Properties

Label 380.2.u.b.61.2
Level $380$
Weight $2$
Character 380.61
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 61.2
Root \(-0.478554 + 0.828880i\) of defining polynomial
Character \(\chi\) \(=\) 380.61
Dual form 380.2.u.b.81.2

$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

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

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 0.994450 + 0.105207i \(0.0335506\pi\)
−0.898495 + 0.438984i \(0.855338\pi\)
\(4\) 0 0
\(5\) 0.766044 0.642788i 0.342585 0.287463i
\(6\) 0 0
\(7\) −2.28066 + 3.95023i −0.862010 + 1.49305i 0.00797511 + 0.999968i \(0.497461\pi\)
−0.869985 + 0.493077i \(0.835872\pi\)
\(8\) 0 0
\(9\) 1.95827 0.712751i 0.652756 0.237584i
\(10\) 0 0
\(11\) −0.558879 0.968007i −0.168508 0.291865i 0.769387 0.638783i \(-0.220562\pi\)
−0.937896 + 0.346918i \(0.887228\pi\)
\(12\) 0 0
\(13\) −0.897380 + 5.08930i −0.248889 + 1.41152i 0.562397 + 0.826867i \(0.309879\pi\)
−0.811286 + 0.584650i \(0.801232\pi\)
\(14\) 0 0
\(15\) 0.733187 + 0.615217i 0.189308 + 0.158848i
\(16\) 0 0
\(17\) 6.80290 + 2.47605i 1.64994 + 0.600531i 0.988736 0.149671i \(-0.0478216\pi\)
0.661209 + 0.750202i \(0.270044\pi\)
\(18\) 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 0.227480 0.973783i \(-0.426952\pi\)
−0.919488 + 0.393119i \(0.871396\pi\)
\(24\) 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 −0.0981710 0.995170i \(-0.531299\pi\)
0.564479 + 0.825447i \(0.309077\pi\)
\(30\) 0 0
\(31\) 1.37022 2.37328i 0.246098 0.426254i −0.716342 0.697750i \(-0.754185\pi\)
0.962440 + 0.271495i \(0.0875181\pi\)
\(32\) 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 0.858652 + 0.512560i \(0.171303\pi\)
−0.631563 + 0.775325i \(0.717586\pi\)
\(42\) 0 0
\(43\) 3.16372 2.65467i 0.482462 0.404834i −0.368853 0.929488i \(-0.620250\pi\)
0.851316 + 0.524654i \(0.175805\pi\)
\(44\) 0 0
\(45\) 1.04197 1.80475i 0.155328 0.269036i
\(46\) 0 0
\(47\) 2.48547 0.904639i 0.362544 0.131955i −0.154324 0.988020i \(-0.549320\pi\)
0.516868 + 0.856065i \(0.327098\pi\)
\(48\) 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 −0.942425 0.334418i \(-0.891460\pi\)
−0.492988 0.870036i \(-0.664095\pi\)
\(54\) 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 0.496731 0.867905i \(-0.334534\pi\)
−0.177360 + 0.984146i \(0.556756\pi\)
\(60\) 0 0
\(61\) 3.64703 + 3.06022i 0.466954 + 0.391821i 0.845682 0.533687i \(-0.179194\pi\)
−0.378728 + 0.925508i \(0.623638\pi\)
\(62\) 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 0.510855 0.859667i \(-0.329329\pi\)
0.943921 + 0.330171i \(0.107107\pi\)
\(68\) 0 0
\(69\) 2.07325 3.59098i 0.249590 0.432303i
\(70\) 0 0
\(71\) 0.524118 0.439787i 0.0622013 0.0521931i −0.611157 0.791509i \(-0.709296\pi\)
0.673358 + 0.739316i \(0.264851\pi\)
\(72\) 0 0
\(73\) −2.28024 12.9319i −0.266882 1.51356i −0.763623 0.645662i \(-0.776581\pi\)
0.496741 0.867899i \(-0.334530\pi\)
\(74\) 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 −0.601499 0.798874i \(-0.705430\pi\)
0.291993 0.956420i \(-0.405681\pi\)
\(80\) 0 0
\(81\) 1.22158 1.02502i 0.135731 0.113892i
\(82\) 0 0
\(83\) 1.88033 3.25683i 0.206393 0.357484i −0.744182 0.667976i \(-0.767161\pi\)
0.950576 + 0.310493i \(0.100494\pi\)
\(84\) 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 −0.661393 0.750039i \(-0.730035\pi\)
0.878035 0.478597i \(-0.158854\pi\)
\(90\) 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 0.503031 0.864268i \(-0.332218\pi\)
−0.170197 + 0.985410i \(0.554440\pi\)
\(98\) 0 0
\(99\) −1.78438 1.49727i −0.179337 0.150482i
\(100\) 0 0
\(101\) 1.83378 10.3999i 0.182468 1.03483i −0.746697 0.665164i \(-0.768362\pi\)
0.929165 0.369665i \(-0.120527\pi\)
\(102\) 0 0
\(103\) 5.77623 + 10.0047i 0.569149 + 0.985794i 0.996650 + 0.0817799i \(0.0260605\pi\)
−0.427502 + 0.904015i \(0.640606\pi\)
\(104\) 0 0
\(105\) −4.10240 + 1.49315i −0.400354 + 0.145717i
\(106\) 0 0
\(107\) −3.88420 + 6.72763i −0.375499 + 0.650384i −0.990402 0.138219i \(-0.955862\pi\)
0.614902 + 0.788603i \(0.289195\pi\)
\(108\) 0 0
\(109\) −10.1216 + 8.49299i −0.969469 + 0.813481i −0.982467 0.186435i \(-0.940307\pi\)
0.0129986 + 0.999916i \(0.495862\pi\)
\(110\) 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 0.934954 + 0.354769i \(0.115441\pi\)
−0.999908 + 0.0136008i \(0.995671\pi\)
\(128\) 0 0
\(129\) 3.02802 + 2.54081i 0.266602 + 0.223706i
\(130\) 0 0
\(131\) −2.58430 0.940609i −0.225791 0.0821814i 0.226647 0.973977i \(-0.427224\pi\)
−0.452439 + 0.891796i \(0.649446\pi\)
\(132\) 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 0.712208 0.701968i \(-0.247695\pi\)
−0.567630 + 0.823284i \(0.692140\pi\)
\(138\) 0 0
\(139\) 1.53264 8.69203i 0.129997 0.737248i −0.848217 0.529649i \(-0.822324\pi\)
0.978214 0.207600i \(-0.0665651\pi\)
\(140\) 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 0.658495 + 0.752585i \(0.271194\pi\)
−0.361383 + 0.932417i \(0.617695\pi\)
\(150\) 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 −0.998950 0.0458101i \(-0.985413\pi\)
−0.128352 + 0.991729i \(0.540969\pi\)
\(158\) 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 0.789755 0.613422i \(-0.210207\pi\)
−0.926117 + 0.377237i \(0.876874\pi\)
\(164\) 0 0
\(165\) 0.185772 1.05356i 0.0144623 0.0820198i
\(166\) 0 0
\(167\) 16.4620 + 13.8132i 1.27387 + 1.06890i 0.994059 + 0.108843i \(0.0347147\pi\)
0.279806 + 0.960056i \(0.409730\pi\)
\(168\) 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 −0.0817929 0.996649i \(-0.526065\pi\)
−0.703291 + 0.710902i \(0.748287\pi\)
\(174\) 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 0.985664 + 0.168718i \(0.0539627\pi\)
−0.346718 + 0.937969i \(0.612704\pi\)
\(180\) 0 0
\(181\) −10.8910 + 3.96399i −0.809519 + 0.294641i −0.713425 0.700732i \(-0.752857\pi\)
−0.0960938 + 0.995372i \(0.530635\pi\)
\(182\) 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 0.937180 + 0.348845i \(0.113426\pi\)
−0.761349 + 0.648342i \(0.775463\pi\)
\(194\) 0 0
\(195\) −3.78897 + 3.17932i −0.271334 + 0.227676i
\(196\) 0 0
\(197\) −1.70220 + 2.94830i −0.121277 + 0.210057i −0.920271 0.391281i \(-0.872032\pi\)
0.798995 + 0.601338i \(0.205365\pi\)
\(198\) 0 0
\(199\) 17.3891 6.32911i 1.23268 0.448659i 0.358166 0.933658i \(-0.383402\pi\)
0.874515 + 0.484999i \(0.161180\pi\)
\(200\) 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 −0.223878 0.974617i \(-0.571872\pi\)
−0.797972 + 0.602694i \(0.794094\pi\)
\(212\) 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 −0.999417 0.0341558i \(-0.989126\pi\)
−0.139910 + 0.990164i \(0.544681\pi\)
\(224\) 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 −0.291482 0.956576i \(-0.594148\pi\)
0.891428 + 0.453161i \(0.149704\pi\)
\(234\) 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 0.974129 0.225992i \(-0.0725622\pi\)
−0.682779 + 0.730625i \(0.739229\pi\)
\(240\) 0 0
\(241\) −2.31012 + 13.1014i −0.148808 + 0.843933i 0.815422 + 0.578867i \(0.196505\pi\)
−0.964230 + 0.265066i \(0.914606\pi\)
\(242\) 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 −0.0779560 0.996957i \(-0.524839\pi\)
−0.995348 + 0.0963480i \(0.969284\pi\)
\(252\) 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 −0.266918 0.963719i \(-0.586005\pi\)
0.414996 + 0.909823i \(0.363783\pi\)
\(258\) 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 −0.975169 0.221462i \(-0.928917\pi\)
0.840615 0.541634i \(-0.182194\pi\)
\(264\) 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 −0.873439 0.486933i \(-0.838116\pi\)
0.654224 0.756301i \(-0.272995\pi\)
\(270\) 0 0
\(271\) −1.02160 + 0.857226i −0.0620579 + 0.0520728i −0.673289 0.739379i \(-0.735119\pi\)
0.611231 + 0.791452i \(0.290675\pi\)
\(272\) 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 −0.883338 0.468736i \(-0.844710\pi\)
0.0357322 0.999361i \(-0.488624\pi\)
\(278\) 0 0
\(279\) 0.991688 5.62414i 0.0593708 0.336709i
\(280\) 0 0
\(281\) 9.31199 + 7.81369i 0.555507 + 0.466126i 0.876801 0.480854i \(-0.159673\pi\)
−0.321294 + 0.946980i \(0.604118\pi\)
\(282\) 0 0
\(283\) −1.65082 0.600850i −0.0981312 0.0357168i 0.292488 0.956269i \(-0.405517\pi\)
−0.390619 + 0.920552i \(0.627739\pi\)
\(284\) 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 0.956305 0.292370i \(-0.0944440\pi\)
−0.731353 + 0.681999i \(0.761111\pi\)
\(294\) 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 −0.999949 0.0101104i \(-0.996782\pi\)
0.936187 0.351503i \(-0.114329\pi\)
\(308\) 0 0
\(309\) −8.47012 + 7.10727i −0.481848 + 0.404319i
\(310\) 0 0
\(311\) 14.5028 25.1196i 0.822379 1.42440i −0.0815274 0.996671i \(-0.525980\pi\)
0.903906 0.427731i \(-0.140687\pi\)
\(312\) 0 0
\(313\) −12.8655 + 4.68265i −0.727200 + 0.264679i −0.678979 0.734158i \(-0.737577\pi\)
−0.0482209 + 0.998837i \(0.515355\pi\)
\(314\) 0 0
\(315\) 4.75278 + 8.23205i 0.267789 + 0.463824i
\(316\) 0 0
\(317\) −0.782232 + 4.43626i −0.0439345 + 0.249165i −0.998863 0.0476705i \(-0.984820\pi\)
0.954929 + 0.296836i \(0.0959314\pi\)
\(318\) 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 0.571866 0.820347i \(-0.306220\pi\)
−0.996374 + 0.0850767i \(0.972886\pi\)
\(332\) 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 −0.967983 0.251016i \(-0.919235\pi\)
0.0791136 + 0.996866i \(0.474791\pi\)
\(338\) 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 −0.567588 0.823312i \(-0.692124\pi\)
0.712244 + 0.701932i \(0.247679\pi\)
\(348\) 0 0
\(349\) −4.55638 + 7.89188i −0.243897 + 0.422443i −0.961821 0.273679i \(-0.911759\pi\)
0.717924 + 0.696122i \(0.245093\pi\)
\(350\) 0 0
\(351\) −23.6295 + 8.60042i −1.26125 + 0.459057i
\(352\) 0 0
\(353\) −12.4350 21.5381i −0.661850 1.14636i −0.980129 0.198361i \(-0.936438\pi\)
0.318279 0.947997i \(-0.396895\pi\)
\(354\) 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 −0.189138 0.981951i \(-0.560569\pi\)
−0.776074 + 0.630642i \(0.782792\pi\)
\(360\) 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 −0.737520 0.675325i \(-0.764003\pi\)
0.924017 0.382351i \(-0.124885\pi\)
\(368\) 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 −0.814167 0.580630i \(-0.802806\pi\)
0.909924 + 0.414774i \(0.136139\pi\)
\(374\) 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 0.737451 + 0.675400i \(0.236029\pi\)
−0.461977 + 0.886892i \(0.652860\pi\)
\(384\) 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 −0.0411892 0.999151i \(-0.513115\pi\)
0.610689 + 0.791870i \(0.290892\pi\)
\(390\) 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 0.440556 0.897725i \(-0.354781\pi\)
−0.239561 + 0.970881i \(0.577004\pi\)
\(398\) 0 0
\(399\) 18.5980 4.02980i 0.931065 0.201742i
\(400\) 0 0
\(401\) 0.433821 + 0.157898i 0.0216640 + 0.00788506i 0.352829 0.935688i \(-0.385220\pi\)
−0.331165 + 0.943573i \(0.607442\pi\)
\(402\) 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 0.522378 0.852714i \(-0.325045\pi\)
0.948279 + 0.317438i \(0.102823\pi\)
\(410\) 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 0.999926 + 0.0121424i \(0.00386514\pi\)
−0.935470 + 0.353405i \(0.885024\pi\)
\(422\) 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 −0.999589 0.0286575i \(-0.990877\pi\)
0.949108 + 0.314950i \(0.101988\pi\)
\(432\) 0 0
\(433\) −14.2376 11.9468i −0.684216 0.574126i 0.233019 0.972472i \(-0.425140\pi\)
−0.917235 + 0.398347i \(0.869584\pi\)
\(434\) 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 0.00992755 0.999951i \(-0.496840\pi\)
−0.635151 + 0.772388i \(0.719062\pi\)
\(440\) 0 0
\(441\) −22.0394 18.4932i −1.04949 0.880630i
\(442\) 0 0
\(443\) −2.65351 + 15.0488i −0.126072 + 0.714991i 0.854593 + 0.519298i \(0.173807\pi\)
−0.980665 + 0.195692i \(0.937305\pi\)
\(444\) 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 −0.167645 0.985847i \(-0.553616\pi\)
0.937591 0.347739i \(-0.113051\pi\)
\(450\) 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 −0.998644 0.0520545i \(-0.983423\pi\)
−0.122149 + 0.992512i \(0.538979\pi\)
\(462\) 0 0
\(463\) 15.2496 26.4132i 0.708711 1.22752i −0.256624 0.966511i \(-0.582610\pi\)
0.965335 0.261012i \(-0.0840563\pi\)
\(464\) 0 0
\(465\) 2.46471 0.897081i 0.114298 0.0416011i
\(466\) 0 0
\(467\) 3.74239 + 6.48201i 0.173177 + 0.299952i 0.939529 0.342469i \(-0.111263\pi\)
−0.766352 + 0.642421i \(0.777930\pi\)
\(468\) 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 0.531718 0.846922i \(-0.321547\pi\)
−0.741723 + 0.670706i \(0.765991\pi\)
\(480\) 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 −0.930185 0.367091i \(-0.880354\pi\)
0.783003 + 0.622018i \(0.213687\pi\)
\(488\) 0 0
\(489\) 2.55288 2.14212i 0.115445 0.0968699i
\(490\) 0 0
\(491\) 5.01124 + 28.4202i 0.226154 + 1.28258i 0.860467 + 0.509507i \(0.170172\pi\)
−0.634312 + 0.773077i \(0.718717\pi\)
\(492\) 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 −0.832453 0.554096i \(-0.813064\pi\)
0.401124 + 0.916024i \(0.368619\pi\)
\(500\) 0 0
\(501\) −10.2839 + 17.8123i −0.459452 + 0.795794i
\(502\) 0 0
\(503\) −14.4854 + 5.27226i −0.645872 + 0.235078i −0.644125 0.764920i \(-0.722778\pi\)
−0.00174715 + 0.999998i \(0.500556\pi\)
\(504\) 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 0.535479 0.844548i \(-0.320131\pi\)
−0.738733 + 0.673998i \(0.764575\pi\)
\(510\) 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 0.990726 0.135872i \(-0.0433835\pi\)
−0.613032 + 0.790058i \(0.710050\pi\)
\(522\) 0 0
\(523\) 0.113607 0.0413496i 0.00496770 0.00180809i −0.339535 0.940593i \(-0.610270\pi\)
0.344503 + 0.938785i \(0.388048\pi\)
\(524\) 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 0.591764 0.806112i \(-0.298432\pi\)
0.971476 + 0.237139i \(0.0762097\pi\)
\(542\) 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 0.472127 0.881531i \(-0.343486\pi\)
−0.786154 + 0.618030i \(0.787931\pi\)
\(548\) 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 −0.544527 0.838744i \(-0.683291\pi\)
0.798555 0.601922i \(-0.205598\pi\)
\(558\) 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 0.0987270 0.995115i \(-0.468523\pi\)
0.812431 0.583057i \(-0.198144\pi\)
\(564\) 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 −0.886812 0.462130i \(-0.847085\pi\)
0.843622 + 0.536937i \(0.180419\pi\)
\(578\) 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 −0.322975 0.946407i \(-0.604683\pi\)
−0.855752 + 0.517385i \(0.826905\pi\)
\(588\) 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 0.452648 0.891689i \(-0.350480\pi\)
−0.799541 + 0.600611i \(0.794924\pi\)
\(594\) 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 −0.770322 0.637655i \(-0.779905\pi\)
−0.180225 + 0.983625i \(0.557683\pi\)
\(600\) 0 0
\(601\) −20.6916 + 35.8388i −0.844026 + 1.46190i 0.0424380 + 0.999099i \(0.486487\pi\)
−0.886464 + 0.462797i \(0.846846\pi\)
\(602\) 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 −0.522081 0.852896i \(-0.674844\pi\)
0.749280 + 0.662253i \(0.230400\pi\)
\(614\) 0 0
\(615\) −4.00727 + 6.94079i −0.161589 + 0.279880i
\(616\) 0 0
\(617\) −15.4866 + 5.63667i −0.623468 + 0.226924i −0.634386 0.773017i \(-0.718747\pi\)
0.0109180 + 0.999940i \(0.496525\pi\)
\(618\) 0 0
\(619\) 5.27186 + 9.13112i 0.211894 + 0.367011i 0.952307 0.305141i \(-0.0987036\pi\)
−0.740413 + 0.672152i \(0.765370\pi\)
\(620\) 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 0.371124 0.928583i \(-0.378972\pi\)
−0.850031 + 0.526733i \(0.823417\pi\)
\(632\) 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 −0.594446 0.804135i \(-0.702629\pi\)
0.688694 + 0.725052i \(0.258184\pi\)
\(642\) 0 0
\(643\) 3.53665 + 20.0573i 0.139472 + 0.790983i 0.971641 + 0.236462i \(0.0759877\pi\)
−0.832169 + 0.554522i \(0.812901\pi\)
\(644\) 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 −0.872350 0.488881i \(-0.837405\pi\)
0.859559 + 0.511037i \(0.170738\pi\)
\(654\) 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 −0.989396 0.145241i \(-0.953604\pi\)
0.979404 + 0.201911i \(0.0647153\pi\)
\(660\) 0 0
\(661\) −1.31742 1.10545i −0.0512418 0.0429970i 0.616807 0.787114i \(-0.288426\pi\)
−0.668049 + 0.744117i \(0.732870\pi\)
\(662\) 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 0.994983 + 0.100042i \(0.0318977\pi\)
−0.410853 + 0.911702i \(0.634769\pi\)
\(674\) 0 0
\(675\) 4.57244 1.66423i 0.175993 0.0640563i
\(676\) 0 0
\(677\) 13.5349 23.4432i 0.520190 0.900995i −0.479535 0.877523i \(-0.659195\pi\)
0.999724 0.0234721i \(-0.00747210\pi\)
\(678\) 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 −0.803493 0.595314i \(-0.797028\pi\)
0.917303 + 0.398189i \(0.130361\pi\)
\(692\) 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 0.545073 0.838389i \(-0.316502\pi\)
−0.121356 + 0.992609i \(0.538724\pi\)
\(702\) 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 −0.787159 0.616750i \(-0.788449\pi\)
0.950629 0.310331i \(-0.100440\pi\)
\(710\) 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 0.981952 + 0.189132i \(0.0605676\pi\)
−0.858046 + 0.513574i \(0.828321\pi\)
\(720\) 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 −0.742105 0.670284i \(-0.766172\pi\)
0.531235 + 0.847224i \(0.321728\pi\)
\(728\) 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 0.835011 0.550234i \(-0.185461\pi\)
−0.894022 + 0.448024i \(0.852128\pi\)
\(734\) 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 0.369070 0.929402i \(-0.379676\pi\)
−0.314684 + 0.949196i \(0.601899\pi\)
\(740\) 0 0
\(741\) 18.2386 11.4969i 0.670010 0.422350i
\(742\) 0 0
\(743\) −10.6647 3.88164i −0.391251 0.142404i 0.138901 0.990306i \(-0.455643\pi\)
−0.530152 + 0.847903i \(0.677865\pi\)
\(744\) 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 −0.791074 0.611721i \(-0.790478\pi\)
−0.212791 + 0.977098i \(0.568255\pi\)
\(752\) 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 0.822607 + 0.568610i \(0.192519\pi\)
−0.578522 + 0.815667i \(0.696370\pi\)
\(758\) 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 −0.496343 0.868127i \(-0.665324\pi\)
0.177800 + 0.984067i \(0.443102\pi\)
\(770\) 0 0
\(771\) 1.20894 + 2.09394i 0.0435388 + 0.0754115i
\(772\) 0 0
\(773\) 2.61084 14.8068i 0.0939054 0.532564i −0.901172 0.433462i \(-0.857292\pi\)
0.995077 0.0991019i \(-0.0315970\pi\)
\(774\) 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