LMFDB - Embedded newform 756.2.cf.a.659.45

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.45
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.45

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.409728 - 1.35356i) q^{2} +(-0.446307 - 1.67356i) q^{3} +(-1.66425 + 1.10918i) q^{4} +(-0.512035 + 1.40680i) q^{5} +(-2.08240 + 1.28981i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(2.18323 + 1.79819i) q^{8} +(-2.60162 + 1.49384i) q^{9} +(2.11399 + 0.116662i) q^{10} +(-0.394383 + 0.143544i) q^{11} +(2.59905 + 2.29018i) q^{12} +(-1.30935 + 1.09868i) q^{13} +(0.168460 + 1.40414i) q^{14} +(2.58290 + 0.229055i) q^{15} +(1.53943 - 3.69191i) q^{16} +(1.20192 - 0.693931i) q^{17} +(3.08797 + 2.90938i) q^{18} +(3.55084 + 2.05008i) q^{19} +(-0.708251 - 2.90921i) q^{20} +(0.148916 + 1.72564i) q^{21} +(0.355885 + 0.475007i) q^{22} +(0.450800 + 2.55662i) q^{23} +(2.03499 - 4.45632i) q^{24} +(2.11331 + 1.77327i) q^{25} +(2.02360 + 1.32213i) q^{26} +(3.66116 + 3.68726i) q^{27} +(1.83157 - 0.803339i) q^{28} +(4.96486 - 5.91689i) q^{29} +(-0.748246 - 3.58996i) q^{30} +(2.98692 - 0.526675i) q^{31} +(-5.62796 - 0.571026i) q^{32} +(0.416245 + 0.595960i) q^{33} +(-1.43174 - 1.34255i) q^{34} +(0.748545 - 1.29652i) q^{35} +(2.67279 - 5.37180i) q^{36} +(3.90195 + 6.75837i) q^{37} +(1.32002 - 5.64625i) q^{38} +(2.42308 + 1.70094i) q^{39} +(-3.64759 + 2.15064i) q^{40} +(0.0493633 + 0.0588289i) q^{41} +(2.27474 - 0.908608i) q^{42} +(0.727821 + 1.99967i) q^{43} +(0.497134 - 0.676335i) q^{44} +(-0.769427 - 4.42487i) q^{45} +(3.27583 - 1.65770i) q^{46} +(-0.389288 + 2.20776i) q^{47} +(-6.86569 - 0.928601i) q^{48} +(0.939693 + 0.342020i) q^{49} +(1.53435 - 3.58704i) q^{50} +(-1.69776 - 1.70179i) q^{51} +(0.960450 - 3.28078i) q^{52} -7.46475i q^{53} +(3.49084 - 6.46638i) q^{54} -0.628319i q^{55} +(-1.83781 - 2.14999i) q^{56} +(1.84617 - 6.85752i) q^{57} +(-10.0431 - 4.29592i) q^{58} +(-3.56282 - 1.29676i) q^{59} +(-4.55264 + 2.48370i) q^{60} +(-2.06347 + 11.7025i) q^{61} +(-1.93671 - 3.82718i) q^{62} +(2.82150 - 1.01938i) q^{63} +(1.53302 + 7.85174i) q^{64} +(-0.875189 - 2.40456i) q^{65} +(0.636120 - 0.807595i) q^{66} +(2.44302 + 2.91147i) q^{67} +(-1.23060 + 2.48802i) q^{68} +(4.07746 - 1.89548i) q^{69} +(-2.06161 - 0.481980i) q^{70} +(4.04964 + 7.01418i) q^{71} +(-8.36616 - 1.41680i) q^{72} +(-0.567827 + 0.983506i) q^{73} +(7.54912 - 8.05062i) q^{74} +(2.02450 - 4.32817i) q^{75} +(-8.18338 + 0.526698i) q^{76} +(0.413318 - 0.0728791i) q^{77} +(1.30951 - 3.97670i) q^{78} +(-5.11154 + 6.09170i) q^{79} +(4.40555 + 4.05605i) q^{80} +(4.53685 - 7.77283i) q^{81} +(0.0594029 - 0.0909201i) q^{82} +(-6.45846 - 5.41929i) q^{83} +(-2.16188 - 2.70671i) q^{84} +(0.360798 + 2.04619i) q^{85} +(2.40846 - 1.80447i) q^{86} +(-12.1181 - 5.66825i) q^{87} +(-1.11915 - 0.395787i) q^{88} +(-7.55188 - 4.36008i) q^{89} +(-5.67407 + 2.85446i) q^{90} +(1.48024 - 0.854619i) q^{91} +(-3.58600 - 3.75482i) q^{92} +(-2.21451 - 4.76374i) q^{93} +(3.14784 - 0.377658i) q^{94} +(-4.70221 + 3.94562i) q^{95} +(1.55615 + 9.67359i) q^{96} +(5.87823 - 2.13950i) q^{97} +(0.0779259 - 1.41206i) q^{98} +(0.811603 - 0.962594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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 $

$2$	−0.409728	−	1.35356i	−0.289722	−	0.957111i
$2$	−0.409728	−	1.35356i	−0.289722	−	0.957111i
$3$	−0.446307	−	1.67356i	−0.257675	−	0.966232i
$3$	−0.446307	−	1.67356i	−0.257675	−	0.966232i
$4$	−1.66425	+	1.10918i	−0.832123	+	0.554592i
$5$	−0.512035	+	1.40680i	−0.228989	+	0.629142i	−0.999970	−	0.00771601i	$-0.997544\pi$
$5$	−0.512035	+	1.40680i	−0.228989	+	0.629142i	0.770981	+	0.636858i	$0.219766\pi$
$6$	−2.08240	+	1.28981i	−0.850137	+	0.526562i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	2.18323	+	1.79819i	0.771890	+	0.635757i
$9$	−2.60162	+	1.49384i	−0.867207	+	0.497948i
$10$	2.11399	+	0.116662i	0.668501	+	0.0368918i
$11$	−0.394383	+	0.143544i	−0.118911	+	0.0432801i	−0.400790	−	0.916170i	$-0.631264\pi$
$11$	−0.394383	+	0.143544i	−0.118911	+	0.0432801i	0.281879	+	0.959450i	$0.409042\pi$
$12$	2.59905	+	2.29018i	0.750281	+	0.661119i
$13$	−1.30935	+	1.09868i	−0.363149	+	0.304718i	−0.806044	−	0.591855i	$-0.798396\pi$
$13$	−1.30935	+	1.09868i	−0.363149	+	0.304718i	0.442895	+	0.896573i	$0.353951\pi$
$14$	0.168460	+	1.40414i	0.0450230	+	0.375273i
$15$	2.58290	+	0.229055i	0.666901	+	0.0591419i
$16$	1.53943	−	3.69191i	0.384856	−	0.922976i
$17$	1.20192	−	0.693931i	0.291509	−	0.168303i	−0.347113	−	0.937823i	$-0.612838\pi$
$17$	1.20192	−	0.693931i	0.291509	−	0.168303i	0.638622	+	0.769520i	$0.279505\pi$
$18$	3.08797	+	2.90938i	0.727840	+	0.685747i
$19$	3.55084	+	2.05008i	0.814619	+	0.470320i	0.848557	−	0.529104i	$-0.177472\pi$
$19$	3.55084	+	2.05008i	0.814619	+	0.470320i	−0.0339384	+	0.999424i	$0.510805\pi$
$20$	−0.708251	−	2.90921i	−0.158370	−	0.650518i
$21$	0.148916	+	1.72564i	0.0324960	+	0.376565i
$22$	0.355885	+	0.475007i	0.0758749	+	0.101272i
$23$	0.450800	+	2.55662i	0.0939984	+	0.533091i	0.995050	+	0.0993788i	$0.0316856\pi$
$23$	0.450800	+	2.55662i	0.0939984	+	0.533091i	−0.901051	+	0.433713i	$0.857203\pi$
$24$	2.03499	−	4.45632i	0.415391	−	0.909643i
$25$	2.11331	+	1.77327i	0.422661	+	0.354655i
$26$	2.02360	+	1.32213i	0.396861	+	0.259290i
$27$	3.66116	+	3.68726i	0.704591	+	0.709613i
$28$	1.83157	−	0.803339i	0.346134	−	0.151817i
$29$	4.96486	−	5.91689i	0.921952	−	1.09874i	−0.0728941	−	0.997340i	$-0.523224\pi$
$29$	4.96486	−	5.91689i	0.921952	−	1.09874i	0.994846	−	0.101400i	$-0.0323320\pi$
$30$	−0.748246	−	3.58996i	−0.136610	−	0.655433i
$31$	2.98692	−	0.526675i	0.536467	−	0.0945936i	0.101151	−	0.994871i	$-0.467748\pi$
$31$	2.98692	−	0.526675i	0.536467	−	0.0945936i	0.435317	+	0.900277i	$0.356636\pi$
$32$	−5.62796	−	0.571026i	−0.994892	−	0.100944i
$33$	0.416245	+	0.595960i	0.0724590	+	0.103743i
$34$	−1.43174	−	1.34255i	−0.245541	−	0.230246i
$35$	0.748545	−	1.29652i	0.126527	−	0.219151i
$36$	2.67279	−	5.37180i	0.445465	−	0.895300i
$37$	3.90195	+	6.75837i	0.641476	+	1.11107i	0.985103	+	0.171964i	$0.0550111\pi$
$37$	3.90195	+	6.75837i	0.641476	+	1.11107i	−0.343627	+	0.939106i	$0.611656\pi$
$38$	1.32002	−	5.64625i	0.214136	−	0.915943i
$39$	2.42308	+	1.70094i	0.388003	+	0.272368i
$40$	−3.64759	+	2.15064i	−0.576735	+	0.340047i
$41$	0.0493633	+	0.0588289i	0.00770926	+	0.00918754i	0.769885	−	0.638182i	$-0.220313\pi$
$41$	0.0493633	+	0.0588289i	0.00770926	+	0.00918754i	−0.762176	+	0.647370i	$0.775869\pi$
$42$	2.27474	−	0.908608i	0.351000	−	0.140201i
$43$	0.727821	+	1.99967i	0.110992	+	0.304947i	0.982736	−	0.185014i	$-0.0592331\pi$
$43$	0.727821	+	1.99967i	0.110992	+	0.304947i	−0.871744	+	0.489961i	$0.837011\pi$
$44$	0.497134	−	0.676335i	0.0749458	−	0.101961i
$45$	−0.769427	−	4.42487i	−0.114699	−	0.659620i
$46$	3.27583	−	1.65770i	0.482994	−	0.244415i
$47$	−0.389288	+	2.20776i	−0.0567835	+	0.322035i	−0.999947	−	0.0102938i	$-0.996723\pi$
$47$	−0.389288	+	2.20776i	−0.0567835	+	0.322035i	0.943164	+	0.332329i	$0.107834\pi$
$48$	−6.86569	−	0.928601i	−0.990977	−	0.134032i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	1.53435	−	3.58704i	0.216990	−	0.507285i
$51$	−1.69776	−	1.70179i	−0.237734	−	0.238298i
$52$	0.960450	−	3.28078i	0.133190	−	0.454962i
$53$		−	7.46475i		−	1.02536i	−0.858579	−	0.512681i	$-0.828652\pi$
$53$		−	7.46475i		−	1.02536i	0.858579	−	0.512681i	$-0.171348\pi$
$54$	3.49084	−	6.46638i	0.475043	−	0.879962i
$55$		−	0.628319i		−	0.0847225i
$56$	−1.83781	−	2.14999i	−0.245588	−	0.287304i
$57$	1.84617	−	6.85752i	0.244531	−	0.908300i
$58$	−10.0431	−	4.29592i	−1.31872	−	0.564081i
$59$	−3.56282	−	1.29676i	−0.463840	−	0.168824i	0.0995200	−	0.995036i	$-0.468269\pi$
$59$	−3.56282	−	1.29676i	−0.463840	−	0.168824i	−0.563360	+	0.826212i	$0.690492\pi$
$60$	−4.55264	+	2.48370i	−0.587743	+	0.320645i
$61$	−2.06347	+	11.7025i	−0.264200	+	1.49835i	0.507104	+	0.861885i	$0.330716\pi$
$61$	−2.06347	+	11.7025i	−0.264200	+	1.49835i	−0.771304	+	0.636467i	$0.780395\pi$
$62$	−1.93671	−	3.82718i	−0.245963	−	0.486053i
$63$	2.82150	−	1.01938i	0.355475	−	0.128430i
$64$	1.53302	+	7.85174i	0.191627	+	0.981468i
$65$	−0.875189	−	2.40456i	−0.108554	−	0.298249i
$66$	0.636120	−	0.807595i	0.0783010	−	0.0994080i
$67$	2.44302	+	2.91147i	0.298462	+	0.355693i	0.894345	−	0.447378i	$-0.147642\pi$
$67$	2.44302	+	2.91147i	0.298462	+	0.355693i	−0.595883	+	0.803071i	$0.703198\pi$
$68$	−1.23060	+	2.48802i	−0.149232	+	0.301717i
$69$	4.07746	−	1.89548i	0.490869	−	0.228189i
$70$	−2.06161	−	0.481980i	−0.246410	−	0.0576076i
$71$	4.04964	+	7.01418i	0.480604	+	0.832430i	0.999752	−	0.0222539i	$-0.00708422\pi$
$71$	4.04964	+	7.01418i	0.480604	+	0.832430i	−0.519149	+	0.854684i	$0.673751\pi$
$72$	−8.36616	−	1.41680i	−0.985962	−	0.166971i
$73$	−0.567827	+	0.983506i	−0.0664592	+	0.115111i	−0.897340	−	0.441339i	$-0.854504\pi$
$73$	−0.567827	+	0.983506i	−0.0664592	+	0.115111i	0.830881	+	0.556450i	$0.187837\pi$
$74$	7.54912	−	8.05062i	0.877567	−	0.935865i
$75$	2.02450	−	4.32817i	0.233769	−	0.499774i
$76$	−8.18338	+	0.526698i	−0.938699	+	0.0604164i
$77$	0.413318	−	0.0728791i	0.0471019	−	0.00830534i
$78$	1.30951	−	3.97670i	0.148273	−	0.450273i
$79$	−5.11154	+	6.09170i	−0.575093	+	0.685369i	−0.972668	−	0.232200i	$-0.925408\pi$
$79$	−5.11154	+	6.09170i	−0.575093	+	0.685369i	0.397575	+	0.917570i	$0.369852\pi$
$80$	4.40555	+	4.05605i	0.492555	+	0.453481i
$81$	4.53685	−	7.77283i	0.504095	−	0.863648i
$82$	0.0594029	−	0.0909201i	0.00655995	−	0.0100404i
$83$	−6.45846	−	5.41929i	−0.708909	−	0.594845i	0.215384	−	0.976529i	$-0.430900\pi$
$83$	−6.45846	−	5.41929i	−0.708909	−	0.594845i	−0.924293	+	0.381685i	$0.875344\pi$
$84$	−2.16188	−	2.70671i	−0.235880	−	0.295326i
$85$	0.360798	+	2.04619i	0.0391340	+	0.221940i
$86$	2.40846	−	1.80447i	0.259711	−	0.194581i
$87$	−12.1181	−	5.66825i	−1.29920	−	0.607701i
$88$	−1.11915	−	0.395787i	−0.119302	−	0.0421910i
$89$	−7.55188	−	4.36008i	−0.800498	−	0.462168i	0.0431474	−	0.999069i	$-0.486261\pi$
$89$	−7.55188	−	4.36008i	−0.800498	−	0.462168i	−0.843645	+	0.536901i	$0.819595\pi$
$90$	−5.67407	+	2.85446i	−0.598099	+	0.300886i
$91$	1.48024	−	0.854619i	0.155172	−	0.0895884i
$92$	−3.58600	−	3.75482i	−0.373866	−	0.391467i
$93$	−2.21451	−	4.76374i	−0.229634	−	0.493977i
$94$	3.14784	−	0.377658i	0.324675	−	0.0389525i
$95$	−4.70221	+	3.94562i	−0.482437	+	0.404813i
$96$	1.55615	+	9.67359i	0.158824	+	0.987307i
$97$	5.87823	−	2.13950i	0.596844	−	0.217233i	−0.0258931	−	0.999665i	$-0.508243\pi$
$97$	5.87823	−	2.13950i	0.596844	−	0.217233i	0.622737	+	0.782431i	$0.286021\pi$
$98$	0.0779259	−	1.41206i	0.00787170	−	0.142640i
$99$	0.811603	−	0.962594i	0.0815692	−	0.0967443i
$100$	−5.48394	−	0.607120i	−0.548394	−	0.0607120i
$101$	9.48303	+	1.67211i	0.943596	+	0.166382i	0.624222	−	0.781247i	$-0.285416\pi$
$101$	9.48303	+	1.67211i	0.943596	+	0.166382i	0.319375	+	0.947629i	$0.396527\pi$
$102$	−1.60785	+	2.99529i	−0.159201	+	0.296578i
$103$	−4.91431	+	13.5020i	−0.484222	+	1.33039i	0.421620	+	0.906772i	$0.361462\pi$
$103$	−4.91431	+	13.5020i	−0.484222	+	1.33039i	−0.905842	+	0.423616i	$0.860761\pi$
$104$	−4.83425	+	0.0442027i	−0.474038	+	0.00433443i
$105$	−2.50388	−	0.674091i	−0.244354	−	0.0657846i
$106$	−10.1040	+	3.05852i	−0.981385	+	0.297070i
$107$	8.50784			0.822484			0.411242	−	0.911526i	$-0.365095\pi$
$107$	8.50784			0.822484			0.411242	+	0.911526i	$0.365095\pi$
$108$	−10.1829	−	2.07560i	−0.979852	−	0.199725i
$109$	14.5309			1.39180			0.695902	−	0.718137i	$-0.255005\pi$
$109$	14.5309			1.39180			0.695902	+	0.718137i	$0.255005\pi$
$110$	−0.850467	+	0.257440i	−0.0810889	+	0.0245460i
$111$	9.56909	−	9.54646i	0.908258	−	0.906110i
$112$	−2.15713	+	3.36850i	−0.203830	+	0.318293i
$113$	2.27013	−	6.23714i	0.213556	−	0.586740i	−0.785946	−	0.618295i	$-0.787824\pi$
$113$	2.27013	−	6.23714i	0.213556	−	0.586740i	0.999502	+	0.0315547i	$0.0100459\pi$
$114$	−10.0385	+	0.310819i	−0.940190	+	0.0291109i
$115$	−3.82748	−	0.674888i	−0.356915	−	0.0629337i
$116$	−1.69983	+	15.3541i	−0.157825	+	1.42559i
$117$	1.76518	−	4.81431i	0.163191	−	0.445083i
$118$	−0.295454	+	5.35381i	−0.0271988	+	0.492858i
$119$	−1.30416	+	0.474677i	−0.119552	+	0.0435135i
$120$	5.22718	+	5.14463i	0.477174	+	0.469638i
$121$	−8.29156	+	6.95744i	−0.753778	+	0.632495i
$122$	16.6855	−	2.00182i	1.51063	−	0.181236i
$123$	0.0764227	−	0.108868i	0.00689080	−	0.00981633i
$124$	−4.38679	+	4.18956i	−0.393946	+	0.376234i
$125$	−10.0593	+	5.80775i	−0.899733	+	0.519461i
$126$	−2.53584	−	3.40140i	−0.225911	−	0.303020i
$127$	5.60926	+	3.23851i	0.497742	+	0.287371i	0.727781	−	0.685810i	$-0.240552\pi$
$127$	5.60926	+	3.23851i	0.497742	+	0.287371i	−0.230039	+	0.973181i	$0.573885\pi$
$128$	9.99968	−	5.29211i	0.883855	−	0.467761i
$129$	3.02174	−	2.11052i	0.266050	−	0.185821i
$130$	−2.89613	+	2.16984i	−0.254007	+	0.190307i
$131$	2.58213	+	14.6440i	0.225602	+	1.27945i	0.861531	+	0.507705i	$0.169506\pi$
$131$	2.58213	+	14.6440i	0.225602	+	1.27945i	−0.635929	+	0.771748i	$0.719383\pi$
$132$	−1.35376	−	0.530132i	−0.117830	−	0.0461421i
$133$	−3.14090	−	2.63553i	−0.272351	−	0.228530i
$134$	2.93988	−	4.49968i	0.253967	−	0.388713i
$135$	−7.06189	+	3.26253i	−0.607791	+	0.280794i
$136$	3.87190	+	0.646275i	0.332013	+	0.0554176i
$137$	2.56179	−	3.05303i	0.218869	−	0.260838i	−0.645426	−	0.763822i	$-0.723320\pi$
$137$	2.56179	−	3.05303i	0.218869	−	0.260838i	0.864295	+	0.502985i	$0.167765\pi$
$138$	−4.23629	−	4.74245i	−0.360617	−	0.403704i
$139$	8.51102	−	1.50072i	0.721895	−	0.127290i	0.199383	−	0.979922i	$-0.436106\pi$
$139$	8.51102	−	1.50072i	0.721895	−	0.127290i	0.522512	+	0.852632i	$0.324995\pi$
$140$	0.192313	+	2.98800i	0.0162534	+	0.252532i
$141$	3.86857	−	0.333842i	0.325792	−	0.0281146i
$142$	7.83486	−	8.35533i	0.657487	−	0.701164i
$143$	0.358678	−	0.621249i	0.0299942	−	0.0519515i
$144$	1.51013	+	11.9046i	0.125844	+	0.992050i
$145$	5.78172	+	10.0142i	0.480146	+	0.831637i
$146$	1.56389	+	0.365618i	0.129428	+	0.0302588i
$147$	0.153001	−	1.72528i	0.0126193	−	0.142299i
$148$	−13.9901	−	6.91962i	−1.14998	−	0.568789i
$149$	12.8897	+	15.3613i	1.05596	+	1.25845i	0.964904	+	0.262603i	$0.0845808\pi$
$149$	12.8897	+	15.3613i	1.05596	+	1.25845i	0.0910592	+	0.995845i	$0.470975\pi$
$150$	−6.68793	−	0.966907i	−0.546067	−	0.0789477i
$151$	5.29405	+	14.5453i	0.430824	+	1.18368i	0.945308	+	0.326179i	$0.105761\pi$
$151$	5.29405	+	14.5453i	0.430824	+	1.18368i	−0.514484	+	0.857500i	$0.672016\pi$
$152$	4.06588	+	10.8609i	0.329787	+	0.880935i
$153$	−2.09032	+	3.60083i	−0.168993	+	0.291110i
$154$	−0.267994	−	0.529590i	−0.0215956	−	0.0426755i
$155$	−0.788480	+	4.47169i	−0.0633322	+	0.359175i
$156$	−5.91924	−	0.143137i	−0.473919	−	0.0114602i
$157$	3.15920	+	1.14985i	0.252131	+	0.0917683i	0.464994	−	0.885314i	$-0.346056\pi$
$157$	3.15920	+	1.14985i	0.252131	+	0.0917683i	−0.212863	+	0.977082i	$0.568279\pi$
$158$	10.3398	+	4.42283i	0.822592	+	0.351862i
$159$	−12.4927	+	3.33157i	−0.990737	+	0.264211i
$160$	3.68503	−	7.62505i	0.291327	−	0.602813i
$161$		−	2.59606i		−	0.204598i
$162$	−12.3799	−	2.95615i	−0.972654	−	0.232257i
$163$		−	17.7942i		−	1.39375i	−0.717193	−	0.696875i	$-0.754573\pi$
$163$		−	17.7942i		−	1.39375i	0.717193	−	0.696875i	$-0.245427\pi$
$164$	−0.147405	−	0.0431528i	−0.0115104	−	0.00336967i
$165$	−1.05153	+	0.280423i	−0.0818616	+	0.0218309i
$166$	−4.68912	+	10.9624i	−0.363946	+	0.850844i
$167$	−9.03502	−	3.28848i	−0.699151	−	0.254470i	−0.0321025	−	0.999485i	$-0.510220\pi$
$167$	−9.03502	−	3.28848i	−0.699151	−	0.254470i	−0.667048	+	0.745015i	$0.732443\pi$
$168$	−2.77791	+	4.03525i	−0.214320	+	0.311326i
$169$	−1.75011	+	9.92539i	−0.134624	+	0.763492i
$170$	2.62181	−	1.32674i	0.201083	−	0.101756i
$171$	−12.3004	−	0.0291211i	−0.940638	−	0.00222694i
$172$	−3.42927	−	2.52066i	−0.261480	−	0.192198i
$173$	−5.99882	−	16.4816i	−0.456082	−	1.25307i	−0.928379	−	0.371635i	$-0.878797\pi$
$173$	−5.99882	−	16.4816i	−0.456082	−	1.25307i	0.472297	−	0.881439i	$-0.343425\pi$
$174$	−2.70717	+	18.7251i	−0.205230	+	1.41954i
$175$	−1.77327	−	2.11331i	−0.134047	−	0.159751i
$176$	−0.0771737	+	1.67700i	−0.00581719	+	0.126409i
$177$	−0.580098	+	6.54136i	−0.0436028	+	0.491678i
$178$	−2.80741	+	12.0084i	−0.210424	+	0.900065i
$179$	5.38997	+	9.33570i	0.402865	+	0.697783i	0.994070	−	0.108738i	$-0.0346811\pi$
$179$	5.38997	+	9.33570i	0.402865	+	0.697783i	−0.591205	+	0.806521i	$0.701348\pi$
$180$	6.18850	+	6.51063i	0.461264	+	0.485274i
$181$	−5.81285	+	10.0681i	−0.432066	+	0.748360i	−0.997051	−	0.0767412i	$-0.975548\pi$
$181$	−5.81285	+	10.0681i	−0.432066	+	0.748360i	0.564985	+	0.825101i	$0.308882\pi$
$182$	−1.76328	−	1.65344i	−0.130703	−	0.122561i
$183$	20.5058	−	1.76957i	1.51583	−	0.130810i
$184$	−3.61308	+	6.39232i	−0.266360	+	0.471248i
$185$	−11.5056	+	2.02875i	−0.845911	+	0.149157i
$186$	−5.54066	+	4.94931i	−0.406261	+	0.362901i
$187$	−0.374409	+	0.446203i	−0.0273795	+	0.0326296i
$188$	−1.80094	−	4.10605i	−0.131347	−	0.299464i
$189$	−2.96526	−	4.26700i	−0.215691	−	0.310378i
$190$	7.26727	+	4.74809i	0.527223	+	0.344463i
$191$	11.6748	+	9.79634i	0.844761	+	0.708838i	0.958629	−	0.284657i	$-0.0918798\pi$
$191$	11.6748	+	9.79634i	0.844761	+	0.708838i	−0.113869	+	0.993496i	$0.536324\pi$
$192$	12.4562	−	6.06989i	0.898948	−	0.438056i
$193$	−3.12755	−	17.7372i	−0.225126	−	1.27675i	−0.862445	−	0.506151i	$-0.831068\pi$
$193$	−3.12755	−	17.7372i	−0.225126	−	1.27675i	0.637319	−	0.770600i	$-0.280043\pi$
$194$	−5.30442	−	7.07992i	−0.380835	−	0.508308i
$195$	−3.63358	+	2.53786i	−0.260206	+	0.181740i
$196$	−1.94324	+	0.473086i	−0.138803	+	0.0337918i
$197$	−4.41385	−	2.54834i	−0.314474	−	0.181562i	0.334453	−	0.942412i	$-0.391448\pi$
$197$	−4.41385	−	2.54834i	−0.314474	−	0.181562i	−0.648927	+	0.760851i	$0.724782\pi$
$198$	−1.63546	−	0.704151i	−0.116227	−	0.0500419i
$199$	−8.39995	+	4.84971i	−0.595456	+	0.343787i	−0.767252	−	0.641346i	$-0.778376\pi$
$199$	−8.39995	+	4.84971i	−0.595456	+	0.343787i	0.171796	+	0.985133i	$0.445043\pi$
$200$	1.42515	+	7.67160i	0.100774	+	0.542464i
$201$	3.78220	−	5.38795i	0.266775	−	0.380037i
$202$	−1.62216	−	13.5210i	−0.114135	−	0.951331i
$203$	−5.91689	+	4.96486i	−0.415284	+	0.348465i
$204$	4.71309	+	0.949062i	0.329982	+	0.0664476i
$205$	−0.108036	+	0.0393221i	−0.00754560	+	0.00274637i
$206$	20.2892	+	1.11968i	1.41362	+	0.0780116i
$207$	−4.99200	−	5.97792i	−0.346968	−	0.415494i
$208$	2.04056	+	6.52534i	0.141487	+	0.452451i
$209$	−1.69467	−	0.298816i	−0.117223	−	0.0206695i
$210$	0.113489	+	3.66535i	0.00783151	+	0.252933i
$211$	8.75683	−	24.0592i	0.602845	−	1.65630i	−0.142636	−	0.989775i	$-0.545558\pi$
$211$	8.75683	−	24.0592i	0.602845	−	1.65630i	0.745481	−	0.666527i	$-0.232220\pi$
$212$	8.27977	+	12.4232i	0.568657	+	0.853227i
$213$	9.93128	−	9.90780i	0.680480	−	0.678871i
$214$	−3.48590	−	11.5159i	−0.238291	−	0.787209i
$215$	−3.18581			−0.217271
$216$	1.36278	+	14.6336i	0.0927252	+	0.995692i
$217$	−3.03300			−0.205894
$218$	−5.95370	−	19.6684i	−0.403236	−	1.33211i
$219$	1.89938	+	0.511349i	0.128348	+	0.0345538i
$220$	0.696921	+	1.04568i	0.0469864	+	0.0704995i
$221$	−0.811335	+	2.22913i	−0.0545763	+	0.149947i
$222$	−16.8424	−	9.04088i	−1.13039	−	0.606784i
$223$	−2.06723	−	0.364508i	−0.138432	−	0.0244093i	0.104003	−	0.994577i	$-0.466835\pi$
$223$	−2.06723	−	0.364508i	−0.138432	−	0.0244093i	−0.242435	+	0.970168i	$0.577946\pi$
$224$	5.44330	+	1.53964i	0.363696	+	0.102871i
$225$	−8.14701	−	1.45643i	−0.543134	−	0.0970956i
$226$	−9.37247	−	0.517227i	−0.623448	−	0.0344054i
$227$	−3.38603	+	1.23241i	−0.224739	+	0.0817983i	−0.451935	−	0.892051i	$-0.649266\pi$
$227$	−3.38603	+	1.23241i	−0.224739	+	0.0817983i	0.227197	+	0.973849i	$0.427044\pi$
$228$	4.53376	+	13.4603i	0.300256	+	0.891432i
$229$	−13.5151	+	11.3405i	−0.893104	+	0.749403i	−0.968830	−	0.247725i	$-0.920317\pi$
$229$	−13.5151	+	11.3405i	−0.893104	+	0.749403i	0.0757263	+	0.997129i	$0.475872\pi$
$230$	0.654726	+	5.45724i	0.0431714	+	0.359840i
$231$	−0.306434	−	0.659187i	−0.0201619	−	0.0433713i
$232$	21.4792	−	3.99019i	1.41018	−	0.261969i
$233$	−24.1439	+	13.9395i	−1.58172	+	0.913208i	−0.587114	+	0.809504i	$0.699736\pi$
$233$	−24.1439	+	13.9395i	−1.58172	+	0.913208i	−0.994608	+	0.103704i	$0.966931\pi$
$234$	−7.23970	−	0.416723i	−0.473274	−	0.0272420i
$235$	−2.90656	−	1.67810i	−0.189603	−	0.109467i
$236$	7.36775	−	1.79369i	0.479600	−	0.116759i
$237$	12.4761	+	5.83571i	0.810413	+	0.379070i
$238$	1.17686	+	1.57077i	0.0762842	+	0.101818i
$239$	3.12107	+	17.7004i	0.201885	+	1.14495i	0.902267	+	0.431178i	$0.141902\pi$
$239$	3.12107	+	17.7004i	0.201885	+	1.14495i	−0.700382	+	0.713768i	$0.746987\pi$
$240$	4.82183	−	9.18320i	0.311248	−	0.592773i
$241$	−5.81130	−	4.87626i	−0.374339	−	0.314107i	0.436136	−	0.899881i	$-0.356346\pi$
$241$	−5.81130	−	4.87626i	−0.374339	−	0.314107i	−0.810475	+	0.585773i	$0.800791\pi$
$242$	12.8146	+	8.37245i	0.823753	+	0.538202i
$243$	−15.0332	−	4.12364i	−0.964377	−	0.264531i
$244$	−9.54610	−	21.7646i	−0.611127	−	1.39334i
$245$	−0.962310	+	1.14684i	−0.0614797	+	0.0732687i
$246$	−0.178672	−	0.0588362i	−0.0113917	−	0.00375126i
$247$	−6.90168	+	1.21695i	−0.439143	+	0.0774328i
$248$	7.46821	+	4.22120i	0.474232	+	0.268047i
$249$	−6.18707	+	13.2273i	−0.392090	+	0.838247i
$250$	11.9827	+	11.2363i	0.757854	+	0.710645i
$251$	9.19225	−	15.9215i	0.580210	−	1.00495i	−0.415244	−	0.909710i	$-0.636304\pi$
$251$	9.19225	−	15.9215i	0.580210	−	1.00495i	0.995454	−	0.0952431i	$-0.0303628\pi$
$252$	−3.56498	+	4.82606i	−0.224573	+	0.304013i
$253$	−0.544774	−	0.943577i	−0.0342497	−	0.0593222i
$254$	2.08524	−	8.91938i	0.130840	−	0.559652i
$255$	3.26339	−	1.51705i	0.204362	−	0.0950010i
$256$	−11.2603	−	11.3668i	−0.703771	−	0.710427i
$257$	−12.8195	−	15.2777i	−0.799658	−	0.952995i	0.199983	−	0.979799i	$-0.435911\pi$
$257$	−12.8195	−	15.2777i	−0.799658	−	0.952995i	−0.999641	+	0.0268044i	$0.991467\pi$
$258$	−4.09481	−	3.22537i	−0.254932	−	0.200803i
$259$	−2.66909	−	7.33327i	−0.165849	−	0.455667i
$260$	4.12363	+	3.03104i	0.255737	+	0.187977i
$261$	−4.07777	+	22.8102i	−0.252407	+	1.41192i
$262$	18.7636	−	9.49513i	1.15922	−	0.586611i
$263$	−0.299556	+	1.69887i	−0.0184714	+	0.104757i	−0.992650	−	0.121024i	$-0.961382\pi$
$263$	−0.299556	+	1.69887i	−0.0184714	+	0.104757i	0.974178	+	0.225781i	$0.0724933\pi$
$264$	−0.162890	+	2.04961i	−0.0100252	+	0.126145i
$265$	10.5014	+	3.82221i	0.645098	+	0.234796i
$266$	−2.28043	+	5.33125i	−0.139822	+	0.326880i
$267$	−3.92641	+	14.5845i	−0.240292	+	0.892555i
$268$	−7.29513	−	2.13565i	−0.445621	−	0.130456i
$269$		−	14.2014i		−	0.865873i	−0.901424	−	0.432937i	$-0.857477\pi$
$269$		−	14.2014i		−	0.865873i	0.901424	−	0.432937i	$-0.142523\pi$
$270$	7.30949	+	8.22194i	0.444841	+	0.500371i
$271$		−	28.7696i		−	1.74763i	−0.486260	−	0.873814i	$-0.661639\pi$
$271$		−	28.7696i		−	1.74763i	0.486260	−	0.873814i	$-0.338361\pi$
$272$	−0.711655	−	5.50564i	−0.0431504	−	0.333829i
$273$	−2.09090	−	2.09586i	−0.126547	−	0.126847i
$274$	−5.18209	−	2.21663i	−0.313062	−	0.133911i
$275$	−1.08799	−	0.395998i	−0.0656086	−	0.0238796i
$276$	−4.68346	+	7.67719i	−0.281911	+	0.462113i
$277$	0.295936	−	1.67834i	0.0177811	−	0.100842i	−0.974626	−	0.223841i	$-0.928140\pi$
$277$	0.295936	−	1.67834i	0.0177811	−	0.100842i	0.992407	+	0.123000i	$0.0392514\pi$
$278$	−5.51852	−	10.9053i	−0.330979	−	0.654055i
$279$	−6.98407	+	5.83221i	−0.418125	+	0.349165i
$280$	3.96563	−	1.48457i	0.236992	−	0.0887202i
$281$	−5.88953	−	16.1814i	−0.351340	−	0.965299i	−0.981940	−	0.189191i	$-0.939413\pi$
$281$	−5.88953	−	16.1814i	−0.351340	−	0.965299i	0.630600	−	0.776108i	$-0.282809\pi$
$282$	−2.03694	−	5.09955i	−0.121298	−	0.303674i
$283$	4.89320	+	5.83149i	0.290870	+	0.346646i	0.891614	−	0.452796i	$-0.149573\pi$
$283$	4.89320	+	5.83149i	0.290870	+	0.346646i	−0.600744	+	0.799442i	$0.705129\pi$
$284$	−14.5196	−	7.18153i	−0.861580	−	0.426145i
$285$	8.70188	+	6.10848i	0.515455	+	0.361835i
$286$	−0.987858	−	0.230949i	−0.0584133	−	0.0136563i
$287$	−0.0383979	−	0.0665070i	−0.00226655	−	0.00392579i
$288$	15.4948	−	6.92171i	0.913042	−	0.407865i
$289$	−7.53692	+	13.0543i	−0.443348	+	0.767902i
$290$	11.1859	−	11.9290i	0.656860	−	0.700496i
$291$	−6.20408	−	8.88271i	−0.363690	−	0.520713i
$292$	−0.145884	−	2.26662i	−0.00853721	−	0.132644i
$293$	−24.6896	+	4.35345i	−1.44238	+	0.254331i	−0.839440	−	0.543453i	$-0.817117\pi$
$293$	−24.6896	+	4.35345i	−1.44238	+	0.254331i	−0.602944	+	0.797784i	$0.706006\pi$
$294$	−2.39796	+	0.499801i	−0.139852	+	0.0291490i
$295$	3.64858	−	4.34820i	0.212428	−	0.253162i
$296$	−3.63398	+	21.7716i	−0.211221	+	1.26545i
$297$	−1.97318	−	0.928656i	−0.114496	−	0.0538861i
$298$	15.5112	−	23.7409i	0.898539	−	1.37527i
$299$	−3.39915	−	2.85223i	−0.196578	−	0.164949i
$300$	1.43147	+	9.44868i	0.0826459	+	0.545520i
$301$	−0.369524	−	2.09568i	−0.0212990	−	0.120793i
$302$	17.5188	−	13.1254i	1.00809	−	0.755284i
$303$	−1.43396	−	16.6167i	−0.0823786	−	0.954605i
$304$	13.0350	−	9.95343i	0.747606	−	0.570868i
$305$	−15.4066	−	8.89498i	−0.882177	−	0.509325i
$306$	5.73040	+	1.35401i	0.327585	+	0.0774038i
$307$	18.9740	−	10.9546i	1.08290	−	0.625215i	0.151225	−	0.988499i	$-0.451678\pi$
$307$	18.9740	−	10.9546i	1.08290	−	0.625215i	0.931678	+	0.363285i	$0.118345\pi$
$308$	−0.607026	+	0.579734i	−0.0345885	+	0.0330334i
$309$	24.7897	+	2.19839i	1.41023	+	0.125062i
$310$	6.37576	−	0.764924i	0.362119	−	0.0434448i
$311$	−2.84001	+	2.38305i	−0.161042	+	0.135131i	−0.719748	−	0.694236i	$-0.755743\pi$
$311$	−2.84001	+	2.38305i	−0.161042	+	0.135131i	0.558706	+	0.829366i	$0.311298\pi$
$312$	2.23154	+	8.07070i	0.126336	+	0.456913i
$313$	−24.1489	+	8.78949i	−1.36498	+	0.496811i	−0.917590	−	0.397528i	$-0.869868\pi$
$313$	−24.1489	+	8.78949i	−1.36498	+	0.496811i	−0.447388	+	0.894340i	$0.647646\pi$
$314$	0.261983	−	4.74729i	0.0147845	−	0.267905i
$315$	−0.0106330	+	4.49125i	−0.000599099	+	0.253054i
$316$	1.75005	−	15.8077i	0.0984481	−	0.889253i
$317$	34.2319	+	6.03601i	1.92265	+	0.339016i	0.999020	−	0.0442581i	$-0.0140924\pi$
$317$	34.2319	+	6.03601i	1.92265	+	0.339016i	0.923635	+	0.383274i	$0.125204\pi$
$318$	9.62810	+	15.5446i	0.539917	+	0.871698i
$319$	−1.10873	+	3.04620i	−0.0620767	+	0.170554i
$320$	−11.8308	−	1.86371i	−0.661363	−	0.104185i
$321$	−3.79711	−	14.2384i	−0.211934	−	0.794710i
$322$	−3.51392	+	1.06368i	−0.195823	+	0.0592764i
$323$	5.69045			0.316625
$324$	1.07106	+	17.9681i	0.0595031	+	0.998228i
$325$	−4.71532			−0.261559
$326$	−24.0855	+	7.29079i	−1.33397	+	0.403800i
$327$	−6.48522	−	24.3183i	−0.358634	−	1.34480i
$328$	0.00198602	+	0.217202i	0.000109659	+	0.0119930i
$329$	0.766748	−	2.10662i	0.0422722	−	0.116142i
$330$	0.810411	+	1.30841i	0.0446117	+	0.0720257i
$331$	14.6605	+	2.58505i	0.805816	+	0.142087i	0.561358	−	0.827573i	$-0.310279\pi$
$331$	14.6605	+	2.58505i	0.805816	+	0.142087i	0.244458	+	0.969660i	$0.421390\pi$
$332$	16.7595	+	1.85542i	0.919795	+	0.101829i
$333$	−20.2474	−	11.7538i	−1.10955	−	0.644105i
$334$	−0.749247	+	13.5768i	−0.0409970	+	0.742890i
$335$	−5.34678	+	1.94607i	−0.292126	+	0.106325i
$336$	6.60013	+	2.10671i	0.360067	+	0.114930i
$337$	3.73692	−	3.13564i	0.203563	−	0.170809i	−0.535307	−	0.844657i	$-0.679804\pi$
$337$	3.73692	−	3.13564i	0.203563	−	0.170809i	0.738870	+	0.673848i	$0.235360\pi$
$338$	14.1517	−	1.69783i	0.769750	−	0.0923498i
$339$	−11.4514	−	1.01553i	−0.621955	−	0.0551560i
$340$	−2.87005	−	3.00517i	−0.155650	−	0.162978i
$341$	−1.10239	+	0.636466i	−0.0596978	+	0.0344666i
$342$	5.00042	+	16.6613i	0.270392	+	0.900940i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	−2.00679	+	5.67451i	−0.108199	+	0.305949i
$345$	0.578764	+	6.70674i	0.0311596	+	0.361079i
$346$	−19.8510	+	14.8727i	−1.06719	+	0.799563i
$347$	−3.13986	−	17.8070i	−0.168557	−	0.955932i	−0.945321	−	0.326141i	$-0.894252\pi$
$347$	−3.13986	−	17.8070i	−0.168557	−	0.955932i	0.776764	−	0.629791i	$-0.216860\pi$
$348$	26.4547	−	4.00787i	1.41812	−	0.214844i
$349$	19.2724	+	16.1715i	1.03163	+	0.865638i	0.991044	−	0.133538i	$-0.0426337\pi$
$349$	19.2724	+	16.1715i	1.03163	+	0.865638i	0.0405839	+	0.999176i	$0.487078\pi$
$350$	−2.13392	+	3.26611i	−0.114063	+	0.174581i
$351$	−8.84486	−	0.805485i	−0.472104	−	0.0429936i
$352$	2.30154	−	0.582655i	0.122673	−	0.0310556i
$353$	−10.9581	+	13.0594i	−0.583242	+	0.695080i	−0.974292	−	0.225289i	$-0.927667\pi$
$353$	−10.9581	+	13.0594i	−0.583242	+	0.695080i	0.391050	+	0.920369i	$0.372112\pi$
$354$	9.09180	−	1.89498i	0.483223	−	0.100717i
$355$	−11.9411	+	2.10554i	−0.633769	+	0.111751i
$356$	17.4043	−	1.12017i	0.922427	−	0.0593691i
$357$	1.37646	+	1.97075i	0.0728499	+	0.104303i
$358$	10.4280	−	11.1207i	0.551137	−	0.587749i
$359$	8.35026	−	14.4631i	0.440710	−	0.763332i	−0.557032	−	0.830491i	$-0.688060\pi$
$359$	8.35026	−	14.4631i	0.440710	−	0.763332i	0.997742	+	0.0671586i	$0.0213934\pi$
$360$	6.27692	−	11.0441i	0.330823	−	0.582075i
$361$	−1.09435	−	1.89547i	−0.0575974	−	0.0997616i
$362$	16.0095	+	3.74283i	0.841442	+	0.196719i
$363$	15.3443	+	10.7713i	0.805366	+	0.565345i
$364$	−1.51556	+	3.06416i	−0.0794369	+	0.160605i
$365$	−1.09285	−	1.30241i	−0.0572025	−	0.0681713i
$366$	−10.7970	−	27.0308i	−0.564370	−	1.41292i
$367$	9.53151	+	26.1876i	0.497541	+	1.36698i	0.893644	+	0.448777i	$0.148140\pi$
$367$	9.53151	+	26.1876i	0.497541	+	1.36698i	−0.396103	+	0.918206i	$0.629638\pi$
$368$	10.1328	+	2.27141i	0.528207	+	0.118405i
$369$	−0.216306	−	0.0793094i	−0.0112604	−	0.00412868i
$370$	7.46022	+	14.7423i	0.387839	+	0.766417i
$371$	−1.29624	+	7.35134i	−0.0672974	+	0.381663i
$372$	8.96935	+	5.47174i	0.465039	+	0.283697i
$373$	11.8231	+	4.30326i	0.612178	+	0.222815i	0.629456	−	0.777036i	$-0.283278\pi$
$373$	11.8231	+	4.30326i	0.612178	+	0.222815i	−0.0172781	+	0.999851i	$0.505500\pi$
$374$	0.757369	+	0.323963i	0.0391626	+	0.0167517i
$375$	14.2092	+	14.2429i	0.733759	+	0.735498i
$376$	−4.81989	+	4.12005i	−0.248567	+	0.212475i
$377$			13.2021i			0.679941i
$378$	−4.56068	+	5.76196i	−0.234576	+	0.296363i
$379$		−	34.2066i		−	1.75708i	−0.477673	−	0.878538i	$-0.658520\pi$
$379$		−	34.2066i		−	1.75708i	0.477673	−	0.878538i	$-0.341480\pi$
$380$	3.44922	−	11.7821i	0.176941	−	0.604409i
$381$	2.91639	−	10.8328i	0.149411	−	0.554982i
$382$	8.47642	−	19.8164i	0.433692	−	1.01390i
$383$	−23.6448	−	8.60601i	−1.20819	−	0.439746i	−0.342117	−	0.939658i	$-0.611144\pi$
$383$	−23.6448	−	8.60601i	−1.20819	−	0.439746i	−0.866077	+	0.499911i	$0.833366\pi$
$384$	−13.3196	−	14.3732i	−0.679713	−	0.733478i
$385$	−0.109106	+	0.618774i	−0.00556058	+	0.0315356i
$386$	−22.7269	+	11.5007i	−1.15677	+	0.585373i
$387$	−4.88071	−	4.11513i	−0.248100	−	0.209184i
$388$	−7.40972	+	10.0807i	−0.376171	+	0.511769i
$389$	2.93085	+	8.05245i	0.148600	+	0.408276i	0.991551	−	0.129714i	$-0.0414061\pi$
$389$	2.93085	+	8.05245i	0.148600	+	0.408276i	−0.842951	+	0.537990i	$0.819184\pi$
$390$	4.92392	+	3.87844i	0.249332	+	0.196392i
$391$	2.31594	+	2.76003i	0.117122	+	0.139581i
$392$	1.43655	+	2.43646i	0.0725568	+	0.123060i
$393$	23.3552	−	10.8571i	1.17812	−	0.547667i
$394$	−1.64085	+	7.01853i	−0.0826647	+	0.353589i
$395$	−5.95254	−	10.3101i	−0.299505	−	0.518757i
$396$	−0.283014	+	2.50221i	−0.0142220	+	0.125741i
$397$	11.7528	−	20.3565i	0.589857	−	1.02166i	−0.404394	−	0.914585i	$-0.632517\pi$
$397$	11.7528	−	20.3565i	0.589857	−	1.02166i	0.994251	−	0.107077i	$-0.0341492\pi$
$398$	10.0061	+	9.38276i	0.501559	+	0.470315i
$399$	−3.00892	+	6.43275i	−0.150634	+	0.322040i
$400$	9.80004	−	5.07230i	0.490002	−	0.253615i
$401$	2.02145	−	0.356437i	0.100947	−	0.0177996i	−0.122947	−	0.992413i	$-0.539234\pi$
$401$	2.02145	−	0.356437i	0.100947	−	0.0177996i	0.223893	+	0.974614i	$0.428123\pi$
$402$	−8.84258	−	2.91183i	−0.441028	−	0.145229i
$403$	−3.33229	+	3.97127i	−0.165993	+	0.197823i
$404$	−17.6368	+	7.73561i	−0.877462	+	0.384861i
$405$	8.61182	+	10.3624i	0.427925	+	0.514913i
$406$	9.14455	+	5.97462i	0.453837	+	0.296515i
$407$	−2.50899	−	2.10529i	−0.124366	−	0.104355i
$408$	−0.646474	−	6.76830i	−0.0320052	−	0.335081i
$409$	−4.11968	−	23.3638i	−0.203705	−	1.15527i	−0.899465	−	0.436993i	$-0.856043\pi$
$409$	−4.11968	−	23.3638i	−0.203705	−	1.15527i	0.695760	−	0.718275i	$-0.255068\pi$
$410$	0.0974904	+	0.130122i	0.00481471	+	0.00642629i
$411$	−6.25278	−	2.92473i	−0.308427	−	0.144267i
$412$	−6.79753	−	27.9215i	−0.334890	−	1.37559i
$413$	3.28351	+	1.89574i	0.161571	+	0.0932832i
$414$	−6.04610	+	9.20629i	−0.297150	+	0.452464i
$415$	10.9308	−	6.31092i	0.536574	−	0.309791i
$416$	7.99636	−	5.43564i	0.392054	−	0.266504i
$417$	−6.31008	−	13.5739i	−0.309006	−	0.664718i
$418$	0.289889	+	2.41627i	0.0141789	+	0.118184i
$419$	−26.9927	+	22.6495i	−1.31868	+	1.10650i	−0.332095	+	0.943246i	$0.607755\pi$
$419$	−26.9927	+	22.6495i	−1.31868	+	1.10650i	−0.986584	+	0.163256i	$0.947800\pi$
$420$	4.91477	−	1.65541i	0.239816	−	0.0807758i
$421$	13.3381	−	4.85465i	0.650057	−	0.236601i	0.00411921	−	0.999992i	$-0.498689\pi$
$421$	13.3381	−	4.85465i	0.650057	−	0.236601i	0.645938	+	0.763390i	$0.276467\pi$
$422$	−36.1534	−	1.99516i	−1.75992	−	0.0971227i
$423$	−2.28527	−	6.32529i	−0.111114	−	0.307546i
$424$	13.4230	−	16.2973i	0.651881	−	0.791466i
$425$	3.77056	+	0.664852i	0.182899	+	0.0322500i
$426$	−17.4799	−	9.38308i	−0.846905	−	0.454612i
$427$	4.06424	−	11.1664i	0.196682	−	0.540380i
$428$	−14.1591	+	9.43675i	−0.684408	+	0.456143i
$429$	−1.19978	−	0.323003i	−0.0579259	−	0.0155947i
$430$	1.30532	+	4.31219i	0.0629480	+	0.207952i
$431$	6.70554			0.322995			0.161497	−	0.986873i	$-0.448368\pi$
$431$	6.70554			0.322995			0.161497	+	0.986873i	$0.448368\pi$
$432$	19.2491	−	7.84041i	0.926123	−	0.377222i
$433$	−26.7749			−1.28672			−0.643361	−	0.765563i	$-0.722460\pi$
$433$	−26.7749			−1.28672			−0.643361	+	0.765563i	$0.722460\pi$
$434$	1.24271	+	4.10535i	0.0596518	+	0.197063i
$435$	14.1790	−	14.1455i	0.679832	−	0.678225i
$436$	−24.1829	+	16.1174i	−1.15815	+	0.771883i
$437$	−3.64054	+	10.0023i	−0.174151	+	0.478476i
$438$	−0.0860902	−	2.78044i	−0.00411355	−	0.132855i
$439$	−12.8065	−	2.25813i	−0.611220	−	0.107775i	−0.140535	−	0.990076i	$-0.544882\pi$
$439$	−12.8065	−	2.25813i	−0.611220	−	0.107775i	−0.470685	+	0.882301i	$0.655993\pi$
$440$	1.12984	−	1.37177i	0.0538629	−	0.0653964i
$441$	−2.95565	+	0.513949i	−0.140745	+	0.0244737i
$442$	3.34968	+	0.184855i	0.159328	+	0.00879264i
$443$	33.4990	−	12.1926i	1.59159	−	0.579290i	0.613903	−	0.789381i	$-0.289598\pi$
$443$	33.4990	−	12.1926i	1.59159	−	0.579290i	0.977682	+	0.210091i	$0.0673762\pi$
$444$	−5.33654	+	26.5015i	−0.253261	+	1.25771i
$445$	10.0006	−	8.39150i	0.474074	−	0.397795i
$446$	0.353619	+	2.94747i	0.0167443	+	0.139567i
$447$	19.9554	−	28.4275i	0.943856	−	1.34458i
$448$	−0.146286	−	7.99866i	−0.00691137	−	0.377901i
$449$	4.95460	−	2.86054i	0.233822	−	0.134997i	−0.378512	−	0.925596i	$-0.623564\pi$
$449$	4.95460	−	2.86054i	0.233822	−	0.134997i	0.612334	+	0.790599i	$0.290231\pi$
$450$	1.36669	+	11.6242i	0.0644265	+	0.547970i
$451$	−0.0279126	−	0.0161153i	−0.00131435	−	0.000758842i
$452$	3.14007	+	12.8981i	0.147696	+	0.606676i
$453$	21.9797	−	15.3516i	1.03270	−	0.721281i
$454$	3.05550	+	4.07824i	0.143402	+	0.191401i
$455$	0.444345	+	2.52001i	0.0208312	+	0.118140i
$456$	16.3617	−	11.6518i	0.766209	−	0.545645i
$457$	9.64021	+	8.08910i	0.450950	+	0.378392i	0.839788	−	0.542914i	$-0.182679\pi$
$457$	9.64021	+	8.08910i	0.450950	+	0.378392i	−0.388838	+	0.921306i	$0.627123\pi$
$458$	20.8876	+	13.6470i	0.976014	+	0.637681i
$459$	6.95914	+	1.89121i	0.324825	+	0.0882741i
$460$	7.11844	−	3.12220i	0.331899	−	0.145573i
$461$	−6.61302	+	7.88109i	−0.307999	+	0.367059i	−0.897734	−	0.440538i	$-0.854788\pi$
$461$	−6.61302	+	7.88109i	−0.307999	+	0.367059i	0.589735	+	0.807597i	$0.299232\pi$
$462$	−0.766693	+	0.684864i	−0.0356698	+	0.0318628i
$463$	−7.98464	+	1.40791i	−0.371078	+	0.0654310i	−0.356077	−	0.934456i	$-0.615886\pi$
$463$	−7.98464	+	1.40791i	−0.371078	+	0.0654310i	−0.0150004	+	0.999887i	$0.504775\pi$
$464$	−14.2016	−	27.4384i	−0.659291	−	1.27380i
$465$	7.83555	−	0.676177i	0.363365	−	0.0313570i
$466$	28.7604	+	26.9689i	1.33230	+	1.24931i
$467$	14.7410	−	25.5322i	0.682134	−	1.18149i	−0.292195	−	0.956359i	$-0.594386\pi$
$467$	14.7410	−	25.5322i	0.682134	−	1.18149i	0.974328	−	0.225131i	$-0.0722811\pi$
$468$	2.40225	+	9.97011i	0.111044	+	0.460868i
$469$	−1.90033	−	3.29147i	−0.0877490	−	0.151986i
$470$	−1.08051	+	4.62177i	−0.0498403	+	0.213186i
$471$	0.514380	−	5.80030i	0.0237014	−	0.267264i
$472$	−5.44665	−	9.23777i	−0.250702	−	0.425203i
$473$	−0.574081	−	0.684163i	−0.0263963	−	0.0314578i
$474$	2.78715	−	19.2783i	0.128018	−	0.885480i
$475$	3.86866	+	10.6291i	0.177506	+	0.487695i
$476$	1.64394	−	2.23653i	0.0753501	−	0.102511i
$477$	11.1512	+	19.4204i	0.510577	+	0.889201i
$478$	22.6798	−	11.4769i	1.03735	−	0.524942i
$479$	1.57116	−	8.91048i	0.0717880	−	0.407130i	−0.927645	−	0.373463i	$-0.878170\pi$
$479$	1.57116	−	8.91048i	0.0717880	−	0.407130i	0.999433	−	0.0336672i	$-0.0107186\pi$
$480$	−14.4056	−	2.76402i	−0.657525	−	0.126160i
$481$	−12.5343	−	4.56211i	−0.571515	−	0.208014i
$482$	−4.21925	+	9.86387i	−0.192182	+	0.449287i
$483$	−4.34466	+	1.15864i	−0.197689	+	0.0527199i
$484$	6.08211	−	20.7757i	0.276459	−	0.944352i
$485$			9.36501i			0.425243i
$486$	0.577919	+	22.0378i	0.0262149	+	0.999656i
$487$		−	34.8599i		−	1.57965i	−0.613331	−	0.789826i	$-0.710171\pi$
$487$		−	34.8599i		−	1.57965i	0.613331	−	0.789826i	$-0.289829\pi$
$488$	−25.5484	+	21.8388i	−1.15652	+	0.988596i
$489$	−29.7797	+	7.94168i	−1.34669	+	0.359135i
$490$	1.94660	+	0.832653i	0.0879383	+	0.0376154i
$491$	−7.26051	−	2.64261i	−0.327662	−	0.119259i	0.172951	−	0.984930i	$-0.444670\pi$
$491$	−7.26051	−	2.64261i	−0.327662	−	0.119259i	−0.500613	+	0.865671i	$0.666892\pi$
$492$	−0.00643113	+	0.265950i	−0.000289938	+	0.0119900i
$493$	1.86147	−	10.5569i	0.0838364	−	0.475460i
$494$	4.47503	+	8.84321i	0.201341	+	0.397875i
$495$	0.938611	+	1.63465i	0.0421874	+	0.0734719i
$496$	2.65371	−	11.8382i	0.119155	−	0.531552i
$497$	−2.77012	−	7.61083i	−0.124257	−	0.341392i
$498$	20.4390	+	2.95496i	0.915892	+	0.132415i
$499$	16.6571	+	19.8512i	0.745676	+	0.888661i	0.996852	−	0.0792797i	$-0.0252620\pi$
$499$	16.6571	+	19.8512i	0.745676	+	0.888661i	−0.251177	+	0.967941i	$0.580818\pi$
$500$	10.2993	−	20.8231i	0.460599	−	0.931240i
$501$	−1.47108	+	16.5883i	−0.0657230	+	0.741112i
$502$	−25.3170	−	5.91879i	−1.12995	−	0.264169i
$503$	−14.0325	−	24.3051i	−0.625680	−	1.08371i	−0.988409	−	0.151815i	$-0.951488\pi$
$503$	−14.0325	−	24.3051i	−0.625680	−	1.08371i	0.362728	−	0.931895i	$-0.381845\pi$
$504$	7.99304	+	2.84804i	0.356038	+	0.126862i
$505$	−7.20797	+	12.4846i	−0.320751	+	0.555556i
$506$	−1.05398	+	1.12399i	−0.0468550	+	0.0499677i
$507$	17.3918	−	1.50085i	0.772399	−	0.0666549i
$508$	−12.9273	+	0.832025i	−0.573556	+	0.0369151i
$509$	5.53057	−	0.975189i	0.245138	−	0.0432245i	−0.0497289	−	0.998763i	$-0.515836\pi$
$509$	5.53057	−	0.975189i	0.245138	−	0.0432245i	0.294867	+	0.955538i	$0.404725\pi$
$510$	−3.39052	−	3.79562i	−0.150135	−	0.168073i
$511$	0.729985	−	0.869962i	0.0322926	−	0.0384849i
$512$	−10.7720	+	19.8988i	−0.476060	+	0.879413i
$513$	5.44104	+	20.5985i	0.240228	+	0.909448i
$514$	−15.4267	+	23.6116i	−0.680444	+	1.04146i
$515$	−16.4783	−	13.8269i	−0.726121	−	0.609288i
$516$	−2.68797	+	6.86409i	−0.118331	+	0.302175i
$517$	−0.163382	−	0.926584i	−0.00718552	−	0.0407511i
$518$	−8.83241	+	6.61742i	−0.388074	+	0.290753i
$519$	−24.9057	+	17.3953i	−1.09324	+	0.763567i
$520$	2.41312	−	6.82348i	0.105822	−	0.299229i
$521$	26.1150	+	15.0775i	1.14412	+	0.660557i	0.947447	−	0.319912i	$-0.103653\pi$
$521$	26.1150	+	15.0775i	1.14412	+	0.660557i	0.196672	+	0.980469i	$0.436987\pi$
$522$	32.5458	−	3.82650i	1.42449	−	0.167481i
$523$	3.42303	−	1.97629i	0.149679	−	0.0864171i	−0.423290	−	0.905994i	$-0.639125\pi$
$523$	3.42303	−	1.97629i	0.149679	−	0.0864171i	0.572969	+	0.819577i	$0.305792\pi$
$524$	−20.5402	−	21.5072i	−0.897302	−	0.939545i
$525$	−2.74532	+	3.91087i	−0.119816	+	0.170684i
$526$	2.42225	−	0.290607i	0.105615	−	0.0126711i
$527$	3.22458	−	2.70574i	0.140465	−	0.117864i
$528$	2.84101	−	0.619302i	0.123639	−	0.0269517i
$529$	15.2799	−	5.56142i	0.664342	−	0.241801i
$530$	0.870852	−	15.7804i	0.0378274	−	0.685456i
$531$	11.2063	−	1.94862i	0.486311	−	0.0845630i
$532$	8.15052	+	0.902333i	0.353370	+	0.0391211i
$533$	−0.129268	−	0.0227934i	−0.00559922	−	0.000987293i
$534$	21.3497	−	0.661046i	0.923892	−	0.0286063i
$535$	−4.35631	+	11.9689i	−0.188340	+	0.517459i
$536$	0.0982890	+	10.7494i	0.00424544	+	0.464305i
$537$	13.2183	−	13.1870i	0.570411	−	0.569062i
$538$	−19.2224	+	5.81871i	−0.828737	+	0.250862i
$539$	−0.419694			−0.0180775
$540$	8.13397	−	13.2626i	0.350031	−	0.570731i
$541$	−33.7362			−1.45043			−0.725217	−	0.688520i	$-0.758261\pi$
$541$	−33.7362			−1.45043			−0.725217	+	0.688520i	$0.758261\pi$
$542$	−38.9413	+	11.7877i	−1.67267	+	0.506326i
$543$	19.4440	+	5.23468i	0.834421	+	0.224642i
$544$	−7.16063	+	3.21908i	−0.307009	+	0.138017i
$545$	−7.44030	+	20.4421i	−0.318708	+	0.875642i
$546$	−1.98017	+	3.68889i	−0.0847433	+	0.157870i
$547$	28.2799	+	4.98651i	1.20916	+	0.213208i	0.741654	−	0.670782i	$-0.234042\pi$
$547$	28.2799	+	4.98651i	1.20916	+	0.213208i	0.467506	+	0.883990i	$0.345153\pi$
$548$	−0.877088	+	7.92249i	−0.0374674	+	0.338432i
$549$	−12.1134	−	33.5280i	−0.516986	−	1.43094i
$550$	−0.0902241	+	1.63492i	−0.00384717	+	0.0697131i
$551$	29.7595	−	10.8316i	1.26780	−	0.461441i
$552$	12.3105	+	3.19378i	0.523969	+	0.135936i
$553$	6.09170	−	5.11154i	0.259045	−	0.217365i
$554$	−2.39298	+	0.287095i	−0.101668	+	0.0121975i
$555$	8.53029	+	18.3500i	0.362091	+	0.778912i
$556$	−12.4998	+	11.9378i	−0.530112	+	0.506277i
$557$	−22.9604	+	13.2562i	−0.972863	+	0.561683i	−0.900108	−	0.435667i	$-0.856512\pi$
$557$	−22.9604	+	13.2562i	−0.972863	+	0.561683i	−0.0727551	+	0.997350i	$0.523179\pi$
$558$	10.7558	+	7.06373i	0.455330	+	0.299032i
$559$	−3.14997	−	1.81863i	−0.133229	−	0.0769200i
$560$	−3.63429	−	4.75945i	−0.153577	−	0.201123i
$561$	0.913850	+	0.427453i	0.0385828	+	0.0180471i
$562$	−19.4893	+	14.6018i	−0.822107	+	0.615939i
$563$	−4.59859	−	26.0799i	−0.193807	−	1.09914i	−0.914107	−	0.405473i	$-0.867107\pi$
$563$	−4.59859	−	26.0799i	−0.193807	−	1.09914i	0.720300	−	0.693663i	$-0.244004\pi$
$564$	−6.06796	+	4.84655i	−0.255507	+	0.204076i
$565$	7.61204	+	6.38726i	0.320241	+	0.268714i
$566$	5.88838	−	9.01256i	0.247507	−	0.378826i
$567$	−5.81767	+	6.86693i	−0.244319	+	0.288384i
$568$	−3.77153	+	22.5956i	−0.158250	+	0.948091i
$569$	−8.17379	+	9.74114i	−0.342663	+	0.408370i	−0.909662	−	0.415348i	$-0.863660\pi$
$569$	−8.17379	+	9.74114i	−0.342663	+	0.408370i	0.566999	+	0.823718i	$0.308104\pi$
$570$	4.70279	−	14.2813i	0.196978	−	0.598179i
$571$	−3.72670	+	0.657118i	−0.155958	+	0.0274995i	−0.251082	−	0.967966i	$-0.580786\pi$
$571$	−3.72670	+	0.657118i	−0.155958	+	0.0274995i	0.0951242	+	0.995465i	$0.469675\pi$
$572$	0.0921502	+	1.43175i	0.00385299	+	0.0598645i
$573$	11.1842	−	23.9107i	0.467228	−	0.998885i
$574$	−0.0742885	+	0.0792236i	−0.00310074	+	0.00330673i
$575$	−3.58090	+	6.20230i	−0.149334	+	0.258654i
$576$	−15.7176	−	18.1372i	−0.654901	−	0.755715i
$577$	−9.12824	−	15.8106i	−0.380014	−	0.658203i	0.611050	−	0.791592i	$-0.290747\pi$
$577$	−9.12824	−	15.8106i	−0.380014	−	0.658203i	−0.991064	+	0.133389i	$0.957414\pi$
$578$	20.7579	+	4.85294i	0.863415	+	0.201856i
$579$	−28.2884	+	13.1504i	−1.17563	+	0.546511i
$580$	−20.7298	−	10.2532i	−0.860759	−	0.425739i
$581$	5.41929	+	6.45846i	0.224830	+	0.267942i
$582$	−9.48128	+	12.0371i	−0.393012	+	0.498953i
$583$	1.07152	+	2.94397i	0.0443777	+	0.121927i
$584$	−3.00823	+	1.12616i	−0.124482	+	0.0466009i
$585$	5.86895	+	4.94836i	0.242651	+	0.204590i
$586$	16.0087	+	31.6351i	0.661313	+	1.30684i
$587$	−6.45620	+	36.6149i	−0.266476	+	1.51126i	0.498323	+	0.866991i	$0.333949\pi$
$587$	−6.45620	+	36.6149i	−0.266476	+	1.51126i	−0.764799	+	0.644269i	$0.777162\pi$
$588$	1.65902	+	3.04099i	0.0684169	+	0.125409i
$589$	11.6858	+	4.25329i	0.481506	+	0.175254i
$590$	−7.38048	−	3.15698i	−0.303849	−	0.129971i
$591$	−2.29487	+	8.52419i	−0.0943983	+	0.350639i
$592$	30.9580	−	4.00161i	1.27237	−	0.164465i
$593$		−	10.8240i		−	0.444488i	−0.974991	−	0.222244i	$-0.928662\pi$
$593$		−	10.8240i		−	0.444488i	0.974991	−	0.222244i	$-0.0713382\pi$
$594$	−0.448522	+	3.05132i	−0.0184031	+	0.125197i
$595$		−	2.07775i		−	0.0851795i
$596$	−38.4901	−	11.2680i	−1.57662	−	0.461555i
$597$	11.8652	+	11.8934i	0.485612	+	0.486763i
$598$	−2.46793	+	5.76959i	−0.100921	+	0.235936i
$599$	−32.9706	−	12.0003i	−1.34714	−	0.490320i	−0.435088	−	0.900388i	$-0.643283\pi$
$599$	−32.9706	−	12.0003i	−1.34714	−	0.490320i	−0.912055	+	0.410068i	$0.865505\pi$
$600$	12.2028	−	5.80897i	0.498179	−	0.237150i
$601$	−4.47792	+	25.3955i	−0.182658	+	1.03591i	0.746269	+	0.665644i	$0.231843\pi$
$601$	−4.47792	+	25.3955i	−0.182658	+	1.03591i	−0.928928	+	0.370262i	$0.879268\pi$
$602$	−2.68522	+	1.35883i	−0.109441	+	0.0553818i
$603$	−10.7051	−	3.92506i	−0.435945	−	0.159841i
$604$	−24.9440	−	18.3349i	−1.01496	−	0.746035i
$605$	−5.54219	−	15.2270i	−0.225322	−	0.619067i
$606$	−21.9042	+	8.74928i	−0.889796	+	0.355415i
$607$	24.7555	+	29.5024i	1.00479	+	1.19747i	0.980249	+	0.197767i	$0.0633691\pi$
$607$	24.7555	+	29.5024i	1.00479	+	1.19747i	0.0245445	+	0.999699i	$0.492186\pi$
$608$	−18.8133	−	13.5654i	−0.762982	−	0.550149i
$609$	10.9498	+	7.68643i	0.443706	+	0.311470i
$610$	−5.72738	+	24.4982i	−0.231895	+	0.991904i
$611$	−1.91590	−	3.31844i	−0.0775091	−	0.134250i
$612$	−0.515171	−	8.31122i	−0.0208245	−	0.335961i
$613$	0.165105	−	0.285970i	0.00666851	−	0.0115502i	−0.862672	−	0.505764i	$-0.831211\pi$
$613$	0.165105	−	0.285970i	0.00666851	−	0.0115502i	0.869340	+	0.494214i	$0.164544\pi$
$614$	−22.6019	−	21.1940i	−0.912140	−	0.855321i
$615$	0.114025	+	0.163256i	0.00459795	+	0.00658312i
$616$	1.03342	+	0.584112i	0.0416377	+	0.0235346i
$617$	−14.8654	+	2.62117i	−0.598457	+	0.105524i	−0.464667	−	0.885485i	$-0.653826\pi$
$617$	−14.8654	+	2.62117i	−0.598457	+	0.105524i	−0.133790	+	0.991010i	$0.542715\pi$
$618$	−7.18138	−	34.4550i	−0.288878	−	1.38598i
$619$	−21.8857	+	26.0823i	−0.879659	+	1.04834i	0.118804	+	0.992918i	$0.462094\pi$
$619$	−21.8857	+	26.0823i	−0.879659	+	1.04834i	−0.998463	+	0.0554195i	$0.982350\pi$
$620$	−3.64770	−	8.31656i	−0.146495	−	0.334001i
$621$	−7.77645	+	11.0224i	−0.312058	+	0.442314i
$622$	4.38924	+	2.86772i	0.175992	+	0.114985i
$623$	6.68003	+	5.60521i	0.267630	+	0.224568i
$624$	10.0098	−	6.32731i	0.400714	−	0.253295i
$625$	−0.624407	−	3.54119i	−0.0249763	−	0.141648i
$626$	21.7916	+	29.0857i	0.870967	+	1.16250i
$627$	0.256256	+	2.96950i	0.0102339	+	0.118590i
$628$	−6.53308	+	1.59049i	−0.260698	+	0.0634674i
$629$	9.37969	+	5.41537i	0.373993	+	0.215925i
$630$	6.08354	−	1.82580i	0.242374	−	0.0727417i
$631$	−28.5466	+	16.4814i	−1.13642	+	0.656114i	−0.945542	−	0.325499i	$-0.894468\pi$
$631$	−28.5466	+	16.4814i	−1.13642	+	0.656114i	−0.190881	+	0.981613i	$0.561134\pi$
$632$	−22.1137	+	4.10807i	−0.879637	+	0.163410i
$633$	−44.1728	−	3.91731i	−1.75571	−	0.155699i
$634$	−5.85568	−	48.8080i	−0.232559	−	1.93841i
$635$	−7.42809	+	6.23290i	−0.294775	+	0.247345i
$636$	17.0956	−	19.4013i	0.677886	−	0.769310i
$637$	−1.60616	+	0.584594i	−0.0636383	+	0.0231625i
$638$	4.57749	+	0.252612i	0.181224	+	0.0100010i
$639$	−21.0137	−	12.1987i	−0.831290	−	0.482573i
$640$	2.32478	+	16.7773i	0.0918949	+	0.663182i
$641$	20.5795	+	3.62873i	0.812843	+	0.143326i	0.564593	−	0.825370i	$-0.309033\pi$
$641$	20.5795	+	3.62873i	0.812843	+	0.143326i	0.248250	+	0.968696i	$0.420144\pi$
$642$	−17.7167	+	10.9735i	−0.699224	+	0.433089i
$643$	−10.2697	+	28.2159i	−0.404999	+	1.11272i	0.554787	+	0.831992i	$0.312800\pi$
$643$	−10.2697	+	28.2159i	−0.404999	+	1.11272i	−0.959786	+	0.280733i	$0.909423\pi$
$644$	2.87950	+	4.32047i	0.113468	+	0.170251i
$645$	1.42185	+	5.33166i	0.0559853	+	0.209934i
$646$	−2.33154	−	7.70236i	−0.0917332	−	0.303045i
$647$	44.4202			1.74634			0.873169	−	0.487418i	$-0.162061\pi$
$647$	44.4202			1.74634			0.873169	+	0.487418i	$0.162061\pi$
$648$	23.8821	−	8.81178i	0.938176	−	0.346159i
$649$	1.59126			0.0624624
$650$	1.93200	+	6.38246i	0.0757792	+	0.250341i
$651$	1.35365	+	5.07592i	0.0530537	+	0.198941i
$652$	19.7370	+	29.6139i	0.772962	+	1.15977i
$653$	8.89730	−	24.4451i	0.348178	−	0.956612i	−0.634765	−	0.772705i	$-0.718903\pi$
$653$	8.89730	−	24.4451i	0.348178	−	0.956612i	0.982944	−	0.183907i	$-0.0588746\pi$
$654$	−30.2591	+	18.7420i	−1.18322	+	0.732871i
$655$	−21.9234	−	3.86568i	−0.856617	−	0.151045i
$656$	0.293182	−	0.0916820i	0.0114468	−	0.00357958i
$657$	0.00806590	−	3.40696i	0.000314681	−	0.132918i
$658$	−3.16560	−	0.174696i	−0.123408	−	0.00681035i
$659$	−38.2340	+	13.9160i	−1.48938	+	0.542092i	−0.953287	−	0.302065i	$-0.902324\pi$
$659$	−38.2340	+	13.9160i	−1.48938	+	0.542092i	−0.536097	+	0.844156i	$0.680102\pi$
$660$	1.43897	−	1.63303i	0.0560116	−	0.0635657i
$661$	10.8086	−	9.06947i	0.420405	−	0.352761i	−0.407912	−	0.913021i	$-0.633743\pi$
$661$	10.8086	−	9.06947i	0.420405	−	0.352761i	0.828317	+	0.560260i	$0.189299\pi$
$662$	−2.50782	−	20.9031i	−0.0974693	−	0.812421i
$663$	4.09268	+	0.362946i	0.158947	+	0.0140956i
$664$	−4.35541	−	23.4451i	−0.169023	−	0.909848i
$665$	5.31593	−	3.06915i	0.206143	−	0.119017i
$666$	−7.61357	+	32.2219i	−0.295020	+	1.24857i
$667$	17.3654	+	10.0259i	0.672390	+	0.388205i
$668$	18.6840	−	4.54866i	0.722906	−	0.175993i
$669$	0.312592	+	3.62232i	0.0120855	+	0.140047i
$670$	4.82484	+	6.43982i	0.186400	+	0.248792i
$671$	−0.866025	−	4.91147i	−0.0334325	−	0.189605i
$672$	0.147293	−	9.79685i	0.00568195	−	0.377922i
$673$	−5.18952	−	4.35453i	−0.200041	−	0.167855i	0.537264	−	0.843414i	$-0.319458\pi$
$673$	−5.18952	−	4.35453i	−0.200041	−	0.167855i	−0.737306	+	0.675559i	$0.763902\pi$
$674$	−5.77540	−	3.77337i	−0.222460	−	0.145345i
$675$	1.19864	+	14.2846i	0.0461355	+	0.549813i
$676$	−8.09646	−	18.4595i	−0.311402	−	0.709980i
$677$	8.47196	−	10.0965i	0.325604	−	0.388040i	−0.578265	−	0.815849i	$-0.696270\pi$
$677$	8.47196	−	10.0965i	0.325604	−	0.388040i	0.903869	+	0.427809i	$0.140715\pi$
$678$	3.31739	+	15.9163i	0.127404	+	0.611260i
$679$	−6.16045	+	1.08625i	−0.236416	+	0.0416866i
$680$	−2.89173	+	5.11609i	−0.110893	+	0.196193i
$681$	3.57373	+	5.11670i	0.136946	+	0.196072i
$682$	1.31318	+	1.23137i	0.0502841	+	0.0471518i
$683$	−15.0679	+	26.0984i	−0.576559	+	0.998629i	0.419312	+	0.907842i	$0.362271\pi$
$683$	−15.0679	+	26.0984i	−0.576559	+	0.998629i	−0.995870	+	0.0907864i	$0.971062\pi$
$684$	20.5033	−	13.5950i	0.783961	−	0.519817i
$685$	2.98328	+	5.16720i	0.113985	+	0.197428i
$686$	−0.321945	+	1.37708i	−0.0122919	+	0.0525772i
$687$	25.0110	+	17.5570i	0.954228	+	0.669842i
$688$	8.50302	+	0.391300i	0.324175	+	0.0149182i
$689$	8.20135	+	9.77399i	0.312446	+	0.372359i
$690$	8.84083	−	3.53133i	0.336565	−	0.134435i
$691$	−1.83215	−	5.03378i	−0.0696982	−	0.191494i	0.899953	−	0.435987i	$-0.143601\pi$
$691$	−1.83215	−	5.03378i	−0.0696982	−	0.191494i	−0.969651	+	0.244493i	$0.921378\pi$
$692$	28.2646	+	20.7757i	1.07446	+	0.789772i
$693$	−0.966426	+	0.807036i	−0.0367115	+	0.0306568i
$694$	−22.8164	+	11.5460i	−0.866099	+	0.438282i
$695$	−2.24671	+	12.7418i	−0.0852227	+	0.483322i
$696$	−16.2641	−	34.1659i	−0.616490	−	1.29505i
$697$	0.100154	+	0.0364531i	0.00379361	+	0.00138076i
$698$	13.9926	−	32.7122i	0.529627	−	1.23818i
$699$	34.1043	+	34.1851i	1.28994	+	1.29300i
$700$	5.29521	+	1.55017i	0.200140	+	0.0585911i
$701$			7.04437i			0.266062i	0.991112	+	0.133031i	$0.0424710\pi$
$701$			7.04437i			0.266062i	−0.991112	+	0.133031i	$0.957529\pi$
$702$	2.53372	+	12.3021i	0.0956290	+	0.464312i
$703$			31.9972i			1.20680i
$704$	−1.73166	−	2.87654i	−0.0652646	−	0.108414i
$705$	−1.51119	+	5.61326i	−0.0569148	+	0.211407i
$706$	22.1665	+	9.48166i	0.834247	+	0.356847i
$707$	−9.04860	−	3.29342i	−0.340308	−	0.123862i
$708$	−6.29014	−	11.5299i	−0.236398	−	0.433319i
$709$	7.12587	−	40.4128i	0.267618	−	1.51774i	−0.493858	−	0.869543i	$-0.664414\pi$
$709$	7.12587	−	40.4128i	0.267618	−	1.51774i	0.761476	−	0.648193i	$-0.224475\pi$
$710$	7.74260	+	15.3003i	0.290574	+	0.574211i
$711$	4.19824	−	23.4841i	0.157446	−	0.880724i
$712$	−8.64726	−	23.0988i	−0.324070	−	0.865664i
$713$	2.69301	+	7.39899i	0.100854	+	0.277094i
$714$	2.10355	−	2.67059i	0.0787233	−	0.0999442i
$715$	0.690320	+	0.822691i	0.0258165	+	0.0307669i
$716$	−19.3252	−	9.55843i	−0.722218	−	0.357215i
$717$	28.2298	−	13.1231i	1.05426	−	0.490092i
$718$	−22.9980	−	5.37664i	−0.858277	−	0.200655i
$719$	17.6776	+	30.6185i	0.659263	+	1.14188i	0.980807	+	0.194982i	$0.0624650\pi$
$719$	17.6776	+	30.6185i	0.659263	+	1.14188i	−0.321544	+	0.946895i	$0.604202\pi$
$720$	−17.5207	−	3.97111i	−0.652957	−	0.147994i
$721$	7.18425	−	12.4435i	0.267555	−	0.463419i
$722$	−2.11725	+	2.25790i	−0.0787957	+	0.0840302i
$723$	−5.56710	+	11.9019i	−0.207043	+	0.442635i
$724$	−1.49341	−	23.2034i	−0.0555023	−	0.862347i
$725$	20.9845	−	3.70014i	0.779346	−	0.137420i
$726$	8.29257	−	25.1827i	0.307766	−	0.934618i
$727$	−24.1980	+	28.8381i	−0.897454	+	1.06954i	0.0997642	+	0.995011i	$0.468191\pi$
$727$	−24.1980	+	28.8381i	−0.897454	+	1.06954i	−0.997219	+	0.0745333i	$0.976253\pi$
$728$	4.76849	+	0.795928i	0.176732	+	0.0294991i
$729$	−0.191764	+	26.9993i	−0.00710237	+	0.999975i
$730$	−1.31512	+	2.01288i	−0.0486747	+	0.0744999i
$731$	2.26242	+	1.89839i	0.0836785	+	0.0702146i
$732$	−32.1639	+	25.6897i	−1.18881	+	0.949518i
$733$	−7.60443	−	43.1269i	−0.280876	−	1.59293i	−0.719654	−	0.694333i	$-0.755700\pi$
$733$	−7.60443	−	43.1269i	−0.280876	−	1.59293i	0.438778	−	0.898595i	$-0.355411\pi$
$734$	31.5412	−	23.6313i	1.16421	−	0.872246i
$735$	2.34879	+	1.09864i	0.0866364	+	0.0405241i
$736$	−1.07719	−	14.6460i	−0.0397058	−	0.539857i
$737$	−1.38141	−	0.797556i	−0.0508848	−	0.0293784i
$738$	−0.0187233	+	0.325278i	−0.000689213	+	0.0119737i
$739$	−13.7563	+	7.94220i	−0.506034	+	0.292159i	−0.731202	−	0.682161i	$-0.761040\pi$
$739$	−13.7563	+	7.94220i	−0.506034	+	0.292159i	0.225168	+	0.974320i	$0.427707\pi$
$740$	16.8979	−	16.1382i	0.621181	−	0.593252i
$741$	5.11691	+	11.0073i	0.187974	+	0.404361i
$742$	10.4816	−	1.25752i	0.384791	−	0.0461648i
$743$	12.9852	−	10.8959i	0.476381	−	0.399731i	−0.372734	−	0.927938i	$-0.621580\pi$
$743$	12.9852	−	10.8959i	0.476381	−	0.399731i	0.849116	+	0.528207i	$0.177135\pi$
$744$	3.73133	−	14.3825i	0.136797	−	0.527287i
$745$	−28.2103	+	10.2677i	−1.03355	+	0.376180i
$746$	0.980456	−	17.7665i	0.0358970	−	0.650476i
$747$	24.8981	+	4.45100i	0.910972	+	0.162854i
$748$	0.128187	−	1.15788i	0.00468699	−	0.0423363i
$749$	−8.37859	−	1.47737i	−0.306147	−	0.0539820i
$750$	13.4566	−	25.0687i	0.491367	−	0.915378i
$751$	5.05737	−	13.8950i	0.184546	−	0.507036i	−0.812575	−	0.582856i	$-0.801935\pi$
$751$	5.05737	−	13.8950i	0.184546	−	0.507036i	0.997122	+	0.0758197i	$0.0241573\pi$
$752$	7.55157	+	4.83590i	0.275377	+	0.176347i
$753$	−30.7481	−	8.27795i	−1.12052	−	0.301665i
$754$	17.8698	−	5.40926i	0.650779	−	0.196994i
$755$	−23.1731			−0.843356
$756$	9.66779	+	3.81232i	0.351614	+	0.138653i
$757$	−15.8482			−0.576013			−0.288006	−	0.957628i	$-0.592992\pi$
$757$	−15.8482			−0.576013			−0.288006	+	0.957628i	$0.592992\pi$
$758$	−46.3007	+	14.0154i	−1.68172	+	0.509063i
$759$	−1.33600	+	1.33284i	−0.0484937	+	0.0483790i
$760$	−17.3610	+	0.158743i	−0.629750	+	0.00575821i
$761$	−13.1918	+	36.2441i	−0.478201	+	1.31385i	0.432817	+	0.901482i	$0.357520\pi$
$761$	−13.1918	+	36.2441i	−0.478201	+	1.31385i	−0.911018	+	0.412366i	$0.864703\pi$
$762$	−15.8578	+	0.491001i	−0.574467	+	0.0177871i
$763$	−14.3101	−	2.52326i	−0.518060	−	0.0913480i
$764$	−30.2957	−	3.35400i	−1.09606	−	0.121343i
$765$	−3.99534	−	4.78442i	−0.144452	−	0.172981i
$766$	−1.96079	+	35.5308i	−0.0708463	+	1.28378i
$767$	6.08971	−	2.21647i	0.219887	−	0.0800322i
$768$	−13.9975	+	23.9180i	−0.505092	+	0.863065i
$769$	35.7354	−	29.9856i	1.28865	−	1.08131i	0.296664	−	0.954982i	$-0.404126\pi$
$769$	35.7354	−	29.9856i	1.28865	−	1.08131i	0.991989	−	0.126326i	$-0.0403186\pi$
$770$	0.882251	−	0.105847i	0.0317941	−	0.00381446i
$771$	−19.8467	+	28.2727i	−0.714762	+	1.01822i
$772$	24.8788	+	26.0500i	0.895408	+	0.937561i
$773$	23.5978	−	13.6242i	0.848752	−	0.490027i	−0.0114775	−	0.999934i	$-0.503653\pi$
$773$	23.5978	−	13.6242i	0.848752	−	0.490027i	0.860230	+	0.509907i	$0.170320\pi$
$774$	−3.57031	+	8.29242i	−0.128332	+	0.298065i
$775$	7.24622	+	4.18361i	0.260292	+	0.150280i
$776$	16.6808	+	5.89915i	0.598805	+	0.211767i
$777$	−11.0814	+	7.73978i	−0.397544	+	0.277663i
$778$	9.69862	−	7.26640i	0.347712	−	0.260513i
$779$	0.0546774	+	0.310091i	0.00195902	+	0.0111102i
$780$	3.23222	−	8.25392i	0.115732	−	0.295538i
$781$	−2.60395	−	2.18497i	−0.0931767	−	0.0781846i
$782$	2.78696	−	4.26563i	0.0996615	−	0.152539i
$783$	39.9943	−	3.35597i	1.42928	−	0.119933i
$784$	2.70929	−	2.94274i	0.0967605	−	0.105098i
$785$	−3.23524	+	3.85560i	−0.115471	+	0.137612i
$786$	−24.2650	−	27.1642i	−0.865504	−	0.968916i
$787$	19.9240	−	3.51315i	0.710215	−	0.125230i	0.193142	−	0.981171i	$-0.438132\pi$
$787$	19.9240	−	3.51315i	0.710215	−	0.125230i	0.517074	+	0.855941i	$0.327021\pi$
$788$	10.1723	−	0.654709i	0.362373	−	0.0233230i
$789$	2.97685	−	0.256890i	0.105979	−	0.00914554i
$790$	−11.5164	+	12.2814i	−0.409735	+	0.436954i
$791$	−3.31871	+	5.74818i	−0.118000	+	0.204382i
$792$	3.50285	−	0.642149i	0.124468	−	0.0228178i
$793$	−10.1555	−	17.5898i	−0.360631	−	0.624632i
$794$	−32.3692	−	7.56751i	−1.14874	−	0.268561i
$795$	1.70984	−	19.2807i	0.0606418	−	0.683815i
$796$	8.60035	−	17.3882i	0.304831	−	0.616308i
$797$	−7.98897	−	9.52089i	−0.282984	−	0.337247i	0.605763	−	0.795645i	$-0.292868\pi$
$797$	−7.98897	−	9.52089i	−0.282984	−	0.337247i	−0.888747	+	0.458398i	$0.848423\pi$
$798$	9.93995	+	1.43707i	0.351870	+	0.0508716i
$799$	1.06414	+	2.92370i	0.0376466	+	0.103433i
$800$	−10.8810	−	11.1867i	−0.384702	−	0.395508i
$801$	26.1604	+	0.0619343i	0.924333	+	0.00218834i
$802$	−1.31071	−	2.59012i	−0.0462826	−	0.0914602i
$803$	0.0827655	−	0.469386i	0.00292073	−	0.0165643i
$804$	−0.318280	+	13.1620i	−0.0112249	+	0.464189i
$805$	3.65214	+	1.32927i	0.128721	+	0.0468506i
$806$	6.74068	+	2.88331i	0.237430	+	0.101560i
$807$	−23.7669	+	6.33817i	−0.836634	+	0.223114i
$808$	17.6969	+	20.7029i	0.622574	+	0.728326i
$809$		−	10.9139i		−	0.383713i	−0.981423	−	0.191857i	$-0.938549\pi$
$809$		−	10.9139i		−	0.383713i	0.981423	−	0.191857i	$-0.0614509\pi$
$810$	10.4976	−	15.9024i	0.368850	−	0.558753i
$811$			11.8843i			0.417314i	0.977989	+	0.208657i	$0.0669093\pi$
$811$			11.8843i			0.417314i	−0.977989	+	0.208657i	$0.933091\pi$
$812$	4.34022	−	14.8257i	0.152312	−	0.520279i
$813$	−48.1477	+	12.8401i	−1.68861	+	0.450321i
$814$	−1.82163	+	4.25866i	−0.0638481	+	0.149266i
$815$	25.0330	+	9.11125i	0.876866	+	0.319153i
$816$	−8.89642	+	3.64821i	−0.311437	+	0.127713i
$817$	−1.51511	+	8.59260i	−0.0530069	+	0.300617i
$818$	−29.9364	+	15.1491i	−1.04670	+	0.529674i
$819$	−2.57436	+	4.43465i	−0.0899555	+	0.154959i
$820$	0.136184	−	0.185274i	0.00475575	−	0.00647004i
$821$	8.33221	+	22.8926i	0.290796	+	0.798956i	0.995951	+	0.0899020i	$0.0286554\pi$
$821$	8.33221	+	22.8926i	0.290796	+	0.798956i	−0.705155	+	0.709054i	$0.749122\pi$
$822$	−1.39686	+	9.66185i	−0.0487211	+	0.336996i
$823$	4.00746	+	4.77590i	0.139691	+	0.166477i	0.831354	−	0.555743i	$-0.187566\pi$
$823$	4.00746	+	4.77590i	0.139691	+	0.166477i	−0.691663	+	0.722220i	$0.743122\pi$
$824$	−35.0082	+	20.6411i	−1.21957	+	0.719066i
$825$	−0.177147	+	1.99756i	−0.00616747	+	0.0695462i
$826$	1.22064	−	5.22117i	0.0424717	−	0.181668i
$827$	5.56715	+	9.64259i	0.193589	+	0.335306i	0.946437	−	0.322888i	$-0.104654\pi$
$827$	5.56715	+	9.64259i	0.193589	+	0.335306i	−0.752848	+	0.658194i	$0.771321\pi$
$828$	14.9385	+	4.41168i	0.519149	+	0.153317i
$829$	2.05923	−	3.56668i	0.0715198	−	0.123876i	−0.828048	−	0.560658i	$-0.810548\pi$
$829$	2.05923	−	3.56668i	0.0715198	−	0.123876i	0.899568	+	0.436782i	$0.143882\pi$
$830$	−13.0209	−	12.2098i	−0.451961	−	0.423808i
$831$	−2.94088	+	0.253786i	−0.102018	+	0.00880375i
$832$	−10.6338	−	8.59641i	−0.368660	−	0.298027i
$833$	1.36678	−	0.241000i	0.0473560	−	0.00835014i
$834$	−15.7877	+	14.1027i	−0.546684	+	0.488336i
$835$	9.25248	−	11.0267i	0.320195	−	0.381594i
$836$	3.15179	−	1.38239i	0.109007	−	0.0478111i
$837$	12.8776	+	9.08532i	0.445115	+	0.314034i
$838$	41.7172	+	27.2560i	1.44110	+	0.941544i
$839$	−1.24668	−	1.04609i	−0.0430401	−	0.0361150i	0.621014	−	0.783800i	$-0.286721\pi$
$839$	−1.24668	−	1.04609i	−0.0430401	−	0.0361150i	−0.664054	+	0.747685i	$0.731166\pi$
$840$	−4.25442	−	5.97416i	−0.146791	−	0.206128i
$841$	−5.32396	−	30.1937i	−0.183585	−	1.04116i
$842$	−12.0360	−	16.0648i	−0.414789	−	0.553628i
$843$	−24.4520	+	17.0784i	−0.842171	+	0.588210i
$844$	12.1125	+	49.7533i	0.416930	+	1.71258i
$845$	−13.0670	−	7.54421i	−0.449517	−	0.259529i
$846$	−7.62532	+	5.68491i	−0.262164	+	0.195451i
$847$	9.37374	−	5.41193i	0.322085	−	0.185956i
$848$	−27.5591	−	11.4914i	−0.946385	−	0.394617i
$849$	7.57549	−	10.7917i	0.259990	−	0.370370i
$850$	−0.644989	−	5.37609i	−0.0221230	−	0.184398i
$851$	−15.5196	+	13.0225i	−0.532004	+	0.446404i
$852$	−5.53853	+	27.5046i	−0.189747	+	0.942293i
$853$	26.2309	−	9.54728i	0.898130	−	0.326893i	0.148627	−	0.988893i	$-0.452515\pi$
$853$	26.2309	−	9.54728i	0.898130	−	0.326893i	0.749503	+	0.662001i	$0.230292\pi$
$854$	−16.7796	−	0.925996i	−0.574187	−	0.0316869i
$855$	6.33922	−	17.2894i	0.216797	−	0.591285i
$856$	18.5746	+	15.2987i	0.634867	+	0.522900i
$857$	−12.5693	−	2.21630i	−0.429358	−	0.0757073i	−0.0452067	−	0.998978i	$-0.514395\pi$
$857$	−12.5693	−	2.21630i	−0.429358	−	0.0757073i	−0.384151	+	0.923270i	$0.625506\pi$
$858$	0.0543804	+	1.75632i	0.00185652	+	0.0599597i
$859$	7.07078	−	19.4268i	0.241252	−	0.662834i	−0.758683	−	0.651460i	$-0.774157\pi$
$859$	7.07078	−	19.4268i	0.241252	−	0.662834i	0.999935	−	0.0113747i	$-0.00362077\pi$
$860$	5.30197	−	3.53365i	0.180796	−	0.120496i
$861$	−0.0941664	+	0.0939438i	−0.00320918	+	0.00320160i
$862$	−2.74745	−	9.07635i	−0.0935786	−	0.309142i
$863$	14.1984			0.483318			0.241659	−	0.970361i	$-0.422308\pi$
$863$	14.1984			0.483318			0.241659	+	0.970361i	$0.422308\pi$
$864$	−18.4994	−	22.8424i	−0.629361	−	0.777113i
$865$	26.2580			0.892799
$866$	10.9704	+	36.2415i	0.372791	+	1.23154i
$867$	25.2110	+	6.78727i	0.856211	+	0.230508i
$868$	5.04766	−	3.36415i	0.171329	−	0.114187i
$869$	1.14148	−	3.13619i	0.0387221	−	0.106388i
$870$	−24.9563	−	13.3963i	−0.846098	−	0.454179i
$871$	−6.39754	−	1.12806i	−0.216772	−	0.0382228i
$872$	31.7243	+	26.1293i	1.07432	+	0.884848i
$873$	−12.0968	+	14.3473i	−0.409416	+	0.485583i
$874$	15.0304	+	0.829462i	0.508410	+	0.0280570i
$875$	10.9150	−	3.97274i	0.368994	−	0.134303i
$876$	−3.72822	+	1.25575i	−0.125965	+	0.0424280i
$877$	−16.6200	+	13.9458i	−0.561216	+	0.470916i	−0.878718	−	0.477341i	$-0.841601\pi$
$877$	−16.6200	+	13.9458i	−0.561216	+	0.470916i	0.317502	+	0.948258i	$0.397156\pi$
$878$	2.19067	+	18.2596i	0.0739315	+	0.616230i
$879$	18.3049	+	39.3767i	0.617410	+	1.32814i
$880$	−2.31969	−	0.967251i	−0.0781969	−	0.0326060i
$881$	22.3336	−	12.8943i	0.752439	−	0.434421i	−0.0741357	−	0.997248i	$-0.523620\pi$
$881$	22.3336	−	12.8943i	0.752439	−	0.434421i	0.826574	+	0.562827i	$0.190286\pi$
$882$	1.90667	+	3.79007i	0.0642010	+	0.127618i
$883$	−43.2521	−	24.9716i	−1.45555	−	0.840362i	−0.456762	−	0.889589i	$-0.650991\pi$
$883$	−43.2521	−	24.9716i	−1.45555	−	0.840362i	−0.998788	+	0.0492272i	$0.984324\pi$
$884$	−1.12225	−	4.60973i	−0.0377453	−	0.155042i
$885$	−8.90537	−	4.16548i	−0.299351	−	0.140021i
$886$	−30.2289	−	40.3472i	−1.01556	−	1.35549i
$887$	2.87180	+	16.2868i	0.0964257	+	0.546857i	0.994301	+	0.106608i	$0.0339989\pi$
$887$	2.87180	+	16.2868i	0.0964257	+	0.546857i	−0.897875	+	0.440250i	$0.854890\pi$
$888$	38.0579	−	3.63510i	1.27714	−	0.121986i
$889$	−4.96169	−	4.16335i	−0.166410	−	0.139634i
$890$	−15.4559	−	10.0982i	−0.518084	−	0.338491i
$891$	−0.673518	+	3.71671i	−0.0225637	+	0.124515i
$892$	3.84468	−	1.68630i	0.128730	−	0.0564616i
$893$	−5.90839	+	7.04134i	−0.197717	+	0.235630i
$894$	−46.6546	−	15.3632i	−1.56036	−	0.513822i
$895$	−15.8933	+	2.80242i	−0.531256	+	0.0936747i
$896$	−10.7667	+	3.47529i	−0.359691	+	0.116101i
$897$	−3.25631	+	6.96166i	−0.108725	+	0.232443i
$898$	−5.90196	−	5.53431i	−0.196951	−	0.184682i
$899$	11.7134	−	20.2882i	0.390663	−	0.676648i
$900$	15.1741	−	6.61267i	0.505803	−	0.220422i
$901$	−5.18002	−	8.97206i	−0.172571	−	0.298903i
$902$	−0.0103765	+	0.0443843i	−0.000345500	+	0.00147783i
$903$	−3.34232	+	1.55374i	−0.111226	+	0.0517051i
$904$	16.1718	−	9.53499i	0.537866	−	0.317129i
$905$	−11.1875	−	13.3328i	−0.371886	−	0.443197i
$906$	−29.7850	−	23.4608i	−0.989540	−	0.779433i
$907$	−9.85736	−	27.0829i	−0.327308	−	0.899272i	−0.988790	−	0.149311i	$-0.952294\pi$
$907$	−9.85736	−	27.0829i	−0.327308	−	0.899272i	0.661482	−	0.749961i	$-0.269928\pi$
$908$	4.26822	−	5.80677i	0.141646	−	0.192704i
$909$	−27.1691	+	9.81597i	−0.901143	+	0.325575i
$910$	3.22892	−	1.63397i	0.107038	−	0.0541654i
$911$	−2.05438	+	11.6509i	−0.0680645	+	0.386013i	0.931677	+	0.363287i	$0.118346\pi$
$911$	−2.05438	+	11.6509i	−0.0680645	+	0.386013i	−0.999742	+	0.0227258i	$0.992766\pi$
$912$	−22.4753	−	17.3725i	−0.744231	−	0.575262i
$913$	3.32502	+	1.21021i	0.110042	+	0.0400520i
$914$	6.99921	−	16.3629i	0.231513	−	0.541238i
$915$	−8.01025	+	29.7537i	−0.264811	+	0.983628i
$916$	9.91375	−	33.8642i	0.327559	−	1.11890i
$917$		−	14.8699i		−	0.491048i
$918$	−0.291493	−	10.1945i	−0.00962070	−	0.336468i
$919$		−	16.6494i		−	0.549211i	−0.961557	−	0.274606i	$-0.911453\pi$
$919$		−	16.6494i		−	0.549211i	0.961557	−	0.274606i	$-0.0885473\pi$
$920$	−7.14271	−	8.35598i	−0.235488	−	0.275489i
$921$	−26.8015	−	26.8650i	−0.883140	−	0.885233i
$922$	13.3771	+	5.72201i	0.440550	+	0.188444i
$923$	−13.0087	−	4.73479i	−0.428187	−	0.155847i
$924$	1.24114	+	0.757157i	0.0408305	+	0.0249086i
$925$	−3.73844	+	21.2017i	−0.122919	+	0.697109i
$926$	5.17722	+	10.2308i	0.170134	+	0.336206i
$927$	−7.38466	−	42.4682i	−0.242544	−	1.39484i
$928$	−31.3207	+	30.4650i	−1.02815	+	1.00006i
$929$	−19.1043	−	52.4886i	−0.626791	−	1.72209i	−0.689719	−	0.724077i	$-0.742266\pi$
$929$	−19.1043	−	52.4886i	−0.626791	−	1.72209i	0.0629283	−	0.998018i	$-0.479956\pi$
$930$	−4.12569	−	10.3288i	−0.135287	−	0.338696i
$931$	2.63553	+	3.14090i	0.0863760	+	0.102939i
$932$	24.7200	−	49.9788i	0.809730	−	1.63711i
$933$	5.25570	+	3.68936i	0.172064	+	0.120784i
$934$	−40.5992	−	9.49159i	−1.32845	−	0.310574i
$935$	−0.436010	−	0.755191i	−0.0142591	−	0.0246974i
$936$	12.5109	−	7.33662i	0.408930	−	0.239805i
$937$	8.98185	−	15.5570i	0.293424	−	0.508226i	−0.681193	−	0.732104i	$-0.738538\pi$
$937$	8.98185	−	15.5570i	0.293424	−	0.508226i	0.974617	+	0.223878i	$0.0718718\pi$
$938$	−3.67658	+	3.92081i	−0.120044	+	0.128019i
$939$	25.4876	+	36.4919i	0.831756	+	1.19087i
$940$	6.69855	−	0.431131i	0.218483	−	0.0140620i
$941$	38.1202	−	6.72162i	1.24268	−	0.219119i	0.486618	−	0.873615i	$-0.338230\pi$
$941$	38.1202	−	6.72162i	1.24268	−	0.219119i	0.756065	+	0.654496i	$0.227119\pi$
$942$	−8.06181	+	1.68030i	−0.262668	+	0.0547472i
$943$	−0.128150	+	0.152723i	−0.00417314	+	0.00497335i
$944$	−10.2722	+	11.1573i	−0.334332	+	0.363140i
$945$	7.52114	−	1.98668i	0.244663	−	0.0646268i
$946$	−0.690838	+	1.05737i	−0.0224611	+	0.0343782i
$947$	23.1920	+	19.4604i	0.753640	+	0.632379i	0.936463	−	0.350767i	$-0.114079\pi$
$947$	23.1920	+	19.4604i	0.753640	+	0.632379i	−0.182823	+	0.983146i	$0.558524\pi$
$948$	−27.2363	+	4.12627i	−0.884592	+	0.134015i
$949$	−0.337069	−	1.91162i	−0.0109417	−	0.0620536i
$950$	12.8020	−	9.59149i	0.415350	−	0.311189i
$951$	−5.17630	−	59.9831i	−0.167853	−	1.94509i
$952$	−3.70085	−	1.30881i	−0.119945	−	0.0424186i
$953$	21.5757	+	12.4567i	0.698905	+	0.403513i	0.806939	−	0.590634i	$-0.201122\pi$
$953$	21.5757	+	12.4567i	0.698905	+	0.403513i	−0.108035	+	0.994147i	$0.534456\pi$
$954$	21.7178	−	23.0509i	0.703139	−	0.746300i
$955$	−19.7594	+	11.4081i	−0.639401	+	0.369158i
$956$	−24.8273	−	25.9961i	−0.802971	−	0.840772i
$957$	5.59283	+	0.495981i	0.180791	+	0.0160328i
$958$	−12.7046	+	1.52422i	−0.410467	+	0.0492453i
$959$	−3.05303	+	2.56179i	−0.0985874	+	0.0827247i
$960$	2.16114	+	20.6314i	0.0697505	+	0.665875i
$961$	−20.4861	+	7.45635i	−0.660844	+	0.240527i
$962$	−1.03943	+	18.8351i	−0.0335126	+	0.607269i
$963$	−22.1342	+	12.7094i	−0.713264	+	0.409555i
$964$	15.0801	+	1.66950i	0.485697	+	0.0537709i
$965$	26.5542	+	4.68221i	0.854809	+	0.150726i
$966$	3.34842	+	5.40603i	0.107734	+	0.173936i
$967$	18.5727	−	51.0281i	0.597258	−	1.64095i	−0.159455	−	0.987205i	$-0.550974\pi$
$967$	18.5727	−	51.0281i	0.597258	−	1.64095i	0.756713	−	0.653747i	$-0.226804\pi$
$968$	−30.6132	+	0.279916i	−0.983946	+	0.00899685i
$969$	−2.53969	−	9.52332i	−0.0815866	−	0.305933i
$970$	12.6761	−	3.83711i	0.407005	−	0.123202i
$971$	−0.980675			−0.0314714			−0.0157357	−	0.999876i	$-0.505009\pi$
$971$	−0.980675			−0.0314714			−0.0157357	+	0.999876i	$0.505009\pi$
$972$	29.5927	−	9.81177i	0.949187	−	0.314713i
$973$	−8.64231			−0.277060
$974$	−47.1849	+	14.2831i	−1.51190	+	0.457659i
$975$	2.10448	+	7.89138i	0.0673973	+	0.252726i
$976$	40.0280	+	25.6333i	1.28126	+	0.820501i
$977$	−5.69149	+	15.6372i	−0.182087	+	0.500280i	−0.996832	−	0.0795401i	$-0.974655\pi$
$977$	−5.69149	+	15.6372i	−0.182087	+	0.500280i	0.814745	+	0.579820i	$0.196877\pi$
$978$	22.9511	+	37.0547i	0.733896	+	1.18488i
$979$	3.60420	+	0.635517i	0.115191	+	0.0203112i
$980$	0.329469	−	2.97600i	0.0105245	−	0.0950647i
$981$	−37.8038	+	21.7068i	−1.20698	+	0.693046i
$982$	−0.602092	+	10.9103i	−0.0192135	+	0.348161i
$983$	31.4528	−	11.4479i	1.00319	−	0.365131i	0.212376	−	0.977188i	$-0.431880\pi$
$983$	31.4528	−	11.4479i	1.00319	−	0.365131i	0.790814	+	0.612057i	$0.209658\pi$
$984$	0.362615	−	0.100263i	0.0115597	−	0.00319625i
$985$	5.84506	−	4.90458i	0.186239	−	0.156273i
$986$	−15.0521	+	1.80586i	−0.479357	+	0.0575103i
$987$	−3.86777	−	0.343000i	−0.123112	−	0.0109178i
$988$	10.1363	−	9.68053i	0.322477	−	0.307979i
$989$	−4.78429	+	2.76221i	−0.152132	+	0.0878332i
$990$	1.82802	−	1.94023i	0.0580982	−	0.0616645i
$991$	−1.37910	−	0.796222i	−0.0438084	−	0.0252928i	0.477936	−	0.878395i	$-0.341385\pi$
$991$	−1.37910	−	0.796222i	−0.0438084	−	0.0252928i	−0.521744	+	0.853102i	$0.674718\pi$
$992$	−17.1110	+	1.25850i	−0.543276	+	0.0399573i
$993$	−2.21686	−	25.6891i	−0.0703500	−	0.815218i
$994$	−9.16672	+	6.86789i	−0.290751	+	0.217836i
$995$	−2.52153	−	14.3003i	−0.0799378	−	0.453350i
$996$	−4.37471	−	28.8761i	−0.138618	−	0.914974i
$997$	35.1408	+	29.4866i	1.11292	+	0.933850i	0.998225	−	0.0595506i	$-0.0189668\pi$
$997$	35.1408	+	29.4866i	1.11292	+	0.933850i	0.114694	+	0.993401i	$0.463411\pi$
$998$	20.0449	−	30.6800i	0.634509	−	0.971159i
$999$	−10.6342	+	39.1310i	−0.336451	+	1.23805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.45	yes	648
4.3	odd	2	inner	756.2.cf.a.659.105	yes	648
27.5	odd	18	inner	756.2.cf.a.491.105	yes	648
108.59	even	18	inner	756.2.cf.a.491.45	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.45	✓	648	108.59	even	18	inner
756.2.cf.a.491.105	yes	648	27.5	odd	18	inner
756.2.cf.a.659.45	yes	648	1.1	even	1	trivial
756.2.cf.a.659.105	yes	648	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.409728 - 1.35356i) q^{2} +(-0.446307 - 1.67356i) q^{3} +(-1.66425 + 1.10918i) q^{4} +(-0.512035 + 1.40680i) q^{5} +(-2.08240 + 1.28981i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(2.18323 + 1.79819i) q^{8} +(-2.60162 + 1.49384i) q^{9} +(2.11399 + 0.116662i) q^{10} +(-0.394383 + 0.143544i) q^{11} +(2.59905 + 2.29018i) q^{12} +(-1.30935 + 1.09868i) q^{13} +(0.168460 + 1.40414i) q^{14} +(2.58290 + 0.229055i) q^{15} +(1.53943 - 3.69191i) q^{16} +(1.20192 - 0.693931i) q^{17} +(3.08797 + 2.90938i) q^{18} +(3.55084 + 2.05008i) q^{19} +(-0.708251 - 2.90921i) q^{20} +(0.148916 + 1.72564i) q^{21} +(0.355885 + 0.475007i) q^{22} +(0.450800 + 2.55662i) q^{23} +(2.03499 - 4.45632i) q^{24} +(2.11331 + 1.77327i) q^{25} +(2.02360 + 1.32213i) q^{26} +(3.66116 + 3.68726i) q^{27} +(1.83157 - 0.803339i) q^{28} +(4.96486 - 5.91689i) q^{29} +(-0.748246 - 3.58996i) q^{30} +(2.98692 - 0.526675i) q^{31} +(-5.62796 - 0.571026i) q^{32} +(0.416245 + 0.595960i) q^{33} +(-1.43174 - 1.34255i) q^{34} +(0.748545 - 1.29652i) q^{35} +(2.67279 - 5.37180i) q^{36} +(3.90195 + 6.75837i) q^{37} +(1.32002 - 5.64625i) q^{38} +(2.42308 + 1.70094i) q^{39} +(-3.64759 + 2.15064i) q^{40} +(0.0493633 + 0.0588289i) q^{41} +(2.27474 - 0.908608i) q^{42} +(0.727821 + 1.99967i) q^{43} +(0.497134 - 0.676335i) q^{44} +(-0.769427 - 4.42487i) q^{45} +(3.27583 - 1.65770i) q^{46} +(-0.389288 + 2.20776i) q^{47} +(-6.86569 - 0.928601i) q^{48} +(0.939693 + 0.342020i) q^{49} +(1.53435 - 3.58704i) q^{50} +(-1.69776 - 1.70179i) q^{51} +(0.960450 - 3.28078i) q^{52} -7.46475i q^{53} +(3.49084 - 6.46638i) q^{54} -0.628319i q^{55} +(-1.83781 - 2.14999i) q^{56} +(1.84617 - 6.85752i) q^{57} +(-10.0431 - 4.29592i) q^{58} +(-3.56282 - 1.29676i) q^{59} +(-4.55264 + 2.48370i) q^{60} +(-2.06347 + 11.7025i) q^{61} +(-1.93671 - 3.82718i) q^{62} +(2.82150 - 1.01938i) q^{63} +(1.53302 + 7.85174i) q^{64} +(-0.875189 - 2.40456i) q^{65} +(0.636120 - 0.807595i) q^{66} +(2.44302 + 2.91147i) q^{67} +(-1.23060 + 2.48802i) q^{68} +(4.07746 - 1.89548i) q^{69} +(-2.06161 - 0.481980i) q^{70} +(4.04964 + 7.01418i) q^{71} +(-8.36616 - 1.41680i) q^{72} +(-0.567827 + 0.983506i) q^{73} +(7.54912 - 8.05062i) q^{74} +(2.02450 - 4.32817i) q^{75} +(-8.18338 + 0.526698i) q^{76} +(0.413318 - 0.0728791i) q^{77} +(1.30951 - 3.97670i) q^{78} +(-5.11154 + 6.09170i) q^{79} +(4.40555 + 4.05605i) q^{80} +(4.53685 - 7.77283i) q^{81} +(0.0594029 - 0.0909201i) q^{82} +(-6.45846 - 5.41929i) q^{83} +(-2.16188 - 2.70671i) q^{84} +(0.360798 + 2.04619i) q^{85} +(2.40846 - 1.80447i) q^{86} +(-12.1181 - 5.66825i) q^{87} +(-1.11915 - 0.395787i) q^{88} +(-7.55188 - 4.36008i) q^{89} +(-5.67407 + 2.85446i) q^{90} +(1.48024 - 0.854619i) q^{91} +(-3.58600 - 3.75482i) q^{92} +(-2.21451 - 4.76374i) q^{93} +(3.14784 - 0.377658i) q^{94} +(-4.70221 + 3.94562i) q^{95} +(1.55615 + 9.67359i) q^{96} +(5.87823 - 2.13950i) q^{97} +(0.0779259 - 1.41206i) q^{98} +(0.811603 - 0.962594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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