LMFDB - Embedded newform 240.2.bl.a.109.11

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			109.11
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382275 + 1.36157i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.38805 - 1.75308i) q^{5} +(-0.692464 - 1.23308i) q^{6} +4.66030 q^{7} +(2.07020 - 1.92725i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.382275 + 1.36157i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.38805 - 1.75308i) q^{5} +(-0.692464 - 1.23308i) q^{6} +4.66030 q^{7} +(2.07020 - 1.92725i) q^{8} -1.00000i q^{9} +(1.85633 + 2.56009i) 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} +(-4.19536 + 1.54885i) 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} +(-3.12288 - 0.497636i) q^{30} +3.84716 q^{31} +(-5.54158 + 1.13618i) q^{32} +1.74872i q^{33} +(4.36804 + 1.22637i) q^{34} +(6.46874 - 8.16990i) q^{35} +(-1.04099 + 1.70773i) q^{36} +(2.33317 + 2.33317i) q^{37} +(-6.51931 + 3.66106i) q^{38} -5.83322i q^{39} +(-0.505089 - 6.30435i) q^{40} +6.81590i q^{41} +(-3.22709 - 5.74653i) q^{42} +(-1.31751 - 1.31751i) q^{43} +(-3.39888 + 0.824453i) q^{44} +(-1.75308 - 1.38805i) q^{45} +(-0.273310 + 0.973462i) q^{46} -1.18427i q^{47} +(-3.80999 - 1.21817i) q^{48} +14.7184 q^{49} +(7.06473 + 0.299245i) 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} +(1.87136 - 4.06177i) 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} +(8.65103 + 11.9308i) q^{70} -6.23269i q^{71} +(-1.92725 - 2.07020i) q^{72} -5.34334 q^{73} +(-4.06868 + 2.28486i) q^{74} +(4.25209 + 2.63054i) q^{75} +(-2.49261 - 10.2760i) q^{76} +(5.76261 - 5.76261i) q^{77} +(7.94233 + 2.22990i) q^{78} -13.0275 q^{79} +(8.77689 + 1.72228i) q^{80} -1.00000 q^{81} +(-9.28031 - 2.60555i) q^{82} +(4.88079 - 4.88079i) q^{83} +(9.05793 - 2.19715i) q^{84} +(-5.62407 - 4.45301i) q^{85} +(2.29754 - 1.29023i) q^{86} +1.75736 q^{87} +(0.176758 - 4.94297i) q^{88} -2.20498i q^{89} +(2.56009 - 1.85633i) 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
$5$	1.38805	−	1.75308i	0.620757	−	0.784003i
$5$	1.38805	−	1.75308i	0.620757	−	0.784003i
$6$	−0.692464	−	1.23308i	−0.282697	−	0.503404i
$7$	4.66030			1.76143			0.880714	−	0.473649i	$-0.157064\pi$
$7$	4.66030			1.76143			0.880714	+	0.473649i	$0.157064\pi$
$8$	2.07020	−	1.92725i	0.731925	−	0.681386i
$9$		−	1.00000i		−	0.333333i
$10$	1.85633	+	2.56009i	0.587022	+	0.809571i
$11$	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	$0.549949\pi$
$13$	−4.12471	+	4.12471i	−1.14399	+	1.14399i	−0.987713	+	0.156276i	$0.950051\pi$
$14$	−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	$-0.872807\pi$
$17$		−	3.20810i		−	0.778078i	0.921221	−	0.389039i	$-0.127193\pi$
$18$	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	$0.542589\pi$
$20$	−4.19536	+	1.54885i	−0.938111	+	0.346334i
$21$	−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	$-0.476251\pi$
$23$	0.714957			0.149079			0.0745394	+	0.997218i	$0.476251\pi$
$24$	−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	$0.802171\pi$
$30$	−3.12288	−	0.497636i	−0.570157	−	0.0908555i
$31$	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
$35$	6.46874	−	8.16990i	1.09342	−	1.38096i
$36$	−1.04099	+	1.70773i	−0.173498	+	0.284622i
$37$	2.33317	+	2.33317i	0.383571	+	0.383571i	0.872387	−	0.488816i	$-0.162571\pi$
$37$	2.33317	+	2.33317i	0.383571	+	0.383571i	−0.488816	+	0.872387i	$0.662571\pi$
$38$	−6.51931	+	3.66106i	−1.05757	+	0.593902i
$39$		−	5.83322i		−	0.934064i
$40$	−0.505089	−	6.30435i	−0.0798616	−	0.996806i
$41$			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	0.599475	−	0.800394i	$-0.295376\pi$
$43$	−1.31751	−	1.31751i	−0.200919	−	0.200919i	−0.800394	+	0.599475i	$0.795376\pi$
$44$	−3.39888	+	0.824453i	−0.512400	+	0.124291i
$45$	−1.75308	−	1.38805i	−0.261334	−	0.206919i
$46$	−0.273310	+	0.973462i	−0.0402974	+	0.143529i
$47$		−	1.18427i		−	0.172743i	−0.996263	−	0.0863716i	$-0.972473\pi$
$47$		−	1.18427i		−	0.172743i	0.996263	−	0.0863716i	$-0.0275272\pi$
$48$	−3.80999	−	1.21817i	−0.549925	−	0.175828i
$49$	14.7184			2.10263
$50$	7.06473	+	0.299245i	0.999104	+	0.0423197i
$51$	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	$-0.887295\pi$
$53$	−9.35268	−	9.35268i	−1.28469	−	1.28469i	−0.346722	−	0.937968i	$-0.612705\pi$
$54$	−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	$0.444295\pi$
$60$	1.87136	−	4.06177i	0.241592	−	0.524373i
$61$	−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	−0.979688	−	0.200529i	$-0.935734\pi$
$67$	−6.37769	+	6.37769i	−0.779159	+	0.779159i	0.200529	+	0.979688i	$0.435734\pi$
$68$	−3.33958	+	5.47857i	−0.404984	+	0.664374i
$69$	−0.505551	+	0.505551i	−0.0608612	+	0.0608612i
$70$	8.65103	+	11.9308i	1.03400	+	1.42600i
$71$		−	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	$-0.601232\pi$
$73$	−5.34334			−0.625391			−0.312695	+	0.949853i	$0.601232\pi$
$74$	−4.06868	+	2.28486i	−0.472975	+	0.265609i
$75$	4.25209	+	2.63054i	0.490989	+	0.303748i
$76$	−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	$0.761812\pi$
$80$	8.77689	+	1.72228i	0.981286	+	0.192557i
$81$	−1.00000			−0.111111
$82$	−9.28031	−	2.60555i	−1.02484	−	0.287735i
$83$	4.88079	−	4.88079i	0.535736	−	0.535736i	−0.386537	−	0.922274i	$-0.626329\pi$
$83$	4.88079	−	4.88079i	0.535736	−	0.535736i	0.922274	+	0.386537i	$0.126329\pi$
$84$	9.05793	−	2.19715i	0.988301	−	0.239728i
$85$	−5.62407	−	4.45301i	−0.610016	−	0.482997i
$86$	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	$-0.0372841\pi$
$90$	2.56009	−	1.85633i	0.269857	−	0.195674i
$91$	−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	$-0.877540\pi$
$97$		−	7.39253i		−	0.750598i	0.926904	−	0.375299i	$-0.122460\pi$
$98$	−5.62647	+	20.0401i	−0.568359	+	2.02435i
$99$	−1.23653	−	1.23653i	−0.124276	−	0.124276i
$100$	−3.10811	+	9.50472i	−0.310811	+	0.950472i
$101$	−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	$-0.421117\pi$
$103$	4.97884			0.490580			0.245290	+	0.969450i	$0.421117\pi$
$104$	−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	0.858490	−	0.512830i	$-0.171403\pi$
$107$	3.57553	+	3.57553i	0.345660	+	0.345660i	−0.512830	+	0.858490i	$0.671403\pi$
$108$	−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	$0.909357\pi$
$110$	5.46104	+	0.870226i	0.520690	+	0.0829728i
$111$	−3.29960			−0.313184
$112$	8.54091	+	16.5695i	0.807040	+	1.56567i
$113$		−	3.56470i		−	0.335339i	−0.985843	−	0.167669i	$-0.946376\pi$
$113$		−	3.56470i		−	0.335339i	0.985843	−	0.167669i	$-0.0536241\pi$
$114$	2.02109	−	7.19861i	0.189292	−	0.674211i
$115$	0.992399	−	1.25338i	0.0925417	−	0.116878i
$116$	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
$120$	4.81500	+	4.10070i	0.439548	+	0.374341i
$121$			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
$125$	−10.1234	−	4.74520i	−0.905464	−	0.424424i
$126$	6.34531	+	1.78151i	0.565285	+	0.158710i
$127$			8.87279i			0.787333i	0.919253	+	0.393666i	$0.128793\pi$
$127$			8.87279i			0.787333i	−0.919253	+	0.393666i	$0.871207\pi$
$128$	10.6463	+	3.82841i	0.941007	+	0.338387i
$129$	1.86325			0.164050
$130$	−18.2164	−	2.90282i	−1.59769	−	0.254594i
$131$	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	$-0.355823\pi$
$137$	10.2443			0.875232			0.437616	+	0.899162i	$0.355823\pi$
$138$	−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	$0.188384\pi$
$140$	−19.5516	+	7.21812i	−1.65241	+	0.610043i
$141$	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	$0.917569\pi$
$150$	−5.20712	+	4.78392i	−0.425159	+	0.390606i
$151$			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
$155$	5.34006	−	6.74439i	0.428924	−	0.541723i
$156$	−6.07231	+	9.96158i	−0.486174	+	0.797565i
$157$	8.09742	−	8.09742i	0.646245	−	0.646245i	−0.305839	−	0.952083i	$-0.598937\pi$
$157$	8.09742	−	8.09742i	0.646245	−	0.646245i	0.952083	+	0.305839i	$0.0989369\pi$
$158$	4.98009	−	17.7378i	0.396194	−	1.41115i
$159$	13.2267			1.04894
$160$	−5.70019	+	11.2919i	−0.450639	+	0.892706i
$161$	3.33191			0.262592
$162$	0.382275	−	1.36157i	0.0300343	−	0.106975i
$163$	−5.72054	+	5.72054i	−0.448067	+	0.448067i	−0.894712	−	0.446644i	$-0.852619\pi$
$163$	−5.72054	+	5.72054i	−0.448067	+	0.448067i	0.446644	+	0.894712i	$0.352619\pi$
$164$	7.09526	−	11.6397i	0.554046	−	0.908910i
$165$	3.06566	+	2.42732i	0.238661	+	0.188966i
$166$	4.77972	+	8.51133i	0.370978	+	0.660607i
$167$	−22.8308			−1.76670			−0.883349	−	0.468716i	$-0.844717\pi$
$167$	−22.8308			−1.76670			−0.883349	+	0.468716i	$0.844717\pi$
$168$	−0.471055	+	13.1729i	−0.0363427	+	1.01631i
$169$		−	21.0265i		−	1.61742i
$170$	8.21301	−	5.95527i	0.629909	−	0.456748i
$171$	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	−0.532444	−	0.846465i	$-0.678726\pi$
$173$	4.13030	−	4.13030i	0.314021	−	0.314021i	0.846465	+	0.532444i	$0.178726\pi$
$174$	−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	$0.532762\pi$
$180$	1.54885	+	4.19536i	0.115445	+	0.312704i
$181$	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
$190$	−2.63100	+	16.5106i	−0.190873	+	1.19781i
$191$	−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	$0.104234\pi$
$193$			8.93675i			0.643281i	−0.946862	+	0.321641i	$0.895766\pi$
$194$	10.0654	+	2.82598i	0.722656	+	0.202894i
$195$	−10.2261	−	8.09683i	−0.732309	−	0.579826i
$196$	−25.1350	−	15.3216i	−1.79536	−	1.09440i
$197$	−10.2868	−	10.2868i	−0.732907	−	0.732907i	0.238288	−	0.971195i	$-0.423414\pi$
$197$	−10.2868	−	10.2868i	−0.732907	−	0.732907i	−0.971195	+	0.238288i	$0.923414\pi$
$198$	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	$-0.184473\pi$
$200$	−11.7532	−	7.86532i	−0.831074	−	0.556162i
$201$		−	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
$205$	11.9489	+	9.46083i	0.834544	+	0.660773i
$206$	−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
$210$	−14.5535	−	2.31913i	−1.00429	−	0.160035i
$211$	−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
$220$	−3.27249	+	7.10291i	−0.220631	+	0.478878i
$221$	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	$-0.947642\pi$
$223$		−	4.89051i		−	0.327493i	0.986502	−	0.163746i	$-0.0523579\pi$
$224$	−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	−0.785105	−	0.619362i	$-0.787391\pi$
$227$	−2.49717	+	2.49717i	−0.165743	+	0.165743i	0.619362	+	0.785105i	$0.287391\pi$
$228$	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	$0.345386\pi$
$230$	1.32719	+	1.83035i	0.0875125	+	0.120690i
$231$			8.14956i			0.536202i
$232$	−4.96739	−	0.177631i	−0.326125	−	0.0116621i
$233$	9.08796			0.595372			0.297686	−	0.954664i	$-0.403785\pi$
$233$	9.08796			0.595372			0.297686	+	0.954664i	$0.403785\pi$
$234$	−7.19285	+	4.03930i	−0.470211	+	0.264057i
$235$	−2.07612	−	1.64383i	−0.135431	−	0.107231i
$236$	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	$0.610199\pi$
$240$	−7.42403	+	4.98836i	−0.479219	+	0.321997i
$241$	−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
$245$	20.4299	−	25.8026i	1.30522	−	1.64847i
$246$	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
$250$	10.3308	−	11.9697i	0.653379	−	0.757031i
$251$	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	$0.278817\pi$
$257$			24.6284i			1.53628i	−0.640283	+	0.768139i	$0.721183\pi$
$258$	−0.712272	+	2.53694i	−0.0443441	+	0.157943i
$259$	10.8733	+	10.8733i	0.675632	+	0.675632i
$260$	10.9161	−	23.6932i	0.676986	−	1.46939i
$261$	−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	$-0.575985\pi$
$263$	−7.66921			−0.472904			−0.236452	+	0.971643i	$0.575985\pi$
$264$	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	$0.794725\pi$
$270$	−0.497636	+	3.12288i	−0.0302852	+	0.190052i
$271$	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
$275$	−7.43572	−	4.60007i	−0.448391	−	0.277395i
$276$	1.38962	−	0.337074i	0.0836451	−	0.0202895i
$277$	−20.6009	−	20.6009i	−1.23779	−	1.23779i	−0.960903	−	0.276885i	$-0.910698\pi$
$277$	−20.6009	−	20.6009i	−1.23779	−	1.23779i	−0.276885	−	0.960903i	$-0.589302\pi$
$278$	3.14095	+	5.59315i	0.188382	+	0.335455i
$279$		−	3.84716i		−	0.230323i
$280$	−2.35387	−	29.3802i	−0.140670	−	1.75580i
$281$			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	0.965067	−	0.262002i	$-0.0843828\pi$
$283$	11.8274	+	11.8274i	0.703065	+	0.703065i	−0.262002	+	0.965067i	$0.584383\pi$
$284$	−6.48815	+	10.6438i	−0.385001	+	0.631592i
$285$	−7.33864	+	9.26856i	−0.434703	+	0.549022i
$286$	−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
$290$	0.874527	−	5.48802i	0.0513540	−	0.322268i
$291$	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	0.838720	−	0.544562i	$-0.183304\pi$
$293$	5.03517	+	5.03517i	0.294158	+	0.294158i	−0.544562	+	0.838720i	$0.683304\pi$
$294$	−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
$300$	−4.52308	−	8.91862i	−0.261140	−	0.514917i
$301$	−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	−0.437159	−	0.899384i	$-0.644015\pi$
$307$	8.09883	−	8.09883i	0.462224	−	0.462224i	0.899384	+	0.437159i	$0.144015\pi$
$308$	−15.8398	+	3.84219i	−0.902555	+	0.218929i
$309$	−3.52057	+	3.52057i	−0.200278	+	0.200278i
$310$	7.14158	+	9.84907i	0.405614	+	0.559389i
$311$		−	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	$-0.326368\pi$
$313$	18.3580			1.03766			0.518829	+	0.854878i	$0.326368\pi$
$314$	7.92974	+	14.1206i	0.447501	+	0.796873i
$315$	−8.16990	−	6.46874i	−0.460322	−	0.364472i
$316$	22.2475	+	13.5614i	1.25152	+	0.762891i
$317$	−0.514929	+	0.514929i	−0.0289213	+	0.0289213i	−0.721420	−	0.692498i	$-0.756510\pi$
$317$	−0.514929	+	0.514929i	−0.0289213	+	0.0289213i	0.692498	+	0.721420i	$0.256510\pi$
$318$	−5.05623	+	18.0090i	−0.283539	+	1.00990i
$319$	−3.07313			−0.172062
$320$	−13.1957	−	12.0778i	−0.737662	−	0.675170i
$321$	−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
$325$	24.8034	+	15.3445i	1.37585	+	0.851160i
$326$	−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
$330$	−4.47688	+	3.24619i	−0.246444	+	0.178697i
$331$	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	$-0.843690\pi$
$337$		−	17.3135i		−	0.943127i	0.881832	−	0.471564i	$-0.156310\pi$
$338$	28.6290	+	8.03791i	1.55721	+	0.437204i
$339$	2.52062	+	2.52062i	0.136901	+	0.136901i
$340$	4.96888	+	13.4591i	0.269475	+	0.729923i
$341$	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	0.884374	−	0.466779i	$-0.154586\pi$
$347$	7.77893	+	7.77893i	0.417595	+	0.417595i	−0.466779	+	0.884374i	$0.654586\pi$
$348$	−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	$0.494676\pi$
$350$	32.9238	+	1.39457i	1.75985	+	0.0745430i
$351$	−5.83322			−0.311355
$352$	−5.44742	+	8.25726i	−0.290348	+	0.440114i
$353$			19.0971i			1.01644i	0.861228	+	0.508219i	$0.169696\pi$
$353$			19.0971i			1.01644i	−0.861228	+	0.508219i	$0.830304\pi$
$354$	11.9894	+	3.36614i	0.637227	+	0.178908i
$355$	−10.9264	−	8.65132i	−0.579915	−	0.459164i
$356$	−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	$0.733921\pi$
$360$	−6.30435	+	0.505089i	−0.332269	+	0.0266205i
$361$			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
$365$	−7.41684	+	9.36733i	−0.388215	+	0.490308i
$366$	−2.40188	+	8.55491i	−0.125548	+	0.447172i
$367$			15.5388i			0.811117i	0.914069	+	0.405558i	$0.132923\pi$
$367$			15.5388i			0.811117i	−0.914069	+	0.405558i	$0.867077\pi$
$368$	1.31030	+	2.54199i	0.0683041	+	0.132511i
$369$	6.81590			0.354822
$370$	−1.64200	+	10.3043i	−0.0853636	+	0.535693i
$371$	−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	0.725985	−	0.687710i	$-0.241384\pi$
$373$	0.739215	+	0.739215i	0.0382751	+	0.0382751i	−0.687710	+	0.725985i	$0.741384\pi$
$374$	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	$0.261308\pi$
$380$	−21.4746	−	9.89389i	−1.10162	−	0.507546i
$381$	−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	$-0.864590\pi$
$383$		−	16.1529i		−	0.825374i	0.910873	−	0.412687i	$-0.135410\pi$
$384$	−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	$0.196149\pi$
$390$	14.9336	−	10.8284i	0.756191	−	0.548315i
$391$		−	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
$395$	−18.0829	+	22.8383i	−0.909848	+	1.14912i
$396$	0.824453	+	3.39888i	0.0414303	+	0.170800i
$397$	0.887688	−	0.887688i	0.0445518	−	0.0445518i	−0.684480	−	0.729032i	$-0.739971\pi$
$397$	0.887688	−	0.887688i	0.0445518	−	0.0445518i	0.729032	+	0.684480i	$0.239971\pi$
$398$	21.0372	+	5.90643i	1.05450	+	0.296063i
$399$	−24.6390			−1.23349
$400$	15.2021	−	12.9960i	0.760105	−	0.649800i
$401$	−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
$405$	−1.38805	+	1.75308i	−0.0689729	+	0.0871115i
$406$	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	$-0.0157206\pi$
$410$	−17.4493	+	12.6525i	−0.861760	+	0.624864i
$411$	−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	$0.623892\pi$
$420$	8.72111	−	18.9291i	0.425546	−	0.923644i
$421$	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
$430$	0.927218	−	5.81869i	0.0447144	−	0.280602i
$431$	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	$-0.986329\pi$
$433$		−	1.78691i		−	0.0858734i	0.999078	−	0.0429367i	$-0.0136714\pi$
$434$	−6.85377	+	24.4114i	−0.328991	+	1.17179i
$435$	2.43931	−	3.08080i	0.116956	−	0.147713i
$436$	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	$-0.0377687\pi$
$440$	−8.42009	−	7.17098i	−0.401412	−	0.341863i
$441$		−	14.7184i		−	0.700875i
$442$	−23.0754	+	12.9585i	−1.09758	+	0.616371i
$443$	−3.68515	−	3.68515i	−0.175087	−	0.175087i	0.614123	−	0.789210i	$-0.289510\pi$
$443$	−3.68515	−	3.68515i	−0.175087	−	0.175087i	−0.789210	+	0.614123i	$0.789510\pi$
$444$	5.63484	+	3.43484i	0.267418	+	0.163010i
$445$	−3.86552	−	3.06063i	−0.183243	−	0.145088i
$446$	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	$0.708008\pi$
$450$	0.299245	−	7.06473i	0.0141066	−	0.333035i
$451$	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	$-0.510040\pi$
$457$	−1.34836			−0.0630735			−0.0315367	+	0.999503i	$0.510040\pi$
$458$	−6.18671	−	11.0168i	−0.289086	−	0.514780i
$459$	2.26847	−	2.26847i	0.105883	−	0.105883i
$460$	−2.99950	+	1.10736i	−0.139853	+	0.0516311i
$461$	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	$0.0159115\pi$
$463$			2.15031i			0.0999334i	−0.998751	+	0.0499667i	$0.984088\pi$
$464$	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	−0.483178	−	0.875522i	$-0.660517\pi$
$467$	8.47864	−	8.47864i	0.392345	−	0.392345i	0.875522	+	0.483178i	$0.160517\pi$
$468$	−2.75014	−	11.3377i	−0.127125	−	0.524084i
$469$	−29.7219	+	29.7219i	−1.37243	+	1.37243i
$470$	3.03183	−	2.19839i	0.139848	−	0.101404i
$471$			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
$475$	13.9076	−	22.4808i	0.638126	−	1.03149i
$476$	−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	$0.614806\pi$
$480$	−3.95396	−	12.0152i	−0.180473	−	0.548419i
$481$	−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
$485$	−12.9597	−	10.2612i	−0.588471	−	0.465939i
$486$	0.692464	+	1.23308i	0.0314108	+	0.0559338i
$487$	21.0712			0.954827			0.477414	−	0.878679i	$-0.341574\pi$
$487$	21.0712			0.954827			0.477414	+	0.878679i	$0.341574\pi$
$488$	−17.7600	−	0.635088i	−0.803959	−	0.0287491i
$489$		−	8.09007i		−	0.365846i
$490$	27.3221	+	37.6804i	1.23429	+	1.70223i
$491$	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	$0.681414\pi$
$500$	12.3483	+	18.6418i	0.552235	+	0.833689i
$501$	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	$-0.710446\pi$
$503$	−27.5418			−1.22803			−0.614014	+	0.789295i	$0.710446\pi$
$504$	−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	$0.916263\pi$
$510$	−1.59646	+	10.0185i	−0.0706927	+	0.443626i
$511$	−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
$515$	6.91090	−	8.72833i	0.304530	−	0.384616i
$516$	−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
$520$	28.0870	+	23.9203i	1.23170	+	1.04897i
$521$			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	$0.108208\pi$
$523$	29.1859	+	29.1859i	1.27621	+	1.27621i	0.333436	+	0.942773i	$0.391792\pi$
$524$	−4.32318	−	17.8227i	−0.188859	−	0.778587i
$525$	19.8160	+	12.2591i	0.864842	+	0.535030i
$526$	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
$530$	6.58208	−	41.3053i	0.285907	−	1.79419i
$531$	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
$540$	−4.06177	−	1.87136i	−0.174791	−	0.0805306i
$541$	−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	−0.180187	−	0.983632i	$-0.557670\pi$
$547$	18.7910	−	18.7910i	0.803445	−	0.803445i	0.983632	+	0.180187i	$0.0576705\pi$
$548$	−17.4946	−	10.6642i	−0.747330	−	0.455552i
$549$	−4.44284	+	4.44284i	−0.189616	+	0.189616i
$550$	9.10579	−	8.36574i	0.388272	−	0.356716i
$551$		−	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
$555$	−4.58003	+	5.78448i	−0.194411	+	0.245538i
$556$	−8.81616	+	2.13850i	−0.373888	+	0.0906927i
$557$	30.7121	−	30.7121i	1.30132	−	1.30132i	0.373810	−	0.927505i	$-0.378051\pi$
$557$	30.7121	−	30.7121i	1.30132	−	1.30132i	0.927505	−	0.373810i	$-0.121949\pi$
$558$	5.23817	+	1.47067i	0.221749	+	0.0622585i
$559$	10.8687			0.459698
$560$	40.9029	+	8.02635i	1.72846	+	0.339175i
$561$	5.61006			0.236857
$562$	−11.3655	−	3.19098i	−0.479424	−	0.134603i
$563$	20.7316	−	20.7316i	0.873734	−	0.873734i	−0.119143	−	0.992877i	$-0.538015\pi$
$563$	20.7316	−	20.7316i	0.873734	−	0.873734i	0.992877	+	0.119143i	$0.0380148\pi$
$564$	−0.558335	−	2.30179i	−0.0235102	−	0.0969227i
$565$	−6.24922	−	4.94799i	−0.262907	−	0.208164i
$566$	−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	$-0.167622\pi$
$570$	−9.81439	−	13.5352i	−0.411080	−	0.566927i
$571$	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	$0.0583025\pi$
$577$			8.75032i			0.364281i	−0.983273	+	0.182140i	$0.941697\pi$
$578$	−2.56434	+	9.13355i	−0.106663	+	0.379906i
$579$	−6.31924	−	6.31924i	−0.262619	−	0.262619i
$580$	7.13801	+	3.28866i	0.296390	+	0.136554i
$581$	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	0.983073	−	0.183216i	$-0.0586506\pi$
$587$	19.3790	+	19.3790i	0.799857	+	0.799857i	−0.183216	+	0.983073i	$0.558651\pi$
$588$	28.6072	−	6.93913i	1.17974	−	0.286165i
$589$	14.3825	+	14.3825i	0.592620	+	0.592620i
$590$	−27.4986	−	4.38196i	−1.13210	−	0.180402i
$591$	14.5478			0.598416
$592$	−4.01948	+	12.5715i	−0.165200	+	0.516684i
$593$			19.4757i			0.799769i	0.916565	+	0.399885i	$0.130950\pi$
$593$			19.4757i			0.799769i	−0.916565	+	0.399885i	$0.869050\pi$
$594$	−0.668492	+	2.38100i	−0.0274286	+	0.0976936i
$595$	−26.2098	−	20.7524i	−1.07450	−	0.850764i
$596$	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	$-0.126083\pi$
$600$	13.8724	−	2.74912i	0.566337	−	0.112232i
$601$		−	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
$605$	13.9230	+	11.0239i	0.566049	+	0.448185i
$606$	15.7517	+	4.42246i	0.639869	+	0.179650i
$607$		−	11.3757i		−	0.461724i	−0.972986	−	0.230862i	$-0.925845\pi$
$607$		−	11.3757i		−	0.461724i	0.972986	−	0.230862i	$-0.0741546\pi$
$608$	−24.9646	−	16.4695i	−1.01245	−	0.667925i
$609$	8.18983			0.331869
$610$	3.12671	−	19.6214i	0.126597	−	0.794449i
$611$	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	0.855938	−	0.517079i	$-0.172981\pi$
$613$	8.38974	+	8.38974i	0.338859	+	0.338859i	−0.517079	+	0.855938i	$0.672981\pi$
$614$	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	$-0.887718\pi$
$617$	−46.6201			−1.87686			−0.938428	+	0.345476i	$0.887718\pi$
$618$	−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	$0.224778\pi$
$620$	−16.1402	+	5.95869i	−0.648207	+	0.239307i
$621$	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
$630$	11.9308	−	8.65103i	0.475334	−	0.344665i
$631$			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
$635$	15.5548	+	12.3159i	0.617272	+	0.488742i
$636$	−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
$640$	21.4891	−	13.3498i	0.849433	−	0.527697i
$641$	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	−0.587687	−	0.809088i	$-0.699961\pi$
$643$	5.61417	−	5.61417i	0.221401	−	0.221401i	0.809088	+	0.587687i	$0.199961\pi$
$644$	−5.69001	−	3.46847i	−0.224218	−	0.136677i
$645$	2.58629	−	3.26643i	0.101835	−	0.128615i
$646$	11.7450	+	20.9146i	0.462102	+	0.822873i
$647$	12.5530			0.493508			0.246754	−	0.969078i	$-0.420636\pi$
$647$	12.5530			0.493508			0.246754	+	0.969078i	$0.420636\pi$
$648$	−2.07020	+	1.92725i	−0.0813250	+	0.0757095i
$649$			15.3984i			0.604442i
$650$	−30.3743	+	27.9057i	−1.19138	+	1.09455i
$651$	−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	$-0.348041\pi$
$653$	34.4380	−	34.4380i	1.34766	−	1.34766i	0.888196	−	0.459466i	$-0.151959\pi$
$654$	−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	$0.550921\pi$
$660$	−2.70851	−	7.33651i	−0.105429	−	0.285573i
$661$	−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
$670$	−28.1665	−	4.48839i	−1.08817	−	0.173402i
$671$	−10.9874			−0.424165
$672$	14.5172	−	22.0054i	0.560014	−	0.848877i
$673$			8.51817i			0.328351i	0.986431	+	0.164176i	$0.0524964\pi$
$673$			8.51817i			0.328351i	−0.986431	+	0.164176i	$0.947504\pi$
$674$	23.5735	+	6.61852i	0.908018	+	0.254936i
$675$	2.63054	−	4.25209i	0.101249	−	0.163663i
$676$	−21.8883	+	35.9076i	−0.841858	+	1.38106i
$677$	19.0779	+	19.0779i	0.733223	+	0.733223i	0.971257	−	0.238034i	$-0.0765029\pi$
$677$	19.0779	+	19.0779i	0.733223	+	0.733223i	−0.238034	+	0.971257i	$0.576503\pi$
$678$	−4.39557	+	2.46843i	−0.168811	+	0.0947993i
$679$		−	34.4514i		−	1.32212i
$680$	−20.2250	+	1.62037i	−0.775593	+	0.0621385i
$681$		−	3.53153i		−	0.135329i
$682$	4.65863	+	8.29569i	0.178388	+	0.317658i
$683$	−13.3669	−	13.3669i	−0.511471	−	0.511471i	0.403506	−	0.914977i	$-0.367791\pi$
$683$	−13.3669	−	13.3669i	−0.511471	−	0.511471i	−0.914977	+	0.403506i	$0.867791\pi$
$684$	−10.2760	+	2.49261i	−0.392913	+	0.0953074i
$685$	14.2197	−	17.9592i	0.543306	−	0.686185i
$686$	−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
$690$	−2.23272	−	0.355788i	−0.0849983	−	0.0135446i
$691$	−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
$700$	−14.4847	+	44.2948i	−0.547471	+	1.67419i
$701$	−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	$0.406839\pi$
$710$	15.9563	−	11.5699i	0.598828	−	0.434211i
$711$			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
$715$	17.8827	+	14.1591i	0.668773	+	0.529520i
$716$	−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	$0.591652\pi$
$720$	1.72228	−	8.77689i	0.0641857	−	0.327095i
$721$	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
$725$	−4.62280	+	7.47246i	−0.171687	+	0.277520i
$726$	9.79311	−	5.49954i	0.363457	−	0.204107i
$727$	40.6950			1.50930			0.754648	−	0.656130i	$-0.227808\pi$
$727$	40.6950			1.50930			0.754648	+	0.656130i	$0.227808\pi$
$728$	−2.74777	+	76.8404i	−0.101839	+	2.84790i
$729$			1.00000i			0.0370370i
$730$	−9.91898	−	13.6794i	−0.367118	−	0.506298i
$731$	−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	−0.271679	−	0.962388i	$-0.587579\pi$
$733$	18.7002	−	18.7002i	0.690709	−	0.690709i	0.962388	+	0.271679i	$0.0875788\pi$
$734$	−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	$0.822836\pi$
$740$	−13.4022	−	6.17475i	−0.492676	−	0.226988i
$741$	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	$-0.415743\pi$
$743$	14.2625			0.523240			0.261620	+	0.965171i	$0.415743\pi$
$744$	−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
$750$	1.15886	+	15.7689i	0.0423156	+	0.575797i
$751$	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
$755$	35.5378	+	28.1380i	1.29335	+	1.02405i
$756$	−2.19715	−	9.05793i	−0.0799094	−	0.329434i
$757$	3.26487	+	3.26487i	0.118664	+	0.118664i	0.763945	−	0.645281i	$-0.223260\pi$
$757$	3.26487	+	3.26487i	0.118664	+	0.118664i	−0.645281	+	0.763945i	$0.723260\pi$
$758$	−0.957576	−	1.70517i	−0.0347807	−	0.0619346i
$759$			1.25026i			0.0453816i
$760$	21.6804	−	25.4569i	0.786431	−	0.923420i
$761$			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
$765$	−4.45301	+	5.62407i	−0.160999	+	0.203339i
$766$	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	$0.417997\pi$
$770$	25.4501	+	4.05551i	0.917157	+	0.146151i
$771$	−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	0.955601	−	0.294663i	$-0.0952074\pi$
$773$	18.3760	+	18.3760i	0.660938	+	0.660938i	−0.294663	+	0.955601i	$0.595207\pi$
$774$	−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
$780$	9.03482	+	24.4725i	0.323498	+	0.876255i
$781$	−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	−0.922811	−	0.385253i	$-0.874114\pi$
$787$	−15.0804	+	15.0804i	−0.537558	+	0.537558i	0.385253	+	0.922811i	$0.374114\pi$
$788$	6.85871	+	28.2756i	0.244331	+	1.00728i
$789$	5.42295	−	5.42295i	0.193062	−	0.193062i
$790$	−24.1833	−	33.3516i	−0.860403	−	1.18660i
$791$		−	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
$795$	18.3594	−	23.1875i	0.651139	−	0.822376i
$796$	−16.0840	+	26.3857i	−0.570083	+	0.935217i
$797$	−26.8036	+	26.8036i	−0.949431	+	0.949431i	−0.998782	−	0.0493502i	$-0.984285\pi$
$797$	−26.8036	+	26.8036i	−0.949431	+	0.949431i	0.0493502	+	0.998782i	$0.484285\pi$
$798$	9.41887	−	33.5477i	0.333424	−	1.18757i
$799$	−3.79925			−0.134408
$800$	11.8836	+	25.6667i	0.420147	+	0.907456i
$801$	−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
$805$	4.62487	−	5.84113i	0.163005	−	0.205873i
$806$	−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	$-0.241464\pi$
$810$	−1.85633	−	2.56009i	−0.0652246	−	0.0899524i
$811$	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
$820$	−10.5568	−	28.5952i	−0.368661	−	0.998586i
$821$	−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	$-0.884171\pi$
$823$	−53.6190			−1.86904			−0.934520	+	0.355910i	$0.884171\pi$
$824$	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	$-0.857862\pi$
$827$	−38.3567	−	38.3567i	−1.33379	−	1.33379i	−0.431849	−	0.901946i	$-0.642138\pi$
$828$	−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	$-0.527765\pi$
$830$	21.5556	+	3.43492i	0.748205	+	0.119228i
$831$	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
$835$	−31.6903	+	40.0243i	−1.09669	+	1.38510i
$836$	−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	$-0.171813\pi$
$840$	22.4394	+	19.1105i	0.774231	+	0.659374i
$841$		−	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
$845$	−36.8613	−	29.1859i	−1.26807	−	1.00403i
$846$	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
$850$	0.960008	−	22.6643i	0.0329280	−	0.777381i
$851$	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	0.656701	−	0.754151i	$-0.271951\pi$
$853$	−2.84613	−	2.84613i	−0.0974497	−	0.0974497i	−0.754151	+	0.656701i	$0.771951\pi$
$854$	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	$-0.549532\pi$
$857$	−9.07410			−0.309965			−0.154983	+	0.987917i	$0.549532\pi$
$858$	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	$0.998806\pi$
$860$	7.56808	+	3.48681i	0.258069	+	0.118899i
$861$	−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	$0.143430\pi$
$863$			25.5875i			0.871008i	−0.900187	+	0.435504i	$0.856570\pi$
$864$	−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
$870$	3.26224	+	4.49900i	0.110600	+	0.152530i
$871$		−	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
$875$	−47.1780	−	22.1141i	−1.59491	−	0.747592i
$876$	−10.3855	+	2.51917i	−0.350894	+	0.0851150i
$877$	28.2401	−	28.2401i	0.953600	−	0.953600i	−0.0453704	−	0.998970i	$-0.514447\pi$
$877$	28.2401	−	28.2401i	0.953600	−	0.953600i	0.998970	+	0.0453704i	$0.0144468\pi$
$878$	6.75405	+	1.89627i	0.227938	+	0.0639961i
$879$	−7.12081			−0.240179
$880$	12.9826	−	8.72324i	0.437642	−	0.294060i
$881$	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	−0.636556	−	0.771231i	$-0.719641\pi$
$883$	4.00191	−	4.00191i	0.134675	−	0.134675i	0.771231	+	0.636556i	$0.219641\pi$
$884$	−8.82270	−	36.3723i	−0.296740	−	1.22333i
$885$	−15.4369	−	12.2226i	−0.518905	−	0.410857i
$886$	6.42632	−	3.60884i	0.215897	−	0.121241i
$887$	40.4073			1.35675			0.678373	−	0.734718i	$-0.262685\pi$
$887$	40.4073			1.35675			0.678373	+	0.734718i	$0.262685\pi$
$888$	−6.83082	+	6.35916i	−0.229227	+	0.213399i
$889$			41.3499i			1.38683i
$890$	5.64495	−	4.09316i	0.189219	−	0.137203i
$891$	−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
$900$	9.50472	+	3.10811i	0.316824	+	0.103604i
$901$	−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	0.519085	−	0.854723i	$-0.326273\pi$
$907$	−10.1082	−	10.1082i	−0.335637	−	0.335637i	−0.854723	+	0.519085i	$0.826273\pi$
$908$	6.86401	−	1.66498i	0.227790	−	0.0552542i
$909$	8.18037	+	8.18037i	0.271326	+	0.271326i
$910$	−84.8940	−	13.5280i	−2.81421	−	0.448450i
$911$	−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
$915$	8.72132	−	11.0149i	0.288318	−	0.364140i
$916$	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	$0.917372\pi$
$920$	−0.361117	−	4.50734i	−0.0119057	−	0.148603i
$921$			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
$925$	8.67972	−	14.0302i	0.285387	−	0.461311i
$926$	−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	$0.261393\pi$
$930$	−12.0142	−	1.91448i	−0.393961	−	0.0627784i
$931$	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	$-0.225316\pi$
$937$	46.5132			1.51952			0.759761	+	0.650203i	$0.225316\pi$
$938$	−29.1065	−	51.8304i	−0.950360	−	1.69232i
$939$	−12.9811	+	12.9811i	−0.423622	+	0.423622i
$940$	1.83426	+	4.96843i	0.0598269	+	0.162052i
$941$	−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	−0.331007	−	0.943628i	$-0.607388\pi$
$947$	18.8524	−	18.8524i	0.612622	−	0.612622i	0.943628	+	0.331007i	$0.107388\pi$
$948$	−25.3207	+	6.14195i	−0.822379	+	0.199481i
$949$	22.0397	−	22.0397i	0.715440	−	0.715440i
$950$	25.2926	+	27.5300i	0.820600	+	0.893192i
$951$		−	0.728219i		−	0.0236141i
$952$	−28.8137	−	30.9508i	−0.933857	−	1.00312i
$953$	15.9773			0.517557			0.258778	−	0.965937i	$-0.416680\pi$
$953$	15.9773			0.517557			0.258778	+	0.965937i	$0.416680\pi$
$954$	−9.15901	−	16.3096i	−0.296534	−	0.528043i
$955$	−16.4587	+	20.7870i	−0.532591	+	0.672652i
$956$	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
$960$	17.8711	−	0.790462i	0.576786	−	0.0255120i
$961$	−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
$965$	15.6669	+	12.4047i	0.504335	+	0.399321i
$966$	−2.30723	−	4.10852i	−0.0742339	−	0.132190i
$967$	−46.0281			−1.48017			−0.740083	−	0.672516i	$-0.765214\pi$
$967$	−46.0281			−1.48017			−0.740083	+	0.672516i	$0.765214\pi$
$968$	15.3062	+	16.4414i	0.491959	+	0.528448i
$969$			16.9612i			0.544872i
$970$	18.9255	−	13.7229i	0.607663	−	0.440617i
$971$	−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	$-0.818490\pi$
$977$		−	33.7468i		−	1.07965i	0.841776	−	0.539827i	$-0.181510\pi$
$978$	11.0152	+	3.09263i	0.352226	+	0.0988914i
$979$	−2.72653	−	2.72653i	−0.0871403	−	0.0871403i
$980$	−61.7489	+	22.7966i	−1.97250	+	0.728211i
$981$	−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	$-0.493957\pi$
$983$	1.19047			0.0379700			0.0189850	+	0.999820i	$0.493957\pi$
$984$	−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
$990$	0.870226	−	5.46104i	0.0276576	−	0.173563i
$991$	−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
$995$	−27.0865	−	21.4465i	−0.858699	−	0.679899i
$996$	7.18538	−	11.7876i	0.227678	−	0.373504i
$997$	−27.5653	−	27.5653i	−0.873002	−	0.873002i	0.119797	−	0.992798i	$-0.461776\pi$
$997$	−27.5653	−	27.5653i	−0.873002	−	0.873002i	−0.992798	+	0.119797i	$0.961776\pi$
$998$	−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.109.11	✓	48
3.2	odd	2		720.2.bm.h.109.14		48
4.3	odd	2		960.2.bl.a.529.21		48
5.4	even	2	inner	240.2.bl.a.109.14	yes	48
8.3	odd	2		1920.2.bl.b.289.1		48
8.5	even	2		1920.2.bl.a.289.24		48
15.14	odd	2		720.2.bm.h.109.11		48
16.3	odd	4		1920.2.bl.b.1249.24		48
16.5	even	4	inner	240.2.bl.a.229.14	yes	48
16.11	odd	4		960.2.bl.a.49.10		48
16.13	even	4		1920.2.bl.a.1249.1		48
20.19	odd	2		960.2.bl.a.529.10		48
40.19	odd	2		1920.2.bl.b.289.24		48
40.29	even	2		1920.2.bl.a.289.1		48
48.5	odd	4		720.2.bm.h.469.11		48
80.19	odd	4		1920.2.bl.b.1249.1		48
80.29	even	4		1920.2.bl.a.1249.24		48
80.59	odd	4		960.2.bl.a.49.21		48
80.69	even	4	inner	240.2.bl.a.229.11	yes	48
240.149	odd	4		720.2.bm.h.469.14		48

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

\(f(q)\)	\(=\)	\(q+(-0.382275 + 1.36157i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.38805 - 1.75308i) q^{5} +(-0.692464 - 1.23308i) q^{6} +4.66030 q^{7} +(2.07020 - 1.92725i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.382275 + 1.36157i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.70773 - 1.04099i) q^{4} +(1.38805 - 1.75308i) q^{5} +(-0.692464 - 1.23308i) q^{6} +4.66030 q^{7} +(2.07020 - 1.92725i) q^{8} -1.00000i q^{9} +(1.85633 + 2.56009i) 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} +(-4.19536 + 1.54885i) 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} +(-3.12288 - 0.497636i) q^{30} +3.84716 q^{31} +(-5.54158 + 1.13618i) q^{32} +1.74872i q^{33} +(4.36804 + 1.22637i) q^{34} +(6.46874 - 8.16990i) q^{35} +(-1.04099 + 1.70773i) q^{36} +(2.33317 + 2.33317i) q^{37} +(-6.51931 + 3.66106i) q^{38} -5.83322i q^{39} +(-0.505089 - 6.30435i) q^{40} +6.81590i q^{41} +(-3.22709 - 5.74653i) q^{42} +(-1.31751 - 1.31751i) q^{43} +(-3.39888 + 0.824453i) q^{44} +(-1.75308 - 1.38805i) q^{45} +(-0.273310 + 0.973462i) q^{46} -1.18427i q^{47} +(-3.80999 - 1.21817i) q^{48} +14.7184 q^{49} +(7.06473 + 0.299245i) 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} +(1.87136 - 4.06177i) 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} +(8.65103 + 11.9308i) q^{70} -6.23269i q^{71} +(-1.92725 - 2.07020i) q^{72} -5.34334 q^{73} +(-4.06868 + 2.28486i) q^{74} +(4.25209 + 2.63054i) q^{75} +(-2.49261 - 10.2760i) q^{76} +(5.76261 - 5.76261i) q^{77} +(7.94233 + 2.22990i) q^{78} -13.0275 q^{79} +(8.77689 + 1.72228i) q^{80} -1.00000 q^{81} +(-9.28031 - 2.60555i) q^{82} +(4.88079 - 4.88079i) q^{83} +(9.05793 - 2.19715i) q^{84} +(-5.62407 - 4.45301i) q^{85} +(2.29754 - 1.29023i) q^{86} +1.75736 q^{87} +(0.176758 - 4.94297i) q^{88} -2.20498i q^{89} +(2.56009 - 1.85633i) 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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