Properties

Label 1323.2.h.c.226.3
Level $1323$
Weight $2$
Character 1323.226
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 226.3
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.c.802.3

$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 0.976423 0.215867i \(-0.0692579\pi\)
−0.675158 + 0.737673i \(0.735925\pi\)
\(6\) 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 −0.714137 0.700006i \(-0.753181\pi\)
0.963291 + 0.268458i \(0.0865140\pi\)
\(12\) 0 0
\(13\) 1.68479 2.91815i 0.467277 0.809348i −0.532024 0.846729i \(-0.678568\pi\)
0.999301 + 0.0373813i \(0.0119016\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0418891 −0.0104723
\(17\) 0.233956 + 0.405223i 0.0567426 + 0.0982810i 0.893001 0.450054i \(-0.148595\pi\)
−0.836259 + 0.548335i \(0.815262\pi\)
\(18\) 0 0
\(19\) 1.61334 2.79439i 0.370126 0.641077i −0.619459 0.785029i \(-0.712648\pi\)
0.989585 + 0.143953i \(0.0459813\pi\)
\(20\) −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 0.779152 + 0.626835i \(0.215650\pi\)
0.153279 + 0.988183i \(0.451017\pi\)
\(24\) 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 0.995239 + 0.0974595i \(0.0310717\pi\)
−0.413217 + 0.910632i \(0.635595\pi\)
\(30\) 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 0.184263 + 0.982877i \(0.441010\pi\)
−0.943328 + 0.331862i \(0.892323\pi\)
\(38\) 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 −0.701536 0.712634i \(-0.747502\pi\)
0.967927 + 0.251231i \(0.0808353\pi\)
\(42\) 0 0
\(43\) 2.20574 + 3.82045i 0.336372 + 0.582613i 0.983747 0.179558i \(-0.0574668\pi\)
−0.647376 + 0.762171i \(0.724133\pi\)
\(44\) −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 0.845642 0.533751i \(-0.179218\pi\)
−0.885063 + 0.465472i \(0.845885\pi\)
\(54\) 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 0.799800 0.600266i \(-0.204939\pi\)
−0.919746 + 0.392514i \(0.871605\pi\)
\(74\) −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 −0.901187 0.433431i \(-0.857303\pi\)
0.0752309 0.997166i \(-0.476031\pi\)
\(84\) 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 −0.518195 0.855263i \(-0.673396\pi\)
0.999777 + 0.0211385i \(0.00672911\pi\)
\(90\) 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 0.910195 0.414181i \(-0.135932\pi\)
−0.813788 + 0.581161i \(0.802598\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95336 + 3.38332i −0.195336 + 0.338332i
\(101\) −0.854570 + 1.48016i −0.0850329 + 0.147281i −0.905405 0.424548i \(-0.860433\pi\)
0.820372 + 0.571830i \(0.193766\pi\)
\(102\) 0 0
\(103\) 1.81908 + 3.15074i 0.179239 + 0.310451i 0.941620 0.336677i \(-0.109303\pi\)
−0.762381 + 0.647128i \(0.775970\pi\)
\(104\) −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 −0.640712 0.767781i \(-0.721361\pi\)
0.985274 + 0.170982i \(0.0546941\pi\)
\(108\) 0 0
\(109\) −0.201867 0.349643i −0.0193353 0.0334898i 0.856196 0.516651i \(-0.172822\pi\)
−0.875531 + 0.483162i \(0.839488\pi\)
\(110\) 1.95811 0.186699
\(111\) 0 0
\(112\) 0 0
\(113\) 7.18479 12.4444i 0.675888 1.17067i −0.300320 0.953839i \(-0.597093\pi\)
0.976208 0.216835i \(-0.0695732\pi\)
\(114\) 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 0.666000 0.745952i \(-0.268005\pi\)
−0.979013 + 0.203797i \(0.934672\pi\)
\(132\) 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 −0.805925 0.592017i \(-0.798332\pi\)
0.915665 + 0.401943i \(0.131665\pi\)
\(138\) 0 0
\(139\) 3.06670 5.31169i 0.260114 0.450531i −0.706158 0.708055i \(-0.749573\pi\)
0.966272 + 0.257523i \(0.0829064\pi\)
\(140\) 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 0.874719 0.484630i \(-0.161046\pi\)
−0.857062 + 0.515214i \(0.827712\pi\)
\(150\) 0 0
\(151\) 1.23530 2.13960i 0.100527 0.174118i −0.811375 0.584526i \(-0.801280\pi\)
0.911902 + 0.410408i \(0.134614\pi\)
\(152\) −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 −0.810698 0.585464i \(-0.800912\pi\)
0.912376 + 0.409353i \(0.134246\pi\)
\(164\) −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 −0.0656422 + 0.997843i \(0.520910\pi\)
−0.831337 + 0.555769i \(0.812424\pi\)
\(168\) 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 0.661391 0.750041i \(-0.269966\pi\)
−0.980250 + 0.197761i \(0.936633\pi\)
\(180\) 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 0.923270 0.384151i \(-0.125506\pi\)
−0.794319 + 0.607500i \(0.792172\pi\)
\(200\) −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 −0.948668 0.316273i \(-0.897569\pi\)
0.748234 + 0.663435i \(0.230902\pi\)
\(212\) 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 0.722722 0.691139i \(-0.242891\pi\)
−0.959905 + 0.280327i \(0.909557\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.31820 10.9434i 0.420280 0.727947i
\(227\) −5.97178 + 10.3434i −0.396361 + 0.686517i −0.993274 0.115789i \(-0.963060\pi\)
0.596913 + 0.802306i \(0.296394\pi\)
\(228\) 0 0
\(229\) 8.77631 + 15.2010i 0.579955 + 1.00451i 0.995484 + 0.0949315i \(0.0302632\pi\)
−0.415529 + 0.909580i \(0.636403\pi\)
\(230\) −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 −0.466865 0.884328i \(-0.654617\pi\)
0.999284 0.0378470i \(-0.0120499\pi\)
\(234\) 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 −0.999910 0.0134062i \(-0.995733\pi\)
0.511565 + 0.859244i \(0.329066\pi\)
\(240\) 0 0
\(241\) 7.81908 13.5430i 0.503671 0.872384i −0.496320 0.868140i \(-0.665316\pi\)
0.999991 0.00424420i \(-0.00135097\pi\)
\(242\) 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 0.898776 + 0.438409i \(0.144458\pi\)
−0.0697146 + 0.997567i \(0.522209\pi\)
\(258\) 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 −0.877120 0.480270i \(-0.840539\pi\)
0.854487 + 0.519473i \(0.173872\pi\)
\(264\) 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 −0.986381 0.164478i \(-0.947406\pi\)
0.350749 0.936470i \(-0.385927\pi\)
\(270\) 0 0
\(271\) −3.47906 + 6.02590i −0.211338 + 0.366047i −0.952133 0.305683i \(-0.901115\pi\)
0.740796 + 0.671730i \(0.234449\pi\)
\(272\) −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 0.462138 + 0.886808i \(0.347083\pi\)
−0.999067 + 0.0431811i \(0.986251\pi\)
\(278\) 2.69681 4.67102i 0.161744 0.280149i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1552 + 19.3214i 0.665465 + 1.15262i 0.979159 + 0.203095i \(0.0651001\pi\)
−0.313694 + 0.949524i \(0.601567\pi\)
\(282\) 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 −0.608998 0.793171i \(-0.708428\pi\)
0.991406 + 0.130822i \(0.0417618\pi\)
\(294\) 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 0.135161 + 0.990824i \(0.456845\pi\)
−0.925659 + 0.378359i \(0.876489\pi\)
\(338\) 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 0.845785 0.533524i \(-0.179132\pi\)
−0.884938 + 0.465710i \(0.845799\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.65910 8.06980i 0.248331 0.430122i
\(353\) 7.16637 12.4125i 0.381428 0.660652i −0.609839 0.792525i \(-0.708766\pi\)
0.991267 + 0.131873i \(0.0420992\pi\)
\(354\) 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 0.445593 + 0.895235i \(0.352993\pi\)
−0.998093 + 0.0617224i \(0.980341\pi\)
\(360\) 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 −0.664678 0.747130i \(-0.731431\pi\)
0.979373 + 0.202063i \(0.0647645\pi\)
\(368\) −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 0.875959 0.482386i \(-0.160230\pi\)
−0.855738 + 0.517410i \(0.826896\pi\)
\(374\) 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 0.947734 0.319061i \(-0.103367\pi\)
−0.750182 + 0.661232i \(0.770034\pi\)
\(384\) 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 −0.789431 0.613840i \(-0.789624\pi\)
0.926316 + 0.376747i \(0.122957\pi\)
\(390\) 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 −0.221711 0.975112i \(-0.571164\pi\)
0.955328 0.295549i \(-0.0955026\pi\)
\(398\) 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 −0.973721 0.227743i \(-0.926865\pi\)
0.289629 0.957139i \(-0.406468\pi\)
\(402\) 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 −0.863877 0.503704i \(-0.831970\pi\)
0.868158 + 0.496287i \(0.165304\pi\)
\(420\) 0 0
\(421\) 12.3525 + 21.3952i 0.602025 + 1.04274i 0.992514 + 0.122130i \(0.0389724\pi\)
−0.390490 + 0.920607i \(0.627694\pi\)
\(422\) −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 −0.966283 0.257481i \(-0.917108\pi\)
0.260157 0.965566i \(-0.416226\pi\)
\(432\) 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 0.854560 0.519352i \(-0.173827\pi\)
−0.877052 + 0.480395i \(0.840493\pi\)
\(462\) 0 0
\(463\) 0.222811 0.385920i 0.0103549 0.0179352i −0.860802 0.508941i \(-0.830037\pi\)
0.871156 + 0.491006i \(0.163371\pi\)
\(464\) −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 0.133317 + 0.991074i \(0.457437\pi\)
−0.924953 + 0.380081i \(0.875896\pi\)
\(468\) 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 −0.999997 0.00245553i \(-0.999218\pi\)
0.502125 + 0.864795i \(0.332552\pi\)
\(480\) 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 0.558256 0.829669i \(-0.311471\pi\)
−0.997642 + 0.0686297i \(0.978137\pi\)
\(488\) −21.6732 −0.981101
\(489\) 0 0
\(490\) 0 0
\(491\) 13.0783 22.6523i 0.590216 1.02228i −0.403987 0.914765i \(-0.632376\pi\)
0.994203 0.107519i \(-0.0342908\pi\)
\(492\) 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 0.980510 0.196470i \(-0.0629479\pi\)
−0.660403 + 0.750911i \(0.729615\pi\)
\(500\) −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 −0.996807 0.0798442i \(-0.974558\pi\)
0.429257 0.903183i \(-0.358776\pi\)
\(510\) 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 0.534526 0.845152i \(-0.320490\pi\)
−0.999186 + 0.0403370i \(0.987157\pi\)
\(522\) 0 0
\(523\) −10.4029 + 18.0183i −0.454885 + 0.787884i −0.998682 0.0513330i \(-0.983653\pi\)
0.543796 + 0.839217i \(0.316986\pi\)
\(524\) 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 0.421486 + 0.906835i \(0.361509\pi\)
−0.996085 + 0.0884001i \(0.971825\pi\)
\(542\) −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 −0.928446 0.371467i \(-0.878855\pi\)
0.142523 0.989792i \(-0.454479\pi\)
\(548\) −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 0.973400 + 0.229114i \(0.0735827\pi\)
−0.288282 + 0.957546i \(0.593084\pi\)
\(558\) 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 0.973398 + 0.229121i \(0.0735852\pi\)
−0.288274 + 0.957548i \(0.593082\pi\)
\(578\) 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 0.667531 0.744582i \(-0.267351\pi\)
−0.978592 + 0.205808i \(0.934018\pi\)
\(588\) 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 −0.0464729 0.998920i \(-0.514798\pi\)
0.888326 0.459213i \(-0.151869\pi\)
\(594\) 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 0.973402 0.229102i \(-0.0735791\pi\)
−0.685110 + 0.728440i \(0.740246\pi\)
\(602\) 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 −0.773986 0.633203i \(-0.781740\pi\)
−0.161377 0.986893i \(-0.551594\pi\)
\(608\) 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 0.999162 + 0.0409421i \(0.0130359\pi\)
−0.464124 + 0.885770i \(0.653631\pi\)
\(614\) 5.54933 0.223953
\(615\) 0 0
\(616\) 0 0
\(617\) −1.12495 + 1.94847i −0.0452889 + 0.0784426i −0.887781 0.460266i \(-0.847754\pi\)
0.842492 + 0.538708i \(0.181087\pi\)
\(618\) 0 0
\(619\) −3.09539 + 5.36137i −0.124414 + 0.215492i −0.921504 0.388369i \(-0.873038\pi\)
0.797090 + 0.603861i \(0.206372\pi\)
\(620\) −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 −0.813705 0.581278i \(-0.802553\pi\)
0.910254 + 0.414050i \(0.135886\pi\)
\(642\) 0 0
\(643\) 20.1839 34.9596i 0.795976 1.37867i −0.126242 0.992000i \(-0.540291\pi\)
0.922218 0.386671i \(-0.126375\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.32770 0.0522375
\(647\) −1.14038 1.97519i −0.0448329 0.0776528i 0.842738 0.538324i \(-0.180942\pi\)
−0.887571 + 0.460671i \(0.847609\pi\)
\(648\) 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 0.998930 0.0462542i \(-0.0147284\pi\)
−0.539522 + 0.841971i \(0.681395\pi\)
\(654\) 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 −0.776101 0.630609i \(-0.782805\pi\)
−0.158073 0.987427i \(-0.550528\pi\)
\(660\) 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 −0.999965 0.00838731i \(-0.997330\pi\)
0.492719 0.870189i \(-0.336003\pi\)
\(674\) −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 0.977664 + 0.210172i \(0.0674025\pi\)
−0.306818 + 0.951768i \(0.599264\pi\)
\(684\) 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 −0.999830 0.0184300i \(-0.994133\pi\)
0.515876 + 0.856663i \(0.327467\pi\)
\(720\) 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 0.944720 0.327878i \(-0.106333\pi\)
−0.756311 + 0.654213i \(0.773000\pi\)
\(728\) 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 −0.947372 0.320135i \(-0.896272\pi\)
0.196441 0.980516i \(-0.437062\pi\)
\(734\) 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 0.999267 0.0382877i \(-0.0121903\pi\)
−0.532791 + 0.846247i \(0.678857\pi\)
\(740\) 15.2618 0.561034
\(741\) 0 0
\(742\) 0 0
\(743\) −11.2221 + 19.4372i −0.411699 + 0.713083i −0.995076 0.0991184i \(-0.968398\pi\)
0.583377 + 0.812202i \(0.301731\pi\)
\(744\) 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 0.555978 0.831197i \(-0.312344\pi\)
−0.997827 + 0.0658924i \(0.979011\pi\)
\(752\) 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 0.651561 0.758596i \(-0.274114\pi\)
−0.982744 + 0.184970i \(0.940781\pi\)
\(762\) 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 −0.983310 0.181936i \(-0.941764\pi\)
0.649217 + 0.760604i \(0.275097\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.782814 0.0281741
\(773\) −1.48040 2.56413i −0.0532463 0.0922253i 0.838174 0.545403i \(-0.183624\pi\)
−0.891420 + 0.453178i \(0.850290\pi\)
\(774\) 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