−6.95416	+	0.799757i	−0.286785	+	0.0329814i
$589$	−14.0801	+	24.3875i	−0.580162	+	1.00487i
$590$	5.96029	−	10.3235i	0.245381	−	0.425013i
$591$	13.2710			0.545898
$592$	−1.15751			−0.0475734
$593$	−2.77524	+	4.80686i	−0.113966	+	0.197394i	−0.917366	−	0.398045i	$-0.869689\pi$
$593$	−2.77524	+	4.80686i	−0.113966	+	0.197394i	0.803400	+	0.595439i	$0.203022\pi$
$594$	1.05939	−	1.83493i	0.0434675	−	0.0752879i
$595$	1.40262	−	0.920656i	0.0575018	−	0.0377432i
$596$	11.6820	+	20.2338i	0.478513	+	0.828809i
$597$	−9.51093	+	16.4734i	−0.389256	+	0.674212i
$598$	0.151068	+	17.2683i	0.00617761	+	0.706152i
$599$	−7.94019	−	13.7528i	−0.324427	−	0.561925i	0.656969	−	0.753918i	$-0.271838\pi$
$599$	−7.94019	−	13.7528i	−0.324427	−	0.561925i	−0.981396	+	0.191993i	$0.938505\pi$
$600$	3.30278			0.134835
$601$	19.1239	+	33.1235i	0.780078	+	1.35114i	0.931896	+	0.362727i	$0.118154\pi$
$601$	19.1239	+	33.1235i	0.780078	+	1.35114i	−0.151817	+	0.988409i	$0.548513\pi$
$602$	−17.7547	+	11.6539i	−0.723627	+	0.474977i
$603$	−3.35848			−0.136768
$604$	−2.93692	−	5.08689i	−0.119501	−	0.206983i
$605$	8.48202			0.344843
$606$	−3.01725	−	5.22602i	−0.122567	−	0.212293i
$607$	9.66094	+	16.7332i	0.392125	+	0.679181i	0.992730	−	0.120365i	$-0.0384066\pi$
$607$	9.66094	+	16.7332i	0.392125	+	0.679181i	−0.600604	+	0.799546i	$0.705073\pi$
$608$	−3.13815	−	5.43544i	−0.127269	−	0.220436i
$609$	8.24001	+	4.14786i	0.333902	+	0.168080i
$610$	−13.2683			−0.537217
$611$	−25.0155	−	14.1524i	−1.01202	−	0.572544i
$612$	0.243381	+	0.421549i	0.00983810	+	0.0170401i
$613$	15.2625	−	26.4355i	0.616448	−	1.06772i	−0.373680	−	0.927558i	$-0.621904\pi$
$613$	15.2625	−	26.4355i	0.616448	−	1.06772i	0.990129	−	0.140162i	$-0.0447625\pi$
$614$	12.0673			0.486997
$615$	8.23152	−	14.2574i	0.331927	−	0.574914i
$616$	−4.68642	+	3.07609i	−0.188821	+	0.123939i
$617$	−12.5446	+	21.7279i	−0.505026	+	0.874731i	0.494957	+	0.868917i	$0.335184\pi$
$617$	−12.5446	+	21.7279i	−0.505026	+	0.874731i	−0.999983	+	0.00581322i	$0.998150\pi$
$618$	−5.64770	−	9.78210i	−0.227184	−	0.393494i
$619$	9.35717	+	16.2071i	0.376096	+	0.651418i	0.990490	−	0.137581i	$-0.0439328\pi$
$619$	9.35717	+	16.2071i	0.376096	+	0.651418i	−0.614394	+	0.788999i	$0.710599\pi$
$620$	5.84524			0.234751
$621$	−4.78954			−0.192198
$622$	−0.755881	−	1.30923i	−0.0303081	−	0.0524951i
$623$	−22.2077	−	11.1789i	−0.889734	−	0.447875i
$624$	−3.13815	−	1.77539i	−0.125627	−	0.0710725i
$625$	−1.21110	+	2.09769i	−0.0484441	+	0.0839076i
$626$	0.862908	−	1.49460i	0.0344887	−	0.0597362i
$627$	6.64908	−	11.5165i	0.265539	−	0.459926i
$628$	−3.12248	−	5.40829i	−0.124600	−	0.215814i
$629$	0.563433			0.0224655
$630$	−3.07876	−	1.54979i	−0.122661	−	0.0617449i
$631$	−14.4362	+	25.0042i	−0.574695	+	0.995401i	0.421379	+	0.906884i	$0.361546\pi$
$631$	−14.4362	+	25.0042i	−0.574695	+	0.995401i	−0.996075	+	0.0885169i	$0.971787\pi$
$632$	7.16738	−	12.4143i	0.285103	−	0.493813i
$633$	3.97500			0.157992
$634$	10.6520	−	18.4499i	0.423046	−	0.732737i
$635$	6.75633			0.268117
$636$	−8.58119			−0.340266
$637$	−20.1403	+	15.2108i	−0.797988	+	0.602674i
$638$	7.38771			0.292482
$639$	−2.93480			−0.116099
$640$	−0.651388	+	1.12824i	−0.0257484	+	0.0445975i
$641$	2.19822			0.0868243			0.0434121	−	0.999057i	$-0.486177\pi$
$641$	2.19822			0.0868243			0.0434121	+	0.999057i	$0.486177\pi$
$642$	−7.01462	+	12.1497i	−0.276845	+	0.479509i
$643$	8.74713	−	15.1505i	0.344953	−	0.597476i	−0.640392	−	0.768048i	$-0.721228\pi$
$643$	8.74713	−	15.1505i	0.344953	−	0.597476i	0.985345	+	0.170572i	$0.0545615\pi$
$644$	11.3188	+	5.69765i	0.446022	+	0.224519i
$645$	−10.4575			−0.411765
$646$	1.52753	+	2.64576i	0.0601000	+	0.104096i
$647$	−16.0868	+	27.8631i	−0.632436	+	1.09541i	0.354616	+	0.935012i	$0.384612\pi$
$647$	−16.0868	+	27.8631i	−0.632436	+	1.09541i	−0.987052	+	0.160400i	$0.948722\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	9.69360	−	16.7898i	0.380507	−	0.659058i
$650$	10.2604	−	6.04415i	0.402447	−	0.237071i
$651$	10.6032	+	5.33746i	0.415574	+	0.209192i
$652$	1.30383	+	2.25831i	0.0510621	+	0.0884421i
$653$	47.5661			1.86141			0.930703	−	0.365775i	$-0.119196\pi$
$653$	47.5661			1.86141			0.930703	+	0.365775i	$0.119196\pi$
$654$	−11.0000			−0.430134
$655$	−5.25261	−	9.09779i	−0.205236	−	0.355480i
$656$	−6.31845	−	10.9439i	−0.246694	−	0.427287i
$657$	−8.09337	+	14.0181i	−0.315752	+	0.546899i
$658$	−17.6315	+	11.5730i	−0.687347	+	0.451163i
$659$	−3.69892	+	6.40672i	−0.144090	+	0.249570i	−0.929033	−	0.369997i	$-0.879359\pi$
$659$	−3.69892	+	6.40672i	−0.144090	+	0.249570i	0.784943	+	0.619568i	$0.212692\pi$
$660$	−2.76031			−0.107445
$661$	−6.11485	+	10.5912i	−0.237840	+	0.411951i	−0.960094	−	0.279677i	$-0.909773\pi$
$661$	−6.11485	+	10.5912i	−0.237840	+	0.411951i	0.722254	+	0.691628i	$0.243106\pi$
$662$	8.21691	+	14.2321i	0.319359	+	0.553146i
$663$	1.52753	+	0.864193i	0.0593245	+	0.0335625i
$664$	−3.48676			−0.135313
$665$	−19.3232	−	9.72692i	−0.749321	−	0.377194i
$666$	−0.578756	−	1.00243i	−0.0224263	−	0.0388435i
$667$	−8.34999	−	14.4626i	−0.323313	−	0.559994i
$668$	−3.45416	−	5.98279i	−0.133646	−	0.231481i
$669$	−19.1603			−0.740779
$670$	2.18767	+	3.78916i	0.0845172	+	0.146388i
$671$	−21.5791			−0.833051
$672$	−2.21184	+	1.45181i	−0.0853236	+	0.0560049i
$673$	24.4511	+	42.3506i	0.942521	+	1.63249i	0.760640	+	0.649174i	$0.224885\pi$
$673$	24.4511	+	42.3506i	0.942521	+	1.63249i	0.181882	+	0.983320i	$0.441781\pi$
$674$	12.9178			0.497576
$675$	1.65139	+	2.86029i	0.0635619	+	0.110093i
$676$	−12.9980	+	0.227438i	−0.499923	+	0.00874761i
$677$	−9.74027	+	16.8707i	−0.374349	+	0.648392i	−0.990229	−	0.139448i	$-0.955467\pi$
$677$	−9.74027	+	16.8707i	−0.374349	+	0.648392i	0.615880	+	0.787840i	$0.288801\pi$
$678$	−3.56552	−	6.17566i	−0.136933	−	0.237175i
$679$	−3.09039	+	2.02848i	−0.118598	+	0.0778460i
$680$	0.317071	−	0.549183i	0.0121591	−	0.0210602i
$681$	0.591256	−	1.02409i	0.0226570	−	0.0392430i
$682$	9.50650			0.364023
$683$	−18.1603			−0.694883			−0.347442	−	0.937702i	$-0.612950\pi$
$683$	−18.1603			−0.694883			−0.347442	+	0.937702i	$0.612950\pi$
$684$	3.13815	−	5.43544i	0.119990	−	0.207829i
$685$	−4.42400	+	7.66259i	−0.169032	+	0.292773i
$686$	3.16527	+	18.2478i	0.120850	+	0.696703i
$687$	7.51599	+	13.0181i	0.286753	+	0.496671i
$688$	−4.01356	+	6.95169i	−0.153015	+	0.265031i
$689$	−26.6584	+	15.7038i	−1.01560	+	0.598266i
$690$	3.11985	+	5.40373i	0.118771	+	0.205717i
$691$	37.0049			1.40773			0.703866	−	0.710333i	$-0.251456\pi$
$691$	37.0049			1.40773			0.703866	+	0.710333i	$0.251456\pi$
$692$	3.86355	+	6.69186i	0.146870	+	0.254386i
$693$	−5.00718	−	2.52052i	−0.190207	−	0.0957465i
$694$	16.0387			0.608822
$695$	−8.40970	−	14.5660i	−0.318998	−	0.552521i
$696$	3.48676			0.132165
$697$	3.07558	+	5.32707i	0.116496	+	0.201777i
$698$	3.81951	+	6.61558i	0.144570	+	0.250403i
$699$	−2.59706	−	4.49824i	−0.0982298	−	0.170139i
$700$	−0.500000	−	8.72401i	−0.0188982	−	0.329736i
$701$	36.3972			1.37470			0.687352	−	0.726325i	$-0.258773\pi$
$701$	36.3972			1.37470			0.687352	+	0.726325i	$0.258773\pi$
$702$	−0.0315412	−	3.60541i	−0.00119044	−	0.136078i
$703$	−3.63244	−	6.29158i	−0.137000	−	0.237291i
$704$	−1.05939	+	1.83493i	−0.0399274	+	0.0691563i
$705$	−10.3850			−0.391120
$706$	−16.1956	+	28.0515i	−0.609528	+	1.05573i
$707$	−13.3473	+	8.76096i	−0.501978	+	0.329490i
$708$	4.57507	−	7.92425i	0.171942	−	0.297812i
$709$	0.165683	+	0.286972i	0.00622236	+	0.0107774i	0.869120	−	0.494602i	$-0.164686\pi$
$709$	0.165683	+	0.286972i	0.00622236	+	0.0107774i	−0.862897	+	0.505379i	$0.831353\pi$
$710$	1.91169	+	3.31115i	0.0717446	+	0.124265i
$711$	14.3348			0.537596
$712$	−9.39720			−0.352175
$713$	−10.7448	−	18.6105i	−0.402394	−	0.696968i
$714$	1.07664	−	0.706688i	0.0402922	−	0.0264471i
$715$	−8.57519	+	5.05142i	−0.320694	+	0.188912i
$716$	−9.57539	+	16.5851i	−0.357849	+	0.619813i
$717$	−12.6989	+	21.9952i	−0.474250	+	0.821425i
$718$	−1.57507	+	2.72810i	−0.0587810	+	0.101812i
$719$	−23.7931	−	41.2108i	−0.887333	−	1.53691i	−0.843017	−	0.537887i	$-0.819223\pi$
$719$	−23.7931	−	41.2108i	−0.887333	−	1.53691i	−0.0443159	−	0.999018i	$-0.514111\pi$
$720$	−1.30278			−0.0485516
$721$	−24.9836	+	16.3988i	−0.930439	+	0.610724i
$722$	10.1960	−	17.6599i	0.379455	−	0.657235i
$723$	5.92875	−	10.2689i	0.220492	−	0.381904i
$724$	13.0972			0.486753
$725$	−5.75800	+	9.97314i	−0.213847	+	0.370393i
$726$	6.51073			0.241636
$727$	−32.9021			−1.22027			−0.610136	−	0.792297i	$-0.708885\pi$
$727$	−32.9021			−1.22027			−0.610136	+	0.792297i	$0.708885\pi$
$728$	−4.21447	+	8.55793i	−0.156199	+	0.317178i
$729$	1.00000			0.0370370
$730$	21.0877			0.780491
$731$	1.95365	−	3.38382i	0.0722583	−	0.125155i
$732$	−10.1846			−0.376435
$733$	−10.5040	+	18.1935i	−0.387974	+	0.671991i	−0.992177	−	0.124839i	$-0.960158\pi$
$733$	−10.5040	+	18.1935i	−0.387974	+	0.671991i	0.604203	+	0.796831i	$0.293492\pi$
$734$	−2.23463	+	3.87049i	−0.0824816	+	0.142862i
$735$	−3.62754	+	8.36689i	−0.133804	+	0.308618i
$736$	4.78954			0.176545
$737$	3.55796	+	6.16256i	0.131059	+	0.227001i
$738$	6.31845	−	10.9439i	0.232585	−	0.402850i
$739$	−3.26085	+	5.64796i	−0.119952	+	0.207763i	−0.919749	−	0.392508i	$-0.871607\pi$
$739$	−3.26085	+	5.64796i	−0.119952	+	0.207763i	0.799796	+	0.600272i	$0.204941\pi$
$740$	−0.753989	+	1.30595i	−0.0277172	+	0.0480076i
$741$	−0.197962	−	22.6287i	−0.00727231	−	0.831284i
$742$	1.29909	+	22.6665i	0.0476910	+	0.832113i
$743$	−8.64802	−	14.9788i	−0.317265	−	0.549519i	0.662651	−	0.748928i	$-0.269431\pi$
$743$	−8.64802	−	14.9788i	−0.317265	−	0.549519i	−0.979916	+	0.199409i	$0.936098\pi$
$744$	4.48676			0.164493
$745$	30.4380			1.11516
$746$	2.47615	+	4.28883i	0.0906585	+	0.157025i
$747$	−1.74338	−	3.01962i	−0.0637870	−	0.110482i
$748$	0.515673	−	0.893172i	0.0188549	−	0.0326576i
$749$	33.1543	+	16.6892i	1.21143	+	0.609810i
$750$	5.40833	−	9.36750i	0.197484	−	0.342053i
$751$	−9.62426			−0.351194			−0.175597	−	0.984462i	$-0.556186\pi$
$751$	−9.62426			−0.351194			−0.175597	+	0.984462i	$0.556186\pi$
$752$	−3.98570	+	6.90344i	−0.145344	+	0.251743i
$753$	10.7397	+	18.6017i	0.391376	+	0.677883i
$754$	10.8320	−	6.38085i	0.394478	−	0.232377i
$755$	−7.65229			−0.278495
$756$	−2.36323	−	1.18960i	−0.0859498	−	0.0432654i
$757$	−19.5740	−	33.9032i	−0.711429	−	1.23223i	−0.964321	−	0.264737i	$-0.914715\pi$
$757$	−19.5740	−	33.9032i	−0.711429	−	1.23223i	0.252891	−	0.967495i	$-0.418619\pi$
$758$	−6.55920	−	11.3609i	−0.238241	−	0.412645i
$759$	5.07401	+	8.78844i	0.184175	+	0.319000i
$760$	−8.17661			−0.296597
$761$	5.18879	+	8.98725i	0.188094	+	0.325788i	0.944615	−	0.328182i	$-0.106436\pi$
$761$	5.18879	+	8.98725i	0.188094	+	0.325788i	−0.756521	+	0.653969i	$0.773103\pi$
$762$	5.18610			0.187873
$763$	1.66527	+	29.0556i	0.0602867	+	1.05188i
$764$	5.74444	+	9.94966i	0.207827	+	0.359966i
$765$	0.634142			0.0229275
$766$	−6.09000	−	10.5482i	−0.220041	−	0.381122i
$767$	−0.288606	−	32.9900i	−0.0104210	−	1.19120i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	17.5102	+	30.3285i	0.631434	+	1.09368i	0.987259	+	0.159123i	$0.0508665\pi$
$769$	17.5102	+	30.3285i	0.631434	+	1.09368i	−0.355825	+	0.934553i	$0.615800\pi$
$770$	0.417877	+	7.29112i	0.0150592	+	0.262754i
$771$	3.42294	−	5.92871i	0.123274	−	0.213517i
$772$	0.138150	−	0.239283i	0.00497213	−	0.00861198i
$773$	20.1234			0.723789			0.361894	−	0.932219i	$-0.382130\pi$
$773$	20.1234			0.723789			0.361894	+	0.932219i	$0.382130\pi$
$774$	−8.02712			−0.288529
$775$	−7.40938	+	12.8334i	−0.266153	+	0.460990i
$776$	−0.698602	+	1.21001i	−0.0250784	+	0.0434370i
$777$	−2.56023	+	1.68049i	−0.0918477	+	0.0602873i
$778$	−3.34598	−	5.79541i	−0.119959	−	0.207776i
$779$	39.6565	−	68.6870i	1.42084	−	2.46097i
$780$	−4.04721	+	2.38411i	−0.144914	+	0.0853648i
$781$	3.10911	+	5.38514i	0.111253	+	0.192696i
$782$	−2.33137			−0.0833695
$783$	1.74338	+	3.01962i	0.0623034	+	0.107913i
$784$	4.16969	+	5.62260i	0.148918	+	0.200807i
$785$	−8.13577			−0.290378
$786$	−4.03186	−	6.98339i	−0.143812	−	0.249089i
$787$	1.90307			0.0678370			0.0339185	−	0.999425i	$-0.489201\pi$
$787$	1.90307			0.0678370			0.0339185	+	0.999425i	$0.489201\pi$
$788$	−6.63552	−	11.4931i	−0.236381	−	0.409423i
$789$	−7.69998	−	13.3368i	−0.274127	−	0.474801i
$790$	−9.33749	−	16.1730i	−0.332213	−	0.575410i
$791$	−15.7727	+	10.3529i	−0.560813	+	0.368108i
$792$	−2.11879			−0.0752879
$793$	−31.6397	+	18.6381i	−1.12356	+	0.661858i
$794$	12.2912	+	21.2890i	0.436200	+	0.755520i
$795$	−5.58968	+	9.68162i	−0.198246	+	0.343372i
$796$	19.0219			0.674212
$797$	10.9112	−	18.8987i	0.386494	−	0.669427i	−0.605481	−	0.795859i	$-0.707019\pi$
$797$	10.9112	−	18.8987i	0.386494	−	0.669427i	0.991975	+	0.126433i	$0.0403527\pi$
$798$	−14.8323	−	7.46630i	−0.525059	−	0.264304i
$799$	1.94009	−	3.36034i	0.0686355	−	0.118880i
$800$	−1.65139	−	2.86029i	−0.0583854	−	0.101126i
$801$	−4.69860	−	8.13822i	−0.166017	−	0.287550i
$802$	−34.6545			−1.22369
$803$	34.2963			1.21029
$804$	1.67924	+	2.90853i	0.0592223	+	0.102576i
$805$	13.8012	−	9.05887i	0.486428	−	0.319283i
$806$	13.9386	−	8.21087i	0.490967	−	0.289216i
$807$	5.86566	−	10.1596i	0.206481	−	0.357636i
$808$	−3.01725	+	5.22602i	−0.106146	+	0.183851i
$809$	−22.9519	+	39.7538i	−0.806944	+	1.39767i	0.108026	+	0.994148i	$0.465547\pi$
$809$	−22.9519	+	39.7538i	−0.806944	+	1.39767i	−0.914971	+	0.403520i	$0.867786\pi$
$810$	−0.651388	−	1.12824i	−0.0228874	−	0.0396422i
$811$	3.66652			0.128749			0.0643744	−	0.997926i	$-0.479495\pi$
$811$	3.66652			0.128749			0.0643744	+	0.997926i	$0.479495\pi$
$812$	−0.527853	−	9.20999i	−0.0185240	−	0.323207i
$813$	13.0428	−	22.5908i	0.457431	−	0.792293i
$814$	−1.22626	+	2.12395i	−0.0429804	+	0.0744443i
$815$	3.39720			0.118999
$816$	0.243381	−	0.421549i	0.00852004	−	0.0147571i
$817$	−50.3806			−1.76259
$818$	23.9090			0.835957
$819$	−9.51862	+	0.629129i	−0.332608	+	0.0219835i
$820$	−16.4630			−0.574914
$821$	−20.3484			−0.710162			−0.355081	−	0.934835i	$-0.615547\pi$
$821$	−20.3484			−0.710162			−0.355081	+	0.934835i	$0.615547\pi$
$822$	−3.39583	+	5.88174i	−0.118443	+	0.205149i
$823$	27.7345			0.966763			0.483381	−	0.875410i	$-0.339408\pi$
$823$	27.7345			0.966763			0.483381	+	0.875410i	$0.339408\pi$
$824$	−5.64770	+	9.78210i	−0.196747	+	0.340776i
$825$	3.49894	−	6.06035i	0.121818	−	0.210994i
$826$	−21.6239	−	10.8850i	−0.752390	−	0.378738i
$827$	36.6640			1.27493			0.637466	−	0.770478i	$-0.279983\pi$
$827$	36.6640			1.27493			0.637466	+	0.770478i	$0.279983\pi$
$828$	2.39477	+	4.14786i	0.0832240	+	0.144148i
$829$	−7.23120	+	12.5248i	−0.251150	+	0.435005i	−0.963843	−	0.266472i	$-0.914142\pi$
$829$	−7.23120	+	12.5248i	−0.251150	+	0.435005i	0.712693	+	0.701476i	$0.247475\pi$
$830$	−2.27123	+	3.93389i	−0.0788357	+	0.136547i
$831$	−11.7153	+	20.2916i	−0.406400	+	0.703906i
$832$	0.0315412	+	3.60541i	0.00109349	+	0.124995i
$833$	−2.02965	−	2.73687i	−0.0703232	−	0.0948270i
$834$	−6.45522	−	11.1808i	−0.223526	−	0.387158i
$835$	−9.00000			−0.311458
$836$	−13.2982			−0.459926
$837$	2.24338	+	3.88565i	0.0775426	+	0.134308i
$838$	6.09738	+	10.5610i	0.210630	+	0.364823i
$839$	−2.51779	+	4.36094i	−0.0869237	+	0.150556i	−0.906209	−	0.422829i	$-0.861037\pi$
$839$	−2.51779	+	4.36094i	−0.0869237	+	0.150556i	0.819286	+	0.573386i	$0.194370\pi$
$840$	0.197224	+	3.44117i	0.00680489	+	0.118732i
$841$	8.42124	−	14.5860i	0.290388	−	0.502966i
$842$	−14.0504			−0.484210
$843$	−3.07876	+	5.33256i	−0.106038	+	0.183663i
$844$	−1.98750	−	3.44245i	−0.0684126	−	0.118494i
$845$	−8.21014	+	14.8130i	−0.282437	+	0.509582i
$846$	−7.97141			−0.274063
$847$	−0.985646	−	17.1976i	−0.0338672	−	0.590915i
$848$	4.29060	+	7.43153i	0.147340	+	0.255200i
$849$	−10.9661	−	18.9939i	−0.376357	−	0.651870i
$850$	0.803833	+	1.39228i	0.0275713	+	0.0477548i
$851$	5.54394			0.190044
$852$	1.46740	+	2.54161i	0.0502723	+	0.0870742i
$853$	21.9833			0.752693			0.376346	−	0.926479i	$-0.377180\pi$
$853$	21.9833			0.752693			0.376346	+	0.926479i	$0.377180\pi$
$854$	1.54183	+	26.9018i	0.0527603	+	0.920562i
$855$	−4.08831	−	7.08115i	−0.139817	−	0.242170i
$856$	14.0292			0.479509
$857$	21.6450	+	37.4902i	0.739378	+	1.28064i	0.952776	+	0.303675i	$0.0982137\pi$
$857$	21.6450	+	37.4902i	0.739378	+	1.28064i	−0.213397	+	0.976965i	$0.568453\pi$
$858$	−6.58225	+	3.87743i	−0.224714	+	0.132373i
$859$	22.6834	−	39.2888i	0.773947	−	1.34052i	−0.161438	−	0.986883i	$-0.551613\pi$
$859$	22.6834	−	39.2888i	0.773947	−	1.34052i	0.935385	−	0.353632i	$-0.115054\pi$
$860$	5.22877	+	9.05649i	0.178299	+	0.308824i
$861$	−29.8639	−	15.0329i	−1.01776	−	0.512319i
$862$	8.65171	−	14.9852i	0.294678	−	0.510398i
$863$	−6.76755	+	11.7217i	−0.230370	+	0.399012i	−0.957917	−	0.287045i	$-0.907327\pi$
$863$	−6.76755	+	11.7217i	−0.230370	+	0.399012i	0.727547	+	0.686058i	$0.240660\pi$
$864$	−1.00000			−0.0340207
$865$	10.0667			0.342277
$866$	−10.1803	+	17.6328i	−0.345941	+	0.599187i
$867$	8.38153	−	14.5172i	0.284652	−	0.493031i
$868$	−0.679241	−	11.8514i	−0.0230549	−	0.402263i
$869$	−15.1862	−	26.3032i	−0.515155	−	0.892275i
$870$	2.27123	−	3.93389i	0.0770021	−	0.133371i
$871$	10.5394	+	5.96262i	0.357115	+	0.202036i
$872$	5.50000	+	9.52628i	0.186254	+	0.322601i
$873$	−1.39720			−0.0472882
$874$	15.0303	+	26.0332i	0.508407	+	0.880587i
$875$	−25.5622	−	12.8675i	−0.864161	−	0.435002i
$876$	16.1867			0.546899
$877$	−9.71091	−	16.8198i	−0.327914	−	0.567964i	0.654184	−	0.756336i	$-0.273012\pi$
$877$	−9.71091	−	16.8198i	−0.327914	−	0.567964i	−0.982098	+	0.188372i	$0.939679\pi$
$878$	−4.04398			−0.136478
$879$	−8.74075	−	15.1394i	−0.294818	−	0.510640i
$880$	1.38015	+	2.39050i	0.0465250	+	0.0805836i
$881$	−2.77059	−	4.79881i	−0.0933437	−	0.161676i	0.815572	−	0.578655i	$-0.196422\pi$
$881$	−2.77059	−	4.79881i	−0.0933437	−	0.161676i	−0.908916	+	0.416979i	$0.863089\pi$
$882$	−2.78447	+	6.42236i	−0.0937581	+	0.216252i
$883$	51.6940			1.73964			0.869821	−	0.493367i	$-0.164234\pi$
$883$	51.6940			1.73964			0.869821	+	0.493367i	$0.164234\pi$
$884$	−0.0153530	−	1.75498i	−0.000516379	−	0.0590263i
$885$	−5.96029	−	10.3235i	−0.200353	−	0.347021i
$886$	−10.1092	+	17.5097i	−0.339627	+	0.588250i
$887$	−3.54837			−0.119143			−0.0595713	−	0.998224i	$-0.518973\pi$
$887$	−3.54837			−0.119143			−0.0595713	+	0.998224i	$0.518973\pi$
$888$	−0.578756	+	1.00243i	−0.0194218	+	0.0336395i
$889$	−0.785113	−	13.6987i	−0.0263318	−	0.459438i
$890$	−6.12122	+	10.6023i	−0.205184	+	0.355389i
$891$	−1.05939	−	1.83493i	−0.0354911	−	0.0614723i
$892$	9.58013	+	16.5933i	0.320767	+	0.555584i
$893$	−50.0310			−1.67422
$894$	23.3640			0.781409
$895$	12.4746	+	21.6066i	0.416979	+	0.722229i
$896$	2.36323	+	1.18960i	0.0789499	+	0.0397418i
$897$	15.0303	+	8.50330i	0.501847	+	0.283917i
$898$	19.8059	−	34.3047i	0.660930	−	1.14476i
$899$	−7.82214	+	13.5483i	−0.260883	+	0.451862i
$900$	1.65139	−	2.86029i	0.0550463	−	0.0953429i
$901$	−2.08850	−	3.61739i	−0.0695780	−	0.120513i
$902$	−26.7749			−0.891507
$903$	1.21521	+	21.2030i	0.0404396	+	0.705590i
$904$	−3.56552	+	6.17566i	−0.118587	+	0.205399i
$905$	8.53135	−	14.7767i	0.283592	−	0.491195i
$906$	−5.87384			−0.195145
$907$	21.8453	−	37.8372i	0.725362	−	1.25636i	−0.233463	−	0.972366i	$-0.575006\pi$
$907$	21.8453	−	37.8372i	0.725362	−	1.25636i	0.958825	−	0.283998i	$-0.0916608\pi$
$908$	−1.18251			−0.0392430
$909$	−6.03449			−0.200151
$910$	6.91012	+	10.3295i	0.229068	+	0.342418i
$911$	−5.97013			−0.197799			−0.0988996	−	0.995097i	$-0.531532\pi$
$911$	−5.97013			−0.197799			−0.0988996	+	0.995097i	$0.531532\pi$
$912$	−6.27630			−0.207829
$913$	−3.69386	+	6.39795i	−0.122249	+	0.211741i
$914$	6.64742			0.219877
$915$	−6.63414	+	11.4907i	−0.219318	+	0.379870i
$916$	7.51599	−	13.0181i	0.248335	−	0.430130i
$917$	−17.8357	+	11.7070i	−0.588986	+	0.386600i
$918$	0.486762			0.0160655
$919$	28.8290	+	49.9332i	0.950980	+	1.64715i	0.743311	+	0.668946i	$0.233254\pi$
$919$	28.8290	+	49.9332i	0.950980	+	1.64715i	0.207668	+	0.978199i	$0.433413\pi$
$920$	3.11985	−	5.40373i	0.102858	−	0.178156i
$921$	6.03366	−	10.4506i	0.198816	−	0.344359i
$922$	10.2371	−	17.7311i	0.337140	−	0.583943i
$923$	9.20985	+	5.21042i	0.303146	+	0.171503i
$924$	0.320759	+	5.59660i	0.0105522	+	0.184115i
$925$	−1.91150	−	3.31081i	−0.0628497	−	0.108859i
$926$	−17.2668			−0.567423
$927$	−11.2954			−0.370990
$928$	−1.74338	−	3.01962i	−0.0572293	−	0.0991240i
$929$	−2.05959	−	3.56731i	−0.0675729	−	0.117040i	0.830259	−	0.557377i	$-0.188192\pi$
$929$	−2.05959	−	3.56731i	−0.0675729	−	0.117040i	−0.897832	+	0.440337i	$0.854859\pi$
$930$	2.92262	−	5.06213i	0.0958366	−	0.165994i
$931$	−17.4762	+	40.3087i	−0.572759	+	1.32106i
$932$	−2.59706	+	4.49824i	−0.0850695	+	0.147345i
$933$	−1.51176			−0.0494929
$934$	−4.37922	+	7.58503i	−0.143292	+	0.248190i
$935$	−0.671807	−	1.16360i	−0.0219704	−	0.0380539i
$936$	−3.10661	+	1.83002i	−0.101543	+	0.0598161i
$937$	22.6483			0.739888			0.369944	−	0.929054i	$-0.379377\pi$
$937$	22.6483			0.739888			0.369944	+	0.929054i	$0.379377\pi$
$938$	7.42843	−	4.87589i	0.242547	−	0.159204i
$939$	−0.862908	−	1.49460i	−0.0281599	−	0.0487744i
$940$	5.19248	+	8.99364i	0.169360	+	0.293340i
$941$	10.0011	+	17.3223i	0.326025	+	0.564692i	0.981719	−	0.190334i	$-0.0609572\pi$
$941$	10.0011	+	17.3223i	0.326025	+	0.564692i	−0.655694	+	0.755027i	$0.727624\pi$
$942$	−6.24495			−0.203472
$943$	30.2625	+	52.4161i	0.985481	+	1.70690i
$944$	−9.15014			−0.297812
$945$	−2.88153	+	1.89139i	−0.0937362	+	0.0615269i
$946$	8.50388	+	14.7292i	0.276485	+	0.478886i
$947$	7.53183			0.244752			0.122376	−	0.992484i	$-0.460949\pi$
$947$	7.53183			0.244752			0.122376	+	0.992484i	$0.460949\pi$
$948$	−7.16738	−	12.4143i	−0.232786	−	0.403197i
$949$	50.2859	−	29.6221i	1.63235	−	0.961574i
$950$	10.3646	−	17.9520i	0.336272	−	0.582441i
$951$	−10.6520	−	18.4499i	−0.345416	−	0.598278i
$952$	−1.15033	−	0.579054i	−0.0372824	−	0.0187672i
$953$	−2.65075	+	4.59123i	−0.0858661	+	0.148724i	−0.905760	−	0.423791i	$-0.860699\pi$
$953$	−2.65075	+	4.59123i	−0.0858661	+	0.148724i	0.819894	+	0.572516i	$0.194032\pi$
$954$	−4.29060	+	7.43153i	−0.138913	+	0.240605i
$955$	14.9674			0.484335
$956$	25.3978			0.821425
$957$	3.69386	−	6.39795i	0.119405	−	0.206816i
$958$	−13.5126	+	23.4046i	−0.436573	+	0.756167i
$959$	16.0502	+	8.07937i	0.518289	+	0.260896i
$960$	0.651388	+	1.12824i	0.0210235	+	0.0364137i
$961$	5.43448	−	9.41280i	0.175306	−	0.303639i
$962$	0.0365092	+	4.17331i	0.00117711	+	0.134553i
$963$	7.01462	+	12.1497i	0.226043	+	0.391518i
$964$	−11.8575			−0.381904
$965$	−0.179979	−	0.311732i	−0.00579372	−	0.0100350i
$966$	10.5937	−	6.95352i	0.340846	−	0.223726i
$967$	−7.46926			−0.240195			−0.120098	−	0.992762i	$-0.538321\pi$
$967$	−7.46926			−0.240195			−0.120098	+	0.992762i	$0.538321\pi$
$968$	−3.25537	−	5.63846i	−0.104631	−	0.181227i
$969$	3.05507			0.0981429
$970$	0.910122	+	1.57638i	0.0292223	+	0.0506144i
$971$	1.64395	+	2.84741i	0.0527570	+	0.0913778i	0.891198	−	0.453615i	$-0.149866\pi$
$971$	1.64395	+	2.84741i	0.0527570	+	0.0913778i	−0.838441	+	0.544993i	$0.816532\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−28.5558	+	18.7436i	−0.915458	+	0.600891i
$974$	−21.9435			−0.703114
$975$	−0.104173	−	11.9079i	−0.00333622	−	0.381357i
$976$	5.09231	+	8.82015i	0.163001	+	0.282326i
$977$	0.416499	−	0.721397i	0.0133250	−	0.0230795i	−0.859286	−	0.511495i	$-0.829092\pi$
$977$	0.416499	−	0.721397i	0.0133250	−	0.0230795i	0.872611	+	0.488416i	$0.162425\pi$
$978$	2.60767			0.0833840
$979$	−9.95535	+	17.2432i	−0.318174	+	0.551094i
$980$	9.05971	−	1.04190i	0.289402	−	0.0332824i
$981$	−5.50000	+	9.52628i	−0.175601	+	0.304151i
$982$	7.09020	+	12.2806i	0.226257	+	0.391889i
$983$	20.9860	+	36.3487i	0.669348	+	1.15934i	0.978087	+	0.208198i	$0.0667598\pi$
$983$	20.9860	+	36.3487i	0.669348	+	1.15934i	−0.308739	+	0.951147i	$0.599907\pi$
$984$	−12.6369			−0.402850
$985$	−17.2892			−0.550879
$986$	0.848612	+	1.46984i	0.0270253	+	0.0468092i
$987$	1.20677	+	21.0558i	0.0384120	+	0.670214i
$988$	−19.4980	+	11.4858i	−0.620314	+	0.365411i
$989$	19.2231	−	33.2954i	0.611259	−	1.05873i
$990$	−1.38015	+	2.39050i	−0.0438642	+	0.0759749i
$991$	25.9607	−	44.9653i	0.824670	−	1.42837i	−0.0775015	−	0.996992i	$-0.524694\pi$
$991$	25.9607	−	44.9653i	0.824670	−	1.42837i	0.902171	−	0.431378i	$-0.141972\pi$
$992$	−2.24338	−	3.88565i	−0.0712274	−	0.123370i
$993$	16.4338			0.521511
$994$	6.49131	−	4.26079i	0.205892	−	0.135144i
$995$	12.3906	−	21.4612i	0.392809	−	0.680364i
$996$	−1.74338	+	3.01962i	−0.0552411	+	0.0956805i
$997$	−48.5174			−1.53656			−0.768281	−	0.640113i	$-0.778888\pi$
$997$	−48.5174			−1.53656			−0.768281	+	0.640113i	$0.778888\pi$
$998$	−14.7488	+	25.5456i	−0.466864	+	0.808632i
$999$	−1.15751			−0.0366220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.b.289.3	✓	8
3.2	odd	2		1638.2.m.i.289.1		8
7.4	even	3		546.2.k.d.445.4	yes	8
13.9	even	3		546.2.k.d.373.4	yes	8
21.11	odd	6		1638.2.p.g.991.2		8
39.35	odd	6		1638.2.p.g.919.2		8
91.74	even	3	inner	546.2.j.b.529.3	yes	8
273.74	odd	6		1638.2.m.i.1621.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.b.289.3	✓	8	1.1	even	1	trivial
546.2.j.b.529.3	yes	8	91.74	even	3	inner
546.2.k.d.373.4	yes	8	13.9	even	3
546.2.k.d.445.4	yes	8	7.4	even	3
1638.2.m.i.289.1		8	3.2	odd	2
1638.2.m.i.1621.1		8	273.74	odd	6
1638.2.p.g.919.2		8	39.35	odd	6
1638.2.p.g.991.2		8	21.11	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.36323 - 1.18960i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.651388 - 1.12824i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.36323 - 1.18960i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.651388 + 1.12824i) q^{10} +(-1.05939 + 1.83493i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0315412 + 3.60541i) q^{13} +(2.36323 + 1.18960i) q^{14} +(0.651388 + 1.12824i) q^{15} +1.00000 q^{16} -0.486762 q^{17} +(0.500000 + 0.866025i) q^{18} +(3.13815 + 5.43544i) q^{19} +(0.651388 - 1.12824i) q^{20} +(2.21184 - 1.45181i) q^{21} +(1.05939 - 1.83493i) q^{22} -4.78954 q^{23} +(0.500000 - 0.866025i) q^{24} +(1.65139 + 2.86029i) q^{25} +(-0.0315412 - 3.60541i) q^{26} +1.00000 q^{27} +(-2.36323 - 1.18960i) q^{28} +(1.74338 + 3.01962i) q^{29} +(-0.651388 - 1.12824i) q^{30} +(2.24338 + 3.88565i) q^{31} -1.00000 q^{32} +(-1.05939 - 1.83493i) q^{33} +0.486762 q^{34} +(-2.88153 + 1.89139i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.15751 q^{37} +(-3.13815 - 5.43544i) q^{38} +(-3.13815 - 1.77539i) q^{39} +(-0.651388 + 1.12824i) q^{40} +(-6.31845 - 10.9439i) q^{41} +(-2.21184 + 1.45181i) q^{42} +(-4.01356 + 6.95169i) q^{43} +(-1.05939 + 1.83493i) q^{44} -1.30278 q^{45} +4.78954 q^{46} +(-3.98570 + 6.90344i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(4.16969 + 5.62260i) q^{49} +(-1.65139 - 2.86029i) q^{50} +(0.243381 - 0.421549i) q^{51} +(0.0315412 + 3.60541i) q^{52} +(4.29060 + 7.43153i) q^{53} -1.00000 q^{54} +(1.38015 + 2.39050i) q^{55} +(2.36323 + 1.18960i) q^{56} -6.27630 q^{57} +(-1.74338 - 3.01962i) q^{58} -9.15014 q^{59} +(0.651388 + 1.12824i) q^{60} +(5.09231 + 8.82015i) q^{61} +(-2.24338 - 3.88565i) q^{62} +(0.151388 + 2.64142i) q^{63} +1.00000 q^{64} +(4.08831 + 2.31294i) q^{65} +(1.05939 + 1.83493i) q^{66} +(1.67924 - 2.90853i) q^{67} -0.486762 q^{68} +(2.39477 - 4.14786i) q^{69} +(2.88153 - 1.89139i) q^{70} +(1.46740 - 2.54161i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-8.09337 - 14.0181i) q^{73} +1.15751 q^{74} -3.30278 q^{75} +(3.13815 + 5.43544i) q^{76} +(4.68642 - 3.07609i) q^{77} +(3.13815 + 1.77539i) q^{78} +(-7.16738 + 12.4143i) q^{79} +(0.651388 - 1.12824i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.31845 + 10.9439i) q^{82} +3.48676 q^{83} +(2.21184 - 1.45181i) q^{84} +(-0.317071 + 0.549183i) q^{85} +(4.01356 - 6.95169i) q^{86} -3.48676 q^{87} +(1.05939 - 1.83493i) q^{88} +9.39720 q^{89} +1.30278 q^{90} +(4.21447 - 8.55793i) q^{91} -4.78954 q^{92} -4.48676 q^{93} +(3.98570 - 6.90344i) q^{94} +8.17661 q^{95} +(0.500000 - 0.866025i) q^{96} +(0.698602 - 1.21001i) q^{97} +(-4.16969 - 5.62260i) q^{98} +2.11879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 7 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} + 12 q^{17} + 4 q^{18} + 2 q^{19} - 2 q^{20} + 3 q^{21} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} - 7 q^{26} + 8 q^{27} + 3 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} - 8 q^{32} - 2 q^{33} - 12 q^{34} + 8 q^{35} - 4 q^{36} + 24 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} - 6 q^{41} - 3 q^{42} - 4 q^{43} - 2 q^{44} + 4 q^{45} + 8 q^{46} - 17 q^{47} - 4 q^{48} + 17 q^{49} - 6 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} - 8 q^{54} + 25 q^{55} - 3 q^{56} - 4 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} + 12 q^{65} + 2 q^{66} - 7 q^{67} + 12 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 4 q^{72} - 19 q^{73} - 24 q^{74} - 12 q^{75} + 2 q^{76} - 10 q^{77} + 2 q^{78} + 24 q^{79} - 2 q^{80} - 4 q^{81} + 6 q^{82} + 12 q^{83} + 3 q^{84} - 3 q^{85} + 4 q^{86} - 12 q^{87} + 2 q^{88} + 14 q^{89} - 4 q^{90} + 40 q^{91} - 8 q^{92} - 20 q^{93} + 17 q^{94} + 24 q^{95} + 4 q^{96} - 25 q^{97} - 17 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 4 * q^6 + 3 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 7 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 + 12 * q^17 + 4 * q^18 + 2 * q^19 - 2 * q^20 + 3 * q^21 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 - 7 * q^26 + 8 * q^27 + 3 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 - 8 * q^32 - 2 * q^33 - 12 * q^34 + 8 * q^35 - 4 * q^36 + 24 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 - 6 * q^41 - 3 * q^42 - 4 * q^43 - 2 * q^44 + 4 * q^45 + 8 * q^46 - 17 * q^47 - 4 * q^48 + 17 * q^49 - 6 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 - 8 * q^54 + 25 * q^55 - 3 * q^56 - 4 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 + 12 * q^65 + 2 * q^66 - 7 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 4 * q^72 - 19 * q^73 - 24 * q^74 - 12 * q^75 + 2 * q^76 - 10 * q^77 + 2 * q^78 + 24 * q^79 - 2 * q^80 - 4 * q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 3 * q^85 + 4 * q^86 - 12 * q^87 + 2 * q^88 + 14 * q^89 - 4 * q^90 + 40 * q^91 - 8 * q^92 - 20 * q^93 + 17 * q^94 + 24 * q^95 + 4 * q^96 - 25 * q^97 - 17 * q^98 + 4 * q^99

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