Properties

Label 380.2.u.b.321.2
Level $380$
Weight $2$
Character 380.321
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 321.2
Root \(0.443231 + 0.767698i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.b.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +O(q^{10})\) \(q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +(1.03842 - 1.79860i) q^{11} +(3.22410 - 2.70534i) q^{13} +(0.833001 + 0.303188i) q^{15} +(0.340401 - 1.93051i) q^{17} +(0.207532 - 4.35396i) q^{19} +(0.141750 - 0.803906i) q^{21} +(-0.570023 - 0.207471i) q^{23} +(0.766044 - 0.642788i) q^{25} +(-2.31109 + 4.00292i) q^{27} +(-1.31313 - 7.44714i) q^{29} +(1.07398 + 1.86019i) q^{31} +(-1.73001 + 0.629673i) q^{33} +(-0.705421 - 0.591918i) q^{35} +3.88044 q^{37} -3.73090 q^{39} +(-4.50081 - 3.77663i) q^{41} +(-0.638807 + 0.232507i) q^{43} +(1.10709 + 1.91754i) q^{45} +(1.88450 + 10.6875i) q^{47} +(3.07601 - 5.32780i) q^{49} +(-1.33117 + 1.11699i) q^{51} +(4.25090 + 1.54720i) q^{53} +(-0.360640 + 2.04529i) q^{55} +(-2.62184 + 2.83838i) q^{57} +(-1.02661 + 5.82217i) q^{59} +(6.55984 + 2.38759i) q^{61} +(1.56193 - 1.31062i) q^{63} +(-2.10438 + 3.64489i) q^{65} +(1.32744 + 7.52828i) q^{67} +(0.268866 + 0.465690i) q^{69} +(-10.8097 + 3.93442i) q^{71} +(2.42577 + 2.03547i) q^{73} -0.886461 q^{75} +1.91248 q^{77} +(-2.36217 - 1.98209i) q^{79} +(-2.39169 + 0.870503i) q^{81} +(-5.06043 - 8.76492i) q^{83} +(0.340401 + 1.93051i) q^{85} +(-3.35172 + 5.80535i) q^{87} +(2.60677 - 2.18734i) q^{89} +(3.64195 + 1.32556i) q^{91} +(0.330641 - 1.87516i) q^{93} +(1.29412 + 4.16236i) q^{95} +(-3.29871 + 18.7079i) q^{97} +(-4.32119 - 1.57279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\)

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
\(3\) −0.679069 0.569806i −0.392061 0.328978i 0.425355 0.905027i \(-0.360149\pi\)
−0.817415 + 0.576049i \(0.804594\pi\)
\(4\) 0 0
\(5\) −0.939693 + 0.342020i −0.420243 + 0.152956i
\(6\) 0 0
\(7\) 0.460431 + 0.797489i 0.174026 + 0.301423i 0.939824 0.341659i \(-0.110989\pi\)
−0.765797 + 0.643082i \(0.777656\pi\)
\(8\) 0 0
\(9\) −0.384489 2.18055i −0.128163 0.726849i
\(10\) 0 0
\(11\) 1.03842 1.79860i 0.313096 0.542298i −0.665935 0.746010i \(-0.731967\pi\)
0.979031 + 0.203712i \(0.0653005\pi\)
\(12\) 0 0
\(13\) 3.22410 2.70534i 0.894203 0.750326i −0.0748453 0.997195i \(-0.523846\pi\)
0.969049 + 0.246869i \(0.0794019\pi\)
\(14\) 0 0
\(15\) 0.833001 + 0.303188i 0.215080 + 0.0782827i
\(16\) 0 0
\(17\) 0.340401 1.93051i 0.0825594 0.468218i −0.915297 0.402779i \(-0.868044\pi\)
0.997857 0.0654386i \(-0.0208447\pi\)
\(18\) 0 0
\(19\) 0.207532 4.35396i 0.0476111 0.998866i
\(20\) 0 0
\(21\) 0.141750 0.803906i 0.0309325 0.175427i
\(22\) 0 0
\(23\) −0.570023 0.207471i −0.118858 0.0432608i 0.281906 0.959442i \(-0.409033\pi\)
−0.400764 + 0.916181i \(0.631255\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) −2.31109 + 4.00292i −0.444769 + 0.770362i
\(28\) 0 0
\(29\) −1.31313 7.44714i −0.243843 1.38290i −0.823165 0.567802i \(-0.807794\pi\)
0.579323 0.815098i \(-0.303317\pi\)
\(30\) 0 0
\(31\) 1.07398 + 1.86019i 0.192893 + 0.334100i 0.946208 0.323560i \(-0.104880\pi\)
−0.753315 + 0.657660i \(0.771546\pi\)
\(32\) 0 0
\(33\) −1.73001 + 0.629673i −0.301157 + 0.109612i
\(34\) 0 0
\(35\) −0.705421 0.591918i −0.119238 0.100052i
\(36\) 0 0
\(37\) 3.88044 0.637940 0.318970 0.947765i \(-0.396663\pi\)
0.318970 + 0.947765i \(0.396663\pi\)
\(38\) 0 0
\(39\) −3.73090 −0.597422
\(40\) 0 0
\(41\) −4.50081 3.77663i −0.702909 0.589811i 0.219691 0.975570i \(-0.429495\pi\)
−0.922600 + 0.385759i \(0.873940\pi\)
\(42\) 0 0
\(43\) −0.638807 + 0.232507i −0.0974171 + 0.0354569i −0.390269 0.920701i \(-0.627618\pi\)
0.292852 + 0.956158i \(0.405396\pi\)
\(44\) 0 0
\(45\) 1.10709 + 1.91754i 0.165036 + 0.285850i
\(46\) 0 0
\(47\) 1.88450 + 10.6875i 0.274883 + 1.55894i 0.739334 + 0.673339i \(0.235141\pi\)
−0.464451 + 0.885599i \(0.653748\pi\)
\(48\) 0 0
\(49\) 3.07601 5.32780i 0.439430 0.761114i
\(50\) 0 0
\(51\) −1.33117 + 1.11699i −0.186402 + 0.156410i
\(52\) 0 0
\(53\) 4.25090 + 1.54720i 0.583907 + 0.212525i 0.617047 0.786926i \(-0.288329\pi\)
−0.0331407 + 0.999451i \(0.510551\pi\)
\(54\) 0 0
\(55\) −0.360640 + 2.04529i −0.0486287 + 0.275787i
\(56\) 0 0
\(57\) −2.62184 + 2.83838i −0.347271 + 0.375953i
\(58\) 0 0
\(59\) −1.02661 + 5.82217i −0.133653 + 0.757982i 0.842136 + 0.539266i \(0.181298\pi\)
−0.975788 + 0.218716i \(0.929813\pi\)
\(60\) 0 0
\(61\) 6.55984 + 2.38759i 0.839902 + 0.305699i 0.725916 0.687783i \(-0.241416\pi\)
0.113986 + 0.993482i \(0.463638\pi\)
\(62\) 0 0
\(63\) 1.56193 1.31062i 0.196785 0.165122i
\(64\) 0 0
\(65\) −2.10438 + 3.64489i −0.261016 + 0.452093i
\(66\) 0 0
\(67\) 1.32744 + 7.52828i 0.162172 + 0.919726i 0.951932 + 0.306309i \(0.0990942\pi\)
−0.789760 + 0.613417i \(0.789795\pi\)
\(68\) 0 0
\(69\) 0.268866 + 0.465690i 0.0323677 + 0.0560625i
\(70\) 0 0
\(71\) −10.8097 + 3.93442i −1.28288 + 0.466930i −0.891383 0.453251i \(-0.850264\pi\)
−0.391495 + 0.920180i \(0.628042\pi\)
\(72\) 0 0
\(73\) 2.42577 + 2.03547i 0.283915 + 0.238233i 0.773612 0.633660i \(-0.218448\pi\)
−0.489697 + 0.871893i \(0.662892\pi\)
\(74\) 0 0
\(75\) −0.886461 −0.102360
\(76\) 0 0
\(77\) 1.91248 0.217948
\(78\) 0 0
\(79\) −2.36217 1.98209i −0.265765 0.223003i 0.500161 0.865933i \(-0.333274\pi\)
−0.765925 + 0.642930i \(0.777719\pi\)
\(80\) 0 0
\(81\) −2.39169 + 0.870503i −0.265743 + 0.0967225i
\(82\) 0 0
\(83\) −5.06043 8.76492i −0.555454 0.962075i −0.997868 0.0652636i \(-0.979211\pi\)
0.442414 0.896811i \(-0.354122\pi\)
\(84\) 0 0
\(85\) 0.340401 + 1.93051i 0.0369217 + 0.209393i
\(86\) 0 0
\(87\) −3.35172 + 5.80535i −0.359342 + 0.622399i
\(88\) 0 0
\(89\) 2.60677 2.18734i 0.276317 0.231858i −0.494089 0.869412i \(-0.664498\pi\)
0.770406 + 0.637554i \(0.220054\pi\)
\(90\) 0 0
\(91\) 3.64195 + 1.32556i 0.381780 + 0.138957i
\(92\) 0 0
\(93\) 0.330641 1.87516i 0.0342859 0.194445i
\(94\) 0 0
\(95\) 1.29412 + 4.16236i 0.132774 + 0.427049i
\(96\) 0 0
\(97\) −3.29871 + 18.7079i −0.334933 + 1.89950i 0.0929607 + 0.995670i \(0.470367\pi\)
−0.427894 + 0.903829i \(0.640744\pi\)
\(98\) 0 0
\(99\) −4.32119 1.57279i −0.434296 0.158071i
\(100\) 0 0
\(101\) 9.57643 8.03558i 0.952890 0.799570i −0.0268917 0.999638i \(-0.508561\pi\)
0.979782 + 0.200069i \(0.0641165\pi\)
\(102\) 0 0
\(103\) −0.347379 + 0.601678i −0.0342283 + 0.0592851i −0.882632 0.470064i \(-0.844231\pi\)
0.848404 + 0.529350i \(0.177564\pi\)
\(104\) 0 0
\(105\) 0.141750 + 0.803906i 0.0138334 + 0.0784532i
\(106\) 0 0
\(107\) 3.22893 + 5.59267i 0.312152 + 0.540664i 0.978828 0.204684i \(-0.0656167\pi\)
−0.666676 + 0.745348i \(0.732283\pi\)
\(108\) 0 0
\(109\) 1.58055 0.575274i 0.151389 0.0551013i −0.265214 0.964190i \(-0.585443\pi\)
0.416603 + 0.909088i \(0.363220\pi\)
\(110\) 0 0
\(111\) −2.63508 2.21110i −0.250111 0.209868i
\(112\) 0 0
\(113\) −17.7924 −1.67376 −0.836882 0.547383i \(-0.815624\pi\)
−0.836882 + 0.547383i \(0.815624\pi\)
\(114\) 0 0
\(115\) 0.606605 0.0565663
\(116\) 0 0
\(117\) −7.13875 5.99012i −0.659978 0.553787i
\(118\) 0 0
\(119\) 1.69629 0.617400i 0.155499 0.0565970i
\(120\) 0 0
\(121\) 3.34336 + 5.79087i 0.303942 + 0.526443i
\(122\) 0 0
\(123\) 0.904414 + 5.12919i 0.0815482 + 0.462483i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) 2.51384 2.10936i 0.223067 0.187176i −0.524404 0.851469i \(-0.675712\pi\)
0.747472 + 0.664294i \(0.231268\pi\)
\(128\) 0 0
\(129\) 0.566278 + 0.206108i 0.0498580 + 0.0181468i
\(130\) 0 0
\(131\) −1.19306 + 6.76619i −0.104238 + 0.591164i 0.887284 + 0.461224i \(0.152590\pi\)
−0.991522 + 0.129940i \(0.958521\pi\)
\(132\) 0 0
\(133\) 3.56779 1.83919i 0.309366 0.159478i
\(134\) 0 0
\(135\) 0.802632 4.55195i 0.0690796 0.391770i
\(136\) 0 0
\(137\) −3.71112 1.35074i −0.317063 0.115401i 0.178587 0.983924i \(-0.442848\pi\)
−0.495649 + 0.868523i \(0.665070\pi\)
\(138\) 0 0
\(139\) 13.2455 11.1143i 1.12347 0.942701i 0.124693 0.992195i \(-0.460205\pi\)
0.998774 + 0.0494941i \(0.0157609\pi\)
\(140\) 0 0
\(141\) 4.81012 8.33138i 0.405085 0.701628i
\(142\) 0 0
\(143\) −1.51785 8.60814i −0.126929 0.719849i
\(144\) 0 0
\(145\) 3.78101 + 6.54891i 0.313996 + 0.543857i
\(146\) 0 0
\(147\) −5.12464 + 1.86521i −0.422673 + 0.153840i
\(148\) 0 0
\(149\) −2.44856 2.05459i −0.200594 0.168319i 0.536957 0.843609i \(-0.319574\pi\)
−0.737551 + 0.675291i \(0.764018\pi\)
\(150\) 0 0
\(151\) −11.8963 −0.968110 −0.484055 0.875038i \(-0.660837\pi\)
−0.484055 + 0.875038i \(0.660837\pi\)
\(152\) 0 0
\(153\) −4.34045 −0.350905
\(154\) 0 0
\(155\) −1.64544 1.38068i −0.132165 0.110899i
\(156\) 0 0
\(157\) 18.4402 6.71170i 1.47169 0.535652i 0.523132 0.852252i \(-0.324763\pi\)
0.948559 + 0.316600i \(0.102541\pi\)
\(158\) 0 0
\(159\) −2.00505 3.47285i −0.159011 0.275415i
\(160\) 0 0
\(161\) −0.0969998 0.550113i −0.00764465 0.0433550i
\(162\) 0 0
\(163\) 9.37242 16.2335i 0.734105 1.27151i −0.221010 0.975271i \(-0.570935\pi\)
0.955115 0.296235i \(-0.0957312\pi\)
\(164\) 0 0
\(165\) 1.41032 1.18340i 0.109793 0.0921275i
\(166\) 0 0
\(167\) 4.73371 + 1.72293i 0.366306 + 0.133324i 0.518614 0.855009i \(-0.326448\pi\)
−0.152308 + 0.988333i \(0.548671\pi\)
\(168\) 0 0
\(169\) 0.818517 4.64204i 0.0629629 0.357080i
\(170\) 0 0
\(171\) −9.57380 + 1.22152i −0.732127 + 0.0934117i
\(172\) 0 0
\(173\) −2.60163 + 14.7546i −0.197799 + 1.12177i 0.710578 + 0.703618i \(0.248434\pi\)
−0.908377 + 0.418153i \(0.862678\pi\)
\(174\) 0 0
\(175\) 0.865327 + 0.314953i 0.0654125 + 0.0238082i
\(176\) 0 0
\(177\) 4.01464 3.36869i 0.301759 0.253206i
\(178\) 0 0
\(179\) 1.18715 2.05620i 0.0887316 0.153688i −0.818244 0.574872i \(-0.805052\pi\)
0.906975 + 0.421184i \(0.138385\pi\)
\(180\) 0 0
\(181\) −2.19843 12.4679i −0.163408 0.926732i −0.950691 0.310140i \(-0.899624\pi\)
0.787283 0.616592i \(-0.211487\pi\)
\(182\) 0 0
\(183\) −3.09412 5.35918i −0.228724 0.396162i
\(184\) 0 0
\(185\) −3.64642 + 1.32719i −0.268090 + 0.0975768i
\(186\) 0 0
\(187\) −3.11874 2.61693i −0.228065 0.191369i
\(188\) 0 0
\(189\) −4.25638 −0.309606
\(190\) 0 0
\(191\) 21.7998 1.57737 0.788687 0.614795i \(-0.210761\pi\)
0.788687 + 0.614795i \(0.210761\pi\)
\(192\) 0 0
\(193\) −4.94729 4.15127i −0.356114 0.298815i 0.447126 0.894471i \(-0.352448\pi\)
−0.803240 + 0.595656i \(0.796892\pi\)
\(194\) 0 0
\(195\) 3.50590 1.27604i 0.251063 0.0913794i
\(196\) 0 0
\(197\) −4.73539 8.20194i −0.337383 0.584364i 0.646557 0.762866i \(-0.276208\pi\)
−0.983940 + 0.178502i \(0.942875\pi\)
\(198\) 0 0
\(199\) 4.28855 + 24.3216i 0.304007 + 1.72411i 0.628142 + 0.778099i \(0.283816\pi\)
−0.324135 + 0.946011i \(0.605073\pi\)
\(200\) 0 0
\(201\) 3.38824 5.86860i 0.238988 0.413939i
\(202\) 0 0
\(203\) 5.33441 4.47610i 0.374402 0.314161i
\(204\) 0 0
\(205\) 5.52107 + 2.00950i 0.385608 + 0.140350i
\(206\) 0 0
\(207\) −0.233233 + 1.32273i −0.0162108 + 0.0919363i
\(208\) 0 0
\(209\) −7.61552 4.89451i −0.526776 0.338560i
\(210\) 0 0
\(211\) −0.338736 + 1.92107i −0.0233196 + 0.132252i −0.994245 0.107130i \(-0.965834\pi\)
0.970925 + 0.239382i \(0.0769449\pi\)
\(212\) 0 0
\(213\) 9.58240 + 3.48771i 0.656575 + 0.238974i
\(214\) 0 0
\(215\) 0.520760 0.436970i 0.0355156 0.0298011i
\(216\) 0 0
\(217\) −0.988989 + 1.71298i −0.0671369 + 0.116285i
\(218\) 0 0
\(219\) −0.487446 2.76444i −0.0329385 0.186804i
\(220\) 0 0
\(221\) −4.12520 7.14506i −0.277491 0.480628i
\(222\) 0 0
\(223\) 22.0336 8.01957i 1.47548 0.537030i 0.525896 0.850549i \(-0.323730\pi\)
0.949582 + 0.313518i \(0.101508\pi\)
\(224\) 0 0
\(225\) −1.69617 1.42325i −0.113078 0.0948834i
\(226\) 0 0
\(227\) −4.14223 −0.274929 −0.137465 0.990507i \(-0.543895\pi\)
−0.137465 + 0.990507i \(0.543895\pi\)
\(228\) 0 0
\(229\) 0.644603 0.0425965 0.0212983 0.999773i \(-0.493220\pi\)
0.0212983 + 0.999773i \(0.493220\pi\)
\(230\) 0 0
\(231\) −1.29871 1.08975i −0.0854488 0.0717000i
\(232\) 0 0
\(233\) −1.96247 + 0.714281i −0.128566 + 0.0467941i −0.405502 0.914094i \(-0.632903\pi\)
0.276936 + 0.960888i \(0.410681\pi\)
\(234\) 0 0
\(235\) −5.42621 9.39847i −0.353967 0.613088i
\(236\) 0 0
\(237\) 0.474665 + 2.69196i 0.0308328 + 0.174861i
\(238\) 0 0
\(239\) 3.10456 5.37725i 0.200817 0.347825i −0.747975 0.663727i \(-0.768974\pi\)
0.948792 + 0.315902i \(0.102307\pi\)
\(240\) 0 0
\(241\) −7.33621 + 6.15581i −0.472567 + 0.396531i −0.847730 0.530428i \(-0.822031\pi\)
0.375163 + 0.926959i \(0.377587\pi\)
\(242\) 0 0
\(243\) 15.1504 + 5.51430i 0.971899 + 0.353742i
\(244\) 0 0
\(245\) −1.06829 + 6.05855i −0.0682503 + 0.387067i
\(246\) 0 0
\(247\) −11.1098 14.5990i −0.706901 0.928913i
\(248\) 0 0
\(249\) −1.55793 + 8.83544i −0.0987296 + 0.559924i
\(250\) 0 0
\(251\) −9.59301 3.49157i −0.605506 0.220386i 0.0210300 0.999779i \(-0.493305\pi\)
−0.626536 + 0.779393i \(0.715528\pi\)
\(252\) 0 0
\(253\) −0.965082 + 0.809800i −0.0606742 + 0.0509117i
\(254\) 0 0
\(255\) 0.868862 1.50491i 0.0544102 0.0942413i
\(256\) 0 0
\(257\) −0.128277 0.727493i −0.00800168 0.0453798i 0.980545 0.196292i \(-0.0628900\pi\)
−0.988547 + 0.150912i \(0.951779\pi\)
\(258\) 0 0
\(259\) 1.78667 + 3.09461i 0.111018 + 0.192290i
\(260\) 0 0
\(261\) −15.7340 + 5.72670i −0.973908 + 0.354474i
\(262\) 0 0
\(263\) −16.5311 13.8712i −1.01935 0.855336i −0.0298039 0.999556i \(-0.509488\pi\)
−0.989546 + 0.144220i \(0.953933\pi\)
\(264\) 0 0
\(265\) −4.52372 −0.277890
\(266\) 0 0
\(267\) −3.01654 −0.184609
\(268\) 0 0
\(269\) −7.00867 5.88097i −0.427326 0.358569i 0.403616 0.914929i \(-0.367753\pi\)
−0.830942 + 0.556359i \(0.812198\pi\)
\(270\) 0 0
\(271\) 4.87686 1.77503i 0.296248 0.107826i −0.189620 0.981858i \(-0.560726\pi\)
0.485868 + 0.874032i \(0.338503\pi\)
\(272\) 0 0
\(273\) −1.71782 2.97535i −0.103967 0.180077i
\(274\) 0 0
\(275\) −0.360640 2.04529i −0.0217474 0.123336i
\(276\) 0 0
\(277\) 11.7053 20.2742i 0.703303 1.21816i −0.263998 0.964523i \(-0.585041\pi\)
0.967301 0.253633i \(-0.0816255\pi\)
\(278\) 0 0
\(279\) 3.64330 3.05709i 0.218119 0.183023i
\(280\) 0 0
\(281\) 17.4286 + 6.34349i 1.03970 + 0.378421i 0.804767 0.593590i \(-0.202290\pi\)
0.234935 + 0.972011i \(0.424512\pi\)
\(282\) 0 0
\(283\) −3.82002 + 21.6644i −0.227077 + 1.28782i 0.631599 + 0.775295i \(0.282399\pi\)
−0.858675 + 0.512520i \(0.828712\pi\)
\(284\) 0 0
\(285\) 1.49294 3.56393i 0.0884341 0.211109i
\(286\) 0 0
\(287\) 0.939510 5.32823i 0.0554575 0.314515i
\(288\) 0 0
\(289\) 12.3638 + 4.50005i 0.727281 + 0.264709i
\(290\) 0 0
\(291\) 12.8999 10.8243i 0.756207 0.634533i
\(292\) 0 0
\(293\) −11.7723 + 20.3902i −0.687745 + 1.19121i 0.284821 + 0.958581i \(0.408066\pi\)
−0.972566 + 0.232629i \(0.925267\pi\)
\(294\) 0 0
\(295\) −1.02661 5.82217i −0.0597713 0.338980i
\(296\) 0 0
\(297\) 4.79977 + 8.31344i 0.278511 + 0.482395i
\(298\) 0 0
\(299\) −2.39909 + 0.873197i −0.138743 + 0.0504983i
\(300\) 0 0
\(301\) −0.479548 0.402388i −0.0276407 0.0231933i
\(302\) 0 0
\(303\) −11.0818 −0.636631
\(304\) 0 0
\(305\) −6.98084 −0.399722
\(306\) 0 0
\(307\) 2.98192 + 2.50213i 0.170187 + 0.142804i 0.723903 0.689902i \(-0.242346\pi\)
−0.553716 + 0.832706i \(0.686791\pi\)
\(308\) 0 0
\(309\) 0.578734 0.210642i 0.0329230 0.0119830i
\(310\) 0 0
\(311\) 12.5567 + 21.7489i 0.712028 + 1.23327i 0.964095 + 0.265559i \(0.0855564\pi\)
−0.252067 + 0.967710i \(0.581110\pi\)
\(312\) 0 0
\(313\) 4.10192 + 23.2631i 0.231854 + 1.31491i 0.849139 + 0.528169i \(0.177121\pi\)
−0.617285 + 0.786740i \(0.711767\pi\)
\(314\) 0 0
\(315\) −1.01948 + 1.76579i −0.0574411 + 0.0994910i
\(316\) 0 0
\(317\) 4.96644 4.16734i 0.278943 0.234061i −0.492572 0.870271i \(-0.663943\pi\)
0.771516 + 0.636210i \(0.219499\pi\)
\(318\) 0 0
\(319\) −14.7580 5.37148i −0.826290 0.300745i
\(320\) 0 0
\(321\) 0.994074 5.63767i 0.0554838 0.314664i
\(322\) 0 0
\(323\) −8.33472 1.88274i −0.463756 0.104758i
\(324\) 0 0
\(325\) 0.730843 4.14482i 0.0405399 0.229913i
\(326\) 0 0
\(327\) −1.40110 0.509958i −0.0774809 0.0282008i
\(328\) 0 0
\(329\) −7.65552 + 6.42374i −0.422062 + 0.354152i
\(330\) 0 0
\(331\) −9.62278 + 16.6671i −0.528916 + 0.916109i 0.470515 + 0.882392i \(0.344068\pi\)
−0.999431 + 0.0337175i \(0.989265\pi\)
\(332\) 0 0
\(333\) −1.49199 8.46148i −0.0817604 0.463686i
\(334\) 0 0
\(335\) −3.82221 6.62026i −0.208830 0.361703i
\(336\) 0 0
\(337\) −15.9785 + 5.81569i −0.870402 + 0.316801i −0.738330 0.674439i \(-0.764385\pi\)
−0.132072 + 0.991240i \(0.542163\pi\)
\(338\) 0 0
\(339\) 12.0822 + 10.1382i 0.656217 + 0.550631i
\(340\) 0 0
\(341\) 4.46099 0.241576
\(342\) 0 0
\(343\) 12.1112 0.653942
\(344\) 0 0
\(345\) −0.411927 0.345648i −0.0221774 0.0186090i
\(346\) 0 0
\(347\) 17.2902 6.29311i 0.928186 0.337832i 0.166696 0.986008i \(-0.446690\pi\)
0.761490 + 0.648176i \(0.224468\pi\)
\(348\) 0 0
\(349\) 15.7745 + 27.3223i 0.844392 + 1.46253i 0.886148 + 0.463402i \(0.153372\pi\)
−0.0417557 + 0.999128i \(0.513295\pi\)
\(350\) 0 0
\(351\) 3.37809 + 19.1581i 0.180309 + 1.02258i
\(352\) 0 0
\(353\) −16.3730 + 28.3588i −0.871444 + 1.50939i −0.0109414 + 0.999940i \(0.503483\pi\)
−0.860503 + 0.509446i \(0.829850\pi\)
\(354\) 0 0
\(355\) 8.81217 7.39429i 0.467701 0.392448i
\(356\) 0 0
\(357\) −1.50370 0.547302i −0.0795842 0.0289663i
\(358\) 0 0
\(359\) −2.42755 + 13.7673i −0.128121 + 0.726612i 0.851284 + 0.524706i \(0.175825\pi\)
−0.979405 + 0.201906i \(0.935286\pi\)
\(360\) 0 0
\(361\) −18.9139 1.80717i −0.995466 0.0951143i
\(362\) 0 0
\(363\) 1.02930 5.83747i 0.0540244 0.306388i
\(364\) 0 0
\(365\) −2.97565 1.08305i −0.155753 0.0566893i
\(366\) 0 0
\(367\) 4.11551 3.45332i 0.214828 0.180262i −0.529023 0.848607i \(-0.677442\pi\)
0.743851 + 0.668345i \(0.232997\pi\)
\(368\) 0 0
\(369\) −6.50461 + 11.2663i −0.338617 + 0.586501i
\(370\) 0 0
\(371\) 0.723369 + 4.10243i 0.0375555 + 0.212988i
\(372\) 0 0
\(373\) 16.1702 + 28.0076i 0.837260 + 1.45018i 0.892177 + 0.451686i \(0.149177\pi\)
−0.0549172 + 0.998491i \(0.517490\pi\)
\(374\) 0 0
\(375\) 0.833001 0.303188i 0.0430160 0.0156565i
\(376\) 0 0
\(377\) −24.3807 20.4578i −1.25567 1.05363i
\(378\) 0 0
\(379\) −33.8059 −1.73649 −0.868247 0.496133i \(-0.834753\pi\)
−0.868247 + 0.496133i \(0.834753\pi\)
\(380\) 0 0
\(381\) −2.90900 −0.149033
\(382\) 0 0
\(383\) −0.548598 0.460328i −0.0280320 0.0235217i 0.628664 0.777677i \(-0.283602\pi\)
−0.656696 + 0.754155i \(0.728047\pi\)
\(384\) 0 0
\(385\) −1.79715 + 0.654108i −0.0915911 + 0.0333364i
\(386\) 0 0
\(387\) 0.752607 + 1.30355i 0.0382571 + 0.0662633i
\(388\) 0 0
\(389\) 3.64903 + 20.6947i 0.185013 + 1.04926i 0.925938 + 0.377674i \(0.123276\pi\)
−0.740925 + 0.671587i \(0.765613\pi\)
\(390\) 0 0
\(391\) −0.594562 + 1.02981i −0.0300683 + 0.0520798i
\(392\) 0 0
\(393\) 4.66559 3.91489i 0.235348 0.197480i
\(394\) 0 0
\(395\) 2.89763 + 1.05465i 0.145796 + 0.0530652i
\(396\) 0 0
\(397\) 3.55616 20.1680i 0.178479 1.01220i −0.755573 0.655064i \(-0.772642\pi\)
0.934052 0.357138i \(-0.116247\pi\)
\(398\) 0 0
\(399\) −3.47075 0.784011i −0.173755 0.0392497i
\(400\) 0 0
\(401\) −2.62785 + 14.9033i −0.131229 + 0.744235i 0.846183 + 0.532892i \(0.178895\pi\)
−0.977412 + 0.211343i \(0.932216\pi\)
\(402\) 0 0
\(403\) 8.49507 + 3.09195i 0.423170 + 0.154021i
\(404\) 0 0
\(405\) 1.94972 1.63601i 0.0968824 0.0812940i
\(406\) 0 0
\(407\) 4.02953 6.97935i 0.199736 0.345954i
\(408\) 0 0
\(409\) −0.528547 2.99754i −0.0261349 0.148219i 0.968948 0.247265i \(-0.0795319\pi\)
−0.995083 + 0.0990465i \(0.968421\pi\)
\(410\) 0 0
\(411\) 1.75045 + 3.03186i 0.0863432 + 0.149551i
\(412\) 0 0
\(413\) −5.11580 + 1.86200i −0.251732 + 0.0916229i
\(414\) 0 0
\(415\) 7.75302 + 6.50556i 0.380581 + 0.319345i
\(416\) 0 0
\(417\) −15.3276 −0.750595
\(418\) 0 0
\(419\) −3.89744 −0.190402 −0.0952011 0.995458i \(-0.530349\pi\)
−0.0952011 + 0.995458i \(0.530349\pi\)
\(420\) 0 0
\(421\) 2.18162 + 1.83059i 0.106325 + 0.0892177i 0.694401 0.719589i \(-0.255670\pi\)
−0.588075 + 0.808806i \(0.700114\pi\)
\(422\) 0 0
\(423\) 22.5801 8.21849i 1.09788 0.399597i
\(424\) 0 0
\(425\) −0.980146 1.69766i −0.0475441 0.0823488i
\(426\) 0 0
\(427\) 1.11628 + 6.33072i 0.0540204 + 0.306365i
\(428\) 0 0
\(429\) −3.87425 + 6.71040i −0.187051 + 0.323981i
\(430\) 0 0
\(431\) 18.4177 15.4543i 0.887152 0.744409i −0.0804852 0.996756i \(-0.525647\pi\)
0.967637 + 0.252347i \(0.0812025\pi\)
\(432\) 0 0
\(433\) 13.7914 + 5.01965i 0.662771 + 0.241229i 0.651432 0.758707i \(-0.274168\pi\)
0.0113389 + 0.999936i \(0.496391\pi\)
\(434\) 0 0
\(435\) 1.16404 6.60161i 0.0558115 0.316523i
\(436\) 0 0
\(437\) −1.02162 + 2.43880i −0.0488707 + 0.116663i
\(438\) 0 0
\(439\) −1.22539 + 6.94955i −0.0584849 + 0.331684i −0.999986 0.00532619i \(-0.998305\pi\)
0.941501 + 0.337010i \(0.109416\pi\)
\(440\) 0 0
\(441\) −12.8002 4.65890i −0.609534 0.221852i
\(442\) 0 0
\(443\) −7.89296 + 6.62298i −0.375006 + 0.314667i −0.810738 0.585409i \(-0.800934\pi\)
0.435732 + 0.900076i \(0.356489\pi\)
\(444\) 0 0
\(445\) −1.70145 + 2.94699i −0.0806564 + 0.139701i
\(446\) 0 0
\(447\) 0.492026 + 2.79042i 0.0232720 + 0.131982i
\(448\) 0 0
\(449\) 0.920622 + 1.59456i 0.0434468 + 0.0752521i 0.886931 0.461902i \(-0.152833\pi\)
−0.843484 + 0.537154i \(0.819499\pi\)
\(450\) 0 0
\(451\) −11.4664 + 4.17343i −0.539931 + 0.196519i
\(452\) 0 0
\(453\) 8.07843 + 6.77861i 0.379558 + 0.318487i
\(454\) 0 0
\(455\) −3.87568 −0.181695
\(456\) 0 0
\(457\) −10.3531 −0.484297 −0.242148 0.970239i \(-0.577852\pi\)
−0.242148 + 0.970239i \(0.577852\pi\)
\(458\) 0 0
\(459\) 6.94099 + 5.82418i 0.323978 + 0.271849i
\(460\) 0 0
\(461\) 12.3814 4.50647i 0.576660 0.209887i −0.0371922 0.999308i \(-0.511841\pi\)
0.613852 + 0.789421i \(0.289619\pi\)
\(462\) 0 0
\(463\) −15.0532 26.0728i −0.699579 1.21171i −0.968612 0.248576i \(-0.920037\pi\)
0.269033 0.963131i \(-0.413296\pi\)
\(464\) 0 0
\(465\) 0.330641 + 1.87516i 0.0153331 + 0.0869584i
\(466\) 0 0
\(467\) 20.3663 35.2754i 0.942438 1.63235i 0.181636 0.983366i \(-0.441861\pi\)
0.760801 0.648985i \(-0.224806\pi\)
\(468\) 0 0
\(469\) −5.39253 + 4.52487i −0.249004 + 0.208939i
\(470\) 0 0
\(471\) −16.3466 5.94966i −0.753210 0.274146i
\(472\) 0 0
\(473\) −0.245165 + 1.39040i −0.0112727 + 0.0639306i
\(474\) 0 0
\(475\) −2.63969 3.46872i −0.121117 0.159156i
\(476\) 0 0
\(477\) 1.73932 9.86418i 0.0796381 0.451650i
\(478\) 0 0
\(479\) 28.1142 + 10.2327i 1.28457 + 0.467545i 0.891941 0.452153i \(-0.149344\pi\)
0.392628 + 0.919697i \(0.371566\pi\)
\(480\) 0 0
\(481\) 12.5109 10.4979i 0.570448 0.478663i
\(482\) 0 0
\(483\) −0.247588 + 0.428836i −0.0112657 + 0.0195127i
\(484\) 0 0
\(485\) −3.29871 18.7079i −0.149787 0.849482i
\(486\) 0 0
\(487\) −12.1450 21.0357i −0.550341 0.953219i −0.998250 0.0591397i \(-0.981164\pi\)
0.447908 0.894079i \(-0.352169\pi\)
\(488\) 0 0
\(489\) −15.6145 + 5.68320i −0.706111 + 0.257003i
\(490\) 0 0
\(491\) 6.17437 + 5.18091i 0.278645 + 0.233811i 0.771390 0.636363i \(-0.219562\pi\)
−0.492745 + 0.870174i \(0.664006\pi\)
\(492\) 0 0
\(493\) −14.8238 −0.667630
\(494\) 0 0
\(495\) 4.59852 0.206688
\(496\) 0 0
\(497\) −8.11479 6.80911i −0.363998 0.305430i
\(498\) 0 0
\(499\) 9.34595 3.40165i 0.418382 0.152279i −0.124247 0.992251i \(-0.539651\pi\)
0.542629 + 0.839973i \(0.317429\pi\)
\(500\) 0 0
\(501\) −2.23278 3.86729i −0.0997532 0.172778i
\(502\) 0 0
\(503\) −1.97979 11.2279i −0.0882744 0.500629i −0.996602 0.0823692i \(-0.973751\pi\)
0.908328 0.418260i \(-0.137360\pi\)
\(504\) 0 0
\(505\) −6.25057 + 10.8263i −0.278147 + 0.481764i
\(506\) 0 0
\(507\) −3.20089 + 2.68587i −0.142157 + 0.119284i
\(508\) 0 0
\(509\) 26.1717 + 9.52573i 1.16004 + 0.422220i 0.849112 0.528213i \(-0.177138\pi\)
0.310929 + 0.950433i \(0.399360\pi\)
\(510\) 0 0
\(511\) −0.506361 + 2.87172i −0.0224001 + 0.127037i
\(512\) 0 0
\(513\) 16.9489 + 10.8931i 0.748313 + 0.480942i
\(514\) 0 0
\(515\) 0.120643 0.684203i 0.00531618 0.0301496i
\(516\) 0 0
\(517\) 21.1795 + 7.70871i 0.931474 + 0.339029i
\(518\) 0 0
\(519\) 10.1740 8.53696i 0.446587 0.374731i
\(520\) 0 0
\(521\) 18.6901 32.3722i 0.818829 1.41825i −0.0877173 0.996145i \(-0.527957\pi\)
0.906546 0.422107i \(-0.138709\pi\)
\(522\) 0 0
\(523\) −6.76998 38.3944i −0.296030 1.67887i −0.662985 0.748633i \(-0.730711\pi\)
0.366954 0.930239i \(-0.380401\pi\)
\(524\) 0 0
\(525\) −0.408154 0.706943i −0.0178133 0.0308535i
\(526\) 0 0
\(527\) 3.95671 1.44012i 0.172357 0.0627328i
\(528\) 0 0
\(529\) −17.3371 14.5476i −0.753789 0.632504i
\(530\) 0 0
\(531\) 13.0902 0.568068
\(532\) 0 0
\(533\) −24.7281 −1.07109
\(534\) 0 0
\(535\) −4.94701 4.15103i −0.213878 0.179465i
\(536\) 0 0
\(537\) −1.97779 + 0.719857i −0.0853480 + 0.0310641i
\(538\) 0 0
\(539\) −6.38839 11.0650i −0.275167 0.476604i
\(540\) 0 0
\(541\) 1.44443 + 8.19179i 0.0621011 + 0.352193i 0.999986 + 0.00524684i \(0.00167013\pi\)
−0.937885 + 0.346946i \(0.887219\pi\)
\(542\) 0 0
\(543\) −5.61141 + 9.71925i −0.240809 + 0.417093i
\(544\) 0 0
\(545\) −1.28848 + 1.08116i −0.0551924 + 0.0463119i
\(546\) 0 0
\(547\) −41.9506 15.2688i −1.79368 0.652846i −0.998947 0.0458869i \(-0.985389\pi\)
−0.794733 0.606959i \(-0.792389\pi\)
\(548\) 0 0
\(549\) 2.68406 15.2221i 0.114553 0.649662i
\(550\) 0 0
\(551\) −32.6971 + 4.17180i −1.39294 + 0.177725i
\(552\) 0 0
\(553\) 0.493085 2.79642i 0.0209681 0.118916i
\(554\) 0 0
\(555\) 3.23241 + 1.17650i 0.137208 + 0.0499397i
\(556\) 0 0
\(557\) 20.7113 17.3788i 0.877565 0.736365i −0.0881117 0.996111i \(-0.528083\pi\)
0.965677 + 0.259746i \(0.0836388\pi\)
\(558\) 0 0
\(559\) −1.43057 + 2.47781i −0.0605065 + 0.104800i
\(560\) 0 0
\(561\) 0.626693 + 3.55415i 0.0264590 + 0.150056i
\(562\) 0 0
\(563\) 17.4197 + 30.1718i 0.734153 + 1.27159i 0.955094 + 0.296303i \(0.0957540\pi\)
−0.220941 + 0.975287i \(0.570913\pi\)
\(564\) 0 0
\(565\) 16.7193 6.08534i 0.703388 0.256012i
\(566\) 0 0
\(567\) −1.79542 1.50654i −0.0754007 0.0632687i
\(568\) 0 0
\(569\) 26.2259 1.09945 0.549723 0.835347i \(-0.314733\pi\)
0.549723 + 0.835347i \(0.314733\pi\)
\(570\) 0 0
\(571\) −29.6016 −1.23879 −0.619393 0.785081i \(-0.712621\pi\)
−0.619393 + 0.785081i \(0.712621\pi\)
\(572\) 0 0
\(573\) −14.8035 12.4216i −0.618426 0.518921i
\(574\) 0 0
\(575\) −0.570023 + 0.207471i −0.0237716 + 0.00865215i
\(576\) 0 0
\(577\) 14.6753 + 25.4183i 0.610940 + 1.05818i 0.991082 + 0.133252i \(0.0425418\pi\)
−0.380142 + 0.924928i \(0.624125\pi\)
\(578\) 0 0
\(579\) 0.994131 + 5.63800i 0.0413147 + 0.234307i
\(580\) 0 0
\(581\) 4.65995 8.07127i 0.193327 0.334853i
\(582\) 0 0
\(583\) 7.19703 6.03902i 0.298071 0.250111i
\(584\) 0 0
\(585\) 8.75697 + 3.18728i 0.362056 + 0.131778i
\(586\) 0 0
\(587\) 0.701381 3.97773i 0.0289491 0.164179i −0.966906 0.255133i \(-0.917881\pi\)
0.995855 + 0.0909546i \(0.0289918\pi\)
\(588\) 0 0
\(589\) 8.32208 4.29002i 0.342905 0.176767i
\(590\) 0 0
\(591\) −1.45786 + 8.26794i −0.0599684 + 0.340097i
\(592\) 0 0
\(593\) 8.77518 + 3.19390i 0.360353 + 0.131158i 0.515851 0.856678i \(-0.327476\pi\)
−0.155498 + 0.987836i \(0.549698\pi\)
\(594\) 0 0
\(595\) −1.38283 + 1.16033i −0.0566905 + 0.0475690i
\(596\) 0 0
\(597\) 10.9464 18.9597i 0.448005 0.775967i
\(598\) 0 0
\(599\) 2.49742 + 14.1636i 0.102042 + 0.578707i 0.992361 + 0.123370i \(0.0393702\pi\)
−0.890319 + 0.455337i \(0.849519\pi\)
\(600\) 0 0
\(601\) −22.6873 39.2956i −0.925435 1.60290i −0.790860 0.611997i \(-0.790366\pi\)
−0.134575 0.990903i \(-0.542967\pi\)
\(602\) 0 0
\(603\) 15.9054 5.78909i 0.647718 0.235750i
\(604\) 0 0
\(605\) −5.12233 4.29814i −0.208252 0.174744i
\(606\) 0 0
\(607\) −5.07790 −0.206105 −0.103053 0.994676i \(-0.532861\pi\)
−0.103053 + 0.994676i \(0.532861\pi\)
\(608\) 0 0
\(609\) −6.17294 −0.250140
\(610\) 0 0
\(611\) 34.9892 + 29.3594i 1.41551 + 1.18776i
\(612\) 0 0
\(613\) −12.0467 + 4.38465i −0.486563 + 0.177095i −0.573641 0.819107i \(-0.694469\pi\)
0.0870775 + 0.996202i \(0.472247\pi\)
\(614\) 0 0
\(615\) −2.60416 4.51053i −0.105010 0.181882i
\(616\) 0 0
\(617\) 3.09892 + 17.5748i 0.124758 + 0.707536i 0.981452 + 0.191711i \(0.0614035\pi\)
−0.856694 + 0.515825i \(0.827485\pi\)
\(618\) 0 0
\(619\) 8.02039 13.8917i 0.322367 0.558355i −0.658609 0.752485i \(-0.728855\pi\)
0.980976 + 0.194130i \(0.0621883\pi\)
\(620\) 0 0
\(621\) 2.14786 1.80227i 0.0861908 0.0723227i
\(622\) 0 0
\(623\) 2.94462 + 1.07175i 0.117974 + 0.0429389i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) 2.38254 + 7.66308i 0.0951493 + 0.306034i
\(628\) 0 0
\(629\) 1.32091 7.49123i 0.0526680 0.298695i
\(630\) 0 0
\(631\) −24.3557 8.86476i −0.969586 0.352900i −0.191803 0.981433i \(-0.561433\pi\)
−0.777783 + 0.628533i \(0.783656\pi\)
\(632\) 0 0
\(633\) 1.32466 1.11152i 0.0526506 0.0441791i
\(634\) 0 0
\(635\) −1.64079 + 2.84194i −0.0651129 + 0.112779i
\(636\) 0 0
\(637\) −4.49616 25.4990i −0.178144 1.01031i
\(638\) 0 0
\(639\) 12.7354 + 22.0584i 0.503805 + 0.872616i
\(640\) 0 0
\(641\) −5.01574 + 1.82558i −0.198110 + 0.0721061i −0.439170 0.898404i \(-0.644727\pi\)
0.241060 + 0.970510i \(0.422505\pi\)
\(642\) 0 0
\(643\) −2.90330 2.43616i −0.114495 0.0960727i 0.583743 0.811939i \(-0.301588\pi\)
−0.698238 + 0.715866i \(0.746032\pi\)
\(644\) 0 0
\(645\) −0.602620 −0.0237281
\(646\) 0 0
\(647\) 30.2823 1.19052 0.595260 0.803533i \(-0.297049\pi\)
0.595260 + 0.803533i \(0.297049\pi\)
\(648\) 0 0
\(649\) 9.40570 + 7.89232i 0.369206 + 0.309801i
\(650\) 0 0
\(651\) 1.64766 0.599698i 0.0645768 0.0235040i
\(652\) 0 0
\(653\) −11.4949 19.9098i −0.449831 0.779131i 0.548543 0.836122i \(-0.315183\pi\)
−0.998375 + 0.0569914i \(0.981849\pi\)
\(654\) 0 0
\(655\) −1.19306 6.76619i −0.0466168 0.264377i
\(656\) 0 0
\(657\) 3.50575 6.07213i 0.136772 0.236896i
\(658\) 0 0
\(659\) 0.410633 0.344562i 0.0159960 0.0134222i −0.634755 0.772714i \(-0.718899\pi\)
0.650751 + 0.759292i \(0.274454\pi\)
\(660\) 0 0
\(661\) 28.0558 + 10.2115i 1.09124 + 0.397180i 0.824081 0.566472i \(-0.191692\pi\)
0.267162 + 0.963652i \(0.413914\pi\)
\(662\) 0 0
\(663\) −1.27000 + 7.20255i −0.0493229 + 0.279724i
\(664\) 0 0
\(665\) −2.72358 + 2.94853i −0.105616 + 0.114339i
\(666\) 0 0
\(667\) −0.796553 + 4.51748i −0.0308427 + 0.174917i
\(668\) 0 0
\(669\) −19.5319 7.10904i −0.755148 0.274851i
\(670\) 0 0
\(671\) 11.1062 9.31921i 0.428750 0.359764i
\(672\) 0 0
\(673\) 11.2524 19.4898i 0.433750 0.751277i −0.563443 0.826155i \(-0.690523\pi\)
0.997193 + 0.0748782i \(0.0238568\pi\)
\(674\) 0 0
\(675\) 0.802632 + 4.55195i 0.0308933 + 0.175205i
\(676\) 0 0
\(677\) 8.55072 + 14.8103i 0.328631 + 0.569206i 0.982240 0.187626i \(-0.0600794\pi\)
−0.653609 + 0.756832i \(0.726746\pi\)
\(678\) 0 0
\(679\) −16.4382 + 5.98300i −0.630839 + 0.229607i
\(680\) 0 0
\(681\) 2.81286 + 2.36027i 0.107789 + 0.0904456i
\(682\) 0 0
\(683\) −50.9124 −1.94811 −0.974054 0.226316i \(-0.927332\pi\)
−0.974054 + 0.226316i \(0.927332\pi\)
\(684\) 0 0
\(685\) 3.94929 0.150895
\(686\) 0 0
\(687\) −0.437730 0.367299i −0.0167004 0.0140133i
\(688\) 0 0
\(689\) 17.8910 6.51180i 0.681594 0.248080i
\(690\) 0 0
\(691\) 13.5121 + 23.4037i 0.514026 + 0.890318i 0.999868 + 0.0162718i \(0.00517971\pi\)
−0.485842 + 0.874047i \(0.661487\pi\)
\(692\) 0 0
\(693\) −0.735330 4.17026i −0.0279329 0.158415i
\(694\) 0 0
\(695\) −8.64538 + 14.9742i −0.327938 + 0.568005i
\(696\) 0 0
\(697\) −8.82291 + 7.40330i −0.334192 + 0.280420i
\(698\) 0 0
\(699\) 1.73965 + 0.633182i 0.0657998 + 0.0239492i
\(700\) 0 0
\(701\) 7.76496 44.0373i 0.293278 1.66326i −0.380839 0.924641i \(-0.624365\pi\)
0.674118 0.738624i \(-0.264524\pi\)
\(702\) 0 0
\(703\) 0.805315 16.8953i 0.0303730 0.637217i
\(704\) 0 0
\(705\) −1.67054 + 9.47409i −0.0629161 + 0.356815i
\(706\) 0 0
\(707\) 10.8176 + 3.93727i 0.406837 + 0.148076i
\(708\) 0 0
\(709\) −27.6472 + 23.1988i −1.03831 + 0.871249i −0.991817 0.127669i \(-0.959250\pi\)
−0.0464974 + 0.998918i \(0.514806\pi\)
\(710\) 0 0
\(711\) −3.41382 + 5.91292i −0.128028 + 0.221752i
\(712\) 0 0
\(713\) −0.226258 1.28317i −0.00847342 0.0480552i
\(714\) 0 0
\(715\) 4.37047 + 7.56987i 0.163446 + 0.283097i
\(716\) 0 0
\(717\) −5.17220 + 1.88253i −0.193159 + 0.0703042i
\(718\) 0 0
\(719\) −17.5573 14.7323i −0.654776 0.549423i 0.253740 0.967273i \(-0.418339\pi\)
−0.908516 + 0.417850i \(0.862784\pi\)
\(720\) 0 0
\(721\) −0.639776 −0.0238265
\(722\) 0 0
\(723\) 8.48941 0.315725
\(724\) 0 0
\(725\) −5.79285 4.86078i −0.215141 0.180525i
\(726\) 0 0
\(727\) −43.9640 + 16.0016i −1.63053 + 0.593466i −0.985347 0.170559i \(-0.945443\pi\)
−0.645186 + 0.764025i \(0.723220\pi\)
\(728\) 0 0
\(729\) −3.32832 5.76481i −0.123271 0.213512i
\(730\) 0 0
\(731\) 0.231406 + 1.31237i 0.00855887 + 0.0485398i
\(732\) 0 0
\(733\) −9.44660 + 16.3620i −0.348918 + 0.604344i −0.986058 0.166405i \(-0.946784\pi\)
0.637139 + 0.770749i \(0.280118\pi\)
\(734\) 0 0
\(735\) 4.17764 3.50546i 0.154095 0.129301i
\(736\) 0 0
\(737\) 14.9188 + 5.43000i 0.549541 + 0.200017i
\(738\) 0 0
\(739\) −3.11918 + 17.6897i −0.114741 + 0.650727i 0.872138 + 0.489261i \(0.162733\pi\)
−0.986878 + 0.161466i \(0.948378\pi\)
\(740\) 0 0
\(741\) −0.774282 + 16.2442i −0.0284440 + 0.596745i
\(742\) 0 0
\(743\) −0.940109 + 5.33163i −0.0344893 + 0.195598i −0.997184 0.0749906i \(-0.976107\pi\)
0.962695 + 0.270589i \(0.0872184\pi\)
\(744\) 0 0
\(745\) 3.00361 + 1.09322i 0.110044 + 0.0400526i
\(746\) 0 0
\(747\) −17.1666 + 14.4045i −0.628094 + 0.527034i
\(748\) 0 0
\(749\) −2.97340 + 5.15007i −0.108646 + 0.188180i
\(750\) 0 0
\(751\) −1.33116 7.54938i −0.0485747 0.275481i 0.950840 0.309682i \(-0.100222\pi\)
−0.999415 + 0.0342010i \(0.989111\pi\)
\(752\) 0 0
\(753\) 4.52480 + 7.83718i 0.164893 + 0.285603i
\(754\) 0 0
\(755\) 11.1789 4.06879i 0.406842 0.148078i
\(756\) 0 0
\(757\) −5.89669 4.94791i −0.214319 0.179835i 0.529308 0.848430i \(-0.322452\pi\)
−0.743627 + 0.668595i \(0.766896\pi\)
\(758\) 0 0
\(759\) 1.11679 0.0405368
\(760\) 0 0
\(761\) 25.8527 0.937161 0.468581 0.883421i \(-0.344766\pi\)
0.468581 + 0.883421i \(0.344766\pi\)
\(762\) 0 0
\(763\) 1.18651 + 0.995600i 0.0429545 + 0.0360431i
\(764\) 0 0
\(765\) 4.07869 1.48452i 0.147465 0.0536730i
\(766\) 0 0
\(767\) 12.4411 + 21.5486i 0.449221 + 0.778073i
\(768\) 0 0
\(769\) −8.31408 47.1515i −0.299814 1.70033i −0.646966 0.762519i \(-0.723963\pi\)
0.347153 0.937809i \(-0.387149\pi\)
\(770\) 0 0
\(771\) −0.327422 + 0.567111i −0.0117918 + 0.0204240i
\(772\) 0 0
\(773\) 6.51612 5.46768i 0.234369 0.196659i −0.518038 0.855358i \(-0.673337\pi\)
0.752407 + 0.658699i \(0.228893\pi\)
\(774\) 0 0
\(775\) 2.01843 + 0.734647i 0.0725040 + 0.0263893i
\(776\) 0 0
\(777\) 0.550053 3.11951i 0.0197331 0.111912i
\(778\) 0 0
\(779\) −17.3774 + 18.8126i −0.622608 + 0.674030i
\(780\) 0 0
\(781\) −4.14861 + 23.5280i −0.148449 + 0.841896i
\(782\) 0 0
\(783\) 32.8451 + 11.9546i 1.17379 + 0.427224i
\(784\) 0 0
\(785\) −15.0326 + 12.6139i −0.536537 + 0.450208i
\(786\) 0 0
\(787\) −10.1390 + 17.5612i −0.361415