Properties

Label 1568.2.i.v.961.1
Level $1568$
Weight $2$
Character 1568.961
Analytic conductor $12.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1568,2,Mod(961,1568)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
 
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("1568.961");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.i (of order \(3\), degree \(2\), not 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: \(12.5205430369\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 224)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1568.961
Dual form 1568.2.i.v.1537.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.618034 - 1.07047i) q^{3} +(-1.61803 + 2.80252i) q^{5} +(0.736068 - 1.27491i) q^{9} +O(q^{10})\) \(q+(-0.618034 - 1.07047i) q^{3} +(-1.61803 + 2.80252i) q^{5} +(0.736068 - 1.27491i) q^{9} +(3.23607 + 5.60503i) q^{11} +0.763932 q^{13} +4.00000 q^{15} +(-2.23607 - 3.87298i) q^{17} +(0.618034 - 1.07047i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-2.73607 - 4.73901i) q^{25} -5.52786 q^{27} -4.47214 q^{29} +(1.23607 + 2.14093i) q^{31} +(4.00000 - 6.92820i) q^{33} +(2.23607 - 3.87298i) q^{37} +(-0.472136 - 0.817763i) q^{39} -8.47214 q^{41} +6.47214 q^{43} +(2.38197 + 4.12569i) q^{45} +(-5.23607 + 9.06914i) q^{47} +(-2.76393 + 4.78727i) q^{51} +(5.00000 + 8.66025i) q^{53} -20.9443 q^{55} -1.52786 q^{57} +(4.61803 + 7.99867i) q^{59} +(-5.61803 + 9.73072i) q^{61} +(-1.23607 + 2.14093i) q^{65} +(-2.00000 - 3.46410i) q^{67} +4.94427 q^{69} -4.94427 q^{71} +(1.47214 + 2.54981i) q^{73} +(-3.38197 + 5.85774i) q^{75} +(-6.47214 + 11.2101i) q^{79} +(1.20820 + 2.09267i) q^{81} -9.23607 q^{83} +14.4721 q^{85} +(2.76393 + 4.78727i) q^{87} +(3.00000 - 5.19615i) q^{89} +(1.52786 - 2.64634i) q^{93} +(2.00000 + 3.46410i) q^{95} +12.4721 q^{97} +9.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9} + 4 q^{11} + 12 q^{13} + 16 q^{15} - 2 q^{19} - 8 q^{23} - 2 q^{25} - 40 q^{27} - 4 q^{31} + 16 q^{33} + 16 q^{39} - 16 q^{41} + 8 q^{43} + 14 q^{45} - 12 q^{47} - 20 q^{51} + 20 q^{53} - 48 q^{55} - 24 q^{57} + 14 q^{59} - 18 q^{61} + 4 q^{65} - 8 q^{67} - 16 q^{69} + 16 q^{71} - 12 q^{73} - 18 q^{75} - 8 q^{79} - 22 q^{81} - 28 q^{83} + 40 q^{85} + 20 q^{87} + 12 q^{89} + 24 q^{93} + 8 q^{95} + 32 q^{97} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(1471\) \(1473\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.618034 1.07047i −0.356822 0.618034i 0.630606 0.776103i \(-0.282806\pi\)
−0.987428 + 0.158069i \(0.949473\pi\)
\(4\) 0 0
\(5\) −1.61803 + 2.80252i −0.723607 + 1.25332i 0.235938 + 0.971768i \(0.424184\pi\)
−0.959545 + 0.281556i \(0.909150\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.736068 1.27491i 0.245356 0.424969i
\(10\) 0 0
\(11\) 3.23607 + 5.60503i 0.975711 + 1.68998i 0.677568 + 0.735460i \(0.263034\pi\)
0.298143 + 0.954521i \(0.403633\pi\)
\(12\) 0 0
\(13\) 0.763932 0.211877 0.105938 0.994373i \(-0.466215\pi\)
0.105938 + 0.994373i \(0.466215\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) −2.23607 3.87298i −0.542326 0.939336i −0.998770 0.0495842i \(-0.984210\pi\)
0.456444 0.889752i \(-0.349123\pi\)
\(18\) 0 0
\(19\) 0.618034 1.07047i 0.141787 0.245582i −0.786383 0.617740i \(-0.788049\pi\)
0.928170 + 0.372158i \(0.121382\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −2.73607 4.73901i −0.547214 0.947802i
\(26\) 0 0
\(27\) −5.52786 −1.06384
\(28\) 0 0
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 0 0
\(31\) 1.23607 + 2.14093i 0.222004 + 0.384523i 0.955417 0.295261i \(-0.0954067\pi\)
−0.733412 + 0.679784i \(0.762073\pi\)
\(32\) 0 0
\(33\) 4.00000 6.92820i 0.696311 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.23607 3.87298i 0.367607 0.636715i −0.621584 0.783348i \(-0.713510\pi\)
0.989191 + 0.146633i \(0.0468437\pi\)
\(38\) 0 0
\(39\) −0.472136 0.817763i −0.0756023 0.130947i
\(40\) 0 0
\(41\) −8.47214 −1.32313 −0.661563 0.749890i \(-0.730106\pi\)
−0.661563 + 0.749890i \(0.730106\pi\)
\(42\) 0 0
\(43\) 6.47214 0.986991 0.493496 0.869748i \(-0.335719\pi\)
0.493496 + 0.869748i \(0.335719\pi\)
\(44\) 0 0
\(45\) 2.38197 + 4.12569i 0.355083 + 0.615021i
\(46\) 0 0
\(47\) −5.23607 + 9.06914i −0.763759 + 1.32287i 0.177141 + 0.984185i \(0.443315\pi\)
−0.940900 + 0.338684i \(0.890018\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.76393 + 4.78727i −0.387028 + 0.670352i
\(52\) 0 0
\(53\) 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i \(0.0743197\pi\)
−0.286064 + 0.958211i \(0.592347\pi\)
\(54\) 0 0
\(55\) −20.9443 −2.82413
\(56\) 0 0
\(57\) −1.52786 −0.202371
\(58\) 0 0
\(59\) 4.61803 + 7.99867i 0.601217 + 1.04134i 0.992637 + 0.121126i \(0.0386505\pi\)
−0.391420 + 0.920212i \(0.628016\pi\)
\(60\) 0 0
\(61\) −5.61803 + 9.73072i −0.719316 + 1.24589i 0.241956 + 0.970287i \(0.422211\pi\)
−0.961271 + 0.275604i \(0.911122\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.23607 + 2.14093i −0.153315 + 0.265550i
\(66\) 0 0
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) 0 0
\(69\) 4.94427 0.595220
\(70\) 0 0
\(71\) −4.94427 −0.586777 −0.293389 0.955993i \(-0.594783\pi\)
−0.293389 + 0.955993i \(0.594783\pi\)
\(72\) 0 0
\(73\) 1.47214 + 2.54981i 0.172300 + 0.298433i 0.939224 0.343306i \(-0.111547\pi\)
−0.766923 + 0.641739i \(0.778213\pi\)
\(74\) 0 0
\(75\) −3.38197 + 5.85774i −0.390516 + 0.676393i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.47214 + 11.2101i −0.728172 + 1.26123i 0.229483 + 0.973313i \(0.426297\pi\)
−0.957655 + 0.287918i \(0.907037\pi\)
\(80\) 0 0
\(81\) 1.20820 + 2.09267i 0.134245 + 0.232519i
\(82\) 0 0
\(83\) −9.23607 −1.01379 −0.506895 0.862008i \(-0.669207\pi\)
−0.506895 + 0.862008i \(0.669207\pi\)
\(84\) 0 0
\(85\) 14.4721 1.56972
\(86\) 0 0
\(87\) 2.76393 + 4.78727i 0.296325 + 0.513249i
\(88\) 0 0
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.52786 2.64634i 0.158432 0.274412i
\(94\) 0 0
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) 12.4721 1.26635 0.633177 0.774007i \(-0.281751\pi\)
0.633177 + 0.774007i \(0.281751\pi\)
\(98\) 0 0
\(99\) 9.52786 0.957586
\(100\) 0 0
\(101\) 0.854102 + 1.47935i 0.0849863 + 0.147201i 0.905385 0.424591i \(-0.139582\pi\)
−0.820399 + 0.571791i \(0.806249\pi\)
\(102\) 0 0
\(103\) 2.76393 4.78727i 0.272338 0.471704i −0.697122 0.716953i \(-0.745536\pi\)
0.969460 + 0.245249i \(0.0788697\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.47214 + 7.74597i −0.432338 + 0.748831i −0.997074 0.0764405i \(-0.975644\pi\)
0.564736 + 0.825271i \(0.308978\pi\)
\(108\) 0 0
\(109\) −4.23607 7.33708i −0.405742 0.702765i 0.588666 0.808377i \(-0.299653\pi\)
−0.994407 + 0.105611i \(0.966320\pi\)
\(110\) 0 0
\(111\) −5.52786 −0.524682
\(112\) 0 0
\(113\) −12.4721 −1.17328 −0.586640 0.809848i \(-0.699550\pi\)
−0.586640 + 0.809848i \(0.699550\pi\)
\(114\) 0 0
\(115\) −6.47214 11.2101i −0.603530 1.04534i
\(116\) 0 0
\(117\) 0.562306 0.973942i 0.0519852 0.0900410i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −15.4443 + 26.7503i −1.40402 + 2.43184i
\(122\) 0 0
\(123\) 5.23607 + 9.06914i 0.472120 + 0.817736i
\(124\) 0 0
\(125\) 1.52786 0.136656
\(126\) 0 0
\(127\) 8.94427 0.793676 0.396838 0.917889i \(-0.370108\pi\)
0.396838 + 0.917889i \(0.370108\pi\)
\(128\) 0 0
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 0 0
\(131\) −5.85410 + 10.1396i −0.511475 + 0.885901i 0.488436 + 0.872600i \(0.337567\pi\)
−0.999912 + 0.0133016i \(0.995766\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 8.94427 15.4919i 0.769800 1.33333i
\(136\) 0 0
\(137\) −7.47214 12.9421i −0.638388 1.10572i −0.985787 0.168002i \(-0.946268\pi\)
0.347399 0.937717i \(-0.387065\pi\)
\(138\) 0 0
\(139\) 1.23607 0.104842 0.0524210 0.998625i \(-0.483306\pi\)
0.0524210 + 0.998625i \(0.483306\pi\)
\(140\) 0 0
\(141\) 12.9443 1.09010
\(142\) 0 0
\(143\) 2.47214 + 4.28187i 0.206730 + 0.358068i
\(144\) 0 0
\(145\) 7.23607 12.5332i 0.600923 1.04083i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.47214 + 2.54981i −0.120602 + 0.208889i −0.920005 0.391906i \(-0.871816\pi\)
0.799403 + 0.600795i \(0.205149\pi\)
\(150\) 0 0
\(151\) 4.47214 + 7.74597i 0.363937 + 0.630358i 0.988605 0.150533i \(-0.0480989\pi\)
−0.624668 + 0.780891i \(0.714766\pi\)
\(152\) 0 0
\(153\) −6.58359 −0.532252
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −0.381966 0.661585i −0.0304842 0.0528002i 0.850381 0.526168i \(-0.176372\pi\)
−0.880865 + 0.473368i \(0.843038\pi\)
\(158\) 0 0
\(159\) 6.18034 10.7047i 0.490133 0.848935i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.70820 2.95870i 0.133797 0.231743i −0.791340 0.611376i \(-0.790616\pi\)
0.925137 + 0.379633i \(0.123950\pi\)
\(164\) 0 0
\(165\) 12.9443 + 22.4201i 1.00771 + 1.74541i
\(166\) 0 0
\(167\) 23.4164 1.81202 0.906008 0.423261i \(-0.139114\pi\)
0.906008 + 0.423261i \(0.139114\pi\)
\(168\) 0 0
\(169\) −12.4164 −0.955108
\(170\) 0 0
\(171\) −0.909830 1.57587i −0.0695764 0.120510i
\(172\) 0 0
\(173\) −2.85410 + 4.94345i −0.216993 + 0.375844i −0.953887 0.300165i \(-0.902958\pi\)
0.736894 + 0.676008i \(0.236292\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.70820 9.88690i 0.429055 0.743145i
\(178\) 0 0
\(179\) 3.52786 + 6.11044i 0.263685 + 0.456716i 0.967218 0.253947i \(-0.0817287\pi\)
−0.703533 + 0.710662i \(0.748395\pi\)
\(180\) 0 0
\(181\) −12.1803 −0.905358 −0.452679 0.891674i \(-0.649532\pi\)
−0.452679 + 0.891674i \(0.649532\pi\)
\(182\) 0 0
\(183\) 13.8885 1.02667
\(184\) 0 0
\(185\) 7.23607 + 12.5332i 0.532006 + 0.921462i
\(186\) 0 0
\(187\) 14.4721 25.0665i 1.05831 1.83304i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.47214 + 4.28187i −0.178877 + 0.309825i −0.941496 0.337023i \(-0.890580\pi\)
0.762619 + 0.646848i \(0.223913\pi\)
\(192\) 0 0
\(193\) −0.236068 0.408882i −0.0169925 0.0294320i 0.857404 0.514644i \(-0.172076\pi\)
−0.874397 + 0.485212i \(0.838742\pi\)
\(194\) 0 0
\(195\) 3.05573 0.218825
\(196\) 0 0
\(197\) 10.9443 0.779747 0.389874 0.920868i \(-0.372519\pi\)
0.389874 + 0.920868i \(0.372519\pi\)
\(198\) 0 0
\(199\) −7.70820 13.3510i −0.546420 0.946427i −0.998516 0.0544581i \(-0.982657\pi\)
0.452096 0.891969i \(-0.350676\pi\)
\(200\) 0 0
\(201\) −2.47214 + 4.28187i −0.174371 + 0.302019i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 13.7082 23.7433i 0.957422 1.65830i
\(206\) 0 0
\(207\) 2.94427 + 5.09963i 0.204641 + 0.354449i
\(208\) 0 0
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) 3.05573 + 5.29268i 0.209375 + 0.362648i
\(214\) 0 0
\(215\) −10.4721 + 18.1383i −0.714194 + 1.23702i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.81966 3.15174i 0.122961 0.212975i
\(220\) 0 0
\(221\) −1.70820 2.95870i −0.114906 0.199023i
\(222\) 0 0
\(223\) 12.9443 0.866813 0.433406 0.901199i \(-0.357312\pi\)
0.433406 + 0.901199i \(0.357312\pi\)
\(224\) 0 0
\(225\) −8.05573 −0.537049
\(226\) 0 0
\(227\) 8.61803 + 14.9269i 0.571999 + 0.990731i 0.996361 + 0.0852385i \(0.0271652\pi\)
−0.424362 + 0.905493i \(0.639501\pi\)
\(228\) 0 0
\(229\) −11.7984 + 20.4354i −0.779658 + 1.35041i 0.152480 + 0.988307i \(0.451274\pi\)
−0.932139 + 0.362102i \(0.882059\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.94427 13.7599i 0.520447 0.901440i −0.479271 0.877667i \(-0.659099\pi\)
0.999717 0.0237728i \(-0.00756784\pi\)
\(234\) 0 0
\(235\) −16.9443 29.3483i −1.10532 1.91447i
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) −13.8885 −0.898375 −0.449188 0.893437i \(-0.648287\pi\)
−0.449188 + 0.893437i \(0.648287\pi\)
\(240\) 0 0
\(241\) −6.23607 10.8012i −0.401700 0.695766i 0.592231 0.805768i \(-0.298247\pi\)
−0.993931 + 0.110003i \(0.964914\pi\)
\(242\) 0 0
\(243\) −6.79837 + 11.7751i −0.436116 + 0.755375i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.472136 0.817763i 0.0300413 0.0520330i
\(248\) 0 0
\(249\) 5.70820 + 9.88690i 0.361743 + 0.626557i
\(250\) 0 0
\(251\) 4.29180 0.270896 0.135448 0.990784i \(-0.456753\pi\)
0.135448 + 0.990784i \(0.456753\pi\)
\(252\) 0 0
\(253\) −25.8885 −1.62760
\(254\) 0 0
\(255\) −8.94427 15.4919i −0.560112 0.970143i
\(256\) 0 0
\(257\) 7.00000 12.1244i 0.436648 0.756297i −0.560781 0.827964i \(-0.689499\pi\)
0.997429 + 0.0716680i \(0.0228322\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.29180 + 5.70156i −0.203757 + 0.352918i
\(262\) 0 0
\(263\) −5.52786 9.57454i −0.340863 0.590392i 0.643730 0.765252i \(-0.277386\pi\)
−0.984593 + 0.174861i \(0.944052\pi\)
\(264\) 0 0
\(265\) −32.3607 −1.98790
\(266\) 0 0
\(267\) −7.41641 −0.453877
\(268\) 0 0
\(269\) 2.09017 + 3.62028i 0.127440 + 0.220732i 0.922684 0.385557i \(-0.125991\pi\)
−0.795244 + 0.606289i \(0.792657\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 17.7082 30.6715i 1.06784 1.84956i
\(276\) 0 0
\(277\) −3.94427 6.83168i −0.236988 0.410476i 0.722860 0.690994i \(-0.242827\pi\)
−0.959849 + 0.280518i \(0.909494\pi\)
\(278\) 0 0
\(279\) 3.63932 0.217880
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) 3.09017 + 5.35233i 0.183692 + 0.318163i 0.943135 0.332410i \(-0.107862\pi\)
−0.759443 + 0.650574i \(0.774529\pi\)
\(284\) 0 0
\(285\) 2.47214 4.28187i 0.146437 0.253636i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.50000 + 2.59808i −0.0882353 + 0.152828i
\(290\) 0 0
\(291\) −7.70820 13.3510i −0.451863 0.782650i
\(292\) 0 0
\(293\) −12.7639 −0.745677 −0.372838 0.927896i \(-0.621615\pi\)
−0.372838 + 0.927896i \(0.621615\pi\)
\(294\) 0 0
\(295\) −29.8885 −1.74018
\(296\) 0 0
\(297\) −17.8885 30.9839i −1.03800 1.79787i
\(298\) 0 0
\(299\) −1.52786 + 2.64634i −0.0883587 + 0.153042i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.05573 1.82857i 0.0606500 0.105049i
\(304\) 0 0
\(305\) −18.1803 31.4893i −1.04100 1.80307i
\(306\) 0 0
\(307\) 1.81966 0.103853 0.0519267 0.998651i \(-0.483464\pi\)
0.0519267 + 0.998651i \(0.483464\pi\)
\(308\) 0 0
\(309\) −6.83282 −0.388705
\(310\) 0 0
\(311\) −4.00000 6.92820i −0.226819 0.392862i 0.730044 0.683400i \(-0.239499\pi\)
−0.956864 + 0.290537i \(0.906166\pi\)
\(312\) 0 0
\(313\) 4.23607 7.33708i 0.239437 0.414717i −0.721116 0.692814i \(-0.756371\pi\)
0.960553 + 0.278098i \(0.0897039\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.52786 + 7.84249i −0.254310 + 0.440478i −0.964708 0.263322i \(-0.915182\pi\)
0.710398 + 0.703800i \(0.248515\pi\)
\(318\) 0 0
\(319\) −14.4721 25.0665i −0.810284 1.40345i
\(320\) 0 0
\(321\) 11.0557 0.617071
\(322\) 0 0
\(323\) −5.52786 −0.307579
\(324\) 0 0
\(325\) −2.09017 3.62028i −0.115942 0.200817i
\(326\) 0 0
\(327\) −5.23607 + 9.06914i −0.289555 + 0.501524i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.2361 + 19.4614i −0.617590 + 1.06970i 0.372334 + 0.928099i \(0.378558\pi\)
−0.989924 + 0.141599i \(0.954776\pi\)
\(332\) 0 0
\(333\) −3.29180 5.70156i −0.180389 0.312443i
\(334\) 0 0
\(335\) 12.9443 0.707221
\(336\) 0 0
\(337\) 10.3607 0.564382 0.282191 0.959358i \(-0.408939\pi\)
0.282191 + 0.959358i \(0.408939\pi\)
\(338\) 0 0
\(339\) 7.70820 + 13.3510i 0.418652 + 0.725127i
\(340\) 0 0
\(341\) −8.00000 + 13.8564i −0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) 0 0
\(347\) −3.23607 5.60503i −0.173721 0.300894i 0.765997 0.642844i \(-0.222246\pi\)
−0.939718 + 0.341950i \(0.888913\pi\)
\(348\) 0 0
\(349\) 26.6525 1.42667 0.713337 0.700821i \(-0.247183\pi\)
0.713337 + 0.700821i \(0.247183\pi\)
\(350\) 0 0
\(351\) −4.22291 −0.225402
\(352\) 0 0
\(353\) 7.94427 + 13.7599i 0.422831 + 0.732365i 0.996215 0.0869220i \(-0.0277031\pi\)
−0.573384 + 0.819287i \(0.694370\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.47214 14.6742i 0.447142 0.774473i −0.551056 0.834468i \(-0.685775\pi\)
0.998199 + 0.0599949i \(0.0191084\pi\)
\(360\) 0 0
\(361\) 8.73607 + 15.1313i 0.459793 + 0.796385i
\(362\) 0 0
\(363\) 38.1803 2.00395
\(364\) 0 0
\(365\) −9.52786 −0.498711
\(366\) 0 0
\(367\) 11.4164 + 19.7738i 0.595932 + 1.03218i 0.993415 + 0.114574i \(0.0365504\pi\)
−0.397483 + 0.917610i \(0.630116\pi\)
\(368\) 0 0
\(369\) −6.23607 + 10.8012i −0.324637 + 0.562287i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.47214 + 2.54981i −0.0762243 + 0.132024i −0.901618 0.432533i \(-0.857620\pi\)
0.825394 + 0.564558i \(0.190953\pi\)
\(374\) 0 0
\(375\) −0.944272 1.63553i −0.0487620 0.0844582i
\(376\) 0 0
\(377\) −3.41641 −0.175954
\(378\) 0 0
\(379\) −4.58359 −0.235443 −0.117722 0.993047i \(-0.537559\pi\)
−0.117722 + 0.993047i \(0.537559\pi\)
\(380\) 0 0
\(381\) −5.52786 9.57454i −0.283201 0.490519i
\(382\) 0 0
\(383\) 7.70820 13.3510i 0.393871 0.682204i −0.599086 0.800685i \(-0.704469\pi\)
0.992956 + 0.118481i \(0.0378024\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.76393 8.25137i 0.242164 0.419441i
\(388\) 0 0
\(389\) 2.23607 + 3.87298i 0.113373 + 0.196368i 0.917128 0.398592i \(-0.130501\pi\)
−0.803755 + 0.594960i \(0.797168\pi\)
\(390\) 0 0
\(391\) 17.8885 0.904663
\(392\) 0 0
\(393\) 14.4721 0.730023
\(394\) 0 0
\(395\) −20.9443 36.2765i −1.05382 1.82527i
\(396\) 0 0
\(397\) 7.61803 13.1948i 0.382338 0.662229i −0.609058 0.793126i \(-0.708452\pi\)
0.991396 + 0.130897i \(0.0417856\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7639 20.3757i 0.587463 1.01752i −0.407101 0.913383i \(-0.633460\pi\)
0.994563 0.104132i \(-0.0332065\pi\)
\(402\) 0 0
\(403\) 0.944272 + 1.63553i 0.0470375 + 0.0814714i
\(404\) 0 0
\(405\) −7.81966 −0.388562
\(406\) 0 0
\(407\) 28.9443 1.43471
\(408\) 0 0
\(409\) 10.7082 + 18.5472i 0.529487 + 0.917098i 0.999408 + 0.0343897i \(0.0109487\pi\)
−0.469922 + 0.882708i \(0.655718\pi\)
\(410\) 0 0
\(411\) −9.23607 + 15.9973i −0.455582 + 0.789091i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 14.9443 25.8842i 0.733585 1.27061i
\(416\) 0 0
\(417\) −0.763932 1.32317i −0.0374099 0.0647959i
\(418\) 0 0
\(419\) 22.1803 1.08358 0.541790 0.840514i \(-0.317747\pi\)
0.541790 + 0.840514i \(0.317747\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 7.70820 + 13.3510i 0.374786 + 0.649148i
\(424\) 0 0
\(425\) −12.2361 + 21.1935i −0.593536 + 1.02804i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 3.05573 5.29268i 0.147532 0.255533i
\(430\) 0 0
\(431\) 14.0000 + 24.2487i 0.674356 + 1.16802i 0.976657 + 0.214807i \(0.0689121\pi\)
−0.302300 + 0.953213i \(0.597755\pi\)
\(432\) 0 0
\(433\) 9.41641 0.452524 0.226262 0.974067i \(-0.427349\pi\)
0.226262 + 0.974067i \(0.427349\pi\)
\(434\) 0 0
\(435\) −17.8885 −0.857690
\(436\) 0 0
\(437\) 2.47214 + 4.28187i 0.118258 + 0.204829i
\(438\) 0 0
\(439\) 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i \(-0.556744\pi\)
0.940963 0.338508i \(-0.109922\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.94427 12.0278i 0.329932 0.571460i −0.652566 0.757732i \(-0.726307\pi\)
0.982498 + 0.186273i \(0.0596407\pi\)
\(444\) 0 0
\(445\) 9.70820 + 16.8151i 0.460213 + 0.797112i
\(446\) 0 0
\(447\) 3.63932 0.172134
\(448\) 0 0
\(449\) −7.88854 −0.372283 −0.186142 0.982523i \(-0.559598\pi\)
−0.186142 + 0.982523i \(0.559598\pi\)
\(450\) 0 0
\(451\) −27.4164 47.4866i −1.29099 2.23606i
\(452\) 0 0
\(453\) 5.52786 9.57454i 0.259722 0.449851i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.76393 6.51932i 0.176069 0.304961i −0.764462 0.644669i \(-0.776995\pi\)
0.940531 + 0.339708i \(0.110328\pi\)
\(458\) 0 0
\(459\) 12.3607 + 21.4093i 0.576947 + 0.999302i
\(460\) 0 0
\(461\) 21.7082 1.01105 0.505526 0.862811i \(-0.331298\pi\)
0.505526 + 0.862811i \(0.331298\pi\)
\(462\) 0 0
\(463\) −35.7771 −1.66270 −0.831351 0.555748i \(-0.812432\pi\)
−0.831351 + 0.555748i \(0.812432\pi\)
\(464\) 0 0
\(465\) 4.94427 + 8.56373i 0.229285 + 0.397133i
\(466\) 0 0
\(467\) 16.0344 27.7725i 0.741985 1.28516i −0.209605 0.977786i \(-0.567218\pi\)
0.951590 0.307370i \(-0.0994490\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.472136 + 0.817763i −0.0217549 + 0.0376806i
\(472\) 0 0
\(473\) 20.9443 + 36.2765i 0.963019 + 1.66800i
\(474\) 0 0
\(475\) −6.76393 −0.310350
\(476\) 0 0
\(477\) 14.7214 0.674045
\(478\) 0 0
\(479\) 4.29180 + 7.43361i 0.196097 + 0.339650i 0.947260 0.320467i \(-0.103840\pi\)
−0.751162 + 0.660117i \(0.770507\pi\)
\(480\) 0 0
\(481\) 1.70820 2.95870i 0.0778874 0.134905i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −20.1803 + 34.9534i −0.916342 + 1.58715i
\(486\) 0 0
\(487\) −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i \(-0.316364\pi\)
−0.998579 + 0.0532853i \(0.983031\pi\)
\(488\) 0 0
\(489\) −4.22291 −0.190967
\(490\) 0 0
\(491\) 37.8885 1.70989 0.854943 0.518722i \(-0.173592\pi\)
0.854943 + 0.518722i \(0.173592\pi\)
\(492\) 0 0
\(493\) 10.0000 + 17.3205i 0.450377 + 0.780076i
\(494\) 0 0
\(495\) −15.4164 + 26.7020i −0.692916 + 1.20017i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −10.9443 + 18.9560i −0.489933 + 0.848589i −0.999933 0.0115857i \(-0.996312\pi\)
0.510000 + 0.860174i \(0.329645\pi\)
\(500\) 0 0
\(501\) −14.4721 25.0665i −0.646567 1.11989i
\(502\) 0 0
\(503\) −4.94427 −0.220454 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(504\) 0 0
\(505\) −5.52786 −0.245987
\(506\) 0 0
\(507\) 7.67376 + 13.2913i 0.340804 + 0.590289i
\(508\) 0 0
\(509\) 20.5623 35.6150i 0.911408 1.57861i 0.0993316 0.995054i \(-0.468330\pi\)
0.812077 0.583551i \(-0.198337\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −3.41641 + 5.91739i −0.150838 + 0.261259i
\(514\) 0 0
\(515\) 8.94427 + 15.4919i 0.394132 + 0.682656i
\(516\) 0 0
\(517\) −67.7771 −2.98083
\(518\) 0 0
\(519\) 7.05573 0.309712
\(520\) 0 0
\(521\) 3.29180 + 5.70156i 0.144216 + 0.249790i 0.929080 0.369878i \(-0.120601\pi\)
−0.784864 + 0.619668i \(0.787267\pi\)
\(522\) 0 0
\(523\) 2.14590 3.71680i 0.0938336 0.162525i −0.815288 0.579056i \(-0.803421\pi\)
0.909121 + 0.416532i \(0.136755\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.52786 9.57454i 0.240798 0.417074i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 13.5967 0.590049
\(532\) 0 0
\(533\) −6.47214 −0.280339
\(534\) 0 0
\(535\) −14.4721 25.0665i −0.625685 1.08372i
\(536\) 0 0
\(537\) 4.36068 7.55292i 0.188177 0.325933i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.52786 4.37839i 0.108681 0.188242i −0.806555 0.591159i \(-0.798671\pi\)
0.915236 + 0.402917i \(0.132004\pi\)
\(542\) 0 0
\(543\) 7.52786 + 13.0386i 0.323052 + 0.559542i
\(544\) 0 0
\(545\) 27.4164 1.17439
\(546\) 0 0
\(547\) −4.58359 −0.195980 −0.0979901 0.995187i \(-0.531241\pi\)
−0.0979901 + 0.995187i \(0.531241\pi\)
\(548\) 0 0
\(549\) 8.27051 + 14.3249i 0.352977 + 0.611374i
\(550\) 0 0
\(551\) −2.76393 + 4.78727i −0.117747 + 0.203945i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 8.94427 15.4919i 0.379663 0.657596i
\(556\) 0 0
\(557\) −4.52786 7.84249i −0.191852 0.332297i 0.754012 0.656860i \(-0.228116\pi\)
−0.945864 + 0.324563i \(0.894783\pi\)
\(558\) 0 0
\(559\) 4.94427 0.209120
\(560\) 0 0
\(561\) −35.7771 −1.51051
\(562\) 0 0
\(563\) 8.90983 + 15.4323i 0.375505 + 0.650393i 0.990402 0.138214i \(-0.0441361\pi\)
−0.614898 + 0.788607i \(0.710803\pi\)
\(564\) 0 0
\(565\) 20.1803 34.9534i 0.848993 1.47050i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.1803 + 22.8290i −0.552549 + 0.957042i 0.445541 + 0.895261i \(0.353011\pi\)
−0.998090 + 0.0617808i \(0.980322\pi\)
\(570\) 0 0
\(571\) 7.23607 + 12.5332i 0.302820 + 0.524500i 0.976774 0.214274i \(-0.0687386\pi\)
−0.673954 + 0.738774i \(0.735405\pi\)
\(572\) 0 0
\(573\) 6.11146 0.255310
\(574\) 0 0
\(575\) 21.8885 0.912815
\(576\) 0 0
\(577\) 3.00000 + 5.19615i 0.124892 + 0.216319i 0.921691 0.387926i \(-0.126808\pi\)
−0.796799 + 0.604245i \(0.793475\pi\)
\(578\) 0 0
\(579\) −0.291796 + 0.505406i −0.0121266 + 0.0210039i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −32.3607 + 56.0503i −1.34024 + 2.32137i
\(584\) 0 0
\(585\) 1.81966 + 3.15174i 0.0752337 + 0.130309i
\(586\) 0 0
\(587\) −3.70820 −0.153054 −0.0765270 0.997068i \(-0.524383\pi\)
−0.0765270 + 0.997068i \(0.524383\pi\)
\(588\) 0 0
\(589\) 3.05573 0.125909
\(590\) 0 0
\(591\) −6.76393 11.7155i −0.278231 0.481910i
\(592\) 0 0
\(593\) −16.4164 + 28.4341i −0.674141 + 1.16765i 0.302578 + 0.953125i \(0.402153\pi\)
−0.976719 + 0.214522i \(0.931181\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −9.52786 + 16.5027i −0.389950 + 0.675412i
\(598\) 0 0
\(599\) −8.94427 15.4919i −0.365453 0.632983i 0.623396 0.781907i \(-0.285753\pi\)
−0.988849 + 0.148923i \(0.952419\pi\)
\(600\) 0 0
\(601\) 29.7771 1.21463 0.607316 0.794460i \(-0.292246\pi\)
0.607316 + 0.794460i \(0.292246\pi\)
\(602\) 0 0
\(603\) −5.88854 −0.239800
\(604\) 0 0
\(605\) −49.9787 86.5657i −2.03192 3.51940i
\(606\) 0 0
\(607\) −4.94427 + 8.56373i −0.200682 + 0.347591i −0.948748 0.316033i \(-0.897649\pi\)
0.748066 + 0.663624i \(0.230982\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 0 0
\(613\) −14.7082 25.4754i −0.594059 1.02894i −0.993679 0.112259i \(-0.964191\pi\)
0.399620 0.916681i \(-0.369142\pi\)
\(614\) 0 0
\(615\) −33.8885 −1.36652
\(616\) 0 0
\(617\) 34.3607 1.38331 0.691654 0.722229i \(-0.256882\pi\)
0.691654 + 0.722229i \(0.256882\pi\)
\(618\) 0 0
\(619\) 24.0344 + 41.6289i 0.966026 + 1.67321i 0.706833 + 0.707380i \(0.250123\pi\)
0.259192 + 0.965826i \(0.416544\pi\)
\(620\) 0 0
\(621\) 11.0557 19.1491i 0.443651 0.768426i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11.2082 19.4132i 0.448328 0.776527i
\(626\) 0 0
\(627\) −4.94427 8.56373i −0.197455 0.342002i
\(628\) 0 0
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −44.9443 −1.78920 −0.894602 0.446865i \(-0.852541\pi\)
−0.894602 + 0.446865i \(0.852541\pi\)
\(632\) 0 0
\(633\) 7.41641 + 12.8456i 0.294776 + 0.510567i
\(634\) 0 0
\(635\) −14.4721 + 25.0665i −0.574309 + 0.994733i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −3.63932 + 6.30349i −0.143969 + 0.249362i
\(640\) 0 0
\(641\) −7.29180 12.6298i −0.288009 0.498846i 0.685326 0.728237i \(-0.259660\pi\)
−0.973334 + 0.229391i \(0.926327\pi\)
\(642\) 0 0
\(643\) −43.7082 −1.72368 −0.861842 0.507177i \(-0.830689\pi\)
−0.861842 + 0.507177i \(0.830689\pi\)
\(644\) 0 0
\(645\) 25.8885 1.01936
\(646\) 0 0
\(647\) 10.1803 + 17.6329i 0.400230 + 0.693219i 0.993753 0.111598i \(-0.0355967\pi\)
−0.593523 + 0.804817i \(0.702263\pi\)
\(648\) 0 0
\(649\) −29.8885 + 51.7685i −1.17323 + 2.03209i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.70820 8.15485i 0.184246 0.319124i −0.759076 0.651002i \(-0.774349\pi\)
0.943322 + 0.331878i \(0.107682\pi\)
\(654\) 0 0
\(655\) −18.9443 32.8124i −0.740214 1.28209i
\(656\) 0 0
\(657\) 4.33437 0.169100
\(658\) 0 0
\(659\) 37.3050 1.45319 0.726597 0.687064i \(-0.241101\pi\)
0.726597 + 0.687064i \(0.241101\pi\)
\(660\) 0 0
\(661\) 11.3262 + 19.6176i 0.440540 + 0.763037i 0.997730 0.0673481i \(-0.0214538\pi\)
−0.557190 + 0.830385i \(0.688120\pi\)
\(662\) 0 0
\(663\) −2.11146 + 3.65715i −0.0820022 + 0.142032i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.94427 15.4919i 0.346324 0.599850i
\(668\) 0 0
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) −72.7214 −2.80738
\(672\) 0 0
\(673\) −2.94427 −0.113493 −0.0567467 0.998389i \(-0.518073\pi\)
−0.0567467 + 0.998389i \(0.518073\pi\)
\(674\) 0 0
\(675\) 15.1246 + 26.1966i 0.582147 + 1.00831i
\(676\) 0 0
\(677\) −9.90983 + 17.1643i −0.380866 + 0.659679i −0.991186 0.132476i \(-0.957707\pi\)
0.610321 + 0.792155i \(0.291041\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 10.6525 18.4506i 0.408204 0.707030i
\(682\) 0 0
\(683\) −11.8885 20.5916i −0.454902 0.787914i 0.543780 0.839228i \(-0.316993\pi\)
−0.998683 + 0.0513135i \(0.983659\pi\)
\(684\) 0 0
\(685\) 48.3607 1.84777
\(686\) 0 0
\(687\) 29.1672 1.11280
\(688\) 0 0
\(689\) 3.81966 + 6.61585i 0.145517 + 0.252044i
\(690\) 0 0
\(691\) 7.09017 12.2805i 0.269723 0.467174i −0.699067 0.715056i \(-0.746401\pi\)
0.968790 + 0.247882i \(0.0797346\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 18.9443 + 32.8124i 0.717565 + 1.24286i
\(698\) 0 0
\(699\) −19.6393 −0.742827
\(700\) 0 0
\(701\) −41.4164 −1.56428 −0.782138 0.623105i \(-0.785871\pi\)
−0.782138 + 0.623105i \(0.785871\pi\)
\(702\) 0 0
\(703\) −2.76393 4.78727i −0.104244 0.180555i
\(704\) 0 0
\(705\) −20.9443 + 36.2765i −0.788807 + 1.36625i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.819660 + 1.41969i −0.0307830 + 0.0533177i −0.881006 0.473104i \(-0.843133\pi\)
0.850223 + 0.526422i \(0.176467\pi\)
\(710\) 0 0
\(711\) 9.52786 + 16.5027i 0.357323 + 0.618901i
\(712\) 0 0
\(713\) −9.88854 −0.370329
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 0 0
\(717\) 8.58359 + 14.8672i 0.320560 + 0.555226i
\(718\) 0 0
\(719\) −25.5967 + 44.3349i −0.954598 + 1.65341i −0.219311 + 0.975655i \(0.570381\pi\)
−0.735286 + 0.677757i \(0.762952\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −7.70820 + 13.3510i −0.286671 + 0.496529i
\(724\) 0 0
\(725\) 12.2361 + 21.1935i 0.454436 + 0.787107i
\(726\) 0 0
\(727\) 12.3607 0.458432 0.229216 0.973376i \(-0.426384\pi\)
0.229216 + 0.973376i \(0.426384\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 0 0
\(731\) −14.4721 25.0665i −0.535271 0.927117i
\(732\) 0 0
\(733\) 2.38197 4.12569i 0.0879799 0.152386i −0.818677 0.574254i \(-0.805292\pi\)
0.906657 + 0.421868i \(0.138626\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 12.9443 22.4201i 0.476808 0.825856i
\(738\) 0 0
\(739\) 1.70820 + 2.95870i 0.0628373 + 0.108837i 0.895733 0.444593i \(-0.146652\pi\)
−0.832895 + 0.553431i \(0.813318\pi\)
\(740\) 0 0
\(741\) −1.16718 −0.0428776
\(742\) 0 0
\(743\) 24.9443 0.915117 0.457558 0.889180i \(-0.348724\pi\)
0.457558 + 0.889180i \(0.348724\pi\)
\(744\) 0 0
\(745\) −4.76393 8.25137i −0.174537 0.302307i
\(746\) 0 0
\(747\) −6.79837 + 11.7751i −0.248739 + 0.430829i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −18.0000 + 31.1769i −0.656829 + 1.13766i 0.324603 + 0.945851i \(0.394769\pi\)
−0.981432 + 0.191811i \(0.938564\pi\)
\(752\) 0 0
\(753\) −2.65248 4.59422i −0.0966616 0.167423i
\(754\) 0 0
\(755\) −28.9443 −1.05339
\(756\) 0 0
\(757\) 39.3050 1.42856 0.714281 0.699859i \(-0.246754\pi\)
0.714281 + 0.699859i \(0.246754\pi\)
\(758\) 0 0
\(759\) 16.0000 + 27.7128i 0.580763 + 1.00591i
\(760\) 0 0
\(761\) 1.76393 3.05522i 0.0639425 0.110752i −0.832282 0.554353i \(-0.812966\pi\)
0.896224 + 0.443601i \(0.146299\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 10.6525 18.4506i 0.385141 0.667084i
\(766\) 0 0
\(767\) 3.52786 + 6.11044i 0.127384 + 0.220635i
\(768\) 0 0
\(769\) −18.3607 −0.662103 −0.331052 0.943613i \(-0.607403\pi\)
−0.331052 + 0.943613i \(0.607403\pi\)
\(770\) 0 0
\(771\) −17.3050 −0.623223
\(772\) 0 0
\(773\) −20.0902 34.7972i −0.722593 1.25157i −0.959957 0.280147i \(-0.909617\pi\)
0.237364 0.971421i \(-0.423717\pi\)
\(774\) 0 0
\(775\) 6.76393 11.7155i 0.242968 0.420832i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.23607 + 9.06914i −0.187602 + 0.324936i
\(780\) 0 0
\(781\) −16.0000 27.7128i −0.572525 0.991642i
\(782\) 0 0
\(783\) 24.7214 0.883469
\(784\) 0 0
\(785\) 2.47214 0.0882343
\(786\) 0 0
\(787\) 6.14590 + 10.6450i 0.219078 + 0.379454i 0.954526 0.298127i \(-0.0963619\pi\)
−0.735449 + 0.677580i \(0.763029\pi\)
\(788\) 0 0
\(789\) −6.83282 + 11.8348i −0.243255 + 0.421329i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4.29180 + 7.43361i −0.152406 + 0.263975i
\(794\) 0 0
\(795\)