LMFDB - Embedded newform 165.2.s.a.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(4,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("165.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.s (of order $10$, degree $4$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	165.64
Dual form			165.2.s.a.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00341 - 0.650947i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.97188 + 1.43266i) q^{4} +(-2.23165 - 0.140493i) q^{5} +(-0.650947 - 2.00341i) q^{6} +(1.94929 - 2.68296i) q^{7} +(-0.541555 - 0.745386i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.00341 - 0.650947i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.97188 + 1.43266i) q^{4} +(-2.23165 - 0.140493i) q^{5} +(-0.650947 - 2.00341i) q^{6} +(1.94929 - 2.68296i) q^{7} +(-0.541555 - 0.745386i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(4.37946 + 1.73415i) q^{10} +(3.31267 - 0.162019i) q^{11} +2.43738i q^{12} +(2.37658 + 0.772198i) q^{13} +(-5.65169 + 4.10619i) q^{14} +(-1.19807 - 1.88802i) q^{15} +(-0.906636 - 2.79034i) q^{16} +(6.47687 - 2.10446i) q^{17} +(1.23818 - 1.70420i) q^{18} +(-0.928503 + 0.674597i) q^{19} +(-4.19927 - 3.47422i) q^{20} +3.31633 q^{21} +(-6.74209 - 1.83178i) q^{22} -5.89026i q^{23} +(0.284712 - 0.876254i) q^{24} +(4.96052 + 0.627062i) q^{25} +(-4.25861 - 3.09406i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(7.68753 - 2.49783i) q^{28} +(-0.908175 - 0.659827i) q^{29} +(1.17122 + 4.56236i) q^{30} +(-0.338908 + 1.04305i) q^{31} +8.02306i q^{32} +(2.07821 + 2.58477i) q^{33} -14.3457 q^{34} +(-4.72706 + 5.71358i) q^{35} +(-1.97188 + 1.43266i) q^{36} +(-6.78238 + 9.33514i) q^{37} +(2.29930 - 0.747087i) q^{38} +(0.772198 + 2.37658i) q^{39} +(1.10384 + 1.73953i) q^{40} +(0.754463 - 0.548149i) q^{41} +(-6.64396 - 2.15875i) q^{42} -0.552188i q^{43} +(6.76431 + 4.42643i) q^{44} +(0.823234 - 2.07901i) q^{45} +(-3.83425 + 11.8006i) q^{46} +(1.25449 + 1.72666i) q^{47} +(1.72452 - 2.37360i) q^{48} +(-1.23546 - 3.80234i) q^{49} +(-9.52978 - 4.48530i) q^{50} +(5.50956 + 4.00293i) q^{51} +(3.58005 + 4.92751i) q^{52} +(-11.0661 - 3.59560i) q^{53} +2.10651 q^{54} +(-7.41547 - 0.103836i) q^{55} -3.05549 q^{56} +(-1.09152 - 0.354657i) q^{57} +(1.38993 + 1.91308i) q^{58} +(6.79443 + 4.93644i) q^{59} +(0.342435 - 5.43938i) q^{60} +(-2.53800 - 7.81115i) q^{61} +(1.35794 - 1.86905i) q^{62} +(1.94929 + 2.68296i) q^{63} +(3.40931 - 10.4928i) q^{64} +(-5.19521 - 2.05717i) q^{65} +(-2.48096 - 6.53116i) q^{66} -4.15419i q^{67} +(15.7866 + 5.12938i) q^{68} +(4.76532 - 3.46221i) q^{69} +(13.1895 - 8.36956i) q^{70} +(3.87323 + 11.9206i) q^{71} +(0.876254 - 0.284712i) q^{72} +(3.37248 - 4.64182i) q^{73} +(19.6646 - 14.2871i) q^{74} +(2.40842 + 4.38173i) q^{75} -2.79736 q^{76} +(6.02265 - 9.20358i) q^{77} -5.26393i q^{78} +(1.19514 - 3.67825i) q^{79} +(1.63127 + 6.35443i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.86831 + 0.607052i) q^{82} +(-5.78295 + 1.87899i) q^{83} +(6.53941 + 4.75116i) q^{84} +(-14.7498 + 3.78647i) q^{85} +(-0.359446 + 1.10626i) q^{86} -1.12257i q^{87} +(-1.91476 - 2.38147i) q^{88} -12.5950 q^{89} +(-3.00260 + 3.62923i) q^{90} +(6.70442 - 4.87105i) q^{91} +(8.43872 - 11.6149i) q^{92} +(-1.04305 + 0.338908i) q^{93} +(-1.38930 - 4.27582i) q^{94} +(2.16687 - 1.37502i) q^{95} +(-6.49079 + 4.71583i) q^{96} +(-2.72832 - 0.886486i) q^{97} +8.42187i q^{98} +(-0.869581 + 3.20060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

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 $

$2$	−2.00341	−	0.650947i	−1.41662	−	0.460289i	−0.502096	−	0.864812i	$-0.667438\pi$
$2$	−2.00341	−	0.650947i	−1.41662	−	0.460289i	−0.914528	+	0.404523i	$0.867438\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	1.97188	+	1.43266i	0.985942	+	0.716328i
$5$	−2.23165	−	0.140493i	−0.998024	−	0.0628303i
$5$	−2.23165	−	0.140493i	−0.998024	−	0.0628303i
$6$	−0.650947	−	2.00341i	−0.265748	−	0.817888i
$7$	1.94929	−	2.68296i	0.736761	−	1.01407i	−0.262037	−	0.965058i	$-0.584394\pi$
$7$	1.94929	−	2.68296i	0.736761	−	1.01407i	0.998798	−	0.0490073i	$-0.0156058\pi$
$8$	−0.541555	−	0.745386i	−0.191469	−	0.263534i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	4.37946	+	1.73415i	1.38491	+	0.548387i
$11$	3.31267	−	0.162019i	0.998806	−	0.0488505i
$11$	3.31267	−	0.162019i	0.998806	−	0.0488505i
$12$			2.43738i			0.703611i
$13$	2.37658	+	0.772198i	0.659145	+	0.214169i	0.619442	−	0.785042i	$-0.287359\pi$
$13$	2.37658	+	0.772198i	0.659145	+	0.214169i	0.0397029	+	0.999212i	$0.487359\pi$
$14$	−5.65169	+	4.10619i	−1.51048	+	1.09743i
$15$	−1.19807	−	1.88802i	−0.309340	−	0.487485i
$16$	−0.906636	−	2.79034i	−0.226659	−	0.697584i
$17$	6.47687	−	2.10446i	1.57087	−	0.510408i	0.611188	−	0.791486i	$-0.290692\pi$
$17$	6.47687	−	2.10446i	1.57087	−	0.510408i	0.959685	+	0.281078i	$0.0906920\pi$
$18$	1.23818	−	1.70420i	0.291841	−	0.401684i
$19$	−0.928503	+	0.674597i	−0.213013	+	0.154763i	−0.689176	−	0.724594i	$-0.742027\pi$
$19$	−0.928503	+	0.674597i	−0.213013	+	0.154763i	0.476163	+	0.879357i	$0.342027\pi$
$20$	−4.19927	−	3.47422i	−0.938986	−	0.776860i
$21$	3.31633			0.723682
$22$	−6.74209	−	1.83178i	−1.43742	−	0.390537i
$23$		−	5.89026i		−	1.22820i	−0.789226	−	0.614102i	$-0.789518\pi$
$23$		−	5.89026i		−	1.22820i	0.789226	−	0.614102i	$-0.210482\pi$
$24$	0.284712	−	0.876254i	0.0581167	−	0.178865i
$25$	4.96052	+	0.627062i	0.992105	+	0.125412i
$26$	−4.25861	−	3.09406i	−0.835181	−	0.606795i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	7.68753	−	2.49783i	1.45281	−	0.472046i
$29$	−0.908175	−	0.659827i	−0.168644	−	0.122527i	0.500262	−	0.865874i	$-0.333237\pi$
$29$	−0.908175	−	0.659827i	−0.168644	−	0.122527i	−0.668906	+	0.743347i	$0.733237\pi$
$30$	1.17122	+	4.56236i	0.213835	+	0.832970i
$31$	−0.338908	+	1.04305i	−0.0608697	+	0.187338i	−0.976867	−	0.213846i	$-0.931401\pi$
$31$	−0.338908	+	1.04305i	−0.0608697	+	0.187338i	0.915998	+	0.401183i	$0.131401\pi$
$32$			8.02306i			1.41829i
$33$	2.07821	+	2.58477i	0.361770	+	0.449951i
$34$	−14.3457			−2.46027
$35$	−4.72706	+	5.71358i	−0.799020	+	0.965771i
$36$	−1.97188	+	1.43266i	−0.328647	+	0.238776i
$37$	−6.78238	+	9.33514i	−1.11502	+	1.53469i	−0.301203	+	0.953560i	$0.597388\pi$
$37$	−6.78238	+	9.33514i	−1.11502	+	1.53469i	−0.813812	+	0.581128i	$0.802612\pi$
$38$	2.29930	−	0.747087i	0.372995	−	0.121194i
$39$	0.772198	+	2.37658i	0.123651	+	0.380558i
$40$	1.10384	+	1.73953i	0.174532	+	0.275043i
$41$	0.754463	−	0.548149i	0.117827	−	0.0856066i	−0.527311	−	0.849672i	$-0.676800\pi$
$41$	0.754463	−	0.548149i	0.117827	−	0.0856066i	0.645138	+	0.764066i	$0.276800\pi$
$42$	−6.64396	−	2.15875i	−1.02519	−	0.333103i
$43$		−	0.552188i		−	0.0842079i	−0.999113	−	0.0421040i	$-0.986594\pi$
$43$		−	0.552188i		−	0.0842079i	0.999113	−	0.0421040i	$-0.0134061\pi$
$44$	6.76431	+	4.42643i	1.01976	+	0.667309i
$45$	0.823234	−	2.07901i	0.122721	−	0.309921i
$46$	−3.83425	+	11.8006i	−0.565329	+	1.73990i
$47$	1.25449	+	1.72666i	0.182987	+	0.251860i	0.890649	−	0.454691i	$-0.150250\pi$
$47$	1.25449	+	1.72666i	0.182987	+	0.251860i	−0.707663	+	0.706551i	$0.750250\pi$
$48$	1.72452	−	2.37360i	0.248913	−	0.342600i
$49$	−1.23546	−	3.80234i	−0.176494	−	0.543192i
$50$	−9.52978	−	4.48530i	−1.34771	−	0.634317i
$51$	5.50956	+	4.00293i	0.771493	+	0.560522i
$52$	3.58005	+	4.92751i	0.496463	+	0.683323i
$53$	−11.0661	−	3.59560i	−1.52005	−	0.493893i	−0.574258	−	0.818674i	$-0.694709\pi$
$53$	−11.0661	−	3.59560i	−1.52005	−	0.493893i	−0.945789	+	0.324781i	$0.894709\pi$
$54$	2.10651			0.286660
$55$	−7.41547	−	0.103836i	−0.999902	−	0.0140013i
$56$	−3.05549			−0.408307
$57$	−1.09152	−	0.354657i	−0.144575	−	0.0469754i
$58$	1.38993	+	1.91308i	0.182507	+	0.251199i
$59$	6.79443	+	4.93644i	0.884559	+	0.642670i	0.934454	−	0.356085i	$-0.115889\pi$
$59$	6.79443	+	4.93644i	0.884559	+	0.642670i	−0.0498947	+	0.998754i	$0.515889\pi$
$60$	0.342435	−	5.43938i	0.0442081	−	0.702221i
$61$	−2.53800	−	7.81115i	−0.324957	−	1.00012i	−0.971460	−	0.237204i	$-0.923769\pi$
$61$	−2.53800	−	7.81115i	−0.324957	−	1.00012i	0.646503	−	0.762912i	$-0.276231\pi$
$62$	1.35794	−	1.86905i	0.172459	−	0.237369i
$63$	1.94929	+	2.68296i	0.245587	+	0.338022i
$64$	3.40931	−	10.4928i	0.426164	−	1.31160i
$65$	−5.19521	−	2.05717i	−0.644386	−	0.255160i
$66$	−2.48096	−	6.53116i	−0.305385	−	0.803930i
$67$		−	4.15419i		−	0.507515i	−0.967268	−	0.253757i	$-0.918334\pi$
$67$		−	4.15419i		−	0.507515i	0.967268	−	0.253757i	$-0.0816665\pi$
$68$	15.7866	+	5.12938i	1.91441	+	0.622029i
$69$	4.76532	−	3.46221i	0.573677	−	0.416801i
$70$	13.1895	−	8.36956i	1.57644	−	1.00035i
$71$	3.87323	+	11.9206i	0.459668	+	1.41471i	0.865566	+	0.500795i	$0.166959\pi$
$71$	3.87323	+	11.9206i	0.459668	+	1.41471i	−0.405897	+	0.913919i	$0.633041\pi$
$72$	0.876254	−	0.284712i	0.103268	−	0.0335537i
$73$	3.37248	−	4.64182i	0.394719	−	0.543284i	−0.564690	−	0.825303i	$-0.691004\pi$
$73$	3.37248	−	4.64182i	0.394719	−	0.543284i	0.959409	+	0.282019i	$0.0910041\pi$
$74$	19.6646	−	14.2871i	2.28596	−	1.66085i
$75$	2.40842	+	4.38173i	0.278100	+	0.505958i
$76$	−2.79736			−0.320880
$77$	6.02265	−	9.20358i	0.686344	−	1.04885i
$78$		−	5.26393i		−	0.596022i
$79$	1.19514	−	3.67825i	0.134463	−	0.413835i	−0.861043	−	0.508532i	$-0.830188\pi$
$79$	1.19514	−	3.67825i	0.134463	−	0.413835i	0.995506	+	0.0946970i	$0.0301882\pi$
$80$	1.63127	+	6.35443i	0.182382	+	0.710447i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.86831	+	0.607052i	−0.206321	+	0.0670377i
$83$	−5.78295	+	1.87899i	−0.634761	+	0.206246i	−0.608683	−	0.793414i	$-0.708302\pi$
$83$	−5.78295	+	1.87899i	−0.634761	+	0.206246i	−0.0260781	+	0.999660i	$0.508302\pi$
$84$	6.53941	+	4.75116i	0.713508	+	0.518394i
$85$	−14.7498	+	3.78647i	−1.59984	+	0.410701i
$86$	−0.359446	+	1.10626i	−0.0387600	+	0.119291i
$87$		−	1.12257i		−	0.120352i
$88$	−1.91476	−	2.38147i	−0.204114	−	0.253866i
$89$	−12.5950			−1.33506			−0.667531	−	0.744582i	$-0.732649\pi$
$89$	−12.5950			−1.33506			−0.667531	+	0.744582i	$0.732649\pi$
$90$	−3.00260	+	3.62923i	−0.316502	+	0.382554i
$91$	6.70442	−	4.87105i	0.702814	−	0.510624i
$92$	8.43872	−	11.6149i	0.879798	−	1.21094i
$93$	−1.04305	+	0.338908i	−0.108159	+	0.0351431i
$94$	−1.38930	−	4.27582i	−0.143295	−	0.441017i
$95$	2.16687	−	1.37502i	0.222316	−	0.141074i
$96$	−6.49079	+	4.71583i	−0.662463	+	0.481308i
$97$	−2.72832	−	0.886486i	−0.277019	−	0.0900090i	0.167213	−	0.985921i	$-0.446523\pi$
$97$	−2.72832	−	0.886486i	−0.277019	−	0.0900090i	−0.444232	+	0.895912i	$0.646523\pi$
$98$			8.42187i			0.850737i
$99$	−0.869581	+	3.20060i	−0.0873962	+	0.321672i
$100$	8.88321	+	8.34322i	0.888321	+	0.834322i
$101$	3.05000	−	9.38694i	0.303487	−	0.934036i	−0.676751	−	0.736212i	$-0.736613\pi$
$101$	3.05000	−	9.38694i	0.303487	−	0.934036i	0.980238	−	0.197824i	$-0.0633873\pi$
$102$	−8.43221	−	11.6059i	−0.834913	−	1.14916i
$103$	−4.53743	+	6.24523i	−0.447086	+	0.615361i	−0.971768	−	0.235937i	$-0.924184\pi$
$103$	−4.53743	+	6.24523i	−0.447086	+	0.615361i	0.524682	+	0.851298i	$0.324184\pi$
$104$	−0.711463	−	2.18966i	−0.0697647	−	0.214714i
$105$	−7.40088	−	0.465920i	−0.722252	−	0.0454691i
$106$	19.8294	+	14.4069i	1.92600	+	1.39932i
$107$	9.11737	+	12.5490i	0.881409	+	1.21316i	0.976029	+	0.217642i	$0.0698366\pi$
$107$	9.11737	+	12.5490i	0.881409	+	1.21316i	−0.0946194	+	0.995514i	$0.530163\pi$
$108$	−2.31809	−	0.753192i	−0.223058	−	0.0724760i
$109$	−6.79834			−0.651163			−0.325581	−	0.945514i	$-0.605560\pi$
$109$	−6.79834			−0.651163			−0.325581	+	0.945514i	$0.605560\pi$
$110$	14.7886	+	5.03511i	1.41004	+	0.480079i
$111$	−11.5389			−1.09522
$112$	−9.25367	−	3.00670i	−0.874390	−	0.284106i
$113$	−0.177211	−	0.243910i	−0.0166706	−	0.0229451i	0.800600	−	0.599199i	$-0.204514\pi$
$113$	−0.177211	−	0.243910i	−0.0166706	−	0.0229451i	−0.817271	+	0.576254i	$0.804514\pi$
$114$	1.95590	+	1.42104i	0.183187	+	0.133093i
$115$	−0.827539	+	13.1450i	−0.0771684	+	1.22578i
$116$	−0.845508	−	2.60221i	−0.0785034	−	0.241609i
$117$	−1.46881	+	2.02164i	−0.135791	+	0.186901i
$118$	−10.3987	−	14.3125i	−0.957274	−	1.31757i
$119$	6.97909	−	21.4794i	0.639772	−	1.96902i
$120$	−0.758486	+	1.91549i	−0.0692399	+	0.174860i
$121$	10.9475	−	1.07343i	0.995227	−	0.0975844i
$122$			17.3010i			1.56636i
$123$	0.886924	+	0.288179i	0.0799713	+	0.0259842i
$124$	−2.16262	+	1.57124i	−0.194209	+	0.141101i
$125$	−10.9821	−	2.09630i	−0.982265	−	0.187499i
$126$	−2.15875	−	6.64396i	−0.192317	−	0.591891i
$127$	6.37720	−	2.07208i	0.565885	−	0.183867i	−0.0120823	−	0.999927i	$-0.503846\pi$
$127$	6.37720	−	2.07208i	0.565885	−	0.183867i	0.577968	+	0.816060i	$0.303846\pi$
$128$	−4.22884	+	5.82050i	−0.373780	+	0.514464i
$129$	0.446730	−	0.324568i	0.0393324	−	0.0285766i
$130$	9.06902	+	7.50316i	0.795406	+	0.658070i
$131$	−8.07729			−0.705716			−0.352858	−	0.935677i	$-0.614790\pi$
$131$	−8.07729			−0.705716			−0.352858	+	0.935677i	$0.614790\pi$
$132$	0.394902	+	8.07423i	0.0343718	+	0.702771i
$133$			3.80612i			0.330033i
$134$	−2.70416	+	8.32254i	−0.233604	+	0.718958i
$135$	2.16584	−	0.556001i	0.186406	−	0.0478530i
$136$	−5.07622	−	3.68809i	−0.435282	−	0.316251i
$137$	6.12273	−	1.98939i	0.523100	−	0.169965i	−0.0355519	−	0.999368i	$-0.511319\pi$
$137$	6.12273	−	1.98939i	0.523100	−	0.169965i	0.558652	+	0.829402i	$0.311319\pi$
$138$	−11.8006	+	3.83425i	−1.00453	+	0.326393i
$139$	5.64344	+	4.10020i	0.478670	+	0.347774i	0.800811	−	0.598918i	$-0.204402\pi$
$139$	5.64344	+	4.10020i	0.478670	+	0.347774i	−0.322140	+	0.946692i	$0.604402\pi$
$140$	−17.5068	+	4.49424i	−1.47960	+	0.379833i
$141$	−0.659526	+	2.02981i	−0.0555421	+	0.170941i
$142$		−	26.4031i		−	2.21570i
$143$	7.99793	+	2.17298i	0.668820	+	0.181714i
$144$	2.93393			0.244495
$145$	1.93403	+	1.60010i	0.160612	+	0.132881i
$146$	−9.77805	+	7.10417i	−0.809237	+	0.587945i
$147$	2.34998	−	3.23447i	0.193823	−	0.266774i
$148$	−26.7481	+	8.69099i	−2.19868	+	0.714395i
$149$	5.87766	+	18.0896i	0.481516	+	1.48196i	0.836963	+	0.547259i	$0.184329\pi$
$149$	5.87766	+	18.0896i	0.481516	+	1.48196i	−0.355447	+	0.934696i	$0.615671\pi$
$150$	−1.97278	−	10.3461i	−0.161077	−	0.844759i
$151$	−3.15582	+	2.29284i	−0.256817	+	0.186589i	−0.708743	−	0.705467i	$-0.750737\pi$
$151$	−3.15582	+	2.29284i	−0.256817	+	0.186589i	0.451925	+	0.892056i	$0.350737\pi$
$152$	1.00567	+	0.326762i	0.0815707	+	0.0265039i
$153$			6.81019i			0.550571i
$154$	−18.0569	+	14.5181i	−1.45506	+	1.16990i
$155$	0.902865	−	2.28011i	0.0725199	−	0.183143i
$156$	−1.88214	+	5.79264i	−0.150692	+	0.463782i
$157$	10.8060	+	14.8732i	0.862413	+	1.18701i	0.980989	+	0.194065i	$0.0621673\pi$
$157$	10.8060	+	14.8732i	0.862413	+	1.18701i	−0.118575	+	0.992945i	$0.537833\pi$
$158$	−4.78869	+	6.59107i	−0.380968	+	0.524357i
$159$	−3.59560	−	11.0661i	−0.285149	−	0.877600i
$160$	1.12718	−	17.9047i	0.0891115	−	1.41549i
$161$	−15.8034	−	11.4818i	−1.24548	−	0.904894i
$162$	1.23818	+	1.70420i	0.0972802	+	0.133895i
$163$	16.7120	+	5.43005i	1.30898	+	0.425314i	0.878698	−	0.477379i	$-0.158413\pi$
$163$	16.7120	+	5.43005i	1.30898	+	0.425314i	0.430285	+	0.902693i	$0.358413\pi$
$164$	2.27302			0.177493
$165$	−4.27470	−	6.06028i	−0.332785	−	0.471792i
$166$	12.8087			0.994151
$167$	−11.4865	−	3.73220i	−0.888855	−	0.288807i	−0.171226	−	0.985232i	$-0.554773\pi$
$167$	−11.4865	−	3.73220i	−0.888855	−	0.288807i	−0.717629	+	0.696425i	$0.754773\pi$
$168$	−1.79597	−	2.47194i	−0.138562	−	0.190715i
$169$	−5.46537	−	3.97083i	−0.420413	−	0.305448i
$170$	32.0146	+	2.01547i	2.45541	+	0.154580i
$171$	−0.354657	−	1.09152i	−0.0271213	−	0.0834707i
$172$	0.791097	−	1.08885i	0.0603206	−	0.0830241i
$173$	−14.2500	−	19.6135i	−1.08341	−	1.49119i	−0.855711	−	0.517454i	$-0.826880\pi$
$173$	−14.2500	−	19.6135i	−1.08341	−	1.49119i	−0.227698	−	0.973732i	$-0.573120\pi$
$174$	−0.730731	+	2.24896i	−0.0553966	+	0.170493i
$175$	11.3519	−	12.0866i	0.858121	−	0.913660i
$176$	−3.45547	−	9.09656i	−0.260466	−	0.685679i
$177$			8.39837i			0.631260i
$178$	25.2329	+	8.19865i	1.89128	+	0.614515i
$179$	−16.1310	+	11.7198i	−1.20569	+	0.875982i	−0.994832	−	0.101535i	$-0.967625\pi$
$179$	−16.1310	+	11.7198i	−1.20569	+	0.875982i	−0.210854	+	0.977517i	$0.567625\pi$
$180$	4.60183	−	2.92015i	0.343000	−	0.217655i
$181$	−1.58615	−	4.88168i	−0.117898	−	0.362852i	0.874643	−	0.484768i	$-0.161096\pi$
$181$	−1.58615	−	4.88168i	−0.117898	−	0.362852i	−0.992540	+	0.121916i	$0.961096\pi$
$182$	−16.6025	+	5.39448i	−1.23066	+	0.399865i
$183$	4.82756	−	6.64456i	0.356863	−	0.491180i
$184$	−4.39052	+	3.18990i	−0.323674	+	0.235163i
$185$	16.4474	−	19.8799i	1.20924	−	1.46160i
$186$	2.31027			0.169397
$187$	21.1148	−	8.02076i	1.54406	−	0.586536i
$188$			5.20204i			0.379397i
$189$	−1.02480	+	3.15401i	−0.0745433	+	0.229421i
$190$	−5.23619	+	1.34420i	−0.379873	+	0.0975187i
$191$	2.27606	+	1.65365i	0.164690	+	0.119654i	0.667078	−	0.744988i	$-0.267545\pi$
$191$	2.27606	+	1.65365i	0.164690	+	0.119654i	−0.502388	+	0.864642i	$0.667545\pi$
$192$	10.4928	−	3.40931i	0.757252	−	0.246046i
$193$	−18.3584	+	5.96502i	−1.32147	+	0.429371i	−0.882999	−	0.469374i	$-0.844480\pi$
$193$	−18.3584	+	5.96502i	−1.32147	+	0.429371i	−0.438470	+	0.898746i	$0.644480\pi$
$194$	4.88889	+	3.55199i	0.351002	+	0.255018i
$195$	−1.38938	−	5.41219i	−0.0994958	−	0.387575i
$196$	3.01128	−	9.26776i	0.215091	−	0.661983i
$197$			3.57956i			0.255033i	0.991836	+	0.127516i	$0.0407006\pi$
$197$			3.57956i			0.255033i	−0.991836	+	0.127516i	$0.959299\pi$
$198$	3.82555	−	5.84606i	0.271870	−	0.415461i
$199$	−12.7087			−0.900893			−0.450447	−	0.892803i	$-0.648735\pi$
$199$	−12.7087			−0.900893			−0.450447	+	0.892803i	$0.648735\pi$
$200$	−2.21899	−	4.03710i	−0.156906	−	0.285466i
$201$	3.36081	−	2.44177i	0.237053	−	0.172229i
$202$	−12.2208	+	16.8205i	−0.859853	+	1.18349i
$203$	−3.54059	+	1.15041i	−0.248500	+	0.0807427i
$204$	5.12938	+	15.7866i	0.359129	+	1.10528i
$205$	−1.76071	+	1.11728i	−0.122973	+	0.0780343i
$206$	13.1556	−	9.55813i	0.916597	−	0.665947i
$207$	5.60197	+	1.82019i	0.389364	+	0.126512i
$208$		−	7.33157i		−	0.508353i
$209$	−2.96652	+	2.38515i	−0.205199	+	0.164984i
$210$	14.5237	+	5.75101i	1.00223	+	0.396857i
$211$	−1.08007	+	3.32412i	−0.0743552	+	0.228842i	−0.981326	−	0.192352i	$-0.938389\pi$
$211$	−1.08007	+	3.32412i	−0.0743552	+	0.228842i	0.906971	+	0.421193i	$0.138389\pi$
$212$	−16.6698	−	22.9440i	−1.14489	−	1.57580i
$213$	−7.36733	+	10.1403i	−0.504801	+	0.694799i
$214$	−10.0971	−	31.0757i	−0.690223	−	2.12429i
$215$	−0.0775785	+	1.23229i	−0.00529081	+	0.0840416i
$216$	0.745386	+	0.541555i	0.0507171	+	0.0368481i
$217$	2.13784	+	2.94249i	0.145126	+	0.199749i
$218$	13.6199	+	4.42536i	0.922453	+	0.299723i
$219$	5.73761			0.387712
$220$	−14.4737	−	10.8286i	−0.975815	−	0.730063i
$221$	17.0179			1.14475
$222$	23.1171	+	7.51119i	1.55152	+	0.504118i
$223$	−3.05976	−	4.21140i	−0.204897	−	0.282016i	0.694185	−	0.719796i	$-0.255765\pi$
$223$	−3.05976	−	4.21140i	−0.204897	−	0.282016i	−0.899082	+	0.437780i	$0.855765\pi$
$224$	21.5256	+	15.6392i	1.43824	+	1.04494i
$225$	−2.12926	+	4.52397i	−0.141950	+	0.301598i
$226$	0.196253	+	0.604005i	0.0130546	+	0.0401778i
$227$	−5.70295	+	7.84944i	−0.378518	+	0.520985i	−0.955191	−	0.295990i	$-0.904351\pi$
$227$	−5.70295	+	7.84944i	−0.378518	+	0.520985i	0.576673	+	0.816975i	$0.304351\pi$
$228$	−1.64425	−	2.26312i	−0.108893	−	0.149878i
$229$	−5.71715	+	17.5956i	−0.377800	+	1.16275i	0.563770	+	0.825932i	$0.309350\pi$
$229$	−5.71715	+	17.5956i	−0.377800	+	1.16275i	−0.941570	+	0.336817i	$0.890650\pi$
$230$	10.2146	−	25.7961i	0.673531	−	1.70095i
$231$	10.9859	−	0.537307i	0.722818	−	0.0353522i
$232$			1.03427i			0.0679034i
$233$	−14.2224	−	4.62115i	−0.931742	−	0.302741i	−0.196467	−	0.980510i	$-0.562947\pi$
$233$	−14.2224	−	4.62115i	−0.931742	−	0.302741i	−0.735275	+	0.677769i	$0.762947\pi$
$234$	4.25861	−	3.09406i	0.278394	−	0.202265i
$235$	−2.55701	−	4.02955i	−0.166801	−	0.262859i
$236$	6.32559	+	19.4682i	0.411761	+	1.26727i
$237$	3.67825	−	1.19514i	0.238928	−	0.0776324i
$238$	−27.9639	+	38.4891i	−1.81263	+	2.49488i
$239$	−1.21932	+	0.885887i	−0.0788712	+	0.0573033i	−0.626522	−	0.779404i	$-0.715522\pi$
$239$	−1.21932	+	0.885887i	−0.0788712	+	0.0573033i	0.547651	+	0.836707i	$0.315522\pi$
$240$	−4.18201	+	5.05477i	−0.269947	+	0.326284i
$241$	−7.09571			−0.457075			−0.228537	−	0.973535i	$-0.573394\pi$
$241$	−7.09571			−0.457075			−0.228537	+	0.973535i	$0.573394\pi$
$242$	−22.6311	−	4.97573i	−1.45478	−	0.319852i
$243$		−	1.00000i		−	0.0641500i
$244$	6.18607	−	19.0388i	0.396022	−	1.21883i
$245$	2.22290	+	8.65907i	0.142016	+	0.553208i
$246$	−1.58928	−	1.15468i	−0.101329	−	0.0736198i
$247$	−2.72758	+	0.886246i	−0.173552	+	0.0563905i
$248$	0.961014	−	0.312252i	0.0610244	−	0.0198280i
$249$	−4.91927	−	3.57406i	−0.311746	−	0.226497i
$250$	20.6370	+	11.3485i	1.30520	+	0.717741i
$251$	−4.22692	+	13.0091i	−0.266801	+	0.821129i	0.724472	+	0.689304i	$0.242084\pi$
$251$	−4.22692	+	13.0091i	−0.266801	+	0.821129i	−0.991273	+	0.131825i	$0.957916\pi$
$252$			8.08315i			0.509191i
$253$	−0.954333	−	19.5125i	−0.0599984	−	1.22674i
$254$	−14.1250			−0.886279
$255$	−11.7330	−	9.70719i	−0.734750	−	0.607888i
$256$	−5.59047	+	4.06172i	−0.349405	+	0.253857i
$257$	4.88104	−	6.71817i	0.304471	−	0.419068i	−0.629176	−	0.777263i	$-0.716608\pi$
$257$	4.88104	−	6.71817i	0.304471	−	0.419068i	0.933647	+	0.358195i	$0.116608\pi$
$258$	−1.10626	+	0.359446i	−0.0688727	+	0.0223781i
$259$	11.8250	+	36.3937i	0.734773	+	2.26140i
$260$	−7.29713	−	11.4994i	−0.452549	−	0.713166i
$261$	0.908175	−	0.659827i	0.0562146	−	0.0408423i
$262$	16.1821	+	5.25789i	0.999735	+	0.324834i
$263$			11.1345i			0.686582i	0.939229	+	0.343291i	$0.111542\pi$
$263$			11.1345i			0.686582i	−0.939229	+	0.343291i	$0.888458\pi$
$264$	0.801187	−	2.94887i	0.0493096	−	0.181490i
$265$	24.1905	+	9.57882i	1.48601	+	0.588422i
$266$	2.47759	−	7.62522i	0.151910	−	0.467532i
$267$	−7.40313	−	10.1895i	−0.453064	−	0.623589i
$268$	5.95153	−	8.19157i	0.363547	−	0.500380i
$269$	−7.03209	−	21.6426i	−0.428754	−	1.31957i	−0.899353	−	0.437223i	$-0.855962\pi$
$269$	−7.03209	−	21.6426i	−0.428754	−	1.31957i	0.470599	−	0.882347i	$-0.344038\pi$
$270$	−4.70099	−	0.295949i	−0.286093	−	0.0180109i
$271$	−6.30586	−	4.58148i	−0.383054	−	0.278305i	0.379549	−	0.925172i	$-0.376079\pi$
$271$	−6.30586	−	4.58148i	−0.383054	−	0.278305i	−0.762603	+	0.646867i	$0.776079\pi$
$272$	−11.7443	−	16.1647i	−0.712105	−	0.980128i
$273$	7.88152	+	2.56086i	0.477011	+	0.154990i
$274$	−13.5613			−0.819269
$275$	16.5341	+	1.27355i	0.997047	+	0.0767978i
$276$	14.3568			0.864179
$277$	−9.00383	−	2.92552i	−0.540988	−	0.175778i	0.0257612	−	0.999668i	$-0.491799\pi$
$277$	−9.00383	−	2.92552i	−0.540988	−	0.175778i	−0.566749	+	0.823891i	$0.691799\pi$
$278$	−8.63711	−	11.8880i	−0.518019	−	0.712992i
$279$	−0.887273	−	0.644641i	−0.0531196	−	0.0385937i
$280$	6.81879	+	0.429275i	0.407501	+	0.0256541i
$281$	9.67271	+	29.7696i	0.577026	+	1.77590i	0.629175	+	0.777263i	$0.283393\pi$
$281$	9.67271	+	29.7696i	0.577026	+	1.77590i	−0.0521495	+	0.998639i	$0.516607\pi$
$282$	2.64260	−	3.63723i	0.157365	−	0.216594i
$283$	14.3492	+	19.7500i	0.852972	+	1.17402i	0.983200	+	0.182531i	$0.0584291\pi$
$283$	14.3492	+	19.7500i	0.852972	+	1.17402i	−0.130228	+	0.991484i	$0.541571\pi$
$284$	−9.44055	+	29.0550i	−0.560194	+	1.72410i
$285$	2.38607	+	0.944820i	0.141338	+	0.0559663i
$286$	−14.6086	−	9.55960i	−0.863826	−	0.565271i
$287$		−	3.09270i		−	0.182556i
$288$	−7.63038	−	2.47926i	−0.449624	−	0.146092i
$289$	23.7678	−	17.2684i	1.39811	−	1.01579i
$290$	−2.83307	−	4.46460i	−0.166364	−	0.262170i
$291$	−0.886486	−	2.72832i	−0.0519667	−	0.159937i
$292$	13.3003	−	4.32152i	0.778340	−	0.252898i
$293$	6.94742	−	9.56230i	0.405873	−	0.558636i	−0.556333	−	0.830959i	$-0.687792\pi$
$293$	6.94742	−	9.56230i	0.405873	−	0.558636i	0.962206	+	0.272324i	$0.0877922\pi$
$294$	−6.81343	+	4.95025i	−0.397367	+	0.288704i
$295$	−14.4692	−	11.9710i	−0.842432	−	0.696977i
$296$	10.6313			0.617933
$297$	−3.10047	+	1.17776i	−0.179907	+	0.0683405i
$298$		−	40.0669i		−	2.32101i
$299$	4.54845	−	13.9987i	0.263044	−	0.809565i
$300$	−1.52839	+	12.0907i	−0.0882415	+	0.698056i
$301$	−1.48150	−	1.07637i	−0.0853923	−	0.0620412i
$302$	7.81492	−	2.53922i	0.449698	−	0.146116i
$303$	9.38694	−	3.05000i	0.539266	−	0.175218i
$304$	2.72417	+	1.97922i	0.156242	+	0.113516i
$305$	4.56651	+	17.7883i	0.261478	+	1.01856i
$306$	4.43307	−	13.6436i	0.253422	−	0.779952i
$307$		−	22.3217i		−	1.27396i	−0.770878	−	0.636982i	$-0.780182\pi$
$307$		−	22.3217i		−	1.27396i	0.770878	−	0.636982i	$-0.219818\pi$
$308$	25.0615	−	9.52000i	1.42801	−	0.542453i
$309$	−7.71953			−0.439149
$310$	−3.29304	+	3.98028i	−0.187032	+	0.226065i
$311$	15.7624	−	11.4521i	0.893804	−	0.649386i	−0.0430633	−	0.999072i	$-0.513712\pi$
$311$	15.7624	−	11.4521i	0.893804	−	0.649386i	0.936867	+	0.349686i	$0.113712\pi$
$312$	1.35328	−	1.86264i	0.0766146	−	0.105451i
$313$	−16.5034	+	5.36228i	−0.932827	+	0.303094i	−0.735718	−	0.677288i	$-0.763155\pi$
$313$	−16.5034	+	5.36228i	−0.932827	+	0.303094i	−0.197109	+	0.980382i	$0.563155\pi$
$314$	−11.9672	−	36.8312i	−0.675348	−	2.07851i
$315$	−3.97319	−	6.26130i	−0.223864	−	0.352784i
$316$	7.62634	−	5.54086i	0.429015	−	0.311698i
$317$	−0.790059	−	0.256706i	−0.0443741	−	0.0144180i	0.286746	−	0.958007i	$-0.407426\pi$
$317$	−0.790059	−	0.256706i	−0.0443741	−	0.0144180i	−0.331120	+	0.943589i	$0.607426\pi$
$318$			24.5105i			1.37448i
$319$	−3.11538	−	2.03865i	−0.174428	−	0.114142i
$320$	−9.08256	+	22.9373i	−0.507731	+	1.28223i
$321$	−4.79328	+	14.7522i	−0.267535	+	0.823388i
$322$	24.1865	+	33.2899i	1.34786	+	1.85518i
$323$	−4.59413	+	6.32328i	−0.255624	+	0.351837i
$324$	−0.753192	−	2.31809i	−0.0418440	−	0.128783i
$325$	11.3049	+	5.32077i	0.627081	+	0.295143i
$326$	−29.9462	−	21.7572i	−1.65857	−	1.20502i
$327$	−3.99596	−	5.49997i	−0.220977	−	0.304149i
$328$	−0.817166	−	0.265513i	−0.0451205	−	0.0146605i
$329$	7.07794			0.390220
$330$	4.61905	+	14.9238i	0.254271	+	0.821529i
$331$	−31.5311			−1.73311			−0.866554	−	0.499084i	$-0.833670\pi$
$331$	−31.5311			−1.73311			−0.866554	+	0.499084i	$0.833670\pi$
$332$	−14.0953	−	4.57982i	−0.773577	−	0.251351i
$333$	−6.78238	−	9.33514i	−0.371672	−	0.511563i
$334$	20.5828	+	14.9543i	1.12624	+	0.818261i
$335$	−0.583634	+	9.27069i	−0.0318873	+	0.506512i
$336$	−3.00670	−	9.25367i	−0.164029	−	0.504829i
$337$	9.54207	−	13.1335i	0.519790	−	0.715429i	−0.465742	−	0.884921i	$-0.654212\pi$
$337$	9.54207	−	13.1335i	0.519790	−	0.715429i	0.985532	+	0.169491i	$0.0542124\pi$
$338$	8.36458	+	11.5129i	0.454973	+	0.626217i
$339$	0.0931652	−	0.286733i	0.00506004	−	0.0155732i
$340$	−34.5096	−	13.6649i	−1.87154	−	0.741083i
$341$	−0.953695	+	3.51019i	−0.0516455	+	0.190087i
$342$			2.41763i			0.130730i
$343$	9.46829	+	3.07643i	0.511239	+	0.166112i
$344$	−0.411594	+	0.299040i	−0.0221916	+	0.0161232i
$345$	−11.1209	+	7.05695i	−0.598732	+	0.379933i
$346$	15.7813	+	48.5698i	0.848408	+	2.61113i
$347$	−11.8406	+	3.84726i	−0.635639	+	0.206532i	−0.609071	−	0.793115i	$-0.708458\pi$
$347$	−11.8406	+	3.84726i	−0.635639	+	0.206532i	−0.0265674	+	0.999647i	$0.508458\pi$
$348$	1.60825	−	2.21357i	0.0862113	−	0.118660i
$349$	26.3980	−	19.1793i	1.41305	−	1.02664i	0.420182	−	0.907440i	$-0.361966\pi$
$349$	26.3980	−	19.1793i	1.41305	−	1.02664i	0.992870	−	0.119203i	$-0.0380338\pi$
$350$	−30.6102	+	16.8249i	−1.63618	+	0.899329i
$351$	−2.49889			−0.133381
$352$	1.29989	+	26.5777i	0.0692842	+	1.41660i
$353$		−	15.7921i		−	0.840530i	−0.907402	−	0.420265i	$-0.861937\pi$
$353$		−	15.7921i		−	0.840530i	0.907402	−	0.420265i	$-0.138063\pi$
$354$	5.46690	−	16.8254i	0.290562	−	0.894259i
$355$	−6.96895	−	27.1467i	−0.369873	−	1.44080i
$356$	−24.8358	−	18.0443i	−1.31629	−	0.956343i
$357$	21.4794	−	6.97909i	1.13681	−	0.369373i
$358$	39.9460	−	12.9792i	2.11121	−	0.685974i
$359$	14.6935	+	10.6755i	0.775494	+	0.563429i	0.903623	−	0.428328i	$-0.140897\pi$
$359$	14.6935	+	10.6755i	0.775494	+	0.563429i	−0.128129	+	0.991757i	$0.540897\pi$
$360$	−1.99549	+	0.512271i	−0.105172	+	0.0269990i
$361$	−5.46429	+	16.8173i	−0.287594	+	0.885123i
$362$			10.8125i			0.568292i
$363$	7.30320	+	8.22577i	0.383319	+	0.431741i
$364$	20.1989			1.05871
$365$	−8.17834	+	9.88512i	−0.428074	+	0.517411i
$366$	−13.9968	+	10.1693i	−0.731626	+	0.531558i
$367$	0.277462	−	0.381893i	0.0144834	−	0.0199347i	−0.801714	−	0.597708i	$-0.796078\pi$
$367$	0.277462	−	0.381893i	0.0144834	−	0.0199347i	0.816197	+	0.577773i	$0.196078\pi$
$368$	−16.4358	+	5.34032i	−0.856776	+	0.278383i
$369$	0.288179	+	0.886924i	0.0150020	+	0.0461714i
$370$	−45.8917	+	29.1212i	−2.38579	+	1.51394i
$371$	−31.2179	+	22.6811i	−1.62075	+	1.17755i
$372$	−2.54231	−	0.826048i	−0.131813	−	0.0428286i
$373$			15.4102i			0.797910i	0.916970	+	0.398955i	$0.130627\pi$
$373$			15.4102i			0.797910i	−0.916970	+	0.398955i	$0.869373\pi$
$374$	−47.5226	+	2.32428i	−2.45733	+	0.120186i
$375$	−4.75915	−	10.1168i	−0.245761	−	0.522432i
$376$	0.607653	−	1.87017i	0.0313373	−	0.0964464i
$377$	−1.64883	−	2.26942i	−0.0849192	−	0.116881i
$378$	4.10619	−	5.65169i	0.211200	−	0.290692i
$379$	5.95617	+	18.3312i	0.305948	+	0.941611i	0.979322	+	0.202309i	$0.0648444\pi$
$379$	5.95617	+	18.3312i	0.305948	+	0.941611i	−0.673374	+	0.739302i	$0.735156\pi$
$380$	6.24274	+	0.393010i	0.320246	+	0.0201610i
$381$	5.42477	+	3.94133i	0.277920	+	0.201920i
$382$	−3.48344	−	4.79454i	−0.178228	−	0.245310i
$383$	−7.08369	−	2.30163i	−0.361960	−	0.117608i	0.122390	−	0.992482i	$-0.460944\pi$
$383$	−7.08369	−	2.30163i	−0.361960	−	0.117608i	−0.484350	+	0.874874i	$0.660944\pi$
$384$	−7.19453			−0.367144
$385$	−14.7335	+	19.6930i	−0.750887	+	1.00365i
$386$	40.6624			2.06966
$387$	0.525162	+	0.170636i	0.0266955	+	0.00867390i
$388$	−4.10990	−	5.65680i	−0.208649	−	0.287180i
$389$	−0.577492	−	0.419572i	−0.0292800	−	0.0212732i	0.573049	−	0.819521i	$-0.305760\pi$
$389$	−0.577492	−	0.419572i	−0.0292800	−	0.0212732i	−0.602329	+	0.798248i	$0.705760\pi$
$390$	−0.739544	+	11.7472i	−0.0374483	+	0.594845i
$391$	−12.3958	−	38.1505i	−0.626885	−	1.92935i
$392$	−2.16515	+	2.98007i	−0.109356	+	0.150516i
$393$	−4.74771	−	6.53467i	−0.239490	−	0.329630i
$394$	2.33010	−	7.17132i	0.117389	−	0.361286i
$395$	−3.18389	+	8.04066i	−0.160199	+	0.404569i
$396$	−6.30007	+	5.06539i	−0.316590	+	0.254546i
$397$			0.764171i			0.0383526i	0.999816	+	0.0191763i	$0.00610438\pi$
$397$			0.764171i			0.0383526i	−0.999816	+	0.0191763i	$0.993896\pi$
$398$	25.4607	+	8.27267i	1.27623	+	0.414672i
$399$	−3.07922	+	2.23718i	−0.154154	+	0.111999i
$400$	−2.74767	−	14.4101i	−0.137384	−	0.720503i
$401$	−4.86839	−	14.9834i	−0.243116	−	0.748234i	−0.995941	−	0.0900128i	$-0.971309\pi$
$401$	−4.86839	−	14.9834i	−0.243116	−	0.748234i	0.752825	−	0.658221i	$-0.228691\pi$
$402$	−8.32254	+	2.70416i	−0.415091	+	0.134871i
$403$	−1.61089	+	2.21719i	−0.0802439	+	0.110446i
$404$	19.4625	−	14.1403i	0.968296	−	0.703508i
$405$	1.72286	+	1.42539i	0.0856098	+	0.0708283i
$406$	7.84210			0.389197
$407$	−20.9553	+	32.0231i	−1.03871	+	1.58732i
$408$		−	6.27456i		−	0.310637i
$409$	0.809935	−	2.49272i	0.0400487	−	0.123257i	−0.929033	−	0.369996i	$-0.879359\pi$
$409$	0.809935	−	2.49272i	0.0400487	−	0.123257i	0.969082	+	0.246739i	$0.0793590\pi$
$410$	4.25471	−	1.09224i	0.210125	−	0.0539421i
$411$	5.20830	+	3.78405i	0.256907	+	0.186654i
$412$	−17.8945	+	5.81429i	−0.881601	+	0.286450i
$413$	26.4886	−	8.60666i	1.30342	−	0.423506i
$414$	−10.0382	−	7.29318i	−0.493350	−	0.358440i
$415$	13.1695	−	3.38079i	0.646465	−	0.165957i
$416$	−6.19539	+	19.0674i	−0.303754	+	0.934858i
$417$			6.97567i			0.341600i
$418$	7.49576	−	2.84738i	0.366630	−	0.139270i
$419$	18.0078			0.879737			0.439868	−	0.898062i	$-0.355025\pi$
$419$	18.0078			0.879737			0.439868	+	0.898062i	$0.355025\pi$
$420$	−13.9262	−	11.5217i	−0.679527	−	0.562199i
$421$	−0.947495	+	0.688395i	−0.0461781	+	0.0335503i	−0.610635	−	0.791912i	$-0.709086\pi$
$421$	−0.947495	+	0.688395i	−0.0461781	+	0.0335503i	0.564457	+	0.825463i	$0.309086\pi$
$422$	4.32765	−	5.95650i	0.210667	−	0.289958i
$423$	−2.02981	+	0.659526i	−0.0986929	+	0.0320673i
$424$	3.31280	+	10.1957i	0.160884	+	0.495149i
$425$	33.4483	−	6.37784i	1.62248	−	0.309371i
$426$	21.3606	−	15.5193i	1.03492	−	0.751915i
$427$	−25.9043	−	8.41683i	−1.25360	−	0.407319i
$428$			37.8072i			1.82748i
$429$	2.94308	+	7.74771i	0.142093	+	0.374063i
$430$	0.957578	−	2.41828i	0.0461785	−	0.116620i
$431$	10.8441	−	33.3746i	0.522340	−	1.60760i	−0.247177	−	0.968970i	$-0.579503\pi$
$431$	10.8441	−	33.3746i	0.522340	−	1.60760i	0.769517	−	0.638626i	$-0.220497\pi$
$432$	1.72452	+	2.37360i	0.0829712	+	0.114200i
$433$	10.7130	−	14.7452i	0.514834	−	0.708608i	−0.469891	−	0.882724i	$-0.655707\pi$
$433$	10.7130	−	14.7452i	0.514834	−	0.708608i	0.984725	+	0.174116i	$0.0557069\pi$
$434$	−2.36757	−	7.28663i	−0.113647	−	0.349769i
$435$	−0.157712	+	2.50517i	−0.00756173	+	0.120114i
$436$	−13.4055	−	9.73969i	−0.642009	−	0.466446i
$437$	3.97355	+	5.46912i	0.190081	+	0.261624i
$438$	−11.4948	−	3.73488i	−0.549242	−	0.178460i
$439$	19.8155			0.945743			0.472871	−	0.881131i	$-0.343218\pi$
$439$	19.8155			0.945743			0.472871	+	0.881131i	$0.343218\pi$
$440$	3.93849	+	5.58362i	0.187760	+	0.266189i
$441$	3.99802			0.190382
$442$	−34.0938	−	11.0777i	−1.62168	−	0.526914i
$443$	9.80922	+	13.5012i	0.466050	+	0.641463i	0.975750	−	0.218890i	$-0.0702435\pi$
$443$	9.80922	+	13.5012i	0.466050	+	0.641463i	−0.509700	+	0.860352i	$0.670243\pi$
$444$	−22.7533	−	16.5312i	−1.07982	−	0.784538i
$445$	28.1075	+	1.76950i	1.33242	+	0.0838824i
$446$	3.38856	+	10.4289i	0.160453	+	0.493823i
$447$	−11.1800	+	15.3879i	−0.528794	+	0.727823i
$448$	−21.5061	−	29.6005i	−1.01607	−	1.39849i
$449$	4.07811	−	12.5511i	0.192458	−	0.592325i	−0.807539	−	0.589815i	$-0.799201\pi$
$449$	4.07811	−	12.5511i	0.192458	−	0.592325i	0.999997	−	0.00251063i	$-0.000799160\pi$
$450$	7.21064	−	7.67732i	0.339913	−	0.361912i
$451$	2.41047	−	1.93807i	0.113505	−	0.0912603i
$452$		−	0.734843i		−	0.0345641i
$453$	−3.70989	−	1.20542i	−0.174306	−	0.0566354i
$454$	16.5349	−	12.0133i	0.776022	−	0.563813i
$455$	−15.6463	+	9.92855i	−0.733508	+	0.465458i
$456$	0.326762	+	1.00567i	0.0153020	+	0.0470948i
$457$	−20.2264	+	6.57194i	−0.946149	+	0.307423i	−0.741150	−	0.671340i	$-0.765719\pi$
$457$	−20.2264	+	6.57194i	−0.946149	+	0.307423i	−0.204999	+	0.978762i	$0.565719\pi$
$458$	22.9076	−	31.5296i	1.07040	−	1.47328i
$459$	−5.50956	+	4.00293i	−0.257164	+	0.186841i
$460$	−20.4641	+	24.7348i	−0.954143	+	1.15327i
$461$	−20.0772			−0.935086			−0.467543	−	0.883970i	$-0.654861\pi$
$461$	−20.0772			−0.935086			−0.467543	+	0.883970i	$0.654861\pi$
$462$	−22.3590	−	6.07478i	−1.04023	−	0.282624i
$463$			0.962526i			0.0447324i	0.999750	+	0.0223662i	$0.00711997\pi$
$463$			0.962526i			0.0447324i	−0.999750	+	0.0223662i	$0.992880\pi$
$464$	−1.01776	+	3.13234i	−0.0472482	+	0.145415i
$465$	2.37534	−	0.609783i	0.110154	−	0.0282780i
$466$	25.4852	+	18.5161i	1.18058	+	0.857742i
$467$	14.1831	−	4.60838i	0.656317	−	0.213250i	0.0381194	−	0.999273i	$-0.487863\pi$
$467$	14.1831	−	4.60838i	0.656317	−	0.213250i	0.618197	+	0.786023i	$0.287863\pi$
$468$	−5.79264	+	1.88214i	−0.267765	+	0.0870020i
$469$	−11.1455	−	8.09771i	−0.514653	−	0.373917i
$470$	2.49971	+	9.73732i	0.115303	+	0.449149i
$471$	−5.68106	+	17.4845i	−0.261769	+	0.805643i
$472$		−	7.73783i		−	0.356162i
$473$	−0.0894649	−	1.82922i	−0.00411360	−	0.0841074i
$474$	−8.14701			−0.374204
$475$	−5.02887	+	2.76412i	−0.230741	+	0.126827i
$476$	44.5346	−	32.3563i	2.04124	−	1.48305i
$477$	6.83923	−	9.41340i	0.313147	−	0.431010i
$478$	3.01946	−	0.981082i	0.138107	−	0.0448737i
$479$	0.146946	+	0.452253i	0.00671413	+	0.0206640i	0.954357	−	0.298667i	$-0.0965419\pi$
$479$	0.146946	+	0.452253i	0.00671413	+	0.0206640i	−0.947643	+	0.319331i	$0.896542\pi$
$480$	15.1477	−	9.61218i	0.691395	−	0.438734i
$481$	−23.3274	+	16.9484i	−1.06364	+	0.772780i
$482$	14.2156	+	4.61893i	0.647503	+	0.210387i
$483$		−	19.5340i		−	0.888829i
$484$	23.1250	+	13.5673i	1.05114	+	0.616697i
$485$	5.96412	+	2.36164i	0.270817	+	0.107236i
$486$	−0.650947	+	2.00341i	−0.0295276	+	0.0908765i
$487$	20.7799	+	28.6011i	0.941629	+	1.29604i	0.955147	+	0.296132i	$0.0956969\pi$
$487$	20.7799	+	28.6011i	0.941629	+	1.29604i	−0.0135183	+	0.999909i	$0.504303\pi$
$488$	−4.44786	+	6.12196i	−0.201345	+	0.277128i
$489$	5.43005	+	16.7120i	0.245555	+	0.755741i
$490$	1.18321	−	18.7947i	0.0534521	−	0.849056i
$491$	24.3779	+	17.7116i	1.10016	+	0.799314i	0.981086	−	0.193572i	$-0.0620072\pi$
$491$	24.3779	+	17.7116i	1.10016	+	0.799314i	0.119075	+	0.992885i	$0.462007\pi$
$492$	1.33605	+	1.83891i	0.0602338	+	0.0829047i
$493$	−7.27072	−	2.36240i	−0.327457	−	0.106397i
$494$	6.04137			0.271814
$495$	2.39026	−	7.02045i	0.107434	−	0.315546i
$496$	3.21773			0.144480
$497$	39.5326	+	12.8449i	1.77328	+	0.576173i
$498$	7.52879	+	10.3625i	0.337373	+	0.464354i
$499$	−29.5127	−	21.4422i	−1.32117	−	0.959887i	−0.999917	−	0.0128935i	$-0.995896\pi$
$499$	−29.5127	−	21.4422i	−1.32117	−	0.959887i	−0.321254	−	0.946993i	$-0.604104\pi$
$500$	−18.6520	−	19.8672i	−0.834145	−	0.888487i
$501$	−3.73220	−	11.4865i	−0.166743	−	0.513181i
$502$	16.9365	−	23.3111i	0.755914	−	1.04043i
$503$	9.06666	+	12.4792i	0.404262	+	0.556420i	0.961807	−	0.273727i	$-0.0882566\pi$
$503$	9.06666	+	12.4792i	0.404262	+	0.556420i	−0.557545	+	0.830147i	$0.688257\pi$
$504$	0.944199	−	2.90595i	0.0420580	−	0.129441i
$505$	−8.12534	+	20.5199i	−0.361573	+	0.913122i
$506$	−10.7897	+	39.7127i	−0.479659	+	1.76544i
$507$		−	6.75557i		−	0.300025i
$508$	15.5437	+	5.05045i	0.689639	+	0.224077i
$509$	10.2238	−	7.42806i	0.453164	−	0.329243i	−0.337680	−	0.941261i	$-0.609642\pi$
$509$	10.2238	−	7.42806i	0.453164	−	0.329243i	0.790844	+	0.612018i	$0.209642\pi$
$510$	17.1872	+	27.0851i	0.761061	+	1.19935i
$511$	−5.87991	−	18.0965i	−0.260112	−	0.800542i
$512$	27.5288	−	8.94464i	1.21661	−	0.395301i
$513$	0.674597	−	0.928503i	0.0297842	−	0.0409944i
$514$	−14.1519	+	10.2819i	−0.624213	+	0.453517i
$515$	11.0034	−	13.2997i	0.484866	−	0.586055i
$516$	1.34589			0.0592497
$517$	4.43547	+	5.51660i	0.195072	+	0.242620i
$518$		−	80.6091i		−	3.54176i
$519$	7.49168	−	23.0570i	0.328848	−	1.01209i
$520$	1.28011	+	4.98651i	0.0561364	+	0.218673i
$521$	7.43033	+	5.39845i	0.325529	+	0.236510i	0.738531	−	0.674220i	$-0.235520\pi$
$521$	7.43033	+	5.39845i	0.325529	+	0.236510i	−0.413002	+	0.910730i	$0.635520\pi$
$522$	−2.24896	+	0.730731i	−0.0984342	+	0.0319832i
$523$	31.9404	−	10.3781i	1.39665	−	0.453801i	0.488547	−	0.872537i	$-0.337527\pi$
$523$	31.9404	−	10.3781i	1.39665	−	0.453801i	0.908108	+	0.418737i	$0.137527\pi$
$524$	−15.9275	−	11.5720i	−0.695795	−	0.505525i
$525$	16.4507	+	2.07954i	0.717968	+	0.0907586i
$526$	7.24796	−	22.3069i	0.316026	−	0.972629i
$527$			7.46893i			0.325352i
$528$	5.32820	−	8.14236i	0.231880	−	0.354351i
$529$	−11.6952			−0.508486
$530$	−42.2282	−	34.9371i	−1.83428	−	1.51757i
$531$	−6.79443	+	4.93644i	−0.294853	+	0.214223i
$532$	−5.45287	+	7.50523i	−0.236412	+	0.325393i
$533$	2.21632	−	0.720127i	0.0959996	−	0.0311922i
$534$	8.19865	+	25.2329i	0.354790	+	1.09193i
$535$	−18.5837	−	29.2859i	−0.803445	−	1.26614i
$536$	−3.09648	+	2.24972i	−0.133747	+	0.0971731i
$537$	−18.9631	−	6.16149i	−0.818319	−	0.265888i
$538$			47.9364i			2.06669i
$539$	−4.70870	−	12.3957i	−0.202818	−	0.533921i
$540$	5.06734	+	2.00654i	0.218064	+	0.0863476i
$541$	13.7829	−	42.4194i	0.592573	−	1.82375i	0.0261178	−	0.999659i	$-0.491685\pi$
$541$	13.7829	−	42.4194i	0.592573	−	1.82375i	0.566455	−	0.824093i	$-0.308315\pi$
$542$	9.65093	+	13.2834i	0.414543	+	0.570569i
$543$	3.01704	−	4.15260i	0.129474	−	0.178205i
$544$	16.8842	+	51.9643i	0.723906	+	2.22795i
$545$	15.1715	+	0.955118i	0.649876	+	0.0409128i
$546$	−14.1229	−	10.2609i	−0.604405	−	0.439126i
$547$	−11.3037	−	15.5582i	−0.483310	−	0.665219i	0.495827	−	0.868421i	$-0.334865\pi$
$547$	−11.3037	−	15.5582i	−0.483310	−	0.665219i	−0.979137	+	0.203202i	$0.934865\pi$
$548$	14.9234	+	4.84891i	0.637497	+	0.207135i
$549$	8.21313			0.350528
$550$	−32.2957	−	13.3143i	−1.37709	−	0.567723i
$551$	1.28836			0.0548860
$552$	−5.16137	−	1.67703i	−0.219682	−	0.0713791i
$553$	−7.53895	−	10.3765i	−0.320589	−	0.441252i
$554$	16.1340	+	11.7220i	0.685468	+	0.498022i
$555$	25.7507	+	1.62113i	1.09306	+	0.0688131i
$556$	5.25402	+	16.1702i	0.222820	+	0.685770i
$557$	−19.6126	+	26.9944i	−0.831011	+	1.14379i	0.156723	+	0.987643i	$0.449907\pi$
$557$	−19.6126	+	26.9944i	−0.831011	+	1.14379i	−0.987734	+	0.156145i	$0.950093\pi$
$558$	1.35794	+	1.86905i	0.0574863	+	0.0791231i
$559$	0.426399	−	1.31232i	0.0180348	−	0.0555053i
$560$	20.2285	+	8.00997i	0.854811	+	0.338483i
$561$	18.8999	+	12.3677i	0.797953	+	0.522165i
$562$		−	65.9370i		−	2.78139i
$563$	1.98975	+	0.646509i	0.0838580	+	0.0272471i	0.350646	−	0.936508i	$-0.385962\pi$
$563$	1.98975	+	0.646509i	0.0838580	+	0.0272471i	−0.266788	+	0.963755i	$0.585962\pi$
$564$	−4.20853	+	3.05768i	−0.177211	+	0.128752i
$565$	0.361205	+	0.569218i	0.0151960	+	0.0239472i
$566$	−15.8911	−	48.9079i	−0.667955	−	2.05575i
$567$	−3.15401	+	1.02480i	−0.132456	+	0.0430376i
$568$	6.78788	−	9.34271i	0.284813	−	0.392011i
$569$	−7.53693	+	5.47590i	−0.315964	+	0.229562i	−0.734452	−	0.678661i	$-0.762561\pi$
$569$	−7.53693	+	5.47590i	−0.315964	+	0.229562i	0.418487	+	0.908223i	$0.362561\pi$
$570$	−4.16524	−	3.44606i	−0.174463	−	0.144340i
$571$	2.32989			0.0975029			0.0487514	−	0.998811i	$-0.484476\pi$
$571$	2.32989			0.0975029			0.0487514	+	0.998811i	$0.484476\pi$
$572$	12.6578	+	15.7432i	0.529251	+	0.658254i
$573$			2.81336i			0.117530i
$574$	−2.01318	+	6.19594i	−0.0840286	+	0.258614i
$575$	3.69356	−	29.2188i	0.154032	−	1.21851i
$576$	8.92570	+	6.48490i	0.371904	+	0.270204i
$577$	−28.0207	+	9.10449i	−1.16652	+	0.379025i	−0.827342	−	0.561698i	$-0.810148\pi$
$577$	−28.0207	+	9.10449i	−1.16652	+	0.379025i	−0.339176	+	0.940723i	$0.610148\pi$
$578$	−58.8575	+	19.1240i	−2.44815	+	0.795452i
$579$	−15.6166	−	11.3461i	−0.649005	−	0.471530i
$580$	1.52129	+	5.92600i	0.0631680	+	0.246064i
$581$	−6.23136	+	19.1781i	−0.258520	+	0.795643i
$582$			6.04300i			0.250491i
$583$	−37.2409	−	10.1181i	−1.54236	−	0.419049i
$584$	−5.28634			−0.218750
$585$	3.56189	−	4.30524i	0.147266	−	0.178000i
$586$	−20.1431	+	14.6348i	−0.832103	+	0.604558i
$587$	24.4029	−	33.5877i	1.00722	−	1.38631i	0.0864248	−	0.996258i	$-0.472456\pi$
$587$	24.4029	−	33.5877i	1.00722	−	1.38631i	0.920791	−	0.390056i	$-0.127544\pi$
$588$	9.26776	−	3.01128i	0.382196	−	0.124183i
$589$	−0.388962	−	1.19710i	−0.0160269	−	0.0493258i
$590$	21.1954	+	33.4015i	0.872599	+	1.37512i
$591$	−2.89592	+	2.10401i	−0.119122	+	0.0865475i
$592$	32.1973	+	10.4615i	1.32330	+	0.429967i
$593$		−	9.36964i		−	0.384765i	−0.981320	−	0.192383i	$-0.938379\pi$
$593$		−	9.36964i		−	0.384765i	0.981320	−	0.192383i	$-0.0616214\pi$
$594$	6.97816	−	0.341294i	0.286317	−	0.0140035i
$595$	−18.5926	+	46.9541i	−0.762222	+	1.92493i
$596$	−14.3261	+	44.0912i	−0.586820	+	1.80605i
$597$	−7.46997	−	10.2815i	−0.305725	−	0.420795i
$598$	−18.2248	+	25.0843i	−0.745268	+	1.02577i
$599$	−0.406983	−	1.25256i	−0.0166289	−	0.0511784i	0.942398	−	0.334494i	$-0.108566\pi$
$599$	−0.406983	−	1.25256i	−0.0166289	−	0.0511784i	−0.959027	+	0.283316i	$0.908566\pi$
$600$	1.96179	−	4.16815i	0.0800896	−	0.170164i
$601$	−12.6422	−	9.18512i	−0.515688	−	0.374669i	0.299289	−	0.954162i	$-0.403250\pi$
$601$	−12.6422	−	9.18512i	−0.515688	−	0.374669i	−0.814977	+	0.579493i	$0.803250\pi$
$602$	2.26739	+	3.12080i	0.0924120	+	0.127194i
$603$	3.95087	+	1.28371i	0.160892	+	0.0522769i
$604$	−9.50777			−0.386866
$605$	−24.5818	+	0.857471i	−0.999392	+	0.0348611i
$606$	−20.7913			−0.844588
$607$	−23.0273	−	7.48201i	−0.934647	−	0.303685i	−0.198186	−	0.980165i	$-0.563505\pi$
$607$	−23.0273	−	7.48201i	−0.934647	−	0.303685i	−0.736462	+	0.676479i	$0.763505\pi$
$608$	−5.41233	−	7.44943i	−0.219499	−	0.302114i
$609$	−3.01180	−	2.18820i	−0.122044	−	0.0886705i
$610$	2.43067	−	38.6099i	0.0984150	−	1.56327i
$611$	1.64808	+	5.07227i	0.0666742	+	0.205202i
$612$	−9.75666	+	13.4289i	−0.394390	+	0.542831i
$613$	−2.40187	−	3.30589i	−0.0970105	−	0.133524i	0.757752	−	0.652542i	$-0.226298\pi$
$613$	−2.40187	−	3.30589i	−0.0970105	−	0.133524i	−0.854763	+	0.519019i	$0.826298\pi$
$614$	−14.5302	+	44.7194i	−0.586392	+	1.80473i
$615$	−1.93882	−	0.767722i	−0.0781807	−	0.0309575i
$616$	−10.1218	+	0.495047i	−0.407820	+	0.0199460i
$617$		−	16.9835i		−	0.683731i	−0.939749	−	0.341866i	$-0.888941\pi$
$617$		−	16.9835i		−	0.683731i	0.939749	−	0.341866i	$-0.111059\pi$
$618$	15.4654	+	5.02501i	0.622109	+	0.202135i
$619$	−25.9942	+	18.8859i	−1.04480	+	0.759089i	−0.971216	−	0.238200i	$-0.923442\pi$
$619$	−25.9942	+	18.8859i	−1.04480	+	0.759089i	−0.0735802	+	0.997289i	$0.523442\pi$
$620$	5.04696	−	3.20262i	0.202691	−	0.128620i
$621$	1.82019	+	5.60197i	0.0730417	+	0.224799i
$622$	−39.0332	+	12.6827i	−1.56509	+	0.508528i
$623$	−24.5512	+	33.7918i	−0.983623	+	1.35384i
$624$	5.93136	−	4.30939i	0.237444	−	0.172514i
$625$	24.2136	+	6.22111i	0.968544	+	0.248844i
$626$	36.5536			1.46098
$627$	−3.67330	−	0.998011i	−0.146698	−	0.0398567i
$628$			44.8095i			1.78809i
$629$	−24.2831	+	74.7358i	−0.968232	+	2.97991i
$630$	3.88415	+	15.1303i	0.154748	+	0.602805i
$631$	5.10947	+	3.71225i	0.203405	+	0.147782i	0.684825	−	0.728708i	$-0.259879\pi$
$631$	5.10947	+	3.71225i	0.203405	+	0.147782i	−0.481420	+	0.876490i	$0.659879\pi$
$632$	−3.38895	+	1.10114i	−0.134805	+	0.0438008i
$633$	−3.32412	+	1.08007i	−0.132122	+	0.0429290i
$634$	1.41571	+	1.02857i	0.0562250	+	0.0408499i
$635$	−14.5228	+	3.72820i	−0.576320	+	0.147949i
$636$	8.76384	−	26.9723i	0.347509	−	1.06952i
$637$		−	9.99059i		−	0.395842i
$638$	4.91434	+	6.11219i	0.194560	+	0.241984i
$639$	−12.5340			−0.495839
$640$	10.2550	−	12.3952i	0.405365	−	0.489963i
$641$	−11.8814	+	8.63236i	−0.469288	+	0.340958i	−0.797164	−	0.603763i	$-0.793667\pi$
$641$	−11.8814	+	8.63236i	−0.469288	+	0.340958i	0.327876	+	0.944721i	$0.393667\pi$
$642$	19.2058	−	26.4345i	0.757993	−	1.04329i
$643$	15.3605	−	4.99093i	0.605759	−	0.196823i	0.00995196	−	0.999950i	$-0.496832\pi$
$643$	15.3605	−	4.99093i	0.605759	−	0.196823i	0.595807	+	0.803127i	$0.296832\pi$
$644$	−14.7129	−	45.2816i	−0.579769	−	1.78434i
$645$	−1.04254	+	0.661560i	−0.0410501	+	0.0260489i
$646$	13.3200	−	9.67758i	0.524070	−	0.380759i
$647$	−26.4273	−	8.58676i	−1.03897	−	0.337581i	−0.260637	−	0.965437i	$-0.583933\pi$
$647$	−26.4273	−	8.58676i	−1.03897	−	0.337581i	−0.778329	+	0.627856i	$0.783933\pi$
$648$			0.921348i			0.0361940i
$649$	23.3075	+	15.2519i	0.914898	+	0.598691i
$650$	−19.1847	−	18.0186i	−0.752488	−	0.706746i
$651$	−1.12393	+	3.45910i	−0.0440503	+	0.135573i
$652$	25.1747	+	34.6499i	0.985916	+	1.35700i
$653$	−20.0232	+	27.5595i	−0.783568	+	1.07849i	0.211312	+	0.977419i	$0.432227\pi$
$653$	−20.0232	+	27.5595i	−0.783568	+	1.07849i	−0.994879	+	0.101070i	$0.967773\pi$
$654$	4.42536	+	13.6199i	0.173045	+	0.532579i
$655$	18.0257	+	1.13480i	0.704322	+	0.0443404i
$656$	−2.21354	−	1.60823i	−0.0864244	−	0.0627910i
$657$	3.37248	+	4.64182i	0.131573	+	0.181095i
$658$	−14.1800	−	4.60737i	−0.552795	−	0.179614i
$659$	−14.4196			−0.561709			−0.280855	−	0.959750i	$-0.590618\pi$
$659$	−14.4196			−0.561709			−0.280855	+	0.959750i	$0.590618\pi$
$660$	0.253089	−	18.0743i	0.00985147	−	0.703542i
$661$	26.4275			1.02791			0.513956	−	0.857817i	$-0.328179\pi$
$661$	26.4275			1.02791			0.513956	+	0.857817i	$0.328179\pi$
$662$	63.1697	+	20.5251i	2.45516	+	0.797730i
$663$	10.0029	+	13.7678i	0.388479	+	0.534695i
$664$	4.53236	+	3.29295i	0.175890	+	0.127791i
$665$	0.534733	−	8.49393i	0.0207361	−	0.329381i
$666$	7.51119	+	23.1171i	0.291053	+	0.895769i
$667$	−3.88656	+	5.34939i	−0.150488	+	0.207129i
$668$	−17.3032	−	23.8157i	−0.669479	−	0.921459i
$669$	1.60861	−	4.95080i	0.0621925	−	0.191409i
$670$	7.20399	−	18.1931i	0.278314	−	0.702860i
$671$	−9.67309	−	25.4645i	−0.373426	−	0.983047i
$672$			26.6071i			1.02639i
$673$	34.5357	+	11.2213i	1.33125	+	0.432550i	0.886345	−	0.463026i	$-0.153236\pi$
$673$	34.5357	+	11.2213i	1.33125	+	0.432550i	0.444908	+	0.895576i	$0.353236\pi$
$674$	−27.6659	+	20.1005i	−1.06565	+	0.774241i
$675$	−4.91151	+	0.936515i	−0.189044	+	0.0360465i
$676$	−5.08824	−	15.6600i	−0.195702	−	0.602308i
$677$	10.7890	−	3.50556i	0.414655	−	0.134730i	−0.0942574	−	0.995548i	$-0.530048\pi$
$677$	10.7890	−	3.50556i	0.414655	−	0.134730i	0.508913	+	0.860818i	$0.330048\pi$
$678$	−0.373296	+	0.513798i	−0.0143363	+	0.0197323i
$679$	−7.69669	+	5.59198i	−0.295372	+	0.214600i
$680$	10.8102	+	8.94370i	0.414552	+	0.342975i
$681$	−9.70244			−0.371798
$682$	4.19559	−	6.41154i	0.160657	−	0.245511i
$683$			39.4269i			1.50863i	0.656514	+	0.754314i	$0.272030\pi$
$683$			39.4269i			1.50863i	−0.656514	+	0.754314i	$0.727970\pi$
$684$	0.864433	−	2.66045i	0.0330524	−	0.101725i
$685$	−13.9433	+	3.57943i	−0.532745	+	0.136763i
$686$	−16.9663	−	12.3267i	−0.647775	−	0.470636i
$687$	−17.5956	+	5.71715i	−0.671313	+	0.218123i
$688$	−1.54079	+	0.500634i	−0.0587421	+	0.0190865i
$689$	−23.5230	−	17.0905i	−0.896155	−	0.651095i
$690$	26.8735	−	6.89880i	1.02306	−	0.262633i
$691$	4.56613	−	14.0531i	0.173704	−	0.534606i	−0.825868	−	0.563864i	$-0.809314\pi$
$691$	4.56613	−	14.0531i	0.173704	−	0.534606i	0.999572	+	0.0292578i	$0.00931437\pi$
$692$		−	59.0909i		−	2.24630i
$693$	6.89203	+	8.57194i	0.261806	+	0.325621i
$694$	26.2260			0.995526
$695$	−12.0181	−	9.94307i	−0.455874	−	0.377162i
$696$	−0.836745	+	0.607931i	−0.0317167	+	0.0230436i
$697$	3.73300	−	5.13804i	0.141398	−	0.194617i
$698$	−65.3707	+	21.2402i	−2.47432	+	0.803954i
$699$	−4.62115	−	14.2224i	−0.174788	−	0.537942i
$700$	39.7005	−	7.56999i	1.50054	−	0.286119i
$701$	5.76774	−	4.19051i	0.217845	−	0.158273i	−0.473511	−	0.880788i	$-0.657014\pi$
$701$	5.76774	−	4.19051i	0.217845	−	0.158273i	0.691356	+	0.722514i	$0.257014\pi$
$702$	5.00629	+	1.62664i	0.188950	+	0.0613937i
$703$		−	13.2431i		−	0.499472i
$704$	9.59389	−	35.3115i	0.361583	−	1.33085i
$705$	1.75701	−	4.43717i	0.0661727	−	0.167114i
$706$	−10.2798	+	31.6381i	−0.386887	+	1.19071i
$707$	−19.2395	−	26.4809i	−0.723576	−	0.995917i
$708$	−12.0320	+	16.5606i	−0.452190	+	0.622386i
$709$	1.65473	+	5.09274i	0.0621447	+	0.191262i	0.977309	−	0.211820i	$-0.0679390\pi$
$709$	1.65473	+	5.09274i	0.0621447	+	0.191262i	−0.915164	+	0.403082i	$0.867939\pi$
$710$	−3.70944	+	58.9225i	−0.139213	+	2.21132i
$711$	3.12890	+	2.27328i	0.117343	+	0.0852548i
$712$	6.82086	+	9.38811i	0.255623	+	0.351834i
$713$	6.14385	+	1.99626i	0.230089	+	0.0747604i
$714$	−47.5751			−1.78045
$715$	−17.5433	−	5.97299i	−0.656082	−	0.223377i
$716$	−48.5989			−1.81623
$717$	−1.43340	−	0.465738i	−0.0535311	−	0.0173933i
$718$	−22.4880	−	30.9520i	−0.839243	−	1.15512i
$719$	−32.9940	−	23.9716i	−1.23047	−	0.893989i	−0.233545	−	0.972346i	$-0.575033\pi$
$719$	−32.9940	−	23.9716i	−1.23047	−	0.893989i	−0.996925	+	0.0783569i	$0.975033\pi$
$720$	−6.54751	−	0.412197i	−0.244011	−	0.0153617i
$721$	7.91098	+	24.3475i	0.294620	+	0.906749i
$722$	21.8944	−	30.1351i	0.814825	−	1.12151i
$723$	−4.17075	−	5.74055i	−0.155112	−	0.213493i
$724$	3.86606	−	11.8985i	0.143681	−	0.442204i
$725$	−4.09127	−	3.84257i	−0.151946	−	0.142710i
$726$	−9.27676	−	21.2336i	−0.344293	−	0.788052i
$727$			28.6101i			1.06109i	0.847656	+	0.530546i	$0.178013\pi$
$727$			28.6101i			1.06109i	−0.847656	+	0.530546i	$0.821987\pi$
$728$	−7.26162	−	2.35944i	−0.269134	−	0.0874468i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	22.8193	−	14.4803i	0.844579	−	0.535939i
$731$	−1.16206	−	3.57646i	−0.0429804	−	0.132280i
$732$	19.0388	−	6.18607i	0.703693	−	0.228644i
$733$	2.58397	−	3.55653i	0.0954412	−	0.131364i	−0.758626	−	0.651527i	$-0.774129\pi$
$733$	2.58397	−	3.55653i	0.0954412	−	0.131364i	0.854067	+	0.520163i	$0.174129\pi$
$734$	−0.804462	+	0.584476i	−0.0296932	+	0.0215734i
$735$	−5.69875	+	6.88804i	−0.210201	+	0.254069i
$736$	47.2579			1.74195
$737$	−0.673056	−	13.7614i	−0.0247924	−	0.506909i
$738$		−	1.96446i		−	0.0723129i
$739$	3.25000	−	10.0025i	0.119553	−	0.367947i	−0.873316	−	0.487154i	$-0.838035\pi$
$739$	3.25000	−	10.0025i	0.119553	−	0.367947i	0.992869	+	0.119207i	$0.0380352\pi$
$740$	60.9134	−	15.6373i	2.23922	−	0.574839i
$741$	−2.32022	−	1.68574i	−0.0852355	−	0.0619272i
$742$	77.3064	−	25.1184i	2.83801	−	0.922125i
$743$	32.8020	−	10.6580i	1.20339	−	0.391005i	0.362382	−	0.932030i	$-0.381964\pi$
$743$	32.8020	−	10.6580i	1.20339	−	0.391005i	0.841007	+	0.541025i	$0.181964\pi$
$744$	0.817487	+	0.593939i	0.0299705	+	0.0217749i
$745$	−10.5754	−	41.1954i	−0.387453	−	1.50928i
$746$	10.0312	−	30.8729i	0.367269	−	1.13034i
$747$		−	6.08055i		−	0.222476i
$748$	53.1268	+	14.4342i	1.94251	+	0.527766i
$749$	51.4408			1.87961
$750$	2.94899	+	23.3661i	0.107682	+	0.853211i
$751$	1.92630	−	1.39954i	0.0702918	−	0.0510700i	−0.552084	−	0.833788i	$-0.686167\pi$
$751$	1.92630	−	1.39954i	0.0702918	−	0.0510700i	0.622376	+	0.782718i	$0.286167\pi$
$752$	3.68060	−	5.06591i	0.134218	−	0.184735i
$753$	−13.0091	+	4.22692i	−0.474079	+	0.154038i
$754$	1.82601	+	5.61989i	0.0664995	+	0.204664i
$755$	7.36482	−	4.67345i	0.268033	−	0.170084i
$756$	−6.53941	+	4.75116i	−0.237836	+	0.172798i
$757$	7.98459	+	2.59435i	0.290205	+	0.0942932i	0.450502	−	0.892776i	$-0.351245\pi$
$757$	7.98459	+	2.59435i	0.290205	+	0.0942932i	−0.160297	+	0.987069i	$0.551245\pi$
$758$		−	40.6021i		−	1.47473i
$759$	15.2250	−	12.2412i	0.552631	−	0.444328i
$760$	−2.19840	−	0.870508i	−0.0797442	−	0.0315767i
$761$	3.23481	−	9.95573i	0.117262	−	0.360895i	−0.875150	−	0.483851i	$-0.839238\pi$
$761$	3.23481	−	9.95573i	0.117262	−	0.360895i	0.992412	+	0.122956i	$0.0392375\pi$
$762$	−8.30245	−	11.4273i	−0.300766	−	0.413969i
$763$	−13.2519	+	18.2397i	−0.479752	+	0.660322i
$764$	2.11900	+	6.52162i	0.0766628	+	0.235944i
$765$	0.956783	−	15.1980i	0.0345925	−	0.549483i
$766$	12.6933	+	9.22222i	0.458627	+	0.333212i
$767$	12.3356	+	16.9785i	0.445413	+	0.613058i
$768$	−6.57200	−	2.13537i	−0.237146	−	0.0770536i
$769$	9.70799			0.350079			0.175040	−	0.984561i	$-0.443995\pi$
$769$	9.70799			0.350079			0.175040	+	0.984561i	$0.443995\pi$
$770$	42.3363	−	29.8625i	1.52569	−	1.07617i
$771$	8.30411			0.299065
$772$	−44.7465	−	14.5390i	−1.61046	−	0.523271i
$773$	−18.7855	−	25.8560i	−0.675668	−	0.929977i	0.324204	−	0.945987i	$-0.394904\pi$
$773$	−18.7855	−	25.8560i	−0.675668	−	0.929977i	−0.999872	+	0.0160101i	$0.994904\pi$
$774$	−0.941041	−	0.683706i	−0.0338250	−	0.0245753i
$775$	−2.33522	+	4.96157i	−0.0838835	+	0.178225i
$776$	0.816762	+	2.51374i	0.0293201	+	0.0902378i
$777$	−22.4926	+	30.9584i	−0.806917	+	1.11063i
$778$	0.883833	+	1.21649i	0.0316869	+	0.0436133i
$779$	−0.330741	+	1.01792i	−0.0118500	+	0.0364706i
$780$	5.01410	−	12.6627i	0.179534	−	0.453398i
$781$	14.7621	+	38.8614i	0.528229	+	1.39057i
$782$			84.5001i			3.02172i
$783$	1.06762	+	0.346892i	0.0381537	+	0.0123969i
$784$	−9.48971	+	6.89468i	−0.338918	+	0.246239i
$785$	−22.0257	−	34.7099i	−0.786129	−	1.23885i
$786$	5.25789	+	16.1821i	0.187543	+	0.577197i
$787$	−44.1971	+	14.3605i	−1.57545	+	0.511896i	−0.960881	−	0.276963i	$-0.910672\pi$
$787$	−44.1971	+	14.3605i	−1.57545	+	0.511896i	−0.614574	+	0.788859i	$0.710672\pi$
$788$	−5.12828	+	7.05847i	−0.182687	+	0.251448i
$789$	−9.00799	+	6.54469i	−0.320693	+	0.232997i
$790$	11.6127	−	14.0362i	0.413161	−	0.499385i
$791$	−0.999835			−0.0355500
$792$	2.85661	−	1.08513i	0.101505	−	0.0385583i
$793$		−	20.5237i		−	0.728817i
$794$	0.497435	−	1.53095i	0.0176533	−	0.0543313i
$795$	6.46941	+	25.2008i	0.229446	+	0.893782i
$796$	−25.0600	−	18.2072i	−0.888228	−	0.645336i
$797$	−30.6576	+	9.96126i	−1.08595	+	0.352846i	−0.796680	−	0.604402i	$-0.793412\pi$
$797$	−30.6576	+	9.96126i	−1.08595	+	0.352846i	−0.289269	+	0.957248i	$0.593412\pi$
$798$	7.62522	−	2.47759i	0.269930	−	0.0877056i
$799$	11.7589	+	8.54334i	0.416000	+	0.302242i
$800$	−5.03095	+	39.7986i	−0.177871	+	1.40709i
$801$	3.89206	−	11.9785i	0.137519	−	0.423240i
$802$			33.1869i			1.17187i
$803$	10.4198	−	15.9232i	0.367708	−	0.561918i
$804$	10.1253			0.357093
$805$	33.6545	+	27.8436i	1.18616	+	0.981360i
$806$	4.67054	−	3.39334i	0.164513	−	0.119525i
$807$	13.3758	−	18.4103i	0.470852	−	0.648072i
$808$	−8.64864	+	2.81011i	−0.304258	+	0.0988595i
$809$	−6.55046	−	20.1603i	−0.230302	−	0.708797i	−0.997710	−	0.0676376i	$-0.978454\pi$
$809$	−6.55046	−	20.1603i	−0.230302	−	0.708797i	0.767408	−	0.641159i	$-0.221546\pi$
$810$	−2.52375	−	3.97714i	−0.0886754	−	0.139742i
$811$	19.0967	−	13.8746i	0.670578	−	0.487203i	−0.199641	−	0.979869i	$-0.563978\pi$
$811$	19.0967	−	13.8746i	0.670578	−	0.487203i	0.870218	+	0.492666i	$0.163978\pi$
$812$	−8.62976	−	2.80398i	−0.302845	−	0.0984004i
$813$		−	7.79448i		−	0.273364i
$814$	62.8273	−	50.5145i	2.20210	−	1.77053i
$815$	−36.5324	−	14.4659i	−1.27967	−	0.506718i
$816$	6.17436	−	19.0027i	0.216146	−	0.665228i
$817$	0.372505	+	0.512709i	0.0130323	+	0.0179374i
$818$	−3.24526	+	4.46672i	−0.113468	+	0.156175i
$819$	2.56086	+	7.88152i	0.0894837	+	0.275403i
$820$	−5.07259	−	0.319343i	−0.177143	−	0.0111520i
$821$	36.0153	+	26.1667i	1.25694	+	0.913223i	0.998603	−	0.0528314i	$-0.0168246\pi$
$821$	36.0153	+	26.1667i	1.25694	+	0.913223i	0.258340	+	0.966054i	$0.416825\pi$
$822$	−7.97114	−	10.9713i	−0.278026	−	0.382669i
$823$	−0.129751	−	0.0421588i	−0.00452285	−	0.00146956i	0.306755	−	0.951789i	$-0.400757\pi$
$823$	−0.129751	−	0.0421588i	−0.00452285	−	0.00146956i	−0.311278	+	0.950319i	$0.600757\pi$
$824$	7.11238			0.247771
$825$	8.68821	+	14.1250i	0.302485	+	0.491769i
$826$	−58.6700			−2.04139
$827$	−11.1951	−	3.63750i	−0.389291	−	0.126488i	0.107830	−	0.994169i	$-0.465610\pi$
$827$	−11.1951	−	3.63750i	−0.389291	−	0.126488i	−0.497121	+	0.867681i	$0.665610\pi$
$828$	8.43872	+	11.6149i	0.293266	+	0.403646i
$829$	8.92262	+	6.48266i	0.309895	+	0.225152i	0.731852	−	0.681464i	$-0.238656\pi$
$829$	8.92262	+	6.48266i	0.309895	+	0.225152i	−0.421956	+	0.906616i	$0.638656\pi$
$830$	−28.5846	−	1.79954i	−0.992187	−	0.0624628i
$831$	−2.92552	−	9.00383i	−0.101485	−	0.312339i
$832$	16.2050	−	22.3043i	0.561808	−	0.773263i
$833$	−16.0038	−	22.0273i	−0.554498	−	0.763202i
$834$	4.54080	−	13.9751i	0.157235	−	0.483919i
$835$	25.1096	+	9.94275i	0.868953	+	0.344083i
$836$	−9.26673	+	0.453226i	−0.320497	+	0.0156751i
$837$		−	1.09673i		−	0.0379085i
$838$	−36.0769	−	11.7221i	−1.24626	−	0.404933i
$839$	−8.56769	+	6.22479i	−0.295790	+	0.214904i	−0.725775	−	0.687932i	$-0.758519\pi$
$839$	−8.56769	+	6.22479i	−0.295790	+	0.214904i	0.429985	+	0.902836i	$0.358519\pi$
$840$	3.66069	+	5.76884i	0.126306	+	0.199044i
$841$	−8.57208	−	26.3822i	−0.295589	−	0.909730i
$842$	2.34633	−	0.762368i	0.0808598	−	0.0262730i
$843$	−18.3986	+	25.3235i	−0.633681	+	0.872188i
$844$	−6.89209	+	5.00740i	−0.237236	+	0.172362i
$845$	11.6389	+	9.62934i	0.400391	+	0.331259i
$846$	4.49586			0.154571
$847$	18.4599	−	31.4642i	0.634288	−	1.08112i
$848$			34.1381i			1.17231i
$849$	−7.54383	+	23.2175i	−0.258903	+	0.796823i
$850$	−71.1623	−	8.99565i	−2.44085	−	0.308548i
$851$	54.9864	+	39.9500i	1.88491	+	1.36947i
$852$	−29.0550	+	9.44055i	−0.995409	+	0.323428i
$853$	−42.3992	+	13.7763i	−1.45172	+	0.471693i	−0.925530	−	0.378674i	$-0.876380\pi$
$853$	−42.3992	+	13.7763i	−1.45172	+	0.471693i	−0.526190	+	0.850367i	$0.676380\pi$
$854$	46.4181	+	33.7247i	1.58839	+	1.15404i
$855$	0.638118	+	2.48572i	0.0218232	+	0.0850098i
$856$	4.41628	−	13.5919i	0.150945	−	0.464562i
$857$		−	24.3105i		−	0.830430i	−0.909723	−	0.415215i	$-0.863706\pi$
$857$		−	24.3105i		−	0.830430i	0.909723	−	0.415215i	$-0.136294\pi$
$858$	−0.852855	−	17.4376i	−0.0291160	−	0.595311i
$859$	35.5045			1.21140			0.605699	−	0.795694i	$-0.292893\pi$
$859$	35.5045			1.21140			0.605699	+	0.795694i	$0.292893\pi$
$860$	−1.91843	+	2.31879i	−0.0654178	+	0.0790701i
$861$	2.50205	−	1.81784i	0.0852695	−	0.0619519i
$862$	−43.4502	+	59.8040i	−1.47992	+	2.03693i
$863$	11.1007	−	3.60684i	0.377873	−	0.122778i	−0.113921	−	0.993490i	$-0.536341\pi$
$863$	11.1007	−	3.60684i	0.377873	−	0.122778i	0.491794	+	0.870711i	$0.336341\pi$
$864$	−2.47926	−	7.63038i	−0.0843462	−	0.259591i
$865$	29.0455	+	45.7725i	0.987577	+	1.55631i
$866$	−31.0609	+	22.5670i	−1.05549	+	0.766859i
$867$	27.9408	+	9.07851i	0.948919	+	0.308322i
$868$			8.86503i			0.300899i
$869$	3.36314	−	12.3784i	0.114087	−	0.419910i
$870$	1.94670	−	4.91623i	0.0659992	−	0.166676i
$871$	3.20786	−	9.87276i	0.108694	−	0.334526i
$872$	3.68167	+	5.06739i	0.124677	+	0.171603i
$873$	1.68620	−	2.32085i	0.0570691	−	0.0785489i
$874$	−4.40054	−	13.5435i	−0.148850	−	0.458115i
$875$	−27.0315	+	25.3782i	−0.913831	+	0.857939i
$876$	11.3139	+	8.22003i	0.382261	+	0.277729i
$877$	15.5657	+	21.4243i	0.525615	+	0.723447i	0.986454	−	0.164036i	$-0.0524515\pi$
$877$	15.5657	+	21.4243i	0.525615	+	0.723447i	−0.460839	+	0.887484i	$0.652451\pi$
$878$	−39.6986	−	12.8989i	−1.33976	−	0.435315i
$879$	11.8197			0.398667
$880$	6.43339	+	20.7858i	0.216870	+	0.700689i
$881$	10.3488			0.348658			0.174329	−	0.984687i	$-0.444224\pi$
$881$	10.3488			0.348658			0.174329	+	0.984687i	$0.444224\pi$
$882$	−8.00967	−	2.60250i	−0.269700	−	0.0876307i
$883$	−1.59377	−	2.19364i	−0.0536346	−	0.0738217i	0.781357	−	0.624084i	$-0.214528\pi$
$883$	−1.59377	−	2.19364i	−0.0536346	−	0.0738217i	−0.834992	+	0.550262i	$0.814528\pi$
$884$	33.5573	+	24.3808i	1.12865	+	0.820015i
$885$	1.17991	−	18.7422i	0.0396623	−	0.630013i
$886$	−10.8633	−	33.4338i	−0.364959	−	1.12323i
$887$	0.0721054	−	0.0992445i	0.00242106	−	0.00333230i	−0.807805	−	0.589450i	$-0.799344\pi$
$887$	0.0721054	−	0.0992445i	0.00242106	−	0.00333230i	0.810226	+	0.586118i	$0.199344\pi$
$888$	6.24893	+	8.60092i	0.209700	+	0.288628i
$889$	6.87169	−	21.1489i	0.230469	−	0.709311i
$890$	−55.1590	−	21.8416i	−1.84894	−	0.732131i
$891$	−2.77523	−	1.81606i	−0.0929739	−	0.0608403i
$892$		−	12.6880i		−	0.424825i
$893$	−2.32960	−	0.756933i	−0.0779571	−	0.0253298i
$894$	32.4148	−	23.5507i	1.08411	−	0.787654i
$895$	37.6453	−	23.8883i	1.25834	−	0.798498i
$896$	7.37296	+	22.6916i	0.246313	+	0.758075i
$897$	13.9987	−	4.54845i	0.467403	−	0.151868i
$898$	−16.3403	+	22.4904i	−0.545282	+	0.750516i
$899$	0.996022	−	0.723652i	0.0332192	−	0.0241352i
$900$	−10.6799	+	5.87024i	−0.355998	+	0.195675i
$901$	−79.2406			−2.63989
$902$	−6.09075	+	2.31366i	−0.202800	+	0.0770365i
$903$		−	1.83124i		−	0.0609398i
$904$	−0.0858376	+	0.264181i	−0.00285491	+	0.00878652i
$905$	2.85390	+	11.1170i	0.0948667	+	0.369543i
$906$	6.64777	+	4.82989i	0.220857	+	0.160462i
$907$	13.1424	−	4.27023i	0.436387	−	0.141791i	−0.0825812	−	0.996584i	$-0.526316\pi$
$907$	13.1424	−	4.27023i	0.436387	−	0.141791i	0.518968	+	0.854794i	$0.326316\pi$
$908$	−22.4911	+	7.30780i	−0.746393	+	0.242518i
$909$	7.98501	+	5.80145i	0.264846	+	0.192422i
$910$	37.8088	−	9.70605i	1.25335	−	0.321753i
$911$	7.18645	−	22.1176i	0.238098	−	0.732790i	−0.758598	−	0.651559i	$-0.774115\pi$
$911$	7.18645	−	22.1176i	0.238098	−	0.732790i	0.996695	−	0.0812302i	$-0.0258849\pi$
$912$			3.36725i			0.111501i
$913$	−18.8525	+	7.16142i	−0.623928	+	0.237009i
$914$	44.7997			1.48184
$915$	−11.7069	+	14.1501i	−0.387019	+	0.467788i
$916$	−36.4820	+	26.5057i	−1.20540	+	0.875773i
$917$	−15.7450	+	21.6711i	−0.519945	+	0.715642i
$918$	13.6436	−	4.43307i	0.450306	−	0.146313i
$919$	−8.16663	−	25.1343i	−0.269392	−	0.829104i	−0.990649	−	0.136436i	$-0.956435\pi$
$919$	−8.16663	−	25.1343i	−0.269392	−	0.829104i	0.721257	−	0.692668i	$-0.243565\pi$
$920$	10.2463	−	6.50190i	0.337809	−	0.214361i
$921$	18.0586	−	13.1203i	0.595051	−	0.432330i
$922$	40.2228	+	13.0692i	1.32467	+	0.430410i
$923$			31.3212i			1.03095i
$924$	22.4326	+	14.6795i	0.737980	+	0.482920i
$925$	−39.4978	+	42.0542i	−1.29868	+	1.38273i
$926$	0.626554	−	1.92833i	0.0205898	−	0.0633690i
$927$	−4.53743	−	6.24523i	−0.149029	−	0.205120i
$928$	5.29383	−	7.28634i	0.173779	−	0.239186i
$929$	2.48284	+	7.64138i	0.0814592	+	0.250706i	0.983489	−	0.180968i	$-0.0579231\pi$
$929$	2.48284	+	7.64138i	0.0814592	+	0.250706i	−0.902030	+	0.431674i	$0.857923\pi$
$930$	−5.15572	−	0.324576i	−0.169063	−	0.0106433i
$931$	3.71217	+	2.69705i	0.121662	+	0.0883923i
$932$	−21.4244	−	29.4882i	−0.701781	−	0.965919i
$933$	18.5298	+	6.02070i	0.606639	+	0.197109i
$934$	−31.4144			−1.02791
$935$	−48.2476	+	14.9331i	−1.57787	+	0.488363i
$936$	2.30234			0.0752545
$937$	12.8309	+	4.16903i	0.419169	+	0.136196i	0.511005	−	0.859578i	$-0.329274\pi$
$937$	12.8309	+	4.16903i	0.419169	+	0.136196i	−0.0918359	+	0.995774i	$0.529274\pi$
$938$	17.0579	+	23.4782i	0.556960	+	0.766590i
$939$	−14.0386	−	10.1997i	−0.458133	−	0.332853i
$940$	0.730849	−	11.6091i	0.0238377	−	0.378648i
$941$	−9.85889	−	30.3425i	−0.321391	−	0.989138i	−0.973044	−	0.230621i	$-0.925924\pi$
$941$	−9.85889	−	30.3425i	−0.321391	−	0.989138i	0.651653	−	0.758517i	$-0.274076\pi$
$942$	22.7630	−	31.3305i	0.741657	−	1.02080i
$943$	−3.22874	−	4.44398i	−0.105142	−	0.144716i
$944$	7.61426	−	23.4343i	0.247823	−	0.762721i
$945$	2.73011	−	6.89468i	0.0888106	−	0.224284i
$946$	−1.01149	+	3.72290i	−0.0328863	+	0.121042i
$947$		−	10.2719i		−	0.333793i	−0.985974	−	0.166896i	$-0.946625\pi$
$947$		−	10.2719i		−	0.333793i	0.985974	−	0.166896i	$-0.0533745\pi$
$948$	8.96529	+	2.91300i	0.291179	+	0.0946099i
$949$	11.5994	−	8.42745i	0.376532	−	0.273567i
$950$	11.8742	−	2.26414i	0.385250	−	0.0734585i
$951$	−0.256706	−	0.790059i	−0.00832425	−	0.0256194i
$952$	−19.7900	+	6.43017i	−0.641399	+	0.208403i
$953$	5.78043	−	7.95608i	0.187247	−	0.257723i	−0.705065	−	0.709143i	$-0.749082\pi$
$953$	5.78043	−	7.95608i	0.187247	−	0.257723i	0.892312	+	0.451420i	$0.149082\pi$
$954$	−19.8294	+	14.4069i	−0.642001	+	0.466441i
$955$	−4.84704	−	4.01014i	−0.156846	−	0.129765i
$956$	−3.67353			−0.118810
$957$	−0.181877	−	3.71868i	−0.00587924	−	0.120208i
$958$		−	1.00170i		−	0.0323635i
$959$	6.59748	−	20.3050i	0.213044	−	0.655681i
$960$	−23.8952	+	6.13424i	−0.771215	+	0.197982i
$961$	24.1064	+	17.5143i	0.777627	+	0.564979i
$962$	57.7669	−	18.7696i	1.86248	−	0.605157i
$963$	−14.7522	+	4.79328i	−0.475383	+	0.154461i
$964$	−13.9919	−	10.1657i	−0.450649	−	0.327416i
$965$	41.8077	−	10.7326i	1.34584	−	0.345495i
$966$	−12.7156	+	39.1347i	−0.409118	+	1.25914i
$967$			3.85001i			0.123808i	0.998082	+	0.0619041i	$0.0197173\pi$
$967$			3.85001i			0.123808i	−0.998082	+	0.0619041i	$0.980283\pi$
$968$	−6.72879	−	7.57880i	−0.216272	−	0.243592i
$969$	−7.81600			−0.251086
$970$	−10.4113	−	8.61365i	−0.334286	−	0.276568i
$971$	−17.3065	+	12.5739i	−0.555392	+	0.403516i	−0.829769	−	0.558106i	$-0.811528\pi$
$971$	−17.3065	+	12.5739i	−0.555392	+	0.403516i	0.274378	+	0.961622i	$0.411528\pi$
$972$	1.43266	−	1.97188i	0.0459525	−	0.0632482i
$973$	22.0014	−	7.14868i	0.705332	−	0.229176i
$974$	−23.0129	−	70.8264i	−0.737381	−	2.26942i
$975$	2.34024	+	12.2733i	0.0749478	+	0.393060i
$976$	−19.4947	+	14.1637i	−0.624011	+	0.453370i
$977$	15.8523	+	5.15071i	0.507159	+	0.164786i	0.551410	−	0.834235i	$-0.314090\pi$
$977$	15.8523	+	5.15071i	0.507159	+	0.164786i	−0.0442509	+	0.999020i	$0.514090\pi$
$978$		−	37.0156i		−	1.18363i
$979$	−41.7229	+	2.04062i	−1.33347	+	0.0652185i
$980$	−8.02217	+	20.2593i	−0.256259	+	0.647161i
$981$	2.10080	−	6.46561i	0.0670735	−	0.206431i
$982$	−37.3097	−	51.3524i	−1.19060	−	1.63872i
$983$	30.4808	−	41.9532i	0.972186	−	1.33810i	0.0312510	−	0.999512i	$-0.490051\pi$
$983$	30.4808	−	41.9532i	0.972186	−	1.33810i	0.940935	−	0.338588i	$-0.109949\pi$
$984$	−0.265513	−	0.817166i	−0.00846426	−	0.0260503i
$985$	0.502902	−	7.98832i	0.0160238	−	0.254529i
$986$	13.0284	+	9.46570i	0.414910	+	0.301449i
$987$	4.16031	+	5.72618i	0.132424	+	0.182266i
$988$	−6.64816	−	2.16012i	−0.211506	−	0.0687226i
$989$	−3.25253			−0.103425
$990$	−9.35861	+	12.5089i	−0.297436	+	0.397559i
$991$	19.8195			0.629588			0.314794	−	0.949160i	$-0.398065\pi$
$991$	19.8195			0.629588			0.314794	+	0.949160i	$0.398065\pi$
$992$	−8.36846	−	2.71908i	−0.265699	−	0.0863308i
$993$	−18.5335	−	25.5092i	−0.588144	−	0.809510i
$994$	−70.8386	−	51.4672i	−2.24686	−	1.63244i
$995$	28.3613	+	1.78548i	0.899114	+	0.0566034i
$996$	−4.57982	−	14.0953i	−0.145117	−	0.446625i
$997$	30.3647	−	41.7934i	0.961658	−	1.32361i	0.0155088	−	0.999880i	$-0.495063\pi$
$997$	30.3647	−	41.7934i	0.961658	−	1.32361i	0.946150	−	0.323730i	$-0.104937\pi$
$998$	45.1683	+	62.1688i	1.42978	+	1.96792i
$999$	3.56571	−	10.9741i	0.112814	−	0.347206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.64.3	yes	48
3.2	odd	2		495.2.ba.c.64.10		48
5.2	odd	4		825.2.n.o.526.5		24
5.3	odd	4		825.2.n.p.526.2		24
5.4	even	2	inner	165.2.s.a.64.10	yes	48
11.4	even	5		1815.2.c.j.364.5		24
11.5	even	5	inner	165.2.s.a.49.10	yes	48
11.7	odd	10		1815.2.c.k.364.20		24
15.14	odd	2		495.2.ba.c.64.3		48
33.5	odd	10		495.2.ba.c.379.3		48
55.4	even	10		1815.2.c.j.364.20		24
55.7	even	20		9075.2.a.dx.1.3		12
55.18	even	20		9075.2.a.ea.1.10		12
55.27	odd	20		825.2.n.o.676.5		24
55.29	odd	10		1815.2.c.k.364.5		24
55.37	odd	20		9075.2.a.dz.1.10		12
55.38	odd	20		825.2.n.p.676.2		24
55.48	odd	20		9075.2.a.dy.1.3		12
55.49	even	10	inner	165.2.s.a.49.3	✓	48
165.104	odd	10		495.2.ba.c.379.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.3	✓	48	55.49	even	10	inner
165.2.s.a.49.10	yes	48	11.5	even	5	inner
165.2.s.a.64.3	yes	48	1.1	even	1	trivial
165.2.s.a.64.10	yes	48	5.4	even	2	inner
495.2.ba.c.64.3		48	15.14	odd	2
495.2.ba.c.64.10		48	3.2	odd	2
495.2.ba.c.379.3		48	33.5	odd	10
495.2.ba.c.379.10		48	165.104	odd	10
825.2.n.o.526.5		24	5.2	odd	4
825.2.n.o.676.5		24	55.27	odd	20
825.2.n.p.526.2		24	5.3	odd	4
825.2.n.p.676.2		24	55.38	odd	20
1815.2.c.j.364.5		24	11.4	even	5
1815.2.c.j.364.20		24	55.4	even	10
1815.2.c.k.364.5		24	55.29	odd	10
1815.2.c.k.364.20		24	11.7	odd	10
9075.2.a.dx.1.3		12	55.7	even	20
9075.2.a.dy.1.3		12	55.48	odd	20
9075.2.a.dz.1.10		12	55.37	odd	20
9075.2.a.ea.1.10		12	55.18	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00341 - 0.650947i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.97188 + 1.43266i) q^{4} +(-2.23165 - 0.140493i) q^{5} +(-0.650947 - 2.00341i) q^{6} +(1.94929 - 2.68296i) q^{7} +(-0.541555 - 0.745386i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.00341 - 0.650947i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.97188 + 1.43266i) q^{4} +(-2.23165 - 0.140493i) q^{5} +(-0.650947 - 2.00341i) q^{6} +(1.94929 - 2.68296i) q^{7} +(-0.541555 - 0.745386i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(4.37946 + 1.73415i) q^{10} +(3.31267 - 0.162019i) q^{11} +2.43738i q^{12} +(2.37658 + 0.772198i) q^{13} +(-5.65169 + 4.10619i) q^{14} +(-1.19807 - 1.88802i) q^{15} +(-0.906636 - 2.79034i) q^{16} +(6.47687 - 2.10446i) q^{17} +(1.23818 - 1.70420i) q^{18} +(-0.928503 + 0.674597i) q^{19} +(-4.19927 - 3.47422i) q^{20} +3.31633 q^{21} +(-6.74209 - 1.83178i) q^{22} -5.89026i q^{23} +(0.284712 - 0.876254i) q^{24} +(4.96052 + 0.627062i) q^{25} +(-4.25861 - 3.09406i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(7.68753 - 2.49783i) q^{28} +(-0.908175 - 0.659827i) q^{29} +(1.17122 + 4.56236i) q^{30} +(-0.338908 + 1.04305i) q^{31} +8.02306i q^{32} +(2.07821 + 2.58477i) q^{33} -14.3457 q^{34} +(-4.72706 + 5.71358i) q^{35} +(-1.97188 + 1.43266i) q^{36} +(-6.78238 + 9.33514i) q^{37} +(2.29930 - 0.747087i) q^{38} +(0.772198 + 2.37658i) q^{39} +(1.10384 + 1.73953i) q^{40} +(0.754463 - 0.548149i) q^{41} +(-6.64396 - 2.15875i) q^{42} -0.552188i q^{43} +(6.76431 + 4.42643i) q^{44} +(0.823234 - 2.07901i) q^{45} +(-3.83425 + 11.8006i) q^{46} +(1.25449 + 1.72666i) q^{47} +(1.72452 - 2.37360i) q^{48} +(-1.23546 - 3.80234i) q^{49} +(-9.52978 - 4.48530i) q^{50} +(5.50956 + 4.00293i) q^{51} +(3.58005 + 4.92751i) q^{52} +(-11.0661 - 3.59560i) q^{53} +2.10651 q^{54} +(-7.41547 - 0.103836i) q^{55} -3.05549 q^{56} +(-1.09152 - 0.354657i) q^{57} +(1.38993 + 1.91308i) q^{58} +(6.79443 + 4.93644i) q^{59} +(0.342435 - 5.43938i) q^{60} +(-2.53800 - 7.81115i) q^{61} +(1.35794 - 1.86905i) q^{62} +(1.94929 + 2.68296i) q^{63} +(3.40931 - 10.4928i) q^{64} +(-5.19521 - 2.05717i) q^{65} +(-2.48096 - 6.53116i) q^{66} -4.15419i q^{67} +(15.7866 + 5.12938i) q^{68} +(4.76532 - 3.46221i) q^{69} +(13.1895 - 8.36956i) q^{70} +(3.87323 + 11.9206i) q^{71} +(0.876254 - 0.284712i) q^{72} +(3.37248 - 4.64182i) q^{73} +(19.6646 - 14.2871i) q^{74} +(2.40842 + 4.38173i) q^{75} -2.79736 q^{76} +(6.02265 - 9.20358i) q^{77} -5.26393i q^{78} +(1.19514 - 3.67825i) q^{79} +(1.63127 + 6.35443i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.86831 + 0.607052i) q^{82} +(-5.78295 + 1.87899i) q^{83} +(6.53941 + 4.75116i) q^{84} +(-14.7498 + 3.78647i) q^{85} +(-0.359446 + 1.10626i) q^{86} -1.12257i q^{87} +(-1.91476 - 2.38147i) q^{88} -12.5950 q^{89} +(-3.00260 + 3.62923i) q^{90} +(6.70442 - 4.87105i) q^{91} +(8.43872 - 11.6149i) q^{92} +(-1.04305 + 0.338908i) q^{93} +(-1.38930 - 4.27582i) q^{94} +(2.16687 - 1.37502i) q^{95} +(-6.49079 + 4.71583i) q^{96} +(-2.72832 - 0.886486i) q^{97} +8.42187i q^{98} +(-0.869581 + 3.20060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

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