Properties

Label 380.2.u.a.301.2
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 301.2
Root \(-0.124000 - 0.703239i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.a.101.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.671023 - 0.244232i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(1.15961 + 2.00851i) q^{7} +(-1.90751 + 1.60059i) q^{9} +O(q^{10})\) \(q+(0.671023 - 0.244232i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(1.15961 + 2.00851i) q^{7} +(-1.90751 + 1.60059i) q^{9} +(-1.57458 + 2.72725i) q^{11} +(5.20266 + 1.89361i) q^{13} +(0.124000 + 0.703239i) q^{15} +(-2.31628 - 1.94359i) q^{17} +(4.24875 - 0.973710i) q^{19} +(1.26867 + 1.06454i) q^{21} +(-0.283534 - 1.60800i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(-1.96020 + 3.39516i) q^{27} +(3.91367 - 3.28396i) q^{29} +(1.01198 + 1.75281i) q^{31} +(-0.390495 + 2.21461i) q^{33} +(-2.17936 + 0.793222i) q^{35} -3.94230 q^{37} +3.95359 q^{39} +(6.75417 - 2.45832i) q^{41} +(-0.0418722 + 0.237469i) q^{43} +(-1.24504 - 2.15647i) q^{45} +(-5.49214 + 4.60845i) q^{47} +(0.810595 - 1.40399i) q^{49} +(-2.02896 - 0.738482i) q^{51} +(-0.521860 - 2.95961i) q^{53} +(-2.41239 - 2.02424i) q^{55} +(2.61320 - 1.69106i) q^{57} +(-0.466370 - 0.391331i) q^{59} +(-1.87362 - 10.6258i) q^{61} +(-5.42678 - 1.97519i) q^{63} +(-2.76828 + 4.79480i) q^{65} +(-11.5028 + 9.65202i) q^{67} +(-0.582984 - 1.00976i) q^{69} +(0.791928 - 4.49124i) q^{71} +(13.6128 - 4.95465i) q^{73} -0.714088 q^{75} -7.30359 q^{77} +(-4.11398 + 1.49737i) q^{79} +(0.811064 - 4.59977i) q^{81} +(-2.97839 - 5.15872i) q^{83} +(2.31628 - 1.94359i) q^{85} +(1.82412 - 3.15946i) q^{87} +(8.52005 + 3.10104i) q^{89} +(2.22974 + 12.6455i) q^{91} +(1.10716 + 0.929014i) q^{93} +(0.221130 + 4.35329i) q^{95} +(7.30113 + 6.12637i) q^{97} +(-1.36169 - 7.72250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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
\(3\) 0.671023 0.244232i 0.387415 0.141008i −0.140967 0.990014i \(-0.545021\pi\)
0.528382 + 0.849007i \(0.322799\pi\)
\(4\) 0 0
\(5\) −0.173648 + 0.984808i −0.0776578 + 0.440419i
\(6\) 0 0
\(7\) 1.15961 + 2.00851i 0.438293 + 0.759145i 0.997558 0.0698437i \(-0.0222501\pi\)
−0.559265 + 0.828989i \(0.688917\pi\)
\(8\) 0 0
\(9\) −1.90751 + 1.60059i −0.635837 + 0.533531i
\(10\) 0 0
\(11\) −1.57458 + 2.72725i −0.474752 + 0.822295i −0.999582 0.0289120i \(-0.990796\pi\)
0.524829 + 0.851207i \(0.324129\pi\)
\(12\) 0 0
\(13\) 5.20266 + 1.89361i 1.44296 + 0.525194i 0.940616 0.339474i \(-0.110249\pi\)
0.502344 + 0.864668i \(0.332471\pi\)
\(14\) 0 0
\(15\) 0.124000 + 0.703239i 0.0320167 + 0.181576i
\(16\) 0 0
\(17\) −2.31628 1.94359i −0.561780 0.471389i 0.317127 0.948383i \(-0.397282\pi\)
−0.878907 + 0.476994i \(0.841726\pi\)
\(18\) 0 0
\(19\) 4.24875 0.973710i 0.974730 0.223384i
\(20\) 0 0
\(21\) 1.26867 + 1.06454i 0.276846 + 0.232302i
\(22\) 0 0
\(23\) −0.283534 1.60800i −0.0591210 0.335292i 0.940873 0.338759i \(-0.110007\pi\)
−0.999994 + 0.00346778i \(0.998896\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) −1.96020 + 3.39516i −0.377240 + 0.653400i
\(28\) 0 0
\(29\) 3.91367 3.28396i 0.726751 0.609817i −0.202493 0.979284i \(-0.564904\pi\)
0.929244 + 0.369467i \(0.120460\pi\)
\(30\) 0 0
\(31\) 1.01198 + 1.75281i 0.181757 + 0.314813i 0.942479 0.334265i \(-0.108488\pi\)
−0.760722 + 0.649078i \(0.775155\pi\)
\(32\) 0 0
\(33\) −0.390495 + 2.21461i −0.0679764 + 0.385513i
\(34\) 0 0
\(35\) −2.17936 + 0.793222i −0.368379 + 0.134079i
\(36\) 0 0
\(37\) −3.94230 −0.648110 −0.324055 0.946038i \(-0.605046\pi\)
−0.324055 + 0.946038i \(0.605046\pi\)
\(38\) 0 0
\(39\) 3.95359 0.633081
\(40\) 0 0
\(41\) 6.75417 2.45832i 1.05482 0.383925i 0.244343 0.969689i \(-0.421428\pi\)
0.810482 + 0.585764i \(0.199205\pi\)
\(42\) 0 0
\(43\) −0.0418722 + 0.237469i −0.00638544 + 0.0362137i −0.987834 0.155512i \(-0.950297\pi\)
0.981449 + 0.191726i \(0.0614084\pi\)
\(44\) 0 0
\(45\) −1.24504 2.15647i −0.185600 0.321468i
\(46\) 0 0
\(47\) −5.49214 + 4.60845i −0.801110 + 0.672211i −0.948468 0.316872i \(-0.897368\pi\)
0.147358 + 0.989083i \(0.452923\pi\)
\(48\) 0 0
\(49\) 0.810595 1.40399i 0.115799 0.200570i
\(50\) 0 0
\(51\) −2.02896 0.738482i −0.284112 0.103408i
\(52\) 0 0
\(53\) −0.521860 2.95961i −0.0716829 0.406534i −0.999443 0.0333580i \(-0.989380\pi\)
0.927761 0.373176i \(-0.121731\pi\)
\(54\) 0 0
\(55\) −2.41239 2.02424i −0.325287 0.272948i
\(56\) 0 0
\(57\) 2.61320 1.69106i 0.346127 0.223987i
\(58\) 0 0
\(59\) −0.466370 0.391331i −0.0607162 0.0509470i 0.611925 0.790916i \(-0.290396\pi\)
−0.672641 + 0.739969i \(0.734840\pi\)
\(60\) 0 0
\(61\) −1.87362 10.6258i −0.239893 1.36050i −0.832060 0.554685i \(-0.812839\pi\)
0.592167 0.805815i \(-0.298272\pi\)
\(62\) 0 0
\(63\) −5.42678 1.97519i −0.683710 0.248850i
\(64\) 0 0
\(65\) −2.76828 + 4.79480i −0.343363 + 0.594722i
\(66\) 0 0
\(67\) −11.5028 + 9.65202i −1.40529 + 1.17918i −0.446604 + 0.894732i \(0.647367\pi\)
−0.958691 + 0.284450i \(0.908189\pi\)
\(68\) 0 0
\(69\) −0.582984 1.00976i −0.0701830 0.121561i
\(70\) 0 0
\(71\) 0.791928 4.49124i 0.0939845 0.533013i −0.901069 0.433675i \(-0.857217\pi\)
0.995054 0.0993375i \(-0.0316723\pi\)
\(72\) 0 0
\(73\) 13.6128 4.95465i 1.59326 0.579898i 0.615224 0.788352i \(-0.289066\pi\)
0.978032 + 0.208454i \(0.0668433\pi\)
\(74\) 0 0
\(75\) −0.714088 −0.0824557
\(76\) 0 0
\(77\) −7.30359 −0.832322
\(78\) 0 0
\(79\) −4.11398 + 1.49737i −0.462859 + 0.168467i −0.562915 0.826515i \(-0.690320\pi\)
0.100056 + 0.994982i \(0.468098\pi\)
\(80\) 0 0
\(81\) 0.811064 4.59977i 0.0901182 0.511086i
\(82\) 0 0
\(83\) −2.97839 5.15872i −0.326920 0.566243i 0.654979 0.755647i \(-0.272678\pi\)
−0.981899 + 0.189405i \(0.939344\pi\)
\(84\) 0 0
\(85\) 2.31628 1.94359i 0.251236 0.210812i
\(86\) 0 0
\(87\) 1.82412 3.15946i 0.195566 0.338730i
\(88\) 0 0
\(89\) 8.52005 + 3.10104i 0.903123 + 0.328710i 0.751504 0.659729i \(-0.229329\pi\)
0.151620 + 0.988439i \(0.451551\pi\)
\(90\) 0 0
\(91\) 2.22974 + 12.6455i 0.233740 + 1.32560i
\(92\) 0 0
\(93\) 1.10716 + 0.929014i 0.114807 + 0.0963342i
\(94\) 0 0
\(95\) 0.221130 + 4.35329i 0.0226874 + 0.446638i
\(96\) 0 0
\(97\) 7.30113 + 6.12637i 0.741317 + 0.622039i 0.933191 0.359381i \(-0.117012\pi\)
−0.191874 + 0.981420i \(0.561457\pi\)
\(98\) 0 0
\(99\) −1.36169 7.72250i −0.136855 0.776141i
\(100\) 0 0
\(101\) −17.8871 6.51036i −1.77983 0.647805i −0.999755 0.0221177i \(-0.992959\pi\)
−0.780074 0.625687i \(-0.784819\pi\)
\(102\) 0 0
\(103\) 3.18075 5.50922i 0.313409 0.542840i −0.665689 0.746229i \(-0.731862\pi\)
0.979098 + 0.203389i \(0.0651957\pi\)
\(104\) 0 0
\(105\) −1.26867 + 1.06454i −0.123809 + 0.103888i
\(106\) 0 0
\(107\) −8.89168 15.4008i −0.859591 1.48886i −0.872319 0.488937i \(-0.837385\pi\)
0.0127277 0.999919i \(-0.495949\pi\)
\(108\) 0 0
\(109\) 3.15487 17.8922i 0.302182 1.71376i −0.334300 0.942467i \(-0.608500\pi\)
0.636482 0.771292i \(-0.280389\pi\)
\(110\) 0 0
\(111\) −2.64537 + 0.962837i −0.251088 + 0.0913884i
\(112\) 0 0
\(113\) −7.92400 −0.745427 −0.372714 0.927946i \(-0.621573\pi\)
−0.372714 + 0.927946i \(0.621573\pi\)
\(114\) 0 0
\(115\) 1.63281 0.152260
\(116\) 0 0
\(117\) −12.9550 + 4.71525i −1.19769 + 0.435925i
\(118\) 0 0
\(119\) 1.21773 6.90608i 0.111629 0.633079i
\(120\) 0 0
\(121\) 0.541422 + 0.937770i 0.0492202 + 0.0852518i
\(122\) 0 0
\(123\) 3.93180 3.29918i 0.354519 0.297477i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) −6.28578 2.28784i −0.557773 0.203013i 0.0477237 0.998861i \(-0.484803\pi\)
−0.605497 + 0.795848i \(0.707026\pi\)
\(128\) 0 0
\(129\) 0.0299004 + 0.169574i 0.00263258 + 0.0149301i
\(130\) 0 0
\(131\) 8.75979 + 7.35034i 0.765347 + 0.642202i 0.939513 0.342514i \(-0.111279\pi\)
−0.174166 + 0.984716i \(0.555723\pi\)
\(132\) 0 0
\(133\) 6.88261 + 7.40453i 0.596798 + 0.642054i
\(134\) 0 0
\(135\) −3.00320 2.51998i −0.258474 0.216886i
\(136\) 0 0
\(137\) 0.429370 + 2.43508i 0.0366836 + 0.208043i 0.997640 0.0686553i \(-0.0218709\pi\)
−0.960957 + 0.276698i \(0.910760\pi\)
\(138\) 0 0
\(139\) 20.7828 + 7.56434i 1.76278 + 0.641599i 0.999987 0.00504701i \(-0.00160652\pi\)
0.762791 + 0.646646i \(0.223829\pi\)
\(140\) 0 0
\(141\) −2.55982 + 4.43373i −0.215575 + 0.373388i
\(142\) 0 0
\(143\) −13.3563 + 11.2073i −1.11691 + 0.937202i
\(144\) 0 0
\(145\) 2.55447 + 4.42447i 0.212137 + 0.367432i
\(146\) 0 0
\(147\) 0.201028 1.14008i 0.0165805 0.0940326i
\(148\) 0 0
\(149\) 12.9595 4.71687i 1.06168 0.386421i 0.248623 0.968600i \(-0.420022\pi\)
0.813061 + 0.582179i \(0.197800\pi\)
\(150\) 0 0
\(151\) 1.98891 0.161856 0.0809278 0.996720i \(-0.474212\pi\)
0.0809278 + 0.996720i \(0.474212\pi\)
\(152\) 0 0
\(153\) 7.52922 0.608701
\(154\) 0 0
\(155\) −1.90191 + 0.692237i −0.152765 + 0.0556018i
\(156\) 0 0
\(157\) −0.00345031 + 0.0195677i −0.000275365 + 0.00156167i −0.984945 0.172867i \(-0.944697\pi\)
0.984670 + 0.174429i \(0.0558079\pi\)
\(158\) 0 0
\(159\) −1.07301 1.85851i −0.0850955 0.147390i
\(160\) 0 0
\(161\) 2.90090 2.43414i 0.228623 0.191837i
\(162\) 0 0
\(163\) −5.04459 + 8.73749i −0.395123 + 0.684373i −0.993117 0.117128i \(-0.962631\pi\)
0.597994 + 0.801501i \(0.295965\pi\)
\(164\) 0 0
\(165\) −2.11315 0.769125i −0.164509 0.0598763i
\(166\) 0 0
\(167\) 2.43270 + 13.7965i 0.188248 + 1.06761i 0.921711 + 0.387879i \(0.126792\pi\)
−0.733462 + 0.679730i \(0.762097\pi\)
\(168\) 0 0
\(169\) 13.5234 + 11.3474i 1.04026 + 0.872880i
\(170\) 0 0
\(171\) −6.54603 + 8.65788i −0.500587 + 0.662085i
\(172\) 0 0
\(173\) −2.91704 2.44769i −0.221779 0.186094i 0.525128 0.851023i \(-0.324017\pi\)
−0.746907 + 0.664929i \(0.768462\pi\)
\(174\) 0 0
\(175\) −0.402729 2.28399i −0.0304435 0.172654i
\(176\) 0 0
\(177\) −0.408521 0.148689i −0.0307063 0.0111762i
\(178\) 0 0
\(179\) −5.29756 + 9.17564i −0.395958 + 0.685819i −0.993223 0.116225i \(-0.962921\pi\)
0.597265 + 0.802044i \(0.296254\pi\)
\(180\) 0 0
\(181\) 5.61443 4.71107i 0.417317 0.350171i −0.409824 0.912165i \(-0.634410\pi\)
0.827142 + 0.561994i \(0.189965\pi\)
\(182\) 0 0
\(183\) −3.85242 6.67259i −0.284779 0.493252i
\(184\) 0 0
\(185\) 0.684573 3.88241i 0.0503308 0.285440i
\(186\) 0 0
\(187\) 8.94780 3.25673i 0.654328 0.238156i
\(188\) 0 0
\(189\) −9.09229 −0.661367
\(190\) 0 0
\(191\) 17.9346 1.29770 0.648850 0.760917i \(-0.275250\pi\)
0.648850 + 0.760917i \(0.275250\pi\)
\(192\) 0 0
\(193\) 4.86560 1.77093i 0.350234 0.127475i −0.160912 0.986969i \(-0.551444\pi\)
0.511146 + 0.859494i \(0.329221\pi\)
\(194\) 0 0
\(195\) −0.686533 + 3.89352i −0.0491637 + 0.278821i
\(196\) 0 0
\(197\) 0.651384 + 1.12823i 0.0464092 + 0.0803831i 0.888297 0.459270i \(-0.151889\pi\)
−0.841888 + 0.539653i \(0.818556\pi\)
\(198\) 0 0
\(199\) −9.31228 + 7.81393i −0.660130 + 0.553915i −0.910126 0.414332i \(-0.864015\pi\)
0.249996 + 0.968247i \(0.419571\pi\)
\(200\) 0 0
\(201\) −5.36133 + 9.28609i −0.378159 + 0.654990i
\(202\) 0 0
\(203\) 11.1342 + 4.05252i 0.781469 + 0.284431i
\(204\) 0 0
\(205\) 1.24812 + 7.07844i 0.0871725 + 0.494380i
\(206\) 0 0
\(207\) 3.11460 + 2.61346i 0.216480 + 0.181648i
\(208\) 0 0
\(209\) −4.03443 + 13.1206i −0.279068 + 0.907569i
\(210\) 0 0
\(211\) 20.4402 + 17.1514i 1.40716 + 1.18075i 0.957812 + 0.287396i \(0.0927897\pi\)
0.449352 + 0.893355i \(0.351655\pi\)
\(212\) 0 0
\(213\) −0.565506 3.20714i −0.0387478 0.219750i
\(214\) 0 0
\(215\) −0.226590 0.0824721i −0.0154533 0.00562455i
\(216\) 0 0
\(217\) −2.34702 + 4.06515i −0.159326 + 0.275961i
\(218\) 0 0
\(219\) 7.92441 6.64937i 0.535482 0.449323i
\(220\) 0 0
\(221\) −8.37041 14.4980i −0.563055 0.975239i
\(222\) 0 0
\(223\) 1.94159 11.0113i 0.130018 0.737372i −0.848181 0.529706i \(-0.822302\pi\)
0.978200 0.207666i \(-0.0665866\pi\)
\(224\) 0 0
\(225\) 2.33991 0.851657i 0.155994 0.0567771i
\(226\) 0 0
\(227\) 0.565133 0.0375092 0.0187546 0.999824i \(-0.494030\pi\)
0.0187546 + 0.999824i \(0.494030\pi\)
\(228\) 0 0
\(229\) −2.02689 −0.133941 −0.0669705 0.997755i \(-0.521333\pi\)
−0.0669705 + 0.997755i \(0.521333\pi\)
\(230\) 0 0
\(231\) −4.90088 + 1.78377i −0.322454 + 0.117364i
\(232\) 0 0
\(233\) −5.05833 + 28.6872i −0.331382 + 1.87936i 0.129006 + 0.991644i \(0.458821\pi\)
−0.460388 + 0.887718i \(0.652290\pi\)
\(234\) 0 0
\(235\) −3.58474 6.20895i −0.233842 0.405027i
\(236\) 0 0
\(237\) −2.39487 + 2.00954i −0.155564 + 0.130533i
\(238\) 0 0
\(239\) −4.93291 + 8.54405i −0.319084 + 0.552669i −0.980297 0.197529i \(-0.936708\pi\)
0.661214 + 0.750198i \(0.270042\pi\)
\(240\) 0 0
\(241\) −4.80460 1.74873i −0.309492 0.112646i 0.182605 0.983186i \(-0.441547\pi\)
−0.492096 + 0.870541i \(0.663769\pi\)
\(242\) 0 0
\(243\) −2.62148 14.8672i −0.168168 0.953728i
\(244\) 0 0
\(245\) 1.24190 + 1.04208i 0.0793423 + 0.0665761i
\(246\) 0 0
\(247\) 23.9487 + 2.97961i 1.52382 + 0.189588i
\(248\) 0 0
\(249\) −3.25849 2.73420i −0.206498 0.173273i
\(250\) 0 0
\(251\) −5.36940 30.4514i −0.338914 1.92208i −0.384521 0.923116i \(-0.625633\pi\)
0.0456071 0.998959i \(-0.485478\pi\)
\(252\) 0 0
\(253\) 4.83186 + 1.75865i 0.303777 + 0.110566i
\(254\) 0 0
\(255\) 1.07959 1.86990i 0.0676065 0.117098i
\(256\) 0 0
\(257\) 10.5875 8.88396i 0.660429 0.554166i −0.249786 0.968301i \(-0.580360\pi\)
0.910215 + 0.414135i \(0.135916\pi\)
\(258\) 0 0
\(259\) −4.57154 7.91814i −0.284062 0.492009i
\(260\) 0 0
\(261\) −2.20909 + 12.5284i −0.136739 + 0.775488i
\(262\) 0 0
\(263\) 21.5805 7.85467i 1.33071 0.484340i 0.423837 0.905739i \(-0.360683\pi\)
0.906875 + 0.421399i \(0.138461\pi\)
\(264\) 0 0
\(265\) 3.00527 0.184612
\(266\) 0 0
\(267\) 6.47452 0.396234
\(268\) 0 0
\(269\) −25.3054 + 9.21042i −1.54290 + 0.561569i −0.966738 0.255767i \(-0.917672\pi\)
−0.576161 + 0.817337i \(0.695450\pi\)
\(270\) 0 0
\(271\) 0.247964 1.40628i 0.0150628 0.0854251i −0.976350 0.216197i \(-0.930635\pi\)
0.991412 + 0.130772i \(0.0417457\pi\)
\(272\) 0 0
\(273\) 4.58463 + 7.94082i 0.277475 + 0.480600i
\(274\) 0 0
\(275\) 2.41239 2.02424i 0.145473 0.122066i
\(276\) 0 0
\(277\) −4.29459 + 7.43844i −0.258037 + 0.446933i −0.965716 0.259601i \(-0.916409\pi\)
0.707679 + 0.706534i \(0.249742\pi\)
\(278\) 0 0
\(279\) −4.73589 1.72372i −0.283531 0.103197i
\(280\) 0 0
\(281\) −0.717482 4.06904i −0.0428014 0.242739i 0.955900 0.293694i \(-0.0948846\pi\)
−0.998701 + 0.0509551i \(0.983773\pi\)
\(282\) 0 0
\(283\) −21.6523 18.1684i −1.28710 1.08000i −0.992224 0.124465i \(-0.960279\pi\)
−0.294872 0.955537i \(-0.595277\pi\)
\(284\) 0 0
\(285\) 1.21160 + 2.86715i 0.0717688 + 0.169835i
\(286\) 0 0
\(287\) 12.7698 + 10.7151i 0.753776 + 0.632493i
\(288\) 0 0
\(289\) −1.36441 7.73795i −0.0802594 0.455173i
\(290\) 0 0
\(291\) 6.39548 + 2.32776i 0.374910 + 0.136456i
\(292\) 0 0
\(293\) −15.5670 + 26.9629i −0.909436 + 1.57519i −0.0945860 + 0.995517i \(0.530153\pi\)
−0.814850 + 0.579672i \(0.803181\pi\)
\(294\) 0 0
\(295\) 0.466370 0.391331i 0.0271531 0.0227842i
\(296\) 0 0
\(297\) −6.17296 10.6919i −0.358192 0.620406i
\(298\) 0 0
\(299\) 1.56980 8.90280i 0.0907841 0.514862i
\(300\) 0 0
\(301\) −0.525514 + 0.191271i −0.0302901 + 0.0110247i
\(302\) 0 0
\(303\) −13.5927 −0.780878
\(304\) 0 0
\(305\) 10.7898 0.617820
\(306\) 0 0
\(307\) 7.77449 2.82968i 0.443714 0.161499i −0.110494 0.993877i \(-0.535243\pi\)
0.554208 + 0.832378i \(0.313021\pi\)
\(308\) 0 0
\(309\) 0.788827 4.47366i 0.0448748 0.254498i
\(310\) 0 0
\(311\) −6.16019 10.6698i −0.349313 0.605027i 0.636815 0.771017i \(-0.280252\pi\)
−0.986128 + 0.165990i \(0.946918\pi\)
\(312\) 0 0
\(313\) −0.677188 + 0.568228i −0.0382769 + 0.0321181i −0.661725 0.749746i \(-0.730176\pi\)
0.623449 + 0.781864i \(0.285731\pi\)
\(314\) 0 0
\(315\) 2.88753 5.00135i 0.162694 0.281794i
\(316\) 0 0
\(317\) −11.7423 4.27383i −0.659511 0.240042i −0.00948585 0.999955i \(-0.503019\pi\)
−0.650025 + 0.759913i \(0.725242\pi\)
\(318\) 0 0
\(319\) 2.79380 + 15.8444i 0.156422 + 0.887116i
\(320\) 0 0
\(321\) −9.72791 8.16268i −0.542959 0.455597i
\(322\) 0 0
\(323\) −11.7338 6.00244i −0.652885 0.333985i
\(324\) 0 0
\(325\) −4.24125 3.55883i −0.235262 0.197408i
\(326\) 0 0
\(327\) −2.25285 12.7766i −0.124583 0.706546i
\(328\) 0 0
\(329\) −15.6249 5.68699i −0.861427 0.313534i
\(330\) 0 0
\(331\) −3.01501 + 5.22215i −0.165720 + 0.287035i −0.936911 0.349569i \(-0.886328\pi\)
0.771191 + 0.636604i \(0.219661\pi\)
\(332\) 0 0
\(333\) 7.51998 6.31001i 0.412092 0.345786i
\(334\) 0 0
\(335\) −7.50794 13.0041i −0.410203 0.710492i
\(336\) 0 0
\(337\) 2.84817 16.1528i 0.155150 0.879899i −0.803499 0.595306i \(-0.797031\pi\)
0.958649 0.284592i \(-0.0918582\pi\)
\(338\) 0 0
\(339\) −5.31719 + 1.93530i −0.288790 + 0.105111i
\(340\) 0 0
\(341\) −6.37377 −0.345159
\(342\) 0 0
\(343\) 19.9945 1.07960
\(344\) 0 0
\(345\) 1.09565 0.398785i 0.0589879 0.0214698i
\(346\) 0 0
\(347\) 1.88989 10.7181i 0.101454 0.575377i −0.891123 0.453762i \(-0.850082\pi\)
0.992577 0.121615i \(-0.0388073\pi\)
\(348\) 0 0
\(349\) −1.22388 2.11982i −0.0655127 0.113471i 0.831409 0.555662i \(-0.187535\pi\)
−0.896921 + 0.442190i \(0.854202\pi\)
\(350\) 0 0
\(351\) −16.6274 + 13.9520i −0.887504 + 0.744705i
\(352\) 0 0
\(353\) −11.7923 + 20.4248i −0.627639 + 1.08710i 0.360385 + 0.932804i \(0.382645\pi\)
−0.988024 + 0.154299i \(0.950688\pi\)
\(354\) 0 0
\(355\) 4.28550 + 1.55979i 0.227450 + 0.0827852i
\(356\) 0 0
\(357\) −0.869564 4.93154i −0.0460222 0.261005i
\(358\) 0 0
\(359\) −10.3699 8.70141i −0.547304 0.459243i 0.326723 0.945120i \(-0.394056\pi\)
−0.874027 + 0.485877i \(0.838500\pi\)
\(360\) 0 0
\(361\) 17.1038 8.27411i 0.900199 0.435479i
\(362\) 0 0
\(363\) 0.592340 + 0.497033i 0.0310898 + 0.0260874i
\(364\) 0 0
\(365\) 2.51554 + 14.2663i 0.131669 + 0.746735i
\(366\) 0 0
\(367\) −7.01361 2.55274i −0.366107 0.133252i 0.152414 0.988317i \(-0.451295\pi\)
−0.518522 + 0.855065i \(0.673517\pi\)
\(368\) 0 0
\(369\) −8.94890 + 15.4999i −0.465861 + 0.806895i
\(370\) 0 0
\(371\) 5.33925 4.48016i 0.277200 0.232599i
\(372\) 0 0
\(373\) −11.4309 19.7989i −0.591869 1.02515i −0.993981 0.109556i \(-0.965057\pi\)
0.402112 0.915591i \(-0.368276\pi\)
\(374\) 0 0
\(375\) 0.124000 0.703239i 0.00640333 0.0363151i
\(376\) 0 0
\(377\) 26.5801 9.67436i 1.36894 0.498255i
\(378\) 0 0
\(379\) −21.3110 −1.09467 −0.547337 0.836913i \(-0.684358\pi\)
−0.547337 + 0.836913i \(0.684358\pi\)
\(380\) 0 0
\(381\) −4.77667 −0.244716
\(382\) 0 0
\(383\) 14.8002 5.38683i 0.756255 0.275254i 0.0650198 0.997884i \(-0.479289\pi\)
0.691235 + 0.722630i \(0.257067\pi\)
\(384\) 0 0
\(385\) 1.26826 7.19264i 0.0646363 0.366571i
\(386\) 0 0
\(387\) −0.300219 0.519995i −0.0152610 0.0264328i
\(388\) 0 0
\(389\) 14.7732 12.3962i 0.749033 0.628513i −0.186214 0.982509i \(-0.559622\pi\)
0.935247 + 0.353996i \(0.115177\pi\)
\(390\) 0 0
\(391\) −2.46855 + 4.27565i −0.124840 + 0.216229i
\(392\) 0 0
\(393\) 7.67321 + 2.79282i 0.387062 + 0.140879i
\(394\) 0 0
\(395\) −0.760233 4.31150i −0.0382515 0.216935i
\(396\) 0 0
\(397\) −12.0637 10.1227i −0.605462 0.508043i 0.287734 0.957710i \(-0.407098\pi\)
−0.893196 + 0.449667i \(0.851543\pi\)
\(398\) 0 0
\(399\) 6.42682 + 3.28765i 0.321743 + 0.164588i
\(400\) 0 0
\(401\) 12.6661 + 10.6281i 0.632515 + 0.530743i 0.901709 0.432343i \(-0.142313\pi\)
−0.269194 + 0.963086i \(0.586757\pi\)
\(402\) 0 0
\(403\) 1.94587 + 11.0356i 0.0969306 + 0.549721i
\(404\) 0 0
\(405\) 4.38905 + 1.59748i 0.218094 + 0.0793796i
\(406\) 0 0
\(407\) 6.20745 10.7516i 0.307692 0.532938i
\(408\) 0 0
\(409\) −24.5460 + 20.5965i −1.21372 + 1.01843i −0.214590 + 0.976704i \(0.568842\pi\)
−0.999129 + 0.0417273i \(0.986714\pi\)
\(410\) 0 0
\(411\) 0.882843 + 1.52913i 0.0435474 + 0.0754264i
\(412\) 0 0
\(413\) 0.245183 1.39050i 0.0120647 0.0684221i
\(414\) 0 0
\(415\) 5.59754 2.03734i 0.274772 0.100009i
\(416\) 0 0
\(417\) 15.7932 0.773397
\(418\) 0 0
\(419\) −14.3431 −0.700706 −0.350353 0.936618i \(-0.613938\pi\)
−0.350353 + 0.936618i \(0.613938\pi\)
\(420\) 0 0
\(421\) −26.6417 + 9.69680i −1.29844 + 0.472593i −0.896488 0.443068i \(-0.853890\pi\)
−0.401951 + 0.915661i \(0.631668\pi\)
\(422\) 0 0
\(423\) 3.10006 17.5813i 0.150730 0.854834i
\(424\) 0 0
\(425\) 1.51184 + 2.61859i 0.0733352 + 0.127020i
\(426\) 0 0
\(427\) 19.1694 16.0851i 0.927674 0.778411i
\(428\) 0 0
\(429\) −6.22523 + 10.7824i −0.300557 + 0.520579i
\(430\) 0 0
\(431\) 8.90106 + 3.23972i 0.428749 + 0.156052i 0.547376 0.836887i \(-0.315627\pi\)
−0.118627 + 0.992939i \(0.537849\pi\)
\(432\) 0 0
\(433\) 1.88247 + 10.6760i 0.0904658 + 0.513057i 0.996043 + 0.0888752i \(0.0283272\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(434\) 0 0
\(435\) 2.79471 + 2.34504i 0.133996 + 0.112436i
\(436\) 0 0
\(437\) −2.77039 6.55592i −0.132526 0.313612i
\(438\) 0 0
\(439\) 6.82279 + 5.72500i 0.325634 + 0.273239i 0.790918 0.611922i \(-0.209603\pi\)
−0.465284 + 0.885161i \(0.654048\pi\)
\(440\) 0 0
\(441\) 0.700999 + 3.97556i 0.0333809 + 0.189312i
\(442\) 0 0
\(443\) −24.4075 8.88360i −1.15963 0.422073i −0.310668 0.950518i \(-0.600553\pi\)
−0.848967 + 0.528446i \(0.822775\pi\)
\(444\) 0 0
\(445\) −4.53342 + 7.85212i −0.214905 + 0.372226i
\(446\) 0 0
\(447\) 7.54411 6.33026i 0.356824 0.299411i
\(448\) 0 0
\(449\) −0.721317 1.24936i −0.0340410 0.0589608i 0.848503 0.529191i \(-0.177504\pi\)
−0.882544 + 0.470230i \(0.844171\pi\)
\(450\) 0 0
\(451\) −3.93052 + 22.2911i −0.185081 + 1.04965i
\(452\) 0 0
\(453\) 1.33461 0.485757i 0.0627053 0.0228229i
\(454\) 0 0
\(455\) −12.8405 −0.601973
\(456\) 0 0
\(457\) 17.0470 0.797427 0.398713 0.917076i \(-0.369457\pi\)
0.398713 + 0.917076i \(0.369457\pi\)
\(458\) 0 0
\(459\) 11.1392 4.05433i 0.519932 0.189240i
\(460\) 0 0
\(461\) 5.87148 33.2988i 0.273462 1.55088i −0.470343 0.882484i \(-0.655870\pi\)
0.743805 0.668396i \(-0.233019\pi\)
\(462\) 0 0
\(463\) −13.6374 23.6208i −0.633786 1.09775i −0.986771 0.162121i \(-0.948167\pi\)
0.352985 0.935629i \(-0.385167\pi\)
\(464\) 0 0
\(465\) −1.10716 + 0.929014i −0.0513431 + 0.0430820i
\(466\) 0 0
\(467\) −5.46671 + 9.46862i −0.252969 + 0.438156i −0.964342 0.264659i \(-0.914740\pi\)
0.711373 + 0.702815i \(0.248074\pi\)
\(468\) 0 0
\(469\) −32.7250 11.9109i −1.51110 0.549996i
\(470\) 0 0
\(471\) 0.00246382 + 0.0139730i 0.000113527 + 0.000643843i
\(472\) 0 0
\(473\) −0.581705 0.488108i −0.0267468 0.0224432i
\(474\) 0 0
\(475\) −4.32555 0.538170i −0.198470 0.0246929i
\(476\) 0 0
\(477\) 5.73258 + 4.81021i 0.262477 + 0.220244i
\(478\) 0 0
\(479\) −1.00848 5.71936i −0.0460785 0.261324i 0.953062 0.302775i \(-0.0979131\pi\)
−0.999141 + 0.0414508i \(0.986802\pi\)
\(480\) 0 0
\(481\) −20.5105 7.46519i −0.935196 0.340384i
\(482\) 0 0
\(483\) 1.35207 2.34186i 0.0615214 0.106558i
\(484\) 0 0
\(485\) −7.30113 + 6.12637i −0.331527 + 0.278184i
\(486\) 0 0
\(487\) 16.3401 + 28.3019i 0.740442 + 1.28248i 0.952294 + 0.305181i \(0.0987170\pi\)
−0.211853 + 0.977302i \(0.567950\pi\)
\(488\) 0 0
\(489\) −1.25106 + 7.09511i −0.0565748 + 0.320852i
\(490\) 0 0
\(491\) 34.3475 12.5015i 1.55008 0.564184i 0.581645 0.813443i \(-0.302409\pi\)
0.968437 + 0.249259i \(0.0801872\pi\)
\(492\) 0 0
\(493\) −15.4478 −0.695735
\(494\) 0 0
\(495\) 7.84164 0.352455
\(496\) 0 0
\(497\) 9.93903 3.61751i 0.445827 0.162268i
\(498\) 0 0
\(499\) −2.22383 + 12.6120i −0.0995523 + 0.564589i 0.893705 + 0.448656i \(0.148097\pi\)
−0.993257 + 0.115934i \(0.963014\pi\)
\(500\) 0 0
\(501\) 5.00196 + 8.66365i 0.223471 + 0.387063i
\(502\) 0 0
\(503\) −29.7181 + 24.9364i −1.32506 + 1.11186i −0.339858 + 0.940477i \(0.610379\pi\)
−0.985204 + 0.171383i \(0.945176\pi\)
\(504\) 0 0
\(505\) 9.51751 16.4848i 0.423524 0.733564i
\(506\) 0 0
\(507\) 11.8459 + 4.31155i 0.526095 + 0.191483i
\(508\) 0 0
\(509\) 1.35459 + 7.68223i 0.0600409 + 0.340509i 1.00000 0.000778981i \(-0.000247957\pi\)
−0.939959 + 0.341288i \(0.889137\pi\)
\(510\) 0 0
\(511\) 25.7370 + 21.5959i 1.13854 + 0.955348i
\(512\) 0 0
\(513\) −5.02249 + 16.3339i −0.221748 + 0.721158i
\(514\) 0 0
\(515\) 4.87319 + 4.08910i 0.214739 + 0.180187i
\(516\) 0 0
\(517\) −3.92059 22.2348i −0.172427 0.977884i
\(518\) 0 0
\(519\) −2.55521 0.930020i −0.112161 0.0408233i
\(520\) 0 0
\(521\) −11.8725 + 20.5638i −0.520145 + 0.900918i 0.479580 + 0.877498i \(0.340789\pi\)
−0.999726 + 0.0234202i \(0.992544\pi\)
\(522\) 0 0
\(523\) −32.0810 + 26.9192i −1.40280 + 1.17709i −0.442966 + 0.896538i \(0.646074\pi\)
−0.959838 + 0.280554i \(0.909482\pi\)
\(524\) 0 0
\(525\) −0.828065 1.43425i −0.0361397 0.0625959i
\(526\) 0 0
\(527\) 1.06270 6.02686i 0.0462919 0.262534i
\(528\) 0 0
\(529\) 19.1077 6.95462i 0.830767 0.302375i
\(530\) 0 0
\(531\) 1.51597 0.0657874
\(532\) 0 0
\(533\) 39.7948 1.72370
\(534\) 0 0
\(535\) 16.7109 6.08227i 0.722475 0.262959i
\(536\) 0 0
\(537\) −1.31379 + 7.45090i −0.0566944 + 0.321530i
\(538\) 0 0
\(539\) 2.55269 + 4.42138i 0.109952 + 0.190442i
\(540\) 0 0
\(541\) 4.29180 3.60124i 0.184519 0.154830i −0.545849 0.837883i \(-0.683793\pi\)
0.730368 + 0.683054i \(0.239349\pi\)
\(542\) 0 0
\(543\) 2.61682 4.53246i 0.112298 0.194507i
\(544\) 0 0
\(545\) 17.0725 + 6.21388i 0.731306 + 0.266174i
\(546\) 0 0
\(547\) 7.13453 + 40.4619i 0.305050 + 1.73003i 0.623268 + 0.782008i \(0.285805\pi\)
−0.318218 + 0.948018i \(0.603084\pi\)
\(548\) 0 0
\(549\) 20.5816 + 17.2700i 0.878401 + 0.737066i
\(550\) 0 0
\(551\) 13.4306 17.7635i 0.572163 0.756752i
\(552\) 0 0
\(553\) −7.77811 6.52661i −0.330759 0.277539i
\(554\) 0 0
\(555\) −0.488845 2.77238i −0.0207503 0.117681i
\(556\) 0 0
\(557\) 1.84636 + 0.672021i 0.0782329 + 0.0284744i 0.380840 0.924641i \(-0.375635\pi\)
−0.302607 + 0.953115i \(0.597857\pi\)
\(558\) 0 0
\(559\) −0.667521 + 1.15618i −0.0282331 + 0.0489012i
\(560\) 0 0
\(561\) 5.20878 4.37068i 0.219915 0.184530i
\(562\) 0 0
\(563\) 8.21286 + 14.2251i 0.346131 + 0.599516i 0.985559 0.169335i \(-0.0541620\pi\)
−0.639428 + 0.768851i \(0.720829\pi\)
\(564\) 0 0
\(565\) 1.37599 7.80362i 0.0578883 0.328301i
\(566\) 0 0
\(567\) 10.1792 3.70493i 0.427486 0.155592i
\(568\) 0 0
\(569\) −14.9560 −0.626989 −0.313494 0.949590i \(-0.601500\pi\)
−0.313494 + 0.949590i \(0.601500\pi\)
\(570\) 0 0
\(571\) −41.0971 −1.71986 −0.859930 0.510412i \(-0.829493\pi\)
−0.859930 + 0.510412i \(0.829493\pi\)
\(572\) 0 0
\(573\) 12.0345 4.38020i 0.502749 0.182986i
\(574\) 0 0
\(575\) −0.283534 + 1.60800i −0.0118242 + 0.0670583i
\(576\) 0 0
\(577\) −0.00404408 0.00700455i −0.000168357 0.000291603i 0.865941 0.500146i \(-0.166720\pi\)
−0.866110 + 0.499854i \(0.833387\pi\)
\(578\) 0 0
\(579\) 2.83241 2.37668i 0.117711 0.0987712i
\(580\) 0 0
\(581\) 6.90755 11.9642i 0.286574 0.496360i
\(582\) 0 0
\(583\) 8.89330 + 3.23690i 0.368323 + 0.134059i
\(584\) 0 0
\(585\) −2.39400 13.5770i −0.0989795 0.561341i
\(586\) 0 0
\(587\) 19.7483 + 16.5708i 0.815100 + 0.683950i 0.951819 0.306660i \(-0.0992114\pi\)
−0.136719 + 0.990610i \(0.543656\pi\)
\(588\) 0 0
\(589\) 6.00639 + 6.46186i 0.247489 + 0.266256i
\(590\) 0 0
\(591\) 0.712644 + 0.597979i 0.0293143 + 0.0245976i
\(592\) 0 0
\(593\) 7.66557 + 43.4736i 0.314787 + 1.78525i 0.573410 + 0.819268i \(0.305620\pi\)
−0.258623 + 0.965978i \(0.583269\pi\)
\(594\) 0 0
\(595\) 6.58970 + 2.39845i 0.270151 + 0.0983271i
\(596\) 0 0
\(597\) −4.34034 + 7.51769i −0.177638 + 0.307678i
\(598\) 0 0
\(599\) 16.8792 14.1633i 0.689665 0.578698i −0.229148 0.973392i \(-0.573594\pi\)
0.918813 + 0.394694i \(0.129149\pi\)
\(600\) 0 0
\(601\) −14.7335 25.5192i −0.600993 1.04095i −0.992671 0.120848i \(-0.961439\pi\)
0.391678 0.920102i \(-0.371895\pi\)
\(602\) 0 0
\(603\) 6.49283 36.8227i 0.264409 1.49954i
\(604\) 0 0
\(605\) −1.01754 + 0.370354i −0.0413689 + 0.0150570i
\(606\) 0 0
\(607\) −48.9118 −1.98527 −0.992635 0.121143i \(-0.961344\pi\)
−0.992635 + 0.121143i \(0.961344\pi\)
\(608\) 0 0
\(609\) 8.46107 0.342860
\(610\) 0 0
\(611\) −37.3004 + 13.5762i −1.50901 + 0.549235i
\(612\) 0 0
\(613\) 1.42748 8.09563i 0.0576553 0.326979i −0.942315 0.334728i \(-0.891355\pi\)
0.999970 + 0.00774885i \(0.00246656\pi\)
\(614\) 0 0
\(615\) 2.56630 + 4.44497i 0.103483 + 0.179238i
\(616\) 0 0
\(617\) 23.2296 19.4920i 0.935190 0.784718i −0.0415517 0.999136i \(-0.513230\pi\)
0.976742 + 0.214419i \(0.0687857\pi\)
\(618\) 0 0
\(619\) 2.79735 4.84515i 0.112435 0.194743i −0.804317 0.594201i \(-0.797468\pi\)
0.916751 + 0.399458i \(0.130802\pi\)
\(620\) 0 0
\(621\) 6.01521 + 2.18936i 0.241382 + 0.0878560i
\(622\) 0 0
\(623\) 3.65149 + 20.7086i 0.146294 + 0.829673i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) 0.497270 + 9.78954i 0.0198590 + 0.390957i
\(628\) 0 0
\(629\) 9.13146 + 7.66220i 0.364095 + 0.305512i
\(630\) 0 0
\(631\) 0.0628199 + 0.356269i 0.00250082 + 0.0141829i 0.986033 0.166552i \(-0.0532634\pi\)
−0.983532 + 0.180735i \(0.942152\pi\)
\(632\) 0 0
\(633\) 17.9048 + 6.51681i 0.711652 + 0.259020i
\(634\) 0 0
\(635\) 3.34460 5.79301i 0.132726 0.229889i
\(636\) 0 0
\(637\) 6.87587 5.76954i 0.272432 0.228598i
\(638\) 0 0
\(639\) 5.67804 + 9.83465i 0.224620 + 0.389053i
\(640\) 0 0
\(641\) −6.77181 + 38.4048i −0.267470 + 1.51690i 0.494437 + 0.869214i \(0.335374\pi\)
−0.761907 + 0.647686i \(0.775737\pi\)
\(642\) 0 0
\(643\) −1.65858 + 0.603673i −0.0654079 + 0.0238065i −0.374517 0.927220i \(-0.622191\pi\)
0.309109 + 0.951027i \(0.399969\pi\)
\(644\) 0 0
\(645\) −0.172189 −0.00677995
\(646\) 0 0
\(647\) −31.8882 −1.25366 −0.626828 0.779158i \(-0.715647\pi\)
−0.626828 + 0.779158i \(0.715647\pi\)
\(648\) 0 0
\(649\) 1.80159 0.655725i 0.0707186 0.0257395i
\(650\) 0 0
\(651\) −0.582060 + 3.30103i −0.0228127 + 0.129377i
\(652\) 0 0
\(653\) 10.2106 + 17.6853i 0.399573 + 0.692081i 0.993673 0.112310i \(-0.0358250\pi\)
−0.594100 + 0.804391i \(0.702492\pi\)
\(654\) 0 0
\(655\) −8.75979 + 7.35034i −0.342273 + 0.287201i
\(656\) 0 0
\(657\) −18.0362 + 31.2396i −0.703658 + 1.21877i
\(658\) 0 0
\(659\) 24.1407 + 8.78649i 0.940387 + 0.342273i 0.766319 0.642461i \(-0.222086\pi\)
0.174068 + 0.984734i \(0.444309\pi\)
\(660\) 0 0
\(661\) −0.441437 2.50351i −0.0171699 0.0973753i 0.975019 0.222123i \(-0.0712988\pi\)
−0.992188 + 0.124748i \(0.960188\pi\)
\(662\) 0 0
\(663\) −9.15761 7.68415i −0.355652 0.298428i
\(664\) 0 0
\(665\) −8.48719 + 5.49227i −0.329119 + 0.212981i
\(666\) 0 0
\(667\) −6.39028 5.36208i −0.247433 0.207621i
\(668\) 0 0
\(669\) −1.38647 7.86304i −0.0536039 0.304003i
\(670\) 0 0
\(671\) 31.9295 + 11.6214i 1.23262 + 0.448638i
\(672\) 0 0
\(673\) 1.09447 1.89568i 0.0421888 0.0730731i −0.844160 0.536091i \(-0.819900\pi\)
0.886349 + 0.463018i \(0.153234\pi\)
\(674\) 0 0
\(675\) 3.00320 2.51998i 0.115593 0.0969942i
\(676\) 0 0
\(677\) 17.8893 + 30.9853i 0.687544 + 1.19086i 0.972630 + 0.232359i \(0.0746443\pi\)
−0.285087 + 0.958502i \(0.592022\pi\)
\(678\) 0 0
\(679\) −3.83839 + 21.7686i −0.147304 + 0.835402i
\(680\) 0 0
\(681\) 0.379217 0.138024i 0.0145316 0.00528909i
\(682\) 0 0
\(683\) −22.0944 −0.845420 −0.422710 0.906265i \(-0.638921\pi\)
−0.422710 + 0.906265i \(0.638921\pi\)
\(684\) 0 0
\(685\) −2.47265 −0.0944749
\(686\) 0 0
\(687\) −1.36009 + 0.495033i −0.0518907 + 0.0188867i
\(688\) 0 0
\(689\) 2.88931 16.3861i 0.110074 0.624260i
\(690\) 0 0
\(691\) −20.2387 35.0544i −0.769916 1.33353i −0.937608 0.347694i \(-0.886965\pi\)
0.167693 0.985839i \(-0.446368\pi\)
\(692\) 0 0
\(693\) 13.9317 11.6901i 0.529221 0.444069i
\(694\) 0 0
\(695\) −11.0583 + 19.1536i −0.419466 + 0.726536i
\(696\) 0 0
\(697\) −20.4225 7.43318i −0.773557 0.281552i
\(698\) 0 0
\(699\) 3.61209 + 20.4852i 0.136622 + 0.774821i
\(700\) 0 0
\(701\) 13.2392 + 11.1090i 0.500037 + 0.419581i 0.857607 0.514305i \(-0.171950\pi\)
−0.357570 + 0.933886i \(0.616395\pi\)
\(702\) 0 0
\(703\) −16.7498 + 3.83866i −0.631732 + 0.144778i
\(704\) 0 0
\(705\) −3.92187 3.29084i −0.147706 0.123940i
\(706\) 0 0
\(707\) −7.66596 43.4758i −0.288308 1.63508i
\(708\) 0 0
\(709\) −15.2703 5.55795i −0.573490 0.208733i 0.0389627 0.999241i \(-0.487595\pi\)
−0.612452 + 0.790507i \(0.709817\pi\)
\(710\) 0 0
\(711\) 5.45080 9.44105i 0.204421 0.354067i
\(712\) 0 0
\(713\) 2.53158 2.12425i 0.0948086 0.0795538i
\(714\) 0 0
\(715\) −8.71773 15.0996i −0.326025 0.564691i
\(716\) 0 0
\(717\) −1.22336 + 6.93803i −0.0456873 + 0.259106i
\(718\) 0 0
\(719\) −38.8579 + 14.1431i −1.44915 + 0.527449i −0.942355 0.334615i \(-0.891394\pi\)
−0.506800 + 0.862064i \(0.669172\pi\)
\(720\) 0 0
\(721\) 14.7538 0.549459
\(722\) 0 0
\(723\) −3.65109 −0.135786
\(724\) 0 0
\(725\) −4.80083 + 1.74736i −0.178298 + 0.0648953i
\(726\) 0 0
\(727\) 5.68484 32.2403i 0.210839 1.19573i −0.677143 0.735851i \(-0.736782\pi\)
0.887983 0.459877i \(-0.152107\pi\)
\(728\) 0 0
\(729\) 1.61598 + 2.79896i 0.0598511 + 0.103665i
\(730\) 0 0
\(731\) 0.558529 0.468662i 0.0206579 0.0173341i
\(732\) 0 0
\(733\) 21.5832 37.3832i 0.797194 1.38078i −0.124243 0.992252i \(-0.539650\pi\)
0.921437 0.388528i \(-0.127016\pi\)
\(734\) 0 0
\(735\) 1.08786 + 0.395947i 0.0401262 + 0.0146047i
\(736\) 0 0
\(737\) −8.21135 46.5689i −0.302469 1.71539i
\(738\) 0 0
\(739\) −19.8020 16.6158i −0.728427 0.611223i 0.201275 0.979535i \(-0.435491\pi\)
−0.929702 + 0.368312i \(0.879936\pi\)
\(740\) 0 0
\(741\) 16.7978 3.84965i 0.617083 0.141420i
\(742\) 0 0
\(743\) −10.6605 8.94520i −0.391095 0.328167i 0.425945 0.904749i \(-0.359942\pi\)
−0.817039 + 0.576582i \(0.804386\pi\)
\(744\) 0 0
\(745\) 2.39482 + 13.5817i 0.0877394 + 0.497595i
\(746\) 0 0
\(747\) 13.9383 + 5.07313i 0.509976 + 0.185616i
\(748\) 0 0
\(749\) 20.6218 35.7180i 0.753505 1.30511i
\(750\) 0 0
\(751\) −9.12380 + 7.65578i −0.332932 + 0.279363i −0.793893 0.608057i \(-0.791949\pi\)
0.460961 + 0.887420i \(0.347505\pi\)
\(752\) 0 0
\(753\) −11.0402 19.1222i −0.402328 0.696852i
\(754\) 0 0
\(755\) −0.345371 + 1.95870i −0.0125694 + 0.0712843i
\(756\) 0 0
\(757\) −34.8317 + 12.6777i −1.26598 + 0.460778i −0.885771 0.464123i \(-0.846370\pi\)
−0.380208 + 0.924901i \(0.624147\pi\)
\(758\) 0 0
\(759\) 3.67181 0.133278
\(760\) 0 0
\(761\) 0.464156 0.0168257 0.00841283 0.999965i \(-0.497322\pi\)
0.00841283 + 0.999965i \(0.497322\pi\)
\(762\) 0 0
\(763\) 39.5950 14.4114i 1.43344 0.521728i
\(764\) 0 0
\(765\) −1.30744 + 7.41483i −0.0472704 + 0.268084i
\(766\) 0 0
\(767\) −1.68534 2.91909i −0.0608540 0.105402i
\(768\) 0 0
\(769\) 3.80822 3.19548i 0.137328 0.115232i −0.571536 0.820577i \(-0.693652\pi\)
0.708864 + 0.705345i \(0.249208\pi\)
\(770\) 0 0
\(771\) 4.93470 8.54715i 0.177719 0.307818i
\(772\) 0 0
\(773\) −35.9253 13.0757i −1.29214 0.470302i −0.397713 0.917510i \(-0.630196\pi\)
−0.894430 + 0.447208i \(0.852418\pi\)
\(774\) 0 0
\(775\) −0.351458 1.99322i −0.0126247 0.0715985i
\(776\) 0 0
\(777\) −5.00147 4.19673i −0.179427 0.150557i
\(778\) 0 0
\(779\) 26.3031 17.0214i 0.942407 0.609855i
\(780\) 0 0
\(781\) 11.0018 + 9.23159i 0.393674 + 0.330332i
\(782\) 0 0
\(783\) 3.47801 + 19.7248i 0.124294 + 0.704906i
\(784\) 0 0
\(785\) −0.0186713 0.00679578i −0.000666406 0.000242552i
\(786\) 0 0
\(787\) −11.9870 + 20.7621i −0.427291 + 0.740090i