Properties

Label 380.2.u.b.81.3
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 81.3
Root \(-0.754364 - 1.30660i\) of defining polynomial
Character \(\chi\) \(=\) 380.81
Dual form 380.2.u.b.61.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.261988 - 1.48581i) q^{3} +(0.766044 + 0.642788i) q^{5} +(1.67550 + 2.90204i) q^{7} +(0.680094 + 0.247534i) q^{9} +O(q^{10})\) \(q+(0.261988 - 1.48581i) q^{3} +(0.766044 + 0.642788i) q^{5} +(1.67550 + 2.90204i) q^{7} +(0.680094 + 0.247534i) q^{9} +(1.23765 - 2.14367i) q^{11} +(0.324617 + 1.84100i) q^{13} +(1.15575 - 0.969791i) q^{15} +(0.341929 - 0.124452i) q^{17} +(-3.65925 + 2.36853i) q^{19} +(4.75084 - 1.72916i) q^{21} +(5.71972 - 4.79941i) q^{23} +(0.173648 + 0.984808i) q^{25} +(2.80906 - 4.86543i) q^{27} +(-3.04312 - 1.10761i) q^{29} +(-3.78440 - 6.55477i) q^{31} +(-2.86083 - 2.40052i) q^{33} +(-0.581894 + 3.30008i) q^{35} +3.34885 q^{37} +2.82041 q^{39} +(-1.49157 + 8.45909i) q^{41} +(-8.07036 - 6.77184i) q^{43} +(0.361870 + 0.626778i) q^{45} +(11.0714 + 4.02966i) q^{47} +(-2.11458 + 3.66255i) q^{49} +(-0.0953303 - 0.540645i) q^{51} +(-2.01573 + 1.69140i) q^{53} +(2.32601 - 0.846600i) q^{55} +(2.56050 + 6.05746i) q^{57} +(-11.3091 + 4.11618i) q^{59} +(-8.67810 + 7.28179i) q^{61} +(0.421140 + 2.38841i) q^{63} +(-0.934699 + 1.61895i) q^{65} +(-2.31034 - 0.840895i) q^{67} +(-5.63250 - 9.75578i) q^{69} +(-0.0802996 - 0.0673793i) q^{71} +(-1.34598 + 7.63341i) q^{73} +1.50873 q^{75} +8.29469 q^{77} +(0.948370 - 5.37847i) q^{79} +(-4.82989 - 4.05276i) q^{81} +(0.462244 + 0.800630i) q^{83} +(0.341929 + 0.124452i) q^{85} +(-2.44295 + 4.23132i) q^{87} +(-1.38660 - 7.86382i) q^{89} +(-4.79876 + 4.02664i) q^{91} +(-10.7306 + 3.90562i) q^{93} +(-4.32560 - 0.537720i) q^{95} +(-6.64008 + 2.41679i) q^{97} +(1.37235 - 1.15154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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
\(3\) 0.261988 1.48581i 0.151259 0.857831i −0.810868 0.585229i \(-0.801005\pi\)
0.962127 0.272602i \(-0.0878842\pi\)
\(4\) 0 0
\(5\) 0.766044 + 0.642788i 0.342585 + 0.287463i
\(6\) 0 0
\(7\) 1.67550 + 2.90204i 0.633278 + 1.09687i 0.986877 + 0.161473i \(0.0516244\pi\)
−0.353599 + 0.935397i \(0.615042\pi\)
\(8\) 0 0
\(9\) 0.680094 + 0.247534i 0.226698 + 0.0825113i
\(10\) 0 0
\(11\) 1.23765 2.14367i 0.373164 0.646340i −0.616886 0.787052i \(-0.711606\pi\)
0.990050 + 0.140713i \(0.0449394\pi\)
\(12\) 0 0
\(13\) 0.324617 + 1.84100i 0.0900327 + 0.510601i 0.996157 + 0.0875887i \(0.0279161\pi\)
−0.906124 + 0.423012i \(0.860973\pi\)
\(14\) 0 0
\(15\) 1.15575 0.969791i 0.298414 0.250399i
\(16\) 0 0
\(17\) 0.341929 0.124452i 0.0829299 0.0301840i −0.300222 0.953869i \(-0.597061\pi\)
0.383152 + 0.923685i \(0.374839\pi\)
\(18\) 0 0
\(19\) −3.65925 + 2.36853i −0.839488 + 0.543378i
\(20\) 0 0
\(21\) 4.75084 1.72916i 1.03672 0.377334i
\(22\) 0 0
\(23\) 5.71972 4.79941i 1.19264 1.00075i 0.192834 0.981231i \(-0.438232\pi\)
0.999810 0.0195150i \(-0.00621220\pi\)
\(24\) 0 0
\(25\) 0.173648 + 0.984808i 0.0347296 + 0.196962i
\(26\) 0 0
\(27\) 2.80906 4.86543i 0.540603 0.936352i
\(28\) 0 0
\(29\) −3.04312 1.10761i −0.565094 0.205677i 0.0436461 0.999047i \(-0.486103\pi\)
−0.608740 + 0.793370i \(0.708325\pi\)
\(30\) 0 0
\(31\) −3.78440 6.55477i −0.679698 1.17727i −0.975072 0.221890i \(-0.928777\pi\)
0.295373 0.955382i \(-0.404556\pi\)
\(32\) 0 0
\(33\) −2.86083 2.40052i −0.498006 0.417876i
\(34\) 0 0
\(35\) −0.581894 + 3.30008i −0.0983580 + 0.557816i
\(36\) 0 0
\(37\) 3.34885 0.550548 0.275274 0.961366i \(-0.411231\pi\)
0.275274 + 0.961366i \(0.411231\pi\)
\(38\) 0 0
\(39\) 2.82041 0.451627
\(40\) 0 0
\(41\) −1.49157 + 8.45909i −0.232943 + 1.32109i 0.613958 + 0.789339i \(0.289576\pi\)
−0.846902 + 0.531750i \(0.821535\pi\)
\(42\) 0 0
\(43\) −8.07036 6.77184i −1.23072 1.03270i −0.998192 0.0601056i \(-0.980856\pi\)
−0.232527 0.972590i \(-0.574699\pi\)
\(44\) 0 0
\(45\) 0.361870 + 0.626778i 0.0539445 + 0.0934346i
\(46\) 0 0
\(47\) 11.0714 + 4.02966i 1.61493 + 0.587786i 0.982406 0.186756i \(-0.0597975\pi\)
0.632522 + 0.774542i \(0.282020\pi\)
\(48\) 0 0
\(49\) −2.11458 + 3.66255i −0.302082 + 0.523222i
\(50\) 0 0
\(51\) −0.0953303 0.540645i −0.0133489 0.0757054i
\(52\) 0 0
\(53\) −2.01573 + 1.69140i −0.276882 + 0.232331i −0.770645 0.637265i \(-0.780066\pi\)
0.493763 + 0.869597i \(0.335621\pi\)
\(54\) 0 0
\(55\) 2.32601 0.846600i 0.313640 0.114156i
\(56\) 0 0
\(57\) 2.56050 + 6.05746i 0.339146 + 0.802330i
\(58\) 0 0
\(59\) −11.3091 + 4.11618i −1.47232 + 0.535881i −0.948730 0.316089i \(-0.897630\pi\)
−0.523591 + 0.851970i \(0.675408\pi\)
\(60\) 0 0
\(61\) −8.67810 + 7.28179i −1.11112 + 0.932338i −0.998122 0.0612578i \(-0.980489\pi\)
−0.112995 + 0.993596i \(0.536044\pi\)
\(62\) 0 0
\(63\) 0.421140 + 2.38841i 0.0530587 + 0.300911i
\(64\) 0 0
\(65\) −0.934699 + 1.61895i −0.115935 + 0.200806i
\(66\) 0 0
\(67\) −2.31034 0.840895i −0.282253 0.102732i 0.197015 0.980401i \(-0.436875\pi\)
−0.479267 + 0.877669i \(0.659098\pi\)
\(68\) 0 0
\(69\) −5.63250 9.75578i −0.678074 1.17446i
\(70\) 0 0
\(71\) −0.0802996 0.0673793i −0.00952980 0.00799646i 0.638010 0.770028i \(-0.279758\pi\)
−0.647540 + 0.762031i \(0.724202\pi\)
\(72\) 0 0
\(73\) −1.34598 + 7.63341i −0.157535 + 0.893423i 0.798897 + 0.601468i \(0.205417\pi\)
−0.956432 + 0.291956i \(0.905694\pi\)
\(74\) 0 0
\(75\) 1.50873 0.174213
\(76\) 0 0
\(77\) 8.29469 0.945267
\(78\) 0 0
\(79\) 0.948370 5.37847i 0.106700 0.605125i −0.883828 0.467812i \(-0.845042\pi\)
0.990528 0.137313i \(-0.0438466\pi\)
\(80\) 0 0
\(81\) −4.82989 4.05276i −0.536655 0.450307i
\(82\) 0 0
\(83\) 0.462244 + 0.800630i 0.0507378 + 0.0878805i 0.890279 0.455416i \(-0.150509\pi\)
−0.839541 + 0.543296i \(0.817176\pi\)
\(84\) 0 0
\(85\) 0.341929 + 0.124452i 0.0370874 + 0.0134987i
\(86\) 0 0
\(87\) −2.44295 + 4.23132i −0.261912 + 0.453645i
\(88\) 0 0
\(89\) −1.38660 7.86382i −0.146980 0.833563i −0.965756 0.259451i \(-0.916458\pi\)
0.818777 0.574112i \(-0.194653\pi\)
\(90\) 0 0
\(91\) −4.79876 + 4.02664i −0.503047 + 0.422106i
\(92\) 0 0
\(93\) −10.7306 + 3.90562i −1.11271 + 0.404993i
\(94\) 0 0
\(95\) −4.32560 0.537720i −0.443798 0.0551689i
\(96\) 0 0
\(97\) −6.64008 + 2.41679i −0.674198 + 0.245388i −0.656354 0.754453i \(-0.727902\pi\)
−0.0178439 + 0.999841i \(0.505680\pi\)
\(98\) 0 0
\(99\) 1.37235 1.15154i 0.137926 0.115734i
\(100\) 0 0
\(101\) −0.0936052 0.530861i −0.00931406 0.0528227i 0.979796 0.199997i \(-0.0640933\pi\)
−0.989111 + 0.147174i \(0.952982\pi\)
\(102\) 0 0
\(103\) 3.81344 6.60507i 0.375749 0.650817i −0.614690 0.788769i \(-0.710719\pi\)
0.990439 + 0.137952i \(0.0440521\pi\)
\(104\) 0 0
\(105\) 4.75084 + 1.72916i 0.463634 + 0.168749i
\(106\) 0 0
\(107\) 4.25568 + 7.37105i 0.411412 + 0.712586i 0.995044 0.0994318i \(-0.0317025\pi\)
−0.583633 + 0.812018i \(0.698369\pi\)
\(108\) 0 0
\(109\) −10.0485 8.43168i −0.962471 0.807609i 0.0188826 0.999822i \(-0.493989\pi\)
−0.981353 + 0.192213i \(0.938434\pi\)
\(110\) 0 0
\(111\) 0.877359 4.97575i 0.0832752 0.472277i
\(112\) 0 0
\(113\) −13.9017 −1.30776 −0.653880 0.756598i \(-0.726860\pi\)
−0.653880 + 0.756598i \(0.726860\pi\)
\(114\) 0 0
\(115\) 7.46656 0.696260
\(116\) 0 0
\(117\) −0.234939 + 1.33241i −0.0217201 + 0.123181i
\(118\) 0 0
\(119\) 0.934065 + 0.783774i 0.0856256 + 0.0718484i
\(120\) 0 0
\(121\) 2.43646 + 4.22008i 0.221497 + 0.383644i
\(122\) 0 0
\(123\) 12.1778 + 4.43236i 1.09804 + 0.399652i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) 0.295034 + 1.67322i 0.0261801 + 0.148474i 0.995096 0.0989168i \(-0.0315378\pi\)
−0.968916 + 0.247391i \(0.920427\pi\)
\(128\) 0 0
\(129\) −12.1760 + 10.2169i −1.07204 + 0.899544i
\(130\) 0 0
\(131\) 4.40967 1.60499i 0.385275 0.140228i −0.142119 0.989850i \(-0.545392\pi\)
0.527394 + 0.849621i \(0.323169\pi\)
\(132\) 0 0
\(133\) −13.0046 6.65083i −1.12764 0.576700i
\(134\) 0 0
\(135\) 5.27930 1.92151i 0.454370 0.165377i
\(136\) 0 0
\(137\) 9.17290 7.69698i 0.783694 0.657597i −0.160482 0.987039i \(-0.551305\pi\)
0.944176 + 0.329441i \(0.106860\pi\)
\(138\) 0 0
\(139\) −2.26678 12.8556i −0.192266 1.09039i −0.916259 0.400587i \(-0.868806\pi\)
0.723993 0.689807i \(-0.242305\pi\)
\(140\) 0 0
\(141\) 8.88786 15.3942i 0.748493 1.29643i
\(142\) 0 0
\(143\) 4.34825 + 1.58263i 0.363619 + 0.132346i
\(144\) 0 0
\(145\) −1.61921 2.80456i −0.134468 0.232906i
\(146\) 0 0
\(147\) 4.88785 + 4.10140i 0.403143 + 0.338277i
\(148\) 0 0
\(149\) −0.928070 + 5.26334i −0.0760304 + 0.431190i 0.922904 + 0.385031i \(0.125809\pi\)
−0.998934 + 0.0461591i \(0.985302\pi\)
\(150\) 0 0
\(151\) −19.7726 −1.60907 −0.804534 0.593907i \(-0.797585\pi\)
−0.804534 + 0.593907i \(0.797585\pi\)
\(152\) 0 0
\(153\) 0.263350 0.0212906
\(154\) 0 0
\(155\) 1.31431 7.45381i 0.105568 0.598705i
\(156\) 0 0
\(157\) −2.31736 1.94449i −0.184945 0.155187i 0.545615 0.838036i \(-0.316296\pi\)
−0.730560 + 0.682849i \(0.760741\pi\)
\(158\) 0 0
\(159\) 1.98499 + 3.43811i 0.157420 + 0.272660i
\(160\) 0 0
\(161\) 23.5115 + 8.55748i 1.85296 + 0.674424i
\(162\) 0 0
\(163\) −3.62815 + 6.28414i −0.284178 + 0.492211i −0.972410 0.233280i \(-0.925054\pi\)
0.688231 + 0.725491i \(0.258387\pi\)
\(164\) 0 0
\(165\) −0.648496 3.67781i −0.0504854 0.286317i
\(166\) 0 0
\(167\) −2.02319 + 1.69766i −0.156559 + 0.131369i −0.717702 0.696350i \(-0.754806\pi\)
0.561143 + 0.827719i \(0.310362\pi\)
\(168\) 0 0
\(169\) 8.93211 3.25102i 0.687085 0.250079i
\(170\) 0 0
\(171\) −3.07492 + 0.705034i −0.235145 + 0.0539153i
\(172\) 0 0
\(173\) 11.3682 4.13769i 0.864309 0.314583i 0.128449 0.991716i \(-0.459000\pi\)
0.735860 + 0.677133i \(0.236778\pi\)
\(174\) 0 0
\(175\) −2.56701 + 2.15398i −0.194048 + 0.162825i
\(176\) 0 0
\(177\) 3.15300 + 17.8815i 0.236994 + 1.34406i
\(178\) 0 0
\(179\) 9.09890 15.7598i 0.680084 1.17794i −0.294871 0.955537i \(-0.595277\pi\)
0.974955 0.222403i \(-0.0713900\pi\)
\(180\) 0 0
\(181\) 19.2341 + 7.00064i 1.42966 + 0.520353i 0.936834 0.349775i \(-0.113742\pi\)
0.492825 + 0.870128i \(0.335964\pi\)
\(182\) 0 0
\(183\) 8.54578 + 14.8017i 0.631722 + 1.09417i
\(184\) 0 0
\(185\) 2.56537 + 2.15260i 0.188610 + 0.158262i
\(186\) 0 0
\(187\) 0.156404 0.887008i 0.0114374 0.0648645i
\(188\) 0 0
\(189\) 18.8262 1.36941
\(190\) 0 0
\(191\) 6.70464 0.485131 0.242565 0.970135i \(-0.422011\pi\)
0.242565 + 0.970135i \(0.422011\pi\)
\(192\) 0 0
\(193\) −1.82646 + 10.3584i −0.131471 + 0.745612i 0.845781 + 0.533531i \(0.179135\pi\)
−0.977252 + 0.212081i \(0.931976\pi\)
\(194\) 0 0
\(195\) 2.16056 + 1.81293i 0.154721 + 0.129826i
\(196\) 0 0
\(197\) −6.09112 10.5501i −0.433975 0.751666i 0.563237 0.826296i \(-0.309556\pi\)
−0.997211 + 0.0746295i \(0.976223\pi\)
\(198\) 0 0
\(199\) −16.6310 6.05321i −1.17894 0.429100i −0.323115 0.946360i \(-0.604730\pi\)
−0.855829 + 0.517259i \(0.826952\pi\)
\(200\) 0 0
\(201\) −1.85469 + 3.21241i −0.130820 + 0.226586i
\(202\) 0 0
\(203\) −1.88442 10.6871i −0.132260 0.750086i
\(204\) 0 0
\(205\) −6.58000 + 5.52128i −0.459567 + 0.385623i
\(206\) 0 0
\(207\) 5.07796 1.84823i 0.352943 0.128461i
\(208\) 0 0
\(209\) 0.548482 + 10.7756i 0.0379393 + 0.745364i
\(210\) 0 0
\(211\) −18.9353 + 6.89188i −1.30356 + 0.474457i −0.898154 0.439681i \(-0.855092\pi\)
−0.405405 + 0.914137i \(0.632869\pi\)
\(212\) 0 0
\(213\) −0.121150 + 0.101657i −0.00830107 + 0.00696543i
\(214\) 0 0
\(215\) −1.82940 10.3751i −0.124764 0.707573i
\(216\) 0 0
\(217\) 12.6815 21.9650i 0.860876 1.49108i
\(218\) 0 0
\(219\) 10.9891 + 3.99972i 0.742578 + 0.270276i
\(220\) 0 0
\(221\) 0.340112 + 0.589091i 0.0228784 + 0.0396265i
\(222\) 0 0
\(223\) 14.8141 + 12.4305i 0.992028 + 0.832411i 0.985860 0.167570i \(-0.0535921\pi\)
0.00616830 + 0.999981i \(0.498037\pi\)
\(224\) 0 0
\(225\) −0.125676 + 0.712746i −0.00837842 + 0.0475164i
\(226\) 0 0
\(227\) 5.01480 0.332844 0.166422 0.986055i \(-0.446779\pi\)
0.166422 + 0.986055i \(0.446779\pi\)
\(228\) 0 0
\(229\) 15.4150 1.01865 0.509325 0.860574i \(-0.329895\pi\)
0.509325 + 0.860574i \(0.329895\pi\)
\(230\) 0 0
\(231\) 2.17311 12.3243i 0.142980 0.810879i
\(232\) 0 0
\(233\) −6.63763 5.56963i −0.434845 0.364879i 0.398931 0.916981i \(-0.369381\pi\)
−0.833776 + 0.552102i \(0.813826\pi\)
\(234\) 0 0
\(235\) 5.89096 + 10.2034i 0.384284 + 0.665600i
\(236\) 0 0
\(237\) −7.74291 2.81819i −0.502956 0.183061i
\(238\) 0 0
\(239\) −6.11195 + 10.5862i −0.395349 + 0.684765i −0.993146 0.116883i \(-0.962710\pi\)
0.597796 + 0.801648i \(0.296043\pi\)
\(240\) 0 0
\(241\) −0.270059 1.53158i −0.0173960 0.0986577i 0.974874 0.222759i \(-0.0715063\pi\)
−0.992270 + 0.124101i \(0.960395\pi\)
\(242\) 0 0
\(243\) 5.62418 4.71924i 0.360791 0.302740i
\(244\) 0 0
\(245\) −3.97410 + 1.44646i −0.253896 + 0.0924106i
\(246\) 0 0
\(247\) −5.54831 5.96780i −0.353030 0.379722i
\(248\) 0 0
\(249\) 1.31068 0.477050i 0.0830612 0.0302318i
\(250\) 0 0
\(251\) −5.05420 + 4.24098i −0.319018 + 0.267688i −0.788208 0.615410i \(-0.788991\pi\)
0.469189 + 0.883098i \(0.344546\pi\)
\(252\) 0 0
\(253\) −3.20935 18.2011i −0.201770 1.14430i
\(254\) 0 0
\(255\) 0.274493 0.475435i 0.0171894 0.0297729i
\(256\) 0 0
\(257\) 27.4725 + 9.99916i 1.71368 + 0.623730i 0.997263 0.0739369i \(-0.0235563\pi\)
0.716422 + 0.697667i \(0.245779\pi\)
\(258\) 0 0
\(259\) 5.61099 + 9.71852i 0.348650 + 0.603879i
\(260\) 0 0
\(261\) −1.79544 1.50655i −0.111135 0.0932533i
\(262\) 0 0
\(263\) 3.62948 20.5838i 0.223804 1.26925i −0.641156 0.767411i \(-0.721545\pi\)
0.864959 0.501842i \(-0.167344\pi\)
\(264\) 0 0
\(265\) −2.63135 −0.161642
\(266\) 0 0
\(267\) −12.0474 −0.737288
\(268\) 0 0
\(269\) 4.36839 24.7744i 0.266345 1.51052i −0.498831 0.866699i \(-0.666237\pi\)
0.765176 0.643821i \(-0.222652\pi\)
\(270\) 0 0
\(271\) −17.1970 14.4300i −1.04464 0.876559i −0.0521227 0.998641i \(-0.516599\pi\)
−0.992520 + 0.122081i \(0.961043\pi\)
\(272\) 0 0
\(273\) 4.72559 + 8.18496i 0.286006 + 0.495376i
\(274\) 0 0
\(275\) 2.32601 + 0.846600i 0.140264 + 0.0510519i
\(276\) 0 0
\(277\) −1.31202 + 2.27248i −0.0788314 + 0.136540i −0.902746 0.430174i \(-0.858452\pi\)
0.823915 + 0.566714i \(0.191786\pi\)
\(278\) 0 0
\(279\) −0.951219 5.39463i −0.0569480 0.322968i
\(280\) 0 0
\(281\) −8.76242 + 7.35254i −0.522722 + 0.438616i −0.865580 0.500771i \(-0.833050\pi\)
0.342857 + 0.939387i \(0.388605\pi\)
\(282\) 0 0
\(283\) −19.9029 + 7.24406i −1.18310 + 0.430614i −0.857297 0.514822i \(-0.827858\pi\)
−0.325806 + 0.945437i \(0.605636\pi\)
\(284\) 0 0
\(285\) −1.93220 + 6.28614i −0.114454 + 0.372359i
\(286\) 0 0
\(287\) −27.0478 + 9.84458i −1.59658 + 0.581107i
\(288\) 0 0
\(289\) −12.9213 + 10.8423i −0.760078 + 0.637781i
\(290\) 0 0
\(291\) 1.85127 + 10.4991i 0.108523 + 0.615465i
\(292\) 0 0
\(293\) 13.4334 23.2673i 0.784788 1.35929i −0.144338 0.989528i \(-0.546105\pi\)
0.929126 0.369764i \(-0.120561\pi\)
\(294\) 0 0
\(295\) −11.3091 4.11618i −0.658442 0.239653i
\(296\) 0 0
\(297\) −6.95323 12.0434i −0.403468 0.698826i
\(298\) 0 0
\(299\) 10.6924 + 8.97201i 0.618359 + 0.518865i
\(300\) 0 0
\(301\) 6.13031 34.7667i 0.353345 2.00392i
\(302\) 0 0
\(303\) −0.813281 −0.0467217
\(304\) 0 0
\(305\) −11.3285 −0.648665
\(306\) 0 0
\(307\) −0.736789 + 4.17854i −0.0420508 + 0.238482i −0.998588 0.0531297i \(-0.983080\pi\)
0.956537 + 0.291612i \(0.0941914\pi\)
\(308\) 0 0
\(309\) −8.81478 7.39648i −0.501455 0.420771i
\(310\) 0 0
\(311\) 16.5037 + 28.5852i 0.935839 + 1.62092i 0.773131 + 0.634246i \(0.218689\pi\)
0.162707 + 0.986674i \(0.447977\pi\)
\(312\) 0 0
\(313\) 7.30450 + 2.65862i 0.412875 + 0.150274i 0.540102 0.841599i \(-0.318386\pi\)
−0.127227 + 0.991874i \(0.540608\pi\)
\(314\) 0 0
\(315\) −1.21263 + 2.10033i −0.0683237 + 0.118340i
\(316\) 0 0
\(317\) −2.10897 11.9606i −0.118452 0.671772i −0.984983 0.172650i \(-0.944767\pi\)
0.866532 0.499122i \(-0.166344\pi\)
\(318\) 0 0
\(319\) −6.14065 + 5.15262i −0.343810 + 0.288491i
\(320\) 0 0
\(321\) 12.0669 4.39199i 0.673508 0.245137i
\(322\) 0 0
\(323\) −0.956433 + 1.26527i −0.0532174 + 0.0704014i
\(324\) 0 0
\(325\) −1.75666 + 0.639372i −0.0974419 + 0.0354660i
\(326\) 0 0
\(327\) −15.1604 + 12.7211i −0.838374 + 0.703479i
\(328\) 0 0
\(329\) 6.85583 + 38.8814i 0.377974 + 2.14360i
\(330\) 0 0
\(331\) −14.9145 + 25.8326i −0.819774 + 1.41989i 0.0860741 + 0.996289i \(0.472568\pi\)
−0.905848 + 0.423602i \(0.860766\pi\)
\(332\) 0 0
\(333\) 2.27753 + 0.828955i 0.124808 + 0.0454264i
\(334\) 0 0
\(335\) −1.22931 2.12922i −0.0671642 0.116332i
\(336\) 0 0
\(337\) −17.4827 14.6697i −0.952341 0.799109i 0.0273495 0.999626i \(-0.491293\pi\)
−0.979690 + 0.200517i \(0.935738\pi\)
\(338\) 0 0
\(339\) −3.64207 + 20.6552i −0.197810 + 1.12184i
\(340\) 0 0
\(341\) −18.7350 −1.01456
\(342\) 0 0
\(343\) 9.28509 0.501348
\(344\) 0 0
\(345\) 1.95615 11.0939i 0.105315 0.597273i
\(346\) 0 0
\(347\) −26.5831 22.3059i −1.42706 1.19744i −0.947427 0.319972i \(-0.896327\pi\)
−0.479630 0.877471i \(-0.659229\pi\)
\(348\) 0 0
\(349\) 6.05693 + 10.4909i 0.324220 + 0.561565i 0.981354 0.192208i \(-0.0615649\pi\)
−0.657134 + 0.753774i \(0.728232\pi\)
\(350\) 0 0
\(351\) 9.86911 + 3.59206i 0.526774 + 0.191730i
\(352\) 0 0
\(353\) −15.8193 + 27.3998i −0.841976 + 1.45835i 0.0462448 + 0.998930i \(0.485275\pi\)
−0.888221 + 0.459416i \(0.848059\pi\)
\(354\) 0 0
\(355\) −0.0182024 0.103231i −0.000966085 0.00547894i
\(356\) 0 0
\(357\) 1.40925 1.18250i 0.0745854 0.0625846i
\(358\) 0 0
\(359\) 0.327164 0.119078i 0.0172671 0.00628470i −0.333372 0.942795i \(-0.608187\pi\)
0.350639 + 0.936511i \(0.385964\pi\)
\(360\) 0 0
\(361\) 7.78015 17.3340i 0.409482 0.912318i
\(362\) 0 0
\(363\) 6.90855 2.51450i 0.362605 0.131977i
\(364\) 0 0
\(365\) −5.93774 + 4.98236i −0.310796 + 0.260788i
\(366\) 0 0
\(367\) 0.812336 + 4.60699i 0.0424036 + 0.240483i 0.998641 0.0521076i \(-0.0165939\pi\)
−0.956238 + 0.292590i \(0.905483\pi\)
\(368\) 0 0
\(369\) −3.10832 + 5.38376i −0.161813 + 0.280268i
\(370\) 0 0
\(371\) −8.28586 3.01581i −0.430180 0.156573i
\(372\) 0 0
\(373\) 8.99161 + 15.5739i 0.465568 + 0.806388i 0.999227 0.0393123i \(-0.0125167\pi\)
−0.533659 + 0.845700i \(0.679183\pi\)
\(374\) 0 0
\(375\) 1.15575 + 0.969791i 0.0596828 + 0.0500798i
\(376\) 0 0
\(377\) 1.05125 5.96193i 0.0541421 0.307055i
\(378\) 0 0
\(379\) 8.98539 0.461548 0.230774 0.973007i \(-0.425874\pi\)
0.230774 + 0.973007i \(0.425874\pi\)
\(380\) 0 0
\(381\) 2.56338 0.131326
\(382\) 0 0
\(383\) −2.05099 + 11.6317i −0.104801 + 0.594354i 0.886499 + 0.462730i \(0.153130\pi\)
−0.991300 + 0.131624i \(0.957981\pi\)
\(384\) 0 0
\(385\) 6.35410 + 5.33172i 0.323835 + 0.271730i
\(386\) 0 0
\(387\) −3.81235 6.60318i −0.193792 0.335658i
\(388\) 0 0
\(389\) 3.11727 + 1.13459i 0.158052 + 0.0575262i 0.419834 0.907601i \(-0.362088\pi\)
−0.261783 + 0.965127i \(0.584310\pi\)
\(390\) 0 0
\(391\) 1.35844 2.35289i 0.0686992 0.118991i
\(392\) 0 0
\(393\) −1.22942 6.97240i −0.0620162 0.351711i
\(394\) 0 0
\(395\) 4.18371 3.51055i 0.210505 0.176635i
\(396\) 0 0
\(397\) −28.3418 + 10.3156i −1.42243 + 0.517723i −0.934753 0.355299i \(-0.884379\pi\)
−0.487680 + 0.873022i \(0.662157\pi\)
\(398\) 0 0
\(399\) −13.2889 + 17.5799i −0.665277 + 0.880097i
\(400\) 0 0
\(401\) 12.9553 4.71536i 0.646959 0.235474i 0.00236276 0.999997i \(-0.499248\pi\)
0.644596 + 0.764524i \(0.277026\pi\)
\(402\) 0 0
\(403\) 10.8388 9.09486i 0.539921 0.453047i
\(404\) 0 0
\(405\) −1.09485 6.20919i −0.0544034 0.308537i
\(406\) 0 0
\(407\) 4.14469 7.17882i 0.205445 0.355841i
\(408\) 0 0
\(409\) 25.9524 + 9.44591i 1.28326 + 0.467070i 0.891511 0.453000i \(-0.149646\pi\)
0.391754 + 0.920070i \(0.371868\pi\)
\(410\) 0 0
\(411\) −9.03304 15.6457i −0.445567 0.771744i
\(412\) 0 0
\(413\) −30.8937 25.9229i −1.52018 1.27558i
\(414\) 0 0
\(415\) −0.160536 + 0.910442i −0.00788038 + 0.0446919i
\(416\) 0 0
\(417\) −19.6947 −0.964456
\(418\) 0 0
\(419\) 21.2139 1.03637 0.518184 0.855269i \(-0.326608\pi\)
0.518184 + 0.855269i \(0.326608\pi\)
\(420\) 0 0
\(421\) 5.42288 30.7547i 0.264295 1.49889i −0.506741 0.862099i \(-0.669150\pi\)
0.771036 0.636792i \(-0.219739\pi\)
\(422\) 0 0
\(423\) 6.53211 + 5.48109i 0.317602 + 0.266500i
\(424\) 0 0
\(425\) 0.181936 + 0.315123i 0.00882521 + 0.0152857i
\(426\) 0 0
\(427\) −35.6722 12.9836i −1.72630 0.628322i
\(428\) 0 0
\(429\) 3.49067 6.04602i 0.168531 0.291905i
\(430\) 0 0
\(431\) 1.69732 + 9.62595i 0.0817568 + 0.463666i 0.998009 + 0.0630649i \(0.0200875\pi\)
−0.916253 + 0.400601i \(0.868801\pi\)
\(432\) 0 0
\(433\) 15.1630 12.7233i 0.728690 0.611443i −0.201084 0.979574i \(-0.564447\pi\)
0.929774 + 0.368131i \(0.120002\pi\)
\(434\) 0 0
\(435\) −4.59125 + 1.67108i −0.220133 + 0.0801220i
\(436\) 0 0
\(437\) −9.56230 + 31.1095i −0.457427 + 1.48817i
\(438\) 0 0
\(439\) −21.4219 + 7.79694i −1.02241 + 0.372128i −0.798187 0.602410i \(-0.794207\pi\)
−0.224225 + 0.974537i \(0.571985\pi\)
\(440\) 0 0
\(441\) −2.34472 + 1.96745i −0.111653 + 0.0936882i
\(442\) 0 0
\(443\) −2.22149 12.5987i −0.105546 0.598581i −0.991001 0.133856i \(-0.957264\pi\)
0.885455 0.464725i \(-0.153847\pi\)
\(444\) 0 0
\(445\) 3.99257 6.91533i 0.189266 0.327818i
\(446\) 0 0
\(447\) 7.57717 + 2.75786i 0.358388 + 0.130443i
\(448\) 0 0
\(449\) −7.14276 12.3716i −0.337088 0.583853i 0.646796 0.762663i \(-0.276109\pi\)
−0.983884 + 0.178810i \(0.942775\pi\)
\(450\) 0 0
\(451\) 16.2874 + 13.6668i 0.766945 + 0.643544i
\(452\) 0 0
\(453\) −5.18017 + 29.3782i −0.243386 + 1.38031i
\(454\) 0 0
\(455\) −6.26434 −0.293677
\(456\) 0 0
\(457\) 29.7160 1.39005 0.695027 0.718984i \(-0.255392\pi\)
0.695027 + 0.718984i \(0.255392\pi\)
\(458\) 0 0
\(459\) 0.354985 2.01322i 0.0165693 0.0939691i
\(460\) 0 0
\(461\) 17.1209 + 14.3662i 0.797402 + 0.669099i 0.947565 0.319562i \(-0.103536\pi\)
−0.150164 + 0.988661i \(0.547980\pi\)
\(462\) 0 0
\(463\) 19.2984 + 33.4259i 0.896874 + 1.55343i 0.831468 + 0.555573i \(0.187501\pi\)
0.0654067 + 0.997859i \(0.479166\pi\)
\(464\) 0 0
\(465\) −10.7306 3.90562i −0.497619 0.181119i
\(466\) 0 0
\(467\) −7.24255 + 12.5445i −0.335145 + 0.580489i −0.983513 0.180839i \(-0.942119\pi\)
0.648367 + 0.761328i \(0.275452\pi\)
\(468\) 0 0
\(469\) −1.43065 8.11363i −0.0660613 0.374653i
\(470\) 0 0
\(471\) −3.49626 + 2.93371i −0.161099 + 0.135178i
\(472\) 0 0
\(473\) −24.5048 + 8.91902i −1.12673 + 0.410097i
\(474\) 0 0
\(475\) −2.96797 3.19236i −0.136180 0.146476i
\(476\) 0 0
\(477\) −1.78956 + 0.651348i −0.0819385 + 0.0298232i
\(478\) 0 0
\(479\) 11.5193 9.66583i 0.526330 0.441643i −0.340502 0.940244i \(-0.610597\pi\)
0.866832 + 0.498601i \(0.166153\pi\)
\(480\) 0 0
\(481\) 1.08710 + 6.16523i 0.0495673 + 0.281110i
\(482\) 0 0
\(483\) 18.8745 32.6915i 0.858818 1.48752i
\(484\) 0 0
\(485\) −6.64008 2.41679i −0.301511 0.109741i
\(486\) 0 0
\(487\) −0.424122 0.734601i −0.0192188 0.0332879i 0.856256 0.516552i \(-0.172785\pi\)
−0.875475 + 0.483264i \(0.839451\pi\)
\(488\) 0 0
\(489\) 8.38648 + 7.03709i 0.379250 + 0.318228i
\(490\) 0 0
\(491\) 4.71762 26.7549i 0.212903 1.20743i −0.671605 0.740909i \(-0.734395\pi\)
0.884508 0.466525i \(-0.154494\pi\)
\(492\) 0 0
\(493\) −1.17838 −0.0530714
\(494\) 0 0
\(495\) 1.79147 0.0805206
\(496\) 0 0
\(497\) 0.0609962 0.345927i 0.00273605 0.0155169i
\(498\) 0 0
\(499\) 8.19888 + 6.87968i 0.367032 + 0.307977i 0.807586 0.589749i \(-0.200774\pi\)
−0.440554 + 0.897726i \(0.645218\pi\)
\(500\) 0 0
\(501\) 1.99234 + 3.45084i 0.0890113 + 0.154172i
\(502\) 0 0
\(503\) −29.3209 10.6719i −1.30736 0.475839i −0.407970 0.912995i \(-0.633763\pi\)
−0.899385 + 0.437157i \(0.855986\pi\)
\(504\) 0 0
\(505\) 0.269525 0.466832i 0.0119937 0.0207737i
\(506\) 0 0
\(507\) −2.49029 14.1231i −0.110598 0.627230i
\(508\) 0 0
\(509\) 33.1668 27.8302i 1.47009 1.23355i 0.554040 0.832490i \(-0.313085\pi\)
0.916051 0.401063i \(-0.131359\pi\)
\(510\) 0 0
\(511\) −24.4077 + 8.88367i −1.07973 + 0.392990i
\(512\) 0 0
\(513\) 1.24488 + 24.4571i 0.0549626 + 1.07981i
\(514\) 0 0
\(515\) 7.16692 2.60855i 0.315812 0.114946i
\(516\) 0 0
\(517\) 22.3407 18.7461i 0.982543 0.824452i
\(518\) 0 0
\(519\) −3.16948 17.9750i −0.139125 0.789015i
\(520\) 0 0
\(521\) −18.3439 + 31.7726i −0.803663 + 1.39198i 0.113527 + 0.993535i \(0.463785\pi\)
−0.917190 + 0.398450i \(0.869548\pi\)
\(522\) 0 0
\(523\) 36.6256 + 13.3306i 1.60153 + 0.582908i 0.979739 0.200278i \(-0.0641847\pi\)
0.621787 + 0.783186i \(0.286407\pi\)
\(524\) 0 0
\(525\) 2.52787 + 4.37840i 0.110325 + 0.191089i
\(526\) 0 0
\(527\) −2.10975 1.77029i −0.0919021 0.0771150i
\(528\) 0 0
\(529\) 5.68689 32.2520i 0.247256 1.40226i
\(530\) 0 0
\(531\) −8.71015 −0.377988
\(532\) 0 0
\(533\) −16.0574 −0.695521
\(534\) 0 0
\(535\) −1.47798 + 8.38205i −0.0638987 + 0.362387i
\(536\) 0 0
\(537\) −21.0322 17.6481i −0.907605 0.761571i
\(538\) 0 0
\(539\) 5.23419 + 9.06589i 0.225453 + 0.390496i
\(540\) 0 0
\(541\) 23.2295 + 8.45486i 0.998716 + 0.363503i 0.789089 0.614279i \(-0.210553\pi\)
0.209627 + 0.977781i \(0.432775\pi\)
\(542\) 0 0
\(543\) 15.4407 26.7441i 0.662623 1.14770i
\(544\) 0 0
\(545\) −2.27781 12.9181i −0.0975706 0.553350i
\(546\) 0 0
\(547\) 11.9613 10.0368i 0.511430 0.429141i −0.350202 0.936674i \(-0.613887\pi\)
0.861632 + 0.507533i \(0.169443\pi\)
\(548\) 0 0
\(549\) −7.70442 + 2.80418i −0.328816 + 0.119679i
\(550\) 0 0
\(551\) 13.7589 3.15472i 0.586150 0.134396i
\(552\) 0 0
\(553\) 17.1976 6.25940i 0.731314 0.266177i
\(554\) 0 0
\(555\) 3.87044 3.24769i 0.164291 0.137857i
\(556\) 0 0
\(557\) 0.785151 + 4.45281i 0.0332679 + 0.188672i 0.996913 0.0785138i \(-0.0250175\pi\)
−0.963645 + 0.267185i \(0.913906\pi\)
\(558\) 0 0
\(559\) 9.84715 17.0558i 0.416490 0.721382i
\(560\) 0 0
\(561\) −1.27695 0.464771i −0.0539127 0.0196226i
\(562\) 0 0
\(563\) 7.56521 + 13.1033i 0.318835 + 0.552239i 0.980245 0.197785i \(-0.0633749\pi\)
−0.661410 + 0.750025i \(0.730042\pi\)
\(564\) 0 0
\(565\) −10.6493 8.93583i −0.448020 0.375933i
\(566\) 0 0
\(567\) 3.66883 20.8069i 0.154076 0.873810i
\(568\) 0 0
\(569\) −2.59851 −0.108935 −0.0544676 0.998516i \(-0.517346\pi\)
−0.0544676 + 0.998516i \(0.517346\pi\)
\(570\) 0 0
\(571\) 39.1787 1.63958 0.819790 0.572665i \(-0.194090\pi\)
0.819790 + 0.572665i \(0.194090\pi\)
\(572\) 0 0
\(573\) 1.75653 9.96180i 0.0733802 0.416160i
\(574\) 0 0
\(575\) 5.71972 + 4.79941i 0.238529 + 0.200149i
\(576\) 0 0
\(577\) −4.88434 8.45993i −0.203338 0.352191i 0.746264 0.665650i \(-0.231846\pi\)
−0.949602 + 0.313459i \(0.898512\pi\)
\(578\) 0 0
\(579\) 14.9120 + 5.42753i 0.619723 + 0.225561i
\(580\) 0 0
\(581\) −1.54898 + 2.68290i −0.0642623 + 0.111306i
\(582\) 0 0
\(583\) 1.13103 + 6.41440i 0.0468426 + 0.265657i
\(584\) 0 0
\(585\) −1.03643 + 0.869666i −0.0428510 + 0.0359562i
\(586\) 0 0
\(587\) 5.08774 1.85178i 0.209993 0.0764313i −0.234882 0.972024i \(-0.575470\pi\)
0.444875 + 0.895593i \(0.353248\pi\)
\(588\) 0 0
\(589\) 29.3732 + 15.0221i 1.21030 + 0.618973i
\(590\) 0 0
\(591\) −17.2713 + 6.28623i −0.710445 + 0.258581i
\(592\) 0 0
\(593\) −2.38413 + 2.00052i −0.0979043 + 0.0821515i −0.690426 0.723403i \(-0.742577\pi\)
0.592522 + 0.805555i \(0.298132\pi\)
\(594\) 0 0
\(595\) 0.211735 + 1.20081i 0.00868030 + 0.0492285i
\(596\) 0 0
\(597\) −13.3510 + 23.1247i −0.546421 + 0.946429i
\(598\) 0 0
\(599\) 16.8738 + 6.14155i 0.689444 + 0.250937i 0.662897 0.748711i \(-0.269327\pi\)
0.0265467 + 0.999648i \(0.491549\pi\)
\(600\) 0 0
\(601\) −20.1403 34.8839i −0.821538 1.42295i −0.904537 0.426396i \(-0.859783\pi\)
0.0829986 0.996550i \(-0.473550\pi\)
\(602\) 0 0
\(603\) −1.36310 1.14378i −0.0555097 0.0465781i
\(604\) 0 0
\(605\) −0.846175 + 4.79890i −0.0344019 + 0.195103i
\(606\) 0 0
\(607\) 30.5465 1.23984 0.619922 0.784663i \(-0.287164\pi\)
0.619922 + 0.784663i \(0.287164\pi\)
\(608\) 0 0
\(609\) −16.3726 −0.663452
\(610\) 0 0
\(611\) −3.82462 + 21.6905i −0.154728 + 0.877504i
\(612\) 0 0
\(613\) 24.0219 + 20.1568i 0.970235 + 0.814124i 0.982588 0.185800i \(-0.0594876\pi\)
−0.0123524 + 0.999924i \(0.503932\pi\)
\(614\) 0 0
\(615\) 6.47967 + 11.2231i 0.261286 + 0.452560i
\(616\) 0 0
\(617\) 41.0154 + 14.9284i 1.65122 + 0.600994i 0.988947 0.148270i \(-0.0473703\pi\)
0.662271 + 0.749264i \(0.269593\pi\)
\(618\) 0 0
\(619\) −1.34573 + 2.33087i −0.0540895 + 0.0936857i −0.891802 0.452425i \(-0.850559\pi\)
0.837713 + 0.546111i \(0.183892\pi\)
\(620\) 0 0
\(621\) −7.28419 41.3107i −0.292304 1.65774i
\(622\) 0 0
\(623\) 20.4979 17.1998i 0.821231 0.689095i
\(624\) 0 0
\(625\) −0.939693 + 0.342020i −0.0375877 + 0.0136808i
\(626\) 0 0
\(627\) 16.1542 + 2.00814i 0.645135 + 0.0801973i
\(628\) 0 0
\(629\) 1.14507 0.416771i 0.0456569 0.0166177i
\(630\) 0 0
\(631\) −17.9778 + 15.0852i −0.715685 + 0.600531i −0.926188 0.377062i \(-0.876934\pi\)
0.210503 + 0.977593i \(0.432490\pi\)
\(632\) 0 0
\(633\) 5.27919 + 29.9398i 0.209829 + 1.19000i
\(634\) 0 0
\(635\) −0.849517 + 1.47141i −0.0337121 + 0.0583910i
\(636\) 0 0
\(637\) −7.42918 2.70400i −0.294355 0.107136i
\(638\) 0 0
\(639\) −0.0379326 0.0657011i −0.00150059 0.00259910i
\(640\) 0 0
\(641\) 29.5691 + 24.8114i 1.16791 + 0.979991i 0.999983 0.00580901i \(-0.00184908\pi\)
0.167924 + 0.985800i \(0.446294\pi\)
\(642\) 0 0
\(643\) −4.94981 + 28.0718i −0.195201 + 1.10704i 0.716930 + 0.697145i \(0.245547\pi\)
−0.912132 + 0.409897i \(0.865564\pi\)
\(644\) 0 0
\(645\) −15.8946 −0.625850
\(646\) 0 0
\(647\) −8.39487 −0.330036 −0.165018 0.986291i \(-0.552768\pi\)
−0.165018 + 0.986291i \(0.552768\pi\)
\(648\) 0 0
\(649\) −5.17296 + 29.3373i −0.203057 + 1.15159i
\(650\) 0 0
\(651\) −29.3133 24.5968i −1.14888 0.964025i
\(652\) 0 0
\(653\) −2.14161 3.70938i −0.0838077 0.145159i 0.821075 0.570821i \(-0.193375\pi\)
−0.904883 + 0.425661i \(0.860041\pi\)
\(654\) 0 0
\(655\) 4.40967 + 1.60499i 0.172300 + 0.0627121i
\(656\) 0 0
\(657\) −2.80492 + 4.85826i −0.109430 + 0.189539i
\(658\) 0 0
\(659\) −2.57762 14.6184i −0.100410 0.569453i −0.992955 0.118494i \(-0.962193\pi\)
0.892545 0.450959i \(-0.148918\pi\)
\(660\) 0 0
\(661\) −32.4321 + 27.2137i −1.26146 + 1.05849i −0.265937 + 0.963990i \(0.585681\pi\)
−0.995525 + 0.0945016i \(0.969874\pi\)
\(662\) 0 0
\(663\) 0.964380 0.351006i 0.0374534 0.0136319i
\(664\) 0 0
\(665\) −5.68705 13.4540i −0.220534 0.521726i
\(666\) 0 0
\(667\) −22.7217 + 8.27001i −0.879787 + 0.320216i
\(668\) 0 0
\(669\) 22.3505 18.7543i 0.864121 0.725083i
\(670\) 0 0
\(671\) 4.86931 + 27.6152i 0.187978 + 1.06607i
\(672\) 0 0
\(673\) −2.96569 + 5.13672i −0.114319 + 0.198006i −0.917507 0.397719i \(-0.869802\pi\)
0.803188 + 0.595725i \(0.203135\pi\)
\(674\) 0 0
\(675\) 5.27930 + 1.92151i 0.203200 + 0.0739588i
\(676\) 0 0
\(677\) 4.02585 + 6.97297i 0.154726 + 0.267993i 0.932959 0.359982i \(-0.117217\pi\)
−0.778233 + 0.627975i \(0.783884\pi\)
\(678\) 0 0
\(679\) −18.1391 15.2205i −0.696114 0.584109i
\(680\) 0 0
\(681\) 1.31382 7.45102i 0.0503456 0.285524i
\(682\) 0 0
\(683\) −42.4980 −1.62614 −0.813071 0.582164i \(-0.802206\pi\)
−0.813071 + 0.582164i \(0.802206\pi\)
\(684\) 0 0
\(685\) 11.9744 0.457517
\(686\) 0 0
\(687\) 4.03854 22.9037i 0.154080 0.873830i
\(688\) 0 0
\(689\) −3.76820 3.16190i −0.143557 0.120459i
\(690\) 0 0
\(691\) 12.1536 + 21.0507i 0.462345 + 0.800805i 0.999077 0.0429478i \(-0.0136749\pi\)
−0.536733 + 0.843752i \(0.680342\pi\)
\(692\) 0 0
\(693\) 5.64117 + 2.05322i 0.214290 + 0.0779953i
\(694\) 0 0
\(695\) 6.52694 11.3050i 0.247581 0.428823i
\(696\) 0 0
\(697\) 0.542740 + 3.07803i 0.0205578 + 0.116589i
\(698\) 0 0
\(699\) −10.0144 + 8.40305i −0.378778 + 0.317833i
\(700\) 0 0
\(701\) 16.0317 5.83508i 0.605511 0.220388i −0.0210272 0.999779i \(-0.506694\pi\)
0.626538 + 0.779391i \(0.284471\pi\)
\(702\) 0 0
\(703\) −12.2543 + 7.93185i −0.462179 + 0.299155i
\(704\) 0 0
\(705\) 16.7037 6.07965i 0.629098 0.228973i
\(706\) 0 0
\(707\) 1.38375 1.16110i 0.0520412 0.0436678i
\(708\) 0 0
\(709\) −2.01281 11.4152i −0.0755928 0.428708i −0.998993 0.0448691i \(-0.985713\pi\)
0.923400 0.383839i \(-0.125398\pi\)
\(710\) 0 0
\(711\) 1.97633 3.42311i 0.0741184 0.128377i
\(712\) 0 0
\(713\) −53.1047 19.3285i −1.98879 0.723860i
\(714\) 0 0
\(715\) 2.31365 + 4.00736i 0.0865257 + 0.149867i
\(716\) 0 0
\(717\) 14.1278 + 11.8546i 0.527613 + 0.442719i
\(718\) 0 0
\(719\) 2.09646 11.8896i 0.0781848 0.443408i −0.920435 0.390895i \(-0.872166\pi\)
0.998620 0.0525135i \(-0.0167232\pi\)
\(720\) 0 0
\(721\) 25.5576 0.951815
\(722\) 0 0
\(723\) −2.34638 −0.0872629
\(724\) 0 0
\(725\) 0.562347 3.18923i 0.0208850 0.118445i
\(726\) 0 0
\(727\) −2.84897 2.39057i −0.105662 0.0886612i 0.588426 0.808551i \(-0.299748\pi\)
−0.694088 + 0.719890i \(0.744192\pi\)
\(728\) 0 0
\(729\) −14.9959 25.9736i −0.555403 0.961986i
\(730\) 0 0
\(731\) −3.60226 1.31111i −0.133234 0.0484933i
\(732\) 0 0
\(733\) −4.28268 + 7.41782i −0.158184 + 0.273984i −0.934214 0.356713i \(-0.883897\pi\)
0.776030 + 0.630697i \(0.217231\pi\)
\(734\) 0 0
\(735\) 1.10799 + 6.28370i 0.0408687 + 0.231778i
\(736\) 0 0
\(737\) −4.66198 + 3.91187i −0.171726 + 0.144095i
\(738\) 0 0
\(739\) 2.60103 0.946697i 0.0956804 0.0348248i −0.293736 0.955886i \(-0.594899\pi\)
0.389417 + 0.921062i \(0.372677\pi\)
\(740\) 0 0
\(741\) −10.3206 + 6.68022i −0.379136 + 0.245404i
\(742\) 0 0
\(743\) 20.3640 7.41189i 0.747083 0.271916i 0.0597050 0.998216i \(-0.480984\pi\)
0.687378 + 0.726300i \(0.258762\pi\)
\(744\) 0 0
\(745\) −4.09416 + 3.43540i −0.149998 + 0.125863i
\(746\) 0 0
\(747\) 0.116186 + 0.658924i 0.00425103 + 0.0241088i
\(748\) 0 0
\(749\) −14.2607 + 24.7003i −0.521076 + 0.902530i
\(750\) 0 0
\(751\) 32.8421 + 11.9535i 1.19843 + 0.436191i 0.862674 0.505760i \(-0.168788\pi\)
0.335751 + 0.941951i \(0.391010\pi\)
\(752\) 0 0
\(753\) 4.97713 + 8.62065i 0.181377 + 0.314154i
\(754\) 0 0
\(755\) −15.1467 12.7096i −0.551243 0.462548i
\(756\) 0 0
\(757\) −4.00158 + 22.6941i −0.145440 + 0.824831i 0.821573 + 0.570103i \(0.193097\pi\)
−0.967013 + 0.254727i \(0.918014\pi\)
\(758\) 0 0
\(759\) −27.8842 −1.01213
\(760\) 0 0
\(761\) −27.9096 −1.01172 −0.505862 0.862615i \(-0.668825\pi\)
−0.505862 + 0.862615i \(0.668825\pi\)
\(762\) 0 0
\(763\) 7.63292 43.2884i 0.276330 1.56715i
\(764\) 0 0
\(765\) 0.201738 + 0.169278i 0.00729384 + 0.00612026i
\(766\) 0 0
\(767\) −11.2490 19.4839i −0.406178 0.703521i
\(768\) 0 0
\(769\) −24.7790 9.01883i −0.893554 0.325227i −0.145888 0.989301i \(-0.546604\pi\)
−0.747667 + 0.664074i \(0.768826\pi\)
\(770\) 0 0
\(771\) 22.0543 38.1991i 0.794265 1.37571i
\(772\) 0 0
\(773\) −1.47221 8.34931i −0.0529516 0.300304i 0.946818 0.321770i \(-0.104278\pi\)
−0.999770 + 0.0214661i \(0.993167\pi\)
\(774\) 0 0
\(775\) 5.79804 4.86513i 0.208272 0.174761i
\(776\) 0 0
\(777\) 15.9099 5.79071i 0.570763 0.207741i
\(778\) 0 0
\(779\) −14.5776 34.4867i −0.522296 1.23561i
\(780\) 0 0
\(781\) −0.243821 + 0.0887437i −0.00872461 + 0.00317550i
\(782\) 0 0
\(783\) −13.9373 + 11.6948i −0.498078 + 0.417937i
\(784\) 0 0
\(785\) −0.525302 2.97914i −0.0187488 0.106330i
\(786\) 0 0
\(787\) −12.0148 + 20.8103i −0.428283 + 0.741807i