Properties

Label 380.2.u.b.81.2
Level $380$
Weight $2$
Character 380.81
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 81.2
Root \(-0.478554 - 0.828880i\) of defining polynomial
Character \(\chi\) \(=\) 380.81
Dual form 380.2.u.b.61.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.166200 - 0.942568i) q^{3} +(0.766044 + 0.642788i) q^{5} +(-2.28066 - 3.95023i) q^{7} +(1.95827 + 0.712751i) q^{9} +O(q^{10})\) \(q+(0.166200 - 0.942568i) q^{3} +(0.766044 + 0.642788i) q^{5} +(-2.28066 - 3.95023i) q^{7} +(1.95827 + 0.712751i) q^{9} +(-0.558879 + 0.968007i) q^{11} +(-0.897380 - 5.08930i) q^{13} +(0.733187 - 0.615217i) q^{15} +(6.80290 - 2.47605i) q^{17} +(-3.68742 - 2.32442i) q^{19} +(-4.10240 + 1.49315i) q^{21} +(-3.31875 + 2.78477i) q^{23} +(0.173648 + 0.984808i) q^{25} +(2.43294 - 4.21398i) q^{27} +(2.51115 + 0.913983i) q^{29} +(1.37022 + 2.37328i) q^{31} +(0.819526 + 0.687664i) q^{33} +(0.792067 - 4.49203i) q^{35} -0.491893 q^{37} -4.94615 q^{39} +(1.45408 - 8.24648i) q^{41} +(3.16372 + 2.65467i) q^{43} +(1.04197 + 1.80475i) q^{45} +(2.48547 + 0.904639i) q^{47} +(-6.90286 + 11.9561i) q^{49} +(-1.20320 - 6.82371i) q^{51} +(-10.4500 + 8.76856i) q^{53} +(-1.05035 + 0.382296i) q^{55} +(-2.80377 + 3.08933i) q^{57} +(2.45313 - 0.892868i) q^{59} +(3.64703 - 3.06022i) q^{61} +(-1.65062 - 9.36114i) q^{63} +(2.58390 - 4.47545i) q^{65} +(11.9079 + 4.33411i) q^{67} +(2.07325 + 3.59098i) q^{69} +(0.524118 + 0.439787i) q^{71} +(-2.28024 + 12.9319i) q^{73} +0.957108 q^{75} +5.09846 q^{77} +(-2.75095 + 15.6014i) q^{79} +(1.22158 + 1.02502i) q^{81} +(1.88033 + 3.25683i) q^{83} +(6.80290 + 2.47605i) q^{85} +(1.27884 - 2.21502i) q^{87} +(2.04379 + 11.5909i) q^{89} +(-18.0573 + 15.1518i) q^{91} +(2.46471 - 0.897081i) q^{93} +(-1.33063 - 4.15084i) q^{95} +(3.27804 - 1.19311i) q^{97} +(-1.78438 + 1.49727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\)

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
\(3\) 0.166200 0.942568i 0.0959557 0.544192i −0.898495 0.438984i \(-0.855338\pi\)
0.994450 0.105207i \(-0.0335506\pi\)
\(4\) 0 0
\(5\) 0.766044 + 0.642788i 0.342585 + 0.287463i
\(6\) 0 0
\(7\) −2.28066 3.95023i −0.862010 1.49305i −0.869985 0.493077i \(-0.835872\pi\)
0.00797511 0.999968i \(-0.497461\pi\)
\(8\) 0 0
\(9\) 1.95827 + 0.712751i 0.652756 + 0.237584i
\(10\) 0 0
\(11\) −0.558879 + 0.968007i −0.168508 + 0.291865i −0.937896 0.346918i \(-0.887228\pi\)
0.769387 + 0.638783i \(0.220562\pi\)
\(12\) 0 0
\(13\) −0.897380 5.08930i −0.248889 1.41152i −0.811286 0.584650i \(-0.801232\pi\)
0.562397 0.826867i \(-0.309879\pi\)
\(14\) 0 0
\(15\) 0.733187 0.615217i 0.189308 0.158848i
\(16\) 0 0
\(17\) 6.80290 2.47605i 1.64994 0.600531i 0.661209 0.750202i \(-0.270044\pi\)
0.988736 + 0.149671i \(0.0478216\pi\)
\(18\) 0 0
\(19\) −3.68742 2.32442i −0.845953 0.533257i
\(20\) 0 0
\(21\) −4.10240 + 1.49315i −0.895218 + 0.325833i
\(22\) 0 0
\(23\) −3.31875 + 2.78477i −0.692008 + 0.580664i −0.919488 0.393119i \(-0.871396\pi\)
0.227480 + 0.973783i \(0.426952\pi\)
\(24\) 0 0
\(25\) 0.173648 + 0.984808i 0.0347296 + 0.196962i
\(26\) 0 0
\(27\) 2.43294 4.21398i 0.468220 0.810981i
\(28\) 0 0
\(29\) 2.51115 + 0.913983i 0.466308 + 0.169722i 0.564479 0.825447i \(-0.309077\pi\)
−0.0981710 + 0.995170i \(0.531299\pi\)
\(30\) 0 0
\(31\) 1.37022 + 2.37328i 0.246098 + 0.426254i 0.962440 0.271495i \(-0.0875181\pi\)
−0.716342 + 0.697750i \(0.754185\pi\)
\(32\) 0 0
\(33\) 0.819526 + 0.687664i 0.142661 + 0.119707i
\(34\) 0 0
\(35\) 0.792067 4.49203i 0.133884 0.759292i
\(36\) 0 0
\(37\) −0.491893 −0.0808666 −0.0404333 0.999182i \(-0.512874\pi\)
−0.0404333 + 0.999182i \(0.512874\pi\)
\(38\) 0 0
\(39\) −4.94615 −0.792018
\(40\) 0 0
\(41\) 1.45408 8.24648i 0.227089 1.28788i −0.631563 0.775325i \(-0.717586\pi\)
0.858652 0.512560i \(-0.171303\pi\)
\(42\) 0 0
\(43\) 3.16372 + 2.65467i 0.482462 + 0.404834i 0.851316 0.524654i \(-0.175805\pi\)
−0.368853 + 0.929488i \(0.620250\pi\)
\(44\) 0 0
\(45\) 1.04197 + 1.80475i 0.155328 + 0.269036i
\(46\) 0 0
\(47\) 2.48547 + 0.904639i 0.362544 + 0.131955i 0.516868 0.856065i \(-0.327098\pi\)
−0.154324 + 0.988020i \(0.549320\pi\)
\(48\) 0 0
\(49\) −6.90286 + 11.9561i −0.986124 + 1.70802i
\(50\) 0 0
\(51\) −1.20320 6.82371i −0.168482 0.955510i
\(52\) 0 0
\(53\) −10.4500 + 8.76856i −1.43541 + 1.20445i −0.492988 + 0.870036i \(0.664095\pi\)
−0.942425 + 0.334418i \(0.891460\pi\)
\(54\) 0 0
\(55\) −1.05035 + 0.382296i −0.141629 + 0.0515488i
\(56\) 0 0
\(57\) −2.80377 + 3.08933i −0.371368 + 0.409192i
\(58\) 0 0
\(59\) 2.45313 0.892868i 0.319371 0.116241i −0.177360 0.984146i \(-0.556756\pi\)
0.496731 + 0.867905i \(0.334534\pi\)
\(60\) 0 0
\(61\) 3.64703 3.06022i 0.466954 0.391821i −0.378728 0.925508i \(-0.623638\pi\)
0.845682 + 0.533687i \(0.179194\pi\)
\(62\) 0 0
\(63\) −1.65062 9.36114i −0.207959 1.17939i
\(64\) 0 0
\(65\) 2.58390 4.47545i 0.320494 0.555112i
\(66\) 0 0
\(67\) 11.9079 + 4.33411i 1.45478 + 0.529495i 0.943921 0.330171i \(-0.107107\pi\)
0.510855 + 0.859667i \(0.329329\pi\)
\(68\) 0 0
\(69\) 2.07325 + 3.59098i 0.249590 + 0.432303i
\(70\) 0 0
\(71\) 0.524118 + 0.439787i 0.0622013 + 0.0521931i 0.673358 0.739316i \(-0.264851\pi\)
−0.611157 + 0.791509i \(0.709296\pi\)
\(72\) 0 0
\(73\) −2.28024 + 12.9319i −0.266882 + 1.51356i 0.496741 + 0.867899i \(0.334530\pi\)
−0.763623 + 0.645662i \(0.776581\pi\)
\(74\) 0 0
\(75\) 0.957108 0.110517
\(76\) 0 0
\(77\) 5.09846 0.581024
\(78\) 0 0
\(79\) −2.75095 + 15.6014i −0.309506 + 1.75529i 0.291993 + 0.956420i \(0.405681\pi\)
−0.601499 + 0.798874i \(0.705430\pi\)
\(80\) 0 0
\(81\) 1.22158 + 1.02502i 0.135731 + 0.113892i
\(82\) 0 0
\(83\) 1.88033 + 3.25683i 0.206393 + 0.357484i 0.950576 0.310493i \(-0.100494\pi\)
−0.744182 + 0.667976i \(0.767161\pi\)
\(84\) 0 0
\(85\) 6.80290 + 2.47605i 0.737878 + 0.268565i
\(86\) 0 0
\(87\) 1.27884 2.21502i 0.137106 0.237475i
\(88\) 0 0
\(89\) 2.04379 + 11.5909i 0.216642 + 1.22864i 0.878035 + 0.478597i \(0.158854\pi\)
−0.661393 + 0.750039i \(0.730035\pi\)
\(90\) 0 0
\(91\) −18.0573 + 15.1518i −1.89292 + 1.58834i
\(92\) 0 0
\(93\) 2.46471 0.897081i 0.255579 0.0930230i
\(94\) 0 0
\(95\) −1.33063 4.15084i −0.136519 0.425867i
\(96\) 0 0
\(97\) 3.27804 1.19311i 0.332835 0.121142i −0.170197 0.985410i \(-0.554440\pi\)
0.503031 + 0.864268i \(0.332218\pi\)
\(98\) 0 0
\(99\) −1.78438 + 1.49727i −0.179337 + 0.150482i
\(100\) 0 0
\(101\) 1.83378 + 10.3999i 0.182468 + 1.03483i 0.929165 + 0.369665i \(0.120527\pi\)
−0.746697 + 0.665164i \(0.768362\pi\)
\(102\) 0 0
\(103\) 5.77623 10.0047i 0.569149 0.985794i −0.427502 0.904015i \(-0.640606\pi\)
0.996650 0.0817799i \(-0.0260605\pi\)
\(104\) 0 0
\(105\) −4.10240 1.49315i −0.400354 0.145717i
\(106\) 0 0
\(107\) −3.88420 6.72763i −0.375499 0.650384i 0.614902 0.788603i \(-0.289195\pi\)
−0.990402 + 0.138219i \(0.955862\pi\)
\(108\) 0 0
\(109\) −10.1216 8.49299i −0.969469 0.813481i 0.0129986 0.999916i \(-0.495862\pi\)
−0.982467 + 0.186435i \(0.940307\pi\)
\(110\) 0 0
\(111\) −0.0817526 + 0.463642i −0.00775961 + 0.0440070i
\(112\) 0 0
\(113\) −1.84103 −0.173190 −0.0865950 0.996244i \(-0.527599\pi\)
−0.0865950 + 0.996244i \(0.527599\pi\)
\(114\) 0 0
\(115\) −4.33233 −0.403991
\(116\) 0 0
\(117\) 1.87009 10.6058i 0.172890 0.980507i
\(118\) 0 0
\(119\) −25.2961 21.2259i −2.31889 1.94578i
\(120\) 0 0
\(121\) 4.87531 + 8.44428i 0.443210 + 0.767662i
\(122\) 0 0
\(123\) −7.53120 2.74113i −0.679066 0.247160i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −0.731989 4.15132i −0.0649536 0.368370i −0.999908 0.0136008i \(-0.995671\pi\)
0.934954 0.354769i \(-0.115441\pi\)
\(128\) 0 0
\(129\) 3.02802 2.54081i 0.266602 0.223706i
\(130\) 0 0
\(131\) −2.58430 + 0.940609i −0.225791 + 0.0821814i −0.452439 0.891796i \(-0.649446\pi\)
0.226647 + 0.973977i \(0.427224\pi\)
\(132\) 0 0
\(133\) −0.772191 + 19.8674i −0.0669574 + 1.72272i
\(134\) 0 0
\(135\) 4.57244 1.66423i 0.393533 0.143234i
\(136\) 0 0
\(137\) 1.69224 1.41996i 0.144578 0.121315i −0.567630 0.823284i \(-0.692140\pi\)
0.712208 + 0.701968i \(0.247695\pi\)
\(138\) 0 0
\(139\) 1.53264 + 8.69203i 0.129997 + 0.737248i 0.978214 + 0.207600i \(0.0665651\pi\)
−0.848217 + 0.529649i \(0.822324\pi\)
\(140\) 0 0
\(141\) 1.26577 2.19238i 0.106597 0.184631i
\(142\) 0 0
\(143\) 5.42800 + 1.97563i 0.453912 + 0.165211i
\(144\) 0 0
\(145\) 1.33615 + 2.31429i 0.110962 + 0.192191i
\(146\) 0 0
\(147\) 10.1222 + 8.49352i 0.834864 + 0.700534i
\(148\) 0 0
\(149\) 3.62671 20.5681i 0.297111 1.68500i −0.361383 0.932417i \(-0.617695\pi\)
0.658495 0.752585i \(-0.271194\pi\)
\(150\) 0 0
\(151\) 5.73130 0.466407 0.233203 0.972428i \(-0.425079\pi\)
0.233203 + 0.972428i \(0.425079\pi\)
\(152\) 0 0
\(153\) 15.0867 1.21969
\(154\) 0 0
\(155\) −0.475871 + 2.69880i −0.0382229 + 0.216773i
\(156\) 0 0
\(157\) −14.1251 11.8523i −1.12730 0.945919i −0.128352 0.991729i \(-0.540969\pi\)
−0.998950 + 0.0458101i \(0.985413\pi\)
\(158\) 0 0
\(159\) 6.52818 + 11.3071i 0.517718 + 0.896714i
\(160\) 0 0
\(161\) 18.5694 + 6.75872i 1.46348 + 0.532661i
\(162\) 0 0
\(163\) −1.74094 + 3.01540i −0.136361 + 0.236185i −0.926117 0.377237i \(-0.876874\pi\)
0.789755 + 0.613422i \(0.210207\pi\)
\(164\) 0 0
\(165\) 0.185772 + 1.05356i 0.0144623 + 0.0820198i
\(166\) 0 0
\(167\) 16.4620 13.8132i 1.27387 1.06890i 0.279806 0.960056i \(-0.409730\pi\)
0.994059 0.108843i \(-0.0347147\pi\)
\(168\) 0 0
\(169\) −12.8797 + 4.68781i −0.990742 + 0.360601i
\(170\) 0 0
\(171\) −5.56423 7.18004i −0.425507 0.549071i
\(172\) 0 0
\(173\) −10.3262 + 3.75842i −0.785084 + 0.285747i −0.703291 0.710902i \(-0.748287\pi\)
−0.0817929 + 0.996649i \(0.526065\pi\)
\(174\) 0 0
\(175\) 3.49418 2.93197i 0.264135 0.221636i
\(176\) 0 0
\(177\) −0.433877 2.46064i −0.0326122 0.184953i
\(178\) 0 0
\(179\) 8.54852 14.8065i 0.638946 1.10669i −0.346718 0.937969i \(-0.612704\pi\)
0.985664 0.168718i \(-0.0539627\pi\)
\(180\) 0 0
\(181\) −10.8910 3.96399i −0.809519 0.294641i −0.0960938 0.995372i \(-0.530635\pi\)
−0.713425 + 0.700732i \(0.752857\pi\)
\(182\) 0 0
\(183\) −2.27833 3.94618i −0.168419 0.291710i
\(184\) 0 0
\(185\) −0.376812 0.316182i −0.0277037 0.0232462i
\(186\) 0 0
\(187\) −1.40516 + 7.96907i −0.102756 + 0.582756i
\(188\) 0 0
\(189\) −22.1949 −1.61444
\(190\) 0 0
\(191\) 25.8688 1.87180 0.935901 0.352262i \(-0.114587\pi\)
0.935901 + 0.352262i \(0.114587\pi\)
\(192\) 0 0
\(193\) 2.44272 13.8534i 0.175831 0.997187i −0.761349 0.648342i \(-0.775463\pi\)
0.937180 0.348845i \(-0.113426\pi\)
\(194\) 0 0
\(195\) −3.78897 3.17932i −0.271334 0.227676i
\(196\) 0 0
\(197\) −1.70220 2.94830i −0.121277 0.210057i 0.798995 0.601338i \(-0.205365\pi\)
−0.920271 + 0.391281i \(0.872032\pi\)
\(198\) 0 0
\(199\) 17.3891 + 6.32911i 1.23268 + 0.448659i 0.874515 0.484999i \(-0.161180\pi\)
0.358166 + 0.933658i \(0.383402\pi\)
\(200\) 0 0
\(201\) 6.06427 10.5036i 0.427741 0.740869i
\(202\) 0 0
\(203\) −2.11665 12.0041i −0.148559 0.842522i
\(204\) 0 0
\(205\) 6.41463 5.38251i 0.448017 0.375931i
\(206\) 0 0
\(207\) −8.48385 + 3.08787i −0.589668 + 0.214622i
\(208\) 0 0
\(209\) 4.31087 2.27039i 0.298189 0.157046i
\(210\) 0 0
\(211\) −14.8432 + 5.40250i −1.02185 + 0.371923i −0.797972 0.602694i \(-0.794094\pi\)
−0.223878 + 0.974617i \(0.571872\pi\)
\(212\) 0 0
\(213\) 0.501638 0.420924i 0.0343716 0.0288412i
\(214\) 0 0
\(215\) 0.717156 + 4.06720i 0.0489097 + 0.277380i
\(216\) 0 0
\(217\) 6.25001 10.8253i 0.424278 0.734871i
\(218\) 0 0
\(219\) 11.8102 + 4.29856i 0.798058 + 0.290469i
\(220\) 0 0
\(221\) −18.7061 32.4000i −1.25831 2.17946i
\(222\) 0 0
\(223\) −17.0138 14.2763i −1.13933 0.956008i −0.139910 0.990164i \(-0.544681\pi\)
−0.999417 + 0.0341558i \(0.989126\pi\)
\(224\) 0 0
\(225\) −0.361873 + 2.05228i −0.0241249 + 0.136819i
\(226\) 0 0
\(227\) −5.60932 −0.372304 −0.186152 0.982521i \(-0.559602\pi\)
−0.186152 + 0.982521i \(0.559602\pi\)
\(228\) 0 0
\(229\) 1.04017 0.0687366 0.0343683 0.999409i \(-0.489058\pi\)
0.0343683 + 0.999409i \(0.489058\pi\)
\(230\) 0 0
\(231\) 0.847365 4.80565i 0.0557525 0.316188i
\(232\) 0 0
\(233\) 9.15779 + 7.68430i 0.599947 + 0.503415i 0.891428 0.453161i \(-0.149704\pi\)
−0.291482 + 0.956576i \(0.594148\pi\)
\(234\) 0 0
\(235\) 1.32249 + 2.29063i 0.0862699 + 0.149424i
\(236\) 0 0
\(237\) 14.2482 + 5.18591i 0.925517 + 0.336861i
\(238\) 0 0
\(239\) 4.50416 7.80144i 0.291350 0.504633i −0.682779 0.730625i \(-0.739229\pi\)
0.974129 + 0.225992i \(0.0725622\pi\)
\(240\) 0 0
\(241\) −2.31012 13.1014i −0.148808 0.843933i −0.964230 0.265066i \(-0.914606\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(242\) 0 0
\(243\) 12.3516 10.3642i 0.792358 0.664867i
\(244\) 0 0
\(245\) −12.9731 + 4.72184i −0.828824 + 0.301667i
\(246\) 0 0
\(247\) −8.52062 + 20.8523i −0.542154 + 1.32680i
\(248\) 0 0
\(249\) 3.38230 1.23105i 0.214344 0.0780149i
\(250\) 0 0
\(251\) −17.0043 + 14.2683i −1.07330 + 0.900609i −0.995348 0.0963480i \(-0.969284\pi\)
−0.0779560 + 0.996957i \(0.524839\pi\)
\(252\) 0 0
\(253\) −0.840890 4.76892i −0.0528663 0.299820i
\(254\) 0 0
\(255\) 3.46449 6.00067i 0.216955 0.375776i
\(256\) 0 0
\(257\) 2.37388 + 0.864022i 0.148079 + 0.0538962i 0.414996 0.909823i \(-0.363783\pi\)
−0.266918 + 0.963719i \(0.586005\pi\)
\(258\) 0 0
\(259\) 1.12184 + 1.94309i 0.0697079 + 0.120738i
\(260\) 0 0
\(261\) 4.26605 + 3.57964i 0.264062 + 0.221574i
\(262\) 0 0
\(263\) −2.18211 + 12.3753i −0.134554 + 0.763096i 0.840615 + 0.541634i \(0.182194\pi\)
−0.975169 + 0.221462i \(0.928917\pi\)
\(264\) 0 0
\(265\) −13.6415 −0.837988
\(266\) 0 0
\(267\) 11.2649 0.689401
\(268\) 0 0
\(269\) −3.59540 + 20.3905i −0.219216 + 1.24323i 0.654224 + 0.756301i \(0.272995\pi\)
−0.873439 + 0.486933i \(0.838116\pi\)
\(270\) 0 0
\(271\) −1.02160 0.857226i −0.0620579 0.0520728i 0.611231 0.791452i \(-0.290675\pi\)
−0.673289 + 0.739379i \(0.735119\pi\)
\(272\) 0 0
\(273\) 11.2805 + 19.5384i 0.682728 + 1.18252i
\(274\) 0 0
\(275\) −1.05035 0.382296i −0.0633384 0.0230533i
\(276\) 0 0
\(277\) −14.1070 + 24.4340i −0.847606 + 1.46810i 0.0357322 + 0.999361i \(0.488624\pi\)
−0.883338 + 0.468736i \(0.844710\pi\)
\(278\) 0 0
\(279\) 0.991688 + 5.62414i 0.0593708 + 0.336709i
\(280\) 0 0
\(281\) 9.31199 7.81369i 0.555507 0.466126i −0.321294 0.946980i \(-0.604118\pi\)
0.876801 + 0.480854i \(0.159673\pi\)
\(282\) 0 0
\(283\) −1.65082 + 0.600850i −0.0981312 + 0.0357168i −0.390619 0.920552i \(-0.627739\pi\)
0.292488 + 0.956269i \(0.405517\pi\)
\(284\) 0 0
\(285\) −4.13359 + 0.564335i −0.244853 + 0.0334283i
\(286\) 0 0
\(287\) −35.8918 + 13.0635i −2.11862 + 0.771116i
\(288\) 0 0
\(289\) 27.1258 22.7612i 1.59564 1.33890i
\(290\) 0 0
\(291\) −0.579775 3.28807i −0.0339870 0.192750i
\(292\) 0 0
\(293\) 3.85056 6.66937i 0.224952 0.389629i −0.731353 0.681999i \(-0.761111\pi\)
0.956305 + 0.292370i \(0.0944440\pi\)
\(294\) 0 0
\(295\) 2.45313 + 0.892868i 0.142827 + 0.0519848i
\(296\) 0 0
\(297\) 2.71944 + 4.71021i 0.157798 + 0.273314i
\(298\) 0 0
\(299\) 17.1507 + 14.3911i 0.991850 + 0.832261i
\(300\) 0 0
\(301\) 3.27119 18.5518i 0.188548 1.06931i
\(302\) 0 0
\(303\) 10.1074 0.580654
\(304\) 0 0
\(305\) 4.76086 0.272606
\(306\) 0 0
\(307\) −1.11720 + 6.33598i −0.0637623 + 0.361614i 0.936187 + 0.351503i \(0.114329\pi\)
−0.999949 + 0.0101104i \(0.996782\pi\)
\(308\) 0 0
\(309\) −8.47012 7.10727i −0.481848 0.404319i
\(310\) 0 0
\(311\) 14.5028 + 25.1196i 0.822379 + 1.42440i 0.903906 + 0.427731i \(0.140687\pi\)
−0.0815274 + 0.996671i \(0.525980\pi\)
\(312\) 0 0
\(313\) −12.8655 4.68265i −0.727200 0.264679i −0.0482209 0.998837i \(-0.515355\pi\)
−0.678979 + 0.734158i \(0.737577\pi\)
\(314\) 0 0
\(315\) 4.75278 8.23205i 0.267789 0.463824i
\(316\) 0 0
\(317\) −0.782232 4.43626i −0.0439345 0.249165i 0.954929 0.296836i \(-0.0959314\pi\)
−0.998863 + 0.0476705i \(0.984820\pi\)
\(318\) 0 0
\(319\) −2.28817 + 1.92000i −0.128113 + 0.107500i
\(320\) 0 0
\(321\) −6.98680 + 2.54299i −0.389965 + 0.141936i
\(322\) 0 0
\(323\) −30.8405 6.68250i −1.71601 0.371824i
\(324\) 0 0
\(325\) 4.85615 1.76749i 0.269371 0.0980430i
\(326\) 0 0
\(327\) −9.68742 + 8.12871i −0.535715 + 0.449519i
\(328\) 0 0
\(329\) −2.09501 11.8814i −0.115501 0.655041i
\(330\) 0 0
\(331\) −7.72326 + 13.3771i −0.424509 + 0.735271i −0.996374 0.0850767i \(-0.972886\pi\)
0.571866 + 0.820347i \(0.306220\pi\)
\(332\) 0 0
\(333\) −0.963257 0.350597i −0.0527862 0.0192126i
\(334\) 0 0
\(335\) 6.33604 + 10.9743i 0.346175 + 0.599592i
\(336\) 0 0
\(337\) −16.3175 13.6920i −0.888869 0.745850i 0.0791136 0.996866i \(-0.474791\pi\)
−0.967983 + 0.251016i \(0.919235\pi\)
\(338\) 0 0
\(339\) −0.305980 + 1.73530i −0.0166186 + 0.0942485i
\(340\) 0 0
\(341\) −3.06314 −0.165878
\(342\) 0 0
\(343\) 31.0432 1.67617
\(344\) 0 0
\(345\) −0.720033 + 4.08351i −0.0387653 + 0.219849i
\(346\) 0 0
\(347\) 2.69463 + 2.26106i 0.144655 + 0.121380i 0.712244 0.701932i \(-0.247679\pi\)
−0.567588 + 0.823312i \(0.692124\pi\)
\(348\) 0 0
\(349\) −4.55638 7.89188i −0.243897 0.422443i 0.717924 0.696122i \(-0.245093\pi\)
−0.961821 + 0.273679i \(0.911759\pi\)
\(350\) 0 0
\(351\) −23.6295 8.60042i −1.26125 0.459057i
\(352\) 0 0
\(353\) −12.4350 + 21.5381i −0.661850 + 1.14636i 0.318279 + 0.947997i \(0.396895\pi\)
−0.980129 + 0.198361i \(0.936438\pi\)
\(354\) 0 0
\(355\) 0.118808 + 0.673793i 0.00630567 + 0.0357612i
\(356\) 0 0
\(357\) −24.2111 + 20.3155i −1.28139 + 1.07521i
\(358\) 0 0
\(359\) −18.2882 + 6.65634i −0.965212 + 0.351308i −0.776074 0.630642i \(-0.782792\pi\)
−0.189138 + 0.981951i \(0.560569\pi\)
\(360\) 0 0
\(361\) 8.19419 + 17.1422i 0.431273 + 0.902221i
\(362\) 0 0
\(363\) 8.76958 3.19187i 0.460284 0.167530i
\(364\) 0 0
\(365\) −10.0592 + 8.44068i −0.526523 + 0.441805i
\(366\) 0 0
\(367\) 3.57276 + 20.2622i 0.186497 + 1.05768i 0.924017 + 0.382351i \(0.124885\pi\)
−0.737520 + 0.675325i \(0.764003\pi\)
\(368\) 0 0
\(369\) 8.72516 15.1124i 0.454214 0.786721i
\(370\) 0 0
\(371\) 58.4707 + 21.2816i 3.03565 + 1.10488i
\(372\) 0 0
\(373\) 1.84938 + 3.20322i 0.0957572 + 0.165856i 0.909924 0.414774i \(-0.136139\pi\)
−0.814167 + 0.580630i \(0.802806\pi\)
\(374\) 0 0
\(375\) 0.733187 + 0.615217i 0.0378616 + 0.0317697i
\(376\) 0 0
\(377\) 2.39808 13.6002i 0.123507 0.700444i
\(378\) 0 0
\(379\) −6.68304 −0.343285 −0.171642 0.985159i \(-0.554907\pi\)
−0.171642 + 0.985159i \(0.554907\pi\)
\(380\) 0 0
\(381\) −4.03456 −0.206697
\(382\) 0 0
\(383\) 5.39114 30.5747i 0.275474 1.56229i −0.461977 0.886892i \(-0.652860\pi\)
0.737451 0.675400i \(-0.236029\pi\)
\(384\) 0 0
\(385\) 3.90565 + 3.27723i 0.199050 + 0.167023i
\(386\) 0 0
\(387\) 4.30328 + 7.45350i 0.218748 + 0.378883i
\(388\) 0 0
\(389\) 11.2323 + 4.08822i 0.569500 + 0.207281i 0.610689 0.791870i \(-0.290892\pi\)
−0.0411892 + 0.999151i \(0.513115\pi\)
\(390\) 0 0
\(391\) −15.6819 + 27.1619i −0.793068 + 1.37363i
\(392\) 0 0
\(393\) 0.457076 + 2.59221i 0.0230564 + 0.130760i
\(394\) 0 0
\(395\) −12.1357 + 10.1831i −0.610615 + 0.512367i
\(396\) 0 0
\(397\) 4.00480 1.45763i 0.200995 0.0731562i −0.239561 0.970881i \(-0.577004\pi\)
0.440556 + 0.897725i \(0.354781\pi\)
\(398\) 0 0
\(399\) 18.5980 + 4.02980i 0.931065 + 0.201742i
\(400\) 0 0
\(401\) 0.433821 0.157898i 0.0216640 0.00788506i −0.331165 0.943573i \(-0.607442\pi\)
0.352829 + 0.935688i \(0.385220\pi\)
\(402\) 0 0
\(403\) 10.8487 9.10317i 0.540414 0.453461i
\(404\) 0 0
\(405\) 0.276909 + 1.57043i 0.0137597 + 0.0780352i
\(406\) 0 0
\(407\) 0.274909 0.476156i 0.0136267 0.0236022i
\(408\) 0 0
\(409\) 29.7422 + 10.8253i 1.47066 + 0.535276i 0.948279 0.317438i \(-0.102823\pi\)
0.522378 + 0.852714i \(0.325045\pi\)
\(410\) 0 0
\(411\) −1.05715 1.83104i −0.0521456 0.0903188i
\(412\) 0 0
\(413\) −9.12181 7.65411i −0.448855 0.376634i
\(414\) 0 0
\(415\) −0.653033 + 3.70353i −0.0320561 + 0.181799i
\(416\) 0 0
\(417\) 8.44755 0.413678
\(418\) 0 0
\(419\) 23.8430 1.16481 0.582403 0.812900i \(-0.302112\pi\)
0.582403 + 0.812900i \(0.302112\pi\)
\(420\) 0 0
\(421\) 1.32252 7.50041i 0.0644559 0.365547i −0.935470 0.353405i \(-0.885024\pi\)
0.999926 0.0121424i \(-0.00386514\pi\)
\(422\) 0 0
\(423\) 4.22244 + 3.54305i 0.205302 + 0.172269i
\(424\) 0 0
\(425\) 3.61975 + 6.26958i 0.175583 + 0.304119i
\(426\) 0 0
\(427\) −20.4062 7.42726i −0.987526 0.359430i
\(428\) 0 0
\(429\) 2.76430 4.78791i 0.133462 0.231162i
\(430\) 0 0
\(431\) −1.04802 5.94360i −0.0504812 0.286293i 0.949108 0.314950i \(-0.101988\pi\)
−0.999589 + 0.0286575i \(0.990877\pi\)
\(432\) 0 0
\(433\) −14.2376 + 11.9468i −0.684216 + 0.574126i −0.917235 0.398347i \(-0.869584\pi\)
0.233019 + 0.972472i \(0.425140\pi\)
\(434\) 0 0
\(435\) 2.40344 0.874781i 0.115236 0.0419425i
\(436\) 0 0
\(437\) 18.7106 2.55445i 0.895049 0.122196i
\(438\) 0 0
\(439\) −13.0999 + 4.76797i −0.625223 + 0.227563i −0.635151 0.772388i \(-0.719062\pi\)
0.00992755 + 0.999951i \(0.496840\pi\)
\(440\) 0 0
\(441\) −22.0394 + 18.4932i −1.04949 + 0.880630i
\(442\) 0 0
\(443\) −2.65351 15.0488i −0.126072 0.714991i −0.980665 0.195692i \(-0.937305\pi\)
0.854593 0.519298i \(-0.173807\pi\)
\(444\) 0 0
\(445\) −5.88487 + 10.1929i −0.278970 + 0.483189i
\(446\) 0 0
\(447\) −18.7840 6.83683i −0.888455 0.323371i
\(448\) 0 0
\(449\) 16.3149 + 28.2582i 0.769947 + 1.33359i 0.937591 + 0.347739i \(0.113051\pi\)
−0.167645 + 0.985847i \(0.553616\pi\)
\(450\) 0 0
\(451\) 7.17000 + 6.01635i 0.337622 + 0.283299i
\(452\) 0 0
\(453\) 0.952543 5.40214i 0.0447544 0.253815i
\(454\) 0 0
\(455\) −23.5721 −1.10508
\(456\) 0 0
\(457\) −19.5721 −0.915546 −0.457773 0.889069i \(-0.651353\pi\)
−0.457773 + 0.889069i \(0.651353\pi\)
\(458\) 0 0
\(459\) 6.11702 34.6914i 0.285518 1.61925i
\(460\) 0 0
\(461\) −24.0645 20.1925i −1.12079 0.940457i −0.122149 0.992512i \(-0.538979\pi\)
−0.998644 + 0.0520545i \(0.983423\pi\)
\(462\) 0 0
\(463\) 15.2496 + 26.4132i 0.708711 + 1.22752i 0.965335 + 0.261012i \(0.0840563\pi\)
−0.256624 + 0.966511i \(0.582610\pi\)
\(464\) 0 0
\(465\) 2.46471 + 0.897081i 0.114298 + 0.0416011i
\(466\) 0 0
\(467\) 3.74239 6.48201i 0.173177 0.299952i −0.766352 0.642421i \(-0.777930\pi\)
0.939529 + 0.342469i \(0.111263\pi\)
\(468\) 0 0
\(469\) −10.0371 56.9234i −0.463472 2.62848i
\(470\) 0 0
\(471\) −13.5192 + 11.3440i −0.622932 + 0.522702i
\(472\) 0 0
\(473\) −4.33788 + 1.57886i −0.199456 + 0.0725960i
\(474\) 0 0
\(475\) 1.64879 4.03503i 0.0756516 0.185140i
\(476\) 0 0
\(477\) −26.7136 + 9.72296i −1.22313 + 0.445184i
\(478\) 0 0
\(479\) −4.59620 + 3.85667i −0.210006 + 0.176216i −0.741723 0.670706i \(-0.765991\pi\)
0.531718 + 0.846922i \(0.321547\pi\)
\(480\) 0 0
\(481\) 0.441415 + 2.50339i 0.0201268 + 0.114145i
\(482\) 0 0
\(483\) 9.45679 16.3796i 0.430299 0.745299i
\(484\) 0 0
\(485\) 3.27804 + 1.19311i 0.148848 + 0.0541763i
\(486\) 0 0
\(487\) −3.24803 5.62576i −0.147182 0.254927i 0.783003 0.622018i \(-0.213687\pi\)
−0.930185 + 0.367091i \(0.880354\pi\)
\(488\) 0 0
\(489\) 2.55288 + 2.14212i 0.115445 + 0.0968699i
\(490\) 0 0
\(491\) 5.01124 28.4202i 0.226154 1.28258i −0.634312 0.773077i \(-0.718717\pi\)
0.860467 0.509507i \(-0.170172\pi\)
\(492\) 0 0
\(493\) 19.3461 0.871306
\(494\) 0 0
\(495\) −2.32935 −0.104696
\(496\) 0 0
\(497\) 0.541922 3.07339i 0.0243085 0.137860i
\(498\) 0 0
\(499\) −9.63514 8.08484i −0.431328 0.361927i 0.401124 0.916024i \(-0.368619\pi\)
−0.832453 + 0.554096i \(0.813064\pi\)
\(500\) 0 0
\(501\) −10.2839 17.8123i −0.459452 0.795794i
\(502\) 0 0
\(503\) −14.4854 5.27226i −0.645872 0.235078i −0.00174715 0.999998i \(-0.500556\pi\)
−0.644125 + 0.764920i \(0.722778\pi\)
\(504\) 0 0
\(505\) −5.28017 + 9.14552i −0.234964 + 0.406970i
\(506\) 0 0
\(507\) 2.27798 + 12.9191i 0.101169 + 0.573755i
\(508\) 0 0
\(509\) −4.58561 + 3.84778i −0.203254 + 0.170550i −0.738733 0.673998i \(-0.764575\pi\)
0.535479 + 0.844548i \(0.320131\pi\)
\(510\) 0 0
\(511\) 56.2843 20.4858i 2.48987 0.906239i
\(512\) 0 0
\(513\) −18.7663 + 9.88356i −0.828554 + 0.436370i
\(514\) 0 0
\(515\) 10.8558 3.95117i 0.478362 0.174109i
\(516\) 0 0
\(517\) −2.26478 + 1.90037i −0.0996047 + 0.0835783i
\(518\) 0 0
\(519\) 1.82635 + 10.3578i 0.0801680 + 0.454655i
\(520\) 0 0
\(521\) 8.62104 14.9321i 0.377695 0.654187i −0.613032 0.790058i \(-0.710050\pi\)
0.990726 + 0.135872i \(0.0433835\pi\)
\(522\) 0 0
\(523\) 0.113607 + 0.0413496i 0.00496770 + 0.00180809i 0.344503 0.938785i \(-0.388048\pi\)
−0.339535 + 0.940593i \(0.610270\pi\)
\(524\) 0 0
\(525\) −2.18284 3.78080i −0.0952671 0.165007i
\(526\) 0 0
\(527\) 15.1978 + 12.7525i 0.662027 + 0.555507i
\(528\) 0 0
\(529\) −0.734698 + 4.16668i −0.0319434 + 0.181160i
\(530\) 0 0
\(531\) 5.44028 0.236088
\(532\) 0 0
\(533\) −43.2737 −1.87439
\(534\) 0 0
\(535\) 1.34897 7.65037i 0.0583209 0.330754i
\(536\) 0 0
\(537\) −12.5353 10.5184i −0.540940 0.453902i
\(538\) 0 0
\(539\) −7.71574 13.3640i −0.332340 0.575630i
\(540\) 0 0
\(541\) 36.3600 + 13.2340i 1.56324 + 0.568973i 0.971476 0.237139i \(-0.0762097\pi\)
0.591764 + 0.806112i \(0.298432\pi\)
\(542\) 0 0
\(543\) −5.54640 + 9.60665i −0.238019 + 0.412261i
\(544\) 0 0
\(545\) −2.29437 13.0120i −0.0982800 0.557373i
\(546\) 0 0
\(547\) −7.34449 + 6.16276i −0.314028 + 0.263501i −0.786154 0.618030i \(-0.787931\pi\)
0.472127 + 0.881531i \(0.343486\pi\)
\(548\) 0 0
\(549\) 9.32303 3.39331i 0.397897 0.144823i
\(550\) 0 0
\(551\) −7.13519 9.20719i −0.303969 0.392240i
\(552\) 0 0
\(553\) 67.9030 24.7147i 2.88753 1.05098i
\(554\) 0 0
\(555\) −0.360649 + 0.302621i −0.0153087 + 0.0128455i
\(556\) 0 0
\(557\) 5.99528 + 34.0009i 0.254028 + 1.44067i 0.798555 + 0.601922i \(0.205598\pi\)
−0.544527 + 0.838744i \(0.683291\pi\)
\(558\) 0 0
\(559\) 10.6714 18.4834i 0.451351 0.781762i
\(560\) 0 0
\(561\) 7.27784 + 2.64892i 0.307271 + 0.111837i
\(562\) 0 0
\(563\) 21.6196 + 37.4463i 0.911158 + 1.57817i 0.812431 + 0.583057i \(0.198144\pi\)
0.0987270 + 0.995115i \(0.468523\pi\)
\(564\) 0 0
\(565\) −1.41031 1.18339i −0.0593324 0.0497858i
\(566\) 0 0
\(567\) 1.26307 7.16324i 0.0530440 0.300828i
\(568\) 0 0
\(569\) −0.172138 −0.00721638 −0.00360819 0.999993i \(-0.501149\pi\)
−0.00360819 + 0.999993i \(0.501149\pi\)
\(570\) 0 0
\(571\) −28.8203 −1.20609 −0.603046 0.797706i \(-0.706046\pi\)
−0.603046 + 0.797706i \(0.706046\pi\)
\(572\) 0 0
\(573\) 4.29940 24.3831i 0.179610 1.01862i
\(574\) 0 0
\(575\) −3.31875 2.78477i −0.138402 0.116133i
\(576\) 0 0
\(577\) −1.03745 1.79692i −0.0431898 0.0748069i 0.843622 0.536937i \(-0.180419\pi\)
−0.886812 + 0.462130i \(0.847085\pi\)
\(578\) 0 0
\(579\) −12.6517 4.60486i −0.525789 0.191371i
\(580\) 0 0
\(581\) 8.57682 14.8555i 0.355826 0.616309i
\(582\) 0 0
\(583\) −2.64776 15.0162i −0.109659 0.621908i
\(584\) 0 0
\(585\) 8.24986 6.92245i 0.341090 0.286208i
\(586\) 0 0
\(587\) −28.5583 + 10.3944i −1.17873 + 0.429022i −0.855752 0.517385i \(-0.826905\pi\)
−0.322975 + 0.946407i \(0.604683\pi\)
\(588\) 0 0
\(589\) 0.463930 11.9363i 0.0191159 0.491825i
\(590\) 0 0
\(591\) −3.06187 + 1.11443i −0.125949 + 0.0458416i
\(592\) 0 0
\(593\) −8.44741 + 7.08822i −0.346894 + 0.291078i −0.799541 0.600611i \(-0.794924\pi\)
0.452648 + 0.891689i \(0.350480\pi\)
\(594\) 0 0
\(595\) −5.73416 32.5200i −0.235078 1.33319i
\(596\) 0 0
\(597\) 8.85569 15.3385i 0.362439 0.627763i
\(598\) 0 0
\(599\) −23.2641 8.46746i −0.950547 0.345971i −0.180225 0.983625i \(-0.557683\pi\)
−0.770322 + 0.637655i \(0.779905\pi\)
\(600\) 0 0
\(601\) −20.6916 35.8388i −0.844026 1.46190i −0.886464 0.462797i \(-0.846846\pi\)
0.0424380 0.999099i \(-0.486487\pi\)
\(602\) 0 0
\(603\) 20.2296 + 16.9747i 0.823814 + 0.691262i
\(604\) 0 0
\(605\) −1.69318 + 9.60248i −0.0688374 + 0.390396i
\(606\) 0 0
\(607\) 27.0263 1.09696 0.548481 0.836163i \(-0.315206\pi\)
0.548481 + 0.836163i \(0.315206\pi\)
\(608\) 0 0
\(609\) −11.6665 −0.472749
\(610\) 0 0
\(611\) 2.37356 13.4611i 0.0960239 0.544579i
\(612\) 0 0
\(613\) 5.62519 + 4.72010i 0.227199 + 0.190643i 0.749280 0.662253i \(-0.230400\pi\)
−0.522081 + 0.852896i \(0.674844\pi\)
\(614\) 0 0
\(615\) −4.00727 6.94079i −0.161589 0.279880i
\(616\) 0 0
\(617\) −15.4866 5.63667i −0.623468 0.226924i 0.0109180 0.999940i \(-0.496525\pi\)
−0.634386 + 0.773017i \(0.718747\pi\)
\(618\) 0 0
\(619\) 5.27186 9.13112i 0.211894 0.367011i −0.740413 0.672152i \(-0.765370\pi\)
0.952307 + 0.305141i \(0.0987036\pi\)
\(620\) 0 0
\(621\) 3.66061 + 20.7603i 0.146895 + 0.833083i
\(622\) 0 0
\(623\) 41.1256 34.5085i 1.64766 1.38255i
\(624\) 0 0
\(625\) −0.939693 + 0.342020i −0.0375877 + 0.0136808i
\(626\) 0 0
\(627\) −1.42352 4.44063i −0.0568501 0.177342i
\(628\) 0 0
\(629\) −3.34629 + 1.21795i −0.133425 + 0.0485629i
\(630\) 0 0
\(631\) −12.0300 + 10.0944i −0.478907 + 0.401850i −0.850031 0.526733i \(-0.823417\pi\)
0.371124 + 0.928583i \(0.378972\pi\)
\(632\) 0 0
\(633\) 2.62527 + 14.8886i 0.104345 + 0.591771i
\(634\) 0 0
\(635\) 2.10768 3.65061i 0.0836407 0.144870i
\(636\) 0 0
\(637\) 67.0427 + 24.4016i 2.65633 + 0.966825i
\(638\) 0 0
\(639\) 0.712904 + 1.23479i 0.0282020 + 0.0488474i
\(640\) 0 0
\(641\) 2.38617 + 2.00224i 0.0942481 + 0.0790836i 0.688694 0.725052i \(-0.258184\pi\)
−0.594446 + 0.804135i \(0.702629\pi\)
\(642\) 0 0
\(643\) 3.53665 20.0573i 0.139472 0.790983i −0.832169 0.554522i \(-0.812901\pi\)
0.971641 0.236462i \(-0.0759877\pi\)
\(644\) 0 0
\(645\) 3.95280 0.155641
\(646\) 0 0
\(647\) −2.01187 −0.0790946 −0.0395473 0.999218i \(-0.512592\pi\)
−0.0395473 + 0.999218i \(0.512592\pi\)
\(648\) 0 0
\(649\) −0.506703 + 2.87366i −0.0198898 + 0.112801i
\(650\) 0 0
\(651\) −9.16485 7.69022i −0.359199 0.301404i
\(652\) 0 0
\(653\) −0.326876 0.566166i −0.0127916 0.0221558i 0.859559 0.511037i \(-0.170738\pi\)
−0.872350 + 0.488881i \(0.837405\pi\)
\(654\) 0 0
\(655\) −2.58430 0.940609i −0.100977 0.0367526i
\(656\) 0 0
\(657\) −13.6825 + 23.6988i −0.533806 + 0.924579i
\(658\) 0 0
\(659\) −0.256516 1.45477i −0.00999243 0.0566699i 0.979404 0.201911i \(-0.0647153\pi\)
−0.989396 + 0.145241i \(0.953604\pi\)
\(660\) 0 0
\(661\) −1.31742 + 1.10545i −0.0512418 + 0.0429970i −0.668049 0.744117i \(-0.732870\pi\)
0.616807 + 0.787114i \(0.288426\pi\)
\(662\) 0 0
\(663\) −33.6482 + 12.2469i −1.30679 + 0.475631i
\(664\) 0 0
\(665\) −13.3620 + 14.7229i −0.518157 + 0.570931i
\(666\) 0 0
\(667\) −10.8791 + 3.95967i −0.421241 + 0.153319i
\(668\) 0 0
\(669\) −16.2840 + 13.6639i −0.629577 + 0.528278i
\(670\) 0 0
\(671\) 0.924067 + 5.24064i 0.0356732 + 0.202313i
\(672\) 0 0
\(673\) 15.1537 26.2469i 0.584130 1.01174i −0.410853 0.911702i \(-0.634769\pi\)
0.994983 0.100042i \(-0.0318977\pi\)
\(674\) 0 0
\(675\) 4.57244 + 1.66423i 0.175993 + 0.0640563i
\(676\) 0 0
\(677\) 13.5349 + 23.4432i 0.520190 + 0.900995i 0.999724 + 0.0234721i \(0.00747210\pi\)
−0.479535 + 0.877523i \(0.659195\pi\)
\(678\) 0 0
\(679\) −12.1892 10.2279i −0.467777 0.392512i
\(680\) 0 0
\(681\) −0.932270 + 5.28717i −0.0357247 + 0.202605i
\(682\) 0 0
\(683\) −49.3960 −1.89008 −0.945042 0.326948i \(-0.893980\pi\)
−0.945042 + 0.326948i \(0.893980\pi\)
\(684\) 0 0
\(685\) 2.20906 0.0844038
\(686\) 0 0
\(687\) 0.172877 0.980433i 0.00659566 0.0374059i
\(688\) 0 0
\(689\) 54.0034 + 45.3142i 2.05737 + 1.72633i
\(690\) 0 0
\(691\) 2.99171 + 5.18179i 0.113810 + 0.197125i 0.917303 0.398189i \(-0.130361\pi\)
−0.803493 + 0.595314i \(0.797028\pi\)
\(692\) 0 0
\(693\) 9.98415 + 3.63393i 0.379267 + 0.138042i
\(694\) 0 0
\(695\) −4.41306 + 7.64364i −0.167397 + 0.289940i
\(696\) 0 0
\(697\) −10.5268 59.7003i −0.398730 2.26131i
\(698\) 0 0
\(699\) 8.76499 7.35470i 0.331522 0.278180i
\(700\) 0 0
\(701\) 11.2185 4.08320i 0.423717 0.154220i −0.121356 0.992609i \(-0.538724\pi\)
0.545073 + 0.838389i \(0.316502\pi\)
\(702\) 0 0
\(703\) 1.81382 + 1.14336i 0.0684094 + 0.0431227i
\(704\) 0 0
\(705\) 2.37887 0.865837i 0.0895933 0.0326093i
\(706\) 0 0
\(707\) 36.8997 30.9625i 1.38776 1.16447i
\(708\) 0 0
\(709\) 4.35271 + 24.6854i 0.163469 + 0.927080i 0.950629 + 0.310331i \(0.100440\pi\)
−0.787159 + 0.616750i \(0.788449\pi\)
\(710\) 0 0
\(711\) −16.5070 + 28.5909i −0.619061 + 1.07224i
\(712\) 0 0
\(713\) −11.1564 4.06061i −0.417812 0.152071i
\(714\) 0 0
\(715\) 2.88818 + 5.00248i 0.108012 + 0.187082i
\(716\) 0 0
\(717\) −6.60479 5.54208i −0.246660 0.206973i
\(718\) 0 0
\(719\) 3.32244 18.8425i 0.123906 0.702706i −0.858046 0.513574i \(-0.828321\pi\)
0.981952 0.189132i \(-0.0605676\pi\)
\(720\) 0 0
\(721\) −52.6946 −1.96245
\(722\) 0 0
\(723\) −12.7329 −0.473540
\(724\) 0 0
\(725\) −0.464041 + 2.63171i −0.0172341 + 0.0977392i
\(726\) 0 0
\(727\) −5.68566 4.77084i −0.210870 0.176941i 0.531235 0.847224i \(-0.321728\pi\)
−0.742105 + 0.670284i \(0.766172\pi\)
\(728\) 0 0
\(729\) −5.32418 9.22175i −0.197192 0.341546i
\(730\) 0 0
\(731\) 28.0955 + 10.2259i 1.03915 + 0.378220i
\(732\) 0 0
\(733\) −1.59766 + 2.76722i −0.0590108 + 0.102210i −0.894022 0.448024i \(-0.852128\pi\)
0.835011 + 0.550234i \(0.185461\pi\)
\(734\) 0 0
\(735\) 2.29451 + 13.0128i 0.0846344 + 0.479986i
\(736\) 0 0
\(737\) −10.8505 + 9.10465i −0.399683 + 0.335374i
\(738\) 0 0
\(739\) 1.47844 0.538109i 0.0543853 0.0197946i −0.314684 0.949196i \(-0.601899\pi\)
0.369070 + 0.929402i \(0.379676\pi\)
\(740\) 0 0
\(741\) 18.2386 + 11.4969i 0.670010 + 0.422350i
\(742\) 0 0
\(743\) −10.6647 + 3.88164i −0.391251 + 0.142404i −0.530152 0.847903i \(-0.677865\pi\)
0.138901 + 0.990306i \(0.455643\pi\)
\(744\) 0 0
\(745\) 15.9991 13.4249i 0.586163 0.491849i
\(746\) 0 0
\(747\) 1.36088 + 7.71795i 0.0497921 + 0.282385i
\(748\) 0 0
\(749\) −17.7171 + 30.6869i −0.647369 + 1.12128i
\(750\) 0 0
\(751\) −27.5103 10.0129i −1.00386 0.365377i −0.212791 0.977098i \(-0.568255\pi\)
−0.791074 + 0.611721i \(0.790478\pi\)
\(752\) 0 0
\(753\) 10.6227 + 18.3991i 0.387114 + 0.670501i
\(754\) 0 0
\(755\) 4.39043 + 3.68401i 0.159784 + 0.134075i
\(756\) 0 0
\(757\) 6.71567 38.0865i 0.244085 1.38428i −0.578522 0.815667i \(-0.696370\pi\)
0.822607 0.568610i \(-0.192519\pi\)
\(758\) 0 0
\(759\) −4.63479 −0.168232
\(760\) 0 0
\(761\) 31.8253 1.15367 0.576833 0.816862i \(-0.304288\pi\)
0.576833 + 0.816862i \(0.304288\pi\)
\(762\) 0 0
\(763\) −10.4654 + 59.3521i −0.378872 + 2.14869i
\(764\) 0 0
\(765\) 11.5571 + 9.69754i 0.417847 + 0.350615i
\(766\) 0 0
\(767\) −6.74546 11.6835i −0.243565 0.421866i
\(768\) 0 0
\(769\) −8.83346 3.21512i −0.318543 0.115940i 0.177800 0.984067i \(-0.443102\pi\)
−0.496343 + 0.868127i \(0.665324\pi\)
\(770\) 0 0
\(771\) 1.20894 2.09394i 0.0435388 0.0754115i
\(772\) 0 0
\(773\) 2.61084 + 14.8068i 0.0939054 + 0.532564i 0.995077 + 0.0991019i \(0.0315970\pi\)
−0.901172 + 0.433462i \(0.857292\pi\)
\(774\) 0 0
\(775\) −2.09929 + 1.76152i −0.0754088 + 0.0632755i
\(776\) 0 0
\(777\) 2.01794 0.734471i 0.0723933 0.0263490i
\(778\) 0 0
\(779\) −24.5301 + 27.0284i −0.878880 + 0.968393i
\(780\) 0 0
\(781\) −0.718636 + 0.261562i −0.0257148 + 0.00935942i
\(782\) 0 0
\(783\) 9.96098 8.35826i 0.355976 0.298700i
\(784\) 0 0
\(785\) −3.20189 18.1588i −0.114280 0.648116i
\(786\) 0 0
\(787\) −13.6930 + 23.7170i −0.488104 + 0.845421i