LMFDB - Embedded newform 756.2.cf.a.659.51

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			659.51
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.51

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0840789 + 1.41171i) q^{2} +(0.0831113 - 1.73006i) q^{3} +(-1.98586 - 0.237390i) q^{4} +(-0.685235 + 1.88267i) q^{5} +(2.43535 + 0.262790i) q^{6} +(0.984808 + 0.173648i) q^{7} +(0.502096 - 2.78350i) q^{8} +(-2.98619 - 0.287574i) q^{9} +(-2.60017 - 1.12565i) q^{10} +(1.63809 - 0.596218i) q^{11} +(-0.575746 + 3.41592i) q^{12} +(2.68625 - 2.25403i) q^{13} +(-0.327943 + 1.37566i) q^{14} +(3.20017 + 1.34197i) q^{15} +(3.88729 + 0.942848i) q^{16} +(-4.11959 + 2.37845i) q^{17} +(0.657047 - 4.19145i) q^{18} +(4.53176 + 2.61641i) q^{19} +(1.80771 - 3.57605i) q^{20} +(0.382270 - 1.68934i) q^{21} +(0.703958 + 2.36265i) q^{22} +(0.487878 + 2.76689i) q^{23} +(-4.77389 - 1.09999i) q^{24} +(0.755328 + 0.633795i) q^{25} +(2.95619 + 3.98173i) q^{26} +(-0.745705 + 5.14237i) q^{27} +(-1.91447 - 0.578625i) q^{28} +(4.70723 - 5.60985i) q^{29} +(-2.16354 + 4.40489i) q^{30} +(8.83361 - 1.55760i) q^{31} +(-1.65787 + 5.40846i) q^{32} +(-0.895345 - 2.88355i) q^{33} +(-3.01131 - 6.01565i) q^{34} +(-1.00175 + 1.73508i) q^{35} +(5.86188 + 1.27997i) q^{36} +(1.06468 + 1.84408i) q^{37} +(-4.07464 + 6.17755i) q^{38} +(-3.67635 - 4.83470i) q^{39} +(4.89636 + 2.85264i) q^{40} +(0.796665 + 0.949428i) q^{41} +(2.35272 + 0.681692i) q^{42} +(-0.282664 - 0.776612i) q^{43} +(-3.39456 + 0.795138i) q^{44} +(2.58765 - 5.42494i) q^{45} +(-3.94707 + 0.456106i) q^{46} +(-0.00999803 + 0.0567016i) q^{47} +(1.95426 - 6.64687i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-0.958244 + 1.01302i) q^{50} +(3.77246 + 7.32480i) q^{51} +(-5.86961 + 3.83851i) q^{52} +9.02236i q^{53} +(-7.19684 - 1.48509i) q^{54} +3.49254i q^{55} +(0.977818 - 2.65403i) q^{56} +(4.90317 - 7.62274i) q^{57} +(7.52372 + 7.11692i) q^{58} +(6.96582 + 2.53535i) q^{59} +(-6.03653 - 3.42465i) q^{60} +(0.697015 - 3.95297i) q^{61} +(1.45617 + 12.6015i) q^{62} +(-2.89088 - 0.801751i) q^{63} +(-7.49580 - 2.79517i) q^{64} +(2.40288 + 6.60187i) q^{65} +(4.14602 - 1.02152i) q^{66} +(3.21429 + 3.83064i) q^{67} +(8.74556 - 3.74532i) q^{68} +(4.82742 - 0.614096i) q^{69} +(-2.36520 - 1.56006i) q^{70} +(1.83610 + 3.18021i) q^{71} +(-2.29982 + 8.16767i) q^{72} +(7.20477 - 12.4790i) q^{73} +(-2.69282 + 1.34797i) q^{74} +(1.15928 - 1.25408i) q^{75} +(-8.37833 - 6.27162i) q^{76} +(1.71674 - 0.302708i) q^{77} +(7.13431 - 4.78344i) q^{78} +(-6.42945 + 7.66232i) q^{79} +(-4.43878 + 6.67241i) q^{80} +(8.83460 + 1.71750i) q^{81} +(-1.40730 + 1.04483i) q^{82} +(7.59781 + 6.37532i) q^{83} +(-1.16017 + 3.26405i) q^{84} +(-1.65494 - 9.38562i) q^{85} +(1.12012 - 0.333743i) q^{86} +(-9.31414 - 8.61001i) q^{87} +(-0.837094 - 4.85900i) q^{88} +(-6.38186 - 3.68457i) q^{89} +(7.44089 + 4.10914i) q^{90} +(3.03685 - 1.75333i) q^{91} +(-0.312024 - 5.61048i) q^{92} +(-1.96057 - 15.4121i) q^{93} +(-0.0792057 - 0.0188817i) q^{94} +(-8.03115 + 6.73894i) q^{95} +(9.21915 + 3.31771i) q^{96} +(1.64617 - 0.599159i) q^{97} +(-0.561842 + 1.29782i) q^{98} +(-5.06311 + 1.30934i) 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 $

$2$	−0.0840789	+	1.41171i	−0.0594527	+	0.998231i
$2$	−0.0840789	+	1.41171i	−0.0594527	+	0.998231i
$3$	0.0831113	−	1.73006i	0.0479843	−	0.998848i
$3$	0.0831113	−	1.73006i	0.0479843	−	0.998848i
$4$	−1.98586	−	0.237390i	−0.992931	−	0.118695i
$5$	−0.685235	+	1.88267i	−0.306447	+	0.841955i	0.686896	+	0.726756i	$0.258973\pi$
$5$	−0.685235	+	1.88267i	−0.306447	+	0.841955i	−0.993342	+	0.115199i	$0.963249\pi$
$6$	2.43535	+	0.262790i	0.994228	+	0.107284i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	0.502096	−	2.78350i	0.177518	−	0.984118i
$9$	−2.98619	−	0.287574i	−0.995395	−	0.0958581i
$10$	−2.60017	−	1.12565i	−0.822247	−	0.355961i
$11$	1.63809	−	0.596218i	0.493904	−	0.179766i	−0.0830462	−	0.996546i	$-0.526465\pi$
$11$	1.63809	−	0.596218i	0.493904	−	0.179766i	0.576950	+	0.816779i	$0.304243\pi$
$12$	−0.575746	+	3.41592i	−0.166204	+	0.986091i
$13$	2.68625	−	2.25403i	0.745032	−	0.625156i	−0.189152	−	0.981948i	$-0.560574\pi$
$13$	2.68625	−	2.25403i	0.745032	−	0.625156i	0.934184	+	0.356791i	$0.116129\pi$
$14$	−0.327943	+	1.37566i	−0.0876464	+	0.367662i
$15$	3.20017	+	1.34197i	0.826281	+	0.346494i
$16$	3.88729	+	0.942848i	0.971823	+	0.235712i
$17$	−4.11959	+	2.37845i	−0.999148	+	0.576858i	−0.907996	−	0.418979i	$-0.862388\pi$
$17$	−4.11959	+	2.37845i	−0.999148	+	0.576858i	−0.0911517	+	0.995837i	$0.529055\pi$
$18$	0.657047	−	4.19145i	0.154868	−	0.987935i
$19$	4.53176	+	2.61641i	1.03966	+	0.600246i	0.919736	−	0.392538i	$-0.128403\pi$
$19$	4.53176	+	2.61641i	1.03966	+	0.600246i	0.119920	+	0.992784i	$0.461736\pi$
$20$	1.80771	−	3.57605i	0.404216	−	0.799629i
$21$	0.382270	−	1.68934i	0.0834181	−	0.368644i
$22$	0.703958	+	2.36265i	0.150084	+	0.503718i
$23$	0.487878	+	2.76689i	0.101730	+	0.576937i	0.992476	+	0.122437i	$0.0390709\pi$
$23$	0.487878	+	2.76689i	0.101730	+	0.576937i	−0.890747	+	0.454500i	$0.849818\pi$
$24$	−4.77389	−	1.09999i	−0.974466	−	0.224535i
$25$	0.755328	+	0.633795i	0.151066	+	0.126759i
$26$	2.95619	+	3.98173i	0.579756	+	0.780882i
$27$	−0.745705	+	5.14237i	−0.143511	+	0.989649i
$28$	−1.91447	−	0.578625i	−0.361801	−	0.109350i
$29$	4.70723	−	5.60985i	0.874110	−	1.04172i	−0.124663	−	0.992199i	$-0.539785\pi$
$29$	4.70723	−	5.60985i	0.874110	−	1.04172i	0.998773	−	0.0495246i	$-0.0157706\pi$
$30$	−2.16354	+	4.40489i	−0.395006	+	0.804219i
$31$	8.83361	−	1.55760i	1.58656	−	0.279754i	0.690383	−	0.723444i	$-0.257442\pi$
$31$	8.83361	−	1.55760i	1.58656	−	0.279754i	0.896180	+	0.443691i	$0.146331\pi$
$32$	−1.65787	+	5.40846i	−0.293073	+	0.956090i
$33$	−0.895345	−	2.88355i	−0.155860	−	0.501961i
$34$	−3.01131	−	6.01565i	−0.516436	−	1.03168i
$35$	−1.00175	+	1.73508i	−0.169326	+	0.293282i
$36$	5.86188	+	1.27997i	0.976980	+	0.213329i
$37$	1.06468	+	1.84408i	0.175032	+	0.303164i	0.940172	−	0.340699i	$-0.110664\pi$
$37$	1.06468	+	1.84408i	0.175032	+	0.303164i	−0.765140	+	0.643864i	$0.777330\pi$
$38$	−4.07464	+	6.17755i	−0.660994	+	1.00213i
$39$	−3.67635	−	4.83470i	−0.588686	−	0.774172i
$40$	4.89636	+	2.85264i	0.774183	+	0.451041i
$41$	0.796665	+	0.949428i	0.124418	+	0.148276i	0.824658	−	0.565632i	$-0.191368\pi$
$41$	0.796665	+	0.949428i	0.124418	+	0.148276i	−0.700239	+	0.713908i	$0.746923\pi$
$42$	2.35272	+	0.681692i	0.363033	+	0.105187i
$43$	−0.282664	−	0.776612i	−0.0431058	−	0.118432i	0.916272	−	0.400556i	$-0.131183\pi$
$43$	−0.282664	−	0.776612i	−0.0431058	−	0.118432i	−0.959378	+	0.282124i	$0.908961\pi$
$44$	−3.39456	+	0.795138i	−0.511750	+	0.119872i
$45$	2.58765	−	5.42494i	0.385744	−	0.808703i
$46$	−3.94707	+	0.456106i	−0.581964	+	0.0672491i
$47$	−0.00999803	+	0.0567016i	−0.00145836	+	0.00827078i	−0.985528	−	0.169511i	$-0.945781\pi$
$47$	−0.00999803	+	0.0567016i	−0.00145836	+	0.00827078i	0.984070	+	0.177782i	$0.0568922\pi$
$48$	1.95426	−	6.64687i	0.282073	−	0.959393i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−0.958244	+	1.01302i	−0.135516	+	0.143262i
$51$	3.77246	+	7.32480i	0.528250	+	1.02568i
$52$	−5.86961	+	3.83851i	−0.813969	+	0.532305i
$53$			9.02236i			1.23932i	0.784872	+	0.619658i	$0.212729\pi$
$53$			9.02236i			1.23932i	−0.784872	+	0.619658i	$0.787271\pi$
$54$	−7.19684	−	1.48509i	−0.979366	−	0.202095i
$55$			3.49254i			0.470934i
$56$	0.977818	−	2.65403i	0.130666	−	0.354660i
$57$	4.90317	−	7.62274i	0.649441	−	1.00966i
$58$	7.52372	+	7.11692i	0.987913	+	0.934497i
$59$	6.96582	+	2.53535i	0.906872	+	0.330074i	0.753003	−	0.658017i	$-0.228604\pi$
$59$	6.96582	+	2.53535i	0.906872	+	0.330074i	0.153869	+	0.988091i	$0.450827\pi$
$60$	−6.03653	−	3.42465i	−0.779312	−	0.442120i
$61$	0.697015	−	3.95297i	0.0892437	−	0.506126i	−0.907116	−	0.420880i	$-0.861721\pi$
$61$	0.697015	−	3.95297i	0.0892437	−	0.506126i	0.996360	−	0.0852459i	$-0.0271676\pi$
$62$	1.45617	+	12.6015i	0.184933	+	1.60039i
$63$	−2.89088	−	0.801751i	−0.364217	−	0.101011i
$64$	−7.49580	−	2.79517i	−0.936975	−	0.349396i
$65$	2.40288	+	6.60187i	0.298041	+	0.818861i
$66$	4.14602	−	1.02152i	0.510339	−	0.125741i
$67$	3.21429	+	3.83064i	0.392688	+	0.467987i	0.925776	−	0.378072i	$-0.123413\pi$
$67$	3.21429	+	3.83064i	0.392688	+	0.467987i	−0.533088	+	0.846060i	$0.678969\pi$
$68$	8.74556	−	3.74532i	1.06055	−	0.454186i
$69$	4.82742	−	0.614096i	0.581154	−	0.0739284i
$70$	−2.36520	−	1.56006i	−0.282696	−	0.186463i
$71$	1.83610	+	3.18021i	0.217905	+	0.377422i	0.954167	−	0.299274i	$-0.0967445\pi$
$71$	1.83610	+	3.18021i	0.217905	+	0.377422i	−0.736263	+	0.676696i	$0.763411\pi$
$72$	−2.29982	+	8.16767i	−0.271036	+	0.962569i
$73$	7.20477	−	12.4790i	0.843254	−	1.46056i	−0.0438743	−	0.999037i	$-0.513970\pi$
$73$	7.20477	−	12.4790i	0.843254	−	1.46056i	0.887129	−	0.461522i	$-0.152697\pi$
$74$	−2.69282	+	1.34797i	−0.313034	+	0.156698i
$75$	1.15928	−	1.25408i	0.133862	−	0.144809i
$76$	−8.37833	−	6.27162i	−0.961060	−	0.719404i
$77$	1.71674	−	0.302708i	0.195641	−	0.0344967i
$78$	7.13431	−	4.78344i	0.807802	−	0.541618i
$79$	−6.42945	+	7.66232i	−0.723370	+	0.862078i	−0.994954	−	0.100336i	$-0.968008\pi$
$79$	−6.42945	+	7.66232i	−0.723370	+	0.862078i	0.271584	+	0.962415i	$0.412453\pi$
$80$	−4.43878	+	6.67241i	−0.496271	+	0.745998i
$81$	8.83460	+	1.71750i	0.981622	+	0.190833i
$82$	−1.40730	+	1.04483i	−0.155410	+	0.115383i
$83$	7.59781	+	6.37532i	0.833968	+	0.699782i	0.956198	−	0.292719i	$-0.0945602\pi$
$83$	7.59781	+	6.37532i	0.833968	+	0.699782i	−0.122230	+	0.992502i	$0.539005\pi$
$84$	−1.16017	+	3.26405i	−0.126585	+	0.356137i
$85$	−1.65494	−	9.38562i	−0.179503	−	1.01801i
$86$	1.12012	−	0.333743i	0.120785	−	0.0359884i
$87$	−9.31414	−	8.61001i	−0.998580	−	0.923090i
$88$	−0.837094	−	4.85900i	−0.0892346	−	0.517971i
$89$	−6.38186	−	3.68457i	−0.676476	−	0.390563i	0.122050	−	0.992524i	$-0.461053\pi$
$89$	−6.38186	−	3.68457i	−0.676476	−	0.390563i	−0.798526	+	0.601961i	$0.794386\pi$
$90$	7.44089	+	4.10914i	0.784339	+	0.433141i
$91$	3.03685	−	1.75333i	0.318349	−	0.183799i
$92$	−0.312024	−	5.61048i	−0.0325308	−	0.584933i
$93$	−1.96057	−	15.4121i	−0.203301	−	1.59816i
$94$	−0.0792057	−	0.0188817i	−0.00816945	−	0.00194750i
$95$	−8.03115	+	6.73894i	−0.823979	+	0.691400i
$96$	9.21915	+	3.31771i	0.940926	+	0.338612i
$97$	1.64617	−	0.599159i	0.167144	−	0.0608353i	−0.257093	−	0.966387i	$-0.582765\pi$
$97$	1.64617	−	0.599159i	0.167144	−	0.0608353i	0.424237	+	0.905551i	$0.360542\pi$
$98$	−0.561842	+	1.29782i	−0.0567546	+	0.131099i
$99$	−5.06311	+	1.30934i	−0.508862	+	0.131594i
$100$	−1.34952	−	1.43794i	−0.134952	−	0.143794i
$101$	−8.66479	−	1.52784i	−0.862179	−	0.152025i	−0.274962	−	0.961455i	$-0.588665\pi$
$101$	−8.66479	−	1.52784i	−0.862179	−	0.152025i	−0.587217	+	0.809430i	$0.699776\pi$
$102$	−10.6577	+	4.70977i	−1.05527	+	0.466337i
$103$	4.05714	−	11.1469i	0.399762	−	1.09834i	−0.562639	−	0.826703i	$-0.690214\pi$
$103$	4.05714	−	11.1469i	0.399762	−	1.09834i	0.962401	−	0.271633i	$-0.0875638\pi$
$104$	−4.92536	−	8.60894i	−0.482971	−	0.844176i
$105$	2.91852	+	1.87728i	0.284819	+	0.183204i
$106$	−12.7370	−	0.758589i	−1.23712	−	0.0736807i
$107$	−9.94228			−0.961156			−0.480578	−	0.876952i	$-0.659573\pi$
$107$	−9.94228			−0.961156			−0.480578	+	0.876952i	$0.659573\pi$
$108$	2.70162	−	10.0350i	0.259963	−	0.965619i
$109$	−18.2137			−1.74455			−0.872277	−	0.489012i	$-0.837357\pi$
$109$	−18.2137			−1.74455			−0.872277	+	0.489012i	$0.837357\pi$
$110$	−4.93046	−	0.293649i	−0.470101	−	0.0279983i
$111$	3.27884	−	1.68869i	0.311214	−	0.160283i
$112$	3.66451	+	1.60355i	0.346264	+	0.151521i
$113$	1.42358	−	3.91125i	0.133919	−	0.367940i	−0.854549	−	0.519371i	$-0.826166\pi$
$113$	1.42358	−	3.91125i	0.133919	−	0.367940i	0.988468	+	0.151432i	$0.0483884\pi$
$114$	10.3489	+	7.56278i	0.969259	+	0.708319i
$115$	−5.54345	−	0.977460i	−0.516930	−	0.0911486i
$116$	−10.6796	+	10.0229i	−0.991578	+	0.930607i
$117$	−8.66985	+	5.95846i	−0.801528	+	0.550860i
$118$	−4.16486	+	9.62056i	−0.383407	+	0.885644i
$119$	−4.47002	+	1.62695i	−0.409766	+	0.149143i
$120$	5.34216	−	8.23390i	0.487670	−	0.751648i
$121$	−6.09861	+	5.11734i	−0.554419	+	0.465213i
$122$	5.52185	+	1.31635i	0.499925	+	0.119176i
$123$	1.70878	−	1.29937i	0.154075	−	0.117160i
$124$	−17.9121	+	0.996172i	−1.60855	+	0.0894589i
$125$	−10.3862	+	5.99647i	−0.928969	+	0.536340i
$126$	1.37490	−	4.01368i	0.122486	−	0.357567i
$127$	−6.82321	−	3.93938i	−0.605462	−	0.349564i	0.165725	−	0.986172i	$-0.447004\pi$
$127$	−6.82321	−	3.93938i	−0.605462	−	0.349564i	−0.771187	+	0.636608i	$0.780337\pi$
$128$	4.57622	−	10.3469i	0.404484	−	0.914545i
$129$	−1.36707	+	0.424478i	−0.120364	+	0.0373732i
$130$	−9.52197	+	2.83710i	−0.835132	+	0.248830i
$131$	−3.38016	−	19.1699i	−0.295326	−	1.67488i	−0.665874	−	0.746065i	$-0.731941\pi$
$131$	−3.38016	−	19.1699i	−0.295326	−	1.67488i	0.370547	−	0.928814i	$-0.379170\pi$
$132$	1.09351	+	5.93887i	0.0951775	+	0.516912i
$133$	4.00857	+	3.36359i	0.347587	+	0.291660i
$134$	−5.67802	+	4.21558i	−0.490506	+	0.364170i
$135$	−9.17039	−	4.92765i	−0.789261	−	0.424104i
$136$	4.55199	+	12.6611i	0.390330	+	1.08568i
$137$	5.39694	−	6.43182i	0.461091	−	0.549507i	−0.484531	−	0.874774i	$-0.661010\pi$
$137$	5.39694	−	6.43182i	0.461091	−	0.549507i	0.945622	+	0.325267i	$0.105454\pi$
$138$	0.461042	+	6.86657i	0.0392465	+	0.584521i
$139$	10.8304	−	1.90969i	0.918621	−	0.161978i	0.305705	−	0.952126i	$-0.401108\pi$
$139$	10.8304	−	1.90969i	0.918621	−	0.161978i	0.612915	+	0.790149i	$0.289997\pi$
$140$	2.40122	−	3.20782i	0.202940	−	0.271110i
$141$	0.0972660	+	0.0220097i	0.00819128	+	0.00185355i
$142$	−4.64392	+	2.32465i	−0.389709	+	0.195080i
$143$	3.05644	−	5.29391i	0.255592	−	0.442699i
$144$	−11.3370	−	3.93341i	−0.944753	−	0.327784i
$145$	7.33594	+	12.7062i	0.609217	+	1.05519i
$146$	17.0110	+	11.2203i	1.40784	+	0.928597i
$147$	0.669813	−	1.59729i	0.0552452	−	0.131743i
$148$	−1.67654	−	3.91483i	−0.137811	−	0.321797i
$149$	−8.45271	−	10.0736i	−0.692473	−	0.825258i	0.299179	−	0.954197i	$-0.403287\pi$
$149$	−8.45271	−	10.0736i	−0.692473	−	0.825258i	−0.991652	+	0.128939i	$0.958843\pi$
$150$	1.67293	+	1.74201i	0.136595	+	0.142234i
$151$	−7.15326	−	19.6534i	−0.582124	−	1.59937i	−0.784543	−	0.620074i	$-0.787103\pi$
$151$	−7.15326	−	19.6534i	−0.582124	−	1.59937i	0.202419	−	0.979299i	$-0.435120\pi$
$152$	9.55816	−	11.3005i	0.775270	−	0.916590i
$153$	12.9858	−	5.91780i	1.04984	−	0.478425i
$154$	0.282994	+	2.44899i	0.0228043	+	0.197346i
$155$	−3.12065	+	17.6981i	−0.250657	+	1.42154i
$156$	6.15300	+	10.4738i	0.492634	+	0.838573i
$157$	−9.12094	−	3.31975i	−0.727930	−	0.264945i	−0.0486418	−	0.998816i	$-0.515489\pi$
$157$	−9.12094	−	3.31975i	−0.727930	−	0.264945i	−0.679288	+	0.733871i	$0.737711\pi$
$158$	−10.2764	−	9.72077i	−0.817547	−	0.773343i
$159$	15.6092	+	0.749860i	1.23789	+	0.0594677i
$160$	−9.04631	−	6.82729i	−0.715174	−	0.539745i
$161$			2.80958i			0.221426i
$162$	−3.16742	+	12.3275i	−0.248856	+	0.968541i
$163$		−	3.37250i		−	0.264155i	−0.991239	−	0.132077i	$-0.957835\pi$
$163$		−	3.37250i		−	0.264155i	0.991239	−	0.132077i	$-0.0421648\pi$
$164$	−1.35668	−	2.07455i	−0.105939	−	0.161995i
$165$	6.04229	+	0.290269i	0.470391	+	0.0225974i
$166$	−9.63893	+	10.1899i	−0.748126	+	0.790889i
$167$	16.3768	+	5.96067i	1.26728	+	0.461251i	0.886204	−	0.463295i	$-0.153333\pi$
$167$	16.3768	+	5.96067i	1.26728	+	0.461251i	0.381072	+	0.924545i	$0.375555\pi$
$168$	−4.51035	−	1.91226i	−0.347981	−	0.147534i
$169$	−0.122141	+	0.692694i	−0.00939543	+	0.0532841i
$170$	13.3889	−	1.54716i	1.02689	−	0.118662i
$171$	−12.7802	−	9.11630i	−0.977330	−	0.697141i
$172$	0.376971	+	1.60934i	0.0287437	+	0.122711i
$173$	6.64339	+	18.2526i	0.505088	+	1.38772i	0.886249	+	0.463209i	$0.153302\pi$
$173$	6.64339	+	18.2526i	0.505088	+	1.38772i	−0.381162	+	0.924508i	$0.624476\pi$
$174$	12.9380	−	12.4250i	0.980825	−	0.941934i
$175$	0.633795	+	0.755328i	0.0479104	+	0.0570974i
$176$	6.92989	−	0.773197i	0.522360	−	0.0582819i
$177$	4.96523	−	11.8405i	0.373210	−	0.889989i
$178$	5.73813	−	8.69955i	0.430091	−	0.652059i
$179$	8.73210	+	15.1244i	0.652668	+	1.13045i	0.982473	+	0.186405i	$0.0596837\pi$
$179$	8.73210	+	15.1244i	0.652668	+	1.13045i	−0.329805	+	0.944049i	$0.606983\pi$
$180$	−6.42654	+	10.1589i	−0.479006	+	0.757200i
$181$	−7.47039	+	12.9391i	−0.555269	+	0.961755i	0.442613	+	0.896713i	$0.354051\pi$
$181$	−7.47039	+	12.9391i	−0.555269	+	0.961755i	−0.997883	+	0.0650421i	$0.979282\pi$
$182$	2.21986	+	4.43458i	0.164547	+	0.328713i
$183$	−6.78093	−	1.53441i	−0.501261	−	0.113427i
$184$	7.94662	+	0.0312346i	0.585832	+	0.00230264i
$185$	−4.20134	+	0.740810i	−0.308889	+	0.0544654i
$186$	21.9223	−	1.47193i	1.60742	−	0.107927i
$187$	−5.33021	+	6.35229i	−0.389783	+	0.464526i
$188$	0.0333151	−	0.110228i	0.00242975	−	0.00803921i
$189$	−1.62734	+	4.93475i	−0.118371	+	0.358950i
$190$	−8.83819	−	11.9043i	−0.641190	−	0.863627i
$191$	4.98067	+	4.17928i	0.360389	+	0.302402i	0.804946	−	0.593348i	$-0.202194\pi$
$191$	4.98067	+	4.17928i	0.360389	+	0.302402i	−0.444557	+	0.895751i	$0.646639\pi$
$192$	−5.45879	+	12.7358i	−0.393954	+	0.919130i
$193$	−0.130871	−	0.742204i	−0.00942027	−	0.0534250i	0.979735	−	0.200297i	$-0.0641906\pi$
$193$	−0.130871	−	0.742204i	−0.00942027	−	0.0534250i	−0.989156	+	0.146872i	$0.953080\pi$
$194$	0.707431	+	2.37430i	0.0507906	+	0.170465i
$195$	11.6213	−	3.60843i	0.832219	−	0.258405i
$196$	−1.78491	−	0.902279i	−0.127493	−	0.0644485i
$197$	−8.70216	−	5.02419i	−0.620003	−	0.357959i	0.156867	−	0.987620i	$-0.449861\pi$
$197$	−8.70216	−	5.02419i	−0.620003	−	0.357959i	−0.776870	+	0.629661i	$0.783194\pi$
$198$	−1.42271	−	7.25774i	−0.101108	−	0.515785i
$199$	18.1924	−	10.5034i	1.28963	−	0.744567i	0.311040	−	0.950397i	$-0.399323\pi$
$199$	18.1924	−	10.5034i	1.28963	−	0.744567i	0.978588	+	0.205830i	$0.0659895\pi$
$200$	2.14342	−	1.78423i	0.151563	−	0.126164i
$201$	6.89437	−	5.24253i	0.486291	−	0.369780i
$202$	2.88539	−	12.1037i	0.203015	−	0.851616i
$203$	5.60985	−	4.70723i	0.393735	−	0.330383i
$204$	−5.75275	−	15.4416i	−0.402773	−	1.08113i
$205$	−2.33336	+	0.849274i	−0.162969	+	0.0593159i
$206$	15.3951	+	6.66473i	1.07263	+	0.464354i
$207$	−0.661206	−	8.40275i	−0.0459570	−	0.584032i
$208$	12.5675	−	6.22936i	0.871397	−	0.431928i
$209$	8.98339	+	1.58401i	0.621394	+	0.109569i
$210$	−2.89557	+	3.96227i	−0.199813	+	0.273423i
$211$	1.98316	−	5.44868i	0.136526	−	0.375103i	−0.852523	−	0.522690i	$-0.824929\pi$
$211$	1.98316	−	5.44868i	0.136526	−	0.375103i	0.989049	+	0.147587i	$0.0471508\pi$
$212$	2.14182	−	17.9171i	0.147101	−	1.23055i
$213$	5.65455	−	2.91224i	0.387443	−	0.199543i
$214$	0.835935	−	14.0356i	0.0571434	−	0.959456i
$215$	1.65579			0.112924
$216$	13.9394	+	4.65763i	0.948455	+	0.316912i
$217$	8.96988			0.608915
$218$	1.53139	−	25.7125i	0.103718	−	1.74147i
$219$	−20.9906	−	13.5018i	−1.41841	−	0.912367i
$220$	0.829095	−	6.93570i	0.0558976	−	0.467605i
$221$	−5.70516	+	15.6748i	−0.383771	+	1.05440i
$222$	2.10826	+	4.77076i	0.141497	+	0.320193i
$223$	−26.7751	−	4.72116i	−1.79299	−	0.316153i	−0.824623	−	0.565682i	$-0.808613\pi$
$223$	−26.7751	−	4.72116i	−1.79299	−	0.316153i	−0.968367	+	0.249530i	$0.919724\pi$
$224$	−2.57185	+	5.03841i	−0.171839	+	0.336643i
$225$	−2.07329	−	2.10984i	−0.138219	−	0.140656i
$226$	5.40187	+	2.33854i	0.359327	+	0.155557i
$227$	3.36725	−	1.22558i	0.223492	−	0.0813445i	−0.227847	−	0.973697i	$-0.573169\pi$
$227$	3.36725	−	1.22558i	0.223492	−	0.0813445i	0.451339	+	0.892352i	$0.350946\pi$
$228$	−11.5466	+	13.9737i	−0.764692	+	0.925433i
$229$	−2.49175	+	2.09082i	−0.164659	+	0.138166i	−0.721394	−	0.692525i	$-0.756498\pi$
$229$	−2.49175	+	2.09082i	−0.164659	+	0.138166i	0.556735	+	0.830690i	$0.312054\pi$
$230$	1.84598	−	7.74357i	0.121720	−	0.510596i
$231$	−0.381020	−	2.99521i	−0.0250693	−	0.197071i
$232$	−13.2516	−	15.9193i	−0.870009	−	1.04515i
$233$	−20.8736	+	12.0514i	−1.36747	+	0.789511i	−0.990605	−	0.136757i	$-0.956332\pi$
$233$	−20.8736	+	12.0514i	−1.36747	+	0.789511i	−0.376868	+	0.926267i	$0.622999\pi$
$234$	−7.68268	−	12.7403i	−0.502233	−	0.832860i
$235$	−0.0998994	−	0.0576769i	−0.00651672	−	0.00376243i
$236$	−13.2313	−	6.68847i	−0.861283	−	0.435382i
$237$	12.7219	+	11.7601i	0.826375	+	0.763903i
$238$	−1.92096	−	6.44717i	−0.124517	−	0.417908i
$239$	−1.74173	−	9.87785i	−0.112663	−	0.638945i	−0.987881	−	0.155215i	$-0.950393\pi$
$239$	−1.74173	−	9.87785i	−0.112663	−	0.638945i	0.875217	−	0.483730i	$-0.160718\pi$
$240$	11.1747	+	8.23389i	0.721326	+	0.531495i
$241$	9.02888	+	7.57613i	0.581601	+	0.488021i	0.885473	−	0.464692i	$-0.153835\pi$
$241$	9.02888	+	7.57613i	0.581601	+	0.488021i	−0.303871	+	0.952713i	$0.598279\pi$
$242$	−6.71145	−	9.03974i	−0.431428	−	0.581097i
$243$	3.70563	−	15.1416i	0.237716	−	0.971335i
$244$	−2.32257	+	7.68459i	−0.148688	+	0.491955i
$245$	−1.28782	+	1.53477i	−0.0822759	+	0.0980526i
$246$	1.69066	+	2.52155i	0.107792	+	0.160768i
$247$	18.0709	−	3.18639i	1.14982	−	0.202745i
$248$	0.0997198	−	25.3705i	0.00633222	−	1.61103i
$249$	11.6611	−	12.6148i	0.738994	−	0.799429i
$250$	−7.59203	−	15.1665i	−0.480162	−	0.959213i
$251$	0.862478	−	1.49386i	0.0544391	−	0.0942913i	−0.837522	−	0.546404i	$-0.815996\pi$
$251$	0.862478	−	1.49386i	0.0544391	−	0.0942913i	0.891961	+	0.452113i	$0.149330\pi$
$252$	5.55056	+	2.27843i	0.349653	+	0.143528i
$253$	2.44886	+	4.24155i	0.153958	+	0.266664i
$254$	6.13496	−	9.30119i	0.384942	−	0.583609i
$255$	−16.3752	+	2.08308i	−1.02545	+	0.130448i
$256$	14.2221	+	7.33025i	0.888880	+	0.458141i
$257$	14.6240	+	17.4282i	0.912220	+	1.08714i	0.995883	+	0.0906472i	$0.0288936\pi$
$257$	14.6240	+	17.4282i	0.912220	+	1.08714i	−0.0836632	+	0.996494i	$0.526662\pi$
$258$	−0.484299	−	1.96560i	−0.0301512	−	0.122373i
$259$	0.728283	+	2.00094i	0.0452533	+	0.124332i
$260$	−3.20457	−	13.6808i	−0.198739	−	0.848448i
$261$	−15.6699	+	15.3984i	−0.969942	+	0.953136i
$262$	27.3465	−	3.16004i	1.68947	−	0.195228i
$263$	−3.42026	+	19.3973i	−0.210902	+	1.19609i	0.676975	+	0.736006i	$0.263291\pi$
$263$	−3.42026	+	19.3973i	−0.210902	+	1.19609i	−0.887877	+	0.460080i	$0.847821\pi$
$264$	−8.47592	+	1.04438i	−0.521657	+	0.0642773i
$265$	−16.9861	−	6.18244i	−1.04345	−	0.379784i
$266$	−5.08546	+	5.37614i	−0.311810	+	0.329632i
$267$	−6.90491	+	10.7347i	−0.422574	+	0.656955i
$268$	−5.47378	−	8.37016i	−0.334364	−	0.511289i
$269$		−	22.7513i		−	1.38717i	−0.720373	−	0.693587i	$-0.756029\pi$
$269$		−	22.7513i		−	1.38717i	0.720373	−	0.693587i	$-0.243971\pi$
$270$	7.72745	−	12.5316i	0.470278	−	0.762651i
$271$		−	11.2542i		−	0.683644i	−0.939765	−	0.341822i	$-0.888956\pi$
$271$		−	11.2542i		−	0.683644i	0.939765	−	0.341822i	$-0.111044\pi$
$272$	−18.2566	+	5.36157i	−1.10697	+	0.325093i
$273$	−2.78096	−	5.39964i	−0.168311	−	0.326801i
$274$	8.62611	+	8.15970i	0.521122	+	0.492945i
$275$	1.61518	+	0.587877i	0.0973989	+	0.0354503i
$276$	−9.73238	+	0.0735249i	−0.585820	+	0.00442568i
$277$	−4.91764	+	27.8893i	−0.295473	+	1.67571i	0.369803	+	0.929110i	$0.379425\pi$
$277$	−4.91764	+	27.8893i	−0.295473	+	1.67571i	−0.665275	+	0.746598i	$0.731686\pi$
$278$	1.78532	+	15.4499i	0.107077	+	0.926626i
$279$	−26.8267	+	2.11097i	−1.60607	+	0.126381i
$280$	4.32662	+	3.65954i	0.258565	+	0.218700i
$281$	−6.73648	−	18.5083i	−0.401865	−	1.10411i	−0.961363	−	0.275283i	$-0.911228\pi$
$281$	−6.73648	−	18.5083i	−0.401865	−	1.10411i	0.559499	−	0.828831i	$-0.310994\pi$
$282$	−0.0392494	+	0.135461i	−0.00233727	+	0.00806659i
$283$	20.9433	+	24.9592i	1.24495	+	1.48367i	0.813531	+	0.581522i	$0.197542\pi$
$283$	20.9433	+	24.9592i	1.24495	+	1.48367i	0.431419	+	0.902152i	$0.358013\pi$
$284$	−2.89128	−	6.75133i	−0.171566	−	0.400618i
$285$	10.9913	+	14.4544i	0.651066	+	0.856206i
$286$	7.21649	+	4.75992i	0.426720	+	0.281460i
$287$	0.619695	+	1.07334i	0.0365795	+	0.0633575i
$288$	6.50604	−	15.6739i	0.383372	−	0.923594i
$289$	2.81402	−	4.87403i	0.165531	−	0.286708i
$290$	−18.5543	+	9.28791i	−1.08955	+	0.545405i
$291$	−0.899762	−	2.89777i	−0.0527450	−	0.169870i
$292$	−17.2701	+	23.0713i	−1.01065	+	1.35014i
$293$	−27.6340	+	4.87262i	−1.61439	+	0.284661i	−0.906674	−	0.421832i	$-0.861387\pi$
$293$	−27.6340	+	4.87262i	−1.61439	+	0.284661i	−0.707720	+	0.706493i	$0.750276\pi$
$294$	2.19860	+	1.07988i	0.128225	+	0.0629800i
$295$	−9.54645	+	11.3770i	−0.555816	+	0.662395i
$296$	5.66757	−	2.03763i	0.329421	−	0.118435i
$297$	1.84443	+	8.86828i	0.107025	+	0.514590i
$298$	14.9316	−	11.0858i	0.864967	−	0.642185i
$299$	7.54723	+	6.33288i	0.436468	+	0.366240i
$300$	−2.59987	+	2.21524i	−0.150104	+	0.127897i
$301$	−0.143512	−	0.813897i	−0.00827190	−	0.0469123i
$302$	28.3464	−	8.44591i	1.63115	−	0.486007i
$303$	−3.36338	+	14.8636i	−0.193221	+	0.853891i
$304$	15.1494	+	14.4435i	0.868876	+	0.828392i
$305$	6.96452	+	4.02097i	0.398787	+	0.230240i
$306$	7.26239	+	18.8298i	0.415163	+	1.07643i
$307$	−14.5246	+	8.38577i	−0.828962	+	0.478601i	−0.853497	−	0.521098i	$-0.825523\pi$
$307$	−14.5246	+	8.38577i	−0.828962	+	0.478601i	0.0245353	+	0.999699i	$0.492189\pi$
$308$	−3.48107	+	0.193598i	−0.198352	+	0.0110313i
$309$	−18.9475	−	7.94551i	−1.07789	−	0.452004i
$310$	−24.7222	−	5.89349i	−1.40413	−	0.334728i
$311$	16.9969	−	14.2621i	0.963805	−	0.808729i	−0.0177628	−	0.999842i	$-0.505654\pi$
$311$	16.9969	−	14.2621i	0.963805	−	0.808729i	0.981568	+	0.191114i	$0.0612099\pi$
$312$	−15.3033	+	7.80564i	−0.866378	+	0.441908i
$313$	7.63759	−	2.77986i	0.431702	−	0.157127i	−0.117024	−	0.993129i	$-0.537335\pi$
$313$	7.63759	−	2.77986i	0.431702	−	0.157127i	0.548726	+	0.836002i	$0.315113\pi$
$314$	5.45341	−	12.5970i	0.307754	−	0.710891i
$315$	3.49037	−	4.89318i	0.196660	−	0.275700i
$316$	14.5870	−	13.6900i	0.820581	−	0.770124i
$317$	−13.1057	−	2.31088i	−0.736088	−	0.129792i	−0.206978	−	0.978346i	$-0.566363\pi$
$317$	−13.1057	−	2.31088i	−0.736088	−	0.129792i	−0.529110	+	0.848554i	$0.677474\pi$
$318$	−2.37099	+	21.9726i	−0.132958	+	1.23216i
$319$	4.36619	−	11.9960i	0.244460	−	0.671647i
$320$	10.3988	−	12.1968i	0.581309	−	0.681819i
$321$	−0.826315	+	17.2007i	−0.0461204	+	0.960049i
$322$	−3.96631	−	0.236226i	−0.221034	−	0.0131644i
$323$	−24.8920			−1.38503
$324$	−17.1366	−	5.50797i	−0.952032	−	0.305998i
$325$	3.45760			0.191793
$326$	4.76101	+	0.283556i	0.263688	+	0.0157047i
$327$	−1.51376	+	31.5107i	−0.0837112	+	1.74254i
$328$	3.04274	−	1.74082i	0.168007	−	0.0961205i
$329$	−0.0196923	+	0.0541041i	−0.00108567	+	0.00298285i
$330$	−0.917805	+	8.50556i	−0.0505235	+	0.468216i
$331$	24.5999	+	4.33762i	1.35213	+	0.238417i	0.802331	−	0.596880i	$-0.203593\pi$
$331$	24.5999	+	4.33762i	1.35213	+	0.238417i	0.549799	+	0.835297i	$0.314704\pi$
$332$	−13.5748	−	14.4642i	−0.745012	−	0.793823i
$333$	−2.64902	−	5.81293i	−0.145165	−	0.318547i
$334$	−9.79170	+	22.6182i	−0.535778	+	1.23761i
$335$	−9.41437	+	3.42655i	−0.514362	+	0.187213i
$336$	3.07879	−	6.20654i	0.167962	−	0.338594i
$337$	16.7491	−	14.0542i	0.912383	−	0.765580i	−0.0601881	−	0.998187i	$-0.519170\pi$
$337$	16.7491	−	14.0542i	0.912383	−	0.765580i	0.972571	+	0.232607i	$0.0747256\pi$
$338$	−0.967615	−	0.230668i	−0.0526313	−	0.0125467i
$339$	−6.64837	−	2.78794i	−0.361090	−	0.151420i
$340$	1.05842	+	19.0314i	0.0574010	+	1.03212i
$341$	13.5416	−	7.81825i	0.733319	−	0.423382i
$342$	13.9441	−	17.2755i	0.754013	−	0.934154i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	−2.30363	+	0.396862i	−0.124203	+	0.0213974i
$345$	−2.15178	+	9.50924i	−0.115848	+	0.511960i
$346$	−26.3259	+	7.84390i	−1.41529	+	0.421691i
$347$	2.30236	+	13.0573i	0.123597	+	0.700955i	0.982131	+	0.188198i	$0.0602647\pi$
$347$	2.30236	+	13.0573i	0.123597	+	0.700955i	−0.858534	+	0.512757i	$0.828624\pi$
$348$	16.4527	+	19.3094i	0.881955	+	1.03509i
$349$	17.5168	+	14.6984i	0.937654	+	0.786785i	0.977176	−	0.212433i	$-0.0681388\pi$
$349$	17.5168	+	14.6984i	0.937654	+	0.786785i	−0.0395212	+	0.999219i	$0.512583\pi$
$350$	−1.11959	+	0.831229i	−0.0598448	+	0.0444311i
$351$	9.58791	+	15.4945i	0.511765	+	0.827037i
$352$	0.508874	+	9.84802i	0.0271231	+	0.524901i
$353$	13.1438	−	15.6641i	0.699572	−	0.833718i	−0.292906	−	0.956141i	$-0.594622\pi$
$353$	13.1438	−	15.6641i	0.699572	−	0.833718i	0.992478	+	0.122424i	$0.0390667\pi$
$354$	16.2979	+	8.00502i	0.866226	+	0.425462i
$355$	−7.24545	+	1.27757i	−0.384548	+	0.0678063i
$356$	11.7988	+	8.83203i	0.625335	+	0.468097i
$357$	2.44321	+	7.86860i	0.129308	+	0.416450i
$358$	−22.0855	+	11.0556i	−1.16726	+	0.584305i
$359$	−2.44547	+	4.23569i	−0.129067	+	0.223551i	−0.923315	−	0.384042i	$-0.874532\pi$
$359$	−2.44547	+	4.23569i	−0.129067	+	0.223551i	0.794248	+	0.607593i	$0.207865\pi$
$360$	−13.8011	−	9.92657i	−0.727382	−	0.523176i
$361$	4.19120	+	7.25938i	0.220590	+	0.382072i
$362$	−17.6382	−	11.6339i	−0.927041	−	0.611466i
$363$	8.34642	+	10.9762i	0.438074	+	0.576104i
$364$	−6.44699	+	2.76095i	−0.337914	+	0.144713i
$365$	18.5569	+	22.1153i	0.971313	+	1.15757i
$366$	2.73628	−	9.44371i	0.143028	−	0.493631i
$367$	0.0608091	+	0.167072i	0.00317421	+	0.00872107i	0.941270	−	0.337656i	$-0.109634\pi$
$367$	0.0608091	+	0.167072i	0.00317421	+	0.00872107i	−0.938095	+	0.346377i	$0.887412\pi$
$368$	−0.712237	+	11.2157i	−0.0371279	+	0.584659i
$369$	−2.10596	−	3.06427i	−0.109632	−	0.159519i
$370$	−0.692566	−	5.99337i	−0.0360048	−	0.311580i
$371$	−1.56672	+	8.88529i	−0.0813398	+	0.461301i
$372$	0.234736	+	31.0717i	0.0121705	+	1.61099i
$373$	19.0554	+	6.93558i	0.986649	+	0.359111i	0.784422	−	0.620228i	$-0.212960\pi$
$373$	19.0554	+	6.93558i	0.986649	+	0.359111i	0.202227	+	0.979339i	$0.435182\pi$
$374$	−8.51945	−	8.05881i	−0.440530	−	0.416711i
$375$	9.51102	+	18.4671i	0.491147	+	0.953635i
$376$	0.152809	+	0.0562992i	0.00788054	+	0.00290341i
$377$		−	25.6797i		−	1.32257i
$378$	−6.82962	−	2.71224i	−0.351278	−	0.139503i
$379$			19.1041i			0.981312i	0.871353	+	0.490656i	$0.163243\pi$
$379$			19.1041i			0.981312i	−0.871353	+	0.490656i	$0.836757\pi$
$380$	17.5485	−	11.4761i	0.900220	−	0.588710i
$381$	−7.38244	+	11.4771i	−0.378214	+	0.587991i
$382$	−6.31871	+	6.67989i	−0.323293	+	0.341773i
$383$	−17.1625	−	6.24664i	−0.876963	−	0.319188i	−0.135979	−	0.990712i	$-0.543418\pi$
$383$	−17.1625	−	6.24664i	−0.876963	−	0.319188i	−0.740983	+	0.671523i	$0.765640\pi$
$384$	−17.5204	−	8.77705i	−0.894083	−	0.447902i
$385$	−0.606473	+	3.43948i	−0.0309087	+	0.175292i
$386$	1.05878	−	0.122348i	0.0538906	−	0.00622734i
$387$	0.620752	+	2.40039i	0.0315546	+	0.122019i
$388$	−3.41131	+	0.799060i	−0.173183	+	0.0405661i
$389$	−4.76768	−	13.0991i	−0.241731	−	0.664151i	−0.999927	−	0.0121232i	$-0.996141\pi$
$389$	−4.76768	−	13.0991i	−0.241731	−	0.664151i	0.758195	−	0.652027i	$-0.226081\pi$
$390$	4.11696	+	16.7093i	0.208470	+	0.846110i
$391$	−8.59076	−	10.2381i	−0.434454	−	0.517762i
$392$	1.42383	−	2.44391i	0.0719143	−	0.123436i
$393$	−33.4459	+	4.25464i	−1.68712	+	0.214618i
$394$	7.82438	−	11.8625i	0.394187	−	0.597625i
$395$	−10.0199	−	17.3550i	−0.504157	−	0.873226i
$396$	10.3655	−	1.39824i	0.520884	−	0.0702642i
$397$	−6.02168	+	10.4298i	−0.302219	+	0.523459i	−0.976638	−	0.214890i	$-0.931061\pi$
$397$	−6.02168	+	10.4298i	−0.302219	+	0.523459i	0.674419	+	0.738349i	$0.264394\pi$
$398$	13.2982	+	26.5656i	0.666578	+	1.33161i
$399$	6.15236	−	6.65550i	0.308003	−	0.333192i
$400$	2.33861	+	3.17591i	0.116930	+	0.158795i
$401$	0.898441	−	0.158419i	0.0448660	−	0.00791109i	−0.151170	−	0.988508i	$-0.548304\pi$
$401$	0.898441	−	0.158419i	0.0448660	−	0.00791109i	0.196036	+	0.980597i	$0.437193\pi$
$402$	6.82127	+	10.1736i	0.340214	+	0.507415i
$403$	20.2184	−	24.0954i	1.00715	−	1.20028i
$404$	16.8444	+	5.09101i	0.838039	+	0.253287i
$405$	−9.28727	+	15.4557i	−0.461488	+	0.768002i
$406$	6.17358	+	8.31528i	0.306390	+	0.412680i
$407$	2.84351	+	2.38599i	0.140948	+	0.118269i
$408$	22.2828	−	6.82292i	1.10316	−	0.337785i
$409$	−1.12082	−	6.35646i	−0.0554208	−	0.314307i	0.944477	−	0.328576i	$-0.106569\pi$
$409$	−1.12082	−	6.35646i	−0.0554208	−	0.314307i	−0.999898	+	0.0142695i	$0.995458\pi$
$410$	−1.00274	−	3.36544i	−0.0495220	−	0.166207i
$411$	−10.6789	−	9.87156i	−0.526749	−	0.486928i
$412$	−10.7031	+	21.1731i	−0.527303	+	1.04312i
$413$	6.41973	+	3.70643i	0.315894	+	0.182382i
$414$	11.9179	−	0.226939i	0.585731	−	0.0111534i
$415$	−17.2089	+	9.93557i	−0.844752	+	0.487718i
$416$	7.73740	+	18.2654i	0.379357	+	0.895534i
$417$	−2.40374	−	18.8959i	−0.117712	−	0.925335i
$418$	−2.99149	+	12.5488i	−0.146318	+	0.613781i
$419$	−5.01219	+	4.20573i	−0.244862	+	0.205463i	−0.756956	−	0.653466i	$-0.773314\pi$
$419$	−5.01219	+	4.20573i	−0.244862	+	0.205463i	0.512094	+	0.858929i	$0.328870\pi$
$420$	−5.35013	−	4.42085i	−0.261060	−	0.215716i
$421$	−14.9816	+	5.45285i	−0.730158	+	0.265756i	−0.680232	−	0.732997i	$-0.738121\pi$
$421$	−14.9816	+	5.45285i	−0.730158	+	0.265756i	−0.0499262	+	0.998753i	$0.515899\pi$
$422$	7.52522	+	3.25777i	0.366322	+	0.158586i
$423$	0.0461619	−	0.166446i	0.00224447	−	0.00809290i
$424$	25.1138	+	4.53009i	1.21963	+	0.220000i
$425$	−4.61909	−	0.814470i	−0.224059	−	0.0395076i
$426$	3.63581	+	8.22745i	0.176156	+	0.398621i
$427$	1.37285	−	3.77188i	0.0664370	−	0.182534i
$428$	19.7440	+	2.36020i	0.954361	+	0.114085i
$429$	−8.90473	−	5.72780i	−0.429925	−	0.276541i
$430$	−0.139217	+	2.33750i	−0.00671365	+	0.112724i
$431$	−18.2528			−0.879208			−0.439604	−	0.898192i	$-0.644881\pi$
$431$	−18.2528			−0.879208			−0.439604	+	0.898192i	$0.644881\pi$
$432$	−7.74725	+	19.2868i	−0.372740	+	0.927936i
$433$	−28.5758			−1.37326			−0.686632	−	0.727005i	$-0.740912\pi$
$433$	−28.5758			−1.37326			−0.686632	+	0.727005i	$0.740912\pi$
$434$	−0.754177	+	12.6629i	−0.0362017	+	0.607838i
$435$	22.5922	−	11.6356i	1.08321	−	0.557882i
$436$	36.1698	+	4.32375i	1.73222	+	0.207070i
$437$	−5.02838	+	13.8154i	−0.240540	+	0.660878i
$438$	20.8255	−	28.4975i	0.995082	−	1.36166i
$439$	−0.603074	−	0.106338i	−0.0287831	−	0.00507524i	0.159238	−	0.987240i	$-0.449096\pi$
$439$	−0.603074	−	0.106338i	−0.0287831	−	0.00507524i	−0.188021	+	0.982165i	$0.560207\pi$
$440$	9.72150	+	1.75359i	0.463454	+	0.0835991i
$441$	−2.70774	−	1.29157i	−0.128940	−	0.0615032i
$442$	−21.6486	−	9.37197i	−1.02972	−	0.445779i
$443$	−0.195223	+	0.0710553i	−0.00927532	+	0.00337594i	−0.346654	−	0.937993i	$-0.612682\pi$
$443$	−0.195223	+	0.0710553i	−0.00927532	+	0.00337594i	0.337378	+	0.941369i	$0.390460\pi$
$444$	−6.91221	+	2.57514i	−0.328039	+	0.122211i
$445$	11.3099	−	9.49013i	0.536140	−	0.449875i
$446$	8.91614	−	37.4017i	0.422192	−	1.77102i
$447$	−18.1303	+	13.7864i	−0.857535	+	0.652076i
$448$	−6.89655	−	4.05434i	−0.325831	−	0.191550i
$449$	−32.0144	+	18.4835i	−1.51085	+	0.872292i	−0.510935	+	0.859619i	$0.670701\pi$
$449$	−32.0144	+	18.4835i	−1.51085	+	0.872292i	−0.999920	+	0.0126729i	$0.995966\pi$
$450$	3.15281	−	2.74949i	0.148625	−	0.129612i
$451$	1.87108	+	1.08027i	0.0881056	+	0.0508678i
$452$	−3.75553	+	7.42926i	−0.176645	+	0.349443i
$453$	−34.5960	+	10.7421i	−1.62546	+	0.504709i
$454$	1.44705	+	4.85663i	0.0679134	+	0.227933i
$455$	1.21998	+	6.91883i	0.0571933	+	0.324360i
$456$	−18.7561	−	17.4754i	−0.878333	−	0.818358i
$457$	3.83236	+	3.21573i	0.179270	+	0.150426i	0.728007	−	0.685569i	$-0.240447\pi$
$457$	3.83236	+	3.21573i	0.179270	+	0.150426i	−0.548737	+	0.835995i	$0.684891\pi$
$458$	−2.74214	−	3.69342i	−0.128132	−	0.172582i
$459$	−9.15884	−	22.9581i	−0.427498	−	1.07159i
$460$	10.7765	+	3.25706i	0.502456	+	0.151861i
$461$	15.5814	−	18.5692i	0.725700	−	0.864855i	−0.269472	−	0.963008i	$-0.586849\pi$
$461$	15.5814	−	18.5692i	0.725700	−	0.864855i	0.995171	+	0.0981531i	$0.0312935\pi$
$462$	4.26042	−	0.286057i	0.198212	−	0.0133086i
$463$	9.96973	−	1.75793i	0.463333	−	0.0816980i	0.0628912	−	0.998020i	$-0.479968\pi$
$463$	9.96973	−	1.75793i	0.463333	−	0.0816980i	0.400441	+	0.916322i	$0.368857\pi$
$464$	23.5876	−	17.3689i	1.09503	−	0.806333i
$465$	30.3593	+	6.86981i	1.40788	+	0.318580i
$466$	−15.2580	−	30.4807i	−0.706814	−	1.41199i
$467$	−0.556444	+	0.963790i	−0.0257492	+	0.0445989i	−0.878613	−	0.477535i	$-0.841530\pi$
$467$	−0.556444	+	0.963790i	−0.0257492	+	0.0445989i	0.852864	+	0.522134i	$0.174864\pi$
$468$	18.6316	−	9.77455i	0.861246	−	0.451829i
$469$	2.50027	+	4.33060i	0.115452	+	0.199969i
$470$	0.0898227	−	0.136180i	0.00414321	−	0.00628150i
$471$	−6.50141	+	15.5038i	−0.299569	+	0.714379i
$472$	10.5547	−	18.1164i	0.485818	−	0.833875i
$473$	−0.926059	−	1.10363i	−0.0425802	−	0.0507451i
$474$	−17.6716	+	16.9709i	−0.811682	+	0.779497i
$475$	1.76469	+	4.84845i	0.0809696	+	0.222462i
$476$	9.26306	−	2.16977i	0.424572	−	0.0994511i
$477$	2.59460	−	26.9424i	0.118798	−	1.23361i
$478$	14.0911	−	1.62830i	0.644513	−	0.0744769i
$479$	3.57944	−	20.3000i	0.163549	−	0.927532i	−0.786999	−	0.616954i	$-0.788366\pi$
$479$	3.57944	−	20.3000i	0.163549	−	0.927532i	0.950548	−	0.310578i	$-0.100523\pi$
$480$	−12.5634	+	15.0832i	−0.573440	+	0.688451i
$481$	7.01661	+	2.55384i	0.319930	+	0.116445i
$482$	−11.4544	+	12.1092i	−0.521736	+	0.551558i
$483$	4.86072	+	0.233507i	0.221171	+	0.0106250i
$484$	13.3258	−	8.71458i	0.605718	−	0.396117i
$485$			3.50977i			0.159370i
$486$	21.0640	+	6.50437i	0.955484	+	0.295044i
$487$		−	42.2218i		−	1.91325i	−0.291318	−	0.956626i	$-0.594094\pi$
$487$		−	42.2218i		−	1.91325i	0.291318	−	0.956626i	$-0.405906\pi$
$488$	−10.6531	−	3.92492i	−0.482245	−	0.177673i
$489$	−5.83462	−	0.280293i	−0.263851	−	0.0126753i
$490$	−2.05837	−	1.94707i	−0.0929876	−	0.0879598i
$491$	−25.4312	−	9.25619i	−1.14769	−	0.417726i	−0.303007	−	0.952988i	$-0.597991\pi$
$491$	−25.4312	−	9.25619i	−1.14769	−	0.417726i	−0.844686	+	0.535262i	$0.820213\pi$
$492$	−3.70185	+	2.17471i	−0.166892	+	0.0980437i
$493$	−6.04911	+	34.3062i	−0.272438	+	1.54507i
$494$	2.97888	+	25.7788i	0.134026	+	1.15984i
$495$	1.00436	−	10.4294i	0.0451428	−	0.468765i
$496$	35.8074	+	2.27390i	1.60780	+	0.102101i
$497$	1.25596	+	3.45073i	0.0563377	+	0.154787i
$498$	16.8280	+	17.5228i	0.754080	+	0.785215i
$499$	20.0662	+	23.9139i	0.898285	+	1.07053i	0.997151	+	0.0754336i	$0.0240341\pi$
$499$	20.0662	+	23.9139i	0.898285	+	1.07053i	−0.0988658	+	0.995101i	$0.531521\pi$
$500$	22.0490	−	9.44258i	0.986063	−	0.422285i
$501$	11.6734	−	27.8374i	0.521529	−	1.24368i
$502$	2.03638	+	1.34317i	0.0908880	+	0.0599487i
$503$	−5.34666	−	9.26069i	−0.238396	−	0.412914i	0.721858	−	0.692041i	$-0.243288\pi$
$503$	−5.34666	−	9.26069i	−0.238396	−	0.412914i	−0.960254	+	0.279127i	$0.909955\pi$
$504$	−3.68318	+	7.64423i	−0.164062	+	0.340501i
$505$	8.81383	−	15.2660i	0.392210	−	0.679328i
$506$	−6.19374	+	3.10046i	−0.275345	+	0.137832i
$507$	1.18825	+	0.268881i	0.0527719	+	0.0119414i
$508$	12.6148	+	9.44284i	0.559691	+	0.418958i
$509$	2.67638	−	0.471919i	0.118629	−	0.0209174i	−0.114019	−	0.993479i	$-0.536372\pi$
$509$	2.67638	−	0.471919i	0.118629	−	0.0209174i	0.232647	+	0.972561i	$0.425261\pi$
$510$	−1.56391	−	23.2922i	−0.0692510	−	1.03140i
$511$	9.26227	−	11.0383i	0.409739	−	0.488308i
$512$	−11.5440	+	19.4612i	−0.510177	+	0.860070i
$513$	−16.8339	+	21.3529i	−0.743234	+	0.942752i
$514$	−25.8332	+	19.1795i	−1.13945	+	0.845973i
$515$	18.2058	+	15.2765i	0.802244	+	0.673163i
$516$	2.81559	−	0.518425i	0.123949	−	0.0228224i
$517$	0.0174288	+	0.0988436i	0.000766518	+	0.00434714i
$518$	−2.88599	+	0.859889i	−0.126803	+	0.0377813i
$519$	32.1301	−	9.97644i	1.41035	−	0.437917i
$520$	19.5828	−	3.37367i	0.858763	−	0.147945i
$521$	−9.48007	−	5.47332i	−0.415329	−	0.239790i	0.277748	−	0.960654i	$-0.410412\pi$
$521$	−9.48007	−	5.47332i	−0.415329	−	0.239790i	−0.693077	+	0.720864i	$0.743745\pi$
$522$	−20.4206	−	23.4161i	−0.893784	−	1.02489i
$523$	−16.4289	+	9.48522i	−0.718385	+	0.414760i	−0.814158	−	0.580643i	$-0.802801\pi$
$523$	−16.4289	+	9.48522i	−0.718385	+	0.414760i	0.0957729	+	0.995403i	$0.469468\pi$
$524$	2.16180	+	38.8711i	0.0944386	+	1.69809i
$525$	1.35943	−	1.03372i	0.0593306	−	0.0451155i
$526$	−27.0958	−	6.45932i	−1.18143	−	0.281640i
$527$	−32.6862	+	27.4270i	−1.42383	+	1.19474i
$528$	−0.761721	−	12.0534i	−0.0331497	−	0.524555i
$529$	14.1953	−	5.16665i	0.617185	−	0.224637i
$530$	10.1560	−	23.4597i	0.441148	−	1.01902i
$531$	−20.0721	−	9.57421i	−0.871055	−	0.415485i
$532$	−7.16199	−	7.63122i	−0.310511	−	0.330856i
$533$	4.28009	+	0.754695i	0.185391	+	0.0326895i
$534$	−14.5738	−	10.6503i	−0.630670	−	0.460884i
$535$	6.81280	−	18.7180i	0.294543	−	0.809250i
$536$	12.2765	−	7.02364i	0.530264	−	0.303375i
$537$	26.8919	−	13.8500i	1.16047	−	0.597672i
$538$	32.1184	+	1.91291i	1.38472	+	0.0824713i
$539$	1.74322			0.0750860
$540$	17.0413	+	11.9626i	0.733343	+	0.514788i
$541$	−17.3929			−0.747781			−0.373891	−	0.927473i	$-0.621976\pi$
$541$	−17.3929			−0.747781			−0.373891	+	0.927473i	$0.621976\pi$
$542$	15.8877	+	0.946240i	0.682435	+	0.0406445i
$543$	21.7645	+	13.9996i	0.934003	+	0.600779i
$544$	−6.03400	−	26.2238i	−0.258706	−	1.12434i
$545$	12.4807	−	34.2903i	0.534613	−	1.46884i
$546$	7.85656	−	3.47191i	0.336230	−	0.148584i
$547$	−43.1805	−	7.61388i	−1.84626	−	0.325546i	−0.862645	−	0.505809i	$-0.831194\pi$
$547$	−43.1805	−	7.61388i	−1.84626	−	0.325546i	−0.983618	+	0.180263i	$0.942305\pi$
$548$	−12.2444	+	11.4915i	−0.523056	+	0.490893i
$549$	−3.21819	+	11.6039i	−0.137349	+	0.495241i
$550$	−0.965715	+	2.23074i	−0.0411782	+	0.0951190i
$551$	36.0097	−	13.1065i	1.53406	−	0.558354i
$552$	0.714491	−	13.7455i	0.0304108	−	0.585047i
$553$	−7.66232	+	6.42945i	−0.325835	+	0.273408i
$554$	−38.9583	−	9.28720i	−1.65518	−	0.394575i
$555$	0.932463	+	7.33012i	0.0395809	+	0.311146i
$556$	−21.9610	+	1.22135i	−0.931353	+	0.0517967i
$557$	37.7417	−	21.7902i	1.59917	−	0.923279i	0.607517	−	0.794307i	$-0.292166\pi$
$557$	37.7417	−	21.7902i	1.59917	−	0.923279i	0.991648	−	0.128972i	$-0.0411677\pi$
$558$	−0.724526	−	38.0491i	−0.0306717	−	1.61075i
$559$	−2.50981	−	1.44904i	−0.106154	−	0.0612879i
$560$	−5.53000	+	5.80025i	−0.233685	+	0.245105i
$561$	10.5468	+	9.74950i	0.445287	+	0.411624i
$562$	26.6948	−	7.95381i	1.12605	−	0.335511i
$563$	−1.20102	−	6.81131i	−0.0506169	−	0.287062i	0.948984	−	0.315325i	$-0.102114\pi$
$563$	−1.20102	−	6.81131i	−0.0506169	−	0.287062i	−0.999601	+	0.0282628i	$0.991002\pi$
$564$	−0.187932	−	0.0667982i	−0.00791336	−	0.00281271i
$565$	6.38811	+	5.36026i	0.268750	+	0.225508i
$566$	−36.9962	+	27.4674i	−1.55506	+	1.15454i
$567$	8.40214	+	3.22552i	0.352857	+	0.135459i
$568$	9.77404	−	3.51401i	0.410109	−	0.147445i
$569$	23.5561	−	28.0730i	0.987522	−	1.17688i	0.00329152	−	0.999995i	$-0.498952\pi$
$569$	23.5561	−	28.0730i	0.987522	−	1.17688i	0.984231	−	0.176889i	$-0.0566033\pi$
$570$	−21.3296	+	14.3012i	−0.893399	+	0.599010i
$571$	−33.1800	+	5.85053i	−1.38854	+	0.244837i	−0.817426	−	0.576033i	$-0.804600\pi$
$571$	−33.1800	+	5.85053i	−1.38854	+	0.244837i	−0.571114	+	0.820871i	$0.693489\pi$
$572$	−7.32639	+	9.78740i	−0.306332	+	0.409232i
$573$	7.64434	−	8.26950i	0.319347	−	0.345463i
$574$	−1.56736	+	0.784586i	−0.0654201	+	0.0327480i
$575$	−1.38514	+	2.39912i	−0.0577641	+	0.100050i
$576$	21.5800	+	10.5025i	0.899168	+	0.437604i
$577$	11.5245	+	19.9610i	0.479771	+	0.830988i	0.999731	−	0.0232028i	$-0.00738633\pi$
$577$	11.5245	+	19.9610i	0.479771	+	0.830988i	−0.519960	+	0.854191i	$0.674053\pi$
$578$	6.64413	+	4.38239i	0.276359	+	0.182284i
$579$	−1.29493	+	0.164728i	−0.0538155	+	0.00684585i
$580$	−11.5518	−	26.9743i	−0.479663	−	1.12005i
$581$	6.37532	+	7.59781i	0.264493	+	0.315210i
$582$	4.16647	−	1.02656i	0.172706	−	0.0425524i
$583$	5.37929	+	14.7795i	0.222787	+	0.612103i
$584$	−31.1179	−	26.3202i	−1.28767	−	1.08914i
$585$	−5.27693	−	20.4054i	−0.218174	−	0.843660i
$586$	−4.55530	−	39.4209i	−0.188178	−	1.62846i
$587$	−2.76739	+	15.6947i	−0.114222	+	0.647788i	0.872910	+	0.487882i	$0.162230\pi$
$587$	−2.76739	+	15.6947i	−0.114222	+	0.647788i	−0.987132	+	0.159906i	$0.948881\pi$
$588$	−1.70934	+	3.01300i	−0.0704919	+	0.124254i
$589$	44.1071	+	16.0537i	1.81740	+	0.661480i
$590$	−15.2584	−	14.4334i	−0.628179	−	0.594214i
$591$	−9.41538	+	14.6377i	−0.387297	+	0.602113i
$592$	2.40003	+	8.17230i	0.0986406	+	0.335879i
$593$			8.14603i			0.334517i	0.985913	+	0.167259i	$0.0534915\pi$
$593$			8.14603i			0.334517i	−0.985913	+	0.167259i	$0.946509\pi$
$594$	−12.6745	+	1.85817i	−0.520043	+	0.0762418i
$595$		−	9.53041i		−	0.390709i
$596$	14.3946	+	22.0113i	0.589624	+	0.901617i
$597$	−16.6595	−	32.3469i	−0.681827	−	1.32387i
$598$	−9.57476	+	10.1221i	−0.391541	+	0.413922i
$599$	−25.3928	−	9.24221i	−1.03752	−	0.377627i	−0.233581	−	0.972337i	$-0.575044\pi$
$599$	−25.3928	−	9.24221i	−1.03752	−	0.377627i	−0.803940	+	0.594711i	$0.797267\pi$
$600$	−2.90868	−	3.85652i	−0.118746	−	0.157442i
$601$	6.76894	−	38.3886i	0.276111	−	1.56590i	−0.459300	−	0.888281i	$-0.651900\pi$
$601$	6.76894	−	38.3886i	0.276111	−	1.56590i	0.735411	−	0.677622i	$-0.236989\pi$
$602$	1.16105	−	0.134166i	0.0473211	−	0.00546820i
$603$	−8.49687	−	12.3634i	−0.346019	−	0.503475i
$604$	9.53985	+	40.7271i	0.388171	+	1.65716i
$605$	−5.45528	−	14.9882i	−0.221789	−	0.609359i
$606$	−20.7003	−	5.99784i	−0.840893	−	0.243646i
$607$	4.74162	+	5.65084i	0.192456	+	0.229361i	0.853640	−	0.520864i	$-0.174390\pi$
$607$	4.74162	+	5.65084i	0.192456	+	0.229361i	−0.661184	+	0.750224i	$0.729946\pi$
$608$	−21.6638	+	20.1722i	−0.878584	+	0.818089i
$609$	−7.67752	−	10.0966i	−0.311109	−	0.409134i
$610$	−6.26201	+	9.49381i	−0.253542	+	0.384393i
$611$	0.100950	+	0.174851i	0.00408401	+	0.00707371i
$612$	−27.1929	+	8.66921i	−1.09921	+	0.350432i
$613$	−4.76433	+	8.25207i	−0.192430	+	0.333298i	−0.946055	−	0.324006i	$-0.894970\pi$
$613$	−4.76433	+	8.25207i	−0.192430	+	0.333298i	0.753625	+	0.657304i	$0.228303\pi$
$614$	−10.6171	−	21.2096i	−0.428471	−	0.855950i
$615$	1.27536	+	4.10743i	0.0514276	+	0.165628i
$616$	0.0193797	−	4.93054i	0.000780832	−	0.198657i
$617$	16.2690	−	2.86866i	0.654965	−	0.115488i	0.163717	−	0.986507i	$-0.447652\pi$
$617$	16.2690	−	2.86866i	0.654965	−	0.115488i	0.491249	+	0.871019i	$0.336541\pi$
$618$	12.8099	−	26.0804i	0.515288	−	1.04911i
$619$	−10.7932	+	12.8629i	−0.433817	+	0.517003i	−0.938019	−	0.346583i	$-0.887342\pi$
$619$	−10.7932	+	12.8629i	−0.433817	+	0.517003i	0.504203	+	0.863585i	$0.331787\pi$
$620$	10.3985	−	34.4051i	0.417615	−	1.38174i
$621$	−14.5922	+	0.445560i	−0.585564	+	0.0178797i
$622$	18.7049	+	25.1939i	0.749997	+	1.01018i
$623$	−5.64508	−	4.73679i	−0.226166	−	0.189775i
$624$	−9.73264	−	22.2601i	−0.389617	−	0.891119i
$625$	−3.31629	−	18.8076i	−0.132651	−	0.752304i
$626$	3.28220	+	11.0158i	0.131183	+	0.440280i
$627$	3.48705	−	15.4101i	0.139260	−	0.615421i
$628$	17.3248	+	8.75779i	0.691337	+	0.349474i
$629$	−8.77208	−	5.06456i	−0.349766	−	0.201937i
$630$	6.61430	+	5.33880i	0.263520	+	0.212703i
$631$	14.6008	−	8.42977i	0.581248	−	0.335584i	−0.180381	−	0.983597i	$-0.557733\pi$
$631$	14.6008	−	8.42977i	0.581248	−	0.335584i	0.761629	+	0.648013i	$0.224400\pi$
$632$	18.0999	+	21.7436i	0.719976	+	0.864915i
$633$	−9.26169	−	3.88382i	−0.368119	−	0.154368i
$634$	4.36421	−	18.3071i	0.173325	−	0.727069i
$635$	12.0921	−	10.1464i	0.479859	−	0.402649i
$636$	−30.8197	−	5.19458i	−1.22208	−	0.205979i
$637$	3.29518	−	1.19935i	0.130560	−	0.0475198i
$638$	16.5678	+	7.17241i	0.655925	+	0.283958i
$639$	−4.56838	−	10.0247i	−0.180722	−	0.396572i
$640$	16.3440	+	15.7056i	0.646053	+	0.620817i
$641$	−15.0975	−	2.66209i	−0.596314	−	0.105146i	−0.132658	−	0.991162i	$-0.542351\pi$
$641$	−15.0975	−	2.66209i	−0.596314	−	0.105146i	−0.463655	+	0.886016i	$0.653462\pi$
$642$	−24.2129	−	2.61273i	−0.955609	−	0.103116i
$643$	15.1620	−	41.6572i	0.597931	−	1.64280i	−0.157460	−	0.987525i	$-0.550330\pi$
$643$	15.1620	−	41.6572i	0.597931	−	1.64280i	0.755390	−	0.655275i	$-0.227447\pi$
$644$	0.666966	−	5.57943i	0.0262821	−	0.219860i
$645$	0.137615	−	2.86461i	0.00541859	−	0.112794i
$646$	2.09289	−	35.1403i	0.0823436	−	1.38258i
$647$	−3.43767			−0.135149			−0.0675744	−	0.997714i	$-0.521526\pi$
$647$	−3.43767			−0.135149			−0.0675744	+	0.997714i	$0.521526\pi$
$648$	9.21649	−	23.7288i	0.362058	−	0.932156i
$649$	12.9223			0.507244
$650$	−0.290711	+	4.88113i	−0.0114026	+	0.191454i
$651$	0.745498	−	15.5184i	0.0292184	−	0.608214i
$652$	−0.800600	+	6.69733i	−0.0313539	+	0.262288i
$653$	−11.6144	+	31.9104i	−0.454508	+	1.24875i	0.475013	+	0.879979i	$0.342443\pi$
$653$	−11.6144	+	31.9104i	−0.454508	+	1.24875i	−0.929521	+	0.368770i	$0.879779\pi$
$654$	−44.3567	−	4.78638i	−1.73448	−	0.187162i
$655$	38.4067	+	6.77214i	1.50067	+	0.264609i
$656$	2.20170	+	4.44184i	0.0859620	+	0.173425i
$657$	−25.1034	+	35.1928i	−0.979378	+	1.37300i
$658$	−0.0747237	−	0.0323488i	−0.00291303	−	0.00126109i
$659$	34.8234	−	12.6747i	1.35653	−	0.493736i	0.441549	−	0.897237i	$-0.354429\pi$
$659$	34.8234	−	12.6747i	1.35653	−	0.493736i	0.914979	+	0.403501i	$0.132207\pi$
$660$	−11.9302	−	2.01081i	−0.464384	−	0.0782709i
$661$	14.8549	−	12.4647i	0.577787	−	0.484821i	−0.306432	−	0.951892i	$-0.599135\pi$
$661$	14.8549	−	12.4647i	0.577787	−	0.484821i	0.884220	+	0.467071i	$0.154691\pi$
$662$	−8.19179	+	34.3632i	−0.318383	+	1.33556i
$663$	26.6441	+	11.1730i	1.03477	+	0.433924i
$664$	21.5606	−	17.9475i	0.836712	−	0.696499i
$665$	−9.07935	+	5.24196i	−0.352082	+	0.203275i
$666$	8.42891	−	3.25090i	0.326614	−	0.125970i
$667$	17.8184	+	10.2875i	0.689932	+	0.398332i
$668$	−31.1071	−	15.7248i	−1.20357	−	0.608410i
$669$	−10.3932	+	45.9300i	−0.401824	+	1.77575i
$670$	−4.04575	−	13.5785i	−0.156301	−	0.524583i
$671$	−1.21505	−	6.89091i	−0.0469066	−	0.266021i
$672$	8.50298	+	4.86820i	0.328010	+	0.187795i
$673$	7.61356	+	6.38854i	0.293481	+	0.246260i	0.777625	−	0.628729i	$-0.216424\pi$
$673$	7.61356	+	6.38854i	0.293481	+	0.246260i	−0.484144	+	0.874989i	$0.660869\pi$
$674$	18.4322	+	24.8266i	0.709982	+	0.956285i
$675$	−3.82246	+	3.41155i	−0.147127	+	0.131311i
$676$	0.406993	−	1.34660i	0.0156536	−	0.0517923i
$677$	6.53994	−	7.79399i	0.251350	−	0.299548i	−0.625585	−	0.780156i	$-0.715140\pi$
$677$	6.53994	−	7.79399i	0.251350	−	0.299548i	0.876935	+	0.480608i	$0.159584\pi$
$678$	4.49476	−	9.15118i	0.172620	−	0.351449i
$679$	1.72521	−	0.304201i	0.0662074	−	0.0116742i
$680$	−26.9559	−	0.105951i	−1.03371	−	0.00406305i
$681$	−1.84046	−	5.92739i	−0.0705267	−	0.227138i
$682$	9.89856	+	19.7742i	0.379035	+	0.757193i
$683$	22.1261	−	38.3235i	0.846630	−	1.46641i	−0.0375677	−	0.999294i	$-0.511961\pi$
$683$	22.1261	−	38.3235i	0.846630	−	1.46641i	0.884198	−	0.467112i	$-0.154706\pi$
$684$	23.2157	+	21.1376i	0.887674	+	0.808217i
$685$	8.41081	+	14.5680i	0.321361	+	0.556613i
$686$	−0.778670	+	1.18054i	−0.0297298	+	0.0450732i
$687$	3.41015	+	4.48463i	0.130105	+	0.171099i
$688$	−0.366568	−	3.28542i	−0.0139753	−	0.125256i
$689$	20.3367	+	24.2363i	0.774766	+	0.923331i
$690$	−13.2434	−	3.83723i	−0.504167	−	0.146081i
$691$	7.12434	+	19.5740i	0.271023	+	0.744628i	0.998300	+	0.0582847i	$0.0185631\pi$
$691$	7.12434	+	19.5740i	0.271023	+	0.744628i	−0.727277	+	0.686344i	$0.759215\pi$
$692$	−8.85987	−	37.8241i	−0.336802	−	1.43786i
$693$	−5.21355	+	0.410251i	−0.198047	+	0.0155841i
$694$	−18.6268	+	2.15243i	−0.707063	+	0.0817050i
$695$	−3.82605	+	21.6986i	−0.145130	+	0.823075i
$696$	−28.6426	+	21.6029i	−1.08569	+	0.818856i
$697$	−5.54010	−	2.01643i	−0.209846	−	0.0763778i
$698$	−22.2227	+	23.4929i	−0.841140	+	0.889219i
$699$	19.1147	+	37.1140i	0.722984	+	1.40378i
$700$	−1.07932	−	1.65043i	−0.0407945	−	0.0623805i
$701$			48.7163i			1.83999i	0.391931	+	0.919994i	$0.371807\pi$
$701$			48.7163i			1.83999i	−0.391931	+	0.919994i	$0.628193\pi$
$702$	−22.6800	+	12.2326i	−0.856000	+	0.461690i
$703$			11.1425i			0.420249i
$704$	−13.9454	−	0.109628i	−0.525585	−	0.00413174i
$705$	−0.108087	+	0.168038i	−0.00407079	+	0.00632867i
$706$	21.0081	+	19.8722i	0.790651	+	0.747902i
$707$	−8.26785	−	3.00925i	−0.310944	−	0.113175i
$708$	−12.6711	+	22.3350i	−0.476209	+	0.839399i
$709$	8.63356	−	48.9634i	0.324240	−	1.83886i	−0.190721	−	0.981644i	$-0.561083\pi$
$709$	8.63356	−	48.9634i	0.324240	−	1.83886i	0.514961	−	0.857214i	$-0.327806\pi$
$710$	−1.19437	−	10.3359i	−0.0448239	−	0.387899i
$711$	21.4030	−	21.0322i	0.802676	−	0.788768i
$712$	−13.4603	+	15.9139i	−0.504447	+	0.596400i
$713$	8.61944	+	23.6817i	0.322801	+	0.886887i
$714$	−11.3136	+	2.78753i	−0.423402	+	0.104321i
$715$	7.87230	+	9.38184i	0.294407	+	0.350861i
$716$	−13.7504	−	32.1080i	−0.513875	−	1.19993i
$717$	−17.2340	+	2.19233i	−0.643615	+	0.0818741i
$718$	−5.77396	−	3.80844i	−0.215482	−	0.142130i
$719$	−16.0943	−	27.8761i	−0.600216	−	1.03960i	−0.992788	−	0.119883i	$-0.961748\pi$
$719$	−16.0943	−	27.8761i	−0.600216	−	1.03960i	0.392573	−	0.919721i	$-0.371585\pi$
$720$	15.1738	−	18.6486i	0.565495	−	0.694991i
$721$	5.93114	−	10.2730i	0.220887	−	0.382588i
$722$	−10.6005	+	5.30641i	−0.394511	+	0.197484i
$723$	13.8575	−	14.9908i	0.515367	−	0.557514i
$724$	17.9068	−	23.9218i	0.665500	−	0.889048i
$725$	7.11100	−	1.25386i	0.264096	−	0.0465672i
$726$	−16.1971	+	10.8599i	−0.601129	+	0.403048i
$727$	−4.61912	+	5.50485i	−0.171314	+	0.204164i	−0.844869	−	0.534973i	$-0.820322\pi$
$727$	−4.61912	+	5.50485i	−0.171314	+	0.204164i	0.673556	+	0.739137i	$0.264766\pi$
$728$	−3.35560	−	9.33343i	−0.124367	−	0.345920i
$729$	−25.8878	−	7.66938i	−0.958809	−	0.284051i
$730$	−32.7806	+	24.3376i	−1.21327	+	0.900774i
$731$	3.01159	+	2.52702i	0.111388	+	0.0934653i
$732$	13.1017	+	4.65686i	0.484254	+	0.172122i
$733$	−7.59105	−	43.0510i	−0.280382	−	1.59012i	−0.721330	−	0.692592i	$-0.756469\pi$
$733$	−7.59105	−	43.0510i	−0.280382	−	1.59012i	0.440948	−	0.897533i	$-0.354642\pi$
$734$	−0.240970	+	0.0717977i	−0.00889435	+	0.00265010i
$735$	2.54820	+	2.35556i	0.0939917	+	0.0868861i
$736$	−15.7735	−	1.94848i	−0.581418	−	0.0718218i
$737$	7.54921	+	4.35854i	0.278079	+	0.160549i
$738$	4.50293	−	2.71536i	0.165755	−	0.0999540i
$739$	−39.3259	+	22.7048i	−1.44663	+	0.835210i	−0.998279	−	0.0586495i	$-0.981321\pi$
$739$	−39.3259	+	22.7048i	−1.44663	+	0.835210i	−0.448347	+	0.893859i	$0.647987\pi$
$740$	8.51914	−	0.473788i	0.313170	−	0.0174168i
$741$	−4.01073	−	31.5285i	−0.147338	−	1.15823i
$742$	−12.4117	−	2.95882i	−0.455649	−	0.108622i
$743$	−23.5736	+	19.7806i	−0.864830	+	0.725678i	−0.963003	−	0.269491i	$-0.913145\pi$
$743$	−23.5736	+	19.7806i	−0.864830	+	0.725678i	0.0981732	+	0.995169i	$0.468700\pi$
$744$	−43.8840	−	2.28109i	−1.60887	−	0.0836289i
$745$	24.7573	−	9.01091i	0.907036	−	0.330134i
$746$	−11.3932	+	26.3175i	−0.417135	+	0.963554i
$747$	−20.8551	−	21.2228i	−0.763048	−	0.776502i
$748$	12.0930	−	11.3494i	0.442165	−	0.414976i
$749$	−9.79123	−	1.72646i	−0.357764	−	0.0630834i
$750$	−26.8698	+	11.8741i	−0.981148	+	0.433582i
$751$	−5.66164	+	15.5552i	−0.206596	+	0.567618i	−0.999108	−	0.0422389i	$-0.986551\pi$
$751$	−5.66164	+	15.5552i	−0.206596	+	0.567618i	0.792511	+	0.609857i	$0.208773\pi$
$752$	−0.0923263	+	0.210989i	−0.00336679	+	0.00769398i
$753$	−2.51277	−	1.61629i	−0.0915705	−	0.0589009i
$754$	36.2524	+	2.15912i	1.32023	+	0.0786306i
$755$	41.9026			1.52499
$756$	4.40313	−	9.41342i	0.160140	−	0.342363i
$757$	−50.0347			−1.81854			−0.909271	−	0.416205i	$-0.863360\pi$
$757$	−50.0347			−1.81854			−0.909271	+	0.416205i	$0.863360\pi$
$758$	−26.9695	−	1.60625i	−0.979576	−	0.0583417i
$759$	7.54164	−	3.88414i	0.273744	−	0.140985i
$760$	14.7255	+	25.7383i	0.534148	+	0.933628i
$761$	1.70579	−	4.68662i	0.0618349	−	0.169890i	−0.904928	−	0.425565i	$-0.860075\pi$
$761$	1.70579	−	4.68662i	0.0618349	−	0.169890i	0.966763	+	0.255675i	$0.0822977\pi$
$762$	−15.5817	−	11.3869i	−0.564465	−	0.412503i
$763$	−17.9370	−	3.16277i	−0.649362	−	0.114500i
$764$	−8.89881	−	9.48184i	−0.321948	−	0.343041i
$765$	2.24289	+	28.5031i	0.0810918	+	1.03053i
$766$	10.2615	−	23.7033i	0.370762	−	0.856435i
$767$	24.4267	−	8.89059i	0.881997	−	0.321021i
$768$	13.8638	−	23.9958i	0.500265	−	0.865872i
$769$	−36.5306	+	30.6528i	−1.31733	+	1.10537i	−0.330464	+	0.943819i	$0.607205\pi$
$769$	−36.5306	+	30.6528i	−1.31733	+	1.10537i	−0.986864	+	0.161551i	$0.948350\pi$
$770$	−4.80456	−	1.14535i	−0.173144	−	0.0412756i
$771$	31.3672	−	23.8518i	1.12966	−	0.859003i
$772$	0.0836988	+	1.50498i	0.00301239	+	0.0541655i
$773$	−23.2548	+	13.4262i	−0.836416	+	0.482905i	−0.856044	−	0.516902i	$-0.827085\pi$
$773$	−23.2548	+	13.4262i	−0.836416	+	0.482905i	0.0196282	+	0.999807i	$0.493752\pi$
$774$	−3.44086	+	0.674501i	−0.123679	+	0.0242444i
$775$	7.65947	+	4.42220i	0.275136	+	0.158850i
$776$	−0.841224	−	4.88297i	−0.0301982	−	0.175288i
$777$	3.52227	−	1.09367i	0.126361	−	0.0392352i
$778$	18.8930	−	5.62924i	0.677347	−	0.201818i
$779$	1.12620	+	6.38698i	0.0403502	+	0.228837i
$780$	−23.9349	+	4.40706i	−0.857007	+	0.157798i
$781$	4.90380	+	4.11478i	0.175472	+	0.147238i
$782$	15.1755	−	11.2669i	0.542675	−	0.402903i
$783$	25.3377	+	28.3896i	0.905496	+	1.01456i
$784$	3.33039	+	2.21552i	0.118942	+	0.0791257i
$785$	12.5000	−	14.8969i	0.446143	−	0.531693i
$786$	−3.19424	−	47.5736i	−0.113935	−	1.69690i
$787$	−4.24842	+	0.749112i	−0.151440	+	0.0267030i	−0.248854	−	0.968541i	$-0.580054\pi$
$787$	−4.24842	+	0.749112i	−0.151440	+	0.0267030i	0.0974142	+	0.995244i	$0.468943\pi$
$788$	16.0886	+	12.0432i	0.573132	+	0.429020i
$789$	33.2741	+	7.52937i	1.18459	+	0.268053i
$790$	25.3428	−	12.6861i	0.901655	−	0.451350i
$791$	2.08113	−	3.60463i	0.0739966	−	0.128166i
$792$	1.10239	+	14.7506i	0.0391719	+	0.524140i
$793$	−7.03777	−	12.1898i	−0.249919	−	0.432872i
$794$	−14.2176	−	9.37780i	−0.504565	−	0.332806i
$795$	−12.1077	+	28.8731i	−0.429416	+	1.02402i
$796$	−38.6211	+	16.5396i	−1.36889	+	0.586231i
$797$	−32.2934	−	38.4858i	−1.14389	−	1.36324i	−0.921547	−	0.388267i	$-0.873074\pi$
$797$	−32.2934	−	38.4858i	−1.14389	−	1.36324i	−0.222343	−	0.974968i	$-0.571371\pi$
$798$	8.87837	+	9.24495i	0.314291	+	0.327268i
$799$	−0.0936741	−	0.257367i	−0.00331395	−	0.00910500i
$800$	−4.68009	+	3.03441i	−0.165466	+	0.107283i
$801$	17.9978	+	12.8381i	0.635922	+	0.453610i
$802$	0.148103	+	1.28166i	0.00522969	+	0.0452570i
$803$	4.36188	−	24.7374i	0.153927	−	0.872965i
$804$	−14.9358	+	8.77428i	−0.526744	+	0.309445i
$805$	−5.28950	−	1.92522i	−0.186430	−	0.0678551i
$806$	32.3158	+	30.5685i	1.13827	+	1.07673i
$807$	−39.3611	−	1.89089i	−1.38558	−	0.0665626i
$808$	−8.60330	+	23.3514i	−0.302663	+	0.821498i
$809$		−	53.9333i		−	1.89619i	−0.317982	−	0.948097i	$-0.603005\pi$
$809$		−	53.9333i		−	1.89619i	0.317982	−	0.948097i	$-0.396995\pi$
$810$	−21.0382	−	14.4104i	−0.739207	−	0.506331i
$811$		−	20.3561i		−	0.714799i	−0.933952	−	0.357400i	$-0.883663\pi$
$811$		−	20.3561i		−	0.714799i	0.933952	−	0.357400i	$-0.116337\pi$
$812$	−12.2578	+	8.01618i	−0.430166	+	0.281313i
$813$	−19.4704	−	0.935351i	−0.682857	−	0.0328042i
$814$	−3.60741	+	3.81361i	−0.126440	+	0.133667i
$815$	6.34931	+	2.31096i	0.222407	+	0.0809494i
$816$	7.75848	+	32.0305i	0.271601	+	1.12129i
$817$	0.750973	−	4.25898i	0.0262732	−	0.149003i
$818$	9.06773	−	1.04783i	0.317046	−	0.0366363i
$819$	−9.57281	+	4.36244i	−0.334501	+	0.152436i
$820$	4.83534	−	1.13262i	0.168857	−	0.0395529i
$821$	9.07423	+	24.9313i	0.316693	+	0.870107i	0.991264	+	0.131896i	$0.0421066\pi$
$821$	9.07423	+	24.9313i	0.316693	+	0.870107i	−0.674571	+	0.738210i	$0.735671\pi$
$822$	14.8337	−	14.2455i	0.517383	−	0.496868i
$823$	−8.52193	−	10.1560i	−0.297056	−	0.354017i	0.596785	−	0.802401i	$-0.296444\pi$
$823$	−8.52193	−	10.1560i	−0.297056	−	0.354017i	−0.893841	+	0.448383i	$0.852000\pi$
$824$	−28.9904	−	16.8899i	−1.00993	−	0.588386i
$825$	1.15130	−	2.74549i	0.0400831	−	0.0955857i
$826$	−5.77218	+	8.75118i	−0.200840	+	0.304492i
$827$	3.43494	+	5.94950i	0.119445	+	0.206884i	0.919548	−	0.392978i	$-0.128555\pi$
$827$	3.43494	+	5.94950i	0.119445	+	0.206884i	−0.800103	+	0.599863i	$0.795222\pi$
$828$	−0.681668	+	16.8437i	−0.0236896	+	0.585358i
$829$	2.11338	−	3.66048i	0.0734008	−	0.127134i	−0.826989	−	0.562218i	$-0.809948\pi$
$829$	2.11338	−	3.66048i	0.0734008	−	0.127134i	0.900390	+	0.435084i	$0.143281\pi$
$830$	−12.5793	−	25.1294i	−0.436632	−	0.872254i
$831$	47.8414	+	10.8257i	1.65960	+	0.375540i
$832$	−26.4360	+	9.38725i	−0.916504	+	0.325444i
$833$	−4.68463	+	0.826026i	−0.162313	+	0.0286201i
$834$	26.8776	−	1.80464i	0.930696	−	0.0624897i
$835$	−22.4439	+	26.7477i	−0.776705	+	0.925641i
$836$	−17.4637	−	5.27820i	−0.603996	−	0.182550i
$837$	1.42250	+	46.5872i	0.0491687	+	1.61029i
$838$	−5.51586	−	7.42939i	−0.190542	−	0.256644i
$839$	−5.82912	−	4.89121i	−0.201244	−	0.168863i	0.536597	−	0.843839i	$-0.319710\pi$
$839$	−5.82912	−	4.89121i	−0.201244	−	0.168863i	−0.737840	+	0.674976i	$0.764154\pi$
$840$	6.69080	−	7.18115i	0.230855	−	0.247773i
$841$	−4.27669	−	24.2543i	−0.147472	−	0.836355i
$842$	−6.43822	−	21.6082i	−0.221876	−	0.744666i
$843$	−32.5803	+	10.1162i	−1.12213	+	0.348422i
$844$	−5.23174	+	10.3495i	−0.180084	+	0.356246i
$845$	−1.22042	−	0.704609i	−0.0419837	−	0.0242393i
$846$	0.231093	+	0.0791619i	0.00794514	+	0.00272164i
$847$	−6.89458	+	3.98059i	−0.236900	+	0.136775i
$848$	−8.50671	+	35.0725i	−0.292122	+	1.20440i
$849$	44.9215	−	34.1587i	1.54170	−	1.17232i
$850$	1.53817	−	6.45235i	0.0527586	−	0.221314i
$851$	−4.58293	+	3.84553i	−0.157101	+	0.131823i
$852$	−11.9205	+	4.44097i	−0.408389	+	0.152145i
$853$	−24.8556	+	9.04669i	−0.851038	+	0.309753i	−0.730464	−	0.682952i	$-0.760696\pi$
$853$	−24.8556	+	9.04669i	−0.851038	+	0.309753i	−0.120575	+	0.992704i	$0.538474\pi$
$854$	5.20938	+	2.25521i	0.178261	+	0.0771716i
$855$	25.9205	−	17.8142i	0.886461	−	0.609231i
$856$	−4.99197	+	27.6744i	−0.170622	+	0.945891i
$857$	13.0042	+	2.29299i	0.444215	+	0.0783271i	0.391282	−	0.920271i	$-0.372032\pi$
$857$	13.0042	+	2.29299i	0.444215	+	0.0783271i	0.0529332	+	0.998598i	$0.483143\pi$
$858$	8.83470	−	12.0893i	0.301612	−	0.412723i
$859$	1.22382	−	3.36243i	0.0417563	−	0.114725i	−0.917062	−	0.398745i	$-0.869446\pi$
$859$	1.22382	−	3.36243i	0.0417563	−	0.114725i	0.958818	+	0.284020i	$0.0916682\pi$
$860$	−3.28818	−	0.393069i	−0.112126	−	0.0134036i
$861$	1.90845	−	0.982900i	0.0650397	−	0.0334971i
$862$	1.53468	−	25.7678i	0.0522713	−	0.877653i
$863$	−2.31089			−0.0786638			−0.0393319	−	0.999226i	$-0.512523\pi$
$863$	−2.31089			−0.0786638			−0.0393319	+	0.999226i	$0.512523\pi$
$864$	−26.5760	−	12.5585i	−0.904134	−	0.427249i
$865$	−38.9158			−1.32318
$866$	2.40262	−	40.3408i	0.0816443	−	1.37083i
$867$	−8.19847	−	5.27351i	−0.278435	−	0.179098i
$868$	−17.8129	−	2.12936i	−0.604611	−	0.0722753i
$869$	−5.96364	+	16.3850i	−0.202302	+	0.555822i
$870$	14.5265	+	32.8719i	0.492495	+	1.11446i
$871$	17.2688	+	3.04495i	0.585131	+	0.103174i
$872$	−9.14501	+	50.6979i	−0.309689	+	1.71685i
$873$	−5.08809	+	1.31580i	−0.172206	+	0.0445331i
$874$	−19.0805	−	8.26021i	−0.645409	−	0.279406i
$875$	−11.2697	+	4.10183i	−0.380985	+	0.138667i
$876$	38.4792	+	31.7957i	1.30009	+	1.07428i
$877$	3.89176	−	3.26557i	0.131415	−	0.110271i	−0.574711	−	0.818356i	$-0.694886\pi$
$877$	3.89176	−	3.26557i	0.131415	−	0.110271i	0.706126	+	0.708086i	$0.250441\pi$
$878$	0.200825	−	0.842426i	0.00677750	−	0.0284305i
$879$	6.13320	+	48.2133i	0.206868	+	1.62619i
$880$	−3.29293	+	13.5765i	−0.111005	+	0.457664i
$881$	18.2490	−	10.5360i	0.614823	−	0.354968i	−0.160028	−	0.987113i	$-0.551158\pi$
$881$	18.2490	−	10.5360i	0.614823	−	0.354968i	0.774851	+	0.632144i	$0.217825\pi$
$882$	2.05098	−	3.71396i	0.0690602	−	0.125055i
$883$	−7.82974	−	4.52050i	−0.263492	−	0.152127i	0.362435	−	0.932009i	$-0.381946\pi$
$883$	−7.82974	−	4.52050i	−0.263492	−	0.152127i	−0.625926	+	0.779882i	$0.715279\pi$
$884$	15.0507	−	29.7736i	0.506210	−	1.00140i
$885$	18.8894	+	17.4614i	0.634962	+	0.586960i
$886$	−0.0838956	−	0.281573i	−0.00281853	−	0.00945963i
$887$	−2.18693	−	12.4027i	−0.0734300	−	0.416442i	−0.999259	−	0.0384986i	$-0.987743\pi$
$887$	−2.18693	−	12.4027i	−0.0734300	−	0.416442i	0.925829	−	0.377943i	$-0.123369\pi$
$888$	−3.05418	−	9.97456i	−0.102492	−	0.334724i
$889$	−6.03549	−	5.06438i	−0.202424	−	0.169854i
$890$	12.4464	+	16.7642i	0.417204	+	0.561938i
$891$	15.4959	−	2.45392i	0.519133	−	0.0822093i
$892$	52.0508	+	15.7317i	1.74279	+	0.526737i
$893$	−0.193663	+	0.230799i	−0.00648070	+	0.00772339i
$894$	−17.9381	−	26.7539i	−0.599940	−	0.894786i
$895$	−34.4579	+	6.07585i	−1.15180	+	0.203093i
$896$	6.30341	−	9.39505i	0.210582	−	0.313867i
$897$	11.5835	−	12.5308i	0.386761	−	0.418391i
$898$	−23.4017	−	46.7492i	−0.780925	−	1.56004i
$899$	32.8439	−	56.8872i	1.09540	−	1.89730i
$900$	3.61640	+	4.68203i	0.120547	+	0.156068i
$901$	−21.4592	−	37.1684i	−0.714910	−	1.23826i
$902$	−1.68234	+	2.55060i	−0.0560159	+	0.0849255i
$903$	−1.42001	+	0.180640i	−0.0472551	+	0.00601131i
$904$	−10.1722	−	5.92636i	−0.338323	−	0.197108i
$905$	−19.2410	−	22.9306i	−0.639594	−	0.762238i
$906$	−12.2560	−	49.7428i	−0.407178	−	1.65259i
$907$	9.77670	+	26.8613i	0.324630	+	0.891913i	0.989445	+	0.144906i	$0.0462879\pi$
$907$	9.77670	+	26.8613i	0.324630	+	0.891913i	−0.664816	+	0.747007i	$0.731490\pi$
$908$	−6.97783	+	1.63448i	−0.231568	+	0.0542420i
$909$	25.4353	+	7.05418i	0.843636	+	0.233972i
$910$	−9.86996	+	1.14053i	−0.327186	+	0.0378081i
$911$	−2.79436	+	15.8476i	−0.0925813	+	0.525055i	0.902880	+	0.429892i	$0.141448\pi$
$911$	−2.79436	+	15.8476i	−0.0925813	+	0.525055i	−0.995462	+	0.0951629i	$0.969663\pi$
$912$	26.2472	−	25.0088i	0.869130	−	0.828126i
$913$	16.2470	+	5.91343i	0.537698	+	0.195706i
$914$	−4.86191	+	5.13981i	−0.160818	+	0.170010i
$915$	7.53532	−	11.7148i	0.249110	−	0.387280i
$916$	5.44461	−	3.56057i	0.179895	−	0.117645i
$917$		−	19.4656i		−	0.642810i
$918$	33.1802	−	10.9994i	1.09511	−	0.363033i
$919$			18.9862i			0.626298i	0.949704	+	0.313149i	$0.101384\pi$
$919$			18.9862i			0.626298i	−0.949704	+	0.313149i	$0.898616\pi$
$920$	−5.50411	+	14.9394i	−0.181465	+	0.492539i
$921$	13.3007	+	25.8253i	0.438273	+	0.850972i
$922$	24.9043	+	23.5578i	0.820181	+	0.775834i
$923$	12.1005	+	4.40423i	0.398294	+	0.144967i
$924$	0.0456191	+	6.03853i	0.00150076	+	0.198653i
$925$	−0.364586	+	2.06767i	−0.0119875	+	0.0679846i
$926$	1.64345	+	14.2222i	0.0540071	+	0.467370i
$927$	−15.3209	+	32.1200i	−0.503205	+	1.05496i
$928$	22.5367	+	34.7593i	0.739804	+	1.14103i
$929$	12.4245	+	34.1361i	0.407635	+	1.11997i	0.958430	+	0.285327i	$0.0921024\pi$
$929$	12.4245	+	34.1361i	0.407635	+	1.11997i	−0.550795	+	0.834641i	$0.685675\pi$
$930$	−12.2508	+	42.2810i	−0.401718	+	1.38645i
$931$	3.36359	+	4.00857i	0.110237	+	0.131376i
$932$	44.3129	−	18.9771i	1.45152	−	0.621617i
$933$	−23.2616	−	30.5909i	−0.761549	−	1.00150i
$934$	−1.31381	−	0.866574i	−0.0429891	−	0.0283552i
$935$	−8.30682	−	14.3878i	−0.271662	−	0.470532i
$936$	12.2323	+	27.1243i	0.399826	+	0.886585i
$937$	−28.7723	+	49.8350i	−0.939949	+	1.62804i	−0.174387	+	0.984677i	$0.555794\pi$
$937$	−28.7723	+	49.8350i	−0.939949	+	1.62804i	−0.765562	+	0.643362i	$0.777539\pi$
$938$	−6.32378	+	3.16555i	−0.206479	+	0.103359i
$939$	−4.17454	−	13.4445i	−0.136231	−	0.438745i
$940$	0.184694	+	0.138254i	0.00602407	+	0.00450933i
$941$	20.7461	−	3.65811i	0.676305	−	0.119251i	0.175062	−	0.984557i	$-0.443987\pi$
$941$	20.7461	−	3.65811i	0.676305	−	0.119251i	0.501243	+	0.865307i	$0.332876\pi$
$942$	−21.3403	−	10.4817i	−0.695305	−	0.341511i
$943$	−2.23829	+	2.66749i	−0.0728887	+	0.0868654i
$944$	24.6877	+	16.4234i	0.803516	+	0.534535i
$945$	−8.17539	−	6.44521i	−0.265946	−	0.209663i
$946$	1.63588	−	1.21454i	0.0531869	−	0.0394880i
$947$	−16.9741	−	14.2430i	−0.551585	−	0.462835i	0.323892	−	0.946094i	$-0.395008\pi$
$947$	−16.9741	−	14.2430i	−0.551585	−	0.462835i	−0.875477	+	0.483259i	$0.839453\pi$
$948$	−22.4722	−	26.3740i	−0.729862	−	0.856589i
$949$	−8.77431	−	49.7616i	−0.284826	−	1.61533i
$950$	−6.99299	+	2.08358i	−0.226883	+	0.0676004i
$951$	−5.08718	+	22.4815i	−0.164963	+	0.729012i
$952$	2.28426	+	13.2592i	0.0740332	+	0.429733i
$953$	−28.4194	−	16.4079i	−0.920594	−	0.531505i	−0.0367694	−	0.999324i	$-0.511707\pi$
$953$	−28.4194	−	16.4079i	−0.920594	−	0.531505i	−0.883824	+	0.467819i	$0.845040\pi$
$954$	37.8168	+	5.92811i	1.22436	+	0.191930i
$955$	−11.2811	+	6.51317i	−0.365049	+	0.210761i
$956$	1.11393	+	20.0295i	0.0360271	+	0.647801i
$957$	−20.3909	−	8.55075i	−0.659143	−	0.276407i
$958$	28.3568	+	6.75995i	0.916168	+	0.218404i
$959$	6.43182	−	5.39694i	0.207694	−	0.174276i
$960$	−20.2368	−	19.0041i	−0.653140	−	0.613356i
$961$	46.4760	−	16.9159i	1.49923	−	0.545674i
$962$	−4.19523	+	9.69070i	−0.135260	+	0.312441i
$963$	29.6895	+	2.85914i	0.956730	+	0.0921346i
$964$	−16.1316	−	17.1885i	−0.519564	−	0.553605i
$965$	1.48700	+	0.262198i	0.0478683	+	0.00844046i
$966$	−0.738329	+	6.84231i	−0.0237554	+	0.220148i
$967$	2.41554	−	6.63665i	0.0776786	−	0.213420i	−0.894775	−	0.446518i	$-0.852664\pi$
$967$	2.41554	−	6.63665i	0.0776786	−	0.213420i	0.972453	+	0.233098i	$0.0748862\pi$
$968$	11.1821	+	19.5449i	0.359405	+	0.628197i
$969$	−2.06880	+	43.0645i	−0.0664596	+	1.38343i
$970$	−4.95478	−	0.295097i	−0.159088	−	0.00947500i
$971$	4.05569			0.130153			0.0650767	−	0.997880i	$-0.479271\pi$
$971$	4.05569			0.130153			0.0650767	+	0.997880i	$0.479271\pi$
$972$	−10.9533	+	29.1895i	−0.351328	+	0.936252i
$973$	10.9975			0.352562
$974$	59.6050	+	3.54996i	1.90987	+	0.113748i
$975$	0.287365	−	5.98184i	0.00920306	−	0.191572i
$976$	6.43656	−	14.7092i	0.206029	−	0.470829i
$977$	0.710504	−	1.95209i	0.0227310	−	0.0624530i	−0.927808	−	0.373058i	$-0.878309\pi$
$977$	0.710504	−	1.95209i	0.0227310	−	0.0624530i	0.950539	+	0.310605i	$0.100532\pi$
$978$	0.886262	−	8.21324i	0.0283395	−	0.262630i
$979$	−12.6509	−	2.23069i	−0.404324	−	0.0712933i
$980$	2.92177	−	2.74212i	0.0933326	−	0.0875937i
$981$	54.3894	+	5.23778i	1.73652	+	0.167230i
$982$	15.2053	−	35.1232i	0.485221	−	1.12083i
$983$	19.0433	−	6.93119i	0.607386	−	0.221071i	−0.0199729	−	0.999801i	$-0.506358\pi$
$983$	19.0433	−	6.93119i	0.607386	−	0.221071i	0.627359	+	0.778730i	$0.284136\pi$
$984$	−2.75882	−	5.40879i	−0.0879481	−	0.172426i
$985$	15.4219	−	12.9405i	0.491383	−	0.412320i
$986$	−47.9219	−	11.4240i	−1.52614	−	0.363815i
$987$	0.0919664	+	0.0385654i	0.00292732	+	0.00122755i
$988$	−36.6428	+	2.03787i	−1.16576	+	0.0648333i
$989$	2.01090	−	1.16099i	0.0639427	−	0.0369174i
$990$	14.6388	+	2.29476i	0.465252	+	0.0729323i
$991$	−33.8168	−	19.5241i	−1.07423	−	0.620204i	−0.144892	−	0.989447i	$-0.546284\pi$
$991$	−33.8168	−	19.5241i	−1.07423	−	0.620204i	−0.929333	+	0.369243i	$0.879617\pi$
$992$	−6.22073	+	50.3585i	−0.197508	+	1.59889i
$993$	9.54885	−	42.1986i	0.303023	−	1.33913i
$994$	−4.97704	+	1.48293i	−0.157862	+	0.0470356i
$995$	7.30834	+	41.4476i	0.231690	+	1.31398i
$996$	−26.1520	+	22.2830i	−0.828658	+	0.706063i
$997$	−17.5014	−	14.6855i	−0.554276	−	0.465093i	0.322110	−	0.946702i	$-0.395608\pi$
$997$	−17.5014	−	14.6855i	−0.554276	−	0.465093i	−0.876386	+	0.481609i	$0.840052\pi$
$998$	−35.4467	+	26.3170i	−1.12205	+	0.833050i
$999$	−10.2769	+	4.09983i	−0.325145	+	0.129713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.51	yes	648
4.3	odd	2	inner	756.2.cf.a.659.9	yes	648
27.5	odd	18	inner	756.2.cf.a.491.9	✓	648
108.59	even	18	inner	756.2.cf.a.491.51	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.9	✓	648	27.5	odd	18	inner
756.2.cf.a.491.51	yes	648	108.59	even	18	inner
756.2.cf.a.659.9	yes	648	4.3	odd	2	inner
756.2.cf.a.659.51	yes	648	1.1	even	1	trivial

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+(-0.0840789 + 1.41171i) q^{2} +(0.0831113 - 1.73006i) q^{3} +(-1.98586 - 0.237390i) q^{4} +(-0.685235 + 1.88267i) q^{5} +(2.43535 + 0.262790i) q^{6} +(0.984808 + 0.173648i) q^{7} +(0.502096 - 2.78350i) q^{8} +(-2.98619 - 0.287574i) q^{9} +(-2.60017 - 1.12565i) q^{10} +(1.63809 - 0.596218i) q^{11} +(-0.575746 + 3.41592i) q^{12} +(2.68625 - 2.25403i) q^{13} +(-0.327943 + 1.37566i) q^{14} +(3.20017 + 1.34197i) q^{15} +(3.88729 + 0.942848i) q^{16} +(-4.11959 + 2.37845i) q^{17} +(0.657047 - 4.19145i) q^{18} +(4.53176 + 2.61641i) q^{19} +(1.80771 - 3.57605i) q^{20} +(0.382270 - 1.68934i) q^{21} +(0.703958 + 2.36265i) q^{22} +(0.487878 + 2.76689i) q^{23} +(-4.77389 - 1.09999i) q^{24} +(0.755328 + 0.633795i) q^{25} +(2.95619 + 3.98173i) q^{26} +(-0.745705 + 5.14237i) q^{27} +(-1.91447 - 0.578625i) q^{28} +(4.70723 - 5.60985i) q^{29} +(-2.16354 + 4.40489i) q^{30} +(8.83361 - 1.55760i) q^{31} +(-1.65787 + 5.40846i) q^{32} +(-0.895345 - 2.88355i) q^{33} +(-3.01131 - 6.01565i) q^{34} +(-1.00175 + 1.73508i) q^{35} +(5.86188 + 1.27997i) q^{36} +(1.06468 + 1.84408i) q^{37} +(-4.07464 + 6.17755i) q^{38} +(-3.67635 - 4.83470i) q^{39} +(4.89636 + 2.85264i) q^{40} +(0.796665 + 0.949428i) q^{41} +(2.35272 + 0.681692i) q^{42} +(-0.282664 - 0.776612i) q^{43} +(-3.39456 + 0.795138i) q^{44} +(2.58765 - 5.42494i) q^{45} +(-3.94707 + 0.456106i) q^{46} +(-0.00999803 + 0.0567016i) q^{47} +(1.95426 - 6.64687i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-0.958244 + 1.01302i) q^{50} +(3.77246 + 7.32480i) q^{51} +(-5.86961 + 3.83851i) q^{52} +9.02236i q^{53} +(-7.19684 - 1.48509i) q^{54} +3.49254i q^{55} +(0.977818 - 2.65403i) q^{56} +(4.90317 - 7.62274i) q^{57} +(7.52372 + 7.11692i) q^{58} +(6.96582 + 2.53535i) q^{59} +(-6.03653 - 3.42465i) q^{60} +(0.697015 - 3.95297i) q^{61} +(1.45617 + 12.6015i) q^{62} +(-2.89088 - 0.801751i) q^{63} +(-7.49580 - 2.79517i) q^{64} +(2.40288 + 6.60187i) q^{65} +(4.14602 - 1.02152i) q^{66} +(3.21429 + 3.83064i) q^{67} +(8.74556 - 3.74532i) q^{68} +(4.82742 - 0.614096i) q^{69} +(-2.36520 - 1.56006i) q^{70} +(1.83610 + 3.18021i) q^{71} +(-2.29982 + 8.16767i) q^{72} +(7.20477 - 12.4790i) q^{73} +(-2.69282 + 1.34797i) q^{74} +(1.15928 - 1.25408i) q^{75} +(-8.37833 - 6.27162i) q^{76} +(1.71674 - 0.302708i) q^{77} +(7.13431 - 4.78344i) q^{78} +(-6.42945 + 7.66232i) q^{79} +(-4.43878 + 6.67241i) q^{80} +(8.83460 + 1.71750i) q^{81} +(-1.40730 + 1.04483i) q^{82} +(7.59781 + 6.37532i) q^{83} +(-1.16017 + 3.26405i) q^{84} +(-1.65494 - 9.38562i) q^{85} +(1.12012 - 0.333743i) q^{86} +(-9.31414 - 8.61001i) q^{87} +(-0.837094 - 4.85900i) q^{88} +(-6.38186 - 3.68457i) q^{89} +(7.44089 + 4.10914i) q^{90} +(3.03685 - 1.75333i) q^{91} +(-0.312024 - 5.61048i) q^{92} +(-1.96057 - 15.4121i) q^{93} +(-0.0792057 - 0.0188817i) q^{94} +(-8.03115 + 6.73894i) q^{95} +(9.21915 + 3.31771i) q^{96} +(1.64617 - 0.599159i) q^{97} +(-0.561842 + 1.29782i) q^{98} +(-5.06311 + 1.30934i) 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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