LMFDB - Embedded newform 820.2.j.c.483.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.3
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41313 - 0.0554718i) q^{2} -1.54369i q^{3} +(1.99385 + 0.156777i) q^{4} +(-1.38671 + 1.75415i) q^{5} +(-0.0856310 + 2.18142i) q^{6} -2.96451 q^{7} +(-2.80886 - 0.332148i) q^{8} +0.617035 q^{9} +(2.05690 - 2.40191i) q^{10} +(2.13724 + 2.13724i) q^{11} +(0.242015 - 3.07787i) q^{12} +2.06129 q^{13} +(4.18923 + 0.164447i) q^{14} +(2.70786 + 2.14064i) q^{15} +(3.95084 + 0.625179i) q^{16} -4.42100 q^{17} +(-0.871947 - 0.0342280i) q^{18} +(-2.99818 - 2.99818i) q^{19} +(-3.03989 + 3.28010i) q^{20} +4.57628i q^{21} +(-2.90163 - 3.13874i) q^{22} +(5.19993 - 5.19993i) q^{23} +(-0.512732 + 4.33599i) q^{24} +(-1.15408 - 4.86499i) q^{25} +(-2.91287 - 0.114344i) q^{26} -5.58356i q^{27} +(-5.91078 - 0.464768i) q^{28} +(3.21653 + 3.21653i) q^{29} +(-3.70779 - 3.17520i) q^{30} -9.27745i q^{31} +(-5.54835 - 1.10262i) q^{32} +(3.29922 - 3.29922i) q^{33} +(6.24742 + 0.245241i) q^{34} +(4.11091 - 5.20020i) q^{35} +(1.23027 + 0.0967370i) q^{36} +(-3.03923 + 3.03923i) q^{37} +(4.07049 + 4.40312i) q^{38} -3.18199i q^{39} +(4.47770 - 4.46656i) q^{40} +(-5.60860 - 3.08927i) q^{41} +(0.253854 - 6.46685i) q^{42} +(-5.76865 - 5.76865i) q^{43} +(3.92625 + 4.59639i) q^{44} +(-0.855647 + 1.08237i) q^{45} +(-7.63661 + 7.05971i) q^{46} +4.71449i q^{47} +(0.965080 - 6.09886i) q^{48} +1.78834 q^{49} +(1.36099 + 6.93885i) q^{50} +6.82463i q^{51} +(4.10990 + 0.323164i) q^{52} +6.29275 q^{53} +(-0.309730 + 7.89028i) q^{54} +(-6.71276 + 0.785311i) q^{55} +(8.32690 + 0.984657i) q^{56} +(-4.62825 + 4.62825i) q^{57} +(-4.36693 - 4.72378i) q^{58} +1.86980 q^{59} +(5.06344 + 4.69264i) q^{60} -2.79777i q^{61} +(-0.514637 + 13.1102i) q^{62} -1.82921 q^{63} +(7.77936 + 1.86591i) q^{64} +(-2.85841 + 3.61582i) q^{65} +(-4.84523 + 4.47920i) q^{66} -7.93540i q^{67} +(-8.81479 - 0.693112i) q^{68} +(-8.02706 - 8.02706i) q^{69} +(-6.09770 + 7.12050i) q^{70} +(-1.98163 - 1.98163i) q^{71} +(-1.73316 - 0.204947i) q^{72} +(-0.828844 + 0.828844i) q^{73} +(4.46341 - 4.12623i) q^{74} +(-7.51001 + 1.78154i) q^{75} +(-5.50787 - 6.44796i) q^{76} +(-6.33587 - 6.33587i) q^{77} +(-0.176511 + 4.49655i) q^{78} +(1.53706 - 1.53706i) q^{79} +(-6.57532 + 6.06343i) q^{80} -6.76816 q^{81} +(7.75429 + 4.67665i) q^{82} +(1.78572 - 1.78572i) q^{83} +(-0.717456 + 9.12439i) q^{84} +(6.13063 - 7.75509i) q^{85} +(7.83182 + 8.47182i) q^{86} +(4.96531 - 4.96531i) q^{87} +(-5.29332 - 6.71308i) q^{88} +(-5.58411 - 5.58411i) q^{89} +(1.26918 - 1.48206i) q^{90} -6.11073 q^{91} +(11.1831 - 9.55263i) q^{92} -14.3215 q^{93} +(0.261521 - 6.66217i) q^{94} +(9.41686 - 1.10166i) q^{95} +(-1.70209 + 8.56492i) q^{96} -9.67761 q^{97} +(-2.52715 - 0.0992025i) q^{98} +(1.31875 + 1.31875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.41313	−	0.0554718i	−0.999230	−	0.0392245i
$2$	−1.41313	−	0.0554718i	−0.999230	−	0.0392245i
$3$		−	1.54369i		−	0.891247i	−0.895220	−	0.445624i	$-0.852982\pi$
$3$		−	1.54369i		−	0.891247i	0.895220	−	0.445624i	$-0.147018\pi$
$4$	1.99385	+	0.156777i	0.996923	+	0.0783886i
$5$	−1.38671	+	1.75415i	−0.620155	+	0.784480i
$5$	−1.38671	+	1.75415i	−0.620155	+	0.784480i
$6$	−0.0856310	+	2.18142i	−0.0349587	+	0.890561i
$7$	−2.96451			−1.12048			−0.560240	−	0.828330i	$-0.689291\pi$
$7$	−2.96451			−1.12048			−0.560240	+	0.828330i	$0.689291\pi$
$8$	−2.80886	−	0.332148i	−0.993081	−	0.117432i
$9$	0.617035			0.205678
$10$	2.05690	−	2.40191i	0.650448	−	0.759551i
$11$	2.13724	+	2.13724i	0.644402	+	0.644402i	0.951634	−	0.307233i	$-0.0994030\pi$
$11$	2.13724	+	2.13724i	0.644402	+	0.644402i	−0.307233	+	0.951634i	$0.599403\pi$
$12$	0.242015	−	3.07787i	0.0698636	−	0.888505i
$13$	2.06129			0.571700			0.285850	−	0.958274i	$-0.407724\pi$
$13$	2.06129			0.571700			0.285850	+	0.958274i	$0.407724\pi$
$14$	4.18923	+	0.164447i	1.11962	+	0.0439503i
$15$	2.70786	+	2.14064i	0.699165	+	0.552711i
$16$	3.95084	+	0.625179i	0.987710	+	0.156295i
$17$	−4.42100			−1.07225			−0.536125	−	0.844139i	$-0.680112\pi$
$17$	−4.42100			−1.07225			−0.536125	+	0.844139i	$0.680112\pi$
$18$	−0.871947	−	0.0342280i	−0.205520	−	0.00806762i
$19$	−2.99818	−	2.99818i	−0.687830	−	0.687830i	0.273922	−	0.961752i	$-0.411679\pi$
$19$	−2.99818	−	2.99818i	−0.687830	−	0.687830i	−0.961752	+	0.273922i	$0.911679\pi$
$20$	−3.03989	+	3.28010i	−0.679741	+	0.733453i
$21$			4.57628i			0.998626i
$22$	−2.90163	−	3.13874i	−0.618629	−	0.669182i
$23$	5.19993	−	5.19993i	1.08426	−	1.08426i	0.0881540	−	0.996107i	$-0.471903\pi$
$23$	5.19993	−	5.19993i	1.08426	−	1.08426i	0.996107	−	0.0881540i	$-0.0280968\pi$
$24$	−0.512732	+	4.33599i	−0.104661	+	0.885081i
$25$	−1.15408	−	4.86499i	−0.230817	−	0.972997i
$26$	−2.91287	−	0.114344i	−0.571260	−	0.0224246i
$27$		−	5.58356i		−	1.07456i
$28$	−5.91078	−	0.464768i	−1.11703	−	0.0878329i
$29$	3.21653	+	3.21653i	0.597294	+	0.597294i	0.939592	−	0.342298i	$-0.111205\pi$
$29$	3.21653	+	3.21653i	0.597294	+	0.597294i	−0.342298	+	0.939592i	$0.611205\pi$
$30$	−3.70779	−	3.17520i	−0.676948	−	0.579710i
$31$		−	9.27745i		−	1.66628i	−0.553062	−	0.833140i	$-0.686541\pi$
$31$		−	9.27745i		−	1.66628i	0.553062	−	0.833140i	$-0.313459\pi$
$32$	−5.54835	−	1.10262i	−0.980820	−	0.194917i
$33$	3.29922	−	3.29922i	0.574321	−	0.574321i
$34$	6.24742	+	0.245241i	1.07142	+	0.0420584i
$35$	4.11091	−	5.20020i	0.694871	−	0.878994i
$36$	1.23027	+	0.0967370i	0.205045	+	0.0161228i
$37$	−3.03923	+	3.03923i	−0.499647	+	0.499647i	−0.911328	−	0.411681i	$-0.864942\pi$
$37$	−3.03923	+	3.03923i	−0.499647	+	0.499647i	0.411681	+	0.911328i	$0.364942\pi$
$38$	4.07049	+	4.40312i	0.660321	+	0.714281i
$39$		−	3.18199i		−	0.509526i
$40$	4.47770	−	4.46656i	0.707987	−	0.706226i
$41$	−5.60860	−	3.08927i	−0.875916	−	0.482463i
$41$	−5.60860	−	3.08927i	−0.875916	−	0.482463i
$42$	0.253854	−	6.46685i	0.0391706	−	0.997857i
$43$	−5.76865	−	5.76865i	−0.879710	−	0.879710i	0.113794	−	0.993504i	$-0.463700\pi$
$43$	−5.76865	−	5.76865i	−0.879710	−	0.879710i	−0.993504	+	0.113794i	$0.963700\pi$
$44$	3.92625	+	4.59639i	0.591905	+	0.692932i
$45$	−0.855647	+	1.08237i	−0.127552	+	0.161350i
$46$	−7.63661	+	7.05971i	−1.12596	+	1.04090i
$47$			4.71449i			0.687679i	0.939028	+	0.343840i	$0.111728\pi$
$47$			4.71449i			0.687679i	−0.939028	+	0.343840i	$0.888272\pi$
$48$	0.965080	−	6.09886i	0.139297	−	0.880294i
$49$	1.78834			0.255477
$50$	1.36099	+	6.93885i	0.192474	+	0.981302i
$51$			6.82463i			0.955640i
$52$	4.10990	+	0.323164i	0.569941	+	0.0448147i
$53$	6.29275			0.864375			0.432188	−	0.901784i	$-0.357742\pi$
$53$	6.29275			0.864375			0.432188	+	0.901784i	$0.357742\pi$
$54$	−0.309730	+	7.89028i	−0.0421490	+	1.07373i
$55$	−6.71276	+	0.785311i	−0.905148	+	0.105891i
$56$	8.32690	+	0.984657i	1.11273	+	0.131580i
$57$	−4.62825	+	4.62825i	−0.613027	+	0.613027i
$58$	−4.36693	−	4.72378i	−0.573406	−	0.620263i
$59$	1.86980			0.243428			0.121714	−	0.992565i	$-0.461161\pi$
$59$	1.86980			0.243428			0.121714	+	0.992565i	$0.461161\pi$
$60$	5.06344	+	4.69264i	0.653688	+	0.605817i
$61$		−	2.79777i		−	0.358218i	−0.983829	−	0.179109i	$-0.942679\pi$
$61$		−	2.79777i		−	0.358218i	0.983829	−	0.179109i	$-0.0573214\pi$
$62$	−0.514637	+	13.1102i	−0.0653590	+	1.66500i
$63$	−1.82921			−0.230459
$64$	7.77936	+	1.86591i	0.972419	+	0.233239i
$65$	−2.85841	+	3.61582i	−0.354542	+	0.448487i
$66$	−4.84523	+	4.47920i	−0.596407	+	0.551352i
$67$		−	7.93540i		−	0.969463i	−0.874663	−	0.484732i	$-0.838917\pi$
$67$		−	7.93540i		−	0.969463i	0.874663	−	0.484732i	$-0.161083\pi$
$68$	−8.81479	−	0.693112i	−1.06895	−	0.0840521i
$69$	−8.02706	−	8.02706i	−0.966345	−	0.966345i
$70$	−6.09770	+	7.12050i	−0.728815	+	0.851062i
$71$	−1.98163	−	1.98163i	−0.235177	−	0.235177i	0.579673	−	0.814849i	$-0.303180\pi$
$71$	−1.98163	−	1.98163i	−0.235177	−	0.235177i	−0.814849	+	0.579673i	$0.803180\pi$
$72$	−1.73316	−	0.204947i	−0.204255	−	0.0241532i
$73$	−0.828844	+	0.828844i	−0.0970089	+	0.0970089i	−0.753946	−	0.656937i	$-0.771852\pi$
$73$	−0.828844	+	0.828844i	−0.0970089	+	0.0970089i	0.656937	+	0.753946i	$0.271852\pi$
$74$	4.46341	−	4.12623i	0.518861	−	0.479664i
$75$	−7.51001	+	1.78154i	−0.867181	+	0.205715i
$76$	−5.50787	−	6.44796i	−0.631796	−	0.739632i
$77$	−6.33587	−	6.33587i	−0.722040	−	0.722040i
$78$	−0.176511	+	4.49655i	−0.0199859	+	0.509134i
$79$	1.53706	−	1.53706i	0.172933	−	0.172933i	−0.615334	−	0.788267i	$-0.710979\pi$
$79$	1.53706	−	1.53706i	0.172933	−	0.172933i	0.788267	+	0.615334i	$0.210979\pi$
$80$	−6.57532	+	6.06343i	−0.735143	+	0.677912i
$81$	−6.76816			−0.752018
$82$	7.75429	+	4.67665i	0.856318	+	0.516450i
$83$	1.78572	−	1.78572i	0.196008	−	0.196008i	−0.602278	−	0.798286i	$-0.705740\pi$
$83$	1.78572	−	1.78572i	0.196008	−	0.196008i	0.798286	+	0.602278i	$0.205740\pi$
$84$	−0.717456	+	9.12439i	−0.0782808	+	0.995553i
$85$	6.13063	−	7.75509i	0.664961	−	0.841158i
$86$	7.83182	+	8.47182i	0.844527	+	0.913539i
$87$	4.96531	−	4.96531i	0.532337	−	0.532337i
$88$	−5.29332	−	6.71308i	−0.564270	−	0.715616i
$89$	−5.58411	−	5.58411i	−0.591915	−	0.591915i	0.346233	−	0.938148i	$-0.387460\pi$
$89$	−5.58411	−	5.58411i	−0.591915	−	0.591915i	−0.938148	+	0.346233i	$0.887460\pi$
$90$	1.26918	−	1.48206i	0.133783	−	0.156223i
$91$	−6.11073			−0.640579
$92$	11.1831	−	9.55263i	1.16592	−	0.995931i
$93$	−14.3215			−1.48507
$94$	0.261521	−	6.66217i	0.0269739	−	0.687150i
$95$	9.41686	−	1.10166i	0.966150	−	0.113028i
$96$	−1.70209	+	8.56492i	−0.173719	+	0.874153i
$97$	−9.67761			−0.982612			−0.491306	−	0.870987i	$-0.663480\pi$
$97$	−9.67761			−0.982612			−0.491306	+	0.870987i	$0.663480\pi$
$98$	−2.52715	−	0.0992025i	−0.255281	−	0.0100210i
$99$	1.31875	+	1.31875i	0.132539	+	0.132539i
$100$	−1.53834	−	9.88097i	−0.153834	−	0.988097i
$101$	−8.19176	−	8.19176i	−0.815111	−	0.815111i	0.170284	−	0.985395i	$-0.445531\pi$
$101$	−8.19176	−	8.19176i	−0.815111	−	0.815111i	−0.985395	+	0.170284i	$0.945531\pi$
$102$	0.378575	−	9.64406i	0.0374845	−	0.954904i
$103$	4.74151	+	4.74151i	0.467195	+	0.467195i	0.901004	−	0.433810i	$-0.142831\pi$
$103$	4.74151	+	4.74151i	0.467195	+	0.467195i	−0.433810	+	0.901004i	$0.642831\pi$
$104$	−5.78988	−	0.684654i	−0.567744	−	0.0671359i
$105$	−8.02748	−	6.34596i	−0.783401	−	0.619302i
$106$	−8.89244	−	0.349070i	−0.863710	−	0.0339047i
$107$	−11.9643	−	11.9643i	−1.15663	−	1.15663i	−0.985196	−	0.171434i	$-0.945160\pi$
$107$	−11.9643	−	11.9643i	−1.15663	−	1.15663i	−0.171434	−	0.985196i	$-0.554840\pi$
$108$	0.875375	−	11.1328i	0.0842330	−	1.07125i
$109$	12.8867	−	12.8867i	1.23432	−	1.23432i	0.272030	−	0.962289i	$-0.412305\pi$
$109$	12.8867	−	12.8867i	1.23432	−	1.23432i	0.962289	−	0.272030i	$-0.0876950\pi$
$110$	9.52953	−	0.737374i	0.908605	−	0.0703059i
$111$	4.69162	+	4.69162i	0.445309	+	0.445309i
$112$	−11.7123	−	1.85335i	−1.10671	−	0.175125i
$113$	9.80373	+	9.80373i	0.922257	+	0.922257i	0.997189	−	0.0749316i	$-0.0238738\pi$
$113$	9.80373	+	9.80373i	0.922257	+	0.922257i	−0.0749316	+	0.997189i	$0.523874\pi$
$114$	6.79703	−	6.28356i	0.636601	−	0.588509i
$115$	1.91067	+	16.3322i	0.178171	+	1.52299i
$116$	5.90898	+	6.91753i	0.548635	+	0.642277i
$117$	1.27189			0.117586
$118$	−2.64227	−	0.103721i	−0.243240	−	0.00954832i
$119$	13.1061			1.20144
$120$	−6.89497	−	6.91216i	−0.629422	−	0.630991i
$121$		−	1.86443i		−	0.169493i
$122$	−0.155197	+	3.95360i	−0.0140509	+	0.357942i
$123$	−4.76887	+	8.65791i	−0.429994	+	0.780658i
$124$	1.45449	−	18.4978i	0.130617	−	1.66115i
$125$	10.1343	+	4.72188i	0.906439	+	0.422338i
$126$	2.58490	+	0.101469i	0.230281	+	0.00903962i
$127$	−6.95229	−	6.95229i	−0.616916	−	0.616916i	0.327823	−	0.944739i	$-0.393685\pi$
$127$	−6.95229	−	6.95229i	−0.616916	−	0.616916i	−0.944739	+	0.327823i	$0.893685\pi$
$128$	−10.8897	−	3.06830i	−0.962522	−	0.271202i
$129$	−8.90497	+	8.90497i	−0.784039	+	0.784039i
$130$	4.23987	−	4.95104i	0.371861	−	0.434235i
$131$	−4.01067			−0.350414			−0.175207	−	0.984532i	$-0.556059\pi$
$131$	−4.01067			−0.350414			−0.175207	+	0.984532i	$0.556059\pi$
$132$	7.09539	−	6.06090i	0.617574	−	0.527534i
$133$	8.88815	+	8.88815i	0.770700	+	0.770700i
$134$	−0.440191	+	11.2137i	−0.0380267	+	0.968717i
$135$	9.79441	+	7.74277i	0.842968	+	0.666392i
$136$	12.4180	+	1.46843i	1.06483	+	0.125916i
$137$	22.6174			1.93234			0.966169	−	0.257910i	$-0.0830337\pi$
$137$	22.6174			1.93234			0.966169	+	0.257910i	$0.0830337\pi$
$138$	10.8980	+	11.7885i	0.927697	+	1.00351i
$139$	−9.40066			−0.797354			−0.398677	−	0.917092i	$-0.630530\pi$
$139$	−9.40066			−0.797354			−0.398677	+	0.917092i	$0.630530\pi$
$140$	9.01180	−	9.72390i	0.761636	−	0.821820i
$141$	7.27769			0.612892
$142$	2.69037	+	2.91022i	0.225771	+	0.244220i
$143$	4.40547	+	4.40547i	0.368404	+	0.368404i
$144$	2.43781	+	0.385757i	0.203151	+	0.0321464i
$145$	−10.1027	+	1.18189i	−0.838979	+	0.0981504i
$146$	1.21724	−	1.12528i	0.100739	−	0.0931291i
$147$		−	2.76064i		−	0.227693i
$148$	−6.53624	+	5.58328i	−0.537276	+	0.458943i
$149$	−7.69811	+	7.69811i	−0.630654	+	0.630654i	−0.948232	−	0.317578i	$-0.897130\pi$
$149$	−7.69811	+	7.69811i	−0.630654	+	0.630654i	0.317578	+	0.948232i	$0.397130\pi$
$150$	10.7114	−	2.10095i	0.874583	−	0.171542i
$151$	5.75534	+	5.75534i	0.468363	+	0.468363i	0.901384	−	0.433021i	$-0.142552\pi$
$151$	5.75534	+	5.75534i	0.468363	+	0.468363i	−0.433021	+	0.901384i	$0.642552\pi$
$152$	7.42562	+	9.41730i	0.602298	+	0.763844i
$153$	−2.72791			−0.220538
$154$	8.60192	+	9.30484i	0.693162	+	0.749806i
$155$	16.2740	+	12.8651i	1.30716	+	1.03335i
$156$	0.498863	−	6.34439i	0.0399410	−	0.507958i
$157$		−	19.5013i		−	1.55637i	−0.628035	−	0.778185i	$-0.716141\pi$
$157$		−	19.5013i		−	1.55637i	0.628035	−	0.778185i	$-0.283859\pi$
$158$	−2.25733	+	2.08680i	−0.179583	+	0.166017i
$159$		−	9.71402i		−	0.770372i
$160$	9.62810	−	8.20364i	0.761168	−	0.648555i
$161$	−15.4153	+	15.4153i	−1.21489	+	1.21489i
$162$	9.56426	+	0.375442i	0.751440	+	0.0294975i
$163$	2.85841	−	2.85841i	0.223888	−	0.223888i	−0.586246	−	0.810133i	$-0.699395\pi$
$163$	2.85841	−	2.85841i	0.223888	−	0.223888i	0.810133	+	0.586246i	$0.199395\pi$
$164$	−10.6984	−	7.03884i	−0.835401	−	0.549641i
$165$	1.21227	+	10.3624i	0.0943754	+	0.806711i
$166$	−2.62250	+	2.42439i	−0.203546	+	0.188169i
$167$	−7.56711			−0.585561			−0.292780	−	0.956180i	$-0.594580\pi$
$167$	−7.56711			−0.585561			−0.292780	+	0.956180i	$0.594580\pi$
$168$	1.52000	−	12.8541i	0.117271	−	0.991716i
$169$	−8.75107			−0.673159
$170$	−9.09354	+	10.6188i	−0.697443	+	0.814428i
$171$	−1.84998	−	1.84998i	−0.141472	−	0.141472i
$172$	−10.5974	−	12.4062i	−0.808044	−	0.945962i
$173$	12.2848	−	12.2848i	0.933995	−	0.933995i	−0.0639574	−	0.997953i	$-0.520372\pi$
$173$	12.2848	−	12.2848i	0.933995	−	0.933995i	0.997953	+	0.0639574i	$0.0203722\pi$
$174$	−7.29203	+	6.74116i	−0.552808	+	0.511046i
$175$	3.42130	+	14.4223i	0.258626	+	1.09022i
$176$	7.10773	+	9.78005i	0.535766	+	0.737199i
$177$		−	2.88639i		−	0.216954i
$178$	7.58129	+	8.20081i	0.568242	+	0.614677i
$179$	5.99824	+	5.99824i	0.448329	+	0.448329i	0.894799	−	0.446469i	$-0.147319\pi$
$179$	5.99824	+	5.99824i	0.448329	+	0.448329i	−0.446469	+	0.894799i	$0.647319\pi$
$180$	−1.87572	+	2.02394i	−0.139808	+	0.150855i
$181$	11.1195	+	11.1195i	0.826507	+	0.826507i	0.987032	−	0.160525i	$-0.0513187\pi$
$181$	11.1195	+	11.1195i	0.826507	+	0.826507i	−0.160525	+	0.987032i	$0.551319\pi$
$182$	8.63523	+	0.338973i	0.640086	+	0.0251264i
$183$	−4.31888			−0.319261
$184$	−16.3330	+	12.8787i	−1.20409	+	0.949432i
$185$	−1.11674	−	9.54580i	−0.0821045	−	0.701821i
$186$	20.2380	+	0.794438i	1.48392	+	0.0582510i
$187$	−9.44873	−	9.44873i	−0.690959	−	0.690959i
$188$	−0.739125	+	9.39997i	−0.0539062	+	0.685563i
$189$			16.5526i			1.20402i
$190$	−13.3683	+	1.03441i	−0.969840	+	0.0750440i
$191$	−10.2338	+	10.2338i	−0.740493	+	0.740493i	−0.972673	−	0.232180i	$-0.925414\pi$
$191$	−10.2338	+	10.2338i	−0.740493	+	0.740493i	0.232180	+	0.972673i	$0.425414\pi$
$192$	2.88038	−	12.0089i	0.207874	−	0.866666i
$193$	6.36563			0.458208			0.229104	−	0.973402i	$-0.426420\pi$
$193$	6.36563			0.458208			0.229104	+	0.973402i	$0.426420\pi$
$194$	13.6757	+	0.536834i	0.981856	+	0.0385425i
$195$	5.58168	+	4.41249i	0.399713	+	0.315985i
$196$	3.56568	+	0.280371i	0.254691	+	0.0200265i
$197$	15.9470	+	15.9470i	1.13618	+	1.13618i	0.989129	+	0.147051i	$0.0469782\pi$
$197$	15.9470	+	15.9470i	1.13618	+	1.13618i	0.147051	+	0.989129i	$0.453022\pi$
$198$	−1.79041	−	1.93671i	−0.127239	−	0.137636i
$199$	5.01409	+	5.01409i	0.355440	+	0.355440i	0.862129	−	0.506689i	$-0.169131\pi$
$199$	5.01409	+	5.01409i	0.355440	+	0.355440i	−0.506689	+	0.862129i	$0.669131\pi$
$200$	1.62576	+	14.0484i	0.114959	+	0.993370i
$201$	−12.2498			−0.864031
$202$	11.1216	+	12.0304i	0.782511	+	0.846456i
$203$	−9.53544	−	9.53544i	−0.669256	−	0.669256i
$204$	−1.06995	+	13.6073i	−0.0749112	+	0.952699i
$205$	13.1965	−	5.55440i	0.921686	−	0.387936i
$206$	−6.43733	−	6.96337i	−0.448510	−	0.485161i
$207$	3.20854	−	3.20854i	0.223009	−	0.223009i
$208$	8.14384	+	1.28868i	0.564674	+	0.0893537i
$209$		−	12.8157i		−	0.886478i
$210$	10.9918	+	9.41293i	0.758507	+	0.649554i
$211$	5.64148	−	5.64148i	0.388375	−	0.388375i	−0.485732	−	0.874108i	$-0.661447\pi$
$211$	5.64148	−	5.64148i	0.388375	−	0.388375i	0.874108	+	0.485732i	$0.161447\pi$
$212$	12.5468	+	0.986559i	0.861716	+	0.0677572i
$213$	−3.05902	+	3.05902i	−0.209601	+	0.209601i
$214$	16.2433	+	17.5707i	1.11037	+	1.20111i
$215$	18.1185	−	2.11964i	1.23567	−	0.144558i
$216$	−1.85457	+	15.6834i	−0.126187	+	1.06712i
$217$			27.5031i			1.86703i
$218$	−18.9253	+	17.4956i	−1.28178	+	1.18495i
$219$	1.27947	+	1.27947i	0.0864589	+	0.0864589i
$220$	−13.5073	+	0.513382i	−0.910664	+	0.0346122i
$221$	−9.11297			−0.613005
$222$	−6.36959	−	6.89010i	−0.427499	−	0.462433i
$223$	−9.08787	+	9.08787i	−0.608569	+	0.608569i	−0.942572	−	0.334003i	$-0.891600\pi$
$223$	−9.08787	+	9.08787i	−0.608569	+	0.608569i	0.334003	+	0.942572i	$0.391600\pi$
$224$	16.4482	+	3.26872i	1.09899	+	0.218401i
$225$	−0.712109	−	3.00187i	−0.0474740	−	0.200124i
$226$	−13.3101	−	14.3977i	−0.885372	−	0.957722i
$227$			23.0174i			1.52772i	0.645384	+	0.763858i	$0.276697\pi$
$227$			23.0174i			1.52772i	−0.645384	+	0.763858i	$0.723303\pi$
$228$	−9.95362	+	8.50241i	−0.659195	+	0.563086i
$229$	5.54681	−	5.54681i	0.366544	−	0.366544i	−0.499671	−	0.866215i	$-0.666546\pi$
$229$	5.54681	−	5.54681i	0.366544	−	0.366544i	0.866215	+	0.499671i	$0.166546\pi$
$230$	−1.79404	−	23.1855i	−0.118296	−	1.52881i
$231$	−9.78059	+	9.78059i	−0.643516	+	0.643516i
$232$	−7.96640	−	10.1031i	−0.523020	−	0.663303i
$233$	−15.7716			−1.03323			−0.516615	−	0.856218i	$-0.672808\pi$
$233$	−15.7716			−1.03323			−0.516615	+	0.856218i	$0.672808\pi$
$234$	−1.79734	−	0.0705540i	−0.117496	−	0.00461226i
$235$	−8.26992	−	6.53762i	−0.539470	−	0.426467i
$236$	3.72810	+	0.293142i	0.242679	+	0.0190819i
$237$	−2.37274	−	2.37274i	−0.154126	−	0.154126i
$238$	−18.5206	−	0.727020i	−1.20051	−	0.0471257i
$239$	−4.45150	+	4.45150i	−0.287944	+	0.287944i	−0.836267	−	0.548323i	$-0.815267\pi$
$239$	−4.45150	+	4.45150i	−0.287944	+	0.287944i	0.548323	+	0.836267i	$0.315267\pi$
$240$	9.36003	+	10.1502i	0.604187	+	0.655194i
$241$		−	3.53074i		−	0.227435i	−0.993513	−	0.113717i	$-0.963724\pi$
$241$		−	3.53074i		−	0.227435i	0.993513	−	0.113717i	$-0.0362758\pi$
$242$	−0.103423	+	2.63467i	−0.00664828	+	0.169363i
$243$		−	6.30278i		−	0.404323i
$244$	0.438626	−	5.57832i	0.0280802	−	0.357115i
$245$	−2.47991	+	3.13702i	−0.158435	+	0.200417i
$246$	7.21928	−	11.9702i	0.460284	−	0.763191i
$247$	−6.18013	−	6.18013i	−0.393232	−	0.393232i
$248$	−3.08149	+	26.0590i	−0.195675	+	1.65475i
$249$	−2.75659	−	2.75659i	−0.174692	−	0.174692i
$250$	−14.0591	−	7.23477i	−0.889175	−	0.457567i
$251$	18.8286			1.18845			0.594226	−	0.804298i	$-0.297458\pi$
$251$	18.8286			1.18845			0.594226	+	0.804298i	$0.297458\pi$
$252$	−3.64716	−	0.286778i	−0.229749	−	0.0180653i
$253$	22.2270			1.39740
$254$	9.43879	+	10.2101i	0.592243	+	0.640639i
$255$	−11.9714	−	9.46377i	−0.749680	−	0.592644i
$256$	15.2183	+	4.93997i	0.951144	+	0.308748i
$257$		−	11.5190i		−	0.718534i	−0.933235	−	0.359267i	$-0.883027\pi$
$257$		−	11.5190i		−	0.718534i	0.933235	−	0.359267i	$-0.116973\pi$
$258$	13.0778	−	12.0899i	0.814189	−	0.752682i
$259$	9.00985	−	9.00985i	0.559845	−	0.559845i
$260$	−6.26611	+	6.76125i	−0.388608	+	0.419315i
$261$	1.98471	+	1.98471i	0.122850	+	0.122850i
$262$	5.66758	+	0.222479i	0.350144	+	0.0137448i
$263$	17.2632			1.06450			0.532248	−	0.846589i	$-0.321347\pi$
$263$	17.2632			1.06450			0.532248	+	0.846589i	$0.321347\pi$
$264$	−10.3629	+	8.17122i	−0.637791	+	0.502904i
$265$	−8.72620	+	11.0384i	−0.536046	+	0.678085i
$266$	−12.0670	−	13.0531i	−0.739877	−	0.800338i
$267$	−8.62012	+	8.62012i	−0.527543	+	0.527543i
$268$	1.24409	−	15.8220i	0.0759948	−	0.966480i
$269$		−	25.7301i		−	1.56879i	−0.620260	−	0.784396i	$-0.712973\pi$
$269$		−	25.7301i		−	1.56879i	0.620260	−	0.784396i	$-0.287027\pi$
$270$	−13.4112	−	11.4848i	−0.816181	−	0.698944i
$271$			7.22865i			0.439109i	0.975600	+	0.219555i	$0.0704604\pi$
$271$			7.22865i			0.439109i	−0.975600	+	0.219555i	$0.929540\pi$
$272$	−17.4667	−	2.76392i	−1.05907	−	0.167587i
$273$			9.43305i			0.570914i
$274$	−31.9613	−	1.25463i	−1.93085	−	0.0757950i
$275$	7.93108	−	12.8642i	0.478262	−	0.775740i
$276$	−14.7463	−	17.2632i	−0.887621	−	1.03912i
$277$	2.59863	−	2.59863i	0.156136	−	0.156136i	−0.624716	−	0.780852i	$-0.714785\pi$
$277$	2.59863	−	2.59863i	0.156136	−	0.156136i	0.780852	+	0.624716i	$0.214785\pi$
$278$	13.2843	+	0.521471i	0.796740	+	0.0312758i
$279$		−	5.72451i		−	0.342717i
$280$	−13.2742	+	13.2412i	−0.793286	+	0.791312i
$281$	12.2283	+	12.2283i	0.729479	+	0.729479i	0.970516	−	0.241037i	$-0.0774875\pi$
$281$	12.2283	+	12.2283i	0.729479	+	0.729479i	−0.241037	+	0.970516i	$0.577487\pi$
$282$	−10.2843	−	0.403707i	−0.612420	−	0.0240404i
$283$	−15.8069	+	15.8069i	−0.939625	+	0.939625i	−0.998278	−	0.0586539i	$-0.981319\pi$
$283$	−15.8069	+	15.8069i	−0.939625	+	0.939625i	0.0586539	+	0.998278i	$0.481319\pi$
$284$	−3.64040	−	4.26175i	−0.216018	−	0.252888i
$285$	−1.70061	−	14.5367i	−0.100736	−	0.861078i
$286$	−5.98111	−	6.46987i	−0.353670	−	0.382571i
$287$	16.6268	+	9.15819i	0.981447	+	0.540591i
$288$	−3.42353	−	0.680353i	−0.201733	−	0.0400902i
$289$	2.54523			0.149719
$290$	14.3419	−	1.10974i	0.842184	−	0.0651663i
$291$			14.9392i			0.875751i
$292$	−1.78253	+	1.52264i	−0.104315	+	0.0891060i
$293$			18.1339i			1.05939i	0.848187	+	0.529696i	$0.177694\pi$
$293$			18.1339i			1.05939i	−0.848187	+	0.529696i	$0.822306\pi$
$294$	−0.153137	+	3.90113i	−0.00893116	+	0.227518i
$295$	−2.59287	+	3.27991i	−0.150963	+	0.190964i
$296$	9.54625	−	7.52730i	0.554864	−	0.437515i
$297$	11.9334	−	11.9334i	0.692447	−	0.692447i
$298$	11.3054	−	10.4514i	0.654906	−	0.605432i
$299$	10.7186	−	10.7186i	0.619872	−	0.619872i
$300$	−15.2531	+	2.37472i	−0.880638	+	0.137105i
$301$	17.1012	+	17.1012i	0.985698	+	0.985698i
$302$	−7.81375	−	8.45227i	−0.449631	−	0.486373i
$303$	−12.6455	+	12.6455i	−0.726465	+	0.726465i
$304$	−9.97094	−	13.7197i	−0.571873	−	0.786881i
$305$	4.90771	+	3.87969i	0.281014	+	0.222150i
$306$	3.85488	+	0.151322i	0.220369	+	0.00865050i
$307$	18.3006	−	18.3006i	1.04447	−	1.04447i	0.0455084	−	0.998964i	$-0.485509\pi$
$307$	18.3006	−	18.3006i	1.04447	−	1.04447i	0.998964	−	0.0455084i	$-0.0144908\pi$
$308$	−11.6394	−	13.6261i	−0.663218	−	0.776417i
$309$	7.31940	−	7.31940i	0.416386	−	0.416386i
$310$	−22.2836	−	19.0828i	−1.26562	−	1.08383i
$311$	−13.2570	+	13.2570i	−0.751733	+	0.751733i	−0.974803	−	0.223070i	$-0.928392\pi$
$311$	−13.2570	+	13.2570i	−0.751733	+	0.751733i	0.223070	+	0.974803i	$0.428392\pi$
$312$	−1.05689	+	8.93775i	−0.0598347	+	0.506000i
$313$		−	25.8327i		−	1.46015i	−0.683365	−	0.730077i	$-0.739484\pi$
$313$		−	25.8327i		−	1.46015i	0.683365	−	0.730077i	$-0.260516\pi$
$314$	−1.08177	+	27.5577i	−0.0610478	+	1.55517i
$315$	2.53658	−	3.20870i	0.142920	−	0.180790i
$316$	3.30565	−	2.82369i	0.185957	−	0.158845i
$317$			17.1768i			0.964743i	0.875967	+	0.482371i	$0.160224\pi$
$317$			17.1768i			0.964743i	−0.875967	+	0.482371i	$0.839776\pi$
$318$	−0.538854	+	13.7271i	−0.0302175	+	0.769779i
$319$			13.7490i			0.769794i
$320$	−14.0608	+	11.0587i	−0.786022	+	0.618199i
$321$	−18.4691	+	18.4691i	−1.03084	+	1.03084i
$322$	22.6388	−	20.9286i	1.26161	−	1.16631i
$323$	13.2550	+	13.2550i	0.737526	+	0.737526i
$324$	−13.4947	−	1.06109i	−0.749704	−	0.0589497i
$325$	−2.37890	−	10.0282i	−0.131958	−	0.556262i
$326$	−4.19785	+	3.88073i	−0.232497	+	0.214934i
$327$	−19.8930	−	19.8930i	−1.10008	−	1.10008i
$328$	14.7277	+	10.5402i	0.813199	+	0.581986i
$329$		−	13.9762i		−	0.770531i
$330$	−1.13827	−	14.7106i	−0.0626599	−	0.809792i
$331$	−16.7610	−	16.7610i	−0.921268	−	0.921268i	0.0758511	−	0.997119i	$-0.475833\pi$
$331$	−16.7610	−	16.7610i	−0.921268	−	0.921268i	−0.997119	+	0.0758511i	$0.975833\pi$
$332$	3.84041	−	3.28049i	0.210770	−	0.180040i
$333$	−1.87531	+	1.87531i	−0.102766	+	0.102766i
$334$	10.6933	+	0.419761i	0.585110	+	0.0229683i
$335$	13.9199	+	11.0041i	0.760524	+	0.601217i
$336$	−2.86099	+	18.0801i	−0.156080	+	0.986353i
$337$	24.4784	+	24.4784i	1.33342	+	1.33342i	0.902289	+	0.431133i	$0.141886\pi$
$337$	24.4784	+	24.4784i	1.33342	+	1.33342i	0.431133	+	0.902289i	$0.358114\pi$
$338$	12.3664	+	0.485438i	0.672641	+	0.0264043i
$339$	15.1339	−	15.1339i	0.821959	−	0.821959i
$340$	13.4394	−	14.5013i	0.728852	−	0.786444i
$341$	19.8281	−	19.8281i	1.07375	−	1.07375i
$342$	2.51163	+	2.71688i	0.135814	+	0.146912i
$343$	15.4500			0.834223
$344$	14.2873	+	18.1193i	0.770317	+	0.976930i
$345$	25.2119	−	2.94948i	1.35736	−	0.158795i
$346$	−18.0414	+	16.6785i	−0.969912	+	0.896641i
$347$		−	18.6010i		−	0.998551i	−0.866443	−	0.499276i	$-0.833599\pi$
$347$		−	18.6010i		−	0.998551i	0.866443	−	0.499276i	$-0.166401\pi$
$348$	10.6785	−	9.12161i	0.572428	−	0.488969i
$349$	−19.6738			−1.05311			−0.526557	−	0.850140i	$-0.676517\pi$
$349$	−19.6738			−1.05311			−0.526557	+	0.850140i	$0.676517\pi$
$350$	−4.03469	−	20.5703i	−0.215663	−	1.09953i
$351$		−	11.5094i		−	0.614324i
$352$	−9.50160	−	14.2147i	−0.506437	−	0.757647i
$353$	−18.0827	−	18.0827i	−0.962445	−	0.962445i	0.0368750	−	0.999320i	$-0.488260\pi$
$353$	−18.0827	−	18.0827i	−0.962445	−	0.962445i	−0.999320	+	0.0368750i	$0.988260\pi$
$354$	−0.160113	+	4.07883i	−0.00850991	+	0.216787i
$355$	6.22403	−	0.728136i	0.330337	−	0.0386454i
$356$	−10.2584	−	12.0093i	−0.543694	−	0.636493i
$357$		−	20.2317i		−	1.07078i
$358$	−8.14353	−	8.80900i	−0.430399	−	0.465570i
$359$	1.48120			0.0781748			0.0390874	−	0.999236i	$-0.487555\pi$
$359$	1.48120			0.0781748			0.0390874	+	0.999236i	$0.487555\pi$
$360$	2.76290	−	2.75602i	0.145617	−	0.145255i
$361$		−	1.02181i		−	0.0537794i
$362$	−15.0964	−	16.3301i	−0.793452	−	0.858290i
$363$	−2.87809			−0.151060
$364$	−12.1839	−	0.958023i	−0.638608	−	0.0502141i
$365$	−0.304552	−	2.60328i	−0.0159410	−	0.136262i
$366$	6.10311	+	0.239576i	0.319015	+	0.0125228i
$367$	−8.09969	+	8.09969i	−0.422800	+	0.422800i	−0.886167	−	0.463366i	$-0.846641\pi$
$367$	−8.09969	+	8.09969i	−0.422800	+	0.422800i	0.463366	+	0.886167i	$0.346641\pi$
$368$	23.7950	−	17.2932i	1.24040	−	0.901472i
$369$	−3.46070	−	1.90619i	−0.180157	−	0.0992322i
$370$	1.04857	+	13.5514i	0.0545128	+	0.704501i
$371$	−18.6549			−0.968516
$372$	−28.5548	−	2.24528i	−1.48050	−	0.116412i
$373$	3.43345	+	3.43345i	0.177777	+	0.177777i	0.790386	−	0.612609i	$-0.209880\pi$
$373$	3.43345	+	3.43345i	0.177777	+	0.177777i	−0.612609	+	0.790386i	$0.709880\pi$
$374$	12.8281	+	13.8764i	0.663325	+	0.717530i
$375$	7.28910	−	15.6442i	0.376407	−	0.807861i
$376$	1.56591	−	13.2423i	0.0807556	−	0.682921i
$377$	6.63020	+	6.63020i	0.341473	+	0.341473i
$378$	0.918200	−	23.3908i	0.0472271	−	1.20309i
$379$	−3.87141			−0.198861			−0.0994306	−	0.995044i	$-0.531702\pi$
$379$	−3.87141			−0.198861			−0.0994306	+	0.995044i	$0.531702\pi$
$380$	18.9485	−	0.720187i	0.972037	−	0.0369448i
$381$	−10.7321	+	10.7321i	−0.549824	+	0.549824i
$382$	15.0294	−	13.8940i	0.768969	−	0.710878i
$383$	−35.7374			−1.82609			−0.913047	−	0.407855i	$-0.866277\pi$
$383$	−35.7374			−1.82609			−0.913047	+	0.407855i	$0.866277\pi$
$384$	−4.73649	+	16.8103i	−0.241708	+	0.857846i
$385$	19.9001	−	2.32807i	1.01420	−	0.118649i
$386$	−8.99543	−	0.353113i	−0.457855	−	0.0179730i
$387$	−3.55945	−	3.55945i	−0.180937	−	0.180937i
$388$	−19.2957	−	1.51723i	−0.979589	−	0.0770256i
$389$	−13.0931			−0.663846			−0.331923	−	0.943307i	$-0.607697\pi$
$389$	−13.0931			−0.663846			−0.331923	+	0.943307i	$0.607697\pi$
$390$	−7.64285	−	6.54502i	−0.387011	−	0.331420i
$391$	−22.9889	+	22.9889i	−1.16260	+	1.16260i
$392$	−5.02320	−	0.593994i	−0.253710	−	0.0300012i
$393$			6.19122i			0.312306i
$394$	−21.6506	−	23.4198i	−1.09074	−	1.17987i
$395$	0.564782	+	4.82770i	0.0284173	+	0.242908i
$396$	2.42263	+	2.83613i	0.121742	+	0.142521i
$397$			35.0451i			1.75886i	0.476027	+	0.879431i	$0.342076\pi$
$397$			35.0451i			1.75886i	−0.476027	+	0.879431i	$0.657924\pi$
$398$	−6.80740	−	7.36368i	−0.341224	−	0.369108i
$399$	13.7205	−	13.7205i	0.686885	−	0.686885i
$400$	−1.51811	−	19.9423i	−0.0759056	−	0.997115i
$401$		−	4.35670i		−	0.217563i	−0.994066	−	0.108782i	$-0.965305\pi$
$401$		−	4.35670i		−	0.217563i	0.994066	−	0.108782i	$-0.0346950\pi$
$402$	17.3104	+	0.679516i	0.863366	+	0.0338912i
$403$		−	19.1236i		−	0.952612i
$404$	−15.0488	−	17.6174i	−0.748707	−	0.876498i
$405$	9.38547	−	11.8724i	0.466368	−	0.589943i
$406$	12.9458	+	14.0037i	0.642490	+	0.694993i
$407$	−12.9911			−0.643946
$408$	2.26679	−	19.1694i	0.112223	−	0.949028i
$409$			10.2545i			0.507052i	0.967329	+	0.253526i	$0.0815903\pi$
$409$			10.2545i			0.507052i	−0.967329	+	0.253526i	$0.918410\pi$
$410$	−18.9565	+	7.11703i	−0.936193	+	0.351485i
$411$		−	34.9142i		−	1.72219i
$412$	8.71048	+	10.1972i	0.429134	+	0.502380i
$413$	−5.54306			−0.272756
$414$	−4.71205	+	4.35608i	−0.231585	+	0.214090i
$415$	0.656149	+	5.60869i	0.0322091	+	0.275320i
$416$	−11.4368	−	2.27282i	−0.560734	−	0.111434i
$417$			14.5117i			0.710639i
$418$	−0.710908	+	18.1101i	−0.0347716	+	0.885795i
$419$			10.0143i			0.489231i	0.969620	+	0.244615i	$0.0786617\pi$
$419$			10.0143i			0.489231i	−0.969620	+	0.244615i	$0.921338\pi$
$420$	−15.0106	−	13.9114i	−0.732445	−	0.678806i
$421$	9.92673	−	9.92673i	0.483799	−	0.483799i	−0.422544	−	0.906343i	$-0.638863\pi$
$421$	9.92673	−	9.92673i	0.483799	−	0.483799i	0.906343	+	0.422544i	$0.138863\pi$
$422$	−8.28506	+	7.65917i	−0.403310	+	0.372843i
$423$			2.90900i			0.141441i
$424$	−17.6754	−	2.09012i	−0.858395	−	0.101505i
$425$	5.10220	+	21.5081i	0.247493	+	1.04330i
$426$	4.49247	−	4.15309i	0.217661	−	0.201218i
$427$			8.29403i			0.401376i
$428$	−21.9792	−	25.7306i	−1.06240	−	1.24374i
$429$	6.80067	−	6.80067i	0.328339	−	0.328339i
$430$	−25.7213	+	1.99026i	−1.24039	+	0.0959786i
$431$	−27.1267			−1.30665			−0.653323	−	0.757079i	$-0.726626\pi$
$431$	−27.1267			−1.30665			−0.653323	+	0.757079i	$0.726626\pi$
$432$	3.49073	−	22.0598i	0.167948	−	1.06135i
$433$	17.9466	+	17.9466i	0.862459	+	0.862459i	0.991623	−	0.129164i	$-0.0412295\pi$
$433$	17.9466	+	17.9466i	0.862459	+	0.862459i	−0.129164	+	0.991623i	$0.541229\pi$
$434$	1.52565	−	38.8654i	0.0732335	−	1.86560i
$435$	1.82446	+	15.5953i	0.0874763	+	0.747738i
$436$	27.7144	−	23.6737i	1.32728	−	1.13376i
$437$	−31.1807			−1.49157
$438$	−1.73708	−	1.87903i	−0.0830010	−	0.0897837i
$439$	10.8545	−	10.8545i	0.518057	−	0.518057i	−0.398926	−	0.916983i	$-0.630617\pi$
$439$	10.8545	−	10.8545i	0.518057	−	0.518057i	0.916983	+	0.398926i	$0.130617\pi$
$440$	19.1160	+	0.0238032i	0.911321	+	0.00113477i
$441$	1.10347			0.0525461
$442$	12.8778	+	0.505513i	0.612533	+	0.0240448i
$443$	−28.9513	−	28.9513i	−1.37552	−	1.37552i	−0.852037	−	0.523481i	$-0.824633\pi$
$443$	−28.9513	−	28.9513i	−1.37552	−	1.37552i	−0.523481	−	0.852037i	$-0.675367\pi$
$444$	8.61883	+	10.0899i	0.409032	+	0.478846i
$445$	17.5389	−	2.05184i	0.831424	−	0.0972665i
$446$	13.3464	−	12.3382i	0.631971	−	0.584230i
$447$	11.8835	+	11.8835i	0.562069	+	0.562069i
$448$	−23.0620	−	5.53152i	−1.08958	−	0.261340i
$449$	−30.5714			−1.44275			−0.721376	−	0.692543i	$-0.756490\pi$
$449$	−30.5714			−1.44275			−0.721376	+	0.692543i	$0.756490\pi$
$450$	0.839781	+	4.28151i	0.0395876	+	0.201832i
$451$	−5.38440	−	18.5894i	−0.253541	−	0.875342i
$452$	18.0101	+	21.0841i	0.847125	+	0.991714i
$453$	8.88443	−	8.88443i	0.417427	−	0.417427i
$454$	1.27681	−	32.5264i	0.0599239	−	1.52654i
$455$	8.47380	−	10.7191i	0.397258	−	0.502521i
$456$	14.5374	−	11.4628i	0.680774	−	0.536796i
$457$	−6.22884			−0.291373			−0.145686	−	0.989331i	$-0.546539\pi$
$457$	−6.22884			−0.291373			−0.145686	+	0.989331i	$0.546539\pi$
$458$	−8.14603	+	7.53065i	−0.380639	+	0.351884i
$459$			24.6849i			1.15219i
$460$	1.24907	+	32.8635i	0.0582380	+	1.53227i
$461$	29.8643			1.39092			0.695460	−	0.718565i	$-0.255201\pi$
$461$	29.8643			1.39092			0.695460	+	0.718565i	$0.255201\pi$
$462$	14.3638	−	13.2787i	0.668262	−	0.617779i
$463$			34.2640i			1.59238i	0.605044	+	0.796192i	$0.293155\pi$
$463$			34.2640i			1.59238i	−0.605044	+	0.796192i	$0.706845\pi$
$464$	10.6971	+	14.7189i	0.496600	+	0.683307i
$465$	19.8597	−	25.1220i	0.920971	−	1.16501i
$466$	22.2872	+	0.874878i	1.03244	+	0.0405279i
$467$	15.6866	+	15.6866i	0.725889	+	0.725889i	0.969798	−	0.243909i	$-0.0784298\pi$
$467$	15.6866	+	15.6866i	0.725889	+	0.725889i	−0.243909	+	0.969798i	$0.578430\pi$
$468$	2.53595	+	0.199403i	0.117224	+	0.00921742i
$469$			23.5246i			1.08626i
$470$	11.3238	+	9.69722i	0.522327	+	0.447300i
$471$	−30.1038			−1.38711
$472$	−5.25201	−	0.621051i	−0.241743	−	0.0285862i
$473$		−	24.6579i		−	1.13377i
$474$	3.22136	+	3.48461i	0.147962	+	0.160053i
$475$	−11.1260	+	18.0463i	−0.510494	+	0.828019i
$476$	26.1316	+	2.05474i	1.19774	+	0.0941788i
$477$	3.88284			0.177783
$478$	6.53747	−	6.04360i	0.299017	−	0.276428i
$479$	−20.5525	+	20.5525i	−0.939067	+	0.939067i	−0.998247	−	0.0591805i	$-0.981151\pi$
$479$	−20.5525	+	20.5525i	−0.939067	+	0.939067i	0.0591805	+	0.998247i	$0.481151\pi$
$480$	−12.6638	−	14.8628i	−0.578022	−	0.678389i
$481$	−6.26475	+	6.26475i	−0.285648	+	0.285648i
$482$	−0.195856	+	4.98937i	−0.00892101	+	0.227260i
$483$	23.7963	+	23.7963i	1.08277	+	1.08277i
$484$	0.292299	−	3.71738i	0.0132863	−	0.168972i
$485$	13.4200	−	16.9760i	0.609372	−	0.770839i
$486$	−0.349626	+	8.90661i	−0.0158594	+	0.404012i
$487$	−21.1914	+	21.1914i	−0.960273	+	0.960273i	−0.999240	−	0.0389676i	$-0.987593\pi$
$487$	−21.1914	+	21.1914i	−0.960273	+	0.960273i	0.0389676	+	0.999240i	$0.487593\pi$
$488$	−0.929273	+	7.85853i	−0.0420662	+	0.355739i
$489$	−4.41248	−	4.41248i	−0.199539	−	0.199539i
$490$	3.67843	−	4.29544i	0.166175	−	0.194048i
$491$		−	23.7640i		−	1.07245i	−0.844074	−	0.536227i	$-0.819849\pi$
$491$		−	23.7640i		−	1.07245i	0.844074	−	0.536227i	$-0.180151\pi$
$492$	−10.8657	+	16.5149i	−0.489866	+	0.744549i
$493$	−14.2203	−	14.2203i	−0.640448	−	0.640448i
$494$	8.39048	+	9.07612i	0.377505	+	0.408354i
$495$	−4.14201	+	0.484564i	−0.186169	+	0.0217795i
$496$	5.80007	−	36.6538i	0.260431	−	1.64580i
$497$	5.87458	+	5.87458i	0.263511	+	0.263511i
$498$	3.74249	+	4.04832i	0.167705	+	0.181410i
$499$	1.32382	−	1.32382i	0.0592624	−	0.0592624i	−0.676854	−	0.736117i	$-0.736657\pi$
$499$	1.32382	−	1.32382i	0.0592624	−	0.0592624i	0.736117	+	0.676854i	$0.236657\pi$
$500$	19.4659	+	11.0035i	0.870543	+	0.492093i
$501$			11.6812i			0.521880i
$502$	−26.6072	−	1.04446i	−1.18754	−	0.0466164i
$503$		−	7.86192i		−	0.350546i	−0.984520	−	0.175273i	$-0.943919\pi$
$503$		−	7.86192i		−	0.350546i	0.984520	−	0.175273i	$-0.0560808\pi$
$504$	5.13798	+	0.607568i	0.228864	+	0.0270632i
$505$	25.7291	−	3.01000i	1.14493	−	0.133943i
$506$	−31.4095	−	1.23297i	−1.39632	−	0.0548122i
$507$			13.5089i			0.599951i
$508$	−12.7718	−	14.9517i	−0.566658	−	0.663376i
$509$	18.0015	−	18.0015i	0.797904	−	0.797904i	−0.184860	−	0.982765i	$-0.559183\pi$
$509$	18.0015	−	18.0015i	0.797904	−	0.797904i	0.982765	+	0.184860i	$0.0591833\pi$
$510$	16.3922	+	14.0376i	0.725857	+	0.621594i
$511$	2.45712	−	2.45712i	0.108697	−	0.108697i
$512$	−21.2313	−	7.82498i	−0.938301	−	0.345818i
$513$	−16.7405	+	16.7405i	−0.739113	+	0.739113i
$514$	−0.638978	+	16.2778i	−0.0281841	+	0.717981i
$515$	−14.8924	+	1.74223i	−0.656238	+	0.0767718i
$516$	−19.1512	+	16.3590i	−0.843086	+	0.720167i
$517$	−10.0760	+	10.0760i	−0.443141	+	0.443141i
$518$	−13.2318	+	12.2323i	−0.581374	+	0.537454i
$519$	−18.9639	−	18.9639i	−0.832421	−	0.832421i
$520$	9.22985	−	9.20690i	0.404756	−	0.403749i
$521$	−11.6549	+	11.6549i	−0.510612	+	0.510612i	−0.914714	−	0.404102i	$-0.867584\pi$
$521$	−11.6549	+	11.6549i	−0.510612	+	0.510612i	0.404102	+	0.914714i	$0.367584\pi$
$522$	−2.69455	−	2.91474i	−0.117937	−	0.127575i
$523$	−12.8140	+	12.8140i	−0.560318	+	0.560318i	−0.929398	−	0.369079i	$-0.879673\pi$
$523$	−12.8140	+	12.8140i	−0.560318	+	0.560318i	0.369079	+	0.929398i	$0.379673\pi$
$524$	−7.99666	−	0.628782i	−0.349336	−	0.0274685i
$525$	22.2635	−	5.28140i	0.971660	−	0.230499i
$526$	−24.3951	−	0.957622i	−1.06368	−	0.0417543i
$527$			41.0156i			1.78667i
$528$	15.0973	−	10.9721i	0.657026	−	0.477500i
$529$		−	31.0786i		−	1.35124i
$530$	12.9435	−	15.1146i	0.562231	−	0.656537i
$531$	1.15373			0.0500677
$532$	16.3281	+	19.1151i	0.707915	+	0.828743i
$533$	−11.5610	−	6.36790i	−0.500761	−	0.275824i
$534$	12.6595	−	11.7031i	0.547829	−	0.506444i
$535$	37.5781	−	4.39618i	1.62464	−	0.190063i
$536$	−2.63573	+	22.2894i	−0.113846	+	0.962755i
$537$	9.25939	−	9.25939i	0.399572	−	0.399572i
$538$	−1.42729	+	36.3599i	−0.0615351	+	1.56758i
$539$	3.82211	+	3.82211i	0.164630	+	0.164630i
$540$	18.3146	+	16.9734i	0.788137	+	0.730420i
$541$		−	42.2366i		−	1.81589i	−0.419087	−	0.907946i	$-0.637650\pi$
$541$		−	42.2366i		−	1.81589i	0.419087	−	0.907946i	$-0.362350\pi$
$542$	0.400986	−	10.2150i	0.0172238	−	0.438771i
$543$	17.1650	−	17.1650i	0.736622	−	0.736622i
$544$	24.5293	+	4.87467i	1.05168	+	0.209000i
$545$	4.73510	+	40.4752i	0.202830	+	1.73377i
$546$	0.523268	−	13.3301i	0.0223938	−	0.570475i
$547$			11.8730i			0.507653i	0.967250	+	0.253827i	$0.0816892\pi$
$547$			11.8730i			0.507653i	−0.967250	+	0.253827i	$0.918311\pi$
$548$	45.0957	+	3.54590i	1.92639	+	0.151473i
$549$		−	1.72632i		−	0.0736776i
$550$	−11.9212	+	17.7388i	−0.508322	+	0.756383i
$551$		−	19.2875i		−	0.821674i
$552$	19.8807	+	25.2130i	0.846179	+	1.07314i
$553$	−4.55665	+	4.55665i	−0.193768	+	0.193768i
$554$	−3.81634	+	3.52804i	−0.162141	+	0.149892i
$555$	−14.7357	+	1.72390i	−0.625496	+	0.0731754i
$556$	−18.7435	−	1.47381i	−0.794900	−	0.0625034i
$557$	−37.9898			−1.60968			−0.804840	−	0.593492i	$-0.797749\pi$
$557$	−37.9898			−1.60968			−0.804840	+	0.593492i	$0.797749\pi$
$558$	−0.317549	+	8.08945i	−0.0134429	+	0.342454i
$559$	−11.8909	−	11.8909i	−0.502930	−	0.502930i
$560$	19.4926	−	17.9751i	0.823714	−	0.759587i
$561$	−14.5859	+	14.5859i	−0.615816	+	0.615816i
$562$	−16.6018	−	17.9584i	−0.700304	−	0.757531i
$563$		−	26.0989i		−	1.09994i	−0.835185	−	0.549969i	$-0.814639\pi$
$563$		−	26.0989i		−	1.09994i	0.835185	−	0.549969i	$-0.185361\pi$
$564$	14.5106	+	1.14098i	0.611006	+	0.0480438i
$565$	−30.7921	+	3.60230i	−1.29543	+	0.151550i
$566$	23.2140	−	21.4603i	0.975758	−	0.902045i
$567$	20.0643			0.842622
$568$	4.90793	+	6.22433i	0.205932	+	0.261167i
$569$	−33.8234			−1.41795			−0.708976	−	0.705232i	$-0.750843\pi$
$569$	−33.8234			−1.41795			−0.708976	+	0.705232i	$0.750843\pi$
$570$	1.59680	+	20.6365i	0.0668828	+	0.864367i
$571$	17.2518	+	17.2518i	0.721964	+	0.721964i	0.969005	−	0.247041i	$-0.0794582\pi$
$571$	17.2518	+	17.2518i	0.721964	+	0.721964i	−0.247041	+	0.969005i	$0.579458\pi$
$572$	8.09316	+	9.47451i	0.338392	+	0.396149i
$573$	15.7978	+	15.7978i	0.659963	+	0.659963i
$574$	−22.9877	−	13.8640i	−0.959487	−	0.578672i
$575$	−31.2988	−	19.2964i	−1.30525	−	0.804717i
$576$	4.80013	+	1.15133i	0.200005	+	0.0479722i
$577$			24.9786i			1.03987i	0.854205	+	0.519937i	$0.174045\pi$
$577$			24.9786i			1.03987i	−0.854205	+	0.519937i	$0.825955\pi$
$578$	−3.59673	−	0.141189i	−0.149604	−	0.00587267i
$579$		−	9.82653i		−	0.408376i
$580$	−20.3284	+	0.772635i	−0.844092	+	0.0320819i
$581$	−5.29379	+	5.29379i	−0.219623	+	0.219623i
$582$	0.828703	−	21.1109i	0.0343509	−	0.875077i
$583$	13.4491	+	13.4491i	0.557005	+	0.557005i
$584$	2.60340	−	2.05281i	0.107730	−	0.0849457i
$585$	−1.76374	+	2.23108i	−0.0729216	+	0.0922440i
$586$	1.00592	−	25.6255i	0.0415541	−	1.05858i
$587$	−23.1395			−0.955070			−0.477535	−	0.878613i	$-0.658470\pi$
$587$	−23.1395			−0.955070			−0.477535	+	0.878613i	$0.658470\pi$
$588$	0.432805	−	5.50428i	0.0178486	−	0.226993i
$589$	−27.8155	+	27.8155i	−1.14612	+	1.14612i
$590$	3.84599	−	4.49110i	0.158337	−	0.184896i
$591$	24.6172	−	24.6172i	1.01262	−	1.01262i
$592$	−13.9076	+	10.1075i	−0.571599	+	0.415414i
$593$			22.5816i			0.927314i	0.886015	+	0.463657i	$0.153463\pi$
$593$			22.5816i			0.927314i	−0.886015	+	0.463657i	$0.846537\pi$
$594$	−17.5254	+	16.2014i	−0.719074	+	0.664753i
$595$	−18.1743	+	22.9901i	−0.745076	+	0.942502i
$596$	−16.5557	+	14.1420i	−0.678149	+	0.579277i
$597$	7.74018	−	7.74018i	0.316785	−	0.316785i
$598$	−15.7413	+	14.5521i	−0.643709	+	0.595081i
$599$	30.7814			1.25770			0.628848	−	0.777528i	$-0.283527\pi$
$599$	30.7814			1.25770			0.628848	+	0.777528i	$0.283527\pi$
$600$	21.6863	−	2.50966i	0.885339	−	0.102456i
$601$	5.29646	+	5.29646i	0.216047	+	0.216047i	0.806830	−	0.590783i	$-0.201181\pi$
$601$	5.29646	+	5.29646i	0.216047	+	0.216047i	−0.590783	+	0.806830i	$0.701181\pi$
$602$	−23.2175	−	25.1148i	−0.946276	−	1.02360i
$603$		−	4.89642i		−	0.199397i
$604$	10.5729	+	12.3776i	0.430207	+	0.503636i
$605$	3.27048	+	2.58541i	0.132964	+	0.105112i
$606$	18.5711	−	17.1682i	0.754401	−	0.697411i
$607$	18.0562	−	18.0562i	0.732877	−	0.732877i	−0.238312	−	0.971189i	$-0.576594\pi$
$607$	18.0562	−	18.0562i	0.732877	−	0.732877i	0.971189	+	0.238312i	$0.0765940\pi$
$608$	13.3291	+	19.9408i	0.540568	+	0.808707i
$609$	−14.7197	+	14.7197i	−0.596473	+	0.596473i
$610$	−6.71999	−	5.75472i	−0.272084	−	0.233002i
$611$			9.71795i			0.393146i
$612$	−5.43903	−	0.427674i	−0.219860	−	0.0172877i
$613$	5.56262	−	5.56262i	0.224672	−	0.224672i	−0.585790	−	0.810463i	$-0.699216\pi$
$613$	5.56262	−	5.56262i	0.224672	−	0.224672i	0.810463	+	0.585790i	$0.199216\pi$
$614$	−26.8763	+	24.8459i	−1.08464	+	1.00270i
$615$	−8.57425	−	20.3713i	−0.345747	−	0.821450i
$616$	15.6921	+	19.9010i	0.632253	+	0.801834i
$617$	−31.7482	−	31.7482i	−1.27813	−	1.27813i	−0.941711	−	0.336423i	$-0.890783\pi$
$617$	−31.7482	−	31.7482i	−1.27813	−	1.27813i	−0.336423	−	0.941711i	$-0.609217\pi$
$618$	−10.7492	+	9.93721i	−0.432398	+	0.399733i
$619$	16.3590			0.657525			0.328763	−	0.944413i	$-0.393368\pi$
$619$	16.3590			0.657525			0.328763	+	0.944413i	$0.393368\pi$
$620$	30.4310	+	28.2025i	1.22214	+	1.13264i
$621$	−29.0342	−	29.0342i	−1.16510	−	1.16510i
$622$	19.4691	−	17.9983i	0.780641	−	0.721668i
$623$	16.5542	+	16.5542i	0.663229	+	0.663229i
$624$	1.98931	−	12.5715i	0.0796362	−	0.503264i
$625$	−22.3362	+	11.2292i	−0.893447	+	0.449168i
$626$	−1.43299	+	36.5049i	−0.0572738	+	1.45903i
$627$	−19.7833			−0.790071
$628$	3.05735	−	38.8825i	0.122002	−	1.55158i
$629$	13.4364	−	13.4364i	0.535746	−	0.535746i
$630$	−3.76249	+	4.39359i	−0.149901	+	0.175045i
$631$		−	35.5160i		−	1.41387i	−0.707280	−	0.706934i	$-0.750078\pi$
$631$		−	35.5160i		−	1.41387i	0.707280	−	0.706934i	$-0.249922\pi$
$632$	−4.82793	+	3.80686i	−0.192045	+	0.151429i
$633$	−8.70867	−	8.70867i	−0.346139	−	0.346139i
$634$	0.952825	−	24.2729i	0.0378415	−	0.964000i
$635$	21.8361	−	2.55456i	0.866541	−	0.101375i
$636$	1.52294	−	19.3683i	0.0603884	−	0.768002i
$637$	3.68630			0.146056
$638$	0.762680	−	19.4290i	0.0301948	−	0.769202i
$639$	−1.22274	−	1.22274i	−0.0483707	−	0.0483707i
$640$	20.4831	−	14.8473i	0.809665	−	0.586892i
$641$	25.6964	+	25.6964i	1.01495	+	1.01495i	0.999887	+	0.0150587i	$0.00479353\pi$
$641$	25.6964	+	25.6964i	1.01495	+	1.01495i	0.0150587	+	0.999887i	$0.495206\pi$
$642$	27.1236	−	25.0746i	1.07048	−	0.989615i
$643$			21.6776i			0.854879i	0.904044	+	0.427440i	$0.140584\pi$
$643$			21.6776i			0.854879i	−0.904044	+	0.427440i	$0.859416\pi$
$644$	−33.1524	+	28.3189i	−1.30639	+	1.11592i
$645$	−3.27206	−	27.9693i	−0.128837	−	1.10129i
$646$	−17.9956	−	19.4662i	−0.708029	−	0.765887i
$647$	−11.9198	+	11.9198i	−0.468618	+	0.468618i	−0.901467	−	0.432849i	$-0.857508\pi$
$647$	−11.9198	+	11.9198i	−0.468618	+	0.468618i	0.432849	+	0.901467i	$0.357508\pi$
$648$	19.0108	+	2.24803i	0.746815	+	0.0883110i
$649$	3.99621	+	3.99621i	0.156865	+	0.156865i
$650$	2.80541	+	14.3030i	0.110037	+	0.561010i
$651$	42.4562			1.66399
$652$	6.14736	−	5.25109i	0.240749	−	0.205649i
$653$	29.0297			1.13602			0.568010	−	0.823022i	$-0.307713\pi$
$653$	29.0297			1.13602			0.568010	+	0.823022i	$0.307713\pi$
$654$	27.0077	+	29.2147i	1.05609	+	1.14239i
$655$	5.56163	−	7.03532i	0.217311	−	0.274893i
$656$	−20.2273	−	15.7116i	−0.789745	−	0.613435i
$657$	−0.511426	+	0.511426i	−0.0199526	+	0.0199526i
$658$	−0.775283	+	19.7501i	−0.0302237	+	0.769938i
$659$	8.94014	−	8.94014i	0.348258	−	0.348258i	−0.511202	−	0.859460i	$-0.670800\pi$
$659$	8.94014	−	8.94014i	0.348258	−	0.348258i	0.859460	+	0.511202i	$0.170800\pi$
$660$	0.792500	+	20.8511i	0.0308480	+	0.811627i
$661$		−	21.5704i		−	0.838989i	−0.907758	−	0.419495i	$-0.862207\pi$
$661$		−	21.5704i		−	0.838989i	0.907758	−	0.419495i	$-0.137793\pi$
$662$	22.7556	+	24.6152i	0.884423	+	0.956695i
$663$			14.0676i			0.546339i
$664$	−5.60896	+	4.42271i	−0.217670	+	0.171634i
$665$	−27.9164	+	3.26588i	−1.08255	+	0.126645i
$666$	2.75408	−	2.54602i	0.106718	−	0.0986564i
$667$	33.4514			1.29524
$668$	−15.0877	−	1.18635i	−0.583759	−	0.0459013i
$669$	14.0288	+	14.0288i	0.542385	+	0.542385i
$670$	−19.0601	−	16.3223i	−0.736356	−	0.630585i
$671$	5.97950	−	5.97950i	0.230836	−	0.230836i
$672$	5.04588	−	25.3908i	0.194649	−	0.979472i
$673$			10.1260i			0.390327i	0.980771	+	0.195164i	$0.0625238\pi$
$673$			10.1260i			0.390327i	−0.980771	+	0.195164i	$0.937476\pi$
$674$	−33.2331	−	35.9488i	−1.28009	−	1.38470i
$675$	−27.1640	+	6.44390i	−1.04554	+	0.248026i
$676$	−17.4483	−	1.37197i	−0.671088	−	0.0527680i
$677$	−14.7928	−	14.7928i	−0.568534	−	0.568534i	0.363183	−	0.931718i	$-0.381690\pi$
$677$	−14.7928	−	14.7928i	−0.568534	−	0.568534i	−0.931718	+	0.363183i	$0.881690\pi$
$678$	−22.2256	+	20.5466i	−0.853567	+	0.789086i
$679$	28.6894			1.10100
$680$	−19.7959	+	19.7467i	−0.759139	+	0.757250i
$681$	35.5316			1.36157
$682$	−29.1195	+	26.9197i	−1.11504	+	1.03081i
$683$	19.8031			0.757746			0.378873	−	0.925449i	$-0.376312\pi$
$683$	19.8031			0.757746			0.378873	+	0.925449i	$0.376312\pi$
$684$	−3.39854	−	3.97861i	−0.129947	−	0.152126i
$685$	−31.3638	+	39.6744i	−1.19835	+	1.51588i
$686$	−21.8328	−	0.857041i	−0.833581	−	0.0327220i
$687$	−8.56254	−	8.56254i	−0.326681	−	0.326681i
$688$	−19.1846	−	26.3974i	−0.731405	−	1.00639i
$689$	12.9712			0.494163
$690$	−35.7911	+	2.76944i	−1.36254	+	0.105431i
$691$	21.0786	−	21.0786i	0.801867	−	0.801867i	−0.181520	−	0.983387i	$-0.558102\pi$
$691$	21.0786	−	21.0786i	0.801867	−	0.801867i	0.983387	+	0.181520i	$0.0581017\pi$
$692$	26.4200	−	22.5680i	1.00434	−	0.857907i
$693$	−3.90945	−	3.90945i	−0.148508	−	0.148508i
$694$	−1.03183	+	26.2855i	−0.0391677	+	0.997783i
$695$	13.0360	−	16.4902i	0.494482	−	0.625508i
$696$	−15.5960	+	12.2976i	−0.591167	+	0.466140i
$697$	24.7956	+	13.6577i	0.939201	+	0.517321i
$698$	27.8015	+	1.09134i	1.05230	+	0.0413079i
$699$			24.3464i			0.920864i
$700$	4.56044	+	29.2923i	0.172369	+	1.10714i
$701$	15.4811			0.584714			0.292357	−	0.956309i	$-0.405560\pi$
$701$	15.4811			0.584714			0.292357	+	0.956309i	$0.405560\pi$
$702$	−0.638445	+	16.2642i	−0.0240966	+	0.613852i
$703$	18.2243			0.687344
$704$	12.6384	+	20.6142i	0.476329	+	0.776928i
$705$	−10.0920	+	12.7662i	−0.380088	+	0.480801i
$706$	24.5500	+	26.5562i	0.923953	+	0.999456i
$707$	24.2846	+	24.2846i	0.913316	+	0.913316i
$708$	0.452520	−	5.75501i	0.0170067	−	0.216287i
$709$	7.17183	+	7.17183i	0.269344	+	0.269344i	0.828836	−	0.559492i	$-0.189004\pi$
$709$	7.17183	+	7.17183i	0.269344	+	0.269344i	−0.559492	+	0.828836i	$0.689004\pi$
$710$	−8.83573	+	0.683689i	−0.331599	+	0.0256584i
$711$	0.948422	−	0.948422i	0.0355686	−	0.0355686i
$712$	13.8302	+	17.5397i	0.518310	+	0.657329i
$713$	−48.2421	−	48.2421i	−1.80668	−	1.80668i
$714$	−1.12229	+	28.5899i	−0.0420006	+	1.06995i
$715$	−13.8370	+	1.61876i	−0.517473	+	0.0605381i
$716$	11.0192	+	12.8999i	0.411806	+	0.482094i
$717$	6.87172	+	6.87172i	0.256629	+	0.256629i
$718$	−2.09312	−	0.0821649i	−0.0781146	−	0.00306637i
$719$	−9.68519	−	9.68519i	−0.361197	−	0.361197i	0.503057	−	0.864253i	$-0.332209\pi$
$719$	−9.68519	−	9.68519i	−0.361197	−	0.361197i	−0.864253	+	0.503057i	$0.832209\pi$
$720$	−4.05720	+	3.74135i	−0.151203	+	0.139432i
$721$	−14.0563	−	14.0563i	−0.523483	−	0.523483i
$722$	−0.0566816	+	1.44394i	−0.00210947	+	0.0537380i
$723$	−5.45035			−0.202701
$724$	20.4273	+	23.9139i	0.759175	+	0.888752i
$725$	11.9362	−	19.3605i	0.443300	−	0.719031i
$726$	4.06710	+	0.159653i	0.150944	+	0.00592526i
$727$	28.5846			1.06015			0.530073	−	0.847952i	$-0.322165\pi$
$727$	28.5846			1.06015			0.530073	+	0.847952i	$0.322165\pi$
$728$	17.1642	+	2.02967i	0.636146	+	0.0752245i
$729$	−30.0340			−1.11237
$730$	0.285962	+	3.69566i	0.0105839	+	0.136782i
$731$	25.5032	+	25.5032i	0.943269	+	0.943269i
$732$	−8.61117	−	0.677101i	−0.318278	−	0.0250264i
$733$	−4.86128	+	4.86128i	−0.179555	+	0.179555i	−0.791162	−	0.611607i	$-0.790524\pi$
$733$	−4.86128	+	4.86128i	−0.179555	+	0.179555i	0.611607	+	0.791162i	$0.290524\pi$
$734$	11.8952	−	10.9966i	0.439059	−	0.405891i
$735$	4.84257	+	3.82820i	0.178621	+	0.141205i
$736$	−34.5846	+	23.1175i	−1.27481	+	0.852124i
$737$	16.9598	−	16.9598i	0.624724	−	0.624724i
$738$	4.78466	+	2.88565i	0.176126	+	0.106222i
$739$	−48.5523			−1.78603			−0.893013	−	0.450031i	$-0.851413\pi$
$739$	−48.5523			−1.78603			−0.893013	+	0.450031i	$0.851413\pi$
$740$	−0.730048	−	19.2079i	−0.0268371	−	0.706098i
$741$	−9.54018	+	9.54018i	−0.350467	+	0.350467i
$742$	26.3618	+	1.03482i	0.967771	+	0.0379895i
$743$	−1.48445	−	1.48445i	−0.0544594	−	0.0544594i	0.679353	−	0.733812i	$-0.262261\pi$
$743$	−1.48445	−	1.48445i	−0.0544594	−	0.0544594i	−0.733812	+	0.679353i	$0.762261\pi$
$744$	40.2270	+	4.75685i	1.47479	+	0.174395i
$745$	−2.82861	−	24.1787i	−0.103632	−	0.885838i
$746$	−4.66143	−	5.04235i	−0.170667	−	0.184614i
$747$	1.10185	−	1.10185i	0.0403146	−	0.0403146i
$748$	−17.3580	−	20.3207i	−0.634670	−	0.742997i
$749$	35.4682	+	35.4682i	1.29598	+	1.29598i
$750$	−11.1682	+	21.7028i	−0.407806	+	0.792475i
$751$	11.4482	+	11.4482i	0.417751	+	0.417751i	0.884428	−	0.466677i	$-0.154549\pi$
$751$	11.4482	+	11.4482i	0.417751	+	0.417751i	−0.466677	+	0.884428i	$0.654549\pi$
$752$	−2.94740	+	18.6262i	−0.107481	+	0.679228i
$753$		−	29.0655i		−	1.05920i
$754$	−9.00152	−	9.73710i	−0.327816	−	0.354604i
$755$	−18.0767	+	2.11475i	−0.657878	+	0.0769637i
$756$	−2.59506	+	33.0032i	−0.0943815	+	1.20032i
$757$	11.4281			0.415362			0.207681	−	0.978197i	$-0.433408\pi$
$757$	11.4281			0.415362			0.207681	+	0.978197i	$0.433408\pi$
$758$	5.47079	+	0.214754i	0.198708	+	0.00780023i
$759$		−	34.3115i		−	1.24543i
$760$	−26.8165	−	0.0333918i	−0.972738	−	0.00121125i
$761$	−10.4760			−0.379755			−0.189877	−	0.981808i	$-0.560809\pi$
$761$	−10.4760			−0.379755			−0.189877	+	0.981808i	$0.560809\pi$
$762$	15.7612	−	14.5705i	0.570968	−	0.527835i
$763$	−38.2027	+	38.2027i	−1.38303	+	1.38303i
$764$	−22.0091	+	18.8002i	−0.796261	+	0.680169i
$765$	3.78281	−	4.78516i	0.136768	−	0.173008i
$766$	50.5014	+	1.98242i	1.82469	+	0.0716276i
$767$	3.85421			0.139167
$768$	7.62576	−	23.4923i	0.275171	−	0.847704i
$769$		−	16.0229i		−	0.577800i	−0.957359	−	0.288900i	$-0.906711\pi$
$769$		−	16.0229i		−	0.577800i	0.957359	−	0.288900i	$-0.0932895\pi$
$770$	−28.2504	+	2.18596i	−1.01808	+	0.0787764i
$771$	−17.7817			−0.640391
$772$	12.6921	+	0.997985i	0.456798	+	0.0359183i
$773$			19.6802i			0.707848i	0.935274	+	0.353924i	$0.115153\pi$
$773$			19.6802i			0.707848i	−0.935274	+	0.353924i	$0.884847\pi$
$774$	4.83250	+	5.22740i	0.173701	+	0.187895i
$775$	−45.1347	+	10.7070i	−1.62129	+	0.384605i
$776$	27.1830	+	3.21440i	0.975814	+	0.115390i
$777$	−13.9084	−	13.9084i	−0.498960	−	0.498960i
$778$	18.5022	+	0.726297i	0.663335	+	0.0260390i
$779$	7.55340	+	26.0778i	0.270629	+	0.934334i
$780$	10.4372	+	9.67290i	0.373713	+	0.346345i
$781$		−	8.47045i		−	0.303097i
$782$	33.7614	−	31.2110i	1.20731	−	1.11610i
$783$	17.9597	−	17.9597i	0.641827	−	0.641827i
$784$	7.06545	+	1.11803i	0.252338	+	0.0399298i
$785$	34.2081	+	27.0426i	1.22094	+	0.965190i
$786$	0.343438	−	8.74896i	0.0122500	−	0.312065i
$787$	22.5369	−	22.5369i	0.803353	−	0.803353i	−0.180265	−	0.983618i	$-0.557695\pi$
$787$	22.5369	−	22.5369i	0.803353	−	0.803353i	0.983618	+	0.180265i	$0.0576955\pi$
$788$	29.2958	+	34.2961i	1.04362	+	1.22175i
$789$		−	26.6490i		−	0.948729i
$790$	−0.530307	−	6.85348i	−0.0188675	−	0.243836i
$791$	−29.0633	−	29.0633i	−1.03337	−	1.03337i
$792$	−3.26616	−	4.14220i	−0.116058	−	0.147187i
$793$		−	5.76702i		−	0.204793i
$794$	1.94401	−	49.5231i	0.0689904	−	1.75751i
$795$	17.0399	+	13.4705i	0.604341	+	0.477750i
$796$	9.21123	+	10.7834i	0.326483	+	0.382208i
$797$	−17.4581	+	17.4581i	−0.618396	+	0.618396i	−0.945120	−	0.326724i	$-0.894055\pi$
$797$	−17.4581	+	17.4581i	−0.618396	+	0.618396i	0.326724	+	0.945120i	$0.394055\pi$
$798$	−20.1499	+	18.6277i	−0.713299	+	0.659413i
$799$		−	20.8428i		−	0.737364i
$800$	1.03905	+	28.2652i	0.0367359	+	0.999325i
$801$	−3.44559	−	3.44559i	−0.121744	−	0.121744i
$802$	−0.241674	+	6.15657i	−0.00853381	+	0.217396i
$803$	−3.54287			−0.125025
$804$	−24.4241	−	1.92048i	−0.861373	−	0.0677302i
$805$	−5.66422	−	48.4172i	−0.199637	−	1.70648i
$806$	−1.06082	+	27.0240i	−0.0373657	+	0.951879i
$807$	−39.7192			−1.39818
$808$	20.2886	+	25.7304i	0.713751	+	0.905191i
$809$	25.9195	+	25.9195i	0.911280	+	0.911280i	0.996373	−	0.0850929i	$-0.0271187\pi$
$809$	25.9195	+	25.9195i	0.911280	+	0.911280i	−0.0850929	+	0.996373i	$0.527119\pi$
$810$	−13.9214	+	16.2565i	−0.489149	+	0.571196i
$811$	37.1832			1.30568			0.652839	−	0.757496i	$-0.273578\pi$
$811$	37.1832			1.30568			0.652839	+	0.757496i	$0.273578\pi$
$812$	−17.5172	−	20.5071i	−0.614735	−	0.719659i
$813$	11.1588			0.391355
$814$	18.3581	+	0.720641i	0.643451	+	0.0252585i
$815$	1.05030	+	8.97785i	0.0367904	+	0.314480i
$816$	−4.26662	+	26.9630i	−0.149361	+	0.943895i
$817$			34.5909i			1.21018i
$818$	0.568835	−	14.4909i	0.0198889	−	0.506662i
$819$	−3.77053			−0.131753
$820$	27.1827	−	9.00571i	0.949260	−	0.314493i
$821$	5.36728			0.187319			0.0936597	−	0.995604i	$-0.470143\pi$
$821$	5.36728			0.187319			0.0936597	+	0.995604i	$0.470143\pi$
$822$	−1.93675	+	49.3382i	−0.0675521	+	1.72087i
$823$			26.3813i			0.919594i	0.888024	+	0.459797i	$0.152078\pi$
$823$			26.3813i			0.919594i	−0.888024	+	0.459797i	$0.847922\pi$
$824$	−11.7433	−	14.8931i	−0.409099	−	0.518826i
$825$	−19.8583	−	12.2431i	−0.691376	−	0.426250i
$826$	7.83303	+	0.307483i	0.272546	+	0.0106987i
$827$	12.5425			0.436144			0.218072	−	0.975933i	$-0.430023\pi$
$827$	12.5425			0.436144			0.218072	+	0.975933i	$0.430023\pi$
$828$	6.90036	−	5.89431i	0.239804	−	0.204841i
$829$	21.0122			0.729784			0.364892	−	0.931050i	$-0.381106\pi$
$829$	21.0122			0.729784			0.364892	+	0.931050i	$0.381106\pi$
$830$	−0.616096	−	7.96218i	−0.0213850	−	0.276371i
$831$	−4.01147	−	4.01147i	−0.139156	−	0.139156i
$832$	16.0355	+	3.84619i	0.555932	+	0.133343i
$833$	−7.90625			−0.273935
$834$	0.804988	−	20.5068i	0.0278745	−	0.710092i
$835$	10.4934	−	13.2739i	0.363138	−	0.459361i
$836$	2.00920	−	25.5524i	0.0694897	−	0.883750i
$837$	−51.8013			−1.79051
$838$	0.555512	−	14.1515i	0.0191898	−	0.488854i
$839$	−31.9387	−	31.9387i	−1.10265	−	1.10265i	−0.994090	−	0.108555i	$-0.965378\pi$
$839$	−31.9387	−	31.9387i	−1.10265	−	1.10265i	−0.108555	−	0.994090i	$-0.534622\pi$
$840$	20.4402	+	20.4912i	0.705255	+	0.707014i
$841$		−	8.30792i		−	0.286480i
$842$	−14.5784	+	13.4771i	−0.502404	+	0.464450i
$843$	18.8766	−	18.8766i	0.650146	−	0.650146i
$844$	12.1327	−	10.3638i	0.417625	−	0.356736i
$845$	12.1352	−	15.3507i	0.417463	−	0.528080i
$846$	0.161368	−	4.11079i	0.00554793	−	0.141332i
$847$			5.52711i			0.189914i
$848$	24.8617	+	3.93409i	0.853753	+	0.135097i
$849$	24.4009	+	24.4009i	0.837438	+	0.837438i
$850$	−6.01695	−	30.6767i	−0.206380	−	1.05220i
$851$			31.6076i			1.08350i
$852$	−6.57880	+	5.61963i	−0.225386	+	0.192525i
$853$	15.4377	−	15.4377i	0.528577	−	0.528577i	−0.391571	−	0.920148i	$-0.628068\pi$
$853$	15.4377	−	15.4377i	0.528577	−	0.528577i	0.920148	+	0.391571i	$0.128068\pi$
$854$	0.460084	−	11.7205i	0.0157438	−	0.401067i
$855$	5.81053	−	0.679761i	0.198716	−	0.0232473i
$856$	29.6320	+	37.5798i	1.01280	+	1.28445i
$857$	−11.2527	+	11.2527i	−0.384383	+	0.384383i	−0.872679	−	0.488295i	$-0.837619\pi$
$857$	−11.2527	+	11.2527i	−0.384383	+	0.384383i	0.488295	+	0.872679i	$0.337619\pi$
$858$	−9.98744	+	9.23295i	−0.340966	+	0.315208i
$859$		−	5.66627i		−	0.193330i	−0.995317	−	0.0966652i	$-0.969182\pi$
$859$		−	5.66627i		−	0.193330i	0.995317	−	0.0966652i	$-0.0308176\pi$
$860$	36.4578	−	1.38567i	1.24320	−	0.0472511i
$861$	14.1374	−	25.6665i	0.481800	−	0.874712i
$862$	38.3334	+	1.50477i	1.30564	+	0.0512525i
$863$	11.0287	+	11.0287i	0.375422	+	0.375422i	0.869447	−	0.494026i	$-0.164475\pi$
$863$	11.0287	+	11.0287i	0.375422	+	0.375422i	−0.494026	+	0.869447i	$0.664475\pi$
$864$	−6.15653	+	30.9796i	−0.209449	+	1.05395i
$865$	4.51395	+	38.5848i	0.153479	+	1.31192i
$866$	−24.3653	−	26.3563i	−0.827966	−	0.895625i
$867$		−	3.92904i		−	0.133437i
$868$	−4.31186	+	54.8370i	−0.146354	+	1.86129i
$869$	6.57015			0.222877
$870$	−1.71309	−	22.1393i	−0.0580793	−	0.750594i
$871$		−	16.3572i		−	0.554242i
$872$	−40.4771	+	31.9165i	−1.37073	+	1.08083i
$873$	−5.97142			−0.202102
$874$	44.0622	+	1.72965i	1.49043	+	0.0585062i
$875$	−30.0432	−	13.9981i	−1.01565	−	0.473221i
$876$	2.35048	+	2.75167i	0.0794155	+	0.0929702i
$877$	19.8199	−	19.8199i	0.669270	−	0.669270i	−0.288277	−	0.957547i	$-0.593082\pi$
$877$	19.8199	−	19.8199i	0.669270	−	0.669270i	0.957547	+	0.288277i	$0.0930823\pi$
$878$	−15.9409	+	14.7366i	−0.537979	+	0.497338i
$879$	27.9930			0.944181
$880$	−27.0120	−	1.09404i	−0.910575	−	0.0368800i
$881$		−	15.9214i		−	0.536406i	−0.963362	−	0.268203i	$-0.913570\pi$
$881$		−	15.9214i		−	0.536406i	0.963362	−	0.268203i	$-0.0864298\pi$
$882$	−1.55934	−	0.0612114i	−0.0525057	−	0.00206109i
$883$	10.2171			0.343831			0.171916	−	0.985112i	$-0.445004\pi$
$883$	10.2171			0.343831			0.171916	+	0.985112i	$0.445004\pi$
$884$	−18.1699	−	1.42871i	−0.611119	−	0.0480526i
$885$	5.06316	+	4.00258i	0.170196	+	0.134545i
$886$	39.3058	+	42.5178i	1.32051	+	1.42841i
$887$		−	19.9340i		−	0.669319i	−0.942339	−	0.334659i	$-0.891379\pi$
$887$		−	19.9340i		−	0.669319i	0.942339	−	0.334659i	$-0.108621\pi$
$888$	−11.6198	−	14.7364i	−0.389934	−	0.494521i
$889$	20.6101	+	20.6101i	0.691242	+	0.691242i
$890$	−24.8985	+	1.92659i	−0.834599	+	0.0645794i
$891$	−14.4652	−	14.4652i	−0.484602	−	0.484602i
$892$	−19.5446	+	16.6950i	−0.654401	+	0.558991i
$893$	14.1349	−	14.1349i	0.473006	−	0.473006i
$894$	−16.1336	−	17.4520i	−0.539589	−	0.583683i
$895$	−18.8396	+	2.20401i	−0.629739	+	0.0736718i
$896$	32.2827	+	9.09603i	1.07849	+	0.303877i
$897$	−16.5461	−	16.5461i	−0.552459	−	0.552459i
$898$	43.2012	+	1.69585i	1.44164	+	0.0565912i
$899$	29.8412	−	29.8412i	0.995259	−	0.995259i
$900$	−0.949212	−	6.09690i	−0.0316404	−	0.203230i
$901$	−27.8202			−0.926826
$902$	6.57764	+	26.5679i	0.219012	+	0.884613i
$903$	26.3989	−	26.3989i	0.878501	−	0.878501i
$904$	−24.2810	−	30.7936i	−0.807573	−	1.02418i
$905$	−34.9248	+	4.08578i	−1.16094	+	0.135816i
$906$	−13.0476	+	12.0620i	−0.433479	+	0.400732i
$907$	7.01709	−	7.01709i	0.232999	−	0.232999i	−0.580944	−	0.813943i	$-0.697317\pi$
$907$	7.01709	−	7.01709i	0.232999	−	0.232999i	0.813943	+	0.580944i	$0.197317\pi$
$908$	−3.60860	+	45.8931i	−0.119756	+	1.52302i
$909$	−5.05460	−	5.05460i	−0.167650	−	0.167650i
$910$	−12.5691	+	14.6774i	−0.416663	+	0.486552i
$911$	−0.588254			−0.0194897			−0.00974486	−	0.999953i	$-0.503102\pi$
$911$	−0.588254			−0.0194897			−0.00974486	+	0.999953i	$0.503102\pi$
$912$	−21.1790	+	15.3920i	−0.701306	+	0.509680i
$913$	7.63302			0.252616
$914$	8.80213	+	0.345525i	0.291149	+	0.0114290i
$915$	5.98902	−	7.57596i	0.197991	−	0.250453i
$916$	11.9291	−	10.1899i	0.394149	−	0.336683i
$917$	11.8897			0.392632
$918$	1.36932	−	34.8829i	0.0451942	−	1.15131i
$919$	23.5896	+	23.5896i	0.778150	+	0.778150i	0.979516	−	0.201366i	$-0.0645380\pi$
$919$	23.5896	+	23.5896i	0.778150	+	0.778150i	−0.201366	+	0.979516i	$0.564538\pi$
$920$	0.0579135	−	46.5096i	0.00190935	−	1.53338i
$921$	−28.2504	−	28.2504i	−0.930883	−	0.930883i
$922$	−42.2020	−	1.65663i	−1.38985	−	0.0545581i
$923$	−4.08473	−	4.08473i	−0.134451	−	0.134451i
$924$	−21.0344	+	17.9676i	−0.691980	+	0.591091i
$925$	18.2934	+	11.2783i	0.601482	+	0.370828i
$926$	1.90069	−	48.4193i	0.0624604	−	1.59116i
$927$	2.92568	+	2.92568i	0.0960918	+	0.0960918i
$928$	−14.2998	−	21.3930i	−0.469415	−	0.702260i
$929$	30.7912	−	30.7912i	1.01023	−	1.01023i	0.0102800	−	0.999947i	$-0.496728\pi$
$929$	30.7912	−	30.7912i	1.01023	−	1.01023i	0.999947	−	0.0102800i	$-0.00327228\pi$
$930$	−29.4578	+	34.3989i	−0.965959	+	1.12798i
$931$	−5.36177	−	5.36177i	−0.175725	−	0.175725i
$932$	−31.4461	−	2.47262i	−1.03005	−	0.0809935i
$933$	20.4646	+	20.4646i	0.669980	+	0.669980i
$934$	−21.2970	−	23.0373i	−0.696858	−	0.753803i
$935$	29.6771	−	3.47186i	0.970545	−	0.113542i
$936$	−3.57255	−	0.422455i	−0.116773	−	0.0138084i
$937$	17.2613			0.563902			0.281951	−	0.959429i	$-0.409018\pi$
$937$	17.2613			0.563902			0.281951	+	0.959429i	$0.409018\pi$
$938$	1.30495	−	33.2432i	0.0426082	−	1.08543i
$939$	−39.8776			−1.30136
$940$	−15.4640	−	14.3315i	−0.504380	−	0.467443i
$941$			56.7672i			1.85056i	0.379289	+	0.925278i	$0.376169\pi$
$941$			56.7672i			1.85056i	−0.379289	+	0.925278i	$0.623831\pi$
$942$	42.5405	+	1.66991i	1.38604	+	0.0544087i
$943$	−45.2284	+	13.1003i	−1.47284	+	0.426605i
$944$	7.38729	+	1.16896i	0.240436	+	0.0380465i
$945$	−29.0357	−	22.9536i	−0.944530	−	0.746679i
$946$	−1.36782	+	34.8448i	−0.0444717	+	1.13290i
$947$	−28.9392	−	28.9392i	−0.940398	−	0.940398i	0.0579230	−	0.998321i	$-0.481552\pi$
$947$	−28.9392	−	28.9392i	−0.940398	−	0.940398i	−0.998321	+	0.0579230i	$0.981552\pi$
$948$	−4.35889	−	5.10288i	−0.141570	−	0.165734i
$949$	−1.70849	+	1.70849i	−0.0554599	+	0.0554599i
$950$	16.7234	−	24.8845i	0.542580	−	0.807358i
$951$	26.5155			0.859824
$952$	−36.8132	−	4.35317i	−1.19312	−	0.141087i
$953$	−3.64179	−	3.64179i	−0.117969	−	0.117969i	0.645658	−	0.763627i	$-0.276583\pi$
$953$	−3.64179	−	3.64179i	−0.117969	−	0.117969i	−0.763627	+	0.645658i	$0.776583\pi$
$954$	−5.48694	−	0.215388i	−0.177646	−	0.00697345i
$955$	−3.76034	−	32.1430i	−0.121682	−	1.04012i
$956$	−9.57351	+	8.17772i	−0.309629	+	0.264486i
$957$	21.2241			0.686077
$958$	30.1833	−	27.9031i	0.975179	−	0.901510i
$959$	−67.0497			−2.16515
$960$	17.0711	+	21.7054i	0.550968	+	0.700540i
$961$	−55.0711			−1.77649
$962$	9.20039	−	8.50536i	0.296633	−	0.274224i
$963$	−7.38237	−	7.38237i	−0.237893	−	0.237893i
$964$	0.553539	−	7.03975i	0.0178283	−	0.226735i
$965$	−8.82726	+	11.1663i	−0.284160	+	0.359455i
$966$	−32.3072	−	34.9472i	−1.03947	−	1.12441i
$967$			9.73391i			0.313021i	0.987676	+	0.156511i	$0.0500246\pi$
$967$			9.73391i			0.313021i	−0.987676	+	0.156511i	$0.949975\pi$
$968$	−0.619265	+	5.23690i	−0.0199039	+	0.168320i
$969$	20.4615	−	20.4615i	0.657318	−	0.657318i
$970$	−19.9059	+	23.2447i	−0.639138	+	0.746344i
$971$	40.0375	+	40.0375i	1.28487	+	1.28487i	0.937865	+	0.347000i	$0.112800\pi$
$971$	40.0375	+	40.0375i	1.28487	+	1.28487i	0.347000	+	0.937865i	$0.387200\pi$
$972$	0.988131	−	12.5668i	0.0316943	−	0.403079i
$973$	27.8684			0.893419
$974$	31.1216	−	28.7705i	0.997200	−	0.921868i
$975$	−15.4803	+	3.67228i	−0.495767	+	0.117607i
$976$	1.74911	−	11.0535i	0.0559875	−	0.353815i
$977$			0.823965i			0.0263610i	0.999913	+	0.0131805i	$0.00419560\pi$
$977$			0.823965i			0.0263610i	−0.999913	+	0.0131805i	$0.995804\pi$
$978$	5.99062	+	6.48016i	0.191559	+	0.207213i
$979$		−	23.8692i		−	0.762862i
$980$	−5.43636	+	5.86594i	−0.173658	+	0.187381i
$981$	7.95152	−	7.95152i	0.253873	−	0.253873i
$982$	−1.31823	+	33.5815i	−0.0420665	+	1.07163i
$983$	16.1528	−	16.1528i	0.515195	−	0.515195i	−0.400919	−	0.916114i	$-0.631309\pi$
$983$	16.1528	−	16.1528i	0.515195	−	0.515195i	0.916114	+	0.400919i	$0.131309\pi$
$984$	16.2708	−	22.7349i	0.518693	−	0.724761i
$985$	−50.0874	+	5.85962i	−1.59592	+	0.186703i
$986$	19.3062	+	20.8838i	0.614834	+	0.665077i
$987$	−21.5748			−0.686734
$988$	−11.3533	−	13.2911i	−0.361197	−	0.422847i
$989$	−59.9931			−1.90767
$990$	5.88005	−	0.454985i	0.186880	−	0.0144604i
$991$	15.8979	+	15.8979i	0.505013	+	0.505013i	0.912991	−	0.407979i	$-0.133766\pi$
$991$	15.8979	+	15.8979i	0.505013	+	0.505013i	−0.407979	+	0.912991i	$0.633766\pi$
$992$	−10.2295	+	51.4746i	−0.324786	+	1.63432i
$993$	−25.8737	+	25.8737i	−0.821078	+	0.821078i
$994$	−7.97565	−	8.62740i	−0.252972	−	0.273644i
$995$	−15.7485	+	1.84239i	−0.499263	+	0.0584076i
$996$	−5.06405	−	5.92839i	−0.160460	−	0.187848i
$997$		−	26.9189i		−	0.852530i	−0.904598	−	0.426265i	$-0.859829\pi$
$997$		−	26.9189i		−	0.852530i	0.904598	−	0.426265i	$-0.140171\pi$
$998$	−1.94416	+	1.79729i	−0.0615413	+	0.0568923i
$999$	16.9698	+	16.9698i	0.536899	+	0.536899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.3	✓	240
4.3	odd	2	inner	820.2.j.c.483.61	yes	240
5.2	odd	4		820.2.s.c.647.60	yes	240
20.7	even	4		820.2.s.c.647.118	yes	240
41.9	even	4		820.2.s.c.583.118	yes	240
164.91	odd	4		820.2.s.c.583.60	yes	240
205.132	odd	4	inner	820.2.j.c.747.61	yes	240
820.747	even	4	inner	820.2.j.c.747.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.3	✓	240	1.1	even	1	trivial
820.2.j.c.483.61	yes	240	4.3	odd	2	inner
820.2.j.c.747.3	yes	240	820.747	even	4	inner
820.2.j.c.747.61	yes	240	205.132	odd	4	inner
820.2.s.c.583.60	yes	240	164.91	odd	4
820.2.s.c.583.118	yes	240	41.9	even	4
820.2.s.c.647.60	yes	240	5.2	odd	4
820.2.s.c.647.118	yes	240	20.7	even	4

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41313 - 0.0554718i) q^{2} -1.54369i q^{3} +(1.99385 + 0.156777i) q^{4} +(-1.38671 + 1.75415i) q^{5} +(-0.0856310 + 2.18142i) q^{6} -2.96451 q^{7} +(-2.80886 - 0.332148i) q^{8} +0.617035 q^{9} +(2.05690 - 2.40191i) q^{10} +(2.13724 + 2.13724i) q^{11} +(0.242015 - 3.07787i) q^{12} +2.06129 q^{13} +(4.18923 + 0.164447i) q^{14} +(2.70786 + 2.14064i) q^{15} +(3.95084 + 0.625179i) q^{16} -4.42100 q^{17} +(-0.871947 - 0.0342280i) q^{18} +(-2.99818 - 2.99818i) q^{19} +(-3.03989 + 3.28010i) q^{20} +4.57628i q^{21} +(-2.90163 - 3.13874i) q^{22} +(5.19993 - 5.19993i) q^{23} +(-0.512732 + 4.33599i) q^{24} +(-1.15408 - 4.86499i) q^{25} +(-2.91287 - 0.114344i) q^{26} -5.58356i q^{27} +(-5.91078 - 0.464768i) q^{28} +(3.21653 + 3.21653i) q^{29} +(-3.70779 - 3.17520i) q^{30} -9.27745i q^{31} +(-5.54835 - 1.10262i) q^{32} +(3.29922 - 3.29922i) q^{33} +(6.24742 + 0.245241i) q^{34} +(4.11091 - 5.20020i) q^{35} +(1.23027 + 0.0967370i) q^{36} +(-3.03923 + 3.03923i) q^{37} +(4.07049 + 4.40312i) q^{38} -3.18199i q^{39} +(4.47770 - 4.46656i) q^{40} +(-5.60860 - 3.08927i) q^{41} +(0.253854 - 6.46685i) q^{42} +(-5.76865 - 5.76865i) q^{43} +(3.92625 + 4.59639i) q^{44} +(-0.855647 + 1.08237i) q^{45} +(-7.63661 + 7.05971i) q^{46} +4.71449i q^{47} +(0.965080 - 6.09886i) q^{48} +1.78834 q^{49} +(1.36099 + 6.93885i) q^{50} +6.82463i q^{51} +(4.10990 + 0.323164i) q^{52} +6.29275 q^{53} +(-0.309730 + 7.89028i) q^{54} +(-6.71276 + 0.785311i) q^{55} +(8.32690 + 0.984657i) q^{56} +(-4.62825 + 4.62825i) q^{57} +(-4.36693 - 4.72378i) q^{58} +1.86980 q^{59} +(5.06344 + 4.69264i) q^{60} -2.79777i q^{61} +(-0.514637 + 13.1102i) q^{62} -1.82921 q^{63} +(7.77936 + 1.86591i) q^{64} +(-2.85841 + 3.61582i) q^{65} +(-4.84523 + 4.47920i) q^{66} -7.93540i q^{67} +(-8.81479 - 0.693112i) q^{68} +(-8.02706 - 8.02706i) q^{69} +(-6.09770 + 7.12050i) q^{70} +(-1.98163 - 1.98163i) q^{71} +(-1.73316 - 0.204947i) q^{72} +(-0.828844 + 0.828844i) q^{73} +(4.46341 - 4.12623i) q^{74} +(-7.51001 + 1.78154i) q^{75} +(-5.50787 - 6.44796i) q^{76} +(-6.33587 - 6.33587i) q^{77} +(-0.176511 + 4.49655i) q^{78} +(1.53706 - 1.53706i) q^{79} +(-6.57532 + 6.06343i) q^{80} -6.76816 q^{81} +(7.75429 + 4.67665i) q^{82} +(1.78572 - 1.78572i) q^{83} +(-0.717456 + 9.12439i) q^{84} +(6.13063 - 7.75509i) q^{85} +(7.83182 + 8.47182i) q^{86} +(4.96531 - 4.96531i) q^{87} +(-5.29332 - 6.71308i) q^{88} +(-5.58411 - 5.58411i) q^{89} +(1.26918 - 1.48206i) q^{90} -6.11073 q^{91} +(11.1831 - 9.55263i) q^{92} -14.3215 q^{93} +(0.261521 - 6.66217i) q^{94} +(9.41686 - 1.10166i) q^{95} +(-1.70209 + 8.56492i) q^{96} -9.67761 q^{97} +(-2.52715 - 0.0992025i) q^{98} +(1.31875 + 1.31875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

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