Properties

Label 285.2.k.a.77.2
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 77.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 285.77
Dual form 285.2.k.a.248.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +1.73205i q^{3} +(-1.86603 - 1.23205i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-0.633975 - 0.633975i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +1.73205i q^{3} +(-1.86603 - 1.23205i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-0.633975 - 0.633975i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +(3.09808 - 0.633975i) q^{10} -3.73205i q^{11} +(-0.267949 + 0.267949i) q^{13} +1.26795 q^{14} +(2.13397 - 3.23205i) q^{15} +4.00000 q^{16} +(-5.09808 + 5.09808i) q^{17} +(3.00000 - 3.00000i) q^{18} -1.00000i q^{19} +(1.09808 - 1.09808i) q^{21} +(3.73205 + 3.73205i) q^{22} +(0.464102 + 0.464102i) q^{23} +(3.46410 - 3.46410i) q^{24} +(1.96410 + 4.59808i) q^{25} -0.535898i q^{26} -5.19615i q^{27} +(1.09808 + 5.36603i) q^{30} -5.26795 q^{31} +6.46410 q^{33} -10.1962i q^{34} +(0.401924 + 1.96410i) q^{35} +(-4.46410 - 4.46410i) q^{37} +(1.00000 + 1.00000i) q^{38} +(-0.464102 - 0.464102i) q^{39} +(1.26795 + 6.19615i) q^{40} -9.66025i q^{41} +2.19615i q^{42} +(-5.09808 + 5.09808i) q^{43} +(5.59808 + 3.69615i) q^{45} -0.928203 q^{46} +(-8.56218 + 8.56218i) q^{47} +6.92820i q^{48} -6.19615i q^{49} +(-6.56218 - 2.63397i) q^{50} +(-8.83013 - 8.83013i) q^{51} +(5.73205 + 5.73205i) q^{53} +(5.19615 + 5.19615i) q^{54} +(-4.59808 + 6.96410i) q^{55} +2.53590i q^{56} +1.73205 q^{57} -0.196152 q^{59} -7.73205 q^{61} +(5.26795 - 5.26795i) q^{62} +(1.90192 + 1.90192i) q^{63} +8.00000i q^{64} +(0.830127 - 0.169873i) q^{65} +(-6.46410 + 6.46410i) q^{66} +(-2.19615 - 2.19615i) q^{67} +(-0.803848 + 0.803848i) q^{69} +(-2.36603 - 1.56218i) q^{70} +10.7321i q^{71} +(6.00000 + 6.00000i) q^{72} +(5.36603 - 5.36603i) q^{73} +8.92820 q^{74} +(-7.96410 + 3.40192i) q^{75} +(-2.36603 + 2.36603i) q^{77} +0.928203 q^{78} +10.3923i q^{79} +(-7.46410 - 4.92820i) q^{80} +9.00000 q^{81} +(9.66025 + 9.66025i) q^{82} +(-0.267949 - 0.267949i) q^{83} +(15.7942 - 3.23205i) q^{85} -10.1962i q^{86} +(-7.46410 + 7.46410i) q^{88} -7.26795 q^{89} +(-9.29423 + 1.90192i) q^{90} +0.339746 q^{91} -9.12436i q^{93} -17.1244i q^{94} +(-1.23205 + 1.86603i) q^{95} +(-6.46410 - 6.46410i) q^{97} +(6.19615 + 6.19615i) q^{98} +11.1962i 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
\(5\) −1.86603 1.23205i −0.834512 0.550990i
\(6\) −1.73205 1.73205i −0.707107 0.707107i
\(7\) −0.633975 0.633975i −0.239620 0.239620i 0.577073 0.816693i \(-0.304195\pi\)
−0.816693 + 0.577073i \(0.804195\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −3.00000 −1.00000
\(10\) 3.09808 0.633975i 0.979698 0.200480i
\(11\) 3.73205i 1.12526i −0.826710 0.562628i \(-0.809790\pi\)
0.826710 0.562628i \(-0.190210\pi\)
\(12\) 0 0
\(13\) −0.267949 + 0.267949i −0.0743157 + 0.0743157i −0.743288 0.668972i \(-0.766735\pi\)
0.668972 + 0.743288i \(0.266735\pi\)
\(14\) 1.26795 0.338874
\(15\) 2.13397 3.23205i 0.550990 0.834512i
\(16\) 4.00000 1.00000
\(17\) −5.09808 + 5.09808i −1.23647 + 1.23647i −0.275029 + 0.961436i \(0.588688\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) 1.00000i 0.229416i
\(20\) 0 0
\(21\) 1.09808 1.09808i 0.239620 0.239620i
\(22\) 3.73205 + 3.73205i 0.795676 + 0.795676i
\(23\) 0.464102 + 0.464102i 0.0967719 + 0.0967719i 0.753835 0.657063i \(-0.228202\pi\)
−0.657063 + 0.753835i \(0.728202\pi\)
\(24\) 3.46410 3.46410i 0.707107 0.707107i
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) 0.535898i 0.105098i
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.09808 + 5.36603i 0.200480 + 0.979698i
\(31\) −5.26795 −0.946152 −0.473076 0.881022i \(-0.656856\pi\)
−0.473076 + 0.881022i \(0.656856\pi\)
\(32\) 0 0
\(33\) 6.46410 1.12526
\(34\) 10.1962i 1.74863i
\(35\) 0.401924 + 1.96410i 0.0679375 + 0.331994i
\(36\) 0 0
\(37\) −4.46410 4.46410i −0.733894 0.733894i 0.237495 0.971389i \(-0.423674\pi\)
−0.971389 + 0.237495i \(0.923674\pi\)
\(38\) 1.00000 + 1.00000i 0.162221 + 0.162221i
\(39\) −0.464102 0.464102i −0.0743157 0.0743157i
\(40\) 1.26795 + 6.19615i 0.200480 + 0.979698i
\(41\) 9.66025i 1.50868i −0.656485 0.754339i \(-0.727957\pi\)
0.656485 0.754339i \(-0.272043\pi\)
\(42\) 2.19615i 0.338874i
\(43\) −5.09808 + 5.09808i −0.777449 + 0.777449i −0.979396 0.201947i \(-0.935273\pi\)
0.201947 + 0.979396i \(0.435273\pi\)
\(44\) 0 0
\(45\) 5.59808 + 3.69615i 0.834512 + 0.550990i
\(46\) −0.928203 −0.136856
\(47\) −8.56218 + 8.56218i −1.24892 + 1.24892i −0.292725 + 0.956197i \(0.594562\pi\)
−0.956197 + 0.292725i \(0.905438\pi\)
\(48\) 6.92820i 1.00000i
\(49\) 6.19615i 0.885165i
\(50\) −6.56218 2.63397i −0.928032 0.372500i
\(51\) −8.83013 8.83013i −1.23647 1.23647i
\(52\) 0 0
\(53\) 5.73205 + 5.73205i 0.787358 + 0.787358i 0.981060 0.193703i \(-0.0620497\pi\)
−0.193703 + 0.981060i \(0.562050\pi\)
\(54\) 5.19615 + 5.19615i 0.707107 + 0.707107i
\(55\) −4.59808 + 6.96410i −0.620004 + 0.939039i
\(56\) 2.53590i 0.338874i
\(57\) 1.73205 0.229416
\(58\) 0 0
\(59\) −0.196152 −0.0255369 −0.0127684 0.999918i \(-0.504064\pi\)
−0.0127684 + 0.999918i \(0.504064\pi\)
\(60\) 0 0
\(61\) −7.73205 −0.989988 −0.494994 0.868896i \(-0.664830\pi\)
−0.494994 + 0.868896i \(0.664830\pi\)
\(62\) 5.26795 5.26795i 0.669030 0.669030i
\(63\) 1.90192 + 1.90192i 0.239620 + 0.239620i
\(64\) 8.00000i 1.00000i
\(65\) 0.830127 0.169873i 0.102965 0.0210702i
\(66\) −6.46410 + 6.46410i −0.795676 + 0.795676i
\(67\) −2.19615 2.19615i −0.268303 0.268303i 0.560113 0.828416i \(-0.310758\pi\)
−0.828416 + 0.560113i \(0.810758\pi\)
\(68\) 0 0
\(69\) −0.803848 + 0.803848i −0.0967719 + 0.0967719i
\(70\) −2.36603 1.56218i −0.282794 0.186716i
\(71\) 10.7321i 1.27366i 0.771004 + 0.636830i \(0.219755\pi\)
−0.771004 + 0.636830i \(0.780245\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 5.36603 5.36603i 0.628046 0.628046i −0.319530 0.947576i \(-0.603525\pi\)
0.947576 + 0.319530i \(0.103525\pi\)
\(74\) 8.92820 1.03788
\(75\) −7.96410 + 3.40192i −0.919615 + 0.392820i
\(76\) 0 0
\(77\) −2.36603 + 2.36603i −0.269634 + 0.269634i
\(78\) 0.928203 0.105098
\(79\) 10.3923i 1.16923i 0.811312 + 0.584613i \(0.198754\pi\)
−0.811312 + 0.584613i \(0.801246\pi\)
\(80\) −7.46410 4.92820i −0.834512 0.550990i
\(81\) 9.00000 1.00000
\(82\) 9.66025 + 9.66025i 1.06680 + 1.06680i
\(83\) −0.267949 0.267949i −0.0294112 0.0294112i 0.692248 0.721659i \(-0.256620\pi\)
−0.721659 + 0.692248i \(0.756620\pi\)
\(84\) 0 0
\(85\) 15.7942 3.23205i 1.71312 0.350565i
\(86\) 10.1962i 1.09948i
\(87\) 0 0
\(88\) −7.46410 + 7.46410i −0.795676 + 0.795676i
\(89\) −7.26795 −0.770401 −0.385201 0.922833i \(-0.625868\pi\)
−0.385201 + 0.922833i \(0.625868\pi\)
\(90\) −9.29423 + 1.90192i −0.979698 + 0.200480i
\(91\) 0.339746 0.0356151
\(92\) 0 0
\(93\) 9.12436i 0.946152i
\(94\) 17.1244i 1.76624i
\(95\) −1.23205 + 1.86603i −0.126406 + 0.191450i
\(96\) 0 0
\(97\) −6.46410 6.46410i −0.656330 0.656330i 0.298180 0.954510i \(-0.403621\pi\)
−0.954510 + 0.298180i \(0.903621\pi\)
\(98\) 6.19615 + 6.19615i 0.625906 + 0.625906i
\(99\) 11.1962i 1.12526i
\(100\) 0 0
\(101\) 18.3923i 1.83010i 0.403337 + 0.915051i \(0.367850\pi\)
−0.403337 + 0.915051i \(0.632150\pi\)
\(102\) 17.6603 1.74863
\(103\) 5.66025 5.66025i 0.557721 0.557721i −0.370937 0.928658i \(-0.620963\pi\)
0.928658 + 0.370937i \(0.120963\pi\)
\(104\) 1.07180 0.105098
\(105\) −3.40192 + 0.696152i −0.331994 + 0.0679375i
\(106\) −11.4641 −1.11349
\(107\) −0.535898 + 0.535898i −0.0518073 + 0.0518073i −0.732536 0.680729i \(-0.761663\pi\)
0.680729 + 0.732536i \(0.261663\pi\)
\(108\) 0 0
\(109\) 3.07180i 0.294225i −0.989120 0.147112i \(-0.953002\pi\)
0.989120 0.147112i \(-0.0469979\pi\)
\(110\) −2.36603 11.5622i −0.225592 1.10241i
\(111\) 7.73205 7.73205i 0.733894 0.733894i
\(112\) −2.53590 2.53590i −0.239620 0.239620i
\(113\) −1.46410 1.46410i −0.137731 0.137731i 0.634880 0.772611i \(-0.281050\pi\)
−0.772611 + 0.634880i \(0.781050\pi\)
\(114\) −1.73205 + 1.73205i −0.162221 + 0.162221i
\(115\) −0.294229 1.43782i −0.0274370 0.134078i
\(116\) 0 0
\(117\) 0.803848 0.803848i 0.0743157 0.0743157i
\(118\) 0.196152 0.196152i 0.0180573 0.0180573i
\(119\) 6.46410 0.592563
\(120\) −10.7321 + 2.19615i −0.979698 + 0.200480i
\(121\) −2.92820 −0.266200
\(122\) 7.73205 7.73205i 0.700027 0.700027i
\(123\) 16.7321 1.50868
\(124\) 0 0
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) −3.80385 −0.338874
\(127\) −11.2679 11.2679i −0.999869 0.999869i 0.000131185 1.00000i \(-0.499958\pi\)
−1.00000 0.000131185i \(0.999958\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −8.83013 8.83013i −0.777449 0.777449i
\(130\) −0.660254 + 1.00000i −0.0579081 + 0.0877058i
\(131\) 2.46410i 0.215290i −0.994189 0.107645i \(-0.965669\pi\)
0.994189 0.107645i \(-0.0343309\pi\)
\(132\) 0 0
\(133\) −0.633975 + 0.633975i −0.0549726 + 0.0549726i
\(134\) 4.39230 0.379437
\(135\) −6.40192 + 9.69615i −0.550990 + 0.834512i
\(136\) 20.3923 1.74863
\(137\) 5.56218 5.56218i 0.475209 0.475209i −0.428387 0.903596i \(-0.640918\pi\)
0.903596 + 0.428387i \(0.140918\pi\)
\(138\) 1.60770i 0.136856i
\(139\) 10.4641i 0.887554i −0.896137 0.443777i \(-0.853638\pi\)
0.896137 0.443777i \(-0.146362\pi\)
\(140\) 0 0
\(141\) −14.8301 14.8301i −1.24892 1.24892i
\(142\) −10.7321 10.7321i −0.900614 0.900614i
\(143\) 1.00000 + 1.00000i 0.0836242 + 0.0836242i
\(144\) −12.0000 −1.00000
\(145\) 0 0
\(146\) 10.7321i 0.888191i
\(147\) 10.7321 0.885165
\(148\) 0 0
\(149\) 13.3923 1.09714 0.548570 0.836105i \(-0.315172\pi\)
0.548570 + 0.836105i \(0.315172\pi\)
\(150\) 4.56218 11.3660i 0.372500 0.928032i
\(151\) 2.73205 0.222331 0.111166 0.993802i \(-0.464542\pi\)
0.111166 + 0.993802i \(0.464542\pi\)
\(152\) −2.00000 + 2.00000i −0.162221 + 0.162221i
\(153\) 15.2942 15.2942i 1.23647 1.23647i
\(154\) 4.73205i 0.381320i
\(155\) 9.83013 + 6.49038i 0.789575 + 0.521320i
\(156\) 0 0
\(157\) 14.6603 + 14.6603i 1.17002 + 1.17002i 0.982205 + 0.187810i \(0.0601390\pi\)
0.187810 + 0.982205i \(0.439861\pi\)
\(158\) −10.3923 10.3923i −0.826767 0.826767i
\(159\) −9.92820 + 9.92820i −0.787358 + 0.787358i
\(160\) 0 0
\(161\) 0.588457i 0.0463769i
\(162\) −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
\(165\) −12.0622 7.96410i −0.939039 0.620004i
\(166\) 0.535898 0.0415938
\(167\) −4.00000 + 4.00000i −0.309529 + 0.309529i −0.844727 0.535198i \(-0.820237\pi\)
0.535198 + 0.844727i \(0.320237\pi\)
\(168\) −4.39230 −0.338874
\(169\) 12.8564i 0.988954i
\(170\) −12.5622 + 19.0263i −0.963475 + 1.45925i
\(171\) 3.00000i 0.229416i
\(172\) 0 0
\(173\) −8.19615 8.19615i −0.623142 0.623142i 0.323192 0.946334i \(-0.395244\pi\)
−0.946334 + 0.323192i \(0.895244\pi\)
\(174\) 0 0
\(175\) 1.66987 4.16025i 0.126231 0.314486i
\(176\) 14.9282i 1.12526i
\(177\) 0.339746i 0.0255369i
\(178\) 7.26795 7.26795i 0.544756 0.544756i
\(179\) 8.92820 0.667325 0.333663 0.942693i \(-0.391715\pi\)
0.333663 + 0.942693i \(0.391715\pi\)
\(180\) 0 0
\(181\) 10.9282 0.812287 0.406143 0.913809i \(-0.366873\pi\)
0.406143 + 0.913809i \(0.366873\pi\)
\(182\) −0.339746 + 0.339746i −0.0251836 + 0.0251836i
\(183\) 13.3923i 0.989988i
\(184\) 1.85641i 0.136856i
\(185\) 2.83013 + 13.8301i 0.208075 + 1.01681i
\(186\) 9.12436 + 9.12436i 0.669030 + 0.669030i
\(187\) 19.0263 + 19.0263i 1.39134 + 1.39134i
\(188\) 0 0
\(189\) −3.29423 + 3.29423i −0.239620 + 0.239620i
\(190\) −0.633975 3.09808i −0.0459934 0.224758i
\(191\) 4.07180i 0.294625i −0.989090 0.147312i \(-0.952938\pi\)
0.989090 0.147312i \(-0.0470623\pi\)
\(192\) −13.8564 −1.00000
\(193\) 1.80385 1.80385i 0.129844 0.129844i −0.639198 0.769042i \(-0.720734\pi\)
0.769042 + 0.639198i \(0.220734\pi\)
\(194\) 12.9282 0.928191
\(195\) 0.294229 + 1.43782i 0.0210702 + 0.102965i
\(196\) 0 0
\(197\) 14.1244 14.1244i 1.00632 1.00632i 0.00633876 0.999980i \(-0.497982\pi\)
0.999980 0.00633876i \(-0.00201770\pi\)
\(198\) −11.1962 11.1962i −0.795676 0.795676i
\(199\) 0.803848i 0.0569832i 0.999594 + 0.0284916i \(0.00907039\pi\)
−0.999594 + 0.0284916i \(0.990930\pi\)
\(200\) 5.26795 13.1244i 0.372500 0.928032i
\(201\) 3.80385 3.80385i 0.268303 0.268303i
\(202\) −18.3923 18.3923i −1.29408 1.29408i
\(203\) 0 0
\(204\) 0 0
\(205\) −11.9019 + 18.0263i −0.831266 + 1.25901i
\(206\) 11.3205i 0.788737i
\(207\) −1.39230 1.39230i −0.0967719 0.0967719i
\(208\) −1.07180 + 1.07180i −0.0743157 + 0.0743157i
\(209\) −3.73205 −0.258151
\(210\) 2.70577 4.09808i 0.186716 0.282794i
\(211\) 14.0526 0.967418 0.483709 0.875229i \(-0.339289\pi\)
0.483709 + 0.875229i \(0.339289\pi\)
\(212\) 0 0
\(213\) −18.5885 −1.27366
\(214\) 1.07180i 0.0732665i
\(215\) 15.7942 3.23205i 1.07716 0.220424i
\(216\) −10.3923 + 10.3923i −0.707107 + 0.707107i
\(217\) 3.33975 + 3.33975i 0.226717 + 0.226717i
\(218\) 3.07180 + 3.07180i 0.208048 + 0.208048i
\(219\) 9.29423 + 9.29423i 0.628046 + 0.628046i
\(220\) 0 0
\(221\) 2.73205i 0.183778i
\(222\) 15.4641i 1.03788i
\(223\) −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
\(225\) −5.89230 13.7942i −0.392820 0.919615i
\(226\) 2.92820 0.194781
\(227\) −11.1962 + 11.1962i −0.743115 + 0.743115i −0.973176 0.230061i \(-0.926107\pi\)
0.230061 + 0.973176i \(0.426107\pi\)
\(228\) 0 0
\(229\) 23.2487i 1.53632i 0.640259 + 0.768159i \(0.278827\pi\)
−0.640259 + 0.768159i \(0.721173\pi\)
\(230\) 1.73205 + 1.14359i 0.114208 + 0.0754063i
\(231\) −4.09808 4.09808i −0.269634 0.269634i
\(232\) 0 0
\(233\) −7.16987 7.16987i −0.469714 0.469714i 0.432108 0.901822i \(-0.357770\pi\)
−0.901822 + 0.432108i \(0.857770\pi\)
\(234\) 1.60770i 0.105098i
\(235\) 26.5263 5.42820i 1.73038 0.354097i
\(236\) 0 0
\(237\) −18.0000 −1.16923
\(238\) −6.46410 + 6.46410i −0.419005 + 0.419005i
\(239\) −25.0526 −1.62052 −0.810258 0.586074i \(-0.800673\pi\)
−0.810258 + 0.586074i \(0.800673\pi\)
\(240\) 8.53590 12.9282i 0.550990 0.834512i
\(241\) −16.1962 −1.04329 −0.521643 0.853164i \(-0.674681\pi\)
−0.521643 + 0.853164i \(0.674681\pi\)
\(242\) 2.92820 2.92820i 0.188232 0.188232i
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −7.63397 + 11.5622i −0.487717 + 0.738680i
\(246\) −16.7321 + 16.7321i −1.06680 + 1.06680i
\(247\) 0.267949 + 0.267949i 0.0170492 + 0.0170492i
\(248\) 10.5359 + 10.5359i 0.669030 + 0.669030i
\(249\) 0.464102 0.464102i 0.0294112 0.0294112i
\(250\) 9.00000 + 13.0000i 0.569210 + 0.822192i
\(251\) 16.8564i 1.06397i 0.846755 + 0.531983i \(0.178553\pi\)
−0.846755 + 0.531983i \(0.821447\pi\)
\(252\) 0 0
\(253\) 1.73205 1.73205i 0.108893 0.108893i
\(254\) 22.5359 1.41403
\(255\) 5.59808 + 27.3564i 0.350565 + 1.71312i
\(256\) 0 0
\(257\) 16.7321 16.7321i 1.04372 1.04372i 0.0447170 0.999000i \(-0.485761\pi\)
0.999000 0.0447170i \(-0.0142386\pi\)
\(258\) 17.6603 1.09948
\(259\) 5.66025i 0.351711i
\(260\) 0 0
\(261\) 0 0
\(262\) 2.46410 + 2.46410i 0.152233 + 0.152233i
\(263\) 6.02628 + 6.02628i 0.371596 + 0.371596i 0.868058 0.496462i \(-0.165368\pi\)
−0.496462 + 0.868058i \(0.665368\pi\)
\(264\) −12.9282 12.9282i −0.795676 0.795676i
\(265\) −3.63397 17.7583i −0.223233 1.09089i
\(266\) 1.26795i 0.0777430i
\(267\) 12.5885i 0.770401i
\(268\) 0 0
\(269\) −5.80385 −0.353867 −0.176933 0.984223i \(-0.556618\pi\)
−0.176933 + 0.984223i \(0.556618\pi\)
\(270\) −3.29423 16.0981i −0.200480 0.979698i
\(271\) −8.39230 −0.509796 −0.254898 0.966968i \(-0.582042\pi\)
−0.254898 + 0.966968i \(0.582042\pi\)
\(272\) −20.3923 + 20.3923i −1.23647 + 1.23647i
\(273\) 0.588457i 0.0356151i
\(274\) 11.1244i 0.672047i
\(275\) 17.1603 7.33013i 1.03480 0.442023i
\(276\) 0 0
\(277\) 1.83013 + 1.83013i 0.109962 + 0.109962i 0.759947 0.649985i \(-0.225225\pi\)
−0.649985 + 0.759947i \(0.725225\pi\)
\(278\) 10.4641 + 10.4641i 0.627595 + 0.627595i
\(279\) 15.8038 0.946152
\(280\) 3.12436 4.73205i 0.186716 0.282794i
\(281\) 12.0000i 0.715860i −0.933748 0.357930i \(-0.883483\pi\)
0.933748 0.357930i \(-0.116517\pi\)
\(282\) 29.6603 1.76624
\(283\) −8.83013 + 8.83013i −0.524897 + 0.524897i −0.919046 0.394150i \(-0.871039\pi\)
0.394150 + 0.919046i \(0.371039\pi\)
\(284\) 0 0
\(285\) −3.23205 2.13397i −0.191450 0.126406i
\(286\) −2.00000 −0.118262
\(287\) −6.12436 + 6.12436i −0.361509 + 0.361509i
\(288\) 0 0
\(289\) 34.9808i 2.05769i
\(290\) 0 0
\(291\) 11.1962 11.1962i 0.656330 0.656330i
\(292\) 0 0
\(293\) −8.00000 8.00000i −0.467365 0.467365i 0.433695 0.901060i \(-0.357210\pi\)
−0.901060 + 0.433695i \(0.857210\pi\)
\(294\) −10.7321 + 10.7321i −0.625906 + 0.625906i
\(295\) 0.366025 + 0.241670i 0.0213108 + 0.0140706i
\(296\) 17.8564i 1.03788i
\(297\) −19.3923 −1.12526
\(298\) −13.3923 + 13.3923i −0.775795 + 0.775795i
\(299\) −0.248711 −0.0143833
\(300\) 0 0
\(301\) 6.46410 0.372585
\(302\) −2.73205 + 2.73205i −0.157212 + 0.157212i
\(303\) −31.8564 −1.83010
\(304\) 4.00000i 0.229416i
\(305\) 14.4282 + 9.52628i 0.826157 + 0.545473i
\(306\) 30.5885i 1.74863i
\(307\) −14.5885 14.5885i −0.832607 0.832607i 0.155266 0.987873i \(-0.450377\pi\)
−0.987873 + 0.155266i \(0.950377\pi\)
\(308\) 0 0
\(309\) 9.80385 + 9.80385i 0.557721 + 0.557721i
\(310\) −16.3205 + 3.33975i −0.926943 + 0.189685i
\(311\) 5.73205i 0.325035i −0.986706 0.162517i \(-0.948039\pi\)
0.986706 0.162517i \(-0.0519614\pi\)
\(312\) 1.85641i 0.105098i
\(313\) 1.73205 1.73205i 0.0979013 0.0979013i −0.656460 0.754361i \(-0.727947\pi\)
0.754361 + 0.656460i \(0.227947\pi\)
\(314\) −29.3205 −1.65465
\(315\) −1.20577 5.89230i −0.0679375 0.331994i
\(316\) 0 0
\(317\) 18.8564 18.8564i 1.05908 1.05908i 0.0609399 0.998141i \(-0.480590\pi\)
0.998141 0.0609399i \(-0.0194098\pi\)
\(318\) 19.8564i 1.11349i
\(319\) 0 0
\(320\) 9.85641 14.9282i 0.550990 0.834512i
\(321\) −0.928203 0.928203i −0.0518073 0.0518073i
\(322\) 0.588457 + 0.588457i 0.0327934 + 0.0327934i
\(323\) 5.09808 + 5.09808i 0.283665 + 0.283665i
\(324\) 0 0
\(325\) −1.75833 0.705771i −0.0975346 0.0391492i
\(326\) 22.0000i 1.21847i
\(327\) 5.32051 0.294225
\(328\) −19.3205 + 19.3205i −1.06680 + 1.06680i
\(329\) 10.8564 0.598533
\(330\) 20.0263 4.09808i 1.10241 0.225592i
\(331\) 35.3205 1.94139 0.970695 0.240313i \(-0.0772502\pi\)
0.970695 + 0.240313i \(0.0772502\pi\)
\(332\) 0 0
\(333\) 13.3923 + 13.3923i 0.733894 + 0.733894i
\(334\) 8.00000i 0.437741i
\(335\) 1.39230 + 6.80385i 0.0760697 + 0.371734i
\(336\) 4.39230 4.39230i 0.239620 0.239620i
\(337\) −9.92820 9.92820i −0.540824 0.540824i 0.382947 0.923770i \(-0.374909\pi\)
−0.923770 + 0.382947i \(0.874909\pi\)
\(338\) −12.8564 12.8564i −0.699296 0.699296i
\(339\) 2.53590 2.53590i 0.137731 0.137731i
\(340\) 0 0
\(341\) 19.6603i 1.06466i
\(342\) −3.00000 3.00000i −0.162221 0.162221i
\(343\) −8.36603 + 8.36603i −0.451723 + 0.451723i
\(344\) 20.3923 1.09948
\(345\) 2.49038 0.509619i 0.134078 0.0274370i
\(346\) 16.3923 0.881256
\(347\) 18.0981 18.0981i 0.971556 0.971556i −0.0280509 0.999606i \(-0.508930\pi\)
0.999606 + 0.0280509i \(0.00893004\pi\)
\(348\) 0 0
\(349\) 3.73205i 0.199772i −0.994999 0.0998860i \(-0.968152\pi\)
0.994999 0.0998860i \(-0.0318478\pi\)
\(350\) 2.49038 + 5.83013i 0.133116 + 0.311633i
\(351\) 1.39230 + 1.39230i 0.0743157 + 0.0743157i
\(352\) 0 0
\(353\) 25.7321 + 25.7321i 1.36958 + 1.36958i 0.861038 + 0.508541i \(0.169815\pi\)
0.508541 + 0.861038i \(0.330185\pi\)
\(354\) 0.339746 + 0.339746i 0.0180573 + 0.0180573i
\(355\) 13.2224 20.0263i 0.701774 1.06288i
\(356\) 0 0
\(357\) 11.1962i 0.592563i
\(358\) −8.92820 + 8.92820i −0.471870 + 0.471870i
\(359\) −21.9282 −1.15733 −0.578663 0.815567i \(-0.696425\pi\)
−0.578663 + 0.815567i \(0.696425\pi\)
\(360\) −3.80385 18.5885i −0.200480 0.979698i
\(361\) −1.00000 −0.0526316
\(362\) −10.9282 + 10.9282i −0.574374 + 0.574374i
\(363\) 5.07180i 0.266200i
\(364\) 0 0
\(365\) −16.6244 + 3.40192i −0.870159 + 0.178065i
\(366\) 13.3923 + 13.3923i 0.700027 + 0.700027i
\(367\) −23.7846 23.7846i −1.24155 1.24155i −0.959359 0.282187i \(-0.908940\pi\)
−0.282187 0.959359i \(-0.591060\pi\)
\(368\) 1.85641 + 1.85641i 0.0967719 + 0.0967719i
\(369\) 28.9808i 1.50868i
\(370\) −16.6603 11.0000i −0.866125 0.571863i
\(371\) 7.26795i 0.377333i
\(372\) 0 0
\(373\) 18.5885 18.5885i 0.962474 0.962474i −0.0368471 0.999321i \(-0.511731\pi\)
0.999321 + 0.0368471i \(0.0117314\pi\)
\(374\) −38.0526 −1.96765
\(375\) 19.0526 + 3.46410i 0.983870 + 0.178885i
\(376\) 34.2487 1.76624
\(377\) 0 0
\(378\) 6.58846i 0.338874i
\(379\) 14.5359i 0.746659i 0.927699 + 0.373329i \(0.121784\pi\)
−0.927699 + 0.373329i \(0.878216\pi\)
\(380\) 0 0
\(381\) 19.5167 19.5167i 0.999869 0.999869i
\(382\) 4.07180 + 4.07180i 0.208331 + 0.208331i
\(383\) −15.7846 15.7846i −0.806556 0.806556i 0.177555 0.984111i \(-0.443181\pi\)
−0.984111 + 0.177555i \(0.943181\pi\)
\(384\) 13.8564 13.8564i 0.707107 0.707107i
\(385\) 7.33013 1.50000i 0.373578 0.0764471i
\(386\) 3.60770i 0.183627i
\(387\) 15.2942 15.2942i 0.777449 0.777449i
\(388\) 0 0
\(389\) −36.1244 −1.83158 −0.915789 0.401660i \(-0.868433\pi\)
−0.915789 + 0.401660i \(0.868433\pi\)
\(390\) −1.73205 1.14359i −0.0877058 0.0579081i
\(391\) −4.73205 −0.239310
\(392\) −12.3923 + 12.3923i −0.625906 + 0.625906i
\(393\) 4.26795 0.215290
\(394\) 28.2487i 1.42315i
\(395\) 12.8038 19.3923i 0.644231 0.975733i
\(396\) 0 0
\(397\) −10.4904 10.4904i −0.526497 0.526497i 0.393029 0.919526i \(-0.371427\pi\)
−0.919526 + 0.393029i \(0.871427\pi\)
\(398\) −0.803848 0.803848i −0.0402932 0.0402932i
\(399\) −1.09808 1.09808i −0.0549726 0.0549726i
\(400\) 7.85641 + 18.3923i 0.392820 + 0.919615i
\(401\) 31.7128i 1.58366i −0.610740 0.791831i \(-0.709128\pi\)
0.610740 0.791831i \(-0.290872\pi\)
\(402\) 7.60770i 0.379437i
\(403\) 1.41154 1.41154i 0.0703140 0.0703140i
\(404\) 0 0
\(405\) −16.7942 11.0885i −0.834512 0.550990i
\(406\) 0 0
\(407\) −16.6603 + 16.6603i −0.825818 + 0.825818i
\(408\) 35.3205i 1.74863i
\(409\) 20.1962i 0.998635i −0.866419 0.499318i \(-0.833584\pi\)
0.866419 0.499318i \(-0.166416\pi\)
\(410\) −6.12436 29.9282i −0.302460 1.47805i
\(411\) 9.63397 + 9.63397i 0.475209 + 0.475209i
\(412\) 0 0
\(413\) 0.124356 + 0.124356i 0.00611914 + 0.00611914i
\(414\) 2.78461 0.136856
\(415\) 0.169873 + 0.830127i 0.00833874 + 0.0407493i
\(416\) 0 0
\(417\) 18.1244 0.887554
\(418\) 3.73205 3.73205i 0.182541 0.182541i
\(419\) −22.9282 −1.12012 −0.560058 0.828453i \(-0.689221\pi\)
−0.560058 + 0.828453i \(0.689221\pi\)
\(420\) 0 0
\(421\) −0.588457 −0.0286797 −0.0143398 0.999897i \(-0.504565\pi\)
−0.0143398 + 0.999897i \(0.504565\pi\)
\(422\) −14.0526 + 14.0526i −0.684068 + 0.684068i
\(423\) 25.6865 25.6865i 1.24892 1.24892i
\(424\) 22.9282i 1.11349i
\(425\) −33.4545 13.4282i −1.62278 0.651364i
\(426\) 18.5885 18.5885i 0.900614 0.900614i
\(427\) 4.90192 + 4.90192i 0.237221 + 0.237221i
\(428\) 0 0
\(429\) −1.73205 + 1.73205i −0.0836242 + 0.0836242i
\(430\) −12.5622 + 19.0263i −0.605802 + 0.917529i
\(431\) 35.5167i 1.71078i 0.517987 + 0.855389i \(0.326682\pi\)
−0.517987 + 0.855389i \(0.673318\pi\)
\(432\) 20.7846i 1.00000i
\(433\) −29.1244 + 29.1244i −1.39963 + 1.39963i −0.598517 + 0.801110i \(0.704243\pi\)
−0.801110 + 0.598517i \(0.795757\pi\)
\(434\) −6.67949 −0.320626
\(435\) 0 0
\(436\) 0 0
\(437\) 0.464102 0.464102i 0.0222010 0.0222010i
\(438\) −18.5885 −0.888191
\(439\) 9.85641i 0.470421i −0.971945 0.235210i \(-0.924422\pi\)
0.971945 0.235210i \(-0.0755779\pi\)
\(440\) 23.1244 4.73205i 1.10241 0.225592i
\(441\) 18.5885i 0.885165i
\(442\) 2.73205 + 2.73205i 0.129950 + 0.129950i
\(443\) −10.1699 10.1699i −0.483185 0.483185i 0.422962 0.906147i \(-0.360990\pi\)
−0.906147 + 0.422962i \(0.860990\pi\)
\(444\) 0 0
\(445\) 13.5622 + 8.95448i 0.642909 + 0.424483i
\(446\) 18.0000i 0.852325i
\(447\) 23.1962i 1.09714i
\(448\) 5.07180 5.07180i 0.239620 0.239620i
\(449\) −19.8564 −0.937082 −0.468541 0.883442i \(-0.655220\pi\)
−0.468541 + 0.883442i \(0.655220\pi\)
\(450\) 19.6865 + 7.90192i 0.928032 + 0.372500i
\(451\) −36.0526 −1.69765
\(452\) 0 0
\(453\) 4.73205i 0.222331i
\(454\) 22.3923i 1.05092i
\(455\) −0.633975 0.418584i −0.0297212 0.0196235i
\(456\) −3.46410 3.46410i −0.162221 0.162221i
\(457\) −16.3660 16.3660i −0.765570 0.765570i 0.211753 0.977323i \(-0.432083\pi\)
−0.977323 + 0.211753i \(0.932083\pi\)
\(458\) −23.2487 23.2487i −1.08634 1.08634i
\(459\) 26.4904 + 26.4904i 1.23647 + 1.23647i
\(460\) 0 0
\(461\) 13.0000i 0.605470i 0.953075 + 0.302735i \(0.0978998\pi\)
−0.953075 + 0.302735i \(0.902100\pi\)
\(462\) 8.19615 0.381320
\(463\) −11.2942 + 11.2942i −0.524887 + 0.524887i −0.919043 0.394156i \(-0.871037\pi\)
0.394156 + 0.919043i \(0.371037\pi\)
\(464\) 0 0
\(465\) −11.2417 + 17.0263i −0.521320 + 0.789575i
\(466\) 14.3397 0.664276
\(467\) 11.2224 11.2224i 0.519312 0.519312i −0.398051 0.917363i \(-0.630313\pi\)
0.917363 + 0.398051i \(0.130313\pi\)
\(468\) 0 0
\(469\) 2.78461i 0.128581i
\(470\) −21.0981 + 31.9545i −0.973182 + 1.47395i
\(471\) −25.3923 + 25.3923i −1.17002 + 1.17002i
\(472\) 0.392305 + 0.392305i 0.0180573 + 0.0180573i
\(473\) 19.0263 + 19.0263i 0.874829 + 0.874829i
\(474\) 18.0000 18.0000i 0.826767 0.826767i
\(475\) 4.59808 1.96410i 0.210974 0.0901192i
\(476\) 0 0
\(477\) −17.1962 17.1962i −0.787358 0.787358i
\(478\) 25.0526 25.0526i 1.14588 1.14588i
\(479\) 0.928203 0.0424107 0.0212053 0.999775i \(-0.493250\pi\)
0.0212053 + 0.999775i \(0.493250\pi\)
\(480\) 0 0
\(481\) 2.39230 0.109080
\(482\) 16.1962 16.1962i 0.737715 0.737715i
\(483\) 1.01924 0.0463769
\(484\) 0 0
\(485\) 4.09808 + 20.0263i 0.186084 + 0.909347i
\(486\) −15.5885 15.5885i −0.707107 0.707107i
\(487\) 17.0526 + 17.0526i 0.772725 + 0.772725i 0.978582 0.205857i \(-0.0659981\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(488\) 15.4641 + 15.4641i 0.700027 + 0.700027i
\(489\) −19.0526 19.0526i −0.861586 0.861586i
\(490\) −3.92820 19.1962i −0.177458 0.867194i
\(491\) 2.67949i 0.120924i −0.998171 0.0604619i \(-0.980743\pi\)
0.998171 0.0604619i \(-0.0192574\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.535898 −0.0241112
\(495\) 13.7942 20.8923i 0.620004 0.939039i
\(496\) −21.0718 −0.946152
\(497\) 6.80385 6.80385i 0.305194 0.305194i
\(498\) 0.928203i 0.0415938i
\(499\) 12.8564i 0.575532i 0.957701 + 0.287766i \(0.0929125\pi\)
−0.957701 + 0.287766i \(0.907087\pi\)
\(500\) 0 0
\(501\) −6.92820 6.92820i −0.309529 0.309529i
\(502\) −16.8564 16.8564i −0.752338 0.752338i
\(503\) −23.9282 23.9282i −1.06691 1.06691i −0.997595 0.0693107i \(-0.977920\pi\)
−0.0693107 0.997595i \(-0.522080\pi\)
\(504\) 7.60770i 0.338874i
\(505\) 22.6603 34.3205i 1.00837 1.52724i
\(506\) 3.46410i 0.153998i
\(507\) −22.2679 −0.988954
\(508\) 0 0
\(509\) 18.7321 0.830284 0.415142 0.909757i \(-0.363732\pi\)
0.415142 + 0.909757i \(0.363732\pi\)
\(510\) −32.9545 21.7583i −1.45925 0.963475i
\(511\) −6.80385 −0.300984
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −5.19615 −0.229416
\(514\) 33.4641i 1.47604i
\(515\) −17.5359 + 3.58846i −0.772724 + 0.158126i
\(516\) 0 0
\(517\) 31.9545 + 31.9545i 1.40536 + 1.40536i
\(518\) −5.66025 5.66025i −0.248697 0.248697i
\(519\) 14.1962 14.1962i 0.623142 0.623142i
\(520\) −2.00000 1.32051i −0.0877058 0.0579081i
\(521\) 16.0000i 0.700973i 0.936568 + 0.350486i \(0.113984\pi\)
−0.936568 + 0.350486i \(0.886016\pi\)
\(522\) 0 0
\(523\) 22.3923 22.3923i 0.979147 0.979147i −0.0206398 0.999787i \(-0.506570\pi\)
0.999787 + 0.0206398i \(0.00657033\pi\)
\(524\) 0 0
\(525\) 7.20577 + 2.89230i 0.314486 + 0.126231i
\(526\) −12.0526 −0.525517
\(527\) 26.8564 26.8564i 1.16988 1.16988i
\(528\) 25.8564 1.12526
\(529\) 22.5692i 0.981270i
\(530\) 21.3923 + 14.1244i 0.929222 + 0.613523i
\(531\) 0.588457 0.0255369
\(532\) 0 0
\(533\) 2.58846 + 2.58846i 0.112119 + 0.112119i
\(534\) 12.5885 + 12.5885i 0.544756 + 0.544756i
\(535\) 1.66025 0.339746i 0.0717790 0.0146885i
\(536\) 8.78461i 0.379437i
\(537\) 15.4641i 0.667325i
\(538\) 5.80385 5.80385i 0.250222 0.250222i
\(539\) −23.1244 −0.996037
\(540\) 0 0
\(541\) −31.1962 −1.34123 −0.670614 0.741807i \(-0.733969\pi\)
−0.670614 + 0.741807i \(0.733969\pi\)
\(542\) 8.39230 8.39230i 0.360480 0.360480i
\(543\) 18.9282i 0.812287i
\(544\) 0 0
\(545\) −3.78461 + 5.73205i −0.162115 + 0.245534i
\(546\) −0.588457 0.588457i −0.0251836 0.0251836i
\(547\) 16.3205 + 16.3205i 0.697815 + 0.697815i 0.963939 0.266124i \(-0.0857431\pi\)
−0.266124 + 0.963939i \(0.585743\pi\)
\(548\) 0 0
\(549\) 23.1962 0.989988
\(550\) −9.83013 + 24.4904i −0.419158 + 1.04427i
\(551\) 0 0
\(552\) 3.21539 0.136856
\(553\) 6.58846 6.58846i 0.280170 0.280170i
\(554\) −3.66025 −0.155509
\(555\) −23.9545 + 4.90192i −1.01681 + 0.208075i
\(556\) 0 0
\(557\) −5.68653 + 5.68653i −0.240946 + 0.240946i −0.817242 0.576295i \(-0.804498\pi\)
0.576295 + 0.817242i \(0.304498\pi\)
\(558\) −15.8038 + 15.8038i −0.669030 + 0.669030i
\(559\) 2.73205i 0.115553i
\(560\) 1.60770 + 7.85641i 0.0679375 + 0.331994i
\(561\) −32.9545 + 32.9545i −1.39134 + 1.39134i
\(562\) 12.0000 + 12.0000i 0.506189 + 0.506189i
\(563\) −4.12436 4.12436i −0.173821 0.173821i 0.614835 0.788656i \(-0.289223\pi\)
−0.788656 + 0.614835i \(0.789223\pi\)
\(564\) 0 0
\(565\) 0.928203 + 4.53590i 0.0390498 + 0.190827i
\(566\) 17.6603i 0.742316i
\(567\) −5.70577 5.70577i −0.239620 0.239620i
\(568\) 21.4641 21.4641i 0.900614 0.900614i
\(569\) 8.73205 0.366067 0.183033 0.983107i \(-0.441408\pi\)
0.183033 + 0.983107i \(0.441408\pi\)
\(570\) 5.36603 1.09808i 0.224758 0.0459934i
\(571\) −6.53590 −0.273519 −0.136759 0.990604i \(-0.543669\pi\)
−0.136759 + 0.990604i \(0.543669\pi\)
\(572\) 0 0
\(573\) 7.05256 0.294625
\(574\) 12.2487i 0.511251i
\(575\) −1.22243 + 3.04552i −0.0509789 + 0.127007i
\(576\) 24.0000i 1.00000i
\(577\) 21.6865 + 21.6865i 0.902822 + 0.902822i 0.995679 0.0928572i \(-0.0296000\pi\)
−0.0928572 + 0.995679i \(0.529600\pi\)
\(578\) 34.9808 + 34.9808i 1.45501 + 1.45501i
\(579\) 3.12436 + 3.12436i 0.129844 + 0.129844i
\(580\) 0 0
\(581\) 0.339746i 0.0140950i
\(582\) 22.3923i 0.928191i
\(583\) 21.3923 21.3923i 0.885979 0.885979i
\(584\) −21.4641 −0.888191
\(585\) −2.49038 + 0.509619i −0.102965 + 0.0210702i
\(586\) 16.0000 0.660954
\(587\) −12.6865 + 12.6865i −0.523629 + 0.523629i −0.918666 0.395036i \(-0.870732\pi\)
0.395036 + 0.918666i \(0.370732\pi\)
\(588\) 0 0
\(589\) 5.26795i 0.217062i
\(590\) −0.607695 + 0.124356i −0.0250184 + 0.00511964i
\(591\) 24.4641 + 24.4641i 1.00632 + 1.00632i
\(592\) −17.8564 17.8564i −0.733894 0.733894i
\(593\) 4.07180 + 4.07180i 0.167209 + 0.167209i 0.785751 0.618543i \(-0.212277\pi\)
−0.618543 + 0.785751i \(0.712277\pi\)
\(594\) 19.3923 19.3923i 0.795676 0.795676i
\(595\) −12.0622 7.96410i −0.494501 0.326496i
\(596\) 0 0
\(597\) −1.39230 −0.0569832
\(598\) 0.248711 0.248711i 0.0101706 0.0101706i
\(599\) −1.32051 −0.0539545 −0.0269772 0.999636i \(-0.508588\pi\)
−0.0269772 + 0.999636i \(0.508588\pi\)
\(600\) 22.7321 + 9.12436i 0.928032 + 0.372500i
\(601\) 8.19615 0.334328 0.167164 0.985929i \(-0.446539\pi\)
0.167164 + 0.985929i \(0.446539\pi\)
\(602\) −6.46410 + 6.46410i −0.263457 + 0.263457i
\(603\) 6.58846 + 6.58846i 0.268303 + 0.268303i
\(604\) 0 0
\(605\) 5.46410 + 3.60770i 0.222147 + 0.146674i
\(606\) 31.8564 31.8564i 1.29408 1.29408i
\(607\) −12.1244 12.1244i −0.492112 0.492112i 0.416859 0.908971i \(-0.363131\pi\)
−0.908971 + 0.416859i \(0.863131\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −23.9545 + 4.90192i −0.969889 + 0.198473i
\(611\) 4.58846i 0.185629i
\(612\) 0 0
\(613\) −5.36603 + 5.36603i −0.216732 + 0.216732i −0.807120 0.590388i \(-0.798975\pi\)
0.590388 + 0.807120i \(0.298975\pi\)
\(614\) 29.1769 1.17748
\(615\) −31.2224 20.6147i −1.25901 0.831266i
\(616\) 9.46410 0.381320
\(617\) 9.22243 9.22243i 0.371281 0.371281i −0.496663 0.867944i \(-0.665441\pi\)
0.867944 + 0.496663i \(0.165441\pi\)
\(618\) −19.6077 −0.788737
\(619\) 36.7846i 1.47850i 0.673432 + 0.739249i \(0.264819\pi\)
−0.673432 + 0.739249i \(0.735181\pi\)
\(620\) 0 0
\(621\) 2.41154 2.41154i 0.0967719 0.0967719i
\(622\) 5.73205 + 5.73205i 0.229834 + 0.229834i
\(623\) 4.60770 + 4.60770i 0.184603 + 0.184603i
\(624\) −1.85641 1.85641i −0.0743157 0.0743157i
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 3.46410i 0.138453i
\(627\) 6.46410i 0.258151i
\(628\) 0 0
\(629\) 45.5167 1.81487
\(630\) 7.09808 + 4.68653i 0.282794 + 0.186716i
\(631\) 6.66025 0.265141 0.132570 0.991174i \(-0.457677\pi\)
0.132570 + 0.991174i \(0.457677\pi\)
\(632\) 20.7846 20.7846i 0.826767 0.826767i
\(633\) 24.3397i 0.967418i
\(634\) 37.7128i 1.49777i
\(635\) 7.14359 + 34.9090i 0.283485 + 1.38532i
\(636\) 0 0
\(637\) 1.66025 + 1.66025i 0.0657817 + 0.0657817i
\(638\) 0 0
\(639\) 32.1962i 1.27366i
\(640\) 5.07180 + 24.7846i 0.200480 + 0.979698i
\(641\) 30.5885i 1.20817i −0.796919 0.604086i \(-0.793538\pi\)
0.796919 0.604086i \(-0.206462\pi\)
\(642\) 1.85641 0.0732665
\(643\) −23.7583 + 23.7583i −0.936937 + 0.936937i −0.998126 0.0611891i \(-0.980511\pi\)
0.0611891 + 0.998126i \(0.480511\pi\)
\(644\) 0 0
\(645\) 5.59808 + 27.3564i 0.220424 + 1.07716i
\(646\) −10.1962 −0.401162
\(647\) −21.0981 + 21.0981i −0.829451 + 0.829451i −0.987441 0.157990i \(-0.949499\pi\)
0.157990 + 0.987441i \(0.449499\pi\)
\(648\) −18.0000 18.0000i −0.707107 0.707107i
\(649\) 0.732051i 0.0287355i
\(650\) 2.46410 1.05256i 0.0966500 0.0412848i
\(651\) −5.78461 + 5.78461i −0.226717 + 0.226717i
\(652\) 0 0
\(653\) 8.49038 + 8.49038i 0.332254 + 0.332254i 0.853442 0.521188i \(-0.174511\pi\)
−0.521188 + 0.853442i \(0.674511\pi\)
\(654\) −5.32051 + 5.32051i −0.208048 + 0.208048i
\(655\) −3.03590 + 4.59808i −0.118622 + 0.179662i
\(656\) 38.6410i 1.50868i
\(657\) −16.0981 + 16.0981i −0.628046 + 0.628046i
\(658\) −10.8564 + 10.8564i −0.423227 + 0.423227i
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) −22.7846 −0.886219 −0.443109 0.896468i \(-0.646125\pi\)
−0.443109 + 0.896468i \(0.646125\pi\)
\(662\) −35.3205 + 35.3205i −1.37277 + 1.37277i
\(663\) 4.73205 0.183778
\(664\) 1.07180i 0.0415938i
\(665\) 1.96410 0.401924i 0.0761646 0.0155859i
\(666\) −26.7846 −1.03788
\(667\) 0 0
\(668\) 0 0
\(669\) −15.5885 15.5885i −0.602685 0.602685i
\(670\) −8.19615 5.41154i −0.316645 0.209066i
\(671\) 28.8564i 1.11399i
\(672\) 0 0
\(673\) 29.4449 29.4449i 1.13502 1.13502i 0.145685 0.989331i \(-0.453461\pi\)
0.989331 0.145685i \(-0.0465386\pi\)
\(674\) 19.8564 0.764840
\(675\) 23.8923 10.2058i 0.919615 0.392820i
\(676\) 0 0
\(677\) −1.46410 + 1.46410i −0.0562700 + 0.0562700i −0.734682 0.678412i \(-0.762669\pi\)
0.678412 + 0.734682i \(0.262669\pi\)
\(678\) 5.07180i 0.194781i
\(679\) 8.19615i 0.314539i
\(680\) −38.0526 25.1244i −1.45925 0.963475i
\(681\) −19.3923 19.3923i −0.743115 0.743115i
\(682\) −19.6603 19.6603i −0.752830 0.752830i
\(683\) −16.8038 16.8038i −0.642981 0.642981i 0.308306 0.951287i \(-0.400238\pi\)
−0.951287 + 0.308306i \(0.900238\pi\)
\(684\) 0 0
\(685\) −17.2321 + 3.52628i −0.658403 + 0.134732i
\(686\) 16.7321i 0.638833i
\(687\) −40.2679 −1.53632
\(688\) −20.3923 + 20.3923i −0.777449 + 0.777449i
\(689\) −3.07180 −0.117026
\(690\) −1.98076 + 3.00000i −0.0754063 + 0.114208i
\(691\) −9.44486 −0.359300 −0.179650 0.983731i \(-0.557496\pi\)
−0.179650 + 0.983731i \(0.557496\pi\)
\(692\) 0 0
\(693\) 7.09808 7.09808i 0.269634 0.269634i
\(694\) 36.1962i 1.37399i
\(695\) −12.8923 + 19.5263i −0.489033 + 0.740674i
\(696\) 0 0
\(697\) 49.2487 + 49.2487i 1.86543 + 1.86543i
\(698\) 3.73205 + 3.73205i 0.141260 + 0.141260i
\(699\) 12.4186 12.4186i 0.469714 0.469714i
\(700\) 0 0
\(701\) 4.14359i 0.156501i 0.996934 + 0.0782507i \(0.0249335\pi\)
−0.996934 + 0.0782507i \(0.975067\pi\)
\(702\) −2.78461 −0.105098
\(703\) −4.46410 + 4.46410i −0.168367 + 0.168367i
\(704\) 29.8564 1.12526
\(705\) 9.40192 + 45.9449i 0.354097 + 1.73038i
\(706\) −51.4641 −1.93688
\(707\) 11.6603 11.6603i 0.438529 0.438529i
\(708\) 0 0
\(709\) 24.5359i 0.921465i 0.887539 + 0.460733i \(0.152413\pi\)
−0.887539 + 0.460733i \(0.847587\pi\)
\(710\) 6.80385 + 33.2487i 0.255344 + 1.24780i
\(711\) 31.1769i 1.16923i
\(712\) 14.5359 + 14.5359i 0.544756 + 0.544756i
\(713\) −2.44486 2.44486i −0.0915609 0.0915609i
\(714\) −11.1962 11.1962i −0.419005 0.419005i
\(715\) −0.633975 3.09808i −0.0237093 0.115861i
\(716\) 0 0
\(717\) 43.3923i 1.62052i
\(718\) 21.9282 21.9282i 0.818353 0.818353i
\(719\) 21.6410 0.807074 0.403537 0.914963i \(-0.367781\pi\)
0.403537 + 0.914963i \(0.367781\pi\)
\(720\) 22.3923 + 14.7846i 0.834512 + 0.550990i
\(721\) −7.17691 −0.267282
\(722\) 1.00000 1.00000i 0.0372161 0.0372161i
\(723\) 28.0526i 1.04329i
\(724\) 0 0
\(725\) 0 0
\(726\) 5.07180 + 5.07180i 0.188232 + 0.188232i
\(727\) 8.02628 + 8.02628i 0.297678 + 0.297678i 0.840104 0.542426i \(-0.182494\pi\)
−0.542426 + 0.840104i \(0.682494\pi\)
\(728\) −0.679492 0.679492i −0.0251836 0.0251836i
\(729\) −27.0000 −1.00000
\(730\) 13.2224 20.0263i 0.489384 0.741206i
\(731\) 51.9808i 1.92258i
\(732\) 0 0
\(733\) 11.3397 11.3397i 0.418843 0.418843i −0.465962 0.884805i \(-0.654292\pi\)
0.884805 + 0.465962i \(0.154292\pi\)
\(734\) 47.5692 1.75581
\(735\) −20.0263 13.2224i −0.738680 0.487717i
\(736\) 0 0
\(737\) −8.19615 + 8.19615i −0.301909 + 0.301909i
\(738\) −28.9808 28.9808i −1.06680 1.06680i
\(739\) 39.4449i 1.45100i 0.688221 + 0.725501i \(0.258392\pi\)
−0.688221 + 0.725501i \(0.741608\pi\)
\(740\) 0 0
\(741\) −0.464102 + 0.464102i −0.0170492 + 0.0170492i
\(742\) 7.26795 + 7.26795i 0.266815 + 0.266815i
\(743\) −16.2487 16.2487i −0.596107 0.596107i 0.343167 0.939274i \(-0.388500\pi\)
−0.939274 + 0.343167i \(0.888500\pi\)
\(744\) −18.2487 + 18.2487i −0.669030 + 0.669030i
\(745\) −24.9904 16.5000i −0.915577 0.604513i
\(746\) 37.1769i 1.36114i
\(747\) 0.803848 + 0.803848i 0.0294112 + 0.0294112i
\(748\) 0 0
\(749\) 0.679492 0.0248281
\(750\) −22.5167 + 15.5885i −0.822192 + 0.569210i
\(751\) −34.7846 −1.26931 −0.634654 0.772796i \(-0.718857\pi\)
−0.634654 + 0.772796i \(0.718857\pi\)
\(752\) −34.2487 + 34.2487i −1.24892 + 1.24892i
\(753\) −29.1962 −1.06397
\(754\) 0 0
\(755\) −5.09808 3.36603i −0.185538 0.122502i
\(756\) 0 0
\(757\) −5.02628 5.02628i −0.182683 0.182683i 0.609841 0.792524i \(-0.291233\pi\)
−0.792524 + 0.609841i \(0.791233\pi\)
\(758\) −14.5359 14.5359i −0.527968 0.527968i
\(759\) 3.00000 + 3.00000i 0.108893 + 0.108893i
\(760\) 6.19615 1.26795i 0.224758 0.0459934i
\(761\) 46.5167i 1.68623i −0.537735 0.843114i \(-0.680720\pi\)
0.537735 0.843114i \(-0.319280\pi\)
\(762\) 39.0333i 1.41403i
\(763\) −1.94744 + 1.94744i −0.0705021 + 0.0705021i
\(764\) 0 0
\(765\) −47.3827 + 9.69615i −1.71312 + 0.350565i
\(766\) 31.5692 1.14064
\(767\) 0.0525589 0.0525589i 0.00189779 0.00189779i
\(768\) 0 0
\(769\) 23.0000i 0.829401i −0.909958 0.414701i \(-0.863886\pi\)
0.909958 0.414701i \(-0.136114\pi\)
\(770\) −5.83013 + 8.83013i −0.210103 + 0.318216i
\(771\) 28.9808 + 28.9808i 1.04372 + 1.04372i
\(772\) 0 0
\(773\) 5.58846 + 5.58846i 0.201003 + 0.201003i 0.800430 0.599427i \(-0.204605\pi\)
−0.599427 + 0.800430i \(0.704605\pi\)
\(774\) 30.5885i 1.09948i
\(775\) −10.3468 24.2224i −0.371668 0.870095i
\(776\) 25.8564i 0.928191i