Properties

Label 380.2.u.a.301.1
Level $380$
Weight $2$
Character 380.301
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: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) 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 301.1
Root \(0.128174 + 0.726910i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.a.101.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +O(q^{10})\) \(q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +(-1.20808 + 2.09246i) q^{11} +(-2.11186 - 0.768655i) q^{13} +(-0.128174 - 0.726910i) q^{15} +(-0.901391 - 0.756357i) q^{17} +(-3.98240 - 1.77215i) q^{19} +(2.63330 + 2.20960i) q^{21} +(-0.255223 - 1.44744i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(2.01330 - 3.48713i) q^{27} +(-3.72314 + 3.12409i) q^{29} +(-3.60610 - 6.24595i) q^{31} +(0.309690 - 1.75634i) q^{33} +(4.37626 - 1.59283i) q^{35} +2.81439 q^{37} +1.65886 q^{39} +(-5.05804 + 1.84097i) q^{41} +(-1.33878 + 7.59257i) q^{43} +(-1.22759 - 2.12624i) q^{45} +(4.70570 - 3.94855i) q^{47} +(-7.34438 + 12.7208i) q^{49} +(0.816159 + 0.297058i) q^{51} +(0.390796 + 2.21632i) q^{53} +(-1.85089 - 1.55308i) q^{55} +(3.20962 + 0.223809i) q^{57} +(8.78120 + 7.36830i) q^{59} +(-0.285673 - 1.62013i) q^{61} +(10.7445 + 3.91067i) q^{63} +(1.12370 - 1.94630i) q^{65} +(1.80864 - 1.51763i) q^{67} +(0.542437 + 0.939529i) q^{69} +(1.11027 - 6.29664i) q^{71} +(3.18662 - 1.15983i) q^{73} +0.738124 q^{75} +11.2524 q^{77} +(2.11795 - 0.770872i) q^{79} +(0.762904 - 4.32665i) q^{81} +(-5.11094 - 8.85241i) q^{83} +(0.901391 - 0.756357i) q^{85} +(1.79372 - 3.10682i) q^{87} +(5.26955 + 1.91796i) q^{89} +(1.81747 + 10.3074i) q^{91} +(4.07804 + 3.42188i) q^{93} +(2.43676 - 3.61417i) q^{95} +(4.19849 + 3.52295i) q^{97} +(-1.03010 - 5.84198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

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
\(3\) −0.693610 + 0.252453i −0.400456 + 0.145754i −0.534394 0.845236i \(-0.679460\pi\)
0.133938 + 0.990990i \(0.457238\pi\)
\(4\) 0 0
\(5\) −0.173648 + 0.984808i −0.0776578 + 0.440419i
\(6\) 0 0
\(7\) −2.32856 4.03318i −0.880113 1.52440i −0.851215 0.524818i \(-0.824134\pi\)
−0.0288981 0.999582i \(-0.509200\pi\)
\(8\) 0 0
\(9\) −1.88077 + 1.57815i −0.626924 + 0.526052i
\(10\) 0 0
\(11\) −1.20808 + 2.09246i −0.364251 + 0.630901i −0.988656 0.150200i \(-0.952008\pi\)
0.624405 + 0.781101i \(0.285342\pi\)
\(12\) 0 0
\(13\) −2.11186 0.768655i −0.585725 0.213187i 0.0321229 0.999484i \(-0.489773\pi\)
−0.617848 + 0.786297i \(0.711995\pi\)
\(14\) 0 0
\(15\) −0.128174 0.726910i −0.0330944 0.187687i
\(16\) 0 0
\(17\) −0.901391 0.756357i −0.218620 0.183444i 0.526900 0.849927i \(-0.323354\pi\)
−0.745520 + 0.666484i \(0.767799\pi\)
\(18\) 0 0
\(19\) −3.98240 1.77215i −0.913625 0.406558i
\(20\) 0 0
\(21\) 2.63330 + 2.20960i 0.574634 + 0.482175i
\(22\) 0 0
\(23\) −0.255223 1.44744i −0.0532178 0.301813i 0.946568 0.322504i \(-0.104525\pi\)
−0.999786 + 0.0206909i \(0.993413\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) 2.01330 3.48713i 0.387459 0.671099i
\(28\) 0 0
\(29\) −3.72314 + 3.12409i −0.691370 + 0.580128i −0.919304 0.393548i \(-0.871247\pi\)
0.227934 + 0.973677i \(0.426803\pi\)
\(30\) 0 0
\(31\) −3.60610 6.24595i −0.647675 1.12181i −0.983677 0.179945i \(-0.942408\pi\)
0.336002 0.941861i \(-0.390925\pi\)
\(32\) 0 0
\(33\) 0.309690 1.75634i 0.0539100 0.305739i
\(34\) 0 0
\(35\) 4.37626 1.59283i 0.739723 0.269237i
\(36\) 0 0
\(37\) 2.81439 0.462683 0.231341 0.972873i \(-0.425689\pi\)
0.231341 + 0.972873i \(0.425689\pi\)
\(38\) 0 0
\(39\) 1.65886 0.265630
\(40\) 0 0
\(41\) −5.05804 + 1.84097i −0.789933 + 0.287512i −0.705308 0.708901i \(-0.749191\pi\)
−0.0846245 + 0.996413i \(0.526969\pi\)
\(42\) 0 0
\(43\) −1.33878 + 7.59257i −0.204161 + 1.15786i 0.694593 + 0.719403i \(0.255585\pi\)
−0.898754 + 0.438453i \(0.855526\pi\)
\(44\) 0 0
\(45\) −1.22759 2.12624i −0.182998 0.316961i
\(46\) 0 0
\(47\) 4.70570 3.94855i 0.686396 0.575955i −0.231471 0.972842i \(-0.574354\pi\)
0.917868 + 0.396887i \(0.129909\pi\)
\(48\) 0 0
\(49\) −7.34438 + 12.7208i −1.04920 + 1.81726i
\(50\) 0 0
\(51\) 0.816159 + 0.297058i 0.114285 + 0.0415964i
\(52\) 0 0
\(53\) 0.390796 + 2.21632i 0.0536800 + 0.304434i 0.999813 0.0193442i \(-0.00615783\pi\)
−0.946133 + 0.323779i \(0.895047\pi\)
\(54\) 0 0
\(55\) −1.85089 1.55308i −0.249574 0.209417i
\(56\) 0 0
\(57\) 3.20962 + 0.223809i 0.425124 + 0.0296442i
\(58\) 0 0
\(59\) 8.78120 + 7.36830i 1.14322 + 0.959271i 0.999539 0.0303534i \(-0.00966327\pi\)
0.143676 + 0.989625i \(0.454108\pi\)
\(60\) 0 0
\(61\) −0.285673 1.62013i −0.0365767 0.207437i 0.961042 0.276401i \(-0.0891417\pi\)
−0.997619 + 0.0689641i \(0.978031\pi\)
\(62\) 0 0
\(63\) 10.7445 + 3.91067i 1.35368 + 0.492698i
\(64\) 0 0
\(65\) 1.12370 1.94630i 0.139378 0.241409i
\(66\) 0 0
\(67\) 1.80864 1.51763i 0.220961 0.185408i −0.525587 0.850740i \(-0.676154\pi\)
0.746548 + 0.665332i \(0.231710\pi\)
\(68\) 0 0
\(69\) 0.542437 + 0.939529i 0.0653018 + 0.113106i
\(70\) 0 0
\(71\) 1.11027 6.29664i 0.131764 0.747273i −0.845294 0.534302i \(-0.820575\pi\)
0.977058 0.212972i \(-0.0683142\pi\)
\(72\) 0 0
\(73\) 3.18662 1.15983i 0.372966 0.135748i −0.148735 0.988877i \(-0.547520\pi\)
0.521700 + 0.853129i \(0.325298\pi\)
\(74\) 0 0
\(75\) 0.738124 0.0852312
\(76\) 0 0
\(77\) 11.2524 1.28233
\(78\) 0 0
\(79\) 2.11795 0.770872i 0.238289 0.0867299i −0.220116 0.975474i \(-0.570643\pi\)
0.458404 + 0.888744i \(0.348421\pi\)
\(80\) 0 0
\(81\) 0.762904 4.32665i 0.0847671 0.480738i
\(82\) 0 0
\(83\) −5.11094 8.85241i −0.560999 0.971678i −0.997410 0.0719307i \(-0.977084\pi\)
0.436411 0.899747i \(-0.356249\pi\)
\(84\) 0 0
\(85\) 0.901391 0.756357i 0.0977696 0.0820385i
\(86\) 0 0
\(87\) 1.79372 3.10682i 0.192307 0.333086i
\(88\) 0 0
\(89\) 5.26955 + 1.91796i 0.558571 + 0.203303i 0.605851 0.795578i \(-0.292833\pi\)
−0.0472794 + 0.998882i \(0.515055\pi\)
\(90\) 0 0
\(91\) 1.81747 + 10.3074i 0.190523 + 1.08051i
\(92\) 0 0
\(93\) 4.07804 + 3.42188i 0.422873 + 0.354833i
\(94\) 0 0
\(95\) 2.43676 3.61417i 0.250006 0.370806i
\(96\) 0 0
\(97\) 4.19849 + 3.52295i 0.426292 + 0.357701i 0.830550 0.556943i \(-0.188026\pi\)
−0.404259 + 0.914645i \(0.632470\pi\)
\(98\) 0 0
\(99\) −1.03010 5.84198i −0.103529 0.587141i
\(100\) 0 0
\(101\) 11.5198 + 4.19286i 1.14626 + 0.417205i 0.844171 0.536075i \(-0.180093\pi\)
0.302090 + 0.953279i \(0.402316\pi\)
\(102\) 0 0
\(103\) −6.87149 + 11.9018i −0.677068 + 1.17272i 0.298792 + 0.954318i \(0.403416\pi\)
−0.975860 + 0.218398i \(0.929917\pi\)
\(104\) 0 0
\(105\) −2.63330 + 2.20960i −0.256984 + 0.215635i
\(106\) 0 0
\(107\) −7.57368 13.1180i −0.732176 1.26817i −0.955951 0.293525i \(-0.905172\pi\)
0.223776 0.974641i \(-0.428162\pi\)
\(108\) 0 0
\(109\) −2.38654 + 13.5347i −0.228589 + 1.29639i 0.627116 + 0.778926i \(0.284235\pi\)
−0.855704 + 0.517465i \(0.826876\pi\)
\(110\) 0 0
\(111\) −1.95209 + 0.710502i −0.185284 + 0.0674379i
\(112\) 0 0
\(113\) −19.0463 −1.79173 −0.895865 0.444327i \(-0.853443\pi\)
−0.895865 + 0.444327i \(0.853443\pi\)
\(114\) 0 0
\(115\) 1.46977 0.137057
\(116\) 0 0
\(117\) 5.18499 1.88718i 0.479352 0.174470i
\(118\) 0 0
\(119\) −0.951584 + 5.39670i −0.0872315 + 0.494715i
\(120\) 0 0
\(121\) 2.58107 + 4.47055i 0.234643 + 0.406413i
\(122\) 0 0
\(123\) 3.04354 2.55384i 0.274427 0.230272i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) −11.2619 4.09901i −0.999336 0.363729i −0.210008 0.977700i \(-0.567349\pi\)
−0.789328 + 0.613971i \(0.789571\pi\)
\(128\) 0 0
\(129\) −0.988183 5.60426i −0.0870046 0.493428i
\(130\) 0 0
\(131\) 7.33068 + 6.15117i 0.640484 + 0.537430i 0.904167 0.427179i \(-0.140493\pi\)
−0.263683 + 0.964609i \(0.584937\pi\)
\(132\) 0 0
\(133\) 2.12586 + 20.1883i 0.184335 + 1.75055i
\(134\) 0 0
\(135\) 3.08455 + 2.58825i 0.265476 + 0.222761i
\(136\) 0 0
\(137\) −1.98184 11.2395i −0.169320 0.960259i −0.944498 0.328517i \(-0.893451\pi\)
0.775178 0.631742i \(-0.217660\pi\)
\(138\) 0 0
\(139\) −19.6728 7.16031i −1.66862 0.607329i −0.676941 0.736038i \(-0.736695\pi\)
−0.991682 + 0.128708i \(0.958917\pi\)
\(140\) 0 0
\(141\) −2.26709 + 3.92672i −0.190924 + 0.330689i
\(142\) 0 0
\(143\) 4.15969 3.49039i 0.347851 0.291881i
\(144\) 0 0
\(145\) −2.43011 4.20907i −0.201809 0.349544i
\(146\) 0 0
\(147\) 1.88272 10.6774i 0.155284 0.880658i
\(148\) 0 0
\(149\) 19.8946 7.24104i 1.62983 0.593209i 0.644609 0.764512i \(-0.277020\pi\)
0.985218 + 0.171303i \(0.0547978\pi\)
\(150\) 0 0
\(151\) −16.7285 −1.36134 −0.680671 0.732589i \(-0.738312\pi\)
−0.680671 + 0.732589i \(0.738312\pi\)
\(152\) 0 0
\(153\) 2.88896 0.233559
\(154\) 0 0
\(155\) 6.77725 2.46672i 0.544362 0.198132i
\(156\) 0 0
\(157\) 3.44927 19.5618i 0.275282 1.56120i −0.462784 0.886471i \(-0.653149\pi\)
0.738065 0.674729i \(-0.235740\pi\)
\(158\) 0 0
\(159\) −0.830576 1.43860i −0.0658690 0.114088i
\(160\) 0 0
\(161\) −5.24350 + 4.39982i −0.413246 + 0.346755i
\(162\) 0 0
\(163\) 2.78567 4.82492i 0.218191 0.377917i −0.736064 0.676912i \(-0.763318\pi\)
0.954255 + 0.298994i \(0.0966512\pi\)
\(164\) 0 0
\(165\) 1.67588 + 0.609969i 0.130467 + 0.0474860i
\(166\) 0 0
\(167\) 3.98022 + 22.5730i 0.307999 + 1.74675i 0.609043 + 0.793137i \(0.291554\pi\)
−0.301044 + 0.953610i \(0.597335\pi\)
\(168\) 0 0
\(169\) −6.08944 5.10965i −0.468419 0.393050i
\(170\) 0 0
\(171\) 10.2867 2.95184i 0.786644 0.225733i
\(172\) 0 0
\(173\) −19.5400 16.3960i −1.48560 1.24657i −0.899943 0.436008i \(-0.856392\pi\)
−0.585658 0.810558i \(-0.699164\pi\)
\(174\) 0 0
\(175\) 0.808700 + 4.58637i 0.0611320 + 0.346697i
\(176\) 0 0
\(177\) −7.95088 2.89388i −0.597625 0.217518i
\(178\) 0 0
\(179\) −2.19869 + 3.80824i −0.164338 + 0.284641i −0.936420 0.350881i \(-0.885882\pi\)
0.772082 + 0.635523i \(0.219215\pi\)
\(180\) 0 0
\(181\) 5.64119 4.73352i 0.419306 0.351840i −0.408593 0.912717i \(-0.633980\pi\)
0.827899 + 0.560877i \(0.189536\pi\)
\(182\) 0 0
\(183\) 0.607153 + 1.05162i 0.0448821 + 0.0777380i
\(184\) 0 0
\(185\) −0.488714 + 2.77163i −0.0359310 + 0.203775i
\(186\) 0 0
\(187\) 2.67160 0.972384i 0.195367 0.0711078i
\(188\) 0 0
\(189\) −18.7523 −1.36403
\(190\) 0 0
\(191\) −14.9154 −1.07924 −0.539620 0.841908i \(-0.681432\pi\)
−0.539620 + 0.841908i \(0.681432\pi\)
\(192\) 0 0
\(193\) −21.4669 + 7.81332i −1.54522 + 0.562415i −0.967291 0.253670i \(-0.918362\pi\)
−0.577932 + 0.816085i \(0.696140\pi\)
\(194\) 0 0
\(195\) −0.288058 + 1.63366i −0.0206282 + 0.116989i
\(196\) 0 0
\(197\) 0.984224 + 1.70473i 0.0701231 + 0.121457i 0.898955 0.438041i \(-0.144327\pi\)
−0.828832 + 0.559498i \(0.810994\pi\)
\(198\) 0 0
\(199\) −5.86623 + 4.92235i −0.415846 + 0.348936i −0.826580 0.562819i \(-0.809717\pi\)
0.410734 + 0.911755i \(0.365272\pi\)
\(200\) 0 0
\(201\) −0.871360 + 1.50924i −0.0614610 + 0.106454i
\(202\) 0 0
\(203\) 21.2696 + 7.74149i 1.49283 + 0.543346i
\(204\) 0 0
\(205\) −0.934687 5.30088i −0.0652814 0.370229i
\(206\) 0 0
\(207\) 2.76431 + 2.31953i 0.192133 + 0.161218i
\(208\) 0 0
\(209\) 8.51922 6.19211i 0.589287 0.428317i
\(210\) 0 0
\(211\) −1.93264 1.62168i −0.133048 0.111641i 0.573835 0.818971i \(-0.305455\pi\)
−0.706883 + 0.707330i \(0.749899\pi\)
\(212\) 0 0
\(213\) 0.819515 + 4.64770i 0.0561522 + 0.318455i
\(214\) 0 0
\(215\) −7.24475 2.63687i −0.494088 0.179833i
\(216\) 0 0
\(217\) −16.7940 + 29.0881i −1.14005 + 1.97463i
\(218\) 0 0
\(219\) −1.91747 + 1.60895i −0.129570 + 0.108722i
\(220\) 0 0
\(221\) 1.32224 + 2.29018i 0.0889433 + 0.154054i
\(222\) 0 0
\(223\) 3.84787 21.8224i 0.257673 1.46133i −0.531445 0.847093i \(-0.678351\pi\)
0.789118 0.614242i \(-0.210538\pi\)
\(224\) 0 0
\(225\) 2.30711 0.839719i 0.153807 0.0559812i
\(226\) 0 0
\(227\) −14.4646 −0.960049 −0.480024 0.877255i \(-0.659372\pi\)
−0.480024 + 0.877255i \(0.659372\pi\)
\(228\) 0 0
\(229\) 17.0323 1.12553 0.562764 0.826618i \(-0.309738\pi\)
0.562764 + 0.826618i \(0.309738\pi\)
\(230\) 0 0
\(231\) −7.80476 + 2.84070i −0.513515 + 0.186904i
\(232\) 0 0
\(233\) 4.06307 23.0428i 0.266181 1.50958i −0.499472 0.866330i \(-0.666473\pi\)
0.765652 0.643255i \(-0.222416\pi\)
\(234\) 0 0
\(235\) 3.07142 + 5.31986i 0.200358 + 0.347030i
\(236\) 0 0
\(237\) −1.27442 + 1.06937i −0.0827828 + 0.0694630i
\(238\) 0 0
\(239\) −12.0058 + 20.7947i −0.776593 + 1.34510i 0.157302 + 0.987551i \(0.449721\pi\)
−0.933895 + 0.357548i \(0.883613\pi\)
\(240\) 0 0
\(241\) −23.6077 8.59251i −1.52071 0.553492i −0.559382 0.828910i \(-0.688962\pi\)
−0.961325 + 0.275418i \(0.911184\pi\)
\(242\) 0 0
\(243\) 2.66075 + 15.0899i 0.170687 + 0.968015i
\(244\) 0 0
\(245\) −11.2522 9.44175i −0.718879 0.603211i
\(246\) 0 0
\(247\) 7.04811 + 6.80362i 0.448460 + 0.432904i
\(248\) 0 0
\(249\) 5.77982 + 4.84984i 0.366281 + 0.307346i
\(250\) 0 0
\(251\) −2.25159 12.7694i −0.142119 0.805998i −0.969635 0.244556i \(-0.921358\pi\)
0.827516 0.561442i \(-0.189753\pi\)
\(252\) 0 0
\(253\) 3.33705 + 1.21459i 0.209799 + 0.0763604i
\(254\) 0 0
\(255\) −0.434269 + 0.752176i −0.0271950 + 0.0471031i
\(256\) 0 0
\(257\) −1.77328 + 1.48796i −0.110614 + 0.0928163i −0.696417 0.717637i \(-0.745224\pi\)
0.585803 + 0.810453i \(0.300779\pi\)
\(258\) 0 0
\(259\) −6.55348 11.3510i −0.407213 0.705314i
\(260\) 0 0
\(261\) 2.07209 11.7514i 0.128259 0.727392i
\(262\) 0 0
\(263\) 7.50002 2.72978i 0.462471 0.168326i −0.100268 0.994960i \(-0.531970\pi\)
0.562739 + 0.826635i \(0.309748\pi\)
\(264\) 0 0
\(265\) −2.25051 −0.138247
\(266\) 0 0
\(267\) −4.13921 −0.253315
\(268\) 0 0
\(269\) 21.9625 7.99371i 1.33908 0.487385i 0.429557 0.903040i \(-0.358670\pi\)
0.909523 + 0.415654i \(0.136447\pi\)
\(270\) 0 0
\(271\) 4.18967 23.7608i 0.254504 1.44336i −0.542838 0.839837i \(-0.682650\pi\)
0.797342 0.603527i \(-0.206239\pi\)
\(272\) 0 0
\(273\) −3.86275 6.69048i −0.233784 0.404926i
\(274\) 0 0
\(275\) 1.85089 1.55308i 0.111613 0.0936544i
\(276\) 0 0
\(277\) 6.69101 11.5892i 0.402024 0.696326i −0.591946 0.805978i \(-0.701640\pi\)
0.993970 + 0.109652i \(0.0349735\pi\)
\(278\) 0 0
\(279\) 16.6393 + 6.05622i 0.996171 + 0.362576i
\(280\) 0 0
\(281\) 0.871304 + 4.94141i 0.0519777 + 0.294780i 0.999705 0.0243024i \(-0.00773645\pi\)
−0.947727 + 0.319082i \(0.896625\pi\)
\(282\) 0 0
\(283\) 2.46269 + 2.06644i 0.146392 + 0.122837i 0.713042 0.701121i \(-0.247317\pi\)
−0.566651 + 0.823958i \(0.691761\pi\)
\(284\) 0 0
\(285\) −0.777753 + 3.12199i −0.0460701 + 0.184931i
\(286\) 0 0
\(287\) 19.2029 + 16.1132i 1.13351 + 0.951130i
\(288\) 0 0
\(289\) −2.71159 15.3782i −0.159505 0.904599i
\(290\) 0 0
\(291\) −3.80149 1.38363i −0.222847 0.0811098i
\(292\) 0 0
\(293\) −9.11970 + 15.7958i −0.532779 + 0.922800i 0.466489 + 0.884527i \(0.345519\pi\)
−0.999267 + 0.0382724i \(0.987815\pi\)
\(294\) 0 0
\(295\) −8.78120 + 7.36830i −0.511261 + 0.428999i
\(296\) 0 0
\(297\) 4.86446 + 8.42549i 0.282265 + 0.488897i
\(298\) 0 0
\(299\) −0.573588 + 3.25298i −0.0331715 + 0.188125i
\(300\) 0 0
\(301\) 33.7397 12.2802i 1.94472 0.707821i
\(302\) 0 0
\(303\) −9.04873 −0.519836
\(304\) 0 0
\(305\) 1.64513 0.0941996
\(306\) 0 0
\(307\) −16.3329 + 5.94469i −0.932167 + 0.339281i −0.763068 0.646318i \(-0.776308\pi\)
−0.169099 + 0.985599i \(0.554086\pi\)
\(308\) 0 0
\(309\) 1.76149 9.98992i 0.100208 0.568307i
\(310\) 0 0
\(311\) 2.37948 + 4.12138i 0.134928 + 0.233702i 0.925570 0.378577i \(-0.123586\pi\)
−0.790642 + 0.612279i \(0.790253\pi\)
\(312\) 0 0
\(313\) 6.19056 5.19450i 0.349911 0.293611i −0.450843 0.892603i \(-0.648877\pi\)
0.800754 + 0.598993i \(0.204432\pi\)
\(314\) 0 0
\(315\) −5.71702 + 9.90216i −0.322117 + 0.557924i
\(316\) 0 0
\(317\) 10.1397 + 3.69056i 0.569503 + 0.207282i 0.610691 0.791869i \(-0.290892\pi\)
−0.0411875 + 0.999151i \(0.513114\pi\)
\(318\) 0 0
\(319\) −2.03917 11.5647i −0.114171 0.647498i
\(320\) 0 0
\(321\) 8.56487 + 7.18678i 0.478044 + 0.401127i
\(322\) 0 0
\(323\) 2.24932 + 4.60951i 0.125156 + 0.256480i
\(324\) 0 0
\(325\) 1.72161 + 1.44460i 0.0954975 + 0.0801320i
\(326\) 0 0
\(327\) −1.76156 9.99031i −0.0974145 0.552465i
\(328\) 0 0
\(329\) −26.8827 9.78450i −1.48209 0.539437i
\(330\) 0 0
\(331\) −11.4550 + 19.8406i −0.629622 + 1.09054i 0.358006 + 0.933719i \(0.383457\pi\)
−0.987628 + 0.156817i \(0.949877\pi\)
\(332\) 0 0
\(333\) −5.29322 + 4.44154i −0.290067 + 0.243395i
\(334\) 0 0
\(335\) 1.18051 + 2.04470i 0.0644980 + 0.111714i
\(336\) 0 0
\(337\) −5.07731 + 28.7949i −0.276579 + 1.56856i 0.457322 + 0.889301i \(0.348809\pi\)
−0.733901 + 0.679256i \(0.762303\pi\)
\(338\) 0 0
\(339\) 13.2107 4.80831i 0.717509 0.261152i
\(340\) 0 0
\(341\) 17.4259 0.943664
\(342\) 0 0
\(343\) 35.8075 1.93342
\(344\) 0 0
\(345\) −1.01945 + 0.371049i −0.0548853 + 0.0199766i
\(346\) 0 0
\(347\) −4.61087 + 26.1496i −0.247525 + 1.40378i 0.567031 + 0.823696i \(0.308092\pi\)
−0.814556 + 0.580085i \(0.803019\pi\)
\(348\) 0 0
\(349\) 8.16447 + 14.1413i 0.437034 + 0.756965i 0.997459 0.0712400i \(-0.0226956\pi\)
−0.560425 + 0.828205i \(0.689362\pi\)
\(350\) 0 0
\(351\) −6.93221 + 5.81682i −0.370014 + 0.310479i
\(352\) 0 0
\(353\) 1.94078 3.36153i 0.103297 0.178916i −0.809744 0.586783i \(-0.800394\pi\)
0.913041 + 0.407867i \(0.133727\pi\)
\(354\) 0 0
\(355\) 6.00818 + 2.18680i 0.318881 + 0.116063i
\(356\) 0 0
\(357\) −0.702387 3.98343i −0.0371743 0.210826i
\(358\) 0 0
\(359\) 0.264938 + 0.222310i 0.0139829 + 0.0117331i 0.649752 0.760146i \(-0.274873\pi\)
−0.635769 + 0.771879i \(0.719317\pi\)
\(360\) 0 0
\(361\) 12.7190 + 14.1148i 0.669420 + 0.742884i
\(362\) 0 0
\(363\) −2.91886 2.44921i −0.153200 0.128550i
\(364\) 0 0
\(365\) 0.588864 + 3.33961i 0.0308225 + 0.174803i
\(366\) 0 0
\(367\) −3.13757 1.14198i −0.163780 0.0596110i 0.258829 0.965923i \(-0.416663\pi\)
−0.422609 + 0.906312i \(0.638886\pi\)
\(368\) 0 0
\(369\) 6.60767 11.4448i 0.343981 0.595793i
\(370\) 0 0
\(371\) 8.02882 6.73698i 0.416835 0.349766i
\(372\) 0 0
\(373\) −10.4571 18.1123i −0.541450 0.937818i −0.998821 0.0485425i \(-0.984542\pi\)
0.457372 0.889276i \(-0.348791\pi\)
\(374\) 0 0
\(375\) −0.128174 + 0.726910i −0.00661887 + 0.0375375i
\(376\) 0 0
\(377\) 10.2641 3.73583i 0.528628 0.192405i
\(378\) 0 0
\(379\) 16.4497 0.844966 0.422483 0.906371i \(-0.361159\pi\)
0.422483 + 0.906371i \(0.361159\pi\)
\(380\) 0 0
\(381\) 8.84620 0.453205
\(382\) 0 0
\(383\) 22.2497 8.09821i 1.13690 0.413799i 0.296110 0.955154i \(-0.404311\pi\)
0.840794 + 0.541354i \(0.182088\pi\)
\(384\) 0 0
\(385\) −1.95395 + 11.0814i −0.0995827 + 0.564762i
\(386\) 0 0
\(387\) −9.46433 16.3927i −0.481099 0.833287i
\(388\) 0 0
\(389\) −6.89298 + 5.78389i −0.349488 + 0.293255i −0.800584 0.599220i \(-0.795477\pi\)
0.451097 + 0.892475i \(0.351033\pi\)
\(390\) 0 0
\(391\) −0.864728 + 1.49775i −0.0437312 + 0.0757447i
\(392\) 0 0
\(393\) −6.63751 2.41586i −0.334818 0.121864i
\(394\) 0 0
\(395\) 0.391382 + 2.21964i 0.0196926 + 0.111682i
\(396\) 0 0
\(397\) −3.47331 2.91445i −0.174320 0.146272i 0.551453 0.834206i \(-0.314074\pi\)
−0.725774 + 0.687934i \(0.758518\pi\)
\(398\) 0 0
\(399\) −6.57112 13.4661i −0.328967 0.674149i
\(400\) 0 0
\(401\) 29.5693 + 24.8115i 1.47662 + 1.23903i 0.909707 + 0.415250i \(0.136306\pi\)
0.566911 + 0.823779i \(0.308138\pi\)
\(402\) 0 0
\(403\) 2.81461 + 15.9624i 0.140206 + 0.795146i
\(404\) 0 0
\(405\) 4.12844 + 1.50263i 0.205144 + 0.0746662i
\(406\) 0 0
\(407\) −3.40002 + 5.88900i −0.168533 + 0.291907i
\(408\) 0 0
\(409\) 13.6673 11.4682i 0.675804 0.567067i −0.238973 0.971026i \(-0.576811\pi\)
0.914777 + 0.403959i \(0.132366\pi\)
\(410\) 0 0
\(411\) 4.21208 + 7.29554i 0.207767 + 0.359862i
\(412\) 0 0
\(413\) 9.27017 52.5737i 0.456155 2.58698i
\(414\) 0 0
\(415\) 9.60543 3.49609i 0.471512 0.171616i
\(416\) 0 0
\(417\) 15.4529 0.756731
\(418\) 0 0
\(419\) 6.36461 0.310931 0.155466 0.987841i \(-0.450312\pi\)
0.155466 + 0.987841i \(0.450312\pi\)
\(420\) 0 0
\(421\) −24.0784 + 8.76384i −1.17351 + 0.427123i −0.853906 0.520427i \(-0.825773\pi\)
−0.319606 + 0.947551i \(0.603550\pi\)
\(422\) 0 0
\(423\) −2.61892 + 14.8526i −0.127336 + 0.722160i
\(424\) 0 0
\(425\) 0.588341 + 1.01904i 0.0285388 + 0.0494306i
\(426\) 0 0
\(427\) −5.86908 + 4.92475i −0.284025 + 0.238325i
\(428\) 0 0
\(429\) −2.00404 + 3.47110i −0.0967559 + 0.167586i
\(430\) 0 0
\(431\) −0.258943 0.0942475i −0.0124728 0.00453974i 0.335776 0.941942i \(-0.391001\pi\)
−0.348249 + 0.937402i \(0.613224\pi\)
\(432\) 0 0
\(433\) −0.448391 2.54295i −0.0215483 0.122206i 0.972136 0.234417i \(-0.0753180\pi\)
−0.993684 + 0.112210i \(0.964207\pi\)
\(434\) 0 0
\(435\) 2.74814 + 2.30596i 0.131763 + 0.110562i
\(436\) 0 0
\(437\) −1.54868 + 6.21659i −0.0740835 + 0.297380i
\(438\) 0 0
\(439\) 20.6138 + 17.2971i 0.983844 + 0.825543i 0.984665 0.174456i \(-0.0558168\pi\)
−0.000820776 1.00000i \(0.500261\pi\)
\(440\) 0 0
\(441\) −6.26235 35.5155i −0.298207 1.69122i
\(442\) 0 0
\(443\) 10.7671 + 3.91891i 0.511561 + 0.186193i 0.584887 0.811115i \(-0.301139\pi\)
−0.0733256 + 0.997308i \(0.523361\pi\)
\(444\) 0 0
\(445\) −2.80387 + 4.85644i −0.132916 + 0.230218i
\(446\) 0 0
\(447\) −11.9711 + 10.0449i −0.566211 + 0.475108i
\(448\) 0 0
\(449\) −17.4065 30.1490i −0.821464 1.42282i −0.904592 0.426278i \(-0.859824\pi\)
0.0831280 0.996539i \(-0.473509\pi\)
\(450\) 0 0
\(451\) 2.25836 12.8078i 0.106342 0.603096i
\(452\) 0 0
\(453\) 11.6030 4.22316i 0.545158 0.198421i
\(454\) 0 0
\(455\) −10.4664 −0.490672
\(456\) 0 0
\(457\) −8.23172 −0.385064 −0.192532 0.981291i \(-0.561670\pi\)
−0.192532 + 0.981291i \(0.561670\pi\)
\(458\) 0 0
\(459\) −4.45229 + 1.62050i −0.207815 + 0.0756385i
\(460\) 0 0
\(461\) −4.93548 + 27.9905i −0.229868 + 1.30365i 0.623288 + 0.781992i \(0.285796\pi\)
−0.853156 + 0.521655i \(0.825315\pi\)
\(462\) 0 0
\(463\) 3.47770 + 6.02355i 0.161622 + 0.279938i 0.935451 0.353457i \(-0.114994\pi\)
−0.773828 + 0.633395i \(0.781661\pi\)
\(464\) 0 0
\(465\) −4.07804 + 3.42188i −0.189115 + 0.158686i
\(466\) 0 0
\(467\) −16.3197 + 28.2665i −0.755185 + 1.30802i 0.190098 + 0.981765i \(0.439119\pi\)
−0.945282 + 0.326253i \(0.894214\pi\)
\(468\) 0 0
\(469\) −10.3324 3.76069i −0.477106 0.173652i
\(470\) 0 0
\(471\) 2.54599 + 14.4390i 0.117313 + 0.665315i
\(472\) 0 0
\(473\) −14.2698 11.9738i −0.656127 0.550556i
\(474\) 0 0
\(475\) 3.13612 + 3.02733i 0.143895 + 0.138904i
\(476\) 0 0
\(477\) −4.23269 3.55165i −0.193801 0.162619i
\(478\) 0 0
\(479\) −4.77539 27.0826i −0.218193 1.23744i −0.875278 0.483619i \(-0.839322\pi\)
0.657085 0.753816i \(-0.271789\pi\)
\(480\) 0 0
\(481\) −5.94361 2.16330i −0.271005 0.0986378i
\(482\) 0 0
\(483\) 2.52620 4.37550i 0.114946 0.199092i
\(484\) 0 0
\(485\) −4.19849 + 3.52295i −0.190644 + 0.159969i
\(486\) 0 0
\(487\) −15.1932 26.3153i −0.688468 1.19246i −0.972333 0.233597i \(-0.924950\pi\)
0.283866 0.958864i \(-0.408383\pi\)
\(488\) 0 0
\(489\) −0.714101 + 4.04987i −0.0322928 + 0.183141i
\(490\) 0 0
\(491\) −25.1763 + 9.16343i −1.13619 + 0.413540i −0.840536 0.541755i \(-0.817760\pi\)
−0.295655 + 0.955295i \(0.595538\pi\)
\(492\) 0 0
\(493\) 5.71893 0.257568
\(494\) 0 0
\(495\) 5.93211 0.266628
\(496\) 0 0
\(497\) −27.9808 + 10.1842i −1.25511 + 0.456823i
\(498\) 0 0
\(499\) −1.02904 + 5.83598i −0.0460662 + 0.261254i −0.999139 0.0414868i \(-0.986791\pi\)
0.953073 + 0.302741i \(0.0979017\pi\)
\(500\) 0 0
\(501\) −8.45934 14.6520i −0.377935 0.654603i
\(502\) 0 0
\(503\) −11.6839 + 9.80400i −0.520962 + 0.437139i −0.864967 0.501829i \(-0.832661\pi\)
0.344005 + 0.938968i \(0.388216\pi\)
\(504\) 0 0
\(505\) −6.12955 + 10.6167i −0.272761 + 0.472436i
\(506\) 0 0
\(507\) 5.51365 + 2.00680i 0.244870 + 0.0891253i
\(508\) 0 0
\(509\) −0.610129 3.46022i −0.0270435 0.153371i 0.968296 0.249807i \(-0.0803670\pi\)
−0.995339 + 0.0964352i \(0.969256\pi\)
\(510\) 0 0
\(511\) −12.0981 10.1515i −0.535187 0.449075i
\(512\) 0 0
\(513\) −14.1975 + 10.3193i −0.626833 + 0.455608i
\(514\) 0 0
\(515\) −10.5277 8.83382i −0.463907 0.389265i
\(516\) 0 0
\(517\) 2.57731 + 14.6167i 0.113350 + 0.642840i
\(518\) 0 0
\(519\) 17.6924 + 6.43950i 0.776609 + 0.282663i
\(520\) 0 0
\(521\) 20.2771 35.1209i 0.888355 1.53868i 0.0465357 0.998917i \(-0.485182\pi\)
0.841819 0.539759i \(-0.181485\pi\)
\(522\) 0 0
\(523\) −18.5173 + 15.5379i −0.809707 + 0.679425i −0.950538 0.310609i \(-0.899467\pi\)
0.140831 + 0.990034i \(0.455023\pi\)
\(524\) 0 0
\(525\) −1.71877 2.97699i −0.0750131 0.129927i
\(526\) 0 0
\(527\) −1.47366 + 8.35755i −0.0641937 + 0.364061i
\(528\) 0 0
\(529\) 19.5830 7.12762i 0.851434 0.309897i
\(530\) 0 0
\(531\) −28.1438 −1.22133
\(532\) 0 0
\(533\) 12.0970 0.523977
\(534\) 0 0
\(535\) 14.2339 5.18070i 0.615384 0.223981i
\(536\) 0 0
\(537\) 0.563629 3.19650i 0.0243224 0.137939i
\(538\) 0 0
\(539\) −17.7452 30.7357i −0.764342 1.32388i
\(540\) 0 0
\(541\) 25.9983 21.8152i 1.11775 0.937907i 0.119265 0.992862i \(-0.461946\pi\)
0.998489 + 0.0549553i \(0.0175016\pi\)
\(542\) 0 0
\(543\) −2.71779 + 4.70735i −0.116632 + 0.202012i
\(544\) 0 0
\(545\) −12.9147 4.70056i −0.553204 0.201350i
\(546\) 0 0
\(547\) −0.241319 1.36859i −0.0103181 0.0585167i 0.979214 0.202830i \(-0.0650138\pi\)
−0.989532 + 0.144313i \(0.953903\pi\)
\(548\) 0 0
\(549\) 3.09410 + 2.59626i 0.132053 + 0.110806i
\(550\) 0 0
\(551\) 20.3634 5.84340i 0.867509 0.248937i
\(552\) 0 0
\(553\) −8.04085 6.74708i −0.341932 0.286915i
\(554\) 0 0
\(555\) −0.360731 2.04581i −0.0153122 0.0868398i
\(556\) 0 0
\(557\) −10.2344 3.72501i −0.433645 0.157834i 0.115968 0.993253i \(-0.463003\pi\)
−0.549614 + 0.835419i \(0.685225\pi\)
\(558\) 0 0
\(559\) 8.66338 15.0054i 0.366422 0.634662i
\(560\) 0 0
\(561\) −1.60757 + 1.34891i −0.0678716 + 0.0569511i
\(562\) 0 0
\(563\) −13.9598 24.1792i −0.588337 1.01903i −0.994450 0.105207i \(-0.966449\pi\)
0.406113 0.913823i \(-0.366884\pi\)
\(564\) 0 0
\(565\) 3.30736 18.7570i 0.139142 0.789113i
\(566\) 0 0
\(567\) −19.2266 + 6.99792i −0.807442 + 0.293885i
\(568\) 0 0
\(569\) 6.97102 0.292240 0.146120 0.989267i \(-0.453321\pi\)
0.146120 + 0.989267i \(0.453321\pi\)
\(570\) 0 0
\(571\) −22.7164 −0.950652 −0.475326 0.879810i \(-0.657670\pi\)
−0.475326 + 0.879810i \(0.657670\pi\)
\(572\) 0 0
\(573\) 10.3455 3.76544i 0.432188 0.157304i
\(574\) 0 0
\(575\) −0.255223 + 1.44744i −0.0106436 + 0.0603626i
\(576\) 0 0
\(577\) 10.0668 + 17.4362i 0.419086 + 0.725879i 0.995848 0.0910337i \(-0.0290171\pi\)
−0.576761 + 0.816913i \(0.695684\pi\)
\(578\) 0 0
\(579\) 12.9172 10.8388i 0.536819 0.450445i
\(580\) 0 0
\(581\) −23.8023 + 41.2267i −0.987484 + 1.71037i
\(582\) 0 0
\(583\) −5.10967 1.85977i −0.211621 0.0770237i
\(584\) 0 0
\(585\) 0.958147 + 5.43392i 0.0396145 + 0.224665i
\(586\) 0 0
\(587\) 33.2219 + 27.8765i 1.37121 + 1.15059i 0.972337 + 0.233582i \(0.0750446\pi\)
0.398878 + 0.917004i \(0.369400\pi\)
\(588\) 0 0
\(589\) 3.29219 + 31.2644i 0.135652 + 1.28823i
\(590\) 0 0
\(591\) −1.11303 0.933944i −0.0457840 0.0384173i
\(592\) 0 0
\(593\) −0.509542 2.88976i −0.0209244 0.118668i 0.972557 0.232667i \(-0.0747452\pi\)
−0.993481 + 0.113999i \(0.963634\pi\)
\(594\) 0 0
\(595\) −5.14947 1.87425i −0.211108 0.0768369i
\(596\) 0 0
\(597\) 2.82621 4.89514i 0.115669 0.200345i
\(598\) 0 0
\(599\) −24.5081 + 20.5648i −1.00138 + 0.840254i −0.987174 0.159645i \(-0.948965\pi\)
−0.0142009 + 0.999899i \(0.504520\pi\)
\(600\) 0 0
\(601\) −13.3118 23.0567i −0.542998 0.940501i −0.998730 0.0503835i \(-0.983956\pi\)
0.455732 0.890117i \(-0.349378\pi\)
\(602\) 0 0
\(603\) −1.00659 + 5.70863i −0.0409913 + 0.232473i
\(604\) 0 0
\(605\) −4.85083 + 1.76556i −0.197214 + 0.0717801i
\(606\) 0 0
\(607\) 7.23183 0.293531 0.146766 0.989171i \(-0.453114\pi\)
0.146766 + 0.989171i \(0.453114\pi\)
\(608\) 0 0
\(609\) −16.7071 −0.677008
\(610\) 0 0
\(611\) −12.9729 + 4.72173i −0.524826 + 0.191021i
\(612\) 0 0
\(613\) −8.33598 + 47.2757i −0.336687 + 1.90945i 0.0732109 + 0.997316i \(0.476675\pi\)
−0.409898 + 0.912131i \(0.634436\pi\)
\(614\) 0 0
\(615\) 1.98653 + 3.44077i 0.0801047 + 0.138745i
\(616\) 0 0
\(617\) −15.6781 + 13.1555i −0.631175 + 0.529619i −0.901294 0.433208i \(-0.857381\pi\)
0.270119 + 0.962827i \(0.412937\pi\)
\(618\) 0 0
\(619\) 19.9789 34.6044i 0.803019 1.39087i −0.114601 0.993412i \(-0.536559\pi\)
0.917620 0.397459i \(-0.130108\pi\)
\(620\) 0 0
\(621\) −5.56127 2.02414i −0.223166 0.0812258i
\(622\) 0 0
\(623\) −4.53498 25.7191i −0.181690 1.03042i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) −4.34579 + 6.44562i −0.173554 + 0.257413i
\(628\) 0 0
\(629\) −2.53687 2.12868i −0.101152 0.0848762i
\(630\) 0 0
\(631\) −6.92667 39.2831i −0.275746 1.56383i −0.736581 0.676349i \(-0.763561\pi\)
0.460835 0.887486i \(-0.347550\pi\)
\(632\) 0 0
\(633\) 1.74990 + 0.636910i 0.0695521 + 0.0253149i
\(634\) 0 0
\(635\) 5.99235 10.3791i 0.237799 0.411881i
\(636\) 0 0
\(637\) 25.2883 21.2194i 1.00196 0.840742i
\(638\) 0 0
\(639\) 7.84891 + 13.5947i 0.310498 + 0.537798i
\(640\) 0 0
\(641\) −5.64717 + 32.0267i −0.223050 + 1.26498i 0.643328 + 0.765591i \(0.277553\pi\)
−0.866378 + 0.499389i \(0.833558\pi\)
\(642\) 0 0
\(643\) 3.52792 1.28406i 0.139128 0.0506383i −0.271518 0.962433i \(-0.587526\pi\)
0.410645 + 0.911795i \(0.365303\pi\)
\(644\) 0 0
\(645\) 5.69072 0.224072
\(646\) 0 0
\(647\) 25.9437 1.01995 0.509976 0.860188i \(-0.329654\pi\)
0.509976 + 0.860188i \(0.329654\pi\)
\(648\) 0 0
\(649\) −26.0263 + 9.47280i −1.02162 + 0.371840i
\(650\) 0 0
\(651\) 4.30512 24.4155i 0.168731 0.956920i
\(652\) 0 0
\(653\) −3.60013 6.23560i −0.140884 0.244018i 0.786946 0.617022i \(-0.211661\pi\)
−0.927830 + 0.373004i \(0.878328\pi\)
\(654\) 0 0
\(655\) −7.33068 + 6.15117i −0.286433 + 0.240346i
\(656\) 0 0
\(657\) −4.16290 + 7.21036i −0.162410 + 0.281303i
\(658\) 0 0
\(659\) 3.67127 + 1.33623i 0.143012 + 0.0520522i 0.412535 0.910942i \(-0.364644\pi\)
−0.269522 + 0.962994i \(0.586866\pi\)
\(660\) 0 0
\(661\) 1.37423 + 7.79367i 0.0534515 + 0.303139i 0.999800 0.0200098i \(-0.00636975\pi\)
−0.946348 + 0.323149i \(0.895259\pi\)
\(662\) 0 0
\(663\) −1.49528 1.25469i −0.0580719 0.0487281i
\(664\) 0 0
\(665\) −20.2507 1.41210i −0.785290 0.0547589i
\(666\) 0 0
\(667\) 5.47217 + 4.59170i 0.211883 + 0.177791i
\(668\) 0 0
\(669\) 2.84021 + 16.1076i 0.109809 + 0.622757i
\(670\) 0 0
\(671\) 3.73518 + 1.35949i 0.144195 + 0.0524827i
\(672\) 0 0
\(673\) −12.3605 + 21.4089i −0.476460 + 0.825254i −0.999636 0.0269712i \(-0.991414\pi\)
0.523176 + 0.852225i \(0.324747\pi\)
\(674\) 0 0
\(675\) −3.08455 + 2.58825i −0.118724 + 0.0996216i
\(676\) 0 0
\(677\) −3.62242 6.27421i −0.139221 0.241138i 0.787981 0.615699i \(-0.211126\pi\)
−0.927202 + 0.374562i \(0.877793\pi\)
\(678\) 0 0
\(679\) 4.43227 25.1367i 0.170095 0.964657i
\(680\) 0 0
\(681\) 10.0328 3.65164i 0.384457 0.139931i
\(682\) 0 0
\(683\) −28.2210 −1.07984 −0.539922 0.841715i \(-0.681546\pi\)
−0.539922 + 0.841715i \(0.681546\pi\)
\(684\) 0 0
\(685\) 11.4129 0.436066
\(686\) 0 0
\(687\) −11.8138 + 4.29987i −0.450724 + 0.164050i
\(688\) 0 0
\(689\) 0.878275 4.98094i 0.0334596 0.189759i
\(690\) 0 0
\(691\) 2.42568 + 4.20140i 0.0922772 + 0.159829i 0.908469 0.417952i \(-0.137252\pi\)
−0.816192 + 0.577781i \(0.803919\pi\)
\(692\) 0 0
\(693\) −21.1631 + 17.7580i −0.803921 + 0.674570i
\(694\) 0 0
\(695\) 10.4677 18.1305i 0.397061 0.687730i
\(696\) 0 0
\(697\) 5.95171 + 2.16624i 0.225437 + 0.0820523i
\(698\) 0 0
\(699\) 2.99905 + 17.0085i 0.113434 + 0.643319i
\(700\) 0 0
\(701\) 7.95515 + 6.67517i 0.300462 + 0.252118i 0.780537 0.625110i \(-0.214946\pi\)
−0.480075 + 0.877228i \(0.659390\pi\)
\(702\) 0 0
\(703\) −11.2080 4.98751i −0.422719 0.188108i
\(704\) 0 0
\(705\) −3.47339 2.91452i −0.130815 0.109767i
\(706\) 0 0
\(707\) −9.91393 56.2247i −0.372852 2.11455i
\(708\) 0 0
\(709\) 11.7708 + 4.28424i 0.442063 + 0.160898i 0.553456 0.832879i \(-0.313309\pi\)
−0.111392 + 0.993776i \(0.535531\pi\)
\(710\) 0 0
\(711\) −2.76683 + 4.79229i −0.103764 + 0.179725i
\(712\) 0 0
\(713\) −8.12030 + 6.81374i −0.304108 + 0.255177i
\(714\) 0 0
\(715\) 2.71504 + 4.70259i 0.101537 + 0.175867i
\(716\) 0 0
\(717\) 3.07767 17.4543i 0.114938 0.651844i
\(718\) 0 0
\(719\) −28.5351 + 10.3859i −1.06418 + 0.387330i −0.813997 0.580869i \(-0.802713\pi\)
−0.250182 + 0.968199i \(0.580491\pi\)
\(720\) 0 0
\(721\) 64.0027 2.38359
\(722\) 0 0
\(723\) 18.5438 0.689650
\(724\) 0 0
\(725\) 4.56711 1.66229i 0.169618 0.0617360i
\(726\) 0 0
\(727\) 4.79921 27.2176i 0.177993 1.00945i −0.756640 0.653832i \(-0.773160\pi\)
0.934633 0.355615i \(-0.115728\pi\)
\(728\) 0 0
\(729\) 0.935075 + 1.61960i 0.0346324 + 0.0599851i
\(730\) 0 0
\(731\) 6.94946 5.83129i 0.257035 0.215678i
\(732\) 0 0
\(733\) 16.2769 28.1924i 0.601201 1.04131i −0.391439 0.920204i \(-0.628023\pi\)
0.992640 0.121106i \(-0.0386441\pi\)
\(734\) 0 0
\(735\) 10.1883 + 3.70823i 0.375800 + 0.136780i
\(736\) 0 0
\(737\) 0.990593 + 5.61793i 0.0364890 + 0.206939i
\(738\) 0 0
\(739\) 3.18376 + 2.67150i 0.117117 + 0.0982725i 0.699465 0.714667i \(-0.253422\pi\)
−0.582348 + 0.812939i \(0.697866\pi\)
\(740\) 0 0
\(741\) −6.60624 2.93974i −0.242686 0.107994i
\(742\) 0 0
\(743\) 5.58048 + 4.68258i 0.204728 + 0.171787i 0.739387 0.673281i \(-0.235115\pi\)
−0.534659 + 0.845068i \(0.679560\pi\)
\(744\) 0 0
\(745\) 3.67637 + 20.8497i 0.134692 + 0.763875i
\(746\) 0 0
\(747\) 23.5830 + 8.58350i 0.862856 + 0.314054i
\(748\) 0 0
\(749\) −35.2715 + 61.0921i −1.28879 + 2.23226i
\(750\) 0 0
\(751\) 8.54980 7.17413i 0.311987 0.261788i −0.473326 0.880887i \(-0.656947\pi\)
0.785313 + 0.619100i \(0.212502\pi\)
\(752\) 0 0
\(753\) 4.78540 + 8.28856i 0.174390 + 0.302052i
\(754\) 0 0
\(755\) 2.90487 16.4743i 0.105719 0.599562i
\(756\) 0 0
\(757\) 1.18635 0.431797i 0.0431187 0.0156939i −0.320371 0.947292i \(-0.603807\pi\)
0.363489 + 0.931598i \(0.381585\pi\)
\(758\) 0 0
\(759\) −2.62124 −0.0951449
\(760\) 0 0
\(761\) −42.2386 −1.53115 −0.765574 0.643347i \(-0.777545\pi\)
−0.765574 + 0.643347i \(0.777545\pi\)
\(762\) 0 0
\(763\) 60.1452 21.8911i 2.17740 0.792510i
\(764\) 0 0
\(765\) −0.501663 + 2.84507i −0.0181376 + 0.102864i
\(766\) 0 0
\(767\) −12.8810 22.3106i −0.465106 0.805588i
\(768\) 0 0
\(769\) 31.5317 26.4582i 1.13706 0.954109i 0.137724 0.990471i \(-0.456021\pi\)
0.999339 + 0.0363619i \(0.0115769\pi\)
\(770\) 0 0
\(771\) 0.854325 1.47973i 0.0307678 0.0532913i
\(772\) 0 0
\(773\) 29.6767 + 10.8014i 1.06740 + 0.388500i 0.815202 0.579176i \(-0.196626\pi\)
0.252194 + 0.967677i \(0.418848\pi\)
\(774\) 0 0
\(775\) 1.25239 + 7.10263i 0.0449870 + 0.255134i
\(776\) 0 0
\(777\) 7.41114 + 6.21869i 0.265873 + 0.223094i
\(778\) 0 0
\(779\) 23.4056 + 1.63209i 0.838592 + 0.0584758i
\(780\) 0 0
\(781\) 11.8342 + 9.93005i 0.423460 + 0.355325i
\(782\) 0 0
\(783\) 3.39832 + 19.2728i 0.121446 + 0.688754i
\(784\) 0 0
\(785\) 18.6656 + 6.79374i 0.666205 + 0.242479i
\(786\) 0 0
\(787\) 16.8936 29.2607i 0.602194 1.04303i −0.390295 0.920690i \(-