LMFDB - Embedded newform 280.2.s.c.237.22

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			237.22
Character	$\chi$	$=$	280.237
Dual form			280.2.s.c.13.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.255964 - 1.39086i) q^{2} +(1.92461 - 1.92461i) q^{3} +(-1.86896 - 0.712018i) q^{4} +(-2.22709 + 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-0.516406 - 2.59487i) q^{7} +(-1.46870 + 2.41721i) q^{8} -4.40827i q^{9} +O(q^{10})$	\(q+(0.255964 - 1.39086i) 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} +(-0.516406 - 2.59487i) q^{7} +(-1.46870 + 2.41721i) q^{8} -4.40827i q^{9} +(-0.291632 + 3.14880i) q^{10} +5.44500i q^{11} +(-4.96739 + 2.22667i) 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} +(-6.13127 - 1.12836i) q^{18} -3.36836i q^{19} +(4.30488 + 1.21160i) q^{20} +(-5.98799 - 4.00023i) q^{21} +(7.57321 + 1.39372i) 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} +(-0.882447 + 5.21740i) q^{28} -2.04964 q^{29} +(5.49894 + 6.62150i) q^{30} +1.78815i q^{31} +(4.46605 - 3.47194i) q^{32} +(10.4795 + 10.4795i) q^{33} +(-5.59356 - 8.11671i) q^{34} +(1.66952 + 5.67562i) q^{35} +(-3.13877 + 8.23890i) q^{36} +(-1.63966 + 1.63966i) q^{37} +(-4.68490 - 0.862178i) q^{38} -5.48993i q^{39} +(2.78705 - 5.67735i) q^{40} +1.17165i q^{41} +(-7.09646 + 7.30452i) 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} +(10.8693 - 0.624701i) q^{48} +(-6.46665 + 2.68001i) q^{49} +(0.0191611 - 7.07104i) q^{50} -18.9717i q^{51} +(-3.68111 + 1.65009i) 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} +(-0.524635 + 2.85076i) q^{58} +8.44987i q^{59} +(10.6171 - 5.95338i) q^{60} +3.37492 q^{61} +(2.48706 + 0.457703i) q^{62} +(-11.4389 + 2.27645i) 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} +(-12.7209 + 5.70226i) q^{68} -6.14894i q^{69} +(8.32132 - 0.869314i) q^{70} +10.6844 q^{71} +(10.6557 + 6.47444i) 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} +(14.1290 - 2.81183i) q^{77} +(-7.63571 - 1.40522i) q^{78} +5.29897i q^{79} +(-7.18300 - 5.32959i) q^{80} +2.79198 q^{81} +(1.62960 + 0.299900i) 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} +(-13.1617 - 7.99709i) q^{88} +0.578136 q^{89} +(13.8808 + 1.28559i) q^{90} +(-4.43743 - 2.96439i) q^{91} +(-4.12299 + 1.84816i) 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} +(2.07228 + 9.68017i) 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.255964	−	1.39086i	0.180994	−	0.983484i
$2$	0.255964	−	1.39086i	0.180994	−	0.983484i
$3$	1.92461	−	1.92461i	1.11118	−	1.11118i	0.118184	−	0.992992i	$-0.462293\pi$
$3$	1.92461	−	1.92461i	1.11118	−	1.11118i	0.992992	−	0.118184i	$-0.0377072\pi$
$4$	−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
$7$	−0.516406	−	2.59487i	−0.195183	−	0.980767i
$7$	−0.516406	−	2.59487i	−0.195183	−	0.980767i
$8$	−1.46870	+	2.41721i	−0.519265	+	0.854613i
$9$		−	4.40827i		−	1.46942i
$10$	−0.291632	+	3.14880i	−0.0922221	+	0.995738i
$11$			5.44500i			1.64173i	0.571123	+	0.820865i	$0.306508\pi$
$11$			5.44500i			1.64173i	−0.571123	+	0.820865i	$0.693492\pi$
$12$	−4.96739	+	2.22667i	−1.43396	+	0.642785i
$13$	1.42624	−	1.42624i	0.395569	−	0.395569i	−0.481098	−	0.876667i	$-0.659762\pi$
$13$	1.42624	−	1.42624i	0.395569	−	0.395569i	0.876667	+	0.481098i	$0.159762\pi$
$14$	−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	0.219856	−	0.975532i	$-0.429441\pi$
$17$	4.92871	−	4.92871i	1.19539	−	1.19539i	0.975532	−	0.219856i	$-0.0705589\pi$
$18$	−6.13127	−	1.12836i	−1.44515	−	0.265956i
$19$		−	3.36836i		−	0.772754i	−0.922341	−	0.386377i	$-0.873726\pi$
$19$		−	3.36836i		−	0.772754i	0.922341	−	0.386377i	$-0.126274\pi$
$20$	4.30488	+	1.21160i	0.962601	+	0.270922i
$21$	−5.98799	−	4.00023i	−1.30669	−	0.872922i
$22$	7.57321	+	1.39372i	1.61461	+	0.297143i
$23$	1.59745	−	1.59745i	0.333091	−	0.333091i	−0.520668	−	0.853759i	$-0.674317\pi$
$23$	1.59745	−	1.59745i	0.333091	−	0.333091i	0.853759	+	0.520668i	$0.174317\pi$
$24$	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
$28$	−0.882447	+	5.21740i	−0.166767	+	0.985996i
$29$	−2.04964			−0.380609			−0.190305	−	0.981725i	$-0.560948\pi$
$29$	−2.04964			−0.380609			−0.190305	+	0.981725i	$0.560948\pi$
$30$	5.49894	+	6.62150i	1.00397	+	1.20892i
$31$			1.78815i			0.321162i	0.987023	+	0.160581i	$0.0513367\pi$
$31$			1.78815i			0.321162i	−0.987023	+	0.160581i	$0.948663\pi$
$32$	4.46605	−	3.47194i	0.789494	−	0.613758i
$33$	10.4795	+	10.4795i	1.82425	+	1.82425i
$34$	−5.59356	−	8.11671i	−0.959288	−	1.39200i
$35$	1.66952	+	5.67562i	0.282201	+	0.959355i
$36$	−3.13877	+	8.23890i	−0.523128	+	1.37315i
$37$	−1.63966	+	1.63966i	−0.269558	+	0.269558i	−0.828922	−	0.559364i	$-0.811045\pi$
$37$	−1.63966	+	1.63966i	−0.269558	+	0.269558i	0.559364	+	0.828922i	$0.311045\pi$
$38$	−4.68490	−	0.862178i	−0.759992	−	0.139864i
$39$		−	5.48993i		−	0.879093i
$40$	2.78705	−	5.67735i	0.440672	−	0.897668i
$41$			1.17165i			0.182981i	0.995806	+	0.0914904i	$0.0291631\pi$
$41$			1.17165i			0.182981i	−0.995806	+	0.0914904i	$0.970837\pi$
$42$	−7.09646	+	7.30452i	−1.09501	+	1.12711i
$43$	−5.08552	−	5.08552i	−0.775534	−	0.775534i	0.203534	−	0.979068i	$-0.434757\pi$
$43$	−5.08552	−	5.08552i	−0.775534	−	0.775534i	−0.979068	+	0.203534i	$0.934757\pi$
$44$	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	$-0.805426\pi$
$47$	−1.67970	+	1.67970i	−0.245009	+	0.245009i	0.573910	+	0.818919i	$0.305426\pi$
$48$	10.8693	−	0.624701i	1.56885	−	0.0901679i
$49$	−6.46665	+	2.68001i	−0.923807	+	0.382858i
$50$	0.0191611	−	7.07104i	0.00270979	−	0.999996i
$51$		−	18.9717i		−	2.65657i
$52$	−3.68111	+	1.65009i	−0.510478	+	0.228826i
$53$	8.44557	+	8.44557i	1.16009	+	1.16009i	0.984456	+	0.175632i	$0.0561969\pi$
$53$	8.44557	+	8.44557i	1.16009	+	1.16009i	0.175632	+	0.984456i	$0.443803\pi$
$54$	−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
$58$	−0.524635	+	2.85076i	−0.0688880	+	0.374323i
$59$			8.44987i			1.10008i	0.835138	+	0.550040i	$0.185388\pi$
$59$			8.44987i			1.10008i	−0.835138	+	0.550040i	$0.814612\pi$
$60$	10.6171	−	5.95338i	1.37066	−	0.768578i
$61$	3.37492			0.432114			0.216057	−	0.976381i	$-0.430680\pi$
$61$	3.37492			0.432114			0.216057	+	0.976381i	$0.430680\pi$
$62$	2.48706	+	0.457703i	0.315858	+	0.0581283i
$63$	−11.4389	+	2.27645i	−1.44116	+	0.286806i
$64$	−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	$-0.904046\pi$
$67$	−5.38600	+	5.38600i	−0.658005	+	0.658005i	0.296903	+	0.954908i	$0.404046\pi$
$68$	−12.7209	+	5.70226i	−1.54264	+	0.691500i
$69$		−	6.14894i		−	0.740245i
$70$	8.32132	−	0.869314i	0.994587	−	0.103903i
$71$	10.6844			1.26800			0.634001	−	0.773332i	$-0.281411\pi$
$71$	10.6844			1.26800			0.634001	+	0.773332i	$0.281411\pi$
$72$	10.6557	+	6.47444i	1.25579	+	0.763020i
$73$	2.52591	+	2.52591i	0.295636	+	0.295636i	0.839302	−	0.543666i	$-0.182964\pi$
$73$	2.52591	+	2.52591i	0.295636	+	0.295636i	−0.543666	+	0.839302i	$0.682964\pi$
$74$	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
$77$	14.1290	−	2.81183i	1.61015	−	0.320438i
$78$	−7.63571	−	1.40522i	−0.864574	−	0.159110i
$79$			5.29897i			0.596181i	0.954538	+	0.298090i	$0.0963497\pi$
$79$			5.29897i			0.596181i	−0.954538	+	0.298090i	$0.903650\pi$
$80$	−7.18300	−	5.32959i	−0.803084	−	0.595866i
$81$	2.79198			0.310220
$82$	1.62960	+	0.299900i	0.179959	+	0.0331184i
$83$	−0.118255	+	0.118255i	−0.0129802	+	0.0129802i	−0.713567	−	0.700587i	$-0.752922\pi$
$83$	−0.118255	+	0.118255i	−0.0129802	+	0.0129802i	0.700587	+	0.713567i	$0.252922\pi$
$84$	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
$88$	−13.1617	−	7.99709i	−1.40304	−	0.852492i
$89$	0.578136			0.0612823			0.0306411	−	0.999530i	$-0.490245\pi$
$89$	0.578136			0.0612823			0.0306411	+	0.999530i	$0.490245\pi$
$90$	13.8808	+	1.28559i	1.46316	+	0.135513i
$91$	−4.43743	−	2.96439i	−0.465169	−	0.310752i
$92$	−4.12299	+	1.84816i	−0.429851	+	0.192684i
$93$	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	$-0.713881\pi$
$97$	1.57710	−	1.57710i	0.160130	−	0.160130i	0.782624	+	0.622494i	$0.213881\pi$
$98$	2.07228	+	9.68017i	0.209331	+	0.977845i
$99$	24.0030			2.41239
$100$	−9.82990	−	1.83658i	−0.982990	−	0.183658i
$101$	13.0984			1.30334			0.651668	−	0.758504i	$-0.274069\pi$
$101$	13.0984			1.30334			0.651668	+	0.758504i	$0.274069\pi$
$102$	−26.3870	−	4.85608i	−2.61270	−	0.480823i
$103$	−6.28095	−	6.28095i	−0.618880	−	0.618880i	0.326364	−	0.945244i	$-0.394176\pi$
$103$	−6.28095	−	6.28095i	−0.618880	−	0.618880i	−0.945244	+	0.326364i	$0.894176\pi$
$104$	1.35280	+	5.54226i	0.132653	+	0.543463i
$105$	14.1366	+	7.71019i	1.37959	+	0.752437i
$106$	13.9083	−	9.58481i	1.35090	−	0.930959i
$107$	−4.86141	+	4.86141i	−0.469970	+	0.469970i	−0.901905	−	0.431935i	$-0.857831\pi$
$107$	−4.86141	+	4.86141i	−0.469970	+	0.469970i	0.431935	+	0.901905i	$0.357831\pi$
$108$	3.13575	+	6.99542i	0.301738	+	0.673135i
$109$	11.3075			1.08306			0.541530	−	0.840682i	$-0.317845\pi$
$109$	11.3075			1.08306			0.541530	+	0.840682i	$0.317845\pi$
$110$	−17.1452	−	1.58794i	−1.63473	−	0.151404i
$111$			6.31142i			0.599053i
$112$	5.36415	−	9.12282i	0.506864	−	0.862026i
$113$	2.60044	−	2.60044i	0.244629	−	0.244629i	−0.574133	−	0.818762i	$-0.694661\pi$
$113$	2.60044	−	2.60044i	0.244629	−	0.244629i	0.818762	+	0.574133i	$0.194661\pi$
$114$	−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
$118$	11.7526	+	2.16286i	1.08191	+	0.199108i
$119$	−15.3346	−	10.2441i	−1.40572	−	0.939078i
$120$	−5.56270	−	16.2907i	−0.507803	−	1.48713i
$121$	−18.6480			−1.69527
$122$	0.863857	−	4.69403i	0.0782100	−	0.424977i
$123$	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	0.813801	−	0.581143i	$-0.197394\pi$
$127$	2.62192	+	2.62192i	0.232658	+	0.232658i	−0.581143	+	0.813801i	$0.697394\pi$
$128$	−10.8190	+	3.30902i	−0.956272	+	0.292479i
$129$	−19.5753			−1.72351
$130$	4.07502	+	4.90690i	0.357403	+	0.430363i
$131$	−10.5877			−0.925052			−0.462526	−	0.886606i	$-0.653057\pi$
$131$	−10.5877			−0.925052			−0.462526	+	0.886606i	$0.653057\pi$
$132$	−12.1242	−	27.0475i	−1.05528	−	2.35418i
$133$	−8.74043	+	1.73944i	−0.757892	+	0.150829i
$134$	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	0.884295	−	0.466930i	$-0.154640\pi$
$137$	4.88513	+	4.88513i	0.417365	+	0.417365i	−0.466930	+	0.884295i	$0.654640\pi$
$138$	−8.55229	−	1.57391i	−0.728020	−	0.133980i
$139$		−	13.6387i		−	1.15682i	−0.815746	−	0.578410i	$-0.803673\pi$
$139$		−	13.6387i		−	1.15682i	0.815746	−	0.578410i	$-0.196327\pi$
$140$	0.920866	−	11.7963i	0.0778274	−	0.996967i
$141$			6.46553i			0.544496i
$142$	2.73481	−	14.8604i	0.229501	−	1.24706i
$143$	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
$147$	−7.28782	+	17.6038i	−0.601089	+	1.45193i
$148$	4.23193	−	1.89700i	0.347863	−	0.155932i
$149$	−5.97851			−0.489779			−0.244889	−	0.969551i	$-0.578752\pi$
$149$	−5.97851			−0.489779			−0.244889	+	0.969551i	$0.578752\pi$
$150$	−13.5721	−	13.6459i	−1.10816	−	1.11418i
$151$	−9.72084			−0.791071			−0.395535	−	0.918451i	$-0.629441\pi$
$151$	−9.72084			−0.791071			−0.395535	+	0.918451i	$0.629441\pi$
$152$	8.14203	+	4.94712i	0.660406	+	0.401264i
$153$	−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	0.349595	−	0.936901i	$-0.386319\pi$
$157$	−7.35892	−	7.35892i	−0.587306	−	0.587306i	−0.936901	+	0.349595i	$0.886319\pi$
$158$	7.37011	+	1.35635i	0.586335	+	0.107905i
$159$	32.5089			2.57812
$160$	−9.25129	+	8.62634i	−0.731378	+	0.681972i
$161$	−4.97010	−	3.32023i	−0.391698	−	0.261671i
$162$	0.714646	−	3.88324i	0.0561479	−	0.305096i
$163$	6.10986	+	6.10986i	0.478562	+	0.478562i	0.904671	−	0.426110i	$-0.140116\pi$
$163$	6.10986	+	6.10986i	0.478562	+	0.478562i	−0.426110	+	0.904671i	$0.640116\pi$
$164$	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	−0.461149	+	0.887323i	$0.652563\pi$
$167$	−17.4261	+	17.4261i	−1.34847	+	1.34847i	−0.887323	+	0.461149i	$0.847437\pi$
$168$	18.4640	−	8.59909i	1.42453	−	0.663434i
$169$			8.93166i			0.687051i
$170$	14.0822	+	16.9569i	1.08005	+	1.30054i
$171$	−14.8486			−1.13550
$172$	5.88367	+	13.1256i	0.448626	+	1.00082i
$173$	−5.16805	+	5.16805i	−0.392919	+	0.392919i	−0.875727	−	0.482807i	$-0.839617\pi$
$173$	−5.16805	+	5.16805i	−0.392919	+	0.392919i	0.482807	+	0.875727i	$0.339617\pi$
$174$	4.47689	+	6.49633i	0.339392	+	0.492486i
$175$	−4.85433	−	12.3059i	−0.366953	−	0.930240i
$176$	−14.4917	+	16.2591i	−1.09236	+	1.22558i
$177$	16.2627	+	16.2627i	1.22238	+	1.22238i
$178$	0.147982	−	0.804104i	0.0110917	−	0.0602702i
$179$	−13.2310			−0.988932			−0.494466	−	0.869197i	$-0.664636\pi$
$179$	−13.2310			−0.988932			−0.494466	+	0.869197i	$0.664636\pi$
$180$	5.34105	−	18.9771i	0.398098	−	1.41447i
$181$	−3.57015			−0.265367			−0.132684	−	0.991158i	$-0.542359\pi$
$181$	−3.57015			−0.265367			−0.132684	+	0.991158i	$0.542359\pi$
$182$	−5.25886	+	5.41305i	−0.389813	+	0.401242i
$183$	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
$188$	4.33527	−	1.94332i	0.316182	−	0.141731i
$189$	−5.63339	+	8.43270i	−0.409769	+	0.613388i
$190$	10.6063	+	0.982321i	0.769461	+	0.0712650i
$191$	−11.0535			−0.799805			−0.399903	−	0.916558i	$-0.630956\pi$
$191$	−11.0535			−0.799805			−0.399903	+	0.916558i	$0.630956\pi$
$192$	−20.7592	−	6.57161i	−1.49816	−	0.474265i
$193$	−10.6063	+	10.6063i	−0.763455	+	0.763455i	−0.976945	−	0.213490i	$-0.931517\pi$
$193$	−10.6063	+	10.6063i	−0.763455	+	0.763455i	0.213490	+	0.976945i	$0.431517\pi$
$194$	−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	$-0.632414\pi$
$197$	7.16688	−	7.16688i	0.510619	−	0.510619i	0.914716	+	0.404097i	$0.132414\pi$
$198$	6.14391	−	33.3848i	0.436628	−	2.37255i
$199$	5.25225			0.372322			0.186161	−	0.982519i	$-0.440395\pi$
$199$	5.25225			0.372322			0.186161	+	0.982519i	$0.440395\pi$
$200$	−5.07052	+	13.2019i	−0.358540	+	0.933514i
$201$			20.7319i			1.46232i
$202$	3.35271	−	18.2180i	0.235896	−	1.28181i
$203$	1.05845	+	5.31855i	0.0742885	+	0.373289i
$204$	−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
$208$	8.05476	−	0.462938i	0.558497	−	0.0320990i
$209$	18.3407			1.26865
$210$	14.3422	−	17.6884i	0.989707	−	1.22062i
$211$		−	1.94669i		−	0.134016i	−0.997752	−	0.0670078i	$-0.978655\pi$
$211$		−	1.94669i		−	0.134016i	0.997752	−	0.0670078i	$-0.0213452\pi$
$212$	−9.77107	−	21.7979i	−0.671080	−	1.49708i
$213$	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
$217$	4.64002	−	0.923413i	0.314985	−	0.0626853i
$218$	2.89431	−	15.7271i	0.196027	−	1.06517i
$219$	9.72281			0.657007
$220$	−6.59715	+	23.4401i	−0.444780	+	1.58033i
$221$		−	14.0591i		−	0.945717i
$222$	8.77828	+	1.61550i	0.589160	+	0.108425i
$223$	−3.57648	−	3.57648i	−0.239499	−	0.239499i	0.577144	−	0.816643i	$-0.304167\pi$
$223$	−3.57648	−	3.57648i	−0.239499	−	0.239499i	−0.816643	+	0.577144i	$0.804167\pi$
$224$	−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	0.141546	−	0.989932i	$-0.454793\pi$
$227$	−12.7822	−	12.7822i	−0.848385	−	0.848385i	−0.989932	+	0.141546i	$0.954793\pi$
$228$	7.50023	+	16.7320i	0.496715	+	1.10810i
$229$		−	24.8116i		−	1.63960i	−0.572650	−	0.819800i	$-0.694085\pi$
$229$		−	24.8116i		−	1.63960i	0.572650	−	0.819800i	$-0.305915\pi$
$230$	4.56418	+	5.49592i	0.300953	+	0.362390i
$231$	21.7812	−	32.6046i	1.43310	−	2.14523i
$232$	3.01032	−	4.95442i	0.197637	−	0.325274i
$233$	8.73803	−	8.73803i	0.572447	−	0.572447i	−0.360364	−	0.932812i	$-0.617348\pi$
$233$	8.73803	−	8.73803i	0.572447	−	0.572447i	0.932812	+	0.360364i	$0.117348\pi$
$234$	−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
$238$	−18.1732	+	18.7061i	−1.17799	+	1.21253i
$239$			17.8047i			1.15169i	0.817558	+	0.575846i	$0.195327\pi$
$239$			17.8047i			1.15169i	−0.817558	+	0.575846i	$0.804673\pi$
$240$	−24.0819	+	3.56709i	−1.55448	+	0.230255i
$241$		−	28.6845i		−	1.84773i	−0.382719	−	0.923865i	$-0.625012\pi$
$241$		−	28.6845i		−	1.84773i	0.382719	−	0.923865i	$-0.374988\pi$
$242$	−4.77322	+	25.9367i	−0.306834	+	1.66728i
$243$	13.5046	−	13.5046i	0.866320	−	0.866320i
$244$	−6.30760	−	2.40300i	−0.403803	−	0.153837i
$245$	13.8653	−	7.26311i	0.885823	−	0.464023i
$246$	3.71353	−	2.55915i	0.236766	−	0.163165i
$247$	−4.80410	−	4.80410i	−0.305677	−	0.305677i
$248$	−4.32234	−	2.62627i	−0.274469	−	0.166768i
$249$			0.455192i			0.0288466i
$250$	1.37281	+	15.7517i	0.0868243	+	0.996224i
$251$	−7.05563			−0.445348			−0.222674	−	0.974893i	$-0.571478\pi$
$251$	−7.05563			−0.445348			−0.222674	+	0.974893i	$0.571478\pi$
$252$	22.9997	+	3.89006i	1.44885	+	0.245051i
$253$	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	$-0.925902\pi$
$257$	−11.9006	+	11.9006i	−0.742338	+	0.742338i	0.230689	+	0.973027i	$0.425902\pi$
$258$	−5.01057	+	27.2264i	−0.311944	+	1.69504i
$259$	5.10142	+	3.40797i	0.316987	+	0.211761i
$260$	7.86785	−	4.41178i	0.487943	−	0.273607i
$261$			9.03538i			0.559276i
$262$	−2.71007	+	14.7260i	−0.167429	+	0.909774i
$263$	10.7636	−	10.7636i	0.663711	−	0.663711i	−0.292542	−	0.956253i	$-0.594501\pi$
$263$	10.7636	−	10.7636i	0.663711	−	0.663711i	0.956253	+	0.292542i	$0.0945010\pi$
$264$	−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
$268$	13.9012	−	6.23132i	0.849150	−	0.380638i
$269$			11.0154i			0.671623i	0.941929	+	0.335812i	$0.109011\pi$
$269$			11.0154i			0.671623i	−0.941929	+	0.335812i	$0.890989\pi$
$270$	9.32485	−	7.74399i	0.567492	−	0.471284i
$271$			2.75000i			0.167050i	0.996506	+	0.0835252i	$0.0266179\pi$
$271$			2.75000i			0.167050i	−0.996506	+	0.0835252i	$0.973382\pi$
$272$	27.8351	−	1.59979i	1.68775	−	0.0970014i
$273$	−14.2456	+	2.83503i	−0.862185	+	0.171584i
$274$	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	$-0.576303\pi$
$277$	12.2159	−	12.2159i	0.733984	−	0.733984i	0.971406	+	0.237423i	$0.0763026\pi$
$278$	−18.9695	−	3.49102i	−1.13771	−	0.209377i
$279$	7.88266			0.471922
$280$	−16.1712	−	4.30021i	−0.966415	−	0.256987i
$281$	−21.7273			−1.29614			−0.648072	−	0.761579i	$-0.724424\pi$
$281$	−21.7273			−1.29614			−0.648072	+	0.761579i	$0.724424\pi$
$282$	8.99262	+	1.65494i	0.535503	+	0.0985504i
$283$	−11.5844	+	11.5844i	−0.688621	+	0.688621i	−0.961927	−	0.273306i	$-0.911883\pi$
$283$	−11.5844	+	11.5844i	−0.688621	+	0.688621i	0.273306	+	0.961927i	$0.411883\pi$
$284$	−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
$287$	3.04027	−	0.605046i	0.179462	−	0.0357148i
$288$	−15.3052	−	19.6876i	−0.901870	−	1.16010i
$289$		−	31.5844i		−	1.85791i
$290$	0.597742	−	6.45392i	0.0351006	−	0.378987i
$291$		−	6.07060i		−	0.355865i
$292$	−2.92235	−	6.51934i	−0.171017	−	0.381516i
$293$	16.2022	−	16.2022i	0.946542	−	0.946542i	−0.0520995	−	0.998642i	$-0.516591\pi$
$293$	16.2022	−	16.2022i	0.946542	−	0.946542i	0.998642	+	0.0520995i	$0.0165913\pi$
$294$	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
$298$	−1.53028	+	8.31525i	−0.0886469	+	0.481690i
$299$		−	4.55670i		−	0.263521i
$300$	−22.4535	+	15.3840i	−1.29635	+	0.888198i
$301$	−10.5700	+	15.8224i	−0.609247	+	0.911989i
$302$	−2.48818	+	13.5203i	−0.143179	+	0.778006i
$303$	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	0.798895	−	0.601471i	$-0.205418\pi$
$307$	3.45914	+	3.45914i	0.197424	+	0.197424i	−0.601471	+	0.798895i	$0.705418\pi$
$308$	−28.4088	−	4.80492i	−1.61874	−	0.273786i
$309$	−24.1768			−1.37537
$310$	−5.63054	−	0.521483i	−0.319793	−	0.0296182i
$311$			27.5528i			1.56237i	0.624296	+	0.781187i	$0.285386\pi$
$311$			27.5528i			1.56237i	−0.624296	+	0.781187i	$0.714614\pi$
$312$	13.2703	+	8.06308i	0.751284	+	0.456482i
$313$	18.2628	+	18.2628i	1.03227	+	1.03227i	0.999462	+	0.0328132i	$0.0104466\pi$
$313$	18.2628	+	18.2628i	1.03227	+	1.03227i	0.0328132	+	0.999462i	$0.489553\pi$
$314$	−12.1188	+	8.35159i	−0.683905	+	0.471307i
$315$	25.0197	−	7.35971i	1.40970	−	0.414673i
$316$	3.77297	−	9.90359i	0.212246	−	0.557121i
$317$	−0.662461	+	0.662461i	−0.0372075	+	0.0372075i	−0.725466	−	0.688258i	$-0.758376\pi$
$317$	−0.662461	+	0.662461i	−0.0372075	+	0.0372075i	0.688258	+	0.725466i	$0.258376\pi$
$318$	8.32110	−	45.2152i	0.466624	−	2.53554i
$319$		−	11.1603i		−	0.624858i
$320$	9.63001	+	15.0752i	0.538334	+	0.842732i
$321$			18.7126i			1.04444i
$322$	−5.89013	+	6.06283i	−0.328244	+	0.337868i
$323$	−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
$328$	−2.83212	−	1.72080i	−0.156378	−	0.0950155i
$329$	5.22599	+	3.49118i	0.288118	+	0.192475i
$330$	−36.0541	+	29.9418i	−1.98471	+	1.64824i
$331$			0.00988396i			0.000543272i	1.00000		0.000271636i	$8.64644e-5\pi$
$331$			0.00988396i			0.000543272i	−1.00000		0.000271636i	$0.999914\pi$
$332$	0.305215	−	0.136815i	0.0167509	−	0.00750871i
$333$	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	0.936508	+	0.350647i	$0.114038\pi$
$337$	23.6290	+	23.6290i	1.28715	+	1.28715i	0.350647	+	0.936508i	$0.385962\pi$
$338$	12.4227	+	2.28618i	0.675704	+	0.124352i
$339$		−	10.0097i		−	0.543651i
$340$	27.1892	−	15.2459i	1.47454	−	0.826826i
$341$	−9.73649			−0.527261
$342$	−3.80071	+	20.6523i	−0.205519	+	1.11675i
$343$	10.2937	+	15.3961i	0.555806	+	0.831312i
$344$	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	0.230712	−	0.973022i	$-0.425894\pi$
$347$	22.4231	−	22.4231i	1.20373	−	1.20373i	0.973022	−	0.230712i	$-0.0741056\pi$
$348$	10.1814	−	4.56389i	0.545780	−	0.244650i
$349$			25.7980i			1.38093i	0.723363	+	0.690467i	$0.242595\pi$
$349$			25.7980i			1.38093i	−0.723363	+	0.690467i	$0.757405\pi$
$350$	−18.3583	+	3.60181i	−0.981292	+	0.192525i
$351$	−7.73129			−0.412666
$352$	18.9047	+	24.3177i	1.00762	+	1.29614i
$353$	−4.22657	−	4.22657i	−0.224958	−	0.224958i	0.585625	−	0.810582i	$-0.300849\pi$
$353$	−4.22657	−	4.22657i	−0.224958	−	0.224958i	−0.810582	+	0.585625i	$0.800849\pi$
$354$	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
$357$	−49.2291	+	9.79711i	−2.60548	+	0.518518i
$358$	−3.38666	+	18.4024i	−0.178991	+	0.972599i
$359$			7.52162i			0.396976i	0.980103	+	0.198488i	$0.0636031\pi$
$359$			7.52162i			0.396976i	−0.980103	+	0.198488i	$0.936397\pi$
$360$	−25.0273	−	12.2861i	−1.31905	−	0.647533i
$361$	7.65417			0.402851
$362$	−0.913831	+	4.96557i	−0.0480299	+	0.260985i
$363$	−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	$-0.514025\pi$
$367$	18.2949	−	18.2949i	0.954984	−	0.954984i	0.999030	+	0.0440457i	$0.0140247\pi$
$368$	9.02165	−	0.518509i	0.470286	−	0.0270291i
$369$	5.16494			0.268876
$370$	−4.68479	−	5.64114i	−0.243550	−	0.293269i
$371$	17.5538	−	26.2764i	0.911346	−	1.36421i
$372$	−3.98163	−	8.88246i	−0.206438	−	0.460534i
$373$	−12.2045	−	12.2045i	−0.631925	−	0.631925i	0.316626	−	0.948550i	$-0.397450\pi$
$373$	−12.2045	−	12.2045i	−0.631925	−	0.631925i	−0.948550	+	0.316626i	$0.897450\pi$
$374$	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
$378$	10.2867	+	9.99371i	0.529092	+	0.514021i
$379$	−15.3415			−0.788037			−0.394019	−	0.919102i	$-0.628915\pi$
$379$	−15.3415			−0.788037			−0.394019	+	0.919102i	$0.628915\pi$
$380$	4.08109	−	14.5004i	0.209356	−	0.743854i
$381$	10.0924			0.517048
$382$	−2.82930	+	15.3739i	−0.144760	+	0.786596i
$383$	−24.6609	−	24.6609i	−1.26011	−	1.26011i	−0.951037	−	0.309077i	$-0.899980\pi$
$383$	−24.6609	−	24.6609i	−1.26011	−	1.26011i	−0.309077	−	0.951037i	$-0.600020\pi$
$384$	−14.4538	+	27.1909i	−0.737590	+	1.38758i
$385$	−30.9038	+	9.09056i	−1.57500	+	0.463298i
$386$	12.0370	+	17.4666i	0.612666	+	0.889027i
$387$	−22.4183	+	22.4183i	−1.13959	+	1.13959i
$388$	−4.07046	+	1.82462i	−0.206646	+	0.0926309i
$389$	−16.1736			−0.820034			−0.410017	−	0.912078i	$-0.634477\pi$
$389$	−16.1736			−0.820034			−0.410017	+	0.912078i	$0.634477\pi$
$390$	17.2867	+	1.60104i	0.875346	+	0.0810718i
$391$		−	15.7467i		−	0.796347i
$392$	3.01945	−	19.5674i	0.152505	−	0.988303i
$393$	−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	0.516733	−	0.856147i	$-0.327148\pi$
$397$	−6.76277	−	6.76277i	−0.339414	−	0.339414i	−0.856147	+	0.516733i	$0.827148\pi$
$398$	1.34439	−	7.30513i	0.0673880	−	0.366173i
$399$	−13.4742	+	20.1697i	−0.674554	+	1.00975i
$400$	17.0641	+	10.4316i	0.853203	+	0.521579i
$401$	6.46277			0.322736			0.161368	−	0.986894i	$-0.448409\pi$
$401$	6.46277			0.322736			0.161368	+	0.986894i	$0.448409\pi$
$402$	28.8352	+	5.30663i	1.43817	+	0.264671i
$403$	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
$408$	45.8587	+	27.8638i	2.27034	+	1.37947i
$409$	−0.933714			−0.0461692			−0.0230846	−	0.999734i	$-0.507349\pi$
$409$	−0.933714			−0.0461692			−0.0230846	+	0.999734i	$0.507349\pi$
$410$	−3.68929	−	0.341690i	−0.182201	−	0.0168749i
$411$	18.8040			0.927532
$412$	7.26672	+	16.2110i	0.358006	+	0.798660i
$413$	21.9263	−	4.36356i	1.07892	−	0.214717i
$414$	−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
$418$	4.69456	−	25.5093i	0.229618	−	1.24770i
$419$			7.66167i			0.374297i	0.982332	+	0.187149i	$0.0599246\pi$
$419$			7.66167i			0.374297i	−0.982332	+	0.187149i	$0.940075\pi$
$420$	−20.9309	−	24.4756i	−1.02133	−	1.19429i
$421$		−	9.84492i		−	0.479812i	−0.970796	−	0.239906i	$-0.922883\pi$
$421$		−	9.84492i		−	0.479812i	0.970796	−	0.239906i	$-0.0771167\pi$
$422$	−2.70756	−	0.498282i	−0.131802	−	0.0242560i
$423$	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
$427$	−1.74283	−	8.75746i	−0.0843413	−	0.423803i
$428$	12.5472	−	5.62439i	0.606492	−	0.271865i
$429$	29.8927			1.44323
$430$	17.4964	−	14.5302i	0.843750	−	0.700708i
$431$	26.6614			1.28423			0.642117	−	0.766606i	$-0.278056\pi$
$431$	26.6614			1.28423			0.642117	+	0.766606i	$0.278056\pi$
$432$	−0.879747	−	15.3069i	−0.0423268	−	0.736454i
$433$	−4.20698	−	4.20698i	−0.202175	−	0.202175i	0.598756	−	0.800931i	$-0.295662\pi$
$433$	−4.20698	−	4.20698i	−0.202175	−	0.202175i	−0.800931	+	0.598756i	$0.795662\pi$
$434$	−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
$438$	2.48869	−	13.5230i	0.118914	−	0.646156i
$439$	−23.8642			−1.13897			−0.569487	−	0.822000i	$-0.692858\pi$
$439$	−23.8642			−1.13897			−0.569487	+	0.822000i	$0.692858\pi$
$440$	30.9132	+	15.1755i	1.47373	+	0.723464i
$441$	11.8142	+	28.5067i	0.562580	+	1.35746i
$442$	−19.5542	−	3.59862i	−0.930097	−	0.171169i
$443$	−14.2936	−	14.2936i	−0.679110	−	0.679110i	0.280689	−	0.959799i	$-0.409437\pi$
$443$	−14.2936	−	14.2936i	−0.679110	−	0.679110i	−0.959799	+	0.280689i	$0.909437\pi$
$444$	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
$448$	−16.5210	+	13.2309i	−0.780545	+	0.625100i
$449$		−	3.65940i		−	0.172698i	−0.996265	−	0.0863489i	$-0.972480\pi$
$449$		−	3.65940i		−	0.172698i	0.996265	−	0.0863489i	$-0.0275200\pi$
$450$	−31.1710	−	0.0844673i	−1.46942	−	0.00398183i
$451$	−6.37963			−0.300405
$452$	−6.71168	+	3.00857i	−0.315691	+	0.141511i
$453$	−18.7088	+	18.7088i	−0.879018	+	0.879018i
$454$	−21.0500	+	14.5064i	−0.987926	+	0.680821i
$455$	10.4760	+	5.71367i	0.491121	+	0.267861i
$456$	25.1915	−	6.14898i	1.17970	−	0.287952i
$457$	17.1784	+	17.1784i	0.803573	+	0.803573i	0.983652	−	0.180079i	$-0.0576354\pi$
$457$	17.1784	+	17.1784i	0.803573	+	0.803573i	−0.180079	+	0.983652i	$0.557635\pi$
$458$	−34.5094	−	6.35089i	−1.61252	−	0.296757i
$459$	−26.7173			−1.24706
$460$	8.81230	−	4.94137i	0.410875	−	0.230392i
$461$	31.0261			1.44503			0.722516	−	0.691355i	$-0.242986\pi$
$461$	31.0261			1.44503			0.722516	+	0.691355i	$0.242986\pi$
$462$	−39.7731	−	38.6402i	−1.85041	−	1.79770i
$463$	−1.62586	+	1.62586i	−0.0755603	+	0.0755603i	−0.743877	−	0.668317i	$-0.767015\pi$
$463$	−1.62586	+	1.62586i	−0.0755603	+	0.0755603i	0.668317	+	0.743877i	$0.267015\pi$
$464$	−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	0.114609	−	0.993411i	$-0.463439\pi$
$467$	−18.9911	−	18.9911i	−0.878802	−	0.878802i	−0.993411	+	0.114609i	$0.963439\pi$
$468$	7.27403	+	16.2273i	0.336242	+	0.750108i
$469$	16.7573	+	11.1946i	0.773781	+	0.516918i
$470$	−4.79918	−	5.77888i	−0.221370	−	0.266560i
$471$	−28.3261			−1.30520
$472$	−20.4251	−	12.4104i	−0.940143	−	0.571233i
$473$	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
$478$	24.7638	+	4.55737i	1.13267	+	0.208449i
$479$	−36.6913			−1.67647			−0.838234	−	0.545311i	$-0.816411\pi$
$479$	−36.6913			−1.67647			−0.838234	+	0.545311i	$0.816411\pi$
$480$	−1.20278	+	34.4075i	−0.0548991	+	1.57048i
$481$			4.67711i			0.213258i
$482$	−39.8960	−	7.34219i	−1.81721	−	0.334428i
$483$	−15.9557	+	3.17535i	−0.726008	+	0.144483i
$484$	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	0.584422	−	0.811450i	$-0.301321\pi$
$487$	−5.01008	−	5.01008i	−0.227028	−	0.227028i	−0.811450	+	0.584422i	$0.801321\pi$
$488$	−4.95675	+	8.15789i	−0.224382	+	0.369290i
$489$	23.5182			1.06353
$490$	−6.55293	−	21.1438i	−0.296031	−	0.955178i
$491$			34.3152i			1.54862i	0.632804	+	0.774312i	$0.281904\pi$
$491$			34.3152i			1.54862i	−0.632804	+	0.774312i	$0.718096\pi$
$492$	−2.60888	−	5.82004i	−0.117617	−	0.262388i
$493$	−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
$497$	−5.51747	−	27.7245i	−0.247492	−	1.24361i
$498$	0.633106	+	0.116513i	0.0283702	+	0.00522106i
$499$	27.9382			1.25069			0.625343	−	0.780350i	$-0.284959\pi$
$499$	27.9382			1.25069			0.625343	+	0.780350i	$0.284959\pi$
$500$	22.2597	+	2.12248i	0.995485	+	0.0949200i
$501$			67.0770i			2.99678i
$502$	−1.80599	+	9.81337i	−0.0806052	+	0.437992i
$503$	21.4722	+	21.4722i	0.957398	+	0.957398i	0.999129	−	0.0417307i	$-0.0132872\pi$
$503$	21.4722	+	21.4722i	0.957398	+	0.957398i	−0.0417307	+	0.999129i	$0.513287\pi$
$504$	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
$508$	−3.03342	−	6.76714i	−0.134586	−	0.300243i
$509$			31.4811i			1.39538i	0.716401	+	0.697689i	$0.245788\pi$
$509$			31.4811i			1.39538i	−0.716401	+	0.697689i	$0.754212\pi$
$510$	59.7382	+	5.53276i	2.64525	+	0.244995i
$511$	5.25001	−	7.85880i	0.232247	−	0.347653i
$512$	22.5764	+	1.51887i	0.997745	+	0.0671250i
$513$	−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
$518$	6.04577	−	6.22303i	0.265636	−	0.273424i
$519$			19.8930i			0.873205i
$520$	−4.12227	−	12.0723i	−0.180773	−	0.529406i
$521$		−	14.3173i		−	0.627251i	−0.949547	−	0.313626i	$-0.898456\pi$
$521$		−	14.3173i		−	0.627251i	0.949547	−	0.313626i	$-0.101544\pi$
$522$	12.5669	+	2.31273i	0.550039	+	0.101226i
$523$	22.4819	−	22.4819i	0.983065	−	0.983065i	−0.0167944	−	0.999859i	$-0.505346\pi$
$523$	22.4819	−	22.4819i	0.983065	−	0.983065i	0.999859	+	0.0167944i	$0.00534608\pi$
$524$	19.7881	+	7.53864i	0.864445	+	0.329327i
$525$	−33.0268	−	14.3414i	−1.44141	−	0.625911i
$526$	−12.2155	−	17.7257i	−0.532622	−	0.772877i
$527$	8.81329	+	8.81329i	0.383913	+	0.383913i
$528$	3.40150	+	59.1834i	0.148031	+	2.57563i
$529$			17.8963i			0.778101i
$530$	−29.0564	+	24.1304i	−1.26213	+	1.04816i
$531$	37.2493			1.61648
$532$	17.5741	+	2.97240i	0.761933	+	0.128870i
$533$	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
$538$	15.3209	+	2.81956i	0.660531	+	0.121560i
$539$	−14.5926	−	35.2109i	−0.628549	−	1.51664i
$540$	−8.38395	−	14.9517i	−0.360788	−	0.643419i
$541$		−	24.0200i		−	1.03270i	−0.856378	−	0.516350i	$-0.827290\pi$
$541$		−	24.0200i		−	1.03270i	0.856378	−	0.516350i	$-0.172710\pi$
$542$	3.82485	+	0.703900i	0.164291	+	0.0302351i
$543$	−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	−0.233760	+	0.972294i	$0.575103\pi$
$547$	−28.2072	+	28.2072i	−1.20605	+	1.20605i	−0.972294	+	0.233760i	$0.924897\pi$
$548$	−5.65184	−	12.6084i	−0.241435	−	0.538606i
$549$		−	14.8775i		−	0.634958i
$550$	38.5018	+	0.104332i	1.64172	+	0.00444874i
$551$			6.90394i			0.294118i
$552$	14.8633	+	9.03097i	0.632624	+	0.384383i
$553$	13.7501	−	2.73642i	0.584715	−	0.116364i
$554$	−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	$-0.753801\pi$
$557$	−0.398538	+	0.398538i	−0.0168866	+	0.0168866i	0.698613	+	0.715500i	$0.253801\pi$
$558$	2.01768	−	10.9636i	0.0854150	−	0.464128i
$559$	−14.5064			−0.613554
$560$	−10.1202	+	21.3911i	−0.427658	+	0.903941i
$561$	103.301			4.36137
$562$	−5.56141	+	30.2196i	−0.234594	+	1.27474i
$563$	19.3688	−	19.3688i	0.816299	−	0.816299i	−0.169271	−	0.985570i	$-0.554141\pi$
$563$	19.3688	−	19.3688i	0.816299	−	0.816299i	0.985570	+	0.169271i	$0.0541413\pi$
$564$	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
$567$	−1.44179	−	7.24481i	−0.0605496	−	0.304253i
$568$	−15.6922	+	25.8264i	−0.658429	+	1.08365i
$569$			4.05795i			0.170118i	0.996376	+	0.0850591i	$0.0271079\pi$
$569$			4.05795i			0.170118i	−0.996376	+	0.0850591i	$0.972892\pi$
$570$	22.3036	−	18.5224i	0.934194	−	0.775818i
$571$			3.38941i			0.141842i	0.997482	+	0.0709212i	$0.0225939\pi$
$571$			3.38941i			0.141842i	−0.997482	+	0.0709212i	$0.977406\pi$
$572$	−8.98473	−	20.0436i	−0.375670	−	0.838067i
$573$	−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	$-0.745183\pi$
$577$	0.514077	−	0.514077i	0.0214013	−	0.0214013i	0.717726	+	0.696325i	$0.245183\pi$
$578$	−43.9294	−	8.08448i	−1.82722	−	0.336270i
$579$			40.8259i			1.69667i
$580$	−8.82348	−	2.48334i	−0.366375	−	0.103115i
$581$	0.367925	+	0.245789i	0.0152641	+	0.0101970i
$582$	−8.44334	−	1.55385i	−0.349988	−	0.0644094i
$583$	−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	0.996241	+	0.0866239i	$0.0276079\pi$
$587$	26.2357	+	26.2357i	1.08287	+	1.08287i	0.0866239	+	0.996241i	$0.472392\pi$
$588$	26.1549	−	27.7118i	1.07861	−	1.14281i
$589$	6.02314			0.248179
$590$	−26.6070	−	2.46425i	−1.09539	−	0.101452i
$591$		−	27.5869i		−	1.13477i
$592$	−9.26003	+	0.532210i	−0.380585	+	0.0218737i
$593$	21.0385	+	21.0385i	0.863946	+	0.863946i	0.991794	−	0.127848i	$-0.0408068\pi$
$593$	21.0385	+	21.0385i	0.863946	+	0.863946i	−0.127848	+	0.991794i	$0.540807\pi$
$594$	−16.7487	−	24.3037i	−0.687208	−	0.997194i
$595$	36.2021	+	19.7449i	1.48414	+	0.809463i
$596$	11.1736	+	4.25681i	0.457690	+	0.174366i
$597$	10.1085	−	10.1085i	0.413715	−	0.413715i
$598$	−6.33772	−	1.16635i	−0.259169	−	0.0476956i
$599$			41.7664i			1.70653i	0.521478	+	0.853265i	$0.325381\pi$
$599$			41.7664i			1.70653i	−0.521478	+	0.853265i	$0.674619\pi$
$600$	15.6497	+	35.1673i	0.638897	+	1.43570i
$601$			14.0893i			0.574717i	0.957823	+	0.287358i	$0.0927770\pi$
$601$			14.0893i			0.574717i	−0.957823	+	0.287358i	$0.907223\pi$
$602$	19.3012	+	18.7514i	0.786657	+	0.764249i
$603$	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	$-0.681686\pi$
$607$	7.42042	−	7.42042i	0.301186	−	0.301186i	0.841478	+	0.540292i	$0.181686\pi$
$608$	−11.6947	−	15.0433i	−0.474284	−	0.610085i
$609$	12.2733	+	8.19905i	0.497337	+	0.332242i
$610$	−0.984234	+	10.6269i	−0.0398505	+	0.430272i
$611$			4.79131i			0.193836i
$612$	25.1371	+	56.0773i	1.01611	+	2.26679i
$613$	−2.64550	−	2.64550i	−0.106851	−	0.106851i	0.651660	−	0.758511i	$-0.274073\pi$
$613$	−2.64550	−	2.64550i	−0.106851	−	0.106851i	−0.758511	+	0.651660i	$0.774073\pi$
$614$	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	0.776226	−	0.630455i	$-0.217132\pi$
$617$	3.62086	+	3.62086i	0.145771	+	0.145771i	−0.630455	+	0.776226i	$0.717132\pi$
$618$	−6.18838	+	33.6264i	−0.248933	+	1.35265i
$619$			10.2222i			0.410865i	0.978671	+	0.205433i	$0.0658602\pi$
$619$			10.2222i			0.410865i	−0.978671	+	0.205433i	$0.934140\pi$
$620$	−2.16652	+	7.69779i	−0.0870096	+	0.309151i
$621$	−8.65935			−0.347488
$622$	38.3220	+	7.05252i	1.53657	+	0.282780i
$623$	−0.298553	−	1.50018i	−0.0119613	−	0.0601036i
$624$	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
$628$	8.51388	+	18.9933i	0.339741	+	0.757913i
$629$			16.1628i			0.644454i
$630$	−3.83217	−	36.6826i	−0.152677	−	1.46147i
$631$	−10.6864			−0.425419			−0.212710	−	0.977115i	$-0.568229\pi$
$631$	−10.6864			−0.425419			−0.212710	+	0.977115i	$0.568229\pi$
$632$	−12.8087	−	7.78262i	−0.509504	−	0.309576i
$633$	−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
$637$	−5.40068	+	13.0454i	−0.213983	+	0.516876i
$638$	−15.5224	−	2.85664i	−0.614538	−	0.113095i
$639$		−	47.0996i		−	1.86323i
$640$	23.4324	−	9.53524i	0.926248	−	0.376913i
$641$	−38.3191			−1.51351			−0.756757	−	0.653697i	$-0.773217\pi$
$641$	−38.3191			−1.51351			−0.756757	+	0.653697i	$0.773217\pi$
$642$	26.0266	+	4.78976i	1.02719	+	0.189037i
$643$	9.81076	−	9.81076i	0.386899	−	0.386899i	−0.486681	−	0.873580i	$-0.661793\pi$
$643$	9.81076	−	9.81076i	0.386899	−	0.386899i	0.873580	+	0.486681i	$0.161793\pi$
$644$	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	$-0.984489\pi$
$647$	−24.1670	+	24.1670i	−0.950105	+	0.950105i	0.0487085	+	0.998813i	$0.484489\pi$
$648$	−4.10059	+	6.74880i	−0.161086	+	0.265118i
$649$	−46.0096			−1.80603
$650$	−10.0577	−	10.1124i	−0.394495	−	0.396639i
$651$	7.15302	−	10.7074i	0.280349	−	0.419658i
$652$	−7.06879	−	15.7695i	−0.276835	−	0.617580i
$653$	−21.8449	−	21.8449i	−0.854856	−	0.854856i	0.135870	−	0.990727i	$-0.456617\pi$
$653$	−21.8449	−	21.8449i	−0.854856	−	0.854856i	−0.990727	+	0.135870i	$0.956617\pi$
$654$	−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
$658$	6.19340	−	6.37499i	0.241444	−	0.248523i
$659$	−24.3323			−0.947854			−0.473927	−	0.880564i	$-0.657164\pi$
$659$	−24.3323			−0.947854			−0.473927	+	0.880564i	$0.657164\pi$
$660$	32.4161	+	57.8101i	1.26180	+	2.25025i
$661$	−5.32909			−0.207278			−0.103639	−	0.994615i	$-0.533049\pi$
$661$	−5.32909			−0.207278			−0.103639	+	0.994615i	$0.533049\pi$
$662$	0.0137472	+	0.00252994i	0.000534299	+	9.83288e-5i
$663$	−27.0583	−	27.0583i	−1.05086	−	1.05086i
$664$	−0.112166	−	0.459530i	−0.00435289	−	0.0178332i
$665$	19.1175	−	5.62355i	0.741346	−	0.218072i
$666$	11.9033	−	8.20307i	0.461244	−	0.317863i
$667$	−3.27420	+	3.27420i	−0.126778	+	0.126778i
$668$	44.9765	−	20.1611i	1.74019	−	0.780055i
$669$	−13.7667			−0.532250
$670$	−15.3887	−	18.5302i	−0.594518	−	0.715884i
$671$			18.3764i			0.709414i
$672$	−40.6312	+	2.92471i	−1.56738	+	0.112823i
$673$	10.1733	−	10.1733i	0.392150	−	0.392150i	−0.483303	−	0.875453i	$-0.660563\pi$
$673$	10.1733	−	10.1733i	0.392150	−	0.392150i	0.875453	+	0.483303i	$0.160563\pi$
$674$	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	0.457896	−	0.889006i	$-0.348603\pi$
$677$	−11.2171	−	11.2171i	−0.431110	−	0.431110i	−0.889006	+	0.457896i	$0.848603\pi$
$678$	−13.9220	−	2.56211i	−0.534672	−	0.0983974i
$679$	−4.90678	−	3.27793i	−0.188305	−	0.125795i
$680$	−14.2455	−	41.7186i	−0.546288	−	1.59984i
$681$	−49.2016			−1.88541
$682$	−2.49219	+	13.5421i	−0.0954309	+	0.518553i
$683$	24.5690	+	24.5690i	0.940108	+	0.940108i	0.998305	−	0.0581972i	$-0.0185352\pi$
$683$	24.5690	+	24.5690i	0.940108	+	0.940108i	−0.0581972	+	0.998305i	$0.518535\pi$
$684$	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
$688$	−1.65068	−	28.7206i	−0.0629318	−	1.09496i
$689$	24.0909			0.917789
$690$	19.3618	+	1.79323i	0.737091	+	0.0682670i
$691$	26.7358			1.01708			0.508540	−	0.861038i	$-0.330185\pi$
$691$	26.7358			1.01708			0.508540	+	0.861038i	$0.330185\pi$
$692$	13.3386	−	5.97915i	0.507059	−	0.227293i
$693$	−12.3953	−	62.2846i	−0.470858	−	2.36600i
$694$	−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
$698$	35.8813	+	6.60336i	1.35813	+	0.249941i
$699$		−	33.6346i		−	1.27218i
$700$	0.310535	+	26.4557i	0.0117371	+	0.999931i
$701$			6.71634i			0.253673i	0.991924	+	0.126836i	$0.0404823\pi$
$701$			6.71634i			0.253673i	−0.991924	+	0.126836i	$0.959518\pi$
$702$	−1.97893	+	10.7531i	−0.0746900	+	0.405850i
$703$	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
$707$	−6.76407	−	33.9885i	−0.254389	−	1.27827i
$708$	−18.8151	−	41.9738i	−0.707115	−	1.57747i
$709$	−22.7398			−0.854009			−0.427005	−	0.904249i	$-0.640431\pi$
$709$	−22.7398			−0.854009			−0.427005	+	0.904249i	$0.640431\pi$
$710$	−3.11590	+	33.6430i	−0.116938	+	1.26260i
$711$	23.3593			0.876042
$712$	−0.849110	+	1.39748i	−0.0318217	+	0.0523727i
$713$	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
$718$	10.4615	+	1.92526i	0.390420	+	0.0718502i
$719$	32.0992			1.19710			0.598549	−	0.801086i	$-0.295744\pi$
$719$	32.0992			1.19710			0.598549	+	0.801086i	$0.295744\pi$
$720$	−23.4943	+	31.6646i	−0.875579	+	1.18007i
$721$	−13.0547	+	19.5417i	−0.486182	+	0.727772i
$722$	1.95919	−	10.6458i	0.0729135	−	0.396198i
$723$	−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	$-0.850386\pi$
$727$	−11.8273	+	11.8273i	−0.438649	+	0.438649i	0.452908	+	0.891557i	$0.350386\pi$
$728$	13.6828	−	6.37240i	0.507119	−	0.236177i
$729$		−	43.6063i		−	1.61505i
$730$	−8.69024	+	7.21696i	−0.321640	+	0.267112i
$731$	−50.1301			−1.85413
$732$	−16.7645	+	7.51484i	−0.619635	+	0.277757i
$733$	−20.8928	+	20.8928i	−0.771692	+	0.771692i	−0.978402	−	0.206710i	$-0.933724\pi$
$733$	−20.8928	+	20.8928i	−0.771692	+	0.771692i	0.206710	+	0.978402i	$0.433724\pi$
$734$	−20.7627	−	30.1284i	−0.766365	−	1.11206i
$735$	12.7067	−	40.6641i	0.468694	−	1.49992i
$736$	1.58804	−	12.6805i	0.0585361	−	0.467411i
$737$	−29.3268	−	29.3268i	−1.08027	−	1.08027i
$738$	1.32204	−	7.18370i	0.0486649	−	0.264435i
$739$	−3.01684			−0.110976			−0.0554881	−	0.998459i	$-0.517671\pi$
$739$	−3.01684			−0.110976			−0.0554881	+	0.998459i	$0.517671\pi$
$740$	−9.04515	+	5.07194i	−0.332506	+	0.186448i
$741$	−18.4921			−0.679323
$742$	−32.0536	−	31.1406i	−1.17673	−	1.14321i
$743$	−4.12087	+	4.12087i	−0.151180	+	0.151180i	−0.778645	−	0.627465i	$-0.784093\pi$
$743$	−4.12087	+	4.12087i	−0.151180	+	0.151180i	0.627465	+	0.778645i	$0.284093\pi$
$744$	−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
$748$	−31.0488	−	69.2654i	−1.13526	−	2.53260i
$749$	15.1252	+	10.1042i	0.552661	+	0.369201i
$750$	32.9580	+	27.6737i	1.20346	+	1.01050i
$751$	14.2125			0.518620			0.259310	−	0.965794i	$-0.416505\pi$
$751$	14.2125			0.518620			0.259310	+	0.965794i	$0.416505\pi$
$752$	−9.48614	+	0.545205i	−0.345924	+	0.0198816i
$753$	−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	$-0.804148\pi$
$757$	−6.58719	+	6.58719i	−0.239415	+	0.239415i	0.577193	+	0.816608i	$0.304148\pi$
$758$	−3.92686	+	21.3378i	−0.142630	+	0.775022i
$759$	33.4810			1.21528
$760$	−19.1234	−	9.38779i	−0.693677	−	0.340531i
$761$		−	44.9438i		−	1.62921i	−0.580016	−	0.814605i	$-0.696954\pi$
$761$		−	44.9438i		−	1.62921i	0.580016	−	0.814605i	$-0.303046\pi$
$762$	2.58328	−	14.0370i	0.0935825	−	0.508508i
$763$	−5.83924	−	29.3414i	−0.211395	−	1.06223i
$764$	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
$768$	34.1191	+	27.0630i	1.23117	+	0.976552i
$769$	28.3200			1.02125			0.510623	−	0.859805i	$-0.329415\pi$
$769$	28.3200			1.02125			0.510623	+	0.859805i	$0.329415\pi$
$770$	4.73341	+	45.3096i	0.170580	+	1.63284i
$771$			45.8080i			1.64974i
$772$	27.3746	−	12.2709i	0.985233	−	0.441639i
$773$	−32.5722	+	32.5722i	−1.17154	+	1.17154i	−0.189697	+	0.981843i	$0.560751\pi$
$773$	−32.5722	+	32.5722i	−1.17154	+	1.17154i	−0.981843	+	0.189697i	$0.939249\pi$
$774$	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
$777$	16.3773	−	3.25925i	0.587532	−	0.116925i
$778$	−4.13986	+	22.4952i	−0.148421	+	0.806491i
$779$	3.94653			0.141399
$780$	6.65159	−	23.6335i	0.238165	−	0.846216i
$781$			58.1764i			2.08172i
$782$	−21.9015	−	4.03060i	−0.783194	−	0.144134i
$783$	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	0.655888	−	0.754859i	$-0.272295\pi$
$787$	−2.77648	−	2.77648i	−0.0989709	−	0.0989709i	−0.754859	+	0.655888i	$0.772295\pi$
$788$	−18.4976	+	8.29170i	−0.658949	+	0.295379i
$789$		−	41.4315i		−	1.47500i
$790$	−16.6854	−	1.54535i	−0.593640	−	0.0549811i
$791$	−8.09066	−	5.40490i	−0.287671	−	0.192176i
$792$	−35.2533	+	58.0204i	−1.25267	+	2.06166i
$793$	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	0.873367	−	0.487063i	$-0.161932\pi$
$797$	10.9058	+	10.9058i	0.386303	+	0.386303i	−0.487063	+	0.873367i	$0.661932\pi$
$798$	24.6042	+	23.9034i	0.870981	+	0.846171i
$799$			16.5575i			0.585762i
$800$	18.8766	−	21.0636i	0.667389	−	0.744709i
$801$		−	2.54858i		−	0.0900496i
$802$	1.65424	−	8.98879i	0.0584131	−	0.317405i
$803$	−13.7536	+	13.7536i	−0.485354	+	0.485354i
$804$	14.7615	−	38.7473i	0.520599	−	1.36651i
$805$	11.7335	+	6.39954i	0.413551	+	0.225554i
$806$	4.19996	−	2.89436i	0.147937	−	0.101950i
$807$	21.2005	+	21.2005i	0.746292	+	0.746292i
$808$	−19.2376	+	31.6615i	−0.676777	+	1.11385i
$809$		−	26.9265i		−	0.946686i	−0.880878	−	0.473343i	$-0.843047\pi$
$809$		−	26.9265i		−	0.946686i	0.880878	−	0.473343i	$-0.156953\pi$
$810$	−0.814230	+	8.79139i	−0.0286091	+	0.308898i
$811$	−34.6646			−1.21724			−0.608620	−	0.793462i	$-0.708276\pi$
$811$	−34.6646			−1.21724			−0.608620	+	0.793462i	$0.708276\pi$
$812$	1.80870	−	10.6938i	0.0634730	−	0.375279i
$813$	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
$818$	−0.238997	+	1.29866i	−0.00835633	+	0.0454066i
$819$	−13.0678	+	19.5614i	−0.456627	+	0.683530i
$820$	−1.41957	+	5.04381i	−0.0495734	+	0.176138i
$821$		−	28.3630i		−	0.989877i	−0.868928	−	0.494939i	$-0.835191\pi$
$821$		−	28.3630i		−	0.989877i	0.868928	−	0.494939i	$-0.164809\pi$
$822$	4.81314	−	26.1536i	0.167878	−	0.912213i
$823$	2.88581	−	2.88581i	0.100593	−	0.100593i	−0.655019	−	0.755612i	$-0.727339\pi$
$823$	2.88581	−	2.88581i	0.100593	−	0.100593i	0.755612	+	0.655019i	$0.227339\pi$
$824$	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	$-0.712288\pi$
$827$	4.80713	−	4.80713i	0.167160	−	0.167160i	0.785730	+	0.618570i	$0.212288\pi$
$828$	8.14720	+	18.1752i	0.283135	+	0.631633i
$829$		−	24.0249i		−	0.834419i	−0.908810	−	0.417209i	$-0.863008\pi$
$829$		−	24.0249i		−	0.834419i	0.908810	−	0.417209i	$-0.136992\pi$
$830$	−0.337876	−	0.406850i	−0.0117278	−	0.0141220i
$831$		−	47.0218i		−	1.63117i
$832$	−15.3837	−	4.86992i	−0.533333	−	0.168834i
$833$	−18.6633	+	45.0813i	−0.646644	+	1.56197i
$834$	−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
$838$	10.6563	+	1.96111i	0.368115	+	0.0677455i
$839$	28.5858			0.986890			0.493445	−	0.869777i	$-0.335737\pi$
$839$	28.5858			0.986890			0.493445	+	0.869777i	$0.335737\pi$
$840$	−39.3996	+	22.8471i	−1.35941	+	0.788299i
$841$	−24.7990			−0.855136
$842$	−13.6929	−	2.51995i	−0.471888	−	0.0868431i
$843$	−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
$847$	9.62995	+	48.3891i	0.330889	+	1.66267i
$848$	2.74131	+	47.6966i	0.0941369	+	1.63791i
$849$			44.5909i			1.53036i
$850$	−34.7567	−	34.9456i	−1.19214	−	1.19862i
$851$			5.23854i			0.179575i
$852$	−53.0735	+	23.7906i	−1.81827	+	0.815053i
$853$	26.3254	−	26.3254i	0.901366	−	0.901366i	−0.0941884	−	0.995554i	$-0.530026\pi$
$853$	26.3254	−	26.3254i	0.901366	−	0.901366i	0.995554	+	0.0941884i	$0.0300256\pi$
$854$	−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	$-0.915965\pi$
$857$	−20.6212	+	20.6212i	−0.704407	+	0.704407i	0.260946	+	0.965353i	$0.415965\pi$
$858$	7.65145	−	41.5764i	0.261216	−	1.41940i
$859$			11.3102i			0.385899i	0.981209	+	0.192949i	$0.0618053\pi$
$859$			11.3102i			0.385899i	−0.981209	+	0.192949i	$0.938195\pi$
$860$	−15.7310	−	28.0542i	−0.536421	−	0.956639i
$861$	4.68686	−	7.01582i	0.159728	−	0.239099i
$862$	6.82436	−	37.0822i	0.232439	−	1.26302i
$863$	33.8905	−	33.8905i	1.15365	−	1.15365i	0.167832	−	0.985816i	$-0.446323\pi$
$863$	33.8905	−	33.8905i	1.15365	−	1.15365i	0.985816	−	0.167832i	$-0.0536766\pi$
$864$	−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
$868$	−9.32951	−	1.57795i	−0.316664	−	0.0535591i
$869$	−28.8529			−0.978768
$870$	−11.2709	−	13.5717i	−0.382119	−	0.460125i
$871$			15.3635i			0.520573i
$872$	−16.6073	+	27.3326i	−0.562395	+	0.925597i
$873$	−6.95227	−	6.95227i	−0.235299	−	0.235299i
$874$	−8.86118	+	6.10661i	−0.299734	+	0.206559i
$875$	13.2744	+	26.4346i	0.448758	+	0.893653i
$876$	−18.1716	−	6.92282i	−0.613961	−	0.233900i
$877$	−39.5070	+	39.5070i	−1.33406	+	1.33406i	−0.432351	+	0.901705i	$0.642316\pi$
$877$	−39.5070	+	39.5070i	−1.33406	+	1.33406i	−0.901705	+	0.432351i	$0.857684\pi$
$878$	−6.10837	+	33.1916i	−0.206147	+	1.12016i
$879$		−	62.3659i		−	2.10355i
$880$	29.0196	−	39.1114i	0.978251	−	1.31845i
$881$		−	31.8459i		−	1.07292i	−0.843927	−	0.536458i	$-0.819762\pi$
$881$		−	31.8459i		−	1.07292i	0.843927	−	0.536458i	$-0.180238\pi$
$882$	42.6728	−	9.13515i	1.43687	−	0.307596i
$883$	−2.50424	−	2.50424i	−0.0842743	−	0.0842743i	0.663713	−	0.747987i	$-0.268980\pi$
$883$	−2.50424	−	2.50424i	−0.0842743	−	0.0842743i	−0.747987	+	0.663713i	$0.768980\pi$
$884$	−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	$-0.602038\pi$
$887$	18.8809	−	18.8809i	0.633959	−	0.633959i	0.949059	+	0.315100i	$0.102038\pi$
$888$	−15.2560	−	9.26960i	−0.511959	−	0.311067i
$889$	5.44956	−	8.15751i	0.182772	−	0.273594i
$890$	−0.168603	+	1.82044i	−0.00565158	+	0.0610211i
$891$			15.2023i			0.509297i
$892$	4.13780	+	9.23083i	0.138544	+	0.309071i
$893$	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
$898$	−5.08970	−	0.936675i	−0.169846	−	0.0312572i
$899$		−	3.66508i		−	0.122237i
$900$	−8.09615	+	43.3328i	−0.269872	+	1.44443i
$901$	83.2516			2.77351
$902$	−1.63295	+	8.87315i	−0.0543714	+	0.295444i
$903$	10.1088	+	50.7953i	0.336400	+	1.69036i
$904$	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	$-0.595063\pi$
$907$	19.9221	−	19.9221i	0.661504	−	0.661504i	0.955735	+	0.294230i	$0.0950633\pi$
$908$	14.7883	+	32.9907i	0.490768	+	1.09483i
$909$		−	57.7411i		−	1.91515i
$910$	10.6284	−	13.1081i	0.352327	−	0.434528i
$911$	18.3056			0.606492			0.303246	−	0.952912i	$-0.401930\pi$
$911$	18.3056			0.606492			0.303246	+	0.952912i	$0.401930\pi$
$912$	−2.10422	−	36.6117i	−0.0696776	−	1.21234i
$913$	−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
$917$	5.46755	+	27.4737i	0.180554	+	0.907260i
$918$	−6.83866	+	37.1599i	−0.225709	+	1.22646i
$919$		−	48.4316i		−	1.59761i	−0.601590	−	0.798805i	$-0.705466\pi$
$919$		−	48.4316i		−	1.59761i	0.601590	−	0.798805i	$-0.294534\pi$
$920$	−4.61710	−	13.5215i	−0.152221	−	0.445789i
$921$	13.3150			0.438745
$922$	7.94157	−	43.1529i	0.261542	−	1.42117i
$923$	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
$928$	−9.15382	+	7.11624i	−0.300489	+	0.233602i
$929$	−42.8816			−1.40690			−0.703449	−	0.710746i	$-0.748358\pi$
$929$	−42.8816			−1.40690			−0.703449	+	0.710746i	$0.748358\pi$
$930$	−11.8403	+	9.83296i	−0.388257	+	0.322435i
$931$	9.02722	+	21.7820i	0.295855	+	0.713876i
$932$	−22.5527	+	10.1094i	−0.738739	+	0.331146i
$933$	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	$-0.609284\pi$
$937$	18.5200	−	18.5200i	0.605022	−	0.605022i	0.941641	+	0.336619i	$0.109284\pi$
$938$	19.8593	−	20.4416i	0.648431	−	0.667443i
$939$	70.2976			2.29408
$940$	−9.26601	+	5.19578i	−0.302224	+	0.169468i
$941$	−9.80731			−0.319709			−0.159855	−	0.987141i	$-0.551103\pi$
$941$	−9.80731			−0.319709			−0.159855	+	0.987141i	$0.551103\pi$
$942$	−7.25047	+	39.3976i	−0.236233	+	1.28364i
$943$	1.87165	+	1.87165i	0.0609493	+	0.0609493i
$944$	−22.4891	+	25.2318i	−0.731959	+	0.821226i
$945$	10.8580	−	19.9081i	0.353211	−	0.647609i
$946$	−31.4259	−	45.6015i	−1.02174	−	1.48263i
$947$	−7.28661	+	7.28661i	−0.236783	+	0.236783i	−0.815517	−	0.578734i	$-0.803547\pi$
$947$	−7.28661	+	7.28661i	−0.236783	+	0.236783i	0.578734	+	0.815517i	$0.303547\pi$
$948$	−11.7991	−	26.3221i	−0.383216	−	0.854901i
$949$	7.20514			0.233889
$950$	−23.8178	−	0.0645415i	−0.772751	−	0.00209400i
$951$			2.54996i			0.0826882i
$952$	47.2842	−	22.0213i	1.53249	−	0.713714i
$953$	−33.6252	+	33.6252i	−1.08923	+	1.08923i	−0.0936179	+	0.995608i	$0.529843\pi$
$953$	−33.6252	+	33.6252i	−1.08923	+	1.08923i	−0.995608	+	0.0936179i	$0.970157\pi$
$954$	−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
$958$	−9.39164	+	51.0323i	−0.303430	+	1.64878i
$959$	10.1535	−	15.1990i	0.327875	−	0.490800i
$960$	47.5480	+	10.4800i	1.53461	+	0.338240i
$961$	27.8025			0.896855
$962$	6.50519	+	1.19717i	0.209736	+	0.0385983i
$963$	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	0.646192	−	0.763175i	$-0.276361\pi$
$967$	−3.63780	−	3.63780i	−0.116984	−	0.116984i	−0.763175	+	0.646192i	$0.776361\pi$
$968$	27.3884	−	45.0762i	0.880297	−	1.44880i
$969$	−63.9036			−2.05288
$970$	4.50603	+	5.42590i	0.144680	+	0.174215i
$971$	−38.2561			−1.22770			−0.613848	−	0.789424i	$-0.710379\pi$
$971$	−38.2561			−1.22770			−0.613848	+	0.789424i	$0.710379\pi$
$972$	−34.8551	+	15.6241i	−1.11798	+	0.501143i
$973$	−35.3906	+	7.04311i	−1.13457	+	0.225792i
$974$	−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	0.176589	−	0.984285i	$-0.443494\pi$
$977$	−25.2462	−	25.2462i	−0.807696	−	0.807696i	−0.984285	+	0.176589i	$0.943494\pi$
$978$	6.01982	−	32.7105i	0.192493	−	1.04597i
$979$			3.14795i			0.100609i
$980$	−31.0853	+	3.70214i	−0.992983	+	0.118261i
$981$		−	49.8464i		−	1.59147i
$982$	47.7276	+	8.78346i	1.52305	+	0.280291i
$983$	−34.0314	−	34.0314i	−1.08543	−	1.08543i	−0.995992	−	0.0894417i	$-0.971492\pi$
$983$	−34.0314	−	34.0314i	−1.08543	−	1.08543i	−0.0894417	−	0.995992i	$-0.528508\pi$
$984$	−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
$987$	16.7772	−	3.33884i	0.534023	−	0.106276i
$988$	5.55808	+	12.3993i	0.176826	+	0.394474i
$989$	−16.2477			−0.516647
$990$	−7.00005	+	75.5807i	−0.222476	+	2.40211i
$991$	7.42850			0.235974			0.117987	−	0.993015i	$-0.462356\pi$
$991$	7.42850			0.235974			0.117987	+	0.993015i	$0.462356\pi$
$992$	6.20836	+	7.98599i	0.197116	+	0.253555i
$993$	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	0.849313	−	0.527890i	$-0.177017\pi$
$997$	10.1490	+	10.1490i	0.321422	+	0.321422i	−0.527890	+	0.849313i	$0.677017\pi$
$998$	7.15118	−	38.8581i	0.226367	−	1.23003i
$999$	8.88817			0.281209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.237.22	yes	72
4.3	odd	2		1120.2.w.c.657.4		72
5.3	odd	4	inner	280.2.s.c.13.2	yes	72
7.6	odd	2	inner	280.2.s.c.237.21	yes	72
8.3	odd	2		1120.2.w.c.657.33		72
8.5	even	2	inner	280.2.s.c.237.1	yes	72
20.3	even	4		1120.2.w.c.433.3		72
28.27	even	2		1120.2.w.c.657.34		72
35.13	even	4	inner	280.2.s.c.13.1	✓	72
40.3	even	4		1120.2.w.c.433.34		72
40.13	odd	4	inner	280.2.s.c.13.21	yes	72
56.13	odd	2	inner	280.2.s.c.237.2	yes	72
56.27	even	2		1120.2.w.c.657.3		72
140.83	odd	4		1120.2.w.c.433.33		72
280.13	even	4	inner	280.2.s.c.13.22	yes	72
280.83	odd	4		1120.2.w.c.433.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.1	✓	72	35.13	even	4	inner
280.2.s.c.13.2	yes	72	5.3	odd	4	inner
280.2.s.c.13.21	yes	72	40.13	odd	4	inner
280.2.s.c.13.22	yes	72	280.13	even	4	inner
280.2.s.c.237.1	yes	72	8.5	even	2	inner
280.2.s.c.237.2	yes	72	56.13	odd	2	inner
280.2.s.c.237.21	yes	72	7.6	odd	2	inner
280.2.s.c.237.22	yes	72	1.1	even	1	trivial
1120.2.w.c.433.3		72	20.3	even	4
1120.2.w.c.433.4		72	280.83	odd	4
1120.2.w.c.433.33		72	140.83	odd	4
1120.2.w.c.433.34		72	40.3	even	4
1120.2.w.c.657.3		72	56.27	even	2
1120.2.w.c.657.4		72	4.3	odd	2
1120.2.w.c.657.33		72	8.3	odd	2
1120.2.w.c.657.34		72	28.27	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.255964 - 1.39086i) q^{2} +(1.92461 - 1.92461i) q^{3} +(-1.86896 - 0.712018i) q^{4} +(-2.22709 + 0.200181i) q^{5} +(-2.18423 - 3.16949i) q^{6} +(-0.516406 - 2.59487i) q^{7} +(-1.46870 + 2.41721i) q^{8} -4.40827i q^{9} +O(q^{10})\)	\(q+(0.255964 - 1.39086i) 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} +(-0.516406 - 2.59487i) q^{7} +(-1.46870 + 2.41721i) q^{8} -4.40827i q^{9} +(-0.291632 + 3.14880i) q^{10} +5.44500i q^{11} +(-4.96739 + 2.22667i) 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} +(-6.13127 - 1.12836i) q^{18} -3.36836i q^{19} +(4.30488 + 1.21160i) q^{20} +(-5.98799 - 4.00023i) q^{21} +(7.57321 + 1.39372i) 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} +(-0.882447 + 5.21740i) q^{28} -2.04964 q^{29} +(5.49894 + 6.62150i) q^{30} +1.78815i q^{31} +(4.46605 - 3.47194i) q^{32} +(10.4795 + 10.4795i) q^{33} +(-5.59356 - 8.11671i) q^{34} +(1.66952 + 5.67562i) q^{35} +(-3.13877 + 8.23890i) q^{36} +(-1.63966 + 1.63966i) q^{37} +(-4.68490 - 0.862178i) q^{38} -5.48993i q^{39} +(2.78705 - 5.67735i) q^{40} +1.17165i q^{41} +(-7.09646 + 7.30452i) 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} +(10.8693 - 0.624701i) q^{48} +(-6.46665 + 2.68001i) q^{49} +(0.0191611 - 7.07104i) q^{50} -18.9717i q^{51} +(-3.68111 + 1.65009i) 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} +(-0.524635 + 2.85076i) q^{58} +8.44987i q^{59} +(10.6171 - 5.95338i) q^{60} +3.37492 q^{61} +(2.48706 + 0.457703i) q^{62} +(-11.4389 + 2.27645i) 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} +(-12.7209 + 5.70226i) q^{68} -6.14894i q^{69} +(8.32132 - 0.869314i) q^{70} +10.6844 q^{71} +(10.6557 + 6.47444i) 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} +(14.1290 - 2.81183i) q^{77} +(-7.63571 - 1.40522i) q^{78} +5.29897i q^{79} +(-7.18300 - 5.32959i) q^{80} +2.79198 q^{81} +(1.62960 + 0.299900i) 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} +(-13.1617 - 7.99709i) q^{88} +0.578136 q^{89} +(13.8808 + 1.28559i) q^{90} +(-4.43743 - 2.96439i) q^{91} +(-4.12299 + 1.84816i) 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} +(2.07228 + 9.68017i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more