LMFDB - Embedded newform 187.2.m.a.54.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,2,Mod(10,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.m (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			54.4
Character	$\chi$	$=$	187.54
Dual form			187.2.m.a.142.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.657401 - 1.58711i) q^{2} +(-0.508365 - 0.101120i) q^{3} +(-0.672515 + 0.672515i) q^{4} +(0.528726 + 0.791294i) q^{5} +(0.173711 + 0.873306i) q^{6} +(-3.14310 - 2.10015i) q^{7} +(-1.66475 - 0.689561i) q^{8} +(-2.52343 - 1.04524i) q^{9} +(0.908282 - 1.35934i) q^{10} +(1.84861 - 2.75366i) q^{11} +(0.409888 - 0.273879i) q^{12} +(1.94934 - 1.94934i) q^{13} +(-1.26689 + 6.36907i) q^{14} +(-0.188770 - 0.455731i) q^{15} +4.99761i q^{16} +(-4.11560 + 0.248593i) q^{17} +4.69209i q^{18} +(0.754020 + 1.82037i) q^{19} +(-0.887733 - 0.176581i) q^{20} +(1.38547 + 1.38547i) q^{21} +(-5.58563 - 1.12368i) q^{22} +(-1.28830 + 0.256259i) q^{23} +(0.776571 + 0.518888i) q^{24} +(1.56682 - 3.78264i) q^{25} +(-4.37531 - 1.81231i) q^{26} +(2.47004 + 1.65043i) q^{27} +(3.52616 - 0.701397i) q^{28} +(4.63349 + 6.93451i) q^{29} +(-0.599196 + 0.599196i) q^{30} +(1.81159 - 9.10750i) q^{31} +(4.60224 - 1.90631i) q^{32} +(-1.21822 + 1.21293i) q^{33} +(3.10014 + 6.36847i) q^{34} -3.59752i q^{35} +(2.39998 - 0.994105i) q^{36} +(11.1935 + 2.22653i) q^{37} +(2.39342 - 2.39342i) q^{38} +(-1.18810 + 0.793861i) q^{39} +(-0.334549 - 1.68189i) q^{40} +(0.378603 + 0.252974i) q^{41} +(1.28808 - 3.10970i) q^{42} +(3.12639 - 7.54776i) q^{43} +(0.608663 + 3.09509i) q^{44} +(-0.507111 - 2.54942i) q^{45} +(1.25364 + 1.87620i) q^{46} +(-9.27116 - 9.27116i) q^{47} +(0.505359 - 2.54061i) q^{48} +(2.78964 + 6.73479i) q^{49} -7.03348 q^{50} +(2.11737 + 0.289795i) q^{51} +2.62192i q^{52} +(-6.60110 + 2.73427i) q^{53} +(0.995599 - 5.00521i) q^{54} +(3.15636 + 0.00685955i) q^{55} +(3.78428 + 5.66357i) q^{56} +(-0.199242 - 1.00166i) q^{57} +(7.95974 - 11.9126i) q^{58} +(-1.03421 + 2.49681i) q^{59} +(0.433437 + 0.179535i) q^{60} +(1.55057 - 2.32059i) q^{61} +(-15.6455 + 3.11208i) q^{62} +(5.73622 + 8.58486i) q^{63} +(1.01666 + 1.01666i) q^{64} +(2.57317 + 0.511835i) q^{65} +(2.72591 + 1.13606i) q^{66} +4.14849i q^{67} +(2.60062 - 2.93499i) q^{68} +0.680840 q^{69} +(-5.70964 + 2.36501i) q^{70} +(2.53813 + 0.504865i) q^{71} +(3.48011 + 3.48011i) q^{72} +(-8.31205 + 5.55393i) q^{73} +(-3.82489 - 19.2290i) q^{74} +(-1.17902 + 1.76453i) q^{75} +(-1.73131 - 0.717134i) q^{76} +(-11.5935 + 4.77267i) q^{77} +(2.04100 + 1.36375i) q^{78} +(11.3634 - 2.26032i) q^{79} +(-3.95457 + 2.64236i) q^{80} +(4.70525 + 4.70525i) q^{81} +(0.152603 - 0.767188i) q^{82} +(12.5490 - 5.19798i) q^{83} -1.86350 q^{84} +(-2.37274 - 3.12521i) q^{85} -14.0344 q^{86} +(-1.65429 - 3.99381i) q^{87} +(-4.97628 + 3.30942i) q^{88} +(-2.17454 + 2.17454i) q^{89} +(-3.71282 + 2.48083i) q^{90} +(-10.2209 + 2.03306i) q^{91} +(0.694064 - 1.03874i) q^{92} +(-1.84190 + 4.44675i) q^{93} +(-8.61944 + 20.8092i) q^{94} +(-1.04177 + 1.55913i) q^{95} +(-2.53238 + 0.503722i) q^{96} +(10.8775 - 7.26814i) q^{97} +(8.85491 - 8.85491i) q^{98} +(-7.54306 + 5.01643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$-1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−0.657401	−	1.58711i	−0.464852	−	1.12225i	−0.966382	−	0.257112i	$-0.917229\pi$
$2$	−0.657401	−	1.58711i	−0.464852	−	1.12225i	0.501529	−	0.865141i	$-0.332771\pi$
$3$	−0.508365	−	0.101120i	−0.293505	−	0.0583818i	0.0461416	−	0.998935i	$-0.485307\pi$
$3$	−0.508365	−	0.101120i	−0.293505	−	0.0583818i	−0.339647	+	0.940553i	$0.610307\pi$
$4$	−0.672515	+	0.672515i	−0.336257	+	0.336257i
$5$	0.528726	+	0.791294i	0.236453	+	0.353877i	0.930652	−	0.365906i	$-0.119241\pi$
$5$	0.528726	+	0.791294i	0.236453	+	0.353877i	−0.694198	+	0.719784i	$0.744241\pi$
$6$	0.173711	+	0.873306i	0.0709174	+	0.356526i
$7$	−3.14310	−	2.10015i	−1.18798	−	0.793782i	−0.205228	−	0.978714i	$-0.565793\pi$
$7$	−3.14310	−	2.10015i	−1.18798	−	0.793782i	−0.982751	+	0.184932i	$0.940793\pi$
$8$	−1.66475	−	0.689561i	−0.588577	−	0.243797i
$9$	−2.52343	−	1.04524i	−0.841143	−	0.348413i
$10$	0.908282	−	1.35934i	0.287224	−	0.429861i
$11$	1.84861	−	2.75366i	0.557376	−	0.830260i
$11$	1.84861	−	2.75366i	0.557376	−	0.830260i
$12$	0.409888	−	0.273879i	0.118325	−	0.0790619i
$13$	1.94934	−	1.94934i	0.540650	−	0.540650i	−0.383069	−	0.923720i	$-0.625133\pi$
$13$	1.94934	−	1.94934i	0.540650	−	0.540650i	0.923720	+	0.383069i	$0.125133\pi$
$14$	−1.26689	+	6.36907i	−0.338590	+	1.70220i
$15$	−0.188770	−	0.455731i	−0.0487402	−	0.117669i
$16$			4.99761i			1.24940i
$17$	−4.11560	+	0.248593i	−0.998181	+	0.0602926i
$17$	−4.11560	+	0.248593i	−0.998181	+	0.0602926i
$18$			4.69209i			1.10594i
$19$	0.754020	+	1.82037i	0.172984	+	0.417621i	0.986465	−	0.163971i	$-0.0524303\pi$
$19$	0.754020	+	1.82037i	0.172984	+	0.417621i	−0.813481	+	0.581591i	$0.802430\pi$
$20$	−0.887733	−	0.176581i	−0.198503	−	0.0394847i
$21$	1.38547	+	1.38547i	0.302335	+	0.302335i
$22$	−5.58563	−	1.12368i	−1.19086	−	0.239568i
$23$	−1.28830	+	0.256259i	−0.268629	+	0.0534337i	−0.327567	−	0.944828i	$-0.606229\pi$
$23$	−1.28830	+	0.256259i	−0.268629	+	0.0534337i	0.0589376	+	0.998262i	$0.481229\pi$
$24$	0.776571	+	0.518888i	0.158517	+	0.105918i
$25$	1.56682	−	3.78264i	0.313364	−	0.756529i
$26$	−4.37531	−	1.81231i	−0.858069	−	0.355424i
$27$	2.47004	+	1.65043i	0.475360	+	0.317625i
$28$	3.52616	−	0.701397i	0.666382	−	0.132552i
$29$	4.63349	+	6.93451i	0.860418	+	1.28771i	0.956322	+	0.292316i	$0.0944260\pi$
$29$	4.63349	+	6.93451i	0.860418	+	1.28771i	−0.0959035	+	0.995391i	$0.530574\pi$
$30$	−0.599196	+	0.599196i	−0.109398	+	0.109398i
$31$	1.81159	−	9.10750i	0.325372	−	1.63575i	−0.378624	−	0.925551i	$-0.623603\pi$
$31$	1.81159	−	9.10750i	0.325372	−	1.63575i	0.703996	−	0.710204i	$-0.251397\pi$
$32$	4.60224	−	1.90631i	0.813568	−	0.336991i
$33$	−1.21822	+	1.21293i	−0.212065	+	0.211145i
$34$	3.10014	+	6.36847i	0.531670	+	1.09218i
$35$		−	3.59752i		−	0.608091i
$36$	2.39998	−	0.994105i	0.399997	−	0.165684i
$37$	11.1935	+	2.22653i	1.84021	+	0.366040i	0.987660	−	0.156614i	$-0.0500579\pi$
$37$	11.1935	+	2.22653i	1.84021	+	0.366040i	0.852545	+	0.522654i	$0.175058\pi$
$38$	2.39342	−	2.39342i	0.388264	−	0.388264i
$39$	−1.18810	+	0.793861i	−0.190248	+	0.127119i
$40$	−0.334549	−	1.68189i	−0.0528969	−	0.265931i
$41$	0.378603	+	0.252974i	0.0591278	+	0.0395080i	0.584783	−	0.811190i	$-0.301180\pi$
$41$	0.378603	+	0.252974i	0.0591278	+	0.0395080i	−0.525655	+	0.850698i	$0.676180\pi$
$42$	1.28808	−	3.10970i	0.198755	−	0.479838i
$43$	3.12639	−	7.54776i	0.476769	−	1.15102i	−0.484346	−	0.874877i	$-0.660942\pi$
$43$	3.12639	−	7.54776i	0.476769	−	1.15102i	0.961115	−	0.276147i	$-0.0890576\pi$
$44$	0.608663	+	3.09509i	0.0917594	+	0.466603i
$45$	−0.507111	−	2.54942i	−0.0755956	−	0.380045i
$46$	1.25364	+	1.87620i	0.184839	+	0.276631i
$47$	−9.27116	−	9.27116i	−1.35234	−	1.35234i	−0.883041	−	0.469296i	$-0.844508\pi$
$47$	−9.27116	−	9.27116i	−1.35234	−	1.35234i	−0.469296	−	0.883041i	$-0.655492\pi$
$48$	0.505359	−	2.54061i	0.0729423	−	0.366706i
$49$	2.78964	+	6.73479i	0.398520	+	0.962113i
$50$	−7.03348			−0.994685
$51$	2.11737	+	0.289795i	0.296491	+	0.0405794i
$52$			2.62192i			0.363596i
$53$	−6.60110	+	2.73427i	−0.906731	+	0.375580i	−0.786805	−	0.617202i	$-0.788266\pi$
$53$	−6.60110	+	2.73427i	−0.906731	+	0.375580i	−0.119927	+	0.992783i	$0.538266\pi$
$54$	0.995599	−	5.00521i	0.135484	−	0.681123i
$55$	3.15636	+	0.00685955i	0.425604	+	0.000924942i
$56$	3.78428	+	5.66357i	0.505696	+	0.756827i
$57$	−0.199242	−	1.00166i	−0.0263903	−	0.132673i
$58$	7.95974	−	11.9126i	1.04517	−	1.56420i
$59$	−1.03421	+	2.49681i	−0.134643	+	0.325057i	−0.976793	−	0.214187i	$-0.931290\pi$
$59$	−1.03421	+	2.49681i	−0.134643	+	0.325057i	0.842150	+	0.539244i	$0.181290\pi$
$60$	0.433437	+	0.179535i	0.0559564	+	0.0231779i
$61$	1.55057	−	2.32059i	0.198530	−	0.297122i	−0.718825	−	0.695191i	$-0.755320\pi$
$61$	1.55057	−	2.32059i	0.198530	−	0.297122i	0.917355	+	0.398069i	$0.130320\pi$
$62$	−15.6455	+	3.11208i	−1.98698	+	0.395235i
$63$	5.73622	+	8.58486i	0.722696	+	1.08159i
$64$	1.01666	+	1.01666i	0.127082	+	0.127082i
$65$	2.57317	+	0.511835i	0.319162	+	0.0634854i
$66$	2.72591	+	1.13606i	0.335537	+	0.139839i
$67$			4.14849i			0.506819i	0.967359	+	0.253409i	$0.0815519\pi$
$67$			4.14849i			0.506819i	−0.967359	+	0.253409i	$0.918448\pi$
$68$	2.60062	−	2.93499i	0.315372	−	0.355920i
$69$	0.680840			0.0819636
$70$	−5.70964	+	2.36501i	−0.682432	+	0.282673i
$71$	2.53813	+	0.504865i	0.301220	+	0.0599165i	0.343387	−	0.939194i	$-0.388426\pi$
$71$	2.53813	+	0.504865i	0.301220	+	0.0599165i	−0.0421662	+	0.999111i	$0.513426\pi$
$72$	3.48011	+	3.48011i	0.410135	+	0.410135i
$73$	−8.31205	+	5.55393i	−0.972851	+	0.650039i	−0.937004	−	0.349319i	$-0.886413\pi$
$73$	−8.31205	+	5.55393i	−0.972851	+	0.650039i	−0.0358474	+	0.999357i	$0.511413\pi$
$74$	−3.82489	−	19.2290i	−0.444635	−	2.23533i
$75$	−1.17902	+	1.76453i	−0.136141	+	0.203750i
$76$	−1.73131	−	0.717134i	−0.198595	−	0.0822609i
$77$	−11.5935	+	4.77267i	−1.32120	+	0.543897i
$78$	2.04100	+	1.36375i	0.231097	+	0.154414i
$79$	11.3634	−	2.26032i	1.27848	−	0.254306i	0.491280	−	0.871002i	$-0.336529\pi$
$79$	11.3634	−	2.26032i	1.27848	−	0.254306i	0.787201	+	0.616696i	$0.211529\pi$
$80$	−3.95457	+	2.64236i	−0.442135	+	0.295425i
$81$	4.70525	+	4.70525i	0.522806	+	0.522806i
$82$	0.152603	−	0.767188i	0.0168522	−	0.0847218i
$83$	12.5490	−	5.19798i	1.37744	−	0.570553i	0.433642	−	0.901085i	$-0.357228\pi$
$83$	12.5490	−	5.19798i	1.37744	−	0.570553i	0.943795	+	0.330532i	$0.107228\pi$
$84$	−1.86350			−0.203325
$85$	−2.37274	−	3.12521i	−0.257359	−	0.338977i
$86$	−14.0344			−1.51337
$87$	−1.65429	−	3.99381i	−0.177358	−	0.428181i
$88$	−4.97628	+	3.30942i	−0.530473	+	0.352786i
$89$	−2.17454	+	2.17454i	−0.230501	+	0.230501i	−0.812902	−	0.582401i	$-0.802114\pi$
$89$	−2.17454	+	2.17454i	−0.230501	+	0.230501i	0.582401	+	0.812902i	$0.302114\pi$
$90$	−3.71282	+	2.48083i	−0.391366	+	0.261502i
$91$	−10.2209	+	2.03306i	−1.07144	+	0.213123i
$92$	0.694064	−	1.03874i	0.0723611	−	0.108296i
$93$	−1.84190	+	4.44675i	−0.190996	+	0.461106i
$94$	−8.61944	+	20.8092i	−0.889027	+	2.14630i
$95$	−1.04177	+	1.55913i	−0.106884	+	0.159963i
$96$	−2.53238	+	0.503722i	−0.258460	+	0.0514109i
$97$	10.8775	−	7.26814i	1.10445	−	0.737968i	0.136881	−	0.990587i	$-0.456292\pi$
$97$	10.8775	−	7.26814i	1.10445	−	0.737968i	0.967566	+	0.252620i	$0.0812922\pi$
$98$	8.85491	−	8.85491i	0.894481	−	0.894481i
$99$	−7.54306	+	5.01643i	−0.758106	+	0.504171i
$100$	1.49017	+	3.59760i	0.149017	+	0.359760i
$101$	−8.06389			−0.802387			−0.401193	−	0.915993i	$-0.631404\pi$
$101$	−8.06389			−0.802387			−0.401193	+	0.915993i	$0.631404\pi$
$102$	−0.932025	−	3.55100i	−0.0922842	−	0.351601i
$103$	−12.9597			−1.27696			−0.638479	−	0.769639i	$-0.720436\pi$
$103$	−12.9597			−1.27696			−0.638479	+	0.769639i	$0.720436\pi$
$104$	−4.58935	+	1.90097i	−0.450023	+	0.186406i
$105$	−0.363781	+	1.82885i	−0.0355014	+	0.178478i
$106$	8.67914	+	8.67914i	0.842993	+	0.842993i
$107$	5.22279	−	3.48976i	0.504906	−	0.337367i	−0.276890	−	0.960902i	$-0.589304\pi$
$107$	5.22279	−	3.48976i	0.504906	−	0.337367i	0.781796	+	0.623534i	$0.214304\pi$
$108$	−2.77108	+	0.551202i	−0.266647	+	0.0530394i
$109$	−4.99472	−	3.33737i	−0.478407	−	0.319662i	0.292879	−	0.956149i	$-0.405387\pi$
$109$	−4.99472	−	3.33737i	−0.478407	−	0.319662i	−0.771287	+	0.636488i	$0.780387\pi$
$110$	−2.06411	−	5.01399i	−0.196805	−	0.478065i
$111$	−5.46526	−	2.26378i	−0.518739	−	0.214869i
$112$	10.4957	−	15.7080i	0.991753	−	1.48426i
$113$	2.55166	+	12.8281i	0.240040	+	1.20676i	0.893241	+	0.449579i	$0.148426\pi$
$113$	2.55166	+	12.8281i	0.240040	+	1.20676i	−0.653200	+	0.757185i	$0.726574\pi$
$114$	−1.45875	+	0.974709i	−0.136625	+	0.0912898i
$115$	−0.883934	−	0.883934i	−0.0824272	−	0.0824272i
$116$	−7.77966	−	1.54747i	−0.722323	−	0.143679i
$117$	−6.95655	+	2.88150i	−0.643134	+	0.266395i
$118$	4.64259			0.427385
$119$	13.4578	+	7.86204i	1.23368	+	0.720712i
$120$			0.888845i			0.0811401i
$121$	−4.16531	−	10.1809i	−0.378664	−	0.925534i
$122$	−4.70238	−	0.935361i	−0.425733	−	0.0846836i
$123$	−0.166888	−	0.166888i	−0.0150478	−	0.0150478i
$124$	4.90660	+	7.34325i	0.440626	+	0.659443i
$125$	8.48857	−	1.68848i	0.759241	−	0.151022i
$126$	9.85409	−	14.7477i	0.877872	−	1.31383i
$127$	−10.9754	−	4.54617i	−0.973911	−	0.403407i	−0.161744	−	0.986833i	$-0.551712\pi$
$127$	−10.9754	−	4.54617i	−0.973911	−	0.403407i	−0.812167	+	0.583426i	$0.801712\pi$
$128$	4.75781	−	11.4864i	0.420535	−	1.01526i
$129$	−2.35258	+	3.52088i	−0.207133	+	0.309996i
$130$	−0.879267	−	4.42037i	−0.0771168	−	0.387692i
$131$	−1.23232	−	1.84430i	−0.107668	−	0.161137i	0.773723	−	0.633524i	$-0.218392\pi$
$131$	−1.23232	−	1.84430i	−0.107668	−	0.161137i	−0.881391	+	0.472387i	$0.843392\pi$
$132$	0.00355323	−	1.63499i	0.000309269	−	0.142307i
$133$	1.45308	−	7.30514i	0.125998	−	0.633436i
$134$	6.58409	−	2.72722i	0.568779	−	0.235596i
$135$			2.82715i			0.243323i
$136$	7.02286	+	2.42412i	0.602205	+	0.207866i
$137$	−7.19002			−0.614285			−0.307142	−	0.951664i	$-0.599373\pi$
$137$	−7.19002			−0.614285			−0.307142	+	0.951664i	$0.599373\pi$
$138$	−0.447585	−	1.08057i	−0.0381010	−	0.0919839i
$139$	−1.94970	+	9.80179i	−0.165371	+	0.831377i	0.805651	+	0.592390i	$0.201815\pi$
$139$	−1.94970	+	9.80179i	−0.165371	+	0.831377i	−0.971023	+	0.238987i	$0.923185\pi$
$140$	2.41938	+	2.41938i	0.204475	+	0.204475i
$141$	3.77563	+	5.65064i	0.317966	+	0.475869i
$142$	−0.867293	−	4.36018i	−0.0727816	−	0.365898i
$143$	−1.76426	−	8.97140i	−0.147535	−	0.750226i
$144$	5.22369	−	12.6111i	0.435308	−	1.05093i
$145$	−3.03739	+	7.33291i	−0.252242	+	0.608965i
$146$	14.2790	+	9.54094i	1.18174	+	0.789613i
$147$	−0.737134	−	3.70582i	−0.0607978	−	0.305651i
$148$	−9.02519	+	6.03044i	−0.741866	+	0.495699i
$149$	−1.41197	+	1.41197i	−0.115673	+	0.115673i	−0.762574	−	0.646901i	$-0.776065\pi$
$149$	−1.41197	+	1.41197i	−0.115673	+	0.115673i	0.646901	+	0.762574i	$0.276065\pi$
$150$	3.57558	+	0.711227i	0.291945	+	0.0580714i
$151$	7.27022	−	3.01143i	0.591642	−	0.245066i	−0.0667146	−	0.997772i	$-0.521252\pi$
$151$	7.27022	−	3.01143i	0.591642	−	0.245066i	0.658357	+	0.752706i	$0.271252\pi$
$152$		−	3.55039i		−	0.287975i
$153$	10.6453	+	3.67448i	0.860619	+	0.297064i
$154$	15.1963	+	15.2625i	1.22455	+	1.22989i
$155$	8.16454	−	3.38186i	0.655792	−	0.271638i
$156$	0.265129	−	1.33290i	0.0212273	−	0.106717i
$157$	−3.27575	+	3.27575i	−0.261434	+	0.261434i	−0.825636	−	0.564203i	$-0.809184\pi$
$157$	−3.27575	+	3.27575i	−0.261434	+	0.261434i	0.564203	+	0.825636i	$0.309184\pi$
$158$	−11.0577	−	16.5490i	−0.879701	−	1.31656i
$159$	3.63226	−	0.722502i	0.288057	−	0.0572981i
$160$	3.94177	+	2.63381i	0.311624	+	0.208221i
$161$	4.58744	+	1.90018i	0.361541	+	0.149755i
$162$	4.37450	−	10.5610i	0.343693	−	0.829748i
$163$	3.92529	+	2.62279i	0.307452	+	0.205433i	0.699718	−	0.714419i	$-0.253309\pi$
$163$	3.92529	+	2.62279i	0.307452	+	0.205433i	−0.392266	+	0.919852i	$0.628309\pi$
$164$	−0.424745	+	0.0844871i	−0.0331670	+	0.00659733i
$165$	−1.60389	−	0.322659i	−0.124863	−	0.0251190i
$166$	−16.4995	−	16.4995i	−1.28061	−	1.28061i
$167$	−1.95974	−	0.389817i	−0.151649	−	0.0301649i	0.118682	−	0.992932i	$-0.462133\pi$
$167$	−1.95974	−	0.389817i	−0.151649	−	0.0301649i	−0.270331	+	0.962767i	$0.587133\pi$
$168$	−1.35110	−	3.26183i	−0.104239	−	0.251656i
$169$			5.40013i			0.415394i
$170$	−3.40021	+	5.82030i	−0.260784	+	0.446397i
$171$		−	5.38170i		−	0.411549i
$172$	2.97344	+	7.17853i	0.226723	+	0.547358i
$173$	0.102046	−	0.513020i	0.00775841	−	0.0390042i	−0.976712	−	0.214554i	$-0.931170\pi$
$173$	0.102046	−	0.513020i	0.00775841	−	0.0390042i	0.984471	+	0.175550i	$0.0561703\pi$
$174$	−5.25106	+	5.25106i	−0.398082	+	0.398082i
$175$	−12.8688	+	8.59865i	−0.972789	+	0.649997i
$176$	13.7617	+	9.23861i	1.03733	+	0.696386i
$177$	0.778236	−	1.16471i	0.0584958	−	0.0875451i
$178$	4.88078	+	2.02168i	0.365830	+	0.151532i
$179$	−2.16552	−	0.896988i	−0.161859	−	0.0670440i	0.300283	−	0.953850i	$-0.402919\pi$
$179$	−2.16552	−	0.896988i	−0.161859	−	0.0670440i	−0.462142	+	0.886806i	$0.652919\pi$
$180$	2.05556	+	1.37348i	0.153212	+	0.102373i
$181$	−1.34934	−	6.78361i	−0.100296	−	0.504222i	−0.997977	−	0.0635760i	$-0.979749\pi$
$181$	−1.34934	−	6.78361i	−0.100296	−	0.504222i	0.897681	−	0.440646i	$-0.145251\pi$
$182$	9.94590	+	14.8851i	0.737239	+	1.10336i
$183$	−1.02292	+	1.02292i	−0.0756161	+	0.0756161i
$184$	2.32140	+	0.461755i	0.171136	+	0.0340411i
$185$	4.15646	+	10.0346i	0.305589	+	0.737758i
$186$	8.26833			0.606263
$187$	−6.92359	+	11.7925i	−0.506303	+	0.862355i
$188$	12.4700			0.909467
$189$	−4.29743	−	10.3749i	−0.312592	−	0.754665i
$190$	3.15936	+	0.628436i	0.229204	+	0.0455915i
$191$	6.69956	−	6.69956i	0.484763	−	0.484763i	−0.421886	−	0.906649i	$-0.638632\pi$
$191$	6.69956	−	6.69956i	0.484763	−	0.484763i	0.906649	+	0.421886i	$0.138632\pi$
$192$	−0.414029	−	0.619638i	−0.0298800	−	0.0447185i
$193$	0.372707	+	1.87372i	0.0268280	+	0.134874i	0.991878	−	0.127192i	$-0.0405964\pi$
$193$	0.372707	+	1.87372i	0.0268280	+	0.134874i	−0.965050	+	0.262065i	$0.915596\pi$
$194$	−18.6862	−	12.4857i	−1.34159	−	0.896423i
$195$	−1.25635	−	0.520399i	−0.0899693	−	0.0372665i
$196$	−6.40532	−	2.65317i	−0.457523	−	0.189512i
$197$	9.69557	−	14.5105i	0.690781	−	1.03383i	−0.305872	−	0.952073i	$-0.598948\pi$
$197$	9.69557	−	14.5105i	0.690781	−	1.03383i	0.996653	−	0.0817540i	$-0.0260522\pi$
$198$	12.9204	+	8.67383i	0.918214	+	0.616422i
$199$	−11.5787	+	7.73667i	−0.820796	+	0.548438i	−0.893577	−	0.448910i	$-0.851812\pi$
$199$	−11.5787	+	7.73667i	−0.820796	+	0.548438i	0.0727814	+	0.997348i	$0.476812\pi$
$200$	−5.21673	+	5.21673i	−0.368878	+	0.368878i
$201$	0.419496	−	2.10895i	0.0295890	−	0.148754i
$202$	5.30121	+	12.7982i	0.372992	+	0.900481i
$203$		−	31.5269i		−	2.21275i
$204$	−1.61885	+	1.22907i	−0.113342	+	0.0860522i
$205$			0.433340i			0.0302658i
$206$	8.51972	+	20.5684i	0.593597	+	1.43307i
$207$	3.51879	+	0.699930i	0.244573	+	0.0486485i
$208$	9.74205	+	9.74205i	0.675490	+	0.675490i
$209$	6.40656	+	1.28882i	0.443151	+	0.0891498i
$210$	3.14173	−	0.624929i	0.216800	−	0.0431242i
$211$	−4.00595	−	2.67669i	−0.275781	−	0.184271i	0.409987	−	0.912091i	$-0.365533\pi$
$211$	−4.00595	−	2.67669i	−0.275781	−	0.184271i	−0.685767	+	0.727821i	$0.740533\pi$
$212$	2.60051	−	6.27818i	0.178604	−	0.431187i
$213$	−1.23924	−	0.513312i	−0.0849116	−	0.0351716i
$214$	−8.97208	−	5.99495i	−0.613319	−	0.409806i
$215$	7.62550	−	1.51681i	0.520055	−	0.103445i
$216$	−2.97393	−	4.45079i	−0.202350	−	0.302838i
$217$	−24.8211	+	24.8211i	−1.68497	+	1.68497i
$218$	−2.01322	+	10.1211i	−0.136352	+	0.685490i
$219$	4.78717	−	1.98291i	0.323487	−	0.133993i
$220$	−2.12731	+	2.11809i	−0.143423	+	0.142801i
$221$	−7.53813	+	8.50732i	−0.507070	+	0.572264i
$222$			10.1622i			0.682039i
$223$	−0.256015	+	0.106045i	−0.0171440	+	0.00710128i	−0.391239	−	0.920289i	$-0.627953\pi$
$223$	−0.256015	+	0.106045i	−0.0171440	+	0.00710128i	0.374095	+	0.927390i	$0.377953\pi$
$224$	−18.4688	−	3.67367i	−1.23400	−	0.245458i
$225$	−7.90753	+	7.90753i	−0.527169	+	0.527169i
$226$	18.6821	−	12.4829i	1.24271	−	0.830353i
$227$	0.954933	+	4.80077i	0.0633811	+	0.318638i	0.999449	−	0.0331800i	$-0.0105635\pi$
$227$	0.954933	+	4.80077i	0.0633811	+	0.318638i	−0.936068	+	0.351818i	$0.885563\pi$
$228$	0.807623	+	0.539637i	0.0534862	+	0.0357383i
$229$	−0.898685	+	2.16962i	−0.0593868	+	0.143372i	−0.950788	−	0.309844i	$-0.899723\pi$
$229$	−0.898685	+	2.16962i	−0.0593868	+	0.143372i	0.891401	+	0.453216i	$0.149723\pi$
$230$	−0.821797	+	1.98399i	−0.0541877	+	0.130821i
$231$	6.37632	−	1.25393i	0.419531	−	0.0825025i
$232$	−2.93183	−	14.7393i	−0.192484	−	0.967682i
$233$	4.73955	+	7.09323i	0.310498	+	0.464693i	0.953595	−	0.301091i	$-0.0973509\pi$
$233$	4.73955	+	7.09323i	0.310498	+	0.464693i	−0.643097	+	0.765785i	$0.722351\pi$
$234$	9.14649	+	9.14649i	0.597925	+	0.597925i
$235$	2.43431	−	12.2381i	0.158797	−	0.798326i
$236$	−0.983619	−	2.37467i	−0.0640281	−	0.154578i
$237$	−6.00532			−0.390087
$238$	3.63070	−	26.5275i	0.235343	−	1.71952i
$239$			6.82054i			0.441184i	0.975366	+	0.220592i	$0.0707989\pi$
$239$			6.82054i			0.441184i	−0.975366	+	0.220592i	$0.929201\pi$
$240$	2.27756	−	0.943398i	0.147016	−	0.0608961i
$241$	0.213302	−	1.07234i	0.0137400	−	0.0690757i	−0.973307	−	0.229507i	$-0.926289\pi$
$241$	0.213302	−	1.07234i	0.0137400	−	0.0690757i	0.987047	+	0.160431i	$0.0512886\pi$
$242$	−13.4198	+	13.3037i	−0.862661	+	0.855194i
$243$	−6.86748	−	10.2779i	−0.440549	−	0.659328i
$244$	0.517852	+	2.60342i	0.0331521	+	0.166667i
$245$	−3.85424	+	5.76828i	−0.246239	+	0.368522i
$246$	−0.155156	+	0.374581i	−0.00989241	+	0.0238824i
$247$	5.01836	+	2.07867i	0.319311	+	0.132263i
$248$	−9.29602	+	13.9125i	−0.590298	+	0.883443i
$249$	−6.90512	+	1.37351i	−0.437594	+	0.0870429i
$250$	−8.26019	−	12.3623i	−0.522420	−	0.781858i
$251$	13.7391	+	13.7391i	0.867203	+	0.867203i	0.992162	−	0.124959i	$-0.0398799\pi$
$251$	13.7391	+	13.7391i	0.867203	+	0.867203i	−0.124959	+	0.992162i	$0.539880\pi$
$252$	−9.63114	−	1.91575i	−0.606705	−	0.120681i
$253$	−1.67591	+	4.02127i	−0.105364	+	0.252815i
$254$			20.4078i			1.28050i
$255$	0.890194	+	1.82868i	0.0557461	+	0.114517i
$256$	−18.4823			−1.15514
$257$	23.8758	−	9.88969i	1.48933	−	0.616902i	0.518162	−	0.855283i	$-0.326617\pi$
$257$	23.8758	−	9.88969i	1.48933	−	0.616902i	0.971172	+	0.238381i	$0.0766166\pi$
$258$	7.13460	+	1.41916i	0.444181	+	0.0883530i
$259$	−30.5063	−	30.5063i	−1.89557	−	1.89557i
$260$	−2.07471	+	1.38628i	−0.128668	+	0.0859733i
$261$	−4.44407	−	22.3419i	−0.275081	−	1.38293i
$262$	−2.11697	+	3.16827i	−0.130787	+	0.195736i
$263$	−19.5939	−	8.11604i	−1.20821	−	0.500457i	−0.314567	−	0.949235i	$-0.601859\pi$
$263$	−19.5939	−	8.11604i	−1.20821	−	0.500457i	−0.893643	+	0.448779i	$0.851859\pi$
$264$	2.86442	−	1.17919i	0.176293	−	0.0725744i
$265$	−5.65378	−	3.77774i	−0.347309	−	0.232064i
$266$	−12.5493	+	2.49621i	−0.769446	+	0.153052i
$267$	1.32535	−	0.885573i	0.0811103	−	0.0541962i
$268$	−2.78992	−	2.78992i	−0.170422	−	0.170422i
$269$	4.13233	−	20.7746i	0.251953	−	1.26665i	−0.622915	−	0.782289i	$-0.714052\pi$
$269$	4.13233	−	20.7746i	0.251953	−	1.26665i	0.874868	−	0.484362i	$-0.160948\pi$
$270$	4.48699	−	1.85857i	0.273070	−	0.113109i
$271$	24.4544			1.48550			0.742750	−	0.669569i	$-0.233521\pi$
$271$	24.4544			1.48550			0.742750	+	0.669569i	$0.233521\pi$
$272$	−1.24237	−	20.5682i	−0.0753297	−	1.24713i
$273$	5.40153			0.326915
$274$	4.72672	+	11.4113i	0.285552	+	0.689383i
$275$	−7.51968	−	11.3071i	−0.453454	−	0.681845i
$276$	−0.457875	+	0.457875i	−0.0275609	+	0.0275609i
$277$	22.6766	−	15.1520i	1.36250	−	0.910396i	0.362734	−	0.931893i	$-0.381843\pi$
$277$	22.6766	−	15.1520i	1.36250	−	0.910396i	0.999769	+	0.0214970i	$0.00684324\pi$
$278$	16.8382	−	3.34933i	1.00989	−	0.200879i
$279$	−14.0909	+	21.0886i	−0.843602	+	1.26254i
$280$	−2.48071	+	5.98895i	−0.148251	+	0.357908i
$281$	−1.38527	+	3.34435i	−0.0826385	+	0.199507i	−0.959798	−	0.280693i	$-0.909436\pi$
$281$	−1.38527	+	3.34435i	−0.0826385	+	0.199507i	0.877159	+	0.480200i	$0.159436\pi$
$282$	6.48605	−	9.70706i	0.386239	−	0.578047i
$283$	0.832740	−	0.165642i	0.0495012	−	0.00984641i	−0.170278	−	0.985396i	$-0.554466\pi$
$283$	0.832740	−	0.165642i	0.0495012	−	0.00984641i	0.219779	+	0.975550i	$0.429466\pi$
$284$	−2.04646	+	1.36740i	−0.121435	+	0.0811403i
$285$	0.687261	−	0.687261i	0.0407098	−	0.0407098i
$286$	−13.0787	+	8.69787i	−0.773362	+	0.514316i
$287$	−0.658701	−	1.59025i	−0.0388819	−	0.0938693i
$288$	−13.6060			−0.801739
$289$	16.8764	−	2.04622i	0.992730	−	0.120366i
$290$	13.6349			0.800668
$291$	−6.26472	+	2.59493i	−0.367244	+	0.152118i
$292$	1.85487	−	9.32508i	0.108548	−	0.545709i
$293$	10.2818	+	10.2818i	0.600669	+	0.600669i	0.940490	−	0.339821i	$-0.110366\pi$
$293$	10.2818	+	10.2818i	0.600669	+	0.600669i	−0.339821	+	0.940490i	$0.610366\pi$
$294$	−5.39694	+	3.60612i	−0.314756	+	0.210313i
$295$	−2.52253	+	0.501761i	−0.146867	+	0.0292137i
$296$	−17.0991	−	11.4252i	−0.993863	−	0.664078i
$297$	9.11086	−	3.75067i	0.528666	−	0.217636i
$298$	3.16917	+	1.31271i	0.183585	+	0.0760435i
$299$	−2.01180	+	3.01088i	−0.116346	+	0.174123i
$300$	−0.393763	−	1.97958i	−0.0227339	−	0.114291i
$301$	−25.6780	+	17.1575i	−1.48005	+	0.988940i
$302$	−9.55890	−	9.55890i	−0.550053	−	0.550053i
$303$	4.09940	+	0.815422i	0.235504	+	0.0468448i
$304$	−9.09747	+	3.76830i	−0.521776	+	0.216127i
$305$	2.65610			0.152088
$306$	−1.16642	−	19.3108i	−0.0666797	−	1.10392i
$307$			12.0226i			0.686165i	0.939305	+	0.343082i	$0.111471\pi$
$307$			12.0226i			0.686165i	−0.939305	+	0.343082i	$0.888529\pi$
$308$	4.58708	−	11.0065i	0.261373	−	0.627152i
$309$	6.58827	+	1.31049i	0.374793	+	0.0745510i
$310$	−10.7347	−	10.7347i	−0.609693	−	0.609693i
$311$	−9.91203	−	14.8344i	−0.562060	−	0.841182i	0.436218	−	0.899841i	$-0.356318\pi$
$311$	−9.91203	−	14.8344i	−0.562060	−	0.841182i	−0.998278	+	0.0586590i	$0.981318\pi$
$312$	2.52529	−	0.502312i	0.142967	−	0.0284378i
$313$	−0.582763	+	0.872166i	−0.0329397	+	0.0492977i	−0.847574	−	0.530677i	$-0.821938\pi$
$313$	−0.582763	+	0.872166i	−0.0329397	+	0.0492977i	0.814634	+	0.579975i	$0.196938\pi$
$314$	7.35245	+	3.04548i	0.414923	+	0.171867i
$315$	−3.76026	+	9.07807i	−0.211867	+	0.511491i
$316$	−6.12195	+	9.16215i	−0.344387	+	0.515411i
$317$	4.93858	+	24.8279i	0.277378	+	1.39448i	0.828471	+	0.560031i	$0.189211\pi$
$317$	4.93858	+	24.8279i	0.277378	+	1.39448i	−0.551093	+	0.834444i	$0.685789\pi$
$318$	−3.53454	−	5.28981i	−0.198207	−	0.296638i
$319$	27.6608	+	0.0601138i	1.54871	+	0.00336573i
$320$	−0.266942	+	1.34201i	−0.0149225	+	0.0750205i
$321$	−3.00797	+	1.24594i	−0.167889	+	0.0695417i
$322$		−	8.52992i		−	0.475354i
$323$	−3.55578	−	7.30446i	−0.197849	−	0.406431i
$324$	−6.32871			−0.351595
$325$	−4.31940	−	10.4279i	−0.239597	−	0.578438i
$326$	1.58216	−	7.95407i	0.0876279	−	0.440535i
$327$	2.20167	+	2.20167i	0.121753	+	0.121753i
$328$	−0.455837	−	0.682208i	−0.0251694	−	0.0376686i
$329$	9.66932	+	48.6110i	0.533087	+	2.68001i
$330$	0.542305	+	2.75766i	0.0298529	+	0.151804i
$331$	−0.545376	+	1.31665i	−0.0299766	+	0.0723699i	−0.938159	−	0.346205i	$-0.887470\pi$
$331$	−0.545376	+	1.31665i	−0.0299766	+	0.0723699i	0.908182	+	0.418575i	$0.137470\pi$
$332$	−4.94370	+	11.9351i	−0.271321	+	0.655026i
$333$	−25.9188	−	17.3184i	−1.42034	−	0.949042i
$334$	0.669654	+	3.36658i	0.0366419	+	0.184211i
$335$	−3.28267	+	2.19341i	−0.179352	+	0.119839i
$336$	−6.92405	+	6.92405i	−0.377738	+	0.377738i
$337$	13.3535	+	2.65619i	0.727414	+	0.144692i	0.544887	−	0.838509i	$-0.316572\pi$
$337$	13.3535	+	2.65619i	0.727414	+	0.144692i	0.182527	+	0.983201i	$0.441572\pi$
$338$	8.57057	−	3.55005i	0.466178	−	0.193097i
$339$		−	6.77938i		−	0.368205i
$340$	3.69745	+	0.506054i	0.200523	+	0.0274446i
$341$	−21.7300	−	21.8247i	−1.17675	−	1.18187i
$342$	−8.54132	+	3.53793i	−0.461862	+	0.191309i
$343$	0.213636	−	1.07402i	0.0115352	−	0.0579916i
$344$	−10.4093	+	10.4093i	−0.561231	+	0.561231i
$345$	0.359978	+	0.538745i	0.0193805	+	0.0290050i
$346$	−0.881301	+	0.175302i	−0.0473791	+	0.00942428i
$347$	15.3579	+	10.2618i	0.824454	+	0.550883i	0.894711	−	0.446646i	$-0.147382\pi$
$347$	15.3579	+	10.2618i	0.824454	+	0.550883i	−0.0702566	+	0.997529i	$0.522382\pi$
$348$	3.79843	+	1.57336i	0.203617	+	0.0843410i
$349$	−9.29944	+	22.4508i	−0.497787	+	1.20176i	0.452885	+	0.891569i	$0.350395\pi$
$349$	−9.29944	+	22.4508i	−0.497787	+	1.20176i	−0.950673	+	0.310196i	$0.899605\pi$
$350$	22.1069	+	14.7714i	1.18166	+	0.789563i
$351$	8.03221	−	1.59771i	0.428728	−	0.0852793i
$352$	3.25840	−	16.1970i	0.173673	−	0.863304i
$353$	13.6123	+	13.6123i	0.724510	+	0.724510i	0.969520	−	0.245011i	$-0.0787914\pi$
$353$	13.6123	+	13.6123i	0.724510	+	0.724510i	−0.245011	+	0.969520i	$0.578791\pi$
$354$	−2.36013	−	0.469460i	−0.125440	−	0.0249515i
$355$	0.942477	+	2.27534i	0.0500215	+	0.120763i
$356$		−	2.92483i		−	0.155016i
$357$	−6.04648	−	5.35764i	−0.320014	−	0.283557i
$358$			4.02659i			0.212812i
$359$	1.40755	+	3.39813i	0.0742878	+	0.179347i	0.956661	−	0.291203i	$-0.0940556\pi$
$359$	1.40755	+	3.39813i	0.0742878	+	0.179347i	−0.882373	+	0.470550i	$0.844056\pi$
$360$	−0.913767	+	4.59382i	−0.0481598	+	0.242115i
$361$	10.6898	−	10.6898i	0.562623	−	0.562623i
$362$	−9.87925	+	6.60110i	−0.519242	+	0.346946i
$363$	1.08801	+	5.59680i	0.0571055	+	0.293756i
$364$	5.50643	−	8.24096i	0.288616	−	0.431944i
$365$	−8.78958	−	3.64076i	−0.460068	−	0.190566i
$366$	2.29594	+	0.951010i	0.120011	+	0.0497101i
$367$	16.2986	+	10.8904i	0.850782	+	0.568474i	0.902746	−	0.430175i	$-0.141548\pi$
$367$	16.2986	+	10.8904i	0.850782	+	0.568474i	−0.0519638	+	0.998649i	$0.516548\pi$
$368$	−1.28068	−	6.43842i	−0.0667601	−	0.335626i
$369$	−0.690959	−	1.03409i	−0.0359699	−	0.0538327i
$370$	13.1935	−	13.1935i	0.685897	−	0.685897i
$371$	26.4903	+	5.26924i	1.37531	+	0.273566i
$372$	−1.75180	−	4.22921i	−0.0908264	−	0.219274i
$373$	4.01776			0.208032			0.104016	−	0.994576i	$-0.466831\pi$
$373$	4.01776			0.208032			0.104016	+	0.994576i	$0.466831\pi$
$374$	23.2676	+	3.23606i	1.20314	+	0.167332i
$375$	−4.48604			−0.231658
$376$	9.04110	+	21.8272i	0.466259	+	1.12565i
$377$	22.5500	+	4.48548i	1.16138	+	0.231014i
$378$	−13.6410	+	13.6410i	−0.701615	+	0.701615i
$379$	5.42366	+	8.11708i	0.278595	+	0.416946i	0.944208	−	0.329351i	$-0.106830\pi$
$379$	5.42366	+	8.11708i	0.278595	+	0.416946i	−0.665613	+	0.746297i	$0.731830\pi$
$380$	−0.347926	−	1.74914i	−0.0178482	−	0.0897292i
$381$	5.11981	+	3.42095i	0.262296	+	0.175261i
$382$	−15.0372	−	6.22861i	−0.769370	−	0.318683i
$383$	−15.1299	−	6.26701i	−0.773102	−	0.320229i	−0.0389736	−	0.999240i	$-0.512409\pi$
$383$	−15.1299	−	6.26701i	−0.773102	−	0.320229i	−0.734128	+	0.679011i	$0.762409\pi$
$384$	−3.58021	+	5.35816i	−0.182702	+	0.273432i
$385$	−9.90634	−	6.65039i	−0.504874	−	0.338935i
$386$	2.72878	−	1.82331i	0.138891	−	0.0928042i
$387$	−15.7784	+	15.7784i	−0.802062	+	0.802062i
$388$	−2.42738	+	12.2032i	−0.123231	+	0.619526i
$389$	−10.8515	−	26.1979i	−0.550194	−	1.32829i	−0.917333	−	0.398120i	$-0.869663\pi$
$389$	−10.8515	−	26.1979i	−0.550194	−	1.32829i	0.367139	−	0.930166i	$-0.380337\pi$
$390$			2.33608i			0.118292i
$391$	5.23843	−	1.37492i	0.264919	−	0.0695328i
$392$		−	13.1354i		−	0.663435i
$393$	0.439973	+	1.06219i	0.0221937	+	0.0535804i
$394$	−29.4035	−	5.84872i	−1.48133	−	0.294654i
$395$	7.79669	+	7.79669i	0.392294	+	0.392294i
$396$	1.69919	−	8.44645i	0.0853877	−	0.424450i
$397$	−2.81413	+	0.559764i	−0.141237	+	0.0280938i	−0.265202	−	0.964193i	$-0.585439\pi$
$397$	−2.81413	+	0.559764i	−0.141237	+	0.0280938i	0.123965	+	0.992287i	$0.460439\pi$
$398$	19.8908	+	13.2906i	0.997035	+	0.666198i
$399$	−1.47739	+	3.56675i	−0.0739622	+	0.178561i
$400$	18.9042	+	7.83036i	0.945208	+	0.391518i
$401$	−4.30259	−	2.87490i	−0.214861	−	0.143566i	0.443483	−	0.896283i	$-0.353743\pi$
$401$	−4.30259	−	2.87490i	−0.214861	−	0.143566i	−0.658344	+	0.752717i	$0.728743\pi$
$402$	−3.62290	+	0.720640i	−0.180694	+	0.0359422i
$403$	−14.2222	−	21.2850i	−0.708459	−	1.06028i
$404$	5.42309	−	5.42309i	0.269809	−	0.269809i
$405$	−1.23545	+	6.21102i	−0.0613900	+	0.308628i
$406$	−50.0365	+	20.7258i	−2.48327	+	1.02860i
$407$	26.8236	−	26.7072i	1.32959	−	1.32383i
$408$	−3.32505	−	1.94249i	−0.164615	−	0.0961676i
$409$		−	17.8135i		−	0.880822i	−0.897796	−	0.440411i	$-0.854833\pi$
$409$		−	17.8135i		−	0.880822i	0.897796	−	0.440411i	$-0.145167\pi$
$410$	0.687757	−	0.284878i	0.0339659	−	0.0140691i
$411$	3.65516	+	0.727056i	0.180296	+	0.0358630i
$412$	8.71560	−	8.71560i	0.429387	−	0.429387i
$413$	8.49431	−	5.67572i	0.417978	−	0.279284i
$414$	−1.20239	−	6.04482i	−0.0590942	−	0.297087i
$415$	10.7481	+	7.18167i	0.527605	+	0.352534i
$416$	5.25529	−	12.6874i	0.257662	−	0.622050i
$417$	1.98232	−	4.78574i	0.0970745	−	0.234359i
$418$	−2.16618	−	11.0152i	−0.105951	−	0.538769i
$419$	0.772662	+	3.88444i	0.0377470	+	0.189767i	0.995058	−	0.0992917i	$-0.0316577\pi$
$419$	0.772662	+	3.88444i	0.0377470	+	0.189767i	−0.957311	+	0.289059i	$0.906658\pi$
$420$	−0.985282	−	1.47458i	−0.0480768	−	0.0719521i
$421$	10.5297	+	10.5297i	0.513188	+	0.513188i	0.915502	−	0.402314i	$-0.131794\pi$
$421$	10.5297	+	10.5297i	0.513188	+	0.513188i	−0.402314	+	0.915502i	$0.631794\pi$
$422$	−1.61467	+	8.11752i	−0.0786011	+	0.395154i
$423$	13.7045	+	33.0857i	0.666337	+	1.60868i
$424$	12.8746			0.625247
$425$	−5.50808	+	15.9574i	−0.267181	+	0.774046i
$426$			2.30426i			0.111642i
$427$	−9.74719	+	4.03742i	−0.471700	+	0.195384i
$428$	−1.16549	+	5.85932i	−0.0563361	+	0.283221i
$429$	−0.0102994	+	4.73915i	−0.000497257	+	0.228808i
$430$	−7.42034	−	11.1053i	−0.357841	−	0.535546i
$431$	2.25957	+	11.3596i	0.108839	+	0.547173i	0.996274	+	0.0862399i	$0.0274852\pi$
$431$	2.25957	+	11.3596i	0.108839	+	0.547173i	−0.887435	+	0.460933i	$0.847515\pi$
$432$	−8.24820	+	12.3443i	−0.396842	+	0.593916i
$433$	8.60584	−	20.7763i	0.413570	−	0.998447i	−0.570601	−	0.821227i	$-0.693290\pi$
$433$	8.60584	−	20.7763i	0.413570	−	0.998447i	0.984171	−	0.177220i	$-0.0567103\pi$
$434$	55.7112	+	23.0763i	2.67422	+	1.10770i
$435$	2.28561	−	3.42066i	0.109587	−	0.164008i
$436$	5.60345	−	1.11460i	0.268357	−	0.0533795i
$437$	−1.43789	−	2.15195i	−0.0687836	−	0.102942i
$438$	−6.29418	−	6.29418i	−0.300747	−	0.300747i
$439$	−31.9631	−	6.35785i	−1.52551	−	0.303444i	−0.640116	−	0.768278i	$-0.721114\pi$
$439$	−31.9631	−	6.35785i	−1.52551	−	0.303444i	−0.885398	+	0.464835i	$0.846114\pi$
$440$	−5.24981	−	2.18792i	−0.250275	−	0.104305i
$441$		−	19.9106i		−	0.948124i
$442$	18.4576	+	6.37110i	0.877938	+	0.303042i
$443$	2.60044			0.123551			0.0617754	−	0.998090i	$-0.480324\pi$
$443$	2.60044			0.123551			0.0617754	+	0.998090i	$0.480324\pi$
$444$	5.19789	−	2.15304i	0.246681	−	0.102179i
$445$	−2.87044	−	0.570966i	−0.136072	−	0.0270664i
$446$	0.336608	+	0.336608i	0.0159389	+	0.0159389i
$447$	0.860574	−	0.575017i	0.0407038	−	0.0271974i
$448$	−1.06032	−	5.33059i	−0.0500954	−	0.251847i
$449$	15.0420	−	22.5120i	0.709876	−	1.06240i	−0.284722	−	0.958610i	$-0.591901\pi$
$449$	15.0420	−	22.5120i	0.709876	−	1.06240i	0.994599	−	0.103795i	$-0.0330986\pi$
$450$	17.7485	+	7.35167i	0.836672	+	0.346561i
$451$	1.39649	−	0.574894i	0.0657583	−	0.0270707i
$452$	−10.3431	−	6.91104i	−0.486499	−	0.325068i
$453$	−4.00045	+	0.795738i	−0.187957	+	0.0373870i
$454$	6.99156	−	4.67161i	0.328130	−	0.219250i
$455$	−7.01279	−	7.01279i	−0.328765	−	0.328765i
$456$	−0.359016	+	1.80490i	−0.0168125	+	0.0845220i
$457$	31.1830	−	12.9164i	1.45868	−	0.604204i	0.494432	−	0.869216i	$-0.335376\pi$
$457$	31.1830	−	12.9164i	1.45868	−	0.604204i	0.964245	+	0.265012i	$0.0853760\pi$
$458$	4.03421			0.188506
$459$	−10.5760	−	6.17848i	−0.493646	−	0.288387i
$460$	1.18892			0.0554335
$461$	−0.0101577	−	0.0245230i	−0.000473093	−	0.00114215i	0.923643	−	0.383254i	$-0.125197\pi$
$461$	−0.0101577	−	0.0245230i	−0.000473093	−	0.00114215i	−0.924116	+	0.382112i	$0.875197\pi$
$462$	−6.18192	−	9.29556i	−0.287609	−	0.432469i
$463$	24.4046	−	24.4046i	1.13418	−	1.13418i	0.144705	−	0.989475i	$-0.453777\pi$
$463$	24.4046	−	24.4046i	1.13418	−	1.13418i	0.989475	−	0.144705i	$-0.0462232\pi$
$464$	−34.6560	+	23.1564i	−1.60886	+	1.07501i
$465$	−4.49254	+	0.893623i	−0.208337	+	0.0414408i
$466$	8.14193	−	12.1853i	0.377168	−	0.564471i
$467$	−10.7340	+	25.9142i	−0.496710	+	1.19916i	0.454535	+	0.890729i	$0.349805\pi$
$467$	−10.7340	+	25.9142i	−0.496710	+	1.19916i	−0.951245	+	0.308436i	$0.900195\pi$
$468$	2.74054	−	6.61624i	0.126681	−	0.305836i
$469$	8.71245	−	13.0391i	0.402304	−	0.602090i
$470$	−21.0235	+	4.18183i	−0.969741	+	0.192893i
$471$	1.99652	−	1.33404i	0.0919950	−	0.0614691i
$472$	3.44341	−	3.44341i	0.158496	−	0.158496i
$473$	−15.0045	−	22.5619i	−0.689909	−	1.03740i
$474$	3.94790	+	9.53107i	0.181333	+	0.437777i
$475$	8.06721			0.370149
$476$	−14.3379	+	3.76325i	−0.657178	+	0.172488i
$477$	19.5154			0.893548
$478$	10.8249	−	4.48383i	0.495120	−	0.205086i
$479$	6.26939	−	31.5183i	0.286456	−	1.44011i	−0.522701	−	0.852516i	$-0.675075\pi$
$479$	6.26939	−	31.5183i	0.286456	−	1.44011i	0.809156	−	0.587594i	$-0.199925\pi$
$480$	−1.73753	−	1.73753i	−0.0793069	−	0.0793069i
$481$	26.1603	−	17.4798i	1.19281	−	0.797008i
$482$	−1.84215	+	0.366426i	−0.0839075	+	0.0166902i
$483$	−2.13995	−	1.42987i	−0.0973710	−	0.0650612i
$484$	9.64802	+	4.04556i	0.438546	+	0.183889i
$485$	11.5025	+	4.76448i	0.522300	+	0.216344i
$486$	−11.7974	+	17.6561i	−0.535143	+	0.800898i
$487$	3.82119	+	19.2104i	0.173155	+	0.870507i	0.965494	+	0.260426i	$0.0838631\pi$
$487$	3.82119	+	19.2104i	0.173155	+	0.870507i	−0.792339	+	0.610081i	$0.791137\pi$
$488$	−4.18150	+	2.79399i	−0.189288	+	0.126478i
$489$	−1.73026	−	1.73026i	−0.0782451	−	0.0782451i
$490$	11.6887	+	2.32502i	0.528040	+	0.105034i
$491$	−11.3458	+	4.69957i	−0.512027	+	0.212089i	−0.623711	−	0.781655i	$-0.714376\pi$
$491$	−11.3458	+	4.69957i	−0.512027	+	0.212089i	0.111684	+	0.993744i	$0.464376\pi$
$492$	0.224469			0.0101198
$493$	−20.7935	−	27.3879i	−0.936492	−	1.23349i
$494$		−	9.33119i		−	0.419830i
$495$	−7.95768	−	3.31646i	−0.357671	−	0.149064i
$496$	45.5157	+	9.05363i	2.04371	+	0.406520i
$497$	−6.91729	−	6.91729i	−0.310283	−	0.310283i
$498$	6.71934	+	10.0562i	0.301101	+	0.450629i
$499$	−17.4474	+	3.47051i	−0.781054	+	0.155361i	−0.569485	−	0.822002i	$-0.692857\pi$
$499$	−17.4474	+	3.47051i	−0.781054	+	0.155361i	−0.211569	+	0.977363i	$0.567857\pi$
$500$	−4.57316	+	6.84422i	−0.204518	+	0.306083i
$501$	0.956846	+	0.396338i	0.0427487	+	0.0177071i
$502$	12.7733	−	30.8374i	0.570100	−	1.37634i
$503$	−17.1079	+	25.6037i	−0.762802	+	1.14161i	0.223183	+	0.974777i	$0.428355\pi$
$503$	−17.1079	+	25.6037i	−0.762802	+	1.14161i	−0.985984	+	0.166837i	$0.946645\pi$
$504$	−3.62957	−	18.2471i	−0.161674	−	0.812790i
$505$	−4.26358	−	6.38090i	−0.189727	−	0.283946i
$506$	7.48392	+	0.0162644i	0.332701	+	0.000723041i
$507$	0.546062	−	2.74524i	0.0242514	−	0.121920i
$508$	10.4385	−	4.32377i	0.463133	−	0.191836i
$509$		−	17.3198i		−	0.767688i	−0.923398	−	0.383844i	$-0.874600\pi$
$509$		−	17.3198i		−	0.767688i	0.923398	−	0.383844i	$-0.125400\pi$
$510$	2.31710	−	2.61501i	0.102603	−	0.115795i
$511$	37.7897			1.67172
$512$	2.63467	+	6.36066i	0.116437	+	0.281104i
$513$	−1.14192	+	5.74084i	−0.0504172	+	0.253464i
$514$	−31.3920	−	31.3920i	−1.38464	−	1.38464i
$515$	−6.85213	−	10.2549i	−0.301941	−	0.451886i
$516$	−0.785702	−	3.94999i	−0.0345886	−	0.173889i
$517$	−42.6684	+	8.39091i	−1.87655	+	0.369032i
$518$	−28.3619	+	68.4716i	−1.24615	+	3.00847i
$519$	−0.103753	+	0.250482i	−0.00455426	+	0.0109950i
$520$	−3.93074	−	2.62643i	−0.172374	−	0.115177i
$521$	3.29503	+	16.5652i	0.144358	+	0.725737i	0.983369	+	0.181621i	$0.0581346\pi$
$521$	3.29503	+	16.5652i	0.144358	+	0.725737i	−0.839011	+	0.544115i	$0.816865\pi$
$522$	−32.5373	+	21.7408i	−1.42412	+	0.951567i
$523$	−30.2885	+	30.2885i	−1.32443	+	1.32443i	−0.414273	+	0.910153i	$0.635964\pi$
$523$	−30.2885	+	30.2885i	−1.32443	+	1.32443i	−0.910153	+	0.414273i	$0.864036\pi$
$524$	2.06907	+	0.411564i	0.0903879	+	0.0179793i
$525$	7.41155	−	3.06996i	0.323466	−	0.133984i
$526$			36.4330i			1.58856i
$527$	−5.19175	+	37.9332i	−0.226156	+	1.65240i
$528$	−6.06177	−	6.08818i	−0.263805	−	0.264954i
$529$	−19.6552	+	8.14144i	−0.854573	+	0.353976i
$530$	−2.27887	+	11.4566i	−0.0989876	+	0.497644i
$531$	5.21952	−	5.21952i	0.226508	−	0.226508i
$532$	3.93560	+	5.89004i	0.170630	+	0.255366i
$533$	1.23116	−	0.244893i	0.0533275	−	0.0106075i
$534$	−2.27679	−	1.52130i	−0.0985262	−	0.0658331i
$535$	5.52284	+	2.28764i	0.238773	+	0.0989032i
$536$	2.86064	−	6.90619i	0.123561	−	0.298302i
$537$	1.01017	+	0.674975i	0.0435921	+	0.0291273i
$538$	−35.6881	+	7.09881i	−1.53862	+	0.306051i
$539$	23.7023	+	4.76825i	1.02093	+	0.205383i
$540$	−1.90130	−	1.90130i	−0.0818191	−	0.0818191i
$541$	2.24078	+	0.445720i	0.0963389	+	0.0191630i	0.243024	−	0.970020i	$-0.421861\pi$
$541$	2.24078	+	0.445720i	0.0963389	+	0.0191630i	−0.146685	+	0.989183i	$0.546861\pi$
$542$	−16.0763	−	38.8117i	−0.690538	−	1.66711i
$543$			3.58500i			0.153847i
$544$	−18.4671	+	8.98969i	−0.791770	+	0.385430i
$545$		−	5.71684i		−	0.244883i
$546$	−3.55097	−	8.57279i	−0.151967	−	0.366882i
$547$	−4.60540	+	23.1529i	−0.196913	+	0.989947i	0.748268	+	0.663397i	$0.230886\pi$
$547$	−4.60540	+	23.1529i	−0.196913	+	0.989947i	−0.945180	+	0.326549i	$0.894114\pi$
$548$	4.83540	−	4.83540i	0.206558	−	0.206558i
$549$	−6.33833	+	4.23514i	−0.270513	+	0.180751i
$550$	−13.0021	+	19.3678i	−0.554413	+	0.825847i
$551$	−9.12961	+	13.6634i	−0.388934	+	0.582081i
$552$	−1.13343	−	0.469481i	−0.0482419	−	0.0199824i
$553$	−40.4632	−	16.7604i	−1.72067	−	0.712726i
$554$	−38.9554	−	26.0292i	−1.65506	−	1.10587i
$555$	−1.09830	−	5.52154i	−0.0466204	−	0.234376i
$556$	−5.28065	−	7.90305i	−0.223950	−	0.335164i
$557$	22.6614	−	22.6614i	0.960196	−	0.960196i	−0.0390414	−	0.999238i	$-0.512430\pi$
$557$	22.6614	−	22.6614i	0.960196	−	0.960196i	0.999238	+	0.0390414i	$0.0124304\pi$
$558$	42.7332	+	8.50016i	1.80904	+	0.359840i
$559$	−8.61878	−	20.8076i	−0.364536	−	0.880067i
$560$	17.9790			0.759750
$561$	4.71218	−	5.29480i	0.198948	−	0.223547i
$562$	6.21851			0.262312
$563$	−1.29745	−	3.13233i	−0.0546811	−	0.132012i	0.894178	−	0.447711i	$-0.147761\pi$
$563$	−1.29745	−	3.13233i	−0.0546811	−	0.132012i	−0.948859	+	0.315700i	$0.897761\pi$
$564$	−6.33931	−	1.26097i	−0.266933	−	0.0530963i
$565$	−8.80165	+	8.80165i	−0.370288	+	0.370288i
$566$	−0.810335	−	1.21275i	−0.0340609	−	0.0509758i
$567$	−4.90733	−	24.6708i	−0.206088	−	1.03608i
$568$	−3.87721	−	2.59067i	−0.162684	−	0.108702i
$569$	5.51202	+	2.28315i	0.231076	+	0.0957147i	0.495217	−	0.868769i	$-0.335089\pi$
$569$	5.51202	+	2.28315i	0.231076	+	0.0957147i	−0.264141	+	0.964484i	$0.585089\pi$
$570$	−1.54256	−	0.638950i	−0.0646108	−	0.0267627i
$571$	11.5463	−	17.2803i	0.483199	−	0.723158i	−0.507134	−	0.861867i	$-0.669295\pi$
$571$	11.5463	−	17.2803i	0.483199	−	0.723158i	0.990333	+	0.138709i	$0.0442952\pi$
$572$	7.21989	+	4.84691i	0.301879	+	0.202659i
$573$	−4.08328	+	2.72836i	−0.170582	+	0.113979i
$574$	−2.09086	+	2.09086i	−0.0872707	+	0.0872707i
$575$	−1.04920	+	5.27469i	−0.0437547	+	0.219970i
$576$	−1.50281	−	3.62811i	−0.0626172	−	0.151171i
$577$			38.6753i			1.61007i	0.593225	+	0.805037i	$0.297855\pi$
$577$			38.6753i			1.61007i	−0.593225	+	0.805037i	$0.702145\pi$
$578$	−14.3421	−	25.4394i	−0.596554	−	1.05814i
$579$		−	0.990225i		−	0.0411523i
$580$	−2.88880	−	6.97418i	−0.119951	−	0.289587i
$581$	−50.3594	−	10.0171i	−2.08926	−	0.415580i
$582$	8.23686	+	8.23686i	0.341429	+	0.341429i
$583$	−4.67360	+	23.2318i	−0.193561	+	0.962163i
$584$	17.6672	−	3.51423i	0.731075	−	0.145420i
$585$	−5.95822	−	3.98116i	−0.246342	−	0.164601i
$586$	9.55905	−	23.0776i	0.394881	−	0.953326i
$587$	19.0293	+	7.88220i	0.785424	+	0.325333i	0.739102	−	0.673593i	$-0.235250\pi$
$587$	19.0293	+	7.88220i	0.785424	+	0.325333i	0.0463219	+	0.998927i	$0.485250\pi$
$588$	2.98796	+	1.99649i	0.123221	+	0.0823338i
$589$	17.9450	−	3.56947i	0.739409	−	0.147078i
$590$	2.45466	+	3.67366i	0.101057	+	0.151242i
$591$	−6.39619	+	6.39619i	−0.263104	+	0.263104i
$592$	−11.1273	+	55.9409i	−0.457330	+	2.29916i
$593$	−30.1599	+	12.4926i	−1.23852	+	0.513011i	−0.903251	−	0.429112i	$-0.858827\pi$
$593$	−30.1599	+	12.4926i	−1.23852	+	0.513011i	−0.335267	+	0.942123i	$0.608827\pi$
$594$	−11.9422	−	11.9942i	−0.489994	−	0.492129i
$595$	0.894316	+	14.8060i	0.0366634	+	0.606985i
$596$		−	1.89914i		−	0.0777918i
$597$	6.66857	−	2.76221i	0.272926	−	0.113050i
$598$	6.10114	+	1.21359i	0.249494	+	0.0496275i
$599$	3.99691	−	3.99691i	0.163309	−	0.163309i	−0.620722	−	0.784031i	$-0.713160\pi$
$599$	3.99691	−	3.99691i	0.163309	−	0.163309i	0.784031	+	0.620722i	$0.213160\pi$
$600$	3.17952	−	2.12449i	0.129803	−	0.0867318i
$601$	2.63257	+	13.2348i	0.107385	+	0.539860i	0.996602	+	0.0823736i	$0.0262501\pi$
$601$	2.63257	+	13.2348i	0.107385	+	0.539860i	−0.889217	+	0.457486i	$0.848750\pi$
$602$	44.1114	+	29.4743i	1.79785	+	1.20128i
$603$	4.33616	−	10.4684i	0.176582	−	0.426307i
$604$	−2.86411	+	6.91456i	−0.116539	+	0.281350i
$605$	5.85376	−	8.67887i	0.237989	−	0.352846i
$606$	−1.40079	−	7.04224i	−0.0569032	−	0.286072i
$607$	−10.8873	−	16.2940i	−0.441901	−	0.661351i	0.541936	−	0.840420i	$-0.317692\pi$
$607$	−10.8873	−	16.2940i	−0.441901	−	0.661351i	−0.983837	+	0.179069i	$0.942692\pi$
$608$	6.94036	+	6.94036i	0.281469	+	0.281469i
$609$	−3.18800	+	16.0272i	−0.129184	+	0.649454i
$610$	−1.74612	−	4.21551i	−0.0706984	−	0.170681i
$611$	−36.1453			−1.46228
$612$	−9.63025	+	4.68796i	−0.389280	+	0.189500i
$613$			7.23685i			0.292294i	0.989263	+	0.146147i	$0.0466872\pi$
$613$			7.23685i			0.292294i	−0.989263	+	0.146147i	$0.953313\pi$
$614$	19.0811	−	7.90365i	0.770050	−	0.318965i
$615$	0.0438194	−	0.220295i	0.00176697	−	0.00888316i
$616$	22.5912	+	0.0490963i	0.910226	+	0.00197815i
$617$	18.8904	+	28.2715i	0.760499	+	1.13817i	0.986455	+	0.164030i	$0.0524494\pi$
$617$	18.8904	+	28.2715i	0.760499	+	1.13817i	−0.225956	+	0.974137i	$0.572551\pi$
$618$	−2.25125	−	11.3178i	−0.0905585	−	0.455268i
$619$	−3.17007	+	4.74434i	−0.127416	+	0.190691i	−0.889693	−	0.456560i	$-0.849081\pi$
$619$	−3.17007	+	4.74434i	−0.127416	+	0.190691i	0.762277	+	0.647251i	$0.224081\pi$
$620$	−3.21642	+	7.76513i	−0.129175	+	0.311855i
$621$	−3.60510	−	1.49328i	−0.144668	−	0.0599232i
$622$	−17.0276	+	25.4836i	−0.682744	+	1.02180i
$623$	11.4017	−	2.26793i	0.456798	−	0.0908628i
$624$	−3.96740	−	5.93764i	−0.158823	−	0.237696i
$625$	−8.65134	−	8.65134i	−0.346054	−	0.346054i
$626$	1.76733	+	0.351543i	0.0706366	+	0.0140505i
$627$	−3.12655	−	1.30303i	−0.124862	−	0.0520378i
$628$		−	4.40599i		−	0.175818i
$629$	−46.6216	−	6.38089i	−1.85893	−	0.254423i
$630$	16.8799			0.672510
$631$	8.29368	−	3.43535i	0.330166	−	0.136759i	−0.211442	−	0.977391i	$-0.567816\pi$
$631$	8.29368	−	3.43535i	0.330166	−	0.136759i	0.541608	+	0.840631i	$0.317816\pi$
$632$	−20.4758	−	4.07289i	−0.814483	−	0.162011i
$633$	1.76582	+	1.76582i	0.0701849	+	0.0701849i
$634$	36.1579	−	24.1599i	1.43601	−	0.959514i
$635$	−2.20563	−	11.0885i	−0.0875278	−	0.440032i
$636$	−1.95686	+	2.92864i	−0.0775945	+	0.116128i
$637$	18.5664	+	7.69045i	0.735627	+	0.304707i
$638$	−18.0888	−	43.9401i	−0.716144	−	1.73961i
$639$	−5.87708	−	3.92694i	−0.232494	−	0.155347i
$640$	11.6047	−	2.30831i	0.458715	−	0.0912440i
$641$	23.3921	−	15.6301i	0.923932	−	0.617352i	3.79269e−5	−	1.00000i	$-0.499988\pi$
$641$	23.3921	−	15.6301i	0.923932	−	0.617352i	0.923894	+	0.382648i	$0.124988\pi$
$642$	3.95488	+	3.95488i	0.156087	+	0.156087i
$643$	3.04061	−	15.2862i	0.119910	−	0.602828i	−0.873367	−	0.487063i	$-0.838068\pi$
$643$	3.04061	−	15.2862i	0.119910	−	0.602828i	0.993277	−	0.115765i	$-0.0369319\pi$
$644$	−4.36302	+	1.80722i	−0.171927	+	0.0712145i
$645$	−4.02992			−0.158678
$646$	−9.25538	+	10.4454i	−0.364148	+	0.410967i
$647$	−0.0962889			−0.00378551			−0.00189275	−	0.999998i	$-0.500602\pi$
$647$	−0.0962889			−0.00378551			−0.00189275	+	0.999998i	$0.500602\pi$
$648$	−4.58850	−	11.0776i	−0.180253	−	0.435170i
$649$	4.96352	+	7.46349i	0.194835	+	0.292968i
$650$	−13.7107	+	13.7107i	−0.537777	+	0.537777i
$651$	15.1281	−	10.1083i	0.592918	−	0.396175i
$652$	−4.40368	+	0.875946i	−0.172461	+	0.0343047i
$653$	−3.56164	+	5.33037i	−0.139378	+	0.208593i	−0.894591	−	0.446885i	$-0.852533\pi$
$653$	−3.56164	+	5.33037i	−0.139378	+	0.208593i	0.755214	+	0.655479i	$0.227533\pi$
$654$	2.04690	−	4.94166i	0.0800402	−	0.193234i
$655$	0.807822	−	1.95026i	0.0315642	−	0.0762028i
$656$	−1.26427	+	1.89211i	−0.0493613	+	0.0738744i
$657$	26.7800	−	5.32688i	1.04479	−	0.207821i
$658$	70.7941	−	47.3031i	2.75984	−	1.84407i
$659$	13.1075	−	13.1075i	0.510597	−	0.510597i	−0.404112	−	0.914709i	$-0.632419\pi$
$659$	13.1075	−	13.1075i	0.510597	−	0.510597i	0.914709	+	0.404112i	$0.132419\pi$
$660$	1.29563	−	0.861648i	0.0504325	−	0.0335396i
$661$	−2.36908	−	5.71947i	−0.0921467	−	0.222462i	0.871086	−	0.491131i	$-0.163416\pi$
$661$	−2.36908	−	5.71947i	−0.0921467	−	0.222462i	−0.963233	+	0.268669i	$0.913416\pi$
$662$	2.44820			0.0951520
$663$	4.69239	−	3.56257i	0.182237	−	0.138359i
$664$	−24.4753			−0.949826
$665$	6.54880	−	2.71260i	0.253951	−	0.105190i
$666$	−10.4471	+	52.5210i	−0.404816	+	2.03515i
$667$	−7.74636	−	7.74636i	−0.299940	−	0.299940i
$668$	1.58011	−	1.05580i	0.0611364	−	0.0408500i
$669$	0.140872	−	0.0280212i	0.00544644	−	0.00108336i
$670$	5.63921	+	3.76800i	0.217862	+	0.145570i
$671$	−3.52373	−	8.55962i	−0.136032	−	0.330440i
$672$	9.01742	+	3.73514i	0.347854	+	0.144086i
$673$	−16.8784	+	25.2602i	−0.650613	+	0.973711i	0.348722	+	0.937226i	$0.386616\pi$
$673$	−16.8784	+	25.2602i	−0.650613	+	0.973711i	−0.999334	+	0.0364843i	$0.988384\pi$
$674$	−4.56298	−	22.9397i	−0.175760	−	0.883603i
$675$	10.1131	−	6.75736i	0.389254	−	0.260091i
$676$	−3.63167	−	3.63167i	−0.139679	−	0.139679i
$677$	25.9618	+	5.16412i	0.997793	+	0.198473i	0.666862	−	0.745182i	$-0.267637\pi$
$677$	25.9618	+	5.16412i	0.997793	+	0.198473i	0.330931	+	0.943655i	$0.392637\pi$
$678$	−10.7596	+	4.45677i	−0.413219	+	0.171161i
$679$	−49.4533			−1.89784
$680$	1.79498	+	6.83884i	0.0688343	+	0.262257i
$681$		−	2.53711i		−	0.0972222i
$682$	−20.3528	+	48.8354i	−0.779347	+	1.87001i
$683$	25.2142	+	5.01542i	0.964796	+	0.191910i	0.652259	−	0.757996i	$-0.273821\pi$
$683$	25.2142	+	5.01542i	0.964796	+	0.191910i	0.312536	+	0.949906i	$0.398821\pi$
$684$	3.61927	+	3.61927i	0.138386	+	0.138386i
$685$	−3.80155	−	5.68942i	−0.145250	−	0.217381i
$686$	−1.84503	+	0.366999i	−0.0704434	+	0.0140121i
$687$	0.676252	−	1.01208i	0.0258006	−	0.0386134i
$688$	37.7208	+	15.6245i	1.43809	+	0.595677i
$689$	−7.53779	+	18.1978i	−0.287167	+	0.693282i
$690$	0.618395	−	0.925494i	0.0235419	−	0.0352329i
$691$	2.84842	+	14.3200i	0.108359	+	0.544758i	0.996384	+	0.0849626i	$0.0270771\pi$
$691$	2.84842	+	14.3200i	0.108359	+	0.544758i	−0.888025	+	0.459795i	$0.847923\pi$
$692$	0.276386	+	0.413641i	0.0105066	+	0.0157243i
$693$	34.2438	+	0.0744203i	1.30082	+	0.00282699i
$694$	6.19029	−	31.1207i	0.234980	−	1.18133i
$695$	−8.78695	+	3.63967i	−0.333308	+	0.138061i
$696$			7.78941i			0.295257i
$697$	−1.62107	−	0.947025i	−0.0614023	−	0.0358711i
$698$	41.7453			1.58008
$699$	−1.69215	−	4.08522i	−0.0640031	−	0.154517i
$700$	2.87173	−	14.4372i	0.108541	−	0.545674i
$701$	−35.4433	−	35.4433i	−1.33867	−	1.33867i	−0.897345	−	0.441330i	$-0.854507\pi$
$701$	−35.4433	−	35.4433i	−1.33867	−	1.33867i	−0.441330	−	0.897345i	$-0.645493\pi$
$702$	−7.81611	−	11.6976i	−0.295000	−	0.441499i
$703$	4.38705	+	22.0552i	0.165461	+	0.831827i
$704$	4.67893	−	0.920131i	0.176344	−	0.0346788i
$705$	−2.47504	+	5.97527i	−0.0932153	+	0.225042i
$706$	12.6554	−	30.5529i	0.476293	−	1.14987i
$707$	25.3456	+	16.9354i	0.953219	+	0.636920i
$708$	0.259911	+	1.30666i	0.00976806	+	0.0491074i
$709$	27.4062	−	18.3122i	1.02926	−	0.687731i	0.0782654	−	0.996933i	$-0.475062\pi$
$709$	27.4062	−	18.3122i	1.02926	−	0.687731i	0.950996	+	0.309202i	$0.100062\pi$
$710$	2.99162	−	2.99162i	0.112274	−	0.112274i
$711$	−31.0373	−	6.17370i	−1.16399	−	0.231532i
$712$	5.11955	−	2.12059i	0.191863	−	0.0794723i
$713$			12.1974i			0.456797i
$714$	−4.52819	+	13.1185i	−0.169463	+	0.490948i
$715$	6.16620	−	6.13946i	0.230603	−	0.229603i
$716$	2.05958	−	0.853107i	0.0769702	−	0.0318821i
$717$	0.689694	−	3.46733i	0.0257571	−	0.129490i
$718$	4.46787	−	4.46787i	0.166739	−	0.166739i
$719$	4.22477	+	6.32282i	0.157557	+	0.235801i	0.901847	−	0.432056i	$-0.142212\pi$
$719$	4.22477	+	6.32282i	0.157557	+	0.235801i	−0.744289	+	0.667857i	$0.767212\pi$
$720$	12.7410	−	2.53434i	0.474828	−	0.0944493i
$721$	40.7336	+	27.2173i	1.51700	+	1.01363i
$722$	−23.9934	−	9.93840i	−0.892943	−	0.369869i
$723$	−0.216871	+	0.523573i	−0.00806552	+	0.0194719i
$724$	5.46953	+	3.65463i	0.203274	+	0.135823i
$725$	33.4907	−	6.66170i	1.24381	−	0.247410i
$726$	8.16746	−	5.40612i	0.303123	−	0.200640i
$727$	−13.0260	−	13.0260i	−0.483109	−	0.483109i	0.423014	−	0.906123i	$-0.360972\pi$
$727$	−13.0260	−	13.0260i	−0.483109	−	0.483109i	−0.906123	+	0.423014i	$0.860972\pi$
$728$	18.4171	+	3.66339i	0.682583	+	0.135774i
$729$	−5.18751	−	12.5238i	−0.192130	−	0.463843i
$730$			16.3434i			0.604898i
$731$	−10.9907	+	31.8408i	−0.406504	+	1.17768i
$732$		−	1.37585i		−	0.0508530i
$733$	−11.7001	−	28.2466i	−0.432154	−	1.04331i	−0.978592	−	0.205811i	$-0.934017\pi$
$733$	−11.7001	−	28.2466i	−0.432154	−	1.04331i	0.546438	−	0.837499i	$-0.315983\pi$
$734$	6.56948	−	33.0270i	0.242484	−	1.21905i
$735$	2.54265	−	2.54265i	0.0937872	−	0.0937872i
$736$	−5.44055	+	3.63526i	−0.200542	+	0.133998i
$737$	11.4235	+	7.66892i	0.420791	+	0.282488i
$738$	−1.18698	+	1.77644i	−0.0436933	+	0.0653916i
$739$	33.1617	+	13.7360i	1.21987	+	0.505287i	0.897369	−	0.441281i	$-0.145476\pi$
$739$	33.1617	+	13.7360i	1.21987	+	0.505287i	0.322503	+	0.946569i	$0.395476\pi$
$740$	−9.54370	−	3.95313i	−0.350833	−	0.145320i
$741$	−2.34097	−	1.56418i	−0.0859975	−	0.0574617i
$742$	−9.05188	−	45.5069i	−0.332305	−	1.67061i
$743$	−13.5006	−	20.2051i	−0.495291	−	0.741255i	0.496651	−	0.867950i	$-0.334563\pi$
$743$	−13.5006	−	20.2051i	−0.495291	−	0.741255i	−0.991942	+	0.126695i	$0.959563\pi$
$744$	6.13261	−	6.13261i	0.224832	−	0.224832i
$745$	−1.86383	−	0.370738i	−0.0682853	−	0.0135828i
$746$	−2.64128	−	6.37661i	−0.0967040	−	0.233464i
$747$	−37.0997			−1.35741
$748$	−3.27443	−	12.5869i	−0.119725	−	0.460222i
$749$	−23.7447			−0.867614
$750$	2.94912	+	7.11981i	0.107687	+	0.259979i
$751$	−5.40184	−	1.07449i	−0.197116	−	0.0392088i	0.0955449	−	0.995425i	$-0.469541\pi$
$751$	−5.40184	−	1.07449i	−0.197116	−	0.0392088i	−0.292661	+	0.956216i	$0.594541\pi$
$752$	46.3336	−	46.3336i	1.68961	−	1.68961i
$753$	−5.59517	−	8.37377i	−0.203899	−	0.305157i
$754$	−7.70547	−	38.7380i	−0.280617	−	1.41075i
$755$	6.22688	+	4.16066i	0.226619	+	0.151422i
$756$	9.86738	+	4.08720i	0.358873	+	0.148650i
$757$	−21.2260	−	8.79208i	−0.771470	−	0.319554i	−0.0380026	−	0.999278i	$-0.512100\pi$
$757$	−21.2260	−	8.79208i	−0.771470	−	0.319554i	−0.733468	+	0.679724i	$0.762100\pi$
$758$	9.31715	−	13.9441i	0.338414	−	0.506472i
$759$	1.25861	−	1.87480i	0.0456845	−	0.0680511i
$760$	2.80940	−	1.87718i	0.101908	−	0.0680926i
$761$	28.4929	−	28.4929i	1.03287	−	1.03287i	0.0334241	−	0.999441i	$-0.489359\pi$
$761$	28.4929	−	28.4929i	1.03287	−	1.03287i	0.999441	−	0.0334241i	$-0.0106412\pi$
$762$	2.06364	−	10.3746i	0.0747578	−	0.375833i
$763$	8.68992	+	20.9793i	0.314596	+	0.759503i
$764$			9.01110i			0.326010i
$765$	2.72083	+	10.3663i	0.0983719	+	0.374795i
$766$			28.1327i			1.01648i
$767$	2.85110	+	6.88318i	0.102947	+	0.248537i
$768$	9.39577	+	1.86894i	0.339041	+	0.0674394i
$769$	12.5743	+	12.5743i	0.453439	+	0.453439i	0.896494	−	0.443055i	$-0.146105\pi$
$769$	12.5743	+	12.5743i	0.453439	+	0.453439i	−0.443055	+	0.896494i	$0.646105\pi$
$770$	−4.04244	+	20.0944i	−0.145679	+	0.724151i
$771$	−13.1377	+	2.61325i	−0.473142	+	0.0941139i
$772$	−1.51076	−	1.00946i	−0.0543734	−	0.0363311i
$773$	−14.9644	+	36.1271i	−0.538230	+	1.29940i	0.387727	+	0.921774i	$0.373260\pi$
$773$	−14.9644	+	36.1271i	−0.538230	+	1.29940i	−0.925957	+	0.377629i	$0.876740\pi$
$774$	35.4148	+	14.6693i	1.27296	+	0.527276i
$775$	−31.6120	−	21.1224i	−1.13554	−	0.758740i
$776$	−23.1202	+	4.59889i	−0.829966	+	0.165090i
$777$	12.4235	+	18.5931i	0.445692	+	0.667025i
$778$	−34.4450	+	34.4450i	−1.23491	+	1.23491i
$779$	−0.175032	+	0.879944i	−0.00627116	+	0.0315273i
$780$	1.19489	−	0.494941i	0.0427840	−	0.0177217i
$781$	6.08223	−	6.05585i	0.217639	−	0.216695i
$782$	−5.62590	−	7.41007i	−0.201182	−	0.264984i
$783$			24.7758i			0.885415i
$784$	−33.6578	+	13.9415i	−1.20207	+	0.497912i
$785$	−4.32406	−	0.860109i	−0.154332	−	0.0306986i
$786$	1.39657	−	1.39657i	0.0498140	−	0.0498140i
$787$	−30.1855	+	20.1693i	−1.07600	+	0.718957i	−0.961594	−	0.274477i	$-0.911495\pi$
$787$	−30.1855	+	20.1693i	−1.07600	+	0.718957i	−0.114402	+	0.993435i	$0.536495\pi$
$788$	3.23808	+	16.2789i	0.115352	+	0.579912i
$789$	9.14015	+	6.10725i	0.325398	+	0.217424i
$790$	7.24862	−	17.4997i	0.257894	−	0.622612i
$791$	18.9208	−	45.6788i	0.672745	−	1.62415i
$792$	16.0164	−	3.14970i	0.569119	−	0.111920i
$793$	−1.50104	−	7.54623i	−0.0533034	−	0.267974i
$794$	2.73841	+	4.09833i	0.0971827	+	0.145444i
$795$	2.49218	+	2.49218i	0.0883886	+	0.0883886i
$796$	2.58385	−	12.9899i	0.0915823	−	0.460415i
$797$	0.991141	+	2.39283i	0.0351080	+	0.0847583i	0.940461	−	0.339901i	$-0.110394\pi$
$797$	0.991141	+	2.39283i	0.0351080	+	0.0847583i	−0.905353	+	0.424660i	$0.860394\pi$
$798$	6.63204			0.234772
$799$	40.4612	+	35.8517i	1.43141	+	1.26834i
$800$		−	20.3955i		−	0.721088i
$801$	7.76023	−	3.21439i	0.274194	−	0.113575i
$802$	−1.73424	+	8.71863i	−0.0612382	+	0.307865i
$803$	−0.0720553	+	33.1556i	−0.00254278	+	1.17004i
$804$	1.13618	+	1.70042i	0.0400700	+	0.0599691i
$805$	0.921895	+	4.63468i	0.0324925	+	0.163351i
$806$	−24.4319	+	36.5650i	−0.860578	+	1.28795i
$807$	−4.20147	+	10.1432i	−0.147899	+	0.357059i
$808$	13.4243	+	5.56054i	0.472266	+	0.195619i
$809$	−14.2502	+	21.3270i	−0.501011	+	0.749816i	−0.992655	−	0.120980i	$-0.961396\pi$
$809$	−14.2502	+	21.3270i	−0.501011	+	0.749816i	0.491644	+	0.870796i	$0.336396\pi$
$810$	10.6697	−	2.12234i	0.374896	−	0.0745715i
$811$	24.7685	+	37.0687i	0.869739	+	1.30166i	0.952329	+	0.305073i	$0.0986809\pi$
$811$	24.7685	+	37.0687i	0.869739	+	1.30166i	−0.0825897	+	0.996584i	$0.526319\pi$
$812$	21.2023	+	21.2023i	0.744055	+	0.744055i
$813$	−12.4318	−	2.47283i	−0.436001	−	0.0867260i
$814$	−60.0210	−	25.0145i	−2.10373	−	0.876757i
$815$			4.49279i			0.157376i
$816$	−1.44828	+	10.5818i	−0.0506999	+	0.370436i
$817$	16.0971			0.563165
$818$	−28.2720	+	11.7106i	−0.988506	+	0.409452i
$819$	27.9167	+	5.55298i	0.975489	+	0.194037i
$820$	−0.291428	−	0.291428i	−0.0101771	−	0.0101771i
$821$	−32.7618	+	21.8908i	−1.14340	+	0.763993i	−0.975105	−	0.221744i	$-0.928825\pi$
$821$	−32.7618	+	21.8908i	−1.14340	+	0.763993i	−0.168291	+	0.985737i	$0.553825\pi$
$822$	−1.24899	−	6.27909i	−0.0435635	−	0.219008i
$823$	−29.1459	+	43.6199i	−1.01596	+	1.52049i	−0.171282	+	0.985222i	$0.554791\pi$
$823$	−29.1459	+	43.6199i	−1.01596	+	1.52049i	−0.844680	+	0.535272i	$0.820209\pi$
$824$	21.5746	+	8.93651i	0.751588	+	0.311318i
$825$	2.67937	+	6.50854i	0.0932836	+	0.226598i
$826$	−14.5921	−	9.75015i	−0.507725	−	0.339251i
$827$	1.73212	−	0.344541i	0.0602318	−	0.0119809i	−0.164882	−	0.986313i	$-0.552724\pi$
$827$	1.73212	−	0.344541i	0.0602318	−	0.0119809i	0.225114	+	0.974332i	$0.427724\pi$
$828$	−2.83715	+	1.89572i	−0.0985978	+	0.0658809i
$829$	−31.0094	−	31.0094i	−1.07700	−	1.07700i	−0.996777	−	0.0802224i	$-0.974437\pi$
$829$	−31.0094	−	31.0094i	−1.07700	−	1.07700i	−0.0802224	−	0.996777i	$-0.525563\pi$
$830$	4.33224	−	21.7797i	0.150374	−	0.755983i
$831$	−13.0602	+	5.40969i	−0.453052	+	0.187660i
$832$	3.96363			0.137414
$833$	−13.1553	−	27.0243i	−0.455804	−	0.936335i
$834$	−8.89865			−0.308135
$835$	−0.727705	−	1.75684i	−0.0251833	−	0.0607978i
$836$	−5.17526	+	3.44175i	−0.178990	+	0.119036i
$837$	19.5060	−	19.5060i	0.674226	−	0.674226i
$838$	5.65706	−	3.77993i	0.195420	−	0.130575i
$839$	−5.64128	+	1.12212i	−0.194759	+	0.0387399i	−0.291506	−	0.956569i	$-0.594156\pi$
$839$	−5.64128	+	1.12212i	−0.194759	+	0.0387399i	0.0967471	+	0.995309i	$0.469156\pi$
$840$	1.86671	−	2.79373i	0.0644076	−	0.0963927i
$841$	−15.5204	+	37.4695i	−0.535186	+	1.29205i
$842$	9.78955	−	23.6341i	0.337370	−	0.814484i
$843$	1.04241	−	1.56007i	0.0359024	−	0.0537317i
$844$	4.49417	−	0.893946i	0.154696	−	0.0307709i
$845$	−4.27308	+	2.85518i	−0.146999	+	0.0982213i
$846$	43.5011	−	43.5011i	1.49560	−	1.49560i
$847$	−8.28941	+	40.7472i	−0.284827	+	1.40009i
$848$	−13.6648	−	32.9897i	−0.469251	−	1.13287i
$849$	−0.440086			−0.0151037
$850$	28.9470	−	1.74847i	0.992875	−	0.0599721i
$851$	−14.9912			−0.513892
$852$	1.17862	−	0.488201i	0.0403789	−	0.0167255i
$853$	−3.69505	+	18.5763i	−0.126516	+	0.636039i	0.864537	+	0.502569i	$0.167612\pi$
$853$	−3.69505	+	18.5763i	−0.126516	+	0.636039i	−0.991053	+	0.133470i	$0.957388\pi$
$854$	12.8156	+	12.8156i	0.438542	+	0.438542i
$855$	4.25850	−	2.84544i	0.145638	−	0.0973120i
$856$	−11.1010	+	2.20813i	−0.379425	+	0.0754723i
$857$	−30.0017	−	20.0465i	−1.02484	−	0.684774i	−0.0748920	−	0.997192i	$-0.523861\pi$
$857$	−30.0017	−	20.0465i	−1.02484	−	0.684774i	−0.949945	+	0.312417i	$0.898861\pi$
$858$	7.52830	−	3.09917i	0.257012	−	0.105804i
$859$	22.2661	+	9.22291i	0.759709	+	0.314682i	0.728696	−	0.684837i	$-0.240127\pi$
$859$	22.2661	+	9.22291i	0.759709	+	0.314682i	0.0310126	+	0.999519i	$0.490127\pi$
$860$	−4.10819	+	6.14834i	−0.140088	+	0.209657i
$861$	0.174055	+	0.875034i	0.00593178	+	0.0298211i
$862$	16.5435	−	11.0540i	0.563472	−	0.376500i
$863$	−38.0884	−	38.0884i	−1.29654	−	1.29654i	−0.930661	−	0.365882i	$-0.880767\pi$
$863$	−38.0884	−	38.0884i	−1.29654	−	1.29654i	−0.365882	−	0.930661i	$-0.619233\pi$
$864$	14.5139	+	2.88700i	0.493775	+	0.0982179i
$865$	0.459903	−	0.190498i	0.0156372	−	0.00647713i
$866$	−38.6317			−1.31276
$867$	−8.78629	−	0.666318i	−0.298398	−	0.0226293i
$868$		−	33.3852i		−	1.13317i
$869$	14.7823	−	35.4694i	0.501455	−	1.20322i
$870$	−6.93150	−	1.37876i	−0.235000	−	0.0467444i
$871$	8.08683	+	8.08683i	0.274012	+	0.274012i
$872$	6.01363	+	9.00003i	0.203647	+	0.304780i
$873$	−35.0456	+	6.97101i	−1.18611	+	0.235933i
$874$	−2.47011	+	3.69678i	−0.0835527	+	0.125045i
$875$	−30.2265	−	12.5202i	−1.02184	−	0.423260i
$876$	−1.88591	+	4.55298i	−0.0637189	+	0.153831i
$877$	−21.2367	+	31.7829i	−0.717111	+	1.07323i	0.276570	+	0.960994i	$0.410802\pi$
$877$	−21.2367	+	31.7829i	−0.717111	+	1.07323i	−0.993681	+	0.112239i	$0.964198\pi$
$878$	10.9220	+	54.9084i	0.368598	+	1.85307i
$879$	−4.18722	−	6.26661i	−0.141231	−	0.211368i
$880$	−0.0342814	+	15.7742i	−0.00115562	+	0.531750i
$881$	1.06742	−	5.36631i	0.0359624	−	0.180795i	−0.958629	−	0.284658i	$-0.908120\pi$
$881$	1.06742	−	5.36631i	0.0359624	−	0.180795i	0.994592	+	0.103862i	$0.0331201\pi$
$882$	−31.6002	+	13.0892i	−1.06404	+	0.440738i
$883$			37.3981i			1.25855i	0.777184	+	0.629274i	$0.216647\pi$
$883$			37.3981i			1.25855i	−0.777184	+	0.629274i	$0.783353\pi$
$884$	−0.651791	−	10.7908i	−0.0219221	−	0.362934i
$885$	1.33310			0.0448118
$886$	−1.70953	−	4.12718i	−0.0574329	−	0.138655i
$887$	−2.04371	+	10.2744i	−0.0686210	+	0.344981i	−0.999809	−	0.0195589i	$-0.993774\pi$
$887$	−2.04371	+	10.2744i	−0.0686210	+	0.344981i	0.931188	+	0.364540i	$0.118774\pi$
$888$	7.53725	+	7.53725i	0.252934	+	0.252934i
$889$	24.9492	+	37.3391i	0.836768	+	1.25231i
$890$	0.980846	+	4.93105i	0.0328780	+	0.165289i
$891$	21.6548	−	4.25851i	0.725464	−	0.142666i
$892$	0.100857	−	0.243490i	0.00337694	−	0.00815266i
$893$	9.88626	−	23.8675i	0.330831	−	0.798697i
$894$	−1.47836	−	0.987806i	−0.0494436	−	0.0330372i
$895$	−0.435185	−	2.18782i	−0.0145466	−	0.0731308i
$896$	−39.0773	+	26.1106i	−1.30548	+	0.872295i
$897$	1.32719	−	1.32719i	0.0443136	−	0.0443136i
$898$	−45.6175	−	9.07388i	−1.52227	−	0.302799i
$899$	71.5501	−	29.6370i	2.38633	−	0.988449i
$900$		−	10.6359i		−	0.354529i
$901$	26.4878	−	12.8941i	0.882437	−	0.429566i
$902$	−1.83047	−	1.83845i	−0.0609481	−	0.0612136i
$903$	14.7888	−	6.12570i	0.492139	−	0.203851i
$904$	4.59787	−	23.1150i	0.152923	−	0.768795i
$905$	4.65440	−	4.65440i	0.154717	−	0.154717i
$906$	3.89282	+	5.82601i	0.129330	+	0.193556i
$907$	−33.3093	+	6.62564i	−1.10602	+	0.220001i	−0.714131	−	0.700013i	$-0.753178\pi$
$907$	−33.3093	+	6.62564i	−1.10602	+	0.220001i	−0.391887	+	0.920013i	$0.628178\pi$
$908$	−3.87080	−	2.58638i	−0.128457	−	0.0858322i
$909$	20.3486	+	8.42868i	0.674922	+	0.279562i
$910$	−6.51983	+	15.7403i	−0.216130	+	0.521784i
$911$	8.52807	+	5.69827i	0.282547	+	0.188792i	0.688766	−	0.724984i	$-0.258153\pi$
$911$	8.52807	+	5.69827i	0.282547	+	0.188792i	−0.406218	+	0.913776i	$0.633153\pi$
$912$	5.00589	−	0.995734i	0.165762	−	0.0329720i
$913$	8.88476	−	44.1649i	0.294043	−	1.46164i
$914$	−40.9994	−	40.9994i	−1.35614	−	1.35614i
$915$	−1.35027	−	0.268585i	−0.0446385	−	0.00887915i
$916$	−0.854721	−	2.06348i	−0.0282408	−	0.0681792i
$917$			8.38487i			0.276893i
$918$	−2.85323	+	20.8470i	−0.0941707	+	0.688053i
$919$		−	11.6261i		−	0.383509i	−0.981443	−	0.191755i	$-0.938582\pi$
$919$		−	11.6261i		−	0.383509i	0.981443	−	0.191755i	$-0.0614178\pi$
$920$	0.862000	+	2.08105i	0.0284193	+	0.0686102i
$921$	1.21572	−	6.11186i	0.0400595	−	0.201393i
$922$	−0.0322428	+	0.0322428i	−0.00106186	+	0.00106186i
$923$	5.93184	−	3.96353i	0.195249	−	0.130461i
$924$	−3.44489	+	5.13146i	−0.113328	+	0.168813i
$925$	25.9604	−	38.8526i	0.853574	−	1.27746i
$926$	−54.7764	−	22.6891i	−1.80006	−	0.745610i
$927$	32.7029	+	13.5460i	1.07410	+	0.444908i
$928$	34.5438	+	23.0814i	1.13395	+	0.757684i
$929$	−5.73954	−	28.8546i	−0.188308	−	0.946689i	−0.953156	−	0.302478i	$-0.902186\pi$
$929$	−5.73954	−	28.8546i	−0.188308	−	0.946689i	0.764848	−	0.644211i	$-0.222814\pi$
$930$	4.37167	+	6.54267i	0.143353	+	0.214543i
$931$	−10.1563	+	10.1563i	−0.332861	+	0.332861i
$932$	−7.95772	−	1.58289i	−0.260664	−	0.0518493i
$933$	3.53888	+	8.54360i	0.115858	+	0.279705i
$934$	48.1850			1.57666
$935$	−12.9920	+	0.756417i	−0.424885	+	0.0247375i
$936$	13.5679			0.443480
$937$	−5.46105	−	13.1841i	−0.178405	−	0.430707i	0.809228	−	0.587495i	$-0.199886\pi$
$937$	−5.46105	−	13.1841i	−0.178405	−	0.430707i	−0.987632	+	0.156788i	$0.949886\pi$
$938$	−26.4220	−	5.25566i	−0.862709	−	0.171603i
$939$	0.384450	−	0.384450i	0.0125460	−	0.0125460i
$940$	6.59320	+	9.86742i	0.215046	+	0.321840i
$941$	−6.75464	−	33.9578i	−0.220195	−	1.10699i	−0.919777	−	0.392442i	$-0.871630\pi$
$941$	−6.75464	−	33.9578i	−0.220195	−	1.10699i	0.699582	−	0.714552i	$-0.253370\pi$
$942$	−3.42977	−	2.29170i	−0.111748	−	0.0746676i
$943$	−0.552581	−	0.228887i	−0.0179945	−	0.00745358i
$944$	−12.4781	−	5.16859i	−0.406127	−	0.168223i
$945$	5.93745	−	8.88602i	0.193145	−	0.289062i
$946$	−25.9441	+	38.6460i	−0.843514	+	1.25649i
$947$	−19.9224	+	13.3117i	−0.647392	+	0.432574i	−0.835437	−	0.549587i	$-0.814785\pi$
$947$	−19.9224	+	13.3117i	−0.647392	+	0.432574i	0.188044	+	0.982161i	$0.439785\pi$
$948$	4.03867	−	4.03867i	0.131170	−	0.131170i
$949$	−5.37651	+	27.0295i	−0.174529	+	0.877416i
$950$	−5.30339	−	12.8035i	−0.172065	−	0.415401i
$951$		−	13.1210i		−	0.425479i
$952$	−16.9825	−	22.3683i	−0.550407	−	0.724960i
$953$		−	33.3277i		−	1.07959i	−0.841797	−	0.539795i	$-0.818502\pi$
$953$		−	33.3277i		−	1.07959i	0.841797	−	0.539795i	$-0.181498\pi$
$954$	−12.8294	−	30.9730i	−0.415368	−	1.00279i
$955$	8.84354	+	1.75909i	0.286170	+	0.0569228i
$956$	−4.58692	−	4.58692i	−0.148351	−	0.148351i
$957$	−14.0557	−	2.82763i	−0.454357	−	0.0914042i
$958$	−54.1444	+	10.7700i	−1.74933	+	0.347963i
$959$	22.5989	+	15.1001i	0.729757	+	0.487608i
$960$	0.271408	−	0.655237i	0.00875966	−	0.0211477i
$961$	−51.0243	−	21.1350i	−1.64595	−	0.681773i
$962$	−44.9400	−	30.0280i	−1.44892	−	0.968140i
$963$	−16.8270	+	3.34709i	−0.542241	+	0.107858i
$964$	0.577718	+	0.864616i	0.0186070	+	0.0278474i
$965$	−1.28561	+	1.28561i	−0.0413851	+	0.0413851i
$966$	−0.862547	+	4.33632i	−0.0277520	+	0.139519i
$967$	−32.8047	+	13.5882i	−1.05493	+	0.436966i	−0.841649	−	0.540025i	$-0.818415\pi$
$967$	−32.8047	+	13.5882i	−1.05493	+	0.436966i	−0.213280	+	0.976991i	$0.568415\pi$
$968$	−0.0861515	+	19.8208i	−0.00276901	+	0.637065i
$969$	1.06901	+	4.07290i	0.0343414	+	0.130840i
$970$		−	21.3878i		−	0.686721i
$971$	38.5215	−	15.9561i	1.23621	−	0.512056i	0.333684	−	0.942685i	$-0.391708\pi$
$971$	38.5215	−	15.9561i	1.23621	−	0.512056i	0.902529	+	0.430628i	$0.141708\pi$
$972$	11.5305	+	2.29357i	0.369842	+	0.0735662i
$973$	26.7133	−	26.7133i	0.856390	−	0.856390i
$974$	27.9769	−	18.6936i	0.896438	−	0.598981i
$975$	1.14136	+	5.73798i	0.0365526	+	0.183763i
$976$	11.5974	+	7.74915i	0.371224	+	0.248044i
$977$	9.73658	−	23.5062i	0.311501	−	0.752030i	−0.688149	−	0.725569i	$-0.741576\pi$
$977$	9.73658	−	23.5062i	0.311501	−	0.752030i	0.999650	−	0.0264602i	$-0.00842353\pi$
$978$	−1.60863	+	3.88358i	−0.0514384	+	0.124183i
$979$	1.96808	+	10.0078i	0.0629002	+	0.319852i
$980$	−1.28722	−	6.47129i	−0.0411187	−	0.206718i
$981$	9.11548	+	13.6423i	0.291035	+	0.435564i
$982$	14.9174	+	14.9174i	0.476034	+	0.476034i
$983$	4.64483	−	23.3512i	0.148147	−	0.744786i	−0.833265	−	0.552874i	$-0.813531\pi$
$983$	4.64483	−	23.3512i	0.148147	−	0.744786i	0.981412	−	0.191912i	$-0.0614689\pi$
$984$	0.162747	+	0.392905i	0.00518818	+	0.0125254i
$985$	16.6083			0.529185
$986$	−29.7978	+	51.0063i	−0.948954	+	1.62437i
$987$		−	25.6899i		−	0.817718i
$988$	−4.77286	+	1.97698i	−0.151845	+	0.0628963i
$989$	−2.09354	+	10.5250i	−0.0665708	+	0.334674i
$990$	−0.0321856	+	14.8099i	−0.00102293	+	0.470690i
$991$	11.2415	+	16.8241i	0.357099	+	0.534436i	0.965910	−	0.258879i	$-0.0833531\pi$
$991$	11.2415	+	16.8241i	0.357099	+	0.534436i	−0.608811	+	0.793315i	$0.708353\pi$
$992$	−9.02432	−	45.3683i	−0.286522	−	1.44044i
$993$	0.410391	−	0.614193i	0.0130234	−	0.0194908i
$994$	−6.43104	+	15.5259i	−0.203980	+	0.492452i
$995$	−12.2440	−	5.07161i	−0.388160	−	0.160781i
$996$	3.72009	−	5.56751i	0.117876	−	0.176413i
$997$	8.42894	−	1.67662i	0.266947	−	0.0530991i	−0.0598017	−	0.998210i	$-0.519047\pi$
$997$	8.42894	−	1.67662i	0.266947	−	0.0530991i	0.326749	+	0.945111i	$0.394047\pi$
$998$	16.9780	+	25.4094i	0.537430	+	0.804321i
$999$	23.9738	+	23.9738i	0.758496	+	0.758496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.54.4	✓	128
11.10	odd	2	inner	187.2.m.a.54.13	yes	128
17.6	odd	16	inner	187.2.m.a.142.13	yes	128
187.142	even	16	inner	187.2.m.a.142.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.54.4	✓	128	1.1	even	1	trivial
187.2.m.a.54.13	yes	128	11.10	odd	2	inner
187.2.m.a.142.4	yes	128	187.142	even	16	inner
187.2.m.a.142.13	yes	128	17.6	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.m (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.657401 - 1.58711i) q^{2} +(-0.508365 - 0.101120i) q^{3} +(-0.672515 + 0.672515i) q^{4} +(0.528726 + 0.791294i) q^{5} +(0.173711 + 0.873306i) q^{6} +(-3.14310 - 2.10015i) q^{7} +(-1.66475 - 0.689561i) q^{8} +(-2.52343 - 1.04524i) q^{9} +(0.908282 - 1.35934i) q^{10} +(1.84861 - 2.75366i) q^{11} +(0.409888 - 0.273879i) q^{12} +(1.94934 - 1.94934i) q^{13} +(-1.26689 + 6.36907i) q^{14} +(-0.188770 - 0.455731i) q^{15} +4.99761i q^{16} +(-4.11560 + 0.248593i) q^{17} +4.69209i q^{18} +(0.754020 + 1.82037i) q^{19} +(-0.887733 - 0.176581i) q^{20} +(1.38547 + 1.38547i) q^{21} +(-5.58563 - 1.12368i) q^{22} +(-1.28830 + 0.256259i) q^{23} +(0.776571 + 0.518888i) q^{24} +(1.56682 - 3.78264i) q^{25} +(-4.37531 - 1.81231i) q^{26} +(2.47004 + 1.65043i) q^{27} +(3.52616 - 0.701397i) q^{28} +(4.63349 + 6.93451i) q^{29} +(-0.599196 + 0.599196i) q^{30} +(1.81159 - 9.10750i) q^{31} +(4.60224 - 1.90631i) q^{32} +(-1.21822 + 1.21293i) q^{33} +(3.10014 + 6.36847i) q^{34} -3.59752i q^{35} +(2.39998 - 0.994105i) q^{36} +(11.1935 + 2.22653i) q^{37} +(2.39342 - 2.39342i) q^{38} +(-1.18810 + 0.793861i) q^{39} +(-0.334549 - 1.68189i) q^{40} +(0.378603 + 0.252974i) q^{41} +(1.28808 - 3.10970i) q^{42} +(3.12639 - 7.54776i) q^{43} +(0.608663 + 3.09509i) q^{44} +(-0.507111 - 2.54942i) q^{45} +(1.25364 + 1.87620i) q^{46} +(-9.27116 - 9.27116i) q^{47} +(0.505359 - 2.54061i) q^{48} +(2.78964 + 6.73479i) q^{49} -7.03348 q^{50} +(2.11737 + 0.289795i) q^{51} +2.62192i q^{52} +(-6.60110 + 2.73427i) q^{53} +(0.995599 - 5.00521i) q^{54} +(3.15636 + 0.00685955i) q^{55} +(3.78428 + 5.66357i) q^{56} +(-0.199242 - 1.00166i) q^{57} +(7.95974 - 11.9126i) q^{58} +(-1.03421 + 2.49681i) q^{59} +(0.433437 + 0.179535i) q^{60} +(1.55057 - 2.32059i) q^{61} +(-15.6455 + 3.11208i) q^{62} +(5.73622 + 8.58486i) q^{63} +(1.01666 + 1.01666i) q^{64} +(2.57317 + 0.511835i) q^{65} +(2.72591 + 1.13606i) q^{66} +4.14849i q^{67} +(2.60062 - 2.93499i) q^{68} +0.680840 q^{69} +(-5.70964 + 2.36501i) q^{70} +(2.53813 + 0.504865i) q^{71} +(3.48011 + 3.48011i) q^{72} +(-8.31205 + 5.55393i) q^{73} +(-3.82489 - 19.2290i) q^{74} +(-1.17902 + 1.76453i) q^{75} +(-1.73131 - 0.717134i) q^{76} +(-11.5935 + 4.77267i) q^{77} +(2.04100 + 1.36375i) q^{78} +(11.3634 - 2.26032i) q^{79} +(-3.95457 + 2.64236i) q^{80} +(4.70525 + 4.70525i) q^{81} +(0.152603 - 0.767188i) q^{82} +(12.5490 - 5.19798i) q^{83} -1.86350 q^{84} +(-2.37274 - 3.12521i) q^{85} -14.0344 q^{86} +(-1.65429 - 3.99381i) q^{87} +(-4.97628 + 3.30942i) q^{88} +(-2.17454 + 2.17454i) q^{89} +(-3.71282 + 2.48083i) q^{90} +(-10.2209 + 2.03306i) q^{91} +(0.694064 - 1.03874i) q^{92} +(-1.84190 + 4.44675i) q^{93} +(-8.61944 + 20.8092i) q^{94} +(-1.04177 + 1.55913i) q^{95} +(-2.53238 + 0.503722i) q^{96} +(10.8775 - 7.26814i) q^{97} +(8.85491 - 8.85491i) q^{98} +(-7.54306 + 5.01643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9} - 64 q^{12} + 16 q^{14} - 16 q^{15} - 16 q^{20} + 8 q^{22} - 32 q^{23} + 16 q^{26} + 32 q^{27} - 80 q^{31} - 16 q^{34} + 16 q^{36} + 16 q^{37} + 80 q^{38}+ \cdots - 112 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

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