Properties

Label 1710.2.d.d.1369.2
Level $1710$
Weight $2$
Character 1710.1369
Analytic conductor $13.654$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1369.2
Root \(-1.75233 - 1.75233i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1369
Dual form 1710.2.d.d.1369.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.38900 - 1.75233i) q^{5} +0.636672i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.38900 - 1.75233i) q^{5} +0.636672i q^{7} +1.00000i q^{8} +(-1.75233 + 1.38900i) q^{10} -3.50466 q^{11} +0.141336i q^{13} +0.636672 q^{14} +1.00000 q^{16} -2.14134i q^{17} -1.00000 q^{19} +(1.38900 + 1.75233i) q^{20} +3.50466i q^{22} +4.91934i q^{23} +(-1.14134 + 4.86799i) q^{25} +0.141336 q^{26} -0.636672i q^{28} +7.15066 q^{29} -7.78734 q^{31} -1.00000i q^{32} -2.14134 q^{34} +(1.11566 - 0.884340i) q^{35} +3.27334i q^{37} +1.00000i q^{38} +(1.75233 - 1.38900i) q^{40} +4.23132 q^{41} -2.49534i q^{43} +3.50466 q^{44} +4.91934 q^{46} +10.2827i q^{47} +6.59465 q^{49} +(4.86799 + 1.14134i) q^{50} -0.141336i q^{52} +8.14134i q^{53} +(4.86799 + 6.14134i) q^{55} -0.636672 q^{56} -7.15066i q^{58} -5.64600 q^{59} -6.49534 q^{61} +7.78734i q^{62} -1.00000 q^{64} +(0.247668 - 0.196316i) q^{65} +8.37266i q^{67} +2.14134i q^{68} +(-0.884340 - 1.11566i) q^{70} +8.95798 q^{71} +3.69735i q^{73} +3.27334 q^{74} +1.00000 q^{76} -2.23132i q^{77} +4.17997 q^{79} +(-1.38900 - 1.75233i) q^{80} -4.23132i q^{82} -9.00933i q^{83} +(-3.75233 + 2.97432i) q^{85} -2.49534 q^{86} -3.50466i q^{88} -6.77801 q^{89} -0.0899847 q^{91} -4.91934i q^{92} +10.2827 q^{94} +(1.38900 + 1.75233i) q^{95} +14.5653i q^{97} -6.59465i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 2q^{5} + O(q^{10}) \) \( 6q - 6q^{4} - 2q^{5} + 8q^{14} + 6q^{16} - 6q^{19} + 2q^{20} + 10q^{25} - 16q^{26} - 16q^{29} + 8q^{31} + 4q^{34} - 8q^{35} - 4q^{41} + 6q^{49} + 4q^{50} + 4q^{55} - 8q^{56} + 4q^{59} - 60q^{61} - 6q^{64} + 12q^{65} - 20q^{70} + 16q^{71} + 28q^{74} + 6q^{76} - 2q^{80} - 12q^{85} - 36q^{86} - 28q^{89} + 12q^{91} + 28q^{94} + 2q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.38900 1.75233i −0.621181 0.783667i
\(6\) 0 0
\(7\) 0.636672i 0.240639i 0.992735 + 0.120320i \(0.0383920\pi\)
−0.992735 + 0.120320i \(0.961608\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.75233 + 1.38900i −0.554136 + 0.439242i
\(11\) −3.50466 −1.05670 −0.528348 0.849028i \(-0.677188\pi\)
−0.528348 + 0.849028i \(0.677188\pi\)
\(12\) 0 0
\(13\) 0.141336i 0.0391996i 0.999808 + 0.0195998i \(0.00623921\pi\)
−0.999808 + 0.0195998i \(0.993761\pi\)
\(14\) 0.636672 0.170158
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.14134i 0.519350i −0.965696 0.259675i \(-0.916385\pi\)
0.965696 0.259675i \(-0.0836155\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 1.38900 + 1.75233i 0.310591 + 0.391833i
\(21\) 0 0
\(22\) 3.50466i 0.747197i
\(23\) 4.91934i 1.02575i 0.858462 + 0.512877i \(0.171420\pi\)
−0.858462 + 0.512877i \(0.828580\pi\)
\(24\) 0 0
\(25\) −1.14134 + 4.86799i −0.228267 + 0.973599i
\(26\) 0.141336 0.0277183
\(27\) 0 0
\(28\) 0.636672i 0.120320i
\(29\) 7.15066 1.32785 0.663923 0.747801i \(-0.268890\pi\)
0.663923 + 0.747801i \(0.268890\pi\)
\(30\) 0 0
\(31\) −7.78734 −1.39865 −0.699323 0.714805i \(-0.746515\pi\)
−0.699323 + 0.714805i \(0.746515\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −2.14134 −0.367236
\(35\) 1.11566 0.884340i 0.188581 0.149481i
\(36\) 0 0
\(37\) 3.27334i 0.538134i 0.963121 + 0.269067i \(0.0867154\pi\)
−0.963121 + 0.269067i \(0.913285\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 0 0
\(40\) 1.75233 1.38900i 0.277068 0.219621i
\(41\) 4.23132 0.660821 0.330411 0.943837i \(-0.392813\pi\)
0.330411 + 0.943837i \(0.392813\pi\)
\(42\) 0 0
\(43\) 2.49534i 0.380535i −0.981732 0.190268i \(-0.939064\pi\)
0.981732 0.190268i \(-0.0609356\pi\)
\(44\) 3.50466 0.528348
\(45\) 0 0
\(46\) 4.91934 0.725318
\(47\) 10.2827i 1.49988i 0.661505 + 0.749941i \(0.269918\pi\)
−0.661505 + 0.749941i \(0.730082\pi\)
\(48\) 0 0
\(49\) 6.59465 0.942093
\(50\) 4.86799 + 1.14134i 0.688438 + 0.161409i
\(51\) 0 0
\(52\) 0.141336i 0.0195998i
\(53\) 8.14134i 1.11830i 0.829067 + 0.559149i \(0.188872\pi\)
−0.829067 + 0.559149i \(0.811128\pi\)
\(54\) 0 0
\(55\) 4.86799 + 6.14134i 0.656400 + 0.828098i
\(56\) −0.636672 −0.0850788
\(57\) 0 0
\(58\) 7.15066i 0.938928i
\(59\) −5.64600 −0.735047 −0.367523 0.930014i \(-0.619794\pi\)
−0.367523 + 0.930014i \(0.619794\pi\)
\(60\) 0 0
\(61\) −6.49534 −0.831643 −0.415821 0.909446i \(-0.636506\pi\)
−0.415821 + 0.909446i \(0.636506\pi\)
\(62\) 7.78734i 0.988993i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.247668 0.196316i 0.0307194 0.0243501i
\(66\) 0 0
\(67\) 8.37266i 1.02288i 0.859318 + 0.511441i \(0.170888\pi\)
−0.859318 + 0.511441i \(0.829112\pi\)
\(68\) 2.14134i 0.259675i
\(69\) 0 0
\(70\) −0.884340 1.11566i −0.105699 0.133347i
\(71\) 8.95798 1.06312 0.531558 0.847022i \(-0.321607\pi\)
0.531558 + 0.847022i \(0.321607\pi\)
\(72\) 0 0
\(73\) 3.69735i 0.432742i 0.976311 + 0.216371i \(0.0694221\pi\)
−0.976311 + 0.216371i \(0.930578\pi\)
\(74\) 3.27334 0.380518
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 2.23132i 0.254283i
\(78\) 0 0
\(79\) 4.17997 0.470283 0.235142 0.971961i \(-0.424445\pi\)
0.235142 + 0.971961i \(0.424445\pi\)
\(80\) −1.38900 1.75233i −0.155295 0.195917i
\(81\) 0 0
\(82\) 4.23132i 0.467271i
\(83\) 9.00933i 0.988902i −0.869205 0.494451i \(-0.835369\pi\)
0.869205 0.494451i \(-0.164631\pi\)
\(84\) 0 0
\(85\) −3.75233 + 2.97432i −0.406998 + 0.322611i
\(86\) −2.49534 −0.269079
\(87\) 0 0
\(88\) 3.50466i 0.373598i
\(89\) −6.77801 −0.718467 −0.359234 0.933248i \(-0.616962\pi\)
−0.359234 + 0.933248i \(0.616962\pi\)
\(90\) 0 0
\(91\) −0.0899847 −0.00943296
\(92\) 4.91934i 0.512877i
\(93\) 0 0
\(94\) 10.2827 1.06058
\(95\) 1.38900 + 1.75233i 0.142509 + 0.179785i
\(96\) 0 0
\(97\) 14.5653i 1.47889i 0.673219 + 0.739443i \(0.264911\pi\)
−0.673219 + 0.739443i \(0.735089\pi\)
\(98\) 6.59465i 0.666160i
\(99\) 0 0
\(100\) 1.14134 4.86799i 0.114134 0.486799i
\(101\) 16.6167 1.65342 0.826712 0.562626i \(-0.190209\pi\)
0.826712 + 0.562626i \(0.190209\pi\)
\(102\) 0 0
\(103\) 9.06068i 0.892775i −0.894840 0.446388i \(-0.852710\pi\)
0.894840 0.446388i \(-0.147290\pi\)
\(104\) −0.141336 −0.0138591
\(105\) 0 0
\(106\) 8.14134 0.790756
\(107\) 0.0899847i 0.00869915i −0.999991 0.00434958i \(-0.998615\pi\)
0.999991 0.00434958i \(-0.00138452\pi\)
\(108\) 0 0
\(109\) 13.5946 1.30213 0.651066 0.759021i \(-0.274322\pi\)
0.651066 + 0.759021i \(0.274322\pi\)
\(110\) 6.14134 4.86799i 0.585553 0.464145i
\(111\) 0 0
\(112\) 0.636672i 0.0601598i
\(113\) 11.5233i 1.08402i 0.840371 + 0.542011i \(0.182337\pi\)
−0.840371 + 0.542011i \(0.817663\pi\)
\(114\) 0 0
\(115\) 8.62032 6.83299i 0.803849 0.637179i
\(116\) −7.15066 −0.663923
\(117\) 0 0
\(118\) 5.64600i 0.519756i
\(119\) 1.36333 0.124976
\(120\) 0 0
\(121\) 1.28267 0.116607
\(122\) 6.49534i 0.588060i
\(123\) 0 0
\(124\) 7.78734 0.699323
\(125\) 10.1157 4.76166i 0.904772 0.425896i
\(126\) 0 0
\(127\) 3.29200i 0.292118i −0.989276 0.146059i \(-0.953341\pi\)
0.989276 0.146059i \(-0.0466589\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −0.196316 0.247668i −0.0172181 0.0217219i
\(131\) −18.0187 −1.57430 −0.787149 0.616763i \(-0.788444\pi\)
−0.787149 + 0.616763i \(0.788444\pi\)
\(132\) 0 0
\(133\) 0.636672i 0.0552064i
\(134\) 8.37266 0.723287
\(135\) 0 0
\(136\) 2.14134 0.183618
\(137\) 14.4240i 1.23233i 0.787619 + 0.616163i \(0.211314\pi\)
−0.787619 + 0.616163i \(0.788686\pi\)
\(138\) 0 0
\(139\) −15.4720 −1.31232 −0.656158 0.754624i \(-0.727819\pi\)
−0.656158 + 0.754624i \(0.727819\pi\)
\(140\) −1.11566 + 0.884340i −0.0942905 + 0.0747403i
\(141\) 0 0
\(142\) 8.95798i 0.751737i
\(143\) 0.495336i 0.0414220i
\(144\) 0 0
\(145\) −9.93230 12.5303i −0.824833 1.04059i
\(146\) 3.69735 0.305995
\(147\) 0 0
\(148\) 3.27334i 0.269067i
\(149\) −17.1893 −1.40820 −0.704101 0.710100i \(-0.748650\pi\)
−0.704101 + 0.710100i \(0.748650\pi\)
\(150\) 0 0
\(151\) 3.29200 0.267899 0.133950 0.990988i \(-0.457234\pi\)
0.133950 + 0.990988i \(0.457234\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0 0
\(154\) −2.23132 −0.179805
\(155\) 10.8166 + 13.6460i 0.868814 + 1.09607i
\(156\) 0 0
\(157\) 15.1893i 1.21224i 0.795374 + 0.606119i \(0.207274\pi\)
−0.795374 + 0.606119i \(0.792726\pi\)
\(158\) 4.17997i 0.332541i
\(159\) 0 0
\(160\) −1.75233 + 1.38900i −0.138534 + 0.109810i
\(161\) −3.13201 −0.246837
\(162\) 0 0
\(163\) 14.0700i 1.10205i 0.834489 + 0.551024i \(0.185763\pi\)
−0.834489 + 0.551024i \(0.814237\pi\)
\(164\) −4.23132 −0.330411
\(165\) 0 0
\(166\) −9.00933 −0.699260
\(167\) 14.7967i 1.14500i 0.819905 + 0.572500i \(0.194026\pi\)
−0.819905 + 0.572500i \(0.805974\pi\)
\(168\) 0 0
\(169\) 12.9800 0.998463
\(170\) 2.97432 + 3.75233i 0.228120 + 0.287791i
\(171\) 0 0
\(172\) 2.49534i 0.190268i
\(173\) 17.2920i 1.31469i −0.753591 0.657343i \(-0.771680\pi\)
0.753591 0.657343i \(-0.228320\pi\)
\(174\) 0 0
\(175\) −3.09931 0.726656i −0.234286 0.0549301i
\(176\) −3.50466 −0.264174
\(177\) 0 0
\(178\) 6.77801i 0.508033i
\(179\) 17.7360 1.32565 0.662825 0.748774i \(-0.269357\pi\)
0.662825 + 0.748774i \(0.269357\pi\)
\(180\) 0 0
\(181\) 6.17997 0.459354 0.229677 0.973267i \(-0.426233\pi\)
0.229677 + 0.973267i \(0.426233\pi\)
\(182\) 0.0899847i 0.00667011i
\(183\) 0 0
\(184\) −4.91934 −0.362659
\(185\) 5.73599 4.54669i 0.421718 0.334279i
\(186\) 0 0
\(187\) 7.50466i 0.548795i
\(188\) 10.2827i 0.749941i
\(189\) 0 0
\(190\) 1.75233 1.38900i 0.127128 0.100769i
\(191\) −14.6367 −1.05907 −0.529536 0.848287i \(-0.677634\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(192\) 0 0
\(193\) 20.0187i 1.44097i −0.693468 0.720487i \(-0.743918\pi\)
0.693468 0.720487i \(-0.256082\pi\)
\(194\) 14.5653 1.04573
\(195\) 0 0
\(196\) −6.59465 −0.471046
\(197\) 9.94865i 0.708812i 0.935092 + 0.354406i \(0.115317\pi\)
−0.935092 + 0.354406i \(0.884683\pi\)
\(198\) 0 0
\(199\) −9.74870 −0.691067 −0.345534 0.938406i \(-0.612302\pi\)
−0.345534 + 0.938406i \(0.612302\pi\)
\(200\) −4.86799 1.14134i −0.344219 0.0807047i
\(201\) 0 0
\(202\) 16.6167i 1.16915i
\(203\) 4.55263i 0.319532i
\(204\) 0 0
\(205\) −5.87732 7.41468i −0.410490 0.517864i
\(206\) −9.06068 −0.631287
\(207\) 0 0
\(208\) 0.141336i 0.00979990i
\(209\) 3.50466 0.242423
\(210\) 0 0
\(211\) −20.7580 −1.42904 −0.714521 0.699614i \(-0.753355\pi\)
−0.714521 + 0.699614i \(0.753355\pi\)
\(212\) 8.14134i 0.559149i
\(213\) 0 0
\(214\) −0.0899847 −0.00615123
\(215\) −4.37266 + 3.46603i −0.298213 + 0.236381i
\(216\) 0 0
\(217\) 4.95798i 0.336569i
\(218\) 13.5946i 0.920746i
\(219\) 0 0
\(220\) −4.86799 6.14134i −0.328200 0.414049i
\(221\) 0.302648 0.0203583
\(222\) 0 0
\(223\) 10.7267i 0.718310i 0.933278 + 0.359155i \(0.116935\pi\)
−0.933278 + 0.359155i \(0.883065\pi\)
\(224\) 0.636672 0.0425394
\(225\) 0 0
\(226\) 11.5233 0.766520
\(227\) 12.5526i 0.833147i −0.909102 0.416574i \(-0.863231\pi\)
0.909102 0.416574i \(-0.136769\pi\)
\(228\) 0 0
\(229\) −25.4720 −1.68324 −0.841618 0.540074i \(-0.818396\pi\)
−0.841618 + 0.540074i \(0.818396\pi\)
\(230\) −6.83299 8.62032i −0.450554 0.568407i
\(231\) 0 0
\(232\) 7.15066i 0.469464i
\(233\) 3.11203i 0.203876i −0.994791 0.101938i \(-0.967496\pi\)
0.994791 0.101938i \(-0.0325043\pi\)
\(234\) 0 0
\(235\) 18.0187 14.2827i 1.17541 0.931699i
\(236\) 5.64600 0.367523
\(237\) 0 0
\(238\) 1.36333i 0.0883714i
\(239\) −1.54330 −0.0998276 −0.0499138 0.998754i \(-0.515895\pi\)
−0.0499138 + 0.998754i \(0.515895\pi\)
\(240\) 0 0
\(241\) 10.2827 0.662365 0.331183 0.943567i \(-0.392552\pi\)
0.331183 + 0.943567i \(0.392552\pi\)
\(242\) 1.28267i 0.0824533i
\(243\) 0 0
\(244\) 6.49534 0.415821
\(245\) −9.15999 11.5560i −0.585211 0.738287i
\(246\) 0 0
\(247\) 0.141336i 0.00899300i
\(248\) 7.78734i 0.494496i
\(249\) 0 0
\(250\) −4.76166 10.1157i −0.301154 0.639771i
\(251\) 2.51399 0.158682 0.0793409 0.996848i \(-0.474718\pi\)
0.0793409 + 0.996848i \(0.474718\pi\)
\(252\) 0 0
\(253\) 17.2406i 1.08391i
\(254\) −3.29200 −0.206559
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.7967i 1.54677i 0.633934 + 0.773387i \(0.281439\pi\)
−0.633934 + 0.773387i \(0.718561\pi\)
\(258\) 0 0
\(259\) −2.08405 −0.129496
\(260\) −0.247668 + 0.196316i −0.0153597 + 0.0121750i
\(261\) 0 0
\(262\) 18.0187i 1.11320i
\(263\) 22.5653i 1.39144i −0.718314 0.695719i \(-0.755086\pi\)
0.718314 0.695719i \(-0.244914\pi\)
\(264\) 0 0
\(265\) 14.2663 11.3083i 0.876373 0.694666i
\(266\) −0.636672 −0.0390369
\(267\) 0 0
\(268\) 8.37266i 0.511441i
\(269\) −26.5653 −1.61972 −0.809859 0.586625i \(-0.800456\pi\)
−0.809859 + 0.586625i \(0.800456\pi\)
\(270\) 0 0
\(271\) −24.9380 −1.51488 −0.757438 0.652907i \(-0.773549\pi\)
−0.757438 + 0.652907i \(0.773549\pi\)
\(272\) 2.14134i 0.129838i
\(273\) 0 0
\(274\) 14.4240 0.871386
\(275\) 4.00000 17.0607i 0.241209 1.02880i
\(276\) 0 0
\(277\) 18.5467i 1.11436i 0.830391 + 0.557181i \(0.188117\pi\)
−0.830391 + 0.557181i \(0.811883\pi\)
\(278\) 15.4720i 0.927947i
\(279\) 0 0
\(280\) 0.884340 + 1.11566i 0.0528494 + 0.0666735i
\(281\) −24.7967 −1.47925 −0.739623 0.673022i \(-0.764996\pi\)
−0.739623 + 0.673022i \(0.764996\pi\)
\(282\) 0 0
\(283\) 13.5747i 0.806931i −0.914995 0.403465i \(-0.867806\pi\)
0.914995 0.403465i \(-0.132194\pi\)
\(284\) −8.95798 −0.531558
\(285\) 0 0
\(286\) −0.495336 −0.0292898
\(287\) 2.69396i 0.159020i
\(288\) 0 0
\(289\) 12.4147 0.730275
\(290\) −12.5303 + 9.93230i −0.735807 + 0.583245i
\(291\) 0 0
\(292\) 3.69735i 0.216371i
\(293\) 15.6133i 0.912139i −0.889944 0.456070i \(-0.849257\pi\)
0.889944 0.456070i \(-0.150743\pi\)
\(294\) 0 0
\(295\) 7.84232 + 9.89367i 0.456597 + 0.576032i
\(296\) −3.27334 −0.190259
\(297\) 0 0
\(298\) 17.1893i 0.995749i
\(299\) −0.695281 −0.0402091
\(300\) 0 0
\(301\) 1.58871 0.0915717
\(302\) 3.29200i 0.189433i
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) 9.02205 + 11.3820i 0.516601 + 0.651731i
\(306\) 0 0
\(307\) 34.0187i 1.94155i 0.239997 + 0.970774i \(0.422854\pi\)
−0.239997 + 0.970774i \(0.577146\pi\)
\(308\) 2.23132i 0.127141i
\(309\) 0 0
\(310\) 13.6460 10.8166i 0.775041 0.614344i
\(311\) −8.93800 −0.506828 −0.253414 0.967358i \(-0.581553\pi\)
−0.253414 + 0.967358i \(0.581553\pi\)
\(312\) 0 0
\(313\) 18.4240i 1.04139i 0.853744 + 0.520693i \(0.174326\pi\)
−0.853744 + 0.520693i \(0.825674\pi\)
\(314\) 15.1893 0.857182
\(315\) 0 0
\(316\) −4.17997 −0.235142
\(317\) 33.5547i 1.88462i −0.334742 0.942310i \(-0.608649\pi\)
0.334742 0.942310i \(-0.391351\pi\)
\(318\) 0 0
\(319\) −25.0607 −1.40313
\(320\) 1.38900 + 1.75233i 0.0776477 + 0.0979583i
\(321\) 0 0
\(322\) 3.13201i 0.174540i
\(323\) 2.14134i 0.119147i
\(324\) 0 0
\(325\) −0.688023 0.161312i −0.0381647 0.00894798i
\(326\) 14.0700 0.779266
\(327\) 0 0
\(328\) 4.23132i 0.233636i
\(329\) −6.54669 −0.360931
\(330\) 0 0
\(331\) 2.25130 0.123742 0.0618712 0.998084i \(-0.480293\pi\)
0.0618712 + 0.998084i \(0.480293\pi\)
\(332\) 9.00933i 0.494451i
\(333\) 0 0
\(334\) 14.7967 0.809638
\(335\) 14.6717 11.6297i 0.801599 0.635396i
\(336\) 0 0
\(337\) 21.3620i 1.16366i −0.813309 0.581831i \(-0.802336\pi\)
0.813309 0.581831i \(-0.197664\pi\)
\(338\) 12.9800i 0.706020i
\(339\) 0 0
\(340\) 3.75233 2.97432i 0.203499 0.161305i
\(341\) 27.2920 1.47794
\(342\) 0 0
\(343\) 8.65533i 0.467344i
\(344\) 2.49534 0.134539
\(345\) 0 0
\(346\) −17.2920 −0.929624
\(347\) 11.5560i 0.620359i −0.950678 0.310180i \(-0.899611\pi\)
0.950678 0.310180i \(-0.100389\pi\)
\(348\) 0 0
\(349\) 17.1120 0.915986 0.457993 0.888956i \(-0.348568\pi\)
0.457993 + 0.888956i \(0.348568\pi\)
\(350\) −0.726656 + 3.09931i −0.0388414 + 0.165665i
\(351\) 0 0
\(352\) 3.50466i 0.186799i
\(353\) 11.6974i 0.622587i 0.950314 + 0.311294i \(0.100762\pi\)
−0.950314 + 0.311294i \(0.899238\pi\)
\(354\) 0 0
\(355\) −12.4427 15.6974i −0.660388 0.833129i
\(356\) 6.77801 0.359234
\(357\) 0 0
\(358\) 17.7360i 0.937376i
\(359\) −4.47536 −0.236200 −0.118100 0.993002i \(-0.537680\pi\)
−0.118100 + 0.993002i \(0.537680\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 6.17997i 0.324812i
\(363\) 0 0
\(364\) 0.0899847 0.00471648
\(365\) 6.47899 5.13564i 0.339126 0.268811i
\(366\) 0 0
\(367\) 18.7453i 0.978497i 0.872144 + 0.489249i \(0.162729\pi\)
−0.872144 + 0.489249i \(0.837271\pi\)
\(368\) 4.91934i 0.256439i
\(369\) 0 0
\(370\) −4.54669 5.73599i −0.236371 0.298200i
\(371\) −5.18336 −0.269107
\(372\) 0 0
\(373\) 1.69735i 0.0878855i −0.999034 0.0439428i \(-0.986008\pi\)
0.999034 0.0439428i \(-0.0139919\pi\)
\(374\) 7.50466 0.388057
\(375\) 0 0
\(376\) −10.2827 −0.530288
\(377\) 1.01065i 0.0520510i
\(378\) 0 0
\(379\) −2.63667 −0.135437 −0.0677184 0.997704i \(-0.521572\pi\)
−0.0677184 + 0.997704i \(0.521572\pi\)
\(380\) −1.38900 1.75233i −0.0712544 0.0898927i
\(381\) 0 0
\(382\) 14.6367i 0.748877i
\(383\) 12.4953i 0.638482i 0.947674 + 0.319241i \(0.103428\pi\)
−0.947674 + 0.319241i \(0.896572\pi\)
\(384\) 0 0
\(385\) −3.91002 + 3.09931i −0.199273 + 0.157956i
\(386\) −20.0187 −1.01892
\(387\) 0 0
\(388\) 14.5653i 0.739443i
\(389\) −4.51399 −0.228869 −0.114434 0.993431i \(-0.536506\pi\)
−0.114434 + 0.993431i \(0.536506\pi\)
\(390\) 0 0
\(391\) 10.5340 0.532726
\(392\) 6.59465i 0.333080i
\(393\) 0 0
\(394\) 9.94865 0.501206
\(395\) −5.80599 7.32469i −0.292131 0.368545i
\(396\) 0 0
\(397\) 35.6774i 1.79060i −0.445468 0.895298i \(-0.646963\pi\)
0.445468 0.895298i \(-0.353037\pi\)
\(398\) 9.74870i 0.488658i
\(399\) 0 0
\(400\) −1.14134 + 4.86799i −0.0570668 + 0.243400i
\(401\) −15.3434 −0.766210 −0.383105 0.923705i \(-0.625145\pi\)
−0.383105 + 0.923705i \(0.625145\pi\)
\(402\) 0 0
\(403\) 1.10063i 0.0548264i
\(404\) −16.6167 −0.826712
\(405\) 0 0
\(406\) 4.55263 0.225943
\(407\) 11.4720i 0.568644i
\(408\) 0 0
\(409\) −29.3620 −1.45186 −0.725929 0.687770i \(-0.758590\pi\)
−0.725929 + 0.687770i \(0.758590\pi\)
\(410\) −7.41468 + 5.87732i −0.366185 + 0.290260i
\(411\) 0 0
\(412\) 9.06068i 0.446388i
\(413\) 3.59465i 0.176881i
\(414\) 0 0
\(415\) −15.7873 + 12.5140i −0.774970 + 0.614288i
\(416\) 0.141336 0.00692957
\(417\) 0 0
\(418\) 3.50466i 0.171419i
\(419\) 25.1379 1.22807 0.614035 0.789279i \(-0.289546\pi\)
0.614035 + 0.789279i \(0.289546\pi\)
\(420\) 0 0
\(421\) 14.5454 0.708898 0.354449 0.935075i \(-0.384668\pi\)
0.354449 + 0.935075i \(0.384668\pi\)
\(422\) 20.7580i 1.01049i
\(423\) 0 0
\(424\) −8.14134 −0.395378
\(425\) 10.4240 + 2.44398i 0.505639 + 0.118551i
\(426\) 0 0
\(427\) 4.13540i 0.200126i
\(428\) 0.0899847i 0.00434958i
\(429\) 0 0
\(430\) 3.46603 + 4.37266i 0.167147 + 0.210868i
\(431\) −19.4020 −0.934560 −0.467280 0.884109i \(-0.654766\pi\)
−0.467280 + 0.884109i \(0.654766\pi\)
\(432\) 0 0
\(433\) 5.50466i 0.264537i −0.991214 0.132269i \(-0.957774\pi\)
0.991214 0.132269i \(-0.0422262\pi\)
\(434\) −4.95798 −0.237991
\(435\) 0 0
\(436\) −13.5946 −0.651066
\(437\) 4.91934i 0.235324i
\(438\) 0 0
\(439\) −12.2500 −0.584660 −0.292330 0.956318i \(-0.594430\pi\)
−0.292330 + 0.956318i \(0.594430\pi\)
\(440\) −6.14134 + 4.86799i −0.292777 + 0.232072i
\(441\) 0 0
\(442\) 0.302648i 0.0143955i
\(443\) 31.6006i 1.50139i 0.660649 + 0.750695i \(0.270281\pi\)
−0.660649 + 0.750695i \(0.729719\pi\)
\(444\) 0 0
\(445\) 9.41468 + 11.8773i 0.446299 + 0.563039i
\(446\) 10.7267 0.507922
\(447\) 0 0
\(448\) 0.636672i 0.0300799i
\(449\) −36.0187 −1.69983 −0.849913 0.526923i \(-0.823345\pi\)
−0.849913 + 0.526923i \(0.823345\pi\)
\(450\) 0 0
\(451\) −14.8294 −0.698287
\(452\) 11.5233i 0.542011i
\(453\) 0 0
\(454\) −12.5526 −0.589124
\(455\) 0.124989 + 0.157683i 0.00585958 + 0.00739230i
\(456\) 0 0
\(457\) 22.1413i 1.03573i 0.855463 + 0.517864i \(0.173273\pi\)
−0.855463 + 0.517864i \(0.826727\pi\)
\(458\) 25.4720i 1.19023i
\(459\) 0 0
\(460\) −8.62032 + 6.83299i −0.401925 + 0.318590i
\(461\) 2.31537 0.107837 0.0539187 0.998545i \(-0.482829\pi\)
0.0539187 + 0.998545i \(0.482829\pi\)
\(462\) 0 0
\(463\) 15.8387i 0.736086i −0.929809 0.368043i \(-0.880028\pi\)
0.929809 0.368043i \(-0.119972\pi\)
\(464\) 7.15066 0.331961
\(465\) 0 0
\(466\) −3.11203 −0.144162
\(467\) 23.1379i 1.07070i −0.844631 0.535348i \(-0.820180\pi\)
0.844631 0.535348i \(-0.179820\pi\)
\(468\) 0 0
\(469\) −5.33063 −0.246146
\(470\) −14.2827 18.0187i −0.658811 0.831139i
\(471\) 0 0
\(472\) 5.64600i 0.259878i
\(473\) 8.74531i 0.402110i
\(474\) 0 0
\(475\) 1.14134 4.86799i 0.0523681 0.223359i
\(476\) −1.36333 −0.0624880
\(477\) 0 0
\(478\) 1.54330i 0.0705888i
\(479\) −10.1214 −0.462457 −0.231228 0.972900i \(-0.574274\pi\)
−0.231228 + 0.972900i \(0.574274\pi\)
\(480\) 0 0
\(481\) −0.462642 −0.0210946
\(482\) 10.2827i 0.468363i
\(483\) 0 0
\(484\) −1.28267 −0.0583033
\(485\) 25.5233 20.2313i 1.15895 0.918657i
\(486\) 0 0
\(487\) 20.3854i 0.923750i 0.886945 + 0.461875i \(0.152823\pi\)
−0.886945 + 0.461875i \(0.847177\pi\)
\(488\) 6.49534i 0.294030i
\(489\) 0 0
\(490\) −11.5560 + 9.15999i −0.522048 + 0.413806i
\(491\) 7.78734 0.351438 0.175719 0.984440i \(-0.443775\pi\)
0.175719 + 0.984440i \(0.443775\pi\)
\(492\) 0 0
\(493\) 15.3120i 0.689617i
\(494\) −0.141336 −0.00635901
\(495\) 0 0
\(496\) −7.78734 −0.349662
\(497\) 5.70329i 0.255828i
\(498\) 0 0
\(499\) −4.31537 −0.193182 −0.0965912 0.995324i \(-0.530794\pi\)
−0.0965912 + 0.995324i \(0.530794\pi\)
\(500\) −10.1157 + 4.76166i −0.452386 + 0.212948i
\(501\) 0 0
\(502\) 2.51399i 0.112205i
\(503\) 18.5526i 0.827221i 0.910454 + 0.413610i \(0.135732\pi\)
−0.910454 + 0.413610i \(0.864268\pi\)
\(504\) 0 0
\(505\) −23.0807 29.1180i −1.02708 1.29573i
\(506\) −17.2406 −0.766440
\(507\) 0 0
\(508\) 3.29200i 0.146059i
\(509\) −7.73599 −0.342892 −0.171446 0.985194i \(-0.554844\pi\)
−0.171446 + 0.985194i \(0.554844\pi\)
\(510\) 0 0
\(511\) −2.35400 −0.104135
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 24.7967 1.09373
\(515\) −15.8773 + 12.5853i −0.699638 + 0.554575i
\(516\) 0 0
\(517\) 36.0373i 1.58492i
\(518\) 2.08405i 0.0915677i
\(519\) 0 0
\(520\) 0.196316 + 0.247668i 0.00860904 + 0.0108610i
\(521\) −15.2080 −0.666273 −0.333136 0.942879i \(-0.608107\pi\)
−0.333136 + 0.942879i \(0.608107\pi\)
\(522\) 0 0
\(523\) 18.2113i 0.796327i 0.917315 + 0.398163i \(0.130352\pi\)
−0.917315 + 0.398163i \(0.869648\pi\)
\(524\) 18.0187 0.787149
\(525\) 0 0
\(526\) −22.5653 −0.983896
\(527\) 16.6753i 0.726388i
\(528\) 0 0
\(529\) −1.19995 −0.0521715
\(530\) −11.3083 14.2663i −0.491203 0.619690i
\(531\) 0 0
\(532\) 0.636672i 0.0276032i
\(533\) 0.598038i 0.0259039i
\(534\) 0 0
\(535\) −0.157683 + 0.124989i −0.00681724 + 0.00540375i
\(536\) −8.37266 −0.361644
\(537\) 0 0
\(538\) 26.5653i 1.14531i
\(539\) −23.1120 −0.995506
\(540\) 0 0
\(541\) 16.5140 0.709992 0.354996 0.934868i \(-0.384482\pi\)
0.354996 + 0.934868i \(0.384482\pi\)
\(542\) 24.9380i 1.07118i
\(543\) 0 0
\(544\) −2.14134 −0.0918090
\(545\) −18.8830 23.8223i −0.808860 1.02044i
\(546\) 0 0
\(547\) 16.2827i 0.696197i 0.937458 + 0.348098i \(0.113172\pi\)
−0.937458 + 0.348098i \(0.886828\pi\)
\(548\) 14.4240i 0.616163i
\(549\) 0 0
\(550\) −17.0607 4.00000i −0.727470 0.170561i
\(551\) −7.15066 −0.304629
\(552\) 0 0
\(553\) 2.66127i 0.113169i
\(554\) 18.5467 0.787973
\(555\) 0 0
\(556\) 15.4720 0.656158
\(557\) 37.4533i 1.58695i −0.608604 0.793474i \(-0.708270\pi\)
0.608604 0.793474i \(-0.291730\pi\)
\(558\) 0 0
\(559\) 0.352681 0.0149168
\(560\) 1.11566 0.884340i 0.0471453 0.0373702i
\(561\) 0 0
\(562\) 24.7967i 1.04598i
\(563\) 29.1307i 1.22771i −0.789418 0.613856i \(-0.789618\pi\)
0.789418 0.613856i \(-0.210382\pi\)
\(564\) 0 0
\(565\) 20.1927 16.0059i 0.849513 0.673375i
\(566\) −13.5747 −0.570586
\(567\) 0 0
\(568\) 8.95798i 0.375868i
\(569\) 14.8480 0.622461 0.311231 0.950334i \(-0.399259\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(570\) 0 0
\(571\) 41.9087 1.75382 0.876912 0.480651i \(-0.159599\pi\)
0.876912 + 0.480651i \(0.159599\pi\)
\(572\) 0.495336i 0.0207110i
\(573\) 0 0
\(574\) 2.69396 0.112444
\(575\) −23.9473 5.61462i −0.998673 0.234146i
\(576\) 0 0
\(577\) 16.4427i 0.684517i 0.939606 + 0.342259i \(0.111192\pi\)
−0.939606 + 0.342259i \(0.888808\pi\)
\(578\) 12.4147i 0.516383i
\(579\) 0 0
\(580\) 9.93230 + 12.5303i 0.412416 + 0.520294i
\(581\) 5.73599 0.237969
\(582\) 0 0
\(583\) 28.5327i 1.18170i
\(584\) −3.69735 −0.152998
\(585\) 0 0
\(586\) −15.6133 −0.644980
\(587\) 42.5327i 1.75551i 0.479109 + 0.877755i \(0.340960\pi\)
−0.479109 + 0.877755i \(0.659040\pi\)
\(588\) 0 0
\(589\) 7.78734 0.320872
\(590\) 9.89367 7.84232i 0.407316 0.322863i
\(591\) 0 0
\(592\) 3.27334i 0.134534i
\(593\) 3.92273i 0.161087i 0.996751 + 0.0805437i \(0.0256656\pi\)
−0.996751 + 0.0805437i \(0.974334\pi\)
\(594\) 0 0
\(595\) −1.89367 2.38900i −0.0776328 0.0979396i
\(596\) 17.1893 0.704101
\(597\) 0 0
\(598\) 0.695281i 0.0284322i
\(599\) −10.7594 −0.439615 −0.219808 0.975543i \(-0.570543\pi\)
−0.219808 + 0.975543i \(0.570543\pi\)
\(600\) 0 0
\(601\) 25.2220 1.02883 0.514413 0.857542i \(-0.328010\pi\)
0.514413 + 0.857542i \(0.328010\pi\)
\(602\) 1.58871i 0.0647510i
\(603\) 0 0
\(604\) −3.29200 −0.133950
\(605\) −1.78164 2.24767i −0.0724338 0.0913807i
\(606\) 0 0
\(607\) 39.2920i 1.59481i 0.603442 + 0.797407i \(0.293795\pi\)
−0.603442 + 0.797407i \(0.706205\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) 11.3820 9.02205i 0.460843 0.365292i
\(611\) −1.45331 −0.0587947
\(612\) 0 0
\(613\) 9.80599i 0.396060i −0.980196 0.198030i \(-0.936546\pi\)
0.980196 0.198030i \(-0.0634544\pi\)
\(614\) 34.0187 1.37288
\(615\) 0 0
\(616\) 2.23132 0.0899025
\(617\) 35.0093i 1.40942i 0.709494 + 0.704711i \(0.248923\pi\)
−0.709494 + 0.704711i \(0.751077\pi\)
\(618\) 0 0
\(619\) −13.4206 −0.539420 −0.269710 0.962942i \(-0.586928\pi\)
−0.269710 + 0.962942i \(0.586928\pi\)
\(620\) −10.8166 13.6460i −0.434407 0.548037i
\(621\) 0 0
\(622\) 8.93800i 0.358381i
\(623\) 4.31537i 0.172891i
\(624\) 0 0
\(625\) −22.3947 11.1120i −0.895788 0.444481i
\(626\) 18.4240 0.736371
\(627\) 0 0
\(628\) 15.1893i 0.606119i
\(629\) 7.00933 0.279480
\(630\) 0 0
\(631\) 40.5254 1.61329 0.806645 0.591036i \(-0.201281\pi\)
0.806645 + 0.591036i \(0.201281\pi\)
\(632\) 4.17997i 0.166270i
\(633\) 0 0
\(634\) −33.5547 −1.33263
\(635\) −5.76868 + 4.57260i −0.228923 + 0.181458i
\(636\) 0 0
\(637\) 0.932062i 0.0369296i
\(638\) 25.0607i 0.992162i
\(639\) 0 0
\(640\) 1.75233 1.38900i 0.0692670 0.0549052i
\(641\) 26.0700 1.02970 0.514852 0.857279i \(-0.327847\pi\)
0.514852 + 0.857279i \(0.327847\pi\)
\(642\) 0 0
\(643\) 30.1400i 1.18861i −0.804241 0.594303i \(-0.797428\pi\)
0.804241 0.594303i \(-0.202572\pi\)
\(644\) 3.13201 0.123418
\(645\) 0 0
\(646\) 2.14134 0.0842497
\(647\) 20.1086i 0.790552i 0.918562 + 0.395276i \(0.129351\pi\)
−0.918562 + 0.395276i \(0.870649\pi\)
\(648\) 0 0
\(649\) 19.7873 0.776721
\(650\) −0.161312 + 0.688023i −0.00632718 + 0.0269865i
\(651\) 0 0
\(652\) 14.0700i 0.551024i
\(653\) 28.0373i 1.09718i −0.836090 0.548592i \(-0.815164\pi\)
0.836090 0.548592i \(-0.184836\pi\)
\(654\) 0 0
\(655\) 25.0280 + 31.5747i 0.977924 + 1.23372i
\(656\) 4.23132 0.165205
\(657\) 0 0
\(658\) 6.54669i 0.255216i
\(659\) 4.90069 0.190904 0.0954518 0.995434i \(-0.469570\pi\)
0.0954518 + 0.995434i \(0.469570\pi\)
\(660\) 0 0
\(661\) −8.03863 −0.312667 −0.156333 0.987704i \(-0.549967\pi\)
−0.156333 + 0.987704i \(0.549967\pi\)
\(662\) 2.25130i 0.0874991i
\(663\) 0 0
\(664\) 9.00933 0.349630
\(665\) −1.11566 + 0.884340i −0.0432635 + 0.0342932i
\(666\) 0 0
\(667\) 35.1766i 1.36204i
\(668\) 14.7967i 0.572500i
\(669\) 0 0
\(670\) −11.6297 14.6717i −0.449293 0.566816i
\(671\) 22.7640 0.878793
\(672\) 0 0
\(673\) 4.82936i 0.186158i 0.995659 + 0.0930791i \(0.0296709\pi\)
−0.995659 + 0.0930791i \(0.970329\pi\)
\(674\) −21.3620 −0.822834
\(675\) 0 0
\(676\) −12.9800 −0.499232
\(677\) 12.8094i 0.492305i −0.969231 0.246152i \(-0.920834\pi\)
0.969231 0.246152i \(-0.0791663\pi\)
\(678\) 0 0
\(679\) −9.27334 −0.355878
\(680\) −2.97432 3.75233i −0.114060 0.143895i
\(681\) 0 0
\(682\) 27.2920i 1.04506i
\(683\) 37.1307i 1.42077i 0.703815 + 0.710383i \(0.251478\pi\)
−0.703815 + 0.710383i \(0.748522\pi\)
\(684\) 0 0
\(685\) 25.2757 20.0350i 0.965733 0.765498i
\(686\) 8.65533 0.330462
\(687\) 0 0
\(688\) 2.49534i 0.0951338i
\(689\) −1.15066 −0.0438368
\(690\) 0 0
\(691\) −18.1986 −0.692308 −0.346154 0.938178i \(-0.612513\pi\)
−0.346154 + 0.938178i \(0.612513\pi\)
\(692\) 17.2920i 0.657343i
\(693\) 0 0
\(694\) −11.5560 −0.438660
\(695\) 21.4906 + 27.1120i 0.815186 + 1.02842i
\(696\) 0 0
\(697\) 9.06068i 0.343198i
\(698\) 17.1120i 0.647700i
\(699\) 0 0
\(700\) 3.09931 + 0.726656i 0.117143 + 0.0274650i
\(701\) 26.2827 0.992683 0.496341 0.868127i \(-0.334676\pi\)
0.496341 + 0.868127i \(0.334676\pi\)
\(702\) 0 0
\(703\) 3.27334i 0.123456i
\(704\) 3.50466 0.132087
\(705\) 0 0
\(706\) 11.6974 0.440236
\(707\) 10.5794i 0.397879i
\(708\) 0 0
\(709\) 14.9253 0.560531 0.280265 0.959923i \(-0.409578\pi\)
0.280265 + 0.959923i \(0.409578\pi\)
\(710\) −15.6974 + 12.4427i −0.589111 + 0.466965i
\(711\) 0 0
\(712\) 6.77801i 0.254017i
\(713\) 38.3086i 1.43467i
\(714\) 0 0
\(715\) −0.867993 + 0.688023i −0.0324611 + 0.0257306i
\(716\) −17.7360 −0.662825
\(717\) 0 0
\(718\) 4.47536i 0.167019i
\(719\) 32.3327 1.20581 0.602903 0.797814i \(-0.294011\pi\)
0.602903 + 0.797814i \(0.294011\pi\)
\(720\) 0 0
\(721\) 5.76868 0.214837
\(722\) 1.00000i 0.0372161i
\(723\) 0 0
\(724\) −6.17997 −0.229677
\(725\) −8.16131 + 34.8094i −0.303104 + 1.29279i
\(726\) 0 0
\(727\) 42.0246i 1.55861i −0.626647 0.779303i \(-0.715573\pi\)
0.626647 0.779303i \(-0.284427\pi\)
\(728\) 0.0899847i 0.00333506i
\(729\) 0 0
\(730\) −5.13564 6.47899i −0.190078 0.239798i
\(731\) −5.34335 −0.197631
\(732\) 0 0
\(733\) 26.5840i 0.981903i −0.871187 0.490951i \(-0.836649\pi\)
0.871187 0.490951i \(-0.163351\pi\)
\(734\) 18.7453 0.691902
\(735\) 0 0
\(736\) 4.91934 0.181329
\(737\) 29.3434i 1.08088i
\(738\) 0 0
\(739\) −8.14728 −0.299702 −0.149851 0.988709i \(-0.547879\pi\)
−0.149851 + 0.988709i \(0.547879\pi\)
\(740\) −5.73599 + 4.54669i −0.210859 + 0.167140i
\(741\) 0 0
\(742\) 5.18336i 0.190287i
\(743\) 35.8247i 1.31428i 0.753769 + 0.657139i \(0.228234\pi\)
−0.753769 + 0.657139i \(0.771766\pi\)
\(744\) 0 0
\(745\) 23.8760 + 30.1214i 0.874749 + 1.10356i
\(746\) −1.69735 −0.0621445
\(747\) 0 0
\(748\) 7.50466i 0.274398i
\(749\) 0.0572907 0.00209336
\(750\) 0 0
\(751\) −14.8994 −0.543686 −0.271843 0.962342i \(-0.587633\pi\)
−0.271843 + 0.962342i \(0.587633\pi\)
\(752\) 10.2827i 0.374970i
\(753\) 0 0
\(754\) 1.01065 0.0368056
\(755\) −4.57260 5.76868i −0.166414 0.209944i
\(756\) 0 0
\(757\) 47.7920i 1.73703i −0.495664 0.868514i \(-0.665075\pi\)
0.495664 0.868514i \(-0.334925\pi\)
\(758\) 2.63667i 0.0957682i
\(759\) 0 0
\(760\) −1.75233 + 1.38900i −0.0635638 + 0.0503845i
\(761\) 38.9053 1.41032 0.705158 0.709050i \(-0.250876\pi\)
0.705158 + 0.709050i \(0.250876\pi\)
\(762\) 0 0
\(763\) 8.65533i 0.313344i
\(764\) 14.6367 0.529536
\(765\) 0 0
\(766\) 12.4953 0.451475
\(767\) 0.797984i 0.0288135i
\(768\) 0 0
\(769\) −8.74663 −0.315412 −0.157706 0.987486i \(-0.550410\pi\)
−0.157706 + 0.987486i \(0.550410\pi\)
\(770\) 3.09931 + 3.91002i 0.111692 + 0.140907i
\(771\) 0 0
\(772\) 20.0187i 0.720487i
\(773\) 23.4707i 0.844181i −0.906554 0.422090i \(-0.861297\pi\)
0.906554 0.422090i \(-0.138703\pi\)
\(774\) 0 0
\(775\) 8.88797 37.9087i 0.319265 1.36172i
\(776\) −14.5653 −0.522865
\(777\) 0 0
\(778\) 4.51399i 0.161834i
\(779\) −4.23132 −0.151603
\(780\) 0 0
\(781\) −31.3947 −1.12339
\(782\) 10.5340i 0.376694i
\(783\) 0 0
\(784\) 6.59465 0.235523
\(785\) 26.6167 21.0980i 0.949991 0.753020i
\(786\) 0 0
\(787\) 1.26063i 0.0449364i 0.999748 + 0.0224682i \(0.00715246\pi\)
−0.999748 + 0.0224682i \(0.992848\pi\)
\(788\) 9.94865i 0.354406i
\(789\) 0 0
\(790\) −7.32469 + 5.80599i −0.260601 + 0.206568i
\(791\) −7.33657 −0.260859
\(792\) 0 0
\(793\) 0.918026i 0.0326000i
\(794\) −35.6774 −1.26614
\(795\) 0 0
\(796\) 9.74870 0.345534
\(797\) 38.6481i 1.36898i 0.729020 + 0.684492i \(0.239976\pi\)
−0.729020 + 0.684492i \(0.760024\pi\)