Properties

Label 405.2.b.a.244.3
Level $405$
Weight $2$
Character 405.244
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,2,Mod(244,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), 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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.3
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.2.b.a.244.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.792287i q^{2} +1.37228 q^{4} +(0.686141 + 2.12819i) q^{5} +3.46410i q^{7} +2.67181i q^{8} +O(q^{10})\) \(q+0.792287i q^{2} +1.37228 q^{4} +(0.686141 + 2.12819i) q^{5} +3.46410i q^{7} +2.67181i q^{8} +(-1.68614 + 0.543620i) q^{10} -4.37228 q^{11} -5.84096i q^{13} -2.74456 q^{14} +0.627719 q^{16} +0.792287i q^{17} +0.372281 q^{19} +(0.941578 + 2.92048i) q^{20} -3.46410i q^{22} -1.58457i q^{23} +(-4.05842 + 2.92048i) q^{25} +4.62772 q^{26} +4.75372i q^{28} +5.74456 q^{29} +6.37228 q^{31} +5.84096i q^{32} -0.627719 q^{34} +(-7.37228 + 2.37686i) q^{35} -2.37686i q^{37} +0.294954i q^{38} +(-5.68614 + 1.83324i) q^{40} +4.37228 q^{41} +3.46410i q^{43} -6.00000 q^{44} +1.25544 q^{46} +1.87953i q^{47} -5.00000 q^{49} +(-2.31386 - 3.21543i) q^{50} -8.01544i q^{52} -11.9769i q^{53} +(-3.00000 - 9.30506i) q^{55} -9.25544 q^{56} +4.55134i q^{58} -1.62772 q^{59} +9.37228 q^{61} +5.04868i q^{62} -3.37228 q^{64} +(12.4307 - 4.00772i) q^{65} +11.6819i q^{67} +1.08724i q^{68} +(-1.88316 - 5.84096i) q^{70} +13.1168 q^{71} +2.37686i q^{73} +1.88316 q^{74} +0.510875 q^{76} -15.1460i q^{77} -6.74456 q^{79} +(0.430703 + 1.33591i) q^{80} +3.46410i q^{82} -11.9769i q^{83} +(-1.68614 + 0.543620i) q^{85} -2.74456 q^{86} -11.6819i q^{88} +3.00000 q^{89} +20.2337 q^{91} -2.17448i q^{92} -1.48913 q^{94} +(0.255437 + 0.792287i) q^{95} -1.28962i q^{97} -3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{4} - 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{4} - 3 q^{5} - q^{10} - 6 q^{11} + 12 q^{14} + 14 q^{16} - 10 q^{19} + 21 q^{20} + q^{25} + 30 q^{26} + 14 q^{31} - 14 q^{34} - 18 q^{35} - 17 q^{40} + 6 q^{41} - 24 q^{44} + 28 q^{46} - 20 q^{49} - 15 q^{50} - 12 q^{55} - 60 q^{56} - 18 q^{59} + 26 q^{61} - 2 q^{64} + 21 q^{65} - 42 q^{70} + 18 q^{71} + 42 q^{74} + 48 q^{76} - 4 q^{79} - 27 q^{80} - q^{85} + 12 q^{86} + 12 q^{89} + 12 q^{91} + 40 q^{94} + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.792287i 0.560232i 0.959966 + 0.280116i \(0.0903729\pi\)
−0.959966 + 0.280116i \(0.909627\pi\)
\(3\) 0 0
\(4\) 1.37228 0.686141
\(5\) 0.686141 + 2.12819i 0.306851 + 0.951757i
\(6\) 0 0
\(7\) 3.46410i 1.30931i 0.755929 + 0.654654i \(0.227186\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 2.67181i 0.944629i
\(9\) 0 0
\(10\) −1.68614 + 0.543620i −0.533204 + 0.171908i
\(11\) −4.37228 −1.31829 −0.659146 0.752015i \(-0.729082\pi\)
−0.659146 + 0.752015i \(0.729082\pi\)
\(12\) 0 0
\(13\) 5.84096i 1.61999i −0.586436 0.809996i \(-0.699469\pi\)
0.586436 0.809996i \(-0.300531\pi\)
\(14\) −2.74456 −0.733515
\(15\) 0 0
\(16\) 0.627719 0.156930
\(17\) 0.792287i 0.192158i 0.995374 + 0.0960789i \(0.0306301\pi\)
−0.995374 + 0.0960789i \(0.969370\pi\)
\(18\) 0 0
\(19\) 0.372281 0.0854072 0.0427036 0.999088i \(-0.486403\pi\)
0.0427036 + 0.999088i \(0.486403\pi\)
\(20\) 0.941578 + 2.92048i 0.210543 + 0.653039i
\(21\) 0 0
\(22\) 3.46410i 0.738549i
\(23\) 1.58457i 0.330407i −0.986260 0.165203i \(-0.947172\pi\)
0.986260 0.165203i \(-0.0528280\pi\)
\(24\) 0 0
\(25\) −4.05842 + 2.92048i −0.811684 + 0.584096i
\(26\) 4.62772 0.907570
\(27\) 0 0
\(28\) 4.75372i 0.898369i
\(29\) 5.74456 1.06674 0.533369 0.845883i \(-0.320926\pi\)
0.533369 + 0.845883i \(0.320926\pi\)
\(30\) 0 0
\(31\) 6.37228 1.14450 0.572248 0.820081i \(-0.306072\pi\)
0.572248 + 0.820081i \(0.306072\pi\)
\(32\) 5.84096i 1.03255i
\(33\) 0 0
\(34\) −0.627719 −0.107653
\(35\) −7.37228 + 2.37686i −1.24614 + 0.401763i
\(36\) 0 0
\(37\) 2.37686i 0.390754i −0.980728 0.195377i \(-0.937407\pi\)
0.980728 0.195377i \(-0.0625930\pi\)
\(38\) 0.294954i 0.0478478i
\(39\) 0 0
\(40\) −5.68614 + 1.83324i −0.899058 + 0.289861i
\(41\) 4.37228 0.682836 0.341418 0.939912i \(-0.389093\pi\)
0.341418 + 0.939912i \(0.389093\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 1.25544 0.185104
\(47\) 1.87953i 0.274157i 0.990560 + 0.137079i \(0.0437713\pi\)
−0.990560 + 0.137079i \(0.956229\pi\)
\(48\) 0 0
\(49\) −5.00000 −0.714286
\(50\) −2.31386 3.21543i −0.327229 0.454731i
\(51\) 0 0
\(52\) 8.01544i 1.11154i
\(53\) 11.9769i 1.64515i −0.568656 0.822575i \(-0.692536\pi\)
0.568656 0.822575i \(-0.307464\pi\)
\(54\) 0 0
\(55\) −3.00000 9.30506i −0.404520 1.25469i
\(56\) −9.25544 −1.23681
\(57\) 0 0
\(58\) 4.55134i 0.597621i
\(59\) −1.62772 −0.211911 −0.105955 0.994371i \(-0.533790\pi\)
−0.105955 + 0.994371i \(0.533790\pi\)
\(60\) 0 0
\(61\) 9.37228 1.20000 0.599999 0.800001i \(-0.295168\pi\)
0.599999 + 0.800001i \(0.295168\pi\)
\(62\) 5.04868i 0.641182i
\(63\) 0 0
\(64\) −3.37228 −0.421535
\(65\) 12.4307 4.00772i 1.54184 0.497097i
\(66\) 0 0
\(67\) 11.6819i 1.42717i 0.700566 + 0.713587i \(0.252931\pi\)
−0.700566 + 0.713587i \(0.747069\pi\)
\(68\) 1.08724i 0.131847i
\(69\) 0 0
\(70\) −1.88316 5.84096i −0.225080 0.698129i
\(71\) 13.1168 1.55668 0.778341 0.627841i \(-0.216061\pi\)
0.778341 + 0.627841i \(0.216061\pi\)
\(72\) 0 0
\(73\) 2.37686i 0.278191i 0.990279 + 0.139095i \(0.0444194\pi\)
−0.990279 + 0.139095i \(0.955581\pi\)
\(74\) 1.88316 0.218912
\(75\) 0 0
\(76\) 0.510875 0.0586013
\(77\) 15.1460i 1.72605i
\(78\) 0 0
\(79\) −6.74456 −0.758823 −0.379411 0.925228i \(-0.623873\pi\)
−0.379411 + 0.925228i \(0.623873\pi\)
\(80\) 0.430703 + 1.33591i 0.0481541 + 0.149359i
\(81\) 0 0
\(82\) 3.46410i 0.382546i
\(83\) 11.9769i 1.31463i −0.753615 0.657317i \(-0.771691\pi\)
0.753615 0.657317i \(-0.228309\pi\)
\(84\) 0 0
\(85\) −1.68614 + 0.543620i −0.182888 + 0.0589639i
\(86\) −2.74456 −0.295954
\(87\) 0 0
\(88\) 11.6819i 1.24530i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 20.2337 2.12107
\(92\) 2.17448i 0.226705i
\(93\) 0 0
\(94\) −1.48913 −0.153592
\(95\) 0.255437 + 0.792287i 0.0262073 + 0.0812869i
\(96\) 0 0
\(97\) 1.28962i 0.130941i −0.997855 0.0654706i \(-0.979145\pi\)
0.997855 0.0654706i \(-0.0208548\pi\)
\(98\) 3.96143i 0.400165i
\(99\) 0 0
\(100\) −5.56930 + 4.00772i −0.556930 + 0.400772i
\(101\) −16.3723 −1.62910 −0.814551 0.580091i \(-0.803017\pi\)
−0.814551 + 0.580091i \(0.803017\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 15.6060 1.53029
\(105\) 0 0
\(106\) 9.48913 0.921665
\(107\) 13.2665i 1.28252i −0.767323 0.641260i \(-0.778412\pi\)
0.767323 0.641260i \(-0.221588\pi\)
\(108\) 0 0
\(109\) −9.74456 −0.933360 −0.466680 0.884426i \(-0.654550\pi\)
−0.466680 + 0.884426i \(0.654550\pi\)
\(110\) 7.37228 2.37686i 0.702919 0.226625i
\(111\) 0 0
\(112\) 2.17448i 0.205469i
\(113\) 6.13592i 0.577218i −0.957447 0.288609i \(-0.906807\pi\)
0.957447 0.288609i \(-0.0931928\pi\)
\(114\) 0 0
\(115\) 3.37228 1.08724i 0.314467 0.101386i
\(116\) 7.88316 0.731933
\(117\) 0 0
\(118\) 1.28962i 0.118719i
\(119\) −2.74456 −0.251594
\(120\) 0 0
\(121\) 8.11684 0.737895
\(122\) 7.42554i 0.672276i
\(123\) 0 0
\(124\) 8.74456 0.785285
\(125\) −9.00000 6.63325i −0.804984 0.593296i
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 9.01011i 0.796389i
\(129\) 0 0
\(130\) 3.17527 + 9.84868i 0.278489 + 0.863787i
\(131\) 4.37228 0.382008 0.191004 0.981589i \(-0.438826\pi\)
0.191004 + 0.981589i \(0.438826\pi\)
\(132\) 0 0
\(133\) 1.28962i 0.111824i
\(134\) −9.25544 −0.799548
\(135\) 0 0
\(136\) −2.11684 −0.181518
\(137\) 14.3537i 1.22632i −0.789958 0.613161i \(-0.789898\pi\)
0.789958 0.613161i \(-0.210102\pi\)
\(138\) 0 0
\(139\) −11.1168 −0.942918 −0.471459 0.881888i \(-0.656273\pi\)
−0.471459 + 0.881888i \(0.656273\pi\)
\(140\) −10.1168 + 3.26172i −0.855029 + 0.275666i
\(141\) 0 0
\(142\) 10.3923i 0.872103i
\(143\) 25.5383i 2.13562i
\(144\) 0 0
\(145\) 3.94158 + 12.2255i 0.327330 + 1.01528i
\(146\) −1.88316 −0.155851
\(147\) 0 0
\(148\) 3.26172i 0.268112i
\(149\) −10.6277 −0.870657 −0.435328 0.900272i \(-0.643368\pi\)
−0.435328 + 0.900272i \(0.643368\pi\)
\(150\) 0 0
\(151\) 0.883156 0.0718702 0.0359351 0.999354i \(-0.488559\pi\)
0.0359351 + 0.999354i \(0.488559\pi\)
\(152\) 0.994667i 0.0806781i
\(153\) 0 0
\(154\) 12.0000 0.966988
\(155\) 4.37228 + 13.5615i 0.351190 + 1.08928i
\(156\) 0 0
\(157\) 11.4795i 0.916167i −0.888909 0.458084i \(-0.848536\pi\)
0.888909 0.458084i \(-0.151464\pi\)
\(158\) 5.34363i 0.425116i
\(159\) 0 0
\(160\) −12.4307 + 4.00772i −0.982733 + 0.316838i
\(161\) 5.48913 0.432604
\(162\) 0 0
\(163\) 15.1460i 1.18633i −0.805082 0.593164i \(-0.797878\pi\)
0.805082 0.593164i \(-0.202122\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 9.48913 0.736499
\(167\) 13.5615i 1.04942i 0.851282 + 0.524708i \(0.175826\pi\)
−0.851282 + 0.524708i \(0.824174\pi\)
\(168\) 0 0
\(169\) −21.1168 −1.62437
\(170\) −0.430703 1.33591i −0.0330334 0.102459i
\(171\) 0 0
\(172\) 4.75372i 0.362468i
\(173\) 11.1846i 0.850349i 0.905111 + 0.425174i \(0.139787\pi\)
−0.905111 + 0.425174i \(0.860213\pi\)
\(174\) 0 0
\(175\) −10.1168 14.0588i −0.764762 1.06274i
\(176\) −2.74456 −0.206879
\(177\) 0 0
\(178\) 2.37686i 0.178153i
\(179\) 4.88316 0.364984 0.182492 0.983207i \(-0.441584\pi\)
0.182492 + 0.983207i \(0.441584\pi\)
\(180\) 0 0
\(181\) −13.8614 −1.03031 −0.515155 0.857097i \(-0.672266\pi\)
−0.515155 + 0.857097i \(0.672266\pi\)
\(182\) 16.0309i 1.18829i
\(183\) 0 0
\(184\) 4.23369 0.312112
\(185\) 5.05842 1.63086i 0.371903 0.119903i
\(186\) 0 0
\(187\) 3.46410i 0.253320i
\(188\) 2.57924i 0.188110i
\(189\) 0 0
\(190\) −0.627719 + 0.202380i −0.0455395 + 0.0146822i
\(191\) 7.62772 0.551922 0.275961 0.961169i \(-0.411004\pi\)
0.275961 + 0.961169i \(0.411004\pi\)
\(192\) 0 0
\(193\) 11.4795i 0.826316i −0.910659 0.413158i \(-0.864426\pi\)
0.910659 0.413158i \(-0.135574\pi\)
\(194\) 1.02175 0.0733573
\(195\) 0 0
\(196\) −6.86141 −0.490100
\(197\) 6.43087i 0.458181i 0.973405 + 0.229090i \(0.0735751\pi\)
−0.973405 + 0.229090i \(0.926425\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −7.80298 10.8434i −0.551754 0.766741i
\(201\) 0 0
\(202\) 12.9715i 0.912675i
\(203\) 19.8997i 1.39669i
\(204\) 0 0
\(205\) 3.00000 + 9.30506i 0.209529 + 0.649894i
\(206\) −5.48913 −0.382445
\(207\) 0 0
\(208\) 3.66648i 0.254225i
\(209\) −1.62772 −0.112592
\(210\) 0 0
\(211\) −1.86141 −0.128145 −0.0640723 0.997945i \(-0.520409\pi\)
−0.0640723 + 0.997945i \(0.520409\pi\)
\(212\) 16.4356i 1.12880i
\(213\) 0 0
\(214\) 10.5109 0.718509
\(215\) −7.37228 + 2.37686i −0.502785 + 0.162101i
\(216\) 0 0
\(217\) 22.0742i 1.49850i
\(218\) 7.72049i 0.522898i
\(219\) 0 0
\(220\) −4.11684 12.7692i −0.277558 0.860897i
\(221\) 4.62772 0.311294
\(222\) 0 0
\(223\) 18.6101i 1.24623i 0.782132 + 0.623113i \(0.214132\pi\)
−0.782132 + 0.623113i \(0.785868\pi\)
\(224\) −20.2337 −1.35192
\(225\) 0 0
\(226\) 4.86141 0.323376
\(227\) 13.5615i 0.900105i 0.893002 + 0.450053i \(0.148595\pi\)
−0.893002 + 0.450053i \(0.851405\pi\)
\(228\) 0 0
\(229\) 17.6060 1.16344 0.581718 0.813391i \(-0.302381\pi\)
0.581718 + 0.813391i \(0.302381\pi\)
\(230\) 0.861407 + 2.67181i 0.0567995 + 0.176174i
\(231\) 0 0
\(232\) 15.3484i 1.00767i
\(233\) 6.13592i 0.401977i −0.979594 0.200989i \(-0.935585\pi\)
0.979594 0.200989i \(-0.0644154\pi\)
\(234\) 0 0
\(235\) −4.00000 + 1.28962i −0.260931 + 0.0841256i
\(236\) −2.23369 −0.145401
\(237\) 0 0
\(238\) 2.17448i 0.140951i
\(239\) −22.9783 −1.48634 −0.743170 0.669103i \(-0.766679\pi\)
−0.743170 + 0.669103i \(0.766679\pi\)
\(240\) 0 0
\(241\) −1.51087 −0.0973240 −0.0486620 0.998815i \(-0.515496\pi\)
−0.0486620 + 0.998815i \(0.515496\pi\)
\(242\) 6.43087i 0.413392i
\(243\) 0 0
\(244\) 12.8614 0.823367
\(245\) −3.43070 10.6410i −0.219180 0.679827i
\(246\) 0 0
\(247\) 2.17448i 0.138359i
\(248\) 17.0256i 1.08112i
\(249\) 0 0
\(250\) 5.25544 7.13058i 0.332383 0.450978i
\(251\) −20.2337 −1.27714 −0.638570 0.769564i \(-0.720474\pi\)
−0.638570 + 0.769564i \(0.720474\pi\)
\(252\) 0 0
\(253\) 6.92820i 0.435572i
\(254\) 8.23369 0.516628
\(255\) 0 0
\(256\) −13.8832 −0.867697
\(257\) 6.43087i 0.401147i 0.979679 + 0.200573i \(0.0642805\pi\)
−0.979679 + 0.200573i \(0.935720\pi\)
\(258\) 0 0
\(259\) 8.23369 0.511616
\(260\) 17.0584 5.49972i 1.05792 0.341078i
\(261\) 0 0
\(262\) 3.46410i 0.214013i
\(263\) 26.5330i 1.63609i 0.575151 + 0.818047i \(0.304943\pi\)
−0.575151 + 0.818047i \(0.695057\pi\)
\(264\) 0 0
\(265\) 25.4891 8.21782i 1.56578 0.504817i
\(266\) −1.02175 −0.0626475
\(267\) 0 0
\(268\) 16.0309i 0.979242i
\(269\) 29.2337 1.78241 0.891205 0.453601i \(-0.149861\pi\)
0.891205 + 0.453601i \(0.149861\pi\)
\(270\) 0 0
\(271\) 5.25544 0.319245 0.159623 0.987178i \(-0.448972\pi\)
0.159623 + 0.987178i \(0.448972\pi\)
\(272\) 0.497333i 0.0301553i
\(273\) 0 0
\(274\) 11.3723 0.687025
\(275\) 17.7446 12.7692i 1.07004 0.770010i
\(276\) 0 0
\(277\) 22.0742i 1.32631i −0.748481 0.663156i \(-0.769217\pi\)
0.748481 0.663156i \(-0.230783\pi\)
\(278\) 8.80773i 0.528253i
\(279\) 0 0
\(280\) −6.35053 19.6974i −0.379517 1.17714i
\(281\) −1.37228 −0.0818634 −0.0409317 0.999162i \(-0.513033\pi\)
−0.0409317 + 0.999162i \(0.513033\pi\)
\(282\) 0 0
\(283\) 27.7128i 1.64736i 0.567058 + 0.823678i \(0.308082\pi\)
−0.567058 + 0.823678i \(0.691918\pi\)
\(284\) 18.0000 1.06810
\(285\) 0 0
\(286\) −20.2337 −1.19644
\(287\) 15.1460i 0.894042i
\(288\) 0 0
\(289\) 16.3723 0.963075
\(290\) −9.68614 + 3.12286i −0.568790 + 0.183381i
\(291\) 0 0
\(292\) 3.26172i 0.190878i
\(293\) 0.792287i 0.0462859i 0.999732 + 0.0231430i \(0.00736729\pi\)
−0.999732 + 0.0231430i \(0.992633\pi\)
\(294\) 0 0
\(295\) −1.11684 3.46410i −0.0650252 0.201688i
\(296\) 6.35053 0.369117
\(297\) 0 0
\(298\) 8.42020i 0.487769i
\(299\) −9.25544 −0.535256
\(300\) 0 0
\(301\) −12.0000 −0.691669
\(302\) 0.699713i 0.0402640i
\(303\) 0 0
\(304\) 0.233688 0.0134029
\(305\) 6.43070 + 19.9460i 0.368221 + 1.14211i
\(306\) 0 0
\(307\) 15.1460i 0.864429i −0.901771 0.432215i \(-0.857732\pi\)
0.901771 0.432215i \(-0.142268\pi\)
\(308\) 20.7846i 1.18431i
\(309\) 0 0
\(310\) −10.7446 + 3.46410i −0.610250 + 0.196748i
\(311\) −15.8614 −0.899418 −0.449709 0.893175i \(-0.648472\pi\)
−0.449709 + 0.893175i \(0.648472\pi\)
\(312\) 0 0
\(313\) 24.4511i 1.38206i −0.722827 0.691029i \(-0.757158\pi\)
0.722827 0.691029i \(-0.242842\pi\)
\(314\) 9.09509 0.513266
\(315\) 0 0
\(316\) −9.25544 −0.520659
\(317\) 29.4998i 1.65687i −0.560084 0.828436i \(-0.689231\pi\)
0.560084 0.828436i \(-0.310769\pi\)
\(318\) 0 0
\(319\) −25.1168 −1.40627
\(320\) −2.31386 7.17687i −0.129349 0.401199i
\(321\) 0 0
\(322\) 4.34896i 0.242358i
\(323\) 0.294954i 0.0164117i
\(324\) 0 0
\(325\) 17.0584 + 23.7051i 0.946231 + 1.31492i
\(326\) 12.0000 0.664619
\(327\) 0 0
\(328\) 11.6819i 0.645026i
\(329\) −6.51087 −0.358956
\(330\) 0 0
\(331\) 9.11684 0.501107 0.250554 0.968103i \(-0.419387\pi\)
0.250554 + 0.968103i \(0.419387\pi\)
\(332\) 16.4356i 0.902023i
\(333\) 0 0
\(334\) −10.7446 −0.587916
\(335\) −24.8614 + 8.01544i −1.35832 + 0.437930i
\(336\) 0 0
\(337\) 6.92820i 0.377403i 0.982034 + 0.188702i \(0.0604279\pi\)
−0.982034 + 0.188702i \(0.939572\pi\)
\(338\) 16.7306i 0.910025i
\(339\) 0 0
\(340\) −2.31386 + 0.746000i −0.125487 + 0.0404575i
\(341\) −27.8614 −1.50878
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) −9.25544 −0.499020
\(345\) 0 0
\(346\) −8.86141 −0.476392
\(347\) 2.87419i 0.154295i −0.997020 0.0771474i \(-0.975419\pi\)
0.997020 0.0771474i \(-0.0245812\pi\)
\(348\) 0 0
\(349\) 26.6060 1.42418 0.712092 0.702086i \(-0.247748\pi\)
0.712092 + 0.702086i \(0.247748\pi\)
\(350\) 11.1386 8.01544i 0.595383 0.428443i
\(351\) 0 0
\(352\) 25.5383i 1.36120i
\(353\) 1.87953i 0.100037i 0.998748 + 0.0500186i \(0.0159281\pi\)
−0.998748 + 0.0500186i \(0.984072\pi\)
\(354\) 0 0
\(355\) 9.00000 + 27.9152i 0.477670 + 1.48158i
\(356\) 4.11684 0.218192
\(357\) 0 0
\(358\) 3.86886i 0.204476i
\(359\) 10.8832 0.574391 0.287196 0.957872i \(-0.407277\pi\)
0.287196 + 0.957872i \(0.407277\pi\)
\(360\) 0 0
\(361\) −18.8614 −0.992706
\(362\) 10.9822i 0.577212i
\(363\) 0 0
\(364\) 27.7663 1.45535
\(365\) −5.05842 + 1.63086i −0.264770 + 0.0853632i
\(366\) 0 0
\(367\) 16.4356i 0.857934i −0.903320 0.428967i \(-0.858878\pi\)
0.903320 0.428967i \(-0.141122\pi\)
\(368\) 0.994667i 0.0518506i
\(369\) 0 0
\(370\) 1.29211 + 4.00772i 0.0671736 + 0.208352i
\(371\) 41.4891 2.15401
\(372\) 0 0
\(373\) 8.21782i 0.425503i −0.977106 0.212751i \(-0.931758\pi\)
0.977106 0.212751i \(-0.0682424\pi\)
\(374\) 2.74456 0.141918
\(375\) 0 0
\(376\) −5.02175 −0.258977
\(377\) 33.5538i 1.72811i
\(378\) 0 0
\(379\) 1.48913 0.0764912 0.0382456 0.999268i \(-0.487823\pi\)
0.0382456 + 0.999268i \(0.487823\pi\)
\(380\) 0.350532 + 1.08724i 0.0179819 + 0.0557743i
\(381\) 0 0
\(382\) 6.04334i 0.309204i
\(383\) 11.0920i 0.566776i −0.959005 0.283388i \(-0.908542\pi\)
0.959005 0.283388i \(-0.0914584\pi\)
\(384\) 0 0
\(385\) 32.2337 10.3923i 1.64278 0.529641i
\(386\) 9.09509 0.462928
\(387\) 0 0
\(388\) 1.76972i 0.0898440i
\(389\) 0.510875 0.0259024 0.0129512 0.999916i \(-0.495877\pi\)
0.0129512 + 0.999916i \(0.495877\pi\)
\(390\) 0 0
\(391\) 1.25544 0.0634902
\(392\) 13.3591i 0.674735i
\(393\) 0 0
\(394\) −5.09509 −0.256687
\(395\) −4.62772 14.3537i −0.232846 0.722215i
\(396\) 0 0
\(397\) 17.5229i 0.879449i 0.898133 + 0.439724i \(0.144924\pi\)
−0.898133 + 0.439724i \(0.855076\pi\)
\(398\) 12.6766i 0.635420i
\(399\) 0 0
\(400\) −2.54755 + 1.83324i −0.127377 + 0.0916620i
\(401\) 25.3723 1.26703 0.633516 0.773730i \(-0.281611\pi\)
0.633516 + 0.773730i \(0.281611\pi\)
\(402\) 0 0
\(403\) 37.2203i 1.85407i
\(404\) −22.4674 −1.11779
\(405\) 0 0
\(406\) −15.7663 −0.782469
\(407\) 10.3923i 0.515127i
\(408\) 0 0
\(409\) −22.8614 −1.13042 −0.565212 0.824946i \(-0.691206\pi\)
−0.565212 + 0.824946i \(0.691206\pi\)
\(410\) −7.37228 + 2.37686i −0.364091 + 0.117385i
\(411\) 0 0
\(412\) 9.50744i 0.468398i
\(413\) 5.63858i 0.277457i
\(414\) 0 0
\(415\) 25.4891 8.21782i 1.25121 0.403397i
\(416\) 34.1168 1.67272
\(417\) 0 0
\(418\) 1.28962i 0.0630774i
\(419\) 17.4891 0.854400 0.427200 0.904157i \(-0.359500\pi\)
0.427200 + 0.904157i \(0.359500\pi\)
\(420\) 0 0
\(421\) −21.7446 −1.05977 −0.529883 0.848071i \(-0.677764\pi\)
−0.529883 + 0.848071i \(0.677764\pi\)
\(422\) 1.47477i 0.0717906i
\(423\) 0 0
\(424\) 32.0000 1.55406
\(425\) −2.31386 3.21543i −0.112239 0.155972i
\(426\) 0 0
\(427\) 32.4665i 1.57117i
\(428\) 18.2054i 0.879990i
\(429\) 0 0
\(430\) −1.88316 5.84096i −0.0908138 0.281676i
\(431\) −33.3505 −1.60644 −0.803219 0.595683i \(-0.796881\pi\)
−0.803219 + 0.595683i \(0.796881\pi\)
\(432\) 0 0
\(433\) 12.7692i 0.613647i 0.951766 + 0.306823i \(0.0992661\pi\)
−0.951766 + 0.306823i \(0.900734\pi\)
\(434\) −17.4891 −0.839505
\(435\) 0 0
\(436\) −13.3723 −0.640416
\(437\) 0.589907i 0.0282191i
\(438\) 0 0
\(439\) −31.8614 −1.52066 −0.760331 0.649536i \(-0.774963\pi\)
−0.760331 + 0.649536i \(0.774963\pi\)
\(440\) 24.8614 8.01544i 1.18522 0.382121i
\(441\) 0 0
\(442\) 3.66648i 0.174397i
\(443\) 21.4843i 1.02075i −0.859952 0.510375i \(-0.829506\pi\)
0.859952 0.510375i \(-0.170494\pi\)
\(444\) 0 0
\(445\) 2.05842 + 6.38458i 0.0975786 + 0.302658i
\(446\) −14.7446 −0.698175
\(447\) 0 0
\(448\) 11.6819i 0.551919i
\(449\) 10.8832 0.513608 0.256804 0.966464i \(-0.417331\pi\)
0.256804 + 0.966464i \(0.417331\pi\)
\(450\) 0 0
\(451\) −19.1168 −0.900177
\(452\) 8.42020i 0.396053i
\(453\) 0 0
\(454\) −10.7446 −0.504267
\(455\) 13.8832 + 43.0612i 0.650852 + 2.01874i
\(456\) 0 0
\(457\) 20.9870i 0.981730i 0.871236 + 0.490865i \(0.163319\pi\)
−0.871236 + 0.490865i \(0.836681\pi\)
\(458\) 13.9490i 0.651793i
\(459\) 0 0
\(460\) 4.62772 1.49200i 0.215768 0.0695649i
\(461\) 24.0951 1.12222 0.561110 0.827741i \(-0.310374\pi\)
0.561110 + 0.827741i \(0.310374\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i −0.946746 0.321981i \(-0.895651\pi\)
0.946746 0.321981i \(-0.104349\pi\)
\(464\) 3.60597 0.167403
\(465\) 0 0
\(466\) 4.86141 0.225200
\(467\) 18.3152i 0.847525i 0.905773 + 0.423763i \(0.139291\pi\)
−0.905773 + 0.423763i \(0.860709\pi\)
\(468\) 0 0
\(469\) −40.4674 −1.86861
\(470\) −1.02175 3.16915i −0.0471298 0.146182i
\(471\) 0 0
\(472\) 4.34896i 0.200177i
\(473\) 15.1460i 0.696415i
\(474\) 0 0
\(475\) −1.51087 + 1.08724i −0.0693237 + 0.0498860i
\(476\) −3.76631 −0.172629
\(477\) 0 0
\(478\) 18.2054i 0.832694i
\(479\) −18.6060 −0.850128 −0.425064 0.905163i \(-0.639748\pi\)
−0.425064 + 0.905163i \(0.639748\pi\)
\(480\) 0 0
\(481\) −13.8832 −0.633017
\(482\) 1.19705i 0.0545240i
\(483\) 0 0
\(484\) 11.1386 0.506300
\(485\) 2.74456 0.884861i 0.124624 0.0401795i
\(486\) 0 0
\(487\) 9.50744i 0.430823i −0.976523 0.215412i \(-0.930891\pi\)
0.976523 0.215412i \(-0.0691093\pi\)
\(488\) 25.0410i 1.13355i
\(489\) 0 0
\(490\) 8.43070 2.71810i 0.380860 0.122791i
\(491\) −31.6277 −1.42734 −0.713669 0.700483i \(-0.752968\pi\)
−0.713669 + 0.700483i \(0.752968\pi\)
\(492\) 0 0
\(493\) 4.55134i 0.204982i
\(494\) 1.72281 0.0775130
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 45.4381i 2.03818i
\(498\) 0 0
\(499\) 24.3723 1.09105 0.545527 0.838094i \(-0.316330\pi\)
0.545527 + 0.838094i \(0.316330\pi\)
\(500\) −12.3505 9.10268i −0.552333 0.407084i
\(501\) 0 0
\(502\) 16.0309i 0.715494i
\(503\) 3.16915i 0.141305i 0.997501 + 0.0706527i \(0.0225082\pi\)
−0.997501 + 0.0706527i \(0.977492\pi\)
\(504\) 0 0
\(505\) −11.2337 34.8434i −0.499893 1.55051i
\(506\) −5.48913 −0.244021
\(507\) 0 0
\(508\) 14.2612i 0.632737i
\(509\) −0.510875 −0.0226441 −0.0113221 0.999936i \(-0.503604\pi\)
−0.0113221 + 0.999936i \(0.503604\pi\)
\(510\) 0 0
\(511\) −8.23369 −0.364237
\(512\) 7.02078i 0.310277i
\(513\) 0 0
\(514\) −5.09509 −0.224735
\(515\) −14.7446 + 4.75372i −0.649723 + 0.209474i
\(516\) 0 0
\(517\) 8.21782i 0.361419i
\(518\) 6.52344i 0.286624i
\(519\) 0 0
\(520\) 10.7079 + 33.2125i 0.469572 + 1.45647i
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 4.75372i 0.207866i 0.994584 + 0.103933i \(0.0331427\pi\)
−0.994584 + 0.103933i \(0.966857\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) −21.0217 −0.916592
\(527\) 5.04868i 0.219924i
\(528\) 0 0
\(529\) 20.4891 0.890832
\(530\) 6.51087 + 20.1947i 0.282814 + 0.877202i
\(531\) 0 0
\(532\) 1.76972i 0.0767272i
\(533\) 25.5383i 1.10619i
\(534\) 0 0
\(535\) 28.2337 9.10268i 1.22065 0.393543i
\(536\) −31.2119 −1.34815
\(537\) 0 0
\(538\) 23.1615i 0.998562i
\(539\) 21.8614 0.941637
\(540\) 0 0
\(541\) 19.2337 0.826921 0.413460 0.910522i \(-0.364320\pi\)
0.413460 + 0.910522i \(0.364320\pi\)
\(542\) 4.16381i 0.178851i
\(543\) 0 0
\(544\) −4.62772 −0.198412
\(545\) −6.68614 20.7383i −0.286403 0.888332i
\(546\) 0 0
\(547\) 6.92820i 0.296229i −0.988970 0.148114i \(-0.952680\pi\)
0.988970 0.148114i \(-0.0473203\pi\)
\(548\) 19.6974i 0.841430i
\(549\) 0 0
\(550\) 10.1168 + 14.0588i 0.431384 + 0.599469i
\(551\) 2.13859 0.0911071
\(552\) 0 0
\(553\) 23.3639i 0.993532i
\(554\) 17.4891 0.743042
\(555\) 0 0
\(556\) −15.2554 −0.646975
\(557\) 25.0410i 1.06102i 0.847678 + 0.530511i \(0.178000\pi\)
−0.847678 + 0.530511i \(0.822000\pi\)
\(558\) 0 0
\(559\) 20.2337 0.855794
\(560\) −4.62772 + 1.49200i −0.195557 + 0.0630485i
\(561\) 0 0
\(562\) 1.08724i 0.0458625i
\(563\) 32.1716i 1.35587i 0.735122 + 0.677935i \(0.237125\pi\)
−0.735122 + 0.677935i \(0.762875\pi\)
\(564\) 0 0
\(565\) 13.0584 4.21010i 0.549372 0.177120i
\(566\) −21.9565 −0.922901
\(567\) 0 0
\(568\) 35.0458i 1.47049i
\(569\) −20.4891 −0.858949 −0.429474 0.903079i \(-0.641301\pi\)
−0.429474 + 0.903079i \(0.641301\pi\)
\(570\) 0 0
\(571\) 4.13859 0.173195 0.0865974 0.996243i \(-0.472401\pi\)
0.0865974 + 0.996243i \(0.472401\pi\)
\(572\) 35.0458i 1.46534i
\(573\) 0 0
\(574\) −12.0000 −0.500870
\(575\) 4.62772 + 6.43087i 0.192989 + 0.268186i
\(576\) 0 0
\(577\) 18.4077i 0.766325i 0.923681 + 0.383162i \(0.125165\pi\)
−0.923681 + 0.383162i \(0.874835\pi\)
\(578\) 12.9715i 0.539545i
\(579\) 0 0
\(580\) 5.40895 + 16.7769i 0.224595 + 0.696622i
\(581\) 41.4891 1.72126
\(582\) 0 0
\(583\) 52.3663i 2.16879i
\(584\) −6.35053 −0.262787
\(585\) 0 0
\(586\) −0.627719 −0.0259308
\(587\) 16.7306i 0.690546i −0.938502 0.345273i \(-0.887786\pi\)
0.938502 0.345273i \(-0.112214\pi\)
\(588\) 0 0
\(589\) 2.37228 0.0977481
\(590\) 2.74456 0.884861i 0.112992 0.0364291i
\(591\) 0 0
\(592\) 1.49200i 0.0613208i
\(593\) 1.67715i 0.0688722i 0.999407 + 0.0344361i \(0.0109635\pi\)
−0.999407 + 0.0344361i \(0.989036\pi\)
\(594\) 0 0
\(595\) −1.88316 5.84096i −0.0772019 0.239456i
\(596\) −14.5842 −0.597393
\(597\) 0 0
\(598\) 7.33296i 0.299867i
\(599\) −1.62772 −0.0665068 −0.0332534 0.999447i \(-0.510587\pi\)
−0.0332534 + 0.999447i \(0.510587\pi\)
\(600\) 0 0
\(601\) −17.9783 −0.733348 −0.366674 0.930349i \(-0.619504\pi\)
−0.366674 + 0.930349i \(0.619504\pi\)
\(602\) 9.50744i 0.387494i
\(603\) 0 0
\(604\) 1.21194 0.0493131
\(605\) 5.56930 + 17.2742i 0.226424 + 0.702297i
\(606\) 0 0
\(607\) 43.2636i 1.75602i −0.478647 0.878008i \(-0.658872\pi\)
0.478647 0.878008i \(-0.341128\pi\)
\(608\) 2.17448i 0.0881869i
\(609\) 0 0
\(610\) −15.8030 + 5.09496i −0.639844 + 0.206289i
\(611\) 10.9783 0.444132
\(612\) 0 0
\(613\) 30.2921i 1.22348i 0.791057 + 0.611742i \(0.209531\pi\)
−0.791057 + 0.611742i \(0.790469\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 40.4674 1.63048
\(617\) 20.6920i 0.833030i 0.909129 + 0.416515i \(0.136749\pi\)
−0.909129 + 0.416515i \(0.863251\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 6.00000 + 18.6101i 0.240966 + 0.747401i
\(621\) 0 0
\(622\) 12.5668i 0.503882i
\(623\) 10.3923i 0.416359i
\(624\) 0 0
\(625\) 7.94158 23.7051i 0.317663 0.948204i
\(626\) 19.3723 0.774272
\(627\) 0 0
\(628\) 15.7532i 0.628620i
\(629\) 1.88316 0.0750863
\(630\) 0 0
\(631\) 6.37228 0.253677 0.126838 0.991923i \(-0.459517\pi\)
0.126838 + 0.991923i \(0.459517\pi\)
\(632\) 18.0202i 0.716806i
\(633\) 0 0
\(634\) 23.3723 0.928232
\(635\) 22.1168 7.13058i 0.877680 0.282969i
\(636\) 0 0
\(637\) 29.2048i 1.15714i
\(638\) 19.8997i 0.787839i
\(639\) 0 0
\(640\) −19.1753 + 6.18220i −0.757969 + 0.244373i
\(641\) 7.97825 0.315122 0.157561 0.987509i \(-0.449637\pi\)
0.157561 + 0.987509i \(0.449637\pi\)
\(642\) 0 0
\(643\) 1.28962i 0.0508577i 0.999677 + 0.0254288i \(0.00809512\pi\)
−0.999677 + 0.0254288i \(0.991905\pi\)
\(644\) 7.53262 0.296827
\(645\) 0 0
\(646\) −0.233688 −0.00919433
\(647\) 28.7075i 1.12861i 0.825567 + 0.564304i \(0.190855\pi\)
−0.825567 + 0.564304i \(0.809145\pi\)
\(648\) 0 0
\(649\) 7.11684 0.279361
\(650\) −18.7812 + 13.5152i −0.736661 + 0.530108i
\(651\) 0 0
\(652\) 20.7846i 0.813988i
\(653\) 6.33830i 0.248037i −0.992280 0.124018i \(-0.960422\pi\)
0.992280 0.124018i \(-0.0395782\pi\)
\(654\) 0 0
\(655\) 3.00000 + 9.30506i 0.117220 + 0.363579i
\(656\) 2.74456 0.107157
\(657\) 0 0
\(658\) 5.15848i 0.201099i
\(659\) −21.2554 −0.827994 −0.413997 0.910278i \(-0.635868\pi\)
−0.413997 + 0.910278i \(0.635868\pi\)
\(660\) 0 0
\(661\) −15.2337 −0.592522 −0.296261 0.955107i \(-0.595740\pi\)
−0.296261 + 0.955107i \(0.595740\pi\)
\(662\) 7.22316i 0.280736i
\(663\) 0 0
\(664\) 32.0000 1.24184
\(665\) −2.74456 + 0.884861i −0.106430 + 0.0343134i
\(666\) 0 0
\(667\) 9.10268i 0.352457i
\(668\) 18.6101i 0.720047i
\(669\) 0 0
\(670\) −6.35053 19.6974i −0.245342 0.760976i
\(671\) −40.9783 −1.58195
\(672\) 0 0
\(673\) 10.5947i 0.408395i 0.978930 + 0.204198i \(0.0654585\pi\)
−0.978930 + 0.204198i \(0.934542\pi\)
\(674\) −5.48913 −0.211433
\(675\) 0 0
\(676\) −28.9783 −1.11455
\(677\) 26.5330i 1.01975i 0.860250 + 0.509873i \(0.170308\pi\)
−0.860250 + 0.509873i \(0.829692\pi\)
\(678\) 0 0
\(679\) 4.46738 0.171442
\(680\) −1.45245 4.50506i −0.0556990 0.172761i
\(681\) 0 0
\(682\) 22.0742i 0.845266i
\(683\) 27.1229i 1.03783i −0.854826 0.518915i \(-0.826336\pi\)
0.854826 0.518915i \(-0.173664\pi\)
\(684\) 0 0
\(685\) 30.5475 9.84868i 1.16716 0.376299i
\(686\) −5.48913 −0.209576
\(687\) 0 0
\(688\) 2.17448i 0.0829013i
\(689\) −69.9565 −2.66513
\(690\) 0 0
\(691\) 45.7228 1.73938 0.869689 0.493600i \(-0.164319\pi\)
0.869689 + 0.493600i \(0.164319\pi\)
\(692\) 15.3484i 0.583459i
\(693\) 0 0
\(694\) 2.27719 0.0864408
\(695\) −7.62772 23.6588i −0.289336 0.897430i
\(696\) 0 0
\(697\) 3.46410i 0.131212i
\(698\) 21.0796i 0.797873i
\(699\) 0 0
\(700\) −13.8832 19.2926i −0.524734 0.729192i
\(701\) 17.2337 0.650907 0.325454 0.945558i \(-0.394483\pi\)
0.325454 + 0.945558i \(0.394483\pi\)
\(702\) 0 0
\(703\) 0.884861i 0.0333732i
\(704\) 14.7446 0.555707
\(705\) 0 0
\(706\) −1.48913 −0.0560440
\(707\) 56.7152i 2.13300i
\(708\) 0 0
\(709\) −52.3505 −1.96607 −0.983033 0.183430i \(-0.941280\pi\)
−0.983033 + 0.183430i \(0.941280\pi\)
\(710\) −22.1168 + 7.13058i −0.830030 + 0.267606i
\(711\) 0 0
\(712\) 8.01544i 0.300391i
\(713\) 10.0974i 0.378149i
\(714\) 0 0
\(715\) −54.3505 + 17.5229i −2.03259 + 0.655319i
\(716\) 6.70106 0.250431
\(717\) 0 0
\(718\) 8.62258i 0.321792i
\(719\) −10.8832 −0.405873 −0.202937 0.979192i \(-0.565049\pi\)
−0.202937 + 0.979192i \(0.565049\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 14.9436i 0.556145i
\(723\) 0 0
\(724\) −19.0217 −0.706938
\(725\) −23.3139 + 16.7769i −0.865855 + 0.623078i
\(726\) 0 0
\(727\) 48.9022i 1.81368i 0.421473 + 0.906841i \(0.361513\pi\)
−0.421473 + 0.906841i \(0.638487\pi\)
\(728\) 54.0607i 2.00362i
\(729\) 0 0
\(730\) −1.29211 4.00772i −0.0478231 0.148332i
\(731\) −2.74456 −0.101511
\(732\) 0 0
\(733\) 16.4356i 0.607064i 0.952821 + 0.303532i \(0.0981660\pi\)
−0.952821 + 0.303532i \(0.901834\pi\)
\(734\) 13.0217 0.480642
\(735\) 0 0
\(736\) 9.25544 0.341160
\(737\) 51.0767i 1.88143i
\(738\) 0 0
\(739\) −5.62772 −0.207019 −0.103509 0.994628i \(-0.533007\pi\)
−0.103509 + 0.994628i \(0.533007\pi\)
\(740\) 6.94158 2.23800i 0.255177 0.0822705i
\(741\) 0 0
\(742\) 32.8713i 1.20674i
\(743\) 9.39764i 0.344766i −0.985030 0.172383i \(-0.944853\pi\)
0.985030 0.172383i \(-0.0551467\pi\)
\(744\) 0 0
\(745\) −7.29211 22.6179i −0.267162 0.828654i
\(746\) 6.51087 0.238380
\(747\) 0 0
\(748\) 4.75372i 0.173813i
\(749\) 45.9565 1.67921
\(750\) 0 0
\(751\) 21.7228 0.792677 0.396338 0.918105i \(-0.370281\pi\)
0.396338 + 0.918105i \(0.370281\pi\)
\(752\) 1.17981i 0.0430234i
\(753\) 0 0
\(754\) 26.5842 0.968140
\(755\) 0.605969 + 1.87953i 0.0220535 + 0.0684030i
\(756\) 0 0
\(757\) 41.5692i 1.51086i −0.655230 0.755429i \(-0.727428\pi\)
0.655230 0.755429i \(-0.272572\pi\)
\(758\) 1.17981i 0.0428528i
\(759\) 0 0
\(760\) −2.11684 + 0.682481i −0.0767860 + 0.0247562i
\(761\) 32.4891 1.17773 0.588865 0.808231i \(-0.299575\pi\)
0.588865 + 0.808231i \(0.299575\pi\)
\(762\) 0 0
\(763\) 33.7562i 1.22205i
\(764\) 10.4674 0.378696
\(765\) 0 0
\(766\) 8.78806 0.317526
\(767\) 9.50744i 0.343294i
\(768\) 0 0
\(769\) 16.4891 0.594613 0.297307 0.954782i \(-0.403912\pi\)
0.297307 + 0.954782i \(0.403912\pi\)
\(770\) 8.23369 + 25.5383i 0.296722 + 0.920338i
\(771\) 0 0
\(772\) 15.7532i 0.566969i
\(773\) 21.5769i 0.776067i 0.921645 + 0.388034i \(0.126846\pi\)
−0.921645 + 0.388034i \(0.873154\pi\)
\(774\) 0 0
\(775\) −25.8614 + 18.6101i −0.928969 + 0.668496i
\(776\) 3.44563 0.123691
\(777\) 0 0
\(778\) 0.404759i 0.0145113i
\(779\) 1.62772 0.0583191
\(780\) 0 0
\(781\) −57.3505 −2.05216
\(782\) 0.994667i 0.0355692i
\(783\) 0 0
\(784\) −3.13859 −0.112093
\(785\) 24.4307 7.87658i 0.871969 0.281127i
\(786\) 0 0
\(787\) 17.3205i 0.617409i 0.951158 + 0.308705i \(0.0998955\pi\)
−0.951158 + 0.308705i \(0.900105\pi\)
\(788\) 8.82496i 0.314376i
\(789\) 0 0
\(790\) 11.3723 3.66648i 0.404608