LMFDB - Embedded newform 560.2.bd.b.141.3

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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.3
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30578 + 0.543081i) q^{2} +(2.37790 + 2.37790i) q^{3} +(1.41013 - 1.41829i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.39640 - 1.81362i) q^{6} +1.00000i q^{7} +(-1.07107 + 2.61779i) q^{8} +8.30879i q^{9} +O(q^{10})$	\(q+(-1.30578 + 0.543081i) q^{2} +(2.37790 + 2.37790i) q^{3} +(1.41013 - 1.41829i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.39640 - 1.81362i) q^{6} +1.00000i q^{7} +(-1.07107 + 2.61779i) q^{8} +8.30879i q^{9} +(0.539310 - 1.30734i) q^{10} +(-1.25501 + 1.25501i) q^{11} +(6.72568 - 0.0194152i) q^{12} +(-4.11673 - 4.11673i) q^{13} +(-0.543081 - 1.30578i) q^{14} -3.36285 q^{15} +(-0.0230936 - 3.99993i) q^{16} -2.87289 q^{17} +(-4.51235 - 10.8495i) q^{18} +(3.28189 + 3.28189i) q^{19} +(0.00577343 + 1.99999i) q^{20} +(-2.37790 + 2.37790i) q^{21} +(0.957198 - 2.32035i) q^{22} -1.75198i q^{23} +(-8.77172 + 3.67794i) q^{24} -1.00000i q^{25} +(7.61126 + 3.13983i) q^{26} +(-12.6238 + 12.6238i) q^{27} +(1.41829 + 1.41013i) q^{28} +(4.43338 + 4.43338i) q^{29} +(4.39115 - 1.82630i) q^{30} +6.75204 q^{31} +(2.20244 + 5.21049i) q^{32} -5.96859 q^{33} +(3.75137 - 1.56022i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(11.7843 + 11.7164i) q^{36} +(0.623971 - 0.623971i) q^{37} +(-6.06776 - 2.50310i) q^{38} -19.5783i q^{39} +(-1.09370 - 2.60841i) q^{40} +6.40635i q^{41} +(1.81362 - 4.39640i) q^{42} +(3.86088 - 3.86088i) q^{43} +(0.0102470 + 3.54970i) q^{44} +(-5.87520 - 5.87520i) q^{45} +(0.951466 + 2.28770i) q^{46} +0.320755 q^{47} +(9.45652 - 9.56634i) q^{48} -1.00000 q^{49} +(0.543081 + 1.30578i) q^{50} +(-6.83145 - 6.83145i) q^{51} +(-11.6438 + 0.0336125i) q^{52} +(0.669364 - 0.669364i) q^{53} +(9.62812 - 23.3396i) q^{54} -1.77486i q^{55} +(-2.61779 - 1.07107i) q^{56} +15.6080i q^{57} +(-8.19670 - 3.38133i) q^{58} +(8.60128 - 8.60128i) q^{59} +(-4.74205 + 4.76950i) q^{60} +(0.746751 + 0.746751i) q^{61} +(-8.81668 + 3.66690i) q^{62} -8.30879 q^{63} +(-5.70563 - 5.60765i) q^{64} +5.82193 q^{65} +(7.79367 - 3.24143i) q^{66} +(2.91748 + 2.91748i) q^{67} +(-4.05114 + 4.07460i) q^{68} +(4.16602 - 4.16602i) q^{69} +(1.30734 + 0.539310i) q^{70} +12.4076i q^{71} +(-21.7506 - 8.89927i) q^{72} -6.12483i q^{73} +(-0.475902 + 1.15364i) q^{74} +(2.37790 - 2.37790i) q^{75} +(9.28255 - 0.0267962i) q^{76} +(-1.25501 - 1.25501i) q^{77} +(10.6326 + 25.5650i) q^{78} -13.1093 q^{79} +(2.84471 + 2.81205i) q^{80} -35.1096 q^{81} +(-3.47917 - 8.36528i) q^{82} +(-2.87023 - 2.87023i) q^{83} +(0.0194152 + 6.72568i) q^{84} +(2.03144 - 2.03144i) q^{85} +(-2.94469 + 7.13823i) q^{86} +21.0842i q^{87} +(-1.94116 - 4.62957i) q^{88} +16.6114i q^{89} +(10.8624 + 4.48101i) q^{90} +(4.11673 - 4.11673i) q^{91} +(-2.48481 - 2.47051i) q^{92} +(16.0556 + 16.0556i) q^{93} +(-0.418836 + 0.174196i) q^{94} -4.64129 q^{95} +(-7.15283 + 17.6272i) q^{96} +12.2240 q^{97} +(1.30578 - 0.543081i) q^{98} +(-10.4277 - 10.4277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * 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 $

$2$	−1.30578	+	0.543081i	−0.923326	+	0.384017i
$2$	−1.30578	+	0.543081i	−0.923326	+	0.384017i
$3$	2.37790	+	2.37790i	1.37288	+	1.37288i	0.856147	+	0.516733i	$0.172852\pi$
$3$	2.37790	+	2.37790i	1.37288	+	1.37288i	0.516733	+	0.856147i	$0.327148\pi$
$4$	1.41013	−	1.41829i	0.705063	−	0.709145i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−4.39640	−	1.81362i	−1.79482	−	0.740407i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.07107	+	2.61779i	−0.378679	+	0.925528i
$9$			8.30879i			2.76960i
$10$	0.539310	−	1.30734i	0.170545	−	0.413418i
$11$	−1.25501	+	1.25501i	−0.378401	+	0.378401i	−0.870525	−	0.492124i	$-0.836221\pi$
$11$	−1.25501	+	1.25501i	−0.378401	+	0.378401i	0.492124	+	0.870525i	$0.336221\pi$
$12$	6.72568	−	0.0194152i	1.94154	−	0.00560469i
$13$	−4.11673	−	4.11673i	−1.14178	−	1.14178i	−0.988125	−	0.153650i	$-0.950897\pi$
$13$	−4.11673	−	4.11673i	−1.14178	−	1.14178i	−0.153650	−	0.988125i	$-0.549103\pi$
$14$	−0.543081	−	1.30578i	−0.145145	−	0.348985i
$15$	−3.36285			−0.868285
$16$	−0.0230936	−	3.99993i	−0.00577341	−	0.999983i
$17$	−2.87289			−0.696779			−0.348390	−	0.937350i	$-0.613271\pi$
$17$	−2.87289			−0.696779			−0.348390	+	0.937350i	$0.613271\pi$
$18$	−4.51235	−	10.8495i	−1.06357	−	2.55724i
$19$	3.28189	+	3.28189i	0.752917	+	0.752917i	0.975023	−	0.222105i	$-0.0712929\pi$
$19$	3.28189	+	3.28189i	0.752917	+	0.752917i	−0.222105	+	0.975023i	$0.571293\pi$
$20$	0.00577343	+	1.99999i	0.00129098	+	0.447212i
$21$	−2.37790	+	2.37790i	−0.518900	+	0.518900i
$22$	0.957198	−	2.32035i	0.204075	−	0.494700i
$23$		−	1.75198i		−	0.365312i	−0.983177	−	0.182656i	$-0.941530\pi$
$23$		−	1.75198i		−	0.365312i	0.983177	−	0.182656i	$-0.0584695\pi$
$24$	−8.77172	+	3.67794i	−1.79052	+	0.750757i
$25$		−	1.00000i		−	0.200000i
$26$	7.61126	+	3.13983i	1.49269	+	0.615770i
$27$	−12.6238	+	12.6238i	−2.42944	+	2.42944i
$28$	1.41829	+	1.41013i	0.268032	+	0.266489i
$29$	4.43338	+	4.43338i	0.823258	+	0.823258i	0.986574	−	0.163316i	$-0.0522190\pi$
$29$	4.43338	+	4.43338i	0.823258	+	0.823258i	−0.163316	+	0.986574i	$0.552219\pi$
$30$	4.39115	−	1.82630i	0.801711	−	0.333436i
$31$	6.75204			1.21270			0.606351	−	0.795197i	$-0.292633\pi$
$31$	6.75204			1.21270			0.606351	+	0.795197i	$0.292633\pi$
$32$	2.20244	+	5.21049i	0.389341	+	0.921094i
$33$	−5.96859			−1.03900
$34$	3.75137	−	1.56022i	0.643354	−	0.267575i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	11.7843	+	11.7164i	1.96405	+	1.95274i
$37$	0.623971	−	0.623971i	0.102580	−	0.102580i	−0.653954	−	0.756534i	$-0.726891\pi$
$37$	0.623971	−	0.623971i	0.102580	−	0.102580i	0.756534	+	0.653954i	$0.226891\pi$
$38$	−6.06776	−	2.50310i	−0.984321	−	0.406056i
$39$		−	19.5783i		−	3.13504i
$40$	−1.09370	−	2.60841i	−0.172929	−	0.412427i
$41$			6.40635i			1.00050i	0.865880	+	0.500252i	$0.166759\pi$
$41$			6.40635i			1.00050i	−0.865880	+	0.500252i	$0.833241\pi$
$42$	1.81362	−	4.39640i	0.279848	−	0.678380i
$43$	3.86088	−	3.86088i	0.588778	−	0.588778i	−0.348522	−	0.937301i	$-0.613316\pi$
$43$	3.86088	−	3.86088i	0.588778	−	0.588778i	0.937301	+	0.348522i	$0.113316\pi$
$44$	0.0102470	+	3.54970i	0.00154480	+	0.535138i
$45$	−5.87520	−	5.87520i	−0.875823	−	0.875823i
$46$	0.951466	+	2.28770i	0.140286	+	0.337303i
$47$	0.320755			0.0467869			0.0233935	−	0.999726i	$-0.492553\pi$
$47$	0.320755			0.0467869			0.0233935	+	0.999726i	$0.492553\pi$
$48$	9.45652	−	9.56634i	1.36493	−	1.38078i
$49$	−1.00000			−0.142857
$50$	0.543081	+	1.30578i	0.0768033	+	0.184665i
$51$	−6.83145	−	6.83145i	−0.956594	−	0.956594i
$52$	−11.6438	+	0.0336125i	−1.61471	+	0.00466122i
$53$	0.669364	−	0.669364i	0.0919442	−	0.0919442i	−0.659639	−	0.751583i	$-0.729291\pi$
$53$	0.669364	−	0.669364i	0.0919442	−	0.0919442i	0.751583	+	0.659639i	$0.229291\pi$
$54$	9.62812	−	23.3396i	1.31022	−	3.17611i
$55$		−	1.77486i		−	0.239322i
$56$	−2.61779	−	1.07107i	−0.349817	−	0.143127i
$57$			15.6080i			2.06733i
$58$	−8.19670	−	3.38133i	−1.07628	−	0.443991i
$59$	8.60128	−	8.60128i	1.11979	−	1.11979i	0.128020	−	0.991772i	$-0.459138\pi$
$59$	8.60128	−	8.60128i	1.11979	−	1.11979i	0.991772	−	0.128020i	$-0.0408622\pi$
$60$	−4.74205	+	4.76950i	−0.612195	+	0.615740i
$61$	0.746751	+	0.746751i	0.0956116	+	0.0956116i	0.753295	−	0.657683i	$-0.228463\pi$
$61$	0.746751	+	0.746751i	0.0956116	+	0.0956116i	−0.657683	+	0.753295i	$0.728463\pi$
$62$	−8.81668	+	3.66690i	−1.11972	+	0.465697i
$63$	−8.30879			−1.04681
$64$	−5.70563	−	5.60765i	−0.713204	−	0.700957i
$65$	5.82193			0.722122
$66$	7.79367	−	3.24143i	0.959334	−	0.398993i
$67$	2.91748	+	2.91748i	0.356427	+	0.356427i	0.862494	−	0.506067i	$-0.168901\pi$
$67$	2.91748	+	2.91748i	0.356427	+	0.356427i	−0.506067	+	0.862494i	$0.668901\pi$
$68$	−4.05114	+	4.07460i	−0.491273	+	0.494117i
$69$	4.16602	−	4.16602i	0.501530	−	0.501530i
$70$	1.30734	+	0.539310i	0.156257	+	0.0644598i
$71$			12.4076i			1.47251i	0.676705	+	0.736254i	$0.263407\pi$
$71$			12.4076i			1.47251i	−0.676705	+	0.736254i	$0.736593\pi$
$72$	−21.7506	−	8.89927i	−2.56334	−	1.04879i
$73$		−	6.12483i		−	0.716858i	−0.933557	−	0.358429i	$-0.883313\pi$
$73$		−	6.12483i		−	0.716858i	0.933557	−	0.358429i	$-0.116687\pi$
$74$	−0.475902	+	1.15364i	−0.0553225	+	0.134108i
$75$	2.37790	−	2.37790i	0.274576	−	0.274576i
$76$	9.28255	−	0.0267962i	1.06478	−	0.00307374i
$77$	−1.25501	−	1.25501i	−0.143022	−	0.143022i
$78$	10.6326	+	25.5650i	1.20391	+	2.89466i
$79$	−13.1093			−1.47491			−0.737454	−	0.675397i	$-0.763972\pi$
$79$	−13.1093			−1.47491			−0.737454	+	0.675397i	$0.763972\pi$
$80$	2.84471	+	2.81205i	0.318048	+	0.314397i
$81$	−35.1096			−3.90107
$82$	−3.47917	−	8.36528i	−0.384210	−	0.923791i
$83$	−2.87023	−	2.87023i	−0.315049	−	0.315049i	0.531813	−	0.846862i	$-0.321511\pi$
$83$	−2.87023	−	2.87023i	−0.315049	−	0.315049i	−0.846862	+	0.531813i	$0.821511\pi$
$84$	0.0194152	+	6.72568i	0.00211837	+	0.733832i
$85$	2.03144	−	2.03144i	0.220341	−	0.220341i
$86$	−2.94469	+	7.13823i	−0.317534	+	0.769735i
$87$			21.0842i			2.26047i
$88$	−1.94116	−	4.62957i	−0.206928	−	0.493514i
$89$			16.6114i			1.76080i	0.474228	+	0.880402i	$0.342727\pi$
$89$			16.6114i			1.76080i	−0.474228	+	0.880402i	$0.657273\pi$
$90$	10.8624	+	4.48101i	1.14500	+	0.472340i
$91$	4.11673	−	4.11673i	0.431550	−	0.431550i
$92$	−2.48481	−	2.47051i	−0.259060	−	0.257568i
$93$	16.0556	+	16.0556i	1.66489	+	1.66489i
$94$	−0.418836	+	0.174196i	−0.0431996	+	0.0179670i
$95$	−4.64129			−0.476187
$96$	−7.15283	+	17.6272i	−0.730033	+	1.79907i
$97$	12.2240			1.24116			0.620579	−	0.784144i	$-0.286898\pi$
$97$	12.2240			1.24116			0.620579	+	0.784144i	$0.286898\pi$
$98$	1.30578	−	0.543081i	0.131904	−	0.0548595i
$99$	−10.4277	−	10.4277i	−1.04802	−	1.04802i
$100$	−1.41829	−	1.41013i	−0.141829	−	0.141013i
$101$	10.4022	−	10.4022i	1.03506	−	1.03506i	0.0356954	−	0.999363i	$-0.488635\pi$
$101$	10.4022	−	10.4022i	1.03506	−	1.03506i	0.999363	−	0.0356954i	$-0.0113646\pi$
$102$	12.6304	+	5.21034i	1.25060	+	0.515900i
$103$		−	13.1762i		−	1.29829i	−0.760663	−	0.649147i	$-0.775126\pi$
$103$		−	13.1762i		−	1.29829i	0.760663	−	0.649147i	$-0.224874\pi$
$104$	15.1860	−	6.36743i	1.48911	−	0.624378i
$105$		−	3.36285i		−	0.328181i
$106$	−0.510523	+	1.23756i	−0.0495864	+	0.120203i
$107$	−3.71846	+	3.71846i	−0.359477	+	0.359477i	−0.863620	−	0.504143i	$-0.831808\pi$
$107$	−3.71846	+	3.71846i	−0.359477	+	0.359477i	0.504143	+	0.863620i	$0.331808\pi$
$108$	0.103071	+	35.7052i	0.00991804	+	3.43574i
$109$	−2.01248	−	2.01248i	−0.192761	−	0.192761i	0.604127	−	0.796888i	$-0.293522\pi$
$109$	−2.01248	−	2.01248i	−0.192761	−	0.192761i	−0.796888	+	0.604127i	$0.793522\pi$
$110$	0.963893	+	2.31758i	0.0919036	+	0.220972i
$111$	2.96748			0.281661
$112$	3.99993	−	0.0230936i	0.377958	−	0.00218214i
$113$	5.61909			0.528599			0.264300	−	0.964441i	$-0.414859\pi$
$113$	5.61909			0.528599			0.264300	+	0.964441i	$0.414859\pi$
$114$	−8.47641	−	20.3806i	−0.793889	−	1.90882i
$115$	1.23883	+	1.23883i	0.115522	+	0.115522i
$116$	12.5394	−	0.0361979i	1.16426	−	0.00336090i
$117$	34.2050	−	34.2050i	3.16226	−	3.16226i
$118$	−6.56019	+	15.9026i	−0.603914	+	1.46395i
$119$		−	2.87289i		−	0.263358i
$120$	3.60184	−	8.80324i	0.328802	−	0.803622i
$121$			7.84988i			0.713625i
$122$	−1.38064	−	0.569546i	−0.124997	−	0.0515643i
$123$	−15.2336	+	15.2336i	−1.37357	+	1.37357i
$124$	9.52122	−	9.57635i	0.855030	−	0.859981i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	10.8495	−	4.51235i	0.966546	−	0.401992i
$127$	−2.91626			−0.258776			−0.129388	−	0.991594i	$-0.541301\pi$
$127$	−2.91626			−0.258776			−0.129388	+	0.991594i	$0.541301\pi$
$128$	10.4957	+	4.22374i	0.927699	+	0.373330i
$129$	18.3615			1.61664
$130$	−7.60217	+	3.16178i	−0.666754	+	0.277307i
$131$	−10.9855	−	10.9855i	−0.959804	−	0.959804i	0.0394192	−	0.999223i	$-0.487449\pi$
$131$	−10.9855	−	10.9855i	−0.959804	−	0.959804i	−0.999223	+	0.0394192i	$0.987449\pi$
$132$	−8.41646	+	8.46519i	−0.732559	+	0.736801i
$133$	−3.28189	+	3.28189i	−0.284576	+	0.284576i
$134$	−5.39402	−	2.22516i	−0.465972	−	0.192225i
$135$		−	17.8527i		−	1.53651i
$136$	3.07706	−	7.52063i	0.263856	−	0.644888i
$137$		−	3.76211i		−	0.321419i	−0.987002	−	0.160709i	$-0.948622\pi$
$137$		−	3.76211i		−	0.321419i	0.987002	−	0.160709i	$-0.0513782\pi$
$138$	−3.17742	+	7.70240i	−0.270480	+	0.655672i
$139$	3.48738	−	3.48738i	0.295796	−	0.295796i	−0.543569	−	0.839365i	$-0.682927\pi$
$139$	3.48738	−	3.48738i	0.295796	−	0.295796i	0.839365	+	0.543569i	$0.182927\pi$
$140$	−1.99999	+	0.00577343i	−0.169030	+	0.000487944i
$141$	0.762722	+	0.762722i	0.0642328	+	0.0642328i
$142$	−6.73832	−	16.2016i	−0.565467	−	1.35960i
$143$	10.3331			0.864098
$144$	33.2346	−	0.191880i	2.76955	−	0.0159900i
$145$	−6.26974			−0.520674
$146$	3.32628	+	7.99769i	0.275285	+	0.661893i
$147$	−2.37790	−	2.37790i	−0.196126	−	0.196126i
$148$	−0.00509464	−	1.76485i	−0.000418777	−	0.145070i
$149$	13.5536	−	13.5536i	1.11036	−	1.11036i	0.117255	−	0.993102i	$-0.462591\pi$
$149$	13.5536	−	13.5536i	1.11036	−	1.11036i	0.993102	−	0.117255i	$-0.0374094\pi$
$150$	−1.81362	+	4.39640i	−0.148081	+	0.358965i
$151$		−	8.59389i		−	0.699361i	−0.936869	−	0.349680i	$-0.886290\pi$
$151$		−	8.59389i		−	0.699361i	0.936869	−	0.349680i	$-0.113710\pi$
$152$	−12.1064	+	5.07617i	−0.981960	+	0.411732i
$153$		−	23.8703i		−	1.92980i
$154$	2.32035	+	0.957198i	0.186979	+	0.0771333i
$155$	−4.77441	+	4.77441i	−0.383490	+	0.383490i
$156$	−27.7677	−	27.6079i	−2.22320	−	2.21040i
$157$	10.6575	+	10.6575i	0.850559	+	0.850559i	0.990202	−	0.139643i	$-0.0445956\pi$
$157$	10.6575	+	10.6575i	0.850559	+	0.850559i	−0.139643	+	0.990202i	$0.544596\pi$
$158$	17.1178	−	7.11940i	1.36182	−	0.566389i
$159$	3.18336			0.252457
$160$	−5.24174	−	2.12701i	−0.414396	−	0.168155i
$161$	1.75198			0.138075
$162$	45.8454	−	19.0674i	3.60196	−	1.49807i
$163$	13.1625	+	13.1625i	1.03096	+	1.03096i	0.999505	+	0.0314587i	$0.0100153\pi$
$163$	13.1625	+	13.1625i	1.03096	+	1.03096i	0.0314587	+	0.999505i	$0.489985\pi$
$164$	9.08606	+	9.03375i	0.709502	+	0.705417i
$165$	4.22043	−	4.22043i	0.328560	−	0.328560i
$166$	5.30666	+	2.18912i	0.411877	+	0.169909i
$167$			22.5106i			1.74192i	0.491353	+	0.870961i	$0.336502\pi$
$167$			22.5106i			1.74192i	−0.491353	+	0.870961i	$0.663498\pi$
$168$	−3.67794	−	8.77172i	−0.283760	−	0.676753i
$169$			20.8949i			1.60730i
$170$	−1.54938	+	3.75586i	−0.118832	+	0.288061i
$171$	−27.2685	+	27.2685i	−2.08528	+	2.08528i
$172$	−0.0315236	−	10.9202i	−0.00240365	−	0.832655i
$173$	−2.86596	−	2.86596i	−0.217895	−	0.217895i	0.589716	−	0.807611i	$-0.299240\pi$
$173$	−2.86596	−	2.86596i	−0.217895	−	0.217895i	−0.807611	+	0.589716i	$0.799240\pi$
$174$	−11.4505	−	27.5314i	−0.868057	−	2.08715i
$175$	1.00000			0.0755929
$176$	5.04896	+	4.99099i	0.380580	+	0.376210i
$177$	40.9059			3.07468
$178$	−9.02134	−	21.6908i	−0.676178	−	1.62580i
$179$	10.5882	+	10.5882i	0.791402	+	0.791402i	0.981722	−	0.190320i	$-0.0609525\pi$
$179$	10.5882	+	10.5882i	0.791402	+	0.791402i	−0.190320	+	0.981722i	$0.560952\pi$
$180$	−16.6175	+	0.0479702i	−1.23860	+	0.00357549i
$181$	9.40320	−	9.40320i	0.698934	−	0.698934i	−0.265246	−	0.964181i	$-0.585453\pi$
$181$	9.40320	−	9.40320i	0.698934	−	0.698934i	0.964181	+	0.265246i	$0.0854533\pi$
$182$	−3.13983	+	7.61126i	−0.232739	+	0.564184i
$183$			3.55139i			0.262526i
$184$	4.58631	+	1.87648i	0.338107	+	0.138336i
$185$			0.882429i			0.0648775i
$186$	−29.6847	−	12.2456i	−2.17659	−	0.897893i
$187$	3.60552	−	3.60552i	0.263662	−	0.263662i
$188$	0.452305	−	0.454924i	0.0329877	−	0.0331787i
$189$	−12.6238	−	12.6238i	−0.918243	−	0.918243i
$190$	6.06051	−	2.52060i	0.439676	−	0.182864i
$191$	3.59651			0.260234			0.130117	−	0.991499i	$-0.458465\pi$
$191$	3.59651			0.260234			0.130117	+	0.991499i	$0.458465\pi$
$192$	−0.232980	−	26.9018i	−0.0168139	−	1.94147i
$193$	9.49758			0.683651			0.341825	−	0.939763i	$-0.388955\pi$
$193$	9.49758			0.683651			0.341825	+	0.939763i	$0.388955\pi$
$194$	−15.9618	+	6.63862i	−1.14599	+	0.476625i
$195$	13.8440	+	13.8440i	0.991386	+	0.991386i
$196$	−1.41013	+	1.41829i	−0.100723	+	0.101306i
$197$	−12.1400	+	12.1400i	−0.864942	+	0.864942i	−0.991907	−	0.126965i	$-0.959476\pi$
$197$	−12.1400	+	12.1400i	−0.864942	+	0.864942i	0.126965	+	0.991907i	$0.459476\pi$
$198$	19.2793	+	7.95316i	1.37012	+	0.565206i
$199$		−	0.496226i		−	0.0351766i	−0.999845	−	0.0175883i	$-0.994401\pi$
$199$		−	0.496226i		−	0.0351766i	0.999845	−	0.0175883i	$-0.00559881\pi$
$200$	2.61779	+	1.07107i	0.185106	+	0.0757359i
$201$			13.8749i			0.978663i
$202$	−7.93375	+	19.2322i	−0.558217	+	1.35318i
$203$	−4.43338	+	4.43338i	−0.311162	+	0.311162i
$204$	−19.3222	+	0.0557778i	−1.35282	+	0.00390523i
$205$	−4.52997	−	4.52997i	−0.316387	−	0.316387i
$206$	7.15577	+	17.2053i	0.498566	+	1.19875i
$207$	14.5568			1.01177
$208$	−16.3716	+	16.5617i	−1.13516	+	1.14835i
$209$	−8.23764			−0.569810
$210$	1.82630	+	4.39115i	0.126027	+	0.303018i
$211$	−11.9930	−	11.9930i	−0.825635	−	0.825635i	0.161275	−	0.986910i	$-0.448440\pi$
$211$	−11.9930	−	11.9930i	−0.825635	−	0.825635i	−0.986910	+	0.161275i	$0.948440\pi$
$212$	−0.00546527	−	1.89324i	−0.000375356	−	0.130028i
$213$	−29.5039	+	29.5039i	−2.02158	+	2.02158i
$214$	2.83607	−	6.87492i	0.193870	−	0.469960i
$215$			5.46011i			0.372376i
$216$	−19.5254	−	46.5672i	−1.32854	−	3.16850i
$217$			6.75204i			0.458358i
$218$	3.72080	+	1.53492i	0.252005	+	0.103958i
$219$	14.5642	−	14.5642i	0.984159	−	0.984159i
$220$	−2.51726	−	2.50277i	−0.169714	−	0.168737i
$221$	11.8269	+	11.8269i	0.795565	+	0.795565i
$222$	−3.87488	+	1.61158i	−0.260065	+	0.108162i
$223$	2.45569			0.164445			0.0822225	−	0.996614i	$-0.473798\pi$
$223$	2.45569			0.164445			0.0822225	+	0.996614i	$0.473798\pi$
$224$	−5.21049	+	2.20244i	−0.348141	+	0.147157i
$225$	8.30879			0.553919
$226$	−7.33729	+	3.05162i	−0.488070	+	0.202991i
$227$	−18.9413	−	18.9413i	−1.25718	−	1.25718i	−0.952433	−	0.304748i	$-0.901428\pi$
$227$	−18.9413	−	18.9413i	−1.25718	−	1.25718i	−0.304748	−	0.952433i	$-0.598572\pi$
$228$	22.1367	+	22.0092i	1.46604	+	1.45760i
$229$	−6.27061	+	6.27061i	−0.414374	+	0.414374i	−0.883259	−	0.468885i	$-0.844656\pi$
$229$	−6.27061	+	6.27061i	−0.414374	+	0.414374i	0.468885	+	0.883259i	$0.344656\pi$
$230$	−2.29043	−	0.944858i	−0.151027	−	0.0623021i
$231$		−	5.96859i		−	0.392704i
$232$	−16.3541	+	6.85720i	−1.07370	+	0.450197i
$233$			5.69418i			0.373038i	0.982451	+	0.186519i	$0.0597206\pi$
$233$			5.69418i			0.373038i	−0.982451	+	0.186519i	$0.940279\pi$
$234$	−26.0881	+	63.2404i	−1.70544	+	4.13415i
$235$	−0.226808	+	0.226808i	−0.0147953	+	0.0147953i
$236$	−0.0702283	−	24.3280i	−0.00457148	−	1.58362i
$237$	−31.1725	−	31.1725i	−2.02487	−	2.02487i
$238$	1.56022	+	3.75137i	0.101134	+	0.243165i
$239$	−10.4310			−0.674724			−0.337362	−	0.941375i	$-0.609535\pi$
$239$	−10.4310			−0.674724			−0.337362	+	0.941375i	$0.609535\pi$
$240$	0.0776605	+	13.4512i	0.00501297	+	0.868271i
$241$	21.3882			1.37774			0.688869	−	0.724886i	$-0.258107\pi$
$241$	21.3882			1.37774			0.688869	+	0.724886i	$0.258107\pi$
$242$	−4.26312	−	10.2502i	−0.274044	−	0.658909i
$243$	−45.6158	−	45.6158i	−2.92625	−	2.92625i
$244$	2.11212	−	0.00609712i	0.135215	−	0.000390328i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	11.6187	−	28.1649i	0.740780	−	1.79573i
$247$		−	27.0213i		−	1.71932i
$248$	−7.23188	+	17.6754i	−0.459225	+	1.12239i
$249$		−	13.6502i		−	0.865049i
$250$	−1.30734	−	0.539310i	−0.0826836	−	0.0341089i
$251$	17.9204	−	17.9204i	1.13113	−	1.13113i	0.141138	−	0.989990i	$-0.454924\pi$
$251$	17.9204	−	17.9204i	1.13113	−	1.13113i	0.989990	−	0.141138i	$-0.0450760\pi$
$252$	−11.7164	+	11.7843i	−0.738066	+	0.742339i
$253$	2.19876	+	2.19876i	0.138235	+	0.138235i
$254$	3.80799	−	1.58376i	0.238935	−	0.0993742i
$255$	9.66112			0.605003
$256$	−15.9989	+	0.184746i	−0.999933	+	0.0115466i
$257$	−3.22928			−0.201437			−0.100718	−	0.994915i	$-0.532114\pi$
$257$	−3.22928			−0.201437			−0.100718	+	0.994915i	$0.532114\pi$
$258$	−23.9761	+	9.97181i	−1.49269	+	0.620818i
$259$	0.623971	+	0.623971i	0.0387717	+	0.0387717i
$260$	8.20966	−	8.25719i	0.509141	−	0.512089i
$261$	−36.8360	+	36.8360i	−2.28009	+	2.28009i
$262$	20.3106	+	8.37860i	1.25479	+	0.517631i
$263$		−	20.3905i		−	1.25733i	−0.777674	−	0.628667i	$-0.783601\pi$
$263$		−	20.3905i		−	1.25733i	0.777674	−	0.628667i	$-0.216399\pi$
$264$	6.39276	−	15.6245i	0.393447	−	0.961622i
$265$			0.946624i			0.0581506i
$266$	2.50310	−	6.06776i	0.153475	−	0.372038i
$267$	−39.5002	+	39.5002i	−2.41737	+	2.41737i
$268$	8.25185	−	0.0238208i	0.504062	−	0.00145509i
$269$	−10.1704	−	10.1704i	−0.620098	−	0.620098i	0.325459	−	0.945556i	$-0.394481\pi$
$269$	−10.1704	−	10.1704i	−0.620098	−	0.620098i	−0.945556	+	0.325459i	$0.894481\pi$
$270$	9.69546	+	23.3117i	0.590047	+	1.41870i
$271$	9.49943			0.577049			0.288525	−	0.957472i	$-0.406835\pi$
$271$	9.49943			0.577049			0.288525	+	0.957472i	$0.406835\pi$
$272$	0.0663456	+	11.4914i	0.00402279	+	0.696767i
$273$	19.5783			1.18493
$274$	2.04313	+	4.91249i	0.123430	+	0.296774i
$275$	1.25501	+	1.25501i	0.0756802	+	0.0756802i
$276$	−0.0340150	−	11.7832i	−0.00204746	−	0.709268i
$277$	−9.55772	+	9.55772i	−0.574268	+	0.574268i	−0.933318	−	0.359050i	$-0.883101\pi$
$277$	−9.55772	+	9.55772i	−0.574268	+	0.574268i	0.359050	+	0.933318i	$0.383101\pi$
$278$	−2.65982	+	6.44768i	−0.159525	+	0.386706i
$279$			56.1012i			3.35869i
$280$	2.60841	−	1.09370i	0.155883	−	0.0653609i
$281$		−	0.724850i		−	0.0432409i	−0.999766	−	0.0216205i	$-0.993117\pi$
$281$		−	0.724850i		−	0.0432409i	0.999766	−	0.0216205i	$-0.00688255\pi$
$282$	−1.41017	−	0.581728i	−0.0839743	−	0.0346414i
$283$	23.0331	−	23.0331i	1.36917	−	1.36917i	0.507555	−	0.861619i	$-0.330549\pi$
$283$	23.0331	−	23.0331i	1.36917	−	1.36917i	0.861619	−	0.507555i	$-0.169451\pi$
$284$	17.5975	+	17.4962i	1.04422	+	1.03821i
$285$	−11.0365	−	11.0365i	−0.653747	−	0.653747i
$286$	−13.4928	+	5.61172i	−0.797844	+	0.331828i
$287$	−6.40635			−0.378155
$288$	−43.2929	+	18.2996i	−2.55106	+	1.07832i
$289$	−8.74648			−0.514499
$290$	8.18691	−	3.40498i	0.480752	−	0.199947i
$291$	29.0674	+	29.0674i	1.70396	+	1.70396i
$292$	−8.68679	−	8.63678i	−0.508356	−	0.505429i
$293$	5.80663	−	5.80663i	0.339227	−	0.339227i	−0.516849	−	0.856076i	$-0.672895\pi$
$293$	5.80663	−	5.80663i	0.339227	−	0.339227i	0.856076	+	0.516849i	$0.172895\pi$
$294$	4.39640	+	1.81362i	0.256403	+	0.105772i
$295$			12.1641i			0.708218i
$296$	0.965110	+	2.30174i	0.0560959	+	0.133786i
$297$		−	31.6860i		−	1.83861i
$298$	−10.3373	+	25.0588i	−0.598826	+	1.45162i
$299$	−7.21241	+	7.21241i	−0.417105	+	0.417105i
$300$	−0.0194152	−	6.72568i	−0.00112094	−	0.388307i
$301$	3.86088	+	3.86088i	0.222537	+	0.222537i
$302$	4.66718	+	11.2217i	0.268566	+	0.645738i
$303$	49.4707			2.84202
$304$	13.0516	−	13.2031i	0.748558	−	0.757252i
$305$	−1.05606			−0.0604701
$306$	12.9635	+	31.1693i	0.741074	+	1.78183i
$307$	−7.93304	−	7.93304i	−0.452763	−	0.452763i	0.443508	−	0.896271i	$-0.353734\pi$
$307$	−7.93304	−	7.93304i	−0.452763	−	0.452763i	−0.896271	+	0.443508i	$0.853734\pi$
$308$	−3.54970	+	0.0102470i	−0.202263	+	0.000583879i
$309$	31.3317	−	31.3317i	1.78240	−	1.78240i
$310$	3.64144	−	8.82723i	0.206820	−	0.501353i
$311$		−	13.2327i		−	0.750356i	−0.926953	−	0.375178i	$-0.877582\pi$
$311$		−	13.2327i		−	0.750356i	0.926953	−	0.375178i	$-0.122418\pi$
$312$	51.2519	+	20.9697i	2.90157	+	1.18717i
$313$			14.2651i			0.806311i	0.915131	+	0.403156i	$0.132087\pi$
$313$			14.2651i			0.806311i	−0.915131	+	0.403156i	$0.867913\pi$
$314$	−19.7042	−	8.12844i	−1.11197	−	0.458715i
$315$	5.87520	−	5.87520i	0.331030	−	0.331030i
$316$	−18.4857	+	18.5928i	−1.03990	+	1.04592i
$317$	−15.1063	−	15.1063i	−0.848456	−	0.848456i	0.141485	−	0.989940i	$-0.454812\pi$
$317$	−15.1063	−	15.1063i	−0.848456	−	0.848456i	−0.989940	+	0.141485i	$0.954812\pi$
$318$	−4.15677	+	1.72882i	−0.233100	+	0.0969475i
$319$	−11.1279			−0.623043
$320$	7.99970	−	0.0692804i	0.447197	−	0.00387289i
$321$	−17.6842			−0.987038
$322$	−2.28770	+	0.951466i	−0.127488	+	0.0530231i
$323$	−9.42852	−	9.42852i	−0.524617	−	0.524617i
$324$	−49.5089	+	49.7956i	−2.75050	+	2.76642i
$325$	−4.11673	+	4.11673i	−0.228355	+	0.228355i
$326$	−24.3356	−	10.0390i	−1.34782	−	0.556009i
$327$		−	9.57096i		−	0.529275i
$328$	−16.7705	−	6.86163i	−0.925994	−	0.378870i
$329$			0.320755i			0.0176838i
$330$	−3.21892	+	7.80299i	−0.177196	+	0.429541i
$331$	−3.74712	+	3.74712i	−0.205960	+	0.205960i	−0.802548	−	0.596588i	$-0.796523\pi$
$331$	−3.74712	+	3.74712i	−0.205960	+	0.205960i	0.596588	+	0.802548i	$0.296523\pi$
$332$	−8.11821	+	0.0234351i	−0.445545	+	0.00128617i
$333$	5.18445	+	5.18445i	0.284106	+	0.284106i
$334$	−12.2251	−	29.3939i	−0.668926	−	1.60836i
$335$	−4.12594			−0.225424
$336$	9.56634	+	9.45652i	0.521887	+	0.515895i
$337$	−19.7990			−1.07852			−0.539260	−	0.842140i	$-0.681296\pi$
$337$	−19.7990			−1.07852			−0.539260	+	0.842140i	$0.681296\pi$
$338$	−11.3476	−	27.2842i	−0.617230	−	1.48406i
$339$	13.3616	+	13.3616i	0.725703	+	0.725703i
$340$	−0.0165865	−	5.74576i	−0.000899527	−	0.311608i
$341$	−8.47390	+	8.47390i	−0.458888	+	0.458888i
$342$	20.7977	−	50.4158i	1.12461	−	2.72617i
$343$		−	1.00000i		−	0.0539949i
$344$	5.97170	+	14.2422i	0.321973	+	0.767889i
$345$			5.89164i			0.317195i
$346$	5.29877	+	2.18587i	0.284863	+	0.117513i
$347$	3.10476	−	3.10476i	0.166672	−	0.166672i	−0.618843	−	0.785515i	$-0.712398\pi$
$347$	3.10476	−	3.10476i	0.166672	−	0.166672i	0.785515	+	0.618843i	$0.212398\pi$
$348$	29.9036	+	29.7314i	1.60300	+	1.59377i
$349$	−2.23119	−	2.23119i	−0.119433	−	0.119433i	0.644864	−	0.764297i	$-0.276914\pi$
$349$	−2.23119	−	2.23119i	−0.119433	−	0.119433i	−0.764297	+	0.644864i	$0.776914\pi$
$350$	−1.30578	+	0.543081i	−0.0697969	+	0.0290289i
$351$	103.937			5.54775
$352$	−9.30334	−	3.77514i	−0.495870	−	0.201216i
$353$	7.29254			0.388143			0.194071	−	0.980987i	$-0.437831\pi$
$353$	7.29254			0.388143			0.194071	+	0.980987i	$0.437831\pi$
$354$	−53.4142	+	22.2152i	−2.83893	+	1.18073i
$355$	−8.77348	−	8.77348i	−0.465648	−	0.465648i
$356$	23.5598	+	23.4241i	1.24867	+	1.24148i
$357$	6.83145	−	6.83145i	0.361558	−	0.361558i
$358$	−19.5762	−	8.07564i	−1.03463	−	0.426811i
$359$			2.53240i			0.133655i	0.997765	+	0.0668276i	$0.0212877\pi$
$359$			2.53240i			0.133655i	−0.997765	+	0.0668276i	$0.978712\pi$
$360$	21.6728	−	9.08730i	1.14226	−	0.478943i
$361$			2.54162i			0.133769i
$362$	−7.17181	+	17.3852i	−0.376942	+	0.913747i
$363$	−18.6662	+	18.6662i	−0.979721	+	0.979721i
$364$	−0.0336125	−	11.6438i	−0.00176178	−	0.610302i
$365$	4.33091	+	4.33091i	0.226690	+	0.226690i
$366$	−1.92870	−	4.63734i	−0.100815	−	0.242398i
$367$	−29.5810			−1.54412			−0.772059	−	0.635551i	$-0.780773\pi$
$367$	−29.5810			−1.54412			−0.772059	+	0.635551i	$0.780773\pi$
$368$	−7.00779	+	0.0404595i	−0.365306	+	0.00210910i
$369$	−53.2290			−2.77099
$370$	−0.479231	−	1.15226i	−0.0249140	−	0.0599031i
$371$	0.669364	+	0.669364i	0.0347517	+	0.0347517i
$372$	45.4120	−	0.131092i	2.35450	−	0.00679681i
$373$	−8.82536	+	8.82536i	−0.456960	+	0.456960i	−0.897656	−	0.440696i	$-0.854732\pi$
$373$	−8.82536	+	8.82536i	−0.456960	+	0.456960i	0.440696	+	0.897656i	$0.354732\pi$
$374$	−2.74993	+	6.66611i	−0.142195	+	0.344697i
$375$			3.36285i			0.173657i
$376$	−0.343550	+	0.839669i	−0.0177172	+	0.0433026i
$377$		−	36.5020i		−	1.87995i
$378$	23.3396	+	9.62812i	1.20046	+	0.495217i
$379$	19.7712	−	19.7712i	1.01558	−	1.01558i	0.0157014	−	0.999877i	$-0.495002\pi$
$379$	19.7712	−	19.7712i	1.01558	−	1.01558i	0.999877	−	0.0157014i	$-0.00499813\pi$
$380$	−6.54481	+	6.58270i	−0.335742	+	0.337686i
$381$	−6.93456	−	6.93456i	−0.355268	−	0.355268i
$382$	−4.69625	+	1.95320i	−0.240281	+	0.0999343i
$383$	−5.10399			−0.260802			−0.130401	−	0.991461i	$-0.541626\pi$
$383$	−5.10399			−0.260802			−0.130401	+	0.991461i	$0.541626\pi$
$384$	14.9141	+	35.0014i	0.761082	+	1.78616i
$385$	1.77486			0.0904552
$386$	−12.4018	+	5.15796i	−0.631233	+	0.262533i
$387$	32.0792	+	32.0792i	1.63068	+	1.63068i
$388$	17.2373	−	17.3372i	0.875094	−	0.880161i
$389$	−13.6391	+	13.6391i	−0.691529	+	0.691529i	−0.962568	−	0.271039i	$-0.912633\pi$
$389$	−13.6391	+	13.6391i	−0.691529	+	0.691529i	0.271039	+	0.962568i	$0.412633\pi$
$390$	−25.5956	−	10.5588i	−1.29608	−	0.534664i
$391$			5.03324i			0.254542i
$392$	1.07107	−	2.61779i	0.0540971	−	0.132218i
$393$		−	52.2446i		−	2.63539i
$394$	9.25920	−	22.4453i	0.466472	−	1.13078i
$395$	9.26966	−	9.26966i	0.466407	−	0.466407i
$396$	−29.4937	+	0.0851404i	−1.48212	+	0.00427847i
$397$	14.0868	+	14.0868i	0.706996	+	0.706996i	0.965902	−	0.258907i	$-0.0833622\pi$
$397$	14.0868	+	14.0868i	0.706996	+	0.706996i	−0.258907	+	0.965902i	$0.583362\pi$
$398$	0.269491	+	0.647963i	0.0135084	+	0.0324794i
$399$	−15.6080			−0.781377
$400$	−3.99993	+	0.0230936i	−0.199997	+	0.00115468i
$401$	23.2024			1.15867			0.579336	−	0.815089i	$-0.303312\pi$
$401$	23.2024			1.15867			0.579336	+	0.815089i	$0.303312\pi$
$402$	−7.53522	−	18.1176i	−0.375823	−	0.903625i
$403$	−27.7963	−	27.7963i	−1.38463	−	1.38463i
$404$	−0.0849326	−	29.4218i	−0.00422556	−	1.46379i
$405$	24.8262	−	24.8262i	1.23363	−	1.23363i
$406$	3.38133	−	8.19670i	0.167813	−	0.406796i
$407$			1.56619i			0.0776330i
$408$	25.2002	−	10.5663i	1.24760	−	0.523112i
$409$		−	21.8189i		−	1.07887i	−0.842026	−	0.539437i	$-0.818637\pi$
$409$		−	21.8189i		−	1.07887i	0.842026	−	0.539437i	$-0.181363\pi$
$410$	8.37529	+	3.45500i	0.413626	+	0.170631i
$411$	8.94591	−	8.94591i	0.441269	−	0.441269i
$412$	−18.6877	−	18.5802i	−0.920679	−	0.915378i
$413$	8.60128	+	8.60128i	0.423241	+	0.423241i
$414$	−19.0080	+	7.90553i	−0.934192	+	0.388536i
$415$	4.05912			0.199255
$416$	12.3833	−	30.5171i	0.607142	−	1.49622i
$417$	16.5853			0.812183
$418$	10.7566	−	4.47371i	0.526120	−	0.218816i
$419$	−11.8739	−	11.8739i	−0.580078	−	0.580078i	0.354846	−	0.934925i	$-0.384533\pi$
$419$	−11.8739	−	11.8739i	−0.580078	−	0.580078i	−0.934925	+	0.354846i	$0.884533\pi$
$420$	−4.76950	−	4.74205i	−0.232728	−	0.231388i
$421$	−24.0765	+	24.0765i	−1.17342	+	1.17342i	−0.192030	+	0.981389i	$0.561507\pi$
$421$	−24.0765	+	24.0765i	−1.17342	+	1.17342i	−0.981389	+	0.192030i	$0.938493\pi$
$422$	22.1735	+	9.14708i	1.07939	+	0.445273i
$423$			2.66509i			0.129581i
$424$	1.03532	+	2.46919i	0.0502796	+	0.119914i
$425$			2.87289i			0.139356i
$426$	22.5026	−	54.5487i	1.09026	−	2.64289i
$427$	−0.746751	+	0.746751i	−0.0361378	+	0.0361378i
$428$	0.0303608	+	10.5174i	0.00146754	+	0.508376i
$429$	24.5711	+	24.5711i	1.18630	+	1.18630i
$430$	−2.96528	−	7.12970i	−0.142999	−	0.343825i
$431$	−21.2683			−1.02446			−0.512230	−	0.858848i	$-0.671181\pi$
$431$	−21.2683			−1.02446			−0.512230	+	0.858848i	$0.671181\pi$
$432$	50.7857	+	50.2026i	2.44343	+	2.41538i
$433$	−20.2717			−0.974197			−0.487098	−	0.873347i	$-0.661945\pi$
$433$	−20.2717			−0.974197			−0.487098	+	0.873347i	$0.661945\pi$
$434$	−3.66690	−	8.81668i	−0.176017	−	0.423214i
$435$	−14.9088	−	14.9088i	−0.714823	−	0.714823i
$436$	−5.69214	+	0.0164317i	−0.272604	+	0.000786934i
$437$	5.74980	−	5.74980i	0.275050	−	0.275050i
$438$	−11.1081	+	26.9272i	−0.530767	+	1.28663i
$439$			2.45267i			0.117059i	0.998286	+	0.0585297i	$0.0186412\pi$
$439$			2.45267i			0.117059i	−0.998286	+	0.0585297i	$0.981359\pi$
$440$	4.64620	+	1.90099i	0.221499	+	0.0906263i
$441$		−	8.30879i		−	0.395657i
$442$	−21.8663	−	9.02038i	−1.04008	−	0.429056i
$443$	9.64422	−	9.64422i	0.458211	−	0.458211i	−0.439857	−	0.898068i	$-0.644971\pi$
$443$	9.64422	−	9.64422i	0.458211	−	0.458211i	0.898068	+	0.439857i	$0.144971\pi$
$444$	4.18452	−	4.20875i	0.198588	−	0.199738i
$445$	−11.7460	−	11.7460i	−0.556815	−	0.556815i
$446$	−3.20659	+	1.33364i	−0.151836	+	0.0631496i
$447$	64.4583			3.04877
$448$	5.60765	−	5.70563i	0.264937	−	0.269566i
$449$	2.57381			0.121466			0.0607328	−	0.998154i	$-0.480656\pi$
$449$	2.57381			0.121466			0.0607328	+	0.998154i	$0.480656\pi$
$450$	−10.8495	+	4.51235i	−0.511448	+	0.212714i
$451$	−8.04006	−	8.04006i	−0.378592	−	0.378592i
$452$	7.92362	−	7.96950i	0.372696	−	0.374854i
$453$	20.4354	−	20.4354i	0.960138	−	0.960138i
$454$	35.0199	+	14.4465i	1.64357	+	0.678010i
$455$			5.82193i			0.272936i
$456$	−40.8584	−	16.7172i	−1.91337	−	0.782855i
$457$			24.4301i			1.14279i	0.820675	+	0.571395i	$0.193598\pi$
$457$			24.4301i			1.14279i	−0.820675	+	0.571395i	$0.806402\pi$
$458$	4.78259	−	11.5935i	0.223476	−	0.541728i
$459$	36.2667	−	36.2667i	1.69278	−	1.69278i
$460$	3.50394	−	0.0101149i	0.163372	−	0.000471611i
$461$	−18.6632	−	18.6632i	−0.869232	−	0.869232i	0.123155	−	0.992387i	$-0.460699\pi$
$461$	−18.6632	−	18.6632i	−0.869232	−	0.869232i	−0.992387	+	0.123155i	$0.960699\pi$
$462$	3.24143	+	7.79367i	0.150805	+	0.362594i
$463$	15.3925			0.715349			0.357674	−	0.933846i	$-0.383570\pi$
$463$	15.3925			0.715349			0.357674	+	0.933846i	$0.383570\pi$
$464$	17.6308	−	17.8356i	0.818491	−	0.827997i
$465$	−22.7061			−1.05297
$466$	−3.09240	−	7.43534i	−0.143253	−	0.344436i
$467$	−22.3987	−	22.3987i	−1.03649	−	1.03649i	−0.999309	−	0.0371781i	$-0.988163\pi$
$467$	−22.3987	−	22.3987i	−1.03649	−	1.03649i	−0.0371781	−	0.999309i	$-0.511837\pi$
$468$	−0.279280	−	96.7460i	−0.0129097	−	4.47209i
$469$	−2.91748	+	2.91748i	−0.134717	+	0.134717i
$470$	0.172986	−	0.419337i	0.00797926	−	0.0193426i
$471$			50.6847i			2.33543i
$472$	13.3038	+	31.7289i	0.612356	+	1.46044i
$473$			9.69092i			0.445589i
$474$	57.6336	+	23.7752i	2.64720	+	1.09203i
$475$	3.28189	−	3.28189i	0.150583	−	0.150583i
$476$	−4.07460	−	4.05114i	−0.186759	−	0.185684i
$477$	5.56160	+	5.56160i	0.254648	+	0.254648i
$478$	13.6206	−	5.66487i	0.622990	−	0.259105i
$479$	−8.51824			−0.389208			−0.194604	−	0.980882i	$-0.562342\pi$
$479$	−8.51824			−0.389208			−0.194604	+	0.980882i	$0.562342\pi$
$480$	−7.40650	−	17.5221i	−0.338059	−	0.799772i
$481$	−5.13744			−0.234247
$482$	−27.9284	+	11.6156i	−1.27210	+	0.529074i
$483$	4.16602	+	4.16602i	0.189561	+	0.189561i
$484$	11.1334	+	11.0693i	0.506064	+	0.503150i
$485$	−8.64366	+	8.64366i	−0.392488	+	0.392488i
$486$	84.3372	+	34.7911i	3.82561	+	1.57816i
$487$		−	1.15656i		−	0.0524086i	−0.999657	−	0.0262043i	$-0.991658\pi$
$487$		−	1.15656i		−	0.0524086i	0.999657	−	0.0262043i	$-0.00834204\pi$
$488$	−2.75466	+	1.15502i	−0.124697	+	0.0522851i
$489$			62.5980i			2.83078i
$490$	−0.539310	+	1.30734i	−0.0243635	+	0.0590597i
$491$	20.8462	−	20.8462i	0.940777	−	0.940777i	−0.0575650	−	0.998342i	$-0.518334\pi$
$491$	20.8462	−	20.8462i	0.940777	−	0.940777i	0.998342	+	0.0575650i	$0.0183336\pi$
$492$	0.124381	+	43.0870i	0.00560751	+	1.94251i
$493$	−12.7366	−	12.7366i	−0.573629	−	0.573629i
$494$	14.6748	+	35.2839i	0.660249	+	1.58750i
$495$	14.7469			0.662825
$496$	−0.155929	−	27.0077i	−0.00700142	−	1.21268i
$497$	−12.4076			−0.556556
$498$	7.41319	+	17.8242i	0.332193	+	0.798722i
$499$	−7.69505	−	7.69505i	−0.344478	−	0.344478i	0.513570	−	0.858048i	$-0.328323\pi$
$499$	−7.69505	−	7.69505i	−0.344478	−	0.344478i	−0.858048	+	0.513570i	$0.828323\pi$
$500$	1.99999	−	0.00577343i	0.0894423	−	0.000258196i
$501$	−53.5278	+	53.5278i	−2.39145	+	2.39145i
$502$	−13.6679	+	33.1324i	−0.610028	+	1.47877i
$503$			14.7741i			0.658747i	0.944200	+	0.329373i	$0.106837\pi$
$503$			14.7741i			0.658747i	−0.944200	+	0.329373i	$0.893163\pi$
$504$	8.89927	−	21.7506i	0.396405	−	0.968851i
$505$			14.7109i			0.654628i
$506$	−4.06520	−	1.67699i	−0.180720	−	0.0745513i
$507$	−49.6859	+	49.6859i	−2.20663	+	2.20663i
$508$	−4.11229	+	4.13610i	−0.182453	+	0.183510i
$509$	−15.8694	−	15.8694i	−0.703399	−	0.703399i	0.261740	−	0.965139i	$-0.415704\pi$
$509$	−15.8694	−	15.8694i	−0.703399	−	0.703399i	−0.965139	+	0.261740i	$0.915704\pi$
$510$	−12.6153	+	5.24678i	−0.558615	+	0.232331i
$511$	6.12483			0.270947
$512$	20.7908	−	8.92996i	0.918831	−	0.394652i
$513$	−82.8596			−3.65834
$514$	4.21673	−	1.75376i	0.185992	−	0.0773551i
$515$	9.31701	+	9.31701i	0.410557	+	0.410557i
$516$	25.8921	−	26.0420i	1.13983	−	1.14643i
$517$	−0.402552	+	0.402552i	−0.0177042	+	0.0177042i
$518$	−1.15364	−	0.475902i	−0.0506879	−	0.0209100i
$519$		−	13.6299i		−	0.598287i
$520$	−6.23568	+	15.2406i	−0.273453	+	0.668344i
$521$		−	13.0157i		−	0.570229i	−0.958493	−	0.285115i	$-0.907968\pi$
$521$		−	13.0157i		−	0.570229i	0.958493	−	0.285115i	$-0.0920317\pi$
$522$	28.0948	−	68.1047i	1.22968	−	2.98086i
$523$	7.19417	−	7.19417i	0.314579	−	0.314579i	−0.532102	−	0.846681i	$-0.678598\pi$
$523$	7.19417	−	7.19417i	0.314579	−	0.314579i	0.846681	+	0.532102i	$0.178598\pi$
$524$	−31.0714	+	0.0896948i	−1.35736	+	0.00391833i
$525$	2.37790	+	2.37790i	0.103780	+	0.103780i
$526$	11.0737	+	26.6256i	0.482837	+	1.16093i
$527$	−19.3979			−0.844985
$528$	0.137836	+	23.8740i	0.00599856	+	1.03898i
$529$	19.9306			0.866547
$530$	−0.514094	−	1.23608i	−0.0223308	−	0.0536920i
$531$	71.4662	+	71.4662i	3.10137	+	3.10137i
$532$	0.0267962	+	9.28255i	0.00116176	+	0.402450i
$533$	26.3732	−	26.3732i	1.14235	−	1.14235i
$534$	30.1268	−	73.0304i	1.30371	−	3.16033i
$535$		−	5.25870i		−	0.227353i
$536$	−10.7622	+	4.51253i	−0.464855	+	0.194912i
$537$			50.3555i			2.17300i
$538$	18.8036	+	7.75692i	0.810680	+	0.334425i
$539$	1.25501	−	1.25501i	0.0540573	−	0.0540573i
$540$	−25.3203	−	25.1745i	−1.08961	−	1.08334i
$541$	2.11432	+	2.11432i	0.0909018	+	0.0909018i	0.751095	−	0.660194i	$-0.229526\pi$
$541$	2.11432	+	2.11432i	0.0909018	+	0.0909018i	−0.660194	+	0.751095i	$0.729526\pi$
$542$	−12.4042	+	5.15896i	−0.532805	+	0.221596i
$543$	44.7197			1.91911
$544$	−6.32739	−	14.9692i	−0.271285	−	0.641799i
$545$	2.84608			0.121913
$546$	−25.5650	+	10.6326i	−1.09408	+	0.455034i
$547$	18.0722	+	18.0722i	0.772710	+	0.772710i	0.978579	−	0.205870i	$-0.0660023\pi$
$547$	18.0722	+	18.0722i	0.772710	+	0.772710i	−0.205870	+	0.978579i	$0.566002\pi$
$548$	−5.33576	−	5.30505i	−0.227932	−	0.226620i
$549$	−6.20459	+	6.20459i	−0.264806	+	0.264806i
$550$	−2.32035	−	0.957198i	−0.0989400	−	0.0408151i
$551$			29.0997i			1.23969i
$552$	6.44367	+	15.3678i	0.274261	+	0.654099i
$553$		−	13.1093i		−	0.557463i
$554$	7.28967	−	17.6709i	0.309708	−	0.750765i
$555$	−2.09833	+	2.09833i	−0.0890689	+	0.0890689i
$556$	−0.0284740	−	9.86375i	−0.00120757	−	0.418316i
$557$	−14.2207	−	14.2207i	−0.602550	−	0.602550i	0.338438	−	0.940989i	$-0.390101\pi$
$557$	−14.2207	−	14.2207i	−0.602550	−	0.602550i	−0.940989	+	0.338438i	$0.890101\pi$
$558$	−30.4675	−	73.2559i	−1.28979	−	3.10117i
$559$	−31.7884			−1.34450
$560$	−2.81205	+	2.84471i	−0.118831	+	0.120211i
$561$	17.1471			0.723952
$562$	0.393653	+	0.946495i	0.0166052	+	0.0399255i
$563$	−12.1888	−	12.1888i	−0.513695	−	0.513695i	0.401961	−	0.915657i	$-0.368329\pi$
$563$	−12.1888	−	12.1888i	−0.513695	−	0.513695i	−0.915657	+	0.401961i	$0.868329\pi$
$564$	2.15730	−	0.00622753i	0.0908385	−	0.000262226i
$565$	−3.97329	+	3.97329i	−0.167158	+	0.167158i
$566$	−17.5673	+	42.5850i	−0.738409	+	1.78998i
$567$		−	35.1096i		−	1.47446i
$568$	−32.4804	−	13.2893i	−1.36285	−	0.557608i
$569$			5.82007i			0.243990i	0.992531	+	0.121995i	$0.0389292\pi$
$569$			5.82007i			0.243990i	−0.992531	+	0.121995i	$0.961071\pi$
$570$	20.4050	+	8.41754i	0.854672	+	0.352572i
$571$	14.6824	−	14.6824i	0.614439	−	0.614439i	−0.329660	−	0.944100i	$-0.606934\pi$
$571$	14.6824	−	14.6824i	0.614439	−	0.614439i	0.944100	+	0.329660i	$0.106934\pi$
$572$	14.5710	−	14.6553i	0.609243	−	0.612771i
$573$	8.55213	+	8.55213i	0.357270	+	0.357270i
$574$	8.36528	−	3.47917i	0.349160	−	0.145218i
$575$	−1.75198			−0.0730625
$576$	46.5928	−	47.4069i	1.94137	−	1.97529i
$577$	17.8747			0.744131			0.372066	−	0.928206i	$-0.378650\pi$
$577$	17.8747			0.744131			0.372066	+	0.928206i	$0.378650\pi$
$578$	11.4210	−	4.75005i	0.475050	−	0.197576i
$579$	22.5843	+	22.5843i	0.938570	+	0.938570i
$580$	−8.84112	+	8.89232i	−0.367108	+	0.369233i
$581$	2.87023	−	2.87023i	0.119077	−	0.119077i
$582$	−53.7416	−	22.1697i	−2.22766	−	0.918962i
$583$			1.68012i			0.0695836i
$584$	16.0335	+	6.56011i	0.663472	+	0.271459i
$585$			48.3732i			1.99999i
$586$	−4.42871	+	10.7357i	−0.182948	+	0.443486i
$587$	−1.33735	+	1.33735i	−0.0551985	+	0.0551985i	−0.734167	−	0.678969i	$-0.762427\pi$
$587$	−1.33735	+	1.33735i	−0.0551985	+	0.0551985i	0.678969	+	0.734167i	$0.262427\pi$
$588$	−6.72568	+	0.0194152i	−0.277362	+	0.000800670i
$589$	22.1594	+	22.1594i	0.913064	+	0.913064i
$590$	−6.60607	−	15.8836i	−0.271968	−	0.653917i
$591$	−57.7356			−2.37492
$592$	−2.51025	−	2.48143i	−0.103171	−	0.101986i
$593$	−7.99404			−0.328276			−0.164138	−	0.986437i	$-0.552484\pi$
$593$	−7.99404			−0.328276			−0.164138	+	0.986437i	$0.552484\pi$
$594$	17.2081	+	41.3749i	0.706056	+	1.69763i
$595$	2.03144	+	2.03144i	0.0832810	+	0.0832810i
$596$	−0.110664	−	38.3353i	−0.00453296	−	1.57027i
$597$	1.17998	−	1.17998i	0.0482932	−	0.0482932i
$598$	5.50090	−	13.3348i	0.224949	−	0.545299i
$599$			38.0110i			1.55309i	0.630063	+	0.776544i	$0.283029\pi$
$599$			38.0110i			1.55309i	−0.630063	+	0.776544i	$0.716971\pi$
$600$	3.67794	+	8.77172i	0.150151	+	0.358104i
$601$			39.4659i			1.60985i	0.593377	+	0.804925i	$0.297794\pi$
$601$			39.4659i			1.60985i	−0.593377	+	0.804925i	$0.702206\pi$
$602$	−7.13823	−	2.94469i	−0.290933	−	0.120017i
$603$	−24.2407	+	24.2407i	−0.987159	+	0.987159i
$604$	−12.1886	−	12.1185i	−0.495948	−	0.493093i
$605$	−5.55070	−	5.55070i	−0.225668	−	0.225668i
$606$	−64.5979	+	26.8666i	−2.62411	+	1.09138i
$607$	34.6505			1.40642			0.703210	−	0.710983i	$-0.251750\pi$
$607$	34.6505			1.40642			0.703210	+	0.710983i	$0.251750\pi$
$608$	−9.87209	+	24.3285i	−0.400366	+	0.986649i
$609$	−21.0842			−0.854376
$610$	1.37899	−	0.573529i	0.0558336	−	0.0232215i
$611$	−1.32046	−	1.32046i	−0.0534202	−	0.0534202i
$612$	−33.8550	−	33.6601i	−1.36851	−	1.36063i
$613$	11.4856	−	11.4856i	0.463898	−	0.463898i	−0.436033	−	0.899931i	$-0.643617\pi$
$613$	11.4856	−	11.4856i	0.463898	−	0.463898i	0.899931	+	0.436033i	$0.143617\pi$
$614$	14.6671	+	6.05053i	0.591916	+	0.244179i
$615$		−	21.5436i		−	0.868722i
$616$	4.62957	−	1.94116i	0.186531	−	0.0782115i
$617$			19.0156i			0.765540i	0.923844	+	0.382770i	$0.125030\pi$
$617$			19.0156i			0.765540i	−0.923844	+	0.382770i	$0.874970\pi$
$618$	−23.8967	+	57.9281i	−0.961266	+	2.33021i
$619$	−29.4885	+	29.4885i	−1.18524	+	1.18524i	−0.206878	+	0.978367i	$0.566330\pi$
$619$	−29.4885	+	29.4885i	−1.18524	+	1.18524i	−0.978367	+	0.206878i	$0.933670\pi$
$620$	0.0389824	+	13.5040i	0.00156557	+	0.542334i
$621$	22.1165	+	22.1165i	0.887506	+	0.887506i
$622$	7.18642	+	17.2790i	0.288149	+	0.692824i
$623$	−16.6114			−0.665521
$624$	−78.3119	+	0.452134i	−3.13499	+	0.0180999i
$625$	−1.00000			−0.0400000
$626$	−7.74711	−	18.6271i	−0.309637	−	0.744488i
$627$	−19.5883	−	19.5883i	−0.782280	−	0.782280i
$628$	30.1438	−	0.0870168i	1.20287	−	0.00347235i
$629$	−1.79260	+	1.79260i	−0.0714758	+	0.0714758i
$630$	−4.48101	+	10.8624i	−0.178528	+	0.432770i
$631$		−	2.51839i		−	0.100256i	−0.998743	−	0.0501278i	$-0.984037\pi$
$631$		−	2.51839i		−	0.100256i	0.998743	−	0.0501278i	$-0.0159629\pi$
$632$	14.0409	−	34.3173i	0.558517	−	1.36507i
$633$		−	57.0364i		−	2.26699i
$634$	27.9295	+	11.5216i	1.10922	+	0.457580i
$635$	2.06210	−	2.06210i	0.0818321	−	0.0818321i
$636$	4.48893	−	4.51492i	0.177998	−	0.179028i
$637$	4.11673	+	4.11673i	0.163111	+	0.163111i
$638$	14.5306	−	6.04336i	0.575272	−	0.239259i
$639$	−103.092			−4.07825
$640$	−10.4082	+	4.43495i	−0.411421	+	0.175307i
$641$	1.59788			0.0631125			0.0315562	−	0.999502i	$-0.489954\pi$
$641$	1.59788			0.0631125			0.0315562	+	0.999502i	$0.489954\pi$
$642$	23.0917	−	9.60398i	0.911358	−	0.379039i
$643$	4.63689	+	4.63689i	0.182861	+	0.182861i	0.792601	−	0.609740i	$-0.208726\pi$
$643$	4.63689	+	4.63689i	0.182861	+	0.182861i	−0.609740	+	0.792601i	$0.708726\pi$
$644$	2.47051	−	2.48481i	0.0973516	−	0.0979153i
$645$	−12.9836	+	12.9836i	−0.511228	+	0.511228i
$646$	17.4320	+	7.19113i	0.685854	+	0.282931i
$647$		−	27.2170i		−	1.07001i	−0.844849	−	0.535004i	$-0.820310\pi$
$647$		−	27.2170i		−	1.07001i	0.844849	−	0.535004i	$-0.179690\pi$
$648$	37.6047	−	91.9095i	1.47725	−	3.61055i
$649$			21.5895i			0.847461i
$650$	3.13983	−	7.61126i	0.123154	−	0.298538i
$651$	−16.0556	+	16.0556i	−0.629270	+	0.629270i
$652$	37.2289	−	0.107470i	1.45800	−	0.00420884i
$653$	−13.7192	−	13.7192i	−0.536874	−	0.536874i	0.385735	−	0.922610i	$-0.373948\pi$
$653$	−13.7192	−	13.7192i	−0.536874	−	0.536874i	−0.922610	+	0.385735i	$0.873948\pi$
$654$	5.19781	+	12.4976i	0.203250	+	0.488694i
$655$	15.5358			0.607033
$656$	25.6250	−	0.147946i	1.00049	−	0.00577631i
$657$	50.8899			1.98541
$658$	−0.174196	−	0.418836i	−0.00679087	−	0.0163279i
$659$	1.26700	+	1.26700i	0.0493555	+	0.0493555i	0.731354	−	0.681998i	$-0.238889\pi$
$659$	1.26700	+	1.26700i	0.0493555	+	0.0493555i	−0.681998	+	0.731354i	$0.738889\pi$
$660$	−0.0344593	−	11.9371i	−0.00134132	−	0.464652i
$661$	10.0662	−	10.0662i	0.391530	−	0.391530i	−0.483703	−	0.875232i	$-0.660708\pi$
$661$	10.0662	−	10.0662i	0.391530	−	0.391530i	0.875232	+	0.483703i	$0.160708\pi$
$662$	2.85792	−	6.92790i	0.111076	−	0.269261i
$663$			56.2464i			2.18443i
$664$	10.5879	−	4.43945i	0.410889	−	0.172284i
$665$		−	4.64129i		−	0.179982i
$666$	−9.58533	−	3.95417i	−0.371424	−	0.153221i
$667$	7.76718	−	7.76718i	0.300746	−	0.300746i
$668$	31.9265	+	31.7427i	1.23527	+	1.22816i
$669$	5.83937	+	5.83937i	0.225763	+	0.225763i
$670$	5.38757	−	2.24072i	0.208140	−	0.0865667i
$671$	−1.87437			−0.0723591
$672$	−17.6272	−	7.15283i	−0.679984	−	0.275926i
$673$	−30.8918			−1.19079			−0.595396	−	0.803432i	$-0.703005\pi$
$673$	−30.8918			−1.19079			−0.595396	+	0.803432i	$0.703005\pi$
$674$	25.8531	−	10.7525i	0.995825	−	0.414169i
$675$	12.6238	+	12.6238i	0.485888	+	0.485888i
$676$	29.6350	+	29.4644i	1.13981	+	1.13325i
$677$	−0.534249	+	0.534249i	−0.0205328	+	0.0205328i	−0.717299	−	0.696766i	$-0.754622\pi$
$677$	−0.534249	+	0.534249i	−0.0205328	+	0.0205328i	0.696766	+	0.717299i	$0.254622\pi$
$678$	−24.7038	−	10.1909i	−0.948743	−	0.391379i
$679$			12.2240i			0.469113i
$680$	3.14208	+	7.49370i	0.120493	+	0.287370i
$681$		−	90.0811i		−	3.45192i
$682$	6.46304	−	15.6671i	0.247483	−	0.599923i
$683$	5.92660	−	5.92660i	0.226775	−	0.226775i	−0.584569	−	0.811344i	$-0.698736\pi$
$683$	5.92660	−	5.92660i	0.226775	−	0.226775i	0.811344	+	0.584569i	$0.198736\pi$
$684$	0.222644	+	77.1268i	0.00851301	+	2.94902i
$685$	2.66021	+	2.66021i	0.101642	+	0.101642i
$686$	0.543081	+	1.30578i	0.0207349	+	0.0498549i
$687$	−29.8217			−1.13777
$688$	−15.5324	−	15.3541i	−0.592168	−	0.585369i
$689$	−5.51118			−0.209959
$690$	−3.19964	−	7.69319i	−0.121808	−	0.292875i
$691$	−1.14085	−	1.14085i	−0.0433998	−	0.0433998i	0.685074	−	0.728474i	$-0.259770\pi$
$691$	−1.14085	−	1.14085i	−0.0433998	−	0.0433998i	−0.728474	+	0.685074i	$0.759770\pi$
$692$	−8.10613	+	0.0234002i	−0.308149	+	0.000889542i
$693$	10.4277	−	10.4277i	0.396114	−	0.396114i
$694$	−2.36800	+	5.74028i	−0.0898880	+	0.217898i
$695$			4.93190i			0.187078i
$696$	−55.1941	−	22.5826i	−2.09213	−	0.855992i
$697$		−	18.4048i		−	0.697130i
$698$	4.12516	+	1.70173i	0.156140	+	0.0644113i
$699$	−13.5402	+	13.5402i	−0.512136	+	0.512136i
$700$	1.41013	−	1.41829i	0.0532977	−	0.0536063i
$701$	9.14716	+	9.14716i	0.345483	+	0.345483i	0.858424	−	0.512941i	$-0.171444\pi$
$701$	9.14716	+	9.14716i	0.345483	+	0.345483i	−0.512941	+	0.858424i	$0.671444\pi$
$702$	−135.719	+	56.4463i	−5.12239	+	2.13043i
$703$	4.09561			0.154469
$704$	14.1983	−	0.122963i	0.535120	−	0.00463434i
$705$	−1.07865			−0.0406244
$706$	−9.52246	+	3.96044i	−0.358383	+	0.149053i
$707$	10.4022	+	10.4022i	0.391215	+	0.391215i
$708$	57.6825	−	58.0165i	2.16784	−	2.18039i
$709$	−4.35240	+	4.35240i	−0.163458	+	0.163458i	−0.784097	−	0.620639i	$-0.786873\pi$
$709$	−4.35240	+	4.35240i	−0.163458	+	0.163458i	0.620639	+	0.784097i	$0.286873\pi$
$710$	16.2209	+	6.69152i	0.608761	+	0.251128i
$711$		−	108.922i		−	4.08490i
$712$	−43.4851	−	17.7919i	−1.62967	−	0.666780i
$713$		−	11.8294i		−	0.443015i
$714$	−5.21034	+	12.6304i	−0.194992	+	0.472681i
$715$	−7.30661	+	7.30661i	−0.273252	+	0.273252i
$716$	29.9479	−	0.0864516i	1.11921	−	0.00323085i
$717$	−24.8038	−	24.8038i	−0.926314	−	0.926314i
$718$	−1.37530	−	3.30676i	−0.0513258	−	0.123407i
$719$	2.21572			0.0826325			0.0413162	−	0.999146i	$-0.486845\pi$
$719$	2.21572			0.0826325			0.0413162	+	0.999146i	$0.486845\pi$
$720$	−23.3647	+	23.6361i	−0.870752	+	0.880865i
$721$	13.1762			0.490709
$722$	−1.38031	−	3.31879i	−0.0513696	−	0.123513i
$723$	50.8591	+	50.8591i	1.89147	+	1.89147i
$724$	−0.0767759	−	26.5962i	−0.00285335	−	0.988438i
$725$	4.43338	−	4.43338i	0.164652	−	0.164652i
$726$	14.2367	−	34.5112i	0.528373	−	1.28083i
$727$		−	1.86211i		−	0.0690618i	−0.999404	−	0.0345309i	$-0.989006\pi$
$727$		−	1.86211i		−	0.0690618i	0.999404	−	0.0345309i	$-0.0109937\pi$
$728$	6.36743	+	15.1860i	0.235993	+	0.562831i
$729$		−	111.610i		−	4.13372i
$730$	−8.00726	−	3.30318i	−0.296362	−	0.122256i
$731$	−11.0919	+	11.0919i	−0.410248	+	0.410248i
$732$	5.03690	+	5.00791i	0.186169	+	0.185098i
$733$	−22.4099	−	22.4099i	−0.827730	−	0.827730i	0.159473	−	0.987202i	$-0.449021\pi$
$733$	−22.4099	−	22.4099i	−0.827730	−	0.827730i	−0.987202	+	0.159473i	$0.949021\pi$
$734$	38.6263	−	16.0649i	1.42572	−	0.592967i
$735$	3.36285			0.124041
$736$	9.12866	−	3.85863i	0.336487	−	0.142231i
$737$	−7.32296			−0.269745
$738$	69.5054	−	28.9077i	2.55853	−	1.06411i
$739$	−0.402304	−	0.402304i	−0.0147990	−	0.0147990i	0.699669	−	0.714468i	$-0.253331\pi$
$739$	−0.402304	−	0.402304i	−0.0147990	−	0.0147990i	−0.714468	+	0.699669i	$0.753331\pi$
$740$	1.25154	+	1.24434i	0.0460075	+	0.0457427i
$741$	64.2539	−	64.2539i	2.36043	−	2.36043i
$742$	−1.23756	−	0.510523i	−0.0454323	−	0.0187419i
$743$			15.3190i			0.562000i	0.959708	+	0.281000i	$0.0906660\pi$
$743$			15.3190i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$744$	−59.2270	+	24.8336i	−2.17137	+	0.910444i
$745$			19.1677i			0.702251i
$746$	6.73109	−	16.3169i	0.246443	−	0.597403i
$747$	23.8482	−	23.8482i	0.872559	−	0.872559i
$748$	−0.0294386	−	10.1979i	−0.00107638	−	0.372873i
$749$	−3.71846	−	3.71846i	−0.135870	−	0.135870i
$750$	−1.82630	−	4.39115i	−0.0666872	−	0.160342i
$751$	−9.17303			−0.334729			−0.167364	−	0.985895i	$-0.553526\pi$
$751$	−9.17303			−0.334729			−0.167364	+	0.985895i	$0.553526\pi$
$752$	−0.00740740	−	1.28300i	−0.000270120	−	0.0467862i
$753$	85.2259			3.10580
$754$	19.8236	+	47.6636i	0.721932	+	1.73581i
$755$	6.07680	+	6.07680i	0.221157	+	0.221157i
$756$	−35.7052	+	0.103071i	−1.29859	+	0.00374867i
$757$	3.84533	−	3.84533i	0.139761	−	0.139761i	−0.633765	−	0.773526i	$-0.718491\pi$
$757$	3.84533	−	3.84533i	0.139761	−	0.139761i	0.773526	+	0.633765i	$0.218491\pi$
$758$	−15.0795	+	36.5542i	−0.547711	+	1.32771i
$759$			10.4568i			0.379559i
$760$	4.97114	−	12.1499i	0.180322	−	0.440724i
$761$		−	28.0121i		−	1.01544i	−0.861522	−	0.507720i	$-0.830489\pi$
$761$		−	28.0121i		−	1.01544i	0.861522	−	0.507720i	$-0.169511\pi$
$762$	12.8210	+	5.28898i	0.464457	+	0.191600i
$763$	2.01248	−	2.01248i	0.0728568	−	0.0728568i
$764$	5.07153	−	5.10090i	0.183482	−	0.184544i
$765$	16.8788	+	16.8788i	0.610255	+	0.610255i
$766$	6.66470	−	2.77188i	0.240805	−	0.100152i
$767$	−70.8183			−2.55710
$768$	−38.4831	−	37.6045i	−1.38864	−	1.35694i
$769$	46.1009			1.66244			0.831221	−	0.555942i	$-0.187642\pi$
$769$	46.1009			1.66244			0.831221	+	0.555942i	$0.187642\pi$
$770$	−2.31758	+	0.963893i	−0.0835196	+	0.0347363i
$771$	−7.67889	−	7.67889i	−0.276549	−	0.276549i
$772$	13.3928	−	13.4703i	0.482017	−	0.484808i
$773$	14.9964	−	14.9964i	0.539382	−	0.539382i	−0.383966	−	0.923347i	$-0.625442\pi$
$773$	14.9964	−	14.9964i	0.539382	−	0.539382i	0.923347	+	0.383966i	$0.125442\pi$
$774$	−59.3100	−	24.4668i	−2.13186	−	0.879441i
$775$		−	6.75204i		−	0.242540i
$776$	−13.0927	+	31.9998i	−0.470001	+	1.14873i
$777$			2.96748i			0.106458i
$778$	10.4025	−	25.2168i	0.372948	−	0.904065i
$779$	−21.0249	+	21.0249i	−0.753296	+	0.753296i
$780$	39.1565	−	0.113034i	1.40203	−	0.00404727i
$781$	−15.5717	−	15.5717i	−0.557199	−	0.557199i
$782$	−2.73346	−	6.57231i	−0.0977484	−	0.235025i
$783$	−111.932			−4.00011
$784$	0.0230936	+	3.99993i	0.000824773	+	0.142855i
$785$	−15.0719			−0.537941
$786$	28.3730	+	68.2199i	1.01203	+	2.43332i
$787$	31.0487	+	31.0487i	1.10677	+	1.10677i	0.993573	+	0.113195i	$0.0361084\pi$
$787$	31.0487	+	31.0487i	1.10677	+	1.10677i	0.113195	+	0.993573i	$0.463892\pi$
$788$	0.0991219	+	34.3371i	0.00353107	+	1.22321i
$789$	48.4866	−	48.4866i	1.72617	−	1.72617i
$790$	−7.06996	+	17.1383i	−0.251538	+	0.609754i
$791$			5.61909i			0.199792i
$792$	38.4661	−	16.1287i	1.36683	−	0.573107i
$793$		−	6.14834i		−	0.218334i
$794$	−26.0445	−	10.7440i	−0.924286	−	0.381290i
$795$	−2.25097	+	2.25097i	−0.0798338	+	0.0798338i
$796$	−0.703793	−	0.699741i	−0.0249453	−	0.0248017i
$797$	8.69660	+	8.69660i	0.308049	+	0.308049i	0.844153	−	0.536103i	$-0.180104\pi$
$797$	8.69660	+	8.69660i	0.308049	+	0.308049i	−0.536103	+	0.844153i	$0.680104\pi$
$798$	20.3806	−	8.47641i	0.721466	−	0.300062i
$799$	−0.921495			−0.0326002
$800$	5.21049	−	2.20244i	0.184219	−	0.0778682i
$801$	−138.021			−4.87672
$802$	−30.2972	+	12.6008i	−1.06983	+	0.444949i
$803$	7.68676	+	7.68676i	0.271260	+	0.271260i
$804$	19.6787	+	19.5654i	0.694014	+	0.690019i
$805$	−1.23883	+	1.23883i	−0.0436632	+	0.0436632i
$806$	51.3915	+	21.2002i	1.81019	+	0.746746i
$807$		−	48.3681i		−	1.70264i
$808$	16.0893	+	38.3722i	0.566020	+	1.34993i
$809$		−	8.91959i		−	0.313596i	−0.987631	−	0.156798i	$-0.949883\pi$
$809$		−	8.91959i		−	0.313596i	0.987631	−	0.156798i	$-0.0501172\pi$
$810$	−18.9349	+	45.9003i	−0.665306	+	1.61277i
$811$	−0.578400	+	0.578400i	−0.0203104	+	0.0203104i	−0.717189	−	0.696879i	$-0.754572\pi$
$811$	−0.578400	+	0.578400i	−0.0203104	+	0.0203104i	0.696879	+	0.717189i	$0.254572\pi$
$812$	0.0361979	+	12.5394i	0.00127030	+	0.440048i
$813$	22.5887	+	22.5887i	0.792219	+	0.792219i
$814$	−0.850567	−	2.04510i	−0.0298123	−	0.0716806i
$815$	−18.6145			−0.652039
$816$	−27.1676	+	27.4831i	−0.951055	+	0.962101i
$817$	25.3420			0.886603
$818$	11.8494	+	28.4907i	0.414306	+	0.996153i
$819$	34.2050	+	34.2050i	1.19522	+	1.19522i
$820$	−12.8126	+	0.0369866i	−0.447437	+	0.00129163i
$821$	−26.2064	+	26.2064i	−0.914610	+	0.914610i	−0.996631	−	0.0820211i	$-0.973863\pi$
$821$	−26.2064	+	26.2064i	−0.914610	+	0.914610i	0.0820211	+	0.996631i	$0.473863\pi$
$822$	−6.82304	+	16.5398i	−0.237981	+	0.576890i
$823$			26.7591i			0.932762i	0.884584	+	0.466381i	$0.154442\pi$
$823$			26.7591i			0.932762i	−0.884584	+	0.466381i	$0.845558\pi$
$824$	34.4926	+	14.1126i	1.20161	+	0.491637i
$825$			5.96859i			0.207800i
$826$	−15.9026	−	6.56019i	−0.553322	−	0.228258i
$827$	−13.4175	+	13.4175i	−0.466571	+	0.466571i	−0.900802	−	0.434231i	$-0.857020\pi$
$827$	−13.4175	+	13.4175i	−0.466571	+	0.466571i	0.434231	+	0.900802i	$0.357020\pi$
$828$	20.5269	−	20.6458i	0.713360	−	0.717490i
$829$	−18.0315	−	18.0315i	−0.626260	−	0.626260i	0.320865	−	0.947125i	$-0.396026\pi$
$829$	−18.0315	−	18.0315i	−0.626260	−	0.626260i	−0.947125	+	0.320865i	$0.896026\pi$
$830$	−5.30032	+	2.20443i	−0.183977	+	0.0765170i
$831$	−45.4546			−1.57680
$832$	0.403346	+	46.5737i	0.0139835	+	1.61465i
$833$	2.87289			0.0995399
$834$	−21.6567	+	9.00714i	−0.749910	+	0.311892i
$835$	−15.9174	−	15.9174i	−0.550844	−	0.550844i
$836$	−11.6161	+	11.6834i	−0.401751	+	0.404078i
$837$	−85.2360	+	85.2360i	−2.94619	+	2.94619i
$838$	21.9532	+	9.05622i	0.758361	+	0.312842i
$839$		−	32.5735i		−	1.12456i	−0.826947	−	0.562280i	$-0.809924\pi$
$839$		−	32.5735i		−	1.12456i	0.826947	−	0.562280i	$-0.190076\pi$
$840$	8.80324	+	3.60184i	0.303741	+	0.124275i
$841$			10.3097i			0.355507i
$842$	18.3632	−	44.5142i	0.632836	−	1.53406i
$843$	1.72362	−	1.72362i	0.0593646	−	0.0593646i
$844$	−33.9213	+	0.0979216i	−1.16762	+	0.00337060i
$845$	−14.7749	−	14.7749i	−0.508273	−	0.508273i
$846$	−1.44736	−	3.48002i	−0.0497612	−	0.119645i
$847$	−7.84988			−0.269725
$848$	−2.69287	−	2.66195i	−0.0924735	−	0.0914119i
$849$	109.541			3.75942
$850$	−1.56022	−	3.75137i	−0.0535149	−	0.128671i
$851$	−1.09318	−	1.09318i	−0.0374739	−	0.0374739i
$852$	0.240896	+	83.4494i	0.00825295	+	2.85893i
$853$	−8.44932	+	8.44932i	−0.289299	+	0.289299i	−0.836803	−	0.547504i	$-0.815578\pi$
$853$	−8.44932	+	8.44932i	−0.289299	+	0.289299i	0.547504	+	0.836803i	$0.315578\pi$
$854$	0.569546	−	1.38064i	0.0194895	−	0.0472445i
$855$		−	38.5635i		−	1.31885i
$856$	−5.75143	−	13.7169i	−0.196580	−	0.468833i
$857$			36.7236i			1.25445i	0.778836	+	0.627227i	$0.215810\pi$
$857$			36.7236i			1.25445i	−0.778836	+	0.627227i	$0.784190\pi$
$858$	−45.4285	−	18.7403i	−1.55090	−	0.639784i
$859$	32.1071	−	32.1071i	1.09548	−	1.09548i	0.100549	−	0.994932i	$-0.467940\pi$
$859$	32.1071	−	32.1071i	1.09548	−	1.09548i	0.994932	−	0.100549i	$-0.0320598\pi$
$860$	7.74401	+	7.69943i	0.264069	+	0.262548i
$861$	−15.2336	−	15.2336i	−0.519161	−	0.519161i
$862$	27.7718	−	11.5504i	0.945911	−	0.393410i
$863$	4.71972			0.160661			0.0803306	−	0.996768i	$-0.474402\pi$
$863$	4.71972			0.160661			0.0803306	+	0.996768i	$0.474402\pi$
$864$	−93.5791	−	37.9729i	−3.18363	−	1.29186i
$865$	4.05308			0.137809
$866$	26.4704	−	11.0092i	0.899501	−	0.374108i
$867$	−20.7982	−	20.7982i	−0.706345	−	0.706345i
$868$	9.57635	+	9.52122i	0.325042	+	0.323171i
$869$	16.4523	−	16.4523i	0.558107	−	0.558107i
$870$	27.5643	+	11.3709i	0.934518	+	0.385511i
$871$		−	24.0210i		−	0.813919i
$872$	7.42376	−	3.11275i	0.251400	−	0.105411i
$873$			101.566i			3.43750i
$874$	−4.38537	+	10.6306i	−0.148337	+	0.359585i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	−0.118915	−	41.1937i	−0.00401776	−	1.39181i
$877$	33.1265	+	33.1265i	1.11860	+	1.11860i	0.991947	+	0.126657i	$0.0404249\pi$
$877$	33.1265	+	33.1265i	1.11860	+	1.11860i	0.126657	+	0.991947i	$0.459575\pi$
$878$	−1.33200	−	3.20265i	−0.0449528	−	0.108084i
$879$	27.6151			0.931435
$880$	−7.09932	+	0.0409879i	−0.239318	+	0.00138170i
$881$	−52.8233			−1.77966			−0.889831	−	0.456290i	$-0.849178\pi$
$881$	−52.8233			−1.77966			−0.889831	+	0.456290i	$0.849178\pi$
$882$	4.51235	+	10.8495i	0.151939	+	0.365320i
$883$	30.4844	+	30.4844i	1.02588	+	1.02588i	0.999656	+	0.0262253i	$0.00834874\pi$
$883$	30.4844	+	30.4844i	1.02588	+	1.02588i	0.0262253	+	0.999656i	$0.491651\pi$
$884$	33.4515	−	0.0965653i	1.12509	−	0.00324784i
$885$	−28.9249	+	28.9249i	−0.972299	+	0.972299i
$886$	−7.35564	+	17.8308i	−0.247117	+	0.599038i
$887$		−	24.6022i		−	0.826060i	−0.910717	−	0.413030i	$-0.864471\pi$
$887$		−	24.6022i		−	0.826060i	0.910717	−	0.413030i	$-0.135529\pi$
$888$	−3.17837	+	7.76823i	−0.106659	+	0.260685i
$889$		−	2.91626i		−	0.0978081i
$890$	21.7168	+	8.95868i	0.727948	+	0.300296i
$891$	44.0631	−	44.0631i	1.47617	−	1.47617i
$892$	3.46283	−	3.48288i	0.115944	−	0.116615i
$893$	1.05268	+	1.05268i	0.0352267	+	0.0352267i
$894$	−84.1684	+	35.0061i	−2.81501	+	1.17078i
$895$	−14.9740			−0.500527
$896$	−4.22374	+	10.4957i	−0.141105	+	0.350637i
$897$	−34.3008			−1.14527
$898$	−3.36083	+	1.39779i	−0.112152	+	0.0466448i
$899$	29.9343	+	29.9343i	0.998366	+	0.998366i
$900$	11.7164	−	11.7843i	0.390548	−	0.392809i
$901$	−1.92301	+	1.92301i	−0.0640648	+	0.0640648i
$902$	14.8650	+	6.13215i	0.494949	+	0.204178i
$903$			18.3615i			0.611034i
$904$	−6.01842	+	14.7096i	−0.200170	+	0.489233i
$905$			13.2981i			0.442045i
$906$	−15.5860	+	37.7822i	−0.517812	+	1.25523i
$907$	17.4262	−	17.4262i	0.578629	−	0.578629i	−0.355897	−	0.934525i	$-0.615825\pi$
$907$	17.4262	−	17.4262i	0.578629	−	0.578629i	0.934525	+	0.355897i	$0.115825\pi$
$908$	−53.5740	+	0.154654i	−1.77792	+	0.00513236i
$909$	86.4297	+	86.4297i	2.86669	+	2.86669i
$910$	−3.16178	−	7.60217i	−0.104812	−	0.252009i
$911$	37.0743			1.22833			0.614164	−	0.789179i	$-0.289493\pi$
$911$	37.0743			1.22833			0.614164	+	0.789179i	$0.289493\pi$
$912$	62.4310	−	0.360445i	2.06730	−	0.0119355i
$913$	7.20437			0.238430
$914$	−13.2675	−	31.9003i	−0.438850	−	1.05517i
$915$	−2.51121	−	2.51121i	−0.0830182	−	0.0830182i
$916$	0.0511987	+	17.7359i	0.00169165	+	0.586010i
$917$	10.9855	−	10.9855i	0.362772	−	0.362772i
$918$	−27.6606	+	67.0521i	−0.912935	+	2.21305i
$919$			8.82519i			0.291116i	0.989350	+	0.145558i	$0.0464978\pi$
$919$			8.82519i			0.291116i	−0.989350	+	0.145558i	$0.953502\pi$
$920$	−4.56988	+	1.91613i	−0.150665	+	0.0631730i
$921$		−	37.7279i		−	1.24318i
$922$	34.5057	+	14.2344i	1.13638	+	0.468785i
$923$	51.0786	−	51.0786i	1.68127	−	1.68127i
$924$	−8.46519	−	8.41646i	−0.278484	−	0.276881i
$925$	−0.623971	−	0.623971i	−0.0205161	−	0.0205161i
$926$	−20.0992	+	8.35936i	−0.660500	+	0.274706i
$927$	109.479			3.59575
$928$	−13.3358	+	32.8644i	−0.437770	+	1.07883i
$929$	−42.5840			−1.39713			−0.698567	−	0.715544i	$-0.746179\pi$
$929$	−42.5840			−1.39713			−0.698567	+	0.715544i	$0.746179\pi$
$930$	29.6492	−	12.3313i	0.972235	−	0.404358i
$931$	−3.28189	−	3.28189i	−0.107560	−	0.107560i
$932$	8.07599	+	8.02950i	0.264538	+	0.263015i
$933$	31.4659	−	31.4659i	1.03015	−	1.03015i
$934$	41.4120	+	17.0834i	1.35504	+	0.558987i
$935$			5.09898i			0.166754i
$936$	52.9056	+	126.177i	1.72927	+	4.12424i
$937$			10.8663i			0.354987i	0.984122	+	0.177493i	$0.0567988\pi$
$937$			10.8663i			0.354987i	−0.984122	+	0.177493i	$0.943201\pi$
$938$	2.22516	−	5.39402i	0.0726541	−	0.176121i
$939$	−33.9209	+	33.9209i	−1.10697	+	1.10697i
$940$	0.00185186	+	0.641507i	6.04009e−5	+	0.0209237i
$941$	19.2518	+	19.2518i	0.627590	+	0.627590i	0.947461	−	0.319871i	$-0.103640\pi$
$941$	19.2518	+	19.2518i	0.627590	+	0.627590i	−0.319871	+	0.947461i	$0.603640\pi$
$942$	−27.5259	−	66.1831i	−0.896843	−	2.15636i
$943$	11.2238			0.365496
$944$	−34.6032	−	34.2059i	−1.12624	−	1.11331i
$945$	17.8527			0.580748
$946$	−5.26296	−	12.6542i	−0.171113	−	0.411424i
$947$	−20.5171	−	20.5171i	−0.666715	−	0.666715i	0.290239	−	0.956954i	$-0.406265\pi$
$947$	−20.5171	−	20.5171i	−0.666715	−	0.666715i	−0.956954	+	0.290239i	$0.906265\pi$
$948$	−88.1688	+	0.254519i	−2.86359	+	0.00826640i
$949$	−25.2143	+	25.2143i	−0.818490	+	0.818490i
$950$	−2.50310	+	6.06776i	−0.0812111	+	0.196864i
$951$		−	71.8426i		−	2.32965i
$952$	7.52063	+	3.07706i	0.243745	+	0.0997281i
$953$		−	13.5864i		−	0.440105i	−0.975488	−	0.220053i	$-0.929377\pi$
$953$		−	13.5864i		−	0.440105i	0.975488	−	0.220053i	$-0.0706229\pi$
$954$	−10.2826	−	4.24183i	−0.332913	−	0.137334i
$955$	−2.54312	+	2.54312i	−0.0822933	+	0.0822933i
$956$	−14.7090	+	14.7942i	−0.475722	+	0.478477i
$957$	−26.4610	−	26.4610i	−0.855363	−	0.855363i
$958$	11.1230	−	4.62610i	0.359366	−	0.149462i
$959$	3.76211			0.121485
$960$	19.1872	+	18.8577i	0.619264	+	0.608630i
$961$	14.5900			0.470645
$962$	6.70837	−	2.79005i	0.216287	−	0.0899548i
$963$	−30.8959	−	30.8959i	−0.995607	−	0.995607i
$964$	30.1601	−	30.3347i	0.971392	−	0.977016i
$965$	−6.71580	+	6.71580i	−0.216189	+	0.216189i
$966$	−7.70240	−	3.17742i	−0.247821	−	0.102232i
$967$			12.1857i			0.391865i	0.980617	+	0.195932i	$0.0627733\pi$
$967$			12.1857i			0.391865i	−0.980617	+	0.195932i	$0.937227\pi$
$968$	−20.5493	−	8.40774i	−0.660480	−	0.270235i
$969$		−	44.8401i		−	1.44047i
$970$	6.59251	−	15.9809i	0.211673	−	0.513117i
$971$	17.0874	−	17.0874i	0.548360	−	0.548360i	−0.377606	−	0.925966i	$-0.623253\pi$
$971$	17.0874	−	17.0874i	0.548360	−	0.548360i	0.925966	+	0.377606i	$0.123253\pi$
$972$	−129.020	+	0.372447i	−4.13833	+	0.0119462i
$973$	3.48738	+	3.48738i	0.111800	+	0.111800i
$974$	0.628104	+	1.51021i	0.0201258	+	0.0483902i
$975$	−19.5783			−0.627008
$976$	2.96971	−	3.00420i	0.0950580	−	0.0961620i
$977$	−18.8136			−0.601902			−0.300951	−	0.953640i	$-0.597304\pi$
$977$	−18.8136			−0.601902			−0.300951	+	0.953640i	$0.597304\pi$
$978$	−33.9958	−	81.7392i	−1.08707	−	2.61373i
$979$	−20.8475	−	20.8475i	−0.666290	−	0.666290i
$980$	−0.00577343	−	1.99999i	−0.000184426	−	0.0638874i
$981$	16.7213	−	16.7213i	0.533870	−	0.533870i
$982$	−15.8994	+	38.5418i	−0.507370	+	1.22992i
$983$		−	5.95522i		−	0.189942i	−0.995480	−	0.0949710i	$-0.969724\pi$
$983$		−	5.95522i		−	0.189942i	0.995480	−	0.0949710i	$-0.0302758\pi$
$984$	−23.5622	−	56.1947i	−0.751135	−	1.79142i
$985$		−	17.1686i		−	0.547038i
$986$	23.5483	+	9.71421i	0.749929	+	0.309364i
$987$	−0.762722	+	0.762722i	−0.0242777	+	0.0242777i
$988$	−38.3241	−	38.1034i	−1.21925	−	1.21223i
$989$	−6.76417	−	6.76417i	−0.215088	−	0.215088i
$990$	−19.2562	+	8.00878i	−0.612004	+	0.254536i
$991$	−55.2961			−1.75654			−0.878269	−	0.478167i	$-0.841301\pi$
$991$	−55.2961			−1.75654			−0.878269	+	0.478167i	$0.841301\pi$
$992$	14.8710	+	35.1814i	0.472154	+	1.11701i
$993$	−17.8205			−0.565517
$994$	16.2016	−	6.73832i	0.513882	−	0.213727i
$995$	0.350885	+	0.350885i	0.0111238	+	0.0111238i
$996$	−19.3600	−	19.2485i	−0.613445	−	0.609914i
$997$	−10.8008	+	10.8008i	−0.342064	+	0.342064i	−0.857143	−	0.515079i	$-0.827763\pi$
$997$	−10.8008	+	10.8008i	−0.342064	+	0.342064i	0.515079	+	0.857143i	$0.327763\pi$
$998$	14.2271	+	5.86901i	0.450351	+	0.185780i
$999$			15.7537i			0.498426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.3	✓	52
4.3	odd	2		2240.2.bd.b.1681.1		52
16.5	even	4	inner	560.2.bd.b.421.3	yes	52
16.11	odd	4		2240.2.bd.b.561.1		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.3	✓	52	1.1	even	1	trivial
560.2.bd.b.421.3	yes	52	16.5	even	4	inner
2240.2.bd.b.561.1		52	16.11	odd	4
2240.2.bd.b.1681.1		52	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)

\(f(q)\)	\(=\)	\(q+(-1.30578 + 0.543081i) q^{2} +(2.37790 + 2.37790i) q^{3} +(1.41013 - 1.41829i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.39640 - 1.81362i) q^{6} +1.00000i q^{7} +(-1.07107 + 2.61779i) q^{8} +8.30879i q^{9} +O(q^{10})\)	\(q+(-1.30578 + 0.543081i) q^{2} +(2.37790 + 2.37790i) q^{3} +(1.41013 - 1.41829i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-4.39640 - 1.81362i) q^{6} +1.00000i q^{7} +(-1.07107 + 2.61779i) q^{8} +8.30879i q^{9} +(0.539310 - 1.30734i) q^{10} +(-1.25501 + 1.25501i) q^{11} +(6.72568 - 0.0194152i) q^{12} +(-4.11673 - 4.11673i) q^{13} +(-0.543081 - 1.30578i) q^{14} -3.36285 q^{15} +(-0.0230936 - 3.99993i) q^{16} -2.87289 q^{17} +(-4.51235 - 10.8495i) q^{18} +(3.28189 + 3.28189i) q^{19} +(0.00577343 + 1.99999i) q^{20} +(-2.37790 + 2.37790i) q^{21} +(0.957198 - 2.32035i) q^{22} -1.75198i q^{23} +(-8.77172 + 3.67794i) q^{24} -1.00000i q^{25} +(7.61126 + 3.13983i) q^{26} +(-12.6238 + 12.6238i) q^{27} +(1.41829 + 1.41013i) q^{28} +(4.43338 + 4.43338i) q^{29} +(4.39115 - 1.82630i) q^{30} +6.75204 q^{31} +(2.20244 + 5.21049i) q^{32} -5.96859 q^{33} +(3.75137 - 1.56022i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(11.7843 + 11.7164i) q^{36} +(0.623971 - 0.623971i) q^{37} +(-6.06776 - 2.50310i) q^{38} -19.5783i q^{39} +(-1.09370 - 2.60841i) q^{40} +6.40635i q^{41} +(1.81362 - 4.39640i) q^{42} +(3.86088 - 3.86088i) q^{43} +(0.0102470 + 3.54970i) q^{44} +(-5.87520 - 5.87520i) q^{45} +(0.951466 + 2.28770i) q^{46} +0.320755 q^{47} +(9.45652 - 9.56634i) q^{48} -1.00000 q^{49} +(0.543081 + 1.30578i) q^{50} +(-6.83145 - 6.83145i) q^{51} +(-11.6438 + 0.0336125i) q^{52} +(0.669364 - 0.669364i) q^{53} +(9.62812 - 23.3396i) q^{54} -1.77486i q^{55} +(-2.61779 - 1.07107i) q^{56} +15.6080i q^{57} +(-8.19670 - 3.38133i) q^{58} +(8.60128 - 8.60128i) q^{59} +(-4.74205 + 4.76950i) q^{60} +(0.746751 + 0.746751i) q^{61} +(-8.81668 + 3.66690i) q^{62} -8.30879 q^{63} +(-5.70563 - 5.60765i) q^{64} +5.82193 q^{65} +(7.79367 - 3.24143i) q^{66} +(2.91748 + 2.91748i) q^{67} +(-4.05114 + 4.07460i) q^{68} +(4.16602 - 4.16602i) q^{69} +(1.30734 + 0.539310i) q^{70} +12.4076i q^{71} +(-21.7506 - 8.89927i) q^{72} -6.12483i q^{73} +(-0.475902 + 1.15364i) q^{74} +(2.37790 - 2.37790i) q^{75} +(9.28255 - 0.0267962i) q^{76} +(-1.25501 - 1.25501i) q^{77} +(10.6326 + 25.5650i) q^{78} -13.1093 q^{79} +(2.84471 + 2.81205i) q^{80} -35.1096 q^{81} +(-3.47917 - 8.36528i) q^{82} +(-2.87023 - 2.87023i) q^{83} +(0.0194152 + 6.72568i) q^{84} +(2.03144 - 2.03144i) q^{85} +(-2.94469 + 7.13823i) q^{86} +21.0842i q^{87} +(-1.94116 - 4.62957i) q^{88} +16.6114i q^{89} +(10.8624 + 4.48101i) q^{90} +(4.11673 - 4.11673i) q^{91} +(-2.48481 - 2.47051i) q^{92} +(16.0556 + 16.0556i) q^{93} +(-0.418836 + 0.174196i) q^{94} -4.64129 q^{95} +(-7.15283 + 17.6272i) q^{96} +12.2240 q^{97} +(1.30578 - 0.543081i) q^{98} +(-10.4277 - 10.4277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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