LMFDB - Embedded newform 465.2.k.a.218.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.28
Character	$\chi$	$=$	465.218
Dual form			465.2.k.a.32.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.74033 + 1.74033i) q^{2} +(-1.17160 + 1.27567i) q^{3} +4.05749i q^{4} +(-0.384493 + 2.20276i) q^{5} +(-4.25907 + 0.181113i) q^{6} +(1.30230 - 1.30230i) q^{7} +(-3.58070 + 3.58070i) q^{8} +(-0.254684 - 2.98917i) q^{9} +(-4.50267 + 3.16439i) q^{10} +2.55932i q^{11} +(-5.17603 - 4.75377i) q^{12} +(2.37097 + 2.37097i) q^{13} +4.53284 q^{14} +(-2.35953 - 3.07125i) q^{15} -4.34822 q^{16} +(-3.38670 - 3.38670i) q^{17} +(4.75890 - 5.64537i) q^{18} -4.69306i q^{19} +(-8.93768 - 1.56007i) q^{20} +(0.135528 + 3.18708i) q^{21} +(-4.45405 + 4.45405i) q^{22} +(0.268531 - 0.268531i) q^{23} +(-0.372638 - 8.76297i) q^{24} +(-4.70433 - 1.69389i) q^{25} +8.25253i q^{26} +(4.11159 + 3.17723i) q^{27} +(5.28405 + 5.28405i) q^{28} +5.68539 q^{29} +(1.23863 - 9.45135i) q^{30} +1.00000 q^{31} +(-0.405926 - 0.405926i) q^{32} +(-3.26485 - 2.99851i) q^{33} -11.7879i q^{34} +(2.36793 + 3.36937i) q^{35} +(12.1285 - 1.03338i) q^{36} +(-2.80395 + 2.80395i) q^{37} +(8.16747 - 8.16747i) q^{38} +(-5.80242 + 0.246743i) q^{39} +(-6.51068 - 9.26419i) q^{40} -3.76694i q^{41} +(-5.31070 + 5.78243i) q^{42} +(7.57956 + 7.57956i) q^{43} -10.3844 q^{44} +(6.68236 + 0.588304i) q^{45} +0.934666 q^{46} +(-2.85488 - 2.85488i) q^{47} +(5.09439 - 5.54691i) q^{48} +3.60805i q^{49} +(-5.23915 - 11.1350i) q^{50} +(8.28820 - 0.352449i) q^{51} +(-9.62017 + 9.62017i) q^{52} +(-3.33548 + 3.33548i) q^{53} +(1.62610 + 12.6849i) q^{54} +(-5.63757 - 0.984039i) q^{55} +9.32626i q^{56} +(5.98682 + 5.49842i) q^{57} +(9.89445 + 9.89445i) q^{58} +12.5260 q^{59} +(12.4616 - 9.57377i) q^{60} -7.79487 q^{61} +(1.74033 + 1.74033i) q^{62} +(-4.22446 - 3.56111i) q^{63} +7.28355i q^{64} +(-6.13430 + 4.31106i) q^{65} +(-0.463526 - 10.9003i) q^{66} +(-4.02116 + 4.02116i) q^{67} +(13.7415 - 13.7415i) q^{68} +(0.0279457 + 0.657171i) q^{69} +(-1.74285 + 9.98478i) q^{70} -1.18160i q^{71} +(11.6153 + 9.79137i) q^{72} +(3.86864 + 3.86864i) q^{73} -9.75960 q^{74} +(7.67247 - 4.01662i) q^{75} +19.0420 q^{76} +(3.33299 + 3.33299i) q^{77} +(-10.5275 - 9.66870i) q^{78} -4.46527i q^{79} +(1.67186 - 9.57809i) q^{80} +(-8.87027 + 1.52259i) q^{81} +(6.55571 - 6.55571i) q^{82} +(-4.02931 + 4.02931i) q^{83} +(-12.9315 + 0.549903i) q^{84} +(8.76226 - 6.15794i) q^{85} +26.3819i q^{86} +(-6.66103 + 7.25270i) q^{87} +(-9.16415 - 9.16415i) q^{88} -16.4656 q^{89} +(10.6057 + 12.6533i) q^{90} +6.17540 q^{91} +(1.08956 + 1.08956i) q^{92} +(-1.17160 + 1.27567i) q^{93} -9.93684i q^{94} +(10.3377 + 1.80445i) q^{95} +(0.993414 - 0.0422441i) q^{96} +(13.6813 - 13.6813i) q^{97} +(-6.27919 + 6.27919i) q^{98} +(7.65023 - 0.651818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.74033	+	1.74033i	1.23060	+	1.23060i	0.963734	+	0.266864i	$0.0859874\pi$
$2$	1.74033	+	1.74033i	1.23060	+	1.23060i	0.266864	+	0.963734i	$0.414013\pi$
$3$	−1.17160	+	1.27567i	−0.676426	+	0.736510i
$3$	−1.17160	+	1.27567i	−0.676426	+	0.736510i
$4$			4.05749i			2.02874i
$5$	−0.384493	+	2.20276i	−0.171950	+	0.985106i
$5$	−0.384493	+	2.20276i	−0.171950	+	0.985106i
$6$	−4.25907	+	0.181113i	−1.73876	+	0.0739392i
$7$	1.30230	−	1.30230i	0.492222	−	0.492222i	−0.416784	−	0.909006i	$-0.636843\pi$
$7$	1.30230	−	1.30230i	0.492222	−	0.492222i	0.909006	+	0.416784i	$0.136843\pi$
$8$	−3.58070	+	3.58070i	−1.26597	+	1.26597i
$9$	−0.254684	−	2.98917i	−0.0848948	−	0.996390i
$10$	−4.50267	+	3.16439i	−1.42387	+	1.00067i
$11$			2.55932i			0.771663i	0.922569	+	0.385832i	$0.126085\pi$
$11$			2.55932i			0.771663i	−0.922569	+	0.385832i	$0.873915\pi$
$12$	−5.17603	−	4.75377i	−1.49419	−	1.37230i
$13$	2.37097	+	2.37097i	0.657588	+	0.657588i	0.954809	−	0.297221i	$-0.0960597\pi$
$13$	2.37097	+	2.37097i	0.657588	+	0.657588i	−0.297221	+	0.954809i	$0.596060\pi$
$14$	4.53284			1.21145
$15$	−2.35953	−	3.07125i	−0.609229	−	0.792995i
$16$	−4.34822			−1.08705
$17$	−3.38670	−	3.38670i	−0.821396	−	0.821396i	0.164913	−	0.986308i	$-0.447266\pi$
$17$	−3.38670	−	3.38670i	−0.821396	−	0.821396i	−0.986308	+	0.164913i	$0.947266\pi$
$18$	4.75890	−	5.64537i	1.12168	−	1.33063i
$19$		−	4.69306i		−	1.07666i	−0.842733	−	0.538331i	$-0.819055\pi$
$19$		−	4.69306i		−	1.07666i	0.842733	−	0.538331i	$-0.180945\pi$
$20$	−8.93768	−	1.56007i	−1.99853	−	0.348843i
$21$	0.135528	+	3.18708i	0.0295746	+	0.695478i
$22$	−4.45405	+	4.45405i	−0.949607	+	0.949607i
$23$	0.268531	−	0.268531i	0.0559927	−	0.0559927i	−0.678556	−	0.734549i	$-0.737394\pi$
$23$	0.268531	−	0.268531i	0.0559927	−	0.0559927i	0.734549	+	0.678556i	$0.237394\pi$
$24$	−0.372638	−	8.76297i	−0.0760644	−	1.78873i
$25$	−4.70433	−	1.69389i	−0.940866	−	0.338779i
$26$			8.25253i			1.61845i
$27$	4.11159	+	3.17723i	0.791277	+	0.611458i
$28$	5.28405	+	5.28405i	0.998591	+	0.998591i
$29$	5.68539			1.05575			0.527875	−	0.849322i	$-0.322989\pi$
$29$	5.68539			1.05575			0.527875	+	0.849322i	$0.322989\pi$
$30$	1.23863	−	9.45135i	0.226142	−	1.72557i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.405926	−	0.405926i	−0.0717582	−	0.0717582i
$33$	−3.26485	−	2.99851i	−0.568338	−	0.521973i
$34$		−	11.7879i		−	2.02162i
$35$	2.36793	+	3.36937i	0.400253	+	0.569528i
$36$	12.1285	−	1.03338i	2.02142	−	0.172230i
$37$	−2.80395	+	2.80395i	−0.460967	+	0.460967i	−0.898972	−	0.438005i	$-0.855685\pi$
$37$	−2.80395	+	2.80395i	−0.460967	+	0.460967i	0.438005	+	0.898972i	$0.355685\pi$
$38$	8.16747	−	8.16747i	1.32494	−	1.32494i
$39$	−5.80242	+	0.246743i	−0.929131	+	0.0395105i
$40$	−6.51068	−	9.26419i	−1.02943	−	1.46480i
$41$		−	3.76694i		−	0.588297i	−0.955760	−	0.294148i	$-0.904964\pi$
$41$		−	3.76694i		−	0.588297i	0.955760	−	0.294148i	$-0.0950360\pi$
$42$	−5.31070	+	5.78243i	−0.819459	+	0.892248i
$43$	7.57956	+	7.57956i	1.15587	+	1.15587i	0.985355	+	0.170518i	$0.0545441\pi$
$43$	7.57956	+	7.57956i	1.15587	+	1.15587i	0.170518	+	0.985355i	$0.445456\pi$
$44$	−10.3844			−1.56551
$45$	6.68236	+	0.588304i	0.996147	+	0.0876993i
$46$	0.934666			0.137809
$47$	−2.85488	−	2.85488i	−0.416427	−	0.416427i	0.467544	−	0.883970i	$-0.345139\pi$
$47$	−2.85488	−	2.85488i	−0.416427	−	0.416427i	−0.883970	+	0.467544i	$0.845139\pi$
$48$	5.09439	−	5.54691i	0.735312	−	0.800627i
$49$			3.60805i			0.515436i
$50$	−5.23915	−	11.1350i	−0.740928	−	1.57473i
$51$	8.28820	−	0.352449i	1.16058	−	0.0493527i
$52$	−9.62017	+	9.62017i	−1.33408	+	1.33408i
$53$	−3.33548	+	3.33548i	−0.458164	+	0.458164i	−0.898052	−	0.439888i	$-0.855018\pi$
$53$	−3.33548	+	3.33548i	−0.458164	+	0.458164i	0.439888	+	0.898052i	$0.355018\pi$
$54$	1.62610	+	12.6849i	0.221284	+	1.72620i
$55$	−5.63757	−	0.984039i	−0.760170	−	0.132688i
$56$			9.32626i			1.24627i
$57$	5.98682	+	5.49842i	0.792973	+	0.728283i
$58$	9.89445	+	9.89445i	1.29920	+	1.29920i
$59$	12.5260			1.63075			0.815375	−	0.578933i	$-0.196531\pi$
$59$	12.5260			1.63075			0.815375	+	0.578933i	$0.196531\pi$
$60$	12.4616	−	9.57377i	1.60878	−	1.23597i
$61$	−7.79487			−0.998031			−0.499016	−	0.866593i	$-0.666305\pi$
$61$	−7.79487			−0.998031			−0.499016	+	0.866593i	$0.666305\pi$
$62$	1.74033	+	1.74033i	0.221022	+	0.221022i
$63$	−4.22446	−	3.56111i	−0.532232	−	0.448658i
$64$			7.28355i			0.910443i
$65$	−6.13430	+	4.31106i	−0.760866	+	0.534721i
$66$	−0.463526	−	10.9003i	−0.0570562	−	1.34173i
$67$	−4.02116	+	4.02116i	−0.491263	+	0.491263i	−0.908704	−	0.417441i	$-0.862927\pi$
$67$	−4.02116	+	4.02116i	−0.491263	+	0.491263i	0.417441	+	0.908704i	$0.362927\pi$
$68$	13.7415	−	13.7415i	1.66640	−	1.66640i
$69$	0.0279457	+	0.657171i	0.00336426	+	0.0791141i
$70$	−1.74285	+	9.98478i	−0.208310	+	1.19341i
$71$		−	1.18160i		−	0.140230i	−0.997539	−	0.0701152i	$-0.977663\pi$
$71$		−	1.18160i		−	0.140230i	0.997539	−	0.0701152i	$-0.0223367\pi$
$72$	11.6153	+	9.79137i	1.36887	+	1.15392i
$73$	3.86864	+	3.86864i	0.452790	+	0.452790i	0.896279	−	0.443490i	$-0.146260\pi$
$73$	3.86864	+	3.86864i	0.452790	+	0.452790i	−0.443490	+	0.896279i	$0.646260\pi$
$74$	−9.75960			−1.13453
$75$	7.67247	−	4.01662i	0.885941	−	0.463799i
$76$	19.0420			2.18427
$77$	3.33299	+	3.33299i	0.379829	+	0.379829i
$78$	−10.5275	−	9.66870i	−1.19201	−	1.09476i
$79$		−	4.46527i		−	0.502383i	−0.967937	−	0.251191i	$-0.919178\pi$
$79$		−	4.46527i		−	0.502383i	0.967937	−	0.251191i	$-0.0808223\pi$
$80$	1.67186	−	9.57809i	0.186919	−	1.07086i
$81$	−8.87027	+	1.52259i	−0.985586	+	0.169177i
$82$	6.55571	−	6.55571i	0.723957	−	0.723957i
$83$	−4.02931	+	4.02931i	−0.442274	+	0.442274i	−0.892776	−	0.450502i	$-0.851245\pi$
$83$	−4.02931	+	4.02931i	−0.442274	+	0.442274i	0.450502	+	0.892776i	$0.351245\pi$
$84$	−12.9315	+	0.549903i	−1.41095	+	0.0599993i
$85$	8.76226	−	6.15794i	0.950401	−	0.667922i
$86$			26.3819i			2.84483i
$87$	−6.66103	+	7.25270i	−0.714137	+	0.777571i
$88$	−9.16415	−	9.16415i	−0.976901	−	0.976901i
$89$	−16.4656			−1.74535			−0.872675	−	0.488301i	$-0.837617\pi$
$89$	−16.4656			−1.74535			−0.872675	+	0.488301i	$0.837617\pi$
$90$	10.6057	+	12.6533i	1.11793	+	1.33378i
$91$	6.17540			0.647358
$92$	1.08956	+	1.08956i	0.113595	+	0.113595i
$93$	−1.17160	+	1.27567i	−0.121490	+	0.132281i
$94$		−	9.93684i		−	1.02491i
$95$	10.3377	+	1.80445i	1.06063	+	0.185133i
$96$	0.993414	−	0.0422441i	0.101390	−	0.00431152i
$97$	13.6813	−	13.6813i	1.38912	−	1.38912i	0.561959	−	0.827165i	$-0.310048\pi$
$97$	13.6813	−	13.6813i	1.38912	−	1.38912i	0.827165	−	0.561959i	$-0.189952\pi$
$98$	−6.27919	+	6.27919i	−0.634294	+	0.634294i
$99$	7.65023	−	0.651818i	0.768877	−	0.0655102i
$100$	6.87295	−	19.0878i	0.687295	−	1.90878i
$101$		−	18.5916i		−	1.84993i	−0.380047	−	0.924967i	$-0.624092\pi$
$101$		−	18.5916i		−	1.84993i	0.380047	−	0.924967i	$-0.375908\pi$
$102$	15.0376	+	13.8108i	1.48894	+	1.36747i
$103$	2.22600	+	2.22600i	0.219334	+	0.219334i	0.808218	−	0.588884i	$-0.200432\pi$
$103$	2.22600	+	2.22600i	0.219334	+	0.219334i	−0.588884	+	0.808218i	$0.700432\pi$
$104$	−16.9795			−1.66497
$105$	−7.07249	−	0.926873i	−0.690205	−	0.0904536i
$106$	−11.6097			−1.12763
$107$	1.86365	+	1.86365i	0.180166	+	0.180166i	0.791428	−	0.611262i	$-0.209338\pi$
$107$	1.86365	+	1.86365i	0.180166	+	0.180166i	−0.611262	+	0.791428i	$0.709338\pi$
$108$	−12.8916	+	16.6827i	−1.24049	+	1.60530i
$109$		−	18.6614i		−	1.78744i	−0.448629	−	0.893718i	$-0.648088\pi$
$109$		−	18.6614i		−	1.78744i	0.448629	−	0.893718i	$-0.351912\pi$
$110$	−8.09867	−	11.5238i	−0.772178	−	1.09875i
$111$	−0.291803	−	6.86205i	−0.0276967	−	0.651317i
$112$	−5.66267	+	5.66267i	−0.535072	+	0.535072i
$113$	6.99502	−	6.99502i	0.658036	−	0.658036i	−0.296879	−	0.954915i	$-0.595946\pi$
$113$	6.99502	−	6.99502i	0.658036	−	0.658036i	0.954915	+	0.296879i	$0.0959457\pi$
$114$	0.849977	+	19.9881i	0.0796076	+	1.87206i
$115$	0.488263	+	0.694759i	0.0455307	+	0.0647866i
$116$			23.0684i			2.14185i
$117$	6.48338	−	7.69108i	0.599388	−	0.711040i
$118$	21.7994	+	21.7994i	2.00680	+	2.00680i
$119$	−8.82097			−0.808617
$120$	19.4460	+	2.54846i	1.77517	+	0.232642i
$121$	4.44990			0.404536
$122$	−13.5656	−	13.5656i	−1.22818	−	1.22818i
$123$	4.80538	+	4.41336i	0.433287	+	0.397940i
$124$			4.05749i			0.364373i
$125$	5.54003	−	9.71124i	0.495515	−	0.868599i
$126$	−1.15445	−	13.5494i	−0.102846	−	1.20708i
$127$	12.1010	−	12.1010i	1.07379	−	1.07379i	0.0767411	−	0.997051i	$-0.475548\pi$
$127$	12.1010	−	12.1010i	1.07379	−	1.07379i	0.997051	−	0.0767411i	$-0.0244515\pi$
$128$	−13.4876	+	13.4876i	−1.19215	+	1.19215i
$129$	−18.5493	+	0.788794i	−1.63317	+	0.0694494i
$130$	−18.1784	−	3.17304i	−1.59435	−	0.278294i
$131$		−	4.42153i		−	0.386311i	−0.981168	−	0.193155i	$-0.938128\pi$
$131$		−	4.42153i		−	0.386311i	0.981168	−	0.193155i	$-0.0618721\pi$
$132$	12.1664	−	13.2471i	1.05895	−	1.15301i
$133$	−6.11176	−	6.11176i	−0.529957	−	0.529957i
$134$	−13.9963			−1.20909
$135$	−8.57957	+	7.83524i	−0.738411	+	0.674350i
$136$	24.2535			2.07972
$137$	14.4439	+	14.4439i	1.23403	+	1.23403i	0.962403	+	0.271625i	$0.0875611\pi$
$137$	14.4439	+	14.4439i	1.23403	+	1.23403i	0.271625	+	0.962403i	$0.412439\pi$
$138$	−1.09506	+	1.19233i	−0.0932176	+	0.101498i
$139$		−	20.0382i		−	1.69961i	−0.527094	−	0.849807i	$-0.676718\pi$
$139$		−	20.0382i		−	1.69961i	0.527094	−	0.849807i	$-0.323282\pi$
$140$	−13.6712	+	9.60783i	−1.15543	+	0.812009i
$141$	6.98668	−	0.297103i	0.588384	−	0.0250206i
$142$	2.05638	−	2.05638i	0.172567	−	0.172567i
$143$	−6.06806	+	6.06806i	−0.507437	+	0.507437i
$144$	1.10742	+	12.9976i	0.0922853	+	1.08313i
$145$	−2.18599	+	12.5236i	−0.181537	+	1.04003i
$146$			13.4654i			1.11440i
$147$	−4.60269	−	4.22721i	−0.379624	−	0.348654i
$148$	−11.3770	−	11.3770i	−0.935184	−	0.935184i
$149$	−9.91574			−0.812329			−0.406165	−	0.913800i	$-0.633134\pi$
$149$	−9.91574			−0.812329			−0.406165	+	0.913800i	$0.633134\pi$
$150$	20.3428	+	6.36239i	1.66099	+	0.519487i
$151$	10.0111			0.814695			0.407347	−	0.913273i	$-0.366454\pi$
$151$	10.0111			0.814695			0.407347	+	0.913273i	$0.366454\pi$
$152$	16.8045	+	16.8045i	1.36302	+	1.36302i
$153$	−9.26088	+	10.9860i	−0.748698	+	0.888163i
$154$			11.6010i			0.934834i
$155$	−0.384493	+	2.20276i	−0.0308832	+	0.176930i
$156$	−1.00116	−	23.5432i	−0.0801567	−	1.88497i
$157$	−15.3890	+	15.3890i	−1.22818	+	1.22818i	−0.263527	+	0.964652i	$0.584886\pi$
$157$	−15.3890	+	15.3890i	−1.22818	+	1.22818i	−0.964652	+	0.263527i	$0.915114\pi$
$158$	7.77104	−	7.77104i	0.618231	−	0.618231i
$159$	−0.347119	−	8.16286i	−0.0275283	−	0.647357i
$160$	1.05023	−	0.738083i	0.0830283	−	0.0583506i
$161$		−	0.699415i		−	0.0551216i
$162$	−18.0870	−	12.7874i	−1.42105	−	1.00467i
$163$	15.0954	+	15.0954i	1.18237	+	1.18237i	0.979130	+	0.203235i	$0.0651457\pi$
$163$	15.0954	+	15.0954i	1.18237	+	1.18237i	0.203235	+	0.979130i	$0.434854\pi$
$164$	15.2843			1.19350
$165$	7.86032	−	6.03879i	0.611925	−	0.470119i
$166$	−14.0246			−1.08852
$167$	−4.70977	−	4.70977i	−0.364453	−	0.364453i	0.500996	−	0.865449i	$-0.332967\pi$
$167$	−4.70977	−	4.70977i	−0.364453	−	0.364453i	−0.865449	+	0.500996i	$0.832967\pi$
$168$	−11.8973	−	10.9267i	−0.917894	−	0.843013i
$169$		−	1.75702i		−	0.135155i
$170$	25.9660	+	4.53238i	1.99151	+	0.347618i
$171$	−14.0284	+	1.19525i	−1.07278	+	0.0914031i
$172$	−30.7540	+	30.7540i	−2.34497	+	2.34497i
$173$	−2.26329	+	2.26329i	−0.172074	+	0.172074i	−0.787890	−	0.615816i	$-0.788827\pi$
$173$	−2.26329	+	2.26329i	−0.172074	+	0.172074i	0.615816	+	0.787890i	$0.288827\pi$
$174$	−24.2145	+	1.02970i	−1.83569	+	0.0780614i
$175$	−8.33238	+	3.92048i	−0.629869	+	0.296360i
$176$		−	11.1285i		−	0.838840i
$177$	−14.6756	+	15.9791i	−1.10308	+	1.20106i
$178$	−28.6556	−	28.6556i	−2.14782	−	2.14782i
$179$	−1.55392			−0.116145			−0.0580725	−	0.998312i	$-0.518495\pi$
$179$	−1.55392			−0.116145			−0.0580725	+	0.998312i	$0.518495\pi$
$180$	−2.38704	+	27.1136i	−0.177919	+	2.02093i
$181$	−12.4886			−0.928271			−0.464135	−	0.885764i	$-0.653635\pi$
$181$	−12.4886			−0.928271			−0.464135	+	0.885764i	$0.653635\pi$
$182$	10.7472	+	10.7472i	0.796638	+	0.796638i
$183$	9.13251	−	9.94371i	0.675095	−	0.735060i
$184$			1.92306i			0.141770i
$185$	−5.09835	−	7.25455i	−0.374838	−	0.533365i
$186$	−4.25907	+	0.181113i	−0.312290	+	0.0132799i
$187$	8.66764	−	8.66764i	0.633841	−	0.633841i
$188$	11.5836	−	11.5836i	0.844822	−	0.844822i
$189$	9.49221	−	1.21682i	0.690456	−	0.0885103i
$190$	14.8507	+	21.1313i	1.07738	+	1.53303i
$191$		−	6.16936i		−	0.446399i	−0.974773	−	0.223200i	$-0.928350\pi$
$191$		−	6.16936i		−	0.446399i	0.974773	−	0.223200i	$-0.0716502\pi$
$192$	−9.29143	−	8.53344i	−0.670551	−	0.615848i
$193$	−13.8267	−	13.8267i	−0.995270	−	0.995270i	0.00471859	−	0.999989i	$-0.498498\pi$
$193$	−13.8267	−	13.8267i	−0.995270	−	0.995270i	−0.999989	+	0.00471859i	$0.998498\pi$
$194$	47.6199			3.41891
$195$	1.68747	−	12.8762i	0.120842	−	0.922086i
$196$	−14.6396			−1.04569
$197$	−10.2230	−	10.2230i	−0.728359	−	0.728359i	0.241934	−	0.970293i	$-0.422218\pi$
$197$	−10.2230	−	10.2230i	−0.728359	−	0.728359i	−0.970293	+	0.241934i	$0.922218\pi$
$198$	14.4483	+	12.1795i	1.02680	+	0.865562i
$199$			3.18566i			0.225825i	0.993605	+	0.112913i	$0.0360180\pi$
$199$			3.18566i			0.225825i	−0.993605	+	0.112913i	$0.963982\pi$
$200$	22.9101	−	10.7795i	1.61999	−	0.762224i
$201$	−0.418476	−	9.84089i	−0.0295170	−	0.694123i
$202$	32.3555	−	32.3555i	2.27653	−	2.27653i
$203$	7.40406	−	7.40406i	0.519663	−	0.519663i
$204$	1.43006	+	33.6292i	0.100124	+	2.35452i
$205$	8.29767	+	1.44836i	0.579535	+	0.101158i
$206$			7.74794i			0.539825i
$207$	−0.871077	−	0.734295i	−0.0605440	−	0.0510370i
$208$	−10.3095	−	10.3095i	−0.714834	−	0.714834i
$209$	12.0110			0.830821
$210$	−10.6954	−	13.9215i	−0.738052	−	0.960676i
$211$	9.18742			0.632488			0.316244	−	0.948678i	$-0.397578\pi$
$211$	9.18742			0.632488			0.316244	+	0.948678i	$0.397578\pi$
$212$	−13.5337	−	13.5337i	−0.929497	−	0.929497i
$213$	1.50734	+	1.38437i	0.103281	+	0.0948555i
$214$			6.48673i			0.443424i
$215$	−19.6103	+	13.7817i	−1.33741	+	0.939904i
$216$	−26.0991	+	3.34567i	−1.77582	+	0.227644i
$217$	1.30230	−	1.30230i	0.0884056	−	0.0884056i
$218$	32.4769	−	32.4769i	2.19962	−	2.19962i
$219$	−9.46763	+	0.402603i	−0.639763	+	0.0272054i
$220$	3.99272	−	22.8744i	0.269189	−	1.54219i
$221$		−	16.0595i		−	1.08028i
$222$	11.4344	−	12.4501i	0.767426	−	0.835593i
$223$	18.3841	+	18.3841i	1.23109	+	1.23109i	0.963545	+	0.267545i	$0.0862125\pi$
$223$	18.3841	+	18.3841i	1.23109	+	1.23109i	0.267545	+	0.963545i	$0.413788\pi$
$224$	−1.05727			−0.0706419
$225$	−3.86521	+	14.4935i	−0.257681	+	0.966230i
$226$	24.3473			1.61956
$227$	−4.46148	−	4.46148i	−0.296119	−	0.296119i	0.543373	−	0.839492i	$-0.317147\pi$
$227$	−4.46148	−	4.46148i	−0.296119	−	0.296119i	−0.839492	+	0.543373i	$0.817147\pi$
$228$	−22.3097	+	24.2914i	−1.47750	+	1.60874i
$229$			7.03878i			0.465136i	0.972580	+	0.232568i	$0.0747128\pi$
$229$			7.03878i			0.465136i	−0.972580	+	0.232568i	$0.925287\pi$
$230$	−0.359372	+	2.05885i	−0.0236963	+	0.135756i
$231$	−8.15675	+	0.346859i	−0.536675	+	0.0228216i
$232$	−20.3577	+	20.3577i	−1.33655	+	1.33655i
$233$	−6.31425	+	6.31425i	−0.413660	+	0.413660i	−0.883012	−	0.469351i	$-0.844488\pi$
$233$	−6.31425	+	6.31425i	−0.413660	+	0.413660i	0.469351	+	0.883012i	$0.344488\pi$
$234$	24.6682	−	2.10179i	1.61261	−	0.137398i
$235$	7.38630	−	5.19094i	0.481829	−	0.338619i
$236$			50.8242i			3.30837i
$237$	5.69623	+	5.23154i	0.370010	+	0.339825i
$238$	−15.3514	−	15.3514i	−0.995083	−	0.995083i
$239$	6.05585			0.391720			0.195860	−	0.980632i	$-0.437250\pi$
$239$	6.05585			0.391720			0.195860	+	0.980632i	$0.437250\pi$
$240$	10.2598	+	13.3545i	0.662265	+	0.862028i
$241$	−19.4218			−1.25107			−0.625533	−	0.780198i	$-0.715118\pi$
$241$	−19.4218			−1.25107			−0.625533	+	0.780198i	$0.715118\pi$
$242$	7.74428	+	7.74428i	0.497821	+	0.497821i
$243$	8.45012	−	13.0994i	0.542076	−	0.840330i
$244$		−	31.6276i		−	2.02475i
$245$	−7.94768	−	1.38727i	−0.507759	−	0.0886294i
$246$	0.682243	+	16.0436i	0.0434982	+	1.02291i
$247$	11.1271	−	11.1271i	0.708001	−	0.708001i
$248$	−3.58070	+	3.58070i	−0.227375	+	0.227375i
$249$	−0.419324	−	9.86084i	−0.0265736	−	0.624905i
$250$	26.5422	−	7.25928i	1.67868	−	0.459117i
$251$			0.334433i			0.0211092i	0.999944	+	0.0105546i	$0.00335970\pi$
$251$			0.334433i			0.0211092i	−0.999944	+	0.0105546i	$0.996640\pi$
$252$	14.4491	−	17.1407i	0.910211	−	1.07976i
$253$	0.687257	+	0.687257i	0.0432075	+	0.0432075i
$254$	42.1195			2.64281
$255$	−2.41039	+	18.3925i	−0.150945	+	1.15178i
$256$	−32.3787			−2.02367
$257$	−21.6611	−	21.6611i	−1.35118	−	1.35118i	−0.884343	−	0.466838i	$-0.845393\pi$
$257$	−21.6611	−	21.6611i	−1.35118	−	1.35118i	−0.466838	−	0.884343i	$-0.654607\pi$
$258$	−33.6546	−	30.9091i	−2.09525	−	1.92432i
$259$			7.30315i			0.453796i
$260$	−17.4921	−	24.8898i	−1.08481	−	1.54360i
$261$	−1.44798	−	16.9946i	−0.0896278	−	1.05194i
$262$	7.69491	−	7.69491i	0.475393	−	0.475393i
$263$	−9.30589	+	9.30589i	−0.573826	+	0.573826i	−0.933195	−	0.359370i	$-0.882992\pi$
$263$	−9.30589	+	9.30589i	−0.573826	+	0.573826i	0.359370	+	0.933195i	$0.382992\pi$
$264$	22.4272	−	0.953699i	1.38030	−	0.0586961i
$265$	−6.06481	−	8.62975i	−0.372558	−	0.530121i
$266$		−	21.2729i		−	1.30433i
$267$	19.2912	−	21.0047i	1.18060	−	1.28547i
$268$	−16.3158	−	16.3158i	−0.996646	−	0.996646i
$269$	−2.97259			−0.181242			−0.0906210	−	0.995885i	$-0.528885\pi$
$269$	−2.97259			−0.181242			−0.0906210	+	0.995885i	$0.528885\pi$
$270$	−28.5672	−	1.29536i	−1.73854	−	0.0788334i
$271$	4.29904			0.261148			0.130574	−	0.991439i	$-0.458318\pi$
$271$	4.29904			0.261148			0.130574	+	0.991439i	$0.458318\pi$
$272$	14.7261	+	14.7261i	0.892902	+	0.892902i
$273$	−7.23513	+	7.87780i	−0.437890	+	0.476786i
$274$			50.2744i			3.03719i
$275$	4.33521	−	12.0399i	0.261423	−	0.726032i
$276$	−2.66646	+	0.113389i	−0.160502	+	0.00682522i
$277$	−7.69471	+	7.69471i	−0.462330	+	0.462330i	−0.899419	−	0.437088i	$-0.856010\pi$
$277$	−7.69471	+	7.69471i	−0.462330	+	0.462330i	0.437088	+	0.899419i	$0.356010\pi$
$278$	34.8730	−	34.8730i	2.09154	−	2.09154i
$279$	−0.254684	−	2.98917i	−0.0152476	−	0.178957i
$280$	−20.5435	−	3.58588i	−1.22771	−	0.214297i
$281$			14.7446i			0.879591i	0.898098	+	0.439796i	$0.144949\pi$
$281$			14.7446i			0.879591i	−0.898098	+	0.439796i	$0.855051\pi$
$282$	12.6762	+	11.6421i	0.754855	+	0.693274i
$283$	−10.3694	−	10.3694i	−0.616398	−	0.616398i	0.328208	−	0.944606i	$-0.393555\pi$
$283$	−10.3694	−	10.3694i	−0.616398	−	0.616398i	−0.944606	+	0.328208i	$0.893555\pi$
$284$	4.79433			0.284491
$285$	−14.4136	+	11.0734i	−0.853788	+	0.655934i
$286$	−21.1208			−1.24890
$287$	−4.90567	−	4.90567i	−0.289572	−	0.289572i
$288$	−1.11000	+	1.31676i	−0.0654073	+	0.0775911i
$289$			5.93949i			0.349382i
$290$	−25.5995	+	17.9908i	−1.50325	+	1.05645i
$291$	1.42379	+	33.4819i	0.0834641	+	1.96274i
$292$	−15.6969	+	15.6969i	−0.918594	+	0.918594i
$293$	4.21552	−	4.21552i	0.246273	−	0.246273i	−0.573166	−	0.819439i	$-0.694285\pi$
$293$	4.21552	−	4.21552i	0.246273	−	0.246273i	0.819439	+	0.573166i	$0.194285\pi$
$294$	−0.653466	−	15.3669i	−0.0381109	−	0.896218i
$295$	−4.81617	+	27.5919i	−0.280408	+	1.60646i
$296$		−	20.0802i		−	1.16714i
$297$	−8.13154	+	10.5229i	−0.471840	+	0.610599i
$298$	−17.2566	−	17.2566i	−0.999651	−	0.999651i
$299$	1.27336			0.0736402
$300$	16.2974	+	31.1309i	0.940929	+	1.79735i
$301$	19.7417			1.13789
$302$	17.4227	+	17.4227i	1.00256	+	1.00256i
$303$	23.7168	+	21.7820i	1.36250	+	1.25134i
$304$			20.4065i			1.17039i
$305$	2.99707	−	17.1703i	0.171612	−	0.983166i
$306$	−35.2362	+	3.00221i	−2.01432	+	0.171625i
$307$	7.61622	−	7.61622i	0.434681	−	0.434681i	−0.455536	−	0.890217i	$-0.650553\pi$
$307$	7.61622	−	7.61622i	0.434681	−	0.434681i	0.890217	+	0.455536i	$0.150553\pi$
$308$	−13.5236	+	13.5236i	−0.770576	+	0.770576i
$309$	−5.44764	+	0.231656i	−0.309905	+	0.0131785i
$310$	−4.50267	+	3.16439i	−0.255735	+	0.179725i
$311$			7.65741i			0.434212i	0.976148	+	0.217106i	$0.0696618\pi$
$311$			7.65741i			0.434212i	−0.976148	+	0.217106i	$0.930338\pi$
$312$	19.8932	−	21.6602i	1.12623	−	1.22627i
$313$	−2.60386	−	2.60386i	−0.147179	−	0.147179i	0.629678	−	0.776856i	$-0.283187\pi$
$313$	−2.60386	−	2.60386i	−0.147179	−	0.147179i	−0.776856	+	0.629678i	$0.783187\pi$
$314$	−53.5640			−3.02279
$315$	9.46855	−	7.93626i	0.533492	−	0.447158i
$316$	18.1178			1.01921
$317$	8.97912	+	8.97912i	0.504318	+	0.504318i	0.912777	−	0.408459i	$-0.133934\pi$
$317$	8.97912	+	8.97912i	0.504318	+	0.504318i	−0.408459	+	0.912777i	$0.633934\pi$
$318$	13.6019	−	14.8101i	0.762759	−	0.830512i
$319$			14.5507i			0.814684i
$320$	−16.0439	−	2.80047i	−0.896883	−	0.156551i
$321$	−4.56087	+	0.193947i	−0.254563	+	0.0108251i
$322$	1.21721	−	1.21721i	0.0678325	−	0.0678325i
$323$	−15.8940	+	15.8940i	−0.884366	+	0.884366i
$324$	−6.17789	−	35.9910i	−0.343216	−	1.99950i
$325$	−7.13765	−	15.1700i	−0.395926	−	0.841479i
$326$			52.5420i			2.91003i
$327$	23.8058	+	21.8638i	1.31647	+	1.20907i
$328$	13.4883	+	13.4883i	0.744766	+	0.744766i
$329$	−7.43579			−0.409948
$330$	24.1890	+	3.17005i	1.33156	+	0.174505i
$331$	−1.32694			−0.0729354			−0.0364677	−	0.999335i	$-0.511611\pi$
$331$	−1.32694			−0.0729354			−0.0364677	+	0.999335i	$0.511611\pi$
$332$	−16.3489	−	16.3489i	−0.897260	−	0.897260i
$333$	9.09562	+	7.66737i	0.498437	+	0.420169i
$334$		−	16.3931i		−	0.896990i
$335$	−7.31155	−	10.4038i	−0.399473	−	0.568418i
$336$	−0.589305	−	13.8581i	−0.0321492	−	0.756022i
$337$	−12.2571	+	12.2571i	−0.667686	+	0.667686i	−0.957180	−	0.289494i	$-0.906513\pi$
$337$	−12.2571	+	12.2571i	−0.667686	+	0.667686i	0.289494	+	0.957180i	$0.406513\pi$
$338$	3.05779	−	3.05779i	0.166322	−	0.166322i
$339$	0.727961	+	17.1188i	0.0395374	+	0.929764i
$340$	24.9857	+	35.5528i	1.35504	+	1.92812i
$341$			2.55932i			0.138595i
$342$	−26.4941	−	22.3338i	−1.43264	−	1.20768i
$343$	13.8148	+	13.8148i	0.745930	+	0.745930i
$344$	−54.2803			−2.92660
$345$	−1.45834	−	0.191120i	−0.0785142	−	0.0102895i
$346$	−7.87772			−0.423509
$347$	−16.8052	−	16.8052i	−0.902153	−	0.902153i	0.0934693	−	0.995622i	$-0.470204\pi$
$347$	−16.8052	−	16.8052i	−0.902153	−	0.902153i	−0.995622	+	0.0934693i	$0.970204\pi$
$348$	−29.4277	−	27.0270i	−1.57749	−	1.44880i
$349$			18.5688i			0.993965i	0.867761	+	0.496983i	$0.165559\pi$
$349$			18.5688i			0.993965i	−0.867761	+	0.496983i	$0.834441\pi$
$350$	−21.3240	−	7.67815i	−1.13982	−	0.410415i
$351$	2.21534	+	17.2816i	0.118246	+	0.922422i
$352$	1.03889	−	1.03889i	0.0553732	−	0.0553732i
$353$	19.3920	−	19.3920i	1.03213	−	1.03213i	0.0326657	−	0.999466i	$-0.489600\pi$
$353$	19.3920	−	19.3920i	1.03213	−	1.03213i	0.999466	−	0.0326657i	$-0.0103997\pi$
$354$	−53.3492	+	2.26863i	−2.83548	+	0.120576i
$355$	2.60279	+	0.454317i	0.138142	+	0.0241127i
$356$		−	66.8089i		−	3.54087i
$357$	10.3347	−	11.2527i	0.546970	−	0.595555i
$358$	−2.70432	−	2.70432i	−0.142928	−	0.142928i
$359$	2.35818			0.124460			0.0622300	−	0.998062i	$-0.480179\pi$
$359$	2.35818			0.124460			0.0622300	+	0.998062i	$0.480179\pi$
$360$	−26.0341	+	21.8210i	−1.37212	+	1.15007i
$361$	−3.02486			−0.159203
$362$	−21.7343	−	21.7343i	−1.14233	−	1.14233i
$363$	−5.21352	+	5.67661i	−0.273639	+	0.297945i
$364$			25.0566i			1.31332i
$365$	−10.0092	+	7.03423i	−0.523903	+	0.368188i
$366$	33.1989	−	1.41176i	1.73533	−	0.0737936i
$367$	−9.30245	+	9.30245i	−0.485584	+	0.485584i	−0.906909	−	0.421326i	$-0.861565\pi$
$367$	−9.30245	+	9.30245i	−0.485584	+	0.485584i	0.421326	+	0.906909i	$0.361565\pi$
$368$	−1.16763	+	1.16763i	−0.0608671	+	0.0608671i
$369$	−11.2600	+	0.959381i	−0.586173	+	0.0499434i
$370$	3.75250	−	21.4981i	0.195083	−	1.11763i
$371$			8.68757i			0.451036i
$372$	−5.17603	−	4.75377i	−0.268364	−	0.246471i
$373$	−5.91864	−	5.91864i	−0.306455	−	0.306455i	0.537077	−	0.843533i	$-0.319528\pi$
$373$	−5.91864	−	5.91864i	−0.306455	−	0.306455i	−0.843533	+	0.537077i	$0.819528\pi$
$374$	30.1691			1.56001
$375$	5.89764	+	18.4450i	0.304553	+	0.952495i
$376$	20.4449			1.05437
$377$	13.4799	+	13.4799i	0.694249	+	0.694249i
$378$	18.6372	+	14.4019i	0.958595	+	0.740754i
$379$			18.1658i			0.933116i	0.884491	+	0.466558i	$0.154506\pi$
$379$			18.1658i			0.933116i	−0.884491	+	0.466558i	$0.845494\pi$
$380$	−7.32153	+	41.9451i	−0.375586	+	2.15174i
$381$	1.25934	+	29.6146i	0.0645177	+	1.51720i
$382$	10.7367	−	10.7367i	0.549338	−	0.549338i
$383$	−19.5567	+	19.5567i	−0.999299	+	0.999299i	−1.00000		0.000700330i	$-0.999777\pi$
$383$	−19.5567	+	19.5567i	−0.999299	+	0.999299i	0.000700330		1.00000i	$0.499777\pi$
$384$	−1.40364	−	33.0079i	−0.0716290	−	1.68443i
$385$	−8.62329	+	6.06027i	−0.439484	+	0.308860i
$386$		−	48.1261i		−	2.44956i
$387$	20.7262	−	24.5870i	1.05357	−	1.24983i
$388$	55.5116	+	55.5116i	2.81818	+	2.81818i
$389$	31.6425			1.60434			0.802170	−	0.597095i	$-0.203679\pi$
$389$	31.6425			1.60434			0.802170	+	0.597095i	$0.203679\pi$
$390$	25.3456	−	19.4721i	1.28342	−	0.986008i
$391$	−1.81887			−0.0919843
$392$	−12.9194	−	12.9194i	−0.652526	−	0.652526i
$393$	5.64042	+	5.18028i	0.284522	+	0.261311i
$394$		−	35.5828i		−	1.79263i
$395$	9.83594	+	1.71687i	0.494900	+	0.0863849i
$396$	2.64474	+	31.0407i	0.132903	+	1.55985i
$397$	−18.4634	+	18.4634i	−0.926651	+	0.926651i	−0.997488	−	0.0708365i	$-0.977433\pi$
$397$	−18.4634	+	18.4634i	−0.926651	+	0.926651i	0.0708365	+	0.997488i	$0.477433\pi$
$398$	−5.54409	+	5.54409i	−0.277900	+	0.277900i
$399$	14.9572	−	0.636041i	0.748795	−	0.0318419i
$400$	20.4555	+	7.36542i	1.02277	+	0.368271i
$401$		−	1.22570i		−	0.0612083i	−0.999532	−	0.0306041i	$-0.990257\pi$
$401$		−	1.22570i		−	0.0612083i	0.999532	−	0.0306041i	$-0.00974312\pi$
$402$	16.3981	−	17.8547i	0.817863	−	0.890510i
$403$	2.37097	+	2.37097i	0.118106	+	0.118106i
$404$	75.4352			3.75304
$405$	0.0566491	−	20.1245i	0.00281492	−	0.999996i
$406$	25.7710			1.27899
$407$	−7.17621	−	7.17621i	−0.355711	−	0.355711i
$408$	−28.4155	+	30.9396i	−1.40678	+	1.53174i
$409$		−	33.9950i		−	1.68094i	−0.541854	−	0.840472i	$-0.682278\pi$
$409$		−	33.9950i		−	1.68094i	0.541854	−	0.840472i	$-0.317722\pi$
$410$	11.9201	+	16.9613i	0.588689	+	0.837659i
$411$	−35.3483	+	1.50316i	−1.74360	+	0.0741453i
$412$	−9.03196	+	9.03196i	−0.444973	+	0.444973i
$413$	16.3126	−	16.3126i	0.802690	−	0.802690i
$414$	−0.238045	−	2.79387i	−0.0116993	−	0.137311i
$415$	−7.32637	−	10.4248i	−0.359637	−	0.511736i
$416$		−	1.92487i		−	0.0943748i
$417$	25.5621	+	23.4768i	1.25178	+	1.14966i
$418$	20.9032	+	20.9032i	1.02241	+	1.02241i
$419$	25.8945			1.26503			0.632514	−	0.774549i	$-0.282023\pi$
$419$	25.8945			1.26503			0.632514	+	0.774549i	$0.282023\pi$
$420$	3.76077	−	28.6965i	0.183507	−	1.40025i
$421$	−11.4846			−0.559724			−0.279862	−	0.960040i	$-0.590289\pi$
$421$	−11.4846			−0.559724			−0.279862	+	0.960040i	$0.590289\pi$
$422$	15.9891	+	15.9891i	0.778338	+	0.778338i
$423$	−7.80662	+	9.26080i	−0.379571	+	0.450276i
$424$		−	23.8867i		−	1.16004i
$425$	10.1955	+	21.6689i	0.494552	+	1.05109i
$426$	0.214004	+	5.03252i	0.0103685	+	0.243827i
$427$	−10.1512	+	10.1512i	−0.491252	+	0.491252i
$428$	−7.56174	+	7.56174i	−0.365510	+	0.365510i
$429$	−0.631494	−	14.8502i	−0.0304888	−	0.716976i
$430$	−58.1130	−	10.1436i	−2.80246	−	0.489169i
$431$		−	25.7652i		−	1.24107i	−0.784180	−	0.620533i	$-0.786916\pi$
$431$		−	25.7652i		−	1.24107i	0.784180	−	0.620533i	$-0.213084\pi$
$432$	−17.8781	−	13.8153i	−0.860161	−	0.664689i
$433$	2.29857	+	2.29857i	0.110462	+	0.110462i	0.760178	−	0.649715i	$-0.225112\pi$
$433$	2.29857	+	2.29857i	0.110462	+	0.110462i	−0.649715	+	0.760178i	$0.725112\pi$
$434$	4.53284			0.217584
$435$	−13.4149	−	17.4613i	−0.643193	−	0.837204i
$436$	75.7183			3.62625
$437$	−1.26024	−	1.26024i	−0.0602852	−	0.0602852i
$438$	−17.1774	−	15.7761i	−0.820770	−	0.753812i
$439$			4.69778i			0.224213i	0.993696	+	0.112106i	$0.0357597\pi$
$439$			4.69778i			0.224213i	−0.993696	+	0.112106i	$0.964240\pi$
$440$	23.7100	−	16.6629i	1.13033	−	0.794373i
$441$	10.7851	−	0.918915i	0.513575	−	0.0437578i
$442$	27.9488	−	27.9488i	1.32939	−	1.32939i
$443$	12.8335	−	12.8335i	0.609737	−	0.609737i	−0.333140	−	0.942877i	$-0.608108\pi$
$443$	12.8335	−	12.8335i	0.609737	−	0.609737i	0.942877	+	0.333140i	$0.108108\pi$
$444$	27.8427	−	1.18399i	1.32136	−	0.0561895i
$445$	6.33090	−	36.2698i	0.300114	−	1.71935i
$446$			63.9887i			3.02995i
$447$	11.6173	−	12.6492i	0.549481	−	0.598289i
$448$	9.48533	+	9.48533i	0.448140	+	0.448140i
$449$	−38.3820			−1.81136			−0.905679	−	0.423963i	$-0.860639\pi$
$449$	−38.3820			−1.81136			−0.905679	+	0.423963i	$0.860639\pi$
$450$	−31.9501	+	18.4966i	−1.50614	+	0.871939i
$451$	9.64079			0.453967
$452$	28.3822	+	28.3822i	1.33499	+	1.33499i
$453$	−11.7291	+	12.7709i	−0.551081	+	0.600031i
$454$		−	15.5289i		−	0.728806i
$455$	−2.37440	+	13.6030i	−0.111314	+	0.637716i
$456$	−41.1252	+	1.74881i	−1.92586	+	0.0818957i
$457$	7.32388	−	7.32388i	0.342597	−	0.342597i	−0.514746	−	0.857343i	$-0.672114\pi$
$457$	7.32388	−	7.32388i	0.342597	−	0.342597i	0.857343	+	0.514746i	$0.172114\pi$
$458$	−12.2498	+	12.2498i	−0.572395	+	0.572395i
$459$	−3.16441	−	24.6851i	−0.147702	−	1.15220i
$460$	−2.81898	+	1.98112i	−0.131435	+	0.0923701i
$461$		−	29.3813i		−	1.36842i	−0.729284	−	0.684212i	$-0.760147\pi$
$461$		−	29.3813i		−	1.36842i	0.729284	−	0.684212i	$-0.239853\pi$
$462$	−14.7991	−	13.5918i	−0.688515	−	0.632346i
$463$	−7.50791	−	7.50791i	−0.348922	−	0.348922i	0.510786	−	0.859708i	$-0.329354\pi$
$463$	−7.50791	−	7.50791i	−0.348922	−	0.348922i	−0.859708	+	0.510786i	$0.829354\pi$
$464$	−24.7213			−1.14766
$465$	−2.35953	−	3.07125i	−0.109421	−	0.142426i
$466$	−21.9777			−1.01810
$467$	22.5049	+	22.5049i	1.04140	+	1.04140i	0.999105	+	0.0422999i	$0.0134685\pi$
$467$	22.5049	+	22.5049i	1.04140	+	1.04140i	0.0422999	+	0.999105i	$0.486532\pi$
$468$	31.2064	+	26.3062i	1.44252	+	1.21601i
$469$			10.4735i			0.483620i
$470$	21.8885	+	3.82064i	1.00964	+	0.176233i
$471$	−1.60151	−	37.6613i	−0.0737939	−	1.73534i
$472$	−44.8519	+	44.8519i	−2.06448	+	2.06448i
$473$	−19.3985	+	19.3985i	−0.891944	+	0.891944i
$474$	0.808721	+	19.0179i	0.0371458	+	0.873521i
$475$	−7.94955	+	22.0777i	−0.364750	+	1.01300i
$476$		−	35.7910i		−	1.64048i
$477$	10.8198	+	9.12083i	0.495406	+	0.417614i
$478$	10.5392	+	10.5392i	0.482050	+	0.482050i
$479$	14.3792			0.657004			0.328502	−	0.944503i	$-0.393456\pi$
$479$	14.3792			0.657004			0.328502	+	0.944503i	$0.393456\pi$
$480$	−0.288907	+	2.20450i	−0.0131867	+	0.100621i
$481$	−13.2962			−0.606253
$482$	−33.8002	−	33.8002i	−1.53956	−	1.53956i
$483$	0.892224	+	0.819437i	0.0405976	+	0.0372857i
$484$			18.0554i			0.820699i
$485$	24.8763	+	35.3970i	1.12957	+	1.60729i
$486$	37.5033	−	8.09134i	1.70119	−	0.367031i
$487$	−9.90705	+	9.90705i	−0.448931	+	0.448931i	−0.894999	−	0.446068i	$-0.852824\pi$
$487$	−9.90705	+	9.90705i	−0.448931	+	0.448931i	0.446068	+	0.894999i	$0.352824\pi$
$488$	27.9111	−	27.9111i	1.26348	−	1.26348i
$489$	−36.9427	+	1.57096i	−1.67061	+	0.0710412i
$490$	−11.4173	−	16.2459i	−0.515780	−	0.733914i
$491$			16.4515i			0.742445i	0.928544	+	0.371223i	$0.121061\pi$
$491$			16.4515i			0.742445i	−0.928544	+	0.371223i	$0.878939\pi$
$492$	−17.9072	+	19.4978i	−0.807317	+	0.879027i
$493$	−19.2547	−	19.2547i	−0.867189	−	0.867189i
$494$	38.7296			1.74253
$495$	−1.50566	+	17.1023i	−0.0676743	+	0.768690i
$496$	−4.34822			−0.195241
$497$	−1.53880	−	1.53880i	−0.0690244	−	0.0690244i
$498$	16.4313	−	17.8909i	0.736305	−	0.801708i
$499$		−	14.2093i		−	0.636096i	−0.948075	−	0.318048i	$-0.896973\pi$
$499$		−	14.2093i		−	0.636096i	0.948075	−	0.318048i	$-0.103027\pi$
$500$	39.4032	+	22.4786i	1.76216	+	1.00527i
$501$	11.5261	−	0.490139i	0.514949	−	0.0218978i
$502$	−0.582023	+	0.582023i	−0.0259770	+	0.0259770i
$503$	−3.98638	+	3.98638i	−0.177744	+	0.177744i	−0.790372	−	0.612628i	$-0.790113\pi$
$503$	−3.98638	+	3.98638i	−0.177744	+	0.177744i	0.612628	+	0.790372i	$0.290113\pi$
$504$	27.8778	−	2.37525i	1.24178	−	0.105802i
$505$	40.9529	+	7.14834i	1.82238	+	0.318097i
$506$			2.39211i			0.106342i
$507$	2.24138	+	2.05853i	0.0995433	+	0.0914226i
$508$	49.0997	+	49.0997i	2.17845	+	2.17845i
$509$	3.81193			0.168961			0.0844803	−	0.996425i	$-0.473077\pi$
$509$	3.81193			0.168961			0.0844803	+	0.996425i	$0.473077\pi$
$510$	−36.2038	+	27.8140i	−1.60313	+	1.23163i
$511$	10.0762			0.445746
$512$	−29.3743	−	29.3743i	−1.29817	−	1.29817i
$513$	14.9110	−	19.2960i	0.658335	−	0.851938i
$514$		−	75.3948i		−	3.32552i
$515$	−5.75923	+	4.04747i	−0.253782	+	0.178353i
$516$	−3.20052	−	75.2635i	−0.140895	−	3.31329i
$517$	7.30653	−	7.30653i	0.321341	−	0.321341i
$518$	−12.7099	+	12.7099i	−0.558440	+	0.558440i
$519$	−0.235537	−	5.53889i	−0.0103389	−	0.243130i
$520$	6.52848	−	37.4017i	0.286293	−	1.64017i
$521$			8.28196i			0.362839i	0.983406	+	0.181420i	$0.0580692\pi$
$521$			8.28196i			0.362839i	−0.983406	+	0.181420i	$0.941931\pi$
$522$	27.0562	−	32.0961i	1.18422	−	1.40481i
$523$	−4.50113	−	4.50113i	−0.196820	−	0.196820i	0.601815	−	0.798635i	$-0.294444\pi$
$523$	−4.50113	−	4.50113i	−0.196820	−	0.196820i	−0.798635	+	0.601815i	$0.794444\pi$
$524$	17.9403			0.783725
$525$	4.76100	−	15.2226i	0.207787	−	0.664371i
$526$	−32.3906			−1.41230
$527$	−3.38670	−	3.38670i	−0.147527	−	0.147527i
$528$	14.1963	+	13.0382i	0.617814	+	0.567413i
$529$			22.8558i			0.993730i
$530$	4.46384	−	25.5734i	0.193897	−	1.11084i
$531$	−3.19018	−	37.4424i	−0.138442	−	1.62486i
$532$	24.7984	−	24.7984i	1.07515	−	1.07515i
$533$	8.93129	−	8.93129i	0.386857	−	0.386857i
$534$	70.1281	−	2.98214i	3.03474	−	0.129050i
$535$	−4.82174	+	3.38862i	−0.208462	+	0.146503i
$536$		−	28.7971i		−	1.24385i
$537$	1.82057	−	1.98229i	0.0785636	−	0.0855420i
$538$	−5.17328	−	5.17328i	−0.223036	−	0.223036i
$539$	−9.23415			−0.397743
$540$	−31.7914	−	34.8115i	−1.36808	−	1.49805i
$541$	−29.5788			−1.27169			−0.635847	−	0.771815i	$-0.719349\pi$
$541$	−29.5788			−1.27169			−0.635847	+	0.771815i	$0.719349\pi$
$542$	7.48175	+	7.48175i	0.321369	+	0.321369i
$543$	14.6317	−	15.9314i	0.627907	−	0.683681i
$544$			2.74950i			0.117884i
$545$	41.1066	+	7.17517i	1.76081	+	0.307350i
$546$	−26.3015	+	1.11845i	−1.12560	+	0.0478652i
$547$	−0.136930	+	0.136930i	−0.00585468	+	0.00585468i	−0.710028	−	0.704173i	$-0.751318\pi$
$547$	−0.136930	+	0.136930i	−0.00585468	+	0.00585468i	0.704173	+	0.710028i	$0.251318\pi$
$548$	−58.6060	+	58.6060i	−2.50353	+	2.50353i
$549$	1.98523	+	23.3002i	0.0847277	+	0.994428i
$550$	28.4980	−	13.4086i	1.21516	−	0.571747i
$551$		−	26.6819i		−	1.13669i
$552$	−2.45320	−	2.25307i	−0.104415	−	0.0958969i
$553$	−5.81511	−	5.81511i	−0.247284	−	0.247284i
$554$	−26.7826			−1.13789
$555$	15.2277	+	1.99564i	0.646379	+	0.0847101i
$556$	81.3045			3.44808
$557$	1.30891	+	1.30891i	0.0554602	+	0.0554602i	0.734293	−	0.678833i	$-0.237514\pi$
$557$	1.30891	+	1.30891i	0.0554602	+	0.0554602i	−0.678833	+	0.734293i	$0.737514\pi$
$558$	4.75890	−	5.64537i	0.201460	−	0.238988i
$559$			35.9418i			1.52018i
$560$	−10.2963	−	14.6508i	−0.435096	−	0.619108i
$561$	0.902028	+	21.2121i	0.0380837	+	0.895577i
$562$	−25.6605	+	25.6605i	−1.08242	+	1.08242i
$563$	−29.9878	+	29.9878i	−1.26383	+	1.26383i	−0.314615	+	0.949219i	$0.601875\pi$
$563$	−29.9878	+	29.9878i	−1.26383	+	1.26383i	−0.949219	+	0.314615i	$0.898125\pi$
$564$	1.20549	+	28.3483i	0.0507603	+	1.19368i
$565$	12.7188	+	18.0979i	0.535086	+	0.761385i
$566$		−	36.0924i		−	1.51708i
$567$	−9.56885	+	13.5346i	−0.401854	+	0.568399i
$568$	4.23096	+	4.23096i	0.177527	+	0.177527i
$569$	16.0104			0.671189			0.335595	−	0.942007i	$-0.391063\pi$
$569$	16.0104			0.671189			0.335595	+	0.942007i	$0.391063\pi$
$570$	−44.3558	−	5.81297i	−1.85786	−	0.243479i
$571$	15.7012			0.657077			0.328538	−	0.944491i	$-0.393444\pi$
$571$	15.7012			0.657077			0.328538	+	0.944491i	$0.393444\pi$
$572$	−24.6211	−	24.6211i	−1.02946	−	1.02946i
$573$	7.87009	+	7.22805i	0.328778	+	0.301956i
$574$		−	17.0749i		−	0.712695i
$575$	−1.71812	+	0.808397i	−0.0716507	+	0.0337125i
$576$	21.7718	−	1.85501i	0.907157	−	0.0772919i
$577$	−19.5189	+	19.5189i	−0.812581	+	0.812581i	−0.985020	−	0.172439i	$-0.944835\pi$
$577$	−19.5189	+	19.5189i	−0.812581	+	0.812581i	0.172439	+	0.985020i	$0.444835\pi$
$578$	−10.3367	+	10.3367i	−0.429949	+	0.429949i
$579$	33.8379	−	1.43893i	1.40625	−	0.0597998i
$580$	−50.8142	−	8.86963i	−2.10994	−	0.368291i
$581$			10.4947i			0.435394i
$582$	−55.7917	+	60.7474i	−2.31264	+	2.51806i
$583$	−8.53656	−	8.53656i	−0.353548	−	0.353548i
$584$	−27.7049			−1.14644
$585$	14.4488	+	17.2385i	0.597385	+	0.712725i
$586$	14.6728			0.606126
$587$	−18.4221	−	18.4221i	−0.760360	−	0.760360i	0.216027	−	0.976387i	$-0.430690\pi$
$587$	−18.4221	−	18.4221i	−0.760360	−	0.760360i	−0.976387	+	0.216027i	$0.930690\pi$
$588$	17.1518	−	18.6754i	0.707330	−	0.770159i
$589$		−	4.69306i		−	0.193374i
$590$	−56.4006	+	39.6372i	−2.32198	+	1.63184i
$591$	25.0185	−	1.06389i	1.02912	−	0.0437627i
$592$	12.1922	−	12.1922i	0.501096	−	0.501096i
$593$	4.26981	−	4.26981i	0.175340	−	0.175340i	−0.613981	−	0.789321i	$-0.710433\pi$
$593$	4.26981	−	4.26981i	0.175340	−	0.175340i	0.789321	+	0.613981i	$0.210433\pi$
$594$	−32.4648	+	4.16170i	−1.33205	+	0.170757i
$595$	3.39160	−	19.4305i	0.139042	−	0.796573i
$596$		−	40.2330i		−	1.64801i
$597$	−4.06386	−	3.73233i	−0.166323	−	0.152754i
$598$	2.21606	+	2.21606i	0.0906215	+	0.0906215i
$599$	1.20371			0.0491822			0.0245911	−	0.999698i	$-0.492172\pi$
$599$	1.20371			0.0491822			0.0245911	+	0.999698i	$0.492172\pi$
$600$	−13.0905	+	41.8551i	−0.534418	+	1.70873i
$601$	4.03047			0.164406			0.0822031	−	0.996616i	$-0.473804\pi$
$601$	4.03047			0.164406			0.0822031	+	0.996616i	$0.473804\pi$
$602$	34.3570	+	34.3570i	1.40029	+	1.40029i
$603$	13.0441	+	10.9958i	0.531195	+	0.447784i
$604$			40.6201i			1.65281i
$605$	−1.71095	+	9.80207i	−0.0695601	+	0.398511i
$606$	3.36719	+	79.1829i	0.136783	+	3.21659i
$607$	10.5261	−	10.5261i	0.427241	−	0.427241i	−0.460446	−	0.887687i	$-0.652311\pi$
$607$	10.5261	−	10.5261i	0.427241	−	0.427241i	0.887687	+	0.460446i	$0.152311\pi$
$608$	−1.90504	+	1.90504i	−0.0772594	+	0.0772594i
$609$	0.770529	+	18.1198i	0.0312234	+	0.734251i
$610$	35.0978	−	24.6660i	1.42107	−	0.998697i
$611$		−	13.5376i		−	0.547674i
$612$	−44.5754	−	37.5759i	−1.80185	−	1.51892i
$613$	−5.63618	−	5.63618i	−0.227643	−	0.227643i	0.584064	−	0.811707i	$-0.301462\pi$
$613$	−5.63618	−	5.63618i	−0.227643	−	0.227643i	−0.811707	+	0.584064i	$0.801462\pi$
$614$	26.5095			1.06983
$615$	−11.5692	+	8.88821i	−0.466516	+	0.358407i
$616$	−23.8689			−0.961704
$617$	11.1982	+	11.1982i	0.450824	+	0.450824i	0.895628	−	0.444804i	$-0.146727\pi$
$617$	11.1982	+	11.1982i	0.450824	+	0.450824i	−0.444804	+	0.895628i	$0.646727\pi$
$618$	−9.88384	−	9.07752i	−0.397586	−	0.365152i
$619$		−	13.0830i		−	0.525851i	−0.964816	−	0.262926i	$-0.915313\pi$
$619$		−	13.0830i		−	0.525851i	0.964816	−	0.262926i	$-0.0846874\pi$
$620$	−8.93768	−	1.56007i	−0.358946	−	0.0626541i
$621$	1.95728	−	0.250906i	0.0785429	−	0.0100685i
$622$	−13.3264	+	13.3264i	−0.534341	+	0.534341i
$623$	−21.4431	+	21.4431i	−0.859099	+	0.859099i
$624$	25.2302	−	1.07289i	1.01002	−	0.0429501i
$625$	19.2615	+	15.9373i	0.770458	+	0.637491i
$626$		−	9.06314i		−	0.362236i
$627$	−14.0722	+	15.3222i	−0.561989	+	0.611908i
$628$	−62.4408	−	62.4408i	−2.49166	−	2.49166i
$629$	18.9923			0.757273
$630$	30.2901	+	2.66669i	1.20679	+	0.106244i
$631$	26.1928			1.04272			0.521360	−	0.853337i	$-0.325425\pi$
$631$	26.1928			1.04272			0.521360	+	0.853337i	$0.325425\pi$
$632$	15.9888	+	15.9888i	0.636001	+	0.636001i
$633$	−10.7640	+	11.7201i	−0.427831	+	0.465834i
$634$			31.2532i			1.24122i
$635$	22.0029	+	31.3084i	0.873160	+	1.24244i
$636$	33.1207	−	1.40843i	1.31332	−	0.0558478i
$637$	−8.55457	+	8.55457i	−0.338945	+	0.338945i
$638$	−25.3230	+	25.3230i	−1.00255	+	1.00255i
$639$	−3.53201	+	0.300936i	−0.139724	+	0.0119048i
$640$	−24.5241	−	34.8959i	−0.969401	−	1.37938i
$641$		−	4.55409i		−	0.179876i	−0.995947	−	0.0899379i	$-0.971333\pi$
$641$		−	4.55409i		−	0.179876i	0.995947	−	0.0899379i	$-0.0286669\pi$
$642$	−8.27495	−	7.59988i	−0.326586	−	0.299943i
$643$	−27.2969	−	27.2969i	−1.07648	−	1.07648i	−0.996822	−	0.0796607i	$-0.974616\pi$
$643$	−27.2969	−	27.2969i	−1.07648	−	1.07648i	−0.0796607	−	0.996822i	$-0.525384\pi$
$644$	2.83786			0.111828
$645$	5.39455	−	41.1630i	0.212410	−	1.62079i
$646$	−55.3216			−2.17660
$647$	−23.8541	−	23.8541i	−0.937803	−	0.937803i	0.0603727	−	0.998176i	$-0.480771\pi$
$647$	−23.8541	−	23.8541i	−0.937803	−	0.937803i	−0.998176	+	0.0603727i	$0.980771\pi$
$648$	26.3098	−	37.2137i	1.03355	−	1.46189i
$649$			32.0581i			1.25839i
$650$	13.9789	−	38.8226i	0.548297	−	1.52275i
$651$	0.135528	+	3.18708i	0.00531176	+	0.124912i
$652$	−61.2495	+	61.2495i	−2.39872	+	2.39872i
$653$	−5.07325	+	5.07325i	−0.198532	+	0.198532i	−0.799370	−	0.600839i	$-0.794833\pi$
$653$	−5.07325	+	5.07325i	−0.198532	+	0.198532i	0.600839	+	0.799370i	$0.294833\pi$
$654$	3.37982	+	79.4801i	0.132162	+	3.10792i
$655$	9.73957	+	1.70004i	0.380557	+	0.0664262i
$656$			16.3795i			0.639511i
$657$	10.5787	−	12.5493i	0.412716	−	0.489595i
$658$	−12.9407	−	12.9407i	−0.504481	−	0.504481i
$659$	−32.9568			−1.28381			−0.641907	−	0.766782i	$-0.721857\pi$
$659$	−32.9568			−1.28381			−0.641907	+	0.766782i	$0.721857\pi$
$660$	24.5023	+	31.8931i	0.953751	+	1.24144i
$661$	−3.56963			−0.138842			−0.0694212	−	0.997587i	$-0.522115\pi$
$661$	−3.56963			−0.138842			−0.0694212	+	0.997587i	$0.522115\pi$
$662$	−2.30932	−	2.30932i	−0.0897541	−	0.0897541i
$663$	20.4867	+	18.8154i	0.795638	+	0.730730i
$664$		−	28.8555i		−	1.11981i
$665$	15.8127	−	11.1128i	0.613190	−	0.430937i
$666$	2.48562	+	29.1731i	0.0963158	+	1.13043i
$667$	1.52671	−	1.52671i	0.0591143	−	0.0591143i
$668$	19.1098	−	19.1098i	0.739381	−	0.739381i
$669$	−44.9910	+	1.91321i	−1.73945	+	0.0739688i
$670$	5.38147	−	30.8305i	0.207904	−	1.19109i
$671$		−	19.9495i		−	0.770144i
$672$	1.23870	−	1.34873i	0.0477840	−	0.0520285i
$673$	−16.9220	−	16.9220i	−0.652295	−	0.652295i	0.301250	−	0.953545i	$-0.402596\pi$
$673$	−16.9220	−	16.9220i	−0.652295	−	0.652295i	−0.953545	+	0.301250i	$0.902596\pi$
$674$	−42.6627			−1.64331
$675$	−13.9604	−	21.9113i	−0.537336	−	0.843368i
$676$	7.12908			0.274195
$677$	15.8295	+	15.8295i	0.608377	+	0.608377i	0.942522	−	0.334145i	$-0.108448\pi$
$677$	15.8295	+	15.8295i	0.608377	+	0.608377i	−0.334145	+	0.942522i	$0.608448\pi$
$678$	−28.5254	+	31.0592i	−1.09551	+	1.19282i
$679$		−	35.6342i		−	1.36751i
$680$	−9.32530	+	53.4248i	−0.357609	+	2.04875i
$681$	10.9185	−	0.464299i	0.418397	−	0.0177920i
$682$	−4.45405	+	4.45405i	−0.170554	+	0.170554i
$683$	0.807396	−	0.807396i	0.0308941	−	0.0308941i	−0.691491	−	0.722385i	$-0.743046\pi$
$683$	0.807396	−	0.807396i	0.0308941	−	0.0308941i	0.722385	+	0.691491i	$0.243046\pi$
$684$	−4.84971	−	56.9199i	−0.185433	−	2.17639i
$685$	−37.3701	+	26.2630i	−1.42784	+	1.00346i
$686$			48.0846i			1.83588i
$687$	−8.97919	−	8.24667i	−0.342577	−	0.314630i
$688$	−32.9576	−	32.9576i	−1.25650	−	1.25650i
$689$	−15.8167			−0.602566
$690$	−2.20537	−	2.87060i	−0.0839571	−	0.109282i
$691$	−26.8549			−1.02161			−0.510804	−	0.859697i	$-0.670652\pi$
$691$	−26.8549			−1.02161			−0.510804	+	0.859697i	$0.670652\pi$
$692$	−9.18325	−	9.18325i	−0.349095	−	0.349095i
$693$	9.11401	−	10.8117i	0.346212	−	0.410704i
$694$		−	58.4933i		−	2.22037i
$695$	44.1393	+	7.70452i	1.67430	+	0.292249i
$696$	−2.11859	−	49.8209i	−0.0803051	−	1.88846i
$697$	−12.7575	+	12.7575i	−0.483225	+	0.483225i
$698$	−32.3158	+	32.3158i	−1.22317	+	1.22317i
$699$	−0.657114	−	15.4527i	−0.0248544	−	0.584476i
$700$	−15.9073	−	33.8085i	−0.601239	−	1.27784i
$701$		−	3.77870i		−	0.142719i	−0.997451	−	0.0713597i	$-0.977266\pi$
$701$		−	3.77870i		−	0.142719i	0.997451	−	0.0713597i	$-0.0227338\pi$
$702$	−26.2202	+	33.9310i	−0.989617	+	1.28064i
$703$	13.1591	+	13.1591i	0.496306	+	0.496306i
$704$	−18.6409			−0.702556
$705$	−2.03188	+	15.5042i	−0.0765250	+	0.583923i
$706$	67.4969			2.54028
$707$	−24.2118	−	24.2118i	−0.910578	−	0.910578i
$708$	−64.8350	−	59.5458i	−2.43665	−	2.23787i
$709$			18.2349i			0.684825i	0.939550	+	0.342413i	$0.111244\pi$
$709$			18.2349i			0.684825i	−0.939550	+	0.342413i	$0.888756\pi$
$710$	3.73905	+	5.32037i	0.140324	+	0.199670i
$711$	−13.3475	+	1.13724i	−0.500569	+	0.0426497i
$712$	58.9584	−	58.9584i	2.20956	−	2.20956i
$713$	0.268531	−	0.268531i	0.0100566	−	0.0100566i
$714$	37.5691	−	1.59760i	1.40599	−	0.0597885i
$715$	−11.0334	−	15.6996i	−0.412625	−	0.587133i
$716$		−	6.30499i		−	0.235628i
$717$	−7.09506	+	7.72528i	−0.264970	+	0.288506i
$718$	4.10401	+	4.10401i	0.153160	+	0.153160i
$719$	−4.30553			−0.160569			−0.0802845	−	0.996772i	$-0.525583\pi$
$719$	−4.30553			−0.160569			−0.0802845	+	0.996772i	$0.525583\pi$
$720$	−29.0563	−	2.55808i	−1.08287	−	0.0953339i
$721$	5.79782			0.215922
$722$	−5.26425	−	5.26425i	−0.195915	−	0.195915i
$723$	22.7546	−	24.7758i	0.846253	−	0.921422i
$724$		−	50.6723i		−	1.88322i
$725$	−26.7460	−	9.63044i	−0.993320	−	0.357666i
$726$	−18.9524	+	0.805935i	−0.703390	+	0.0299111i
$727$	4.10330	−	4.10330i	0.152183	−	0.152183i	−0.626909	−	0.779092i	$-0.715680\pi$
$727$	4.10330	−	4.10330i	0.152183	−	0.152183i	0.779092	+	0.626909i	$0.215680\pi$
$728$	−22.1123	+	22.1123i	−0.819535	+	0.819535i
$729$	6.81040	+	26.1270i	0.252237	+	0.967665i
$730$	−29.6611	−	5.17735i	−1.09781	−	0.191622i
$731$		−	51.3394i		−	1.89886i
$732$	40.3465	+	37.0550i	1.49125	+	1.36959i
$733$	5.34821	+	5.34821i	0.197541	+	0.197541i	0.798945	−	0.601404i	$-0.205392\pi$
$733$	5.34821	+	5.34821i	0.197541	+	0.197541i	−0.601404	+	0.798945i	$0.705392\pi$
$734$	−32.3786			−1.19512
$735$	11.0812	−	8.51331i	0.408738	−	0.314018i
$736$	−0.218008			−0.00803587
$737$	−10.2914	−	10.2914i	−0.379089	−	0.379089i
$738$	−21.2658	−	17.9265i	−0.782804	−	0.659883i
$739$		−	31.4904i		−	1.15839i	−0.815188	−	0.579197i	$-0.803366\pi$
$739$		−	31.4904i		−	1.15839i	0.815188	−	0.579197i	$-0.196634\pi$
$740$	29.4352	−	20.6865i	1.08206	−	0.760450i
$741$	1.15798	+	27.2311i	0.0425395	+	1.00036i
$742$	−15.1192	+	15.1192i	−0.555044	+	0.555044i
$743$	−15.5001	+	15.5001i	−0.568645	+	0.568645i	−0.931749	−	0.363104i	$-0.881717\pi$
$743$	−15.5001	+	15.5001i	−0.568645	+	0.568645i	0.363104	+	0.931749i	$0.381717\pi$
$744$	−0.372638	−	8.76297i	−0.0136616	−	0.321266i
$745$	3.81253	−	21.8420i	0.139680	−	0.800230i
$746$		−	20.6007i		−	0.754247i
$747$	13.0705	+	11.0181i	0.478224	+	0.403131i
$748$	35.1688	+	35.1688i	1.28590	+	1.28590i
$749$	4.85405			0.177363
$750$	−21.8365	+	42.3642i	−0.797357	+	1.54692i
$751$	−31.1823			−1.13786			−0.568930	−	0.822386i	$-0.692642\pi$
$751$	−31.1823			−1.13786			−0.568930	+	0.822386i	$0.692642\pi$
$752$	12.4136	+	12.4136i	0.452678	+	0.452678i
$753$	−0.426627	−	0.391823i	−0.0155472	−	0.0142788i
$754$			46.9188i			1.70868i
$755$	−3.84921	+	22.0522i	−0.140087	+	0.802561i
$756$	4.93721	+	38.5145i	0.179565	+	1.40076i
$757$	−25.1331	+	25.1331i	−0.913480	+	0.913480i	−0.996544	−	0.0830643i	$-0.973529\pi$
$757$	−25.1331	+	25.1331i	−0.913480	+	0.913480i	0.0830643	+	0.996544i	$0.473529\pi$
$758$	−31.6145	+	31.6145i	−1.14829	+	1.14829i
$759$	−1.68191	+	0.0715218i	−0.0610494	+	0.00259608i
$760$	−43.4774	+	30.5551i	−1.57709	+	1.10835i
$761$			8.72350i			0.316226i	0.987421	+	0.158113i	$0.0505411\pi$
$761$			8.72350i			0.316226i	−0.987421	+	0.158113i	$0.949459\pi$
$762$	−49.3474	+	53.7307i	−1.78767	+	1.94646i
$763$	−24.3026	−	24.3026i	−0.879815	−	0.879815i
$764$	25.0321			0.905629
$765$	−20.6387	−	24.6236i	−0.746195	−	0.890267i
$766$	−68.0701			−2.45947
$767$	29.6988	+	29.6988i	1.07236	+	1.07236i
$768$	37.9350	−	41.3046i	1.36886	−	1.49045i
$769$		−	21.7304i		−	0.783619i	−0.920046	−	0.391809i	$-0.871849\pi$
$769$		−	21.7304i		−	0.783619i	0.920046	−	0.391809i	$-0.128151\pi$
$770$	−25.5542	−	4.46050i	−0.920910	−	0.160745i
$771$	53.0107	−	2.25423i	1.90913	−	0.0811843i
$772$	56.1018	−	56.1018i	2.01915	−	2.01915i
$773$	16.4735	−	16.4735i	0.592511	−	0.592511i	−0.345798	−	0.938309i	$-0.612392\pi$
$773$	16.4735	−	16.4735i	0.592511	−	0.592511i	0.938309	+	0.345798i	$0.112392\pi$
$774$	78.8599	−	6.71905i	2.83456	−	0.241511i
$775$	−4.70433	−	1.69389i	−0.168985	−	0.0608464i
$776$			97.9772i			3.51718i
$777$	−9.31644	−	8.55641i	−0.334225	−	0.306960i
$778$	55.0684	+	55.0684i	1.97430	+	1.97430i
$779$	−17.6785			−0.633398
$780$	52.2451	+	6.84689i	1.87067	+	0.245158i
$781$	3.02409			0.108211
$782$	−3.16543	−	3.16543i	−0.113196	−	0.113196i
$783$	23.3760	+	18.0638i	0.835391	+	0.645548i
$784$		−	15.6886i		−	0.560307i
$785$	−27.9814	−	39.8154i	−0.998700	−	1.42107i
$786$	0.800797	+	18.8316i	0.0285635	+	0.671700i
$787$	−11.1899	+	11.1899i	−0.398878	+	0.398878i	−0.877837	−	0.478959i	$-0.841014\pi$
$787$	−11.1899	+	11.1899i	−0.398878	+	0.398878i	0.478959	+	0.877837i	$0.341014\pi$
$788$	41.4797	−	41.4797i	1.47765	−	1.47765i
$789$	−0.968450	−	22.7741i	−0.0344777	−	0.810779i
$790$	14.1299	+	20.1057i	0.502718	+	0.715328i
$791$		−	18.2192i		−	0.647799i
$792$	−25.0592	+	29.7272i	−0.890441	+	1.05631i
$793$	−18.4814	−	18.4814i	−0.656294	−	0.656294i
$794$	−64.2648			−2.28067
$795$	18.1143	+	2.37394i	0.642448	+	0.0841949i
$796$	−12.9258			−0.458142
$797$	26.6744	+	26.6744i	0.944855	+	0.944855i	0.998557	−	0.0537016i	$-0.0171020\pi$
$797$	26.6744	+	26.6744i	0.944855	+	0.944855i	−0.0537016	+	0.998557i	$0.517102\pi$
$798$	27.1373	+	24.9235i	0.960650	+	0.882281i
$799$			19.3372i			0.684102i
$800$	1.22201	+	2.59720i	0.0432047	+	0.0918250i
$801$	4.19353	+	49.2185i	0.148171	+	1.73905i
$802$	2.13311	−	2.13311i	0.0753228	−	0.0753228i
$803$	−9.90107	+	9.90107i	−0.349401	+	0.349401i
$804$	39.9293	−	1.69796i	1.40820	−	0.0598824i
$805$	1.54064	+	0.268920i	0.0543006	+	0.00947818i
$806$			8.25253i			0.290683i
$807$	3.48270	−	3.79205i	0.122597	−	0.133487i
$808$	66.5710	+	66.5710i	2.34196	+	2.34196i
$809$	−8.76972			−0.308327			−0.154163	−	0.988045i	$-0.549268\pi$
$809$	−8.76972			−0.308327			−0.154163	+	0.988045i	$0.549268\pi$
$810$	35.1219	−	34.9247i	1.23406	−	1.22713i
$811$	−6.06391			−0.212933			−0.106466	−	0.994316i	$-0.533954\pi$
$811$	−6.06391			−0.212933			−0.106466	+	0.994316i	$0.533954\pi$
$812$	30.0419	+	30.0419i	1.05426	+	1.05426i
$813$	−5.03678	+	5.48417i	−0.176648	+	0.192338i
$814$		−	24.9779i		−	0.875475i
$815$	−39.0557	+	27.4476i	−1.36806	+	0.961447i
$816$	−36.0389	+	1.53252i	−1.26161	+	0.0536491i
$817$	35.5714	−	35.5714i	1.24449	−	1.24449i
$818$	59.1625	−	59.1625i	2.06857	−	2.06857i
$819$	−1.57278	−	18.4593i	−0.0549574	−	0.645021i
$820$	−5.87670	+	33.6677i	−0.205223	+	1.17573i
$821$		−	41.6548i		−	1.45376i	−0.686763	−	0.726881i	$-0.740969\pi$
$821$		−	41.6548i		−	1.45376i	0.686763	−	0.726881i	$-0.259031\pi$
$822$	−64.1337	−	58.9017i	−2.23692	−	2.05443i
$823$	33.0974	+	33.0974i	1.15370	+	1.15370i	0.985804	+	0.167898i	$0.0536980\pi$
$823$	33.0974	+	33.0974i	1.15370	+	1.15370i	0.167898	+	0.985804i	$0.446302\pi$
$824$	−15.9413			−0.555341
$825$	10.2798	+	19.6363i	0.357896	+	0.683648i
$826$	56.7785			1.97558
$827$	27.5595	+	27.5595i	0.958338	+	0.958338i	0.999166	−	0.0408287i	$-0.0129998\pi$
$827$	27.5595	+	27.5595i	0.958338	+	0.958338i	−0.0408287	+	0.999166i	$0.513000\pi$
$828$	2.97939	−	3.53438i	0.103541	−	0.122828i
$829$			42.0783i			1.46144i	0.682677	+	0.730720i	$0.260815\pi$
$829$			42.0783i			1.46144i	−0.682677	+	0.730720i	$0.739185\pi$
$830$	5.39237	−	30.8929i	0.187172	−	1.07231i
$831$	−0.800777	−	18.8311i	−0.0277786	−	0.653243i
$832$	−17.2691	+	17.2691i	−0.598697	+	0.598697i
$833$	12.2194	−	12.2194i	0.423377	−	0.423377i
$834$	3.62918	+	85.3438i	0.125668	+	2.95522i
$835$	12.1854	−	8.56364i	0.421693	−	0.296357i
$836$			48.7346i			1.68552i
$837$	4.11159	+	3.17723i	0.142117	+	0.109821i
$838$	45.0649	+	45.0649i	1.55674	+	1.55674i
$839$	−15.8726			−0.547983			−0.273991	−	0.961732i	$-0.588344\pi$
$839$	−15.8726			−0.547983			−0.273991	+	0.961732i	$0.588344\pi$
$840$	28.6433	−	22.0056i	0.988289	−	0.759266i
$841$	3.32367			0.114609
$842$	−19.9869	−	19.9869i	−0.688795	−	0.688795i
$843$	−18.8093	−	17.2749i	−0.647828	−	0.594979i
$844$			37.2778i			1.28316i
$845$	3.87030	+	0.675561i	0.133142	+	0.0232400i
$846$	−29.7029	+	2.53076i	−1.02121	+	0.0870093i
$847$	5.79508	−	5.79508i	0.199121	−	0.199121i
$848$	14.5034	−	14.5034i	0.498049	−	0.498049i
$849$	25.3768	−	1.07913i	0.870931	−	0.0370356i
$850$	−19.9675	+	55.4544i	−0.684880	+	1.90207i
$851$			1.50590i			0.0516216i
$852$	−5.61706	+	6.11600i	−0.192437	+	0.209531i
$853$	19.7306	+	19.7306i	0.675562	+	0.675562i	0.958993	−	0.283431i	$-0.0914727\pi$
$853$	19.7306	+	19.7306i	0.675562	+	0.675562i	−0.283431	+	0.958993i	$0.591473\pi$
$854$	−35.3329			−1.20907
$855$	2.76095	−	31.3607i	0.0944225	−	1.07251i
$856$	−13.3463			−0.456169
$857$	−14.1707	−	14.1707i	−0.484061	−	0.484061i	0.422365	−	0.906426i	$-0.361200\pi$
$857$	−14.1707	−	14.1707i	−0.484061	−	0.484061i	−0.906426	+	0.422365i	$0.861200\pi$
$858$	24.7453	−	26.9433i	0.844790	−	0.919828i
$859$		−	22.6000i		−	0.771102i	−0.922687	−	0.385551i	$-0.874011\pi$
$859$		−	22.6000i		−	0.771102i	0.922687	−	0.385551i	$-0.125989\pi$
$860$	−55.9190	−	79.5684i	−1.90682	−	2.71326i
$861$	12.0055	−	0.510525i	0.409148	−	0.0173987i
$862$	44.8399	−	44.8399i	1.52725	−	1.52725i
$863$	26.4341	−	26.4341i	0.899828	−	0.899828i	−0.0955929	−	0.995421i	$-0.530475\pi$
$863$	26.4341	−	26.4341i	0.899828	−	0.899828i	0.995421	+	0.0955929i	$0.0304747\pi$
$864$	−0.379282	−	2.95872i	−0.0129034	−	0.100658i
$865$	−4.11526	−	5.85570i	−0.139923	−	0.199100i
$866$			8.00054i			0.271869i
$867$	−7.57685	−	6.95874i	−0.257323	−	0.236331i
$868$	5.28405	+	5.28405i	0.179352	+	0.179352i
$869$	11.4281			0.387670
$870$	7.04210	−	53.7346i	0.238750	−	1.82177i
$871$	−19.0681			−0.646097
$872$	66.8208	+	66.8208i	2.26284	+	2.26284i
$873$	−44.3801	−	37.4113i	−1.50204	−	1.26618i
$874$		−	4.38645i		−	0.148374i
$875$	−5.43215	−	19.8617i	−0.183640	−	0.671447i
$876$	−1.63356	−	38.4148i	−0.0551927	−	1.29791i
$877$	9.80802	−	9.80802i	0.331193	−	0.331193i	−0.521846	−	0.853040i	$-0.674757\pi$
$877$	9.80802	−	9.80802i	0.331193	−	0.331193i	0.853040	+	0.521846i	$0.174757\pi$
$878$	−8.17567	+	8.17567i	−0.275916	+	0.275916i
$879$	0.438702	+	10.3165i	0.0147971	+	0.347968i
$880$	24.5134	+	4.27882i	0.826346	+	0.144239i
$881$			17.6496i			0.594629i	0.954780	+	0.297315i	$0.0960910\pi$
$881$			17.6496i			0.594629i	−0.954780	+	0.297315i	$0.903909\pi$
$882$	20.3688	+	17.1704i	0.685853	+	0.578156i
$883$	−13.6543	−	13.6543i	−0.459503	−	0.459503i	0.438990	−	0.898492i	$-0.355336\pi$
$883$	−13.6543	−	13.6543i	−0.459503	−	0.459503i	−0.898492	+	0.438990i	$0.855336\pi$
$884$	65.1613			2.19161
$885$	−29.5556	−	38.4706i	−0.993499	−	1.29318i
$886$	44.6690			1.50068
$887$	−33.6240	−	33.6240i	−1.12898	−	1.12898i	−0.990343	−	0.138639i	$-0.955727\pi$
$887$	−33.6240	−	33.6240i	−1.12898	−	1.12898i	−0.138639	−	0.990343i	$-0.544273\pi$
$888$	25.6158	+	23.5261i	0.859611	+	0.789484i
$889$		−	31.5182i		−	1.05709i
$890$	74.1392	−	52.1035i	2.48515	−	1.74651i
$891$	−3.89679	−	22.7018i	−0.130547	−	0.760540i
$892$	−74.5932	+	74.5932i	−2.49757	+	2.49757i
$893$	−13.3981	+	13.3981i	−0.448351	+	0.448351i
$894$	42.2318	−	1.79587i	1.41244	−	0.0600630i
$895$	0.597469	−	3.42291i	0.0199712	−	0.114415i
$896$			35.1297i			1.17360i
$897$	−1.49187	+	1.62439i	−0.0498122	+	0.0542368i
$898$	−66.7973	−	66.7973i	−2.22905	−	2.22905i
$899$	5.68539			0.189618
$900$	−58.8070	−	15.6830i	−1.96023	−	0.522768i
$901$	22.5926			0.752668
$902$	16.7781	+	16.7781i	0.558651	+	0.558651i
$903$	−23.1294	+	25.1839i	−0.769699	+	0.838068i
$904$			50.0942i			1.66611i
$905$	4.80178	−	27.5094i	0.159617	−	0.914445i
$906$	−42.6381	+	1.81315i	−1.41656	+	0.0602379i
$907$	−4.29022	+	4.29022i	−0.142454	+	0.142454i	−0.774737	−	0.632283i	$-0.782118\pi$
$907$	−4.29022	+	4.29022i	−0.142454	+	0.142454i	0.632283	+	0.774737i	$0.282118\pi$
$908$	18.1024	−	18.1024i	0.600749	−	0.600749i
$909$	−55.5735	+	4.73500i	−1.84326	+	0.157050i
$910$	−27.8058	+	19.5414i	−0.921755	+	0.647790i
$911$		−	1.45363i		−	0.0481610i	−0.999710	−	0.0240805i	$-0.992334\pi$
$911$		−	1.45363i		−	0.0481610i	0.999710	−	0.0240805i	$-0.00766580\pi$
$912$	−26.0320	−	23.9083i	−0.862005	−	0.791683i
$913$	−10.3123	−	10.3123i	−0.341286	−	0.341286i
$914$	25.4919			0.843197
$915$	18.3923	+	23.9400i	0.608029	+	0.791433i
$916$	−28.5598			−0.943641
$917$	−5.75814	−	5.75814i	−0.190150	−	0.190150i
$918$	37.4530	−	48.4672i	1.23613	−	1.59966i
$919$		−	12.9482i		−	0.427122i	−0.976930	−	0.213561i	$-0.931494\pi$
$919$		−	12.9482i		−	0.427122i	0.976930	−	0.213561i	$-0.0685063\pi$
$920$	−4.23605	−	0.739403i	−0.139658	−	0.0243774i
$921$	0.792609	+	18.6390i	0.0261173	+	0.614176i
$922$	51.1331	−	51.1331i	1.68398	−	1.68398i
$923$	2.80154	−	2.80154i	0.0922139	−	0.0922139i
$924$	−1.40738	−	33.0959i	−0.0462993	−	1.08877i
$925$	17.9403	−	8.44113i	0.589874	−	0.277543i
$926$		−	26.1324i		−	0.858766i
$927$	6.08696	−	7.22082i	0.199922	−	0.237163i
$928$	−2.30785	−	2.30785i	−0.0757588	−	0.0757588i
$929$	−34.5433			−1.13333			−0.566664	−	0.823949i	$-0.691766\pi$
$929$	−34.5433			−1.13333			−0.566664	+	0.823949i	$0.691766\pi$
$930$	1.23863	−	9.45135i	0.0406163	−	0.309922i
$931$	16.9328			0.554951
$932$	−25.6200	−	25.6200i	−0.839210	−	0.839210i
$933$	−9.76836	−	8.97146i	−0.319802	−	0.293713i
$934$			78.3320i			2.56310i
$935$	15.7601	+	22.4254i	0.515411	+	0.733389i
$936$	4.32440	+	50.7545i	0.141348	+	1.65896i
$937$	32.2161	−	32.2161i	1.05245	−	1.05245i	0.0539082	−	0.998546i	$-0.482832\pi$
$937$	32.2161	−	32.2161i	1.05245	−	1.05245i	0.998546	−	0.0539082i	$-0.0171678\pi$
$938$	−18.2273	+	18.2273i	−0.595142	+	0.595142i
$939$	6.37237	−	0.270980i	0.207954	−	0.00884309i
$940$	21.0622	+	29.9698i	0.686972	+	0.977507i
$941$		−	19.8742i		−	0.647879i	−0.946078	−	0.323939i	$-0.894993\pi$
$941$		−	19.8742i		−	0.647879i	0.946078	−	0.323939i	$-0.105007\pi$
$942$	62.7558	−	68.3301i	2.04469	−	2.22632i
$943$	−1.01154	−	1.01154i	−0.0329403	−	0.0329403i
$944$	−54.4659			−1.77271
$945$	−0.969327	+	21.3769i	−0.0315322	+	0.695392i
$946$	−67.5195			−2.19525
$947$	−16.6962	−	16.6962i	−0.542555	−	0.542555i	0.381722	−	0.924277i	$-0.375331\pi$
$947$	−16.6962	−	16.6962i	−0.542555	−	0.542555i	−0.924277	+	0.381722i	$0.875331\pi$
$948$	−21.2269	+	23.1124i	−0.689417	+	0.750655i
$949$			18.3448i			0.595498i
$950$	−52.2573	+	24.5877i	−1.69545	+	0.797729i
$951$	−21.9744	+	0.934443i	−0.712569	+	0.0303014i
$952$	31.5853	−	31.5853i	1.02368	−	1.02368i
$953$	−1.45649	+	1.45649i	−0.0471804	+	0.0471804i	−0.730303	−	0.683123i	$-0.760621\pi$
$953$	−1.45649	+	1.45649i	−0.0471804	+	0.0471804i	0.683123	+	0.730303i	$0.260621\pi$
$954$	2.95680	+	34.7033i	0.0957301	+	1.12356i
$955$	13.5896	+	2.37207i	0.439750	+	0.0767585i
$956$			24.5715i			0.794699i
$957$	−18.5620	−	17.0477i	−0.600023	−	0.551074i
$958$	25.0246	+	25.0246i	0.808508	+	0.808508i
$959$	37.6205			1.21483
$960$	22.3696	−	17.1858i	0.721977	−	0.554668i
$961$	1.00000			0.0322581
$962$	−23.1397	−	23.1397i	−0.746054	−	0.746054i
$963$	5.09612	−	6.04541i	0.164220	−	0.194811i
$964$		−	78.8035i		−	2.53809i
$965$	35.7733	−	25.1407i	1.15158	−	0.809309i
$966$	0.126673	+	2.97885i	0.00407565	+	0.0958430i
$967$	3.93466	−	3.93466i	0.126530	−	0.126530i	−0.641006	−	0.767536i	$-0.721483\pi$
$967$	3.93466	−	3.93466i	0.126530	−	0.126530i	0.767536	+	0.641006i	$0.221483\pi$
$968$	−15.9337	+	15.9337i	−0.512130	+	0.512130i
$969$	−1.65407	−	38.8971i	−0.0531362	−	1.24955i
$970$	−18.3095	+	104.895i	−0.587882	+	3.36798i
$971$			50.7595i			1.62895i	0.580199	+	0.814475i	$0.302975\pi$
$971$			50.7595i			1.62895i	−0.580199	+	0.814475i	$0.697025\pi$
$972$	53.1508	+	34.2863i	1.70481	+	1.09973i
$973$	−26.0956	−	26.0956i	−0.836587	−	0.836587i
$974$	−34.4830			−1.10491
$975$	27.7145	+	8.66791i	0.887573	+	0.277595i
$976$	33.8938			1.08491
$977$	18.6011	+	18.6011i	0.595101	+	0.595101i	0.939005	−	0.343904i	$-0.111749\pi$
$977$	18.6011	+	18.6011i	0.595101	+	0.595101i	−0.343904	+	0.939005i	$0.611749\pi$
$978$	−67.0264	−	61.5585i	−2.14327	−	1.96842i
$979$		−	42.1407i		−	1.34682i
$980$	5.62883	−	32.2476i	0.179806	−	1.03011i
$981$	−55.7820	+	4.75276i	−1.78098	+	0.151744i
$982$	−28.6310	+	28.6310i	−0.913652	+	0.913652i
$983$	7.45897	−	7.45897i	0.237904	−	0.237904i	−0.578078	−	0.815982i	$-0.696197\pi$
$983$	7.45897	−	7.45897i	0.237904	−	0.237904i	0.815982	+	0.578078i	$0.196197\pi$
$984$	−33.0096	+	1.40370i	−1.05231	+	0.0447485i
$985$	26.4495	−	18.5882i	0.842752	−	0.592269i
$986$		−	67.0191i		−	2.13432i
$987$	8.71180	−	9.48563i	0.277300	−	0.301931i
$988$	45.1481	+	45.1481i	1.43635	+	1.43635i
$989$	4.07070			0.129441
$990$	−32.3839	+	27.1432i	−1.02923	+	0.862668i
$991$	−9.46326			−0.300610			−0.150305	−	0.988640i	$-0.548026\pi$
$991$	−9.46326			−0.300610			−0.150305	+	0.988640i	$0.548026\pi$
$992$	−0.405926	−	0.405926i	−0.0128882	−	0.0128882i
$993$	1.55465	−	1.69275i	0.0493354	−	0.0537176i
$994$		−	5.35602i		−	0.169883i
$995$	−7.01725	−	1.22486i	−0.222462	−	0.0388308i
$996$	40.0102	−	1.70140i	1.26777	−	0.0539109i
$997$	31.8233	−	31.8233i	1.00785	−	1.00785i	0.00788547	−	0.999969i	$-0.497490\pi$
$997$	31.8233	−	31.8233i	1.00785	−	1.00785i	0.999969	−	0.00788547i	$-0.00251005\pi$
$998$	24.7288	−	24.7288i	0.782778	−	0.782778i
$999$	−20.4375	+	2.61991i	−0.646615	+	0.0828902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.218.28	yes	60
3.2	odd	2	inner	465.2.k.a.218.3	yes	60
5.2	odd	4	inner	465.2.k.a.32.3	✓	60
15.2	even	4	inner	465.2.k.a.32.28	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.3	✓	60	5.2	odd	4	inner
465.2.k.a.32.28	yes	60	15.2	even	4	inner
465.2.k.a.218.3	yes	60	3.2	odd	2	inner
465.2.k.a.218.28	yes	60	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74033 + 1.74033i) q^{2} +(-1.17160 + 1.27567i) q^{3} +4.05749i q^{4} +(-0.384493 + 2.20276i) q^{5} +(-4.25907 + 0.181113i) q^{6} +(1.30230 - 1.30230i) q^{7} +(-3.58070 + 3.58070i) q^{8} +(-0.254684 - 2.98917i) q^{9} +(-4.50267 + 3.16439i) q^{10} +2.55932i q^{11} +(-5.17603 - 4.75377i) q^{12} +(2.37097 + 2.37097i) q^{13} +4.53284 q^{14} +(-2.35953 - 3.07125i) q^{15} -4.34822 q^{16} +(-3.38670 - 3.38670i) q^{17} +(4.75890 - 5.64537i) q^{18} -4.69306i q^{19} +(-8.93768 - 1.56007i) q^{20} +(0.135528 + 3.18708i) q^{21} +(-4.45405 + 4.45405i) q^{22} +(0.268531 - 0.268531i) q^{23} +(-0.372638 - 8.76297i) q^{24} +(-4.70433 - 1.69389i) q^{25} +8.25253i q^{26} +(4.11159 + 3.17723i) q^{27} +(5.28405 + 5.28405i) q^{28} +5.68539 q^{29} +(1.23863 - 9.45135i) q^{30} +1.00000 q^{31} +(-0.405926 - 0.405926i) q^{32} +(-3.26485 - 2.99851i) q^{33} -11.7879i q^{34} +(2.36793 + 3.36937i) q^{35} +(12.1285 - 1.03338i) q^{36} +(-2.80395 + 2.80395i) q^{37} +(8.16747 - 8.16747i) q^{38} +(-5.80242 + 0.246743i) q^{39} +(-6.51068 - 9.26419i) q^{40} -3.76694i q^{41} +(-5.31070 + 5.78243i) q^{42} +(7.57956 + 7.57956i) q^{43} -10.3844 q^{44} +(6.68236 + 0.588304i) q^{45} +0.934666 q^{46} +(-2.85488 - 2.85488i) q^{47} +(5.09439 - 5.54691i) q^{48} +3.60805i q^{49} +(-5.23915 - 11.1350i) q^{50} +(8.28820 - 0.352449i) q^{51} +(-9.62017 + 9.62017i) q^{52} +(-3.33548 + 3.33548i) q^{53} +(1.62610 + 12.6849i) q^{54} +(-5.63757 - 0.984039i) q^{55} +9.32626i q^{56} +(5.98682 + 5.49842i) q^{57} +(9.89445 + 9.89445i) q^{58} +12.5260 q^{59} +(12.4616 - 9.57377i) q^{60} -7.79487 q^{61} +(1.74033 + 1.74033i) q^{62} +(-4.22446 - 3.56111i) q^{63} +7.28355i q^{64} +(-6.13430 + 4.31106i) q^{65} +(-0.463526 - 10.9003i) q^{66} +(-4.02116 + 4.02116i) q^{67} +(13.7415 - 13.7415i) q^{68} +(0.0279457 + 0.657171i) q^{69} +(-1.74285 + 9.98478i) q^{70} -1.18160i q^{71} +(11.6153 + 9.79137i) q^{72} +(3.86864 + 3.86864i) q^{73} -9.75960 q^{74} +(7.67247 - 4.01662i) q^{75} +19.0420 q^{76} +(3.33299 + 3.33299i) q^{77} +(-10.5275 - 9.66870i) q^{78} -4.46527i q^{79} +(1.67186 - 9.57809i) q^{80} +(-8.87027 + 1.52259i) q^{81} +(6.55571 - 6.55571i) q^{82} +(-4.02931 + 4.02931i) q^{83} +(-12.9315 + 0.549903i) q^{84} +(8.76226 - 6.15794i) q^{85} +26.3819i q^{86} +(-6.66103 + 7.25270i) q^{87} +(-9.16415 - 9.16415i) q^{88} -16.4656 q^{89} +(10.6057 + 12.6533i) q^{90} +6.17540 q^{91} +(1.08956 + 1.08956i) q^{92} +(-1.17160 + 1.27567i) q^{93} -9.93684i q^{94} +(10.3377 + 1.80445i) q^{95} +(0.993414 - 0.0422441i) q^{96} +(13.6813 - 13.6813i) q^{97} +(-6.27919 + 6.27919i) q^{98} +(7.65023 - 0.651818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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