LMFDB - Embedded newform 552.2.b.c.413.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(413,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("552.413");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.b (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			413.2
Character	$\chi$	$=$	552.413
Dual form			552.2.b.c.413.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} +2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} -1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +O(q^{10})$	\(q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} +2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} -1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +(0.226295 - 4.00580i) q^{10} -5.25468i q^{11} +(-1.25931 - 3.22710i) q^{12} +4.42296i q^{13} +(-0.120473 + 2.13257i) q^{14} +(4.34739 - 2.29055i) q^{15} +(3.89853 + 0.895261i) q^{16} +5.44908 q^{17} +(2.59248 - 3.35843i) q^{18} +0.278059 q^{19} +(-0.639039 + 5.63799i) q^{20} +(-2.31442 + 1.21942i) q^{21} +(-0.419136 + 7.41941i) q^{22} +(-2.74274 + 3.93413i) q^{23} +(1.52069 + 4.65699i) q^{24} -3.04882 q^{25} +(0.352794 - 6.24505i) q^{26} +(5.16121 + 0.601614i) q^{27} +(0.340205 - 3.00149i) q^{28} +3.90617 q^{29} +(-6.32106 + 2.88740i) q^{30} -0.0236931 q^{31} +(-5.43316 - 1.57504i) q^{32} +(-8.05210 + 4.24248i) q^{33} +(-7.69390 - 0.434642i) q^{34} +4.28495 q^{35} +(-3.92837 + 4.53519i) q^{36} +10.9457 q^{37} +(-0.392609 - 0.0221792i) q^{38} +(6.77760 - 3.57097i) q^{39} +(1.35201 - 7.90965i) q^{40} -7.21720i q^{41} +(3.36514 - 1.53717i) q^{42} +7.36445 q^{43} +(1.18361 - 10.4425i) q^{44} +(-7.01993 - 4.81248i) q^{45} +(4.18645 - 5.33607i) q^{46} +6.38523i q^{47} +(-1.77569 - 6.69678i) q^{48} +4.71882 q^{49} +(4.30481 + 0.243187i) q^{50} +(-4.39943 - 8.35000i) q^{51} +(-0.996265 + 8.78964i) q^{52} -9.62419i q^{53} +(-7.23944 - 1.26114i) q^{54} +14.9077 q^{55} +(-0.719769 + 4.21086i) q^{56} +(-0.224497 - 0.426089i) q^{57} +(-5.51537 - 0.311573i) q^{58} +9.58456 q^{59} +(9.15541 - 3.57271i) q^{60} +4.91803 q^{61} +(0.0334538 + 0.00188987i) q^{62} +(3.73720 + 2.56202i) q^{63} +(7.54579 + 2.65727i) q^{64} -12.5481 q^{65} +(11.7077 - 5.34795i) q^{66} -11.7718 q^{67} +(10.8288 + 1.22740i) q^{68} +(8.24294 + 1.02658i) q^{69} +(-6.05018 - 0.341786i) q^{70} +5.13535i q^{71} +(5.90846 - 6.09017i) q^{72} -10.4463 q^{73} +(-15.4549 - 0.873077i) q^{74} +(2.46153 + 4.67191i) q^{75} +(0.552580 + 0.0626324i) q^{76} -7.93644 q^{77} +(-9.85456 + 4.50147i) q^{78} -13.3643i q^{79} +(-2.53989 + 11.0603i) q^{80} +(-3.24512 - 8.39459i) q^{81} +(-0.575675 + 10.1904i) q^{82} +2.01019i q^{83} +(-4.87407 + 1.90200i) q^{84} +15.4593i q^{85} +(-10.3983 - 0.587420i) q^{86} +(-3.15373 - 5.98569i) q^{87} +(-2.50415 + 14.6500i) q^{88} +13.9059 q^{89} +(9.52801 + 7.35498i) q^{90} +6.68025 q^{91} +(-6.33673 + 7.20040i) q^{92} +(0.0191292 + 0.0363066i) q^{93} +(0.509313 - 9.01570i) q^{94} +0.788866i q^{95} +(1.97304 + 9.59724i) q^{96} +10.1465i q^{97} +(-6.66280 - 0.376394i) q^{98} +(13.0021 + 8.91352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) $ 80 * q - 12 * q^6 - 4 * q^9	$ 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) $ 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41196	−	0.0797643i	−0.998408	−	0.0564019i
$2$	−1.41196	−	0.0797643i	−0.998408	−	0.0564019i
$3$	−0.807372	−	1.53237i	−0.466136	−	0.884713i
$3$	−0.807372	−	1.53237i	−0.466136	−	0.884713i
$4$	1.98728	+	0.225248i	0.993638	+	0.112624i
$5$			2.83704i			1.26876i	0.773020	+	0.634382i	$0.218745\pi$
$5$			2.83704i			1.26876i	−0.773020	+	0.634382i	$0.781255\pi$
$6$	1.01775	+	2.22805i	0.415495	+	0.909596i
$7$		−	1.51036i		−	0.570861i	−0.958399	−	0.285431i	$-0.907863\pi$
$7$		−	1.51036i		−	0.570861i	0.958399	−	0.285431i	$-0.0921366\pi$
$8$	−2.78799	−	0.476556i	−0.985704	−	0.168488i
$9$	−1.69630	+	2.47438i	−0.565434	+	0.824794i
$10$	0.226295	−	4.00580i	0.0715607	−	1.26674i
$11$		−	5.25468i		−	1.58434i	−0.610297	−	0.792172i	$-0.708950\pi$
$11$		−	5.25468i		−	1.58434i	0.610297	−	0.792172i	$-0.291050\pi$
$12$	−1.25931	−	3.22710i	−0.363530	−	0.931582i
$13$			4.42296i			1.22671i	0.789808	+	0.613354i	$0.210180\pi$
$13$			4.42296i			1.22671i	−0.789808	+	0.613354i	$0.789820\pi$
$14$	−0.120473	+	2.13257i	−0.0321976	+	0.569952i
$15$	4.34739	−	2.29055i	1.12249	−	0.591417i
$16$	3.89853	+	0.895261i	0.974632	+	0.223815i
$17$	5.44908			1.32160			0.660798	−	0.750564i	$-0.270218\pi$
$17$	5.44908			1.32160			0.660798	+	0.750564i	$0.270218\pi$
$18$	2.59248	−	3.35843i	0.611054	−	0.791589i
$19$	0.278059			0.0637912			0.0318956	−	0.999491i	$-0.489846\pi$
$19$	0.278059			0.0637912			0.0318956	+	0.999491i	$0.489846\pi$
$20$	−0.639039	+	5.63799i	−0.142894	+	1.26069i
$21$	−2.31442	+	1.21942i	−0.505048	+	0.266099i
$22$	−0.419136	+	7.41941i	−0.0893600	+	1.58182i
$23$	−2.74274	+	3.93413i	−0.571900	+	0.820323i
$23$	−2.74274	+	3.93413i	−0.571900	+	0.820323i
$24$	1.52069	+	4.65699i	0.310409	+	0.950603i
$25$	−3.04882			−0.609763
$26$	0.352794	−	6.24505i	0.0691887	−	1.22476i
$27$	5.16121	+	0.601614i	0.993275	+	0.115781i
$28$	0.340205	−	3.00149i	0.0642928	−	0.567229i
$29$	3.90617			0.725358			0.362679	−	0.931914i	$-0.381862\pi$
$29$	3.90617			0.725358			0.362679	+	0.931914i	$0.381862\pi$
$30$	−6.32106	+	2.88740i	−1.15406	+	0.527165i
$31$	−0.0236931			−0.00425542			−0.00212771	−	0.999998i	$-0.500677\pi$
$31$	−0.0236931			−0.00425542			−0.00212771	+	0.999998i	$0.500677\pi$
$32$	−5.43316	−	1.57504i	−0.960457	−	0.278430i
$33$	−8.05210	+	4.24248i	−1.40169	+	0.738521i
$34$	−7.69390	−	0.434642i	−1.31949	−	0.0745405i
$35$	4.28495			0.724288
$36$	−3.92837	+	4.53519i	−0.654728	+	0.755864i
$37$	10.9457			1.79946			0.899732	−	0.436443i	$-0.143762\pi$
$37$	10.9457			1.79946			0.899732	+	0.436443i	$0.143762\pi$
$38$	−0.392609	−	0.0221792i	−0.0636896	−	0.00359794i
$39$	6.77760	−	3.57097i	1.08528	−	0.571813i
$40$	1.35201	−	7.90965i	0.213771	−	1.25063i
$41$		−	7.21720i		−	1.12714i	−0.826069	−	0.563569i	$-0.809428\pi$
$41$		−	7.21720i		−	1.12714i	0.826069	−	0.563569i	$-0.190572\pi$
$42$	3.36514	−	1.53717i	0.519253	−	0.237190i
$43$	7.36445			1.12307			0.561534	−	0.827454i	$-0.310211\pi$
$43$	7.36445			1.12307			0.561534	+	0.827454i	$0.310211\pi$
$44$	1.18361	−	10.4425i	0.178436	−	1.57426i
$45$	−7.01993	−	4.81248i	−1.04647	−	0.717403i
$46$	4.18645	−	5.33607i	0.617258	−	0.786761i
$47$			6.38523i			0.931381i	0.884948	+	0.465691i	$0.154194\pi$
$47$			6.38523i			0.931381i	−0.884948	+	0.465691i	$0.845806\pi$
$48$	−1.77569	−	6.69678i	−0.256299	−	0.966598i
$49$	4.71882			0.674118
$50$	4.30481	+	0.243187i	0.608792	+	0.0343918i
$51$	−4.39943	−	8.35000i	−0.616044	−	1.16923i
$52$	−0.996265	+	8.78964i	−0.138157	+	1.21890i
$53$		−	9.62419i		−	1.32198i	−0.750393	−	0.660992i	$-0.770136\pi$
$53$		−	9.62419i		−	1.32198i	0.750393	−	0.660992i	$-0.229864\pi$
$54$	−7.23944	−	1.26114i	−0.985163	−	0.171619i
$55$	14.9077			2.01016
$56$	−0.719769	+	4.21086i	−0.0961832	+	0.562700i
$57$	−0.224497	−	0.426089i	−0.0297354	−	0.0564369i
$58$	−5.51537	−	0.311573i	−0.724203	−	0.0409115i
$59$	9.58456			1.24780			0.623902	−	0.781503i	$-0.285547\pi$
$59$	9.58456			1.24780			0.623902	+	0.781503i	$0.285547\pi$
$60$	9.15541	−	3.57271i	1.18196	−	0.461235i
$61$	4.91803			0.629690			0.314845	−	0.949143i	$-0.398048\pi$
$61$	4.91803			0.629690			0.314845	+	0.949143i	$0.398048\pi$
$62$	0.0334538	+	0.00188987i	0.00424864	+	0.000240013i
$63$	3.73720	+	2.56202i	0.470843	+	0.322784i
$64$	7.54579	+	2.65727i	0.943224	+	0.332158i
$65$	−12.5481			−1.55640
$66$	11.7077	−	5.34795i	1.44111	−	0.658287i
$67$	−11.7718			−1.43815			−0.719074	−	0.694933i	$-0.755434\pi$
$67$	−11.7718			−1.43815			−0.719074	+	0.694933i	$0.755434\pi$
$68$	10.8288	+	1.22740i	1.31319	+	0.148844i
$69$	8.24294	+	1.02658i	0.992334	+	0.123585i
$70$	−6.05018	−	0.341786i	−0.723135	−	0.0408512i
$71$			5.13535i			0.609454i	0.952440	+	0.304727i	$0.0985653\pi$
$71$			5.13535i			0.609454i	−0.952440	+	0.304727i	$0.901435\pi$
$72$	5.90846	−	6.09017i	0.696318	−	0.717733i
$73$	−10.4463			−1.22265			−0.611325	−	0.791380i	$-0.709363\pi$
$73$	−10.4463			−1.22265			−0.611325	+	0.791380i	$0.709363\pi$
$74$	−15.4549	−	0.873077i	−1.79660	−	0.101493i
$75$	2.46153	+	4.67191i	0.284233	+	0.539465i
$76$	0.552580	+	0.0626324i	0.0633853	+	0.00718443i
$77$	−7.93644			−0.904441
$78$	−9.85456	+	4.50147i	−1.11581	+	0.509691i
$79$		−	13.3643i		−	1.50360i	−0.659392	−	0.751799i	$-0.729186\pi$
$79$		−	13.3643i		−	1.50360i	0.659392	−	0.751799i	$-0.270814\pi$
$80$	−2.53989	+	11.0603i	−0.283969	+	1.23658i
$81$	−3.24512	−	8.39459i	−0.360569	−	0.932733i
$82$	−0.575675	+	10.1904i	−0.0635726	+	1.12534i
$83$			2.01019i			0.220647i	0.993896	+	0.110323i	$0.0351887\pi$
$83$			2.01019i			0.220647i	−0.993896	+	0.110323i	$0.964811\pi$
$84$	−4.87407	+	1.90200i	−0.531804	+	0.207525i
$85$			15.4593i			1.67679i
$86$	−10.3983	−	0.587420i	−1.12128	−	0.0633431i
$87$	−3.15373	−	5.98569i	−0.338115	−	0.641733i
$88$	−2.50415	+	14.6500i	−0.266943	+	1.56169i
$89$	13.9059			1.47402			0.737012	−	0.675880i	$-0.236236\pi$
$89$	13.9059			1.47402			0.737012	+	0.675880i	$0.236236\pi$
$90$	9.52801	+	7.35498i	1.00434	+	0.775283i
$91$	6.68025			0.700280
$92$	−6.33673	+	7.20040i	−0.660650	+	0.750694i
$93$	0.0191292	+	0.0363066i	0.00198360	+	0.00376482i
$94$	0.509313	−	9.01570i	0.0525317	−	0.929899i
$95$			0.788866i			0.0809360i
$96$	1.97304	+	9.59724i	0.201373	+	0.979515i
$97$			10.1465i			1.03023i	0.857123	+	0.515113i	$0.172250\pi$
$97$			10.1465i			1.03023i	−0.857123	+	0.515113i	$0.827750\pi$
$98$	−6.66280	−	0.376394i	−0.673044	−	0.0380215i
$99$	13.0021	+	8.91352i	1.30676	+	0.895842i
$100$	−6.05884	−	0.686741i	−0.605884	−	0.0686741i
$101$	7.70417			0.766594			0.383297	−	0.923625i	$-0.374789\pi$
$101$	7.70417			0.766594			0.383297	+	0.923625i	$0.374789\pi$
$102$	5.54580	+	12.1408i	0.549116	+	1.20212i
$103$			3.66936i			0.361553i	0.983524	+	0.180777i	$0.0578611\pi$
$103$			3.66936i			0.361553i	−0.983524	+	0.180777i	$0.942139\pi$
$104$	2.10779	−	12.3312i	0.206686	−	1.20917i
$105$	−3.45954	−	6.56611i	−0.337617	−	0.640787i
$106$	−0.767667	+	13.5890i	−0.0745624	+	1.31988i
$107$			6.54109i			0.632352i	0.948701	+	0.316176i	$0.102399\pi$
$107$			6.54109i			0.632352i	−0.948701	+	0.316176i	$0.897601\pi$
$108$	10.1212	+	2.35813i	0.973916	+	0.226911i
$109$	−0.715038			−0.0684882			−0.0342441	−	0.999413i	$-0.510902\pi$
$109$	−0.715038			−0.0684882			−0.0342441	+	0.999413i	$0.510902\pi$
$110$	−21.0492	−	1.18911i	−2.00696	−	0.113377i
$111$	−8.83725	−	16.7729i	−0.838795	−	1.59201i
$112$	1.35216	−	5.88816i	0.127767	−	0.556379i
$113$	2.54869			0.239760			0.119880	−	0.992788i	$-0.461749\pi$
$113$	2.54869			0.239760			0.119880	+	0.992788i	$0.461749\pi$
$114$	0.282995	+	0.619529i	0.0265049	+	0.0580242i
$115$	−11.1613	−	7.78127i	−1.04080	−	0.725607i
$116$	7.76264	+	0.879858i	0.720743	+	0.0816928i
$117$	−10.9441	−	7.50268i	−1.01178	−	0.693623i
$118$	−13.5330	−	0.764506i	−1.24582	−	0.0703785i
$119$		−	8.23005i		−	0.754448i
$120$	−13.2121	+	4.31425i	−1.20609	+	0.393836i
$121$	−16.6116			−1.51015
$122$	−6.94408	−	0.392283i	−0.628687	−	0.0355157i
$123$	−11.0594	+	5.82696i	−0.997193	+	0.525399i
$124$	−0.0470848	−	0.00533684i	−0.00422834	−	0.000479263i
$125$			5.53560i			0.495119i
$126$	−5.07242	−	3.91557i	−0.451887	−	0.348827i
$127$	−1.27108			−0.112790			−0.0563950	−	0.998409i	$-0.517961\pi$
$127$	−1.27108			−0.112790			−0.0563950	+	0.998409i	$0.517961\pi$
$128$	−10.4424	−	4.35385i	−0.922988	−	0.384829i
$129$	−5.94585	−	11.2850i	−0.523503	−	0.993593i
$130$	17.7175	+	1.00089i	1.55393	+	0.0877841i
$131$	−10.9007			−0.952399			−0.476199	−	0.879337i	$-0.657986\pi$
$131$	−10.9007			−0.952399			−0.476199	+	0.879337i	$0.657986\pi$
$132$	−16.9573	+	6.61725i	−1.47595	+	0.575958i
$133$		−	0.419969i		−	0.0364159i
$134$	16.6213	+	0.938965i	1.43586	+	0.0811143i
$135$	−1.70680	+	14.6426i	−0.146898	+	1.26023i
$136$	−15.1920	−	2.59679i	−1.30270	−	0.222673i
$137$	−9.56299			−0.817021			−0.408511	−	0.912754i	$-0.633952\pi$
$137$	−9.56299			−0.817021			−0.408511	+	0.912754i	$0.633952\pi$
$138$	−11.5568	−	2.10698i	−0.983784	−	0.179358i
$139$			19.6353i			1.66545i	0.553690	+	0.832723i	$0.313219\pi$
$139$			19.6353i			1.66545i	−0.553690	+	0.832723i	$0.686781\pi$
$140$	8.51537	+	0.965177i	0.719680	+	0.0815724i
$141$	9.78452	−	5.15525i	0.824005	−	0.434151i
$142$	0.409618	−	7.25093i	0.0343744	−	0.608484i
$143$	23.2412			1.94353
$144$	−8.82829	+	8.12781i	−0.735691	+	0.677317i
$145$			11.0820i			0.920308i
$146$	14.7498	+	0.833243i	1.22070	+	0.0689597i
$147$	−3.80984	−	7.23097i	−0.314231	−	0.596401i
$148$	21.7521	+	2.46550i	1.78801	+	0.202663i
$149$		−	13.2630i		−	1.08655i	−0.839556	−	0.543274i	$-0.817185\pi$
$149$		−	13.2630i		−	1.08655i	0.839556	−	0.543274i	$-0.182815\pi$
$150$	−3.10293	−	6.79290i	−0.253353	−	0.554638i
$151$	0.702221			0.0571460			0.0285730	−	0.999592i	$-0.490904\pi$
$151$	0.702221			0.0571460			0.0285730	+	0.999592i	$0.490904\pi$
$152$	−0.775227	−	0.132511i	−0.0628792	−	0.0107480i
$153$	−9.24329	+	13.4831i	−0.747275	+	1.09004i
$154$	11.2059	+	0.633044i	0.903001	+	0.0510122i
$155$		−	0.0672185i		−	0.00539912i
$156$	14.2733	−	5.56986i	1.14278	−	0.445946i
$157$	−7.53792			−0.601592			−0.300796	−	0.953689i	$-0.597252\pi$
$157$	−7.53792			−0.601592			−0.300796	+	0.953689i	$0.597252\pi$
$158$	−1.06599	+	18.8698i	−0.0848057	+	1.50120i
$159$	−14.7478	+	7.77030i	−1.16958	+	0.616225i
$160$	4.46845	−	15.4141i	0.353262	−	1.21859i
$161$	5.94194	+	4.14251i	0.468291	+	0.326476i
$162$	3.91240	+	12.1117i	0.307387	+	0.951585i
$163$			4.73461i			0.370843i	0.982659	+	0.185421i	$0.0593650\pi$
$163$			4.73461i			0.370843i	−0.982659	+	0.185421i	$0.940635\pi$
$164$	1.62566	−	14.3426i	0.126943	−	1.11997i
$165$	−12.0361	−	22.8442i	−0.937009	−	1.77841i
$166$	0.160341	−	2.83831i	0.0124449	−	0.220296i
$167$			12.7163i			0.984019i	0.870590	+	0.492009i	$0.163737\pi$
$167$			12.7163i			0.984019i	−0.870590	+	0.492009i	$0.836263\pi$
$168$	7.03371	−	2.29678i	0.542662	−	0.177200i
$169$	−6.56258			−0.504814
$170$	1.23310	−	21.8279i	0.0945743	−	1.67412i
$171$	−0.471673	+	0.688025i	−0.0360697	+	0.0526146i
$172$	14.6352	+	1.65883i	1.11592	+	0.126485i
$173$	5.13533			0.390432			0.195216	−	0.980760i	$-0.437459\pi$
$173$	5.13533			0.390432			0.195216	+	0.980760i	$0.437459\pi$
$174$	3.97551	+	8.70312i	0.301382	+	0.659782i
$175$			4.60480i			0.348090i
$176$	4.70431	−	20.4855i	0.354601	−	1.54415i
$177$	−7.73830	−	14.6871i	−0.581646	−	1.10395i
$178$	−19.6346	−	1.10920i	−1.47168	−	0.0831377i
$179$	−16.0763			−1.20160			−0.600799	−	0.799400i	$-0.705151\pi$
$179$	−16.0763			−1.20160			−0.600799	+	0.799400i	$0.705151\pi$
$180$	−12.8665	−	11.1450i	−0.959014	−	0.830696i
$181$	−17.9778			−1.33628			−0.668138	−	0.744037i	$-0.732909\pi$
$181$	−17.9778			−1.33628			−0.668138	+	0.744037i	$0.732909\pi$
$182$	−9.43226	−	0.532845i	−0.699165	−	0.0394971i
$183$	−3.97068	−	7.53623i	−0.293521	−	0.557094i
$184$	9.52156	−	9.66126i	0.701939	−	0.712237i
$185$			31.0535i			2.28310i
$186$	−0.0241137	−	0.0527894i	−0.00176810	−	0.00387071i
$187$		−	28.6332i		−	2.09386i
$188$	−1.43826	+	12.6892i	−0.104896	+	0.925456i
$189$	0.908651	−	7.79526i	0.0660946	−	0.567022i
$190$	0.0629234	−	1.11385i	0.00456494	−	0.0808071i
$191$	17.2840			1.25063			0.625313	−	0.780374i	$-0.284971\pi$
$191$	17.2840			1.25063			0.625313	+	0.780374i	$0.284971\pi$
$192$	−2.02035	−	13.7083i	−0.145806	−	0.989313i
$193$	6.00676			0.432376			0.216188	−	0.976352i	$-0.430638\pi$
$193$	6.00676			0.432376			0.216188	+	0.976352i	$0.430638\pi$
$194$	0.809332	−	14.3265i	0.0581066	−	1.02859i
$195$	10.1310	+	19.2284i	0.725496	+	1.37697i
$196$	9.37760	+	1.06291i	0.669829	+	0.0759219i
$197$	−3.33454			−0.237576			−0.118788	−	0.992920i	$-0.537901\pi$
$197$	−3.33454			−0.237576			−0.118788	+	0.992920i	$0.537901\pi$
$198$	−17.6475	−	13.6227i	−1.25415	−	0.968120i
$199$		−	5.44215i		−	0.385784i	−0.981220	−	0.192892i	$-0.938213\pi$
$199$		−	5.44215i		−	0.385784i	0.981220	−	0.192892i	$-0.0617867\pi$
$200$	8.50007	+	1.45293i	0.601046	+	0.102738i
$201$	9.50418	+	18.0387i	0.670373	+	1.27235i
$202$	−10.8780	−	0.614518i	−0.765373	−	0.0432373i
$203$		−	5.89971i		−	0.414078i
$204$	−6.86206	−	17.5847i	−0.480440	−	1.23118i
$205$	20.4755			1.43007
$206$	0.292684	−	5.18100i	0.0203923	−	0.360978i
$207$	−5.08203	−	13.4601i	−0.353225	−	0.935538i
$208$	−3.95970	+	17.2430i	−0.274556	+	1.19559i
$209$		−	1.46111i		−	0.101067i
$210$	4.36101	+	9.54706i	0.300938	+	0.658809i
$211$		−	6.98441i		−	0.480826i	−0.970671	−	0.240413i	$-0.922717\pi$
$211$		−	6.98441i		−	0.480826i	0.970671	−	0.240413i	$-0.0772829\pi$
$212$	2.16783	−	19.1259i	0.148887	−	1.31357i
$213$	7.86925	−	4.14614i	0.539192	−	0.284089i
$214$	0.521746	−	9.23578i	0.0356658	−	0.631345i
$215$			20.8933i			1.42491i
$216$	−14.1027	−	4.13690i	−0.959567	−	0.281480i
$217$			0.0357851i			0.00242925i
$218$	1.00961	+	0.0570345i	0.0683792	+	0.00386286i
$219$	8.43406	+	16.0076i	0.569921	+	1.08169i
$220$	29.6258	+	3.35795i	1.99737	+	0.226393i
$221$			24.1011i			1.62121i
$222$	11.1400	+	24.3875i	0.747668	+	1.63678i
$223$	3.51479			0.235368			0.117684	−	0.993051i	$-0.462453\pi$
$223$	3.51479			0.235368			0.117684	+	0.993051i	$0.462453\pi$
$224$	−2.37887	+	8.20601i	−0.158945	+	0.548287i
$225$	5.17171	−	7.54393i	0.344781	−	0.502929i
$226$	−3.59865	−	0.203294i	−0.239379	−	0.0135229i
$227$			3.95674i			0.262618i	0.991341	+	0.131309i	$0.0419180\pi$
$227$			3.95674i			0.262618i	−0.991341	+	0.131309i	$0.958082\pi$
$228$	−0.350162	−	0.897324i	−0.0231900	−	0.0594267i
$229$	−14.4693			−0.956161			−0.478081	−	0.878316i	$-0.658667\pi$
$229$	−14.4693			−0.956161			−0.478081	+	0.878316i	$0.658667\pi$
$230$	15.1387	+	11.8771i	0.998214	+	0.783155i
$231$	6.40765	+	12.1615i	0.421593	+	0.800171i
$232$	−10.8904	−	1.86151i	−0.714988	−	0.122214i
$233$		−	6.38619i		−	0.418373i	−0.977876	−	0.209186i	$-0.932918\pi$
$233$		−	6.38619i		−	0.418373i	0.977876	−	0.209186i	$-0.0670816\pi$
$234$	14.8542	+	11.4664i	0.971049	+	0.749585i
$235$	−18.1152			−1.18170
$236$	19.0472	+	2.15891i	1.23986	+	0.140533i
$237$	−20.4790	+	10.7899i	−1.33025	+	0.700882i
$238$	−0.656465	+	11.6205i	−0.0425523	+	0.753247i
$239$			3.65421i			0.236371i	0.992992	+	0.118185i	$0.0377077\pi$
$239$			3.65421i			0.236371i	−0.992992	+	0.118185i	$0.962292\pi$
$240$	18.9991	−	5.03771i	1.22638	−	0.325183i
$241$		−	14.5478i		−	0.937107i	−0.883435	−	0.468553i	$-0.844775\pi$
$241$		−	14.5478i		−	0.937107i	0.883435	−	0.468553i	$-0.155225\pi$
$242$	23.4550	+	1.32502i	1.50774	+	0.0851752i
$243$	−10.2436	+	11.7503i	−0.657126	+	0.753780i
$244$	9.77348	+	1.10778i	0.625683	+	0.0709183i
$245$			13.3875i			0.855296i
$246$	16.0802	−	7.34531i	1.02524	−	0.468320i
$247$			1.22985i			0.0782532i
$248$	0.0660563	+	0.0112911i	0.00419458	+	0.000716986i
$249$	3.08035	−	1.62297i	0.195209	−	0.102851i
$250$	0.441543	−	7.81605i	0.0279256	−	0.494331i
$251$		−	5.58993i		−	0.352833i	−0.984316	−	0.176417i	$-0.943549\pi$
$251$		−	5.58993i		−	0.352833i	0.984316	−	0.176417i	$-0.0564506\pi$
$252$	6.84975	+	5.93324i	0.431494	+	0.373759i
$253$	20.6726	+	14.4122i	1.29967	+	0.906087i
$254$	1.79471	+	0.101387i	0.112610	+	0.00636156i
$255$	23.6893	−	12.4814i	1.48348	−	0.781615i
$256$	14.3970	+	6.98040i	0.899813	+	0.436275i
$257$		−	3.98354i		−	0.248486i	−0.992252	−	0.124243i	$-0.960350\pi$
$257$		−	3.98354i		−	0.248486i	0.992252	−	0.124243i	$-0.0396503\pi$
$258$	7.49517	+	16.4083i	0.466629	+	1.02154i
$259$		−	16.5319i		−	1.02724i
$260$	−24.9366	−	2.82645i	−1.54650	−	0.175289i
$261$	−6.62604	+	9.66535i	−0.410142	+	0.598270i
$262$	15.3914	+	0.869487i	0.950883	+	0.0537171i
$263$	−8.31685			−0.512839			−0.256419	−	0.966566i	$-0.582543\pi$
$263$	−8.31685			−0.512839			−0.256419	+	0.966566i	$0.582543\pi$
$264$	24.4710	−	7.99072i	1.50608	−	0.491795i
$265$	27.3042			1.67729
$266$	−0.0334985	+	0.592980i	−0.00205393	+	0.0363579i
$267$	−11.2272	−	21.3090i	−0.687096	−	1.30409i
$268$	−23.3937	−	2.65157i	−1.42900	−	0.161970i
$269$	6.72690			0.410146			0.205073	−	0.978747i	$-0.434257\pi$
$269$	6.72690			0.410146			0.205073	+	0.978747i	$0.434257\pi$
$270$	3.57790	−	20.5386i	0.217744	−	1.24994i
$271$	−11.4000			−0.692500			−0.346250	−	0.938142i	$-0.612545\pi$
$271$	−11.4000			−0.692500			−0.346250	+	0.938142i	$0.612545\pi$
$272$	21.2434	+	4.87835i	1.28807	+	0.295793i
$273$	−5.39344	−	10.2366i	−0.326426	−	0.619547i
$274$	13.5026	+	0.762785i	0.815721	+	0.0460815i
$275$			16.0205i			0.966075i
$276$	16.1498	+	3.89680i	0.972102	+	0.234560i
$277$			24.3492i			1.46300i	0.681842	+	0.731500i	$0.261179\pi$
$277$			24.3492i			1.46300i	−0.681842	+	0.731500i	$0.738821\pi$
$278$	1.56620	−	27.7243i	0.0939343	−	1.66279i
$279$	0.0401907	−	0.0586259i	0.00240616	−	0.00350984i
$280$	−11.9464	−	2.04202i	−0.713934	−	0.122034i
$281$	−3.27622			−0.195443			−0.0977215	−	0.995214i	$-0.531155\pi$
$281$	−3.27622			−0.195443			−0.0977215	+	0.995214i	$0.531155\pi$
$282$	−14.2266	+	6.49857i	−0.847180	+	0.386984i
$283$	20.5517			1.22167			0.610836	−	0.791757i	$-0.290833\pi$
$283$	20.5517			1.22167			0.610836	+	0.791757i	$0.290833\pi$
$284$	−1.15673	+	10.2054i	−0.0686393	+	0.605577i
$285$	1.20883	−	0.636908i	0.0716051	−	0.0377272i
$286$	−32.8157	−	1.85382i	−1.94044	−	0.109619i
$287$	−10.9005			−0.643439
$288$	13.1135	−	10.7720i	0.772722	−	0.634745i
$289$	12.6925			0.746616
$290$	0.883946	−	15.6473i	0.0519071	−	0.918843i
$291$	15.5482	−	8.19203i	0.911453	−	0.480225i
$292$	−20.7597	−	2.35302i	−1.21487	−	0.137700i
$293$		−	2.96154i		−	0.173015i	−0.996251	−	0.0865076i	$-0.972429\pi$
$293$		−	2.96154i		−	0.173015i	0.996251	−	0.0865076i	$-0.0275707\pi$
$294$	4.80258	+	10.5138i	0.280092	+	0.613174i
$295$			27.1918i			1.58317i
$296$	−30.5165	−	5.21624i	−1.77374	−	0.303188i
$297$	3.16129	−	27.1205i	0.183436	−	1.57369i
$298$	−1.05791	+	18.7269i	−0.0612833	+	1.08482i
$299$	−17.4005	−	12.1310i	−1.00630	−	0.701555i
$300$	3.83939	+	9.83882i	0.221667	+	0.568045i
$301$		−	11.1229i		−	0.641116i
$302$	−0.991510	−	0.0560122i	−0.0570550	−	0.00322314i
$303$	−6.22013	−	11.8056i	−0.357337	−	0.678215i
$304$	1.08402	+	0.248936i	0.0621729	+	0.0142774i
$305$			13.9527i			0.798928i
$306$	14.1266	−	18.3003i	0.807566	−	1.04616i
$307$		−	16.2366i		−	0.926672i	−0.886183	−	0.463336i	$-0.846652\pi$
$307$		−	16.2366i		−	0.926672i	0.886183	−	0.463336i	$-0.153348\pi$
$308$	−15.7719	−	1.78767i	−0.898687	−	0.101862i
$309$	5.62282	−	2.96254i	0.319871	−	0.168533i
$310$	−0.00536164	+	0.0949100i	−0.000304520	+	0.00539052i
$311$			5.86765i			0.332724i	0.986065	+	0.166362i	$0.0532020\pi$
$311$			5.86765i			0.332724i	−0.986065	+	0.166362i	$0.946798\pi$
$312$	−20.5977	+	6.72594i	−1.16611	+	0.380781i
$313$			11.2752i			0.637313i	0.947870	+	0.318656i	$0.103232\pi$
$313$			11.2752i			0.637313i	−0.947870	+	0.318656i	$0.896768\pi$
$314$	10.6433	+	0.601257i	0.600634	+	0.0339309i
$315$	−7.26856	+	10.6026i	−0.409537	+	0.597388i
$316$	3.01028	−	26.5585i	0.169341	−	1.49403i
$317$	−29.8569			−1.67693			−0.838466	−	0.544954i	$-0.816547\pi$
$317$	−29.8569			−1.67693			−0.838466	+	0.544954i	$0.816547\pi$
$318$	21.4431	−	9.79502i	1.20247	−	0.549277i
$319$		−	20.5257i		−	1.14922i
$320$	−7.53878	+	21.4077i	−0.421431	+	1.19673i
$321$	10.0234	−	5.28109i	0.559450	−	0.294762i
$322$	−8.05937	−	6.32303i	−0.449131	−	0.352368i
$323$	1.51517			0.0843062
$324$	−4.55808	−	17.4133i	−0.253226	−	0.967407i
$325$		−	13.4848i		−	0.748002i
$326$	0.377653	−	6.68509i	0.0209162	−	0.370253i
$327$	0.577301	+	1.09570i	0.0319248	+	0.0605924i
$328$	−3.43940	+	20.1215i	−0.189909	+	1.11102i
$329$	9.64397			0.531689
$330$	15.1724	+	33.2151i	0.835211	+	1.82843i
$331$		−	29.3591i		−	1.61372i	−0.590740	−	0.806862i	$-0.701164\pi$
$331$		−	29.3591i		−	1.61372i	0.590740	−	0.806862i	$-0.298836\pi$
$332$	−0.452792	+	3.99480i	−0.0248502	+	0.219243i
$333$	−18.5672	+	27.0838i	−1.01748	+	1.48419i
$334$	1.01431	−	17.9550i	0.0555005	−	0.982452i
$335$		−	33.3970i		−	1.82467i
$336$	−10.1145	+	2.68193i	−0.551793	+	0.146311i
$337$		−	35.2740i		−	1.92150i	−0.277417	−	0.960750i	$-0.589478\pi$
$337$		−	35.2740i		−	1.92150i	0.277417	−	0.960750i	$-0.410522\pi$
$338$	9.26612	+	0.523460i	0.504010	+	0.0284724i
$339$	−2.05774	−	3.90553i	−0.111761	−	0.212119i
$340$	−3.48218	+	30.7218i	−0.188848	+	1.66613i
$341$			0.124500i			0.00674205i
$342$	0.720864	−	0.933842i	0.0389798	−	0.0504964i
$343$		−	17.6996i		−	0.955689i
$344$	−20.5320	−	3.50957i	−1.10701	−	0.189223i
$345$	−2.91244	+	23.3856i	−0.156801	+	1.25904i
$346$	−7.25090	−	0.409616i	−0.389811	−	0.0220211i
$347$	13.5906			0.729581			0.364790	−	0.931090i	$-0.381141\pi$
$347$	13.5906			0.729581			0.364790	+	0.931090i	$0.381141\pi$
$348$	−4.91907	−	12.6056i	−0.263690	−	0.675730i
$349$		−	22.5138i		−	1.20514i	−0.798067	−	0.602568i	$-0.794144\pi$
$349$		−	22.5138i		−	1.20514i	0.798067	−	0.602568i	$-0.205856\pi$
$350$	0.367299	−	6.50180i	0.0196329	−	0.347536i
$351$	−2.66091	+	22.8278i	−0.142029	+	1.21846i
$352$	−8.27632	+	28.5495i	−0.441129	+	1.52169i
$353$		−	12.0054i		−	0.638984i	−0.947589	−	0.319492i	$-0.896488\pi$
$353$		−	12.0054i		−	0.638984i	0.947589	−	0.319492i	$-0.103512\pi$
$354$	9.75469	+	21.3548i	0.518456	+	1.13500i
$355$	−14.5692			−0.773254
$356$	27.6349	+	3.13228i	1.46465	+	0.166011i
$357$	−12.6115	+	6.64471i	−0.667470	+	0.351675i
$358$	22.6991	+	1.28231i	1.19969	+	0.0677724i
$359$	12.3407			0.651317			0.325658	−	0.945488i	$-0.394414\pi$
$359$	12.3407			0.651317			0.325658	+	0.945488i	$0.394414\pi$
$360$	17.2781	+	16.7625i	0.910634	+	0.883464i
$361$	−18.9227			−0.995931
$362$	25.3839	+	1.43398i	1.33415	+	0.0753685i
$363$	13.4118	+	25.4551i	0.703935	+	1.33605i
$364$	13.2755	+	1.50471i	0.695825	+	0.0788685i
$365$		−	29.6367i		−	1.55125i
$366$	5.00533	+	10.9576i	0.261633	+	0.572763i
$367$			10.4677i			0.546408i	0.961956	+	0.273204i	$0.0880834\pi$
$367$			10.4677i			0.546408i	−0.961956	+	0.273204i	$0.911917\pi$
$368$	−14.2147	+	12.8818i	−0.740993	+	0.671513i
$369$	17.8581	+	12.2425i	0.929655	+	0.637322i
$370$	2.47696	−	43.8463i	0.128771	−	2.27946i
$371$	−14.5360			−0.754669
$372$	0.0298369	+	0.0764601i	0.00154697	+	0.00396427i
$373$	19.0982			0.988867			0.494433	−	0.869216i	$-0.335376\pi$
$373$	19.0982			0.988867			0.494433	+	0.869216i	$0.335376\pi$
$374$	−2.28390	+	40.4289i	−0.118098	+	2.09053i
$375$	8.48257	−	4.46928i	0.438038	−	0.230793i
$376$	3.04292	−	17.8020i	0.156927	−	0.918066i
$377$			17.2768i			0.889802i
$378$	−1.90476	+	10.9341i	−0.0979705	+	0.562391i
$379$	−27.6320			−1.41936			−0.709680	−	0.704524i	$-0.751161\pi$
$379$	−27.6320			−1.41936			−0.709680	+	0.704524i	$0.751161\pi$
$380$	−0.177691	+	1.56769i	−0.00911535	+	0.0804210i
$381$	1.02623	+	1.94776i	0.0525755	+	0.0997867i
$382$	−24.4044	−	1.37865i	−1.24864	−	0.0705377i
$383$	−24.5172			−1.25277			−0.626384	−	0.779514i	$-0.715466\pi$
$383$	−24.5172			−1.25277			−0.626384	+	0.779514i	$0.715466\pi$
$384$	1.75922	+	19.5168i	0.0897747	+	0.995962i
$385$		−	22.5160i		−	1.14752i
$386$	−8.48132	−	0.479125i	−0.431688	−	0.0243868i
$387$	−12.4923	+	18.2224i	−0.635021	+	0.926299i
$388$	−2.28549	+	20.1640i	−0.116028	+	1.02367i
$389$			17.6113i			0.892929i	0.894801	+	0.446465i	$0.147317\pi$
$389$			17.6113i			0.892929i	−0.894801	+	0.446465i	$0.852683\pi$
$390$	−12.7709	−	27.9578i	−0.646678	−	1.41570i
$391$	−14.9454	+	21.4374i	−0.755821	+	1.08414i
$392$	−13.1560	−	2.24878i	−0.664480	−	0.113581i
$393$	8.80092	+	16.7039i	0.443948	+	0.842600i
$394$	4.70824	+	0.265977i	0.237198	+	0.0133997i
$395$	37.9150			1.90771
$396$	23.8309	+	20.6423i	1.19755	+	1.03732i
$397$		−	26.0926i		−	1.30955i	−0.755825	−	0.654774i	$-0.772764\pi$
$397$		−	26.0926i		−	1.30955i	0.755825	−	0.654774i	$-0.227236\pi$
$398$	−0.434090	+	7.68412i	−0.0217589	+	0.385170i
$399$	−0.643547	+	0.339071i	−0.0322176	+	0.0169748i
$400$	−11.8859	−	2.72949i	−0.594294	−	0.136474i
$401$	5.82998			0.291135			0.145568	−	0.989348i	$-0.453499\pi$
$401$	5.82998			0.291135			0.145568	+	0.989348i	$0.453499\pi$
$402$	−11.9807	−	26.2280i	−0.597543	−	1.30813i
$403$		−	0.104794i		−	0.00522015i
$404$	15.3103	+	1.73535i	0.761716	+	0.0863370i
$405$	23.8158	−	9.20654i	1.18342	−	0.457477i
$406$	−0.470586	+	8.33017i	−0.0233548	+	0.413419i
$407$		−	57.5162i		−	2.85097i
$408$	8.28634	+	25.3763i	0.410235	+	1.25631i
$409$	33.6916			1.66594			0.832971	−	0.553317i	$-0.186638\pi$
$409$	33.6916			1.66594			0.832971	+	0.553317i	$0.186638\pi$
$410$	−28.9106	−	1.63321i	−1.42779	−	0.0806587i
$411$	7.72089	+	14.6540i	0.380843	+	0.722829i
$412$	−0.826518	+	7.29204i	−0.0407196	+	0.359253i
$413$		−	14.4761i		−	0.712323i
$414$	6.10200	+	19.4105i	0.299897	+	0.953972i
$415$	−5.70299			−0.279949
$416$	6.96633	−	24.0307i	0.341552	−	1.17820i
$417$	30.0885	−	15.8530i	1.47344	−	0.776325i
$418$	−0.116545	+	2.06304i	−0.00570038	+	0.100906i
$419$			17.4910i			0.854490i	0.904136	+	0.427245i	$0.140516\pi$
$419$			17.4910i			0.854490i	−0.904136	+	0.427245i	$0.859484\pi$
$420$	−5.39606	−	13.8279i	−0.263301	−	0.674734i
$421$	−18.6829			−0.910550			−0.455275	−	0.890351i	$-0.650459\pi$
$421$	−18.6829			−0.910550			−0.455275	+	0.890351i	$0.650459\pi$
$422$	−0.557106	+	9.86172i	−0.0271195	+	0.480061i
$423$	−15.7995	−	10.8313i	−0.768197	−	0.526635i
$424$	−4.58646	+	26.8322i	−0.222738	+	1.30308i
$425$	−16.6132			−0.805861
$426$	−11.4418	+	5.22651i	−0.554357	+	0.253225i
$427$		−	7.42798i		−	0.359465i
$428$	−1.47337	+	12.9990i	−0.0712181	+	0.628328i
$429$	−18.7643	−	35.6141i	−0.905950	−	1.71947i
$430$	1.66654	−	29.5005i	0.0803675	−	1.42264i
$431$	−3.99271			−0.192322			−0.0961610	−	0.995366i	$-0.530656\pi$
$431$	−3.99271			−0.192322			−0.0961610	+	0.995366i	$0.530656\pi$
$432$	19.5825	+	6.96603i	0.942164	+	0.335153i
$433$		−	20.4619i		−	0.983336i	−0.870783	−	0.491668i	$-0.836387\pi$
$433$		−	20.4619i		−	0.983336i	0.870783	−	0.491668i	$-0.163613\pi$
$434$	0.00285437	−	0.0505272i	0.000137014	−	0.00242538i
$435$	16.9817	−	8.94727i	0.814208	−	0.428989i
$436$	−1.42098	−	0.161061i	−0.0680525	−	0.00771343i
$437$	−0.762644	+	1.09392i	−0.0364822	+	0.0523294i
$438$	−10.6317	−	23.2749i	−0.508004	−	1.11212i
$439$	13.4074			0.639900			0.319950	−	0.947434i	$-0.396334\pi$
$439$	13.4074			0.639900			0.319950	+	0.947434i	$0.396334\pi$
$440$	−41.5627	−	7.10437i	−1.98142	−	0.338688i
$441$	−8.00455	+	11.6762i	−0.381169	+	0.556008i
$442$	1.92240	−	34.0298i	0.0914395	−	1.61863i
$443$	35.7620			1.69910			0.849552	−	0.527505i	$-0.176873\pi$
$443$	35.7620			1.69910			0.849552	+	0.527505i	$0.176873\pi$
$444$	−13.7840	−	35.3229i	−0.654160	−	1.67635i
$445$			39.4517i			1.87019i
$446$	−4.96275	−	0.280355i	−0.234993	−	0.0132752i
$447$	−20.3238	+	10.7082i	−0.961283	+	0.506479i
$448$	4.01342	−	11.3968i	0.189616	−	0.538450i
$449$			12.9815i			0.612636i	0.951929	+	0.306318i	$0.0990971\pi$
$449$			12.9815i			0.612636i	−0.951929	+	0.306318i	$0.900903\pi$
$450$	−7.90400	+	10.2392i	−0.372598	+	0.482682i
$451$	−37.9241			−1.78577
$452$	5.06494	+	0.574088i	0.238235	+	0.0270028i
$453$	−0.566954	−	1.07606i	−0.0266378	−	0.0505578i
$454$	0.315607	−	5.58677i	0.0148122	−	0.262200i
$455$			18.9522i			0.888491i
$456$	0.422841	+	1.29492i	0.0198013	+	0.0606401i
$457$			23.2473i			1.08746i	0.839259	+	0.543732i	$0.182989\pi$
$457$			23.2473i			1.08746i	−0.839259	+	0.543732i	$0.817011\pi$
$458$	20.4302	+	1.15414i	0.954639	+	0.0539293i
$459$	28.1238	+	3.27824i	1.31271	+	0.153015i
$460$	−20.4279	−	17.9776i	−0.952454	−	0.838209i
$461$	−26.5945			−1.23863			−0.619314	−	0.785143i	$-0.712589\pi$
$461$	−26.5945			−1.23863			−0.619314	+	0.785143i	$0.712589\pi$
$462$	−8.07731	−	17.6827i	−0.375790	−	0.822675i
$463$	−22.2831			−1.03558			−0.517791	−	0.855507i	$-0.673246\pi$
$463$	−22.2831			−1.03558			−0.517791	+	0.855507i	$0.673246\pi$
$464$	15.2283	+	3.49704i	0.706956	+	0.162346i
$465$	−0.103003	+	0.0542703i	−0.00477667	+	0.00251673i
$466$	−0.509390	+	9.01705i	−0.0235970	+	0.417707i
$467$			9.03811i			0.418234i	0.977891	+	0.209117i	$0.0670589\pi$
$467$			9.03811i			0.418234i	−0.977891	+	0.209117i	$0.932941\pi$
$468$	−20.0590	−	17.3750i	−0.927225	−	0.803161i
$469$			17.7795i			0.820983i
$470$	25.5779	+	1.44494i	1.17982	+	0.0666503i
$471$	6.08590	+	11.5509i	0.280424	+	0.532236i
$472$	−26.7217	−	4.56758i	−1.22996	−	0.210240i
$473$		−	38.6978i		−	1.77933i
$474$	29.7762	−	13.6015i	1.36767	−	0.624737i
$475$	−0.847752			−0.0388975
$476$	1.85381	−	16.3554i	0.0849691	−	0.749648i
$477$	23.8139	+	16.3255i	1.09036	+	0.747495i
$478$	0.291475	−	5.15960i	0.0133318	−	0.235995i
$479$	−9.04841			−0.413432			−0.206716	−	0.978401i	$-0.566278\pi$
$479$	−9.04841			−0.413432			−0.206716	+	0.978401i	$0.566278\pi$
$480$	−27.2278	+	5.59761i	−1.24277	+	0.255495i
$481$			48.4124i			2.20742i
$482$	−1.16040	+	20.5410i	−0.0528546	+	0.935615i
$483$	1.55050	−	12.4498i	0.0705501	−	0.566485i
$484$	−33.0119	−	3.74174i	−1.50054	−	0.170079i
$485$	−28.7862			−1.30711
$486$	15.4008	−	15.7739i	0.698595	−	0.715517i
$487$	−12.0729			−0.547076			−0.273538	−	0.961861i	$-0.588194\pi$
$487$	−12.0729			−0.547076			−0.273538	+	0.961861i	$0.588194\pi$
$488$	−13.7114	−	2.34372i	−0.620687	−	0.106095i
$489$	7.25516	−	3.82259i	0.328090	−	0.172863i
$490$	1.06785	−	18.9027i	0.0482403	−	0.853935i
$491$	−1.06548			−0.0480844			−0.0240422	−	0.999711i	$-0.507654\pi$
$491$	−1.06548			−0.0480844			−0.0240422	+	0.999711i	$0.507654\pi$
$492$	−23.2906	+	9.08867i	−1.05002	+	0.409749i
$493$	21.2850			0.958630
$494$	0.0980978	−	1.73650i	0.00441363	−	0.0781286i
$495$	−25.2880	+	36.8874i	−1.13661	+	1.65797i
$496$	−0.0923684	−	0.0212116i	−0.00414746	−	0.000952427i
$497$	7.75622			0.347914
$498$	−4.47879	+	2.04587i	−0.200699	+	0.0916776i
$499$			15.7374i			0.704501i	0.935906	+	0.352250i	$0.114583\pi$
$499$			15.7374i			0.704501i	−0.935906	+	0.352250i	$0.885417\pi$
$500$	−1.24688	+	11.0008i	−0.0557623	+	0.491969i
$501$	19.4861	−	10.2668i	0.870574	−	0.458687i
$502$	−0.445877	+	7.89277i	−0.0199004	+	0.352271i
$503$	−0.610236			−0.0272091			−0.0136045	−	0.999907i	$-0.504331\pi$
$503$	−0.610236			−0.0272091			−0.0136045	+	0.999907i	$0.504331\pi$
$504$	−9.19833	−	8.92387i	−0.409726	−	0.397501i
$505$			21.8571i			0.972627i
$506$	−28.0393	−	21.9984i	−1.24650	−	0.977949i
$507$	5.29844	+	10.0563i	0.235312	+	0.446615i
$508$	−2.52598	−	0.286308i	−0.112072	−	0.0127029i
$509$	34.2520			1.51819			0.759095	−	0.650979i	$-0.225642\pi$
$509$	34.2520			1.51819			0.759095	+	0.650979i	$0.225642\pi$
$510$	−34.4440	+	15.7337i	−1.52520	+	0.696699i
$511$			15.7777i			0.697963i
$512$	−19.7713	−	11.0044i	−0.873774	−	0.486332i
$513$	1.43512	+	0.167284i	0.0633622	+	0.00738578i
$514$	−0.317744	+	5.62461i	−0.0140151	+	0.248091i
$515$	−10.4101			−0.458726
$516$	−9.27410	−	23.7658i	−0.408269	−	1.04623i
$517$	33.5523			1.47563
$518$	−1.31866	+	23.3425i	−0.0579385	+	1.02561i
$519$	−4.14612	−	7.86922i	−0.181995	−	0.345420i
$520$	34.9841	+	5.97989i	1.53415	+	0.262235i
$521$	−12.3295			−0.540165			−0.270083	−	0.962837i	$-0.587051\pi$
$521$	−12.3295			−0.540165			−0.270083	+	0.962837i	$0.587051\pi$
$522$	10.1267	−	13.1186i	0.443233	−	0.574185i
$523$	0.786343			0.0343844			0.0171922	−	0.999852i	$-0.494527\pi$
$523$	0.786343			0.0343844			0.0171922	+	0.999852i	$0.494527\pi$
$524$	−21.6627	−	2.45537i	−0.946339	−	0.107263i
$525$	7.05624	−	3.71778i	0.307960	−	0.162257i
$526$	11.7431	+	0.663387i	0.512022	+	0.0289251i
$527$	−0.129106			−0.00562394
$528$	−35.1894	+	9.33068i	−1.53142	+	0.406066i
$529$	−7.95478	−	21.5806i	−0.345860	−	0.938286i
$530$	−38.5526	−	2.17790i	−1.67462	−	0.0946021i
$531$	−16.2583	+	23.7159i	−0.705551	+	1.02918i
$532$	0.0945973	−	0.834593i	0.00410131	−	0.0361842i
$533$	31.9214			1.38267
$534$	14.1527	+	30.9830i	0.612449	+	1.34077i
$535$	−18.5574			−0.802305
$536$	32.8195	+	5.60990i	1.41759	+	0.242311i
$537$	12.9795	+	24.6348i	0.560109	+	1.06307i
$538$	−9.49813	−	0.536566i	−0.409493	−	0.0231330i
$539$		−	24.7959i		−	1.06803i
$540$	−6.69010	+	28.7144i	−0.287896	+	1.23567i
$541$			14.9417i			0.642394i	0.947012	+	0.321197i	$0.104085\pi$
$541$			14.9417i			0.642394i	−0.947012	+	0.321197i	$0.895915\pi$
$542$	16.0964	+	0.909313i	0.691398	+	0.0390583i
$543$	14.5147	+	27.5485i	0.622887	+	1.18222i
$544$	−29.6057	−	8.58251i	−1.26934	−	0.367972i
$545$		−	2.02859i		−	0.0868954i
$546$	6.79882	+	14.8839i	0.290963	+	0.636972i
$547$			26.1652i			1.11874i	0.828917	+	0.559371i	$0.188957\pi$
$547$			26.1652i			1.11874i	−0.828917	+	0.559371i	$0.811043\pi$
$548$	−19.0043	−	2.15405i	−0.811823	−	0.0920164i
$549$	−8.34247	+	12.1691i	−0.356048	+	0.519364i
$550$	1.27787	−	22.6204i	0.0544884	−	0.964537i
$551$	1.08615			0.0462714
$552$	−22.4920	−	6.79031i	−0.957325	−	0.289015i
$553$	−20.1848			−0.858346
$554$	1.94219	−	34.3801i	0.0825159	−	1.46067i
$555$	47.5853	−	25.0717i	2.01988	−	1.06423i
$556$	−4.42282	+	39.0208i	−0.187569	+	1.65485i
$557$			31.3190i			1.32703i	0.748164	+	0.663513i	$0.230935\pi$
$557$			31.3190i			1.32703i	−0.748164	+	0.663513i	$0.769065\pi$
$558$	−0.0614241	+	0.0795717i	−0.00260029	+	0.00336854i
$559$			32.5727i			1.37768i
$560$	16.7050	+	3.83615i	0.705914	+	0.162107i
$561$	−43.8765	+	23.1176i	−1.85247	+	0.976026i
$562$	4.62590	+	0.261325i	0.195132	+	0.0110233i
$563$		−	43.2187i		−	1.82145i	−0.413014	−	0.910725i	$-0.635524\pi$
$563$		−	43.2187i		−	1.82145i	0.413014	−	0.910725i	$-0.364476\pi$
$564$	20.6057	−	8.04096i	0.867658	−	0.338585i
$565$			7.23074i			0.304199i
$566$	−29.0182	−	1.63929i	−1.21973	−	0.0689046i
$567$	−12.6788	+	4.90129i	−0.532461	+	0.205835i
$568$	2.44728	−	14.3173i	0.102686	−	0.600741i
$569$	−9.00515			−0.377515			−0.188758	−	0.982024i	$-0.560446\pi$
$569$	−9.00515			−0.377515			−0.188758	+	0.982024i	$0.560446\pi$
$570$	−1.75763	+	0.802869i	−0.0736190	+	0.0336285i
$571$	39.7928			1.66528			0.832639	−	0.553816i	$-0.186829\pi$
$571$	39.7928			1.66528			0.832639	+	0.553816i	$0.186829\pi$
$572$	46.1867	+	5.23505i	1.93116	+	0.218888i
$573$	−13.9546	−	26.4855i	−0.582963	−	1.10645i
$574$	15.3912	+	0.869474i	0.642414	+	0.0362912i
$575$	8.36210	−	11.9944i	0.348724	−	0.500203i
$576$	−19.3750	+	14.1636i	−0.807293	+	0.590151i
$577$	26.7652			1.11425			0.557126	−	0.830428i	$-0.311904\pi$
$577$	26.7652			1.11425			0.557126	+	0.830428i	$0.311904\pi$
$578$	−17.9213	−	1.01241i	−0.745428	−	0.0421106i
$579$	−4.84969	−	9.20456i	−0.201546	−	0.382529i
$580$	−2.49620	+	22.0229i	−0.103649	+	0.914453i
$581$	3.03610			0.125959
$582$	−22.6069	+	10.3266i	−0.937088	+	0.428053i
$583$	−50.5720			−2.09448
$584$	29.1242	+	4.97825i	1.20517	+	0.206002i
$585$	21.2854	−	31.0489i	0.880044	−	1.28371i
$586$	−0.236225	+	4.18159i	−0.00975838	+	0.172740i
$587$	−31.7614			−1.31094			−0.655468	−	0.755223i	$-0.727528\pi$
$587$	−31.7614			−1.31094			−0.655468	+	0.755223i	$0.727528\pi$
$588$	−5.94244	−	15.2281i	−0.245062	−	0.627996i
$589$	−0.00658810			−0.000271458
$590$	2.16894	−	38.3938i	0.0892937	−	1.58065i
$591$	2.69221	+	5.10974i	0.110743	+	0.210187i
$592$	42.6721	+	9.79927i	1.75381	+	0.402747i
$593$		−	22.6400i		−	0.929712i	−0.885386	−	0.464856i	$-0.846106\pi$
$593$		−	22.6400i		−	0.929712i	0.885386	−	0.464856i	$-0.153894\pi$
$594$	−6.62686	+	38.0409i	−0.271903	+	1.56084i
$595$	23.3490			0.957217
$596$	2.98747	−	26.3572i	0.122372	−	1.07963i
$597$	−8.33938	+	4.39384i	−0.341308	+	0.179828i
$598$	23.6012	+	18.5165i	0.965126	+	0.757195i
$599$		−	14.8241i		−	0.605697i	−0.953039	−	0.302848i	$-0.902062\pi$
$599$		−	14.8241i		−	0.605697i	0.953039	−	0.302848i	$-0.0979376\pi$
$600$	−4.63629	−	14.1983i	−0.189276	−	0.579643i
$601$	4.48110			0.182788			0.0913939	−	0.995815i	$-0.470868\pi$
$601$	4.48110			0.182788			0.0913939	+	0.995815i	$0.470868\pi$
$602$	−0.887214	+	15.7052i	−0.0361601	+	0.640095i
$603$	19.9684	−	29.1278i	0.813178	−	1.18618i
$604$	1.39551	+	0.158174i	0.0567824	+	0.00643602i
$605$		−	47.1279i		−	1.91602i
$606$	7.84092	+	17.1652i	0.318516	+	0.697290i
$607$	38.8731			1.57781			0.788905	−	0.614516i	$-0.210648\pi$
$607$	38.8731			1.57781			0.788905	+	0.614516i	$0.210648\pi$
$608$	−1.51074	−	0.437954i	−0.0612687	−	0.0177614i
$609$	−9.04052	+	4.76326i	−0.366341	+	0.193017i
$610$	1.11293	−	19.7006i	0.0450610	−	0.797656i
$611$	−28.2416			−1.14253
$612$	−21.4060	+	24.7126i	−0.865286	+	0.998947i
$613$	−47.3280			−1.91156			−0.955780	−	0.294084i	$-0.904986\pi$
$613$	−47.3280			−1.91156			−0.955780	+	0.294084i	$0.904986\pi$
$614$	−1.29510	+	22.9255i	−0.0522661	+	0.925197i
$615$	−16.5313	−	31.3760i	−0.666608	−	1.26520i
$616$	22.1267	+	3.78216i	0.891511	+	0.152387i
$617$	18.2646			0.735307			0.367653	−	0.929963i	$-0.380161\pi$
$617$	18.2646			0.735307			0.367653	+	0.929963i	$0.380161\pi$
$618$	−8.17551	+	3.73450i	−0.328867	+	0.150223i
$619$	5.94337			0.238884			0.119442	−	0.992841i	$-0.461889\pi$
$619$	5.94337			0.238884			0.119442	+	0.992841i	$0.461889\pi$
$620$	0.0151409	−	0.133582i	0.000608071	−	0.00536477i
$621$	−16.5227	+	18.6548i	−0.663032	+	0.748591i
$622$	0.468029	−	8.28490i	0.0187663	−	0.332194i
$623$		−	21.0029i		−	0.841463i
$624$	29.6196	−	7.85381i	1.18573	−	0.314404i
$625$	−30.9488			−1.23795
$626$	0.899359	−	15.9202i	0.0359456	−	0.636298i
$627$	−2.23896	+	1.17966i	−0.0894155	+	0.0471111i
$628$	−14.9799	−	1.69790i	−0.597764	−	0.0677538i
$629$	59.6440			2.37816
$630$	11.1086	−	14.3907i	0.442579	−	0.573339i
$631$			12.8561i			0.511794i	0.966704	+	0.255897i	$0.0823709\pi$
$631$			12.8561i			0.511794i	−0.966704	+	0.255897i	$0.917629\pi$
$632$	−6.36882	+	37.2595i	−0.253338	+	1.48210i
$633$	−10.7027	+	5.63901i	−0.425393	+	0.224131i
$634$	42.1569	+	2.38152i	1.67426	+	0.0945821i
$635$		−	3.60610i		−	0.143104i
$636$	−31.0582	+	12.1198i	−1.23154	+	0.480581i
$637$			20.8712i			0.826946i
$638$	−1.63722	+	28.9815i	−0.0648180	+	1.14739i
$639$	−12.7068	−	8.71111i	−0.502674	−	0.344606i
$640$	12.3520	−	29.6256i	0.488258	−	1.17105i
$641$	−37.2339			−1.47065			−0.735326	−	0.677714i	$-0.762971\pi$
$641$	−37.2339			−1.47065			−0.735326	+	0.677714i	$0.762971\pi$
$642$	−14.5739	+	6.65720i	−0.575184	+	0.262739i
$643$	4.26786			0.168308			0.0841541	−	0.996453i	$-0.473181\pi$
$643$	4.26786			0.168308			0.0841541	+	0.996453i	$0.473181\pi$
$644$	10.8752	+	9.57072i	0.428542	+	0.377139i
$645$	32.0162	−	16.8686i	1.26064	−	0.664202i
$646$	−2.13936	−	0.120856i	−0.0841720	−	0.00475503i
$647$		−	1.13278i		−	0.0445340i	−0.999752	−	0.0222670i	$-0.992912\pi$
$647$		−	1.13278i		−	0.0445340i	0.999752	−	0.0222670i	$-0.00708839\pi$
$648$	5.04687	+	24.9505i	0.198260	+	0.980150i
$649$		−	50.3638i		−	1.97695i
$650$	−1.07560	+	19.0400i	−0.0421887	+	0.746811i
$651$	0.0548359	−	0.0288919i	0.00214919	−	0.00113236i
$652$	−1.06646	+	9.40897i	−0.0417659	+	0.368484i
$653$	27.5832			1.07941			0.539707	−	0.841853i	$-0.318535\pi$
$653$	27.5832			1.07941			0.539707	+	0.841853i	$0.318535\pi$
$654$	−0.727730	−	1.59314i	−0.0284565	−	0.0622966i
$655$		−	30.9258i		−	1.20837i
$656$	6.46128	−	28.1364i	0.252270	−	1.09854i
$657$	17.7201	−	25.8482i	0.691327	−	1.00843i
$658$	−13.6169	−	0.769245i	−0.530843	−	0.0299883i
$659$			27.3110i			1.06388i	0.846781	+	0.531942i	$0.178538\pi$
$659$			27.3110i			1.06388i	−0.846781	+	0.531942i	$0.821462\pi$
$660$	−18.7734	−	48.1087i	−0.730755	−	1.87263i
$661$	8.45225			0.328754			0.164377	−	0.986398i	$-0.447439\pi$
$661$	8.45225			0.328754			0.164377	+	0.986398i	$0.447439\pi$
$662$	−2.34181	+	41.4540i	−0.0910171	+	1.61116i
$663$	36.9317	−	19.4585i	1.43431	−	0.755706i
$664$	0.957967	−	5.60439i	0.0371763	−	0.217492i
$665$	1.19147			0.0462032
$666$	28.3765	−	36.7604i	1.09957	−	1.42444i
$667$	−10.7136	+	15.3674i	−0.414832	+	0.595028i
$668$	−2.86433	+	25.2708i	−0.110824	+	0.977758i
$669$	−2.83774	−	5.38595i	−0.109713	−	0.208233i
$670$	−2.66389	+	47.1553i	−0.102915	+	1.82177i
$671$		−	25.8427i		−	0.997645i
$672$	14.4953	−	2.98000i	0.559167	−	0.114956i
$673$	28.7225			1.10717			0.553585	−	0.832793i	$-0.313260\pi$
$673$	28.7225			1.10717			0.553585	+	0.832793i	$0.313260\pi$
$674$	−2.81361	+	49.8056i	−0.108376	+	1.91844i
$675$	−15.7356	−	1.83421i	−0.605662	−	0.0705987i
$676$	−13.0417	−	1.47821i	−0.501602	−	0.0568542i
$677$			7.23891i			0.278214i	0.990277	+	0.139107i	$0.0444232\pi$
$677$			7.23891i			0.278214i	−0.990277	+	0.139107i	$0.955577\pi$
$678$	2.59393	+	5.67859i	0.0996191	+	0.218085i
$679$	15.3249			0.588115
$680$	7.36721	−	43.1003i	0.282520	−	1.65282i
$681$	6.06318	−	3.19456i	0.232342	−	0.122416i
$682$	0.00993064	−	0.175789i	0.000380264	−	0.00673131i
$683$	11.1797			0.427778			0.213889	−	0.976858i	$-0.431387\pi$
$683$	11.1797			0.427778			0.213889	+	0.976858i	$0.431387\pi$
$684$	−1.09232	+	1.26105i	−0.0417659	+	0.0482175i
$685$		−	27.1306i		−	1.03661i
$686$	−1.41180	+	24.9912i	−0.0539026	+	0.954167i
$687$	11.6821	+	22.1724i	0.445701	+	0.845928i
$688$	28.7105	+	6.59310i	1.09458	+	0.251360i
$689$	42.5674			1.62169
$690$	5.97760	−	32.7873i	0.227563	−	1.24819i
$691$		−	9.57423i		−	0.364221i	−0.983278	−	0.182110i	$-0.941707\pi$
$691$		−	9.57423i		−	0.364221i	0.983278	−	0.182110i	$-0.0582928\pi$
$692$	10.2053	+	1.15673i	0.387948	+	0.0439721i
$693$	13.4626	−	19.6378i	0.511402	−	0.745977i
$694$	−19.1894	−	1.08404i	−0.728419	−	0.0411497i
$695$	−55.7062			−2.11306
$696$	5.94006	+	18.1910i	0.225157	+	0.689527i
$697$		−	39.3271i		−	1.48962i
$698$	−1.79580	+	31.7886i	−0.0679719	+	1.20322i
$699$	−9.78599	+	5.15603i	−0.370140	+	0.195019i
$700$	−1.03722	+	9.15100i	−0.0392034	+	0.345875i
$701$			12.8330i			0.484697i	0.970189	+	0.242349i	$0.0779178\pi$
$701$			12.8330i			0.484697i	−0.970189	+	0.242349i	$0.922082\pi$
$702$	5.57795	−	32.0198i	0.210526	−	1.20851i
$703$	3.04356			0.114790
$704$	13.9631	−	39.6507i	0.526253	−	1.49439i
$705$	14.6257	+	27.7591i	0.550835	+	1.04547i
$706$	−0.957603	+	16.9512i	−0.0360399	+	0.637966i
$707$		−	11.6360i		−	0.437618i
$708$	−12.0699	−	30.9303i	−0.453615	−	1.16243i
$709$	2.20392			0.0827701			0.0413850	−	0.999143i	$-0.486823\pi$
$709$	2.20392			0.0827701			0.0413850	+	0.999143i	$0.486823\pi$
$710$	20.5712	+	1.16210i	0.772023	+	0.0436130i
$711$	33.0683	+	22.6698i	1.24016	+	0.850185i
$712$	−38.7696	−	6.62694i	−1.45295	−	0.248355i
$713$	0.0649841	−	0.0932120i	0.00243367	−	0.00349082i
$714$	18.3369	−	8.37614i	0.686242	−	0.313469i
$715$			65.9364i			2.46588i
$716$	−31.9480	−	3.62116i	−1.19395	−	0.135329i
$717$	5.59959	−	2.95030i	0.209120	−	0.110181i
$718$	−17.4246	−	0.984346i	−0.650280	−	0.0367355i
$719$			45.9821i			1.71484i	0.514616	+	0.857421i	$0.327935\pi$
$719$			45.9821i			1.71484i	−0.514616	+	0.857421i	$0.672065\pi$
$720$	−23.0589	−	25.0463i	−0.859356	−	0.933419i
$721$	5.54205			0.206397
$722$	26.7181	+	1.50935i	0.994345	+	0.0561724i
$723$	−22.2926	+	11.7455i	−0.829071	+	0.436820i
$724$	−35.7268	−	4.04946i	−1.32778	−	0.150497i
$725$	−11.9092			−0.442296
$726$	−16.9065	−	37.0115i	−0.627459	−	1.37362i
$727$		−	40.8296i		−	1.51428i	−0.653250	−	0.757142i	$-0.726595\pi$
$727$		−	40.8296i		−	1.51428i	0.653250	−	0.757142i	$-0.273405\pi$
$728$	−18.6245	−	3.18351i	−0.690269	−	0.117989i
$729$	26.2761	+	6.21011i	0.973190	+	0.230004i
$730$	−2.36395	+	41.8459i	−0.0874936	+	1.54878i
$731$	40.1295			1.48424
$732$	−6.19331	−	15.8710i	−0.228911	−	0.586608i
$733$	−10.9115			−0.403024			−0.201512	−	0.979486i	$-0.564586\pi$
$733$	−10.9115			−0.403024			−0.201512	+	0.979486i	$0.564586\pi$
$734$	0.834946	−	14.7800i	0.0308184	−	0.545538i
$735$	20.5146	−	10.8087i	0.756692	−	0.398685i
$736$	21.0981	−	17.0549i	0.777688	−	0.628650i
$737$			61.8568i			2.27852i
$738$	−24.2384	−	18.7105i	−0.892229	−	0.688741i
$739$		−	39.1912i		−	1.44167i	−0.693105	−	0.720836i	$-0.743758\pi$
$739$		−	39.1912i		−	1.44167i	0.693105	−	0.720836i	$-0.256242\pi$
$740$	−6.99474	+	61.7118i	−0.257132	+	2.26857i
$741$	1.88458	−	0.992942i	0.0692316	−	0.0364766i
$742$	20.5242	+	1.15945i	0.753468	+	0.0425648i
$743$	−53.5532			−1.96468			−0.982338	−	0.187113i	$-0.940087\pi$
$743$	−53.5532			−1.96468			−0.982338	+	0.187113i	$0.940087\pi$
$744$	−0.0360298	−	0.110339i	−0.00132092	−	0.00404521i
$745$	37.6277			1.37857
$746$	−26.9659	−	1.52335i	−0.987293	−	0.0557739i
$747$	−4.97397	−	3.40989i	−0.181988	−	0.124761i
$748$	6.44957	−	56.9020i	0.235820	−	2.08054i
$749$	9.87939			0.360985
$750$	−12.3336	+	5.63385i	−0.450358	+	0.205719i
$751$			13.1585i			0.480161i	0.970753	+	0.240081i	$0.0771739\pi$
$751$			13.1585i			0.480161i	−0.970753	+	0.240081i	$0.922826\pi$
$752$	−5.71645	+	24.8930i	−0.208457	+	0.907754i
$753$	−8.56582	+	4.51315i	−0.312156	+	0.164468i
$754$	1.37807	−	24.3942i	0.0501865	−	0.888386i
$755$			1.99223i			0.0725048i
$756$	3.56161	−	15.2867i	0.129535	−	0.555971i
$757$	−16.8295			−0.611680			−0.305840	−	0.952083i	$-0.598937\pi$
$757$	−16.8295			−0.611680			−0.305840	+	0.952083i	$0.598937\pi$
$758$	39.0153	+	2.20405i	1.41710	+	0.0800546i
$759$	5.39433	−	43.3140i	0.195802	−	1.57220i
$760$	0.375939	−	2.19935i	0.0136367	−	0.0797789i
$761$		−	49.7398i		−	1.80307i	−0.432708	−	0.901534i	$-0.642442\pi$
$761$		−	49.7398i		−	1.80307i	0.432708	−	0.901534i	$-0.357558\pi$
$762$	−1.29364	−	2.83202i	−0.0468636	−	0.102593i
$763$			1.07996i			0.0390973i
$764$	34.3481	+	3.89319i	1.24267	+	0.140851i
$765$	−38.2521	−	26.2236i	−1.38301	−	0.948116i
$766$	34.6173	+	1.95559i	1.25077	+	0.0706585i
$767$			42.3921i			1.53069i
$768$	−0.927206	−	27.6973i	−0.0334577	−	0.999440i
$769$			13.3506i			0.481434i	0.970595	+	0.240717i	$0.0773825\pi$
$769$			13.3506i			0.481434i	−0.970595	+	0.240717i	$0.922617\pi$
$770$	−1.79597	+	31.7918i	−0.0647224	+	1.14570i
$771$	−6.10425	+	3.21620i	−0.219839	+	0.115829i
$772$	11.9371	+	1.35301i	0.429625	+	0.0486960i
$773$		−	27.4662i		−	0.987890i	−0.869493	−	0.493945i	$-0.835554\pi$
$773$		−	27.4662i		−	0.987890i	0.869493	−	0.493945i	$-0.164446\pi$
$774$	19.0922	−	24.7330i	0.686255	−	0.889008i
$775$	0.0722360			0.00259480
$776$	4.83539	−	28.2885i	0.173580	−	1.01550i
$777$	−25.3330	+	13.3474i	−0.908816	+	0.478836i
$778$	1.40475	−	24.8665i	0.0503629	−	0.891508i
$779$		−	2.00681i		−	0.0719014i
$780$	15.8019	+	40.4940i	0.565800	+	1.44992i
$781$	26.9846			0.965586
$782$	22.8123	−	29.0767i	0.815765	−	1.03978i
$783$	20.1606	+	2.35001i	0.720479	+	0.0839823i
$784$	18.3965	+	4.22458i	0.657016	+	0.150878i
$785$		−	21.3854i		−	0.763278i
$786$	−11.0942	−	24.2873i	−0.395717	−	0.866298i
$787$	41.9113			1.49398			0.746988	−	0.664837i	$-0.231499\pi$
$787$	41.9113			1.49398			0.746988	+	0.664837i	$0.231499\pi$
$788$	−6.62665	−	0.751100i	−0.236065	−	0.0267568i
$789$	6.71479	+	12.7445i	0.239053	+	0.453715i
$790$	−53.5346	−	3.02426i	−1.90467	−	0.107599i
$791$		−	3.84943i		−	0.136870i
$792$	−32.0019	−	31.0470i	−1.13714	−	1.10321i
$793$			21.7523i			0.772446i
$794$	−2.08125	+	36.8417i	−0.0738610	+	1.30746i
$795$	−22.0447	−	41.8401i	−0.781844	−	1.48392i
$796$	1.22584	−	10.8151i	0.0434486	−	0.383330i
$797$		−	1.43260i		−	0.0507454i	−0.999678	−	0.0253727i	$-0.991923\pi$
$797$		−	1.43260i		−	0.0507454i	0.999678	−	0.0253727i	$-0.00807725\pi$
$798$	0.935709	−	0.427423i	0.0331237	−	0.0151306i
$799$			34.7936i			1.23091i
$800$	16.5647	+	4.80200i	0.585651	+	0.169776i
$801$	−23.5886	+	34.4085i	−0.833463	+	1.21577i
$802$	−8.23171	−	0.465024i	−0.290672	−	0.0164206i
$803$			54.8920i			1.93710i
$804$	14.8242	+	37.9886i	0.522811	+	1.33975i
$805$	−11.7525	+	16.8575i	−0.414221	+	0.594150i
$806$	−0.00835881	+	0.147965i	−0.000294426	+	0.00521184i
$807$	−5.43111	−	10.3081i	−0.191184	−	0.362862i
$808$	−21.4792	−	3.67147i	−0.755634	−	0.129162i
$809$			41.7684i			1.46850i	0.678881	+	0.734248i	$0.262465\pi$
$809$			41.7684i			1.46850i	−0.678881	+	0.734248i	$0.737535\pi$
$810$	−34.3614	+	11.0996i	−1.20734	+	0.390002i
$811$			10.2543i			0.360078i	0.983659	+	0.180039i	$0.0576223\pi$
$811$			10.2543i			0.360078i	−0.983659	+	0.180039i	$0.942378\pi$
$812$	1.32890	−	11.7243i	0.0466352	−	0.411444i
$813$	9.20403	+	17.4690i	0.322800	+	0.612664i
$814$	−4.58774	+	81.2107i	−0.160800	+	2.84643i
$815$	−13.4323			−0.470512
$816$	−9.67588	−	36.4913i	−0.338724	−	1.27745i
$817$	2.04775			0.0716418
$818$	−47.5712	−	2.68739i	−1.66329	−	0.0939622i
$819$	−11.3317	+	16.5295i	−0.395962	+	0.577587i
$820$	40.6905	+	4.61207i	1.42097	+	0.161061i
$821$	−35.9779			−1.25564			−0.627819	−	0.778359i	$-0.716052\pi$
$821$	−35.9779			−1.25564			−0.627819	+	0.778359i	$0.716052\pi$
$822$	−9.73274	−	21.3068i	−0.339468	−	0.743159i
$823$	31.1038			1.08421			0.542106	−	0.840310i	$-0.317627\pi$
$823$	31.1038			1.08421			0.542106	+	0.840310i	$0.317627\pi$
$824$	1.74866	−	10.2302i	0.0609173	−	0.356384i
$825$	24.5494	−	12.9345i	0.854699	−	0.450323i
$826$	−1.15468	+	20.4397i	−0.0401763	+	0.711189i
$827$		−	44.8962i		−	1.56119i	−0.625036	−	0.780596i	$-0.714916\pi$
$827$		−	44.8962i		−	1.56119i	0.625036	−	0.780596i	$-0.285084\pi$
$828$	−7.06753	−	27.8935i	−0.245614	−	0.969368i
$829$		−	24.4025i		−	0.847535i	−0.905771	−	0.423768i	$-0.860707\pi$
$829$		−	24.4025i		−	0.847535i	0.905771	−	0.423768i	$-0.139293\pi$
$830$	8.05241	+	0.454895i	0.279503	+	0.0157896i
$831$	37.3119	−	19.6588i	1.29433	−	0.681957i
$832$	−11.7530	+	33.3747i	−0.407461	+	1.15706i
$833$	25.7132			0.890911
$834$	−43.7484	+	19.9838i	−1.51488	+	0.691984i
$835$	−36.0768			−1.24849
$836$	0.329113	−	2.90363i	0.0113826	−	0.100424i
$837$	−0.122285	−	0.0142541i	−0.00422680	−	0.000492695i
$838$	1.39516	−	24.6966i	0.0481949	−	0.853130i
$839$	42.3798			1.46311			0.731557	−	0.681780i	$-0.238794\pi$
$839$	42.3798			1.46311			0.731557	+	0.681780i	$0.238794\pi$
$840$	6.51606	+	19.9549i	0.224825	+	0.688511i
$841$	−13.7418			−0.473856
$842$	26.3796	+	1.49023i	0.909100	+	0.0513567i
$843$	2.64513	+	5.02038i	0.0911030	+	0.172911i
$844$	1.57323	−	13.8799i	0.0541527	−	0.477767i
$845$		−	18.6183i		−	0.640490i
$846$	21.4443	+	16.5536i	0.737271	+	0.569124i
$847$			25.0895i			0.862085i
$848$	8.61616	−	37.5202i	0.295880	−	1.28845i
$849$	−16.5929	−	31.4928i	−0.569466	−	1.08083i
$850$	23.4573	+	1.32514i	0.804578	+	0.0454520i
$851$	−30.0212	+	43.0619i	−1.02911	+	1.47614i
$852$	16.5723	−	6.46698i	0.567757	−	0.221555i
$853$			39.5979i			1.35581i	0.735151	+	0.677903i	$0.237111\pi$
$853$			39.5979i			1.35581i	−0.735151	+	0.677903i	$0.762889\pi$
$854$	−0.592488	+	10.4880i	−0.0202745	+	0.358893i
$855$	−1.95196	−	1.33816i	−0.0667555	−	0.0457640i
$856$	3.11720	−	18.2365i	0.106544	−	0.623311i
$857$		−	45.3290i		−	1.54841i	−0.632935	−	0.774205i	$-0.718150\pi$
$857$		−	45.3290i		−	1.54841i	0.632935	−	0.774205i	$-0.281850\pi$
$858$	23.6538	+	51.7825i	0.807526	+	1.76783i
$859$			24.6318i			0.840426i	0.907426	+	0.420213i	$0.138045\pi$
$859$			24.6318i			0.840426i	−0.907426	+	0.420213i	$0.861955\pi$
$860$	−4.70617	+	41.5207i	−0.160479	+	1.41584i
$861$	8.80079	+	16.7036i	0.299930	+	0.569259i
$862$	5.63755	+	0.318475i	0.192016	+	0.0108473i
$863$			21.3840i			0.727921i	0.931414	+	0.363960i	$0.118576\pi$
$863$			21.3840i			0.727921i	−0.931414	+	0.363960i	$0.881424\pi$
$864$	−27.0941	−	11.3978i	−0.921760	−	0.387760i
$865$			14.5692i			0.495366i
$866$	−1.63213	+	28.8914i	−0.0554620	+	0.981770i
$867$	−10.2475	−	19.4495i	−0.348025	−	0.660541i
$868$	−0.00806054	+	0.0711149i	−0.000273592	+	0.00241380i
$869$	−70.2249			−2.38222
$870$	−24.6911	+	11.2787i	−0.837108	+	0.382383i
$871$		−	52.0660i		−	1.76419i
$872$	1.99352	+	0.340755i	0.0675091	+	0.0115394i
$873$	−25.1064	−	17.2116i	−0.849723	−	0.582524i
$874$	1.16408	−	1.48374i	0.0393756	−	0.0501884i
$875$	8.36072			0.282644
$876$	13.1551	+	33.7113i	0.444470	+	1.13900i
$877$		−	7.10030i		−	0.239760i	−0.992788	−	0.119880i	$-0.961749\pi$
$877$		−	7.10030i		−	0.239760i	0.992788	−	0.119880i	$-0.0382510\pi$
$878$	−18.9307	−	1.06943i	−0.638881	−	0.0360915i
$879$	−4.53817	+	2.39107i	−0.153069	+	0.0806487i
$880$	58.1183	+	13.3463i	1.95917	+	0.449905i
$881$	−21.8256			−0.735323			−0.367661	−	0.929960i	$-0.619841\pi$
$881$	−21.8256			−0.735323			−0.367661	+	0.929960i	$0.619841\pi$
$882$	12.2335	−	15.8478i	0.411922	−	0.533624i
$883$		−	34.5350i		−	1.16220i	−0.813834	−	0.581098i	$-0.802623\pi$
$883$		−	34.5350i		−	1.16220i	0.813834	−	0.581098i	$-0.197377\pi$
$884$	−5.42873	+	47.8955i	−0.182588	+	1.61090i
$885$	41.6679	−	21.9539i	1.40065	−	0.737972i
$886$	−50.4946	−	2.85253i	−1.69640	−	0.0958326i
$887$		−	23.9052i		−	0.802660i	−0.915934	−	0.401330i	$-0.868548\pi$
$887$		−	23.9052i		−	0.802660i	0.915934	−	0.401330i	$-0.131452\pi$
$888$	16.6450	+	50.9740i	0.558569	+	1.71058i
$889$			1.91978i			0.0643874i
$890$	3.14684	−	55.7043i	0.105482	−	1.86721i
$891$	−44.1109	+	17.0521i	−1.47777	+	0.571265i
$892$	6.98485	+	0.791700i	0.233870	+	0.0265081i
$893$			1.77547i			0.0594139i
$894$	29.5506	−	13.4984i	0.988319	−	0.451455i
$895$		−	45.6091i		−	1.52455i
$896$	−6.57586	+	15.7718i	−0.219684	+	0.526898i
$897$	−4.54051	+	36.4582i	−0.151603	+	1.21730i
$898$	1.03546	−	18.3294i	0.0345538	−	0.611661i
$899$	−0.0925495			−0.00308670
$900$	11.9769	−	13.8269i	0.399229	−	0.460898i
$901$		−	52.4430i		−	1.74713i
$902$	53.5473	+	3.02499i	1.78293	+	0.100721i
$903$	−17.0444	+	8.98035i	−0.567203	+	0.298847i
$904$	−7.10572	−	1.21459i	−0.236333	−	0.0403967i
$905$		−	51.0037i		−	1.69542i
$906$	0.714686	+	1.56458i	0.0237438	+	0.0519797i
$907$	−20.9902			−0.696967			−0.348484	−	0.937315i	$-0.613303\pi$
$907$	−20.9902			−0.696967			−0.348484	+	0.937315i	$0.613303\pi$
$908$	−0.891249	+	7.86313i	−0.0295771	+	0.260947i
$909$	−13.0686	+	19.0630i	−0.433458	+	0.632281i
$910$	1.51171	−	26.7597i	0.0501125	−	0.887076i
$911$	−19.5906			−0.649064			−0.324532	−	0.945875i	$-0.605207\pi$
$911$	−19.5906			−0.649064			−0.324532	+	0.945875i	$0.605207\pi$
$912$	−0.493747	−	1.86210i	−0.0163496	−	0.0616604i
$913$	10.5629			0.349581
$914$	1.85431	−	32.8243i	0.0613350	−	1.08573i
$915$	21.3806	−	11.2650i	0.706822	−	0.372409i
$916$	−28.7546	−	3.25920i	−0.950078	−	0.107687i
$917$			16.4639i			0.543688i
$918$	−39.4483	−	6.87203i	−1.30199	−	0.226811i
$919$		−	5.56361i		−	0.183527i	−0.995781	−	0.0917633i	$-0.970750\pi$
$919$		−	5.56361i		−	0.183527i	0.995781	−	0.0917633i	$-0.0292503\pi$
$920$	27.4094	+	27.0131i	0.903661	+	0.890595i
$921$	−24.8805	+	13.1090i	−0.819839	+	0.431956i
$922$	37.5504	+	2.12129i	1.23666	+	0.0698610i
$923$	−22.7135			−0.747623
$924$	9.99441	+	25.6116i	0.328792	+	0.842561i
$925$	−33.3714			−1.09725
$926$	31.4629	+	1.77739i	1.03393	+	0.0584088i
$927$	−9.07940	−	6.22435i	−0.298207	−	0.204434i
$928$	−21.2229	−	6.15237i	−0.696674	−	0.201961i
$929$			15.4930i			0.508309i	0.967164	+	0.254155i	$0.0817972\pi$
$929$			15.4930i			0.508309i	−0.967164	+	0.254155i	$0.918203\pi$
$930$	0.149766	−	0.0684116i	0.00491101	−	0.00224331i
$931$	1.31211			0.0430028
$932$	1.43848	−	12.6911i	0.0471189	−	0.415711i
$933$	8.99140	−	4.73738i	0.294365	−	0.155095i
$934$	0.720918	−	12.7615i	0.0235892	−	0.417568i
$935$	81.2335			2.65662
$936$	26.9366	+	26.1329i	0.880450	+	0.854179i
$937$			3.40862i			0.111355i	0.998449	+	0.0556774i	$0.0177318\pi$
$937$			3.40862i			0.111355i	−0.998449	+	0.0556774i	$0.982268\pi$
$938$	1.41817	−	25.1040i	0.0463050	−	0.819676i
$939$	17.2778	−	9.10329i	0.563839	−	0.297075i
$940$	−35.9998	−	4.08041i	−1.17419	−	0.133088i
$941$			14.3553i			0.467969i	0.972240	+	0.233985i	$0.0751765\pi$
$941$			14.3553i			0.467969i	−0.972240	+	0.233985i	$0.924823\pi$
$942$	−7.67172	−	16.7948i	−0.249958	−	0.547205i
$943$	28.3934	+	19.7949i	0.924617	+	0.644610i
$944$	37.3657	+	8.58068i	1.21615	+	0.279277i
$945$	22.1155	+	2.57788i	0.719417	+	0.0838585i
$946$	−3.08670	+	54.6398i	−0.100357	+	1.77649i
$947$	−10.2010			−0.331490			−0.165745	−	0.986169i	$-0.553003\pi$
$947$	−10.2010			−0.331490			−0.165745	+	0.986169i	$0.553003\pi$
$948$	−43.1278	+	16.8297i	−1.40073	+	0.546604i
$949$		−	46.2037i		−	1.49983i
$950$	1.19699	+	0.0676203i	0.0388356	+	0.00219389i
$951$	24.1056	+	45.7518i	0.781679	+	1.48360i
$952$	−3.92208	+	22.9453i	−0.127115	+	0.743662i
$953$	−10.7012			−0.346645			−0.173323	−	0.984865i	$-0.555450\pi$
$953$	−10.7012			−0.346645			−0.173323	+	0.984865i	$0.555450\pi$
$954$	−32.3221	−	24.9505i	−1.04647	−	0.807803i
$955$			49.0355i			1.58675i
$956$	−0.823104	+	7.26191i	−0.0266211	+	0.234867i
$957$	−31.4529	+	16.5718i	−1.01673	+	0.535692i
$958$	12.7760	+	0.721740i	0.412774	+	0.0233184i
$959$			14.4435i			0.466406i
$960$	38.8911	−	5.73181i	1.25521	−	0.184993i
$961$	−30.9994			−0.999982
$962$	3.86158	−	68.3565i	0.124502	−	2.20390i
$963$	−16.1852	−	11.0957i	−0.521559	−	0.357553i
$964$	3.27687	−	28.9105i	0.105541	−	0.931145i
$965$			17.0414i			0.548583i
$966$	−3.18229	+	17.4550i	−0.102389	+	0.561604i
$967$	6.66228			0.214244			0.107122	−	0.994246i	$-0.465836\pi$
$967$	6.66228			0.214244			0.107122	+	0.994246i	$0.465836\pi$
$968$	46.3131	+	7.91637i	1.48856	+	0.254442i
$969$	−1.22330	−	2.32179i	−0.0392982	−	0.0745868i
$970$	40.6450	+	2.29611i	1.30503	+	0.0737236i
$971$			46.2279i			1.48352i	0.670663	+	0.741762i	$0.266010\pi$
$971$			46.2279i			1.48352i	−0.670663	+	0.741762i	$0.733990\pi$
$972$	−23.0036	+	21.0437i	−0.737839	+	0.674976i
$973$	29.6563			0.950738
$974$	17.0465	+	0.962987i	0.546205	+	0.0308561i
$975$	−20.6637	+	10.8872i	−0.661767	+	0.348671i
$976$	19.1731	+	4.40292i	0.613715	+	0.140934i
$977$	−3.77134			−0.120656			−0.0603280	−	0.998179i	$-0.519215\pi$
$977$	−3.77134			−0.120656			−0.0603280	+	0.998179i	$0.519215\pi$
$978$	−10.5489	+	4.81865i	−0.337317	+	0.154083i
$979$		−	73.0711i		−	2.33536i
$980$	−3.01551	+	26.6047i	−0.0963271	+	0.849855i
$981$	1.21292	−	1.76928i	0.0387256	−	0.0564886i
$982$	1.50442	+	0.0849872i	0.0480079	+	0.00271205i
$983$	−10.4725			−0.334021			−0.167010	−	0.985955i	$-0.553411\pi$
$983$	−10.4725			−0.334021			−0.167010	+	0.985955i	$0.553411\pi$
$984$	33.6104	−	10.9751i	1.07146	−	0.349873i
$985$		−	9.46023i		−	0.301428i
$986$	−30.0537	−	1.69779i	−0.957104	−	0.0540685i
$987$	−7.78627	−	14.7781i	−0.247840	−	0.470392i
$988$	−0.277021	+	2.44404i	−0.00881320	+	0.0777553i
$989$	−20.1988	+	28.9727i	−0.642283	+	0.921279i
$990$	38.6481	−	50.0666i	1.22832	−	1.59122i
$991$	15.3490			0.487576			0.243788	−	0.969829i	$-0.421610\pi$
$991$	15.3490			0.487576			0.243788	+	0.969829i	$0.421610\pi$
$992$	0.128729	+	0.0373176i	0.00408714	+	0.00118484i
$993$	−44.9890	+	23.7037i	−1.42768	+	0.752215i
$994$	−10.9515	−	0.618669i	−0.347360	−	0.0196230i
$995$	15.4396			0.489469
$996$	6.48707	−	2.53144i	0.205551	−	0.0802118i
$997$			49.8784i			1.57967i	0.613323	+	0.789833i	$0.289833\pi$
$997$			49.8784i			1.57967i	−0.613323	+	0.789833i	$0.710167\pi$
$998$	1.25528	−	22.2206i	0.0397352	−	0.703379i
$999$	56.4931	+	6.58509i	1.78736	+	0.208343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.b.c.413.2	yes	80
3.2	odd	2	inner	552.2.b.c.413.79	yes	80
4.3	odd	2		2208.2.b.c.689.56		80
8.3	odd	2		2208.2.b.c.689.25		80
8.5	even	2	inner	552.2.b.c.413.77	yes	80
12.11	even	2		2208.2.b.c.689.27		80
23.22	odd	2	inner	552.2.b.c.413.1	✓	80
24.5	odd	2	inner	552.2.b.c.413.4	yes	80
24.11	even	2		2208.2.b.c.689.54		80
69.68	even	2	inner	552.2.b.c.413.80	yes	80
92.91	even	2		2208.2.b.c.689.55		80
184.45	odd	2	inner	552.2.b.c.413.78	yes	80
184.91	even	2		2208.2.b.c.689.26		80
276.275	odd	2		2208.2.b.c.689.28		80
552.275	odd	2		2208.2.b.c.689.53		80
552.413	even	2	inner	552.2.b.c.413.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.b.c.413.1	✓	80	23.22	odd	2	inner
552.2.b.c.413.2	yes	80	1.1	even	1	trivial
552.2.b.c.413.3	yes	80	552.413	even	2	inner
552.2.b.c.413.4	yes	80	24.5	odd	2	inner
552.2.b.c.413.77	yes	80	8.5	even	2	inner
552.2.b.c.413.78	yes	80	184.45	odd	2	inner
552.2.b.c.413.79	yes	80	3.2	odd	2	inner
552.2.b.c.413.80	yes	80	69.68	even	2	inner
2208.2.b.c.689.25		80	8.3	odd	2
2208.2.b.c.689.26		80	184.91	even	2
2208.2.b.c.689.27		80	12.11	even	2
2208.2.b.c.689.28		80	276.275	odd	2
2208.2.b.c.689.53		80	552.275	odd	2
2208.2.b.c.689.54		80	24.11	even	2
2208.2.b.c.689.55		80	92.91	even	2
2208.2.b.c.689.56		80	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} +2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} -1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +O(q^{10})\)	\(q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} +2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} -1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +(0.226295 - 4.00580i) q^{10} -5.25468i q^{11} +(-1.25931 - 3.22710i) q^{12} +4.42296i q^{13} +(-0.120473 + 2.13257i) q^{14} +(4.34739 - 2.29055i) q^{15} +(3.89853 + 0.895261i) q^{16} +5.44908 q^{17} +(2.59248 - 3.35843i) q^{18} +0.278059 q^{19} +(-0.639039 + 5.63799i) q^{20} +(-2.31442 + 1.21942i) q^{21} +(-0.419136 + 7.41941i) q^{22} +(-2.74274 + 3.93413i) q^{23} +(1.52069 + 4.65699i) q^{24} -3.04882 q^{25} +(0.352794 - 6.24505i) q^{26} +(5.16121 + 0.601614i) q^{27} +(0.340205 - 3.00149i) q^{28} +3.90617 q^{29} +(-6.32106 + 2.88740i) q^{30} -0.0236931 q^{31} +(-5.43316 - 1.57504i) q^{32} +(-8.05210 + 4.24248i) q^{33} +(-7.69390 - 0.434642i) q^{34} +4.28495 q^{35} +(-3.92837 + 4.53519i) q^{36} +10.9457 q^{37} +(-0.392609 - 0.0221792i) q^{38} +(6.77760 - 3.57097i) q^{39} +(1.35201 - 7.90965i) q^{40} -7.21720i q^{41} +(3.36514 - 1.53717i) q^{42} +7.36445 q^{43} +(1.18361 - 10.4425i) q^{44} +(-7.01993 - 4.81248i) q^{45} +(4.18645 - 5.33607i) q^{46} +6.38523i q^{47} +(-1.77569 - 6.69678i) q^{48} +4.71882 q^{49} +(4.30481 + 0.243187i) q^{50} +(-4.39943 - 8.35000i) q^{51} +(-0.996265 + 8.78964i) q^{52} -9.62419i q^{53} +(-7.23944 - 1.26114i) q^{54} +14.9077 q^{55} +(-0.719769 + 4.21086i) q^{56} +(-0.224497 - 0.426089i) q^{57} +(-5.51537 - 0.311573i) q^{58} +9.58456 q^{59} +(9.15541 - 3.57271i) q^{60} +4.91803 q^{61} +(0.0334538 + 0.00188987i) q^{62} +(3.73720 + 2.56202i) q^{63} +(7.54579 + 2.65727i) q^{64} -12.5481 q^{65} +(11.7077 - 5.34795i) q^{66} -11.7718 q^{67} +(10.8288 + 1.22740i) q^{68} +(8.24294 + 1.02658i) q^{69} +(-6.05018 - 0.341786i) q^{70} +5.13535i q^{71} +(5.90846 - 6.09017i) q^{72} -10.4463 q^{73} +(-15.4549 - 0.873077i) q^{74} +(2.46153 + 4.67191i) q^{75} +(0.552580 + 0.0626324i) q^{76} -7.93644 q^{77} +(-9.85456 + 4.50147i) q^{78} -13.3643i q^{79} +(-2.53989 + 11.0603i) q^{80} +(-3.24512 - 8.39459i) q^{81} +(-0.575675 + 10.1904i) q^{82} +2.01019i q^{83} +(-4.87407 + 1.90200i) q^{84} +15.4593i q^{85} +(-10.3983 - 0.587420i) q^{86} +(-3.15373 - 5.98569i) q^{87} +(-2.50415 + 14.6500i) q^{88} +13.9059 q^{89} +(9.52801 + 7.35498i) q^{90} +6.68025 q^{91} +(-6.33673 + 7.20040i) q^{92} +(0.0191292 + 0.0363066i) q^{93} +(0.509313 - 9.01570i) q^{94} +0.788866i q^{95} +(1.97304 + 9.59724i) q^{96} +10.1465i q^{97} +(-6.66280 - 0.376394i) q^{98} +(13.0021 + 8.91352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) \) 80 * q - 12 * q^6 - 4 * q^9	\( 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) \) 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Introduction

L-functions

Modular forms

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