LMFDB - Embedded newform 546.2.j.d.289.4

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:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$1.19003 - 0.764088i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.d.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.61442 - 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.61442 - 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.05781 - 3.56422i) q^{10} +(-2.02237 + 3.50284i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.81454 - 3.11568i) q^{13} +(-2.61442 - 0.405935i) q^{14} +(-2.05781 - 3.56422i) q^{15} +1.00000 q^{16} +0.715381 q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.92440 + 3.33315i) q^{19} +(2.05781 - 3.56422i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-2.02237 + 3.50284i) q^{22} -4.09781 q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.96913 - 10.3388i) q^{25} +(1.81454 - 3.11568i) q^{26} -1.00000 q^{27} +(-2.61442 - 0.405935i) q^{28} +(4.50457 + 7.80214i) q^{29} +(-2.05781 - 3.56422i) q^{30} +(1.82642 + 3.16346i) q^{31} +1.00000 q^{32} +(2.02237 + 3.50284i) q^{33} +0.715381 q^{34} +(-6.82682 + 8.48306i) q^{35} +(-0.500000 - 0.866025i) q^{36} +7.19594 q^{37} +(1.92440 + 3.33315i) q^{38} +(-1.79099 - 3.12928i) q^{39} +(2.05781 - 3.56422i) q^{40} +(-2.88423 - 4.99563i) q^{41} +(-1.65876 + 2.06119i) q^{42} +(1.28209 - 2.22064i) q^{43} +(-2.02237 + 3.50284i) q^{44} -4.11561 q^{45} -4.09781 q^{46} +(1.28800 - 2.23088i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.67043 + 2.12257i) q^{49} +(-5.96913 - 10.3388i) q^{50} +(0.357690 - 0.619538i) q^{51} +(1.81454 - 3.11568i) q^{52} +(-1.35888 - 2.35365i) q^{53} -1.00000 q^{54} +(8.32328 + 14.4163i) q^{55} +(-2.61442 - 0.405935i) q^{56} +3.84879 q^{57} +(4.50457 + 7.80214i) q^{58} +12.9027 q^{59} +(-2.05781 - 3.56422i) q^{60} +(4.71538 + 8.16728i) q^{61} +(1.82642 + 3.16346i) q^{62} +(0.955663 + 2.46713i) q^{63} +1.00000 q^{64} +(-7.37100 - 12.8789i) q^{65} +(2.02237 + 3.50284i) q^{66} +(0.583158 - 1.01006i) q^{67} +0.715381 q^{68} +(-2.04891 + 3.54881i) q^{69} +(-6.82682 + 8.48306i) q^{70} +(5.10254 - 8.83786i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.25673 - 2.17673i) q^{73} +7.19594 q^{74} -11.9383 q^{75} +(1.92440 + 3.33315i) q^{76} +(6.70925 - 8.33697i) q^{77} +(-1.79099 - 3.12928i) q^{78} +(-6.70468 + 11.6129i) q^{79} +(2.05781 - 3.56422i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.88423 - 4.99563i) q^{82} -15.5024 q^{83} +(-1.65876 + 2.06119i) q^{84} +(1.47212 - 2.54978i) q^{85} +(1.28209 - 2.22064i) q^{86} +9.00914 q^{87} +(-2.02237 + 3.50284i) q^{88} -10.9137 q^{89} -4.11561 q^{90} +(-6.00874 + 7.40912i) q^{91} -4.09781 q^{92} +3.65285 q^{93} +(1.28800 - 2.23088i) q^{94} +15.8401 q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.10135 + 5.37170i) q^{97} +(6.67043 + 2.12257i) q^{98} +4.04474 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	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} - 8 q^{17} - 4 q^{18} + 6 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} + 20 q^{23} + 4 q^{24} - 18 q^{25} - 11 q^{26} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 8 q^{32} + 6 q^{33} - 8 q^{34} - 18 q^{35} - 4 q^{36} + 56 q^{37} + 6 q^{38} - 10 q^{39} + 2 q^{40} - 3 q^{42} - 6 q^{43} - 6 q^{44} - 4 q^{45} + 20 q^{46} + q^{47} + 4 q^{48} + 5 q^{49} - 18 q^{50} - 4 q^{51} - 11 q^{52} + 7 q^{53} - 8 q^{54} + q^{55} - 3 q^{56} + 12 q^{57} + 2 q^{58} - 4 q^{59} - 2 q^{60} + 24 q^{61} + 6 q^{62} + 8 q^{64} + 22 q^{65} + 6 q^{66} - 15 q^{67} - 8 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} - 4 q^{72} + q^{73} + 56 q^{74} - 36 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} + 2 q^{80} - 4 q^{81} - 32 q^{83} - 3 q^{84} - 13 q^{85} - 6 q^{86} + 4 q^{87} - 6 q^{88} - 50 q^{89} - 4 q^{90} - 8 q^{91} + 20 q^{92} + 12 q^{93} + q^{94} + 16 q^{95} + 4 q^{96} - q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 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 - 6 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 - 8 * q^17 - 4 * q^18 + 6 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 + 20 * q^23 + 4 * q^24 - 18 * q^25 - 11 * q^26 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 8 * q^32 + 6 * q^33 - 8 * q^34 - 18 * q^35 - 4 * q^36 + 56 * q^37 + 6 * q^38 - 10 * q^39 + 2 * q^40 - 3 * q^42 - 6 * q^43 - 6 * q^44 - 4 * q^45 + 20 * q^46 + q^47 + 4 * q^48 + 5 * q^49 - 18 * q^50 - 4 * q^51 - 11 * q^52 + 7 * q^53 - 8 * q^54 + q^55 - 3 * q^56 + 12 * q^57 + 2 * q^58 - 4 * q^59 - 2 * q^60 + 24 * q^61 + 6 * q^62 + 8 * q^64 + 22 * q^65 + 6 * q^66 - 15 * q^67 - 8 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 - 4 * q^72 + q^73 + 56 * q^74 - 36 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 + 2 * q^80 - 4 * q^81 - 32 * q^83 - 3 * q^84 - 13 * q^85 - 6 * q^86 + 4 * q^87 - 6 * q^88 - 50 * q^89 - 4 * q^90 - 8 * q^91 + 20 * q^92 + 12 * q^93 + q^94 + 16 * q^95 + 4 * q^96 - q^97 + 5 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.05781	−	3.56422i	0.920279	−	1.59397i	0.121296	−	0.992616i	$-0.461295\pi$
$5$	2.05781	−	3.56422i	0.920279	−	1.59397i	0.798983	−	0.601353i	$-0.205372\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.61442	−	0.405935i	−0.988160	−	0.153429i
$7$	−2.61442	−	0.405935i	−0.988160	−	0.153429i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.05781	−	3.56422i	0.650735	−	1.12711i
$11$	−2.02237	+	3.50284i	−0.609767	+	1.05615i	0.381512	+	0.924364i	$0.375404\pi$
$11$	−2.02237	+	3.50284i	−0.609767	+	1.05615i	−0.991279	+	0.131783i	$0.957930\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.81454	−	3.11568i	0.503263	−	0.864133i
$13$	1.81454	−	3.11568i	0.503263	−	0.864133i
$14$	−2.61442	−	0.405935i	−0.698734	−	0.108491i
$15$	−2.05781	−	3.56422i	−0.531323	−	0.920279i
$16$	1.00000			0.250000
$17$	0.715381			0.173505			0.0867527	−	0.996230i	$-0.472351\pi$
$17$	0.715381			0.173505			0.0867527	+	0.996230i	$0.472351\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.92440	+	3.33315i	0.441487	+	0.764677i	0.997800	−	0.0662953i	$-0.0211179\pi$
$19$	1.92440	+	3.33315i	0.441487	+	0.764677i	−0.556313	+	0.830973i	$0.687785\pi$
$20$	2.05781	−	3.56422i	0.460139	−	0.796985i
$21$	−1.65876	+	2.06119i	−0.361972	+	0.449789i
$22$	−2.02237	+	3.50284i	−0.431170	+	0.746809i
$23$	−4.09781			−0.854453			−0.427227	−	0.904145i	$-0.640509\pi$
$23$	−4.09781			−0.854453			−0.427227	+	0.904145i	$0.640509\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−5.96913	−	10.3388i	−1.19383	−	2.06777i
$26$	1.81454	−	3.11568i	0.355861	−	0.611035i
$27$	−1.00000			−0.192450
$28$	−2.61442	−	0.405935i	−0.494080	−	0.0767145i
$29$	4.50457	+	7.80214i	0.836478	+	1.44882i	0.892822	+	0.450410i	$0.148722\pi$
$29$	4.50457	+	7.80214i	0.836478	+	1.44882i	−0.0563442	+	0.998411i	$0.517944\pi$
$30$	−2.05781	−	3.56422i	−0.375702	−	0.650735i
$31$	1.82642	+	3.16346i	0.328035	+	0.568174i	0.982122	−	0.188246i	$-0.0602802\pi$
$31$	1.82642	+	3.16346i	0.328035	+	0.568174i	−0.654087	+	0.756420i	$0.726947\pi$
$32$	1.00000			0.176777
$33$	2.02237	+	3.50284i	0.352049	+	0.609767i
$34$	0.715381			0.122687
$35$	−6.82682	+	8.48306i	−1.15394	+	1.43390i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	7.19594			1.18301			0.591503	−	0.806303i	$-0.298535\pi$
$37$	7.19594			1.18301			0.591503	+	0.806303i	$0.298535\pi$
$38$	1.92440	+	3.33315i	0.312178	+	0.540709i
$39$	−1.79099	−	3.12928i	−0.286787	−	0.501085i
$40$	2.05781	−	3.56422i	0.325368	−	0.563553i
$41$	−2.88423	−	4.99563i	−0.450441	−	0.780187i	0.547972	−	0.836496i	$-0.315400\pi$
$41$	−2.88423	−	4.99563i	−0.450441	−	0.780187i	−0.998413	+	0.0563098i	$0.982067\pi$
$42$	−1.65876	+	2.06119i	−0.255953	+	0.318049i
$43$	1.28209	−	2.22064i	0.195516	−	0.338644i	−0.751553	−	0.659672i	$-0.770695\pi$
$43$	1.28209	−	2.22064i	0.195516	−	0.338644i	0.947070	+	0.321028i	$0.104028\pi$
$44$	−2.02237	+	3.50284i	−0.304883	+	0.528074i
$45$	−4.11561			−0.613519
$46$	−4.09781			−0.604190
$47$	1.28800	−	2.23088i	0.187874	−	0.325408i	−0.756667	−	0.653800i	$-0.773174\pi$
$47$	1.28800	−	2.23088i	0.187874	−	0.325408i	0.944541	+	0.328393i	$0.106507\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	6.67043	+	2.12257i	0.952919	+	0.303225i
$50$	−5.96913	−	10.3388i	−0.844163	−	1.46213i
$51$	0.357690	−	0.619538i	0.0500867	−	0.0867527i
$52$	1.81454	−	3.11568i	0.251631	−	0.432067i
$53$	−1.35888	−	2.35365i	−0.186656	−	0.323298i	0.757477	−	0.652862i	$-0.226432\pi$
$53$	−1.35888	−	2.35365i	−0.186656	−	0.323298i	−0.944133	+	0.329564i	$0.893098\pi$
$54$	−1.00000			−0.136083
$55$	8.32328	+	14.4163i	1.12231	+	1.94390i
$56$	−2.61442	−	0.405935i	−0.349367	−	0.0542453i
$57$	3.84879			0.509785
$58$	4.50457	+	7.80214i	0.591479	+	1.02447i
$59$	12.9027			1.67978			0.839892	−	0.542754i	$-0.182618\pi$
$59$	12.9027			1.67978			0.839892	+	0.542754i	$0.182618\pi$
$60$	−2.05781	−	3.56422i	−0.265662	−	0.460139i
$61$	4.71538	+	8.16728i	0.603743	+	1.04571i	0.992249	+	0.124267i	$0.0396579\pi$
$61$	4.71538	+	8.16728i	0.603743	+	1.04571i	−0.388506	+	0.921446i	$0.627009\pi$
$62$	1.82642	+	3.16346i	0.231956	+	0.401760i
$63$	0.955663	+	2.46713i	0.120402	+	0.310829i
$64$	1.00000			0.125000
$65$	−7.37100	−	12.8789i	−0.914260	−	1.59743i
$66$	2.02237	+	3.50284i	0.248936	+	0.431170i
$67$	0.583158	−	1.01006i	0.0712441	−	0.123398i	−0.828203	−	0.560429i	$-0.810636\pi$
$67$	0.583158	−	1.01006i	0.0712441	−	0.123398i	0.899447	+	0.437030i	$0.143970\pi$
$68$	0.715381			0.0867527
$69$	−2.04891	+	3.54881i	−0.246659	+	0.427227i
$70$	−6.82682	+	8.48306i	−0.815961	+	1.01392i
$71$	5.10254	−	8.83786i	0.605560	−	1.04886i	−0.386402	−	0.922330i	$-0.626282\pi$
$71$	5.10254	−	8.83786i	0.605560	−	1.04886i	0.991963	−	0.126531i	$-0.0403843\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−1.25673	−	2.17673i	−0.147090	−	0.254767i	0.783061	−	0.621945i	$-0.213657\pi$
$73$	−1.25673	−	2.17673i	−0.147090	−	0.254767i	−0.930151	+	0.367178i	$0.880324\pi$
$74$	7.19594			0.836512
$75$	−11.9383			−1.37851
$76$	1.92440	+	3.33315i	0.220743	+	0.382339i
$77$	6.70925	−	8.33697i	0.764590	−	0.950086i
$78$	−1.79099	−	3.12928i	−0.202789	−	0.354321i
$79$	−6.70468	+	11.6129i	−0.754336	+	1.30655i	0.191368	+	0.981518i	$0.438708\pi$
$79$	−6.70468	+	11.6129i	−0.754336	+	1.30655i	−0.945704	+	0.325030i	$0.894626\pi$
$80$	2.05781	−	3.56422i	0.230070	−	0.398492i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.88423	−	4.99563i	−0.318510	−	0.551675i
$83$	−15.5024			−1.70161			−0.850807	−	0.525479i	$-0.823886\pi$
$83$	−15.5024			−1.70161			−0.850807	+	0.525479i	$0.823886\pi$
$84$	−1.65876	+	2.06119i	−0.180986	+	0.224894i
$85$	1.47212	−	2.54978i	0.159673	−	0.276562i
$86$	1.28209	−	2.22064i	0.138251	−	0.239458i
$87$	9.00914			0.965881
$88$	−2.02237	+	3.50284i	−0.215585	+	0.373404i
$89$	−10.9137			−1.15685			−0.578425	−	0.815736i	$-0.696332\pi$
$89$	−10.9137			−1.15685			−0.578425	+	0.815736i	$0.696332\pi$
$90$	−4.11561			−0.433824
$91$	−6.00874	+	7.40912i	−0.629887	+	0.776687i
$92$	−4.09781			−0.427227
$93$	3.65285			0.378783
$94$	1.28800	−	2.23088i	0.132847	−	0.230098i
$95$	15.8401			1.62516
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−3.10135	+	5.37170i	−0.314895	+	0.545414i	−0.979415	−	0.201856i	$-0.935303\pi$
$97$	−3.10135	+	5.37170i	−0.314895	+	0.545414i	0.664520	+	0.747270i	$0.268636\pi$
$98$	6.67043	+	2.12257i	0.673816	+	0.214412i
$99$	4.04474			0.406511
$100$	−5.96913	−	10.3388i	−0.596913	−	1.03388i
$101$	−8.15325	+	14.1218i	−0.811278	+	1.40518i	0.100692	+	0.994918i	$0.467894\pi$
$101$	−8.15325	+	14.1218i	−0.811278	+	1.40518i	−0.911970	+	0.410257i	$0.865439\pi$
$102$	0.357690	−	0.619538i	0.0354166	−	0.0613434i
$103$	1.46023	−	2.52920i	0.143881	−	0.249209i	−0.785074	−	0.619402i	$-0.787375\pi$
$103$	1.46023	−	2.52920i	0.143881	−	0.249209i	0.928955	+	0.370193i	$0.120708\pi$
$104$	1.81454	−	3.11568i	0.177930	−	0.305517i
$105$	3.93314	+	10.1537i	0.383835	+	0.990903i
$106$	−1.35888	−	2.35365i	−0.131986	−	0.228606i
$107$	−4.03877			−0.390442			−0.195221	−	0.980759i	$-0.562542\pi$
$107$	−4.03877			−0.390442			−0.195221	+	0.980759i	$0.562542\pi$
$108$	−1.00000			−0.0962250
$109$	6.93314	+	12.0085i	0.664074	+	1.15021i	0.979535	+	0.201272i	$0.0645074\pi$
$109$	6.93314	+	12.0085i	0.664074	+	1.15021i	−0.315461	+	0.948938i	$0.602159\pi$
$110$	8.32328	+	14.4163i	0.793594	+	1.37454i
$111$	3.59797	−	6.23187i	0.341504	−	0.591503i
$112$	−2.61442	−	0.405935i	−0.247040	−	0.0383572i
$113$	−7.30902	+	12.6596i	−0.687575	+	1.19091i	0.285045	+	0.958514i	$0.407991\pi$
$113$	−7.30902	+	12.6596i	−0.687575	+	1.19091i	−0.972620	+	0.232401i	$0.925342\pi$
$114$	3.84879			0.360472
$115$	−8.43251	+	14.6055i	−0.786335	+	1.36197i
$116$	4.50457	+	7.80214i	0.418239	+	0.724411i
$117$	−3.60553	−	0.0135995i	−0.333331	−	0.00125727i
$118$	12.9027			1.18779
$119$	−1.87031	−	0.290398i	−0.171451	−	0.0266207i
$120$	−2.05781	−	3.56422i	−0.187851	−	0.325368i
$121$	−2.67994	−	4.64180i	−0.243631	−	0.421982i
$122$	4.71538	+	8.16728i	0.426911	+	0.739431i
$123$	−5.76846			−0.520124
$124$	1.82642	+	3.16346i	0.164018	+	0.284087i
$125$	−28.5552			−2.55405
$126$	0.955663	+	2.46713i	0.0851372	+	0.219789i
$127$	−1.26603	−	2.19283i	−0.112342	−	0.194582i	0.804372	−	0.594126i	$-0.202502\pi$
$127$	−1.26603	−	2.19283i	−0.112342	−	0.194582i	−0.916714	+	0.399544i	$0.869169\pi$
$128$	1.00000			0.0883883
$129$	−1.28209	−	2.22064i	−0.112881	−	0.195516i
$130$	−7.37100	−	12.8789i	−0.646480	−	1.12955i
$131$	6.21657	−	10.7674i	0.543144	−	0.940753i	−0.455577	−	0.890196i	$-0.650567\pi$
$131$	6.21657	−	10.7674i	0.543144	−	0.940753i	0.998721	−	0.0505568i	$-0.0160996\pi$
$132$	2.02237	+	3.50284i	0.176025	+	0.304883i
$133$	−3.67815	−	9.49545i	−0.318936	−	0.823360i
$134$	0.583158	−	1.01006i	0.0503772	−	0.0872558i
$135$	−2.05781	+	3.56422i	−0.177108	+	0.306760i
$136$	0.715381			0.0613434
$137$	−10.3848			−0.887234			−0.443617	−	0.896216i	$-0.646305\pi$
$137$	−10.3848			−0.887234			−0.443617	+	0.896216i	$0.646305\pi$
$138$	−2.04891	+	3.54881i	−0.174415	+	0.302095i
$139$	−0.636394	+	1.10227i	−0.0539783	+	0.0934931i	−0.891752	−	0.452525i	$-0.850524\pi$
$139$	−0.636394	+	1.10227i	−0.0539783	+	0.0934931i	0.837774	+	0.546018i	$0.183857\pi$
$140$	−6.82682	+	8.48306i	−0.576972	+	0.716950i
$141$	−1.28800	−	2.23088i	−0.108469	−	0.187874i
$142$	5.10254	−	8.83786i	0.428196	−	0.741657i
$143$	7.24406	+	12.6571i	0.605779	+	1.05844i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	37.0781			3.07917
$146$	−1.25673	−	2.17673i	−0.104008	−	0.180147i
$147$	5.17342	−	4.71548i	0.426696	−	0.388926i
$148$	7.19594			0.591503
$149$	−11.6810	−	20.2320i	−0.956942	−	1.65747i	−0.729859	−	0.683598i	$-0.760414\pi$
$149$	−11.6810	−	20.2320i	−0.956942	−	1.65747i	−0.227083	−	0.973875i	$-0.572919\pi$
$150$	−11.9383			−0.974755
$151$	1.19832	+	2.07555i	0.0975178	+	0.168906i	0.910657	−	0.413164i	$-0.135576\pi$
$151$	1.19832	+	2.07555i	0.0975178	+	0.168906i	−0.813139	+	0.582070i	$0.802243\pi$
$152$	1.92440	+	3.33315i	0.156089	+	0.270354i
$153$	−0.357690	−	0.619538i	−0.0289176	−	0.0500867i
$154$	6.70925	−	8.33697i	0.540647	−	0.671812i
$155$	15.0337			1.20754
$156$	−1.79099	−	3.12928i	−0.143394	−	0.250543i
$157$	5.79083	+	10.0300i	0.462158	+	0.800482i	0.999068	−	0.0431579i	$-0.0137419\pi$
$157$	5.79083	+	10.0300i	0.462158	+	0.800482i	−0.536910	+	0.843640i	$0.680409\pi$
$158$	−6.70468	+	11.6129i	−0.533396	+	0.923869i
$159$	−2.71776			−0.215532
$160$	2.05781	−	3.56422i	0.162684	−	0.281777i
$161$	10.7134	+	1.66344i	0.844336	+	0.131098i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−8.95432	−	15.5093i	−0.701356	−	1.21478i	−0.967990	−	0.250987i	$-0.919245\pi$
$163$	−8.95432	−	15.5093i	−0.701356	−	1.21478i	0.266634	−	0.963798i	$-0.414088\pi$
$164$	−2.88423	−	4.99563i	−0.225220	−	0.390093i
$165$	16.6466			1.29593
$166$	−15.5024			−1.20322
$167$	3.15398	+	5.46286i	0.244062	+	0.422728i	0.961868	−	0.273516i	$-0.0881865\pi$
$167$	3.15398	+	5.46286i	0.244062	+	0.422728i	−0.717805	+	0.696244i	$0.754853\pi$
$168$	−1.65876	+	2.06119i	−0.127976	+	0.159024i
$169$	−6.41489	−	11.3070i	−0.493453	−	0.869773i
$170$	1.47212	−	2.54978i	0.112906	−	0.195559i
$171$	1.92440	−	3.33315i	0.147162	−	0.254892i
$172$	1.28209	−	2.22064i	0.0977582	−	0.169322i
$173$	1.82563	+	3.16209i	0.138800	+	0.240409i	0.927043	−	0.374956i	$-0.122342\pi$
$173$	1.82563	+	3.16209i	0.138800	+	0.240409i	−0.788242	+	0.615365i	$0.789009\pi$
$174$	9.00914			0.682981
$175$	11.4090	+	29.4532i	0.862436	+	2.22645i
$176$	−2.02237	+	3.50284i	−0.152442	+	0.264037i
$177$	6.45133	−	11.1740i	0.484912	−	0.839892i
$178$	−10.9137			−0.818016
$179$	−6.25956	+	10.8419i	−0.467861	+	0.810360i	−0.999326	−	0.0367210i	$-0.988309\pi$
$179$	−6.25956	+	10.8419i	−0.467861	+	0.810360i	0.531464	+	0.847081i	$0.321642\pi$
$180$	−4.11561			−0.306760
$181$	−18.1728			−1.35077			−0.675385	−	0.737465i	$-0.736023\pi$
$181$	−18.1728			−1.35077			−0.675385	+	0.737465i	$0.736023\pi$
$182$	−6.00874	+	7.40912i	−0.445397	+	0.549200i
$183$	9.43076			0.697142
$184$	−4.09781			−0.302095
$185$	14.8079	−	25.6480i	1.08870	−	1.88568i
$186$	3.65285			0.267840
$187$	−1.44676	+	2.50587i	−0.105798	+	0.183247i
$188$	1.28800	−	2.23088i	0.0939371	−	0.162704i
$189$	2.61442	+	0.405935i	0.190171	+	0.0295274i
$190$	15.8401			1.14916
$191$	−2.23004	−	3.86254i	−0.161360	−	0.279483i	0.773997	−	0.633190i	$-0.218255\pi$
$191$	−2.23004	−	3.86254i	−0.161360	−	0.279483i	−0.935357	+	0.353706i	$0.884921\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	4.34243	−	7.52130i	0.312575	−	0.541395i	−0.666344	−	0.745644i	$-0.732142\pi$
$193$	4.34243	−	7.52130i	0.312575	−	0.541395i	0.978919	+	0.204249i	$0.0654752\pi$
$194$	−3.10135	+	5.37170i	−0.222664	+	0.385666i
$195$	−14.8389	−	0.0559702i	−1.06264	−	0.00400811i
$196$	6.67043	+	2.12257i	0.476460	+	0.151612i
$197$	−1.23397	−	2.13730i	−0.0879166	−	0.152276i	0.818714	−	0.574202i	$-0.194688\pi$
$197$	−1.23397	−	2.13730i	−0.0879166	−	0.152276i	−0.906630	+	0.421926i	$0.861354\pi$
$198$	4.04474			0.287447
$199$	20.5681			1.45804			0.729018	−	0.684494i	$-0.239977\pi$
$199$	20.5681			1.45804			0.729018	+	0.684494i	$0.239977\pi$
$200$	−5.96913	−	10.3388i	−0.422081	−	0.731066i
$201$	−0.583158	−	1.01006i	−0.0411328	−	0.0712441i
$202$	−8.15325	+	14.1218i	−0.573660	+	0.993609i
$203$	−8.60970	−	22.2267i	−0.604282	−	1.56001i
$204$	0.357690	−	0.619538i	0.0250433	−	0.0433763i
$205$	−23.7407			−1.65813
$206$	1.46023	−	2.52920i	0.101739	−	0.176217i
$207$	2.04891	+	3.54881i	0.142409	+	0.246659i
$208$	1.81454	−	3.11568i	0.125816	−	0.216033i
$209$	−15.5673			−1.07682
$210$	3.93314	+	10.1537i	0.271412	+	0.700674i
$211$	2.22726	+	3.85773i	0.153331	+	0.265577i	0.932450	−	0.361299i	$-0.117667\pi$
$211$	2.22726	+	3.85773i	0.153331	+	0.265577i	−0.779119	+	0.626876i	$0.784333\pi$
$212$	−1.35888	−	2.35365i	−0.0933281	−	0.161649i
$213$	−5.10254	−	8.83786i	−0.349620	−	0.605560i
$214$	−4.03877			−0.276084
$215$	−5.27657	−	9.13929i	−0.359859	−	0.623294i
$216$	−1.00000			−0.0680414
$217$	−3.49089	−	9.01203i	−0.236977	−	0.611777i
$218$	6.93314	+	12.0085i	0.469571	+	0.813321i
$219$	−2.51347			−0.169844
$220$	8.32328	+	14.4163i	0.561155	+	0.971950i
$221$	1.29809	−	2.22890i	0.0873188	−	0.149932i
$222$	3.59797	−	6.23187i	0.241480	−	0.418256i
$223$	−2.49662	−	4.32427i	−0.167186	−	0.289574i	0.770243	−	0.637750i	$-0.220135\pi$
$223$	−2.49662	−	4.32427i	−0.167186	−	0.289574i	−0.937429	+	0.348175i	$0.886801\pi$
$224$	−2.61442	−	0.405935i	−0.174684	−	0.0271227i
$225$	−5.96913	+	10.3388i	−0.397942	+	0.689256i
$226$	−7.30902	+	12.6596i	−0.486189	+	0.842104i
$227$	−1.57273			−0.104385			−0.0521927	−	0.998637i	$-0.516621\pi$
$227$	−1.57273			−0.104385			−0.0521927	+	0.998637i	$0.516621\pi$
$228$	3.84879			0.254892
$229$	0.828619	−	1.43521i	0.0547567	−	0.0948413i	−0.837348	−	0.546671i	$-0.815895\pi$
$229$	0.828619	−	1.43521i	0.0547567	−	0.0948413i	0.892104	+	0.451829i	$0.149228\pi$
$230$	−8.43251	+	14.6055i	−0.556023	+	0.963060i
$231$	−3.86540	−	9.97887i	−0.254325	−	0.656561i
$232$	4.50457	+	7.80214i	0.295739	+	0.512236i
$233$	−3.86181	+	6.68885i	−0.252996	+	0.438201i	−0.964349	−	0.264633i	$-0.914749\pi$
$233$	−3.86181	+	6.68885i	−0.252996	+	0.438201i	0.711354	+	0.702834i	$0.248082\pi$
$234$	−3.60553	−	0.0135995i	−0.235701	−	0.000889026i
$235$	−5.30091	−	9.18145i	−0.345793	−	0.598932i
$236$	12.9027			0.839892
$237$	6.70468	+	11.6129i	0.435516	+	0.754336i
$238$	−1.87031	−	0.290398i	−0.121234	−	0.0188237i
$239$	−28.7630			−1.86052			−0.930261	−	0.366899i	$-0.880420\pi$
$239$	−28.7630			−1.86052			−0.930261	+	0.366899i	$0.880420\pi$
$240$	−2.05781	−	3.56422i	−0.132831	−	0.230070i
$241$	25.6204			1.65036			0.825178	−	0.564872i	$-0.191075\pi$
$241$	25.6204			1.65036			0.825178	+	0.564872i	$0.191075\pi$
$242$	−2.67994	−	4.64180i	−0.172273	−	0.298386i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.71538	+	8.16728i	0.301871	+	0.522856i
$245$	21.2918	−	19.4071i	1.36028	−	1.23987i
$246$	−5.76846			−0.367784
$247$	13.8769	+	0.0523416i	0.882967	+	0.00333042i
$248$	1.82642	+	3.16346i	0.115978	+	0.200880i
$249$	−7.75122	+	13.4255i	−0.491213	+	0.850807i
$250$	−28.5552			−1.80599
$251$	0.339652	−	0.588295i	0.0214387	−	0.0371329i	−0.855107	−	0.518452i	$-0.826509\pi$
$251$	0.339652	−	0.588295i	0.0214387	−	0.0371329i	0.876546	+	0.481319i	$0.159842\pi$
$252$	0.955663	+	2.46713i	0.0602011	+	0.155414i
$253$	8.28729	−	14.3540i	0.521017	−	0.902428i
$254$	−1.26603	−	2.19283i	−0.0794379	−	0.137590i
$255$	−1.47212	−	2.54978i	−0.0921874	−	0.159673i
$256$	1.00000			0.0625000
$257$	−2.44587			−0.152569			−0.0762846	−	0.997086i	$-0.524306\pi$
$257$	−2.44587			−0.152569			−0.0762846	+	0.997086i	$0.524306\pi$
$258$	−1.28209	−	2.22064i	−0.0798192	−	0.138251i
$259$	−18.8133	−	2.92108i	−1.16900	−	0.181507i
$260$	−7.37100	−	12.8789i	−0.457130	−	0.798715i
$261$	4.50457	−	7.80214i	0.278826	−	0.482941i
$262$	6.21657	−	10.7674i	0.384061	−	0.665213i
$263$	−12.6596	+	21.9271i	−0.780625	+	1.35208i	0.150953	+	0.988541i	$0.451766\pi$
$263$	−12.6596	+	21.9271i	−0.780625	+	1.35208i	−0.931578	+	0.363541i	$0.881568\pi$
$264$	2.02237	+	3.50284i	0.124468	+	0.215585i
$265$	−11.1852			−0.687103
$266$	−3.67815	−	9.49545i	−0.225522	−	0.582204i
$267$	−5.45685	+	9.45154i	−0.333954	+	0.578425i
$268$	0.583158	−	1.01006i	0.0356220	−	0.0616992i
$269$	−13.5665			−0.827167			−0.413583	−	0.910466i	$-0.635723\pi$
$269$	−13.5665			−0.827167			−0.413583	+	0.910466i	$0.635723\pi$
$270$	−2.05781	+	3.56422i	−0.125234	+	0.216912i
$271$	−4.85940			−0.295188			−0.147594	−	0.989048i	$-0.547153\pi$
$271$	−4.85940			−0.295188			−0.147594	+	0.989048i	$0.547153\pi$
$272$	0.715381			0.0433763
$273$	3.41211	+	8.90828i	0.206511	+	0.539154i
$274$	−10.3848			−0.627369
$275$	48.2871			2.91182
$276$	−2.04891	+	3.54881i	−0.123330	+	0.213613i
$277$	12.0625			0.724767			0.362384	−	0.932029i	$-0.381963\pi$
$277$	12.0625			0.724767			0.362384	+	0.932029i	$0.381963\pi$
$278$	−0.636394	+	1.10227i	−0.0381684	+	0.0661096i
$279$	1.82642	−	3.16346i	0.109345	−	0.189391i
$280$	−6.82682	+	8.48306i	−0.407981	+	0.506960i
$281$	18.3963			1.09743			0.548716	−	0.836009i	$-0.315117\pi$
$281$	18.3963			1.09743			0.548716	+	0.836009i	$0.315117\pi$
$282$	−1.28800	−	2.23088i	−0.0766994	−	0.132847i
$283$	0.347153	−	0.601286i	0.0206361	−	0.0357428i	−0.855523	−	0.517765i	$-0.826764\pi$
$283$	0.347153	−	0.601286i	0.0206361	−	0.0357428i	0.876159	+	0.482022i	$0.160098\pi$
$284$	5.10254	−	8.83786i	0.302780	−	0.524431i
$285$	7.92007	−	13.7180i	0.469144	−	0.812582i
$286$	7.24406	+	12.6571i	0.428350	+	0.748430i
$287$	5.51270	+	14.2315i	0.325404	+	0.840060i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−16.4882			−0.969896
$290$	37.0781			2.17730
$291$	3.10135	+	5.37170i	0.181805	+	0.314895i
$292$	−1.25673	−	2.17673i	−0.0735448	−	0.127383i
$293$	5.44518	−	9.43133i	0.318111	−	0.550984i	−0.661983	−	0.749519i	$-0.730285\pi$
$293$	5.44518	−	9.43133i	0.318111	−	0.550984i	0.980094	+	0.198535i	$0.0636183\pi$
$294$	5.17342	−	4.71548i	0.301720	−	0.275012i
$295$	26.5512	−	45.9880i	1.54587	−	2.67752i
$296$	7.19594			0.418256
$297$	2.02237	−	3.50284i	0.117350	−	0.203256i
$298$	−11.6810	−	20.2320i	−0.676661	−	1.17201i
$299$	−7.43565	+	12.7675i	−0.430015	+	0.738362i
$300$	−11.9383			−0.689256
$301$	−4.25335	+	5.28525i	−0.245159	+	0.304637i
$302$	1.19832	+	2.07555i	0.0689555	+	0.119434i
$303$	8.15325	+	14.1218i	0.468392	+	0.811278i
$304$	1.92440	+	3.33315i	0.110372	+	0.191169i
$305$	38.8134			2.22245
$306$	−0.357690	−	0.619538i	−0.0204478	−	0.0354166i
$307$	23.7724			1.35676			0.678382	−	0.734709i	$-0.262681\pi$
$307$	23.7724			1.35676			0.678382	+	0.734709i	$0.262681\pi$
$308$	6.70925	−	8.33697i	0.382295	−	0.475043i
$309$	−1.46023	−	2.52920i	−0.0830697	−	0.143881i
$310$	15.0337			0.853857
$311$	−10.9242	−	18.9212i	−0.619454	−	1.07293i	−0.989586	−	0.143946i	$-0.954021\pi$
$311$	−10.9242	−	18.9212i	−0.619454	−	1.07293i	0.370132	−	0.928979i	$-0.379312\pi$
$312$	−1.79099	−	3.12928i	−0.101395	−	0.177160i
$313$	16.0323	−	27.7688i	0.906199	−	1.56958i	0.0868992	−	0.996217i	$-0.472304\pi$
$313$	16.0323	−	27.7688i	0.906199	−	1.56958i	0.819300	−	0.573365i	$-0.194362\pi$
$314$	5.79083	+	10.0300i	0.326795	+	0.566026i
$315$	10.7600	+	1.67067i	0.606255	+	0.0941316i
$316$	−6.70468	+	11.6129i	−0.377168	+	0.653274i
$317$	10.3068	−	17.8520i	0.578889	−	1.00267i	−0.416718	−	0.909036i	$-0.636820\pi$
$317$	10.3068	−	17.8520i	0.578889	−	1.00267i	0.995607	−	0.0936296i	$-0.0298469\pi$
$318$	−2.71776			−0.152404
$319$	−36.4396			−2.04023
$320$	2.05781	−	3.56422i	0.115035	−	0.199246i
$321$	−2.01938	+	3.49768i	−0.112711	+	0.195221i
$322$	10.7134	+	1.66344i	0.597036	+	0.0927002i
$323$	1.37668	+	2.38447i	0.0766003	+	0.132676i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−43.0437	−	0.162354i	−2.38764	−	0.00900579i
$326$	−8.95432	−	15.5093i	−0.495934	−	0.858982i
$327$	13.8663			0.766807
$328$	−2.88423	−	4.99563i	−0.159255	−	0.275838i
$329$	−4.27298	+	5.30963i	−0.235577	+	0.292730i
$330$	16.6466			0.916363
$331$	−5.99781	−	10.3885i	−0.329669	−	0.571004i	0.652777	−	0.757550i	$-0.273604\pi$
$331$	−5.99781	−	10.3885i	−0.329669	−	0.571004i	−0.982446	+	0.186546i	$0.940271\pi$
$332$	−15.5024			−0.850807
$333$	−3.59797	−	6.23187i	−0.197168	−	0.341504i
$334$	3.15398	+	5.46286i	0.172578	+	0.298914i
$335$	−2.40005	−	4.15701i	−0.131129	−	0.227122i
$336$	−1.65876	+	2.06119i	−0.0904929	+	0.112447i
$337$	−17.6146			−0.959526			−0.479763	−	0.877398i	$-0.659277\pi$
$337$	−17.6146			−0.959526			−0.479763	+	0.877398i	$0.659277\pi$
$338$	−6.41489	−	11.3070i	−0.348924	−	0.615022i
$339$	7.30902	+	12.6596i	0.396972	+	0.687575i
$340$	1.47212	−	2.54978i	0.0798367	−	0.138281i
$341$	−14.7748			−0.800100
$342$	1.92440	−	3.33315i	0.104059	−	0.180236i
$343$	−16.5777	−	8.25707i	−0.895113	−	0.445840i
$344$	1.28209	−	2.22064i	0.0691255	−	0.119729i
$345$	8.43251	+	14.6055i	0.453991	+	0.786335i
$346$	1.82563	+	3.16209i	0.0981467	+	0.169995i
$347$	−15.8504			−0.850893			−0.425447	−	0.904984i	$-0.639883\pi$
$347$	−15.8504			−0.850893			−0.425447	+	0.904984i	$0.639883\pi$
$348$	9.00914			0.482941
$349$	5.15206	+	8.92363i	0.275783	+	0.477671i	0.970332	−	0.241775i	$-0.0777294\pi$
$349$	5.15206	+	8.92363i	0.275783	+	0.477671i	−0.694549	+	0.719445i	$0.744396\pi$
$350$	11.4090	+	29.4532i	0.609834	+	1.57434i
$351$	−1.81454	+	3.11568i	−0.0968530	+	0.166303i
$352$	−2.02237	+	3.50284i	−0.107793	+	0.186702i
$353$	8.00975	−	13.8733i	0.426316	−	0.738401i	−0.570226	−	0.821488i	$-0.693145\pi$
$353$	8.00975	−	13.8733i	0.426316	−	0.738401i	0.996542	+	0.0830868i	$0.0264779\pi$
$354$	6.45133	−	11.1740i	0.342884	−	0.593893i
$355$	−21.0001	−	36.3732i	−1.11457	−	1.93049i
$356$	−10.9137			−0.578425
$357$	−1.18665	+	1.47454i	−0.0628040	+	0.0780408i
$358$	−6.25956	+	10.8419i	−0.330828	+	0.573011i
$359$	4.55623	−	7.89162i	0.240469	−	0.416504i	−0.720379	−	0.693580i	$-0.756032\pi$
$359$	4.55623	−	7.89162i	0.240469	−	0.416504i	0.960848	+	0.277077i	$0.0893656\pi$
$360$	−4.11561			−0.216912
$361$	2.09340	−	3.62588i	0.110179	−	0.190836i
$362$	−18.1728			−0.955139
$363$	−5.35989			−0.281321
$364$	−6.00874	+	7.40912i	−0.314944	+	0.388343i
$365$	−10.3445			−0.541454
$366$	9.43076			0.492954
$367$	−5.11189	+	8.85406i	−0.266839	+	0.462178i	−0.968044	−	0.250782i	$-0.919312\pi$
$367$	−5.11189	+	8.85406i	−0.266839	+	0.462178i	0.701205	+	0.712960i	$0.252646\pi$
$368$	−4.09781			−0.213613
$369$	−2.88423	+	4.99563i	−0.150147	+	0.260062i
$370$	14.8079	−	25.6480i	0.769824	−	1.33337i
$371$	2.59726	+	6.70504i	0.134843	+	0.348109i
$372$	3.65285			0.189391
$373$	14.0796	+	24.3866i	0.729015	+	1.26269i	0.957300	+	0.289097i	$0.0933550\pi$
$373$	14.0796	+	24.3866i	0.729015	+	1.26269i	−0.228284	+	0.973594i	$0.573312\pi$
$374$	−1.44676	+	2.50587i	−0.0748104	+	0.129575i
$375$	−14.2776	+	24.7295i	−0.737292	+	1.27703i
$376$	1.28800	−	2.23088i	0.0664236	−	0.115049i
$377$	32.4827	+	0.122520i	1.67294	+	0.00631008i
$378$	2.61442	+	0.405935i	0.134472	+	0.0208790i
$379$	−3.08112	−	5.33666i	−0.158267	−	0.274126i	0.775977	−	0.630761i	$-0.217257\pi$
$379$	−3.08112	−	5.33666i	−0.158267	−	0.274126i	−0.934244	+	0.356635i	$0.883924\pi$
$380$	15.8401			0.812582
$381$	−2.53206			−0.129722
$382$	−2.23004	−	3.86254i	−0.114099	−	0.197625i
$383$	9.48159	+	16.4226i	0.484487	+	0.839156i	0.999841	−	0.0178215i	$-0.00567306\pi$
$383$	9.48159	+	16.4226i	0.484487	+	0.839156i	−0.515354	+	0.856977i	$0.672340\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−15.9085	−	41.0692i	−0.810772	−	2.09308i
$386$	4.34243	−	7.52130i	0.221024	−	0.382824i
$387$	−2.56417			−0.130344
$388$	−3.10135	+	5.37170i	−0.157447	+	0.272707i
$389$	1.08192	+	1.87394i	0.0548554	+	0.0950123i	0.892149	−	0.451741i	$-0.149197\pi$
$389$	1.08192	+	1.87394i	0.0548554	+	0.0950123i	−0.837294	+	0.546753i	$0.815864\pi$
$390$	−14.8389	−	0.0559702i	−0.751399	−	0.00283416i
$391$	−2.93150			−0.148252
$392$	6.67043	+	2.12257i	0.336908	+	0.107206i
$393$	−6.21657	−	10.7674i	−0.313584	−	0.543144i
$394$	−1.23397	−	2.13730i	−0.0621664	−	0.107675i
$395$	27.5939	+	47.7940i	1.38840	+	2.40478i
$396$	4.04474			0.203256
$397$	−10.3858	−	17.9888i	−0.521249	−	0.902830i	−0.999695	−	0.0247127i	$-0.992133\pi$
$397$	−10.3858	−	17.9888i	−0.521249	−	0.902830i	0.478445	−	0.878117i	$-0.341200\pi$
$398$	20.5681			1.03099
$399$	−10.0624	−	1.56236i	−0.503749	−	0.0782157i
$400$	−5.96913	−	10.3388i	−0.298457	−	0.516942i
$401$	2.30807			0.115259			0.0576297	−	0.998338i	$-0.481646\pi$
$401$	2.30807			0.115259			0.0576297	+	0.998338i	$0.481646\pi$
$402$	−0.583158	−	1.01006i	−0.0290853	−	0.0503772i
$403$	13.1704	+	0.0496768i	0.656066	+	0.00247458i
$404$	−8.15325	+	14.1218i	−0.405639	+	0.702588i
$405$	2.05781	+	3.56422i	0.102253	+	0.177108i
$406$	−8.60970	−	22.2267i	−0.427292	−	1.10309i
$407$	−14.5528	+	25.2063i	−0.721358	+	1.24943i
$408$	0.357690	−	0.619538i	0.0177083	−	0.0306717i
$409$	16.0313			0.792698			0.396349	−	0.918100i	$-0.370277\pi$
$409$	16.0313			0.792698			0.396349	+	0.918100i	$0.370277\pi$
$410$	−23.7407			−1.17247
$411$	−5.19240	+	8.99351i	−0.256122	+	0.443617i
$412$	1.46023	−	2.52920i	0.0719405	−	0.124605i
$413$	−33.7330	−	5.23764i	−1.65989	−	0.257727i
$414$	2.04891	+	3.54881i	0.100698	+	0.174415i
$415$	−31.9010	+	55.2542i	−1.56596	+	2.71232i
$416$	1.81454	−	3.11568i	0.0889652	−	0.152759i
$417$	0.636394	+	1.10227i	0.0311644	+	0.0539783i
$418$	−15.5673			−0.761424
$419$	1.48519	+	2.57242i	0.0725561	+	0.125671i	0.900021	−	0.435847i	$-0.143551\pi$
$419$	1.48519	+	2.57242i	0.0725561	+	0.125671i	−0.827465	+	0.561518i	$0.810218\pi$
$420$	3.93314	+	10.1537i	0.191917	+	0.495451i
$421$	34.3026			1.67181			0.835903	−	0.548878i	$-0.184945\pi$
$421$	34.3026			1.67181			0.835903	+	0.548878i	$0.184945\pi$
$422$	2.22726	+	3.85773i	0.108422	+	0.187792i
$423$	−2.57600			−0.125250
$424$	−1.35888	−	2.35365i	−0.0659929	−	0.114303i
$425$	−4.27020	−	7.39621i	−0.207135	−	0.358769i
$426$	−5.10254	−	8.83786i	−0.247219	−	0.428196i
$427$	−9.01263	−	23.2669i	−0.436152	−	1.12596i
$428$	−4.03877			−0.195221
$429$	14.5834	+	0.0550063i	0.704093	+	0.00265573i
$430$	−5.27657	−	9.13929i	−0.254459	−	0.440736i
$431$	11.7248	−	20.3079i	0.564762	−	0.978196i	−0.432310	−	0.901725i	$-0.642301\pi$
$431$	11.7248	−	20.3079i	0.564762	−	0.978196i	0.997072	−	0.0764711i	$-0.0243653\pi$
$432$	−1.00000			−0.0481125
$433$	0.402426	−	0.697022i	0.0193394	−	0.0334968i	−0.856194	−	0.516655i	$-0.827177\pi$
$433$	0.402426	−	0.697022i	0.0193394	−	0.0334968i	0.875533	+	0.483158i	$0.160510\pi$
$434$	−3.49089	−	9.01203i	−0.167568	−	0.432591i
$435$	18.5391	−	32.1106i	0.888880	−	1.53959i
$436$	6.93314	+	12.0085i	0.332037	+	0.575105i
$437$	−7.88581	−	13.6586i	−0.377230	−	0.653381i
$438$	−2.51347			−0.120098
$439$	−1.59775			−0.0762566			−0.0381283	−	0.999273i	$-0.512140\pi$
$439$	−1.59775			−0.0762566			−0.0381283	+	0.999273i	$0.512140\pi$
$440$	8.32328	+	14.4163i	0.396797	+	0.687272i
$441$	−1.49702	−	6.83805i	−0.0712865	−	0.325621i
$442$	1.29809	−	2.22890i	0.0617437	−	0.106018i
$443$	−3.27335	+	5.66960i	−0.155521	+	0.269371i	−0.933249	−	0.359231i	$-0.883039\pi$
$443$	−3.27335	+	5.66960i	−0.155521	+	0.269371i	0.777727	+	0.628602i	$0.216372\pi$
$444$	3.59797	−	6.23187i	0.170752	−	0.295751i
$445$	−22.4583	+	38.8989i	−1.06462	+	1.84398i
$446$	−2.49662	−	4.32427i	−0.118218	−	0.204760i
$447$	−23.3619			−1.10498
$448$	−2.61442	−	0.405935i	−0.123520	−	0.0191786i
$449$	−6.34113	+	10.9832i	−0.299257	+	0.518328i	−0.975966	−	0.217923i	$-0.930072\pi$
$449$	−6.34113	+	10.9832i	−0.299257	+	0.518328i	0.676710	+	0.736250i	$0.263405\pi$
$450$	−5.96913	+	10.3388i	−0.281388	+	0.487378i
$451$	23.3319			1.09866
$452$	−7.30902	+	12.6596i	−0.343788	+	0.595457i
$453$	2.39664			0.112604
$454$	−1.57273			−0.0738117
$455$	14.0429	+	36.6630i	0.658343	+	1.71879i
$456$	3.84879			0.180236
$457$	−10.7551			−0.503100			−0.251550	−	0.967844i	$-0.580940\pi$
$457$	−10.7551			−0.503100			−0.251550	+	0.967844i	$0.580940\pi$
$458$	0.828619	−	1.43521i	0.0387188	−	0.0670629i
$459$	−0.715381			−0.0333911
$460$	−8.43251	+	14.6055i	−0.393168	+	0.680986i
$461$	9.19640	−	15.9286i	0.428319	−	0.741870i	−0.568405	−	0.822749i	$-0.692439\pi$
$461$	9.19640	−	15.9286i	0.428319	−	0.741870i	0.996724	+	0.0808788i	$0.0257727\pi$
$462$	−3.86540	−	9.97887i	−0.179835	−	0.464259i
$463$	−34.6818			−1.61180			−0.805901	−	0.592050i	$-0.798319\pi$
$463$	−34.6818			−1.61180			−0.805901	+	0.592050i	$0.798319\pi$
$464$	4.50457	+	7.80214i	0.209119	+	0.362205i
$465$	7.51685	−	13.0196i	0.348586	−	0.603768i
$466$	−3.86181	+	6.68885i	−0.178895	+	0.309855i
$467$	14.1236	−	24.4627i	0.653561	−	1.13200i	−0.328692	−	0.944437i	$-0.606608\pi$
$467$	14.1236	−	24.4627i	0.653561	−	1.13200i	0.982253	−	0.187563i	$-0.0600589\pi$
$468$	−3.60553	−	0.0135995i	−0.166665	−	0.000628636i
$469$	−1.93464	+	2.40400i	−0.0893334	+	0.111006i
$470$	−5.30091	−	9.18145i	−0.244513	−	0.423509i
$471$	11.5817			0.533654
$472$	12.9027			0.593893
$473$	5.18570	+	8.98189i	0.238439	+	0.412988i
$474$	6.70468	+	11.6129i	0.307956	+	0.533396i
$475$	22.9739	−	39.7920i	1.05412	−	1.82578i
$476$	−1.87031	−	0.290398i	−0.0857255	−	0.0133104i
$477$	−1.35888	+	2.35365i	−0.0622187	+	0.107766i
$478$	−28.7630			−1.31559
$479$	6.22925	−	10.7894i	0.284622	−	0.492979i	−0.687896	−	0.725810i	$-0.741465\pi$
$479$	6.22925	−	10.7894i	0.284622	−	0.492979i	0.972517	+	0.232830i	$0.0747987\pi$
$480$	−2.05781	−	3.56422i	−0.0939256	−	0.162684i
$481$	13.0573	−	22.4202i	0.595363	−	1.02227i
$482$	25.6204			1.16698
$483$	6.79730	−	8.44638i	0.309288	−	0.384323i
$484$	−2.67994	−	4.64180i	−0.121816	−	0.210991i
$485$	12.7640	+	22.1078i	0.579582	+	1.00387i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	8.34097			0.377966			0.188983	−	0.981980i	$-0.439481\pi$
$487$	8.34097			0.377966			0.188983	+	0.981980i	$0.439481\pi$
$488$	4.71538	+	8.16728i	0.213455	+	0.369715i
$489$	−17.9086			−0.809856
$490$	21.2918	−	19.4071i	0.961865	−	0.876723i
$491$	8.82502	+	15.2854i	0.398268	+	0.689820i	0.993512	−	0.113725i	$-0.0362781\pi$
$491$	8.82502	+	15.2854i	0.398268	+	0.689820i	−0.595245	+	0.803545i	$0.702945\pi$
$492$	−5.76846			−0.260062
$493$	3.22248	+	5.58150i	0.145133	+	0.251378i
$494$	13.8769	+	0.0523416i	0.624352	+	0.00235496i
$495$	8.32328	−	14.4163i	0.374104	−	0.647967i
$496$	1.82642	+	3.16346i	0.0820088	+	0.142043i
$497$	−16.9278	+	21.0346i	−0.759316	+	0.943532i
$498$	−7.75122	+	13.4255i	−0.347340	+	0.601611i
$499$	−18.9853	+	32.8834i	−0.849897	+	1.47207i	0.0314021	+	0.999507i	$0.490003\pi$
$499$	−18.9853	+	32.8834i	−0.849897	+	1.47207i	−0.881299	+	0.472558i	$0.843331\pi$
$500$	−28.5552			−1.27703
$501$	6.30796			0.281819
$502$	0.339652	−	0.588295i	0.0151594	−	0.0262569i
$503$	−10.4517	+	18.1029i	−0.466019	+	0.807169i	−0.999247	−	0.0388027i	$-0.987646\pi$
$503$	−10.4517	+	18.1029i	−0.466019	+	0.807169i	0.533228	+	0.845972i	$0.320979\pi$
$504$	0.955663	+	2.46713i	0.0425686	+	0.109895i
$505$	33.5556	+	58.1200i	1.49320	+	2.58631i
$506$	8.28729	−	14.3540i	0.368415	−	0.638113i
$507$	−12.9996	−	0.0980666i	−0.577334	−	0.00435529i
$508$	−1.26603	−	2.19283i	−0.0561711	−	0.0972911i
$509$	−15.0211			−0.665797			−0.332899	−	0.942963i	$-0.608027\pi$
$509$	−15.0211			−0.665797			−0.332899	+	0.942963i	$0.608027\pi$
$510$	−1.47212	−	2.54978i	−0.0651864	−	0.112906i
$511$	2.40203	+	6.20104i	0.106259	+	0.274318i
$512$	1.00000			0.0441942
$513$	−1.92440	−	3.33315i	−0.0849641	−	0.147162i
$514$	−2.44587			−0.107883
$515$	−6.00975	−	10.4092i	−0.264821	−	0.458684i
$516$	−1.28209	−	2.22064i	−0.0564407	−	0.0977582i
$517$	5.20962	+	9.02333i	0.229119	+	0.396846i
$518$	−18.8133	−	2.92108i	−0.826607	−	0.128345i
$519$	3.65127			0.160273
$520$	−7.37100	−	12.8789i	−0.323240	−	0.564777i
$521$	10.4549	+	18.1084i	0.458037	+	0.793344i	0.998857	−	0.0477946i	$-0.0152193\pi$
$521$	10.4549	+	18.1084i	0.458037	+	0.793344i	−0.540820	+	0.841138i	$0.681886\pi$
$522$	4.50457	−	7.80214i	0.197160	−	0.341491i
$523$	−12.3678			−0.540806			−0.270403	−	0.962747i	$-0.587157\pi$
$523$	−12.3678			−0.540806			−0.270403	+	0.962747i	$0.587157\pi$
$524$	6.21657	−	10.7674i	0.271572	−	0.470377i
$525$	31.2117	+	4.84616i	1.36219	+	0.211504i
$526$	−12.6596	+	21.9271i	−0.551985	+	0.956067i
$527$	1.30659	+	2.26308i	0.0569159	+	0.0985812i
$528$	2.02237	+	3.50284i	0.0880123	+	0.152442i
$529$	−6.20792			−0.269910
$530$	−11.1852			−0.485855
$531$	−6.45133	−	11.1740i	−0.279964	−	0.484912i
$532$	−3.67815	−	9.49545i	−0.159468	−	0.411680i
$533$	−20.7983	−	0.0784481i	−0.900876	−	0.00339796i
$534$	−5.45685	+	9.45154i	−0.236141	+	0.409008i
$535$	−8.31100	+	14.3951i	−0.359316	+	0.622353i
$536$	0.583158	−	1.01006i	0.0251886	−	0.0436279i
$537$	6.25956	+	10.8419i	0.270120	+	0.467861i
$538$	−13.5665			−0.584895
$539$	−20.9251	+	19.0729i	−0.901308	+	0.821527i
$540$	−2.05781	+	3.56422i	−0.0885539	+	0.153380i
$541$	2.37409	−	4.11204i	0.102070	−	0.176791i	−0.810467	−	0.585784i	$-0.800787\pi$
$541$	2.37409	−	4.11204i	0.102070	−	0.176791i	0.912537	+	0.408993i	$0.134120\pi$
$542$	−4.85940			−0.208729
$543$	−9.08638	+	15.7381i	−0.389934	+	0.675385i
$544$	0.715381			0.0306717
$545$	57.0682			2.44453
$546$	3.41211	+	8.90828i	0.146025	+	0.381239i
$547$	2.85148			0.121921			0.0609603	−	0.998140i	$-0.480584\pi$
$547$	2.85148			0.121921			0.0609603	+	0.998140i	$0.480584\pi$
$548$	−10.3848			−0.443617
$549$	4.71538	−	8.16728i	0.201248	−	0.348571i
$550$	48.2871			2.05897
$551$	−17.3371	+	30.0288i	−0.738587	+	1.27927i
$552$	−2.04891	+	3.54881i	−0.0872073	+	0.151047i
$553$	22.2430	−	27.6393i	0.945867	−	1.17534i
$554$	12.0625			0.512488
$555$	−14.8079	−	25.6480i	−0.628559	−	1.08870i
$556$	−0.636394	+	1.10227i	−0.0269891	+	0.0467466i
$557$	−7.04985	+	12.2107i	−0.298712	+	0.517384i	−0.975842	−	0.218480i	$-0.929890\pi$
$557$	−7.04985	+	12.2107i	−0.298712	+	0.517384i	0.677130	+	0.735864i	$0.263224\pi$
$558$	1.82642	−	3.16346i	0.0773187	−	0.133920i
$559$	−4.59239	−	8.02400i	−0.194238	−	0.339379i
$560$	−6.82682	+	8.48306i	−0.288486	+	0.358475i
$561$	1.44676	+	2.50587i	0.0610824	+	0.105798i
$562$	18.3963			0.776002
$563$	−0.914813			−0.0385548			−0.0192774	−	0.999814i	$-0.506137\pi$
$563$	−0.914813			−0.0385548			−0.0192774	+	0.999814i	$0.506137\pi$
$564$	−1.28800	−	2.23088i	−0.0542346	−	0.0939371i
$565$	30.0811	+	52.1020i	1.26552	+	2.19195i
$566$	0.347153	−	0.601286i	0.0145919	−	0.0252740i
$567$	1.65876	−	2.06119i	0.0696615	−	0.0865619i
$568$	5.10254	−	8.83786i	0.214098	−	0.370828i
$569$	−22.0768			−0.925509			−0.462755	−	0.886486i	$-0.653139\pi$
$569$	−22.0768			−0.925509			−0.462755	+	0.886486i	$0.653139\pi$
$570$	7.92007	−	13.7180i	0.331735	−	0.574582i
$571$	−1.38518	−	2.39921i	−0.0579682	−	0.100404i	0.835585	−	0.549361i	$-0.185129\pi$
$571$	−1.38518	−	2.39921i	−0.0579682	−	0.100404i	−0.893553	+	0.448957i	$0.851796\pi$
$572$	7.24406	+	12.6571i	0.302889	+	0.529220i
$573$	−4.46007			−0.186322
$574$	5.51270	+	14.2315i	0.230096	+	0.594012i
$575$	24.4604	+	42.3666i	1.02007	+	1.76681i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−13.6418	−	23.6282i	−0.567914	−	0.983656i	−0.996772	−	0.0802839i	$-0.974417\pi$
$577$	−13.6418	−	23.6282i	−0.567914	−	0.983656i	0.428858	−	0.903372i	$-0.358916\pi$
$578$	−16.4882			−0.685820
$579$	−4.34243	−	7.52130i	−0.180465	−	0.312575i
$580$	37.0781			1.53959
$581$	40.5299	+	6.29298i	1.68147	+	0.261077i
$582$	3.10135	+	5.37170i	0.128555	+	0.222664i
$583$	10.9926			0.455267
$584$	−1.25673	−	2.17673i	−0.0520040	−	0.0900736i
$585$	−7.46794	+	12.8229i	−0.308761	+	0.530162i
$586$	5.44518	−	9.43133i	0.224938	−	0.389604i
$587$	−15.1737	−	26.2816i	−0.626286	−	1.08476i	−0.988291	−	0.152583i	$-0.951241\pi$
$587$	−15.1737	−	26.2816i	−0.626286	−	1.08476i	0.362005	−	0.932176i	$-0.382092\pi$
$588$	5.17342	−	4.71548i	0.213348	−	0.194463i
$589$	−7.02952	+	12.1755i	−0.289646	+	0.501682i
$590$	26.5512	−	45.9880i	1.09309	−	1.89330i
$591$	−2.46794			−0.101517
$592$	7.19594			0.295751
$593$	−21.2192	+	36.7527i	−0.871367	+	1.50925i	−0.0107847	+	0.999942i	$0.503433\pi$
$593$	−21.2192	+	36.7527i	−0.871367	+	1.50925i	−0.860583	+	0.509311i	$0.829900\pi$
$594$	2.02237	−	3.50284i	0.0829788	−	0.143723i
$595$	−4.88378	+	6.06862i	−0.200215	+	0.248789i
$596$	−11.6810	−	20.2320i	−0.478471	−	0.828736i
$597$	10.2841	−	17.8125i	0.420899	−	0.729018i
$598$	−7.43565	+	12.7675i	−0.304066	+	0.522100i
$599$	15.1759	+	26.2854i	0.620071	+	1.07399i	0.989472	+	0.144724i	$0.0462294\pi$
$599$	15.1759	+	26.2854i	0.620071	+	1.07399i	−0.369401	+	0.929270i	$0.620437\pi$
$600$	−11.9383			−0.487378
$601$	−2.44125	−	4.22836i	−0.0995805	−	0.172479i	0.811931	−	0.583754i	$-0.198417\pi$
$601$	−2.44125	−	4.22836i	−0.0995805	−	0.172479i	−0.911511	+	0.411275i	$0.865083\pi$
$602$	−4.25335	+	5.28525i	−0.173354	+	0.215411i
$603$	−1.16632			−0.0474960
$604$	1.19832	+	2.07555i	0.0487589	+	0.0844529i
$605$	−22.0592			−0.896834
$606$	8.15325	+	14.1218i	0.331203	+	0.573660i
$607$	6.39843	+	11.0824i	0.259704	+	0.449821i	0.966163	−	0.257933i	$-0.0830415\pi$
$607$	6.39843	+	11.0824i	0.259704	+	0.449821i	−0.706458	+	0.707755i	$0.749708\pi$
$608$	1.92440	+	3.33315i	0.0780445	+	0.135177i
$609$	−23.5537	−	3.65712i	−0.954445	−	0.148194i
$610$	38.8134			1.57151
$611$	−4.61358	−	8.06102i	−0.186646	−	0.326114i
$612$	−0.357690	−	0.619538i	−0.0144588	−	0.0250433i
$613$	−2.02495	+	3.50732i	−0.0817871	+	0.141659i	−0.904018	−	0.427495i	$-0.859396\pi$
$613$	−2.02495	+	3.50732i	−0.0817871	+	0.141659i	0.822231	+	0.569155i	$0.192729\pi$
$614$	23.7724			0.959377
$615$	−11.8704	+	20.5601i	−0.478660	+	0.829063i
$616$	6.70925	−	8.33697i	0.270324	−	0.335906i
$617$	−7.16474	+	12.4097i	−0.288441	+	0.499595i	−0.973438	−	0.228951i	$-0.926470\pi$
$617$	−7.16474	+	12.4097i	−0.288441	+	0.499595i	0.684996	+	0.728546i	$0.259804\pi$
$618$	−1.46023	−	2.52920i	−0.0587391	−	0.101739i
$619$	−18.3950	−	31.8611i	−0.739358	−	1.28061i	−0.952785	−	0.303646i	$-0.901796\pi$
$619$	−18.3950	−	31.8611i	−0.739358	−	1.28061i	0.213427	−	0.976959i	$-0.431537\pi$
$620$	15.0337			0.603768
$621$	4.09781			0.164440
$622$	−10.9242	−	18.9212i	−0.438020	−	0.758673i
$623$	28.5330	+	4.43025i	1.14315	+	0.177494i
$624$	−1.79099	−	3.12928i	−0.0716968	−	0.125271i
$625$	−28.9154	+	50.0829i	−1.15662	+	2.00332i
$626$	16.0323	−	27.7688i	0.640779	−	1.10986i
$627$	−7.78367	+	13.4817i	−0.310850	+	0.538408i
$628$	5.79083	+	10.0300i	0.231079	+	0.400241i
$629$	5.14784			0.205258
$630$	10.7600	+	1.67067i	0.428687	+	0.0665611i
$631$	−18.8504	+	32.6498i	−0.750422	+	1.29977i	0.197197	+	0.980364i	$0.436816\pi$
$631$	−18.8504	+	32.6498i	−0.750422	+	1.29977i	−0.947618	+	0.319405i	$0.896517\pi$
$632$	−6.70468	+	11.6129i	−0.266698	+	0.461935i
$633$	4.45453			0.177052
$634$	10.3068	−	17.8520i	0.409336	−	0.708992i
$635$	−10.4210			−0.413544
$636$	−2.71776			−0.107766
$637$	18.7170	−	16.9314i	0.741595	−	0.670848i
$638$	−36.4396			−1.44266
$639$	−10.2051			−0.403707
$640$	2.05781	−	3.56422i	0.0813419	−	0.140888i
$641$	−1.18808			−0.0469264			−0.0234632	−	0.999725i	$-0.507469\pi$
$641$	−1.18808			−0.0469264			−0.0234632	+	0.999725i	$0.507469\pi$
$642$	−2.01938	+	3.49768i	−0.0796987	+	0.138042i
$643$	−14.9781	+	25.9429i	−0.590679	+	1.02309i	0.403462	+	0.914996i	$0.367807\pi$
$643$	−14.9781	+	25.9429i	−0.590679	+	1.02309i	−0.994141	+	0.108090i	$0.965527\pi$
$644$	10.7134	+	1.66344i	0.422168	+	0.0655489i
$645$	−10.5531			−0.415529
$646$	1.37668	+	2.38447i	0.0541646	+	0.0938158i
$647$	15.2109	−	26.3460i	0.598002	−	1.03577i	−0.395114	−	0.918632i	$-0.629295\pi$
$647$	15.2109	−	26.3460i	0.598002	−	1.03577i	0.993116	−	0.117138i	$-0.0373718\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−26.0939	+	45.1960i	−1.02428	+	1.77410i
$650$	−43.0437	−	0.162354i	−1.68831	−	0.00636806i
$651$	−9.55009	−	1.48282i	−0.374298	−	0.0581162i
$652$	−8.95432	−	15.5093i	−0.350678	−	0.607392i
$653$	−12.2930			−0.481061			−0.240530	−	0.970642i	$-0.577321\pi$
$653$	−12.2930			−0.481061			−0.240530	+	0.970642i	$0.577321\pi$
$654$	13.8663			0.542214
$655$	−25.5850	−	44.3145i	−0.999688	−	1.73151i
$656$	−2.88423	−	4.99563i	−0.112610	−	0.195047i
$657$	−1.25673	+	2.17673i	−0.0490299	+	0.0849222i
$658$	−4.27298	+	5.30963i	−0.166578	+	0.206991i
$659$	17.0038	−	29.4514i	0.662374	−	1.14727i	−0.317616	−	0.948219i	$-0.602882\pi$
$659$	17.0038	−	29.4514i	0.662374	−	1.14727i	0.979990	−	0.199046i	$-0.0637844\pi$
$660$	16.6466			0.647967
$661$	−6.90834	+	11.9656i	−0.268703	+	0.465408i	−0.968527	−	0.248908i	$-0.919928\pi$
$661$	−6.90834	+	11.9656i	−0.268703	+	0.465408i	0.699824	+	0.714315i	$0.253262\pi$
$662$	−5.99781	−	10.3885i	−0.233111	−	0.403761i
$663$	−1.28124	−	2.23862i	−0.0497591	−	0.0869410i
$664$	−15.5024			−0.601611
$665$	−41.4128	−	6.43006i	−1.60592	−	0.249347i
$666$	−3.59797	−	6.23187i	−0.139419	−	0.241480i
$667$	−18.4589	−	31.9717i	−0.714731	−	1.23795i
$668$	3.15398	+	5.46286i	0.122031	+	0.211364i
$669$	−4.99324			−0.193050
$670$	−2.40005	−	4.15701i	−0.0927221	−	0.160599i
$671$	−38.1449			−1.47257
$672$	−1.65876	+	2.06119i	−0.0639881	+	0.0795122i
$673$	19.8004	+	34.2952i	0.763248	+	1.32198i	0.941168	+	0.337939i	$0.109730\pi$
$673$	19.8004	+	34.2952i	0.763248	+	1.32198i	−0.177920	+	0.984045i	$0.556937\pi$
$674$	−17.6146			−0.678487
$675$	5.96913	+	10.3388i	0.229752	+	0.397942i
$676$	−6.41489	−	11.3070i	−0.246726	−	0.434886i
$677$	16.8735	−	29.2258i	0.648503	−	1.12324i	−0.334978	−	0.942226i	$-0.608729\pi$
$677$	16.8735	−	29.2258i	0.648503	−	1.12324i	0.983481	−	0.181013i	$-0.0579378\pi$
$678$	7.30902	+	12.6596i	0.280701	+	0.486189i
$679$	10.2888	−	12.7850i	0.394849	−	0.490642i
$680$	1.47212	−	2.54978i	0.0564530	−	0.0977795i
$681$	−0.786363	+	1.36202i	−0.0301335	+	0.0521927i
$682$	−14.7748			−0.565756
$683$	16.7899			0.642448			0.321224	−	0.947003i	$-0.395906\pi$
$683$	16.7899			0.642448			0.321224	+	0.947003i	$0.395906\pi$
$684$	1.92440	−	3.33315i	0.0735811	−	0.127446i
$685$	−21.3699	+	37.0138i	−0.816503	+	1.41422i
$686$	−16.5777	−	8.25707i	−0.632940	−	0.315256i
$687$	−0.828619	−	1.43521i	−0.0316138	−	0.0547567i
$688$	1.28209	−	2.22064i	0.0488791	−	0.0846610i
$689$	−9.79894	−	0.0369601i	−0.373310	−	0.00140807i
$690$	8.43251	+	14.6055i	0.321020	+	0.556023i
$691$	−3.35925			−0.127792			−0.0638960	−	0.997957i	$-0.520353\pi$
$691$	−3.35925			−0.127792			−0.0638960	+	0.997957i	$0.520353\pi$
$692$	1.82563	+	3.16209i	0.0694002	+	0.120205i
$693$	−10.5747	−	1.64190i	−0.401698	−	0.0623706i
$694$	−15.8504			−0.601672
$695$	2.61915	+	4.53651i	0.0993501	+	0.172079i
$696$	9.00914			0.341491
$697$	−2.06332	−	3.57378i	−0.0781539	−	0.135367i
$698$	5.15206	+	8.92363i	0.195008	+	0.337764i
$699$	3.86181	+	6.68885i	0.146067	+	0.252996i
$700$	11.4090	+	29.4532i	0.431218	+	1.11323i
$701$	−51.6652			−1.95137			−0.975683	−	0.219186i	$-0.929660\pi$
$701$	−51.6652			−1.95137			−0.975683	+	0.219186i	$0.929660\pi$
$702$	−1.81454	+	3.11568i	−0.0684854	+	0.117594i
$703$	13.8478	+	23.9852i	0.522281	+	0.904618i
$704$	−2.02237	+	3.50284i	−0.0762209	+	0.132018i
$705$	−10.6018			−0.399288
$706$	8.00975	−	13.8733i	0.301451	−	0.522128i
$707$	27.0486	−	33.6108i	1.01727	−	1.26406i
$708$	6.45133	−	11.1740i	0.242456	−	0.419946i
$709$	9.65303	+	16.7195i	0.362527	+	0.627916i	0.988376	−	0.152029i	$-0.0485806\pi$
$709$	9.65303	+	16.7195i	0.362527	+	0.627916i	−0.625849	+	0.779944i	$0.715247\pi$
$710$	−21.0001	−	36.3732i	−0.788119	−	1.36506i
$711$	13.4094			0.502891
$712$	−10.9137			−0.409008
$713$	−7.48434	−	12.9633i	−0.280291	−	0.485478i
$714$	−1.18665	+	1.47454i	−0.0444091	+	0.0551832i
$715$	60.0196	+	0.226385i	2.24461	+	0.00846631i
$716$	−6.25956	+	10.8419i	−0.233931	+	0.405180i
$717$	−14.3815	+	24.9095i	−0.537086	+	0.930261i
$718$	4.55623	−	7.89162i	0.170037	−	0.294513i
$719$	4.27657	+	7.40724i	0.159489	+	0.276243i	0.934685	−	0.355478i	$-0.115682\pi$
$719$	4.27657	+	7.40724i	0.159489	+	0.276243i	−0.775195	+	0.631721i	$0.782349\pi$
$720$	−4.11561			−0.153380
$721$	−4.84436	+	6.01963i	−0.180413	+	0.224183i
$722$	2.09340	−	3.62588i	0.0779084	−	0.134941i
$723$	12.8102	−	22.1879i	0.476417	−	0.825178i
$724$	−18.1728			−0.675385
$725$	53.7767	−	93.1440i	1.99722	−	3.45928i
$726$	−5.35989			−0.198924
$727$	37.0524			1.37420			0.687100	−	0.726563i	$-0.258884\pi$
$727$	37.0524			1.37420			0.687100	+	0.726563i	$0.258884\pi$
$728$	−6.00874	+	7.40912i	−0.222699	+	0.274600i
$729$	1.00000			0.0370370
$730$	−10.3445			−0.382866
$731$	0.917180	−	1.58860i	0.0339231	−	0.0587566i
$732$	9.43076			0.348571
$733$	7.89197	−	13.6693i	0.291497	−	0.504887i	−0.682667	−	0.730729i	$-0.739180\pi$
$733$	7.89197	−	13.6693i	0.291497	−	0.504887i	0.974164	+	0.225843i	$0.0725135\pi$
$734$	−5.11189	+	8.85406i	−0.188683	+	0.326809i
$735$	−6.16114	−	28.1428i	−0.227257	−	1.03806i
$736$	−4.09781			−0.151047
$737$	2.35872	+	4.08542i	0.0868845	+	0.150488i
$738$	−2.88423	+	4.99563i	−0.106170	+	0.183892i
$739$	18.1725	−	31.4757i	0.668487	−	1.15785i	−0.309840	−	0.950789i	$-0.600276\pi$
$739$	18.1725	−	31.4757i	0.668487	−	1.15785i	0.978327	−	0.207065i	$-0.0663911\pi$
$740$	14.8079	−	25.6480i	0.544348	−	0.942838i
$741$	6.98379	−	11.9916i	0.256556	−	0.440522i
$742$	2.59726	+	6.70504i	0.0953483	+	0.246150i
$743$	−15.1149	−	26.1797i	−0.554511	−	0.960441i	−0.997941	−	0.0641324i	$-0.979572\pi$
$743$	−15.1149	−	26.1797i	−0.554511	−	0.960441i	0.443430	−	0.896309i	$-0.353761\pi$
$744$	3.65285			0.133920
$745$	−96.1487			−3.52262
$746$	14.0796	+	24.3866i	0.515492	+	0.892858i
$747$	7.75122	+	13.4255i	0.283602	+	0.491213i
$748$	−1.44676	+	2.50587i	−0.0528989	+	0.0916236i
$749$	10.5591	+	1.63948i	0.385819	+	0.0599052i
$750$	−14.2776	+	24.7295i	−0.521344	+	0.902995i
$751$	30.7238			1.12113			0.560563	−	0.828112i	$-0.310585\pi$
$751$	30.7238			1.12113			0.560563	+	0.828112i	$0.310585\pi$
$752$	1.28800	−	2.23088i	0.0469686	−	0.0813520i
$753$	−0.339652	−	0.588295i	−0.0123776	−	0.0214387i
$754$	32.4827	+	0.122520i	1.18295	+	0.00446190i
$755$	9.86363			0.358974
$756$	2.61442	+	0.405935i	0.0950857	+	0.0147637i
$757$	−7.78491	−	13.4839i	−0.282947	−	0.490079i	0.689162	−	0.724607i	$-0.257979\pi$
$757$	−7.78491	−	13.4839i	−0.282947	−	0.490079i	−0.972109	+	0.234528i	$0.924646\pi$
$758$	−3.08112	−	5.33666i	−0.111911	−	0.193836i
$759$	−8.28729	−	14.3540i	−0.300809	−	0.521017i
$760$	15.8401			0.574582
$761$	−11.9278	−	20.6596i	−0.432382	−	0.748908i	0.564696	−	0.825299i	$-0.308994\pi$
$761$	−11.9278	−	20.6596i	−0.432382	−	0.748908i	−0.997078	+	0.0763911i	$0.975660\pi$
$762$	−2.53206			−0.0917270
$763$	−13.2515	−	34.2098i	−0.479736	−	1.23848i
$764$	−2.23004	−	3.86254i	−0.0806799	−	0.139742i
$765$	−2.94423			−0.106449
$766$	9.48159	+	16.4226i	0.342584	+	0.593373i
$767$	23.4124	−	40.2005i	0.845373	−	1.45156i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−23.2870	−	40.3342i	−0.839750	−	1.45449i	−0.890104	−	0.455758i	$-0.849368\pi$
$769$	−23.2870	−	40.3342i	−0.839750	−	1.45449i	0.0503539	−	0.998731i	$-0.483965\pi$
$770$	−15.9085	−	41.0692i	−0.573302	−	1.48003i
$771$	−1.22293	+	2.11818i	−0.0440429	+	0.0762846i
$772$	4.34243	−	7.52130i	0.156287	−	0.270698i
$773$	7.50660			0.269994			0.134997	−	0.990846i	$-0.456898\pi$
$773$	7.50660			0.269994			0.134997	+	0.990846i	$0.456898\pi$
$774$	−2.56417			−0.0921673
$775$	21.8043	−	37.7662i	0.783234	−	1.35660i
$776$	−3.10135	+	5.37170i	−0.111332	+	0.192833i
$777$	−11.9364	+	14.8322i	−0.428215	+	0.532103i
$778$	1.08192	+	1.87394i	0.0387886	+	0.0671839i
$779$	11.1008	−	19.2271i	0.397727	−	0.688884i
$780$	−14.8389	−	0.0559702i	−0.531319	−	0.00200405i
$781$	20.6384	+	35.7468i	0.738501	+	1.27912i
$782$	−2.93150			−0.104830
$783$	−4.50457	−	7.80214i	−0.160980	−	0.278826i
$784$	6.67043	+	2.12257i	0.238230	+	0.0758061i
$785$	47.6656			1.70126
$786$	−6.21657	−	10.7674i	−0.221738	−	0.384061i
$787$	42.4895			1.51459			0.757293	−	0.653075i	$-0.226521\pi$
$787$	42.4895			1.51459			0.757293	+	0.653075i	$0.226521\pi$
$788$	−1.23397	−	2.13730i	−0.0439583	−	0.0761380i
$789$	12.6596	+	21.9271i	0.450694	+	0.780625i
$790$	27.5939	+	47.7940i	0.981746	+	1.70043i
$791$	24.2479	−	30.1306i	0.862155	−	1.07132i
$792$	4.04474			0.143723
$793$	34.0029	+	0.128254i	1.20748	+	0.00455442i
$794$	−10.3858	−	17.9888i	−0.368579	−	0.638397i
$795$	−5.59261	+	9.68669i	−0.198350	+	0.343552i
$796$	20.5681			0.729018
$797$	−9.27713	+	16.0685i	−0.328613	+	0.569174i	−0.982237	−	0.187645i	$-0.939914\pi$
$797$	−9.27713	+	16.0685i	−0.328613	+	0.569174i	0.653624	+	0.756819i	$0.273248\pi$
$798$	−10.0624	−	1.56236i	−0.356204	−	0.0553069i
$799$	0.921412	−	1.59593i	0.0325972	−	0.0564600i
$800$	−5.96913	−	10.3388i	−0.211041	−	0.365533i
$801$	5.45685	+	9.45154i	0.192808	+	0.333954i
$802$	2.30807			0.0815007
$803$	10.1663			0.358761
$804$	−0.583158	−	1.01006i	−0.0205664	−	0.0356220i
$805$	27.9750	−	34.7620i	0.985991	−	1.22520i
$806$	13.1704	+	0.0496768i	0.463909	+	0.00174979i
$807$	−6.78327	+	11.7490i	−0.238783	+	0.413583i
$808$	−8.15325	+	14.1218i	−0.286830	+	0.496804i
$809$	−18.6681	+	32.3340i	−0.656334	+	1.13680i	0.325224	+	0.945637i	$0.394560\pi$
$809$	−18.6681	+	32.3340i	−0.656334	+	1.13680i	−0.981558	+	0.191167i	$0.938773\pi$
$810$	2.05781	+	3.56422i	0.0723039	+	0.125234i
$811$	19.9446			0.700350			0.350175	−	0.936684i	$-0.386122\pi$
$811$	19.9446			0.700350			0.350175	+	0.936684i	$0.386122\pi$
$812$	−8.60970	−	22.2267i	−0.302141	−	0.780003i
$813$	−2.42970	+	4.20837i	−0.0852133	+	0.147594i
$814$	−14.5528	+	25.2063i	−0.510077	+	0.883479i
$815$	−73.7050			−2.58177
$816$	0.357690	−	0.619538i	0.0125217	−	0.0216882i
$817$	9.86896			0.345271
$818$	16.0313			0.560522
$819$	9.42086	+	1.49916i	0.329191	+	0.0523850i
$820$	−23.7407			−0.829063
$821$	24.1262			0.842011			0.421005	−	0.907058i	$-0.361677\pi$
$821$	24.1262			0.842011			0.421005	+	0.907058i	$0.361677\pi$
$822$	−5.19240	+	8.99351i	−0.181106	+	0.313685i
$823$	3.27706			0.114231			0.0571155	−	0.998368i	$-0.481810\pi$
$823$	3.27706			0.114231			0.0571155	+	0.998368i	$0.481810\pi$
$824$	1.46023	−	2.52920i	0.0508696	−	0.0881087i
$825$	24.1436	−	41.8179i	0.840571	−	1.45591i
$826$	−33.7330	−	5.23764i	−1.17372	−	0.182241i
$827$	49.4538			1.71968			0.859838	−	0.510566i	$-0.170564\pi$
$827$	49.4538			1.71968			0.859838	+	0.510566i	$0.170564\pi$
$828$	2.04891	+	3.54881i	0.0712044	+	0.123330i
$829$	−18.2954	+	31.6886i	−0.635426	+	1.10059i	0.350998	+	0.936376i	$0.385842\pi$
$829$	−18.2954	+	31.6886i	−0.635426	+	1.10059i	−0.986425	+	0.164215i	$0.947491\pi$
$830$	−31.9010	+	55.2542i	−1.10730	+	1.91790i
$831$	6.03127	−	10.4465i	0.209222	−	0.362384i
$832$	1.81454	−	3.11568i	0.0629079	−	0.108017i
$833$	4.77190	+	1.51845i	0.165337	+	0.0526111i
$834$	0.636394	+	1.10227i	0.0220365	+	0.0381684i
$835$	25.9611			0.898422
$836$	−15.5673			−0.538408
$837$	−1.82642	−	3.16346i	−0.0631304	−	0.109345i
$838$	1.48519	+	2.57242i	0.0513049	+	0.0888627i
$839$	−21.2148	+	36.7451i	−0.732416	+	1.26858i	0.223431	+	0.974720i	$0.428274\pi$
$839$	−21.2148	+	36.7451i	−0.732416	+	1.26858i	−0.955848	+	0.293862i	$0.905059\pi$
$840$	3.93314	+	10.1537i	0.135706	+	0.350337i
$841$	−26.0823	+	45.1759i	−0.899389	+	1.55779i
$842$	34.3026			1.18214
$843$	9.19816	−	15.9317i	0.316801	−	0.548716i
$844$	2.22726	+	3.85773i	0.0766656	+	0.132789i
$845$	−53.5014	−	0.403604i	−1.84051	−	0.0138844i
$846$	−2.57600			−0.0885648
$847$	5.12224	+	13.2235i	0.176002	+	0.454365i
$848$	−1.35888	−	2.35365i	−0.0466641	−	0.0808245i
$849$	−0.347153	−	0.601286i	−0.0119143	−	0.0206361i
$850$	−4.27020	−	7.39621i	−0.146467	−	0.253688i
$851$	−29.4876			−1.01082
$852$	−5.10254	−	8.83786i	−0.174810	−	0.302780i
$853$	31.5639			1.08073			0.540363	−	0.841432i	$-0.318287\pi$
$853$	31.5639			1.08073			0.540363	+	0.841432i	$0.318287\pi$
$854$	−9.01263	−	23.2669i	−0.308406	−	0.796176i
$855$	−7.92007	−	13.7180i	−0.270861	−	0.469144i
$856$	−4.03877			−0.138042
$857$	−13.0273	−	22.5639i	−0.445004	−	0.770769i	0.553049	−	0.833149i	$-0.313464\pi$
$857$	−13.0273	−	22.5639i	−0.445004	−	0.770769i	−0.998052	+	0.0623801i	$0.980131\pi$
$858$	14.5834	+	0.0550063i	0.497869	+	0.00187789i
$859$	19.9113	−	34.4875i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$859$	19.9113	−	34.4875i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710786\pi$
$860$	−5.27657	−	9.13929i	−0.179930	−	0.311647i
$861$	15.0812	+	2.34162i	0.513966	+	0.0798021i
$862$	11.7248	−	20.3079i	0.399347	−	0.691689i
$863$	10.4795	−	18.1510i	0.356725	−	0.617866i	−0.630687	−	0.776038i	$-0.717227\pi$
$863$	10.4795	−	18.1510i	0.356725	−	0.617866i	0.987412	+	0.158172i	$0.0505600\pi$
$864$	−1.00000			−0.0340207
$865$	15.0272			0.510940
$866$	0.402426	−	0.697022i	0.0136750	−	0.0236858i
$867$	−8.24412	+	14.2792i	−0.279985	+	0.484948i
$868$	−3.49089	−	9.01203i	−0.118489	−	0.305888i
$869$	−27.1187	−	46.9709i	−0.919938	−	1.59338i
$870$	18.5391	−	32.1106i	0.628533	−	1.08865i
$871$	−2.08885	−	3.64972i	−0.0707781	−	0.123666i
$872$	6.93314	+	12.0085i	0.234786	+	0.406661i
$873$	6.20271			0.209930
$874$	−7.88581	−	13.6586i	−0.266742	−	0.462010i
$875$	74.6554	+	11.5915i	2.52381	+	0.391866i
$876$	−2.51347			−0.0849222
$877$	7.24457	+	12.5480i	0.244632	+	0.423714i	0.962028	−	0.272951i	$-0.0879996\pi$
$877$	7.24457	+	12.5480i	0.244632	+	0.423714i	−0.717396	+	0.696665i	$0.754666\pi$
$878$	−1.59775			−0.0539216
$879$	−5.44518	−	9.43133i	−0.183661	−	0.318111i
$880$	8.32328	+	14.4163i	0.280578	+	0.485975i
$881$	−22.1191	−	38.3114i	−0.745211	−	1.29074i	−0.950096	−	0.311957i	$-0.899016\pi$
$881$	−22.1191	−	38.3114i	−0.745211	−	1.29074i	0.204886	−	0.978786i	$-0.434318\pi$
$882$	−1.49702	−	6.83805i	−0.0504071	−	0.230249i
$883$	−51.8997			−1.74656			−0.873282	−	0.487216i	$-0.838012\pi$
$883$	−51.8997			−1.74656			−0.873282	+	0.487216i	$0.838012\pi$
$884$	1.29809	−	2.22890i	0.0436594	−	0.0749659i
$885$	−26.5512	−	45.9880i	−0.892508	−	1.54587i
$886$	−3.27335	+	5.66960i	−0.109970	+	0.190474i
$887$	28.7902			0.966681			0.483340	−	0.875433i	$-0.339423\pi$
$887$	28.7902			0.966681			0.483340	+	0.875433i	$0.339423\pi$
$888$	3.59797	−	6.23187i	0.120740	−	0.209128i
$889$	2.41980	+	6.24692i	0.0811574	+	0.209515i
$890$	−22.4583	+	38.8989i	−0.752803	+	1.30389i
$891$	−2.02237	−	3.50284i	−0.0677519	−	0.117350i
$892$	−2.49662	−	4.32427i	−0.0835929	−	0.144787i
$893$	9.91450			0.331776
$894$	−23.3619			−0.781340
$895$	25.7619	+	44.6210i	0.861126	+	1.49151i
$896$	−2.61442	−	0.405935i	−0.0873418	−	0.0135613i
$897$	7.33912	+	12.8232i	0.245046	+	0.428154i
$898$	−6.34113	+	10.9832i	−0.211606	+	0.366513i
$899$	−16.4545	+	28.5000i	−0.548788	+	0.950529i
$900$	−5.96913	+	10.3388i	−0.198971	+	0.344628i
$901$	−0.972115	−	1.68375i	−0.0323859	−	0.0560939i
$902$	23.3319			0.776867
$903$	2.45048	+	6.32614i	0.0815470	+	0.210521i
$904$	−7.30902	+	12.6596i	−0.243095	+	0.421052i
$905$	−37.3960	+	64.7718i	−1.24309	+	2.15309i
$906$	2.39664			0.0796229
$907$	16.5608	−	28.6841i	0.549892	−	0.952441i	−0.448389	−	0.893838i	$-0.648002\pi$
$907$	16.5608	−	28.6841i	0.549892	−	0.952441i	0.998281	−	0.0586026i	$-0.0186645\pi$
$908$	−1.57273			−0.0521927
$909$	16.3065			0.540852
$910$	14.0429	+	36.6630i	0.465519	+	1.21537i
$911$	−20.6630			−0.684597			−0.342298	−	0.939591i	$-0.611205\pi$
$911$	−20.6630			−0.684597			−0.342298	+	0.939591i	$0.611205\pi$
$912$	3.84879			0.127446
$913$	31.3516	−	54.3026i	1.03759	−	1.79715i
$914$	−10.7551			−0.355745
$915$	19.4067	−	33.6134i	0.641565	−	1.11122i
$916$	0.828619	−	1.43521i	0.0273783	−	0.0474207i
$917$	−20.6236	+	25.6271i	−0.681052	+	0.846280i
$918$	−0.715381			−0.0236111
$919$	−25.8087	−	44.7020i	−0.851350	−	1.47458i	−0.879990	−	0.474992i	$-0.842451\pi$
$919$	−25.8087	−	44.7020i	−0.851350	−	1.47458i	0.0286403	−	0.999590i	$-0.490882\pi$
$920$	−8.43251	+	14.6055i	−0.278011	+	0.481530i
$921$	11.8862	−	20.5875i	0.391664	−	0.678382i
$922$	9.19640	−	15.9286i	0.302867	−	0.524581i
$923$	−18.2772	−	31.9345i	−0.601600	−	1.05114i
$924$	−3.86540	−	9.97887i	−0.127162	−	0.328281i
$925$	−42.9535	−	74.3977i	−1.41230	−	2.44618i
$926$	−34.6818			−1.13972
$927$	−2.92046			−0.0959206
$928$	4.50457	+	7.80214i	0.147870	+	0.256118i
$929$	17.2590	+	29.8935i	0.566250	+	0.980773i	0.996932	+	0.0782698i	$0.0249396\pi$
$929$	17.2590	+	29.8935i	0.566250	+	0.980773i	−0.430682	+	0.902504i	$0.641727\pi$
$930$	7.51685	−	13.0196i	0.246487	−	0.426928i
$931$	5.76170	+	26.3182i	0.188832	+	0.862545i
$932$	−3.86181	+	6.68885i	−0.126498	+	0.219101i
$933$	−21.8484			−0.715283
$934$	14.1236	−	24.4627i	0.462137	−	0.800445i
$935$	5.95432	+	10.3132i	0.194727	+	0.337277i
$936$	−3.60553	−	0.0135995i	−0.117850	−	0.000444513i
$937$	14.3652			0.469291			0.234646	−	0.972081i	$-0.424607\pi$
$937$	14.3652			0.469291			0.234646	+	0.972081i	$0.424607\pi$
$938$	−1.93464	+	2.40400i	−0.0631683	+	0.0784934i
$939$	−16.0323	−	27.7688i	−0.523194	−	0.906199i
$940$	−5.30091	−	9.18145i	−0.172897	−	0.299466i
$941$	4.16447	+	7.21307i	0.135758	+	0.235139i	0.925887	−	0.377801i	$-0.123320\pi$
$941$	4.16447	+	7.21307i	0.135758	+	0.235139i	−0.790129	+	0.612941i	$0.789986\pi$
$942$	11.5817			0.377351
$943$	11.8190	+	20.4712i	0.384881	+	0.666633i
$944$	12.9027			0.419946
$945$	6.82682	−	8.48306i	0.222077	−	0.275954i
$946$	5.18570	+	8.98189i	0.168602	+	0.292027i
$947$	−0.321435			−0.0104452			−0.00522262	−	0.999986i	$-0.501662\pi$
$947$	−0.321435			−0.0104452			−0.00522262	+	0.999986i	$0.501662\pi$
$948$	6.70468	+	11.6129i	0.217758	+	0.377168i
$949$	−9.06238	−	0.0341819i	−0.294177	−	0.00110959i
$950$	22.9739	−	39.7920i	0.745373	−	1.29102i
$951$	−10.3068	−	17.8520i	−0.334222	−	0.578889i
$952$	−1.87031	−	0.290398i	−0.0606171	−	0.00941185i
$953$	−9.79426	+	16.9642i	−0.317267	+	0.549523i	−0.979917	−	0.199407i	$-0.936099\pi$
$953$	−9.79426	+	16.9642i	−0.317267	+	0.549523i	0.662650	+	0.748930i	$0.269432\pi$
$954$	−1.35888	+	2.35365i	−0.0439953	+	0.0762021i
$955$	−18.3559			−0.593984
$956$	−28.7630			−0.930261
$957$	−18.2198	+	31.5576i	−0.588962	+	1.02011i
$958$	6.22925	−	10.7894i	0.201258	−	0.348589i
$959$	27.1503	+	4.21555i	0.876729	+	0.136127i
$960$	−2.05781	−	3.56422i	−0.0664154	−	0.115035i
$961$	8.82835	−	15.2912i	0.284786	−	0.493263i
$962$	13.0573	−	22.4202i	0.420985	−	0.722857i
$963$	2.01938	+	3.49768i	0.0650737	+	0.112711i
$964$	25.6204			0.825178
$965$	−17.8717	−	30.9548i	−0.575312	−	0.996469i
$966$	6.79730	−	8.44638i	0.218699	−	0.271758i
$967$	−21.5461			−0.692875			−0.346437	−	0.938073i	$-0.612609\pi$
$967$	−21.5461			−0.692875			−0.346437	+	0.938073i	$0.612609\pi$
$968$	−2.67994	−	4.64180i	−0.0861366	−	0.149193i
$969$	2.75335			0.0884504
$970$	12.7640	+	22.1078i	0.409826	+	0.709840i
$971$	8.53781	+	14.7879i	0.273991	+	0.474567i	0.969880	−	0.243583i	$-0.0783227\pi$
$971$	8.53781	+	14.7879i	0.273991	+	0.474567i	−0.695889	+	0.718150i	$0.744989\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	2.11125	−	2.62346i	0.0676837	−	0.0841043i
$974$	8.34097			0.267262
$975$	−21.6625	+	37.1958i	−0.693754	+	1.19122i
$976$	4.71538	+	8.16728i	0.150936	+	0.261428i
$977$	−4.36043	+	7.55249i	−0.139503	+	0.241626i	−0.927308	−	0.374298i	$-0.877884\pi$
$977$	−4.36043	+	7.55249i	−0.139503	+	0.241626i	0.787806	+	0.615924i	$0.211217\pi$
$978$	−17.9086			−0.572655
$979$	22.0715	−	38.2290i	0.705409	−	1.22180i
$980$	21.2918	−	19.4071i	0.680141	−	0.619937i
$981$	6.93314	−	12.0085i	0.221358	−	0.383403i
$982$	8.82502	+	15.2854i	0.281618	+	0.487776i
$983$	11.0826	+	19.1956i	0.353480	+	0.612245i	0.986857	−	0.161598i	$-0.0516649\pi$
$983$	11.0826	+	19.1956i	0.353480	+	0.612245i	−0.633377	+	0.773844i	$0.718332\pi$
$984$	−5.76846			−0.183892
$985$	−10.1571			−0.323631
$986$	3.22248	+	5.58150i	0.102625	+	0.177751i
$987$	2.46179	+	6.35532i	0.0783596	+	0.202292i
$988$	13.8769	+	0.0523416i	0.441484	+	0.00166521i
$989$	−5.25375	+	9.09976i	−0.167060	+	0.289356i
$990$	8.32328	−	14.4163i	0.264531	−	0.458182i
$991$	−8.97605	+	15.5470i	−0.285134	+	0.493866i	−0.972642	−	0.232311i	$-0.925371\pi$
$991$	−8.97605	+	15.5470i	−0.285134	+	0.493866i	0.687508	+	0.726177i	$0.258705\pi$
$992$	1.82642	+	3.16346i	0.0579890	+	0.100440i
$993$	−11.9956			−0.380669
$994$	−16.9278	+	21.0346i	−0.536917	+	0.667178i
$995$	42.3252	−	73.3095i	1.34180	−	2.32407i
$996$	−7.75122	+	13.4255i	−0.245607	+	0.425403i
$997$	58.9494			1.86694			0.933472	−	0.358649i	$-0.116763\pi$
$997$	58.9494			1.86694			0.933472	+	0.358649i	$0.116763\pi$
$998$	−18.9853	+	32.8834i	−0.600968	+	1.04091i
$999$	−7.19594			−0.227670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.d.289.4	✓	8
3.2	odd	2		1638.2.m.g.289.1		8
7.4	even	3		546.2.k.b.445.4	yes	8
13.9	even	3		546.2.k.b.373.4	yes	8
21.11	odd	6		1638.2.p.i.991.1		8
39.35	odd	6		1638.2.p.i.919.1		8
91.74	even	3	inner	546.2.j.d.529.4	yes	8
273.74	odd	6		1638.2.m.g.1621.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.4	✓	8	1.1	even	1	trivial
546.2.j.d.529.4	yes	8	91.74	even	3	inner
546.2.k.b.373.4	yes	8	13.9	even	3
546.2.k.b.445.4	yes	8	7.4	even	3
1638.2.m.g.289.1		8	3.2	odd	2
1638.2.m.g.1621.1		8	273.74	odd	6
1638.2.p.i.919.1		8	39.35	odd	6
1638.2.p.i.991.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.61442 - 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(2.05781 - 3.56422i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.61442 - 0.405935i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.05781 - 3.56422i) q^{10} +(-2.02237 + 3.50284i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.81454 - 3.11568i) q^{13} +(-2.61442 - 0.405935i) q^{14} +(-2.05781 - 3.56422i) q^{15} +1.00000 q^{16} +0.715381 q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.92440 + 3.33315i) q^{19} +(2.05781 - 3.56422i) q^{20} +(-1.65876 + 2.06119i) q^{21} +(-2.02237 + 3.50284i) q^{22} -4.09781 q^{23} +(0.500000 - 0.866025i) q^{24} +(-5.96913 - 10.3388i) q^{25} +(1.81454 - 3.11568i) q^{26} -1.00000 q^{27} +(-2.61442 - 0.405935i) q^{28} +(4.50457 + 7.80214i) q^{29} +(-2.05781 - 3.56422i) q^{30} +(1.82642 + 3.16346i) q^{31} +1.00000 q^{32} +(2.02237 + 3.50284i) q^{33} +0.715381 q^{34} +(-6.82682 + 8.48306i) q^{35} +(-0.500000 - 0.866025i) q^{36} +7.19594 q^{37} +(1.92440 + 3.33315i) q^{38} +(-1.79099 - 3.12928i) q^{39} +(2.05781 - 3.56422i) q^{40} +(-2.88423 - 4.99563i) q^{41} +(-1.65876 + 2.06119i) q^{42} +(1.28209 - 2.22064i) q^{43} +(-2.02237 + 3.50284i) q^{44} -4.11561 q^{45} -4.09781 q^{46} +(1.28800 - 2.23088i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.67043 + 2.12257i) q^{49} +(-5.96913 - 10.3388i) q^{50} +(0.357690 - 0.619538i) q^{51} +(1.81454 - 3.11568i) q^{52} +(-1.35888 - 2.35365i) q^{53} -1.00000 q^{54} +(8.32328 + 14.4163i) q^{55} +(-2.61442 - 0.405935i) q^{56} +3.84879 q^{57} +(4.50457 + 7.80214i) q^{58} +12.9027 q^{59} +(-2.05781 - 3.56422i) q^{60} +(4.71538 + 8.16728i) q^{61} +(1.82642 + 3.16346i) q^{62} +(0.955663 + 2.46713i) q^{63} +1.00000 q^{64} +(-7.37100 - 12.8789i) q^{65} +(2.02237 + 3.50284i) q^{66} +(0.583158 - 1.01006i) q^{67} +0.715381 q^{68} +(-2.04891 + 3.54881i) q^{69} +(-6.82682 + 8.48306i) q^{70} +(5.10254 - 8.83786i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.25673 - 2.17673i) q^{73} +7.19594 q^{74} -11.9383 q^{75} +(1.92440 + 3.33315i) q^{76} +(6.70925 - 8.33697i) q^{77} +(-1.79099 - 3.12928i) q^{78} +(-6.70468 + 11.6129i) q^{79} +(2.05781 - 3.56422i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.88423 - 4.99563i) q^{82} -15.5024 q^{83} +(-1.65876 + 2.06119i) q^{84} +(1.47212 - 2.54978i) q^{85} +(1.28209 - 2.22064i) q^{86} +9.00914 q^{87} +(-2.02237 + 3.50284i) q^{88} -10.9137 q^{89} -4.11561 q^{90} +(-6.00874 + 7.40912i) q^{91} -4.09781 q^{92} +3.65285 q^{93} +(1.28800 - 2.23088i) q^{94} +15.8401 q^{95} +(0.500000 - 0.866025i) q^{96} +(-3.10135 + 5.37170i) q^{97} +(6.67043 + 2.12257i) q^{98} +4.04474 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	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} - 8 q^{17} - 4 q^{18} + 6 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} + 20 q^{23} + 4 q^{24} - 18 q^{25} - 11 q^{26} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 8 q^{32} + 6 q^{33} - 8 q^{34} - 18 q^{35} - 4 q^{36} + 56 q^{37} + 6 q^{38} - 10 q^{39} + 2 q^{40} - 3 q^{42} - 6 q^{43} - 6 q^{44} - 4 q^{45} + 20 q^{46} + q^{47} + 4 q^{48} + 5 q^{49} - 18 q^{50} - 4 q^{51} - 11 q^{52} + 7 q^{53} - 8 q^{54} + q^{55} - 3 q^{56} + 12 q^{57} + 2 q^{58} - 4 q^{59} - 2 q^{60} + 24 q^{61} + 6 q^{62} + 8 q^{64} + 22 q^{65} + 6 q^{66} - 15 q^{67} - 8 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} - 4 q^{72} + q^{73} + 56 q^{74} - 36 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} + 2 q^{80} - 4 q^{81} - 32 q^{83} - 3 q^{84} - 13 q^{85} - 6 q^{86} + 4 q^{87} - 6 q^{88} - 50 q^{89} - 4 q^{90} - 8 q^{91} + 20 q^{92} + 12 q^{93} + q^{94} + 16 q^{95} + 4 q^{96} - q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 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 - 6 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 - 8 * q^17 - 4 * q^18 + 6 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 + 20 * q^23 + 4 * q^24 - 18 * q^25 - 11 * q^26 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 8 * q^32 + 6 * q^33 - 8 * q^34 - 18 * q^35 - 4 * q^36 + 56 * q^37 + 6 * q^38 - 10 * q^39 + 2 * q^40 - 3 * q^42 - 6 * q^43 - 6 * q^44 - 4 * q^45 + 20 * q^46 + q^47 + 4 * q^48 + 5 * q^49 - 18 * q^50 - 4 * q^51 - 11 * q^52 + 7 * q^53 - 8 * q^54 + q^55 - 3 * q^56 + 12 * q^57 + 2 * q^58 - 4 * q^59 - 2 * q^60 + 24 * q^61 + 6 * q^62 + 8 * q^64 + 22 * q^65 + 6 * q^66 - 15 * q^67 - 8 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 - 4 * q^72 + q^73 + 56 * q^74 - 36 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 + 2 * q^80 - 4 * q^81 - 32 * q^83 - 3 * q^84 - 13 * q^85 - 6 * q^86 + 4 * q^87 - 6 * q^88 - 50 * q^89 - 4 * q^90 - 8 * q^91 + 20 * q^92 + 12 * q^93 + q^94 + 16 * q^95 + 4 * q^96 - q^97 + 5 * q^98 + 12 * q^99

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