LMFDB - Embedded newform 273.2.k.c.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	273.211
Dual form			273.2.k.c.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.277479 + 0.480608i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.846011 - 1.46533i) q^{4} +1.35690 q^{5} +(0.277479 - 0.480608i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.277479 + 0.480608i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.846011 - 1.46533i) q^{4} +1.35690 q^{5} +(0.277479 - 0.480608i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.376510 + 0.652135i) q^{10} +(-0.568532 - 0.984726i) q^{11} -1.69202 q^{12} +(1.37047 - 3.33494i) q^{13} -0.554958 q^{14} +(-0.678448 - 1.17511i) q^{15} +(-1.12349 - 1.94594i) q^{16} +(0.277479 - 0.480608i) q^{17} -0.554958 q^{18} +(2.05496 - 3.55929i) q^{19} +(1.14795 - 1.98831i) q^{20} +1.00000 q^{21} +(0.315511 - 0.546482i) q^{22} +(3.39493 + 5.88019i) q^{23} +(-1.02446 - 1.77441i) q^{24} -3.15883 q^{25} +(1.98307 - 0.266717i) q^{26} +1.00000 q^{27} +(0.846011 + 1.46533i) q^{28} +(4.51842 + 7.82613i) q^{29} +(0.376510 - 0.652135i) q^{30} -8.63102 q^{31} +(2.67241 - 4.62874i) q^{32} +(-0.568532 + 0.984726i) q^{33} +0.307979 q^{34} +(-0.678448 + 1.17511i) q^{35} +(0.846011 + 1.46533i) q^{36} +(2.59030 + 4.48653i) q^{37} +2.28083 q^{38} +(-3.57338 + 0.480608i) q^{39} +2.78017 q^{40} +(-0.109916 - 0.190381i) q^{41} +(0.277479 + 0.480608i) q^{42} +(-1.94989 + 3.37730i) q^{43} -1.92394 q^{44} +(-0.678448 + 1.17511i) q^{45} +(-1.88404 + 3.26326i) q^{46} -8.13706 q^{47} +(-1.12349 + 1.94594i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.876510 - 1.51816i) q^{50} -0.554958 q^{51} +(-3.72737 - 4.82959i) q^{52} +7.98792 q^{53} +(0.277479 + 0.480608i) q^{54} +(-0.771438 - 1.33617i) q^{55} +(-1.02446 + 1.77441i) q^{56} -4.10992 q^{57} +(-2.50753 + 4.34317i) q^{58} +(-1.94989 + 3.37730i) q^{59} -2.29590 q^{60} +(-5.46077 + 9.45833i) q^{61} +(-2.39493 - 4.14814i) q^{62} +(-0.500000 - 0.866025i) q^{63} -1.52781 q^{64} +(1.85958 - 4.52516i) q^{65} -0.631023 q^{66} +(-0.381355 - 0.660525i) q^{67} +(-0.469501 - 0.813199i) q^{68} +(3.39493 - 5.88019i) q^{69} -0.753020 q^{70} +(-2.25182 + 3.90027i) q^{71} +(-1.02446 + 1.77441i) q^{72} +8.50365 q^{73} +(-1.43751 + 2.48984i) q^{74} +(1.57942 + 2.73563i) q^{75} +(-3.47703 - 6.02240i) q^{76} +1.13706 q^{77} +(-1.22252 - 1.58403i) q^{78} -3.74094 q^{79} +(-1.52446 - 2.64044i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.0609989 - 0.105653i) q^{82} -11.0586 q^{83} +(0.846011 - 1.46533i) q^{84} +(0.376510 - 0.652135i) q^{85} -2.16421 q^{86} +(4.51842 - 7.82613i) q^{87} +(-1.16487 - 2.01762i) q^{88} +(4.30194 + 7.45117i) q^{89} -0.753020 q^{90} +(2.20291 + 2.85433i) q^{91} +11.4886 q^{92} +(4.31551 + 7.47468i) q^{93} +(-2.25786 - 3.91074i) q^{94} +(2.78836 - 4.82959i) q^{95} -5.34481 q^{96} +(7.47434 - 12.9459i) q^{97} +(0.277479 - 0.480608i) q^{98} +1.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.277479	+	0.480608i	0.196207	+	0.339841i	0.947296	−	0.320361i	$-0.103804\pi$
$2$	0.277479	+	0.480608i	0.196207	+	0.339841i	−0.751088	+	0.660202i	$0.770471\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.846011	−	1.46533i	0.423005	−	0.732667i
$5$	1.35690			0.606822			0.303411	−	0.952860i	$-0.401874\pi$
$5$	1.35690			0.606822			0.303411	+	0.952860i	$0.401874\pi$
$6$	0.277479	−	0.480608i	0.113280	−	0.196207i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	2.04892			0.724402
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.376510	+	0.652135i	0.119063	+	0.206223i
$11$	−0.568532	−	0.984726i	−0.171419	−	0.296906i	0.767497	−	0.641052i	$-0.221502\pi$
$11$	−0.568532	−	0.984726i	−0.171419	−	0.296906i	−0.938916	+	0.344146i	$0.888168\pi$
$12$	−1.69202			−0.488445
$13$	1.37047	−	3.33494i	0.380100	−	0.924945i
$13$	1.37047	−	3.33494i	0.380100	−	0.924945i
$14$	−0.554958			−0.148319
$15$	−0.678448	−	1.17511i	−0.175175	−	0.303411i
$16$	−1.12349	−	1.94594i	−0.280872	−	0.486485i
$17$	0.277479	−	0.480608i	0.0672986	−	0.116565i	−0.830413	−	0.557149i	$-0.811895\pi$
$17$	0.277479	−	0.480608i	0.0672986	−	0.116565i	0.897711	+	0.440584i	$0.145229\pi$
$18$	−0.554958			−0.130805
$19$	2.05496	−	3.55929i	0.471440	−	0.816558i	−0.528026	−	0.849228i	$-0.677068\pi$
$19$	2.05496	−	3.55929i	0.471440	−	0.816558i	0.999466	+	0.0326704i	$0.0104011\pi$
$20$	1.14795	−	1.98831i	0.256689	−	0.444599i
$21$	1.00000			0.218218
$22$	0.315511	−	0.546482i	0.0672672	−	0.116510i
$23$	3.39493	+	5.88019i	0.707891	+	1.22610i	0.965638	+	0.259891i	$0.0836867\pi$
$23$	3.39493	+	5.88019i	0.707891	+	1.22610i	−0.257746	+	0.966213i	$0.582980\pi$
$24$	−1.02446	−	1.77441i	−0.209117	−	0.362201i
$25$	−3.15883			−0.631767
$26$	1.98307	−	0.266717i	0.388913	−	0.0523076i
$27$	1.00000			0.192450
$28$	0.846011	+	1.46533i	0.159881	+	0.276922i
$29$	4.51842	+	7.82613i	0.839049	+	1.45328i	0.890691	+	0.454610i	$0.150221\pi$
$29$	4.51842	+	7.82613i	0.839049	+	1.45328i	−0.0516414	+	0.998666i	$0.516445\pi$
$30$	0.376510	−	0.652135i	0.0687410	−	0.119063i
$31$	−8.63102			−1.55018			−0.775089	−	0.631852i	$-0.782295\pi$
$31$	−8.63102			−1.55018			−0.775089	+	0.631852i	$0.782295\pi$
$32$	2.67241	−	4.62874i	0.472419	−	0.818254i
$33$	−0.568532	+	0.984726i	−0.0989687	+	0.171419i
$34$	0.307979			0.0528179
$35$	−0.678448	+	1.17511i	−0.114679	+	0.198629i
$36$	0.846011	+	1.46533i	0.141002	+	0.244222i
$37$	2.59030	+	4.48653i	0.425843	+	0.737582i	0.996499	−	0.0836077i	$-0.0266442\pi$
$37$	2.59030	+	4.48653i	0.425843	+	0.737582i	−0.570656	+	0.821189i	$0.693311\pi$
$38$	2.28083			0.370000
$39$	−3.57338	+	0.480608i	−0.572198	+	0.0769588i
$40$	2.78017			0.439583
$41$	−0.109916	−	0.190381i	−0.0171660	−	0.0297324i	0.857315	−	0.514793i	$-0.172131\pi$
$41$	−0.109916	−	0.190381i	−0.0171660	−	0.0297324i	−0.874481	+	0.485060i	$0.838798\pi$
$42$	0.277479	+	0.480608i	0.0428159	+	0.0741594i
$43$	−1.94989	+	3.37730i	−0.297355	+	0.515034i	−0.975530	−	0.219867i	$-0.929438\pi$
$43$	−1.94989	+	3.37730i	−0.297355	+	0.515034i	0.678175	+	0.734900i	$0.262771\pi$
$44$	−1.92394			−0.290044
$45$	−0.678448	+	1.17511i	−0.101137	+	0.175175i
$46$	−1.88404	+	3.26326i	−0.277787	+	0.481141i
$47$	−8.13706			−1.18691			−0.593456	−	0.804866i	$-0.702237\pi$
$47$	−8.13706			−1.18691			−0.593456	+	0.804866i	$0.702237\pi$
$48$	−1.12349	+	1.94594i	−0.162162	+	0.280872i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.876510	−	1.51816i	−0.123957	−	0.214700i
$51$	−0.554958			−0.0777097
$52$	−3.72737	−	4.82959i	−0.516893	−	0.669743i
$53$	7.98792			1.09722			0.548612	−	0.836077i	$-0.315156\pi$
$53$	7.98792			1.09722			0.548612	+	0.836077i	$0.315156\pi$
$54$	0.277479	+	0.480608i	0.0377601	+	0.0654024i
$55$	−0.771438	−	1.33617i	−0.104021	−	0.180169i
$56$	−1.02446	+	1.77441i	−0.136899	+	0.237116i
$57$	−4.10992			−0.544372
$58$	−2.50753	+	4.34317i	−0.329255	+	0.570287i
$59$	−1.94989	+	3.37730i	−0.253854	+	0.439687i	−0.964583	−	0.263778i	$-0.915031\pi$
$59$	−1.94989	+	3.37730i	−0.253854	+	0.439687i	0.710730	+	0.703465i	$0.248365\pi$
$60$	−2.29590			−0.296399
$61$	−5.46077	+	9.45833i	−0.699180	+	1.21102i	0.269571	+	0.962981i	$0.413118\pi$
$61$	−5.46077	+	9.45833i	−0.699180	+	1.21102i	−0.968751	+	0.248035i	$0.920215\pi$
$62$	−2.39493	−	4.14814i	−0.304156	−	0.526814i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	−1.52781			−0.190976
$65$	1.85958	−	4.52516i	0.230653	−	0.561278i
$66$	−0.631023			−0.0776735
$67$	−0.381355	−	0.660525i	−0.0465899	−	0.0806960i	0.841790	−	0.539805i	$-0.181502\pi$
$67$	−0.381355	−	0.660525i	−0.0465899	−	0.0806960i	−0.888380	+	0.459109i	$0.848169\pi$
$68$	−0.469501	−	0.813199i	−0.0569353	−	0.0986148i
$69$	3.39493	−	5.88019i	0.408701	−	0.707891i
$70$	−0.753020			−0.0900032
$71$	−2.25182	+	3.90027i	−0.267242	+	0.462877i	−0.968149	−	0.250376i	$-0.919446\pi$
$71$	−2.25182	+	3.90027i	−0.267242	+	0.462877i	0.700906	+	0.713253i	$0.252779\pi$
$72$	−1.02446	+	1.77441i	−0.120734	+	0.209117i
$73$	8.50365			0.995277			0.497638	−	0.867385i	$-0.334201\pi$
$73$	8.50365			0.995277			0.497638	+	0.867385i	$0.334201\pi$
$74$	−1.43751	+	2.48984i	−0.167107	+	0.289438i
$75$	1.57942	+	2.73563i	0.182375	+	0.315883i
$76$	−3.47703	−	6.02240i	−0.398843	−	0.690816i
$77$	1.13706			0.129580
$78$	−1.22252	−	1.58403i	−0.138423	−	0.179357i
$79$	−3.74094			−0.420888			−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094			−0.420888			−0.210444	+	0.977606i	$0.567491\pi$
$80$	−1.52446	−	2.64044i	−0.170440	−	0.295210i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.0609989	−	0.105653i	0.00673620	−	0.0116674i
$83$	−11.0586			−1.21384			−0.606920	−	0.794763i	$-0.707595\pi$
$83$	−11.0586			−1.21384			−0.606920	+	0.794763i	$0.707595\pi$
$84$	0.846011	−	1.46533i	0.0923073	−	0.159881i
$85$	0.376510	−	0.652135i	0.0408383	−	0.0707339i
$86$	−2.16421			−0.233373
$87$	4.51842	−	7.82613i	0.484425	−	0.839049i
$88$	−1.16487	−	2.01762i	−0.124176	−	0.215079i
$89$	4.30194	+	7.45117i	0.456004	+	0.789823i	0.998745	−	0.0500773i	$-0.0159468\pi$
$89$	4.30194	+	7.45117i	0.456004	+	0.789823i	−0.542741	+	0.839900i	$0.682613\pi$
$90$	−0.753020			−0.0793753
$91$	2.20291	+	2.85433i	0.230927	+	0.299215i
$92$	11.4886			1.19777
$93$	4.31551	+	7.47468i	0.447498	+	0.775089i
$94$	−2.25786	−	3.91074i	−0.232881	−	0.403362i
$95$	2.78836	−	4.82959i	0.286080	−	0.495505i
$96$	−5.34481			−0.545503
$97$	7.47434	−	12.9459i	0.758905	−	1.31446i	−0.184505	−	0.982832i	$-0.559068\pi$
$97$	7.47434	−	12.9459i	0.758905	−	1.31446i	0.943410	−	0.331630i	$-0.107599\pi$
$98$	0.277479	−	0.480608i	0.0280296	−	0.0485487i
$99$	1.13706			0.114279
$100$	−2.67241	+	4.62874i	−0.267241	+	0.462874i
$101$	−2.12618	−	3.68265i	−0.211563	−	0.366437i	0.740641	−	0.671901i	$-0.234522\pi$
$101$	−2.12618	−	3.68265i	−0.211563	−	0.366437i	−0.952204	+	0.305464i	$0.901189\pi$
$102$	−0.153989	−	0.266717i	−0.0152472	−	0.0264089i
$103$	6.08575			0.599647			0.299824	−	0.953995i	$-0.403072\pi$
$103$	6.08575			0.599647			0.299824	+	0.953995i	$0.403072\pi$
$104$	2.80798	−	6.83301i	0.275345	−	0.670032i
$105$	1.35690			0.132419
$106$	2.21648	+	3.83906i	0.215284	+	0.372882i
$107$	6.42812	+	11.1338i	0.621429	+	1.07635i	0.989220	+	0.146439i	$0.0467811\pi$
$107$	6.42812	+	11.1338i	0.621429	+	1.07635i	−0.367790	+	0.929909i	$0.619886\pi$
$108$	0.846011	−	1.46533i	0.0814074	−	0.141002i
$109$	−6.84117			−0.655265			−0.327632	−	0.944805i	$-0.606251\pi$
$109$	−6.84117			−0.655265			−0.327632	+	0.944805i	$0.606251\pi$
$110$	0.428116	−	0.741519i	0.0408193	−	0.0707010i
$111$	2.59030	−	4.48653i	0.245861	−	0.425843i
$112$	2.24698			0.212320
$113$	−9.31551	+	16.1349i	−0.876330	+	1.51785i	−0.0209900	+	0.999780i	$0.506682\pi$
$113$	−9.31551	+	16.1349i	−0.876330	+	1.51785i	−0.855340	+	0.518068i	$0.826652\pi$
$114$	−1.14042	−	1.97526i	−0.106810	−	0.185000i
$115$	4.60656	+	7.97880i	0.429564	+	0.744027i
$116$	15.2905			1.41969
$117$	2.20291	+	2.85433i	0.203659	+	0.263883i
$118$	−2.16421			−0.199232
$119$	0.277479	+	0.480608i	0.0254365	+	0.0440572i
$120$	−1.39008	−	2.40770i	−0.126897	−	0.219792i
$121$	4.85354	−	8.40658i	0.441231	−	0.764235i
$122$	−6.06100			−0.548737
$123$	−0.109916	+	0.190381i	−0.00991082	+	0.0171660i
$124$	−7.30194	+	12.6473i	−0.655733	+	1.13576i
$125$	−11.0707			−0.990192
$126$	0.277479	−	0.480608i	0.0247198	−	0.0428159i
$127$	−2.30947	−	4.00012i	−0.204932	−	0.354953i	0.745179	−	0.666865i	$-0.232364\pi$
$127$	−2.30947	−	4.00012i	−0.204932	−	0.354953i	−0.950111	+	0.311911i	$0.899031\pi$
$128$	−5.76875	−	9.99177i	−0.509890	−	0.883156i
$129$	3.89977			0.343356
$130$	2.69083	−	0.361908i	0.236001	−	0.0317414i
$131$	−3.35690			−0.293293			−0.146647	−	0.989189i	$-0.546848\pi$
$131$	−3.35690			−0.293293			−0.146647	+	0.989189i	$0.546848\pi$
$132$	0.961968	+	1.66618i	0.0837285	+	0.145022i
$133$	2.05496	+	3.55929i	0.178187	+	0.308630i
$134$	0.211636	−	0.366564i	0.0182825	−	0.0316663i
$135$	1.35690			0.116783
$136$	0.568532	−	0.984726i	0.0487512	−	0.0844395i
$137$	10.7567	−	18.6311i	0.919004	−	1.59176i	0.118074	−	0.993005i	$-0.462328\pi$
$137$	10.7567	−	18.6311i	0.919004	−	1.59176i	0.800931	−	0.598757i	$-0.204339\pi$
$138$	3.76809			0.320761
$139$	4.04623	−	7.00827i	0.343197	−	0.594434i	−0.641828	−	0.766849i	$-0.721824\pi$
$139$	4.04623	−	7.00827i	0.343197	−	0.594434i	0.985024	+	0.172415i	$0.0551569\pi$
$140$	1.14795	+	1.98831i	0.0970194	+	0.168042i
$141$	4.06853	+	7.04690i	0.342632	+	0.593456i
$142$	−2.49934			−0.209740
$143$	−4.06315	+	0.546482i	−0.339778	+	0.0456991i
$144$	2.24698			0.187248
$145$	6.13102	+	10.6192i	0.509154	+	0.881880i
$146$	2.35958	+	4.08692i	0.195281	+	0.338236i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	8.76569			0.720536
$149$	−1.62953	+	2.82243i	−0.133496	+	0.231222i	−0.925022	−	0.379913i	$-0.875954\pi$
$149$	−1.62953	+	2.82243i	−0.133496	+	0.231222i	0.791526	+	0.611136i	$0.209287\pi$
$150$	−0.876510	+	1.51816i	−0.0715668	+	0.123957i
$151$	−6.81163			−0.554322			−0.277161	−	0.960823i	$-0.589394\pi$
$151$	−6.81163			−0.554322			−0.277161	+	0.960823i	$0.589394\pi$
$152$	4.21044	−	7.29269i	0.341512	−	0.591516i
$153$	0.277479	+	0.480608i	0.0224329	+	0.0388548i
$154$	0.315511	+	0.546482i	0.0254246	+	0.0440367i
$155$	−11.7114			−0.940682
$156$	−2.31886	+	5.64279i	−0.185658	+	0.451785i
$157$	24.4306			1.94977			0.974886	−	0.222705i	$-0.0714888\pi$
$157$	24.4306			1.94977			0.974886	+	0.222705i	$0.0714888\pi$
$158$	−1.03803	−	1.79792i	−0.0825814	−	0.143035i
$159$	−3.99396	−	6.91774i	−0.316742	−	0.548612i
$160$	3.62618	−	6.28072i	0.286675	−	0.496535i
$161$	−6.78986			−0.535116
$162$	0.277479	−	0.480608i	0.0218008	−	0.0377601i
$163$	5.77413	−	10.0011i	0.452265	−	0.783345i	−0.546262	−	0.837614i	$-0.683950\pi$
$163$	5.77413	−	10.0011i	0.452265	−	0.783345i	0.998526	+	0.0542694i	$0.0172830\pi$
$164$	−0.371961			−0.0290453
$165$	−0.771438	+	1.33617i	−0.0600564	+	0.104021i
$166$	−3.06853	−	5.31485i	−0.238164	−	0.412513i
$167$	−2.41185	−	4.17745i	−0.186635	−	0.323261i	0.757491	−	0.652845i	$-0.226425\pi$
$167$	−2.41185	−	4.17745i	−0.186635	−	0.323261i	−0.944126	+	0.329584i	$0.893091\pi$
$168$	2.04892			0.158077
$169$	−9.24363	−	9.14086i	−0.711048	−	0.703143i
$170$	0.417895			0.0320511
$171$	2.05496	+	3.55929i	0.157147	+	0.272186i
$172$	3.29925	+	5.71447i	0.251565	+	0.435724i
$173$	10.8128	−	18.7284i	0.822084	−	1.42389i	−0.0820441	−	0.996629i	$-0.526145\pi$
$173$	10.8128	−	18.7284i	0.822084	−	1.42389i	0.904128	−	0.427262i	$-0.140522\pi$
$174$	5.01507			0.380191
$175$	1.57942	−	2.73563i	0.119393	−	0.206794i
$176$	−1.27748	+	2.21266i	−0.0962936	+	0.166785i
$177$	3.89977			0.293125
$178$	−2.38740	+	4.13509i	−0.178943	+	0.309938i
$179$	−12.7044	−	22.0047i	−0.949571	−	1.64471i	−0.746329	−	0.665577i	$-0.768185\pi$
$179$	−12.7044	−	22.0047i	−0.949571	−	1.64471i	−0.203242	−	0.979128i	$-0.565148\pi$
$180$	1.14795	+	1.98831i	0.0855630	+	0.148200i
$181$	−7.67994			−0.570845			−0.285423	−	0.958402i	$-0.592134\pi$
$181$	−7.67994			−0.570845			−0.285423	+	0.958402i	$0.592134\pi$
$182$	−0.760553	+	1.85075i	−0.0563759	+	0.137187i
$183$	10.9215			0.807344
$184$	6.95593	+	12.0480i	0.512798	+	0.888192i
$185$	3.51477	+	6.08776i	0.258411	+	0.447581i
$186$	−2.39493	+	4.14814i	−0.175605	+	0.304156i
$187$	−0.631023			−0.0461449
$188$	−6.88404	+	11.9235i	−0.502070	+	0.869611i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	3.09485			0.224524
$191$	−4.75182	+	8.23040i	−0.343830	+	0.595531i	−0.985140	−	0.171751i	$-0.945058\pi$
$191$	−4.75182	+	8.23040i	−0.343830	+	0.595531i	0.641311	+	0.767281i	$0.278391\pi$
$192$	0.763906	+	1.32312i	0.0551301	+	0.0954882i
$193$	4.67576	+	8.09865i	0.336569	+	0.582954i	0.983785	−	0.179353i	$-0.0574003\pi$
$193$	4.67576	+	8.09865i	0.336569	+	0.582954i	−0.647216	+	0.762306i	$0.724067\pi$
$194$	8.29590			0.595611
$195$	−4.84870	+	0.652135i	−0.347223	+	0.0467003i
$196$	−1.69202			−0.120859
$197$	−8.75786	−	15.1691i	−0.623972	−	1.08075i	−0.988739	−	0.149652i	$-0.952185\pi$
$197$	−8.75786	−	15.1691i	−0.623972	−	1.08075i	0.364767	−	0.931099i	$-0.381149\pi$
$198$	0.315511	+	0.546482i	0.0224224	+	0.0388368i
$199$	8.79470	−	15.2329i	0.623440	−	1.07983i	−0.365401	−	0.930850i	$-0.619068\pi$
$199$	8.79470	−	15.2329i	0.623440	−	1.07983i	0.988840	−	0.148979i	$-0.0475987\pi$
$200$	−6.47219			−0.457653
$201$	−0.381355	+	0.660525i	−0.0268987	+	0.0465899i
$202$	1.17994	−	2.04372i	0.0830203	−	0.143795i
$203$	−9.03684			−0.634262
$204$	−0.469501	+	0.813199i	−0.0328716	+	0.0569353i
$205$	−0.149145	−	0.258327i	−0.0104167	−	0.0180423i
$206$	1.68867	+	2.92486i	0.117655	+	0.203785i
$207$	−6.78986			−0.471928
$208$	−8.02930	+	1.07992i	−0.556732	+	0.0748787i
$209$	−4.67324			−0.323254
$210$	0.376510	+	0.652135i	0.0259817	+	0.0450016i
$211$	−0.681136	−	1.17976i	−0.0468914	−	0.0812182i	0.841627	−	0.540059i	$-0.181598\pi$
$211$	−0.681136	−	1.17976i	−0.0468914	−	0.0812182i	−0.888518	+	0.458841i	$0.848265\pi$
$212$	6.75786	−	11.7050i	0.464132	−	0.803900i
$213$	4.50365			0.308585
$214$	−3.56734	+	6.17881i	−0.243858	+	0.422374i
$215$	−2.64579	+	4.58265i	−0.180442	+	0.312534i
$216$	2.04892			0.139411
$217$	4.31551	−	7.47468i	0.292956	−	0.507415i
$218$	−1.89828	−	3.28792i	−0.128568	−	0.222686i
$219$	−4.25182	−	7.36438i	−0.287312	−	0.497638i
$220$	−2.61058			−0.176005
$221$	−1.22252	−	1.58403i	−0.0822357	−	0.106554i
$222$	2.87502			0.192959
$223$	5.14310	+	8.90812i	0.344408	+	0.596532i	0.985246	−	0.171144i	$-0.0547464\pi$
$223$	5.14310	+	8.90812i	0.344408	+	0.596532i	−0.640838	+	0.767676i	$0.721413\pi$
$224$	2.67241	+	4.62874i	0.178558	+	0.309271i
$225$	1.57942	−	2.73563i	0.105294	−	0.182375i
$226$	−10.3394			−0.687769
$227$	−2.80409	+	4.85683i	−0.186114	+	0.322359i	−0.943951	−	0.330084i	$-0.892923\pi$
$227$	−2.80409	+	4.85683i	−0.186114	+	0.322359i	0.757837	+	0.652444i	$0.226256\pi$
$228$	−3.47703	+	6.02240i	−0.230272	+	0.398843i
$229$	−1.88040			−0.124260			−0.0621300	−	0.998068i	$-0.519789\pi$
$229$	−1.88040			−0.124260			−0.0621300	+	0.998068i	$0.519789\pi$
$230$	−2.55645	+	4.42790i	−0.168567	+	0.291967i
$231$	−0.568532	−	0.984726i	−0.0374066	−	0.0647902i
$232$	9.25786	+	16.0351i	0.607809	+	1.05276i
$233$	−6.38404			−0.418233			−0.209116	−	0.977891i	$-0.567059\pi$
$233$	−6.38404			−0.418233			−0.209116	+	0.977891i	$0.567059\pi$
$234$	−0.760553	+	1.85075i	−0.0497189	+	0.120987i
$235$	−11.0411			−0.720245
$236$	3.29925	+	5.71447i	0.214763	+	0.371980i
$237$	1.87047	+	3.23975i	0.121500	+	0.210444i
$238$	−0.153989	+	0.266717i	−0.00998164	+	0.0172887i
$239$	1.90217			0.123041			0.0615204	−	0.998106i	$-0.480405\pi$
$239$	1.90217			0.123041			0.0615204	+	0.998106i	$0.480405\pi$
$240$	−1.52446	+	2.64044i	−0.0984034	+	0.170440i
$241$	−6.60603	+	11.4420i	−0.425532	+	0.737043i	−0.996470	−	0.0839503i	$-0.973246\pi$
$241$	−6.60603	+	11.4420i	−0.425532	+	0.737043i	0.570938	+	0.820993i	$0.306580\pi$
$242$	5.38703			0.346291
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	9.23974	+	16.0037i	0.591514	+	1.02453i
$245$	−0.678448	−	1.17511i	−0.0433444	−	0.0750748i
$246$	−0.121998			−0.00777830
$247$	−9.05376	−	11.7311i	−0.576077	−	0.746429i
$248$	−17.6843			−1.12295
$249$	5.52930	+	9.57703i	0.350405	+	0.606920i
$250$	−3.07188	−	5.32066i	−0.194283	−	0.336508i
$251$	−3.77024	+	6.53025i	−0.237976	+	0.412186i	−0.960133	−	0.279543i	$-0.909817\pi$
$251$	−3.77024	+	6.53025i	−0.237976	+	0.412186i	0.722158	+	0.691728i	$0.243150\pi$
$252$	−1.69202			−0.106587
$253$	3.86025	−	6.68615i	0.242692	−	0.420354i
$254$	1.28166	−	2.21990i	0.0804185	−	0.139289i
$255$	−0.753020			−0.0471560
$256$	1.67360	−	2.89877i	0.104600	−	0.181173i
$257$	−6.70895	−	11.6202i	−0.418493	−	0.724851i	0.577295	−	0.816535i	$-0.304108\pi$
$257$	−6.70895	−	11.6202i	−0.418493	−	0.724851i	−0.995788	+	0.0916848i	$0.970775\pi$
$258$	1.08211	+	1.87426i	0.0673689	+	0.116686i
$259$	−5.18060			−0.321907
$260$	−5.05765	−	6.55325i	−0.313662	−	0.406415i
$261$	−9.03684			−0.559366
$262$	−0.931468	−	1.61335i	−0.0575463	−	0.0996731i
$263$	5.59903	+	9.69781i	0.345251	+	0.597992i	0.985399	−	0.170259i	$-0.0544604\pi$
$263$	5.59903	+	9.69781i	0.345251	+	0.597992i	−0.640148	+	0.768251i	$0.721127\pi$
$264$	−1.16487	+	2.01762i	−0.0716931	+	0.124176i
$265$	10.8388			0.665821
$266$	−1.14042	+	1.97526i	−0.0699234	+	0.121111i
$267$	4.30194	−	7.45117i	0.263274	−	0.456004i
$268$	−1.29052			−0.0788311
$269$	−6.95862	+	12.0527i	−0.424274	+	0.734865i	−0.996352	−	0.0853346i	$-0.972804\pi$
$269$	−6.95862	+	12.0527i	−0.424274	+	0.734865i	0.572078	+	0.820199i	$0.306137\pi$
$270$	0.376510	+	0.652135i	0.0229137	+	0.0396877i
$271$	−0.991271	−	1.71693i	−0.0602154	−	0.104296i	0.834346	−	0.551241i	$-0.185845\pi$
$271$	−0.991271	−	1.71693i	−0.0602154	−	0.104296i	−0.894562	+	0.446945i	$0.852512\pi$
$272$	−1.24698			−0.0756092
$273$	1.37047	−	3.33494i	0.0829446	−	0.201840i
$274$	11.9390			0.721261
$275$	1.79590	+	3.11058i	0.108297	+	0.187575i
$276$	−5.74429	−	9.94940i	−0.345766	−	0.598884i
$277$	−4.89977	+	8.48665i	−0.294399	+	0.509914i	−0.974845	−	0.222884i	$-0.928453\pi$
$277$	−4.89977	+	8.48665i	−0.294399	+	0.509914i	0.680446	+	0.732798i	$0.261786\pi$
$278$	4.49098			0.269351
$279$	4.31551	−	7.47468i	0.258363	−	0.447498i
$280$	−1.39008	+	2.40770i	−0.0830734	+	0.143887i
$281$	−25.7603			−1.53673			−0.768366	−	0.640011i	$-0.778930\pi$
$281$	−25.7603			−1.53673			−0.768366	+	0.640011i	$0.778930\pi$
$282$	−2.25786	+	3.91074i	−0.134454	+	0.232881i
$283$	0.0244587	+	0.0423637i	0.00145392	+	0.00251826i	0.866751	−	0.498740i	$-0.166204\pi$
$283$	0.0244587	+	0.0423637i	0.00145392	+	0.00251826i	−0.865298	+	0.501259i	$0.832871\pi$
$284$	3.81013	+	6.59935i	0.226090	+	0.391599i
$285$	−5.57673			−0.330337
$286$	−1.39008	−	1.80115i	−0.0821974	−	0.106504i
$287$	0.219833			0.0129763
$288$	2.67241	+	4.62874i	0.157473	+	0.272751i
$289$	8.34601	+	14.4557i	0.490942	+	0.850336i
$290$	−3.40246	+	5.89324i	−0.199799	+	0.346063i
$291$	−14.9487			−0.876308
$292$	7.19418	−	12.4607i	0.421007	−	0.729206i
$293$	−10.6610	+	18.4654i	−0.622822	+	1.07876i	0.366136	+	0.930561i	$0.380680\pi$
$293$	−10.6610	+	18.4654i	−0.622822	+	1.07876i	−0.988958	+	0.148197i	$0.952653\pi$
$294$	−0.554958			−0.0323658
$295$	−2.64579	+	4.58265i	−0.154044	+	0.266812i
$296$	5.30731	+	9.19254i	0.308481	+	0.534305i
$297$	−0.568532	−	0.984726i	−0.0329896	−	0.0571396i
$298$	−1.80864			−0.104772
$299$	24.2627	−	3.26326i	1.40315	−	0.188719i
$300$	5.34481			0.308583
$301$	−1.94989	−	3.37730i	−0.112390	−	0.194664i
$302$	−1.89008	−	3.27372i	−0.108762	−	0.188381i
$303$	−2.12618	+	3.68265i	−0.122146	+	0.211563i
$304$	−9.23490			−0.529658
$305$	−7.40970	+	12.8340i	−0.424278	+	0.734871i
$306$	−0.153989	+	0.266717i	−0.00880298	+	0.0152472i
$307$	−23.6528			−1.34994			−0.674968	−	0.737847i	$-0.735843\pi$
$307$	−23.6528			−1.34994			−0.674968	+	0.737847i	$0.735843\pi$
$308$	0.961968	−	1.66618i	0.0548132	−	0.0949393i
$309$	−3.04288	−	5.27042i	−0.173103	−	0.299824i
$310$	−3.24967	−	5.62859i	−0.184569	−	0.319682i
$311$	16.5851			0.940454			0.470227	−	0.882545i	$-0.344172\pi$
$311$	16.5851			0.940454			0.470227	+	0.882545i	$0.344172\pi$
$312$	−7.32155	+	0.984726i	−0.414501	+	0.0557491i
$313$	−6.90648			−0.390377			−0.195189	−	0.980766i	$-0.562532\pi$
$313$	−6.90648			−0.390377			−0.195189	+	0.980766i	$0.562532\pi$
$314$	6.77897	+	11.7415i	0.382559	+	0.662612i
$315$	−0.678448	−	1.17511i	−0.0382262	−	0.0662097i
$316$	−3.16487	+	5.48172i	−0.178038	+	0.308371i
$317$	26.0562			1.46346			0.731731	−	0.681593i	$-0.238713\pi$
$317$	26.0562			1.46346			0.731731	+	0.681593i	$0.238713\pi$
$318$	2.21648	−	3.83906i	0.124294	−	0.215284i
$319$	5.13773	−	8.89880i	0.287658	−	0.498237i
$320$	−2.07308			−0.115889
$321$	6.42812	−	11.1338i	0.358782	−	0.621429i
$322$	−1.88404	−	3.26326i	−0.104994	−	0.181854i
$323$	−1.14042	−	1.97526i	−0.0634544	−	0.109906i
$324$	−1.69202			−0.0940012
$325$	−4.32908	+	10.5345i	−0.240134	+	0.584350i
$326$	6.40880			0.354950
$327$	3.42058	+	5.92462i	0.189159	+	0.327632i
$328$	−0.225209	−	0.390074i	−0.0124351	−	0.0215382i
$329$	4.06853	−	7.04690i	0.224305	−	0.388508i
$330$	−0.856232			−0.0471340
$331$	1.75033	−	3.03166i	0.0962069	−	0.166635i	−0.813905	−	0.580998i	$-0.802662\pi$
$331$	1.75033	−	3.03166i	0.0962069	−	0.166635i	0.910112	+	0.414363i	$0.135996\pi$
$332$	−9.35570	+	16.2045i	−0.513461	+	0.889340i
$333$	−5.18060			−0.283895
$334$	1.33848	−	2.31831i	0.0732383	−	0.126852i
$335$	−0.517458	−	0.896264i	−0.0282718	−	0.0489681i
$336$	−1.12349	−	1.94594i	−0.0612914	−	0.106160i
$337$	−4.14782			−0.225946			−0.112973	−	0.993598i	$-0.536037\pi$
$337$	−4.14782			−0.225946			−0.112973	+	0.993598i	$0.536037\pi$
$338$	1.82826	−	6.97896i	0.0994441	−	0.379605i
$339$	18.6310			1.01190
$340$	−0.637063	−	1.10343i	−0.0345496	−	0.0598417i
$341$	4.90701	+	8.49919i	0.265729	+	0.460257i
$342$	−1.14042	+	1.97526i	−0.0616666	+	0.106810i
$343$	1.00000			0.0539949
$344$	−3.99516	+	6.91981i	−0.215404	+	0.373091i
$345$	4.60656	−	7.97880i	0.248009	−	0.429564i
$346$	12.0013			0.645195
$347$	5.78717	−	10.0237i	0.310671	−	0.538099i	−0.667836	−	0.744308i	$-0.732779\pi$
$347$	5.78717	−	10.0237i	0.310671	−	0.538099i	0.978508	+	0.206209i	$0.0661128\pi$
$348$	−7.64526	−	13.2420i	−0.409829	−	0.709845i
$349$	6.50634	+	11.2693i	0.348276	+	0.603232i	0.985943	−	0.167080i	$-0.0534338\pi$
$349$	6.50634	+	11.2693i	0.348276	+	0.603232i	−0.637667	+	0.770312i	$0.720100\pi$
$350$	1.75302			0.0937029
$351$	1.37047	−	3.33494i	0.0731502	−	0.178006i
$352$	−6.07739			−0.323926
$353$	−13.0957	−	22.6824i	−0.697013	−	1.20726i	−0.969497	−	0.245101i	$-0.921179\pi$
$353$	−13.0957	−	22.6824i	−0.697013	−	1.20726i	0.272485	−	0.962160i	$-0.412155\pi$
$354$	1.08211	+	1.87426i	0.0575132	+	0.0996159i
$355$	−3.05549	+	5.29226i	−0.162169	+	0.280884i
$356$	14.5579			0.771569
$357$	0.277479	−	0.480608i	0.0146857	−	0.0254365i
$358$	7.05041	−	12.2117i	0.372626	−	0.645407i
$359$	11.0750			0.584516			0.292258	−	0.956339i	$-0.405593\pi$
$359$	11.0750			0.584516			0.292258	+	0.956339i	$0.405593\pi$
$360$	−1.39008	+	2.40770i	−0.0732638	+	0.126897i
$361$	1.05429	+	1.82609i	0.0554892	+	0.0961101i
$362$	−2.13102	−	3.69104i	−0.112004	−	0.193997i
$363$	−9.70709			−0.509490
$364$	6.04623	−	0.813199i	0.316909	−	0.0426232i
$365$	11.5386			0.603956
$366$	3.03050	+	5.24898i	0.158407	+	0.274369i
$367$	6.68545	+	11.5795i	0.348978	+	0.604447i	0.986068	−	0.166342i	$-0.0531956\pi$
$367$	6.68545	+	11.5795i	0.348978	+	0.604447i	−0.637091	+	0.770789i	$0.719862\pi$
$368$	7.62833	−	13.2127i	0.397654	−	0.688758i
$369$	0.219833			0.0114440
$370$	−1.95055	+	3.37845i	−0.101404	+	0.175637i
$371$	−3.99396	+	6.91774i	−0.207356	+	0.359151i
$372$	14.6039			0.757176
$373$	18.3654	−	31.8098i	0.950924	−	1.64705i	0.207492	−	0.978237i	$-0.433470\pi$
$373$	18.3654	−	31.8098i	0.950924	−	1.64705i	0.743432	−	0.668811i	$-0.233197\pi$
$374$	−0.175096	−	0.303274i	−0.00905398	−	0.0156819i
$375$	5.53534	+	9.58750i	0.285844	+	0.495096i
$376$	−16.6722			−0.859802
$377$	32.2920	−	4.34317i	1.66312	−	0.223685i
$378$	−0.554958			−0.0285440
$379$	−16.6407	−	28.8226i	−0.854776	−	1.48052i	−0.876853	−	0.480759i	$-0.840361\pi$
$379$	−16.6407	−	28.8226i	−0.854776	−	1.48052i	0.0220768	−	0.999756i	$-0.492972\pi$
$380$	−4.71797	−	8.17177i	−0.242027	−	0.419203i
$381$	−2.30947	+	4.00012i	−0.118318	+	0.204932i
$382$	−5.27413			−0.269848
$383$	8.81163	−	15.2622i	0.450253	−	0.779861i	−0.548148	−	0.836381i	$-0.684667\pi$
$383$	8.81163	−	15.2622i	0.450253	−	0.779861i	0.998401	+	0.0565199i	$0.0180004\pi$
$384$	−5.76875	+	9.99177i	−0.294385	+	0.509890i
$385$	1.54288			0.0786323
$386$	−2.59485	+	4.49441i	−0.132074	+	0.228760i
$387$	−1.94989	−	3.37730i	−0.0991183	−	0.171678i
$388$	−12.6468	−	21.9048i	−0.642042	−	1.11205i
$389$	29.6340			1.50250			0.751252	−	0.660016i	$-0.229450\pi$
$389$	29.6340			1.50250			0.751252	+	0.660016i	$0.229450\pi$
$390$	−1.65883	−	2.14937i	−0.0839983	−	0.108838i
$391$	3.76809			0.190560
$392$	−1.02446	−	1.77441i	−0.0517430	−	0.0896215i
$393$	1.67845	+	2.90716i	0.0846665	+	0.146647i
$394$	4.86025	−	8.41820i	0.244856	−	0.424103i
$395$	−5.07606			−0.255405
$396$	0.961968	−	1.66618i	0.0483407	−	0.0837285i
$397$	−9.59999	+	16.6277i	−0.481810	+	0.834519i	−0.999782	−	0.0208785i	$-0.993354\pi$
$397$	−9.59999	+	16.6277i	−0.481810	+	0.834519i	0.517972	+	0.855397i	$0.326687\pi$
$398$	9.76138			0.489294
$399$	2.05496	−	3.55929i	0.102877	−	0.178187i
$400$	3.54892	+	6.14691i	0.177446	+	0.307345i
$401$	−6.24967	−	10.8247i	−0.312094	−	0.540562i	0.666722	−	0.745307i	$-0.267697\pi$
$401$	−6.24967	−	10.8247i	−0.312094	−	0.540562i	−0.978815	+	0.204745i	$0.934364\pi$
$402$	−0.423272			−0.0211109
$403$	−11.8286	+	28.7839i	−0.589222	+	1.43383i
$404$	−7.19508			−0.357969
$405$	−0.678448	−	1.17511i	−0.0337123	−	0.0583915i
$406$	−2.50753	−	4.34317i	−0.124447	−	0.215548i
$407$	2.94534	−	5.10147i	0.145995	−	0.252871i
$408$	−1.13706			−0.0562930
$409$	8.39104	−	14.5337i	0.414910	−	0.718646i	−0.580509	−	0.814254i	$-0.697146\pi$
$409$	8.39104	−	14.5337i	0.414910	−	0.718646i	0.995419	+	0.0956082i	$0.0304796\pi$
$410$	0.0827692	−	0.143360i	0.00408768	−	0.00708007i
$411$	−21.5133			−1.06117
$412$	5.14861	−	8.91766i	0.253654	−	0.439341i
$413$	−1.94989	−	3.37730i	−0.0959476	−	0.166186i
$414$	−1.88404	−	3.26326i	−0.0925957	−	0.160380i
$415$	−15.0054			−0.736585
$416$	−11.7741	−	15.2559i	−0.577274	−	0.747980i
$417$	−8.09246			−0.396289
$418$	−1.29672	−	2.24599i	−0.0634249	−	0.109855i
$419$	7.18210	+	12.4398i	0.350868	+	0.607722i	0.986402	−	0.164352i	$-0.0525531\pi$
$419$	7.18210	+	12.4398i	0.350868	+	0.607722i	−0.635533	+	0.772073i	$0.719220\pi$
$420$	1.14795	−	1.98831i	0.0560141	−	0.0970194i
$421$	−22.5526			−1.09914			−0.549572	−	0.835446i	$-0.685209\pi$
$421$	−22.5526			−1.09914			−0.549572	+	0.835446i	$0.685209\pi$
$422$	0.378002	−	0.654719i	0.0184009	−	0.0318712i
$423$	4.06853	−	7.04690i	0.197819	−	0.342632i
$424$	16.3666			0.794832
$425$	−0.876510	+	1.51816i	−0.0425170	+	0.0736416i
$426$	1.24967	+	2.16449i	0.0605466	+	0.104870i
$427$	−5.46077	−	9.45833i	−0.264265	−	0.457721i
$428$	21.7530			1.05147
$429$	2.50484	+	3.24555i	0.120935	+	0.156697i
$430$	−2.93661			−0.141616
$431$	−2.24482	−	3.88815i	−0.108129	−	0.187286i	0.806883	−	0.590711i	$-0.201153\pi$
$431$	−2.24482	−	3.88815i	−0.108129	−	0.187286i	−0.915012	+	0.403426i	$0.867819\pi$
$432$	−1.12349	−	1.94594i	−0.0540539	−	0.0936242i
$433$	−9.68060	+	16.7673i	−0.465220	+	0.805785i	−0.999211	−	0.0397051i	$-0.987358\pi$
$433$	−9.68060	+	16.7673i	−0.465220	+	0.805785i	0.533991	+	0.845490i	$0.320691\pi$
$434$	4.78986			0.229920
$435$	6.13102	−	10.6192i	0.293960	−	0.509154i
$436$	−5.78770	+	10.0246i	−0.277181	+	0.480091i
$437$	27.9057			1.33491
$438$	2.35958	−	4.08692i	0.112745	−	0.195281i
$439$	−13.6434	−	23.6311i	−0.651164	−	1.12785i	−0.982841	−	0.184456i	$-0.940948\pi$
$439$	−13.6434	−	23.6311i	−0.651164	−	1.12785i	0.331677	−	0.943393i	$-0.392386\pi$
$440$	−1.58061	−	2.73770i	−0.0753528	−	0.130515i
$441$	1.00000			0.0476190
$442$	0.422075	−	1.02709i	0.0200761	−	0.0488537i
$443$	−16.2319			−0.771202			−0.385601	−	0.922666i	$-0.626006\pi$
$443$	−16.2319			−0.771202			−0.385601	+	0.922666i	$0.626006\pi$
$444$	−4.38285	−	7.59131i	−0.208001	−	0.360268i
$445$	5.83728	+	10.1105i	0.276714	+	0.479282i
$446$	−2.85421	+	4.94363i	−0.135151	+	0.234088i
$447$	3.25906			0.154148
$448$	0.763906	−	1.32312i	0.0360911	−	0.0625117i
$449$	12.1235	−	20.9985i	0.572143	−	0.990980i	−0.424203	−	0.905567i	$-0.639446\pi$
$449$	12.1235	−	20.9985i	0.572143	−	0.990980i	0.996346	−	0.0854133i	$-0.0272211\pi$
$450$	1.75302			0.0826382
$451$	−0.124982	+	0.216475i	−0.00588516	+	0.0101934i
$452$	15.7620	+	27.3007i	0.741384	+	1.28412i
$453$	3.40581	+	5.89904i	0.160019	+	0.277161i
$454$	−3.11231			−0.146068
$455$	2.98911	+	3.87303i	0.140132	+	0.181570i
$456$	−8.42088			−0.394344
$457$	15.7451	+	27.2713i	0.736526	+	1.27570i	0.954051	+	0.299645i	$0.0968683\pi$
$457$	15.7451	+	27.2713i	0.736526	+	1.27570i	−0.217525	+	0.976055i	$0.569798\pi$
$458$	−0.521770	−	0.903733i	−0.0243807	−	0.0422287i
$459$	0.277479	−	0.480608i	0.0129516	−	0.0224329i
$460$	15.5888			0.726832
$461$	−20.4284	+	35.3830i	−0.951446	+	1.64795i	−0.209147	+	0.977884i	$0.567069\pi$
$461$	−20.4284	+	35.3830i	−0.951446	+	1.64795i	−0.742299	+	0.670068i	$0.766265\pi$
$462$	0.315511	−	0.546482i	0.0146789	−	0.0254246i
$463$	39.0941			1.81686			0.908429	−	0.418040i	$-0.137283\pi$
$463$	39.0941			1.81686			0.908429	+	0.418040i	$0.137283\pi$
$464$	10.1528	−	17.5852i	0.471332	−	0.816370i
$465$	5.85570	+	10.1424i	0.271552	+	0.470341i
$466$	−1.77144	−	3.06822i	−0.0820603	−	0.142133i
$467$	9.39804			0.434890			0.217445	−	0.976073i	$-0.430228\pi$
$467$	9.39804			0.434890			0.217445	+	0.976073i	$0.430228\pi$
$468$	6.04623	−	0.813199i	0.279487	−	0.0375901i
$469$	0.762709			0.0352186
$470$	−3.06369	−	5.30646i	−0.141317	−	0.244769i
$471$	−12.2153	−	21.1575i	−0.562851	−	0.974886i
$472$	−3.99516	+	6.91981i	−0.183892	+	0.318510i
$473$	4.43429			0.203889
$474$	−1.03803	+	1.79792i	−0.0476784	+	0.0825814i
$475$	−6.49127	+	11.2432i	−0.297840	+	0.515874i
$476$	0.939001			0.0430390
$477$	−3.99396	+	6.91774i	−0.182871	+	0.316742i
$478$	0.527811	+	0.914196i	0.0241415	+	0.0418143i
$479$	1.01693	+	1.76137i	0.0464645	+	0.0804789i	0.888322	−	0.459221i	$-0.151871\pi$
$479$	1.01693	+	1.76137i	0.0464645	+	0.0804789i	−0.841858	+	0.539699i	$0.818538\pi$
$480$	−7.25236			−0.331023
$481$	18.5122	−	2.48984i	0.844086	−	0.113527i
$482$	−7.33214			−0.333970
$483$	3.39493	+	5.88019i	0.154475	+	0.267558i
$484$	−8.21230	−	14.2241i	−0.373286	−	0.646551i
$485$	10.1419	−	17.5663i	0.460520	−	0.797645i
$486$	−0.554958			−0.0251734
$487$	15.1441	−	26.2303i	0.686243	−	1.18861i	−0.286801	−	0.957990i	$-0.592592\pi$
$487$	15.1441	−	26.2303i	0.686243	−	1.18861i	0.973044	−	0.230618i	$-0.0740747\pi$
$488$	−11.1887	+	19.3793i	−0.506487	+	0.877262i
$489$	−11.5483			−0.522230
$490$	0.376510	−	0.652135i	0.0170090	−	0.0294604i
$491$	14.5945	+	25.2784i	0.658640	+	1.14080i	0.980968	+	0.194170i	$0.0622012\pi$
$491$	14.5945	+	25.2784i	0.658640	+	1.14080i	−0.322328	+	0.946628i	$0.604465\pi$
$492$	0.185981	+	0.322128i	0.00838466	+	0.0145227i
$493$	5.01507			0.225867
$494$	3.12581	−	7.60643i	0.140637	−	0.342230i
$495$	1.54288			0.0693471
$496$	9.69687	+	16.7955i	0.435402	+	0.754139i
$497$	−2.25182	−	3.90027i	−0.101008	−	0.174951i
$498$	−3.06853	+	5.31485i	−0.137504	+	0.238164i
$499$	1.24937			0.0559296			0.0279648	−	0.999609i	$-0.491097\pi$
$499$	1.24937			0.0559296			0.0279648	+	0.999609i	$0.491097\pi$
$500$	−9.36592	+	16.2223i	−0.418857	+	0.725481i
$501$	−2.41185	+	4.17745i	−0.107754	+	0.186635i
$502$	−4.18465			−0.186770
$503$	−10.5097	+	18.2033i	−0.468604	+	0.811646i	−0.999356	−	0.0358814i	$-0.988576\pi$
$503$	−10.5097	+	18.2033i	−0.468604	+	0.811646i	0.530752	+	0.847527i	$0.321909\pi$
$504$	−1.02446	−	1.77441i	−0.0456330	−	0.0790387i
$505$	−2.88500	−	4.99697i	−0.128381	−	0.222362i
$506$	4.28455			0.190472
$507$	−3.29440	+	12.5756i	−0.146310	+	0.558504i
$508$	−7.81535			−0.346750
$509$	−11.8388	−	20.5054i	−0.524744	−	0.908884i	−0.999585	−	0.0288121i	$-0.990828\pi$
$509$	−11.8388	−	20.5054i	−0.524744	−	0.908884i	0.474840	−	0.880072i	$-0.342506\pi$
$510$	−0.208947	−	0.361908i	−0.00925235	−	0.0160255i
$511$	−4.25182	+	7.36438i	−0.188090	+	0.325781i
$512$	−21.2174			−0.937687
$513$	2.05496	−	3.55929i	0.0907286	−	0.157147i
$514$	3.72318	−	6.44875i	0.164223	−	0.284442i
$515$	8.25773			0.363879
$516$	3.29925	−	5.71447i	0.145241	−	0.251565i
$517$	4.62618	+	8.01278i	0.203459	+	0.352401i
$518$	−1.43751	−	2.48984i	−0.0631605	−	0.109397i
$519$	−21.6256			−0.949260
$520$	3.81013	−	9.27169i	0.167085	−	0.406590i
$521$	2.47783			0.108556			0.0542778	−	0.998526i	$-0.482714\pi$
$521$	2.47783			0.108556			0.0542778	+	0.998526i	$0.482714\pi$
$522$	−2.50753	−	4.34317i	−0.109752	−	0.190096i
$523$	−3.55280	−	6.15363i	−0.155353	−	0.269080i	0.777834	−	0.628469i	$-0.216318\pi$
$523$	−3.55280	−	6.15363i	−0.155353	−	0.269080i	−0.933188	+	0.359390i	$0.882985\pi$
$524$	−2.83997	+	4.91897i	−0.124065	+	0.214886i
$525$	−3.15883			−0.137863
$526$	−3.10723	+	5.38188i	−0.135482	+	0.234661i
$527$	−2.39493	+	4.14814i	−0.104325	+	0.180696i
$528$	2.55496			0.111190
$529$	−11.5511	+	20.0070i	−0.502221	+	0.869872i
$530$	3.00753	+	5.20920i	0.130639	+	0.226273i
$531$	−1.94989	−	3.37730i	−0.0846179	−	0.146562i
$532$	6.95407			0.301497
$533$	−0.785544	+	0.105653i	−0.0340257	+	0.00457635i
$534$	4.77479			0.206625
$535$	8.72228	+	15.1074i	0.377097	+	0.653152i
$536$	−0.781364	−	1.35336i	−0.0337498	−	0.0584563i
$537$	−12.7044	+	22.0047i	−0.548235	+	0.949571i
$538$	−7.72348			−0.332983
$539$	−0.568532	+	0.984726i	−0.0244884	+	0.0424151i
$540$	1.14795	−	1.98831i	0.0493998	−	0.0855630i
$541$	−35.7157			−1.53554			−0.767769	−	0.640727i	$-0.778633\pi$
$541$	−35.7157			−1.53554			−0.767769	+	0.640727i	$0.778633\pi$
$542$	0.550114	−	0.952825i	0.0236294	−	0.0409273i
$543$	3.83997	+	6.65102i	0.164789	+	0.285423i
$544$	−1.48307	−	2.56876i	−0.0635863	−	0.110135i
$545$	−9.28275			−0.397629
$546$	1.98307	−	0.266717i	0.0848677	−	0.0114144i
$547$	10.1395			0.433532			0.216766	−	0.976224i	$-0.430449\pi$
$547$	10.1395			0.433532			0.216766	+	0.976224i	$0.430449\pi$
$548$	−18.2005	−	31.5242i	−0.777487	−	1.34665i
$549$	−5.46077	−	9.45833i	−0.233060	−	0.403672i
$550$	−0.996648	+	1.72624i	−0.0424972	+	0.0736073i
$551$	37.1406			1.58224
$552$	6.95593	−	12.0480i	0.296064	−	0.512798i
$553$	1.87047	−	3.23975i	0.0795404	−	0.137768i
$554$	−5.43834			−0.231053
$555$	3.51477	−	6.08776i	0.149194	−	0.258411i
$556$	−6.84631	−	11.8582i	−0.290348	−	0.502898i
$557$	−1.81671	−	3.14663i	−0.0769764	−	0.133327i	0.824968	−	0.565180i	$-0.191193\pi$
$557$	−1.81671	−	3.14663i	−0.0769764	−	0.133327i	−0.901944	+	0.431853i	$0.857860\pi$
$558$	4.78986			0.202771
$559$	8.59083	+	11.1312i	0.363354	+	0.470801i
$560$	3.04892			0.128840
$561$	0.315511	+	0.546482i	0.0133209	+	0.0230725i
$562$	−7.14795	−	12.3806i	−0.301518	−	0.522245i
$563$	−19.9182	+	34.4993i	−0.839452	+	1.45397i	0.0509022	+	0.998704i	$0.483790\pi$
$563$	−19.9182	+	34.4993i	−0.839452	+	1.45397i	−0.890354	+	0.455269i	$0.849543\pi$
$564$	13.7681			0.579741
$565$	−12.6402	+	21.8934i	−0.531776	+	0.921064i
$566$	−0.0135735	+	0.0235101i	−0.000570538	+	0.000988201i
$567$	1.00000			0.0419961
$568$	−4.61380	+	7.99134i	−0.193591	+	0.335309i
$569$	−1.34063	−	2.32205i	−0.0562023	−	0.0973452i	0.836555	−	0.547882i	$-0.184566\pi$
$569$	−1.34063	−	2.32205i	−0.0562023	−	0.0973452i	−0.892758	+	0.450537i	$0.851233\pi$
$570$	−1.54743	−	2.68022i	−0.0648145	−	0.112262i
$571$	−6.76138			−0.282955			−0.141477	−	0.989941i	$-0.545185\pi$
$571$	−6.76138			−0.282955			−0.141477	+	0.989941i	$0.545185\pi$
$572$	−2.63669	+	6.41621i	−0.110246	+	0.268275i
$573$	9.50365			0.397021
$574$	0.0609989	+	0.105653i	0.00254605	+	0.00440988i
$575$	−10.7240	−	18.5745i	−0.447222	−	0.774612i
$576$	0.763906	−	1.32312i	0.0318294	−	0.0551301i
$577$	−6.73556			−0.280405			−0.140203	−	0.990123i	$-0.544775\pi$
$577$	−6.73556			−0.280405			−0.140203	+	0.990123i	$0.544775\pi$
$578$	−4.63169	+	8.02232i	−0.192653	+	0.333684i
$579$	4.67576	−	8.09865i	0.194318	−	0.336569i
$580$	20.7476			0.861499
$581$	5.52930	−	9.57703i	0.229394	−	0.397322i
$582$	−4.14795	−	7.18446i	−0.171938	−	0.297805i
$583$	−4.54138	−	7.86591i	−0.188085	−	0.325773i
$584$	17.4233			0.720980
$585$	2.98911	+	3.87303i	0.123585	+	0.160130i
$586$	−11.8328			−0.488809
$587$	11.6265	+	20.1376i	0.479876	+	0.831169i	0.999734	−	0.0230834i	$-0.00734834\pi$
$587$	11.6265	+	20.1376i	0.479876	+	0.831169i	−0.519858	+	0.854253i	$0.674015\pi$
$588$	0.846011	+	1.46533i	0.0348889	+	0.0604293i
$589$	−17.7364	+	30.7203i	−0.730815	+	1.26581i
$590$	−2.93661			−0.120898
$591$	−8.75786	+	15.1691i	−0.360250	+	0.623972i
$592$	5.82036	−	10.0812i	0.239215	−	0.414333i
$593$	−25.4717			−1.04600			−0.522999	−	0.852333i	$-0.675187\pi$
$593$	−25.4717			−1.04600			−0.522999	+	0.852333i	$0.675187\pi$
$594$	0.315511	−	0.546482i	0.0129456	−	0.0224224i
$595$	0.376510	+	0.652135i	0.0154354	+	0.0267349i
$596$	2.75720	+	4.77561i	0.112939	+	0.195617i
$597$	−17.5894			−0.719886
$598$	8.30074	+	10.7554i	0.339443	+	0.439819i
$599$	−16.7453			−0.684192			−0.342096	−	0.939665i	$-0.611137\pi$
$599$	−16.7453			−0.684192			−0.342096	+	0.939665i	$0.611137\pi$
$600$	3.23609	+	5.60508i	0.132113	+	0.228826i
$601$	−0.206259	−	0.357251i	−0.00841348	−	0.0145726i	0.861788	−	0.507269i	$-0.169345\pi$
$601$	−0.206259	−	0.357251i	−0.00841348	−	0.0145726i	−0.870201	+	0.492696i	$0.836011\pi$
$602$	1.08211	−	1.87426i	0.0441033	−	0.0763892i
$603$	0.762709			0.0310599
$604$	−5.76271	+	9.98130i	−0.234481	+	0.406134i
$605$	6.58575	−	11.4069i	0.267749	−	0.463755i
$606$	−2.35988			−0.0958636
$607$	20.5057	−	35.5169i	0.832300	−	1.44159i	−0.0639107	−	0.997956i	$-0.520357\pi$
$607$	20.5057	−	35.5169i	0.832300	−	1.44159i	0.896210	−	0.443630i	$-0.146309\pi$
$608$	−10.9834	−	19.0238i	−0.445434	−	0.771515i
$609$	4.51842	+	7.82613i	0.183096	+	0.317131i
$610$	−8.22414			−0.332986
$611$	−11.1516	+	27.1366i	−0.451145	+	1.09783i
$612$	0.939001			0.0379569
$613$	−14.4248	−	24.9844i	−0.582611	−	1.00911i	−0.995169	−	0.0981800i	$-0.968698\pi$
$613$	−14.4248	−	24.9844i	−0.582611	−	1.00911i	0.412558	−	0.910931i	$-0.364635\pi$
$614$	−6.56315	−	11.3677i	−0.264867	−	0.458764i
$615$	−0.149145	+	0.258327i	−0.00601410	+	0.0104167i
$616$	2.32975			0.0938683
$617$	1.65428	−	2.86531i	0.0665990	−	0.115353i	−0.830803	−	0.556566i	$-0.812119\pi$
$617$	1.65428	−	2.86531i	0.0665990	−	0.115353i	0.897402	+	0.441213i	$0.145452\pi$
$618$	1.68867	−	2.92486i	0.0679282	−	0.117655i
$619$	−36.0737			−1.44992			−0.724962	−	0.688789i	$-0.758143\pi$
$619$	−36.0737			−1.44992			−0.724962	+	0.688789i	$0.758143\pi$
$620$	−9.90797	+	17.1611i	−0.397914	+	0.689207i
$621$	3.39493	+	5.88019i	0.136234	+	0.235964i
$622$	4.60202	+	7.97092i	0.184524	+	0.319605i
$623$	−8.60388			−0.344707
$624$	4.94989	+	6.41362i	0.198154	+	0.256750i
$625$	0.772398			0.0308959
$626$	−1.91640	−	3.31931i	−0.0765949	−	0.132666i
$627$	2.33662	+	4.04714i	0.0933155	+	0.161627i
$628$	20.6685	−	35.7989i	0.824764	−	1.42853i
$629$	2.87502			0.114634
$630$	0.376510	−	0.652135i	0.0150005	−	0.0259817i
$631$	19.2315	−	33.3100i	0.765596	−	1.32605i	−0.174335	−	0.984686i	$-0.555778\pi$
$631$	19.2315	−	33.3100i	0.765596	−	1.32605i	0.939931	−	0.341364i	$-0.110889\pi$
$632$	−7.66487			−0.304892
$633$	−0.681136	+	1.17976i	−0.0270727	+	0.0468914i
$634$	7.23005	+	12.5228i	0.287142	+	0.497345i
$635$	−3.13371	−	5.42775i	−0.124358	−	0.215394i
$636$	−13.5157			−0.535934
$637$	−3.57338	+	0.480608i	−0.141582	+	0.0190424i
$638$	5.70245			0.225762
$639$	−2.25182	−	3.90027i	−0.0890808	−	0.154292i
$640$	−7.82759	−	13.5578i	−0.309413	−	0.535919i
$641$	2.13049	−	3.69012i	0.0841493	−	0.145751i	−0.820879	−	0.571102i	$-0.806516\pi$
$641$	2.13049	−	3.69012i	0.0841493	−	0.145751i	0.905028	+	0.425351i	$0.139849\pi$
$642$	7.13467			0.281583
$643$	1.79829	−	3.11473i	0.0709176	−	0.122833i	−0.828386	−	0.560158i	$-0.810741\pi$
$643$	1.79829	−	3.11473i	0.0709176	−	0.122833i	0.899304	+	0.437325i	$0.144074\pi$
$644$	−5.74429	+	9.94940i	−0.226357	+	0.392061i
$645$	5.29159			0.208356
$646$	0.632883	−	1.09619i	0.0249004	−	0.0431288i
$647$	22.3572	+	38.7238i	0.878952	+	1.52239i	0.852493	+	0.522739i	$0.175090\pi$
$647$	22.3572	+	38.7238i	0.878952	+	1.52239i	0.0264594	+	0.999650i	$0.491577\pi$
$648$	−1.02446	−	1.77441i	−0.0402445	−	0.0697056i
$649$	4.43429			0.174061
$650$	−6.26420	+	0.842515i	−0.245702	+	0.0330462i
$651$	−8.63102			−0.338276
$652$	−9.76995	−	16.9220i	−0.382621	−	0.662718i
$653$	16.5978	+	28.7483i	0.649523	+	1.12501i	0.983237	+	0.182333i	$0.0583649\pi$
$653$	16.5978	+	28.7483i	0.649523	+	1.12501i	−0.333713	+	0.942675i	$0.608302\pi$
$654$	−1.89828	+	3.28792i	−0.0742286	+	0.128568i
$655$	−4.55496			−0.177977
$656$	−0.246980	+	0.427781i	−0.00964293	+	0.0167021i
$657$	−4.25182	+	7.36438i	−0.165879	+	0.287312i
$658$	4.51573			0.176041
$659$	−23.8735	+	41.3500i	−0.929978	+	1.61077i	−0.146624	+	0.989192i	$0.546841\pi$
$659$	−23.8735	+	41.3500i	−0.929978	+	1.61077i	−0.783354	+	0.621576i	$0.786493\pi$
$660$	1.30529	+	2.26083i	0.0508083	+	0.0880026i
$661$	−3.64526	−	6.31378i	−0.141784	−	0.245577i	0.786384	−	0.617738i	$-0.211951\pi$
$661$	−3.64526	−	6.31378i	−0.141784	−	0.245577i	−0.928169	+	0.372160i	$0.878617\pi$
$662$	1.94272			0.0755060
$663$	−0.760553	+	1.85075i	−0.0295374	+	0.0718772i
$664$	−22.6582			−0.879308
$665$	2.78836	+	4.82959i	0.108128	+	0.187283i
$666$	−1.43751	−	2.48984i	−0.0557023	−	0.0964793i
$667$	−30.6794	+	53.1383i	−1.18791	+	2.05752i
$668$	−8.16182			−0.315790
$669$	5.14310	−	8.90812i	0.198844	−	0.344408i
$670$	0.287168	−	0.497389i	0.0110943	−	0.0192158i
$671$	12.4185			0.479410
$672$	2.67241	−	4.62874i	0.103090	−	0.178558i
$673$	16.9421	+	29.3446i	0.653071	+	1.13115i	0.982374	+	0.186927i	$0.0598529\pi$
$673$	16.9421	+	29.3446i	0.653071	+	1.13115i	−0.329303	+	0.944224i	$0.606814\pi$
$674$	−1.15093	−	1.99347i	−0.0443323	−	0.0767857i
$675$	−3.15883			−0.121584
$676$	−21.2146	+	5.81173i	−0.815947	+	0.223528i
$677$	−36.2989			−1.39508			−0.697540	−	0.716546i	$-0.745722\pi$
$677$	−36.2989			−1.39508			−0.697540	+	0.716546i	$0.745722\pi$
$678$	5.16972	+	8.95422i	0.198542	+	0.343885i
$679$	7.47434	+	12.9459i	0.286839	+	0.496820i
$680$	0.771438	−	1.33617i	0.0295833	−	0.0512398i
$681$	5.60819			0.214906
$682$	−2.72318	+	4.71669i	−0.104276	+	0.180612i
$683$	0.568236	−	0.984214i	0.0217430	−	0.0376599i	−0.854949	−	0.518712i	$-0.826412\pi$
$683$	0.568236	−	0.984214i	0.0217430	−	0.0376599i	0.876692	+	0.481052i	$0.159745\pi$
$684$	6.95407			0.265895
$685$	14.5957	−	25.2805i	0.557672	−	0.965917i
$686$	0.277479	+	0.480608i	0.0105942	+	0.0183497i
$687$	0.940198	+	1.62847i	0.0358708	+	0.0621300i
$688$	8.76271			0.334075
$689$	10.9472	−	26.6392i	0.417055	−	1.01487i
$690$	5.11290			0.194645
$691$	17.7301	+	30.7094i	0.674483	+	1.16824i	0.976620	+	0.214974i	$0.0689668\pi$
$691$	17.7301	+	30.7094i	0.674483	+	1.16824i	−0.302137	+	0.953265i	$0.597700\pi$
$692$	−18.2955	−	31.6888i	−0.695492	−	1.20463i
$693$	−0.568532	+	0.984726i	−0.0215967	+	0.0374066i
$694$	6.42327			0.243824
$695$	5.49031	−	9.50950i	0.208259	−	0.360716i
$696$	9.25786	−	16.0351i	0.350918	−	0.607809i
$697$	−0.121998			−0.00462100
$698$	−3.61074	+	6.25399i	−0.136669	+	0.236717i
$699$	3.19202	+	5.52874i	0.120733	+	0.209116i
$700$	−2.67241	−	4.62874i	−0.101007	−	0.174950i
$701$	31.7265			1.19829			0.599146	−	0.800640i	$-0.295507\pi$
$701$	31.7265			1.19829			0.599146	+	0.800640i	$0.295507\pi$
$702$	1.98307	−	0.266717i	0.0748463	−	0.0100666i
$703$	21.2918			0.803037
$704$	0.868609	+	1.50447i	0.0327369	+	0.0567020i
$705$	5.52057	+	9.56191i	0.207917	+	0.360123i
$706$	7.26755	−	12.5878i	0.273518	−	0.473747i
$707$	4.25236			0.159926
$708$	3.29925	−	5.71447i	0.123993	−	0.214763i
$709$	17.5913	−	30.4690i	0.660654	−	1.14429i	−0.319790	−	0.947488i	$-0.603613\pi$
$709$	17.5913	−	30.4690i	0.660654	−	1.14429i	0.980444	−	0.196797i	$-0.0630541\pi$
$710$	−3.39134			−0.127275
$711$	1.87047	−	3.23975i	0.0701481	−	0.121500i
$712$	8.81431	+	15.2668i	0.330330	+	0.572149i
$713$	−29.3017	−	50.7520i	−1.09736	−	1.90068i
$714$	0.307979			0.0115258
$715$	−5.51328	+	0.741519i	−0.206185	+	0.0277312i
$716$	−42.9922			−1.60670
$717$	−0.951083	−	1.64732i	−0.0355188	−	0.0615204i
$718$	3.07308	+	5.32273i	0.114686	+	0.198643i
$719$	0.970992	−	1.68181i	0.0362119	−	0.0627209i	−0.847351	−	0.531033i	$-0.821804\pi$
$719$	0.970992	−	1.68181i	0.0362119	−	0.0627209i	0.883563	+	0.468312i	$0.155138\pi$
$720$	3.04892			0.113626
$721$	−3.04288	+	5.27042i	−0.113323	+	0.196281i
$722$	−0.585089	+	1.01340i	−0.0217748	+	0.0377150i
$723$	13.2121			0.491362
$724$	−6.49731	+	11.2537i	−0.241471	+	0.418239i
$725$	−14.2729	−	24.7214i	−0.530083	−	0.918131i
$726$	−2.69351	−	4.66530i	−0.0999657	−	0.173146i
$727$	8.95838			0.332248			0.166124	−	0.986105i	$-0.446875\pi$
$727$	8.95838			0.332248			0.166124	+	0.986105i	$0.446875\pi$
$728$	4.51357	+	5.84829i	0.167284	+	0.216752i
$729$	1.00000			0.0370370
$730$	3.20171	+	5.54552i	0.118501	+	0.205249i
$731$	1.08211	+	1.87426i	0.0400231	+	0.0693221i
$732$	9.23974	−	16.0037i	0.341511	−	0.591514i
$733$	9.11662			0.336730			0.168365	−	0.985725i	$-0.446151\pi$
$733$	9.11662			0.336730			0.168365	+	0.985725i	$0.446151\pi$
$734$	−3.71014	+	6.42616i	−0.136944	+	0.237194i
$735$	−0.678448	+	1.17511i	−0.0250249	+	0.0433444i
$736$	36.2905			1.33769
$737$	−0.433624	+	0.751059i	−0.0159728	+	0.0276656i
$738$	0.0609989	+	0.105653i	0.00224540	+	0.00388915i
$739$	14.4167	+	24.9705i	0.530327	+	0.918553i	0.999374	+	0.0353799i	$0.0112641\pi$
$739$	14.4167	+	24.9705i	0.530327	+	0.918553i	−0.469047	+	0.883173i	$0.655403\pi$
$740$	11.8941			0.437237
$741$	−5.63251	+	13.7063i	−0.206916	+	0.503514i
$742$	−4.43296			−0.162739
$743$	−25.1005	−	43.4754i	−0.920849	−	1.59496i	−0.798105	−	0.602519i	$-0.794164\pi$
$743$	−25.1005	−	43.4754i	−0.920849	−	1.59496i	−0.122744	−	0.992438i	$-0.539169\pi$
$744$	8.84213	+	15.3150i	0.324168	+	0.561476i
$745$	−2.21110	+	3.82974i	−0.0810086	+	0.140311i
$746$	20.3840			0.746313
$747$	5.52930	−	9.57703i	0.202307	−	0.350405i
$748$	−0.533852	+	0.924659i	−0.0195196	+	0.0338089i
$749$	−12.8562			−0.469756
$750$	−3.07188	+	5.32066i	−0.112169	+	0.194283i
$751$	4.01477	+	6.95379i	0.146501	+	0.253747i	0.929932	−	0.367732i	$-0.119865\pi$
$751$	4.01477	+	6.95379i	0.146501	+	0.253747i	−0.783431	+	0.621479i	$0.786532\pi$
$752$	9.14191	+	15.8342i	0.333371	+	0.577416i
$753$	7.54048			0.274790
$754$	11.0477	+	14.3147i	0.402334	+	0.521309i
$755$	−9.24267			−0.336375
$756$	0.846011	+	1.46533i	0.0307691	+	0.0532937i
$757$	−23.3751	−	40.4868i	−0.849582	−	1.47152i	−0.881582	−	0.472031i	$-0.843521\pi$
$757$	−23.3751	−	40.4868i	−0.849582	−	1.47152i	0.0320005	−	0.999488i	$-0.489812\pi$
$758$	9.23490	−	15.9953i	0.335427	−	0.580976i
$759$	−7.72050			−0.280236
$760$	5.71313	−	9.89543i	0.207237	−	0.358945i
$761$	−3.15668	+	5.46753i	−0.114429	+	0.198198i	−0.917552	−	0.397617i	$-0.869837\pi$
$761$	−3.15668	+	5.46753i	−0.114429	+	0.198198i	0.803122	+	0.595815i	$0.203171\pi$
$762$	−2.56332			−0.0928592
$763$	3.42058	−	5.92462i	0.123833	−	0.214486i
$764$	8.04019	+	13.9260i	0.290884	+	0.503826i
$765$	0.376510	+	0.652135i	0.0136128	+	0.0235780i
$766$	9.78017			0.353372
$767$	8.59083	+	11.1312i	0.310197	+	0.401926i
$768$	−3.34721			−0.120782
$769$	−20.9366	−	36.2633i	−0.754993	−	1.30769i	−0.945378	−	0.325977i	$-0.894307\pi$
$769$	−20.9366	−	36.2633i	−0.754993	−	1.30769i	0.190384	−	0.981710i	$-0.439027\pi$
$770$	0.428116	+	0.741519i	0.0154282	+	0.0267225i
$771$	−6.70895	+	11.6202i	−0.241617	+	0.418493i
$772$	15.8230			0.569481
$773$	19.6320	−	34.0036i	0.706113	−	1.22302i	−0.260175	−	0.965561i	$-0.583780\pi$
$773$	19.6320	−	34.0036i	0.706113	−	1.22302i	0.966288	−	0.257463i	$-0.0828864\pi$
$774$	1.08211	−	1.87426i	0.0388955	−	0.0673689i
$775$	27.2640			0.979350
$776$	15.3143	−	26.5252i	0.549752	−	0.952198i
$777$	2.59030	+	4.48653i	0.0929266	+	0.160954i
$778$	8.22282	+	14.2423i	0.294802	+	0.510612i
$779$	−0.903493			−0.0323710
$780$	−3.14646	+	7.65667i	−0.112661	+	0.274153i
$781$	5.12093			0.183241
$782$	1.04556	+	1.81097i	0.0373893	+	0.0647602i
$783$	4.51842	+	7.82613i	0.161475	+	0.279683i
$784$	−1.12349	+	1.94594i	−0.0401246	+	0.0694979i
$785$	33.1497			1.18316
$786$	−0.931468	+	1.61335i	−0.0332244	+	0.0575463i
$787$	18.0027	−	31.1816i	0.641727	−	1.11150i	−0.343321	−	0.939218i	$-0.611552\pi$
$787$	18.0027	−	31.1816i	0.641727	−	1.11150i	0.985047	−	0.172285i	$-0.0551149\pi$
$788$	−29.6370			−1.05577
$789$	5.59903	−	9.69781i	0.199331	−	0.345251i
$790$	−1.40850	−	2.43960i	−0.0501122	−	0.0867969i
$791$	−9.31551	−	16.1349i	−0.331221	−	0.573692i
$792$	2.32975			0.0827840
$793$	24.0591	+	31.1737i	0.854365	+	1.10701i
$794$	−10.6552			−0.378138
$795$	−5.41939	−	9.38665i	−0.192206	−	0.332910i
$796$	−14.8808	−	25.7743i	−0.527437	−	0.913547i
$797$	9.07553	−	15.7193i	0.321472	−	0.556806i	−0.659320	−	0.751862i	$-0.729156\pi$
$797$	9.07553	−	15.7193i	0.321472	−	0.556806i	0.980792	+	0.195057i	$0.0624891\pi$
$798$	2.28083			0.0807406
$799$	−2.25786	+	3.91074i	−0.0798775	+	0.138352i
$800$	−8.44169	+	14.6214i	−0.298459	+	0.516946i
$801$	−8.60388			−0.304003
$802$	3.46830	−	6.00728i	0.122470	−	0.212124i
$803$	−4.83459	−	8.37376i	−0.170609	−	0.295504i
$804$	0.645260	+	1.11762i	0.0227566	+	0.0394155i
$805$	−9.21313			−0.324720
$806$	−17.1160	+	2.30204i	−0.602884	+	0.0810860i
$807$	13.9172			0.489910
$808$	−4.35636	−	7.54544i	−0.153256	−	0.265448i
$809$	−18.6417	−	32.2883i	−0.655406	−	1.13520i	−0.981792	−	0.189960i	$-0.939164\pi$
$809$	−18.6417	−	32.2883i	−0.655406	−	1.13520i	0.326386	−	0.945237i	$-0.394169\pi$
$810$	0.376510	−	0.652135i	0.0132292	−	0.0229137i
$811$	37.7657			1.32613			0.663066	−	0.748561i	$-0.269255\pi$
$811$	37.7657			1.32613			0.663066	+	0.748561i	$0.269255\pi$
$812$	−7.64526	+	13.2420i	−0.268296	+	0.464702i
$813$	−0.991271	+	1.71693i	−0.0347654	+	0.0602154i
$814$	3.26908			0.114581
$815$	7.83489	−	13.5704i	0.274444	−	0.475351i
$816$	0.623490	+	1.07992i	0.0218265	+	0.0378046i
$817$	8.01387	+	13.8804i	0.280370	+	0.485615i
$818$	9.31336			0.325634
$819$	−3.57338	+	0.480608i	−0.124864	+	0.0167938i
$820$	−0.504713			−0.0176253
$821$	−0.807315	−	1.39831i	−0.0281755	−	0.0488013i	0.851594	−	0.524202i	$-0.175636\pi$
$821$	−0.807315	−	1.39831i	−0.0281755	−	0.0488013i	−0.879769	+	0.475401i	$0.842303\pi$
$822$	−5.96950	−	10.3395i	−0.208210	−	0.360631i
$823$	−17.0550	+	29.5401i	−0.594498	+	1.02970i	0.399119	+	0.916899i	$0.369316\pi$
$823$	−17.0550	+	29.5401i	−0.594498	+	1.02970i	−0.993617	+	0.112802i	$0.964017\pi$
$824$	12.4692			0.434385
$825$	1.79590	−	3.11058i	0.0625251	−	0.108297i
$826$	1.08211	−	1.87426i	0.0376513	−	0.0652139i
$827$	23.1360			0.804517			0.402259	−	0.915526i	$-0.368225\pi$
$827$	23.1360			0.804517			0.402259	+	0.915526i	$0.368225\pi$
$828$	−5.74429	+	9.94940i	−0.199628	+	0.345766i
$829$	−0.195669	−	0.338909i	−0.00679588	−	0.0117708i	0.862607	−	0.505874i	$-0.168830\pi$
$829$	−0.195669	−	0.338909i	−0.00679588	−	0.0117708i	−0.869403	+	0.494103i	$0.835497\pi$
$830$	−4.16368	−	7.21170i	−0.144523	−	0.250322i
$831$	9.79954			0.339942
$832$	−2.09382	+	5.09516i	−0.0725901	+	0.176643i
$833$	−0.554958			−0.0192282
$834$	−2.24549	−	3.88930i	−0.0777549	−	0.134675i
$835$	−3.27263	−	5.66837i	−0.113254	−	0.196162i
$836$	−3.95361	+	6.84785i	−0.136738	+	0.236838i
$837$	−8.63102			−0.298332
$838$	−3.98576	+	6.90354i	−0.137686	+	0.238479i
$839$	12.2690	−	21.2506i	0.423574	−	0.733653i	−0.572712	−	0.819757i	$-0.694109\pi$
$839$	12.2690	−	21.2506i	0.423574	−	0.733653i	0.996286	+	0.0861044i	$0.0274419\pi$
$840$	2.78017			0.0959249
$841$	−26.3322	+	45.6087i	−0.908007	+	1.57271i
$842$	−6.25786	−	10.8389i	−0.215660	−	0.373535i
$843$	12.8802	+	22.3091i	0.443616	+	0.768366i
$844$	−2.30499			−0.0793412
$845$	−12.5426	−	12.4032i	−0.431480	−	0.426683i
$846$	4.51573			0.155254
$847$	4.85354	+	8.40658i	0.166770	+	0.288854i
$848$	−8.97434	−	15.5440i	−0.308180	−	0.533784i
$849$	0.0244587	−	0.0423637i	0.000839419	−	0.00145392i
$850$	−0.972853			−0.0333686
$851$	−17.5878	+	30.4629i	−0.602901	+	1.04426i
$852$	3.81013	−	6.59935i	0.130533	−	0.226090i
$853$	−19.6786			−0.673783			−0.336891	−	0.941544i	$-0.609376\pi$
$853$	−19.6786			−0.673783			−0.336891	+	0.941544i	$0.609376\pi$
$854$	3.03050	−	5.24898i	0.103702	−	0.179616i
$855$	2.78836	+	4.82959i	0.0953600	+	0.165168i
$856$	13.1707	+	22.8123i	0.450165	+	0.779708i
$857$	−22.5429			−0.770050			−0.385025	−	0.922906i	$-0.625807\pi$
$857$	−22.5429			−0.770050			−0.385025	+	0.922906i	$0.625807\pi$
$858$	−0.864797	+	2.10442i	−0.0295237	+	0.0718438i
$859$	−23.8931			−0.815221			−0.407610	−	0.913156i	$-0.633638\pi$
$859$	−23.8931			−0.815221			−0.407610	+	0.913156i	$0.633638\pi$
$860$	4.47674	+	7.75394i	0.152655	+	0.264407i
$861$	−0.109916	−	0.190381i	−0.00374594	−	0.00648815i
$862$	1.24578	−	2.15776i	0.0424315	−	0.0734936i
$863$	15.5821			0.530421			0.265211	−	0.964191i	$-0.414559\pi$
$863$	15.5821			0.530421			0.265211	+	0.964191i	$0.414559\pi$
$864$	2.67241	−	4.62874i	0.0909171	−	0.157473i
$865$	14.6719	−	25.4124i	0.498859	−	0.864049i
$866$	−10.7447			−0.365118
$867$	8.34601	−	14.4557i	0.283445	−	0.490942i
$868$	−7.30194	−	12.6473i	−0.247844	−	0.429278i
$869$	2.12684	+	3.68380i	0.0721482	+	0.124964i
$870$	6.80492			0.230708
$871$	−2.72545	+	0.366564i	−0.0923482	+	0.0124205i
$872$	−14.0170			−0.474675
$873$	7.47434	+	12.9459i	0.252968	+	0.438154i
$874$	7.74326	+	13.4117i	0.261920	+	0.453658i
$875$	5.53534	−	9.58750i	0.187129	−	0.324117i
$876$	−14.3884			−0.486137
$877$	−8.83848	+	15.3087i	−0.298454	+	0.516938i	−0.975782	−	0.218743i	$-0.929804\pi$
$877$	−8.83848	+	15.3087i	−0.298454	+	0.516938i	0.677328	+	0.735681i	$0.263138\pi$
$878$	7.57152	−	13.1142i	0.255526	−	0.442584i
$879$	21.3220			0.719173
$880$	−1.73341	+	3.00235i	−0.0584331	+	0.101209i
$881$	−22.7684	−	39.4360i	−0.767086	−	1.32863i	−0.939137	−	0.343544i	$-0.888372\pi$
$881$	−22.7684	−	39.4360i	−0.767086	−	1.32863i	0.172050	−	0.985088i	$-0.444961\pi$
$882$	0.277479	+	0.480608i	0.00934321	+	0.0161829i
$883$	7.13361			0.240065			0.120032	−	0.992770i	$-0.461700\pi$
$883$	7.13361			0.240065			0.120032	+	0.992770i	$0.461700\pi$
$884$	−3.35540	+	0.451291i	−0.112854	+	0.0151786i
$885$	5.29159			0.177875
$886$	−4.50402	−	7.80119i	−0.151315	−	0.262086i
$887$	21.4590	+	37.1682i	0.720524	+	1.24798i	0.960790	+	0.277277i	$0.0894321\pi$
$887$	21.4590	+	37.1682i	0.720524	+	1.24798i	−0.240266	+	0.970707i	$0.577235\pi$
$888$	5.30731	−	9.19254i	0.178102	−	0.308481i
$889$	4.61894			0.154914
$890$	−3.23945	+	5.61089i	−0.108587	+	0.188077i
$891$	−0.568532	+	0.984726i	−0.0190465	+	0.0329896i
$892$	17.4045			0.582745
$893$	−16.7213	+	28.9622i	−0.559558	+	0.969183i
$894$	0.904321	+	1.56633i	0.0302450	+	0.0523859i
$895$	−17.2385	−	29.8580i	−0.576221	−	0.998044i
$896$	11.5375			0.385441
$897$	−14.9574	−	19.3805i	−0.499414	−	0.647096i
$898$	13.4561			0.449034
$899$	−38.9986	−	67.5475i	−1.30068	−	2.25284i
$900$	−2.67241	−	4.62874i	−0.0890802	−	0.154291i
$901$	2.21648	−	3.83906i	0.0738417	−	0.127898i
$902$	−0.138719			−0.00461885
$903$	−1.94989	+	3.37730i	−0.0648881	+	0.112390i
$904$	−19.0867	+	33.0592i	−0.634815	+	1.09953i
$905$	−10.4209			−0.346402
$906$	−1.89008	+	3.27372i	−0.0627938	+	0.108762i
$907$	−17.4629	−	30.2467i	−0.579847	−	1.00432i	−0.995496	−	0.0947995i	$-0.969779\pi$
$907$	−17.4629	−	30.2467i	−0.579847	−	1.00432i	0.415649	−	0.909525i	$-0.363554\pi$
$908$	4.74459	+	8.21787i	0.157455	+	0.272719i
$909$	4.25236			0.141042
$910$	−1.03199	+	2.51128i	−0.0342102	+	0.0832480i
$911$	56.0810			1.85805			0.929023	−	0.370023i	$-0.120650\pi$
$911$	56.0810			1.85805			0.929023	+	0.370023i	$0.120650\pi$
$912$	4.61745	+	7.99766i	0.152899	+	0.264829i
$913$	6.28717	+	10.8897i	0.208075	+	0.360396i
$914$	−8.73788	+	15.1345i	−0.289023	+	0.500603i
$915$	14.8194			0.489914
$916$	−1.59083	+	2.75541i	−0.0525626	+	0.0910412i
$917$	1.67845	−	2.90716i	0.0554272	−	0.0960028i
$918$	0.307979			0.0101648
$919$	15.8041	−	27.3735i	0.521329	−	0.902968i	−0.478363	−	0.878162i	$-0.658770\pi$
$919$	15.8041	−	27.3735i	0.521329	−	0.902968i	0.999692	−	0.0248062i	$-0.00789687\pi$
$920$	9.43847	+	16.3479i	0.311177	+	0.538975i
$921$	11.8264	+	20.4839i	0.389693	+	0.674968i
$922$	−22.6738			−0.746723
$923$	9.92112	+	12.8549i	0.326557	+	0.423124i
$924$	−1.92394			−0.0632928
$925$	−8.18233	−	14.1722i	−0.269033	−	0.465980i
$926$	10.8478	+	18.7889i	0.356481	+	0.617443i
$927$	−3.04288	+	5.27042i	−0.0999412	+	0.173103i
$928$	48.3002			1.58553
$929$	−12.2615	+	21.2376i	−0.402287	+	0.696782i	−0.994002	−	0.109366i	$-0.965118\pi$
$929$	−12.2615	+	21.2376i	−0.402287	+	0.696782i	0.591714	+	0.806148i	$0.298451\pi$
$930$	−3.24967	+	5.62859i	−0.106561	+	0.184569i
$931$	−4.10992			−0.134697
$932$	−5.40097	+	9.35475i	−0.176915	+	0.306425i
$933$	−8.29254	−	14.3631i	−0.271486	−	0.470227i
$934$	2.60776	+	4.51677i	0.0853285	+	0.147793i
$935$	−0.856232			−0.0280018
$936$	4.51357	+	5.84829i	0.147531	+	0.191157i
$937$	−11.1943			−0.365703			−0.182852	−	0.983141i	$-0.558533\pi$
$937$	−11.1943			−0.365703			−0.182852	+	0.983141i	$0.558533\pi$
$938$	0.211636	+	0.366564i	0.00691015	+	0.0119687i
$939$	3.45324	+	5.98118i	0.112692	+	0.195189i
$940$	−9.34093	+	16.1790i	−0.304668	+	0.527700i
$941$	9.92931			0.323686			0.161843	−	0.986816i	$-0.448256\pi$
$941$	9.92931			0.323686			0.161843	+	0.986816i	$0.448256\pi$
$942$	6.77897	−	11.7415i	0.220871	−	0.382559i
$943$	0.746316	−	1.29266i	0.0243034	−	0.0420947i
$944$	8.76271			0.285202
$945$	−0.678448	+	1.17511i	−0.0220699	+	0.0382262i
$946$	1.23042	+	2.13115i	0.0400045	+	0.0692898i
$947$	22.1301	+	38.3305i	0.719132	+	1.24557i	0.961344	+	0.275350i	$0.0887938\pi$
$947$	22.1301	+	38.3305i	0.719132	+	1.24557i	−0.242212	+	0.970223i	$0.577873\pi$
$948$	6.32975			0.205581
$949$	11.6540	−	28.3591i	0.378305	−	0.920577i
$950$	−7.20477			−0.233754
$951$	−13.0281	−	22.5653i	−0.422465	−	0.731731i
$952$	0.568532	+	0.984726i	0.0184262	+	0.0319151i
$953$	−15.5656	+	26.9604i	−0.504219	+	0.873334i	0.495769	+	0.868455i	$0.334886\pi$
$953$	−15.5656	+	26.9604i	−0.504219	+	0.873334i	−0.999988	+	0.00487907i	$0.998447\pi$
$954$	−4.43296			−0.143522
$955$	−6.44773	+	11.1678i	−0.208644	+	0.361381i
$956$	1.60925	−	2.78731i	0.0520469	−	0.0901479i
$957$	−10.2755			−0.332158
$958$	−0.564351	+	0.977485i	−0.0182334	+	0.0315811i
$959$	10.7567	+	18.6311i	0.347351	+	0.601629i
$960$	1.03654	+	1.79534i	0.0334542	+	0.0579444i
$961$	43.4946			1.40305
$962$	6.33340	+	8.20625i	0.204197	+	0.264580i
$963$	−12.8562			−0.414286
$964$	11.1775	+	19.3601i	0.360005	+	0.623546i
$965$	6.34452	+	10.9890i	0.204237	+	0.353749i
$966$	−1.88404	+	3.26326i	−0.0606181	+	0.104994i
$967$	−15.9745			−0.513706			−0.256853	−	0.966451i	$-0.582686\pi$
$967$	−15.9745			−0.513706			−0.256853	+	0.966451i	$0.582686\pi$
$968$	9.94451	−	17.2244i	0.319629	−	0.553613i
$969$	−1.14042	+	1.97526i	−0.0366354	+	0.0634544i
$970$	11.2567			0.361430
$971$	18.9263	−	32.7812i	0.607372	−	1.05200i	−0.384299	−	0.923209i	$-0.625557\pi$
$971$	18.9263	−	32.7812i	0.607372	−	1.05200i	0.991672	−	0.128791i	$-0.0411098\pi$
$972$	0.846011	+	1.46533i	0.0271358	+	0.0470006i
$973$	4.04623	+	7.00827i	0.129716	+	0.224675i
$974$	16.8086			0.538584
$975$	11.2877	−	1.51816i	0.361496	−	0.0486200i
$976$	24.5405			0.785522
$977$	0.961968	+	1.66618i	0.0307761	+	0.0533057i	0.881003	−	0.473110i	$-0.156869\pi$
$977$	0.961968	+	1.66618i	0.0307761	+	0.0533057i	−0.850227	+	0.526416i	$0.823535\pi$
$978$	−3.20440	−	5.55018i	−0.102465	−	0.177475i
$979$	4.89158	−	8.47246i	0.156335	−	0.270781i
$980$	−2.29590			−0.0733397
$981$	3.42058	−	5.92462i	0.109211	−	0.189159i
$982$	−8.09933	+	14.0284i	−0.258460	+	0.447666i
$983$	47.7922			1.52434			0.762168	−	0.647379i	$-0.224135\pi$
$983$	47.7922			1.52434			0.762168	+	0.647379i	$0.224135\pi$
$984$	−0.225209	+	0.390074i	−0.00717941	+	0.0124351i
$985$	−11.8835	−	20.5828i	−0.378640	−	0.655824i
$986$	1.39158	+	2.41028i	0.0443168	+	0.0767589i
$987$	−8.13706			−0.259006
$988$	−24.8495	+	3.34218i	−0.790568	+	0.106329i
$989$	−26.4789			−0.841980
$990$	0.428116	+	0.741519i	0.0136064	+	0.0235670i
$991$	−22.0341	−	38.1643i	−0.699938	−	1.21233i	−0.968488	−	0.249062i	$-0.919878\pi$
$991$	−22.0341	−	38.1643i	−0.699938	−	1.21233i	0.268550	−	0.963266i	$-0.413456\pi$
$992$	−23.0656	+	39.9508i	−0.732334	+	1.26844i
$993$	−3.50066			−0.111090
$994$	1.24967	−	2.16449i	0.0396371	−	0.0686534i
$995$	11.9335	−	20.6694i	0.378317	−	0.655265i
$996$	18.7114			0.592893
$997$	−24.1172	+	41.7722i	−0.763800	+	1.32294i	0.177079	+	0.984197i	$0.443335\pi$
$997$	−24.1172	+	41.7722i	−0.763800	+	1.32294i	−0.940879	+	0.338743i	$0.889998\pi$
$998$	0.346675	+	0.600458i	0.0109738	+	0.0190072i
$999$	2.59030	+	4.48653i	0.0819535	+	0.141948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.c.211.2	yes	6
3.2	odd	2		819.2.o.e.757.2		6
13.3	even	3		3549.2.a.i.1.2		3
13.9	even	3	inner	273.2.k.c.22.2	✓	6
13.10	even	6		3549.2.a.u.1.2		3
39.35	odd	6		819.2.o.e.568.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.2	✓	6	13.9	even	3	inner
273.2.k.c.211.2	yes	6	1.1	even	1	trivial
819.2.o.e.568.2		6	39.35	odd	6
819.2.o.e.757.2		6	3.2	odd	2
3549.2.a.i.1.2		3	13.3	even	3
3549.2.a.u.1.2		3	13.10	even	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277479 + 0.480608i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.846011 - 1.46533i) q^{4} +1.35690 q^{5} +(0.277479 - 0.480608i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.277479 + 0.480608i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.846011 - 1.46533i) q^{4} +1.35690 q^{5} +(0.277479 - 0.480608i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.04892 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.376510 + 0.652135i) q^{10} +(-0.568532 - 0.984726i) q^{11} -1.69202 q^{12} +(1.37047 - 3.33494i) q^{13} -0.554958 q^{14} +(-0.678448 - 1.17511i) q^{15} +(-1.12349 - 1.94594i) q^{16} +(0.277479 - 0.480608i) q^{17} -0.554958 q^{18} +(2.05496 - 3.55929i) q^{19} +(1.14795 - 1.98831i) q^{20} +1.00000 q^{21} +(0.315511 - 0.546482i) q^{22} +(3.39493 + 5.88019i) q^{23} +(-1.02446 - 1.77441i) q^{24} -3.15883 q^{25} +(1.98307 - 0.266717i) q^{26} +1.00000 q^{27} +(0.846011 + 1.46533i) q^{28} +(4.51842 + 7.82613i) q^{29} +(0.376510 - 0.652135i) q^{30} -8.63102 q^{31} +(2.67241 - 4.62874i) q^{32} +(-0.568532 + 0.984726i) q^{33} +0.307979 q^{34} +(-0.678448 + 1.17511i) q^{35} +(0.846011 + 1.46533i) q^{36} +(2.59030 + 4.48653i) q^{37} +2.28083 q^{38} +(-3.57338 + 0.480608i) q^{39} +2.78017 q^{40} +(-0.109916 - 0.190381i) q^{41} +(0.277479 + 0.480608i) q^{42} +(-1.94989 + 3.37730i) q^{43} -1.92394 q^{44} +(-0.678448 + 1.17511i) q^{45} +(-1.88404 + 3.26326i) q^{46} -8.13706 q^{47} +(-1.12349 + 1.94594i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.876510 - 1.51816i) q^{50} -0.554958 q^{51} +(-3.72737 - 4.82959i) q^{52} +7.98792 q^{53} +(0.277479 + 0.480608i) q^{54} +(-0.771438 - 1.33617i) q^{55} +(-1.02446 + 1.77441i) q^{56} -4.10992 q^{57} +(-2.50753 + 4.34317i) q^{58} +(-1.94989 + 3.37730i) q^{59} -2.29590 q^{60} +(-5.46077 + 9.45833i) q^{61} +(-2.39493 - 4.14814i) q^{62} +(-0.500000 - 0.866025i) q^{63} -1.52781 q^{64} +(1.85958 - 4.52516i) q^{65} -0.631023 q^{66} +(-0.381355 - 0.660525i) q^{67} +(-0.469501 - 0.813199i) q^{68} +(3.39493 - 5.88019i) q^{69} -0.753020 q^{70} +(-2.25182 + 3.90027i) q^{71} +(-1.02446 + 1.77441i) q^{72} +8.50365 q^{73} +(-1.43751 + 2.48984i) q^{74} +(1.57942 + 2.73563i) q^{75} +(-3.47703 - 6.02240i) q^{76} +1.13706 q^{77} +(-1.22252 - 1.58403i) q^{78} -3.74094 q^{79} +(-1.52446 - 2.64044i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.0609989 - 0.105653i) q^{82} -11.0586 q^{83} +(0.846011 - 1.46533i) q^{84} +(0.376510 - 0.652135i) q^{85} -2.16421 q^{86} +(4.51842 - 7.82613i) q^{87} +(-1.16487 - 2.01762i) q^{88} +(4.30194 + 7.45117i) q^{89} -0.753020 q^{90} +(2.20291 + 2.85433i) q^{91} +11.4886 q^{92} +(4.31551 + 7.47468i) q^{93} +(-2.25786 - 3.91074i) q^{94} +(2.78836 - 4.82959i) q^{95} -5.34481 q^{96} +(7.47434 - 12.9459i) q^{97} +(0.277479 - 0.480608i) q^{98} +1.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - 3 q^{3} + 2 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 7 q^{10} + 2 q^{11} - 6 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} + 13 q^{19} - 7 q^{20} + 6 q^{21} - 13 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 4 q^{26} + 6 q^{27} - q^{29} + 7 q^{30} - 22 q^{31} - 7 q^{32} + 2 q^{33} + 12 q^{34} + 4 q^{37} + 36 q^{38} + 6 q^{39} + 14 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 42 q^{44} + 9 q^{46} - 38 q^{47} - 2 q^{48} - 3 q^{49} - 10 q^{50} - 4 q^{51} + 10 q^{53} + 2 q^{54} + 14 q^{55} + 3 q^{56} - 26 q^{57} + 10 q^{58} + 11 q^{59} + 14 q^{60} - 7 q^{61} + 9 q^{62} - 3 q^{63} - 22 q^{64} + 26 q^{66} + 15 q^{67} + 7 q^{68} - 3 q^{69} - 14 q^{70} + 18 q^{71} + 3 q^{72} - 12 q^{73} - 33 q^{74} + q^{75} + 14 q^{76} - 4 q^{77} - 7 q^{78} + 6 q^{79} - 3 q^{81} + 20 q^{82} - 4 q^{83} + 7 q^{85} + 10 q^{86} - q^{87} - 9 q^{88} + 17 q^{89} - 14 q^{90} + 56 q^{92} + 11 q^{93} - q^{94} + 14 q^{95} + 14 q^{96} + 13 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 3 * q^3 + 2 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 7 * q^10 + 2 * q^11 - 6 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 + 13 * q^19 - 7 * q^20 + 6 * q^21 - 13 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 4 * q^26 + 6 * q^27 - q^29 + 7 * q^30 - 22 * q^31 - 7 * q^32 + 2 * q^33 + 12 * q^34 + 4 * q^37 + 36 * q^38 + 6 * q^39 + 14 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 42 * q^44 + 9 * q^46 - 38 * q^47 - 2 * q^48 - 3 * q^49 - 10 * q^50 - 4 * q^51 + 10 * q^53 + 2 * q^54 + 14 * q^55 + 3 * q^56 - 26 * q^57 + 10 * q^58 + 11 * q^59 + 14 * q^60 - 7 * q^61 + 9 * q^62 - 3 * q^63 - 22 * q^64 + 26 * q^66 + 15 * q^67 + 7 * q^68 - 3 * q^69 - 14 * q^70 + 18 * q^71 + 3 * q^72 - 12 * q^73 - 33 * q^74 + q^75 + 14 * q^76 - 4 * q^77 - 7 * q^78 + 6 * q^79 - 3 * q^81 + 20 * q^82 - 4 * q^83 + 7 * q^85 + 10 * q^86 - q^87 - 9 * q^88 + 17 * q^89 - 14 * q^90 + 56 * q^92 + 11 * q^93 - q^94 + 14 * q^95 + 14 * q^96 + 13 * q^97 + 2 * q^98 - 4 * q^99

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