Properties

Label 285.2.k.a.77.1
Level $285$
Weight $2$
Character 285.77
Analytic conductor $2.276$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [285,2,Mod(77,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.k (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: \(2.27573645761\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 285.77
Dual form 285.2.k.a.248.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} -1.73205i q^{3} +(-0.133975 + 2.23205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.36603 - 2.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} -1.73205i q^{3} +(-0.133975 + 2.23205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.36603 - 2.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +(-2.09808 - 2.36603i) q^{10} -0.267949i q^{11} +(-3.73205 + 3.73205i) q^{13} +4.73205 q^{14} +(3.86603 + 0.232051i) q^{15} +4.00000 q^{16} +(0.0980762 - 0.0980762i) q^{17} +(3.00000 - 3.00000i) q^{18} -1.00000i q^{19} +(-4.09808 + 4.09808i) q^{21} +(0.267949 + 0.267949i) q^{22} +(-6.46410 - 6.46410i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(-4.96410 - 0.598076i) q^{25} -7.46410i q^{26} +5.19615i q^{27} +(-4.09808 + 3.63397i) q^{30} -8.73205 q^{31} -0.464102 q^{33} +0.196152i q^{34} +(5.59808 - 4.96410i) q^{35} +(2.46410 + 2.46410i) q^{37} +(1.00000 + 1.00000i) q^{38} +(6.46410 + 6.46410i) q^{39} +(4.73205 - 4.19615i) q^{40} +7.66025i q^{41} -8.19615i q^{42} +(0.0980762 - 0.0980762i) q^{43} +(0.401924 - 6.69615i) q^{45} +12.9282 q^{46} +(3.56218 - 3.56218i) q^{47} -6.92820i q^{48} +4.19615i q^{49} +(5.56218 - 4.36603i) q^{50} +(-0.169873 - 0.169873i) q^{51} +(2.26795 + 2.26795i) q^{53} +(-5.19615 - 5.19615i) q^{54} +(0.598076 + 0.0358984i) q^{55} +9.46410i q^{56} -1.73205 q^{57} +10.1962 q^{59} -4.26795 q^{61} +(8.73205 - 8.73205i) q^{62} +(7.09808 + 7.09808i) q^{63} +8.00000i q^{64} +(-7.83013 - 8.83013i) q^{65} +(0.464102 - 0.464102i) q^{66} +(8.19615 + 8.19615i) q^{67} +(-11.1962 + 11.1962i) q^{69} +(-0.633975 + 10.5622i) q^{70} +7.26795i q^{71} +(6.00000 + 6.00000i) q^{72} +(3.63397 - 3.63397i) q^{73} -4.92820 q^{74} +(-1.03590 + 8.59808i) q^{75} +(-0.633975 + 0.633975i) q^{77} -12.9282 q^{78} -10.3923i q^{79} +(-0.535898 + 8.92820i) q^{80} +9.00000 q^{81} +(-7.66025 - 7.66025i) q^{82} +(-3.73205 - 3.73205i) q^{83} +(0.205771 + 0.232051i) q^{85} +0.196152i q^{86} +(-0.535898 + 0.535898i) q^{88} -10.7321 q^{89} +(6.29423 + 7.09808i) q^{90} +17.6603 q^{91} +15.1244i q^{93} +7.12436i q^{94} +(2.23205 + 0.133975i) q^{95} +(0.464102 + 0.464102i) q^{97} +(-4.19615 - 4.19615i) q^{98} +0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{5} - 6 q^{7} - 8 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{5} - 6 q^{7} - 8 q^{8} - 12 q^{9} + 2 q^{10} - 8 q^{13} + 12 q^{14} + 12 q^{15} + 16 q^{16} - 10 q^{17} + 12 q^{18} - 6 q^{21} + 8 q^{22} - 12 q^{23} - 6 q^{25} - 6 q^{30} - 28 q^{31} + 12 q^{33} + 12 q^{35} - 4 q^{37} + 4 q^{38} + 12 q^{39} + 12 q^{40} - 10 q^{43} + 12 q^{45} + 24 q^{46} - 10 q^{47} - 2 q^{50} - 18 q^{51} + 16 q^{53} - 8 q^{55} + 20 q^{59} - 24 q^{61} + 28 q^{62} + 18 q^{63} - 14 q^{65} - 12 q^{66} + 12 q^{67} - 24 q^{69} - 6 q^{70} + 24 q^{72} + 18 q^{73} + 8 q^{74} - 18 q^{75} - 6 q^{77} - 24 q^{78} - 16 q^{80} + 36 q^{81} + 4 q^{82} - 8 q^{83} + 32 q^{85} - 16 q^{88} - 36 q^{89} - 6 q^{90} + 36 q^{91} + 2 q^{95} - 12 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) −0.133975 + 2.23205i −0.0599153 + 0.998203i
\(6\) 1.73205 + 1.73205i 0.707107 + 0.707107i
\(7\) −2.36603 2.36603i −0.894274 0.894274i 0.100649 0.994922i \(-0.467908\pi\)
−0.994922 + 0.100649i \(0.967908\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −3.00000 −1.00000
\(10\) −2.09808 2.36603i −0.663470 0.748203i
\(11\) 0.267949i 0.0807897i −0.999184 0.0403949i \(-0.987138\pi\)
0.999184 0.0403949i \(-0.0128616\pi\)
\(12\) 0 0
\(13\) −3.73205 + 3.73205i −1.03508 + 1.03508i −0.0357229 + 0.999362i \(0.511373\pi\)
−0.999362 + 0.0357229i \(0.988627\pi\)
\(14\) 4.73205 1.26469
\(15\) 3.86603 + 0.232051i 0.998203 + 0.0599153i
\(16\) 4.00000 1.00000
\(17\) 0.0980762 0.0980762i 0.0237870 0.0237870i −0.695113 0.718900i \(-0.744646\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) 1.00000i 0.229416i
\(20\) 0 0
\(21\) −4.09808 + 4.09808i −0.894274 + 0.894274i
\(22\) 0.267949 + 0.267949i 0.0571270 + 0.0571270i
\(23\) −6.46410 6.46410i −1.34786 1.34786i −0.887984 0.459874i \(-0.847894\pi\)
−0.459874 0.887984i \(-0.652106\pi\)
\(24\) −3.46410 + 3.46410i −0.707107 + 0.707107i
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 7.46410i 1.46383i
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −4.09808 + 3.63397i −0.748203 + 0.663470i
\(31\) −8.73205 −1.56832 −0.784161 0.620557i \(-0.786907\pi\)
−0.784161 + 0.620557i \(0.786907\pi\)
\(32\) 0 0
\(33\) −0.464102 −0.0807897
\(34\) 0.196152i 0.0336399i
\(35\) 5.59808 4.96410i 0.946248 0.839086i
\(36\) 0 0
\(37\) 2.46410 + 2.46410i 0.405096 + 0.405096i 0.880024 0.474929i \(-0.157526\pi\)
−0.474929 + 0.880024i \(0.657526\pi\)
\(38\) 1.00000 + 1.00000i 0.162221 + 0.162221i
\(39\) 6.46410 + 6.46410i 1.03508 + 1.03508i
\(40\) 4.73205 4.19615i 0.748203 0.663470i
\(41\) 7.66025i 1.19633i 0.801373 + 0.598165i \(0.204103\pi\)
−0.801373 + 0.598165i \(0.795897\pi\)
\(42\) 8.19615i 1.26469i
\(43\) 0.0980762 0.0980762i 0.0149565 0.0149565i −0.699589 0.714545i \(-0.746634\pi\)
0.714545 + 0.699589i \(0.246634\pi\)
\(44\) 0 0
\(45\) 0.401924 6.69615i 0.0599153 0.998203i
\(46\) 12.9282 1.90616
\(47\) 3.56218 3.56218i 0.519597 0.519597i −0.397852 0.917449i \(-0.630244\pi\)
0.917449 + 0.397852i \(0.130244\pi\)
\(48\) 6.92820i 1.00000i
\(49\) 4.19615i 0.599450i
\(50\) 5.56218 4.36603i 0.786611 0.617449i
\(51\) −0.169873 0.169873i −0.0237870 0.0237870i
\(52\) 0 0
\(53\) 2.26795 + 2.26795i 0.311527 + 0.311527i 0.845501 0.533974i \(-0.179302\pi\)
−0.533974 + 0.845501i \(0.679302\pi\)
\(54\) −5.19615 5.19615i −0.707107 0.707107i
\(55\) 0.598076 + 0.0358984i 0.0806446 + 0.00484054i
\(56\) 9.46410i 1.26469i
\(57\) −1.73205 −0.229416
\(58\) 0 0
\(59\) 10.1962 1.32743 0.663713 0.747987i \(-0.268980\pi\)
0.663713 + 0.747987i \(0.268980\pi\)
\(60\) 0 0
\(61\) −4.26795 −0.546455 −0.273227 0.961949i \(-0.588091\pi\)
−0.273227 + 0.961949i \(0.588091\pi\)
\(62\) 8.73205 8.73205i 1.10897 1.10897i
\(63\) 7.09808 + 7.09808i 0.894274 + 0.894274i
\(64\) 8.00000i 1.00000i
\(65\) −7.83013 8.83013i −0.971208 1.09524i
\(66\) 0.464102 0.464102i 0.0571270 0.0571270i
\(67\) 8.19615 + 8.19615i 1.00132 + 1.00132i 0.999999 + 0.00132026i \(0.000420252\pi\)
0.00132026 + 0.999999i \(0.499580\pi\)
\(68\) 0 0
\(69\) −11.1962 + 11.1962i −1.34786 + 1.34786i
\(70\) −0.633975 + 10.5622i −0.0757745 + 1.26242i
\(71\) 7.26795i 0.862547i 0.902221 + 0.431273i \(0.141936\pi\)
−0.902221 + 0.431273i \(0.858064\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 3.63397 3.63397i 0.425325 0.425325i −0.461708 0.887032i \(-0.652763\pi\)
0.887032 + 0.461708i \(0.152763\pi\)
\(74\) −4.92820 −0.572892
\(75\) −1.03590 + 8.59808i −0.119615 + 0.992820i
\(76\) 0 0
\(77\) −0.633975 + 0.633975i −0.0722481 + 0.0722481i
\(78\) −12.9282 −1.46383
\(79\) 10.3923i 1.16923i −0.811312 0.584613i \(-0.801246\pi\)
0.811312 0.584613i \(-0.198754\pi\)
\(80\) −0.535898 + 8.92820i −0.0599153 + 0.998203i
\(81\) 9.00000 1.00000
\(82\) −7.66025 7.66025i −0.845934 0.845934i
\(83\) −3.73205 3.73205i −0.409646 0.409646i 0.471969 0.881615i \(-0.343543\pi\)
−0.881615 + 0.471969i \(0.843543\pi\)
\(84\) 0 0
\(85\) 0.205771 + 0.232051i 0.0223190 + 0.0251694i
\(86\) 0.196152i 0.0211517i
\(87\) 0 0
\(88\) −0.535898 + 0.535898i −0.0571270 + 0.0571270i
\(89\) −10.7321 −1.13760 −0.568798 0.822478i \(-0.692591\pi\)
−0.568798 + 0.822478i \(0.692591\pi\)
\(90\) 6.29423 + 7.09808i 0.663470 + 0.748203i
\(91\) 17.6603 1.85130
\(92\) 0 0
\(93\) 15.1244i 1.56832i
\(94\) 7.12436i 0.734821i
\(95\) 2.23205 + 0.133975i 0.229004 + 0.0137455i
\(96\) 0 0
\(97\) 0.464102 + 0.464102i 0.0471224 + 0.0471224i 0.730275 0.683153i \(-0.239392\pi\)
−0.683153 + 0.730275i \(0.739392\pi\)
\(98\) −4.19615 4.19615i −0.423875 0.423875i
\(99\) 0.803848i 0.0807897i
\(100\) 0 0
\(101\) 2.39230i 0.238043i −0.992892 0.119022i \(-0.962024\pi\)
0.992892 0.119022i \(-0.0379758\pi\)
\(102\) 0.339746 0.0336399
\(103\) −11.6603 + 11.6603i −1.14892 + 1.14892i −0.162153 + 0.986766i \(0.551844\pi\)
−0.986766 + 0.162153i \(0.948156\pi\)
\(104\) 14.9282 1.46383
\(105\) −8.59808 9.69615i −0.839086 0.946248i
\(106\) −4.53590 −0.440565
\(107\) −7.46410 + 7.46410i −0.721582 + 0.721582i −0.968927 0.247345i \(-0.920442\pi\)
0.247345 + 0.968927i \(0.420442\pi\)
\(108\) 0 0
\(109\) 16.9282i 1.62143i −0.585443 0.810714i \(-0.699079\pi\)
0.585443 0.810714i \(-0.300921\pi\)
\(110\) −0.633975 + 0.562178i −0.0604471 + 0.0536016i
\(111\) 4.26795 4.26795i 0.405096 0.405096i
\(112\) −9.46410 9.46410i −0.894274 0.894274i
\(113\) 5.46410 + 5.46410i 0.514019 + 0.514019i 0.915756 0.401736i \(-0.131593\pi\)
−0.401736 + 0.915756i \(0.631593\pi\)
\(114\) 1.73205 1.73205i 0.162221 0.162221i
\(115\) 15.2942 13.5622i 1.42619 1.26468i
\(116\) 0 0
\(117\) 11.1962 11.1962i 1.03508 1.03508i
\(118\) −10.1962 + 10.1962i −0.938632 + 0.938632i
\(119\) −0.464102 −0.0425441
\(120\) −7.26795 8.19615i −0.663470 0.748203i
\(121\) 10.9282 0.993473
\(122\) 4.26795 4.26795i 0.386402 0.386402i
\(123\) 13.2679 1.19633
\(124\) 0 0
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) −14.1962 −1.26469
\(127\) −14.7321 14.7321i −1.30726 1.30726i −0.923386 0.383872i \(-0.874591\pi\)
−0.383872 0.923386i \(-0.625409\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −0.169873 0.169873i −0.0149565 0.0149565i
\(130\) 16.6603 + 1.00000i 1.46120 + 0.0877058i
\(131\) 4.46410i 0.390030i 0.980800 + 0.195015i \(0.0624756\pi\)
−0.980800 + 0.195015i \(0.937524\pi\)
\(132\) 0 0
\(133\) −2.36603 + 2.36603i −0.205160 + 0.205160i
\(134\) −16.3923 −1.41608
\(135\) −11.5981 0.696152i −0.998203 0.0599153i
\(136\) −0.392305 −0.0336399
\(137\) −6.56218 + 6.56218i −0.560645 + 0.560645i −0.929491 0.368846i \(-0.879753\pi\)
0.368846 + 0.929491i \(0.379753\pi\)
\(138\) 22.3923i 1.90616i
\(139\) 3.53590i 0.299911i −0.988693 0.149955i \(-0.952087\pi\)
0.988693 0.149955i \(-0.0479130\pi\)
\(140\) 0 0
\(141\) −6.16987 6.16987i −0.519597 0.519597i
\(142\) −7.26795 7.26795i −0.609913 0.609913i
\(143\) 1.00000 + 1.00000i 0.0836242 + 0.0836242i
\(144\) −12.0000 −1.00000
\(145\) 0 0
\(146\) 7.26795i 0.601500i
\(147\) 7.26795 0.599450
\(148\) 0 0
\(149\) −7.39230 −0.605601 −0.302801 0.953054i \(-0.597922\pi\)
−0.302801 + 0.953054i \(0.597922\pi\)
\(150\) −7.56218 9.63397i −0.617449 0.786611i
\(151\) −0.732051 −0.0595734 −0.0297867 0.999556i \(-0.509483\pi\)
−0.0297867 + 0.999556i \(0.509483\pi\)
\(152\) −2.00000 + 2.00000i −0.162221 + 0.162221i
\(153\) −0.294229 + 0.294229i −0.0237870 + 0.0237870i
\(154\) 1.26795i 0.102174i
\(155\) 1.16987 19.4904i 0.0939665 1.56551i
\(156\) 0 0
\(157\) −2.66025 2.66025i −0.212311 0.212311i 0.592937 0.805249i \(-0.297968\pi\)
−0.805249 + 0.592937i \(0.797968\pi\)
\(158\) 10.3923 + 10.3923i 0.826767 + 0.826767i
\(159\) 3.92820 3.92820i 0.311527 0.311527i
\(160\) 0 0
\(161\) 30.5885i 2.41071i
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) −11.0000 + 11.0000i −0.861586 + 0.861586i −0.991522 0.129936i \(-0.958523\pi\)
0.129936 + 0.991522i \(0.458523\pi\)
\(164\) 0 0
\(165\) 0.0621778 1.03590i 0.00484054 0.0806446i
\(166\) 7.46410 0.579327
\(167\) −4.00000 + 4.00000i −0.309529 + 0.309529i −0.844727 0.535198i \(-0.820237\pi\)
0.535198 + 0.844727i \(0.320237\pi\)
\(168\) 16.3923 1.26469
\(169\) 14.8564i 1.14280i
\(170\) −0.437822 0.0262794i −0.0335794 0.00201554i
\(171\) 3.00000i 0.229416i
\(172\) 0 0
\(173\) 2.19615 + 2.19615i 0.166970 + 0.166970i 0.785646 0.618676i \(-0.212331\pi\)
−0.618676 + 0.785646i \(0.712331\pi\)
\(174\) 0 0
\(175\) 10.3301 + 13.1603i 0.780884 + 0.994822i
\(176\) 1.07180i 0.0807897i
\(177\) 17.6603i 1.32743i
\(178\) 10.7321 10.7321i 0.804401 0.804401i
\(179\) −4.92820 −0.368351 −0.184176 0.982893i \(-0.558962\pi\)
−0.184176 + 0.982893i \(0.558962\pi\)
\(180\) 0 0
\(181\) −2.92820 −0.217652 −0.108826 0.994061i \(-0.534709\pi\)
−0.108826 + 0.994061i \(0.534709\pi\)
\(182\) −17.6603 + 17.6603i −1.30907 + 1.30907i
\(183\) 7.39230i 0.546455i
\(184\) 25.8564i 1.90616i
\(185\) −5.83013 + 5.16987i −0.428639 + 0.380097i
\(186\) −15.1244 15.1244i −1.10897 1.10897i
\(187\) −0.0262794 0.0262794i −0.00192174 0.00192174i
\(188\) 0 0
\(189\) 12.2942 12.2942i 0.894274 0.894274i
\(190\) −2.36603 + 2.09808i −0.171650 + 0.152210i
\(191\) 17.9282i 1.29724i −0.761113 0.648620i \(-0.775347\pi\)
0.761113 0.648620i \(-0.224653\pi\)
\(192\) 13.8564 1.00000
\(193\) 12.1962 12.1962i 0.877898 0.877898i −0.115419 0.993317i \(-0.536821\pi\)
0.993317 + 0.115419i \(0.0368210\pi\)
\(194\) −0.928203 −0.0666411
\(195\) −15.2942 + 13.5622i −1.09524 + 0.971208i
\(196\) 0 0
\(197\) −10.1244 + 10.1244i −0.721330 + 0.721330i −0.968876 0.247546i \(-0.920376\pi\)
0.247546 + 0.968876i \(0.420376\pi\)
\(198\) −0.803848 0.803848i −0.0571270 0.0571270i
\(199\) 11.1962i 0.793674i 0.917889 + 0.396837i \(0.129892\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(200\) 8.73205 + 11.1244i 0.617449 + 0.786611i
\(201\) 14.1962 14.1962i 1.00132 1.00132i
\(202\) 2.39230 + 2.39230i 0.168322 + 0.168322i
\(203\) 0 0
\(204\) 0 0
\(205\) −17.0981 1.02628i −1.19418 0.0716785i
\(206\) 23.3205i 1.62482i
\(207\) 19.3923 + 19.3923i 1.34786 + 1.34786i
\(208\) −14.9282 + 14.9282i −1.03508 + 1.03508i
\(209\) −0.267949 −0.0185344
\(210\) 18.2942 + 1.09808i 1.26242 + 0.0757745i
\(211\) −24.0526 −1.65585 −0.827923 0.560841i \(-0.810478\pi\)
−0.827923 + 0.560841i \(0.810478\pi\)
\(212\) 0 0
\(213\) 12.5885 0.862547
\(214\) 14.9282i 1.02047i
\(215\) 0.205771 + 0.232051i 0.0140335 + 0.0158257i
\(216\) 10.3923 10.3923i 0.707107 0.707107i
\(217\) 20.6603 + 20.6603i 1.40251 + 1.40251i
\(218\) 16.9282 + 16.9282i 1.14652 + 1.14652i
\(219\) −6.29423 6.29423i −0.425325 0.425325i
\(220\) 0 0
\(221\) 0.732051i 0.0492431i
\(222\) 8.53590i 0.572892i
\(223\) −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i \(-0.890135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(224\) 0 0
\(225\) 14.8923 + 1.79423i 0.992820 + 0.119615i
\(226\) −10.9282 −0.726933
\(227\) −0.803848 + 0.803848i −0.0533532 + 0.0533532i −0.733280 0.679927i \(-0.762012\pi\)
0.679927 + 0.733280i \(0.262012\pi\)
\(228\) 0 0
\(229\) 25.2487i 1.66848i −0.551400 0.834241i \(-0.685906\pi\)
0.551400 0.834241i \(-0.314094\pi\)
\(230\) −1.73205 + 28.8564i −0.114208 + 1.90274i
\(231\) 1.09808 + 1.09808i 0.0722481 + 0.0722481i
\(232\) 0 0
\(233\) −15.8301 15.8301i −1.03707 1.03707i −0.999286 0.0377800i \(-0.987971\pi\)
−0.0377800 0.999286i \(-0.512029\pi\)
\(234\) 22.3923i 1.46383i
\(235\) 7.47372 + 8.42820i 0.487532 + 0.549795i
\(236\) 0 0
\(237\) −18.0000 −1.16923
\(238\) 0.464102 0.464102i 0.0300832 0.0300832i
\(239\) 13.0526 0.844300 0.422150 0.906526i \(-0.361276\pi\)
0.422150 + 0.906526i \(0.361276\pi\)
\(240\) 15.4641 + 0.928203i 0.998203 + 0.0599153i
\(241\) −5.80385 −0.373859 −0.186929 0.982373i \(-0.559854\pi\)
−0.186929 + 0.982373i \(0.559854\pi\)
\(242\) −10.9282 + 10.9282i −0.702492 + 0.702492i
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −9.36603 0.562178i −0.598373 0.0359162i
\(246\) −13.2679 + 13.2679i −0.845934 + 0.845934i
\(247\) 3.73205 + 3.73205i 0.237465 + 0.237465i
\(248\) 17.4641 + 17.4641i 1.10897 + 1.10897i
\(249\) −6.46410 + 6.46410i −0.409646 + 0.409646i
\(250\) 9.00000 + 13.0000i 0.569210 + 0.822192i
\(251\) 10.8564i 0.685250i −0.939472 0.342625i \(-0.888684\pi\)
0.939472 0.342625i \(-0.111316\pi\)
\(252\) 0 0
\(253\) −1.73205 + 1.73205i −0.108893 + 0.108893i
\(254\) 29.4641 1.84874
\(255\) 0.401924 0.356406i 0.0251694 0.0223190i
\(256\) 0 0
\(257\) 13.2679 13.2679i 0.827632 0.827632i −0.159557 0.987189i \(-0.551007\pi\)
0.987189 + 0.159557i \(0.0510065\pi\)
\(258\) 0.339746 0.0211517
\(259\) 11.6603i 0.724533i
\(260\) 0 0
\(261\) 0 0
\(262\) −4.46410 4.46410i −0.275793 0.275793i
\(263\) −13.0263 13.0263i −0.803235 0.803235i 0.180365 0.983600i \(-0.442272\pi\)
−0.983600 + 0.180365i \(0.942272\pi\)
\(264\) 0.928203 + 0.928203i 0.0571270 + 0.0571270i
\(265\) −5.36603 + 4.75833i −0.329632 + 0.292302i
\(266\) 4.73205i 0.290141i
\(267\) 18.5885i 1.13760i
\(268\) 0 0
\(269\) −16.1962 −0.987497 −0.493748 0.869605i \(-0.664374\pi\)
−0.493748 + 0.869605i \(0.664374\pi\)
\(270\) 12.2942 10.9019i 0.748203 0.663470i
\(271\) 12.3923 0.752779 0.376389 0.926462i \(-0.377165\pi\)
0.376389 + 0.926462i \(0.377165\pi\)
\(272\) 0.392305 0.392305i 0.0237870 0.0237870i
\(273\) 30.5885i 1.85130i
\(274\) 13.1244i 0.792871i
\(275\) −0.160254 + 1.33013i −0.00966368 + 0.0802097i
\(276\) 0 0
\(277\) −6.83013 6.83013i −0.410383 0.410383i 0.471489 0.881872i \(-0.343717\pi\)
−0.881872 + 0.471489i \(0.843717\pi\)
\(278\) 3.53590 + 3.53590i 0.212069 + 0.212069i
\(279\) 26.1962 1.56832
\(280\) −21.1244 1.26795i −1.26242 0.0757745i
\(281\) 12.0000i 0.715860i −0.933748 0.357930i \(-0.883483\pi\)
0.933748 0.357930i \(-0.116517\pi\)
\(282\) 12.3397 0.734821
\(283\) −0.169873 + 0.169873i −0.0100979 + 0.0100979i −0.712138 0.702040i \(-0.752273\pi\)
0.702040 + 0.712138i \(0.252273\pi\)
\(284\) 0 0
\(285\) 0.232051 3.86603i 0.0137455 0.229004i
\(286\) −2.00000 −0.118262
\(287\) 18.1244 18.1244i 1.06985 1.06985i
\(288\) 0 0
\(289\) 16.9808i 0.998868i
\(290\) 0 0
\(291\) 0.803848 0.803848i 0.0471224 0.0471224i
\(292\) 0 0
\(293\) −8.00000 8.00000i −0.467365 0.467365i 0.433695 0.901060i \(-0.357210\pi\)
−0.901060 + 0.433695i \(0.857210\pi\)
\(294\) −7.26795 + 7.26795i −0.423875 + 0.423875i
\(295\) −1.36603 + 22.7583i −0.0795331 + 1.32504i
\(296\) 9.85641i 0.572892i
\(297\) 1.39230 0.0807897
\(298\) 7.39230 7.39230i 0.428225 0.428225i
\(299\) 48.2487 2.79030
\(300\) 0 0
\(301\) −0.464102 −0.0267504
\(302\) 0.732051 0.732051i 0.0421248 0.0421248i
\(303\) −4.14359 −0.238043
\(304\) 4.00000i 0.229416i
\(305\) 0.571797 9.52628i 0.0327410 0.545473i
\(306\) 0.588457i 0.0336399i
\(307\) 16.5885 + 16.5885i 0.946753 + 0.946753i 0.998652 0.0518991i \(-0.0165274\pi\)
−0.0518991 + 0.998652i \(0.516527\pi\)
\(308\) 0 0
\(309\) 20.1962 + 20.1962i 1.14892 + 1.14892i
\(310\) 18.3205 + 20.6603i 1.04053 + 1.17342i
\(311\) 2.26795i 0.128604i −0.997930 0.0643018i \(-0.979518\pi\)
0.997930 0.0643018i \(-0.0204820\pi\)
\(312\) 25.8564i 1.46383i
\(313\) −1.73205 + 1.73205i −0.0979013 + 0.0979013i −0.754361 0.656460i \(-0.772053\pi\)
0.656460 + 0.754361i \(0.272053\pi\)
\(314\) 5.32051 0.300254
\(315\) −16.7942 + 14.8923i −0.946248 + 0.839086i
\(316\) 0 0
\(317\) −8.85641 + 8.85641i −0.497425 + 0.497425i −0.910636 0.413210i \(-0.864407\pi\)
0.413210 + 0.910636i \(0.364407\pi\)
\(318\) 7.85641i 0.440565i
\(319\) 0 0
\(320\) −17.8564 1.07180i −0.998203 0.0599153i
\(321\) 12.9282 + 12.9282i 0.721582 + 0.721582i
\(322\) −30.5885 30.5885i −1.70463 1.70463i
\(323\) −0.0980762 0.0980762i −0.00545711 0.00545711i
\(324\) 0 0
\(325\) 20.7583 16.2942i 1.15146 0.903841i
\(326\) 22.0000i 1.21847i
\(327\) −29.3205 −1.62143
\(328\) 15.3205 15.3205i 0.845934 0.845934i
\(329\) −16.8564 −0.929324
\(330\) 0.973721 + 1.09808i 0.0536016 + 0.0604471i
\(331\) 0.679492 0.0373483 0.0186741 0.999826i \(-0.494055\pi\)
0.0186741 + 0.999826i \(0.494055\pi\)
\(332\) 0 0
\(333\) −7.39230 7.39230i −0.405096 0.405096i
\(334\) 8.00000i 0.437741i
\(335\) −19.3923 + 17.1962i −1.05951 + 0.939526i
\(336\) −16.3923 + 16.3923i −0.894274 + 0.894274i
\(337\) 3.92820 + 3.92820i 0.213983 + 0.213983i 0.805957 0.591974i \(-0.201651\pi\)
−0.591974 + 0.805957i \(0.701651\pi\)
\(338\) 14.8564 + 14.8564i 0.808082 + 0.808082i
\(339\) 9.46410 9.46410i 0.514019 0.514019i
\(340\) 0 0
\(341\) 2.33975i 0.126704i
\(342\) −3.00000 3.00000i −0.162221 0.162221i
\(343\) −6.63397 + 6.63397i −0.358201 + 0.358201i
\(344\) −0.392305 −0.0211517
\(345\) −23.4904 26.4904i −1.26468 1.42619i
\(346\) −4.39230 −0.236132
\(347\) 12.9019 12.9019i 0.692612 0.692612i −0.270194 0.962806i \(-0.587088\pi\)
0.962806 + 0.270194i \(0.0870879\pi\)
\(348\) 0 0
\(349\) 0.267949i 0.0143430i −0.999974 0.00717150i \(-0.997717\pi\)
0.999974 0.00717150i \(-0.00228278\pi\)
\(350\) −23.4904 2.83013i −1.25561 0.151277i
\(351\) −19.3923 19.3923i −1.03508 1.03508i
\(352\) 0 0
\(353\) 22.2679 + 22.2679i 1.18520 + 1.18520i 0.978378 + 0.206825i \(0.0663132\pi\)
0.206825 + 0.978378i \(0.433687\pi\)
\(354\) 17.6603 + 17.6603i 0.938632 + 0.938632i
\(355\) −16.2224 0.973721i −0.860997 0.0516797i
\(356\) 0 0
\(357\) 0.803848i 0.0425441i
\(358\) 4.92820 4.92820i 0.260464 0.260464i
\(359\) −8.07180 −0.426013 −0.213007 0.977051i \(-0.568326\pi\)
−0.213007 + 0.977051i \(0.568326\pi\)
\(360\) −14.1962 + 12.5885i −0.748203 + 0.663470i
\(361\) −1.00000 −0.0526316
\(362\) 2.92820 2.92820i 0.153903 0.153903i
\(363\) 18.9282i 0.993473i
\(364\) 0 0
\(365\) 7.62436 + 8.59808i 0.399077 + 0.450044i
\(366\) −7.39230 7.39230i −0.386402 0.386402i
\(367\) 17.7846 + 17.7846i 0.928349 + 0.928349i 0.997599 0.0692503i \(-0.0220607\pi\)
−0.0692503 + 0.997599i \(0.522061\pi\)
\(368\) −25.8564 25.8564i −1.34786 1.34786i
\(369\) 22.9808i 1.19633i
\(370\) 0.660254 11.0000i 0.0343250 0.571863i
\(371\) 10.7321i 0.557180i
\(372\) 0 0
\(373\) −12.5885 + 12.5885i −0.651806 + 0.651806i −0.953428 0.301622i \(-0.902472\pi\)
0.301622 + 0.953428i \(0.402472\pi\)
\(374\) 0.0525589 0.00271776
\(375\) −19.0526 3.46410i −0.983870 0.178885i
\(376\) −14.2487 −0.734821
\(377\) 0 0
\(378\) 24.5885i 1.26469i
\(379\) 21.4641i 1.10254i 0.834328 + 0.551268i \(0.185856\pi\)
−0.834328 + 0.551268i \(0.814144\pi\)
\(380\) 0 0
\(381\) −25.5167 + 25.5167i −1.30726 + 1.30726i
\(382\) 17.9282 + 17.9282i 0.917287 + 0.917287i
\(383\) 25.7846 + 25.7846i 1.31753 + 1.31753i 0.915724 + 0.401808i \(0.131618\pi\)
0.401808 + 0.915724i \(0.368382\pi\)
\(384\) −13.8564 + 13.8564i −0.707107 + 0.707107i
\(385\) −1.33013 1.50000i −0.0677895 0.0764471i
\(386\) 24.3923i 1.24154i
\(387\) −0.294229 + 0.294229i −0.0149565 + 0.0149565i
\(388\) 0 0
\(389\) −11.8756 −0.602119 −0.301060 0.953605i \(-0.597340\pi\)
−0.301060 + 0.953605i \(0.597340\pi\)
\(390\) 1.73205 28.8564i 0.0877058 1.46120i
\(391\) −1.26795 −0.0641229
\(392\) 8.39230 8.39230i 0.423875 0.423875i
\(393\) 7.73205 0.390030
\(394\) 20.2487i 1.02012i
\(395\) 23.1962 + 1.39230i 1.16713 + 0.0700545i
\(396\) 0 0
\(397\) 15.4904 + 15.4904i 0.777440 + 0.777440i 0.979395 0.201955i \(-0.0647294\pi\)
−0.201955 + 0.979395i \(0.564729\pi\)
\(398\) −11.1962 11.1962i −0.561212 0.561212i
\(399\) 4.09808 + 4.09808i 0.205160 + 0.205160i
\(400\) −19.8564 2.39230i −0.992820 0.119615i
\(401\) 23.7128i 1.18416i 0.805879 + 0.592081i \(0.201693\pi\)
−0.805879 + 0.592081i \(0.798307\pi\)
\(402\) 28.3923i 1.41608i
\(403\) 32.5885 32.5885i 1.62335 1.62335i
\(404\) 0 0
\(405\) −1.20577 + 20.0885i −0.0599153 + 0.998203i
\(406\) 0 0
\(407\) 0.660254 0.660254i 0.0327276 0.0327276i
\(408\) 0.679492i 0.0336399i
\(409\) 9.80385i 0.484769i −0.970180 0.242385i \(-0.922070\pi\)
0.970180 0.242385i \(-0.0779296\pi\)
\(410\) 18.1244 16.0718i 0.895098 0.793729i
\(411\) 11.3660 + 11.3660i 0.560645 + 0.560645i
\(412\) 0 0
\(413\) −24.1244 24.1244i −1.18708 1.18708i
\(414\) −38.7846 −1.90616
\(415\) 8.83013 7.83013i 0.433454 0.384366i
\(416\) 0 0
\(417\) −6.12436 −0.299911
\(418\) 0.267949 0.267949i 0.0131058 0.0131058i
\(419\) −9.07180 −0.443186 −0.221593 0.975139i \(-0.571126\pi\)
−0.221593 + 0.975139i \(0.571126\pi\)
\(420\) 0 0
\(421\) 30.5885 1.49079 0.745395 0.666623i \(-0.232261\pi\)
0.745395 + 0.666623i \(0.232261\pi\)
\(422\) 24.0526 24.0526i 1.17086 1.17086i
\(423\) −10.6865 + 10.6865i −0.519597 + 0.519597i
\(424\) 9.07180i 0.440565i
\(425\) −0.545517 + 0.428203i −0.0264615 + 0.0207709i
\(426\) −12.5885 + 12.5885i −0.609913 + 0.609913i
\(427\) 10.0981 + 10.0981i 0.488680 + 0.488680i
\(428\) 0 0
\(429\) 1.73205 1.73205i 0.0836242 0.0836242i
\(430\) −0.437822 0.0262794i −0.0211137 0.00126731i
\(431\) 9.51666i 0.458401i −0.973379 0.229201i \(-0.926389\pi\)
0.973379 0.229201i \(-0.0736112\pi\)
\(432\) 20.7846i 1.00000i
\(433\) −4.87564 + 4.87564i −0.234309 + 0.234309i −0.814488 0.580180i \(-0.802982\pi\)
0.580180 + 0.814488i \(0.302982\pi\)
\(434\) −41.3205 −1.98345
\(435\) 0 0
\(436\) 0 0
\(437\) −6.46410 + 6.46410i −0.309220 + 0.309220i
\(438\) 12.5885 0.601500
\(439\) 17.8564i 0.852240i 0.904667 + 0.426120i \(0.140120\pi\)
−0.904667 + 0.426120i \(0.859880\pi\)
\(440\) −1.12436 1.26795i −0.0536016 0.0604471i
\(441\) 12.5885i 0.599450i
\(442\) −0.732051 0.732051i −0.0348201 0.0348201i
\(443\) −18.8301 18.8301i −0.894646 0.894646i 0.100310 0.994956i \(-0.468017\pi\)
−0.994956 + 0.100310i \(0.968017\pi\)
\(444\) 0 0
\(445\) 1.43782 23.9545i 0.0681593 1.13555i
\(446\) 18.0000i 0.852325i
\(447\) 12.8038i 0.605601i
\(448\) 18.9282 18.9282i 0.894274 0.894274i
\(449\) 7.85641 0.370767 0.185383 0.982666i \(-0.440647\pi\)
0.185383 + 0.982666i \(0.440647\pi\)
\(450\) −16.6865 + 13.0981i −0.786611 + 0.617449i
\(451\) 2.05256 0.0966512
\(452\) 0 0
\(453\) 1.26795i 0.0595734i
\(454\) 1.60770i 0.0754529i
\(455\) −2.36603 + 39.4186i −0.110921 + 1.84797i
\(456\) 3.46410 + 3.46410i 0.162221 + 0.162221i
\(457\) −14.6340 14.6340i −0.684548 0.684548i 0.276473 0.961022i \(-0.410834\pi\)
−0.961022 + 0.276473i \(0.910834\pi\)
\(458\) 25.2487 + 25.2487i 1.17979 + 1.17979i
\(459\) 0.509619 + 0.509619i 0.0237870 + 0.0237870i
\(460\) 0 0
\(461\) 13.0000i 0.605470i 0.953075 + 0.302735i \(0.0978998\pi\)
−0.953075 + 0.302735i \(0.902100\pi\)
\(462\) −2.19615 −0.102174
\(463\) 4.29423 4.29423i 0.199570 0.199570i −0.600246 0.799816i \(-0.704931\pi\)
0.799816 + 0.600246i \(0.204931\pi\)
\(464\) 0 0
\(465\) −33.7583 2.02628i −1.56551 0.0939665i
\(466\) 31.6603 1.46663
\(467\) −18.2224 + 18.2224i −0.843234 + 0.843234i −0.989278 0.146044i \(-0.953346\pi\)
0.146044 + 0.989278i \(0.453346\pi\)
\(468\) 0 0
\(469\) 38.7846i 1.79091i
\(470\) −15.9019 0.954483i −0.733501 0.0440270i
\(471\) −4.60770 + 4.60770i −0.212311 + 0.212311i
\(472\) −20.3923 20.3923i −0.938632 0.938632i
\(473\) −0.0262794 0.0262794i −0.00120833 0.00120833i
\(474\) 18.0000 18.0000i 0.826767 0.826767i
\(475\) −0.598076 + 4.96410i −0.0274416 + 0.227769i
\(476\) 0 0
\(477\) −6.80385 6.80385i −0.311527 0.311527i
\(478\) −13.0526 + 13.0526i −0.597010 + 0.597010i
\(479\) −12.9282 −0.590705 −0.295352 0.955388i \(-0.595437\pi\)
−0.295352 + 0.955388i \(0.595437\pi\)
\(480\) 0 0
\(481\) −18.3923 −0.838617
\(482\) 5.80385 5.80385i 0.264358 0.264358i
\(483\) 52.9808 2.41071
\(484\) 0 0
\(485\) −1.09808 + 0.973721i −0.0498611 + 0.0442144i
\(486\) 15.5885 + 15.5885i 0.707107 + 0.707107i
\(487\) −21.0526 21.0526i −0.953983 0.953983i 0.0450043 0.998987i \(-0.485670\pi\)
−0.998987 + 0.0450043i \(0.985670\pi\)
\(488\) 8.53590 + 8.53590i 0.386402 + 0.386402i
\(489\) 19.0526 + 19.0526i 0.861586 + 0.861586i
\(490\) 9.92820 8.80385i 0.448511 0.397717i
\(491\) 37.3205i 1.68425i −0.539282 0.842125i \(-0.681304\pi\)
0.539282 0.842125i \(-0.318696\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −7.46410 −0.335826
\(495\) −1.79423 0.107695i −0.0806446 0.00484054i
\(496\) −34.9282 −1.56832
\(497\) 17.1962 17.1962i 0.771353 0.771353i
\(498\) 12.9282i 0.579327i
\(499\) 14.8564i 0.665064i −0.943092 0.332532i \(-0.892097\pi\)
0.943092 0.332532i \(-0.107903\pi\)
\(500\) 0 0
\(501\) 6.92820 + 6.92820i 0.309529 + 0.309529i
\(502\) 10.8564 + 10.8564i 0.484545 + 0.484545i
\(503\) −10.0718 10.0718i −0.449079 0.449079i 0.445969 0.895048i \(-0.352859\pi\)
−0.895048 + 0.445969i \(0.852859\pi\)
\(504\) 28.3923i 1.26469i
\(505\) 5.33975 + 0.320508i 0.237616 + 0.0142624i
\(506\) 3.46410i 0.153998i
\(507\) −25.7321 −1.14280
\(508\) 0 0
\(509\) 15.2679 0.676740 0.338370 0.941013i \(-0.390124\pi\)
0.338370 + 0.941013i \(0.390124\pi\)
\(510\) −0.0455173 + 0.758330i −0.00201554 + 0.0335794i
\(511\) −17.1962 −0.760713
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 5.19615 0.229416
\(514\) 26.5359i 1.17045i
\(515\) −24.4641 27.5885i −1.07802 1.21569i
\(516\) 0 0
\(517\) −0.954483 0.954483i −0.0419781 0.0419781i
\(518\) 11.6603 + 11.6603i 0.512322 + 0.512322i
\(519\) 3.80385 3.80385i 0.166970 0.166970i
\(520\) −2.00000 + 33.3205i −0.0877058 + 1.46120i
\(521\) 16.0000i 0.700973i 0.936568 + 0.350486i \(0.113984\pi\)
−0.936568 + 0.350486i \(0.886016\pi\)
\(522\) 0 0
\(523\) 1.60770 1.60770i 0.0702996 0.0702996i −0.671083 0.741382i \(-0.734171\pi\)
0.741382 + 0.671083i \(0.234171\pi\)
\(524\) 0 0
\(525\) 22.7942 17.8923i 0.994822 0.780884i
\(526\) 26.0526 1.13595
\(527\) −0.856406 + 0.856406i −0.0373057 + 0.0373057i
\(528\) −1.85641 −0.0807897
\(529\) 60.5692i 2.63344i
\(530\) 0.607695 10.1244i 0.0263966 0.439774i
\(531\) −30.5885 −1.32743
\(532\) 0 0
\(533\) −28.5885 28.5885i −1.23830 1.23830i
\(534\) −18.5885 18.5885i −0.804401 0.804401i
\(535\) −15.6603 17.6603i −0.677052 0.763519i
\(536\) 32.7846i 1.41608i
\(537\) 8.53590i 0.368351i
\(538\) 16.1962 16.1962i 0.698266 0.698266i
\(539\) 1.12436 0.0484294
\(540\) 0 0
\(541\) −20.8038 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(542\) −12.3923 + 12.3923i −0.532295 + 0.532295i
\(543\) 5.07180i 0.217652i
\(544\) 0 0
\(545\) 37.7846 + 2.26795i 1.61851 + 0.0971483i
\(546\) 30.5885 + 30.5885i 1.30907 + 1.30907i
\(547\) −18.3205 18.3205i −0.783328 0.783328i 0.197063 0.980391i \(-0.436860\pi\)
−0.980391 + 0.197063i \(0.936860\pi\)
\(548\) 0 0
\(549\) 12.8038 0.546455
\(550\) −1.16987 1.49038i −0.0498836 0.0635501i
\(551\) 0 0
\(552\) 44.7846 1.90616
\(553\) −24.5885 + 24.5885i −1.04561 + 1.04561i
\(554\) 13.6603 0.580369
\(555\) 8.95448 + 10.0981i 0.380097 + 0.428639i
\(556\) 0 0
\(557\) 30.6865 30.6865i 1.30023 1.30023i 0.371996 0.928234i \(-0.378674\pi\)
0.928234 0.371996i \(-0.121326\pi\)
\(558\) −26.1962 + 26.1962i −1.10897 + 1.10897i
\(559\) 0.732051i 0.0309625i
\(560\) 22.3923 19.8564i 0.946248 0.839086i
\(561\) −0.0455173 + 0.0455173i −0.00192174 + 0.00192174i
\(562\) 12.0000 + 12.0000i 0.506189 + 0.506189i
\(563\) 20.1244 + 20.1244i 0.848140 + 0.848140i 0.989901 0.141761i \(-0.0452763\pi\)
−0.141761 + 0.989901i \(0.545276\pi\)
\(564\) 0 0
\(565\) −12.9282 + 11.4641i −0.543894 + 0.482298i
\(566\) 0.339746i 0.0142806i
\(567\) −21.2942 21.2942i −0.894274 0.894274i
\(568\) 14.5359 14.5359i 0.609913 0.609913i
\(569\) 5.26795 0.220844 0.110422 0.993885i \(-0.464780\pi\)
0.110422 + 0.993885i \(0.464780\pi\)
\(570\) 3.63397 + 4.09808i 0.152210 + 0.171650i
\(571\) −13.4641 −0.563455 −0.281728 0.959494i \(-0.590907\pi\)
−0.281728 + 0.959494i \(0.590907\pi\)
\(572\) 0 0
\(573\) −31.0526 −1.29724
\(574\) 36.2487i 1.51299i
\(575\) 28.2224 + 35.9545i 1.17696 + 1.49941i
\(576\) 24.0000i 1.00000i
\(577\) −14.6865 14.6865i −0.611408 0.611408i 0.331905 0.943313i \(-0.392309\pi\)
−0.943313 + 0.331905i \(0.892309\pi\)
\(578\) −16.9808 16.9808i −0.706307 0.706307i
\(579\) −21.1244 21.1244i −0.877898 0.877898i
\(580\) 0 0
\(581\) 17.6603i 0.732671i
\(582\) 1.60770i 0.0666411i
\(583\) 0.607695 0.607695i 0.0251682 0.0251682i
\(584\) −14.5359 −0.601500
\(585\) 23.4904 + 26.4904i 0.971208 + 1.09524i
\(586\) 16.0000 0.660954
\(587\) 23.6865 23.6865i 0.977648 0.977648i −0.0221077 0.999756i \(-0.507038\pi\)
0.999756 + 0.0221077i \(0.00703768\pi\)
\(588\) 0 0
\(589\) 8.73205i 0.359798i
\(590\) −21.3923 24.1244i −0.880707 0.993184i
\(591\) 17.5359 + 17.5359i 0.721330 + 0.721330i
\(592\) 9.85641 + 9.85641i 0.405096 + 0.405096i
\(593\) 17.9282 + 17.9282i 0.736223 + 0.736223i 0.971845 0.235622i \(-0.0757126\pi\)
−0.235622 + 0.971845i \(0.575713\pi\)
\(594\) −1.39230 + 1.39230i −0.0571270 + 0.0571270i
\(595\) 0.0621778 1.03590i 0.00254904 0.0424677i
\(596\) 0 0
\(597\) 19.3923 0.793674
\(598\) −48.2487 + 48.2487i −1.97304 + 1.97304i
\(599\) 33.3205 1.36144 0.680720 0.732544i \(-0.261667\pi\)
0.680720 + 0.732544i \(0.261667\pi\)
\(600\) 19.2679 15.1244i 0.786611 0.617449i
\(601\) −2.19615 −0.0895829 −0.0447915 0.998996i \(-0.514262\pi\)
−0.0447915 + 0.998996i \(0.514262\pi\)
\(602\) 0.464102 0.464102i 0.0189154 0.0189154i
\(603\) −24.5885 24.5885i −1.00132 1.00132i
\(604\) 0 0
\(605\) −1.46410 + 24.3923i −0.0595242 + 0.991688i
\(606\) 4.14359 4.14359i 0.168322 0.168322i
\(607\) 12.1244 + 12.1244i 0.492112 + 0.492112i 0.908971 0.416859i \(-0.136869\pi\)
−0.416859 + 0.908971i \(0.636869\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 8.95448 + 10.0981i 0.362556 + 0.408859i
\(611\) 26.5885i 1.07565i
\(612\) 0 0
\(613\) −3.63397 + 3.63397i −0.146775 + 0.146775i −0.776676 0.629901i \(-0.783096\pi\)
0.629901 + 0.776676i \(0.283096\pi\)
\(614\) −33.1769 −1.33891
\(615\) −1.77757 + 29.6147i −0.0716785 + 1.19418i
\(616\) 2.53590 0.102174
\(617\) −20.2224 + 20.2224i −0.814124 + 0.814124i −0.985249 0.171125i \(-0.945260\pi\)
0.171125 + 0.985249i \(0.445260\pi\)
\(618\) −40.3923 −1.62482
\(619\) 4.78461i 0.192310i −0.995366 0.0961549i \(-0.969346\pi\)
0.995366 0.0961549i \(-0.0306544\pi\)
\(620\) 0 0
\(621\) 33.5885 33.5885i 1.34786 1.34786i
\(622\) 2.26795 + 2.26795i 0.0909365 + 0.0909365i
\(623\) 25.3923 + 25.3923i 1.01732 + 1.01732i
\(624\) 25.8564 + 25.8564i 1.03508 + 1.03508i
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 3.46410i 0.138453i
\(627\) 0.464102i 0.0185344i
\(628\) 0 0
\(629\) 0.483340 0.0192720
\(630\) 1.90192 31.6865i 0.0757745 1.26242i
\(631\) −10.6603 −0.424378 −0.212189 0.977229i \(-0.568059\pi\)
−0.212189 + 0.977229i \(0.568059\pi\)
\(632\) −20.7846 + 20.7846i −0.826767 + 0.826767i
\(633\) 41.6603i 1.65585i
\(634\) 17.7128i 0.703466i
\(635\) 34.8564 30.9090i 1.38323 1.22658i
\(636\) 0 0
\(637\) −15.6603 15.6603i −0.620482 0.620482i
\(638\) 0 0
\(639\) 21.8038i 0.862547i
\(640\) 18.9282 16.7846i 0.748203 0.663470i
\(641\) 0.588457i 0.0232427i 0.999932 + 0.0116213i \(0.00369927\pi\)
−0.999932 + 0.0116213i \(0.996301\pi\)
\(642\) −25.8564 −1.02047
\(643\) −1.24167 + 1.24167i −0.0489667 + 0.0489667i −0.731166 0.682199i \(-0.761024\pi\)
0.682199 + 0.731166i \(0.261024\pi\)
\(644\) 0 0
\(645\) 0.401924 0.356406i 0.0158257 0.0140335i
\(646\) 0.196152 0.00771751
\(647\) −15.9019 + 15.9019i −0.625169 + 0.625169i −0.946849 0.321679i \(-0.895753\pi\)
0.321679 + 0.946849i \(0.395753\pi\)
\(648\) −18.0000 18.0000i −0.707107 0.707107i
\(649\) 2.73205i 0.107242i
\(650\) −4.46410 + 37.0526i −0.175096 + 1.45332i
\(651\) 35.7846 35.7846i 1.40251 1.40251i
\(652\) 0 0
\(653\) −17.4904 17.4904i −0.684452 0.684452i 0.276548 0.961000i \(-0.410809\pi\)
−0.961000 + 0.276548i \(0.910809\pi\)
\(654\) 29.3205 29.3205i 1.14652 1.14652i
\(655\) −9.96410 0.598076i −0.389330 0.0233688i
\(656\) 30.6410i 1.19633i
\(657\) −10.9019 + 10.9019i −0.425325 + 0.425325i
\(658\) 16.8564 16.8564i 0.657131 0.657131i
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) 18.7846 0.730637 0.365318 0.930883i \(-0.380960\pi\)
0.365318 + 0.930883i \(0.380960\pi\)
\(662\) −0.679492 + 0.679492i −0.0264092 + 0.0264092i
\(663\) 1.26795 0.0492431
\(664\) 14.9282i 0.579327i
\(665\) −4.96410 5.59808i −0.192500 0.217084i
\(666\) 14.7846 0.572892
\(667\) 0 0
\(668\) 0 0
\(669\) 15.5885 + 15.5885i 0.602685 + 0.602685i
\(670\) 2.19615 36.5885i 0.0848448 1.41354i
\(671\) 1.14359i 0.0441479i
\(672\) 0 0
\(673\) −29.4449 + 29.4449i −1.13502 + 1.13502i −0.145685 + 0.989331i \(0.546539\pi\)
−0.989331 + 0.145685i \(0.953461\pi\)
\(674\) −7.85641 −0.302617
\(675\) 3.10770 25.7942i 0.119615 0.992820i
\(676\) 0 0
\(677\) 5.46410 5.46410i 0.210002 0.210002i −0.594266 0.804269i \(-0.702557\pi\)
0.804269 + 0.594266i \(0.202557\pi\)
\(678\) 18.9282i 0.726933i
\(679\) 2.19615i 0.0842806i
\(680\) 0.0525589 0.875644i 0.00201554 0.0335794i
\(681\) 1.39230 + 1.39230i 0.0533532 + 0.0533532i
\(682\) −2.33975 2.33975i −0.0895935 0.0895935i
\(683\) −27.1962 27.1962i −1.04063 1.04063i −0.999139 0.0414931i \(-0.986789\pi\)
−0.0414931 0.999139i \(-0.513211\pi\)
\(684\) 0 0
\(685\) −13.7679 15.5263i −0.526046 0.593229i
\(686\) 13.2679i 0.506573i
\(687\) −43.7321 −1.66848
\(688\) 0.392305 0.392305i 0.0149565 0.0149565i
\(689\) −16.9282 −0.644913
\(690\) 49.9808 + 3.00000i 1.90274 + 0.114208i
\(691\) 49.4449 1.88097 0.940486 0.339833i \(-0.110371\pi\)
0.940486 + 0.339833i \(0.110371\pi\)
\(692\) 0 0
\(693\) 1.90192 1.90192i 0.0722481 0.0722481i
\(694\) 25.8038i 0.979501i
\(695\) 7.89230 + 0.473721i 0.299372 + 0.0179692i
\(696\) 0 0
\(697\) 0.751289 + 0.751289i 0.0284571 + 0.0284571i
\(698\) 0.267949 + 0.267949i 0.0101420 + 0.0101420i
\(699\) −27.4186 + 27.4186i −1.03707 + 1.03707i
\(700\) 0 0
\(701\) 31.8564i 1.20320i 0.798798 + 0.601600i \(0.205470\pi\)
−0.798798 + 0.601600i \(0.794530\pi\)
\(702\) 38.7846 1.46383
\(703\) 2.46410 2.46410i 0.0929354 0.0929354i
\(704\) 2.14359 0.0807897
\(705\) 14.5981 12.9449i 0.549795 0.487532i
\(706\) −44.5359 −1.67613
\(707\) −5.66025 + 5.66025i −0.212876 + 0.212876i
\(708\) 0 0
\(709\) 31.4641i 1.18166i 0.806796 + 0.590830i \(0.201199\pi\)
−0.806796 + 0.590830i \(0.798801\pi\)
\(710\) 17.1962 15.2487i 0.645360 0.572274i
\(711\) 31.1769i 1.16923i
\(712\) 21.4641 + 21.4641i 0.804401 + 0.804401i
\(713\) 56.4449 + 56.4449i 2.11388 + 2.11388i
\(714\) −0.803848 0.803848i −0.0300832 0.0300832i
\(715\) −2.36603 + 2.09808i −0.0884843 + 0.0784636i
\(716\) 0 0
\(717\) 22.6077i 0.844300i
\(718\) 8.07180 8.07180i 0.301237 0.301237i
\(719\) −47.6410 −1.77671 −0.888355 0.459157i \(-0.848151\pi\)
−0.888355 + 0.459157i \(0.848151\pi\)
\(720\) 1.60770 26.7846i 0.0599153 0.998203i
\(721\) 55.1769 2.05490
\(722\) 1.00000 1.00000i 0.0372161 0.0372161i
\(723\) 10.0526i 0.373859i
\(724\) 0 0
\(725\) 0 0
\(726\) 18.9282 + 18.9282i 0.702492 + 0.702492i
\(727\) −11.0263 11.0263i −0.408942 0.408942i 0.472427 0.881370i \(-0.343378\pi\)
−0.881370 + 0.472427i \(0.843378\pi\)
\(728\) −35.3205 35.3205i −1.30907 1.30907i
\(729\) −27.0000 −1.00000
\(730\) −16.2224 0.973721i −0.600419 0.0360390i
\(731\) 0.0192379i 0.000711539i
\(732\) 0 0
\(733\) 28.6603 28.6603i 1.05859 1.05859i 0.0604174 0.998173i \(-0.480757\pi\)
0.998173 0.0604174i \(-0.0192432\pi\)
\(734\) −35.5692 −1.31288
\(735\) −0.973721 + 16.2224i −0.0359162 + 0.598373i
\(736\) 0 0
\(737\) 2.19615 2.19615i 0.0808963 0.0808963i
\(738\) 22.9808 + 22.9808i 0.845934 + 0.845934i
\(739\) 19.4449i 0.715291i −0.933857 0.357645i \(-0.883580\pi\)
0.933857 0.357645i \(-0.116420\pi\)
\(740\) 0 0
\(741\) 6.46410 6.46410i 0.237465 0.237465i
\(742\) 10.7321 + 10.7321i 0.393986 + 0.393986i
\(743\) 32.2487 + 32.2487i 1.18309 + 1.18309i 0.978939 + 0.204151i \(0.0654434\pi\)
0.204151 + 0.978939i \(0.434557\pi\)
\(744\) 30.2487 30.2487i 1.10897 1.10897i
\(745\) 0.990381 16.5000i 0.0362848 0.604513i
\(746\) 25.1769i 0.921792i
\(747\) 11.1962 + 11.1962i 0.409646 + 0.409646i
\(748\) 0 0
\(749\) 35.3205 1.29058
\(750\) 22.5167 15.5885i 0.822192 0.569210i
\(751\) 6.78461 0.247574 0.123787 0.992309i \(-0.460496\pi\)
0.123787 + 0.992309i \(0.460496\pi\)
\(752\) 14.2487 14.2487i 0.519597 0.519597i
\(753\) −18.8038 −0.685250
\(754\) 0 0
\(755\) 0.0980762 1.63397i 0.00356936 0.0594664i
\(756\) 0 0
\(757\) 14.0263 + 14.0263i 0.509794 + 0.509794i 0.914463 0.404669i \(-0.132613\pi\)
−0.404669 + 0.914463i \(0.632613\pi\)
\(758\) −21.4641 21.4641i −0.779611 0.779611i
\(759\) 3.00000 + 3.00000i 0.108893 + 0.108893i
\(760\) −4.19615 4.73205i −0.152210 0.171650i
\(761\) 1.48334i 0.0537710i −0.999639 0.0268855i \(-0.991441\pi\)
0.999639 0.0268855i \(-0.00855895\pi\)
\(762\) 51.0333i 1.84874i
\(763\) −40.0526 + 40.0526i −1.45000 + 1.45000i
\(764\) 0 0
\(765\) −0.617314 0.696152i −0.0223190 0.0251694i
\(766\) −51.5692 −1.86327
\(767\) −38.0526 + 38.0526i −1.37400 + 1.37400i
\(768\) 0 0
\(769\) 23.0000i 0.829401i −0.909958 0.414701i \(-0.863886\pi\)
0.909958 0.414701i \(-0.136114\pi\)
\(770\) 2.83013 + 0.169873i 0.101991 + 0.00612180i
\(771\) −22.9808 22.9808i −0.827632 0.827632i
\(772\) 0 0
\(773\) −25.5885 25.5885i −0.920353 0.920353i 0.0767013 0.997054i \(-0.475561\pi\)
−0.997054 + 0.0767013i \(0.975561\pi\)
\(774\) 0.588457i 0.0211517i
\(775\) 43.3468 + 5.22243i 1.55706 + 0.187595i
\(776\) 1.85641i