LMFDB - Embedded newform 287.2.l.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(27,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("287.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.7
Character	$\chi$	$=$	287.27
Dual form			287.2.l.a.202.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17122 - 1.17122i) q^{2} +(-0.481548 - 1.16256i) q^{3} +0.743529i q^{4} +(0.511687 + 0.511687i) q^{5} +(-0.797616 + 1.92562i) q^{6} +(1.67326 - 2.04944i) q^{7} +(-1.47161 + 1.47161i) q^{8} +(1.00167 - 1.00167i) q^{9} +O(q^{10})$	\(q+(-1.17122 - 1.17122i) q^{2} +(-0.481548 - 1.16256i) q^{3} +0.743529i q^{4} +(0.511687 + 0.511687i) q^{5} +(-0.797616 + 1.92562i) q^{6} +(1.67326 - 2.04944i) q^{7} +(-1.47161 + 1.47161i) q^{8} +(1.00167 - 1.00167i) q^{9} -1.19860i q^{10} +(-1.13792 - 2.74717i) q^{11} +(0.864396 - 0.358044i) q^{12} +(-2.33554 - 5.63849i) q^{13} +(-4.36011 + 0.440588i) q^{14} +(0.348465 - 0.841268i) q^{15} +4.93422 q^{16} +(-1.66048 + 4.00875i) q^{17} -2.34635 q^{18} +(-2.33753 + 5.64329i) q^{19} +(-0.380454 + 0.380454i) q^{20} +(-3.18835 - 0.958361i) q^{21} +(-1.88480 + 4.55030i) q^{22} +4.21773i q^{23} +(2.41948 + 1.00218i) q^{24} -4.47635i q^{25} +(-3.86849 + 9.33937i) q^{26} +(-5.13452 - 2.12679i) q^{27} +(1.52382 + 1.24412i) q^{28} +(5.26342 - 2.18018i) q^{29} +(-1.39344 + 0.577183i) q^{30} -1.26834 q^{31} +(-2.83586 - 2.83586i) q^{32} +(-2.64579 + 2.64579i) q^{33} +(6.63993 - 2.75035i) q^{34} +(1.90486 - 0.192485i) q^{35} +(0.744767 + 0.744767i) q^{36} -7.10280 q^{37} +(9.34732 - 3.87178i) q^{38} +(-5.43040 + 5.43040i) q^{39} -1.50601 q^{40} +(6.06831 - 2.04342i) q^{41} +(2.61181 + 4.85672i) q^{42} +(-1.81789 - 1.81789i) q^{43} +(2.04260 - 0.846073i) q^{44} +1.02508 q^{45} +(4.93991 - 4.93991i) q^{46} +(-1.59005 + 3.83872i) q^{47} +(-2.37606 - 5.73632i) q^{48} +(-1.40040 - 6.85849i) q^{49} +(-5.24281 + 5.24281i) q^{50} +5.46000 q^{51} +(4.19238 - 1.73654i) q^{52} +(0.570585 + 1.37751i) q^{53} +(3.52273 + 8.50462i) q^{54} +(0.823435 - 1.98795i) q^{55} +(0.553587 + 5.47836i) q^{56} +7.68628 q^{57} +(-8.71812 - 3.61117i) q^{58} -8.50571i q^{59} +(0.625507 + 0.259093i) q^{60} +(9.97575 - 9.97575i) q^{61} +(1.48551 + 1.48551i) q^{62} +(-0.376805 - 3.72890i) q^{63} -3.22559i q^{64} +(1.69008 - 4.08021i) q^{65} +6.19762 q^{66} +(11.7724 + 4.87630i) q^{67} +(-2.98062 - 1.23461i) q^{68} +(4.90336 - 2.03104i) q^{69} +(-2.45646 - 2.00557i) q^{70} +(-5.88668 + 2.43834i) q^{71} +2.94812i q^{72} +(9.42192 - 9.42192i) q^{73} +(8.31897 + 8.31897i) q^{74} +(-5.20402 + 2.15558i) q^{75} +(-4.19595 - 1.73802i) q^{76} +(-7.53419 - 2.26465i) q^{77} +12.7204 q^{78} +(4.48251 + 10.8217i) q^{79} +(2.52478 + 2.52478i) q^{80} +2.74362i q^{81} +(-9.50065 - 4.71405i) q^{82} -9.04038i q^{83} +(0.712569 - 2.37063i) q^{84} +(-2.90087 + 1.20158i) q^{85} +4.25832i q^{86} +(-5.06918 - 5.06918i) q^{87} +(5.71733 + 2.36819i) q^{88} +(6.93110 + 16.7332i) q^{89} +(-1.20060 - 1.20060i) q^{90} +(-15.4637 - 4.64812i) q^{91} -3.13601 q^{92} +(0.610766 + 1.47452i) q^{93} +(6.35830 - 2.63370i) q^{94} +(-4.08368 + 1.69152i) q^{95} +(-1.93125 + 4.66245i) q^{96} +(4.66294 + 1.93145i) q^{97} +(-6.39265 + 9.67300i) q^{98} +(-3.89156 - 1.61194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 104 * q - 8 * q^2 - 4 * q^7 + 8 * q^8 + 8 * q^9	$ 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{11} - 8 q^{14} - 32 q^{15} - 96 q^{16} - 16 q^{18} - 24 q^{21} + 24 q^{22} + 12 q^{28} - 16 q^{29} + 48 q^{30} - 72 q^{32} - 44 q^{35} + 56 q^{36} + 32 q^{37} - 8 q^{39} - 8 q^{42} - 32 q^{43} + 72 q^{44} - 88 q^{46} - 12 q^{49} + 80 q^{50} + 32 q^{51} - 8 q^{53} + 104 q^{56} - 32 q^{57} - 96 q^{58} + 112 q^{60} - 132 q^{63} + 80 q^{65} + 56 q^{67} + 148 q^{70} - 104 q^{71} + 32 q^{74} - 16 q^{77} - 168 q^{78} - 124 q^{84} + 8 q^{85} - 64 q^{88} + 8 q^{91} + 104 q^{92} - 64 q^{93} - 8 q^{95} - 8 q^{98} + 8 q^{99}+O(q^{100}) $ 104 * q - 8 * q^2 - 4 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^11 - 8 * q^14 - 32 * q^15 - 96 * q^16 - 16 * q^18 - 24 * q^21 + 24 * q^22 + 12 * q^28 - 16 * q^29 + 48 * q^30 - 72 * q^32 - 44 * q^35 + 56 * q^36 + 32 * q^37 - 8 * q^39 - 8 * q^42 - 32 * q^43 + 72 * q^44 - 88 * q^46 - 12 * q^49 + 80 * q^50 + 32 * q^51 - 8 * q^53 + 104 * q^56 - 32 * q^57 - 96 * q^58 + 112 * q^60 - 132 * q^63 + 80 * q^65 + 56 * q^67 + 148 * q^70 - 104 * q^71 + 32 * q^74 - 16 * q^77 - 168 * q^78 - 124 * q^84 + 8 * q^85 - 64 * q^88 + 8 * q^91 + 104 * q^92 - 64 * q^93 - 8 * q^95 - 8 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.17122	−	1.17122i	−0.828180	−	0.828180i	0.159085	−	0.987265i	$-0.449146\pi$
$2$	−1.17122	−	1.17122i	−0.828180	−	0.828180i	−0.987265	+	0.159085i	$0.949146\pi$
$3$	−0.481548	−	1.16256i	−0.278022	−	0.671204i	0.721759	−	0.692144i	$-0.243334\pi$
$3$	−0.481548	−	1.16256i	−0.278022	−	0.671204i	−0.999781	+	0.0209408i	$0.993334\pi$
$4$			0.743529i			0.371764i
$5$	0.511687	+	0.511687i	0.228833	+	0.228833i	0.812205	−	0.583372i	$-0.198267\pi$
$5$	0.511687	+	0.511687i	0.228833	+	0.228833i	−0.583372	+	0.812205i	$0.698267\pi$
$6$	−0.797616	+	1.92562i	−0.325625	+	0.786129i
$7$	1.67326	−	2.04944i	0.632433	−	0.774615i
$7$	1.67326	−	2.04944i	0.632433	−	0.774615i
$8$	−1.47161	+	1.47161i	−0.520292	+	0.520292i
$9$	1.00167	−	1.00167i	0.333889	−	0.333889i
$10$		−	1.19860i		−	0.379030i
$11$	−1.13792	−	2.74717i	−0.343094	−	0.828303i	−0.997399	−	0.0720725i	$-0.977039\pi$
$11$	−1.13792	−	2.74717i	−0.343094	−	0.828303i	0.654305	−	0.756231i	$-0.272961\pi$
$12$	0.864396	−	0.358044i	0.249530	−	0.103359i
$13$	−2.33554	−	5.63849i	−0.647762	−	1.56384i	−0.815976	−	0.578085i	$-0.803800\pi$
$13$	−2.33554	−	5.63849i	−0.647762	−	1.56384i	0.168215	−	0.985750i	$-0.446200\pi$
$14$	−4.36011	+	0.440588i	−1.16529	+	0.117752i
$15$	0.348465	−	0.841268i	0.0899732	−	0.217214i
$16$	4.93422			1.23356
$17$	−1.66048	+	4.00875i	−0.402725	+	0.972264i	0.584277	+	0.811554i	$0.301378\pi$
$17$	−1.66048	+	4.00875i	−0.402725	+	0.972264i	−0.987002	+	0.160710i	$0.948622\pi$
$18$	−2.34635			−0.553040
$19$	−2.33753	+	5.64329i	−0.536265	+	1.29466i	0.391047	+	0.920371i	$0.372113\pi$
$19$	−2.33753	+	5.64329i	−0.536265	+	1.29466i	−0.927312	+	0.374288i	$0.877887\pi$
$20$	−0.380454	+	0.380454i	−0.0850721	+	0.0850721i
$21$	−3.18835	−	0.958361i	−0.695754	−	0.209132i
$22$	−1.88480	+	4.55030i	−0.401840	+	0.970128i
$23$			4.21773i			0.879458i	0.898130	+	0.439729i	$0.144926\pi$
$23$			4.21773i			0.879458i	−0.898130	+	0.439729i	$0.855074\pi$
$24$	2.41948	+	1.00218i	0.493875	+	0.204570i
$25$		−	4.47635i		−	0.895271i
$26$	−3.86849	+	9.33937i	−0.758674	+	1.83160i
$27$	−5.13452	−	2.12679i	−0.988139	−	0.409301i
$28$	1.52382	+	1.24412i	0.287974	+	0.235116i
$29$	5.26342	−	2.18018i	0.977393	−	0.404849i	0.163934	−	0.986471i	$-0.447582\pi$
$29$	5.26342	−	2.18018i	0.977393	−	0.404849i	0.813459	+	0.581622i	$0.197582\pi$
$30$	−1.39344	+	0.577183i	−0.254407	+	0.105379i
$31$	−1.26834			−0.227800			−0.113900	−	0.993492i	$-0.536334\pi$
$31$	−1.26834			−0.227800			−0.113900	+	0.993492i	$0.536334\pi$
$32$	−2.83586	−	2.83586i	−0.501314	−	0.501314i
$33$	−2.64579	+	2.64579i	−0.460572	+	0.460572i
$34$	6.63993	−	2.75035i	1.13874	−	0.471681i
$35$	1.90486	−	0.192485i	0.321980	−	0.0325360i
$36$	0.744767	+	0.744767i	0.124128	+	0.124128i
$37$	−7.10280			−1.16769			−0.583847	−	0.811864i	$-0.698453\pi$
$37$	−7.10280			−1.16769			−0.583847	+	0.811864i	$0.698453\pi$
$38$	9.34732	−	3.87178i	1.51633	−	0.628086i
$39$	−5.43040	+	5.43040i	−0.869560	+	0.869560i
$40$	−1.50601			−0.238120
$41$	6.06831	−	2.04342i	0.947711	−	0.319128i
$41$	6.06831	−	2.04342i	0.947711	−	0.319128i
$42$	2.61181	+	4.85672i	0.403011	+	0.749409i
$43$	−1.81789	−	1.81789i	−0.277226	−	0.277226i	0.554775	−	0.832001i	$-0.312804\pi$
$43$	−1.81789	−	1.81789i	−0.277226	−	0.277226i	−0.832001	+	0.554775i	$0.812804\pi$
$44$	2.04260	−	0.846073i	0.307934	−	0.127550i
$45$	1.02508			0.152810
$46$	4.93991	−	4.93991i	0.728350	−	0.728350i
$47$	−1.59005	+	3.83872i	−0.231933	+	0.559935i	−0.996405	−	0.0847221i	$-0.973000\pi$
$47$	−1.59005	+	3.83872i	−0.231933	+	0.559935i	0.764472	+	0.644657i	$0.223000\pi$
$48$	−2.37606	−	5.73632i	−0.342955	−	0.827967i
$49$	−1.40040	−	6.85849i	−0.200057	−	0.979784i
$50$	−5.24281	+	5.24281i	−0.741445	+	0.741445i
$51$	5.46000			0.764553
$52$	4.19238	−	1.73654i	0.581378	−	0.240815i
$53$	0.570585	+	1.37751i	0.0783759	+	0.189216i	0.958211	−	0.286064i	$-0.0923469\pi$
$53$	0.570585	+	1.37751i	0.0783759	+	0.189216i	−0.879835	+	0.475280i	$0.842347\pi$
$54$	3.52273	+	8.50462i	0.479382	+	1.15733i
$55$	0.823435	−	1.98795i	0.111032	−	0.268055i
$56$	0.553587	+	5.47836i	0.0739762	+	0.732076i
$57$	7.68628			1.01807
$58$	−8.71812	−	3.61117i	−1.14475	−	0.474169i
$59$		−	8.50571i		−	1.10735i	−0.832733	−	0.553675i	$-0.813225\pi$
$59$		−	8.50571i		−	1.10735i	0.832733	−	0.553675i	$-0.186775\pi$
$60$	0.625507	+	0.259093i	0.0807526	+	0.0334488i
$61$	9.97575	−	9.97575i	1.27726	−	1.27726i	0.335072	−	0.942193i	$-0.391239\pi$
$61$	9.97575	−	9.97575i	1.27726	−	1.27726i	0.942193	−	0.335072i	$-0.108761\pi$
$62$	1.48551	+	1.48551i	0.188660	+	0.188660i
$63$	−0.376805	−	3.72890i	−0.0474729	−	0.469797i
$64$		−	3.22559i		−	0.403199i
$65$	1.69008	−	4.08021i	0.209628	−	0.506087i
$66$	6.19762			0.762874
$67$	11.7724	+	4.87630i	1.43823	+	0.595735i	0.959369	−	0.282156i	$-0.0910495\pi$
$67$	11.7724	+	4.87630i	1.43823	+	0.595735i	0.478862	+	0.877890i	$0.341049\pi$
$68$	−2.98062	−	1.23461i	−0.361453	−	0.149719i
$69$	4.90336	−	2.03104i	0.590295	−	0.244508i
$70$	−2.45646	−	2.00557i	−0.293603	−	0.239711i
$71$	−5.88668	+	2.43834i	−0.698621	+	0.289378i	−0.703587	−	0.710610i	$-0.748419\pi$
$71$	−5.88668	+	2.43834i	−0.698621	+	0.289378i	0.00496602	+	0.999988i	$0.498419\pi$
$72$			2.94812i			0.347439i
$73$	9.42192	−	9.42192i	1.10275	−	1.10275i	0.108675	−	0.994077i	$-0.465339\pi$
$73$	9.42192	−	9.42192i	1.10275	−	1.10275i	0.994077	−	0.108675i	$-0.0346608\pi$
$74$	8.31897	+	8.31897i	0.967060	+	0.967060i
$75$	−5.20402	+	2.15558i	−0.600909	+	0.248905i
$76$	−4.19595	−	1.73802i	−0.481308	−	0.199364i
$77$	−7.53419	−	2.26465i	−0.858600	−	0.258080i
$78$	12.7204			1.44030
$79$	4.48251	+	10.8217i	0.504322	+	1.21754i	0.947109	+	0.320913i	$0.103990\pi$
$79$	4.48251	+	10.8217i	0.504322	+	1.21754i	−0.442787	+	0.896627i	$0.646010\pi$
$80$	2.52478	+	2.52478i	0.282279	+	0.282279i
$81$			2.74362i			0.304847i
$82$	−9.50065	−	4.71405i	−1.04917	−	0.520580i
$83$		−	9.04038i		−	0.992311i	−0.868234	−	0.496155i	$-0.834745\pi$
$83$		−	9.04038i		−	0.992311i	0.868234	−	0.496155i	$-0.165255\pi$
$84$	0.712569	−	2.37063i	0.0777477	−	0.258657i
$85$	−2.90087	+	1.20158i	−0.314643	+	0.130330i
$86$			4.25832i			0.459186i
$87$	−5.06918	−	5.06918i	−0.543473	−	0.543473i
$88$	5.71733	+	2.36819i	0.609469	+	0.252450i
$89$	6.93110	+	16.7332i	0.734695	+	1.77371i	0.626269	+	0.779607i	$0.284581\pi$
$89$	6.93110	+	16.7332i	0.734695	+	1.77371i	0.108427	+	0.994104i	$0.465419\pi$
$90$	−1.20060	−	1.20060i	−0.126554	−	0.126554i
$91$	−15.4637	−	4.64812i	−1.62104	−	0.487255i
$92$	−3.13601			−0.326951
$93$	0.610766	+	1.47452i	0.0633335	+	0.152900i
$94$	6.35830	−	2.63370i	0.655809	−	0.271645i
$95$	−4.08368	+	1.69152i	−0.418977	+	0.173546i
$96$	−1.93125	+	4.66245i	−0.197108	+	0.475860i
$97$	4.66294	+	1.93145i	0.473450	+	0.196109i	0.606633	−	0.794982i	$-0.292520\pi$
$97$	4.66294	+	1.93145i	0.473450	+	0.196109i	−0.133183	+	0.991091i	$0.542520\pi$
$98$	−6.39265	+	9.67300i	−0.645755	+	0.977121i
$99$	−3.89156	−	1.61194i	−0.391116	−	0.162006i
$100$	3.32830			0.332830
$101$	2.26599	−	5.47059i	0.225475	−	0.544344i	−0.770142	−	0.637872i	$-0.779815\pi$
$101$	2.26599	−	5.47059i	0.225475	−	0.544344i	0.995617	+	0.0935288i	$0.0298147\pi$
$102$	−6.39488	−	6.39488i	−0.633188	−	0.633188i
$103$	4.01398	+	4.01398i	0.395510	+	0.395510i	0.876646	−	0.481136i	$-0.159776\pi$
$103$	4.01398	+	4.01398i	0.395510	+	0.395510i	−0.481136	+	0.876646i	$0.659776\pi$
$104$	11.7346	+	4.86065i	1.15068	+	0.476626i
$105$	−1.14105	−	2.12182i	−0.111356	−	0.207068i
$106$	0.945094	−	2.28166i	0.0917956	−	0.221614i
$107$		−	14.3187i		−	1.38424i	−0.721782	−	0.692120i	$-0.756677\pi$
$107$		−	14.3187i		−	1.38424i	0.721782	−	0.692120i	$-0.243323\pi$
$108$	1.58133	−	3.81766i	0.152163	−	0.367355i
$109$	−1.29345	+	3.12266i	−0.123890	+	0.299097i	−0.973640	−	0.228088i	$-0.926753\pi$
$109$	−1.29345	+	3.12266i	−0.123890	+	0.299097i	0.849751	+	0.527185i	$0.176753\pi$
$110$	−3.29276	+	1.36391i	−0.313952	+	0.130043i
$111$	3.42034	+	8.25742i	0.324644	+	0.783760i
$112$	8.25624	−	10.1124i	0.780141	−	0.955531i
$113$			12.3311i			1.16001i	0.814613	+	0.580006i	$0.196950\pi$
$113$			12.3311i			1.16001i	−0.814613	+	0.580006i	$0.803050\pi$
$114$	−9.00235	−	9.00235i	−0.843148	−	0.843148i
$115$	−2.15816	+	2.15816i	−0.201249	+	0.201249i
$116$	1.62103	+	3.91351i	0.150509	+	0.363360i
$117$	−7.98731	−	3.30845i	−0.738427	−	0.305867i
$118$	−9.96209	+	9.96209i	−0.917084	+	0.917084i
$119$	5.43727	+	10.1107i	0.498434	+	0.926849i
$120$	0.725214	+	1.75082i	0.0662026	+	0.159827i
$121$	1.52608	−	1.52608i	0.138734	−	0.138734i
$122$	−23.3677			−2.11561
$123$	−5.29778	−	6.07077i	−0.477684	−	0.547383i
$124$		−	0.943047i		−	0.0846881i
$125$	4.84893	−	4.84893i	0.433701	−	0.433701i
$126$	−3.92605	+	4.80870i	−0.349761	+	0.428393i
$127$		−	18.6026i		−	1.65071i	−0.564614	−	0.825355i	$-0.690975\pi$
$127$		−	18.6026i		−	1.65071i	0.564614	−	0.825355i	$-0.309025\pi$
$128$	−9.44961	+	9.44961i	−0.835236	+	0.835236i
$129$	−1.23801	+	2.98881i	−0.109000	+	0.263150i
$130$	−6.75829	+	2.79938i	−0.592741	+	0.245522i
$131$	8.76221	+	8.76221i	0.765558	+	0.765558i	0.977321	−	0.211763i	$-0.0679205\pi$
$131$	8.76221	+	8.76221i	0.765558	+	0.765558i	−0.211763	+	0.977321i	$0.567920\pi$
$132$	−1.96722	−	1.96722i	−0.171224	−	0.171224i
$133$	7.65428	+	14.2333i	0.663710	+	1.23418i
$134$	−8.07690	−	19.4994i	−0.697738	−	1.68449i
$135$	−1.53902	−	3.71552i	−0.132458	−	0.319781i
$136$	−3.45573	−	8.34288i	−0.296327	−	0.715396i
$137$	−14.6169	−	6.05451i	−1.24880	−	0.517272i	−0.342349	−	0.939573i	$-0.611222\pi$
$137$	−14.6169	−	6.05451i	−1.24880	−	0.517272i	−0.906456	+	0.422301i	$0.861222\pi$
$138$	−8.12173	−	3.36413i	−0.691368	−	0.286374i
$139$			9.67908i			0.820969i	0.911868	+	0.410484i	$0.134640\pi$
$139$			9.67908i			0.820969i	−0.911868	+	0.410484i	$0.865360\pi$
$140$	0.143118	+	1.41632i	0.0120957	+	0.119701i
$141$	5.22842			0.440313
$142$	9.75046	+	4.03877i	0.818241	+	0.338926i
$143$	−12.8323	+	12.8323i	−1.07309	+	1.07309i
$144$	4.94244	−	4.94244i	0.411870	−	0.411870i
$145$	3.80880	+	1.57765i	0.316303	+	0.131017i
$146$	−22.0703			−1.82656
$147$	−7.29904	+	4.93073i	−0.602015	+	0.406680i
$148$		−	5.28114i		−	0.434107i
$149$	8.55004	+	3.54154i	0.700447	+	0.290134i	0.704345	−	0.709858i	$-0.251241\pi$
$149$	8.55004	+	3.54154i	0.700447	+	0.290134i	−0.00389833	+	0.999992i	$0.501241\pi$
$150$	8.61974	+	3.57041i	0.703798	+	0.291523i
$151$	−0.641779	−	1.54939i	−0.0522272	−	0.126088i	0.895612	−	0.444835i	$-0.146738\pi$
$151$	−0.641779	−	1.54939i	−0.0522272	−	0.126088i	−0.947840	+	0.318748i	$0.896738\pi$
$152$	−4.86479	−	11.7446i	−0.394586	−	0.952616i
$153$	2.35218	+	5.67867i	0.190163	+	0.459093i
$154$	6.17181	+	11.4766i	0.497339	+	0.924813i
$155$	−0.648993	−	0.648993i	−0.0521284	−	0.0521284i
$156$	−4.03766	−	4.03766i	−0.323271	−	0.323271i
$157$	8.40223	−	3.48032i	0.670571	−	0.277760i	−0.0213082	−	0.999773i	$-0.506783\pi$
$157$	8.40223	−	3.48032i	0.670571	−	0.277760i	0.691879	+	0.722013i	$0.256783\pi$
$158$	7.42465	−	17.9247i	0.590673	−	1.42601i
$159$	1.32668	−	1.32668i	0.105212	−	0.105212i
$160$		−	2.90214i		−	0.229435i
$161$	8.64399	+	7.05737i	0.681241	+	0.556198i
$162$	3.21340	−	3.21340i	0.252468	−	0.252468i
$163$			5.01158i			0.392537i	0.980550	+	0.196269i	$0.0628824\pi$
$163$			5.01158i			0.392537i	−0.980550	+	0.196269i	$0.937118\pi$
$164$	1.51934	+	4.51197i	0.118641	+	0.352325i
$165$	−2.70763			−0.210789
$166$	−10.5883	+	10.5883i	−0.821812	+	0.821812i
$167$	−2.76046	−	6.66435i	−0.213611	−	0.515703i	0.780362	−	0.625328i	$-0.215035\pi$
$167$	−2.76046	−	6.66435i	−0.213611	−	0.515703i	−0.993973	+	0.109625i	$0.965035\pi$
$168$	6.10233	−	3.28167i	0.470805	−	0.253186i
$169$	−17.1454	+	17.1454i	−1.31888	+	1.31888i
$170$	4.80488	+	1.99025i	0.368518	+	0.152645i
$171$	3.31127	+	7.99411i	0.253219	+	0.611325i
$172$	1.35166	−	1.35166i	0.103063	−	0.103063i
$173$	−10.0409	−	10.0409i	−0.763394	−	0.763394i	0.213540	−	0.976934i	$-0.431501\pi$
$173$	−10.0409	−	10.0409i	−0.763394	−	0.763394i	−0.976934	+	0.213540i	$0.931501\pi$
$174$			11.8743i			0.900187i
$175$	−9.17401	−	7.49010i	−0.693490	−	0.566199i
$176$	−5.61473	−	13.5552i	−0.423226	−	1.02176i
$177$	−9.88839	+	4.09590i	−0.743257	+	0.307867i
$178$	11.4804	−	27.7161i	0.860493	−	2.07741i
$179$	−6.21354	+	15.0008i	−0.464422	+	1.12121i	0.502141	+	0.864786i	$0.332546\pi$
$179$	−6.21354	+	15.0008i	−0.464422	+	1.12121i	−0.966563	+	0.256428i	$0.917454\pi$
$180$			0.762175i			0.0568092i
$181$	0.651241	−	1.57223i	0.0484063	−	0.116863i	−0.897827	−	0.440349i	$-0.854855\pi$
$181$	0.651241	−	1.57223i	0.0484063	−	0.116863i	0.946233	+	0.323486i	$0.104855\pi$
$182$	12.6675	+	23.5554i	0.938975	+	1.74605i
$183$	−16.4012	−	6.79360i	−1.21241	−	0.502197i
$184$	−6.20685	−	6.20685i	−0.457575	−	0.457575i
$185$	−3.63441	−	3.63441i	−0.267207	−	0.267207i
$186$	1.01165	−	2.44233i	0.0741776	−	0.179081i
$187$	12.9022			0.943502
$188$	−2.85420	−	1.18225i	−0.208164	−	0.0862243i
$189$	−12.9501	+	6.96421i	−0.941982	+	0.506572i
$190$	6.76404	+	2.80176i	0.490715	+	0.203261i
$191$	5.82524	−	14.0634i	0.421500	−	1.01759i	−0.560406	−	0.828218i	$-0.689355\pi$
$191$	5.82524	−	14.0634i	0.421500	−	1.01759i	0.981905	−	0.189372i	$-0.0606453\pi$
$192$	−3.74994	+	1.55328i	−0.270629	+	0.112098i
$193$	3.36134	−	1.39231i	0.241954	−	0.100221i	−0.258411	−	0.966035i	$-0.583199\pi$
$193$	3.36134	−	1.39231i	0.241954	−	0.100221i	0.500366	+	0.865814i	$0.333199\pi$
$194$	−3.19918	−	7.72351i	−0.229688	−	0.554516i
$195$	−5.55733			−0.397969
$196$	5.09948	−	1.04124i	0.364249	−	0.0743740i
$197$	10.3236	+	10.3236i	0.735526	+	0.735526i	0.971709	−	0.236183i	$-0.0758964\pi$
$197$	10.3236	+	10.3236i	0.735526	+	0.735526i	−0.236183	+	0.971709i	$0.575896\pi$
$198$	2.66995	+	6.44582i	0.189745	+	0.458085i
$199$	11.7422	+	4.86377i	0.832381	+	0.344784i	0.757845	−	0.652435i	$-0.226252\pi$
$199$	11.7422	+	4.86377i	0.832381	+	0.344784i	0.0745363	+	0.997218i	$0.476252\pi$
$200$	6.58744	+	6.58744i	0.465802	+	0.465802i
$201$		−	16.0343i		−	1.13097i
$202$	−9.06126	+	3.75330i	−0.637548	+	0.264081i
$203$	4.33893	−	14.4351i	0.304533	−	1.01314i
$204$			4.05967i			0.284234i
$205$	4.15067	+	2.05949i	0.289895	+	0.143841i
$206$		−	9.40254i		−	0.655106i
$207$	4.22476	+	4.22476i	0.293641	+	0.293641i
$208$	−11.5241	−	27.8216i	−0.799050	−	1.92908i
$209$	18.1630			1.25636
$210$	−1.14869	+	3.82155i	−0.0792673	+	0.263712i
$211$	5.14224	+	2.12999i	0.354006	+	0.146634i	0.552598	−	0.833448i	$-0.313637\pi$
$211$	5.14224	+	2.12999i	0.354006	+	0.146634i	−0.198591	+	0.980082i	$0.563637\pi$
$212$	−1.02422	+	0.424246i	−0.0703438	+	0.0291373i
$213$	5.66943	+	5.66943i	0.388463	+	0.388463i
$214$	−16.7704	+	16.7704i	−1.14640	+	1.14640i
$215$		−	1.86038i		−	0.126877i
$216$	10.6858	−	4.42621i	0.727077	−	0.301165i
$217$	−2.12226	+	2.59938i	−0.144069	+	0.176458i
$218$	5.17225	−	2.14242i	0.350309	−	0.145103i
$219$	−15.4906	−	6.41643i	−1.04676	−	0.433582i
$220$	1.47810	+	0.612248i	0.0996533	+	0.0412777i
$221$	26.4814			1.78133
$222$	5.66531	−	13.6773i	0.380231	−	0.917958i
$223$			14.7817i			0.989857i	0.868934	+	0.494929i	$0.164806\pi$
$223$			14.7817i			0.989857i	−0.868934	+	0.494929i	$0.835194\pi$
$224$	−10.5571	+	1.06679i	−0.705373	+	0.0712778i
$225$	−4.48381	−	4.48381i	−0.298921	−	0.298921i
$226$	14.4425	−	14.4425i	0.960698	−	0.960698i
$227$	−11.0032	−	4.55769i	−0.730311	−	0.302505i	−0.0136313	−	0.999907i	$-0.504339\pi$
$227$	−11.0032	−	4.55769i	−0.730311	−	0.302505i	−0.716680	+	0.697402i	$0.754339\pi$
$228$			5.71497i			0.378483i
$229$	12.9319	+	5.35658i	0.854566	+	0.353973i	0.766580	−	0.642149i	$-0.221957\pi$
$229$	12.9319	+	5.35658i	0.854566	+	0.353973i	0.0879860	+	0.996122i	$0.471957\pi$
$230$	5.05537			0.333341
$231$	0.995287	+	9.84947i	0.0654851	+	0.648048i
$232$	−4.53733	+	10.9541i	−0.297890	+	0.719170i
$233$	1.44964	+	3.49973i	0.0949688	+	0.229275i	0.964224	−	0.265089i	$-0.0854012\pi$
$233$	1.44964	+	3.49973i	0.0949688	+	0.229275i	−0.869255	+	0.494364i	$0.835401\pi$
$234$	5.47999	+	13.2299i	0.358238	+	0.864863i
$235$	−2.77783	+	1.15062i	−0.181206	+	0.0750579i
$236$	6.32424			0.411673
$237$	10.4224	−	10.4224i	0.677005	−	0.677005i
$238$	5.47366	−	18.2102i	0.354805	−	1.18039i
$239$	1.86870	+	4.51144i	0.120876	+	0.291821i	0.972723	−	0.231970i	$-0.0745172\pi$
$239$	1.86870	+	4.51144i	0.120876	+	0.291821i	−0.851847	+	0.523791i	$0.824517\pi$
$240$	1.71940	−	4.15100i	0.110987	−	0.267946i
$241$	4.04536	−	4.04536i	0.260584	−	0.260584i	−0.564707	−	0.825291i	$-0.691011\pi$
$241$	4.04536	−	4.04536i	0.260584	−	0.260584i	0.825291	+	0.564707i	$0.191011\pi$
$242$	−3.57475			−0.229794
$243$	−12.2139	+	5.05918i	−0.783525	+	0.324546i
$244$	7.41726	+	7.41726i	0.474841	+	0.474841i
$245$	2.79284	−	4.22597i	0.178428	−	0.269987i
$246$	−0.905345	+	13.3151i	−0.0577227	+	0.848940i
$247$	37.2790			2.37201
$248$	1.86650	−	1.86650i	0.118523	−	0.118523i
$249$	−10.5100	+	4.35337i	−0.666043	+	0.275884i
$250$	−11.3584			−0.718365
$251$	−11.0014	−	11.0014i	−0.694403	−	0.694403i	0.268795	−	0.963197i	$-0.413375\pi$
$251$	−11.0014	−	11.0014i	−0.694403	−	0.694403i	−0.963197	+	0.268795i	$0.913375\pi$
$252$	2.77254	−	0.280165i	0.174654	−	0.0176487i
$253$	11.5868	−	4.79942i	0.728458	−	0.301737i
$254$	−21.7877	+	21.7877i	−1.36708	+	1.36708i
$255$	2.79381	+	2.79381i	0.174955	+	0.174955i
$256$	15.6840			0.980251
$257$	1.33847	−	0.554412i	0.0834914	−	0.0345833i	−0.340547	−	0.940228i	$-0.610612\pi$
$257$	1.33847	−	0.554412i	0.0834914	−	0.0345833i	0.424038	+	0.905644i	$0.360612\pi$
$258$	4.95054	−	2.05058i	0.308207	−	0.127664i
$259$	−11.8848	+	14.5568i	−0.738488	+	0.904513i
$260$	3.03375	+	1.25662i	0.188145	+	0.0779323i
$261$	3.08838	−	7.45600i	0.191166	−	0.461515i
$262$		−	20.5250i		−	1.26804i
$263$	−3.14046	−	1.30082i	−0.193649	−	0.0802122i	0.283751	−	0.958898i	$-0.408421\pi$
$263$	−3.14046	−	1.30082i	−0.193649	−	0.0802122i	−0.477401	+	0.878686i	$0.658421\pi$
$264$		−	7.78713i		−	0.479265i
$265$	−0.412895	+	0.996817i	−0.0253639	+	0.0612340i
$266$	7.70551	−	25.6353i	0.472455	−	1.57180i
$267$	16.1156	−	16.1156i	0.986260	−	0.986260i
$268$	−3.62567	+	8.75313i	−0.221473	+	0.534683i
$269$	−6.33287			−0.386122			−0.193061	−	0.981187i	$-0.561842\pi$
$269$	−6.33287			−0.386122			−0.193061	+	0.981187i	$0.561842\pi$
$270$	−2.54917	+	6.15423i	−0.155137	+	0.374535i
$271$	−4.16294			−0.252881			−0.126440	−	0.991974i	$-0.540355\pi$
$271$	−4.16294			−0.252881			−0.126440	+	0.991974i	$0.540355\pi$
$272$	−8.19316	+	19.7800i	−0.496784	+	1.19934i
$273$	2.04280	+	20.2158i	0.123636	+	1.22351i
$274$	10.0284	+	24.2108i	0.605841	+	1.46263i
$275$	−12.2973	+	5.09371i	−0.741556	+	0.307162i
$276$	1.51014	+	3.64579i	0.0908995	+	0.219451i
$277$		−	8.02085i		−	0.481926i	−0.970534	−	0.240963i	$-0.922537\pi$
$277$		−	8.02085i		−	0.481926i	0.970534	−	0.240963i	$-0.0774633\pi$
$278$	11.3364	−	11.3364i	0.679910	−	0.679910i
$279$	−1.27045	+	1.27045i	−0.0760600	+	0.0760600i
$280$	−2.51994	+	3.08647i	−0.150595	+	0.184452i
$281$	−0.280294	+	0.676690i	−0.0167210	+	0.0403680i	−0.932020	−	0.362408i	$-0.881955\pi$
$281$	−0.280294	+	0.676690i	−0.0167210	+	0.0403680i	0.915299	+	0.402776i	$0.131955\pi$
$282$	−6.12365	−	6.12365i	−0.364658	−	0.364658i
$283$			0.305045i			0.0181331i	0.999959	+	0.00906653i	$0.00288600\pi$
$283$			0.305045i			0.0181331i	−0.999959	+	0.00906653i	$0.997114\pi$
$284$	−1.81298	−	4.37692i	−0.107580	−	0.259722i
$285$	3.93297	+	3.93297i	0.232969	+	0.232969i
$286$	30.0589			1.77742
$287$	5.96601	−	15.8558i	0.352162	−	0.935939i
$288$	−5.68117			−0.334766
$289$	−1.29205	−	1.29205i	−0.0760030	−	0.0760030i
$290$	−2.61316	−	6.30874i	−0.153450	−	0.370462i
$291$		−	6.35103i		−	0.372304i
$292$	7.00547	+	7.00547i	0.409964	+	0.409964i
$293$	2.69064	−	6.49579i	0.157189	−	0.379488i	−0.825590	−	0.564270i	$-0.809158\pi$
$293$	2.69064	−	6.49579i	0.157189	−	0.379488i	0.982780	+	0.184782i	$0.0591578\pi$
$294$	14.3238	+	2.77381i	0.835381	+	0.161772i
$295$	4.35226	−	4.35226i	0.253398	−	0.253398i
$296$	10.4525	−	10.4525i	0.607542	−	0.607542i
$297$			16.5255i			0.958908i
$298$	−5.86607	−	14.1619i	−0.339812	−	0.820379i
$299$	23.7816	−	9.85068i	1.37533	−	0.569680i
$300$	−1.60273	−	3.86934i	−0.0925338	−	0.223396i
$301$	−6.76747	+	0.683851i	−0.390070	+	0.0394165i
$302$	−1.06302	+	2.56635i	−0.0611698	+	0.147677i
$303$	−7.45106			−0.428052
$304$	−11.5339	+	27.8452i	−0.661513	+	1.59703i
$305$	10.2089			0.584561
$306$	3.89606	−	9.40592i	0.222723	−	0.537701i
$307$	−14.7488	+	14.7488i	−0.841760	+	0.841760i	−0.989088	−	0.147328i	$-0.952933\pi$
$307$	−14.7488	+	14.7488i	−0.841760	+	0.841760i	0.147328	+	0.989088i	$0.452933\pi$
$308$	1.68383	−	5.60188i	0.0959450	−	0.319197i
$309$	2.73357	−	6.59941i	0.155507	−	0.375428i
$310$			1.52023i			0.0863433i
$311$	−14.3481	−	5.94316i	−0.813604	−	0.337006i	−0.0632131	−	0.998000i	$-0.520135\pi$
$311$	−14.3481	−	5.94316i	−0.813604	−	0.337006i	−0.750391	+	0.660994i	$0.770135\pi$
$312$		−	15.9829i		−	0.904851i
$313$	−0.423317	+	1.02198i	−0.0239273	+	0.0577656i	−0.935392	−	0.353614i	$-0.884953\pi$
$313$	−0.423317	+	1.02198i	−0.0239273	+	0.0577656i	0.911464	+	0.411379i	$0.134953\pi$
$314$	−13.9171	−	5.76466i	−0.785388	−	0.325319i
$315$	1.71522	−	2.10084i	0.0966419	−	0.118369i
$316$	−8.04627	+	3.33287i	−0.452638	+	0.187489i
$317$	−18.3843	+	7.61504i	−1.03257	+	0.427703i	−0.833638	−	0.552311i	$-0.813746\pi$
$317$	−18.3843	+	7.61504i	−1.03257	+	0.427703i	−0.198928	+	0.980014i	$0.563746\pi$
$318$	−3.10767			−0.174269
$319$	−11.9787	−	11.9787i	−0.670676	−	0.670676i
$320$	1.65050	−	1.65050i	0.0922655	−	0.0922655i
$321$	−16.6463	+	6.89513i	−0.929107	+	0.384849i
$322$	−1.85828	−	18.3898i	−0.103558	−	1.02482i
$323$	−18.7411	−	18.7411i	−1.04278	−	1.04278i
$324$	−2.03996			−0.113331
$325$	−25.2399	+	10.4547i	−1.40006	+	0.579922i
$326$	5.86968	−	5.86968i	0.325091	−	0.325091i
$327$	4.25314			0.235199
$328$	−5.92307	+	11.9373i	−0.327047	+	0.659127i
$329$	5.20665	+	9.68189i	0.287052	+	0.533780i
$330$	3.17124	+	3.17124i	0.174571	+	0.174571i
$331$	−29.3008	+	12.1368i	−1.61052	+	0.667099i	−0.992853	−	0.119342i	$-0.961922\pi$
$331$	−29.3008	+	12.1368i	−1.61052	+	0.667099i	−0.617666	+	0.786440i	$0.711922\pi$
$332$	6.72178			0.368906
$333$	−7.11463	+	7.11463i	−0.389879	+	0.389879i
$334$	−4.57232	+	11.0386i	−0.250186	+	0.604003i
$335$	3.52866	+	8.51893i	0.192791	+	0.465439i
$336$	−15.7320	−	4.72877i	−0.858252	−	0.257975i
$337$	−22.2434	+	22.2434i	−1.21167	+	1.21167i	−0.241198	+	0.970476i	$0.577540\pi$
$337$	−22.2434	+	22.2434i	−1.21167	+	1.21167i	−0.970476	+	0.241198i	$0.922460\pi$
$338$	40.1623			2.18454
$339$	14.3356	−	5.93800i	0.778604	−	0.322508i
$340$	−0.893408	−	2.15688i	−0.0484519	−	0.116973i
$341$	1.44326	+	3.48435i	0.0781571	+	0.188688i
$342$	5.48465	−	13.2411i	0.296576	−	0.715998i
$343$	−16.3993	−	8.60601i	−0.885478	−	0.464681i
$344$	5.35045			0.288477
$345$	3.54824	+	1.46973i	0.191031	+	0.0791276i
$346$			23.5202i			1.26446i
$347$	20.5587	+	8.51569i	1.10365	+	0.457146i	0.858746	−	0.512401i	$-0.171244\pi$
$347$	20.5587	+	8.51569i	1.10365	+	0.457146i	0.244903	+	0.969548i	$0.421244\pi$
$348$	3.76908	−	3.76908i	0.202044	−	0.202044i
$349$	8.56272	+	8.56272i	0.458352	+	0.458352i	0.898114	−	0.439762i	$-0.144937\pi$
$349$	8.56272	+	8.56272i	0.458352	+	0.458352i	−0.439762	+	0.898114i	$0.644937\pi$
$350$	1.97223	+	19.5174i	0.105420	+	1.04325i
$351$			33.9181i			1.81042i
$352$	−4.56362	+	11.0176i	−0.243242	+	0.587238i
$353$	31.6872			1.68654			0.843269	−	0.537491i	$-0.180628\pi$
$353$	31.6872			1.68654			0.843269	+	0.537491i	$0.180628\pi$
$354$	16.3787	+	6.78429i	0.870520	+	0.360581i
$355$	−4.25981	−	1.76447i	−0.226087	−	0.0936483i
$356$	−12.4416	+	5.15347i	−0.659403	+	0.273134i
$357$	9.13601	−	11.1899i	0.483529	−	0.592234i
$358$	24.8468	−	10.2919i	1.31319	−	0.543942i
$359$			3.47594i			0.183453i	0.995784	+	0.0917266i	$0.0292386\pi$
$359$			3.47594i			0.183453i	−0.995784	+	0.0917266i	$0.970761\pi$
$360$	−1.50851	+	1.50851i	−0.0795057	+	0.0795057i
$361$	−12.9476	−	12.9476i	−0.681454	−	0.681454i
$362$	−2.60419	+	1.07869i	−0.136873	+	0.0566946i
$363$	−2.50903	−	1.03927i	−0.131690	−	0.0545478i
$364$	3.45601	−	11.4977i	0.181144	−	0.602644i
$365$	9.64215			0.504693
$366$	11.2526	+	27.1663i	0.588185	+	1.42000i
$367$	9.82394	+	9.82394i	0.512806	+	0.512806i	0.915385	−	0.402579i	$-0.131886\pi$
$367$	9.82394	+	9.82394i	0.512806	+	0.512806i	−0.402579	+	0.915385i	$0.631886\pi$
$368$			20.8112i			1.08486i
$369$	4.03160	−	8.12525i	0.209877	−	0.422983i
$370$			8.51341i			0.442591i
$371$	3.77787	+	1.13556i	0.196137	+	0.0589554i
$372$	−1.09635	+	0.454122i	−0.0568429	+	0.0235451i
$373$		−	8.65907i		−	0.448350i	−0.974549	−	0.224175i	$-0.928031\pi$
$373$		−	8.65907i		−	0.448350i	0.974549	−	0.224175i	$-0.0719686\pi$
$374$	−15.1114	−	15.1114i	−0.781390	−	0.781390i
$375$	−7.97215	−	3.30217i	−0.411680	−	0.170523i
$376$	−3.30916	−	7.98903i	−0.170657	−	0.412003i
$377$	−24.5859	−	24.5859i	−1.26624	−	1.26624i
$378$	23.3241	+	7.01083i	1.19966	+	0.360598i
$379$	1.54341			0.0792797			0.0396398	−	0.999214i	$-0.487379\pi$
$379$	1.54341			0.0792797			0.0396398	+	0.999214i	$0.487379\pi$
$380$	−1.25769	−	3.03633i	−0.0645181	−	0.155761i
$381$	−21.6266	+	8.95801i	−1.10796	+	0.458933i
$382$	−23.2940	+	9.64870i	−1.19183	+	0.493670i
$383$	−1.34061	+	3.23653i	−0.0685022	+	0.165379i	−0.954423	−	0.298458i	$-0.903528\pi$
$383$	−1.34061	+	3.23653i	−0.0685022	+	0.165379i	0.885921	+	0.463837i	$0.153528\pi$
$384$	15.5362	+	6.43529i	0.792827	+	0.328400i
$385$	−2.69636	−	5.01394i	−0.137419	−	0.255534i
$386$	−5.56759	−	2.30617i	−0.283383	−	0.117381i
$387$	−3.64184			−0.185125
$388$	−1.43609	+	3.46703i	−0.0729065	+	0.176012i
$389$	−8.53738	−	8.53738i	−0.432862	−	0.432862i	0.456739	−	0.889601i	$-0.349017\pi$
$389$	−8.53738	−	8.53738i	−0.432862	−	0.432862i	−0.889601	+	0.456739i	$0.849017\pi$
$390$	6.50888	+	6.50888i	0.329590	+	0.329590i
$391$	−16.9078	−	7.00345i	−0.855065	−	0.354180i
$392$	12.1539	+	8.03218i	0.613862	+	0.405686i
$393$	5.96716	−	14.4060i	0.301004	−	0.726687i
$394$		−	24.1825i		−	1.21830i
$395$	−3.24370	+	7.83098i	−0.163208	+	0.394020i
$396$	1.19852	−	2.89348i	0.0602279	−	0.145403i
$397$	30.9569	−	12.8228i	1.55368	−	0.643556i	0.569704	−	0.821850i	$-0.307058\pi$
$397$	30.9569	−	12.8228i	1.55368	−	0.643556i	0.983977	+	0.178294i	$0.0570579\pi$
$398$	−8.05616	−	19.4493i	−0.403819	−	0.974904i
$399$	12.8612	−	15.7526i	0.643863	−	0.788615i
$400$		−	22.0873i		−	1.10437i
$401$	−19.3223	−	19.3223i	−0.964910	−	0.964910i	0.0344948	−	0.999405i	$-0.489018\pi$
$401$	−19.3223	−	19.3223i	−0.964910	−	0.964910i	−0.999405	+	0.0344948i	$0.989018\pi$
$402$	−18.7798	+	18.7798i	−0.936649	+	0.936649i
$403$	2.96226	+	7.15152i	0.147560	+	0.356242i
$404$	4.06754	+	1.68483i	0.202368	+	0.0838234i
$405$	−1.40388	+	1.40388i	−0.0697592	+	0.0697592i
$406$	−21.9886	+	11.8248i	−1.09127	+	0.586857i
$407$	8.08239	+	19.5126i	0.400629	+	0.967204i
$408$	−8.03499	+	8.03499i	−0.397791	+	0.397791i
$409$	−33.1778			−1.64053			−0.820267	−	0.571980i	$-0.806175\pi$
$409$	−33.1778			−1.64053			−0.820267	+	0.571980i	$0.806175\pi$
$410$	−2.44924	−	7.27348i	−0.120959	−	0.359212i
$411$			19.9085i			0.982015i
$412$	−2.98451	+	2.98451i	−0.147036	+	0.147036i
$413$	−17.4319	−	14.2323i	−0.857769	−	0.700324i
$414$		−	9.89627i		−	0.486375i
$415$	4.62585	−	4.62585i	0.227074	−	0.227074i
$416$	−9.36670	+	22.6132i	−0.459240	+	1.10870i
$417$	11.2525	−	4.66094i	0.551037	−	0.228247i
$418$	−21.2729	−	21.2729i	−1.04049	−	1.04049i
$419$	5.37335	+	5.37335i	0.262505	+	0.262505i	0.826071	−	0.563566i	$-0.190571\pi$
$419$	5.37335	+	5.37335i	0.262505	+	0.262505i	−0.563566	+	0.826071i	$0.690571\pi$
$420$	1.57763	−	0.848407i	0.0769805	−	0.0413980i
$421$	1.09587	+	2.64567i	0.0534095	+	0.128942i	0.948332	−	0.317280i	$-0.102769\pi$
$421$	1.09587	+	2.64567i	0.0534095	+	0.128942i	−0.894923	+	0.446221i	$0.852769\pi$
$422$	−3.52802	−	8.51740i	−0.171741	−	0.414621i
$423$	2.25242	+	5.43781i	0.109516	+	0.264395i
$424$	−2.86684	−	1.18748i	−0.139226	−	0.0576693i
$425$	17.9446	+	7.43288i	0.870439	+	0.360548i
$426$		−	13.2803i		−	0.643435i
$427$	−3.75266	−	37.1367i	−0.181604	−	1.79717i
$428$	10.6464			0.514611
$429$	21.0976	+	8.73891i	1.01860	+	0.421918i
$430$	−2.17893	+	2.17893i	−0.105077	+	0.105077i
$431$	16.7887	−	16.7887i	0.808683	−	0.808683i	−0.175752	−	0.984435i	$-0.556236\pi$
$431$	16.7887	−	16.7887i	0.808683	−	0.808683i	0.984435	+	0.175752i	$0.0562356\pi$
$432$	−25.3349	−	10.4940i	−1.21892	−	0.504895i
$433$	3.05517			0.146822			0.0734111	−	0.997302i	$-0.476611\pi$
$433$	3.05517			0.146822			0.0734111	+	0.997302i	$0.476611\pi$
$434$	5.53010	−	0.558816i	0.265453	−	0.0268240i
$435$		−	5.18766i		−	0.248729i
$436$	−2.32179	−	0.961716i	−0.111194	−	0.0460579i
$437$	−23.8019	−	9.85906i	−1.13860	−	0.471623i
$438$	10.6279	+	25.6581i	0.507822	+	1.22599i
$439$	−0.199489	−	0.481608i	−0.00952108	−	0.0229859i	0.919048	−	0.394147i	$-0.128960\pi$
$439$	−0.199489	−	0.481608i	−0.00952108	−	0.0229859i	−0.928569	+	0.371161i	$0.878960\pi$
$440$	1.71371	+	4.13726i	0.0816978	+	0.197236i
$441$	−8.27264	−	5.46718i	−0.393935	−	0.260342i
$442$	−31.0156	−	31.0156i	−1.47526	−	1.47526i
$443$	11.2410	+	11.2410i	0.534077	+	0.534077i	0.921783	−	0.387706i	$-0.126733\pi$
$443$	11.2410	+	11.2410i	0.534077	+	0.534077i	−0.387706	+	0.921783i	$0.626733\pi$
$444$	−6.13963	+	2.54312i	−0.291374	+	0.120691i
$445$	−5.01559	+	12.1087i	−0.237762	+	0.574007i
$446$	17.3127	−	17.3127i	0.819780	−	0.819780i
$447$		−	11.6453i		−	0.550806i
$448$	−6.61066	−	5.39726i	−0.312324	−	0.254997i
$449$	−8.70897	+	8.70897i	−0.411002	+	0.411002i	−0.882087	−	0.471086i	$-0.843862\pi$
$449$	−8.70897	+	8.70897i	−0.411002	+	0.411002i	0.471086	+	0.882087i	$0.343862\pi$
$450$			10.5031i			0.495120i
$451$	−12.5189	−	14.3455i	−0.589490	−	0.675501i
$452$	−9.16852			−0.431251
$453$	−1.49221	+	1.49221i	−0.0701102	+	0.0701102i
$454$	7.54918	+	18.2253i	0.354301	+	0.855358i
$455$	−5.53419	−	10.2910i	−0.259447	−	0.482448i
$456$	−11.3112	+	11.3112i	−0.529696	+	0.529696i
$457$	9.81846	+	4.06694i	0.459288	+	0.190243i	0.600317	−	0.799762i	$-0.295041\pi$
$457$	9.81846	+	4.06694i	0.459288	+	0.190243i	−0.141029	+	0.990005i	$0.545041\pi$
$458$	−8.87243	−	21.4199i	−0.414581	−	1.00089i
$459$	17.0515	−	17.0515i	0.795896	−	0.795896i
$460$	−1.60465	−	1.60465i	−0.0748173	−	0.0748173i
$461$		−	30.3927i		−	1.41553i	−0.706448	−	0.707765i	$-0.749704\pi$
$461$		−	30.3927i		−	1.41553i	0.706448	−	0.707765i	$-0.250296\pi$
$462$	10.3702	−	12.7016i	0.482467	−	0.590934i
$463$	2.40405	+	5.80389i	0.111726	+	0.269730i	0.969846	−	0.243719i	$-0.0783675\pi$
$463$	2.40405	+	5.80389i	0.111726	+	0.269730i	−0.858120	+	0.513449i	$0.828368\pi$
$464$	25.9709	−	10.7575i	1.20567	−	0.499404i
$465$	−0.441971	+	1.06701i	−0.0204959	+	0.0494815i
$466$	2.40112	−	5.79681i	0.111230	−	0.268532i
$467$			16.7396i			0.774615i	0.921951	+	0.387307i	$0.126595\pi$
$467$			16.7396i			0.774615i	−0.921951	+	0.387307i	$0.873405\pi$
$468$	2.45993	−	5.93879i	0.113710	−	0.274521i
$469$	29.6920	−	15.9675i	1.37105	−	0.737313i
$470$	4.60109	+	1.90583i	0.212232	+	0.0879095i
$471$	−8.09215	−	8.09215i	−0.372866	−	0.372866i
$472$	12.5171	+	12.5171i	0.576145	+	0.576145i
$473$	−2.92545	+	7.06267i	−0.134513	+	0.324742i
$474$	−24.4138			−1.12136
$475$	25.2613	+	10.4636i	1.15907	+	0.480103i
$476$	−7.51761	+	4.04277i	−0.344569	+	0.185300i
$477$	1.95134	+	0.808273i	0.0893459	+	0.0370083i
$478$	3.09524	−	7.47257i	0.141573	−	0.341787i
$479$	−19.7337	+	8.17397i	−0.901656	+	0.373478i	−0.784857	−	0.619677i	$-0.787263\pi$
$479$	−19.7337	+	8.17397i	−0.901656	+	0.373478i	−0.116799	+	0.993156i	$0.537263\pi$
$480$	−3.37391	+	1.39752i	−0.153997	+	0.0637878i
$481$	16.5889	+	40.0491i	0.756387	+	1.82608i
$482$	−9.47604			−0.431622
$483$	4.04211	−	13.4476i	0.183923	−	0.611887i
$484$	1.13468	+	1.13468i	0.0515764	+	0.0515764i
$485$	1.39767	+	3.37427i	0.0634648	+	0.153218i
$486$	20.2307	+	8.37982i	0.917682	+	0.380116i
$487$	13.2527	+	13.2527i	0.600537	+	0.600537i	0.940455	−	0.339918i	$-0.110399\pi$
$487$	13.2527	+	13.2527i	0.600537	+	0.600537i	−0.339918	+	0.940455i	$0.610399\pi$
$488$			29.3608i			1.32910i
$489$	5.82625	−	2.41331i	0.263472	−	0.109134i
$490$	−8.22058	+	1.67852i	−0.371368	+	0.0758276i
$491$		−	0.832265i		−	0.0375596i	−0.999824	−	0.0187798i	$-0.994022\pi$
$491$		−	0.832265i		−	0.0375596i	0.999824	−	0.0187798i	$-0.00597814\pi$
$492$	4.51379	−	3.93905i	0.203497	−	0.177586i
$493$			24.7199i			1.11333i
$494$	−43.6620	−	43.6620i	−1.96445	−	1.96445i
$495$	−1.16645	−	2.81607i	−0.0524282	−	0.126573i
$496$	−6.25827			−0.281005
$497$	−4.85272	+	16.1444i	−0.217674	+	0.724174i
$498$	17.4083	+	7.21076i	0.780085	+	0.323122i
$499$	−22.0789	+	9.14538i	−0.988387	+	0.409403i	−0.817526	−	0.575892i	$-0.804655\pi$
$499$	−22.0789	+	9.14538i	−0.988387	+	0.409403i	−0.170861	+	0.985295i	$0.554655\pi$
$500$	3.60532	+	3.60532i	0.161235	+	0.161235i
$501$	−6.41840	+	6.41840i	−0.286753	+	0.286753i
$502$			25.7702i			1.15018i
$503$	−4.39926	+	1.82224i	−0.196154	+	0.0812494i	−0.478598	−	0.878034i	$-0.658855\pi$
$503$	−4.39926	+	1.82224i	−0.196154	+	0.0812494i	0.282444	+	0.959284i	$0.408855\pi$
$504$	6.04199	+	4.93297i	0.269132	+	0.219732i
$505$	3.95871	−	1.63975i	0.176160	−	0.0729679i
$506$	−19.1920	−	7.94957i	−0.853187	−	0.353402i
$507$	28.1889	+	11.6762i	1.25191	+	0.518560i
$508$	13.8315			0.613675
$509$	3.98593	−	9.62288i	0.176673	−	0.426527i	−0.810592	−	0.585612i	$-0.800854\pi$
$509$	3.98593	−	9.62288i	0.176673	−	0.426527i	0.987265	+	0.159085i	$0.0508544\pi$
$510$		−	6.54436i		−	0.289789i
$511$	−3.54432	−	35.0750i	−0.156791	−	1.55163i
$512$	0.529729	+	0.529729i	0.0234109	+	0.0234109i
$513$	24.0042	−	24.0042i	1.05981	−	1.05981i
$514$	−2.21699	−	0.918306i	−0.0977871	−	0.0405048i
$515$			4.10781i			0.181012i
$516$	−2.22227	−	0.920492i	−0.0978298	−	0.0405224i
$517$	12.3550			0.543371
$518$	30.9690	−	3.12941i	1.36070	−	0.137498i
$519$	−6.83795	+	16.5083i	−0.300153	+	0.724633i
$520$	3.51734	+	8.49160i	0.154245	+	0.372381i
$521$	5.99890	+	14.4826i	0.262817	+	0.634495i	0.999111	−	0.0421664i	$-0.0134260\pi$
$521$	5.99890	+	14.4826i	0.262817	+	0.634495i	−0.736294	+	0.676662i	$0.763426\pi$
$522$	−12.3498	+	5.11547i	−0.540537	+	0.223898i
$523$	−24.9956			−1.09298			−0.546491	−	0.837465i	$-0.684037\pi$
$523$	−24.9956			−1.09298			−0.546491	+	0.837465i	$0.684037\pi$
$524$	−6.51496	+	6.51496i	−0.284607	+	0.284607i
$525$	−4.28996	+	14.2722i	−0.187229	+	0.622888i
$526$	2.15463	+	5.20174i	0.0939463	+	0.226807i
$527$	2.10605	−	5.08445i	0.0917409	−	0.221482i
$528$	−13.0549	+	13.0549i	−0.568142	+	0.568142i
$529$	5.21073			0.226553
$530$	1.65109	−	0.683903i	0.0717187	−	0.0297068i
$531$	−8.51988	−	8.51988i	−0.369731	−	0.369731i
$532$	−10.5829	+	5.69118i	−0.458826	+	0.246744i
$533$	−25.6946	−	29.4436i	−1.11296	−	1.27535i
$534$	−37.7500			−1.63360
$535$	7.32669	−	7.32669i	0.316761	−	0.316761i
$536$	−24.5004	+	10.1484i	−1.05826	+	0.438344i
$537$	20.4315			0.881682
$538$	7.41721	+	7.41721i	0.319778	+	0.319778i
$539$	−17.2479	+	11.6515i	−0.742920	+	0.501866i
$540$	2.76259	−	1.14430i	0.118883	−	0.0492430i
$541$	−6.34005	+	6.34005i	−0.272580	+	0.272580i	−0.830138	−	0.557558i	$-0.811738\pi$
$541$	−6.34005	+	6.34005i	−0.272580	+	0.272580i	0.557558	+	0.830138i	$0.311738\pi$
$542$	4.87573	+	4.87573i	0.209431	+	0.209431i
$543$	−2.14142			−0.0918970
$544$	16.0771	−	6.65936i	0.689301	−	0.285518i
$545$	−2.25967	+	0.935985i	−0.0967935	+	0.0400932i
$546$	21.2846	−	26.0697i	0.910896	−	1.11568i
$547$	4.40083	+	1.82289i	0.188166	+	0.0779409i	0.474777	−	0.880106i	$-0.342529\pi$
$547$	4.40083	+	1.82289i	0.188166	+	0.0779409i	−0.286611	+	0.958047i	$0.592529\pi$
$548$	4.50170	−	10.8681i	0.192303	−	0.464261i
$549$		−	19.9847i		−	0.852928i
$550$	20.3688	+	8.43702i	0.868527	+	0.359756i
$551$			34.7992i			1.48250i
$552$	−4.22694	+	10.2047i	−0.179910	+	0.434342i
$553$	29.6789	+	8.92096i	1.26207	+	0.379358i
$554$	−9.39421	+	9.39421i	−0.399122	+	0.399122i
$555$	−2.47507	+	5.97536i	−0.105061	+	0.253640i
$556$	−7.19667			−0.305207
$557$	−10.5447	+	25.4571i	−0.446792	+	1.07865i	0.526725	+	0.850035i	$0.323420\pi$
$557$	−10.5447	+	25.4571i	−0.446792	+	1.07865i	−0.973517	+	0.228615i	$0.926580\pi$
$558$	2.97597			0.125983
$559$	−6.00441	+	14.4959i	−0.253960	+	0.613113i
$560$	9.39899	−	0.949766i	0.397180	−	0.0401349i
$561$	−6.21302	−	14.9996i	−0.262314	−	0.633282i
$562$	1.12084	−	0.464268i	0.0472799	−	0.0195840i
$563$	−8.65783	−	20.9018i	−0.364884	−	0.880908i	−0.994571	−	0.104059i	$-0.966817\pi$
$563$	−8.65783	−	20.9018i	−0.364884	−	0.880908i	0.629687	−	0.776849i	$-0.283183\pi$
$564$			3.88748i			0.163692i
$565$	−6.30966	+	6.30966i	−0.265449	+	0.265449i
$566$	0.357276	−	0.357276i	0.0150174	−	0.0150174i
$567$	5.62289	+	4.59080i	0.236139	+	0.192795i
$568$	5.07460	−	12.2512i	0.212926	−	0.514048i
$569$	23.5617	+	23.5617i	0.987756	+	0.987756i	0.999926	−	0.0121696i	$-0.00387381\pi$
$569$	23.5617	+	23.5617i	0.987756	+	0.987756i	−0.0121696	+	0.999926i	$0.503874\pi$
$570$		−	9.21278i		−	0.385881i
$571$	−6.53444	−	15.7755i	−0.273458	−	0.660186i	0.726169	−	0.687517i	$-0.241299\pi$
$571$	−6.53444	−	15.7755i	−0.273458	−	0.660186i	−0.999626	+	0.0273309i	$0.991299\pi$
$572$	−9.54115	−	9.54115i	−0.398935	−	0.398935i
$573$	−19.1546			−0.800196
$574$	−25.5582	+	11.5832i	−1.06678	+	0.483472i
$575$	18.8801			0.787353
$576$	−3.23097	−	3.23097i	−0.134624	−	0.134624i
$577$	16.1671	+	39.0307i	0.673043	+	1.62487i	0.776411	+	0.630227i	$0.217038\pi$
$577$	16.1671	+	39.0307i	0.673043	+	1.62487i	−0.103368	+	0.994643i	$0.532962\pi$
$578$			3.02656i			0.125888i
$579$	−3.23729	−	3.23729i	−0.134537	−	0.134537i
$580$	−1.17303	+	2.83195i	−0.0487075	+	0.117590i
$581$	−18.5277	−	15.1269i	−0.768659	−	0.627570i
$582$	−7.43847	+	7.43847i	−0.308335	+	0.308335i
$583$	3.13499	−	3.13499i	0.129838	−	0.129838i
$584$			27.7308i			1.14751i
$585$	−2.39411	−	5.77990i	−0.0989843	−	0.238969i
$586$	−10.7594	+	4.45668i	−0.444465	+	0.184104i
$587$	−1.91182	−	4.61553i	−0.0789091	−	0.190503i	0.879502	−	0.475896i	$-0.157876\pi$
$587$	−1.91182	−	4.61553i	−0.0789091	−	0.190503i	−0.958411	+	0.285392i	$0.907876\pi$
$588$	−3.66614	−	5.42704i	−0.151189	−	0.223808i
$589$	2.96478	−	7.15760i	0.122161	−	0.294924i
$590$	−10.1949			−0.419719
$591$	7.03049	−	16.9731i	0.289196	−	0.698180i
$592$	−35.0468			−1.44041
$593$	−12.1062	+	29.2269i	−0.497141	+	1.20020i	0.453876	+	0.891065i	$0.350041\pi$
$593$	−12.1062	+	29.2269i	−0.497141	+	1.20020i	−0.951017	+	0.309139i	$0.899959\pi$
$594$	19.3551	−	19.3551i	0.794148	−	0.794148i
$595$	−2.39135	+	7.95571i	−0.0980356	+	0.326152i
$596$	−2.63324	+	6.35720i	−0.107862	+	0.260401i
$597$		−	15.9931i		−	0.654555i
$598$	−39.3910	−	16.3163i	−1.61082	−	0.667222i
$599$			1.67810i			0.0685652i	0.999412	+	0.0342826i	$0.0109146\pi$
$599$			1.67810i			0.0685652i	−0.999412	+	0.0342826i	$0.989085\pi$
$600$	4.48612	−	10.8305i	0.183145	−	0.442151i
$601$	7.92222	+	3.28149i	0.323154	+	0.133855i	0.538363	−	0.842713i	$-0.319043\pi$
$601$	7.92222	+	3.28149i	0.323154	+	0.133855i	−0.215208	+	0.976568i	$0.569043\pi$
$602$	8.72716	+	7.12528i	0.355693	+	0.290405i
$603$	16.6765	−	6.90761i	0.679118	−	0.281300i
$604$	1.15202	−	0.477181i	0.0468749	−	0.0194162i
$605$	1.56175			0.0634940
$606$	8.72686	+	8.72686i	0.354504	+	0.354504i
$607$	23.0320	−	23.0320i	0.934840	−	0.934840i	−0.0631631	−	0.998003i	$-0.520119\pi$
$607$	23.0320	−	23.0320i	0.934840	−	0.934840i	0.998003	+	0.0631631i	$0.0201188\pi$
$608$	22.6325	−	9.37467i	0.917868	−	0.380193i
$609$	−18.8710	+	1.90691i	−0.764692	+	0.0772720i
$610$	−11.9569	−	11.9569i	−0.484122	−	0.484122i
$611$	25.3582			1.02588
$612$	−4.22225	+	1.74891i	−0.170674	+	0.0706957i
$613$	27.4046	−	27.4046i	1.10686	−	1.10686i	0.113301	−	0.993561i	$-0.463858\pi$
$613$	27.4046	−	27.4046i	1.10686	−	1.10686i	0.993561	−	0.113301i	$-0.0361424\pi$
$614$	34.5483			1.39426
$615$	0.395529	−	5.81714i	0.0159493	−	0.234570i
$616$	14.4200	−	7.75471i	0.581000	−	0.312446i
$617$	−9.93890	−	9.93890i	−0.400125	−	0.400125i	0.478152	−	0.878277i	$-0.341307\pi$
$617$	−9.93890	−	9.93890i	−0.400125	−	0.400125i	−0.878277	+	0.478152i	$0.841307\pi$
$618$	−10.9310	+	4.52777i	−0.439710	+	0.182134i
$619$	38.2012			1.53543			0.767717	−	0.640789i	$-0.221393\pi$
$619$	38.2012			1.53543			0.767717	+	0.640789i	$0.221393\pi$
$620$	0.482545	−	0.482545i	0.0193795	−	0.0193795i
$621$	8.97023	−	21.6560i	0.359963	−	0.869027i
$622$	9.84402	+	23.7656i	0.394709	+	0.952912i
$623$	45.8911	+	13.7941i	1.83859	+	0.552648i
$624$	−26.7948	+	26.7948i	−1.07265	+	1.07265i
$625$	−17.4195			−0.696780
$626$	1.69276	−	0.701166i	0.0676565	−	0.0280242i
$627$	−8.74634	−	21.1155i	−0.349295	−	0.843273i
$628$	2.58772	+	6.24730i	0.103261	+	0.249294i
$629$	11.7940	−	28.4733i	0.470259	−	1.13531i
$630$	−4.46946	+	0.451638i	−0.178067	+	0.0179937i
$631$	−7.72347			−0.307467			−0.153733	−	0.988112i	$-0.549130\pi$
$631$	−7.72347			−0.307467			−0.153733	+	0.988112i	$0.549130\pi$
$632$	−22.5219	−	9.32886i	−0.895871	−	0.371082i
$633$		−	7.00385i		−	0.278378i
$634$	30.4511	+	12.6132i	1.20937	+	0.500936i
$635$	9.51868	−	9.51868i	0.377737	−	0.377737i
$636$	0.986422	+	0.986422i	0.0391142	+	0.0391142i
$637$	−35.4008	+	23.9144i	−1.40263	+	0.947523i
$638$			28.0594i			1.11088i
$639$	−3.45408	+	8.33889i	−0.136641	+	0.329881i
$640$	−9.67049			−0.382260
$641$	18.7441	+	7.76406i	0.740347	+	0.306662i	0.720796	−	0.693147i	$-0.243776\pi$
$641$	18.7441	+	7.76406i	0.740347	+	0.306662i	0.0195508	+	0.999809i	$0.493776\pi$
$642$	27.5723	+	11.4208i	1.08819	+	0.450744i
$643$	−37.5019	+	15.5338i	−1.47893	+	0.612593i	−0.968876	−	0.247548i	$-0.920375\pi$
$643$	−37.5019	+	15.5338i	−1.47893	+	0.612593i	−0.510056	+	0.860141i	$0.670375\pi$
$644$	−5.24735	+	6.42705i	−0.206775	+	0.253261i
$645$	−2.16281	+	0.895864i	−0.0851604	+	0.0352746i
$646$			43.9000i			1.72722i
$647$	7.19260	−	7.19260i	0.282770	−	0.282770i	−0.551443	−	0.834213i	$-0.685922\pi$
$647$	7.19260	−	7.19260i	0.282770	−	0.282770i	0.834213	+	0.551443i	$0.185922\pi$
$648$	−4.03754	−	4.03754i	−0.158610	−	0.158610i
$649$	−23.3666	+	9.67878i	−0.917221	+	0.379925i
$650$	41.8063	+	17.3167i	1.63978	+	0.679218i
$651$	4.04391	+	1.21553i	0.158493	+	0.0476403i
$652$	−3.72625			−0.145931
$653$	10.7581	+	25.9723i	0.420996	+	1.01637i	0.982054	+	0.188597i	$0.0603941\pi$
$653$	10.7581	+	25.9723i	0.420996	+	1.01637i	−0.561059	+	0.827776i	$0.689606\pi$
$654$	−4.98137	−	4.98137i	−0.194787	−	0.194787i
$655$			8.96702i			0.350370i
$656$	29.9424	−	10.0827i	1.16905	−	0.393663i
$657$		−	18.8752i		−	0.736393i
$658$	5.24150	−	17.4378i	0.204335	−	0.679797i
$659$	16.4357	−	6.80787i	0.640242	−	0.265197i	−0.0388554	−	0.999245i	$-0.512371\pi$
$659$	16.4357	−	6.80787i	0.640242	−	0.265197i	0.679098	+	0.734048i	$0.262371\pi$
$660$		−	2.01320i		−	0.0783637i
$661$	8.66169	+	8.66169i	0.336901	+	0.336901i	0.855200	−	0.518299i	$-0.173434\pi$
$661$	8.66169	+	8.66169i	0.336901	+	0.336901i	−0.518299	+	0.855200i	$0.673434\pi$
$662$	48.5327	+	20.1029i	1.88628	+	0.781322i
$663$	−12.7520	−	30.7862i	−0.495248	−	1.19564i
$664$	13.3039	+	13.3039i	0.516292	+	0.516292i
$665$	−3.36640	+	11.1996i	−0.130543	+	0.434302i
$666$	16.6656			0.645781
$667$	9.19542	+	22.1997i	0.356048	+	0.859576i
$668$	4.95513	−	2.05248i	0.191720	−	0.0794130i
$669$	17.1846	−	7.11810i	0.664396	−	0.275202i
$670$	5.84473	−	14.1104i	0.225802	−	0.545133i
$671$	−38.7567	−	16.0535i	−1.49618	−	0.619740i
$672$	6.32393	+	11.7595i	0.243951	+	0.453632i
$673$	11.3564	+	4.70399i	0.437758	+	0.181325i	0.590668	−	0.806915i	$-0.298864\pi$
$673$	11.3564	+	4.70399i	0.437758	+	0.181325i	−0.152910	+	0.988240i	$0.548864\pi$
$674$	52.1039			2.00697
$675$	−9.52025	+	22.9839i	−0.366435	+	0.884652i
$676$	−12.7481	−	12.7481i	−0.490312	−	0.490312i
$677$	−1.91275	−	1.91275i	−0.0735131	−	0.0735131i	0.669394	−	0.742907i	$-0.266554\pi$
$677$	−1.91275	−	1.91275i	−0.0735131	−	0.0735131i	−0.742907	+	0.669394i	$0.766554\pi$
$678$	−23.7449	−	9.83547i	−0.911919	−	0.377729i
$679$	11.7607	−	6.32459i	0.451335	−	0.242715i
$680$	2.50069	−	6.03720i	0.0958970	−	0.231516i
$681$			14.9867i			0.574290i
$682$	2.39056	−	5.77133i	0.0915394	−	0.220996i
$683$	−9.29304	+	22.4354i	−0.355588	+	0.858466i	0.640321	+	0.768108i	$0.278801\pi$
$683$	−9.29304	+	22.4354i	−0.355588	+	0.858466i	−0.995909	+	0.0903589i	$0.971199\pi$
$684$	−5.94385	+	2.46202i	−0.227269	+	0.0941378i
$685$	−4.38125	−	10.5773i	−0.167399	−	0.404137i
$686$	9.12766	+	29.2868i	0.348496	+	1.11817i
$687$		−	17.6136i		−	0.672000i
$688$	−8.96989	−	8.96989i	−0.341974	−	0.341974i
$689$	6.43447	−	6.43447i	0.245134	−	0.245134i
$690$	−2.43440	−	5.87717i	−0.0926761	−	0.223740i
$691$	10.3496	+	4.28693i	0.393716	+	0.163082i	0.570753	−	0.821122i	$-0.306651\pi$
$691$	10.3496	+	4.28693i	0.393716	+	0.163082i	−0.177037	+	0.984204i	$0.556651\pi$
$692$	7.46568	−	7.46568i	0.283803	−	0.283803i
$693$	−9.81516	+	5.27832i	−0.372847	+	0.200507i
$694$	−14.1051	−	34.0526i	−0.535421	−	1.29262i
$695$	−4.95266	+	4.95266i	−0.187865	+	0.187865i
$696$	14.9197			0.565529
$697$	−1.88475	+	27.7194i	−0.0713899	+	1.04995i
$698$		−	20.0577i		−	0.759196i
$699$	3.37057	−	3.37057i	0.127487	−	0.127487i
$700$	5.56911	−	6.82114i	0.210492	−	0.257815i
$701$		−	37.5756i		−	1.41921i	−0.704600	−	0.709605i	$-0.748873\pi$
$701$		−	37.5756i		−	1.41921i	0.704600	−	0.709605i	$-0.251127\pi$
$702$	39.7257	−	39.7257i	1.49935	−	1.49935i
$703$	16.6030	−	40.0831i	0.626193	−	1.51176i
$704$	−8.86126	+	3.67045i	−0.333971	+	0.138335i
$705$	2.67532	+	2.67532i	0.100758	+	0.100758i
$706$	−37.1128	−	37.1128i	−1.39676	−	1.39676i
$707$	−7.42004	−	13.7977i	−0.279059	−	0.518917i
$708$	−3.04542	−	7.35230i	−0.114454	−	0.276316i
$709$	−18.9117	−	45.6569i	−0.710244	−	1.71468i	−0.699390	−	0.714740i	$-0.746545\pi$
$709$	−18.9117	−	45.6569i	−0.710244	−	1.71468i	−0.0108541	−	0.999941i	$-0.503455\pi$
$710$	2.92260	+	7.05577i	0.109683	+	0.264798i
$711$	15.3297	+	6.34978i	0.574910	+	0.238136i
$712$	−34.8245	−	14.4248i	−1.30510	−	0.540592i
$713$		−	5.34952i		−	0.200341i
$714$	−23.8062	+	2.40561i	−0.890926	+	0.0900278i
$715$	−13.1322			−0.491116
$716$	−11.1535	−	4.61995i	−0.416827	−	0.172656i
$717$	4.34495	−	4.34495i	0.162265	−	0.162265i
$718$	4.07110	−	4.07110i	0.151932	−	0.151932i
$719$	16.7517	+	6.93876i	0.624731	+	0.258772i	0.672513	−	0.740086i	$-0.265215\pi$
$719$	16.7517	+	6.93876i	0.624731	+	0.258772i	−0.0477812	+	0.998858i	$0.515215\pi$
$720$	5.05797			0.188499
$721$	14.9429	−	1.50997i	0.556501	−	0.0562343i
$722$			30.3291i			1.12873i
$723$	−6.65100	−	2.75493i	−0.247353	−	0.102457i
$724$	1.16900	+	0.484216i	0.0434456	+	0.0179957i
$725$	−9.75926	−	23.5609i	−0.362450	−	0.875031i
$726$	1.72141	+	4.15586i	0.0638876	+	0.154238i
$727$	9.34959	+	22.5719i	0.346757	+	0.837145i	0.996999	+	0.0774181i	$0.0246676\pi$
$727$	9.34959	+	22.5719i	0.346757	+	0.837145i	−0.650242	+	0.759727i	$0.725332\pi$
$728$	29.5967	−	15.9163i	1.09693	−	0.589898i
$729$	17.5833	+	17.5833i	0.651233	+	0.651233i
$730$	−11.2931	−	11.2931i	−0.417977	−	0.417977i
$731$	10.3060	−	4.26890i	0.381183	−	0.157891i
$732$	5.05123	−	12.1948i	0.186699	−	0.450731i
$733$	−0.642315	+	0.642315i	−0.0237244	+	0.0237244i	−0.718869	−	0.695145i	$-0.755340\pi$
$733$	−0.642315	+	0.642315i	−0.0237244	+	0.0237244i	0.695145	+	0.718869i	$0.255340\pi$
$734$		−	23.0121i		−	0.849391i
$735$	−6.25782	−	1.21183i	−0.230823	−	0.0446991i
$736$	11.9609	−	11.9609i	0.440885	−	0.440885i
$737$		−	37.8897i		−	1.39568i
$738$	−14.2384	+	4.79457i	−0.524122	+	0.176491i
$739$	21.7771			0.801084			0.400542	−	0.916278i	$-0.368822\pi$
$739$	21.7771			0.801084			0.400542	+	0.916278i	$0.368822\pi$
$740$	2.70229	−	2.70229i	0.0993381	−	0.0993381i
$741$	−17.9516	−	43.3390i	−0.659469	−	1.59210i
$742$	−3.09473	−	5.75472i	−0.113611	−	0.211262i
$743$	−10.1353	+	10.1353i	−0.371830	+	0.371830i	−0.868143	−	0.496314i	$-0.834687\pi$
$743$	−10.1353	+	10.1353i	−0.371830	+	0.371830i	0.496314	+	0.868143i	$0.334687\pi$
$744$	−3.06872	−	1.27111i	−0.112505	−	0.0466010i
$745$	2.56278	+	6.18711i	0.0938931	+	0.226678i
$746$	−10.1417	+	10.1417i	−0.371314	+	0.371314i
$747$	−9.05544	−	9.05544i	−0.331321	−	0.331321i
$748$			9.59315i			0.350760i
$749$	−29.3453	−	23.9589i	−1.07225	−	0.875440i
$750$	5.46959	+	13.2048i	0.199721	+	0.482169i
$751$	19.3701	−	8.02336i	0.706825	−	0.292776i	−0.000165072	−	1.00000i	$-0.500053\pi$
$751$	19.3701	−	8.02336i	0.706825	−	0.292776i	0.706990	+	0.707223i	$0.250053\pi$
$752$	−7.84566	+	18.9411i	−0.286102	+	0.690711i
$753$	−7.49208	+	18.0875i	−0.273027	+	0.659144i
$754$			57.5911i			2.09734i
$755$	0.464414	−	1.12119i	0.0169017	−	0.0408044i
$756$	−5.17809	−	9.62878i	−0.188325	−	0.350195i
$757$	19.9077	+	8.24604i	0.723558	+	0.299707i	0.713902	−	0.700246i	$-0.246926\pi$
$757$	19.9077	+	8.24604i	0.723558	+	0.299707i	0.00965610	+	0.999953i	$0.496926\pi$
$758$	−1.80768	−	1.80768i	−0.0656578	−	0.0656578i
$759$	−11.1592	−	11.1592i	−0.405054	−	0.405054i
$760$	3.52033	−	8.49883i	0.127696	−	0.308285i
$761$	−32.0527			−1.16191			−0.580955	−	0.813936i	$-0.697321\pi$
$761$	−32.0527			−1.16191			−0.580955	+	0.813936i	$0.697321\pi$
$762$	35.8214	+	14.8377i	1.29767	+	0.537513i
$763$	4.23543	+	7.87587i	0.153333	+	0.285126i
$764$	10.4565	+	4.33123i	0.378304	+	0.156699i
$765$	−1.70212	+	4.10928i	−0.0615403	+	0.148571i
$766$	5.36086	−	2.22054i	0.193696	−	0.0802314i
$767$	−47.9594	+	19.8654i	−1.73171	+	0.717299i
$768$	−7.55260	−	18.2336i	−0.272531	−	0.657948i
$769$	18.9428			0.683094			0.341547	−	0.939865i	$-0.389049\pi$
$769$	18.9428			0.683094			0.341547	+	0.939865i	$0.389049\pi$
$770$	−2.71440	+	9.03048i	−0.0978203	+	0.325436i
$771$	−1.28907	−	1.28907i	−0.0464249	−	0.0464249i
$772$	1.03522	+	2.49925i	0.0372585	+	0.0899500i
$773$	−5.49237	−	2.27502i	−0.197547	−	0.0818266i	0.281717	−	0.959498i	$-0.409096\pi$
$773$	−5.49237	−	2.27502i	−0.197547	−	0.0818266i	−0.479264	+	0.877671i	$0.659096\pi$
$774$	4.26541	+	4.26541i	0.153317	+	0.153317i
$775$			5.67753i			0.203943i
$776$	−9.70437	+	4.01968i	−0.348367	+	0.144298i
$777$	22.6462	+	6.80705i	0.812428	+	0.244202i
$778$			19.9984i			0.716976i
$779$	−2.65324	+	39.0218i	−0.0950622	+	1.39810i
$780$		−	4.13204i		−	0.147951i
$781$	13.3971	+	13.3971i	0.479386	+	0.479386i
$782$	11.6002	+	28.0054i	0.414824	+	1.00147i
$783$	−31.6619			−1.13151
$784$	−6.90987	−	33.8413i	−0.246781	−	1.20862i
$785$	6.08015	+	2.51848i	0.217010	+	0.0898884i
$786$	−23.8615	+	9.88377i	−0.851113	+	0.352542i
$787$	18.8534	+	18.8534i	0.672051	+	0.672051i	0.958189	−	0.286138i	$-0.0923715\pi$
$787$	18.8534	+	18.8534i	0.672051	+	0.672051i	−0.286138	+	0.958189i	$0.592371\pi$
$788$	−7.67589	+	7.67589i	−0.273442	+	0.273442i
$789$			4.27738i			0.152279i
$790$	12.9709	−	5.37273i	0.461485	−	0.191153i
$791$	25.2718	+	20.6331i	0.898562	+	0.733629i
$792$	8.09899	−	3.35471i	0.287785	−	0.119204i
$793$	−79.5469	−	32.9494i	−2.82479	−	1.17007i
$794$	−51.2757	−	21.2391i	−1.81971	−	0.753748i
$795$	1.35769			0.0481522
$796$	−3.61635	+	8.73065i	−0.128178	+	0.309450i
$797$		−	17.7508i		−	0.628767i	−0.949296	−	0.314383i	$-0.898202\pi$
$797$		−	17.7508i		−	0.628767i	0.949296	−	0.314383i	$-0.101798\pi$
$798$	−33.5131	+	3.38649i	−1.18635	+	0.119880i
$799$	−12.7482	−	12.7482i	−0.450999	−	0.450999i
$800$	−12.6943	+	12.6943i	−0.448812	+	0.448812i
$801$	23.7037	+	9.81839i	0.837529	+	0.346916i
$802$			45.2615i			1.59824i
$803$	−36.6050	−	15.1623i	−1.29176	−	0.535065i
$804$	11.9220			0.420455
$805$	0.811852	+	8.03418i	0.0286140	+	0.283168i
$806$	4.90656	−	11.8455i	0.172826	−	0.417240i
$807$	3.04958	+	7.36233i	0.107350	+	0.259166i
$808$	4.71591	+	11.3852i	0.165905	+	0.400530i
$809$	32.3959	−	13.4188i	1.13898	−	0.471780i	0.268155	−	0.963376i	$-0.413586\pi$
$809$	32.3959	−	13.4188i	1.13898	−	0.471780i	0.870824	+	0.491596i	$0.163586\pi$
$810$	3.28851			0.115546
$811$	−25.2913	+	25.2913i	−0.888097	+	0.888097i	−0.994340	−	0.106243i	$-0.966118\pi$
$811$	−25.2913	+	25.2913i	−0.888097	+	0.888097i	0.106243	+	0.994340i	$0.466118\pi$
$812$	10.7329	+	3.22612i	0.376651	+	0.113215i
$813$	2.00465	+	4.83966i	0.0703063	+	0.169734i
$814$	13.3873	−	32.3199i	0.469226	−	1.13281i
$815$	−2.56436	+	2.56436i	−0.0898256	+	0.0898256i
$816$	26.9409			0.943119
$817$	14.5083	−	6.00952i	0.507580	−	0.210246i
$818$	38.8586	+	38.8586i	1.35866	+	1.35866i
$819$	−20.1453	+	10.8336i	−0.703935	+	0.378557i
$820$	−1.53129	+	3.08614i	−0.0534749	+	0.107773i
$821$	−47.8794			−1.67100			−0.835502	−	0.549487i	$-0.814823\pi$
$821$	−47.8794			−1.67100			−0.835502	+	0.549487i	$0.814823\pi$
$822$	23.3173	−	23.3173i	0.813285	−	0.813285i
$823$	8.54351	−	3.53884i	0.297808	−	0.123356i	−0.228776	−	0.973479i	$-0.573472\pi$
$823$	8.54351	−	3.53884i	0.297808	−	0.123356i	0.526584	+	0.850123i	$0.323472\pi$
$824$	−11.8140			−0.411561
$825$	11.8435	+	11.8435i	0.412337	+	0.412337i
$826$	3.74752	+	37.0859i	0.130393	+	1.29038i
$827$	−5.85930	+	2.42700i	−0.203748	+	0.0843951i	−0.482224	−	0.876048i	$-0.660171\pi$
$827$	−5.85930	+	2.42700i	−0.203748	+	0.0843951i	0.278476	+	0.960443i	$0.410171\pi$
$828$	−3.14123	+	3.14123i	−0.109165	+	0.109165i
$829$	−19.6516	−	19.6516i	−0.682529	−	0.682529i	0.278040	−	0.960569i	$-0.410315\pi$
$829$	−19.6516	−	19.6516i	−0.682529	−	0.682529i	−0.960569	+	0.278040i	$0.910315\pi$
$830$	−10.8358			−0.376116
$831$	−9.32471	+	3.86242i	−0.323471	+	0.133986i
$832$	−18.1875	+	7.53350i	−0.630538	+	0.261177i
$833$	29.8193	+	5.77453i	1.03318	+	0.200076i
$834$	−18.6382	−	7.72019i	−0.645387	−	0.267328i
$835$	1.99757	−	4.82255i	0.0691287	−	0.166891i
$836$			13.5047i			0.467070i
$837$	6.51231	+	2.69749i	0.225099	+	0.0932389i
$838$		−	12.5868i		−	0.434804i
$839$	−11.0164	+	26.5960i	−0.380329	+	0.918196i	0.611572	+	0.791188i	$0.290537\pi$
$839$	−11.0164	+	26.5960i	−0.380329	+	0.918196i	−0.991902	+	0.127008i	$0.959463\pi$
$840$	4.80167	+	1.44330i	0.165673	+	0.0497985i
$841$	2.44434	−	2.44434i	0.0842875	−	0.0842875i
$842$	1.81516	−	4.38218i	0.0625544	−	0.151020i
$843$	0.921667			0.0317439
$844$	−1.58371	+	3.82340i	−0.0545134	+	0.131607i
$845$	−17.5462			−0.603607
$846$	3.73081	−	9.00698i	0.128268	−	0.309666i
$847$	−0.574076	−	5.68112i	−0.0197255	−	0.195206i
$848$	2.81539	+	6.79696i	0.0966810	+	0.233409i
$849$	0.354633	−	0.146894i	0.0121710	−	0.00504138i
$850$	−12.3115	−	29.7227i	−0.422282	−	1.01948i
$851$		−	29.9577i		−	1.02694i
$852$	−4.21539	+	4.21539i	−0.144417	+	0.144417i
$853$	−35.7708	+	35.7708i	−1.22477	+	1.22477i	−0.258852	+	0.965917i	$0.583344\pi$
$853$	−35.7708	+	35.7708i	−1.22477	+	1.22477i	−0.965917	+	0.258852i	$0.916656\pi$
$854$	−39.1002	+	47.8906i	−1.33798	+	1.63878i
$855$	−2.39615	+	5.78481i	−0.0819465	+	0.197836i
$856$	21.0715	+	21.0715i	0.720210	+	0.720210i
$857$			29.9228i			1.02214i	0.859538	+	0.511072i	$0.170751\pi$
$857$			29.9228i			1.02214i	−0.859538	+	0.511072i	$0.829249\pi$
$858$	−14.4748	−	34.9452i	−0.494161	−	1.19301i
$859$	−29.2941	−	29.2941i	−0.999503	−	0.999503i	0.000496414	−	1.00000i	$-0.499842\pi$
$859$	−29.2941	−	29.2941i	−0.999503	−	0.999503i	−1.00000		0.000496414i	$0.999842\pi$
$860$	1.38325			0.0471684
$861$	−21.3062	+	0.699492i	−0.726114	+	0.0238386i
$862$	−39.3266			−1.33947
$863$	10.4199	+	10.4199i	0.354697	+	0.354697i	0.861854	−	0.507157i	$-0.169304\pi$
$863$	10.4199	+	10.4199i	0.354697	+	0.354697i	−0.507157	+	0.861854i	$0.669304\pi$
$864$	8.52951	+	20.5921i	0.290180	+	0.700556i
$865$		−	10.2756i		−	0.349380i
$866$	−3.57829	−	3.57829i	−0.121595	−	0.121595i
$867$	−0.879901	+	2.12427i	−0.0298830	+	0.0721440i
$868$	−1.93272	−	1.57796i	−0.0656007	−	0.0535595i
$869$	24.6284	−	24.6284i	0.835463	−	0.835463i
$870$	−6.07591	+	6.07591i	−0.205993	+	0.205993i
$871$		−	77.7675i		−	2.63505i
$872$	−2.69189	−	6.49879i	−0.0911588	−	0.220077i
$873$	6.60538	−	2.73604i	0.223558	−	0.0926008i
$874$	16.3302	+	39.4245i	0.552376	+	1.33355i
$875$	−1.82406	−	18.0511i	−0.0616645	−	0.610238i
$876$	4.77080	−	11.5177i	0.161190	−	0.389148i
$877$	13.9118			0.469767			0.234884	−	0.972023i	$-0.424529\pi$
$877$	13.9118			0.469767			0.234884	+	0.972023i	$0.424529\pi$
$878$	−0.330425	+	0.797717i	−0.0111513	+	0.0269216i
$879$	−8.84741			−0.298416
$880$	4.06301	−	9.80898i	0.136964	−	0.330661i
$881$	−24.1045	+	24.1045i	−0.812100	+	0.812100i	−0.984948	−	0.172848i	$-0.944703\pi$
$881$	−24.1045	+	24.1045i	−0.812100	+	0.812100i	0.172848	+	0.984948i	$0.444703\pi$
$882$	3.28582	+	16.0924i	0.110639	+	0.541860i
$883$	−19.3827	+	46.7941i	−0.652281	+	1.57475i	0.157179	+	0.987570i	$0.449760\pi$
$883$	−19.3827	+	46.7941i	−0.652281	+	1.57475i	−0.809460	+	0.587175i	$0.800240\pi$
$884$			19.6897i			0.662235i
$885$	−7.15558	−	2.96394i	−0.240532	−	0.0996317i
$886$		−	26.3315i		−	0.884623i
$887$	0.555376	−	1.34080i	0.0186477	−	0.0450195i	−0.914281	−	0.405080i	$-0.867244\pi$
$887$	0.555376	−	1.34080i	0.0186477	−	0.0450195i	0.932929	+	0.360060i	$0.117244\pi$
$888$	−17.1851	−	7.11830i	−0.576694	−	0.238874i
$889$	−38.1248	−	31.1269i	−1.27866	−	1.04396i
$890$	20.0564	−	8.30762i	0.672291	−	0.278472i
$891$	7.53721	−	3.12201i	0.252506	−	0.104591i
$892$	−10.9906			−0.367994
$893$	−17.9462	−	17.9462i	−0.600547	−	0.600547i
$894$	−13.6393	+	13.6393i	−0.456166	+	0.456166i
$895$	−10.8551	+	4.49634i	−0.362846	+	0.150296i
$896$	3.55474	+	35.1781i	0.118755	+	1.17522i
$897$	−22.9040	−	22.9040i	−0.764742	−	0.764742i
$898$	20.4003			0.680767
$899$	−6.67581	+	2.76521i	−0.222651	+	0.0922249i
$900$	3.33384	−	3.33384i	0.111128	−	0.111128i
$901$	−6.46955			−0.215532
$902$	−2.13937	+	31.4641i	−0.0712331	+	1.04764i
$903$	4.05388	+	7.53827i	0.134905	+	0.250858i
$904$	−18.1465	−	18.1465i	−0.603545	−	0.603545i
$905$	1.13772	−	0.471260i	0.0378192	−	0.0156652i
$906$	3.49543			0.116128
$907$	−9.67522	+	9.67522i	−0.321260	+	0.321260i	−0.849251	−	0.527990i	$-0.822946\pi$
$907$	−9.67522	+	9.67522i	−0.321260	+	0.321260i	0.527990	+	0.849251i	$0.322946\pi$
$908$	3.38878	−	8.18123i	0.112460	−	0.271504i
$909$	−3.20993	−	7.74946i	−0.106467	−	0.257033i
$910$	−5.57123	+	18.5348i	−0.184685	+	0.614422i
$911$	24.0571	−	24.0571i	0.797047	−	0.797047i	−0.185582	−	0.982629i	$-0.559417\pi$
$911$	24.0571	−	24.0571i	0.797047	−	0.797047i	0.982629	+	0.185582i	$0.0594171\pi$
$912$	37.9258			1.25585
$913$	−24.8355	+	10.2872i	−0.821934	+	0.340456i
$914$	−6.73632	−	16.2629i	−0.222817	−	0.537929i
$915$	−4.91608	−	11.8685i	−0.162521	−	0.392360i
$916$	−3.98277	+	9.61526i	−0.131594	+	0.317697i
$917$	32.6191	−	3.29615i	1.07718	−	0.108849i
$918$	−39.9423			−1.31829
$919$	54.1053	+	22.4111i	1.78477	+	0.739275i	0.991453	+	0.130464i	$0.0416466\pi$
$919$	54.1053	+	22.4111i	1.78477	+	0.739275i	0.793315	+	0.608811i	$0.208353\pi$
$920$		−	6.35193i		−	0.209417i
$921$	24.2486	+	10.0441i	0.799020	+	0.330965i
$922$	−35.5967	+	35.5967i	−1.17231	+	1.17231i
$923$	27.4971	+	27.4971i	0.905080	+	0.905080i
$924$	−7.32336	+	0.740024i	−0.240921	+	0.0243450i
$925$			31.7946i			1.04540i
$926$	3.98198	−	9.61334i	0.130856	−	0.315914i
$927$	8.04134			0.264112
$928$	−21.1090	−	8.74364i	−0.692937	−	0.287024i
$929$	−27.3139	−	11.3138i	−0.896139	−	0.371193i	−0.113405	−	0.993549i	$-0.536176\pi$
$929$	−27.3139	−	11.3138i	−0.896139	−	0.371193i	−0.782734	+	0.622356i	$0.786176\pi$
$930$	1.76736	−	0.732064i	0.0579539	−	0.0240053i
$931$	41.9779	+	8.12905i	1.37577	+	0.266419i
$932$	−2.60215	+	1.07785i	−0.0852363	+	0.0353060i
$933$			19.5424i			0.639789i
$934$	19.6058	−	19.6058i	0.641520	−	0.641520i
$935$	6.60189	+	6.60189i	0.215905	+	0.215905i
$936$	16.6229	−	6.88545i	0.543338	−	0.225058i
$937$	−13.7837	−	5.70938i	−0.450292	−	0.186517i	0.146000	−	0.989285i	$-0.453360\pi$
$937$	−13.7837	−	5.70938i	−0.450292	−	0.186517i	−0.596292	+	0.802767i	$0.703360\pi$
$938$	−53.4775	−	16.0744i	−1.74610	−	0.524848i
$939$	1.39196			0.0454248
$940$	−0.855515	−	2.06540i	−0.0279038	−	0.0673658i
$941$	−2.32274	−	2.32274i	−0.0757191	−	0.0757191i	0.668233	−	0.743952i	$-0.267051\pi$
$941$	−2.32274	−	2.32274i	−0.0757191	−	0.0757191i	−0.743952	+	0.668233i	$0.767051\pi$
$942$			18.9554i			0.617601i
$943$	8.61860	+	25.5945i	0.280660	+	0.833473i
$944$		−	41.9691i		−	1.36598i
$945$	−10.1899	−	3.06291i	−0.331478	−	0.0996364i
$946$	11.6983	−	4.84561i	0.380345	−	0.157544i
$947$			12.9367i			0.420385i	0.977660	+	0.210192i	$0.0674090\pi$
$947$			12.9367i			0.420385i	−0.977660	+	0.210192i	$0.932591\pi$
$948$	7.74932	+	7.74932i	0.251686	+	0.251686i
$949$	−75.1307	−	31.1201i	−2.43884	−	1.01020i
$950$	−17.3315	−	41.8419i	−0.562307	−	1.35753i
$951$	17.7059	+	17.7059i	0.574152	+	0.574152i
$952$	−22.8806	−	6.87750i	−0.741563	−	0.222901i
$953$	−31.6805			−1.02623			−0.513117	−	0.858319i	$-0.671509\pi$
$953$	−31.6805			−1.02623			−0.513117	+	0.858319i	$0.671509\pi$
$954$	−1.33879	−	3.23213i	−0.0433450	−	0.104644i
$955$	10.1768	−	4.21535i	0.329312	−	0.136405i
$956$	−3.35438	+	1.38943i	−0.108489	+	0.0449374i
$957$	−8.15760	+	19.6942i	−0.263698	+	0.636623i
$958$	32.6861	+	13.5390i	1.05604	+	0.437426i
$959$	−36.8662	+	19.8256i	−1.19047	+	0.640203i
$960$	−2.71359	−	1.12401i	−0.0875807	−	0.0362771i
$961$	−29.3913			−0.948107
$962$	27.4771	−	66.3357i	0.885898	−	2.13875i
$963$	−14.3425	−	14.3425i	−0.462182	−	0.462182i
$964$	3.00784	+	3.00784i	0.0968760	+	0.0968760i
$965$	2.43238	+	1.00753i	0.0783011	+	0.0324334i
$966$	−20.4844	+	11.0159i	−0.659073	+	0.354432i
$967$	11.1190	−	26.8436i	0.357563	−	0.863233i	−0.638079	−	0.769971i	$-0.720271\pi$
$967$	11.1190	−	26.8436i	0.357563	−	0.863233i	0.995642	−	0.0932617i	$-0.0297293\pi$
$968$			4.49157i			0.144365i
$969$	−12.7629	+	30.8124i	−0.410003	+	0.989836i
$970$	2.31504	−	5.58900i	0.0743314	−	0.179452i
$971$	−5.16153	+	2.13798i	−0.165641	+	0.0686109i	−0.463963	−	0.885854i	$-0.653573\pi$
$971$	−5.16153	+	2.13798i	−0.165641	+	0.0686109i	0.298322	+	0.954465i	$0.403573\pi$
$972$	−3.76164	−	9.08141i	−0.120655	−	0.291286i
$973$	19.8367	+	16.1956i	0.635935	+	0.519208i
$974$		−	31.0437i		−	0.994705i
$975$	24.3084	+	24.3084i	0.778492	+	0.778492i
$976$	49.2226	−	49.2226i	1.57558	−	1.57558i
$977$	−20.7343	−	50.0571i	−0.663350	−	1.60147i	−0.792519	−	0.609847i	$-0.791231\pi$
$977$	−20.7343	−	50.0571i	−0.663350	−	1.60147i	0.129169	−	0.991623i	$-0.458769\pi$
$978$	−9.65038	−	3.99732i	−0.308585	−	0.127820i
$979$	38.0819	−	38.0819i	1.21710	−	1.21710i
$980$	3.14213	+	2.07655i	0.100372	+	0.0663330i
$981$	1.83226	+	4.42347i	0.0584996	+	0.141230i
$982$	−0.974768	+	0.974768i	−0.0311061	+	0.0311061i
$983$	58.6008			1.86907			0.934537	−	0.355866i	$-0.115814\pi$
$983$	58.6008			1.86907			0.934537	+	0.355866i	$0.115814\pi$
$984$	16.7300	+	1.13754i	0.533335	+	0.0362635i
$985$			10.5649i			0.336626i
$986$	28.9525	−	28.9525i	0.922035	−	0.922035i
$987$	8.74851	−	10.7153i	0.278468	−	0.341073i
$988$			27.7180i			0.881827i
$989$	7.66739	−	7.66739i	0.243809	−	0.243809i
$990$	−1.93207	+	4.66442i	−0.0614051	+	0.148245i
$991$	−31.9224	+	13.2227i	−1.01405	+	0.420032i	−0.826930	−	0.562305i	$-0.809915\pi$
$991$	−31.9224	+	13.2227i	−1.01405	+	0.420032i	−0.187118	+	0.982338i	$0.559915\pi$
$992$	3.59683	+	3.59683i	0.114200	+	0.114200i
$993$	28.2195	+	28.2195i	0.895518	+	0.895518i
$994$	24.5923	−	13.2251i	0.780020	−	0.419473i
$995$	3.51959	+	8.49705i	0.111579	+	0.269375i
$996$	−3.23686	−	7.81447i	−0.102564	−	0.247611i
$997$	−8.99439	−	21.7144i	−0.284855	−	0.687702i	0.715080	−	0.699042i	$-0.246390\pi$
$997$	−8.99439	−	21.7144i	−0.284855	−	0.687702i	−0.999936	+	0.0113407i	$0.996390\pi$
$998$	36.5706	+	15.1480i	1.15762	+	0.479503i
$999$	36.4695	+	15.1062i	1.15384	+	0.477937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.l.a.27.7	✓	104
7.6	odd	2	inner	287.2.l.a.27.8	yes	104
41.38	odd	8	inner	287.2.l.a.202.8	yes	104
287.202	even	8	inner	287.2.l.a.202.7	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.l.a.27.7	✓	104	1.1	even	1	trivial
287.2.l.a.27.8	yes	104	7.6	odd	2	inner
287.2.l.a.202.7	yes	104	287.202	even	8	inner
287.2.l.a.202.8	yes	104	41.38	odd	8	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17122 - 1.17122i) q^{2} +(-0.481548 - 1.16256i) q^{3} +0.743529i q^{4} +(0.511687 + 0.511687i) q^{5} +(-0.797616 + 1.92562i) q^{6} +(1.67326 - 2.04944i) q^{7} +(-1.47161 + 1.47161i) q^{8} +(1.00167 - 1.00167i) q^{9} +O(q^{10})\)	\(q+(-1.17122 - 1.17122i) q^{2} +(-0.481548 - 1.16256i) q^{3} +0.743529i q^{4} +(0.511687 + 0.511687i) q^{5} +(-0.797616 + 1.92562i) q^{6} +(1.67326 - 2.04944i) q^{7} +(-1.47161 + 1.47161i) q^{8} +(1.00167 - 1.00167i) q^{9} -1.19860i q^{10} +(-1.13792 - 2.74717i) q^{11} +(0.864396 - 0.358044i) q^{12} +(-2.33554 - 5.63849i) q^{13} +(-4.36011 + 0.440588i) q^{14} +(0.348465 - 0.841268i) q^{15} +4.93422 q^{16} +(-1.66048 + 4.00875i) q^{17} -2.34635 q^{18} +(-2.33753 + 5.64329i) q^{19} +(-0.380454 + 0.380454i) q^{20} +(-3.18835 - 0.958361i) q^{21} +(-1.88480 + 4.55030i) q^{22} +4.21773i q^{23} +(2.41948 + 1.00218i) q^{24} -4.47635i q^{25} +(-3.86849 + 9.33937i) q^{26} +(-5.13452 - 2.12679i) q^{27} +(1.52382 + 1.24412i) q^{28} +(5.26342 - 2.18018i) q^{29} +(-1.39344 + 0.577183i) q^{30} -1.26834 q^{31} +(-2.83586 - 2.83586i) q^{32} +(-2.64579 + 2.64579i) q^{33} +(6.63993 - 2.75035i) q^{34} +(1.90486 - 0.192485i) q^{35} +(0.744767 + 0.744767i) q^{36} -7.10280 q^{37} +(9.34732 - 3.87178i) q^{38} +(-5.43040 + 5.43040i) q^{39} -1.50601 q^{40} +(6.06831 - 2.04342i) q^{41} +(2.61181 + 4.85672i) q^{42} +(-1.81789 - 1.81789i) q^{43} +(2.04260 - 0.846073i) q^{44} +1.02508 q^{45} +(4.93991 - 4.93991i) q^{46} +(-1.59005 + 3.83872i) q^{47} +(-2.37606 - 5.73632i) q^{48} +(-1.40040 - 6.85849i) q^{49} +(-5.24281 + 5.24281i) q^{50} +5.46000 q^{51} +(4.19238 - 1.73654i) q^{52} +(0.570585 + 1.37751i) q^{53} +(3.52273 + 8.50462i) q^{54} +(0.823435 - 1.98795i) q^{55} +(0.553587 + 5.47836i) q^{56} +7.68628 q^{57} +(-8.71812 - 3.61117i) q^{58} -8.50571i q^{59} +(0.625507 + 0.259093i) q^{60} +(9.97575 - 9.97575i) q^{61} +(1.48551 + 1.48551i) q^{62} +(-0.376805 - 3.72890i) q^{63} -3.22559i q^{64} +(1.69008 - 4.08021i) q^{65} +6.19762 q^{66} +(11.7724 + 4.87630i) q^{67} +(-2.98062 - 1.23461i) q^{68} +(4.90336 - 2.03104i) q^{69} +(-2.45646 - 2.00557i) q^{70} +(-5.88668 + 2.43834i) q^{71} +2.94812i q^{72} +(9.42192 - 9.42192i) q^{73} +(8.31897 + 8.31897i) q^{74} +(-5.20402 + 2.15558i) q^{75} +(-4.19595 - 1.73802i) q^{76} +(-7.53419 - 2.26465i) q^{77} +12.7204 q^{78} +(4.48251 + 10.8217i) q^{79} +(2.52478 + 2.52478i) q^{80} +2.74362i q^{81} +(-9.50065 - 4.71405i) q^{82} -9.04038i q^{83} +(0.712569 - 2.37063i) q^{84} +(-2.90087 + 1.20158i) q^{85} +4.25832i q^{86} +(-5.06918 - 5.06918i) q^{87} +(5.71733 + 2.36819i) q^{88} +(6.93110 + 16.7332i) q^{89} +(-1.20060 - 1.20060i) q^{90} +(-15.4637 - 4.64812i) q^{91} -3.13601 q^{92} +(0.610766 + 1.47452i) q^{93} +(6.35830 - 2.63370i) q^{94} +(-4.08368 + 1.69152i) q^{95} +(-1.93125 + 4.66245i) q^{96} +(4.66294 + 1.93145i) q^{97} +(-6.39265 + 9.67300i) q^{98} +(-3.89156 - 1.61194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 104 * q - 8 * q^2 - 4 * q^7 + 8 * q^8 + 8 * q^9	\( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{11} - 8 q^{14} - 32 q^{15} - 96 q^{16} - 16 q^{18} - 24 q^{21} + 24 q^{22} + 12 q^{28} - 16 q^{29} + 48 q^{30} - 72 q^{32} - 44 q^{35} + 56 q^{36} + 32 q^{37} - 8 q^{39} - 8 q^{42} - 32 q^{43} + 72 q^{44} - 88 q^{46} - 12 q^{49} + 80 q^{50} + 32 q^{51} - 8 q^{53} + 104 q^{56} - 32 q^{57} - 96 q^{58} + 112 q^{60} - 132 q^{63} + 80 q^{65} + 56 q^{67} + 148 q^{70} - 104 q^{71} + 32 q^{74} - 16 q^{77} - 168 q^{78} - 124 q^{84} + 8 q^{85} - 64 q^{88} + 8 q^{91} + 104 q^{92} - 64 q^{93} - 8 q^{95} - 8 q^{98} + 8 q^{99}+O(q^{100}) \) 104 * q - 8 * q^2 - 4 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^11 - 8 * q^14 - 32 * q^15 - 96 * q^16 - 16 * q^18 - 24 * q^21 + 24 * q^22 + 12 * q^28 - 16 * q^29 + 48 * q^30 - 72 * q^32 - 44 * q^35 + 56 * q^36 + 32 * q^37 - 8 * q^39 - 8 * q^42 - 32 * q^43 + 72 * q^44 - 88 * q^46 - 12 * q^49 + 80 * q^50 + 32 * q^51 - 8 * q^53 + 104 * q^56 - 32 * q^57 - 96 * q^58 + 112 * q^60 - 132 * q^63 + 80 * q^65 + 56 * q^67 + 148 * q^70 - 104 * q^71 + 32 * q^74 - 16 * q^77 - 168 * q^78 - 124 * q^84 + 8 * q^85 - 64 * q^88 + 8 * q^91 + 104 * q^92 - 64 * q^93 - 8 * q^95 - 8 * q^98 + 8 * q^99

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