Properties

Label 1323.2.h.c.802.3
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
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] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.3
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.c.226.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.879385 q^{2} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +O(q^{10})\) \(q+0.879385 q^{2} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +(0.592396 - 1.02606i) q^{10} +(0.826352 + 1.43128i) q^{11} +(1.68479 + 2.91815i) q^{13} -0.0418891 q^{16} +(0.233956 - 0.405223i) q^{17} +(1.61334 + 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(1.48158 + 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +9.23442 q^{31} +5.63816 q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 - 7.99724i) q^{37} +(1.41875 + 2.45734i) q^{38} +(-1.91147 + 3.31077i) q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 - 1.75573i) q^{44} +(3.93242 - 6.81115i) q^{46} -9.35504 q^{47} +(1.40033 + 2.42544i) q^{50} +(-2.06670 - 3.57964i) q^{52} +(-0.286989 + 0.497079i) q^{53} +2.22668 q^{55} +(2.75624 - 4.77396i) q^{58} +10.3969 q^{59} +7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} +4.53983 q^{65} +0.596267 q^{67} +(-0.286989 + 0.497079i) q^{68} +0.554378 q^{71} +(-1.02481 + 1.77503i) q^{73} +(-4.06031 - 7.03266i) q^{74} +(-1.97906 - 3.42782i) q^{76} -2.40373 q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(1.93969 - 3.35965i) q^{86} +(-2.34477 - 4.06126i) q^{88} +(4.54323 + 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} -8.22668 q^{94} +4.34730 q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} + 15 q^{44} - 6 q^{47} - 6 q^{50} + 21 q^{52} + 6 q^{53} + 9 q^{58} + 6 q^{59} + 12 q^{61} + 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} + 6 q^{68} - 18 q^{71} + 21 q^{73} - 30 q^{74} - 15 q^{76} - 42 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 12 q^{89} + 3 q^{92} - 36 q^{94} + 24 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.879385 0.621819 0.310910 0.950439i \(-0.399366\pi\)
0.310910 + 0.950439i \(0.399366\pi\)
\(3\) 0 0
\(4\) −1.22668 −0.613341
\(5\) 0.673648 1.16679i 0.301265 0.521806i −0.675158 0.737673i \(-0.735925\pi\)
0.976423 + 0.215867i \(0.0692579\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.83750 −1.00321
\(9\) 0 0
\(10\) 0.592396 1.02606i 0.187332 0.324469i
\(11\) 0.826352 + 1.43128i 0.249154 + 0.431548i 0.963291 0.268458i \(-0.0865140\pi\)
−0.714137 + 0.700006i \(0.753181\pi\)
\(12\) 0 0
\(13\) 1.68479 + 2.91815i 0.467277 + 0.809348i 0.999301 0.0373813i \(-0.0119016\pi\)
−0.532024 + 0.846729i \(0.678568\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0418891 −0.0104723
\(17\) 0.233956 0.405223i 0.0567426 0.0982810i −0.836259 0.548335i \(-0.815262\pi\)
0.893001 + 0.450054i \(0.148595\pi\)
\(18\) 0 0
\(19\) 1.61334 + 2.79439i 0.370126 + 0.641077i 0.989585 0.143953i \(-0.0459813\pi\)
−0.619459 + 0.785029i \(0.712648\pi\)
\(20\) −0.826352 + 1.43128i −0.184778 + 0.320045i
\(21\) 0 0
\(22\) 0.726682 + 1.25865i 0.154929 + 0.268345i
\(23\) 4.47178 7.74535i 0.932431 1.61502i 0.153279 0.988183i \(-0.451017\pi\)
0.779152 0.626835i \(-0.215650\pi\)
\(24\) 0 0
\(25\) 1.59240 + 2.75811i 0.318479 + 0.551622i
\(26\) 1.48158 + 2.56617i 0.290562 + 0.503268i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.13429 5.42874i 0.582022 1.00809i −0.413217 0.910632i \(-0.635595\pi\)
0.995239 0.0974595i \(-0.0310717\pi\)
\(30\) 0 0
\(31\) 9.23442 1.65855 0.829276 0.558840i \(-0.188753\pi\)
0.829276 + 0.558840i \(0.188753\pi\)
\(32\) 5.63816 0.996695
\(33\) 0 0
\(34\) 0.205737 0.356347i 0.0352836 0.0611130i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.61721 7.99724i −0.759065 1.31474i −0.943328 0.331862i \(-0.892323\pi\)
0.184263 0.982877i \(-0.441010\pi\)
\(38\) 1.41875 + 2.45734i 0.230151 + 0.398634i
\(39\) 0 0
\(40\) −1.91147 + 3.31077i −0.302231 + 0.523479i
\(41\) 1.70574 + 2.95442i 0.266391 + 0.461403i 0.967927 0.251231i \(-0.0808353\pi\)
−0.701536 + 0.712634i \(0.747502\pi\)
\(42\) 0 0
\(43\) 2.20574 3.82045i 0.336372 0.582613i −0.647376 0.762171i \(-0.724133\pi\)
0.983747 + 0.179558i \(0.0574668\pi\)
\(44\) −1.01367 1.75573i −0.152817 0.264686i
\(45\) 0 0
\(46\) 3.93242 6.81115i 0.579803 1.00425i
\(47\) −9.35504 −1.36457 −0.682286 0.731085i \(-0.739014\pi\)
−0.682286 + 0.731085i \(0.739014\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.40033 + 2.42544i 0.198037 + 0.343009i
\(51\) 0 0
\(52\) −2.06670 3.57964i −0.286600 0.496406i
\(53\) −0.286989 + 0.497079i −0.0394210 + 0.0682791i −0.885063 0.465472i \(-0.845885\pi\)
0.845642 + 0.533751i \(0.179218\pi\)
\(54\) 0 0
\(55\) 2.22668 0.300246
\(56\) 0 0
\(57\) 0 0
\(58\) 2.75624 4.77396i 0.361913 0.626851i
\(59\) 10.3969 1.35356 0.676782 0.736183i \(-0.263374\pi\)
0.676782 + 0.736183i \(0.263374\pi\)
\(60\) 0 0
\(61\) 7.63816 0.977966 0.488983 0.872293i \(-0.337368\pi\)
0.488983 + 0.872293i \(0.337368\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) 4.53983 0.563097
\(66\) 0 0
\(67\) 0.596267 0.0728456 0.0364228 0.999336i \(-0.488404\pi\)
0.0364228 + 0.999336i \(0.488404\pi\)
\(68\) −0.286989 + 0.497079i −0.0348025 + 0.0602797i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.554378 0.0657925 0.0328963 0.999459i \(-0.489527\pi\)
0.0328963 + 0.999459i \(0.489527\pi\)
\(72\) 0 0
\(73\) −1.02481 + 1.77503i −0.119946 + 0.207752i −0.919746 0.392514i \(-0.871605\pi\)
0.799800 + 0.600266i \(0.204939\pi\)
\(74\) −4.06031 7.03266i −0.472001 0.817530i
\(75\) 0 0
\(76\) −1.97906 3.42782i −0.227013 0.393198i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.40373 −0.270441 −0.135221 0.990816i \(-0.543174\pi\)
−0.135221 + 0.990816i \(0.543174\pi\)
\(80\) −0.0282185 + 0.0488759i −0.00315492 + 0.00546449i
\(81\) 0 0
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) −7.52481 + 13.0334i −0.825956 + 1.43060i 0.0752309 + 0.997166i \(0.476031\pi\)
−0.901187 + 0.433431i \(0.857303\pi\)
\(84\) 0 0
\(85\) −0.315207 0.545955i −0.0341891 0.0592172i
\(86\) 1.93969 3.35965i 0.209162 0.362280i
\(87\) 0 0
\(88\) −2.34477 4.06126i −0.249953 0.432932i
\(89\) 4.54323 + 7.86911i 0.481582 + 0.834124i 0.999777 0.0211385i \(-0.00672911\pi\)
−0.518195 + 0.855263i \(0.673396\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.48545 + 9.50108i −0.571898 + 0.990556i
\(93\) 0 0
\(94\) −8.22668 −0.848517
\(95\) 4.34730 0.446023
\(96\) 0 0
\(97\) 0.949493 1.64457i 0.0964064 0.166981i −0.813788 0.581161i \(-0.802598\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95336 3.38332i −0.195336 0.338332i
\(101\) −0.854570 1.48016i −0.0850329 0.147281i 0.820372 0.571830i \(-0.193766\pi\)
−0.905405 + 0.424548i \(0.860433\pi\)
\(102\) 0 0
\(103\) 1.81908 3.15074i 0.179239 0.310451i −0.762381 0.647128i \(-0.775970\pi\)
0.941620 + 0.336677i \(0.109303\pi\)
\(104\) −4.78059 8.28023i −0.468776 0.811943i
\(105\) 0 0
\(106\) −0.252374 + 0.437124i −0.0245127 + 0.0424573i
\(107\) 3.56418 + 6.17334i 0.344562 + 0.596799i 0.985274 0.170982i \(-0.0546941\pi\)
−0.640712 + 0.767781i \(0.721361\pi\)
\(108\) 0 0
\(109\) −0.201867 + 0.349643i −0.0193353 + 0.0334898i −0.875531 0.483162i \(-0.839488\pi\)
0.856196 + 0.516651i \(0.172822\pi\)
\(110\) 1.95811 0.186699
\(111\) 0 0
\(112\) 0 0
\(113\) 7.18479 + 12.4444i 0.675888 + 1.17067i 0.976208 + 0.216835i \(0.0695732\pi\)
−0.300320 + 0.953839i \(0.597093\pi\)
\(114\) 0 0
\(115\) −6.02481 10.4353i −0.561817 0.973095i
\(116\) −3.84477 + 6.65934i −0.356978 + 0.618304i
\(117\) 0 0
\(118\) 9.14290 0.841672
\(119\) 0 0
\(120\) 0 0
\(121\) 4.13429 7.16079i 0.375844 0.650981i
\(122\) 6.71688 0.608118
\(123\) 0 0
\(124\) −11.3277 −1.01726
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) −6.84255 −0.604802
\(129\) 0 0
\(130\) 3.99226 0.350144
\(131\) −3.58260 + 6.20524i −0.313013 + 0.542154i −0.979013 0.203797i \(-0.934672\pi\)
0.666000 + 0.745952i \(0.268005\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.524348 0.0452968
\(135\) 0 0
\(136\) −0.663848 + 1.14982i −0.0569245 + 0.0985961i
\(137\) 1.28446 + 2.22475i 0.109739 + 0.190074i 0.915665 0.401943i \(-0.131665\pi\)
−0.805925 + 0.592017i \(0.798332\pi\)
\(138\) 0 0
\(139\) 3.06670 + 5.31169i 0.260114 + 0.450531i 0.966272 0.257523i \(-0.0829064\pi\)
−0.706158 + 0.708055i \(0.749573\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.487511 0.0409111
\(143\) −2.78446 + 4.82283i −0.232848 + 0.403305i
\(144\) 0 0
\(145\) −4.22281 7.31412i −0.350685 0.607405i
\(146\) −0.901207 + 1.56094i −0.0745844 + 0.129184i
\(147\) 0 0
\(148\) 5.66385 + 9.81007i 0.465565 + 0.806383i
\(149\) 0.215537 0.373321i 0.0176575 0.0305837i −0.857062 0.515214i \(-0.827712\pi\)
0.874719 + 0.484630i \(0.161046\pi\)
\(150\) 0 0
\(151\) 1.23530 + 2.13960i 0.100527 + 0.174118i 0.911902 0.410408i \(-0.134614\pi\)
−0.811375 + 0.584526i \(0.801280\pi\)
\(152\) −4.57785 7.92907i −0.371313 0.643132i
\(153\) 0 0
\(154\) 0 0
\(155\) 6.22075 10.7747i 0.499663 0.865441i
\(156\) 0 0
\(157\) 10.1334 0.808734 0.404367 0.914597i \(-0.367492\pi\)
0.404367 + 0.914597i \(0.367492\pi\)
\(158\) −2.11381 −0.168166
\(159\) 0 0
\(160\) 3.79813 6.57856i 0.300269 0.520081i
\(161\) 0 0
\(162\) 0 0
\(163\) 1.29813 + 2.24843i 0.101678 + 0.176111i 0.912376 0.409353i \(-0.134246\pi\)
−0.810698 + 0.585464i \(0.800912\pi\)
\(164\) −2.09240 3.62414i −0.163389 0.282998i
\(165\) 0 0
\(166\) −6.61721 + 11.4613i −0.513595 + 0.889573i
\(167\) −11.5915 20.0771i −0.896979 1.55361i −0.831337 0.555769i \(-0.812424\pi\)
−0.0656422 0.997843i \(-0.520910\pi\)
\(168\) 0 0
\(169\) 0.822948 1.42539i 0.0633037 0.109645i
\(170\) −0.277189 0.480105i −0.0212594 0.0368224i
\(171\) 0 0
\(172\) −2.70574 + 4.68647i −0.206311 + 0.357340i
\(173\) 4.75196 0.361285 0.180643 0.983549i \(-0.442182\pi\)
0.180643 + 0.983549i \(0.442182\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.0346151 0.0599551i −0.00260921 0.00451929i
\(177\) 0 0
\(178\) 3.99525 + 6.91998i 0.299457 + 0.518674i
\(179\) −4.26604 + 7.38901i −0.318859 + 0.552280i −0.980250 0.197761i \(-0.936633\pi\)
0.661391 + 0.750041i \(0.269966\pi\)
\(180\) 0 0
\(181\) −17.2344 −1.28102 −0.640512 0.767948i \(-0.721278\pi\)
−0.640512 + 0.767948i \(0.721278\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −12.6887 + 21.9774i −0.935421 + 1.62020i
\(185\) −12.4415 −0.914718
\(186\) 0 0
\(187\) 0.773318 0.0565506
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) −12.9094 −0.934092 −0.467046 0.884233i \(-0.654682\pi\)
−0.467046 + 0.884233i \(0.654682\pi\)
\(192\) 0 0
\(193\) −0.638156 −0.0459355 −0.0229677 0.999736i \(-0.507311\pi\)
−0.0229677 + 0.999736i \(0.507311\pi\)
\(194\) 0.834970 1.44621i 0.0599473 0.103832i
\(195\) 0 0
\(196\) 0 0
\(197\) −11.4456 −0.815467 −0.407733 0.913101i \(-0.633681\pi\)
−0.407733 + 0.913101i \(0.633681\pi\)
\(198\) 0 0
\(199\) 1.81908 3.15074i 0.128951 0.223350i −0.794319 0.607500i \(-0.792172\pi\)
0.923270 + 0.384151i \(0.125506\pi\)
\(200\) −4.51842 7.82613i −0.319500 0.553391i
\(201\) 0 0
\(202\) −0.751497 1.30163i −0.0528751 0.0915824i
\(203\) 0 0
\(204\) 0 0
\(205\) 4.59627 0.321017
\(206\) 1.59967 2.77071i 0.111454 0.193045i
\(207\) 0 0
\(208\) −0.0705744 0.122238i −0.00489345 0.00847571i
\(209\) −2.66637 + 4.61830i −0.184437 + 0.319454i
\(210\) 0 0
\(211\) −2.91147 5.04282i −0.200434 0.347162i 0.748234 0.663435i \(-0.230902\pi\)
−0.948668 + 0.316273i \(0.897569\pi\)
\(212\) 0.352044 0.609758i 0.0241785 0.0418784i
\(213\) 0 0
\(214\) 3.13429 + 5.42874i 0.214255 + 0.371101i
\(215\) −2.97178 5.14728i −0.202674 0.351041i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.177519 + 0.307471i −0.0120231 + 0.0208246i
\(219\) 0 0
\(220\) −2.73143 −0.184153
\(221\) 1.57667 0.106058
\(222\) 0 0
\(223\) −3.54189 + 6.13473i −0.237182 + 0.410812i −0.959905 0.280327i \(-0.909557\pi\)
0.722722 + 0.691139i \(0.242891\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.31820 + 10.9434i 0.420280 + 0.727947i
\(227\) −5.97178 10.3434i −0.396361 0.686517i 0.596913 0.802306i \(-0.296394\pi\)
−0.993274 + 0.115789i \(0.963060\pi\)
\(228\) 0 0
\(229\) 8.77631 15.2010i 0.579955 1.00451i −0.415529 0.909580i \(-0.636403\pi\)
0.995484 0.0949315i \(-0.0302632\pi\)
\(230\) −5.29813 9.17664i −0.349349 0.605089i
\(231\) 0 0
\(232\) −8.89352 + 15.4040i −0.583888 + 1.01132i
\(233\) 8.12701 + 14.0764i 0.532418 + 0.922175i 0.999284 + 0.0378470i \(0.0120499\pi\)
−0.466865 + 0.884328i \(0.654617\pi\)
\(234\) 0 0
\(235\) −6.30200 + 10.9154i −0.411097 + 0.712042i
\(236\) −12.7537 −0.830196
\(237\) 0 0
\(238\) 0 0
\(239\) −7.54963 13.0763i −0.488345 0.845838i 0.511565 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134062i \(0.995733\pi\)
\(240\) 0 0
\(241\) 7.81908 + 13.5430i 0.503671 + 0.872384i 0.999991 + 0.00424420i \(0.00135097\pi\)
−0.496320 + 0.868140i \(0.665316\pi\)
\(242\) 3.63563 6.29710i 0.233707 0.404793i
\(243\) 0 0
\(244\) −9.36959 −0.599826
\(245\) 0 0
\(246\) 0 0
\(247\) −5.43629 + 9.41593i −0.345903 + 0.599121i
\(248\) −26.2026 −1.66387
\(249\) 0 0
\(250\) 9.69728 0.613310
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) −18.2662 −1.14612
\(255\) 0 0
\(256\) −16.1010 −1.00631
\(257\) 13.2909 23.0204i 0.829061 1.43598i −0.0697146 0.997567i \(-0.522209\pi\)
0.898776 0.438409i \(-0.144458\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −5.56893 −0.345370
\(261\) 0 0
\(262\) −3.15048 + 5.45680i −0.194637 + 0.337122i
\(263\) −0.367059 0.635765i −0.0226338 0.0392029i 0.854487 0.519473i \(-0.173872\pi\)
−0.877120 + 0.480270i \(0.840539\pi\)
\(264\) 0 0
\(265\) 0.386659 + 0.669713i 0.0237523 + 0.0411402i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.731429 −0.0446792
\(269\) −10.4251 + 18.0569i −0.635632 + 1.10095i 0.350749 + 0.936470i \(0.385927\pi\)
−0.986381 + 0.164478i \(0.947406\pi\)
\(270\) 0 0
\(271\) −3.47906 6.02590i −0.211338 0.366047i 0.740796 0.671730i \(-0.234449\pi\)
−0.952133 + 0.305683i \(0.901115\pi\)
\(272\) −0.00980018 + 0.0169744i −0.000594223 + 0.00102922i
\(273\) 0 0
\(274\) 1.12954 + 1.95642i 0.0682379 + 0.118191i
\(275\) −2.63176 + 4.55834i −0.158701 + 0.274878i
\(276\) 0 0
\(277\) −8.93629 15.4781i −0.536930 0.929989i −0.999067 0.0431811i \(-0.986251\pi\)
0.462138 0.886808i \(-0.347083\pi\)
\(278\) 2.69681 + 4.67102i 0.161744 + 0.280149i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1552 19.3214i 0.665465 1.15262i −0.313694 0.949524i \(-0.601567\pi\)
0.979159 0.203095i \(-0.0651001\pi\)
\(282\) 0 0
\(283\) −18.5945 −1.10533 −0.552665 0.833404i \(-0.686389\pi\)
−0.552665 + 0.833404i \(0.686389\pi\)
\(284\) −0.680045 −0.0403532
\(285\) 0 0
\(286\) −2.44862 + 4.24113i −0.144790 + 0.250783i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.39053 + 14.5328i 0.493561 + 0.854872i
\(290\) −3.71348 6.43193i −0.218063 0.377696i
\(291\) 0 0
\(292\) 1.25712 2.17740i 0.0735675 0.127423i
\(293\) 6.54576 + 11.3376i 0.382407 + 0.662349i 0.991406 0.130822i \(-0.0417618\pi\)
−0.608998 + 0.793171i \(0.708428\pi\)
\(294\) 0 0
\(295\) 7.00387 12.1311i 0.407781 0.706298i
\(296\) 13.1013 + 22.6922i 0.761499 + 1.31895i
\(297\) 0 0
\(298\) 0.189540 0.328293i 0.0109798 0.0190175i
\(299\) 30.1361 1.74282
\(300\) 0 0
\(301\) 0 0
\(302\) 1.08630 + 1.88153i 0.0625098 + 0.108270i
\(303\) 0 0
\(304\) −0.0675813 0.117054i −0.00387606 0.00671353i
\(305\) 5.14543 8.91215i 0.294626 0.510308i
\(306\) 0 0
\(307\) 6.31046 0.360157 0.180078 0.983652i \(-0.442365\pi\)
0.180078 + 0.983652i \(0.442365\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 5.47044 9.47508i 0.310700 0.538148i
\(311\) 9.52435 0.540076 0.270038 0.962850i \(-0.412964\pi\)
0.270038 + 0.962850i \(0.412964\pi\)
\(312\) 0 0
\(313\) −17.6287 −0.996431 −0.498215 0.867053i \(-0.666011\pi\)
−0.498215 + 0.867053i \(0.666011\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) −8.07697 −0.453648 −0.226824 0.973936i \(-0.572834\pi\)
−0.226824 + 0.973936i \(0.572834\pi\)
\(318\) 0 0
\(319\) 10.3601 0.580054
\(320\) 3.39646 5.88284i 0.189868 0.328861i
\(321\) 0 0
\(322\) 0 0
\(323\) 1.50980 0.0840075
\(324\) 0 0
\(325\) −5.36571 + 9.29369i −0.297636 + 0.515521i
\(326\) 1.14156 + 1.97724i 0.0632251 + 0.109509i
\(327\) 0 0
\(328\) −4.84002 8.38316i −0.267246 0.462883i
\(329\) 0 0
\(330\) 0 0
\(331\) 23.0496 1.26692 0.633461 0.773775i \(-0.281634\pi\)
0.633461 + 0.773775i \(0.281634\pi\)
\(332\) 9.23055 15.9878i 0.506592 0.877444i
\(333\) 0 0
\(334\) −10.1934 17.6555i −0.557759 0.966066i
\(335\) 0.401674 0.695720i 0.0219458 0.0380112i
\(336\) 0 0
\(337\) −14.5116 25.1348i −0.790498 1.36918i −0.925659 0.378359i \(-0.876489\pi\)
0.135161 0.990824i \(-0.456845\pi\)
\(338\) 0.723689 1.25347i 0.0393635 0.0681795i
\(339\) 0 0
\(340\) 0.386659 + 0.669713i 0.0209695 + 0.0363203i
\(341\) 7.63088 + 13.2171i 0.413235 + 0.715745i
\(342\) 0 0
\(343\) 0 0
\(344\) −6.25877 + 10.8405i −0.337450 + 0.584481i
\(345\) 0 0
\(346\) 4.17881 0.224654
\(347\) −12.9463 −0.694991 −0.347496 0.937682i \(-0.612968\pi\)
−0.347496 + 0.937682i \(0.612968\pi\)
\(348\) 0 0
\(349\) −0.731429 + 1.26687i −0.0391525 + 0.0678141i −0.884938 0.465710i \(-0.845799\pi\)
0.845785 + 0.533524i \(0.179132\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.65910 + 8.06980i 0.248331 + 0.430122i
\(353\) 7.16637 + 12.4125i 0.381428 + 0.660652i 0.991267 0.131873i \(-0.0420992\pi\)
−0.609839 + 0.792525i \(0.708766\pi\)
\(354\) 0 0
\(355\) 0.373455 0.646844i 0.0198210 0.0343309i
\(356\) −5.57310 9.65289i −0.295374 0.511602i
\(357\) 0 0
\(358\) −3.75150 + 6.49778i −0.198273 + 0.343418i
\(359\) −10.4684 18.1318i −0.552500 0.956958i −0.998093 0.0617224i \(-0.980341\pi\)
0.445593 0.895235i \(-0.352993\pi\)
\(360\) 0 0
\(361\) 4.29426 7.43788i 0.226014 0.391467i
\(362\) −15.1557 −0.796566
\(363\) 0 0
\(364\) 0 0
\(365\) 1.38073 + 2.39149i 0.0722707 + 0.125176i
\(366\) 0 0
\(367\) 6.02869 + 10.4420i 0.314695 + 0.545067i 0.979373 0.202063i \(-0.0647645\pi\)
−0.664678 + 0.747130i \(0.731431\pi\)
\(368\) −0.187319 + 0.324446i −0.00976466 + 0.0169129i
\(369\) 0 0
\(370\) −10.9409 −0.568789
\(371\) 0 0
\(372\) 0 0
\(373\) 0.390530 0.676417i 0.0202209 0.0350235i −0.855738 0.517410i \(-0.826896\pi\)
0.875959 + 0.482386i \(0.160230\pi\)
\(374\) 0.680045 0.0351643
\(375\) 0 0
\(376\) 26.5449 1.36895
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) −5.33275 −0.273564
\(381\) 0 0
\(382\) −11.3523 −0.580837
\(383\) 3.86618 6.69642i 0.197553 0.342171i −0.750182 0.661232i \(-0.770034\pi\)
0.947734 + 0.319061i \(0.103367\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.561185 −0.0285636
\(387\) 0 0
\(388\) −1.16473 + 2.01736i −0.0591300 + 0.102416i
\(389\) 2.69981 + 4.67620i 0.136886 + 0.237093i 0.926316 0.376747i \(-0.122957\pi\)
−0.789431 + 0.613840i \(0.789624\pi\)
\(390\) 0 0
\(391\) −2.09240 3.62414i −0.105817 0.183280i
\(392\) 0 0
\(393\) 0 0
\(394\) −10.0651 −0.507073
\(395\) −1.61927 + 2.80466i −0.0814743 + 0.141118i
\(396\) 0 0
\(397\) 14.6172 + 25.3178i 0.733617 + 1.27066i 0.955328 + 0.295549i \(0.0955026\pi\)
−0.221711 + 0.975112i \(0.571164\pi\)
\(398\) 1.59967 2.77071i 0.0801842 0.138883i
\(399\) 0 0
\(400\) −0.0667040 0.115535i −0.00333520 0.00577674i
\(401\) −13.6989 + 23.7272i −0.684092 + 1.18488i 0.289629 + 0.957139i \(0.406468\pi\)
−0.973721 + 0.227743i \(0.926865\pi\)
\(402\) 0 0
\(403\) 15.5581 + 26.9474i 0.775003 + 1.34235i
\(404\) 1.04829 + 1.81568i 0.0521542 + 0.0903337i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.63088 13.2171i 0.378249 0.655146i
\(408\) 0 0
\(409\) −9.02498 −0.446256 −0.223128 0.974789i \(-0.571627\pi\)
−0.223128 + 0.974789i \(0.571627\pi\)
\(410\) 4.04189 0.199615
\(411\) 0 0
\(412\) −2.23143 + 3.86495i −0.109935 + 0.190412i
\(413\) 0 0
\(414\) 0 0
\(415\) 10.1382 + 17.5598i 0.497662 + 0.861977i
\(416\) 9.49912 + 16.4530i 0.465733 + 0.806673i
\(417\) 0 0
\(418\) −2.34477 + 4.06126i −0.114686 + 0.198643i
\(419\) 0.0876485 + 0.151812i 0.00428191 + 0.00741649i 0.868158 0.496287i \(-0.165304\pi\)
−0.863877 + 0.503704i \(0.831970\pi\)
\(420\) 0 0
\(421\) 12.3525 21.3952i 0.602025 1.04274i −0.390490 0.920607i \(-0.627694\pi\)
0.992514 0.122130i \(-0.0389724\pi\)
\(422\) −2.56031 4.43458i −0.124634 0.215872i
\(423\) 0 0
\(424\) 0.814330 1.41046i 0.0395474 0.0684980i
\(425\) 1.49020 0.0722853
\(426\) 0 0
\(427\) 0 0
\(428\) −4.37211 7.57272i −0.211334 0.366041i
\(429\) 0 0
\(430\) −2.61334 4.52644i −0.126026 0.218284i
\(431\) −14.6596 + 25.3911i −0.706126 + 1.22305i 0.260157 + 0.965566i \(0.416226\pi\)
−0.966283 + 0.257481i \(0.917108\pi\)
\(432\) 0 0
\(433\) 19.6554 0.944578 0.472289 0.881444i \(-0.343428\pi\)
0.472289 + 0.881444i \(0.343428\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.247626 0.428901i 0.0118591 0.0205406i
\(437\) 28.8580 1.38047
\(438\) 0 0
\(439\) −21.9299 −1.04666 −0.523330 0.852130i \(-0.675310\pi\)
−0.523330 + 0.852130i \(0.675310\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) 18.7101 0.888942 0.444471 0.895793i \(-0.353392\pi\)
0.444471 + 0.895793i \(0.353392\pi\)
\(444\) 0 0
\(445\) 12.2422 0.580334
\(446\) −3.11468 + 5.39479i −0.147485 + 0.255451i
\(447\) 0 0
\(448\) 0 0
\(449\) −6.68004 −0.315251 −0.157625 0.987499i \(-0.550384\pi\)
−0.157625 + 0.987499i \(0.550384\pi\)
\(450\) 0 0
\(451\) −2.81908 + 4.88279i −0.132745 + 0.229921i
\(452\) −8.81345 15.2653i −0.414550 0.718022i
\(453\) 0 0
\(454\) −5.25150 9.09586i −0.246465 0.426890i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.4287 −0.908837 −0.454418 0.890788i \(-0.650153\pi\)
−0.454418 + 0.890788i \(0.650153\pi\)
\(458\) 7.71776 13.3676i 0.360627 0.624625i
\(459\) 0 0
\(460\) 7.39053 + 12.8008i 0.344585 + 0.596839i
\(461\) −0.482926 + 0.836452i −0.0224921 + 0.0389575i −0.877052 0.480395i \(-0.840493\pi\)
0.854560 + 0.519352i \(0.173827\pi\)
\(462\) 0 0
\(463\) 0.222811 + 0.385920i 0.0103549 + 0.0179352i 0.871156 0.491006i \(-0.163371\pi\)
−0.860802 + 0.508941i \(0.830037\pi\)
\(464\) −0.131292 + 0.227405i −0.00609509 + 0.0105570i
\(465\) 0 0
\(466\) 7.14677 + 12.3786i 0.331068 + 0.573426i
\(467\) −17.1074 29.6309i −0.791637 1.37115i −0.924953 0.380081i \(-0.875896\pi\)
0.133317 0.991074i \(-0.457437\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −5.54189 + 9.59883i −0.255628 + 0.442761i
\(471\) 0 0
\(472\) −29.5012 −1.35790
\(473\) 7.29086 0.335234
\(474\) 0 0
\(475\) −5.13816 + 8.89955i −0.235755 + 0.408339i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.63903 11.4991i −0.303662 0.525959i
\(479\) −10.8965 18.8732i −0.497872 0.862339i 0.502125 0.864795i \(-0.332552\pi\)
−0.999997 + 0.00245553i \(0.999218\pi\)
\(480\) 0 0
\(481\) 15.5581 26.9474i 0.709388 1.22870i
\(482\) 6.87598 + 11.9095i 0.313192 + 0.542465i
\(483\) 0 0
\(484\) −5.07145 + 8.78401i −0.230521 + 0.399273i
\(485\) −1.27925 2.21572i −0.0580877 0.100611i
\(486\) 0 0
\(487\) −9.69640 + 16.7947i −0.439386 + 0.761039i −0.997642 0.0686297i \(-0.978137\pi\)
0.558256 + 0.829669i \(0.311471\pi\)
\(488\) −21.6732 −0.981101
\(489\) 0 0
\(490\) 0 0
\(491\) 13.0783 + 22.6523i 0.590216 + 1.02228i 0.994203 + 0.107519i \(0.0342908\pi\)
−0.403987 + 0.914765i \(0.632376\pi\)
\(492\) 0 0
\(493\) −1.46657 2.54017i −0.0660509 0.114403i
\(494\) −4.78059 + 8.28023i −0.215089 + 0.372545i
\(495\) 0 0
\(496\) −0.386821 −0.0173688
\(497\) 0 0
\(498\) 0 0
\(499\) 7.15064 12.3853i 0.320107 0.554441i −0.660403 0.750911i \(-0.729615\pi\)
0.980510 + 0.196470i \(0.0629479\pi\)
\(500\) −13.5270 −0.604947
\(501\) 0 0
\(502\) −16.7656 −0.748284
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) 12.9982 0.577842
\(507\) 0 0
\(508\) 25.4801 1.13050
\(509\) −12.8045 + 22.1781i −0.567551 + 0.983027i 0.429257 + 0.903183i \(0.358776\pi\)
−0.996807 + 0.0798442i \(0.974558\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.473897 −0.0209435
\(513\) 0 0
\(514\) 11.6878 20.2438i 0.515526 0.892917i
\(515\) −2.45084 4.24497i −0.107997 0.187056i
\(516\) 0 0
\(517\) −7.73055 13.3897i −0.339989 0.588879i
\(518\) 0 0
\(519\) 0 0
\(520\) −12.8817 −0.564902
\(521\) −10.6061 + 18.3702i −0.464660 + 0.804815i −0.999186 0.0403370i \(-0.987157\pi\)
0.534526 + 0.845152i \(0.320490\pi\)
\(522\) 0 0
\(523\) −10.4029 18.0183i −0.454885 0.787884i 0.543796 0.839217i \(-0.316986\pi\)
−0.998682 + 0.0513330i \(0.983653\pi\)
\(524\) 4.39470 7.61185i 0.191984 0.332525i
\(525\) 0 0
\(526\) −0.322786 0.559082i −0.0140741 0.0243771i
\(527\) 2.16044 3.74200i 0.0941104 0.163004i
\(528\) 0 0
\(529\) −28.4937 49.3525i −1.23885 2.14576i
\(530\) 0.340022 + 0.588936i 0.0147696 + 0.0255817i
\(531\) 0 0
\(532\) 0 0
\(533\) −5.74763 + 9.95518i −0.248957 + 0.431207i
\(534\) 0 0
\(535\) 9.60401 0.415217
\(536\) −1.69190 −0.0730791
\(537\) 0 0
\(538\) −9.16772 + 15.8790i −0.395248 + 0.684590i
\(539\) 0 0
\(540\) 0 0
\(541\) −13.3648 23.1486i −0.574599 0.995235i −0.996085 0.0884001i \(-0.971825\pi\)
0.421486 0.906835i \(-0.361509\pi\)
\(542\) −3.05943 5.29909i −0.131414 0.227615i
\(543\) 0 0
\(544\) 1.31908 2.28471i 0.0565550 0.0979561i
\(545\) 0.271974 + 0.471073i 0.0116501 + 0.0201786i
\(546\) 0 0
\(547\) −18.3812 + 31.8372i −0.785923 + 1.36126i 0.142523 + 0.989792i \(0.454479\pi\)
−0.928446 + 0.371467i \(0.878855\pi\)
\(548\) −1.57563 2.72907i −0.0673074 0.116580i
\(549\) 0 0
\(550\) −2.31433 + 4.00854i −0.0986834 + 0.170925i
\(551\) 20.2267 0.861686
\(552\) 0 0
\(553\) 0 0
\(554\) −7.85844 13.6112i −0.333873 0.578285i
\(555\) 0 0
\(556\) −3.76187 6.51575i −0.159539 0.276329i
\(557\) 16.1694 28.0062i 0.685118 1.18666i −0.288282 0.957546i \(-0.593084\pi\)
0.973400 0.229114i \(-0.0735827\pi\)
\(558\) 0 0
\(559\) 14.8648 0.628716
\(560\) 0 0
\(561\) 0 0
\(562\) 9.80974 16.9910i 0.413799 0.716721i
\(563\) 17.7419 0.747730 0.373865 0.927483i \(-0.378032\pi\)
0.373865 + 0.927483i \(0.378032\pi\)
\(564\) 0 0
\(565\) 19.3601 0.814485
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) 26.6013 1.11519 0.557593 0.830115i \(-0.311725\pi\)
0.557593 + 0.830115i \(0.311725\pi\)
\(570\) 0 0
\(571\) −10.0172 −0.419208 −0.209604 0.977786i \(-0.567218\pi\)
−0.209604 + 0.977786i \(0.567218\pi\)
\(572\) 3.41565 5.91608i 0.142815 0.247364i
\(573\) 0 0
\(574\) 0 0
\(575\) 28.4834 1.18784
\(576\) 0 0
\(577\) 16.4572 28.5048i 0.685124 1.18667i −0.288274 0.957548i \(-0.593082\pi\)
0.973398 0.229121i \(-0.0735852\pi\)
\(578\) 7.37851 + 12.7800i 0.306905 + 0.531576i
\(579\) 0 0
\(580\) 5.18004 + 8.97210i 0.215090 + 0.372546i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.948615 −0.0392876
\(584\) 2.90791 5.03665i 0.120330 0.208418i
\(585\) 0 0
\(586\) 5.75624 + 9.97011i 0.237788 + 0.411861i
\(587\) −7.53643 + 13.0535i −0.311062 + 0.538774i −0.978592 0.205808i \(-0.934018\pi\)
0.667531 + 0.744582i \(0.267351\pi\)
\(588\) 0 0
\(589\) 14.8983 + 25.8046i 0.613873 + 1.06326i
\(590\) 6.15910 10.6679i 0.253566 0.439189i
\(591\) 0 0
\(592\) 0.193411 + 0.334997i 0.00794913 + 0.0137683i
\(593\) 20.5005 + 35.5079i 0.841853 + 1.45813i 0.888326 + 0.459213i \(0.151869\pi\)
−0.0464729 + 0.998920i \(0.514798\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.264396 + 0.457947i −0.0108301 + 0.0187582i
\(597\) 0 0
\(598\) 26.5012 1.08372
\(599\) −6.07367 −0.248164 −0.124082 0.992272i \(-0.539599\pi\)
−0.124082 + 0.992272i \(0.539599\pi\)
\(600\) 0 0
\(601\) 7.06758 12.2414i 0.288293 0.499338i −0.685110 0.728440i \(-0.740246\pi\)
0.973402 + 0.229102i \(0.0735791\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.51532 2.62461i −0.0616575 0.106794i
\(605\) −5.57011 9.64771i −0.226457 0.392235i
\(606\) 0 0
\(607\) −23.0449 + 39.9149i −0.935363 + 1.62010i −0.161377 + 0.986893i \(0.551594\pi\)
−0.773986 + 0.633203i \(0.781740\pi\)
\(608\) 9.09627 + 15.7552i 0.368902 + 0.638958i
\(609\) 0 0
\(610\) 4.52481 7.83721i 0.183204 0.317319i
\(611\) −15.7613 27.2994i −0.637634 1.10441i
\(612\) 0 0
\(613\) 13.2469 22.9443i 0.535038 0.926712i −0.464124 0.885770i \(-0.653631\pi\)
0.999162 0.0409421i \(-0.0130359\pi\)
\(614\) 5.54933 0.223953
\(615\) 0 0
\(616\) 0 0
\(617\) −1.12495 1.94847i −0.0452889 0.0784426i 0.842492 0.538708i \(-0.181087\pi\)
−0.887781 + 0.460266i \(0.847754\pi\)
\(618\) 0 0
\(619\) −3.09539 5.36137i −0.124414 0.215492i 0.797090 0.603861i \(-0.206372\pi\)
−0.921504 + 0.388369i \(0.873038\pi\)
\(620\) −7.63088 + 13.2171i −0.306464 + 0.530811i
\(621\) 0 0
\(622\) 8.37557 0.335830
\(623\) 0 0
\(624\) 0 0
\(625\) −0.533433 + 0.923933i −0.0213373 + 0.0369573i
\(626\) −15.5024 −0.619600
\(627\) 0 0
\(628\) −12.4305 −0.496030
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) 6.82058 0.271308
\(633\) 0 0
\(634\) −7.10277 −0.282087
\(635\) −13.9927 + 24.2361i −0.555284 + 0.961781i
\(636\) 0 0
\(637\) 0 0
\(638\) 9.11051 0.360689
\(639\) 0 0
\(640\) −4.60947 + 7.98384i −0.182205 + 0.315589i
\(641\) 2.44444 + 4.23389i 0.0965496 + 0.167229i 0.910254 0.414050i \(-0.135886\pi\)
−0.813705 + 0.581278i \(0.802553\pi\)
\(642\) 0 0
\(643\) 20.1839 + 34.9596i 0.795976 + 1.37867i 0.922218 + 0.386671i \(0.126375\pi\)
−0.126242 + 0.992000i \(0.540291\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.32770 0.0522375
\(647\) −1.14038 + 1.97519i −0.0448329 + 0.0776528i −0.887571 0.460671i \(-0.847609\pi\)
0.842738 + 0.538324i \(0.180942\pi\)
\(648\) 0 0
\(649\) 8.59152 + 14.8809i 0.337247 + 0.584128i
\(650\) −4.71853 + 8.17273i −0.185076 + 0.320561i
\(651\) 0 0
\(652\) −1.59240 2.75811i −0.0623631 0.108016i
\(653\) 11.7396 20.3336i 0.459407 0.795717i −0.539522 0.841971i \(-0.681395\pi\)
0.998930 + 0.0462542i \(0.0147284\pi\)
\(654\) 0 0
\(655\) 4.82682 + 8.36030i 0.188599 + 0.326664i
\(656\) −0.0714517 0.123758i −0.00278972 0.00483194i
\(657\) 0 0
\(658\) 0 0
\(659\) −23.9812 + 41.5366i −0.934174 + 1.61804i −0.158073 + 0.987427i \(0.550528\pi\)
−0.776101 + 0.630609i \(0.782805\pi\)
\(660\) 0 0
\(661\) 29.3090 1.13999 0.569995 0.821648i \(-0.306945\pi\)
0.569995 + 0.821648i \(0.306945\pi\)
\(662\) 20.2695 0.787797
\(663\) 0 0
\(664\) 21.3516 36.9821i 0.828604 1.43518i
\(665\) 0 0
\(666\) 0 0
\(667\) −28.0317 48.5523i −1.08539 1.87995i
\(668\) 14.2191 + 24.6282i 0.550154 + 0.952894i
\(669\) 0 0
\(670\) 0.353226 0.611806i 0.0136463 0.0236361i
\(671\) 6.31180 + 10.9324i 0.243664 + 0.422039i
\(672\) 0 0
\(673\) −13.1591 + 22.7922i −0.507246 + 0.878576i 0.492719 + 0.870189i \(0.336003\pi\)
−0.999965 + 0.00838731i \(0.997330\pi\)
\(674\) −12.7613 22.1032i −0.491547 0.851384i
\(675\) 0 0
\(676\) −1.00950 + 1.74850i −0.0388267 + 0.0672499i
\(677\) −35.8907 −1.37939 −0.689697 0.724098i \(-0.742256\pi\)
−0.689697 + 0.724098i \(0.742256\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.894400 + 1.54915i 0.0342987 + 0.0594070i
\(681\) 0 0
\(682\) 6.71048 + 11.6229i 0.256958 + 0.445064i
\(683\) 17.5321 30.3665i 0.670847 1.16194i −0.306818 0.951768i \(-0.599264\pi\)
0.977664 0.210172i \(-0.0674025\pi\)
\(684\) 0 0
\(685\) 3.46110 0.132242
\(686\) 0 0
\(687\) 0 0
\(688\) −0.0923963 + 0.160035i −0.00352257 + 0.00610128i
\(689\) −1.93407 −0.0736821
\(690\) 0 0
\(691\) 2.06687 0.0786273 0.0393136 0.999227i \(-0.487483\pi\)
0.0393136 + 0.999227i \(0.487483\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) 8.26352 0.313453
\(696\) 0 0
\(697\) 1.59627 0.0604629
\(698\) −0.643208 + 1.11407i −0.0243458 + 0.0421681i
\(699\) 0 0
\(700\) 0 0
\(701\) 7.36009 0.277987 0.138993 0.990293i \(-0.455613\pi\)
0.138993 + 0.990293i \(0.455613\pi\)
\(702\) 0 0
\(703\) 14.8983 25.8046i 0.561899 0.973237i
\(704\) 4.16637 + 7.21637i 0.157026 + 0.271977i
\(705\) 0 0
\(706\) 6.30200 + 10.9154i 0.237179 + 0.410806i
\(707\) 0 0
\(708\) 0 0
\(709\) 9.10876 0.342086 0.171043 0.985264i \(-0.445286\pi\)
0.171043 + 0.985264i \(0.445286\pi\)
\(710\) 0.328411 0.568825i 0.0123251 0.0213476i
\(711\) 0 0
\(712\) −12.8914 22.3286i −0.483126 0.836799i
\(713\) 41.2943 71.5239i 1.54648 2.67859i
\(714\) 0 0
\(715\) 3.75150 + 6.49778i 0.140298 + 0.243003i
\(716\) 5.23308 9.06396i 0.195569 0.338736i
\(717\) 0 0
\(718\) −9.20574 15.9448i −0.343555 0.595055i
\(719\) −12.9768 22.4765i −0.483954 0.838233i 0.515876 0.856663i \(-0.327467\pi\)
−0.999830 + 0.0184300i \(0.994133\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.77631 6.54076i 0.140540 0.243422i
\(723\) 0 0
\(724\) 21.1411 0.785705
\(725\) 19.9641 0.741448
\(726\) 0 0
\(727\) 5.08007 8.79894i 0.188409 0.326335i −0.756311 0.654213i \(-0.773000\pi\)
0.944720 + 0.327878i \(0.106333\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.21419 + 2.10304i 0.0449393 + 0.0778372i
\(731\) −1.03209 1.78763i −0.0381732 0.0661179i
\(732\) 0 0
\(733\) −20.3307 + 35.2138i −0.750931 + 1.30065i 0.196441 + 0.980516i \(0.437062\pi\)
−0.947372 + 0.320135i \(0.896272\pi\)
\(734\) 5.30154 + 9.18253i 0.195683 + 0.338933i
\(735\) 0 0
\(736\) 25.2126 43.6695i 0.929349 1.60968i
\(737\) 0.492726 + 0.853427i 0.0181498 + 0.0314364i
\(738\) 0 0
\(739\) 12.6809 21.9640i 0.466475 0.807959i −0.532791 0.846247i \(-0.678857\pi\)
0.999267 + 0.0382877i \(0.0121903\pi\)
\(740\) 15.2618 0.561034
\(741\) 0 0
\(742\) 0 0
\(743\) −11.2221 19.4372i −0.411699 0.713083i 0.583377 0.812202i \(-0.301731\pi\)
−0.995076 + 0.0991184i \(0.968398\pi\)
\(744\) 0 0
\(745\) −0.290393 0.502975i −0.0106392 0.0184276i
\(746\) 0.343426 0.594831i 0.0125737 0.0217783i
\(747\) 0 0
\(748\) −0.948615 −0.0346848
\(749\) 0 0
\(750\) 0 0
\(751\) −12.1086 + 20.9727i −0.441849 + 0.765305i −0.997827 0.0658924i \(-0.979011\pi\)
0.555978 + 0.831197i \(0.312344\pi\)
\(752\) 0.391874 0.0142902
\(753\) 0 0
\(754\) 18.5748 0.676454
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) −6.08883 −0.221156
\(759\) 0 0
\(760\) −12.3354 −0.447453
\(761\) −9.13610 + 15.8242i −0.331183 + 0.573626i −0.982744 0.184970i \(-0.940781\pi\)
0.651561 + 0.758596i \(0.274114\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 15.8357 0.572917
\(765\) 0 0
\(766\) 3.39986 5.88874i 0.122842 0.212769i
\(767\) 17.5167 + 30.3398i 0.632490 + 1.09550i
\(768\) 0 0
\(769\) −9.26470 16.0469i −0.334094 0.578667i 0.649217 0.760604i \(-0.275097\pi\)
−0.983310 + 0.181936i \(0.941764\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.782814 0.0281741
\(773\) −1.48040 + 2.56413i −0.0532463 + 0.0922253i −0.891420 0.453178i \(-0.850290\pi\)
0.838174 + 0.545403i \(0.183624\pi\)
\(774\) 0 0
\(775\) 14.7049 + 25.4696i 0.528214 + 0.914894i
\(776\) −2.69418 + 4.66646i −0.0967155 + 0.167516i
\(777\) 0 0
\(778\) 2.37417 + 4.11218i 0.0851181 + 0.147429i
\(779\) −5.50387 + 9.53298i −0.197197 + 0.341555i
\(780\) 0 0
\(781\) 0.458111 + 0.793471i 0.0163925 + 0.0283926i
\(782\) −1.84002 3.18701i −0.0657991 0.113967i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.82635 11.8236i 0.243643 0.422002i
\(786\) 0 0
\(787\) −33.4020 −1.19065 −0.595326 0.803484i \(-0.702977\pi\)