LMFDB - Embedded newform 560.2.bc.a.251.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.20
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.883798 + 1.10404i) q^{2} +(1.16174 - 1.16174i) q^{3} +(-0.437803 - 1.95149i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.255863 + 2.30935i) q^{6} +(2.48811 + 0.899608i) q^{7} +(2.54145 + 1.24137i) q^{8} +0.300718i q^{9} +O(q^{10})$	\(q+(-0.883798 + 1.10404i) q^{2} +(1.16174 - 1.16174i) q^{3} +(-0.437803 - 1.95149i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.255863 + 2.30935i) q^{6} +(2.48811 + 0.899608i) q^{7} +(2.54145 + 1.24137i) q^{8} +0.300718i q^{9} +(0.155734 + 1.40561i) q^{10} +(-3.08981 + 3.08981i) q^{11} +(-2.77574 - 1.75852i) q^{12} +(3.64354 + 3.64354i) q^{13} +(-3.19219 + 1.95190i) q^{14} -1.64295i q^{15} +(-3.61666 + 1.70874i) q^{16} -1.90479i q^{17} +(-0.332005 - 0.265774i) q^{18} +(2.96251 - 2.96251i) q^{19} +(-1.68949 - 1.07034i) q^{20} +(3.93565 - 1.84543i) q^{21} +(-0.680503 - 6.14204i) q^{22} +0.655690 q^{23} +(4.39466 - 1.51036i) q^{24} -1.00000i q^{25} +(-7.24276 + 0.802457i) q^{26} +(3.83458 + 3.83458i) q^{27} +(0.666275 - 5.24939i) q^{28} +(2.68009 - 2.68009i) q^{29} +(1.81388 + 1.45203i) q^{30} +3.01437 q^{31} +(1.30988 - 5.50311i) q^{32} +7.17911i q^{33} +(2.10296 + 1.68345i) q^{34} +(2.39548 - 1.12324i) q^{35} +(0.586850 - 0.131656i) q^{36} +(-6.08074 - 6.08074i) q^{37} +(0.652467 + 5.88899i) q^{38} +8.46569 q^{39} +(2.67486 - 0.919296i) q^{40} +7.27882 q^{41} +(-1.44089 + 5.97610i) q^{42} +(-0.168678 + 0.168678i) q^{43} +(7.38247 + 4.67702i) q^{44} +(0.212640 + 0.212640i) q^{45} +(-0.579497 + 0.723907i) q^{46} -8.95609 q^{47} +(-2.21650 + 6.18673i) q^{48} +(5.38141 + 4.47665i) q^{49} +(1.10404 + 0.883798i) q^{50} +(-2.21287 - 2.21287i) q^{51} +(5.51519 - 8.70549i) q^{52} +(-6.49178 - 6.49178i) q^{53} +(-7.62251 + 0.844532i) q^{54} +4.36965i q^{55} +(5.20668 + 5.37499i) q^{56} -6.88334i q^{57} +(0.590266 + 5.32758i) q^{58} +(-7.08273 - 7.08273i) q^{59} +(-3.20620 + 0.719289i) q^{60} +(3.27600 + 3.27600i) q^{61} +(-2.66410 + 3.32799i) q^{62} +(-0.270529 + 0.748222i) q^{63} +(4.91798 + 6.30979i) q^{64} +5.15274 q^{65} +(-7.92602 - 6.34488i) q^{66} +(-0.886744 - 0.886744i) q^{67} +(-3.71718 + 0.833922i) q^{68} +(0.761741 - 0.761741i) q^{69} +(-0.877017 + 3.63742i) q^{70} -15.5247 q^{71} +(-0.373304 + 0.764262i) q^{72} +6.26678 q^{73} +(12.0875 - 1.33923i) q^{74} +(-1.16174 - 1.16174i) q^{75} +(-7.07832 - 4.48433i) q^{76} +(-10.4674 + 4.90818i) q^{77} +(-7.48195 + 9.34645i) q^{78} +12.3148i q^{79} +(-1.34910 + 3.76562i) q^{80} +8.00741 q^{81} +(-6.43300 + 8.03610i) q^{82} +(-2.44679 + 2.44679i) q^{83} +(-5.32439 - 6.87247i) q^{84} +(-1.34689 - 1.34689i) q^{85} +(-0.0371499 - 0.335305i) q^{86} -6.22713i q^{87} +(-11.6882 + 4.01700i) q^{88} +12.5968 q^{89} +(-0.422694 + 0.0468321i) q^{90} +(5.78778 + 12.3433i) q^{91} +(-0.287063 - 1.27957i) q^{92} +(3.50192 - 3.50192i) q^{93} +(7.91537 - 9.88787i) q^{94} -4.18963i q^{95} +(-4.87145 - 7.91492i) q^{96} +13.2440i q^{97} +(-9.69848 + 1.98483i) q^{98} +(-0.929163 - 0.929163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.883798	+	1.10404i	−0.624939	+	0.780673i
$2$	−0.883798	+	1.10404i	−0.624939	+	0.780673i
$3$	1.16174	−	1.16174i	0.670731	−	0.670731i	−0.287153	−	0.957885i	$-0.592709\pi$
$3$	1.16174	−	1.16174i	0.670731	−	0.670731i	0.957885	+	0.287153i	$0.0927090\pi$
$4$	−0.437803	−	1.95149i	−0.218902	−	0.975747i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.255863	+	2.30935i	0.104456	+	0.942788i
$7$	2.48811	+	0.899608i	0.940418	+	0.340020i
$7$	2.48811	+	0.899608i	0.940418	+	0.340020i
$8$	2.54145	+	1.24137i	0.898540	+	0.438892i
$9$			0.300718i			0.100239i
$10$	0.155734	+	1.40561i	0.0492474	+	0.444494i
$11$	−3.08981	+	3.08981i	−0.931613	+	0.931613i	−0.997807	−	0.0661940i	$-0.978914\pi$
$11$	−3.08981	+	3.08981i	−0.931613	+	0.931613i	0.0661940	+	0.997807i	$0.478914\pi$
$12$	−2.77574	−	1.75852i	−0.801288	−	0.507640i
$13$	3.64354	+	3.64354i	1.01054	+	1.01054i	0.999944	+	0.0105914i	$0.00337140\pi$
$13$	3.64354	+	3.64354i	1.01054	+	1.01054i	0.0105914	+	0.999944i	$0.496629\pi$
$14$	−3.19219	+	1.95190i	−0.853149	+	0.521668i
$15$		−	1.64295i		−	0.424208i
$16$	−3.61666	+	1.70874i	−0.904164	+	0.427185i
$17$		−	1.90479i		−	0.461979i	−0.972956	−	0.230989i	$-0.925804\pi$
$17$		−	1.90479i		−	0.461979i	0.972956	−	0.230989i	$-0.0741963\pi$
$18$	−0.332005	−	0.265774i	−0.0782543	−	0.0626436i
$19$	2.96251	−	2.96251i	0.679647	−	0.679647i	−0.280273	−	0.959920i	$-0.590425\pi$
$19$	2.96251	−	2.96251i	0.679647	−	0.679647i	0.959920	+	0.280273i	$0.0904250\pi$
$20$	−1.68949	−	1.07034i	−0.377781	−	0.239335i
$21$	3.93565	−	1.84543i	0.858830	−	0.402706i
$22$	−0.680503	−	6.14204i	−0.145084	−	1.30949i
$23$	0.655690			0.136721			0.0683604	−	0.997661i	$-0.478223\pi$
$23$	0.655690			0.136721			0.0683604	+	0.997661i	$0.478223\pi$
$24$	4.39466	−	1.51036i	0.897057	−	0.308300i
$25$		−	1.00000i		−	0.200000i
$26$	−7.24276	+	0.802457i	−1.42042	+	0.157375i
$27$	3.83458	+	3.83458i	0.737965	+	0.737965i
$28$	0.666275	−	5.24939i	0.125914	−	0.992041i
$29$	2.68009	−	2.68009i	0.497680	−	0.497680i	−0.413035	−	0.910715i	$-0.635531\pi$
$29$	2.68009	−	2.68009i	0.497680	−	0.497680i	0.910715	+	0.413035i	$0.135531\pi$
$30$	1.81388	+	1.45203i	0.331168	+	0.265104i
$31$	3.01437			0.541398			0.270699	−	0.962664i	$-0.412745\pi$
$31$	3.01437			0.541398			0.270699	+	0.962664i	$0.412745\pi$
$32$	1.30988	−	5.50311i	0.231555	−	0.972822i
$33$			7.17911i			1.24972i
$34$	2.10296	+	1.68345i	0.360654	+	0.288709i
$35$	2.39548	−	1.12324i	0.404910	−	0.189863i
$36$	0.586850	−	0.131656i	0.0978084	−	0.0219426i
$37$	−6.08074	−	6.08074i	−0.999667	−	0.999667i	0.000333113	−	1.00000i	$-0.499894\pi$
$37$	−6.08074	−	6.08074i	−0.999667	−	0.999667i	−1.00000		0.000333113i	$0.999894\pi$
$38$	0.652467	+	5.88899i	0.105844	+	0.955321i
$39$	8.46569			1.35559
$40$	2.67486	−	0.919296i	0.422933	−	0.145353i
$41$	7.27882			1.13676			0.568380	−	0.822766i	$-0.307570\pi$
$41$	7.27882			1.13676			0.568380	+	0.822766i	$0.307570\pi$
$42$	−1.44089	+	5.97610i	−0.222335	+	0.922132i
$43$	−0.168678	+	0.168678i	−0.0257232	+	0.0257232i	−0.719851	−	0.694128i	$-0.755790\pi$
$43$	−0.168678	+	0.168678i	−0.0257232	+	0.0257232i	0.694128	+	0.719851i	$0.255790\pi$
$44$	7.38247	+	4.67702i	1.11295	+	0.705087i
$45$	0.212640	+	0.212640i	0.0316985	+	0.0316985i
$46$	−0.579497	+	0.723907i	−0.0854422	+	0.106734i
$47$	−8.95609			−1.30638			−0.653190	−	0.757194i	$-0.726570\pi$
$47$	−8.95609			−1.30638			−0.653190	+	0.757194i	$0.726570\pi$
$48$	−2.21650	+	6.18673i	−0.319924	+	0.892978i
$49$	5.38141	+	4.47665i	0.768773	+	0.639522i
$50$	1.10404	+	0.883798i	0.156135	+	0.124988i
$51$	−2.21287	−	2.21287i	−0.309864	−	0.309864i
$52$	5.51519	−	8.70549i	0.764819	−	1.20723i
$53$	−6.49178	−	6.49178i	−0.891714	−	0.891714i	0.102971	−	0.994684i	$-0.467165\pi$
$53$	−6.49178	−	6.49178i	−0.891714	−	0.891714i	−0.994684	+	0.102971i	$0.967165\pi$
$54$	−7.62251	+	0.844532i	−1.03729	+	0.114926i
$55$			4.36965i			0.589204i
$56$	5.20668	+	5.37499i	0.695771	+	0.718263i
$57$		−	6.88334i		−	0.911721i
$58$	0.590266	+	5.32758i	0.0775057	+	0.699545i
$59$	−7.08273	−	7.08273i	−0.922094	−	0.922094i	0.0750837	−	0.997177i	$-0.476078\pi$
$59$	−7.08273	−	7.08273i	−0.922094	−	0.922094i	−0.997177	+	0.0750837i	$0.976078\pi$
$60$	−3.20620	+	0.719289i	−0.413919	+	0.0928598i
$61$	3.27600	+	3.27600i	0.419448	+	0.419448i	0.885014	−	0.465565i	$-0.154149\pi$
$61$	3.27600	+	3.27600i	0.419448	+	0.419448i	−0.465565	+	0.885014i	$0.654149\pi$
$62$	−2.66410	+	3.32799i	−0.338341	+	0.422655i
$63$	−0.270529	+	0.748222i	−0.0340834	+	0.0942671i
$64$	4.91798	+	6.30979i	0.614748	+	0.788724i
$65$	5.15274			0.639119
$66$	−7.92602	−	6.34488i	−0.975626	−	0.781001i
$67$	−0.886744	−	0.886744i	−0.108333	−	0.108333i	0.650863	−	0.759196i	$-0.274407\pi$
$67$	−0.886744	−	0.886744i	−0.108333	−	0.108333i	−0.759196	+	0.650863i	$0.774407\pi$
$68$	−3.71718	+	0.833922i	−0.450774	+	0.101128i
$69$	0.761741	−	0.761741i	0.0917029	−	0.0917029i
$70$	−0.877017	+	3.63742i	−0.104824	+	0.434755i
$71$	−15.5247			−1.84244			−0.921222	−	0.389038i	$-0.872807\pi$
$71$	−15.5247			−1.84244			−0.921222	+	0.389038i	$0.872807\pi$
$72$	−0.373304	+	0.764262i	−0.0439943	+	0.0900692i
$73$	6.26678			0.733471			0.366736	−	0.930325i	$-0.380475\pi$
$73$	6.26678			0.733471			0.366736	+	0.930325i	$0.380475\pi$
$74$	12.0875	−	1.33923i	1.40514	−	0.155682i
$75$	−1.16174	−	1.16174i	−0.134146	−	0.134146i
$76$	−7.07832	−	4.48433i	−0.811940	−	0.514388i
$77$	−10.4674	+	4.90818i	−1.19287	+	0.559339i
$78$	−7.48195	+	9.34645i	−0.847165	+	1.05828i
$79$			12.3148i			1.38552i	0.721168	+	0.692760i	$0.243605\pi$
$79$			12.3148i			1.38552i	−0.721168	+	0.692760i	$0.756395\pi$
$80$	−1.34910	+	3.76562i	−0.150834	+	0.421010i
$81$	8.00741			0.889713
$82$	−6.43300	+	8.03610i	−0.710406	+	0.887439i
$83$	−2.44679	+	2.44679i	−0.268570	+	0.268570i	−0.828524	−	0.559954i	$-0.810819\pi$
$83$	−2.44679	+	2.44679i	−0.268570	+	0.268570i	0.559954	+	0.828524i	$0.310819\pi$
$84$	−5.32439	−	6.87247i	−0.580938	−	0.749847i
$85$	−1.34689	−	1.34689i	−0.146091	−	0.146091i
$86$	−0.0371499	−	0.335305i	−0.00400598	−	0.0361568i
$87$		−	6.22713i		−	0.667619i
$88$	−11.6882	+	4.01700i	−1.24597	+	0.428214i
$89$	12.5968			1.33525			0.667627	−	0.744496i	$-0.267310\pi$
$89$	12.5968			1.33525			0.667627	+	0.744496i	$0.267310\pi$
$90$	−0.422694	+	0.0468321i	−0.0445558	+	0.00493654i
$91$	5.78778	+	12.3433i	0.606724	+	1.29393i
$92$	−0.287063	−	1.27957i	−0.0299284	−	0.133405i
$93$	3.50192	−	3.50192i	0.363132	−	0.363132i
$94$	7.91537	−	9.88787i	0.816408	−	1.01986i
$95$		−	4.18963i		−	0.429847i
$96$	−4.87145	−	7.91492i	−0.497190	−	0.807813i
$97$			13.2440i			1.34472i	0.740222	+	0.672362i	$0.234720\pi$
$97$			13.2440i			1.34472i	−0.740222	+	0.672362i	$0.765280\pi$
$98$	−9.69848	+	1.98483i	−0.979694	+	0.200498i
$99$	−0.929163	−	0.929163i	−0.0933844	−	0.0933844i
$100$	−1.95149	+	0.437803i	−0.195149	+	0.0437803i
$101$	−1.62825	+	1.62825i	−0.162017	+	0.162017i	−0.783460	−	0.621443i	$-0.786547\pi$
$101$	−1.62825	+	1.62825i	−0.162017	+	0.162017i	0.621443	+	0.783460i	$0.286547\pi$
$102$	4.39882	−	0.487365i	0.435548	−	0.0482563i
$103$		−	17.7281i		−	1.74680i	−0.487001	−	0.873401i	$-0.661909\pi$
$103$		−	17.7281i		−	1.74680i	0.487001	−	0.873401i	$-0.338091\pi$
$104$	4.73689	+	13.7829i	0.464491	+	1.35152i
$105$	1.47801	−	4.08784i	0.144239	−	0.398933i
$106$	12.9046	−	1.42976i	1.25340	−	0.138870i
$107$	−9.36421	+	9.36421i	−0.905272	+	0.905272i	−0.995886	−	0.0906139i	$-0.971117\pi$
$107$	−9.36421	+	9.36421i	−0.905272	+	0.905272i	0.0906139	+	0.995886i	$0.471117\pi$
$108$	5.80436	−	9.16195i	0.558525	−	0.881609i
$109$	2.52170	−	2.52170i	0.241535	−	0.241535i	−0.575950	−	0.817485i	$-0.695368\pi$
$109$	2.52170	−	2.52170i	0.241535	−	0.241535i	0.817485	+	0.575950i	$0.195368\pi$
$110$	−4.82426	−	3.86189i	−0.459976	−	0.368217i
$111$	−14.1285			−1.34102
$112$	−10.5358	+	0.997969i	−0.995544	+	0.0942992i
$113$	1.25495			0.118056			0.0590279	−	0.998256i	$-0.481200\pi$
$113$	1.25495			0.118056			0.0590279	+	0.998256i	$0.481200\pi$
$114$	7.59948	+	6.08348i	0.711756	+	0.569770i
$115$	0.463643	−	0.463643i	0.0432349	−	0.0432349i
$116$	−6.40353	−	4.05682i	−0.594553	−	0.376667i
$117$	−1.09568	+	1.09568i	−0.101296	+	0.101296i
$118$	14.0793	−	1.55991i	1.29611	−	0.143601i
$119$	1.71356	−	4.73933i	0.157082	−	0.434453i
$120$	2.03951	−	4.17548i	0.186181	−	0.381167i
$121$		−	8.09385i		−	0.735805i
$122$	−6.51214	+	0.721509i	−0.589582	+	0.0653224i
$123$	8.45610	−	8.45610i	0.762461	−	0.762461i
$124$	−1.31970	−	5.88253i	−0.118513	−	0.528267i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−0.586973	−	0.959951i	−0.0522917	−	0.0855192i
$127$		−	12.2925i		−	1.09078i	−0.838183	−	0.545389i	$-0.816382\pi$
$127$		−	12.2925i		−	1.09078i	0.838183	−	0.545389i	$-0.183618\pi$
$128$	−11.3128	−	0.146933i	−0.999916	−	0.0129871i
$129$			0.391921i			0.0345067i
$130$	−4.55398	+	5.68882i	−0.399410	+	0.498943i
$131$	6.73342	−	6.73342i	0.588302	−	0.588302i	−0.348870	−	0.937171i	$-0.613434\pi$
$131$	6.73342	−	6.73342i	0.588302	−	0.588302i	0.937171	+	0.348870i	$0.113434\pi$
$132$	14.0100	−	3.14304i	1.21941	−	0.273567i
$133$	10.0362	−	4.70597i	0.870246	−	0.408059i
$134$	1.76270	−	0.195298i	0.152274	−	0.0168711i
$135$	5.42291			0.466730
$136$	2.36455	−	4.84093i	0.202759	−	0.415106i
$137$			17.0309i			1.45505i	0.686080	+	0.727526i	$0.259330\pi$
$137$			17.0309i			1.45505i	−0.686080	+	0.727526i	$0.740670\pi$
$138$	0.167767	+	1.51422i	0.0142813	+	0.128899i
$139$	−10.9977	−	10.9977i	−0.932812	−	0.932812i	0.0650691	−	0.997881i	$-0.479273\pi$
$139$	−10.9977	−	10.9977i	−0.932812	−	0.932812i	−0.997881	+	0.0650691i	$0.979273\pi$
$140$	−3.24075	−	4.18301i	−0.273893	−	0.353529i
$141$	−10.4047	+	10.4047i	−0.876230	+	0.876230i
$142$	13.7207	−	17.1399i	1.15142	−	1.43835i
$143$	−22.5157			−1.88286
$144$	−0.513850	−	1.08760i	−0.0428208	−	0.0906330i
$145$		−	3.79022i		−	0.314760i
$146$	−5.53857	+	6.91877i	−0.458375	+	0.572602i
$147$	11.4525	−	1.05109i	0.944587	−	0.0866928i
$148$	−9.20435	+	14.5287i	−0.756593	+	1.19425i
$149$	−0.189559	−	0.189559i	−0.0155293	−	0.0155293i	0.699299	−	0.714829i	$-0.253495\pi$
$149$	−0.189559	−	0.189559i	−0.0155293	−	0.0155293i	−0.714829	+	0.699299i	$0.753495\pi$
$150$	2.30935	−	0.255863i	0.188558	−	0.0208911i
$151$	−8.33315			−0.678142			−0.339071	−	0.940761i	$-0.610113\pi$
$151$	−8.33315			−0.678142			−0.339071	+	0.940761i	$0.610113\pi$
$152$	11.2067	−	3.85151i	0.908982	−	0.312398i
$153$	0.572805			0.0463085
$154$	3.83226	−	15.8943i	0.308812	−	1.28080i
$155$	2.13148	−	2.13148i	0.171205	−	0.171205i
$156$	−3.70631	−	16.5207i	−0.296742	−	1.32272i
$157$	−15.2438	−	15.2438i	−1.21659	−	1.21659i	−0.968819	−	0.247770i	$-0.920302\pi$
$157$	−15.2438	−	15.2438i	−1.21659	−	1.21659i	−0.247770	−	0.968819i	$-0.579698\pi$
$158$	−13.5960	−	10.8838i	−1.08164	−	0.865866i
$159$	−15.0835			−1.19620
$160$	−2.96507	−	4.81751i	−0.234409	−	0.380857i
$161$	1.63143	+	0.589864i	0.128575	+	0.0464878i
$162$	−7.07693	+	8.84049i	−0.556016	+	0.694575i
$163$	−5.83870	−	5.83870i	−0.457323	−	0.457323i	0.440453	−	0.897776i	$-0.354818\pi$
$163$	−5.83870	−	5.83870i	−0.457323	−	0.457323i	−0.897776	+	0.440453i	$0.854818\pi$
$164$	−3.18669	−	14.2046i	−0.248839	−	1.10919i
$165$	5.07640	+	5.07640i	0.395197	+	0.395197i
$166$	−0.538884	−	4.86382i	−0.0418255	−	0.377505i
$167$			4.19425i			0.324561i	0.986745	+	0.162281i	$0.0518850\pi$
$167$			4.19425i			0.324561i	−0.986745	+	0.162281i	$0.948115\pi$
$168$	12.2931	+	0.195537i	0.948437	+	0.0150860i
$169$			13.5507i			1.04236i
$170$	2.67739	−	0.296640i	0.205347	−	0.0227513i
$171$	0.890883	+	0.890883i	0.0681275	+	0.0681275i
$172$	0.403022	+	0.255327i	0.0307302	+	0.0194685i
$173$	−15.7848	−	15.7848i	−1.20010	−	1.20010i	−0.974137	−	0.225959i	$-0.927448\pi$
$173$	−15.7848	−	15.7848i	−1.20010	−	1.20010i	−0.225959	−	0.974137i	$-0.572552\pi$
$174$	6.87500	+	5.50353i	0.521192	+	0.417221i
$175$	0.899608	−	2.48811i	0.0680040	−	0.188084i
$176$	5.89509	−	16.4545i	0.444359	−	1.24030i
$177$	−16.4566			−1.23695
$178$	−11.1330	+	13.9073i	−0.834453	+	1.04240i
$179$	4.18280	+	4.18280i	0.312637	+	0.312637i	0.845930	−	0.533293i	$-0.179046\pi$
$179$	4.18280	+	4.18280i	0.312637	+	0.312637i	−0.533293	+	0.845930i	$0.679046\pi$
$180$	0.321871	−	0.508060i	0.0239909	−	0.0378686i
$181$	5.91259	−	5.91259i	0.439479	−	0.439479i	−0.452357	−	0.891837i	$-0.649417\pi$
$181$	5.91259	−	5.91259i	0.439479	−	0.439479i	0.891837	+	0.452357i	$0.149417\pi$
$182$	−18.7427	−	4.51904i	−1.38930	−	0.334973i
$183$	7.61171			0.562674
$184$	1.66641	+	0.813956i	0.122849	+	0.0600056i
$185$	−8.59946			−0.632245
$186$	0.771267	+	6.96124i	0.0565520	+	0.510423i
$187$	5.88543	+	5.88543i	0.430385	+	0.430385i
$188$	3.92101	+	17.4778i	0.285969	+	1.27470i
$189$	6.09125	+	12.9905i	0.443073	+	0.944918i
$190$	4.62551	+	3.70278i	0.335570	+	0.268628i
$191$			14.8787i			1.07659i	0.842758	+	0.538293i	$0.180930\pi$
$191$			14.8787i			1.07659i	−0.842758	+	0.538293i	$0.819070\pi$
$192$	13.0438	+	1.61692i	0.941352	+	0.116691i
$193$	−4.17202			−0.300309			−0.150154	−	0.988663i	$-0.547977\pi$
$193$	−4.17202			−0.300309			−0.150154	+	0.988663i	$0.547977\pi$
$194$	−14.6219	−	11.7050i	−1.04979	−	0.840371i
$195$	5.98615	−	5.98615i	0.428677	−	0.428677i
$196$	6.38016	−	12.4617i	0.455726	−	0.890120i
$197$	11.7586	+	11.7586i	0.837765	+	0.837765i	0.988564	−	0.150799i	$-0.0481847\pi$
$197$	11.7586	+	11.7586i	0.837765	+	0.837765i	−0.150799	+	0.988564i	$0.548185\pi$
$198$	1.84702	−	0.204640i	0.131262	−	0.0145431i
$199$			20.0732i			1.42295i	0.702711	+	0.711476i	$0.251973\pi$
$199$			20.0732i			1.42295i	−0.702711	+	0.711476i	$0.748027\pi$
$200$	1.24137	−	2.54145i	0.0877784	−	0.179708i
$201$	−2.06033			−0.145325
$202$	−0.358608	−	3.23670i	−0.0252316	−	0.227733i
$203$	9.07939	−	4.25733i	0.637248	−	0.298806i
$204$	−3.34960	+	5.28720i	−0.234519	+	0.370178i
$205$	5.14690	−	5.14690i	0.359475	−	0.359475i
$206$	19.5725	+	15.6681i	1.36368	+	1.09165i
$207$			0.197178i			0.0137048i
$208$	−19.4033	−	6.95156i	−1.34538	−	0.482004i
$209$			18.3072i			1.26634i
$210$	3.20688	+	5.24461i	0.221295	+	0.361912i
$211$	−5.82363	−	5.82363i	−0.400915	−	0.400915i	0.477640	−	0.878555i	$-0.341492\pi$
$211$	−5.82363	−	5.82363i	−0.400915	−	0.400915i	−0.878555	+	0.477640i	$0.841492\pi$
$212$	−9.82654	+	15.5108i	−0.674889	+	1.06528i
$213$	−18.0357	+	18.0357i	−1.23578	+	1.23578i
$214$	−2.06238	−	18.6145i	−0.140982	−	1.27246i
$215$			0.238547i			0.0162688i
$216$	4.98526	+	14.5055i	0.339204	+	0.986978i
$217$	7.50010	+	2.71175i	0.509140	+	0.184086i
$218$	0.555382	+	5.01273i	0.0376152	+	0.339505i
$219$	7.28038	−	7.28038i	0.491962	−	0.491962i
$220$	8.52735	−	1.91305i	0.574914	−	0.128978i
$221$	6.94016	−	6.94016i	0.466846	−	0.466846i
$222$	12.4867	−	15.5984i	0.838053	−	1.04689i
$223$	−13.0612			−0.874642			−0.437321	−	0.899305i	$-0.644073\pi$
$223$	−13.0612			−0.874642			−0.437321	+	0.899305i	$0.644073\pi$
$224$	8.20976	−	12.5140i	0.548538	−	0.836126i
$225$	0.300718			0.0200479
$226$	−1.10912	+	1.38551i	−0.0737777	+	0.0921630i
$227$	−6.47580	+	6.47580i	−0.429814	+	0.429814i	−0.888565	−	0.458751i	$-0.848297\pi$
$227$	−6.47580	+	6.47580i	−0.429814	+	0.429814i	0.458751	+	0.888565i	$0.348297\pi$
$228$	−13.4328	+	3.01355i	−0.889609	+	0.199577i
$229$	16.6199	−	16.6199i	1.09827	−	1.09827i	0.103660	−	0.994613i	$-0.466945\pi$
$229$	16.6199	−	16.6199i	1.09827	−	1.09827i	0.994613	−	0.103660i	$-0.0330552\pi$
$230$	0.102113	+	0.921646i	0.00673314	+	0.0607715i
$231$	−6.45839	+	17.8624i	−0.424931	+	1.17526i
$232$	10.1383	−	3.48433i	0.665613	−	0.228758i
$233$		−	20.6706i		−	1.35418i	−0.735902	−	0.677088i	$-0.763242\pi$
$233$		−	20.6706i		−	1.35418i	0.735902	−	0.677088i	$-0.236758\pi$
$234$	−0.241314	−	2.17803i	−0.0157752	−	0.142382i
$235$	−6.33291	+	6.33291i	−0.413114	+	0.413114i
$236$	−10.7211	+	16.9228i	−0.697882	+	1.10158i
$237$	14.3066	+	14.3066i	0.929311	+	0.929311i
$238$	3.71796	+	6.08044i	0.240999	+	0.394137i
$239$			4.70064i			0.304059i	0.988376	+	0.152030i	$0.0485809\pi$
$239$			4.70064i			0.304059i	−0.988376	+	0.152030i	$0.951419\pi$
$240$	2.80738	+	5.94198i	0.181215	+	0.383553i
$241$			3.80524i			0.245117i	0.992461	+	0.122558i	$0.0391099\pi$
$241$			3.80524i			0.245117i	−0.992461	+	0.122558i	$0.960890\pi$
$242$	8.93593	+	7.15333i	0.574423	+	0.459833i
$243$	−2.20120	+	2.20120i	−0.141207	+	0.141207i
$244$	4.95884	−	7.82733i	0.317457	−	0.501093i
$245$	6.97070	−	0.639761i	0.445342	−	0.0408728i
$246$	1.86238	+	16.8093i	0.118741	+	1.07172i
$247$	21.5881			1.37361
$248$	7.66089	+	3.74196i	0.486467	+	0.237615i
$249$			5.68507i			0.360277i
$250$	1.40561	−	0.155734i	0.0888987	−	0.00984949i
$251$	−8.25157	−	8.25157i	−0.520835	−	0.520835i	0.396989	−	0.917823i	$-0.370055\pi$
$251$	−8.25157	−	8.25157i	−0.520835	−	0.520835i	−0.917823	+	0.396989i	$0.870055\pi$
$252$	1.57859	+	0.200361i	0.0994417	+	0.0126216i
$253$	−2.02596	+	2.02596i	−0.127371	+	0.127371i
$254$	13.5713	+	10.8640i	0.851542	+	0.681671i
$255$	−3.12947			−0.195975
$256$	10.1604	−	12.3599i	0.635025	−	0.772491i
$257$			10.3771i			0.647307i	0.946176	+	0.323654i	$0.104911\pi$
$257$			10.3771i			0.647307i	−0.946176	+	0.323654i	$0.895089\pi$
$258$	−0.432696	−	0.346379i	−0.0269385	−	0.0215646i
$259$	−9.65928	−	20.5998i	−0.600198	−	1.28001i
$260$	−2.25589	−	10.0555i	−0.139904	−	0.623618i
$261$	0.805952	+	0.805952i	0.0498872	+	0.0498872i
$262$	1.48298	+	13.3849i	0.0916186	+	0.826924i
$263$	−24.4187			−1.50572			−0.752862	−	0.658178i	$-0.771327\pi$
$263$	−24.4187			−1.50572			−0.752862	+	0.658178i	$0.771327\pi$
$264$	−8.91196	+	18.2454i	−0.548493	+	1.12293i
$265$	−9.18076			−0.563969
$266$	−3.67437	+	15.2394i	−0.225290	+	0.934390i
$267$	14.6342	−	14.6342i	0.895597	−	0.895597i
$268$	−1.34226	+	2.11870i	−0.0819913	+	0.129420i
$269$	−13.6160	−	13.6160i	−0.830183	−	0.830183i	0.157359	−	0.987541i	$-0.449702\pi$
$269$	−13.6160	−	13.6160i	−0.830183	−	0.830183i	−0.987541	+	0.157359i	$0.949702\pi$
$270$	−4.79276	+	5.98711i	−0.291678	+	0.364364i
$271$	−5.57441			−0.338621			−0.169311	−	0.985563i	$-0.554154\pi$
$271$	−5.57441			−0.338621			−0.169311	+	0.985563i	$0.554154\pi$
$272$	3.25479	+	6.88896i	0.197351	+	0.417705i
$273$	21.0636	+	7.61580i	1.27483	+	0.460929i
$274$	−18.8028	−	15.0519i	−1.13592	−	0.909319i
$275$	3.08981	+	3.08981i	0.186323	+	0.186323i
$276$	−1.82003	−	1.15304i	−0.109553	−	0.0694049i
$277$	10.7412	+	10.7412i	0.645377	+	0.645377i	0.951872	−	0.306496i	$-0.0991564\pi$
$277$	10.7412	+	10.7412i	0.645377	+	0.645377i	−0.306496	+	0.951872i	$0.599156\pi$
$278$	21.8616	−	2.42214i	1.31117	−	0.145271i
$279$			0.906478i			0.0542694i
$280$	7.48237	+	0.119016i	0.447157	+	0.00711257i
$281$			8.61214i			0.513757i	0.966444	+	0.256879i	$0.0826941\pi$
$281$			8.61214i			0.513757i	−0.966444	+	0.256879i	$0.917306\pi$
$282$	−2.29153	−	20.6828i	−0.136459	−	1.23164i
$283$	3.17809	+	3.17809i	0.188918	+	0.188918i	0.795228	−	0.606310i	$-0.207351\pi$
$283$	3.17809	+	3.17809i	0.188918	+	0.188918i	−0.606310	+	0.795228i	$0.707351\pi$
$284$	6.79677	+	30.2964i	0.403314	+	1.79776i
$285$	−4.86726	−	4.86726i	−0.288311	−	0.288311i
$286$	19.8993	−	24.8582i	1.17667	−	1.46989i
$287$	18.1105	+	6.54809i	1.06903	+	0.386521i
$288$	1.65489	+	0.393904i	0.0975152	+	0.0232110i
$289$	13.3718			0.786576
$290$	4.18455	+	3.34978i	0.245725	+	0.196706i
$291$	15.3861	+	15.3861i	0.901949	+	0.901949i
$292$	−2.74362	−	12.2296i	−0.160558	−	0.715683i
$293$	−2.49809	+	2.49809i	−0.145940	+	0.145940i	−0.776302	−	0.630362i	$-0.782907\pi$
$293$	−2.49809	+	2.49809i	−0.145940	+	0.145940i	0.630362	+	0.776302i	$0.282907\pi$
$294$	−8.96125	+	13.5730i	−0.522631	+	0.791592i
$295$	−10.0165			−0.583183
$296$	−7.90545	−	23.0024i	−0.459495	−	1.33699i
$297$	−23.6962			−1.37500
$298$	0.376813	−	0.0417488i	0.0218282	−	0.00241844i
$299$	2.38903	+	2.38903i	0.138161	+	0.138161i
$300$	−1.75852	+	2.77574i	−0.101528	+	0.160258i
$301$	−0.571435	+	0.267946i	−0.0329370	+	0.0154442i
$302$	7.36482	−	9.20012i	0.423798	−	0.529407i
$303$			3.78321i			0.217340i
$304$	−5.65222	+	15.7766i	−0.324177	+	0.904848i
$305$	4.63296			0.265282
$306$	−0.506243	+	0.632399i	−0.0289400	+	0.0361518i
$307$	6.43361	−	6.43361i	0.367185	−	0.367185i	−0.499264	−	0.866450i	$-0.666396\pi$
$307$	6.43361	−	6.43361i	0.367185	−	0.367185i	0.866450	+	0.499264i	$0.166396\pi$
$308$	14.1609	+	18.2783i	0.806895	+	1.04150i
$309$	−20.5955	−	20.5955i	−1.17163	−	1.17163i
$310$	0.469441	+	4.23704i	0.0266624	+	0.240648i
$311$			1.47719i			0.0837637i	0.999123	+	0.0418818i	$0.0133353\pi$
$311$			1.47719i			0.0837637i	−0.999123	+	0.0418818i	$0.986665\pi$
$312$	21.5152	+	10.5091i	1.21806	+	0.594960i
$313$	26.5456			1.50045			0.750224	−	0.661184i	$-0.229946\pi$
$313$	26.5456			1.50045			0.750224	+	0.661184i	$0.229946\pi$
$314$	30.3022	−	3.35732i	1.71005	−	0.189464i
$315$	0.337780	+	0.720365i	0.0190317	+	0.0405880i
$316$	24.0322	−	5.39145i	1.35192	−	0.303293i
$317$	−5.52565	+	5.52565i	−0.310352	+	0.310352i	−0.845046	−	0.534694i	$-0.820427\pi$
$317$	−5.52565	+	5.52565i	−0.310352	+	0.310352i	0.534694	+	0.845046i	$0.320427\pi$
$318$	13.3308	−	16.6528i	0.747553	−	0.933842i
$319$			16.5619i			0.927290i
$320$	7.93923	+	0.984156i	0.443817	+	0.0550160i
$321$			21.7576i			1.21439i
$322$	−2.09309	+	1.27984i	−0.116643	+	0.0713228i
$323$	−5.64296	−	5.64296i	−0.313983	−	0.313983i
$324$	−3.50567	−	15.6264i	−0.194760	−	0.868134i
$325$	3.64354	−	3.64354i	0.202107	−	0.202107i
$326$	11.6064	−	1.28592i	0.642818	−	0.0712207i
$327$		−	5.85912i		−	0.324010i
$328$	18.4988	+	9.03574i	1.02142	+	0.498915i
$329$	−22.2838	−	8.05697i	−1.22854	−	0.444195i
$330$	−10.0911	+	1.11803i	−0.555494	+	0.0615457i
$331$	−14.7924	+	14.7924i	−0.813062	+	0.813062i	−0.985092	−	0.172029i	$-0.944968\pi$
$331$	−14.7924	+	14.7924i	−0.813062	+	0.813062i	0.172029	+	0.985092i	$0.444968\pi$
$332$	5.84611	+	3.70368i	0.320847	+	0.203266i
$333$	1.82859	−	1.82859i	0.100206	−	0.100206i
$334$	−4.63062	−	3.70687i	−0.253376	−	0.202831i
$335$	−1.25405			−0.0685158
$336$	−11.0805	+	13.3993i	−0.604493	+	0.730992i
$337$	−29.0873			−1.58449			−0.792244	−	0.610204i	$-0.791087\pi$
$337$	−29.0873			−1.58449			−0.792244	+	0.610204i	$0.791087\pi$
$338$	−14.9605	−	11.9761i	−0.813745	−	0.651414i
$339$	1.45793	−	1.45793i	0.0791837	−	0.0791837i
$340$	−2.03877	+	3.21812i	−0.110568	+	0.174527i
$341$	−9.31384	+	9.31384i	−0.504373	+	0.504373i
$342$	−1.77093	+	0.196209i	−0.0957609	+	0.0106098i
$343$	9.36233	+	15.9796i	0.505518	+	0.862816i
$344$	−0.638081	+	0.219295i	−0.0344030	+	0.0118236i
$345$		−	1.07726i		−	0.0579980i
$346$	31.3776	−	3.47646i	1.68687	−	0.186896i
$347$	−7.32687	+	7.32687i	−0.393327	+	0.393327i	−0.875872	−	0.482544i	$-0.839713\pi$
$347$	−7.32687	+	7.32687i	−0.393327	+	0.393327i	0.482544	+	0.875872i	$0.339713\pi$
$348$	−12.1522	+	2.72626i	−0.651427	+	0.146143i
$349$	8.65818	+	8.65818i	0.463462	+	0.463462i	0.899788	−	0.436327i	$-0.143721\pi$
$349$	8.65818	+	8.65818i	0.463462	+	0.463462i	−0.436327	+	0.899788i	$0.643721\pi$
$350$	1.95190	+	3.19219i	0.104334	+	0.170630i
$351$			27.9429i			1.49148i
$352$	12.9563	+	21.0508i	0.690573	+	1.12201i
$353$		−	8.56359i		−	0.455794i	−0.973685	−	0.227897i	$-0.926815\pi$
$353$		−	8.56359i		−	0.455794i	0.973685	−	0.227897i	$-0.0731850\pi$
$354$	14.5443	−	18.1687i	0.773021	−	0.965657i
$355$	−10.9776	+	10.9776i	−0.582632	+	0.582632i
$356$	−5.51491	−	24.5825i	−0.292290	−	1.30287i
$357$	−3.51515	−	7.49658i	−0.186042	−	0.396761i
$358$	−8.31473	+	0.921225i	−0.439447	+	0.0486883i
$359$	2.20627			0.116443			0.0582213	−	0.998304i	$-0.481457\pi$
$359$	2.20627			0.116443			0.0582213	+	0.998304i	$0.481457\pi$
$360$	0.276449	+	0.804381i	0.0145702	+	0.0423946i
$361$			1.44703i			0.0761595i
$362$	1.30220	+	11.7533i	0.0684419	+	0.617738i
$363$	−9.40295	−	9.40295i	−0.493527	−	0.493527i
$364$	21.5539	−	16.6987i	1.12973	−	0.875252i
$365$	4.43128	−	4.43128i	0.231944	−	0.231944i
$366$	−6.72721	+	8.40363i	−0.351637	+	0.439265i
$367$	−9.33617			−0.487344			−0.243672	−	0.969858i	$-0.578352\pi$
$367$	−9.33617			−0.487344			−0.243672	+	0.969858i	$0.578352\pi$
$368$	−2.37140	+	1.12040i	−0.123618	+	0.0584051i
$369$			2.18888i			0.113948i
$370$	7.60018	−	9.49414i	0.395115	−	0.493577i
$371$	−10.3122	−	21.9923i	−0.535384	−	1.14178i
$372$	−8.36713	−	5.30082i	−0.433815	−	0.274835i
$373$	−4.81520	−	4.81520i	−0.249321	−	0.249321i	0.571371	−	0.820692i	$-0.306412\pi$
$373$	−4.81520	−	4.81520i	−0.249321	−	0.249321i	−0.820692	+	0.571371i	$0.806412\pi$
$374$	−11.6993	+	1.29621i	−0.604955	+	0.0670256i
$375$	−1.64295			−0.0848415
$376$	−22.7615	−	11.1179i	−1.17383	−	0.573360i
$377$	19.5300			1.00585
$378$	−19.7254	−	4.75598i	−1.01457	−	0.244621i
$379$	21.6084	−	21.6084i	1.10995	−	1.10995i	0.116791	−	0.993156i	$-0.462739\pi$
$379$	21.6084	−	21.6084i	1.10995	−	1.10995i	0.993156	−	0.116791i	$-0.0372608\pi$
$380$	−8.17603	+	1.83423i	−0.419421	+	0.0940942i
$381$	−14.2806	−	14.2806i	−0.731619	−	0.731619i
$382$	−16.4267	−	13.1498i	−0.840461	−	0.672800i
$383$	33.5735			1.71553			0.857764	−	0.514044i	$-0.171853\pi$
$383$	33.5735			1.71553			0.857764	+	0.514044i	$0.171853\pi$
$384$	−13.3132	+	12.9718i	−0.679385	+	0.661964i
$385$	−3.93097	+	10.8722i	−0.200341	+	0.554098i
$386$	3.68723	−	4.60608i	0.187675	−	0.234443i
$387$	−0.0507247	−	0.0507247i	−0.00257848	−	0.00257848i
$388$	25.8456	−	5.79827i	1.31211	−	0.294363i
$389$	−22.3390	−	22.3390i	−1.13263	−	1.13263i	−0.989738	−	0.142896i	$-0.954359\pi$
$389$	−22.3390	−	22.3390i	−1.13263	−	1.13263i	−0.142896	−	0.989738i	$-0.545641\pi$
$390$	1.31840	+	11.8995i	0.0667596	+	0.602553i
$391$		−	1.24895i		−	0.0631621i
$392$	8.11941	+	18.0576i	0.410092	+	0.912044i
$393$		−	15.6450i		−	0.789184i
$394$	−23.3742	+	2.58973i	−1.17757	+	0.130469i
$395$	8.70786	+	8.70786i	0.438140	+	0.438140i
$396$	−1.40647	+	2.22005i	−0.0706775	+	0.111562i
$397$	−13.8135	−	13.8135i	−0.693282	−	0.693282i	0.269671	−	0.962953i	$-0.413085\pi$
$397$	−13.8135	−	13.8135i	−0.693282	−	0.693282i	−0.962953	+	0.269671i	$0.913085\pi$
$398$	−22.1616	−	17.7407i	−1.11086	−	0.889258i
$399$	6.19231	−	17.1265i	0.310003	−	0.857399i
$400$	1.70874	+	3.61666i	0.0854371	+	0.180833i
$401$	2.34938			0.117322			0.0586611	−	0.998278i	$-0.481317\pi$
$401$	2.34938			0.117322			0.0586611	+	0.998278i	$0.481317\pi$
$402$	1.82092	−	2.27469i	0.0908191	−	0.113451i
$403$	10.9830	+	10.9830i	0.547101	+	0.547101i
$404$	3.89038	+	2.46467i	0.193554	+	0.122622i
$405$	5.66210	−	5.66210i	0.281352	−	0.281352i
$406$	−3.32408	+	13.7866i	−0.164971	+	0.684218i
$407$	37.5766			1.86260
$408$	−2.87691	−	8.37090i	−0.142428	−	0.414421i
$409$	−31.3208			−1.54871			−0.774356	−	0.632750i	$-0.781926\pi$
$409$	−31.3208			−1.54871			−0.774356	+	0.632750i	$0.781926\pi$
$410$	1.13356	+	10.2312i	0.0559825	+	0.505283i
$411$	19.7855	+	19.7855i	0.975948	+	0.975948i
$412$	−34.5963	+	7.76143i	−1.70444	+	0.382378i
$413$	−11.2510	−	23.9943i	−0.553623	−	1.18068i
$414$	−0.217692	−	0.174265i	−0.0106990	−	0.00856468i
$415$			3.46028i			0.169859i
$416$	24.8234	−	15.2782i	1.21707	−	0.749076i
$417$	−25.5529			−1.25133
$418$	−20.2119	−	16.1799i	−0.988595	−	0.791383i
$419$	10.4710	−	10.4710i	0.511544	−	0.511544i	−0.403455	−	0.914999i	$-0.632191\pi$
$419$	10.4710	−	10.4710i	0.511544	−	0.511544i	0.914999	+	0.403455i	$0.132191\pi$
$420$	−8.62448	−	1.09466i	−0.420831	−	0.0534137i
$421$	20.6186	+	20.6186i	1.00489	+	1.00489i	0.999988	+	0.00490286i	$0.00156064\pi$
$421$	20.6186	+	20.6186i	1.00489	+	1.00489i	0.00490286	+	0.999988i	$0.498439\pi$
$422$	11.5764	−	1.28260i	0.563531	−	0.0624361i
$423$		−	2.69326i		−	0.130951i
$424$	−8.43983	−	24.5573i	−0.409875	−	1.19261i
$425$	−1.90479			−0.0923958
$426$	−3.97220	−	35.8520i	−0.192454	−	1.73703i
$427$	5.20394	+	11.0982i	0.251836	+	0.537078i
$428$	22.3739	+	14.1745i	1.08148	+	0.685151i
$429$	−26.1574	+	26.1574i	−1.26289	+	1.26289i
$430$	−0.263365	−	0.210827i	−0.0127006	−	0.0101670i
$431$		−	18.8920i		−	0.909997i	−0.890492	−	0.454999i	$-0.849640\pi$
$431$		−	18.8920i		−	0.909997i	0.890492	−	0.454999i	$-0.150360\pi$
$432$	−20.4207	−	7.31605i	−0.982489	−	0.351994i
$433$		−	25.8925i		−	1.24431i	−0.782892	−	0.622157i	$-0.786256\pi$
$433$		−	25.8925i		−	1.24431i	0.782892	−	0.622157i	$-0.213744\pi$
$434$	−9.62246	+	5.88376i	−0.461893	+	0.282430i
$435$	−4.40325	−	4.40325i	−0.211120	−	0.211120i
$436$	−6.02509	−	3.81707i	−0.288549	−	0.182805i
$437$	1.94249	−	1.94249i	0.0929219	−	0.0929219i
$438$	1.60344	+	14.4722i	0.0766153	+	0.691508i
$439$		−	2.69090i		−	0.128430i	−0.997936	−	0.0642148i	$-0.979546\pi$
$439$		−	2.69090i		−	0.128430i	0.997936	−	0.0642148i	$-0.0204543\pi$
$440$	−5.42437	+	11.1053i	−0.258597	+	0.529423i
$441$	−1.34621	+	1.61829i	−0.0641053	+	0.0770614i
$442$	1.52851	+	13.7959i	0.0727038	+	0.656204i
$443$	23.8127	−	23.8127i	1.13138	−	1.13138i	0.141429	−	0.989948i	$-0.454830\pi$
$443$	23.8127	−	23.8127i	1.13138	−	1.13138i	0.989948	−	0.141429i	$-0.0451697\pi$
$444$	6.18549	+	27.5716i	0.293551	+	1.30849i
$445$	8.90726	−	8.90726i	0.422245	−	0.422245i
$446$	11.5435	−	14.4201i	0.546598	−	0.682810i
$447$	−0.440438			−0.0208320
$448$	6.56016	+	20.1237i	0.309938	+	0.950757i
$449$	12.6452			0.596763			0.298381	−	0.954447i	$-0.403553\pi$
$449$	12.6452			0.596763			0.298381	+	0.954447i	$0.403553\pi$
$450$	−0.265774	+	0.332005i	−0.0125287	+	0.0156509i
$451$	−22.4902	+	22.4902i	−1.05902	+	1.05902i
$452$	−0.549421	−	2.44903i	−0.0258426	−	0.115193i
$453$	−9.68096	+	9.68096i	−0.454851	+	0.454851i
$454$	−1.42624	−	12.8728i	−0.0669367	−	0.604152i
$455$	12.8206	+	4.63545i	0.601039	+	0.217313i
$456$	8.54480	−	17.4937i	0.400147	−	0.819218i
$457$		−	35.0394i		−	1.63907i	−0.573027	−	0.819536i	$-0.694231\pi$
$457$		−	35.0394i		−	1.63907i	0.573027	−	0.819536i	$-0.305769\pi$
$458$	3.66038	+	33.0376i	0.171038	+	1.54375i
$459$	7.30406	−	7.30406i	0.340924	−	0.340924i
$460$	−1.10778	−	0.701811i	−0.0516505	−	0.0327221i
$461$	−21.7115	−	21.7115i	−1.01120	−	1.01120i	−0.999937	−	0.0112676i	$-0.996413\pi$
$461$	−21.7115	−	21.7115i	−1.01120	−	1.01120i	−0.0112676	−	0.999937i	$-0.503587\pi$
$462$	−14.0129	−	22.9171i	−0.651940	−	1.06620i
$463$			0.418425i			0.0194459i	0.999953	+	0.00972294i	$0.00309496\pi$
$463$			0.418425i			0.0194459i	−0.999953	+	0.00972294i	$0.996905\pi$
$464$	−5.11338	+	14.2725i	−0.237383	+	0.662586i
$465$		−	4.95246i		−	0.229665i
$466$	22.8211	+	18.2686i	1.05717	+	0.846277i
$467$	18.9158	−	18.9158i	0.875320	−	0.875320i	−0.117726	−	0.993046i	$-0.537560\pi$
$467$	18.9158	−	18.9158i	0.875320	−	0.875320i	0.993046	+	0.117726i	$0.0375604\pi$
$468$	2.61790	+	1.65852i	0.121013	+	0.0766650i
$469$	−1.40860	−	3.00404i	−0.0650430	−	0.138714i
$470$	−1.39477	−	12.5888i	−0.0643359	−	0.580678i
$471$	−35.4187			−1.63201
$472$	−9.20813	−	26.7928i	−0.423838	−	1.23324i
$473$		−	1.04237i		−	0.0479281i
$474$	−28.4391	+	3.15089i	−1.30625	+	0.144725i
$475$	−2.96251	−	2.96251i	−0.135929	−	0.135929i
$476$	−9.99897	−	1.26911i	−0.458302	−	0.0581697i
$477$	1.95220	−	1.95220i	0.0893850	−	0.0893850i
$478$	−5.18969	−	4.15442i	−0.237371	−	0.190019i
$479$	26.0182			1.18880			0.594401	−	0.804169i	$-0.297389\pi$
$479$	26.0182			1.18880			0.594401	+	0.804169i	$0.297389\pi$
$480$	−9.04133	−	2.15206i	−0.412678	−	0.0982276i
$481$		−	44.3108i		−	2.02040i
$482$	−4.20113	−	3.36306i	−0.191356	−	0.153183i
$483$	2.58057	−	1.21003i	0.117420	−	0.0550582i
$484$	−15.7951	+	3.54352i	−0.717959	+	0.161069i
$485$	9.36492	+	9.36492i	0.425239	+	0.425239i
$486$	−0.484795	−	4.37562i	−0.0219907	−	0.198482i
$487$	−10.0152			−0.453831			−0.226915	−	0.973914i	$-0.572864\pi$
$487$	−10.0152			−0.453831			−0.226915	+	0.973914i	$0.572864\pi$
$488$	4.25906	+	12.3925i	0.192799	+	0.560983i
$489$	−13.5661			−0.613481
$490$	−5.45437	+	8.26135i	−0.246403	+	0.373210i
$491$	−27.3123	+	27.3123i	−1.23259	+	1.23259i	−0.269619	+	0.962967i	$0.586898\pi$
$491$	−27.3123	+	27.3123i	−1.23259	+	1.23259i	−0.962967	+	0.269619i	$0.913102\pi$
$492$	−20.2041	−	12.7999i	−0.910873	−	0.577065i
$493$	−5.10500	−	5.10500i	−0.229918	−	0.229918i
$494$	−19.0795	+	23.8340i	−0.858426	+	1.07234i
$495$	−1.31403			−0.0590615
$496$	−10.9020	+	5.15079i	−0.489512	+	0.231277i
$497$	−38.6272	−	13.9661i	−1.73267	−	0.626467i
$498$	−6.27654	−	5.02445i	−0.281258	−	0.225151i
$499$	18.1053	+	18.1053i	0.810503	+	0.810503i	0.984709	−	0.174206i	$-0.0557358\pi$
$499$	18.1053	+	18.1053i	0.810503	+	0.810503i	−0.174206	+	0.984709i	$0.555736\pi$
$500$	−1.07034	+	1.68949i	−0.0478671	+	0.0755562i
$501$	4.87263	+	4.87263i	0.217693	+	0.217693i
$502$	16.4028	−	1.81734i	0.732092	−	0.0811117i
$503$		−	2.52704i		−	0.112675i	−0.998412	−	0.0563375i	$-0.982058\pi$
$503$		−	2.52704i		−	0.112675i	0.998412	−	0.0563375i	$-0.0179423\pi$
$504$	−1.61636	+	1.56574i	−0.0719984	+	0.0697438i
$505$			2.30270i			0.102469i
$506$	−0.446199	−	4.02727i	−0.0198360	−	0.179034i
$507$	15.7424	+	15.7424i	0.699145	+	0.699145i
$508$	−23.9886	+	5.38168i	−1.06432	+	0.238773i
$509$	25.0178	+	25.0178i	1.10889	+	1.10889i	0.993296	+	0.115597i	$0.0368781\pi$
$509$	25.0178	+	25.0178i	1.10889	+	1.10889i	0.115597	+	0.993296i	$0.463122\pi$
$510$	2.76582	−	3.45505i	0.122472	−	0.152992i
$511$	15.5925	+	5.63765i	0.689770	+	0.249395i
$512$	4.66602	+	22.1411i	0.206211	+	0.978508i
$513$	22.7200			1.00311
$514$	−11.4567	−	9.17128i	−0.505335	−	0.404528i
$515$	−12.5357	−	12.5357i	−0.552387	−	0.552387i
$516$	0.764831	−	0.171584i	0.0336698	−	0.00755357i
$517$	27.6726	−	27.6726i	1.21704	−	1.21704i
$518$	31.2799	+	7.54187i	1.37436	+	0.331371i
$519$	−36.6757			−1.60988
$520$	13.0955	+	6.39647i	0.574274	+	0.280504i
$521$	3.39271			0.148637			0.0743187	−	0.997235i	$-0.476322\pi$
$521$	3.39271			0.148637			0.0743187	+	0.997235i	$0.476322\pi$
$522$	−1.60210	+	0.177504i	−0.0701221	+	0.00776913i
$523$	23.0833	+	23.0833i	1.00936	+	1.00936i	0.999956	+	0.00940786i	$0.00299466\pi$
$523$	23.0833	+	23.0833i	1.00936	+	1.00936i	0.00940786	+	0.999956i	$0.497005\pi$
$524$	−16.0881	−	10.1923i	−0.702814	−	0.445253i
$525$	−1.84543	−	3.93565i	−0.0805412	−	0.171766i
$526$	21.5812	−	26.9592i	0.940986	−	1.17548i
$527$		−	5.74174i		−	0.250114i
$528$	−12.2673	−	25.9644i	−0.533864	−	1.12995i
$529$	−22.5701			−0.981307
$530$	8.11393	−	10.1359i	0.352447	−	0.440276i
$531$	2.12991	−	2.12991i	0.0924302	−	0.0924302i
$532$	−13.5775	−	17.5252i	−0.588661	−	0.759815i
$533$	26.5206	+	26.5206i	1.14874	+	1.14874i
$534$	3.22305	+	29.0903i	0.139475	+	1.25886i
$535$			13.2430i			0.572544i
$536$	−1.15284	−	3.35440i	−0.0497951	−	0.144888i
$537$	9.71866			0.419391
$538$	27.0664	−	2.99881i	1.16692	−	0.129288i
$539$	−30.4595	+	2.79553i	−1.31199	+	0.120412i
$540$	−2.37417	−	10.5828i	−0.102168	−	0.455410i
$541$	−6.72937	+	6.72937i	−0.289318	+	0.289318i	−0.836811	−	0.547492i	$-0.815583\pi$
$541$	−6.72937	+	6.72937i	−0.289318	+	0.289318i	0.547492	+	0.836811i	$0.315583\pi$
$542$	4.92665	−	6.15436i	0.211618	−	0.264353i
$543$		−	13.7378i		−	0.589545i
$544$	−10.4823	−	2.49503i	−0.449423	−	0.106974i
$545$		−	3.56622i		−	0.152760i
$546$	−27.0241	+	16.5242i	−1.15652	+	0.707170i
$547$	11.9959	+	11.9959i	0.512908	+	0.512908i	0.915416	−	0.402508i	$-0.131862\pi$
$547$	11.9959	+	11.9959i	0.512908	+	0.512908i	−0.402508	+	0.915416i	$0.631862\pi$
$548$	33.2358	−	7.45621i	1.41976	−	0.318513i
$549$	−0.985153	+	0.985153i	−0.0420453	+	0.0420453i
$550$	−6.14204	+	0.680503i	−0.261897	+	0.0290168i
$551$		−	15.8796i		−	0.676493i
$552$	2.88154	−	0.990325i	0.122646	−	0.0421510i
$553$	−11.0785	+	30.6405i	−0.471104	+	1.30297i
$554$	−21.3518	+	2.36566i	−0.907150	+	0.100507i
$555$	−9.99034	+	9.99034i	−0.424066	+	0.424066i
$556$	−16.6471	+	26.2767i	−0.705994	+	1.11438i
$557$	1.78658	−	1.78658i	0.0756996	−	0.0756996i	−0.668243	−	0.743943i	$-0.732953\pi$
$557$	1.78658	−	1.78658i	0.0756996	−	0.0756996i	0.743943	+	0.668243i	$0.232953\pi$
$558$	−1.00079	−	0.801143i	−0.0423667	−	0.0339151i
$559$	−1.22917			−0.0519884
$560$	−6.74430	+	8.15564i	−0.284999	+	0.344639i
$561$	13.6747			0.577346
$562$	−9.50814	−	7.61139i	−0.401077	−	0.321067i
$563$	25.1096	−	25.1096i	1.05824	−	1.05824i	0.0600469	−	0.998196i	$-0.480875\pi$
$563$	25.1096	−	25.1096i	1.05824	−	1.05824i	0.998196	−	0.0600469i	$-0.0191250\pi$
$564$	24.8598	+	15.7494i	1.04679	+	0.663170i
$565$	0.887384	−	0.887384i	0.0373325	−	0.0373325i
$566$	−6.31752	+	0.699946i	−0.265545	+	0.0294209i
$567$	19.9233	+	7.20353i	0.836702	+	0.302520i
$568$	−39.4553	−	19.2720i	−1.65551	−	0.808633i
$569$			16.9846i			0.712030i	0.934480	+	0.356015i	$0.115865\pi$
$569$			16.9846i			0.712030i	−0.934480	+	0.356015i	$0.884135\pi$
$570$	9.67531	−	1.07197i	0.405254	−	0.0448999i
$571$	24.7972	−	24.7972i	1.03773	−	1.03773i	0.0384723	−	0.999260i	$-0.487751\pi$
$571$	24.7972	−	24.7972i	1.03773	−	1.03773i	0.999260	−	0.0384723i	$-0.0122491\pi$
$572$	9.85744	+	43.9392i	0.412160	+	1.83719i
$573$	17.2852	+	17.2852i	0.722099	+	0.722099i
$574$	−23.2354	+	14.2075i	−0.969826	+	0.593011i
$575$		−	0.655690i		−	0.0273441i
$576$	−1.89747	+	1.47893i	−0.0790613	+	0.0616220i
$577$			38.0906i			1.58573i	0.609397	+	0.792865i	$0.291412\pi$
$577$			38.0906i			1.58573i	−0.609397	+	0.792865i	$0.708588\pi$
$578$	−11.8180	+	14.7630i	−0.491562	+	0.614059i
$579$	−4.84681	+	4.84681i	−0.201427	+	0.201427i
$580$	−7.39659	+	1.65937i	−0.307126	+	0.0689016i
$581$	−8.28904	+	3.88674i	−0.343887	+	0.161249i
$582$	−30.5850	+	3.38865i	−1.26779	+	0.140464i
$583$	40.1167			1.66146
$584$	15.9267	+	7.77942i	0.659053	+	0.321915i
$585$			1.54952i			0.0640649i
$586$	−0.550183	−	4.96580i	−0.0227278	−	0.205135i
$587$	−19.8295	−	19.8295i	−0.818450	−	0.818450i	0.167434	−	0.985883i	$-0.446452\pi$
$587$	−19.8295	−	19.8295i	−0.818450	−	0.818450i	−0.985883	+	0.167434i	$0.946452\pi$
$588$	−7.06515	−	21.8893i	−0.291362	−	0.902701i
$589$	8.93012	−	8.93012i	0.367959	−	0.367959i
$590$	8.85256	−	11.0586i	0.364454	−	0.455276i
$591$	27.3209			1.12383
$592$	32.3823	+	11.6015i	1.33091	+	0.476820i
$593$		−	5.85503i		−	0.240437i	−0.992747	−	0.120219i	$-0.961640\pi$
$593$		−	5.85503i		−	0.240437i	0.992747	−	0.120219i	$-0.0383595\pi$
$594$	20.9427	−	26.1616i	0.859288	−	1.07342i
$595$	−2.13954	−	4.56288i	−0.0877125	−	0.187060i
$596$	−0.286934	+	0.452914i	−0.0117533	+	0.0185521i
$597$	23.3199	+	23.3199i	0.954418	+	0.954418i
$598$	−4.74900	+	0.526163i	−0.194201	+	0.0215164i
$599$	16.4465			0.671985			0.335992	−	0.941865i	$-0.390928\pi$
$599$	16.4465			0.671985			0.335992	+	0.941865i	$0.390928\pi$
$600$	−1.51036	−	4.39466i	−0.0616601	−	0.179411i
$601$	−7.56096			−0.308418			−0.154209	−	0.988038i	$-0.549283\pi$
$601$	−7.56096			−0.308418			−0.154209	+	0.988038i	$0.549283\pi$
$602$	0.209210	−	0.867696i	0.00852675	−	0.0353647i
$603$	0.266660	−	0.266660i	0.0108592	−	0.0108592i
$604$	3.64828	+	16.2621i	0.148446	+	0.661695i
$605$	−5.72322	−	5.72322i	−0.232682	−	0.232682i
$606$	−4.17681	−	3.34359i	−0.169671	−	0.135824i
$607$	−28.9016			−1.17308			−0.586540	−	0.809920i	$-0.699510\pi$
$607$	−28.9016			−1.17308			−0.586540	+	0.809920i	$0.699510\pi$
$608$	−12.4225	−	20.1836i	−0.503800	−	0.818551i
$609$	5.60198	−	15.4938i	0.227004	−	0.627841i
$610$	−4.09460	+	5.11497i	−0.165785	+	0.207099i
$611$	−32.6319	−	32.6319i	−1.32014	−	1.32014i
$612$	−0.250776	−	1.11782i	−0.0101370	−	0.0451854i
$613$	−31.1495	−	31.1495i	−1.25811	−	1.25811i	−0.951992	−	0.306122i	$-0.900968\pi$
$613$	−31.1495	−	31.1495i	−1.25811	−	1.25811i	−0.306122	−	0.951992i	$-0.599032\pi$
$614$	1.41695	+	12.7890i	0.0571832	+	0.516120i
$615$		−	11.9587i		−	0.482223i
$616$	−32.6953	−	0.520059i	−1.31733	−	0.0209538i
$617$			4.76961i			0.192017i	0.995381	+	0.0960085i	$0.0306076\pi$
$617$			4.76961i			0.192017i	−0.995381	+	0.0960085i	$0.969392\pi$
$618$	40.9404	−	4.53597i	1.64686	−	0.182463i
$619$	33.1839	+	33.1839i	1.33377	+	1.33377i	0.901966	+	0.431807i	$0.142124\pi$
$619$	33.1839	+	33.1839i	1.33377	+	1.33377i	0.431807	+	0.901966i	$0.357876\pi$
$620$	−5.09275	−	3.22641i	−0.204530	−	0.129576i
$621$	2.51429	+	2.51429i	0.100895	+	0.100895i
$622$	−1.63087	−	1.30554i	−0.0653921	−	0.0523472i
$623$	31.3422	+	11.3322i	1.25570	+	0.454013i
$624$	−30.6175	+	14.4657i	−1.22568	+	0.579090i
$625$	−1.00000			−0.0400000
$626$	−23.4610	+	29.3074i	−0.937689	+	1.17136i
$627$	21.2682	+	21.2682i	0.849371	+	0.849371i
$628$	−23.0744	+	36.4220i	−0.920769	+	1.45340i
$629$	−11.5825	+	11.5825i	−0.461825	+	0.461825i
$630$	−1.09384	−	0.263735i	−0.0435796	−	0.0105075i
$631$	12.8457			0.511380			0.255690	−	0.966759i	$-0.417697\pi$
$631$	12.8457			0.511380			0.255690	+	0.966759i	$0.417697\pi$
$632$	−15.2872	+	31.2974i	−0.608093	+	1.24494i
$633$	−13.5311			−0.537812
$634$	−1.21698	−	10.9841i	−0.0483323	−	0.436234i
$635$	−8.69208	−	8.69208i	−0.344935	−	0.344935i
$636$	6.60362	+	29.4354i	0.261850	+	1.16719i
$637$	3.29652	+	35.9182i	0.130613	+	1.42313i
$638$	−18.2850	−	14.6374i	−0.723910	−	0.579500i
$639$		−	4.66857i		−	0.184686i
$640$	−8.10322	+	7.89543i	−0.320308	+	0.312094i
$641$	39.7192			1.56881			0.784407	−	0.620246i	$-0.212967\pi$
$641$	39.7192			1.56881			0.784407	+	0.620246i	$0.212967\pi$
$642$	−24.0212	−	19.2293i	−0.948041	−	0.758919i
$643$	−21.0735	+	21.0735i	−0.831057	+	0.831057i	−0.987661	−	0.156605i	$-0.949945\pi$
$643$	−21.0735	+	21.0735i	−0.831057	+	0.831057i	0.156605	+	0.987661i	$0.449945\pi$
$644$	0.436870	−	3.44197i	0.0172151	−	0.135633i
$645$	0.277130	+	0.277130i	0.0109120	+	0.0109120i
$646$	11.2173	−	1.24281i	0.441338	−	0.0488978i
$647$		−	21.7509i		−	0.855117i	−0.903988	−	0.427559i	$-0.859374\pi$
$647$		−	21.7509i		−	0.855117i	0.903988	−	0.427559i	$-0.140626\pi$
$648$	20.3505	+	9.94019i	0.799442	+	0.390488i
$649$	43.7686			1.71807
$650$	0.802457	+	7.24276i	0.0314749	+	0.284084i
$651$	11.8635	−	5.56282i	0.464968	−	0.218024i
$652$	−8.83799	+	13.9504i	−0.346122	+	0.546340i
$653$	−12.1669	+	12.1669i	−0.476129	+	0.476129i	−0.903891	−	0.427762i	$-0.859302\pi$
$653$	−12.1669	+	12.1669i	−0.476129	+	0.476129i	0.427762	+	0.903891i	$0.359302\pi$
$654$	6.46870	+	5.17828i	0.252946	+	0.202487i
$655$		−	9.52249i		−	0.372075i
$656$	−26.3250	+	12.4376i	−1.02782	+	0.485608i
$657$			1.88454i			0.0735228i
$658$	28.5896	−	17.4814i	1.11454	−	0.681496i
$659$	−5.00285	−	5.00285i	−0.194883	−	0.194883i	0.602919	−	0.797802i	$-0.294004\pi$
$659$	−5.00285	−	5.00285i	−0.194883	−	0.194883i	−0.797802	+	0.602919i	$0.794004\pi$
$660$	7.68410	−	12.1290i	0.299103	−	0.472122i
$661$	−14.4182	+	14.4182i	−0.560804	+	0.560804i	−0.929536	−	0.368732i	$-0.879792\pi$
$661$	−14.4182	+	14.4182i	−0.560804	+	0.560804i	0.368732	+	0.929536i	$0.379792\pi$
$662$	−3.25789	−	29.4048i	−0.126621	−	1.14285i
$663$		−	16.1253i		−	0.626256i
$664$	−9.25579	+	3.18102i	−0.359194	+	0.123448i
$665$	3.76902	−	10.4243i	0.146156	−	0.404236i
$666$	0.402731	+	3.63494i	0.0156055	+	0.140851i
$667$	1.75731	−	1.75731i	0.0680432	−	0.0680432i
$668$	8.18506	−	1.83626i	0.316689	−	0.0710470i
$669$	−15.1737	+	15.1737i	−0.586650	+	0.586650i
$670$	1.10832	−	1.38451i	0.0428182	−	0.0534885i
$671$	−20.2444			−0.781527
$672$	−5.00039	−	24.0756i	−0.192894	−	0.928737i
$673$	6.26349			0.241440			0.120720	−	0.992687i	$-0.461480\pi$
$673$	6.26349			0.241440			0.120720	+	0.992687i	$0.461480\pi$
$674$	25.7073	−	32.1136i	0.990209	−	1.23697i
$675$	3.83458	−	3.83458i	0.147593	−	0.147593i
$676$	26.4441	−	5.93255i	1.01708	−	0.228175i
$677$	−27.7880	+	27.7880i	−1.06798	+	1.06798i	−0.0704674	+	0.997514i	$0.522449\pi$
$677$	−27.7880	+	27.7880i	−1.06798	+	1.06798i	−0.997514	+	0.0704674i	$0.977551\pi$
$678$	0.321095	+	2.89812i	0.0123316	+	0.111302i
$679$	−11.9144	+	32.9526i	−0.457233	+	1.26460i
$680$	−1.75106	−	5.09505i	−0.0671502	−	0.195386i
$681$			15.0464i			0.576580i
$682$	−2.05129	−	18.5144i	−0.0785480	−	0.708953i
$683$	1.81836	−	1.81836i	0.0695774	−	0.0695774i	−0.671462	−	0.741039i	$-0.734333\pi$
$683$	1.81836	−	1.81836i	0.0695774	−	0.0695774i	0.741039	+	0.671462i	$0.234333\pi$
$684$	1.34852	−	2.12858i	0.0515620	−	0.0813884i
$685$	12.0427	+	12.0427i	0.460128	+	0.460128i
$686$	−25.9165	−	3.78634i	−0.989496	−	0.144563i
$687$		−	38.6160i		−	1.47329i
$688$	0.321824	−	0.898279i	0.0122694	−	0.0342466i
$689$		−	47.3060i		−	1.80222i
$690$	1.18934	+	0.952084i	0.0452775	+	0.0362452i
$691$	−19.4464	+	19.4464i	−0.739776	+	0.739776i	−0.972535	−	0.232759i	$-0.925225\pi$
$691$	−19.4464	+	19.4464i	−0.739776	+	0.739776i	0.232759	+	0.972535i	$0.425225\pi$
$692$	−23.8933	+	37.7146i	−0.908287	+	1.43369i
$693$	−1.47598	−	3.14774i	−0.0560678	−	0.119573i
$694$	−1.61368	−	14.5646i	−0.0612544	−	0.552866i
$695$	−15.5531			−0.589962
$696$	7.73020	−	15.8260i	0.293012	−	0.599882i
$697$		−	13.8646i		−	0.525159i
$698$	−17.2110	+	1.90689i	−0.651448	+	0.0721768i
$699$	−24.0139	−	24.0139i	−0.908288	−	0.908288i
$700$	−5.24939	−	0.666275i	−0.198408	−	0.0251828i
$701$	25.1291	−	25.1291i	0.949115	−	0.949115i	−0.0496520	−	0.998767i	$-0.515811\pi$
$701$	25.1291	−	25.1291i	0.949115	−	0.949115i	0.998767	+	0.0496520i	$0.0158112\pi$
$702$	−30.8500	−	24.6958i	−1.16436	−	0.932084i
$703$	−36.0285			−1.35884
$704$	−34.6917	−	4.30042i	−1.30749	−	0.162078i
$705$			14.7144i			0.554177i
$706$	9.45454	+	7.56848i	0.355826	+	0.284844i
$707$	−5.51606	+	2.58649i	−0.207453	+	0.0972748i
$708$	7.20476	+	32.1150i	0.270771	+	1.20695i
$709$	−13.5498	−	13.5498i	−0.508873	−	0.508873i	0.405307	−	0.914180i	$-0.367164\pi$
$709$	−13.5498	−	13.5498i	−0.508873	−	0.508873i	−0.914180	+	0.405307i	$0.867164\pi$
$710$	−2.41772	−	21.8217i	−0.0907356	−	0.818955i
$711$	−3.70328			−0.138884
$712$	32.0141	+	15.6373i	1.19978	+	0.586032i
$713$	1.97649			0.0740203
$714$	11.3832	+	2.74460i	0.426005	+	0.102714i
$715$	−15.9210	+	15.9210i	−0.595411	+	0.595411i
$716$	6.33147	−	9.99396i	0.236618	−	0.373492i
$717$	5.46093	+	5.46093i	0.203942	+	0.203942i
$718$	−1.94990	+	2.43581i	−0.0727695	+	0.0909036i
$719$	47.9742			1.78914			0.894568	−	0.446931i	$-0.147483\pi$
$719$	47.9742			1.78914			0.894568	+	0.446931i	$0.147483\pi$
$720$	−1.13239	−	0.405699i	−0.0422018	−	0.0151195i
$721$	15.9483	−	44.1095i	0.593948	−	1.64272i
$722$	−1.59758	−	1.27888i	−0.0594557	−	0.0475951i
$723$	4.42070	+	4.42070i	0.164407	+	0.164407i
$724$	−14.1269	−	8.94983i	−0.525024	−	0.332618i
$725$	−2.68009	−	2.68009i	−0.0995360	−	0.0995360i
$726$	18.6915	−	2.07092i	0.693708	−	0.0768590i
$727$		−	12.6465i		−	0.469034i	−0.972112	−	0.234517i	$-0.924649\pi$
$727$		−	12.6465i		−	0.469034i	0.972112	−	0.234517i	$-0.0753509\pi$
$728$	−0.613259	+	38.5547i	−0.0227289	+	1.42893i
$729$			29.1367i			1.07914i
$730$	0.975951	+	8.80867i	0.0361216	+	0.326023i
$731$	0.321296	+	0.321296i	0.0118836	+	0.0118836i
$732$	−3.33243	−	14.8542i	−0.123170	−	0.549027i
$733$	18.8835	+	18.8835i	0.697477	+	0.697477i	0.963866	−	0.266389i	$-0.0858305\pi$
$733$	18.8835	+	18.8835i	0.697477	+	0.697477i	−0.266389	+	0.963866i	$0.585830\pi$
$734$	8.25129	−	10.3075i	0.304561	−	0.380457i
$735$	7.35491	−	8.84138i	0.271290	−	0.326119i
$736$	0.858872	−	3.60833i	0.0316584	−	0.133005i
$737$	5.47974			0.201849
$738$	−2.41660	−	1.93452i	−0.0889564	−	0.0712108i
$739$	−5.82858	−	5.82858i	−0.214408	−	0.214408i	0.591729	−	0.806137i	$-0.298445\pi$
$739$	−5.82858	−	5.82858i	−0.214408	−	0.214408i	−0.806137	+	0.591729i	$0.798445\pi$
$740$	3.76487	+	16.7818i	0.138399	+	0.616911i
$741$	25.0797	−	25.0797i	0.921326	−	0.921326i
$742$	33.3943	+	8.05167i	1.22594	+	0.295586i
$743$	3.18943			0.117009			0.0585043	−	0.998287i	$-0.481367\pi$
$743$	3.18943			0.117009			0.0585043	+	0.998287i	$0.481367\pi$
$744$	13.2472	−	4.55278i	0.485665	−	0.166913i
$745$	−0.268078			−0.00982160
$746$	9.57182	−	1.06050i	0.350449	−	0.0388278i
$747$	−0.735795	−	0.735795i	−0.0269213	−	0.0269213i
$748$	8.90872	−	14.0620i	0.325735	−	0.514159i
$749$	−31.7233	+	14.8751i	−1.15915	+	0.543524i
$750$	1.45203	−	1.81388i	0.0530208	−	0.0662335i
$751$		−	18.1496i		−	0.662287i	−0.943580	−	0.331144i	$-0.892566\pi$
$751$		−	18.1496i		−	0.662287i	0.943580	−	0.331144i	$-0.107434\pi$
$752$	32.3911	−	15.3036i	1.18118	−	0.558067i
$753$	−19.1724			−0.698680
$754$	−17.2606	+	21.5619i	−0.628593	+	0.785237i
$755$	−5.89243	+	5.89243i	−0.214447	+	0.214447i
$756$	22.6841	−	17.5743i	0.825012	−	0.639171i
$757$	−13.7316	−	13.7316i	−0.499085	−	0.499085i	0.412068	−	0.911153i	$-0.364807\pi$
$757$	−13.7316	−	13.7316i	−0.499085	−	0.499085i	−0.911153	+	0.412068i	$0.864807\pi$
$758$	4.75905	+	42.9539i	0.172857	+	1.56016i
$759$			4.70727i			0.170863i
$760$	5.20089	−	10.6477i	0.188656	−	0.386234i
$761$	49.6904			1.80128			0.900638	−	0.434571i	$-0.143100\pi$
$761$	49.6904			1.80128			0.900638	+	0.434571i	$0.143100\pi$
$762$	28.3876	−	3.14519i	1.02837	−	0.113938i
$763$	8.54281	−	4.00573i	0.309271	−	0.145017i
$764$	29.0357	−	6.51395i	1.05047	−	0.235666i
$765$	0.405034	−	0.405034i	0.0146440	−	0.0146440i
$766$	−29.6722	+	37.0665i	−1.07210	+	1.33927i
$767$		−	51.6124i		−	1.86362i
$768$	−2.55520	−	26.1627i	−0.0922027	−	0.944065i
$769$		−	3.60667i		−	0.130060i	−0.997883	−	0.0650298i	$-0.979286\pi$
$769$		−	3.60667i		−	0.130060i	0.997883	−	0.0650298i	$-0.0207143\pi$
$770$	−8.52913	−	13.9488i	−0.307369	−	0.502678i
$771$	12.0555	+	12.0555i	0.434169	+	0.434169i
$772$	1.82653	+	8.14168i	0.0657381	+	0.293026i
$773$	21.3669	−	21.3669i	0.768515	−	0.768515i	−0.209330	−	0.977845i	$-0.567128\pi$
$773$	21.3669	−	21.3669i	0.768515	−	0.768515i	0.977845	+	0.209330i	$0.0671283\pi$
$774$	0.100832	−	0.0111717i	0.00362434	−	0.000401557i
$775$		−	3.01437i		−	0.108280i
$776$	−16.4408	+	33.6590i	−0.590189	+	1.20829i
$777$	−35.1532	−	12.7101i	−1.26112	−	0.455972i
$778$	44.4063	−	4.91997i	1.59204	−	0.176390i
$779$	21.5636	−	21.5636i	0.772596	−	0.772596i
$780$	−14.3027	−	9.06117i	−0.512118	−	0.324442i
$781$	47.9684	−	47.9684i	1.71644	−	1.71644i
$782$	1.37889	+	1.10382i	0.0493089	+	0.0394725i
$783$	20.5540			0.734541
$784$	−27.1122	−	6.99507i	−0.968291	−	0.249824i
$785$	−21.5580			−0.769438
$786$	17.2727	+	13.8270i	0.616095	+	0.493192i
$787$	−16.9931	+	16.9931i	−0.605738	+	0.605738i	−0.941829	−	0.336091i	$-0.890895\pi$
$787$	−16.9931	+	16.9931i	−0.605738	+	0.605738i	0.336091	+	0.941829i	$0.390895\pi$
$788$	17.7989	−	28.0948i	0.634058	−	1.00083i
$789$	−28.3682	+	28.3682i	−1.00994	+	1.00994i
$790$	−17.3098	+	1.91783i	−0.615855	+	0.0682333i
$791$	3.12246	+	1.12896i	0.111022	+	0.0401413i
$792$	−1.20799	−	3.51486i	−0.0429240	−	0.124895i
$793$			23.8724i			0.847735i
$794$	27.4591	−	3.04231i	0.974486	−	0.107968i
$795$	−10.6657	+	10.6657i	−0.378272	+	0.378272i
$796$	39.1727	−	8.78812i	1.38844	−	0.311487i
$797$	16.5746	+	16.5746i	0.587104	+	0.587104i	0.936846	−	0.349742i	$-0.113731\pi$
$797$	16.5746	+	16.5746i	0.587104	+	0.587104i	−0.349742	+	0.936846i	$0.613731\pi$
$798$	13.4356	+	21.9729i	0.475615	+	0.777834i
$799$			17.0595i			0.603520i
$800$	−5.50311	−	1.30988i	−0.194564	−	0.0463111i
$801$			3.78808i			0.133845i
$802$	−2.07637	+	2.59380i	−0.0733193	+	0.0915904i
$803$	−19.3632	+	19.3632i	−0.683311	+	0.683311i
$804$	0.902021	+	4.02073i	0.0318118	+	0.141800i
$805$	1.57069	−	0.736498i	0.0553596	−	0.0259582i
$806$	−21.8324	+	2.41891i	−0.769013	+	0.0852023i
$807$	−31.6365			−1.11366
$808$	−6.15940	+	2.11686i	−0.216687	+	0.0744709i
$809$			25.7007i			0.903588i	0.892122	+	0.451794i	$0.149216\pi$
$809$			25.7007i			0.903588i	−0.892122	+	0.451794i	$0.850784\pi$
$810$	1.24703	+	11.2553i	0.0438161	+	0.395472i
$811$	1.45385	+	1.45385i	0.0510514	+	0.0510514i	0.732172	−	0.681120i	$-0.238507\pi$
$811$	1.45385	+	1.45385i	0.0510514	+	0.0510514i	−0.681120	+	0.732172i	$0.738507\pi$
$812$	−12.2831	−	15.8545i	−0.431054	−	0.556384i
$813$	−6.47602	+	6.47602i	−0.227124	+	0.227124i
$814$	−33.2101	+	41.4861i	−1.16401	+	1.45409i
$815$	−8.25717			−0.289236
$816$	11.7844	+	4.22196i	0.412537	+	0.147798i
$817$			0.999423i			0.0349654i
$818$	27.6812	−	34.5793i	0.967851	−	1.20904i
$819$	−3.71185	+	1.74049i	−0.129703	+	0.0608177i
$820$	−12.2975	−	7.79082i	−0.429447	−	0.272067i
$821$	−10.1678	−	10.1678i	−0.354859	−	0.354859i	0.507055	−	0.861914i	$-0.330734\pi$
$821$	−10.1678	−	10.1678i	−0.354859	−	0.354859i	−0.861914	+	0.507055i	$0.830734\pi$
$822$	−39.3304	+	4.35759i	−1.37181	+	0.151988i
$823$	−46.5085			−1.62119			−0.810593	−	0.585610i	$-0.800855\pi$
$823$	−46.5085			−1.62119			−0.810593	+	0.585610i	$0.800855\pi$
$824$	22.0072	−	45.0552i	0.766657	−	1.56957i
$825$	7.17911			0.249945
$826$	36.4342	+	8.78464i	1.26771	+	0.305657i
$827$	−17.9248	+	17.9248i	−0.623305	+	0.623305i	−0.946375	−	0.323070i	$-0.895285\pi$
$827$	−17.9248	+	17.9248i	−0.623305	+	0.623305i	0.323070	+	0.946375i	$0.395285\pi$
$828$	0.384792	−	0.0863252i	0.0133724	−	0.00300001i
$829$	−14.2329	−	14.2329i	−0.494331	−	0.494331i	0.415337	−	0.909668i	$-0.363664\pi$
$829$	−14.2329	−	14.2329i	−0.494331	−	0.494331i	−0.909668	+	0.415337i	$0.863664\pi$
$830$	−3.82029	−	3.05819i	−0.132604	−	0.106151i
$831$	24.9570			0.865748
$832$	−5.07110	+	40.9088i	−0.175809	+	1.41826i
$833$	8.52707	−	10.2504i	0.295445	−	0.355157i
$834$	22.5836	−	28.2114i	0.782006	−	0.976881i
$835$	2.96579	+	2.96579i	0.102635	+	0.102635i
$836$	35.7264	−	8.01496i	1.23562	−	0.277203i
$837$	11.5589	+	11.5589i	0.399532	+	0.399532i
$838$	2.30616	+	20.8147i	0.0796648	+	0.719033i
$839$			43.8985i			1.51554i	0.652519	+	0.757772i	$0.273712\pi$
$839$			43.8985i			1.51554i	−0.652519	+	0.757772i	$0.726288\pi$
$840$	8.83084	−	8.55430i	0.304693	−	0.295152i
$841$			14.6343i			0.504629i
$842$	−40.9865	+	4.54107i	−1.41249	+	0.156496i
$843$	10.0051	+	10.0051i	0.344593	+	0.344593i
$844$	−8.81517	+	13.9144i	−0.303431	+	0.478953i
$845$	9.58181	+	9.58181i	0.329624	+	0.329624i
$846$	2.97347	+	2.38030i	0.102230	+	0.0818364i
$847$	7.28129	−	20.1384i	0.250188	−	0.691964i
$848$	34.5713	+	12.3858i	1.18718	+	0.425329i
$849$	7.38423			0.253426
$850$	1.68345	−	2.10296i	0.0577417	−	0.0721309i
$851$	−3.98708	−	3.98708i	−0.136675	−	0.136675i
$852$	43.0926	+	27.3004i	1.47633	+	0.935297i
$853$	−8.35675	+	8.35675i	−0.286130	+	0.286130i	−0.835548	−	0.549418i	$-0.814849\pi$
$853$	−8.35675	+	8.35675i	−0.286130	+	0.286130i	0.549418	+	0.835548i	$0.314849\pi$
$854$	−16.8520	−	4.06318i	−0.576664	−	0.139039i
$855$	1.25990			0.0430876
$856$	−35.4232	+	12.1742i	−1.21074	+	0.416107i
$857$	25.7773			0.880535			0.440267	−	0.897867i	$-0.354884\pi$
$857$	25.7773			0.880535			0.440267	+	0.897867i	$0.354884\pi$
$858$	−5.76093	−	51.9966i	−0.196675	−	1.77513i
$859$	−3.99405	−	3.99405i	−0.136275	−	0.136275i	0.635679	−	0.771954i	$-0.280720\pi$
$859$	−3.99405	−	3.99405i	−0.136275	−	0.136275i	−0.771954	+	0.635679i	$0.780720\pi$
$860$	0.465523	−	0.104437i	0.0158742	−	0.00356126i
$861$	28.6469	−	13.4326i	0.976284	−	0.457780i
$862$	20.8575	+	16.6967i	0.710411	+	0.568693i
$863$		−	4.95262i		−	0.168589i	−0.996441	−	0.0842945i	$-0.973136\pi$
$863$		−	4.95262i		−	0.168589i	0.996441	−	0.0842945i	$-0.0268636\pi$
$864$	26.1249	−	16.0793i	0.888788	−	0.547028i
$865$	−22.3231			−0.759007
$866$	28.5863	+	22.8837i	0.971403	+	0.777621i
$867$	15.5345	−	15.5345i	0.527581	−	0.527581i
$868$	2.00840	−	15.8236i	0.0681696	−	0.537089i
$869$	−38.0503	−	38.0503i	−1.29077	−	1.29077i
$870$	8.75294	−	0.969777i	0.296752	−	0.0328785i
$871$		−	6.46177i		−	0.218949i
$872$	9.53916	−	3.27841i	0.323037	−	0.111021i
$873$	−3.98272			−0.134795
$874$	0.427816	+	3.86135i	0.0144711	+	0.130612i
$875$	−1.12324	−	2.39548i	−0.0379725	−	0.0809820i
$876$	−17.3950	−	11.0202i	−0.587722	−	0.372339i
$877$	20.9265	−	20.9265i	0.706637	−	0.706637i	−0.259190	−	0.965826i	$-0.583455\pi$
$877$	20.9265	−	20.9265i	0.706637	−	0.706637i	0.965826	+	0.259190i	$0.0834555\pi$
$878$	2.97086	+	2.37821i	0.100262	+	0.0802607i
$879$			5.80427i			0.195773i
$880$	−7.46660	−	15.8035i	−0.251699	−	0.532737i
$881$			10.0400i			0.338257i	0.985594	+	0.169128i	$0.0540953\pi$
$881$			10.0400i			0.338257i	−0.985594	+	0.169128i	$0.945905\pi$
$882$	−0.596876	−	2.91651i	−0.0200978	−	0.0982040i
$883$	22.3597	+	22.3597i	0.752465	+	0.752465i	0.974939	−	0.222474i	$-0.0714131\pi$
$883$	22.3597	+	22.3597i	0.752465	+	0.752465i	−0.222474	+	0.974939i	$0.571413\pi$
$884$	−16.5821	−	10.5053i	−0.557717	−	0.353330i
$885$	−11.6366	+	11.6366i	−0.391159	+	0.391159i
$886$	5.24455	+	47.3358i	0.176194	+	1.59028i
$887$		−	25.9525i		−	0.871400i	−0.900092	−	0.435700i	$-0.856501\pi$
$887$		−	25.9525i		−	0.871400i	0.900092	−	0.435700i	$-0.143499\pi$
$888$	−35.9069	−	17.5387i	−1.20496	−	0.588561i
$889$	11.0584	−	30.5850i	0.370887	−	1.02579i
$890$	1.96175	+	17.7062i	0.0657578	+	0.593512i
$891$	−24.7414	+	24.7414i	−0.828868	+	0.828868i
$892$	5.71824	+	25.4888i	0.191461	+	0.853429i
$893$	−26.5325	+	26.5325i	−0.887878	+	0.887878i
$894$	0.389258	−	0.486260i	0.0130187	−	0.0162630i
$895$	5.91537			0.197729
$896$	−28.0152	−	10.5426i	−0.935923	−	0.352205i
$897$	5.55086			0.185338
$898$	−11.1758	+	13.9608i	−0.372941	+	0.465877i
$899$	8.07879	−	8.07879i	0.269443	−	0.269443i
$900$	−0.131656	−	0.586850i	−0.00438852	−	0.0195617i
$901$	−12.3655	+	12.3655i	−0.411953	+	0.411953i
$902$	−4.95326	−	44.7068i	−0.164926	−	1.48857i
$903$	−0.352575	+	0.975143i	−0.0117330	+	0.0324507i
$904$	3.18940	+	1.55786i	0.106078	+	0.0518137i
$905$		−	8.36167i		−	0.277951i
$906$	−2.13215	−	19.2442i	−0.0708358	−	0.639344i
$907$	−23.5825	+	23.5825i	−0.783045	+	0.783045i	−0.980343	−	0.197298i	$-0.936783\pi$
$907$	−23.5825	+	23.5825i	−0.783045	+	0.783045i	0.197298	+	0.980343i	$0.436783\pi$
$908$	15.4726	+	9.80236i	0.513477	+	0.325303i
$909$	−0.489646	−	0.489646i	−0.0162405	−	0.0162405i
$910$	−16.4485	+	10.0576i	−0.545263	+	0.333408i
$911$		−	24.0854i		−	0.797984i	−0.916954	−	0.398992i	$-0.869360\pi$
$911$		−	24.0854i		−	0.797984i	0.916954	−	0.398992i	$-0.130640\pi$
$912$	11.7619	+	24.8947i	0.389474	+	0.824345i
$913$		−	15.1202i		−	0.500407i
$914$	38.6848	+	30.9677i	1.27958	+	1.02432i
$915$	5.38229	−	5.38229i	0.177933	−	0.177933i
$916$	−39.7098	−	25.1573i	−1.31205	−	0.831222i
$917$	22.8109	−	10.6961i	0.753284	−	0.353215i
$918$	1.60865	+	14.5193i	0.0530935	+	0.479207i
$919$	21.0056			0.692909			0.346455	−	0.938067i	$-0.387385\pi$
$919$	21.0056			0.692909			0.346455	+	0.938067i	$0.387385\pi$
$920$	1.75388	−	0.602773i	0.0578237	−	0.0198728i
$921$		−	14.9484i		−	0.492565i
$922$	43.1589	−	4.78176i	1.42136	−	0.157479i
$923$	−56.5648	−	56.5648i	−1.86185	−	1.86185i
$924$	37.6860	+	4.78326i	1.23978	+	0.157358i
$925$	−6.08074	+	6.08074i	−0.199933	+	0.199933i
$926$	−0.461958	−	0.369803i	−0.0151809	−	0.0121525i
$927$	5.33117			0.175099
$928$	−11.2382	−	18.2594i	−0.368913	−	0.599394i
$929$			2.00319i			0.0657224i	0.999460	+	0.0328612i	$0.0104619\pi$
$929$			2.00319i			0.0657224i	−0.999460	+	0.0328612i	$0.989538\pi$
$930$	5.46771	+	4.37697i	0.179293	+	0.143527i
$931$	29.2046	−	2.68036i	0.957144	−	0.0878452i
$932$	−40.3385	+	9.04966i	−1.32133	+	0.296431i
$933$	1.71611	+	1.71611i	0.0561829	+	0.0561829i
$934$	4.16604	+	37.6016i	0.136317	+	1.23036i
$935$	8.32326			0.272200
$936$	−4.14476	+	1.42447i	−0.135476	+	0.0465603i
$937$	−48.2490			−1.57623			−0.788113	−	0.615531i	$-0.788942\pi$
$937$	−48.2490			−1.57623			−0.788113	+	0.615531i	$0.788942\pi$
$938$	4.56149	+	1.09982i	0.148938	+	0.0359104i
$939$	30.8391	−	30.8391i	1.00640	−	1.00640i
$940$	15.1312	+	9.58607i	0.493526	+	0.312663i
$941$	4.58268	+	4.58268i	0.149391	+	0.149391i	0.777846	−	0.628455i	$-0.216312\pi$
$941$	4.58268	+	4.58268i	0.149391	+	0.149391i	−0.628455	+	0.777846i	$0.716312\pi$
$942$	31.3030	−	39.1036i	1.01991	−	1.27406i
$943$	4.77265			0.155419
$944$	37.7184	+	13.5133i	1.22763	+	0.439819i
$945$	13.4928	+	4.87850i	0.438921	+	0.158697i
$946$	1.15081	+	0.921242i	0.0374162	+	0.0299522i
$947$	2.50849	+	2.50849i	0.0815151	+	0.0815151i	0.746689	−	0.665174i	$-0.231642\pi$
$947$	2.50849	+	2.50849i	0.0815151	+	0.0815151i	−0.665174	+	0.746689i	$0.731642\pi$
$948$	21.6557	−	34.1826i	0.703345	−	1.11020i
$949$	22.8333	+	22.8333i	0.741199	+	0.741199i
$950$	5.88899	−	0.652467i	0.191064	−	0.0211688i
$951$			12.8387i			0.416325i
$952$	10.2382	−	9.91761i	0.331822	−	0.321432i
$953$		−	2.28997i		−	0.0741795i	−0.999312	−	0.0370897i	$-0.988191\pi$
$953$		−	2.28997i		−	0.0741795i	0.999312	−	0.0370897i	$-0.0118087\pi$
$954$	0.429954	+	3.88065i	0.0139203	+	0.125641i
$955$	10.5208	+	10.5208i	0.340446	+	0.340446i
$956$	9.17327	−	2.05796i	0.296685	−	0.0665591i
$957$	19.2407	+	19.2407i	0.621962	+	0.621962i
$958$	−22.9948	+	28.7251i	−0.742929	+	0.928066i
$959$	−15.3212	+	42.3749i	−0.494746	+	1.36836i
$960$	10.3667	−	8.08000i	0.334583	−	0.260781i
$961$	−21.9135			−0.706889
$962$	48.9208	+	39.1618i	1.57727	+	1.26263i
$963$	−2.81599	−	2.81599i	−0.0907440	−	0.0907440i
$964$	7.42589	−	1.66595i	0.239172	−	0.0536565i
$965$	−2.95007	+	2.95007i	−0.0949660	+	0.0949660i
$966$	−0.944779	+	3.91847i	−0.0303978	+	0.126075i
$967$	30.3317			0.975402			0.487701	−	0.873011i	$-0.337836\pi$
$967$	30.3317			0.975402			0.487701	+	0.873011i	$0.337836\pi$
$968$	10.0475	−	20.5702i	0.322939	−	0.661150i
$969$	−13.1113			−0.421196
$970$	−18.6159	+	2.06254i	−0.597722	+	0.0662242i
$971$	11.5680	+	11.5680i	0.371236	+	0.371236i	0.867927	−	0.496691i	$-0.165452\pi$
$971$	11.5680	+	11.5680i	0.371236	+	0.371236i	−0.496691	+	0.867927i	$0.665452\pi$
$972$	5.25932	+	3.33193i	0.168693	+	0.106872i
$973$	−17.4699	−	37.2571i	−0.560059	−	1.19441i
$974$	8.85138	−	11.0571i	0.283617	−	0.354293i
$975$		−	8.46569i		−	0.271119i
$976$	−17.4460	−	6.25032i	−0.558432	−	0.200068i
$977$	−0.542253			−0.0173482			−0.00867410	−	0.999962i	$-0.502761\pi$
$977$	−0.542253			−0.0173482			−0.00867410	+	0.999962i	$0.502761\pi$
$978$	11.9897	−	14.9775i	0.383388	−	0.478928i
$979$	−38.9216	+	38.9216i	−1.24394	+	1.24394i
$980$	−4.30029	−	13.3232i	−0.137368	−	0.425594i
$981$	0.758322	+	0.758322i	0.0242113	+	0.0242113i
$982$	−6.01529	−	54.2924i	−0.191956	−	1.73254i
$983$		−	11.7834i		−	0.375832i	−0.982185	−	0.187916i	$-0.939827\pi$
$983$		−	11.7834i		−	0.375832i	0.982185	−	0.187916i	$-0.0601733\pi$
$984$	31.9880	−	10.9936i	1.01974	−	0.350464i
$985$	16.6292			0.529849
$986$	10.1479	−	1.12433i	0.323175	−	0.0358060i
$987$	−35.2481	+	16.5278i	−1.12196	+	0.526087i
$988$	−9.45132	−	42.1289i	−0.300687	−	1.34030i
$989$	−0.110601	+	0.110601i	−0.00351689	+	0.00351689i
$990$	1.16134	−	1.45075i	0.0369098	−	0.0461077i
$991$			31.4105i			0.997788i	0.866663	+	0.498894i	$0.166260\pi$
$991$			31.4105i			0.997788i	−0.866663	+	0.498894i	$0.833740\pi$
$992$	3.94845	−	16.5884i	0.125364	−	0.526683i
$993$			34.3698i			1.09069i
$994$	49.5578	−	30.3027i	1.57188	−	0.961143i
$995$	14.1939	+	14.1939i	0.449977	+	0.449977i
$996$	11.0944	−	2.48894i	0.351539	−	0.0788652i
$997$	−17.6622	+	17.6622i	−0.559368	+	0.559368i	−0.929128	−	0.369759i	$-0.879440\pi$
$997$	−17.6622	+	17.6622i	−0.559368	+	0.559368i	0.369759	+	0.929128i	$0.379440\pi$
$998$	−35.9903	+	3.98753i	−1.13925	+	0.126223i
$999$		−	46.6341i		−	1.47544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.20	yes	128
7.6	odd	2	inner	560.2.bc.a.251.19	✓	128
16.3	odd	4	inner	560.2.bc.a.531.19	yes	128
112.83	even	4	inner	560.2.bc.a.531.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.19	✓	128	7.6	odd	2	inner
560.2.bc.a.251.20	yes	128	1.1	even	1	trivial
560.2.bc.a.531.19	yes	128	16.3	odd	4	inner
560.2.bc.a.531.20	yes	128	112.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883798 + 1.10404i) q^{2} +(1.16174 - 1.16174i) q^{3} +(-0.437803 - 1.95149i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.255863 + 2.30935i) q^{6} +(2.48811 + 0.899608i) q^{7} +(2.54145 + 1.24137i) q^{8} +0.300718i q^{9} +O(q^{10})\)	\(q+(-0.883798 + 1.10404i) q^{2} +(1.16174 - 1.16174i) q^{3} +(-0.437803 - 1.95149i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.255863 + 2.30935i) q^{6} +(2.48811 + 0.899608i) q^{7} +(2.54145 + 1.24137i) q^{8} +0.300718i q^{9} +(0.155734 + 1.40561i) q^{10} +(-3.08981 + 3.08981i) q^{11} +(-2.77574 - 1.75852i) q^{12} +(3.64354 + 3.64354i) q^{13} +(-3.19219 + 1.95190i) q^{14} -1.64295i q^{15} +(-3.61666 + 1.70874i) q^{16} -1.90479i q^{17} +(-0.332005 - 0.265774i) q^{18} +(2.96251 - 2.96251i) q^{19} +(-1.68949 - 1.07034i) q^{20} +(3.93565 - 1.84543i) q^{21} +(-0.680503 - 6.14204i) q^{22} +0.655690 q^{23} +(4.39466 - 1.51036i) q^{24} -1.00000i q^{25} +(-7.24276 + 0.802457i) q^{26} +(3.83458 + 3.83458i) q^{27} +(0.666275 - 5.24939i) q^{28} +(2.68009 - 2.68009i) q^{29} +(1.81388 + 1.45203i) q^{30} +3.01437 q^{31} +(1.30988 - 5.50311i) q^{32} +7.17911i q^{33} +(2.10296 + 1.68345i) q^{34} +(2.39548 - 1.12324i) q^{35} +(0.586850 - 0.131656i) q^{36} +(-6.08074 - 6.08074i) q^{37} +(0.652467 + 5.88899i) q^{38} +8.46569 q^{39} +(2.67486 - 0.919296i) q^{40} +7.27882 q^{41} +(-1.44089 + 5.97610i) q^{42} +(-0.168678 + 0.168678i) q^{43} +(7.38247 + 4.67702i) q^{44} +(0.212640 + 0.212640i) q^{45} +(-0.579497 + 0.723907i) q^{46} -8.95609 q^{47} +(-2.21650 + 6.18673i) q^{48} +(5.38141 + 4.47665i) q^{49} +(1.10404 + 0.883798i) q^{50} +(-2.21287 - 2.21287i) q^{51} +(5.51519 - 8.70549i) q^{52} +(-6.49178 - 6.49178i) q^{53} +(-7.62251 + 0.844532i) q^{54} +4.36965i q^{55} +(5.20668 + 5.37499i) q^{56} -6.88334i q^{57} +(0.590266 + 5.32758i) q^{58} +(-7.08273 - 7.08273i) q^{59} +(-3.20620 + 0.719289i) q^{60} +(3.27600 + 3.27600i) q^{61} +(-2.66410 + 3.32799i) q^{62} +(-0.270529 + 0.748222i) q^{63} +(4.91798 + 6.30979i) q^{64} +5.15274 q^{65} +(-7.92602 - 6.34488i) q^{66} +(-0.886744 - 0.886744i) q^{67} +(-3.71718 + 0.833922i) q^{68} +(0.761741 - 0.761741i) q^{69} +(-0.877017 + 3.63742i) q^{70} -15.5247 q^{71} +(-0.373304 + 0.764262i) q^{72} +6.26678 q^{73} +(12.0875 - 1.33923i) q^{74} +(-1.16174 - 1.16174i) q^{75} +(-7.07832 - 4.48433i) q^{76} +(-10.4674 + 4.90818i) q^{77} +(-7.48195 + 9.34645i) q^{78} +12.3148i q^{79} +(-1.34910 + 3.76562i) q^{80} +8.00741 q^{81} +(-6.43300 + 8.03610i) q^{82} +(-2.44679 + 2.44679i) q^{83} +(-5.32439 - 6.87247i) q^{84} +(-1.34689 - 1.34689i) q^{85} +(-0.0371499 - 0.335305i) q^{86} -6.22713i q^{87} +(-11.6882 + 4.01700i) q^{88} +12.5968 q^{89} +(-0.422694 + 0.0468321i) q^{90} +(5.78778 + 12.3433i) q^{91} +(-0.287063 - 1.27957i) q^{92} +(3.50192 - 3.50192i) q^{93} +(7.91537 - 9.88787i) q^{94} -4.18963i q^{95} +(-4.87145 - 7.91492i) q^{96} +13.2440i q^{97} +(-9.69848 + 1.98483i) q^{98} +(-0.929163 - 0.929163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

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