LMFDB - Embedded newform 770.2.l.c.573.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.2
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.02780 + 2.02780i) q^{3} -1.00000i q^{4} +(-0.515374 - 2.17587i) q^{5} -2.86774i q^{6} +(1.43371 - 2.22362i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.22391i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.02780 + 2.02780i) q^{3} -1.00000i q^{4} +(-0.515374 - 2.17587i) q^{5} -2.86774i q^{6} +(1.43371 - 2.22362i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.22391i q^{9} +(1.90299 + 1.17414i) q^{10} -1.00000 q^{11} +(2.02780 + 2.02780i) q^{12} +(-0.426099 + 0.426099i) q^{13} +(0.558546 + 2.58612i) q^{14} +(5.45728 + 3.36714i) q^{15} -1.00000 q^{16} +(3.58943 + 3.58943i) q^{17} +(3.69386 + 3.69386i) q^{18} -8.41042 q^{19} +(-2.17587 + 0.515374i) q^{20} +(1.60176 + 7.41631i) q^{21} +(0.707107 - 0.707107i) q^{22} +(1.54023 + 1.54023i) q^{23} -2.86774 q^{24} +(-4.46878 + 2.24277i) q^{25} -0.602596i q^{26} +(4.50963 + 4.50963i) q^{27} +(-2.22362 - 1.43371i) q^{28} +2.15950i q^{29} +(-6.23981 + 1.47796i) q^{30} +8.89990i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.02780 - 2.02780i) q^{33} -5.07622 q^{34} +(-5.57719 - 1.97357i) q^{35} -5.22391 q^{36} +(-2.82821 + 2.82821i) q^{37} +(5.94706 - 5.94706i) q^{38} -1.72808i q^{39} +(1.17414 - 1.90299i) q^{40} -12.0902i q^{41} +(-6.37674 - 4.11151i) q^{42} +(7.79227 + 7.79227i) q^{43} +1.00000i q^{44} +(-11.3665 + 2.69227i) q^{45} -2.17822 q^{46} +(5.76637 + 5.76637i) q^{47} +(2.02780 - 2.02780i) q^{48} +(-2.88894 - 6.37605i) q^{49} +(1.57403 - 4.74578i) q^{50} -14.5573 q^{51} +(0.426099 + 0.426099i) q^{52} +(-7.26064 - 7.26064i) q^{53} -6.37758 q^{54} +(0.515374 + 2.17587i) q^{55} +(2.58612 - 0.558546i) q^{56} +(17.0546 - 17.0546i) q^{57} +(-1.52700 - 1.52700i) q^{58} -5.29339 q^{59} +(3.36714 - 5.45728i) q^{60} +5.58589i q^{61} +(-6.29318 - 6.29318i) q^{62} +(-11.6160 - 7.48958i) q^{63} +1.00000i q^{64} +(1.14674 + 0.707534i) q^{65} +2.86774i q^{66} +(-2.95352 + 2.95352i) q^{67} +(3.58943 - 3.58943i) q^{68} -6.24656 q^{69} +(5.33919 - 2.54814i) q^{70} -10.8092 q^{71} +(3.69386 - 3.69386i) q^{72} +(-6.37937 + 6.37937i) q^{73} -3.99970i q^{74} +(4.51389 - 13.6096i) q^{75} +8.41042i q^{76} +(-1.43371 + 2.22362i) q^{77} +(1.22194 + 1.22194i) q^{78} +12.8442i q^{79} +(0.515374 + 2.17587i) q^{80} -2.61748 q^{81} +(8.54906 + 8.54906i) q^{82} +(-5.16803 + 5.16803i) q^{83} +(7.41631 - 1.60176i) q^{84} +(5.96022 - 9.66002i) q^{85} -11.0199 q^{86} +(-4.37903 - 4.37903i) q^{87} +(-0.707107 - 0.707107i) q^{88} +5.16538 q^{89} +(6.13362 - 9.94106i) q^{90} +(0.336577 + 1.55839i) q^{91} +(1.54023 - 1.54023i) q^{92} +(-18.0472 - 18.0472i) q^{93} -8.15488 q^{94} +(4.33451 + 18.2999i) q^{95} +2.86774i q^{96} +(1.87168 + 1.87168i) q^{97} +(6.55134 + 2.46576i) q^{98} +5.22391i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−2.02780	+	2.02780i	−1.17075	+	1.17075i	−0.188716	+	0.982032i	$0.560433\pi$
$3$	−2.02780	+	2.02780i	−1.17075	+	1.17075i	−0.982032	+	0.188716i	$0.939567\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.515374	−	2.17587i	−0.230482	−	0.973077i
$5$	−0.515374	−	2.17587i	−0.230482	−	0.973077i
$6$		−	2.86774i		−	1.17075i
$7$	1.43371	−	2.22362i	0.541892	−	0.840448i
$7$	1.43371	−	2.22362i	0.541892	−	0.840448i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	5.22391i		−	1.74130i
$10$	1.90299	+	1.17414i	0.601779	+	0.371297i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.02780	+	2.02780i	0.585374	+	0.585374i
$13$	−0.426099	+	0.426099i	−0.118179	+	0.118179i	−0.763723	−	0.645544i	$-0.776631\pi$
$13$	−0.426099	+	0.426099i	−0.118179	+	0.118179i	0.645544	+	0.763723i	$0.276631\pi$
$14$	0.558546	+	2.58612i	0.149278	+	0.691170i
$15$	5.45728	+	3.36714i	1.40906	+	0.869391i
$16$	−1.00000			−0.250000
$17$	3.58943	+	3.58943i	0.870565	+	0.870565i	0.992534	−	0.121969i	$-0.0389207\pi$
$17$	3.58943	+	3.58943i	0.870565	+	0.870565i	−0.121969	+	0.992534i	$0.538921\pi$
$18$	3.69386	+	3.69386i	0.870651	+	0.870651i
$19$	−8.41042			−1.92948			−0.964741	−	0.263200i	$-0.915222\pi$
$19$	−8.41042			−1.92948			−0.964741	+	0.263200i	$0.915222\pi$
$20$	−2.17587	+	0.515374i	−0.486538	+	0.115241i
$21$	1.60176	+	7.41631i	0.349533	+	1.61837i
$22$	0.707107	−	0.707107i	0.150756	−	0.150756i
$23$	1.54023	+	1.54023i	0.321161	+	0.321161i	0.849212	−	0.528052i	$-0.177077\pi$
$23$	1.54023	+	1.54023i	0.321161	+	0.321161i	−0.528052	+	0.849212i	$0.677077\pi$
$24$	−2.86774			−0.585374
$25$	−4.46878	+	2.24277i	−0.893756	+	0.448554i
$26$		−	0.602596i		−	0.118179i
$27$	4.50963	+	4.50963i	0.867878	+	0.867878i
$28$	−2.22362	−	1.43371i	−0.420224	−	0.270946i
$29$			2.15950i			0.401010i	0.979693	+	0.200505i	$0.0642583\pi$
$29$			2.15950i			0.401010i	−0.979693	+	0.200505i	$0.935742\pi$
$30$	−6.23981	+	1.47796i	−1.13923	+	0.269837i
$31$			8.89990i			1.59847i	0.601020	+	0.799234i	$0.294761\pi$
$31$			8.89990i			1.59847i	−0.601020	+	0.799234i	$0.705239\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.02780	−	2.02780i	0.352994	−	0.352994i
$34$	−5.07622			−0.870565
$35$	−5.57719	−	1.97357i	−0.942717	−	0.333594i
$36$	−5.22391			−0.870651
$37$	−2.82821	+	2.82821i	−0.464955	+	0.464955i	−0.900276	−	0.435320i	$-0.856635\pi$
$37$	−2.82821	+	2.82821i	−0.464955	+	0.464955i	0.435320	+	0.900276i	$0.356635\pi$
$38$	5.94706	−	5.94706i	0.964741	−	0.964741i
$39$		−	1.72808i		−	0.276715i
$40$	1.17414	−	1.90299i	0.185649	−	0.300890i
$41$		−	12.0902i		−	1.88817i	−0.329699	−	0.944086i	$-0.606947\pi$
$41$		−	12.0902i		−	1.88817i	0.329699	−	0.944086i	$-0.393053\pi$
$42$	−6.37674	−	4.11151i	−0.983953	−	0.634419i
$43$	7.79227	+	7.79227i	1.18831	+	1.18831i	0.977535	+	0.210775i	$0.0675987\pi$
$43$	7.79227	+	7.79227i	1.18831	+	1.18831i	0.210775	+	0.977535i	$0.432401\pi$
$44$			1.00000i			0.150756i
$45$	−11.3665	+	2.69227i	−1.69442	+	0.401339i
$46$	−2.17822			−0.321161
$47$	5.76637	+	5.76637i	0.841112	+	0.841112i	0.989004	−	0.147892i	$-0.0472488\pi$
$47$	5.76637	+	5.76637i	0.841112	+	0.841112i	−0.147892	+	0.989004i	$0.547249\pi$
$48$	2.02780	−	2.02780i	0.292687	−	0.292687i
$49$	−2.88894	−	6.37605i	−0.412705	−	0.910865i
$50$	1.57403	−	4.74578i	0.222601	−	0.671155i
$51$	−14.5573			−2.03843
$52$	0.426099	+	0.426099i	0.0590894	+	0.0590894i
$53$	−7.26064	−	7.26064i	−0.997326	−	0.997326i	0.00267086	−	0.999996i	$-0.499150\pi$
$53$	−7.26064	−	7.26064i	−0.997326	−	0.997326i	−0.999996	+	0.00267086i	$0.999150\pi$
$54$	−6.37758			−0.867878
$55$	0.515374	+	2.17587i	0.0694930	+	0.293394i
$56$	2.58612	−	0.558546i	0.345585	−	0.0746389i
$57$	17.0546	−	17.0546i	2.25894	−	2.25894i
$58$	−1.52700	−	1.52700i	−0.200505	−	0.200505i
$59$	−5.29339			−0.689140			−0.344570	−	0.938761i	$-0.611975\pi$
$59$	−5.29339			−0.689140			−0.344570	+	0.938761i	$0.611975\pi$
$60$	3.36714	−	5.45728i	0.434695	−	0.704532i
$61$			5.58589i			0.715199i	0.933875	+	0.357600i	$0.116405\pi$
$61$			5.58589i			0.715199i	−0.933875	+	0.357600i	$0.883595\pi$
$62$	−6.29318	−	6.29318i	−0.799234	−	0.799234i
$63$	−11.6160	−	7.48958i	−1.46347	−	0.943598i
$64$			1.00000i			0.125000i
$65$	1.14674	+	0.707534i	0.142235	+	0.0877588i
$66$			2.86774i			0.352994i
$67$	−2.95352	+	2.95352i	−0.360830	+	0.360830i	−0.864118	−	0.503289i	$-0.832123\pi$
$67$	−2.95352	+	2.95352i	−0.360830	+	0.360830i	0.503289	+	0.864118i	$0.332123\pi$
$68$	3.58943	−	3.58943i	0.435283	−	0.435283i
$69$	−6.24656			−0.751997
$70$	5.33919	−	2.54814i	0.638156	−	0.304561i
$71$	−10.8092			−1.28282			−0.641409	−	0.767199i	$-0.721650\pi$
$71$	−10.8092			−1.28282			−0.641409	+	0.767199i	$0.721650\pi$
$72$	3.69386	−	3.69386i	0.435326	−	0.435326i
$73$	−6.37937	+	6.37937i	−0.746649	+	0.746649i	−0.973848	−	0.227199i	$-0.927043\pi$
$73$	−6.37937	+	6.37937i	−0.746649	+	0.746649i	0.227199	+	0.973848i	$0.427043\pi$
$74$		−	3.99970i		−	0.464955i
$75$	4.51389	−	13.6096i	0.521219	−	1.57151i
$76$			8.41042i			0.964741i
$77$	−1.43371	+	2.22362i	−0.163387	+	0.253405i
$78$	1.22194	+	1.22194i	0.138358	+	0.138358i
$79$			12.8442i			1.44509i	0.691325	+	0.722544i	$0.257027\pi$
$79$			12.8442i			1.44509i	−0.691325	+	0.722544i	$0.742973\pi$
$80$	0.515374	+	2.17587i	0.0576206	+	0.243269i
$81$	−2.61748			−0.290831
$82$	8.54906	+	8.54906i	0.944086	+	0.944086i
$83$	−5.16803	+	5.16803i	−0.567265	+	0.567265i	−0.931361	−	0.364096i	$-0.881378\pi$
$83$	−5.16803	+	5.16803i	−0.567265	+	0.567265i	0.364096	+	0.931361i	$0.381378\pi$
$84$	7.41631	−	1.60176i	0.809186	−	0.174767i
$85$	5.96022	−	9.66002i	0.646477	−	1.04778i
$86$	−11.0199			−1.18831
$87$	−4.37903	−	4.37903i	−0.469481	−	0.469481i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	5.16538			0.547530			0.273765	−	0.961797i	$-0.411731\pi$
$89$	5.16538			0.547530			0.273765	+	0.961797i	$0.411731\pi$
$90$	6.13362	−	9.94106i	0.646541	−	1.04788i
$91$	0.336577	+	1.55839i	0.0352829	+	0.163363i
$92$	1.54023	−	1.54023i	0.160580	−	0.160580i
$93$	−18.0472	−	18.0472i	−1.87140	−	1.87140i
$94$	−8.15488			−0.841112
$95$	4.33451	+	18.2999i	0.444711	+	1.87753i
$96$			2.86774i			0.292687i
$97$	1.87168	+	1.87168i	0.190040	+	0.190040i	0.795714	−	0.605673i	$-0.207096\pi$
$97$	1.87168	+	1.87168i	0.190040	+	0.190040i	−0.605673	+	0.795714i	$0.707096\pi$
$98$	6.55134	+	2.46576i	0.661785	+	0.249080i
$99$			5.22391i			0.525022i
$100$	2.24277	+	4.46878i	0.224277	+	0.446878i
$101$		−	9.29425i		−	0.924812i	−0.886668	−	0.462406i	$-0.846986\pi$
$101$		−	9.29425i		−	0.924812i	0.886668	−	0.462406i	$-0.153014\pi$
$102$	10.2935	−	10.2935i	1.01921	−	1.01921i
$103$	−1.77914	+	1.77914i	−0.175304	+	0.175304i	−0.789305	−	0.614001i	$-0.789559\pi$
$103$	−1.77914	+	1.77914i	−0.175304	+	0.175304i	0.614001	+	0.789305i	$0.289559\pi$
$104$	−0.602596			−0.0590894
$105$	15.3114	−	7.30739i	1.49424	−	0.713129i
$106$	10.2681			0.997326
$107$	−1.79160	+	1.79160i	−0.173200	+	0.173200i	−0.788384	−	0.615184i	$-0.789082\pi$
$107$	−1.79160	+	1.79160i	−0.173200	+	0.173200i	0.615184	+	0.788384i	$0.289082\pi$
$108$	4.50963	−	4.50963i	0.433939	−	0.433939i
$109$			9.12492i			0.874009i	0.899459	+	0.437004i	$0.143961\pi$
$109$			9.12492i			0.874009i	−0.899459	+	0.437004i	$0.856039\pi$
$110$	−1.90299	−	1.17414i	−0.181443	−	0.111950i
$111$		−	11.4701i		−	1.08869i
$112$	−1.43371	+	2.22362i	−0.135473	+	0.210112i
$113$	3.31405	+	3.31405i	0.311760	+	0.311760i	0.845591	−	0.533831i	$-0.179248\pi$
$113$	3.31405	+	3.31405i	0.311760	+	0.311760i	−0.533831	+	0.845591i	$0.679248\pi$
$114$			24.1189i			2.25894i
$115$	2.55754	−	4.14514i	0.238492	−	0.386536i
$116$	2.15950			0.200505
$117$	2.22590	+	2.22590i	0.205785	+	0.205785i
$118$	3.74299	−	3.74299i	0.344570	−	0.344570i
$119$	13.1277	−	2.83531i	1.20342	−	0.259912i
$120$	1.47796	+	6.23981i	0.134918	+	0.569614i
$121$	1.00000			0.0909091
$122$	−3.94982	−	3.94982i	−0.357600	−	0.357600i
$123$	24.5165	+	24.5165i	2.21057	+	2.21057i
$124$	8.89990			0.799234
$125$	7.18306	+	8.56760i	0.642472	+	0.766309i
$126$	13.5097	−	2.91779i	1.20354	−	0.259938i
$127$	−2.15002	+	2.15002i	−0.190783	+	0.190783i	−0.796035	−	0.605251i	$-0.793073\pi$
$127$	−2.15002	+	2.15002i	−0.190783	+	0.190783i	0.605251	+	0.796035i	$0.293073\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−31.6022			−2.78242
$130$	−1.31117	+	0.310562i	−0.114997	+	0.0272381i
$131$		−	8.21641i		−	0.717871i	−0.933362	−	0.358936i	$-0.883140\pi$
$131$		−	8.21641i		−	0.717871i	0.933362	−	0.358936i	$-0.116860\pi$
$132$	−2.02780	−	2.02780i	−0.176497	−	0.176497i
$133$	−12.0581	+	18.7015i	−1.04557	+	1.62163i
$134$		−	4.17691i		−	0.360830i
$135$	7.48820	−	12.1365i	0.644481	−	1.04454i
$136$			5.07622i			0.435283i
$137$	−11.3647	+	11.3647i	−0.970948	+	0.970948i	−0.999590	−	0.0286418i	$-0.990882\pi$
$137$	−11.3647	+	11.3647i	−0.970948	+	0.970948i	0.0286418	+	0.999590i	$0.490882\pi$
$138$	4.41698	−	4.41698i	0.375998	−	0.375998i
$139$	5.67194			0.481088			0.240544	−	0.970638i	$-0.422674\pi$
$139$	5.67194			0.481088			0.240544	+	0.970638i	$0.422674\pi$
$140$	−1.97357	+	5.57719i	−0.166797	+	0.471358i
$141$	−23.3860			−1.96946
$142$	7.64327	−	7.64327i	0.641409	−	0.641409i
$143$	0.426099	−	0.426099i	0.0356322	−	0.0356322i
$144$			5.22391i			0.435326i
$145$	4.69879	−	1.11295i	0.390213	−	0.0924256i
$146$		−	9.02179i		−	0.746649i
$147$	18.7875	+	7.07116i	1.54957	+	0.583219i
$148$	2.82821	+	2.82821i	0.232478	+	0.232478i
$149$			8.66778i			0.710092i	0.934849	+	0.355046i	$0.115535\pi$
$149$			8.66778i			0.710092i	−0.934849	+	0.355046i	$0.884465\pi$
$150$	6.43167	+	12.8153i	0.525143	+	1.04636i
$151$	−23.5639			−1.91761			−0.958803	−	0.284071i	$-0.908315\pi$
$151$	−23.5639			−1.91761			−0.958803	+	0.284071i	$0.908315\pi$
$152$	−5.94706	−	5.94706i	−0.482371	−	0.482371i
$153$	18.7509	−	18.7509i	1.51592	−	1.51592i
$154$	−0.558546	−	2.58612i	−0.0450089	−	0.208396i
$155$	19.3650	−	4.58677i	1.55543	−	0.368419i
$156$	−1.72808			−0.138358
$157$	−4.17299	−	4.17299i	−0.333041	−	0.333041i	0.520699	−	0.853740i	$-0.325671\pi$
$157$	−4.17299	−	4.17299i	−0.333041	−	0.333041i	−0.853740	+	0.520699i	$0.825671\pi$
$158$	−9.08223	−	9.08223i	−0.722544	−	0.722544i
$159$	29.4462			2.33523
$160$	−1.90299	−	1.17414i	−0.150445	−	0.0928243i
$161$	5.63314	−	1.21664i	0.443954	−	0.0958843i
$162$	1.85084	−	1.85084i	0.145416	−	0.145416i
$163$	5.46200	+	5.46200i	0.427817	+	0.427817i	0.887884	−	0.460067i	$-0.152175\pi$
$163$	5.46200	+	5.46200i	0.427817	+	0.427817i	−0.460067	+	0.887884i	$0.652175\pi$
$164$	−12.0902			−0.944086
$165$	−5.45728	−	3.36714i	−0.424849	−	0.262131i
$166$		−	7.30870i		−	0.567265i
$167$	3.85669	+	3.85669i	0.298440	+	0.298440i	0.840402	−	0.541963i	$-0.182319\pi$
$167$	3.85669	+	3.85669i	0.298440	+	0.298440i	−0.541963	+	0.840402i	$0.682319\pi$
$168$	−4.11151	+	6.37674i	−0.317210	+	0.491976i
$169$			12.6369i			0.972068i
$170$	2.61615	+	11.0452i	0.200650	+	0.847127i
$171$			43.9352i			3.35981i
$172$	7.79227	−	7.79227i	0.594155	−	0.594155i
$173$	−2.87563	+	2.87563i	−0.218630	+	0.218630i	−0.807921	−	0.589291i	$-0.799407\pi$
$173$	−2.87563	+	2.87563i	−0.218630	+	0.218630i	0.589291	+	0.807921i	$0.299407\pi$
$174$	6.19289			0.469481
$175$	−1.41989	+	13.1523i	−0.107333	+	0.994223i
$176$	1.00000			0.0753778
$177$	10.7339	−	10.7339i	0.806810	−	0.806810i
$178$	−3.65248	+	3.65248i	−0.273765	+	0.273765i
$179$			4.88835i			0.365373i	0.983171	+	0.182686i	$0.0584793\pi$
$179$			4.88835i			0.365373i	−0.983171	+	0.182686i	$0.941521\pi$
$180$	2.69227	+	11.3665i	0.200670	+	0.847210i
$181$		−	14.7856i		−	1.09900i	−0.835492	−	0.549502i	$-0.814817\pi$
$181$		−	14.7856i		−	1.09900i	0.835492	−	0.549502i	$-0.185183\pi$
$182$	−1.33994	−	0.863949i	−0.0993231	−	0.0640401i
$183$	−11.3270	−	11.3270i	−0.837318	−	0.837318i
$184$			2.17822i			0.160580i
$185$	7.61139	+	4.69622i	0.559601	+	0.345273i
$186$	25.5225			1.87140
$187$	−3.58943	−	3.58943i	−0.262485	−	0.262485i
$188$	5.76637	−	5.76637i	0.420556	−	0.420556i
$189$	16.4932	−	3.56217i	1.19970	−	0.259110i
$190$	−16.0050	−	9.87505i	−1.16112	−	0.716411i
$191$	14.2893			1.03394			0.516968	−	0.856005i	$-0.327061\pi$
$191$	14.2893			1.03394			0.516968	+	0.856005i	$0.327061\pi$
$192$	−2.02780	−	2.02780i	−0.146344	−	0.146344i
$193$	−16.4264	−	16.4264i	−1.18240	−	1.18240i	−0.979121	−	0.203280i	$-0.934840\pi$
$193$	−16.4264	−	16.4264i	−1.18240	−	1.18240i	−0.203280	−	0.979121i	$-0.565160\pi$
$194$	−2.64696			−0.190040
$195$	−3.76008	+	0.890610i	−0.269265	+	0.0637779i
$196$	−6.37605	+	2.88894i	−0.455432	+	0.206353i
$197$	7.38893	−	7.38893i	0.526439	−	0.526439i	−0.393070	−	0.919509i	$-0.628587\pi$
$197$	7.38893	−	7.38893i	0.526439	−	0.526439i	0.919509	+	0.393070i	$0.128587\pi$
$198$	−3.69386	−	3.69386i	−0.262511	−	0.262511i
$199$	22.9111			1.62413			0.812064	−	0.583569i	$-0.198344\pi$
$199$	22.9111			1.62413			0.812064	+	0.583569i	$0.198344\pi$
$200$	−4.74578	−	1.57403i	−0.335577	−	0.111301i
$201$		−	11.9783i		−	0.844881i
$202$	6.57203	+	6.57203i	0.462406	+	0.462406i
$203$	4.80191	+	3.09611i	0.337028	+	0.217304i
$204$			14.5573i			1.01921i
$205$	−26.3067	+	6.23098i	−1.83734	+	0.435190i
$206$		−	2.51609i		−	0.175304i
$207$	8.04603	−	8.04603i	0.559238	−	0.559238i
$208$	0.426099	−	0.426099i	0.0295447	−	0.0295447i
$209$	8.41042			0.581761
$210$	−5.65968	+	15.9939i	−0.390555	+	1.10368i
$211$	−23.0484			−1.58672			−0.793359	−	0.608754i	$-0.791670\pi$
$211$	−23.0484			−1.58672			−0.793359	+	0.608754i	$0.791670\pi$
$212$	−7.26064	+	7.26064i	−0.498663	+	0.498663i
$213$	21.9189	−	21.9189i	1.50186	−	1.50186i
$214$		−	2.53370i		−	0.173200i
$215$	12.9390	−	20.9709i	0.882432	−	1.43020i
$216$			6.37758i			0.433939i
$217$	19.7900	+	12.7599i	1.34343	+	0.866198i
$218$	−6.45229	−	6.45229i	−0.437004	−	0.437004i
$219$		−	25.8721i		−	1.74828i
$220$	2.17587	−	0.515374i	0.146697	−	0.0347465i
$221$	−3.05891			−0.205765
$222$	8.11056	+	8.11056i	0.544345	+	0.544345i
$223$	−0.570760	+	0.570760i	−0.0382209	+	0.0382209i	−0.725959	−	0.687738i	$-0.758604\pi$
$223$	−0.570760	+	0.570760i	−0.0382209	+	0.0382209i	0.687738	+	0.725959i	$0.258604\pi$
$224$	−0.558546	−	2.58612i	−0.0373194	−	0.172793i
$225$	11.7160	+	23.3445i	0.781068	+	1.55630i
$226$	−4.68678			−0.311760
$227$	−7.07099	−	7.07099i	−0.469318	−	0.469318i	0.432376	−	0.901694i	$-0.357675\pi$
$227$	−7.07099	−	7.07099i	−0.469318	−	0.469318i	−0.901694	+	0.432376i	$0.857675\pi$
$228$	−17.0546	−	17.0546i	−1.12947	−	1.12947i
$229$	9.03758			0.597220			0.298610	−	0.954375i	$-0.403477\pi$
$229$	9.03758			0.597220			0.298610	+	0.954375i	$0.403477\pi$
$230$	1.12260	+	4.73951i	0.0740219	+	0.312514i
$231$	−1.60176	−	7.41631i	−0.105388	−	0.487958i
$232$	−1.52700	+	1.52700i	−0.100252	+	0.100252i
$233$	9.20906	+	9.20906i	0.603306	+	0.603306i	0.941188	−	0.337883i	$-0.109711\pi$
$233$	9.20906	+	9.20906i	0.603306	+	0.603306i	−0.337883	+	0.941188i	$0.609711\pi$
$234$	−3.14790			−0.205785
$235$	9.57501	−	15.5187i	0.624605	−	1.01233i
$236$			5.29339i			0.344570i
$237$	−26.0454	−	26.0454i	−1.69183	−	1.69183i
$238$	−7.27785	+	11.2876i	−0.471753	+	0.731665i
$239$		−	12.4264i		−	0.803798i	−0.915684	−	0.401899i	$-0.868350\pi$
$239$		−	12.4264i		−	0.803798i	0.915684	−	0.401899i	$-0.131650\pi$
$240$	−5.45728	−	3.36714i	−0.352266	−	0.217348i
$241$		−	4.20260i		−	0.270713i	−0.990797	−	0.135357i	$-0.956782\pi$
$241$		−	4.20260i		−	0.270713i	0.990797	−	0.135357i	$-0.0432180\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	−8.22117	+	8.22117i	−0.527388	+	0.527388i
$244$	5.58589			0.357600
$245$	−12.3845	+	9.57199i	−0.791220	+	0.611532i
$246$	−34.6715			−2.21057
$247$	3.58367	−	3.58367i	0.228024	−	0.228024i
$248$	−6.29318	+	6.29318i	−0.399617	+	0.399617i
$249$		−	20.9594i		−	1.32825i
$250$	−11.1374	−	0.979019i	−0.704391	−	0.0619186i
$251$		−	17.1523i		−	1.08264i	−0.840816	−	0.541321i	$-0.817925\pi$
$251$		−	17.1523i		−	1.08264i	0.840816	−	0.541321i	$-0.182075\pi$
$252$	−7.48958	+	11.6160i	−0.471799	+	0.731737i
$253$	−1.54023	−	1.54023i	−0.0968336	−	0.0968336i
$254$		−	3.04059i		−	0.190783i
$255$	7.50244	+	31.6747i	0.469821	+	1.98354i
$256$	1.00000			0.0625000
$257$	1.49092	+	1.49092i	0.0930013	+	0.0930013i	0.752077	−	0.659075i	$-0.229052\pi$
$257$	1.49092	+	1.49092i	0.0930013	+	0.0930013i	−0.659075	+	0.752077i	$0.729052\pi$
$258$	22.3462	−	22.3462i	1.39121	−	1.39121i
$259$	2.23401	+	10.3437i	0.138815	+	0.642726i
$260$	0.707534	−	1.14674i	0.0438794	−	0.0711175i
$261$	11.2810			0.698279
$262$	5.80988	+	5.80988i	0.358936	+	0.358936i
$263$	3.56672	+	3.56672i	0.219933	+	0.219933i	0.808470	−	0.588537i	$-0.200296\pi$
$263$	3.56672	+	3.56672i	0.219933	+	0.219933i	−0.588537	+	0.808470i	$0.700296\pi$
$264$	2.86774			0.176497
$265$	−12.0562	+	19.5401i	−0.740608	+	1.20034i
$266$	−4.69761	−	21.7504i	−0.288029	−	1.33360i
$267$	−10.4743	+	10.4743i	−0.641019	+	0.641019i
$268$	2.95352	+	2.95352i	0.180415	+	0.180415i
$269$	−9.82406			−0.598983			−0.299492	−	0.954099i	$-0.596817\pi$
$269$	−9.82406			−0.598983			−0.299492	+	0.954099i	$0.596817\pi$
$270$	3.28684	+	13.8767i	0.200031	+	0.844512i
$271$		−	15.2931i		−	0.928991i	−0.885575	−	0.464496i	$-0.846236\pi$
$271$		−	15.2931i		−	0.928991i	0.885575	−	0.464496i	$-0.153764\pi$
$272$	−3.58943	−	3.58943i	−0.217641	−	0.217641i
$273$	−3.84260	−	2.47758i	−0.232565	−	0.149950i
$274$		−	16.0720i		−	0.970948i
$275$	4.46878	−	2.24277i	0.269478	−	0.135244i
$276$			6.24656i			0.375998i
$277$	−0.579409	+	0.579409i	−0.0348133	+	0.0348133i	−0.724299	−	0.689486i	$-0.757837\pi$
$277$	−0.579409	+	0.579409i	−0.0348133	+	0.0348133i	0.689486	+	0.724299i	$0.257837\pi$
$278$	−4.01067	+	4.01067i	−0.240544	+	0.240544i
$279$	46.4922			2.78342
$280$	−2.54814	−	5.33919i	−0.152281	−	0.319078i
$281$	−0.942528			−0.0562265			−0.0281133	−	0.999605i	$-0.508950\pi$
$281$	−0.942528			−0.0562265			−0.0281133	+	0.999605i	$0.508950\pi$
$282$	16.5364	−	16.5364i	0.984730	−	0.984730i
$283$	−5.18279	+	5.18279i	−0.308085	+	0.308085i	−0.844166	−	0.536081i	$-0.819904\pi$
$283$	−5.18279	+	5.18279i	−0.308085	+	0.308085i	0.536081	+	0.844166i	$0.319904\pi$
$284$			10.8092i			0.641409i
$285$	−45.8980	−	28.3190i	−2.71876	−	1.67747i
$286$			0.602596i			0.0356322i
$287$	−26.8840	−	17.3339i	−1.58691	−	1.02319i
$288$	−3.69386	−	3.69386i	−0.217663	−	0.217663i
$289$			8.76806i			0.515768i
$290$	−2.53557	+	4.10952i	−0.148894	+	0.241319i
$291$	−7.59077			−0.444979
$292$	6.37937	+	6.37937i	0.373324	+	0.373324i
$293$	−6.20707	+	6.20707i	−0.362621	+	0.362621i	−0.864777	−	0.502156i	$-0.832540\pi$
$293$	−6.20707	+	6.20707i	−0.362621	+	0.362621i	0.502156	+	0.864777i	$0.332540\pi$
$294$	−18.2848	+	8.28471i	−1.06639	+	0.483174i
$295$	2.72807	+	11.5177i	0.158835	+	0.670586i
$296$	−3.99970			−0.232478
$297$	−4.50963	−	4.50963i	−0.261675	−	0.261675i
$298$	−6.12905	−	6.12905i	−0.355046	−	0.355046i
$299$	−1.31259			−0.0759088
$300$	−13.6096	−	4.51389i	−0.785753	−	0.260610i
$301$	28.4989	−	6.15514i	1.64265	−	0.354776i
$302$	16.6622	−	16.6622i	0.958803	−	0.958803i
$303$	18.8468	+	18.8468i	1.08272	+	1.08272i
$304$	8.41042			0.482371
$305$	12.1541	−	2.87882i	0.695944	−	0.164841i
$306$			26.5177i			1.51592i
$307$	14.8025	+	14.8025i	0.844821	+	0.844821i	0.989481	−	0.144660i	$-0.0462089\pi$
$307$	14.8025	+	14.8025i	0.844821	+	0.844821i	−0.144660	+	0.989481i	$0.546209\pi$
$308$	2.22362	+	1.43371i	0.126702	+	0.0816934i
$309$		−	7.21547i		−	0.410474i
$310$	−10.4498	+	16.9364i	−0.593507	+	0.961925i
$311$			6.78114i			0.384523i	0.981344	+	0.192261i	$0.0615822\pi$
$311$			6.78114i			0.384523i	−0.981344	+	0.192261i	$0.938418\pi$
$312$	1.22194	−	1.22194i	0.0691788	−	0.0691788i
$313$	−5.84790	+	5.84790i	−0.330543	+	0.330543i	−0.852793	−	0.522250i	$-0.825093\pi$
$313$	−5.84790	+	5.84790i	−0.330543	+	0.330543i	0.522250	+	0.852793i	$0.325093\pi$
$314$	5.90149			0.333041
$315$	−10.3098	+	29.1347i	−0.580889	+	1.64155i
$316$	12.8442			0.722544
$317$	0.591595	−	0.591595i	0.0332273	−	0.0332273i	−0.690298	−	0.723525i	$-0.742521\pi$
$317$	0.591595	−	0.591595i	0.0332273	−	0.0332273i	0.723525	+	0.690298i	$0.242521\pi$
$318$	−20.8216	+	20.8216i	−1.16762	+	1.16762i
$319$		−	2.15950i		−	0.120909i
$320$	2.17587	−	0.515374i	0.121635	−	0.0288103i
$321$		−	7.26598i		−	0.405548i
$322$	−3.12294	+	4.84352i	−0.174035	+	0.269919i
$323$	−30.1886	−	30.1886i	−1.67974	−	1.67974i
$324$			2.61748i			0.145416i
$325$	0.948502	−	2.85979i	0.0526134	−	0.158632i
$326$	−7.72444			−0.427817
$327$	−18.5035	−	18.5035i	−1.02324	−	1.02324i
$328$	8.54906	−	8.54906i	0.472043	−	0.472043i
$329$	21.0895	−	4.55488i	1.16270	−	0.251118i
$330$	6.23981	−	1.47796i	0.343490	−	0.0813588i
$331$	25.5299			1.40325			0.701626	−	0.712545i	$-0.252458\pi$
$331$	25.5299			1.40325			0.701626	+	0.712545i	$0.252458\pi$
$332$	5.16803	+	5.16803i	0.283632	+	0.283632i
$333$	14.7743	+	14.7743i	0.809627	+	0.809627i
$334$	−5.45418			−0.298440
$335$	7.94862	+	4.90429i	0.434280	+	0.267950i
$336$	−1.60176	−	7.41631i	−0.0873833	−	0.404593i
$337$	−5.60086	+	5.60086i	−0.305098	+	0.305098i	−0.843005	−	0.537906i	$-0.819215\pi$
$337$	−5.60086	+	5.60086i	−0.305098	+	0.305098i	0.537906	+	0.843005i	$0.319215\pi$
$338$	−8.93562	−	8.93562i	−0.486034	−	0.486034i
$339$	−13.4404			−0.729984
$340$	−9.66002	−	5.96022i	−0.523888	−	0.323238i
$341$		−	8.89990i		−	0.481956i
$342$	−31.0669	−	31.0669i	−1.67991	−	1.67991i
$343$	−18.3198	−	2.71754i	−0.989176	−	0.146733i
$344$			11.0199i			0.594155i
$345$	3.21931	+	13.5917i	0.173322	+	0.731750i
$346$		−	4.06676i		−	0.218630i
$347$	−4.02552	+	4.02552i	−0.216101	+	0.216101i	−0.806853	−	0.590752i	$-0.798831\pi$
$347$	−4.02552	+	4.02552i	−0.216101	+	0.216101i	0.590752	+	0.806853i	$0.298831\pi$
$348$	−4.37903	+	4.37903i	−0.234741	+	0.234741i
$349$	−16.2397			−0.869291			−0.434645	−	0.900602i	$-0.643126\pi$
$349$	−16.2397			−0.869291			−0.434645	+	0.900602i	$0.643126\pi$
$350$	−8.29609	−	10.3041i	−0.443445	−	0.550778i
$351$	−3.84310			−0.205129
$352$	−0.707107	+	0.707107i	−0.0376889	+	0.0376889i
$353$	9.51040	−	9.51040i	0.506188	−	0.506188i	−0.407166	−	0.913354i	$-0.633483\pi$
$353$	9.51040	−	9.51040i	0.506188	−	0.506188i	0.913354	+	0.407166i	$0.133483\pi$
$354$			15.1800i			0.806810i
$355$	5.57079	+	23.5194i	0.295667	+	1.24828i
$356$		−	5.16538i		−	0.273765i
$357$	−20.8709	+	32.3698i	−1.10461	+	1.71319i
$358$	−3.45659	−	3.45659i	−0.182686	−	0.182686i
$359$		−	1.40979i		−	0.0744056i	−0.999308	−	0.0372028i	$-0.988155\pi$
$359$		−	1.40979i		−	0.0744056i	0.999308	−	0.0372028i	$-0.0118448\pi$
$360$	−9.94106	−	6.13362i	−0.523940	−	0.323270i
$361$	51.7351			2.72290
$362$	10.4550	+	10.4550i	0.549502	+	0.549502i
$363$	−2.02780	+	2.02780i	−0.106432	+	0.106432i
$364$	1.55839	−	0.336577i	0.0816816	−	0.0176415i
$365$	17.1684	+	10.5929i	0.898636	+	0.554457i
$366$	16.0188			0.837318
$367$	−8.25094	−	8.25094i	−0.430695	−	0.430695i	0.458169	−	0.888865i	$-0.348505\pi$
$367$	−8.25094	−	8.25094i	−0.430695	−	0.430695i	−0.888865	+	0.458169i	$0.848505\pi$
$368$	−1.54023	−	1.54023i	−0.0802902	−	0.0802902i
$369$	−63.1581			−3.28788
$370$	−8.70280	+	2.06134i	−0.452437	+	0.107164i
$371$	−26.5545	+	5.73521i	−1.37864	+	0.297757i
$372$	−18.0472	+	18.0472i	−0.935702	+	0.935702i
$373$	−11.6166	−	11.6166i	−0.601482	−	0.601482i	0.339224	−	0.940706i	$-0.389836\pi$
$373$	−11.6166	−	11.6166i	−0.601482	−	0.601482i	−0.940706	+	0.339224i	$0.889836\pi$
$374$	5.07622			0.262485
$375$	−31.9391	−	2.80757i	−1.64933	−	0.144982i
$376$			8.15488i			0.420556i
$377$	−0.920163	−	0.920163i	−0.0473908	−	0.0473908i
$378$	−9.14361	+	14.1813i	−0.470297	+	0.729406i
$379$			21.7176i			1.11556i	0.829990	+	0.557779i	$0.188346\pi$
$379$			21.7176i			1.11556i	−0.829990	+	0.557779i	$0.811654\pi$
$380$	18.2999	−	4.33451i	0.938767	−	0.222356i
$381$		−	8.71960i		−	0.446719i
$382$	−10.1040	+	10.1040i	−0.516968	+	0.516968i
$383$	−7.72049	+	7.72049i	−0.394499	+	0.394499i	−0.876287	−	0.481789i	$-0.839987\pi$
$383$	−7.72049	+	7.72049i	−0.394499	+	0.394499i	0.481789	+	0.876287i	$0.339987\pi$
$384$	2.86774			0.146344
$385$	5.57719	+	1.97357i	0.284240	+	0.100583i
$386$	23.2305			1.18240
$387$	40.7061	−	40.7061i	2.06921	−	2.06921i
$388$	1.87168	−	1.87168i	0.0950202	−	0.0950202i
$389$		−	0.447748i		−	0.0227017i	−0.999936	−	0.0113509i	$-0.996387\pi$
$389$		−	0.447748i		−	0.0227017i	0.999936	−	0.0113509i	$-0.00361317\pi$
$390$	2.02902	−	3.28853i	0.102743	−	0.166521i
$391$			11.0571i			0.559183i
$392$	2.46576	−	6.55134i	0.124540	−	0.330892i
$393$	16.6612	+	16.6612i	0.840447	+	0.840447i
$394$			10.4495i			0.526439i
$395$	27.9473	−	6.61958i	1.40618	−	0.333067i
$396$	5.22391			0.262511
$397$	12.5668	+	12.5668i	0.630712	+	0.630712i	0.948247	−	0.317535i	$-0.102855\pi$
$397$	12.5668	+	12.5668i	0.630712	+	0.630712i	−0.317535	+	0.948247i	$0.602855\pi$
$398$	−16.2006	+	16.2006i	−0.812064	+	0.812064i
$399$	−13.4715	−	62.3743i	−0.674418	−	3.12262i
$400$	4.46878	−	2.24277i	0.223439	−	0.112138i
$401$	30.1252			1.50438			0.752189	−	0.658947i	$-0.228998\pi$
$401$	30.1252			1.50438			0.752189	+	0.658947i	$0.228998\pi$
$402$	8.46991	+	8.46991i	0.422441	+	0.422441i
$403$	−3.79224	−	3.79224i	−0.188905	−	0.188905i
$404$	−9.29425			−0.462406
$405$	1.34898	+	5.69528i	0.0670314	+	0.283001i
$406$	−5.58474	+	1.20618i	−0.277166	+	0.0598618i
$407$	2.82821	−	2.82821i	0.140189	−	0.140189i
$408$	−10.2935	−	10.2935i	−0.509606	−	0.509606i
$409$	−3.90891			−0.193283			−0.0966416	−	0.995319i	$-0.530810\pi$
$409$	−3.90891			−0.193283			−0.0966416	+	0.995319i	$0.530810\pi$
$410$	14.1956	−	23.0076i	0.701073	−	1.13626i
$411$		−	46.0904i		−	2.27347i
$412$	1.77914	+	1.77914i	0.0876520	+	0.0876520i
$413$	−7.58920	+	11.7705i	−0.373440	+	0.579187i
$414$			11.3788i			0.559238i
$415$	13.9084	+	8.58147i	0.682737	+	0.421248i
$416$			0.602596i			0.0295447i
$417$	−11.5015	+	11.5015i	−0.563232	+	0.563232i
$418$	−5.94706	+	5.94706i	−0.290880	+	0.290880i
$419$	10.6110			0.518382			0.259191	−	0.965826i	$-0.416544\pi$
$419$	10.6110			0.518382			0.259191	+	0.965826i	$0.416544\pi$
$420$	−7.30739	−	15.3114i	−0.356564	−	0.747119i
$421$	−16.6336			−0.810670			−0.405335	−	0.914168i	$-0.632845\pi$
$421$	−16.6336			−0.810670			−0.405335	+	0.914168i	$0.632845\pi$
$422$	16.2977	−	16.2977i	0.793359	−	0.793359i
$423$	30.1230	−	30.1230i	1.46463	−	1.46463i
$424$		−	10.2681i		−	0.498663i
$425$	−24.0907	−	7.99011i	−1.16857	−	0.387577i
$426$			30.9980i			1.50186i
$427$	12.4209	+	8.00855i	0.601088	+	0.387561i
$428$	1.79160	+	1.79160i	0.0866001	+	0.0866001i
$429$			1.72808i			0.0834327i
$430$	5.67939	+	23.9779i	0.273884	+	1.15632i
$431$	1.81164			0.0872634			0.0436317	−	0.999048i	$-0.486107\pi$
$431$	1.81164			0.0872634			0.0436317	+	0.999048i	$0.486107\pi$
$432$	−4.50963	−	4.50963i	−0.216970	−	0.216970i
$433$	9.59089	−	9.59089i	0.460909	−	0.460909i	−0.438045	−	0.898953i	$-0.644329\pi$
$433$	9.59089	−	9.59089i	0.460909	−	0.460909i	0.898953	+	0.438045i	$0.144329\pi$
$434$	−23.0162	+	4.97100i	−1.10481	+	0.238616i
$435$	−7.27134	+	11.7850i	−0.348634	+	0.565049i
$436$	9.12492			0.437004
$437$	−12.9540	−	12.9540i	−0.619674	−	0.619674i
$438$	18.2944	+	18.2944i	0.874138	+	0.874138i
$439$	−28.0553			−1.33901			−0.669503	−	0.742809i	$-0.733493\pi$
$439$	−28.0553			−1.33901			−0.669503	+	0.742809i	$0.733493\pi$
$440$	−1.17414	+	1.90299i	−0.0559751	+	0.0907217i
$441$	−33.3079	+	15.0915i	−1.58609	+	0.718645i
$442$	2.16298	−	2.16298i	0.102882	−	0.102882i
$443$	−16.2533	−	16.2533i	−0.772218	−	0.772218i	0.206276	−	0.978494i	$-0.433866\pi$
$443$	−16.2533	−	16.2533i	−0.772218	−	0.772218i	−0.978494	+	0.206276i	$0.933866\pi$
$444$	−11.4701			−0.544345
$445$	−2.66211	−	11.2392i	−0.126196	−	0.532788i
$446$		−	0.807176i		−	0.0382209i
$447$	−17.5765	−	17.5765i	−0.831339	−	0.831339i
$448$	2.22362	+	1.43371i	0.105056	+	0.0677365i
$449$		−	0.726179i		−	0.0342705i	−0.999853	−	0.0171352i	$-0.994545\pi$
$449$		−	0.726179i		−	0.0342705i	0.999853	−	0.0171352i	$-0.00545459\pi$
$450$	−24.7915	−	8.22257i	−1.16868	−	0.387616i
$451$			12.0902i			0.569305i
$452$	3.31405	−	3.31405i	0.155880	−	0.155880i
$453$	47.7829	−	47.7829i	2.24503	−	2.24503i
$454$	9.99989			0.469318
$455$	3.21737	−	1.53550i	0.150833	−	0.0719853i
$456$	24.1189			1.12947
$457$	0.0698758	−	0.0698758i	0.00326865	−	0.00326865i	−0.705471	−	0.708739i	$-0.749264\pi$
$457$	0.0698758	−	0.0698758i	0.00326865	−	0.00326865i	0.708739	+	0.705471i	$0.249264\pi$
$458$	−6.39053	+	6.39053i	−0.298610	+	0.298610i
$459$			32.3740i			1.51109i
$460$	−4.14514	−	2.55754i	−0.193268	−	0.119246i
$461$			16.0772i			0.748792i	0.927269	+	0.374396i	$0.122150\pi$
$461$			16.0772i			0.748792i	−0.927269	+	0.374396i	$0.877850\pi$
$462$	6.37674	+	4.11151i	0.296673	+	0.191285i
$463$	−11.0468	−	11.0468i	−0.513388	−	0.513388i	0.402175	−	0.915563i	$-0.368254\pi$
$463$	−11.0468	−	11.0468i	−0.513388	−	0.513388i	−0.915563	+	0.402175i	$0.868254\pi$
$464$		−	2.15950i		−	0.100252i
$465$	−29.9672	+	48.5692i	−1.38969	+	2.25234i
$466$	−13.0236			−0.603306
$467$	22.4774	+	22.4774i	1.04013	+	1.04013i	0.999160	+	0.0409712i	$0.0130452\pi$
$467$	22.4774	+	22.4774i	1.04013	+	1.04013i	0.0409712	+	0.999160i	$0.486955\pi$
$468$	2.22590	−	2.22590i	0.102892	−	0.102892i
$469$	2.33299	+	10.8020i	0.107728	+	0.498789i
$470$	4.20281	+	17.7439i	0.193861	+	0.818466i
$471$	16.9239			0.779813
$472$	−3.74299	−	3.74299i	−0.172285	−	0.172285i
$473$	−7.79227	−	7.79227i	−0.358289	−	0.358289i
$474$	36.8338			1.69183
$475$	37.5843	−	18.8626i	1.72449	−	0.865477i
$476$	−2.83531	−	13.1277i	−0.129956	−	0.601709i
$477$	−37.9289	+	37.9289i	−1.73665	+	1.73665i
$478$	8.78680	+	8.78680i	0.401899	+	0.401899i
$479$	−27.7653			−1.26863			−0.634314	−	0.773076i	$-0.718717\pi$
$479$	−27.7653			−1.26863			−0.634314	+	0.773076i	$0.718717\pi$
$480$	6.23981	−	1.47796i	0.284807	−	0.0674592i
$481$		−	2.41020i		−	0.109896i
$482$	2.97169	+	2.97169i	0.135357	+	0.135357i
$483$	−8.95576	+	13.8899i	−0.407501	+	0.632014i
$484$		−	1.00000i		−	0.0454545i
$485$	3.10791	−	5.03714i	0.141123	−	0.228725i
$486$		−	11.6265i		−	0.527388i
$487$	5.01532	−	5.01532i	0.227266	−	0.227266i	−0.584284	−	0.811549i	$-0.698624\pi$
$487$	5.01532	−	5.01532i	0.227266	−	0.227266i	0.811549	+	0.584284i	$0.198624\pi$
$488$	−3.94982	+	3.94982i	−0.178800	+	0.178800i
$489$	−22.1516			−1.00173
$490$	1.98878	−	15.5256i	0.0898439	−	0.701376i
$491$	−2.98425			−0.134677			−0.0673387	−	0.997730i	$-0.521451\pi$
$491$	−2.98425			−0.134677			−0.0673387	+	0.997730i	$0.521451\pi$
$492$	24.5165	−	24.5165i	1.10529	−	1.10529i
$493$	−7.75139	+	7.75139i	−0.349105	+	0.349105i
$494$			5.06808i			0.228024i
$495$	11.3665	−	2.69227i	0.510887	−	0.121008i
$496$		−	8.89990i		−	0.399617i
$497$	−15.4973	+	24.0356i	−0.695150	+	1.07814i
$498$	14.8205	+	14.8205i	0.664124	+	0.664124i
$499$		−	16.0277i		−	0.717500i	−0.933434	−	0.358750i	$-0.883203\pi$
$499$		−	16.0277i		−	0.717500i	0.933434	−	0.358750i	$-0.116797\pi$
$500$	8.56760	−	7.18306i	0.383155	−	0.321236i
$501$	−15.6412			−0.698795
$502$	12.1285	+	12.1285i	0.541321	+	0.541321i
$503$	3.97613	−	3.97613i	0.177287	−	0.177287i	−0.612885	−	0.790172i	$-0.709991\pi$
$503$	3.97613	−	3.97613i	0.177287	−	0.177287i	0.790172	+	0.612885i	$0.209991\pi$
$504$	−2.91779	−	13.5097i	−0.129969	−	0.601768i
$505$	−20.2230	+	4.79001i	−0.899913	+	0.213153i
$506$	2.17822			0.0968336
$507$	−25.6250	−	25.6250i	−1.13805	−	1.13805i
$508$	2.15002	+	2.15002i	0.0953917	+	0.0953917i
$509$	22.4464			0.994919			0.497459	−	0.867487i	$-0.334266\pi$
$509$	22.4464			0.994919			0.497459	+	0.867487i	$0.334266\pi$
$510$	−27.7024	−	17.0923i	−1.22668	−	0.756861i
$511$	5.03909	+	23.3315i	0.222916	+	1.03212i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−37.9279	−	37.9279i	−1.67456	−	1.67456i
$514$	−2.10849			−0.0930013
$515$	4.78810	+	2.95425i	0.210989	+	0.130180i
$516$			31.6022i			1.39121i
$517$	−5.76637	−	5.76637i	−0.253605	−	0.253605i
$518$	−8.89379	−	5.73441i	−0.390771	−	0.251956i
$519$		−	11.6624i		−	0.511922i
$520$	0.310562	+	1.31117i	0.0136190	+	0.0574985i
$521$			8.26619i			0.362148i	0.983469	+	0.181074i	$0.0579574\pi$
$521$			8.26619i			0.362148i	−0.983469	+	0.181074i	$0.942043\pi$
$522$	−7.97690	+	7.97690i	−0.349140	+	0.349140i
$523$	−26.7002	+	26.7002i	−1.16752	+	1.16752i	−0.184731	+	0.982789i	$0.559141\pi$
$523$	−26.7002	+	26.7002i	−1.16752	+	1.16752i	−0.982789	+	0.184731i	$0.940859\pi$
$524$	−8.21641			−0.358936
$525$	−23.7910	−	29.5495i	−1.03832	−	1.28965i
$526$	−5.04410			−0.219933
$527$	−31.9456	+	31.9456i	−1.39157	+	1.39157i
$528$	−2.02780	+	2.02780i	−0.0882485	+	0.0882485i
$529$		−	18.2554i		−	0.793711i
$530$	−5.29191	−	22.3420i	−0.229866	−	0.970474i
$531$			27.6522i			1.20000i
$532$	18.7015	+	12.0581i	0.810815	+	0.522786i
$533$	5.15163	+	5.15163i	0.223142	+	0.223142i
$534$		−	14.8130i		−	0.641019i
$535$	4.82161	+	2.97493i	0.208457	+	0.128617i
$536$	−4.17691			−0.180415
$537$	−9.91258	−	9.91258i	−0.427759	−	0.427759i
$538$	6.94666	−	6.94666i	0.299492	−	0.299492i
$539$	2.88894	+	6.37605i	0.124435	+	0.274636i
$540$	−12.1365	−	7.48820i	−0.522271	−	0.322241i
$541$	−40.0365			−1.72131			−0.860653	−	0.509192i	$-0.829944\pi$
$541$	−40.0365			−1.72131			−0.860653	+	0.509192i	$0.829944\pi$
$542$	10.8139	+	10.8139i	0.464496	+	0.464496i
$543$	29.9822	+	29.9822i	1.28666	+	1.28666i
$544$	5.07622			0.217641
$545$	19.8546	−	4.70275i	0.850477	−	0.201444i
$546$	4.46904	−	0.965215i	0.191257	−	0.0413074i
$547$	30.2959	−	30.2959i	1.29536	−	1.29536i	0.363937	−	0.931423i	$-0.381432\pi$
$547$	30.2959	−	30.2959i	1.29536	−	1.29536i	0.931423	−	0.363937i	$-0.118568\pi$
$548$	11.3647	+	11.3647i	0.485474	+	0.485474i
$549$	29.1801			1.24538
$550$	−1.57403	+	4.74578i	−0.0671167	+	0.202361i
$551$		−	18.1623i		−	0.773741i
$552$	−4.41698	−	4.41698i	−0.187999	−	0.187999i
$553$	28.5606	+	18.4149i	1.21452	+	0.783082i
$554$		−	0.819409i		−	0.0348133i
$555$	−24.9573	+	5.91138i	−1.05938	+	0.250924i
$556$		−	5.67194i		−	0.240544i
$557$	25.7599	−	25.7599i	1.09148	−	1.09148i	0.0961126	−	0.995370i	$-0.469359\pi$
$557$	25.7599	−	25.7599i	1.09148	−	1.09148i	0.995370	−	0.0961126i	$-0.0306409\pi$
$558$	−32.8750	+	32.8750i	−1.39171	+	1.39171i
$559$	−6.64056			−0.280866
$560$	5.57719	+	1.97357i	0.235679	+	0.0833986i
$561$	14.5573			0.614608
$562$	0.666468	−	0.666468i	0.0281133	−	0.0281133i
$563$	12.8967	−	12.8967i	0.543530	−	0.543530i	−0.381032	−	0.924562i	$-0.624431\pi$
$563$	12.8967	−	12.8967i	0.543530	−	0.543530i	0.924562	+	0.381032i	$0.124431\pi$
$564$			23.3860i			0.984730i
$565$	5.50296	−	8.91891i	0.231511	−	0.375221i
$566$		−	7.32957i		−	0.308085i
$567$	−3.75271	+	5.82027i	−0.157599	+	0.244428i
$568$	−7.64327	−	7.64327i	−0.320705	−	0.320705i
$569$			2.99532i			0.125570i	0.998027	+	0.0627852i	$0.0199983\pi$
$569$			2.99532i			0.125570i	−0.998027	+	0.0627852i	$0.980002\pi$
$570$	52.4794	−	12.4302i	2.19812	−	0.520645i
$571$	−9.50725			−0.397866			−0.198933	−	0.980013i	$-0.563748\pi$
$571$	−9.50725			−0.397866			−0.198933	+	0.980013i	$0.563748\pi$
$572$	−0.426099	−	0.426099i	−0.0178161	−	0.0178161i
$573$	−28.9757	+	28.9757i	−1.21048	+	1.21048i
$574$	31.2667	−	6.75294i	1.30505	−	0.281862i
$575$	−10.3373	−	3.42858i	−0.431097	−	0.142981i
$576$	5.22391			0.217663
$577$	15.9068	+	15.9068i	0.662207	+	0.662207i	0.955900	−	0.293693i	$-0.0948843\pi$
$577$	15.9068	+	15.9068i	0.662207	+	0.662207i	−0.293693	+	0.955900i	$0.594884\pi$
$578$	−6.19995	−	6.19995i	−0.257884	−	0.257884i
$579$	66.6189			2.76859
$580$	−1.11295	−	4.69879i	−0.0462128	−	0.195107i
$581$	4.08225	+	18.9012i	0.169360	+	0.784153i
$582$	5.36749	−	5.36749i	0.222489	−	0.222489i
$583$	7.26064	+	7.26064i	0.300705	+	0.300705i
$584$	−9.02179			−0.373324
$585$	3.69609	−	5.99044i	0.152815	−	0.247674i
$586$		−	8.77812i		−	0.362621i
$587$	−3.92882	−	3.92882i	−0.162160	−	0.162160i	0.621363	−	0.783523i	$-0.286579\pi$
$587$	−3.92882	−	3.92882i	−0.162160	−	0.162160i	−0.783523	+	0.621363i	$0.786579\pi$
$588$	7.07116	−	18.7875i	0.291610	−	0.774783i
$589$		−	74.8519i		−	3.08422i
$590$	−10.0733	−	6.21520i	−0.414711	−	0.255876i
$591$			29.9665i			1.23266i
$592$	2.82821	−	2.82821i	0.116239	−	0.116239i
$593$	−15.4926	+	15.4926i	−0.636206	+	0.636206i	−0.949617	−	0.313411i	$-0.898528\pi$
$593$	−15.4926	+	15.4926i	−0.636206	+	0.636206i	0.313411	+	0.949617i	$0.398528\pi$
$594$	6.37758			0.261675
$595$	−12.9349	−	27.1029i	−0.530281	−	1.11111i
$596$	8.66778			0.355046
$597$	−46.4591	+	46.4591i	−1.90144	+	1.90144i
$598$	0.928138	−	0.928138i	0.0379544	−	0.0379544i
$599$		−	39.8627i		−	1.62874i	−0.580343	−	0.814372i	$-0.697081\pi$
$599$		−	39.8627i		−	1.62874i	0.580343	−	0.814372i	$-0.302919\pi$
$600$	12.8153	−	6.43167i	0.523181	−	0.262572i
$601$		−	7.61079i		−	0.310451i	−0.987879	−	0.155225i	$-0.950390\pi$
$601$		−	7.61079i		−	0.310451i	0.987879	−	0.155225i	$-0.0496104\pi$
$602$	−15.7994	+	24.5041i	−0.643936	+	0.998712i
$603$	15.4289	+	15.4289i	0.628313	+	0.628313i
$604$			23.5639i			0.958803i
$605$	−0.515374	−	2.17587i	−0.0209529	−	0.0884615i
$606$	−26.6534			−1.08272
$607$	−26.6599	−	26.6599i	−1.08209	−	1.08209i	−0.996314	−	0.0857789i	$-0.972662\pi$
$607$	−26.6599	−	26.6599i	−1.08209	−	1.08209i	−0.0857789	−	0.996314i	$-0.527338\pi$
$608$	−5.94706	+	5.94706i	−0.241185	+	0.241185i
$609$	−16.0156	+	3.45901i	−0.648983	+	0.140166i
$610$	−6.55864	+	10.6299i	−0.265551	+	0.430392i
$611$	−4.91409			−0.198803
$612$	−18.7509	−	18.7509i	−0.757959	−	0.757959i
$613$	12.4086	+	12.4086i	0.501181	+	0.501181i	0.911805	−	0.410624i	$-0.134689\pi$
$613$	12.4086	+	12.4086i	0.501181	+	0.501181i	−0.410624	+	0.911805i	$0.634689\pi$
$614$	−20.9338			−0.844821
$615$	40.7094	−	65.9796i	1.64156	−	2.66056i
$616$	−2.58612	+	0.558546i	−0.104198	+	0.0225045i
$617$	31.5560	−	31.5560i	1.27040	−	1.27040i	0.324517	−	0.945880i	$-0.394798\pi$
$617$	31.5560	−	31.5560i	1.27040	−	1.27040i	0.945880	−	0.324517i	$-0.105202\pi$
$618$	5.10211	+	5.10211i	0.205237	+	0.205237i
$619$	−34.3669			−1.38132			−0.690660	−	0.723179i	$-0.742680\pi$
$619$	−34.3669			−1.38132			−0.690660	+	0.723179i	$0.742680\pi$
$620$	−4.58677	−	19.3650i	−0.184209	−	0.777716i
$621$			13.8918i			0.557457i
$622$	−4.79499	−	4.79499i	−0.192261	−	0.192261i
$623$	7.40568	−	11.4858i	0.296702	−	0.460170i
$624$			1.72808i			0.0691788i
$625$	14.9400	−	20.0449i	0.597599	−	0.801795i
$626$		−	8.27017i		−	0.330543i
$627$	−17.0546	+	17.0546i	−0.681095	+	0.681095i
$628$	−4.17299	+	4.17299i	−0.166520	+	0.166520i
$629$	−20.3034			−0.809548
$630$	−13.3113	−	27.8914i	−0.530333	−	1.11122i
$631$	−42.0556			−1.67421			−0.837103	−	0.547046i	$-0.815752\pi$
$631$	−42.0556			−1.67421			−0.837103	+	0.547046i	$0.815752\pi$
$632$	−9.08223	+	9.08223i	−0.361272	+	0.361272i
$633$	46.7374	−	46.7374i	1.85765	−	1.85765i
$634$			0.836641i			0.0332273i
$635$	5.78622	+	3.57009i	0.229619	+	0.141675i
$636$		−	29.4462i		−	1.16762i
$637$	3.94781	+	1.48586i	0.156418	+	0.0588718i
$638$	1.52700	+	1.52700i	0.0604545	+	0.0604545i
$639$			56.4664i			2.23377i
$640$	−1.17414	+	1.90299i	−0.0464121	+	0.0752224i
$641$	−4.25025			−0.167875			−0.0839373	−	0.996471i	$-0.526750\pi$
$641$	−4.25025			−0.167875			−0.0839373	+	0.996471i	$0.526750\pi$
$642$	5.13782	+	5.13782i	0.202774	+	0.202774i
$643$	22.9980	−	22.9980i	0.906954	−	0.906954i	−0.0890713	−	0.996025i	$-0.528390\pi$
$643$	22.9980	−	22.9980i	0.906954	−	0.906954i	0.996025	+	0.0890713i	$0.0283899\pi$
$644$	−1.21664	−	5.63314i	−0.0479422	−	0.221977i
$645$	16.2870	+	68.7622i	0.641299	+	2.70751i
$646$	42.6932			1.67974
$647$	−1.82489	−	1.82489i	−0.0717437	−	0.0717437i	0.670324	−	0.742068i	$-0.266155\pi$
$647$	−1.82489	−	1.82489i	−0.0717437	−	0.0717437i	−0.742068	+	0.670324i	$0.766155\pi$
$648$	−1.85084	−	1.85084i	−0.0727078	−	0.0727078i
$649$	5.29339			0.207784
$650$	1.35148	+	2.69287i	0.0530095	+	0.105623i
$651$	−66.0044	+	14.2555i	−2.58692	+	0.558718i
$652$	5.46200	−	5.46200i	0.213909	−	0.213909i
$653$	16.4879	+	16.4879i	0.645221	+	0.645221i	0.951834	−	0.306613i	$-0.0991958\pi$
$653$	16.4879	+	16.4879i	0.645221	+	0.645221i	−0.306613	+	0.951834i	$0.599196\pi$
$654$	26.1679			1.02324
$655$	−17.8778	+	4.23453i	−0.698544	+	0.165457i
$656$			12.0902i			0.472043i
$657$	33.3252	+	33.3252i	1.30014	+	1.30014i
$658$	−11.6918	+	18.1333i	−0.455792	+	0.706910i
$659$		−	33.9192i		−	1.32130i	−0.750692	−	0.660652i	$-0.770280\pi$
$659$		−	33.9192i		−	1.32130i	0.750692	−	0.660652i	$-0.229720\pi$
$660$	−3.36714	+	5.45728i	−0.131066	+	0.212424i
$661$		−	29.9551i		−	1.16512i	−0.812789	−	0.582558i	$-0.802052\pi$
$661$		−	29.9551i		−	1.16512i	0.812789	−	0.582558i	$-0.197948\pi$
$662$	−18.0524	+	18.0524i	−0.701626	+	0.701626i
$663$	6.20284	−	6.20284i	0.240899	−	0.240899i
$664$	−7.30870			−0.283632
$665$	46.9065	+	16.5986i	1.81896	+	0.643665i
$666$	−20.8940			−0.809627
$667$	−3.32614	+	3.32614i	−0.128789	+	0.128789i
$668$	3.85669	−	3.85669i	0.149220	−	0.149220i
$669$		−	2.31477i		−	0.0894941i
$670$	−9.08838	+	2.15267i	−0.351115	+	0.0831648i
$671$		−	5.58589i		−	0.215641i
$672$	6.37674	+	4.11151i	0.245988	+	0.158605i
$673$	12.4436	+	12.4436i	0.479665	+	0.479665i	0.905024	−	0.425359i	$-0.139852\pi$
$673$	12.4436	+	12.4436i	0.479665	+	0.479665i	−0.425359	+	0.905024i	$0.639852\pi$
$674$		−	7.92081i		−	0.305098i
$675$	−30.2666	−	10.0385i	−1.16496	−	0.386381i
$676$	12.6369			0.486034
$677$	32.0812	+	32.0812i	1.23298	+	1.23298i	0.962813	+	0.270167i	$0.0870789\pi$
$677$	32.0812	+	32.0812i	1.23298	+	1.23298i	0.270167	+	0.962813i	$0.412921\pi$
$678$	9.50383	−	9.50383i	0.364992	−	0.364992i
$679$	6.84535	−	1.47845i	0.262701	−	0.0567376i
$680$	11.0452	−	2.61615i	0.423563	−	0.100325i
$681$	28.6770			1.09891
$682$	6.29318	+	6.29318i	0.240978	+	0.240978i
$683$	13.8362	+	13.8362i	0.529429	+	0.529429i	0.920402	−	0.390973i	$-0.127861\pi$
$683$	13.8362	+	13.8362i	0.529429	+	0.529429i	−0.390973	+	0.920402i	$0.627861\pi$
$684$	43.9352			1.67991
$685$	30.5850	+	18.8709i	1.16859	+	0.721020i
$686$	14.8756	−	11.0325i	0.567955	−	0.421221i
$687$	−18.3264	+	18.3264i	−0.699194	+	0.699194i
$688$	−7.79227	−	7.79227i	−0.297077	−	0.297077i
$689$	6.18751			0.235725
$690$	−11.8872	−	7.33436i	−0.452536	−	0.279214i
$691$			34.0869i			1.29673i	0.761331	+	0.648363i	$0.224546\pi$
$691$			34.0869i			1.29673i	−0.761331	+	0.648363i	$0.775454\pi$
$692$	2.87563	+	2.87563i	0.109315	+	0.109315i
$693$	11.6160	+	7.48958i	0.441254	+	0.284506i
$694$		−	5.69294i		−	0.216101i
$695$	−2.92317	−	12.3414i	−0.110882	−	0.468135i
$696$		−	6.19289i		−	0.234741i
$697$	43.3970	−	43.3970i	1.64378	−	1.64378i
$698$	11.4832	−	11.4832i	0.434645	−	0.434645i
$699$	−37.3482			−1.41264
$700$	13.1523	+	1.41989i	0.497112	+	0.0536667i
$701$	29.0158			1.09591			0.547957	−	0.836507i	$-0.315406\pi$
$701$	29.0158			1.09591			0.547957	+	0.836507i	$0.315406\pi$
$702$	2.71748	−	2.71748i	0.102565	−	0.102565i
$703$	23.7864	−	23.7864i	0.897123	−	0.897123i
$704$		−	1.00000i		−	0.0376889i
$705$	12.0526	+	50.8849i	0.453925	+	1.91643i
$706$			13.4497i			0.506188i
$707$	−20.6668	−	13.3253i	−0.777256	−	0.501149i
$708$	−10.7339	−	10.7339i	−0.403405	−	0.403405i
$709$		−	21.9587i		−	0.824676i	−0.911031	−	0.412338i	$-0.864712\pi$
$709$		−	21.9587i		−	0.824676i	0.911031	−	0.412338i	$-0.135288\pi$
$710$	−20.5699	−	12.6916i	−0.771974	−	0.476307i
$711$	67.0970			2.51633
$712$	3.65248	+	3.65248i	0.136882	+	0.136882i
$713$	−13.7079	+	13.7079i	−0.513365	+	0.513365i
$714$	−8.13091	−	37.6469i	−0.304292	−	1.40890i
$715$	−1.14674	−	0.707534i	−0.0428855	−	0.0264603i
$716$	4.88835			0.182686
$717$	25.1982	+	25.1982i	0.941045	+	0.941045i
$718$	0.996869	+	0.996869i	0.0372028	+	0.0372028i
$719$	−2.79425			−0.104208			−0.0521040	−	0.998642i	$-0.516593\pi$
$719$	−2.79425			−0.104208			−0.0521040	+	0.998642i	$0.516593\pi$
$720$	11.3665	−	2.69227i	0.423605	−	0.100335i
$721$	1.40535	+	6.50691i	0.0523380	+	0.242330i
$722$	−36.5823	+	36.5823i	−1.36145	+	1.36145i
$723$	8.52201	+	8.52201i	0.316937	+	0.316937i
$724$	−14.7856			−0.549502
$725$	−4.84327	−	9.65035i	−0.179874	−	0.358405i
$726$		−	2.86774i		−	0.106432i
$727$	24.8864	+	24.8864i	0.922987	+	0.922987i	0.997239	−	0.0742528i	$-0.0236572\pi$
$727$	24.8864	+	24.8864i	0.922987	+	0.922987i	−0.0742528	+	0.997239i	$0.523657\pi$
$728$	−0.863949	+	1.33994i	−0.0320201	+	0.0496615i
$729$		−	41.1941i		−	1.52571i
$730$	−19.6302	+	4.64960i	−0.726547	+	0.172089i
$731$			55.9396i			2.06900i
$732$	−11.3270	+	11.3270i	−0.418659	+	0.418659i
$733$	−29.9216	+	29.9216i	−1.10518	+	1.10518i	−0.111404	+	0.993775i	$0.535535\pi$
$733$	−29.9216	+	29.9216i	−1.10518	+	1.10518i	−0.993775	+	0.111404i	$0.964465\pi$
$734$	11.6686			0.430695
$735$	5.70329	−	44.5234i	0.210369	−	1.64227i
$736$	2.17822			0.0802902
$737$	2.95352	−	2.95352i	0.108794	−	0.108794i
$738$	44.6595	−	44.6595i	1.64394	−	1.64394i
$739$			17.0239i			0.626234i	0.949715	+	0.313117i	$0.101373\pi$
$739$			17.0239i			0.626234i	−0.949715	+	0.313117i	$0.898627\pi$
$740$	4.69622	−	7.61139i	0.172637	−	0.279800i
$741$			14.5339i			0.533917i
$742$	14.7215	−	22.8323i	0.540443	−	0.838200i
$743$	−10.6681	−	10.6681i	−0.391375	−	0.391375i	0.483802	−	0.875177i	$-0.339255\pi$
$743$	−10.6681	−	10.6681i	−0.391375	−	0.391375i	−0.875177	+	0.483802i	$0.839255\pi$
$744$		−	25.5225i		−	0.935702i
$745$	18.8599	−	4.46715i	0.690974	−	0.163664i
$746$	16.4283			0.601482
$747$	26.9973	+	26.9973i	0.987780	+	0.987780i
$748$	−3.58943	+	3.58943i	−0.131243	+	0.131243i
$749$	1.41519	+	6.55246i	0.0517099	+	0.239422i
$750$	24.5696	−	20.5991i	0.897155	−	0.752173i
$751$	38.1976			1.39385			0.696925	−	0.717144i	$-0.254551\pi$
$751$	38.1976			1.39385			0.696925	+	0.717144i	$0.254551\pi$
$752$	−5.76637	−	5.76637i	−0.210278	−	0.210278i
$753$	34.7813	+	34.7813i	1.26750	+	1.26750i
$754$	1.30131			0.0473908
$755$	12.1442	+	51.2720i	0.441974	+	1.86598i
$756$	−3.56217	−	16.4932i	−0.129555	−	0.599851i
$757$	−7.19653	+	7.19653i	−0.261562	+	0.261562i	−0.825689	−	0.564126i	$-0.809213\pi$
$757$	−7.19653	+	7.19653i	−0.261562	+	0.261562i	0.564126	+	0.825689i	$0.309213\pi$
$758$	−15.3567	−	15.3567i	−0.557779	−	0.557779i
$759$	6.24656			0.226736
$760$	−9.87505	+	16.0050i	−0.358206	+	0.580561i
$761$			23.6421i			0.857026i	0.903536	+	0.428513i	$0.140962\pi$
$761$			23.6421i			0.857026i	−0.903536	+	0.428513i	$0.859038\pi$
$762$	6.16569	+	6.16569i	0.223359	+	0.223359i
$763$	20.2903	+	13.0825i	0.734559	+	0.473619i
$764$		−	14.2893i		−	0.516968i
$765$	−50.4631	−	31.1356i	−1.82450	−	1.12571i
$766$		−	10.9184i		−	0.394499i
$767$	2.25551	−	2.25551i	0.0814417	−	0.0814417i
$768$	−2.02780	+	2.02780i	−0.0731718	+	0.0731718i
$769$	−43.9970			−1.58657			−0.793286	−	0.608849i	$-0.791632\pi$
$769$	−43.9970			−1.58657			−0.793286	+	0.608849i	$0.791632\pi$
$770$	−5.33919	+	2.54814i	−0.192411	+	0.0918286i
$771$	−6.04658			−0.217762
$772$	−16.4264	+	16.4264i	−0.591200	+	0.591200i
$773$	−8.26578	+	8.26578i	−0.297300	+	0.297300i	−0.839955	−	0.542656i	$-0.817419\pi$
$773$	−8.26578	+	8.26578i	−0.297300	+	0.297300i	0.542656	+	0.839955i	$0.317419\pi$
$774$			57.5671i			2.06921i
$775$	−19.9604	−	39.7717i	−0.716999	−	1.42864i
$776$			2.64696i			0.0950202i
$777$	−25.5050	−	16.4448i	−0.914988	−	0.589953i
$778$	0.316605	+	0.316605i	0.0113509	+	0.0113509i
$779$			101.684i			3.64320i
$780$	0.890610	+	3.76008i	0.0318890	+	0.134632i
$781$	10.8092			0.386784
$782$	−7.81857	−	7.81857i	−0.279591	−	0.279591i
$783$	−9.73856	+	9.73856i	−0.348028	+	0.348028i
$784$	2.88894	+	6.37605i	0.103176	+	0.227716i
$785$	−6.92921	+	11.2305i	−0.247314	+	0.400834i
$786$	−23.5625			−0.840447
$787$	−6.56389	−	6.56389i	−0.233977	−	0.233977i	0.580373	−	0.814351i	$-0.302907\pi$
$787$	−6.56389	−	6.56389i	−0.233977	−	0.233977i	−0.814351	+	0.580373i	$0.802907\pi$
$788$	−7.38893	−	7.38893i	−0.263220	−	0.263220i
$789$	−14.4651			−0.514973
$790$	−15.0810	+	24.4425i	−0.536557	+	0.869624i
$791$	12.1206	−	2.61778i	0.430958	−	0.0930776i
$792$	−3.69386	+	3.69386i	−0.131256	+	0.131256i
$793$	−2.38014	−	2.38014i	−0.0845214	−	0.0845214i
$794$	−17.7722			−0.630712
$795$	−15.1758	−	64.0709i	−0.538230	−	2.27236i
$796$		−	22.9111i		−	0.812064i
$797$	26.2139	+	26.2139i	0.928545	+	0.928545i	0.997612	−	0.0690671i	$-0.0220023\pi$
$797$	26.2139	+	26.2139i	0.928545	+	0.928545i	−0.0690671	+	0.997612i	$0.522002\pi$
$798$	53.6311	+	34.5795i	1.89852	+	1.22410i
$799$			41.3960i			1.46449i
$800$	−1.57403	+	4.74578i	−0.0556503	+	0.167789i
$801$		−	26.9835i		−	0.953415i
$802$	−21.3017	+	21.3017i	−0.752189	+	0.752189i
$803$	6.37937	−	6.37937i	0.225123	−	0.225123i
$804$	−11.9783			−0.422441
$805$	−5.55041	−	11.6299i	−0.195626	−	0.409901i
$806$	5.36304			0.188905
$807$	19.9212	−	19.9212i	0.701259	−	0.701259i
$808$	6.57203	−	6.57203i	0.231203	−	0.231203i
$809$		−	37.9827i		−	1.33540i	−0.744430	−	0.667701i	$-0.767279\pi$
$809$		−	37.9827i		−	1.33540i	0.744430	−	0.667701i	$-0.232721\pi$
$810$	−4.98105	−	3.07330i	−0.175016	−	0.107985i
$811$			13.0899i			0.459647i	0.973232	+	0.229824i	$0.0738149\pi$
$811$			13.0899i			0.459647i	−0.973232	+	0.229824i	$0.926185\pi$
$812$	3.09611	−	4.80191i	0.108652	−	0.168514i
$813$	31.0113	+	31.0113i	1.08761	+	1.08761i
$814$			3.99970i			0.140189i
$815$	9.06961	−	14.6996i	0.317695	−	0.514903i
$816$	14.5573			0.509606
$817$	−65.5362	−	65.5362i	−2.29282	−	2.29282i
$818$	2.76402	−	2.76402i	0.0966416	−	0.0966416i
$819$	8.14086	−	1.75825i	0.284465	−	0.0614382i
$820$	6.23098	+	26.3067i	0.217595	+	0.918668i
$821$	−27.7689			−0.969143			−0.484571	−	0.874752i	$-0.661024\pi$
$821$	−27.7689			−0.969143			−0.484571	+	0.874752i	$0.661024\pi$
$822$	32.5908	+	32.5908i	1.13674	+	1.13674i
$823$	9.38975	+	9.38975i	0.327306	+	0.327306i	0.851561	−	0.524255i	$-0.175656\pi$
$823$	9.38975	+	9.38975i	0.327306	+	0.327306i	−0.524255	+	0.851561i	$0.675656\pi$
$824$	−2.51609			−0.0876520
$825$	−4.51389	+	13.6096i	−0.157154	+	0.473827i
$826$	−2.95660	−	13.6893i	−0.102873	−	0.476313i
$827$	−24.7960	+	24.7960i	−0.862242	+	0.862242i	−0.991598	−	0.129356i	$-0.958709\pi$
$827$	−24.7960	+	24.7960i	−0.862242	+	0.862242i	0.129356	+	0.991598i	$0.458709\pi$
$828$	−8.04603	−	8.04603i	−0.279619	−	0.279619i
$829$	49.8882			1.73269			0.866345	−	0.499446i	$-0.166463\pi$
$829$	49.8882			1.73269			0.866345	+	0.499446i	$0.166463\pi$
$830$	−15.9027	+	3.76671i	−0.551992	+	0.130745i
$831$		−	2.34985i		−	0.0815153i
$832$	−0.426099	−	0.426099i	−0.0147723	−	0.0147723i
$833$	12.5168	−	33.2561i	0.433680	−	1.15225i
$834$		−	16.2656i		−	0.563232i
$835$	6.40400	−	10.3793i	0.221620	−	0.359190i
$836$		−	8.41042i		−	0.290880i
$837$	−40.1352	+	40.1352i	−1.38728	+	1.38728i
$838$	−7.50312	+	7.50312i	−0.259191	+	0.259191i
$839$	−17.8018			−0.614586			−0.307293	−	0.951615i	$-0.599423\pi$
$839$	−17.8018			−0.614586			−0.307293	+	0.951615i	$0.599423\pi$
$840$	15.9939	+	5.65968i	0.551842	+	0.195278i
$841$	24.3365			0.839191
$842$	11.7617	−	11.7617i	0.405335	−	0.405335i
$843$	1.91125	−	1.91125i	0.0658271	−	0.0658271i
$844$			23.0484i			0.793359i
$845$	27.4961	−	6.51272i	0.945896	−	0.224044i
$846$			42.6003i			1.46463i
$847$	1.43371	−	2.22362i	0.0492629	−	0.0764044i
$848$	7.26064	+	7.26064i	0.249331	+	0.249331i
$849$		−	21.0193i		−	0.721380i
$850$	22.6845	−	11.3848i	0.778073	−	0.390495i
$851$	−8.71221			−0.298651
$852$	−21.9189	−	21.9189i	−0.750929	−	0.750929i
$853$	−3.44126	+	3.44126i	−0.117826	+	0.117826i	−0.763562	−	0.645735i	$-0.776551\pi$
$853$	−3.44126	+	3.44126i	−0.117826	+	0.117826i	0.645735	+	0.763562i	$0.276551\pi$
$854$	−14.4458	+	3.11998i	−0.494324	+	0.106763i
$855$	95.5972	−	22.6431i	3.26935	−	0.774377i
$856$	−2.53370			−0.0866001
$857$	−22.5691	−	22.5691i	−0.770947	−	0.770947i	0.207325	−	0.978272i	$-0.433524\pi$
$857$	−22.5691	−	22.5691i	−0.770947	−	0.770947i	−0.978272	+	0.207325i	$0.933524\pi$
$858$	−1.22194	−	1.22194i	−0.0417164	−	0.0417164i
$859$	−2.29802			−0.0784073			−0.0392036	−	0.999231i	$-0.512482\pi$
$859$	−2.29802			−0.0784073			−0.0392036	+	0.999231i	$0.512482\pi$
$860$	−20.9709	−	12.9390i	−0.715100	−	0.441216i
$861$	89.6647	−	19.3656i	3.05577	−	0.659979i
$862$	−1.28102	+	1.28102i	−0.0436317	+	0.0436317i
$863$	−36.9127	−	36.9127i	−1.25652	−	1.25652i	−0.952742	−	0.303781i	$-0.901751\pi$
$863$	−36.9127	−	36.9127i	−1.25652	−	1.25652i	−0.303781	−	0.952742i	$-0.598249\pi$
$864$	6.37758			0.216970
$865$	7.73902	+	4.77497i	0.263135	+	0.162354i
$866$			13.5636i			0.460909i
$867$	−17.7798	−	17.7798i	−0.603834	−	0.603834i
$868$	12.7599	−	19.7900i	0.433099	−	0.671715i
$869$		−	12.8442i		−	0.435710i
$870$	−3.19165	−	13.4749i	−0.108207	−	0.456841i
$871$		−	2.51698i		−	0.0852848i
$872$	−6.45229	+	6.45229i	−0.218502	+	0.218502i
$873$	9.77749	−	9.77749i	0.330918	−	0.330918i
$874$	18.3197			0.619674
$875$	29.3495	−	3.68889i	0.992194	−	0.124707i
$876$	−25.8721			−0.874138
$877$	−10.0112	+	10.0112i	−0.338054	+	0.338054i	−0.855634	−	0.517581i	$-0.826833\pi$
$877$	−10.0112	+	10.0112i	−0.338054	+	0.338054i	0.517581	+	0.855634i	$0.326833\pi$
$878$	19.8381	−	19.8381i	0.669503	−	0.669503i
$879$		−	25.1733i		−	0.849075i
$880$	−0.515374	−	2.17587i	−0.0173733	−	0.0733484i
$881$		−	18.8482i		−	0.635013i	−0.948256	−	0.317507i	$-0.897154\pi$
$881$		−	18.8482i		−	0.635013i	0.948256	−	0.317507i	$-0.102846\pi$
$882$	12.8809	−	34.2236i	0.433723	−	1.15237i
$883$	−14.1209	−	14.1209i	−0.475207	−	0.475207i	0.428388	−	0.903595i	$-0.359082\pi$
$883$	−14.1209	−	14.1209i	−0.475207	−	0.475207i	−0.903595	+	0.428388i	$0.859082\pi$
$884$			3.05891i			0.102882i
$885$	−28.8875	−	17.8236i	−0.971043	−	0.599132i
$886$	22.9856			0.772218
$887$	−13.9657	−	13.9657i	−0.468921	−	0.468921i	0.432644	−	0.901565i	$-0.357581\pi$
$887$	−13.9657	−	13.9657i	−0.468921	−	0.468921i	−0.901565	+	0.432644i	$0.857581\pi$
$888$	8.11056	−	8.11056i	0.272173	−	0.272173i
$889$	1.69831	+	7.86333i	0.0569594	+	0.263728i
$890$	9.82969	+	6.06491i	0.329492	+	0.203296i
$891$	2.61748			0.0876889
$892$	0.570760	+	0.570760i	0.0191105	+	0.0191105i
$893$	−48.4976	−	48.4976i	−1.62291	−	1.62291i
$894$	24.8569			0.831339
$895$	10.6364	−	2.51933i	0.355536	−	0.0842119i
$896$	−2.58612	+	0.558546i	−0.0863963	+	0.0186597i
$897$	2.66165	−	2.66165i	0.0888700	−	0.0888700i
$898$	0.513486	+	0.513486i	0.0171352	+	0.0171352i
$899$	−19.2194			−0.641002
$900$	23.3445	−	11.7160i	0.778150	−	0.390534i
$901$		−	52.1232i		−	1.73647i
$902$	−8.54906	−	8.54906i	−0.284653	−	0.284653i
$903$	−45.3085	+	70.2713i	−1.50777	+	2.33848i
$904$			4.68678i			0.155880i
$905$	−32.1715	+	7.62011i	−1.06942	+	0.253301i
$906$			67.5752i			2.24503i
$907$	26.6916	−	26.6916i	0.886282	−	0.886282i	−0.107882	−	0.994164i	$-0.534407\pi$
$907$	26.6916	−	26.6916i	0.886282	−	0.886282i	0.994164	+	0.107882i	$0.0344069\pi$
$908$	−7.07099	+	7.07099i	−0.234659	+	0.234659i
$909$	−48.5523			−1.61038
$910$	−1.18927	+	3.36079i	−0.0394238	+	0.111409i
$911$	−7.75809			−0.257037			−0.128518	−	0.991707i	$-0.541022\pi$
$911$	−7.75809			−0.257037			−0.128518	+	0.991707i	$0.541022\pi$
$912$	−17.0546	+	17.0546i	−0.564734	+	0.564734i
$913$	5.16803	−	5.16803i	0.171037	−	0.171037i
$914$			0.0988193i			0.00326865i
$915$	−18.8084	+	30.4838i	−0.621788	+	1.00776i
$916$		−	9.03758i		−	0.298610i
$917$	−18.2702	−	11.7800i	−0.603334	−	0.389009i
$918$	−22.8919	−	22.8919i	−0.755545	−	0.755545i
$919$			50.2619i			1.65799i	0.559259	+	0.828993i	$0.311086\pi$
$919$			50.2619i			1.65799i	−0.559259	+	0.828993i	$0.688914\pi$
$920$	4.73951	−	1.12260i	0.156257	−	0.0370109i
$921$	−60.0327			−1.97815
$922$	−11.3683	−	11.3683i	−0.374396	−	0.374396i
$923$	4.60580	−	4.60580i	0.151602	−	0.151602i
$924$	−7.41631	+	1.60176i	−0.243979	+	0.0526941i
$925$	6.29563	−	18.9817i	0.206999	−	0.624114i
$926$	15.6225			0.513388
$927$	9.29407	+	9.29407i	0.305257	+	0.305257i
$928$	1.52700	+	1.52700i	0.0501262	+	0.0501262i
$929$	−12.0444			−0.395165			−0.197582	−	0.980286i	$-0.563309\pi$
$929$	−12.0444			−0.395165			−0.197582	+	0.980286i	$0.563309\pi$
$930$	−13.1537	−	55.5336i	−0.431325	−	1.82102i
$931$	24.2972	+	53.6253i	0.796308	+	1.75750i
$932$	9.20906	−	9.20906i	0.301653	−	0.301653i
$933$	−13.7508	−	13.7508i	−0.450180	−	0.450180i
$934$	−31.7879			−1.04013
$935$	−5.96022	+	9.66002i	−0.194920	+	0.315917i
$936$			3.14790i			0.102892i
$937$	12.5006	+	12.5006i	0.408377	+	0.408377i	0.881172	−	0.472796i	$-0.156755\pi$
$937$	12.5006	+	12.5006i	0.408377	+	0.408377i	−0.472796	+	0.881172i	$0.656755\pi$
$938$	−9.28783	−	5.98848i	−0.303259	−	0.195531i
$939$		−	23.7167i		−	0.773964i
$940$	−15.5187	−	9.57501i	−0.506164	−	0.312302i
$941$			4.21197i			0.137306i	0.997641	+	0.0686532i	$0.0218702\pi$
$941$			4.21197i			0.137306i	−0.997641	+	0.0686532i	$0.978130\pi$
$942$	−11.9670	+	11.9670i	−0.389907	+	0.389907i
$943$	18.6217	−	18.6217i	0.606407	−	0.606407i
$944$	5.29339			0.172285
$945$	−16.2510	−	34.0511i	−0.528644	−	1.10768i
$946$	11.0199			0.358289
$947$	−1.71025	+	1.71025i	−0.0555756	+	0.0555756i	−0.734348	−	0.678773i	$-0.762512\pi$
$947$	−1.71025	+	1.71025i	−0.0555756	+	0.0555756i	0.678773	+	0.734348i	$0.262512\pi$
$948$	−26.0454	+	26.0454i	−0.845917	+	0.845917i
$949$		−	5.43649i		−	0.176476i
$950$	−13.2382	+	39.9140i	−0.429505	+	1.29498i
$951$			2.39927i			0.0778015i
$952$	11.2876	+	7.27785i	0.365832	+	0.235876i
$953$	−31.7354	−	31.7354i	−1.02801	−	1.02801i	−0.999596	−	0.0284158i	$-0.990954\pi$
$953$	−31.7354	−	31.7354i	−1.02801	−	1.02801i	−0.0284158	−	0.999596i	$-0.509046\pi$
$954$		−	53.6396i		−	1.73665i
$955$	−7.36432	−	31.0916i	−0.238304	−	1.00610i
$956$	−12.4264			−0.401899
$957$	4.37903	+	4.37903i	0.141554	+	0.141554i
$958$	19.6330	−	19.6330i	0.634314	−	0.634314i
$959$	8.97698	+	41.5643i	0.289882	+	1.34218i
$960$	−3.36714	+	5.45728i	−0.108674	+	0.176133i
$961$	−48.2081			−1.55510
$962$	1.70427	+	1.70427i	0.0549478	+	0.0549478i
$963$	9.35913	+	9.35913i	0.301594	+	0.301594i
$964$	−4.20260			−0.135357
$965$	−27.2760	+	44.2075i	−0.878044	+	1.42309i
$966$	−3.48899	−	16.1544i	−0.112256	−	0.519758i
$967$	−33.1110	+	33.1110i	−1.06478	+	1.06478i	−0.0670257	+	0.997751i	$0.521351\pi$
$967$	−33.1110	+	33.1110i	−1.06478	+	1.06478i	−0.997751	+	0.0670257i	$0.978649\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	122.433			3.93311
$970$	1.36417	+	5.75942i	0.0438009	+	0.184924i
$971$		−	28.9848i		−	0.930166i	−0.885267	−	0.465083i	$-0.846025\pi$
$971$		−	28.9848i		−	0.930166i	0.885267	−	0.465083i	$-0.153975\pi$
$972$	8.22117	+	8.22117i	0.263694	+	0.263694i
$973$	8.13193	−	12.6122i	0.260698	−	0.404329i
$974$			7.09273i			0.227266i
$975$	3.87569	+	7.72243i	0.124122	+	0.247316i
$976$		−	5.58589i		−	0.178800i
$977$	−36.3736	+	36.3736i	−1.16369	+	1.16369i	−0.180033	+	0.983661i	$0.557621\pi$
$977$	−36.3736	+	36.3736i	−1.16369	+	1.16369i	−0.983661	+	0.180033i	$0.942379\pi$
$978$	15.6636	−	15.6636i	0.500866	−	0.500866i
$979$	−5.16538			−0.165086
$980$	9.57199	+	12.3845i	0.305766	+	0.395610i
$981$	47.6677			1.52191
$982$	2.11018	−	2.11018i	0.0673387	−	0.0673387i
$983$	−3.19868	+	3.19868i	−0.102022	+	0.102022i	−0.756275	−	0.654253i	$-0.772983\pi$
$983$	−3.19868	+	3.19868i	−0.102022	+	0.102022i	0.654253	+	0.756275i	$0.272983\pi$
$984$			34.6715i			1.10529i
$985$	−19.8854	−	12.2692i	−0.633601	−	0.390931i
$986$		−	10.9621i		−	0.349105i
$987$	−33.5289	+	52.0016i	−1.06724	+	1.65523i
$988$	−3.58367	−	3.58367i	−0.114012	−	0.114012i
$989$			24.0038i			0.763277i
$990$	−6.13362	+	9.94106i	−0.194939	+	0.315948i
$991$	−46.3404			−1.47205			−0.736026	−	0.676953i	$-0.763300\pi$
$991$	−46.3404			−1.47205			−0.736026	+	0.676953i	$0.763300\pi$
$992$	6.29318	+	6.29318i	0.199809	+	0.199809i
$993$	−51.7695	+	51.7695i	−1.64286	+	1.64286i
$994$	−6.03745	−	27.9540i	−0.191496	−	0.886646i
$995$	−11.8078	−	49.8515i	−0.374333	−	1.58040i
$996$	−20.9594			−0.664124
$997$	19.8201	+	19.8201i	0.627708	+	0.627708i	0.947491	−	0.319783i	$-0.103610\pi$
$997$	19.8201	+	19.8201i	0.627708	+	0.627708i	−0.319783	+	0.947491i	$0.603610\pi$
$998$	11.3333	+	11.3333i	0.358750	+	0.358750i
$999$	−25.5084			−0.807049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.2	✓	40
5.2	odd	4	inner	770.2.l.c.727.9	yes	40
7.6	odd	2	inner	770.2.l.c.573.9	yes	40
35.27	even	4	inner	770.2.l.c.727.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.2	✓	40	1.1	even	1	trivial
770.2.l.c.573.9	yes	40	7.6	odd	2	inner
770.2.l.c.727.2	yes	40	35.27	even	4	inner
770.2.l.c.727.9	yes	40	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.02780 + 2.02780i) q^{3} -1.00000i q^{4} +(-0.515374 - 2.17587i) q^{5} -2.86774i q^{6} +(1.43371 - 2.22362i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.22391i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.02780 + 2.02780i) q^{3} -1.00000i q^{4} +(-0.515374 - 2.17587i) q^{5} -2.86774i q^{6} +(1.43371 - 2.22362i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.22391i q^{9} +(1.90299 + 1.17414i) q^{10} -1.00000 q^{11} +(2.02780 + 2.02780i) q^{12} +(-0.426099 + 0.426099i) q^{13} +(0.558546 + 2.58612i) q^{14} +(5.45728 + 3.36714i) q^{15} -1.00000 q^{16} +(3.58943 + 3.58943i) q^{17} +(3.69386 + 3.69386i) q^{18} -8.41042 q^{19} +(-2.17587 + 0.515374i) q^{20} +(1.60176 + 7.41631i) q^{21} +(0.707107 - 0.707107i) q^{22} +(1.54023 + 1.54023i) q^{23} -2.86774 q^{24} +(-4.46878 + 2.24277i) q^{25} -0.602596i q^{26} +(4.50963 + 4.50963i) q^{27} +(-2.22362 - 1.43371i) q^{28} +2.15950i q^{29} +(-6.23981 + 1.47796i) q^{30} +8.89990i q^{31} +(0.707107 - 0.707107i) q^{32} +(2.02780 - 2.02780i) q^{33} -5.07622 q^{34} +(-5.57719 - 1.97357i) q^{35} -5.22391 q^{36} +(-2.82821 + 2.82821i) q^{37} +(5.94706 - 5.94706i) q^{38} -1.72808i q^{39} +(1.17414 - 1.90299i) q^{40} -12.0902i q^{41} +(-6.37674 - 4.11151i) q^{42} +(7.79227 + 7.79227i) q^{43} +1.00000i q^{44} +(-11.3665 + 2.69227i) q^{45} -2.17822 q^{46} +(5.76637 + 5.76637i) q^{47} +(2.02780 - 2.02780i) q^{48} +(-2.88894 - 6.37605i) q^{49} +(1.57403 - 4.74578i) q^{50} -14.5573 q^{51} +(0.426099 + 0.426099i) q^{52} +(-7.26064 - 7.26064i) q^{53} -6.37758 q^{54} +(0.515374 + 2.17587i) q^{55} +(2.58612 - 0.558546i) q^{56} +(17.0546 - 17.0546i) q^{57} +(-1.52700 - 1.52700i) q^{58} -5.29339 q^{59} +(3.36714 - 5.45728i) q^{60} +5.58589i q^{61} +(-6.29318 - 6.29318i) q^{62} +(-11.6160 - 7.48958i) q^{63} +1.00000i q^{64} +(1.14674 + 0.707534i) q^{65} +2.86774i q^{66} +(-2.95352 + 2.95352i) q^{67} +(3.58943 - 3.58943i) q^{68} -6.24656 q^{69} +(5.33919 - 2.54814i) q^{70} -10.8092 q^{71} +(3.69386 - 3.69386i) q^{72} +(-6.37937 + 6.37937i) q^{73} -3.99970i q^{74} +(4.51389 - 13.6096i) q^{75} +8.41042i q^{76} +(-1.43371 + 2.22362i) q^{77} +(1.22194 + 1.22194i) q^{78} +12.8442i q^{79} +(0.515374 + 2.17587i) q^{80} -2.61748 q^{81} +(8.54906 + 8.54906i) q^{82} +(-5.16803 + 5.16803i) q^{83} +(7.41631 - 1.60176i) q^{84} +(5.96022 - 9.66002i) q^{85} -11.0199 q^{86} +(-4.37903 - 4.37903i) q^{87} +(-0.707107 - 0.707107i) q^{88} +5.16538 q^{89} +(6.13362 - 9.94106i) q^{90} +(0.336577 + 1.55839i) q^{91} +(1.54023 - 1.54023i) q^{92} +(-18.0472 - 18.0472i) q^{93} -8.15488 q^{94} +(4.33451 + 18.2999i) q^{95} +2.86774i q^{96} +(1.87168 + 1.87168i) q^{97} +(6.55134 + 2.46576i) q^{98} +5.22391i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more