LMFDB - Embedded newform 465.2.k.a.32.29

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			32.29
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.93363 - 1.93363i) q^{2} +(0.963170 + 1.43955i) q^{3} -5.47785i q^{4} +(1.96536 - 1.06648i) q^{5} +(4.64597 + 0.921141i) q^{6} +(1.12676 + 1.12676i) q^{7} +(-6.72487 - 6.72487i) q^{8} +(-1.14461 + 2.77306i) q^{9} +(1.73810 - 5.86244i) q^{10} +0.704412i q^{11} +(7.88564 - 5.27610i) q^{12} +(-4.82163 + 4.82163i) q^{13} +4.35746 q^{14} +(3.42822 + 1.80203i) q^{15} -15.0511 q^{16} +(-1.83808 + 1.83808i) q^{17} +(3.14883 + 7.57532i) q^{18} -1.74662i q^{19} +(-5.84200 - 10.7659i) q^{20} +(-0.536764 + 2.70728i) q^{21} +(1.36207 + 1.36207i) q^{22} +(-2.24021 - 2.24021i) q^{23} +(3.20359 - 16.1580i) q^{24} +(2.72526 - 4.19201i) q^{25} +18.6465i q^{26} +(-5.09441 + 1.02321i) q^{27} +(6.17221 - 6.17221i) q^{28} +4.83228 q^{29} +(10.1134 - 3.14445i) q^{30} +1.00000 q^{31} +(-15.6536 + 15.6536i) q^{32} +(-1.01404 + 0.678468i) q^{33} +7.10835i q^{34} +(3.41614 + 1.01282i) q^{35} +(15.1904 + 6.26998i) q^{36} +(-6.24498 - 6.24498i) q^{37} +(-3.37732 - 3.37732i) q^{38} +(-11.5850 - 2.29692i) q^{39} +(-20.3887 - 6.04486i) q^{40} +5.49292i q^{41} +(4.19698 + 6.27278i) q^{42} +(0.999538 - 0.999538i) q^{43} +3.85866 q^{44} +(0.707847 + 6.67075i) q^{45} -8.66347 q^{46} +(5.28289 - 5.28289i) q^{47} +(-14.4968 - 21.6669i) q^{48} -4.46084i q^{49} +(-2.83617 - 13.3754i) q^{50} +(-4.41640 - 0.875625i) q^{51} +(26.4122 + 26.4122i) q^{52} +(2.76712 + 2.76712i) q^{53} +(-7.87219 + 11.8292i) q^{54} +(0.751239 + 1.38442i) q^{55} -15.1546i q^{56} +(2.51435 - 1.68230i) q^{57} +(9.34383 - 9.34383i) q^{58} -1.42235 q^{59} +(9.87125 - 18.7793i) q^{60} +4.88455 q^{61} +(1.93363 - 1.93363i) q^{62} +(-4.41426 + 1.83488i) q^{63} +30.4342i q^{64} +(-4.33407 + 14.6184i) q^{65} +(-0.648863 + 3.27268i) q^{66} +(-6.87690 - 6.87690i) q^{67} +(10.0687 + 10.0687i) q^{68} +(1.06719 - 5.38260i) q^{69} +(8.56397 - 4.64713i) q^{70} +14.6338i q^{71} +(26.3458 - 10.9512i) q^{72} +(5.99532 - 5.99532i) q^{73} -24.1510 q^{74} +(8.65950 - 0.114483i) q^{75} -9.56774 q^{76} +(-0.793701 + 0.793701i) q^{77} +(-26.8425 + 17.9597i) q^{78} +11.7893i q^{79} +(-29.5809 + 16.0517i) q^{80} +(-6.37975 - 6.34813i) q^{81} +(10.6213 + 10.6213i) q^{82} +(8.42829 + 8.42829i) q^{83} +(14.8301 + 2.94031i) q^{84} +(-1.65222 + 5.57276i) q^{85} -3.86547i q^{86} +(4.65430 + 6.95630i) q^{87} +(4.73708 - 4.73708i) q^{88} +12.0272 q^{89} +(14.2675 + 11.5301i) q^{90} -10.8656 q^{91} +(-12.2715 + 12.2715i) q^{92} +(0.963170 + 1.43955i) q^{93} -20.4303i q^{94} +(-1.86273 - 3.43274i) q^{95} +(-37.6112 - 7.45704i) q^{96} +(0.0249208 + 0.0249208i) q^{97} +(-8.62561 - 8.62561i) q^{98} +(-1.95338 - 0.806274i) 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 $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.93363	−	1.93363i	1.36728	−	1.36728i	0.502992	−	0.864291i	$-0.332233\pi$
$2$	1.93363	−	1.93363i	1.36728	−	1.36728i	0.864291	−	0.502992i	$-0.167767\pi$
$3$	0.963170	+	1.43955i	0.556087	+	0.831124i
$3$	0.963170	+	1.43955i	0.556087	+	0.831124i
$4$		−	5.47785i		−	2.73892i
$5$	1.96536	−	1.06648i	0.878934	−	0.476943i
$5$	1.96536	−	1.06648i	0.878934	−	0.476943i
$6$	4.64597	+	0.921141i	1.89671	+	0.376054i
$7$	1.12676	+	1.12676i	0.425874	+	0.425874i	0.887220	−	0.461346i	$-0.152633\pi$
$7$	1.12676	+	1.12676i	0.425874	+	0.425874i	−0.461346	+	0.887220i	$0.652633\pi$
$8$	−6.72487	−	6.72487i	−2.37760	−	2.37760i
$9$	−1.14461	+	2.77306i	−0.381535	+	0.924354i
$10$	1.73810	−	5.86244i	0.549636	−	1.85387i
$11$			0.704412i			0.212388i	0.994345	+	0.106194i	$0.0338665\pi$
$11$			0.704412i			0.212388i	−0.994345	+	0.106194i	$0.966134\pi$
$12$	7.88564	−	5.27610i	2.27639	−	1.52308i
$13$	−4.82163	+	4.82163i	−1.33728	+	1.33728i	−0.438594	+	0.898685i	$0.644523\pi$
$13$	−4.82163	+	4.82163i	−1.33728	+	1.33728i	−0.898685	+	0.438594i	$0.855477\pi$
$14$	4.35746			1.16458
$15$	3.42822	+	1.80203i	0.885162	+	0.465282i
$16$	−15.0511			−3.76278
$17$	−1.83808	+	1.83808i	−0.445801	+	0.445801i	−0.893956	−	0.448155i	$-0.852081\pi$
$17$	−1.83808	+	1.83808i	−0.445801	+	0.445801i	0.448155	+	0.893956i	$0.352081\pi$
$18$	3.14883	+	7.57532i	0.742187	+	1.78552i
$19$		−	1.74662i		−	0.400703i	−0.979724	−	0.200351i	$-0.935792\pi$
$19$		−	1.74662i		−	0.400703i	0.979724	−	0.200351i	$-0.0642084\pi$
$20$	−5.84200	−	10.7659i	−1.30631	−	2.40734i
$21$	−0.536764	+	2.70728i	−0.117131	+	0.590777i
$22$	1.36207	+	1.36207i	0.290395	+	0.290395i
$23$	−2.24021	−	2.24021i	−0.467116	−	0.467116i	0.433863	−	0.900979i	$-0.357150\pi$
$23$	−2.24021	−	2.24021i	−0.467116	−	0.467116i	−0.900979	+	0.433863i	$0.857150\pi$
$24$	3.20359	−	16.1580i	0.653930	−	3.29824i
$25$	2.72526	−	4.19201i	0.545051	−	0.838403i
$26$			18.6465i			3.65688i
$27$	−5.09441	+	1.02321i	−0.980420	+	0.196918i
$28$	6.17221	−	6.17221i	1.16644	−	1.16644i
$29$	4.83228			0.897331			0.448665	−	0.893700i	$-0.351899\pi$
$29$	4.83228			0.897331			0.448665	+	0.893700i	$0.351899\pi$
$30$	10.1134	−	3.14445i	1.84644	−	0.574095i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−15.6536	+	15.6536i	−2.76719	+	2.76719i
$33$	−1.01404	+	0.678468i	−0.176521	+	0.118106i
$34$			7.10835i			1.21907i
$35$	3.41614	+	1.01282i	0.577433	+	0.171198i
$36$	15.1904	+	6.26998i	2.53174	+	1.04500i
$37$	−6.24498	−	6.24498i	−1.02667	−	1.02667i	−0.999635	−	0.0270342i	$-0.991394\pi$
$37$	−6.24498	−	6.24498i	−1.02667	−	1.02667i	−0.0270342	−	0.999635i	$-0.508606\pi$
$38$	−3.37732	−	3.37732i	−0.547874	−	0.547874i
$39$	−11.5850	−	2.29692i	−1.85509	−	0.367802i
$40$	−20.3887	−	6.04486i	−3.22374	−	0.955776i
$41$			5.49292i			0.857851i	0.903340	+	0.428925i	$0.141108\pi$
$41$			5.49292i			0.857851i	−0.903340	+	0.428925i	$0.858892\pi$
$42$	4.19698	+	6.27278i	0.647608	+	0.967912i
$43$	0.999538	−	0.999538i	0.152428	−	0.152428i	−0.626773	−	0.779202i	$-0.715625\pi$
$43$	0.999538	−	0.999538i	0.152428	−	0.152428i	0.779202	+	0.626773i	$0.215625\pi$
$44$	3.85866			0.581715
$45$	0.707847	+	6.67075i	0.105520	+	0.994417i
$46$	−8.66347			−1.27736
$47$	5.28289	−	5.28289i	0.770589	−	0.770589i	−0.207620	−	0.978209i	$-0.566572\pi$
$47$	5.28289	−	5.28289i	0.770589	−	0.770589i	0.978209	+	0.207620i	$0.0665718\pi$
$48$	−14.4968	−	21.6669i	−2.09243	−	3.12734i
$49$		−	4.46084i		−	0.637262i
$50$	−2.83617	−	13.3754i	−0.401095	−	1.89157i
$51$	−4.41640	−	0.875625i	−0.618420	−	0.122612i
$52$	26.4122	+	26.4122i	3.66271	+	3.66271i
$53$	2.76712	+	2.76712i	0.380094	+	0.380094i	0.871136	−	0.491042i	$-0.163384\pi$
$53$	2.76712	+	2.76712i	0.380094	+	0.380094i	−0.491042	+	0.871136i	$0.663384\pi$
$54$	−7.87219	+	11.8292i	−1.07127	+	1.60975i
$55$	0.751239	+	1.38442i	0.101297	+	0.186675i
$56$		−	15.1546i		−	2.02512i
$57$	2.51435	−	1.68230i	0.333034	−	0.222825i
$58$	9.34383	−	9.34383i	1.22691	−	1.22691i
$59$	−1.42235			−0.185175			−0.0925873	−	0.995705i	$-0.529514\pi$
$59$	−1.42235			−0.185175			−0.0925873	+	0.995705i	$0.529514\pi$
$60$	9.87125	−	18.7793i	1.27437	−	2.42439i
$61$	4.88455			0.625402			0.312701	−	0.949852i	$-0.398766\pi$
$61$	4.88455			0.625402			0.312701	+	0.949852i	$0.398766\pi$
$62$	1.93363	−	1.93363i	0.245571	−	0.245571i
$63$	−4.41426	+	1.83488i	−0.556145	+	0.231173i
$64$			30.4342i			3.80428i
$65$	−4.33407	+	14.6184i	−0.537575	+	1.81319i
$66$	−0.648863	+	3.27268i	−0.0798695	+	0.402839i
$67$	−6.87690	−	6.87690i	−0.840147	−	0.840147i	0.148730	−	0.988878i	$-0.452481\pi$
$67$	−6.87690	−	6.87690i	−0.840147	−	0.840147i	−0.988878	+	0.148730i	$0.952481\pi$
$68$	10.0687	+	10.0687i	1.22101	+	1.22101i
$69$	1.06719	−	5.38260i	0.128475	−	0.647988i
$70$	8.56397	−	4.64713i	1.02359	−	0.555439i
$71$			14.6338i			1.73671i	0.495941	+	0.868356i	$0.334823\pi$
$71$			14.6338i			1.73671i	−0.495941	+	0.868356i	$0.665177\pi$
$72$	26.3458	−	10.9512i	3.10489	−	1.29061i
$73$	5.99532	−	5.99532i	0.701699	−	0.701699i	−0.263076	−	0.964775i	$-0.584737\pi$
$73$	5.99532	−	5.99532i	0.701699	−	0.701699i	0.964775	+	0.263076i	$0.0847369\pi$
$74$	−24.1510			−2.80749
$75$	8.65950	−	0.114483i	0.999913	−	0.0132193i
$76$	−9.56774			−1.09749
$77$	−0.793701	+	0.793701i	−0.0904506	+	0.0904506i
$78$	−26.8425	+	17.9597i	−3.03932	+	2.03354i
$79$			11.7893i			1.32640i	0.748442	+	0.663201i	$0.230802\pi$
$79$			11.7893i			1.32640i	−0.748442	+	0.663201i	$0.769198\pi$
$80$	−29.5809	+	16.0517i	−3.30724	+	1.79463i
$81$	−6.37975	−	6.34813i	−0.708862	−	0.705348i
$82$	10.6213	+	10.6213i	1.17292	+	1.17292i
$83$	8.42829	+	8.42829i	0.925125	+	0.925125i	0.997386	−	0.0722611i	$-0.0230215\pi$
$83$	8.42829	+	8.42829i	0.925125	+	0.925125i	−0.0722611	+	0.997386i	$0.523021\pi$
$84$	14.8301	+	2.94031i	1.61809	+	0.320814i
$85$	−1.65222	+	5.57276i	−0.179208	+	0.604451i
$86$		−	3.86547i		−	0.416825i
$87$	4.65430	+	6.95630i	0.498994	+	0.745794i
$88$	4.73708	−	4.73708i	0.504975	−	0.504975i
$89$	12.0272			1.27488			0.637438	−	0.770501i	$-0.279994\pi$
$89$	12.0272			1.27488			0.637438	+	0.770501i	$0.279994\pi$
$90$	14.2675	+	11.5301i	1.50392	+	1.21537i
$91$	−10.8656			−1.13903
$92$	−12.2715	+	12.2715i	−1.27940	+	1.27940i
$93$	0.963170	+	1.43955i	0.0998761	+	0.149274i
$94$		−	20.4303i		−	2.10723i
$95$	−1.86273	−	3.43274i	−0.191112	−	0.352191i
$96$	−37.6112	−	7.45704i	−3.83867	−	0.761081i
$97$	0.0249208	+	0.0249208i	0.00253032	+	0.00253032i	0.708371	−	0.705840i	$-0.249430\pi$
$97$	0.0249208	+	0.0249208i	0.00253032	+	0.00253032i	−0.705840	+	0.708371i	$0.749430\pi$
$98$	−8.62561	−	8.62561i	−0.871318	−	0.871318i
$99$	−1.95338	−	0.806274i	−0.196322	−	0.0810336i
$100$	−22.9632	−	14.9285i	−2.29632	−	1.49285i
$101$		−	9.87984i		−	0.983081i	−0.870855	−	0.491541i	$-0.836434\pi$
$101$		−	9.87984i		−	0.983081i	0.870855	−	0.491541i	$-0.163566\pi$
$102$	−10.2328	+	6.84655i	−1.01320	+	0.677909i
$103$	−3.02060	+	3.02060i	−0.297629	+	0.297629i	−0.840085	−	0.542456i	$-0.817495\pi$
$103$	−3.02060	+	3.02060i	−0.297629	+	0.297629i	0.542456	+	0.840085i	$0.317495\pi$
$104$	64.8497			6.35904
$105$	1.83232	+	5.89322i	0.178816	+	0.575120i
$106$	10.7012			1.03939
$107$	−8.51336	+	8.51336i	−0.823018	+	0.823018i	−0.986540	−	0.163522i	$-0.947714\pi$
$107$	−8.51336	+	8.51336i	−0.823018	+	0.823018i	0.163522	+	0.986540i	$0.447714\pi$
$108$	5.60502	+	27.9064i	0.539343	+	2.68530i
$109$		−	12.2850i		−	1.17668i	−0.808612	−	0.588342i	$-0.799781\pi$
$109$		−	12.2850i		−	1.17668i	0.808612	−	0.588342i	$-0.200219\pi$
$110$	4.12957	+	1.22434i	0.393739	+	0.116736i
$111$	2.97498	−	15.0049i	0.282373	−	1.42421i
$112$	−16.9590	−	16.9590i	−1.60247	−	1.60247i
$113$	−0.541732	−	0.541732i	−0.0509619	−	0.0509619i	0.681167	−	0.732128i	$-0.261473\pi$
$113$	−0.541732	−	0.541732i	−0.0509619	−	0.0509619i	−0.732128	+	0.681167i	$0.761473\pi$
$114$	1.60889	−	8.11476i	0.150686	−	0.760017i
$115$	−6.79194	−	2.01368i	−0.633352	−	0.187777i
$116$		−	26.4705i		−	2.45772i
$117$	−7.85181	−	18.8895i	−0.725900	−	1.74634i
$118$	−2.75030	+	2.75030i	−0.253186	+	0.253186i
$119$	−4.14215			−0.379710
$120$	−10.9359	−	35.1728i	−0.998308	−	3.21082i
$121$	10.5038			0.954891
$122$	9.44490	−	9.44490i	0.855101	−	0.855101i
$123$	−7.90734	+	5.29062i	−0.712980	+	0.477039i
$124$		−	5.47785i		−	0.491925i
$125$	0.885415	−	11.1452i	0.0791939	−	0.996859i
$126$	−4.98758	+	12.0835i	−0.444329	+	1.07649i
$127$	−15.0880	−	15.0880i	−1.33884	−	1.33884i	−0.897182	−	0.441661i	$-0.854389\pi$
$127$	−15.0880	−	15.0880i	−1.33884	−	1.33884i	−0.441661	−	0.897182i	$-0.645611\pi$
$128$	27.5413	+	27.5413i	2.43433	+	2.43433i
$129$	2.40161	+	0.476159i	0.211450	+	0.0419235i
$130$	19.8860	+	36.6470i	1.74412	+	3.21416i
$131$		−	1.42034i		−	0.124096i	−0.998073	−	0.0620480i	$-0.980237\pi$
$131$		−	1.42034i		−	0.124096i	0.998073	−	0.0620480i	$-0.0197632\pi$
$132$	3.71655	+	5.55474i	0.323484	+	0.483478i
$133$	1.96802	−	1.96802i	0.170649	−	0.170649i
$134$	−26.5948			−2.29744
$135$	−8.92110	+	7.44405i	−0.767806	+	0.640682i
$136$	24.7218			2.11987
$137$	−2.82944	+	2.82944i	−0.241736	+	0.241736i	−0.817568	−	0.575832i	$-0.804678\pi$
$137$	−2.82944	+	2.82944i	−0.241736	+	0.241736i	0.575832	+	0.817568i	$0.304678\pi$
$138$	−8.34440	−	12.4715i	−0.710322	−	1.06164i
$139$			8.86933i			0.752286i	0.926562	+	0.376143i	$0.122750\pi$
$139$			8.86933i			0.752286i	−0.926562	+	0.376143i	$0.877250\pi$
$140$	5.54808	−	18.7131i	0.468898	−	1.58155i
$141$	12.6933	+	2.51666i	1.06897	+	0.211941i
$142$	28.2964	+	28.2964i	2.37458	+	2.37458i
$143$	−3.39641	−	3.39641i	−0.284022	−	0.284022i
$144$	17.2276	−	41.7378i	1.43564	−	3.47815i
$145$	9.49715	−	5.15351i	0.788695	−	0.427976i
$146$		−	23.1855i		−	1.91884i
$147$	6.42159	−	4.29654i	0.529644	−	0.354373i
$148$	−34.2091	+	34.2091i	−2.81197	+	2.81197i
$149$	2.80986			0.230192			0.115096	−	0.993354i	$-0.463282\pi$
$149$	2.80986			0.230192			0.115096	+	0.993354i	$0.463282\pi$
$150$	16.5229	−	16.9656i	1.34909	−	1.38524i
$151$	4.13581			0.336567			0.168284	−	0.985739i	$-0.446178\pi$
$151$	4.13581			0.336567			0.168284	+	0.985739i	$0.446178\pi$
$152$	−11.7458	+	11.7458i	−0.952712	+	0.952712i
$153$	−2.99324	−	7.20100i	−0.241989	−	0.582167i
$154$			3.06945i			0.247343i
$155$	1.96536	−	1.06648i	0.157861	−	0.0856615i
$156$	−12.5822	+	63.4610i	−1.00738	+	5.08095i
$157$	0.0365923	+	0.0365923i	0.00292038	+	0.00292038i	0.708565	−	0.705645i	$-0.249343\pi$
$157$	0.0365923	+	0.0365923i	0.00292038	+	0.00292038i	−0.705645	+	0.708565i	$0.749343\pi$
$158$	22.7962	+	22.7962i	1.81357	+	1.81357i
$159$	−1.31820	+	6.64862i	−0.104540	+	0.527270i
$160$	−14.0707	+	47.4591i	−1.11239	+	3.75197i
$161$		−	5.04835i		−	0.397865i
$162$	−24.6110	+	0.0611521i	−1.93362	+	0.00480456i
$163$	−11.4864	+	11.4864i	−0.899686	+	0.899686i	−0.995408	−	0.0957224i	$-0.969484\pi$
$163$	−11.4864	+	11.4864i	−0.899686	+	0.899686i	0.0957224	+	0.995408i	$0.469484\pi$
$164$	30.0894			2.34959
$165$	−1.26937	+	2.41488i	−0.0988204	+	0.187998i
$166$	32.5944			2.52981
$167$	7.54391	−	7.54391i	0.583765	−	0.583765i	−0.352171	−	0.935936i	$-0.614556\pi$
$167$	7.54391	−	7.54391i	0.583765	−	0.583765i	0.935936	+	0.352171i	$0.114556\pi$
$168$	21.8158	−	14.5965i	1.68313	−	1.12614i
$169$		−	33.4962i		−	2.57663i
$170$	7.58088	+	13.9704i	0.581427	+	1.07148i
$171$	4.84349	+	1.99920i	0.370391	+	0.152882i
$172$	−5.47532	−	5.47532i	−0.417489	−	0.417489i
$173$	2.95265	+	2.95265i	0.224486	+	0.224486i	0.810384	−	0.585899i	$-0.199258\pi$
$173$	2.95265	+	2.95265i	0.224486	+	0.224486i	−0.585899	+	0.810384i	$0.699258\pi$
$174$	22.4506	+	4.45121i	1.70198	+	0.337445i
$175$	7.79408	−	1.65268i	0.589177	−	0.124931i
$176$		−	10.6022i		−	0.799171i
$177$	−1.36997	−	2.04755i	−0.102973	−	0.153903i
$178$	23.2561	−	23.2561i	1.74312	−	1.74312i
$179$	−10.7325			−0.802185			−0.401092	−	0.916038i	$-0.631369\pi$
$179$	−10.7325			−0.802185			−0.401092	+	0.916038i	$0.631369\pi$
$180$	36.5414	−	3.87748i	2.72363	−	0.289010i
$181$	4.01997			0.298802			0.149401	−	0.988777i	$-0.452265\pi$
$181$	4.01997			0.298802			0.149401	+	0.988777i	$0.452265\pi$
$182$	−21.0101	+	21.0101i	−1.55737	+	1.55737i
$183$	4.70465	+	7.03155i	0.347778	+	0.519787i
$184$			30.1303i			2.22123i
$185$	−18.9337	−	5.61349i	−1.39204	−	0.412712i
$186$	4.64597	+	0.921141i	0.340659	+	0.0675414i
$187$	−1.29477	−	1.29477i	−0.0946828	−	0.0946828i
$188$	−28.9389	−	28.9389i	−2.11059	−	2.11059i
$189$	−6.89308	−	4.58725i	−0.501398	−	0.333673i
$190$	−10.2395	−	3.03581i	−0.742850	−	0.220241i
$191$		−	18.5014i		−	1.33872i	−0.742940	−	0.669358i	$-0.766569\pi$
$191$		−	18.5014i		−	1.33872i	0.742940	−	0.669358i	$-0.233431\pi$
$192$	−43.8115	+	29.3133i	−3.16183	+	2.11551i
$193$	4.56932	−	4.56932i	0.328907	−	0.328907i	−0.523264	−	0.852171i	$-0.675286\pi$
$193$	4.56932	−	4.56932i	0.328907	−	0.328907i	0.852171	+	0.523264i	$0.175286\pi$
$194$	0.0963751			0.00691933
$195$	−25.2183	+	7.84088i	−1.80592	+	0.561497i
$196$	−24.4358			−1.74541
$197$	−5.02143	+	5.02143i	−0.357762	+	0.357762i	−0.862987	−	0.505226i	$-0.831409\pi$
$197$	−5.02143	+	5.02143i	−0.357762	+	0.357762i	0.505226	+	0.862987i	$0.331409\pi$
$198$	−5.33615	+	2.21807i	−0.379223	+	0.157632i
$199$			3.15220i			0.223454i	0.993739	+	0.111727i	$0.0356381\pi$
$199$			3.15220i			0.223454i	−0.993739	+	0.111727i	$0.964362\pi$
$200$	−46.5178	+	9.86377i	−3.28930	+	0.697474i
$201$	3.27601	−	16.5233i	0.231072	−	1.16546i
$202$	−19.1040	−	19.1040i	−1.34415	−	1.34415i
$203$	5.44480	+	5.44480i	0.382150	+	0.382150i
$204$	−4.79654	+	24.1924i	−0.335825	+	1.69380i
$205$	5.85807	+	10.7956i	0.409146	+	0.753994i
$206$			11.6815i			0.813886i
$207$	8.77640	−	3.64808i	0.610002	−	0.253559i
$208$	72.5710	−	72.5710i	5.03189	−	5.03189i
$209$	1.23034			0.0851045
$210$	14.9383	+	7.85228i	1.03084	+	0.541859i
$211$	23.0125			1.58425			0.792124	−	0.610361i	$-0.208975\pi$
$211$	23.0125			1.58425			0.792124	+	0.610361i	$0.208975\pi$
$212$	15.1579	−	15.1579i	1.04105	−	1.04105i
$213$	−21.0661	+	14.0948i	−1.44342	+	0.965763i
$214$			32.9234i			2.25060i
$215$	0.898465	−	3.03043i	0.0612748	−	0.206674i
$216$	41.1403	+	27.3783i	2.79924	+	1.86286i
$217$	1.12676	+	1.12676i	0.0764893	+	0.0764893i
$218$	−23.7545	−	23.7545i	−1.60886	−	1.60886i
$219$	14.4051	+	2.85605i	0.973405	+	0.192994i
$220$	7.58365	−	4.11517i	0.511289	−	0.277445i
$221$		−	17.7251i		−	1.19232i
$222$	−23.2615	−	34.7665i	−1.56121	−	2.33338i
$223$	−9.93645	+	9.93645i	−0.665394	+	0.665394i	−0.956646	−	0.291252i	$-0.905928\pi$
$223$	−9.93645	+	9.93645i	−0.665394	+	0.665394i	0.291252	+	0.956646i	$0.405928\pi$
$224$	−35.2756			−2.35695
$225$	8.50537	+	12.3555i	0.567025	+	0.823701i
$226$	−2.09502			−0.139359
$227$	−1.51169	+	1.51169i	−0.100334	+	0.100334i	−0.755492	−	0.655158i	$-0.772602\pi$
$227$	−1.51169	+	1.51169i	−0.100334	+	0.100334i	0.655158	+	0.755492i	$0.272602\pi$
$228$	−9.21536	−	13.7732i	−0.610302	−	0.912155i
$229$		−	8.23863i		−	0.544424i	−0.962237	−	0.272212i	$-0.912245\pi$
$229$		−	8.23863i		−	0.544424i	0.962237	−	0.272212i	$-0.0877552\pi$
$230$	−17.0268	+	9.23939i	−1.12272	+	0.609227i
$231$	−1.90704	−	0.378103i	−0.125474	−	0.0248773i
$232$	−32.4964	−	32.4964i	−2.13350	−	2.13350i
$233$	1.85236	+	1.85236i	0.121352	+	0.121352i	0.765175	−	0.643823i	$-0.222652\pi$
$233$	1.85236	+	1.85236i	0.121352	+	0.121352i	−0.643823	+	0.765175i	$0.722652\pi$
$234$	−51.7079	−	21.3429i	−3.38025	−	1.39523i
$235$	4.74869	−	16.0169i	0.309770	−	1.04482i
$236$			7.79144i			0.507179i
$237$	−16.9713	+	11.3551i	−1.10240	+	0.737594i
$238$	−8.00938	+	8.00938i	−0.519171	+	0.519171i
$239$	−7.32482			−0.473803			−0.236902	−	0.971534i	$-0.576132\pi$
$239$	−7.32482			−0.473803			−0.236902	+	0.971534i	$0.576132\pi$
$240$	−51.5986	−	27.1226i	−3.33068	−	1.75076i
$241$	−19.7394			−1.27153			−0.635763	−	0.771884i	$-0.719314\pi$
$241$	−19.7394			−1.27153			−0.635763	+	0.771884i	$0.719314\pi$
$242$	20.3105	−	20.3105i	1.30561	−	1.30561i
$243$	2.99366	−	15.2983i	0.192043	−	0.981386i
$244$		−	26.7568i		−	1.71293i
$245$	−4.75738	−	8.76713i	−0.303938	−	0.560112i
$246$	−5.05976	+	25.5200i	−0.322598	+	1.62709i
$247$	8.42157	+	8.42157i	0.535852	+	0.535852i
$248$	−6.72487	−	6.72487i	−0.427030	−	0.427030i
$249$	−4.01506	+	20.2508i	−0.254444	+	1.28334i
$250$	−19.8387	−	23.2628i	−1.25471	−	1.47127i
$251$		−	18.6805i		−	1.17911i	−0.807730	−	0.589553i	$-0.799304\pi$
$251$		−	18.6805i		−	1.17911i	0.807730	−	0.589553i	$-0.200696\pi$
$252$	10.0512	+	24.1807i	0.633164	+	1.52324i
$253$	1.57803	−	1.57803i	0.0992099	−	0.0992099i
$254$	−58.3492			−3.66115
$255$	−9.61364	+	2.98907i	−0.602029	+	0.187183i
$256$	45.6410			2.85256
$257$	−10.4990	+	10.4990i	−0.654909	+	0.654909i	−0.954171	−	0.299262i	$-0.903259\pi$
$257$	−10.4990	+	10.4990i	−0.654909	+	0.654909i	0.299262	+	0.954171i	$0.403259\pi$
$258$	5.56454	−	3.72311i	0.346433	−	0.231791i
$259$		−	14.0732i		−	0.874464i
$260$	80.0773	+	23.7414i	4.96618	+	1.47238i
$261$	−5.53105	+	13.4002i	−0.342363	+	0.829452i
$262$	−2.74642	−	2.74642i	−0.169674	−	0.169674i
$263$	−2.04156	−	2.04156i	−0.125888	−	0.125888i	0.641356	−	0.767244i	$-0.278372\pi$
$263$	−2.04156	−	2.04156i	−0.125888	−	0.125888i	−0.767244	+	0.641356i	$0.778372\pi$
$264$	11.3819	+	2.25665i	0.700506	+	0.138887i
$265$	8.38946	+	2.48731i	0.515360	+	0.152794i
$266$		−	7.61085i		−	0.466651i
$267$	11.5842	+	17.3137i	0.708942	+	1.05958i
$268$	−37.6706	+	37.6706i	−2.30110	+	2.30110i
$269$	7.42815			0.452903			0.226451	−	0.974022i	$-0.427288\pi$
$269$	7.42815			0.452903			0.226451	+	0.974022i	$0.427288\pi$
$270$	−2.85607	+	31.6442i	−0.173815	+	1.92580i
$271$	−9.00413			−0.546962			−0.273481	−	0.961877i	$-0.588175\pi$
$271$	−9.00413			−0.546962			−0.273481	+	0.961877i	$0.588175\pi$
$272$	27.6652	−	27.6652i	1.67745	−	1.67745i
$273$	−10.4654	−	15.6416i	−0.633397	−	0.946672i
$274$			10.9422i			0.661042i
$275$	2.95290	+	1.91970i	0.178067	+	0.115762i
$276$	−29.4851	−	5.84590i	−1.77479	−	0.351882i
$277$	−4.37266	−	4.37266i	−0.262728	−	0.262728i	0.563434	−	0.826161i	$-0.309480\pi$
$277$	−4.37266	−	4.37266i	−0.262728	−	0.262728i	−0.826161	+	0.563434i	$0.809480\pi$
$278$	17.1500	+	17.1500i	1.02859	+	1.02859i
$279$	−1.14461	+	2.77306i	−0.0685258	+	0.166019i
$280$	−16.1620	−	29.7842i	−0.965866	−	1.77995i
$281$			30.7914i			1.83686i	0.395582	+	0.918431i	$0.370543\pi$
$281$			30.7914i			1.83686i	−0.395582	+	0.918431i	$0.629457\pi$
$282$	29.4105	−	19.6779i	1.75137	−	1.17180i
$283$	−12.0318	+	12.0318i	−0.715214	+	0.715214i	−0.967621	−	0.252407i	$-0.918778\pi$
$283$	−12.0318	+	12.0318i	−0.715214	+	0.715214i	0.252407	+	0.967621i	$0.418778\pi$
$284$	80.1618			4.75673
$285$	3.14747	−	5.98781i	0.186440	−	0.354687i
$286$	−13.1348			−0.776678
$287$	−6.18919	+	6.18919i	−0.365336	+	0.365336i
$288$	−25.4912	−	61.3256i	−1.50208	−	3.61364i
$289$			10.2429i			0.602523i
$290$	8.39899	−	28.3289i	0.493206	−	1.66353i
$291$	−0.0118717	+	0.0598776i	−0.000695933	+	0.00351009i
$292$	−32.8415	−	32.8415i	−1.92190	−	1.92190i
$293$	15.2115	+	15.2115i	0.888663	+	0.888663i	0.994395	−	0.105732i	$-0.0337185\pi$
$293$	15.2115	+	15.2115i	0.888663	+	0.888663i	−0.105732	+	0.994395i	$0.533719\pi$
$294$	4.10906	−	20.7249i	0.239645	−	1.20870i
$295$	−2.79543	+	1.51691i	−0.162756	+	0.0883177i
$296$			83.9934i			4.88202i
$297$	−0.720764	−	3.58856i	−0.0418230	−	0.208230i
$298$	5.43322	−	5.43322i	0.314738	−	0.314738i
$299$	21.6029			1.24933
$300$	−0.627120	−	47.4354i	−0.0362068	−	2.73869i
$301$	2.25247			0.129830
$302$	7.99712	−	7.99712i	0.460182	−	0.460182i
$303$	14.2225	−	9.51597i	0.817063	−	0.546678i
$304$			26.2887i			1.50776i
$305$	9.59988	−	5.20925i	0.549687	−	0.298281i
$306$	−19.7119	−	8.13626i	−1.12685	−	0.465119i
$307$	6.07251	+	6.07251i	0.346576	+	0.346576i	0.858833	−	0.512256i	$-0.171190\pi$
$307$	6.07251	+	6.07251i	0.346576	+	0.346576i	−0.512256	+	0.858833i	$0.671190\pi$
$308$	4.34778	+	4.34778i	0.247738	+	0.247738i
$309$	−7.25767	−	1.43895i	−0.412874	−	0.0818592i
$310$	1.73810	−	5.86244i	0.0987176	−	0.332964i
$311$			4.62811i			0.262436i	0.991354	+	0.131218i	$0.0418888\pi$
$311$			4.62811i			0.262436i	−0.991354	+	0.131218i	$0.958111\pi$
$312$	62.4613	+	93.3544i	3.53617	+	5.28515i
$313$	−13.9086	+	13.9086i	−0.786161	+	0.786161i	−0.980863	−	0.194701i	$-0.937626\pi$
$313$	−13.9086	+	13.9086i	−0.786161	+	0.786161i	0.194701	+	0.980863i	$0.437626\pi$
$314$	0.141512			0.00798598
$315$	−6.71875	+	8.31389i	−0.378559	+	0.468435i
$316$	64.5801			3.63291
$317$	−5.08343	+	5.08343i	−0.285514	+	0.285514i	−0.835303	−	0.549790i	$-0.814708\pi$
$317$	−5.08343	+	5.08343i	−0.285514	+	0.285514i	0.549790	+	0.835303i	$0.314708\pi$
$318$	10.3071	+	15.4049i	0.577991	+	0.863863i
$319$			3.40391i			0.190582i
$320$	32.4574	+	59.8141i	1.81442	+	3.34371i
$321$	−20.4552	−	4.05559i	−1.14170	−	0.226361i
$322$	−9.76163	−	9.76163i	−0.543994	−	0.543994i
$323$	3.21044	+	3.21044i	0.178634	+	0.178634i
$324$	−34.7741	+	34.9473i	−1.93189	+	1.94152i
$325$	7.07217	+	33.3525i	0.392293	+	1.85006i
$326$			44.4210i			2.46025i
$327$	17.6848	−	11.8325i	0.977971	−	0.654339i
$328$	36.9392	−	36.9392i	2.03963	−	2.03963i
$329$	11.9051			0.656348
$330$	2.21499	+	7.12397i	0.121931	+	0.392162i
$331$	−25.8277			−1.41962			−0.709809	−	0.704394i	$-0.751219\pi$
$331$	−25.8277			−1.41962			−0.709809	+	0.704394i	$0.751219\pi$
$332$	46.1689	−	46.1689i	2.53385	−	2.53385i
$333$	24.4658	−	10.1697i	1.34072	−	0.557295i
$334$		−	29.1743i		−	1.59634i
$335$	−20.8496	−	6.18151i	−1.13914	−	0.337732i
$336$	8.07891	−	40.7477i	0.440741	−	2.22297i
$337$	−11.2502	−	11.2502i	−0.612837	−	0.612837i	0.330848	−	0.943684i	$-0.392665\pi$
$337$	−11.2502	−	11.2502i	−0.612837	−	0.612837i	−0.943684	+	0.330848i	$0.892665\pi$
$338$	−64.7693	−	64.7693i	−3.52298	−	3.52298i
$339$	0.258070	−	1.30163i	0.0140164	−	0.0706949i
$340$	30.5268	+	9.05060i	1.65555	+	0.490838i
$341$			0.704412i			0.0381460i
$342$	13.2312	−	5.49982i	0.715463	−	0.297396i
$343$	12.9136	−	12.9136i	0.697268	−	0.697268i
$344$	−13.4435			−0.724827
$345$	−3.64300	−	11.7169i	−0.196133	−	0.630814i
$346$	11.4187			0.613871
$347$	−4.48313	+	4.48313i	−0.240667	+	0.240667i	−0.817126	−	0.576459i	$-0.804434\pi$
$347$	−4.48313	+	4.48313i	−0.240667	+	0.240667i	0.576459	+	0.817126i	$0.304434\pi$
$348$	38.1056	−	25.4956i	2.04267	−	1.36671i
$349$		−	31.3177i		−	1.67640i	−0.545365	−	0.838199i	$-0.683609\pi$
$349$		−	31.3177i		−	1.67640i	0.545365	−	0.838199i	$-0.316391\pi$
$350$	11.8752	−	18.2665i	0.634756	−	0.976388i
$351$	19.6298	−	29.4969i	1.04776	−	1.57443i
$352$	−11.0266	−	11.0266i	−0.587718	−	0.587718i
$353$	7.74450	+	7.74450i	0.412198	+	0.412198i	0.882504	−	0.470306i	$-0.155856\pi$
$353$	7.74450	+	7.74450i	0.412198	+	0.412198i	−0.470306	+	0.882504i	$0.655856\pi$
$354$	−6.60821	−	1.31019i	−0.351222	−	0.0696357i
$355$	15.6066	+	28.7606i	0.828313	+	1.52646i
$356$		−	65.8830i		−	3.49179i
$357$	−3.98959	−	5.96283i	−0.211152	−	0.315586i
$358$	−20.7527	+	20.7527i	−1.09681	+	1.09681i
$359$	−7.01325			−0.370145			−0.185073	−	0.982725i	$-0.559252\pi$
$359$	−7.01325			−0.370145			−0.185073	+	0.982725i	$0.559252\pi$
$360$	40.0998	−	49.6202i	2.11344	−	2.61521i
$361$	15.9493			0.839437
$362$	7.77313	−	7.77313i	0.408547	−	0.408547i
$363$	10.1170	+	15.1207i	0.531002	+	0.793633i
$364$			59.5202i			3.11971i
$365$	5.38908	−	18.1768i	0.282077	−	0.951418i
$366$	22.6935	+	4.49936i	1.18621	+	0.235185i
$367$	−7.10790	−	7.10790i	−0.371029	−	0.371029i	0.496823	−	0.867852i	$-0.334500\pi$
$367$	−7.10790	−	7.10790i	−0.371029	−	0.371029i	−0.867852	+	0.496823i	$0.834500\pi$
$368$	33.7177	+	33.7177i	1.75766	+	1.75766i
$369$	−15.2322	−	6.28723i	−0.792958	−	0.327300i
$370$	−47.4653	+	25.7564i	−2.46760	+	1.33901i
$371$			6.23575i			0.323744i
$372$	7.88564	−	5.27610i	0.408851	−	0.273553i
$373$	12.4652	−	12.4652i	0.645426	−	0.645426i	−0.306458	−	0.951884i	$-0.599144\pi$
$373$	12.4652	−	12.4652i	0.645426	−	0.645426i	0.951884	+	0.306458i	$0.0991440\pi$
$374$	−5.00720			−0.258916
$375$	16.8969	−	9.46015i	0.872553	−	0.488520i
$376$	−71.0536			−3.66431
$377$	−23.2994	+	23.2994i	−1.19998	+	1.19998i
$378$	−22.1987	+	4.45862i	−1.14178	+	0.229327i
$379$			22.8420i			1.17332i	0.809835	+	0.586658i	$0.199557\pi$
$379$			22.8420i			1.17332i	−0.809835	+	0.586658i	$0.800443\pi$
$380$	−18.8040	+	10.2038i	−0.964626	+	0.523442i
$381$	7.18761	−	36.2522i	0.368232	−	1.85726i
$382$	−35.7749	−	35.7749i	−1.83040	−	1.83040i
$383$	4.23470	+	4.23470i	0.216383	+	0.216383i	0.806972	−	0.590589i	$-0.201105\pi$
$383$	4.23470	+	4.23470i	0.216383	+	0.216383i	−0.590589	+	0.806972i	$0.701105\pi$
$384$	−13.1201	+	66.1741i	−0.669533	+	3.37693i
$385$	−0.713442	+	2.40637i	−0.0363604	+	0.122640i
$386$		−	17.6707i		−	0.899417i
$387$	1.62770	+	3.91586i	0.0827409	+	0.199054i
$388$	0.136512	−	0.136512i	0.00693036	−	0.00693036i
$389$	36.8239			1.86705			0.933524	−	0.358515i	$-0.116717\pi$
$389$	36.8239			1.86705			0.933524	+	0.358515i	$0.116717\pi$
$390$	−33.6015	+	63.9243i	−1.70148	+	3.23693i
$391$	8.23538			0.416481
$392$	−29.9986	+	29.9986i	−1.51516	+	1.51516i
$393$	2.04465	−	1.36803i	0.103139	−	0.0690081i
$394$			19.4192i			0.978323i
$395$	12.5730	+	23.1702i	0.632618	+	1.16582i
$396$	−4.41665	+	10.7003i	−0.221945	+	0.537711i
$397$	1.82340	+	1.82340i	0.0915136	+	0.0915136i	0.751382	−	0.659868i	$-0.229388\pi$
$397$	1.82340	+	1.82340i	0.0915136	+	0.0915136i	−0.659868	+	0.751382i	$0.729388\pi$
$398$	6.09519	+	6.09519i	0.305524	+	0.305524i
$399$	4.72860	+	0.937524i	0.236726	+	0.0469349i
$400$	−41.0182	+	63.0946i	−2.05091	+	3.15473i
$401$			13.9250i			0.695384i	0.937609	+	0.347692i	$0.113034\pi$
$401$			13.9250i			0.695384i	−0.937609	+	0.347692i	$0.886966\pi$
$402$	−25.6153	−	38.2845i	−1.27757	−	1.90946i
$403$	−4.82163	+	4.82163i	−0.240182	+	0.240182i
$404$	−54.1203			−2.69259
$405$	−19.3086	−	5.67248i	−0.959453	−	0.281868i
$406$	21.0565			1.04501
$407$	4.39904	−	4.39904i	0.218052	−	0.218052i
$408$	23.8113	+	35.5882i	1.17883	+	1.76188i
$409$		−	20.1681i		−	0.997248i	−0.866818	−	0.498624i	$-0.833839\pi$
$409$		−	20.1681i		−	0.997248i	0.866818	−	0.498624i	$-0.166161\pi$
$410$	32.2020	+	9.54726i	1.59034	+	0.471506i
$411$	−6.79836	−	1.34789i	−0.335338	−	0.0664864i
$412$	16.5464	+	16.5464i	0.815184	+	0.815184i
$413$	−1.60265	−	1.60265i	−0.0788611	−	0.0788611i
$414$	9.91626	−	24.0244i	0.487358	−	1.18073i
$415$	25.5532	+	7.57602i	1.25436	+	0.371892i
$416$		−	150.952i		−	7.40101i
$417$	−12.7678	+	8.54267i	−0.625244	+	0.418336i
$418$	2.37903	−	2.37903i	0.116362	−	0.116362i
$419$	−5.84177			−0.285389			−0.142695	−	0.989767i	$-0.545577\pi$
$419$	−5.84177			−0.285389			−0.142695	+	0.989767i	$0.545577\pi$
$420$	32.2822	−	10.0372i	1.57521	−	0.489764i
$421$	−4.63552			−0.225921			−0.112961	−	0.993599i	$-0.536033\pi$
$421$	−4.63552			−0.225921			−0.112961	+	0.993599i	$0.536033\pi$
$422$	44.4977	−	44.4977i	2.16611	−	2.16611i
$423$	8.60296	+	20.6966i	0.418290	+	1.00630i
$424$		−	37.2171i		−	1.80742i
$425$	2.69602	+	12.7145i	0.130776	+	0.616745i
$426$	−13.4798	+	67.9882i	−0.653098	+	3.29404i
$427$	5.50370	+	5.50370i	0.266343	+	0.266343i
$428$	46.6349	+	46.6349i	2.25418	+	2.25418i
$429$	1.61798	−	8.16063i	0.0781168	−	0.393999i
$430$	−4.12244	−	7.59703i	−0.198802	−	0.366362i
$431$			22.2597i			1.07221i	0.844151	+	0.536105i	$0.180105\pi$
$431$			22.2597i			1.07221i	−0.844151	+	0.536105i	$0.819895\pi$
$432$	76.6767	−	15.4005i	3.68911	−	0.740959i
$433$	−10.3136	+	10.3136i	−0.495638	+	0.495638i	−0.910077	−	0.414439i	$-0.863978\pi$
$433$	−10.3136	+	10.3136i	−0.495638	+	0.495638i	0.414439	+	0.910077i	$0.363978\pi$
$434$	4.35746			0.209165
$435$	16.5661	+	8.70791i	0.794284	+	0.417512i
$436$	−67.2951			−3.22285
$437$	−3.91280	+	3.91280i	−0.187175	+	0.187175i
$438$	33.3766	−	22.3316i	1.59480	−	1.06704i
$439$			18.3671i			0.876613i	0.898826	+	0.438307i	$0.144422\pi$
$439$			18.3671i			0.876613i	−0.898826	+	0.438307i	$0.855578\pi$
$440$	4.25807	−	14.3620i	0.202995	−	0.684683i
$441$	12.3702	+	5.10590i	0.589056	+	0.243138i
$442$	−34.2738	−	34.2738i	−1.63024	−	1.63024i
$443$	−14.0924	−	14.0924i	−0.669552	−	0.669552i	0.288060	−	0.957612i	$-0.406990\pi$
$443$	−14.0924	−	14.0924i	−0.669552	−	0.669552i	−0.957612	+	0.288060i	$0.906990\pi$
$444$	−82.1948	−	16.2965i	−3.90079	−	0.773397i
$445$	23.6377	−	12.8267i	1.12053	−	0.608043i
$446$			38.4268i			1.81956i
$447$	2.70637	+	4.04493i	0.128007	+	0.191319i
$448$	−34.2920	+	34.2920i	−1.62014	+	1.62014i
$449$	11.1950			0.528325			0.264163	−	0.964478i	$-0.414904\pi$
$449$	11.1950			0.528325			0.264163	+	0.964478i	$0.414904\pi$
$450$	40.3372	+	7.44474i	1.90152	+	0.350948i
$451$	−3.86928			−0.182197
$452$	−2.96753	+	2.96753i	−0.139581	+	0.139581i
$453$	3.98349	+	5.95370i	0.187160	+	0.279729i
$454$			5.84610i			0.274371i
$455$	−21.3548	+	11.5879i	−1.00113	+	0.543250i
$456$	−28.2219	−	5.59547i	−1.32161	−	0.262032i
$457$	21.3153	+	21.3153i	0.997087	+	0.997087i	0.999996	−	0.00290829i	$-0.000925739\pi$
$457$	21.3153	+	21.3153i	0.997087	+	0.997087i	−0.00290829	+	0.999996i	$0.500926\pi$
$458$	−15.9305	−	15.9305i	−0.744382	−	0.744382i
$459$	7.48320	−	11.2447i	0.349286	−	0.524858i
$460$	−11.0306	+	37.2052i	−0.514306	+	1.73470i
$461$		−	33.6981i		−	1.56948i	−0.619827	−	0.784738i	$-0.712797\pi$
$461$		−	33.6981i		−	1.56948i	0.619827	−	0.784738i	$-0.287203\pi$
$462$	−4.41862	+	2.95640i	−0.205573	+	0.137544i
$463$	9.27527	−	9.27527i	0.431058	−	0.431058i	−0.457930	−	0.888988i	$-0.651409\pi$
$463$	9.27527	−	9.27527i	0.431058	−	0.431058i	0.888988	+	0.457930i	$0.151409\pi$
$464$	−72.7312			−3.37646
$465$	3.42822	+	1.80203i	0.158980	+	0.0835671i
$466$	7.16357			0.331846
$467$	−18.2501	+	18.2501i	−0.844515	+	0.844515i	−0.989442	−	0.144927i	$-0.953705\pi$
$467$	−18.2501	+	18.2501i	−0.844515	+	0.844515i	0.144927	+	0.989442i	$0.453705\pi$
$468$	−103.474	+	43.0111i	−4.78309	+	1.98819i
$469$		−	15.4972i		−	0.715594i
$470$	−21.7885	−	40.1529i	−1.00503	−	1.85211i
$471$	−0.0174318	+	0.0879211i	−0.000803216	+	0.00405119i
$472$	9.56515	+	9.56515i	0.440272	+	0.440272i
$473$	0.704086	+	0.704086i	0.0323739	+	0.0323739i
$474$	−10.8596	+	54.7728i	−0.498799	+	2.51580i
$475$	−7.32187	−	4.75999i	−0.335950	−	0.218403i
$476$			22.6901i			1.04000i
$477$	−10.8407	+	4.50614i	−0.496360	+	0.206322i
$478$	−14.1635	+	14.1635i	−0.647823	+	0.647823i
$479$	32.4048			1.48061			0.740306	−	0.672270i	$-0.234681\pi$
$479$	32.4048			1.48061			0.740306	+	0.672270i	$0.234681\pi$
$480$	−81.8722	+	25.4557i	−3.73694	+	1.16189i
$481$	60.2220			2.74589
$482$	−38.1687	+	38.1687i	−1.73854	+	1.73854i
$483$	7.26734	−	4.86242i	0.330676	−	0.221248i
$484$		−	57.5383i		−	2.61538i
$485$	0.0755556	+	0.0224008i	0.00343080	+	0.00101717i
$486$	−23.7926	−	35.3699i	−1.07926	−	1.60441i
$487$	−10.1603	−	10.1603i	−0.460405	−	0.460405i	0.438383	−	0.898788i	$-0.355551\pi$
$487$	−10.1603	−	10.1603i	−0.460405	−	0.460405i	−0.898788	+	0.438383i	$0.855551\pi$
$488$	−32.8480	−	32.8480i	−1.48696	−	1.48696i
$489$	−27.5986	−	5.47189i	−1.24805	−	0.247447i
$490$	−26.1514	−	7.75339i	−1.18140	−	0.350262i
$491$			0.554814i			0.0250384i	0.999922	+	0.0125192i	$0.00398509\pi$
$491$			0.554814i			0.0250384i	−0.999922	+	0.0125192i	$0.996015\pi$
$492$	28.9812	+	43.3152i	1.30657	+	1.95280i
$493$	−8.88213	+	8.88213i	−0.400031	+	0.400031i
$494$	32.5684			1.46532
$495$	−4.69896	+	0.498616i	−0.211202	+	0.0224111i
$496$	−15.0511			−0.675816
$497$	−16.4887	+	16.4887i	−0.739621	+	0.739621i
$498$	31.3939	+	46.9212i	1.40680	+	2.10259i
$499$			7.71945i			0.345570i	0.984960	+	0.172785i	$0.0552766\pi$
$499$			7.71945i			0.345570i	−0.984960	+	0.172785i	$0.944723\pi$
$500$	−61.0519	−	4.85017i	−2.73032	−	0.216906i
$501$	18.1259	+	3.59376i	0.809806	+	0.160557i
$502$	−36.1213	−	36.1213i	−1.61217	−	1.61217i
$503$	18.6078	+	18.6078i	0.829681	+	0.829681i	0.987473	−	0.157791i	$-0.0504373\pi$
$503$	18.6078	+	18.6078i	0.829681	+	0.829681i	−0.157791	+	0.987473i	$0.550437\pi$
$504$	42.0247	+	17.3461i	1.87193	+	0.772655i
$505$	−10.5366	−	19.4174i	−0.468873	−	0.864064i
$506$		−	6.10265i		−	0.271296i
$507$	48.2195	−	32.2626i	2.14150	−	1.43283i
$508$	−82.6498	+	82.6498i	−3.66699	+	3.66699i
$509$	22.1578			0.982126			0.491063	−	0.871124i	$-0.336609\pi$
$509$	22.1578			0.982126			0.491063	+	0.871124i	$0.336609\pi$
$510$	−12.8095	+	24.3690i	−0.567212	+	1.07908i
$511$	13.5105			0.597671
$512$	33.1702	−	33.1702i	1.46593	−	1.46593i
$513$	1.78717	+	8.89802i	0.0789055	+	0.392857i
$514$			40.6023i			1.79089i
$515$	−2.71516	+	9.15797i	−0.119644	+	0.403548i
$516$	2.60833	−	13.1557i	0.114825	−	0.579146i
$517$	3.72133	+	3.72133i	0.163664	+	0.163664i
$518$	−27.2123	−	27.2123i	−1.19564	−	1.19564i
$519$	−1.40658	+	7.09439i	−0.0617421	+	0.311409i
$520$	127.453	−	69.1607i	5.58918	−	3.03290i
$521$		−	42.7144i		−	1.87135i	−0.352863	−	0.935675i	$-0.614792\pi$
$521$		−	42.7144i		−	1.87135i	0.352863	−	0.935675i	$-0.385208\pi$
$522$	15.2160	+	36.6060i	0.665987	+	1.60220i
$523$	3.75838	−	3.75838i	0.164343	−	0.164343i	−0.620145	−	0.784487i	$-0.712926\pi$
$523$	3.75838	−	3.75838i	0.164343	−	0.164343i	0.784487	+	0.620145i	$0.212926\pi$
$524$	−7.78043			−0.339889
$525$	9.88615	+	9.62816i	0.431467	+	0.420207i
$526$	−7.89525			−0.344249
$527$	−1.83808	+	1.83808i	−0.0800682	+	0.0800682i
$528$	15.2624	−	10.2117i	0.664210	−	0.444408i
$529$		−	12.9629i		−	0.563605i
$530$	21.0316	−	11.4126i	0.913556	−	0.495730i
$531$	1.62803	−	3.94427i	0.0706507	−	0.171167i
$532$	−10.7805	−	10.7805i	−0.467395	−	0.467395i
$533$	−26.4848	−	26.4848i	−1.14719	−	1.14719i
$534$	55.8778	+	11.0787i	2.41807	+	0.479423i
$535$	−7.65249	+	25.8111i	−0.330846	+	1.11591i
$536$			92.4926i			3.99507i
$537$	−10.3372	−	15.4500i	−0.446084	−	0.666715i
$538$	14.3633	−	14.3633i	0.619246	−	0.619246i
$539$	3.14227			0.135347
$540$	40.7774	+	48.8685i	1.75478	+	2.10296i
$541$	−19.5017			−0.838445			−0.419223	−	0.907883i	$-0.637697\pi$
$541$	−19.5017			−0.838445			−0.419223	+	0.907883i	$0.637697\pi$
$542$	−17.4107	+	17.4107i	−0.747852	+	0.747852i
$543$	3.87191	+	5.78694i	0.166160	+	0.248341i
$544$		−	57.5452i		−	2.46723i
$545$	−13.1016	−	24.1443i	−0.561211	−	1.03423i
$546$	−50.4813	−	10.0088i	−2.16040	−	0.428336i
$547$	8.53154	+	8.53154i	0.364782	+	0.364782i	0.865570	−	0.500788i	$-0.166956\pi$
$547$	8.53154	+	8.53154i	0.364782	+	0.364782i	−0.500788	+	0.865570i	$0.666956\pi$
$548$	15.4993	+	15.4993i	0.662096	+	0.662096i
$549$	−5.59088	+	13.5452i	−0.238613	+	0.578093i
$550$	9.42182	−	1.99783i	0.401748	−	0.0851878i
$551$		−	8.44016i		−	0.359563i
$552$	−43.3740	+	29.0206i	−1.84612	+	1.23520i
$553$	−13.2837	+	13.2837i	−0.564880	+	0.564880i
$554$	−16.9102			−0.718446
$555$	−10.1555	−	32.6628i	−0.431078	−	1.38646i
$556$	48.5848			2.06046
$557$	5.37770	−	5.37770i	0.227861	−	0.227861i	−0.583938	−	0.811798i	$-0.698489\pi$
$557$	5.37770	−	5.37770i	0.227861	−	0.227861i	0.811798	+	0.583938i	$0.198489\pi$
$558$	3.14883	+	7.57532i	0.133301	+	0.320689i
$559$			9.63880i			0.407678i
$560$	−51.4168	−	15.2441i	−2.17276	−	0.644181i
$561$	0.616801	−	3.11096i	0.0260413	−	0.131345i
$562$	59.5392	+	59.5392i	2.51151	+	2.51151i
$563$	10.1122	+	10.1122i	0.426178	+	0.426178i	0.887324	−	0.461146i	$-0.152562\pi$
$563$	10.1122	+	10.1122i	0.426178	+	0.426178i	−0.461146	+	0.887324i	$0.652562\pi$
$564$	13.7859	−	69.5321i	0.580491	−	2.92783i
$565$	−1.64244	−	0.486953i	−0.0690981	−	0.0204863i
$566$			46.5299i			1.95580i
$567$	−0.0356343	−	14.3412i	−0.00149650	−	0.602275i
$568$	98.4105	−	98.4105i	4.12921	−	4.12921i
$569$	3.27264			0.137196			0.0685982	−	0.997644i	$-0.478147\pi$
$569$	3.27264			0.137196			0.0685982	+	0.997644i	$0.478147\pi$
$570$	−5.49216	−	17.6642i	−0.230041	−	0.739874i
$571$	−16.4203			−0.687168			−0.343584	−	0.939122i	$-0.611641\pi$
$571$	−16.4203			−0.687168			−0.343584	+	0.939122i	$0.611641\pi$
$572$	−18.6050	+	18.6050i	−0.777916	+	0.777916i
$573$	26.6337	−	17.8200i	1.11264	−	0.744442i
$574$			23.9352i			0.999036i
$575$	−15.4961	+	3.28585i	−0.646233	+	0.137029i
$576$	−84.3960	−	34.8352i	−3.51650	−	1.45147i
$577$	16.2388	+	16.2388i	0.676029	+	0.676029i	0.959099	−	0.283070i	$-0.0913529\pi$
$577$	16.2388	+	16.2388i	0.676029	+	0.676029i	−0.283070	+	0.959099i	$0.591353\pi$
$578$	19.8060	+	19.8060i	0.823820	+	0.823820i
$579$	10.9788	+	2.17673i	0.456263	+	0.0904617i
$580$	−28.2301	−	52.0239i	−1.17219	−	2.16018i
$581$			18.9933i			0.787974i
$582$	0.0928256	+	0.138737i	0.00384775	+	0.00575082i
$583$	−1.94919	+	1.94919i	−0.0807274	+	0.0807274i
$584$	−80.6356			−3.33672
$585$	−35.5769	−	28.7509i	−1.47092	−	1.18870i
$586$	58.8267			2.43011
$587$	−6.59866	+	6.59866i	−0.272356	+	0.272356i	−0.830048	−	0.557692i	$-0.811687\pi$
$587$	−6.59866	+	6.59866i	−0.272356	+	0.272356i	0.557692	+	0.830048i	$0.311687\pi$
$588$	−23.5358	−	35.1765i	−0.970601	−	1.45066i
$589$		−	1.74662i		−	0.0719683i
$590$	−2.47219	+	8.33847i	−0.101779	+	0.343289i
$591$	−12.0651	−	2.39210i	−0.496291	−	0.0983980i
$592$	93.9941	+	93.9941i	3.86313	+	3.86313i
$593$	−9.33347	−	9.33347i	−0.383280	−	0.383280i	0.489003	−	0.872282i	$-0.337361\pi$
$593$	−9.33347	−	9.33347i	−0.383280	−	0.383280i	−0.872282	+	0.489003i	$0.837361\pi$
$594$	−8.33265	−	5.54526i	−0.341893	−	0.227525i
$595$	−8.14080	+	4.41750i	−0.333740	+	0.181100i
$596$		−	15.3920i		−	0.630480i
$597$	−4.53775	+	3.03611i	−0.185718	+	0.124260i
$598$	41.7721	−	41.7721i	1.70819	−	1.70819i
$599$	23.7487			0.970348			0.485174	−	0.874418i	$-0.338756\pi$
$599$	23.7487			0.970348			0.485174	+	0.874418i	$0.338756\pi$
$600$	−59.0039	−	57.4642i	−2.40882	−	2.34596i
$601$	−31.2501			−1.27472			−0.637360	−	0.770566i	$-0.719973\pi$
$601$	−31.2501			−1.27472			−0.637360	+	0.770566i	$0.719973\pi$
$602$	4.35545	−	4.35545i	0.177515	−	0.177515i
$603$	26.9414	−	11.1987i	1.09714	−	0.456048i
$604$		−	22.6553i		−	0.921832i
$605$	20.6437	−	11.2021i	0.839287	−	0.455429i
$606$	9.10073	−	45.9015i	0.369692	−	1.86462i
$607$	28.4393	+	28.4393i	1.15431	+	1.15431i	0.985679	+	0.168635i	$0.0539360\pi$
$607$	28.4393	+	28.4393i	1.15431	+	1.15431i	0.168635	+	0.985679i	$0.446064\pi$
$608$	27.3409	+	27.3409i	1.10882	+	1.10882i
$609$	−2.59379	+	13.0823i	−0.105106	+	0.530123i
$610$	8.48984	−	28.6354i	0.343744	−	1.15941i
$611$			50.9443i			2.06099i
$612$	−39.4460	+	16.3965i	−1.59451	+	0.662790i
$613$	−23.7604	+	23.7604i	−0.959673	+	0.959673i	−0.999218	−	0.0395446i	$-0.987409\pi$
$613$	−23.7604	+	23.7604i	−0.959673	+	0.959673i	0.0395446	+	0.999218i	$0.487409\pi$
$614$	23.4840			0.947736
$615$	−9.89841	+	18.8309i	−0.399143	+	0.759337i
$616$	10.6751			0.430111
$617$	27.8802	−	27.8802i	1.12242	−	1.12242i	0.131039	−	0.991377i	$-0.458169\pi$
$617$	27.8802	−	27.8802i	1.12242	−	1.12242i	0.991377	−	0.131039i	$-0.0418314\pi$
$618$	−16.8160	+	11.2512i	−0.676441	+	0.452591i
$619$			11.4690i			0.460980i	0.973075	+	0.230490i	$0.0740328\pi$
$619$			11.4690i			0.460980i	−0.973075	+	0.230490i	$0.925967\pi$
$620$	−5.84200	−	10.7659i	−0.234620	−	0.432370i
$621$	13.7048	+	9.12034i	0.549953	+	0.365986i
$622$	8.94906	+	8.94906i	0.358825	+	0.358825i
$623$	13.5517	+	13.5517i	0.542937	+	0.542937i
$624$	174.368	+	34.5713i	6.98030	+	1.38396i
$625$	−10.1460	−	22.8486i	−0.405839	−	0.913945i
$626$			53.7882i			2.14981i
$627$	1.18503	+	1.77114i	0.0473255	+	0.0707324i
$628$	0.200447	−	0.200447i	0.00799871	−	0.00799871i
$629$	22.9576			0.915379
$630$	3.08442	+	29.0676i	0.122886	+	1.15808i
$631$	−23.1740			−0.922543			−0.461272	−	0.887259i	$-0.652607\pi$
$631$	−23.1740			−0.922543			−0.461272	+	0.887259i	$0.652607\pi$
$632$	79.2817	−	79.2817i	3.15365	−	3.15365i
$633$	22.1650	+	33.1277i	0.880979	+	1.31671i
$634$			19.6589i			0.780756i
$635$	−45.7443	−	13.5623i	−1.81531	−	0.538204i
$636$	36.4202	+	7.22090i	1.44415	+	0.286327i
$637$	21.5085	+	21.5085i	0.852198	+	0.852198i
$638$	6.58191	+	6.58191i	0.260580	+	0.260580i
$639$	−40.5805	−	16.7499i	−1.60534	−	0.662617i
$640$	83.5007	+	24.7563i	3.30065	+	0.978581i
$641$			25.6636i			1.01365i	0.862049	+	0.506825i	$0.169181\pi$
$641$			25.6636i			1.01365i	−0.862049	+	0.506825i	$0.830819\pi$
$642$	−47.3948	+	31.7108i	−1.87052	+	1.25153i
$643$	8.93412	−	8.93412i	0.352327	−	0.352327i	−0.508648	−	0.860975i	$-0.669854\pi$
$643$	8.93412	−	8.93412i	0.352327	−	0.352327i	0.860975	+	0.508648i	$0.169854\pi$
$644$	−27.6541			−1.08972
$645$	5.22783	−	1.62544i	0.205846	−	0.0640015i
$646$	12.4156			0.488485
$647$	19.4396	−	19.4396i	0.764250	−	0.764250i	−0.212838	−	0.977088i	$-0.568271\pi$
$647$	19.4396	−	19.4396i	0.764250	−	0.764250i	0.977088	+	0.212838i	$0.0682705\pi$
$648$	0.212678	+	85.5934i	0.00835478	+	3.36243i
$649$		−	1.00192i		−	0.0393289i
$650$	78.1664	+	50.8165i	3.06594	+	1.99319i
$651$	−0.536764	+	2.70728i	−0.0210374	+	0.106107i
$652$	62.9209	+	62.9209i	2.46417	+	2.46417i
$653$	18.1468	+	18.1468i	0.710138	+	0.710138i	0.966564	−	0.256426i	$-0.0825451\pi$
$653$	18.1468	+	18.1468i	0.710138	+	0.710138i	−0.256426	+	0.966564i	$0.582545\pi$
$654$	11.3162	−	57.0755i	0.442497	−	2.23183i
$655$	−1.51476	−	2.79148i	−0.0591867	−	0.109072i
$656$		−	82.6748i		−	3.22791i
$657$	9.76312	+	23.4877i	0.380896	+	0.916342i
$658$	23.0200	−	23.0200i	0.897414	−	0.897414i
$659$	14.6325			0.570001			0.285001	−	0.958527i	$-0.408006\pi$
$659$	14.6325			0.570001			0.285001	+	0.958527i	$0.408006\pi$
$660$	13.2283	+	6.95343i	0.514912	+	0.270662i
$661$	−18.4216			−0.716516			−0.358258	−	0.933623i	$-0.616629\pi$
$661$	−18.4216			−0.716516			−0.358258	+	0.933623i	$0.616629\pi$
$662$	−49.9412	+	49.9412i	−1.94102	+	1.94102i
$663$	25.5162	−	17.0723i	0.990966	−	0.663033i
$664$		−	113.358i		−	4.39916i
$665$	1.76901	−	5.96671i	0.0685994	−	0.231379i
$666$	27.6433	−	66.9722i	1.07116	−	2.59512i
$667$	−10.8253	−	10.8253i	−0.419158	−	0.419158i
$668$	−41.3244	−	41.3244i	−1.59889	−	1.59889i
$669$	−23.8745	−	4.73352i	−0.923042	−	0.183008i
$670$	−52.2682	+	28.3627i	−2.01930	+	1.09575i
$671$			3.44073i			0.132828i
$672$	−33.9764	−	50.7809i	−1.31067	−	1.95892i
$673$	−21.6700	+	21.6700i	−0.835316	+	0.835316i	−0.988238	−	0.152922i	$-0.951132\pi$
$673$	−21.6700	+	21.6700i	−0.835316	+	0.835316i	0.152922	+	0.988238i	$0.451132\pi$
$674$	−43.5074			−1.67584
$675$	−9.59424	+	24.1444i	−0.369283	+	0.929317i
$676$	−183.487			−7.05720
$677$	6.96192	−	6.96192i	0.267568	−	0.267568i	−0.560551	−	0.828120i	$-0.689411\pi$
$677$	6.96192	−	6.96192i	0.267568	−	0.267568i	0.828120	+	0.560551i	$0.189411\pi$
$678$	−2.01786	−	3.01589i	−0.0774955	−	0.115824i
$679$			0.0561593i			0.00215520i
$680$	48.5871	−	26.3652i	1.86323	−	1.01106i
$681$	−3.63217	−	0.720138i	−0.139185	−	0.0275957i
$682$	1.36207	+	1.36207i	0.0521564	+	0.0521564i
$683$	−31.6521	−	31.6521i	−1.21114	−	1.21114i	−0.970654	−	0.240482i	$-0.922695\pi$
$683$	−31.6521	−	31.6521i	−1.21114	−	1.21114i	−0.240482	−	0.970654i	$-0.577305\pi$
$684$	10.9513	−	26.5319i	0.418733	−	1.01447i
$685$	−2.54333	+	8.57840i	−0.0971757	+	0.327764i
$686$		−	49.9402i		−	1.90672i
$687$	11.8599	−	7.93521i	0.452484	−	0.302747i
$688$	−15.0442	+	15.0442i	−0.573554	+	0.573554i
$689$	−26.6841			−1.01658
$690$	−29.7003	−	15.6118i	−1.13067	−	0.594333i
$691$	−43.8725			−1.66899			−0.834494	−	0.551018i	$-0.814240\pi$
$691$	−43.8725			−1.66899			−0.834494	+	0.551018i	$0.814240\pi$
$692$	16.1742	−	16.1742i	0.614850	−	0.614850i
$693$	−1.29251	−	3.10946i	−0.0490983	−	0.118119i
$694$			17.3374i			0.658119i
$695$	9.45893	+	17.4314i	0.358798	+	0.661210i
$696$	15.4806	−	78.0799i	0.586792	−	2.95961i
$697$	−10.0965	−	10.0965i	−0.382430	−	0.382430i
$698$	−60.5568	−	60.5568i	−2.29211	−	2.29211i
$699$	−0.882427	+	4.45071i	−0.0333765	+	0.168341i
$700$	−9.05314	−	42.6948i	−0.342176	−	1.61371i
$701$		−	27.8916i		−	1.05345i	−0.850036	−	0.526725i	$-0.823420\pi$
$701$		−	27.8916i		−	1.05345i	0.850036	−	0.526725i	$-0.176580\pi$
$702$	−19.0794	−	94.9929i	−0.720104	−	3.58528i
$703$	−10.9076	+	10.9076i	−0.411389	+	0.411389i
$704$	−21.4382			−0.807983
$705$	27.6309	−	8.59098i	1.04064	−	0.323555i
$706$	29.9500			1.12718
$707$	11.1322	−	11.1322i	0.418669	−	0.418669i
$708$	−11.2162	+	7.50448i	−0.421529	+	0.282036i
$709$			48.4320i			1.81890i	0.415813	+	0.909450i	$0.363497\pi$
$709$			48.4320i			1.81890i	−0.415813	+	0.909450i	$0.636503\pi$
$710$	85.7899	+	25.4350i	3.21964	+	0.954560i
$711$	−32.6925	−	13.4941i	−1.22606	−	0.506069i
$712$	−80.8811	−	80.8811i	−3.03115	−	3.03115i
$713$	−2.24021	−	2.24021i	−0.0838965	−	0.0838965i
$714$	−19.2443	−	3.81550i	−0.720200	−	0.142792i
$715$	−10.2974	−	3.05297i	−0.385099	−	0.114175i
$716$			58.7910i			2.19712i
$717$	−7.05505	−	10.5444i	−0.263476	−	0.393789i
$718$	−13.5610	+	13.5610i	−0.506093	+	0.506093i
$719$	−18.5941			−0.693441			−0.346721	−	0.937968i	$-0.612705\pi$
$719$	−18.5941			−0.693441			−0.346721	+	0.937968i	$0.612705\pi$
$720$	−10.6539	−	100.402i	−0.397048	−	3.74178i
$721$	−6.80698			−0.253505
$722$	30.8401	−	30.8401i	1.14775	−	1.14775i
$723$	−19.0124	−	28.4158i	−0.707079	−	1.05680i
$724$		−	22.0208i		−	0.818396i
$725$	13.1692	−	20.2570i	0.489091	−	0.752325i
$726$	48.8004	+	9.67549i	1.81115	+	0.359091i
$727$	7.52952	+	7.52952i	0.279254	+	0.279254i	0.832811	−	0.553557i	$-0.186730\pi$
$727$	7.52952	+	7.52952i	0.279254	+	0.279254i	−0.553557	+	0.832811i	$0.686730\pi$
$728$	73.0699	+	73.0699i	2.70815	+	2.70815i
$729$	24.9061	−	10.4254i	0.922447	−	0.386124i
$730$	−24.7268	−	45.5677i	−0.915178	−	1.68654i
$731$			3.67447i			0.135905i
$732$	38.5178	−	25.7714i	1.42366	−	0.952537i
$733$	25.9926	−	25.9926i	0.960058	−	0.960058i	−0.0391744	−	0.999232i	$-0.512473\pi$
$733$	25.9926	−	25.9926i	0.960058	−	0.960058i	0.999232	+	0.0391744i	$0.0124728\pi$
$734$	−27.4881			−1.01460
$735$	8.03856	−	15.2927i	0.296507	−	0.564081i
$736$	70.1346			2.58520
$737$	4.84417	−	4.84417i	0.178437	−	0.178437i
$738$	−41.6107	+	17.2963i	−1.53171	+	0.636686i
$739$		−	23.0919i		−	0.849449i	−0.905323	−	0.424724i	$-0.860371\pi$
$739$		−	23.0919i		−	0.849449i	0.905323	−	0.424724i	$-0.139629\pi$
$740$	−30.7499	+	103.716i	−1.13039	+	3.81268i
$741$	−4.01186	+	20.2347i	−0.147379	+	0.743339i
$742$	12.0576	+	12.0576i	0.442650	+	0.442650i
$743$	−21.8621	−	21.8621i	−0.802041	−	0.802041i	0.181373	−	0.983414i	$-0.441946\pi$
$743$	−21.8621	−	21.8621i	−0.802041	−	0.802041i	−0.983414	+	0.181373i	$0.941946\pi$
$744$	3.20359	−	16.1580i	0.117449	−	0.592381i
$745$	5.52237	−	2.99665i	0.202324	−	0.109789i
$746$		−	48.2063i		−	1.76496i
$747$	−33.0192	+	13.7251i	−1.20811	+	0.502175i
$748$	−7.09254	+	7.09254i	−0.259329	+	0.259329i
$749$	−19.1850			−0.701004
$750$	14.3799	−	50.9648i	0.525081	−	1.86097i
$751$	29.6285			1.08116			0.540580	−	0.841292i	$-0.318205\pi$
$751$	29.6285			1.08116			0.540580	+	0.841292i	$0.318205\pi$
$752$	−79.5136	+	79.5136i	−2.89956	+	2.89956i
$753$	26.8916	−	17.9925i	0.979983	−	0.655685i
$754$			90.1050i			3.28143i
$755$	8.12834	−	4.41074i	0.295820	−	0.160523i
$756$	−25.1283	+	37.7593i	−0.913907	+	1.37329i
$757$	−25.9551	−	25.9551i	−0.943354	−	0.943354i	0.0551252	−	0.998479i	$-0.482444\pi$
$757$	−25.9551	−	25.9551i	−0.943354	−	0.943354i	−0.998479	+	0.0551252i	$0.982444\pi$
$758$	44.1680	+	44.1680i	1.60425	+	1.60425i
$759$	3.79156	+	0.751741i	0.137625	+	0.0272865i
$760$	−10.5581	+	35.6114i	−0.382982	+	1.29176i
$761$			6.25906i			0.226891i	0.993544	+	0.113445i	$0.0361887\pi$
$761$			6.25906i			0.226891i	−0.993544	+	0.113445i	$0.963811\pi$
$762$	−56.2002	−	83.9966i	−2.03592	−	3.04287i
$763$	13.8422	−	13.8422i	0.501120	−	0.501120i
$764$	−101.348			−3.66664
$765$	−13.5625	−	10.9603i	−0.490353	−	0.396271i
$766$	16.3767			0.591714
$767$	6.85806	−	6.85806i	0.247630	−	0.247630i
$768$	43.9601	+	65.7025i	1.58627	+	2.37084i
$769$			12.0496i			0.434519i	0.976114	+	0.217259i	$0.0697117\pi$
$769$			12.0496i			0.434519i	−0.976114	+	0.217259i	$0.930288\pi$
$770$	3.27349	+	6.03256i	0.117969	+	0.217398i
$771$	−25.2261	−	5.00150i	−0.908497	−	0.180125i
$772$	−25.0300	−	25.0300i	−0.900851	−	0.900851i
$773$	−29.0226	−	29.0226i	−1.04387	−	1.04387i	−0.998992	−	0.0448789i	$-0.985710\pi$
$773$	−29.0226	−	29.0226i	−1.04387	−	1.04387i	−0.0448789	−	0.998992i	$-0.514290\pi$
$774$	10.7192	+	4.42444i	0.385294	+	0.159033i
$775$	2.72526	−	4.19201i	0.0978941	−	0.150582i
$776$		−	0.335178i		−	0.0120322i
$777$	20.2590	−	13.5548i	0.726788	−	0.486277i
$778$	71.2039	−	71.2039i	2.55278	−	2.55278i
$779$	9.59407			0.343743
$780$	42.9512	+	138.142i	1.53790	+	4.94628i
$781$	−10.3082			−0.368857
$782$	15.9242	−	15.9242i	0.569448	−	0.569448i
$783$	−24.6176	+	4.94445i	−0.879761	+	0.176700i
$784$			67.1407i			2.39788i
$785$	0.110942	+	0.0328921i	0.00395968	+	0.00117397i
$786$	1.30834	−	6.59887i	0.0466668	−	0.235374i
$787$	3.08781	+	3.08781i	0.110069	+	0.110069i	0.759996	−	0.649928i	$-0.225201\pi$
$787$	3.08781	+	3.08781i	0.110069	+	0.110069i	−0.649928	+	0.759996i	$0.725201\pi$
$788$	27.5066	+	27.5066i	0.979883	+	0.979883i
$789$	0.972558	−	4.90530i	0.0346240	−	0.174633i
$790$	69.1142	+	20.4910i	2.45897	+	0.729038i
$791$		−	1.22080i		−	0.0434067i
$792$	7.71413	+	18.5583i	0.274110	+	0.659441i
$793$	−23.5515	+	23.5515i	−0.836337	+	0.836337i
$794$	7.05155			0.250250
$795$	4.49987	+	14.4727i	0.159594	+	0.513295i
$796$	17.2673			0.612023
$797$	8.82182	−	8.82182i	0.312485	−	0.312485i	−0.533387	−	0.845872i	$-0.679081\pi$
$797$	8.82182	−	8.82182i	0.312485	−	0.312485i	0.845872	+	0.533387i	$0.179081\pi$
$798$	10.9562	−	7.33054i	0.387845	−	0.259498i
$799$			19.4208i			0.687058i
$800$	22.9600	+	108.280i	0.811760	+	3.82828i
$801$	−13.7664	+	33.3521i	−0.486410	+	1.17844i
$802$	26.9259	+	26.9259i	0.950786	+	0.950786i
$803$	4.22318	+	4.22318i	0.149033	+	0.149033i
$804$	−90.5120	−	17.9455i	−3.19211	−	0.632889i
$805$	−5.38394	−	9.92180i	−0.189759	−	0.349698i
$806$			18.6465i			0.656795i
$807$	7.15458	+	10.6932i	0.251853	+	0.376418i
$808$	−66.4407	+	66.4407i	−2.33738	+	2.33738i
$809$	21.9850			0.772950			0.386475	−	0.922300i	$-0.373693\pi$
$809$	21.9850			0.772950			0.386475	+	0.922300i	$0.373693\pi$
$810$	−48.3042	+	26.3673i	−1.69724	+	0.926451i
$811$	14.1952			0.498461			0.249230	−	0.968444i	$-0.419822\pi$
$811$	14.1952			0.498461			0.249230	+	0.968444i	$0.419822\pi$
$812$	29.8258	−	29.8258i	1.04668	−	1.04668i
$813$	−8.67251	−	12.9619i	−0.304158	−	0.454594i
$814$		−	17.0122i		−	0.596278i
$815$	−10.3249	+	34.8249i	−0.361666	+	1.21986i
$816$	66.4718	+	13.1792i	2.32698	+	0.461363i
$817$	−1.74582	−	1.74582i	−0.0610784	−	0.0610784i
$818$	−38.9976	−	38.9976i	−1.36352	−	1.36352i
$819$	12.4368	−	30.1310i	0.434578	−	1.05286i
$820$	59.1364	−	32.0896i	2.06513	−	1.12062i
$821$			29.1708i			1.01807i	0.860746	+	0.509034i	$0.169997\pi$
$821$			29.1708i			1.01807i	−0.860746	+	0.509034i	$0.830003\pi$
$822$	−15.7518	+	10.5392i	−0.549408	+	0.367597i
$823$	16.4285	−	16.4285i	0.572662	−	0.572662i	−0.360210	−	0.932871i	$-0.617295\pi$
$823$	16.4285	−	16.4285i	0.572662	−	0.572662i	0.932871	+	0.360210i	$0.117295\pi$
$824$	40.6264			1.41529
$825$	0.0806431	+	6.09985i	0.00280763	+	0.212370i
$826$	−6.19785			−0.215651
$827$	−19.1727	+	19.1727i	−0.666699	+	0.666699i	−0.956950	−	0.290252i	$-0.906261\pi$
$827$	−19.1727	+	19.1727i	−0.666699	+	0.666699i	0.290252	+	0.956950i	$0.406261\pi$
$828$	−19.9837	−	48.0758i	−0.694480	−	1.67075i
$829$		−	6.17333i		−	0.214409i	−0.994237	−	0.107204i	$-0.965810\pi$
$829$		−	6.17333i		−	0.214409i	0.994237	−	0.107204i	$-0.0341899\pi$
$830$	64.0596	−	34.7611i	2.22354	−	1.20658i
$831$	2.08305	−	10.5063i	0.0722600	−	0.364459i
$832$	−146.742	−	146.742i	−5.08738	−	5.08738i
$833$	8.19939	+	8.19939i	0.284092	+	0.284092i
$834$	−8.16990	+	41.2066i	−0.282901	+	1.42687i
$835$	6.78107	−	22.8719i	0.234669	−	0.791514i
$836$		−	6.73963i		−	0.233095i
$837$	−5.09441	+	1.02321i	−0.176089	+	0.0353675i
$838$	−11.2958	+	11.2958i	−0.390207	+	0.390207i
$839$	−42.1371			−1.45474			−0.727368	−	0.686248i	$-0.759257\pi$
$839$	−42.1371			−1.45474			−0.727368	+	0.686248i	$0.759257\pi$
$840$	27.3091	−	51.9533i	0.942252	−	1.79256i
$841$	−5.64912			−0.194797
$842$	−8.96338	+	8.96338i	−0.308899	+	0.308899i
$843$	−44.3258	+	29.6574i	−1.52666	+	1.02145i
$844$		−	126.059i		−	4.33913i
$845$	−35.7229	−	65.8320i	−1.22891	−	2.26469i
$846$	56.6546	+	23.3847i	1.94782	+	0.803982i
$847$	11.8352	+	11.8352i	0.406664	+	0.406664i
$848$	−41.6484	−	41.6484i	−1.43021	−	1.43021i
$849$	−28.9089	−	5.73168i	−0.992152	−	0.196711i
$850$	29.7983	+	19.3721i	1.02207	+	0.664456i
$851$			27.9801i			0.959147i
$852$	77.2094	+	115.397i	2.64515	+	3.95343i
$853$	−0.537052	+	0.537052i	−0.0183883	+	0.0183883i	−0.716241	−	0.697853i	$-0.754139\pi$
$853$	−0.537052	+	0.537052i	−0.0183883	+	0.0183883i	0.697853	+	0.716241i	$0.254139\pi$
$854$	21.2842			0.728331
$855$	11.6513	−	1.23634i	0.398466	−	0.0422820i
$856$	114.503			3.91362
$857$	21.3288	−	21.3288i	0.728579	−	0.728579i	−0.241758	−	0.970337i	$-0.577724\pi$
$857$	21.3288	−	21.3288i	0.728579	−	0.728579i	0.970337	+	0.241758i	$0.0777239\pi$
$858$	−12.6511	−	18.9082i	−0.431900	−	0.645516i
$859$			6.51296i			0.222219i	0.993808	+	0.111110i	$0.0354405\pi$
$859$			6.51296i			0.222219i	−0.993808	+	0.111110i	$0.964560\pi$
$860$	−16.6003	−	4.92166i	−0.566064	−	0.167827i
$861$	−14.8709	−	2.94840i	−0.506799	−	0.100481i
$862$	43.0419	+	43.0419i	1.46601	+	1.46601i
$863$	35.2927	+	35.2927i	1.20138	+	1.20138i	0.973747	+	0.227631i	$0.0730980\pi$
$863$	35.2927	+	35.2927i	1.20138	+	1.20138i	0.227631	+	0.973747i	$0.426902\pi$
$864$	63.7288	−	95.7628i	2.16810	−	3.25792i
$865$	8.95194	+	2.65408i	0.304375	+	0.0902414i
$866$			39.8852i			1.35536i
$867$	−14.7452	+	9.86566i	−0.500772	+	0.335055i
$868$	6.17221	−	6.17221i	0.209498	−	0.209498i
$869$	−8.30453			−0.281712
$870$	48.8706	−	15.1948i	1.65687	−	0.515153i
$871$	66.3157			2.24702
$872$	−82.6147	+	82.6147i	−2.79769	+	2.79769i
$873$	−0.0976313	+	0.0405824i	−0.00330432	+	0.00137351i
$874$			15.1318i			0.511841i
$875$	13.5556	−	11.5603i	0.458263	−	0.390810i
$876$	15.6450	−	78.9089i	0.528596	−	2.66608i
$877$	16.5377	+	16.5377i	0.558438	+	0.558438i	0.928863	−	0.370425i	$-0.120788\pi$
$877$	16.5377	+	16.5377i	0.558438	+	0.558438i	−0.370425	+	0.928863i	$0.620788\pi$
$878$	35.5151	+	35.5151i	1.19858	+	1.19858i
$879$	−7.24642	+	36.5489i	−0.244416	+	1.23276i
$880$	−11.3070	−	20.8371i	−0.381159	−	0.702419i
$881$		−	0.468258i		−	0.0157760i	−0.999969	−	0.00788800i	$-0.997489\pi$
$881$		−	0.468258i		−	0.0157760i	0.999969	−	0.00788800i	$-0.00251085\pi$
$882$	33.7923	−	14.0464i	1.13784	−	0.472968i
$883$	−1.46417	+	1.46417i	−0.0492734	+	0.0492734i	−0.731314	−	0.682041i	$-0.761093\pi$
$883$	−1.46417	+	1.46417i	−0.0492734	+	0.0492734i	0.682041	+	0.731314i	$0.261093\pi$
$884$	−97.0955			−3.26568
$885$	−4.87614	−	2.56312i	−0.163910	−	0.0861584i
$886$	−54.4991			−1.83093
$887$	−1.09095	+	1.09095i	−0.0366304	+	0.0366304i	−0.725185	−	0.688554i	$-0.758246\pi$
$887$	−1.09095	+	1.09095i	−0.0366304	+	0.0366304i	0.688554	+	0.725185i	$0.258246\pi$
$888$	−120.913	+	80.9000i	−4.05757	+	2.71483i
$889$		−	34.0010i		−	1.14036i
$890$	20.9044	−	70.5086i	0.700718	−	2.36345i
$891$	4.47170	−	4.49397i	0.149807	−	0.150554i
$892$	54.4304	+	54.4304i	1.82246	+	1.82246i
$893$	−9.22722	−	9.22722i	−0.308777	−	0.308777i
$894$	13.0545	+	2.58828i	0.436608	+	0.0865649i
$895$	−21.0932	+	11.4460i	−0.705068	+	0.382596i
$896$			62.0648i			2.07344i
$897$	20.8073	+	31.0985i	0.694735	+	1.03835i
$898$	21.6470	−	21.6470i	0.722370	−	0.722370i
$899$	4.83228			0.161165
$900$	67.6816	−	46.5912i	2.25605	−	1.55304i
$901$	−10.1724			−0.338892
$902$	−7.48176	+	7.48176i	−0.249115	+	0.249115i
$903$	2.16952	+	3.24255i	0.0721970	+	0.107905i
$904$			7.28617i			0.242334i
$905$	7.90067	−	4.28720i	0.262627	−	0.142511i
$906$	19.2148	+	3.80966i	0.638370	+	0.126568i
$907$	−11.6212	−	11.6212i	−0.385876	−	0.385876i	0.487338	−	0.873214i	$-0.337968\pi$
$907$	−11.6212	−	11.6212i	−0.385876	−	0.385876i	−0.873214	+	0.487338i	$0.837968\pi$
$908$	8.28081	+	8.28081i	0.274808	+	0.274808i
$909$	27.3974	+	11.3085i	0.908715	+	0.375080i
$910$	−18.8855	+	63.6990i	−0.626050	+	2.11160i
$911$			6.71279i			0.222405i	0.993798	+	0.111202i	$0.0354702\pi$
$911$			6.71279i			0.222405i	−0.993798	+	0.111202i	$0.964530\pi$
$912$	−37.8438	+	25.3205i	−1.25313	+	0.838444i
$913$	−5.93698	+	5.93698i	−0.196486	+	0.196486i
$914$	82.4318			2.72660
$915$	16.7453	+	8.80210i	0.553582	+	0.290988i
$916$	−45.1300			−1.49114
$917$	1.60038	−	1.60038i	0.0528493	−	0.0528493i
$918$	−7.27336	−	36.2128i	−0.240057	−	1.19520i
$919$		−	17.4804i		−	0.576624i	−0.957537	−	0.288312i	$-0.906906\pi$
$919$		−	17.4804i		−	0.576624i	0.957537	−	0.288312i	$-0.0930940\pi$
$920$	32.1332	+	59.2167i	1.05940	+	1.95232i
$921$	−2.89282	+	14.5905i	−0.0953216	+	0.480775i
$922$	−65.1596	−	65.1596i	−2.14592	−	2.14592i
$923$	−70.5588	−	70.5588i	−2.32247	−	2.32247i
$924$	−2.07119	+	10.4465i	−0.0681372	+	0.343664i
$925$	−43.1982	+	9.15988i	−1.42035	+	0.301175i
$926$		−	35.8699i		−	1.17876i
$927$	−4.91892	−	11.8337i	−0.161559	−	0.388671i
$928$	−75.6424	+	75.6424i	−2.48308	+	2.48308i
$929$	−20.7835			−0.681884			−0.340942	−	0.940084i	$-0.610746\pi$
$929$	−20.7835			−0.681884			−0.340942	+	0.940084i	$0.610746\pi$
$930$	10.1134	−	3.14445i	0.331630	−	0.103111i
$931$	−7.79140			−0.255353
$932$	10.1470	−	10.1470i	0.332375	−	0.332375i
$933$	−6.66240	+	4.45766i	−0.218117	+	0.145937i
$934$			70.5780i			2.30938i
$935$	−3.92552	−	1.16384i	−0.128378	−	0.0380617i
$936$	−74.2274	+	179.832i	−2.42620	+	5.87800i
$937$	15.0275	+	15.0275i	0.490927	+	0.490927i	0.908598	−	0.417671i	$-0.137153\pi$
$937$	15.0275	+	15.0275i	0.490927	+	0.490927i	−0.417671	+	0.908598i	$0.637153\pi$
$938$	−29.9659	−	29.9659i	−0.978420	−	0.978420i
$939$	−33.4185	−	6.62577i	−1.09057	−	0.216224i
$940$	−87.7379	−	26.0126i	−2.86170	−	0.848438i
$941$		−	3.71889i		−	0.121232i	−0.998161	−	0.0606162i	$-0.980693\pi$
$941$		−	3.71889i		−	0.121232i	0.998161	−	0.0606162i	$-0.0193066\pi$
$942$	0.136300	+	0.203714i	0.00444090	+	0.00663735i
$943$	12.3053	−	12.3053i	0.400716	−	0.400716i
$944$	21.4080			0.696772
$945$	−18.4396	−	1.66428i	−0.599839	−	0.0541390i
$946$	2.72288			0.0885286
$947$	−15.3124	+	15.3124i	−0.497586	+	0.497586i	−0.910686	−	0.413100i	$-0.864446\pi$
$947$	−15.3124	+	15.3124i	−0.497586	+	0.497586i	0.413100	+	0.910686i	$0.364446\pi$
$948$	62.2016	+	92.9662i	2.02021	+	3.01940i
$949$			57.8144i			1.87674i
$950$	−23.3619	+	4.95372i	−0.757959	+	0.160720i
$951$	−12.2141	−	2.42164i	−0.396068	−	0.0785270i
$952$	27.8554	+	27.8554i	0.902800	+	0.902800i
$953$	−23.4013	−	23.4013i	−0.758043	−	0.758043i	0.217923	−	0.975966i	$-0.430072\pi$
$953$	−23.4013	−	23.4013i	−0.758043	−	0.758043i	−0.975966	+	0.217923i	$0.930072\pi$
$954$	−12.2486	+	29.6751i	−0.396564	+	0.960765i
$955$	−19.7313	−	36.3619i	−0.638491	−	1.17664i
$956$			40.1243i			1.29771i
$957$	−4.90010	+	3.27855i	−0.158398	+	0.105980i
$958$	62.6588	−	62.6588i	2.02442	−	2.02442i
$959$	−6.37619			−0.205898
$960$	−54.8434	+	104.335i	−1.77006	+	3.36740i
$961$	1.00000			0.0322581
$962$	116.447	−	116.447i	3.75440	−	3.75440i
$963$	−13.8636	−	33.3525i	−0.446749	−	1.07477i
$964$			108.129i			3.48261i
$965$	4.10727	−	13.8534i	0.132218	−	0.445957i
$966$	4.65024	−	23.4545i	0.149619	−	0.754635i
$967$	13.5129	+	13.5129i	0.434545	+	0.434545i	0.890171	−	0.455626i	$-0.150585\pi$
$967$	13.5129	+	13.5129i	0.434545	+	0.434545i	−0.455626	+	0.890171i	$0.650585\pi$
$968$	−70.6368	−	70.6368i	−2.27035	−	2.27035i
$969$	−1.52939	+	7.71378i	−0.0491310	+	0.247802i
$970$	0.189411	−	0.102782i	0.00608163	−	0.00330012i
$971$		−	37.4937i		−	1.20323i	−0.798787	−	0.601614i	$-0.794524\pi$
$971$		−	37.4937i		−	1.20323i	0.798787	−	0.601614i	$-0.205476\pi$
$972$	−83.8018	−	16.3988i	−2.68794	−	0.525992i
$973$	−9.99358	+	9.99358i	−0.320379	+	0.320379i
$974$	−39.2924			−1.25901
$975$	−41.2009	+	42.3049i	−1.31948	+	1.35484i
$976$	−73.5180			−2.35325
$977$	6.09991	−	6.09991i	0.195153	−	0.195153i	−0.602765	−	0.797919i	$-0.705934\pi$
$977$	6.09991	−	6.09991i	0.195153	−	0.195153i	0.797919	+	0.602765i	$0.205934\pi$
$978$	−63.9462	+	42.7850i	−2.04477	+	1.36811i
$979$			8.47207i			0.270769i
$980$	−48.0250	+	26.0602i	−1.53410	+	0.832462i
$981$	34.0669	+	14.0614i	1.08767	+	0.448947i
$982$	1.07280	+	1.07280i	0.0342346	+	0.0342346i
$983$	19.8321	+	19.8321i	0.632546	+	0.632546i	0.948706	−	0.316160i	$-0.102394\pi$
$983$	19.8321	+	19.8321i	0.632546	+	0.632546i	−0.316160	+	0.948706i	$0.602394\pi$
$984$	88.7546	+	17.5971i	2.82939	+	0.560974i
$985$	−4.51366	+	15.2241i	−0.143817	+	0.485081i
$986$			34.3495i			1.09391i
$987$	11.4666	+	17.1379i	0.364986	+	0.545507i
$988$	46.1321	−	46.1321i	1.46766	−	1.46766i
$989$	−4.47835			−0.142403
$990$	−8.12191	+	10.0502i	−0.258131	+	0.319416i
$991$	−10.9125			−0.346647			−0.173323	−	0.984865i	$-0.555451\pi$
$991$	−10.9125			−0.346647			−0.173323	+	0.984865i	$0.555451\pi$
$992$	−15.6536	+	15.6536i	−0.497002	+	0.497002i
$993$	−24.8765	−	37.1802i	−0.789431	−	1.17988i
$994$			63.7663i			2.02254i
$995$	3.36175	+	6.19520i	0.106575	+	0.196401i
$996$	110.931	+	21.9939i	3.51498	+	0.696904i
$997$	−7.81551	−	7.81551i	−0.247520	−	0.247520i	0.572432	−	0.819952i	$-0.306000\pi$
$997$	−7.81551	−	7.81551i	−0.247520	−	0.247520i	−0.819952	+	0.572432i	$0.806000\pi$
$998$	14.9266	+	14.9266i	0.472492	+	0.472492i
$999$	38.2045	+	25.4246i	1.20874	+	0.804397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.32.29	yes	60
3.2	odd	2	inner	465.2.k.a.32.2	✓	60
5.3	odd	4	inner	465.2.k.a.218.2	yes	60
15.8	even	4	inner	465.2.k.a.218.29	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.2	✓	60	3.2	odd	2	inner
465.2.k.a.32.29	yes	60	1.1	even	1	trivial
465.2.k.a.218.2	yes	60	5.3	odd	4	inner
465.2.k.a.218.29	yes	60	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(1.93363 - 1.93363i) q^{2} +(0.963170 + 1.43955i) q^{3} -5.47785i q^{4} +(1.96536 - 1.06648i) q^{5} +(4.64597 + 0.921141i) q^{6} +(1.12676 + 1.12676i) q^{7} +(-6.72487 - 6.72487i) q^{8} +(-1.14461 + 2.77306i) q^{9} +(1.73810 - 5.86244i) q^{10} +0.704412i q^{11} +(7.88564 - 5.27610i) q^{12} +(-4.82163 + 4.82163i) q^{13} +4.35746 q^{14} +(3.42822 + 1.80203i) q^{15} -15.0511 q^{16} +(-1.83808 + 1.83808i) q^{17} +(3.14883 + 7.57532i) q^{18} -1.74662i q^{19} +(-5.84200 - 10.7659i) q^{20} +(-0.536764 + 2.70728i) q^{21} +(1.36207 + 1.36207i) q^{22} +(-2.24021 - 2.24021i) q^{23} +(3.20359 - 16.1580i) q^{24} +(2.72526 - 4.19201i) q^{25} +18.6465i q^{26} +(-5.09441 + 1.02321i) q^{27} +(6.17221 - 6.17221i) q^{28} +4.83228 q^{29} +(10.1134 - 3.14445i) q^{30} +1.00000 q^{31} +(-15.6536 + 15.6536i) q^{32} +(-1.01404 + 0.678468i) q^{33} +7.10835i q^{34} +(3.41614 + 1.01282i) q^{35} +(15.1904 + 6.26998i) q^{36} +(-6.24498 - 6.24498i) q^{37} +(-3.37732 - 3.37732i) q^{38} +(-11.5850 - 2.29692i) q^{39} +(-20.3887 - 6.04486i) q^{40} +5.49292i q^{41} +(4.19698 + 6.27278i) q^{42} +(0.999538 - 0.999538i) q^{43} +3.85866 q^{44} +(0.707847 + 6.67075i) q^{45} -8.66347 q^{46} +(5.28289 - 5.28289i) q^{47} +(-14.4968 - 21.6669i) q^{48} -4.46084i q^{49} +(-2.83617 - 13.3754i) q^{50} +(-4.41640 - 0.875625i) q^{51} +(26.4122 + 26.4122i) q^{52} +(2.76712 + 2.76712i) q^{53} +(-7.87219 + 11.8292i) q^{54} +(0.751239 + 1.38442i) q^{55} -15.1546i q^{56} +(2.51435 - 1.68230i) q^{57} +(9.34383 - 9.34383i) q^{58} -1.42235 q^{59} +(9.87125 - 18.7793i) q^{60} +4.88455 q^{61} +(1.93363 - 1.93363i) q^{62} +(-4.41426 + 1.83488i) q^{63} +30.4342i q^{64} +(-4.33407 + 14.6184i) q^{65} +(-0.648863 + 3.27268i) q^{66} +(-6.87690 - 6.87690i) q^{67} +(10.0687 + 10.0687i) q^{68} +(1.06719 - 5.38260i) q^{69} +(8.56397 - 4.64713i) q^{70} +14.6338i q^{71} +(26.3458 - 10.9512i) q^{72} +(5.99532 - 5.99532i) q^{73} -24.1510 q^{74} +(8.65950 - 0.114483i) q^{75} -9.56774 q^{76} +(-0.793701 + 0.793701i) q^{77} +(-26.8425 + 17.9597i) q^{78} +11.7893i q^{79} +(-29.5809 + 16.0517i) q^{80} +(-6.37975 - 6.34813i) q^{81} +(10.6213 + 10.6213i) q^{82} +(8.42829 + 8.42829i) q^{83} +(14.8301 + 2.94031i) q^{84} +(-1.65222 + 5.57276i) q^{85} -3.86547i q^{86} +(4.65430 + 6.95630i) q^{87} +(4.73708 - 4.73708i) q^{88} +12.0272 q^{89} +(14.2675 + 11.5301i) q^{90} -10.8656 q^{91} +(-12.2715 + 12.2715i) q^{92} +(0.963170 + 1.43955i) q^{93} -20.4303i q^{94} +(-1.86273 - 3.43274i) q^{95} +(-37.6112 - 7.45704i) q^{96} +(0.0249208 + 0.0249208i) q^{97} +(-8.62561 - 8.62561i) q^{98} +(-1.95338 - 0.806274i) 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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