LMFDB - Embedded newform 560.2.bd.a.141.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.10
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.560807 - 1.29827i) q^{2} +(0.693100 + 0.693100i) q^{3} +(-1.37099 + 1.45615i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.511134 - 1.28852i) q^{6} -1.00000i q^{7} +(2.65934 + 0.963293i) q^{8} -2.03922i q^{9} +O(q^{10})$	\(q+(-0.560807 - 1.29827i) q^{2} +(0.693100 + 0.693100i) q^{3} +(-1.37099 + 1.45615i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.511134 - 1.28852i) q^{6} -1.00000i q^{7} +(2.65934 + 0.963293i) q^{8} -2.03922i q^{9} +(1.31456 + 0.521463i) q^{10} +(-0.309578 + 0.309578i) q^{11} +(-1.95949 + 0.0590251i) q^{12} +(3.90010 + 3.90010i) q^{13} +(-1.29827 + 0.560807i) q^{14} -0.980192 q^{15} +(-0.240762 - 3.99275i) q^{16} +0.135722 q^{17} +(-2.64746 + 1.14361i) q^{18} +(2.90848 + 2.90848i) q^{19} +(-0.0602179 - 1.99909i) q^{20} +(0.693100 - 0.693100i) q^{21} +(0.575529 + 0.228302i) q^{22} +0.323600i q^{23} +(1.17553 + 2.51084i) q^{24} -1.00000i q^{25} +(2.87617 - 7.25057i) q^{26} +(3.49269 - 3.49269i) q^{27} +(1.45615 + 1.37099i) q^{28} +(5.89806 + 5.89806i) q^{29} +(0.549698 + 1.27255i) q^{30} +6.72094 q^{31} +(-5.04863 + 2.55173i) q^{32} -0.429138 q^{33} +(-0.0761138 - 0.176203i) q^{34} +(0.707107 + 0.707107i) q^{35} +(2.96942 + 2.79576i) q^{36} +(3.99371 - 3.99371i) q^{37} +(2.14488 - 5.40707i) q^{38} +5.40632i q^{39} +(-2.56159 + 1.19928i) q^{40} +3.21576i q^{41} +(-1.28852 - 0.511134i) q^{42} +(1.58254 - 1.58254i) q^{43} +(-0.0263640 - 0.875223i) q^{44} +(1.44195 + 1.44195i) q^{45} +(0.420120 - 0.181477i) q^{46} -0.680548 q^{47} +(2.60050 - 2.93425i) q^{48} -1.00000 q^{49} +(-1.29827 + 0.560807i) q^{50} +(0.0940689 + 0.0940689i) q^{51} +(-11.0262 + 0.332137i) q^{52} +(1.42777 - 1.42777i) q^{53} +(-6.49316 - 2.57572i) q^{54} -0.437810i q^{55} +(0.963293 - 2.65934i) q^{56} +4.03173i q^{57} +(4.34958 - 10.9649i) q^{58} +(-3.10583 + 3.10583i) q^{59} +(1.34383 - 1.42731i) q^{60} +(3.16789 + 3.16789i) q^{61} +(-3.76915 - 8.72558i) q^{62} -2.03922 q^{63} +(6.14413 + 5.12344i) q^{64} -5.51558 q^{65} +(0.240663 + 0.557135i) q^{66} +(-9.61703 - 9.61703i) q^{67} +(-0.186074 + 0.197632i) q^{68} +(-0.224287 + 0.224287i) q^{69} +(0.521463 - 1.31456i) q^{70} -0.0650839i q^{71} +(1.96437 - 5.42298i) q^{72} +3.41976i q^{73} +(-7.42460 - 2.94520i) q^{74} +(0.693100 - 0.693100i) q^{75} +(-8.22268 + 0.247689i) q^{76} +(0.309578 + 0.309578i) q^{77} +(7.01885 - 3.03190i) q^{78} -9.73291 q^{79} +(2.99354 + 2.65305i) q^{80} -1.27611 q^{81} +(4.17491 - 1.80342i) q^{82} +(-11.8341 - 11.8341i) q^{83} +(0.0590251 + 1.95949i) q^{84} +(-0.0959699 + 0.0959699i) q^{85} +(-2.94205 - 1.16706i) q^{86} +8.17589i q^{87} +(-1.12149 + 0.525058i) q^{88} -1.93694i q^{89} +(1.06338 - 2.68069i) q^{90} +(3.90010 - 3.90010i) q^{91} +(-0.471212 - 0.443653i) q^{92} +(4.65829 + 4.65829i) q^{93} +(0.381656 + 0.883533i) q^{94} -4.11321 q^{95} +(-5.26781 - 1.73060i) q^{96} +8.46136 q^{97} +(0.560807 + 1.29827i) q^{98} +(0.631300 + 0.631300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.560807	−	1.29827i	−0.396550	−	0.918013i
$2$	−0.560807	−	1.29827i	−0.396550	−	0.918013i
$3$	0.693100	+	0.693100i	0.400162	+	0.400162i	0.878290	−	0.478128i	$-0.158685\pi$
$3$	0.693100	+	0.693100i	0.400162	+	0.400162i	−0.478128	+	0.878290i	$0.658685\pi$
$4$	−1.37099	+	1.45615i	−0.685496	+	0.728076i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.511134	−	1.28852i	0.208669	−	0.526038i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.65934	+	0.963293i	0.940217	+	0.340575i
$9$		−	2.03922i		−	0.679741i
$10$	1.31456	+	0.521463i	0.415701	+	0.164901i
$11$	−0.309578	+	0.309578i	−0.0933414	+	0.0933414i	−0.752236	−	0.658894i	$-0.771024\pi$
$11$	−0.309578	+	0.309578i	−0.0933414	+	0.0933414i	0.658894	+	0.752236i	$0.271024\pi$
$12$	−1.95949	+	0.0590251i	−0.565657	+	0.0170391i
$13$	3.90010	+	3.90010i	1.08169	+	1.08169i	0.996352	+	0.0853418i	$0.0271982\pi$
$13$	3.90010	+	3.90010i	1.08169	+	1.08169i	0.0853418	+	0.996352i	$0.472802\pi$
$14$	−1.29827	+	0.560807i	−0.346976	+	0.149882i
$15$	−0.980192			−0.253084
$16$	−0.240762	−	3.99275i	−0.0601906	−	0.998187i
$17$	0.135722			0.0329174			0.0164587	−	0.999865i	$-0.494761\pi$
$17$	0.135722			0.0329174			0.0164587	+	0.999865i	$0.494761\pi$
$18$	−2.64746	+	1.14361i	−0.624012	+	0.269552i
$19$	2.90848	+	2.90848i	0.667250	+	0.667250i	0.957079	−	0.289829i	$-0.0935983\pi$
$19$	2.90848	+	2.90848i	0.667250	+	0.667250i	−0.289829	+	0.957079i	$0.593598\pi$
$20$	−0.0602179	−	1.99909i	−0.0134651	−	0.447011i
$21$	0.693100	−	0.693100i	0.151247	−	0.151247i
$22$	0.575529	+	0.228302i	0.122703	+	0.0486741i
$23$			0.323600i			0.0674753i	0.999431	+	0.0337377i	$0.0107411\pi$
$23$			0.323600i			0.0674753i	−0.999431	+	0.0337377i	$0.989259\pi$
$24$	1.17553	+	2.51084i	0.239954	+	0.512524i
$25$		−	1.00000i		−	0.200000i
$26$	2.87617	−	7.25057i	0.564063	−	1.42195i
$27$	3.49269	−	3.49269i	0.672168	−	0.672168i
$28$	1.45615	+	1.37099i	0.275187	+	0.259093i
$29$	5.89806	+	5.89806i	1.09524	+	1.09524i	0.994959	+	0.100282i	$0.0319746\pi$
$29$	5.89806	+	5.89806i	1.09524	+	1.09524i	0.100282	+	0.994959i	$0.468025\pi$
$30$	0.549698	+	1.27255i	0.100361	+	0.232335i
$31$	6.72094			1.20712			0.603559	−	0.797319i	$-0.293749\pi$
$31$	6.72094			1.20712			0.603559	+	0.797319i	$0.293749\pi$
$32$	−5.04863	+	2.55173i	−0.892480	+	0.451087i
$33$	−0.429138			−0.0747033
$34$	−0.0761138	−	0.176203i	−0.0130534	−	0.0302186i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	2.96942	+	2.79576i	0.494904	+	0.465960i
$37$	3.99371	−	3.99371i	0.656562	−	0.656562i	−0.298003	−	0.954565i	$-0.596320\pi$
$37$	3.99371	−	3.99371i	0.656562	−	0.656562i	0.954565	+	0.298003i	$0.0963205\pi$
$38$	2.14488	−	5.40707i	0.347946	−	0.877142i
$39$			5.40632i			0.865704i
$40$	−2.56159	+	1.19928i	−0.405022	+	0.189623i
$41$			3.21576i			0.502217i	0.967959	+	0.251109i	$0.0807951\pi$
$41$			3.21576i			0.502217i	−0.967959	+	0.251109i	$0.919205\pi$
$42$	−1.28852	−	0.511134i	−0.198824	−	0.0788696i
$43$	1.58254	−	1.58254i	0.241335	−	0.241335i	−0.576067	−	0.817402i	$-0.695413\pi$
$43$	1.58254	−	1.58254i	0.241335	−	0.241335i	0.817402	+	0.576067i	$0.195413\pi$
$44$	−0.0263640	−	0.875223i	−0.00397452	−	0.131945i
$45$	1.44195	+	1.44195i	0.214953	+	0.214953i
$46$	0.420120	−	0.181477i	0.0619432	−	0.0267574i
$47$	−0.680548			−0.0992682			−0.0496341	−	0.998767i	$-0.515806\pi$
$47$	−0.680548			−0.0992682			−0.0496341	+	0.998767i	$0.515806\pi$
$48$	2.60050	−	2.93425i	0.375350	−	0.423522i
$49$	−1.00000			−0.142857
$50$	−1.29827	+	0.560807i	−0.183603	+	0.0793100i
$51$	0.0940689	+	0.0940689i	0.0131723	+	0.0131723i
$52$	−11.0262	+	0.332137i	−1.52905	+	0.0460590i
$53$	1.42777	−	1.42777i	0.196120	−	0.196120i	−0.602215	−	0.798334i	$-0.705715\pi$
$53$	1.42777	−	1.42777i	0.196120	−	0.196120i	0.798334	+	0.602215i	$0.205715\pi$
$54$	−6.49316	−	2.57572i	−0.883607	−	0.350511i
$55$		−	0.437810i		−	0.0590343i
$56$	0.963293	−	2.65934i	0.128725	−	0.355369i
$57$			4.03173i			0.534016i
$58$	4.34958	−	10.9649i	0.571128	−	1.43976i
$59$	−3.10583	+	3.10583i	−0.404345	+	0.404345i	−0.879761	−	0.475416i	$-0.842298\pi$
$59$	−3.10583	+	3.10583i	−0.404345	+	0.404345i	0.475416	+	0.879761i	$0.342298\pi$
$60$	1.34383	−	1.42731i	0.173488	−	0.184265i
$61$	3.16789	+	3.16789i	0.405607	+	0.405607i	0.880203	−	0.474597i	$-0.157406\pi$
$61$	3.16789	+	3.16789i	0.405607	+	0.405607i	−0.474597	+	0.880203i	$0.657406\pi$
$62$	−3.76915	−	8.72558i	−0.478683	−	1.10815i
$63$	−2.03922			−0.256918
$64$	6.14413	+	5.12344i	0.768017	+	0.640430i
$65$	−5.51558			−0.684123
$66$	0.240663	+	0.557135i	0.0296236	+	0.0685786i
$67$	−9.61703	−	9.61703i	−1.17491	−	1.17491i	−0.981025	−	0.193882i	$-0.937892\pi$
$67$	−9.61703	−	9.61703i	−1.17491	−	1.17491i	−0.193882	−	0.981025i	$-0.562108\pi$
$68$	−0.186074	+	0.197632i	−0.0225648	+	0.0239664i
$69$	−0.224287	+	0.224287i	−0.0270010	+	0.0270010i
$70$	0.521463	−	1.31456i	0.0623267	−	0.157120i
$71$		−	0.0650839i		−	0.00772404i	−0.999993	−	0.00386202i	$-0.998771\pi$
$71$		−	0.0650839i		−	0.00772404i	0.999993	−	0.00386202i	$-0.00122932\pi$
$72$	1.96437	−	5.42298i	0.231503	−	0.639105i
$73$			3.41976i			0.400253i	0.979770	+	0.200126i	$0.0641353\pi$
$73$			3.41976i			0.400253i	−0.979770	+	0.200126i	$0.935865\pi$
$74$	−7.42460	−	2.94520i	−0.863093	−	0.342373i
$75$	0.693100	−	0.693100i	0.0800323	−	0.0800323i
$76$	−8.22268	+	0.247689i	−0.943206	+	0.0284118i
$77$	0.309578	+	0.309578i	0.0352797	+	0.0352797i
$78$	7.01885	−	3.03190i	0.794728	−	0.343295i
$79$	−9.73291			−1.09504			−0.547519	−	0.836793i	$-0.684428\pi$
$79$	−9.73291			−1.09504			−0.547519	+	0.836793i	$0.684428\pi$
$80$	2.99354	+	2.65305i	0.334688	+	0.296620i
$81$	−1.27611			−0.141790
$82$	4.17491	−	1.80342i	0.461042	−	0.199154i
$83$	−11.8341	−	11.8341i	−1.29897	−	1.29897i	−0.929075	−	0.369890i	$-0.879395\pi$
$83$	−11.8341	−	11.8341i	−1.29897	−	1.29897i	−0.369890	−	0.929075i	$-0.620605\pi$
$84$	0.0590251	+	1.95949i	0.00644017	+	0.213798i
$85$	−0.0959699	+	0.0959699i	−0.0104094	+	0.0104094i
$86$	−2.94205	−	1.16706i	−0.317250	−	0.125847i
$87$			8.17589i			0.876547i
$88$	−1.12149	+	0.525058i	−0.119551	+	0.0559714i
$89$		−	1.93694i		−	0.205315i	−0.994717	−	0.102658i	$-0.967265\pi$
$89$		−	1.93694i		−	0.205315i	0.994717	−	0.102658i	$-0.0327346\pi$
$90$	1.06338	−	2.68069i	0.112090	−	0.282569i
$91$	3.90010	−	3.90010i	0.408842	−	0.408842i
$92$	−0.471212	−	0.443653i	−0.0491272	−	0.0462541i
$93$	4.65829	+	4.65829i	0.483042	+	0.483042i
$94$	0.381656	+	0.883533i	0.0393648	+	0.0911295i
$95$	−4.11321			−0.422006
$96$	−5.26781	−	1.73060i	−0.537644	−	0.176629i
$97$	8.46136			0.859121			0.429560	−	0.903038i	$-0.358669\pi$
$97$	8.46136			0.859121			0.429560	+	0.903038i	$0.358669\pi$
$98$	0.560807	+	1.29827i	0.0566500	+	0.131145i
$99$	0.631300	+	0.631300i	0.0634480	+	0.0634480i
$100$	1.45615	+	1.37099i	0.145615	+	0.137099i
$101$	4.75568	−	4.75568i	0.473208	−	0.473208i	−0.429743	−	0.902951i	$-0.641396\pi$
$101$	4.75568	−	4.75568i	0.473208	−	0.473208i	0.902951	+	0.429743i	$0.141396\pi$
$102$	0.0693721	−	0.174881i	0.00686886	−	0.0173158i
$103$		−	3.01465i		−	0.297042i	−0.988909	−	0.148521i	$-0.952549\pi$
$103$		−	3.01465i		−	0.297042i	0.988909	−	0.148521i	$-0.0474513\pi$
$104$	6.61474	+	14.1286i	0.648629	+	1.38543i
$105$			0.980192i			0.0956569i
$106$	−2.65434	−	1.05293i	−0.257812	−	0.102269i
$107$	−10.9587	+	10.9587i	−1.05941	+	1.05941i	−0.0612941	+	0.998120i	$0.519523\pi$
$107$	−10.9587	+	10.9587i	−1.05941	+	1.05941i	−0.998120	+	0.0612941i	$0.980477\pi$
$108$	0.297441	+	9.87433i	0.0286212	+	0.950158i
$109$	10.2426	+	10.2426i	0.981063	+	0.981063i	0.999824	−	0.0187613i	$-0.00597227\pi$
$109$	10.2426	+	10.2426i	0.981063	+	0.981063i	−0.0187613	+	0.999824i	$0.505972\pi$
$110$	−0.568394	+	0.245527i	−0.0541942	+	0.0234101i
$111$	5.53608			0.525462
$112$	−3.99275	+	0.240762i	−0.377279	+	0.0227499i
$113$	−9.34555			−0.879155			−0.439577	−	0.898205i	$-0.644872\pi$
$113$	−9.34555			−0.879155			−0.439577	+	0.898205i	$0.644872\pi$
$114$	5.23426	−	2.26102i	0.490233	−	0.211764i
$115$	−0.228820	−	0.228820i	−0.0213376	−	0.0213376i
$116$	−16.6747	+	0.502284i	−1.54820	+	0.0466359i
$117$	7.95318	−	7.95318i	0.735272	−	0.735272i
$118$	5.77397	+	2.29043i	0.531537	+	0.210851i
$119$		−	0.135722i		−	0.0124416i
$120$	−2.60666	−	0.944211i	−0.237954	−	0.0861943i
$121$			10.8083i			0.982575i
$122$	2.33619	−	5.88934i	0.211509	−	0.533196i
$123$	−2.22884	+	2.22884i	−0.200968	+	0.200968i
$124$	−9.21436	+	9.78672i	−0.827474	+	0.878874i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.14361	+	2.64746i	0.101881	+	0.235854i
$127$	1.08102			0.0959246			0.0479623	−	0.998849i	$-0.484727\pi$
$127$	1.08102			0.0959246			0.0479623	+	0.998849i	$0.484727\pi$
$128$	3.20592	−	10.8500i	0.283366	−	0.959012i
$129$	2.19371			0.193146
$130$	3.09317	+	7.16069i	0.271289	+	0.628034i
$131$	−9.08357	−	9.08357i	−0.793635	−	0.793635i	0.188448	−	0.982083i	$-0.439654\pi$
$131$	−9.08357	−	9.08357i	−0.793635	−	0.793635i	−0.982083	+	0.188448i	$0.939654\pi$
$132$	0.588344	−	0.624890i	0.0512088	−	0.0543897i
$133$	2.90848	−	2.90848i	0.252197	−	0.252197i
$134$	−7.09217	+	17.8788i	−0.612670	+	1.54449i
$135$			4.93941i			0.425116i
$136$	0.360930	+	0.130740i	0.0309495	+	0.0112109i
$137$		−	13.4874i		−	1.15231i	−0.817341	−	0.576155i	$-0.804553\pi$
$137$		−	13.4874i		−	1.15231i	0.817341	−	0.576155i	$-0.195447\pi$
$138$	0.416967	+	0.165403i	0.0354946	+	0.0140800i
$139$	4.71327	−	4.71327i	0.399775	−	0.399775i	−0.478379	−	0.878154i	$-0.658775\pi$
$139$	4.71327	−	4.71327i	0.399775	−	0.399775i	0.878154	+	0.478379i	$0.158775\pi$
$140$	−1.99909	+	0.0602179i	−0.168954	+	0.00508934i
$141$	−0.471688	−	0.471688i	−0.0397233	−	0.0397233i
$142$	−0.0844962	+	0.0364995i	−0.00709077	+	0.00306297i
$143$	−2.41477			−0.201934
$144$	−8.14211	+	0.490969i	−0.678509	+	0.0409141i
$145$	−8.34111			−0.692692
$146$	4.43976	−	1.91782i	0.367437	−	0.158720i
$147$	−0.693100	−	0.693100i	−0.0571659	−	0.0571659i
$148$	0.340108	+	11.2908i	0.0279567	+	0.928098i
$149$	−10.8354	+	10.8354i	−0.887673	+	0.887673i	−0.994299	−	0.106626i	$-0.965995\pi$
$149$	−10.8354	+	10.8354i	−0.887673	+	0.887673i	0.106626	+	0.994299i	$0.465995\pi$
$150$	−1.28852	−	0.511134i	−0.105208	−	0.0417339i
$151$			3.12247i			0.254103i	0.991896	+	0.127051i	$0.0405513\pi$
$151$			3.12247i			0.254103i	−0.991896	+	0.127051i	$0.959449\pi$
$152$	4.93290	+	10.5363i	0.400111	+	0.854609i
$153$		−	0.276768i		−	0.0223753i
$154$	0.228302	−	0.575529i	0.0183971	−	0.0463774i
$155$	−4.75243	+	4.75243i	−0.381724	+	0.381724i
$156$	−7.87243	−	7.41202i	−0.630299	−	0.593437i
$157$	14.8487	+	14.8487i	1.18505	+	1.18505i	0.978418	+	0.206634i	$0.0662510\pi$
$157$	14.8487	+	14.8487i	1.18505	+	1.18505i	0.206634	+	0.978418i	$0.433749\pi$
$158$	5.45828	+	12.6359i	0.434237	+	1.00526i
$159$	1.97918			0.156959
$160$	1.76557	−	5.37427i	0.139581	−	0.424873i
$161$	0.323600			0.0255033
$162$	0.715651	+	1.65673i	0.0562268	+	0.130165i
$163$	−6.29767	−	6.29767i	−0.493272	−	0.493272i	0.416064	−	0.909335i	$-0.363409\pi$
$163$	−6.29767	−	6.29767i	−0.493272	−	0.493272i	−0.909335	+	0.416064i	$0.863409\pi$
$164$	−4.68264	−	4.40878i	−0.365652	−	0.344268i
$165$	0.303446	−	0.303446i	0.0236233	−	0.0236233i
$166$	−8.72720	+	22.0005i	−0.677362	+	1.70757i
$167$			8.01636i			0.620324i	0.950684	+	0.310162i	$0.100383\pi$
$167$			8.01636i			0.620324i	−0.950684	+	0.310162i	$0.899617\pi$
$168$	2.51084	−	1.17553i	0.193716	−	0.0906939i
$169$			17.4216i			1.34012i
$170$	0.178415	+	0.0707740i	0.0136838	+	0.00542812i
$171$	5.93103	−	5.93103i	0.453558	−	0.453558i
$172$	0.134770	+	4.47406i	0.0102761	+	0.341144i
$173$	−17.0091	−	17.0091i	−1.29318	−	1.29318i	−0.932812	−	0.360364i	$-0.882652\pi$
$173$	−17.0091	−	17.0091i	−1.29318	−	1.29318i	−0.360364	−	0.932812i	$-0.617348\pi$
$174$	10.6145	−	4.58509i	0.804682	−	0.347595i
$175$	−1.00000			−0.0755929
$176$	1.31060	+	1.16153i	0.0987904	+	0.0875539i
$177$	−4.30531			−0.323607
$178$	−2.51466	+	1.08625i	−0.188482	+	0.0814178i
$179$	−1.41099	−	1.41099i	−0.105462	−	0.105462i	0.652407	−	0.757869i	$-0.273759\pi$
$179$	−1.41099	−	1.41099i	−0.105462	−	0.105462i	−0.757869	+	0.652407i	$0.773759\pi$
$180$	−4.07660	+	0.122798i	−0.303852	+	0.00915281i
$181$	−8.67319	+	8.67319i	−0.644673	+	0.644673i	−0.951701	−	0.307028i	$-0.900666\pi$
$181$	−8.67319	+	8.67319i	−0.644673	+	0.644673i	0.307028	+	0.951701i	$0.400666\pi$
$182$	−7.25057	−	2.87617i	−0.537448	−	0.213196i
$183$			4.39133i			0.324616i
$184$	−0.311722	+	0.860562i	−0.0229804	+	0.0634415i
$185$			5.64796i			0.415246i
$186$	3.43530	−	8.66010i	0.251888	−	0.634989i
$187$	−0.0420166	+	0.0420166i	−0.00307256	+	0.00307256i
$188$	0.933026	−	0.990982i	0.0680479	−	0.0722748i
$189$	−3.49269	−	3.49269i	−0.254056	−	0.254056i
$190$	2.30671	+	5.34004i	0.167347	+	0.387407i
$191$	−17.5146			−1.26731			−0.633655	−	0.773616i	$-0.718446\pi$
$191$	−17.5146			−1.26731			−0.633655	+	0.773616i	$0.718446\pi$
$192$	0.707445	+	7.80956i	0.0510554	+	0.563606i
$193$	6.90209			0.496823			0.248412	−	0.968655i	$-0.420091\pi$
$193$	6.90209			0.496823			0.248412	+	0.968655i	$0.420091\pi$
$194$	−4.74519	−	10.9851i	−0.340685	−	0.788684i
$195$	−3.82285	−	3.82285i	−0.273760	−	0.273760i
$196$	1.37099	−	1.45615i	0.0979280	−	0.104011i
$197$	14.8423	−	14.8423i	1.05747	−	1.05747i	0.0592238	−	0.998245i	$-0.481137\pi$
$197$	14.8423	−	14.8423i	1.05747	−	1.05747i	0.998245	−	0.0592238i	$-0.0188626\pi$
$198$	0.465558	−	1.17363i	0.0330858	−	0.0834064i
$199$		−	15.0068i		−	1.06381i	−0.846805	−	0.531904i	$-0.821477\pi$
$199$		−	15.0068i		−	1.06381i	0.846805	−	0.531904i	$-0.178523\pi$
$200$	0.963293	−	2.65934i	0.0681151	−	0.188043i
$201$		−	13.3311i		−	0.940305i
$202$	−8.84116	−	3.50713i	−0.622062	−	0.246760i
$203$	5.89806	−	5.89806i	0.413962	−	0.413962i
$204$	−0.265946	+	0.00801100i	−0.0186200	+	0.000560882i
$205$	−2.27388	−	2.27388i	−0.158815	−	0.158815i
$206$	−3.91382	+	1.69063i	−0.272689	+	0.117792i
$207$	0.659894			0.0458658
$208$	14.6331	−	16.5111i	1.01462	−	1.14484i
$209$	−1.80080			−0.124564
$210$	1.27255	−	0.549698i	0.0878143	−	0.0379328i
$211$	18.3866	+	18.3866i	1.26579	+	1.26579i	0.948244	+	0.317542i	$0.102857\pi$
$211$	18.3866	+	18.3866i	1.26579	+	1.26579i	0.317542	+	0.948244i	$0.397143\pi$
$212$	0.121591	+	4.03652i	0.00835088	+	0.277229i
$213$	0.0451096	−	0.0451096i	0.00309086	−	0.00309086i
$214$	20.3730	+	8.08157i	1.39267	+	0.552445i
$215$			2.23805i			0.152633i
$216$	12.6527	−	5.92375i	0.860908	−	0.403060i
$217$		−	6.72094i		−	0.456247i
$218$	7.55350	−	19.0417i	0.511588	−	1.28967i
$219$	−2.37024	+	2.37024i	−0.160166	+	0.160166i
$220$	0.637518	+	0.600234i	0.0429815	+	0.0404678i
$221$	0.529330	+	0.529330i	0.0356066	+	0.0356066i
$222$	−3.10467	−	7.18731i	−0.208372	−	0.482381i
$223$	−24.5317			−1.64276			−0.821381	−	0.570379i	$-0.806796\pi$
$223$	−24.5317			−1.64276			−0.821381	+	0.570379i	$0.806796\pi$
$224$	2.55173	+	5.04863i	0.170495	+	0.337326i
$225$	−2.03922			−0.135948
$226$	5.24104	+	12.1330i	0.348629	+	0.807076i
$227$	−1.42944	−	1.42944i	−0.0948751	−	0.0948751i	0.658076	−	0.752951i	$-0.271370\pi$
$227$	−1.42944	−	1.42944i	−0.0948751	−	0.0948751i	−0.752951	+	0.658076i	$0.771370\pi$
$228$	−5.87081	−	5.52747i	−0.388804	−	0.366066i
$229$	6.60836	−	6.60836i	0.436693	−	0.436693i	−0.454205	−	0.890897i	$-0.650076\pi$
$229$	6.60836	−	6.60836i	0.436693	−	0.436693i	0.890897	+	0.454205i	$0.150076\pi$
$230$	−0.168746	+	0.425393i	−0.0111268	+	0.0280496i
$231$			0.429138i			0.0282352i
$232$	10.0034	+	21.3665i	0.656753	+	1.40278i
$233$		−	19.6736i		−	1.28886i	−0.764662	−	0.644431i	$-0.777094\pi$
$233$		−	19.6736i		−	1.28886i	0.764662	−	0.644431i	$-0.222906\pi$
$234$	−14.7855	−	5.86515i	−0.966562	−	0.383417i
$235$	0.481220	−	0.481220i	0.0313914	−	0.0313914i
$236$	−0.264496	−	8.78064i	−0.0172172	−	0.571571i
$237$	−6.74588	−	6.74588i	−0.438192	−	0.438192i
$238$	−0.176203	+	0.0761138i	−0.0114216	+	0.00493372i
$239$	−12.0048			−0.776529			−0.388264	−	0.921548i	$-0.626925\pi$
$239$	−12.0048			−0.776529			−0.388264	+	0.921548i	$0.626925\pi$
$240$	0.235993	+	3.91366i	0.0152333	+	0.252626i
$241$	−6.64503			−0.428044			−0.214022	−	0.976829i	$-0.568656\pi$
$241$	−6.64503			−0.428044			−0.214022	+	0.976829i	$0.568656\pi$
$242$	14.0321	−	6.06138i	0.902016	−	0.389640i
$243$	−11.3625	−	11.3625i	−0.728907	−	0.728907i
$244$	−8.95608	+	0.269781i	−0.573354	+	0.0172709i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	4.14358	+	1.64368i	0.264185	+	0.104797i
$247$			22.6867i			1.44352i
$248$	17.8732	+	6.47424i	1.13495	+	0.411114i
$249$		−	16.4045i		−	1.03959i
$250$	0.521463	−	1.31456i	0.0329802	−	0.0831403i
$251$	10.9695	−	10.9695i	0.692390	−	0.692390i	−0.270367	−	0.962757i	$-0.587145\pi$
$251$	10.9695	−	10.9695i	0.692390	−	0.692390i	0.962757	+	0.270367i	$0.0871452\pi$
$252$	2.79576	−	2.96942i	0.176116	−	0.187056i
$253$	−0.100180	−	0.100180i	−0.00629824	−	0.00629824i
$254$	−0.606241	−	1.40345i	−0.0380389	−	0.0880601i
$255$	−0.133034			−0.00833088
$256$	−15.8841	+	1.92261i	−0.992754	+	0.120163i
$257$	19.5226			1.21779			0.608894	−	0.793252i	$-0.291614\pi$
$257$	19.5226			1.21779			0.608894	+	0.793252i	$0.291614\pi$
$258$	−1.23025	−	2.84802i	−0.0765920	−	0.177310i
$259$	−3.99371	−	3.99371i	−0.248157	−	0.248157i
$260$	7.56181	−	8.03152i	0.468964	−	0.498094i
$261$	12.0275	−	12.0275i	0.744481	−	0.744481i
$262$	−6.69877	+	16.8870i	−0.413851	+	1.04328i
$263$			13.7663i			0.848864i	0.905460	+	0.424432i	$0.139526\pi$
$263$			13.7663i			0.848864i	−0.905460	+	0.424432i	$0.860474\pi$
$264$	−1.14122	−	0.413385i	−0.0702373	−	0.0254421i
$265$			2.01918i			0.124037i
$266$	−5.40707	−	2.14488i	−0.331529	−	0.131511i
$267$	1.34249	−	1.34249i	0.0821592	−	0.0821592i
$268$	27.1887	−	0.818996i	1.66082	−	0.0500281i
$269$	12.9825	+	12.9825i	0.791555	+	0.791555i	0.981747	−	0.190192i	$-0.0609110\pi$
$269$	12.9825	+	12.9825i	0.791555	+	0.791555i	−0.190192	+	0.981747i	$0.560911\pi$
$270$	6.41266	−	2.77005i	0.390262	−	0.168580i
$271$	31.3454			1.90410			0.952050	−	0.305943i	$-0.0989718\pi$
$271$	31.3454			1.90410			0.952050	+	0.305943i	$0.0989718\pi$
$272$	−0.0326768	−	0.541904i	−0.00198132	−	0.0328577i
$273$	5.40632			0.327205
$274$	−17.5103	+	7.56385i	−1.05784	+	0.456949i
$275$	0.309578	+	0.309578i	0.0186683	+	0.0186683i
$276$	−0.0191005	−	0.634093i	−0.00114972	−	0.0381679i
$277$	18.5159	−	18.5159i	1.11251	−	1.11251i	0.119703	−	0.992810i	$-0.461806\pi$
$277$	18.5159	−	18.5159i	1.11251	−	1.11251i	0.992810	−	0.119703i	$-0.0381941\pi$
$278$	−8.76232	−	3.47585i	−0.525529	−	0.208468i
$279$		−	13.7055i		−	0.820528i
$280$	1.19928	+	2.56159i	0.0716709	+	0.153084i
$281$			12.9375i			0.771789i	0.922543	+	0.385894i	$0.126107\pi$
$281$			12.9375i			0.771789i	−0.922543	+	0.385894i	$0.873893\pi$
$282$	−0.347851	+	0.876903i	−0.0207142	+	0.0522188i
$283$	17.9460	−	17.9460i	1.06678	−	1.06678i	0.0691738	−	0.997605i	$-0.477964\pi$
$283$	17.9460	−	17.9460i	1.06678	−	1.06678i	0.997605	−	0.0691738i	$-0.0220363\pi$
$284$	0.0947721	+	0.0892295i	0.00562369	+	0.00529480i
$285$	−2.85086	−	2.85086i	−0.168871	−	0.168871i
$286$	1.35422	+	3.13502i	0.0800768	+	0.185378i
$287$	3.21576			0.189820
$288$	5.20356	+	10.2953i	0.306623	+	0.606656i
$289$	−16.9816			−0.998916
$290$	4.67775	+	10.8290i	0.274687	+	0.635900i
$291$	5.86457	+	5.86457i	0.343787	+	0.343787i
$292$	−4.97970	−	4.68847i	−0.291415	−	0.274372i
$293$	−15.4346	+	15.4346i	−0.901701	+	0.901701i	−0.995583	−	0.0938824i	$-0.970072\pi$
$293$	−15.4346	+	15.4346i	−0.901701	+	0.901701i	0.0938824	+	0.995583i	$0.470072\pi$
$294$	−0.511134	+	1.28852i	−0.0298099	+	0.0751482i
$295$		−	4.39231i		−	0.255730i
$296$	14.4677	−	6.77351i	0.840920	−	0.393702i
$297$			2.16252i			0.125482i
$298$	20.1439	+	7.99070i	1.16690	+	0.462889i
$299$	−1.26207	+	1.26207i	−0.0729876	+	0.0729876i
$300$	0.0590251	+	1.95949i	0.00340782	+	0.113131i
$301$	−1.58254	−	1.58254i	−0.0912159	−	0.0912159i
$302$	4.05380	−	1.75110i	0.233270	−	0.100765i
$303$	6.59233			0.378719
$304$	10.9126	−	12.3131i	0.625878	−	0.706202i
$305$	−4.48007			−0.256528
$306$	−0.359318	+	0.155213i	−0.0205409	+	0.00887294i
$307$	−17.5986	−	17.5986i	−1.00440	−	1.00440i	−0.999990	−	0.00441329i	$-0.998595\pi$
$307$	−17.5986	−	17.5986i	−1.00440	−	1.00440i	−0.00441329	−	0.999990i	$-0.501405\pi$
$308$	−0.875223	+	0.0263640i	−0.0498705	+	0.00150223i
$309$	2.08945	−	2.08945i	0.118865	−	0.118865i
$310$	8.83511	+	3.50472i	0.501800	+	0.199055i
$311$		−	21.5204i		−	1.22031i	−0.792281	−	0.610156i	$-0.791107\pi$
$311$		−	21.5204i		−	1.22031i	0.792281	−	0.610156i	$-0.208893\pi$
$312$	−5.20787	+	14.3772i	−0.294838	+	0.813950i
$313$		−	3.64750i		−	0.206169i	−0.994673	−	0.103084i	$-0.967129\pi$
$313$		−	3.64750i		−	0.206169i	0.994673	−	0.103084i	$-0.0328712\pi$
$314$	10.9503	−	27.6048i	0.617961	−	1.55783i
$315$	1.44195	−	1.44195i	0.0812446	−	0.0812446i
$316$	13.3437	−	14.1726i	0.750644	−	0.797271i
$317$	3.93808	+	3.93808i	0.221184	+	0.221184i	0.808997	−	0.587813i	$-0.200011\pi$
$317$	3.93808	+	3.93808i	0.221184	+	0.221184i	−0.587813	+	0.808997i	$0.700011\pi$
$318$	−1.10994	−	2.56950i	−0.0622422	−	0.144091i
$319$	−3.65182			−0.204463
$320$	−7.96738	+	0.721742i	−0.445390	+	0.0403466i
$321$	−15.1909			−0.847873
$322$	−0.181477	−	0.420120i	−0.0101133	−	0.0234123i
$323$	0.394744	+	0.394744i	0.0219641	+	0.0219641i
$324$	1.74954	−	1.85821i	0.0971965	−	0.103234i
$325$	3.90010	−	3.90010i	0.216339	−	0.216339i
$326$	−4.64428	+	11.7078i	−0.257223	+	0.648437i
$327$			14.1983i			0.785167i
$328$	−3.09772	+	8.55178i	−0.171043	+	0.472193i
$329$			0.680548i			0.0375198i
$330$	−0.564129	−	0.223779i	−0.0310543	−	0.0123186i
$331$	21.2836	−	21.2836i	1.16985	−	1.16985i	0.187610	−	0.982244i	$-0.439926\pi$
$331$	21.2836	−	21.2836i	1.16985	−	1.16985i	0.982244	−	0.187610i	$-0.0600742\pi$
$332$	33.4568	−	1.00781i	1.83618	−	0.0553106i
$333$	−8.14408	−	8.14408i	−0.446293	−	0.446293i
$334$	10.4074	−	4.49563i	0.569466	−	0.245990i
$335$	13.6005			0.743076
$336$	−2.93425	−	2.60050i	−0.160076	−	0.141869i
$337$	−34.4581			−1.87705			−0.938525	−	0.345210i	$-0.887808\pi$
$337$	−34.4581			−1.87705			−0.938525	+	0.345210i	$0.887808\pi$
$338$	22.6179	−	9.77014i	1.23025	−	0.531426i
$339$	−6.47740	−	6.47740i	−0.351804	−	0.351804i
$340$	−0.00817290	−	0.271321i	−0.000443238	−	0.0147144i
$341$	−2.08066	+	2.08066i	−0.112674	+	0.112674i
$342$	−11.0262	−	4.37390i	−0.596230	−	0.236513i
$343$			1.00000i			0.0539949i
$344$	5.73294	−	2.68405i	0.309100	−	0.144714i
$345$		−	0.317190i		−	0.0170770i
$346$	−12.5435	+	31.6211i	−0.674343	+	1.69996i
$347$	3.36137	−	3.36137i	0.180448	−	0.180448i	−0.611103	−	0.791551i	$-0.709274\pi$
$347$	3.36137	−	3.36137i	0.180448	−	0.180448i	0.791551	+	0.611103i	$0.209274\pi$
$348$	−11.9053	−	11.2091i	−0.638193	−	0.600869i
$349$	−18.0194	−	18.0194i	−0.964558	−	0.964558i	0.0348347	−	0.999393i	$-0.488910\pi$
$349$	−18.0194	−	18.0194i	−0.964558	−	0.964558i	−0.999393	+	0.0348347i	$0.988910\pi$
$350$	0.560807	+	1.29827i	0.0299764	+	0.0693953i
$351$	27.2437			1.45416
$352$	0.772985	−	2.35291i	0.0412002	−	0.125410i
$353$	−26.9842			−1.43623			−0.718113	−	0.695927i	$-0.754994\pi$
$353$	−26.9842			−1.43623			−0.718113	+	0.695927i	$0.754994\pi$
$354$	2.41444	+	5.58943i	0.128326	+	0.297075i
$355$	0.0460213	+	0.0460213i	0.00244255	+	0.00244255i
$356$	2.82048	+	2.65553i	0.149485	+	0.140743i
$357$	0.0940689	−	0.0940689i	0.00497866	−	0.00497866i
$358$	−1.04055	+	2.62312i	−0.0549945	+	0.138636i
$359$			19.7103i			1.04027i	0.854084	+	0.520135i	$0.174119\pi$
$359$			19.7103i			1.04027i	−0.854084	+	0.520135i	$0.825881\pi$
$360$	2.44561	+	5.22365i	0.128895	+	0.275310i
$361$		−	2.08154i		−	0.109555i
$362$	16.1241	+	6.39613i	0.847463	+	0.336173i
$363$	−7.49125	+	7.49125i	−0.393189	+	0.393189i
$364$	0.332137	+	11.0262i	0.0174087	+	0.577927i
$365$	−2.41814	−	2.41814i	−0.126571	−	0.126571i
$366$	5.70112	−	2.46269i	0.298002	−	0.128727i
$367$	2.56944			0.134124			0.0670620	−	0.997749i	$-0.478637\pi$
$367$	2.56944			0.134124			0.0670620	+	0.997749i	$0.478637\pi$
$368$	1.29205	−	0.0779108i	0.0673530	−	0.00406138i
$369$	6.55765			0.341378
$370$	7.33256	−	3.16741i	0.381202	−	0.164666i
$371$	−1.42777	−	1.42777i	−0.0741263	−	0.0741263i
$372$	−13.1697	+	0.396704i	−0.682815	+	0.0205682i
$373$	−19.2765	+	19.2765i	−0.998098	+	0.998098i	−0.999998	−	0.00189970i	$-0.999395\pi$
$373$	−19.2765	+	19.2765i	−0.998098	+	0.998098i	0.00189970	+	0.999998i	$0.499395\pi$
$374$	0.0781119	+	0.0309856i	0.00403907	+	0.00160223i
$375$			0.980192i			0.0506169i
$376$	−1.80981	−	0.655567i	−0.0933336	−	0.0338083i
$377$			46.0060i			2.36943i
$378$	−2.57572	+	6.49316i	−0.132481	+	0.333972i
$379$	−14.4037	+	14.4037i	−0.739866	+	0.739866i	−0.972552	−	0.232686i	$-0.925249\pi$
$379$	−14.4037	+	14.4037i	−0.739866	+	0.739866i	0.232686	+	0.972552i	$0.425249\pi$
$380$	5.63917	−	5.98946i	0.289283	−	0.307253i
$381$	0.749252	+	0.749252i	0.0383854	+	0.0383854i
$382$	9.82228	+	22.7386i	0.502552	+	1.16341i
$383$	−20.8400			−1.06487			−0.532436	−	0.846470i	$-0.678723\pi$
$383$	−20.8400			−1.06487			−0.532436	+	0.846470i	$0.678723\pi$
$384$	9.74214	−	5.29810i	0.497152	−	0.270368i
$385$	−0.437810			−0.0223129
$386$	−3.87074	−	8.96075i	−0.197015	−	0.456090i
$387$	−3.22715	−	3.22715i	−0.164045	−	0.164045i
$388$	−11.6005	+	12.3210i	−0.588924	+	0.625506i
$389$	18.7508	−	18.7508i	0.950704	−	0.950704i	−0.0481365	−	0.998841i	$-0.515328\pi$
$389$	18.7508	−	18.7508i	0.950704	−	0.950704i	0.998841	+	0.0481365i	$0.0153283\pi$
$390$	−2.81920	+	7.10695i	−0.142756	+	0.359874i
$391$			0.0439197i			0.00222111i
$392$	−2.65934	−	0.963293i	−0.134317	−	0.0486536i
$393$		−	12.5916i		−	0.635164i
$394$	−27.5929	−	10.9456i	−1.39011	−	0.551431i
$395$	6.88220	−	6.88220i	0.346281	−	0.346281i
$396$	−1.78478	+	0.0537621i	−0.0896884	+	0.00270165i
$397$	2.75234	+	2.75234i	0.138136	+	0.138136i	0.772794	−	0.634657i	$-0.218859\pi$
$397$	2.75234	+	2.75234i	0.138136	+	0.138136i	−0.634657	+	0.772794i	$0.718859\pi$
$398$	−19.4829	+	8.41594i	−0.976589	+	0.421853i
$399$	4.03173			0.201839
$400$	−3.99275	+	0.240762i	−0.199637	+	0.0120381i
$401$	−12.3353			−0.615996			−0.307998	−	0.951387i	$-0.599659\pi$
$401$	−12.3353			−0.615996			−0.307998	+	0.951387i	$0.599659\pi$
$402$	−17.3074	+	7.47618i	−0.863212	+	0.372878i
$403$	26.2124	+	26.2124i	1.30573	+	1.30573i
$404$	0.404999	+	13.4450i	0.0201494	+	0.668914i
$405$	0.902346	−	0.902346i	0.0448379	−	0.0448379i
$406$	−10.9649	−	4.34958i	−0.544180	−	0.215866i
$407$			2.47273i			0.122569i
$408$	0.159545	+	0.340777i	0.00789865	+	0.0168710i
$409$		−	4.60054i		−	0.227482i	−0.993510	−	0.113741i	$-0.963717\pi$
$409$		−	4.60054i		−	0.227482i	0.993510	−	0.113741i	$-0.0362834\pi$
$410$	−1.67690	+	4.22732i	−0.0828161	+	0.208772i
$411$	9.34815	−	9.34815i	0.461110	−	0.461110i
$412$	4.38979	+	4.13306i	0.216269	+	0.203621i
$413$	3.10583	+	3.10583i	0.152828	+	0.152828i
$414$	−0.370073	−	0.856718i	−0.0181881	−	0.0421054i
$415$	16.7360			0.821538
$416$	−29.6422	−	9.73815i	−1.45333	−	0.477452i
$417$	6.53354			0.319949
$418$	1.00990	+	2.33792i	0.0493959	+	0.114351i
$419$	19.4100	+	19.4100i	0.948243	+	0.948243i	0.998725	−	0.0504821i	$-0.0160758\pi$
$419$	19.4100	+	19.4100i	0.948243	+	0.948243i	−0.0504821	+	0.998725i	$0.516076\pi$
$420$	−1.42731	−	1.34383i	−0.0696455	−	0.0655724i
$421$	−22.0371	+	22.0371i	−1.07402	+	1.07402i	−0.0769891	+	0.997032i	$0.524531\pi$
$421$	−22.0371	+	22.0371i	−1.07402	+	1.07402i	−0.997032	+	0.0769891i	$0.975469\pi$
$422$	13.5594	−	34.1820i	0.660060	−	1.66396i
$423$			1.38779i			0.0674767i
$424$	5.17229	−	2.42157i	0.251189	−	0.117602i
$425$		−	0.135722i		−	0.00658348i
$426$	−0.0838621	−	0.0332666i	−0.00406313	−	0.00161177i
$427$	3.16789	−	3.16789i	0.153305	−	0.153305i
$428$	−0.933251	−	30.9817i	−0.0451104	−	1.49756i
$429$	−1.67368	−	1.67368i	−0.0808061	−	0.0808061i
$430$	2.90558	−	1.25511i	0.140119	−	0.0605268i
$431$	−1.30164			−0.0626979			−0.0313490	−	0.999509i	$-0.509980\pi$
$431$	−1.30164			−0.0626979			−0.0313490	+	0.999509i	$0.509980\pi$
$432$	−14.7863	−	13.1045i	−0.711407	−	0.630491i
$433$	−10.8225			−0.520097			−0.260048	−	0.965596i	$-0.583739\pi$
$433$	−10.8225			−0.520097			−0.260048	+	0.965596i	$0.583739\pi$
$434$	−8.72558	+	3.76915i	−0.418841	+	0.180925i
$435$	−5.78122	−	5.78122i	−0.277189	−	0.277189i
$436$	−28.9573	+	0.872270i	−1.38680	+	0.0417741i
$437$	−0.941184	+	0.941184i	−0.0450229	+	0.0450229i
$438$	4.40644	+	1.74795i	0.210548	+	0.0835205i
$439$		−	8.63059i		−	0.411916i	−0.978561	−	0.205958i	$-0.933969\pi$
$439$		−	8.63059i		−	0.411916i	0.978561	−	0.205958i	$-0.0660310\pi$
$440$	0.421739	−	1.16428i	0.0201056	−	0.0555051i
$441$			2.03922i			0.0971059i
$442$	0.390359	−	0.984062i	0.0185675	−	0.0468071i
$443$	−13.1032	+	13.1032i	−0.622552	+	0.622552i	−0.946183	−	0.323631i	$-0.895096\pi$
$443$	−13.1032	+	13.1032i	−0.622552	+	0.622552i	0.323631	+	0.946183i	$0.395096\pi$
$444$	−7.58993	+	8.06139i	−0.360202	+	0.382576i
$445$	1.36962	+	1.36962i	0.0649264	+	0.0649264i
$446$	13.7575	+	31.8487i	0.651438	+	1.50808i
$447$	−15.0201			−0.710425
$448$	5.12344	−	6.14413i	0.242060	−	0.290283i
$449$	0.831625			0.0392468			0.0196234	−	0.999807i	$-0.493753\pi$
$449$	0.831625			0.0392468			0.0196234	+	0.999807i	$0.493753\pi$
$450$	1.14361	+	2.64746i	0.0539103	+	0.124802i
$451$	−0.995529	−	0.995529i	−0.0468776	−	0.0468776i
$452$	12.8127	−	13.6085i	0.602657	−	0.640092i
$453$	−2.16418	+	2.16418i	−0.101682	+	0.101682i
$454$	−1.05415	+	2.65743i	−0.0494738	+	0.124719i
$455$			5.51558i			0.258574i
$456$	−3.88374	+	10.7217i	−0.181873	+	0.502091i
$457$			9.92424i			0.464236i	0.972688	+	0.232118i	$0.0745656\pi$
$457$			9.92424i			0.464236i	−0.972688	+	0.232118i	$0.925434\pi$
$458$	−12.2854	−	4.87340i	−0.574060	−	0.227719i
$459$	0.474034	−	0.474034i	0.0221260	−	0.0221260i
$460$	0.646907	−	0.0194865i	0.0301622	−	0.000908565i
$461$	16.4744	+	16.4744i	0.767288	+	0.767288i	0.977628	−	0.210340i	$-0.0674571\pi$
$461$	16.4744	+	16.4744i	0.767288	+	0.767288i	−0.210340	+	0.977628i	$0.567457\pi$
$462$	0.557135	−	0.240663i	0.0259203	−	0.0111967i
$463$	−1.33606			−0.0620920			−0.0310460	−	0.999518i	$-0.509884\pi$
$463$	−1.33606			−0.0620920			−0.0310460	+	0.999518i	$0.509884\pi$
$464$	22.1294	−	24.9695i	1.02733	−	1.15918i
$465$	−6.58781			−0.305503
$466$	−25.5416	+	11.0331i	−1.18319	+	0.511098i
$467$	10.7235	+	10.7235i	0.496224	+	0.496224i	0.910260	−	0.414036i	$-0.135881\pi$
$467$	10.7235	+	10.7235i	0.496224	+	0.496224i	−0.414036	+	0.910260i	$0.635881\pi$
$468$	0.677301	+	22.4848i	0.0313082	+	1.03936i
$469$	−9.61703	+	9.61703i	−0.444073	+	0.444073i
$470$	−0.894624	−	0.354881i	−0.0412659	−	0.0163694i
$471$			20.5832i			0.948425i
$472$	−11.2513	+	5.26763i	−0.517882	+	0.242462i
$473$			0.979839i			0.0450530i
$474$	−4.97482	+	12.5411i	−0.228501	+	0.576031i
$475$	2.90848	−	2.90848i	0.133450	−	0.133450i
$476$	0.197632	+	0.186074i	0.00905845	+	0.00852868i
$477$	−2.91155	−	2.91155i	−0.133311	−	0.133311i
$478$	6.73240	+	15.5855i	0.307933	+	0.712864i
$479$	−3.30214			−0.150878			−0.0754392	−	0.997150i	$-0.524036\pi$
$479$	−3.30214			−0.150878			−0.0754392	+	0.997150i	$0.524036\pi$
$480$	4.94862	−	2.50119i	0.225873	−	0.114163i
$481$	31.1518			1.42040
$482$	3.72658	+	8.62702i	0.169741	+	0.392950i
$483$	0.224287	+	0.224287i	0.0102054	+	0.0102054i
$484$	−15.7386	−	14.8181i	−0.715390	−	0.673551i
$485$	−5.98308	+	5.98308i	−0.271678	+	0.271678i
$486$	−8.37941	+	21.1238i	−0.380098	+	0.958194i
$487$			23.3095i			1.05625i	0.849165	+	0.528127i	$0.177106\pi$
$487$			23.3095i			1.05625i	−0.849165	+	0.528127i	$0.822894\pi$
$488$	5.37288	+	11.4761i	0.243219	+	0.519498i
$489$		−	8.72983i		−	0.394777i
$490$	−1.31456	−	0.521463i	−0.0593859	−	0.0235573i
$491$	11.4467	−	11.4467i	0.516583	−	0.516583i	−0.399953	−	0.916536i	$-0.630973\pi$
$491$	11.4467	−	11.4467i	0.516583	−	0.516583i	0.916536	+	0.399953i	$0.130973\pi$
$492$	−0.189810	−	6.30126i	−0.00855732	−	0.284083i
$493$	0.800496	+	0.800496i	0.0360525	+	0.0360525i
$494$	29.4534	−	12.7229i	1.32517	−	0.572428i
$495$	−0.892793			−0.0401281
$496$	−1.61815	−	26.8350i	−0.0726571	−	1.20493i
$497$	−0.0650839			−0.00291941
$498$	−21.2974	+	9.19975i	−0.954359	+	0.412250i
$499$	12.6032	+	12.6032i	0.564197	+	0.564197i	0.930497	−	0.366300i	$-0.119376\pi$
$499$	12.6032	+	12.6032i	0.564197	+	0.564197i	−0.366300	+	0.930497i	$0.619376\pi$
$500$	−1.99909	+	0.0602179i	−0.0894022	+	0.00269303i
$501$	−5.55614	+	5.55614i	−0.248230	+	0.248230i
$502$	−20.3931	−	8.08958i	−0.910190	−	0.361056i
$503$			15.3644i			0.685065i	0.939506	+	0.342532i	$0.111285\pi$
$503$			15.3644i			0.685065i	−0.939506	+	0.342532i	$0.888715\pi$
$504$	−5.42298	−	1.96437i	−0.241559	−	0.0875000i
$505$			6.72555i			0.299283i
$506$	−0.0738785	+	0.186241i	−0.00328430	+	0.00827944i
$507$	−12.0749	+	12.0749i	−0.536265	+	0.536265i
$508$	−1.48206	+	1.57412i	−0.0657560	+	0.0698405i
$509$	−11.2336	−	11.2336i	−0.497922	−	0.497922i	0.412868	−	0.910791i	$-0.364527\pi$
$509$	−11.2336	−	11.2336i	−0.497922	−	0.497922i	−0.910791	+	0.412868i	$0.864527\pi$
$510$	0.0746061	+	0.172713i	0.00330361	+	0.00764786i
$511$	3.41976			0.151281
$512$	11.4039	+	19.5435i	0.503988	+	0.863711i
$513$	20.3168			0.897008
$514$	−10.9484	−	25.3456i	−0.482914	−	1.11795i
$515$	2.13168	+	2.13168i	0.0939330	+	0.0939330i
$516$	−3.00756	+	3.19438i	−0.132401	+	0.140625i
$517$	0.210683	−	0.210683i	0.00926583	−	0.00926583i
$518$	−2.94520	+	7.42460i	−0.129405	+	0.326218i
$519$		−	23.5780i		−	1.03496i
$520$	−14.6678	−	5.31311i	−0.643224	−	0.232995i
$521$		−	41.8678i		−	1.83426i	−0.398588	−	0.917130i	$-0.630500\pi$
$521$		−	41.8678i		−	1.83426i	0.398588	−	0.917130i	$-0.369500\pi$
$522$	−22.3599	−	8.86977i	−0.978667	−	0.388219i
$523$	−1.27567	+	1.27567i	−0.0557810	+	0.0557810i	−0.734447	−	0.678666i	$-0.762558\pi$
$523$	−1.27567	+	1.27567i	−0.0557810	+	0.0557810i	0.678666	+	0.734447i	$0.262558\pi$
$524$	25.6806	−	0.773565i	1.12186	−	0.0337934i
$525$	−0.693100	−	0.693100i	−0.0302494	−	0.0302494i
$526$	17.8723	−	7.72021i	0.779268	−	0.336617i
$527$	0.912180			0.0397352
$528$	0.103320	+	1.71344i	0.00449644	+	0.0745678i
$529$	22.8953			0.995447
$530$	2.62143	−	1.13237i	0.113868	−	0.0491869i
$531$	6.33349	+	6.33349i	0.274850	+	0.274850i
$532$	0.247689	+	8.22268i	0.0107387	+	0.356498i
$533$	−12.5418	+	12.5418i	−0.543245	+	0.543245i
$534$	−2.49579	−	0.990035i	−0.108004	−	0.0428430i
$535$		−	15.4979i		−	0.670032i
$536$	−16.3109	−	34.8389i	−0.704523	−	1.50481i
$537$		−	1.95591i		−	0.0844037i
$538$	9.57405	−	24.1354i	0.412767	−	1.04055i
$539$	0.309578	−	0.309578i	0.0133345	−	0.0133345i
$540$	−7.19253	−	6.77188i	−0.309517	−	0.291416i
$541$	−32.1395	−	32.1395i	−1.38179	−	1.38179i	−0.841449	−	0.540336i	$-0.818297\pi$
$541$	−32.1395	−	32.1395i	−1.38179	−	1.38179i	−0.540336	−	0.841449i	$-0.681703\pi$
$542$	−17.5787	−	40.6947i	−0.755071	−	1.74799i
$543$	−12.0228			−0.515947
$544$	−0.685210	+	0.346326i	−0.0293781	+	0.0148486i
$545$	−14.4852			−0.620479
$546$	−3.03190	−	7.01885i	−0.129753	−	0.300379i
$547$	−17.6296	−	17.6296i	−0.753786	−	0.753786i	0.221398	−	0.975184i	$-0.428938\pi$
$547$	−17.6296	−	17.6296i	−0.753786	−	0.753786i	−0.975184	+	0.221398i	$0.928938\pi$
$548$	19.6398	+	18.4912i	0.838970	+	0.789904i
$549$	6.46004	−	6.46004i	0.275708	−	0.275708i
$550$	0.228302	−	0.575529i	0.00973482	−	0.0245406i
$551$			34.3087i			1.46160i
$552$	−0.812510	+	0.380401i	−0.0345827	+	0.0161909i
$553$			9.73291i			0.413885i
$554$	−34.4224	−	13.6547i	−1.46247	−	0.580134i
$555$	−3.91460	+	3.91460i	−0.166166	+	0.166166i
$556$	0.401387	+	13.3251i	0.0170226	+	0.565111i
$557$	10.6558	+	10.6558i	0.451502	+	0.451502i	0.895853	−	0.444351i	$-0.146566\pi$
$557$	10.6558	+	10.6558i	0.451502	+	0.451502i	−0.444351	+	0.895853i	$0.646566\pi$
$558$	−17.7934	+	7.68614i	−0.753255	+	0.325380i
$559$	12.3441			0.522100
$560$	2.65305	−	2.99354i	0.112112	−	0.126500i
$561$	−0.0582434			−0.00245904
$562$	16.7964	−	7.25546i	0.708512	−	0.306053i
$563$	26.0860	+	26.0860i	1.09939	+	1.09939i	0.994482	+	0.104911i	$0.0334557\pi$
$563$	26.0860	+	26.0860i	1.09939	+	1.09939i	0.104911	+	0.994482i	$0.466544\pi$
$564$	1.33353	−	0.0401694i	0.0561518	−	0.00169144i
$565$	6.60830	−	6.60830i	0.278013	−	0.278013i
$566$	−33.3629	−	13.2344i	−1.40235	−	0.556285i
$567$			1.27611i			0.0535916i
$568$	0.0626948	−	0.173080i	0.00263062	−	0.00726227i
$569$		−	25.5848i		−	1.07257i	−0.844037	−	0.536286i	$-0.819827\pi$
$569$		−	25.5848i		−	1.07257i	0.844037	−	0.536286i	$-0.180173\pi$
$570$	−2.10240	+	5.29996i	−0.0880597	+	0.221991i
$571$	−8.48163	+	8.48163i	−0.354945	+	0.354945i	−0.861946	−	0.507001i	$-0.830754\pi$
$571$	−8.48163	+	8.48163i	−0.354945	+	0.354945i	0.507001	+	0.861946i	$0.330754\pi$
$572$	3.31064	−	3.51628i	0.138425	−	0.147023i
$573$	−12.1393	−	12.1393i	−0.507128	−	0.507128i
$574$	−1.80342	−	4.17491i	−0.0752732	−	0.174257i
$575$	0.323600			0.0134951
$576$	10.4478	−	12.5293i	0.435327	−	0.522053i
$577$	−18.8326			−0.784013			−0.392006	−	0.919962i	$-0.628219\pi$
$577$	−18.8326			−0.784013			−0.392006	+	0.919962i	$0.628219\pi$
$578$	9.52338	+	22.0466i	0.396120	+	0.917018i
$579$	4.78384	+	4.78384i	0.198809	+	0.198809i
$580$	11.4356	−	12.1459i	0.474837	−	0.504332i
$581$	−11.8341	+	11.8341i	−0.490963	+	0.490963i
$582$	4.32488	−	10.9027i	0.179272	−	0.451930i
$583$			0.884016i			0.0366122i
$584$	−3.29423	+	9.09429i	−0.136316	+	0.376325i
$585$			11.2475i			0.465027i
$586$	28.6941	+	11.3824i	1.18534	+	0.470204i
$587$	9.45348	−	9.45348i	0.390187	−	0.390187i	−0.484567	−	0.874754i	$-0.661023\pi$
$587$	9.45348	−	9.45348i	0.390187	−	0.390187i	0.874754	+	0.484567i	$0.161023\pi$
$588$	1.95949	−	0.0590251i	0.0808082	−	0.00243415i
$589$	19.5477	+	19.5477i	0.805449	+	0.805449i
$590$	−5.70239	+	2.46324i	−0.234764	+	0.101410i
$591$	20.5744			0.846316
$592$	−16.9074	−	14.9843i	−0.694891	−	0.615853i
$593$	29.2596			1.20155			0.600774	−	0.799419i	$-0.294859\pi$
$593$	29.2596			1.20155			0.600774	+	0.799419i	$0.294859\pi$
$594$	2.80753	−	1.21276i	0.115194	−	0.0497600i
$595$	0.0959699	+	0.0959699i	0.00393438	+	0.00393438i
$596$	−0.922756	−	30.6333i	−0.0377976	−	1.25479i
$597$	10.4012	−	10.4012i	0.425695	−	0.425695i
$598$	2.34629	+	0.930729i	0.0959469	+	0.0380603i
$599$		−	8.33292i		−	0.340474i	−0.985403	−	0.170237i	$-0.945547\pi$
$599$		−	8.33292i		−	0.340474i	0.985403	−	0.170237i	$-0.0544533\pi$
$600$	2.51084	−	1.17553i	0.102505	−	0.0479907i
$601$			29.1988i			1.19104i	0.803340	+	0.595521i	$0.203054\pi$
$601$			29.1988i			1.19104i	−0.803340	+	0.595521i	$0.796946\pi$
$602$	−1.16706	+	2.94205i	−0.0475657	+	0.119909i
$603$	−19.6113	+	19.6113i	−0.798633	+	0.798633i
$604$	−4.54679	−	4.28088i	−0.185006	−	0.174186i
$605$	−7.64264	−	7.64264i	−0.310717	−	0.310717i
$606$	−3.69702	−	8.55860i	−0.150181	−	0.347669i
$607$	35.7165			1.44969			0.724844	−	0.688913i	$-0.241912\pi$
$607$	35.7165			1.44969			0.724844	+	0.688913i	$0.241912\pi$
$608$	−22.1055	−	7.26216i	−0.896495	−	0.294520i
$609$	8.17589			0.331304
$610$	2.51245	+	5.81633i	0.101726	+	0.235496i
$611$	−2.65421	−	2.65421i	−0.107378	−	0.107378i
$612$	0.403016	+	0.379446i	0.0162910	+	0.0153382i
$613$	17.8439	−	17.8439i	0.720710	−	0.720710i	−0.248040	−	0.968750i	$-0.579786\pi$
$613$	17.8439	−	17.8439i	0.720710	−	0.720710i	0.968750	+	0.248040i	$0.0797863\pi$
$614$	−12.9782	+	32.7170i	−0.523759	+	1.32035i
$615$		−	3.15206i		−	0.127103i
$616$	0.525058	+	1.12149i	0.0211552	+	0.0451860i
$617$		−	25.8401i		−	1.04028i	−0.854080	−	0.520142i	$-0.825879\pi$
$617$		−	25.8401i		−	1.04028i	0.854080	−	0.520142i	$-0.174121\pi$
$618$	−3.88445	−	1.54089i	−0.156255	−	0.0619836i
$619$	4.74341	−	4.74341i	0.190654	−	0.190654i	−0.605325	−	0.795979i	$-0.706957\pi$
$619$	4.74341	−	4.74341i	0.190654	−	0.190654i	0.795979	+	0.605325i	$0.206957\pi$
$620$	−0.404721	−	13.4358i	−0.0162540	−	0.539595i
$621$	1.13023	+	1.13023i	0.0453548	+	0.0453548i
$622$	−27.9393	+	12.0688i	−1.12026	+	0.483915i
$623$	−1.93694			−0.0776018
$624$	21.5861	−	1.30164i	0.864135	−	0.0521073i
$625$	−1.00000			−0.0400000
$626$	−4.73543	+	2.04554i	−0.189266	+	0.0817563i
$627$	−1.24814	−	1.24814i	−0.0498458	−	0.0498458i
$628$	−41.9793	+	1.26453i	−1.67516	+	0.0504601i
$629$	0.542035	−	0.542035i	0.0216123	−	0.0216123i
$630$	−2.68069	−	1.06338i	−0.106801	−	0.0423661i
$631$		−	28.5165i		−	1.13522i	−0.823297	−	0.567611i	$-0.807868\pi$
$631$		−	28.5165i		−	1.13522i	0.823297	−	0.567611i	$-0.192132\pi$
$632$	−25.8831	−	9.37564i	−1.02957	−	0.372943i
$633$			25.4875i			1.01304i
$634$	2.90417	−	7.32117i	0.115339	−	0.290761i
$635$	−0.764394	+	0.764394i	−0.0303340	+	0.0303340i
$636$	−2.71344	+	2.88199i	−0.107595	+	0.114278i
$637$	−3.90010	−	3.90010i	−0.154528	−	0.154528i
$638$	2.04797	+	4.74104i	0.0810797	+	0.187699i
$639$	−0.132721			−0.00525035
$640$	5.40517	+	9.93902i	0.213658	+	0.392874i
$641$	−50.3612			−1.98915			−0.994573	−	0.104040i	$-0.966823\pi$
$641$	−50.3612			−1.98915			−0.994573	+	0.104040i	$0.966823\pi$
$642$	8.51916	+	19.7218i	0.336224	+	0.778359i
$643$	−1.55555	−	1.55555i	−0.0613451	−	0.0613451i	0.675769	−	0.737114i	$-0.263812\pi$
$643$	−1.55555	−	1.55555i	−0.0613451	−	0.0613451i	−0.737114	+	0.675769i	$0.763812\pi$
$644$	−0.443653	+	0.471212i	−0.0174824	+	0.0185683i
$645$	−1.55119	+	1.55119i	−0.0610780	+	0.0610780i
$646$	0.291108	−	0.733858i	0.0114535	−	0.0288733i
$647$		−	7.16846i		−	0.281821i	−0.990022	−	0.140911i	$-0.954997\pi$
$647$		−	7.16846i		−	0.281821i	0.990022	−	0.140911i	$-0.0450030\pi$
$648$	−3.39361	−	1.22927i	−0.133313	−	0.0482902i
$649$		−	1.92300i		−	0.0754843i
$650$	−7.25057	−	2.87617i	−0.284391	−	0.112813i
$651$	4.65829	−	4.65829i	0.182573	−	0.182573i
$652$	17.8044	−	0.536316i	0.697275	−	0.0210037i
$653$	23.7196	+	23.7196i	0.928219	+	0.928219i	0.997591	−	0.0693715i	$-0.0220994\pi$
$653$	23.7196	+	23.7196i	0.928219	+	0.928219i	−0.0693715	+	0.997591i	$0.522099\pi$
$654$	18.4332	−	7.96249i	0.720794	−	0.311358i
$655$	12.8461			0.501939
$656$	12.8397	−	0.774234i	0.501307	−	0.0302288i
$657$	6.97366			0.272068
$658$	0.883533	−	0.381656i	0.0344437	−	0.0148785i
$659$	26.1670	+	26.1670i	1.01932	+	1.01932i	0.999810	+	0.0195118i	$0.00621119\pi$
$659$	26.1670	+	26.1670i	1.01932	+	1.01932i	0.0195118	+	0.999810i	$0.493789\pi$
$660$	0.0258418	+	0.857886i	0.00100589	+	0.0333932i
$661$	−15.6684	+	15.6684i	−0.609430	+	0.609430i	−0.942797	−	0.333367i	$-0.891815\pi$
$661$	−15.6684	+	15.6684i	−0.609430	+	0.609430i	0.333367	+	0.942797i	$0.391815\pi$
$662$	−39.5678	−	15.6958i	−1.53785	−	0.610035i
$663$			0.733757i			0.0284968i
$664$	−20.0712	−	42.8707i	−0.778914	−	1.66371i
$665$			4.11321i			0.159503i
$666$	−6.00593	+	15.1404i	−0.232725	+	0.586680i
$667$	−1.90861	+	1.90861i	−0.0739018	+	0.0739018i
$668$	−11.6730	−	10.9904i	−0.451644	−	0.425230i
$669$	−17.0029	−	17.0029i	−0.657370	−	0.657370i
$670$	−7.62727	−	17.6571i	−0.294667	−	0.682154i
$671$	−1.96142			−0.0757198
$672$	−1.73060	+	5.26781i	−0.0667593	+	0.203210i
$673$	6.94799			0.267825			0.133913	−	0.990993i	$-0.457246\pi$
$673$	6.94799			0.267825			0.133913	+	0.990993i	$0.457246\pi$
$674$	19.3243	+	44.7358i	0.744345	+	1.72316i
$675$	−3.49269	−	3.49269i	−0.134434	−	0.134434i
$676$	−25.3685	−	23.8849i	−0.975711	−	0.918648i
$677$	6.32882	−	6.32882i	0.243236	−	0.243236i	−0.574951	−	0.818188i	$-0.694979\pi$
$677$	6.32882	−	6.32882i	0.243236	−	0.243236i	0.818188	+	0.574951i	$0.194979\pi$
$678$	−4.77682	+	12.0420i	−0.183453	+	0.462469i
$679$		−	8.46136i		−	0.324717i
$680$	−0.347663	+	0.162769i	−0.0133323	+	0.00624191i
$681$		−	1.98149i		−	0.0759307i
$682$	3.86810	+	1.53440i	0.148117	+	0.0587553i
$683$	−14.3200	+	14.3200i	−0.547941	+	0.547941i	−0.925845	−	0.377904i	$-0.876645\pi$
$683$	−14.3200	+	14.3200i	−0.547941	+	0.547941i	0.377904	+	0.925845i	$0.376645\pi$
$684$	0.505093	+	16.7679i	0.0193127	+	0.641136i
$685$	9.53706	+	9.53706i	0.364392	+	0.364392i
$686$	1.29827	−	0.560807i	0.0495680	−	0.0214117i
$687$	9.16051			0.349495
$688$	−6.69969	−	5.93766i	−0.255423	−	0.226371i
$689$	11.1369			0.424283
$690$	−0.411798	+	0.177882i	−0.0156769	+	0.00677187i
$691$	14.6792	+	14.6792i	0.558422	+	0.558422i	0.928858	−	0.370436i	$-0.120792\pi$
$691$	14.6792	+	14.6792i	0.558422	+	0.558422i	−0.370436	+	0.928858i	$0.620792\pi$
$692$	48.0871	−	1.44851i	1.82800	−	0.0550641i
$693$	0.631300	−	0.631300i	0.0239811	−	0.0239811i
$694$	−6.24903	−	2.47888i	−0.237210	−	0.0940969i
$695$			6.66558i			0.252840i
$696$	−7.87577	+	21.7424i	−0.298530	+	0.824145i
$697$			0.436449i			0.0165317i
$698$	−13.2886	+	33.4995i	−0.502981	+	1.26797i
$699$	13.6358	−	13.6358i	0.515753	−	0.515753i
$700$	1.37099	−	1.45615i	0.0518186	−	0.0550374i
$701$	1.80600	+	1.80600i	0.0682116	+	0.0682116i	0.740390	−	0.672178i	$-0.234641\pi$
$701$	1.80600	+	1.80600i	0.0682116	+	0.0682116i	−0.672178	+	0.740390i	$0.734641\pi$
$702$	−15.2784	−	35.3695i	−0.576647	−	1.33494i
$703$	23.2312			0.876182
$704$	−3.48820	+	0.315986i	−0.131466	+	0.0119092i
$705$	0.667068			0.0251232
$706$	15.1329	+	35.0327i	0.569536	+	1.31847i
$707$	−4.75568	−	4.75568i	−0.178856	−	0.178856i
$708$	5.90254	−	6.26918i	0.221831	−	0.235610i
$709$	−22.7049	+	22.7049i	−0.852700	+	0.852700i	−0.990465	−	0.137765i	$-0.956008\pi$
$709$	−22.7049	+	22.7049i	−0.852700	+	0.852700i	0.137765	+	0.990465i	$0.456008\pi$
$710$	0.0339388	−	0.0855569i	0.00127370	−	0.00321089i
$711$			19.8476i			0.744343i
$712$	1.86584	−	5.15097i	0.0699253	−	0.193041i
$713$			2.17490i			0.0814506i
$714$	−0.174881	−	0.0693721i	−0.00654476	−	0.00259618i
$715$	1.70750	−	1.70750i	0.0638570	−	0.0638570i
$716$	3.98906	−	0.120161i	0.149078	−	0.00449062i
$717$	−8.32056	−	8.32056i	−0.310737	−	0.310737i
$718$	25.5892	−	11.0537i	0.954982	−	0.412520i
$719$	−42.2576			−1.57594			−0.787971	−	0.615713i	$-0.788868\pi$
$719$	−42.2576			−1.57594			−0.787971	+	0.615713i	$0.788868\pi$
$720$	5.41017	−	6.10451i	0.201625	−	0.227502i
$721$	−3.01465			−0.112271
$722$	−2.70240	+	1.16734i	−0.100573	+	0.0434440i
$723$	−4.60567	−	4.60567i	−0.171287	−	0.171287i
$724$	−0.738617	−	24.5204i	−0.0274505	−	0.911292i
$725$	5.89806	−	5.89806i	0.219048	−	0.219048i
$726$	13.9268	+	5.52450i	0.516871	+	0.205033i
$727$		−	30.9379i		−	1.14742i	−0.819057	−	0.573712i	$-0.805503\pi$
$727$		−	30.9379i		−	1.14742i	0.819057	−	0.573712i	$-0.194497\pi$
$728$	14.1286	−	6.61474i	0.523641	−	0.245159i
$729$		−	11.9224i		−	0.441571i
$730$	−1.78328	+	4.49549i	−0.0660021	+	0.166386i
$731$	0.214785	−	0.214785i	0.00794411	−	0.00794411i
$732$	−6.39445	−	6.02048i	−0.236346	−	0.222523i
$733$	−27.0144	−	27.0144i	−0.997799	−	0.997799i	0.00219862	−	0.999998i	$-0.499300\pi$
$733$	−27.0144	−	27.0144i	−0.997799	−	0.997799i	−0.999998	+	0.00219862i	$0.999300\pi$
$734$	−1.44096	−	3.33582i	−0.0531869	−	0.123128i
$735$	0.980192			0.0361549
$736$	−0.825742	−	1.63374i	−0.0304372	−	0.0602204i
$737$	5.95445			0.219335
$738$	−3.67758	−	8.51358i	−0.135373	−	0.313389i
$739$	15.6159	+	15.6159i	0.574440	+	0.574440i	0.933366	−	0.358926i	$-0.116857\pi$
$739$	15.6159	+	15.6159i	0.574440	+	0.574440i	−0.358926	+	0.933366i	$0.616857\pi$
$740$	−8.22430	−	7.74331i	−0.302331	−	0.284650i
$741$	−15.7242	+	15.7242i	−0.577641	+	0.577641i
$742$	−1.05293	+	2.65434i	−0.0386541	+	0.0974437i
$743$		−	43.0094i		−	1.57786i	−0.614483	−	0.788930i	$-0.710635\pi$
$743$		−	43.0094i		−	1.57786i	0.614483	−	0.788930i	$-0.289365\pi$
$744$	7.90066	+	16.8752i	0.289652	+	0.618676i
$745$		−	15.3236i		−	0.561414i
$746$	35.8364	+	14.2156i	1.31206	+	0.520471i
$747$	−24.1325	+	24.1325i	−0.882961	+	0.882961i
$748$	−0.00357818	−	0.118787i	−0.000130831	−	0.00434328i
$749$	10.9587	+	10.9587i	0.400421	+	0.400421i
$750$	1.27255	−	0.549698i	0.0464670	−	0.0200721i
$751$	−34.4189			−1.25596			−0.627982	−	0.778228i	$-0.716119\pi$
$751$	−34.4189			−1.25596			−0.627982	+	0.778228i	$0.716119\pi$
$752$	0.163850	+	2.71726i	0.00597501	+	0.0990882i
$753$	15.2059			0.554135
$754$	59.7281	−	25.8005i	2.17517	−	0.939598i
$755$	−2.20792	−	2.20792i	−0.0803544	−	0.0803544i
$756$	9.87433	−	0.297441i	0.359126	−	0.0108178i
$757$	22.8179	−	22.8179i	0.829330	−	0.829330i	−0.158094	−	0.987424i	$-0.550535\pi$
$757$	22.8179	−	22.8179i	0.829330	−	0.829330i	0.987424	+	0.158094i	$0.0505348\pi$
$758$	26.7775	+	10.6221i	0.972601	+	0.385813i
$759$		−	0.138869i		−	0.00504063i
$760$	−10.9384	−	3.96222i	−0.396777	−	0.143725i
$761$			3.90788i			0.141661i	0.997488	+	0.0708303i	$0.0225649\pi$
$761$			3.90788i			0.141661i	−0.997488	+	0.0708303i	$0.977435\pi$
$762$	0.552543	−	1.39291i	0.0200165	−	0.0504600i
$763$	10.2426	−	10.2426i	0.370807	−	0.370807i
$764$	24.0123	−	25.5039i	0.868735	−	0.922698i
$765$	0.195704	+	0.195704i	0.00707570	+	0.00707570i
$766$	11.6872	+	27.0558i	0.422275	+	0.977567i
$767$	−24.2261			−0.874755
$768$	−12.3418	−	9.67669i	−0.445347	−	0.349177i
$769$	34.4887			1.24370			0.621848	−	0.783138i	$-0.286382\pi$
$769$	34.4887			1.24370			0.621848	+	0.783138i	$0.286382\pi$
$770$	0.245527	+	0.568394i	0.00884817	+	0.0204835i
$771$	13.5311	+	13.5311i	0.487312	+	0.487312i
$772$	−9.46270	+	10.0505i	−0.340570	+	0.361725i
$773$	5.32068	−	5.32068i	0.191372	−	0.191372i	−0.604917	−	0.796289i	$-0.706794\pi$
$773$	5.32068	−	5.32068i	0.191372	−	0.191372i	0.796289	+	0.604917i	$0.206794\pi$
$774$	−2.37989	+	5.99951i	−0.0855435	+	0.215648i
$775$		−	6.72094i		−	0.241423i
$776$	22.5016	+	8.15077i	0.807760	+	0.292595i
$777$		−	5.53608i		−	0.198606i
$778$	−34.8591	−	13.8280i	−1.24976	−	0.495757i
$779$	−9.35295	+	9.35295i	−0.335104	+	0.335104i
$780$	10.8077	−	0.325557i	0.386979	−	0.0116568i
$781$	0.0201486	+	0.0201486i	0.000720972	+	0.000720972i
$782$	0.0570195	−	0.0246305i	0.00203901	−	0.000880783i
$783$	41.2001			1.47237
$784$	0.240762	+	3.99275i	0.00859866	+	0.142598i
$785$	−20.9992			−0.749493
$786$	−16.3473	+	7.06148i	−0.583089	+	0.251874i
$787$	−23.2661	−	23.2661i	−0.829346	−	0.829346i	0.158080	−	0.987426i	$-0.449469\pi$
$787$	−23.2661	−	23.2661i	−0.829346	−	0.829346i	−0.987426	+	0.158080i	$0.949469\pi$
$788$	1.26398	+	41.9613i	0.0450275	+	1.49481i
$789$	−9.54139	+	9.54139i	−0.339683	+	0.339683i
$790$	−12.7945	−	5.07535i	−0.455209	−	0.180573i
$791$			9.34555i			0.332289i
$792$	1.07071	+	2.28697i	0.0380461	+	0.0812638i
$793$			24.7102i			0.877484i
$794$	2.02974	−	5.11681i	0.0720329	−	0.181589i
$795$	−1.39949	+	1.39949i	−0.0496348	+	0.0496348i
$796$	21.8523	+	20.5743i	0.774533	+	0.729236i
$797$	18.2953	+	18.2953i	0.648052	+	0.648052i	0.952522	−	0.304470i	$-0.0984793\pi$
$797$	18.2953	+	18.2953i	0.648052	+	0.648052i	−0.304470	+	0.952522i	$0.598479\pi$
$798$	−2.26102	−	5.23426i	−0.0800393	−	0.185291i
$799$	−0.0923654			−0.00326765
$800$	2.55173	+	5.04863i	0.0902174	+	0.178496i
$801$	−3.94985			−0.139561
$802$	6.91772	+	16.0145i	0.244273	+	0.565492i
$803$	−1.05868	−	1.05868i	−0.0373602	−	0.0373602i
$804$	19.4122	+	18.2769i	0.684614	+	0.644575i
$805$	−0.228820	+	0.228820i	−0.00806485	+	0.00806485i
$806$	19.3306	−	48.7307i	0.680890	−	1.71647i
$807$			17.9963i			0.633500i
$808$	17.2281	−	8.06584i	0.606081	−	0.283755i
$809$		−	53.5224i		−	1.88175i	−0.338756	−	0.940874i	$-0.610006\pi$
$809$		−	53.5224i		−	1.88175i	0.338756	−	0.940874i	$-0.389994\pi$
$810$	−1.67753	−	0.665444i	−0.0589423	−	0.0233813i
$811$	−20.9531	+	20.9531i	−0.735764	+	0.735764i	−0.971755	−	0.235991i	$-0.924166\pi$
$811$	−20.9531	+	20.9531i	−0.735764	+	0.735764i	0.235991	+	0.971755i	$0.424166\pi$
$812$	0.502284	+	16.6747i	0.0176267	+	0.585166i
$813$	21.7255	+	21.7255i	0.761947	+	0.761947i
$814$	3.21027	−	1.38673i	0.112520	−	0.0486047i
$815$	8.90625			0.311972
$816$	0.352945	−	0.398242i	0.0123556	−	0.0139413i
$817$	9.20554			0.322061
$818$	−5.97273	+	2.58001i	−0.208832	+	0.0902081i
$819$	−7.95318	−	7.95318i	−0.277907	−	0.277907i
$820$	6.42860	−	0.193646i	0.224496	−	0.00676242i
$821$	−19.4435	+	19.4435i	−0.678581	+	0.678581i	−0.959679	−	0.281098i	$-0.909301\pi$
$821$	−19.4435	+	19.4435i	−0.678581	+	0.678581i	0.281098	+	0.959679i	$0.409301\pi$
$822$	−17.3789	−	6.89388i	−0.606158	−	0.240452i
$823$		−	29.7445i		−	1.03683i	−0.855129	−	0.518415i	$-0.826522\pi$
$823$		−	29.7445i		−	1.03683i	0.855129	−	0.518415i	$-0.173478\pi$
$824$	2.90399	−	8.01696i	0.101165	−	0.279284i
$825$			0.429138i			0.0149407i
$826$	2.29043	−	5.77397i	0.0796942	−	0.200902i
$827$	−19.1821	+	19.1821i	−0.667026	+	0.667026i	−0.957026	−	0.290001i	$-0.906344\pi$
$827$	−19.1821	+	19.1821i	−0.667026	+	0.667026i	0.290001	+	0.957026i	$0.406344\pi$
$828$	−0.904709	+	0.960906i	−0.0314408	+	0.0333938i
$829$	14.9094	+	14.9094i	0.517827	+	0.517827i	0.916913	−	0.399087i	$-0.130673\pi$
$829$	14.9094	+	14.9094i	0.517827	+	0.517827i	−0.399087	+	0.916913i	$0.630673\pi$
$830$	−9.38566	−	21.7278i	−0.325781	−	0.754183i
$831$	25.6667			0.890369
$832$	3.98082	+	43.9447i	0.138010	+	1.52351i
$833$	−0.135722			−0.00470249
$834$	−3.66405	−	8.48228i	−0.126876	−	0.293717i
$835$	−5.66842	−	5.66842i	−0.196164	−	0.196164i
$836$	2.46889	−	2.62224i	0.0853882	−	0.0906922i
$837$	23.4742	−	23.4742i	0.811386	−	0.811386i
$838$	14.3141	−	36.0847i	0.494474	−	1.24653i
$839$			21.7565i			0.751119i	0.926798	+	0.375560i	$0.122549\pi$
$839$			21.7565i			0.751119i	−0.926798	+	0.375560i	$0.877451\pi$
$840$	−0.944211	+	2.60666i	−0.0325784	+	0.0899383i
$841$			40.5741i			1.39911i
$842$	40.9685	+	16.2515i	1.41187	+	0.560062i
$843$	−8.96701	+	8.96701i	−0.308840	+	0.308840i
$844$	−51.9816	+	1.56582i	−1.78928	+	0.0538978i
$845$	−12.3189	−	12.3189i	−0.423784	−	0.423784i
$846$	1.80172	−	0.778282i	0.0619445	−	0.0267579i
$847$	10.8083			0.371378
$848$	−6.04449	−	5.35698i	−0.207569	−	0.183960i
$849$	24.8767			0.853767
$850$	−0.176203	+	0.0761138i	−0.00604372	+	0.00261068i
$851$	1.29237	+	1.29237i	0.0443018	+	0.0443018i
$852$	0.00384158	+	0.127531i	0.000131610	+	0.00436916i
$853$	−24.4556	+	24.4556i	−0.837343	+	0.837343i	−0.988508	−	0.151166i	$-0.951697\pi$
$853$	−24.4556	+	24.4556i	−0.837343	+	0.837343i	0.151166	+	0.988508i	$0.451697\pi$
$854$	−5.88934	−	2.33619i	−0.201529	−	0.0799428i
$855$			8.38775i			0.286855i
$856$	−39.6992	+	18.5864i	−1.35689	+	0.635269i
$857$			29.3468i			1.00247i	0.865312	+	0.501234i	$0.167120\pi$
$857$			29.3468i			1.00247i	−0.865312	+	0.501234i	$0.832880\pi$
$858$	−1.23427	+	3.11149i	−0.0421374	+	0.106225i
$859$	−20.7157	+	20.7157i	−0.706812	+	0.706812i	−0.965863	−	0.259052i	$-0.916590\pi$
$859$	−20.7157	+	20.7157i	−0.706812	+	0.706812i	0.259052	+	0.965863i	$0.416590\pi$
$860$	−3.25894	−	3.06834i	−0.111129	−	0.104630i
$861$	2.22884	+	2.22884i	0.0759587	+	0.0759587i
$862$	0.729970	+	1.68988i	0.0248629	+	0.0575575i
$863$	6.61496			0.225176			0.112588	−	0.993642i	$-0.464086\pi$
$863$	6.61496			0.225176			0.112588	+	0.993642i	$0.464086\pi$
$864$	−8.72088	+	26.5457i	−0.296690	+	0.903103i
$865$	24.0545			0.817876
$866$	6.06934	+	14.0505i	0.206244	+	0.477456i
$867$	−11.7699	−	11.7699i	−0.399728	−	0.399728i
$868$	9.78672	+	9.21436i	0.332183	+	0.312756i
$869$	3.01310	−	3.01310i	0.102212	−	0.102212i
$870$	−4.26342	+	10.7477i	−0.144544	+	0.364382i
$871$		−	75.0148i		−	2.54178i
$872$	17.3719	+	37.1051i	0.588286	+	1.25654i
$873$		−	17.2546i		−	0.583980i
$874$	1.74973	+	0.694085i	0.0591855	+	0.0234778i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−0.201852	−	6.70100i	−0.00681994	−	0.226406i
$877$	−18.3321	−	18.3321i	−0.619031	−	0.619031i	0.326252	−	0.945283i	$-0.394214\pi$
$877$	−18.3321	−	18.3321i	−0.619031	−	0.619031i	−0.945283	+	0.326252i	$0.894214\pi$
$878$	−11.2048	+	4.84009i	−0.378144	+	0.163345i
$879$	−21.3955			−0.721652
$880$	−1.74806	+	0.105408i	−0.0589273	+	0.00355331i
$881$	32.4870			1.09452			0.547258	−	0.836964i	$-0.315672\pi$
$881$	32.4870			1.09452			0.547258	+	0.836964i	$0.315672\pi$
$882$	2.64746	−	1.14361i	0.0891445	−	0.0385074i
$883$	−20.6914	−	20.6914i	−0.696321	−	0.696321i	0.267294	−	0.963615i	$-0.413871\pi$
$883$	−20.6914	−	20.6914i	−0.696321	−	0.696321i	−0.963615	+	0.267294i	$0.913871\pi$
$884$	−1.49649	+	0.0450782i	−0.0503325	+	0.00151615i
$885$	3.04431	−	3.04431i	0.102333	−	0.102333i
$886$	24.3598	+	9.66309i	0.818384	+	0.324638i
$887$			53.7245i			1.80389i	0.431848	+	0.901947i	$0.357862\pi$
$887$			53.7245i			1.80389i	−0.431848	+	0.901947i	$0.642138\pi$
$888$	14.7223	+	5.33287i	0.494048	+	0.178959i
$889$		−	1.08102i		−	0.0362561i
$890$	1.01004	−	2.54623i	0.0338567	−	0.0853498i
$891$	0.395056	−	0.395056i	0.0132349	−	0.0132349i
$892$	33.6327	−	35.7219i	1.12611	−	1.19606i
$893$	−1.97936	−	1.97936i	−0.0662367	−	0.0662367i
$894$	8.42336	+	19.5001i	0.281719	+	0.652180i
$895$	1.99543			0.0667000
$896$	−10.8500	−	3.20592i	−0.362472	−	0.107102i
$897$	−1.74949			−0.0584137
$898$	−0.466381	−	1.07967i	−0.0155633	−	0.0360291i
$899$	39.6405	+	39.6405i	1.32208	+	1.32208i
$900$	2.79576	−	2.96942i	0.0931920	−	0.0989808i
$901$	0.193780	−	0.193780i	0.00645576	−	0.00645576i
$902$	−0.734163	+	1.85076i	−0.0244450	+	0.0616236i
$903$		−	2.19371i		−	0.0730022i
$904$	−24.8529	−	9.00250i	−0.826597	−	0.299419i
$905$		−	12.2657i		−	0.407727i
$906$	4.02337	+	1.59600i	0.133668	+	0.0530235i
$907$	−3.48928	+	3.48928i	−0.115860	+	0.115860i	−0.762660	−	0.646800i	$-0.776107\pi$
$907$	−3.48928	+	3.48928i	−0.115860	+	0.115860i	0.646800	+	0.762660i	$0.276107\pi$
$908$	4.04123	−	0.121732i	0.134113	−	0.00403983i
$909$	−9.69790	−	9.69790i	−0.321659	−	0.321659i
$910$	7.16069	−	3.09317i	0.237375	−	0.102538i
$911$	−22.2692			−0.737812			−0.368906	−	0.929467i	$-0.620268\pi$
$911$	−22.2692			−0.737812			−0.368906	+	0.929467i	$0.620268\pi$
$912$	16.0977	−	0.970689i	0.533047	−	0.0321427i
$913$	7.32719			0.242495
$914$	12.8843	−	5.56558i	0.426175	−	0.184093i
$915$	−3.10514	−	3.10514i	−0.102653	−	0.102653i
$916$	0.562775	+	18.6828i	0.0185946	+	0.617297i
$917$	−9.08357	+	9.08357i	−0.299966	+	0.299966i
$918$	−0.881265	−	0.349581i	−0.0290861	−	0.0115379i
$919$		−	26.0336i		−	0.858771i	−0.903121	−	0.429385i	$-0.858730\pi$
$919$		−	26.0336i		−	0.858771i	0.903121	−	0.429385i	$-0.141270\pi$
$920$	−0.388089	−	0.828930i	−0.0127949	−	0.0273290i
$921$		−	24.3951i		−	0.803847i
$922$	12.1492	−	30.6271i	0.400112	−	1.00865i
$923$	0.253834	−	0.253834i	0.00835504	−	0.00835504i
$924$	−0.624890	−	0.588344i	−0.0205574	−	0.0193551i
$925$	−3.99371	−	3.99371i	−0.131312	−	0.131312i
$926$	0.749272	+	1.73456i	0.0246226	+	0.0570013i
$927$	−6.14755			−0.201912
$928$	−44.8274	−	14.7268i	−1.47153	−	0.483432i
$929$	42.4661			1.39327			0.696635	−	0.717426i	$-0.254680\pi$
$929$	42.4661			1.39327			0.696635	+	0.717426i	$0.254680\pi$
$930$	3.69449	+	8.55274i	0.121147	+	0.280455i
$931$	−2.90848	−	2.90848i	−0.0953214	−	0.0953214i
$932$	28.6478	+	26.9724i	0.938390	+	0.883510i
$933$	14.9158	−	14.9158i	0.488322	−	0.488322i
$934$	7.90815	−	19.9358i	0.258762	−	0.652318i
$935$		−	0.0594205i		−	0.00194326i
$936$	28.8114	−	13.4889i	0.941731	−	0.440900i
$937$			9.48009i			0.309701i	0.987938	+	0.154851i	$0.0494896\pi$
$937$			9.48009i			0.309701i	−0.987938	+	0.154851i	$0.950510\pi$
$938$	17.8788	+	7.09217i	0.583762	+	0.231568i
$939$	2.52808	−	2.52808i	0.0825009	−	0.0825009i
$940$	0.0409812	+	1.36048i	0.00133666	+	0.0443740i
$941$	−13.7087	−	13.7087i	−0.446890	−	0.446890i	0.447429	−	0.894319i	$-0.352340\pi$
$941$	−13.7087	−	13.7087i	−0.446890	−	0.446890i	−0.894319	+	0.447429i	$0.852340\pi$
$942$	26.7225	−	11.5432i	0.870666	−	0.376098i
$943$	−1.04062			−0.0338873
$944$	13.1486	+	11.6530i	0.427950	+	0.379274i
$945$	4.93941			0.160679
$946$	1.27209	−	0.549500i	0.0413593	−	0.0178658i
$947$	6.07651	+	6.07651i	0.197460	+	0.197460i	0.798910	−	0.601450i	$-0.205410\pi$
$947$	6.07651	+	6.07651i	0.197460	+	0.197460i	−0.601450	+	0.798910i	$0.705410\pi$
$948$	19.0716	−	0.574486i	0.619416	−	0.0186584i
$949$	−13.3374	+	13.3374i	−0.432951	+	0.432951i
$950$	−5.40707	−	2.14488i	−0.175428	−	0.0695892i
$951$			5.45896i			0.177019i
$952$	0.130740	−	0.360930i	0.00423731	−	0.0116978i
$953$		−	1.75041i		−	0.0567014i	−0.999598	−	0.0283507i	$-0.990974\pi$
$953$		−	1.75041i		−	0.0567014i	0.999598	−	0.0283507i	$-0.00902551\pi$
$954$	−2.14715	+	5.41279i	−0.0695166	+	0.175245i
$955$	12.3847	−	12.3847i	0.400758	−	0.400758i
$956$	16.4585	−	17.4809i	0.532307	−	0.565372i
$957$	−2.53108	−	2.53108i	−0.0818181	−	0.0818181i
$958$	1.85186	+	4.28705i	0.0598309	+	0.138508i
$959$	−13.4874			−0.435532
$960$	−6.02243	−	5.02195i	−0.194373	−	0.162083i
$961$	14.1711			0.457132
$962$	−17.4701	−	40.4433i	−0.563259	−	1.30394i
$963$	22.3472	+	22.3472i	0.720128	+	0.720128i
$964$	9.11028	−	9.67618i	0.293422	−	0.311649i
$965$	−4.88051	+	4.88051i	−0.157109	+	0.157109i
$966$	0.165403	−	0.416967i	0.00532175	−	0.0134157i
$967$		−	59.9164i		−	1.92678i	−0.268101	−	0.963391i	$-0.586396\pi$
$967$		−	59.9164i		−	1.92678i	0.268101	−	0.963391i	$-0.413604\pi$
$968$	−10.4116	+	28.7430i	−0.334641	+	0.923834i
$969$			0.547194i			0.0175784i
$970$	11.1230	+	4.41228i	0.357138	+	0.141670i
$971$	9.20182	−	9.20182i	0.295301	−	0.295301i	−0.543869	−	0.839170i	$-0.683041\pi$
$971$	9.20182	−	9.20182i	0.295301	−	0.295301i	0.839170	+	0.543869i	$0.183041\pi$
$972$	32.1235	−	0.967645i	1.03036	−	0.0310372i
$973$	−4.71327	−	4.71327i	−0.151101	−	0.151101i
$974$	30.2620	−	13.0721i	0.969656	−	0.418858i
$975$	5.40632			0.173141
$976$	11.8859	−	13.4113i	0.380458	−	0.429285i
$977$	−46.6946			−1.49389			−0.746946	−	0.664884i	$-0.768481\pi$
$977$	−46.6946			−1.49389			−0.746946	+	0.664884i	$0.768481\pi$
$978$	−11.3336	+	4.89575i	−0.362410	+	0.156549i
$979$	0.599635	+	0.599635i	0.0191644	+	0.0191644i
$980$	0.0602179	+	1.99909i	0.00192359	+	0.0638587i
$981$	20.8870	−	20.8870i	0.666869	−	0.666869i
$982$	−21.2803	−	8.44149i	−0.679081	−	0.269379i
$983$		−	29.9292i		−	0.954595i	−0.878742	−	0.477297i	$-0.841616\pi$
$983$		−	29.9292i		−	0.954595i	0.878742	−	0.477297i	$-0.158384\pi$
$984$	−8.07427	+	3.78021i	−0.257398	+	0.120509i
$985$			20.9902i			0.668802i
$986$	0.590334	−	1.48818i	0.0188001	−	0.0473933i
$987$	−0.471688	+	0.471688i	−0.0150140	+	0.0150140i
$988$	−33.0353	−	31.1033i	−1.05099	−	0.989527i
$989$	0.512110	+	0.512110i	0.0162841	+	0.0162841i
$990$	0.500684	+	1.15908i	0.0159128	+	0.0368381i
$991$	1.68004			0.0533683			0.0266842	−	0.999644i	$-0.491505\pi$
$991$	1.68004			0.0533683			0.0266842	+	0.999644i	$0.491505\pi$
$992$	−33.9316	+	17.1501i	−1.07733	+	0.544515i
$993$	29.5034			0.936261
$994$	0.0364995	+	0.0844962i	0.00115769	+	0.00268006i
$995$	10.6114	+	10.6114i	0.336405	+	0.336405i
$996$	23.8874	+	22.4904i	0.756903	+	0.712636i
$997$	19.3826	−	19.3826i	0.613853	−	0.613853i	−0.330095	−	0.943948i	$-0.607081\pi$
$997$	19.3826	−	19.3826i	0.613853	−	0.613853i	0.943948	+	0.330095i	$0.107081\pi$
$998$	9.29435	−	23.4303i	0.294208	−	0.741672i
$999$		−	27.8976i		−	0.882640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.10	✓	44
4.3	odd	2		2240.2.bd.a.1681.8		44
16.5	even	4	inner	560.2.bd.a.421.10	yes	44
16.11	odd	4		2240.2.bd.a.561.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.10	✓	44	1.1	even	1	trivial
560.2.bd.a.421.10	yes	44	16.5	even	4	inner
2240.2.bd.a.561.8		44	16.11	odd	4
2240.2.bd.a.1681.8		44	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.560807 - 1.29827i) q^{2} +(0.693100 + 0.693100i) q^{3} +(-1.37099 + 1.45615i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.511134 - 1.28852i) q^{6} -1.00000i q^{7} +(2.65934 + 0.963293i) q^{8} -2.03922i q^{9} +O(q^{10})\)	\(q+(-0.560807 - 1.29827i) q^{2} +(0.693100 + 0.693100i) q^{3} +(-1.37099 + 1.45615i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.511134 - 1.28852i) q^{6} -1.00000i q^{7} +(2.65934 + 0.963293i) q^{8} -2.03922i q^{9} +(1.31456 + 0.521463i) q^{10} +(-0.309578 + 0.309578i) q^{11} +(-1.95949 + 0.0590251i) q^{12} +(3.90010 + 3.90010i) q^{13} +(-1.29827 + 0.560807i) q^{14} -0.980192 q^{15} +(-0.240762 - 3.99275i) q^{16} +0.135722 q^{17} +(-2.64746 + 1.14361i) q^{18} +(2.90848 + 2.90848i) q^{19} +(-0.0602179 - 1.99909i) q^{20} +(0.693100 - 0.693100i) q^{21} +(0.575529 + 0.228302i) q^{22} +0.323600i q^{23} +(1.17553 + 2.51084i) q^{24} -1.00000i q^{25} +(2.87617 - 7.25057i) q^{26} +(3.49269 - 3.49269i) q^{27} +(1.45615 + 1.37099i) q^{28} +(5.89806 + 5.89806i) q^{29} +(0.549698 + 1.27255i) q^{30} +6.72094 q^{31} +(-5.04863 + 2.55173i) q^{32} -0.429138 q^{33} +(-0.0761138 - 0.176203i) q^{34} +(0.707107 + 0.707107i) q^{35} +(2.96942 + 2.79576i) q^{36} +(3.99371 - 3.99371i) q^{37} +(2.14488 - 5.40707i) q^{38} +5.40632i q^{39} +(-2.56159 + 1.19928i) q^{40} +3.21576i q^{41} +(-1.28852 - 0.511134i) q^{42} +(1.58254 - 1.58254i) q^{43} +(-0.0263640 - 0.875223i) q^{44} +(1.44195 + 1.44195i) q^{45} +(0.420120 - 0.181477i) q^{46} -0.680548 q^{47} +(2.60050 - 2.93425i) q^{48} -1.00000 q^{49} +(-1.29827 + 0.560807i) q^{50} +(0.0940689 + 0.0940689i) q^{51} +(-11.0262 + 0.332137i) q^{52} +(1.42777 - 1.42777i) q^{53} +(-6.49316 - 2.57572i) q^{54} -0.437810i q^{55} +(0.963293 - 2.65934i) q^{56} +4.03173i q^{57} +(4.34958 - 10.9649i) q^{58} +(-3.10583 + 3.10583i) q^{59} +(1.34383 - 1.42731i) q^{60} +(3.16789 + 3.16789i) q^{61} +(-3.76915 - 8.72558i) q^{62} -2.03922 q^{63} +(6.14413 + 5.12344i) q^{64} -5.51558 q^{65} +(0.240663 + 0.557135i) q^{66} +(-9.61703 - 9.61703i) q^{67} +(-0.186074 + 0.197632i) q^{68} +(-0.224287 + 0.224287i) q^{69} +(0.521463 - 1.31456i) q^{70} -0.0650839i q^{71} +(1.96437 - 5.42298i) q^{72} +3.41976i q^{73} +(-7.42460 - 2.94520i) q^{74} +(0.693100 - 0.693100i) q^{75} +(-8.22268 + 0.247689i) q^{76} +(0.309578 + 0.309578i) q^{77} +(7.01885 - 3.03190i) q^{78} -9.73291 q^{79} +(2.99354 + 2.65305i) q^{80} -1.27611 q^{81} +(4.17491 - 1.80342i) q^{82} +(-11.8341 - 11.8341i) q^{83} +(0.0590251 + 1.95949i) q^{84} +(-0.0959699 + 0.0959699i) q^{85} +(-2.94205 - 1.16706i) q^{86} +8.17589i q^{87} +(-1.12149 + 0.525058i) q^{88} -1.93694i q^{89} +(1.06338 - 2.68069i) q^{90} +(3.90010 - 3.90010i) q^{91} +(-0.471212 - 0.443653i) q^{92} +(4.65829 + 4.65829i) q^{93} +(0.381656 + 0.883533i) q^{94} -4.11321 q^{95} +(-5.26781 - 1.73060i) q^{96} +8.46136 q^{97} +(0.560807 + 1.29827i) q^{98} +(0.631300 + 0.631300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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