LMFDB - Embedded newform 560.2.bd.a.141.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.7
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.914710 + 1.07857i) q^{2} +(-1.42818 - 1.42818i) q^{3} +(-0.326610 - 1.97315i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.84676 - 0.234016i) q^{6} -1.00000i q^{7} +(2.42693 + 1.45259i) q^{8} +1.07940i q^{9} +O(q^{10})$	\(q+(-0.914710 + 1.07857i) q^{2} +(-1.42818 - 1.42818i) q^{3} +(-0.326610 - 1.97315i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.84676 - 0.234016i) q^{6} -1.00000i q^{7} +(2.42693 + 1.45259i) q^{8} +1.07940i q^{9} +(0.115864 + 1.40946i) q^{10} +(1.52244 - 1.52244i) q^{11} +(-2.35156 + 3.28447i) q^{12} +(3.04533 + 3.04533i) q^{13} +(1.07857 + 0.914710i) q^{14} -2.01975 q^{15} +(-3.78665 + 1.28890i) q^{16} +4.23034 q^{17} +(-1.16420 - 0.987337i) q^{18} +(-4.95147 - 4.95147i) q^{19} +(-1.62618 - 1.16428i) q^{20} +(-1.42818 + 1.42818i) q^{21} +(0.249461 + 3.03464i) q^{22} -0.679888i q^{23} +(-1.39153 - 5.54065i) q^{24} -1.00000i q^{25} +(-6.07019 + 0.498996i) q^{26} +(-2.74297 + 2.74297i) q^{27} +(-1.97315 + 0.326610i) q^{28} +(-6.70532 - 6.70532i) q^{29} +(1.84749 - 2.17844i) q^{30} +3.91859 q^{31} +(2.07352 - 5.26313i) q^{32} -4.34864 q^{33} +(-3.86954 + 4.56271i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(2.12982 - 0.352542i) q^{36} +(-2.96978 + 2.96978i) q^{37} +(9.86965 - 0.811328i) q^{38} -8.69856i q^{39} +(2.74323 - 0.688960i) q^{40} -7.19853i q^{41} +(-0.234016 - 2.84676i) q^{42} +(5.87122 - 5.87122i) q^{43} +(-3.50125 - 2.50676i) q^{44} +(0.763250 + 0.763250i) q^{45} +(0.733304 + 0.621900i) q^{46} -9.08441 q^{47} +(7.24881 + 3.56724i) q^{48} -1.00000 q^{49} +(1.07857 + 0.914710i) q^{50} +(-6.04169 - 6.04169i) q^{51} +(5.01426 - 7.00354i) q^{52} +(0.694448 - 0.694448i) q^{53} +(-0.449451 - 5.46749i) q^{54} -2.15306i q^{55} +(1.45259 - 2.42693i) q^{56} +14.1432i q^{57} +(13.3656 - 1.09871i) q^{58} +(-1.02293 + 1.02293i) q^{59} +(0.659672 + 3.98528i) q^{60} +(3.24288 + 3.24288i) q^{61} +(-3.58437 + 4.22645i) q^{62} +1.07940 q^{63} +(3.77996 + 7.05067i) q^{64} +4.30675 q^{65} +(3.97774 - 4.69029i) q^{66} +(-8.40320 - 8.40320i) q^{67} +(-1.38167 - 8.34711i) q^{68} +(-0.971002 + 0.971002i) q^{69} +(1.40946 - 0.115864i) q^{70} -9.32988i q^{71} +(-1.56792 + 2.61962i) q^{72} +7.80075i q^{73} +(-0.486615 - 5.91959i) q^{74} +(-1.42818 + 1.42818i) q^{75} +(-8.15280 + 11.3872i) q^{76} +(-1.52244 - 1.52244i) q^{77} +(9.38198 + 7.95667i) q^{78} +7.64996 q^{79} +(-1.76618 + 3.58896i) q^{80} +11.0731 q^{81} +(7.76409 + 6.58457i) q^{82} +(-7.17767 - 7.17767i) q^{83} +(3.28447 + 2.35156i) q^{84} +(2.99130 - 2.99130i) q^{85} +(0.962033 + 11.7030i) q^{86} +19.1528i q^{87} +(5.90634 - 1.48337i) q^{88} +12.8679i q^{89} +(-1.52137 + 0.125063i) q^{90} +(3.04533 - 3.04533i) q^{91} +(-1.34152 + 0.222058i) q^{92} +(-5.59645 - 5.59645i) q^{93} +(8.30960 - 9.79813i) q^{94} -7.00244 q^{95} +(-10.4781 + 4.55533i) q^{96} +1.52512 q^{97} +(0.914710 - 1.07857i) q^{98} +(1.64332 + 1.64332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.914710	+	1.07857i	−0.646798	+	0.762661i
$2$	−0.914710	+	1.07857i	−0.646798	+	0.762661i
$3$	−1.42818	−	1.42818i	−0.824560	−	0.824560i	0.162198	−	0.986758i	$-0.448142\pi$
$3$	−1.42818	−	1.42818i	−0.824560	−	0.824560i	−0.986758	+	0.162198i	$0.948142\pi$
$4$	−0.326610	−	1.97315i	−0.163305	−	0.986576i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	2.84676	−	0.234016i	1.16218	−	0.0955366i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.42693	+	1.45259i	0.858049	+	0.513568i
$9$			1.07940i			0.359799i
$10$	0.115864	+	1.40946i	0.0366393	+	0.445710i
$11$	1.52244	−	1.52244i	0.459033	−	0.459033i	−0.439305	−	0.898338i	$-0.644775\pi$
$11$	1.52244	−	1.52244i	0.459033	−	0.459033i	0.898338	+	0.439305i	$0.144775\pi$
$12$	−2.35156	+	3.28447i	−0.678836	+	0.948146i
$13$	3.04533	+	3.04533i	0.844623	+	0.844623i	0.989456	−	0.144833i	$-0.0462645\pi$
$13$	3.04533	+	3.04533i	0.844623	+	0.844623i	−0.144833	+	0.989456i	$0.546265\pi$
$14$	1.07857	+	0.914710i	0.288259	+	0.244467i
$15$	−2.01975			−0.521498
$16$	−3.78665	+	1.28890i	−0.946663	+	0.322226i
$17$	4.23034			1.02601			0.513005	−	0.858386i	$-0.328532\pi$
$17$	4.23034			1.02601			0.513005	+	0.858386i	$0.328532\pi$
$18$	−1.16420	−	0.987337i	−0.274405	−	0.232717i
$19$	−4.95147	−	4.95147i	−1.13595	−	1.13595i	−0.989170	−	0.146776i	$-0.953110\pi$
$19$	−4.95147	−	4.95147i	−1.13595	−	1.13595i	−0.146776	−	0.989170i	$-0.546890\pi$
$20$	−1.62618	−	1.16428i	−0.363624	−	0.260341i
$21$	−1.42818	+	1.42818i	−0.311655	+	0.311655i
$22$	0.249461	+	3.03464i	0.0531852	+	0.646988i
$23$		−	0.679888i		−	0.141766i	−0.997485	−	0.0708832i	$-0.977418\pi$
$23$		−	0.679888i		−	0.141766i	0.997485	−	0.0708832i	$-0.0225818\pi$
$24$	−1.39153	−	5.54065i	−0.284045	−	1.13098i
$25$		−	1.00000i		−	0.200000i
$26$	−6.07019	+	0.498996i	−1.19046	+	0.0978611i
$27$	−2.74297	+	2.74297i	−0.527884	+	0.527884i
$28$	−1.97315	+	0.326610i	−0.372891	+	0.0617235i
$29$	−6.70532	−	6.70532i	−1.24515	−	1.24515i	−0.957838	−	0.287310i	$-0.907239\pi$
$29$	−6.70532	−	6.70532i	−1.24515	−	1.24515i	−0.287310	−	0.957838i	$-0.592761\pi$
$30$	1.84749	−	2.17844i	0.337304	−	0.397726i
$31$	3.91859			0.703799			0.351899	−	0.936038i	$-0.385536\pi$
$31$	3.91859			0.703799			0.351899	+	0.936038i	$0.385536\pi$
$32$	2.07352	−	5.26313i	0.366550	−	0.930398i
$33$	−4.34864			−0.757001
$34$	−3.86954	+	4.56271i	−0.663621	+	0.782498i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	2.12982	−	0.352542i	0.354969	−	0.0587571i
$37$	−2.96978	+	2.96978i	−0.488228	+	0.488228i	−0.907747	−	0.419519i	$-0.862199\pi$
$37$	−2.96978	+	2.96978i	−0.488228	+	0.488228i	0.419519	+	0.907747i	$0.362199\pi$
$38$	9.86965	−	0.811328i	1.60107	−	0.131615i
$39$		−	8.69856i		−	1.39289i
$40$	2.74323	−	0.688960i	0.433743	−	0.108934i
$41$		−	7.19853i		−	1.12422i	−0.827062	−	0.562111i	$-0.809990\pi$
$41$		−	7.19853i		−	1.12422i	0.827062	−	0.562111i	$-0.190010\pi$
$42$	−0.234016	−	2.84676i	−0.0361094	−	0.439264i
$43$	5.87122	−	5.87122i	0.895352	−	0.895352i	−0.0996688	−	0.995021i	$-0.531778\pi$
$43$	5.87122	−	5.87122i	0.895352	−	0.895352i	0.995021	+	0.0996688i	$0.0317783\pi$
$44$	−3.50125	−	2.50676i	−0.527833	−	0.377908i
$45$	0.763250	+	0.763250i	0.113779	+	0.113779i
$46$	0.733304	+	0.621900i	0.108120	+	0.0916942i
$47$	−9.08441			−1.32510			−0.662548	−	0.749019i	$-0.730525\pi$
$47$	−9.08441			−1.32510			−0.662548	+	0.749019i	$0.730525\pi$
$48$	7.24881	+	3.56724i	1.04628	+	0.514886i
$49$	−1.00000			−0.142857
$50$	1.07857	+	0.914710i	0.152532	+	0.129360i
$51$	−6.04169	−	6.04169i	−0.846006	−	0.846006i
$52$	5.01426	−	7.00354i	0.695353	−	0.971216i
$53$	0.694448	−	0.694448i	0.0953898	−	0.0953898i	−0.657802	−	0.753191i	$-0.728513\pi$
$53$	0.694448	−	0.694448i	0.0953898	−	0.0953898i	0.753191	+	0.657802i	$0.228513\pi$
$54$	−0.449451	−	5.46749i	−0.0611626	−	0.744031i
$55$		−	2.15306i		−	0.290318i
$56$	1.45259	−	2.42693i	0.194111	−	0.324312i
$57$			14.1432i			1.87331i
$58$	13.3656	−	1.09871i	1.75498	−	0.144267i
$59$	−1.02293	+	1.02293i	−0.133175	+	0.133175i	−0.770552	−	0.637377i	$-0.780019\pi$
$59$	−1.02293	+	1.02293i	−0.133175	+	0.133175i	0.637377	+	0.770552i	$0.280019\pi$
$60$	0.659672	+	3.98528i	0.0851632	+	0.514497i
$61$	3.24288	+	3.24288i	0.415208	+	0.415208i	0.883548	−	0.468340i	$-0.155148\pi$
$61$	3.24288	+	3.24288i	0.415208	+	0.415208i	−0.468340	+	0.883548i	$0.655148\pi$
$62$	−3.58437	+	4.22645i	−0.455216	+	0.536760i
$63$	1.07940			0.135991
$64$	3.77996	+	7.05067i	0.472495	+	0.881333i
$65$	4.30675			0.534186
$66$	3.97774	−	4.69029i	0.489626	−	0.577335i
$67$	−8.40320	−	8.40320i	−1.02661	−	1.02661i	−0.999636	−	0.0269785i	$-0.991411\pi$
$67$	−8.40320	−	8.40320i	−1.02661	−	1.02661i	−0.0269785	−	0.999636i	$-0.508589\pi$
$68$	−1.38167	−	8.34711i	−0.167553	−	1.01224i
$69$	−0.971002	+	0.971002i	−0.116895	+	0.116895i
$70$	1.40946	−	0.115864i	0.168463	−	0.0138484i
$71$		−	9.32988i		−	1.10725i	−0.832765	−	0.553626i	$-0.813244\pi$
$71$		−	9.32988i		−	1.10725i	0.832765	−	0.553626i	$-0.186756\pi$
$72$	−1.56792	+	2.61962i	−0.184782	+	0.308725i
$73$			7.80075i			0.913009i	0.889721	+	0.456504i	$0.150899\pi$
$73$			7.80075i			0.913009i	−0.889721	+	0.456504i	$0.849101\pi$
$74$	−0.486615	−	5.91959i	−0.0565679	−	0.688138i
$75$	−1.42818	+	1.42818i	−0.164912	+	0.164912i
$76$	−8.15280	+	11.3872i	−0.935191	+	1.30620i
$77$	−1.52244	−	1.52244i	−0.173498	−	0.173498i
$78$	9.38198	+	7.95667i	1.06230	+	0.900915i
$79$	7.64996			0.860688			0.430344	−	0.902665i	$-0.358392\pi$
$79$	7.64996			0.860688			0.430344	+	0.902665i	$0.358392\pi$
$80$	−1.76618	+	3.58896i	−0.197464	+	0.401258i
$81$	11.0731			1.23034
$82$	7.76409	+	6.58457i	0.857400	+	0.727144i
$83$	−7.17767	−	7.17767i	−0.787852	−	0.787852i	0.193290	−	0.981142i	$-0.438084\pi$
$83$	−7.17767	−	7.17767i	−0.787852	−	0.787852i	−0.981142	+	0.193290i	$0.938084\pi$
$84$	3.28447	+	2.35156i	0.358365	+	0.256576i
$85$	2.99130	−	2.99130i	0.324453	−	0.324453i
$86$	0.962033	+	11.7030i	0.103739	+	1.26196i
$87$			19.1528i			2.05340i
$88$	5.90634	−	1.48337i	0.629618	−	0.158128i
$89$			12.8679i			1.36400i	0.731354	+	0.681998i	$0.238889\pi$
$89$			12.8679i			1.36400i	−0.731354	+	0.681998i	$0.761111\pi$
$90$	−1.52137	+	0.125063i	−0.160366	+	0.0131828i
$91$	3.04533	−	3.04533i	0.319237	−	0.319237i
$92$	−1.34152	+	0.222058i	−0.139863	+	0.0231512i
$93$	−5.59645	−	5.59645i	−0.580325	−	0.580325i
$94$	8.30960	−	9.79813i	0.857070	−	1.01060i
$95$	−7.00244			−0.718435
$96$	−10.4781	+	4.55533i	−1.06941	+	0.464926i
$97$	1.52512			0.154853			0.0774263	−	0.996998i	$-0.475330\pi$
$97$	1.52512			0.154853			0.0774263	+	0.996998i	$0.475330\pi$
$98$	0.914710	−	1.07857i	0.0923997	−	0.108952i
$99$	1.64332	+	1.64332i	0.165160	+	0.165160i
$100$	−1.97315	+	0.326610i	−0.197315	+	0.0326610i
$101$	−1.12960	+	1.12960i	−0.112400	+	0.112400i	−0.761070	−	0.648670i	$-0.775326\pi$
$101$	−1.12960	+	1.12960i	−0.112400	+	0.112400i	0.648670	+	0.761070i	$0.275326\pi$
$102$	12.0428	−	0.989967i	1.19241	−	0.0980214i
$103$			18.1607i			1.78943i	0.446638	+	0.894715i	$0.352621\pi$
$103$			18.1607i			1.78943i	−0.446638	+	0.894715i	$0.647379\pi$
$104$	2.96718	+	11.8144i	0.290956	+	1.15850i
$105$			2.01975i			0.197108i
$106$	0.113789	+	1.38423i	0.0110522	+	0.134448i
$107$	2.32172	−	2.32172i	0.224450	−	0.224450i	−0.585920	−	0.810369i	$-0.699267\pi$
$107$	2.32172	−	2.32172i	0.224450	−	0.224450i	0.810369	+	0.585920i	$0.199267\pi$
$108$	6.30817	+	4.51641i	0.607004	+	0.434591i
$109$	−8.57935	−	8.57935i	−0.821753	−	0.821753i	0.164606	−	0.986359i	$-0.447365\pi$
$109$	−8.57935	−	8.57935i	−0.821753	−	0.821753i	−0.986359	+	0.164606i	$0.947365\pi$
$110$	2.32221	+	1.96942i	0.221414	+	0.187777i
$111$	8.48275			0.805147
$112$	1.28890	+	3.78665i	0.121790	+	0.357805i
$113$	−3.80024			−0.357497			−0.178748	−	0.983895i	$-0.557205\pi$
$113$	−3.80024			−0.357497			−0.178748	+	0.983895i	$0.557205\pi$
$114$	−15.2544	−	12.9369i	−1.42870	−	1.21165i
$115$	−0.480753	−	0.480753i	−0.0448305	−	0.0448305i
$116$	−11.0406	+	15.4206i	−1.02509	+	1.43177i
$117$	−3.28713	+	3.28713i	−0.303895	+	0.303895i
$118$	−0.167614	−	2.03899i	−0.0154301	−	0.187704i
$119$		−	4.23034i		−	0.387795i
$120$	−4.90179	−	2.93387i	−0.447470	−	0.267825i
$121$			6.36435i			0.578577i
$122$	−6.46395	+	0.531365i	−0.585219	+	0.0481075i
$123$	−10.2808	+	10.2808i	−0.926988	+	0.926988i
$124$	−1.27985	−	7.73196i	−0.114934	−	0.694351i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−0.987337	+	1.16420i	−0.0879589	+	0.103715i
$127$	13.8740			1.23112			0.615561	−	0.788089i	$-0.288929\pi$
$127$	13.8740			1.23112			0.615561	+	0.788089i	$0.288929\pi$
$128$	−11.0622	−	2.37238i	−0.977768	−	0.209691i
$129$	−16.7703			−1.47654
$130$	−3.93943	+	4.64511i	−0.345511	+	0.407403i
$131$	−12.5691	−	12.5691i	−1.09817	−	1.09817i	−0.994625	−	0.103547i	$-0.966981\pi$
$131$	−12.5691	−	12.5691i	−1.09817	−	1.09817i	−0.103547	−	0.994625i	$-0.533019\pi$
$132$	1.42031	+	8.58052i	0.123622	+	0.746839i
$133$	−4.95147	+	4.95147i	−0.429347	+	0.429347i
$134$	16.7499	−	1.37691i	1.44697	−	0.118947i
$135$			3.87914i			0.333863i
$136$	10.2667	+	6.14496i	0.880366	+	0.526926i
$137$		−	18.7604i		−	1.60281i	−0.598122	−	0.801405i	$-0.704086\pi$
$137$		−	18.7604i		−	1.60281i	0.598122	−	0.801405i	$-0.295914\pi$
$138$	−0.159104	−	1.93548i	−0.0135439	−	0.164759i
$139$	−2.68745	+	2.68745i	−0.227947	+	0.227947i	−0.811834	−	0.583888i	$-0.801531\pi$
$139$	−2.68745	+	2.68745i	−0.227947	+	0.227947i	0.583888	+	0.811834i	$0.301531\pi$
$140$	−1.16428	+	1.62618i	−0.0983996	+	0.137437i
$141$	12.9742	+	12.9742i	1.09262	+	1.09262i
$142$	10.0629	+	8.53414i	0.844459	+	0.716169i
$143$	9.27267			0.775420
$144$	−1.39124	−	4.08730i	−0.115937	−	0.340609i
$145$	−9.48276			−0.787500
$146$	−8.41363	−	7.13543i	−0.696317	−	0.590532i
$147$	1.42818	+	1.42818i	0.117794	+	0.117794i
$148$	6.82978	+	4.88986i	0.561404	+	0.401944i
$149$	6.04099	−	6.04099i	0.494897	−	0.494897i	−0.414948	−	0.909845i	$-0.636200\pi$
$149$	6.04099	−	6.04099i	0.494897	−	0.494897i	0.909845	+	0.414948i	$0.136200\pi$
$150$	−0.234016	−	2.84676i	−0.0191073	−	0.232437i
$151$			9.29710i			0.756587i	0.925686	+	0.378293i	$0.123489\pi$
$151$			9.29710i			0.756587i	−0.925686	+	0.378293i	$0.876511\pi$
$152$	−4.82440	−	19.2093i	−0.391311	−	1.55808i
$153$			4.56623i			0.369157i
$154$	3.03464	−	0.249461i	0.244539	−	0.0201021i
$155$	2.77086	−	2.77086i	0.222561	−	0.222561i
$156$	−17.1636	+	2.84104i	−1.37419	+	0.227465i
$157$	12.1540	+	12.1540i	0.969995	+	0.969995i	0.999563	−	0.0295682i	$-0.00941323\pi$
$157$	12.1540	+	12.1540i	0.969995	+	0.969995i	−0.0295682	+	0.999563i	$0.509413\pi$
$158$	−6.99750	+	8.25099i	−0.556691	+	0.656413i
$159$	−1.98359			−0.157309
$160$	−2.25539	−	5.18779i	−0.178304	−	0.410131i
$161$	−0.679888			−0.0535826
$162$	−10.1287	+	11.9431i	−0.795784	+	0.938336i
$163$	−3.91678	−	3.91678i	−0.306786	−	0.306786i	0.536876	−	0.843661i	$-0.319604\pi$
$163$	−3.91678	−	3.91678i	−0.306786	−	0.306786i	−0.843661	+	0.536876i	$0.819604\pi$
$164$	−14.2038	+	2.35111i	−1.10913	+	0.183591i
$165$	−3.07495	+	3.07495i	−0.239385	+	0.239385i
$166$	14.3071	−	1.17610i	1.11044	−	0.0912834i
$167$			8.49777i			0.657577i	0.944403	+	0.328789i	$0.106640\pi$
$167$			8.49777i			0.657577i	−0.944403	+	0.328789i	$0.893360\pi$
$168$	−5.54065	+	1.39153i	−0.427471	+	0.107359i
$169$			5.54809i			0.426776i
$170$	0.490143	+	5.96250i	0.0375923	+	0.457303i
$171$	5.34461	−	5.34461i	0.408713	−	0.408713i
$172$	−13.5024	−	9.66720i	−1.02955	−	0.737117i
$173$	0.845971	+	0.845971i	0.0643180	+	0.0643180i	0.738534	−	0.674216i	$-0.235518\pi$
$173$	0.845971	+	0.845971i	0.0643180	+	0.0643180i	−0.674216	+	0.738534i	$0.735518\pi$
$174$	−20.6576	−	17.5193i	−1.56605	−	1.32813i
$175$	−1.00000			−0.0755929
$176$	−3.80267	+	7.72723i	−0.286637	+	0.582462i
$177$	2.92187			0.219621
$178$	−13.8789	−	11.7704i	−1.04027	−	0.882229i
$179$	10.2027	+	10.2027i	0.762583	+	0.762583i	0.976789	−	0.214206i	$-0.0687163\pi$
$179$	10.2027	+	10.2027i	0.762583	+	0.762583i	−0.214206	+	0.976789i	$0.568716\pi$
$180$	1.25672	−	1.75529i	0.0936705	−	0.130832i
$181$	14.5927	−	14.5927i	1.08467	−	1.08467i	0.0885978	−	0.996067i	$-0.471761\pi$
$181$	14.5927	−	14.5927i	1.08467	−	1.08467i	0.996067	−	0.0885978i	$-0.0282386\pi$
$182$	0.498996	+	6.07019i	0.0369880	+	0.449952i
$183$		−	9.26283i		−	0.684728i
$184$	0.987599	−	1.65004i	0.0728067	−	0.121642i
$185$			4.19990i			0.308783i
$186$	11.1553	−	0.917011i	0.817944	−	0.0672385i
$187$	6.44045	−	6.44045i	0.470972	−	0.470972i
$188$	2.96706	+	17.9249i	0.216395	+	1.30731i
$189$	2.74297	+	2.74297i	0.199521	+	0.199521i
$190$	6.40520	−	7.55259i	0.464682	−	0.547923i
$191$	8.56503			0.619744			0.309872	−	0.950778i	$-0.399714\pi$
$191$	8.56503			0.619744			0.309872	+	0.950778i	$0.399714\pi$
$192$	4.67116	−	15.4681i	0.337112	−	1.11631i
$193$	0.754755			0.0543285			0.0271642	−	0.999631i	$-0.491352\pi$
$193$	0.754755			0.0543285			0.0271642	+	0.999631i	$0.491352\pi$
$194$	−1.39504	+	1.64494i	−0.100158	+	0.118100i
$195$	−6.15081	−	6.15081i	−0.440469	−	0.440469i
$196$	0.326610	+	1.97315i	0.0233293	+	0.140939i
$197$	14.9983	−	14.9983i	1.06858	−	1.06858i	0.0711139	−	0.997468i	$-0.477345\pi$
$197$	14.9983	−	14.9983i	1.06858	−	1.06858i	0.997468	−	0.0711139i	$-0.0226554\pi$
$198$	−3.27559	+	0.269268i	−0.232786	+	0.0191360i
$199$		−	3.58826i		−	0.254365i	−0.991879	−	0.127183i	$-0.959407\pi$
$199$		−	3.58826i		−	0.254365i	0.991879	−	0.127183i	$-0.0405934\pi$
$200$	1.45259	−	2.42693i	0.102714	−	0.171610i
$201$			24.0026i			1.69301i
$202$	−0.185092	−	2.25161i	−0.0130230	−	0.158423i
$203$	−6.70532	+	6.70532i	−0.470622	+	0.470622i
$204$	−9.94790	+	13.8945i	−0.696492	+	0.972806i
$205$	−5.09013	−	5.09013i	−0.355510	−	0.355510i
$206$	−19.5875	−	16.6118i	−1.36473	−	1.15740i
$207$	0.733869			0.0510074
$208$	−15.4567	−	7.60647i	−1.07173	−	0.527414i
$209$	−15.0766			−1.04287
$210$	−2.17844	−	1.84749i	−0.150326	−	0.127489i
$211$	7.38510	+	7.38510i	0.508411	+	0.508411i	0.914039	−	0.405627i	$-0.132947\pi$
$211$	7.38510	+	7.38510i	0.508411	+	0.508411i	−0.405627	+	0.914039i	$0.632947\pi$
$212$	−1.59706	−	1.14344i	−0.109687	−	0.0785316i
$213$	−13.3247	+	13.3247i	−0.912997	+	0.912997i
$214$	0.380428	+	4.62784i	0.0260056	+	0.316353i
$215$		−	8.30315i		−	0.566270i
$216$	−10.6414	+	2.67257i	−0.724055	+	0.181846i
$217$		−	3.91859i		−	0.266011i
$218$	17.1010	−	1.40578i	1.15823	−	0.0952113i
$219$	11.1409	−	11.1409i	0.752831	−	0.752831i
$220$	−4.24830	+	0.703210i	−0.286421	+	0.0474104i
$221$	12.8828	+	12.8828i	0.866591	+	0.866591i
$222$	−7.75926	+	9.14921i	−0.520767	+	0.614055i
$223$	22.9924			1.53968			0.769841	−	0.638235i	$-0.220335\pi$
$223$	22.9924			1.53968			0.769841	+	0.638235i	$0.220335\pi$
$224$	−5.26313	−	2.07352i	−0.351657	−	0.138543i
$225$	1.07940			0.0719599
$226$	3.47612	−	4.09881i	0.231228	−	0.272649i
$227$	18.9580	+	18.9580i	1.25829	+	1.25829i	0.951911	+	0.306375i	$0.0991161\pi$
$227$	18.9580	+	18.9580i	1.25829	+	1.25829i	0.306375	+	0.951911i	$0.400884\pi$
$228$	27.9067	−	4.61931i	1.84816	−	0.305921i
$229$	2.75673	−	2.75673i	0.182170	−	0.182170i	−0.610131	−	0.792301i	$-0.708883\pi$
$229$	2.75673	−	2.75673i	0.182170	−	0.182170i	0.792301	+	0.610131i	$0.208883\pi$
$230$	0.958274	−	0.0787742i	0.0631867	−	0.00519422i
$231$			4.34864i			0.286119i
$232$	−6.53325	−	26.0134i	−0.428929	−	1.70787i
$233$		−	0.416171i		−	0.0272643i	−0.999907	−	0.0136321i	$-0.995661\pi$
$233$		−	0.416171i		−	0.0272643i	0.999907	−	0.0136321i	$-0.00433938\pi$
$234$	−0.538615	−	6.55215i	−0.0352104	−	0.428327i
$235$	−6.42365	+	6.42365i	−0.419032	+	0.419032i
$236$	2.35250	+	1.68430i	0.153135	+	0.109639i
$237$	−10.9255	−	10.9255i	−0.709689	−	0.709689i
$238$	4.56271	+	3.86954i	0.295756	+	0.250825i
$239$	19.1283			1.23730			0.618652	−	0.785665i	$-0.287679\pi$
$239$	19.1283			1.23730			0.618652	+	0.785665i	$0.287679\pi$
$240$	7.64810	−	2.60326i	0.493683	−	0.168040i
$241$	24.1343			1.55462			0.777312	−	0.629115i	$-0.216583\pi$
$241$	24.1343			1.55462			0.777312	+	0.629115i	$0.216583\pi$
$242$	−6.86437	−	5.82154i	−0.441259	−	0.374223i
$243$	−7.58548	−	7.58548i	−0.486609	−	0.486609i
$244$	5.33953	−	7.45785i	0.341828	−	0.477440i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−1.68457	−	20.4925i	−0.107404	−	1.30655i
$247$		−	30.1577i		−	1.91889i
$248$	9.51013	+	5.69210i	0.603894	+	0.361449i
$249$			20.5020i			1.29926i
$250$	1.40946	−	0.115864i	0.0891420	−	0.00732786i
$251$	−7.30607	+	7.30607i	−0.461155	+	0.461155i	−0.899034	−	0.437879i	$-0.855730\pi$
$251$	−7.30607	+	7.30607i	−0.461155	+	0.461155i	0.437879	+	0.899034i	$0.355730\pi$
$252$	−0.352542	−	2.12982i	−0.0222081	−	0.134166i
$253$	−1.03509	−	1.03509i	−0.0650754	−	0.0650754i
$254$	−12.6907	+	14.9641i	−0.796287	+	0.938930i
$255$	−8.54425			−0.535061
$256$	12.6775	−	9.76125i	0.792341	−	0.610078i
$257$	−8.79746			−0.548771			−0.274385	−	0.961620i	$-0.588474\pi$
$257$	−8.79746			−0.548771			−0.274385	+	0.961620i	$0.588474\pi$
$258$	15.3400	−	18.0879i	0.955025	−	1.12610i
$259$	2.96978	+	2.96978i	0.184533	+	0.184533i
$260$	−1.40663	−	8.49787i	−0.0872354	−	0.527015i
$261$	7.23772	−	7.23772i	0.448003	−	0.448003i
$262$	25.0538	−	2.05953i	1.54783	−	0.127238i
$263$			9.74140i			0.600681i	0.953832	+	0.300340i	$0.0971002\pi$
$263$			9.74140i			0.600681i	−0.953832	+	0.300340i	$0.902900\pi$
$264$	−10.5538	−	6.31679i	−0.649543	−	0.388772i
$265$		−	0.982098i		−	0.0603298i
$266$	−0.811328	−	9.86965i	−0.0497457	−	0.605147i
$267$	18.3777	−	18.3777i	1.12470	−	1.12470i
$268$	−13.8362	+	19.3254i	−0.845182	+	1.18048i
$269$	−9.08854	−	9.08854i	−0.554138	−	0.554138i	0.373494	−	0.927633i	$-0.378160\pi$
$269$	−9.08854	−	9.08854i	−0.554138	−	0.554138i	−0.927633	+	0.373494i	$0.878160\pi$
$270$	−4.18391	−	3.54829i	−0.254625	−	0.215942i
$271$	16.2292			0.985857			0.492928	−	0.870070i	$-0.335926\pi$
$271$	16.2292			0.985857			0.492928	+	0.870070i	$0.335926\pi$
$272$	−16.0188	+	5.45250i	−0.971285	+	0.330606i
$273$	−8.69856			−0.526461
$274$	20.2344	+	17.1603i	1.22240	+	1.03669i
$275$	−1.52244	−	1.52244i	−0.0918066	−	0.0918066i
$276$	2.23307	+	1.59879i	0.134415	+	0.0962361i
$277$	19.1344	−	19.1344i	1.14968	−	1.14968i	0.163059	−	0.986616i	$-0.447864\pi$
$277$	19.1344	−	19.1344i	1.14968	−	1.14968i	0.986616	−	0.163059i	$-0.0521362\pi$
$278$	−0.440355	−	5.35683i	−0.0264107	−	0.321281i
$279$			4.22971i			0.253226i
$280$	−0.688960	−	2.74323i	−0.0411733	−	0.163940i
$281$		−	8.79118i		−	0.524438i	−0.965008	−	0.262219i	$-0.915546\pi$
$281$		−	8.79118i		−	0.524438i	0.965008	−	0.262219i	$-0.0844542\pi$
$282$	−25.8611	+	2.12589i	−1.54001	+	0.126595i
$283$	−21.1767	+	21.1767i	−1.25882	+	1.25882i	−0.307166	+	0.951656i	$0.599381\pi$
$283$	−21.1767	+	21.1767i	−1.25882	+	1.25882i	−0.951656	+	0.307166i	$0.900619\pi$
$284$	−18.4093	+	3.04723i	−1.09239	+	0.180820i
$285$	10.0007	+	10.0007i	0.592393	+	0.592393i
$286$	−8.48181	+	10.0012i	−0.501540	+	0.591383i
$287$	−7.19853			−0.424916
$288$	5.68101	+	2.23816i	0.334757	+	0.131885i
$289$	0.895811			0.0526948
$290$	8.67398	−	10.2278i	0.509354	−	0.600596i
$291$	−2.17815	−	2.17815i	−0.127685	−	0.127685i
$292$	15.3921	−	2.54780i	0.900752	−	0.149099i
$293$	4.60081	−	4.60081i	0.268782	−	0.268782i	−0.559827	−	0.828609i	$-0.689132\pi$
$293$	4.60081	−	4.60081i	0.268782	−	0.268782i	0.828609	+	0.559827i	$0.189132\pi$
$294$	−2.84676	+	0.234016i	−0.166026	+	0.0136481i
$295$			1.44665i			0.0842270i
$296$	−11.5213	+	2.89356i	−0.669662	+	0.168185i
$297$			8.35200i			0.484632i
$298$	0.989852	+	12.0414i	0.0573406	+	0.697538i
$299$	2.07048	−	2.07048i	0.119739	−	0.119739i
$300$	3.28447	+	2.35156i	0.189629	+	0.135767i
$301$	−5.87122	−	5.87122i	−0.338411	−	0.338411i
$302$	−10.0275	−	8.50415i	−0.577020	−	0.489359i
$303$	3.22655			0.185360
$304$	25.1315	+	12.3675i	1.44139	+	0.709327i
$305$	4.58612			0.262601
$306$	−4.92498	−	4.17677i	−0.281542	−	0.238770i
$307$	7.02452	+	7.02452i	0.400911	+	0.400911i	0.878554	−	0.477643i	$-0.158509\pi$
$307$	7.02452	+	7.02452i	0.400911	+	0.400911i	−0.477643	+	0.878554i	$0.658509\pi$
$308$	−2.50676	+	3.50125i	−0.142836	+	0.199502i
$309$	25.9368	−	25.9368i	1.47549	−	1.47549i
$310$	0.454022	+	5.52309i	0.0257867	+	0.313690i
$311$		−	20.0671i		−	1.13790i	−0.822372	−	0.568950i	$-0.807350\pi$
$311$		−	20.0671i		−	1.13790i	0.822372	−	0.568950i	$-0.192650\pi$
$312$	12.6355	−	21.1108i	0.715342	−	1.19516i
$313$		−	26.2786i		−	1.48536i	−0.669648	−	0.742678i	$-0.733555\pi$
$313$		−	26.2786i		−	1.48536i	0.669648	−	0.742678i	$-0.266445\pi$
$314$	−24.2263	+	1.99150i	−1.36717	+	0.112387i
$315$	0.763250	−	0.763250i	0.0430043	−	0.0430043i
$316$	−2.49856	−	15.0945i	−0.140555	−	0.849134i
$317$	9.81470	+	9.81470i	0.551249	+	0.551249i	0.926801	−	0.375553i	$-0.122547\pi$
$317$	9.81470	+	9.81470i	0.551249	+	0.551249i	−0.375553	+	0.926801i	$0.622547\pi$
$318$	1.81441	−	2.13944i	0.101747	−	0.119974i
$319$	−20.4169			−1.14313
$320$	7.65841	+	2.31274i	0.428118	+	0.129286i
$321$	−6.63168			−0.370145
$322$	0.621900	−	0.733304i	0.0346571	−	0.0408654i
$323$	−20.9464	−	20.9464i	−1.16549	−	1.16549i
$324$	−3.61659	−	21.8489i	−0.200921	−	1.21383i
$325$	3.04533	−	3.04533i	0.168925	−	0.168925i
$326$	7.80723	−	0.641788i	0.432402	−	0.0355453i
$327$			24.5057i			1.35517i
$328$	10.4565	−	17.4703i	0.577365	−	0.964636i
$329$			9.08441i			0.500840i
$330$	−0.503849	−	6.12923i	−0.0277360	−	0.337403i
$331$	−5.73252	+	5.73252i	−0.315088	+	0.315088i	−0.846877	−	0.531789i	$-0.821520\pi$
$331$	−5.73252	+	5.73252i	−0.315088	+	0.315088i	0.531789	+	0.846877i	$0.321520\pi$
$332$	−11.8183	+	16.5069i	−0.648615	+	0.905935i
$333$	−3.20557	−	3.20557i	−0.175664	−	0.175664i
$334$	−9.16541	−	7.77300i	−0.501509	−	0.425320i
$335$	−11.8839			−0.649288
$336$	3.56724	−	7.24881i	0.194609	−	0.395455i
$337$	−24.4896			−1.33403			−0.667017	−	0.745043i	$-0.732429\pi$
$337$	−24.4896			−1.33403			−0.667017	+	0.745043i	$0.732429\pi$
$338$	−5.98398	−	5.07489i	−0.325486	−	0.276038i
$339$	5.42743	+	5.42743i	0.294778	+	0.294778i
$340$	−6.87929	−	4.92531i	−0.373082	−	0.267112i
$341$	5.96581	−	5.96581i	0.323067	−	0.323067i
$342$	0.875746	+	10.6533i	0.0473549	+	0.576064i
$343$			1.00000i			0.0539949i
$344$	22.7775	−	5.72054i	1.22808	−	0.308431i
$345$			1.37320i			0.0739308i
$346$	−1.68625	+	0.138617i	−0.0906536	+	0.00745212i
$347$	−16.9156	+	16.9156i	−0.908079	+	0.908079i	−0.996117	−	0.0880378i	$-0.971940\pi$
$347$	−16.9156	+	16.9156i	−0.908079	+	0.908079i	0.0880378	+	0.996117i	$0.471940\pi$
$348$	37.7914	−	6.25551i	2.02583	−	0.335330i
$349$	−8.97985	−	8.97985i	−0.480680	−	0.480680i	0.424669	−	0.905349i	$-0.360391\pi$
$349$	−8.97985	−	8.97985i	−0.480680	−	0.480680i	−0.905349	+	0.424669i	$0.860391\pi$
$350$	0.914710	−	1.07857i	0.0488933	−	0.0576518i
$351$	−16.7065			−0.891726
$352$	−4.85598	−	11.1696i	−0.258825	−	0.595342i
$353$	−17.7023			−0.942197			−0.471098	−	0.882081i	$-0.656142\pi$
$353$	−17.7023			−0.942197			−0.471098	+	0.882081i	$0.656142\pi$
$354$	−2.67266	+	3.15143i	−0.142050	+	0.167496i
$355$	−6.59722	−	6.59722i	−0.350144	−	0.350144i
$356$	25.3903	−	4.20279i	1.34568	−	0.222747i
$357$	−6.04169	+	6.04169i	−0.319760	+	0.319760i
$358$	−20.3367	+	1.67177i	−1.07483	+	0.0883556i
$359$			3.84682i			0.203027i	0.994834	+	0.101514i	$0.0323686\pi$
$359$			3.84682i			0.203027i	−0.994834	+	0.101514i	$0.967631\pi$
$360$	0.743662	+	2.96104i	0.0391945	+	0.156061i
$361$			30.0342i			1.58075i
$362$	2.39110	+	29.0872i	0.125673	+	1.52879i
$363$	9.08944	−	9.08944i	0.477072	−	0.477072i
$364$	−7.00354	−	5.01426i	−0.367085	−	0.262819i
$365$	5.51596	+	5.51596i	0.288719	+	0.288719i
$366$	9.99057	+	8.47280i	0.522216	+	0.442881i
$367$	2.13101			0.111238			0.0556189	−	0.998452i	$-0.482287\pi$
$367$	2.13101			0.111238			0.0556189	+	0.998452i	$0.482287\pi$
$368$	0.876309	+	2.57450i	0.0456808	+	0.134205i
$369$	7.77008			0.404494
$370$	−4.52987	−	3.84169i	−0.235497	−	0.199720i
$371$	−0.694448	−	0.694448i	−0.0360539	−	0.0360539i
$372$	−9.21478	+	12.8705i	−0.477764	+	0.667304i
$373$	−24.1317	+	24.1317i	−1.24949	+	1.24949i	−0.293550	+	0.955944i	$0.594837\pi$
$373$	−24.1317	+	24.1317i	−1.24949	+	1.24949i	−0.955944	+	0.293550i	$0.905163\pi$
$374$	1.05531	+	12.8376i	0.0545685	+	0.663816i
$375$			2.01975i			0.104300i
$376$	−22.0472	−	13.1959i	−1.13700	−	0.680528i
$377$		−	40.8399i		−	2.10336i
$378$	−5.46749	+	0.449451i	−0.281217	+	0.0231173i
$379$	−4.74362	+	4.74362i	−0.243663	+	0.243663i	−0.818364	−	0.574701i	$-0.805119\pi$
$379$	−4.74362	+	4.74362i	−0.243663	+	0.243663i	0.574701	+	0.818364i	$0.305119\pi$
$380$	2.28707	+	13.8169i	0.117324	+	0.708791i
$381$	−19.8146	−	19.8146i	−1.01513	−	1.01513i
$382$	−7.83453	+	9.23796i	−0.400849	+	0.472655i
$383$	13.0622			0.667445			0.333723	−	0.942671i	$-0.391695\pi$
$383$	13.0622			0.667445			0.333723	+	0.942671i	$0.391695\pi$
$384$	12.4106	+	19.1870i	0.633326	+	0.979131i
$385$	−2.15306			−0.109730
$386$	−0.690383	+	0.814054i	−0.0351395	+	0.0414342i
$387$	6.33738	+	6.33738i	0.322147	+	0.322147i
$388$	−0.498120	−	3.00929i	−0.0252882	−	0.152774i
$389$	17.9652	−	17.9652i	0.910870	−	0.910870i	−0.0854704	−	0.996341i	$-0.527239\pi$
$389$	17.9652	−	17.9652i	0.910870	−	0.910870i	0.996341	+	0.0854704i	$0.0272393\pi$
$390$	12.2603	−	1.00785i	0.620823	−	0.0510343i
$391$		−	2.87616i		−	0.145454i
$392$	−2.42693	−	1.45259i	−0.122578	−	0.0733669i
$393$			35.9020i			1.81102i
$394$	2.45755	+	29.8957i	0.123810	+	1.50612i
$395$	5.40934	−	5.40934i	0.272173	−	0.272173i
$396$	2.70579	−	3.77924i	0.135971	−	0.189914i
$397$	−5.26206	−	5.26206i	−0.264095	−	0.264095i	0.562620	−	0.826715i	$-0.309793\pi$
$397$	−5.26206	−	5.26206i	−0.264095	−	0.264095i	−0.826715	+	0.562620i	$0.809793\pi$
$398$	3.87018	+	3.28222i	0.193994	+	0.164523i
$399$	14.1432			0.708045
$400$	1.28890	+	3.78665i	0.0644451	+	0.189333i
$401$	29.6525			1.48078			0.740389	−	0.672179i	$-0.234641\pi$
$401$	29.6525			1.48078			0.740389	+	0.672179i	$0.234641\pi$
$402$	−25.8884	−	21.9554i	−1.29119	−	1.09504i
$403$	11.9334	+	11.9334i	0.594445	+	0.594445i
$404$	2.59781	+	1.85994i	0.129246	+	0.0925353i
$405$	7.82986	−	7.82986i	0.389069	−	0.389069i
$406$	−1.09871	−	13.3656i	−0.0545279	−	0.663322i
$407$			9.04261i			0.448226i
$408$	−5.88665	−	23.4389i	−0.291432	−	1.16040i
$409$			24.0794i			1.19065i	0.803486	+	0.595324i	$0.202976\pi$
$409$			24.0794i			1.19065i	−0.803486	+	0.595324i	$0.797024\pi$
$410$	10.1460	−	0.834048i	0.501077	−	0.0411907i
$411$	−26.7933	+	26.7933i	−1.32161	+	1.32161i
$412$	35.8339	−	5.93148i	1.76541	−	0.292223i
$413$	1.02293	+	1.02293i	0.0503352	+	0.0503352i
$414$	−0.671278	+	0.791527i	−0.0329915	+	0.0389014i
$415$	−10.1508			−0.498281
$416$	22.3425	−	9.71340i	1.09543	−	0.476239i
$417$	7.67633			0.375911
$418$	13.7908	−	16.2612i	0.674528	−	0.795359i
$419$	−3.50849	−	3.50849i	−0.171401	−	0.171401i	0.616194	−	0.787595i	$-0.288674\pi$
$419$	−3.50849	−	3.50849i	−0.171401	−	0.171401i	−0.787595	+	0.616194i	$0.788674\pi$
$420$	3.98528	−	0.659672i	0.194462	−	0.0321887i
$421$	−13.9576	+	13.9576i	−0.680251	+	0.680251i	−0.960057	−	0.279806i	$-0.909730\pi$
$421$	−13.9576	+	13.9576i	−0.680251	+	0.680251i	0.279806	+	0.960057i	$0.409730\pi$
$422$	−14.7205	+	1.21009i	−0.716585	+	0.0589064i
$423$		−	9.80569i		−	0.476769i
$424$	2.69412	−	0.676626i	0.130838	−	0.0328599i
$425$		−	4.23034i		−	0.205202i
$426$	−2.18334	−	26.5599i	−0.105783	−	1.28683i
$427$	3.24288	−	3.24288i	0.156934	−	0.156934i
$428$	−5.33941	−	3.82282i	−0.258090	−	0.184783i
$429$	−13.2430	−	13.2430i	−0.639380	−	0.639380i
$430$	8.95550	+	7.59498i	0.431873	+	0.366262i
$431$	−13.2702			−0.639202			−0.319601	−	0.947552i	$-0.603549\pi$
$431$	−13.2702			−0.639202			−0.319601	+	0.947552i	$0.603549\pi$
$432$	6.85124	−	13.9221i	0.329630	−	0.669826i
$433$	10.5548			0.507231			0.253615	−	0.967305i	$-0.418380\pi$
$433$	10.5548			0.507231			0.253615	+	0.967305i	$0.418380\pi$
$434$	4.22645	+	3.58437i	0.202876	+	0.172055i
$435$	13.5431	+	13.5431i	0.649342	+	0.649342i
$436$	−14.1263	+	19.7305i	−0.676525	+	0.944918i
$437$	−3.36644	+	3.36644i	−0.161039	+	0.161039i
$438$	1.82550	+	22.2069i	0.0872257	+	1.06108i
$439$			17.2905i			0.825228i	0.910906	+	0.412614i	$0.135384\pi$
$439$			17.2905i			0.825228i	−0.910906	+	0.412614i	$0.864616\pi$
$440$	3.12751	−	5.22531i	0.149098	−	0.249107i
$441$		−	1.07940i		−	0.0513999i
$442$	−25.6790	+	2.11092i	−1.22142	+	0.100406i
$443$	0.726214	−	0.726214i	0.0345035	−	0.0345035i	−0.689645	−	0.724148i	$-0.742233\pi$
$443$	0.726214	−	0.726214i	0.0345035	−	0.0345035i	0.724148	+	0.689645i	$0.242233\pi$
$444$	−2.77055	−	16.7378i	−0.131485	−	0.794339i
$445$	9.09898	+	9.09898i	0.431333	+	0.431333i
$446$	−21.0314	+	24.7988i	−0.995864	+	1.17426i
$447$	−17.2552			−0.816145
$448$	7.05067	−	3.77996i	0.333113	−	0.178586i
$449$	−33.3417			−1.57349			−0.786746	−	0.617277i	$-0.788236\pi$
$449$	−33.3417			−1.57349			−0.786746	+	0.617277i	$0.788236\pi$
$450$	−0.987337	+	1.16420i	−0.0465435	+	0.0548810i
$451$	−10.9593	−	10.9593i	−0.516055	−	0.516055i
$452$	1.24120	+	7.49845i	0.0583810	+	0.352698i
$453$	13.2779	−	13.2779i	0.623852	−	0.623852i
$454$	−37.7885	+	3.10638i	−1.77350	+	0.145790i
$455$		−	4.30675i		−	0.201904i
$456$	−20.5443	+	34.3245i	−0.962074	+	1.60739i
$457$		−	31.2939i		−	1.46386i	−0.681377	−	0.731932i	$-0.738619\pi$
$457$		−	31.2939i		−	1.46386i	0.681377	−	0.731932i	$-0.261381\pi$
$458$	0.451707	+	5.49493i	0.0211069	+	0.256761i
$459$	−11.6037	+	11.6037i	−0.541614	+	0.541614i
$460$	−0.791580	+	1.10562i	−0.0369076	+	0.0515497i
$461$	18.5211	+	18.5211i	0.862614	+	0.862614i	0.991641	−	0.129027i	$-0.0411854\pi$
$461$	18.5211	+	18.5211i	0.862614	+	0.862614i	−0.129027	+	0.991641i	$0.541185\pi$
$462$	−4.69029	−	3.97774i	−0.218212	−	0.185061i
$463$	−8.78852			−0.408437			−0.204219	−	0.978925i	$-0.565465\pi$
$463$	−8.78852			−0.408437			−0.204219	+	0.978925i	$0.565465\pi$
$464$	34.0332	+	16.7482i	1.57995	+	0.777516i
$465$	−7.91457			−0.367029
$466$	0.448868	+	0.380676i	0.0207934	+	0.0176345i
$467$	−20.3190	−	20.3190i	−0.940250	−	0.940250i	0.0580630	−	0.998313i	$-0.481508\pi$
$467$	−20.3190	−	20.3190i	−0.940250	−	0.940250i	−0.998313	+	0.0580630i	$0.981508\pi$
$468$	7.55960	+	5.41239i	0.349443	+	0.250188i
$469$	−8.40320	+	8.40320i	−0.388024	+	0.388024i
$470$	−1.05255	−	12.8041i	−0.0485506	−	0.590609i
$471$		−	34.7162i		−	1.59964i
$472$	−3.96849	+	0.996681i	−0.182664	+	0.0458760i
$473$		−	17.8771i		−	0.821992i
$474$	21.7776	−	1.79021i	1.00028	−	0.0822272i
$475$	−4.95147	+	4.95147i	−0.227189	+	0.227189i
$476$	−8.34711	+	1.38167i	−0.382589	+	0.0633289i
$477$	0.749586	+	0.749586i	0.0343212	+	0.0343212i
$478$	−17.4968	+	20.6311i	−0.800286	+	0.943645i
$479$	−7.61876			−0.348110			−0.174055	−	0.984736i	$-0.555687\pi$
$479$	−7.61876			−0.348110			−0.174055	+	0.984736i	$0.555687\pi$
$480$	−4.18800	+	10.6302i	−0.191155	+	0.485201i
$481$	−18.0879			−0.824738
$482$	−22.0758	+	26.0304i	−1.00553	+	1.18565i
$483$	0.971002	+	0.971002i	0.0441821	+	0.0441821i
$484$	12.5578	−	2.07866i	0.570810	−	0.0944846i
$485$	1.07842	−	1.07842i	0.0489687	−	0.0489687i
$486$	15.1200	−	1.24293i	0.685855	−	0.0563802i
$487$		−	3.96186i		−	0.179529i	−0.995963	−	0.0897646i	$-0.971389\pi$
$487$		−	3.96186i		−	0.179529i	0.995963	−	0.0897646i	$-0.0286115\pi$
$488$	3.15966	+	12.5808i	0.143031	+	0.569506i
$489$			11.1877i			0.505927i
$490$	−0.115864	−	1.40946i	−0.00523419	−	0.0636729i
$491$	4.54089	−	4.54089i	0.204927	−	0.204927i	−0.597180	−	0.802107i	$-0.703712\pi$
$491$	4.54089	−	4.54089i	0.204927	−	0.204927i	0.802107	+	0.597180i	$0.203712\pi$
$492$	23.6434	+	16.9278i	1.06593	+	0.763162i
$493$	−28.3658	−	28.3658i	−1.27753	−	1.27753i
$494$	32.5271	+	27.5856i	1.46346	+	1.24113i
$495$	2.32400			0.104456
$496$	−14.8383	+	5.05068i	−0.666260	+	0.226782i
$497$	−9.32988			−0.418502
$498$	−22.1128	−	18.7534i	−0.990897	−	0.840360i
$499$	29.8861	+	29.8861i	1.33788	+	1.33788i	0.898106	+	0.439778i	$0.144943\pi$
$499$	29.8861	+	29.8861i	1.33788	+	1.33788i	0.439778	+	0.898106i	$0.355057\pi$
$500$	−1.16428	+	1.62618i	−0.0520682	+	0.0727248i
$501$	12.1364	−	12.1364i	0.542212	−	0.542212i
$502$	−1.19714	−	14.5630i	−0.0534311	−	0.649979i
$503$			16.3831i			0.730487i	0.930912	+	0.365243i	$0.119014\pi$
$503$			16.3831i			0.730487i	−0.930912	+	0.365243i	$0.880986\pi$
$504$	2.61962	+	1.56792i	0.116687	+	0.0698409i
$505$			1.59750i			0.0710877i
$506$	2.06322	−	0.169605i	0.0917212	−	0.00753988i
$507$	7.92367	−	7.92367i	0.351902	−	0.351902i
$508$	−4.53140	−	27.3756i	−0.201049	−	1.21460i
$509$	22.5555	+	22.5555i	0.999753	+	0.999753i	1.00000		0.000246942i	$-7.86042e-5\pi$
$509$	22.5555	+	22.5555i	0.999753	+	0.999753i	−0.000246942		1.00000i	$0.500079\pi$
$510$	7.81551	−	9.21554i	0.346077	−	0.408071i
$511$	7.80075			0.345085
$512$	−1.06805	+	22.6022i	−0.0472015	+	0.998885i
$513$	27.1634			1.19930
$514$	8.04713	−	9.48865i	0.354944	−	0.418526i
$515$	12.8416	+	12.8416i	0.565867	+	0.565867i
$516$	5.47735	+	33.0904i	0.241127	+	1.45672i
$517$	−13.8305	+	13.8305i	−0.608263	+	0.608263i
$518$	−5.91959	+	0.486615i	−0.260092	+	0.0213807i
$519$		−	2.41640i		−	0.106068i
$520$	10.4522	+	6.25594i	0.458358	+	0.274341i
$521$		−	33.2930i		−	1.45859i	−0.684198	−	0.729296i	$-0.739848\pi$
$521$		−	33.2930i		−	1.45859i	0.684198	−	0.729296i	$-0.260152\pi$
$522$	1.18594	+	14.4268i	0.0519073	+	0.631442i
$523$	−13.8252	+	13.8252i	−0.604532	+	0.604532i	−0.941512	−	0.336980i	$-0.890595\pi$
$523$	−13.8252	+	13.8252i	−0.604532	+	0.604532i	0.336980	+	0.941512i	$0.390595\pi$
$524$	−20.6956	+	28.9060i	−0.904092	+	1.26277i
$525$	1.42818	+	1.42818i	0.0623309	+	0.0623309i
$526$	−10.5067	−	8.91056i	−0.458116	−	0.388519i
$527$	16.5770			0.722104
$528$	16.4668	−	5.60497i	0.716625	−	0.243925i
$529$	22.5378			0.979902
$530$	1.05926	+	0.898335i	0.0460112	+	0.0390212i
$531$	−1.10415	−	1.10415i	−0.0479161	−	0.0479161i
$532$	11.3872	+	8.15280i	0.493698	+	0.353469i
$533$	21.9219	−	21.9219i	0.949543	−	0.949543i
$534$	3.01129	+	36.6318i	0.130311	+	1.58521i
$535$		−	3.28341i		−	0.141954i
$536$	−8.18755	−	32.6004i	−0.353648	−	1.40812i
$537$		−	29.1425i		−	1.25759i
$538$	18.1160	−	1.48921i	0.781035	−	0.0642045i
$539$	−1.52244	+	1.52244i	−0.0655761	+	0.0655761i
$540$	7.65413	−	1.26697i	0.329381	−	0.0545216i
$541$	14.8108	+	14.8108i	0.636766	+	0.636766i	0.949756	−	0.312990i	$-0.101331\pi$
$541$	14.8108	+	14.8108i	0.636766	+	0.636766i	−0.312990	+	0.949756i	$0.601331\pi$
$542$	−14.8451	+	17.5043i	−0.637650	+	0.751875i
$543$	−41.6820			−1.78874
$544$	8.77171	−	22.2648i	0.376084	−	0.954597i
$545$	−12.1330			−0.519722
$546$	7.95667	−	9.38198i	0.340514	−	0.401512i
$547$	27.0140	+	27.0140i	1.15503	+	1.15503i	0.985529	+	0.169505i	$0.0542168\pi$
$547$	27.0140	+	27.0140i	1.15503	+	1.15503i	0.169505	+	0.985529i	$0.445783\pi$
$548$	−37.0171	+	6.12734i	−1.58129	+	0.261747i
$549$	−3.50036	+	3.50036i	−0.149392	+	0.149392i
$550$	3.03464	−	0.249461i	0.129398	−	0.0106370i
$551$			66.4025i			2.82884i
$552$	−3.76702	+	0.946083i	−0.160335	+	0.0402680i
$553$		−	7.64996i		−	0.325309i
$554$	3.13529	+	38.1402i	0.133206	+	1.62042i
$555$	5.99821	−	5.99821i	0.254610	−	0.254610i
$556$	6.18049	+	4.42500i	0.262111	+	0.187662i
$557$	14.9099	+	14.9099i	0.631751	+	0.631751i	0.948507	−	0.316756i	$-0.102594\pi$
$557$	14.9099	+	14.9099i	0.631751	+	0.631751i	−0.316756	+	0.948507i	$0.602594\pi$
$558$	−4.56203	−	3.86896i	−0.193126	−	0.163786i
$559$	35.7596			1.51247
$560$	3.58896	+	1.76618i	0.151661	+	0.0746345i
$561$	−18.3962			−0.776690
$562$	9.48187	+	8.04138i	0.399968	+	0.339205i
$563$	11.0902	+	11.0902i	0.467396	+	0.467396i	0.901070	−	0.433674i	$-0.142783\pi$
$563$	11.0902	+	11.0902i	0.467396	+	0.467396i	−0.433674	+	0.901070i	$0.642783\pi$
$564$	21.3625	−	29.8375i	0.899524	−	1.25639i
$565$	−2.68718	+	2.68718i	−0.113050	+	0.113050i
$566$	−3.46992	−	42.2109i	−0.145852	−	1.77426i
$567$		−	11.0731i		−	0.465026i
$568$	13.5525	−	22.6429i	0.568650	−	0.950077i
$569$		−	33.1950i		−	1.39161i	−0.718233	−	0.695803i	$-0.755049\pi$
$569$		−	33.1950i		−	1.39161i	0.718233	−	0.695803i	$-0.244951\pi$
$570$	−19.9343	+	1.63868i	−0.834954	+	0.0686368i
$571$	−10.7914	+	10.7914i	−0.451606	+	0.451606i	−0.895887	−	0.444281i	$-0.853459\pi$
$571$	−10.7914	+	10.7914i	−0.451606	+	0.451606i	0.444281	+	0.895887i	$0.353459\pi$
$572$	−3.02855	−	18.2964i	−0.126630	−	0.765010i
$573$	−12.2324	−	12.2324i	−0.511016	−	0.511016i
$574$	6.58457	−	7.76409i	0.274835	−	0.324067i
$575$	−0.679888			−0.0283533
$576$	−7.61048	+	4.08008i	−0.317103	+	0.170003i
$577$	−8.50740			−0.354168			−0.177084	−	0.984196i	$-0.556666\pi$
$577$	−8.50740			−0.354168			−0.177084	+	0.984196i	$0.556666\pi$
$578$	−0.819407	+	0.966191i	−0.0340829	+	0.0401883i
$579$	−1.07793	−	1.07793i	−0.0447971	−	0.0447971i
$580$	3.09717	+	18.7109i	0.128603	+	0.776929i
$581$	−7.17767	+	7.17767i	−0.297780	+	0.297780i
$582$	4.34165	−	0.356902i	0.179967	−	0.0147941i
$583$		−	2.11451i		−	0.0875741i
$584$	−11.3313	+	18.9319i	−0.468893	+	0.783406i
$585$			4.64870i			0.192200i
$586$	0.753870	+	9.17069i	0.0311421	+	0.378838i
$587$	29.2585	−	29.2585i	1.20763	−	1.20763i	0.235835	−	0.971793i	$-0.424218\pi$
$587$	29.2585	−	29.2585i	1.20763	−	1.20763i	0.971793	−	0.235835i	$-0.0757823\pi$
$588$	2.35156	−	3.28447i	0.0969766	−	0.135449i
$589$	−19.4028	−	19.4028i	−0.799477	−	0.799477i
$590$	−1.56030	−	1.32326i	−0.0642367	−	0.0544778i
$591$	−42.8405			−1.76222
$592$	7.41776	−	15.0733i	0.304868	−	0.619507i
$593$	16.7356			0.687249			0.343624	−	0.939107i	$-0.388345\pi$
$593$	16.7356			0.687249			0.343624	+	0.939107i	$0.388345\pi$
$594$	−9.00819	−	7.63966i	−0.369610	−	0.313459i
$595$	−2.99130	−	2.99130i	−0.122632	−	0.122632i
$596$	−13.8928	−	9.94674i	−0.569073	−	0.407434i
$597$	−5.12468	+	5.12468i	−0.209739	+	0.209739i
$598$	0.339261	+	4.12704i	0.0138734	+	0.168767i
$599$		−	12.3404i		−	0.504215i	−0.967699	−	0.252108i	$-0.918876\pi$
$599$		−	12.3404i		−	0.504215i	0.967699	−	0.252108i	$-0.0811237\pi$
$600$	−5.54065	+	1.39153i	−0.226196	+	0.0568089i
$601$			16.7912i			0.684925i	0.939531	+	0.342463i	$0.111261\pi$
$601$			16.7912i			0.684925i	−0.939531	+	0.342463i	$0.888739\pi$
$602$	11.7030	−	0.962033i	0.476977	−	0.0392096i
$603$	9.07040	−	9.07040i	0.369375	−	0.369375i
$604$	18.3446	−	3.03653i	0.746430	−	0.123554i
$605$	4.50028	+	4.50028i	0.182962	+	0.182962i
$606$	−2.95136	+	3.48005i	−0.119891	+	0.141367i
$607$	22.6479			0.919251			0.459625	−	0.888113i	$-0.347984\pi$
$607$	22.6479			0.919251			0.459625	+	0.888113i	$0.347984\pi$
$608$	−36.3272	+	15.7932i	−1.47326	+	0.640500i
$609$	19.1528			0.776112
$610$	−4.19497	+	4.94644i	−0.169849	+	0.200275i
$611$	−27.6650	−	27.6650i	−1.11921	−	1.11921i
$612$	9.00985	−	1.49138i	0.364202	−	0.0602853i
$613$	−22.4499	+	22.4499i	−0.906743	+	0.906743i	−0.996008	−	0.0892648i	$-0.971548\pi$
$613$	−22.4499	+	22.4499i	−0.906743	+	0.906743i	0.0892648	+	0.996008i	$0.471548\pi$
$614$	−14.0018	+	1.15101i	−0.565067	+	0.0464510i
$615$			14.5392i			0.586279i
$616$	−1.48337	−	5.90634i	−0.0597667	−	0.237973i
$617$			5.27185i			0.212237i	0.994354	+	0.106118i	$0.0338423\pi$
$617$			5.27185i			0.212237i	−0.994354	+	0.106118i	$0.966158\pi$
$618$	4.24990	+	51.6992i	0.170956	+	2.07965i
$619$	9.69037	−	9.69037i	0.389489	−	0.389489i	−0.485016	−	0.874505i	$-0.661186\pi$
$619$	9.69037	−	9.69037i	0.389489	−	0.389489i	0.874505	+	0.485016i	$0.161186\pi$
$620$	−6.37231	−	4.56233i	−0.255918	−	0.183228i
$621$	1.86491	+	1.86491i	0.0748362	+	0.0748362i
$622$	21.6437	+	18.3556i	0.867833	+	0.735991i
$623$	12.8679			0.515542
$624$	11.2116	+	32.9384i	0.448823	+	1.31859i
$625$	−1.00000			−0.0400000
$626$	28.3433	+	24.0373i	1.13282	+	0.960726i
$627$	21.5322	+	21.5322i	0.859912	+	0.859912i
$628$	20.0121	−	27.9513i	0.798568	−	1.11538i
$629$	−12.5632	+	12.5632i	−0.500927	+	0.500927i
$630$	0.125063	+	1.52137i	0.00498263	+	0.0606127i
$631$			7.99096i			0.318115i	0.987269	+	0.159057i	$0.0508455\pi$
$631$			7.99096i			0.318115i	−0.987269	+	0.159057i	$0.949154\pi$
$632$	18.5659	+	11.1123i	0.738512	+	0.442022i
$633$		−	21.0945i		−	0.838432i
$634$	−19.5634	+	1.60820i	−0.776962	+	0.0638697i
$635$	9.81043	−	9.81043i	0.389315	−	0.389315i
$636$	0.647862	+	3.91393i	0.0256894	+	0.155197i
$637$	−3.04533	−	3.04533i	−0.120660	−	0.120660i
$638$	18.6756	−	22.0210i	0.739372	−	0.871819i
$639$	10.0707			0.398389
$640$	−9.49967	+	6.14461i	−0.375507	+	0.242887i
$641$	29.3348			1.15866			0.579328	−	0.815094i	$-0.303315\pi$
$641$	29.3348			1.15866			0.579328	+	0.815094i	$0.303315\pi$
$642$	6.06607	−	7.15271i	0.239409	−	0.282295i
$643$	−1.12280	−	1.12280i	−0.0442788	−	0.0442788i	0.684621	−	0.728900i	$-0.259968\pi$
$643$	−1.12280	−	1.12280i	−0.0442788	−	0.0442788i	−0.728900	+	0.684621i	$0.759968\pi$
$644$	0.222058	+	1.34152i	0.00875032	+	0.0528633i
$645$	−11.8584	+	11.8584i	−0.466924	+	0.466924i
$646$	41.7520	−	3.43220i	1.64271	−	0.135038i
$647$			18.2087i			0.715858i	0.933749	+	0.357929i	$0.116517\pi$
$647$			18.2087i			0.715858i	−0.933749	+	0.357929i	$0.883483\pi$
$648$	26.8736	+	16.0847i	1.05569	+	0.631866i
$649$			3.11471i			0.122263i
$650$	0.498996	+	6.07019i	0.0195722	+	0.238092i
$651$	−5.59645	+	5.59645i	−0.219342	+	0.219342i
$652$	−6.44914	+	9.00766i	−0.252568	+	0.352767i
$653$	−0.00152781	−	0.00152781i	−5.97879e−5	−	5.97879e-5i	0.707077	−	0.707137i	$-0.250013\pi$
$653$	−0.00152781	−	0.00152781i	−5.97879e−5	−	5.97879e-5i	−0.707137	+	0.707077i	$0.750013\pi$
$654$	−26.4310	−	22.4156i	−1.03354	−	0.876521i
$655$	−17.7755			−0.694545
$656$	9.27820	+	27.2583i	0.362253	+	1.06426i
$657$	−8.42012			−0.328500
$658$	−9.79813	−	8.30960i	−0.381971	−	0.323942i
$659$	8.94514	+	8.94514i	0.348453	+	0.348453i	0.859533	−	0.511080i	$-0.170754\pi$
$659$	8.94514	+	8.94514i	0.348453	+	0.348453i	−0.511080	+	0.859533i	$0.670754\pi$
$660$	7.07166	+	5.06303i	0.275264	+	0.197078i
$661$	−5.25836	+	5.25836i	−0.204527	+	0.204527i	−0.801936	−	0.597410i	$-0.796197\pi$
$661$	−5.25836	+	5.25836i	−0.204527	+	0.204527i	0.597410	+	0.801936i	$0.296197\pi$
$662$	−0.939307	−	11.4265i	−0.0365072	−	0.444103i
$663$		−	36.7979i		−	1.42911i
$664$	−6.99347	−	27.8459i	−0.271399	−	1.08063i
$665$			7.00244i			0.271543i
$666$	6.38959	−	0.525252i	0.247592	−	0.0203531i
$667$	−4.55887	+	4.55887i	−0.176520	+	0.176520i
$668$	16.7674	−	2.77546i	0.648750	−	0.107386i
$669$	−32.8372	−	32.8372i	−1.26956	−	1.26956i
$670$	10.8703	−	12.8176i	0.419958	−	0.495187i
$671$	9.87418			0.381188
$672$	4.55533	+	10.4781i	0.175726	+	0.404200i
$673$	−31.8824			−1.22898			−0.614488	−	0.788926i	$-0.710637\pi$
$673$	−31.8824			−1.22898			−0.614488	+	0.788926i	$0.710637\pi$
$674$	22.4009	−	26.4136i	0.862850	−	1.01742i
$675$	2.74297	+	2.74297i	0.105577	+	0.105577i
$676$	10.9472	−	1.81206i	0.421047	−	0.0696947i
$677$	−32.7562	+	32.7562i	−1.25892	+	1.25892i	−0.307313	+	0.951608i	$0.599430\pi$
$677$	−32.7562	+	32.7562i	−1.25892	+	1.25892i	−0.951608	+	0.307313i	$0.900570\pi$
$678$	−10.8184	+	0.889317i	−0.415477	+	0.0341540i
$679$		−	1.52512i		−	0.0585288i
$680$	11.6048	−	2.91454i	0.445025	−	0.111767i
$681$		−	54.1508i		−	2.07507i
$682$	0.977534	+	11.8915i	0.0374317	+	0.455350i
$683$	−10.0732	+	10.0732i	−0.385442	+	0.385442i	−0.873058	−	0.487616i	$-0.837867\pi$
$683$	−10.0732	+	10.0732i	−0.385442	+	0.385442i	0.487616	+	0.873058i	$0.337867\pi$
$684$	−12.2913	−	8.80012i	−0.469971	−	0.336481i
$685$	−13.2656	−	13.2656i	−0.506853	−	0.506853i
$686$	−1.07857	−	0.914710i	−0.0411798	−	0.0349238i
$687$	−7.87422			−0.300420
$688$	−14.6648	+	29.7997i	−0.559091	+	1.13610i
$689$	4.22965			0.161137
$690$	−1.48109	−	1.25608i	−0.0563842	−	0.0478183i
$691$	−28.5203	−	28.5203i	−1.08497	−	1.08497i	−0.996038	−	0.0889269i	$-0.971656\pi$
$691$	−28.5203	−	28.5203i	−1.08497	−	1.08497i	−0.0889269	−	0.996038i	$-0.528344\pi$
$692$	1.39293	−	1.94553i	0.0529511	−	0.0739580i
$693$	1.64332	−	1.64332i	0.0624245	−	0.0624245i
$694$	−2.77173	−	33.7176i	−0.105213	−	1.27990i
$695$			3.80063i			0.144166i
$696$	−27.8212	+	46.4825i	−1.05456	+	1.76192i
$697$		−	30.4522i		−	1.15346i
$698$	17.8993	−	1.47140i	0.677499	−	0.0556934i
$699$	−0.594368	+	0.594368i	−0.0224810	+	0.0224810i
$700$	0.326610	+	1.97315i	0.0123447	+	0.0745781i
$701$	−8.90484	−	8.90484i	−0.336331	−	0.336331i	0.518653	−	0.854985i	$-0.326434\pi$
$701$	−8.90484	−	8.90484i	−0.336331	−	0.336331i	−0.854985	+	0.518653i	$0.826434\pi$
$702$	15.2816	−	18.0190i	0.576766	−	0.680085i
$703$	29.4095			1.10920
$704$	16.4890	+	4.97946i	0.621452	+	0.187670i
$705$	18.3482			0.691035
$706$	16.1924	−	19.0931i	0.609411	−	0.718577i
$707$	1.12960	+	1.12960i	0.0424831	+	0.0424831i
$708$	−0.954311	−	5.76528i	−0.0358652	−	0.216673i
$709$	27.5017	−	27.5017i	1.03285	−	1.03285i	0.0334080	−	0.999442i	$-0.489364\pi$
$709$	27.5017	−	27.5017i	1.03285	−	1.03285i	0.999442	−	0.0334080i	$-0.0106361\pi$
$710$	13.1501	−	1.08099i	0.493514	−	0.0405690i
$711$			8.25735i			0.309675i
$712$	−18.6918	+	31.2295i	−0.700505	+	1.17037i
$713$		−	2.66420i		−	0.0997750i
$714$	−0.989967	−	12.0428i	−0.0370486	−	0.450689i
$715$	6.55677	−	6.55677i	0.245209	−	0.245209i
$716$	16.7991	−	23.4637i	0.627812	−	0.876879i
$717$	−27.3186	−	27.3186i	−1.02023	−	1.02023i
$718$	−4.14905	−	3.51873i	−0.154841	−	0.131318i
$719$	28.2950			1.05523			0.527613	−	0.849485i	$-0.323087\pi$
$719$	28.2950			1.05523			0.527613	+	0.849485i	$0.323087\pi$
$720$	−3.87392	−	1.90641i	−0.144372	−	0.0710476i
$721$	18.1607			0.676341
$722$	−32.3938	−	27.4726i	−1.20557	−	1.02242i
$723$	−34.4681	−	34.4681i	−1.28188	−	1.28188i
$724$	−33.5597	−	24.0274i	−1.24724	−	0.892973i
$725$	−6.70532	+	6.70532i	−0.249030	+	0.249030i
$726$	1.48936	+	18.1178i	0.0552753	+	0.672414i
$727$			10.0207i			0.371648i	0.982583	+	0.185824i	$0.0594955\pi$
$727$			10.0207i			0.371648i	−0.982583	+	0.185824i	$0.940505\pi$
$728$	11.8144	−	2.96718i	0.437872	−	0.109971i
$729$		−	11.5524i		−	0.427867i
$730$	−10.9948	+	0.903823i	−0.406937	+	0.0334520i
$731$	24.8373	−	24.8373i	0.918639	−	0.918639i
$732$	−18.2770	+	3.02533i	−0.675536	+	0.111820i
$733$	−14.1699	−	14.1699i	−0.523378	−	0.523378i	0.395212	−	0.918590i	$-0.370671\pi$
$733$	−14.1699	−	14.1699i	−0.523378	−	0.523378i	−0.918590	+	0.395212i	$0.870671\pi$
$734$	−1.94926	+	2.29844i	−0.0719484	+	0.0848368i
$735$	2.01975			0.0744997
$736$	−3.57833	−	1.40976i	−0.131899	−	0.0519645i
$737$	−25.5867			−0.942500
$738$	−7.10737	+	8.38054i	−0.261626	+	0.308492i
$739$	−35.7497	−	35.7497i	−1.31508	−	1.31508i	−0.917623	−	0.397453i	$-0.869894\pi$
$739$	−35.7497	−	35.7497i	−1.31508	−	1.31508i	−0.397453	−	0.917623i	$-0.630106\pi$
$740$	8.28703	−	1.37173i	0.304637	−	0.0504258i
$741$	−43.0707	+	43.0707i	−1.58224	+	1.58224i
$742$	1.38423	−	0.113789i	0.0508166	−	0.00417734i
$743$			14.7322i			0.540472i	0.962794	+	0.270236i	$0.0871017\pi$
$743$			14.7322i			0.540472i	−0.962794	+	0.270236i	$0.912898\pi$
$744$	−5.45283	−	21.7115i	−0.199910	−	0.795983i
$745$		−	8.54325i		−	0.313001i
$746$	−3.95413	−	48.1012i	−0.144771	−	1.76111i
$747$	7.74756	−	7.74756i	0.283469	−	0.283469i
$748$	−14.8115	−	10.6045i	−0.541562	−	0.387737i
$749$	−2.32172	−	2.32172i	−0.0848340	−	0.0848340i
$750$	−2.17844	−	1.84749i	−0.0795452	−	0.0674607i
$751$	15.0294			0.548430			0.274215	−	0.961668i	$-0.411582\pi$
$751$	15.0294			0.548430			0.274215	+	0.961668i	$0.411582\pi$
$752$	34.3995	−	11.7089i	1.25442	−	0.426980i
$753$	20.8688			0.760500
$754$	44.0485	+	37.3566i	1.60415	+	1.36045i
$755$	6.57404	+	6.57404i	0.239254	+	0.239254i
$756$	4.51641	−	6.30817i	0.164260	−	0.229426i
$757$	−28.0160	+	28.0160i	−1.01826	+	1.01826i	−0.0184297	+	0.999830i	$0.505867\pi$
$757$	−28.0160	+	28.0160i	−1.01826	+	1.01826i	−0.999830	+	0.0184297i	$0.994133\pi$
$758$	−0.777270	−	9.45534i	−0.0282317	−	0.343433i
$759$			2.95659i			0.107317i
$760$	−16.9944	−	10.1717i	−0.616452	−	0.368966i
$761$		−	5.35351i		−	0.194065i	−0.995281	−	0.0970323i	$-0.969065\pi$
$761$		−	5.35351i		−	0.194065i	0.995281	−	0.0970323i	$-0.0309350\pi$
$762$	39.4961	−	3.24675i	1.43079	−	0.117617i
$763$	−8.57935	+	8.57935i	−0.310593	+	0.310593i
$764$	−2.79743	−	16.9001i	−0.101207	−	0.611424i
$765$	3.22881	+	3.22881i	0.116738	+	0.116738i
$766$	−11.9481	+	14.0884i	−0.431702	+	0.509035i
$767$	−6.23034			−0.224965
$768$	−32.0465	−	4.16487i	−1.15638	−	0.150287i
$769$	5.53347			0.199542			0.0997709	−	0.995010i	$-0.468189\pi$
$769$	5.53347			0.199542			0.0997709	+	0.995010i	$0.468189\pi$
$770$	1.96942	−	2.32221i	0.0709730	−	0.0836867i
$771$	12.5644	+	12.5644i	0.452494	+	0.452494i
$772$	−0.246511	−	1.48925i	−0.00887212	−	0.0535992i
$773$	25.0955	−	25.0955i	0.902623	−	0.902623i	−0.0930393	−	0.995662i	$-0.529658\pi$
$773$	25.0955	−	25.0955i	0.902623	−	0.902623i	0.995662	+	0.0930393i	$0.0296582\pi$
$774$	−12.6321	+	1.03842i	−0.454053	+	0.0373251i
$775$		−	3.91859i		−	0.140760i
$776$	3.70136	+	2.21538i	0.132871	+	0.0795274i
$777$		−	8.48275i		−	0.304317i
$778$	2.94370	+	35.8096i	0.105537	+	1.28383i
$779$	−35.6433	+	35.6433i	−1.27705	+	1.27705i
$780$	−10.1276	+	14.1454i	−0.362625	+	0.506487i
$781$	−14.2042	−	14.2042i	−0.508266	−	0.508266i
$782$	3.10213	+	2.63085i	0.110932	+	0.0940791i
$783$	36.7850			1.31459
$784$	3.78665	−	1.28890i	0.135238	−	0.0460322i
$785$	17.1883			0.613478
$786$	−38.7227	−	32.8399i	−1.38119	−	1.17136i
$787$	18.4623	+	18.4623i	0.658108	+	0.658108i	0.954932	−	0.296824i	$-0.0959274\pi$
$787$	18.4623	+	18.4623i	0.658108	+	0.658108i	−0.296824	+	0.954932i	$0.595927\pi$
$788$	−34.4924	−	24.6953i	−1.22874	−	0.879732i
$789$	13.9125	−	13.9125i	0.495297	−	0.495297i
$790$	0.886352	+	10.7823i	0.0315350	+	0.383617i
$791$			3.80024i			0.135121i
$792$	1.60115	+	6.37529i	0.0568943	+	0.226536i
$793$			19.7513i			0.701388i
$794$	10.4887	−	0.862220i	0.372231	−	0.0305990i
$795$	−1.40261	+	1.40261i	−0.0497456	+	0.0497456i
$796$	−7.08018	+	1.17196i	−0.250950	+	0.0415391i
$797$	6.72328	+	6.72328i	0.238151	+	0.238151i	0.816084	−	0.577933i	$-0.196141\pi$
$797$	6.72328	+	6.72328i	0.238151	+	0.238151i	−0.577933	+	0.816084i	$0.696141\pi$
$798$	−12.9369	+	15.2544i	−0.457962	+	0.539999i
$799$	−38.4302			−1.35956
$800$	−5.26313	−	2.07352i	−0.186080	−	0.0733101i
$801$	−13.8896			−0.490765
$802$	−27.1235	+	31.9822i	−0.957764	+	1.12933i
$803$	11.8762	+	11.8762i	0.419101	+	0.419101i
$804$	47.3607	−	7.83949i	1.67028	−	0.276477i
$805$	−0.480753	+	0.480753i	−0.0169443	+	0.0169443i
$806$	−23.7866	+	1.95536i	−0.837846	+	0.0688745i
$807$			25.9602i			0.913841i
$808$	−4.38231	+	1.10061i	−0.154169	+	0.0387194i
$809$			30.9713i			1.08889i	0.838795	+	0.544447i	$0.183260\pi$
$809$			30.9713i			1.08889i	−0.838795	+	0.544447i	$0.816740\pi$
$810$	1.28297	+	15.6071i	0.0450789	+	0.548377i
$811$	29.5092	−	29.5092i	1.03621	−	1.03621i	0.0368872	−	0.999319i	$-0.488256\pi$
$811$	29.5092	−	29.5092i	1.03621	−	1.03621i	0.999319	−	0.0368872i	$-0.0117442\pi$
$812$	15.4206	+	11.0406i	0.541159	+	0.387449i
$813$	−23.1783	−	23.1783i	−0.812898	−	0.812898i
$814$	−9.75306	−	8.27137i	−0.341845	−	0.289911i
$815$	−5.53916			−0.194028
$816$	30.6649	+	15.0906i	1.07349	+	0.528278i
$817$	−58.1423			−2.03414
$818$	−25.9712	−	22.0256i	−0.908061	−	0.770109i
$819$	3.28713	+	3.28713i	0.114861	+	0.114861i
$820$	−8.38110	+	11.7061i	−0.292681	+	0.408794i
$821$	16.6064	−	16.6064i	0.579568	−	0.579568i	−0.355216	−	0.934784i	$-0.615593\pi$
$821$	16.6064	−	16.6064i	0.579568	−	0.579568i	0.934784	+	0.355216i	$0.115593\pi$
$822$	−4.39023	−	53.4064i	−0.153127	−	1.86276i
$823$		−	35.3414i		−	1.23192i	−0.787775	−	0.615962i	$-0.788767\pi$
$823$		−	35.3414i		−	1.23192i	0.787775	−	0.615962i	$-0.211233\pi$
$824$	−26.3801	+	44.0748i	−0.918995	+	1.53542i
$825$			4.34864i			0.151400i
$826$	−2.03899	+	0.167614i	−0.0709455	+	0.00583202i
$827$	13.6565	−	13.6565i	0.474882	−	0.474882i	−0.428609	−	0.903490i	$-0.640996\pi$
$827$	13.6565	−	13.6565i	0.474882	−	0.474882i	0.903490	+	0.428609i	$0.140996\pi$
$828$	−0.239689	−	1.44804i	−0.00832978	−	0.0503227i
$829$	13.1434	+	13.1434i	0.456489	+	0.456489i	0.897501	−	0.441012i	$-0.145381\pi$
$829$	13.1434	+	13.1434i	0.456489	+	0.456489i	−0.441012	+	0.897501i	$0.645381\pi$
$830$	9.28500	−	10.9483i	0.322287	−	0.380020i
$831$	−54.6548			−1.89595
$832$	−9.96039	+	32.9828i	−0.345314	+	1.14347i
$833$	−4.23034			−0.146573
$834$	−7.02162	+	8.27943i	−0.243139	+	0.286693i
$835$	6.00883	+	6.00883i	0.207944	+	0.207944i
$836$	4.92418	+	29.7485i	0.170306	+	1.02887i
$837$	−10.7485	+	10.7485i	−0.371524	+	0.371524i
$838$	6.99339	−	0.574886i	0.241582	−	0.0198591i
$839$		−	22.5764i		−	0.779425i	−0.920937	−	0.389713i	$-0.872574\pi$
$839$		−	22.5764i		−	0.779425i	0.920937	−	0.389713i	$-0.127426\pi$
$840$	−2.93387	+	4.90179i	−0.101228	+	0.169128i
$841$			60.9228i			2.10078i
$842$	−2.28703	−	27.8213i	−0.0788163	−	0.958786i
$843$	−12.5554	+	12.5554i	−0.432430	+	0.432430i
$844$	12.1599	−	16.9840i	0.418560	−	0.584612i
$845$	3.92309	+	3.92309i	0.134958	+	0.134958i
$846$	10.5761	+	8.96937i	0.363613	+	0.308373i
$847$	6.36435			0.218682
$848$	−1.73456	+	3.52471i	−0.0595649	+	0.121039i
$849$	60.4882			2.07595
$850$	4.56271	+	3.86954i	0.156500	+	0.132724i
$851$	2.01911	+	2.01911i	0.0692143	+	0.0692143i
$852$	30.6437	+	21.9397i	1.04984	+	0.751643i
$853$	−11.1452	+	11.1452i	−0.381603	+	0.381603i	−0.871680	−	0.490076i	$-0.836969\pi$
$853$	−11.1452	+	11.1452i	−0.381603	+	0.381603i	0.490076	+	0.871680i	$0.336969\pi$
$854$	0.531365	+	6.46395i	0.0181829	+	0.221192i
$855$		−	7.55842i		−	0.258493i
$856$	9.00718	−	2.26214i	0.307859	−	0.0773184i
$857$			30.0667i			1.02706i	0.858072	+	0.513530i	$0.171662\pi$
$857$			30.0667i			1.02706i	−0.858072	+	0.513530i	$0.828338\pi$
$858$	26.3971	−	2.16995i	0.901180	−	0.0740809i
$859$	−33.9373	+	33.9373i	−1.15793	+	1.15793i	−0.173005	+	0.984921i	$0.555348\pi$
$859$	−33.9373	+	33.9373i	−1.15793	+	1.15793i	−0.984921	+	0.173005i	$0.944652\pi$
$860$	−16.3834	+	2.71189i	−0.558668	+	0.0924748i
$861$	10.2808	+	10.2808i	0.350369	+	0.350369i
$862$	12.1384	−	14.3128i	0.413435	−	0.487495i
$863$	−46.1679			−1.57157			−0.785787	−	0.618497i	$-0.787742\pi$
$863$	−46.1679			−1.57157			−0.785787	+	0.618497i	$0.787742\pi$
$864$	8.74898	+	20.1242i	0.297646	+	0.684638i
$865$	1.19638			0.0406783
$866$	−9.65457	+	11.3840i	−0.328076	+	0.386845i
$867$	−1.27938	−	1.27938i	−0.0434500	−	0.0434500i
$868$	−7.73196	+	1.27985i	−0.262440	+	0.0434409i
$869$	11.6466	−	11.6466i	0.395084	−	0.395084i
$870$	−26.9951	+	2.21912i	−0.915221	+	0.0752351i
$871$		−	51.1811i		−	1.73420i
$872$	−8.35918	−	33.2838i	−0.283078	−	1.12713i
$873$			1.64621i			0.0557158i
$874$	−0.551612	−	6.71025i	−0.0186586	−	0.226978i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	−25.6214	−	18.3439i	−0.865666	−	0.619783i
$877$	8.76639	+	8.76639i	0.296020	+	0.296020i	0.839453	−	0.543433i	$-0.182876\pi$
$877$	8.76639	+	8.76639i	0.296020	+	0.296020i	−0.543433	+	0.839453i	$0.682876\pi$
$878$	−18.6489	−	15.8158i	−0.629370	−	0.533756i
$879$	−13.1416			−0.443254
$880$	2.77508	+	8.15287i	0.0935479	+	0.274833i
$881$	18.5740			0.625775			0.312888	−	0.949790i	$-0.398704\pi$
$881$	18.5740			0.625775			0.312888	+	0.949790i	$0.398704\pi$
$882$	1.16420	+	0.987337i	0.0392007	+	0.0332454i
$883$	13.6335	+	13.6335i	0.458802	+	0.458802i	0.898262	−	0.439460i	$-0.144830\pi$
$883$	13.6335	+	13.6335i	0.458802	+	0.458802i	−0.439460	+	0.898262i	$0.644830\pi$
$884$	21.2121	−	29.6274i	0.713439	−	0.996476i
$885$	2.06607	−	2.06607i	0.0694502	−	0.0694502i
$886$	0.118994	+	1.44754i	0.00399770	+	0.0486312i
$887$			22.5386i			0.756771i	0.925648	+	0.378386i	$0.123521\pi$
$887$			22.5386i			0.756771i	−0.925648	+	0.378386i	$0.876479\pi$
$888$	20.5870	+	12.3220i	0.690855	+	0.413498i
$889$		−	13.8740i		−	0.465321i
$890$	−18.1368	+	1.49092i	−0.607947	+	0.0499758i
$891$	16.8581	−	16.8581i	0.564768	−	0.564768i
$892$	−7.50954	−	45.3674i	−0.251438	−	1.51901i
$893$	44.9812	+	44.9812i	1.50524	+	1.50524i
$894$	15.7836	−	18.6109i	0.527881	−	0.622443i
$895$	14.4287			0.482300
$896$	−2.37238	+	11.0622i	−0.0792557	+	0.369561i
$897$	−5.91405			−0.197464
$898$	30.4980	−	35.9612i	1.01773	−	1.20004i
$899$	−26.2754	−	26.2754i	−0.876333	−	0.876333i
$900$	−0.352542	−	2.12982i	−0.0117514	−	0.0709939i
$901$	2.93775	−	2.93775i	0.0978708	−	0.0978708i
$902$	21.8450	−	1.79575i	0.727358	−	0.0597920i
$903$			16.7703i			0.558081i
$904$	−9.22292	−	5.52020i	−0.306750	−	0.183599i
$905$		−	20.6372i		−	0.686003i
$906$	2.17567	+	26.4666i	0.0722817	+	0.879293i
$907$	28.4879	−	28.4879i	0.945924	−	0.945924i	−0.0526874	−	0.998611i	$-0.516779\pi$
$907$	28.4879	−	28.4879i	0.945924	−	0.945924i	0.998611	+	0.0526874i	$0.0167787\pi$
$908$	31.2151	−	43.5988i	1.03591	−	1.44688i
$909$	−1.21929	−	1.21929i	−0.0404413	−	0.0404413i
$910$	4.64511	+	3.93943i	0.153984	+	0.130591i
$911$	−41.5669			−1.37717			−0.688586	−	0.725155i	$-0.741768\pi$
$911$	−41.5669			−1.37717			−0.688586	+	0.725155i	$0.741768\pi$
$912$	−18.2292	−	53.5553i	−0.603629	−	1.77339i
$913$	−21.8551			−0.723300
$914$	33.7525	+	28.6248i	1.11643	+	0.946825i
$915$	−6.54981	−	6.54981i	−0.216530	−	0.216530i
$916$	−6.33982	−	4.53907i	−0.209474	−	0.149975i
$917$	−12.5691	+	12.5691i	−0.415070	+	0.415070i
$918$	−1.90133	−	23.1294i	−0.0627533	−	0.763383i
$919$			52.7198i			1.73907i	0.493875	+	0.869533i	$0.335580\pi$
$919$			52.7198i			1.73907i	−0.493875	+	0.869533i	$0.664420\pi$
$920$	−0.468416	−	1.86509i	−0.0154432	−	0.0614902i
$921$		−	20.0646i		−	0.661150i
$922$	−36.9177	+	3.03479i	−1.21582	+	0.0999456i
$923$	28.4126	−	28.4126i	0.935211	−	0.935211i
$924$	8.58052	−	1.42031i	0.282278	−	0.0467248i
$925$	2.96978	+	2.96978i	0.0976456	+	0.0976456i
$926$	8.03895	−	9.47900i	0.264176	−	0.311499i
$927$	−19.6027			−0.643836
$928$	−49.1946	+	21.3873i	−1.61489	+	0.702074i
$929$	26.6152			0.873217			0.436608	−	0.899652i	$-0.356180\pi$
$929$	26.6152			0.873217			0.436608	+	0.899652i	$0.356180\pi$
$930$	7.23954	−	8.53639i	0.237394	−	0.279919i
$931$	4.95147	+	4.95147i	0.162278	+	0.162278i
$932$	−0.821169	+	0.135926i	−0.0268983	+	0.00445240i
$933$	−28.6594	+	28.6594i	−0.938267	+	0.938267i
$934$	40.5013	−	3.32938i	1.32524	−	0.108941i
$935$		−	9.10817i		−	0.297869i
$936$	−12.7525	+	3.20277i	−0.416827	+	0.104686i
$937$		−	30.8713i		−	1.00852i	−0.863551	−	0.504261i	$-0.831765\pi$
$937$		−	30.8713i		−	1.00852i	0.863551	−	0.504261i	$-0.168235\pi$
$938$	−1.37691	−	16.7499i	−0.0449579	−	0.546904i
$939$	−37.5306	+	37.5306i	−1.22477	+	1.22477i
$940$	14.7729	+	10.5768i	0.481837	+	0.344977i
$941$	8.65597	+	8.65597i	0.282177	+	0.282177i	0.833977	−	0.551800i	$-0.186059\pi$
$941$	8.65597	+	8.65597i	0.282177	+	0.282177i	−0.551800	+	0.833977i	$0.686059\pi$
$942$	37.4437	+	31.7553i	1.21998	+	1.03464i
$943$	−4.89419			−0.159377
$944$	2.55503	−	5.19195i	0.0831591	−	0.168984i
$945$	3.87914			0.126188
$946$	19.2817	+	16.3524i	0.626902	+	0.531663i
$947$	3.78061	+	3.78061i	0.122853	+	0.122853i	0.765860	−	0.643007i	$-0.222313\pi$
$947$	3.78061	+	3.78061i	0.122853	+	0.122853i	−0.643007	+	0.765860i	$0.722313\pi$
$948$	−17.9893	+	25.1261i	−0.584266	+	0.816058i
$949$	−23.7559	+	23.7559i	−0.771148	+	0.771148i
$950$	−0.811328	−	9.86965i	−0.0263230	−	0.320214i
$951$		−	28.0343i		−	0.909075i
$952$	6.14496	−	10.2667i	0.199159	−	0.332747i
$953$		−	39.0313i		−	1.26435i	−0.774826	−	0.632174i	$-0.782163\pi$
$953$		−	39.0313i		−	1.26435i	0.774826	−	0.632174i	$-0.217837\pi$
$954$	−1.49413	+	0.122824i	−0.0483743	+	0.00397658i
$955$	6.05639	−	6.05639i	0.195980	−	0.195980i
$956$	−6.24749	−	37.7430i	−0.202058	−	1.22069i
$957$	29.1590	+	29.1590i	0.942578	+	0.942578i
$958$	6.96896	−	8.21734i	0.225157	−	0.265490i
$959$	−18.7604			−0.605805
$960$	−7.63458	−	14.2406i	−0.246405	−	0.459613i
$961$	−15.6447			−0.504667
$962$	16.5452	−	19.5090i	0.533438	−	0.628996i
$963$	2.50607	+	2.50607i	0.0807568	+	0.0807568i
$964$	−7.88249	−	47.6205i	−0.253878	−	1.53375i
$965$	0.533693	−	0.533693i	0.0171802	−	0.0171802i
$966$	−1.93548	+	0.159104i	−0.0622729	+	0.00511910i
$967$		−	20.8819i		−	0.671517i	−0.941948	−	0.335758i	$-0.891007\pi$
$967$		−	20.8819i		−	0.671517i	0.941948	−	0.335758i	$-0.108993\pi$
$968$	−9.24480	+	15.4458i	−0.297139	+	0.496448i
$969$			59.8306i			1.92203i
$970$	0.176706	+	2.14960i	0.00567369	+	0.0690194i
$971$	25.2166	−	25.2166i	0.809240	−	0.809240i	−0.175279	−	0.984519i	$-0.556083\pi$
$971$	25.2166	−	25.2166i	0.809240	−	0.809240i	0.984519	+	0.175279i	$0.0560826\pi$
$972$	−12.4898	+	17.4448i	−0.400611	+	0.559542i
$973$	2.68745	+	2.68745i	0.0861557	+	0.0861557i
$974$	4.27313	+	3.62396i	0.136920	+	0.116119i
$975$	−8.69856			−0.278577
$976$	−16.4594	−	8.09989i	−0.526853	−	0.259271i
$977$	18.4664			0.590793			0.295396	−	0.955375i	$-0.404548\pi$
$977$	18.4664			0.590793			0.295396	+	0.955375i	$0.404548\pi$
$978$	−12.0667	−	10.2335i	−0.385851	−	0.327232i
$979$	19.5906	+	19.5906i	0.626119	+	0.626119i
$980$	1.62618	+	1.16428i	0.0519463	+	0.0371916i
$981$	9.26054	−	9.26054i	0.295666	−	0.295666i
$982$	0.744051	+	9.05124i	0.0237436	+	0.288837i
$983$			34.0066i			1.08464i	0.840172	+	0.542321i	$0.182454\pi$
$983$			34.0066i			1.08464i	−0.840172	+	0.542321i	$0.817546\pi$
$984$	−39.8845	+	10.0170i	−1.27147	+	0.319329i
$985$		−	21.2107i		−	0.675831i
$986$	56.5409	−	4.64791i	1.80063	−	0.148020i
$987$	12.9742	−	12.9742i	0.412972	−	0.412972i
$988$	−59.5058	+	9.84983i	−1.89313	+	0.313365i
$989$	−3.99177	−	3.99177i	−0.126931	−	0.126931i
$990$	−2.12579	+	2.50659i	−0.0675621	+	0.0796647i
$991$	26.6856			0.847696			0.423848	−	0.905733i	$-0.360679\pi$
$991$	26.6856			0.847696			0.423848	+	0.905733i	$0.360679\pi$
$992$	8.12528	−	20.6240i	0.257978	−	0.654813i
$993$	16.3741			0.519617
$994$	8.53414	−	10.0629i	0.270686	−	0.319176i
$995$	−2.53728	−	2.53728i	−0.0804373	−	0.0804373i
$996$	40.4536	−	6.69617i	1.28182	−	0.212176i
$997$	−30.8022	+	30.8022i	−0.975516	+	0.975516i	−0.999707	−	0.0241912i	$-0.992299\pi$
$997$	−30.8022	+	30.8022i	−0.975516	+	0.975516i	0.0241912	+	0.999707i	$0.492299\pi$
$998$	−59.5712	+	4.89701i	−1.88569	+	0.155012i
$999$		−	16.2920i		−	0.515456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.7	✓	44
4.3	odd	2		2240.2.bd.a.1681.19		44
16.5	even	4	inner	560.2.bd.a.421.7	yes	44
16.11	odd	4		2240.2.bd.a.561.19		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.7	✓	44	1.1	even	1	trivial
560.2.bd.a.421.7	yes	44	16.5	even	4	inner
2240.2.bd.a.561.19		44	16.11	odd	4
2240.2.bd.a.1681.19		44	4.3	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.914710 + 1.07857i) q^{2} +(-1.42818 - 1.42818i) q^{3} +(-0.326610 - 1.97315i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.84676 - 0.234016i) q^{6} -1.00000i q^{7} +(2.42693 + 1.45259i) q^{8} +1.07940i q^{9} +O(q^{10})\)	\(q+(-0.914710 + 1.07857i) q^{2} +(-1.42818 - 1.42818i) q^{3} +(-0.326610 - 1.97315i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.84676 - 0.234016i) q^{6} -1.00000i q^{7} +(2.42693 + 1.45259i) q^{8} +1.07940i q^{9} +(0.115864 + 1.40946i) q^{10} +(1.52244 - 1.52244i) q^{11} +(-2.35156 + 3.28447i) q^{12} +(3.04533 + 3.04533i) q^{13} +(1.07857 + 0.914710i) q^{14} -2.01975 q^{15} +(-3.78665 + 1.28890i) q^{16} +4.23034 q^{17} +(-1.16420 - 0.987337i) q^{18} +(-4.95147 - 4.95147i) q^{19} +(-1.62618 - 1.16428i) q^{20} +(-1.42818 + 1.42818i) q^{21} +(0.249461 + 3.03464i) q^{22} -0.679888i q^{23} +(-1.39153 - 5.54065i) q^{24} -1.00000i q^{25} +(-6.07019 + 0.498996i) q^{26} +(-2.74297 + 2.74297i) q^{27} +(-1.97315 + 0.326610i) q^{28} +(-6.70532 - 6.70532i) q^{29} +(1.84749 - 2.17844i) q^{30} +3.91859 q^{31} +(2.07352 - 5.26313i) q^{32} -4.34864 q^{33} +(-3.86954 + 4.56271i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(2.12982 - 0.352542i) q^{36} +(-2.96978 + 2.96978i) q^{37} +(9.86965 - 0.811328i) q^{38} -8.69856i q^{39} +(2.74323 - 0.688960i) q^{40} -7.19853i q^{41} +(-0.234016 - 2.84676i) q^{42} +(5.87122 - 5.87122i) q^{43} +(-3.50125 - 2.50676i) q^{44} +(0.763250 + 0.763250i) q^{45} +(0.733304 + 0.621900i) q^{46} -9.08441 q^{47} +(7.24881 + 3.56724i) q^{48} -1.00000 q^{49} +(1.07857 + 0.914710i) q^{50} +(-6.04169 - 6.04169i) q^{51} +(5.01426 - 7.00354i) q^{52} +(0.694448 - 0.694448i) q^{53} +(-0.449451 - 5.46749i) q^{54} -2.15306i q^{55} +(1.45259 - 2.42693i) q^{56} +14.1432i q^{57} +(13.3656 - 1.09871i) q^{58} +(-1.02293 + 1.02293i) q^{59} +(0.659672 + 3.98528i) q^{60} +(3.24288 + 3.24288i) q^{61} +(-3.58437 + 4.22645i) q^{62} +1.07940 q^{63} +(3.77996 + 7.05067i) q^{64} +4.30675 q^{65} +(3.97774 - 4.69029i) q^{66} +(-8.40320 - 8.40320i) q^{67} +(-1.38167 - 8.34711i) q^{68} +(-0.971002 + 0.971002i) q^{69} +(1.40946 - 0.115864i) q^{70} -9.32988i q^{71} +(-1.56792 + 2.61962i) q^{72} +7.80075i q^{73} +(-0.486615 - 5.91959i) q^{74} +(-1.42818 + 1.42818i) q^{75} +(-8.15280 + 11.3872i) q^{76} +(-1.52244 - 1.52244i) q^{77} +(9.38198 + 7.95667i) q^{78} +7.64996 q^{79} +(-1.76618 + 3.58896i) q^{80} +11.0731 q^{81} +(7.76409 + 6.58457i) q^{82} +(-7.17767 - 7.17767i) q^{83} +(3.28447 + 2.35156i) q^{84} +(2.99130 - 2.99130i) q^{85} +(0.962033 + 11.7030i) q^{86} +19.1528i q^{87} +(5.90634 - 1.48337i) q^{88} +12.8679i q^{89} +(-1.52137 + 0.125063i) q^{90} +(3.04533 - 3.04533i) q^{91} +(-1.34152 + 0.222058i) q^{92} +(-5.59645 - 5.59645i) q^{93} +(8.30960 - 9.79813i) q^{94} -7.00244 q^{95} +(-10.4781 + 4.55533i) q^{96} +1.52512 q^{97} +(0.914710 - 1.07857i) q^{98} +(1.64332 + 1.64332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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