Properties

Label 880.2.bo.d.81.2
Level $880$
Weight $2$
Character 880.81
Analytic conductor $7.027$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(81,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 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("880.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bo (of order \(5\), degree \(4\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.2
Root \(1.69513 + 1.23158i\) of defining polynomial
Character \(\chi\) \(=\) 880.81
Dual form 880.2.bo.d.641.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.400166 - 1.23158i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(0.0703870 + 0.216629i) q^{7} +(1.07039 + 0.777682i) q^{9} +O(q^{10})\) \(q+(0.400166 - 1.23158i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(0.0703870 + 0.216629i) q^{7} +(1.07039 + 0.777682i) q^{9} +(3.12020 - 1.12443i) q^{11} +(2.70598 + 1.96601i) q^{13} +(0.400166 + 1.23158i) q^{15} +(-4.89440 + 3.55599i) q^{17} +(0.686443 - 2.11265i) q^{19} +0.294963 q^{21} +3.47726 q^{23} +(0.309017 - 0.951057i) q^{25} +(4.52905 - 3.29055i) q^{27} +(0.00951362 + 0.0292799i) q^{29} +(1.79298 + 1.30268i) q^{31} +(-0.136234 - 4.29274i) q^{33} +(-0.184276 - 0.133884i) q^{35} +(2.70306 + 8.31916i) q^{37} +(3.50415 - 2.54591i) q^{39} +(3.16446 - 9.73920i) q^{41} +3.74411 q^{43} -1.32307 q^{45} +(1.64211 - 5.05390i) q^{47} +(5.62115 - 4.08400i) q^{49} +(2.42093 + 7.45085i) q^{51} +(8.25427 + 5.99708i) q^{53} +(-1.86337 + 2.74369i) q^{55} +(-2.32722 - 1.69082i) q^{57} +(-2.57843 - 7.93560i) q^{59} +(1.81667 - 1.31989i) q^{61} +(-0.0931270 + 0.286615i) q^{63} -3.34478 q^{65} -3.47330 q^{67} +(1.39148 - 4.28253i) q^{69} +(-12.1868 + 8.85423i) q^{71} +(-1.13220 - 3.48457i) q^{73} +(-1.04765 - 0.761160i) q^{75} +(0.463206 + 0.596780i) q^{77} +(-9.40175 - 6.83077i) q^{79} +(-1.01366 - 3.11972i) q^{81} +(1.23192 - 0.895044i) q^{83} +(1.86950 - 5.75372i) q^{85} +0.0398677 q^{87} -10.0058 q^{89} +(-0.235429 + 0.724575i) q^{91} +(2.32185 - 1.68692i) q^{93} +(0.686443 + 2.11265i) q^{95} +(6.74372 + 4.89960i) q^{97} +(4.21427 + 1.22295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9} - 3 q^{11} - 4 q^{13} - q^{15} - 3 q^{17} - 9 q^{19} - 4 q^{21} + 22 q^{23} - 2 q^{25} + 8 q^{27} - 17 q^{29} + 4 q^{31} + 21 q^{33} - 6 q^{35} + 24 q^{37} + 13 q^{39} - 4 q^{41} + 14 q^{43} - 8 q^{45} + 12 q^{47} - 15 q^{49} + 17 q^{51} + 35 q^{53} - 3 q^{55} - q^{57} - 21 q^{59} - 22 q^{61} - 5 q^{63} + 6 q^{65} - 14 q^{67} + 3 q^{69} - 40 q^{71} + 9 q^{73} - q^{75} - 4 q^{77} - 41 q^{79} + 24 q^{81} + 7 q^{83} - 8 q^{85} + 46 q^{87} - 24 q^{89} + 18 q^{91} + 3 q^{93} - 9 q^{95} + 4 q^{97} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.400166 1.23158i 0.231036 0.711055i −0.766587 0.642141i \(-0.778047\pi\)
0.997623 0.0689142i \(-0.0219535\pi\)
\(4\) 0 0
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) 0.0703870 + 0.216629i 0.0266038 + 0.0818780i 0.963477 0.267792i \(-0.0862939\pi\)
−0.936873 + 0.349670i \(0.886294\pi\)
\(8\) 0 0
\(9\) 1.07039 + 0.777682i 0.356796 + 0.259227i
\(10\) 0 0
\(11\) 3.12020 1.12443i 0.940776 0.339029i
\(12\) 0 0
\(13\) 2.70598 + 1.96601i 0.750504 + 0.545273i 0.895983 0.444088i \(-0.146472\pi\)
−0.145479 + 0.989361i \(0.546472\pi\)
\(14\) 0 0
\(15\) 0.400166 + 1.23158i 0.103322 + 0.317993i
\(16\) 0 0
\(17\) −4.89440 + 3.55599i −1.18707 + 0.862455i −0.992951 0.118524i \(-0.962184\pi\)
−0.194116 + 0.980979i \(0.562184\pi\)
\(18\) 0 0
\(19\) 0.686443 2.11265i 0.157481 0.484676i −0.840923 0.541155i \(-0.817987\pi\)
0.998404 + 0.0564789i \(0.0179874\pi\)
\(20\) 0 0
\(21\) 0.294963 0.0643662
\(22\) 0 0
\(23\) 3.47726 0.725059 0.362529 0.931972i \(-0.381913\pi\)
0.362529 + 0.931972i \(0.381913\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0 0
\(27\) 4.52905 3.29055i 0.871617 0.633266i
\(28\) 0 0
\(29\) 0.00951362 + 0.0292799i 0.00176664 + 0.00543714i 0.951936 0.306297i \(-0.0990901\pi\)
−0.950169 + 0.311734i \(0.899090\pi\)
\(30\) 0 0
\(31\) 1.79298 + 1.30268i 0.322030 + 0.233968i 0.737041 0.675848i \(-0.236222\pi\)
−0.415011 + 0.909816i \(0.636222\pi\)
\(32\) 0 0
\(33\) −0.136234 4.29274i −0.0237152 0.747271i
\(34\) 0 0
\(35\) −0.184276 0.133884i −0.0311483 0.0226305i
\(36\) 0 0
\(37\) 2.70306 + 8.31916i 0.444380 + 1.36766i 0.883162 + 0.469068i \(0.155410\pi\)
−0.438782 + 0.898594i \(0.644590\pi\)
\(38\) 0 0
\(39\) 3.50415 2.54591i 0.561112 0.407672i
\(40\) 0 0
\(41\) 3.16446 9.73920i 0.494205 1.52101i −0.323986 0.946062i \(-0.605023\pi\)
0.818191 0.574946i \(-0.194977\pi\)
\(42\) 0 0
\(43\) 3.74411 0.570972 0.285486 0.958383i \(-0.407845\pi\)
0.285486 + 0.958383i \(0.407845\pi\)
\(44\) 0 0
\(45\) −1.32307 −0.197232
\(46\) 0 0
\(47\) 1.64211 5.05390i 0.239527 0.737188i −0.756962 0.653459i \(-0.773317\pi\)
0.996489 0.0837286i \(-0.0266829\pi\)
\(48\) 0 0
\(49\) 5.62115 4.08400i 0.803021 0.583429i
\(50\) 0 0
\(51\) 2.42093 + 7.45085i 0.338998 + 1.04333i
\(52\) 0 0
\(53\) 8.25427 + 5.99708i 1.13381 + 0.823762i 0.986245 0.165290i \(-0.0528561\pi\)
0.147566 + 0.989052i \(0.452856\pi\)
\(54\) 0 0
\(55\) −1.86337 + 2.74369i −0.251257 + 0.369959i
\(56\) 0 0
\(57\) −2.32722 1.69082i −0.308247 0.223955i
\(58\) 0 0
\(59\) −2.57843 7.93560i −0.335683 1.03313i −0.966384 0.257102i \(-0.917233\pi\)
0.630701 0.776026i \(-0.282767\pi\)
\(60\) 0 0
\(61\) 1.81667 1.31989i 0.232601 0.168994i −0.465380 0.885111i \(-0.654082\pi\)
0.697980 + 0.716117i \(0.254082\pi\)
\(62\) 0 0
\(63\) −0.0931270 + 0.286615i −0.0117329 + 0.0361102i
\(64\) 0 0
\(65\) −3.34478 −0.414869
\(66\) 0 0
\(67\) −3.47330 −0.424332 −0.212166 0.977234i \(-0.568052\pi\)
−0.212166 + 0.977234i \(0.568052\pi\)
\(68\) 0 0
\(69\) 1.39148 4.28253i 0.167514 0.515557i
\(70\) 0 0
\(71\) −12.1868 + 8.85423i −1.44631 + 1.05080i −0.459631 + 0.888110i \(0.652018\pi\)
−0.986677 + 0.162694i \(0.947982\pi\)
\(72\) 0 0
\(73\) −1.13220 3.48457i −0.132515 0.407838i 0.862681 0.505749i \(-0.168784\pi\)
−0.995195 + 0.0979113i \(0.968784\pi\)
\(74\) 0 0
\(75\) −1.04765 0.761160i −0.120972 0.0878912i
\(76\) 0 0
\(77\) 0.463206 + 0.596780i 0.0527872 + 0.0680094i
\(78\) 0 0
\(79\) −9.40175 6.83077i −1.05778 0.768522i −0.0841031 0.996457i \(-0.526803\pi\)
−0.973676 + 0.227935i \(0.926803\pi\)
\(80\) 0 0
\(81\) −1.01366 3.11972i −0.112629 0.346636i
\(82\) 0 0
\(83\) 1.23192 0.895044i 0.135221 0.0982439i −0.518119 0.855309i \(-0.673367\pi\)
0.653340 + 0.757065i \(0.273367\pi\)
\(84\) 0 0
\(85\) 1.86950 5.75372i 0.202775 0.624078i
\(86\) 0 0
\(87\) 0.0398677 0.00427426
\(88\) 0 0
\(89\) −10.0058 −1.06062 −0.530309 0.847805i \(-0.677924\pi\)
−0.530309 + 0.847805i \(0.677924\pi\)
\(90\) 0 0
\(91\) −0.235429 + 0.724575i −0.0246796 + 0.0759561i
\(92\) 0 0
\(93\) 2.32185 1.68692i 0.240764 0.174926i
\(94\) 0 0
\(95\) 0.686443 + 2.11265i 0.0704275 + 0.216754i
\(96\) 0 0
\(97\) 6.74372 + 4.89960i 0.684721 + 0.497479i 0.874921 0.484267i \(-0.160913\pi\)
−0.190200 + 0.981745i \(0.560913\pi\)
\(98\) 0 0
\(99\) 4.21427 + 1.22295i 0.423550 + 0.122911i
\(100\) 0 0
\(101\) −1.39376 1.01263i −0.138685 0.100760i 0.516280 0.856420i \(-0.327316\pi\)
−0.654964 + 0.755660i \(0.727316\pi\)
\(102\) 0 0
\(103\) 0.603980 + 1.85886i 0.0595119 + 0.183159i 0.976393 0.216002i \(-0.0693016\pi\)
−0.916881 + 0.399160i \(0.869302\pi\)
\(104\) 0 0
\(105\) −0.238630 + 0.173375i −0.0232879 + 0.0169197i
\(106\) 0 0
\(107\) −4.14096 + 12.7446i −0.400322 + 1.23206i 0.524417 + 0.851462i \(0.324283\pi\)
−0.924739 + 0.380603i \(0.875717\pi\)
\(108\) 0 0
\(109\) 7.46306 0.714831 0.357416 0.933945i \(-0.383658\pi\)
0.357416 + 0.933945i \(0.383658\pi\)
\(110\) 0 0
\(111\) 11.3274 1.07515
\(112\) 0 0
\(113\) 1.63548 5.03348i 0.153853 0.473510i −0.844190 0.536044i \(-0.819918\pi\)
0.998043 + 0.0625337i \(0.0199181\pi\)
\(114\) 0 0
\(115\) −2.81316 + 2.04388i −0.262329 + 0.190593i
\(116\) 0 0
\(117\) 1.36752 + 4.20878i 0.126427 + 0.389102i
\(118\) 0 0
\(119\) −1.11483 0.809973i −0.102197 0.0742501i
\(120\) 0 0
\(121\) 8.47131 7.01690i 0.770119 0.637900i
\(122\) 0 0
\(123\) −10.7283 7.79459i −0.967341 0.702814i
\(124\) 0 0
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) −9.86456 + 7.16702i −0.875338 + 0.635970i −0.932014 0.362422i \(-0.881950\pi\)
0.0566759 + 0.998393i \(0.481950\pi\)
\(128\) 0 0
\(129\) 1.49827 4.61119i 0.131915 0.405992i
\(130\) 0 0
\(131\) 2.06530 0.180446 0.0902229 0.995922i \(-0.471242\pi\)
0.0902229 + 0.995922i \(0.471242\pi\)
\(132\) 0 0
\(133\) 0.505978 0.0438739
\(134\) 0 0
\(135\) −1.72994 + 5.32422i −0.148890 + 0.458236i
\(136\) 0 0
\(137\) −11.6851 + 8.48974i −0.998328 + 0.725328i −0.961729 0.274002i \(-0.911652\pi\)
−0.0365990 + 0.999330i \(0.511652\pi\)
\(138\) 0 0
\(139\) 5.04999 + 15.5423i 0.428334 + 1.31828i 0.899765 + 0.436374i \(0.143738\pi\)
−0.471431 + 0.881903i \(0.656262\pi\)
\(140\) 0 0
\(141\) −5.56719 4.04480i −0.468842 0.340633i
\(142\) 0 0
\(143\) 10.6538 + 3.09166i 0.890920 + 0.258537i
\(144\) 0 0
\(145\) −0.0249070 0.0180960i −0.00206841 0.00150279i
\(146\) 0 0
\(147\) −2.78040 8.55718i −0.229323 0.705785i
\(148\) 0 0
\(149\) −12.1204 + 8.80602i −0.992946 + 0.721417i −0.960564 0.278058i \(-0.910309\pi\)
−0.0323814 + 0.999476i \(0.510309\pi\)
\(150\) 0 0
\(151\) −3.80960 + 11.7247i −0.310021 + 0.954146i 0.667735 + 0.744399i \(0.267264\pi\)
−0.977756 + 0.209747i \(0.932736\pi\)
\(152\) 0 0
\(153\) −8.00433 −0.647112
\(154\) 0 0
\(155\) −2.21625 −0.178014
\(156\) 0 0
\(157\) −6.44122 + 19.8240i −0.514065 + 1.58213i 0.270911 + 0.962605i \(0.412675\pi\)
−0.784976 + 0.619526i \(0.787325\pi\)
\(158\) 0 0
\(159\) 10.6890 7.76599i 0.847690 0.615883i
\(160\) 0 0
\(161\) 0.244754 + 0.753275i 0.0192893 + 0.0593664i
\(162\) 0 0
\(163\) 0.457082 + 0.332090i 0.0358014 + 0.0260113i 0.605542 0.795813i \(-0.292956\pi\)
−0.569741 + 0.821825i \(0.692956\pi\)
\(164\) 0 0
\(165\) 2.63343 + 3.39283i 0.205012 + 0.264131i
\(166\) 0 0
\(167\) −18.1506 13.1872i −1.40454 1.02046i −0.994088 0.108575i \(-0.965371\pi\)
−0.410451 0.911883i \(-0.634629\pi\)
\(168\) 0 0
\(169\) −0.560083 1.72376i −0.0430833 0.132597i
\(170\) 0 0
\(171\) 2.37773 1.72752i 0.181830 0.132107i
\(172\) 0 0
\(173\) 0.669243 2.05972i 0.0508816 0.156597i −0.922387 0.386267i \(-0.873764\pi\)
0.973269 + 0.229669i \(0.0737644\pi\)
\(174\) 0 0
\(175\) 0.227777 0.0172183
\(176\) 0 0
\(177\) −10.8052 −0.812165
\(178\) 0 0
\(179\) 6.84683 21.0724i 0.511756 1.57502i −0.277352 0.960768i \(-0.589457\pi\)
0.789108 0.614254i \(-0.210543\pi\)
\(180\) 0 0
\(181\) 7.23000 5.25290i 0.537402 0.390445i −0.285717 0.958314i \(-0.592232\pi\)
0.823119 + 0.567869i \(0.192232\pi\)
\(182\) 0 0
\(183\) −0.898582 2.76555i −0.0664251 0.204435i
\(184\) 0 0
\(185\) −7.07670 5.14152i −0.520289 0.378012i
\(186\) 0 0
\(187\) −11.2731 + 16.5988i −0.824367 + 1.21383i
\(188\) 0 0
\(189\) 1.03161 + 0.749512i 0.0750389 + 0.0545190i
\(190\) 0 0
\(191\) 3.55618 + 10.9448i 0.257316 + 0.791938i 0.993364 + 0.115009i \(0.0366897\pi\)
−0.736048 + 0.676929i \(0.763310\pi\)
\(192\) 0 0
\(193\) −6.72449 + 4.88563i −0.484039 + 0.351675i −0.802887 0.596131i \(-0.796704\pi\)
0.318848 + 0.947806i \(0.396704\pi\)
\(194\) 0 0
\(195\) −1.33846 + 4.11937i −0.0958494 + 0.294994i
\(196\) 0 0
\(197\) 3.64765 0.259885 0.129942 0.991522i \(-0.458521\pi\)
0.129942 + 0.991522i \(0.458521\pi\)
\(198\) 0 0
\(199\) 6.34757 0.449967 0.224984 0.974363i \(-0.427767\pi\)
0.224984 + 0.974363i \(0.427767\pi\)
\(200\) 0 0
\(201\) −1.38990 + 4.27766i −0.0980357 + 0.301723i
\(202\) 0 0
\(203\) −0.00567324 + 0.00412185i −0.000398184 + 0.000289297i
\(204\) 0 0
\(205\) 3.16446 + 9.73920i 0.221015 + 0.680215i
\(206\) 0 0
\(207\) 3.72201 + 2.70420i 0.258698 + 0.187955i
\(208\) 0 0
\(209\) −0.233694 7.36376i −0.0161650 0.509362i
\(210\) 0 0
\(211\) −15.5771 11.3174i −1.07237 0.779122i −0.0960325 0.995378i \(-0.530615\pi\)
−0.976337 + 0.216256i \(0.930615\pi\)
\(212\) 0 0
\(213\) 6.02798 + 18.5522i 0.413030 + 1.27118i
\(214\) 0 0
\(215\) −3.02905 + 2.20074i −0.206580 + 0.150089i
\(216\) 0 0
\(217\) −0.155995 + 0.480104i −0.0105896 + 0.0325916i
\(218\) 0 0
\(219\) −4.74460 −0.320611
\(220\) 0 0
\(221\) −20.2353 −1.36117
\(222\) 0 0
\(223\) 6.71498 20.6666i 0.449669 1.38394i −0.427613 0.903962i \(-0.640645\pi\)
0.877282 0.479976i \(-0.159355\pi\)
\(224\) 0 0
\(225\) 1.07039 0.777682i 0.0713591 0.0518454i
\(226\) 0 0
\(227\) 1.85557 + 5.71085i 0.123158 + 0.379043i 0.993561 0.113298i \(-0.0361415\pi\)
−0.870403 + 0.492341i \(0.836141\pi\)
\(228\) 0 0
\(229\) 18.7756 + 13.6413i 1.24073 + 0.901440i 0.997647 0.0685670i \(-0.0218427\pi\)
0.243079 + 0.970007i \(0.421843\pi\)
\(230\) 0 0
\(231\) 0.920344 0.331666i 0.0605542 0.0218220i
\(232\) 0 0
\(233\) −19.5930 14.2351i −1.28358 0.932576i −0.283925 0.958846i \(-0.591637\pi\)
−0.999655 + 0.0262707i \(0.991637\pi\)
\(234\) 0 0
\(235\) 1.64211 + 5.05390i 0.107120 + 0.329680i
\(236\) 0 0
\(237\) −12.1749 + 8.84559i −0.790846 + 0.574583i
\(238\) 0 0
\(239\) 5.68197 17.4873i 0.367536 1.13116i −0.580841 0.814017i \(-0.697276\pi\)
0.948378 0.317144i \(-0.102724\pi\)
\(240\) 0 0
\(241\) −12.3990 −0.798692 −0.399346 0.916800i \(-0.630763\pi\)
−0.399346 + 0.916800i \(0.630763\pi\)
\(242\) 0 0
\(243\) 12.5468 0.804879
\(244\) 0 0
\(245\) −2.14709 + 6.60805i −0.137172 + 0.422173i
\(246\) 0 0
\(247\) 6.01100 4.36725i 0.382471 0.277881i
\(248\) 0 0
\(249\) −0.609348 1.87538i −0.0386159 0.118847i
\(250\) 0 0
\(251\) −17.6317 12.8101i −1.11290 0.808569i −0.129782 0.991542i \(-0.541428\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(252\) 0 0
\(253\) 10.8498 3.90994i 0.682118 0.245816i
\(254\) 0 0
\(255\) −6.33807 4.60488i −0.396905 0.288369i
\(256\) 0 0
\(257\) 4.54531 + 13.9890i 0.283529 + 0.872611i 0.986836 + 0.161725i \(0.0517058\pi\)
−0.703307 + 0.710886i \(0.748294\pi\)
\(258\) 0 0
\(259\) −1.61191 + 1.17112i −0.100159 + 0.0727699i
\(260\) 0 0
\(261\) −0.0125872 + 0.0387394i −0.000779128 + 0.00239791i
\(262\) 0 0
\(263\) −27.4694 −1.69384 −0.846918 0.531724i \(-0.821544\pi\)
−0.846918 + 0.531724i \(0.821544\pi\)
\(264\) 0 0
\(265\) −10.2028 −0.626755
\(266\) 0 0
\(267\) −4.00399 + 12.3230i −0.245040 + 0.754157i
\(268\) 0 0
\(269\) 1.14812 0.834158i 0.0700022 0.0508595i −0.552234 0.833689i \(-0.686224\pi\)
0.622236 + 0.782830i \(0.286224\pi\)
\(270\) 0 0
\(271\) −3.19827 9.84328i −0.194281 0.597936i −0.999984 0.00561654i \(-0.998212\pi\)
0.805703 0.592320i \(-0.201788\pi\)
\(272\) 0 0
\(273\) 0.798164 + 0.579900i 0.0483071 + 0.0350972i
\(274\) 0 0
\(275\) −0.105203 3.31496i −0.00634396 0.199899i
\(276\) 0 0
\(277\) −14.4052 10.4660i −0.865524 0.628840i 0.0638580 0.997959i \(-0.479660\pi\)
−0.929382 + 0.369119i \(0.879660\pi\)
\(278\) 0 0
\(279\) 0.906117 + 2.78874i 0.0542478 + 0.166958i
\(280\) 0 0
\(281\) −13.8660 + 10.0742i −0.827176 + 0.600978i −0.918759 0.394819i \(-0.870807\pi\)
0.0915833 + 0.995797i \(0.470807\pi\)
\(282\) 0 0
\(283\) −3.06707 + 9.43947i −0.182318 + 0.561118i −0.999892 0.0147061i \(-0.995319\pi\)
0.817574 + 0.575824i \(0.195319\pi\)
\(284\) 0 0
\(285\) 2.87660 0.170395
\(286\) 0 0
\(287\) 2.33253 0.137685
\(288\) 0 0
\(289\) 6.05681 18.6409i 0.356283 1.09653i
\(290\) 0 0
\(291\) 8.73287 6.34480i 0.511930 0.371939i
\(292\) 0 0
\(293\) −5.59429 17.2175i −0.326822 1.00586i −0.970611 0.240652i \(-0.922639\pi\)
0.643789 0.765203i \(-0.277361\pi\)
\(294\) 0 0
\(295\) 6.75043 + 4.90447i 0.393025 + 0.285549i
\(296\) 0 0
\(297\) 10.4316 15.3598i 0.605300 0.891265i
\(298\) 0 0
\(299\) 9.40940 + 6.83633i 0.544160 + 0.395355i
\(300\) 0 0
\(301\) 0.263537 + 0.811083i 0.0151900 + 0.0467501i
\(302\) 0 0
\(303\) −1.80487 + 1.31132i −0.103687 + 0.0753331i
\(304\) 0 0
\(305\) −0.693906 + 2.13562i −0.0397329 + 0.122285i
\(306\) 0 0
\(307\) 6.00433 0.342685 0.171343 0.985211i \(-0.445189\pi\)
0.171343 + 0.985211i \(0.445189\pi\)
\(308\) 0 0
\(309\) 2.53103 0.143985
\(310\) 0 0
\(311\) 4.59712 14.1485i 0.260679 0.802287i −0.731979 0.681328i \(-0.761403\pi\)
0.992657 0.120959i \(-0.0385971\pi\)
\(312\) 0 0
\(313\) 1.95733 1.42208i 0.110635 0.0803808i −0.531092 0.847314i \(-0.678218\pi\)
0.641727 + 0.766933i \(0.278218\pi\)
\(314\) 0 0
\(315\) −0.0931270 0.286615i −0.00524711 0.0161490i
\(316\) 0 0
\(317\) −15.5635 11.3075i −0.874133 0.635095i 0.0575596 0.998342i \(-0.481668\pi\)
−0.931693 + 0.363247i \(0.881668\pi\)
\(318\) 0 0
\(319\) 0.0626077 + 0.0806618i 0.00350536 + 0.00451620i
\(320\) 0 0
\(321\) 14.0389 + 10.1999i 0.783576 + 0.569302i
\(322\) 0 0
\(323\) 4.15285 + 12.7812i 0.231071 + 0.711163i
\(324\) 0 0
\(325\) 2.70598 1.96601i 0.150101 0.109055i
\(326\) 0 0
\(327\) 2.98646 9.19137i 0.165151 0.508284i
\(328\) 0 0
\(329\) 1.21041 0.0667318
\(330\) 0 0
\(331\) 13.8876 0.763330 0.381665 0.924301i \(-0.375351\pi\)
0.381665 + 0.924301i \(0.375351\pi\)
\(332\) 0 0
\(333\) −3.57634 + 11.0068i −0.195982 + 0.603171i
\(334\) 0 0
\(335\) 2.80996 2.04156i 0.153525 0.111542i
\(336\) 0 0
\(337\) −0.953253 2.93381i −0.0519270 0.159815i 0.921730 0.387832i \(-0.126776\pi\)
−0.973657 + 0.228017i \(0.926776\pi\)
\(338\) 0 0
\(339\) −5.54469 4.02845i −0.301146 0.218796i
\(340\) 0 0
\(341\) 7.05925 + 2.04853i 0.382280 + 0.110934i
\(342\) 0 0
\(343\) 2.57030 + 1.86743i 0.138783 + 0.100832i
\(344\) 0 0
\(345\) 1.39148 + 4.28253i 0.0749147 + 0.230564i
\(346\) 0 0
\(347\) −23.1556 + 16.8235i −1.24306 + 0.903134i −0.997798 0.0663235i \(-0.978873\pi\)
−0.245259 + 0.969458i \(0.578873\pi\)
\(348\) 0 0
\(349\) 5.19773 15.9970i 0.278228 0.856298i −0.710119 0.704081i \(-0.751359\pi\)
0.988347 0.152216i \(-0.0486410\pi\)
\(350\) 0 0
\(351\) 18.7248 0.999455
\(352\) 0 0
\(353\) −14.6656 −0.780573 −0.390287 0.920693i \(-0.627624\pi\)
−0.390287 + 0.920693i \(0.627624\pi\)
\(354\) 0 0
\(355\) 4.65494 14.3264i 0.247059 0.760369i
\(356\) 0 0
\(357\) −1.44367 + 1.04889i −0.0764070 + 0.0555129i
\(358\) 0 0
\(359\) 9.54113 + 29.3646i 0.503561 + 1.54980i 0.803176 + 0.595742i \(0.203142\pi\)
−0.299614 + 0.954060i \(0.596858\pi\)
\(360\) 0 0
\(361\) 11.3792 + 8.26749i 0.598907 + 0.435131i
\(362\) 0 0
\(363\) −5.25197 13.2410i −0.275657 0.694974i
\(364\) 0 0
\(365\) 2.96415 + 2.15358i 0.155151 + 0.112724i
\(366\) 0 0
\(367\) 1.12218 + 3.45371i 0.0585773 + 0.180282i 0.976064 0.217485i \(-0.0697852\pi\)
−0.917486 + 0.397767i \(0.869785\pi\)
\(368\) 0 0
\(369\) 10.9612 7.96377i 0.570617 0.414577i
\(370\) 0 0
\(371\) −0.718147 + 2.21023i −0.0372843 + 0.114749i
\(372\) 0 0
\(373\) 29.2244 1.51318 0.756590 0.653890i \(-0.226864\pi\)
0.756590 + 0.653890i \(0.226864\pi\)
\(374\) 0 0
\(375\) 1.29496 0.0668716
\(376\) 0 0
\(377\) −0.0318209 + 0.0979348i −0.00163886 + 0.00504390i
\(378\) 0 0
\(379\) 2.95555 2.14734i 0.151817 0.110301i −0.509284 0.860599i \(-0.670090\pi\)
0.661101 + 0.750297i \(0.270090\pi\)
\(380\) 0 0
\(381\) 4.87933 + 15.0170i 0.249975 + 0.769345i
\(382\) 0 0
\(383\) −11.5255 8.37373i −0.588923 0.427878i 0.253007 0.967465i \(-0.418581\pi\)
−0.841930 + 0.539587i \(0.818581\pi\)
\(384\) 0 0
\(385\) −0.725520 0.210540i −0.0369759 0.0107301i
\(386\) 0 0
\(387\) 4.00765 + 2.91173i 0.203720 + 0.148012i
\(388\) 0 0
\(389\) −2.54825 7.84271i −0.129201 0.397641i 0.865442 0.501010i \(-0.167038\pi\)
−0.994643 + 0.103368i \(0.967038\pi\)
\(390\) 0 0
\(391\) −17.0191 + 12.3651i −0.860693 + 0.625330i
\(392\) 0 0
\(393\) 0.826461 2.54358i 0.0416894 0.128307i
\(394\) 0 0
\(395\) 11.6212 0.584726
\(396\) 0 0
\(397\) −2.57097 −0.129033 −0.0645167 0.997917i \(-0.520551\pi\)
−0.0645167 + 0.997917i \(0.520551\pi\)
\(398\) 0 0
\(399\) 0.202475 0.623154i 0.0101364 0.0311967i
\(400\) 0 0
\(401\) 31.5282 22.9066i 1.57444 1.14390i 0.651708 0.758470i \(-0.274053\pi\)
0.922737 0.385431i \(-0.125947\pi\)
\(402\) 0 0
\(403\) 2.29070 + 7.05005i 0.114108 + 0.351188i
\(404\) 0 0
\(405\) 2.65379 + 1.92809i 0.131868 + 0.0958078i
\(406\) 0 0
\(407\) 17.7884 + 22.9180i 0.881739 + 1.13601i
\(408\) 0 0
\(409\) 2.76891 + 2.01173i 0.136914 + 0.0994735i 0.654134 0.756379i \(-0.273033\pi\)
−0.517220 + 0.855852i \(0.673033\pi\)
\(410\) 0 0
\(411\) 5.77984 + 17.7885i 0.285098 + 0.877442i
\(412\) 0 0
\(413\) 1.53759 1.11713i 0.0756600 0.0549702i
\(414\) 0 0
\(415\) −0.470553 + 1.44821i −0.0230985 + 0.0710899i
\(416\) 0 0
\(417\) 21.1624 1.03633
\(418\) 0 0
\(419\) −10.5914 −0.517426 −0.258713 0.965954i \(-0.583298\pi\)
−0.258713 + 0.965954i \(0.583298\pi\)
\(420\) 0 0
\(421\) 0.732540 2.25453i 0.0357018 0.109879i −0.931617 0.363440i \(-0.881602\pi\)
0.967319 + 0.253561i \(0.0816020\pi\)
\(422\) 0 0
\(423\) 5.68803 4.13259i 0.276561 0.200934i
\(424\) 0 0
\(425\) 1.86950 + 5.75372i 0.0906838 + 0.279096i
\(426\) 0 0
\(427\) 0.413796 + 0.300640i 0.0200250 + 0.0145490i
\(428\) 0 0
\(429\) 8.07094 11.8839i 0.389668 0.573761i
\(430\) 0 0
\(431\) −21.2254 15.4211i −1.02239 0.742810i −0.0556186 0.998452i \(-0.517713\pi\)
−0.966771 + 0.255642i \(0.917713\pi\)
\(432\) 0 0
\(433\) −6.19078 19.0533i −0.297510 0.915641i −0.982367 0.186963i \(-0.940135\pi\)
0.684857 0.728677i \(-0.259865\pi\)
\(434\) 0 0
\(435\) −0.0322536 + 0.0234336i −0.00154644 + 0.00112356i
\(436\) 0 0
\(437\) 2.38694 7.34624i 0.114183 0.351418i
\(438\) 0 0
\(439\) −21.9546 −1.04783 −0.523917 0.851769i \(-0.675530\pi\)
−0.523917 + 0.851769i \(0.675530\pi\)
\(440\) 0 0
\(441\) 9.19285 0.437755
\(442\) 0 0
\(443\) −5.04993 + 15.5421i −0.239929 + 0.738427i 0.756500 + 0.653994i \(0.226908\pi\)
−0.996429 + 0.0844329i \(0.973092\pi\)
\(444\) 0 0
\(445\) 8.09490 5.88129i 0.383735 0.278800i
\(446\) 0 0
\(447\) 5.99516 + 18.4512i 0.283561 + 0.872712i
\(448\) 0 0
\(449\) 30.7811 + 22.3638i 1.45265 + 1.05541i 0.985203 + 0.171392i \(0.0548264\pi\)
0.467448 + 0.884021i \(0.345174\pi\)
\(450\) 0 0
\(451\) −1.07732 33.9465i −0.0507289 1.59848i
\(452\) 0 0
\(453\) 12.9155 + 9.38368i 0.606824 + 0.440884i
\(454\) 0 0
\(455\) −0.235429 0.724575i −0.0110371 0.0339686i
\(456\) 0 0
\(457\) 23.7055 17.2231i 1.10890 0.805660i 0.126407 0.991978i \(-0.459656\pi\)
0.982489 + 0.186318i \(0.0596555\pi\)
\(458\) 0 0
\(459\) −10.4658 + 32.2105i −0.488504 + 1.50346i
\(460\) 0 0
\(461\) −12.1136 −0.564188 −0.282094 0.959387i \(-0.591029\pi\)
−0.282094 + 0.959387i \(0.591029\pi\)
\(462\) 0 0
\(463\) 3.92452 0.182388 0.0911940 0.995833i \(-0.470932\pi\)
0.0911940 + 0.995833i \(0.470932\pi\)
\(464\) 0 0
\(465\) −0.886867 + 2.72950i −0.0411275 + 0.126577i
\(466\) 0 0
\(467\) 28.4609 20.6780i 1.31701 0.956865i 0.317047 0.948410i \(-0.397309\pi\)
0.999964 0.00845484i \(-0.00269129\pi\)
\(468\) 0 0
\(469\) −0.244475 0.752418i −0.0112888 0.0347434i
\(470\) 0 0
\(471\) 21.8374 + 15.8658i 1.00621 + 0.731057i
\(472\) 0 0
\(473\) 11.6824 4.21000i 0.537157 0.193576i
\(474\) 0 0
\(475\) −1.79713 1.30569i −0.0824580 0.0599092i
\(476\) 0 0
\(477\) 4.17144 + 12.8384i 0.190997 + 0.587829i
\(478\) 0 0
\(479\) 28.2934 20.5564i 1.29276 0.939244i 0.292902 0.956143i \(-0.405379\pi\)
0.999857 + 0.0168983i \(0.00537914\pi\)
\(480\) 0 0
\(481\) −9.04113 + 27.8257i −0.412240 + 1.26874i
\(482\) 0 0
\(483\) 1.02566 0.0466693
\(484\) 0 0
\(485\) −8.33570 −0.378504
\(486\) 0 0
\(487\) −3.28735 + 10.1174i −0.148964 + 0.458464i −0.997499 0.0706745i \(-0.977485\pi\)
0.848535 + 0.529139i \(0.177485\pi\)
\(488\) 0 0
\(489\) 0.591904 0.430044i 0.0267668 0.0194472i
\(490\) 0 0
\(491\) −8.99192 27.6743i −0.405800 1.24892i −0.920226 0.391388i \(-0.871995\pi\)
0.514426 0.857535i \(-0.328005\pi\)
\(492\) 0 0
\(493\) −0.150683 0.109477i −0.00678641 0.00493061i
\(494\) 0 0
\(495\) −4.12825 + 1.48770i −0.185551 + 0.0668673i
\(496\) 0 0
\(497\) −2.77587 2.01679i −0.124515 0.0904654i
\(498\) 0 0
\(499\) 7.15335 + 22.0158i 0.320228 + 0.985561i 0.973549 + 0.228479i \(0.0733754\pi\)
−0.653321 + 0.757081i \(0.726625\pi\)
\(500\) 0 0
\(501\) −23.5044 + 17.0770i −1.05010 + 0.762942i
\(502\) 0 0
\(503\) −3.91243 + 12.0412i −0.174447 + 0.536891i −0.999608 0.0280059i \(-0.991084\pi\)
0.825161 + 0.564897i \(0.191084\pi\)
\(504\) 0 0
\(505\) 1.72279 0.0766630
\(506\) 0 0
\(507\) −2.34708 −0.104237
\(508\) 0 0
\(509\) 3.04711 9.37803i 0.135061 0.415674i −0.860539 0.509385i \(-0.829873\pi\)
0.995599 + 0.0937109i \(0.0298729\pi\)
\(510\) 0 0
\(511\) 0.675166 0.490536i 0.0298676 0.0217001i
\(512\) 0 0
\(513\) −3.84285 11.8271i −0.169666 0.522179i
\(514\) 0 0
\(515\) −1.58124 1.14884i −0.0696778 0.0506239i
\(516\) 0 0
\(517\) −0.559046 17.6156i −0.0245868 0.774735i
\(518\) 0 0
\(519\) −2.26891 1.64846i −0.0995939 0.0723592i
\(520\) 0 0
\(521\) −0.779230 2.39822i −0.0341387 0.105068i 0.932535 0.361079i \(-0.117592\pi\)
−0.966674 + 0.256011i \(0.917592\pi\)
\(522\) 0 0
\(523\) 16.7639 12.1797i 0.733033 0.532580i −0.157488 0.987521i \(-0.550340\pi\)
0.890522 + 0.454941i \(0.150340\pi\)
\(524\) 0 0
\(525\) 0.0911485 0.280526i 0.00397805 0.0122432i
\(526\) 0 0
\(527\) −13.4079 −0.584057
\(528\) 0 0
\(529\) −10.9087 −0.474290
\(530\) 0 0
\(531\) 3.41145 10.4994i 0.148044 0.455634i
\(532\) 0 0
\(533\) 27.7103 20.1327i 1.20027 0.872046i
\(534\) 0 0
\(535\) −4.14096 12.7446i −0.179029 0.550996i
\(536\) 0 0
\(537\) −23.2125 16.8649i −1.00169 0.727773i
\(538\) 0 0
\(539\) 12.9469 19.0635i 0.557663 0.821123i
\(540\) 0 0
\(541\) −21.6636 15.7395i −0.931390 0.676694i 0.0149428 0.999888i \(-0.495243\pi\)
−0.946333 + 0.323194i \(0.895243\pi\)
\(542\) 0 0
\(543\) −3.57619 11.0064i −0.153469 0.472329i
\(544\) 0 0
\(545\) −6.03774 + 4.38667i −0.258628 + 0.187904i
\(546\) 0 0
\(547\) 1.41231 4.34665i 0.0603862 0.185849i −0.916313 0.400463i \(-0.868849\pi\)
0.976699 + 0.214614i \(0.0688492\pi\)
\(548\) 0 0
\(549\) 2.97099 0.126799
\(550\) 0 0
\(551\) 0.0683889 0.00291346
\(552\) 0 0
\(553\) 0.817981 2.51749i 0.0347841 0.107054i
\(554\) 0 0
\(555\) −9.16406 + 6.65808i −0.388993 + 0.282620i
\(556\) 0 0
\(557\) −9.82160 30.2278i −0.416155 1.28079i −0.911214 0.411933i \(-0.864854\pi\)
0.495059 0.868859i \(-0.335146\pi\)
\(558\) 0 0
\(559\) 10.1315 + 7.36097i 0.428517 + 0.311336i
\(560\) 0 0
\(561\) 15.9317 + 20.5260i 0.672639 + 0.866607i
\(562\) 0 0
\(563\) −7.52271 5.46557i −0.317044 0.230346i 0.417869 0.908507i \(-0.362777\pi\)
−0.734913 + 0.678161i \(0.762777\pi\)
\(564\) 0 0
\(565\) 1.63548 + 5.03348i 0.0688051 + 0.211760i
\(566\) 0 0
\(567\) 0.604473 0.439176i 0.0253855 0.0184436i
\(568\) 0 0
\(569\) −14.5753 + 44.8582i −0.611029 + 1.88055i −0.162724 + 0.986672i \(0.552028\pi\)
−0.448305 + 0.893881i \(0.647972\pi\)
\(570\) 0 0
\(571\) 4.32635 0.181052 0.0905260 0.995894i \(-0.471145\pi\)
0.0905260 + 0.995894i \(0.471145\pi\)
\(572\) 0 0
\(573\) 14.9025 0.622561
\(574\) 0 0
\(575\) 1.07453 3.30707i 0.0448111 0.137914i
\(576\) 0 0
\(577\) −7.10111 + 5.15926i −0.295623 + 0.214783i −0.725703 0.688008i \(-0.758485\pi\)
0.430080 + 0.902791i \(0.358485\pi\)
\(578\) 0 0
\(579\) 3.32614 + 10.2368i 0.138230 + 0.425428i
\(580\) 0 0
\(581\) 0.280604 + 0.203871i 0.0116414 + 0.00845798i
\(582\) 0 0
\(583\) 32.4983 + 9.43073i 1.34594 + 0.390581i
\(584\) 0 0
\(585\) −3.58021 2.60117i −0.148023 0.107545i
\(586\) 0 0
\(587\) 6.39416 + 19.6792i 0.263915 + 0.812247i 0.991941 + 0.126698i \(0.0404379\pi\)
−0.728026 + 0.685549i \(0.759562\pi\)
\(588\) 0 0
\(589\) 3.98289 2.89374i 0.164112 0.119234i
\(590\) 0 0
\(591\) 1.45967 4.49239i 0.0600426 0.184792i
\(592\) 0 0
\(593\) −46.8273 −1.92296 −0.961482 0.274866i \(-0.911366\pi\)
−0.961482 + 0.274866i \(0.911366\pi\)
\(594\) 0 0
\(595\) 1.37801 0.0564929
\(596\) 0 0
\(597\) 2.54008 7.81755i 0.103958 0.319951i
\(598\) 0 0
\(599\) −25.0840 + 18.2246i −1.02490 + 0.744635i −0.967282 0.253703i \(-0.918351\pi\)
−0.0576205 + 0.998339i \(0.518351\pi\)
\(600\) 0 0
\(601\) 12.9877 + 39.9719i 0.529778 + 1.63049i 0.754669 + 0.656105i \(0.227797\pi\)
−0.224891 + 0.974384i \(0.572203\pi\)
\(602\) 0 0
\(603\) −3.71778 2.70112i −0.151400 0.109998i
\(604\) 0 0
\(605\) −2.72900 + 10.6561i −0.110950 + 0.433232i
\(606\) 0 0
\(607\) 8.78543 + 6.38299i 0.356590 + 0.259078i 0.751628 0.659587i \(-0.229269\pi\)
−0.395039 + 0.918665i \(0.629269\pi\)
\(608\) 0 0
\(609\) 0.00280617 + 0.00863649i 0.000113712 + 0.000349968i
\(610\) 0 0
\(611\) 14.3796 10.4474i 0.581735 0.422655i
\(612\) 0 0
\(613\) −11.4399 + 35.2084i −0.462054 + 1.42205i 0.400597 + 0.916254i \(0.368803\pi\)
−0.862651 + 0.505800i \(0.831197\pi\)
\(614\) 0 0
\(615\) 13.2609 0.534733
\(616\) 0 0
\(617\) 37.3620 1.50414 0.752068 0.659085i \(-0.229056\pi\)
0.752068 + 0.659085i \(0.229056\pi\)
\(618\) 0 0
\(619\) 12.2758 37.7811i 0.493407 1.51855i −0.326017 0.945364i \(-0.605707\pi\)
0.819424 0.573187i \(-0.194293\pi\)
\(620\) 0 0
\(621\) 15.7487 11.4421i 0.631973 0.459155i
\(622\) 0 0
\(623\) −0.704281 2.16756i −0.0282164 0.0868413i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 0 0
\(627\) −9.16260 2.65891i −0.365919 0.106187i
\(628\) 0 0
\(629\) −42.8127 31.1053i −1.70705 1.24025i
\(630\) 0 0
\(631\) −2.29915 7.07604i −0.0915276 0.281693i 0.894806 0.446456i \(-0.147314\pi\)
−0.986333 + 0.164763i \(0.947314\pi\)
\(632\) 0 0
\(633\) −20.1717 + 14.6556i −0.801754 + 0.582508i
\(634\) 0 0
\(635\) 3.76793 11.5965i 0.149526 0.460192i
\(636\) 0 0
\(637\) 23.2399 0.920798
\(638\) 0 0
\(639\) −19.9304 −0.788433
\(640\) 0 0
\(641\) −0.576593 + 1.77457i −0.0227741 + 0.0700913i −0.961798 0.273761i \(-0.911732\pi\)
0.939024 + 0.343853i \(0.111732\pi\)
\(642\) 0 0
\(643\) 36.9990 26.8813i 1.45910 1.06010i 0.475501 0.879715i \(-0.342267\pi\)
0.983597 0.180382i \(-0.0577333\pi\)
\(644\) 0 0
\(645\) 1.49827 + 4.61119i 0.0589942 + 0.181565i
\(646\) 0 0
\(647\) −27.5385 20.0079i −1.08265 0.786591i −0.104507 0.994524i \(-0.533327\pi\)
−0.978143 + 0.207933i \(0.933327\pi\)
\(648\) 0 0
\(649\) −16.9683 21.8614i −0.666063 0.858135i
\(650\) 0 0
\(651\) 0.528864 + 0.384242i 0.0207278 + 0.0150596i
\(652\) 0 0
\(653\) 0.960362 + 2.95569i 0.0375819 + 0.115665i 0.968087 0.250613i \(-0.0806320\pi\)
−0.930506 + 0.366278i \(0.880632\pi\)
\(654\) 0 0
\(655\) −1.67086 + 1.21395i −0.0652859 + 0.0474330i
\(656\) 0 0
\(657\) 1.49799 4.61033i 0.0584420 0.179866i
\(658\) 0 0
\(659\) 10.1518 0.395459 0.197729 0.980257i \(-0.436643\pi\)
0.197729 + 0.980257i \(0.436643\pi\)
\(660\) 0 0
\(661\) −44.7642 −1.74113 −0.870564 0.492056i \(-0.836246\pi\)
−0.870564 + 0.492056i \(0.836246\pi\)
\(662\) 0 0
\(663\) −8.09746 + 24.9214i −0.314479 + 0.967868i
\(664\) 0 0
\(665\) −0.409345 + 0.297407i −0.0158737 + 0.0115329i
\(666\) 0 0
\(667\) 0.0330813 + 0.101814i 0.00128091 + 0.00394225i
\(668\) 0 0
\(669\) −22.7655 16.5401i −0.880166 0.639478i
\(670\) 0 0
\(671\) 4.18425 6.16103i 0.161531 0.237844i
\(672\) 0 0
\(673\) 4.34015 + 3.15330i 0.167300 + 0.121551i 0.668285 0.743905i \(-0.267029\pi\)
−0.500985 + 0.865456i \(0.667029\pi\)
\(674\) 0 0
\(675\) −1.72994 5.32422i −0.0665856 0.204929i
\(676\) 0 0
\(677\) 9.15379 6.65062i 0.351809 0.255604i −0.397819 0.917464i \(-0.630233\pi\)
0.749627 + 0.661860i \(0.230233\pi\)
\(678\) 0 0
\(679\) −0.586725 + 1.80575i −0.0225164 + 0.0692984i
\(680\) 0 0
\(681\) 7.77592 0.297974
\(682\) 0 0
\(683\) −31.0817 −1.18931 −0.594655 0.803981i \(-0.702711\pi\)
−0.594655 + 0.803981i \(0.702711\pi\)
\(684\) 0 0
\(685\) 4.46332 13.7367i 0.170535 0.524852i
\(686\) 0 0
\(687\) 24.3137 17.6649i 0.927625 0.673959i
\(688\) 0 0
\(689\) 10.5456 + 32.4560i 0.401755 + 1.23647i
\(690\) 0 0
\(691\) 3.20162 + 2.32611i 0.121795 + 0.0884895i 0.647015 0.762477i \(-0.276017\pi\)
−0.525220 + 0.850967i \(0.676017\pi\)
\(692\) 0 0
\(693\) 0.0317044 + 0.999013i 0.00120435 + 0.0379494i
\(694\) 0 0
\(695\) −13.2210 9.60564i −0.501502 0.364363i
\(696\) 0 0
\(697\) 19.1444 + 58.9204i 0.725145 + 2.23177i
\(698\) 0 0
\(699\) −25.3722 + 18.4340i −0.959665 + 0.697238i
\(700\) 0 0
\(701\) 7.08605 21.8086i 0.267636 0.823700i −0.723438 0.690389i \(-0.757439\pi\)
0.991074 0.133311i \(-0.0425608\pi\)
\(702\) 0 0
\(703\) 19.4310 0.732854
\(704\) 0 0
\(705\) 6.88142 0.259169
\(706\) 0 0
\(707\) 0.121262 0.373205i 0.00456052 0.0140358i
\(708\) 0 0
\(709\) −26.2985 + 19.1070i −0.987660 + 0.717577i −0.959407 0.282024i \(-0.908994\pi\)
−0.0282525 + 0.999601i \(0.508994\pi\)
\(710\) 0 0
\(711\) −4.75134 14.6231i −0.178189 0.548410i
\(712\) 0 0
\(713\) 6.23467 + 4.52976i 0.233490 + 0.169641i
\(714\) 0 0
\(715\) −10.4364 + 3.76097i −0.390298 + 0.140652i
\(716\) 0 0
\(717\) −19.2634 13.9956i −0.719403 0.522677i
\(718\) 0 0
\(719\) −9.40526 28.9464i −0.350757 1.07952i −0.958429 0.285331i \(-0.907897\pi\)
0.607672 0.794188i \(-0.292103\pi\)
\(720\) 0 0
\(721\) −0.360170 + 0.261679i −0.0134134 + 0.00974544i
\(722\) 0 0
\(723\) −4.96167 + 15.2704i −0.184526 + 0.567914i
\(724\) 0 0
\(725\) 0.0307867 0.00114339
\(726\) 0 0
\(727\) −36.6338 −1.35867 −0.679337 0.733827i \(-0.737732\pi\)
−0.679337 + 0.733827i \(0.737732\pi\)
\(728\) 0 0
\(729\) 8.06178 24.8116i 0.298585 0.918949i
\(730\) 0 0
\(731\) −18.3252 + 13.3140i −0.677782 + 0.492438i
\(732\) 0 0
\(733\) 9.94139 + 30.5964i 0.367194 + 1.13011i 0.948596 + 0.316489i \(0.102504\pi\)
−0.581402 + 0.813616i \(0.697496\pi\)
\(734\) 0 0
\(735\) 7.27917 + 5.28863i 0.268496 + 0.195074i
\(736\) 0 0
\(737\) −10.8374 + 3.90549i −0.399201 + 0.143861i
\(738\) 0 0
\(739\) 16.8109 + 12.2138i 0.618398 + 0.449292i 0.852362 0.522953i \(-0.175170\pi\)
−0.233964 + 0.972245i \(0.575170\pi\)
\(740\) 0 0
\(741\) −2.97323 9.15066i −0.109224 0.336158i
\(742\) 0 0
\(743\) −30.6146 + 22.2428i −1.12314 + 0.816010i −0.984682 0.174358i \(-0.944215\pi\)
−0.138459 + 0.990368i \(0.544215\pi\)
\(744\) 0 0
\(745\) 4.62960 14.2484i 0.169615 0.522022i
\(746\) 0 0
\(747\) 2.01469 0.0737138
\(748\) 0 0
\(749\) −3.05231 −0.111529
\(750\) 0 0
\(751\) 4.03103 12.4062i 0.147094 0.452710i −0.850180 0.526492i \(-0.823507\pi\)
0.997274 + 0.0737821i \(0.0235069\pi\)
\(752\) 0 0
\(753\) −22.8323 + 16.5887i −0.832057 + 0.604525i
\(754\) 0 0
\(755\) −3.80960 11.7247i −0.138646 0.426707i
\(756\) 0 0
\(757\) −33.3075 24.1993i −1.21058 0.879540i −0.215299 0.976548i \(-0.569073\pi\)
−0.995284 + 0.0970086i \(0.969073\pi\)
\(758\) 0 0
\(759\) −0.473719 14.9270i −0.0171949 0.541815i
\(760\) 0 0
\(761\) 35.3819 + 25.7065i 1.28259 + 0.931858i 0.999628 0.0272718i \(-0.00868196\pi\)
0.282965 + 0.959130i \(0.408682\pi\)
\(762\) 0 0
\(763\) 0.525302 + 1.61671i 0.0190172 + 0.0585290i
\(764\) 0 0
\(765\) 6.47564 4.70483i 0.234127 0.170103i
\(766\) 0 0
\(767\) 8.62429 26.5428i 0.311405 0.958406i
\(768\) 0 0
\(769\) −17.3914 −0.627151 −0.313575 0.949563i \(-0.601527\pi\)
−0.313575 + 0.949563i \(0.601527\pi\)
\(770\) 0 0
\(771\) 19.0475 0.685979
\(772\) 0 0
\(773\) 7.68850 23.6628i 0.276536 0.851091i −0.712273 0.701903i \(-0.752334\pi\)
0.988809 0.149188i \(-0.0476660\pi\)
\(774\) 0 0
\(775\) 1.79298 1.30268i 0.0644059 0.0467936i
\(776\) 0 0
\(777\) 0.797302 + 2.45384i 0.0286031 + 0.0880311i
\(778\) 0 0
\(779\) −18.4033 13.3708i −0.659368 0.479059i
\(780\) 0 0
\(781\) −28.0693 + 41.3302i −1.00440 + 1.47891i
\(782\) 0 0
\(783\) 0.139435 + 0.101305i 0.00498299 + 0.00362035i
\(784\) 0 0
\(785\) −6.44122 19.8240i −0.229897 0.707550i
\(786\) 0 0
\(787\) 21.8953 15.9079i 0.780484 0.567055i −0.124641 0.992202i \(-0.539778\pi\)
0.905124 + 0.425147i \(0.139778\pi\)
\(788\) 0