LMFDB - Embedded newform 546.2.o.b.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (of order $4$, 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 $\Q(i)$
Coefficient field:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.2
Root			$1.65222i$ of defining polynomial
Character	$\chi$	$=$	546.265
Dual form			546.2.o.b.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -0.652223 q^{10} +(1.60525 + 1.60525i) q^{11} -1.00000 q^{12} +(2.51608 + 2.58251i) q^{13} +(2.06644 - 1.65222i) q^{14} +(0.461191 - 0.461191i) q^{15} -1.00000 q^{16} +6.40303 q^{17} +(0.707107 - 0.707107i) q^{18} +(2.52763 + 2.52763i) q^{19} +(0.461191 - 0.461191i) q^{20} +(-0.292893 + 2.62949i) q^{21} -2.27016 q^{22} -8.51280i q^{23} +(0.707107 - 0.707107i) q^{24} -4.57461i q^{25} +(-3.60525 - 0.0469777i) q^{26} +1.00000i q^{27} +(-0.292893 + 2.62949i) q^{28} +7.91120 q^{29} +0.652223i q^{30} +(0.922382 + 0.922382i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.60525 - 1.60525i) q^{33} +(-4.52763 + 4.52763i) q^{34} +(-1.07762 - 1.34778i) q^{35} +1.00000i q^{36} +(-0.953022 - 0.953022i) q^{37} -3.57461 q^{38} +(2.58251 - 2.51608i) q^{39} +0.652223i q^{40} +(-3.89486 - 3.89486i) q^{41} +(-1.65222 - 2.06644i) q^{42} +4.17620i q^{43} +(1.60525 - 1.60525i) q^{44} +(-0.461191 - 0.461191i) q^{45} +(6.01946 + 6.01946i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 + 1.54032i) q^{49} +(3.23473 + 3.23473i) q^{50} -6.40303i q^{51} +(2.58251 - 2.51608i) q^{52} +9.10072 q^{53} +(-0.707107 - 0.707107i) q^{54} +1.48065i q^{55} +(-1.65222 - 2.06644i) q^{56} +(2.52763 - 2.52763i) q^{57} +(-5.59406 + 5.59406i) q^{58} +(1.17834 - 1.17834i) q^{59} +(-0.461191 - 0.461191i) q^{60} +14.4874i q^{61} -1.30445 q^{62} +(2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-0.0306399 + 2.35142i) q^{65} +2.27016i q^{66} +(3.47602 - 3.47602i) q^{67} -6.40303i q^{68} -8.51280 q^{69} +(1.71501 + 0.191032i) q^{70} +(-8.29326 + 8.29326i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.89851 + 5.89851i) q^{73} +1.34778 q^{74} -4.57461 q^{75} +(2.52763 - 2.52763i) q^{76} +(-3.75081 - 4.69114i) q^{77} +(-0.0469777 + 3.60525i) q^{78} -9.18813 q^{79} +(-0.461191 - 0.461191i) q^{80} +1.00000 q^{81} +5.50817 q^{82} +(9.98882 + 9.98882i) q^{83} +(2.62949 + 0.292893i) q^{84} +(2.95302 + 2.95302i) q^{85} +(-2.95302 - 2.95302i) q^{86} -7.91120i q^{87} +2.27016i q^{88} +(8.54709 - 8.54709i) q^{89} +0.652223 q^{90} +(-5.85959 - 7.52763i) q^{91} -8.51280 q^{92} +(0.922382 - 0.922382i) q^{93} +2.00000i q^{94} +2.33144i q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.272296 + 0.272296i) q^{97} +(-5.91760 + 3.73926i) q^{98} +(-1.60525 - 1.60525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{12} + 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} + 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 12 q^{22} - 16 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} - 8 q^{34} - 24 q^{35} - 4 q^{37} - 4 q^{38} - 4 q^{39} + 12 q^{41} - 4 q^{42} + 4 q^{45} + 24 q^{46} + 32 q^{49} - 8 q^{50} - 4 q^{52} + 40 q^{53} - 4 q^{56} - 8 q^{57} + 4 q^{58} - 8 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{65} + 32 q^{67} - 28 q^{69} + 8 q^{70} - 12 q^{71} + 20 q^{73} + 20 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 44 q^{83} + 20 q^{85} - 20 q^{86} + 16 q^{89} - 4 q^{90} - 28 q^{91} - 28 q^{92} - 8 q^{93} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^12 + 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 + 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 12 * q^22 - 16 * q^26 - 8 * q^28 + 12 * q^29 - 8 * q^31 - 8 * q^34 - 24 * q^35 - 4 * q^37 - 4 * q^38 - 4 * q^39 + 12 * q^41 - 4 * q^42 + 4 * q^45 + 24 * q^46 + 32 * q^49 - 8 * q^50 - 4 * q^52 + 40 * q^53 - 4 * q^56 - 8 * q^57 + 4 * q^58 - 8 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^65 + 32 * q^67 - 28 * q^69 + 8 * q^70 - 12 * q^71 + 20 * q^73 + 20 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 44 * q^83 + 20 * q^85 - 20 * q^86 + 16 * q^89 - 4 * q^90 - 28 * q^91 - 28 * q^92 - 8 * q^93 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		−	1.00000i		−	0.500000i
$5$	0.461191	+	0.461191i	0.206251	+	0.206251i	0.802672	−	0.596421i	$-0.203411\pi$
$5$	0.461191	+	0.461191i	0.206251	+	0.206251i	−0.596421	+	0.802672i	$0.703411\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−2.62949	−	0.292893i	−0.993854	−	0.110703i
$7$	−2.62949	−	0.292893i	−0.993854	−	0.110703i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−0.652223			−0.206251
$11$	1.60525	+	1.60525i	0.484000	+	0.484000i	0.906406	−	0.422407i	$-0.138815\pi$
$11$	1.60525	+	1.60525i	0.484000	+	0.484000i	−0.422407	+	0.906406i	$0.638815\pi$
$12$	−1.00000			−0.288675
$13$	2.51608	+	2.58251i	0.697834	+	0.716260i
$13$	2.51608	+	2.58251i	0.697834	+	0.716260i
$14$	2.06644	−	1.65222i	0.552278	−	0.441575i
$15$	0.461191	−	0.461191i	0.119079	−	0.119079i
$16$	−1.00000			−0.250000
$17$	6.40303			1.55296			0.776482	−	0.630140i	$-0.217002\pi$
$17$	6.40303			1.55296			0.776482	+	0.630140i	$0.217002\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	2.52763	+	2.52763i	0.579878	+	0.579878i	0.934869	−	0.354992i	$-0.115516\pi$
$19$	2.52763	+	2.52763i	0.579878	+	0.579878i	−0.354992	+	0.934869i	$0.615516\pi$
$20$	0.461191	−	0.461191i	0.103125	−	0.103125i
$21$	−0.292893	+	2.62949i	−0.0639145	+	0.573802i
$22$	−2.27016			−0.484000
$23$		−	8.51280i		−	1.77504i	−0.460768	−	0.887521i	$-0.652426\pi$
$23$		−	8.51280i		−	1.77504i	0.460768	−	0.887521i	$-0.347574\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	4.57461i		−	0.914921i
$26$	−3.60525	−	0.0469777i	−0.707047	−	0.00921308i
$27$			1.00000i			0.192450i
$28$	−0.292893	+	2.62949i	−0.0553516	+	0.496927i
$29$	7.91120			1.46907			0.734537	−	0.678569i	$-0.237400\pi$
$29$	7.91120			1.46907			0.734537	+	0.678569i	$0.237400\pi$
$30$			0.652223i			0.119079i
$31$	0.922382	+	0.922382i	0.165665	+	0.165665i	0.785071	−	0.619406i	$-0.212627\pi$
$31$	0.922382	+	0.922382i	0.165665	+	0.165665i	−0.619406	+	0.785071i	$0.712627\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.60525	−	1.60525i	0.279437	−	0.279437i
$34$	−4.52763	+	4.52763i	−0.776482	+	0.776482i
$35$	−1.07762	−	1.34778i	−0.182151	−	0.227816i
$36$			1.00000i			0.166667i
$37$	−0.953022	−	0.953022i	−0.156676	−	0.156676i	0.624416	−	0.781092i	$-0.285337\pi$
$37$	−0.953022	−	0.953022i	−0.156676	−	0.156676i	−0.781092	+	0.624416i	$0.785337\pi$
$38$	−3.57461			−0.579878
$39$	2.58251	−	2.51608i	0.413533	−	0.402894i
$40$			0.652223i			0.103125i
$41$	−3.89486	−	3.89486i	−0.608275	−	0.608275i	0.334220	−	0.942495i	$-0.391527\pi$
$41$	−3.89486	−	3.89486i	−0.608275	−	0.608275i	−0.942495	+	0.334220i	$0.891527\pi$
$42$	−1.65222	−	2.06644i	−0.254944	−	0.318858i
$43$			4.17620i			0.636865i	0.947946	+	0.318433i	$0.103156\pi$
$43$			4.17620i			0.636865i	−0.947946	+	0.318433i	$0.896844\pi$
$44$	1.60525	−	1.60525i	0.242000	−	0.242000i
$45$	−0.461191	−	0.461191i	−0.0687503	−	0.0687503i
$46$	6.01946	+	6.01946i	0.887521	+	0.887521i
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$			1.00000i			0.144338i
$49$	6.82843	+	1.54032i	0.975490	+	0.220046i
$50$	3.23473	+	3.23473i	0.457461	+	0.457461i
$51$		−	6.40303i		−	0.896604i
$52$	2.58251	−	2.51608i	0.358130	−	0.348917i
$53$	9.10072			1.25008			0.625040	−	0.780593i	$-0.285083\pi$
$53$	9.10072			1.25008			0.625040	+	0.780593i	$0.285083\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$			1.48065i			0.199651i
$56$	−1.65222	−	2.06644i	−0.220788	−	0.276139i
$57$	2.52763	−	2.52763i	0.334792	−	0.334792i
$58$	−5.59406	+	5.59406i	−0.734537	+	0.734537i
$59$	1.17834	−	1.17834i	0.153407	−	0.153407i	−0.626231	−	0.779638i	$-0.715403\pi$
$59$	1.17834	−	1.17834i	0.153407	−	0.153407i	0.779638	+	0.626231i	$0.215403\pi$
$60$	−0.461191	−	0.461191i	−0.0595395	−	0.0595395i
$61$			14.4874i			1.85492i	0.373918	+	0.927462i	$0.378014\pi$
$61$			14.4874i			1.85492i	−0.373918	+	0.927462i	$0.621986\pi$
$62$	−1.30445			−0.165665
$63$	2.62949	+	0.292893i	0.331285	+	0.0369011i
$64$			1.00000i			0.125000i
$65$	−0.0306399	+	2.35142i	−0.00380041	+	0.291658i
$66$			2.27016i			0.279437i
$67$	3.47602	−	3.47602i	0.424663	−	0.424663i	−0.462142	−	0.886806i	$-0.652919\pi$
$67$	3.47602	−	3.47602i	0.424663	−	0.424663i	0.886806	+	0.462142i	$0.152919\pi$
$68$		−	6.40303i		−	0.776482i
$69$	−8.51280			−1.02482
$70$	1.71501	+	0.191032i	0.204983	+	0.0228327i
$71$	−8.29326	+	8.29326i	−0.984229	+	0.984229i	−0.999878	−	0.0156481i	$-0.995019\pi$
$71$	−8.29326	+	8.29326i	−0.984229	+	0.984229i	0.0156481	+	0.999878i	$0.495019\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−5.89851	+	5.89851i	−0.690368	+	0.690368i	−0.962313	−	0.271945i	$-0.912333\pi$
$73$	−5.89851	+	5.89851i	−0.690368	+	0.690368i	0.271945	+	0.962313i	$0.412333\pi$
$74$	1.34778			0.156676
$75$	−4.57461			−0.528230
$76$	2.52763	−	2.52763i	0.289939	−	0.289939i
$77$	−3.75081	−	4.69114i	−0.427444	−	0.534605i
$78$	−0.0469777	+	3.60525i	−0.00531917	+	0.408214i
$79$	−9.18813			−1.03375			−0.516873	−	0.856062i	$-0.672904\pi$
$79$	−9.18813			−1.03375			−0.516873	+	0.856062i	$0.672904\pi$
$80$	−0.461191	−	0.461191i	−0.0515627	−	0.0515627i
$81$	1.00000			0.111111
$82$	5.50817			0.608275
$83$	9.98882	+	9.98882i	1.09642	+	1.09642i	0.994826	+	0.101589i	$0.0323926\pi$
$83$	9.98882	+	9.98882i	1.09642	+	1.09642i	0.101589	+	0.994826i	$0.467607\pi$
$84$	2.62949	+	0.292893i	0.286901	+	0.0319573i
$85$	2.95302	+	2.95302i	0.320300	+	0.320300i
$86$	−2.95302	−	2.95302i	−0.318433	−	0.318433i
$87$		−	7.91120i		−	0.848170i
$88$			2.27016i			0.242000i
$89$	8.54709	−	8.54709i	0.905989	−	0.905989i	−0.0899564	−	0.995946i	$-0.528673\pi$
$89$	8.54709	−	8.54709i	0.905989	−	0.905989i	0.995946	+	0.0899564i	$0.0286728\pi$
$90$	0.652223			0.0687503
$91$	−5.85959	−	7.52763i	−0.614252	−	0.789110i
$92$	−8.51280			−0.887521
$93$	0.922382	−	0.922382i	0.0956466	−	0.0956466i
$94$			2.00000i			0.206284i
$95$			2.33144i			0.239201i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	0.272296	+	0.272296i	0.0276474	+	0.0276474i	0.720795	−	0.693148i	$-0.243777\pi$
$97$	0.272296	+	0.272296i	0.0276474	+	0.0276474i	−0.693148	+	0.720795i	$0.743777\pi$
$98$	−5.91760	+	3.73926i	−0.597768	+	0.377722i
$99$	−1.60525	−	1.60525i	−0.161333	−	0.161333i
$100$	−4.57461			−0.457461
$101$	−8.03892			−0.799902			−0.399951	−	0.916536i	$-0.630973\pi$
$101$	−8.03892			−0.799902			−0.399951	+	0.916536i	$0.630973\pi$
$102$	4.52763	+	4.52763i	0.448302	+	0.448302i
$103$	−7.62934			−0.751741			−0.375870	−	0.926672i	$-0.622656\pi$
$103$	−7.62934			−0.751741			−0.375870	+	0.926672i	$0.622656\pi$
$104$	−0.0469777	+	3.60525i	−0.00460654	+	0.353523i
$105$	−1.34778	+	1.07762i	−0.131530	+	0.105165i
$106$	−6.43518	+	6.43518i	−0.625040	+	0.625040i
$107$	−14.3986			−1.39197			−0.695984	−	0.718058i	$-0.745031\pi$
$107$	−14.3986			−1.39197			−0.695984	+	0.718058i	$0.745031\pi$
$108$	1.00000			0.0962250
$109$	−10.6815	+	10.6815i	−1.02310	+	1.02310i	−0.0233724	+	0.999727i	$0.507440\pi$
$109$	−10.6815	+	10.6815i	−1.02310	+	1.02310i	−0.999727	+	0.0233724i	$0.992560\pi$
$110$	−1.04698	−	1.04698i	−0.0998254	−	0.0998254i
$111$	−0.953022	+	0.953022i	−0.0904569	+	0.0904569i
$112$	2.62949	+	0.292893i	0.248463	+	0.0276758i
$113$	15.0256			1.41349			0.706745	−	0.707469i	$-0.250163\pi$
$113$	15.0256			1.41349			0.706745	+	0.707469i	$0.250163\pi$
$114$			3.57461i			0.334792i
$115$	3.92603	−	3.92603i	0.366104	−	0.366104i
$116$		−	7.91120i		−	0.734537i
$117$	−2.51608	−	2.58251i	−0.232611	−	0.238753i
$118$			1.66642i			0.153407i
$119$	−16.8367	−	1.87540i	−1.54342	−	0.171918i
$120$	0.652223			0.0595395
$121$		−	5.84638i		−	0.531489i
$122$	−10.2442	−	10.2442i	−0.927462	−	0.927462i
$123$	−3.89486	+	3.89486i	−0.351188	+	0.351188i
$124$	0.922382	−	0.922382i	0.0828324	−	0.0828324i
$125$	4.41572	−	4.41572i	0.394954	−	0.394954i
$126$	−2.06644	+	1.65222i	−0.184093	+	0.147192i
$127$		−	15.7970i		−	1.40176i	−0.713280	−	0.700879i	$-0.752791\pi$
$127$		−	15.7970i		−	1.40176i	0.713280	−	0.700879i	$-0.247209\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	4.17620			0.367694
$130$	−1.64104	−	1.68437i	−0.143929	−	0.147729i
$131$			1.75522i			0.153355i	0.997056	+	0.0766773i	$0.0244311\pi$
$131$			1.75522i			0.153355i	−0.997056	+	0.0766773i	$0.975569\pi$
$132$	−1.60525	−	1.60525i	−0.139719	−	0.139719i
$133$	−5.90604	−	7.38669i	−0.512119	−	0.640508i
$134$			4.91583i			0.424663i
$135$	−0.461191	+	0.461191i	−0.0396930	+	0.0396930i
$136$	4.52763	+	4.52763i	0.388241	+	0.388241i
$137$	−1.82994	−	1.82994i	−0.156342	−	0.156342i	0.624602	−	0.780944i	$-0.285261\pi$
$137$	−1.82994	−	1.82994i	−0.156342	−	0.156342i	−0.780944	+	0.624602i	$0.785261\pi$
$138$	6.01946	−	6.01946i	0.512410	−	0.512410i
$139$		−	13.8448i		−	1.17430i	−0.809479	−	0.587149i	$-0.800250\pi$
$139$		−	13.8448i		−	1.17430i	0.809479	−	0.587149i	$-0.199750\pi$
$140$	−1.34778	+	1.07762i	−0.113908	+	0.0910753i
$141$	−1.41421	−	1.41421i	−0.119098	−	0.119098i
$142$		−	11.7284i		−	0.984229i
$143$	−0.106647	+	8.18448i	−0.00891825	+	0.684421i
$144$	1.00000			0.0833333
$145$	3.64858	+	3.64858i	0.302998	+	0.302998i
$146$		−	8.34175i		−	0.690368i
$147$	1.54032	−	6.82843i	0.127043	−	0.563199i
$148$	−0.953022	+	0.953022i	−0.0783380	+	0.0783380i
$149$	−3.12824	+	3.12824i	−0.256276	+	0.256276i	−0.823537	−	0.567262i	$-0.808003\pi$
$149$	−3.12824	+	3.12824i	−0.256276	+	0.256276i	0.567262	+	0.823537i	$0.308003\pi$
$150$	3.23473	−	3.23473i	0.264115	−	0.264115i
$151$	11.5502	+	11.5502i	0.939943	+	0.939943i	0.998296	−	0.0583534i	$-0.0185850\pi$
$151$	11.5502	+	11.5502i	0.939943	+	0.939943i	−0.0583534	+	0.998296i	$0.518585\pi$
$152$			3.57461i			0.289939i
$153$	−6.40303			−0.517654
$154$	5.96936	+	0.664914i	0.481025	+	0.0535803i
$155$			0.850789i			0.0683370i
$156$	−2.51608	−	2.58251i	−0.201447	−	0.206766i
$157$		−	18.5294i		−	1.47880i	−0.673264	−	0.739402i	$-0.735108\pi$
$157$		−	18.5294i		−	1.47880i	0.673264	−	0.739402i	$-0.264892\pi$
$158$	6.49699	−	6.49699i	0.516873	−	0.516873i
$159$		−	9.10072i		−	0.721734i
$160$	0.652223			0.0515627
$161$	−2.49334	+	22.3843i	−0.196503	+	1.76413i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−13.1032	−	13.1032i	−1.02632	−	1.02632i	−0.999644	−	0.0266792i	$-0.991507\pi$
$163$	−13.1032	−	13.1032i	−1.02632	−	1.02632i	−0.0266792	−	0.999644i	$-0.508493\pi$
$164$	−3.89486	+	3.89486i	−0.304138	+	0.304138i
$165$	1.48065			0.115268
$166$	−14.1263			−1.09642
$167$	9.82552	−	9.82552i	0.760322	−	0.760322i	−0.216059	−	0.976380i	$-0.569320\pi$
$167$	9.82552	−	9.82552i	0.760322	−	0.760322i	0.976380	+	0.216059i	$0.0693202\pi$
$168$	−2.06644	+	1.65222i	−0.159429	+	0.127472i
$169$	−0.338732	+	12.9956i	−0.0260563	+	0.999660i
$170$	−4.17620			−0.320300
$171$	−2.52763	−	2.52763i	−0.193293	−	0.193293i
$172$	4.17620			0.318433
$173$	−10.9940			−0.835856			−0.417928	−	0.908480i	$-0.637244\pi$
$173$	−10.9940			−0.835856			−0.417928	+	0.908480i	$0.637244\pi$
$174$	5.59406	+	5.59406i	0.424085	+	0.424085i
$175$	−1.33987	+	12.0289i	−0.101285	+	0.909298i
$176$	−1.60525	−	1.60525i	−0.121000	−	0.121000i
$177$	−1.17834	−	1.17834i	−0.0885695	−	0.0885695i
$178$			12.0874i			0.905989i
$179$			2.54656i			0.190339i	0.995461	+	0.0951695i	$0.0303393\pi$
$179$			2.54656i			0.190339i	−0.995461	+	0.0951695i	$0.969661\pi$
$180$	−0.461191	+	0.461191i	−0.0343752	+	0.0343752i
$181$	−13.8933			−1.03268			−0.516339	−	0.856384i	$-0.672705\pi$
$181$	−13.8933			−1.03268			−0.516339	+	0.856384i	$0.672705\pi$
$182$	9.46619	+	1.17948i	0.701681	+	0.0874288i
$183$	14.4874			1.07094
$184$	6.01946	−	6.01946i	0.443760	−	0.443760i
$185$		−	0.879051i		−	0.0646291i
$186$			1.30445i			0.0956466i
$187$	10.2784	+	10.2784i	0.751634	+	0.751634i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$	0.292893	−	2.62949i	0.0213048	−	0.191267i
$190$	−1.64858	−	1.64858i	−0.119600	−	0.119600i
$191$	−10.2290			−0.740142			−0.370071	−	0.929004i	$-0.620667\pi$
$191$	−10.2290			−0.740142			−0.370071	+	0.929004i	$0.620667\pi$
$192$	1.00000			0.0721688
$193$	12.3940	+	12.3940i	0.892139	+	0.892139i	0.994724	−	0.102585i	$-0.0327115\pi$
$193$	12.3940	+	12.3940i	0.892139	+	0.892139i	−0.102585	+	0.994724i	$0.532712\pi$
$194$	−0.385084			−0.0276474
$195$	2.35142	+	0.0306399i	0.168389	+	0.00219417i
$196$	1.54032	−	6.82843i	0.110023	−	0.487745i
$197$	8.84638	−	8.84638i	0.630278	−	0.630278i	−0.317860	−	0.948138i	$-0.602964\pi$
$197$	8.84638	−	8.84638i	0.630278	−	0.630278i	0.948138	+	0.317860i	$0.102964\pi$
$198$	2.27016			0.161333
$199$	−7.40980			−0.525267			−0.262633	−	0.964896i	$-0.584591\pi$
$199$	−7.40980			−0.525267			−0.262633	+	0.964896i	$0.584591\pi$
$200$	3.23473	−	3.23473i	0.228730	−	0.228730i
$201$	−3.47602	−	3.47602i	−0.245179	−	0.245179i
$202$	5.68437	−	5.68437i	0.399951	−	0.399951i
$203$	−20.8024	−	2.31714i	−1.46004	−	0.162631i
$204$	−6.40303			−0.448302
$205$		−	3.59255i		−	0.250915i
$206$	5.39475	−	5.39475i	0.375870	−	0.375870i
$207$			8.51280i			0.591681i
$208$	−2.51608	−	2.58251i	−0.174458	−	0.179065i
$209$			8.11492i			0.561321i
$210$	0.191032	−	1.71501i	0.0131824	−	0.118347i
$211$	14.6299			1.00716			0.503581	−	0.863948i	$-0.332016\pi$
$211$	14.6299			1.00716			0.503581	+	0.863948i	$0.332016\pi$
$212$		−	9.10072i		−	0.625040i
$213$	8.29326	+	8.29326i	0.568245	+	0.568245i
$214$	10.1814	−	10.1814i	0.695984	−	0.695984i
$215$	−1.92603	+	1.92603i	−0.131354	+	0.131354i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−2.15524	−	2.69555i	−0.146307	−	0.182986i
$218$		−	15.1059i		−	1.02310i
$219$	5.89851	+	5.89851i	0.398584	+	0.398584i
$220$	1.48065			0.0998254
$221$	16.1105	+	16.5359i	1.08371	+	1.11233i
$222$		−	1.34778i		−	0.0904569i
$223$	−11.0574	−	11.0574i	−0.740458	−	0.740458i	0.232208	−	0.972666i	$-0.425405\pi$
$223$	−11.0574	−	11.0574i	−0.740458	−	0.740458i	−0.972666	+	0.232208i	$0.925405\pi$
$224$	−2.06644	+	1.65222i	−0.138070	+	0.110394i
$225$			4.57461i			0.304974i
$226$	−10.6247	+	10.6247i	−0.706745	+	0.706745i
$227$	9.31423	+	9.31423i	0.618207	+	0.618207i	0.945071	−	0.326864i	$-0.105992\pi$
$227$	9.31423	+	9.31423i	0.618207	+	0.618207i	−0.326864	+	0.945071i	$0.605992\pi$
$228$	−2.52763	−	2.52763i	−0.167396	−	0.167396i
$229$	−15.5860	+	15.5860i	−1.02995	+	1.02995i	−0.0304148	+	0.999537i	$0.509683\pi$
$229$	−15.5860	+	15.5860i	−1.02995	+	1.02995i	−0.999537	+	0.0304148i	$0.990317\pi$
$230$			5.55224i			0.366104i
$231$	−4.69114	+	3.75081i	−0.308654	+	0.246785i
$232$	5.59406	+	5.59406i	0.367268	+	0.367268i
$233$			14.4240i			0.944948i	0.881345	+	0.472474i	$0.156639\pi$
$233$			14.4240i			0.944948i	−0.881345	+	0.472474i	$0.843361\pi$
$234$	3.60525	+	0.0469777i	0.235682	+	0.00307103i
$235$	1.30445			0.0850927
$236$	−1.17834	−	1.17834i	−0.0767034	−	0.0767034i
$237$			9.18813i			0.596833i
$238$	13.2315	−	10.5792i	0.857668	−	0.685750i
$239$	3.83747	−	3.83747i	0.248225	−	0.248225i	−0.572017	−	0.820242i	$-0.693839\pi$
$239$	3.83747	−	3.83747i	0.248225	−	0.248225i	0.820242	+	0.572017i	$0.193839\pi$
$240$	−0.461191	+	0.461191i	−0.0297698	+	0.0297698i
$241$	−14.2110	+	14.2110i	−0.915412	+	0.915412i	−0.996691	−	0.0812794i	$-0.974099\pi$
$241$	−14.2110	+	14.2110i	−0.915412	+	0.915412i	0.0812794	+	0.996691i	$0.474099\pi$
$242$	4.13401	+	4.13401i	0.265744	+	0.265744i
$243$		−	1.00000i		−	0.0641500i
$244$	14.4874			0.927462
$245$	2.43883	+	3.85959i	0.155811	+	0.246580i
$246$		−	5.50817i		−	0.351188i
$247$	−0.167927	+	12.8873i	−0.0106849	+	0.820001i
$248$			1.30445i			0.0828324i
$249$	9.98882	−	9.98882i	0.633016	−	0.633016i
$250$			6.24478i			0.394954i
$251$	−5.39399			−0.340465			−0.170233	−	0.985404i	$-0.554452\pi$
$251$	−5.39399			−0.340465			−0.170233	+	0.985404i	$0.554452\pi$
$252$	0.292893	−	2.62949i	0.0184505	−	0.165642i
$253$	13.6651	−	13.6651i	0.859119	−	0.859119i
$254$	11.1702	+	11.1702i	0.700879	+	0.700879i
$255$	2.95302	−	2.95302i	0.184925	−	0.184925i
$256$	1.00000			0.0625000
$257$	4.38508			0.273534			0.136767	−	0.990603i	$-0.456329\pi$
$257$	4.38508			0.273534			0.136767	+	0.990603i	$0.456329\pi$
$258$	−2.95302	+	2.95302i	−0.183847	+	0.183847i
$259$	2.22683	+	2.78510i	0.138368	+	0.173057i
$260$	2.35142	+	0.0306399i	0.145829	+	0.00190021i
$261$	−7.91120			−0.489691
$262$	−1.24113	−	1.24113i	−0.0766773	−	0.0766773i
$263$	−12.4336			−0.766687			−0.383343	−	0.923606i	$-0.625227\pi$
$263$	−12.4336			−0.766687			−0.383343	+	0.923606i	$0.625227\pi$
$264$	2.27016			0.139719
$265$	4.19717	+	4.19717i	0.257830	+	0.257830i
$266$	9.39939	+	1.04698i	0.576313	+	0.0641943i
$267$	−8.54709	−	8.54709i	−0.523073	−	0.523073i
$268$	−3.47602	−	3.47602i	−0.212332	−	0.212332i
$269$			29.7839i			1.81596i	0.419016	+	0.907979i	$0.362375\pi$
$269$			29.7839i			1.81596i	−0.419016	+	0.907979i	$0.637625\pi$
$270$		−	0.652223i		−	0.0396930i
$271$	14.7173	−	14.7173i	0.894010	−	0.894010i	−0.100888	−	0.994898i	$-0.532168\pi$
$271$	14.7173	−	14.7173i	0.894010	−	0.894010i	0.994898	+	0.100888i	$0.0321682\pi$
$272$	−6.40303			−0.388241
$273$	−7.52763	+	5.85959i	−0.455593	+	0.354639i
$274$	2.58792			0.156342
$275$	7.34336	−	7.34336i	0.442821	−	0.442821i
$276$			8.51280i			0.512410i
$277$		−	24.1271i		−	1.44965i	−0.688930	−	0.724827i	$-0.741919\pi$
$277$		−	24.1271i		−	1.44965i	0.688930	−	0.724827i	$-0.258081\pi$
$278$	9.78973	+	9.78973i	0.587149	+	0.587149i
$279$	−0.922382	−	0.922382i	−0.0552216	−	0.0552216i
$280$	0.191032	−	1.71501i	0.0114163	−	0.102492i
$281$	−7.70534	−	7.70534i	−0.459662	−	0.459662i	0.438882	−	0.898545i	$-0.355374\pi$
$281$	−7.70534	−	7.70534i	−0.459662	−	0.459662i	−0.898545	+	0.438882i	$0.855374\pi$
$282$	2.00000			0.119098
$283$	−6.39133			−0.379925			−0.189962	−	0.981791i	$-0.560837\pi$
$283$	−6.39133			−0.379925			−0.189962	+	0.981791i	$0.560837\pi$
$284$	8.29326	+	8.29326i	0.492115	+	0.492115i
$285$	2.33144			0.138103
$286$	−5.71189	−	5.86271i	−0.337751	−	0.346670i
$287$	9.10072	+	11.3823i	0.537199	+	0.671875i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	23.9988			1.41170
$290$	−5.15987			−0.302998
$291$	0.272296	−	0.272296i	0.0159622	−	0.0159622i
$292$	5.89851	+	5.89851i	0.345184	+	0.345184i
$293$	8.93819	−	8.93819i	0.522175	−	0.522175i	−0.396053	−	0.918228i	$-0.629620\pi$
$293$	8.93819	−	8.93819i	0.522175	−	0.522175i	0.918228	+	0.396053i	$0.129620\pi$
$294$	3.73926	+	5.91760i	0.218078	+	0.345121i
$295$	1.08688			0.0632806
$296$		−	1.34778i		−	0.0783380i
$297$	−1.60525	+	1.60525i	−0.0931458	+	0.0931458i
$298$		−	4.42400i		−	0.256276i
$299$	21.9844	−	21.4188i	1.27139	−	1.23868i
$300$			4.57461i			0.264115i
$301$	1.22318	−	10.9813i	0.0705030	−	0.632951i
$302$	−16.3345			−0.939943
$303$			8.03892i			0.461824i
$304$	−2.52763	−	2.52763i	−0.144969	−	0.144969i
$305$	−6.68147	+	6.68147i	−0.382580	+	0.382580i
$306$	4.52763	−	4.52763i	0.258827	−	0.258827i
$307$	1.27177	−	1.27177i	0.0725838	−	0.0725838i	−0.669883	−	0.742467i	$-0.733656\pi$
$307$	1.27177	−	1.27177i	0.0725838	−	0.0725838i	0.742467	+	0.669883i	$0.233656\pi$
$308$	−4.69114	+	3.75081i	−0.267303	+	0.213722i
$309$			7.62934i			0.434018i
$310$	−0.601599	−	0.601599i	−0.0341685	−	0.0341685i
$311$	−1.52201			−0.0863053			−0.0431527	−	0.999068i	$-0.513740\pi$
$311$	−1.52201			−0.0863053			−0.0431527	+	0.999068i	$0.513740\pi$
$312$	3.60525	+	0.0469777i	0.204107	+	0.00265959i
$313$			3.48506i			0.196987i	0.995138	+	0.0984937i	$0.0314024\pi$
$313$			3.48506i			0.196987i	−0.995138	+	0.0984937i	$0.968598\pi$
$314$	13.1022	+	13.1022i	0.739402	+	0.739402i
$315$	1.07762	+	1.34778i	0.0607169	+	0.0759386i
$316$			9.18813i			0.516873i
$317$	3.61566	−	3.61566i	0.203076	−	0.203076i	−0.598241	−	0.801316i	$-0.704133\pi$
$317$	3.61566	−	3.61566i	0.203076	−	0.203076i	0.801316	+	0.598241i	$0.204133\pi$
$318$	6.43518	+	6.43518i	0.360867	+	0.360867i
$319$	12.6994	+	12.6994i	0.711031	+	0.711031i
$320$	−0.461191	+	0.461191i	−0.0257814	+	0.0257814i
$321$			14.3986i			0.803653i
$322$	−14.0650	−	17.5912i	−0.783814	−	0.980317i
$323$	16.1845	+	16.1845i	0.900529	+	0.900529i
$324$		−	1.00000i		−	0.0555556i
$325$	11.8140	−	11.5101i	0.655321	−	0.638463i
$326$	18.5307			1.02632
$327$	10.6815	+	10.6815i	0.590687	+	0.590687i
$328$		−	5.50817i		−	0.304138i
$329$	−4.13287	+	3.30445i	−0.227853	+	0.182180i
$330$	−1.04698	+	1.04698i	−0.0576342	+	0.0576342i
$331$	4.50162	−	4.50162i	0.247431	−	0.247431i	−0.572484	−	0.819916i	$-0.694020\pi$
$331$	4.50162	−	4.50162i	0.247431	−	0.247431i	0.819916	+	0.572484i	$0.194020\pi$
$332$	9.98882	−	9.98882i	0.548208	−	0.548208i
$333$	0.953022	+	0.953022i	0.0522253	+	0.0522253i
$334$			13.8954i			0.760322i
$335$	3.20622			0.175174
$336$	0.292893	−	2.62949i	0.0159786	−	0.143450i
$337$		−	20.7331i		−	1.12940i	−0.825295	−	0.564701i	$-0.808991\pi$
$337$		−	20.7331i		−	1.12940i	0.825295	−	0.564701i	$-0.191009\pi$
$338$	−8.94975	−	9.42879i	−0.486802	−	0.512858i
$339$		−	15.0256i		−	0.816079i
$340$	2.95302	−	2.95302i	0.160150	−	0.160150i
$341$			2.96130i			0.160363i
$342$	3.57461			0.193293
$343$	−17.5041	−	6.05025i	−0.945134	−	0.326683i
$344$	−2.95302	+	2.95302i	−0.159216	+	0.159216i
$345$	−3.92603	−	3.92603i	−0.211370	−	0.211370i
$346$	7.77391	−	7.77391i	0.417928	−	0.417928i
$347$	0.161276			0.00865778			0.00432889	−	0.999991i	$-0.498622\pi$
$347$	0.161276			0.00865778			0.00432889	+	0.999991i	$0.498622\pi$
$348$	−7.91120			−0.424085
$349$	7.17995	−	7.17995i	0.384334	−	0.384334i	−0.488327	−	0.872661i	$-0.662393\pi$
$349$	7.17995	−	7.17995i	0.384334	−	0.384334i	0.872661	+	0.488327i	$0.162393\pi$
$350$	−7.55827	−	9.45313i	−0.404006	−	0.505291i
$351$	−2.58251	+	2.51608i	−0.137844	+	0.134298i
$352$	2.27016			0.121000
$353$	−9.44711	−	9.44711i	−0.502819	−	0.502819i	0.409494	−	0.912313i	$-0.365705\pi$
$353$	−9.44711	−	9.44711i	−0.502819	−	0.502819i	−0.912313	+	0.409494i	$0.865705\pi$
$354$	1.66642			0.0885695
$355$	−7.64956			−0.405997
$356$	−8.54709	−	8.54709i	−0.452995	−	0.452995i
$357$	−1.87540	+	16.8367i	−0.0992569	+	0.891093i
$358$	−1.80069	−	1.80069i	−0.0951695	−	0.0951695i
$359$	−19.1933	−	19.1933i	−1.01298	−	1.01298i	−0.999915	−	0.0130682i	$-0.995840\pi$
$359$	−19.1933	−	19.1933i	−1.01298	−	1.01298i	−0.0130682	−	0.999915i	$-0.504160\pi$
$360$		−	0.652223i		−	0.0343752i
$361$		−	6.22220i		−	0.327484i
$362$	9.82401	−	9.82401i	0.516339	−	0.516339i
$363$	−5.84638			−0.306855
$364$	−7.52763	+	5.85959i	−0.394555	+	0.307126i
$365$	−5.44068			−0.284778
$366$	−10.2442	+	10.2442i	−0.535470	+	0.535470i
$367$			24.3142i			1.26919i	0.772844	+	0.634596i	$0.218834\pi$
$367$			24.3142i			1.26919i	−0.772844	+	0.634596i	$0.781166\pi$
$368$			8.51280i			0.443760i
$369$	3.89486	+	3.89486i	0.202758	+	0.202758i
$370$	0.621583	+	0.621583i	0.0323146	+	0.0323146i
$371$	−23.9303	−	2.66554i	−1.24240	−	0.138388i
$372$	−0.922382	−	0.922382i	−0.0478233	−	0.0478233i
$373$	9.74654			0.504657			0.252328	−	0.967642i	$-0.418804\pi$
$373$	9.74654			0.504657			0.252328	+	0.967642i	$0.418804\pi$
$374$	−14.5359			−0.751634
$375$	−4.41572	−	4.41572i	−0.228027	−	0.228027i
$376$	2.00000			0.103142
$377$	19.9052	+	20.4308i	1.02517	+	1.05224i
$378$	1.65222	+	2.06644i	0.0849812	+	0.106286i
$379$	14.5776	−	14.5776i	0.748802	−	0.748802i	−0.225452	−	0.974254i	$-0.572386\pi$
$379$	14.5776	−	14.5776i	0.748802	−	0.748802i	0.974254	+	0.225452i	$0.0723859\pi$
$380$	2.33144			0.119600
$381$	−15.7970			−0.809306
$382$	7.23297	−	7.23297i	0.370071	−	0.370071i
$383$	−20.8642	−	20.8642i	−1.06611	−	1.06611i	−0.997654	−	0.0684580i	$-0.978192\pi$
$383$	−20.8642	−	20.8642i	−1.06611	−	1.06611i	−0.0684580	−	0.997654i	$-0.521808\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	0.433672	−	3.89335i	0.0221020	−	0.198424i
$386$	−17.5277			−0.892139
$387$		−	4.17620i		−	0.212288i
$388$	0.272296	−	0.272296i	0.0138237	−	0.0138237i
$389$		−	6.09321i		−	0.308938i	−0.987998	−	0.154469i	$-0.950633\pi$
$389$		−	6.09321i		−	0.308938i	0.987998	−	0.154469i	$-0.0493667\pi$
$390$	−1.68437	+	1.64104i	−0.0852915	+	0.0830974i
$391$		−	54.5077i		−	2.75657i
$392$	3.73926	+	5.91760i	0.188861	+	0.298884i
$393$	1.75522			0.0885393
$394$			12.5107i			0.630278i
$395$	−4.23748	−	4.23748i	−0.213211	−	0.213211i
$396$	−1.60525	+	1.60525i	−0.0806666	+	0.0806666i
$397$	−26.9792	+	26.9792i	−1.35405	+	1.35405i	−0.472972	+	0.881077i	$0.656819\pi$
$397$	−26.9792	+	26.9792i	−1.35405	+	1.35405i	−0.881077	+	0.472972i	$0.843181\pi$
$398$	5.23952	−	5.23952i	0.262633	−	0.262633i
$399$	−7.38669	+	5.90604i	−0.369797	+	0.295672i
$400$			4.57461i			0.228730i
$401$	21.4604	+	21.4604i	1.07168	+	1.07168i	0.997224	+	0.0744583i	$0.0237228\pi$
$401$	21.4604	+	21.4604i	1.07168	+	1.07168i	0.0744583	+	0.997224i	$0.476277\pi$
$402$	4.91583			0.245179
$403$	−0.0612798	+	4.70285i	−0.00305256	+	0.234265i
$404$			8.03892i			0.399951i
$405$	0.461191	+	0.461191i	0.0229168	+	0.0229168i
$406$	16.3480	−	13.0711i	0.811337	−	0.648706i
$407$		−	3.05967i		−	0.151662i
$408$	4.52763	−	4.52763i	0.224151	−	0.224151i
$409$	4.20898	+	4.20898i	0.208121	+	0.208121i	0.803468	−	0.595348i	$-0.202986\pi$
$409$	4.20898	+	4.20898i	0.208121	+	0.208121i	−0.595348	+	0.803468i	$0.702986\pi$
$410$	2.54032	+	2.54032i	0.125457	+	0.125457i
$411$	−1.82994	+	1.82994i	−0.0902642	+	0.0902642i
$412$			7.62934i			0.375870i
$413$	−3.44356	+	2.75330i	−0.169447	+	0.135481i
$414$	−6.01946	−	6.01946i	−0.295840	−	0.295840i
$415$			9.21351i			0.452273i
$416$	3.60525	+	0.0469777i	0.176762	+	0.00230327i
$417$	−13.8448			−0.677981
$418$	−5.73812	−	5.73812i	−0.280661	−	0.280661i
$419$			3.78685i			0.185000i	0.995713	+	0.0924998i	$0.0294858\pi$
$419$			3.78685i			0.185000i	−0.995713	+	0.0924998i	$0.970514\pi$
$420$	1.07762	+	1.34778i	0.0525824	+	0.0657648i
$421$	−16.2730	+	16.2730i	−0.793099	+	0.793099i	−0.981997	−	0.188897i	$-0.939509\pi$
$421$	−16.2730	+	16.2730i	−0.793099	+	0.793099i	0.188897	+	0.981997i	$0.439509\pi$
$422$	−10.3449	+	10.3449i	−0.503581	+	0.503581i
$423$	−1.41421	+	1.41421i	−0.0687614	+	0.0687614i
$424$	6.43518	+	6.43518i	0.312520	+	0.312520i
$425$		−	29.2913i		−	1.42084i
$426$	−11.7284			−0.568245
$427$	4.24327	−	38.0945i	0.205346	−	1.84352i
$428$			14.3986i			0.695984i
$429$	8.18448	+	0.106647i	0.395151	+	0.00514895i
$430$		−	2.72382i		−	0.131354i
$431$	−17.7084	+	17.7084i	−0.852982	+	0.852982i	−0.990499	−	0.137518i	$-0.956088\pi$
$431$	−17.7084	+	17.7084i	−0.852982	+	0.852982i	0.137518	+	0.990499i	$0.456088\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−13.2092			−0.634796			−0.317398	−	0.948292i	$-0.602809\pi$
$433$	−13.2092			−0.634796			−0.317398	+	0.948292i	$0.602809\pi$
$434$	3.43003	+	0.382063i	0.164647	+	0.0183396i
$435$	3.64858	−	3.64858i	0.174936	−	0.174936i
$436$	10.6815	+	10.6815i	0.511550	+	0.511550i
$437$	21.5172	−	21.5172i	1.02931	−	1.02931i
$438$	−8.34175			−0.398584
$439$	−27.2638			−1.30123			−0.650616	−	0.759407i	$-0.725489\pi$
$439$	−27.2638			−1.30123			−0.650616	+	0.759407i	$0.725489\pi$
$440$	−1.04698	+	1.04698i	−0.0499127	+	0.0499127i
$441$	−6.82843	−	1.54032i	−0.325163	−	0.0733485i
$442$	−23.0845	−	0.300799i	−1.09802	−	0.0143076i
$443$	22.3627			1.06248			0.531242	−	0.847220i	$-0.321725\pi$
$443$	22.3627			1.06248			0.531242	+	0.847220i	$0.321725\pi$
$444$	0.953022	+	0.953022i	0.0452284	+	0.0452284i
$445$	7.88368			0.373722
$446$	15.6375			0.740458
$447$	3.12824	+	3.12824i	0.147961	+	0.147961i
$448$	0.292893	−	2.62949i	0.0138379	−	0.124232i
$449$	3.36702	+	3.36702i	0.158899	+	0.158899i	0.782079	−	0.623179i	$-0.214159\pi$
$449$	3.36702	+	3.36702i	0.158899	+	0.158899i	−0.623179	+	0.782079i	$0.714159\pi$
$450$	−3.23473	−	3.23473i	−0.152487	−	0.152487i
$451$		−	12.5044i		−	0.588810i
$452$		−	15.0256i		−	0.706745i
$453$	11.5502	−	11.5502i	0.542676	−	0.542676i
$454$	−13.1723			−0.618207
$455$	0.769283	−	6.17407i	0.0360646	−	0.289445i
$456$	3.57461			0.167396
$457$	−12.5030	+	12.5030i	−0.584866	+	0.584866i	−0.936237	−	0.351370i	$-0.885716\pi$
$457$	−12.5030	+	12.5030i	−0.584866	+	0.584866i	0.351370	+	0.936237i	$0.385716\pi$
$458$		−	22.0419i		−	1.02995i
$459$			6.40303i			0.298868i
$460$	−3.92603	−	3.92603i	−0.183052	−	0.183052i
$461$	4.03719	+	4.03719i	0.188031	+	0.188031i	0.794844	−	0.606814i	$-0.207553\pi$
$461$	4.03719	+	4.03719i	0.188031	+	0.188031i	−0.606814	+	0.794844i	$0.707553\pi$
$462$	0.664914	−	5.96936i	0.0309346	−	0.277720i
$463$	−12.8250	−	12.8250i	−0.596028	−	0.596028i	0.343225	−	0.939253i	$-0.388481\pi$
$463$	−12.8250	−	12.8250i	−0.596028	−	0.596028i	−0.939253	+	0.343225i	$0.888481\pi$
$464$	−7.91120			−0.367268
$465$	0.850789			0.0394544
$466$	−10.1993	−	10.1993i	−0.472474	−	0.472474i
$467$	17.0280			0.787964			0.393982	−	0.919118i	$-0.371097\pi$
$467$	17.0280			0.787964			0.393982	+	0.919118i	$0.371097\pi$
$468$	−2.58251	+	2.51608i	−0.119377	+	0.116306i
$469$	−10.1583	+	8.12205i	−0.469065	+	0.375041i
$470$	−0.922382	+	0.922382i	−0.0425463	+	0.0425463i
$471$	−18.5294			−0.853788
$472$	1.66642			0.0767034
$473$	−6.70383	+	6.70383i	−0.308243	+	0.308243i
$474$	−6.49699	−	6.49699i	−0.298417	−	0.298417i
$475$	11.5629	−	11.5629i	0.530542	−	0.530542i
$476$	−1.87540	+	16.8367i	−0.0859590	+	0.771709i
$477$	−9.10072			−0.416693
$478$			5.42701i			0.248225i
$479$	−22.7406	+	22.7406i	−1.03905	+	1.03905i	−0.0398390	+	0.999206i	$0.512685\pi$
$479$	−22.7406	+	22.7406i	−1.03905	+	1.03905i	−0.999206	+	0.0398390i	$0.987315\pi$
$480$		−	0.652223i		−	0.0297698i
$481$	0.0633154	−	4.85907i	0.00288693	−	0.221554i
$482$		−	20.0974i		−	0.915412i
$483$	22.3843	+	2.49334i	1.01852	+	0.113451i
$484$	−5.84638			−0.265744
$485$			0.251161i			0.0114046i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−8.40745	+	8.40745i	−0.380978	+	0.380978i	−0.871454	−	0.490477i	$-0.836823\pi$
$487$	−8.40745	+	8.40745i	−0.380978	+	0.380978i	0.490477	+	0.871454i	$0.336823\pi$
$488$	−10.2442	+	10.2442i	−0.463731	+	0.463731i
$489$	−13.1032	+	13.1032i	−0.592548	+	0.592548i
$490$	−4.45366	−	1.00463i	−0.201196	−	0.0453846i
$491$		−	12.3150i		−	0.555767i	−0.960615	−	0.277884i	$-0.910367\pi$
$491$		−	12.3150i		−	0.555767i	0.960615	−	0.277884i	$-0.0896329\pi$
$492$	3.89486	+	3.89486i	0.175594	+	0.175594i
$493$	50.6557			2.28142
$494$	−8.99398	−	9.23146i	−0.404658	−	0.415343i
$495$		−	1.48065i		−	0.0665503i
$496$	−0.922382	−	0.922382i	−0.0414162	−	0.0414162i
$497$	24.2361	−	19.3780i	1.08714	−	0.869222i
$498$			14.1263i			0.633016i
$499$	4.13266	−	4.13266i	0.185003	−	0.185003i	−0.608529	−	0.793532i	$-0.708240\pi$
$499$	4.13266	−	4.13266i	0.185003	−	0.185003i	0.793532	+	0.608529i	$0.208240\pi$
$500$	−4.41572	−	4.41572i	−0.197477	−	0.197477i
$501$	−9.82552	−	9.82552i	−0.438972	−	0.438972i
$502$	3.81412	−	3.81412i	0.170233	−	0.170233i
$503$			32.1557i			1.43375i	0.697201	+	0.716875i	$0.254428\pi$
$503$			32.1557i			1.43375i	−0.697201	+	0.716875i	$0.745572\pi$
$504$	1.65222	+	2.06644i	0.0735959	+	0.0920464i
$505$	−3.70748	−	3.70748i	−0.164981	−	0.164981i
$506$			19.3254i			0.859119i
$507$	12.9956	+	0.338732i	0.577154	+	0.0150436i
$508$	−15.7970			−0.700879
$509$	−25.9435	−	25.9435i	−1.14992	−	1.14992i	−0.986567	−	0.163357i	$-0.947768\pi$
$509$	−25.9435	−	25.9435i	−1.14992	−	1.14992i	−0.163357	−	0.986567i	$-0.552232\pi$
$510$			4.17620i			0.184925i
$511$	17.2377	−	13.7824i	0.762551	−	0.609699i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.52763	+	2.52763i	−0.111597	+	0.111597i
$514$	−3.10072	+	3.10072i	−0.136767	+	0.136767i
$515$	−3.51858	−	3.51858i	−0.155047	−	0.155047i
$516$		−	4.17620i		−	0.183847i
$517$	4.54032			0.199683
$518$	−3.54397	−	0.394755i	−0.155713	−	0.0173445i
$519$			10.9940i			0.482582i
$520$	−1.68437	+	1.64104i	−0.0738646	+	0.0719644i
$521$			3.85949i			0.169087i	0.996420	+	0.0845437i	$0.0269433\pi$
$521$			3.85949i			0.169087i	−0.996420	+	0.0845437i	$0.973057\pi$
$522$	5.59406	−	5.59406i	0.244846	−	0.244846i
$523$			36.3670i			1.59022i	0.606467	+	0.795109i	$0.292586\pi$
$523$			36.3670i			1.59022i	−0.606467	+	0.795109i	$0.707414\pi$
$524$	1.75522			0.0766773
$525$	12.0289	+	1.33987i	0.524983	+	0.0584768i
$526$	8.79186	−	8.79186i	0.383343	−	0.383343i
$527$	5.90604	+	5.90604i	0.257271	+	0.257271i
$528$	−1.60525	+	1.60525i	−0.0698593	+	0.0698593i
$529$	−49.4678			−2.15077
$530$	−5.93570			−0.257830
$531$	−1.17834	+	1.17834i	−0.0511356	+	0.0511356i
$532$	−7.38669	+	5.90604i	−0.320254	+	0.256060i
$533$	0.258761	−	19.8583i	0.0112082	−	0.860158i
$534$	12.0874			0.523073
$535$	−6.64052	−	6.64052i	−0.287095	−	0.287095i
$536$	4.91583			0.212332
$537$	2.54656			0.109892
$538$	−21.0604	−	21.0604i	−0.907979	−	0.907979i
$539$	8.48871	+	13.4339i	0.365635	+	0.578639i
$540$	0.461191	+	0.461191i	0.0198465	+	0.0198465i
$541$	18.4800	+	18.4800i	0.794518	+	0.794518i	0.982225	−	0.187707i	$-0.0601055\pi$
$541$	18.4800	+	18.4800i	0.794518	+	0.794518i	−0.187707	+	0.982225i	$0.560105\pi$
$542$			20.8134i			0.894010i
$543$			13.8933i			0.596217i
$544$	4.52763	−	4.52763i	0.194120	−	0.194120i
$545$	−9.85240			−0.422030
$546$	1.17948	−	9.46619i	0.0504770	−	0.405116i
$547$	3.22661			0.137960			0.0689800	−	0.997618i	$-0.478026\pi$
$547$	3.22661			0.137960			0.0689800	+	0.997618i	$0.478026\pi$
$548$	−1.82994	+	1.82994i	−0.0781711	+	0.0781711i
$549$		−	14.4874i		−	0.618308i
$550$			10.3851i			0.442821i
$551$	19.9966	+	19.9966i	0.851883	+	0.851883i
$552$	−6.01946	−	6.01946i	−0.256205	−	0.256205i
$553$	24.1601	+	2.69114i	1.02739	+	0.114439i
$554$	17.0604	+	17.0604i	0.724827	+	0.724827i
$555$	−0.879051			−0.0373136
$556$	−13.8448			−0.587149
$557$	−27.1310	−	27.1310i	−1.14958	−	1.14958i	−0.986636	−	0.162939i	$-0.947903\pi$
$557$	−27.1310	−	27.1310i	−1.14958	−	1.14958i	−0.162939	−	0.986636i	$-0.552097\pi$
$558$	1.30445			0.0552216
$559$	−10.7851	+	10.5076i	−0.456161	+	0.444426i
$560$	1.07762	+	1.34778i	0.0455377	+	0.0569540i
$561$	10.2784	−	10.2784i	0.433956	−	0.433956i
$562$	10.8970			0.459662
$563$	2.30304			0.0970614			0.0485307	−	0.998822i	$-0.484546\pi$
$563$	2.30304			0.0970614			0.0485307	+	0.998822i	$0.484546\pi$
$564$	−1.41421	+	1.41421i	−0.0595491	+	0.0595491i
$565$	6.92968	+	6.92968i	0.291534	+	0.291534i
$566$	4.51935	−	4.51935i	0.189962	−	0.189962i
$567$	−2.62949	−	0.292893i	−0.110428	−	0.0123004i
$568$	−11.7284			−0.492115
$569$			5.19115i			0.217624i	0.994062	+	0.108812i	$0.0347047\pi$
$569$			5.19115i			0.217624i	−0.994062	+	0.108812i	$0.965295\pi$
$570$	−1.64858	+	1.64858i	−0.0690513	+	0.0690513i
$571$			11.8508i			0.495941i	0.968768	+	0.247970i	$0.0797636\pi$
$571$			11.8508i			0.495941i	−0.968768	+	0.247970i	$0.920236\pi$
$572$	8.18448	+	0.106647i	0.342210	+	0.00445913i
$573$			10.2290i			0.427321i
$574$	−14.4837	−	1.61331i	−0.604537	−	0.0673381i
$575$	−38.9427			−1.62402
$576$		−	1.00000i		−	0.0416667i
$577$	−29.5340	−	29.5340i	−1.22952	−	1.22952i	−0.964147	−	0.265369i	$-0.914506\pi$
$577$	−29.5340	−	29.5340i	−1.22952	−	1.22952i	−0.265369	−	0.964147i	$-0.585494\pi$
$578$	−16.9697	+	16.9697i	−0.705848	+	0.705848i
$579$	12.3940	−	12.3940i	0.515077	−	0.515077i
$580$	3.64858	−	3.64858i	0.151499	−	0.151499i
$581$	−23.3398	−	29.1911i	−0.968299	−	1.21105i
$582$			0.385084i			0.0159622i
$583$	14.6089	+	14.6089i	0.605038	+	0.605038i
$584$	−8.34175			−0.345184
$585$	0.0306399	−	2.35142i	0.00126680	−	0.0972194i
$586$			12.6405i			0.522175i
$587$	−11.2384	−	11.2384i	−0.463857	−	0.463857i	0.436060	−	0.899917i	$-0.356373\pi$
$587$	−11.2384	−	11.2384i	−0.463857	−	0.463857i	−0.899917	+	0.436060i	$0.856373\pi$
$588$	−6.82843	−	1.54032i	−0.281600	−	0.0635217i
$589$			4.66288i			0.192131i
$590$	−0.768540	+	0.768540i	−0.0316403	+	0.0316403i
$591$	−8.84638	−	8.84638i	−0.363891	−	0.363891i
$592$	0.953022	+	0.953022i	0.0391690	+	0.0391690i
$593$	7.99323	−	7.99323i	0.328243	−	0.328243i	−0.523675	−	0.851918i	$-0.675439\pi$
$593$	7.99323	−	7.99323i	0.328243	−	0.328243i	0.851918	+	0.523675i	$0.175439\pi$
$594$		−	2.27016i		−	0.0931458i
$595$	−6.90002	−	8.62986i	−0.282873	−	0.353790i
$596$	3.12824	+	3.12824i	0.128138	+	0.128138i
$597$			7.40980i			0.303263i
$598$	−0.399911	+	30.6907i	−0.0163536	+	1.25504i
$599$	25.0503			1.02353			0.511764	−	0.859126i	$-0.328992\pi$
$599$	25.0503			1.02353			0.511764	+	0.859126i	$0.328992\pi$
$600$	−3.23473	−	3.23473i	−0.132057	−	0.132057i
$601$			11.5478i			0.471046i	0.971869	+	0.235523i	$0.0756803\pi$
$601$			11.5478i			0.471046i	−0.971869	+	0.235523i	$0.924320\pi$
$602$	6.90002	+	8.62986i	0.281224	+	0.351727i
$603$	−3.47602	+	3.47602i	−0.141554	+	0.141554i
$604$	11.5502	−	11.5502i	0.469971	−	0.469971i
$605$	2.69630	−	2.69630i	0.109620	−	0.109620i
$606$	−5.68437	−	5.68437i	−0.230912	−	0.230912i
$607$			15.2350i			0.618369i	0.951002	+	0.309185i	$0.100056\pi$
$607$			15.2350i			0.618369i	−0.951002	+	0.309185i	$0.899944\pi$
$608$	3.57461			0.144969
$609$	−2.31714	+	20.8024i	−0.0938951	+	0.842957i
$610$		−	9.44903i		−	0.382580i
$611$	7.21049	+	0.0939553i	0.291705	+	0.00380103i
$612$			6.40303i			0.258827i
$613$	11.5903	−	11.5903i	0.468129	−	0.468129i	−0.433179	−	0.901308i	$-0.642608\pi$
$613$	11.5903	−	11.5903i	0.468129	−	0.468129i	0.901308	+	0.433179i	$0.142608\pi$
$614$			1.79855i			0.0725838i
$615$	−3.59255			−0.144866
$616$	0.664914	−	5.96936i	0.0267902	−	0.240512i
$617$	14.5420	−	14.5420i	0.585441	−	0.585441i	−0.350952	−	0.936393i	$-0.614142\pi$
$617$	14.5420	−	14.5420i	0.585441	−	0.585441i	0.936393	+	0.350952i	$0.114142\pi$
$618$	−5.39475	−	5.39475i	−0.217009	−	0.217009i
$619$	−7.62482	+	7.62482i	−0.306467	+	0.306467i	−0.843538	−	0.537070i	$-0.819531\pi$
$619$	−7.62482	+	7.62482i	−0.306467	+	0.306467i	0.537070	+	0.843538i	$0.319531\pi$
$620$	0.850789			0.0341685
$621$	8.51280			0.341607
$622$	1.07622	−	1.07622i	0.0431527	−	0.0431527i
$623$	−24.9779	+	19.9711i	−1.00072	+	0.800125i
$624$	−2.58251	+	2.51608i	−0.103383	+	0.100724i
$625$	−18.8000			−0.752002
$626$	−2.46431	−	2.46431i	−0.0984937	−	0.0984937i
$627$	8.11492			0.324079
$628$	−18.5294			−0.739402
$629$	−6.10223	−	6.10223i	−0.243312	−	0.243312i
$630$	−1.71501	−	0.191032i	−0.0683278	−	0.00761088i
$631$	28.8742	+	28.8742i	1.14946	+	1.14946i	0.986658	+	0.162807i	$0.0520548\pi$
$631$	28.8742	+	28.8742i	1.14946	+	1.14946i	0.162807	+	0.986658i	$0.447945\pi$
$632$	−6.49699	−	6.49699i	−0.258436	−	0.258436i
$633$		−	14.6299i		−	0.581485i
$634$			5.11331i			0.203076i
$635$	7.28545	−	7.28545i	0.289114	−	0.289114i
$636$	−9.10072			−0.360867
$637$	13.2029	+	21.5101i	0.523120	+	0.852259i
$638$	−17.9597			−0.711031
$639$	8.29326	−	8.29326i	0.328076	−	0.328076i
$640$		−	0.652223i		−	0.0257814i
$641$		−	13.9110i		−	0.549453i	−0.961522	−	0.274726i	$-0.911413\pi$
$641$		−	13.9110i		−	0.549453i	0.961522	−	0.274726i	$-0.0885873\pi$
$642$	−10.1814	−	10.1814i	−0.401826	−	0.401826i
$643$	31.6768	+	31.6768i	1.24921	+	1.24921i	0.956068	+	0.293144i	$0.0947017\pi$
$643$	31.6768	+	31.6768i	1.24921	+	1.24921i	0.293144	+	0.956068i	$0.405298\pi$
$644$	22.3843	+	2.49334i	0.882066	+	0.0982514i
$645$	1.92603	+	1.92603i	0.0758373	+	0.0758373i
$646$	−22.8883			−0.900529
$647$	2.61086			0.102644			0.0513218	−	0.998682i	$-0.483657\pi$
$647$	2.61086			0.102644			0.0513218	+	0.998682i	$0.483657\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	3.78305			0.148498
$650$	−0.214904	+	16.4926i	−0.00842924	+	0.646892i
$651$	−2.69555	+	2.15524i	−0.105647	+	0.0844703i
$652$	−13.1032	+	13.1032i	−0.513162	+	0.513162i
$653$	2.35132			0.0920144			0.0460072	−	0.998941i	$-0.485350\pi$
$653$	2.35132			0.0920144			0.0460072	+	0.998941i	$0.485350\pi$
$654$	−15.1059			−0.590687
$655$	−0.809494	+	0.809494i	−0.0316295	+	0.0316295i
$656$	3.89486	+	3.89486i	0.152069	+	0.152069i
$657$	5.89851	−	5.89851i	0.230123	−	0.230123i
$658$	0.585786	−	5.25898i	0.0228363	−	0.205016i
$659$	13.1002			0.510312			0.255156	−	0.966900i	$-0.417873\pi$
$659$	13.1002			0.510312			0.255156	+	0.966900i	$0.417873\pi$
$660$		−	1.48065i		−	0.0576342i
$661$	−12.5885	+	12.5885i	−0.489636	+	0.489636i	−0.908191	−	0.418555i	$-0.862537\pi$
$661$	−12.5885	+	12.5885i	−0.489636	+	0.489636i	0.418555	+	0.908191i	$0.362537\pi$
$662$			6.36625i			0.247431i
$663$	16.5359	−	16.1105i	0.642201	−	0.625680i
$664$			14.1263i			0.548208i
$665$	0.682863	−	6.13049i	0.0264803	−	0.237730i
$666$	−1.34778			−0.0522253
$667$		−	67.3465i		−	2.60767i
$668$	−9.82552	−	9.82552i	−0.380161	−	0.380161i
$669$	−11.0574	+	11.0574i	−0.427503	+	0.427503i
$670$	−2.26714	+	2.26714i	−0.0875872	+	0.0875872i
$671$	−23.2559	+	23.2559i	−0.897782	+	0.897782i
$672$	1.65222	+	2.06644i	0.0637359	+	0.0797145i
$673$		−	7.32134i		−	0.282217i	−0.989994	−	0.141109i	$-0.954933\pi$
$673$		−	7.32134i		−	0.282217i	0.989994	−	0.141109i	$-0.0450667\pi$
$674$	14.6605	+	14.6605i	0.564701	+	0.564701i
$675$	4.57461			0.176077
$676$	12.9956	+	0.338732i	0.499830	+	0.0130282i
$677$		−	27.2432i		−	1.04704i	−0.852013	−	0.523520i	$-0.824619\pi$
$677$		−	27.2432i		−	1.04704i	0.852013	−	0.523520i	$-0.175381\pi$
$678$	10.6247	+	10.6247i	0.408039	+	0.408039i
$679$	−0.636245	−	0.795752i	−0.0244168	−	0.0305381i
$680$			4.17620i			0.160150i
$681$	9.31423	−	9.31423i	0.356922	−	0.356922i
$682$	−2.09396	−	2.09396i	−0.0801817	−	0.0801817i
$683$	−3.89033	−	3.89033i	−0.148859	−	0.148859i	0.628749	−	0.777608i	$-0.283567\pi$
$683$	−3.89033	−	3.89033i	−0.148859	−	0.148859i	−0.777608	+	0.628749i	$0.783567\pi$
$684$	−2.52763	+	2.52763i	−0.0966463	+	0.0966463i
$685$		−	1.68790i		−	0.0644914i
$686$	16.6555	−	8.09911i	0.635908	−	0.309226i
$687$	15.5860	+	15.5860i	0.594643	+	0.594643i
$688$		−	4.17620i		−	0.159216i
$689$	22.8981	+	23.5027i	0.872348	+	0.895382i
$690$	5.55224			0.211370
$691$	7.75081	+	7.75081i	0.294855	+	0.294855i	0.838995	−	0.544140i	$-0.183144\pi$
$691$	7.75081	+	7.75081i	0.294855	+	0.294855i	−0.544140	+	0.838995i	$0.683144\pi$
$692$			10.9940i			0.417928i
$693$	3.75081	+	4.69114i	0.142481	+	0.178202i
$694$	−0.114040	+	0.114040i	−0.00432889	+	0.00432889i
$695$	6.38508	−	6.38508i	0.242200	−	0.242200i
$696$	5.59406	−	5.59406i	0.212042	−	0.212042i
$697$	−24.9389	−	24.9389i	−0.944630	−	0.944630i
$698$			10.1540i			0.384334i
$699$	14.4240			0.545566
$700$	12.0289	+	1.33987i	0.454649	+	0.0506424i
$701$		−	5.02289i		−	0.189712i	−0.995491	−	0.0948559i	$-0.969761\pi$
$701$		−	5.02289i		−	0.189712i	0.995491	−	0.0948559i	$-0.0302390\pi$
$702$	0.0469777	−	3.60525i	0.00177306	−	0.136071i
$703$		−	4.81777i		−	0.181706i
$704$	−1.60525	+	1.60525i	−0.0605000	+	0.0605000i
$705$		−	1.30445i		−	0.0491283i
$706$	13.3602			0.502819
$707$	21.1382	+	2.35454i	0.794986	+	0.0885518i
$708$	−1.17834	+	1.17834i	−0.0442847	+	0.0442847i
$709$	4.80002	+	4.80002i	0.180269	+	0.180269i	0.791473	−	0.611204i	$-0.209315\pi$
$709$	4.80002	+	4.80002i	0.180269	+	0.180269i	−0.611204	+	0.791473i	$0.709315\pi$
$710$	5.40906	−	5.40906i	0.202998	−	0.202998i
$711$	9.18813			0.344582
$712$	12.0874			0.452995
$713$	7.85206	−	7.85206i	0.294062	−	0.294062i
$714$	−10.5792	−	13.2315i	−0.395918	−	0.495175i
$715$	−3.82380	+	3.72543i	−0.143002	+	0.139323i
$716$	2.54656			0.0951695
$717$	−3.83747	−	3.83747i	−0.143313	−	0.143313i
$718$	27.1434			1.01298
$719$	−23.2670			−0.867713			−0.433857	−	0.900982i	$-0.642848\pi$
$719$	−23.2670			−0.867713			−0.433857	+	0.900982i	$0.642848\pi$
$720$	0.461191	+	0.461191i	0.0171876	+	0.0171876i
$721$	20.0613	+	2.23458i	0.747120	+	0.0832201i
$722$	4.39976	+	4.39976i	0.163742	+	0.163742i
$723$	14.2110	+	14.2110i	0.528513	+	0.528513i
$724$			13.8933i			0.516339i
$725$		−	36.1906i		−	1.34409i
$726$	4.13401	−	4.13401i	0.153428	−	0.153428i
$727$	29.8368			1.10659			0.553293	−	0.832987i	$-0.313371\pi$
$727$	29.8368			1.10659			0.553293	+	0.832987i	$0.313371\pi$
$728$	1.17948	−	9.46619i	0.0437144	−	0.350840i
$729$	−1.00000			−0.0370370
$730$	3.84714	−	3.84714i	0.142389	−	0.142389i
$731$			26.7404i			0.989028i
$732$		−	14.4874i		−	0.535470i
$733$	11.7443	+	11.7443i	0.433784	+	0.433784i	0.889913	−	0.456129i	$-0.150765\pi$
$733$	11.7443	+	11.7443i	0.433784	+	0.433784i	−0.456129	+	0.889913i	$0.650765\pi$
$734$	−17.1928	−	17.1928i	−0.634596	−	0.634596i
$735$	3.85959	−	2.43883i	0.142363	−	0.0899576i
$736$	−6.01946	−	6.01946i	−0.221880	−	0.221880i
$737$	11.1597			0.411074
$738$	−5.50817			−0.202758
$739$	−21.9136	−	21.9136i	−0.806103	−	0.806103i	0.177938	−	0.984042i	$-0.443057\pi$
$739$	−21.9136	−	21.9136i	−0.806103	−	0.806103i	−0.984042	+	0.177938i	$0.943057\pi$
$740$	−0.879051			−0.0323146
$741$	12.8873	+	0.167927i	0.473428	+	0.00616894i
$742$	18.8061	−	15.0364i	0.690392	−	0.552004i
$743$	8.70770	−	8.70770i	0.319454	−	0.319454i	−0.529103	−	0.848558i	$-0.677472\pi$
$743$	8.70770	−	8.70770i	0.319454	−	0.319454i	0.848558	+	0.529103i	$0.177472\pi$
$744$	1.30445			0.0478233
$745$	−2.88544			−0.105714
$746$	−6.89184	+	6.89184i	−0.252328	+	0.252328i
$747$	−9.98882	−	9.98882i	−0.365472	−	0.365472i
$748$	10.2784	−	10.2784i	0.375817	−	0.375817i
$749$	37.8610	+	4.21726i	1.38341	+	0.154095i
$750$	6.24478			0.228027
$751$			34.2765i			1.25077i	0.780318	+	0.625384i	$0.215057\pi$
$751$			34.2765i			1.25077i	−0.780318	+	0.625384i	$0.784943\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$			5.39399i			0.196568i
$754$	−28.5218	−	0.371650i	−1.03870	−	0.0135347i
$755$			10.6537i			0.387728i
$756$	−2.62949	−	0.292893i	−0.0956336	−	0.0106524i
$757$	−28.0153			−1.01823			−0.509117	−	0.860697i	$-0.670028\pi$
$757$	−28.0153			−1.01823			−0.509117	+	0.860697i	$0.670028\pi$
$758$			20.6159i			0.748802i
$759$	−13.6651	−	13.6651i	−0.496013	−	0.496013i
$760$	−1.64858	+	1.64858i	−0.0598002	+	0.0598002i
$761$	−24.7400	+	24.7400i	−0.896824	+	0.896824i	−0.995154	−	0.0983300i	$-0.968650\pi$
$761$	−24.7400	+	24.7400i	−0.896824	+	0.896824i	0.0983300	+	0.995154i	$0.468650\pi$
$762$	11.1702	−	11.1702i	0.404653	−	0.404653i
$763$	31.2153	−	24.9583i	1.13007	−	0.903550i
$764$			10.2290i			0.370071i
$765$	−2.95302	−	2.95302i	−0.106767	−	0.106767i
$766$	29.5065			1.06611
$767$	6.00787	+	0.0782847i	0.216932	+	0.00282670i
$768$		−	1.00000i		−	0.0360844i
$769$	−24.3745	−	24.3745i	−0.878968	−	0.878968i	0.114460	−	0.993428i	$-0.463486\pi$
$769$	−24.3745	−	24.3745i	−0.878968	−	0.878968i	−0.993428	+	0.114460i	$0.963486\pi$
$770$	2.44636	+	3.05967i	0.0881608	+	0.110263i
$771$		−	4.38508i		−	0.157925i
$772$	12.3940	−	12.3940i	0.446069	−	0.446069i
$773$	−21.0774	−	21.0774i	−0.758100	−	0.758100i	0.217876	−	0.975976i	$-0.430087\pi$
$773$	−21.0774	−	21.0774i	−0.758100	−	0.758100i	−0.975976	+	0.217876i	$0.930087\pi$
$774$	2.95302	+	2.95302i	0.106144	+	0.106144i
$775$	4.21954	−	4.21954i	0.151570	−	0.151570i
$776$			0.385084i			0.0138237i
$777$	2.78510	−	2.22683i	0.0999148	−	0.0798870i
$778$	4.30855	+	4.30855i	0.154469	+	0.154469i
$779$		−	19.6895i		−	0.705451i
$780$	0.0306399	−	2.35142i	0.00109708	−	0.0841945i
$781$	−26.6254			−0.952733
$782$	38.5428	+	38.5428i	1.37829	+	1.37829i
$783$			7.91120i			0.282723i
$784$	−6.82843	−	1.54032i	−0.243872	−	0.0550114i
$785$	8.54558	−	8.54558i	0.305005	−	0.305005i
$786$	−1.24113	+	1.24113i	−0.0442697	+	0.0442697i
$787$	5.03100	−	5.03100i	0.179336	−	0.179336i	−0.611730	−	0.791066i	$-0.709526\pi$
$787$	5.03100	−	5.03100i	0.179336	−	0.179336i	0.791066	+	0.611730i	$0.209526\pi$
$788$	−8.84638	−	8.84638i	−0.315139	−	0.315139i
$789$			12.4336i			0.442647i
$790$	5.99271			0.213211
$791$	−39.5097	−	4.40090i	−1.40480	−	0.156478i
$792$		−	2.27016i		−	0.0806666i
$793$	−37.4139	+	36.4514i	−1.32861	+	1.29443i
$794$		−	38.1544i		−	1.35405i
$795$	4.19717	−	4.19717i	0.148858	−	0.148858i
$796$			7.40980i			0.262633i
$797$	−35.6777			−1.26377			−0.631884	−	0.775063i	$-0.717718\pi$
$797$	−35.6777			−1.26377			−0.631884	+	0.775063i	$0.717718\pi$
$798$	1.04698	−	9.39939i	0.0370626	−	0.332735i
$799$	9.05526	−	9.05526i	0.320352	−	0.320352i
$800$	−3.23473	−	3.23473i	−0.114365	−	0.114365i
$801$	−8.54709	+	8.54709i	−0.301996	+	0.301996i
$802$	−30.3496			−1.07168
$803$	−18.9371			−0.668276
$804$	−3.47602	+	3.47602i	−0.122590	+	0.122590i
$805$	−11.4734	+	9.17354i	−0.404383	+	0.323325i
$806$	−3.28208	−	3.36875i	−0.115606	−	0.118659i
$807$	29.7839			1.04844
$808$	−5.68437	−	5.68437i	−0.199976	−	0.199976i
$809$	−24.7540			−0.870306			−0.435153	−	0.900357i	$-0.643306\pi$
$809$	−24.7540			−0.870306			−0.435153	+	0.900357i	$0.643306\pi$
$810$	−0.652223			−0.0229168
$811$	19.5605	+	19.5605i	0.686863	+	0.686863i	0.961537	−	0.274674i	$-0.0885701\pi$
$811$	19.5605	+	19.5605i	0.686863	+	0.686863i	−0.274674	+	0.961537i	$0.588570\pi$
$812$	−2.31714	+	20.8024i	−0.0813156	+	0.730022i
$813$	−14.7173	−	14.7173i	−0.516157	−	0.516157i
$814$	2.16351	+	2.16351i	0.0758311	+	0.0758311i
$815$		−	12.0862i		−	0.423360i
$816$			6.40303i			0.224151i
$817$	−10.5559	+	10.5559i	−0.369304	+	0.369304i
$818$	−5.95240			−0.208121
$819$	5.85959	+	7.52763i	0.204751	+	0.263037i
$820$	−3.59255			−0.125457
$821$	8.90959	−	8.90959i	0.310947	−	0.310947i	−0.534329	−	0.845276i	$-0.679436\pi$
$821$	8.90959	−	8.90959i	0.310947	−	0.310947i	0.845276	+	0.534329i	$0.179436\pi$
$822$		−	2.58792i		−	0.0902642i
$823$			6.11934i			0.213307i	0.994296	+	0.106653i	$0.0340135\pi$
$823$			6.11934i			0.213307i	−0.994296	+	0.106653i	$0.965986\pi$
$824$	−5.39475	−	5.39475i	−0.187935	−	0.187935i
$825$	−7.34336	−	7.34336i	−0.255663	−	0.255663i
$826$	0.488084	−	4.38185i	0.0169826	−	0.152464i
$827$	−26.8873	−	26.8873i	−0.934964	−	0.934964i	0.0630466	−	0.998011i	$-0.479918\pi$
$827$	−26.8873	−	26.8873i	−0.934964	−	0.934964i	−0.998011	+	0.0630466i	$0.979918\pi$
$828$	8.51280			0.295840
$829$	31.1247			1.08101			0.540503	−	0.841342i	$-0.318234\pi$
$829$	31.1247			1.08101			0.540503	+	0.841342i	$0.318234\pi$
$830$	−6.51494	−	6.51494i	−0.226137	−	0.226137i
$831$	−24.1271			−0.836959
$832$	−2.58251	+	2.51608i	−0.0895325	+	0.0872292i
$833$	43.7226	+	9.86271i	1.51490	+	0.341723i
$834$	9.78973	−	9.78973i	0.338991	−	0.338991i
$835$	9.06289			0.313634
$836$	8.11492			0.280661
$837$	−0.922382	+	0.922382i	−0.0318822	+	0.0318822i
$838$	−2.67771	−	2.67771i	−0.0924998	−	0.0924998i
$839$	−9.22932	+	9.22932i	−0.318632	+	0.318632i	−0.848241	−	0.529610i	$-0.822338\pi$
$839$	−9.22932	+	9.22932i	−0.318632	+	0.318632i	0.529610	+	0.848241i	$0.322338\pi$
$840$	−1.71501	−	0.191032i	−0.0591736	−	0.00659122i
$841$	33.5871			1.15818
$842$		−	23.0136i		−	0.793099i
$843$	−7.70534	+	7.70534i	−0.265386	+	0.265386i
$844$		−	14.6299i		−	0.503581i
$845$	−6.14967	+	5.83723i	−0.211555	+	0.200807i
$846$		−	2.00000i		−	0.0687614i
$847$	−1.71236	+	15.3730i	−0.0588375	+	0.528222i
$848$	−9.10072			−0.312520
$849$			6.39133i			0.219350i
$850$	20.7121	+	20.7121i	0.710419	+	0.710419i
$851$	−8.11289	+	8.11289i	−0.278106	+	0.278106i
$852$	8.29326	−	8.29326i	0.284123	−	0.284123i
$853$	9.34638	−	9.34638i	0.320014	−	0.320014i	−0.528758	−	0.848772i	$-0.677342\pi$
$853$	9.34638	−	9.34638i	0.320014	−	0.320014i	0.848772	+	0.528758i	$0.177342\pi$
$854$	23.9364	+	29.9373i	0.819088	+	1.02443i
$855$		−	2.33144i		−	0.0797335i
$856$	−10.1814	−	10.1814i	−0.347992	−	0.347992i
$857$	55.3845			1.89190			0.945949	−	0.324315i	$-0.105134\pi$
$857$	55.3845			1.89190			0.945949	+	0.324315i	$0.105134\pi$
$858$	−5.86271	+	5.71189i	−0.200150	+	0.195001i
$859$			42.0994i			1.43641i	0.695830	+	0.718206i	$0.255037\pi$
$859$			42.0994i			1.43641i	−0.695830	+	0.718206i	$0.744963\pi$
$860$	1.92603	+	1.92603i	0.0656770	+	0.0656770i
$861$	11.3823	−	9.10072i	0.387907	−	0.310152i
$862$		−	25.0434i		−	0.852982i
$863$	−3.47410	+	3.47410i	−0.118260	+	0.118260i	−0.763760	−	0.645500i	$-0.776649\pi$
$863$	−3.47410	+	3.47410i	−0.118260	+	0.118260i	0.645500	+	0.763760i	$0.276649\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−5.07032	−	5.07032i	−0.172396	−	0.172396i
$866$	9.34034	−	9.34034i	0.317398	−	0.317398i
$867$		−	23.9988i		−	0.815043i
$868$	−2.69555	+	2.15524i	−0.0914931	+	0.0731534i
$869$	−14.7492	−	14.7492i	−0.500332	−	0.500332i
$870$			5.15987i			0.174936i
$871$	17.7228	+	0.230934i	0.600514	+	0.00782491i
$872$	−15.1059			−0.511550
$873$	−0.272296	−	0.272296i	−0.00921581	−	0.00921581i
$874$			30.4299i			1.02931i
$875$	−12.9044	+	10.3178i	−0.436249	+	0.348804i
$876$	5.89851	−	5.89851i	0.199292	−	0.199292i
$877$	16.8673	−	16.8673i	0.569570	−	0.569570i	−0.362438	−	0.932008i	$-0.618056\pi$
$877$	16.8673	−	16.8673i	0.569570	−	0.569570i	0.932008	+	0.362438i	$0.118056\pi$
$878$	19.2784	−	19.2784i	0.650616	−	0.650616i
$879$	−8.93819	−	8.93819i	−0.301478	−	0.301478i
$880$		−	1.48065i		−	0.0499127i
$881$	28.2254			0.950939			0.475470	−	0.879732i	$-0.342278\pi$
$881$	28.2254			0.950939			0.475470	+	0.879732i	$0.342278\pi$
$882$	5.91760	−	3.73926i	0.199256	−	0.125907i
$883$			42.1795i			1.41945i	0.704478	+	0.709726i	$0.251181\pi$
$883$			42.1795i			1.41945i	−0.704478	+	0.709726i	$0.748819\pi$
$884$	16.5359	−	16.1105i	0.556163	−	0.541855i
$885$		−	1.08688i		−	0.0365351i
$886$	−15.8128	+	15.8128i	−0.531242	+	0.531242i
$887$		−	57.2398i		−	1.92192i	−0.276682	−	0.960962i	$-0.589235\pi$
$887$		−	57.2398i		−	1.92192i	0.276682	−	0.960962i	$-0.410765\pi$
$888$	−1.34778			−0.0452284
$889$	−4.62684	+	41.5381i	−0.155179	+	1.39314i
$890$	−5.57461	+	5.57461i	−0.186861	+	0.186861i
$891$	1.60525	+	1.60525i	0.0537777	+	0.0537777i
$892$	−11.0574	+	11.0574i	−0.370229	+	0.370229i
$893$	7.14921			0.239239
$894$	−4.42400			−0.147961
$895$	−1.17445	+	1.17445i	−0.0392576	+	0.0392576i
$896$	1.65222	+	2.06644i	0.0551969	+	0.0690348i
$897$	−21.4188	−	21.9844i	−0.715154	−	0.734038i
$898$	−4.76168			−0.158899
$899$	7.29715	+	7.29715i	0.243374	+	0.243374i
$900$	4.57461			0.152487
$901$	58.2722			1.94133
$902$	8.84196	+	8.84196i	0.294405	+	0.294405i
$903$	−10.9813	−	1.22318i	−0.365434	−	0.0407049i
$904$	10.6247	+	10.6247i	0.353372	+	0.353372i
$905$	−6.40745	−	6.40745i	−0.212991	−	0.212991i
$906$			16.3345i			0.542676i
$907$			28.7641i			0.955097i	0.878605	+	0.477549i	$0.158475\pi$
$907$			28.7641i			0.955097i	−0.878605	+	0.477549i	$0.841525\pi$
$908$	9.31423	−	9.31423i	0.309104	−	0.309104i
$909$	8.03892			0.266634
$910$	3.82176	+	4.90969i	0.126690	+	0.162755i
$911$	27.0639			0.896666			0.448333	−	0.893867i	$-0.352018\pi$
$911$	27.0639			0.896666			0.448333	+	0.893867i	$0.352018\pi$
$912$	−2.52763	+	2.52763i	−0.0836981	+	0.0836981i
$913$			32.0690i			1.06133i
$914$		−	17.6819i		−	0.584866i
$915$	6.68147	+	6.68147i	0.220883	+	0.220883i
$916$	15.5860	+	15.5860i	0.514976	+	0.514976i
$917$	0.514093	−	4.61534i	0.0169768	−	0.152412i
$918$	−4.52763	−	4.52763i	−0.149434	−	0.149434i
$919$	38.1464			1.25833			0.629167	−	0.777270i	$-0.283396\pi$
$919$	38.1464			1.25833			0.629167	+	0.777270i	$0.283396\pi$
$920$	5.55224			0.183052
$921$	−1.27177	−	1.27177i	−0.0419063	−	0.0419063i
$922$	−5.70945			−0.188031
$923$	−42.2839	−	0.550975i	−1.39179	−	0.0181356i
$924$	3.75081	+	4.69114i	0.123393	+	0.154327i
$925$	−4.35970	+	4.35970i	−0.143346	+	0.143346i
$926$	18.1373			0.596028
$927$	7.62934			0.250580
$928$	5.59406	−	5.59406i	0.183634	−	0.183634i
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	0.501159	−	0.865355i	$-0.332907\pi$
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	−0.865355	+	0.501159i	$0.832907\pi$
$930$	−0.601599	+	0.601599i	−0.0197272	+	0.0197272i
$931$	13.3664	+	21.1531i	0.438065	+	0.693264i
$932$	14.4240			0.472474
$933$			1.52201i			0.0498284i
$934$	−12.0406	+	12.0406i	−0.393982	+	0.393982i
$935$			9.48065i			0.310050i
$936$	0.0469777	−	3.60525i	0.00153551	−	0.117841i
$937$		−	47.2311i		−	1.54297i	−0.636245	−	0.771487i	$-0.719513\pi$
$937$		−	47.2311i		−	1.54297i	0.636245	−	0.771487i	$-0.280487\pi$
$938$	1.43981	−	12.9261i	0.0470116	−	0.422053i
$939$	3.48506			0.113731
$940$		−	1.30445i		−	0.0425463i
$941$	−27.0580	−	27.0580i	−0.882065	−	0.882065i	0.111680	−	0.993744i	$-0.464377\pi$
$941$	−27.0580	−	27.0580i	−0.882065	−	0.882065i	−0.993744	+	0.111680i	$0.964377\pi$
$942$	13.1022	−	13.1022i	0.426894	−	0.426894i
$943$	−33.1562	+	33.1562i	−1.07971	+	1.07971i
$944$	−1.17834	+	1.17834i	−0.0383517	+	0.0383517i
$945$	1.34778	−	1.07762i	0.0438432	−	0.0350549i
$946$		−	9.48065i		−	0.308243i
$947$	−14.2815	−	14.2815i	−0.464085	−	0.464085i	0.435907	−	0.899992i	$-0.356428\pi$
$947$	−14.2815	−	14.2815i	−0.464085	−	0.464085i	−0.899992	+	0.435907i	$0.856428\pi$
$948$	9.18813			0.298417
$949$	−30.0741	−	0.391876i	−0.976245	−	0.0127208i
$950$			16.3524i			0.530542i
$951$	−3.61566	−	3.61566i	−0.117246	−	0.117246i
$952$	−10.5792	−	13.2315i	−0.342875	−	0.428834i
$953$			6.01656i			0.194895i	0.995241	+	0.0974477i	$0.0310679\pi$
$953$			6.01656i			0.194895i	−0.995241	+	0.0974477i	$0.968932\pi$
$954$	6.43518	−	6.43518i	0.208347	−	0.208347i
$955$	−4.71751	−	4.71751i	−0.152655	−	0.152655i
$956$	−3.83747	−	3.83747i	−0.124113	−	0.124113i
$957$	12.6994	−	12.6994i	0.410514	−	0.410514i
$958$		−	32.1601i		−	1.03905i
$959$	4.27582	+	5.34778i	0.138074	+	0.172689i
$960$	0.461191	+	0.461191i	0.0148849	+	0.0148849i
$961$		−	29.2984i		−	0.945110i
$962$	3.39111	+	3.48065i	0.109334	+	0.112221i
$963$	14.3986			0.463989
$964$	14.2110	+	14.2110i	0.457706	+	0.457706i
$965$			11.4320i			0.368009i
$966$	−17.5912	+	14.0650i	−0.565986	+	0.452535i
$967$	−29.0413	+	29.0413i	−0.933906	+	0.933906i	−0.997947	−	0.0640416i	$-0.979601\pi$
$967$	−29.0413	+	29.0413i	−0.933906	+	0.933906i	0.0640416	+	0.997947i	$0.479601\pi$
$968$	4.13401	−	4.13401i	0.132872	−	0.132872i
$969$	16.1845	−	16.1845i	0.519920	−	0.519920i
$970$	−0.177597	−	0.177597i	−0.00570231	−	0.00570231i
$971$			37.3180i			1.19759i	0.800902	+	0.598795i	$0.204354\pi$
$971$			37.3180i			1.19759i	−0.800902	+	0.598795i	$0.795646\pi$
$972$	−1.00000			−0.0320750
$973$	−4.05504	+	36.4047i	−0.129999	+	1.16708i
$974$		−	11.8899i		−	0.380978i
$975$	−11.5101	−	11.8140i	−0.368617	−	0.378350i
$976$		−	14.4874i		−	0.463731i
$977$	−4.00859	+	4.00859i	−0.128246	+	0.128246i	−0.768316	−	0.640070i	$-0.778905\pi$
$977$	−4.00859	+	4.00859i	−0.128246	+	0.128246i	0.640070	+	0.768316i	$0.278905\pi$
$978$		−	18.5307i		−	0.592548i
$979$	27.4403			0.876997
$980$	3.85959	−	2.43883i	0.123290	−	0.0779055i
$981$	10.6815	−	10.6815i	0.341033	−	0.341033i
$982$	8.70800	+	8.70800i	0.277884	+	0.277884i
$983$	−20.0717	+	20.0717i	−0.640188	+	0.640188i	−0.950601	−	0.310414i	$-0.899532\pi$
$983$	−20.0717	+	20.0717i	−0.640188	+	0.640188i	0.310414	+	0.950601i	$0.399532\pi$
$984$	−5.50817			−0.175594
$985$	8.15974			0.259991
$986$	−35.8190	+	35.8190i	−1.14071	+	1.14071i
$987$	3.30445	+	4.13287i	0.105182	+	0.131551i
$988$	12.8873	+	0.167927i	0.410001	+	0.00534246i
$989$	35.5512			1.13046
$990$	1.04698	+	1.04698i	0.0332751	+	0.0332751i
$991$	−16.1309			−0.512415			−0.256208	−	0.966622i	$-0.582473\pi$
$991$	−16.1309			−0.512415			−0.256208	+	0.966622i	$0.582473\pi$
$992$	1.30445			0.0414162
$993$	−4.50162	−	4.50162i	−0.142855	−	0.142855i
$994$	−3.43518	+	30.8398i	−0.108957	+	0.978180i
$995$	−3.41733	−	3.41733i	−0.108337	−	0.108337i
$996$	−9.98882	−	9.98882i	−0.316508	−	0.316508i
$997$			32.1324i			1.01764i	0.860872	+	0.508821i	$0.169919\pi$
$997$			32.1324i			1.01764i	−0.860872	+	0.508821i	$0.830081\pi$
$998$			5.84446i			0.185003i
$999$	0.953022	−	0.953022i	0.0301523	−	0.0301523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.b.265.2	✓	8
3.2	odd	2		1638.2.x.c.811.3		8
7.6	odd	2		546.2.o.c.265.1	yes	8
13.8	odd	4		546.2.o.c.307.1	yes	8
21.20	even	2		1638.2.x.a.811.4		8
39.8	even	4		1638.2.x.a.307.4		8
91.34	even	4	inner	546.2.o.b.307.2	yes	8
273.125	odd	4		1638.2.x.c.307.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.2	✓	8	1.1	even	1	trivial
546.2.o.b.307.2	yes	8	91.34	even	4	inner
546.2.o.c.265.1	yes	8	7.6	odd	2
546.2.o.c.307.1	yes	8	13.8	odd	4
1638.2.x.a.307.4		8	39.8	even	4
1638.2.x.a.811.4		8	21.20	even	2
1638.2.x.c.307.3		8	273.125	odd	4
1638.2.x.c.811.3		8	3.2	odd	2

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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -0.652223 q^{10} +(1.60525 + 1.60525i) q^{11} -1.00000 q^{12} +(2.51608 + 2.58251i) q^{13} +(2.06644 - 1.65222i) q^{14} +(0.461191 - 0.461191i) q^{15} -1.00000 q^{16} +6.40303 q^{17} +(0.707107 - 0.707107i) q^{18} +(2.52763 + 2.52763i) q^{19} +(0.461191 - 0.461191i) q^{20} +(-0.292893 + 2.62949i) q^{21} -2.27016 q^{22} -8.51280i q^{23} +(0.707107 - 0.707107i) q^{24} -4.57461i q^{25} +(-3.60525 - 0.0469777i) q^{26} +1.00000i q^{27} +(-0.292893 + 2.62949i) q^{28} +7.91120 q^{29} +0.652223i q^{30} +(0.922382 + 0.922382i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.60525 - 1.60525i) q^{33} +(-4.52763 + 4.52763i) q^{34} +(-1.07762 - 1.34778i) q^{35} +1.00000i q^{36} +(-0.953022 - 0.953022i) q^{37} -3.57461 q^{38} +(2.58251 - 2.51608i) q^{39} +0.652223i q^{40} +(-3.89486 - 3.89486i) q^{41} +(-1.65222 - 2.06644i) q^{42} +4.17620i q^{43} +(1.60525 - 1.60525i) q^{44} +(-0.461191 - 0.461191i) q^{45} +(6.01946 + 6.01946i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 + 1.54032i) q^{49} +(3.23473 + 3.23473i) q^{50} -6.40303i q^{51} +(2.58251 - 2.51608i) q^{52} +9.10072 q^{53} +(-0.707107 - 0.707107i) q^{54} +1.48065i q^{55} +(-1.65222 - 2.06644i) q^{56} +(2.52763 - 2.52763i) q^{57} +(-5.59406 + 5.59406i) q^{58} +(1.17834 - 1.17834i) q^{59} +(-0.461191 - 0.461191i) q^{60} +14.4874i q^{61} -1.30445 q^{62} +(2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-0.0306399 + 2.35142i) q^{65} +2.27016i q^{66} +(3.47602 - 3.47602i) q^{67} -6.40303i q^{68} -8.51280 q^{69} +(1.71501 + 0.191032i) q^{70} +(-8.29326 + 8.29326i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.89851 + 5.89851i) q^{73} +1.34778 q^{74} -4.57461 q^{75} +(2.52763 - 2.52763i) q^{76} +(-3.75081 - 4.69114i) q^{77} +(-0.0469777 + 3.60525i) q^{78} -9.18813 q^{79} +(-0.461191 - 0.461191i) q^{80} +1.00000 q^{81} +5.50817 q^{82} +(9.98882 + 9.98882i) q^{83} +(2.62949 + 0.292893i) q^{84} +(2.95302 + 2.95302i) q^{85} +(-2.95302 - 2.95302i) q^{86} -7.91120i q^{87} +2.27016i q^{88} +(8.54709 - 8.54709i) q^{89} +0.652223 q^{90} +(-5.85959 - 7.52763i) q^{91} -8.51280 q^{92} +(0.922382 - 0.922382i) q^{93} +2.00000i q^{94} +2.33144i q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.272296 + 0.272296i) q^{97} +(-5.91760 + 3.73926i) q^{98} +(-1.60525 - 1.60525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{12} + 16 q^{13} - 4 q^{14} - 4 q^{15} - 8 q^{16} + 4 q^{17} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 12 q^{22} - 16 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} - 8 q^{34} - 24 q^{35} - 4 q^{37} - 4 q^{38} - 4 q^{39} + 12 q^{41} - 4 q^{42} + 4 q^{45} + 24 q^{46} + 32 q^{49} - 8 q^{50} - 4 q^{52} + 40 q^{53} - 4 q^{56} - 8 q^{57} + 4 q^{58} - 8 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{65} + 32 q^{67} - 28 q^{69} + 8 q^{70} - 12 q^{71} + 20 q^{73} + 20 q^{74} - 12 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 24 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 44 q^{83} + 20 q^{85} - 20 q^{86} + 16 q^{89} - 4 q^{90} - 28 q^{91} - 28 q^{92} - 8 q^{93} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^12 + 16 * q^13 - 4 * q^14 - 4 * q^15 - 8 * q^16 + 4 * q^17 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 12 * q^22 - 16 * q^26 - 8 * q^28 + 12 * q^29 - 8 * q^31 - 8 * q^34 - 24 * q^35 - 4 * q^37 - 4 * q^38 - 4 * q^39 + 12 * q^41 - 4 * q^42 + 4 * q^45 + 24 * q^46 + 32 * q^49 - 8 * q^50 - 4 * q^52 + 40 * q^53 - 4 * q^56 - 8 * q^57 + 4 * q^58 - 8 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^65 + 32 * q^67 - 28 * q^69 + 8 * q^70 - 12 * q^71 + 20 * q^73 + 20 * q^74 - 12 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 24 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 44 * q^83 + 20 * q^85 - 20 * q^86 + 16 * q^89 - 4 * q^90 - 28 * q^91 - 28 * q^92 - 8 * q^93 - 8 * q^97 - 16 * q^98

Introduction

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