Properties

Label 416.2.i.f.321.1
Level $416$
Weight $2$
Character 416.321
Analytic conductor $3.322$
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] = [416,2,Mod(289,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.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: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) 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 321.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 416.321
Dual form 416.2.i.f.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.207107 + 0.358719i) q^{3} -2.82843 q^{5} +(-0.792893 - 1.37333i) q^{7} +(1.41421 + 2.44949i) q^{9} +(2.62132 - 4.54026i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(0.585786 - 1.01461i) q^{15} +(0.0857864 + 0.148586i) q^{17} +(-3.62132 - 6.27231i) q^{19} +0.656854 q^{21} +(3.62132 - 6.27231i) q^{23} +3.00000 q^{25} -2.41421 q^{27} +(1.32843 - 2.30090i) q^{29} -5.65685 q^{31} +(1.08579 + 1.88064i) q^{33} +(2.24264 + 3.88437i) q^{35} +(-4.74264 + 8.21449i) q^{37} +(1.44975 + 0.358719i) q^{39} +(0.0857864 - 0.148586i) q^{41} +(5.03553 + 8.72180i) q^{43} +(-4.00000 - 6.92820i) q^{45} +6.00000 q^{47} +(2.24264 - 3.88437i) q^{49} -0.0710678 q^{51} +2.82843 q^{53} +(-7.41421 + 12.8418i) q^{55} +3.00000 q^{57} +(-3.62132 - 6.27231i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(2.24264 - 3.88437i) q^{63} +(2.82843 + 9.79796i) q^{65} +(-2.37868 + 4.11999i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-0.621320 - 1.07616i) q^{71} -4.48528 q^{73} +(-0.621320 + 1.07616i) q^{75} -8.31371 q^{77} -6.00000 q^{79} +(-3.74264 + 6.48244i) q^{81} +4.00000 q^{83} +(-0.242641 - 0.420266i) q^{85} +(0.550253 + 0.953065i) q^{87} +(7.32843 - 12.6932i) q^{89} +(-3.96447 + 4.11999i) q^{91} +(1.17157 - 2.02922i) q^{93} +(10.2426 + 17.7408i) q^{95} +(4.50000 + 7.79423i) q^{97} +14.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{7} + 2 q^{11} - 4 q^{13} + 8 q^{15} + 6 q^{17} - 6 q^{19} - 20 q^{21} + 6 q^{23} + 12 q^{25} - 4 q^{27} - 6 q^{29} + 10 q^{33} - 8 q^{35} - 2 q^{37} - 14 q^{39} + 6 q^{41} + 6 q^{43}+ \cdots + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.207107 + 0.358719i −0.119573 + 0.207107i −0.919599 0.392859i \(-0.871486\pi\)
0.800025 + 0.599966i \(0.204819\pi\)
\(4\) 0 0
\(5\) −2.82843 −1.26491 −0.632456 0.774597i \(-0.717953\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 0 0
\(7\) −0.792893 1.37333i −0.299685 0.519070i 0.676378 0.736554i \(-0.263548\pi\)
−0.976064 + 0.217484i \(0.930215\pi\)
\(8\) 0 0
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) 0 0
\(11\) 2.62132 4.54026i 0.790358 1.36894i −0.135388 0.990793i \(-0.543228\pi\)
0.925745 0.378147i \(-0.123439\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 0 0
\(15\) 0.585786 1.01461i 0.151249 0.261972i
\(16\) 0 0
\(17\) 0.0857864 + 0.148586i 0.0208063 + 0.0360375i 0.876241 0.481873i \(-0.160043\pi\)
−0.855435 + 0.517911i \(0.826710\pi\)
\(18\) 0 0
\(19\) −3.62132 6.27231i −0.830788 1.43897i −0.897414 0.441189i \(-0.854557\pi\)
0.0666264 0.997778i \(-0.478776\pi\)
\(20\) 0 0
\(21\) 0.656854 0.143337
\(22\) 0 0
\(23\) 3.62132 6.27231i 0.755097 1.30787i −0.190228 0.981740i \(-0.560923\pi\)
0.945326 0.326127i \(-0.105744\pi\)
\(24\) 0 0
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) −2.41421 −0.464616
\(28\) 0 0
\(29\) 1.32843 2.30090i 0.246683 0.427267i −0.715921 0.698182i \(-0.753993\pi\)
0.962603 + 0.270915i \(0.0873261\pi\)
\(30\) 0 0
\(31\) −5.65685 −1.01600 −0.508001 0.861357i \(-0.669615\pi\)
−0.508001 + 0.861357i \(0.669615\pi\)
\(32\) 0 0
\(33\) 1.08579 + 1.88064i 0.189011 + 0.327377i
\(34\) 0 0
\(35\) 2.24264 + 3.88437i 0.379075 + 0.656578i
\(36\) 0 0
\(37\) −4.74264 + 8.21449i −0.779685 + 1.35045i 0.152438 + 0.988313i \(0.451288\pi\)
−0.932123 + 0.362142i \(0.882046\pi\)
\(38\) 0 0
\(39\) 1.44975 + 0.358719i 0.232145 + 0.0574411i
\(40\) 0 0
\(41\) 0.0857864 0.148586i 0.0133976 0.0232053i −0.859249 0.511558i \(-0.829069\pi\)
0.872646 + 0.488352i \(0.162402\pi\)
\(42\) 0 0
\(43\) 5.03553 + 8.72180i 0.767912 + 1.33006i 0.938693 + 0.344753i \(0.112037\pi\)
−0.170782 + 0.985309i \(0.554629\pi\)
\(44\) 0 0
\(45\) −4.00000 6.92820i −0.596285 1.03280i
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 2.24264 3.88437i 0.320377 0.554910i
\(50\) 0 0
\(51\) −0.0710678 −0.00995148
\(52\) 0 0
\(53\) 2.82843 0.388514 0.194257 0.980951i \(-0.437770\pi\)
0.194257 + 0.980951i \(0.437770\pi\)
\(54\) 0 0
\(55\) −7.41421 + 12.8418i −0.999732 + 1.73159i
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) −3.62132 6.27231i −0.471456 0.816585i 0.528011 0.849238i \(-0.322938\pi\)
−0.999467 + 0.0326522i \(0.989605\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) 2.24264 3.88437i 0.282546 0.489384i
\(64\) 0 0
\(65\) 2.82843 + 9.79796i 0.350823 + 1.21529i
\(66\) 0 0
\(67\) −2.37868 + 4.11999i −0.290602 + 0.503337i −0.973952 0.226753i \(-0.927189\pi\)
0.683350 + 0.730091i \(0.260522\pi\)
\(68\) 0 0
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) −0.621320 1.07616i −0.0737372 0.127717i 0.826799 0.562497i \(-0.190159\pi\)
−0.900536 + 0.434781i \(0.856826\pi\)
\(72\) 0 0
\(73\) −4.48528 −0.524962 −0.262481 0.964937i \(-0.584541\pi\)
−0.262481 + 0.964937i \(0.584541\pi\)
\(74\) 0 0
\(75\) −0.621320 + 1.07616i −0.0717439 + 0.124264i
\(76\) 0 0
\(77\) −8.31371 −0.947435
\(78\) 0 0
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 0 0
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −0.242641 0.420266i −0.0263181 0.0455842i
\(86\) 0 0
\(87\) 0.550253 + 0.953065i 0.0589933 + 0.102179i
\(88\) 0 0
\(89\) 7.32843 12.6932i 0.776812 1.34548i −0.156959 0.987605i \(-0.550169\pi\)
0.933771 0.357872i \(-0.116498\pi\)
\(90\) 0 0
\(91\) −3.96447 + 4.11999i −0.415589 + 0.431893i
\(92\) 0 0
\(93\) 1.17157 2.02922i 0.121486 0.210421i
\(94\) 0 0
\(95\) 10.2426 + 17.7408i 1.05087 + 1.82017i
\(96\) 0 0
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) 0 0
\(99\) 14.8284 1.49031
\(100\) 0 0
\(101\) −3.08579 + 5.34474i −0.307047 + 0.531821i −0.977715 0.209936i \(-0.932674\pi\)
0.670668 + 0.741758i \(0.266008\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) −1.85786 −0.181309
\(106\) 0 0
\(107\) −5.37868 + 9.31615i −0.519977 + 0.900626i 0.479754 + 0.877403i \(0.340726\pi\)
−0.999730 + 0.0232227i \(0.992607\pi\)
\(108\) 0 0
\(109\) 8.48528 0.812743 0.406371 0.913708i \(-0.366794\pi\)
0.406371 + 0.913708i \(0.366794\pi\)
\(110\) 0 0
\(111\) −1.96447 3.40256i −0.186459 0.322956i
\(112\) 0 0
\(113\) 2.91421 + 5.04757i 0.274146 + 0.474835i 0.969919 0.243426i \(-0.0782715\pi\)
−0.695773 + 0.718262i \(0.744938\pi\)
\(114\) 0 0
\(115\) −10.2426 + 17.7408i −0.955131 + 1.65434i
\(116\) 0 0
\(117\) 7.07107 7.34847i 0.653720 0.679366i
\(118\) 0 0
\(119\) 0.136039 0.235626i 0.0124707 0.0215998i
\(120\) 0 0
\(121\) −8.24264 14.2767i −0.749331 1.29788i
\(122\) 0 0
\(123\) 0.0355339 + 0.0615465i 0.00320398 + 0.00554946i
\(124\) 0 0
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −2.20711 + 3.82282i −0.195849 + 0.339221i −0.947179 0.320707i \(-0.896080\pi\)
0.751329 + 0.659927i \(0.229413\pi\)
\(128\) 0 0
\(129\) −4.17157 −0.367287
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) −5.74264 + 9.94655i −0.497950 + 0.862475i
\(134\) 0 0
\(135\) 6.82843 0.587697
\(136\) 0 0
\(137\) −10.3284 17.8894i −0.882417 1.52839i −0.848646 0.528962i \(-0.822582\pi\)
−0.0337713 0.999430i \(-0.510752\pi\)
\(138\) 0 0
\(139\) −3.62132 6.27231i −0.307156 0.532010i 0.670583 0.741835i \(-0.266044\pi\)
−0.977739 + 0.209824i \(0.932711\pi\)
\(140\) 0 0
\(141\) −1.24264 + 2.15232i −0.104649 + 0.181258i
\(142\) 0 0
\(143\) −18.3492 4.54026i −1.53444 0.379676i
\(144\) 0 0
\(145\) −3.75736 + 6.50794i −0.312032 + 0.540455i
\(146\) 0 0
\(147\) 0.928932 + 1.60896i 0.0766170 + 0.132705i
\(148\) 0 0
\(149\) 7.32843 + 12.6932i 0.600368 + 1.03987i 0.992765 + 0.120072i \(0.0383126\pi\)
−0.392397 + 0.919796i \(0.628354\pi\)
\(150\) 0 0
\(151\) 16.9706 1.38104 0.690522 0.723311i \(-0.257381\pi\)
0.690522 + 0.723311i \(0.257381\pi\)
\(152\) 0 0
\(153\) −0.242641 + 0.420266i −0.0196163 + 0.0339765i
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) 16.4853 1.31567 0.657834 0.753163i \(-0.271473\pi\)
0.657834 + 0.753163i \(0.271473\pi\)
\(158\) 0 0
\(159\) −0.585786 + 1.01461i −0.0464559 + 0.0804640i
\(160\) 0 0
\(161\) −11.4853 −0.905167
\(162\) 0 0
\(163\) −12.6213 21.8608i −0.988578 1.71227i −0.624807 0.780779i \(-0.714822\pi\)
−0.363771 0.931488i \(-0.618511\pi\)
\(164\) 0 0
\(165\) −3.07107 5.31925i −0.239082 0.414103i
\(166\) 0 0
\(167\) −4.86396 + 8.42463i −0.376385 + 0.651917i −0.990533 0.137273i \(-0.956166\pi\)
0.614149 + 0.789190i \(0.289500\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) 10.2426 17.7408i 0.783274 1.35667i
\(172\) 0 0
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) −2.37868 4.11999i −0.179811 0.311442i
\(176\) 0 0
\(177\) 3.00000 0.225494
\(178\) 0 0
\(179\) 10.6213 18.3967i 0.793875 1.37503i −0.129676 0.991556i \(-0.541394\pi\)
0.923551 0.383475i \(-0.125273\pi\)
\(180\) 0 0
\(181\) 16.4853 1.22534 0.612671 0.790338i \(-0.290095\pi\)
0.612671 + 0.790338i \(0.290095\pi\)
\(182\) 0 0
\(183\) 2.89949 0.214337
\(184\) 0 0
\(185\) 13.4142 23.2341i 0.986233 1.70820i
\(186\) 0 0
\(187\) 0.899495 0.0657776
\(188\) 0 0
\(189\) 1.91421 + 3.31552i 0.139239 + 0.241168i
\(190\) 0 0
\(191\) −7.62132 13.2005i −0.551459 0.955156i −0.998170 0.0604770i \(-0.980738\pi\)
0.446710 0.894679i \(-0.352596\pi\)
\(192\) 0 0
\(193\) 1.25736 2.17781i 0.0905067 0.156762i −0.817218 0.576329i \(-0.804485\pi\)
0.907724 + 0.419567i \(0.137818\pi\)
\(194\) 0 0
\(195\) −4.10051 1.01461i −0.293643 0.0726579i
\(196\) 0 0
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) 0 0
\(199\) −9.10660 15.7731i −0.645550 1.11813i −0.984174 0.177204i \(-0.943295\pi\)
0.338624 0.940922i \(-0.390038\pi\)
\(200\) 0 0
\(201\) −0.985281 1.70656i −0.0694964 0.120371i
\(202\) 0 0
\(203\) −4.21320 −0.295709
\(204\) 0 0
\(205\) −0.242641 + 0.420266i −0.0169468 + 0.0293527i
\(206\) 0 0
\(207\) 20.4853 1.42383
\(208\) 0 0
\(209\) −37.9706 −2.62648
\(210\) 0 0
\(211\) −8.20711 + 14.2151i −0.565001 + 0.978610i 0.432049 + 0.901850i \(0.357791\pi\)
−0.997050 + 0.0767595i \(0.975543\pi\)
\(212\) 0 0
\(213\) 0.514719 0.0352679
\(214\) 0 0
\(215\) −14.2426 24.6690i −0.971340 1.68241i
\(216\) 0 0
\(217\) 4.48528 + 7.76874i 0.304481 + 0.527376i
\(218\) 0 0
\(219\) 0.928932 1.60896i 0.0627714 0.108723i
\(220\) 0 0
\(221\) 0.428932 0.445759i 0.0288531 0.0299850i
\(222\) 0 0
\(223\) 6.44975 11.1713i 0.431907 0.748085i −0.565130 0.825002i \(-0.691174\pi\)
0.997038 + 0.0769166i \(0.0245075\pi\)
\(224\) 0 0
\(225\) 4.24264 + 7.34847i 0.282843 + 0.489898i
\(226\) 0 0
\(227\) 4.86396 + 8.42463i 0.322832 + 0.559162i 0.981071 0.193647i \(-0.0620316\pi\)
−0.658239 + 0.752809i \(0.728698\pi\)
\(228\) 0 0
\(229\) −8.48528 −0.560723 −0.280362 0.959894i \(-0.590454\pi\)
−0.280362 + 0.959894i \(0.590454\pi\)
\(230\) 0 0
\(231\) 1.72183 2.98229i 0.113288 0.196220i
\(232\) 0 0
\(233\) −3.51472 −0.230257 −0.115128 0.993351i \(-0.536728\pi\)
−0.115128 + 0.993351i \(0.536728\pi\)
\(234\) 0 0
\(235\) −16.9706 −1.10704
\(236\) 0 0
\(237\) 1.24264 2.15232i 0.0807182 0.139808i
\(238\) 0 0
\(239\) 24.9706 1.61521 0.807606 0.589723i \(-0.200763\pi\)
0.807606 + 0.589723i \(0.200763\pi\)
\(240\) 0 0
\(241\) 10.2279 + 17.7153i 0.658838 + 1.14114i 0.980917 + 0.194429i \(0.0622852\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) −5.17157 8.95743i −0.331757 0.574619i
\(244\) 0 0
\(245\) −6.34315 + 10.9867i −0.405249 + 0.701911i
\(246\) 0 0
\(247\) −18.1066 + 18.8169i −1.15210 + 1.19729i
\(248\) 0 0
\(249\) −0.828427 + 1.43488i −0.0524994 + 0.0909317i
\(250\) 0 0
\(251\) 3.86396 + 6.69258i 0.243891 + 0.422432i 0.961819 0.273685i \(-0.0882427\pi\)
−0.717928 + 0.696117i \(0.754909\pi\)
\(252\) 0 0
\(253\) −18.9853 32.8835i −1.19359 2.06737i
\(254\) 0 0
\(255\) 0.201010 0.0125877
\(256\) 0 0
\(257\) 11.3995 19.7445i 0.711081 1.23163i −0.253371 0.967369i \(-0.581539\pi\)
0.964452 0.264259i \(-0.0851274\pi\)
\(258\) 0 0
\(259\) 15.0416 0.934641
\(260\) 0 0
\(261\) 7.51472 0.465149
\(262\) 0 0
\(263\) −0.378680 + 0.655892i −0.0233504 + 0.0404441i −0.877464 0.479642i \(-0.840767\pi\)
0.854114 + 0.520086i \(0.174100\pi\)
\(264\) 0 0
\(265\) −8.00000 −0.491436
\(266\) 0 0
\(267\) 3.03553 + 5.25770i 0.185772 + 0.321766i
\(268\) 0 0
\(269\) 5.74264 + 9.94655i 0.350135 + 0.606452i 0.986273 0.165124i \(-0.0528024\pi\)
−0.636138 + 0.771575i \(0.719469\pi\)
\(270\) 0 0
\(271\) −8.37868 + 14.5123i −0.508969 + 0.881559i 0.490978 + 0.871172i \(0.336640\pi\)
−0.999946 + 0.0103871i \(0.996694\pi\)
\(272\) 0 0
\(273\) −0.656854 2.27541i −0.0397546 0.137714i
\(274\) 0 0
\(275\) 7.86396 13.6208i 0.474215 0.821364i
\(276\) 0 0
\(277\) 1.74264 + 3.01834i 0.104705 + 0.181355i 0.913618 0.406574i \(-0.133277\pi\)
−0.808913 + 0.587929i \(0.799943\pi\)
\(278\) 0 0
\(279\) −8.00000 13.8564i −0.478947 0.829561i
\(280\) 0 0
\(281\) 26.1421 1.55951 0.779755 0.626085i \(-0.215344\pi\)
0.779755 + 0.626085i \(0.215344\pi\)
\(282\) 0 0
\(283\) 3.79289 6.56948i 0.225464 0.390515i −0.730994 0.682383i \(-0.760943\pi\)
0.956459 + 0.291868i \(0.0942768\pi\)
\(284\) 0 0
\(285\) −8.48528 −0.502625
\(286\) 0 0
\(287\) −0.272078 −0.0160603
\(288\) 0 0
\(289\) 8.48528 14.6969i 0.499134 0.864526i
\(290\) 0 0
\(291\) −3.72792 −0.218535
\(292\) 0 0
\(293\) 10.1569 + 17.5922i 0.593370 + 1.02775i 0.993775 + 0.111408i \(0.0355361\pi\)
−0.400405 + 0.916338i \(0.631131\pi\)
\(294\) 0 0
\(295\) 10.2426 + 17.7408i 0.596350 + 1.03291i
\(296\) 0 0
\(297\) −6.32843 + 10.9612i −0.367213 + 0.636031i
\(298\) 0 0
\(299\) −25.3492 6.27231i −1.46598 0.362737i
\(300\) 0 0
\(301\) 7.98528 13.8309i 0.460264 0.797201i
\(302\) 0 0
\(303\) −1.27817 2.21386i −0.0734292 0.127183i
\(304\) 0 0
\(305\) 9.89949 + 17.1464i 0.566843 + 0.981802i
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 3.51472 0.198664 0.0993318 0.995054i \(-0.468329\pi\)
0.0993318 + 0.995054i \(0.468329\pi\)
\(314\) 0 0
\(315\) −6.34315 + 10.9867i −0.357396 + 0.619028i
\(316\) 0 0
\(317\) 5.31371 0.298448 0.149224 0.988803i \(-0.452323\pi\)
0.149224 + 0.988803i \(0.452323\pi\)
\(318\) 0 0
\(319\) −6.96447 12.0628i −0.389935 0.675388i
\(320\) 0 0
\(321\) −2.22792 3.85887i −0.124350 0.215381i
\(322\) 0 0
\(323\) 0.621320 1.07616i 0.0345712 0.0598791i
\(324\) 0 0
\(325\) −3.00000 10.3923i −0.166410 0.576461i
\(326\) 0 0
\(327\) −1.75736 + 3.04384i −0.0971822 + 0.168324i
\(328\) 0 0
\(329\) −4.75736 8.23999i −0.262282 0.454285i
\(330\) 0 0
\(331\) −0.621320 1.07616i −0.0341509 0.0591510i 0.848445 0.529284i \(-0.177539\pi\)
−0.882596 + 0.470133i \(0.844206\pi\)
\(332\) 0 0
\(333\) −26.8284 −1.47019
\(334\) 0 0
\(335\) 6.72792 11.6531i 0.367586 0.636677i
\(336\) 0 0
\(337\) −12.4853 −0.680117 −0.340058 0.940404i \(-0.610447\pi\)
−0.340058 + 0.940404i \(0.610447\pi\)
\(338\) 0 0
\(339\) −2.41421 −0.131122
\(340\) 0 0
\(341\) −14.8284 + 25.6836i −0.803004 + 1.39084i
\(342\) 0 0
\(343\) −18.2132 −0.983421
\(344\) 0 0
\(345\) −4.24264 7.34847i −0.228416 0.395628i
\(346\) 0 0
\(347\) 11.3787 + 19.7085i 0.610840 + 1.05801i 0.991099 + 0.133125i \(0.0425013\pi\)
−0.380260 + 0.924880i \(0.624165\pi\)
\(348\) 0 0
\(349\) 8.22792 14.2512i 0.440431 0.762848i −0.557291 0.830317i \(-0.688159\pi\)
0.997721 + 0.0674693i \(0.0214925\pi\)
\(350\) 0 0
\(351\) 2.41421 + 8.36308i 0.128861 + 0.446388i
\(352\) 0 0
\(353\) 1.67157 2.89525i 0.0889688 0.154099i −0.818107 0.575066i \(-0.804976\pi\)
0.907076 + 0.420968i \(0.138310\pi\)
\(354\) 0 0
\(355\) 1.75736 + 3.04384i 0.0932709 + 0.161550i
\(356\) 0 0
\(357\) 0.0563492 + 0.0975997i 0.00298232 + 0.00516552i
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) −16.7279 + 28.9736i −0.880417 + 1.52493i
\(362\) 0 0
\(363\) 6.82843 0.358399
\(364\) 0 0
\(365\) 12.6863 0.664031
\(366\) 0 0
\(367\) −16.8640 + 29.2092i −0.880292 + 1.52471i −0.0292747 + 0.999571i \(0.509320\pi\)
−0.851017 + 0.525138i \(0.824014\pi\)
\(368\) 0 0
\(369\) 0.485281 0.0252627
\(370\) 0 0
\(371\) −2.24264 3.88437i −0.116432 0.201666i
\(372\) 0 0
\(373\) −10.2574 17.7663i −0.531106 0.919902i −0.999341 0.0362985i \(-0.988443\pi\)
0.468235 0.883604i \(-0.344890\pi\)
\(374\) 0 0
\(375\) −1.17157 + 2.02922i −0.0604998 + 0.104789i
\(376\) 0 0
\(377\) −9.29899 2.30090i −0.478922 0.118503i
\(378\) 0 0
\(379\) −4.69239 + 8.12745i −0.241032 + 0.417479i −0.961008 0.276519i \(-0.910819\pi\)
0.719977 + 0.693998i \(0.244152\pi\)
\(380\) 0 0
\(381\) −0.914214 1.58346i −0.0468366 0.0811233i
\(382\) 0 0
\(383\) 4.86396 + 8.42463i 0.248537 + 0.430478i 0.963120 0.269072i \(-0.0867170\pi\)
−0.714583 + 0.699550i \(0.753384\pi\)
\(384\) 0 0
\(385\) 23.5147 1.19842
\(386\) 0 0
\(387\) −14.2426 + 24.6690i −0.723994 + 1.25399i
\(388\) 0 0
\(389\) 28.6274 1.45147 0.725734 0.687976i \(-0.241500\pi\)
0.725734 + 0.687976i \(0.241500\pi\)
\(390\) 0 0
\(391\) 1.24264 0.0628430
\(392\) 0 0
\(393\) 0.828427 1.43488i 0.0417886 0.0723800i
\(394\) 0 0
\(395\) 16.9706 0.853882
\(396\) 0 0
\(397\) −2.74264 4.75039i −0.137649 0.238415i 0.788957 0.614448i \(-0.210621\pi\)
−0.926606 + 0.376033i \(0.877288\pi\)
\(398\) 0 0
\(399\) −2.37868 4.11999i −0.119083 0.206258i
\(400\) 0 0
\(401\) 8.57107 14.8455i 0.428019 0.741350i −0.568678 0.822560i \(-0.692545\pi\)
0.996697 + 0.0812099i \(0.0258784\pi\)
\(402\) 0 0
\(403\) 5.65685 + 19.5959i 0.281788 + 0.976142i
\(404\) 0 0
\(405\) 10.5858 18.3351i 0.526012 0.911079i
\(406\) 0 0
\(407\) 24.8640 + 43.0656i 1.23246 + 2.13468i
\(408\) 0 0
\(409\) 13.7426 + 23.8030i 0.679530 + 1.17698i 0.975123 + 0.221666i \(0.0711495\pi\)
−0.295593 + 0.955314i \(0.595517\pi\)
\(410\) 0 0
\(411\) 8.55635 0.422054
\(412\) 0 0
\(413\) −5.74264 + 9.94655i −0.282577 + 0.489438i
\(414\) 0 0
\(415\) −11.3137 −0.555368
\(416\) 0 0
\(417\) 3.00000 0.146911
\(418\) 0 0
\(419\) −6.86396 + 11.8887i −0.335326 + 0.580802i −0.983547 0.180650i \(-0.942180\pi\)
0.648221 + 0.761452i \(0.275513\pi\)
\(420\) 0 0
\(421\) −16.4853 −0.803443 −0.401722 0.915762i \(-0.631588\pi\)
−0.401722 + 0.915762i \(0.631588\pi\)
\(422\) 0 0
\(423\) 8.48528 + 14.6969i 0.412568 + 0.714590i
\(424\) 0 0
\(425\) 0.257359 + 0.445759i 0.0124838 + 0.0216225i
\(426\) 0 0
\(427\) −5.55025 + 9.61332i −0.268596 + 0.465221i
\(428\) 0 0
\(429\) 5.42893 5.64191i 0.262111 0.272394i
\(430\) 0 0
\(431\) −12.3492 + 21.3895i −0.594842 + 1.03030i 0.398727 + 0.917070i \(0.369452\pi\)
−0.993569 + 0.113227i \(0.963881\pi\)
\(432\) 0 0
\(433\) 9.74264 + 16.8747i 0.468201 + 0.810949i 0.999340 0.0363365i \(-0.0115688\pi\)
−0.531138 + 0.847285i \(0.678235\pi\)
\(434\) 0 0
\(435\) −1.55635 2.69568i −0.0746212 0.129248i
\(436\) 0 0
\(437\) −52.4558 −2.50930
\(438\) 0 0
\(439\) 6.96447 12.0628i 0.332396 0.575726i −0.650585 0.759433i \(-0.725476\pi\)
0.982981 + 0.183707i \(0.0588097\pi\)
\(440\) 0 0
\(441\) 12.6863 0.604109
\(442\) 0 0
\(443\) 4.97056 0.236159 0.118079 0.993004i \(-0.462326\pi\)
0.118079 + 0.993004i \(0.462326\pi\)
\(444\) 0 0
\(445\) −20.7279 + 35.9018i −0.982598 + 1.70191i
\(446\) 0 0
\(447\) −6.07107 −0.287152
\(448\) 0 0
\(449\) −14.7426 25.5350i −0.695748 1.20507i −0.969928 0.243393i \(-0.921740\pi\)
0.274180 0.961679i \(-0.411594\pi\)
\(450\) 0 0
\(451\) −0.449747 0.778985i −0.0211778 0.0366810i
\(452\) 0 0
\(453\) −3.51472 + 6.08767i −0.165136 + 0.286024i
\(454\) 0 0
\(455\) 11.2132 11.6531i 0.525683 0.546306i
\(456\) 0 0
\(457\) −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 0 0
\(459\) −0.207107 0.358719i −0.00966692 0.0167436i
\(460\) 0 0
\(461\) −20.3995 35.3330i −0.950099 1.64562i −0.745204 0.666836i \(-0.767648\pi\)
−0.204895 0.978784i \(-0.565685\pi\)
\(462\) 0 0
\(463\) 29.6569 1.37827 0.689135 0.724633i \(-0.257990\pi\)
0.689135 + 0.724633i \(0.257990\pi\)
\(464\) 0 0
\(465\) −3.31371 + 5.73951i −0.153670 + 0.266163i
\(466\) 0 0
\(467\) −26.9706 −1.24805 −0.624024 0.781405i \(-0.714503\pi\)
−0.624024 + 0.781405i \(0.714503\pi\)
\(468\) 0 0
\(469\) 7.54416 0.348357
\(470\) 0 0
\(471\) −3.41421 + 5.91359i −0.157319 + 0.272484i
\(472\) 0 0
\(473\) 52.7990 2.42770
\(474\) 0 0
\(475\) −10.8640 18.8169i −0.498473 0.863380i
\(476\) 0 0
\(477\) 4.00000 + 6.92820i 0.183147 + 0.317221i
\(478\) 0 0
\(479\) 8.62132 14.9326i 0.393918 0.682286i −0.599044 0.800716i \(-0.704453\pi\)
0.992962 + 0.118430i \(0.0377860\pi\)
\(480\) 0 0
\(481\) 33.1985 + 8.21449i 1.51372 + 0.374549i
\(482\) 0 0
\(483\) 2.37868 4.11999i 0.108234 0.187466i
\(484\) 0 0
\(485\) −12.7279 22.0454i −0.577945 1.00103i
\(486\) 0 0
\(487\) −3.44975 5.97514i −0.156323 0.270759i 0.777217 0.629233i \(-0.216631\pi\)
−0.933540 + 0.358473i \(0.883297\pi\)
\(488\) 0 0
\(489\) 10.4558 0.472830
\(490\) 0 0
\(491\) 10.1066 17.5051i 0.456105 0.789996i −0.542646 0.839961i \(-0.682578\pi\)
0.998751 + 0.0499650i \(0.0159110\pi\)
\(492\) 0 0
\(493\) 0.455844 0.0205302
\(494\) 0 0
\(495\) −41.9411 −1.88511
\(496\) 0 0
\(497\) −0.985281 + 1.70656i −0.0441959 + 0.0765496i
\(498\) 0 0
\(499\) −6.34315 −0.283958 −0.141979 0.989870i \(-0.545347\pi\)
−0.141979 + 0.989870i \(0.545347\pi\)
\(500\) 0 0
\(501\) −2.01472 3.48960i −0.0900110 0.155904i
\(502\) 0 0
\(503\) −11.6213 20.1287i −0.518169 0.897495i −0.999777 0.0211085i \(-0.993280\pi\)
0.481608 0.876387i \(-0.340053\pi\)
\(504\) 0 0
\(505\) 8.72792 15.1172i 0.388387 0.672707i
\(506\) 0 0
\(507\) −0.207107 5.38079i −0.00919794 0.238969i
\(508\) 0 0
\(509\) −11.5711 + 20.0417i −0.512879 + 0.888332i 0.487010 + 0.873396i \(0.338088\pi\)
−0.999888 + 0.0149353i \(0.995246\pi\)
\(510\) 0 0
\(511\) 3.55635 + 6.15978i 0.157324 + 0.272493i
\(512\) 0 0
\(513\) 8.74264 + 15.1427i 0.385997 + 0.668566i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 15.7279 27.2416i 0.691713 1.19808i
\(518\) 0 0
\(519\) −3.72792 −0.163638
\(520\) 0 0
\(521\) −14.8284 −0.649645 −0.324823 0.945775i \(-0.605305\pi\)
−0.324823 + 0.945775i \(0.605305\pi\)
\(522\) 0 0
\(523\) 6.79289 11.7656i 0.297032 0.514475i −0.678423 0.734671i \(-0.737336\pi\)
0.975456 + 0.220196i \(0.0706697\pi\)
\(524\) 0 0
\(525\) 1.97056 0.0860024
\(526\) 0 0
\(527\) −0.485281 0.840532i −0.0211392 0.0366141i
\(528\) 0 0
\(529\) −14.7279 25.5095i −0.640344 1.10911i
\(530\) 0 0
\(531\) 10.2426 17.7408i 0.444493 0.769884i
\(532\) 0 0
\(533\) −0.600505 0.148586i −0.0260108 0.00643599i
\(534\) 0 0
\(535\) 15.2132 26.3500i 0.657724 1.13921i
\(536\) 0 0
\(537\) 4.39949 + 7.62015i 0.189852 + 0.328834i
\(538\) 0 0
\(539\) −11.7574 20.3643i −0.506425 0.877154i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) −3.41421 + 5.91359i −0.146518 + 0.253776i
\(544\) 0 0
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 0 0
\(549\) 9.89949 17.1464i 0.422500 0.731792i
\(550\) 0 0
\(551\) −19.2426 −0.819764
\(552\) 0 0
\(553\) 4.75736 + 8.23999i 0.202303 + 0.350400i
\(554\) 0 0
\(555\) 5.55635 + 9.62388i 0.235854 + 0.408511i
\(556\) 0 0
\(557\) 1.32843 2.30090i 0.0562873 0.0974924i −0.836509 0.547954i \(-0.815407\pi\)
0.892796 + 0.450461i \(0.148740\pi\)
\(558\) 0 0
\(559\) 25.1777 26.1654i 1.06490 1.10668i
\(560\) 0 0
\(561\) −0.186292 + 0.322666i −0.00786523 + 0.0136230i
\(562\) 0 0
\(563\) 13.3492 + 23.1216i 0.562603 + 0.974458i 0.997268 + 0.0738655i \(0.0235335\pi\)
−0.434665 + 0.900592i \(0.643133\pi\)
\(564\) 0 0
\(565\) −8.24264 14.2767i −0.346770 0.600624i
\(566\) 0 0
\(567\) 11.8701 0.498496
\(568\) 0 0
\(569\) −3.98528 + 6.90271i −0.167072 + 0.289377i −0.937389 0.348284i \(-0.886764\pi\)
0.770317 + 0.637661i \(0.220098\pi\)
\(570\) 0 0
\(571\) −16.2843 −0.681476 −0.340738 0.940158i \(-0.610677\pi\)
−0.340738 + 0.940158i \(0.610677\pi\)
\(572\) 0 0
\(573\) 6.31371 0.263759
\(574\) 0 0
\(575\) 10.8640 18.8169i 0.453058 0.784720i
\(576\) 0 0
\(577\) −12.4853 −0.519769 −0.259885 0.965640i \(-0.583685\pi\)
−0.259885 + 0.965640i \(0.583685\pi\)
\(578\) 0 0
\(579\) 0.520815 + 0.902079i 0.0216443 + 0.0374891i
\(580\) 0 0
\(581\) −3.17157 5.49333i −0.131579 0.227902i
\(582\) 0 0
\(583\) 7.41421 12.8418i 0.307065 0.531853i
\(584\) 0 0
\(585\) −20.0000 + 20.7846i −0.826898 + 0.859338i
\(586\) 0 0
\(587\) −19.3492 + 33.5139i −0.798629 + 1.38327i 0.121881 + 0.992545i \(0.461108\pi\)
−0.920509 + 0.390721i \(0.872226\pi\)
\(588\) 0 0
\(589\) 20.4853 + 35.4815i 0.844081 + 1.46199i
\(590\) 0 0
\(591\) −0.621320 1.07616i −0.0255577 0.0442672i
\(592\) 0 0
\(593\) 9.17157 0.376631 0.188316 0.982109i \(-0.439697\pi\)
0.188316 + 0.982109i \(0.439697\pi\)
\(594\) 0 0
\(595\) −0.384776 + 0.666452i −0.0157743 + 0.0273219i
\(596\) 0 0
\(597\) 7.54416 0.308762
\(598\) 0 0
\(599\) −19.9411 −0.814772 −0.407386 0.913256i \(-0.633560\pi\)
−0.407386 + 0.913256i \(0.633560\pi\)
\(600\) 0 0
\(601\) 13.7426 23.8030i 0.560574 0.970943i −0.436872 0.899523i \(-0.643914\pi\)
0.997446 0.0714192i \(-0.0227528\pi\)
\(602\) 0 0
\(603\) −13.4558 −0.547964
\(604\) 0 0
\(605\) 23.3137 + 40.3805i 0.947837 + 1.64170i
\(606\) 0 0
\(607\) 2.20711 + 3.82282i 0.0895837 + 0.155164i 0.907335 0.420408i \(-0.138113\pi\)
−0.817752 + 0.575571i \(0.804780\pi\)
\(608\) 0 0
\(609\) 0.872583 1.51136i 0.0353588 0.0612433i
\(610\) 0 0
\(611\) −6.00000 20.7846i −0.242734 0.840855i
\(612\) 0 0
\(613\) 15.7426 27.2671i 0.635839 1.10131i −0.350497 0.936564i \(-0.613987\pi\)
0.986337 0.164742i \(-0.0526792\pi\)
\(614\) 0 0
\(615\) −0.100505 0.174080i −0.00405276 0.00701958i
\(616\) 0 0
\(617\) 10.8431 + 18.7809i 0.436529 + 0.756090i 0.997419 0.0718003i \(-0.0228744\pi\)
−0.560890 + 0.827890i \(0.689541\pi\)
\(618\) 0 0
\(619\) 28.9706 1.16443 0.582213 0.813037i \(-0.302187\pi\)
0.582213 + 0.813037i \(0.302187\pi\)
\(620\) 0 0
\(621\) −8.74264 + 15.1427i −0.350830 + 0.607656i
\(622\) 0 0
\(623\) −23.2426 −0.931197
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) 7.86396 13.6208i 0.314056 0.543962i
\(628\) 0 0
\(629\) −1.62742 −0.0648894
\(630\) 0 0
\(631\) −0.621320 1.07616i −0.0247344 0.0428412i 0.853393 0.521268i \(-0.174541\pi\)
−0.878128 + 0.478426i \(0.841207\pi\)
\(632\) 0 0
\(633\) −3.39949 5.88810i −0.135118 0.234031i
\(634\) 0 0
\(635\) 6.24264 10.8126i 0.247732 0.429084i
\(636\) 0 0
\(637\) −15.6985 3.88437i −0.621997 0.153904i
\(638\) 0 0
\(639\) 1.75736 3.04384i 0.0695201 0.120412i
\(640\) 0 0
\(641\) −8.39949 14.5484i −0.331760 0.574625i 0.651097 0.758995i \(-0.274309\pi\)
−0.982857 + 0.184369i \(0.940976\pi\)
\(642\) 0 0
\(643\) −21.1066 36.5577i −0.832363 1.44170i −0.896159 0.443732i \(-0.853654\pi\)
0.0637963 0.997963i \(-0.479679\pi\)
\(644\) 0 0
\(645\) 11.7990 0.464585
\(646\) 0 0
\(647\) −7.37868 + 12.7802i −0.290086 + 0.502443i −0.973830 0.227279i \(-0.927017\pi\)
0.683744 + 0.729722i \(0.260351\pi\)
\(648\) 0 0
\(649\) −37.9706 −1.49047
\(650\) 0 0
\(651\) −3.71573 −0.145631
\(652\) 0 0
\(653\) 2.57107 4.45322i 0.100614 0.174268i −0.811324 0.584597i \(-0.801253\pi\)
0.911938 + 0.410329i \(0.134586\pi\)
\(654\) 0 0
\(655\) 11.3137 0.442063
\(656\) 0 0
\(657\) −6.34315 10.9867i −0.247470 0.428630i
\(658\) 0 0
\(659\) −9.10660 15.7731i −0.354743 0.614433i 0.632331 0.774698i \(-0.282098\pi\)
−0.987074 + 0.160266i \(0.948765\pi\)
\(660\) 0 0
\(661\) −13.2279 + 22.9114i −0.514507 + 0.891151i 0.485352 + 0.874319i \(0.338692\pi\)
−0.999858 + 0.0168325i \(0.994642\pi\)
\(662\) 0 0
\(663\) 0.0710678 + 0.246186i 0.00276005 + 0.00956108i
\(664\) 0 0
\(665\) 16.2426 28.1331i 0.629863 1.09095i
\(666\) 0 0
\(667\) −9.62132 16.6646i −0.372539 0.645256i
\(668\) 0 0
\(669\) 2.67157 + 4.62730i 0.103289 + 0.178902i
\(670\) 0 0
\(671\) −36.6985 −1.41673
\(672\) 0 0
\(673\) 20.9853 36.3476i 0.808923 1.40110i −0.104687 0.994505i \(-0.533384\pi\)
0.913610 0.406591i \(-0.133283\pi\)
\(674\) 0 0
\(675\) −7.24264 −0.278769
\(676\) 0 0
\(677\) 25.4558 0.978348 0.489174 0.872186i \(-0.337298\pi\)
0.489174 + 0.872186i \(0.337298\pi\)
\(678\) 0 0
\(679\) 7.13604 12.3600i 0.273856 0.474333i
\(680\) 0 0
\(681\) −4.02944 −0.154408
\(682\) 0 0
\(683\) 0.378680 + 0.655892i 0.0144898 + 0.0250970i 0.873179 0.487399i \(-0.162054\pi\)
−0.858690 + 0.512496i \(0.828721\pi\)
\(684\) 0 0
\(685\) 29.2132 + 50.5988i 1.11618 + 1.93328i
\(686\) 0 0
\(687\) 1.75736 3.04384i 0.0670474 0.116130i
\(688\) 0 0
\(689\) −2.82843 9.79796i −0.107754 0.373273i
\(690\) 0 0
\(691\) 0.964466 1.67050i 0.0366900 0.0635490i −0.847097 0.531438i \(-0.821652\pi\)
0.883787 + 0.467889i \(0.154985\pi\)
\(692\) 0 0
\(693\) −11.7574 20.3643i −0.446625 0.773577i
\(694\) 0 0
\(695\) 10.2426 + 17.7408i 0.388526 + 0.672946i
\(696\) 0 0
\(697\) 0.0294373 0.00111502
\(698\) 0 0
\(699\) 0.727922 1.26080i 0.0275325 0.0476878i
\(700\) 0 0
\(701\) 8.48528 0.320485 0.160242 0.987078i \(-0.448772\pi\)
0.160242 + 0.987078i \(0.448772\pi\)
\(702\) 0 0
\(703\) 68.6985 2.59101
\(704\) 0 0
\(705\) 3.51472 6.08767i 0.132372 0.229275i
\(706\) 0 0
\(707\) 9.78680 0.368070
\(708\) 0 0
\(709\) 1.25736 + 2.17781i 0.0472211 + 0.0817894i 0.888670 0.458548i \(-0.151630\pi\)
−0.841449 + 0.540337i \(0.818297\pi\)
\(710\) 0 0
\(711\) −8.48528 14.6969i −0.318223 0.551178i
\(712\) 0 0
\(713\) −20.4853 + 35.4815i −0.767180 + 1.32879i
\(714\) 0 0
\(715\) 51.8995 + 12.8418i 1.94093 + 0.480256i
\(716\) 0 0
\(717\) −5.17157 + 8.95743i −0.193136 + 0.334521i
\(718\) 0 0
\(719\) −15.6213 27.0569i −0.582577 1.00905i −0.995173 0.0981387i \(-0.968711\pi\)
0.412596 0.910914i \(-0.364622\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −8.47309 −0.315118
\(724\) 0 0
\(725\) 3.98528 6.90271i 0.148010 0.256360i
\(726\) 0 0
\(727\) −12.6863 −0.470509 −0.235254 0.971934i \(-0.575592\pi\)
−0.235254 + 0.971934i \(0.575592\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −0.863961 + 1.49642i −0.0319548 + 0.0553473i
\(732\) 0 0
\(733\) −23.9411 −0.884286 −0.442143 0.896945i \(-0.645782\pi\)
−0.442143 + 0.896945i \(0.645782\pi\)
\(734\) 0 0
\(735\) −2.62742 4.55082i −0.0969137 0.167860i
\(736\) 0 0
\(737\) 12.4706 + 21.5996i 0.459359 + 0.795633i
\(738\) 0 0
\(739\) 6.10660 10.5769i 0.224635 0.389079i −0.731575 0.681761i \(-0.761214\pi\)
0.956210 + 0.292682i \(0.0945477\pi\)
\(740\) 0 0
\(741\) −3.00000 10.3923i −0.110208 0.381771i
\(742\) 0 0
\(743\) 0.621320 1.07616i 0.0227940 0.0394804i −0.854403 0.519610i \(-0.826077\pi\)
0.877197 + 0.480130i \(0.159410\pi\)
\(744\) 0 0
\(745\) −20.7279 35.9018i −0.759412 1.31534i
\(746\) 0 0
\(747\) 5.65685 + 9.79796i 0.206973 + 0.358489i
\(748\) 0 0
\(749\) 17.0589 0.623318
\(750\) 0 0
\(751\) 18.4497 31.9559i 0.673241 1.16609i −0.303739 0.952755i \(-0.598235\pi\)
0.976980 0.213332i \(-0.0684316\pi\)
\(752\) 0 0
\(753\) −3.20101 −0.116651
\(754\) 0 0
\(755\) −48.0000 −1.74690
\(756\) 0 0
\(757\) 3.25736 5.64191i 0.118391 0.205059i −0.800739 0.599013i \(-0.795560\pi\)
0.919130 + 0.393954i \(0.128893\pi\)
\(758\) 0 0
\(759\) 15.7279 0.570887
\(760\) 0 0
\(761\) −6.25736 10.8381i −0.226829 0.392880i 0.730038 0.683407i \(-0.239503\pi\)
−0.956867 + 0.290528i \(0.906169\pi\)
\(762\) 0 0
\(763\) −6.72792 11.6531i −0.243567 0.421871i
\(764\) 0 0
\(765\) 0.686292 1.18869i 0.0248129 0.0429772i
\(766\) 0 0
\(767\) −18.1066 + 18.8169i −0.653791 + 0.679440i
\(768\) 0 0
\(769\) −19.7132 + 34.1443i −0.710876 + 1.23127i 0.253652 + 0.967295i \(0.418368\pi\)
−0.964529 + 0.263978i \(0.914965\pi\)
\(770\) 0 0
\(771\) 4.72183 + 8.17844i 0.170052 + 0.294539i
\(772\) 0 0
\(773\) −2.74264 4.75039i −0.0986459 0.170860i 0.812478 0.582991i \(-0.198118\pi\)
−0.911124 + 0.412131i \(0.864784\pi\)
\(774\) 0 0
\(775\) −16.9706 −0.609601
\(776\) 0 0
\(777\) −3.11522 + 5.39573i −0.111758 + 0.193571i
\(778\) 0 0
\(779\) −1.24264 −0.0445222
\(780\) 0 0
\(781\) −6.51472 −0.233115
\(782\) 0 0
\(783\) −3.20711 + 5.55487i −0.114613 + 0.198515i
\(784\) 0 0
\(785\) −46.6274 −1.66420
\(786\) 0 0
\(787\) 22.0061 + 38.1157i 0.784433 + 1.35868i 0.929337 + 0.369232i \(0.120379\pi\)
−0.144905 + 0.989446i \(0.546288\pi\)
\(788\) 0 0
\(789\) −0.156854 0.271680i −0.00558416 0.00967205i
\(790\) 0 0
\(791\) 4.62132 8.00436i 0.164315 0.284602i