Properties

Label 1008.2.t.g.961.2
Level $1008$
Weight $2$
Character 1008.961
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\), degree \(2\), 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1008.961
Dual form 1008.2.t.g.193.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})\) \(q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} -6.12476 q^{11} +(-0.380438 - 0.658939i) q^{13} +(-1.09097 - 2.84813i) q^{15} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-4.20370 - 1.82454i) q^{21} +0.421067 q^{23} -1.89931 q^{25} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(3.79467 + 9.90650i) q^{33} +(3.26088 - 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(-0.830095 + 1.02359i) q^{39} +(-3.47141 - 6.01266i) q^{41} +(-4.33009 + 7.49994i) q^{43} +(-3.93078 + 3.52918i) q^{45} +(0.830095 + 1.43777i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(-7.46457 + 9.20459i) q^{51} +(-0.112725 - 0.195246i) q^{53} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} +(0.993163 - 1.72021i) q^{59} +(5.17511 + 8.96355i) q^{61} +(-0.346647 + 7.92968i) q^{63} +(-0.669905 - 1.16031i) q^{65} +(3.39248 - 5.87594i) q^{67} +(-0.260877 - 0.681054i) q^{69} -10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(1.17674 + 3.07204i) q^{75} +(-11.3421 + 11.5735i) q^{77} +(-6.72257 - 11.6438i) q^{79} +(0.966208 - 8.94799i) q^{81} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-2.50520 - 0.398611i) q^{87} +(1.30150 - 2.25427i) q^{89} +(-1.94966 - 0.501371i) q^{91} +(-13.1774 - 2.09671i) q^{93} +(-1.71053 + 2.96273i) q^{95} +(-1.81806 + 3.14897i) q^{97} +(13.6722 - 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.619562 1.61745i −0.357704 0.933835i
\(4\) 0 0
\(5\) 1.76088 0.787488 0.393744 0.919220i \(-0.371180\pi\)
0.393744 + 0.919220i \(0.371180\pi\)
\(6\) 0 0
\(7\) 1.85185 1.88962i 0.699933 0.714209i
\(8\) 0 0
\(9\) −2.23229 + 2.00422i −0.744096 + 0.668073i
\(10\) 0 0
\(11\) −6.12476 −1.84669 −0.923343 0.383977i \(-0.874554\pi\)
−0.923343 + 0.383977i \(0.874554\pi\)
\(12\) 0 0
\(13\) −0.380438 0.658939i −0.105515 0.182757i 0.808434 0.588587i \(-0.200316\pi\)
−0.913948 + 0.405831i \(0.866982\pi\)
\(14\) 0 0
\(15\) −1.09097 2.84813i −0.281688 0.735384i
\(16\) 0 0
\(17\) −3.42107 5.92546i −0.829731 1.43714i −0.898250 0.439486i \(-0.855161\pi\)
0.0685191 0.997650i \(-0.478173\pi\)
\(18\) 0 0
\(19\) −0.971410 + 1.68253i −0.222857 + 0.385999i −0.955674 0.294426i \(-0.904872\pi\)
0.732818 + 0.680425i \(0.238205\pi\)
\(20\) 0 0
\(21\) −4.20370 1.82454i −0.917322 0.398147i
\(22\) 0 0
\(23\) 0.421067 0.0877985 0.0438992 0.999036i \(-0.486022\pi\)
0.0438992 + 0.999036i \(0.486022\pi\)
\(24\) 0 0
\(25\) −1.89931 −0.379863
\(26\) 0 0
\(27\) 4.62476 + 2.36887i 0.890036 + 0.455890i
\(28\) 0 0
\(29\) 0.732287 1.26836i 0.135982 0.235528i −0.789990 0.613120i \(-0.789914\pi\)
0.925972 + 0.377592i \(0.123248\pi\)
\(30\) 0 0
\(31\) 3.85185 6.67160i 0.691812 1.19825i −0.279431 0.960166i \(-0.590146\pi\)
0.971243 0.238088i \(-0.0765208\pi\)
\(32\) 0 0
\(33\) 3.79467 + 9.90650i 0.660567 + 1.72450i
\(34\) 0 0
\(35\) 3.26088 3.32738i 0.551189 0.562431i
\(36\) 0 0
\(37\) 1.44282 2.49904i 0.237198 0.410839i −0.722711 0.691150i \(-0.757104\pi\)
0.959909 + 0.280311i \(0.0904376\pi\)
\(38\) 0 0
\(39\) −0.830095 + 1.02359i −0.132922 + 0.163906i
\(40\) 0 0
\(41\) −3.47141 6.01266i −0.542143 0.939020i −0.998781 0.0493667i \(-0.984280\pi\)
0.456638 0.889653i \(-0.349054\pi\)
\(42\) 0 0
\(43\) −4.33009 + 7.49994i −0.660333 + 1.14373i 0.320195 + 0.947352i \(0.396252\pi\)
−0.980528 + 0.196379i \(0.937082\pi\)
\(44\) 0 0
\(45\) −3.93078 + 3.52918i −0.585966 + 0.526100i
\(46\) 0 0
\(47\) 0.830095 + 1.43777i 0.121082 + 0.209720i 0.920195 0.391461i \(-0.128030\pi\)
−0.799113 + 0.601181i \(0.794697\pi\)
\(48\) 0 0
\(49\) −0.141315 6.99857i −0.0201879 0.999796i
\(50\) 0 0
\(51\) −7.46457 + 9.20459i −1.04525 + 1.28890i
\(52\) 0 0
\(53\) −0.112725 0.195246i −0.0154840 0.0268190i 0.858180 0.513350i \(-0.171596\pi\)
−0.873664 + 0.486531i \(0.838262\pi\)
\(54\) 0 0
\(55\) −10.7850 −1.45424
\(56\) 0 0
\(57\) 3.32326 + 0.528775i 0.440176 + 0.0700379i
\(58\) 0 0
\(59\) 0.993163 1.72021i 0.129299 0.223952i −0.794106 0.607779i \(-0.792061\pi\)
0.923405 + 0.383827i \(0.125394\pi\)
\(60\) 0 0
\(61\) 5.17511 + 8.96355i 0.662605 + 1.14766i 0.979929 + 0.199348i \(0.0638823\pi\)
−0.317324 + 0.948317i \(0.602784\pi\)
\(62\) 0 0
\(63\) −0.346647 + 7.92968i −0.0436734 + 0.999046i
\(64\) 0 0
\(65\) −0.669905 1.16031i −0.0830915 0.143919i
\(66\) 0 0
\(67\) 3.39248 5.87594i 0.414457 0.717861i −0.580914 0.813965i \(-0.697305\pi\)
0.995371 + 0.0961042i \(0.0306382\pi\)
\(68\) 0 0
\(69\) −0.260877 0.681054i −0.0314059 0.0819893i
\(70\) 0 0
\(71\) −10.7850 −1.27994 −0.639969 0.768401i \(-0.721053\pi\)
−0.639969 + 0.768401i \(0.721053\pi\)
\(72\) 0 0
\(73\) 0.153353 + 0.265616i 0.0179487 + 0.0310880i 0.874860 0.484375i \(-0.160953\pi\)
−0.856912 + 0.515463i \(0.827620\pi\)
\(74\) 0 0
\(75\) 1.17674 + 3.07204i 0.135878 + 0.354729i
\(76\) 0 0
\(77\) −11.3421 + 11.5735i −1.29256 + 1.31892i
\(78\) 0 0
\(79\) −6.72257 11.6438i −0.756348 1.31003i −0.944701 0.327932i \(-0.893648\pi\)
0.188353 0.982101i \(-0.439685\pi\)
\(80\) 0 0
\(81\) 0.966208 8.94799i 0.107356 0.994221i
\(82\) 0 0
\(83\) 1.56238 2.70612i 0.171494 0.297036i −0.767449 0.641110i \(-0.778474\pi\)
0.938942 + 0.344075i \(0.111807\pi\)
\(84\) 0 0
\(85\) −6.02408 10.4340i −0.653403 1.13173i
\(86\) 0 0
\(87\) −2.50520 0.398611i −0.268586 0.0427356i
\(88\) 0 0
\(89\) 1.30150 2.25427i 0.137959 0.238952i −0.788765 0.614695i \(-0.789279\pi\)
0.926724 + 0.375743i \(0.122612\pi\)
\(90\) 0 0
\(91\) −1.94966 0.501371i −0.204380 0.0525580i
\(92\) 0 0
\(93\) −13.1774 2.09671i −1.36644 0.217418i
\(94\) 0 0
\(95\) −1.71053 + 2.96273i −0.175497 + 0.303970i
\(96\) 0 0
\(97\) −1.81806 + 3.14897i −0.184596 + 0.319729i −0.943440 0.331543i \(-0.892431\pi\)
0.758845 + 0.651272i \(0.225764\pi\)
\(98\) 0 0
\(99\) 13.6722 12.2754i 1.37411 1.23372i
\(100\) 0 0
\(101\) −8.01040 −0.797065 −0.398532 0.917154i \(-0.630480\pi\)
−0.398532 + 0.917154i \(0.630480\pi\)
\(102\) 0 0
\(103\) 6.82846 0.672828 0.336414 0.941714i \(-0.390786\pi\)
0.336414 + 0.941714i \(0.390786\pi\)
\(104\) 0 0
\(105\) −7.40219 3.21278i −0.722380 0.313536i
\(106\) 0 0
\(107\) −1.77292 + 3.07078i −0.171394 + 0.296863i −0.938908 0.344170i \(-0.888160\pi\)
0.767513 + 0.641033i \(0.221494\pi\)
\(108\) 0 0
\(109\) 0.351848 + 0.609419i 0.0337010 + 0.0583718i 0.882384 0.470530i \(-0.155937\pi\)
−0.848683 + 0.528902i \(0.822604\pi\)
\(110\) 0 0
\(111\) −4.93598 0.785381i −0.468503 0.0745451i
\(112\) 0 0
\(113\) 4.25116 + 7.36323i 0.399916 + 0.692674i 0.993715 0.111939i \(-0.0357061\pi\)
−0.593799 + 0.804613i \(0.702373\pi\)
\(114\) 0 0
\(115\) 0.741446 0.0691402
\(116\) 0 0
\(117\) 2.16991 + 0.708458i 0.200608 + 0.0654970i
\(118\) 0 0
\(119\) −17.5322 4.50855i −1.60717 0.413298i
\(120\) 0 0
\(121\) 26.5127 2.41025
\(122\) 0 0
\(123\) −7.57442 + 9.34004i −0.682962 + 0.842163i
\(124\) 0 0
\(125\) −12.1488 −1.08663
\(126\) 0 0
\(127\) 18.9532 1.68183 0.840913 0.541170i \(-0.182018\pi\)
0.840913 + 0.541170i \(0.182018\pi\)
\(128\) 0 0
\(129\) 14.8135 + 2.35703i 1.30426 + 0.207525i
\(130\) 0 0
\(131\) 7.29303 0.637195 0.318598 0.947890i \(-0.396788\pi\)
0.318598 + 0.947890i \(0.396788\pi\)
\(132\) 0 0
\(133\) 1.38044 + 4.95139i 0.119699 + 0.429340i
\(134\) 0 0
\(135\) 8.14364 + 4.17129i 0.700893 + 0.359008i
\(136\) 0 0
\(137\) −8.18194 −0.699031 −0.349515 0.936931i \(-0.613654\pi\)
−0.349515 + 0.936931i \(0.613654\pi\)
\(138\) 0 0
\(139\) 6.23229 + 10.7946i 0.528616 + 0.915589i 0.999443 + 0.0333640i \(0.0106220\pi\)
−0.470828 + 0.882225i \(0.656045\pi\)
\(140\) 0 0
\(141\) 1.81122 2.23342i 0.152532 0.188088i
\(142\) 0 0
\(143\) 2.33009 + 4.03584i 0.194852 + 0.337494i
\(144\) 0 0
\(145\) 1.28947 2.23342i 0.107084 0.185476i
\(146\) 0 0
\(147\) −11.2323 + 4.56462i −0.926423 + 0.376483i
\(148\) 0 0
\(149\) 8.82846 0.723256 0.361628 0.932323i \(-0.382221\pi\)
0.361628 + 0.932323i \(0.382221\pi\)
\(150\) 0 0
\(151\) 14.9863 1.21957 0.609785 0.792567i \(-0.291256\pi\)
0.609785 + 0.792567i \(0.291256\pi\)
\(152\) 0 0
\(153\) 19.5127 + 6.37076i 1.57751 + 0.515045i
\(154\) 0 0
\(155\) 6.78263 11.7479i 0.544794 0.943611i
\(156\) 0 0
\(157\) −9.49028 + 16.4377i −0.757407 + 1.31187i 0.186761 + 0.982405i \(0.440201\pi\)
−0.944169 + 0.329462i \(0.893132\pi\)
\(158\) 0 0
\(159\) −0.245960 + 0.303294i −0.0195059 + 0.0240528i
\(160\) 0 0
\(161\) 0.779752 0.795655i 0.0614530 0.0627064i
\(162\) 0 0
\(163\) 7.51887 13.0231i 0.588924 1.02005i −0.405450 0.914117i \(-0.632885\pi\)
0.994374 0.105929i \(-0.0337815\pi\)
\(164\) 0 0
\(165\) 6.68194 + 17.4441i 0.520189 + 1.35802i
\(166\) 0 0
\(167\) −0.572097 0.990901i −0.0442702 0.0766782i 0.843041 0.537849i \(-0.180763\pi\)
−0.887311 + 0.461171i \(0.847430\pi\)
\(168\) 0 0
\(169\) 6.21053 10.7570i 0.477733 0.827458i
\(170\) 0 0
\(171\) −1.20370 5.70281i −0.0920490 0.436105i
\(172\) 0 0
\(173\) −0.248838 0.431001i −0.0189188 0.0327684i 0.856411 0.516295i \(-0.172689\pi\)
−0.875330 + 0.483526i \(0.839356\pi\)
\(174\) 0 0
\(175\) −3.51724 + 3.58898i −0.265878 + 0.271301i
\(176\) 0 0
\(177\) −3.39768 0.540616i −0.255385 0.0406352i
\(178\) 0 0
\(179\) −4.41423 7.64567i −0.329935 0.571464i 0.652564 0.757734i \(-0.273694\pi\)
−0.982499 + 0.186270i \(0.940360\pi\)
\(180\) 0 0
\(181\) 1.32941 0.0988140 0.0494070 0.998779i \(-0.484267\pi\)
0.0494070 + 0.998779i \(0.484267\pi\)
\(182\) 0 0
\(183\) 11.2918 13.9239i 0.834713 1.02929i
\(184\) 0 0
\(185\) 2.54063 4.40050i 0.186791 0.323531i
\(186\) 0 0
\(187\) 20.9532 + 36.2920i 1.53225 + 2.65394i
\(188\) 0 0
\(189\) 13.0406 4.35224i 0.948566 0.316579i
\(190\) 0 0
\(191\) −8.08414 14.0021i −0.584947 1.01316i −0.994882 0.101044i \(-0.967782\pi\)
0.409934 0.912115i \(-0.365552\pi\)
\(192\) 0 0
\(193\) 7.08414 12.2701i 0.509927 0.883220i −0.490007 0.871719i \(-0.663006\pi\)
0.999934 0.0115011i \(-0.00366101\pi\)
\(194\) 0 0
\(195\) −1.46169 + 1.80242i −0.104674 + 0.129074i
\(196\) 0 0
\(197\) 15.8421 1.12871 0.564353 0.825534i \(-0.309126\pi\)
0.564353 + 0.825534i \(0.309126\pi\)
\(198\) 0 0
\(199\) 4.47141 + 7.74471i 0.316970 + 0.549008i 0.979854 0.199714i \(-0.0640013\pi\)
−0.662884 + 0.748722i \(0.730668\pi\)
\(200\) 0 0
\(201\) −11.6059 1.84665i −0.818616 0.130253i
\(202\) 0 0
\(203\) −1.04063 3.73255i −0.0730378 0.261974i
\(204\) 0 0
\(205\) −6.11273 10.5876i −0.426931 0.739467i
\(206\) 0 0
\(207\) −0.939941 + 0.843910i −0.0653304 + 0.0586558i
\(208\) 0 0
\(209\) 5.94966 10.3051i 0.411546 0.712819i
\(210\) 0 0
\(211\) −11.3856 19.7205i −0.783820 1.35762i −0.929702 0.368314i \(-0.879935\pi\)
0.145882 0.989302i \(-0.453398\pi\)
\(212\) 0 0
\(213\) 6.68194 + 17.4441i 0.457839 + 1.19525i
\(214\) 0 0
\(215\) −7.62476 + 13.2065i −0.520005 + 0.900674i
\(216\) 0 0
\(217\) −5.47373 19.6333i −0.371581 1.33280i
\(218\) 0 0
\(219\) 0.334608 0.412607i 0.0226107 0.0278814i
\(220\) 0 0
\(221\) −2.60301 + 4.50855i −0.175097 + 0.303278i
\(222\) 0 0
\(223\) 6.44282 11.1593i 0.431443 0.747281i −0.565555 0.824711i \(-0.691338\pi\)
0.996998 + 0.0774293i \(0.0246712\pi\)
\(224\) 0 0
\(225\) 4.23981 3.80664i 0.282654 0.253776i
\(226\) 0 0
\(227\) −21.9967 −1.45997 −0.729987 0.683461i \(-0.760474\pi\)
−0.729987 + 0.683461i \(0.760474\pi\)
\(228\) 0 0
\(229\) −3.79863 −0.251020 −0.125510 0.992092i \(-0.540057\pi\)
−0.125510 + 0.992092i \(0.540057\pi\)
\(230\) 0 0
\(231\) 25.7466 + 11.1749i 1.69401 + 0.735251i
\(232\) 0 0
\(233\) −3.33530 + 5.77690i −0.218503 + 0.378458i −0.954350 0.298689i \(-0.903451\pi\)
0.735848 + 0.677147i \(0.236784\pi\)
\(234\) 0 0
\(235\) 1.46169 + 2.53173i 0.0953505 + 0.165152i
\(236\) 0 0
\(237\) −14.6683 + 18.0875i −0.952807 + 1.17491i
\(238\) 0 0
\(239\) 7.82038 + 13.5453i 0.505858 + 0.876172i 0.999977 + 0.00677786i \(0.00215748\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(240\) 0 0
\(241\) 21.4120 1.37927 0.689635 0.724157i \(-0.257771\pi\)
0.689635 + 0.724157i \(0.257771\pi\)
\(242\) 0 0
\(243\) −15.0715 + 3.98104i −0.966840 + 0.255384i
\(244\) 0 0
\(245\) −0.248838 12.3236i −0.0158977 0.787328i
\(246\) 0 0
\(247\) 1.47825 0.0940586
\(248\) 0 0
\(249\) −5.34501 0.850463i −0.338726 0.0538959i
\(250\) 0 0
\(251\) 23.6030 1.48981 0.744904 0.667171i \(-0.232495\pi\)
0.744904 + 0.667171i \(0.232495\pi\)
\(252\) 0 0
\(253\) −2.57893 −0.162136
\(254\) 0 0
\(255\) −13.1442 + 16.2082i −0.823121 + 1.01499i
\(256\) 0 0
\(257\) 20.2599 1.26378 0.631890 0.775058i \(-0.282279\pi\)
0.631890 + 0.775058i \(0.282279\pi\)
\(258\) 0 0
\(259\) −2.05034 7.35422i −0.127402 0.456969i
\(260\) 0 0
\(261\) 0.907394 + 4.29900i 0.0561663 + 0.266102i
\(262\) 0 0
\(263\) 22.4887 1.38671 0.693355 0.720596i \(-0.256132\pi\)
0.693355 + 0.720596i \(0.256132\pi\)
\(264\) 0 0
\(265\) −0.198495 0.343803i −0.0121935 0.0211197i
\(266\) 0 0
\(267\) −4.45254 0.708458i −0.272491 0.0433569i
\(268\) 0 0
\(269\) −12.6706 21.9461i −0.772540 1.33808i −0.936167 0.351556i \(-0.885653\pi\)
0.163627 0.986522i \(-0.447681\pi\)
\(270\) 0 0
\(271\) 6.87880 11.9144i 0.417858 0.723751i −0.577866 0.816132i \(-0.696114\pi\)
0.995724 + 0.0923810i \(0.0294478\pi\)
\(272\) 0 0
\(273\) 0.396990 + 3.46410i 0.0240269 + 0.209657i
\(274\) 0 0
\(275\) 11.6328 0.701487
\(276\) 0 0
\(277\) −3.28263 −0.197234 −0.0986171 0.995125i \(-0.531442\pi\)
−0.0986171 + 0.995125i \(0.531442\pi\)
\(278\) 0 0
\(279\) 4.77292 + 22.6129i 0.285747 + 1.35380i
\(280\) 0 0
\(281\) 0.634479 1.09895i 0.0378498 0.0655578i −0.846480 0.532421i \(-0.821282\pi\)
0.884330 + 0.466863i \(0.154616\pi\)
\(282\) 0 0
\(283\) −4.09617 + 7.09478i −0.243492 + 0.421741i −0.961707 0.274081i \(-0.911626\pi\)
0.718214 + 0.695822i \(0.244960\pi\)
\(284\) 0 0
\(285\) 5.85185 + 0.931107i 0.346634 + 0.0551540i
\(286\) 0 0
\(287\) −17.7902 4.57489i −1.05012 0.270047i
\(288\) 0 0
\(289\) −14.9074 + 25.8204i −0.876906 + 1.51884i
\(290\) 0 0
\(291\) 6.21969 + 0.989636i 0.364605 + 0.0580135i
\(292\) 0 0
\(293\) 7.72545 + 13.3809i 0.451326 + 0.781719i 0.998469 0.0553202i \(-0.0176180\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(294\) 0 0
\(295\) 1.74884 3.02908i 0.101821 0.176360i
\(296\) 0 0
\(297\) −28.3256 14.5088i −1.64362 0.841886i
\(298\) 0 0
\(299\) −0.160190 0.277457i −0.00926402 0.0160458i
\(300\) 0 0
\(301\) 6.15335 + 22.0710i 0.354673 + 1.27215i
\(302\) 0 0
\(303\) 4.96294 + 12.9564i 0.285113 + 0.744327i
\(304\) 0 0
\(305\) 9.11273 + 15.7837i 0.521793 + 0.903772i
\(306\) 0 0
\(307\) −4.89931 −0.279619 −0.139809 0.990178i \(-0.544649\pi\)
−0.139809 + 0.990178i \(0.544649\pi\)
\(308\) 0 0
\(309\) −4.23065 11.0447i −0.240673 0.628310i
\(310\) 0 0
\(311\) −3.84501 + 6.65976i −0.218031 + 0.377640i −0.954206 0.299151i \(-0.903297\pi\)
0.736175 + 0.676791i \(0.236630\pi\)
\(312\) 0 0
\(313\) 0.861564 + 1.49227i 0.0486985 + 0.0843482i 0.889347 0.457233i \(-0.151159\pi\)
−0.840649 + 0.541581i \(0.817826\pi\)
\(314\) 0 0
\(315\) −0.610402 + 13.9632i −0.0343923 + 0.786737i
\(316\) 0 0
\(317\) −16.6014 28.7544i −0.932426 1.61501i −0.779161 0.626824i \(-0.784354\pi\)
−0.153266 0.988185i \(-0.548979\pi\)
\(318\) 0 0
\(319\) −4.48508 + 7.76839i −0.251116 + 0.434946i
\(320\) 0 0
\(321\) 6.06526 + 0.965064i 0.338530 + 0.0538646i
\(322\) 0 0
\(323\) 13.2930 0.739644
\(324\) 0 0
\(325\) 0.722572 + 1.25153i 0.0400811 + 0.0694224i
\(326\) 0 0
\(327\) 0.767713 0.946670i 0.0424546 0.0523510i
\(328\) 0 0
\(329\) 4.25404 + 1.09396i 0.234533 + 0.0603121i
\(330\) 0 0
\(331\) 1.44445 + 2.50187i 0.0793944 + 0.137515i 0.902989 0.429664i \(-0.141368\pi\)
−0.823594 + 0.567179i \(0.808035\pi\)
\(332\) 0 0
\(333\) 1.78783 + 8.47030i 0.0979726 + 0.464169i
\(334\) 0 0
\(335\) 5.97373 10.3468i 0.326380 0.565307i
\(336\) 0 0
\(337\) −4.36156 7.55445i −0.237590 0.411517i 0.722433 0.691441i \(-0.243024\pi\)
−0.960022 + 0.279924i \(0.909691\pi\)
\(338\) 0 0
\(339\) 9.27579 11.4380i 0.503792 0.621228i
\(340\) 0 0
\(341\) −23.5917 + 40.8620i −1.27756 + 2.21280i
\(342\) 0 0
\(343\) −13.4863 12.6933i −0.728193 0.685372i
\(344\) 0 0
\(345\) −0.459372 1.19925i −0.0247317 0.0645656i
\(346\) 0 0
\(347\) 4.84733 8.39583i 0.260219 0.450712i −0.706081 0.708131i \(-0.749539\pi\)
0.966300 + 0.257419i \(0.0828720\pi\)
\(348\) 0 0
\(349\) 14.1992 24.5937i 0.760065 1.31647i −0.182752 0.983159i \(-0.558500\pi\)
0.942817 0.333312i \(-0.108166\pi\)
\(350\) 0 0
\(351\) −0.198495 3.94865i −0.0105949 0.210763i
\(352\) 0 0
\(353\) −4.39372 −0.233854 −0.116927 0.993141i \(-0.537304\pi\)
−0.116927 + 0.993141i \(0.537304\pi\)
\(354\) 0 0
\(355\) −18.9910 −1.00794
\(356\) 0 0
\(357\) 3.56991 + 31.1507i 0.188939 + 1.64867i
\(358\) 0 0
\(359\) −16.0796 + 27.8507i −0.848650 + 1.46990i 0.0337633 + 0.999430i \(0.489251\pi\)
−0.882413 + 0.470475i \(0.844083\pi\)
\(360\) 0 0
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) 0 0
\(363\) −16.4263 42.8830i −0.862155 2.25077i
\(364\) 0 0
\(365\) 0.270036 + 0.467717i 0.0141343 + 0.0244814i
\(366\) 0 0
\(367\) −34.6030 −1.80626 −0.903131 0.429365i \(-0.858738\pi\)
−0.903131 + 0.429365i \(0.858738\pi\)
\(368\) 0 0
\(369\) 19.7999 + 6.46451i 1.03074 + 0.336529i
\(370\) 0 0
\(371\) −0.577690 0.148558i −0.0299921 0.00771274i
\(372\) 0 0
\(373\) 10.9759 0.568312 0.284156 0.958778i \(-0.408287\pi\)
0.284156 + 0.958778i \(0.408287\pi\)
\(374\) 0 0
\(375\) 7.52696 + 19.6501i 0.388690 + 1.01473i
\(376\) 0 0
\(377\) −1.11436 −0.0573925
\(378\) 0 0
\(379\) −33.9877 −1.74583 −0.872916 0.487871i \(-0.837774\pi\)
−0.872916 + 0.487871i \(0.837774\pi\)
\(380\) 0 0
\(381\) −11.7427 30.6559i −0.601596 1.57055i
\(382\) 0 0
\(383\) 21.0241 1.07428 0.537140 0.843493i \(-0.319505\pi\)
0.537140 + 0.843493i \(0.319505\pi\)
\(384\) 0 0
\(385\) −19.9721 + 20.3794i −1.01787 + 1.03863i
\(386\) 0 0
\(387\) −5.36552 25.4205i −0.272745 1.29220i
\(388\) 0 0
\(389\) 13.7382 0.696553 0.348277 0.937392i \(-0.386767\pi\)
0.348277 + 0.937392i \(0.386767\pi\)
\(390\) 0 0
\(391\) −1.44050 2.49501i −0.0728491 0.126178i
\(392\) 0 0
\(393\) −4.51848 11.7961i −0.227927 0.595035i
\(394\) 0 0
\(395\) −11.8376 20.5034i −0.595615 1.03164i
\(396\) 0 0
\(397\) −3.57893 + 6.19889i −0.179622 + 0.311114i −0.941751 0.336311i \(-0.890821\pi\)
0.762129 + 0.647425i \(0.224154\pi\)
\(398\) 0 0
\(399\) 7.15335 5.30048i 0.358116 0.265356i
\(400\) 0 0
\(401\) −9.27936 −0.463389 −0.231695 0.972789i \(-0.574427\pi\)
−0.231695 + 0.972789i \(0.574427\pi\)
\(402\) 0 0
\(403\) −5.86156 −0.291985
\(404\) 0 0
\(405\) 1.70137 15.7563i 0.0845419 0.782937i
\(406\) 0 0
\(407\) −8.83693 + 15.3060i −0.438030 + 0.758691i
\(408\) 0 0
\(409\) −7.58414 + 13.1361i −0.375011 + 0.649539i −0.990329 0.138741i \(-0.955695\pi\)
0.615317 + 0.788279i \(0.289028\pi\)
\(410\) 0 0
\(411\) 5.06922 + 13.2339i 0.250046 + 0.652779i
\(412\) 0 0
\(413\) −1.41135 5.06227i −0.0694481 0.249098i
\(414\) 0 0
\(415\) 2.75116 4.76515i 0.135049 0.233912i
\(416\) 0 0
\(417\) 13.5985 16.7684i 0.665921 0.821150i
\(418\) 0 0
\(419\) 4.16827 + 7.21966i 0.203633 + 0.352703i 0.949696 0.313172i \(-0.101392\pi\)
−0.746063 + 0.665875i \(0.768058\pi\)
\(420\) 0 0
\(421\) −3.50232 + 6.06620i −0.170693 + 0.295649i −0.938662 0.344838i \(-0.887934\pi\)
0.767969 + 0.640486i \(0.221267\pi\)
\(422\) 0 0
\(423\) −4.73461 1.54581i −0.230205 0.0751601i
\(424\) 0 0
\(425\) 6.49768 + 11.2543i 0.315184 + 0.545914i
\(426\) 0 0
\(427\) 26.5212 + 6.82015i 1.28345 + 0.330050i
\(428\) 0 0
\(429\) 5.08414 6.26926i 0.245464 0.302683i
\(430\) 0 0
\(431\) 1.72545 + 2.98857i 0.0831120 + 0.143954i 0.904585 0.426293i \(-0.140181\pi\)
−0.821473 + 0.570247i \(0.806847\pi\)
\(432\) 0 0
\(433\) 28.2599 1.35809 0.679043 0.734099i \(-0.262395\pi\)
0.679043 + 0.734099i \(0.262395\pi\)
\(434\) 0 0
\(435\) −4.41135 0.701905i −0.211508 0.0336538i
\(436\) 0 0
\(437\) −0.409028 + 0.708458i −0.0195665 + 0.0338901i
\(438\) 0 0
\(439\) −14.4480 25.0247i −0.689566 1.19436i −0.971978 0.235071i \(-0.924468\pi\)
0.282412 0.959293i \(-0.408866\pi\)
\(440\) 0 0
\(441\) 14.3421 + 15.3396i 0.682959 + 0.730457i
\(442\) 0 0
\(443\) −6.88044 11.9173i −0.326899 0.566207i 0.654995 0.755633i \(-0.272671\pi\)
−0.981895 + 0.189426i \(0.939337\pi\)
\(444\) 0 0
\(445\) 2.29179 3.96950i 0.108641 0.188172i
\(446\) 0 0
\(447\) −5.46978 14.2796i −0.258711 0.675401i
\(448\) 0 0
\(449\) −20.2003 −0.953309 −0.476655 0.879091i \(-0.658151\pi\)
−0.476655 + 0.879091i \(0.658151\pi\)
\(450\) 0 0
\(451\) 21.2616 + 36.8261i 1.00117 + 1.73407i
\(452\) 0 0
\(453\) −9.28495 24.2396i −0.436245 1.13888i
\(454\) 0 0
\(455\) −3.43310 0.882853i −0.160946 0.0413888i
\(456\) 0 0
\(457\) −10.0149 17.3463i −0.468478 0.811428i 0.530873 0.847451i \(-0.321864\pi\)
−0.999351 + 0.0360237i \(0.988531\pi\)
\(458\) 0 0
\(459\) −1.78495 35.5079i −0.0833145 1.65737i
\(460\) 0 0
\(461\) 5.97661 10.3518i 0.278359 0.482131i −0.692618 0.721304i \(-0.743543\pi\)
0.970977 + 0.239173i \(0.0768763\pi\)
\(462\) 0 0
\(463\) −6.64527 11.5100i −0.308832 0.534913i 0.669275 0.743015i \(-0.266605\pi\)
−0.978107 + 0.208102i \(0.933271\pi\)
\(464\) 0 0
\(465\) −23.2038 3.69204i −1.07605 0.171214i
\(466\) 0 0
\(467\) 5.61505 9.72555i 0.259833 0.450045i −0.706364 0.707849i \(-0.749666\pi\)
0.966197 + 0.257804i \(0.0829990\pi\)
\(468\) 0 0
\(469\) −4.82094 17.2918i −0.222610 0.798463i
\(470\) 0 0
\(471\) 32.4669 + 5.16592i 1.49600 + 0.238033i
\(472\) 0 0
\(473\) 26.5208 45.9354i 1.21943 2.11211i
\(474\) 0 0
\(475\) 1.84501 3.19565i 0.0846550 0.146627i
\(476\) 0 0
\(477\) 0.642950 + 0.209918i 0.0294387 + 0.00961150i
\(478\) 0 0
\(479\) 32.6271 1.49077 0.745385 0.666634i \(-0.232266\pi\)
0.745385 + 0.666634i \(0.232266\pi\)
\(480\) 0 0
\(481\) −2.19562 −0.100111
\(482\) 0 0
\(483\) −1.77004 0.768251i −0.0805394 0.0349566i
\(484\) 0 0
\(485\) −3.20137 + 5.54494i −0.145367 + 0.251783i
\(486\) 0 0
\(487\) −1.84897 3.20251i −0.0837848 0.145120i 0.821088 0.570802i \(-0.193368\pi\)
−0.904873 + 0.425682i \(0.860034\pi\)
\(488\) 0 0
\(489\) −25.7226 4.09280i −1.16321 0.185083i
\(490\) 0 0
\(491\) 18.7804 + 32.5287i 0.847549 + 1.46800i 0.883389 + 0.468641i \(0.155256\pi\)
−0.0358393 + 0.999358i \(0.511410\pi\)
\(492\) 0 0
\(493\) −10.0208 −0.451314
\(494\) 0 0
\(495\) 24.0751 21.6154i 1.08210 0.971541i
\(496\) 0 0
\(497\) −19.9721 + 20.3794i −0.895871 + 0.914143i
\(498\) 0 0
\(499\) 31.7954 1.42336 0.711678 0.702506i \(-0.247936\pi\)
0.711678 + 0.702506i \(0.247936\pi\)
\(500\) 0 0
\(501\) −1.24828 + 1.53926i −0.0557692 + 0.0687692i
\(502\) 0 0
\(503\) −30.8252 −1.37443 −0.687214 0.726455i \(-0.741166\pi\)
−0.687214 + 0.726455i \(0.741166\pi\)
\(504\) 0 0
\(505\) −14.1053 −0.627679
\(506\) 0 0
\(507\) −21.2466 3.38063i −0.943597 0.150139i
\(508\) 0 0
\(509\) 8.01616 0.355310 0.177655 0.984093i \(-0.443149\pi\)
0.177655 + 0.984093i \(0.443149\pi\)
\(510\) 0 0
\(511\) 0.785900 + 0.202101i 0.0347662 + 0.00894042i
\(512\) 0 0
\(513\) −8.47825 + 5.48016i −0.374324 + 0.241955i
\(514\) 0 0
\(515\) 12.0241 0.529844
\(516\) 0 0
\(517\) −5.08414 8.80598i −0.223600 0.387287i
\(518\) 0 0
\(519\) −0.542951 + 0.669515i −0.0238329 + 0.0293885i
\(520\) 0 0
\(521\) 14.8646 + 25.7462i 0.651229 + 1.12796i 0.982825 + 0.184540i \(0.0590795\pi\)
−0.331596 + 0.943421i \(0.607587\pi\)
\(522\) 0 0
\(523\) −13.4698 + 23.3303i −0.588992 + 1.02016i 0.405373 + 0.914152i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(524\) 0 0
\(525\) 7.98414 + 3.46537i 0.348456 + 0.151241i
\(526\) 0 0
\(527\) −52.7097 −2.29607
\(528\) 0 0
\(529\) −22.8227 −0.992291
\(530\) 0 0
\(531\) 1.23065 + 5.83052i 0.0534057 + 0.253023i
\(532\) 0 0
\(533\) −2.64132 + 4.57489i −0.114408 + 0.198161i
\(534\) 0 0
\(535\) −3.12188 + 5.40726i −0.134971 + 0.233776i
\(536\) 0 0
\(537\) −9.63160 + 11.8768i −0.415634 + 0.512520i
\(538\) 0 0
\(539\) 0.865521 + 42.8646i 0.0372806 + 1.84631i
\(540\) 0 0
\(541\) 7.15568 12.3940i 0.307647 0.532859i −0.670201 0.742180i \(-0.733792\pi\)
0.977847 + 0.209321i \(0.0671252\pi\)
\(542\) 0 0
\(543\) −0.823649 2.15025i −0.0353462 0.0922760i
\(544\) 0 0
\(545\) 0.619562 + 1.07311i 0.0265391 + 0.0459671i
\(546\) 0 0
\(547\) −1.02463 + 1.77471i −0.0438101 + 0.0758813i −0.887099 0.461579i \(-0.847283\pi\)
0.843289 + 0.537461i \(0.180616\pi\)
\(548\) 0 0
\(549\) −29.5172 9.63716i −1.25977 0.411304i
\(550\) 0 0
\(551\) 1.42270 + 2.46419i 0.0606091 + 0.104978i
\(552\) 0 0
\(553\) −34.4516 8.85952i −1.46503 0.376745i
\(554\) 0 0
\(555\) −8.69166 1.38296i −0.368940 0.0587033i
\(556\) 0 0
\(557\) 8.84338 + 15.3172i 0.374706 + 0.649010i 0.990283 0.139067i \(-0.0444103\pi\)
−0.615577 + 0.788077i \(0.711077\pi\)
\(558\) 0 0
\(559\) 6.58934 0.278699
\(560\) 0 0
\(561\) 45.7187 56.3759i 1.93025 2.38019i
\(562\) 0 0
\(563\) 0.468531 0.811520i 0.0197462 0.0342015i −0.855983 0.517003i \(-0.827048\pi\)
0.875730 + 0.482802i \(0.160381\pi\)
\(564\) 0 0
\(565\) 7.48577 + 12.9657i 0.314929 + 0.545473i
\(566\) 0 0
\(567\) −15.1190 18.3961i −0.634939 0.772563i
\(568\) 0 0
\(569\) −11.7632 20.3745i −0.493139 0.854142i 0.506830 0.862046i \(-0.330817\pi\)
−0.999969 + 0.00790437i \(0.997484\pi\)
\(570\) 0 0
\(571\) −0.242002 + 0.419160i −0.0101275 + 0.0175413i −0.871045 0.491204i \(-0.836557\pi\)
0.860917 + 0.508745i \(0.169890\pi\)
\(572\) 0 0
\(573\) −17.6391 + 21.7509i −0.736885 + 0.908655i
\(574\) 0 0
\(575\) −0.799737 −0.0333514
\(576\) 0 0
\(577\) −2.23065 3.86360i −0.0928633 0.160844i 0.815852 0.578261i \(-0.196269\pi\)
−0.908715 + 0.417417i \(0.862935\pi\)
\(578\) 0 0
\(579\) −24.2353 3.85616i −1.00718 0.160257i
\(580\) 0 0
\(581\) −2.22025 7.96364i −0.0921114 0.330387i
\(582\) 0 0
\(583\) 0.690415 + 1.19583i 0.0285941 + 0.0495264i
\(584\) 0 0
\(585\) 3.82094 + 1.24751i 0.157976 + 0.0515781i
\(586\) 0 0
\(587\) −8.31518 + 14.4023i −0.343204 + 0.594447i −0.985026 0.172407i \(-0.944846\pi\)
0.641822 + 0.766854i \(0.278179\pi\)
\(588\) 0 0
\(589\) 7.48345 + 12.9617i 0.308350 + 0.534078i
\(590\) 0 0
\(591\) −9.81518 25.6239i −0.403742 1.05402i
\(592\) 0 0
\(593\) 20.7632 35.9629i 0.852642 1.47682i −0.0261726 0.999657i \(-0.508332\pi\)
0.878815 0.477163i \(-0.158335\pi\)
\(594\) 0 0
\(595\) −30.8720 7.93899i −1.26563 0.325467i
\(596\) 0 0
\(597\) 9.75636 12.0306i 0.399301 0.492380i
\(598\) 0 0
\(599\) 7.53831 13.0567i 0.308007 0.533483i −0.669919 0.742434i \(-0.733671\pi\)
0.977926 + 0.208950i \(0.0670047\pi\)
\(600\) 0 0
\(601\) −8.05555 + 13.9526i −0.328593 + 0.569139i −0.982233 0.187666i \(-0.939908\pi\)
0.653640 + 0.756805i \(0.273241\pi\)
\(602\) 0 0
\(603\) 4.20370 + 19.9161i 0.171188 + 0.811044i
\(604\) 0 0
\(605\) 46.6856 1.89804
\(606\) 0 0
\(607\) −19.5732 −0.794451 −0.397225 0.917721i \(-0.630027\pi\)
−0.397225 + 0.917721i \(0.630027\pi\)
\(608\) 0 0
\(609\) −5.39248 + 3.99571i −0.218514 + 0.161914i
\(610\) 0 0
\(611\) 0.631600 1.09396i 0.0255518 0.0442570i
\(612\) 0 0
\(613\) −2.77579 4.80782i −0.112113 0.194186i 0.804509 0.593941i \(-0.202429\pi\)
−0.916622 + 0.399755i \(0.869095\pi\)
\(614\) 0 0
\(615\) −13.3376 + 16.4467i −0.537825 + 0.663194i
\(616\) 0 0
\(617\) 0.634479 + 1.09895i 0.0255431 + 0.0442420i 0.878514 0.477716i \(-0.158535\pi\)
−0.852971 + 0.521958i \(0.825202\pi\)
\(618\) 0 0
\(619\) −4.50232 −0.180964 −0.0904818 0.995898i \(-0.528841\pi\)
−0.0904818 + 0.995898i \(0.528841\pi\)
\(620\) 0 0
\(621\) 1.94733 + 0.997454i 0.0781438 + 0.0400264i
\(622\) 0 0
\(623\) −1.84953 6.63392i −0.0740997 0.265782i
\(624\) 0 0
\(625\) −11.8960 −0.475842
\(626\) 0 0
\(627\) −20.3542 3.23862i −0.812867 0.129338i
\(628\) 0 0
\(629\) −19.7439 −0.787242
\(630\) 0 0
\(631\) 1.69905 0.0676381 0.0338191 0.999428i \(-0.489233\pi\)
0.0338191 + 0.999428i \(0.489233\pi\)
\(632\) 0 0
\(633\) −24.8428 + 30.6338i −0.987414 + 1.21758i
\(634\) 0 0
\(635\) 33.3743 1.32442
\(636\) 0 0
\(637\) −4.55787 + 2.75564i −0.180589 + 0.109183i
\(638\) 0 0
\(639\) 24.0751 21.6154i 0.952397 0.855093i
\(640\) 0 0
\(641\) −0.948577 −0.0374666 −0.0187333 0.999825i \(-0.505963\pi\)
−0.0187333 + 0.999825i \(0.505963\pi\)
\(642\) 0 0
\(643\) 9.84897 + 17.0589i 0.388405 + 0.672738i 0.992235 0.124375i \(-0.0396927\pi\)
−0.603830 + 0.797113i \(0.706359\pi\)
\(644\) 0 0
\(645\) 26.0848 + 4.15044i 1.02709 + 0.163424i
\(646\) 0 0
\(647\) −11.7271 20.3119i −0.461039 0.798543i 0.537974 0.842962i \(-0.319190\pi\)
−0.999013 + 0.0444181i \(0.985857\pi\)
\(648\) 0 0
\(649\) −6.08289 + 10.5359i −0.238774 + 0.413569i
\(650\) 0 0
\(651\) −28.3646 + 21.0175i −1.11170 + 0.823742i
\(652\) 0 0
\(653\) 22.7907 0.891869 0.445935 0.895065i \(-0.352871\pi\)
0.445935 + 0.895065i \(0.352871\pi\)
\(654\) 0 0
\(655\) 12.8421 0.501784
\(656\) 0 0
\(657\) −0.874681 0.285577i −0.0341246 0.0111414i
\(658\) 0 0
\(659\) 13.2398 22.9320i 0.515750 0.893305i −0.484083 0.875022i \(-0.660847\pi\)
0.999833 0.0182828i \(-0.00581993\pi\)
\(660\) 0 0
\(661\) 13.3691 23.1559i 0.519997 0.900662i −0.479732 0.877415i \(-0.659266\pi\)
0.999730 0.0232469i \(-0.00740038\pi\)
\(662\) 0 0
\(663\) 8.90507 + 1.41692i 0.345844 + 0.0550284i
\(664\) 0 0
\(665\) 2.43078 + 8.71878i 0.0942617 + 0.338100i
\(666\) 0 0
\(667\) 0.308342 0.534063i 0.0119390 0.0206790i
\(668\) 0 0
\(669\) −22.0413 3.50707i −0.852167 0.135591i
\(670\) 0 0
\(671\) −31.6963 54.8996i −1.22362 2.11938i
\(672\) 0 0
\(673\) −10.3856 + 17.9885i −0.400337 + 0.693404i −0.993766 0.111482i \(-0.964440\pi\)
0.593429 + 0.804886i \(0.297774\pi\)
\(674\) 0 0
\(675\) −8.78387 4.49923i −0.338091 0.173176i
\(676\) 0 0
\(677\) 10.3490 + 17.9249i 0.397743 + 0.688911i 0.993447 0.114293i \(-0.0364602\pi\)
−0.595704 + 0.803204i \(0.703127\pi\)
\(678\) 0 0
\(679\) 2.58358 + 9.26684i 0.0991487 + 0.355629i
\(680\) 0 0
\(681\) 13.6283 + 35.5786i 0.522239 + 1.36338i
\(682\) 0 0
\(683\) −14.2918 24.7541i −0.546860 0.947190i −0.998487 0.0549828i \(-0.982490\pi\)
0.451627 0.892207i \(-0.350844\pi\)
\(684\) 0 0
\(685\) −14.4074 −0.550478
\(686\) 0 0
\(687\) 2.35348 + 6.14409i 0.0897910 + 0.234412i
\(688\) 0 0
\(689\) −0.0857699 + 0.148558i −0.00326757 + 0.00565960i
\(690\) 0 0
\(691\) −3.34897 5.80059i −0.127401 0.220665i 0.795268 0.606258i \(-0.207330\pi\)
−0.922669 + 0.385593i \(0.873997\pi\)
\(692\) 0 0
\(693\) 2.12313 48.5674i 0.0806510 1.84492i
\(694\) 0 0
\(695\) 10.9743 + 19.0080i 0.416278 + 0.721016i
\(696\) 0 0
\(697\) −23.7518 + 41.1394i −0.899665 + 1.55827i
\(698\) 0 0
\(699\) 11.4103 + 1.81553i 0.431576 + 0.0686695i
\(700\) 0 0
\(701\) −25.1442 −0.949683 −0.474842 0.880071i \(-0.657495\pi\)
−0.474842 + 0.880071i \(0.657495\pi\)
\(702\) 0 0
\(703\) 2.80314 + 4.85518i 0.105722 + 0.183117i
\(704\) 0 0
\(705\) 3.18934 3.93278i 0.120117 0.148117i
\(706\) 0 0
\(707\) −14.8341 + 15.1366i −0.557892 + 0.569271i
\(708\) 0 0
\(709\) −4.43310 7.67836i −0.166489 0.288367i 0.770694 0.637205i \(-0.219910\pi\)
−0.937183 + 0.348838i \(0.886576\pi\)
\(710\) 0 0
\(711\) 38.3435 + 12.5189i 1.43799 + 0.469494i
\(712\) 0 0
\(713\) 1.62188 2.80919i 0.0607401 0.105205i
\(714\) 0 0
\(715\) 4.10301 + 7.10662i 0.153444 + 0.265773i
\(716\) 0 0
\(717\) 17.0636 21.0412i 0.637253 0.785799i
\(718\) 0 0
\(719\) −11.8015 + 20.4408i −0.440122 + 0.762313i −0.997698 0.0678123i \(-0.978398\pi\)
0.557576 + 0.830126i \(0.311731\pi\)
\(720\) 0 0
\(721\) 12.6453 12.9032i 0.470935 0.480540i
\(722\) 0 0
\(723\) −13.2661 34.6329i −0.493371 1.28801i
\(724\) 0 0
\(725\) −1.39084 + 2.40901i −0.0516546 + 0.0894683i
\(726\) 0 0
\(727\) −3.25692 + 5.64115i −0.120792 + 0.209219i −0.920080 0.391730i \(-0.871877\pi\)
0.799288 + 0.600948i \(0.205210\pi\)
\(728\) 0 0
\(729\) 15.7769 + 21.9110i 0.584329 + 0.811517i
\(730\) 0 0
\(731\) 59.2542 2.19159
\(732\) 0 0
\(733\) −23.1981 −0.856842 −0.428421 0.903579i \(-0.640930\pi\)
−0.428421 + 0.903579i \(0.640930\pi\)
\(734\) 0 0
\(735\) −19.7787 + 8.03773i −0.729547 + 0.296476i
\(736\) 0 0
\(737\) −20.7781 + 35.9888i −0.765372 + 1.32566i
\(738\) 0 0
\(739\) 7.57838 + 13.1261i 0.278775 + 0.482853i 0.971081 0.238752i \(-0.0767383\pi\)
−0.692305 + 0.721605i \(0.743405\pi\)
\(740\) 0 0
\(741\) −0.915865 2.39099i −0.0336451 0.0878352i
\(742\) 0 0
\(743\) 5.21737 + 9.03675i 0.191407 + 0.331526i 0.945717 0.324992i \(-0.105362\pi\)
−0.754310 + 0.656518i \(0.772028\pi\)
\(744\) 0 0
\(745\) 15.5458 0.569555
\(746\) 0 0
\(747\) 1.93598 + 9.17220i 0.0708339 + 0.335593i
\(748\) 0 0
\(749\) 2.51943 + 9.03675i 0.0920580 + 0.330196i
\(750\) 0 0
\(751\) −40.2118 −1.46735 −0.733674 0.679501i \(-0.762196\pi\)
−0.733674 + 0.679501i \(0.762196\pi\)
\(752\) 0 0
\(753\) −14.6235 38.1767i −0.532911 1.39124i
\(754\) 0 0
\(755\) 26.3891 0.960397
\(756\) 0 0
\(757\) −21.5206 −0.782181 −0.391091 0.920352i \(-0.627902\pi\)
−0.391091 + 0.920352i \(0.627902\pi\)
\(758\) 0 0
\(759\) 1.59781 + 4.17129i 0.0579968 + 0.151408i
\(760\) 0 0
\(761\) −23.6627 −0.857771 −0.428886 0.903359i \(-0.641094\pi\)
−0.428886 + 0.903359i \(0.641094\pi\)
\(762\) 0 0
\(763\) 1.80314 + 0.463693i 0.0652780 + 0.0167868i
\(764\) 0 0
\(765\) 34.3595 + 11.2181i 1.24227 + 0.405592i
\(766\) 0 0
\(767\) −1.51135 −0.0545717
\(768\) 0 0
\(769\) −5.62764 9.74736i −0.202938 0.351499i 0.746536 0.665345i \(-0.231716\pi\)
−0.949474 + 0.313846i \(0.898382\pi\)
\(770\) 0 0
\(771\) −12.5523 32.7694i −0.452059 1.18016i
\(772\) 0 0
\(773\) 0.138992 + 0.240741i 0.00499919 + 0.00865886i 0.868514 0.495664i \(-0.165075\pi\)
−0.863515 + 0.504323i \(0.831742\pi\)
\(774\) 0 0
\(775\) −7.31587 + 12.6715i −0.262794 + 0.455172i
\(776\) 0 0
\(777\) −10.6248 + 7.87272i −0.381161 + 0.282432i
\(778\) 0 0
\(779\) 13.4887 0.483281
\(780\) 0 0
\(781\) 66.0553 2.36364
\(782\) 0 0
\(783\) 6.39123 4.13116i 0.228404 0.147636i
\(784\) 0 0
\(785\) −16.7112 + 28.9447i −0.596449 + 1.03308i
\(786\) 0 0
\(787\) −14.6940 + 25.4507i −0.523784 + 0.907220i 0.475833 + 0.879536i \(0.342147\pi\)
−0.999617 +