Properties

Label 240.2.bl.a.229.11
Level $240$
Weight $2$
Character 240.229
Analytic conductor $1.916$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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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 229.11
Character \(\chi\) \(=\) 240.229
Dual form 240.2.bl.a.109.11

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.382275 1.36157i −0.270309 0.962774i
\(3\) −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
\(6\) −0.692464 + 1.23308i −0.282697 + 0.503404i
\(7\) 4.66030 1.76143 0.880714 0.473649i \(-0.157064\pi\)
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 0.868506 0.495678i \(-0.165080\pi\)
−0.495678 + 0.868506i \(0.665080\pi\)
\(12\) 1.94364 + 0.471461i 0.561080 + 0.136099i
\(13\) −4.12471 4.12471i −1.14399 1.14399i −0.987713 0.156276i \(-0.950051\pi\)
−0.156276 0.987713i \(-0.549949\pi\)
\(14\) −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 \(0.127193\pi\)
−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 −0.133398 0.991063i \(-0.542589\pi\)
0.991063 + 0.133398i \(0.0425889\pi\)
\(20\) −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 \(-0.476251\pi\)
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 −0.813007 0.582254i \(-0.802171\pi\)
0.582254 + 0.813007i \(0.302171\pi\)
\(30\) −3.12288 + 0.497636i −0.570157 + 0.0908555i
\(31\) 3.84716 0.690970 0.345485 0.938424i \(-0.387714\pi\)
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 −0.488816 0.872387i \(-0.662571\pi\)
0.872387 + 0.488816i \(0.162571\pi\)
\(38\) −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 \(-0.821353\pi\)
0.846598 0.532232i \(-0.178647\pi\)
\(42\) −3.22709 + 5.74653i −0.497951 + 0.886709i
\(43\) −1.31751 + 1.31751i −0.200919 + 0.200919i −0.800394 0.599475i \(-0.795376\pi\)
0.599475 + 0.800394i \(0.295376\pi\)
\(44\) −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 \(0.0275272\pi\)
−0.996263 + 0.0863716i \(0.972473\pi\)
\(48\) −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 −0.346722 + 0.937968i \(0.612705\pi\)
−0.937968 + 0.346722i \(0.887295\pi\)
\(54\) −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 0.174110 0.984726i \(-0.444295\pi\)
−0.984726 + 0.174110i \(0.944295\pi\)
\(60\) 1.87136 + 4.06177i 0.241592 + 0.524373i
\(61\) −4.44284 + 4.44284i −0.568848 + 0.568848i −0.931806 0.362958i \(-0.881767\pi\)
0.362958 + 0.931806i \(0.381767\pi\)
\(62\) −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 \(-0.435734\pi\)
−0.979688 + 0.200529i \(0.935734\pi\)
\(68\) −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 \(0.120588\pi\)
−0.929095 + 0.369842i \(0.879412\pi\)
\(72\) −1.92725 + 2.07020i −0.227129 + 0.243975i
\(73\) −5.34334 −0.625391 −0.312695 0.949853i \(-0.601232\pi\)
−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 \(-0.761812\pi\)
−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 0.922274 0.386537i \(-0.126329\pi\)
−0.386537 + 0.922274i \(0.626329\pi\)
\(84\) 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 \(0.0372841\pi\)
−0.993148 + 0.116864i \(0.962716\pi\)
\(90\) 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 \(0.122460\pi\)
−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
\(100\) −3.10811 9.50472i −0.310811 0.950472i
\(101\) −8.18037 8.18037i −0.813977 0.813977i 0.171250 0.985228i \(-0.445219\pi\)
−0.985228 + 0.171250i \(0.945219\pi\)
\(102\) −3.95585 2.22149i −0.391687 0.219961i
\(103\) 4.97884 0.490580 0.245290 0.969450i \(-0.421117\pi\)
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 −0.512830 0.858490i \(-0.671403\pi\)
0.858490 + 0.512830i \(0.171403\pi\)
\(108\) −0.471461 + 1.94364i −0.0453663 + 0.187027i
\(109\) −7.08685 + 7.08685i −0.678797 + 0.678797i −0.959728 0.280931i \(-0.909357\pi\)
0.280931 + 0.959728i \(0.409357\pi\)
\(110\) 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 \(0.0536241\pi\)
−0.985843 + 0.167669i \(0.946376\pi\)
\(114\) 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 \(-0.871207\pi\)
0.919253 0.393666i \(-0.128793\pi\)
\(128\) 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 −0.364639 0.931149i \(-0.618808\pi\)
0.931149 + 0.364639i \(0.118808\pi\)
\(132\) 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 \(-0.355823\pi\)
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 0.829923 0.557878i \(-0.188384\pi\)
−0.557878 + 0.829923i \(0.688384\pi\)
\(140\) −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 −0.966656 0.256080i \(-0.917569\pi\)
−0.256080 0.966656i \(-0.582431\pi\)
\(150\) −5.20712 4.78392i −0.425159 0.390606i
\(151\) 20.2716i 1.64968i −0.565368 0.824839i \(-0.691266\pi\)
0.565368 0.824839i \(-0.308734\pi\)
\(152\) 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 0.952083 0.305839i \(-0.0989369\pi\)
−0.305839 + 0.952083i \(0.598937\pi\)
\(158\) 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 0.446644 0.894712i \(-0.352619\pi\)
−0.894712 + 0.446644i \(0.852619\pi\)
\(164\) 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 \(-0.844717\pi\)
−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 0.846465 0.532444i \(-0.178726\pi\)
−0.532444 + 0.846465i \(0.678726\pi\)
\(174\) −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 −0.102744 0.994708i \(-0.532762\pi\)
0.994708 + 0.102744i \(0.0327623\pi\)
\(180\) 1.54885 4.19536i 0.115445 0.312704i
\(181\) 15.2918 + 15.2918i 1.13663 + 1.13663i 0.989050 + 0.147579i \(0.0471481\pi\)
0.147579 + 0.989050i \(0.452852\pi\)
\(182\) −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 \(-0.641129\pi\)
−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 \(-0.895766\pi\)
0.946862 0.321641i \(-0.104234\pi\)
\(194\) 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 −0.971195 0.238288i \(-0.923414\pi\)
0.238288 + 0.971195i \(0.423414\pi\)
\(198\) 2.15632 + 1.21093i 0.153243 + 0.0860568i
\(199\) 15.4507i 1.09527i 0.836716 + 0.547637i \(0.184473\pi\)
−0.836716 + 0.547637i \(0.815527\pi\)
\(200\) −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 −0.979412 0.201872i \(-0.935297\pi\)
0.201872 + 0.979412i \(0.435297\pi\)
\(212\) 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 \(0.0523579\pi\)
−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 \(-0.287391\pi\)
−0.785105 + 0.619362i \(0.787391\pi\)
\(228\) 9.02878 5.50369i 0.597945 0.364491i
\(229\) −6.31753 6.31753i −0.417474 0.417474i 0.466858 0.884332i \(-0.345386\pi\)
−0.884332 + 0.466858i \(0.845386\pi\)
\(230\) 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 \(-0.403785\pi\)
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 \(-0.610199\pi\)
−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 \(-0.583280\pi\)
−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 0.990118 0.140240i \(-0.0447874\pi\)
−0.140240 + 0.990118i \(0.544787\pi\)
\(252\) −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 \(-0.721183\pi\)
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
\(260\) 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 \(-0.575985\pi\)
−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 −0.799165 0.601112i \(-0.794725\pi\)
0.601112 + 0.799165i \(0.294725\pi\)
\(270\) −0.497636 3.12288i −0.0302852 0.190052i
\(271\) 22.9657 1.39507 0.697534 0.716552i \(-0.254281\pi\)
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 −0.276885 + 0.960903i \(0.589302\pi\)
−0.960903 + 0.276885i \(0.910698\pi\)
\(278\) 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 \(-0.919904\pi\)
0.968508 0.248981i \(-0.0800955\pi\)
\(282\) −1.46030 0.820063i −0.0869596 0.0488341i
\(283\) 11.8274 11.8274i 0.703065 0.703065i −0.262002 0.965067i \(-0.584383\pi\)
0.965067 + 0.262002i \(0.0843828\pi\)
\(284\) −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 −0.544562 0.838720i \(-0.683304\pi\)
0.838720 + 0.544562i \(0.183304\pi\)
\(294\) −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 0.899384 0.437159i \(-0.144015\pi\)
−0.437159 + 0.899384i \(0.644015\pi\)
\(308\) −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 \(0.0764709\pi\)
−0.971281 + 0.237936i \(0.923529\pi\)
\(312\) −11.2421 + 12.0759i −0.636457 + 0.683664i
\(313\) 18.3580 1.03766 0.518829 0.854878i \(-0.326368\pi\)
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 0.692498 0.721420i \(-0.256510\pi\)
−0.721420 + 0.692498i \(0.756510\pi\)
\(318\) −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 0.998882 + 0.0472642i \(0.0150503\pi\)
0.0472642 + 0.998882i \(0.484950\pi\)
\(332\) −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 \(0.156310\pi\)
−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
\(340\) 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 −0.466779 0.884374i \(-0.654586\pi\)
0.884374 + 0.466779i \(0.154586\pi\)
\(348\) −3.00110 + 1.82939i −0.160876 + 0.0980655i
\(349\) 18.9914 18.9914i 1.01658 1.01658i 0.0167236 0.999860i \(-0.494676\pi\)
0.999860 0.0167236i \(-0.00532353\pi\)
\(350\) 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 \(-0.830304\pi\)
0.861228 0.508219i \(-0.169696\pi\)
\(354\) 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 \(-0.733921\pi\)
0.670502 0.741907i \(-0.266079\pi\)
\(360\) −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 \(-0.867077\pi\)
0.914069 0.405558i \(-0.132923\pi\)
\(368\) 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 −0.687710 0.725985i \(-0.741384\pi\)
0.725985 + 0.687710i \(0.241384\pi\)
\(374\) 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 0.681547 0.731774i \(-0.261308\pi\)
−0.731774 + 0.681547i \(0.761308\pi\)
\(380\) −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 \(0.135410\pi\)
−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 0.816068 0.577955i \(-0.196149\pi\)
−0.577955 + 0.816068i \(0.696149\pi\)
\(390\) 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 0.729032 0.684480i \(-0.239971\pi\)
−0.684480 + 0.729032i \(0.739971\pi\)
\(398\) 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 \(-0.720438\pi\)
−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 \(0.0157206\pi\)
−0.998781 + 0.0493677i \(0.984279\pi\)
\(410\) −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 −0.379464 0.925207i \(-0.623892\pi\)
0.925207 + 0.379464i \(0.123892\pi\)
\(420\) 8.72111 + 18.9291i 0.425546 + 0.923644i
\(421\) 9.76440 + 9.76440i 0.475888 + 0.475888i 0.903814 0.427926i \(-0.140756\pi\)
−0.427926 + 0.903814i \(0.640756\pi\)
\(422\) 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 \(-0.292625\pi\)
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 \(0.0136714\pi\)
−0.999078 + 0.0429367i \(0.986329\pi\)
\(434\) −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 \(0.0377687\pi\)
−0.992969 + 0.118376i \(0.962231\pi\)
\(440\) −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 −0.789210 0.614123i \(-0.789510\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(444\) 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 \(-0.708008\pi\)
−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 \(-0.510040\pi\)
−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 −0.100780 0.994909i \(-0.532134\pi\)
0.994909 + 0.100780i \(0.0321339\pi\)
\(462\) −11.0962 + 3.11537i −0.516241 + 0.144940i
\(463\) 2.15031i 0.0999334i −0.998751 0.0499667i \(-0.984088\pi\)
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 \(-0.160517\pi\)
−0.483178 + 0.875522i \(0.660517\pi\)
\(468\) −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 \(-0.614806\pi\)
−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 \(-0.341574\pi\)
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 0.855206 0.518288i \(-0.173431\pi\)
−0.518288 + 0.855206i \(0.673431\pi\)
\(492\) 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 −0.539573 0.841939i \(-0.681414\pi\)
0.841939 + 0.539573i \(0.181414\pi\)
\(500\) 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 \(-0.710446\pi\)
−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 −0.965597 0.260044i \(-0.916263\pi\)
0.260044 + 0.965597i \(0.416263\pi\)
\(510\) −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 \(-0.999668\pi\)
0.999999 0.00104199i \(-0.000331675\pi\)
\(522\) −1.21691 + 2.16697i −0.0532627 + 0.0948458i
\(523\) 29.1859 29.1859i 1.27621 1.27621i 0.333436 0.942773i \(-0.391792\pi\)
0.942773 0.333436i \(-0.108208\pi\)
\(524\) −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 −0.724323 0.689461i \(-0.757847\pi\)
0.689461 + 0.724323i \(0.257847\pi\)
\(542\) −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 \(-0.0576705\pi\)
−0.180187 + 0.983632i \(0.557670\pi\)
\(548\) −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 0.927505 + 0.373810i \(0.121949\pi\)
0.373810 + 0.927505i \(0.378051\pi\)
\(558\) 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 0.992877 0.119143i \(-0.0380148\pi\)
−0.119143 + 0.992877i \(0.538015\pi\)
\(564\) −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 \(0.167622\pi\)
−0.864521 + 0.502596i \(0.832378\pi\)
\(570\) −9.81439 + 13.5352i −0.411080 + 0.566927i
\(571\) 6.40838 + 6.40838i 0.268182 + 0.268182i 0.828367 0.560185i \(-0.189270\pi\)
−0.560185 + 0.828367i \(0.689270\pi\)
\(572\) 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 \(-0.941697\pi\)
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
\(580\) 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 −0.183216 0.983073i \(-0.558651\pi\)
0.983073 + 0.183216i \(0.0586506\pi\)
\(588\) 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 \(-0.869050\pi\)
0.916565 0.399885i \(-0.130950\pi\)
\(594\) −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 \(0.126083\pi\)
−0.922572 + 0.385825i \(0.873917\pi\)
\(600\) 13.8724 + 2.74912i 0.566337 + 0.112232i
\(601\) 38.2498i 1.56024i 0.625630 + 0.780120i \(0.284842\pi\)
−0.625630 + 0.780120i \(0.715158\pi\)
\(602\) 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 \(0.0741546\pi\)
−0.972986 + 0.230862i \(0.925845\pi\)
\(608\) −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 −0.517079 0.855938i \(-0.672981\pi\)
0.855938 + 0.517079i \(0.172981\pi\)
\(614\) 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 \(-0.887718\pi\)
−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 0.760859 0.648917i \(-0.224778\pi\)
−0.648917 + 0.760859i \(0.724778\pi\)
\(620\) −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 \(-0.837362\pi\)
0.872285 0.488998i \(-0.162638\pi\)
\(632\) −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 \(-0.342054\pi\)
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 \(-0.199961\pi\)
−0.587687 + 0.809088i \(0.699961\pi\)
\(644\) −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 \(-0.420636\pi\)
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 0.888196 + 0.459466i \(0.151959\pi\)
0.459466 + 0.888196i \(0.348041\pi\)
\(654\) −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 −0.159292 0.987232i \(-0.550921\pi\)
0.987232 + 0.159292i \(0.0509210\pi\)
\(660\) −2.70851 + 7.33651i −0.105429 + 0.285573i
\(661\) −1.82514 1.82514i −0.0709896 0.0709896i 0.670721 0.741710i \(-0.265985\pi\)
−0.741710 + 0.670721i \(0.765985\pi\)
\(662\) 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 \(-0.947504\pi\)
0.986431 0.164176i \(-0.0524964\pi\)
\(674\) 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 −0.238034 0.971257i \(-0.576503\pi\)
0.971257 + 0.238034i \(0.0765029\pi\)
\(678\) −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 −0.914977 0.403506i \(-0.867791\pi\)
0.403506 + 0.914977i \(0.367791\pi\)
\(684\) −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 −0.936511 0.350638i \(-0.885965\pi\)
0.350638 + 0.936511i \(0.385965\pi\)
\(692\) −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 −0.910382 0.413768i \(-0.864212\pi\)
0.413768 + 0.910382i \(0.364212\pi\)
\(702\) 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 0.288513 0.957476i \(-0.406839\pi\)
−0.957476 + 0.288513i \(0.906839\pi\)
\(710\) 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 \(-0.591652\pi\)
−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 \(-0.227808\pi\)
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 0.962388 0.271679i \(-0.0875788\pi\)
−0.271679 + 0.962388i \(0.587579\pi\)
\(734\) −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 −0.849069 0.528282i \(-0.822836\pi\)
0.528282 + 0.849069i \(0.322836\pi\)
\(740\) −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 \(-0.415743\pi\)
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 \(-0.345175\pi\)
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 −0.645281 0.763945i \(-0.723260\pi\)
0.763945 + 0.645281i \(0.223260\pi\)
\(758\) −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 \(-0.673348\pi\)
0.518065 0.855341i \(-0.326652\pi\)
\(762\) 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 \(-0.417997\pi\)
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 −0.294663 0.955601i \(-0.595207\pi\)
0.955601 + 0.294663i \(0.0952074\pi\)
\(774\) −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 0.385253 0.922811i \(-0.374114\pi\)
−0.922811 + 0.385253i \(0.874114\pi\)
\(788\) 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 0.0493502 0.998782i \(-0.484285\pi\)
−0.998782 + 0.0493502i \(0.984285\pi\)
\(798\) 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 \(0.241464\pi\)
−0.725813 + 0.687892i \(0.758536\pi\)
\(810\) −1.85633 + 2.56009i −0.0652246 + 0.0899524i
\(811\) 25.8556 + 25.8556i 0.907913 + 0.907913i 0.996104 0.0881903i \(-0.0281084\pi\)
−0.0881903 + 0.996104i \(0.528108\pi\)
\(812\) 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 0.103527 0.994627i \(-0.466987\pi\)
−0.994627 + 0.103527i \(0.966987\pi\)
\(822\) −7.09383 + 12.6321i −0.247426 + 0.440595i
\(823\) −53.6190 −1.86904 −0.934520 0.355910i \(-0.884171\pi\)
−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 −0.431849 + 0.901946i \(0.642138\pi\)
−0.901946 + 0.431849i \(0.857862\pi\)
\(828\) −0.744260 1.22095i −0.0258648 0.0424311i
\(829\) −31.1912 + 31.1912i −1.08331 + 1.08331i −0.0871160 + 0.996198i \(0.527765\pi\)
−0.996198 + 0.0871160i \(0.972235\pi\)
\(830\) 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 \(0.171813\pi\)
−0.857829 + 0.513935i \(0.828187\pi\)
\(840\) 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 −0.754151 0.656701i \(-0.771951\pi\)
0.656701 + 0.754151i \(0.271951\pi\)
\(854\) 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 \(-0.549532\pi\)
−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 −0.999993 0.00375173i \(-0.998806\pi\)
−0.00375173 0.999993i \(-0.501194\pi\)
\(860\) 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 \(-0.856570\pi\)
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
\(870\) 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 0.998970 0.0453704i \(-0.0144468\pi\)
−0.0453704 + 0.998970i \(0.514447\pi\)
\(878\) 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 \(-0.419331\pi\)
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 \(-0.219641\pi\)
−0.636556 + 0.771231i \(0.719641\pi\)
\(884\) −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 \(-0.262685\pi\)
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 −0.854723 0.519085i \(-0.826273\pi\)
0.519085 + 0.854723i \(0.326273\pi\)
\(908\) 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 \(-0.588957\pi\)
−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 \(-0.917372\pi\)
0.966497 0.256678i \(-0.0826279\pi\)
\(920\) −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 \(-0.261393\pi\)
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 \(-0.225316\pi\)
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 −0.795254 0.606276i \(-0.792663\pi\)
0.606276 + 0.795254i \(0.292663\pi\)
\(942\) −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 \(-0.107388\pi\)
−0.331007 + 0.943628i \(0.607388\pi\)
\(948\) −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 \(-0.416680\pi\)
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 \(-0.765214\pi\)
−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 0.313253 0.949670i \(-0.398581\pi\)
−0.949670 + 0.313253i \(0.898581\pi\)
\(972\) −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 \(0.181510\pi\)
−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
\(980\) −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 \(-0.493957\pi\)
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 \(-0.770665\pi\)
−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 −0.992798 0.119797i \(-0.961776\pi\)
0.119797 + 0.992798i \(0.461776\pi\)
\(998\) −11.7785 6.61447i −0.372842 0.209377i
\(999\) 3.29960i 0.104395i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 240.2.bl.a.229.11 yes 48
3.2 odd 2 720.2.bm.h.469.14 48
4.3 odd 2 960.2.bl.a.49.21 48
5.4 even 2 inner 240.2.bl.a.229.14 yes 48
8.3 odd 2 1920.2.bl.b.1249.1 48
8.5 even 2 1920.2.bl.a.1249.24 48
15.14 odd 2 720.2.bm.h.469.11 48
16.3 odd 4 960.2.bl.a.529.10 48
16.5 even 4 1920.2.bl.a.289.1 48
16.11 odd 4 1920.2.bl.b.289.24 48
16.13 even 4 inner 240.2.bl.a.109.14 yes 48
20.19 odd 2 960.2.bl.a.49.10 48
40.19 odd 2 1920.2.bl.b.1249.24 48
40.29 even 2 1920.2.bl.a.1249.1 48
48.29 odd 4 720.2.bm.h.109.11 48
80.19 odd 4 960.2.bl.a.529.21 48
80.29 even 4 inner 240.2.bl.a.109.11 48
80.59 odd 4 1920.2.bl.b.289.1 48
80.69 even 4 1920.2.bl.a.289.24 48
240.29 odd 4 720.2.bm.h.109.14 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bl.a.109.11 48 80.29 even 4 inner
240.2.bl.a.109.14 yes 48 16.13 even 4 inner
240.2.bl.a.229.11 yes 48 1.1 even 1 trivial
240.2.bl.a.229.14 yes 48 5.4 even 2 inner
720.2.bm.h.109.11 48 48.29 odd 4
720.2.bm.h.109.14 48 240.29 odd 4
720.2.bm.h.469.11 48 15.14 odd 2
720.2.bm.h.469.14 48 3.2 odd 2
960.2.bl.a.49.10 48 20.19 odd 2
960.2.bl.a.49.21 48 4.3 odd 2
960.2.bl.a.529.10 48 16.3 odd 4
960.2.bl.a.529.21 48 80.19 odd 4
1920.2.bl.a.289.1 48 16.5 even 4
1920.2.bl.a.289.24 48 80.69 even 4
1920.2.bl.a.1249.1 48 40.29 even 2
1920.2.bl.a.1249.24 48 8.5 even 2
1920.2.bl.b.289.1 48 80.59 odd 4
1920.2.bl.b.289.24 48 16.11 odd 4
1920.2.bl.b.1249.1 48 8.3 odd 2
1920.2.bl.b.1249.24 48 40.19 odd 2