Properties

Label 285.2.k.b.248.1
Level $285$
Weight $2$
Character 285.248
Analytic conductor $2.276$
Analytic rank $0$
Dimension $4$
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: \(0\)
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 248.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 285.248
Dual form 285.2.k.b.77.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} -1.73205 q^{3} +(1.86603 - 1.23205i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-0.633975 + 0.633975i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} -1.73205 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} +(-3.23205 + 2.13397i) 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} -5.19615 q^{27} +(-5.36603 - 1.09808i) q^{30} -5.26795 q^{31} +6.46410i 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} +2.19615 q^{42} +(-5.09808 - 5.09808i) q^{43} +(5.59808 - 3.69615i) q^{45} -0.928203 q^{46} +(8.56218 + 8.56218i) q^{47} -6.92820 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} -1.73205i 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} +(-3.40192 + 7.96410i) q^{75} +(2.36603 + 2.36603i) q^{77} +0.928203i 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} +9.12436 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 \( 4 q + 4 q^{2} + 4 q^{5} - 6 q^{7} + 8 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{13} - 12 q^{14} - 6 q^{15} + 16 q^{16} + 10 q^{17} + 12 q^{18} - 6 q^{21} + 8 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{30} - 28 q^{31} - 12 q^{35} - 4 q^{37} - 4 q^{38} - 12 q^{39} + 12 q^{40} - 12 q^{42} - 10 q^{43} + 12 q^{45} + 24 q^{46} + 10 q^{47} + 2 q^{50} - 18 q^{51} - 16 q^{53} - 8 q^{55} - 20 q^{59} - 24 q^{61} - 28 q^{62} - 18 q^{63} + 14 q^{65} - 12 q^{66} + 12 q^{67} + 24 q^{69} - 6 q^{70} + 24 q^{72} + 18 q^{73} - 8 q^{74} - 24 q^{75} + 6 q^{77} + 16 q^{80} + 36 q^{81} + 4 q^{82} + 8 q^{83} + 32 q^{85} - 16 q^{88} + 36 q^{89} + 6 q^{90} + 36 q^{91} - 12 q^{93} - 2 q^{95} - 12 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) −1.73205 −1.00000
\(4\) 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 −0.816693 0.577073i \(-0.804195\pi\)
0.577073 + 0.816693i \(0.304195\pi\)
\(8\) 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 0.668972 0.743288i \(-0.266735\pi\)
−0.743288 + 0.668972i \(0.766735\pi\)
\(14\) −1.26795 −0.338874
\(15\) −3.23205 + 2.13397i −0.834512 + 0.550990i
\(16\) 4.00000 1.00000
\(17\) 5.09808 + 5.09808i 1.23647 + 1.23647i 0.961436 + 0.275029i \(0.0886875\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 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 \(-0.771798\pi\)
0.657063 + 0.753835i \(0.271798\pi\)
\(24\) −3.46410 + 3.46410i −0.707107 + 0.707107i
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) 0.535898i 0.105098i
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −5.36603 1.09808i −0.979698 0.200480i
\(31\) −5.26795 −0.946152 −0.473076 0.881022i \(-0.656856\pi\)
−0.473076 + 0.881022i \(0.656856\pi\)
\(32\) 0 0
\(33\) 6.46410i 1.12526i
\(34\) 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 −0.971389 0.237495i \(-0.923674\pi\)
0.237495 + 0.971389i \(0.423674\pi\)
\(38\) −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 \(-0.272043\pi\)
\(42\) 2.19615 0.338874
\(43\) −5.09808 5.09808i −0.777449 0.777449i 0.201947 0.979396i \(-0.435273\pi\)
−0.979396 + 0.201947i \(0.935273\pi\)
\(44\) 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 0.956197 + 0.292725i \(0.0945622\pi\)
0.292725 + 0.956197i \(0.405438\pi\)
\(48\) −6.92820 −1.00000
\(49\) 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 \(-0.937950\pi\)
0.193703 + 0.981060i \(0.437950\pi\)
\(54\) −5.19615 5.19615i −0.707107 0.707107i
\(55\) −4.59808 6.96410i −0.620004 0.939039i
\(56\) 2.53590i 0.338874i
\(57\) 1.73205i 0.229416i
\(58\) 0 0
\(59\) 0.196152 0.0255369 0.0127684 0.999918i \(-0.495936\pi\)
0.0127684 + 0.999918i \(0.495936\pi\)
\(60\) 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 −0.828416 0.560113i \(-0.810758\pi\)
0.560113 + 0.828416i \(0.310758\pi\)
\(68\) 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 0.947576 0.319530i \(-0.103525\pi\)
−0.319530 + 0.947576i \(0.603525\pi\)
\(74\) −8.92820 −1.03788
\(75\) −3.40192 + 7.96410i −0.392820 + 0.919615i
\(76\) 0 0
\(77\) 2.36603 + 2.36603i 0.269634 + 0.269634i
\(78\) 0.928203i 0.105098i
\(79\) 10.3923i 1.16923i −0.811312 0.584613i \(-0.801246\pi\)
0.811312 0.584613i \(-0.198754\pi\)
\(80\) 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 \(-0.743380\pi\)
0.721659 + 0.692248i \(0.243380\pi\)
\(84\) 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 \(-0.374132\pi\)
0.385201 + 0.922833i \(0.374132\pi\)
\(90\) 9.29423 + 1.90192i 0.979698 + 0.200480i
\(91\) 0.339746 0.0356151
\(92\) 0 0
\(93\) 9.12436 0.946152
\(94\) 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 −0.954510 0.298180i \(-0.903621\pi\)
0.298180 + 0.954510i \(0.403621\pi\)
\(98\) −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 \(0.632150\pi\)
\(102\) 17.6603i 1.74863i
\(103\) 5.66025 + 5.66025i 0.557721 + 0.557721i 0.928658 0.370937i \(-0.120963\pi\)
−0.370937 + 0.928658i \(0.620963\pi\)
\(104\) −1.07180 −0.105098
\(105\) 0.696152 3.40192i 0.0679375 0.331994i
\(106\) −11.4641 −1.11349
\(107\) 0.535898 + 0.535898i 0.0518073 + 0.0518073i 0.732536 0.680729i \(-0.238337\pi\)
−0.680729 + 0.732536i \(0.738337\pi\)
\(108\) 0 0
\(109\) 3.07180i 0.294225i 0.989120 + 0.147112i \(0.0469979\pi\)
−0.989120 + 0.147112i \(0.953002\pi\)
\(110\) 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 \(-0.718950\pi\)
0.772611 + 0.634880i \(0.218950\pi\)
\(114\) 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
\(120\) −2.19615 + 10.7321i −0.200480 + 0.979698i
\(121\) −2.92820 −0.266200
\(122\) −7.73205 7.73205i −0.700027 0.700027i
\(123\) 16.7321i 1.50868i
\(124\) 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 −1.00000 0.000131185i \(-0.999958\pi\)
0.000131185 1.00000i \(0.499958\pi\)
\(128\) 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
\(135\) −9.69615 + 6.40192i −0.834512 + 0.550990i
\(136\) 20.3923 1.74863
\(137\) −5.56218 5.56218i −0.475209 0.475209i 0.428387 0.903596i \(-0.359082\pi\)
−0.903596 + 0.428387i \(0.859082\pi\)
\(138\) 1.60770 0.136856
\(139\) 10.4641i 0.887554i 0.896137 + 0.443777i \(0.146362\pi\)
−0.896137 + 0.443777i \(0.853638\pi\)
\(140\) 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
\(147\) 10.7321i 0.885165i
\(148\) 0 0
\(149\) −13.3923 −1.09714 −0.548570 0.836105i \(-0.684828\pi\)
−0.548570 + 0.836105i \(0.684828\pi\)
\(150\) −11.3660 + 4.56218i −0.928032 + 0.372500i
\(151\) 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 0.187810 0.982205i \(-0.439861\pi\)
0.982205 0.187810i \(-0.0601390\pi\)
\(158\) 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 0.129936 0.991522i \(-0.458523\pi\)
−0.991522 + 0.129936i \(0.958523\pi\)
\(164\) 0 0
\(165\) 7.96410 + 12.0622i 0.620004 + 0.939039i
\(166\) 0.535898 0.0415938
\(167\) 4.00000 + 4.00000i 0.309529 + 0.309529i 0.844727 0.535198i \(-0.179763\pi\)
−0.535198 + 0.844727i \(0.679763\pi\)
\(168\) 4.39230i 0.338874i
\(169\) 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 \(-0.604756\pi\)
0.946334 + 0.323192i \(0.104756\pi\)
\(174\) 0 0
\(175\) 1.66987 + 4.16025i 0.126231 + 0.314486i
\(176\) 14.9282i 1.12526i
\(177\) −0.339746 −0.0255369
\(178\) 7.26795 + 7.26795i 0.544756 + 0.544756i
\(179\) −8.92820 −0.667325 −0.333663 0.942693i \(-0.608285\pi\)
−0.333663 + 0.942693i \(0.608285\pi\)
\(180\) 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
\(183\) 13.3923 0.989988
\(184\) 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 \(-0.0470623\pi\)
\(192\) 13.8564i 1.00000i
\(193\) 1.80385 + 1.80385i 0.129844 + 0.129844i 0.769042 0.639198i \(-0.220734\pi\)
−0.639198 + 0.769042i \(0.720734\pi\)
\(194\) −12.9282 −0.928191
\(195\) 1.43782 + 0.294229i 0.102965 + 0.0210702i
\(196\) 0 0
\(197\) −14.1244 14.1244i −1.00632 1.00632i −0.999980 0.00633876i \(-0.997982\pi\)
−0.00633876 0.999980i \(-0.502018\pi\)
\(198\) 11.1962 11.1962i 0.795676 0.795676i
\(199\) 0.803848i 0.0569832i −0.999594 0.0284916i \(-0.990930\pi\)
0.999594 0.0284916i \(-0.00907039\pi\)
\(200\) −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
\(210\) 4.09808 2.70577i 0.282794 0.186716i
\(211\) 14.0526 0.967418 0.483709 0.875229i \(-0.339289\pi\)
0.483709 + 0.875229i \(0.339289\pi\)
\(212\) 0 0
\(213\) 18.5885i 1.27366i
\(214\) 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
\(222\) 15.4641 1.03788
\(223\) −9.00000 9.00000i −0.602685 0.602685i 0.338340 0.941024i \(-0.390135\pi\)
−0.941024 + 0.338340i \(0.890135\pi\)
\(224\) 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 \(-0.0738927\pi\)
−0.230061 + 0.973176i \(0.573893\pi\)
\(228\) 0 0
\(229\) 23.2487i 1.53632i −0.640259 0.768159i \(-0.721173\pi\)
0.640259 0.768159i \(-0.278827\pi\)
\(230\) −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 \(-0.642230\pi\)
0.901822 + 0.432108i \(0.142230\pi\)
\(234\) 1.60770i 0.105098i
\(235\) 26.5263 + 5.42820i 1.73038 + 0.354097i
\(236\) 0 0
\(237\) 18.0000i 1.16923i
\(238\) −6.46410 6.46410i −0.419005 0.419005i
\(239\) 25.0526 1.62052 0.810258 0.586074i \(-0.199327\pi\)
0.810258 + 0.586074i \(0.199327\pi\)
\(240\) −12.9282 + 8.53590i −0.834512 + 0.550990i
\(241\) −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
\(243\) −15.5885 −1.00000
\(244\) 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
\(255\) −27.3564 5.59808i −1.71312 0.350565i
\(256\) 0 0
\(257\) −16.7321 16.7321i −1.04372 1.04372i −0.999000 0.0447170i \(-0.985761\pi\)
−0.0447170 0.999000i \(-0.514239\pi\)
\(258\) 17.6603i 1.09948i
\(259\) 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 \(-0.834632\pi\)
0.496462 + 0.868058i \(0.334632\pi\)
\(264\) 12.9282 + 12.9282i 0.795676 + 0.795676i
\(265\) −3.63397 + 17.7583i −0.223233 + 1.09089i
\(266\) 1.26795i 0.0777430i
\(267\) −12.5885 −0.770401
\(268\) 0 0
\(269\) 5.80385 0.353867 0.176933 0.984223i \(-0.443382\pi\)
0.176933 + 0.984223i \(0.443382\pi\)
\(270\) −16.0981 3.29423i −0.979698 0.200480i
\(271\) −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
\(273\) −0.588457 −0.0356151
\(274\) 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 −0.649985 0.759947i \(-0.725225\pi\)
0.759947 + 0.649985i \(0.225225\pi\)
\(278\) −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 \(-0.116517\pi\)
\(282\) 29.6603i 1.76624i
\(283\) −8.83013 8.83013i −0.524897 0.524897i 0.394150 0.919046i \(-0.371039\pi\)
−0.919046 + 0.394150i \(0.871039\pi\)
\(284\) 0 0
\(285\) −2.13397 3.23205i −0.126406 0.191450i
\(286\) −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 \(-0.642790\pi\)
0.901060 + 0.433695i \(0.142790\pi\)
\(294\) 10.7321 10.7321i 0.625906 0.625906i
\(295\) 0.366025 0.241670i 0.0213108 0.0140706i
\(296\) 17.8564i 1.03788i
\(297\) 19.3923i 1.12526i
\(298\) −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
\(303\) 31.8564i 1.83010i
\(304\) 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 −0.987873 0.155266i \(-0.950377\pi\)
0.155266 + 0.987873i \(0.450377\pi\)
\(308\) 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 \(-0.0519614\pi\)
\(312\) 1.85641 0.105098
\(313\) 1.73205 + 1.73205i 0.0979013 + 0.0979013i 0.754361 0.656460i \(-0.227947\pi\)
−0.656460 + 0.754361i \(0.727947\pi\)
\(314\) 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 −0.998141 0.0609399i \(-0.980590\pi\)
−0.0609399 0.998141i \(-0.519410\pi\)
\(318\) 19.8564 1.11349
\(319\) 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
\(327\) 5.32051i 0.294225i
\(328\) −19.3205 19.3205i −1.06680 1.06680i
\(329\) −10.8564 −0.598533
\(330\) −4.09808 + 20.0263i −0.225592 + 1.10241i
\(331\) 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 −0.923770 0.382947i \(-0.874909\pi\)
0.382947 + 0.923770i \(0.374909\pi\)
\(338\) 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
\(345\) 0.509619 2.49038i 0.0274370 0.134078i
\(346\) 16.3923 0.881256
\(347\) −18.0981 18.0981i −0.971556 0.971556i 0.0280509 0.999606i \(-0.491070\pi\)
−0.999606 + 0.0280509i \(0.991070\pi\)
\(348\) 0 0
\(349\) 3.73205i 0.199772i 0.994999 + 0.0998860i \(0.0318478\pi\)
−0.994999 + 0.0998860i \(0.968152\pi\)
\(350\) −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 −0.508541 + 0.861038i \(0.669815\pi\)
−0.861038 + 0.508541i \(0.830185\pi\)
\(354\) −0.339746 0.339746i −0.0180573 0.0180573i
\(355\) 13.2224 + 20.0263i 0.701774 + 1.06288i
\(356\) 0 0
\(357\) 11.1962 0.592563
\(358\) −8.92820 8.92820i −0.471870 0.471870i
\(359\) 21.9282 1.15733 0.578663 0.815567i \(-0.303575\pi\)
0.578663 + 0.815567i \(0.303575\pi\)
\(360\) 3.80385 18.5885i 0.200480 0.979698i
\(361\) −1.00000 −0.0526316
\(362\) 10.9282 + 10.9282i 0.574374 + 0.574374i
\(363\) 5.07180 0.266200
\(364\) 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 −0.282187 + 0.959359i \(0.591060\pi\)
−0.959359 + 0.282187i \(0.908940\pi\)
\(368\) −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 0.999321 0.0368471i \(-0.0117314\pi\)
−0.0368471 + 0.999321i \(0.511731\pi\)
\(374\) 38.0526 1.96765
\(375\) 3.46410 + 19.0526i 0.178885 + 0.983870i
\(376\) 34.2487 1.76624
\(377\) 0 0
\(378\) 6.58846 0.338874
\(379\) 14.5359i 0.746659i −0.927699 0.373329i \(-0.878216\pi\)
0.927699 0.373329i \(-0.121784\pi\)
\(380\) 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 \(-0.556819\pi\)
0.984111 + 0.177555i \(0.0568188\pi\)
\(384\) −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 \(-0.131567\pi\)
0.915789 + 0.401660i \(0.131567\pi\)
\(390\) 1.14359 + 1.73205i 0.0579081 + 0.0877058i
\(391\) −4.73205 −0.239310
\(392\) 12.3923 + 12.3923i 0.625906 + 0.625906i
\(393\) 4.26795i 0.215290i
\(394\) 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 −0.919526 0.393029i \(-0.871427\pi\)
0.393029 + 0.919526i \(0.371427\pi\)
\(398\) 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 \(-0.290872\pi\)
\(402\) 7.60770 0.379437
\(403\) 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
\(408\) −35.3205 −1.74863
\(409\) 20.1962i 0.998635i 0.866419 + 0.499318i \(0.166416\pi\)
−0.866419 + 0.499318i \(0.833584\pi\)
\(410\) 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
\(417\) 18.1244i 0.887554i
\(418\) 3.73205 + 3.73205i 0.182541 + 0.182541i
\(419\) 22.9282 1.12012 0.560058 0.828453i \(-0.310779\pi\)
0.560058 + 0.828453i \(0.310779\pi\)
\(420\) 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 \(0.673318\pi\)
\(432\) −20.7846 −1.00000
\(433\) −29.1244 29.1244i −1.39963 1.39963i −0.801110 0.598517i \(-0.795757\pi\)
−0.598517 0.801110i \(-0.704243\pi\)
\(434\) 6.67949 0.320626
\(435\) 0 0
\(436\) 0 0
\(437\) −0.464102 0.464102i −0.0222010 0.0222010i
\(438\) 18.5885i 0.888191i
\(439\) 9.85641i 0.470421i 0.971945 + 0.235210i \(0.0755779\pi\)
−0.971945 + 0.235210i \(0.924422\pi\)
\(440\) −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 \(-0.639010\pi\)
0.906147 + 0.422962i \(0.139010\pi\)
\(444\) 0 0
\(445\) 13.5622 8.95448i 0.642909 0.424483i
\(446\) 18.0000i 0.852325i
\(447\) 23.1962 1.09714
\(448\) 5.07180 + 5.07180i 0.239620 + 0.239620i
\(449\) 19.8564 0.937082 0.468541 0.883442i \(-0.344780\pi\)
0.468541 + 0.883442i \(0.344780\pi\)
\(450\) 19.6865 7.90192i 0.928032 0.372500i
\(451\) −36.0526 −1.69765
\(452\) 0 0
\(453\) −4.73205 −0.222331
\(454\) 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 −0.977323 0.211753i \(-0.932083\pi\)
0.211753 + 0.977323i \(0.432083\pi\)
\(458\) 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 \(0.902100\pi\)
\(462\) 8.19615i 0.381320i
\(463\) −11.2942 11.2942i −0.524887 0.524887i 0.394156 0.919043i \(-0.371037\pi\)
−0.919043 + 0.394156i \(0.871037\pi\)
\(464\) 0 0
\(465\) 17.0263 11.2417i 0.789575 0.521320i
\(466\) 14.3397 0.664276
\(467\) −11.2224 11.2224i −0.519312 0.519312i 0.398051 0.917363i \(-0.369687\pi\)
−0.917363 + 0.398051i \(0.869687\pi\)
\(468\) 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 \(-0.506750\pi\)
−0.0212053 + 0.999775i \(0.506750\pi\)
\(480\) 0 0
\(481\) 2.39230 0.109080
\(482\) −16.1962 16.1962i −0.737715 0.737715i
\(483\) 1.01924i 0.0463769i
\(484\) 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 −0.205857 0.978582i \(-0.565998\pi\)
0.978582 + 0.205857i \(0.0659981\pi\)
\(488\) −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
\(498\) −0.928203 −0.0415938
\(499\) 12.8564i 0.575532i −0.957701 0.287766i \(-0.907087\pi\)
0.957701 0.287766i \(-0.0929125\pi\)
\(500\) 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 0.0693107 0.997595i \(-0.477920\pi\)
0.997595 0.0693107i \(-0.0220800\pi\)
\(504\) 7.60770i 0.338874i
\(505\) 22.6603 + 34.3205i 1.00837 + 1.52724i
\(506\) 3.46410i 0.153998i
\(507\) 22.2679i 0.988954i
\(508\) 0 0
\(509\) −18.7321 −0.830284 −0.415142 0.909757i \(-0.636268\pi\)
−0.415142 + 0.909757i \(0.636268\pi\)
\(510\) −21.7583 32.9545i −0.963475 1.45925i
\(511\) −6.80385 −0.300984
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 5.19615i 0.229416i
\(514\) 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 0.999787 0.0206398i \(-0.00657033\pi\)
−0.0206398 + 0.999787i \(0.506570\pi\)
\(524\) 0 0
\(525\) −2.89230 7.20577i −0.126231 0.314486i
\(526\) −12.0526 −0.525517
\(527\) −26.8564 26.8564i −1.16988 1.16988i
\(528\) 25.8564i 1.12526i
\(529\) 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
\(537\) 15.4641 0.667325
\(538\) 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
\(543\) −18.9282 −0.812287
\(544\) 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 −0.266124 0.963939i \(-0.585743\pi\)
0.963939 + 0.266124i \(0.0857431\pi\)
\(548\) 0 0
\(549\) −23.1962 −0.989988
\(550\) −9.83013 24.4904i −0.419158 1.04427i
\(551\) 0 0
\(552\) 3.21539i 0.136856i
\(553\) 6.58846 + 6.58846i 0.280170 + 0.280170i
\(554\) 3.66025 0.155509
\(555\) 4.90192 23.9545i 0.208075 1.01681i
\(556\) 0 0
\(557\) 5.68653 + 5.68653i 0.240946 + 0.240946i 0.817242 0.576295i \(-0.195502\pi\)
−0.576295 + 0.817242i \(0.695502\pi\)
\(558\) −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 \(-0.710777\pi\)
0.788656 + 0.614835i \(0.210777\pi\)
\(564\) 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 \(-0.558592\pi\)
−0.183033 + 0.983107i \(0.558592\pi\)
\(570\) 1.09808 5.36603i 0.0459934 0.224758i
\(571\) −6.53590 −0.273519 −0.136759 0.990604i \(-0.543669\pi\)
−0.136759 + 0.990604i \(0.543669\pi\)
\(572\) 0 0
\(573\) 7.05256i 0.294625i
\(574\) 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 −0.0928572 0.995679i \(-0.529600\pi\)
0.995679 + 0.0928572i \(0.0296000\pi\)
\(578\) −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
\(582\) 22.3923 0.928191
\(583\) 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 \(-0.129268\pi\)
−0.395036 + 0.918666i \(0.629268\pi\)
\(588\) 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 \(-0.787723\pi\)
0.618543 + 0.785751i \(0.287723\pi\)
\(594\) −19.3923 + 19.3923i −0.795676 + 0.795676i
\(595\) −12.0622 + 7.96410i −0.494501 + 0.326496i
\(596\) 0 0
\(597\) 1.39230i 0.0569832i
\(598\) 0.248711 + 0.248711i 0.0101706 + 0.0101706i
\(599\) 1.32051 0.0539545 0.0269772 0.999636i \(-0.491412\pi\)
0.0269772 + 0.999636i \(0.491412\pi\)
\(600\) 9.12436 + 22.7321i 0.372500 + 0.928032i
\(601\) 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 −0.908971 0.416859i \(-0.863131\pi\)
0.416859 + 0.908971i \(0.363131\pi\)
\(608\) 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 0.590388 0.807120i \(-0.298975\pi\)
−0.807120 + 0.590388i \(0.798975\pi\)
\(614\) −29.1769 −1.17748
\(615\) 20.6147 + 31.2224i 0.831266 + 1.25901i
\(616\) 9.46410 0.381320
\(617\) −9.22243 9.22243i −0.371281 0.371281i 0.496663 0.867944i \(-0.334559\pi\)
−0.867944 + 0.496663i \(0.834559\pi\)
\(618\) 19.6077i 0.788737i
\(619\) 36.7846i 1.47850i −0.673432 0.739249i \(-0.735181\pi\)
0.673432 0.739249i \(-0.264819\pi\)
\(620\) 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
\(627\) −6.46410 −0.258151
\(628\) 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
\(633\) −24.3397 −0.967418
\(634\) 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 \(-0.206462\pi\)
\(642\) 1.85641i 0.0732665i
\(643\) −23.7583 23.7583i −0.936937 0.936937i 0.0611891 0.998126i \(-0.480511\pi\)
−0.998126 + 0.0611891i \(0.980511\pi\)
\(644\) 0 0
\(645\) 27.3564 + 5.59808i 1.07716 + 0.220424i
\(646\) −10.1962 −0.401162
\(647\) 21.0981 + 21.0981i 0.829451 + 0.829451i 0.987441 0.157990i \(-0.0505013\pi\)
−0.157990 + 0.987441i \(0.550501\pi\)
\(648\) 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 \(-0.825489\pi\)
0.521188 + 0.853442i \(0.325489\pi\)
\(654\) 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 \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 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
\(663\) 4.73205i 0.183778i
\(664\) 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 0.989331 + 0.145685i \(0.0465386\pi\)
0.145685 + 0.989331i \(0.453461\pi\)
\(674\) −19.8564 −0.764840
\(675\) −10.2058 + 23.8923i −0.392820 + 0.919615i
\(676\) 0 0
\(677\) 1.46410 + 1.46410i 0.0562700 + 0.0562700i 0.734682 0.678412i \(-0.237331\pi\)
−0.678412 + 0.734682i \(0.737331\pi\)
\(678\) −5.07180 −0.194781
\(679\) 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 \(-0.599762\pi\)
0.951287 + 0.308306i \(0.0997620\pi\)
\(684\) 0 0
\(685\) −17.2321 3.52628i −0.658403 0.134732i
\(686\) 16.7321i 0.638833i
\(687\) 40.2679i 1.53632i
\(688\) −20.3923 20.3923i −0.777449 0.777449i
\(689\) 3.07180 0.117026
\(690\) 3.00000 1.98076i 0.114208 0.0754063i
\(691\) −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 \(0.975067\pi\)
\(702\) 2.78461i 0.105098i
\(703\) −4.46410 4.46410i −0.168367 0.168367i
\(704\) −29.8564 −1.12526
\(705\) −45.9449 9.40192i −1.73038 0.354097i
\(706\) −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 \(-0.847587\pi\)
0.887539 0.460733i \(-0.152413\pi\)
\(710\) −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
\(717\) −43.3923 −1.62052
\(718\) 21.9282 + 21.9282i 0.818353 + 0.818353i
\(719\) −21.6410 −0.807074 −0.403537 0.914963i \(-0.632219\pi\)
−0.403537 + 0.914963i \(0.632219\pi\)
\(720\) 22.3923 14.7846i 0.834512 0.550990i
\(721\) −7.17691 −0.267282
\(722\) −1.00000 1.00000i −0.0372161 0.0372161i
\(723\) 28.0526 1.04329
\(724\) 0 0
\(725\) 0 0
\(726\) 5.07180 + 5.07180i 0.188232 + 0.188232i
\(727\) 8.02628 8.02628i 0.297678 0.297678i −0.542426 0.840104i \(-0.682494\pi\)
0.840104 + 0.542426i \(0.182494\pi\)
\(728\) 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 0.884805 0.465962i \(-0.154292\pi\)
−0.465962 + 0.884805i \(0.654292\pi\)
\(734\) −47.5692 −1.75581
\(735\) −13.2224 20.0263i −0.487717 0.738680i
\(736\) 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 \(-0.741608\pi\)
0.688221 0.725501i \(-0.258392\pi\)
\(740\) 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 \(-0.611500\pi\)
0.939274 + 0.343167i \(0.111500\pi\)
\(744\) 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
\(750\) −15.5885 + 22.5167i −0.569210 + 0.822192i
\(751\) −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
\(753\) 29.1962i 1.06397i
\(754\) 0 0
\(755\) 5.09808 3.36603i 0.185538 0.122502i
\(756\) 0 0
\(757\) −5.02628 + 5.02628i −0.182683 + 0.182683i −0.792524 0.609841i \(-0.791233\pi\)
0.609841 + 0.792524i \(0.291233\pi\)
\(758\) 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 \(-0.319280\pi\)
\(762\) 39.0333 1.41403
\(763\) −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 \(0.136114\pi\)
−0.909958 + 0.414701i \(0.863886\pi\)
\(770\) 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 \(-0.795395\pi\)
0.599427 + 0.800430i \(0.295395\pi\)
\(774\) 30.5885i 1.09948i
\(775\) −10.3468 + 24.2224i −0.371668 + 0.870095i
\(776\) 25.8564i 0.928191i