Properties

Label 380.2.i.b.201.1
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(121,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(6))
 
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("380.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(-0.956115 - 1.65604i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.b.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28442 + 2.22469i) q^{3} +(0.500000 - 0.866025i) q^{5} +3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +O(q^{10})\) \(q+(-1.28442 + 2.22469i) q^{3} +(0.500000 - 0.866025i) q^{5} +3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(0.500000 + 0.866025i) q^{13} +(1.28442 + 2.22469i) q^{15} +(-2.86834 + 4.96812i) q^{17} +(-4.35327 + 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(2.79949 + 4.84887i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.53871 q^{27} +(-3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(-5.86834 + 10.1643i) q^{33} +(1.78442 - 3.09071i) q^{35} +3.56885 q^{37} -2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(5.65277 - 9.79088i) q^{43} -3.59899 q^{45} +(3.38341 + 5.86024i) q^{47} +5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(1.70051 + 2.94536i) q^{53} +(2.28442 - 3.95674i) q^{55} +(5.09899 - 9.96901i) q^{57} +(3.38341 - 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(-6.42212 - 11.1234i) q^{63} +1.00000 q^{65} +(3.16784 + 5.48686i) q^{67} -14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(6.36834 - 11.0303i) q^{73} +2.56885 q^{75} +16.3055 q^{77} +(-2.43115 + 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} -9.40101 q^{83} +(2.86834 + 4.96812i) q^{85} +17.3830 q^{87} +(-6.13770 - 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(-5.90705 + 10.2313i) q^{93} +(-1.98493 + 3.88073i) q^{95} +(-1.31456 + 2.27689i) q^{97} +(-8.22162 - 14.2403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39} - 6 q^{41} + 5 q^{43} - 16 q^{45} + 6 q^{47} - 6 q^{49} - 24 q^{51} + 13 q^{53} + 5 q^{55} + 25 q^{57} + 6 q^{59} - 7 q^{61} + 5 q^{63} + 6 q^{65} - 4 q^{67} + 30 q^{69} + 9 q^{71} + 18 q^{73} - 2 q^{75} + 40 q^{77} - 32 q^{79} - 23 q^{81} - 62 q^{83} - 3 q^{85} - 12 q^{87} - 2 q^{89} + 2 q^{91} + 14 q^{93} - 6 q^{95} - 11 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.28442 + 2.22469i −0.741563 + 1.28442i 0.210220 + 0.977654i \(0.432582\pi\)
−0.951783 + 0.306771i \(0.900751\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 3.56885 1.34890 0.674449 0.738321i \(-0.264381\pi\)
0.674449 + 0.738321i \(0.264381\pi\)
\(8\) 0 0
\(9\) −1.79949 3.11682i −0.599831 1.03894i
\(10\) 0 0
\(11\) 4.56885 1.37756 0.688780 0.724970i \(-0.258147\pi\)
0.688780 + 0.724970i \(0.258147\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 1.28442 + 2.22469i 0.331637 + 0.574412i
\(16\) 0 0
\(17\) −2.86834 + 4.96812i −0.695676 + 1.20495i 0.274277 + 0.961651i \(0.411562\pi\)
−0.969952 + 0.243295i \(0.921772\pi\)
\(18\) 0 0
\(19\) −4.35327 + 0.221364i −0.998710 + 0.0507843i
\(20\) 0 0
\(21\) −4.58392 + 7.93958i −1.00029 + 1.73256i
\(22\) 0 0
\(23\) 2.79949 + 4.84887i 0.583735 + 1.01106i 0.995032 + 0.0995571i \(0.0317426\pi\)
−0.411297 + 0.911501i \(0.634924\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 1.53871 0.296125
\(28\) 0 0
\(29\) −3.38341 5.86024i −0.628284 1.08822i −0.987896 0.155118i \(-0.950424\pi\)
0.359612 0.933102i \(-0.382909\pi\)
\(30\) 0 0
\(31\) 4.59899 0.826003 0.413001 0.910730i \(-0.364480\pi\)
0.413001 + 0.910730i \(0.364480\pi\)
\(32\) 0 0
\(33\) −5.86834 + 10.1643i −1.02155 + 1.76937i
\(34\) 0 0
\(35\) 1.78442 3.09071i 0.301623 0.522426i
\(36\) 0 0
\(37\) 3.56885 0.586715 0.293358 0.956003i \(-0.405227\pi\)
0.293358 + 0.956003i \(0.405227\pi\)
\(38\) 0 0
\(39\) −2.56885 −0.411345
\(40\) 0 0
\(41\) −5.35327 + 9.27214i −0.836041 + 1.44807i 0.0571390 + 0.998366i \(0.481802\pi\)
−0.893180 + 0.449699i \(0.851531\pi\)
\(42\) 0 0
\(43\) 5.65277 9.79088i 0.862039 1.49310i −0.00791826 0.999969i \(-0.502520\pi\)
0.869957 0.493127i \(-0.164146\pi\)
\(44\) 0 0
\(45\) −3.59899 −0.536506
\(46\) 0 0
\(47\) 3.38341 + 5.86024i 0.493522 + 0.854804i 0.999972 0.00746461i \(-0.00237608\pi\)
−0.506451 + 0.862269i \(0.669043\pi\)
\(48\) 0 0
\(49\) 5.73669 0.819527
\(50\) 0 0
\(51\) −7.36834 12.7623i −1.03177 1.78709i
\(52\) 0 0
\(53\) 1.70051 + 2.94536i 0.233582 + 0.404577i 0.958860 0.283880i \(-0.0916218\pi\)
−0.725277 + 0.688457i \(0.758288\pi\)
\(54\) 0 0
\(55\) 2.28442 3.95674i 0.308032 0.533527i
\(56\) 0 0
\(57\) 5.09899 9.96901i 0.675378 1.32043i
\(58\) 0 0
\(59\) 3.38341 5.86024i 0.440483 0.762939i −0.557242 0.830350i \(-0.688141\pi\)
0.997725 + 0.0674112i \(0.0214739\pi\)
\(60\) 0 0
\(61\) −4.06885 7.04745i −0.520963 0.902334i −0.999703 0.0243773i \(-0.992240\pi\)
0.478740 0.877957i \(-0.341094\pi\)
\(62\) 0 0
\(63\) −6.42212 11.1234i −0.809112 1.40142i
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 3.16784 + 5.48686i 0.387013 + 0.670326i 0.992046 0.125874i \(-0.0401735\pi\)
−0.605033 + 0.796200i \(0.706840\pi\)
\(68\) 0 0
\(69\) −14.3830 −1.73150
\(70\) 0 0
\(71\) 0.515069 0.892126i 0.0611275 0.105876i −0.833842 0.552003i \(-0.813864\pi\)
0.894970 + 0.446127i \(0.147197\pi\)
\(72\) 0 0
\(73\) 6.36834 11.0303i 0.745358 1.29100i −0.204669 0.978831i \(-0.565612\pi\)
0.950027 0.312167i \(-0.101055\pi\)
\(74\) 0 0
\(75\) 2.56885 0.296625
\(76\) 0 0
\(77\) 16.3055 1.85819
\(78\) 0 0
\(79\) −2.43115 + 4.21088i −0.273526 + 0.473761i −0.969762 0.244052i \(-0.921523\pi\)
0.696236 + 0.717813i \(0.254857\pi\)
\(80\) 0 0
\(81\) 3.42212 5.92729i 0.380236 0.658588i
\(82\) 0 0
\(83\) −9.40101 −1.03190 −0.515948 0.856620i \(-0.672560\pi\)
−0.515948 + 0.856620i \(0.672560\pi\)
\(84\) 0 0
\(85\) 2.86834 + 4.96812i 0.311116 + 0.538868i
\(86\) 0 0
\(87\) 17.3830 1.86365
\(88\) 0 0
\(89\) −6.13770 10.6308i −0.650595 1.12686i −0.982979 0.183719i \(-0.941186\pi\)
0.332384 0.943144i \(-0.392147\pi\)
\(90\) 0 0
\(91\) 1.78442 + 3.09071i 0.187059 + 0.323995i
\(92\) 0 0
\(93\) −5.90705 + 10.2313i −0.612533 + 1.06094i
\(94\) 0 0
\(95\) −1.98493 + 3.88073i −0.203650 + 0.398154i
\(96\) 0 0
\(97\) −1.31456 + 2.27689i −0.133474 + 0.231183i −0.925013 0.379935i \(-0.875947\pi\)
0.791540 + 0.611118i \(0.209280\pi\)
\(98\) 0 0
\(99\) −8.22162 14.2403i −0.826304 1.43120i
\(100\) 0 0
\(101\) −4.43719 7.68544i −0.441517 0.764730i 0.556285 0.830992i \(-0.312226\pi\)
−0.997802 + 0.0662612i \(0.978893\pi\)
\(102\) 0 0
\(103\) −4.40101 −0.433645 −0.216822 0.976211i \(-0.569569\pi\)
−0.216822 + 0.976211i \(0.569569\pi\)
\(104\) 0 0
\(105\) 4.58392 + 7.93958i 0.447345 + 0.774824i
\(106\) 0 0
\(107\) −13.9347 −1.34711 −0.673557 0.739135i \(-0.735235\pi\)
−0.673557 + 0.739135i \(0.735235\pi\)
\(108\) 0 0
\(109\) −1.91608 + 3.31875i −0.183527 + 0.317879i −0.943079 0.332568i \(-0.892085\pi\)
0.759552 + 0.650447i \(0.225418\pi\)
\(110\) 0 0
\(111\) −4.58392 + 7.93958i −0.435086 + 0.753592i
\(112\) 0 0
\(113\) −1.70655 −0.160539 −0.0802693 0.996773i \(-0.525578\pi\)
−0.0802693 + 0.996773i \(0.525578\pi\)
\(114\) 0 0
\(115\) 5.59899 0.522108
\(116\) 0 0
\(117\) 1.79949 3.11682i 0.166363 0.288150i
\(118\) 0 0
\(119\) −10.2367 + 17.7305i −0.938396 + 1.62535i
\(120\) 0 0
\(121\) 9.87439 0.897672
\(122\) 0 0
\(123\) −13.7518 23.8187i −1.23995 2.14766i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.53871 13.0574i −0.668952 1.15866i −0.978197 0.207677i \(-0.933410\pi\)
0.309245 0.950982i \(-0.399924\pi\)
\(128\) 0 0
\(129\) 14.5211 + 25.1513i 1.27851 + 2.21445i
\(130\) 0 0
\(131\) 6.78442 11.7510i 0.592758 1.02669i −0.401101 0.916034i \(-0.631372\pi\)
0.993859 0.110653i \(-0.0352943\pi\)
\(132\) 0 0
\(133\) −15.5362 + 0.790014i −1.34716 + 0.0685029i
\(134\) 0 0
\(135\) 0.769355 1.33256i 0.0662156 0.114689i
\(136\) 0 0
\(137\) −3.51507 6.08828i −0.300313 0.520157i 0.675894 0.736999i \(-0.263758\pi\)
−0.976207 + 0.216842i \(0.930424\pi\)
\(138\) 0 0
\(139\) 6.09899 + 10.5638i 0.517309 + 0.896006i 0.999798 + 0.0201039i \(0.00639970\pi\)
−0.482488 + 0.875902i \(0.660267\pi\)
\(140\) 0 0
\(141\) −17.3830 −1.46391
\(142\) 0 0
\(143\) 2.28442 + 3.95674i 0.191033 + 0.330879i
\(144\) 0 0
\(145\) −6.76683 −0.561954
\(146\) 0 0
\(147\) −7.36834 + 12.7623i −0.607731 + 1.05262i
\(148\) 0 0
\(149\) −4.76936 + 8.26077i −0.390721 + 0.676748i −0.992545 0.121880i \(-0.961108\pi\)
0.601824 + 0.798629i \(0.294441\pi\)
\(150\) 0 0
\(151\) 20.4131 1.66119 0.830597 0.556874i \(-0.187999\pi\)
0.830597 + 0.556874i \(0.187999\pi\)
\(152\) 0 0
\(153\) 20.6463 1.66915
\(154\) 0 0
\(155\) 2.29949 3.98284i 0.184700 0.319909i
\(156\) 0 0
\(157\) 7.15277 12.3890i 0.570853 0.988747i −0.425626 0.904899i \(-0.639946\pi\)
0.996479 0.0838472i \(-0.0267207\pi\)
\(158\) 0 0
\(159\) −8.73669 −0.692864
\(160\) 0 0
\(161\) 9.99097 + 17.3049i 0.787399 + 1.36382i
\(162\) 0 0
\(163\) 2.53871 0.198847 0.0994236 0.995045i \(-0.468300\pi\)
0.0994236 + 0.995045i \(0.468300\pi\)
\(164\) 0 0
\(165\) 5.86834 + 10.1643i 0.456850 + 0.791287i
\(166\) 0 0
\(167\) 6.78442 + 11.7510i 0.524995 + 0.909317i 0.999576 + 0.0291058i \(0.00926598\pi\)
−0.474582 + 0.880211i \(0.657401\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 8.52364 + 13.1700i 0.651819 + 1.00714i
\(172\) 0 0
\(173\) −1.18544 + 2.05324i −0.0901271 + 0.156105i −0.907564 0.419913i \(-0.862061\pi\)
0.817437 + 0.576017i \(0.195394\pi\)
\(174\) 0 0
\(175\) −1.78442 3.09071i −0.134890 0.233636i
\(176\) 0 0
\(177\) 8.69148 + 15.0541i 0.653292 + 1.13153i
\(178\) 0 0
\(179\) 17.8744 1.33599 0.667997 0.744164i \(-0.267152\pi\)
0.667997 + 0.744164i \(0.267152\pi\)
\(180\) 0 0
\(181\) −13.2065 22.8744i −0.981635 1.70024i −0.656028 0.754737i \(-0.727765\pi\)
−0.325607 0.945505i \(-0.605569\pi\)
\(182\) 0 0
\(183\) 20.9045 1.54531
\(184\) 0 0
\(185\) 1.78442 3.09071i 0.131194 0.227234i
\(186\) 0 0
\(187\) −13.1050 + 22.6986i −0.958335 + 1.65988i
\(188\) 0 0
\(189\) 5.49143 0.399443
\(190\) 0 0
\(191\) 0.526625 0.0381052 0.0190526 0.999818i \(-0.493935\pi\)
0.0190526 + 0.999818i \(0.493935\pi\)
\(192\) 0 0
\(193\) 2.67037 4.62521i 0.192217 0.332930i −0.753767 0.657141i \(-0.771766\pi\)
0.945985 + 0.324211i \(0.105099\pi\)
\(194\) 0 0
\(195\) −1.28442 + 2.22469i −0.0919796 + 0.159313i
\(196\) 0 0
\(197\) −4.43115 −0.315706 −0.157853 0.987463i \(-0.550457\pi\)
−0.157853 + 0.987463i \(0.550457\pi\)
\(198\) 0 0
\(199\) −6.08392 10.5377i −0.431278 0.746995i 0.565706 0.824607i \(-0.308604\pi\)
−0.996984 + 0.0776123i \(0.975270\pi\)
\(200\) 0 0
\(201\) −16.2754 −1.14798
\(202\) 0 0
\(203\) −12.0749 20.9143i −0.847491 1.46790i
\(204\) 0 0
\(205\) 5.35327 + 9.27214i 0.373889 + 0.647595i
\(206\) 0 0
\(207\) 10.0753 17.4510i 0.700285 1.21293i
\(208\) 0 0
\(209\) −19.8895 + 1.01138i −1.37578 + 0.0699584i
\(210\) 0 0
\(211\) 10.3357 17.9019i 0.711537 1.23242i −0.252743 0.967534i \(-0.581333\pi\)
0.964280 0.264885i \(-0.0853341\pi\)
\(212\) 0 0
\(213\) 1.32314 + 2.29174i 0.0906598 + 0.157027i
\(214\) 0 0
\(215\) −5.65277 9.79088i −0.385516 0.667733i
\(216\) 0 0
\(217\) 16.4131 1.11419
\(218\) 0 0
\(219\) 16.3593 + 28.3352i 1.10546 + 1.91471i
\(220\) 0 0
\(221\) −5.73669 −0.385891
\(222\) 0 0
\(223\) −2.25429 + 3.90454i −0.150958 + 0.261467i −0.931580 0.363536i \(-0.881569\pi\)
0.780622 + 0.625004i \(0.214903\pi\)
\(224\) 0 0
\(225\) −1.79949 + 3.11682i −0.119966 + 0.207788i
\(226\) 0 0
\(227\) −16.6714 −1.10652 −0.553258 0.833010i \(-0.686616\pi\)
−0.553258 + 0.833010i \(0.686616\pi\)
\(228\) 0 0
\(229\) 5.31060 0.350934 0.175467 0.984485i \(-0.443856\pi\)
0.175467 + 0.984485i \(0.443856\pi\)
\(230\) 0 0
\(231\) −20.9432 + 36.2747i −1.37796 + 2.38670i
\(232\) 0 0
\(233\) 1.38594 2.40052i 0.0907961 0.157263i −0.817050 0.576566i \(-0.804392\pi\)
0.907846 + 0.419303i \(0.137726\pi\)
\(234\) 0 0
\(235\) 6.76683 0.441419
\(236\) 0 0
\(237\) −6.24526 10.8171i −0.405673 0.702647i
\(238\) 0 0
\(239\) −8.59899 −0.556222 −0.278111 0.960549i \(-0.589708\pi\)
−0.278111 + 0.960549i \(0.589708\pi\)
\(240\) 0 0
\(241\) −2.83216 4.90545i −0.182436 0.315988i 0.760274 0.649603i \(-0.225065\pi\)
−0.942709 + 0.333615i \(0.891731\pi\)
\(242\) 0 0
\(243\) 11.0990 + 19.2240i 0.712000 + 1.23322i
\(244\) 0 0
\(245\) 2.86834 4.96812i 0.183252 0.317401i
\(246\) 0 0
\(247\) −2.36834 3.65936i −0.150694 0.232840i
\(248\) 0 0
\(249\) 12.0749 20.9143i 0.765215 1.32539i
\(250\) 0 0
\(251\) 11.5598 + 20.0222i 0.729650 + 1.26379i 0.957031 + 0.289984i \(0.0936501\pi\)
−0.227382 + 0.973806i \(0.573017\pi\)
\(252\) 0 0
\(253\) 12.7905 + 22.1537i 0.804130 + 1.39279i
\(254\) 0 0
\(255\) −14.7367 −0.922847
\(256\) 0 0
\(257\) 5.28442 + 9.15289i 0.329633 + 0.570942i 0.982439 0.186584i \(-0.0597415\pi\)
−0.652806 + 0.757525i \(0.726408\pi\)
\(258\) 0 0
\(259\) 12.7367 0.791419
\(260\) 0 0
\(261\) −12.1769 + 21.0909i −0.753729 + 1.30550i
\(262\) 0 0
\(263\) −4.43115 + 7.67498i −0.273236 + 0.473259i −0.969689 0.244344i \(-0.921427\pi\)
0.696452 + 0.717603i \(0.254761\pi\)
\(264\) 0 0
\(265\) 3.40101 0.208922
\(266\) 0 0
\(267\) 31.5337 1.92983
\(268\) 0 0
\(269\) −2.66784 + 4.62083i −0.162661 + 0.281737i −0.935822 0.352472i \(-0.885341\pi\)
0.773161 + 0.634210i \(0.218674\pi\)
\(270\) 0 0
\(271\) −2.23064 + 3.86359i −0.135502 + 0.234696i −0.925789 0.378040i \(-0.876598\pi\)
0.790287 + 0.612737i \(0.209931\pi\)
\(272\) 0 0
\(273\) −9.16784 −0.554863
\(274\) 0 0
\(275\) −2.28442 3.95674i −0.137756 0.238600i
\(276\) 0 0
\(277\) −23.0774 −1.38659 −0.693294 0.720655i \(-0.743841\pi\)
−0.693294 + 0.720655i \(0.743841\pi\)
\(278\) 0 0
\(279\) −8.27585 14.3342i −0.495462 0.858166i
\(280\) 0 0
\(281\) −2.01507 3.49020i −0.120209 0.208208i 0.799641 0.600478i \(-0.205023\pi\)
−0.919850 + 0.392270i \(0.871690\pi\)
\(282\) 0 0
\(283\) −15.9196 + 27.5735i −0.946322 + 1.63908i −0.193239 + 0.981152i \(0.561899\pi\)
−0.753083 + 0.657925i \(0.771434\pi\)
\(284\) 0 0
\(285\) −6.08392 9.40036i −0.360380 0.556829i
\(286\) 0 0
\(287\) −19.1050 + 33.0909i −1.12773 + 1.95329i
\(288\) 0 0
\(289\) −7.95479 13.7781i −0.467929 0.810477i
\(290\) 0 0
\(291\) −3.37692 5.84899i −0.197958 0.342874i
\(292\) 0 0
\(293\) −18.6764 −1.09109 −0.545544 0.838082i \(-0.683677\pi\)
−0.545544 + 0.838082i \(0.683677\pi\)
\(294\) 0 0
\(295\) −3.38341 5.86024i −0.196990 0.341197i
\(296\) 0 0
\(297\) 7.03014 0.407930
\(298\) 0 0
\(299\) −2.79949 + 4.84887i −0.161899 + 0.280417i
\(300\) 0 0
\(301\) 20.1739 34.9422i 1.16280 2.01403i
\(302\) 0 0
\(303\) 22.7970 1.30965
\(304\) 0 0
\(305\) −8.13770 −0.465963
\(306\) 0 0
\(307\) 15.8955 27.5318i 0.907204 1.57132i 0.0892730 0.996007i \(-0.471546\pi\)
0.817931 0.575316i \(-0.195121\pi\)
\(308\) 0 0
\(309\) 5.65277 9.79088i 0.321575 0.556984i
\(310\) 0 0
\(311\) 2.37087 0.134440 0.0672199 0.997738i \(-0.478587\pi\)
0.0672199 + 0.997738i \(0.478587\pi\)
\(312\) 0 0
\(313\) 6.10503 + 10.5742i 0.345077 + 0.597691i 0.985368 0.170442i \(-0.0545195\pi\)
−0.640291 + 0.768132i \(0.721186\pi\)
\(314\) 0 0
\(315\) −12.8442 −0.723691
\(316\) 0 0
\(317\) −14.2216 24.6326i −0.798766 1.38350i −0.920420 0.390930i \(-0.872153\pi\)
0.121655 0.992572i \(-0.461180\pi\)
\(318\) 0 0
\(319\) −15.4583 26.7746i −0.865499 1.49909i
\(320\) 0 0
\(321\) 17.8980 31.0003i 0.998971 1.73027i
\(322\) 0 0
\(323\) 11.3869 22.2625i 0.633586 1.23872i
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 0 0
\(327\) −4.92212 8.52537i −0.272194 0.471454i
\(328\) 0 0
\(329\) 12.0749 + 20.9143i 0.665710 + 1.15304i
\(330\) 0 0
\(331\) −32.5930 −1.79147 −0.895737 0.444584i \(-0.853352\pi\)
−0.895737 + 0.444584i \(0.853352\pi\)
\(332\) 0 0
\(333\) −6.42212 11.1234i −0.351930 0.609561i
\(334\) 0 0
\(335\) 6.33568 0.346155
\(336\) 0 0
\(337\) −5.83216 + 10.1016i −0.317698 + 0.550269i −0.980007 0.198961i \(-0.936243\pi\)
0.662309 + 0.749231i \(0.269577\pi\)
\(338\) 0 0
\(339\) 2.19193 3.79654i 0.119049 0.206200i
\(340\) 0 0
\(341\) 21.0121 1.13787
\(342\) 0 0
\(343\) −4.50857 −0.243440
\(344\) 0 0
\(345\) −7.19148 + 12.4560i −0.387176 + 0.670609i
\(346\) 0 0
\(347\) −15.1613 + 26.2602i −0.813903 + 1.40972i 0.0962092 + 0.995361i \(0.469328\pi\)
−0.910113 + 0.414361i \(0.864005\pi\)
\(348\) 0 0
\(349\) 3.44324 0.184312 0.0921561 0.995745i \(-0.470624\pi\)
0.0921561 + 0.995745i \(0.470624\pi\)
\(350\) 0 0
\(351\) 0.769355 + 1.33256i 0.0410652 + 0.0711269i
\(352\) 0 0
\(353\) −6.53871 −0.348020 −0.174010 0.984744i \(-0.555673\pi\)
−0.174010 + 0.984744i \(0.555673\pi\)
\(354\) 0 0
\(355\) −0.515069 0.892126i −0.0273370 0.0473491i
\(356\) 0 0
\(357\) −26.2965 45.5469i −1.39176 2.41060i
\(358\) 0 0
\(359\) 11.2392 19.4669i 0.593183 1.02742i −0.400617 0.916245i \(-0.631204\pi\)
0.993801 0.111178i \(-0.0354623\pi\)
\(360\) 0 0
\(361\) 18.9020 1.92731i 0.994842 0.101438i
\(362\) 0 0
\(363\) −12.6829 + 21.9674i −0.665680 + 1.15299i
\(364\) 0 0
\(365\) −6.36834 11.0303i −0.333334 0.577352i
\(366\) 0 0
\(367\) −4.29696 7.44256i −0.224300 0.388499i 0.731809 0.681509i \(-0.238676\pi\)
−0.956109 + 0.293011i \(0.905343\pi\)
\(368\) 0 0
\(369\) 38.5327 2.00593
\(370\) 0 0
\(371\) 6.06885 + 10.5116i 0.315079 + 0.545733i
\(372\) 0 0
\(373\) 37.2453 1.92849 0.964243 0.265019i \(-0.0853782\pi\)
0.964243 + 0.265019i \(0.0853782\pi\)
\(374\) 0 0
\(375\) 1.28442 2.22469i 0.0663274 0.114882i
\(376\) 0 0
\(377\) 3.38341 5.86024i 0.174255 0.301818i
\(378\) 0 0
\(379\) 12.1678 0.625020 0.312510 0.949914i \(-0.398830\pi\)
0.312510 + 0.949914i \(0.398830\pi\)
\(380\) 0 0
\(381\) 38.7316 1.98428
\(382\) 0 0
\(383\) 12.5272 21.6977i 0.640108 1.10870i −0.345301 0.938492i \(-0.612223\pi\)
0.985408 0.170207i \(-0.0544436\pi\)
\(384\) 0 0
\(385\) 8.15277 14.1210i 0.415504 0.719673i
\(386\) 0 0
\(387\) −40.6885 −2.06831
\(388\) 0 0
\(389\) −11.0211 19.0891i −0.558793 0.967857i −0.997598 0.0692748i \(-0.977931\pi\)
0.438805 0.898582i \(-0.355402\pi\)
\(390\) 0 0
\(391\) −32.1196 −1.62436
\(392\) 0 0
\(393\) 17.4282 + 30.1865i 0.879135 + 1.52271i
\(394\) 0 0
\(395\) 2.43115 + 4.21088i 0.122324 + 0.211872i
\(396\) 0 0
\(397\) −18.0900 + 31.3327i −0.907909 + 1.57254i −0.0909453 + 0.995856i \(0.528989\pi\)
−0.816964 + 0.576689i \(0.804344\pi\)
\(398\) 0 0
\(399\) 18.1975 35.5779i 0.911016 1.78112i
\(400\) 0 0
\(401\) −13.9583 + 24.1765i −0.697045 + 1.20732i 0.272442 + 0.962172i \(0.412169\pi\)
−0.969487 + 0.245144i \(0.921165\pi\)
\(402\) 0 0
\(403\) 2.29949 + 3.98284i 0.114546 + 0.198399i
\(404\) 0 0
\(405\) −3.42212 5.92729i −0.170047 0.294530i
\(406\) 0 0
\(407\) 16.3055 0.808235
\(408\) 0 0
\(409\) −4.06281 7.03699i −0.200893 0.347957i 0.747924 0.663785i \(-0.231051\pi\)
−0.948816 + 0.315828i \(0.897718\pi\)
\(410\) 0 0
\(411\) 18.0594 0.890803
\(412\) 0 0
\(413\) 12.0749 20.9143i 0.594167 1.02913i
\(414\) 0 0
\(415\) −4.70051 + 8.14151i −0.230739 + 0.399651i
\(416\) 0 0
\(417\) −31.3348 −1.53447
\(418\) 0 0
\(419\) −2.87439 −0.140423 −0.0702115 0.997532i \(-0.522367\pi\)
−0.0702115 + 0.997532i \(0.522367\pi\)
\(420\) 0 0
\(421\) 3.48240 6.03170i 0.169722 0.293967i −0.768600 0.639729i \(-0.779046\pi\)
0.938322 + 0.345763i \(0.112380\pi\)
\(422\) 0 0
\(423\) 12.1769 21.0909i 0.592059 1.02548i
\(424\) 0 0
\(425\) 5.73669 0.278270
\(426\) 0 0
\(427\) −14.5211 25.1513i −0.702726 1.21716i
\(428\) 0 0
\(429\) −11.7367 −0.566653
\(430\) 0 0
\(431\) 5.08996 + 8.81607i 0.245175 + 0.424655i 0.962181 0.272412i \(-0.0878213\pi\)
−0.717006 + 0.697067i \(0.754488\pi\)
\(432\) 0 0
\(433\) 9.88341 + 17.1186i 0.474967 + 0.822666i 0.999589 0.0286689i \(-0.00912683\pi\)
−0.524622 + 0.851335i \(0.675793\pi\)
\(434\) 0 0
\(435\) 8.69148 15.0541i 0.416725 0.721788i
\(436\) 0 0
\(437\) −13.2603 20.4887i −0.634328 0.980109i
\(438\) 0 0
\(439\) −19.3266 + 33.4747i −0.922411 + 1.59766i −0.126737 + 0.991936i \(0.540450\pi\)
−0.795673 + 0.605726i \(0.792883\pi\)
\(440\) 0 0
\(441\) −10.3231 17.8802i −0.491578 0.851438i
\(442\) 0 0
\(443\) −5.35327 9.27214i −0.254342 0.440533i 0.710375 0.703824i \(-0.248525\pi\)
−0.964717 + 0.263291i \(0.915192\pi\)
\(444\) 0 0
\(445\) −12.2754 −0.581910
\(446\) 0 0
\(447\) −12.2518 21.2207i −0.579488 1.00370i
\(448\) 0 0
\(449\) 23.0724 1.08885 0.544426 0.838809i \(-0.316747\pi\)
0.544426 + 0.838809i \(0.316747\pi\)
\(450\) 0 0
\(451\) −24.4583 + 42.3630i −1.15170 + 1.99480i
\(452\) 0 0
\(453\) −26.2191 + 45.4128i −1.23188 + 2.13368i
\(454\) 0 0
\(455\) 3.56885 0.167310
\(456\) 0 0
\(457\) −6.87439 −0.321570 −0.160785 0.986989i \(-0.551403\pi\)
−0.160785 + 0.986989i \(0.551403\pi\)
\(458\) 0 0
\(459\) −4.41355 + 7.64450i −0.206007 + 0.356815i
\(460\) 0 0
\(461\) 1.41355 2.44834i 0.0658357 0.114031i −0.831229 0.555931i \(-0.812362\pi\)
0.897064 + 0.441900i \(0.145695\pi\)
\(462\) 0 0
\(463\) −23.9347 −1.11234 −0.556169 0.831069i \(-0.687729\pi\)
−0.556169 + 0.831069i \(0.687729\pi\)
\(464\) 0 0
\(465\) 5.90705 + 10.2313i 0.273933 + 0.474466i
\(466\) 0 0
\(467\) 33.5508 1.55255 0.776273 0.630397i \(-0.217108\pi\)
0.776273 + 0.630397i \(0.217108\pi\)
\(468\) 0 0
\(469\) 11.3055 + 19.5818i 0.522041 + 0.904202i
\(470\) 0 0
\(471\) 18.3744 + 31.8254i 0.846647 + 1.46644i
\(472\) 0 0
\(473\) 25.8266 44.7331i 1.18751 2.05683i
\(474\) 0 0
\(475\) 2.36834 + 3.65936i 0.108667 + 0.167903i
\(476\) 0 0
\(477\) 6.12010 10.6003i 0.280220 0.485356i
\(478\) 0 0
\(479\) 18.4583 + 31.9707i 0.843382 + 1.46078i 0.887019 + 0.461732i \(0.152772\pi\)
−0.0436379 + 0.999047i \(0.513895\pi\)
\(480\) 0 0
\(481\) 1.78442 + 3.09071i 0.0813628 + 0.140924i
\(482\) 0 0
\(483\) −51.3306 −2.33562
\(484\) 0 0
\(485\) 1.31456 + 2.27689i 0.0596913 + 0.103388i
\(486\) 0 0
\(487\) −12.8744 −0.583394 −0.291697 0.956511i \(-0.594220\pi\)
−0.291697 + 0.956511i \(0.594220\pi\)
\(488\) 0 0
\(489\) −3.26078 + 5.64784i −0.147458 + 0.255404i
\(490\) 0 0
\(491\) 12.3382 21.3704i 0.556815 0.964433i −0.440944 0.897534i \(-0.645356\pi\)
0.997760 0.0668981i \(-0.0213103\pi\)
\(492\) 0 0
\(493\) 38.8192 1.74833
\(494\) 0 0
\(495\) −16.4432 −0.739069
\(496\) 0 0
\(497\) 1.83821 3.18386i 0.0824548 0.142816i
\(498\) 0 0
\(499\) −15.7603 + 27.2977i −0.705529 + 1.22201i 0.260971 + 0.965347i \(0.415957\pi\)
−0.966500 + 0.256666i \(0.917376\pi\)
\(500\) 0 0
\(501\) −34.8563 −1.55727
\(502\) 0 0
\(503\) −6.08645 10.5420i −0.271381 0.470046i 0.697834 0.716259i \(-0.254147\pi\)
−0.969216 + 0.246213i \(0.920814\pi\)
\(504\) 0 0
\(505\) −8.87439 −0.394905
\(506\) 0 0
\(507\) 15.4131 + 26.6963i 0.684520 + 1.18562i
\(508\) 0 0
\(509\) 4.70051 + 8.14151i 0.208346 + 0.360866i 0.951194 0.308594i \(-0.0998586\pi\)
−0.742847 + 0.669461i \(0.766525\pi\)
\(510\) 0 0
\(511\) 22.7277 39.3655i 1.00541 1.74143i
\(512\) 0 0
\(513\) −6.69843 + 0.340615i −0.295743 + 0.0150385i
\(514\) 0 0
\(515\) −2.20051 + 3.81139i −0.0969659 + 0.167950i
\(516\) 0 0
\(517\) 15.4583 + 26.7746i 0.679856 + 1.17754i
\(518\) 0 0
\(519\) −3.04521 5.27446i −0.133670 0.231523i
\(520\) 0 0
\(521\) 8.49649 0.372238 0.186119 0.982527i \(-0.440409\pi\)
0.186119 + 0.982527i \(0.440409\pi\)
\(522\) 0 0
\(523\) −11.2191 19.4320i −0.490577 0.849703i 0.509365 0.860551i \(-0.329880\pi\)
−0.999941 + 0.0108473i \(0.996547\pi\)
\(524\) 0 0
\(525\) 9.16784 0.400117
\(526\) 0 0
\(527\) −13.1915 + 22.8483i −0.574630 + 0.995288i
\(528\) 0 0
\(529\) −4.17434 + 7.23016i −0.181493 + 0.314355i
\(530\) 0 0
\(531\) −24.3537 −1.05686
\(532\) 0 0
\(533\) −10.7065 −0.463752
\(534\) 0 0
\(535\) −6.96733 + 12.0678i −0.301224 + 0.521735i
\(536\) 0 0
\(537\) −22.9583 + 39.7650i −0.990724 + 1.71598i
\(538\) 0 0
\(539\) 26.2101 1.12895
\(540\) 0 0
\(541\) 13.7603 + 23.8336i 0.591603 + 1.02469i 0.994017 + 0.109228i \(0.0348379\pi\)
−0.402414 + 0.915458i \(0.631829\pi\)
\(542\) 0 0
\(543\) 67.8513 2.91178
\(544\) 0 0
\(545\) 1.91608 + 3.31875i 0.0820759 + 0.142160i
\(546\) 0 0
\(547\) 0.425107 + 0.736308i 0.0181763 + 0.0314822i 0.874970 0.484176i \(-0.160881\pi\)
−0.856794 + 0.515659i \(0.827547\pi\)
\(548\) 0 0
\(549\) −14.6437 + 25.3637i −0.624980 + 1.08250i
\(550\) 0 0
\(551\) 16.0262 + 24.7623i 0.682738 + 1.05491i
\(552\) 0 0
\(553\) −8.67641 + 15.0280i −0.368958 + 0.639055i
\(554\) 0 0
\(555\) 4.58392 + 7.93958i 0.194577 + 0.337016i
\(556\) 0 0
\(557\) 19.6950 + 34.1127i 0.834504 + 1.44540i 0.894434 + 0.447200i \(0.147579\pi\)
−0.0599303 + 0.998203i \(0.519088\pi\)
\(558\) 0 0
\(559\) 11.3055 0.478173
\(560\) 0 0
\(561\) −33.6649 58.3092i −1.42133 2.46182i
\(562\) 0 0
\(563\) −22.0774 −0.930452 −0.465226 0.885192i \(-0.654027\pi\)
−0.465226 + 0.885192i \(0.654027\pi\)
\(564\) 0 0
\(565\) −0.853274 + 1.47791i −0.0358975 + 0.0621763i
\(566\) 0 0
\(567\) 12.2130 21.1536i 0.512900 0.888368i
\(568\) 0 0
\(569\) −7.53365 −0.315827 −0.157914 0.987453i \(-0.550477\pi\)
−0.157914 + 0.987453i \(0.550477\pi\)
\(570\) 0 0
\(571\) −38.2824 −1.60207 −0.801035 0.598618i \(-0.795717\pi\)
−0.801035 + 0.598618i \(0.795717\pi\)
\(572\) 0 0
\(573\) −0.676410 + 1.17158i −0.0282574 + 0.0489433i
\(574\) 0 0
\(575\) 2.79949 4.84887i 0.116747 0.202212i
\(576\) 0 0
\(577\) −3.21006 −0.133637 −0.0668183 0.997765i \(-0.521285\pi\)
−0.0668183 + 0.997765i \(0.521285\pi\)
\(578\) 0 0
\(579\) 6.85977 + 11.8815i 0.285082 + 0.493777i
\(580\) 0 0
\(581\) −33.5508 −1.39192
\(582\) 0 0
\(583\) 7.76936 + 13.4569i 0.321774 + 0.557329i
\(584\) 0 0
\(585\) −1.79949 3.11682i −0.0743999 0.128864i
\(586\) 0 0
\(587\) 1.24824 2.16202i 0.0515205 0.0892361i −0.839115 0.543954i \(-0.816927\pi\)
0.890636 + 0.454718i \(0.150260\pi\)
\(588\) 0 0
\(589\) −20.0207 + 1.01805i −0.824937 + 0.0419480i
\(590\) 0 0
\(591\) 5.69148 9.85793i 0.234116 0.405501i
\(592\) 0 0
\(593\) −7.03014 12.1766i −0.288693 0.500031i 0.684805 0.728726i \(-0.259887\pi\)
−0.973498 + 0.228695i \(0.926554\pi\)
\(594\) 0 0
\(595\) 10.2367 + 17.7305i 0.419663 + 0.726878i
\(596\) 0 0
\(597\) 31.2573 1.27928
\(598\) 0 0
\(599\) 11.6678 + 20.2093i 0.476735 + 0.825729i 0.999645 0.0266590i \(-0.00848682\pi\)
−0.522910 + 0.852388i \(0.675153\pi\)
\(600\) 0 0
\(601\) 46.6111 1.90131 0.950653 0.310257i \(-0.100415\pi\)
0.950653 + 0.310257i \(0.100415\pi\)
\(602\) 0 0
\(603\) 11.4010 19.7471i 0.464285 0.804165i
\(604\) 0 0
\(605\) 4.93719 8.55147i 0.200725 0.347667i
\(606\) 0 0
\(607\) 11.1929 0.454307 0.227153 0.973859i \(-0.427058\pi\)
0.227153 + 0.973859i \(0.427058\pi\)
\(608\) 0 0
\(609\) 62.0372 2.51387
\(610\) 0 0
\(611\) −3.38341 + 5.86024i −0.136878 + 0.237080i
\(612\) 0 0
\(613\) −16.9794 + 29.4092i −0.685792 + 1.18783i 0.287395 + 0.957812i \(0.407211\pi\)
−0.973187 + 0.230015i \(0.926123\pi\)
\(614\) 0 0
\(615\) −27.5035 −1.10905
\(616\) 0 0
\(617\) −8.27287 14.3290i −0.333053 0.576865i 0.650056 0.759887i \(-0.274746\pi\)
−0.983109 + 0.183022i \(0.941412\pi\)
\(618\) 0 0
\(619\) 21.4312 0.861391 0.430695 0.902497i \(-0.358268\pi\)
0.430695 + 0.902497i \(0.358268\pi\)
\(620\) 0 0
\(621\) 4.30761 + 7.46100i 0.172859 + 0.299400i
\(622\) 0 0
\(623\) −21.9045 37.9398i −0.877586 1.52002i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 23.2965 45.5469i 0.930373 1.81897i
\(628\) 0 0
\(629\) −10.2367 + 17.7305i −0.408163 + 0.706960i
\(630\) 0 0
\(631\) −10.5035 18.1926i −0.418138 0.724237i 0.577614 0.816310i \(-0.303984\pi\)
−0.995752 + 0.0920733i \(0.970651\pi\)
\(632\) 0 0
\(633\) 26.5508 + 45.9873i 1.05530 + 1.82783i
\(634\) 0 0
\(635\) −15.0774 −0.598329
\(636\) 0 0
\(637\) 2.86834 + 4.96812i 0.113648 + 0.196844i
\(638\) 0 0
\(639\) −3.70746 −0.146665
\(640\) 0 0
\(641\) 15.9106 27.5579i 0.628430 1.08847i −0.359437 0.933169i \(-0.617031\pi\)
0.987867 0.155303i \(-0.0496353\pi\)
\(642\) 0 0
\(643\) 4.44369 7.69670i 0.175242 0.303528i −0.765003 0.644027i \(-0.777263\pi\)
0.940245 + 0.340499i \(0.110596\pi\)
\(644\) 0 0
\(645\) 29.0422 1.14354
\(646\) 0 0
\(647\) 1.37593 0.0540934 0.0270467 0.999634i \(-0.491390\pi\)
0.0270467 + 0.999634i \(0.491390\pi\)
\(648\) 0 0
\(649\) 15.4583 26.7746i 0.606792 1.05099i
\(650\) 0 0
\(651\) −21.0814 + 36.5140i −0.826245 + 1.43110i
\(652\) 0 0
\(653\) −24.7237 −0.967513 −0.483756 0.875203i \(-0.660728\pi\)
−0.483756 + 0.875203i \(0.660728\pi\)
\(654\) 0 0
\(655\) −6.78442 11.7510i −0.265089 0.459148i
\(656\) 0 0
\(657\) −45.8392 −1.78836
\(658\) 0 0
\(659\) 20.9020 + 36.2033i 0.814226 + 1.41028i 0.909882 + 0.414867i \(0.136172\pi\)
−0.0956561 + 0.995414i \(0.530495\pi\)
\(660\) 0 0
\(661\) 11.5211 + 19.9552i 0.448119 + 0.776165i 0.998264 0.0589041i \(-0.0187606\pi\)
−0.550144 + 0.835070i \(0.685427\pi\)
\(662\) 0 0
\(663\) 7.36834 12.7623i 0.286163 0.495648i
\(664\) 0 0
\(665\) −7.08392 + 13.8497i −0.274703 + 0.537070i
\(666\) 0 0
\(667\) 18.9437 32.8114i 0.733503 1.27046i
\(668\) 0 0
\(669\) −5.79092 10.0302i −0.223890 0.387789i
\(670\) 0 0
\(671\) −18.5900 32.1988i −0.717658 1.24302i
\(672\) 0 0
\(673\) 29.5156 1.13774 0.568871 0.822427i \(-0.307380\pi\)
0.568871 + 0.822427i \(0.307380\pi\)
\(674\) 0 0
\(675\) −0.769355 1.33256i −0.0296125 0.0512904i
\(676\) 0 0
\(677\) 12.5035 0.480549 0.240275 0.970705i \(-0.422763\pi\)
0.240275 + 0.970705i \(0.422763\pi\)
\(678\) 0 0
\(679\) −4.69148 + 8.12588i −0.180042 + 0.311843i
\(680\) 0 0
\(681\) 21.4131 37.0886i 0.820552 1.42124i
\(682\) 0 0
\(683\) 12.9045 0.493778 0.246889 0.969044i \(-0.420592\pi\)
0.246889 + 0.969044i \(0.420592\pi\)
\(684\) 0 0
\(685\) −7.03014 −0.268608
\(686\) 0 0
\(687\) −6.82106 + 11.8144i −0.260240 + 0.450748i
\(688\) 0 0
\(689\) −1.70051 + 2.94536i −0.0647841 + 0.112209i
\(690\) 0 0
\(691\) 23.3779 0.889337 0.444669 0.895695i \(-0.353321\pi\)
0.444669 + 0.895695i \(0.353321\pi\)
\(692\) 0 0
\(693\) −29.3417 50.8213i −1.11460 1.93054i
\(694\) 0 0
\(695\) 12.1980 0.462696
\(696\) 0 0
\(697\) −30.7101 53.1914i −1.16323 2.01477i
\(698\) 0 0
\(699\) 3.56028 + 6.16658i 0.134662 + 0.233242i
\(700\) 0 0
\(701\) 5.82314 10.0860i 0.219937 0.380942i −0.734852 0.678228i \(-0.762748\pi\)
0.954788 + 0.297286i \(0.0960816\pi\)
\(702\) 0 0
\(703\) −15.5362 + 0.790014i −0.585958 + 0.0297959i
\(704\) 0 0
\(705\) −8.69148 + 15.0541i −0.327340 + 0.566970i
\(706\) 0 0
\(707\) −15.8357 27.4282i −0.595562 1.03154i
\(708\) 0 0
\(709\) 6.58645 + 11.4081i 0.247359 + 0.428439i 0.962792 0.270243i \(-0.0871039\pi\)
−0.715433 + 0.698681i \(0.753771\pi\)
\(710\) 0 0
\(711\) 17.4994 0.656277
\(712\) 0 0
\(713\) 12.8748 + 22.2999i 0.482167 + 0.835137i
\(714\) 0 0
\(715\) 4.56885 0.170865
\(716\) 0 0
\(717\) 11.0448 19.1301i 0.412474 0.714426i
\(718\) 0 0
\(719\) 2.43972 4.22572i 0.0909863 0.157593i −0.816940 0.576723i \(-0.804331\pi\)
0.907926 + 0.419130i \(0.137665\pi\)
\(720\) 0 0
\(721\) −15.7065 −0.584942
\(722\) 0 0
\(723\) 14.5508 0.541150
\(724\) 0 0
\(725\) −3.38341 + 5.86024i −0.125657 + 0.217644i
\(726\) 0 0
\(727\) −24.9884 + 43.2813i −0.926770 + 1.60521i −0.138081 + 0.990421i \(0.544093\pi\)
−0.788689 + 0.614792i \(0.789240\pi\)
\(728\) 0 0
\(729\) −36.4905 −1.35150
\(730\) 0 0
\(731\) 32.4282 + 56.1672i 1.19940 + 2.07742i
\(732\) 0 0
\(733\) −39.0493 −1.44232 −0.721159 0.692770i \(-0.756390\pi\)
−0.721159 + 0.692770i \(0.756390\pi\)
\(734\) 0 0
\(735\) 7.36834 + 12.7623i 0.271785 + 0.470746i
\(736\) 0 0
\(737\) 14.4734 + 25.0686i 0.533134 + 0.923415i
\(738\) 0 0
\(739\) 12.4020 21.4809i 0.456215 0.790187i −0.542542 0.840028i \(-0.682538\pi\)
0.998757 + 0.0498412i \(0.0158715\pi\)
\(740\) 0 0
\(741\) 11.1829 0.568650i 0.410814 0.0208899i
\(742\) 0 0
\(743\) 9.92817 17.1961i 0.364229 0.630863i −0.624423 0.781086i \(-0.714666\pi\)
0.988652 + 0.150223i \(0.0479992\pi\)
\(744\) 0 0
\(745\) 4.76936 + 8.26077i 0.174736 + 0.302651i
\(746\) 0 0
\(747\) 16.9171 + 29.3012i 0.618963 + 1.07208i
\(748\) 0 0
\(749\) −49.7307 −1.81712
\(750\) 0 0
\(751\) 13.7191 + 23.7622i 0.500617 + 0.867094i 1.00000 0.000712212i \(0.000226704\pi\)
−0.499383 + 0.866381i \(0.666440\pi\)
\(752\) 0 0
\(753\) −59.3909 −2.16432
\(754\) 0 0
\(755\) 10.2065 17.6783i 0.371454 0.643378i
\(756\) 0 0
\(757\) −5.77540 + 10.0033i −0.209910 + 0.363576i −0.951686 0.307073i \(-0.900651\pi\)
0.741776 + 0.670648i \(0.233984\pi\)
\(758\) 0 0
\(759\) −65.7136 −2.38525
\(760\) 0 0
\(761\) −46.9940 −1.70353 −0.851766 0.523922i \(-0.824468\pi\)
−0.851766 + 0.523922i \(0.824468\pi\)
\(762\) 0 0
\(763\) −6.83821 + 11.8441i −0.247560 + 0.428786i
\(764\) 0 0
\(765\) 10.3231 17.8802i 0.373234 0.646460i
\(766\) 0 0
\(767\) 6.76683 0.244336
\(768\) 0 0
\(769\) 6.43719 + 11.1495i 0.232131 + 0.402063i 0.958435 0.285311i \(-0.0920968\pi\)
−0.726304 + 0.687374i \(0.758763\pi\)
\(770\) 0 0
\(771\) −27.1498 −0.977776
\(772\) 0 0
\(773\) 14.0151 + 24.2748i 0.504087 + 0.873104i 0.999989 + 0.00472572i \(0.00150425\pi\)
−0.495902 + 0.868379i \(0.665162\pi\)
\(774\) 0 0
\(775\) −2.29949 3.98284i −0.0826003 0.143068i
\(776\) 0 0
\(777\) −16.3593 + 28.3352i −0.586887 + 1.01652i
\(778\) 0 0
\(779\) 21.2518 41.5492i 0.761423 1.48865i
\(780\) 0 0
\(781\) 2.35327 4.07599i 0.0842068 0.145850i
\(782\) 0 0
\(783\) −5.20609 9.01722i −0.186051 0.322249i
\(784\) 0 0
\(785\) −7.15277 12.3890i −0.255293 0.442181i
\(786\) 0 0
\(787\) 22.3478 0.796612 0.398306 0.917253i \(-0.369598\pi\)
0.398306 + 0.917253i \(0.369598\pi\)
\(788\) 0 0
\(789\) −11.3830 19.7159i −0.405244 0.701903i
\(790\) 0 0