Properties

Label 136.2.n.a.121.1
Level $136$
Weight $2$
Character 136.121
Analytic conductor $1.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.n (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.08596546749\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 121.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 136.121
Dual form 136.2.n.a.9.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70711 + 0.707107i) q^{3} +(0.292893 + 0.707107i) q^{5} +(-1.70711 + 4.12132i) q^{7} +(0.292893 - 0.292893i) q^{9} +O(q^{10})\) \(q+(-1.70711 + 0.707107i) q^{3} +(0.292893 + 0.707107i) q^{5} +(-1.70711 + 4.12132i) q^{7} +(0.292893 - 0.292893i) q^{9} +(1.70711 + 0.707107i) q^{11} +(-1.00000 - 1.00000i) q^{15} +(1.00000 + 4.00000i) q^{17} +(-4.41421 - 4.41421i) q^{19} -8.24264i q^{21} +(4.53553 + 1.87868i) q^{23} +(3.12132 - 3.12132i) q^{25} +(1.82843 - 4.41421i) q^{27} +(-0.878680 - 2.12132i) q^{29} +(5.12132 - 2.12132i) q^{31} -3.41421 q^{33} -3.41421 q^{35} +(1.70711 - 0.707107i) q^{37} +(-3.70711 + 8.94975i) q^{41} +(-1.24264 + 1.24264i) q^{43} +(0.292893 + 0.121320i) q^{45} +7.17157i q^{47} +(-9.12132 - 9.12132i) q^{49} +(-4.53553 - 6.12132i) q^{51} +(7.82843 + 7.82843i) q^{53} +1.41421i q^{55} +(10.6569 + 4.41421i) q^{57} +(8.41421 - 8.41421i) q^{59} +(-4.87868 + 11.7782i) q^{61} +(0.707107 + 1.70711i) q^{63} -1.65685 q^{67} -9.07107 q^{69} +(2.29289 - 0.949747i) q^{71} +(-5.36396 - 12.9497i) q^{73} +(-3.12132 + 7.53553i) q^{75} +(-5.82843 + 5.82843i) q^{77} +(12.5355 + 5.19239i) q^{79} +10.0711i q^{81} +(1.24264 + 1.24264i) q^{83} +(-2.53553 + 1.87868i) q^{85} +(3.00000 + 3.00000i) q^{87} -9.65685i q^{89} +(-7.24264 + 7.24264i) q^{93} +(1.82843 - 4.41421i) q^{95} +(0.778175 + 1.87868i) q^{97} +(0.707107 - 0.292893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{17} - 12 q^{19} + 4 q^{23} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 12 q^{31} - 8 q^{33} - 8 q^{35} + 4 q^{37} - 12 q^{41} + 12 q^{43} + 4 q^{45} - 28 q^{49} - 4 q^{51} + 20 q^{53} + 20 q^{57} + 28 q^{59} - 28 q^{61} + 16 q^{67} - 8 q^{69} + 12 q^{71} + 4 q^{73} - 4 q^{75} - 12 q^{77} + 36 q^{79} - 12 q^{83} + 4 q^{85} + 12 q^{87} - 12 q^{93} - 4 q^{95} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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
\(3\) −1.70711 + 0.707107i −0.985599 + 0.408248i −0.816497 0.577350i \(-0.804087\pi\)
−0.169102 + 0.985599i \(0.554087\pi\)
\(4\) 0 0
\(5\) 0.292893 + 0.707107i 0.130986 + 0.316228i 0.975742 0.218924i \(-0.0702546\pi\)
−0.844756 + 0.535151i \(0.820255\pi\)
\(6\) 0 0
\(7\) −1.70711 + 4.12132i −0.645226 + 1.55771i 0.174314 + 0.984690i \(0.444229\pi\)
−0.819540 + 0.573023i \(0.805771\pi\)
\(8\) 0 0
\(9\) 0.292893 0.292893i 0.0976311 0.0976311i
\(10\) 0 0
\(11\) 1.70711 + 0.707107i 0.514712 + 0.213201i 0.624892 0.780711i \(-0.285143\pi\)
−0.110180 + 0.993912i \(0.535143\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.00000 1.00000i −0.258199 0.258199i
\(16\) 0 0
\(17\) 1.00000 + 4.00000i 0.242536 + 0.970143i
\(18\) 0 0
\(19\) −4.41421 4.41421i −1.01269 1.01269i −0.999918 0.0127716i \(-0.995935\pi\)
−0.0127716 0.999918i \(-0.504065\pi\)
\(20\) 0 0
\(21\) 8.24264i 1.79869i
\(22\) 0 0
\(23\) 4.53553 + 1.87868i 0.945724 + 0.391732i 0.801622 0.597831i \(-0.203971\pi\)
0.144102 + 0.989563i \(0.453971\pi\)
\(24\) 0 0
\(25\) 3.12132 3.12132i 0.624264 0.624264i
\(26\) 0 0
\(27\) 1.82843 4.41421i 0.351881 0.849516i
\(28\) 0 0
\(29\) −0.878680 2.12132i −0.163167 0.393919i 0.821057 0.570846i \(-0.193385\pi\)
−0.984224 + 0.176926i \(0.943385\pi\)
\(30\) 0 0
\(31\) 5.12132 2.12132i 0.919816 0.381000i 0.128010 0.991773i \(-0.459141\pi\)
0.791806 + 0.610772i \(0.209141\pi\)
\(32\) 0 0
\(33\) −3.41421 −0.594338
\(34\) 0 0
\(35\) −3.41421 −0.577107
\(36\) 0 0
\(37\) 1.70711 0.707107i 0.280647 0.116248i −0.237920 0.971285i \(-0.576466\pi\)
0.518567 + 0.855037i \(0.326466\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.70711 + 8.94975i −0.578953 + 1.39772i 0.314801 + 0.949158i \(0.398062\pi\)
−0.893754 + 0.448558i \(0.851938\pi\)
\(42\) 0 0
\(43\) −1.24264 + 1.24264i −0.189501 + 0.189501i −0.795480 0.605979i \(-0.792781\pi\)
0.605979 + 0.795480i \(0.292781\pi\)
\(44\) 0 0
\(45\) 0.292893 + 0.121320i 0.0436619 + 0.0180854i
\(46\) 0 0
\(47\) 7.17157i 1.04608i 0.852308 + 0.523041i \(0.175202\pi\)
−0.852308 + 0.523041i \(0.824798\pi\)
\(48\) 0 0
\(49\) −9.12132 9.12132i −1.30305 1.30305i
\(50\) 0 0
\(51\) −4.53553 6.12132i −0.635102 0.857156i
\(52\) 0 0
\(53\) 7.82843 + 7.82843i 1.07532 + 1.07532i 0.996922 + 0.0783948i \(0.0249795\pi\)
0.0783948 + 0.996922i \(0.475021\pi\)
\(54\) 0 0
\(55\) 1.41421i 0.190693i
\(56\) 0 0
\(57\) 10.6569 + 4.41421i 1.41153 + 0.584677i
\(58\) 0 0
\(59\) 8.41421 8.41421i 1.09544 1.09544i 0.100500 0.994937i \(-0.467956\pi\)
0.994937 0.100500i \(-0.0320443\pi\)
\(60\) 0 0
\(61\) −4.87868 + 11.7782i −0.624651 + 1.50804i 0.221535 + 0.975152i \(0.428893\pi\)
−0.846186 + 0.532888i \(0.821107\pi\)
\(62\) 0 0
\(63\) 0.707107 + 1.70711i 0.0890871 + 0.215075i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.65685 −0.202417 −0.101208 0.994865i \(-0.532271\pi\)
−0.101208 + 0.994865i \(0.532271\pi\)
\(68\) 0 0
\(69\) −9.07107 −1.09203
\(70\) 0 0
\(71\) 2.29289 0.949747i 0.272116 0.112714i −0.242453 0.970163i \(-0.577952\pi\)
0.514569 + 0.857449i \(0.327952\pi\)
\(72\) 0 0
\(73\) −5.36396 12.9497i −0.627804 1.51565i −0.842345 0.538938i \(-0.818826\pi\)
0.214541 0.976715i \(-0.431174\pi\)
\(74\) 0 0
\(75\) −3.12132 + 7.53553i −0.360419 + 0.870129i
\(76\) 0 0
\(77\) −5.82843 + 5.82843i −0.664211 + 0.664211i
\(78\) 0 0
\(79\) 12.5355 + 5.19239i 1.41036 + 0.584189i 0.952418 0.304794i \(-0.0985876\pi\)
0.457939 + 0.888983i \(0.348588\pi\)
\(80\) 0 0
\(81\) 10.0711i 1.11901i
\(82\) 0 0
\(83\) 1.24264 + 1.24264i 0.136398 + 0.136398i 0.772009 0.635612i \(-0.219252\pi\)
−0.635612 + 0.772009i \(0.719252\pi\)
\(84\) 0 0
\(85\) −2.53553 + 1.87868i −0.275017 + 0.203771i
\(86\) 0 0
\(87\) 3.00000 + 3.00000i 0.321634 + 0.321634i
\(88\) 0 0
\(89\) 9.65685i 1.02362i −0.859097 0.511812i \(-0.828974\pi\)
0.859097 0.511812i \(-0.171026\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.24264 + 7.24264i −0.751027 + 0.751027i
\(94\) 0 0
\(95\) 1.82843 4.41421i 0.187593 0.452889i
\(96\) 0 0
\(97\) 0.778175 + 1.87868i 0.0790117 + 0.190751i 0.958449 0.285263i \(-0.0920810\pi\)
−0.879438 + 0.476014i \(0.842081\pi\)
\(98\) 0 0
\(99\) 0.707107 0.292893i 0.0710669 0.0294369i
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −13.6569 −1.34565 −0.672825 0.739802i \(-0.734919\pi\)
−0.672825 + 0.739802i \(0.734919\pi\)
\(104\) 0 0
\(105\) 5.82843 2.41421i 0.568796 0.235603i
\(106\) 0 0
\(107\) −0.636039 1.53553i −0.0614882 0.148446i 0.890149 0.455669i \(-0.150600\pi\)
−0.951637 + 0.307224i \(0.900600\pi\)
\(108\) 0 0
\(109\) 4.77817 11.5355i 0.457666 1.10490i −0.511674 0.859180i \(-0.670974\pi\)
0.969340 0.245724i \(-0.0790257\pi\)
\(110\) 0 0
\(111\) −2.41421 + 2.41421i −0.229147 + 0.229147i
\(112\) 0 0
\(113\) −1.12132 0.464466i −0.105485 0.0436933i 0.329317 0.944219i \(-0.393182\pi\)
−0.434802 + 0.900526i \(0.643182\pi\)
\(114\) 0 0
\(115\) 3.75736i 0.350376i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −18.1924 2.70711i −1.66769 0.248160i
\(120\) 0 0
\(121\) −5.36396 5.36396i −0.487633 0.487633i
\(122\) 0 0
\(123\) 17.8995i 1.61394i
\(124\) 0 0
\(125\) 6.65685 + 2.75736i 0.595407 + 0.246626i
\(126\) 0 0
\(127\) 7.24264 7.24264i 0.642680 0.642680i −0.308533 0.951214i \(-0.599838\pi\)
0.951214 + 0.308533i \(0.0998381\pi\)
\(128\) 0 0
\(129\) 1.24264 3.00000i 0.109408 0.264135i
\(130\) 0 0
\(131\) −0.636039 1.53553i −0.0555710 0.134160i 0.893656 0.448753i \(-0.148132\pi\)
−0.949227 + 0.314593i \(0.898132\pi\)
\(132\) 0 0
\(133\) 25.7279 10.6569i 2.23089 0.924066i
\(134\) 0 0
\(135\) 3.65685 0.314732
\(136\) 0 0
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) −18.1924 + 7.53553i −1.54306 + 0.639156i −0.982044 0.188651i \(-0.939589\pi\)
−0.561014 + 0.827806i \(0.689589\pi\)
\(140\) 0 0
\(141\) −5.07107 12.2426i −0.427061 1.03102i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 1.24264 1.24264i 0.103196 0.103196i
\(146\) 0 0
\(147\) 22.0208 + 9.12132i 1.81625 + 0.752314i
\(148\) 0 0
\(149\) 17.6569i 1.44651i −0.690583 0.723253i \(-0.742646\pi\)
0.690583 0.723253i \(-0.257354\pi\)
\(150\) 0 0
\(151\) 0.0710678 + 0.0710678i 0.00578342 + 0.00578342i 0.709993 0.704209i \(-0.248698\pi\)
−0.704209 + 0.709993i \(0.748698\pi\)
\(152\) 0 0
\(153\) 1.46447 + 0.878680i 0.118395 + 0.0710370i
\(154\) 0 0
\(155\) 3.00000 + 3.00000i 0.240966 + 0.240966i
\(156\) 0 0
\(157\) 7.31371i 0.583697i −0.956464 0.291849i \(-0.905730\pi\)
0.956464 0.291849i \(-0.0942704\pi\)
\(158\) 0 0
\(159\) −18.8995 7.82843i −1.49883 0.620835i
\(160\) 0 0
\(161\) −15.4853 + 15.4853i −1.22041 + 1.22041i
\(162\) 0 0
\(163\) −5.70711 + 13.7782i −0.447015 + 1.07919i 0.526420 + 0.850225i \(0.323534\pi\)
−0.973435 + 0.228965i \(0.926466\pi\)
\(164\) 0 0
\(165\) −1.00000 2.41421i −0.0778499 0.187946i
\(166\) 0 0
\(167\) −1.70711 + 0.707107i −0.132100 + 0.0547176i −0.447754 0.894157i \(-0.647776\pi\)
0.315654 + 0.948874i \(0.397776\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) −2.58579 −0.197740
\(172\) 0 0
\(173\) −22.7782 + 9.43503i −1.73179 + 0.717332i −0.732460 + 0.680810i \(0.761628\pi\)
−0.999333 + 0.0365215i \(0.988372\pi\)
\(174\) 0 0
\(175\) 7.53553 + 18.1924i 0.569633 + 1.37522i
\(176\) 0 0
\(177\) −8.41421 + 20.3137i −0.632451 + 1.52687i
\(178\) 0 0
\(179\) −6.89949 + 6.89949i −0.515692 + 0.515692i −0.916265 0.400573i \(-0.868811\pi\)
0.400573 + 0.916265i \(0.368811\pi\)
\(180\) 0 0
\(181\) −1.12132 0.464466i −0.0833471 0.0345235i 0.340620 0.940201i \(-0.389363\pi\)
−0.423967 + 0.905677i \(0.639363\pi\)
\(182\) 0 0
\(183\) 23.5563i 1.74134i
\(184\) 0 0
\(185\) 1.00000 + 1.00000i 0.0735215 + 0.0735215i
\(186\) 0 0
\(187\) −1.12132 + 7.53553i −0.0819991 + 0.551053i
\(188\) 0 0
\(189\) 15.0711 + 15.0711i 1.09626 + 1.09626i
\(190\) 0 0
\(191\) 3.17157i 0.229487i −0.993395 0.114743i \(-0.963395\pi\)
0.993395 0.114743i \(-0.0366046\pi\)
\(192\) 0 0
\(193\) 1.70711 + 0.707107i 0.122880 + 0.0508987i 0.443276 0.896385i \(-0.353816\pi\)
−0.320396 + 0.947284i \(0.603816\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.36396 + 3.29289i −0.0971782 + 0.234609i −0.964991 0.262282i \(-0.915525\pi\)
0.867813 + 0.496891i \(0.165525\pi\)
\(198\) 0 0
\(199\) 5.22183 + 12.6066i 0.370165 + 0.893658i 0.993722 + 0.111880i \(0.0356872\pi\)
−0.623556 + 0.781778i \(0.714313\pi\)
\(200\) 0 0
\(201\) 2.82843 1.17157i 0.199502 0.0826364i
\(202\) 0 0
\(203\) 10.2426 0.718892
\(204\) 0 0
\(205\) −7.41421 −0.517831
\(206\) 0 0
\(207\) 1.87868 0.778175i 0.130577 0.0540869i
\(208\) 0 0
\(209\) −4.41421 10.6569i −0.305338 0.737150i
\(210\) 0 0
\(211\) 5.80761 14.0208i 0.399812 0.965233i −0.587898 0.808935i \(-0.700044\pi\)
0.987710 0.156297i \(-0.0499558\pi\)
\(212\) 0 0
\(213\) −3.24264 + 3.24264i −0.222182 + 0.222182i
\(214\) 0 0
\(215\) −1.24264 0.514719i −0.0847474 0.0351035i
\(216\) 0 0
\(217\) 24.7279i 1.67864i
\(218\) 0 0
\(219\) 18.3137 + 18.3137i 1.23753 + 1.23753i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −9.58579 9.58579i −0.641912 0.641912i 0.309113 0.951025i \(-0.399968\pi\)
−0.951025 + 0.309113i \(0.899968\pi\)
\(224\) 0 0
\(225\) 1.82843i 0.121895i
\(226\) 0 0
\(227\) 11.3640 + 4.70711i 0.754253 + 0.312422i 0.726475 0.687192i \(-0.241157\pi\)
0.0277772 + 0.999614i \(0.491157\pi\)
\(228\) 0 0
\(229\) −7.00000 + 7.00000i −0.462573 + 0.462573i −0.899498 0.436925i \(-0.856068\pi\)
0.436925 + 0.899498i \(0.356068\pi\)
\(230\) 0 0
\(231\) 5.82843 14.0711i 0.383482 0.925808i
\(232\) 0 0
\(233\) −6.53553 15.7782i −0.428157 1.03366i −0.979871 0.199629i \(-0.936026\pi\)
0.551714 0.834033i \(-0.313974\pi\)
\(234\) 0 0
\(235\) −5.07107 + 2.10051i −0.330800 + 0.137022i
\(236\) 0 0
\(237\) −25.0711 −1.62854
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 0 0
\(241\) 7.36396 3.05025i 0.474354 0.196484i −0.132681 0.991159i \(-0.542359\pi\)
0.607035 + 0.794675i \(0.292359\pi\)
\(242\) 0 0
\(243\) −1.63604 3.94975i −0.104952 0.253376i
\(244\) 0 0
\(245\) 3.77817 9.12132i 0.241379 0.582740i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −3.00000 1.24264i −0.190117 0.0787492i
\(250\) 0 0
\(251\) 4.82843i 0.304768i −0.988321 0.152384i \(-0.951305\pi\)
0.988321 0.152384i \(-0.0486950\pi\)
\(252\) 0 0
\(253\) 6.41421 + 6.41421i 0.403258 + 0.403258i
\(254\) 0 0
\(255\) 3.00000 5.00000i 0.187867 0.313112i
\(256\) 0 0
\(257\) −0.171573 0.171573i −0.0107024 0.0107024i 0.701735 0.712438i \(-0.252409\pi\)
−0.712438 + 0.701735i \(0.752409\pi\)
\(258\) 0 0
\(259\) 8.24264i 0.512173i
\(260\) 0 0
\(261\) −0.878680 0.363961i −0.0543889 0.0225286i
\(262\) 0 0
\(263\) 11.2426 11.2426i 0.693251 0.693251i −0.269695 0.962946i \(-0.586923\pi\)
0.962946 + 0.269695i \(0.0869228\pi\)
\(264\) 0 0
\(265\) −3.24264 + 7.82843i −0.199194 + 0.480896i
\(266\) 0 0
\(267\) 6.82843 + 16.4853i 0.417893 + 1.00888i
\(268\) 0 0
\(269\) 7.36396 3.05025i 0.448989 0.185977i −0.146720 0.989178i \(-0.546871\pi\)
0.595708 + 0.803201i \(0.296871\pi\)
\(270\) 0 0
\(271\) 11.3137 0.687259 0.343629 0.939105i \(-0.388344\pi\)
0.343629 + 0.939105i \(0.388344\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.53553 3.12132i 0.454410 0.188223i
\(276\) 0 0
\(277\) 1.46447 + 3.53553i 0.0879912 + 0.212430i 0.961749 0.273931i \(-0.0883241\pi\)
−0.873758 + 0.486361i \(0.838324\pi\)
\(278\) 0 0
\(279\) 0.878680 2.12132i 0.0526052 0.127000i
\(280\) 0 0
\(281\) 20.3137 20.3137i 1.21181 1.21181i 0.241385 0.970429i \(-0.422398\pi\)
0.970429 0.241385i \(-0.0776016\pi\)
\(282\) 0 0
\(283\) −19.9497 8.26346i −1.18589 0.491211i −0.299475 0.954104i \(-0.596812\pi\)
−0.886414 + 0.462893i \(0.846812\pi\)
\(284\) 0 0
\(285\) 8.82843i 0.522951i
\(286\) 0 0
\(287\) −30.5563 30.5563i −1.80368 1.80368i
\(288\) 0 0
\(289\) −15.0000 + 8.00000i −0.882353 + 0.470588i
\(290\) 0 0
\(291\) −2.65685 2.65685i −0.155748 0.155748i
\(292\) 0 0
\(293\) 15.3137i 0.894636i 0.894375 + 0.447318i \(0.147621\pi\)
−0.894375 + 0.447318i \(0.852379\pi\)
\(294\) 0 0
\(295\) 8.41421 + 3.48528i 0.489894 + 0.202921i
\(296\) 0 0
\(297\) 6.24264 6.24264i 0.362235 0.362235i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −3.00000 7.24264i −0.172917 0.417459i
\(302\) 0 0
\(303\) −17.0711 + 7.07107i −0.980707 + 0.406222i
\(304\) 0 0
\(305\) −9.75736 −0.558705
\(306\) 0 0
\(307\) 18.6274 1.06312 0.531561 0.847020i \(-0.321605\pi\)
0.531561 + 0.847020i \(0.321605\pi\)
\(308\) 0 0
\(309\) 23.3137 9.65685i 1.32627 0.549359i
\(310\) 0 0
\(311\) −2.29289 5.53553i −0.130018 0.313891i 0.845442 0.534067i \(-0.179337\pi\)
−0.975460 + 0.220176i \(0.929337\pi\)
\(312\) 0 0
\(313\) 5.94975 14.3640i 0.336300 0.811899i −0.661765 0.749711i \(-0.730192\pi\)
0.998064 0.0621876i \(-0.0198077\pi\)
\(314\) 0 0
\(315\) −1.00000 + 1.00000i −0.0563436 + 0.0563436i
\(316\) 0 0
\(317\) −15.9497 6.60660i −0.895827 0.371064i −0.113213 0.993571i \(-0.536114\pi\)
−0.782614 + 0.622507i \(0.786114\pi\)
\(318\) 0 0
\(319\) 4.24264i 0.237542i
\(320\) 0 0
\(321\) 2.17157 + 2.17157i 0.121205 + 0.121205i
\(322\) 0 0
\(323\) 13.2426 22.0711i 0.736840 1.22807i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 23.0711i 1.27583i
\(328\) 0 0
\(329\) −29.5563 12.2426i −1.62949 0.674959i
\(330\) 0 0
\(331\) 15.7279 15.7279i 0.864485 0.864485i −0.127370 0.991855i \(-0.540654\pi\)
0.991855 + 0.127370i \(0.0406537\pi\)
\(332\) 0 0
\(333\) 0.292893 0.707107i 0.0160504 0.0387492i
\(334\) 0 0
\(335\) −0.485281 1.17157i −0.0265138 0.0640099i
\(336\) 0 0
\(337\) −3.94975 + 1.63604i −0.215156 + 0.0891207i −0.487658 0.873034i \(-0.662149\pi\)
0.272502 + 0.962155i \(0.412149\pi\)
\(338\) 0 0
\(339\) 2.24264 0.121804
\(340\) 0 0
\(341\) 10.2426 0.554670
\(342\) 0 0
\(343\) 24.3137 10.0711i 1.31282 0.543787i
\(344\) 0 0
\(345\) −2.65685 6.41421i −0.143040 0.345330i
\(346\) 0 0
\(347\) −7.36396 + 17.7782i −0.395318 + 0.954382i 0.593443 + 0.804876i \(0.297768\pi\)
−0.988761 + 0.149506i \(0.952232\pi\)
\(348\) 0 0
\(349\) 1.48528 1.48528i 0.0795053 0.0795053i −0.666236 0.745741i \(-0.732096\pi\)
0.745741 + 0.666236i \(0.232096\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.97056i 0.477455i 0.971087 + 0.238727i \(0.0767302\pi\)
−0.971087 + 0.238727i \(0.923270\pi\)
\(354\) 0 0
\(355\) 1.34315 + 1.34315i 0.0712868 + 0.0712868i
\(356\) 0 0
\(357\) 32.9706 8.24264i 1.74499 0.436247i
\(358\) 0 0
\(359\) 9.72792 + 9.72792i 0.513420 + 0.513420i 0.915573 0.402153i \(-0.131738\pi\)
−0.402153 + 0.915573i \(0.631738\pi\)
\(360\) 0 0
\(361\) 19.9706i 1.05108i
\(362\) 0 0
\(363\) 12.9497 + 5.36396i 0.679685 + 0.281535i
\(364\) 0 0
\(365\) 7.58579 7.58579i 0.397058 0.397058i
\(366\) 0 0
\(367\) 7.94975 19.1924i 0.414973 1.00183i −0.568809 0.822470i \(-0.692596\pi\)
0.983783 0.179365i \(-0.0574043\pi\)
\(368\) 0 0
\(369\) 1.53553 + 3.70711i 0.0799367 + 0.192984i
\(370\) 0 0
\(371\) −45.6274 + 18.8995i −2.36886 + 0.981213i
\(372\) 0 0
\(373\) −31.9411 −1.65385 −0.826924 0.562313i \(-0.809912\pi\)
−0.826924 + 0.562313i \(0.809912\pi\)
\(374\) 0 0
\(375\) −13.3137 −0.687517
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 4.05025 + 9.77817i 0.208047 + 0.502271i 0.993116 0.117138i \(-0.0373721\pi\)
−0.785068 + 0.619409i \(0.787372\pi\)
\(380\) 0 0
\(381\) −7.24264 + 17.4853i −0.371052 + 0.895798i
\(382\) 0 0
\(383\) −10.4142 + 10.4142i −0.532141 + 0.532141i −0.921209 0.389068i \(-0.872797\pi\)
0.389068 + 0.921209i \(0.372797\pi\)
\(384\) 0 0
\(385\) −5.82843 2.41421i −0.297044 0.123040i
\(386\) 0 0
\(387\) 0.727922i 0.0370024i
\(388\) 0 0
\(389\) −2.31371 2.31371i −0.117310 0.117310i 0.646015 0.763325i \(-0.276434\pi\)
−0.763325 + 0.646015i \(0.776434\pi\)
\(390\) 0 0
\(391\) −2.97918 + 20.0208i −0.150664 + 1.01250i
\(392\) 0 0
\(393\) 2.17157 + 2.17157i 0.109541 + 0.109541i
\(394\) 0 0
\(395\) 10.3848i 0.522515i
\(396\) 0 0
\(397\) 6.87868 + 2.84924i 0.345231 + 0.142999i 0.548560 0.836111i \(-0.315176\pi\)
−0.203329 + 0.979110i \(0.565176\pi\)
\(398\) 0 0
\(399\) −36.3848 + 36.3848i −1.82152 + 1.82152i
\(400\) 0 0
\(401\) 0.979185 2.36396i 0.0488982 0.118051i −0.897543 0.440927i \(-0.854650\pi\)
0.946441 + 0.322876i \(0.104650\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −7.12132 + 2.94975i −0.353861 + 0.146574i
\(406\) 0 0
\(407\) 3.41421 0.169236
\(408\) 0 0
\(409\) 18.0000 0.890043 0.445021 0.895520i \(-0.353196\pi\)
0.445021 + 0.895520i \(0.353196\pi\)
\(410\) 0 0
\(411\) −23.8995 + 9.89949i −1.17888 + 0.488306i
\(412\) 0 0
\(413\) 20.3137 + 49.0416i 0.999572 + 2.41318i
\(414\) 0 0
\(415\) −0.514719 + 1.24264i −0.0252665 + 0.0609988i
\(416\) 0 0
\(417\) 25.7279 25.7279i 1.25990 1.25990i
\(418\) 0 0
\(419\) 4.53553 + 1.87868i 0.221575 + 0.0917795i 0.490710 0.871323i \(-0.336738\pi\)
−0.269134 + 0.963103i \(0.586738\pi\)
\(420\) 0 0
\(421\) 11.3137i 0.551396i 0.961244 + 0.275698i \(0.0889090\pi\)
−0.961244 + 0.275698i \(0.911091\pi\)
\(422\) 0 0
\(423\) 2.10051 + 2.10051i 0.102130 + 0.102130i
\(424\) 0 0
\(425\) 15.6066 + 9.36396i 0.757031 + 0.454219i
\(426\) 0 0
\(427\) −40.2132 40.2132i −1.94605 1.94605i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.12132 2.12132i −0.246685 0.102180i 0.255915 0.966699i \(-0.417623\pi\)
−0.502600 + 0.864519i \(0.667623\pi\)
\(432\) 0 0
\(433\) −1.82843 + 1.82843i −0.0878686 + 0.0878686i −0.749675 0.661806i \(-0.769790\pi\)
0.661806 + 0.749675i \(0.269790\pi\)
\(434\) 0 0
\(435\) −1.24264 + 3.00000i −0.0595801 + 0.143839i
\(436\) 0 0
\(437\) −11.7279 28.3137i −0.561023 1.35443i
\(438\) 0 0
\(439\) 17.6066 7.29289i 0.840317 0.348071i 0.0793386 0.996848i \(-0.474719\pi\)
0.760979 + 0.648777i \(0.224719\pi\)
\(440\) 0 0
\(441\) −5.34315 −0.254436
\(442\) 0 0
\(443\) 16.2843 0.773689 0.386845 0.922145i \(-0.373565\pi\)
0.386845 + 0.922145i \(0.373565\pi\)
\(444\) 0 0
\(445\) 6.82843 2.82843i 0.323698 0.134080i
\(446\) 0 0
\(447\) 12.4853 + 30.1421i 0.590534 + 1.42567i
\(448\) 0 0
\(449\) 9.46447 22.8492i 0.446656 1.07832i −0.526911 0.849920i \(-0.676650\pi\)
0.973567 0.228402i \(-0.0733501\pi\)
\(450\) 0 0
\(451\) −12.6569 + 12.6569i −0.595988 + 0.595988i
\(452\) 0 0
\(453\) −0.171573 0.0710678i −0.00806120 0.00333906i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 13.4853 + 13.4853i 0.630815 + 0.630815i 0.948272 0.317458i \(-0.102829\pi\)
−0.317458 + 0.948272i \(0.602829\pi\)
\(458\) 0 0
\(459\) 19.4853 + 2.89949i 0.909495 + 0.135337i
\(460\) 0 0
\(461\) −19.4853 19.4853i −0.907520 0.907520i 0.0885516 0.996072i \(-0.471776\pi\)
−0.996072 + 0.0885516i \(0.971776\pi\)
\(462\) 0 0
\(463\) 4.14214i 0.192501i −0.995357 0.0962507i \(-0.969315\pi\)
0.995357 0.0962507i \(-0.0306850\pi\)
\(464\) 0 0
\(465\) −7.24264 3.00000i −0.335869 0.139122i
\(466\) 0 0
\(467\) 12.4142 12.4142i 0.574461 0.574461i −0.358911 0.933372i \(-0.616852\pi\)
0.933372 + 0.358911i \(0.116852\pi\)
\(468\) 0 0
\(469\) 2.82843 6.82843i 0.130605 0.315307i
\(470\) 0 0
\(471\) 5.17157 + 12.4853i 0.238293 + 0.575291i
\(472\) 0 0
\(473\) −3.00000 + 1.24264i −0.137940 + 0.0571367i
\(474\) 0 0
\(475\) −27.5563 −1.26437
\(476\) 0 0
\(477\) 4.58579 0.209969
\(478\) 0 0
\(479\) 7.46447 3.09188i 0.341060 0.141272i −0.205578 0.978641i \(-0.565907\pi\)
0.546638 + 0.837369i \(0.315907\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 15.4853 37.3848i 0.704605 1.70107i
\(484\) 0 0
\(485\) −1.10051 + 1.10051i −0.0499714 + 0.0499714i
\(486\) 0 0
\(487\) −39.2635 16.2635i −1.77920 0.736968i −0.992876 0.119149i \(-0.961983\pi\)
−0.786321 0.617819i \(-0.788017\pi\)
\(488\) 0 0
\(489\) 27.5563i 1.24614i
\(490\) 0 0
\(491\) 11.5858 + 11.5858i 0.522859 + 0.522859i 0.918434 0.395575i \(-0.129455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(492\) 0 0
\(493\) 7.60660 5.63604i 0.342584 0.253834i
\(494\) 0 0
\(495\) 0.414214 + 0.414214i 0.0186175 + 0.0186175i
\(496\) 0 0
\(497\) 11.0711i 0.496605i
\(498\) 0 0
\(499\) −20.4350 8.46447i −0.914798 0.378922i −0.124906 0.992169i \(-0.539863\pi\)
−0.789891 + 0.613247i \(0.789863\pi\)
\(500\) 0 0
\(501\) 2.41421 2.41421i 0.107859 0.107859i
\(502\) 0 0
\(503\) −1.70711 + 4.12132i −0.0761161 + 0.183761i −0.957357 0.288906i \(-0.906708\pi\)
0.881241 + 0.472667i \(0.156708\pi\)
\(504\) 0 0
\(505\) 2.92893 + 7.07107i 0.130336 + 0.314658i
\(506\) 0 0
\(507\) −22.1924 + 9.19239i −0.985599 + 0.408248i
\(508\) 0 0
\(509\) 18.2843 0.810436 0.405218 0.914220i \(-0.367196\pi\)
0.405218 + 0.914220i \(0.367196\pi\)
\(510\) 0 0
\(511\) 62.5269 2.76603
\(512\) 0 0
\(513\) −27.5563 + 11.4142i −1.21664 + 0.503950i
\(514\) 0 0
\(515\) −4.00000 9.65685i −0.176261 0.425532i
\(516\) 0 0
\(517\) −5.07107 + 12.2426i −0.223025 + 0.538431i
\(518\) 0 0
\(519\) 32.2132 32.2132i 1.41400 1.41400i
\(520\) 0 0
\(521\) 9.02082 + 3.73654i 0.395209 + 0.163701i 0.571432 0.820649i \(-0.306388\pi\)
−0.176223 + 0.984350i \(0.556388\pi\)
\(522\) 0 0
\(523\) 24.1421i 1.05566i −0.849349 0.527831i \(-0.823005\pi\)
0.849349 0.527831i \(-0.176995\pi\)
\(524\) 0 0
\(525\) −25.7279 25.7279i −1.12286 1.12286i
\(526\) 0 0
\(527\) 13.6066 + 18.3640i 0.592713 + 0.799947i
\(528\) 0 0
\(529\) 0.778175 + 0.778175i 0.0338337 + 0.0338337i
\(530\) 0 0
\(531\) 4.92893i 0.213897i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0.899495 0.899495i 0.0388886 0.0388886i
\(536\) 0 0
\(537\) 6.89949 16.6569i 0.297735 0.718796i
\(538\) 0 0
\(539\) −9.12132 22.0208i −0.392883 0.948504i
\(540\) 0 0
\(541\) 0.0502525 0.0208153i 0.00216053 0.000894919i −0.381603 0.924326i \(-0.624628\pi\)
0.383763 + 0.923431i \(0.374628\pi\)
\(542\) 0 0
\(543\) 2.24264 0.0962409
\(544\) 0 0
\(545\) 9.55635 0.409349
\(546\) 0 0
\(547\) 15.2635 6.32233i 0.652618 0.270323i −0.0317103 0.999497i \(-0.510095\pi\)
0.684329 + 0.729174i \(0.260095\pi\)
\(548\) 0 0
\(549\) 2.02082 + 4.87868i 0.0862463 + 0.208217i
\(550\) 0 0
\(551\) −5.48528 + 13.2426i −0.233681 + 0.564155i
\(552\) 0 0
\(553\) −42.7990 + 42.7990i −1.82000 + 1.82000i
\(554\) 0 0
\(555\) −2.41421 1.00000i −0.102478 0.0424476i
\(556\) 0 0
\(557\) 16.0000i 0.677942i −0.940797 0.338971i \(-0.889921\pi\)
0.940797 0.338971i \(-0.110079\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −3.41421 13.6569i −0.144148 0.576593i
\(562\) 0 0
\(563\) 15.5858 + 15.5858i 0.656863 + 0.656863i 0.954636 0.297774i \(-0.0962441\pi\)
−0.297774 + 0.954636i \(0.596244\pi\)
\(564\) 0 0
\(565\) 0.928932i 0.0390805i
\(566\) 0 0
\(567\) −41.5061 17.1924i −1.74309 0.722012i
\(568\) 0 0
\(569\) −32.6569 + 32.6569i −1.36905 + 1.36905i −0.507244 + 0.861802i \(0.669336\pi\)
−0.861802 + 0.507244i \(0.830664\pi\)
\(570\) 0 0
\(571\) 0.150758 0.363961i 0.00630901 0.0152313i −0.920694 0.390286i \(-0.872376\pi\)
0.927003 + 0.375055i \(0.122376\pi\)
\(572\) 0 0
\(573\) 2.24264 + 5.41421i 0.0936877 + 0.226182i
\(574\) 0 0
\(575\) 20.0208 8.29289i 0.834926 0.345838i
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −3.41421 −0.141890
\(580\) 0 0
\(581\) −7.24264 + 3.00000i −0.300475 + 0.124461i
\(582\) 0 0
\(583\) 7.82843 + 18.8995i 0.324220 + 0.782737i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 31.7279 31.7279i 1.30955 1.30955i 0.387814 0.921738i \(-0.373230\pi\)
0.921738 0.387814i \(-0.126770\pi\)
\(588\) 0 0
\(589\) −31.9706 13.2426i −1.31732 0.545654i
\(590\) 0 0
\(591\) 6.58579i 0.270903i
\(592\) 0 0
\(593\) 26.6569 + 26.6569i 1.09467 + 1.09467i 0.995023 + 0.0996425i \(0.0317699\pi\)
0.0996425 + 0.995023i \(0.468230\pi\)
\(594\) 0 0
\(595\) −3.41421 13.6569i −0.139969 0.559876i
\(596\) 0 0
\(597\) −17.8284 17.8284i −0.729669 0.729669i
\(598\) 0 0
\(599\) 39.1716i 1.60051i 0.599662 + 0.800254i \(0.295302\pi\)
−0.599662 + 0.800254i \(0.704698\pi\)
\(600\) 0 0
\(601\) −9.60660 3.97918i −0.391861 0.162314i 0.178048 0.984022i \(-0.443022\pi\)
−0.569910 + 0.821707i \(0.693022\pi\)
\(602\) 0 0
\(603\) −0.485281 + 0.485281i −0.0197622 + 0.0197622i
\(604\) 0 0
\(605\) 2.22183 5.36396i 0.0903300 0.218076i
\(606\) 0 0
\(607\) −2.09188 5.05025i −0.0849069 0.204983i 0.875723 0.482813i \(-0.160385\pi\)
−0.960630 + 0.277830i \(0.910385\pi\)
\(608\) 0 0
\(609\) −17.4853 + 7.24264i −0.708539 + 0.293487i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −6.68629 −0.270057 −0.135028 0.990842i \(-0.543113\pi\)
−0.135028 + 0.990842i \(0.543113\pi\)
\(614\) 0 0
\(615\) 12.6569 5.24264i 0.510374 0.211404i
\(616\) 0 0
\(617\) −7.22183 17.4350i −0.290740 0.701908i 0.709256 0.704951i \(-0.249031\pi\)
−0.999995 + 0.00304356i \(0.999031\pi\)
\(618\) 0 0
\(619\) 7.94975 19.1924i 0.319527 0.771407i −0.679752 0.733442i \(-0.737912\pi\)
0.999279 0.0379649i \(-0.0120875\pi\)
\(620\) 0 0
\(621\) 16.5858 16.5858i 0.665565 0.665565i
\(622\) 0 0
\(623\) 39.7990 + 16.4853i 1.59451 + 0.660469i
\(624\) 0 0
\(625\) 16.5563i 0.662254i
\(626\) 0 0
\(627\) 15.0711 + 15.0711i 0.601880 + 0.601880i
\(628\) 0 0
\(629\) 4.53553 + 6.12132i 0.180844 + 0.244073i
\(630\) 0 0
\(631\) 19.3848 + 19.3848i 0.771696 + 0.771696i 0.978403 0.206707i \(-0.0662747\pi\)
−0.206707 + 0.978403i \(0.566275\pi\)
\(632\) 0 0
\(633\) 28.0416i 1.11455i
\(634\) 0 0
\(635\) 7.24264 + 3.00000i 0.287415 + 0.119051i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.393398 0.949747i 0.0155626 0.0375714i
\(640\) 0 0
\(641\) 15.1213 + 36.5061i 0.597256 + 1.44190i 0.876366 + 0.481645i \(0.159961\pi\)
−0.279110 + 0.960259i \(0.590039\pi\)
\(642\) 0 0
\(643\) −9.02082 + 3.73654i −0.355746 + 0.147355i −0.553397 0.832918i \(-0.686669\pi\)
0.197651 + 0.980272i \(0.436669\pi\)
\(644\) 0 0
\(645\) 2.48528 0.0978579
\(646\) 0 0
\(647\) −45.2548 −1.77915 −0.889576 0.456788i \(-0.849000\pi\)
−0.889576 + 0.456788i \(0.849000\pi\)
\(648\) 0 0
\(649\) 20.3137 8.41421i 0.797383 0.330287i
\(650\) 0 0
\(651\) −17.4853 42.2132i −0.685302 1.65447i
\(652\) 0 0
\(653\) 10.6360 25.6777i 0.416220 1.00484i −0.567212 0.823572i \(-0.691978\pi\)
0.983433 0.181273i \(-0.0580219\pi\)
\(654\) 0 0
\(655\) 0.899495 0.899495i 0.0351462 0.0351462i
\(656\) 0 0
\(657\) −5.36396 2.22183i −0.209268 0.0866817i
\(658\) 0 0
\(659\) 50.7696i 1.97770i 0.148912 + 0.988850i \(0.452423\pi\)
−0.148912 + 0.988850i \(0.547577\pi\)
\(660\) 0 0
\(661\) 20.7990 + 20.7990i 0.808987 + 0.808987i 0.984481 0.175494i \(-0.0561521\pi\)
−0.175494 + 0.984481i \(0.556152\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.0711 + 15.0711i 0.584431 + 0.584431i
\(666\) 0 0
\(667\) 11.2721i 0.436457i
\(668\) 0 0
\(669\) 23.1421 + 9.58579i 0.894727 + 0.370608i
\(670\) 0 0
\(671\) −16.6569 + 16.6569i −0.643031 + 0.643031i
\(672\) 0 0
\(673\) −4.19239 + 10.1213i −0.161605 + 0.390148i −0.983852 0.178981i \(-0.942720\pi\)
0.822248 + 0.569130i \(0.192720\pi\)
\(674\) 0 0
\(675\) −8.07107 19.4853i −0.310656 0.749989i
\(676\) 0 0
\(677\) −42.0919 + 17.4350i −1.61772 + 0.670083i −0.993777 0.111385i \(-0.964471\pi\)
−0.623945 + 0.781468i \(0.714471\pi\)
\(678\) 0 0
\(679\) −9.07107 −0.348116
\(680\) 0 0
\(681\) −22.7279 −0.870936
\(682\) 0 0
\(683\) −37.0208 + 15.3345i −1.41656 + 0.586759i −0.953994 0.299825i \(-0.903072\pi\)
−0.462568 + 0.886584i \(0.653072\pi\)
\(684\) 0 0
\(685\) 4.10051 + 9.89949i 0.156672 + 0.378240i
\(686\) 0 0
\(687\) 7.00000 16.8995i 0.267067 0.644756i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −33.6066 13.9203i −1.27846 0.529554i −0.362931 0.931816i \(-0.618224\pi\)
−0.915524 + 0.402262i \(0.868224\pi\)
\(692\) 0 0
\(693\) 3.41421i 0.129695i
\(694\) 0 0
\(695\) −10.6569 10.6569i −0.404238 0.404238i
\(696\) 0 0
\(697\) −39.5061 5.87868i −1.49640 0.222671i
\(698\) 0 0
\(699\) 22.3137 + 22.3137i 0.843982 + 0.843982i
\(700\) 0 0
\(701\) 51.3137i 1.93809i 0.246880 + 0.969046i \(0.420595\pi\)
−0.246880 + 0.969046i \(0.579405\pi\)
\(702\) 0 0
\(703\) −10.6569 4.41421i −0.401931 0.166485i
\(704\) 0 0
\(705\) 7.17157 7.17157i 0.270097 0.270097i
\(706\) 0 0
\(707\) −17.0711 + 41.2132i −0.642024 + 1.54998i
\(708\) 0 0
\(709\) 15.8076 + 38.1630i 0.593667 + 1.43324i 0.879937 + 0.475091i \(0.157585\pi\)
−0.286270 + 0.958149i \(0.592415\pi\)
\(710\) 0 0
\(711\) 5.19239 2.15076i 0.194730 0.0806597i
\(712\) 0 0
\(713\) 27.2132 1.01914
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 19.3137 8.00000i 0.721284 0.298765i
\(718\) 0 0
\(719\) 8.05025 + 19.4350i 0.300224 + 0.724804i 0.999946 + 0.0103893i \(0.00330708\pi\)
−0.699722 + 0.714415i \(0.746693\pi\)
\(720\) 0 0
\(721\) 23.3137 56.2843i 0.868248 2.09614i
\(722\) 0 0
\(723\) −10.4142 + 10.4142i −0.387309 + 0.387309i
\(724\) 0 0
\(725\) −9.36396 3.87868i −0.347769 0.144051i
\(726\) 0 0
\(727\) 21.7990i 0.808480i 0.914653 + 0.404240i \(0.132464\pi\)
−0.914653 + 0.404240i \(0.867536\pi\)
\(728\) 0 0
\(729\) −15.7782 15.7782i −0.584377 0.584377i
\(730\) 0 0
\(731\) −6.21320 3.72792i −0.229804 0.137882i
\(732\) 0 0
\(733\) 0.514719 + 0.514719i 0.0190116 + 0.0190116i 0.716549 0.697537i \(-0.245721\pi\)
−0.697537 + 0.716549i \(0.745721\pi\)
\(734\) 0 0
\(735\) 18.2426i 0.672890i
\(736\) 0 0
\(737\) −2.82843 1.17157i −0.104186 0.0431554i
\(738\) 0 0
\(739\) −3.58579 + 3.58579i −0.131905 + 0.131905i −0.769977 0.638072i \(-0.779732\pi\)
0.638072 + 0.769977i \(0.279732\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.150758 0.363961i −0.00553076 0.0133524i 0.921090 0.389350i \(-0.127300\pi\)
−0.926621 + 0.375997i \(0.877300\pi\)
\(744\) 0 0
\(745\) 12.4853 5.17157i 0.457425 0.189472i
\(746\) 0 0
\(747\) 0.727922 0.0266333
\(748\) 0 0
\(749\) 7.41421 0.270909
\(750\) 0 0
\(751\) 23.2635 9.63604i 0.848896 0.351624i 0.0845408 0.996420i \(-0.473058\pi\)
0.764355 + 0.644796i \(0.223058\pi\)
\(752\) 0 0
\(753\) 3.41421 + 8.24264i 0.124421 + 0.300379i
\(754\) 0 0
\(755\) −0.0294373 + 0.0710678i −0.00107133 + 0.00258642i
\(756\) 0 0
\(757\) −23.9706 + 23.9706i −0.871225 + 0.871225i −0.992606 0.121381i \(-0.961268\pi\)
0.121381 + 0.992606i \(0.461268\pi\)
\(758\) 0 0
\(759\) −15.4853 6.41421i −0.562080 0.232821i
\(760\) 0 0
\(761\) 36.9706i 1.34018i −0.742279 0.670091i \(-0.766255\pi\)
0.742279 0.670091i \(-0.233745\pi\)
\(762\) 0 0
\(763\) 39.3848 + 39.3848i 1.42582 + 1.42582i
\(764\) 0 0
\(765\) −0.192388 + 1.29289i −0.00695581 + 0.0467447i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 35.5980i 1.28370i −0.766832 0.641848i \(-0.778168\pi\)
0.766832 0.641848i \(-0.221832\pi\)
\(770\) 0 0
\(771\) 0.414214 + 0.171573i 0.0149175 + 0.00617905i
\(772\) 0 0
\(773\) 33.2843 33.2843i 1.19715 1.19715i 0.222136 0.975016i \(-0.428697\pi\)
0.975016 0.222136i \(-0.0713030\pi\)
\(774\) 0 0
\(775\) 9.36396 22.6066i 0.336363 0.812053i
\(776\) 0 0
\(777\) −5.82843 14.0711i −0.209094 0.504797i
\(778\) 0 0
\(779\) 55.8701 23.1421i 2.00175 0.829153i
\(780\) 0 0
\(781\) 4.58579 0.164092
\(782\) 0 0
\(783\) −10.9706 −0.392056
\(784\) 0 0
\(785\) 5.17157 2.14214i 0.184581 0.0764561i
\(786\) 0 0
\(787\) −16.4350 39.6777i −0.585846 1.41436i −0.887442 0.460920i \(-0.847519\pi\)
0.301596 0.953436i \(-0.402481\pi\)
\(788\) 0 0
\(789\) −11.2426 + 27.1421i −0.400249 + 0.966286i
\(790\) 0 0
\(791\) 3.82843 3.82843i 0.136123 0.136123i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 15.6569i 0.555291i
\(796\) 0 0