Properties

Label 162.2.e.b.19.1
Level $162$
Weight $2$
Character 162.19
Analytic conductor $1.294$
Analytic rank $0$
Dimension $12$
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] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} - 1584 x^{3} + 936 x^{2} - 342 x + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 19.1
Root \(0.500000 - 0.677980i\) of defining polynomial
Character \(\chi\) \(=\) 162.19
Dual form 162.2.e.b.145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.77684 - 3.07758i) q^{10} +(-0.773091 + 4.38442i) q^{11} +(4.39657 + 1.60022i) q^{13} +(-0.300233 - 0.109276i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.567354 + 0.982686i) q^{17} +(-0.928896 + 1.60890i) q^{19} +(-2.72228 - 2.28426i) q^{20} +(0.773091 + 4.38442i) q^{22} +(-0.110473 + 0.0926974i) q^{23} +(-7.16859 + 2.60915i) q^{25} +4.67874 q^{26} -0.319501 q^{28} +(-4.09634 + 1.49095i) q^{29} +(0.514546 - 0.431755i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.869237 + 0.729376i) q^{34} +(-0.567702 + 0.983289i) q^{35} +(-3.79438 - 6.57207i) q^{37} +(-0.322602 + 1.82957i) q^{38} +(-3.33937 - 1.21543i) q^{40} +(2.04599 + 0.744678i) q^{41} +(-1.23250 + 6.98988i) q^{43} +(2.22603 + 3.85559i) q^{44} +(-0.0721058 + 0.124891i) q^{46} +(7.91059 + 6.63778i) q^{47} +(-1.19781 - 6.79312i) q^{49} +(-5.84389 + 4.90360i) q^{50} +(4.39657 - 1.60022i) q^{52} -0.805554 q^{53} +15.8212 q^{55} +(-0.300233 + 0.109276i) q^{56} +(-3.33937 + 2.80206i) q^{58} +(-0.517966 - 2.93753i) q^{59} +(-2.67705 - 2.24631i) q^{61} +(0.335846 - 0.581702i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.88720 - 16.3741i) q^{65} +(-6.99437 - 2.54574i) q^{67} +(1.06628 + 0.388093i) q^{68} +(-0.197161 + 1.11816i) q^{70} +(-4.04928 - 7.01356i) q^{71} +(-7.30065 + 12.6451i) q^{73} +(-5.81333 - 4.87797i) q^{74} +(0.322602 + 1.82957i) q^{76} +(1.08965 - 0.914324i) q^{77} +(11.8279 - 4.30501i) q^{79} -3.55368 q^{80} +2.17729 q^{82} +(-5.08715 + 1.85157i) q^{83} +(3.08899 - 2.59197i) q^{85} +(1.23250 + 6.98988i) q^{86} +(3.41047 + 2.86173i) q^{88} +(2.52624 - 4.37558i) q^{89} +(-0.747430 - 1.29459i) q^{91} +(-0.0250421 + 0.142021i) q^{92} +(9.70378 + 3.53189i) q^{94} +(6.20385 + 2.25802i) q^{95} +(3.24273 - 18.3904i) q^{97} +(-3.44896 - 5.97377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 0.342020i 0.664463 0.241845i
\(3\) 0 0
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) −0.617090 3.49969i −0.275971 1.56511i −0.735860 0.677134i \(-0.763222\pi\)
0.459889 0.887977i \(-0.347889\pi\)
\(6\) 0 0
\(7\) −0.244752 0.205371i −0.0925075 0.0776230i 0.595361 0.803458i \(-0.297009\pi\)
−0.687869 + 0.725835i \(0.741453\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0 0
\(10\) −1.77684 3.07758i −0.561886 0.973216i
\(11\) −0.773091 + 4.38442i −0.233096 + 1.32195i 0.613491 + 0.789702i \(0.289765\pi\)
−0.846587 + 0.532250i \(0.821347\pi\)
\(12\) 0 0
\(13\) 4.39657 + 1.60022i 1.21939 + 0.443822i 0.869951 0.493137i \(-0.164150\pi\)
0.349439 + 0.936959i \(0.386372\pi\)
\(14\) −0.300233 0.109276i −0.0802405 0.0292052i
\(15\) 0 0
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) 0.567354 + 0.982686i 0.137604 + 0.238336i 0.926589 0.376075i \(-0.122727\pi\)
−0.788985 + 0.614412i \(0.789393\pi\)
\(18\) 0 0
\(19\) −0.928896 + 1.60890i −0.213103 + 0.369106i −0.952684 0.303962i \(-0.901690\pi\)
0.739581 + 0.673068i \(0.235024\pi\)
\(20\) −2.72228 2.28426i −0.608720 0.510777i
\(21\) 0 0
\(22\) 0.773091 + 4.38442i 0.164824 + 0.934761i
\(23\) −0.110473 + 0.0926974i −0.0230351 + 0.0193288i −0.654233 0.756293i \(-0.727008\pi\)
0.631197 + 0.775622i \(0.282564\pi\)
\(24\) 0 0
\(25\) −7.16859 + 2.60915i −1.43372 + 0.521831i
\(26\) 4.67874 0.917576
\(27\) 0 0
\(28\) −0.319501 −0.0603800
\(29\) −4.09634 + 1.49095i −0.760672 + 0.276862i −0.693089 0.720852i \(-0.743751\pi\)
−0.0675824 + 0.997714i \(0.521529\pi\)
\(30\) 0 0
\(31\) 0.514546 0.431755i 0.0924152 0.0775455i −0.595410 0.803422i \(-0.703010\pi\)
0.687825 + 0.725877i \(0.258566\pi\)
\(32\) −0.173648 0.984808i −0.0306970 0.174091i
\(33\) 0 0
\(34\) 0.869237 + 0.729376i 0.149073 + 0.125087i
\(35\) −0.567702 + 0.983289i −0.0959592 + 0.166206i
\(36\) 0 0
\(37\) −3.79438 6.57207i −0.623793 1.08044i −0.988773 0.149426i \(-0.952258\pi\)
0.364980 0.931015i \(-0.381076\pi\)
\(38\) −0.322602 + 1.82957i −0.0523330 + 0.296795i
\(39\) 0 0
\(40\) −3.33937 1.21543i −0.528000 0.192176i
\(41\) 2.04599 + 0.744678i 0.319529 + 0.116299i 0.496805 0.867862i \(-0.334506\pi\)
−0.177276 + 0.984161i \(0.556729\pi\)
\(42\) 0 0
\(43\) −1.23250 + 6.98988i −0.187955 + 1.06595i 0.734144 + 0.678994i \(0.237584\pi\)
−0.922099 + 0.386953i \(0.873528\pi\)
\(44\) 2.22603 + 3.85559i 0.335586 + 0.581252i
\(45\) 0 0
\(46\) −0.0721058 + 0.124891i −0.0106314 + 0.0184142i
\(47\) 7.91059 + 6.63778i 1.15388 + 0.968219i 0.999803 0.0198400i \(-0.00631569\pi\)
0.154075 + 0.988059i \(0.450760\pi\)
\(48\) 0 0
\(49\) −1.19781 6.79312i −0.171116 0.970446i
\(50\) −5.84389 + 4.90360i −0.826450 + 0.693474i
\(51\) 0 0
\(52\) 4.39657 1.60022i 0.609695 0.221911i
\(53\) −0.805554 −0.110651 −0.0553257 0.998468i \(-0.517620\pi\)
−0.0553257 + 0.998468i \(0.517620\pi\)
\(54\) 0 0
\(55\) 15.8212 2.13333
\(56\) −0.300233 + 0.109276i −0.0401203 + 0.0146026i
\(57\) 0 0
\(58\) −3.33937 + 2.80206i −0.438481 + 0.367929i
\(59\) −0.517966 2.93753i −0.0674334 0.382434i −0.999782 0.0208736i \(-0.993355\pi\)
0.932349 0.361560i \(-0.117756\pi\)
\(60\) 0 0
\(61\) −2.67705 2.24631i −0.342761 0.287611i 0.455114 0.890433i \(-0.349598\pi\)
−0.797876 + 0.602822i \(0.794043\pi\)
\(62\) 0.335846 0.581702i 0.0426525 0.0738763i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 2.88720 16.3741i 0.358113 2.03096i
\(66\) 0 0
\(67\) −6.99437 2.54574i −0.854498 0.311012i −0.122625 0.992453i \(-0.539131\pi\)
−0.731873 + 0.681441i \(0.761353\pi\)
\(68\) 1.06628 + 0.388093i 0.129305 + 0.0470632i
\(69\) 0 0
\(70\) −0.197161 + 1.11816i −0.0235652 + 0.133645i
\(71\) −4.04928 7.01356i −0.480561 0.832356i 0.519190 0.854659i \(-0.326234\pi\)
−0.999751 + 0.0223028i \(0.992900\pi\)
\(72\) 0 0
\(73\) −7.30065 + 12.6451i −0.854477 + 1.48000i 0.0226526 + 0.999743i \(0.492789\pi\)
−0.877129 + 0.480254i \(0.840545\pi\)
\(74\) −5.81333 4.87797i −0.675786 0.567052i
\(75\) 0 0
\(76\) 0.322602 + 1.82957i 0.0370050 + 0.209866i
\(77\) 1.08965 0.914324i 0.124177 0.104197i
\(78\) 0 0
\(79\) 11.8279 4.30501i 1.33074 0.484351i 0.423859 0.905728i \(-0.360675\pi\)
0.906886 + 0.421377i \(0.138453\pi\)
\(80\) −3.55368 −0.397314
\(81\) 0 0
\(82\) 2.17729 0.240442
\(83\) −5.08715 + 1.85157i −0.558387 + 0.203236i −0.605769 0.795641i \(-0.707134\pi\)
0.0473820 + 0.998877i \(0.484912\pi\)
\(84\) 0 0
\(85\) 3.08899 2.59197i 0.335048 0.281139i
\(86\) 1.23250 + 6.98988i 0.132904 + 0.753738i
\(87\) 0 0
\(88\) 3.41047 + 2.86173i 0.363558 + 0.305061i
\(89\) 2.52624 4.37558i 0.267781 0.463810i −0.700508 0.713645i \(-0.747043\pi\)
0.968288 + 0.249835i \(0.0803763\pi\)
\(90\) 0 0
\(91\) −0.747430 1.29459i −0.0783520 0.135710i
\(92\) −0.0250421 + 0.142021i −0.00261082 + 0.0148067i
\(93\) 0 0
\(94\) 9.70378 + 3.53189i 1.00087 + 0.364286i
\(95\) 6.20385 + 2.25802i 0.636502 + 0.231668i
\(96\) 0 0
\(97\) 3.24273 18.3904i 0.329249 1.86726i −0.148708 0.988881i \(-0.547511\pi\)
0.477957 0.878383i \(-0.341377\pi\)
\(98\) −3.44896 5.97377i −0.348398 0.603442i
\(99\) 0 0
\(100\) −3.81433 + 6.60661i −0.381433 + 0.660661i
\(101\) 1.85357 + 1.55533i 0.184438 + 0.154761i 0.730332 0.683093i \(-0.239366\pi\)
−0.545894 + 0.837854i \(0.683810\pi\)
\(102\) 0 0
\(103\) 0.346489 + 1.96504i 0.0341406 + 0.193621i 0.997108 0.0759967i \(-0.0242138\pi\)
−0.962967 + 0.269618i \(0.913103\pi\)
\(104\) 3.58412 3.00743i 0.351452 0.294903i
\(105\) 0 0
\(106\) −0.756973 + 0.275516i −0.0735238 + 0.0267605i
\(107\) −8.87072 −0.857565 −0.428783 0.903408i \(-0.641057\pi\)
−0.428783 + 0.903408i \(0.641057\pi\)
\(108\) 0 0
\(109\) −1.97204 −0.188887 −0.0944434 0.995530i \(-0.530107\pi\)
−0.0944434 + 0.995530i \(0.530107\pi\)
\(110\) 14.8671 5.41116i 1.41752 0.515934i
\(111\) 0 0
\(112\) −0.244752 + 0.205371i −0.0231269 + 0.0194058i
\(113\) 1.67200 + 9.48237i 0.157288 + 0.892026i 0.956664 + 0.291195i \(0.0940527\pi\)
−0.799375 + 0.600832i \(0.794836\pi\)
\(114\) 0 0
\(115\) 0.392584 + 0.329417i 0.0366087 + 0.0307183i
\(116\) −2.17962 + 3.77521i −0.202372 + 0.350519i
\(117\) 0 0
\(118\) −1.49142 2.58322i −0.137297 0.237805i
\(119\) 0.0629545 0.357033i 0.00577103 0.0327291i
\(120\) 0 0
\(121\) −8.28884 3.01689i −0.753530 0.274263i
\(122\) −3.28389 1.19524i −0.297309 0.108212i
\(123\) 0 0
\(124\) 0.116638 0.661487i 0.0104744 0.0594033i
\(125\) 4.67070 + 8.08988i 0.417760 + 0.723581i
\(126\) 0 0
\(127\) −0.0796049 + 0.137880i −0.00706379 + 0.0122348i −0.869536 0.493870i \(-0.835582\pi\)
0.862472 + 0.506105i \(0.168915\pi\)
\(128\) −0.766044 0.642788i −0.0677094 0.0568149i
\(129\) 0 0
\(130\) −2.88720 16.3741i −0.253224 1.43611i
\(131\) 7.26657 6.09738i 0.634883 0.532730i −0.267559 0.963542i \(-0.586217\pi\)
0.902442 + 0.430811i \(0.141773\pi\)
\(132\) 0 0
\(133\) 0.557770 0.203012i 0.0483648 0.0176033i
\(134\) −7.44325 −0.642999
\(135\) 0 0
\(136\) 1.13471 0.0973004
\(137\) 11.0032 4.00484i 0.940067 0.342156i 0.173875 0.984768i \(-0.444371\pi\)
0.766192 + 0.642611i \(0.222149\pi\)
\(138\) 0 0
\(139\) −4.02194 + 3.37481i −0.341136 + 0.286247i −0.797219 0.603690i \(-0.793696\pi\)
0.456083 + 0.889937i \(0.349252\pi\)
\(140\) 0.197161 + 1.11816i 0.0166631 + 0.0945014i
\(141\) 0 0
\(142\) −6.20385 5.20565i −0.520616 0.436849i
\(143\) −10.4150 + 18.0393i −0.870946 + 1.50852i
\(144\) 0 0
\(145\) 7.74567 + 13.4159i 0.643243 + 1.11413i
\(146\) −2.53549 + 14.3795i −0.209839 + 1.19005i
\(147\) 0 0
\(148\) −7.13111 2.59551i −0.586174 0.213350i
\(149\) −15.3097 5.57227i −1.25422 0.456499i −0.372394 0.928075i \(-0.621463\pi\)
−0.881825 + 0.471576i \(0.843685\pi\)
\(150\) 0 0
\(151\) −2.71203 + 15.3807i −0.220702 + 1.25166i 0.650033 + 0.759906i \(0.274755\pi\)
−0.870734 + 0.491754i \(0.836356\pi\)
\(152\) 0.928896 + 1.60890i 0.0753434 + 0.130499i
\(153\) 0 0
\(154\) 0.711218 1.23187i 0.0573116 0.0992665i
\(155\) −1.82853 1.53432i −0.146871 0.123240i
\(156\) 0 0
\(157\) 3.06168 + 17.3637i 0.244349 + 1.38577i 0.822000 + 0.569488i \(0.192859\pi\)
−0.577651 + 0.816284i \(0.696030\pi\)
\(158\) 9.64221 8.09077i 0.767093 0.643667i
\(159\) 0 0
\(160\) −3.33937 + 1.21543i −0.264000 + 0.0960882i
\(161\) 0.0460757 0.00363128
\(162\) 0 0
\(163\) −15.8801 −1.24382 −0.621912 0.783087i \(-0.713644\pi\)
−0.621912 + 0.783087i \(0.713644\pi\)
\(164\) 2.04599 0.744678i 0.159765 0.0581496i
\(165\) 0 0
\(166\) −4.14708 + 3.47981i −0.321876 + 0.270086i
\(167\) 2.35787 + 13.3721i 0.182457 + 1.03477i 0.929179 + 0.369630i \(0.120516\pi\)
−0.746722 + 0.665137i \(0.768373\pi\)
\(168\) 0 0
\(169\) 6.81058 + 5.71475i 0.523891 + 0.439596i
\(170\) 2.01620 3.49215i 0.154635 0.267836i
\(171\) 0 0
\(172\) 3.54885 + 6.14680i 0.270598 + 0.468689i
\(173\) −1.11906 + 6.34650i −0.0850805 + 0.482516i 0.912259 + 0.409615i \(0.134337\pi\)
−0.997339 + 0.0729010i \(0.976774\pi\)
\(174\) 0 0
\(175\) 2.29037 + 0.833627i 0.173136 + 0.0630163i
\(176\) 4.18356 + 1.52269i 0.315348 + 0.114777i
\(177\) 0 0
\(178\) 0.877354 4.97572i 0.0657605 0.372946i
\(179\) −6.25613 10.8359i −0.467605 0.809915i 0.531710 0.846927i \(-0.321550\pi\)
−0.999315 + 0.0370111i \(0.988216\pi\)
\(180\) 0 0
\(181\) −0.152251 + 0.263707i −0.0113168 + 0.0196012i −0.871628 0.490167i \(-0.836936\pi\)
0.860312 + 0.509769i \(0.170269\pi\)
\(182\) −1.14513 0.960878i −0.0848827 0.0712250i
\(183\) 0 0
\(184\) 0.0250421 + 0.142021i 0.00184613 + 0.0104699i
\(185\) −20.6587 + 17.3347i −1.51886 + 1.27448i
\(186\) 0 0
\(187\) −4.74712 + 1.72781i −0.347144 + 0.126350i
\(188\) 10.3265 0.753141
\(189\) 0 0
\(190\) 6.60200 0.478960
\(191\) −13.5247 + 4.92260i −0.978615 + 0.356187i −0.781301 0.624154i \(-0.785444\pi\)
−0.197313 + 0.980341i \(0.563222\pi\)
\(192\) 0 0
\(193\) 2.33692 1.96090i 0.168215 0.141149i −0.554794 0.831988i \(-0.687203\pi\)
0.723009 + 0.690839i \(0.242759\pi\)
\(194\) −3.24273 18.3904i −0.232814 1.32036i
\(195\) 0 0
\(196\) −5.28411 4.43390i −0.377437 0.316707i
\(197\) 11.1321 19.2814i 0.793129 1.37374i −0.130891 0.991397i \(-0.541784\pi\)
0.924020 0.382343i \(-0.124883\pi\)
\(198\) 0 0
\(199\) −12.2817 21.2725i −0.870626 1.50797i −0.861350 0.508012i \(-0.830381\pi\)
−0.00927642 0.999957i \(-0.502953\pi\)
\(200\) −1.32470 + 7.51276i −0.0936705 + 0.531232i
\(201\) 0 0
\(202\) 2.27375 + 0.827576i 0.159980 + 0.0582280i
\(203\) 1.30878 + 0.476359i 0.0918587 + 0.0334338i
\(204\) 0 0
\(205\) 1.34359 7.61986i 0.0938402 0.532194i
\(206\) 0.997676 + 1.72802i 0.0695114 + 0.120397i
\(207\) 0 0
\(208\) 2.33937 4.05190i 0.162206 0.280949i
\(209\) −6.33595 5.31649i −0.438267 0.367750i
\(210\) 0 0
\(211\) −0.524297 2.97344i −0.0360941 0.204700i 0.961428 0.275058i \(-0.0886970\pi\)
−0.997522 + 0.0703579i \(0.977586\pi\)
\(212\) −0.617090 + 0.517800i −0.0423819 + 0.0355627i
\(213\) 0 0
\(214\) −8.33575 + 3.03397i −0.569820 + 0.207398i
\(215\) 25.2230 1.72019
\(216\) 0 0
\(217\) −0.214606 −0.0145684
\(218\) −1.85311 + 0.674476i −0.125508 + 0.0456813i
\(219\) 0 0
\(220\) 12.1197 10.1697i 0.817112 0.685638i
\(221\) 0.921898 + 5.22835i 0.0620136 + 0.351697i
\(222\) 0 0
\(223\) 7.64543 + 6.41527i 0.511976 + 0.429599i 0.861824 0.507208i \(-0.169322\pi\)
−0.349848 + 0.936806i \(0.613767\pi\)
\(224\) −0.159750 + 0.276696i −0.0106738 + 0.0184875i
\(225\) 0 0
\(226\) 4.81433 + 8.33866i 0.320244 + 0.554679i
\(227\) 3.66786 20.8015i 0.243444 1.38064i −0.580633 0.814165i \(-0.697195\pi\)
0.824078 0.566477i \(-0.191694\pi\)
\(228\) 0 0
\(229\) 21.8767 + 7.96248i 1.44566 + 0.526176i 0.941374 0.337364i \(-0.109535\pi\)
0.504281 + 0.863539i \(0.331757\pi\)
\(230\) 0.481576 + 0.175279i 0.0317542 + 0.0115576i
\(231\) 0 0
\(232\) −0.756973 + 4.29301i −0.0496977 + 0.281850i
\(233\) 13.3621 + 23.1439i 0.875383 + 1.51621i 0.856354 + 0.516390i \(0.172724\pi\)
0.0190296 + 0.999819i \(0.493942\pi\)
\(234\) 0 0
\(235\) 18.3486 31.7808i 1.19693 2.07315i
\(236\) −2.28499 1.91734i −0.148740 0.124808i
\(237\) 0 0
\(238\) −0.0629545 0.357033i −0.00408073 0.0231430i
\(239\) 18.4309 15.4654i 1.19220 1.00037i 0.192379 0.981321i \(-0.438380\pi\)
0.999818 0.0190518i \(-0.00606474\pi\)
\(240\) 0 0
\(241\) 1.40157 0.510130i 0.0902831 0.0328604i −0.296484 0.955038i \(-0.595814\pi\)
0.386767 + 0.922178i \(0.373592\pi\)
\(242\) −8.82079 −0.567022
\(243\) 0 0
\(244\) −3.49464 −0.223721
\(245\) −23.0347 + 8.38394i −1.47163 + 0.535630i
\(246\) 0 0
\(247\) −6.65855 + 5.58719i −0.423674 + 0.355504i
\(248\) −0.116638 0.661487i −0.00740653 0.0420045i
\(249\) 0 0
\(250\) 7.15592 + 6.00453i 0.452580 + 0.379760i
\(251\) 7.28748 12.6223i 0.459982 0.796711i −0.538978 0.842320i \(-0.681189\pi\)
0.998959 + 0.0456086i \(0.0145227\pi\)
\(252\) 0 0
\(253\) −0.321019 0.556021i −0.0201823 0.0349568i
\(254\) −0.0276465 + 0.156791i −0.00173469 + 0.00983794i
\(255\) 0 0
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −10.3598 3.77064i −0.646224 0.235206i −0.00194649 0.999998i \(-0.500620\pi\)
−0.644277 + 0.764792i \(0.722842\pi\)
\(258\) 0 0
\(259\) −0.421030 + 2.38778i −0.0261616 + 0.148370i
\(260\) −8.31337 14.3992i −0.515573 0.892999i
\(261\) 0 0
\(262\) 4.74292 8.21497i 0.293018 0.507523i
\(263\) 10.0659 + 8.44626i 0.620688 + 0.520819i 0.898020 0.439955i \(-0.145006\pi\)
−0.277332 + 0.960774i \(0.589450\pi\)
\(264\) 0 0
\(265\) 0.497100 + 2.81919i 0.0305366 + 0.173182i
\(266\) 0.454698 0.381537i 0.0278793 0.0233935i
\(267\) 0 0
\(268\) −6.99437 + 2.54574i −0.427249 + 0.155506i
\(269\) 10.3086 0.628528 0.314264 0.949336i \(-0.398242\pi\)
0.314264 + 0.949336i \(0.398242\pi\)
\(270\) 0 0
\(271\) 1.01454 0.0616288 0.0308144 0.999525i \(-0.490190\pi\)
0.0308144 + 0.999525i \(0.490190\pi\)
\(272\) 1.06628 0.388093i 0.0646525 0.0235316i
\(273\) 0 0
\(274\) 8.96989 7.52663i 0.541891 0.454700i
\(275\) −5.89764 33.4472i −0.355641 2.01694i
\(276\) 0 0
\(277\) −8.29755 6.96247i −0.498552 0.418334i 0.358528 0.933519i \(-0.383279\pi\)
−0.857079 + 0.515185i \(0.827723\pi\)
\(278\) −2.62513 + 4.54686i −0.157445 + 0.272703i
\(279\) 0 0
\(280\) 0.567702 + 0.983289i 0.0339267 + 0.0587628i
\(281\) 1.47197 8.34795i 0.0878103 0.497997i −0.908904 0.417004i \(-0.863080\pi\)
0.996715 0.0809924i \(-0.0258089\pi\)
\(282\) 0 0
\(283\) −5.92408 2.15619i −0.352150 0.128172i 0.159887 0.987135i \(-0.448887\pi\)
−0.512037 + 0.858963i \(0.671109\pi\)
\(284\) −7.61015 2.76987i −0.451580 0.164362i
\(285\) 0 0
\(286\) −3.61709 + 20.5135i −0.213883 + 1.21299i
\(287\) −0.347824 0.602448i −0.0205314 0.0355614i
\(288\) 0 0
\(289\) 7.85622 13.6074i 0.462130 0.800434i
\(290\) 11.8671 + 9.95764i 0.696857 + 0.584733i
\(291\) 0 0
\(292\) 2.53549 + 14.3795i 0.148378 + 0.841495i
\(293\) 1.86383 1.56394i 0.108886 0.0913662i −0.586719 0.809790i \(-0.699581\pi\)
0.695605 + 0.718424i \(0.255136\pi\)
\(294\) 0 0
\(295\) −9.96083 + 3.62544i −0.579942 + 0.211082i
\(296\) −7.58877 −0.441088
\(297\) 0 0
\(298\) −16.2922 −0.943784
\(299\) −0.634037 + 0.230771i −0.0366673 + 0.0133458i
\(300\) 0 0
\(301\) 1.73718 1.45767i 0.100129 0.0840184i
\(302\) 2.71203 + 15.3807i 0.156060 + 0.885058i
\(303\) 0 0
\(304\) 1.42315 + 1.19417i 0.0816233 + 0.0684901i
\(305\) −6.20942 + 10.7550i −0.355550 + 0.615831i
\(306\) 0 0
\(307\) 11.8629 + 20.5471i 0.677050 + 1.17269i 0.975865 + 0.218374i \(0.0700754\pi\)
−0.298815 + 0.954311i \(0.596591\pi\)
\(308\) 0.247003 1.40083i 0.0140743 0.0798194i
\(309\) 0 0
\(310\) −2.24303 0.816395i −0.127395 0.0463681i
\(311\) −10.1493 3.69403i −0.575511 0.209469i 0.0378338 0.999284i \(-0.487954\pi\)
−0.613345 + 0.789815i \(0.710176\pi\)
\(312\) 0 0
\(313\) −2.75948 + 15.6498i −0.155975 + 0.884577i 0.801914 + 0.597439i \(0.203815\pi\)
−0.957889 + 0.287138i \(0.907296\pi\)
\(314\) 8.81577 + 15.2694i 0.497503 + 0.861700i
\(315\) 0 0
\(316\) 6.29350 10.9007i 0.354037 0.613210i
\(317\) 2.47819 + 2.07944i 0.139189 + 0.116793i 0.709724 0.704480i \(-0.248820\pi\)
−0.570535 + 0.821273i \(0.693264\pi\)
\(318\) 0 0
\(319\) −3.37009 19.1127i −0.188689 1.07011i
\(320\) −2.72228 + 2.28426i −0.152180 + 0.127694i
\(321\) 0 0
\(322\) 0.0432970 0.0157588i 0.00241285 0.000878205i
\(323\) −2.10805 −0.117295
\(324\) 0 0
\(325\) −35.6925 −1.97986
\(326\) −14.9224 + 5.43131i −0.826475 + 0.300812i
\(327\) 0 0
\(328\) 1.66790 1.39954i 0.0920946 0.0772765i
\(329\) −0.572924 3.24922i −0.0315863 0.179135i
\(330\) 0 0
\(331\) −13.5311 11.3540i −0.743739 0.624071i 0.190100 0.981765i \(-0.439119\pi\)
−0.933839 + 0.357693i \(0.883563\pi\)
\(332\) −2.70681 + 4.68834i −0.148556 + 0.257306i
\(333\) 0 0
\(334\) 6.78921 + 11.7593i 0.371489 + 0.643438i
\(335\) −4.59316 + 26.0491i −0.250951 + 1.42321i
\(336\) 0 0
\(337\) 9.90706 + 3.60588i 0.539672 + 0.196425i 0.597452 0.801905i \(-0.296180\pi\)
−0.0577798 + 0.998329i \(0.518402\pi\)
\(338\) 8.35441 + 3.04076i 0.454420 + 0.165395i
\(339\) 0 0
\(340\) 0.700218 3.97113i 0.0379746 0.215365i
\(341\) 1.49520 + 2.58977i 0.0809699 + 0.140244i
\(342\) 0 0
\(343\) −2.22020 + 3.84550i −0.119879 + 0.207637i
\(344\) 5.43716 + 4.56232i 0.293152 + 0.245984i
\(345\) 0 0
\(346\) 1.11906 + 6.34650i 0.0601610 + 0.341190i
\(347\) −24.9000 + 20.8936i −1.33670 + 1.12163i −0.354243 + 0.935153i \(0.615261\pi\)
−0.982460 + 0.186473i \(0.940294\pi\)
\(348\) 0 0
\(349\) 18.8599 6.86444i 1.00955 0.367445i 0.216289 0.976329i \(-0.430605\pi\)
0.793259 + 0.608884i \(0.208383\pi\)
\(350\) 2.43736 0.130282
\(351\) 0 0
\(352\) 4.45206 0.237295
\(353\) 10.3705 3.77455i 0.551966 0.200899i −0.0509539 0.998701i \(-0.516226\pi\)
0.602920 + 0.797802i \(0.294004\pi\)
\(354\) 0 0
\(355\) −22.0465 + 18.4992i −1.17011 + 0.981837i
\(356\) −0.877354 4.97572i −0.0464997 0.263713i
\(357\) 0 0
\(358\) −9.58494 8.04272i −0.506580 0.425071i
\(359\) −1.96044 + 3.39557i −0.103468 + 0.179212i −0.913111 0.407711i \(-0.866327\pi\)
0.809643 + 0.586922i \(0.199661\pi\)
\(360\) 0 0
\(361\) 7.77430 + 13.4655i 0.409174 + 0.708710i
\(362\) −0.0528764 + 0.299877i −0.00277912 + 0.0157612i
\(363\) 0 0
\(364\) −1.40471 0.511272i −0.0736268 0.0267980i
\(365\) 48.7591 + 17.7469i 2.55217 + 0.928914i
\(366\) 0 0
\(367\) 5.06206 28.7084i 0.264237 1.49856i −0.506961 0.861969i \(-0.669231\pi\)
0.771198 0.636595i \(-0.219658\pi\)
\(368\) 0.0721058 + 0.124891i 0.00375878 + 0.00651039i
\(369\) 0 0
\(370\) −13.4840 + 23.3550i −0.701001 + 1.21417i
\(371\) 0.197161 + 0.165438i 0.0102361 + 0.00858909i
\(372\) 0 0
\(373\) 1.08909 + 6.17653i 0.0563909 + 0.319809i 0.999935 0.0114395i \(-0.00364140\pi\)
−0.943544 + 0.331248i \(0.892530\pi\)
\(374\) −3.86989 + 3.24722i −0.200107 + 0.167910i
\(375\) 0 0
\(376\) 9.70378 3.53189i 0.500434 0.182143i
\(377\) −20.3957 −1.05043
\(378\) 0 0
\(379\) −26.9562 −1.38465 −0.692324 0.721587i \(-0.743413\pi\)
−0.692324 + 0.721587i \(0.743413\pi\)
\(380\) 6.20385 2.25802i 0.318251 0.115834i
\(381\) 0 0
\(382\) −11.0255 + 9.25146i −0.564111 + 0.473346i
\(383\) 0.565446 + 3.20680i 0.0288929 + 0.163860i 0.995840 0.0911163i \(-0.0290435\pi\)
−0.966947 + 0.254976i \(0.917932\pi\)
\(384\) 0 0
\(385\) −3.87226 3.24922i −0.197349 0.165595i
\(386\) 1.52531 2.64192i 0.0776364 0.134470i
\(387\) 0 0
\(388\) −9.33706 16.1723i −0.474018 0.821022i
\(389\) −0.241315 + 1.36857i −0.0122352 + 0.0693891i −0.990314 0.138846i \(-0.955661\pi\)
0.978079 + 0.208235i \(0.0667719\pi\)
\(390\) 0 0
\(391\) −0.153770 0.0559675i −0.00777646 0.00283040i
\(392\) −6.48192 2.35923i −0.327387 0.119159i
\(393\) 0 0
\(394\) 3.86614 21.9260i 0.194773 1.10461i
\(395\) −22.3651 38.7375i −1.12531 1.94909i
\(396\) 0 0
\(397\) −1.07010 + 1.85347i −0.0537069 + 0.0930230i −0.891629 0.452767i \(-0.850437\pi\)
0.837922 + 0.545790i \(0.183770\pi\)
\(398\) −18.8167 15.7890i −0.943193 0.791433i
\(399\) 0 0
\(400\) 1.32470 + 7.51276i 0.0662351 + 0.375638i
\(401\) 6.55222 5.49796i 0.327202 0.274555i −0.464357 0.885648i \(-0.653714\pi\)
0.791559 + 0.611093i \(0.209270\pi\)
\(402\) 0 0
\(403\) 2.95314 1.07486i 0.147107 0.0535424i
\(404\) 2.41967 0.120383
\(405\) 0 0
\(406\) 1.39278 0.0691225
\(407\) 31.7481 11.5554i 1.57369 0.572778i
\(408\) 0 0
\(409\) 20.8915 17.5300i 1.03302 0.866804i 0.0418096 0.999126i \(-0.486688\pi\)
0.991207 + 0.132322i \(0.0422433\pi\)
\(410\) −1.34359 7.61986i −0.0663550 0.376318i
\(411\) 0 0
\(412\) 1.52853 + 1.28259i 0.0753052 + 0.0631885i
\(413\) −0.476511 + 0.825342i −0.0234476 + 0.0406124i
\(414\) 0 0
\(415\) 9.61916 + 16.6609i 0.472186 + 0.817850i
\(416\) 0.812454 4.60766i 0.0398338 0.225909i
\(417\) 0 0
\(418\) −7.77219 2.82885i −0.380150 0.138363i
\(419\) 15.0495 + 5.47757i 0.735216 + 0.267597i 0.682371 0.731006i \(-0.260949\pi\)
0.0528448 + 0.998603i \(0.483171\pi\)
\(420\) 0 0
\(421\) −3.15120 + 17.8713i −0.153580 + 0.870995i 0.806493 + 0.591244i \(0.201363\pi\)
−0.960073 + 0.279751i \(0.909748\pi\)
\(422\) −1.50965 2.61480i −0.0734888 0.127286i
\(423\) 0 0
\(424\) −0.402777 + 0.697630i −0.0195606 + 0.0338799i
\(425\) −6.63111 5.56416i −0.321656 0.269901i
\(426\) 0 0
\(427\) 0.193885 + 1.09958i 0.00938276 + 0.0532123i
\(428\) −6.79537 + 5.70199i −0.328467 + 0.275616i
\(429\) 0 0
\(430\) 23.7019 8.62677i 1.14301 0.416020i
\(431\) −2.13698 −0.102935 −0.0514673 0.998675i \(-0.516390\pi\)
−0.0514673 + 0.998675i \(0.516390\pi\)
\(432\) 0 0
\(433\) 25.1733 1.20975 0.604876 0.796320i \(-0.293223\pi\)
0.604876 + 0.796320i \(0.293223\pi\)
\(434\) −0.201664 + 0.0733996i −0.00968017 + 0.00352329i
\(435\) 0 0
\(436\) −1.51067 + 1.26760i −0.0723478 + 0.0607071i
\(437\) −0.0465230 0.263845i −0.00222550 0.0126214i
\(438\) 0 0
\(439\) 19.8037 + 16.6173i 0.945179 + 0.793099i 0.978479 0.206346i \(-0.0661573\pi\)
−0.0333002 + 0.999445i \(0.510602\pi\)
\(440\) 7.91059 13.7015i 0.377123 0.653196i
\(441\) 0 0
\(442\) 2.65450 + 4.59773i 0.126262 + 0.218692i
\(443\) −2.42041 + 13.7268i −0.114997 + 0.652181i 0.871755 + 0.489943i \(0.162982\pi\)
−0.986752 + 0.162238i \(0.948129\pi\)
\(444\) 0 0
\(445\) −16.8721 6.14094i −0.799814 0.291108i
\(446\) 9.37850 + 3.41350i 0.444085 + 0.161634i
\(447\) 0 0
\(448\) −0.0554807 + 0.314647i −0.00262122 + 0.0148657i
\(449\) 14.5769 + 25.2479i 0.687927 + 1.19152i 0.972507 + 0.232872i \(0.0748123\pi\)
−0.284581 + 0.958652i \(0.591854\pi\)
\(450\) 0 0
\(451\) −4.84672 + 8.39476i −0.228223 + 0.395294i
\(452\) 7.37598 + 6.18918i 0.346937 + 0.291114i
\(453\) 0 0
\(454\) −3.66786 20.8015i −0.172141 0.976261i
\(455\) −4.06943 + 3.41465i −0.190778 + 0.160081i
\(456\) 0 0
\(457\) −22.3630 + 8.13945i −1.04609 + 0.380747i −0.807188 0.590295i \(-0.799011\pi\)
−0.238907 + 0.971042i \(0.576789\pi\)
\(458\) 23.2807 1.08784
\(459\) 0 0
\(460\) 0.512482 0.0238946
\(461\) 28.9550 10.5388i 1.34857 0.490839i 0.436069 0.899913i \(-0.356370\pi\)
0.912501 + 0.409074i \(0.134148\pi\)
\(462\) 0 0
\(463\) 27.6849 23.2304i 1.28663 1.07961i 0.294334 0.955703i \(-0.404902\pi\)
0.992294 0.123907i \(-0.0395424\pi\)
\(464\) 0.756973 + 4.29301i 0.0351416 + 0.199298i
\(465\) 0 0
\(466\) 20.4720 + 17.1780i 0.948347 + 0.795758i
\(467\) −18.4877 + 32.0217i −0.855509 + 1.48179i 0.0206626 + 0.999787i \(0.493422\pi\)
−0.876172 + 0.481999i \(0.839911\pi\)
\(468\) 0 0
\(469\) 1.18906 + 2.05952i 0.0549058 + 0.0950996i
\(470\) 6.37241 36.1397i 0.293937 1.66700i
\(471\) 0 0
\(472\) −2.80296 1.02019i −0.129017 0.0469582i
\(473\) −29.6937 10.8076i −1.36532 0.496935i
\(474\) 0 0
\(475\) 2.46102 13.9571i 0.112919 0.640398i
\(476\) −0.181270 0.313969i −0.00830850 0.0143908i
\(477\) 0 0
\(478\) 12.0299 20.8365i 0.550236 0.953037i
\(479\) −29.4015 24.6708i −1.34339 1.12724i −0.980741 0.195311i \(-0.937429\pi\)
−0.362647 0.931926i \(-0.618127\pi\)
\(480\) 0 0
\(481\) −6.16553 34.9664i −0.281124 1.59433i
\(482\) 1.14257 0.958731i 0.0520427 0.0436690i
\(483\) 0 0
\(484\) −8.28884 + 3.01689i −0.376765 + 0.137131i
\(485\) −66.3619 −3.01334
\(486\) 0 0
\(487\) 34.3088 1.55468 0.777339 0.629082i \(-0.216569\pi\)
0.777339 + 0.629082i \(0.216569\pi\)
\(488\) −3.28389 + 1.19524i −0.148655 + 0.0541059i
\(489\) 0 0
\(490\) −18.7781 + 15.7567i −0.848306 + 0.711813i
\(491\) 3.02281 + 17.1432i 0.136417 + 0.773661i 0.973862 + 0.227139i \(0.0729373\pi\)
−0.837445 + 0.546522i \(0.815952\pi\)
\(492\) 0 0
\(493\) −3.78921 3.17952i −0.170657 0.143199i
\(494\) −4.34606 + 7.52760i −0.195539 + 0.338683i
\(495\) 0 0
\(496\) −0.335846 0.581702i −0.0150799 0.0261192i
\(497\) −0.449314 + 2.54819i −0.0201545 + 0.114302i
\(498\) 0 0
\(499\) −24.6982 8.98939i −1.10564 0.402421i −0.276248 0.961086i \(-0.589091\pi\)
−0.829393 + 0.558666i \(0.811313\pi\)
\(500\) 8.77804 + 3.19494i 0.392566 + 0.142882i
\(501\) 0 0
\(502\) 2.53091 14.3535i 0.112960 0.640629i
\(503\) −9.08930 15.7431i −0.405272 0.701952i 0.589081 0.808074i \(-0.299490\pi\)
−0.994353 + 0.106122i \(0.966157\pi\)
\(504\) 0 0
\(505\) 4.29937 7.44672i 0.191319 0.331375i
\(506\) −0.491830 0.412694i −0.0218645 0.0183465i
\(507\) 0 0
\(508\) 0.0276465 + 0.156791i 0.00122661 + 0.00695647i
\(509\) 18.8746 15.8376i 0.836600 0.701991i −0.120196 0.992750i \(-0.538352\pi\)
0.956796 + 0.290759i \(0.0939078\pi\)
\(510\) 0 0
\(511\) 4.38379 1.59557i 0.193927 0.0705838i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −11.0246 −0.486275
\(515\) 6.66321 2.42521i 0.293616 0.106868i
\(516\) 0 0
\(517\) −35.2184 + 29.5517i −1.54890 + 1.29968i
\(518\) 0.421030 + 2.38778i 0.0184990 + 0.104913i
\(519\) 0 0
\(520\) −12.7368 10.6875i −0.558547 0.468676i
\(521\) 15.0065 25.9921i 0.657449 1.13873i −0.323825 0.946117i \(-0.604969\pi\)
0.981274 0.192618i \(-0.0616977\pi\)
\(522\) 0 0
\(523\) 13.6719 + 23.6804i 0.597829 + 1.03547i 0.993141 + 0.116924i \(0.0373033\pi\)
−0.395312 + 0.918547i \(0.629363\pi\)
\(524\) 1.64720 9.34172i 0.0719582 0.408095i
\(525\) 0 0
\(526\) 12.3476 + 4.49416i 0.538381 + 0.195955i
\(527\) 0.716210 + 0.260679i 0.0311986 + 0.0113554i
\(528\) 0 0
\(529\) −3.99030 + 22.6301i −0.173491 + 0.983917i
\(530\) 1.43134 + 2.47916i 0.0621735 + 0.107688i
\(531\) 0 0
\(532\) 0.296783 0.514044i 0.0128672 0.0222866i
\(533\) 7.80368 + 6.54807i 0.338015 + 0.283628i
\(534\) 0 0
\(535\) 5.47404 + 31.0448i 0.236663 + 1.34218i
\(536\) −5.70186 + 4.78443i −0.246283 + 0.206656i
\(537\) 0 0
\(538\) 9.68695 3.52576i 0.417634 0.152006i
\(539\) 30.7099 1.32277
\(540\) 0 0
\(541\) 8.65632 0.372164 0.186082 0.982534i \(-0.440421\pi\)
0.186082 + 0.982534i \(0.440421\pi\)
\(542\) 0.953353 0.346992i 0.0409500 0.0149046i
\(543\) 0 0
\(544\) 0.869237 0.729376i 0.0372682 0.0312718i
\(545\) 1.21692 + 6.90152i 0.0521273 + 0.295629i
\(546\) 0 0
\(547\) 21.1005 + 17.7055i 0.902194 + 0.757031i 0.970618 0.240625i \(-0.0773525\pi\)
−0.0684237 + 0.997656i \(0.521797\pi\)
\(548\) 5.85468 10.1406i 0.250100 0.433185i
\(549\) 0 0
\(550\) −16.9816 29.4130i −0.724097 1.25417i
\(551\) 1.40630 7.97552i 0.0599104 0.339769i
\(552\) 0 0
\(553\) −3.77903 1.37545i −0.160701 0.0584903i
\(554\) −10.1785 3.70465i −0.432441 0.157396i
\(555\) 0 0
\(556\) −0.911699 + 5.17050i −0.0386647 + 0.219278i
\(557\) −13.0903 22.6730i −0.554653 0.960687i −0.997930 0.0643022i \(-0.979518\pi\)
0.443278 0.896384i \(-0.353816\pi\)
\(558\) 0 0
\(559\) −16.6042 + 28.7592i −0.702281 + 1.21639i
\(560\) 0.869770 + 0.729824i 0.0367545 + 0.0308407i
\(561\) 0 0
\(562\) −1.47197 8.34795i −0.0620912 0.352137i
\(563\) 3.04293 2.55332i 0.128244 0.107610i −0.576410 0.817161i \(-0.695547\pi\)
0.704654 + 0.709551i \(0.251102\pi\)
\(564\) 0 0
\(565\) 32.1536 11.7030i 1.35271 0.492347i
\(566\) −6.30428 −0.264988
\(567\) 0 0
\(568\) −8.09856 −0.339808
\(569\) −38.0492 + 13.8488i −1.59511 + 0.580571i −0.978418 0.206636i \(-0.933748\pi\)
−0.616688 + 0.787207i \(0.711526\pi\)
\(570\) 0 0
\(571\) 29.3406 24.6197i 1.22787 1.03030i 0.229493 0.973310i \(-0.426293\pi\)
0.998375 0.0569933i \(-0.0181514\pi\)
\(572\) 3.61709 + 20.5135i 0.151238 + 0.857714i
\(573\) 0 0
\(574\) −0.532897 0.447153i −0.0222427 0.0186638i
\(575\) 0.550070 0.952749i 0.0229395 0.0397324i
\(576\) 0 0
\(577\) −4.13928 7.16944i −0.172320 0.298468i 0.766910 0.641754i \(-0.221793\pi\)
−0.939231 + 0.343287i \(0.888460\pi\)
\(578\) 2.72844 15.4737i 0.113488 0.643622i
\(579\) 0 0
\(580\) 14.5571 + 5.29835i 0.604450 + 0.220002i
\(581\) 1.62535 + 0.591578i 0.0674308 + 0.0245428i
\(582\) 0 0
\(583\) 0.622767 3.53189i 0.0257924 0.146276i
\(584\) 7.30065 + 12.6451i 0.302103 + 0.523258i
\(585\) 0 0
\(586\) 1.21653 2.10709i 0.0502543 0.0870430i
\(587\) 10.6808 + 8.96228i 0.440845 + 0.369913i 0.836025 0.548691i \(-0.184874\pi\)
−0.395181 + 0.918603i \(0.629318\pi\)
\(588\) 0 0
\(589\) 0.216689 + 1.22891i 0.00892853 + 0.0506362i
\(590\) −8.12014 + 6.81361i −0.334301 + 0.280512i
\(591\) 0 0
\(592\) −7.13111 + 2.59551i −0.293087 + 0.106675i
\(593\) 41.2342 1.69329 0.846644 0.532160i \(-0.178620\pi\)
0.846644 + 0.532160i \(0.178620\pi\)
\(594\) 0 0
\(595\) −1.28835 −0.0528173
\(596\) −15.3097 + 5.57227i −0.627110 + 0.228249i
\(597\) 0 0
\(598\) −0.516872 + 0.433707i −0.0211365 + 0.0177356i
\(599\) 0.544602 + 3.08859i 0.0222518 + 0.126196i 0.993910 0.110193i \(-0.0351470\pi\)
−0.971658 + 0.236390i \(0.924036\pi\)
\(600\) 0 0
\(601\) −26.6855 22.3918i −1.08853 0.913382i −0.0919256 0.995766i \(-0.529302\pi\)
−0.996601 + 0.0823839i \(0.973747\pi\)
\(602\) 1.13386 1.96391i 0.0462128 0.0800429i
\(603\) 0 0
\(604\) 7.80897 + 13.5255i 0.317742 + 0.550346i
\(605\) −5.44323 + 30.8701i −0.221299 + 1.25505i
\(606\) 0 0
\(607\) 0.726574 + 0.264451i 0.0294907 + 0.0107338i 0.356723 0.934210i \(-0.383894\pi\)
−0.327233 + 0.944944i \(0.606116\pi\)
\(608\) 1.74575 + 0.635402i 0.0707997 + 0.0257690i
\(609\) 0 0
\(610\) −2.15651 + 12.2302i −0.0873145 + 0.495185i
\(611\) 24.1576 + 41.8422i 0.977312 + 1.69275i
\(612\) 0 0
\(613\) −6.99919 + 12.1230i −0.282695 + 0.489642i −0.972048 0.234784i \(-0.924562\pi\)
0.689353 + 0.724426i \(0.257895\pi\)
\(614\) 18.1750 + 15.2506i 0.733483 + 0.615465i
\(615\) 0 0
\(616\) −0.247003 1.40083i −0.00995205 0.0564409i
\(617\) −8.97302 + 7.52926i −0.361240 + 0.303117i −0.805285 0.592888i \(-0.797988\pi\)
0.444045 + 0.896005i \(0.353543\pi\)
\(618\) 0 0
\(619\) −45.1425 + 16.4305i −1.81443 + 0.660398i −0.818073 + 0.575114i \(0.804958\pi\)
−0.996357 + 0.0852845i \(0.972820\pi\)
\(620\) −2.38698 −0.0958634
\(621\) 0 0
\(622\) −10.8006 −0.433065
\(623\) −1.51692 + 0.552114i −0.0607741 + 0.0221200i
\(624\) 0 0
\(625\) −3.78956 + 3.17982i −0.151583 + 0.127193i
\(626\) 2.75948 + 15.6498i 0.110291 + 0.625490i
\(627\) 0 0
\(628\) 13.5065 + 11.3333i 0.538970 + 0.452249i
\(629\) 4.30552 7.45738i 0.171672 0.297345i
\(630\) 0 0
\(631\) −19.7725 34.2469i −0.787130 1.36335i −0.927719 0.373280i \(-0.878233\pi\)
0.140589 0.990068i \(-0.455100\pi\)
\(632\) 2.18571 12.3958i 0.0869429 0.493078i
\(633\) 0 0
\(634\) 3.03994 + 1.10645i 0.120732 + 0.0439427i
\(635\) 0.531660 + 0.193508i 0.0210983 + 0.00767915i
\(636\) 0 0
\(637\) 5.60424 31.7832i 0.222048 1.25930i
\(638\) −9.70378 16.8074i −0.384176 0.665413i
\(639\) 0 0
\(640\) −1.77684 + 3.07758i −0.0702358 + 0.121652i
\(641\) −0.506596 0.425085i −0.0200093 0.0167898i 0.632728 0.774374i \(-0.281935\pi\)
−0.652737 + 0.757584i \(0.726380\pi\)
\(642\) 0 0
\(643\) 0.314901 + 1.78589i 0.0124185 + 0.0704288i 0.990387 0.138323i \(-0.0441711\pi\)
−0.977969 + 0.208752i \(0.933060\pi\)
\(644\) 0.0352961 0.0296169i 0.00139086 0.00116707i
\(645\) 0 0
\(646\) −1.98092 + 0.720997i −0.0779383 + 0.0283672i
\(647\) −4.13765 −0.162668 −0.0813339 0.996687i \(-0.525918\pi\)
−0.0813339 + 0.996687i \(0.525918\pi\)
\(648\) 0 0
\(649\) 13.2798 0.521278
\(650\) −33.5399 + 12.2075i −1.31554 + 0.478819i
\(651\) 0 0
\(652\) −12.1648 + 10.2075i −0.476412 + 0.399757i
\(653\) −4.66662 26.4657i −0.182619 1.03568i −0.928976 0.370139i \(-0.879310\pi\)
0.746357 0.665545i \(-0.231801\pi\)
\(654\) 0 0
\(655\) −25.8231 21.6681i −1.00899 0.846644i
\(656\) 1.08865 1.88559i 0.0425045 0.0736200i
\(657\) 0 0
\(658\) −1.64967 2.85731i −0.0643108 0.111390i
\(659\) −2.51054 + 14.2380i −0.0977969 + 0.554634i 0.896058 + 0.443938i \(0.146419\pi\)
−0.993854 + 0.110696i \(0.964692\pi\)
\(660\) 0 0
\(661\) −20.9378 7.62074i −0.814387 0.296413i −0.0989522 0.995092i \(-0.531549\pi\)
−0.715435 + 0.698680i \(0.753771\pi\)
\(662\) −16.5984 6.04133i −0.645116 0.234803i
\(663\) 0 0
\(664\) −0.940067 + 5.33138i −0.0364817 + 0.206898i
\(665\) −1.05467 1.82675i −0.0408985 0.0708382i
\(666\) 0 0
\(667\) 0.314326 0.544429i 0.0121708 0.0210804i
\(668\) 10.4017 + 8.72804i 0.402453 + 0.337698i
\(669\) 0 0
\(670\) 4.59316 + 26.0491i 0.177449 + 1.00636i
\(671\) 11.9184 10.0007i 0.460104 0.386073i
\(672\) 0 0
\(673\) −23.4002 + 8.51699i −0.902012 + 0.328306i −0.751059 0.660235i \(-0.770457\pi\)
−0.150954 + 0.988541i \(0.548234\pi\)
\(674\) 10.5429 0.406096
\(675\) 0 0
\(676\) 8.89058 0.341945
\(677\) 7.50239 2.73065i 0.288340 0.104947i −0.193801 0.981041i \(-0.562082\pi\)
0.482141 + 0.876094i \(0.339859\pi\)
\(678\) 0 0
\(679\) −4.57053 + 3.83513i −0.175401 + 0.147179i
\(680\) −0.700218 3.97113i −0.0268521 0.152286i
\(681\) 0 0
\(682\) 2.29079 + 1.92220i 0.0877187 + 0.0736048i
\(683\) −17.5306 + 30.3639i −0.670789 + 1.16184i 0.306891 + 0.951745i \(0.400711\pi\)
−0.977681 + 0.210097i \(0.932622\pi\)
\(684\) 0 0
\(685\) −20.8057 36.0365i −0.794944 1.37688i
\(686\) −0.771067 + 4.37294i −0.0294395 + 0.166960i
\(687\) 0 0
\(688\) 6.66967 + 2.42756i 0.254279 + 0.0925498i
\(689\) −3.54168 1.28907i −0.134927 0.0491095i
\(690\) 0 0
\(691\) −0.344177 + 1.95193i −0.0130931 + 0.0742548i −0.990654 0.136397i \(-0.956448\pi\)
0.977561 + 0.210652i \(0.0675587\pi\)
\(692\) 3.22220 + 5.58102i 0.122490 + 0.212159i
\(693\) 0 0
\(694\) −16.2523 + 28.1499i −0.616930 + 1.06855i
\(695\) 14.2927 + 11.9930i 0.542152 + 0.454920i
\(696\) 0 0
\(697\) 0.429014 + 2.43306i 0.0162501 + 0.0921587i
\(698\) 15.3747 12.9009i 0.581942 0.488308i
\(699\) 0 0
\(700\) 2.29037 0.833627i 0.0865679 0.0315081i
\(701\) −42.8694 −1.61916 −0.809578 0.587013i \(-0.800304\pi\)
−0.809578 + 0.587013i \(0.800304\pi\)
\(702\) 0 0
\(703\) 14.0984 0.531730
\(704\) 4.18356 1.52269i 0.157674 0.0573886i
\(705\) 0 0
\(706\) 8.45411 7.09384i 0.318174 0.266980i
\(707\) −0.134245 0.761342i −0.00504881 0.0286332i
\(708\) 0 0
\(709\) 26.9016 + 22.5731i 1.01031 + 0.847752i 0.988379 0.152008i \(-0.0485738\pi\)
0.0219320 + 0.999759i \(0.493018\pi\)
\(710\) −14.3898 + 24.9239i −0.540041 + 0.935379i
\(711\) 0 0
\(712\) −2.52624 4.37558i −0.0946748 0.163982i
\(713\) −0.0168206 + 0.0953942i −0.000629935 + 0.00357254i
\(714\) 0 0
\(715\) 69.5590 + 25.3174i 2.60136 + 0.946818i
\(716\) −11.7577 4.27944i −0.439405 0.159930i
\(717\) 0 0
\(718\) −0.680852 + 3.86130i −0.0254092 + 0.144103i
\(719\) 7.52422 + 13.0323i 0.280606 + 0.486024i 0.971534 0.236899i \(-0.0761312\pi\)
−0.690928 + 0.722924i \(0.742798\pi\)
\(720\) 0 0
\(721\) 0.318758 0.552105i 0.0118712 0.0205615i
\(722\) 11.9109 + 9.99445i 0.443279 + 0.371955i
\(723\) 0 0
\(724\) 0.0528764 + 0.299877i 0.00196513 + 0.0111448i
\(725\) 25.4749 21.3760i 0.946113 0.793883i
\(726\) 0 0
\(727\) −13.7436 + 5.00226i −0.509721 + 0.185523i −0.584061 0.811710i \(-0.698537\pi\)
0.0743399 + 0.997233i \(0.476315\pi\)
\(728\) −1.49486 −0.0554032
\(729\) 0 0
\(730\) 51.8884 1.92048
\(731\) −7.56813 + 2.75457i −0.279917 + 0.101882i
\(732\) 0 0
\(733\) 11.5481 9.69000i 0.426539 0.357908i −0.404105 0.914713i \(-0.632417\pi\)
0.830644 + 0.556804i \(0.187973\pi\)
\(734\) −5.06206 28.7084i −0.186844 1.05964i
\(735\) 0 0
\(736\) 0.110473 + 0.0926974i 0.00407207 + 0.00341687i
\(737\) 16.5689 28.6981i 0.610322 1.05711i
\(738\) 0 0
\(739\) −23.9031 41.4014i −0.879290 1.52297i −0.852122 0.523343i \(-0.824685\pi\)
−0.0271676 0.999631i \(-0.508649\pi\)
\(740\) −4.68296 + 26.5584i −0.172149 + 0.976305i
\(741\) 0 0
\(742\) 0.241854 + 0.0880275i 0.00887873 + 0.00323159i
\(743\) −43.7125 15.9101i −1.60366 0.583683i −0.623485 0.781835i \(-0.714284\pi\)
−0.980171 + 0.198152i \(0.936506\pi\)
\(744\) 0 0
\(745\) −10.0538 + 57.0178i −0.368342 + 2.08897i
\(746\) 3.13591 + 5.43155i 0.114814 + 0.198863i
\(747\) 0 0
\(748\) −2.52589 + 4.37497i −0.0923558 + 0.159965i
\(749\) 2.17113 + 1.82179i 0.0793312 + 0.0665668i
\(750\) 0 0
\(751\) 0.306626 + 1.73897i 0.0111890 + 0.0634557i 0.989891 0.141830i \(-0.0452987\pi\)
−0.978702 + 0.205286i \(0.934188\pi\)
\(752\) 7.91059 6.63778i 0.288470 0.242055i
\(753\) 0 0
\(754\) −19.1657 + 6.97575i −0.697974 + 0.254042i
\(755\) 55.5012 2.01989
\(756\) 0 0
\(757\) 3.34143 0.121446 0.0607232 0.998155i \(-0.480659\pi\)
0.0607232 + 0.998155i \(0.480659\pi\)
\(758\) −25.3306 + 9.21957i −0.920048 + 0.334870i
\(759\) 0 0
\(760\) 5.05743 4.24369i 0.183452 0.153935i
\(761\) −8.29207 47.0267i −0.300587 1.70472i −0.643581 0.765378i \(-0.722552\pi\)
0.342994 0.939338i \(-0.388559\pi\)
\(762\) 0 0
\(763\) 0.482660 + 0.404999i 0.0174735 + 0.0146620i
\(764\) −7.19635 + 12.4645i −0.260355 + 0.450948i
\(765\) 0 0
\(766\) 1.62814 + 2.82001i 0.0588269 + 0.101891i
\(767\) 2.42343 13.7439i 0.0875049 0.496265i
\(768\) 0 0
\(769\) 6.37595 + 2.32066i 0.229923 + 0.0836850i 0.454412 0.890791i \(-0.349849\pi\)
−0.224490 + 0.974476i \(0.572071\pi\)
\(770\) −4.75004 1.72887i −0.171179 0.0623042i
\(771\) 0 0
\(772\) 0.529736 3.00428i 0.0190656 0.108126i
\(773\) −15.0683 26.0991i −0.541970 0.938720i −0.998791 0.0491615i \(-0.984345\pi\)
0.456820 0.889559i \(-0.348988\pi\)
\(774\) 0 0
\(775\) −2.56205 + 4.43760i −0.0920316 + 0.159403i
\(776\) −14.3052 12.0035i −0.513527 0.430900i
\(777\) 0 0
\(778\) 0.241315 + 1.36857i 0.00865158 + 0.0490655i
\(779\) −3.09862 + 2.60005i −0.111020 + 0.0931565i
\(780\) 0 0