LMFDB - Embedded newform 240.2.bl.a.109.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.14
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382275 - 1.36157i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.75308 - 1.38805i) q^{5} +(-0.692464 - 1.23308i) q^{6} -4.66030 q^{7} +(-2.07020 + 1.92725i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.382275 - 1.36157i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.75308 - 1.38805i) q^{5} +(-0.692464 - 1.23308i) q^{6} -4.66030 q^{7} +(-2.07020 + 1.92725i) q^{8} -1.00000i q^{9} +(-1.21977 - 2.91756i) q^{10} +(1.23653 - 1.23653i) q^{11} +(-1.94364 + 0.471461i) q^{12} +(4.12471 - 4.12471i) q^{13} +(-1.78151 + 6.34531i) q^{14} +(0.258116 - 2.22112i) q^{15} +(1.83270 + 3.55545i) q^{16} +3.20810i q^{17} +(-1.36157 - 0.382275i) q^{18} +(3.73847 + 3.73847i) q^{19} +(-4.43874 + 0.545487i) q^{20} +(-3.29533 + 3.29533i) q^{21} +(-1.21093 - 2.15632i) q^{22} -0.714957 q^{23} +(-0.101078 + 2.82662i) q^{24} +(1.14661 - 4.86675i) q^{25} +(-4.03930 - 7.19285i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(7.95854 + 4.85131i) q^{28} +(-1.24264 - 1.24264i) q^{29} +(-2.92553 - 1.20052i) q^{30} +3.84716 q^{31} +(5.54158 - 1.13618i) q^{32} -1.74872i q^{33} +(4.36804 + 1.22637i) q^{34} +(-8.16990 + 6.46874i) q^{35} +(-1.04099 + 1.70773i) q^{36} +(-2.33317 - 2.33317i) q^{37} +(6.51931 - 3.66106i) q^{38} -5.83322i q^{39} +(-0.954103 + 6.25217i) q^{40} +6.81590i q^{41} +(3.22709 + 5.74653i) q^{42} +(1.31751 + 1.31751i) q^{43} +(-3.39888 + 0.824453i) q^{44} +(-1.38805 - 1.75308i) q^{45} +(-0.273310 + 0.973462i) q^{46} +1.18427i q^{47} +(3.80999 + 1.21817i) q^{48} +14.7184 q^{49} +(-6.18809 - 3.42163i) q^{50} +(2.26847 + 2.26847i) q^{51} +(-11.3377 + 2.75014i) q^{52} +(9.35268 + 9.35268i) q^{53} +(-1.23308 + 0.692464i) q^{54} +(0.451373 - 3.88412i) q^{55} +(9.64773 - 8.98156i) q^{56} +5.28700 q^{57} +(-2.16697 + 1.21691i) q^{58} +(-6.22646 + 6.22646i) q^{59} +(-2.75295 + 3.52438i) q^{60} +(-4.44284 - 4.44284i) q^{61} +(1.47067 - 5.23817i) q^{62} +4.66030i q^{63} +(0.571420 - 7.97957i) q^{64} +(1.50565 - 12.9563i) q^{65} +(-2.38100 - 0.668492i) q^{66} +(6.37769 - 6.37769i) q^{67} +(3.33958 - 5.47857i) q^{68} +(-0.505551 + 0.505551i) q^{69} +(5.68448 + 13.5967i) q^{70} -6.23269i q^{71} +(1.92725 + 2.07020i) q^{72} +5.34334 q^{73} +(-4.06868 + 2.28486i) q^{74} +(-2.63054 - 4.25209i) q^{75} +(-2.49261 - 10.2760i) q^{76} +(-5.76261 + 5.76261i) q^{77} +(-7.94233 - 2.22990i) q^{78} -13.0275 q^{79} +(8.14803 + 3.68912i) q^{80} -1.00000 q^{81} +(9.28031 + 2.60555i) q^{82} +(-4.88079 + 4.88079i) q^{83} +(9.05793 - 2.19715i) q^{84} +(4.45301 + 5.62407i) q^{85} +(2.29754 - 1.29023i) q^{86} -1.75736 q^{87} +(-0.176758 + 4.94297i) q^{88} -2.20498i q^{89} +(-2.91756 + 1.21977i) q^{90} +(-19.2224 + 19.2224i) q^{91} +(1.22095 + 0.744260i) q^{92} +(2.72035 - 2.72035i) q^{93} +(1.61246 + 0.452716i) q^{94} +(11.7431 + 1.36466i) q^{95} +(3.11509 - 4.72189i) q^{96} +7.39253i q^{97} +(5.62647 - 20.0401i) q^{98} +(-1.23653 - 1.23653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.382275	−	1.36157i	0.270309	−	0.962774i
$2$	0.382275	−	1.36157i	0.270309	−	0.962774i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.70773	−	1.04099i	−0.853866	−	0.520493i
$5$	1.75308	−	1.38805i	0.784003	−	0.620757i
$5$	1.75308	−	1.38805i	0.784003	−	0.620757i
$6$	−0.692464	−	1.23308i	−0.282697	−	0.503404i
$7$	−4.66030			−1.76143			−0.880714	−	0.473649i	$-0.842936\pi$
$7$	−4.66030			−1.76143			−0.880714	+	0.473649i	$0.842936\pi$
$8$	−2.07020	+	1.92725i	−0.731925	+	0.681386i
$9$		−	1.00000i		−	0.333333i
$10$	−1.21977	−	2.91756i	−0.385725	−	0.922614i
$11$	1.23653	−	1.23653i	0.372828	−	0.372828i	−0.495678	−	0.868506i	$-0.665080\pi$
$11$	1.23653	−	1.23653i	0.372828	−	0.372828i	0.868506	+	0.495678i	$0.165080\pi$
$12$	−1.94364	+	0.471461i	−0.561080	+	0.136099i
$13$	4.12471	−	4.12471i	1.14399	−	1.14399i	0.156276	−	0.987713i	$-0.450051\pi$
$13$	4.12471	−	4.12471i	1.14399	−	1.14399i	0.987713	−	0.156276i	$-0.0499490\pi$
$14$	−1.78151	+	6.34531i	−0.476130	+	1.69586i
$15$	0.258116	−	2.22112i	0.0666453	−	0.573491i
$16$	1.83270	+	3.55545i	0.458174	+	0.888862i
$17$			3.20810i			0.778078i	0.921221	+	0.389039i	$0.127193\pi$
$17$			3.20810i			0.778078i	−0.921221	+	0.389039i	$0.872807\pi$
$18$	−1.36157	−	0.382275i	−0.320925	−	0.0901030i
$19$	3.73847	+	3.73847i	0.857665	+	0.857665i	0.991063	−	0.133398i	$-0.0425889\pi$
$19$	3.73847	+	3.73847i	0.857665	+	0.857665i	−0.133398	+	0.991063i	$0.542589\pi$
$20$	−4.43874	+	0.545487i	−0.992533	+	0.121975i
$21$	−3.29533	+	3.29533i	−0.719100	+	0.719100i
$22$	−1.21093	−	2.15632i	−0.258170	−	0.459728i
$23$	−0.714957			−0.149079			−0.0745394	−	0.997218i	$-0.523749\pi$
$23$	−0.714957			−0.149079			−0.0745394	+	0.997218i	$0.523749\pi$
$24$	−0.101078	+	2.82662i	−0.0206325	+	0.576981i
$25$	1.14661	−	4.86675i	0.229323	−	0.973350i
$26$	−4.03930	−	7.19285i	−0.792172	−	1.41063i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	7.95854	+	4.85131i	1.50402	+	0.916810i
$29$	−1.24264	−	1.24264i	−0.230753	−	0.230753i	0.582254	−	0.813007i	$-0.302171\pi$
$29$	−1.24264	−	1.24264i	−0.230753	−	0.230753i	−0.813007	+	0.582254i	$0.802171\pi$
$30$	−2.92553	−	1.20052i	−0.534127	−	0.219184i
$31$	3.84716			0.690970			0.345485	−	0.938424i	$-0.387714\pi$
$31$	3.84716			0.690970			0.345485	+	0.938424i	$0.387714\pi$
$32$	5.54158	−	1.13618i	0.979622	−	0.200850i
$33$		−	1.74872i		−	0.304413i
$34$	4.36804	+	1.22637i	0.749113	+	0.210322i
$35$	−8.16990	+	6.46874i	−1.38096	+	1.09342i
$36$	−1.04099	+	1.70773i	−0.173498	+	0.284622i
$37$	−2.33317	−	2.33317i	−0.383571	−	0.383571i	0.488816	−	0.872387i	$-0.337429\pi$
$37$	−2.33317	−	2.33317i	−0.383571	−	0.383571i	−0.872387	+	0.488816i	$0.837429\pi$
$38$	6.51931	−	3.66106i	1.05757	−	0.593902i
$39$		−	5.83322i		−	0.934064i
$40$	−0.954103	+	6.25217i	−0.150857	+	0.988556i
$41$			6.81590i			1.06446i	0.846598	+	0.532232i	$0.178647\pi$
$41$			6.81590i			1.06446i	−0.846598	+	0.532232i	$0.821353\pi$
$42$	3.22709	+	5.74653i	0.497951	+	0.886709i
$43$	1.31751	+	1.31751i	0.200919	+	0.200919i	0.800394	−	0.599475i	$-0.204624\pi$
$43$	1.31751	+	1.31751i	0.200919	+	0.200919i	−0.599475	+	0.800394i	$0.704624\pi$
$44$	−3.39888	+	0.824453i	−0.512400	+	0.124291i
$45$	−1.38805	−	1.75308i	−0.206919	−	0.261334i
$46$	−0.273310	+	0.973462i	−0.0402974	+	0.143529i
$47$			1.18427i			0.172743i	0.996263	+	0.0863716i	$0.0275272\pi$
$47$			1.18427i			0.172743i	−0.996263	+	0.0863716i	$0.972473\pi$
$48$	3.80999	+	1.21817i	0.549925	+	0.175828i
$49$	14.7184			2.10263
$50$	−6.18809	−	3.42163i	−0.875128	−	0.483891i
$51$	2.26847	+	2.26847i	0.317649	+	0.317649i
$52$	−11.3377	+	2.75014i	−1.57225	+	0.381375i
$53$	9.35268	+	9.35268i	1.28469	+	1.28469i	0.937968	+	0.346722i	$0.112705\pi$
$53$	9.35268	+	9.35268i	1.28469	+	1.28469i	0.346722	+	0.937968i	$0.387295\pi$
$54$	−1.23308	+	0.692464i	−0.167801	+	0.0942325i
$55$	0.451373	−	3.88412i	0.0608631	−	0.523734i
$56$	9.64773	−	8.98156i	1.28923	−	1.20021i
$57$	5.28700			0.700280
$58$	−2.16697	+	1.21691i	−0.284537	+	0.159788i
$59$	−6.22646	+	6.22646i	−0.810617	+	0.810617i	−0.984726	−	0.174110i	$-0.944295\pi$
$59$	−6.22646	+	6.22646i	−0.810617	+	0.810617i	0.174110	+	0.984726i	$0.444295\pi$
$60$	−2.75295	+	3.52438i	−0.355404	+	0.454996i
$61$	−4.44284	−	4.44284i	−0.568848	−	0.568848i	0.362958	−	0.931806i	$-0.381767\pi$
$61$	−4.44284	−	4.44284i	−0.568848	−	0.568848i	−0.931806	+	0.362958i	$0.881767\pi$
$62$	1.47067	−	5.23817i	0.186776	−	0.665248i
$63$			4.66030i			0.587142i
$64$	0.571420	−	7.97957i	0.0714275	−	0.997446i
$65$	1.50565	−	12.9563i	0.186753	−	1.60703i
$66$	−2.38100	−	0.668492i	−0.293081	−	0.0822857i
$67$	6.37769	−	6.37769i	0.779159	−	0.779159i	−0.200529	−	0.979688i	$-0.564266\pi$
$67$	6.37769	−	6.37769i	0.779159	−	0.779159i	0.979688	+	0.200529i	$0.0642660\pi$
$68$	3.33958	−	5.47857i	0.404984	−	0.664374i
$69$	−0.505551	+	0.505551i	−0.0608612	+	0.0608612i
$70$	5.68448	+	13.5967i	0.679426	+	1.62512i
$71$		−	6.23269i		−	0.739685i	−0.929095	−	0.369842i	$-0.879412\pi$
$71$		−	6.23269i		−	0.739685i	0.929095	−	0.369842i	$-0.120588\pi$
$72$	1.92725	+	2.07020i	0.227129	+	0.243975i
$73$	5.34334			0.625391			0.312695	−	0.949853i	$-0.398768\pi$
$73$	5.34334			0.625391			0.312695	+	0.949853i	$0.398768\pi$
$74$	−4.06868	+	2.28486i	−0.472975	+	0.265609i
$75$	−2.63054	−	4.25209i	−0.303748	−	0.490989i
$76$	−2.49261	−	10.2760i	−0.285922	−	1.17874i
$77$	−5.76261	+	5.76261i	−0.656710	+	0.656710i
$78$	−7.94233	−	2.22990i	−0.899292	−	0.252486i
$79$	−13.0275			−1.46571			−0.732854	−	0.680386i	$-0.761812\pi$
$79$	−13.0275			−1.46571			−0.732854	+	0.680386i	$0.761812\pi$
$80$	8.14803	+	3.68912i	0.910977	+	0.412457i
$81$	−1.00000			−0.111111
$82$	9.28031	+	2.60555i	1.02484	+	0.287735i
$83$	−4.88079	+	4.88079i	−0.535736	+	0.535736i	−0.922274	−	0.386537i	$-0.873671\pi$
$83$	−4.88079	+	4.88079i	−0.535736	+	0.535736i	0.386537	+	0.922274i	$0.373671\pi$
$84$	9.05793	−	2.19715i	0.988301	−	0.239728i
$85$	4.45301	+	5.62407i	0.482997	+	0.610016i
$86$	2.29754	−	1.29023i	0.247750	−	0.139129i
$87$	−1.75736			−0.188409
$88$	−0.176758	+	4.94297i	−0.0188424	+	0.526922i
$89$		−	2.20498i		−	0.233728i	−0.993148	−	0.116864i	$-0.962716\pi$
$89$		−	2.20498i		−	0.233728i	0.993148	−	0.116864i	$-0.0372841\pi$
$90$	−2.91756	+	1.21977i	−0.307538	+	0.128575i
$91$	−19.2224	+	19.2224i	−2.01505	+	2.01505i
$92$	1.22095	+	0.744260i	0.127293	+	0.0775945i
$93$	2.72035	−	2.72035i	0.282087	−	0.282087i
$94$	1.61246	+	0.452716i	0.166313	+	0.0466941i
$95$	11.7431	+	1.36466i	1.20481	+	0.140011i
$96$	3.11509	−	4.72189i	0.317932	−	0.481926i
$97$			7.39253i			0.750598i	0.926904	+	0.375299i	$0.122460\pi$
$97$			7.39253i			0.750598i	−0.926904	+	0.375299i	$0.877540\pi$
$98$	5.62647	−	20.0401i	0.568359	−	2.02435i
$99$	−1.23653	−	1.23653i	−0.124276	−	0.124276i
$100$	−7.02433	+	7.11750i	−0.702433	+	0.711750i
$101$	−8.18037	+	8.18037i	−0.813977	+	0.813977i	−0.985228	−	0.171250i	$-0.945219\pi$
$101$	−8.18037	+	8.18037i	−0.813977	+	0.813977i	0.171250	+	0.985228i	$0.445219\pi$
$102$	3.95585	−	2.22149i	0.391687	−	0.219961i
$103$	−4.97884			−0.490580			−0.245290	−	0.969450i	$-0.578883\pi$
$103$	−4.97884			−0.490580			−0.245290	+	0.969450i	$0.578883\pi$
$104$	−0.589612	+	16.4883i	−0.0578162	+	1.61681i
$105$	−1.20290	+	10.3511i	−0.117391	+	1.01016i
$106$	16.3096	−	9.15901i	1.58413	−	0.889602i
$107$	−3.57553	−	3.57553i	−0.345660	−	0.345660i	0.512830	−	0.858490i	$-0.328597\pi$
$107$	−3.57553	−	3.57553i	−0.345660	−	0.345660i	−0.858490	+	0.512830i	$0.828597\pi$
$108$	0.471461	+	1.94364i	0.0453663	+	0.187027i
$109$	−7.08685	−	7.08685i	−0.678797	−	0.678797i	0.280931	−	0.959728i	$-0.409357\pi$
$109$	−7.08685	−	7.08685i	−0.678797	−	0.678797i	−0.959728	+	0.280931i	$0.909357\pi$
$110$	−5.11594	−	2.09938i	−0.487786	−	0.200168i
$111$	−3.29960			−0.313184
$112$	−8.54091	−	16.5695i	−0.807040	−	1.56567i
$113$			3.56470i			0.335339i	0.985843	+	0.167669i	$0.0536241\pi$
$113$			3.56470i			0.335339i	−0.985843	+	0.167669i	$0.946376\pi$
$114$	2.02109	−	7.19861i	0.189292	−	0.674211i
$115$	−1.25338	+	0.992399i	−0.116878	+	0.0925417i
$116$	0.828527	+	3.41567i	0.0769268	+	0.317137i
$117$	−4.12471	−	4.12471i	−0.381330	−	0.381330i
$118$	6.09753	+	10.8580i	0.561323	+	0.999557i
$119$		−	14.9507i		−	1.37053i
$120$	3.74630	+	5.09561i	0.341989	+	0.465163i
$121$			7.94198i			0.721998i
$122$	−7.74762	+	4.35085i	−0.701437	+	0.393907i
$123$	4.81957	+	4.81957i	0.434566	+	0.434566i
$124$	−6.56991	−	4.00484i	−0.589996	−	0.359645i
$125$	−4.74520	−	10.1234i	−0.424424	−	0.905464i
$126$	6.34531	+	1.78151i	0.565285	+	0.158710i
$127$		−	8.87279i		−	0.787333i	−0.919253	−	0.393666i	$-0.871207\pi$
$127$		−	8.87279i		−	0.787333i	0.919253	−	0.393666i	$-0.128793\pi$
$128$	−10.6463	−	3.82841i	−0.941007	−	0.338387i
$129$	1.86325			0.164050
$130$	−17.0653	−	7.00291i	−1.49673	−	0.614196i
$131$	6.48400	+	6.48400i	0.566509	+	0.566509i	0.931149	−	0.364639i	$-0.118808\pi$
$131$	6.48400	+	6.48400i	0.566509	+	0.566509i	−0.364639	+	0.931149i	$0.618808\pi$
$132$	−1.82039	+	2.98635i	−0.158445	+	0.259928i
$133$	−17.4224	−	17.4224i	−1.51071	−	1.51071i
$134$	−6.24563	−	11.1217i	−0.539540	−	0.960768i
$135$	−2.22112	−	0.258116i	−0.191164	−	0.0222151i
$136$	−6.18280	−	6.64139i	−0.530171	−	0.569494i
$137$	−10.2443			−0.875232			−0.437616	−	0.899162i	$-0.644177\pi$
$137$	−10.2443			−0.875232			−0.437616	+	0.899162i	$0.644177\pi$
$138$	0.495082	+	0.881601i	0.0421442	+	0.0750469i
$139$	3.20737	−	3.20737i	0.272046	−	0.272046i	−0.557878	−	0.829923i	$-0.688384\pi$
$139$	3.20737	−	3.20737i	0.272046	−	0.272046i	0.829923	+	0.557878i	$0.188384\pi$
$140$	20.6859	−	2.54213i	1.74827	−	0.214849i
$141$	0.837404	+	0.837404i	0.0705221	+	0.0705221i
$142$	−8.48623	−	2.38260i	−0.712149	−	0.199944i
$143$		−	10.2007i		−	0.853024i
$144$	3.55545	−	1.83270i	0.296287	−	0.152725i
$145$	−3.90331	−	0.453603i	−0.324152	−	0.0376697i
$146$	2.04262	−	7.27532i	0.169049	−	0.602110i
$147$	10.4075	−	10.4075i	0.858393	−	0.858393i
$148$	1.55563	+	6.41323i	0.127872	+	0.527164i
$149$	−14.9254	+	14.9254i	−1.22274	+	1.22274i	−0.256080	+	0.966656i	$0.582431\pi$
$149$	−14.9254	+	14.9254i	−1.22274	+	1.22274i	−0.966656	+	0.256080i	$0.917569\pi$
$150$	−6.79510	+	1.95618i	−0.554817	+	0.159722i
$151$			20.2716i			1.64968i	0.565368	+	0.824839i	$0.308734\pi$
$151$			20.2716i			1.64968i	−0.565368	+	0.824839i	$0.691266\pi$
$152$	−14.9443	−	0.534401i	−1.21215	−	0.0433456i
$153$	3.20810			0.259359
$154$	5.64328	+	10.0491i	0.454748	+	0.809778i
$155$	6.74439	−	5.34006i	0.541723	−	0.428924i
$156$	−6.07231	+	9.96158i	−0.486174	+	0.797565i
$157$	−8.09742	+	8.09742i	−0.646245	+	0.646245i	−0.952083	−	0.305839i	$-0.901063\pi$
$157$	−8.09742	+	8.09742i	−0.646245	+	0.646245i	0.305839	+	0.952083i	$0.401063\pi$
$158$	−4.98009	+	17.7378i	−0.396194	+	1.41115i
$159$	13.2267			1.04894
$160$	8.13778	−	9.68383i	0.643348	−	0.765574i
$161$	3.33191			0.262592
$162$	−0.382275	+	1.36157i	−0.0300343	+	0.106975i
$163$	5.72054	−	5.72054i	0.448067	−	0.448067i	−0.446644	−	0.894712i	$-0.647381\pi$
$163$	5.72054	−	5.72054i	0.448067	−	0.448067i	0.894712	+	0.446644i	$0.147381\pi$
$164$	7.09526	−	11.6397i	0.554046	−	0.908910i
$165$	−2.42732	−	3.06566i	−0.188966	−	0.238661i
$166$	4.77972	+	8.51133i	0.370978	+	0.660607i
$167$	22.8308			1.76670			0.883349	−	0.468716i	$-0.155283\pi$
$167$	22.8308			1.76670			0.883349	+	0.468716i	$0.155283\pi$
$168$	0.471055	−	13.1729i	0.0363427	−	1.01631i
$169$		−	21.0265i		−	1.61742i
$170$	9.35982	−	3.91314i	0.717865	−	0.300124i
$171$	3.73847	−	3.73847i	0.285888	−	0.285888i
$172$	−0.878447	−	3.62147i	−0.0669809	−	0.276135i
$173$	−4.13030	+	4.13030i	−0.314021	+	0.314021i	−0.846465	−	0.532444i	$-0.821274\pi$
$173$	−4.13030	+	4.13030i	−0.314021	+	0.314021i	0.532444	+	0.846465i	$0.321274\pi$
$174$	−0.671795	+	2.39277i	−0.0509287	+	0.181395i
$175$	−5.34356	+	22.6805i	−0.403935	+	1.71449i
$176$	6.66262	+	2.13024i	0.502214	+	0.160573i
$177$			8.80555i			0.661866i
$178$	−3.00223	−	0.842909i	−0.225027	−	0.0631787i
$179$	11.9337	+	11.9337i	0.891964	+	0.891964i	0.994708	−	0.102744i	$-0.0327623\pi$
$179$	11.9337	+	11.9337i	0.891964	+	0.891964i	−0.102744	+	0.994708i	$0.532762\pi$
$180$	0.545487	+	4.43874i	0.0406582	+	0.330844i
$181$	15.2918	−	15.2918i	1.13663	−	1.13663i	0.147579	−	0.989050i	$-0.452852\pi$
$181$	15.2918	−	15.2918i	1.13663	−	1.13663i	0.989050	−	0.147579i	$-0.0471481\pi$
$182$	18.8243	+	33.5208i	1.39535	+	2.48473i
$183$	−6.28313			−0.464462
$184$	1.48010	−	1.37790i	0.109114	−	0.101580i
$185$	−7.32882	−	0.851680i	−0.538825	−	0.0626168i
$186$	−2.66402	−	4.74386i	−0.195335	−	0.347837i
$187$	3.96691	+	3.96691i	0.290090	+	0.290090i
$188$	1.23281	−	2.02241i	0.0899116	−	0.147500i
$189$	3.29533	+	3.29533i	0.239700	+	0.239700i
$190$	6.34715	−	15.4673i	0.460471	−	1.12212i
$191$	−11.8574			−0.857970			−0.428985	−	0.903312i	$-0.641129\pi$
$191$	−11.8574			−0.857970			−0.428985	+	0.903312i	$0.641129\pi$
$192$	−5.23835	−	6.04646i	−0.378045	−	0.436366i
$193$		−	8.93675i		−	0.643281i	−0.946862	−	0.321641i	$-0.895766\pi$
$193$		−	8.93675i		−	0.643281i	0.946862	−	0.321641i	$-0.104234\pi$
$194$	10.0654	+	2.82598i	0.722656	+	0.202894i
$195$	−8.09683	−	10.2261i	−0.579826	−	0.732309i
$196$	−25.1350	−	15.3216i	−1.79536	−	1.09440i
$197$	10.2868	+	10.2868i	0.732907	+	0.732907i	0.971195	−	0.238288i	$-0.0765861\pi$
$197$	10.2868	+	10.2868i	0.732907	+	0.732907i	−0.238288	+	0.971195i	$0.576586\pi$
$198$	−2.15632	+	1.21093i	−0.153243	+	0.0860568i
$199$		−	15.4507i		−	1.09527i	−0.836716	−	0.547637i	$-0.815527\pi$
$199$		−	15.4507i		−	1.09527i	0.836716	−	0.547637i	$-0.184473\pi$
$200$	7.00573	+	12.2849i	0.495380	+	0.868676i
$201$		−	9.01942i		−	0.636181i
$202$	8.01098	+	14.2653i	0.563650	+	1.00370i
$203$	5.79108	+	5.79108i	0.406454	+	0.406454i
$204$	−1.51249	−	6.23538i	−0.105896	−	0.436564i
$205$	9.46083	+	11.9489i	0.660773	+	0.834544i
$206$	−1.90328	+	6.77903i	−0.132608	+	0.472317i
$207$			0.714957i			0.0496929i
$208$	22.2246	+	7.10586i	1.54100	+	0.492703i
$209$	9.24548			0.639523
$210$	13.6339	+	5.59479i	0.940826	+	0.386077i
$211$	−11.2944	−	11.2944i	−0.777540	−	0.777540i	0.201872	−	0.979412i	$-0.435297\pi$
$211$	−11.2944	−	11.2944i	−0.777540	−	0.777540i	−0.979412	+	0.201872i	$0.935297\pi$
$212$	−6.23586	−	25.7079i	−0.428281	−	1.76563i
$213$	−4.40718	−	4.40718i	−0.301975	−	0.301975i
$214$	−6.23517	+	3.50149i	−0.426227	+	0.239357i
$215$	4.13849	+	0.480934i	0.282243	+	0.0327994i
$216$	2.82662	+	0.101078i	0.192327	+	0.00687751i
$217$	−17.9289			−1.21709
$218$	−12.3583	+	6.94010i	−0.837013	+	0.470043i
$219$	3.77831	−	3.77831i	0.255315	−	0.255315i
$220$	−4.81414	+	6.16316i	−0.324569	+	0.415520i
$221$	13.2325	+	13.2325i	0.890113	+	0.890113i
$222$	−1.26136	+	4.49263i	−0.0846566	+	0.301526i
$223$			4.89051i			0.327493i	0.986502	+	0.163746i	$0.0523579\pi$
$223$			4.89051i			0.327493i	−0.986502	+	0.163746i	$0.947642\pi$
$224$	−25.8254	+	5.29494i	−1.72553	+	0.353783i
$225$	−4.86675	−	1.14661i	−0.324450	−	0.0764409i
$226$	4.85358	+	1.36269i	0.322855	+	0.0906451i
$227$	2.49717	−	2.49717i	0.165743	−	0.165743i	−0.619362	−	0.785105i	$-0.712609\pi$
$227$	2.49717	−	2.49717i	0.165743	−	0.165743i	0.785105	+	0.619362i	$0.212609\pi$
$228$	−9.02878	−	5.50369i	−0.597945	−	0.364491i
$229$	−6.31753	+	6.31753i	−0.417474	+	0.417474i	−0.884332	−	0.466858i	$-0.845386\pi$
$229$	−6.31753	+	6.31753i	−0.417474	+	0.417474i	0.466858	+	0.884332i	$0.345386\pi$
$230$	0.872082	+	2.08593i	0.0575034	+	0.137542i
$231$			8.14956i			0.536202i
$232$	4.96739	+	0.177631i	0.326125	+	0.0116621i
$233$	−9.08796			−0.595372			−0.297686	−	0.954664i	$-0.596215\pi$
$233$	−9.08796			−0.595372			−0.297686	+	0.954664i	$0.596215\pi$
$234$	−7.19285	+	4.03930i	−0.470211	+	0.264057i
$235$	1.64383	+	2.07612i	0.107231	+	0.135431i
$236$	17.1148	−	4.15147i	1.11408	−	0.270238i
$237$	−9.21183	+	9.21183i	−0.598373	+	0.598373i
$238$	−20.3564	−	5.71527i	−1.31951	−	0.370466i
$239$	−10.4917			−0.678652			−0.339326	−	0.940669i	$-0.610199\pi$
$239$	−10.4917			−0.678652			−0.339326	+	0.940669i	$0.610199\pi$
$240$	8.37013	−	3.15292i	0.540290	−	0.203520i
$241$	−8.03087			−0.517314			−0.258657	−	0.965969i	$-0.583280\pi$
$241$	−8.03087			−0.517314			−0.258657	+	0.965969i	$0.583280\pi$
$242$	10.8135	+	3.03602i	0.695121	+	0.195163i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	2.96225	+	12.2121i	0.189639	+	0.781801i
$245$	25.8026	−	20.4299i	1.64847	−	1.30522i
$246$	8.40457	−	4.71977i	0.535856	−	0.300921i
$247$	30.8403			1.96232
$248$	−7.96437	+	7.41443i	−0.505738	+	0.470817i
$249$			6.90248i			0.437427i
$250$	−15.5977	+	2.59100i	−0.986482	+	0.163869i
$251$	13.4646	−	13.4646i	0.849878	−	0.849878i	−0.140240	−	0.990118i	$-0.544787\pi$
$251$	13.4646	−	13.4646i	0.849878	−	0.849878i	0.990118	+	0.140240i	$0.0447874\pi$
$252$	4.85131	−	7.95854i	0.305603	−	0.501341i
$253$	−0.884067	+	0.884067i	−0.0555808	+	0.0555808i
$254$	−12.0809	−	3.39184i	−0.758023	−	0.212823i
$255$	7.12557	+	0.828061i	0.446220	+	0.0518552i
$256$	−9.28245	+	13.0321i	−0.580153	+	0.814507i
$257$		−	24.6284i		−	1.53628i	−0.640283	−	0.768139i	$-0.721183\pi$
$257$		−	24.6284i		−	1.53628i	0.640283	−	0.768139i	$-0.278817\pi$
$258$	0.712272	−	2.53694i	0.0443441	−	0.157943i
$259$	10.8733	+	10.8733i	0.675632	+	0.675632i
$260$	−16.0586	+	20.5585i	−0.995910	+	1.27499i
$261$	−1.24264	+	1.24264i	−0.0769176	+	0.0769176i
$262$	11.3071	−	6.34973i	0.698553	−	0.392288i
$263$	7.66921			0.472904			0.236452	−	0.971643i	$-0.424015\pi$
$263$	7.66921			0.472904			0.236452	+	0.971643i	$0.424015\pi$
$264$	3.37022	+	3.62019i	0.207423	+	0.222807i
$265$	29.3781	+	3.41402i	1.80468	+	0.209722i
$266$	−30.3819	+	17.0616i	−1.86283	+	1.04612i
$267$	−1.55916	−	1.55916i	−0.0954189	−	0.0954189i
$268$	−17.5305	+	4.25230i	−1.07084	+	0.259751i
$269$	−3.24831	−	3.24831i	−0.198053	−	0.198053i	0.601112	−	0.799165i	$-0.294725\pi$
$269$	−3.24831	−	3.24831i	−0.198053	−	0.198053i	−0.799165	+	0.601112i	$0.794725\pi$
$270$	−1.20052	+	2.92553i	−0.0730614	+	0.178042i
$271$	22.9657			1.39507			0.697534	−	0.716552i	$-0.254281\pi$
$271$	22.9657			1.39507			0.697534	+	0.716552i	$0.254281\pi$
$272$	−11.4062	+	5.87947i	−0.691604	+	0.356495i
$273$			27.1846i			1.64528i
$274$	−3.91615	+	13.9483i	−0.236583	+	0.842650i
$275$	−4.60007	−	7.43572i	−0.277395	−	0.448391i
$276$	1.38962	−	0.337074i	0.0836451	−	0.0202895i
$277$	20.6009	+	20.6009i	1.23779	+	1.23779i	0.960903	+	0.276885i	$0.0893021\pi$
$277$	20.6009	+	20.6009i	1.23779	+	1.23779i	0.276885	+	0.960903i	$0.410698\pi$
$278$	−3.14095	−	5.59315i	−0.188382	−	0.335455i
$279$		−	3.84716i		−	0.230323i
$280$	4.44640	−	29.1370i	0.265724	−	1.74127i
$281$			8.34735i			0.497961i	0.968508	+	0.248981i	$0.0800955\pi$
$281$			8.34735i			0.497961i	−0.968508	+	0.248981i	$0.919904\pi$
$282$	1.46030	−	0.820063i	0.0869596	−	0.0488341i
$283$	−11.8274	−	11.8274i	−0.703065	−	0.703065i	0.262002	−	0.965067i	$-0.415617\pi$
$283$	−11.8274	−	11.8274i	−0.703065	−	0.703065i	−0.965067	+	0.262002i	$0.915617\pi$
$284$	−6.48815	+	10.6438i	−0.385001	+	0.631592i
$285$	9.26856	−	7.33864i	0.549022	−	0.434703i
$286$	−13.8889	−	3.89946i	−0.821269	−	0.230580i
$287$		−	31.7641i		−	1.87498i
$288$	−1.13618	−	5.54158i	−0.0669501	−	0.326541i
$289$	6.70811			0.394595
$290$	−2.10975	+	5.14122i	−0.123889	+	0.301903i
$291$	5.22731	+	5.22731i	0.306430	+	0.306430i
$292$	−9.12499	−	5.56234i	−0.534000	−	0.325511i
$293$	−5.03517	−	5.03517i	−0.294158	−	0.294158i	0.544562	−	0.838720i	$-0.316696\pi$
$293$	−5.03517	−	5.03517i	−0.294158	−	0.294158i	−0.838720	+	0.544562i	$0.816696\pi$
$294$	−10.1920	−	18.1490i	−0.594407	−	1.05847i
$295$	−2.27285	+	19.5582i	−0.132331	+	1.13872i
$296$	9.32673	+	0.333518i	0.542105	+	0.0193854i
$297$	−1.74872			−0.101471
$298$	14.6163	+	26.0275i	0.846701	+	1.50773i
$299$	−2.94899	+	2.94899i	−0.170545	+	0.170545i
$300$	0.0658809	+	9.99978i	0.00380363	+	0.577338i
$301$	−6.14001	−	6.14001i	−0.353904	−	0.353904i
$302$	27.6011	+	7.74932i	1.58827	+	0.445923i
$303$			11.5688i			0.664610i
$304$	−6.44047	+	20.1434i	−0.369386	+	1.15531i
$305$	−13.9556	−	1.62178i	−0.799095	−	0.0928627i
$306$	1.22637	−	4.36804i	0.0701072	−	0.249704i
$307$	−8.09883	+	8.09883i	−0.462224	+	0.462224i	−0.899384	−	0.437159i	$-0.855985\pi$
$307$	−8.09883	+	8.09883i	−0.462224	+	0.462224i	0.437159	+	0.899384i	$0.355985\pi$
$308$	15.8398	−	3.84219i	0.902555	−	0.218929i
$309$	−3.52057	+	3.52057i	−0.200278	+	0.200278i
$310$	−4.69264	−	11.2243i	−0.266524	−	0.637499i
$311$		−	8.39210i		−	0.475872i	−0.971281	−	0.237936i	$-0.923529\pi$
$311$		−	8.39210i		−	0.475872i	0.971281	−	0.237936i	$-0.0764709\pi$
$312$	11.2421	+	12.0759i	0.636457	+	0.683664i
$313$	−18.3580			−1.03766			−0.518829	−	0.854878i	$-0.673632\pi$
$313$	−18.3580			−1.03766			−0.518829	+	0.854878i	$0.673632\pi$
$314$	7.92974	+	14.1206i	0.447501	+	0.796873i
$315$	6.46874	+	8.16990i	0.364472	+	0.460322i
$316$	22.2475	+	13.5614i	1.25152	+	0.762891i
$317$	0.514929	−	0.514929i	0.0289213	−	0.0289213i	−0.692498	−	0.721420i	$-0.743490\pi$
$317$	0.514929	−	0.514929i	0.0289213	−	0.0289213i	0.721420	+	0.692498i	$0.243490\pi$
$318$	5.05623	−	18.0090i	0.283539	−	1.00990i
$319$	−3.07313			−0.172062
$320$	−10.0743	−	14.7820i	−0.563172	−	0.826340i
$321$	−5.05657			−0.282230
$322$	1.27371	−	4.53662i	0.0709809	−	0.252816i
$323$	−11.9934	+	11.9934i	−0.667330	+	0.667330i
$324$	1.70773	+	1.04099i	0.0948740	+	0.0578326i
$325$	−15.3445	−	24.8034i	−0.851160	−	1.37585i
$326$	−5.60208	−	9.97572i	−0.310271	−	0.552504i
$327$	−10.0223			−0.554236
$328$	−13.1359	−	14.1102i	−0.725311	−	0.779108i
$329$		−	5.51904i		−	0.304275i
$330$	−5.10200	+	2.13303i	−0.280856	+	0.117420i
$331$	19.0330	−	19.0330i	1.04615	−	1.04615i	0.0472642	−	0.998882i	$-0.484950\pi$
$331$	19.0330	−	19.0330i	1.04615	−	1.04615i	0.998882	−	0.0472642i	$-0.0150503\pi$
$332$	13.4159	−	3.25425i	0.736294	−	0.178600i
$333$	−2.33317	+	2.33317i	−0.127857	+	0.127857i
$334$	8.72763	−	31.0856i	0.477554	−	1.70093i
$335$	2.32806	−	20.0332i	0.127195	−	1.09453i
$336$	−17.7557	−	5.67704i	−0.968653	−	0.309708i
$337$			17.3135i			0.943127i	0.881832	+	0.471564i	$0.156310\pi$
$337$			17.3135i			0.943127i	−0.881832	+	0.471564i	$0.843690\pi$
$338$	−28.6290	−	8.03791i	−1.55721	−	0.437204i
$339$	2.52062	+	2.52062i	0.136901	+	0.136901i
$340$	−1.74997	−	14.2399i	−0.0949057	−	0.772268i
$341$	4.75713	−	4.75713i	0.257613	−	0.257613i
$342$	−3.66106	−	6.51931i	−0.197967	−	0.352524i
$343$	−35.9699			−1.94219
$344$	−5.26669	−	0.188334i	−0.283961	−	0.0101543i
$345$	−0.184542	+	1.58801i	−0.00993540	+	0.0854954i
$346$	4.04477	+	7.20260i	0.217448	+	0.387214i
$347$	−7.77893	−	7.77893i	−0.417595	−	0.417595i	0.466779	−	0.884374i	$-0.345414\pi$
$347$	−7.77893	−	7.77893i	−0.417595	−	0.417595i	−0.884374	+	0.466779i	$0.845414\pi$
$348$	3.00110	+	1.82939i	0.160876	+	0.0980655i
$349$	18.9914	+	18.9914i	1.01658	+	1.01658i	0.999860	+	0.0167236i	$0.00532353\pi$
$349$	18.9914	+	18.9914i	1.01658	+	1.01658i	0.0167236	+	0.999860i	$0.494676\pi$
$350$	28.8383	+	15.9458i	1.54147	+	0.852339i
$351$	−5.83322			−0.311355
$352$	5.44742	−	8.25726i	0.290348	−	0.440114i
$353$		−	19.0971i		−	1.01644i	−0.861228	−	0.508219i	$-0.830304\pi$
$353$		−	19.0971i		−	1.01644i	0.861228	−	0.508219i	$-0.169696\pi$
$354$	11.9894	+	3.36614i	0.637227	+	0.178908i
$355$	−8.65132	−	10.9264i	−0.459164	−	0.579915i
$356$	−2.29535	+	3.76552i	−0.121654	+	0.199572i
$357$	−10.5717	−	10.5717i	−0.559515	−	0.559515i
$358$	20.8104	−	11.6865i	1.09987	−	0.617653i
$359$			28.1143i			1.48381i	0.670502	+	0.741907i	$0.266079\pi$
$359$			28.1143i			1.48381i	−0.670502	+	0.741907i	$0.733921\pi$
$360$	6.25217	+	0.954103i	0.329519	+	0.0502856i
$361$			8.95236i			0.471177i
$362$	−14.9751	−	26.6665i	−0.787075	−	1.40156i
$363$	5.61583	+	5.61583i	0.294754	+	0.294754i
$364$	52.8369	−	12.8164i	2.76941	−	0.671764i
$365$	9.36733	−	7.41684i	0.490308	−	0.388215i
$366$	−2.40188	+	8.55491i	−0.125548	+	0.447172i
$367$		−	15.5388i		−	0.811117i	−0.914069	−	0.405558i	$-0.867077\pi$
$367$		−	15.5388i		−	0.811117i	0.914069	−	0.405558i	$-0.132923\pi$
$368$	−1.31030	−	2.54199i	−0.0683041	−	0.132511i
$369$	6.81590			0.354822
$370$	−3.96124	+	9.65310i	−0.205935	+	0.501841i
$371$	−43.5863	−	43.5863i	−2.26289	−	2.26289i
$372$	−7.47748	+	1.81378i	−0.387689	+	0.0940403i
$373$	−0.739215	−	0.739215i	−0.0382751	−	0.0382751i	0.687710	−	0.725985i	$-0.258616\pi$
$373$	−0.739215	−	0.739215i	−0.0382751	−	0.0382751i	−0.725985	+	0.687710i	$0.758616\pi$
$374$	6.91767	−	3.88477i	0.357704	−	0.200877i
$375$	−10.5137	−	3.80295i	−0.542924	−	0.196384i
$376$	−2.28238	−	2.45167i	−0.117705	−	0.126435i
$377$	−10.2511			−0.527958
$378$	5.74653	−	3.22709i	0.295570	−	0.165984i
$379$	−0.977824	+	0.977824i	−0.0502275	+	0.0502275i	−0.731774	−	0.681547i	$-0.761308\pi$
$379$	−0.977824	+	0.977824i	−0.0502275	+	0.0502275i	0.681547	+	0.731774i	$0.261308\pi$
$380$	−18.6334	−	14.5548i	−0.955874	−	0.746647i
$381$	−6.27401	−	6.27401i	−0.321427	−	0.321427i
$382$	−4.53278	+	16.1446i	−0.231917	+	0.826031i
$383$			16.1529i			0.825374i	0.910873	+	0.412687i	$0.135410\pi$
$383$			16.1529i			0.825374i	−0.910873	+	0.412687i	$0.864590\pi$
$384$	−10.2352	+	4.82096i	−0.522310	+	0.246018i
$385$	−2.10353	+	18.1012i	−0.107206	+	0.922520i
$386$	−12.1680	−	3.41630i	−0.619334	−	0.173885i
$387$	1.31751	−	1.31751i	0.0669730	−	0.0669730i
$388$	7.69552	−	12.6245i	0.390681	−	0.640910i
$389$	4.69632	−	4.69632i	0.238113	−	0.238113i	−0.577955	−	0.816068i	$-0.696149\pi$
$389$	4.69632	−	4.69632i	0.238113	−	0.238113i	0.816068	+	0.577955i	$0.196149\pi$
$390$	−17.0188	+	7.11518i	−0.861780	+	0.360291i
$391$		−	2.29365i		−	0.115995i
$392$	−30.4699	+	28.3660i	−1.53896	+	1.43270i
$393$	9.16976			0.462553
$394$	17.9386	−	10.0738i	0.903735	−	0.507512i
$395$	−22.8383	+	18.0829i	−1.14912	+	0.909848i
$396$	0.824453	+	3.39888i	0.0414303	+	0.170800i
$397$	−0.887688	+	0.887688i	−0.0445518	+	0.0445518i	−0.729032	−	0.684480i	$-0.760029\pi$
$397$	−0.887688	+	0.887688i	−0.0445518	+	0.0445518i	0.684480	+	0.729032i	$0.260029\pi$
$398$	−21.0372	−	5.90643i	−1.05450	−	0.296063i
$399$	−24.6390			−1.23349
$400$	19.4049	−	4.84255i	0.970244	−	0.242128i
$401$	−25.5712			−1.27697			−0.638483	−	0.769636i	$-0.720438\pi$
$401$	−25.5712			−1.27697			−0.638483	+	0.769636i	$0.720438\pi$
$402$	−12.2805	−	3.44790i	−0.612498	−	0.171965i
$403$	15.8684	−	15.8684i	0.790462	−	0.790462i
$404$	22.4855	−	5.45423i	1.11870	−	0.271358i
$405$	−1.75308	+	1.38805i	−0.0871115	+	0.0689729i
$406$	10.0987	−	5.67117i	0.501192	−	0.281455i
$407$	−5.77008			−0.286012
$408$	−9.06807	−	0.324269i	−0.448936	−	0.0160537i
$409$		−	1.99680i		−	0.0987353i	−0.998781	−	0.0493677i	$-0.984279\pi$
$409$		−	1.99680i		−	0.0987353i	0.998781	−	0.0493677i	$-0.0157206\pi$
$410$	19.8858	−	8.31382i	0.982090	−	0.410590i
$411$	−7.24383	+	7.24383i	−0.357312	+	0.357312i
$412$	8.50252	+	5.18290i	0.418889	+	0.255343i
$413$	29.0172	−	29.0172i	1.42784	−	1.42784i
$414$	0.973462	+	0.273310i	0.0478431	+	0.0134325i
$415$	−1.78164	+	15.3312i	−0.0874573	+	0.752581i
$416$	18.1710	−	27.5438i	0.890907	−	1.35045i
$417$		−	4.53591i		−	0.222124i
$418$	3.53432	−	12.5883i	0.172869	−	0.615716i
$419$	11.1711	+	11.1711i	0.545743	+	0.545743i	0.925207	−	0.379464i	$-0.123892\pi$
$419$	11.1711	+	11.1711i	0.545743	+	0.545743i	−0.379464	+	0.925207i	$0.623892\pi$
$420$	12.8296	−	16.4247i	0.626018	−	0.801442i
$421$	9.76440	−	9.76440i	0.475888	−	0.475888i	−0.427926	−	0.903814i	$-0.640756\pi$
$421$	9.76440	−	9.76440i	0.475888	−	0.475888i	0.903814	+	0.427926i	$0.140756\pi$
$422$	−19.6957	+	11.0605i	−0.958771	+	0.538418i
$423$	1.18427			0.0575811
$424$	−37.3868	−	1.33693i	−1.81567	−	0.0649271i
$425$	15.6130	+	3.67845i	0.757342	+	0.178431i
$426$	−7.68543	+	4.31592i	−0.372360	+	0.209107i
$427$	20.7050	+	20.7050i	1.00198	+	1.00198i
$428$	2.38397	+	9.82813i	0.115234	+	0.475061i
$429$	−7.21297	−	7.21297i	−0.348245	−	0.348245i
$430$	2.23687	−	5.45099i	0.107871	−	0.262870i
$431$	25.1772			1.21274			0.606371	−	0.795182i	$-0.292625\pi$
$431$	25.1772			1.21274			0.606371	+	0.795182i	$0.292625\pi$
$432$	1.21817	−	3.80999i	0.0586093	−	0.183308i
$433$			1.78691i			0.0858734i	0.999078	+	0.0429367i	$0.0136714\pi$
$433$			1.78691i			0.0858734i	−0.999078	+	0.0429367i	$0.986329\pi$
$434$	−6.85377	+	24.4114i	−0.328991	+	1.17179i
$435$	−3.08080	+	2.43931i	−0.147713	+	0.116956i
$436$	4.72513	+	19.4798i	0.226293	+	0.932911i
$437$	−2.67285	−	2.67285i	−0.127860	−	0.127860i
$438$	−3.70007	−	6.58878i	−0.176796	−	0.314824i
$439$		−	4.96049i		−	0.236751i	−0.992969	−	0.118376i	$-0.962231\pi$
$439$		−	4.96049i		−	0.236751i	0.992969	−	0.118376i	$-0.0377687\pi$
$440$	6.55124	+	8.91079i	0.312318	+	0.424805i
$441$		−	14.7184i		−	0.700875i
$442$	23.0754	−	12.9585i	1.09758	−	0.616371i
$443$	3.68515	+	3.68515i	0.175087	+	0.175087i	0.789210	−	0.614123i	$-0.210490\pi$
$443$	3.68515	+	3.68515i	0.175087	+	0.175087i	−0.614123	+	0.789210i	$0.710490\pi$
$444$	5.63484	+	3.43484i	0.267418	+	0.163010i
$445$	−3.06063	−	3.86552i	−0.145088	−	0.183243i
$446$	6.65876	+	1.86952i	0.315301	+	0.0885243i
$447$			21.1077i			0.998359i
$448$	−2.66299	+	37.1872i	−0.125814	+	1.75693i
$449$	−25.7644			−1.21590			−0.607949	−	0.793976i	$-0.708008\pi$
$449$	−25.7644			−1.21590			−0.607949	+	0.793976i	$0.708008\pi$
$450$	−3.42163	+	6.18809i	−0.161297	+	0.291709i
$451$	8.42808	+	8.42808i	0.396863	+	0.396863i
$452$	3.71080	−	6.08755i	0.174541	−	0.286334i
$453$	14.3342	+	14.3342i	0.673478	+	0.673478i
$454$	−2.44546	−	4.35467i	−0.114771	−	0.204375i
$455$	−7.01677	+	60.3802i	−0.328951	+	2.83067i
$456$	−10.9451	+	10.1894i	−0.512552	+	0.477161i
$457$	1.34836			0.0630735			0.0315367	−	0.999503i	$-0.489960\pi$
$457$	1.34836			0.0630735			0.0315367	+	0.999503i	$0.489960\pi$
$458$	6.18671	+	11.0168i	0.289086	+	0.514780i
$459$	2.26847	−	2.26847i	0.105883	−	0.105883i
$460$	3.17351	−	0.390000i	0.147966	−	0.0181838i
$461$	19.1978	+	19.1978i	0.894128	+	0.894128i	0.994909	−	0.100780i	$-0.0321339\pi$
$461$	19.1978	+	19.1978i	0.894128	+	0.894128i	−0.100780	+	0.994909i	$0.532134\pi$
$462$	11.0962	+	3.11537i	0.516241	+	0.144940i
$463$		−	2.15031i		−	0.0999334i	−0.998751	−	0.0499667i	$-0.984088\pi$
$463$		−	2.15031i		−	0.0999334i	0.998751	−	0.0499667i	$-0.0159115\pi$
$464$	2.14077	−	6.69554i	0.0993826	−	0.310833i
$465$	0.993013	−	8.54500i	0.0460499	−	0.396265i
$466$	−3.47410	+	12.3739i	−0.160935	+	0.573209i
$467$	−8.47864	+	8.47864i	−0.392345	+	0.392345i	−0.875522	−	0.483178i	$-0.839483\pi$
$467$	−8.47864	+	8.47864i	−0.392345	+	0.392345i	0.483178	+	0.875522i	$0.339483\pi$
$468$	2.75014	+	11.3377i	0.127125	+	0.524084i
$469$	−29.7219	+	29.7219i	−1.37243	+	1.37243i
$470$	3.45517	−	1.44453i	0.159375	−	0.0666313i
$471$			11.4515i			0.527656i
$472$	0.890050	−	24.8899i	0.0409679	−	1.14565i
$473$	3.25830			0.149817
$474$	9.02108	+	16.0640i	0.414352	+	0.737843i
$475$	22.4808	−	13.9076i	1.03149	−	0.638126i
$476$	−15.5635	+	25.5318i	−0.713350	+	1.17025i
$477$	9.35268	−	9.35268i	0.428230	−	0.428230i
$478$	−4.01071	+	14.2852i	−0.183446	+	0.653388i
$479$	−15.4474			−0.705808			−0.352904	−	0.935660i	$-0.614806\pi$
$479$	−15.4474			−0.705808			−0.352904	+	0.935660i	$0.614806\pi$
$480$	−1.09322	−	12.6018i	−0.0498986	−	0.575190i
$481$	−19.2473			−0.877603
$482$	−3.07000	+	10.9346i	−0.139835	+	0.498056i
$483$	2.35602	−	2.35602i	0.107203	−	0.107203i
$484$	8.26749	−	13.5628i	0.375795	−	0.616489i
$485$	10.2612	+	12.9597i	0.465939	+	0.588471i
$486$	0.692464	+	1.23308i	0.0314108	+	0.0559338i
$487$	−21.0712			−0.954827			−0.477414	−	0.878679i	$-0.658426\pi$
$487$	−21.0712			−0.954827			−0.477414	+	0.878679i	$0.658426\pi$
$488$	17.7600	+	0.635088i	0.803959	+	0.0287491i
$489$		−	8.09007i		−	0.365846i
$490$	−17.9530	−	42.9418i	−0.811034	−	1.93991i
$491$	7.46559	−	7.46559i	0.336918	−	0.336918i	−0.518288	−	0.855206i	$-0.673431\pi$
$491$	7.46559	−	7.46559i	0.336918	−	0.336918i	0.855206	+	0.518288i	$0.173431\pi$
$492$	−3.21343	−	13.2476i	−0.144872	−	0.597249i
$493$	3.98652	−	3.98652i	0.179544	−	0.179544i
$494$	11.7895	−	41.9911i	0.530433	−	1.88927i
$495$	−3.88412	−	0.451373i	−0.174578	−	0.0202877i
$496$	7.05067	+	13.6784i	0.316585	+	0.614177i
$497$			29.0462i			1.30290i
$498$	9.39819	+	2.63864i	0.421143	+	0.118240i
$499$	6.75434	+	6.75434i	0.302366	+	0.302366i	0.841939	−	0.539573i	$-0.181414\pi$
$499$	6.75434	+	6.75434i	0.302366	+	0.302366i	−0.539573	+	0.841939i	$0.681414\pi$
$500$	−2.43477	+	22.2277i	−0.108886	+	0.994054i
$501$	16.1438	−	16.1438i	0.721251	−	0.721251i
$502$	−13.1858	−	23.4801i	−0.588510	−	1.04797i
$503$	27.5418			1.22803			0.614014	−	0.789295i	$-0.289554\pi$
$503$	27.5418			1.22803			0.614014	+	0.789295i	$0.289554\pi$
$504$	−8.98156	−	9.64773i	−0.400070	−	0.429744i
$505$	−2.98609	+	25.6957i	−0.132879	+	1.14344i
$506$	0.865761	+	1.54167i	0.0384877	+	0.0685358i
$507$	−14.8680	−	14.8680i	−0.660311	−	0.660311i
$508$	−9.23645	+	15.1523i	−0.409801	+	0.672277i
$509$	−15.9180	−	15.9180i	−0.705552	−	0.705552i	0.260044	−	0.965597i	$-0.416263\pi$
$509$	−15.9180	−	15.9180i	−0.705552	−	0.705552i	−0.965597	+	0.260044i	$0.916263\pi$
$510$	3.85139	−	9.38540i	0.170542	−	0.415592i
$511$	−24.9016			−1.10158
$512$	14.1957	+	17.6205i	0.627366	+	0.778725i
$513$		−	5.28700i		−	0.233427i
$514$	−33.5332	−	9.41482i	−1.47909	−	0.415270i
$515$	−8.72833	+	6.91090i	−0.384616	+	0.304530i
$516$	−3.18192	−	1.93961i	−0.140076	−	0.0853867i
$517$	1.46438	+	1.46438i	0.0644036	+	0.0644036i
$518$	18.9613	−	10.6481i	0.833111	−	0.467851i
$519$			5.84113i			0.256397i
$520$	21.8530	+	29.7238i	0.958318	+	1.30348i
$521$			0.0475676i			0.00208397i	0.999999	+	0.00104199i	$0.000331675\pi$
$521$			0.0475676i			0.00208397i	−0.999999	+	0.00104199i	$0.999668\pi$
$522$	1.21691	+	2.16697i	0.0532627	+	0.0948458i
$523$	−29.1859	−	29.1859i	−1.27621	−	1.27621i	−0.942773	−	0.333436i	$-0.891792\pi$
$523$	−29.1859	−	29.1859i	−1.27621	−	1.27621i	−0.333436	−	0.942773i	$-0.608208\pi$
$524$	−4.32318	−	17.8227i	−0.188859	−	0.778587i
$525$	12.2591	+	19.8160i	0.535030	+	0.864842i
$526$	2.93175	−	10.4422i	0.127830	−	0.455300i
$527$			12.3421i			0.537628i
$528$	6.21749	−	3.20487i	0.270581	−	0.139474i
$529$	−22.4888			−0.977775
$530$	15.8789	−	38.6951i	0.689736	−	1.68081i
$531$	6.22646	+	6.22646i	0.270206	+	0.270206i
$532$	11.6163	+	47.8893i	0.503631	+	2.07626i
$533$	28.1136	+	28.1136i	1.21774	+	1.21774i
$534$	−2.71892	+	1.52687i	−0.117659	+	0.0660742i
$535$	−11.2312	−	1.30518i	−0.485569	−	0.0564279i
$536$	−0.911667	+	25.4945i	−0.0393780	+	1.10119i
$537$	16.8767			0.728285
$538$	−5.66454	+	3.18105i	−0.244216	+	0.137145i
$539$	18.1997	−	18.1997i	0.783919	−	0.783919i
$540$	3.52438	+	2.75295i	0.151665	+	0.118468i
$541$	−0.810856	−	0.810856i	−0.0348614	−	0.0348614i	0.689461	−	0.724323i	$-0.257847\pi$
$541$	−0.810856	−	0.810856i	−0.0348614	−	0.0348614i	−0.724323	+	0.689461i	$0.757847\pi$
$542$	8.77921	−	31.2694i	0.377099	−	1.34313i
$543$		−	21.6259i		−	0.928054i
$544$	3.64498	+	17.7779i	0.156277	+	0.762222i
$545$	−22.2608	−	2.58692i	−0.953547	−	0.110812i
$546$	37.0136	+	10.3920i	1.58404	+	0.444736i
$547$	−18.7910	+	18.7910i	−0.803445	+	0.803445i	−0.983632	−	0.180187i	$-0.942330\pi$
$547$	−18.7910	+	18.7910i	−0.803445	+	0.803445i	0.180187	+	0.983632i	$0.442330\pi$
$548$	17.4946	+	10.6642i	0.747330	+	0.455552i
$549$	−4.44284	+	4.44284i	−0.189616	+	0.189616i
$550$	−11.8827	+	3.42082i	−0.506681	+	0.145864i
$551$		−	9.29117i		−	0.395817i
$552$	0.0722666	−	2.02091i	0.00307587	−	0.0860157i
$553$	60.7120			2.58174
$554$	35.9247	−	20.1743i	1.52630	−	0.857124i
$555$	−5.78448	+	4.58003i	−0.245538	+	0.194411i
$556$	−8.81616	+	2.13850i	−0.373888	+	0.0906927i
$557$	−30.7121	+	30.7121i	−1.30132	+	1.30132i	−0.373810	+	0.927505i	$0.621949\pi$
$557$	−30.7121	+	30.7121i	−1.30132	+	1.30132i	−0.927505	+	0.373810i	$0.878051\pi$
$558$	−5.23817	−	1.47067i	−0.221749	−	0.0622585i
$559$	10.8687			0.459698
$560$	−37.9722	−	17.1924i	−1.60462	−	0.726512i
$561$	5.61006			0.236857
$562$	11.3655	+	3.19098i	0.479424	+	0.134603i
$563$	−20.7316	+	20.7316i	−0.873734	+	0.873734i	−0.992877	−	0.119143i	$-0.961985\pi$
$563$	−20.7316	+	20.7316i	−0.873734	+	0.873734i	0.119143	+	0.992877i	$0.461985\pi$
$564$	−0.558335	−	2.30179i	−0.0235102	−	0.0969227i
$565$	4.94799	+	6.24922i	0.208164	+	0.262907i
$566$	−20.6251	+	11.5825i	−0.866937	+	0.486848i
$567$	4.66030			0.195714
$568$	12.0120	+	12.9029i	0.504011	+	0.541394i
$569$		−	23.9776i		−	1.00519i	−0.864521	−	0.502596i	$-0.832378\pi$
$569$		−	23.9776i		−	1.00519i	0.864521	−	0.502596i	$-0.167622\pi$
$570$	−6.44892	−	15.4251i	−0.270115	−	0.646088i
$571$	6.40838	−	6.40838i	0.268182	−	0.268182i	−0.560185	−	0.828367i	$-0.689270\pi$
$571$	6.40838	−	6.40838i	0.268182	−	0.268182i	0.828367	+	0.560185i	$0.189270\pi$
$572$	−10.6188	+	17.4200i	−0.443993	+	0.728368i
$573$	−8.38444	+	8.38444i	−0.350265	+	0.350265i
$574$	−43.2490	−	12.1426i	−1.80518	−	0.506823i
$575$	−0.819779	+	3.47952i	−0.0341872	+	0.145106i
$576$	−7.97957	−	0.571420i	−0.332482	−	0.0238092i
$577$		−	8.75032i		−	0.364281i	−0.983273	−	0.182140i	$-0.941697\pi$
$577$		−	8.75032i		−	0.364281i	0.983273	−	0.182140i	$-0.0583025\pi$
$578$	2.56434	−	9.13355i	0.106663	−	0.379906i
$579$	−6.31924	−	6.31924i	−0.262619	−	0.262619i
$580$	6.19362	+	4.83793i	0.257176	+	0.200884i
$581$	22.7459	−	22.7459i	0.943660	−	0.943660i
$582$	9.11561	−	5.11907i	0.377854	−	0.212192i
$583$	23.1298			0.957938
$584$	−11.0618	+	10.2979i	−0.457739	+	0.426132i
$585$	−12.9563	−	1.50565i	−0.535677	−	0.0622509i
$586$	−8.78055	+	4.93091i	−0.362721	+	0.203694i
$587$	−19.3790	−	19.3790i	−0.799857	−	0.799857i	0.183216	−	0.983073i	$-0.441349\pi$
$587$	−19.3790	−	19.3790i	−0.799857	−	0.799857i	−0.983073	+	0.183216i	$0.941349\pi$
$588$	−28.6072	+	6.93913i	−1.17974	+	0.286165i
$589$	14.3825	+	14.3825i	0.592620	+	0.592620i
$590$	25.7609	+	10.5712i	1.06056	+	0.435211i
$591$	14.5478			0.598416
$592$	4.01948	−	12.5715i	0.165200	−	0.516684i
$593$		−	19.4757i		−	0.799769i	−0.916565	−	0.399885i	$-0.869050\pi$
$593$		−	19.4757i		−	0.799769i	0.916565	−	0.399885i	$-0.130950\pi$
$594$	−0.668492	+	2.38100i	−0.0274286	+	0.0976936i
$595$	−20.7524	−	26.2098i	−0.850764	−	1.07450i
$596$	41.0257	−	9.95144i	1.68048	−	0.407627i
$597$	−10.9253	−	10.9253i	−0.447144	−	0.447144i
$598$	2.88793	+	5.14258i	0.118096	+	0.210296i
$599$		−	18.8857i		−	0.771651i	−0.922572	−	0.385825i	$-0.873917\pi$
$599$		−	18.8857i		−	0.771651i	0.922572	−	0.385825i	$-0.126083\pi$
$600$	13.6406	+	3.73296i	0.556874	+	0.152398i
$601$		−	38.2498i		−	1.56024i	−0.625630	−	0.780120i	$-0.715158\pi$
$601$		−	38.2498i		−	1.56024i	0.625630	−	0.780120i	$-0.284842\pi$
$602$	−10.7072	+	6.01286i	−0.436393	+	0.245066i
$603$	−6.37769	−	6.37769i	−0.259720	−	0.259720i
$604$	21.1024	−	34.6184i	0.858646	−	1.40860i
$605$	11.0239	+	13.9230i	0.448185	+	0.566049i
$606$	15.7517	+	4.42246i	0.639869	+	0.179650i
$607$			11.3757i			0.461724i	0.972986	+	0.230862i	$0.0741546\pi$
$607$			11.3757i			0.461724i	−0.972986	+	0.230862i	$0.925845\pi$
$608$	24.9646	+	16.4695i	1.01245	+	0.667925i
$609$	8.18983			0.331869
$610$	−7.54303	+	18.3815i	−0.305408	+	0.744246i
$611$	4.88476	+	4.88476i	0.197616	+	0.197616i
$612$	−5.47857	−	3.33958i	−0.221458	−	0.134995i
$613$	−8.38974	−	8.38974i	−0.338859	−	0.338859i	0.517079	−	0.855938i	$-0.327019\pi$
$613$	−8.38974	−	8.38974i	−0.338859	−	0.338859i	−0.855938	+	0.517079i	$0.827019\pi$
$614$	7.93112	+	14.1231i	0.320074	+	0.569961i
$615$	15.1389	+	1.75929i	0.610461	+	0.0709415i
$616$	0.823743	−	23.0357i	0.0331896	−	0.928135i
$617$	46.6201			1.87686			0.938428	−	0.345476i	$-0.112282\pi$
$617$	46.6201			1.87686			0.938428	+	0.345476i	$0.112282\pi$
$618$	3.44767	+	6.13932i	0.138686	+	0.246960i
$619$	2.78509	−	2.78509i	0.111942	−	0.111942i	−0.648917	−	0.760859i	$-0.724778\pi$
$619$	2.78509	−	2.78509i	0.111942	−	0.111942i	0.760859	+	0.648917i	$0.224778\pi$
$620$	−17.0765	+	2.09857i	−0.685811	+	0.0842807i
$621$	0.505551	+	0.505551i	0.0202871	+	0.0202871i
$622$	−11.4264	−	3.20809i	−0.458157	−	0.128633i
$623$			10.2759i			0.411694i
$624$	20.7397	−	10.6905i	0.830254	−	0.427964i
$625$	−22.3706	−	11.1606i	−0.894822	−	0.446423i
$626$	−7.01781	+	24.9957i	−0.280488	+	0.999029i
$627$	6.53754	−	6.53754i	0.261084	−	0.261084i
$628$	22.2575	−	5.39892i	0.888172	−	0.215440i
$629$	7.48504	−	7.48504i	0.298448	−	0.298448i
$630$	13.5967	−	5.68448i	0.541706	−	0.226475i
$631$			24.5670i			0.977997i	0.872285	+	0.488998i	$0.162638\pi$
$631$			24.5670i			0.977997i	−0.872285	+	0.488998i	$0.837362\pi$
$632$	26.9695	−	25.1072i	1.07279	−	0.998713i
$633$	−15.9727			−0.634858
$634$	−0.504266	−	0.897954i	−0.0200270	−	0.0356623i
$635$	−12.3159	−	15.5548i	−0.488742	−	0.617272i
$636$	−22.5876	−	13.7688i	−0.895658	−	0.545969i
$637$	60.7091	−	60.7091i	2.40538	−	2.40538i
$638$	−1.17478	+	4.18428i	−0.0465101	+	0.165657i
$639$	−6.23269			−0.246562
$640$	−23.9779	+	8.06607i	−0.947809	+	0.318839i
$641$	24.1073			0.952179			0.476090	−	0.879397i	$-0.342054\pi$
$641$	24.1073			0.952179			0.476090	+	0.879397i	$0.342054\pi$
$642$	−1.93300	+	6.88486i	−0.0762894	+	0.271724i
$643$	−5.61417	+	5.61417i	−0.221401	+	0.221401i	−0.809088	−	0.587687i	$-0.800039\pi$
$643$	−5.61417	+	5.61417i	−0.221401	+	0.221401i	0.587687	+	0.809088i	$0.300039\pi$
$644$	−5.69001	−	3.46847i	−0.224218	−	0.136677i
$645$	3.26643	−	2.58629i	0.128615	−	0.101835i
$646$	11.7450	+	20.9146i	0.462102	+	0.822873i
$647$	−12.5530			−0.493508			−0.246754	−	0.969078i	$-0.579364\pi$
$647$	−12.5530			−0.493508			−0.246754	+	0.969078i	$0.579364\pi$
$648$	2.07020	−	1.92725i	0.0813250	−	0.0757095i
$649$			15.3984i			0.604442i
$650$	−39.6373	+	11.4109i	−1.55470	+	0.447571i
$651$	−12.6776	+	12.6776i	−0.496876	+	0.496876i
$652$	−15.7242	+	3.81415i	−0.615806	+	0.149374i
$653$	−34.4380	+	34.4380i	−1.34766	+	1.34766i	−0.459466	+	0.888196i	$0.651959\pi$
$653$	−34.4380	+	34.4380i	−1.34766	+	1.34766i	−0.888196	+	0.459466i	$0.848041\pi$
$654$	−3.83128	+	13.6461i	−0.149815	+	0.533603i
$655$	20.3671	+	2.36686i	0.795810	+	0.0924809i
$656$	−24.2336	+	12.4915i	−0.946163	+	0.487710i
$657$		−	5.34334i		−	0.208464i
$658$	−7.51455	−	2.10979i	−0.292948	−	0.0822482i
$659$	21.2540	+	21.2540i	0.827940	+	0.827940i	0.987232	−	0.159292i	$-0.0509210\pi$
$659$	21.2540	+	21.2540i	0.827940	+	0.827940i	−0.159292	+	0.987232i	$0.550921\pi$
$660$	0.953904	+	7.76212i	0.0371307	+	0.302140i
$661$	−1.82514	+	1.82514i	−0.0709896	+	0.0709896i	−0.741710	−	0.670721i	$-0.765985\pi$
$661$	−1.82514	+	1.82514i	−0.0709896	+	0.0709896i	0.670721	+	0.741710i	$0.265985\pi$
$662$	−18.6388	−	33.1905i	−0.724419	−	1.28999i
$663$	18.7135			0.726774
$664$	0.697691	−	19.5107i	0.0270756	−	0.757162i
$665$	−54.7262	−	6.35972i	−2.12219	−	0.246619i
$666$	2.28486	+	4.06868i	0.0885364	+	0.157658i
$667$	0.888436	+	0.888436i	0.0344004	+	0.0344004i
$668$	−38.9888	−	23.7665i	−1.50852	−	0.919554i
$669$	3.45811	+	3.45811i	0.133698	+	0.133698i
$670$	−26.3866	−	10.8280i	−1.01940	−	0.418322i
$671$	−10.9874			−0.424165
$672$	−14.5172	+	22.0054i	−0.560014	+	0.848877i
$673$		−	8.51817i		−	0.328351i	−0.986431	−	0.164176i	$-0.947504\pi$
$673$		−	8.51817i		−	0.328351i	0.986431	−	0.164176i	$-0.0524964\pi$
$674$	23.5735	+	6.61852i	0.908018	+	0.254936i
$675$	−4.25209	+	2.63054i	−0.163663	+	0.101249i
$676$	−21.8883	+	35.9076i	−0.841858	+	1.38106i
$677$	−19.0779	−	19.0779i	−0.733223	−	0.733223i	0.238034	−	0.971257i	$-0.423497\pi$
$677$	−19.0779	−	19.0779i	−0.733223	−	0.733223i	−0.971257	+	0.238034i	$0.923497\pi$
$678$	4.39557	−	2.46843i	0.168811	−	0.0947993i
$679$		−	34.4514i		−	1.32212i
$680$	−20.0576	−	3.06086i	−0.769173	−	0.117378i
$681$		−	3.53153i		−	0.135329i
$682$	−4.65863	−	8.29569i	−0.178388	−	0.317658i
$683$	13.3669	+	13.3669i	0.511471	+	0.511471i	0.914977	−	0.403506i	$-0.132209\pi$
$683$	13.3669	+	13.3669i	0.511471	+	0.511471i	−0.403506	+	0.914977i	$0.632209\pi$
$684$	−10.2760	+	2.49261i	−0.392913	+	0.0953074i
$685$	−17.9592	+	14.2197i	−0.686185	+	0.543306i
$686$	−13.7504	+	48.9755i	−0.524993	+	1.86989i
$687$			8.93433i			0.340866i
$688$	−2.26975	+	7.09896i	−0.0865335	+	0.270645i
$689$	77.1543			2.93934
$690$	2.09163	+	0.858321i	0.0796270	+	0.0326757i
$691$	−15.4008	−	15.4008i	−0.585874	−	0.585874i	0.350638	−	0.936511i	$-0.385965\pi$
$691$	−15.4008	−	15.4008i	−0.585874	−	0.585874i	−0.936511	+	0.350638i	$0.885965\pi$
$692$	11.3530	−	2.75386i	0.431578	−	0.104686i
$693$	5.76261	+	5.76261i	0.218903	+	0.218903i
$694$	−13.5652	+	7.61785i	−0.514929	+	0.289170i
$695$	1.17079	−	10.0748i	0.0444106	−	0.382159i
$696$	3.63808	−	3.38687i	0.137901	−	0.128379i
$697$	−21.8661			−0.828236
$698$	33.1179	−	18.5981i	1.25353	−	0.703948i
$699$	−6.42616	+	6.42616i	−0.243060	+	0.243060i
$700$	32.7355	−	33.1697i	1.23728	−	1.25370i
$701$	−13.1486	−	13.1486i	−0.496614	−	0.496614i	0.413768	−	0.910382i	$-0.364212\pi$
$701$	−13.1486	−	13.1486i	−0.496614	−	0.496614i	−0.910382	+	0.413768i	$0.864212\pi$
$702$	−2.22990	+	7.94233i	−0.0841620	+	0.299764i
$703$		−	17.4450i		−	0.657951i
$704$	−9.16041	−	10.5736i	−0.345246	−	0.398506i
$705$	2.63040	+	0.305678i	0.0990666	+	0.0115125i
$706$	−26.0020	−	7.30036i	−0.978600	−	0.274753i
$707$	38.1230	−	38.1230i	1.43376	−	1.43376i
$708$	9.16646	−	15.0375i	0.344496	−	0.565145i
$709$	−17.8125	+	17.8125i	−0.668963	+	0.668963i	−0.957476	−	0.288513i	$-0.906839\pi$
$709$	−17.8125	+	17.8125i	−0.668963	+	0.668963i	0.288513	+	0.957476i	$0.406839\pi$
$710$	−18.1843	+	7.60245i	−0.682444	+	0.285315i
$711$			13.0275i			0.488569i
$712$	4.24955	+	4.56474i	0.159259	+	0.171071i
$713$	−2.75055			−0.103009
$714$	−18.4354	+	10.3528i	−0.689929	+	0.387445i
$715$	−14.1591	−	17.8827i	−0.529520	−	0.668773i
$716$	−7.95672	−	32.8023i	−0.297357	−	1.22588i
$717$	−7.41876	+	7.41876i	−0.277058	+	0.277058i
$718$	38.2795	+	10.7474i	1.42858	+	0.401089i
$719$	−15.2289			−0.567940			−0.283970	−	0.958833i	$-0.591652\pi$
$719$	−15.2289			−0.567940			−0.283970	+	0.958833i	$0.591652\pi$
$720$	3.68912	−	8.14803i	0.137486	−	0.303659i
$721$	23.2029			0.864120
$722$	12.1892	+	3.42226i	0.453637	+	0.127363i
$723$	−5.67868	+	5.67868i	−0.211193	+	0.211193i
$724$	−42.0328	+	10.1957i	−1.56214	+	0.378922i
$725$	−7.47246	+	4.62280i	−0.277520	+	0.171687i
$726$	9.79311	−	5.49954i	0.363457	−	0.204107i
$727$	−40.6950			−1.50930			−0.754648	−	0.656130i	$-0.772192\pi$
$727$	−40.6950			−1.50930			−0.754648	+	0.656130i	$0.772192\pi$
$728$	2.74777	−	76.8404i	0.101839	−	2.84790i
$729$			1.00000i			0.0370370i
$730$	−6.51764	−	15.5895i	−0.241229	−	0.576994i
$731$	−4.22671	+	4.22671i	−0.156331	+	0.156331i
$732$	10.7299	+	6.54065i	0.396589	+	0.241749i
$733$	−18.7002	+	18.7002i	−0.690709	+	0.690709i	−0.962388	−	0.271679i	$-0.912421\pi$
$733$	−18.7002	+	18.7002i	−0.690709	+	0.690709i	0.271679	+	0.962388i	$0.412421\pi$
$734$	−21.1571	−	5.94008i	−0.780922	−	0.219252i
$735$	3.79905	−	32.6913i	0.140130	−	1.20584i
$736$	−3.96199	+	0.812320i	−0.146041	+	0.0299425i
$737$		−	15.7724i		−	0.580985i
$738$	2.60555	−	9.28031i	0.0959115	−	0.341613i
$739$	−8.72044	−	8.72044i	−0.320786	−	0.320786i	0.528282	−	0.849069i	$-0.322836\pi$
$739$	−8.72044	−	8.72044i	−0.320786	−	0.320786i	−0.849069	+	0.528282i	$0.822836\pi$
$740$	11.6291	+	9.08364i	0.427493	+	0.333921i
$741$	21.8074	−	21.8074i	0.801113	−	0.801113i
$742$	−76.0076	+	42.6837i	−2.79033	+	1.56697i
$743$	−14.2625			−0.523240			−0.261620	−	0.965171i	$-0.584257\pi$
$743$	−14.2625			−0.523240			−0.261620	+	0.965171i	$0.584257\pi$
$744$	−0.388864	+	10.8745i	−0.0142565	+	0.398677i
$745$	−5.44823	+	46.8827i	−0.199608	+	1.71765i
$746$	−1.28908	+	0.723908i	−0.0471964	+	0.0265042i
$747$	4.88079	+	4.88079i	0.178579	+	0.178579i
$748$	−2.64492	−	10.9039i	−0.0967080	−	0.398687i
$749$	16.6630	+	16.6630i	0.608855	+	0.608855i
$750$	−9.19709	+	12.8613i	−0.335830	+	0.469629i
$751$	25.6200			0.934888			0.467444	−	0.884023i	$-0.345175\pi$
$751$	25.6200			0.934888			0.467444	+	0.884023i	$0.345175\pi$
$752$	−4.21060	+	2.17040i	−0.153545	+	0.0791465i
$753$		−	19.0418i		−	0.693922i
$754$	−3.91873	+	13.9575i	−0.142712	+	0.508304i
$755$	28.1380	+	35.5378i	1.02405	+	1.29335i
$756$	−2.19715	−	9.05793i	−0.0799094	−	0.329434i
$757$	−3.26487	−	3.26487i	−0.118664	−	0.118664i	0.645281	−	0.763945i	$-0.276740\pi$
$757$	−3.26487	−	3.26487i	−0.118664	−	0.118664i	−0.763945	+	0.645281i	$0.776740\pi$
$758$	0.957576	+	1.70517i	0.0347807	+	0.0619346i
$759$			1.25026i			0.0453816i
$760$	−26.9405	+	19.8067i	−0.977234	+	0.718464i
$761$			47.1913i			1.71068i	0.518065	+	0.855341i	$0.326652\pi$
$761$			47.1913i			1.71068i	−0.518065	+	0.855341i	$0.673348\pi$
$762$	−10.9409	+	6.14409i	−0.396346	+	0.222577i
$763$	33.0268	+	33.0268i	1.19565	+	1.19565i
$764$	20.2492	+	12.3434i	0.732592	+	0.446568i
$765$	5.62407	−	4.45301i	0.203339	−	0.160999i
$766$	21.9932	+	6.17484i	0.794648	+	0.223106i
$767$			51.3648i			1.85467i
$768$	2.65142	+	15.7788i	0.0956748	+	0.569368i
$769$	14.1306			0.509563			0.254781	−	0.966999i	$-0.417997\pi$
$769$	14.1306			0.509563			0.254781	+	0.966999i	$0.417997\pi$
$770$	23.8418	+	9.78371i	0.859199	+	0.352581i
$771$	−17.4149	−	17.4149i	−0.627183	−	0.627183i
$772$	−9.30303	+	15.2616i	−0.334824	+	0.549276i
$773$	−18.3760	−	18.3760i	−0.660938	−	0.660938i	0.294663	−	0.955601i	$-0.404793\pi$
$773$	−18.3760	−	18.3760i	−0.660938	−	0.660938i	−0.955601	+	0.294663i	$0.904793\pi$
$774$	−1.29023	−	2.29754i	−0.0463764	−	0.0825832i
$775$	4.41120	−	18.7232i	0.158455	−	0.672556i
$776$	−14.2473	−	15.3040i	−0.511447	−	0.549381i
$777$	15.3771			0.551652
$778$	−4.59907	−	8.18964i	−0.164885	−	0.293613i
$779$	−25.4811	+	25.4811i	−0.912954	+	0.912954i
$780$	3.18195	+	25.8922i	0.113932	+	0.927089i
$781$	−7.70693	−	7.70693i	−0.275776	−	0.275776i
$782$	−3.12296	−	0.876805i	−0.111677	−	0.0313545i
$783$			1.75736i			0.0628030i
$784$	26.9743	+	52.3305i	0.963368	+	1.86894i
$785$	−2.95581	+	25.4351i	−0.105497	+	0.907818i
$786$	3.50537	−	12.4852i	0.125032	−	0.445334i
$787$	15.0804	−	15.0804i	0.537558	−	0.537558i	−0.385253	−	0.922811i	$-0.625886\pi$
$787$	15.0804	−	15.0804i	0.537558	−	0.537558i	0.922811	+	0.385253i	$0.125886\pi$
$788$	−6.85871	−	28.2756i	−0.244331	−	1.00728i
$789$	5.42295	−	5.42295i	0.193062	−	0.193062i
$790$	15.8905	+	38.0085i	0.565360	+	1.35228i
$791$		−	16.6126i		−	0.590674i
$792$	4.94297	+	0.176758i	0.175641	+	0.00628081i
$793$	−36.6509			−1.30151
$794$	0.869306	+	1.54799i	0.0308505	+	0.0549360i
$795$	23.1875	−	18.3594i	0.822376	−	0.651139i
$796$	−16.0840	+	26.3857i	−0.570083	+	0.935217i
$797$	26.8036	−	26.8036i	0.949431	−	0.949431i	−0.0493502	−	0.998782i	$-0.515715\pi$
$797$	26.8036	−	26.8036i	0.949431	−	0.949431i	0.998782	+	0.0493502i	$0.0157150\pi$
$798$	−9.41887	+	33.5477i	−0.333424	+	1.18757i
$799$	−3.79925			−0.134408
$800$	0.824541	−	28.2723i	0.0291519	−	0.999575i
$801$	−2.20498			−0.0779092
$802$	−9.77523	+	34.8169i	−0.345175	+	1.22943i
$803$	6.60721	−	6.60721i	0.233163	−	0.233163i
$804$	−9.38909	+	15.4027i	−0.331128	+	0.543213i
$805$	5.84113	−	4.62487i	0.205873	−	0.163005i
$806$	−15.5398	−	27.6720i	−0.547367	−	0.974706i
$807$	−4.59380			−0.161710
$808$	1.16935	−	32.7006i	0.0411377	−	1.15040i
$809$		−	39.1313i		−	1.37578i	−0.725813	−	0.687892i	$-0.758536\pi$
$809$		−	39.1313i		−	1.37578i	0.725813	−	0.687892i	$-0.241464\pi$
$810$	1.21977	+	2.91756i	0.0428583	+	0.102513i
$811$	25.8556	−	25.8556i	0.907913	−	0.907913i	−0.0881903	−	0.996104i	$-0.528108\pi$
$811$	25.8556	−	25.8556i	0.907913	−	0.907913i	0.996104	+	0.0881903i	$0.0281084\pi$
$812$	−3.86118	−	15.9181i	−0.135501	−	0.558614i
$813$	16.2392	−	16.2392i	0.569534	−	0.569534i
$814$	−2.20576	+	7.85636i	−0.0773118	+	0.275365i
$815$	2.08818	−	17.9690i	0.0731456	−	0.629427i
$816$	−3.90801	+	12.2228i	−0.136808	+	0.427885i
$817$			9.85098i			0.344642i
$818$	−2.71878	−	0.763326i	−0.0950598	−	0.0266891i
$819$	19.2224	+	19.2224i	0.671685	+	0.671685i
$820$	−3.71798	−	30.2540i	−0.129838	−	1.05652i
$821$	−25.5328	+	25.5328i	−0.891100	+	0.891100i	−0.994627	−	0.103527i	$-0.966987\pi$
$821$	−25.5328	+	25.5328i	−0.891100	+	0.891100i	0.103527	+	0.994627i	$0.466987\pi$
$822$	7.09383	+	12.6321i	0.247426	+	0.440595i
$823$	53.6190			1.86904			0.934520	−	0.355910i	$-0.115829\pi$
$823$	53.6190			1.86904			0.934520	+	0.355910i	$0.115829\pi$
$824$	10.3072	−	9.59546i	0.359067	−	0.334274i
$825$	−8.51059	−	2.00511i	−0.296301	−	0.0698088i
$826$	−28.4163	−	50.6014i	−0.988730	−	1.76065i
$827$	38.3567	+	38.3567i	1.33379	+	1.33379i	0.901946	+	0.431849i	$0.142138\pi$
$827$	38.3567	+	38.3567i	1.33379	+	1.33379i	0.431849	+	0.901946i	$0.357862\pi$
$828$	0.744260	−	1.22095i	0.0258648	−	0.0424311i
$829$	−31.1912	−	31.1912i	−1.08331	−	1.08331i	−0.996198	−	0.0871160i	$-0.972235\pi$
$829$	−31.1912	−	31.1912i	−1.08331	−	1.08331i	−0.0871160	−	0.996198i	$-0.527765\pi$
$830$	20.1934	+	8.28657i	0.700924	+	0.287631i
$831$	29.1341			1.01065
$832$	−30.5565	−	35.2704i	−1.05936	−	1.22278i
$833$			47.2180i			1.63601i
$834$	−6.17594	−	1.73396i	−0.213855	−	0.0600422i
$835$	40.0243	−	31.6903i	1.38510	−	1.09669i
$836$	−15.7888	−	9.62442i	−0.546067	−	0.332867i
$837$	−2.72035	−	2.72035i	−0.0940291	−	0.0940291i
$838$	19.4806	−	10.9398i	0.672946	−	0.377907i
$839$		−	29.7728i		−	1.02787i	−0.857829	−	0.513935i	$-0.828187\pi$
$839$		−	29.7728i		−	1.02787i	0.857829	−	0.513935i	$-0.171813\pi$
$840$	−17.4589	−	23.7471i	−0.602389	−	0.819351i
$841$		−	25.9117i		−	0.893506i
$842$	−9.56221	−	17.0276i	−0.329535	−	0.586809i
$843$	5.90247	+	5.90247i	0.203292	+	0.203292i
$844$	7.53050	+	31.0452i	0.259211	+	1.06862i
$845$	−29.1859	−	36.8613i	−1.00403	−	1.26807i
$846$	0.452716	−	1.61246i	0.0155647	−	0.0554375i
$847$		−	37.0120i		−	1.27175i
$848$	−16.1124	+	50.3936i	−0.553301	+	1.73052i
$849$	−16.7264			−0.574050
$850$	10.9769	−	19.8520i	0.376505	−	0.680918i
$851$	1.66812	+	1.66812i	0.0571823	+	0.0571823i
$852$	2.93847	+	12.1141i	0.100670	+	0.415022i
$853$	2.84613	+	2.84613i	0.0974497	+	0.0974497i	0.754151	−	0.656701i	$-0.228049\pi$
$853$	2.84613	+	2.84613i	0.0974497	+	0.0974497i	−0.656701	+	0.754151i	$0.728049\pi$
$854$	36.1062	−	20.2762i	1.23553	−	0.693838i
$855$	1.36466	−	11.7431i	0.0466704	−	0.401604i
$856$	14.2930	+	0.511109i	0.488525	+	0.0174694i
$857$	9.07410			0.309965			0.154983	−	0.987917i	$-0.450468\pi$
$857$	9.07410			0.309965			0.154983	+	0.987917i	$0.450468\pi$
$858$	−12.5783	+	7.06361i	−0.429415	+	0.241148i
$859$	−29.4185	+	29.4185i	−1.00374	+	1.00374i	−0.00375173	+	0.999993i	$0.501194\pi$
$859$	−29.4185	+	29.4185i	−1.00374	+	1.00374i	−0.999993	+	0.00375173i	$0.998806\pi$
$860$	−6.56679	−	5.12942i	−0.223926	−	0.174912i
$861$	−22.4606	−	22.4606i	−0.765456	−	0.765456i
$862$	9.62460	−	34.2804i	0.327815	−	1.16760i
$863$		−	25.5875i		−	0.871008i	−0.900187	−	0.435504i	$-0.856570\pi$
$863$		−	25.5875i		−	0.871008i	0.900187	−	0.435504i	$-0.143430\pi$
$864$	−4.72189	−	3.11509i	−0.160642	−	0.105977i
$865$	−1.50769	+	12.9739i	−0.0512630	+	0.441124i
$866$	2.43300	+	0.683091i	0.0826766	+	0.0232124i
$867$	4.74335	−	4.74335i	0.161093	−	0.161093i
$868$	30.6178	+	18.6637i	1.03923	+	0.633489i
$869$	−16.1089	+	16.1089i	−0.546458	+	0.546458i
$870$	2.14357	+	5.12721i	0.0726740	+	0.173829i
$871$		−	52.6123i		−	1.78270i
$872$	28.3293	+	1.01304i	0.959351	+	0.0343058i
$873$	7.39253			0.250199
$874$	−4.66102	+	2.61750i	−0.157662	+	0.0885383i
$875$	22.1141	+	47.1780i	0.747592	+	1.59491i
$876$	−10.3855	+	2.51917i	−0.350894	+	0.0851150i
$877$	−28.2401	+	28.2401i	−0.953600	+	0.953600i	−0.998970	−	0.0453704i	$-0.985553\pi$
$877$	−28.2401	+	28.2401i	−0.953600	+	0.953600i	0.0453704	+	0.998970i	$0.485553\pi$
$878$	−6.75405	−	1.89627i	−0.227938	−	0.0639961i
$879$	−7.12081			−0.240179
$880$	14.6370	−	5.51358i	0.493414	−	0.185863i
$881$	14.8839			0.501453			0.250726	−	0.968058i	$-0.419331\pi$
$881$	14.8839			0.501453			0.250726	+	0.968058i	$0.419331\pi$
$882$	−20.0401	−	5.62647i	−0.674784	−	0.189453i
$883$	−4.00191	+	4.00191i	−0.134675	+	0.134675i	−0.771231	−	0.636556i	$-0.780359\pi$
$883$	−4.00191	+	4.00191i	−0.134675	+	0.134675i	0.636556	+	0.771231i	$0.280359\pi$
$884$	−8.82270	−	36.3723i	−0.296740	−	1.22333i
$885$	12.2226	+	15.4369i	0.410857	+	0.518905i
$886$	6.42632	−	3.60884i	0.215897	−	0.121241i
$887$	−40.4073			−1.35675			−0.678373	−	0.734718i	$-0.737315\pi$
$887$	−40.4073			−1.35675			−0.678373	+	0.734718i	$0.737315\pi$
$888$	6.83082	−	6.35916i	0.229227	−	0.213399i
$889$			41.3499i			1.38683i
$890$	−6.43317	+	2.68957i	−0.215640	+	0.0901545i
$891$	−1.23653	+	1.23653i	−0.0414254	+	0.0414254i
$892$	5.09095	−	8.35168i	0.170458	−	0.279635i
$893$	−4.42735	+	4.42735i	−0.148156	+	0.148156i
$894$	28.7395	+	8.06894i	0.961194	+	0.269866i
$895$	37.4853	+	4.35616i	1.25299	+	0.145610i
$896$	49.6148	+	17.8416i	1.65752	+	0.596044i
$897$			4.17050i			0.139249i
$898$	−9.84909	+	35.0800i	−0.328668	+	1.17063i
$899$	−4.78064	−	4.78064i	−0.159443	−	0.159443i
$900$	7.11750	+	7.02433i	0.237250	+	0.234144i
$901$	−30.0043	+	30.0043i	−0.999589	+	0.999589i
$902$	14.6972	−	8.25355i	0.489365	−	0.274813i
$903$	−8.68328			−0.288962
$904$	−6.87006	−	7.37962i	−0.228495	−	0.245443i
$905$	5.58198	−	48.0336i	0.185551	−	1.59669i
$906$	24.9965	−	14.0374i	0.830454	−	0.466360i
$907$	10.1082	+	10.1082i	0.335637	+	0.335637i	0.854723	−	0.519085i	$-0.173727\pi$
$907$	10.1082	+	10.1082i	0.335637	+	0.335637i	−0.519085	+	0.854723i	$0.673727\pi$
$908$	−6.86401	+	1.66498i	−0.227790	+	0.0552542i
$909$	8.18037	+	8.18037i	0.271326	+	0.271326i
$910$	79.5294	+	32.6356i	2.63637	+	1.08186i
$911$	−16.6514			−0.551686			−0.275843	−	0.961203i	$-0.588957\pi$
$911$	−16.6514			−0.551686			−0.275843	+	0.961203i	$0.588957\pi$
$912$	9.68946	+	18.7977i	0.320850	+	0.622453i
$913$			12.0705i			0.399475i
$914$	0.515443	−	1.83588i	0.0170493	−	0.0607255i
$915$	−11.0149	+	8.72132i	−0.364140	+	0.288318i
$916$	17.3651	−	4.21218i	0.573759	−	0.139175i
$917$	−30.2174	−	30.2174i	−0.997865	−	0.997865i
$918$	−2.22149	−	3.95585i	−0.0733202	−	0.130562i
$919$			15.5624i			0.513355i	0.966497	+	0.256678i	$0.0826279\pi$
$919$			15.5624i			0.513355i	−0.966497	+	0.256678i	$0.917372\pi$
$920$	0.682143	−	4.47004i	0.0224896	−	0.147373i
$921$			11.4535i			0.377405i
$922$	33.4778	−	18.8002i	1.10253	−	0.619152i
$923$	−25.7081	−	25.7081i	−0.846192	−	0.846192i
$924$	8.48358	−	13.9173i	0.279089	−	0.457844i
$925$	−14.0302	+	8.67972i	−0.461311	+	0.285387i
$926$	−2.92779	−	0.822010i	−0.0962133	−	0.0270129i
$927$			4.97884i			0.163527i
$928$	−8.29807	−	5.47433i	−0.272397	−	0.179704i
$929$	41.5344			1.36270			0.681350	−	0.731958i	$-0.261393\pi$
$929$	41.5344			1.36270			0.681350	+	0.731958i	$0.261393\pi$
$930$	−11.2550	−	4.61859i	−0.369066	−	0.151450i
$931$	55.0243	+	55.0243i	1.80335	+	1.80335i
$932$	15.5198	+	9.46044i	0.508368	+	0.309887i
$933$	−5.93411	−	5.93411i	−0.194274	−	0.194274i
$934$	8.30307	+	14.7854i	0.271685	+	0.483794i
$935$	12.4606	+	1.44805i	0.407506	+	0.0473562i
$936$	16.4883	+	0.589612i	0.538937	+	0.0192721i
$937$	−46.5132			−1.51952			−0.759761	−	0.650203i	$-0.774684\pi$
$937$	−46.5132			−1.51952			−0.759761	+	0.650203i	$0.774684\pi$
$938$	29.1065	+	51.8304i	0.950360	+	1.69232i
$939$	−12.9811	+	12.9811i	−0.423622	+	0.423622i
$940$	−0.646002	−	5.25666i	−0.0210703	−	0.171453i
$941$	−5.79704	−	5.79704i	−0.188978	−	0.188978i	0.606276	−	0.795254i	$-0.292663\pi$
$941$	−5.79704	−	5.79704i	−0.188978	−	0.188978i	−0.795254	+	0.606276i	$0.792663\pi$
$942$	15.5920	+	4.37761i	0.508014	+	0.142630i
$943$		−	4.87307i		−	0.158689i
$944$	−33.5491	−	10.7267i	−1.09193	−	0.349123i
$945$	10.3511	+	1.20290i	0.336721	+	0.0391303i
$946$	1.24556	−	4.43639i	0.0404968	−	0.144239i
$947$	−18.8524	+	18.8524i	−0.612622	+	0.612622i	−0.943628	−	0.331007i	$-0.892612\pi$
$947$	−18.8524	+	18.8524i	−0.612622	+	0.612622i	0.331007	+	0.943628i	$0.392612\pi$
$948$	25.3207	−	6.14195i	0.822379	−	0.199481i
$949$	22.0397	−	22.0397i	0.715440	−	0.715440i
$950$	−10.3423	−	35.9257i	−0.335550	−	1.16558i
$951$		−	0.728219i		−	0.0236141i
$952$	28.8137	+	30.9508i	0.933857	+	1.00312i
$953$	−15.9773			−0.517557			−0.258778	−	0.965937i	$-0.583320\pi$
$953$	−15.9773			−0.517557			−0.258778	+	0.965937i	$0.583320\pi$
$954$	−9.15901	−	16.3096i	−0.296534	−	0.528043i
$955$	−20.7870	+	16.4587i	−0.672652	+	0.532591i
$956$	17.9170	+	10.9217i	0.579478	+	0.353234i
$957$	−2.17303	+	2.17303i	−0.0702442	+	0.0702442i
$958$	−5.90514	+	21.0326i	−0.190786	+	0.679533i
$959$	47.7416			1.54166
$960$	−17.5761	−	3.32885i	−0.567266	−	0.107438i
$961$	−16.1994			−0.522560
$962$	−7.35777	+	26.2065i	−0.237224	+	0.844933i
$963$	−3.57553	+	3.57553i	−0.115220	+	0.115220i
$964$	13.7146	+	8.36003i	0.441717	+	0.269258i
$965$	−12.4047	−	15.6669i	−0.399321	−	0.504335i
$966$	−2.30723	−	4.10852i	−0.0742339	−	0.132190i
$967$	46.0281			1.48017			0.740083	−	0.672516i	$-0.234786\pi$
$967$	46.0281			1.48017			0.740083	+	0.672516i	$0.234786\pi$
$968$	−15.3062	−	16.4414i	−0.491959	−	0.528448i
$969$			16.9612i			0.544872i
$970$	21.5682	−	9.01718i	0.692512	−	0.289524i
$971$	−19.8313	+	19.8313i	−0.636416	+	0.636416i	−0.949670	−	0.313253i	$-0.898581\pi$
$971$	−19.8313	+	19.8313i	−0.636416	+	0.636416i	0.313253	+	0.949670i	$0.398581\pi$
$972$	1.94364	−	0.471461i	0.0623422	−	0.0151221i
$973$	−14.9473	+	14.9473i	−0.479189	+	0.479189i
$974$	−8.05499	+	28.6899i	−0.258099	+	0.919282i
$975$	−28.3889	−	6.68845i	−0.909171	−	0.214202i
$976$	7.65393	−	23.9387i	0.244996	−	0.766259i
$977$			33.7468i			1.07965i	0.841776	+	0.539827i	$0.181510\pi$
$977$			33.7468i			1.07965i	−0.841776	+	0.539827i	$0.818490\pi$
$978$	−11.0152	−	3.09263i	−0.352226	−	0.0988914i
$979$	−2.72653	−	2.72653i	−0.0871403	−	0.0871403i
$980$	−65.3311	+	8.02868i	−2.08693	+	0.256467i
$981$	−7.08685	+	7.08685i	−0.226266	+	0.226266i
$982$	−7.31100	−	13.0188i	−0.233303	−	0.415447i
$983$	−1.19047			−0.0379700			−0.0189850	−	0.999820i	$-0.506043\pi$
$983$	−1.19047			−0.0379700			−0.0189850	+	0.999820i	$0.506043\pi$
$984$	−19.2660	−	0.688939i	−0.614176	−	0.0219626i
$985$	32.3124	+	3.75502i	1.02956	+	0.119645i
$986$	−3.90397	−	6.95186i	−0.124328	−	0.221392i
$987$	−3.90255	−	3.90255i	−0.124220	−	0.124220i
$988$	−52.6669	−	32.1043i	−1.67556	−	1.02137i
$989$	−0.941966	−	0.941966i	−0.0299528	−	0.0299528i
$990$	−2.09938	+	5.11594i	−0.0667225	+	0.162595i
$991$	−47.3142			−1.50298			−0.751492	−	0.659742i	$-0.770665\pi$
$991$	−47.3142			−1.50298			−0.751492	+	0.659742i	$0.770665\pi$
$992$	21.3193	−	4.37107i	0.676889	−	0.138781i
$993$		−	26.9167i		−	0.854175i
$994$	39.5484	+	11.1036i	1.25440	+	0.352186i
$995$	−21.4465	−	27.0865i	−0.679899	−	0.858699i
$996$	7.18538	−	11.7876i	0.227678	−	0.373504i
$997$	27.5653	+	27.5653i	0.873002	+	0.873002i	0.992798	−	0.119797i	$-0.0382243\pi$
$997$	27.5653	+	27.5653i	0.873002	+	0.873002i	−0.119797	+	0.992798i	$0.538224\pi$
$998$	11.7785	−	6.61447i	0.372842	−	0.209377i
$999$			3.29960i			0.104395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.14	yes	48
3.2	odd	2		720.2.bm.h.109.11		48
4.3	odd	2		960.2.bl.a.529.10		48
5.4	even	2	inner	240.2.bl.a.109.11	✓	48
8.3	odd	2		1920.2.bl.b.289.24		48
8.5	even	2		1920.2.bl.a.289.1		48
15.14	odd	2		720.2.bm.h.109.14		48
16.3	odd	4		1920.2.bl.b.1249.1		48
16.5	even	4	inner	240.2.bl.a.229.11	yes	48
16.11	odd	4		960.2.bl.a.49.21		48
16.13	even	4		1920.2.bl.a.1249.24		48
20.19	odd	2		960.2.bl.a.529.21		48
40.19	odd	2		1920.2.bl.b.289.1		48
40.29	even	2		1920.2.bl.a.289.24		48
48.5	odd	4		720.2.bm.h.469.14		48
80.19	odd	4		1920.2.bl.b.1249.24		48
80.29	even	4		1920.2.bl.a.1249.1		48
80.59	odd	4		960.2.bl.a.49.10		48
80.69	even	4	inner	240.2.bl.a.229.14	yes	48
240.149	odd	4		720.2.bm.h.469.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.11	✓	48	5.4	even	2	inner
240.2.bl.a.109.14	yes	48	1.1	even	1	trivial
240.2.bl.a.229.11	yes	48	16.5	even	4	inner
240.2.bl.a.229.14	yes	48	80.69	even	4	inner
720.2.bm.h.109.11		48	3.2	odd	2
720.2.bm.h.109.14		48	15.14	odd	2
720.2.bm.h.469.11		48	240.149	odd	4
720.2.bm.h.469.14		48	48.5	odd	4
960.2.bl.a.49.10		48	80.59	odd	4
960.2.bl.a.49.21		48	16.11	odd	4
960.2.bl.a.529.10		48	4.3	odd	2
960.2.bl.a.529.21		48	20.19	odd	2
1920.2.bl.a.289.1		48	8.5	even	2
1920.2.bl.a.289.24		48	40.29	even	2
1920.2.bl.a.1249.1		48	80.29	even	4
1920.2.bl.a.1249.24		48	16.13	even	4
1920.2.bl.b.289.1		48	40.19	odd	2
1920.2.bl.b.289.24		48	8.3	odd	2
1920.2.bl.b.1249.1		48	16.3	odd	4
1920.2.bl.b.1249.24		48	80.19	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382275 - 1.36157i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.75308 - 1.38805i) q^{5} +(-0.692464 - 1.23308i) q^{6} -4.66030 q^{7} +(-2.07020 + 1.92725i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.382275 - 1.36157i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.75308 - 1.38805i) q^{5} +(-0.692464 - 1.23308i) q^{6} -4.66030 q^{7} +(-2.07020 + 1.92725i) q^{8} -1.00000i q^{9} +(-1.21977 - 2.91756i) q^{10} +(1.23653 - 1.23653i) q^{11} +(-1.94364 + 0.471461i) q^{12} +(4.12471 - 4.12471i) q^{13} +(-1.78151 + 6.34531i) q^{14} +(0.258116 - 2.22112i) q^{15} +(1.83270 + 3.55545i) q^{16} +3.20810i q^{17} +(-1.36157 - 0.382275i) q^{18} +(3.73847 + 3.73847i) q^{19} +(-4.43874 + 0.545487i) q^{20} +(-3.29533 + 3.29533i) q^{21} +(-1.21093 - 2.15632i) q^{22} -0.714957 q^{23} +(-0.101078 + 2.82662i) q^{24} +(1.14661 - 4.86675i) q^{25} +(-4.03930 - 7.19285i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(7.95854 + 4.85131i) q^{28} +(-1.24264 - 1.24264i) q^{29} +(-2.92553 - 1.20052i) q^{30} +3.84716 q^{31} +(5.54158 - 1.13618i) q^{32} -1.74872i q^{33} +(4.36804 + 1.22637i) q^{34} +(-8.16990 + 6.46874i) q^{35} +(-1.04099 + 1.70773i) q^{36} +(-2.33317 - 2.33317i) q^{37} +(6.51931 - 3.66106i) q^{38} -5.83322i q^{39} +(-0.954103 + 6.25217i) q^{40} +6.81590i q^{41} +(3.22709 + 5.74653i) q^{42} +(1.31751 + 1.31751i) q^{43} +(-3.39888 + 0.824453i) q^{44} +(-1.38805 - 1.75308i) q^{45} +(-0.273310 + 0.973462i) q^{46} +1.18427i q^{47} +(3.80999 + 1.21817i) q^{48} +14.7184 q^{49} +(-6.18809 - 3.42163i) q^{50} +(2.26847 + 2.26847i) q^{51} +(-11.3377 + 2.75014i) q^{52} +(9.35268 + 9.35268i) q^{53} +(-1.23308 + 0.692464i) q^{54} +(0.451373 - 3.88412i) q^{55} +(9.64773 - 8.98156i) q^{56} +5.28700 q^{57} +(-2.16697 + 1.21691i) q^{58} +(-6.22646 + 6.22646i) q^{59} +(-2.75295 + 3.52438i) q^{60} +(-4.44284 - 4.44284i) q^{61} +(1.47067 - 5.23817i) q^{62} +4.66030i q^{63} +(0.571420 - 7.97957i) q^{64} +(1.50565 - 12.9563i) q^{65} +(-2.38100 - 0.668492i) q^{66} +(6.37769 - 6.37769i) q^{67} +(3.33958 - 5.47857i) q^{68} +(-0.505551 + 0.505551i) q^{69} +(5.68448 + 13.5967i) q^{70} -6.23269i q^{71} +(1.92725 + 2.07020i) q^{72} +5.34334 q^{73} +(-4.06868 + 2.28486i) q^{74} +(-2.63054 - 4.25209i) q^{75} +(-2.49261 - 10.2760i) q^{76} +(-5.76261 + 5.76261i) q^{77} +(-7.94233 - 2.22990i) q^{78} -13.0275 q^{79} +(8.14803 + 3.68912i) q^{80} -1.00000 q^{81} +(9.28031 + 2.60555i) q^{82} +(-4.88079 + 4.88079i) q^{83} +(9.05793 - 2.19715i) q^{84} +(4.45301 + 5.62407i) q^{85} +(2.29754 - 1.29023i) q^{86} -1.75736 q^{87} +(-0.176758 + 4.94297i) q^{88} -2.20498i q^{89} +(-2.91756 + 1.21977i) q^{90} +(-19.2224 + 19.2224i) q^{91} +(1.22095 + 0.744260i) q^{92} +(2.72035 - 2.72035i) q^{93} +(1.61246 + 0.452716i) q^{94} +(11.7431 + 1.36466i) q^{95} +(3.11509 - 4.72189i) q^{96} +7.39253i q^{97} +(5.62647 - 20.0401i) q^{98} +(-1.23653 - 1.23653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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