Properties

Label 405.2.b.a.244.4
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 244.4
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.2.b.a.244.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.52434i q^{2} -4.37228 q^{4} +(-2.18614 - 0.469882i) q^{5} -3.46410i q^{7} -5.98844i q^{8} +O(q^{10})\) \(q+2.52434i q^{2} -4.37228 q^{4} +(-2.18614 - 0.469882i) q^{5} -3.46410i q^{7} -5.98844i q^{8} +(1.18614 - 5.51856i) q^{10} +1.37228 q^{11} -4.10891i q^{13} +8.74456 q^{14} +6.37228 q^{16} +2.52434i q^{17} -5.37228 q^{19} +(9.55842 + 2.05446i) q^{20} +3.46410i q^{22} -5.04868i q^{23} +(4.55842 + 2.05446i) q^{25} +10.3723 q^{26} +15.1460i q^{28} -5.74456 q^{29} +0.627719 q^{31} +4.10891i q^{32} -6.37228 q^{34} +(-1.62772 + 7.57301i) q^{35} -7.57301i q^{37} -13.5615i q^{38} +(-2.81386 + 13.0916i) q^{40} -1.37228 q^{41} -3.46410i q^{43} -6.00000 q^{44} +12.7446 q^{46} -8.51278i q^{47} -5.00000 q^{49} +(-5.18614 + 11.5070i) q^{50} +17.9653i q^{52} +5.34363i q^{53} +(-3.00000 - 0.644810i) q^{55} -20.7446 q^{56} -14.5012i q^{58} -7.37228 q^{59} +3.62772 q^{61} +1.58457i q^{62} +2.37228 q^{64} +(-1.93070 + 8.98266i) q^{65} +8.21782i q^{67} -11.0371i q^{68} +(-19.1168 - 4.10891i) q^{70} -4.11684 q^{71} +7.57301i q^{73} +19.1168 q^{74} +23.4891 q^{76} -4.75372i q^{77} +4.74456 q^{79} +(-13.9307 - 2.99422i) q^{80} -3.46410i q^{82} +5.34363i q^{83} +(1.18614 - 5.51856i) q^{85} +8.74456 q^{86} -8.21782i q^{88} +3.00000 q^{89} -14.2337 q^{91} +22.0742i q^{92} +21.4891 q^{94} +(11.7446 + 2.52434i) q^{95} -18.6101i q^{97} -12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{4} - 3 q^{5}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52434i 1.78498i 0.451071 + 0.892488i \(0.351042\pi\)
−0.451071 + 0.892488i \(0.648958\pi\)
\(3\) 0 0
\(4\) −4.37228 −2.18614
\(5\) −2.18614 0.469882i −0.977672 0.210138i
\(6\) 0 0
\(7\) 3.46410i 1.30931i −0.755929 0.654654i \(-0.772814\pi\)
0.755929 0.654654i \(-0.227186\pi\)
\(8\) 5.98844i 2.11723i
\(9\) 0 0
\(10\) 1.18614 5.51856i 0.375091 1.74512i
\(11\) 1.37228 0.413758 0.206879 0.978366i \(-0.433669\pi\)
0.206879 + 0.978366i \(0.433669\pi\)
\(12\) 0 0
\(13\) 4.10891i 1.13961i −0.821781 0.569804i \(-0.807019\pi\)
0.821781 0.569804i \(-0.192981\pi\)
\(14\) 8.74456 2.33708
\(15\) 0 0
\(16\) 6.37228 1.59307
\(17\) 2.52434i 0.612242i 0.951993 + 0.306121i \(0.0990312\pi\)
−0.951993 + 0.306121i \(0.900969\pi\)
\(18\) 0 0
\(19\) −5.37228 −1.23249 −0.616243 0.787556i \(-0.711346\pi\)
−0.616243 + 0.787556i \(0.711346\pi\)
\(20\) 9.55842 + 2.05446i 2.13733 + 0.459390i
\(21\) 0 0
\(22\) 3.46410i 0.738549i
\(23\) 5.04868i 1.05272i −0.850261 0.526361i \(-0.823556\pi\)
0.850261 0.526361i \(-0.176444\pi\)
\(24\) 0 0
\(25\) 4.55842 + 2.05446i 0.911684 + 0.410891i
\(26\) 10.3723 2.03417
\(27\) 0 0
\(28\) 15.1460i 2.86233i
\(29\) −5.74456 −1.06674 −0.533369 0.845883i \(-0.679074\pi\)
−0.533369 + 0.845883i \(0.679074\pi\)
\(30\) 0 0
\(31\) 0.627719 0.112742 0.0563708 0.998410i \(-0.482047\pi\)
0.0563708 + 0.998410i \(0.482047\pi\)
\(32\) 4.10891i 0.726360i
\(33\) 0 0
\(34\) −6.37228 −1.09284
\(35\) −1.62772 + 7.57301i −0.275135 + 1.28007i
\(36\) 0 0
\(37\) 7.57301i 1.24500i −0.782621 0.622498i \(-0.786118\pi\)
0.782621 0.622498i \(-0.213882\pi\)
\(38\) 13.5615i 2.19996i
\(39\) 0 0
\(40\) −2.81386 + 13.0916i −0.444910 + 2.06996i
\(41\) −1.37228 −0.214314 −0.107157 0.994242i \(-0.534175\pi\)
−0.107157 + 0.994242i \(0.534175\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i −0.964486 0.264135i \(-0.914913\pi\)
0.964486 0.264135i \(-0.0850865\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 12.7446 1.87908
\(47\) 8.51278i 1.24172i −0.783923 0.620858i \(-0.786784\pi\)
0.783923 0.620858i \(-0.213216\pi\)
\(48\) 0 0
\(49\) −5.00000 −0.714286
\(50\) −5.18614 + 11.5070i −0.733431 + 1.62734i
\(51\) 0 0
\(52\) 17.9653i 2.49134i
\(53\) 5.34363i 0.734004i 0.930220 + 0.367002i \(0.119616\pi\)
−0.930220 + 0.367002i \(0.880384\pi\)
\(54\) 0 0
\(55\) −3.00000 0.644810i −0.404520 0.0869462i
\(56\) −20.7446 −2.77211
\(57\) 0 0
\(58\) 14.5012i 1.90410i
\(59\) −7.37228 −0.959789 −0.479895 0.877326i \(-0.659325\pi\)
−0.479895 + 0.877326i \(0.659325\pi\)
\(60\) 0 0
\(61\) 3.62772 0.464482 0.232241 0.972658i \(-0.425394\pi\)
0.232241 + 0.972658i \(0.425394\pi\)
\(62\) 1.58457i 0.201241i
\(63\) 0 0
\(64\) 2.37228 0.296535
\(65\) −1.93070 + 8.98266i −0.239474 + 1.11416i
\(66\) 0 0
\(67\) 8.21782i 1.00397i 0.864877 + 0.501983i \(0.167396\pi\)
−0.864877 + 0.501983i \(0.832604\pi\)
\(68\) 11.0371i 1.33845i
\(69\) 0 0
\(70\) −19.1168 4.10891i −2.28490 0.491109i
\(71\) −4.11684 −0.488579 −0.244290 0.969702i \(-0.578555\pi\)
−0.244290 + 0.969702i \(0.578555\pi\)
\(72\) 0 0
\(73\) 7.57301i 0.886354i 0.896434 + 0.443177i \(0.146149\pi\)
−0.896434 + 0.443177i \(0.853851\pi\)
\(74\) 19.1168 2.22229
\(75\) 0 0
\(76\) 23.4891 2.69439
\(77\) 4.75372i 0.541737i
\(78\) 0 0
\(79\) 4.74456 0.533805 0.266903 0.963724i \(-0.414000\pi\)
0.266903 + 0.963724i \(0.414000\pi\)
\(80\) −13.9307 2.99422i −1.55750 0.334764i
\(81\) 0 0
\(82\) 3.46410i 0.382546i
\(83\) 5.34363i 0.586540i 0.956030 + 0.293270i \(0.0947434\pi\)
−0.956030 + 0.293270i \(0.905257\pi\)
\(84\) 0 0
\(85\) 1.18614 5.51856i 0.128655 0.598572i
\(86\) 8.74456 0.942950
\(87\) 0 0
\(88\) 8.21782i 0.876023i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) −14.2337 −1.49210
\(92\) 22.0742i 2.30140i
\(93\) 0 0
\(94\) 21.4891 2.21643
\(95\) 11.7446 + 2.52434i 1.20497 + 0.258992i
\(96\) 0 0
\(97\) 18.6101i 1.88957i −0.327688 0.944786i \(-0.606269\pi\)
0.327688 0.944786i \(-0.393731\pi\)
\(98\) 12.6217i 1.27498i
\(99\) 0 0
\(100\) −19.9307 8.98266i −1.99307 0.898266i
\(101\) −10.6277 −1.05750 −0.528749 0.848778i \(-0.677339\pi\)
−0.528749 + 0.848778i \(0.677339\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) −24.6060 −2.41281
\(105\) 0 0
\(106\) −13.4891 −1.31018
\(107\) 13.2665i 1.28252i −0.767323 0.641260i \(-0.778412\pi\)
0.767323 0.641260i \(-0.221588\pi\)
\(108\) 0 0
\(109\) 1.74456 0.167099 0.0835494 0.996504i \(-0.473374\pi\)
0.0835494 + 0.996504i \(0.473374\pi\)
\(110\) 1.62772 7.57301i 0.155197 0.722058i
\(111\) 0 0
\(112\) 22.0742i 2.08582i
\(113\) 9.45254i 0.889220i 0.895724 + 0.444610i \(0.146658\pi\)
−0.895724 + 0.444610i \(0.853342\pi\)
\(114\) 0 0
\(115\) −2.37228 + 11.0371i −0.221216 + 1.02922i
\(116\) 25.1168 2.33204
\(117\) 0 0
\(118\) 18.6101i 1.71320i
\(119\) 8.74456 0.801613
\(120\) 0 0
\(121\) −9.11684 −0.828804
\(122\) 9.15759i 0.829089i
\(123\) 0 0
\(124\) −2.74456 −0.246469
\(125\) −9.00000 6.63325i −0.804984 0.593296i
\(126\) 0 0
\(127\) 10.3923i 0.922168i 0.887357 + 0.461084i \(0.152539\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 14.2063i 1.25567i
\(129\) 0 0
\(130\) −22.6753 4.87375i −1.98875 0.427456i
\(131\) −1.37228 −0.119897 −0.0599484 0.998201i \(-0.519094\pi\)
−0.0599484 + 0.998201i \(0.519094\pi\)
\(132\) 0 0
\(133\) 18.6101i 1.61370i
\(134\) −20.7446 −1.79206
\(135\) 0 0
\(136\) 15.1168 1.29626
\(137\) 2.22938i 0.190469i −0.995455 0.0952346i \(-0.969640\pi\)
0.995455 0.0952346i \(-0.0303601\pi\)
\(138\) 0 0
\(139\) 6.11684 0.518824 0.259412 0.965767i \(-0.416471\pi\)
0.259412 + 0.965767i \(0.416471\pi\)
\(140\) 7.11684 33.1113i 0.601483 2.79842i
\(141\) 0 0
\(142\) 10.3923i 0.872103i
\(143\) 5.63858i 0.471522i
\(144\) 0 0
\(145\) 12.5584 + 2.69927i 1.04292 + 0.224162i
\(146\) −19.1168 −1.58212
\(147\) 0 0
\(148\) 33.1113i 2.72174i
\(149\) −16.3723 −1.34127 −0.670635 0.741788i \(-0.733978\pi\)
−0.670635 + 0.741788i \(0.733978\pi\)
\(150\) 0 0
\(151\) 18.1168 1.47433 0.737164 0.675714i \(-0.236165\pi\)
0.737164 + 0.675714i \(0.236165\pi\)
\(152\) 32.1716i 2.60946i
\(153\) 0 0
\(154\) 12.0000 0.966988
\(155\) −1.37228 0.294954i −0.110224 0.0236912i
\(156\) 0 0
\(157\) 21.4294i 1.71025i 0.518419 + 0.855127i \(0.326521\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(158\) 11.9769i 0.952829i
\(159\) 0 0
\(160\) 1.93070 8.98266i 0.152635 0.710142i
\(161\) −17.4891 −1.37834
\(162\) 0 0
\(163\) 4.75372i 0.372340i −0.982518 0.186170i \(-0.940392\pi\)
0.982518 0.186170i \(-0.0596076\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −13.4891 −1.04696
\(167\) 0.294954i 0.0228242i −0.999935 0.0114121i \(-0.996367\pi\)
0.999935 0.0114121i \(-0.00363266\pi\)
\(168\) 0 0
\(169\) −3.88316 −0.298704
\(170\) 13.9307 + 2.99422i 1.06844 + 0.229646i
\(171\) 0 0
\(172\) 15.1460i 1.15487i
\(173\) 7.86797i 0.598190i −0.954223 0.299095i \(-0.903315\pi\)
0.954223 0.299095i \(-0.0966848\pi\)
\(174\) 0 0
\(175\) 7.11684 15.7908i 0.537983 1.19368i
\(176\) 8.74456 0.659146
\(177\) 0 0
\(178\) 7.57301i 0.567621i
\(179\) 22.1168 1.65309 0.826545 0.562870i \(-0.190303\pi\)
0.826545 + 0.562870i \(0.190303\pi\)
\(180\) 0 0
\(181\) 14.8614 1.10464 0.552320 0.833632i \(-0.313743\pi\)
0.552320 + 0.833632i \(0.313743\pi\)
\(182\) 35.9306i 2.66336i
\(183\) 0 0
\(184\) −30.2337 −2.22886
\(185\) −3.55842 + 16.5557i −0.261620 + 1.21720i
\(186\) 0 0
\(187\) 3.46410i 0.253320i
\(188\) 37.2203i 2.71457i
\(189\) 0 0
\(190\) −6.37228 + 29.6472i −0.462294 + 2.15084i
\(191\) 13.3723 0.967584 0.483792 0.875183i \(-0.339259\pi\)
0.483792 + 0.875183i \(0.339259\pi\)
\(192\) 0 0
\(193\) 21.4294i 1.54252i 0.636518 + 0.771262i \(0.280374\pi\)
−0.636518 + 0.771262i \(0.719626\pi\)
\(194\) 46.9783 3.37284
\(195\) 0 0
\(196\) 21.8614 1.56153
\(197\) 23.0140i 1.63968i −0.572593 0.819840i \(-0.694063\pi\)
0.572593 0.819840i \(-0.305937\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 12.3030 27.2978i 0.869952 1.93025i
\(201\) 0 0
\(202\) 26.8280i 1.88761i
\(203\) 19.8997i 1.39669i
\(204\) 0 0
\(205\) 3.00000 + 0.644810i 0.209529 + 0.0450355i
\(206\) 17.4891 1.21853
\(207\) 0 0
\(208\) 26.1831i 1.81547i
\(209\) −7.37228 −0.509951
\(210\) 0 0
\(211\) 26.8614 1.84922 0.924608 0.380921i \(-0.124393\pi\)
0.924608 + 0.380921i \(0.124393\pi\)
\(212\) 23.3639i 1.60464i
\(213\) 0 0
\(214\) 33.4891 2.28927
\(215\) −1.62772 + 7.57301i −0.111009 + 0.516475i
\(216\) 0 0
\(217\) 2.17448i 0.147613i
\(218\) 4.40387i 0.298267i
\(219\) 0 0
\(220\) 13.1168 + 2.81929i 0.884337 + 0.190077i
\(221\) 10.3723 0.697715
\(222\) 0 0
\(223\) 1.28962i 0.0863594i 0.999067 + 0.0431797i \(0.0137488\pi\)
−0.999067 + 0.0431797i \(0.986251\pi\)
\(224\) 14.2337 0.951028
\(225\) 0 0
\(226\) −23.8614 −1.58724
\(227\) 0.294954i 0.0195768i −0.999952 0.00978838i \(-0.996884\pi\)
0.999952 0.00978838i \(-0.00311579\pi\)
\(228\) 0 0
\(229\) −22.6060 −1.49384 −0.746922 0.664911i \(-0.768469\pi\)
−0.746922 + 0.664911i \(0.768469\pi\)
\(230\) −27.8614 5.98844i −1.83713 0.394866i
\(231\) 0 0
\(232\) 34.4010i 2.25853i
\(233\) 9.45254i 0.619257i 0.950858 + 0.309628i \(0.100205\pi\)
−0.950858 + 0.309628i \(0.899795\pi\)
\(234\) 0 0
\(235\) −4.00000 + 18.6101i −0.260931 + 1.21399i
\(236\) 32.2337 2.09823
\(237\) 0 0
\(238\) 22.0742i 1.43086i
\(239\) 22.9783 1.48634 0.743170 0.669103i \(-0.233321\pi\)
0.743170 + 0.669103i \(0.233321\pi\)
\(240\) 0 0
\(241\) −24.4891 −1.57748 −0.788742 0.614725i \(-0.789267\pi\)
−0.788742 + 0.614725i \(0.789267\pi\)
\(242\) 23.0140i 1.47940i
\(243\) 0 0
\(244\) −15.8614 −1.01542
\(245\) 10.9307 + 2.34941i 0.698337 + 0.150098i
\(246\) 0 0
\(247\) 22.0742i 1.40455i
\(248\) 3.75906i 0.238700i
\(249\) 0 0
\(250\) 16.7446 22.7190i 1.05902 1.43688i
\(251\) 14.2337 0.898422 0.449211 0.893426i \(-0.351705\pi\)
0.449211 + 0.893426i \(0.351705\pi\)
\(252\) 0 0
\(253\) 6.92820i 0.435572i
\(254\) −26.2337 −1.64605
\(255\) 0 0
\(256\) −31.1168 −1.94480
\(257\) 23.0140i 1.43557i −0.696263 0.717787i \(-0.745155\pi\)
0.696263 0.717787i \(-0.254845\pi\)
\(258\) 0 0
\(259\) −26.2337 −1.63008
\(260\) 8.44158 39.2747i 0.523524 2.43571i
\(261\) 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
\(265\) 2.51087 11.6819i 0.154242 0.717615i
\(266\) −46.9783 −2.88042
\(267\) 0 0
\(268\) 35.9306i 2.19481i
\(269\) −5.23369 −0.319104 −0.159552 0.987190i \(-0.551005\pi\)
−0.159552 + 0.987190i \(0.551005\pi\)
\(270\) 0 0
\(271\) 16.7446 1.01716 0.508580 0.861015i \(-0.330171\pi\)
0.508580 + 0.861015i \(0.330171\pi\)
\(272\) 16.0858i 0.975344i
\(273\) 0 0
\(274\) 5.62772 0.339983
\(275\) 6.25544 + 2.81929i 0.377217 + 0.170010i
\(276\) 0 0
\(277\) 2.17448i 0.130652i 0.997864 + 0.0653260i \(0.0208087\pi\)
−0.997864 + 0.0653260i \(0.979191\pi\)
\(278\) 15.4410i 0.926088i
\(279\) 0 0
\(280\) 45.3505 + 9.74749i 2.71021 + 0.582524i
\(281\) 4.37228 0.260828 0.130414 0.991460i \(-0.458369\pi\)
0.130414 + 0.991460i \(0.458369\pi\)
\(282\) 0 0
\(283\) 27.7128i 1.64736i −0.567058 0.823678i \(-0.691918\pi\)
0.567058 0.823678i \(-0.308082\pi\)
\(284\) 18.0000 1.06810
\(285\) 0 0
\(286\) 14.2337 0.841656
\(287\) 4.75372i 0.280603i
\(288\) 0 0
\(289\) 10.6277 0.625160
\(290\) −6.81386 + 31.7017i −0.400124 + 1.86159i
\(291\) 0 0
\(292\) 33.1113i 1.93769i
\(293\) 2.52434i 0.147473i 0.997278 + 0.0737367i \(0.0234924\pi\)
−0.997278 + 0.0737367i \(0.976508\pi\)
\(294\) 0 0
\(295\) 16.1168 + 3.46410i 0.938359 + 0.201688i
\(296\) −45.3505 −2.63595
\(297\) 0 0
\(298\) 41.3292i 2.39413i
\(299\) −20.7446 −1.19969
\(300\) 0 0
\(301\) −12.0000 −0.691669
\(302\) 45.7330i 2.63164i
\(303\) 0 0
\(304\) −34.2337 −1.96344
\(305\) −7.93070 1.70460i −0.454111 0.0976051i
\(306\) 0 0
\(307\) 4.75372i 0.271309i −0.990756 0.135655i \(-0.956686\pi\)
0.990756 0.135655i \(-0.0433138\pi\)
\(308\) 20.7846i 1.18431i
\(309\) 0 0
\(310\) 0.744563 3.46410i 0.0422883 0.196748i
\(311\) 12.8614 0.729303 0.364652 0.931144i \(-0.381188\pi\)
0.364652 + 0.931144i \(0.381188\pi\)
\(312\) 0 0
\(313\) 5.39853i 0.305143i −0.988292 0.152572i \(-0.951245\pi\)
0.988292 0.152572i \(-0.0487554\pi\)
\(314\) −54.0951 −3.05276
\(315\) 0 0
\(316\) −20.7446 −1.16697
\(317\) 6.98311i 0.392210i −0.980583 0.196105i \(-0.937171\pi\)
0.980583 0.196105i \(-0.0628294\pi\)
\(318\) 0 0
\(319\) −7.88316 −0.441372
\(320\) −5.18614 1.11469i −0.289914 0.0623132i
\(321\) 0 0
\(322\) 44.1485i 2.46030i
\(323\) 13.5615i 0.754579i
\(324\) 0 0
\(325\) 8.44158 18.7302i 0.468254 1.03896i
\(326\) 12.0000 0.664619
\(327\) 0 0
\(328\) 8.21782i 0.453753i
\(329\) −29.4891 −1.62579
\(330\) 0 0
\(331\) −8.11684 −0.446142 −0.223071 0.974802i \(-0.571608\pi\)
−0.223071 + 0.974802i \(0.571608\pi\)
\(332\) 23.3639i 1.28226i
\(333\) 0 0
\(334\) 0.744563 0.0407407
\(335\) 3.86141 17.9653i 0.210971 0.981550i
\(336\) 0 0
\(337\) 6.92820i 0.377403i −0.982034 0.188702i \(-0.939572\pi\)
0.982034 0.188702i \(-0.0604279\pi\)
\(338\) 9.80240i 0.533180i
\(339\) 0 0
\(340\) −5.18614 + 24.1287i −0.281258 + 1.30856i
\(341\) 0.861407 0.0466478
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) −20.7446 −1.11847
\(345\) 0 0
\(346\) 19.8614 1.06776
\(347\) 23.6588i 1.27007i −0.772483 0.635036i \(-0.780985\pi\)
0.772483 0.635036i \(-0.219015\pi\)
\(348\) 0 0
\(349\) −13.6060 −0.728311 −0.364155 0.931338i \(-0.618642\pi\)
−0.364155 + 0.931338i \(0.618642\pi\)
\(350\) 39.8614 + 17.9653i 2.13068 + 0.960287i
\(351\) 0 0
\(352\) 5.63858i 0.300537i
\(353\) 8.51278i 0.453089i −0.974001 0.226545i \(-0.927257\pi\)
0.974001 0.226545i \(-0.0727429\pi\)
\(354\) 0 0
\(355\) 9.00000 + 1.93443i 0.477670 + 0.102669i
\(356\) −13.1168 −0.695191
\(357\) 0 0
\(358\) 55.8304i 2.95073i
\(359\) 28.1168 1.48395 0.741975 0.670427i \(-0.233889\pi\)
0.741975 + 0.670427i \(0.233889\pi\)
\(360\) 0 0
\(361\) 9.86141 0.519021
\(362\) 37.5152i 1.97176i
\(363\) 0 0
\(364\) 62.2337 3.26193
\(365\) 3.55842 16.5557i 0.186256 0.866564i
\(366\) 0 0
\(367\) 23.3639i 1.21958i −0.792562 0.609792i \(-0.791253\pi\)
0.792562 0.609792i \(-0.208747\pi\)
\(368\) 32.1716i 1.67706i
\(369\) 0 0
\(370\) −41.7921 8.98266i −2.17267 0.466986i
\(371\) 18.5109 0.961037
\(372\) 0 0
\(373\) 11.6819i 0.604867i −0.953170 0.302434i \(-0.902201\pi\)
0.953170 0.302434i \(-0.0977990\pi\)
\(374\) −8.74456 −0.452171
\(375\) 0 0
\(376\) −50.9783 −2.62900
\(377\) 23.6039i 1.21566i
\(378\) 0 0
\(379\) −21.4891 −1.10382 −0.551911 0.833903i \(-0.686101\pi\)
−0.551911 + 0.833903i \(0.686101\pi\)
\(380\) −51.3505 11.0371i −2.63423 0.566192i
\(381\) 0 0
\(382\) 33.7562i 1.72712i
\(383\) 35.3407i 1.80583i −0.429822 0.902913i \(-0.641424\pi\)
0.429822 0.902913i \(-0.358576\pi\)
\(384\) 0 0
\(385\) −2.23369 + 10.3923i −0.113839 + 0.529641i
\(386\) −54.0951 −2.75337
\(387\) 0 0
\(388\) 81.3687i 4.13087i
\(389\) 23.4891 1.19095 0.595473 0.803375i \(-0.296965\pi\)
0.595473 + 0.803375i \(0.296965\pi\)
\(390\) 0 0
\(391\) 12.7446 0.644520
\(392\) 29.9422i 1.51231i
\(393\) 0 0
\(394\) 58.0951 2.92679
\(395\) −10.3723 2.22938i −0.521886 0.112172i
\(396\) 0 0
\(397\) 12.3267i 0.618661i 0.950955 + 0.309331i \(0.100105\pi\)
−0.950955 + 0.309331i \(0.899895\pi\)
\(398\) 40.3894i 2.02454i
\(399\) 0 0
\(400\) 29.0475 + 13.0916i 1.45238 + 0.654579i
\(401\) 19.6277 0.980161 0.490081 0.871677i \(-0.336967\pi\)
0.490081 + 0.871677i \(0.336967\pi\)
\(402\) 0 0
\(403\) 2.57924i 0.128481i
\(404\) 46.4674 2.31184
\(405\) 0 0
\(406\) −50.2337 −2.49306
\(407\) 10.3923i 0.515127i
\(408\) 0 0
\(409\) 5.86141 0.289828 0.144914 0.989444i \(-0.453709\pi\)
0.144914 + 0.989444i \(0.453709\pi\)
\(410\) −1.62772 + 7.57301i −0.0803873 + 0.374004i
\(411\) 0 0
\(412\) 30.2921i 1.49238i
\(413\) 25.5383i 1.25666i
\(414\) 0 0
\(415\) 2.51087 11.6819i 0.123254 0.573443i
\(416\) 16.8832 0.827765
\(417\) 0 0
\(418\) 18.6101i 0.910251i
\(419\) −5.48913 −0.268161 −0.134081 0.990970i \(-0.542808\pi\)
−0.134081 + 0.990970i \(0.542808\pi\)
\(420\) 0 0
\(421\) −10.2554 −0.499819 −0.249910 0.968269i \(-0.580401\pi\)
−0.249910 + 0.968269i \(0.580401\pi\)
\(422\) 67.8073i 3.30081i
\(423\) 0 0
\(424\) 32.0000 1.55406
\(425\) −5.18614 + 11.5070i −0.251565 + 0.558171i
\(426\) 0 0
\(427\) 12.5668i 0.608149i
\(428\) 58.0049i 2.80377i
\(429\) 0 0
\(430\) −19.1168 4.10891i −0.921896 0.198149i
\(431\) 18.3505 0.883914 0.441957 0.897036i \(-0.354284\pi\)
0.441957 + 0.897036i \(0.354284\pi\)
\(432\) 0 0
\(433\) 2.81929i 0.135487i −0.997703 0.0677433i \(-0.978420\pi\)
0.997703 0.0677433i \(-0.0215799\pi\)
\(434\) 5.48913 0.263486
\(435\) 0 0
\(436\) −7.62772 −0.365301
\(437\) 27.1229i 1.29746i
\(438\) 0 0
\(439\) −3.13859 −0.149797 −0.0748984 0.997191i \(-0.523863\pi\)
−0.0748984 + 0.997191i \(0.523863\pi\)
\(440\) −3.86141 + 17.9653i −0.184085 + 0.856463i
\(441\) 0 0
\(442\) 26.1831i 1.24541i
\(443\) 24.9484i 1.18534i −0.805447 0.592668i \(-0.798075\pi\)
0.805447 0.592668i \(-0.201925\pi\)
\(444\) 0 0
\(445\) −6.55842 1.40965i −0.310899 0.0668236i
\(446\) −3.25544 −0.154149
\(447\) 0 0
\(448\) 8.21782i 0.388256i
\(449\) 28.1168 1.32692 0.663458 0.748214i \(-0.269088\pi\)
0.663458 + 0.748214i \(0.269088\pi\)
\(450\) 0 0
\(451\) −1.88316 −0.0886744
\(452\) 41.3292i 1.94396i
\(453\) 0 0
\(454\) 0.744563 0.0349441
\(455\) 31.1168 + 6.68815i 1.45878 + 0.313545i
\(456\) 0 0
\(457\) 8.86263i 0.414577i 0.978280 + 0.207288i \(0.0664638\pi\)
−0.978280 + 0.207288i \(0.933536\pi\)
\(458\) 57.0651i 2.66648i
\(459\) 0 0
\(460\) 10.3723 48.2574i 0.483610 2.25001i
\(461\) −39.0951 −1.82084 −0.910420 0.413685i \(-0.864241\pi\)
−0.910420 + 0.413685i \(0.864241\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i 0.946746 + 0.321981i \(0.104349\pi\)
−0.946746 + 0.321981i \(0.895651\pi\)
\(464\) −36.6060 −1.69939
\(465\) 0 0
\(466\) −23.8614 −1.10536
\(467\) 14.8511i 0.687226i 0.939111 + 0.343613i \(0.111651\pi\)
−0.939111 + 0.343613i \(0.888349\pi\)
\(468\) 0 0
\(469\) 28.4674 1.31450
\(470\) −46.9783 10.0974i −2.16695 0.465756i
\(471\) 0 0
\(472\) 44.1485i 2.03210i
\(473\) 4.75372i 0.218576i
\(474\) 0 0
\(475\) −24.4891 11.0371i −1.12364 0.506418i
\(476\) −38.2337 −1.75244
\(477\) 0 0
\(478\) 58.0049i 2.65308i
\(479\) 21.6060 0.987202 0.493601 0.869688i \(-0.335680\pi\)
0.493601 + 0.869688i \(0.335680\pi\)
\(480\) 0 0
\(481\) −31.1168 −1.41881
\(482\) 61.8188i 2.81577i
\(483\) 0 0
\(484\) 39.8614 1.81188
\(485\) −8.74456 + 40.6844i −0.397070 + 1.84738i
\(486\) 0 0
\(487\) 30.2921i 1.37266i −0.727288 0.686332i \(-0.759220\pi\)
0.727288 0.686332i \(-0.240780\pi\)
\(488\) 21.7244i 0.983416i
\(489\) 0 0
\(490\) −5.93070 + 27.5928i −0.267922 + 1.24652i
\(491\) −37.3723 −1.68659 −0.843294 0.537453i \(-0.819387\pi\)
−0.843294 + 0.537453i \(0.819387\pi\)
\(492\) 0 0
\(493\) 14.5012i 0.653102i
\(494\) −55.7228 −2.50709
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 14.2612i 0.639701i
\(498\) 0 0
\(499\) 18.6277 0.833891 0.416946 0.908931i \(-0.363101\pi\)
0.416946 + 0.908931i \(0.363101\pi\)
\(500\) 39.3505 + 29.0024i 1.75981 + 1.29703i
\(501\) 0 0
\(502\) 35.9306i 1.60366i
\(503\) 10.0974i 0.450219i 0.974334 + 0.225109i \(0.0722739\pi\)
−0.974334 + 0.225109i \(0.927726\pi\)
\(504\) 0 0
\(505\) 23.2337 + 4.99377i 1.03389 + 0.222220i
\(506\) 17.4891 0.777486
\(507\) 0 0
\(508\) 45.4381i 2.01599i
\(509\) −23.4891 −1.04114 −0.520569 0.853820i \(-0.674280\pi\)
−0.520569 + 0.853820i \(0.674280\pi\)
\(510\) 0 0
\(511\) 26.2337 1.16051
\(512\) 50.1369i 2.21576i
\(513\) 0 0
\(514\) 58.0951 2.56246
\(515\) −3.25544 + 15.1460i −0.143452 + 0.667414i
\(516\) 0 0
\(517\) 11.6819i 0.513770i
\(518\) 66.2227i 2.90966i
\(519\) 0 0
\(520\) 53.7921 + 11.5619i 2.35894 + 0.507023i
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 15.1460i 0.662290i 0.943580 + 0.331145i \(0.107435\pi\)
−0.943580 + 0.331145i \(0.892565\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) −66.9783 −2.92039
\(527\) 1.58457i 0.0690251i
\(528\) 0 0
\(529\) −2.48913 −0.108223
\(530\) 29.4891 + 6.33830i 1.28093 + 0.275318i
\(531\) 0 0
\(532\) 81.3687i 3.52778i
\(533\) 5.63858i 0.244234i
\(534\) 0 0
\(535\) −6.23369 + 29.0024i −0.269506 + 1.25388i
\(536\) 49.2119 2.12563
\(537\) 0 0
\(538\) 13.2116i 0.569592i
\(539\) −6.86141 −0.295542
\(540\) 0 0
\(541\) −15.2337 −0.654947 −0.327474 0.944860i \(-0.606197\pi\)
−0.327474 + 0.944860i \(0.606197\pi\)
\(542\) 42.2689i 1.81561i
\(543\) 0 0
\(544\) −10.3723 −0.444708
\(545\) −3.81386 0.819738i −0.163368 0.0351137i
\(546\) 0 0
\(547\) 6.92820i 0.296229i 0.988970 + 0.148114i \(0.0473203\pi\)
−0.988970 + 0.148114i \(0.952680\pi\)
\(548\) 9.74749i 0.416392i
\(549\) 0 0
\(550\) −7.11684 + 15.7908i −0.303463 + 0.673324i
\(551\) 30.8614 1.31474
\(552\) 0 0
\(553\) 16.4356i 0.698915i
\(554\) −5.48913 −0.233211
\(555\) 0 0
\(556\) −26.7446 −1.13422
\(557\) 21.7244i 0.920491i −0.887792 0.460246i \(-0.847761\pi\)
0.887792 0.460246i \(-0.152239\pi\)
\(558\) 0 0
\(559\) −14.2337 −0.602021
\(560\) −10.3723 + 48.2574i −0.438309 + 2.03925i
\(561\) 0 0
\(562\) 11.0371i 0.465573i
\(563\) 0.994667i 0.0419202i 0.999780 + 0.0209601i \(0.00667230\pi\)
−0.999780 + 0.0209601i \(0.993328\pi\)
\(564\) 0 0
\(565\) 4.44158 20.6646i 0.186859 0.869366i
\(566\) 69.9565 2.94049
\(567\) 0 0
\(568\) 24.6535i 1.03444i
\(569\) 2.48913 0.104350 0.0521748 0.998638i \(-0.483385\pi\)
0.0521748 + 0.998638i \(0.483385\pi\)
\(570\) 0 0
\(571\) 32.8614 1.37521 0.687604 0.726086i \(-0.258663\pi\)
0.687604 + 0.726086i \(0.258663\pi\)
\(572\) 24.6535i 1.03081i
\(573\) 0 0
\(574\) −12.0000 −0.500870
\(575\) 10.3723 23.0140i 0.432554 0.959750i
\(576\) 0 0
\(577\) 28.3576i 1.18054i −0.807205 0.590272i \(-0.799021\pi\)
0.807205 0.590272i \(-0.200979\pi\)
\(578\) 26.8280i 1.11590i
\(579\) 0 0
\(580\) −54.9090 11.8020i −2.27997 0.490049i
\(581\) 18.5109 0.767960
\(582\) 0 0
\(583\) 7.33296i 0.303700i
\(584\) 45.3505 1.87662
\(585\) 0 0
\(586\) −6.37228 −0.263237
\(587\) 9.80240i 0.404588i −0.979325 0.202294i \(-0.935160\pi\)
0.979325 0.202294i \(-0.0648397\pi\)
\(588\) 0 0
\(589\) −3.37228 −0.138952
\(590\) −8.74456 + 40.6844i −0.360008 + 1.67495i
\(591\) 0 0
\(592\) 48.2574i 1.98337i
\(593\) 38.1600i 1.56704i −0.621364 0.783522i \(-0.713421\pi\)
0.621364 0.783522i \(-0.286579\pi\)
\(594\) 0 0
\(595\) −19.1168 4.10891i −0.783714 0.168449i
\(596\) 71.5842 2.93220
\(597\) 0 0
\(598\) 52.3663i 2.14142i
\(599\) −7.37228 −0.301223 −0.150612 0.988593i \(-0.548124\pi\)
−0.150612 + 0.988593i \(0.548124\pi\)
\(600\) 0 0
\(601\) 27.9783 1.14126 0.570628 0.821208i \(-0.306700\pi\)
0.570628 + 0.821208i \(0.306700\pi\)
\(602\) 30.2921i 1.23461i
\(603\) 0 0
\(604\) −79.2119 −3.22309
\(605\) 19.9307 + 4.28384i 0.810298 + 0.174163i
\(606\) 0 0
\(607\) 36.3354i 1.47481i −0.675452 0.737404i \(-0.736051\pi\)
0.675452 0.737404i \(-0.263949\pi\)
\(608\) 22.0742i 0.895228i
\(609\) 0 0
\(610\) 4.30298 20.0198i 0.174223 0.810577i
\(611\) −34.9783 −1.41507
\(612\) 0 0
\(613\) 9.50744i 0.384002i 0.981395 + 0.192001i \(0.0614977\pi\)
−0.981395 + 0.192001i \(0.938502\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) −28.4674 −1.14698
\(617\) 22.4241i 0.902760i 0.892332 + 0.451380i \(0.149068\pi\)
−0.892332 + 0.451380i \(0.850932\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 6.00000 + 1.28962i 0.240966 + 0.0517924i
\(621\) 0 0
\(622\) 32.4665i 1.30179i
\(623\) 10.3923i 0.416359i
\(624\) 0 0
\(625\) 16.5584 + 18.7302i 0.662337 + 0.749206i
\(626\) 13.6277 0.544673
\(627\) 0 0
\(628\) 93.6955i 3.73886i
\(629\) 19.1168 0.762238
\(630\) 0 0
\(631\) 0.627719 0.0249891 0.0124945 0.999922i \(-0.496023\pi\)
0.0124945 + 0.999922i \(0.496023\pi\)
\(632\) 28.4125i 1.13019i
\(633\) 0 0
\(634\) 17.6277 0.700086
\(635\) 4.88316 22.7190i 0.193782 0.901578i
\(636\) 0 0
\(637\) 20.5446i 0.814005i
\(638\) 19.8997i 0.787839i
\(639\) 0 0
\(640\) 6.67527 31.0569i 0.263863 1.22763i
\(641\) −37.9783 −1.50005 −0.750025 0.661409i \(-0.769959\pi\)
−0.750025 + 0.661409i \(0.769959\pi\)
\(642\) 0 0
\(643\) 18.6101i 0.733912i 0.930238 + 0.366956i \(0.119600\pi\)
−0.930238 + 0.366956i \(0.880400\pi\)
\(644\) 76.4674 3.01324
\(645\) 0 0
\(646\) 34.2337 1.34691
\(647\) 4.45877i 0.175292i 0.996152 + 0.0876461i \(0.0279345\pi\)
−0.996152 + 0.0876461i \(0.972066\pi\)
\(648\) 0 0
\(649\) −10.1168 −0.397121
\(650\) 47.2812 + 21.3094i 1.85452 + 0.835823i
\(651\) 0 0
\(652\) 20.7846i 0.813988i
\(653\) 20.1947i 0.790280i −0.918621 0.395140i \(-0.870696\pi\)
0.918621 0.395140i \(-0.129304\pi\)
\(654\) 0 0
\(655\) 3.00000 + 0.644810i 0.117220 + 0.0251948i
\(656\) −8.74456 −0.341418
\(657\) 0 0
\(658\) 74.4405i 2.90199i
\(659\) −32.7446 −1.27555 −0.637774 0.770224i \(-0.720144\pi\)
−0.637774 + 0.770224i \(0.720144\pi\)
\(660\) 0 0
\(661\) 19.2337 0.748104 0.374052 0.927408i \(-0.377968\pi\)
0.374052 + 0.927408i \(0.377968\pi\)
\(662\) 20.4897i 0.796353i
\(663\) 0 0
\(664\) 32.0000 1.24184
\(665\) 8.74456 40.6844i 0.339100 1.57767i
\(666\) 0 0
\(667\) 29.0024i 1.12298i
\(668\) 1.28962i 0.0498969i
\(669\) 0 0
\(670\) 45.3505 + 9.74749i 1.75204 + 0.376579i
\(671\) 4.97825 0.192183
\(672\) 0 0
\(673\) 19.2549i 0.742223i 0.928588 + 0.371112i \(0.121023\pi\)
−0.928588 + 0.371112i \(0.878977\pi\)
\(674\) 17.4891 0.673656
\(675\) 0 0
\(676\) 16.9783 0.653010
\(677\) 26.5330i 1.01975i 0.860250 + 0.509873i \(0.170308\pi\)
−0.860250 + 0.509873i \(0.829692\pi\)
\(678\) 0 0
\(679\) −64.4674 −2.47403
\(680\) −33.0475 7.10313i −1.26732 0.272393i
\(681\) 0 0
\(682\) 2.17448i 0.0832652i
\(683\) 0.589907i 0.0225722i 0.999936 + 0.0112861i \(0.00359255\pi\)
−0.999936 + 0.0112861i \(0.996407\pi\)
\(684\) 0 0
\(685\) −1.04755 + 4.87375i −0.0400247 + 0.186216i
\(686\) 17.4891 0.667738
\(687\) 0 0
\(688\) 22.0742i 0.841572i
\(689\) 21.9565 0.836476
\(690\) 0 0
\(691\) −11.7228 −0.445957 −0.222978 0.974823i \(-0.571578\pi\)
−0.222978 + 0.974823i \(0.571578\pi\)
\(692\) 34.4010i 1.30773i
\(693\) 0 0
\(694\) 59.7228 2.26705
\(695\) −13.3723 2.87419i −0.507240 0.109024i
\(696\) 0 0
\(697\) 3.46410i 0.131212i
\(698\) 34.3461i 1.30002i
\(699\) 0 0
\(700\) −31.1168 + 69.0420i −1.17611 + 2.60954i
\(701\) −17.2337 −0.650907 −0.325454 0.945558i \(-0.605517\pi\)
−0.325454 + 0.945558i \(0.605517\pi\)
\(702\) 0 0
\(703\) 40.6844i 1.53444i
\(704\) 3.25544 0.122694
\(705\) 0 0
\(706\) 21.4891 0.808754
\(707\) 36.8155i 1.38459i
\(708\) 0 0
\(709\) −0.649468 −0.0243913 −0.0121956 0.999926i \(-0.503882\pi\)
−0.0121956 + 0.999926i \(0.503882\pi\)
\(710\) −4.88316 + 22.7190i −0.183262 + 0.852630i
\(711\) 0 0
\(712\) 17.9653i 0.673279i
\(713\) 3.16915i 0.118686i
\(714\) 0 0
\(715\) −2.64947 + 12.3267i −0.0990845 + 0.460994i
\(716\) −96.7011 −3.61389
\(717\) 0 0
\(718\) 70.9764i 2.64882i
\(719\) −28.1168 −1.04858 −0.524291 0.851539i \(-0.675669\pi\)
−0.524291 + 0.851539i \(0.675669\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 24.8935i 0.926441i
\(723\) 0 0
\(724\) −64.9783 −2.41490
\(725\) −26.1861 11.8020i −0.972529 0.438313i
\(726\) 0 0
\(727\) 10.7971i 0.400441i 0.979751 + 0.200220i \(0.0641658\pi\)
−0.979751 + 0.200220i \(0.935834\pi\)
\(728\) 85.2376i 3.15911i
\(729\) 0 0
\(730\) 41.7921 + 8.98266i 1.54680 + 0.332463i
\(731\) 8.74456 0.323429
\(732\) 0 0
\(733\) 23.3639i 0.862964i 0.902122 + 0.431482i \(0.142009\pi\)
−0.902122 + 0.431482i \(0.857991\pi\)
\(734\) 58.9783 2.17693
\(735\) 0 0
\(736\) 20.7446 0.764655
\(737\) 11.2772i 0.415400i
\(738\) 0 0
\(739\) −11.3723 −0.418336 −0.209168 0.977880i \(-0.567076\pi\)
−0.209168 + 0.977880i \(0.567076\pi\)
\(740\) 15.5584 72.3861i 0.571939 2.66096i
\(741\) 0 0
\(742\) 46.7277i 1.71543i
\(743\) 42.5639i 1.56152i 0.624833 + 0.780759i \(0.285167\pi\)
−0.624833 + 0.780759i \(0.714833\pi\)
\(744\) 0 0
\(745\) 35.7921 + 7.69304i 1.31132 + 0.281851i
\(746\) 29.4891 1.07967
\(747\) 0 0
\(748\) 15.1460i 0.553794i
\(749\) −45.9565 −1.67921
\(750\) 0 0
\(751\) −35.7228 −1.30354 −0.651772 0.758415i \(-0.725974\pi\)
−0.651772 + 0.758415i \(0.725974\pi\)
\(752\) 54.2458i 1.97814i
\(753\) 0 0
\(754\) −59.5842 −2.16993
\(755\) −39.6060 8.51278i −1.44141 0.309812i
\(756\) 0 0
\(757\) 41.5692i 1.51086i 0.655230 + 0.755429i \(0.272572\pi\)
−0.655230 + 0.755429i \(0.727428\pi\)
\(758\) 54.2458i 1.97030i
\(759\) 0 0
\(760\) 15.1168 70.3316i 0.548346 2.55120i
\(761\) 9.51087 0.344769 0.172384 0.985030i \(-0.444853\pi\)
0.172384 + 0.985030i \(0.444853\pi\)
\(762\) 0 0
\(763\) 6.04334i 0.218784i
\(764\) −58.4674 −2.11528
\(765\) 0 0
\(766\) 89.2119 3.22336
\(767\) 30.2921i 1.09378i
\(768\) 0 0
\(769\) −6.48913 −0.234004 −0.117002 0.993132i \(-0.537328\pi\)
−0.117002 + 0.993132i \(0.537328\pi\)
\(770\) −26.2337 5.63858i −0.945396 0.203200i
\(771\) 0 0
\(772\) 93.6955i 3.37217i
\(773\) 18.2603i 0.656776i −0.944543 0.328388i \(-0.893495\pi\)
0.944543 0.328388i \(-0.106505\pi\)
\(774\) 0 0
\(775\) 2.86141 + 1.28962i 0.102785 + 0.0463245i
\(776\) −111.446 −4.00066
\(777\) 0 0
\(778\) 59.2945i 2.12581i
\(779\) 7.37228 0.264139
\(780\) 0 0
\(781\) −5.64947 −0.202154
\(782\) 32.1716i 1.15045i
\(783\) 0 0
\(784\) −31.8614 −1.13791
\(785\) 10.0693 46.8477i 0.359389 1.67207i
\(786\) 0 0
\(787\) 17.3205i 0.617409i −0.951158 0.308705i \(-0.900105\pi\)
0.951158 0.308705i \(-0.0998955\pi\)
\(788\) 100.624i 3.58457i
\(789\) 0 0
\(790\) 5.62772 26.1831i 0.200225