Properties

Label 720.2.q.g.481.2
Level $720$
Weight $2$
Character 720.481
Analytic conductor $5.749$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(241,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 481.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 720.481
Dual form 720.2.q.g.241.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.724745 + 1.57313i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.72474 + 2.98735i) q^{7} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\) \(q+(0.724745 + 1.57313i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.72474 + 2.98735i) q^{7} +(-1.94949 + 2.28024i) q^{9} +(1.72474 + 0.158919i) q^{15} -2.00000 q^{17} +6.89898 q^{19} +(-3.44949 + 4.87832i) q^{21} +(-3.72474 + 6.45145i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.00000 - 1.41421i) q^{27} +(0.949490 + 1.64456i) q^{29} +(0.550510 - 0.953512i) q^{31} +3.44949 q^{35} -6.00000 q^{37} +(4.94949 - 8.57277i) q^{41} +(5.89898 + 10.2173i) q^{43} +(1.00000 + 2.82843i) q^{45} +(-4.72474 - 8.18350i) q^{47} +(-2.44949 + 4.24264i) q^{49} +(-1.44949 - 3.14626i) q^{51} +7.79796 q^{53} +(5.00000 + 10.8530i) q^{57} +(-0.550510 + 0.953512i) q^{59} +(1.50000 + 2.59808i) q^{61} +(-10.1742 - 1.89097i) q^{63} +(-6.62372 + 11.4726i) q^{67} +(-12.8485 - 1.18386i) q^{69} -9.79796 q^{71} +13.7980 q^{73} +(1.00000 - 1.41421i) q^{75} +(-3.44949 - 5.97469i) q^{79} +(-1.39898 - 8.89060i) q^{81} +(-2.72474 - 4.71940i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(-1.89898 + 2.68556i) q^{87} +2.79796 q^{89} +(1.89898 + 0.174973i) q^{93} +(3.44949 - 5.97469i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{15} - 8 q^{17} + 8 q^{19} - 4 q^{21} - 10 q^{23} - 2 q^{25} - 20 q^{27} - 6 q^{29} + 12 q^{31} + 4 q^{35} - 24 q^{37} + 10 q^{41} + 4 q^{43} + 4 q^{45} - 14 q^{47} + 4 q^{51} - 8 q^{53} + 20 q^{57} - 12 q^{59} + 6 q^{61} - 26 q^{63} - 2 q^{67} - 22 q^{69} + 16 q^{73} + 4 q^{75} - 4 q^{79} + 14 q^{81} - 6 q^{83} - 4 q^{85} + 12 q^{87} - 28 q^{89} - 12 q^{93} + 4 q^{95} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 0.724745 + 1.57313i 0.418432 + 0.908248i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.72474 + 2.98735i 0.651892 + 1.12911i 0.982663 + 0.185399i \(0.0593579\pi\)
−0.330771 + 0.943711i \(0.607309\pi\)
\(8\) 0 0
\(9\) −1.94949 + 2.28024i −0.649830 + 0.760080i
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) 0 0
\(15\) 1.72474 + 0.158919i 0.445327 + 0.0410326i
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 6.89898 1.58273 0.791367 0.611341i \(-0.209370\pi\)
0.791367 + 0.611341i \(0.209370\pi\)
\(20\) 0 0
\(21\) −3.44949 + 4.87832i −0.752740 + 1.06454i
\(22\) 0 0
\(23\) −3.72474 + 6.45145i −0.776663 + 1.34522i 0.157192 + 0.987568i \(0.449756\pi\)
−0.933855 + 0.357652i \(0.883578\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) 0.949490 + 1.64456i 0.176316 + 0.305388i 0.940616 0.339473i \(-0.110249\pi\)
−0.764300 + 0.644861i \(0.776915\pi\)
\(30\) 0 0
\(31\) 0.550510 0.953512i 0.0988746 0.171256i −0.812345 0.583178i \(-0.801809\pi\)
0.911219 + 0.411922i \(0.135142\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.44949 0.583070
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.94949 8.57277i 0.772980 1.33884i −0.162942 0.986636i \(-0.552098\pi\)
0.935923 0.352206i \(-0.114568\pi\)
\(42\) 0 0
\(43\) 5.89898 + 10.2173i 0.899586 + 1.55813i 0.828024 + 0.560692i \(0.189465\pi\)
0.0715617 + 0.997436i \(0.477202\pi\)
\(44\) 0 0
\(45\) 1.00000 + 2.82843i 0.149071 + 0.421637i
\(46\) 0 0
\(47\) −4.72474 8.18350i −0.689175 1.19369i −0.972105 0.234545i \(-0.924640\pi\)
0.282930 0.959140i \(-0.408693\pi\)
\(48\) 0 0
\(49\) −2.44949 + 4.24264i −0.349927 + 0.606092i
\(50\) 0 0
\(51\) −1.44949 3.14626i −0.202969 0.440565i
\(52\) 0 0
\(53\) 7.79796 1.07113 0.535566 0.844493i \(-0.320098\pi\)
0.535566 + 0.844493i \(0.320098\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.00000 + 10.8530i 0.662266 + 1.43752i
\(58\) 0 0
\(59\) −0.550510 + 0.953512i −0.0716703 + 0.124137i −0.899633 0.436646i \(-0.856166\pi\)
0.827963 + 0.560783i \(0.189500\pi\)
\(60\) 0 0
\(61\) 1.50000 + 2.59808i 0.192055 + 0.332650i 0.945931 0.324367i \(-0.105151\pi\)
−0.753876 + 0.657017i \(0.771818\pi\)
\(62\) 0 0
\(63\) −10.1742 1.89097i −1.28183 0.238240i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.62372 + 11.4726i −0.809217 + 1.40160i 0.104190 + 0.994557i \(0.466775\pi\)
−0.913407 + 0.407047i \(0.866558\pi\)
\(68\) 0 0
\(69\) −12.8485 1.18386i −1.54677 0.142520i
\(70\) 0 0
\(71\) −9.79796 −1.16280 −0.581402 0.813617i \(-0.697496\pi\)
−0.581402 + 0.813617i \(0.697496\pi\)
\(72\) 0 0
\(73\) 13.7980 1.61493 0.807464 0.589916i \(-0.200839\pi\)
0.807464 + 0.589916i \(0.200839\pi\)
\(74\) 0 0
\(75\) 1.00000 1.41421i 0.115470 0.163299i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −3.44949 5.97469i −0.388098 0.672205i 0.604096 0.796912i \(-0.293534\pi\)
−0.992194 + 0.124706i \(0.960201\pi\)
\(80\) 0 0
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) 0 0
\(83\) −2.72474 4.71940i −0.299080 0.518021i 0.676846 0.736125i \(-0.263346\pi\)
−0.975926 + 0.218104i \(0.930013\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 0 0
\(87\) −1.89898 + 2.68556i −0.203592 + 0.287923i
\(88\) 0 0
\(89\) 2.79796 0.296583 0.148292 0.988944i \(-0.452623\pi\)
0.148292 + 0.988944i \(0.452623\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.89898 + 0.174973i 0.196915 + 0.0181438i
\(94\) 0 0
\(95\) 3.44949 5.97469i 0.353910 0.612990i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) 0 0
\(105\) 2.50000 + 5.42650i 0.243975 + 0.529573i
\(106\) 0 0
\(107\) 12.3485 1.19377 0.596886 0.802326i \(-0.296405\pi\)
0.596886 + 0.802326i \(0.296405\pi\)
\(108\) 0 0
\(109\) −10.7980 −1.03426 −0.517128 0.855908i \(-0.672999\pi\)
−0.517128 + 0.855908i \(0.672999\pi\)
\(110\) 0 0
\(111\) −4.34847 9.43879i −0.412738 0.895891i
\(112\) 0 0
\(113\) 4.89898 8.48528i 0.460857 0.798228i −0.538147 0.842851i \(-0.680875\pi\)
0.999004 + 0.0446231i \(0.0142087\pi\)
\(114\) 0 0
\(115\) 3.72474 + 6.45145i 0.347334 + 0.601601i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.44949 5.97469i −0.316214 0.547699i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0 0
\(123\) 17.0732 + 1.57313i 1.53944 + 0.141845i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −0.348469 −0.0309216 −0.0154608 0.999880i \(-0.504922\pi\)
−0.0154608 + 0.999880i \(0.504922\pi\)
\(128\) 0 0
\(129\) −11.7980 + 16.6848i −1.03875 + 1.46902i
\(130\) 0 0
\(131\) 1.44949 2.51059i 0.126643 0.219351i −0.795731 0.605650i \(-0.792913\pi\)
0.922374 + 0.386299i \(0.126247\pi\)
\(132\) 0 0
\(133\) 11.8990 + 20.6096i 1.03177 + 1.78708i
\(134\) 0 0
\(135\) −3.72474 + 3.62302i −0.320575 + 0.311820i
\(136\) 0 0
\(137\) −9.79796 16.9706i −0.837096 1.44989i −0.892312 0.451419i \(-0.850918\pi\)
0.0552162 0.998474i \(-0.482415\pi\)
\(138\) 0 0
\(139\) 9.79796 16.9706i 0.831052 1.43942i −0.0661527 0.997810i \(-0.521072\pi\)
0.897205 0.441615i \(-0.145594\pi\)
\(140\) 0 0
\(141\) 9.44949 13.3636i 0.795791 1.12542i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 1.89898 0.157702
\(146\) 0 0
\(147\) −8.44949 0.778539i −0.696902 0.0642128i
\(148\) 0 0
\(149\) 10.5000 18.1865i 0.860194 1.48990i −0.0115483 0.999933i \(-0.503676\pi\)
0.871742 0.489966i \(-0.162991\pi\)
\(150\) 0 0
\(151\) 6.00000 + 10.3923i 0.488273 + 0.845714i 0.999909 0.0134886i \(-0.00429367\pi\)
−0.511636 + 0.859202i \(0.670960\pi\)
\(152\) 0 0
\(153\) 3.89898 4.56048i 0.315214 0.368693i
\(154\) 0 0
\(155\) −0.550510 0.953512i −0.0442180 0.0765879i
\(156\) 0 0
\(157\) 11.8990 20.6096i 0.949642 1.64483i 0.203463 0.979083i \(-0.434780\pi\)
0.746179 0.665745i \(-0.231886\pi\)
\(158\) 0 0
\(159\) 5.65153 + 12.2672i 0.448196 + 0.972854i
\(160\) 0 0
\(161\) −25.6969 −2.02520
\(162\) 0 0
\(163\) 7.79796 0.610783 0.305392 0.952227i \(-0.401213\pi\)
0.305392 + 0.952227i \(0.401213\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.17423 7.22999i 0.323012 0.559473i −0.658096 0.752934i \(-0.728638\pi\)
0.981108 + 0.193461i \(0.0619713\pi\)
\(168\) 0 0
\(169\) 6.50000 + 11.2583i 0.500000 + 0.866025i
\(170\) 0 0
\(171\) −13.4495 + 15.7313i −1.02851 + 1.20300i
\(172\) 0 0
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) 0 0
\(175\) 1.72474 2.98735i 0.130378 0.225822i
\(176\) 0 0
\(177\) −1.89898 0.174973i −0.142736 0.0131518i
\(178\) 0 0
\(179\) 13.7980 1.03131 0.515654 0.856797i \(-0.327549\pi\)
0.515654 + 0.856797i \(0.327549\pi\)
\(180\) 0 0
\(181\) −9.69694 −0.720768 −0.360384 0.932804i \(-0.617354\pi\)
−0.360384 + 0.932804i \(0.617354\pi\)
\(182\) 0 0
\(183\) −3.00000 + 4.24264i −0.221766 + 0.313625i
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −4.39898 17.3759i −0.319979 1.26391i
\(190\) 0 0
\(191\) −7.44949 12.9029i −0.539026 0.933621i −0.998957 0.0456658i \(-0.985459\pi\)
0.459931 0.887955i \(-0.347874\pi\)
\(192\) 0 0
\(193\) 1.10102 1.90702i 0.0792532 0.137271i −0.823675 0.567063i \(-0.808080\pi\)
0.902928 + 0.429792i \(0.141413\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.5959 −1.11116 −0.555582 0.831462i \(-0.687504\pi\)
−0.555582 + 0.831462i \(0.687504\pi\)
\(198\) 0 0
\(199\) −22.8990 −1.62327 −0.811633 0.584168i \(-0.801421\pi\)
−0.811633 + 0.584168i \(0.801421\pi\)
\(200\) 0 0
\(201\) −22.8485 2.10527i −1.61161 0.148494i
\(202\) 0 0
\(203\) −3.27526 + 5.67291i −0.229878 + 0.398160i
\(204\) 0 0
\(205\) −4.94949 8.57277i −0.345687 0.598748i
\(206\) 0 0
\(207\) −7.44949 21.0703i −0.517775 1.46449i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) 0 0
\(213\) −7.10102 15.4135i −0.486554 1.05611i
\(214\) 0 0
\(215\) 11.7980 0.804614
\(216\) 0 0
\(217\) 3.79796 0.257822
\(218\) 0 0
\(219\) 10.0000 + 21.7060i 0.675737 + 1.46676i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.72474 + 4.71940i 0.182462 + 0.316034i 0.942718 0.333589i \(-0.108260\pi\)
−0.760256 + 0.649623i \(0.774927\pi\)
\(224\) 0 0
\(225\) 2.94949 + 0.548188i 0.196633 + 0.0365459i
\(226\) 0 0
\(227\) −4.10102 7.10318i −0.272194 0.471454i 0.697229 0.716848i \(-0.254416\pi\)
−0.969423 + 0.245394i \(0.921083\pi\)
\(228\) 0 0
\(229\) 2.05051 3.55159i 0.135502 0.234696i −0.790287 0.612736i \(-0.790069\pi\)
0.925789 + 0.378041i \(0.123402\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −19.7980 −1.29701 −0.648504 0.761211i \(-0.724605\pi\)
−0.648504 + 0.761211i \(0.724605\pi\)
\(234\) 0 0
\(235\) −9.44949 −0.616417
\(236\) 0 0
\(237\) 6.89898 9.75663i 0.448137 0.633761i
\(238\) 0 0
\(239\) 1.10102 1.90702i 0.0712191 0.123355i −0.828217 0.560408i \(-0.810644\pi\)
0.899436 + 0.437053i \(0.143978\pi\)
\(240\) 0 0
\(241\) 1.84847 + 3.20164i 0.119070 + 0.206236i 0.919400 0.393325i \(-0.128675\pi\)
−0.800329 + 0.599561i \(0.795342\pi\)
\(242\) 0 0
\(243\) 12.9722 8.64420i 0.832167 0.554526i
\(244\) 0 0
\(245\) 2.44949 + 4.24264i 0.156492 + 0.271052i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 5.44949 7.70674i 0.345347 0.488395i
\(250\) 0 0
\(251\) −2.89898 −0.182982 −0.0914910 0.995806i \(-0.529163\pi\)
−0.0914910 + 0.995806i \(0.529163\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −3.44949 0.317837i −0.216015 0.0199037i
\(256\) 0 0
\(257\) −13.8990 + 24.0737i −0.866995 + 1.50168i −0.00194150 + 0.999998i \(0.500618\pi\)
−0.865053 + 0.501680i \(0.832715\pi\)
\(258\) 0 0
\(259\) −10.3485 17.9241i −0.643023 1.11375i
\(260\) 0 0
\(261\) −5.60102 1.04100i −0.346694 0.0644362i
\(262\) 0 0
\(263\) 9.00000 + 15.5885i 0.554964 + 0.961225i 0.997906 + 0.0646755i \(0.0206012\pi\)
−0.442943 + 0.896550i \(0.646065\pi\)
\(264\) 0 0
\(265\) 3.89898 6.75323i 0.239512 0.414848i
\(266\) 0 0
\(267\) 2.02781 + 4.40156i 0.124100 + 0.269371i
\(268\) 0 0
\(269\) 22.5959 1.37770 0.688849 0.724905i \(-0.258116\pi\)
0.688849 + 0.724905i \(0.258116\pi\)
\(270\) 0 0
\(271\) −30.8990 −1.87698 −0.938490 0.345307i \(-0.887775\pi\)
−0.938490 + 0.345307i \(0.887775\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.00000 + 12.1244i 0.420589 + 0.728482i 0.995997 0.0893846i \(-0.0284900\pi\)
−0.575408 + 0.817867i \(0.695157\pi\)
\(278\) 0 0
\(279\) 1.10102 + 3.11416i 0.0659164 + 0.186440i
\(280\) 0 0
\(281\) 4.05051 + 7.01569i 0.241633 + 0.418521i 0.961180 0.275923i \(-0.0889836\pi\)
−0.719546 + 0.694444i \(0.755650\pi\)
\(282\) 0 0
\(283\) −1.82577 + 3.16232i −0.108530 + 0.187980i −0.915175 0.403056i \(-0.867948\pi\)
0.806645 + 0.591037i \(0.201281\pi\)
\(284\) 0 0
\(285\) 11.8990 + 1.09638i 0.704835 + 0.0649437i
\(286\) 0 0
\(287\) 34.1464 2.01560
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 2.00000 2.82843i 0.117242 0.165805i
\(292\) 0 0
\(293\) −8.79796 + 15.2385i −0.513982 + 0.890243i 0.485886 + 0.874022i \(0.338497\pi\)
−0.999868 + 0.0162213i \(0.994836\pi\)
\(294\) 0 0
\(295\) 0.550510 + 0.953512i 0.0320519 + 0.0555156i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −20.3485 + 35.2446i −1.17287 + 2.03146i
\(302\) 0 0
\(303\) −2.00000 + 2.82843i −0.114897 + 0.162489i
\(304\) 0 0
\(305\) 3.00000 0.171780
\(306\) 0 0
\(307\) 4.75255 0.271242 0.135621 0.990761i \(-0.456697\pi\)
0.135621 + 0.990761i \(0.456697\pi\)
\(308\) 0 0
\(309\) 17.2474 + 1.58919i 0.981173 + 0.0904056i
\(310\) 0 0
\(311\) −3.44949 + 5.97469i −0.195603 + 0.338794i −0.947098 0.320945i \(-0.896000\pi\)
0.751495 + 0.659738i \(0.229333\pi\)
\(312\) 0 0
\(313\) 7.79796 + 13.5065i 0.440767 + 0.763430i 0.997747 0.0670957i \(-0.0213733\pi\)
−0.556980 + 0.830526i \(0.688040\pi\)
\(314\) 0 0
\(315\) −6.72474 + 7.86566i −0.378896 + 0.443180i
\(316\) 0 0
\(317\) 12.8990 + 22.3417i 0.724479 + 1.25483i 0.959188 + 0.282769i \(0.0912528\pi\)
−0.234709 + 0.972066i \(0.575414\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 8.94949 + 19.4258i 0.499512 + 1.08424i
\(322\) 0 0
\(323\) −13.7980 −0.767739
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −7.82577 16.9866i −0.432766 0.939362i
\(328\) 0 0
\(329\) 16.2980 28.2289i 0.898536 1.55631i
\(330\) 0 0
\(331\) −3.44949 5.97469i −0.189601 0.328399i 0.755516 0.655130i \(-0.227386\pi\)
−0.945117 + 0.326731i \(0.894053\pi\)
\(332\) 0 0
\(333\) 11.6969 13.6814i 0.640988 0.749738i
\(334\) 0 0
\(335\) 6.62372 + 11.4726i 0.361893 + 0.626817i
\(336\) 0 0
\(337\) 14.8990 25.8058i 0.811599 1.40573i −0.100145 0.994973i \(-0.531931\pi\)
0.911744 0.410758i \(-0.134736\pi\)
\(338\) 0 0
\(339\) 16.8990 + 1.55708i 0.917827 + 0.0845689i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 7.24745 0.391325
\(344\) 0 0
\(345\) −7.44949 + 10.5352i −0.401067 + 0.567194i
\(346\) 0 0
\(347\) −12.7980 + 22.1667i −0.687030 + 1.18997i 0.285764 + 0.958300i \(0.407753\pi\)
−0.972794 + 0.231671i \(0.925581\pi\)
\(348\) 0 0
\(349\) 1.15153 + 1.99451i 0.0616400 + 0.106764i 0.895199 0.445667i \(-0.147034\pi\)
−0.833559 + 0.552431i \(0.813700\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) 0 0
\(355\) −4.89898 + 8.48528i −0.260011 + 0.450352i
\(356\) 0 0
\(357\) 6.89898 9.75663i 0.365133 0.516376i
\(358\) 0 0
\(359\) −28.6969 −1.51457 −0.757283 0.653087i \(-0.773474\pi\)
−0.757283 + 0.653087i \(0.773474\pi\)
\(360\) 0 0
\(361\) 28.5959 1.50505
\(362\) 0 0
\(363\) 18.9722 + 1.74810i 0.995782 + 0.0917517i
\(364\) 0 0
\(365\) 6.89898 11.9494i 0.361109 0.625459i
\(366\) 0 0
\(367\) 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) 0 0
\(369\) 9.89898 + 27.9985i 0.515320 + 1.45755i
\(370\) 0 0
\(371\) 13.4495 + 23.2952i 0.698263 + 1.20943i
\(372\) 0 0
\(373\) −10.7980 + 18.7026i −0.559097 + 0.968385i 0.438475 + 0.898743i \(0.355519\pi\)
−0.997572 + 0.0696412i \(0.977815\pi\)
\(374\) 0 0
\(375\) −0.724745 1.57313i −0.0374257 0.0812362i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −26.8990 −1.38171 −0.690854 0.722994i \(-0.742765\pi\)
−0.690854 + 0.722994i \(0.742765\pi\)
\(380\) 0 0
\(381\) −0.252551 0.548188i −0.0129386 0.0280845i
\(382\) 0 0
\(383\) 1.00000 1.73205i 0.0510976 0.0885037i −0.839345 0.543599i \(-0.817061\pi\)
0.890443 + 0.455095i \(0.150395\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −34.7980 6.46750i −1.76888 0.328762i
\(388\) 0 0
\(389\) 8.29796 + 14.3725i 0.420723 + 0.728714i 0.996010 0.0892375i \(-0.0284430\pi\)
−0.575287 + 0.817952i \(0.695110\pi\)
\(390\) 0 0
\(391\) 7.44949 12.9029i 0.376737 0.652527i
\(392\) 0 0
\(393\) 5.00000 + 0.460702i 0.252217 + 0.0232393i
\(394\) 0 0
\(395\) −6.89898 −0.347125
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −23.7980 + 33.6554i −1.19139 + 1.68488i
\(400\) 0 0
\(401\) −12.7980 + 22.1667i −0.639100 + 1.10695i 0.346531 + 0.938038i \(0.387359\pi\)
−0.985631 + 0.168914i \(0.945974\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −8.39898 3.23375i −0.417349 0.160686i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 4.79796 8.31031i 0.237244 0.410918i −0.722679 0.691184i \(-0.757089\pi\)
0.959922 + 0.280266i \(0.0904226\pi\)
\(410\) 0 0
\(411\) 19.5959 27.7128i 0.966595 1.36697i
\(412\) 0 0
\(413\) −3.79796 −0.186885
\(414\) 0 0
\(415\) −5.44949 −0.267505
\(416\) 0 0
\(417\) 33.7980 + 3.11416i 1.65509 + 0.152501i
\(418\) 0 0
\(419\) 10.0000 17.3205i 0.488532 0.846162i −0.511381 0.859354i \(-0.670866\pi\)
0.999913 + 0.0131919i \(0.00419923\pi\)
\(420\) 0 0
\(421\) −12.7980 22.1667i −0.623734 1.08034i −0.988784 0.149352i \(-0.952281\pi\)
0.365050 0.930988i \(-0.381052\pi\)
\(422\) 0 0
\(423\) 27.8712 + 5.18010i 1.35514 + 0.251865i
\(424\) 0 0
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −5.17423 + 8.96204i −0.250399 + 0.433703i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.8990 −0.717659 −0.358829 0.933403i \(-0.616824\pi\)
−0.358829 + 0.933403i \(0.616824\pi\)
\(432\) 0 0
\(433\) −11.7980 −0.566974 −0.283487 0.958976i \(-0.591491\pi\)
−0.283487 + 0.958976i \(0.591491\pi\)
\(434\) 0 0
\(435\) 1.37628 + 2.98735i 0.0659874 + 0.143232i
\(436\) 0 0
\(437\) −25.6969 + 44.5084i −1.22925 + 2.12913i
\(438\) 0 0
\(439\) −8.89898 15.4135i −0.424725 0.735645i 0.571670 0.820484i \(-0.306296\pi\)
−0.996395 + 0.0848384i \(0.972963\pi\)
\(440\) 0 0
\(441\) −4.89898 13.8564i −0.233285 0.659829i
\(442\) 0 0
\(443\) −4.07321 7.05501i −0.193524 0.335194i 0.752892 0.658145i \(-0.228658\pi\)
−0.946416 + 0.322951i \(0.895325\pi\)
\(444\) 0 0
\(445\) 1.39898 2.42310i 0.0663180 0.114866i
\(446\) 0 0
\(447\) 36.2196 + 3.33729i 1.71313 + 0.157848i
\(448\) 0 0
\(449\) 21.5959 1.01917 0.509587 0.860419i \(-0.329798\pi\)
0.509587 + 0.860419i \(0.329798\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −12.0000 + 16.9706i −0.563809 + 0.797347i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.79796 15.2385i −0.411551 0.712828i 0.583508 0.812107i \(-0.301680\pi\)
−0.995060 + 0.0992796i \(0.968346\pi\)
\(458\) 0 0
\(459\) 10.0000 + 2.82843i 0.466760 + 0.132020i
\(460\) 0 0
\(461\) −6.05051 10.4798i −0.281800 0.488093i 0.690028 0.723783i \(-0.257598\pi\)
−0.971828 + 0.235690i \(0.924265\pi\)
\(462\) 0 0
\(463\) 6.10102 10.5673i 0.283538 0.491103i −0.688715 0.725032i \(-0.741825\pi\)
0.972254 + 0.233929i \(0.0751583\pi\)
\(464\) 0 0
\(465\) 1.10102 1.55708i 0.0510586 0.0722078i
\(466\) 0 0
\(467\) −7.79796 −0.360847 −0.180423 0.983589i \(-0.557747\pi\)
−0.180423 + 0.983589i \(0.557747\pi\)
\(468\) 0 0
\(469\) −45.6969 −2.11009
\(470\) 0 0
\(471\) 41.0454 + 3.78194i 1.89127 + 0.174263i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −3.44949 5.97469i −0.158273 0.274138i
\(476\) 0 0
\(477\) −15.2020 + 17.7812i −0.696054 + 0.814146i
\(478\) 0 0
\(479\) 15.2474 + 26.4094i 0.696674 + 1.20667i 0.969613 + 0.244643i \(0.0786708\pi\)
−0.272939 + 0.962031i \(0.587996\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −18.6237 40.4247i −0.847409 1.83939i
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) 13.5959 0.616090 0.308045 0.951372i \(-0.400325\pi\)
0.308045 + 0.951372i \(0.400325\pi\)
\(488\) 0 0
\(489\) 5.65153 + 12.2672i 0.255571 + 0.554743i
\(490\) 0 0
\(491\) −6.89898 + 11.9494i −0.311347 + 0.539268i −0.978654 0.205514i \(-0.934113\pi\)
0.667308 + 0.744782i \(0.267447\pi\)
\(492\) 0 0
\(493\) −1.89898 3.28913i −0.0855257 0.148135i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.8990 29.2699i −0.758023 1.31293i
\(498\) 0 0
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) 0 0
\(501\) 14.3990 + 1.32673i 0.643299 + 0.0592738i
\(502\) 0 0
\(503\) −25.0454 −1.11672 −0.558360 0.829599i \(-0.688569\pi\)
−0.558360 + 0.829599i \(0.688569\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) −13.0000 + 18.3848i −0.577350 + 0.816497i
\(508\) 0 0
\(509\) 2.05051 3.55159i 0.0908873 0.157421i −0.816997 0.576641i \(-0.804363\pi\)
0.907885 + 0.419220i \(0.137696\pi\)
\(510\) 0 0
\(511\) 23.7980 + 41.2193i 1.05276 + 1.82343i
\(512\) 0 0
\(513\) −34.4949 9.75663i −1.52299 0.430766i
\(514\) 0 0
\(515\) −5.00000 8.66025i −0.220326 0.381616i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −12.0000 + 16.9706i −0.526742 + 0.744925i
\(520\) 0 0
\(521\) 9.20204 0.403149 0.201574 0.979473i \(-0.435394\pi\)
0.201574 + 0.979473i \(0.435394\pi\)
\(522\) 0 0
\(523\) 34.3485 1.50195 0.750977 0.660329i \(-0.229583\pi\)
0.750977 + 0.660329i \(0.229583\pi\)
\(524\) 0 0
\(525\) 5.94949 + 0.548188i 0.259657 + 0.0239249i
\(526\) 0 0
\(527\) −1.10102 + 1.90702i −0.0479612 + 0.0830712i
\(528\) 0 0
\(529\) −16.2474 28.1414i −0.706411 1.22354i
\(530\) 0 0
\(531\) −1.10102 3.11416i −0.0477802 0.135143i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 6.17423 10.6941i 0.266935 0.462346i
\(536\) 0 0
\(537\) 10.0000 + 21.7060i 0.431532 + 0.936684i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.1010 0.520264 0.260132 0.965573i \(-0.416234\pi\)
0.260132 + 0.965573i \(0.416234\pi\)
\(542\) 0 0
\(543\) −7.02781 15.2546i −0.301592 0.654636i
\(544\) 0 0
\(545\) −5.39898 + 9.35131i −0.231267 + 0.400566i
\(546\) 0 0
\(547\) −8.37628 14.5081i −0.358144 0.620323i 0.629507 0.776995i \(-0.283257\pi\)
−0.987651 + 0.156672i \(0.949924\pi\)
\(548\) 0 0
\(549\) −8.84847 1.64456i −0.377643 0.0701883i
\(550\) 0 0
\(551\) 6.55051 + 11.3458i 0.279061 + 0.483348i
\(552\) 0 0
\(553\) 11.8990 20.6096i 0.505996 0.876411i
\(554\) 0 0
\(555\) −10.3485 0.953512i −0.439268 0.0404743i
\(556\) 0 0
\(557\) 43.7980 1.85578 0.927890 0.372855i \(-0.121621\pi\)
0.927890 + 0.372855i \(0.121621\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.17423 + 8.96204i −0.218068 + 0.377705i −0.954217 0.299114i \(-0.903309\pi\)
0.736149 + 0.676819i \(0.236642\pi\)
\(564\) 0 0
\(565\) −4.89898 8.48528i −0.206102 0.356978i
\(566\) 0 0
\(567\) 24.1464 19.5133i 1.01405 0.819480i
\(568\) 0 0
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) 12.8990 22.3417i 0.539805 0.934971i −0.459109 0.888380i \(-0.651831\pi\)
0.998914 0.0465904i \(-0.0148355\pi\)
\(572\) 0 0
\(573\) 14.8990 21.0703i 0.622414 0.880226i
\(574\) 0 0
\(575\) 7.44949 0.310665
\(576\) 0 0
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 0 0
\(579\) 3.79796 + 0.349945i 0.157838 + 0.0145432i
\(580\) 0 0
\(581\) 9.39898 16.2795i 0.389935 0.675388i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.82577 + 6.62642i 0.157906 + 0.273502i 0.934113 0.356976i \(-0.116192\pi\)
−0.776207 + 0.630478i \(0.782859\pi\)
\(588\) 0 0
\(589\) 3.79796 6.57826i 0.156492 0.271052i
\(590\) 0 0
\(591\) −11.3031 24.5344i −0.464946 1.00921i
\(592\) 0 0
\(593\) −31.3939 −1.28919 −0.644596 0.764523i \(-0.722974\pi\)
−0.644596 + 0.764523i \(0.722974\pi\)
\(594\) 0 0
\(595\) −6.89898 −0.282831
\(596\) 0 0
\(597\) −16.5959 36.0231i −0.679226 1.47433i
\(598\) 0 0
\(599\) −12.3485 + 21.3882i −0.504545 + 0.873897i 0.495441 + 0.868641i \(0.335006\pi\)
−0.999986 + 0.00525583i \(0.998327\pi\)
\(600\) 0 0
\(601\) −7.00000 12.1244i −0.285536 0.494563i 0.687203 0.726465i \(-0.258838\pi\)
−0.972739 + 0.231903i \(0.925505\pi\)
\(602\) 0 0
\(603\) −13.2474 37.4694i −0.539478 1.52587i
\(604\) 0 0
\(605\) −5.50000 9.52628i −0.223607 0.387298i
\(606\) 0 0
\(607\) 1.07321 1.85886i 0.0435604 0.0754489i −0.843423 0.537250i \(-0.819463\pi\)
0.886984 + 0.461801i \(0.152797\pi\)
\(608\) 0 0
\(609\) −11.2980 1.04100i −0.457816 0.0421834i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −29.5959 −1.19537 −0.597684 0.801732i \(-0.703912\pi\)
−0.597684 + 0.801732i \(0.703912\pi\)
\(614\) 0 0
\(615\) 9.89898 13.9993i 0.399165 0.564505i
\(616\) 0 0
\(617\) 17.5959 30.4770i 0.708385 1.22696i −0.257071 0.966393i \(-0.582757\pi\)
0.965456 0.260566i \(-0.0839092\pi\)
\(618\) 0 0
\(619\) −12.3485 21.3882i −0.496327 0.859663i 0.503664 0.863900i \(-0.331985\pi\)
−0.999991 + 0.00423617i \(0.998652\pi\)
\(620\) 0 0
\(621\) 27.7474 26.9897i 1.11347 1.08306i
\(622\) 0 0
\(623\) 4.82577 + 8.35847i 0.193340 + 0.334875i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 15.5959 0.620864 0.310432 0.950596i \(-0.399526\pi\)
0.310432 + 0.950596i \(0.399526\pi\)
\(632\) 0 0
\(633\) 20.6969 + 1.90702i 0.822629 + 0.0757974i
\(634\) 0 0
\(635\) −0.174235 + 0.301783i −0.00691429 + 0.0119759i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 19.1010 22.3417i 0.755625 0.883824i
\(640\) 0 0
\(641\) 6.94949 + 12.0369i 0.274488 + 0.475428i 0.970006 0.243081i \(-0.0781582\pi\)
−0.695518 + 0.718509i \(0.744825\pi\)
\(642\) 0 0
\(643\) −10.0732 + 17.4473i −0.397249 + 0.688055i −0.993385 0.114828i \(-0.963368\pi\)
0.596137 + 0.802883i \(0.296702\pi\)
\(644\) 0 0
\(645\) 8.55051 + 18.5597i 0.336676 + 0.730789i
\(646\) 0 0
\(647\) −6.55051 −0.257527 −0.128764 0.991675i \(-0.541101\pi\)
−0.128764 + 0.991675i \(0.541101\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 2.75255 + 5.97469i 0.107881 + 0.234167i
\(652\) 0 0
\(653\) −13.8990 + 24.0737i −0.543909 + 0.942078i 0.454766 + 0.890611i \(0.349723\pi\)
−0.998675 + 0.0514670i \(0.983610\pi\)
\(654\) 0 0
\(655\) −1.44949 2.51059i −0.0566363 0.0980969i
\(656\) 0 0
\(657\) −26.8990 + 31.4626i −1.04943 + 1.22747i
\(658\) 0 0
\(659\) 5.10102 + 8.83523i 0.198708 + 0.344172i 0.948110 0.317944i \(-0.102992\pi\)
−0.749402 + 0.662115i \(0.769659\pi\)
\(660\) 0 0
\(661\) −5.00000 + 8.66025i −0.194477 + 0.336845i −0.946729 0.322031i \(-0.895634\pi\)
0.752252 + 0.658876i \(0.228968\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 23.7980 0.922845
\(666\) 0 0
\(667\) −14.1464 −0.547752
\(668\) 0 0
\(669\) −5.44949 + 7.70674i −0.210689 + 0.297960i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 8.00000 + 13.8564i 0.308377 + 0.534125i 0.978008 0.208569i \(-0.0668807\pi\)
−0.669630 + 0.742695i \(0.733547\pi\)
\(674\) 0 0
\(675\) 1.27526 + 5.03723i 0.0490846 + 0.193883i
\(676\) 0 0
\(677\) −7.10102 12.2993i −0.272914 0.472702i 0.696692 0.717370i \(-0.254654\pi\)
−0.969607 + 0.244668i \(0.921321\pi\)
\(678\) 0 0
\(679\) 3.44949 5.97469i 0.132379 0.229288i
\(680\) 0 0
\(681\) 8.20204 11.5994i 0.314303 0.444491i
\(682\) 0 0
\(683\) −23.3939 −0.895142 −0.447571 0.894248i \(-0.647711\pi\)
−0.447571 + 0.894248i \(0.647711\pi\)
\(684\) 0 0
\(685\) −19.5959 −0.748722
\(686\) 0 0
\(687\) 7.07321 + 0.651729i 0.269860 + 0.0248650i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 19.4495 + 33.6875i 0.739893 + 1.28153i 0.952543 + 0.304404i \(0.0984574\pi\)
−0.212649 + 0.977129i \(0.568209\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.79796 16.9706i −0.371658 0.643730i
\(696\) 0 0
\(697\) −9.89898 + 17.1455i −0.374951 + 0.649433i
\(698\) 0 0
\(699\) −14.3485 31.1448i −0.542709 1.17800i
\(700\) 0 0
\(701\) 30.3939 1.14796 0.573980 0.818869i \(-0.305399\pi\)
0.573980 + 0.818869i \(0.305399\pi\)
\(702\) 0 0
\(703\) −41.3939 −1.56120
\(704\) 0 0
\(705\) −6.84847 14.8653i −0.257928 0.559859i
\(706\) 0 0
\(707\) −3.44949 + 5.97469i −0.129731 + 0.224701i
\(708\) 0 0
\(709\) −4.84847 8.39780i −0.182088 0.315386i 0.760503 0.649334i \(-0.224952\pi\)
−0.942591 + 0.333948i \(0.891619\pi\)
\(710\) 0 0
\(711\) 20.3485 + 3.78194i 0.763127 + 0.141834i
\(712\) 0 0
\(713\) 4.10102 + 7.10318i 0.153584 + 0.266016i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 3.79796 + 0.349945i 0.141837 + 0.0130689i
\(718\) 0 0
\(719\) 28.2929 1.05515 0.527573 0.849510i \(-0.323102\pi\)
0.527573 + 0.849510i \(0.323102\pi\)
\(720\) 0 0
\(721\) 34.4949 1.28466
\(722\) 0 0
\(723\) −3.69694 + 5.22826i −0.137491 + 0.194441i
\(724\) 0 0
\(725\) 0.949490 1.64456i 0.0352632 0.0610776i
\(726\) 0 0
\(727\) −15.6237 27.0611i −0.579452 1.00364i −0.995542 0.0943168i \(-0.969933\pi\)
0.416090 0.909323i \(-0.363400\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) −11.7980 20.4347i −0.436363 0.755803i
\(732\) 0 0
\(733\) 14.7980 25.6308i 0.546575 0.946696i −0.451931 0.892053i \(-0.649265\pi\)
0.998506 0.0546429i \(-0.0174020\pi\)
\(734\) 0 0
\(735\) −4.89898 + 6.92820i −0.180702 + 0.255551i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 33.1010 1.21764 0.608820 0.793308i \(-0.291643\pi\)
0.608820 + 0.793308i \(0.291643\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.52270 + 6.10150i −0.129235 + 0.223842i −0.923381 0.383886i \(-0.874586\pi\)
0.794145 + 0.607728i \(0.207919\pi\)
\(744\) 0 0
\(745\) −10.5000 18.1865i −0.384690 0.666303i
\(746\) 0 0
\(747\) 16.0732 + 2.98735i 0.588088 + 0.109301i
\(748\) 0 0
\(749\) 21.2980 + 36.8891i 0.778210 + 1.34790i
\(750\) 0 0
\(751\) 13.1010 22.6916i 0.478063 0.828029i −0.521621 0.853177i \(-0.674672\pi\)
0.999684 + 0.0251480i \(0.00800571\pi\)
\(752\) 0 0
\(753\) −2.10102 4.56048i −0.0765654 0.166193i
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 31.5959 1.14837 0.574187 0.818724i \(-0.305318\pi\)
0.574187 + 0.818724i \(0.305318\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.5000 + 30.3109i −0.634375 + 1.09877i 0.352273 + 0.935897i \(0.385409\pi\)
−0.986647 + 0.162872i \(0.947924\pi\)
\(762\) 0 0
\(763\) −18.6237 32.2572i −0.674224 1.16779i
\(764\) 0 0
\(765\) −2.00000 5.65685i −0.0723102 0.204524i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 2.60102 4.50510i 0.0937952 0.162458i −0.815310 0.579025i \(-0.803433\pi\)
0.909105 + 0.416567i \(0.136767\pi\)
\(770\) 0 0
\(771\) −47.9444 4.41761i −1.72667 0.159096i
\(772\) 0 0
\(773\) 6.20204 0.223072 0.111536 0.993760i \(-0.464423\pi\)
0.111536 + 0.993760i \(0.464423\pi\)
\(774\) 0 0
\(775\) −1.10102 −0.0395498
\(776\) 0 0
\(777\) 20.6969 29.2699i 0.742499 1.05005i
\(778\) 0 0
\(779\) 34.1464 59.1433i 1.22342 2.11903i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −2.42168 9.56560i −0.0865439 0.341847i
\(784\) 0 0
\(785\) −11.8990 20.6096i −0.424693 0.735589i
\(786\) 0 0
\(787\) −24.7980 + 42.9513i −0.883952 + 1.53105i −0.0370414 + 0.999314i \(0.511793\pi\)
−0.846910 + 0.531736i \(0.821540\pi\)
\(788\) 0 0
\(789\) −18.0000 + 25.4558i −0.640817 + 0.906252i
\(790\) 0 0
\(791\) 33.7980 1.20172
\(792\) 0