LMFDB - Embedded newform 280.2.s.c.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39086 - 0.255964i) q^{2} +(1.92461 + 1.92461i) q^{3} +(1.86896 + 0.712018i) q^{4} +(-2.22709 - 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-2.59487 + 0.516406i) q^{7} +(-2.41721 - 1.46870i) q^{8} +4.40827i q^{9} +O(q^{10})$	\(q+(-1.39086 - 0.255964i) q^{2} +(1.92461 + 1.92461i) q^{3} +(1.86896 + 0.712018i) q^{4} +(-2.22709 - 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-2.59487 + 0.516406i) q^{7} +(-2.41721 - 1.46870i) q^{8} +4.40827i q^{9} +(3.04632 + 0.848477i) q^{10} +5.44500i q^{11} +(2.22667 + 4.96739i) q^{12} +(1.42624 + 1.42624i) q^{13} +(3.74127 - 0.0540545i) q^{14} +(-3.90101 - 4.67155i) q^{15} +(2.98606 + 2.66147i) q^{16} +(-4.92871 - 4.92871i) q^{17} +(1.12836 - 6.13127i) q^{18} +3.36836i q^{19} +(-4.01982 - 1.95986i) q^{20} +(-5.98799 - 4.00023i) q^{21} +(1.39372 - 7.57321i) q^{22} +(1.59745 + 1.59745i) q^{23} +(-1.82551 - 7.47888i) q^{24} +(4.91986 + 0.891641i) q^{25} +(-1.61863 - 2.34877i) q^{26} +(-2.71037 + 2.71037i) q^{27} +(-5.21740 - 0.882447i) q^{28} +2.04964 q^{29} +(4.23000 + 7.49598i) q^{30} +1.78815i q^{31} +(-3.47194 - 4.46605i) q^{32} +(-10.4795 + 10.4795i) q^{33} +(5.59356 + 8.11671i) q^{34} +(5.88237 - 0.630640i) q^{35} +(-3.13877 + 8.23890i) q^{36} +(1.63966 + 1.63966i) q^{37} +(0.862178 - 4.68490i) q^{38} +5.48993i q^{39} +(5.08934 + 3.75481i) q^{40} +1.17165i q^{41} +(7.30452 + 7.09646i) q^{42} +(5.08552 - 5.08552i) q^{43} +(-3.87694 + 10.1765i) q^{44} +(0.882450 - 9.81761i) q^{45} +(-1.81293 - 2.63071i) q^{46} +(1.67970 + 1.67970i) q^{47} +(0.624701 + 10.8693i) q^{48} +(6.46665 - 2.68001i) q^{49} +(-6.61459 - 2.49945i) q^{50} -18.9717i q^{51} +(1.65009 + 3.68111i) q^{52} +(-8.44557 + 8.44557i) q^{53} +(4.46349 - 3.07598i) q^{54} +(1.08998 - 12.1265i) q^{55} +(7.03078 + 2.56282i) q^{56} +(-6.48278 + 6.48278i) q^{57} +(-2.85076 - 0.524635i) q^{58} -8.44987i q^{59} +(-3.96463 - 11.5086i) q^{60} +3.37492 q^{61} +(0.457703 - 2.48706i) q^{62} +(-2.27645 - 11.4389i) q^{63} +(3.68582 + 7.10033i) q^{64} +(-2.89087 - 3.46188i) q^{65} +(17.2579 - 11.8931i) q^{66} +(5.38600 + 5.38600i) q^{67} +(-5.70226 - 12.7209i) q^{68} +6.14894i q^{69} +(-8.34296 - 0.628545i) q^{70} +10.6844 q^{71} +(6.47444 - 10.6557i) q^{72} +(-2.52591 + 2.52591i) q^{73} +(-1.86084 - 2.70023i) q^{74} +(7.75275 + 11.1849i) q^{75} +(-2.39833 + 6.29534i) q^{76} +(-2.81183 - 14.1290i) q^{77} +(1.40522 - 7.63571i) q^{78} -5.29897i q^{79} +(-6.11745 - 6.52509i) q^{80} +2.79198 q^{81} +(0.299900 - 1.62960i) q^{82} +(-0.118255 - 0.118255i) q^{83} +(-8.34311 - 11.7398i) q^{84} +(9.99005 + 11.9633i) q^{85} +(-8.37493 + 5.77152i) q^{86} +(3.94477 + 3.94477i) q^{87} +(7.99709 - 13.1617i) q^{88} -0.578136 q^{89} +(-3.74031 + 13.4290i) q^{90} +(-4.43743 - 2.96439i) q^{91} +(1.84816 + 4.12299i) q^{92} +(-3.44150 + 3.44150i) q^{93} +(-1.90628 - 2.76616i) q^{94} +(0.674280 - 7.50163i) q^{95} +(1.91328 - 15.2776i) q^{96} +(-1.57710 - 1.57710i) q^{97} +(-9.68017 + 2.07228i) q^{98} -24.0030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.39086	−	0.255964i	−0.983484	−	0.180994i
$2$	−1.39086	−	0.255964i	−0.983484	−	0.180994i
$3$	1.92461	+	1.92461i	1.11118	+	1.11118i	0.992992	+	0.118184i	$0.0377072\pi$
$3$	1.92461	+	1.92461i	1.11118	+	1.11118i	0.118184	+	0.992992i	$0.462293\pi$
$4$	1.86896	+	0.712018i	0.934482	+	0.356009i
$5$	−2.22709	−	0.200181i	−0.995985	−	0.0895235i
$5$	−2.22709	−	0.200181i	−0.995985	−	0.0895235i
$6$	−2.18423	−	3.16949i	−0.891708	−	1.29394i
$7$	−2.59487	+	0.516406i	−0.980767	+	0.195183i
$7$	−2.59487	+	0.516406i	−0.980767	+	0.195183i
$8$	−2.41721	−	1.46870i	−0.854613	−	0.519265i
$9$			4.40827i			1.46942i
$10$	3.04632	+	0.848477i	0.963332	+	0.268312i
$11$			5.44500i			1.64173i	0.571123	+	0.820865i	$0.306508\pi$
$11$			5.44500i			1.64173i	−0.571123	+	0.820865i	$0.693492\pi$
$12$	2.22667	+	4.96739i	0.642785	+	1.43396i
$13$	1.42624	+	1.42624i	0.395569	+	0.395569i	0.876667	−	0.481098i	$-0.159762\pi$
$13$	1.42624	+	1.42624i	0.395569	+	0.395569i	−0.481098	+	0.876667i	$0.659762\pi$
$14$	3.74127	−	0.0540545i	0.999896	−	0.0144467i
$15$	−3.90101	−	4.67155i	−1.00724	−	1.20619i
$16$	2.98606	+	2.66147i	0.746515	+	0.665369i
$17$	−4.92871	−	4.92871i	−1.19539	−	1.19539i	−0.975532	−	0.219856i	$-0.929441\pi$
$17$	−4.92871	−	4.92871i	−1.19539	−	1.19539i	−0.219856	−	0.975532i	$-0.570559\pi$
$18$	1.12836	−	6.13127i	0.265956	−	1.44515i
$19$			3.36836i			0.772754i	0.922341	+	0.386377i	$0.126274\pi$
$19$			3.36836i			0.772754i	−0.922341	+	0.386377i	$0.873726\pi$
$20$	−4.01982	−	1.95986i	−0.898859	−	0.438238i
$21$	−5.98799	−	4.00023i	−1.30669	−	0.872922i
$22$	1.39372	−	7.57321i	0.297143	−	1.61461i
$23$	1.59745	+	1.59745i	0.333091	+	0.333091i	0.853759	−	0.520668i	$-0.174317\pi$
$23$	1.59745	+	1.59745i	0.333091	+	0.333091i	−0.520668	+	0.853759i	$0.674317\pi$
$24$	−1.82551	−	7.47888i	−0.372631	−	1.52662i
$25$	4.91986	+	0.891641i	0.983971	+	0.178328i
$26$	−1.61863	−	2.34877i	−0.317440	−	0.460631i
$27$	−2.71037	+	2.71037i	−0.521611	+	0.521611i
$28$	−5.21740	−	0.882447i	−0.985996	−	0.166767i
$29$	2.04964			0.380609			0.190305	−	0.981725i	$-0.439052\pi$
$29$	2.04964			0.380609			0.190305	+	0.981725i	$0.439052\pi$
$30$	4.23000	+	7.49598i	0.772289	+	1.36857i
$31$			1.78815i			0.321162i	0.987023	+	0.160581i	$0.0513367\pi$
$31$			1.78815i			0.321162i	−0.987023	+	0.160581i	$0.948663\pi$
$32$	−3.47194	−	4.46605i	−0.613758	−	0.789494i
$33$	−10.4795	+	10.4795i	−1.82425	+	1.82425i
$34$	5.59356	+	8.11671i	0.959288	+	1.39200i
$35$	5.88237	−	0.630640i	0.994302	−	0.106598i
$36$	−3.13877	+	8.23890i	−0.523128	+	1.37315i
$37$	1.63966	+	1.63966i	0.269558	+	0.269558i	0.828922	−	0.559364i	$-0.188955\pi$
$37$	1.63966	+	1.63966i	0.269558	+	0.269558i	−0.559364	+	0.828922i	$0.688955\pi$
$38$	0.862178	−	4.68490i	0.139864	−	0.759992i
$39$			5.48993i			0.879093i
$40$	5.08934	+	3.75481i	0.804695	+	0.593688i
$41$			1.17165i			0.182981i	0.995806	+	0.0914904i	$0.0291631\pi$
$41$			1.17165i			0.182981i	−0.995806	+	0.0914904i	$0.970837\pi$
$42$	7.30452	+	7.09646i	1.12711	+	1.09501i
$43$	5.08552	−	5.08552i	0.775534	−	0.775534i	−0.203534	−	0.979068i	$-0.565243\pi$
$43$	5.08552	−	5.08552i	0.775534	−	0.775534i	0.979068	+	0.203534i	$0.0652427\pi$
$44$	−3.87694	+	10.1765i	−0.584471	+	1.53417i
$45$	0.882450	−	9.81761i	0.131548	−	1.46352i
$46$	−1.81293	−	2.63071i	−0.267302	−	0.387877i
$47$	1.67970	+	1.67970i	0.245009	+	0.245009i	0.818919	−	0.573910i	$-0.194574\pi$
$47$	1.67970	+	1.67970i	0.245009	+	0.245009i	−0.573910	+	0.818919i	$0.694574\pi$
$48$	0.624701	+	10.8693i	0.0901679	+	1.56885i
$49$	6.46665	−	2.68001i	0.923807	−	0.382858i
$50$	−6.61459	−	2.49945i	−0.935444	−	0.353476i
$51$		−	18.9717i		−	2.65657i
$52$	1.65009	+	3.68111i	0.228826	+	0.510478i
$53$	−8.44557	+	8.44557i	−1.16009	+	1.16009i	−0.175632	+	0.984456i	$0.556197\pi$
$53$	−8.44557	+	8.44557i	−1.16009	+	1.16009i	−0.984456	+	0.175632i	$0.943803\pi$
$54$	4.46349	−	3.07598i	0.607405	−	0.418588i
$55$	1.08998	−	12.1265i	0.146973	−	1.63514i
$56$	7.03078	+	2.56282i	0.939528	+	0.342472i
$57$	−6.48278	+	6.48278i	−0.858666	+	0.858666i
$58$	−2.85076	−	0.524635i	−0.374323	−	0.0688880i
$59$		−	8.44987i		−	1.10008i	−0.835138	−	0.550040i	$-0.814612\pi$
$59$		−	8.44987i		−	1.10008i	0.835138	−	0.550040i	$-0.185388\pi$
$60$	−3.96463	−	11.5086i	−0.511831	−	1.48575i
$61$	3.37492			0.432114			0.216057	−	0.976381i	$-0.430680\pi$
$61$	3.37492			0.432114			0.216057	+	0.976381i	$0.430680\pi$
$62$	0.457703	−	2.48706i	0.0581283	−	0.315858i
$63$	−2.27645	−	11.4389i	−0.286806	−	1.44116i
$64$	3.68582	+	7.10033i	0.460728	+	0.887541i
$65$	−2.89087	−	3.46188i	−0.358568	−	0.429393i
$66$	17.2579	−	11.8931i	2.12430	−	1.46394i
$67$	5.38600	+	5.38600i	0.658005	+	0.658005i	0.954908	−	0.296903i	$-0.0959537\pi$
$67$	5.38600	+	5.38600i	0.658005	+	0.658005i	−0.296903	+	0.954908i	$0.595954\pi$
$68$	−5.70226	−	12.7209i	−0.691500	−	1.54264i
$69$			6.14894i			0.740245i
$70$	−8.34296	−	0.628545i	−0.997174	−	0.0751255i
$71$	10.6844			1.26800			0.634001	−	0.773332i	$-0.281411\pi$
$71$	10.6844			1.26800			0.634001	+	0.773332i	$0.281411\pi$
$72$	6.47444	−	10.6557i	0.763020	−	1.25579i
$73$	−2.52591	+	2.52591i	−0.295636	+	0.295636i	−0.839302	−	0.543666i	$-0.817036\pi$
$73$	−2.52591	+	2.52591i	−0.295636	+	0.295636i	0.543666	+	0.839302i	$0.317036\pi$
$74$	−1.86084	−	2.70023i	−0.216318	−	0.313895i
$75$	7.75275	+	11.1849i	0.895211	+	1.29152i
$76$	−2.39833	+	6.29534i	−0.275108	+	0.722125i
$77$	−2.81183	−	14.1290i	−0.320438	−	1.61015i
$78$	1.40522	−	7.63571i	0.159110	−	0.864574i
$79$		−	5.29897i		−	0.596181i	−0.954538	−	0.298090i	$-0.903650\pi$
$79$		−	5.29897i		−	0.596181i	0.954538	−	0.298090i	$-0.0963497\pi$
$80$	−6.11745	−	6.52509i	−0.683951	−	0.729528i
$81$	2.79198			0.310220
$82$	0.299900	−	1.62960i	0.0331184	−	0.179959i
$83$	−0.118255	−	0.118255i	−0.0129802	−	0.0129802i	0.700587	−	0.713567i	$-0.252922\pi$
$83$	−0.118255	−	0.118255i	−0.0129802	−	0.0129802i	−0.713567	+	0.700587i	$0.752922\pi$
$84$	−8.34311	−	11.7398i	−0.910308	−	1.28092i
$85$	9.99005	+	11.9633i	1.08357	+	1.29760i
$86$	−8.37493	+	5.77152i	−0.903092	+	0.622359i
$87$	3.94477	+	3.94477i	0.422924	+	0.422924i
$88$	7.99709	−	13.1617i	0.852492	−	1.40304i
$89$	−0.578136			−0.0612823			−0.0306411	−	0.999530i	$-0.509755\pi$
$89$	−0.578136			−0.0612823			−0.0306411	+	0.999530i	$0.509755\pi$
$90$	−3.74031	+	13.4290i	−0.394264	+	1.41554i
$91$	−4.43743	−	2.96439i	−0.465169	−	0.310752i
$92$	1.84816	+	4.12299i	0.192684	+	0.429851i
$93$	−3.44150	+	3.44150i	−0.356867	+	0.356867i
$94$	−1.90628	−	2.76616i	−0.196617	−	0.285307i
$95$	0.674280	−	7.50163i	0.0691797	−	0.769651i
$96$	1.91328	−	15.2776i	0.195274	−	1.55926i
$97$	−1.57710	−	1.57710i	−0.160130	−	0.160130i	0.622494	−	0.782624i	$-0.286119\pi$
$97$	−1.57710	−	1.57710i	−0.160130	−	0.160130i	−0.782624	+	0.622494i	$0.786119\pi$
$98$	−9.68017	+	2.07228i	−0.977845	+	0.209331i
$99$	−24.0030			−2.41239
$100$	8.56017	+	5.16947i	0.856017	+	0.516947i
$101$	13.0984			1.30334			0.651668	−	0.758504i	$-0.274069\pi$
$101$	13.0984			1.30334			0.651668	+	0.758504i	$0.274069\pi$
$102$	−4.85608	+	26.3870i	−0.480823	+	2.61270i
$103$	6.28095	−	6.28095i	0.618880	−	0.618880i	−0.326364	−	0.945244i	$-0.605824\pi$
$103$	6.28095	−	6.28095i	0.618880	−	0.618880i	0.945244	+	0.326364i	$0.105824\pi$
$104$	−1.35280	−	5.54226i	−0.132653	−	0.543463i
$105$	12.5350	+	10.1075i	1.22329	+	0.986396i
$106$	13.9083	−	9.58481i	1.35090	−	0.930959i
$107$	4.86141	+	4.86141i	0.469970	+	0.469970i	0.901905	−	0.431935i	$-0.142169\pi$
$107$	4.86141	+	4.86141i	0.469970	+	0.469970i	−0.431935	+	0.901905i	$0.642169\pi$
$108$	−6.99542	+	3.13575i	−0.673135	+	0.301738i
$109$	−11.3075			−1.08306			−0.541530	−	0.840682i	$-0.682155\pi$
$109$	−11.3075			−1.08306			−0.541530	+	0.840682i	$0.682155\pi$
$110$	−4.61996	+	16.5872i	−0.440496	+	1.58153i
$111$			6.31142i			0.599053i
$112$	−9.12282	−	5.36415i	−0.862026	−	0.506864i
$113$	2.60044	+	2.60044i	0.244629	+	0.244629i	0.818762	−	0.574133i	$-0.194661\pi$
$113$	2.60044	+	2.60044i	0.244629	+	0.244629i	−0.574133	+	0.818762i	$0.694661\pi$
$114$	10.6760	−	7.35726i	0.999897	−	0.689071i
$115$	−3.23788	−	3.87744i	−0.301934	−	0.361573i
$116$	3.83071	+	1.45938i	0.355673	+	0.135500i
$117$	−6.28726	+	6.28726i	−0.581258	+	0.581258i
$118$	−2.16286	+	11.7526i	−0.199108	+	1.08191i
$119$	15.3346	+	10.2441i	1.40572	+	0.939078i
$120$	2.56845	+	17.0216i	0.234466	+	1.55385i
$121$	−18.6480			−1.69527
$122$	−4.69403	−	0.863857i	−0.424977	−	0.0782100i
$123$	−2.25497	+	2.25497i	−0.203324	+	0.203324i
$124$	−1.27320	+	3.34200i	−0.114337	+	0.300120i
$125$	−10.7785	−	2.97062i	−0.964056	−	0.265701i
$126$	0.238287	+	16.4925i	0.0212283	+	1.46927i
$127$	2.62192	−	2.62192i	0.232658	−	0.232658i	−0.581143	−	0.813801i	$-0.697394\pi$
$127$	2.62192	−	2.62192i	0.232658	−	0.232658i	0.813801	+	0.581143i	$0.197394\pi$
$128$	−3.30902	−	10.8190i	−0.292479	−	0.956272i
$129$	19.5753			1.72351
$130$	3.13466	+	5.55493i	0.274928	+	0.487200i
$131$	−10.5877			−0.925052			−0.462526	−	0.886606i	$-0.653057\pi$
$131$	−10.5877			−0.925052			−0.462526	+	0.886606i	$0.653057\pi$
$132$	−27.0475	+	12.1242i	−2.35418	+	1.05528i
$133$	−1.73944	−	8.74043i	−0.150829	−	0.757892i
$134$	−6.11254	−	8.86978i	−0.528043	−	0.766233i
$135$	6.57880	−	5.49367i	0.566213	−	0.472820i
$136$	4.67493	+	19.1526i	0.400872	+	1.64232i
$137$	4.88513	−	4.88513i	0.417365	−	0.417365i	−0.466930	−	0.884295i	$-0.654640\pi$
$137$	4.88513	−	4.88513i	0.417365	−	0.417365i	0.884295	+	0.466930i	$0.154640\pi$
$138$	1.57391	−	8.55229i	0.133980	−	0.728020i
$139$			13.6387i			1.15682i	0.815746	+	0.578410i	$0.196327\pi$
$139$			13.6387i			1.15682i	−0.815746	+	0.578410i	$0.803673\pi$
$140$	11.4430	+	3.00971i	0.967108	+	0.254367i
$141$			6.46553i			0.544496i
$142$	−14.8604	−	2.73481i	−1.24706	−	0.229501i
$143$	−7.76589	+	7.76589i	−0.649417	+	0.649417i
$144$	−11.7325	+	13.1634i	−0.977708	+	1.09695i
$145$	−4.56474	−	0.410299i	−0.379081	−	0.0340735i
$146$	4.15973	−	2.86664i	0.344261	−	0.237245i
$147$	17.6038	+	7.28782i	1.45193	+	0.601089i
$148$	1.89700	+	4.23193i	0.155932	+	0.347863i
$149$	5.97851			0.489779			0.244889	−	0.969551i	$-0.421248\pi$
$149$	5.97851			0.489779			0.244889	+	0.969551i	$0.421248\pi$
$150$	−7.92004	−	17.5410i	−0.646669	−	1.43222i
$151$	−9.72084			−0.791071			−0.395535	−	0.918451i	$-0.629441\pi$
$151$	−9.72084			−0.791071			−0.395535	+	0.918451i	$0.629441\pi$
$152$	4.94712	−	8.14203i	0.401264	−	0.660406i
$153$	21.7271	−	21.7271i	1.75653	−	1.75653i
$154$	0.294327	+	20.3712i	0.0237175	+	1.64156i
$155$	0.357954	−	3.98238i	0.0287515	−	0.319872i
$156$	−3.90893	+	10.2605i	−0.312965	+	0.821497i
$157$	−7.35892	+	7.35892i	−0.587306	+	0.587306i	−0.936901	−	0.349595i	$-0.886319\pi$
$157$	−7.35892	+	7.35892i	−0.587306	+	0.587306i	0.349595	+	0.936901i	$0.386319\pi$
$158$	−1.35635	+	7.37011i	−0.107905	+	0.586335i
$159$	−32.5089			−2.57812
$160$	6.83830	+	10.6413i	0.540615	+	0.841270i
$161$	−4.97010	−	3.32023i	−0.391698	−	0.261671i
$162$	−3.88324	−	0.714646i	−0.305096	−	0.0561479i
$163$	−6.10986	+	6.10986i	−0.478562	+	0.478562i	−0.904671	−	0.426110i	$-0.859884\pi$
$163$	−6.10986	+	6.10986i	−0.478562	+	0.478562i	0.426110	+	0.904671i	$0.359884\pi$
$164$	−0.834236	+	2.18977i	−0.0651429	+	0.170992i
$165$	25.4366	−	21.2410i	1.98024	−	1.65361i
$166$	0.134207	+	0.194745i	0.0104165	+	0.0151152i
$167$	17.4261	+	17.4261i	1.34847	+	1.34847i	0.887323	+	0.461149i	$0.152563\pi$
$167$	17.4261	+	17.4261i	1.34847	+	1.34847i	0.461149	+	0.887323i	$0.347437\pi$
$168$	8.59909	+	18.4640i	0.663434	+	1.42453i
$169$		−	8.93166i		−	0.687051i
$170$	−10.8326	−	19.1964i	−0.830819	−	1.47229i
$171$	−14.8486			−1.13550
$172$	13.1256	−	5.88367i	1.00082	−	0.448626i
$173$	−5.16805	−	5.16805i	−0.392919	−	0.392919i	0.482807	−	0.875727i	$-0.339617\pi$
$173$	−5.16805	−	5.16805i	−0.392919	−	0.392919i	−0.875727	+	0.482807i	$0.839617\pi$
$174$	−4.47689	−	6.49633i	−0.339392	−	0.492486i
$175$	−13.2268	+	0.226954i	−0.999853	+	0.0171561i
$176$	−14.4917	+	16.2591i	−1.09236	+	1.22558i
$177$	16.2627	−	16.2627i	1.22238	−	1.22238i
$178$	0.804104	+	0.147982i	0.0602702	+	0.0110917i
$179$	13.2310			0.988932			0.494466	−	0.869197i	$-0.335364\pi$
$179$	13.2310			0.988932			0.494466	+	0.869197i	$0.335364\pi$
$180$	8.63958	−	17.7204i	0.643957	−	1.32080i
$181$	−3.57015			−0.265367			−0.132684	−	0.991158i	$-0.542359\pi$
$181$	−3.57015			−0.265367			−0.132684	+	0.991158i	$0.542359\pi$
$182$	5.41305	+	5.25886i	0.401242	+	0.389813i
$183$	6.49541	+	6.49541i	0.480154	+	0.480154i
$184$	−1.51519	−	6.20755i	−0.111702	−	0.457627i
$185$	−3.32344	−	3.97990i	−0.244344	−	0.292608i
$186$	5.66754	−	3.90574i	0.415564	−	0.286382i
$187$	26.8368	−	26.8368i	1.96250	−	1.96250i
$188$	1.94332	+	4.33527i	0.141731	+	0.316182i
$189$	5.63339	−	8.43270i	0.409769	−	0.613388i
$190$	−2.85797	+	10.2611i	−0.207339	+	0.744419i
$191$	−11.0535			−0.799805			−0.399903	−	0.916558i	$-0.630956\pi$
$191$	−11.0535			−0.799805			−0.399903	+	0.916558i	$0.630956\pi$
$192$	−6.57161	+	20.7592i	−0.474265	+	1.49816i
$193$	−10.6063	−	10.6063i	−0.763455	−	0.763455i	0.213490	−	0.976945i	$-0.431517\pi$
$193$	−10.6063	−	10.6063i	−0.763455	−	0.763455i	−0.976945	+	0.213490i	$0.931517\pi$
$194$	1.78984	+	2.59720i	0.128503	+	0.186468i
$195$	1.09898	−	12.2266i	0.0786995	−	0.875563i
$196$	13.9942	−	0.404465i	0.999583	−	0.0288904i
$197$	−7.16688	−	7.16688i	−0.510619	−	0.510619i	0.404097	−	0.914716i	$-0.367586\pi$
$197$	−7.16688	−	7.16688i	−0.510619	−	0.510619i	−0.914716	+	0.404097i	$0.867586\pi$
$198$	33.3848	+	6.14391i	2.37255	+	0.436628i
$199$	−5.25225			−0.372322			−0.186161	−	0.982519i	$-0.559605\pi$
$199$	−5.25225			−0.372322			−0.186161	+	0.982519i	$0.559605\pi$
$200$	−10.5828	−	9.38109i	−0.748315	−	0.663343i
$201$			20.7319i			1.46232i
$202$	−18.2180	−	3.35271i	−1.28181	−	0.235896i
$203$	−5.31855	+	1.05845i	−0.373289	+	0.0742885i
$204$	13.5082	−	35.4575i	0.945764	−	2.48252i
$205$	0.234542	−	2.60937i	0.0163811	−	0.182246i
$206$	−10.3436	+	7.12820i	−0.720672	+	0.496645i
$207$	−7.04198	+	7.04198i	−0.489452	+	0.489452i
$208$	0.462938	+	8.05476i	0.0320990	+	0.558497i
$209$	−18.3407			−1.26865
$210$	−14.8473	−	17.2667i	−1.02456	−	1.19151i
$211$		−	1.94669i		−	0.134016i	−0.997752	−	0.0670078i	$-0.978655\pi$
$211$		−	1.94669i		−	0.134016i	0.997752	−	0.0670078i	$-0.0213452\pi$
$212$	−21.7979	+	9.77107i	−1.49708	+	0.671080i
$213$	20.5633	+	20.5633i	1.40897	+	1.40897i
$214$	−5.51717	−	8.00586i	−0.377146	−	0.547270i
$215$	−12.3439	+	10.3079i	−0.841848	+	0.702991i
$216$	10.5323	−	2.57081i	0.716630	−	0.174921i
$217$	−0.923413	−	4.64002i	−0.0626853	−	0.314985i
$218$	15.7271	+	2.89431i	1.06517	+	0.196027i
$219$	−9.72281			−0.657007
$220$	10.6714	−	21.8879i	0.719468	−	1.47568i
$221$		−	14.0591i		−	0.945717i
$222$	1.61550	−	8.77828i	0.108425	−	0.589160i
$223$	3.57648	−	3.57648i	0.239499	−	0.239499i	−0.577144	−	0.816643i	$-0.695833\pi$
$223$	3.57648	−	3.57648i	0.239499	−	0.239499i	0.816643	+	0.577144i	$0.195833\pi$
$224$	11.3155	+	9.79588i	0.756049	+	0.654515i
$225$	−3.93059	+	21.6880i	−0.262039	+	1.44587i
$226$	−2.95122	−	4.28245i	−0.196312	−	0.284865i
$227$	−12.7822	+	12.7822i	−0.848385	+	0.848385i	−0.989932	−	0.141546i	$-0.954793\pi$
$227$	−12.7822	+	12.7822i	−0.848385	+	0.848385i	0.141546	+	0.989932i	$0.454793\pi$
$228$	−16.7320	+	7.50023i	−1.10810	+	0.496715i
$229$			24.8116i			1.63960i	0.572650	+	0.819800i	$0.305915\pi$
$229$			24.8116i			1.63960i	−0.572650	+	0.819800i	$0.694085\pi$
$230$	3.51095	+	6.22174i	0.231505	+	0.410250i
$231$	21.7812	−	32.6046i	1.43310	−	2.14523i
$232$	−4.95442	−	3.01032i	−0.325274	−	0.197637i
$233$	8.73803	+	8.73803i	0.572447	+	0.572447i	0.932812	−	0.360364i	$-0.117348\pi$
$233$	8.73803	+	8.73803i	0.572447	+	0.572447i	−0.360364	+	0.932812i	$0.617348\pi$
$234$	10.3540	−	7.13537i	0.676862	−	0.466454i
$235$	−3.40459	−	4.07708i	−0.222091	−	0.265959i
$236$	6.01646	−	15.7925i	0.391638	−	1.02801i
$237$	10.1985	−	10.1985i	0.662462	−	0.662462i
$238$	−18.7061	−	18.1732i	−1.21253	−	1.17799i
$239$		−	17.8047i		−	1.15169i	−0.817558	−	0.575846i	$-0.804673\pi$
$239$		−	17.8047i		−	1.15169i	0.817558	−	0.575846i	$-0.195327\pi$
$240$	0.784562	−	24.3320i	0.0506432	−	1.57062i
$241$		−	28.6845i		−	1.84773i	−0.382719	−	0.923865i	$-0.625012\pi$
$241$		−	28.6845i		−	1.84773i	0.382719	−	0.923865i	$-0.374988\pi$
$242$	25.9367	+	4.77322i	1.66728	+	0.306834i
$243$	13.5046	+	13.5046i	0.866320	+	0.866320i
$244$	6.30760	+	2.40300i	0.403803	+	0.153837i
$245$	−14.9383	+	4.67412i	−0.954373	+	0.298618i
$246$	3.71353	−	2.55915i	0.236766	−	0.163165i
$247$	−4.80410	+	4.80410i	−0.305677	+	0.305677i
$248$	2.62627	−	4.32234i	0.166768	−	0.274469i
$249$		−	0.455192i		−	0.0288466i
$250$	14.2309	+	6.89061i	0.900043	+	0.435801i
$251$	−7.05563			−0.445348			−0.222674	−	0.974893i	$-0.571478\pi$
$251$	−7.05563			−0.445348			−0.222674	+	0.974893i	$0.571478\pi$
$252$	3.89006	−	22.9997i	0.245051	−	1.44885i
$253$	−8.69811	+	8.69811i	−0.546845	+	0.546845i
$254$	−4.31784	+	2.97560i	−0.270925	+	0.186706i
$255$	−3.79777	+	42.2517i	−0.237826	+	2.64591i
$256$	1.83311	+	15.8946i	0.114569	+	0.993415i
$257$	11.9006	+	11.9006i	0.742338	+	0.742338i	0.973027	−	0.230689i	$-0.0740981\pi$
$257$	11.9006	+	11.9006i	0.742338	+	0.742338i	−0.230689	+	0.973027i	$0.574098\pi$
$258$	−27.2264	−	5.01057i	−1.69504	−	0.311944i
$259$	−5.10142	−	3.40797i	−0.316987	−	0.211761i
$260$	−2.93801	−	8.52848i	−0.182207	−	0.528914i
$261$			9.03538i			0.559276i
$262$	14.7260	+	2.71007i	0.909774	+	0.167429i
$263$	10.7636	+	10.7636i	0.663711	+	0.663711i	0.956253	−	0.292542i	$-0.0945010\pi$
$263$	10.7636	+	10.7636i	0.663711	+	0.663711i	−0.292542	+	0.956253i	$0.594501\pi$
$264$	40.7225	−	9.93991i	2.50630	−	0.611759i
$265$	20.4997	−	17.1184i	1.25929	−	1.05157i
$266$	0.182075	+	12.6019i	0.0111637	+	0.772674i
$267$	−1.11269	−	1.11269i	−0.0680954	−	0.0680954i
$268$	6.23132	+	13.9012i	0.380638	+	0.849150i
$269$		−	11.0154i		−	0.671623i	−0.941929	−	0.335812i	$-0.890989\pi$
$269$		−	11.0154i		−	0.671623i	0.941929	−	0.335812i	$-0.109011\pi$
$270$	−10.5564	+	5.95698i	−0.642439	+	0.362530i
$271$			2.75000i			0.167050i	0.996506	+	0.0835252i	$0.0266179\pi$
$271$			2.75000i			0.167050i	−0.996506	+	0.0835252i	$0.973382\pi$
$272$	−1.59979	−	27.8351i	−0.0970014	−	1.68775i
$273$	−2.83503	−	14.2456i	−0.171584	−	0.862185i
$274$	−8.04494	+	5.54410i	−0.486012	+	0.334931i
$275$	−4.85498	+	26.7886i	−0.292766	+	1.61541i
$276$	−4.37816	+	11.4922i	−0.263534	+	0.691746i
$277$	−12.2159	−	12.2159i	−0.733984	−	0.733984i	0.237423	−	0.971406i	$-0.423697\pi$
$277$	−12.2159	−	12.2159i	−0.733984	−	0.733984i	−0.971406	+	0.237423i	$0.923697\pi$
$278$	3.49102	−	18.9695i	0.209377	−	1.13771i
$279$	−7.88266			−0.471922
$280$	−15.1452	−	7.11507i	−0.905096	−	0.425207i
$281$	−21.7273			−1.29614			−0.648072	−	0.761579i	$-0.724424\pi$
$281$	−21.7273			−1.29614			−0.648072	+	0.761579i	$0.724424\pi$
$282$	1.65494	−	8.99262i	0.0985504	−	0.535503i
$283$	−11.5844	−	11.5844i	−0.688621	−	0.688621i	0.273306	−	0.961927i	$-0.411883\pi$
$283$	−11.5844	−	11.5844i	−0.688621	−	0.688621i	−0.961927	+	0.273306i	$0.911883\pi$
$284$	19.9687	+	7.60747i	1.18493	+	0.451420i
$285$	15.7355	−	13.1400i	0.932089	−	0.778347i
$286$	12.7890	−	8.81346i	0.756232	−	0.521151i
$287$	−0.605046	−	3.04027i	−0.0357148	−	0.179462i
$288$	19.6876	−	15.3052i	1.16010	−	0.901870i
$289$			31.5844i			1.85791i
$290$	6.24388	+	1.73908i	0.366653	+	0.102122i
$291$		−	6.07060i		−	0.355865i
$292$	−6.51934	+	2.92235i	−0.381516	+	0.171017i
$293$	16.2022	+	16.2022i	0.946542	+	0.946542i	0.998642	−	0.0520995i	$-0.0165913\pi$
$293$	16.2022	+	16.2022i	0.946542	+	0.946542i	−0.0520995	+	0.998642i	$0.516591\pi$
$294$	−22.6189	−	14.6422i	−1.31916	−	0.853953i
$295$	−1.69150	+	18.8186i	−0.0984830	+	1.09566i
$296$	−1.55523	−	6.37158i	−0.0903960	−	0.370340i
$297$	−14.7580	−	14.7580i	−0.856344	−	0.856344i
$298$	−8.31525	−	1.53028i	−0.481690	−	0.0886469i
$299$			4.55670i			0.263521i
$300$	6.52579	+	26.4242i	0.376766	+	1.52560i
$301$	−10.5700	+	15.8224i	−0.609247	+	0.911989i
$302$	13.5203	+	2.48818i	0.778006	+	0.143179i
$303$	25.2093	+	25.2093i	1.44824	+	1.44824i
$304$	−8.96480	+	10.0581i	−0.514166	+	0.576873i
$305$	−7.51624	−	0.675593i	−0.430379	−	0.0386844i
$306$	−35.7806	+	24.6579i	−2.04544	+	1.40960i
$307$	3.45914	−	3.45914i	0.197424	−	0.197424i	−0.601471	−	0.798895i	$-0.705418\pi$
$307$	3.45914	−	3.45914i	0.197424	−	0.197424i	0.798895	+	0.601471i	$0.205418\pi$
$308$	4.80492	−	28.4088i	0.273786	−	1.61874i
$309$	24.1768			1.37537
$310$	−1.51721	+	5.44729i	−0.0861716	+	0.309385i
$311$			27.5528i			1.56237i	0.624296	+	0.781187i	$0.285386\pi$
$311$			27.5528i			1.56237i	−0.624296	+	0.781187i	$0.714614\pi$
$312$	8.06308	−	13.2703i	0.456482	−	0.751284i
$313$	−18.2628	+	18.2628i	−1.03227	+	1.03227i	−0.0328132	+	0.999462i	$0.510447\pi$
$313$	−18.2628	+	18.2628i	−1.03227	+	1.03227i	−0.999462	+	0.0328132i	$0.989553\pi$
$314$	12.1188	−	8.35159i	0.683905	−	0.471307i
$315$	2.78003	+	25.9311i	0.156637	+	1.46105i
$316$	3.77297	−	9.90359i	0.212246	−	0.557121i
$317$	0.662461	+	0.662461i	0.0372075	+	0.0372075i	0.725466	−	0.688258i	$-0.241624\pi$
$317$	0.662461	+	0.662461i	0.0372075	+	0.0372075i	−0.688258	+	0.725466i	$0.741624\pi$
$318$	45.2152	+	8.32110i	2.53554	+	0.466624i
$319$			11.1603i			0.624858i
$320$	−6.78731	−	16.5509i	−0.379422	−	0.925224i
$321$			18.7126i			1.04444i
$322$	6.06283	+	5.89013i	0.337868	+	0.328244i
$323$	16.6017	−	16.6017i	0.923742	−	0.923742i
$324$	5.21811	+	1.98794i	0.289895	+	0.110441i
$325$	5.74521	+	8.28861i	0.318687	+	0.459769i
$326$	10.0619	−	6.93404i	0.557274	−	0.384041i
$327$	−21.7625	−	21.7625i	−1.20347	−	1.20347i
$328$	1.72080	−	2.83212i	0.0950155	−	0.156378i
$329$	−5.22599	−	3.49118i	−0.288118	−	0.192475i
$330$	−40.8156	+	23.0324i	−2.24683	+	1.26789i
$331$			0.00988396i			0.000543272i	1.00000		0.000271636i	$8.64644e-5\pi$
$331$			0.00988396i			0.000543272i	−1.00000		0.000271636i	$0.999914\pi$
$332$	−0.136815	−	0.305215i	−0.00750871	−	0.0167509i
$333$	−7.22806	+	7.22806i	−0.396095	+	0.396095i
$334$	−19.7768	−	28.6977i	−1.08214	−	1.57027i
$335$	−10.9169	−	13.0733i	−0.596456	−	0.714270i
$336$	−7.23399	−	27.8818i	−0.394647	−	1.52108i
$337$	23.6290	−	23.6290i	1.28715	−	1.28715i	0.350647	−	0.936508i	$-0.385962\pi$
$337$	23.6290	−	23.6290i	1.28715	−	1.28715i	0.936508	−	0.350647i	$-0.114038\pi$
$338$	−2.28618	+	12.4227i	−0.124352	+	0.675704i
$339$			10.0097i			0.543651i
$340$	10.1530	+	29.4721i	0.550621	+	1.59835i
$341$	−9.73649			−0.527261
$342$	20.6523	+	3.80071i	1.11675	+	0.205519i
$343$	−15.3961	+	10.2937i	−0.831312	+	0.555806i
$344$	−19.7619	+	4.82366i	−1.06549	+	0.260074i
$345$	1.23090	−	13.6942i	0.0662694	−	0.737273i
$346$	5.86518	+	8.51085i	0.315314	+	0.457546i
$347$	−22.4231	−	22.4231i	−1.20373	−	1.20373i	−0.973022	−	0.230712i	$-0.925894\pi$
$347$	−22.4231	−	22.4231i	−1.20373	−	1.20373i	−0.230712	−	0.973022i	$-0.574106\pi$
$348$	4.56389	+	10.1814i	0.244650	+	0.545780i
$349$		−	25.7980i		−	1.38093i	−0.723363	−	0.690467i	$-0.757405\pi$
$349$		−	25.7980i		−	1.38093i	0.723363	−	0.690467i	$-0.242595\pi$
$350$	18.4547	+	3.06992i	0.986445	+	0.164094i
$351$	−7.73129			−0.412666
$352$	24.3177	−	18.9047i	1.29614	−	1.00762i
$353$	4.22657	−	4.22657i	0.224958	−	0.224958i	−0.585625	−	0.810582i	$-0.699151\pi$
$353$	4.22657	−	4.22657i	0.224958	−	0.224958i	0.810582	+	0.585625i	$0.199151\pi$
$354$	−26.7818	+	18.4565i	−1.42344	+	0.980950i
$355$	−23.7951	−	2.13881i	−1.26291	−	0.113516i
$356$	−1.08052	−	0.411643i	−0.0572672	−	0.0218171i
$357$	9.79711	+	49.2291i	0.518518	+	2.60548i
$358$	−18.4024	−	3.38666i	−0.972599	−	0.178991i
$359$		−	7.52162i		−	0.396976i	−0.980103	−	0.198488i	$-0.936397\pi$
$359$		−	7.52162i		−	0.396976i	0.980103	−	0.198488i	$-0.0636031\pi$
$360$	−16.5522	+	22.4352i	−0.872378	+	1.18244i
$361$	7.65417			0.402851
$362$	4.96557	+	0.913831i	0.260985	+	0.0480299i
$363$	−35.8902	−	35.8902i	−1.88375	−	1.88375i
$364$	−6.18270	−	8.69987i	−0.324062	−	0.455997i
$365$	6.13108	−	5.11980i	0.320915	−	0.267982i
$366$	−7.37159	−	10.6968i	−0.385319	−	0.559129i
$367$	−18.2949	−	18.2949i	−0.954984	−	0.954984i	0.0440457	−	0.999030i	$-0.485975\pi$
$367$	−18.2949	−	18.2949i	−0.954984	−	0.954984i	−0.999030	+	0.0440457i	$0.985975\pi$
$368$	0.518509	+	9.02165i	0.0270291	+	0.470286i
$369$	−5.16494			−0.268876
$370$	3.60372	+	6.38615i	0.187348	+	0.332000i
$371$	17.5538	−	26.2764i	0.911346	−	1.36421i
$372$	−8.88246	+	3.98163i	−0.460534	+	0.206438i
$373$	12.2045	−	12.2045i	0.631925	−	0.631925i	−0.316626	−	0.948550i	$-0.602550\pi$
$373$	12.2045	−	12.2045i	0.631925	−	0.631925i	0.948550	+	0.316626i	$0.102550\pi$
$374$	−44.1955	+	30.4569i	−2.28529	+	1.57489i
$375$	−15.0271	−	26.4617i	−0.775995	−	1.36648i
$376$	−1.59321	−	6.52716i	−0.0821633	−	0.336612i
$377$	2.92329	+	2.92329i	0.150557	+	0.150557i
$378$	−9.99371	+	10.2867i	−0.514021	+	0.529092i
$379$	15.3415			0.788037			0.394019	−	0.919102i	$-0.371085\pi$
$379$	15.3415			0.788037			0.394019	+	0.919102i	$0.371085\pi$
$380$	6.60151	−	13.5402i	0.338650	−	0.694597i
$381$	10.0924			0.517048
$382$	15.3739	+	2.82930i	0.786596	+	0.144760i
$383$	24.6609	−	24.6609i	1.26011	−	1.26011i	0.309077	−	0.951037i	$-0.399980\pi$
$383$	24.6609	−	24.6609i	1.26011	−	1.26011i	0.951037	−	0.309077i	$-0.100020\pi$
$384$	14.4538	−	27.1909i	0.737590	−	1.38758i
$385$	3.43383	+	32.0295i	0.175004	+	1.63237i
$386$	12.0370	+	17.4666i	0.612666	+	0.889027i
$387$	22.4183	+	22.4183i	1.13959	+	1.13959i
$388$	−1.82462	−	4.07046i	−0.0926309	−	0.206646i
$389$	16.1736			0.820034			0.410017	−	0.912078i	$-0.365523\pi$
$389$	16.1736			0.820034			0.410017	+	0.912078i	$0.365523\pi$
$390$	−4.65808	+	16.7241i	−0.235871	+	0.846858i
$391$		−	15.7467i		−	0.796347i
$392$	−19.5674	−	3.01945i	−0.988303	−	0.152505i
$393$	−20.3772	−	20.3772i	−1.02790	−	1.02790i
$394$	8.13364	+	11.8026i	0.409767	+	0.594605i
$395$	−1.06075	+	11.8013i	−0.0533722	+	0.593787i
$396$	−44.8608	−	17.0906i	−2.25434	−	0.858834i
$397$	−6.76277	+	6.76277i	−0.339414	+	0.339414i	−0.856147	−	0.516733i	$-0.827148\pi$
$397$	−6.76277	+	6.76277i	−0.339414	+	0.339414i	0.516733	+	0.856147i	$0.327148\pi$
$398$	7.30513	+	1.34439i	0.366173	+	0.0673880i
$399$	13.4742	−	20.1697i	0.674554	−	1.00975i
$400$	12.3179	+	15.7566i	0.615895	+	0.787828i
$401$	6.46277			0.322736			0.161368	−	0.986894i	$-0.448409\pi$
$401$	6.46277			0.322736			0.161368	+	0.986894i	$0.448409\pi$
$402$	5.30663	−	28.8352i	0.264671	−	1.43817i
$403$	−2.55034	+	2.55034i	−0.127042	+	0.127042i
$404$	24.4804	+	9.32628i	1.21795	+	0.464000i
$405$	−6.21799	−	0.558900i	−0.308974	−	0.0277720i
$406$	7.66827	−	0.110793i	0.380570	−	0.00549854i
$407$	−8.92795	+	8.92795i	−0.442542	+	0.442542i
$408$	−27.8638	+	45.8587i	−1.37947	+	2.27034i
$409$	0.933714			0.0461692			0.0230846	−	0.999734i	$-0.492651\pi$
$409$	0.933714			0.0461692			0.0230846	+	0.999734i	$0.492651\pi$
$410$	−0.994118	+	3.56922i	−0.0490960	+	0.176271i
$411$	18.8040			0.927532
$412$	16.2110	−	7.26672i	0.798660	−	0.358006i
$413$	4.36356	+	21.9263i	0.214717	+	1.07892i
$414$	11.5969	−	7.99189i	0.569956	−	0.392780i
$415$	0.239693	+	0.287038i	0.0117661	+	0.0140901i
$416$	1.41785	−	11.3215i	0.0695157	−	0.555083i
$417$	−26.2492	+	26.2492i	−1.28543	+	1.28543i
$418$	25.5093	+	4.69456i	1.24770	+	0.229618i
$419$		−	7.66167i		−	0.374297i	−0.982332	−	0.187149i	$-0.940075\pi$
$419$		−	7.66167i		−	0.374297i	0.982332	−	0.187149i	$-0.0599246\pi$
$420$	16.2308	+	27.8158i	0.791980	+	1.35727i
$421$		−	9.84492i		−	0.479812i	−0.970796	−	0.239906i	$-0.922883\pi$
$421$		−	9.84492i		−	0.479812i	0.970796	−	0.239906i	$-0.0771167\pi$
$422$	−0.498282	+	2.70756i	−0.0242560	+	0.131802i
$423$	−7.40455	+	7.40455i	−0.360022	+	0.360022i
$424$	32.8188	−	8.01069i	1.59382	−	0.389034i
$425$	−19.8539	−	28.6432i	−0.963056	−	1.38940i
$426$	−23.3371	−	33.8640i	−1.13069	−	1.64072i
$427$	−8.75746	+	1.74283i	−0.423803	+	0.0843413i
$428$	5.62439	+	12.5472i	0.271865	+	0.606492i
$429$	−29.8927			−1.44323
$430$	19.8071	−	11.1772i	0.955182	−	0.539012i
$431$	26.6614			1.28423			0.642117	−	0.766606i	$-0.278056\pi$
$431$	26.6614			1.28423			0.642117	+	0.766606i	$0.278056\pi$
$432$	−15.3069	+	0.879747i	−0.736454	+	0.0423268i
$433$	4.20698	−	4.20698i	0.202175	−	0.202175i	−0.598756	−	0.800931i	$-0.704338\pi$
$433$	4.20698	−	4.20698i	0.202175	−	0.202175i	0.800931	+	0.598756i	$0.204338\pi$
$434$	0.0966578	+	6.68996i	0.00463972	+	0.321128i
$435$	−7.99569	−	9.57503i	−0.383364	−	0.459087i
$436$	−21.1333	−	8.05113i	−1.01210	−	0.385579i
$437$	−5.38078	+	5.38078i	−0.257398	+	0.257398i
$438$	13.5230	+	2.48869i	0.646156	+	0.118914i
$439$	23.8642			1.13897			0.569487	−	0.822000i	$-0.307142\pi$
$439$	23.8642			1.13897			0.569487	+	0.822000i	$0.307142\pi$
$440$	−20.4450	+	27.7115i	−0.974675	+	1.32109i
$441$	11.8142	+	28.5067i	0.562580	+	1.35746i
$442$	−3.59862	+	19.5542i	−0.171169	+	0.930097i
$443$	14.2936	−	14.2936i	0.679110	−	0.679110i	−0.280689	−	0.959799i	$-0.590563\pi$
$443$	14.2936	−	14.2936i	0.679110	−	0.679110i	0.959799	+	0.280689i	$0.0905629\pi$
$444$	−4.49385	+	11.7958i	−0.213268	+	0.559805i
$445$	1.28756	+	0.115732i	0.0610362	+	0.00548621i
$446$	−5.88982	+	4.05892i	−0.278891	+	0.192195i
$447$	11.5063	+	11.5063i	0.544230	+	0.544230i
$448$	−13.2309	−	16.5210i	−0.625100	−	0.780545i
$449$			3.65940i			0.172698i	0.996265	+	0.0863489i	$0.0275200\pi$
$449$			3.65940i			0.172698i	−0.996265	+	0.0863489i	$0.972480\pi$
$450$	11.0182	−	29.1589i	0.519405	−	1.37456i
$451$	−6.37963			−0.300405
$452$	3.00857	+	6.71168i	0.141511	+	0.315691i
$453$	−18.7088	−	18.7088i	−0.879018	−	0.879018i
$454$	21.0500	−	14.5064i	0.987926	−	0.680821i
$455$	9.28914	+	7.49025i	0.435482	+	0.351148i
$456$	25.1915	−	6.14898i	1.17970	−	0.287952i
$457$	17.1784	−	17.1784i	0.803573	−	0.803573i	−0.180079	−	0.983652i	$-0.557635\pi$
$457$	17.1784	−	17.1784i	0.803573	−	0.803573i	0.983652	+	0.180079i	$0.0576354\pi$
$458$	6.35089	−	34.5094i	0.296757	−	1.61252i
$459$	26.7173			1.24706
$460$	−3.29068	−	9.55223i	−0.153429	−	0.445375i
$461$	31.0261			1.44503			0.722516	−	0.691355i	$-0.242986\pi$
$461$	31.0261			1.44503			0.722516	+	0.691355i	$0.242986\pi$
$462$	−38.6402	+	39.7731i	−1.79770	+	1.85041i
$463$	−1.62586	−	1.62586i	−0.0755603	−	0.0755603i	0.668317	−	0.743877i	$-0.267015\pi$
$463$	−1.62586	−	1.62586i	−0.0755603	−	0.0755603i	−0.743877	+	0.668317i	$0.767015\pi$
$464$	6.12036	+	5.45508i	0.284131	+	0.253246i
$465$	8.35346	−	6.97561i	0.387382	−	0.323486i
$466$	−9.91673	−	14.3900i	−0.459384	−	0.666602i
$467$	−18.9911	+	18.9911i	−0.878802	+	0.878802i	−0.993411	−	0.114609i	$-0.963439\pi$
$467$	−18.9911	+	18.9911i	−0.878802	+	0.878802i	0.114609	+	0.993411i	$0.463439\pi$
$468$	−16.2273	+	7.27403i	−0.750108	+	0.336242i
$469$	−16.7573	−	11.1946i	−0.773781	−	0.516918i
$470$	3.69171	+	6.54208i	0.170286	+	0.301764i
$471$	−28.3261			−1.30520
$472$	−12.4104	+	20.4251i	−0.571233	+	0.940143i
$473$	27.6906	+	27.6906i	1.27322	+	1.27322i
$474$	−16.7950	+	11.5742i	−0.771422	+	0.531619i
$475$	−3.00336	+	16.5718i	−0.137804	+	0.760368i
$476$	21.3658	+	30.0644i	0.979298	+	1.37800i
$477$	−37.2303	−	37.2303i	−1.70466	−	1.70466i
$478$	−4.55737	+	24.7638i	−0.208449	+	1.13267i
$479$	36.6913			1.67647			0.838234	−	0.545311i	$-0.183589\pi$
$479$	36.6913			1.67647			0.838234	+	0.545311i	$0.183589\pi$
$480$	−7.31933	+	33.6415i	−0.334080	+	1.53552i
$481$			4.67711i			0.213258i
$482$	−7.34219	+	39.8960i	−0.334428	+	1.81721i
$483$	−3.17535	−	15.9557i	−0.144483	−	0.726008i
$484$	−34.8525	−	13.2777i	−1.58420	−	0.603533i
$485$	3.19663	+	3.82804i	0.145152	+	0.173822i
$486$	−15.3263	−	22.2396i	−0.695213	−	1.00881i
$487$	−5.01008	+	5.01008i	−0.227028	+	0.227028i	−0.811450	−	0.584422i	$-0.801321\pi$
$487$	−5.01008	+	5.01008i	−0.227028	+	0.227028i	0.584422	+	0.811450i	$0.301321\pi$
$488$	−8.15789	−	4.95675i	−0.369290	−	0.224382i
$489$	−23.5182			−1.06353
$490$	21.9734	−	2.67736i	0.992658	−	0.120951i
$491$			34.3152i			1.54862i	0.632804	+	0.774312i	$0.281904\pi$
$491$			34.3152i			1.54862i	−0.632804	+	0.774312i	$0.718096\pi$
$492$	−5.82004	+	2.60888i	−0.262388	+	0.117617i
$493$	−10.1021	−	10.1021i	−0.454976	−	0.454976i
$494$	7.91149	−	5.45214i	0.355955	−	0.245303i
$495$	53.4569	+	4.80494i	2.40271	+	0.215966i
$496$	−4.75912	+	5.33953i	−0.213691	+	0.239752i
$497$	−27.7245	+	5.51747i	−1.24361	+	0.247492i
$498$	−0.116513	+	0.633106i	−0.00522106	+	0.0283702i
$499$	−27.9382			−1.25069			−0.625343	−	0.780350i	$-0.715041\pi$
$499$	−27.9382			−1.25069			−0.625343	+	0.780350i	$0.715041\pi$
$500$	−18.0294	−	13.2265i	−0.806301	−	0.591505i
$501$			67.0770i			2.99678i
$502$	9.81337	+	1.80599i	0.437992	+	0.0806052i
$503$	−21.4722	+	21.4722i	−0.957398	+	0.957398i	−0.999129	−	0.0417307i	$-0.986713\pi$
$503$	−21.4722	+	21.4722i	−0.957398	+	0.957398i	0.0417307	+	0.999129i	$0.486713\pi$
$504$	−11.2976	+	30.9936i	−0.503236	+	1.38056i
$505$	−29.1712	−	2.62204i	−1.29810	−	0.116679i
$506$	14.3242	−	9.87142i	0.636789	−	0.438838i
$507$	17.1900	−	17.1900i	0.763434	−	0.763434i
$508$	6.76714	−	3.03342i	0.300243	−	0.134586i
$509$		−	31.4811i		−	1.39538i	−0.716401	−	0.697689i	$-0.754212\pi$
$509$		−	31.4811i		−	1.39538i	0.716401	−	0.697689i	$-0.245788\pi$
$510$	16.0971	−	57.7940i	0.712791	−	2.55916i
$511$	5.25001	−	7.85880i	0.232247	−	0.347653i
$512$	1.51887	−	22.5764i	0.0671250	−	0.997745i
$513$	−9.12950	−	9.12950i	−0.403077	−	0.403077i
$514$	−13.5059	−	19.5981i	−0.595719	−	0.864437i
$515$	−15.2456	+	12.7309i	−0.671800	+	0.560991i
$516$	36.5855	+	13.9380i	1.61059	+	0.613585i
$517$	−9.14595	+	9.14595i	−0.402238	+	0.402238i
$518$	6.22303	+	6.04577i	0.273424	+	0.265636i
$519$		−	19.8930i		−	0.873205i
$520$	1.90336	+	12.6139i	0.0834679	+	0.553157i
$521$		−	14.3173i		−	0.627251i	−0.949547	−	0.313626i	$-0.898456\pi$
$521$		−	14.3173i		−	0.627251i	0.949547	−	0.313626i	$-0.101544\pi$
$522$	2.31273	−	12.5669i	0.101226	−	0.550039i
$523$	22.4819	+	22.4819i	0.983065	+	0.983065i	0.999859	−	0.0167944i	$-0.00534608\pi$
$523$	22.4819	+	22.4819i	0.983065	+	0.983065i	−0.0167944	+	0.999859i	$0.505346\pi$
$524$	−19.7881	−	7.53864i	−0.864445	−	0.329327i
$525$	−25.8933	−	25.0197i	−1.13008	−	1.09195i
$526$	−12.2155	−	17.7257i	−0.532622	−	0.772877i
$527$	8.81329	−	8.81329i	0.383913	−	0.383913i
$528$	−59.1834	+	3.40150i	−2.57563	+	0.148031i
$529$		−	17.8963i		−	0.778101i
$530$	−32.8938	+	18.5621i	−1.42882	+	0.806284i
$531$	37.2493			1.61648
$532$	2.97240	−	17.5741i	0.128870	−	0.761933i
$533$	−1.67106	+	1.67106i	−0.0723815	+	0.0723815i
$534$	1.26278	+	1.83240i	0.0546459	+	0.0792956i
$535$	−9.85363	−	11.7999i	−0.426009	−	0.510156i
$536$	−5.10867	−	20.9296i	−0.220661	−	0.904019i
$537$	25.4646	+	25.4646i	1.09888	+	1.09888i
$538$	−2.81956	+	15.3209i	−0.121560	+	0.660531i
$539$	14.5926	+	35.2109i	0.628549	+	1.51664i
$540$	16.2071	−	5.58326i	0.697444	−	0.240265i
$541$		−	24.0200i		−	1.03270i	−0.856378	−	0.516350i	$-0.827290\pi$
$541$		−	24.0200i		−	1.03270i	0.856378	−	0.516350i	$-0.172710\pi$
$542$	0.703900	−	3.82485i	0.0302351	−	0.164291i
$543$	−6.87116	−	6.87116i	−0.294870	−	0.294870i
$544$	−4.89970	+	39.1241i	−0.210073	+	1.67743i
$545$	25.1828	+	2.26354i	1.07871	+	0.0969593i
$546$	0.296756	+	20.5393i	0.0127000	+	0.879001i
$547$	28.2072	+	28.2072i	1.20605	+	1.20605i	0.972294	+	0.233760i	$0.0751028\pi$
$547$	28.2072	+	28.2072i	1.20605	+	1.20605i	0.233760	+	0.972294i	$0.424897\pi$
$548$	12.6084	−	5.65184i	0.538606	−	0.241435i
$549$			14.8775i			0.634958i
$550$	13.6095	−	36.0164i	0.580311	−	1.53575i
$551$			6.90394i			0.294118i
$552$	9.03097	−	14.8633i	0.384383	−	0.632624i
$553$	2.73642	+	13.7501i	0.116364	+	0.584715i
$554$	13.8638	+	20.1174i	0.589015	+	0.854708i
$555$	1.26342	−	14.0561i	0.0536294	−	0.596648i
$556$	−9.71101	+	25.4903i	−0.411839	+	1.08103i
$557$	0.398538	+	0.398538i	0.0168866	+	0.0168866i	0.715500	−	0.698613i	$-0.246199\pi$
$557$	0.398538	+	0.398538i	0.0168866	+	0.0168866i	−0.698613	+	0.715500i	$0.746199\pi$
$558$	10.9636	+	2.01768i	0.464128	+	0.0854150i
$559$	14.5064			0.613554
$560$	19.2435	+	13.7727i	0.813188	+	0.582001i
$561$	103.301			4.36137
$562$	30.2196	+	5.56141i	1.27474	+	0.234594i
$563$	19.3688	+	19.3688i	0.816299	+	0.816299i	0.985570	−	0.169271i	$-0.0541413\pi$
$563$	19.3688	+	19.3688i	0.816299	+	0.816299i	−0.169271	+	0.985570i	$0.554141\pi$
$564$	−4.60357	+	12.0838i	−0.193845	+	0.508822i
$565$	−5.27085	−	6.31196i	−0.221746	−	0.265546i
$566$	13.1470	+	19.0774i	0.552612	+	0.801884i
$567$	−7.24481	+	1.44179i	−0.304253	+	0.0605496i
$568$	−25.8264	−	15.6922i	−1.08365	−	0.658429i
$569$		−	4.05795i		−	0.170118i	−0.996376	−	0.0850591i	$-0.972892\pi$
$569$		−	4.05795i		−	0.170118i	0.996376	−	0.0850591i	$-0.0271079\pi$
$570$	−25.2492	+	14.2482i	−1.05757	+	0.596790i
$571$			3.38941i			0.141842i	0.997482	+	0.0709212i	$0.0225939\pi$
$571$			3.38941i			0.141842i	−0.997482	+	0.0709212i	$0.977406\pi$
$572$	−20.0436	+	8.98473i	−0.838067	+	0.375670i
$573$	−21.2738	−	21.2738i	−0.888724	−	0.888724i
$574$	0.0633330	+	4.38345i	0.00264347	+	0.182962i
$575$	6.43487	+	9.28357i	0.268352	+	0.387151i
$576$	−31.3002	+	16.2481i	−1.30417	+	0.677004i
$577$	−0.514077	−	0.514077i	−0.0214013	−	0.0214013i	0.696325	−	0.717726i	$-0.254817\pi$
$577$	−0.514077	−	0.514077i	−0.0214013	−	0.0214013i	−0.717726	+	0.696325i	$0.754817\pi$
$578$	8.08448	−	43.9294i	0.336270	−	1.82722i
$579$		−	40.8259i		−	1.69667i
$580$	−8.23920	−	4.01701i	−0.342114	−	0.166797i
$581$	0.367925	+	0.245789i	0.0152641	+	0.0101970i
$582$	−1.55385	+	8.44334i	−0.0644094	+	0.349988i
$583$	−45.9861	−	45.9861i	−1.90455	−	1.90455i
$584$	9.81549	−	2.39585i	0.406168	−	0.0991410i
$585$	15.2609	−	12.7437i	0.630960	−	0.526887i
$586$	−18.3878	−	26.6821i	−0.759591	−	1.10223i
$587$	26.2357	−	26.2357i	1.08287	−	1.08287i	0.0866239	−	0.996241i	$-0.472392\pi$
$587$	26.2357	−	26.2357i	1.08287	−	1.08287i	0.996241	−	0.0866239i	$-0.0276079\pi$
$588$	27.7118	+	26.1549i	1.14281	+	1.07861i
$589$	−6.02314			−0.248179
$590$	7.16953	−	25.7410i	0.295165	−	1.05974i
$591$		−	27.5869i		−	1.13477i
$592$	0.532210	+	9.26003i	0.0218737	+	0.380585i
$593$	−21.0385	+	21.0385i	−0.863946	+	0.863946i	−0.991794	−	0.127848i	$-0.959193\pi$
$593$	−21.0385	+	21.0385i	−0.863946	+	0.863946i	0.127848	+	0.991794i	$0.459193\pi$
$594$	16.7487	+	24.3037i	0.687208	+	0.997194i
$595$	−32.1008	−	25.8843i	−1.31600	−	1.06115i
$596$	11.1736	+	4.25681i	0.457690	+	0.174366i
$597$	−10.1085	−	10.1085i	−0.413715	−	0.413715i
$598$	1.16635	−	6.33772i	0.0476956	−	0.259169i
$599$		−	41.7664i		−	1.70653i	−0.521478	−	0.853265i	$-0.674619\pi$
$599$		−	41.7664i		−	1.70653i	0.521478	−	0.853265i	$-0.325381\pi$
$600$	−2.31278	−	38.4227i	−0.0944188	−	1.56860i
$601$			14.0893i			0.574717i	0.957823	+	0.287358i	$0.0927770\pi$
$601$			14.0893i			0.574717i	−0.957823	+	0.287358i	$0.907223\pi$
$602$	18.7514	−	19.3012i	0.764249	−	0.786657i
$603$	−23.7430	+	23.7430i	−0.966888	+	0.966888i
$604$	−18.1679	−	6.92142i	−0.739242	−	0.281628i
$605$	41.5308	+	3.73297i	1.68847	+	0.151767i
$606$	−28.6098	−	41.5152i	−1.16220	−	1.68644i
$607$	−7.42042	−	7.42042i	−0.301186	−	0.301186i	0.540292	−	0.841478i	$-0.318314\pi$
$607$	−7.42042	−	7.42042i	−0.301186	−	0.301186i	−0.841478	+	0.540292i	$0.818314\pi$
$608$	15.0433	−	11.6947i	0.610085	−	0.474284i
$609$	−12.2733	−	8.19905i	−0.497337	−	0.332242i
$610$	10.2811	+	2.86354i	0.416269	+	0.115941i
$611$			4.79131i			0.193836i
$612$	56.0773	−	25.1371i	2.26679	−	1.01611i
$613$	2.64550	−	2.64550i	0.106851	−	0.106851i	−0.651660	−	0.758511i	$-0.725927\pi$
$613$	2.64550	−	2.64550i	0.106851	−	0.106851i	0.758511	+	0.651660i	$0.225927\pi$
$614$	−5.69658	+	3.92575i	−0.229895	+	0.158431i
$615$	5.47342	−	4.57062i	0.220710	−	0.184305i
$616$	−13.9546	+	38.2826i	−0.562246	+	1.54245i
$617$	3.62086	−	3.62086i	0.145771	−	0.145771i	−0.630455	−	0.776226i	$-0.717132\pi$
$617$	3.62086	−	3.62086i	0.145771	−	0.145771i	0.776226	+	0.630455i	$0.217132\pi$
$618$	−33.6264	−	6.18838i	−1.35265	−	0.248933i
$619$		−	10.2222i		−	0.410865i	−0.978671	−	0.205433i	$-0.934140\pi$
$619$		−	10.2222i		−	0.410865i	0.978671	−	0.205433i	$-0.0658602\pi$
$620$	3.50453	−	7.18805i	0.140745	−	0.288679i
$621$	−8.65935			−0.347488
$622$	7.05252	−	38.3220i	0.282780	−	1.53657i
$623$	1.50018	−	0.298553i	0.0601036	−	0.0119613i
$624$	−14.6113	+	16.3933i	−0.584921	+	0.656256i
$625$	23.4100	+	8.77349i	0.936398	+	0.350939i
$626$	30.0756	−	20.7263i	1.20206	−	0.828391i
$627$	−35.2988	−	35.2988i	−1.40970	−	1.40970i
$628$	−18.9933	+	8.51388i	−0.757913	+	0.339741i
$629$		−	16.1628i		−	0.644454i
$630$	2.77079	−	36.7780i	0.110391	−	1.46527i
$631$	−10.6864			−0.425419			−0.212710	−	0.977115i	$-0.568229\pi$
$631$	−10.6864			−0.425419			−0.212710	+	0.977115i	$0.568229\pi$
$632$	−7.78262	+	12.8087i	−0.309576	+	0.509504i
$633$	3.74662	−	3.74662i	0.148915	−	0.148915i
$634$	−0.751822	−	1.09095i	−0.0298587	−	0.0433273i
$635$	−6.36411	+	5.31440i	−0.252552	+	0.210895i
$636$	−60.7580	−	23.1469i	−2.40921	−	0.917835i
$637$	13.0454	+	5.40068i	0.516876	+	0.213983i
$638$	2.85664	−	15.5224i	0.113095	−	0.614538i
$639$			47.0996i			1.86323i
$640$	5.20374	+	24.7572i	0.205696	+	0.978616i
$641$	−38.3191			−1.51351			−0.756757	−	0.653697i	$-0.773217\pi$
$641$	−38.3191			−1.51351			−0.756757	+	0.653697i	$0.773217\pi$
$642$	4.78976	−	26.0266i	0.189037	−	1.02719i
$643$	9.81076	+	9.81076i	0.386899	+	0.386899i	0.873580	−	0.486681i	$-0.161793\pi$
$643$	9.81076	+	9.81076i	0.386899	+	0.386899i	−0.486681	+	0.873580i	$0.661793\pi$
$644$	−6.92487	−	9.74420i	−0.272878	−	0.383975i
$645$	−43.5959	−	3.91860i	−1.71659	−	0.154295i
$646$	−27.3400	+	18.8411i	−1.07568	+	0.741294i
$647$	24.1670	+	24.1670i	0.950105	+	0.950105i	0.998813	−	0.0487085i	$-0.0155105\pi$
$647$	24.1670	+	24.1670i	0.950105	+	0.950105i	−0.0487085	+	0.998813i	$0.515511\pi$
$648$	−6.74880	−	4.10059i	−0.265118	−	0.161086i
$649$	46.0096			1.80603
$650$	−5.86919	−	12.9988i	−0.230208	−	0.509856i
$651$	7.15302	−	10.7074i	0.280349	−	0.419658i
$652$	−15.7695	+	7.06879i	−0.617580	+	0.276835i
$653$	21.8449	−	21.8449i	0.854856	−	0.854856i	−0.135870	−	0.990727i	$-0.543383\pi$
$653$	21.8449	−	21.8449i	0.854856	−	0.854856i	0.990727	+	0.135870i	$0.0433831\pi$
$654$	24.6981	+	35.8389i	0.965773	+	1.40141i
$655$	23.5798	+	2.11945i	0.921338	+	0.0828139i
$656$	−3.11831	+	3.49861i	−0.121750	+	0.136598i
$657$	−11.1349	−	11.1349i	−0.434414	−	0.434414i
$658$	6.37499	+	6.19340i	0.248523	+	0.241444i
$659$	24.3323			0.947854			0.473927	−	0.880564i	$-0.342836\pi$
$659$	24.3323			0.947854			0.473927	+	0.880564i	$0.342836\pi$
$660$	62.6641	−	21.5874i	2.43920	−	0.840288i
$661$	−5.32909			−0.207278			−0.103639	−	0.994615i	$-0.533049\pi$
$661$	−5.32909			−0.207278			−0.103639	+	0.994615i	$0.533049\pi$
$662$	0.00252994	−	0.0137472i	9.83288e−5	−	0.000534299i
$663$	27.0583	−	27.0583i	1.05086	−	1.05086i
$664$	0.112166	+	0.459530i	0.00435289	+	0.0178332i
$665$	2.12422	+	19.8139i	0.0823737	+	0.768351i
$666$	11.9033	−	8.20307i	0.461244	−	0.317863i
$667$	3.27420	+	3.27420i	0.126778	+	0.126778i
$668$	20.1611	+	44.9765i	0.780055	+	1.74019i
$669$	13.7667			0.532250
$670$	11.8376	+	20.9774i	0.457327	+	0.810428i
$671$			18.3764i			0.709414i
$672$	2.92471	+	40.6312i	0.112823	+	1.56738i
$673$	10.1733	+	10.1733i	0.392150	+	0.392150i	0.875453	−	0.483303i	$-0.160563\pi$
$673$	10.1733	+	10.1733i	0.392150	+	0.392150i	−0.483303	+	0.875453i	$0.660563\pi$
$674$	−38.9128	+	26.8164i	−1.49886	+	1.03293i
$675$	−15.7513	+	10.9180i	−0.606268	+	0.420232i
$676$	6.35951	−	16.6930i	0.244596	−	0.642037i
$677$	−11.2171	+	11.2171i	−0.431110	+	0.431110i	−0.889006	−	0.457896i	$-0.848603\pi$
$677$	−11.2171	+	11.2171i	−0.431110	+	0.431110i	0.457896	+	0.889006i	$0.348603\pi$
$678$	2.56211	−	13.9220i	0.0983974	−	0.534672i
$679$	4.90678	+	3.27793i	0.188305	+	0.125795i
$680$	−6.57751	−	43.5903i	−0.252236	−	1.67161i
$681$	−49.2016			−1.88541
$682$	13.5421	+	2.49219i	0.518553	+	0.0954309i
$683$	−24.5690	+	24.5690i	−0.940108	+	0.940108i	−0.998305	−	0.0581972i	$-0.981465\pi$
$683$	−24.5690	+	24.5690i	−0.940108	+	0.940108i	0.0581972	+	0.998305i	$0.481465\pi$
$684$	−27.7516	−	10.5725i	−1.06111	−	0.404249i
$685$	−11.8575	+	9.90172i	−0.453053	+	0.378325i
$686$	24.0486	−	10.3762i	0.918180	−	0.396164i
$687$	−47.7528	+	47.7528i	−1.82188	+	1.82188i
$688$	28.7206	−	1.65068i	1.09496	−	0.0629318i
$689$	−24.0909			−0.917789
$690$	−5.21724	+	18.7317i	−0.198617	+	0.713102i
$691$	26.7358			1.01708			0.508540	−	0.861038i	$-0.330185\pi$
$691$	26.7358			1.01708			0.508540	+	0.861038i	$0.330185\pi$
$692$	−5.97915	−	13.3386i	−0.227293	−	0.507059i
$693$	62.2846	−	12.3953i	2.36600	−	0.470858i
$694$	25.4478	+	36.9268i	0.965985	+	1.40172i
$695$	2.73021	−	30.3746i	0.103563	−	1.15218i
$696$	−3.74165	−	15.3290i	−0.141827	−	0.581046i
$697$	5.77472	−	5.77472i	0.218733	−	0.218733i
$698$	−6.60336	+	35.8813i	−0.249941	+	1.35813i
$699$			33.6346i			1.27218i
$700$	−24.8820	−	8.99356i	−0.940453	−	0.339925i
$701$			6.71634i			0.253673i	0.991924	+	0.126836i	$0.0404823\pi$
$701$			6.71634i			0.253673i	−0.991924	+	0.126836i	$0.959518\pi$
$702$	10.7531	+	1.97893i	0.405850	+	0.0746900i
$703$	−5.52296	+	5.52296i	−0.208302	+	0.208302i
$704$	−38.6613	+	20.0693i	−1.45710	+	0.756390i
$705$	1.29427	−	14.3993i	0.0487452	−	0.542309i
$706$	−6.96040	+	4.79670i	−0.261958	+	0.180526i
$707$	−33.9885	+	6.76407i	−1.27827	+	0.254389i
$708$	41.9738	−	18.8151i	1.57747	−	0.707115i
$709$	22.7398			0.854009			0.427005	−	0.904249i	$-0.359569\pi$
$709$	22.7398			0.854009			0.427005	+	0.904249i	$0.359569\pi$
$710$	32.5481	+	9.06545i	1.22151	+	0.340220i
$711$	23.3593			0.876042
$712$	1.39748	+	0.849110i	0.0523727	+	0.0318217i
$713$	−2.85648	+	2.85648i	−0.106976	+	0.106976i
$714$	−1.02551	−	70.9783i	−0.0383787	−	2.65630i
$715$	18.8499	−	15.7408i	0.704947	−	0.588671i
$716$	24.7283	+	9.42072i	0.924140	+	0.352069i
$717$	34.2672	−	34.2672i	1.27973	−	1.27973i
$718$	−1.92526	+	10.4615i	−0.0718502	+	0.390420i
$719$	−32.0992			−1.19710			−0.598549	−	0.801086i	$-0.704256\pi$
$719$	−32.0992			−1.19710			−0.598549	+	0.801086i	$0.704256\pi$
$720$	28.7644	−	26.9673i	1.07198	−	1.00501i
$721$	−13.0547	+	19.5417i	−0.486182	+	0.727772i
$722$	−10.6458	−	1.95919i	−0.396198	−	0.0729135i
$723$	55.2065	−	55.2065i	2.05315	−	2.05315i
$724$	−6.67249	−	2.54201i	−0.247981	−	0.0944732i
$725$	10.0840	+	1.82755i	0.374509	+	0.0678734i
$726$	40.7315	+	59.1048i	1.51169	+	2.19358i
$727$	11.8273	+	11.8273i	0.438649	+	0.438649i	0.891557	−	0.452908i	$-0.149614\pi$
$727$	11.8273	+	11.8273i	0.438649	+	0.438649i	−0.452908	+	0.891557i	$0.649614\pi$
$728$	6.37240	+	13.6828i	0.236177	+	0.507119i
$729$			43.6063i			1.61505i
$730$	−9.83793	+	5.55157i	−0.364118	+	0.205473i
$731$	−50.1301			−1.85413
$732$	7.51484	+	16.7645i	0.277757	+	0.619635i
$733$	−20.8928	−	20.8928i	−0.771692	−	0.771692i	0.206710	−	0.978402i	$-0.433724\pi$
$733$	−20.8928	−	20.8928i	−0.771692	−	0.771692i	−0.978402	+	0.206710i	$0.933724\pi$
$734$	20.7627	+	30.1284i	0.766365	+	1.11206i
$735$	−37.7463	−	19.7546i	−1.39229	−	0.728658i
$736$	1.58804	−	12.6805i	0.0585361	−	0.467411i
$737$	−29.3268	+	29.3268i	−1.08027	+	1.08027i
$738$	7.18370	+	1.32204i	0.264435	+	0.0486649i
$739$	3.01684			0.110976			0.0554881	−	0.998459i	$-0.482329\pi$
$739$	3.01684			0.110976			0.0554881	+	0.998459i	$0.482329\pi$
$740$	−3.37763	−	9.80464i	−0.124164	−	0.360426i
$741$	−18.4921			−0.679323
$742$	−31.1406	+	32.0536i	−1.14321	+	1.17673i
$743$	−4.12087	−	4.12087i	−0.151180	−	0.151180i	0.627465	−	0.778645i	$-0.284093\pi$
$743$	−4.12087	−	4.12087i	−0.151180	−	0.151180i	−0.778645	+	0.627465i	$0.784093\pi$
$744$	13.3734	−	3.26429i	0.490292	−	0.119675i
$745$	−13.3147	−	1.19678i	−0.487812	−	0.0438467i
$746$	−20.0986	+	13.8508i	−0.735862	+	0.507113i
$747$	0.521301	−	0.521301i	0.0190734	−	0.0190734i
$748$	69.2654	−	31.0488i	2.53260	−	1.13526i
$749$	−15.1252	−	10.1042i	−0.552661	−	0.369201i
$750$	14.1273	+	40.6508i	0.515855	+	1.48436i
$751$	14.2125			0.518620			0.259310	−	0.965794i	$-0.416505\pi$
$751$	14.2125			0.518620			0.259310	+	0.965794i	$0.416505\pi$
$752$	0.545205	+	9.48614i	0.0198816	+	0.345924i
$753$	−13.5794	−	13.5794i	−0.494859	−	0.494859i
$754$	−3.31762	−	4.81414i	−0.120821	−	0.175321i
$755$	21.6492	+	1.94592i	0.787894	+	0.0708194i
$756$	16.5328	−	11.7493i	0.601294	−	0.427319i
$757$	6.58719	+	6.58719i	0.239415	+	0.239415i	0.816608	−	0.577193i	$-0.195852\pi$
$757$	6.58719	+	6.58719i	0.239415	+	0.239415i	−0.577193	+	0.816608i	$0.695852\pi$
$758$	−21.3378	−	3.92686i	−0.775022	−	0.142630i
$759$	−33.4810			−1.21528
$760$	−12.6476	+	17.1427i	−0.458775	+	0.621832i
$761$		−	44.9438i		−	1.62921i	−0.580016	−	0.814605i	$-0.696954\pi$
$761$		−	44.9438i		−	1.62921i	0.580016	−	0.814605i	$-0.303046\pi$
$762$	−14.0370	−	2.58328i	−0.508508	−	0.0935825i
$763$	29.3414	−	5.83924i	1.06223	−	0.211395i
$764$	−20.6587	−	7.87031i	−0.747404	−	0.284738i
$765$	−52.7375	+	44.0388i	−1.90673	+	1.59223i
$766$	−40.6121	+	27.9875i	−1.46737	+	1.01123i
$767$	12.0516	−	12.0516i	0.435157	−	0.435157i
$768$	−27.0630	+	34.1191i	−0.976552	+	1.23117i
$769$	−28.3200			−1.02125			−0.510623	−	0.859805i	$-0.670585\pi$
$769$	−28.3200			−1.02125			−0.510623	+	0.859805i	$0.670585\pi$
$770$	3.42243	−	45.4274i	0.123336	−	1.63709i
$771$			45.8080i			1.64974i
$772$	−12.2709	−	27.3746i	−0.441639	−	0.985233i
$773$	−32.5722	−	32.5722i	−1.17154	−	1.17154i	−0.981843	−	0.189697i	$-0.939249\pi$
$773$	−32.5722	−	32.5722i	−1.17154	−	1.17154i	−0.189697	−	0.981843i	$-0.560751\pi$
$774$	−25.4424	−	36.9189i	−0.914508	−	1.32702i
$775$	−1.59439	+	8.79745i	−0.0572722	+	0.316014i
$776$	1.49589	+	6.12846i	0.0536993	+	0.219999i
$777$	−3.25925	−	16.3773i	−0.116925	−	0.587532i
$778$	−22.4952	−	4.13986i	−0.806491	−	0.148421i
$779$	−3.94653			−0.141399
$780$	10.7595	−	22.0685i	0.385252	−	0.790180i
$781$			58.1764i			2.08172i
$782$	−4.03060	+	21.9015i	−0.144134	+	0.783194i
$783$	−5.55529	+	5.55529i	−0.198530	+	0.198530i
$784$	26.4426	+	9.20816i	0.944378	+	0.328863i
$785$	17.8621	−	14.9159i	0.637525	−	0.532370i
$786$	23.1260	+	33.5576i	0.824876	+	1.19696i
$787$	−2.77648	+	2.77648i	−0.0989709	+	0.0989709i	−0.754859	−	0.655888i	$-0.772295\pi$
$787$	−2.77648	+	2.77648i	−0.0989709	+	0.0989709i	0.655888	+	0.754859i	$0.272295\pi$
$788$	−8.29170	−	18.4976i	−0.295379	−	0.658949i
$789$			41.4315i			1.47500i
$790$	4.49606	−	16.1424i	0.159963	−	0.574320i
$791$	−8.09066	−	5.40490i	−0.287671	−	0.192176i
$792$	58.0204	+	35.2533i	2.06166	+	1.25267i
$793$	4.81345	+	4.81345i	0.170931	+	0.170931i
$794$	11.1371	−	7.67502i	0.395240	−	0.272376i
$795$	72.4002	+	6.50765i	2.56777	+	0.230803i
$796$	−9.81627	−	3.73970i	−0.347928	−	0.132550i
$797$	10.9058	−	10.9058i	0.386303	−	0.386303i	−0.487063	−	0.873367i	$-0.661932\pi$
$797$	10.9058	−	10.9058i	0.386303	−	0.386303i	0.873367	+	0.487063i	$0.161932\pi$
$798$	−23.9034	+	24.6042i	−0.846171	+	0.870981i
$799$		−	16.5575i		−	0.585762i
$800$	−13.0993	−	25.0681i	−0.463131	−	0.886290i
$801$		−	2.54858i		−	0.0900496i
$802$	−8.98879	−	1.65424i	−0.317405	−	0.0584131i
$803$	−13.7536	−	13.7536i	−0.485354	−	0.485354i
$804$	−14.7615	+	38.7473i	−0.520599	+	1.36651i
$805$	10.4042	+	8.38937i	0.366700	+	0.295686i
$806$	4.19996	−	2.89436i	0.147937	−	0.101950i
$807$	21.2005	−	21.2005i	0.746292	−	0.746292i
$808$	−31.6615	−	19.2376i	−1.11385	−	0.676777i
$809$			26.9265i			0.946686i	0.880878	+	0.473343i	$0.156953\pi$
$809$			26.9265i			0.946686i	−0.880878	+	0.473343i	$0.843047\pi$
$810$	8.50527	+	2.36893i	0.298845	+	0.0832357i
$811$	−34.6646			−1.21724			−0.608620	−	0.793462i	$-0.708276\pi$
$811$	−34.6646			−1.21724			−0.608620	+	0.793462i	$0.708276\pi$
$812$	−10.6938	−	1.80870i	−0.375279	−	0.0634730i
$813$	−5.29268	+	5.29268i	−0.185622	+	0.185622i
$814$	14.7027	−	10.1323i	0.515330	−	0.355136i
$815$	14.8303	−	12.3841i	0.519482	−	0.433797i
$816$	50.4928	−	56.6507i	1.76760	−	1.98317i
$817$	17.1298	+	17.1298i	0.599297	+	0.599297i
$818$	−1.29866	−	0.238997i	−0.0454066	−	0.00835633i
$819$	13.0678	−	19.5614i	0.456627	−	0.683530i
$820$	2.29627	−	4.70982i	0.0801891	−	0.164474i
$821$		−	28.3630i		−	0.989877i	−0.868928	−	0.494939i	$-0.835191\pi$
$821$		−	28.3630i		−	0.989877i	0.868928	−	0.494939i	$-0.164809\pi$
$822$	−26.1536	−	4.81314i	−0.912213	−	0.167878i
$823$	2.88581	+	2.88581i	0.100593	+	0.100593i	0.755612	−	0.655019i	$-0.227339\pi$
$823$	2.88581	+	2.88581i	0.100593	+	0.100593i	−0.655019	+	0.755612i	$0.727339\pi$
$824$	−24.4072	+	5.95753i	−0.850266	+	0.207540i
$825$	−60.9017	+	42.2137i	−2.12032	+	1.46969i
$826$	−0.456754	−	31.6132i	−0.0158925	−	1.09997i
$827$	−4.80713	−	4.80713i	−0.167160	−	0.167160i	0.618570	−	0.785730i	$-0.287712\pi$
$827$	−4.80713	−	4.80713i	−0.167160	−	0.167160i	−0.785730	+	0.618570i	$0.787712\pi$
$828$	−18.1752	+	8.14720i	−0.631633	+	0.283135i
$829$			24.0249i			0.834419i	0.908810	+	0.417209i	$0.136992\pi$
$829$			24.0249i			0.834419i	−0.908810	+	0.417209i	$0.863008\pi$
$830$	−0.259907	−	0.460581i	−0.00902151	−	0.0159870i
$831$		−	47.0218i		−	1.63117i
$832$	−4.86992	+	15.3837i	−0.168834	+	0.533333i
$833$	−45.0813	−	18.6633i	−1.56197	−	0.646644i
$834$	43.2278	−	29.7901i	1.49686	−	1.03155i
$835$	−35.3211	−	42.2978i	−1.22234	−	1.46378i
$836$	−34.2781	−	13.0589i	−1.18553	−	0.451652i
$837$	−4.84656	−	4.84656i	−0.167522	−	0.167522i
$838$	−1.96111	+	10.6563i	−0.0677455	+	0.368115i
$839$	−28.5858			−0.986890			−0.493445	−	0.869777i	$-0.664263\pi$
$839$	−28.5858			−0.986890			−0.493445	+	0.869777i	$0.664263\pi$
$840$	−15.4548	−	42.8423i	−0.533242	−	1.47820i
$841$	−24.7990			−0.855136
$842$	−2.51995	+	13.6929i	−0.0868431	+	0.471888i
$843$	−41.8167	−	41.8167i	−1.44024	−	1.44024i
$844$	1.38608	−	3.63829i	0.0477107	−	0.125235i
$845$	−1.78795	+	19.8916i	−0.0615072	+	0.684292i
$846$	12.1940	−	8.40337i	0.419237	−	0.288914i
$847$	48.3891	−	9.62995i	1.66267	−	0.330889i
$848$	−47.6966	+	2.74131i	−1.63791	+	0.0941369i
$849$		−	44.5909i		−	1.53036i
$850$	20.2823	+	44.9205i	0.695678	+	1.54076i
$851$			5.23854i			0.179575i
$852$	23.7906	+	53.0735i	0.815053	+	1.81827i
$853$	26.3254	+	26.3254i	0.901366	+	0.901366i	0.995554	−	0.0941884i	$-0.0300256\pi$
$853$	26.3254	+	26.3254i	0.901366	+	0.901366i	−0.0941884	+	0.995554i	$0.530026\pi$
$854$	12.6265	−	0.182430i	0.432069	−	0.00624261i
$855$	33.0692	+	2.97241i	1.13094	+	0.101654i
$856$	−4.61108	−	18.8910i	−0.157604	−	0.645681i
$857$	20.6212	+	20.6212i	0.704407	+	0.704407i	0.965353	−	0.260946i	$-0.0840346\pi$
$857$	20.6212	+	20.6212i	0.704407	+	0.704407i	−0.260946	+	0.965353i	$0.584035\pi$
$858$	41.5764	+	7.65145i	1.41940	+	0.261216i
$859$		−	11.3102i		−	0.385899i	−0.981209	−	0.192949i	$-0.938195\pi$
$859$		−	11.3102i		−	0.385899i	0.981209	−	0.192949i	$-0.0618053\pi$
$860$	−30.4098	+	10.4760i	−1.03696	+	0.357227i
$861$	4.68686	−	7.01582i	0.159728	−	0.239099i
$862$	−37.0822	−	6.82436i	−1.26302	−	0.232439i
$863$	33.8905	+	33.8905i	1.15365	+	1.15365i	0.985816	+	0.167832i	$0.0536766\pi$
$863$	33.8905	+	33.8905i	1.15365	+	1.15365i	0.167832	+	0.985816i	$0.446323\pi$
$864$	21.5149	+	2.69441i	0.731952	+	0.0916658i
$865$	10.4752	+	12.5442i	0.356166	+	0.426517i
$866$	−6.92814	+	4.77447i	−0.235428	+	0.162243i
$867$	−60.7878	+	60.7878i	−2.06446	+	2.06446i
$868$	1.57795	−	9.32951i	0.0535591	−	0.316664i
$869$	28.8529			0.978768
$870$	8.67000	+	15.3641i	0.293941	+	0.520892i
$871$			15.3635i			0.520573i
$872$	27.3326	+	16.6073i	0.925597	+	0.562395i
$873$	6.95227	−	6.95227i	0.235299	−	0.235299i
$874$	8.86118	−	6.10661i	0.299734	−	0.206559i
$875$	29.5027	+	2.14230i	0.997374	+	0.0724231i
$876$	−18.1716	−	6.92282i	−0.613961	−	0.233900i
$877$	39.5070	+	39.5070i	1.33406	+	1.33406i	0.901705	+	0.432351i	$0.142316\pi$
$877$	39.5070	+	39.5070i	1.33406	+	1.33406i	0.432351	+	0.901705i	$0.357684\pi$
$878$	−33.1916	−	6.10837i	−1.12016	−	0.206147i
$879$			62.3659i			2.10355i
$880$	35.5291	−	33.3095i	1.19769	−	1.12286i
$881$		−	31.8459i		−	1.07292i	−0.843927	−	0.536458i	$-0.819762\pi$
$881$		−	31.8459i		−	1.07292i	0.843927	−	0.536458i	$-0.180238\pi$
$882$	−9.13515	−	42.6728i	−0.307596	−	1.43687i
$883$	2.50424	−	2.50424i	0.0842743	−	0.0842743i	−0.663713	−	0.747987i	$-0.731020\pi$
$883$	2.50424	−	2.50424i	0.0842743	−	0.0842743i	0.747987	+	0.663713i	$0.231020\pi$
$884$	10.0103	−	26.2759i	0.336684	−	0.883756i
$885$	−39.4741	+	32.9631i	−1.32691	+	1.10804i
$886$	−23.5390	+	16.2217i	−0.790809	+	0.544979i
$887$	−18.8809	−	18.8809i	−0.633959	−	0.633959i	0.315100	−	0.949059i	$-0.397962\pi$
$887$	−18.8809	−	18.8809i	−0.633959	−	0.633959i	−0.949059	+	0.315100i	$0.897962\pi$
$888$	9.26960	−	15.2560i	0.311067	−	0.511959i
$889$	−5.44956	+	8.15751i	−0.182772	+	0.273594i
$890$	−1.76119	−	0.490535i	−0.0590352	−	0.0164428i
$891$			15.2023i			0.509297i
$892$	9.23083	−	4.13780i	0.309071	−	0.138544i
$893$	−5.65782	+	5.65782i	−0.189332	+	0.189332i
$894$	−13.0584	−	18.9488i	−0.436740	−	0.633744i
$895$	−29.4666	−	2.64859i	−0.984961	−	0.0885327i
$896$	14.1735	+	26.3650i	0.473502	+	0.880793i
$897$	−8.76988	+	8.76988i	−0.292818	+	0.292818i
$898$	0.936675	−	5.08970i	0.0312572	−	0.169846i
$899$			3.66508i			0.122237i
$900$	−22.7884	+	37.7355i	−0.759614	+	1.25785i
$901$	83.2516			2.77351
$902$	8.87315	+	1.63295i	0.295444	+	0.0543714i
$903$	−50.7953	+	10.1088i	−1.69036	+	0.336400i
$904$	−2.46654	−	10.1051i	−0.0820358	−	0.336090i
$905$	7.95105	+	0.714676i	0.264302	+	0.0237566i
$906$	21.2325	+	30.8101i	0.705404	+	1.02360i
$907$	−19.9221	−	19.9221i	−0.661504	−	0.661504i	0.294230	−	0.955735i	$-0.404937\pi$
$907$	−19.9221	−	19.9221i	−0.661504	−	0.661504i	−0.955735	+	0.294230i	$0.904937\pi$
$908$	−32.9907	+	14.7883i	−1.09483	+	0.490768i
$909$			57.7411i			1.91515i
$910$	−11.0026	−	12.7955i	−0.364734	−	0.424168i
$911$	18.3056			0.606492			0.303246	−	0.952912i	$-0.401930\pi$
$911$	18.3056			0.606492			0.303246	+	0.952912i	$0.401930\pi$
$912$	−36.6117	+	2.10422i	−1.21234	+	0.0696776i
$913$	0.643900	−	0.643900i	0.0213100	−	0.0213100i
$914$	−28.2898	+	19.4957i	−0.935743	+	0.644860i
$915$	−13.1656	−	15.7661i	−0.435241	−	0.521212i
$916$	−17.6663	+	46.3721i	−0.583713	+	1.53218i
$917$	27.4737	−	5.46755i	0.907260	−	0.180554i
$918$	−37.1599	−	6.83866i	−1.22646	−	0.225709i
$919$			48.4316i			1.59761i	0.601590	+	0.798805i	$0.294534\pi$
$919$			48.4316i			1.59761i	−0.601590	+	0.798805i	$0.705466\pi$
$920$	2.13184	+	14.1281i	0.0702847	+	0.465789i
$921$	13.3150			0.438745
$922$	−43.1529	−	7.94157i	−1.42117	−	0.261542i
$923$	15.2385	+	15.2385i	0.501582	+	0.501582i
$924$	63.9235	−	45.4282i	2.10293	−	1.49448i
$925$	6.60490	+	9.52887i	0.217168	+	0.313307i
$926$	1.84518	+	2.67751i	0.0606364	+	0.0879883i
$927$	27.6881	+	27.6881i	0.909397	+	0.909397i
$928$	−7.11624	−	9.15382i	−0.233602	−	0.300489i
$929$	42.8816			1.40690			0.703449	−	0.710746i	$-0.251642\pi$
$929$	42.8816			1.40690			0.703449	+	0.710746i	$0.251642\pi$
$930$	−13.4040	+	7.56389i	−0.439533	+	0.248030i
$931$	9.02722	+	21.7820i	0.295855	+	0.713876i
$932$	10.1094	+	22.5527i	0.331146	+	0.738739i
$933$	−53.0284	+	53.0284i	−1.73607	+	1.73607i
$934$	31.2749	−	21.5528i	1.02335	−	0.705230i
$935$	−65.1403	+	54.3958i	−2.13031	+	1.77893i
$936$	24.4318	−	5.96352i	0.798577	−	0.194924i
$937$	−18.5200	−	18.5200i	−0.605022	−	0.605022i	0.336619	−	0.941641i	$-0.390716\pi$
$937$	−18.5200	−	18.5200i	−0.605022	−	0.605022i	−0.941641	+	0.336619i	$0.890716\pi$
$938$	20.4416	+	19.8593i	0.667443	+	0.648431i
$939$	−70.2976			−2.29408
$940$	−3.46011	−	10.0440i	−0.112856	−	0.327601i
$941$	−9.80731			−0.319709			−0.159855	−	0.987141i	$-0.551103\pi$
$941$	−9.80731			−0.319709			−0.159855	+	0.987141i	$0.551103\pi$
$942$	39.3976	+	7.25047i	1.28364	+	0.236233i
$943$	−1.87165	+	1.87165i	−0.0609493	+	0.0609493i
$944$	22.4891	−	25.2318i	0.731959	−	0.821226i
$945$	−14.2341	+	17.6527i	−0.463036	+	0.574241i
$946$	−31.4259	−	45.6015i	−1.02174	−	1.48263i
$947$	7.28661	+	7.28661i	0.236783	+	0.236783i	0.815517	−	0.578734i	$-0.196453\pi$
$947$	7.28661	+	7.28661i	0.236783	+	0.236783i	−0.578734	+	0.815517i	$0.696453\pi$
$948$	26.3221	−	11.7991i	0.854901	−	0.383216i
$949$	−7.20514			−0.233889
$950$	8.41904	−	22.2803i	0.273150	−	0.722868i
$951$			2.54996i			0.0826882i
$952$	−22.0213	−	47.2842i	−0.713714	−	1.53249i
$953$	−33.6252	−	33.6252i	−1.08923	−	1.08923i	−0.995608	−	0.0936179i	$-0.970157\pi$
$953$	−33.6252	−	33.6252i	−1.08923	−	1.08923i	−0.0936179	−	0.995608i	$-0.529843\pi$
$954$	42.2524	+	61.3117i	1.36797	+	1.98504i
$955$	24.6172	+	2.21270i	0.796594	+	0.0716014i
$956$	12.6773	−	33.2764i	0.410013	−	1.07624i
$957$	−21.4793	+	21.4793i	−0.694326	+	0.694326i
$958$	−51.0323	−	9.39164i	−1.64878	−	0.303430i
$959$	−10.1535	+	15.1990i	−0.327875	+	0.490800i
$960$	18.7911	−	44.9170i	0.606482	−	1.44969i
$961$	27.8025			0.896855
$962$	1.19717	−	6.50519i	0.0385983	−	0.209736i
$963$	−21.4304	+	21.4304i	−0.690584	+	0.690584i
$964$	20.4239	−	53.6103i	0.657809	−	1.72667i
$965$	21.4979	+	25.7443i	0.692043	+	0.828737i
$966$	0.332378	+	23.0048i	0.0106941	+	0.740168i
$967$	−3.63780	+	3.63780i	−0.116984	+	0.116984i	−0.763175	−	0.646192i	$-0.776361\pi$
$967$	−3.63780	+	3.63780i	−0.116984	+	0.116984i	0.646192	+	0.763175i	$0.276361\pi$
$968$	45.0762	+	27.3884i	1.44880	+	0.880297i
$969$	63.9036			2.05288
$970$	−3.46622	−	6.14248i	−0.111294	−	0.197223i
$971$	−38.2561			−1.22770			−0.613848	−	0.789424i	$-0.710379\pi$
$971$	−38.2561			−1.22770			−0.613848	+	0.789424i	$0.710379\pi$
$972$	15.6241	+	34.8551i	0.501143	+	1.11798i
$973$	−7.04311	−	35.3906i	−0.225792	−	1.13457i
$974$	8.25070	−	5.68590i	0.264369	−	0.182188i
$975$	−4.89505	+	27.0097i	−0.156767	+	0.865002i
$976$	10.0777	+	8.98226i	0.322580	+	0.287515i
$977$	−25.2462	+	25.2462i	−0.807696	+	0.807696i	−0.984285	−	0.176589i	$-0.943494\pi$
$977$	−25.2462	+	25.2462i	−0.807696	+	0.807696i	0.176589	+	0.984285i	$0.443494\pi$
$978$	32.7105	+	6.01982i	1.04597	+	0.192493i
$979$		−	3.14795i		−	0.100609i
$980$	−31.2472	−	1.90058i	−0.998155	−	0.0607118i
$981$		−	49.8464i		−	1.59147i
$982$	8.78346	−	47.7276i	0.280291	−	1.52305i
$983$	34.0314	−	34.0314i	1.08543	−	1.08543i	0.0894417	−	0.995992i	$-0.471492\pi$
$983$	34.0314	−	34.0314i	1.08543	−	1.08543i	0.995992	−	0.0894417i	$-0.0285083\pi$
$984$	8.76262	−	2.13886i	0.279342	−	0.0681843i
$985$	14.5266	+	17.3959i	0.462856	+	0.554281i
$986$	11.4648	+	16.6364i	0.365114	+	0.529810i
$987$	−3.33884	−	16.7772i	−0.106276	−	0.534023i
$988$	−12.3993	+	5.55808i	−0.394474	+	0.176826i
$989$	16.2477			0.516647
$990$	−73.1210	−	20.3660i	−2.32394	−	0.647274i
$991$	7.42850			0.235974			0.117987	−	0.993015i	$-0.462356\pi$
$991$	7.42850			0.235974			0.117987	+	0.993015i	$0.462356\pi$
$992$	7.98599	−	6.20836i	0.253555	−	0.197116i
$993$	−0.0190228	+	0.0190228i	−0.000603670	+	0.000603670i
$994$	39.9731	−	0.577539i	1.26787	−	0.0183184i
$995$	11.6972	+	1.05140i	0.370827	+	0.0333316i
$996$	0.324105	−	0.850737i	0.0102697	−	0.0269566i
$997$	10.1490	−	10.1490i	0.321422	−	0.321422i	−0.527890	−	0.849313i	$-0.677017\pi$
$997$	10.1490	−	10.1490i	0.321422	−	0.321422i	0.849313	+	0.527890i	$0.177017\pi$
$998$	38.8581	+	7.15118i	1.23003	+	0.226367i
$999$	−8.88817			−0.281209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.2	yes	72
4.3	odd	2		1120.2.w.c.433.3		72
5.2	odd	4	inner	280.2.s.c.237.22	yes	72
7.6	odd	2	inner	280.2.s.c.13.1	✓	72
8.3	odd	2		1120.2.w.c.433.34		72
8.5	even	2	inner	280.2.s.c.13.21	yes	72
20.7	even	4		1120.2.w.c.657.4		72
28.27	even	2		1120.2.w.c.433.33		72
35.27	even	4	inner	280.2.s.c.237.21	yes	72
40.27	even	4		1120.2.w.c.657.33		72
40.37	odd	4	inner	280.2.s.c.237.1	yes	72
56.13	odd	2	inner	280.2.s.c.13.22	yes	72
56.27	even	2		1120.2.w.c.433.4		72
140.27	odd	4		1120.2.w.c.657.34		72
280.27	odd	4		1120.2.w.c.657.3		72
280.237	even	4	inner	280.2.s.c.237.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.1	✓	72	7.6	odd	2	inner
280.2.s.c.13.2	yes	72	1.1	even	1	trivial
280.2.s.c.13.21	yes	72	8.5	even	2	inner
280.2.s.c.13.22	yes	72	56.13	odd	2	inner
280.2.s.c.237.1	yes	72	40.37	odd	4	inner
280.2.s.c.237.2	yes	72	280.237	even	4	inner
280.2.s.c.237.21	yes	72	35.27	even	4	inner
280.2.s.c.237.22	yes	72	5.2	odd	4	inner
1120.2.w.c.433.3		72	4.3	odd	2
1120.2.w.c.433.4		72	56.27	even	2
1120.2.w.c.433.33		72	28.27	even	2
1120.2.w.c.433.34		72	8.3	odd	2
1120.2.w.c.657.3		72	280.27	odd	4
1120.2.w.c.657.4		72	20.7	even	4
1120.2.w.c.657.33		72	40.27	even	4
1120.2.w.c.657.34		72	140.27	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39086 - 0.255964i) q^{2} +(1.92461 + 1.92461i) q^{3} +(1.86896 + 0.712018i) q^{4} +(-2.22709 - 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-2.59487 + 0.516406i) q^{7} +(-2.41721 - 1.46870i) q^{8} +4.40827i q^{9} +O(q^{10})\)	\(q+(-1.39086 - 0.255964i) q^{2} +(1.92461 + 1.92461i) q^{3} +(1.86896 + 0.712018i) q^{4} +(-2.22709 - 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-2.59487 + 0.516406i) q^{7} +(-2.41721 - 1.46870i) q^{8} +4.40827i q^{9} +(3.04632 + 0.848477i) q^{10} +5.44500i q^{11} +(2.22667 + 4.96739i) q^{12} +(1.42624 + 1.42624i) q^{13} +(3.74127 - 0.0540545i) q^{14} +(-3.90101 - 4.67155i) q^{15} +(2.98606 + 2.66147i) q^{16} +(-4.92871 - 4.92871i) q^{17} +(1.12836 - 6.13127i) q^{18} +3.36836i q^{19} +(-4.01982 - 1.95986i) q^{20} +(-5.98799 - 4.00023i) q^{21} +(1.39372 - 7.57321i) q^{22} +(1.59745 + 1.59745i) q^{23} +(-1.82551 - 7.47888i) q^{24} +(4.91986 + 0.891641i) q^{25} +(-1.61863 - 2.34877i) q^{26} +(-2.71037 + 2.71037i) q^{27} +(-5.21740 - 0.882447i) q^{28} +2.04964 q^{29} +(4.23000 + 7.49598i) q^{30} +1.78815i q^{31} +(-3.47194 - 4.46605i) q^{32} +(-10.4795 + 10.4795i) q^{33} +(5.59356 + 8.11671i) q^{34} +(5.88237 - 0.630640i) q^{35} +(-3.13877 + 8.23890i) q^{36} +(1.63966 + 1.63966i) q^{37} +(0.862178 - 4.68490i) q^{38} +5.48993i q^{39} +(5.08934 + 3.75481i) q^{40} +1.17165i q^{41} +(7.30452 + 7.09646i) q^{42} +(5.08552 - 5.08552i) q^{43} +(-3.87694 + 10.1765i) q^{44} +(0.882450 - 9.81761i) q^{45} +(-1.81293 - 2.63071i) q^{46} +(1.67970 + 1.67970i) q^{47} +(0.624701 + 10.8693i) q^{48} +(6.46665 - 2.68001i) q^{49} +(-6.61459 - 2.49945i) q^{50} -18.9717i q^{51} +(1.65009 + 3.68111i) q^{52} +(-8.44557 + 8.44557i) q^{53} +(4.46349 - 3.07598i) q^{54} +(1.08998 - 12.1265i) q^{55} +(7.03078 + 2.56282i) q^{56} +(-6.48278 + 6.48278i) q^{57} +(-2.85076 - 0.524635i) q^{58} -8.44987i q^{59} +(-3.96463 - 11.5086i) q^{60} +3.37492 q^{61} +(0.457703 - 2.48706i) q^{62} +(-2.27645 - 11.4389i) q^{63} +(3.68582 + 7.10033i) q^{64} +(-2.89087 - 3.46188i) q^{65} +(17.2579 - 11.8931i) q^{66} +(5.38600 + 5.38600i) q^{67} +(-5.70226 - 12.7209i) q^{68} +6.14894i q^{69} +(-8.34296 - 0.628545i) q^{70} +10.6844 q^{71} +(6.47444 - 10.6557i) q^{72} +(-2.52591 + 2.52591i) q^{73} +(-1.86084 - 2.70023i) q^{74} +(7.75275 + 11.1849i) q^{75} +(-2.39833 + 6.29534i) q^{76} +(-2.81183 - 14.1290i) q^{77} +(1.40522 - 7.63571i) q^{78} -5.29897i q^{79} +(-6.11745 - 6.52509i) q^{80} +2.79198 q^{81} +(0.299900 - 1.62960i) q^{82} +(-0.118255 - 0.118255i) q^{83} +(-8.34311 - 11.7398i) q^{84} +(9.99005 + 11.9633i) q^{85} +(-8.37493 + 5.77152i) q^{86} +(3.94477 + 3.94477i) q^{87} +(7.99709 - 13.1617i) q^{88} -0.578136 q^{89} +(-3.74031 + 13.4290i) q^{90} +(-4.43743 - 2.96439i) q^{91} +(1.84816 + 4.12299i) q^{92} +(-3.44150 + 3.44150i) q^{93} +(-1.90628 - 2.76616i) q^{94} +(0.674280 - 7.50163i) q^{95} +(1.91328 - 15.2776i) q^{96} +(-1.57710 - 1.57710i) q^{97} +(-9.68017 + 2.07228i) q^{98} -24.0030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

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