Properties

Label 720.2.q.g.481.1
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 481.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 720.481
Dual form 720.2.q.g.241.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.72474 + 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.724745 - 1.25529i) q^{7} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(-1.72474 + 0.158919i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.724745 - 1.25529i) q^{7} +(2.94949 - 0.548188i) q^{9} +(-0.724745 + 1.57313i) q^{15} -2.00000 q^{17} -2.89898 q^{19} +(1.44949 + 2.04989i) q^{21} +(-1.27526 + 2.20881i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.00000 + 1.41421i) q^{27} +(-3.94949 - 6.84072i) q^{29} +(5.44949 - 9.43879i) q^{31} -1.44949 q^{35} -6.00000 q^{37} +(0.0505103 - 0.0874863i) q^{41} +(-3.89898 - 6.75323i) q^{43} +(1.00000 - 2.82843i) q^{45} +(-2.27526 - 3.94086i) q^{47} +(2.44949 - 4.24264i) q^{49} +(3.44949 - 0.317837i) q^{51} -11.7980 q^{53} +(5.00000 - 0.460702i) q^{57} +(-5.44949 + 9.43879i) q^{59} +(1.50000 + 2.59808i) q^{61} +(-2.82577 - 3.30518i) q^{63} +(5.62372 - 9.74058i) q^{67} +(1.84847 - 4.01229i) q^{69} +9.79796 q^{71} -5.79796 q^{73} +(1.00000 + 1.41421i) q^{75} +(1.44949 + 2.51059i) q^{79} +(8.39898 - 3.23375i) q^{81} +(-0.275255 - 0.476756i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(7.89898 + 11.1708i) q^{87} -16.7980 q^{89} +(-7.89898 + 17.1455i) q^{93} +(-1.44949 + 2.51059i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 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
\(3\) −1.72474 + 0.158919i −0.995782 + 0.0917517i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −0.724745 1.25529i −0.273928 0.474457i 0.695936 0.718104i \(-0.254990\pi\)
−0.969864 + 0.243647i \(0.921656\pi\)
\(8\) 0 0
\(9\) 2.94949 0.548188i 0.983163 0.182729i
\(10\) 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
\(15\) −0.724745 + 1.57313i −0.187128 + 0.406181i
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −2.89898 −0.665072 −0.332536 0.943091i \(-0.607904\pi\)
−0.332536 + 0.943091i \(0.607904\pi\)
\(20\) 0 0
\(21\) 1.44949 + 2.04989i 0.316305 + 0.447322i
\(22\) 0 0
\(23\) −1.27526 + 2.20881i −0.265909 + 0.460568i −0.967801 0.251715i \(-0.919005\pi\)
0.701892 + 0.712283i \(0.252339\pi\)
\(24\) 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
\(29\) −3.94949 6.84072i −0.733402 1.27029i −0.955421 0.295247i \(-0.904598\pi\)
0.222019 0.975042i \(-0.428735\pi\)
\(30\) 0 0
\(31\) 5.44949 9.43879i 0.978757 1.69526i 0.311824 0.950140i \(-0.399060\pi\)
0.666933 0.745117i \(-0.267607\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.44949 −0.245008
\(36\) 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
\(41\) 0.0505103 0.0874863i 0.00788838 0.0136631i −0.862054 0.506816i \(-0.830822\pi\)
0.869943 + 0.493153i \(0.164156\pi\)
\(42\) 0 0
\(43\) −3.89898 6.75323i −0.594589 1.02986i −0.993605 0.112914i \(-0.963982\pi\)
0.399016 0.916944i \(-0.369352\pi\)
\(44\) 0 0
\(45\) 1.00000 2.82843i 0.149071 0.421637i
\(46\) 0 0
\(47\) −2.27526 3.94086i −0.331880 0.574833i 0.651000 0.759077i \(-0.274350\pi\)
−0.982880 + 0.184244i \(0.941016\pi\)
\(48\) 0 0
\(49\) 2.44949 4.24264i 0.349927 0.606092i
\(50\) 0 0
\(51\) 3.44949 0.317837i 0.483025 0.0445061i
\(52\) 0 0
\(53\) −11.7980 −1.62057 −0.810287 0.586033i \(-0.800689\pi\)
−0.810287 + 0.586033i \(0.800689\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.00000 0.460702i 0.662266 0.0610214i
\(58\) 0 0
\(59\) −5.44949 + 9.43879i −0.709463 + 1.22883i 0.255593 + 0.966784i \(0.417729\pi\)
−0.965057 + 0.262042i \(0.915604\pi\)
\(60\) 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
\(63\) −2.82577 3.30518i −0.356013 0.416414i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.62372 9.74058i 0.687047 1.19000i −0.285741 0.958307i \(-0.592240\pi\)
0.972789 0.231694i \(-0.0744268\pi\)
\(68\) 0 0
\(69\) 1.84847 4.01229i 0.222530 0.483023i
\(70\) 0 0
\(71\) 9.79796 1.16280 0.581402 0.813617i \(-0.302504\pi\)
0.581402 + 0.813617i \(0.302504\pi\)
\(72\) 0 0
\(73\) −5.79796 −0.678600 −0.339300 0.940678i \(-0.610190\pi\)
−0.339300 + 0.940678i \(0.610190\pi\)
\(74\) 0 0
\(75\) 1.00000 + 1.41421i 0.115470 + 0.163299i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.44949 + 2.51059i 0.163080 + 0.282463i 0.935972 0.352075i \(-0.114524\pi\)
−0.772892 + 0.634538i \(0.781190\pi\)
\(80\) 0 0
\(81\) 8.39898 3.23375i 0.933220 0.359306i
\(82\) 0 0
\(83\) −0.275255 0.476756i −0.0302132 0.0523308i 0.850523 0.525937i \(-0.176285\pi\)
−0.880737 + 0.473606i \(0.842952\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 0 0
\(87\) 7.89898 + 11.1708i 0.846859 + 1.19764i
\(88\) 0 0
\(89\) −16.7980 −1.78058 −0.890290 0.455394i \(-0.849498\pi\)
−0.890290 + 0.455394i \(0.849498\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.89898 + 17.1455i −0.819086 + 1.77791i
\(94\) 0 0
\(95\) −1.44949 + 2.51059i −0.148715 + 0.257581i
\(96\) 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 0.230351i 0.243975 0.0224799i
\(106\) 0 0
\(107\) −2.34847 −0.227035 −0.113518 0.993536i \(-0.536212\pi\)
−0.113518 + 0.993536i \(0.536212\pi\)
\(108\) 0 0
\(109\) 8.79796 0.842692 0.421346 0.906900i \(-0.361558\pi\)
0.421346 + 0.906900i \(0.361558\pi\)
\(110\) 0 0
\(111\) 10.3485 0.953512i 0.982233 0.0905033i
\(112\) 0 0
\(113\) −4.89898 + 8.48528i −0.460857 + 0.798228i −0.999004 0.0446231i \(-0.985791\pi\)
0.538147 + 0.842851i \(0.319125\pi\)
\(114\) 0 0
\(115\) 1.27526 + 2.20881i 0.118918 + 0.205972i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.44949 + 2.51059i 0.132875 + 0.230145i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0 0
\(123\) −0.0732141 + 0.158919i −0.00660149 + 0.0143292i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.3485 1.27322 0.636610 0.771186i \(-0.280336\pi\)
0.636610 + 0.771186i \(0.280336\pi\)
\(128\) 0 0
\(129\) 7.79796 + 11.0280i 0.686572 + 0.970959i
\(130\) 0 0
\(131\) −3.44949 + 5.97469i −0.301383 + 0.522011i −0.976450 0.215746i \(-0.930782\pi\)
0.675066 + 0.737757i \(0.264115\pi\)
\(132\) 0 0
\(133\) 2.10102 + 3.63907i 0.182182 + 0.315548i
\(134\) 0 0
\(135\) −1.27526 + 5.03723i −0.109756 + 0.433536i
\(136\) 0 0
\(137\) 9.79796 + 16.9706i 0.837096 + 1.44989i 0.892312 + 0.451419i \(0.149082\pi\)
−0.0552162 + 0.998474i \(0.517585\pi\)
\(138\) 0 0
\(139\) −9.79796 + 16.9706i −0.831052 + 1.43942i 0.0661527 + 0.997810i \(0.478928\pi\)
−0.897205 + 0.441615i \(0.854406\pi\)
\(140\) 0 0
\(141\) 4.55051 + 6.43539i 0.383222 + 0.541958i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −7.89898 −0.655975
\(146\) 0 0
\(147\) −3.55051 + 7.70674i −0.292841 + 0.635641i
\(148\) 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
\(153\) −5.89898 + 1.09638i −0.476904 + 0.0886368i
\(154\) 0 0
\(155\) −5.44949 9.43879i −0.437714 0.758142i
\(156\) 0 0
\(157\) 2.10102 3.63907i 0.167680 0.290430i −0.769924 0.638136i \(-0.779706\pi\)
0.937604 + 0.347706i \(0.113039\pi\)
\(158\) 0 0
\(159\) 20.3485 1.87492i 1.61374 0.148690i
\(160\) 0 0
\(161\) 3.69694 0.291360
\(162\) 0 0
\(163\) −11.7980 −0.924087 −0.462044 0.886857i \(-0.652884\pi\)
−0.462044 + 0.886857i \(0.652884\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.17423 + 5.49794i −0.245630 + 0.425443i −0.962308 0.271960i \(-0.912328\pi\)
0.716679 + 0.697403i \(0.245661\pi\)
\(168\) 0 0
\(169\) 6.50000 + 11.2583i 0.500000 + 0.866025i
\(170\) 0 0
\(171\) −8.55051 + 1.58919i −0.653874 + 0.121528i
\(172\) 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
\(175\) −0.724745 + 1.25529i −0.0547856 + 0.0948914i
\(176\) 0 0
\(177\) 7.89898 17.1455i 0.593724 1.28874i
\(178\) 0 0
\(179\) −5.79796 −0.433360 −0.216680 0.976243i \(-0.569523\pi\)
−0.216680 + 0.976243i \(0.569523\pi\)
\(180\) 0 0
\(181\) 19.6969 1.46406 0.732031 0.681271i \(-0.238573\pi\)
0.732031 + 0.681271i \(0.238573\pi\)
\(182\) 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
\(189\) 5.39898 + 5.25153i 0.392718 + 0.381993i
\(190\) 0 0
\(191\) −2.55051 4.41761i −0.184548 0.319647i 0.758876 0.651235i \(-0.225749\pi\)
−0.943424 + 0.331588i \(0.892416\pi\)
\(192\) 0 0
\(193\) 10.8990 18.8776i 0.784526 1.35884i −0.144756 0.989467i \(-0.546240\pi\)
0.929282 0.369371i \(-0.120427\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.5959 1.68114 0.840570 0.541703i \(-0.182220\pi\)
0.840570 + 0.541703i \(0.182220\pi\)
\(198\) 0 0
\(199\) −13.1010 −0.928707 −0.464353 0.885650i \(-0.653713\pi\)
−0.464353 + 0.885650i \(0.653713\pi\)
\(200\) 0 0
\(201\) −8.15153 + 17.6937i −0.574965 + 1.24802i
\(202\) 0 0
\(203\) −5.72474 + 9.91555i −0.401798 + 0.695935i
\(204\) 0 0
\(205\) −0.0505103 0.0874863i −0.00352779 0.00611031i
\(206\) 0 0
\(207\) −2.55051 + 7.21393i −0.177273 + 0.501403i
\(208\) 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
\(213\) −16.8990 + 1.55708i −1.15790 + 0.106689i
\(214\) 0 0
\(215\) −7.79796 −0.531816
\(216\) 0 0
\(217\) −15.7980 −1.07244
\(218\) 0 0
\(219\) 10.0000 0.921404i 0.675737 0.0622627i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.275255 + 0.476756i 0.0184324 + 0.0319259i 0.875094 0.483952i \(-0.160799\pi\)
−0.856662 + 0.515878i \(0.827466\pi\)
\(224\) 0 0
\(225\) −1.94949 2.28024i −0.129966 0.152016i
\(226\) 0 0
\(227\) −13.8990 24.0737i −0.922508 1.59783i −0.795521 0.605926i \(-0.792803\pi\)
−0.126986 0.991904i \(-0.540530\pi\)
\(228\) 0 0
\(229\) 6.94949 12.0369i 0.459235 0.795419i −0.539686 0.841867i \(-0.681457\pi\)
0.998921 + 0.0464480i \(0.0147902\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.202041 −0.0132361 −0.00661807 0.999978i \(-0.502107\pi\)
−0.00661807 + 0.999978i \(0.502107\pi\)
\(234\) 0 0
\(235\) −4.55051 −0.296843
\(236\) 0 0
\(237\) −2.89898 4.09978i −0.188309 0.266309i
\(238\) 0 0
\(239\) 10.8990 18.8776i 0.704996 1.22109i −0.261696 0.965150i \(-0.584282\pi\)
0.966693 0.255939i \(-0.0823847\pi\)
\(240\) 0 0
\(241\) −12.8485 22.2542i −0.827643 1.43352i −0.899883 0.436132i \(-0.856348\pi\)
0.0722401 0.997387i \(-0.476985\pi\)
\(242\) 0 0
\(243\) −13.9722 + 6.91215i −0.896317 + 0.443415i
\(244\) 0 0
\(245\) −2.44949 4.24264i −0.156492 0.271052i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.550510 + 0.778539i 0.0348872 + 0.0493379i
\(250\) 0 0
\(251\) 6.89898 0.435460 0.217730 0.976009i \(-0.430135\pi\)
0.217730 + 0.976009i \(0.430135\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.44949 3.14626i 0.0907706 0.197027i
\(256\) 0 0
\(257\) −4.10102 + 7.10318i −0.255815 + 0.443084i −0.965116 0.261821i \(-0.915677\pi\)
0.709302 + 0.704905i \(0.249010\pi\)
\(258\) 0 0
\(259\) 4.34847 + 7.53177i 0.270201 + 0.468001i
\(260\) 0 0
\(261\) −15.3990 18.0116i −0.953173 1.11489i
\(262\) 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
\(265\) −5.89898 + 10.2173i −0.362371 + 0.627646i
\(266\) 0 0
\(267\) 28.9722 2.66951i 1.77307 0.163371i
\(268\) 0 0
\(269\) −16.5959 −1.01187 −0.505935 0.862571i \(-0.668853\pi\)
−0.505935 + 0.862571i \(0.668853\pi\)
\(270\) 0 0
\(271\) −21.1010 −1.28180 −0.640898 0.767626i \(-0.721438\pi\)
−0.640898 + 0.767626i \(0.721438\pi\)
\(272\) 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
\(279\) 10.8990 30.8270i 0.652505 1.84556i
\(280\) 0 0
\(281\) 8.94949 + 15.5010i 0.533882 + 0.924710i 0.999217 + 0.0395756i \(0.0126006\pi\)
−0.465335 + 0.885135i \(0.654066\pi\)
\(282\) 0 0
\(283\) −9.17423 + 15.8902i −0.545352 + 0.944577i 0.453233 + 0.891392i \(0.350271\pi\)
−0.998585 + 0.0531847i \(0.983063\pi\)
\(284\) 0 0
\(285\) 2.10102 4.56048i 0.124454 0.270139i
\(286\) 0 0
\(287\) −0.146428 −0.00864338
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 2.00000 + 2.82843i 0.117242 + 0.165805i
\(292\) 0 0
\(293\) 10.7980 18.7026i 0.630823 1.09262i −0.356560 0.934272i \(-0.616051\pi\)
0.987384 0.158346i \(-0.0506161\pi\)
\(294\) 0 0
\(295\) 5.44949 + 9.43879i 0.317282 + 0.549548i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −5.65153 + 9.78874i −0.325749 + 0.564214i
\(302\) 0 0
\(303\) −2.00000 2.82843i −0.114897 0.162489i
\(304\) 0 0
\(305\) 3.00000 0.171780
\(306\) 0 0
\(307\) 29.2474 1.66924 0.834620 0.550826i \(-0.185687\pi\)
0.834620 + 0.550826i \(0.185687\pi\)
\(308\) 0 0
\(309\) −7.24745 + 15.7313i −0.412293 + 0.894924i
\(310\) 0 0
\(311\) 1.44949 2.51059i 0.0821930 0.142362i −0.821999 0.569489i \(-0.807141\pi\)
0.904192 + 0.427127i \(0.140474\pi\)
\(312\) 0 0
\(313\) −11.7980 20.4347i −0.666860 1.15504i −0.978777 0.204926i \(-0.934305\pi\)
0.311917 0.950109i \(-0.399029\pi\)
\(314\) 0 0
\(315\) −4.27526 + 0.794593i −0.240883 + 0.0447703i
\(316\) 0 0
\(317\) 3.10102 + 5.37113i 0.174171 + 0.301672i 0.939874 0.341522i \(-0.110942\pi\)
−0.765703 + 0.643194i \(0.777609\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 4.05051 0.373215i 0.226077 0.0208309i
\(322\) 0 0
\(323\) 5.79796 0.322607
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −15.1742 + 1.39816i −0.839137 + 0.0773184i
\(328\) 0 0
\(329\) −3.29796 + 5.71223i −0.181822 + 0.314926i
\(330\) 0 0
\(331\) 1.44949 + 2.51059i 0.0796712 + 0.137994i 0.903108 0.429413i \(-0.141280\pi\)
−0.823437 + 0.567408i \(0.807946\pi\)
\(332\) 0 0
\(333\) −17.6969 + 3.28913i −0.969786 + 0.180243i
\(334\) 0 0
\(335\) −5.62372 9.74058i −0.307257 0.532185i
\(336\) 0 0
\(337\) 5.10102 8.83523i 0.277870 0.481285i −0.692985 0.720952i \(-0.743705\pi\)
0.970855 + 0.239667i \(0.0770381\pi\)
\(338\) 0 0
\(339\) 7.10102 15.4135i 0.385674 0.837146i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −17.2474 −0.931275
\(344\) 0 0
\(345\) −2.55051 3.60697i −0.137315 0.194193i
\(346\) 0 0
\(347\) 6.79796 11.7744i 0.364934 0.632083i −0.623832 0.781559i \(-0.714425\pi\)
0.988765 + 0.149475i \(0.0477584\pi\)
\(348\) 0 0
\(349\) 15.8485 + 27.4504i 0.848349 + 1.46938i 0.882681 + 0.469973i \(0.155736\pi\)
−0.0343315 + 0.999410i \(0.510930\pi\)
\(350\) 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
\(357\) −2.89898 4.09978i −0.153430 0.216983i
\(358\) 0 0
\(359\) 0.696938 0.0367830 0.0183915 0.999831i \(-0.494145\pi\)
0.0183915 + 0.999831i \(0.494145\pi\)
\(360\) 0 0
\(361\) −10.5959 −0.557680
\(362\) 0 0
\(363\) −7.97219 + 17.3045i −0.418432 + 0.908248i
\(364\) 0 0
\(365\) −2.89898 + 5.02118i −0.151740 + 0.262821i
\(366\) 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
\(369\) 0.101021 0.285729i 0.00525892 0.0148745i
\(370\) 0 0
\(371\) 8.55051 + 14.8099i 0.443920 + 0.768893i
\(372\) 0 0
\(373\) 8.79796 15.2385i 0.455541 0.789020i −0.543178 0.839618i \(-0.682779\pi\)
0.998719 + 0.0505973i \(0.0161125\pi\)
\(374\) 0 0
\(375\) 1.72474 0.158919i 0.0890654 0.00820652i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −17.1010 −0.878420 −0.439210 0.898384i \(-0.644742\pi\)
−0.439210 + 0.898384i \(0.644742\pi\)
\(380\) 0 0
\(381\) −24.7474 + 2.28024i −1.26785 + 0.116820i
\(382\) 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
\(387\) −15.2020 17.7812i −0.772763 0.903870i
\(388\) 0 0
\(389\) −11.2980 19.5686i −0.572829 0.992169i −0.996274 0.0862473i \(-0.972512\pi\)
0.423444 0.905922i \(-0.360821\pi\)
\(390\) 0 0
\(391\) 2.55051 4.41761i 0.128985 0.223408i
\(392\) 0 0
\(393\) 5.00000 10.8530i 0.252217 0.547462i
\(394\) 0 0
\(395\) 2.89898 0.145863
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −4.20204 5.94258i −0.210365 0.297501i
\(400\) 0 0
\(401\) 6.79796 11.7744i 0.339474 0.587986i −0.644860 0.764301i \(-0.723084\pi\)
0.984334 + 0.176315i \(0.0564177\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.39898 8.89060i 0.0695158 0.441778i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −14.7980 + 25.6308i −0.731712 + 1.26736i 0.224439 + 0.974488i \(0.427945\pi\)
−0.956151 + 0.292874i \(0.905388\pi\)
\(410\) 0 0
\(411\) −19.5959 27.7128i −0.966595 1.36697i
\(412\) 0 0
\(413\) 15.7980 0.777367
\(414\) 0 0
\(415\) −0.550510 −0.0270235
\(416\) 0 0
\(417\) 14.2020 30.8270i 0.695477 1.50960i
\(418\) 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
\(421\) 6.79796 + 11.7744i 0.331312 + 0.573850i 0.982769 0.184836i \(-0.0591753\pi\)
−0.651457 + 0.758685i \(0.725842\pi\)
\(422\) 0 0
\(423\) −8.87117 10.3763i −0.431331 0.504511i
\(424\) 0 0
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 2.17423 3.76588i 0.105219 0.182244i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.10102 −0.245708 −0.122854 0.992425i \(-0.539205\pi\)
−0.122854 + 0.992425i \(0.539205\pi\)
\(432\) 0 0
\(433\) 7.79796 0.374746 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(434\) 0 0
\(435\) 13.6237 1.25529i 0.653208 0.0601868i
\(436\) 0 0
\(437\) 3.69694 6.40329i 0.176849 0.306311i
\(438\) 0 0
\(439\) 0.898979 + 1.55708i 0.0429059 + 0.0743153i 0.886681 0.462382i \(-0.153005\pi\)
−0.843775 + 0.536697i \(0.819672\pi\)
\(440\) 0 0
\(441\) 4.89898 13.8564i 0.233285 0.659829i
\(442\) 0 0
\(443\) 13.0732 + 22.6435i 0.621127 + 1.07582i 0.989276 + 0.146057i \(0.0466583\pi\)
−0.368149 + 0.929767i \(0.620008\pi\)
\(444\) 0 0
\(445\) −8.39898 + 14.5475i −0.398150 + 0.689616i
\(446\) 0 0
\(447\) −15.2196 + 33.0358i −0.719864 + 1.56254i
\(448\) 0 0
\(449\) −17.5959 −0.830403 −0.415201 0.909730i \(-0.636289\pi\)
−0.415201 + 0.909730i \(0.636289\pi\)
\(450\) 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
\(457\) 10.7980 + 18.7026i 0.505107 + 0.874871i 0.999983 + 0.00590738i \(0.00188039\pi\)
−0.494875 + 0.868964i \(0.664786\pi\)
\(458\) 0 0
\(459\) 10.0000 2.82843i 0.466760 0.132020i
\(460\) 0 0
\(461\) −10.9495 18.9651i −0.509969 0.883291i −0.999933 0.0115492i \(-0.996324\pi\)
0.489965 0.871742i \(-0.337010\pi\)
\(462\) 0 0
\(463\) 15.8990 27.5378i 0.738888 1.27979i −0.214108 0.976810i \(-0.568684\pi\)
0.952996 0.302982i \(-0.0979822\pi\)
\(464\) 0 0
\(465\) 10.8990 + 15.4135i 0.505428 + 0.714783i
\(466\) 0 0
\(467\) 11.7980 0.545944 0.272972 0.962022i \(-0.411993\pi\)
0.272972 + 0.962022i \(0.411993\pi\)
\(468\) 0 0
\(469\) −16.3031 −0.752805
\(470\) 0 0
\(471\) −3.04541 + 6.61037i −0.140325 + 0.304590i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.44949 + 2.51059i 0.0665072 + 0.115194i
\(476\) 0 0
\(477\) −34.7980 + 6.46750i −1.59329 + 0.296127i
\(478\) 0 0
\(479\) −9.24745 16.0171i −0.422527 0.731838i 0.573659 0.819094i \(-0.305523\pi\)
−0.996186 + 0.0872564i \(0.972190\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −6.37628 + 0.587512i −0.290131 + 0.0267327i
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −25.5959 −1.15986 −0.579931 0.814666i \(-0.696920\pi\)
−0.579931 + 0.814666i \(0.696920\pi\)
\(488\) 0 0
\(489\) 20.3485 1.87492i 0.920190 0.0847866i
\(490\) 0 0
\(491\) 2.89898 5.02118i 0.130829 0.226603i −0.793167 0.609004i \(-0.791569\pi\)
0.923996 + 0.382401i \(0.124903\pi\)
\(492\) 0 0
\(493\) 7.89898 + 13.6814i 0.355752 + 0.616181i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.10102 12.2993i −0.318524 0.551700i
\(498\) 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
\(501\) 4.60102 9.98698i 0.205558 0.446185i
\(502\) 0 0
\(503\) 19.0454 0.849193 0.424596 0.905383i \(-0.360416\pi\)
0.424596 + 0.905383i \(0.360416\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) −13.0000 18.3848i −0.577350 0.816497i
\(508\) 0 0
\(509\) 6.94949 12.0369i 0.308031 0.533525i −0.669901 0.742451i \(-0.733663\pi\)
0.977931 + 0.208926i \(0.0669967\pi\)
\(510\) 0 0
\(511\) 4.20204 + 7.27815i 0.185887 + 0.321966i
\(512\) 0 0
\(513\) 14.4949 4.09978i 0.639965 0.181010i
\(514\) 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
\(521\) 28.7980 1.26166 0.630831 0.775920i \(-0.282714\pi\)
0.630831 + 0.775920i \(0.282714\pi\)
\(522\) 0 0
\(523\) 19.6515 0.859301 0.429651 0.902995i \(-0.358637\pi\)
0.429651 + 0.902995i \(0.358637\pi\)
\(524\) 0 0
\(525\) 1.05051 2.28024i 0.0458480 0.0995178i
\(526\) 0 0
\(527\) −10.8990 + 18.8776i −0.474767 + 0.822321i
\(528\) 0 0
\(529\) 8.24745 + 14.2850i 0.358585 + 0.621087i
\(530\) 0 0
\(531\) −10.8990 + 30.8270i −0.472975 + 1.33778i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.17423 + 2.03383i −0.0507666 + 0.0879303i
\(536\) 0 0
\(537\) 10.0000 0.921404i 0.431532 0.0397615i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 21.8990 0.941511 0.470755 0.882264i \(-0.343981\pi\)
0.470755 + 0.882264i \(0.343981\pi\)
\(542\) 0 0
\(543\) −33.9722 + 3.13021i −1.45789 + 0.134330i
\(544\) 0 0
\(545\) 4.39898 7.61926i 0.188432 0.326373i
\(546\) 0 0
\(547\) −20.6237 35.7213i −0.881807 1.52733i −0.849330 0.527862i \(-0.822994\pi\)
−0.0324764 0.999473i \(-0.510339\pi\)
\(548\) 0 0
\(549\) 5.84847 + 6.84072i 0.249607 + 0.291955i
\(550\) 0 0
\(551\) 11.4495 + 19.8311i 0.487765 + 0.844833i
\(552\) 0 0
\(553\) 2.10102 3.63907i 0.0893445 0.154749i
\(554\) 0 0
\(555\) 4.34847 9.43879i 0.184582 0.400654i
\(556\) 0 0
\(557\) 24.2020 1.02547 0.512737 0.858546i \(-0.328632\pi\)
0.512737 + 0.858546i \(0.328632\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.17423 3.76588i 0.0916331 0.158713i −0.816565 0.577253i \(-0.804125\pi\)
0.908198 + 0.418540i \(0.137458\pi\)
\(564\) 0 0
\(565\) 4.89898 + 8.48528i 0.206102 + 0.356978i
\(566\) 0 0
\(567\) −10.1464 8.19955i −0.426110 0.344349i
\(568\) 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
\(571\) 3.10102 5.37113i 0.129774 0.224775i −0.793815 0.608159i \(-0.791908\pi\)
0.923589 + 0.383385i \(0.125242\pi\)
\(572\) 0 0
\(573\) 5.10102 + 7.21393i 0.213098 + 0.301366i
\(574\) 0 0
\(575\) 2.55051 0.106364
\(576\) 0 0
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 0 0
\(579\) −15.7980 + 34.2911i −0.656541 + 1.42509i
\(580\) 0 0
\(581\) −0.398979 + 0.691053i −0.0165525 + 0.0286697i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.1742 + 19.3543i 0.461210 + 0.798839i 0.999022 0.0442259i \(-0.0140821\pi\)
−0.537812 + 0.843065i \(0.680749\pi\)
\(588\) 0 0
\(589\) −15.7980 + 27.3629i −0.650944 + 1.12747i
\(590\) 0 0
\(591\) −40.6969 + 3.74983i −1.67405 + 0.154247i
\(592\) 0 0
\(593\) 27.3939 1.12493 0.562466 0.826821i \(-0.309853\pi\)
0.562466 + 0.826821i \(0.309853\pi\)
\(594\) 0 0
\(595\) 2.89898 0.118847
\(596\) 0 0
\(597\) 22.5959 2.08200i 0.924789 0.0852104i
\(598\) 0 0
\(599\) 2.34847 4.06767i 0.0959559 0.166200i −0.814051 0.580793i \(-0.802743\pi\)
0.910007 + 0.414593i \(0.136076\pi\)
\(600\) 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
\(603\) 11.2474 31.8126i 0.458032 1.29551i
\(604\) 0 0
\(605\) −5.50000 9.52628i −0.223607 0.387298i
\(606\) 0 0
\(607\) −16.0732 + 27.8396i −0.652392 + 1.12998i 0.330149 + 0.943929i \(0.392901\pi\)
−0.982541 + 0.186047i \(0.940432\pi\)
\(608\) 0 0
\(609\) 8.29796 18.0116i 0.336250 0.729865i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.59592 0.387575 0.193788 0.981043i \(-0.437923\pi\)
0.193788 + 0.981043i \(0.437923\pi\)
\(614\) 0 0
\(615\) 0.101021 + 0.142865i 0.00407354 + 0.00576086i
\(616\) 0 0
\(617\) −21.5959 + 37.4052i −0.869419 + 1.50588i −0.00682740 + 0.999977i \(0.502173\pi\)
−0.862592 + 0.505901i \(0.831160\pi\)
\(618\) 0 0
\(619\) 2.34847 + 4.06767i 0.0943929 + 0.163493i 0.909355 0.416021i \(-0.136576\pi\)
−0.814962 + 0.579514i \(0.803242\pi\)
\(620\) 0 0
\(621\) 3.25255 12.8475i 0.130520 0.515553i
\(622\) 0 0
\(623\) 12.1742 + 21.0864i 0.487750 + 0.844808i
\(624\) 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
\(631\) −23.5959 −0.939339 −0.469669 0.882842i \(-0.655627\pi\)
−0.469669 + 0.882842i \(0.655627\pi\)
\(632\) 0 0
\(633\) −8.69694 + 18.8776i −0.345672 + 0.750317i
\(634\) 0 0
\(635\) 7.17423 12.4261i 0.284701 0.493116i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 28.8990 5.37113i 1.14323 0.212478i
\(640\) 0 0
\(641\) 2.05051 + 3.55159i 0.0809903 + 0.140279i 0.903676 0.428218i \(-0.140858\pi\)
−0.822685 + 0.568497i \(0.807525\pi\)
\(642\) 0 0
\(643\) 7.07321 12.2512i 0.278940 0.483139i −0.692181 0.721724i \(-0.743350\pi\)
0.971122 + 0.238585i \(0.0766835\pi\)
\(644\) 0 0
\(645\) 13.4495 1.23924i 0.529573 0.0487951i
\(646\) 0 0
\(647\) −11.4495 −0.450126 −0.225063 0.974344i \(-0.572259\pi\)
−0.225063 + 0.974344i \(0.572259\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 27.2474 2.51059i 1.06791 0.0983978i
\(652\) 0 0
\(653\) −4.10102 + 7.10318i −0.160485 + 0.277969i −0.935043 0.354535i \(-0.884639\pi\)
0.774558 + 0.632503i \(0.217973\pi\)
\(654\) 0 0
\(655\) 3.44949 + 5.97469i 0.134783 + 0.233451i
\(656\) 0 0
\(657\) −17.1010 + 3.17837i −0.667174 + 0.124000i
\(658\) 0 0
\(659\) 14.8990 + 25.8058i 0.580382 + 1.00525i 0.995434 + 0.0954532i \(0.0304300\pi\)
−0.415052 + 0.909798i \(0.636237\pi\)
\(660\) 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
\(665\) 4.20204 0.162948
\(666\) 0 0
\(667\) 20.1464 0.780073
\(668\) 0 0
\(669\) −0.550510 0.778539i −0.0212840 0.0301001i
\(670\) 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
\(675\) 3.72474 + 3.62302i 0.143365 + 0.139450i
\(676\) 0 0
\(677\) −16.8990 29.2699i −0.649481 1.12493i −0.983247 0.182278i \(-0.941653\pi\)
0.333767 0.942656i \(-0.391680\pi\)
\(678\) 0 0
\(679\) −1.44949 + 2.51059i −0.0556263 + 0.0963476i
\(680\) 0 0
\(681\) 27.7980 + 39.3123i 1.06522 + 1.50645i
\(682\) 0 0
\(683\) 35.3939 1.35431 0.677155 0.735841i \(-0.263213\pi\)
0.677155 + 0.735841i \(0.263213\pi\)
\(684\) 0 0
\(685\) 19.5959 0.748722
\(686\) 0 0
\(687\) −10.0732 + 21.8649i −0.384317 + 0.834199i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 14.5505 + 25.2022i 0.553527 + 0.958738i 0.998016 + 0.0629534i \(0.0200520\pi\)
−0.444489 + 0.895784i \(0.646615\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.79796 + 16.9706i 0.371658 + 0.643730i
\(696\) 0 0
\(697\) −0.101021 + 0.174973i −0.00382642 + 0.00662756i
\(698\) 0 0
\(699\) 0.348469 0.0321081i 0.0131803 0.00121444i
\(700\) 0 0
\(701\) −28.3939 −1.07242 −0.536211 0.844084i \(-0.680145\pi\)
−0.536211 + 0.844084i \(0.680145\pi\)
\(702\) 0 0
\(703\) 17.3939 0.656022
\(704\) 0 0
\(705\) 7.84847 0.723161i 0.295590 0.0272358i
\(706\) 0 0
\(707\) 1.44949 2.51059i 0.0545137 0.0944205i
\(708\) 0 0
\(709\) 9.84847 + 17.0580i 0.369867 + 0.640628i 0.989544 0.144228i \(-0.0460699\pi\)
−0.619677 + 0.784857i \(0.712737\pi\)
\(710\) 0 0
\(711\) 5.65153 + 6.61037i 0.211949 + 0.247908i
\(712\) 0 0
\(713\) 13.8990 + 24.0737i 0.520521 + 0.901569i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −15.7980 + 34.2911i −0.589986 + 1.28062i
\(718\) 0 0
\(719\) −40.2929 −1.50267 −0.751335 0.659921i \(-0.770590\pi\)
−0.751335 + 0.659921i \(0.770590\pi\)
\(720\) 0 0
\(721\) −14.4949 −0.539818
\(722\) 0 0
\(723\) 25.6969 + 36.3410i 0.955679 + 1.35153i
\(724\) 0 0
\(725\) −3.94949 + 6.84072i −0.146680 + 0.254058i
\(726\) 0 0
\(727\) −3.37628 5.84788i −0.125219 0.216886i 0.796599 0.604508i \(-0.206630\pi\)
−0.921819 + 0.387622i \(0.873297\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 7.79796 + 13.5065i 0.288418 + 0.499555i
\(732\) 0 0
\(733\) −4.79796 + 8.31031i −0.177217 + 0.306948i −0.940926 0.338612i \(-0.890043\pi\)
0.763710 + 0.645560i \(0.223376\pi\)
\(734\) 0 0
\(735\) 4.89898 + 6.92820i 0.180702 + 0.255551i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 42.8990 1.57806 0.789032 0.614352i \(-0.210582\pi\)
0.789032 + 0.614352i \(0.210582\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.5227 32.0823i 0.679532 1.17698i −0.295590 0.955315i \(-0.595516\pi\)
0.975122 0.221669i \(-0.0711505\pi\)
\(744\) 0 0
\(745\) −10.5000 18.1865i −0.384690 0.666303i
\(746\) 0 0
\(747\) −1.07321 1.25529i −0.0392669 0.0459288i
\(748\) 0 0
\(749\) 1.70204 + 2.94802i 0.0621912 + 0.107718i
\(750\) 0 0
\(751\) 22.8990 39.6622i 0.835596 1.44729i −0.0579489 0.998320i \(-0.518456\pi\)
0.893545 0.448975i \(-0.148211\pi\)
\(752\) 0 0
\(753\) −11.8990 + 1.09638i −0.433623 + 0.0399542i
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) −7.59592 −0.276078 −0.138039 0.990427i \(-0.544080\pi\)
−0.138039 + 0.990427i \(0.544080\pi\)
\(758\) 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
\(763\) −6.37628 11.0440i −0.230837 0.399821i
\(764\) 0 0
\(765\) −2.00000 + 5.65685i −0.0723102 + 0.204524i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 12.3990 21.4757i 0.447119 0.774432i −0.551078 0.834453i \(-0.685784\pi\)
0.998197 + 0.0600212i \(0.0191168\pi\)
\(770\) 0 0
\(771\) 5.94439 12.9029i 0.214082 0.464686i
\(772\) 0 0
\(773\) 25.7980 0.927888 0.463944 0.885865i \(-0.346434\pi\)
0.463944 + 0.885865i \(0.346434\pi\)
\(774\) 0 0
\(775\) −10.8990 −0.391503
\(776\) 0 0
\(777\) −8.69694 12.2993i −0.312001 0.441236i
\(778\) 0 0
\(779\) −0.146428 + 0.253621i −0.00524633 + 0.00908692i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 29.4217 + 28.6182i 1.05145 + 1.02273i
\(784\) 0 0
\(785\) −2.10102 3.63907i −0.0749886 0.129884i
\(786\) 0 0
\(787\) −5.20204 + 9.01020i −0.185433 + 0.321179i −0.943722 0.330739i \(-0.892702\pi\)
0.758290 + 0.651918i \(0.226035\pi\)
\(788\) 0 0
\(789\) −18.0000 25.4558i −0.640817 0.906252i
\(790\) 0 0
\(791\) 14.2020 0.504966
\(792\) 0