Properties

Label 1568.2.i.n.1537.2
Level $1568$
Weight $2$
Character 1568.1537
Analytic conductor $12.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Self dual: no
Analytic conductor: \(12.5205430369\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
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 1537.2
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1568.1537
Dual form 1568.2.i.n.961.2

$q$-expansion

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

Character values

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

\(n\) \(197\) \(1471\) \(1473\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.717194\pi\)
0.987428 + 0.158069i \(0.0505269\pi\)
\(4\) 0 0
\(5\) 1.61803 + 2.80252i 0.723607 + 1.25332i 0.959545 + 0.281556i \(0.0908504\pi\)
−0.235938 + 0.971768i \(0.575816\pi\)
\(6\) 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 0.298143 0.954521i \(-0.403633\pi\)
0.677568 0.735460i \(-0.263034\pi\)
\(12\) 0 0
\(13\) −0.763932 −0.211877 −0.105938 0.994373i \(-0.533785\pi\)
−0.105938 + 0.994373i \(0.533785\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) 2.23607 3.87298i 0.542326 0.939336i −0.456444 0.889752i \(-0.650877\pi\)
0.998770 0.0495842i \(-0.0157896\pi\)
\(18\) 0 0
\(19\) −0.618034 1.07047i −0.141787 0.245582i 0.786383 0.617740i \(-0.211951\pi\)
−0.928170 + 0.372158i \(0.878618\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 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 \(-0.904593\pi\)
0.733412 + 0.679784i \(0.237927\pi\)
\(32\) 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 0.989191 0.146633i \(-0.0468437\pi\)
−0.621584 + 0.783348i \(0.713510\pi\)
\(38\) 0 0
\(39\) −0.472136 + 0.817763i −0.0756023 + 0.130947i
\(40\) 0 0
\(41\) 8.47214 1.32313 0.661563 0.749890i \(-0.269894\pi\)
0.661563 + 0.749890i \(0.269894\pi\)
\(42\) 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 0.940900 + 0.338684i \(0.109982\pi\)
−0.177141 + 0.984185i \(0.556685\pi\)
\(48\) 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 −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) 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 0.391420 + 0.920212i \(0.371984\pi\)
−0.992637 + 0.121126i \(0.961349\pi\)
\(60\) 0 0
\(61\) 5.61803 + 9.73072i 0.719316 + 1.24589i 0.961271 + 0.275604i \(0.0888778\pi\)
−0.241956 + 0.970287i \(0.577789\pi\)
\(62\) 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 −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 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 \(-0.888453\pi\)
0.766923 + 0.641739i \(0.221787\pi\)
\(74\) 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 −0.957655 0.287918i \(-0.907037\pi\)
0.229483 0.973313i \(-0.426297\pi\)
\(80\) 0 0
\(81\) 1.20820 2.09267i 0.134245 0.232519i
\(82\) 0 0
\(83\) 9.23607 1.01379 0.506895 0.862008i \(-0.330793\pi\)
0.506895 + 0.862008i \(0.330793\pi\)
\(84\) 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 \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 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 \(-0.718249\pi\)
−0.633177 + 0.774007i \(0.718249\pi\)
\(98\) 0 0
\(99\) 9.52786 0.957586
\(100\) 0 0
\(101\) −0.854102 + 1.47935i −0.0849863 + 0.147201i −0.905385 0.424591i \(-0.860418\pi\)
0.820399 + 0.571791i \(0.193751\pi\)
\(102\) 0 0
\(103\) −2.76393 4.78727i −0.272338 0.471704i 0.697122 0.716953i \(-0.254464\pi\)
−0.969460 + 0.245249i \(0.921130\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.47214 7.74597i −0.432338 0.748831i 0.564736 0.825271i \(-0.308978\pi\)
−0.997074 + 0.0764405i \(0.975644\pi\)
\(108\) 0 0
\(109\) −4.23607 + 7.33708i −0.405742 + 0.702765i −0.994407 0.105611i \(-0.966320\pi\)
0.588666 + 0.808377i \(0.299653\pi\)
\(110\) 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 0.999912 + 0.0133016i \(0.00423415\pi\)
−0.488436 + 0.872600i \(0.662433\pi\)
\(132\) 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 0.347399 + 0.937717i \(0.387065\pi\)
−0.985787 + 0.168002i \(0.946268\pi\)
\(138\) 0 0
\(139\) −1.23607 −0.104842 −0.0524210 0.998625i \(-0.516694\pi\)
−0.0524210 + 0.998625i \(0.516694\pi\)
\(140\) 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 0.799403 0.600795i \(-0.205149\pi\)
−0.920005 + 0.391906i \(0.871816\pi\)
\(150\) 0 0
\(151\) 4.47214 7.74597i 0.363937 0.630358i −0.624668 0.780891i \(-0.714766\pi\)
0.988605 + 0.150533i \(0.0480989\pi\)
\(152\) 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 \(-0.823628\pi\)
0.880865 + 0.473368i \(0.156962\pi\)
\(158\) 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 0.925137 0.379633i \(-0.123950\pi\)
−0.791340 + 0.611376i \(0.790616\pi\)
\(164\) 0 0
\(165\) 12.9443 22.4201i 1.00771 1.74541i
\(166\) 0 0
\(167\) −23.4164 −1.81202 −0.906008 0.423261i \(-0.860886\pi\)
−0.906008 + 0.423261i \(0.860886\pi\)
\(168\) 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 \(-0.0970417\pi\)
−0.736894 + 0.676008i \(0.763708\pi\)
\(174\) 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 −0.703533 0.710662i \(-0.748395\pi\)
0.967218 + 0.253947i \(0.0817287\pi\)
\(180\) 0 0
\(181\) 12.1803 0.905358 0.452679 0.891674i \(-0.350468\pi\)
0.452679 + 0.891674i \(0.350468\pi\)
\(182\) 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 0.762619 0.646848i \(-0.223913\pi\)
−0.941496 + 0.337023i \(0.890580\pi\)
\(192\) 0 0
\(193\) −0.236068 + 0.408882i −0.0169925 + 0.0294320i −0.874397 0.485212i \(-0.838742\pi\)
0.857404 + 0.514644i \(0.172076\pi\)
\(194\) 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 −0.452096 0.891969i \(-0.649324\pi\)
0.998516 0.0544581i \(-0.0173431\pi\)
\(200\) 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 \(-0.642688\pi\)
−0.433406 + 0.901199i \(0.642688\pi\)
\(224\) 0 0
\(225\) −8.05573 −0.537049
\(226\) 0 0
\(227\) −8.61803 + 14.9269i −0.571999 + 0.990731i 0.424362 + 0.905493i \(0.360499\pi\)
−0.996361 + 0.0852385i \(0.972835\pi\)
\(228\) 0 0
\(229\) 11.7984 + 20.4354i 0.779658 + 1.35041i 0.932139 + 0.362102i \(0.117941\pi\)
−0.152480 + 0.988307i \(0.548726\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.94427 + 13.7599i 0.520447 + 0.901440i 0.999717 + 0.0237728i \(0.00756784\pi\)
−0.479271 + 0.877667i \(0.659099\pi\)
\(234\) 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 \(-0.701753\pi\)
0.993931 + 0.110003i \(0.0350860\pi\)
\(242\) 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 \(-0.543247\pi\)
−0.135448 + 0.990784i \(0.543247\pi\)
\(252\) 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 \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 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 −0.984593 0.174861i \(-0.944052\pi\)
0.643730 + 0.765252i \(0.277386\pi\)
\(264\) 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 \(-0.874009\pi\)
0.795244 + 0.606289i \(0.207343\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 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 −0.959849 0.280518i \(-0.909494\pi\)
0.722860 + 0.690994i \(0.242827\pi\)
\(278\) 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 \(-0.892138\pi\)
0.759443 + 0.650574i \(0.225471\pi\)
\(284\) 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 \(-0.378385\pi\)
0.372838 + 0.927896i \(0.378385\pi\)
\(294\) 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 \(-0.516536\pi\)
−0.0519267 + 0.998651i \(0.516536\pi\)
\(308\) 0 0
\(309\) −6.83282 −0.388705
\(310\) 0 0
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 0 0
\(313\) −4.23607 7.33708i −0.239437 0.414717i 0.721116 0.692814i \(-0.243629\pi\)
−0.960553 + 0.278098i \(0.910296\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.52786 7.84249i −0.254310 0.440478i 0.710398 0.703800i \(-0.248515\pi\)
−0.964708 + 0.263322i \(0.915182\pi\)
\(318\) 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 −0.989924 0.141599i \(-0.954776\pi\)
0.372334 0.928099i \(-0.378558\pi\)
\(332\) 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 −0.939718 0.341950i \(-0.888913\pi\)
0.765997 + 0.642844i \(0.222246\pi\)
\(348\) 0 0
\(349\) −26.6525 −1.42667 −0.713337 0.700821i \(-0.752817\pi\)
−0.713337 + 0.700821i \(0.752817\pi\)
\(350\) 0 0
\(351\) −4.22291 −0.225402
\(352\) 0 0
\(353\) −7.94427 + 13.7599i −0.422831 + 0.732365i −0.996215 0.0869220i \(-0.972297\pi\)
0.573384 + 0.819287i \(0.305630\pi\)
\(354\) 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 0.998199 0.0599949i \(-0.0191084\pi\)
−0.551056 + 0.834468i \(0.685775\pi\)
\(360\) 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 0.397483 + 0.917610i \(0.369884\pi\)
−0.993415 + 0.114574i \(0.963450\pi\)
\(368\) 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 0.825394 0.564558i \(-0.190953\pi\)
−0.901618 + 0.432533i \(0.857620\pi\)
\(374\) 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 \(-0.295531\pi\)
−0.992956 + 0.118481i \(0.962198\pi\)
\(384\) 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 −0.803755 0.594960i \(-0.797168\pi\)
0.917128 + 0.398592i \(0.130501\pi\)
\(390\) 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 \(-0.291548\pi\)
−0.991396 + 0.130897i \(0.958214\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7639 + 20.3757i 0.587463 + 1.01752i 0.994563 + 0.104132i \(0.0332065\pi\)
−0.407101 + 0.913383i \(0.633460\pi\)
\(402\) 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 0.469922 + 0.882708i \(0.344282\pi\)
−0.999408 + 0.0343897i \(0.989051\pi\)
\(410\) 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 \(-0.682253\pi\)
−0.541790 + 0.840514i \(0.682253\pi\)
\(420\) 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 −0.302300 0.953213i \(-0.597755\pi\)
0.976657 0.214807i \(-0.0689121\pi\)
\(432\) 0 0
\(433\) −9.41641 −0.452524 −0.226262 0.974067i \(-0.572651\pi\)
−0.226262 + 0.974067i \(0.572651\pi\)
\(434\) 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 −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.94427 + 12.0278i 0.329932 + 0.571460i 0.982498 0.186273i \(-0.0596407\pi\)
−0.652566 + 0.757732i \(0.726307\pi\)
\(444\) 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 0.940531 0.339708i \(-0.110328\pi\)
−0.764462 + 0.644669i \(0.776995\pi\)
\(458\) 0 0
\(459\) 12.3607 21.4093i 0.576947 0.999302i
\(460\) 0 0
\(461\) −21.7082 −1.01105 −0.505526 0.862811i \(-0.668702\pi\)
−0.505526 + 0.862811i \(0.668702\pi\)
\(462\) 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 −0.951590 0.307370i \(-0.900551\pi\)
0.209605 0.977786i \(-0.432782\pi\)
\(468\) 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 \(-0.896160\pi\)
0.751162 + 0.660117i \(0.229493\pi\)
\(480\) 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 −0.998579 0.0532853i \(-0.983031\pi\)
0.545436 + 0.838152i \(0.316364\pi\)
\(488\) 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 0.510000 0.860174i \(-0.329645\pi\)
−0.999933 + 0.0115857i \(0.996312\pi\)
\(500\) 0 0
\(501\) −14.4721 + 25.0665i −0.646567 + 1.11989i
\(502\) 0 0
\(503\) 4.94427 0.220454 0.110227 0.993906i \(-0.464842\pi\)
0.110227 + 0.993906i \(0.464842\pi\)
\(504\) 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 −0.812077 0.583551i \(-0.801663\pi\)
−0.0993316 0.995054i \(-0.531670\pi\)
\(510\) 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 \(-0.879399\pi\)
0.784864 + 0.619668i \(0.212733\pi\)
\(522\) 0 0
\(523\) −2.14590 3.71680i −0.0938336 0.162525i 0.815288 0.579056i \(-0.196579\pi\)
−0.909121 + 0.416532i \(0.863245\pi\)
\(524\) 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 0.915236 0.402917i \(-0.132004\pi\)
−0.806555 + 0.591159i \(0.798671\pi\)
\(542\) 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 −0.945864 0.324563i \(-0.894783\pi\)
0.754012 + 0.656860i \(0.228116\pi\)
\(558\) 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 \(-0.955864\pi\)
0.614898 + 0.788607i \(0.289197\pi\)
\(564\) 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 −0.998090 0.0617808i \(-0.980322\pi\)
0.445541 0.895261i \(-0.353011\pi\)
\(570\) 0 0
\(571\) 7.23607 12.5332i 0.302820 0.524500i −0.673954 0.738774i \(-0.735405\pi\)
0.976774 + 0.214274i \(0.0687386\pi\)
\(572\) 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 \(-0.873192\pi\)
0.796799 + 0.604245i \(0.206525\pi\)
\(578\) 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 \(-0.475617\pi\)
0.0765270 + 0.997068i \(0.475617\pi\)
\(588\) 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 0.976719 + 0.214522i \(0.0688194\pi\)
−0.302578 + 0.953125i \(0.597847\pi\)
\(594\) 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 −0.988849 0.148923i \(-0.952419\pi\)
0.623396 + 0.781907i \(0.285753\pi\)
\(600\) 0 0
\(601\) −29.7771 −1.21463 −0.607316 0.794460i \(-0.707754\pi\)
−0.607316 + 0.794460i \(0.707754\pi\)
\(602\) 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 \(-0.102351\pi\)
−0.748066 + 0.663624i \(0.769018\pi\)
\(608\) 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 0.399620 + 0.916681i \(0.369142\pi\)
−0.993679 + 0.112259i \(0.964191\pi\)
\(614\) 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 −0.259192 + 0.965826i \(0.583456\pi\)
−0.706833 + 0.707380i \(0.749877\pi\)
\(620\) 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 −0.973334 0.229391i \(-0.926327\pi\)
0.685326 + 0.728237i \(0.259660\pi\)
\(642\) 0 0
\(643\) 43.7082 1.72368 0.861842 0.507177i \(-0.169311\pi\)
0.861842 + 0.507177i \(0.169311\pi\)
\(644\) 0 0
\(645\) 25.8885 1.01936
\(646\) 0 0
\(647\) −10.1803 + 17.6329i −0.400230 + 0.693219i −0.993753 0.111598i \(-0.964403\pi\)
0.593523 + 0.804817i \(0.297737\pi\)
\(648\) 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 0.943322 0.331878i \(-0.107682\pi\)
−0.759076 + 0.651002i \(0.774349\pi\)
\(654\) 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 \(-0.978546\pi\)
0.557190 + 0.830385i \(0.311880\pi\)
\(662\) 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 \(-0.0422927\pi\)
−0.610321 + 0.792155i \(0.708959\pi\)
\(678\) 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 −0.998683 0.0513135i \(-0.983659\pi\)
0.543780 + 0.839228i \(0.316993\pi\)
\(684\) 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 \(-0.253599\pi\)
−0.968790 + 0.247882i \(0.920265\pi\)
\(692\) 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 0.850223 0.526422i \(-0.176467\pi\)
−0.881006 + 0.473104i \(0.843133\pi\)
\(710\) 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 0.735286 + 0.677757i \(0.237048\pi\)
0.219311 + 0.975655i \(0.429619\pi\)
\(720\) 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 \(-0.573616\pi\)
−0.229216 + 0.973376i \(0.573616\pi\)
\(728\) 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 \(-0.194708\pi\)
−0.906657 + 0.421868i \(0.861374\pi\)
\(734\) 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 −0.832895 0.553431i \(-0.813318\pi\)
0.895733 + 0.444593i \(0.146652\pi\)
\(740\) 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 −0.981432 0.191811i \(-0.938564\pi\)
0.324603 0.945851i \(-0.394769\pi\)
\(752\) 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 \(-0.187034\pi\)
−0.896224 + 0.443601i \(0.853701\pi\)
\(762\) 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 \(-0.392597\pi\)
0.331052 + 0.943613i \(0.392597\pi\)
\(770\) 0 0
\(771\) −17.3050 −0.623223
\(772\) 0 0
\(773\) 20.0902 34.7972i 0.722593 1.25157i −0.237364 0.971421i \(-0.576283\pi\)
0.959957 0.280147i \(-0.0903833\pi\)
\(774\) 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 \(-0.903638\pi\)
0.735449 + 0.677580i \(0.236971\pi\)
\(788\) 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
\(795\) 20.0000 34.6410i 0.709327 1.22859i
\(796\) 0 0
\(797\) 52.1803 1.84832 0.924161 0.382003i \(-0.124765\pi\)
0.924161 + 0.382003i \(0.124765\pi\)
\(798\) 0 0
\(799\) 46.8328 1.65683