LMFDB - Embedded newform 465.2.k.a.218.3

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			218.3
Character	$\chi$	$=$	465.218
Dual form			465.2.k.a.32.3

$q$-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} +(1.27567 - 1.17160i) 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} +(4.75377 + 5.17603i) q^{12} +(2.37097 + 2.37097i) q^{13} -4.53284 q^{14} +(-2.09028 - 3.26048i) q^{15} -4.34822 q^{16} +(3.38670 + 3.38670i) q^{17} +(-5.64537 + 4.75890i) 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} +(-3.17723 - 4.11159i) q^{27} +(5.28405 + 5.28405i) q^{28} -5.68539 q^{29} +(-2.03653 + 9.31208i) q^{30} +1.00000 q^{31} +(0.405926 + 0.405926i) q^{32} +(-2.99851 - 3.26485i) 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} +(-5.78243 + 5.31070i) q^{42} +(7.57956 + 7.57956i) q^{43} +10.3844 q^{44} +(-6.48651 - 1.71032i) q^{45} +0.934666 q^{46} +(2.85488 + 2.85488i) q^{47} +(-5.54691 + 5.09439i) 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} +(-5.49842 - 5.98682i) q^{57} +(9.89445 + 9.89445i) q^{58} -12.5260 q^{59} +(13.2293 - 8.48128i) q^{60} -7.79487 q^{61} +(-1.74033 - 1.74033i) q^{62} +(-3.56111 - 4.22446i) 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} +(-9.79137 - 11.6153i) q^{72} +(3.86864 + 3.86864i) q^{73} +9.75960 q^{74} +(-7.98576 + 3.35076i) q^{75} +19.0420 q^{76} +(-3.33299 - 3.33299i) q^{77} +(-9.66870 - 10.5275i) 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} +(-7.25270 + 6.66103i) q^{87} +(-9.16415 - 9.16415i) q^{88} +16.4656 q^{89} +(8.31213 + 14.2652i) q^{90} +6.17540 q^{91} +(-1.08956 - 1.08956i) q^{92} +(1.27567 - 1.17160i) 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	$-0.914013\pi$
$2$	−1.74033	−	1.74033i	−1.23060	−	1.23060i	−0.266864	−	0.963734i	$-0.585987\pi$
$3$	1.27567	−	1.17160i	0.736510	−	0.676426i
$3$	1.27567	−	1.17160i	0.736510	−	0.676426i
$4$			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	$-0.873915\pi$
$11$		−	2.55932i		−	0.771663i	0.922569	−	0.385832i	$-0.126085\pi$
$12$	4.75377	+	5.17603i	1.37230	+	1.49419i
$13$	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
$15$	−2.09028	−	3.26048i	−0.539708	−	0.841852i
$16$	−4.34822			−1.08705
$17$	3.38670	+	3.38670i	0.821396	+	0.821396i	0.986308	−	0.164913i	$-0.0527342\pi$
$17$	3.38670	+	3.38670i	0.821396	+	0.821396i	−0.164913	+	0.986308i	$0.552734\pi$
$18$	−5.64537	+	4.75890i	−1.33063	+	1.12168i
$19$		−	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	−0.734549	−	0.678556i	$-0.762606\pi$
$23$	−0.268531	+	0.268531i	−0.0559927	+	0.0559927i	0.678556	+	0.734549i	$0.262606\pi$
$24$	0.372638	−	8.76297i	0.0760644	−	1.78873i
$25$	−4.70433	−	1.69389i	−0.940866	−	0.338779i
$26$		−	8.25253i		−	1.61845i
$27$	−3.17723	−	4.11159i	−0.611458	−	0.791277i
$28$	5.28405	+	5.28405i	0.998591	+	0.998591i
$29$	−5.68539			−1.05575			−0.527875	−	0.849322i	$-0.677011\pi$
$29$	−5.68539			−1.05575			−0.527875	+	0.849322i	$0.677011\pi$
$30$	−2.03653	+	9.31208i	−0.371818	+	1.70015i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.405926	+	0.405926i	0.0717582	+	0.0717582i
$33$	−2.99851	−	3.26485i	−0.521973	−	0.568338i
$34$		−	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	$0.0950360\pi$
$41$			3.76694i			0.588297i	−0.955760	+	0.294148i	$0.904964\pi$
$42$	−5.78243	+	5.31070i	−0.892248	+	0.819459i
$43$	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
$45$	−6.48651	−	1.71032i	−0.966952	−	0.254960i
$46$	0.934666			0.137809
$47$	2.85488	+	2.85488i	0.416427	+	0.416427i	0.883970	−	0.467544i	$-0.154861\pi$
$47$	2.85488	+	2.85488i	0.416427	+	0.416427i	−0.467544	+	0.883970i	$0.654861\pi$
$48$	−5.54691	+	5.09439i	−0.800627	+	0.735312i
$49$			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	−0.439888	−	0.898052i	$-0.644982\pi$
$53$	3.33548	−	3.33548i	0.458164	−	0.458164i	0.898052	+	0.439888i	$0.144982\pi$
$54$	−1.62610	+	12.6849i	−0.221284	+	1.72620i
$55$	−5.63757	−	0.984039i	−0.760170	−	0.132688i
$56$		−	9.32626i		−	1.24627i
$57$	−5.49842	−	5.98682i	−0.728283	−	0.792973i
$58$	9.89445	+	9.89445i	1.29920	+	1.29920i
$59$	−12.5260			−1.63075			−0.815375	−	0.578933i	$-0.803469\pi$
$59$	−12.5260			−1.63075			−0.815375	+	0.578933i	$0.803469\pi$
$60$	13.2293	−	8.48128i	1.70790	−	1.09493i
$61$	−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
$63$	−3.56111	−	4.22446i	−0.448658	−	0.532232i
$64$			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	$0.0223367\pi$
$71$			1.18160i			0.140230i	−0.997539	+	0.0701152i	$0.977663\pi$
$72$	−9.79137	−	11.6153i	−1.15392	−	1.36887i
$73$	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
$75$	−7.98576	+	3.35076i	−0.922116	+	0.386913i
$76$	19.0420			2.18427
$77$	−3.33299	−	3.33299i	−0.379829	−	0.379829i
$78$	−9.66870	−	10.5275i	−1.09476	−	1.19201i
$79$		−	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	−0.450502	−	0.892776i	$-0.648755\pi$
$83$	4.02931	−	4.02931i	0.442274	−	0.442274i	0.892776	+	0.450502i	$0.148755\pi$
$84$	12.9315	+	0.549903i	1.41095	+	0.0599993i
$85$	8.76226	−	6.15794i	0.950401	−	0.667922i
$86$		−	26.3819i		−	2.84483i
$87$	−7.25270	+	6.66103i	−0.777571	+	0.714137i
$88$	−9.16415	−	9.16415i	−0.976901	−	0.976901i
$89$	16.4656			1.74535			0.872675	−	0.488301i	$-0.162383\pi$
$89$	16.4656			1.74535			0.872675	+	0.488301i	$0.162383\pi$
$90$	8.31213	+	14.2652i	0.876175	+	1.50368i
$91$	6.17540			0.647358
$92$	−1.08956	−	1.08956i	−0.113595	−	0.113595i
$93$	1.27567	−	1.17160i	0.132281	−	0.121490i
$94$		−	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	$0.375908\pi$
$101$			18.5916i			1.84993i	−0.380047	+	0.924967i	$0.624092\pi$
$102$	−13.8108	−	15.0376i	−1.36747	−	1.48894i
$103$	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
$105$	−6.96827	−	1.52395i	−0.680034	−	0.148722i
$106$	−11.6097			−1.12763
$107$	−1.86365	−	1.86365i	−0.180166	−	0.180166i	0.611262	−	0.791428i	$-0.290662\pi$
$107$	−1.86365	−	1.86365i	−0.180166	−	0.180166i	−0.791428	+	0.611262i	$0.790662\pi$
$108$	16.6827	−	12.8916i	1.60530	−	1.24049i
$109$		−	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	−0.954915	−	0.296879i	$-0.904054\pi$
$113$	−6.99502	+	6.99502i	−0.658036	+	0.658036i	0.296879	+	0.954915i	$0.404054\pi$
$114$	−0.849977	+	19.9881i	−0.0796076	+	1.87206i
$115$	0.488263	+	0.694759i	0.0455307	+	0.0647866i
$116$		−	23.0684i		−	2.14185i
$117$	7.69108	−	6.48338i	0.711040	−	0.599388i
$118$	21.7994	+	21.7994i	2.00680	+	2.00680i
$119$	8.82097			0.808617
$120$	−19.1595	−	4.19013i	−1.74901	−	0.382505i
$121$	4.44990			0.404536
$122$	13.5656	+	13.5656i	1.22818	+	1.22818i
$123$	4.41336	+	4.80538i	0.397940	+	0.433287i
$124$			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	$0.0618721\pi$
$131$			4.42153i			0.386311i	−0.981168	+	0.193155i	$0.938128\pi$
$132$	13.2471	−	12.1664i	1.15301	−	1.05895i
$133$	−6.11176	−	6.11176i	−0.529957	−	0.529957i
$134$	13.9963			1.20909
$135$	−10.2785	+	5.41781i	−0.884631	+	0.466291i
$136$	24.2535			2.07972
$137$	−14.4439	−	14.4439i	−1.23403	−	1.23403i	−0.962403	−	0.271625i	$-0.912439\pi$
$137$	−14.4439	−	14.4439i	−1.23403	−	1.23403i	−0.271625	−	0.962403i	$-0.587561\pi$
$138$	1.19233	−	1.09506i	0.101498	−	0.0932176i
$139$		−	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
$147$	4.22721	+	4.60269i	0.348654	+	0.379624i
$148$	−11.3770	−	11.3770i	−0.935184	−	0.935184i
$149$	9.91574			0.812329			0.406165	−	0.913800i	$-0.366866\pi$
$149$	9.91574			0.812329			0.406165	+	0.913800i	$0.366866\pi$
$150$	19.7293	+	8.06642i	1.61089	+	0.658620i
$151$	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
$153$	10.9860	−	9.26088i	0.888163	−	0.748698i
$154$			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
$162$	12.7874	+	18.0870i	1.00467	+	1.42105i
$163$	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
$165$	−8.34460	+	5.34969i	−0.649626	+	0.416473i
$166$	−14.0246			−1.08852
$167$	4.70977	+	4.70977i	0.364453	+	0.364453i	0.865449	−	0.500996i	$-0.167033\pi$
$167$	4.70977	+	4.70977i	0.364453	+	0.364453i	−0.500996	+	0.865449i	$0.667033\pi$
$168$	−10.9267	−	11.8973i	−0.843013	−	0.917894i
$169$		−	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	−0.615816	−	0.787890i	$-0.711173\pi$
$173$	2.26329	−	2.26329i	0.172074	−	0.172074i	0.787890	+	0.615816i	$0.211173\pi$
$174$	24.2145	+	1.02970i	1.83569	+	0.0780614i
$175$	−8.33238	+	3.92048i	−0.629869	+	0.296360i
$176$			11.1285i			0.838840i
$177$	−15.9791	+	14.6756i	−1.20106	+	1.10308i
$178$	−28.6556	−	28.6556i	−2.14782	−	2.14782i
$179$	1.55392			0.116145			0.0580725	−	0.998312i	$-0.481505\pi$
$179$	1.55392			0.116145			0.0580725	+	0.998312i	$0.481505\pi$
$180$	6.93961	−	26.3189i	0.517248	−	1.96170i
$181$	−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
$183$	−9.94371	+	9.13251i	−0.735060	+	0.675095i
$184$			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	$0.0716502\pi$
$191$			6.16936i			0.446399i	−0.974773	+	0.223200i	$0.928350\pi$
$192$	8.53344	+	9.29143i	0.615848	+	0.670551i
$193$	−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
$195$	2.77450	−	12.6865i	0.198686	−	0.908498i
$196$	−14.6396			−1.04569
$197$	10.2230	+	10.2230i	0.728359	+	0.728359i	0.970293	−	0.241934i	$-0.0777817\pi$
$197$	10.2230	+	10.2230i	0.728359	+	0.728359i	−0.241934	+	0.970293i	$0.577782\pi$
$198$	12.1795	+	14.4483i	0.865562	+	1.02680i
$199$			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
$207$	0.734295	+	0.871077i	0.0510370	+	0.0605440i
$208$	−10.3095	−	10.3095i	−0.714834	−	0.714834i
$209$	−12.0110			−0.830821
$210$	9.47492	+	14.7792i	0.653831	+	1.01986i
$211$	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
$213$	1.38437	+	1.50734i	0.0948555	+	0.103281i
$214$			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
$222$	12.4501	−	11.4344i	0.835593	−	0.767426i
$223$	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
$225$	−6.26145	+	13.6306i	−0.417430	+	0.908709i
$226$	24.3473			1.61956
$227$	4.46148	+	4.46148i	0.296119	+	0.296119i	0.839492	−	0.543373i	$-0.182853\pi$
$227$	4.46148	+	4.46148i	0.296119	+	0.296119i	−0.543373	+	0.839492i	$0.682853\pi$
$228$	24.2914	−	22.3097i	1.60874	−	1.47750i
$229$			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	−0.469351	−	0.883012i	$-0.655512\pi$
$233$	6.31425	−	6.31425i	0.413660	−	0.413660i	0.883012	+	0.469351i	$0.155512\pi$
$234$	−24.6682	−	2.10179i	−1.61261	−	0.137398i
$235$	7.38630	−	5.19094i	0.481829	−	0.338619i
$236$		−	50.8242i		−	3.30837i
$237$	−5.23154	−	5.69623i	−0.339825	−	0.370010i
$238$	−15.3514	−	15.3514i	−0.995083	−	0.995083i
$239$	−6.05585			−0.391720			−0.195860	−	0.980632i	$-0.562750\pi$
$239$	−6.05585			−0.391720			−0.195860	+	0.980632i	$0.562750\pi$
$240$	9.08900	+	14.1773i	0.586692	+	0.915139i
$241$	−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
$243$	−13.0994	+	8.45012i	−0.840330	+	0.542076i
$244$		−	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	$-0.996640\pi$
$251$		−	0.334433i		−	0.0211092i	0.999944	−	0.0105546i	$-0.00335970\pi$
$252$	17.1407	−	14.4491i	1.07976	−	0.910211i
$253$	0.687257	+	0.687257i	0.0432075	+	0.0432075i
$254$	−42.1195			−2.64281
$255$	3.96311	−	18.1214i	0.248180	−	1.13481i
$256$	−32.3787			−2.02367
$257$	21.6611	+	21.6611i	1.35118	+	1.35118i	0.884343	+	0.466838i	$0.154607\pi$
$257$	21.6611	+	21.6611i	1.35118	+	1.35118i	0.466838	+	0.884343i	$0.345393\pi$
$258$	−30.9091	−	33.6546i	−1.92432	−	2.09525i
$259$			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	−0.359370	−	0.933195i	$-0.617008\pi$
$263$	9.30589	−	9.30589i	0.573826	−	0.573826i	0.933195	+	0.359370i	$0.117008\pi$
$264$	−22.4272	−	0.953699i	−1.38030	−	0.0586961i
$265$	−6.06481	−	8.62975i	−0.372558	−	0.530121i
$266$			21.2729i			1.30433i
$267$	21.0047	−	19.2912i	1.28547	−	1.18060i
$268$	−16.3158	−	16.3158i	−0.996646	−	0.996646i
$269$	2.97259			0.181242			0.0906210	−	0.995885i	$-0.471115\pi$
$269$	2.97259			0.181242			0.0906210	+	0.995885i	$0.471115\pi$
$270$	27.3167	+	8.45918i	1.66244	+	0.514809i
$271$	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
$273$	7.87780	−	7.23513i	0.476786	−	0.437890i
$274$			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	$-0.855051\pi$
$281$		−	14.7446i		−	0.879591i	0.898098	−	0.439796i	$-0.144949\pi$
$282$	−11.6421	−	12.6762i	−0.693274	−	0.754855i
$283$	−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
$285$	−15.3016	+	9.80982i	−0.906391	+	0.581084i
$286$	−21.1208			−1.24890
$287$	4.90567	+	4.90567i	0.289572	+	0.289572i
$288$	1.31676	−	1.11000i	0.0775911	−	0.0654073i
$289$			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	−0.819439	−	0.573166i	$-0.805715\pi$
$293$	−4.21552	+	4.21552i	−0.246273	+	0.246273i	0.573166	+	0.819439i	$0.305715\pi$
$294$	0.653466	−	15.3669i	0.0381109	−	0.896218i
$295$	−4.81617	+	27.5919i	−0.280408	+	1.60646i
$296$			20.0802i			1.16714i
$297$	−10.5229	+	8.13154i	−0.610599	+	0.471840i
$298$	−17.2566	−	17.2566i	−0.999651	−	0.999651i
$299$	−1.27336			−0.0736402
$300$	−13.5957	−	32.4021i	−0.784946	−	1.87074i
$301$	19.7417			1.13789
$302$	−17.4227	−	17.4227i	−1.00256	−	1.00256i
$303$	21.7820	+	23.7168i	1.25134	+	1.36250i
$304$			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	$-0.930338\pi$
$311$		−	7.65741i		−	0.434212i	0.976148	−	0.217106i	$-0.0696618\pi$
$312$	21.6602	−	19.8932i	1.22627	−	1.12623i
$313$	−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
$315$	−10.6747	+	6.22001i	−0.601451	+	0.350458i
$316$	18.1178			1.01921
$317$	−8.97912	−	8.97912i	−0.504318	−	0.504318i	0.408459	−	0.912777i	$-0.366066\pi$
$317$	−8.97912	−	8.97912i	−0.504318	−	0.504318i	−0.912777	+	0.408459i	$0.866066\pi$
$318$	−14.8101	+	13.6019i	−0.830512	+	0.762759i
$319$			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
$327$	−21.8638	−	23.8058i	−1.20907	−	1.31647i
$328$	13.4883	+	13.4883i	0.744766	+	0.744766i
$329$	7.43579			0.409948
$330$	23.8326	+	5.21213i	1.31194	+	0.286918i
$331$	−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
$333$	7.66737	+	9.09562i	0.420169	+	0.498437i
$334$		−	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
$342$	22.3338	+	26.4941i	1.20768	+	1.43264i
$343$	13.8148	+	13.8148i	0.745930	+	0.745930i
$344$	54.2803			2.92660
$345$	1.43685	+	0.314235i	0.0773572	+	0.0169178i
$346$	−7.87772			−0.423509
$347$	16.8052	+	16.8052i	0.902153	+	0.902153i	0.995622	−	0.0934693i	$-0.0297957\pi$
$347$	16.8052	+	16.8052i	0.902153	+	0.902153i	−0.0934693	+	0.995622i	$0.529796\pi$
$348$	−27.0270	−	29.4277i	−1.44880	−	1.57749i
$349$			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	$0.510400\pi$
$353$	−19.3920	+	19.3920i	−1.03213	+	1.03213i	−0.999466	+	0.0326657i	$0.989600\pi$
$354$	53.3492	+	2.26863i	2.83548	+	0.120576i
$355$	2.60279	+	0.454317i	0.138142	+	0.0241127i
$356$			66.8089i			3.54087i
$357$	11.2527	−	10.3347i	0.595555	−	0.546970i
$358$	−2.70432	−	2.70432i	−0.142928	−	0.142928i
$359$	−2.35818			−0.124460			−0.0622300	−	0.998062i	$-0.519821\pi$
$359$	−2.35818			−0.124460			−0.0622300	+	0.998062i	$0.519821\pi$
$360$	−29.3504	+	17.1021i	−1.54690	+	0.901359i
$361$	−3.02486			−0.159203
$362$	21.7343	+	21.7343i	1.14233	+	1.14233i
$363$	5.67661	−	5.21352i	0.297945	−	0.273639i
$364$			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
$372$	4.75377	+	5.17603i	0.246471	+	0.268364i
$373$	−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
$375$	4.31047	+	18.8791i	0.222592	+	0.974912i
$376$	20.4449			1.05437
$377$	−13.4799	−	13.4799i	−0.694249	−	0.694249i
$378$	14.4019	+	18.6372i	0.740754	+	0.958595i
$379$			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	−0.000700330	−	1.00000i	$-0.500223\pi$
$383$	19.5567	−	19.5567i	0.999299	−	0.999299i	1.00000		0.000700330i	$0.000222922\pi$
$384$	1.40364	−	33.0079i	0.0716290	−	1.68443i
$385$	−8.62329	+	6.06027i	−0.439484	+	0.308860i
$386$			48.1261i			2.44956i
$387$	24.5870	−	20.7262i	1.24983	−	1.05357i
$388$	55.5116	+	55.5116i	2.81818	+	2.81818i
$389$	−31.6425			−1.60434			−0.802170	−	0.597095i	$-0.796321\pi$
$389$	−31.6425			−1.60434			−0.802170	+	0.597095i	$0.796321\pi$
$390$	−26.9072	+	17.2501i	−1.36250	+	0.873493i
$391$	−1.81887			−0.0919843
$392$	12.9194	+	12.9194i	0.652526	+	0.652526i
$393$	5.18028	+	5.64042i	0.261311	+	0.284522i
$394$		−	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	$0.00974312\pi$
$401$			1.22570i			0.0612083i	−0.999532	+	0.0306041i	$0.990257\pi$
$402$	17.8547	−	16.3981i	0.890510	−	0.817863i
$403$	2.37097	+	2.37097i	0.118106	+	0.118106i
$404$	−75.4352			−3.75304
$405$	−6.76446	+	18.9537i	−0.336129	+	0.941816i
$406$	25.7710			1.27899
$407$	7.17621	+	7.17621i	0.355711	+	0.355711i
$408$	30.9396	−	28.4155i	1.53174	−	1.40678i
$409$		−	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
$417$	−23.4768	−	25.5621i	−1.14966	−	1.25178i
$418$	20.9032	+	20.9032i	1.02241	+	1.02241i
$419$	−25.8945			−1.26503			−0.632514	−	0.774549i	$-0.717977\pi$
$419$	−25.8945			−1.26503			−0.632514	+	0.774549i	$0.717977\pi$
$420$	6.18339	−	28.2737i	0.301718	−	1.37961i
$421$	−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
$423$	9.26080	−	7.80662i	0.450276	−	0.379571i
$424$		−	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	$0.213084\pi$
$431$			25.7652i			1.24107i	−0.784180	+	0.620533i	$0.786916\pi$
$432$	13.8153	+	17.8781i	0.664689	+	0.860161i
$433$	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
$435$	11.8841	+	18.5371i	0.569797	+	0.888786i
$436$	75.7183			3.62625
$437$	1.26024	+	1.26024i	0.0602852	+	0.0602852i
$438$	−15.7761	−	17.1774i	−0.753812	−	0.820770i
$439$			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	−0.942877	−	0.333140i	$-0.891892\pi$
$443$	−12.8335	+	12.8335i	−0.609737	+	0.609737i	0.333140	+	0.942877i	$0.391892\pi$
$444$	−27.8427	−	1.18399i	−1.32136	−	0.0561895i
$445$	6.33090	−	36.2698i	0.300114	−	1.71935i
$446$		−	63.9887i		−	3.02995i
$447$	12.6492	−	11.6173i	0.598289	−	0.549481i
$448$	9.48533	+	9.48533i	0.448140	+	0.448140i
$449$	38.3820			1.81136			0.905679	−	0.423963i	$-0.139361\pi$
$449$	38.3820			1.81136			0.905679	+	0.423963i	$0.139361\pi$
$450$	34.6188	−	12.8248i	1.63194	−	0.604567i
$451$	9.64079			0.453967
$452$	−28.3822	−	28.3822i	−1.33499	−	1.33499i
$453$	12.7709	−	11.7291i	0.600031	−	0.551081i
$454$		−	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	$0.239853\pi$
$461$			29.3813i			1.36842i	−0.729284	+	0.684212i	$0.760147\pi$
$462$	13.5918	+	14.7991i	0.632346	+	0.688515i
$463$	−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
$465$	−2.09028	−	3.26048i	−0.0969344	−	0.151201i
$466$	−21.9777			−1.01810
$467$	−22.5049	−	22.5049i	−1.04140	−	1.04140i	−0.999105	−	0.0422999i	$-0.986532\pi$
$467$	−22.5049	−	22.5049i	−1.04140	−	1.04140i	−0.0422999	−	0.999105i	$-0.513468\pi$
$468$	26.3062	+	31.2064i	1.21601	+	1.44252i
$469$			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
$477$	−9.12083	−	10.8198i	−0.417614	−	0.495406i
$478$	10.5392	+	10.5392i	0.482050	+	0.482050i
$479$	−14.3792			−0.657004			−0.328502	−	0.944503i	$-0.606544\pi$
$479$	−14.3792			−0.657004			−0.328502	+	0.944503i	$0.606544\pi$
$480$	0.475014	−	2.17201i	0.0216813	−	0.0991383i
$481$	−13.2962			−0.606253
$482$	33.8002	+	33.8002i	1.53956	+	1.53956i
$483$	0.819437	+	0.892224i	0.0372857	+	0.0405976i
$484$			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	$-0.878939\pi$
$491$		−	16.4515i		−	0.742445i	0.928544	−	0.371223i	$-0.121061\pi$
$492$	−19.4978	+	17.9072i	−0.879027	+	0.807317i
$493$	−19.2547	−	19.2547i	−0.867189	−	0.867189i
$494$	−38.7296			−1.74253
$495$	−4.37726	+	16.6010i	−0.196743	+	0.746161i
$496$	−4.34822			−0.195241
$497$	1.53880	+	1.53880i	0.0690244	+	0.0690244i
$498$	−17.8909	+	16.4313i	−0.801708	+	0.736305i
$499$		−	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	−0.612628	−	0.790372i	$-0.709887\pi$
$503$	3.98638	−	3.98638i	0.177744	−	0.177744i	0.790372	+	0.612628i	$0.209887\pi$
$504$	−27.8778	−	2.37525i	−1.24178	−	0.105802i
$505$	40.9529	+	7.14834i	1.82238	+	0.318097i
$506$		−	2.39211i		−	0.106342i
$507$	−2.05853	−	2.24138i	−0.0914226	−	0.0995433i
$508$	49.0997	+	49.0997i	2.17845	+	2.17845i
$509$	−3.81193			−0.168961			−0.0844803	−	0.996425i	$-0.526923\pi$
$509$	−3.81193			−0.168961			−0.0844803	+	0.996425i	$0.526923\pi$
$510$	−38.4344	+	24.6401i	−1.70190	+	1.09108i
$511$	10.0762			0.445746
$512$	29.3743	+	29.3743i	1.29817	+	1.29817i
$513$	−19.2960	+	14.9110i	−0.851938	+	0.658335i
$514$		−	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	$-0.941931\pi$
$521$		−	8.28196i		−	0.362839i	0.983406	−	0.181420i	$-0.0580692\pi$
$522$	32.0961	−	27.0562i	1.40481	−	1.18422i
$523$	−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
$525$	−6.03614	+	14.7635i	−0.263439	+	0.644332i
$526$	−32.3906			−1.41230
$527$	3.38670	+	3.38670i	0.147527	+	0.147527i
$528$	13.0382	+	14.1963i	0.567413	+	0.617814i
$529$			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
$537$	1.98229	−	1.82057i	0.0855420	−	0.0785636i
$538$	−5.17328	−	5.17328i	−0.223036	−	0.223036i
$539$	9.23415			0.397743
$540$	−21.9827	−	41.7048i	−0.945984	−	1.79469i
$541$	−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
$543$	−15.9314	+	14.6317i	−0.683681	+	0.627907i
$544$			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
$552$	2.25307	+	2.45320i	0.0958969	+	0.104415i
$553$	−5.81511	−	5.81511i	−0.247284	−	0.247284i
$554$	26.7826			1.13789
$555$	15.0033	+	3.28118i	0.636854	+	0.139278i
$556$	81.3045			3.44808
$557$	−1.30891	−	1.30891i	−0.0554602	−	0.0554602i	0.678833	−	0.734293i	$-0.262486\pi$
$557$	−1.30891	−	1.30891i	−0.0554602	−	0.0554602i	−0.734293	+	0.678833i	$0.762486\pi$
$558$	−5.64537	+	4.75890i	−0.238988	+	0.201460i
$559$			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	$-0.398125\pi$
$563$	29.9878	−	29.9878i	1.26383	−	1.26383i	0.949219	−	0.314615i	$-0.101875\pi$
$564$	−1.20549	+	28.3483i	−0.0507603	+	1.19368i
$565$	12.7188	+	18.0979i	0.535086	+	0.761385i
$566$			36.0924i			1.51708i
$567$	−13.5346	+	9.56885i	−0.568399	+	0.401854i
$568$	4.23096	+	4.23096i	0.177527	+	0.177527i
$569$	−16.0104			−0.671189			−0.335595	−	0.942007i	$-0.608937\pi$
$569$	−16.0104			−0.671189			−0.335595	+	0.942007i	$0.608937\pi$
$570$	43.7022	+	9.55757i	1.83048	+	0.400322i
$571$	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
$573$	7.22805	+	7.87009i	0.301956	+	0.328778i
$574$		−	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
$582$	−60.7474	+	55.7917i	−2.51806	+	2.31264i
$583$	−8.53656	−	8.53656i	−0.353548	−	0.353548i
$584$	27.7049			1.14644
$585$	−11.3242	−	19.4344i	−0.468197	−	0.803515i
$586$	14.6728			0.606126
$587$	18.4221	+	18.4221i	0.760360	+	0.760360i	0.976387	−	0.216027i	$-0.0693100\pi$
$587$	18.4221	+	18.4221i	0.760360	+	0.760360i	−0.216027	+	0.976387i	$0.569310\pi$
$588$	−18.6754	+	17.1518i	−0.770159	+	0.707330i
$589$		−	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	−0.789321	−	0.613981i	$-0.789567\pi$
$593$	−4.26981	+	4.26981i	−0.175340	+	0.175340i	0.613981	+	0.789321i	$0.289567\pi$
$594$	32.4648	+	4.16170i	1.33205	+	0.170757i
$595$	3.39160	−	19.4305i	0.139042	−	0.796573i
$596$			40.2330i			1.64801i
$597$	3.73233	+	4.06386i	0.152754	+	0.166323i
$598$	2.21606	+	2.21606i	0.0906215	+	0.0906215i
$599$	−1.20371			−0.0491822			−0.0245911	−	0.999698i	$-0.507828\pi$
$599$	−1.20371			−0.0491822			−0.0245911	+	0.999698i	$0.507828\pi$
$600$	−16.5965	+	40.5927i	−0.677551	+	1.65719i
$601$	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
$603$	10.9958	+	13.0441i	0.447784	+	0.531195i
$604$			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
$612$	37.5759	+	44.5754i	1.51892	+	1.80185i
$613$	−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
$615$	12.2820	−	7.87396i	0.495259	−	0.317509i
$616$	−23.8689			−0.961704
$617$	−11.1982	−	11.1982i	−0.450824	−	0.450824i	0.444804	−	0.895628i	$-0.353273\pi$
$617$	−11.1982	−	11.1982i	−0.450824	−	0.450824i	−0.895628	+	0.444804i	$0.853273\pi$
$618$	−9.07752	−	9.88384i	−0.365152	−	0.397586i
$619$		−	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
$627$	−15.3222	+	14.0722i	−0.611908	+	0.561989i
$628$	−62.4408	−	62.4408i	−2.49166	−	2.49166i
$629$	−18.9923			−0.757273
$630$	29.4023	+	7.75263i	1.17142	+	0.308872i
$631$	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
$633$	11.7201	−	10.7640i	0.465834	−	0.427831i
$634$			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	$0.0286669\pi$
$641$			4.55409i			0.179876i	−0.995947	+	0.0899379i	$0.971333\pi$
$642$	7.59988	+	8.27495i	0.299943	+	0.326586i
$643$	−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
$645$	8.86960	−	40.5564i	0.349240	−	1.59691i
$646$	−55.3216			−2.17660
$647$	23.8541	+	23.8541i	0.937803	+	0.937803i	0.998176	−	0.0603727i	$-0.0192289\pi$
$647$	23.8541	+	23.8541i	0.937803	+	0.937803i	−0.0603727	+	0.998176i	$0.519229\pi$
$648$	−37.2137	+	26.3098i	−1.46189	+	1.03355i
$649$			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	−0.600839	−	0.799370i	$-0.705167\pi$
$653$	5.07325	−	5.07325i	0.198532	−	0.198532i	0.799370	+	0.600839i	$0.205167\pi$
$654$	−3.37982	+	79.4801i	−0.132162	+	3.10792i
$655$	9.73957	+	1.70004i	0.380557	+	0.0664262i
$656$		−	16.3795i		−	0.639511i
$657$	12.5493	−	10.5787i	0.489595	−	0.412716i
$658$	−12.9407	−	12.9407i	−0.504481	−	0.504481i
$659$	32.9568			1.28381			0.641907	−	0.766782i	$-0.278143\pi$
$659$	32.9568			1.28381			0.641907	+	0.766782i	$0.278143\pi$
$660$	−21.7063	−	33.8581i	−0.844916	−	1.31792i
$661$	−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
$663$	18.8154	+	20.4867i	0.730730	+	0.795638i
$664$		−	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
$672$	1.34873	−	1.23870i	0.0520285	−	0.0477840i
$673$	−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
$675$	7.98215	+	24.7242i	0.307233	+	0.951634i
$676$	7.12908			0.274195
$677$	−15.8295	−	15.8295i	−0.608377	−	0.608377i	0.334145	−	0.942522i	$-0.391552\pi$
$677$	−15.8295	−	15.8295i	−0.608377	−	0.608377i	−0.942522	+	0.334145i	$0.891552\pi$
$678$	31.0592	−	28.5254i	1.19282	−	1.09551i
$679$		−	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	−0.722385	−	0.691491i	$-0.756954\pi$
$683$	−0.807396	+	0.807396i	−0.0308941	+	0.0308941i	0.691491	+	0.722385i	$0.256954\pi$
$684$	4.84971	−	56.9199i	0.185433	−	2.17639i
$685$	−37.3701	+	26.2630i	−1.42784	+	1.00346i
$686$		−	48.0846i		−	1.83588i
$687$	8.24667	+	8.97919i	0.314630	+	0.342577i
$688$	−32.9576	−	32.9576i	−1.25650	−	1.25650i
$689$	15.8167			0.602566
$690$	−1.95371	−	3.04746i	−0.0743766	−	0.116015i
$691$	−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
$693$	−10.8117	+	9.11401i	−0.410704	+	0.346212i
$694$		−	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	$0.0227338\pi$
$701$			3.77870i			0.142719i	−0.997451	+	0.0713597i	$0.977266\pi$
$702$	−33.9310	+	26.2202i	−1.28064	+	0.989617i
$703$	13.1591	+	13.1591i	0.496306	+	0.496306i
$704$	18.6409			0.702556
$705$	3.34077	−	15.2758i	0.125821	−	0.575318i
$706$	67.4969			2.54028
$707$	24.2118	+	24.2118i	0.910578	+	0.910578i
$708$	−59.5458	−	64.8350i	−2.23787	−	2.43665i
$709$			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
$717$	−7.72528	+	7.09506i	−0.288506	+	0.264970i
$718$	4.10401	+	4.10401i	0.153160	+	0.153160i
$719$	4.30553			0.160569			0.0802845	−	0.996772i	$-0.474417\pi$
$719$	4.30553			0.160569			0.0802845	+	0.996772i	$0.474417\pi$
$720$	28.2048	+	7.43686i	1.05113	+	0.277155i
$721$	5.79782			0.215922
$722$	5.26425	+	5.26425i	0.195915	+	0.195915i
$723$	−24.7758	+	22.7546i	−0.921422	+	0.846253i
$724$		−	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
$732$	−37.0550	−	40.3465i	−1.36959	−	1.49125i
$733$	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
$735$	11.7640	−	7.54184i	0.433921	−	0.278185i
$736$	−0.218008			−0.00803587
$737$	10.2914	+	10.2914i	0.379089	+	0.379089i
$738$	−17.9265	−	21.2658i	−0.659883	−	0.782804i
$739$		−	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	−0.363104	−	0.931749i	$-0.618283\pi$
$743$	15.5001	−	15.5001i	0.568645	−	0.568645i	0.931749	+	0.363104i	$0.118283\pi$
$744$	0.372638	−	8.76297i	0.0136616	−	0.321266i
$745$	3.81253	−	21.8420i	0.139680	−	0.800230i
$746$			20.6007i			0.754247i
$747$	−11.0181	−	13.0705i	−0.403131	−	0.478224i
$748$	35.1688	+	35.1688i	1.28590	+	1.28590i
$749$	−4.85405			−0.177363
$750$	25.3542	−	40.3574i	0.925804	−	1.47365i
$751$	−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
$753$	−0.391823	−	0.426627i	−0.0142788	−	0.0155472i
$754$			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	$-0.949459\pi$
$761$		−	8.72350i		−	0.316226i	0.987421	−	0.158113i	$-0.0505411\pi$
$762$	−53.7307	+	49.3474i	−1.94646	+	1.78767i
$763$	−24.3026	−	24.3026i	−0.879815	−	0.879815i
$764$	−25.0321			−0.905629
$765$	−16.1755	−	27.7602i	−0.584827	−	1.00367i
$766$	−68.0701			−2.45947
$767$	−29.6988	−	29.6988i	−1.07236	−	1.07236i
$768$	−41.3046	+	37.9350i	−1.49045	+	1.36886i
$769$		−	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	−0.938309	−	0.345798i	$-0.887608\pi$
$773$	−16.4735	+	16.4735i	−0.592511	+	0.592511i	0.345798	+	0.938309i	$0.387608\pi$
$774$	−78.8599	−	6.71905i	−2.83456	−	0.241511i
$775$	−4.70433	−	1.69389i	−0.168985	−	0.0608464i
$776$		−	97.9772i		−	3.51718i
$777$	8.55641	+	9.31644i	0.306960	+	0.334225i
$778$	55.0684	+	55.0684i	1.97430	+	1.97430i
$779$	17.6785			0.633398
$780$	51.4752	+	11.2575i	1.84311	+	0.403084i
$781$	3.02409			0.108211
$782$	3.16543	+	3.16543i	0.113196	+	0.113196i
$783$	18.0638	+	23.3760i	0.645548	+	0.835391i
$784$		−	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
$792$	−29.7272	+	25.0592i	−1.05631	+	0.890441i
$793$	−18.4814	−	18.4814i	−0.656294	−	0.656294i
$794$	64.2648			2.28067
$795$	−17.8474	−	3.90318i	−0.632981	−	0.138431i
$796$	−12.9258			−0.458142
$797$	−26.6744	−	26.6744i	−0.944855	−	0.944855i	0.0537016	−	0.998557i	$-0.482898\pi$
$797$	−26.6744	−	26.6744i	−0.944855	−	0.944855i	−0.998557	+	0.0537016i	$0.982898\pi$
$798$	24.9235	+	27.1373i	0.882281	+	0.960650i
$799$			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
$807$	3.79205	−	3.48270i	0.133487	−	0.122597i
$808$	66.5710	+	66.5710i	2.34196	+	2.34196i
$809$	8.76972			0.308327			0.154163	−	0.988045i	$-0.450732\pi$
$809$	8.76972			0.308327			0.154163	+	0.988045i	$0.450732\pi$
$810$	44.7580	−	21.2132i	1.57264	−	0.745358i
$811$	−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
$813$	5.48417	−	5.03678i	0.192338	−	0.176648i
$814$		−	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	$0.259031\pi$
$821$			41.6548i			1.45376i	−0.686763	+	0.726881i	$0.740969\pi$
$822$	58.9017	+	64.1337i	2.05443	+	2.23692i
$823$	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
$825$	8.57566	+	20.4381i	0.298566	+	0.711563i
$826$	56.7785			1.97558
$827$	−27.5595	−	27.5595i	−0.958338	−	0.958338i	0.0408287	−	0.999166i	$-0.487000\pi$
$827$	−27.5595	−	27.5595i	−0.958338	−	0.958338i	−0.999166	+	0.0408287i	$0.987000\pi$
$828$	−3.53438	+	2.97939i	−0.122828	+	0.103541i
$829$			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
$837$	−3.17723	−	4.11159i	−0.109821	−	0.142117i
$838$	45.0649	+	45.0649i	1.55674	+	1.55674i
$839$	15.8726			0.547983			0.273991	−	0.961732i	$-0.411656\pi$
$839$	15.8726			0.547983			0.273991	+	0.961732i	$0.411656\pi$
$840$	−30.4081	+	19.4945i	−1.04918	+	0.672624i
$841$	3.32367			0.114609
$842$	19.9869	+	19.9869i	0.688795	+	0.688795i
$843$	−17.2749	−	18.8093i	−0.594979	−	0.647828i
$844$			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
$852$	−6.11600	+	5.61706i	−0.209531	+	0.192437i
$853$	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
$855$	−8.02666	+	30.4416i	−0.274506	+	1.04108i
$856$	−13.3463			−0.456169
$857$	14.1707	+	14.1707i	0.484061	+	0.484061i	0.906426	−	0.422365i	$-0.138800\pi$
$857$	14.1707	+	14.1707i	0.484061	+	0.484061i	−0.422365	+	0.906426i	$0.638800\pi$
$858$	−26.9433	+	24.7453i	−0.919828	+	0.844790i
$859$		−	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	−0.995421	−	0.0955929i	$-0.969525\pi$
$863$	−26.4341	+	26.4341i	−0.899828	+	0.899828i	0.0955929	+	0.995421i	$0.469525\pi$
$864$	0.379282	−	2.95872i	0.0129034	−	0.100658i
$865$	−4.11526	−	5.85570i	−0.139923	−	0.199100i
$866$		−	8.00054i		−	0.271869i
$867$	6.95874	+	7.57685i	0.236331	+	0.257323i
$868$	5.28405	+	5.28405i	0.179352	+	0.179352i
$869$	−11.4281			−0.387670
$870$	11.5785	−	52.9428i	0.392547	−	1.79493i
$871$	−19.0681			−0.646097
$872$	−66.8208	−	66.8208i	−2.26284	−	2.26284i
$873$	−37.4113	−	44.3801i	−1.26618	−	1.50204i
$874$		−	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	$-0.903909\pi$
$881$		−	17.6496i		−	0.594629i	0.954780	−	0.297315i	$-0.0960910\pi$
$882$	−17.1704	−	20.3688i	−0.578156	−	0.685853i
$883$	−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
$885$	26.1829	+	40.8409i	0.880129	+	1.37285i
$886$	44.6690			1.50068
$887$	33.6240	+	33.6240i	1.12898	+	1.12898i	0.990343	+	0.138639i	$0.0442729\pi$
$887$	33.6240	+	33.6240i	1.12898	+	1.12898i	0.138639	+	0.990343i	$0.455727\pi$
$888$	23.5261	+	25.6158i	0.789484	+	0.859611i
$889$		−	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
$897$	−1.62439	+	1.49187i	−0.0542368	+	0.0498122i
$898$	−66.7973	−	66.7973i	−2.22905	−	2.22905i
$899$	−5.68539			−0.189618
$900$	−55.3061	−	25.4058i	−1.84354	−	0.846859i
$901$	22.5926			0.752668
$902$	−16.7781	−	16.7781i	−0.558651	−	0.558651i
$903$	25.1839	−	23.1294i	0.838068	−	0.769699i
$904$			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	$0.00766580\pi$
$911$			1.45363i			0.0481610i	−0.999710	+	0.0240805i	$0.992334\pi$
$912$	23.9083	+	26.0320i	0.791683	+	0.862005i
$913$	−10.3123	−	10.3123i	−0.341286	−	0.341286i
$914$	−25.4919			−0.843197
$915$	16.2935	+	25.4150i	0.538646	+	0.840195i
$916$	−28.5598			−0.943641
$917$	5.75814	+	5.75814i	0.190150	+	0.190150i
$918$	−48.4672	+	37.4530i	−1.59966	+	1.23613i
$919$		−	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
$927$	7.22082	−	6.08696i	0.237163	−	0.199922i
$928$	−2.30785	−	2.30785i	−0.0757588	−	0.0757588i
$929$	34.5433			1.13333			0.566664	−	0.823949i	$-0.308234\pi$
$929$	34.5433			1.13333			0.566664	+	0.823949i	$0.308234\pi$
$930$	−2.03653	+	9.31208i	−0.0667805	+	0.305355i
$931$	16.9328			0.554951
$932$	25.6200	+	25.6200i	0.839210	+	0.839210i
$933$	−8.97146	−	9.76836i	−0.293713	−	0.319802i
$934$			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	$0.105007\pi$
$941$			19.8742i			0.647879i	−0.946078	+	0.323939i	$0.894993\pi$
$942$	68.3301	−	62.7558i	2.22632	−	2.04469i
$943$	−1.01154	−	1.01154i	−0.0329403	−	0.0329403i
$944$	54.4659			1.77271
$945$	−6.33004	+	20.4412i	−0.205916	+	0.664953i
$946$	−67.5195			−2.19525
$947$	16.6962	+	16.6962i	0.542555	+	0.542555i	0.924277	−	0.381722i	$-0.124669\pi$
$947$	16.6962	+	16.6962i	0.542555	+	0.542555i	−0.381722	+	0.924277i	$0.624669\pi$
$948$	23.1124	−	21.2269i	0.750655	−	0.689417i
$949$			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	−0.683123	−	0.730303i	$-0.739379\pi$
$953$	1.45649	−	1.45649i	0.0471804	−	0.0471804i	0.730303	+	0.683123i	$0.239379\pi$
$954$	−2.95680	+	34.7033i	−0.0957301	+	1.12356i
$955$	13.5896	+	2.37207i	0.439750	+	0.0767585i
$956$		−	24.5715i		−	0.794699i
$957$	17.0477	+	18.5620i	0.551074	+	0.600023i
$958$	25.0246	+	25.0246i	0.808508	+	0.808508i
$959$	−37.6205			−1.21483
$960$	23.7479	−	15.2247i	0.766459	−	0.491374i
$961$	1.00000			0.0322581
$962$	23.1397	+	23.1397i	0.746054	+	0.746054i
$963$	−6.04541	+	5.09612i	−0.194811	+	0.164220i
$964$		−	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	$-0.697025\pi$
$971$		−	50.7595i		−	1.62895i	0.580199	−	0.814475i	$-0.302975\pi$
$972$	−34.2863	−	53.1508i	−1.09973	−	1.70481i
$973$	−26.0956	−	26.0956i	−0.836587	−	0.836587i
$974$	34.4830			1.10491
$975$	−26.8785	−	10.9894i	−0.860802	−	0.351944i
$976$	33.8938			1.08491
$977$	−18.6011	−	18.6011i	−0.595101	−	0.595101i	0.343904	−	0.939005i	$-0.388251\pi$
$977$	−18.6011	−	18.6011i	−0.595101	−	0.595101i	−0.939005	+	0.343904i	$0.888251\pi$
$978$	−61.5585	−	67.0264i	−1.96842	−	2.14327i
$979$		−	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	−0.815982	−	0.578078i	$-0.803803\pi$
$983$	−7.45897	+	7.45897i	−0.237904	+	0.237904i	0.578078	+	0.815982i	$0.303803\pi$
$984$	33.0096	+	1.40370i	1.05231	+	0.0447485i
$985$	26.4495	−	18.5882i	0.842752	−	0.592269i
$986$			67.0191i			2.13432i
$987$	9.48563	−	8.71180i	0.301931	−	0.277300i
$988$	45.1481	+	45.1481i	1.43635	+	1.43635i
$989$	−4.07070			−0.129441
$990$	36.5091	−	21.2734i	1.16034	−	0.676112i
$991$	−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
$993$	−1.69275	+	1.55465i	−0.0537176	+	0.0493354i
$994$		−	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.218.3	yes	60
3.2	odd	2	inner	465.2.k.a.218.28	yes	60
5.2	odd	4	inner	465.2.k.a.32.28	yes	60
15.2	even	4	inner	465.2.k.a.32.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.3	✓	60	15.2	even	4	inner
465.2.k.a.32.28	yes	60	5.2	odd	4	inner
465.2.k.a.218.3	yes	60	1.1	even	1	trivial
465.2.k.a.218.28	yes	60	3.2	odd	2	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 $\F_{q}$
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} +(1.27567 - 1.17160i) 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} +(4.75377 + 5.17603i) q^{12} +(2.37097 + 2.37097i) q^{13} -4.53284 q^{14} +(-2.09028 - 3.26048i) q^{15} -4.34822 q^{16} +(3.38670 + 3.38670i) q^{17} +(-5.64537 + 4.75890i) 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} +(-3.17723 - 4.11159i) q^{27} +(5.28405 + 5.28405i) q^{28} -5.68539 q^{29} +(-2.03653 + 9.31208i) q^{30} +1.00000 q^{31} +(0.405926 + 0.405926i) q^{32} +(-2.99851 - 3.26485i) 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} +(-5.78243 + 5.31070i) q^{42} +(7.57956 + 7.57956i) q^{43} +10.3844 q^{44} +(-6.48651 - 1.71032i) q^{45} +0.934666 q^{46} +(2.85488 + 2.85488i) q^{47} +(-5.54691 + 5.09439i) 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} +(-5.49842 - 5.98682i) q^{57} +(9.89445 + 9.89445i) q^{58} -12.5260 q^{59} +(13.2293 - 8.48128i) q^{60} -7.79487 q^{61} +(-1.74033 - 1.74033i) q^{62} +(-3.56111 - 4.22446i) 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} +(-9.79137 - 11.6153i) q^{72} +(3.86864 + 3.86864i) q^{73} +9.75960 q^{74} +(-7.98576 + 3.35076i) q^{75} +19.0420 q^{76} +(-3.33299 - 3.33299i) q^{77} +(-9.66870 - 10.5275i) 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} +(-7.25270 + 6.66103i) q^{87} +(-9.16415 - 9.16415i) q^{88} +16.4656 q^{89} +(8.31213 + 14.2652i) q^{90} +6.17540 q^{91} +(-1.08956 - 1.08956i) q^{92} +(1.27567 - 1.17160i) 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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