Properties

Label 72.2.i.b.25.2
Level $72$
Weight $2$
Character 72.25
Analytic conductor $0.575$
Analytic rank $0$
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] = [72,2,Mod(25,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.i (of order \(3\), 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: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 72.25
Dual form 72.2.i.b.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.68614 - 0.396143i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-2.18614 + 3.78651i) q^{7} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\) \(q+(1.68614 - 0.396143i) q^{3} +(-1.18614 - 2.05446i) q^{5} +(-2.18614 + 3.78651i) q^{7} +(2.68614 - 1.33591i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.186141 + 0.322405i) q^{13} +(-2.81386 - 2.99422i) q^{15} -5.37228 q^{17} +0.627719 q^{19} +(-2.18614 + 7.25061i) q^{21} +(0.186141 + 0.322405i) q^{23} +(-0.313859 + 0.543620i) q^{25} +(4.00000 - 3.31662i) q^{27} +(2.18614 - 3.78651i) q^{29} +(-3.18614 - 5.51856i) q^{31} +(-0.500000 + 1.65831i) q^{33} +10.3723 q^{35} +8.74456 q^{37} +(0.441578 + 0.469882i) q^{39} +(5.87228 + 10.1711i) q^{41} +(0.872281 - 1.51084i) q^{43} +(-5.93070 - 3.93398i) q^{45} +(-2.18614 + 3.78651i) q^{47} +(-6.05842 - 10.4935i) q^{49} +(-9.05842 + 2.12819i) q^{51} +0.744563 q^{53} +2.37228 q^{55} +(1.05842 - 0.248667i) q^{57} +(-3.50000 - 6.06218i) q^{59} +(-1.18614 + 2.05446i) q^{61} +(-0.813859 + 13.0916i) q^{63} +(0.441578 - 0.764836i) q^{65} +(1.87228 + 3.24289i) q^{67} +(0.441578 + 0.469882i) q^{69} -4.00000 q^{71} -12.1168 q^{73} +(-0.313859 + 1.04095i) q^{75} +(-2.18614 - 3.78651i) q^{77} +(3.18614 - 5.51856i) q^{79} +(5.43070 - 7.17687i) q^{81} +(-4.81386 + 8.33785i) q^{83} +(6.37228 + 11.0371i) q^{85} +(2.18614 - 7.25061i) q^{87} +6.00000 q^{89} -1.62772 q^{91} +(-7.55842 - 8.04290i) q^{93} +(-0.744563 - 1.28962i) q^{95} +(-0.872281 + 1.51084i) q^{97} +(-0.186141 + 2.99422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} + q^{5} - 3 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} + q^{5} - 3 q^{7} + 5 q^{9} - 2 q^{11} - 5 q^{13} - 17 q^{15} - 10 q^{17} + 14 q^{19} - 3 q^{21} - 5 q^{23} - 7 q^{25} + 16 q^{27} + 3 q^{29} - 7 q^{31} - 2 q^{33} + 30 q^{35} + 12 q^{37} + 19 q^{39} + 12 q^{41} - 8 q^{43} + 5 q^{45} - 3 q^{47} - 7 q^{49} - 19 q^{51} - 20 q^{53} - 2 q^{55} - 13 q^{57} - 14 q^{59} + q^{61} - 9 q^{63} + 19 q^{65} - 4 q^{67} + 19 q^{69} - 16 q^{71} - 14 q^{73} - 7 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} - 25 q^{83} + 14 q^{85} + 3 q^{87} + 24 q^{89} - 18 q^{91} - 13 q^{93} + 20 q^{95} + 8 q^{97} + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) 1.68614 0.396143i 0.973494 0.228714i
\(4\) 0 0
\(5\) −1.18614 2.05446i −0.530458 0.918781i −0.999368 0.0355348i \(-0.988687\pi\)
0.468910 0.883246i \(-0.344647\pi\)
\(6\) 0 0
\(7\) −2.18614 + 3.78651i −0.826284 + 1.43117i 0.0746509 + 0.997210i \(0.476216\pi\)
−0.900934 + 0.433955i \(0.857118\pi\)
\(8\) 0 0
\(9\) 2.68614 1.33591i 0.895380 0.445302i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0 0
\(13\) 0.186141 + 0.322405i 0.0516261 + 0.0894191i 0.890684 0.454624i \(-0.150226\pi\)
−0.839057 + 0.544043i \(0.816893\pi\)
\(14\) 0 0
\(15\) −2.81386 2.99422i −0.726535 0.773104i
\(16\) 0 0
\(17\) −5.37228 −1.30297 −0.651485 0.758662i \(-0.725854\pi\)
−0.651485 + 0.758662i \(0.725854\pi\)
\(18\) 0 0
\(19\) 0.627719 0.144009 0.0720043 0.997404i \(-0.477060\pi\)
0.0720043 + 0.997404i \(0.477060\pi\)
\(20\) 0 0
\(21\) −2.18614 + 7.25061i −0.477055 + 1.58221i
\(22\) 0 0
\(23\) 0.186141 + 0.322405i 0.0388130 + 0.0672261i 0.884779 0.466010i \(-0.154309\pi\)
−0.845966 + 0.533236i \(0.820976\pi\)
\(24\) 0 0
\(25\) −0.313859 + 0.543620i −0.0627719 + 0.108724i
\(26\) 0 0
\(27\) 4.00000 3.31662i 0.769800 0.638285i
\(28\) 0 0
\(29\) 2.18614 3.78651i 0.405956 0.703137i −0.588476 0.808515i \(-0.700272\pi\)
0.994432 + 0.105378i \(0.0336052\pi\)
\(30\) 0 0
\(31\) −3.18614 5.51856i −0.572248 0.991162i −0.996335 0.0855407i \(-0.972738\pi\)
0.424087 0.905621i \(-0.360595\pi\)
\(32\) 0 0
\(33\) −0.500000 + 1.65831i −0.0870388 + 0.288675i
\(34\) 0 0
\(35\) 10.3723 1.75324
\(36\) 0 0
\(37\) 8.74456 1.43760 0.718799 0.695218i \(-0.244692\pi\)
0.718799 + 0.695218i \(0.244692\pi\)
\(38\) 0 0
\(39\) 0.441578 + 0.469882i 0.0707091 + 0.0752413i
\(40\) 0 0
\(41\) 5.87228 + 10.1711i 0.917096 + 1.58846i 0.803803 + 0.594896i \(0.202807\pi\)
0.113293 + 0.993562i \(0.463860\pi\)
\(42\) 0 0
\(43\) 0.872281 1.51084i 0.133022 0.230400i −0.791818 0.610757i \(-0.790865\pi\)
0.924840 + 0.380356i \(0.124199\pi\)
\(44\) 0 0
\(45\) −5.93070 3.93398i −0.884097 0.586444i
\(46\) 0 0
\(47\) −2.18614 + 3.78651i −0.318881 + 0.552319i −0.980255 0.197738i \(-0.936640\pi\)
0.661374 + 0.750057i \(0.269974\pi\)
\(48\) 0 0
\(49\) −6.05842 10.4935i −0.865489 1.49907i
\(50\) 0 0
\(51\) −9.05842 + 2.12819i −1.26843 + 0.298007i
\(52\) 0 0
\(53\) 0.744563 0.102274 0.0511368 0.998692i \(-0.483716\pi\)
0.0511368 + 0.998692i \(0.483716\pi\)
\(54\) 0 0
\(55\) 2.37228 0.319878
\(56\) 0 0
\(57\) 1.05842 0.248667i 0.140191 0.0329367i
\(58\) 0 0
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) −1.18614 + 2.05446i −0.151870 + 0.263046i −0.931915 0.362677i \(-0.881863\pi\)
0.780045 + 0.625723i \(0.215196\pi\)
\(62\) 0 0
\(63\) −0.813859 + 13.0916i −0.102537 + 1.64938i
\(64\) 0 0
\(65\) 0.441578 0.764836i 0.0547710 0.0948662i
\(66\) 0 0
\(67\) 1.87228 + 3.24289i 0.228736 + 0.396182i 0.957434 0.288653i \(-0.0932076\pi\)
−0.728698 + 0.684835i \(0.759874\pi\)
\(68\) 0 0
\(69\) 0.441578 + 0.469882i 0.0531597 + 0.0565671i
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −12.1168 −1.41817 −0.709085 0.705123i \(-0.750892\pi\)
−0.709085 + 0.705123i \(0.750892\pi\)
\(74\) 0 0
\(75\) −0.313859 + 1.04095i −0.0362414 + 0.120199i
\(76\) 0 0
\(77\) −2.18614 3.78651i −0.249134 0.431512i
\(78\) 0 0
\(79\) 3.18614 5.51856i 0.358469 0.620886i −0.629236 0.777214i \(-0.716632\pi\)
0.987705 + 0.156328i \(0.0499656\pi\)
\(80\) 0 0
\(81\) 5.43070 7.17687i 0.603411 0.797430i
\(82\) 0 0
\(83\) −4.81386 + 8.33785i −0.528390 + 0.915198i 0.471062 + 0.882100i \(0.343871\pi\)
−0.999452 + 0.0330979i \(0.989463\pi\)
\(84\) 0 0
\(85\) 6.37228 + 11.0371i 0.691171 + 1.19714i
\(86\) 0 0
\(87\) 2.18614 7.25061i 0.234379 0.777347i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −1.62772 −0.170631
\(92\) 0 0
\(93\) −7.55842 8.04290i −0.783772 0.834009i
\(94\) 0 0
\(95\) −0.744563 1.28962i −0.0763905 0.132312i
\(96\) 0 0
\(97\) −0.872281 + 1.51084i −0.0885667 + 0.153402i −0.906906 0.421334i \(-0.861562\pi\)
0.818339 + 0.574736i \(0.194895\pi\)
\(98\) 0 0
\(99\) −0.186141 + 2.99422i −0.0187078 + 0.300930i
\(100\) 0 0
\(101\) 3.55842 6.16337i 0.354076 0.613278i −0.632883 0.774247i \(-0.718129\pi\)
0.986959 + 0.160969i \(0.0514620\pi\)
\(102\) 0 0
\(103\) 6.18614 + 10.7147i 0.609539 + 1.05575i 0.991316 + 0.131498i \(0.0419786\pi\)
−0.381778 + 0.924254i \(0.624688\pi\)
\(104\) 0 0
\(105\) 17.4891 4.10891i 1.70676 0.400989i
\(106\) 0 0
\(107\) −12.8614 −1.24336 −0.621680 0.783272i \(-0.713549\pi\)
−0.621680 + 0.783272i \(0.713549\pi\)
\(108\) 0 0
\(109\) −4.74456 −0.454447 −0.227223 0.973843i \(-0.572965\pi\)
−0.227223 + 0.973843i \(0.572965\pi\)
\(110\) 0 0
\(111\) 14.7446 3.46410i 1.39949 0.328798i
\(112\) 0 0
\(113\) 2.18614 + 3.78651i 0.205655 + 0.356205i 0.950341 0.311210i \(-0.100734\pi\)
−0.744686 + 0.667415i \(0.767401\pi\)
\(114\) 0 0
\(115\) 0.441578 0.764836i 0.0411774 0.0713213i
\(116\) 0 0
\(117\) 0.930703 + 0.617359i 0.0860436 + 0.0570748i
\(118\) 0 0
\(119\) 11.7446 20.3422i 1.07662 1.86476i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 13.9307 + 14.8236i 1.25609 + 1.33660i
\(124\) 0 0
\(125\) −10.3723 −0.927725
\(126\) 0 0
\(127\) 6.74456 0.598483 0.299242 0.954177i \(-0.403266\pi\)
0.299242 + 0.954177i \(0.403266\pi\)
\(128\) 0 0
\(129\) 0.872281 2.89303i 0.0768001 0.254717i
\(130\) 0 0
\(131\) −9.18614 15.9109i −0.802597 1.39014i −0.917901 0.396808i \(-0.870118\pi\)
0.115305 0.993330i \(-0.463216\pi\)
\(132\) 0 0
\(133\) −1.37228 + 2.37686i −0.118992 + 0.206100i
\(134\) 0 0
\(135\) −11.5584 4.28384i −0.994791 0.368694i
\(136\) 0 0
\(137\) −8.87228 + 15.3672i −0.758010 + 1.31291i 0.185854 + 0.982577i \(0.440495\pi\)
−0.943864 + 0.330335i \(0.892838\pi\)
\(138\) 0 0
\(139\) −2.87228 4.97494i −0.243624 0.421969i 0.718120 0.695919i \(-0.245003\pi\)
−0.961744 + 0.273951i \(0.911670\pi\)
\(140\) 0 0
\(141\) −2.18614 + 7.25061i −0.184106 + 0.610611i
\(142\) 0 0
\(143\) −0.372281 −0.0311317
\(144\) 0 0
\(145\) −10.3723 −0.861371
\(146\) 0 0
\(147\) −14.3723 15.2935i −1.18541 1.26139i
\(148\) 0 0
\(149\) 4.18614 + 7.25061i 0.342942 + 0.593993i 0.984978 0.172682i \(-0.0552432\pi\)
−0.642036 + 0.766675i \(0.721910\pi\)
\(150\) 0 0
\(151\) −0.186141 + 0.322405i −0.0151479 + 0.0262370i −0.873500 0.486824i \(-0.838155\pi\)
0.858352 + 0.513061i \(0.171489\pi\)
\(152\) 0 0
\(153\) −14.4307 + 7.17687i −1.16665 + 0.580216i
\(154\) 0 0
\(155\) −7.55842 + 13.0916i −0.607107 + 1.05154i
\(156\) 0 0
\(157\) 1.55842 + 2.69927i 0.124376 + 0.215425i 0.921489 0.388405i \(-0.126974\pi\)
−0.797113 + 0.603830i \(0.793641\pi\)
\(158\) 0 0
\(159\) 1.25544 0.294954i 0.0995627 0.0233913i
\(160\) 0 0
\(161\) −1.62772 −0.128282
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 4.00000 0.939764i 0.311400 0.0731605i
\(166\) 0 0
\(167\) 9.55842 + 16.5557i 0.739653 + 1.28112i 0.952652 + 0.304064i \(0.0983436\pi\)
−0.212999 + 0.977052i \(0.568323\pi\)
\(168\) 0 0
\(169\) 6.43070 11.1383i 0.494669 0.856793i
\(170\) 0 0
\(171\) 1.68614 0.838574i 0.128942 0.0641274i
\(172\) 0 0
\(173\) 8.18614 14.1788i 0.622381 1.07800i −0.366660 0.930355i \(-0.619499\pi\)
0.989041 0.147640i \(-0.0471678\pi\)
\(174\) 0 0
\(175\) −1.37228 2.37686i −0.103735 0.179674i
\(176\) 0 0
\(177\) −8.30298 8.83518i −0.624091 0.664093i
\(178\) 0 0
\(179\) 22.9783 1.71748 0.858738 0.512416i \(-0.171249\pi\)
0.858738 + 0.512416i \(0.171249\pi\)
\(180\) 0 0
\(181\) −0.510875 −0.0379730 −0.0189865 0.999820i \(-0.506044\pi\)
−0.0189865 + 0.999820i \(0.506044\pi\)
\(182\) 0 0
\(183\) −1.18614 + 3.93398i −0.0876820 + 0.290808i
\(184\) 0 0
\(185\) −10.3723 17.9653i −0.762585 1.32084i
\(186\) 0 0
\(187\) 2.68614 4.65253i 0.196430 0.340227i
\(188\) 0 0
\(189\) 3.81386 + 22.3966i 0.277417 + 1.62912i
\(190\) 0 0
\(191\) −4.93070 + 8.54023i −0.356773 + 0.617949i −0.987420 0.158121i \(-0.949456\pi\)
0.630647 + 0.776070i \(0.282790\pi\)
\(192\) 0 0
\(193\) −0.872281 1.51084i −0.0627882 0.108752i 0.832923 0.553390i \(-0.186666\pi\)
−0.895711 + 0.444637i \(0.853333\pi\)
\(194\) 0 0
\(195\) 0.441578 1.46455i 0.0316221 0.104879i
\(196\) 0 0
\(197\) 15.2554 1.08690 0.543452 0.839440i \(-0.317117\pi\)
0.543452 + 0.839440i \(0.317117\pi\)
\(198\) 0 0
\(199\) −16.2337 −1.15078 −0.575388 0.817881i \(-0.695149\pi\)
−0.575388 + 0.817881i \(0.695149\pi\)
\(200\) 0 0
\(201\) 4.44158 + 4.72627i 0.313285 + 0.333365i
\(202\) 0 0
\(203\) 9.55842 + 16.5557i 0.670870 + 1.16198i
\(204\) 0 0
\(205\) 13.9307 24.1287i 0.972963 1.68522i
\(206\) 0 0
\(207\) 0.930703 + 0.617359i 0.0646884 + 0.0429094i
\(208\) 0 0
\(209\) −0.313859 + 0.543620i −0.0217101 + 0.0376030i
\(210\) 0 0
\(211\) 4.81386 + 8.33785i 0.331400 + 0.574001i 0.982787 0.184745i \(-0.0591458\pi\)
−0.651387 + 0.758746i \(0.725812\pi\)
\(212\) 0 0
\(213\) −6.74456 + 1.58457i −0.462130 + 0.108573i
\(214\) 0 0
\(215\) −4.13859 −0.282250
\(216\) 0 0
\(217\) 27.8614 1.89136
\(218\) 0 0
\(219\) −20.4307 + 4.80001i −1.38058 + 0.324355i
\(220\) 0 0
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) 7.30298 12.6491i 0.489044 0.847049i −0.510877 0.859654i \(-0.670679\pi\)
0.999921 + 0.0126050i \(0.00401240\pi\)
\(224\) 0 0
\(225\) −0.116844 + 1.87953i −0.00778960 + 0.125302i
\(226\) 0 0
\(227\) 7.50000 12.9904i 0.497792 0.862202i −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) 0 0
\(229\) −11.3030 19.5773i −0.746922 1.29371i −0.949291 0.314398i \(-0.898197\pi\)
0.202369 0.979309i \(-0.435136\pi\)
\(230\) 0 0
\(231\) −5.18614 5.51856i −0.341223 0.363094i
\(232\) 0 0
\(233\) 5.37228 0.351950 0.175975 0.984395i \(-0.443692\pi\)
0.175975 + 0.984395i \(0.443692\pi\)
\(234\) 0 0
\(235\) 10.3723 0.676613
\(236\) 0 0
\(237\) 3.18614 10.5672i 0.206962 0.686416i
\(238\) 0 0
\(239\) 6.93070 + 12.0043i 0.448310 + 0.776496i 0.998276 0.0586913i \(-0.0186928\pi\)
−0.549966 + 0.835187i \(0.685359\pi\)
\(240\) 0 0
\(241\) −2.87228 + 4.97494i −0.185020 + 0.320464i −0.943583 0.331135i \(-0.892568\pi\)
0.758563 + 0.651599i \(0.225902\pi\)
\(242\) 0 0
\(243\) 6.31386 14.2525i 0.405034 0.914302i
\(244\) 0 0
\(245\) −14.3723 + 24.8935i −0.918211 + 1.59039i
\(246\) 0 0
\(247\) 0.116844 + 0.202380i 0.00743460 + 0.0128771i
\(248\) 0 0
\(249\) −4.81386 + 15.9658i −0.305066 + 1.01179i
\(250\) 0 0
\(251\) 9.88316 0.623819 0.311910 0.950112i \(-0.399031\pi\)
0.311910 + 0.950112i \(0.399031\pi\)
\(252\) 0 0
\(253\) −0.372281 −0.0234051
\(254\) 0 0
\(255\) 15.1168 + 16.0858i 0.946653 + 1.00733i
\(256\) 0 0
\(257\) −2.24456 3.88770i −0.140012 0.242508i 0.787489 0.616329i \(-0.211381\pi\)
−0.927501 + 0.373821i \(0.878047\pi\)
\(258\) 0 0
\(259\) −19.1168 + 33.1113i −1.18786 + 2.05744i
\(260\) 0 0
\(261\) 0.813859 13.0916i 0.0503766 0.810348i
\(262\) 0 0
\(263\) 10.5584 18.2877i 0.651060 1.12767i −0.331806 0.943348i \(-0.607658\pi\)
0.982866 0.184322i \(-0.0590088\pi\)
\(264\) 0 0
\(265\) −0.883156 1.52967i −0.0542518 0.0939669i
\(266\) 0 0
\(267\) 10.1168 2.37686i 0.619141 0.145462i
\(268\) 0 0
\(269\) −12.7446 −0.777050 −0.388525 0.921438i \(-0.627015\pi\)
−0.388525 + 0.921438i \(0.627015\pi\)
\(270\) 0 0
\(271\) −21.4891 −1.30537 −0.652686 0.757629i \(-0.726358\pi\)
−0.652686 + 0.757629i \(0.726358\pi\)
\(272\) 0 0
\(273\) −2.74456 + 0.644810i −0.166108 + 0.0390257i
\(274\) 0 0
\(275\) −0.313859 0.543620i −0.0189264 0.0327815i
\(276\) 0 0
\(277\) −14.5584 + 25.2159i −0.874731 + 1.51508i −0.0176816 + 0.999844i \(0.505629\pi\)
−0.857049 + 0.515235i \(0.827705\pi\)
\(278\) 0 0
\(279\) −15.9307 10.5672i −0.953746 0.632644i
\(280\) 0 0
\(281\) 6.93070 12.0043i 0.413451 0.716118i −0.581813 0.813322i \(-0.697657\pi\)
0.995264 + 0.0972040i \(0.0309899\pi\)
\(282\) 0 0
\(283\) −11.9307 20.6646i −0.709207 1.22838i −0.965152 0.261691i \(-0.915720\pi\)
0.255945 0.966691i \(-0.417613\pi\)
\(284\) 0 0
\(285\) −1.76631 1.87953i −0.104627 0.111334i
\(286\) 0 0
\(287\) −51.3505 −3.03113
\(288\) 0 0
\(289\) 11.8614 0.697730
\(290\) 0 0
\(291\) −0.872281 + 2.89303i −0.0511340 + 0.169592i
\(292\) 0 0
\(293\) −9.81386 16.9981i −0.573332 0.993040i −0.996221 0.0868582i \(-0.972317\pi\)
0.422889 0.906182i \(-0.361016\pi\)
\(294\) 0 0
\(295\) −8.30298 + 14.3812i −0.483418 + 0.837305i
\(296\) 0 0
\(297\) 0.872281 + 5.12241i 0.0506149 + 0.297233i
\(298\) 0 0
\(299\) −0.0692967 + 0.120025i −0.00400753 + 0.00694125i
\(300\) 0 0
\(301\) 3.81386 + 6.60580i 0.219827 + 0.380752i
\(302\) 0 0
\(303\) 3.55842 11.8020i 0.204426 0.678004i
\(304\) 0 0
\(305\) 5.62772 0.322242
\(306\) 0 0
\(307\) 31.3723 1.79051 0.895255 0.445553i \(-0.146993\pi\)
0.895255 + 0.445553i \(0.146993\pi\)
\(308\) 0 0
\(309\) 14.6753 + 15.6159i 0.834847 + 0.888358i
\(310\) 0 0
\(311\) 5.44158 + 9.42509i 0.308564 + 0.534448i 0.978048 0.208378i \(-0.0668184\pi\)
−0.669485 + 0.742826i \(0.733485\pi\)
\(312\) 0 0
\(313\) −5.61684 + 9.72866i −0.317483 + 0.549896i −0.979962 0.199184i \(-0.936171\pi\)
0.662479 + 0.749080i \(0.269504\pi\)
\(314\) 0 0
\(315\) 27.8614 13.8564i 1.56981 0.780720i
\(316\) 0 0
\(317\) −15.3030 + 26.5055i −0.859501 + 1.48870i 0.0129041 + 0.999917i \(0.495892\pi\)
−0.872405 + 0.488783i \(0.837441\pi\)
\(318\) 0 0
\(319\) 2.18614 + 3.78651i 0.122400 + 0.212004i
\(320\) 0 0
\(321\) −21.6861 + 5.09496i −1.21040 + 0.284373i
\(322\) 0 0
\(323\) −3.37228 −0.187639
\(324\) 0 0
\(325\) −0.233688 −0.0129627
\(326\) 0 0
\(327\) −8.00000 + 1.87953i −0.442401 + 0.103938i
\(328\) 0 0
\(329\) −9.55842 16.5557i −0.526973 0.912744i
\(330\) 0 0
\(331\) 15.9307 27.5928i 0.875631 1.51664i 0.0195412 0.999809i \(-0.493779\pi\)
0.856089 0.516828i \(-0.172887\pi\)
\(332\) 0 0
\(333\) 23.4891 11.6819i 1.28720 0.640166i
\(334\) 0 0
\(335\) 4.44158 7.69304i 0.242669 0.420316i
\(336\) 0 0
\(337\) 9.98913 + 17.3017i 0.544142 + 0.942482i 0.998660 + 0.0517446i \(0.0164782\pi\)
−0.454518 + 0.890738i \(0.650188\pi\)
\(338\) 0 0
\(339\) 5.18614 + 5.51856i 0.281672 + 0.299727i
\(340\) 0 0
\(341\) 6.37228 0.345078
\(342\) 0 0
\(343\) 22.3723 1.20799
\(344\) 0 0
\(345\) 0.441578 1.46455i 0.0237738 0.0788486i
\(346\) 0 0
\(347\) −14.3614 24.8747i −0.770961 1.33534i −0.937037 0.349230i \(-0.886443\pi\)
0.166076 0.986113i \(-0.446890\pi\)
\(348\) 0 0
\(349\) −8.44158 + 14.6212i −0.451867 + 0.782657i −0.998502 0.0547140i \(-0.982575\pi\)
0.546635 + 0.837371i \(0.315909\pi\)
\(350\) 0 0
\(351\) 1.81386 + 0.672262i 0.0968166 + 0.0358827i
\(352\) 0 0
\(353\) 11.9891 20.7658i 0.638117 1.10525i −0.347729 0.937595i \(-0.613047\pi\)
0.985846 0.167656i \(-0.0536196\pi\)
\(354\) 0 0
\(355\) 4.74456 + 8.21782i 0.251815 + 0.436157i
\(356\) 0 0
\(357\) 11.7446 38.9523i 0.621588 2.06157i
\(358\) 0 0
\(359\) 20.2337 1.06789 0.533947 0.845518i \(-0.320708\pi\)
0.533947 + 0.845518i \(0.320708\pi\)
\(360\) 0 0
\(361\) −18.6060 −0.979262
\(362\) 0 0
\(363\) 11.8614 + 12.6217i 0.622562 + 0.662467i
\(364\) 0 0
\(365\) 14.3723 + 24.8935i 0.752280 + 1.30299i
\(366\) 0 0
\(367\) −8.81386 + 15.2661i −0.460080 + 0.796881i −0.998964 0.0454981i \(-0.985513\pi\)
0.538885 + 0.842380i \(0.318846\pi\)
\(368\) 0 0
\(369\) 29.3614 + 19.4762i 1.52849 + 1.01389i
\(370\) 0 0
\(371\) −1.62772 + 2.81929i −0.0845069 + 0.146370i
\(372\) 0 0
\(373\) −10.5584 18.2877i −0.546694 0.946902i −0.998498 0.0547851i \(-0.982553\pi\)
0.451804 0.892117i \(-0.350781\pi\)
\(374\) 0 0
\(375\) −17.4891 + 4.10891i −0.903135 + 0.212183i
\(376\) 0 0
\(377\) 1.62772 0.0838318
\(378\) 0 0
\(379\) −5.88316 −0.302197 −0.151099 0.988519i \(-0.548281\pi\)
−0.151099 + 0.988519i \(0.548281\pi\)
\(380\) 0 0
\(381\) 11.3723 2.67181i 0.582620 0.136881i
\(382\) 0 0
\(383\) −10.6753 18.4901i −0.545481 0.944800i −0.998576 0.0533383i \(-0.983014\pi\)
0.453096 0.891462i \(-0.350320\pi\)
\(384\) 0 0
\(385\) −5.18614 + 8.98266i −0.264310 + 0.457799i
\(386\) 0 0
\(387\) 0.324734 5.22360i 0.0165072 0.265531i
\(388\) 0 0
\(389\) −5.30298 + 9.18504i −0.268872 + 0.465700i −0.968571 0.248738i \(-0.919984\pi\)
0.699699 + 0.714438i \(0.253318\pi\)
\(390\) 0 0
\(391\) −1.00000 1.73205i −0.0505722 0.0875936i
\(392\) 0 0
\(393\) −21.7921 23.1889i −1.09927 1.16973i
\(394\) 0 0
\(395\) −15.1168 −0.760611
\(396\) 0 0
\(397\) −18.2337 −0.915123 −0.457561 0.889178i \(-0.651277\pi\)
−0.457561 + 0.889178i \(0.651277\pi\)
\(398\) 0 0
\(399\) −1.37228 + 4.55134i −0.0687000 + 0.227852i
\(400\) 0 0
\(401\) 8.61684 + 14.9248i 0.430305 + 0.745310i 0.996899 0.0786871i \(-0.0250728\pi\)
−0.566595 + 0.823997i \(0.691739\pi\)
\(402\) 0 0
\(403\) 1.18614 2.05446i 0.0590859 0.102340i
\(404\) 0 0
\(405\) −21.1861 2.64436i −1.05275 0.131399i
\(406\) 0 0
\(407\) −4.37228 + 7.57301i −0.216726 + 0.375380i
\(408\) 0 0
\(409\) −2.87228 4.97494i −0.142025 0.245995i 0.786234 0.617929i \(-0.212028\pi\)
−0.928259 + 0.371934i \(0.878695\pi\)
\(410\) 0 0
\(411\) −8.87228 + 29.4260i −0.437637 + 1.45148i
\(412\) 0 0
\(413\) 30.6060 1.50602
\(414\) 0 0
\(415\) 22.8397 1.12115
\(416\) 0 0
\(417\) −6.81386 7.25061i −0.333676 0.355064i
\(418\) 0 0
\(419\) 6.30298 + 10.9171i 0.307921 + 0.533335i 0.977907 0.209039i \(-0.0670334\pi\)
−0.669986 + 0.742373i \(0.733700\pi\)
\(420\) 0 0
\(421\) 17.5584 30.4121i 0.855745 1.48219i −0.0202069 0.999796i \(-0.506432\pi\)
0.875952 0.482398i \(-0.160234\pi\)
\(422\) 0 0
\(423\) −0.813859 + 13.0916i −0.0395712 + 0.636534i
\(424\) 0 0
\(425\) 1.68614 2.92048i 0.0817898 0.141664i
\(426\) 0 0
\(427\) −5.18614 8.98266i −0.250975 0.434701i
\(428\) 0 0
\(429\) −0.627719 + 0.147477i −0.0303065 + 0.00712025i
\(430\) 0 0
\(431\) −1.25544 −0.0604723 −0.0302361 0.999543i \(-0.509626\pi\)
−0.0302361 + 0.999543i \(0.509626\pi\)
\(432\) 0 0
\(433\) 32.1168 1.54344 0.771719 0.635964i \(-0.219397\pi\)
0.771719 + 0.635964i \(0.219397\pi\)
\(434\) 0 0
\(435\) −17.4891 + 4.10891i −0.838539 + 0.197007i
\(436\) 0 0
\(437\) 0.116844 + 0.202380i 0.00558941 + 0.00968113i
\(438\) 0 0
\(439\) −3.55842 + 6.16337i −0.169834 + 0.294161i −0.938361 0.345656i \(-0.887657\pi\)
0.768527 + 0.639817i \(0.220990\pi\)
\(440\) 0 0
\(441\) −30.2921 20.0935i −1.44248 0.956834i
\(442\) 0 0
\(443\) −15.3614 + 26.6067i −0.729842 + 1.26412i 0.227107 + 0.973870i \(0.427073\pi\)
−0.956950 + 0.290254i \(0.906260\pi\)
\(444\) 0 0
\(445\) −7.11684 12.3267i −0.337371 0.584343i
\(446\) 0 0
\(447\) 9.93070 + 10.5672i 0.469706 + 0.499813i
\(448\) 0 0
\(449\) −15.8832 −0.749572 −0.374786 0.927111i \(-0.622284\pi\)
−0.374786 + 0.927111i \(0.622284\pi\)
\(450\) 0 0
\(451\) −11.7446 −0.553030
\(452\) 0 0
\(453\) −0.186141 + 0.617359i −0.00874565 + 0.0290060i
\(454\) 0 0
\(455\) 1.93070 + 3.34408i 0.0905128 + 0.156773i
\(456\) 0 0
\(457\) 1.87228 3.24289i 0.0875816 0.151696i −0.818907 0.573927i \(-0.805419\pi\)
0.906488 + 0.422231i \(0.138753\pi\)
\(458\) 0 0
\(459\) −21.4891 + 17.8178i −1.00303 + 0.831666i
\(460\) 0 0
\(461\) 3.44158 5.96099i 0.160290 0.277631i −0.774682 0.632350i \(-0.782090\pi\)
0.934973 + 0.354720i \(0.115424\pi\)
\(462\) 0 0
\(463\) −20.6753 35.8106i −0.960861 1.66426i −0.720346 0.693615i \(-0.756017\pi\)
−0.240515 0.970645i \(-0.577316\pi\)
\(464\) 0 0
\(465\) −7.55842 + 25.0684i −0.350513 + 1.16252i
\(466\) 0 0
\(467\) 7.37228 0.341148 0.170574 0.985345i \(-0.445438\pi\)
0.170574 + 0.985345i \(0.445438\pi\)
\(468\) 0 0
\(469\) −16.3723 −0.756002
\(470\) 0 0
\(471\) 3.69702 + 3.93398i 0.170349 + 0.181268i
\(472\) 0 0
\(473\) 0.872281 + 1.51084i 0.0401075 + 0.0694683i
\(474\) 0 0
\(475\) −0.197015 + 0.341241i −0.00903969 + 0.0156572i
\(476\) 0 0
\(477\) 2.00000 0.994667i 0.0915737 0.0455427i
\(478\) 0 0
\(479\) 5.30298 9.18504i 0.242300 0.419675i −0.719069 0.694938i \(-0.755432\pi\)
0.961369 + 0.275263i \(0.0887650\pi\)
\(480\) 0 0
\(481\) 1.62772 + 2.81929i 0.0742176 + 0.128549i
\(482\) 0 0
\(483\) −2.74456 + 0.644810i −0.124882 + 0.0293399i
\(484\) 0 0
\(485\) 4.13859 0.187924
\(486\) 0 0
\(487\) 6.74456 0.305625 0.152813 0.988255i \(-0.451167\pi\)
0.152813 + 0.988255i \(0.451167\pi\)
\(488\) 0 0
\(489\) −20.2337 + 4.75372i −0.914999 + 0.214971i
\(490\) 0 0
\(491\) −0.127719 0.221215i −0.00576386 0.00998330i 0.863129 0.504983i \(-0.168501\pi\)
−0.868893 + 0.495000i \(0.835168\pi\)
\(492\) 0 0
\(493\) −11.7446 + 20.3422i −0.528948 + 0.916166i
\(494\) 0 0
\(495\) 6.37228 3.16915i 0.286413 0.142443i
\(496\) 0 0
\(497\) 8.74456 15.1460i 0.392247 0.679392i
\(498\) 0 0
\(499\) 9.98913 + 17.3017i 0.447175 + 0.774529i 0.998201 0.0599587i \(-0.0190969\pi\)
−0.551026 + 0.834488i \(0.685764\pi\)
\(500\) 0 0
\(501\) 22.6753 + 24.1287i 1.01306 + 1.07799i
\(502\) 0 0
\(503\) 6.51087 0.290306 0.145153 0.989409i \(-0.453633\pi\)
0.145153 + 0.989409i \(0.453633\pi\)
\(504\) 0 0
\(505\) −16.8832 −0.751291
\(506\) 0 0
\(507\) 6.43070 21.3282i 0.285598 0.947220i
\(508\) 0 0
\(509\) 15.5584 + 26.9480i 0.689615 + 1.19445i 0.971962 + 0.235136i \(0.0755535\pi\)
−0.282348 + 0.959312i \(0.591113\pi\)
\(510\) 0 0
\(511\) 26.4891 45.8805i 1.17181 2.02963i
\(512\) 0 0
\(513\) 2.51087 2.08191i 0.110858 0.0919185i
\(514\) 0 0
\(515\) 14.6753 25.4183i 0.646669 1.12006i
\(516\) 0 0
\(517\) −2.18614 3.78651i −0.0961464 0.166530i
\(518\) 0 0
\(519\) 8.18614 27.1504i 0.359332 1.19177i
\(520\) 0 0
\(521\) 12.1168 0.530849 0.265424 0.964132i \(-0.414488\pi\)
0.265424 + 0.964132i \(0.414488\pi\)
\(522\) 0 0
\(523\) −13.4891 −0.589838 −0.294919 0.955522i \(-0.595293\pi\)
−0.294919 + 0.955522i \(0.595293\pi\)
\(524\) 0 0
\(525\) −3.25544 3.46410i −0.142079 0.151186i
\(526\) 0 0
\(527\) 17.1168 + 29.6472i 0.745621 + 1.29145i
\(528\) 0 0
\(529\) 11.4307 19.7986i 0.496987 0.860807i
\(530\) 0 0
\(531\) −17.5000 11.6082i −0.759435 0.503752i
\(532\) 0 0
\(533\) −2.18614 + 3.78651i −0.0946923 + 0.164012i
\(534\) 0 0
\(535\) 15.2554 + 26.4232i 0.659550 + 1.14237i
\(536\) 0 0
\(537\) 38.7446 9.10268i 1.67195 0.392810i
\(538\) 0 0
\(539\) 12.1168 0.521909
\(540\) 0 0
\(541\) 2.23369 0.0960337 0.0480169 0.998847i \(-0.484710\pi\)
0.0480169 + 0.998847i \(0.484710\pi\)
\(542\) 0 0
\(543\) −0.861407 + 0.202380i −0.0369665 + 0.00868494i
\(544\) 0 0
\(545\) 5.62772 + 9.74749i 0.241065 + 0.417537i
\(546\) 0 0
\(547\) 8.12772 14.0776i 0.347516 0.601916i −0.638291 0.769795i \(-0.720359\pi\)
0.985808 + 0.167879i \(0.0536918\pi\)
\(548\) 0 0
\(549\) −0.441578 + 7.10313i −0.0188461 + 0.303154i
\(550\) 0 0
\(551\) 1.37228 2.37686i 0.0584611 0.101258i
\(552\) 0 0
\(553\) 13.9307 + 24.1287i 0.592394 + 1.02606i
\(554\) 0 0
\(555\) −24.6060 26.1831i −1.04447 1.11141i
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) 0.649468 0.0274696
\(560\) 0 0
\(561\) 2.68614 8.90892i 0.113409 0.376135i
\(562\) 0 0
\(563\) −4.87228 8.43904i −0.205342 0.355663i 0.744900 0.667177i \(-0.232497\pi\)
−0.950242 + 0.311514i \(0.899164\pi\)
\(564\) 0 0
\(565\) 5.18614 8.98266i 0.218183 0.377903i
\(566\) 0 0
\(567\) 15.3030 + 36.2530i 0.642665 + 1.52248i
\(568\) 0 0
\(569\) −13.6168 + 23.5851i −0.570848 + 0.988737i 0.425631 + 0.904897i \(0.360052\pi\)
−0.996479 + 0.0838407i \(0.973281\pi\)
\(570\) 0 0
\(571\) 13.2446 + 22.9403i 0.554268 + 0.960020i 0.997960 + 0.0638407i \(0.0203349\pi\)
−0.443692 + 0.896179i \(0.646332\pi\)
\(572\) 0 0
\(573\) −4.93070 + 16.3533i −0.205983 + 0.683169i
\(574\) 0 0
\(575\) −0.233688 −0.00974546
\(576\) 0 0
\(577\) 14.8614 0.618688 0.309344 0.950950i \(-0.399890\pi\)
0.309344 + 0.950950i \(0.399890\pi\)
\(578\) 0 0
\(579\) −2.06930 2.20193i −0.0859970 0.0915092i
\(580\) 0 0
\(581\) −21.0475 36.4554i −0.873199 1.51243i
\(582\) 0 0
\(583\) −0.372281 + 0.644810i −0.0154183 + 0.0267053i
\(584\) 0 0
\(585\) 0.164391 2.64436i 0.00679674 0.109331i
\(586\) 0 0
\(587\) −4.61684 + 7.99661i −0.190558 + 0.330055i −0.945435 0.325810i \(-0.894363\pi\)
0.754878 + 0.655866i \(0.227696\pi\)
\(588\) 0 0
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 25.7228 6.04334i 1.05810 0.248590i
\(592\) 0 0
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −55.7228 −2.28441
\(596\) 0 0
\(597\) −27.3723 + 6.43087i −1.12027 + 0.263198i
\(598\) 0 0
\(599\) −19.9307 34.5210i −0.814346 1.41049i −0.909796 0.415055i \(-0.863762\pi\)
0.0954498 0.995434i \(-0.469571\pi\)
\(600\) 0 0
\(601\) −2.98913 + 5.17732i −0.121929 + 0.211187i −0.920528 0.390676i \(-0.872241\pi\)
0.798599 + 0.601863i \(0.205575\pi\)
\(602\) 0 0
\(603\) 9.36141 + 6.20965i 0.381226 + 0.252877i
\(604\) 0 0
\(605\) 11.8614 20.5446i 0.482235 0.835255i
\(606\) 0 0
\(607\) 5.55842 + 9.62747i 0.225609 + 0.390767i 0.956502 0.291725i \(-0.0942294\pi\)
−0.730893 + 0.682492i \(0.760896\pi\)
\(608\) 0 0
\(609\) 22.6753 + 24.1287i 0.918848 + 0.977744i
\(610\) 0 0
\(611\) −1.62772 −0.0658504
\(612\) 0 0
\(613\) −12.7446 −0.514748 −0.257374 0.966312i \(-0.582857\pi\)
−0.257374 + 0.966312i \(0.582857\pi\)
\(614\) 0 0
\(615\) 13.9307 46.2029i 0.561740 1.86308i
\(616\) 0 0
\(617\) −18.9891 32.8901i −0.764473 1.32411i −0.940525 0.339726i \(-0.889666\pi\)
0.176051 0.984381i \(-0.443668\pi\)
\(618\) 0 0
\(619\) −10.6168 + 18.3889i −0.426727 + 0.739113i −0.996580 0.0826338i \(-0.973667\pi\)
0.569853 + 0.821747i \(0.307000\pi\)
\(620\) 0 0
\(621\) 1.81386 + 0.672262i 0.0727877 + 0.0269769i
\(622\) 0 0
\(623\) −13.1168 + 22.7190i −0.525515 + 0.910219i
\(624\) 0 0
\(625\) 13.8723 + 24.0275i 0.554891 + 0.961100i
\(626\) 0 0
\(627\) −0.313859 + 1.04095i −0.0125343 + 0.0415717i
\(628\) 0 0
\(629\) −46.9783 −1.87315
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) 11.4198 + 12.1518i 0.453897 + 0.482991i
\(634\) 0 0
\(635\) −8.00000 13.8564i −0.317470 0.549875i
\(636\) 0 0
\(637\) 2.25544 3.90653i 0.0893637 0.154782i
\(638\) 0 0
\(639\) −10.7446 + 5.34363i −0.425048 + 0.211391i
\(640\) 0 0
\(641\) −1.61684 + 2.80046i −0.0638615 + 0.110611i −0.896188 0.443674i \(-0.853675\pi\)
0.832327 + 0.554285i \(0.187008\pi\)
\(642\) 0 0
\(643\) −1.50000 2.59808i −0.0591542 0.102458i 0.834932 0.550353i \(-0.185507\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(644\) 0 0
\(645\) −6.97825 + 1.63948i −0.274768 + 0.0645543i
\(646\) 0 0
\(647\) 33.7228 1.32578 0.662890 0.748717i \(-0.269330\pi\)
0.662890 + 0.748717i \(0.269330\pi\)
\(648\) 0 0
\(649\) 7.00000 0.274774
\(650\) 0 0
\(651\) 46.9783 11.0371i 1.84122 0.432579i
\(652\) 0 0
\(653\) 11.4416 + 19.8174i 0.447744 + 0.775515i 0.998239 0.0593237i \(-0.0188944\pi\)
−0.550495 + 0.834838i \(0.685561\pi\)
\(654\) 0 0
\(655\) −21.7921 + 37.7450i −0.851488 + 1.47482i
\(656\) 0 0
\(657\) −32.5475 + 16.1870i −1.26980 + 0.631514i
\(658\) 0 0
\(659\) −9.55842 + 16.5557i −0.372343 + 0.644917i −0.989926 0.141589i \(-0.954779\pi\)
0.617582 + 0.786506i \(0.288112\pi\)
\(660\) 0 0
\(661\) 23.0475 + 39.9195i 0.896446 + 1.55269i 0.832005 + 0.554768i \(0.187193\pi\)
0.0644406 + 0.997922i \(0.479474\pi\)
\(662\) 0 0
\(663\) −2.37228 2.52434i −0.0921318 0.0980372i
\(664\) 0 0
\(665\) 6.51087 0.252481
\(666\) 0 0
\(667\) 1.62772 0.0630255
\(668\) 0 0
\(669\) 7.30298 24.2213i 0.282350 0.936448i
\(670\) 0 0
\(671\) −1.18614 2.05446i −0.0457905 0.0793114i
\(672\) 0 0
\(673\) 0.186141 0.322405i 0.00717520 0.0124278i −0.862416 0.506201i \(-0.831049\pi\)
0.869591 + 0.493773i \(0.164383\pi\)
\(674\) 0 0
\(675\) 0.547547 + 3.21543i 0.0210751 + 0.123762i
\(676\) 0 0
\(677\) 10.3030 17.8453i 0.395976 0.685850i −0.597249 0.802056i \(-0.703740\pi\)
0.993225 + 0.116205i \(0.0370731\pi\)
\(678\) 0 0
\(679\) −3.81386 6.60580i −0.146362 0.253507i
\(680\) 0 0
\(681\) 7.50000 24.8747i 0.287401 0.953200i
\(682\) 0 0
\(683\) −15.3723 −0.588204 −0.294102 0.955774i \(-0.595021\pi\)
−0.294102 + 0.955774i \(0.595021\pi\)
\(684\) 0 0
\(685\) 42.0951 1.60837
\(686\) 0 0
\(687\) −26.8139 28.5326i −1.02301 1.08858i
\(688\) 0 0
\(689\) 0.138593 + 0.240051i 0.00527999 + 0.00914521i
\(690\) 0 0
\(691\) −7.55842 + 13.0916i −0.287536 + 0.498027i −0.973221 0.229872i \(-0.926169\pi\)
0.685685 + 0.727898i \(0.259503\pi\)
\(692\) 0 0
\(693\) −10.9307 7.25061i −0.415223 0.275428i
\(694\) 0 0
\(695\) −6.81386 + 11.8020i −0.258464 + 0.447674i
\(696\) 0 0
\(697\) −31.5475 54.6420i −1.19495 2.06971i
\(698\) 0 0
\(699\) 9.05842 2.12819i 0.342621 0.0804957i
\(700\) 0 0
\(701\) −35.4891 −1.34041 −0.670203 0.742178i \(-0.733793\pi\)
−0.670203 + 0.742178i \(0.733793\pi\)
\(702\) 0 0
\(703\) 5.48913 0.207026
\(704\) 0 0
\(705\) 17.4891 4.10891i 0.658679 0.154751i
\(706\) 0 0
\(707\) 15.5584 + 26.9480i 0.585135 + 1.01348i
\(708\) 0 0
\(709\) 14.3030 24.7735i 0.537160 0.930388i −0.461896 0.886934i \(-0.652831\pi\)
0.999055 0.0434539i \(-0.0138361\pi\)
\(710\) 0 0
\(711\) 1.18614 19.0800i 0.0444838 0.715556i
\(712\) 0 0
\(713\) 1.18614 2.05446i 0.0444213 0.0769400i
\(714\) 0 0
\(715\) 0.441578 + 0.764836i 0.0165141 + 0.0286032i
\(716\) 0 0
\(717\) 16.4416 + 17.4954i 0.614022 + 0.653379i
\(718\) 0 0
\(719\) 45.4891 1.69646 0.848229 0.529630i \(-0.177669\pi\)
0.848229 + 0.529630i \(0.177669\pi\)
\(720\) 0 0
\(721\) −54.0951 −2.01461
\(722\) 0 0
\(723\) −2.87228 + 9.52628i −0.106821 + 0.354286i
\(724\) 0 0
\(725\) 1.37228 + 2.37686i 0.0509652 + 0.0882744i
\(726\) 0 0
\(727\) −5.44158 + 9.42509i −0.201817 + 0.349557i −0.949114 0.314933i \(-0.898018\pi\)
0.747297 + 0.664490i \(0.231351\pi\)
\(728\) 0 0
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 0 0
\(731\) −4.68614 + 8.11663i −0.173323 + 0.300205i
\(732\) 0 0
\(733\) 18.9307 + 32.7889i 0.699221 + 1.21109i 0.968737 + 0.248091i \(0.0798032\pi\)
−0.269515 + 0.962996i \(0.586863\pi\)
\(734\) 0 0
\(735\) −14.3723 + 47.6675i −0.530130 + 1.75824i
\(736\) 0 0
\(737\) −3.74456 −0.137933
\(738\) 0 0
\(739\) 42.1168 1.54929 0.774647 0.632394i \(-0.217928\pi\)
0.774647 + 0.632394i \(0.217928\pi\)
\(740\) 0 0
\(741\) 0.277187 + 0.294954i 0.0101827 + 0.0108354i
\(742\) 0 0
\(743\) −17.8139 30.8545i −0.653527 1.13194i −0.982261 0.187520i \(-0.939955\pi\)
0.328734 0.944423i \(-0.393378\pi\)
\(744\) 0 0
\(745\) 9.93070 17.2005i 0.363833 0.630177i
\(746\) 0 0
\(747\) −1.79211 + 28.8275i −0.0655699 + 1.05474i
\(748\) 0 0
\(749\) 28.1168 48.6998i 1.02737 1.77945i
\(750\) 0 0
\(751\) 18.8139 + 32.5866i 0.686527 + 1.18910i 0.972954 + 0.230998i \(0.0741992\pi\)
−0.286427 + 0.958102i \(0.592467\pi\)
\(752\) 0 0
\(753\) 16.6644 3.91515i 0.607284 0.142676i
\(754\) 0 0
\(755\) 0.883156 0.0321413
\(756\) 0 0
\(757\) 8.51087 0.309333 0.154667 0.987967i \(-0.450570\pi\)
0.154667 + 0.987967i \(0.450570\pi\)
\(758\) 0 0
\(759\) −0.627719 + 0.147477i −0.0227847 + 0.00535307i
\(760\) 0 0
\(761\) 9.67527 + 16.7581i 0.350728 + 0.607479i 0.986377 0.164499i \(-0.0526008\pi\)
−0.635649 + 0.771978i \(0.719267\pi\)
\(762\) 0 0
\(763\) 10.3723 17.9653i 0.375502 0.650388i
\(764\) 0 0
\(765\) 31.8614 + 21.1345i 1.15195 + 0.764118i
\(766\) 0 0
\(767\) 1.30298 2.25684i 0.0470480 0.0814896i
\(768\) 0 0
\(769\) −16.5584 28.6800i −0.597112 1.03423i −0.993245 0.116035i \(-0.962981\pi\)
0.396133 0.918193i \(-0.370352\pi\)
\(770\) 0 0
\(771\) −5.32473 5.66603i −0.191766 0.204057i
\(772\) 0 0
\(773\) 28.9783 1.04228 0.521138 0.853473i \(-0.325508\pi\)
0.521138 + 0.853473i \(0.325508\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −19.1168 + 63.4034i −0.685813 + 2.27458i
\(778\) 0 0
\(779\) 3.68614 + 6.38458i 0.132070 + 0.228751i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 0 0
\(783\) −3.81386 22.3966i −0.136296 0.800390i
\(784\) 0 0
\(785\) 3.69702 6.40342i 0.131952 0.228548i
\(786\) 0 0
\(787\) −21.4198 37.1002i −0.763534 1.32248i −0.941018 0.338357i \(-0.890129\pi\)
0.177484 0.984124i \(-0.443204\pi\)
\(788\) 0 0