Properties

Label 1764.2.e.j.1079.10
Level $1764$
Weight $2$
Character 1764.1079
Analytic conductor $14.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1079.10
Root \(0.670418 + 0.387066i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1079
Dual form 1764.2.e.j.1079.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.03295 - 0.965926i) q^{2} +(0.133975 - 1.99551i) q^{4} +2.73205i q^{5} +(-1.78912 - 2.19067i) q^{8} +O(q^{10})\) \(q+(1.03295 - 0.965926i) q^{2} +(0.133975 - 1.99551i) q^{4} +2.73205i q^{5} +(-1.78912 - 2.19067i) q^{8} +(2.63896 + 2.82207i) q^{10} -5.64415 q^{11} -1.41421 q^{13} +(-3.96410 - 0.534695i) q^{16} -6.19615i q^{17} +4.13180i q^{19} +(5.45183 + 0.366025i) q^{20} +(-5.83013 + 5.45183i) q^{22} -5.64415 q^{23} -2.46410 q^{25} +(-1.46081 + 1.36603i) q^{26} +0.378937i q^{29} +7.15649i q^{31} +(-4.61120 + 3.27671i) q^{32} +(-5.98502 - 6.40032i) q^{34} -3.46410 q^{37} +(3.99102 + 4.26795i) q^{38} +(5.98502 - 4.88798i) q^{40} -5.26795i q^{41} -5.84325i q^{43} +(-0.756172 + 11.2629i) q^{44} +(-5.83013 + 5.45183i) q^{46} -2.13878 q^{47} +(-2.54530 + 2.38014i) q^{50} +(-0.189469 + 2.82207i) q^{52} -0.656339i q^{53} -15.4201i q^{55} +(0.366025 + 0.391424i) q^{58} -13.8253 q^{59} -15.0759 q^{61} +(6.91264 + 7.39230i) q^{62} +(-1.59808 + 7.83876i) q^{64} -3.86370i q^{65} +7.98203i q^{67} +(-12.3645 - 0.830127i) q^{68} -13.9078 q^{71} +13.0053 q^{73} +(-3.57825 + 3.34607i) q^{74} +(8.24504 + 0.553557i) q^{76} -13.8253i q^{79} +(1.46081 - 10.8301i) q^{80} +(-5.08845 - 5.44153i) q^{82} +10.1208 q^{83} +16.9282 q^{85} +(-5.64415 - 6.03579i) q^{86} +(10.0981 + 12.3645i) q^{88} +5.26795i q^{89} +(-0.756172 + 11.2629i) q^{92} +(-2.20925 + 2.06590i) q^{94} -11.2883 q^{95} +9.41902 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 8 q^{16} - 24 q^{22} + 16 q^{25} - 24 q^{46} - 8 q^{58} + 16 q^{64} + 160 q^{85} + 120 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03295 0.965926i 0.730406 0.683013i
\(3\) 0 0
\(4\) 0.133975 1.99551i 0.0669873 0.997754i
\(5\) 2.73205i 1.22181i 0.791704 + 0.610905i \(0.209194\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.78912 2.19067i −0.632551 0.774519i
\(9\) 0 0
\(10\) 2.63896 + 2.82207i 0.834512 + 0.892418i
\(11\) −5.64415 −1.70177 −0.850887 0.525348i \(-0.823935\pi\)
−0.850887 + 0.525348i \(0.823935\pi\)
\(12\) 0 0
\(13\) −1.41421 −0.392232 −0.196116 0.980581i \(-0.562833\pi\)
−0.196116 + 0.980581i \(0.562833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.96410 0.534695i −0.991025 0.133674i
\(17\) 6.19615i 1.50279i −0.659854 0.751394i \(-0.729382\pi\)
0.659854 0.751394i \(-0.270618\pi\)
\(18\) 0 0
\(19\) 4.13180i 0.947901i 0.880552 + 0.473950i \(0.157172\pi\)
−0.880552 + 0.473950i \(0.842828\pi\)
\(20\) 5.45183 + 0.366025i 1.21907 + 0.0818458i
\(21\) 0 0
\(22\) −5.83013 + 5.45183i −1.24299 + 1.16233i
\(23\) −5.64415 −1.17689 −0.588443 0.808539i \(-0.700259\pi\)
−0.588443 + 0.808539i \(0.700259\pi\)
\(24\) 0 0
\(25\) −2.46410 −0.492820
\(26\) −1.46081 + 1.36603i −0.286489 + 0.267900i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.378937i 0.0703669i 0.999381 + 0.0351835i \(0.0112016\pi\)
−0.999381 + 0.0351835i \(0.988798\pi\)
\(30\) 0 0
\(31\) 7.15649i 1.28534i 0.766141 + 0.642672i \(0.222174\pi\)
−0.766141 + 0.642672i \(0.777826\pi\)
\(32\) −4.61120 + 3.27671i −0.815152 + 0.579247i
\(33\) 0 0
\(34\) −5.98502 6.40032i −1.02642 1.09765i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.46410 −0.569495 −0.284747 0.958603i \(-0.591910\pi\)
−0.284747 + 0.958603i \(0.591910\pi\)
\(38\) 3.99102 + 4.26795i 0.647428 + 0.692353i
\(39\) 0 0
\(40\) 5.98502 4.88798i 0.946315 0.772857i
\(41\) 5.26795i 0.822715i −0.911474 0.411358i \(-0.865055\pi\)
0.911474 0.411358i \(-0.134945\pi\)
\(42\) 0 0
\(43\) 5.84325i 0.891088i −0.895260 0.445544i \(-0.853010\pi\)
0.895260 0.445544i \(-0.146990\pi\)
\(44\) −0.756172 + 11.2629i −0.113997 + 1.69795i
\(45\) 0 0
\(46\) −5.83013 + 5.45183i −0.859605 + 0.803828i
\(47\) −2.13878 −0.311973 −0.155986 0.987759i \(-0.549856\pi\)
−0.155986 + 0.987759i \(0.549856\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.54530 + 2.38014i −0.359959 + 0.336603i
\(51\) 0 0
\(52\) −0.189469 + 2.82207i −0.0262746 + 0.391351i
\(53\) 0.656339i 0.0901551i −0.998983 0.0450775i \(-0.985647\pi\)
0.998983 0.0450775i \(-0.0143535\pi\)
\(54\) 0 0
\(55\) 15.4201i 2.07925i
\(56\) 0 0
\(57\) 0 0
\(58\) 0.366025 + 0.391424i 0.0480615 + 0.0513964i
\(59\) −13.8253 −1.79990 −0.899949 0.435995i \(-0.856397\pi\)
−0.899949 + 0.435995i \(0.856397\pi\)
\(60\) 0 0
\(61\) −15.0759 −1.93027 −0.965134 0.261756i \(-0.915698\pi\)
−0.965134 + 0.261756i \(0.915698\pi\)
\(62\) 6.91264 + 7.39230i 0.877906 + 0.938824i
\(63\) 0 0
\(64\) −1.59808 + 7.83876i −0.199760 + 0.979845i
\(65\) 3.86370i 0.479233i
\(66\) 0 0
\(67\) 7.98203i 0.975160i 0.873078 + 0.487580i \(0.162120\pi\)
−0.873078 + 0.487580i \(0.837880\pi\)
\(68\) −12.3645 0.830127i −1.49941 0.100668i
\(69\) 0 0
\(70\) 0 0
\(71\) −13.9078 −1.65055 −0.825273 0.564733i \(-0.808979\pi\)
−0.825273 + 0.564733i \(0.808979\pi\)
\(72\) 0 0
\(73\) 13.0053 1.52216 0.761079 0.648659i \(-0.224670\pi\)
0.761079 + 0.648659i \(0.224670\pi\)
\(74\) −3.57825 + 3.34607i −0.415963 + 0.388972i
\(75\) 0 0
\(76\) 8.24504 + 0.553557i 0.945771 + 0.0634973i
\(77\) 0 0
\(78\) 0 0
\(79\) 13.8253i 1.55547i −0.628595 0.777733i \(-0.716370\pi\)
0.628595 0.777733i \(-0.283630\pi\)
\(80\) 1.46081 10.8301i 0.163324 1.21085i
\(81\) 0 0
\(82\) −5.08845 5.44153i −0.561925 0.600917i
\(83\) 10.1208 1.11090 0.555452 0.831549i \(-0.312545\pi\)
0.555452 + 0.831549i \(0.312545\pi\)
\(84\) 0 0
\(85\) 16.9282 1.83612
\(86\) −5.64415 6.03579i −0.608624 0.650856i
\(87\) 0 0
\(88\) 10.0981 + 12.3645i 1.07646 + 1.31806i
\(89\) 5.26795i 0.558401i 0.960233 + 0.279201i \(0.0900695\pi\)
−0.960233 + 0.279201i \(0.909931\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.756172 + 11.2629i −0.0788364 + 1.17424i
\(93\) 0 0
\(94\) −2.20925 + 2.06590i −0.227867 + 0.213081i
\(95\) −11.2883 −1.15815
\(96\) 0 0
\(97\) 9.41902 0.956357 0.478178 0.878263i \(-0.341297\pi\)
0.478178 + 0.878263i \(0.341297\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.330127 + 4.91713i −0.0330127 + 0.491713i
\(101\) 8.73205i 0.868872i 0.900703 + 0.434436i \(0.143052\pi\)
−0.900703 + 0.434436i \(0.856948\pi\)
\(102\) 0 0
\(103\) 12.3954i 1.22136i 0.791879 + 0.610678i \(0.209103\pi\)
−0.791879 + 0.610678i \(0.790897\pi\)
\(104\) 2.53020 + 3.09808i 0.248107 + 0.303791i
\(105\) 0 0
\(106\) −0.633975 0.677966i −0.0615771 0.0658498i
\(107\) −2.61946 −0.253233 −0.126616 0.991952i \(-0.540412\pi\)
−0.126616 + 0.991952i \(0.540412\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) −14.8947 15.9282i −1.42015 1.51869i
\(111\) 0 0
\(112\) 0 0
\(113\) 9.14162i 0.859971i −0.902836 0.429986i \(-0.858519\pi\)
0.902836 0.429986i \(-0.141481\pi\)
\(114\) 0 0
\(115\) 15.4201i 1.43793i
\(116\) 0.756172 + 0.0507680i 0.0702088 + 0.00471369i
\(117\) 0 0
\(118\) −14.2808 + 13.3542i −1.31466 + 1.22935i
\(119\) 0 0
\(120\) 0 0
\(121\) 20.8564 1.89604
\(122\) −15.5726 + 14.5622i −1.40988 + 1.31840i
\(123\) 0 0
\(124\) 14.2808 + 0.958788i 1.28246 + 0.0861017i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 3.70447i 0.328719i −0.986401 0.164359i \(-0.947444\pi\)
0.986401 0.164359i \(-0.0525557\pi\)
\(128\) 5.92093 + 9.64068i 0.523341 + 0.852123i
\(129\) 0 0
\(130\) −3.73205 3.99102i −0.327323 0.350035i
\(131\) 11.6865 1.02105 0.510527 0.859862i \(-0.329450\pi\)
0.510527 + 0.859862i \(0.329450\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.71005 + 8.24504i 0.666047 + 0.712263i
\(135\) 0 0
\(136\) −13.5737 + 11.0857i −1.16394 + 0.950589i
\(137\) 0.378937i 0.0323748i 0.999869 + 0.0161874i \(0.00515284\pi\)
−0.999869 + 0.0161874i \(0.994847\pi\)
\(138\) 0 0
\(139\) 8.26361i 0.700910i −0.936580 0.350455i \(-0.886027\pi\)
0.936580 0.350455i \(-0.113973\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −14.3660 + 13.4339i −1.20557 + 1.12734i
\(143\) 7.98203 0.667491
\(144\) 0 0
\(145\) −1.03528 −0.0859750
\(146\) 13.4339 12.5622i 1.11179 1.03965i
\(147\) 0 0
\(148\) −0.464102 + 6.91264i −0.0381489 + 0.568216i
\(149\) 4.24264i 0.347571i 0.984784 + 0.173785i \(0.0555999\pi\)
−0.984784 + 0.173785i \(0.944400\pi\)
\(150\) 0 0
\(151\) 5.84325i 0.475517i −0.971324 0.237759i \(-0.923587\pi\)
0.971324 0.237759i \(-0.0764127\pi\)
\(152\) 9.05142 7.39230i 0.734167 0.599595i
\(153\) 0 0
\(154\) 0 0
\(155\) −19.5519 −1.57045
\(156\) 0 0
\(157\) −9.41902 −0.751720 −0.375860 0.926677i \(-0.622653\pi\)
−0.375860 + 0.926677i \(0.622653\pi\)
\(158\) −13.3542 14.2808i −1.06240 1.13612i
\(159\) 0 0
\(160\) −8.95215 12.5980i −0.707730 0.995961i
\(161\) 0 0
\(162\) 0 0
\(163\) 12.2596i 0.960245i 0.877201 + 0.480123i \(0.159408\pi\)
−0.877201 + 0.480123i \(0.840592\pi\)
\(164\) −10.5122 0.705771i −0.820867 0.0551115i
\(165\) 0 0
\(166\) 10.4543 9.77595i 0.811411 0.758761i
\(167\) 2.13878 0.165504 0.0827518 0.996570i \(-0.473629\pi\)
0.0827518 + 0.996570i \(0.473629\pi\)
\(168\) 0 0
\(169\) −11.0000 −0.846154
\(170\) 17.4860 16.3514i 1.34112 1.25409i
\(171\) 0 0
\(172\) −11.6603 0.782847i −0.889086 0.0596915i
\(173\) 7.66025i 0.582398i 0.956662 + 0.291199i \(0.0940542\pi\)
−0.956662 + 0.291199i \(0.905946\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 22.3740 + 3.01790i 1.68650 + 0.227482i
\(177\) 0 0
\(178\) 5.08845 + 5.44153i 0.381395 + 0.407860i
\(179\) 8.66884 0.647939 0.323970 0.946067i \(-0.394982\pi\)
0.323970 + 0.946067i \(0.394982\pi\)
\(180\) 0 0
\(181\) 14.7985 1.09996 0.549981 0.835177i \(-0.314635\pi\)
0.549981 + 0.835177i \(0.314635\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 10.0981 + 12.3645i 0.744440 + 0.911521i
\(185\) 9.46410i 0.695815i
\(186\) 0 0
\(187\) 34.9720i 2.55741i
\(188\) −0.286542 + 4.26795i −0.0208982 + 0.311272i
\(189\) 0 0
\(190\) −11.6603 + 10.9037i −0.845924 + 0.791034i
\(191\) −2.61946 −0.189537 −0.0947687 0.995499i \(-0.530211\pi\)
−0.0947687 + 0.995499i \(0.530211\pi\)
\(192\) 0 0
\(193\) 17.8564 1.28533 0.642666 0.766146i \(-0.277828\pi\)
0.642666 + 0.766146i \(0.277828\pi\)
\(194\) 9.72939 9.09808i 0.698529 0.653204i
\(195\) 0 0
\(196\) 0 0
\(197\) 23.8386i 1.69843i −0.528050 0.849213i \(-0.677077\pi\)
0.528050 0.849213i \(-0.322923\pi\)
\(198\) 0 0
\(199\) 11.2883i 0.800206i −0.916470 0.400103i \(-0.868974\pi\)
0.916470 0.400103i \(-0.131026\pi\)
\(200\) 4.40858 + 5.39804i 0.311734 + 0.381699i
\(201\) 0 0
\(202\) 8.43451 + 9.01978i 0.593450 + 0.634629i
\(203\) 0 0
\(204\) 0 0
\(205\) 14.3923 1.00520
\(206\) 11.9730 + 12.8038i 0.834202 + 0.892086i
\(207\) 0 0
\(208\) 5.60609 + 0.756172i 0.388712 + 0.0524311i
\(209\) 23.3205i 1.61311i
\(210\) 0 0
\(211\) 4.27756i 0.294479i 0.989101 + 0.147240i \(0.0470388\pi\)
−0.989101 + 0.147240i \(0.952961\pi\)
\(212\) −1.30973 0.0879327i −0.0899526 0.00603924i
\(213\) 0 0
\(214\) −2.70577 + 2.53020i −0.184963 + 0.172961i
\(215\) 15.9641 1.08874
\(216\) 0 0
\(217\) 0 0
\(218\) 6.19770 5.79555i 0.419762 0.392525i
\(219\) 0 0
\(220\) −30.7709 2.06590i −2.07458 0.139283i
\(221\) 8.76268i 0.589442i
\(222\) 0 0
\(223\) 3.02469i 0.202548i 0.994859 + 0.101274i \(0.0322919\pi\)
−0.994859 + 0.101274i \(0.967708\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −8.83013 9.44284i −0.587371 0.628129i
\(227\) −2.13878 −0.141956 −0.0709779 0.997478i \(-0.522612\pi\)
−0.0709779 + 0.997478i \(0.522612\pi\)
\(228\) 0 0
\(229\) −5.75839 −0.380525 −0.190263 0.981733i \(-0.560934\pi\)
−0.190263 + 0.981733i \(0.560934\pi\)
\(230\) −14.8947 15.9282i −0.982126 1.05027i
\(231\) 0 0
\(232\) 0.830127 0.677966i 0.0545005 0.0445106i
\(233\) 28.4601i 1.86449i −0.361833 0.932243i \(-0.617849\pi\)
0.361833 0.932243i \(-0.382151\pi\)
\(234\) 0 0
\(235\) 5.84325i 0.381172i
\(236\) −1.85224 + 27.5885i −0.120570 + 1.79586i
\(237\) 0 0
\(238\) 0 0
\(239\) 5.64415 0.365090 0.182545 0.983198i \(-0.441567\pi\)
0.182545 + 0.983198i \(0.441567\pi\)
\(240\) 0 0
\(241\) 1.69161 0.108966 0.0544832 0.998515i \(-0.482649\pi\)
0.0544832 + 0.998515i \(0.482649\pi\)
\(242\) 21.5436 20.1457i 1.38488 1.29502i
\(243\) 0 0
\(244\) −2.01978 + 30.0840i −0.129303 + 1.92593i
\(245\) 0 0
\(246\) 0 0
\(247\) 5.84325i 0.371797i
\(248\) 15.6775 12.8038i 0.995523 0.813045i
\(249\) 0 0
\(250\) 6.69213 + 7.15649i 0.423247 + 0.452616i
\(251\) −23.9461 −1.51146 −0.755732 0.654881i \(-0.772719\pi\)
−0.755732 + 0.654881i \(0.772719\pi\)
\(252\) 0 0
\(253\) 31.8564 2.00280
\(254\) −3.57825 3.82654i −0.224519 0.240098i
\(255\) 0 0
\(256\) 15.4282 + 4.23917i 0.964263 + 0.264948i
\(257\) 23.1244i 1.44246i 0.692697 + 0.721229i \(0.256422\pi\)
−0.692697 + 0.721229i \(0.743578\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7.71005 0.517638i −0.478157 0.0321026i
\(261\) 0 0
\(262\) 12.0716 11.2883i 0.745785 0.697393i
\(263\) 5.64415 0.348033 0.174017 0.984743i \(-0.444325\pi\)
0.174017 + 0.984743i \(0.444325\pi\)
\(264\) 0 0
\(265\) 1.79315 0.110152
\(266\) 0 0
\(267\) 0 0
\(268\) 15.9282 + 1.06939i 0.972970 + 0.0653234i
\(269\) 13.6603i 0.832880i 0.909163 + 0.416440i \(0.136722\pi\)
−0.909163 + 0.416440i \(0.863278\pi\)
\(270\) 0 0
\(271\) 18.4448i 1.12044i −0.828343 0.560221i \(-0.810716\pi\)
0.828343 0.560221i \(-0.189284\pi\)
\(272\) −3.31305 + 24.5622i −0.200883 + 1.48930i
\(273\) 0 0
\(274\) 0.366025 + 0.391424i 0.0221124 + 0.0236468i
\(275\) 13.9078 0.838669
\(276\) 0 0
\(277\) −20.9282 −1.25745 −0.628727 0.777626i \(-0.716424\pi\)
−0.628727 + 0.777626i \(0.716424\pi\)
\(278\) −7.98203 8.53590i −0.478730 0.511949i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.933740i 0.0557023i 0.999612 + 0.0278511i \(0.00886644\pi\)
−0.999612 + 0.0278511i \(0.991134\pi\)
\(282\) 0 0
\(283\) 4.13180i 0.245610i −0.992431 0.122805i \(-0.960811\pi\)
0.992431 0.122805i \(-0.0391890\pi\)
\(284\) −1.86329 + 27.7530i −0.110566 + 1.64684i
\(285\) 0 0
\(286\) 8.24504 7.71005i 0.487540 0.455905i
\(287\) 0 0
\(288\) 0 0
\(289\) −21.3923 −1.25837
\(290\) −1.06939 + 1.00000i −0.0627967 + 0.0587220i
\(291\) 0 0
\(292\) 1.74238 25.9522i 0.101965 1.51874i
\(293\) 6.87564i 0.401679i 0.979624 + 0.200840i \(0.0643670\pi\)
−0.979624 + 0.200840i \(0.935633\pi\)
\(294\) 0 0
\(295\) 37.7714i 2.19913i
\(296\) 6.19770 + 7.58871i 0.360234 + 0.441085i
\(297\) 0 0
\(298\) 4.09808 + 4.38244i 0.237395 + 0.253868i
\(299\) 7.98203 0.461613
\(300\) 0 0
\(301\) 0 0
\(302\) −5.64415 6.03579i −0.324784 0.347321i
\(303\) 0 0
\(304\) 2.20925 16.3789i 0.126709 0.939394i
\(305\) 41.1881i 2.35842i
\(306\) 0 0
\(307\) 7.15649i 0.408443i 0.978925 + 0.204221i \(0.0654662\pi\)
−0.978925 + 0.204221i \(0.934534\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −20.1962 + 18.8857i −1.14706 + 1.07263i
\(311\) −25.5118 −1.44664 −0.723320 0.690513i \(-0.757385\pi\)
−0.723320 + 0.690513i \(0.757385\pi\)
\(312\) 0 0
\(313\) 0.859411 0.0485768 0.0242884 0.999705i \(-0.492268\pi\)
0.0242884 + 0.999705i \(0.492268\pi\)
\(314\) −9.72939 + 9.09808i −0.549061 + 0.513434i
\(315\) 0 0
\(316\) −27.5885 1.85224i −1.55197 0.104196i
\(317\) 4.24264i 0.238290i 0.992877 + 0.119145i \(0.0380154\pi\)
−0.992877 + 0.119145i \(0.961985\pi\)
\(318\) 0 0
\(319\) 2.13878i 0.119749i
\(320\) −21.4159 4.36603i −1.19718 0.244068i
\(321\) 0 0
\(322\) 0 0
\(323\) 25.6013 1.42449
\(324\) 0 0
\(325\) 3.48477 0.193300
\(326\) 11.8419 + 12.6636i 0.655860 + 0.701369i
\(327\) 0 0
\(328\) −11.5403 + 9.42501i −0.637209 + 0.520409i
\(329\) 0 0
\(330\) 0 0
\(331\) 31.9281i 1.75493i −0.479642 0.877464i \(-0.659234\pi\)
0.479642 0.877464i \(-0.340766\pi\)
\(332\) 1.35593 20.1962i 0.0744164 1.10841i
\(333\) 0 0
\(334\) 2.20925 2.06590i 0.120885 0.113041i
\(335\) −21.8073 −1.19146
\(336\) 0 0
\(337\) −22.3923 −1.21979 −0.609893 0.792484i \(-0.708788\pi\)
−0.609893 + 0.792484i \(0.708788\pi\)
\(338\) −11.3625 + 10.6252i −0.618036 + 0.577934i
\(339\) 0 0
\(340\) 2.26795 33.7804i 0.122997 1.83200i
\(341\) 40.3923i 2.18737i
\(342\) 0 0
\(343\) 0 0
\(344\) −12.8006 + 10.4543i −0.690164 + 0.563658i
\(345\) 0 0
\(346\) 7.39924 + 7.91267i 0.397785 + 0.425388i
\(347\) 22.1714 1.19022 0.595110 0.803644i \(-0.297108\pi\)
0.595110 + 0.803644i \(0.297108\pi\)
\(348\) 0 0
\(349\) −22.8033 −1.22063 −0.610316 0.792158i \(-0.708957\pi\)
−0.610316 + 0.792158i \(0.708957\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 26.0263 18.4943i 1.38721 0.985748i
\(353\) 17.8038i 0.947603i −0.880632 0.473802i \(-0.842881\pi\)
0.880632 0.473802i \(-0.157119\pi\)
\(354\) 0 0
\(355\) 37.9967i 2.01665i
\(356\) 10.5122 + 0.705771i 0.557147 + 0.0374058i
\(357\) 0 0
\(358\) 8.95448 8.37345i 0.473259 0.442551i
\(359\) −13.9078 −0.734023 −0.367012 0.930216i \(-0.619619\pi\)
−0.367012 + 0.930216i \(0.619619\pi\)
\(360\) 0 0
\(361\) 1.92820 0.101484
\(362\) 15.2861 14.2942i 0.803419 0.751288i
\(363\) 0 0
\(364\) 0 0
\(365\) 35.5312i 1.85979i
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 22.3740 + 3.01790i 1.16632 + 0.157319i
\(369\) 0 0
\(370\) −9.14162 9.77595i −0.475250 0.508227i
\(371\) 0 0
\(372\) 0 0
\(373\) 3.07180 0.159052 0.0795258 0.996833i \(-0.474659\pi\)
0.0795258 + 0.996833i \(0.474659\pi\)
\(374\) 33.7804 + 36.1244i 1.74674 + 1.86795i
\(375\) 0 0
\(376\) 3.82654 + 4.68536i 0.197339 + 0.241629i
\(377\) 0.535898i 0.0276002i
\(378\) 0 0
\(379\) 20.2416i 1.03974i −0.854245 0.519871i \(-0.825980\pi\)
0.854245 0.519871i \(-0.174020\pi\)
\(380\) −1.51234 + 22.5259i −0.0775817 + 1.15555i
\(381\) 0 0
\(382\) −2.70577 + 2.53020i −0.138439 + 0.129456i
\(383\) −4.27756 −0.218573 −0.109286 0.994010i \(-0.534857\pi\)
−0.109286 + 0.994010i \(0.534857\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.4448 17.2480i 0.938815 0.877898i
\(387\) 0 0
\(388\) 1.26191 18.7957i 0.0640638 0.954209i
\(389\) 21.2875i 1.07932i 0.841883 + 0.539660i \(0.181447\pi\)
−0.841883 + 0.539660i \(0.818553\pi\)
\(390\) 0 0
\(391\) 34.9720i 1.76861i
\(392\) 0 0
\(393\) 0 0
\(394\) −23.0263 24.6241i −1.16005 1.24054i
\(395\) 37.7714 1.90048
\(396\) 0 0
\(397\) −22.2485 −1.11662 −0.558310 0.829633i \(-0.688550\pi\)
−0.558310 + 0.829633i \(0.688550\pi\)
\(398\) −10.9037 11.6603i −0.546551 0.584476i
\(399\) 0 0
\(400\) 9.76795 + 1.31754i 0.488397 + 0.0658771i
\(401\) 15.6307i 0.780559i 0.920696 + 0.390279i \(0.127622\pi\)
−0.920696 + 0.390279i \(0.872378\pi\)
\(402\) 0 0
\(403\) 10.1208i 0.504153i
\(404\) 17.4249 + 1.16987i 0.866920 + 0.0582034i
\(405\) 0 0
\(406\) 0 0
\(407\) 19.5519 0.969152
\(408\) 0 0
\(409\) 4.52004 0.223502 0.111751 0.993736i \(-0.464354\pi\)
0.111751 + 0.993736i \(0.464354\pi\)
\(410\) 14.8665 13.9019i 0.734206 0.686566i
\(411\) 0 0
\(412\) 24.7351 + 1.66067i 1.21861 + 0.0818153i
\(413\) 0 0
\(414\) 0 0
\(415\) 27.6506i 1.35731i
\(416\) 6.52122 4.63397i 0.319729 0.227199i
\(417\) 0 0
\(418\) −22.5259 24.0889i −1.10178 1.17823i
\(419\) −12.2596 −0.598920 −0.299460 0.954109i \(-0.596807\pi\)
−0.299460 + 0.954109i \(0.596807\pi\)
\(420\) 0 0
\(421\) 25.7128 1.25317 0.626583 0.779355i \(-0.284453\pi\)
0.626583 + 0.779355i \(0.284453\pi\)
\(422\) 4.13180 + 4.41851i 0.201133 + 0.215090i
\(423\) 0 0
\(424\) −1.43782 + 1.17427i −0.0698268 + 0.0570276i
\(425\) 15.2679i 0.740604i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.350941 + 5.22715i −0.0169634 + 0.252664i
\(429\) 0 0
\(430\) 16.4901 15.4201i 0.795223 0.743623i
\(431\) 11.6935 0.563257 0.281629 0.959523i \(-0.409125\pi\)
0.281629 + 0.959523i \(0.409125\pi\)
\(432\) 0 0
\(433\) 5.00052 0.240309 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.803848 11.9730i 0.0384973 0.573405i
\(437\) 23.3205i 1.11557i
\(438\) 0 0
\(439\) 36.8896i 1.76064i 0.474377 + 0.880322i \(0.342673\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(440\) −33.7804 + 27.5885i −1.61042 + 1.31523i
\(441\) 0 0
\(442\) 8.46410 + 9.05142i 0.402596 + 0.430532i
\(443\) −28.2207 −1.34081 −0.670404 0.741996i \(-0.733879\pi\)
−0.670404 + 0.741996i \(0.733879\pi\)
\(444\) 0 0
\(445\) −14.3923 −0.682261
\(446\) 2.92163 + 3.12436i 0.138343 + 0.147943i
\(447\) 0 0
\(448\) 0 0
\(449\) 6.86800i 0.324121i 0.986781 + 0.162060i \(0.0518139\pi\)
−0.986781 + 0.162060i \(0.948186\pi\)
\(450\) 0 0
\(451\) 29.7331i 1.40008i
\(452\) −18.2422 1.22474i −0.858040 0.0576072i
\(453\) 0 0
\(454\) −2.20925 + 2.06590i −0.103685 + 0.0969576i
\(455\) 0 0
\(456\) 0 0
\(457\) −9.07180 −0.424361 −0.212180 0.977231i \(-0.568056\pi\)
−0.212180 + 0.977231i \(0.568056\pi\)
\(458\) −5.94813 + 5.56218i −0.277938 + 0.259904i
\(459\) 0 0
\(460\) −30.7709 2.06590i −1.43470 0.0963232i
\(461\) 12.7321i 0.592991i 0.955034 + 0.296495i \(0.0958179\pi\)
−0.955034 + 0.296495i \(0.904182\pi\)
\(462\) 0 0
\(463\) 35.6326i 1.65599i 0.560738 + 0.827994i \(0.310518\pi\)
−0.560738 + 0.827994i \(0.689482\pi\)
\(464\) 0.202616 1.50215i 0.00940620 0.0697354i
\(465\) 0 0
\(466\) −27.4904 29.3979i −1.27347 1.36183i
\(467\) −19.6685 −0.910151 −0.455076 0.890453i \(-0.650388\pi\)
−0.455076 + 0.890453i \(0.650388\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −5.64415 6.03579i −0.260345 0.278410i
\(471\) 0 0
\(472\) 24.7351 + 30.2866i 1.13853 + 1.39406i
\(473\) 32.9802i 1.51643i
\(474\) 0 0
\(475\) 10.1812i 0.467145i
\(476\) 0 0
\(477\) 0 0
\(478\) 5.83013 5.45183i 0.266664 0.249361i
\(479\) 19.6685 0.898678 0.449339 0.893361i \(-0.351659\pi\)
0.449339 + 0.893361i \(0.351659\pi\)
\(480\) 0 0
\(481\) 4.89898 0.223374
\(482\) 1.74735 1.63397i 0.0795898 0.0744255i
\(483\) 0 0
\(484\) 2.79423 41.6191i 0.127010 1.89178i
\(485\) 25.7332i 1.16849i
\(486\) 0 0
\(487\) 10.1208i 0.458618i −0.973354 0.229309i \(-0.926353\pi\)
0.973354 0.229309i \(-0.0736466\pi\)
\(488\) 26.9726 + 33.0263i 1.22099 + 1.49503i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.61946 0.118214 0.0591072 0.998252i \(-0.481175\pi\)
0.0591072 + 0.998252i \(0.481175\pi\)
\(492\) 0 0
\(493\) 2.34795 0.105747
\(494\) −5.64415 6.03579i −0.253942 0.271563i
\(495\) 0 0
\(496\) 3.82654 28.3691i 0.171817 1.27381i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.56569i 0.0700901i 0.999386 + 0.0350451i \(0.0111575\pi\)
−0.999386 + 0.0350451i \(0.988843\pi\)
\(500\) 13.8253 + 0.928203i 0.618285 + 0.0415105i
\(501\) 0 0
\(502\) −24.7351 + 23.1301i −1.10398 + 1.03235i
\(503\) −26.0849 −1.16307 −0.581533 0.813522i \(-0.697547\pi\)
−0.581533 + 0.813522i \(0.697547\pi\)
\(504\) 0 0
\(505\) −23.8564 −1.06160
\(506\) 32.9061 30.7709i 1.46285 1.36793i
\(507\) 0 0
\(508\) −7.39230 0.496305i −0.327980 0.0220200i
\(509\) 10.3397i 0.458301i −0.973391 0.229151i \(-0.926405\pi\)
0.973391 0.229151i \(-0.0735948\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 20.0313 10.5236i 0.885267 0.465084i
\(513\) 0 0
\(514\) 22.3364 + 23.8863i 0.985217 + 1.05358i
\(515\) −33.8649 −1.49227
\(516\) 0 0
\(517\) 12.0716 0.530908
\(518\) 0 0
\(519\) 0 0
\(520\) −8.46410 + 6.91264i −0.371175 + 0.303139i
\(521\) 7.66025i 0.335602i −0.985821 0.167801i \(-0.946333\pi\)
0.985821 0.167801i \(-0.0536666\pi\)
\(522\) 0 0
\(523\) 30.8402i 1.34855i −0.738481 0.674274i \(-0.764457\pi\)
0.738481 0.674274i \(-0.235543\pi\)
\(524\) 1.56569 23.3205i 0.0683977 1.01876i
\(525\) 0 0
\(526\) 5.83013 5.45183i 0.254206 0.237711i
\(527\) 44.3427 1.93160
\(528\) 0 0
\(529\) 8.85641 0.385061
\(530\) 1.85224 1.73205i 0.0804560 0.0752355i
\(531\) 0 0
\(532\) 0 0
\(533\) 7.45001i 0.322696i
\(534\) 0 0
\(535\) 7.15649i 0.309402i
\(536\) 17.4860 14.2808i 0.755280 0.616838i
\(537\) 0 0
\(538\) 13.1948 + 14.1104i 0.568868 + 0.608341i
\(539\) 0 0
\(540\) 0 0
\(541\) −11.8564 −0.509747 −0.254873 0.966974i \(-0.582034\pi\)
−0.254873 + 0.966974i \(0.582034\pi\)
\(542\) −17.8163 19.0526i −0.765276 0.818377i
\(543\) 0 0
\(544\) 20.3030 + 28.5717i 0.870485 + 1.22500i
\(545\) 16.3923i 0.702169i
\(546\) 0 0
\(547\) 9.54773i 0.408231i 0.978947 + 0.204116i \(0.0654319\pi\)
−0.978947 + 0.204116i \(0.934568\pi\)
\(548\) 0.756172 + 0.0507680i 0.0323021 + 0.00216870i
\(549\) 0 0
\(550\) 14.3660 13.4339i 0.612569 0.572822i
\(551\) −1.56569 −0.0667008
\(552\) 0 0
\(553\) 0 0
\(554\) −21.6178 + 20.2151i −0.918452 + 0.858857i
\(555\) 0 0
\(556\) −16.4901 1.10711i −0.699336 0.0469521i
\(557\) 10.4543i 0.442963i −0.975165 0.221481i \(-0.928911\pi\)
0.975165 0.221481i \(-0.0710892\pi\)
\(558\) 0 0
\(559\) 8.26361i 0.349513i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.901924 + 0.964508i 0.0380454 + 0.0406853i
\(563\) 22.3804 0.943221 0.471611 0.881807i \(-0.343673\pi\)
0.471611 + 0.881807i \(0.343673\pi\)
\(564\) 0 0
\(565\) 24.9754 1.05072
\(566\) −3.99102 4.26795i −0.167755 0.179395i
\(567\) 0 0
\(568\) 24.8827 + 30.4673i 1.04405 + 1.27838i
\(569\) 11.6926i 0.490181i −0.969500 0.245091i \(-0.921182\pi\)
0.969500 0.245091i \(-0.0788177\pi\)
\(570\) 0 0
\(571\) 29.7893i 1.24665i −0.781965 0.623323i \(-0.785782\pi\)
0.781965 0.623323i \(-0.214218\pi\)
\(572\) 1.06939 15.9282i 0.0447134 0.665992i
\(573\) 0 0
\(574\) 0 0
\(575\) 13.9078 0.579993
\(576\) 0 0
\(577\) −21.7680 −0.906214 −0.453107 0.891456i \(-0.649684\pi\)
−0.453107 + 0.891456i \(0.649684\pi\)
\(578\) −22.0972 + 20.6634i −0.919122 + 0.859483i
\(579\) 0 0
\(580\) −0.138701 + 2.06590i −0.00575923 + 0.0857819i
\(581\) 0 0
\(582\) 0 0
\(583\) 3.70447i 0.153424i
\(584\) −23.2681 28.4904i −0.962842 1.17894i
\(585\) 0 0
\(586\) 6.64136 + 7.10220i 0.274352 + 0.293389i
\(587\) 18.1028 0.747184 0.373592 0.927593i \(-0.378126\pi\)
0.373592 + 0.927593i \(0.378126\pi\)
\(588\) 0 0
\(589\) −29.5692 −1.21838
\(590\) −36.4843 39.0160i −1.50204 1.60626i
\(591\) 0 0
\(592\) 13.7321 + 1.85224i 0.564384 + 0.0761265i
\(593\) 17.8038i 0.731116i 0.930788 + 0.365558i \(0.119122\pi\)
−0.930788 + 0.365558i \(0.880878\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.46622 + 0.568406i 0.346790 + 0.0232828i
\(597\) 0 0
\(598\) 8.24504 7.71005i 0.337165 0.315287i
\(599\) 30.4350 1.24354 0.621770 0.783200i \(-0.286414\pi\)
0.621770 + 0.783200i \(0.286414\pi\)
\(600\) 0 0
\(601\) −40.2543 −1.64201 −0.821004 0.570923i \(-0.806586\pi\)
−0.821004 + 0.570923i \(0.806586\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −11.6603 0.782847i −0.474449 0.0318536i
\(605\) 56.9808i 2.31660i
\(606\) 0 0
\(607\) 39.1038i 1.58717i −0.608456 0.793587i \(-0.708211\pi\)
0.608456 0.793587i \(-0.291789\pi\)
\(608\) −13.5387 19.0526i −0.549068 0.772683i
\(609\) 0 0
\(610\) −39.7846 42.5452i −1.61083 1.72261i
\(611\) 3.02469 0.122366
\(612\) 0 0
\(613\) −4.39230 −0.177404 −0.0887018 0.996058i \(-0.528272\pi\)
−0.0887018 + 0.996058i \(0.528272\pi\)
\(614\) 6.91264 + 7.39230i 0.278971 + 0.298329i
\(615\) 0 0
\(616\) 0 0
\(617\) 34.8749i 1.40401i −0.712172 0.702005i \(-0.752289\pi\)
0.712172 0.702005i \(-0.247711\pi\)
\(618\) 0 0
\(619\) 5.23892i 0.210570i 0.994442 + 0.105285i \(0.0335755\pi\)
−0.994442 + 0.105285i \(0.966425\pi\)
\(620\) −2.61946 + 39.0160i −0.105200 + 1.56692i
\(621\) 0 0
\(622\) −26.3524 + 24.6425i −1.05664 + 0.988074i
\(623\) 0 0
\(624\) 0 0
\(625\) −31.2487 −1.24995
\(626\) 0.887729 0.830127i 0.0354808 0.0331785i
\(627\) 0 0
\(628\) −1.26191 + 18.7957i −0.0503557 + 0.750031i
\(629\) 21.4641i 0.855830i
\(630\) 0 0
\(631\) 35.6326i 1.41851i 0.704951 + 0.709256i \(0.250969\pi\)
−0.704951 + 0.709256i \(0.749031\pi\)
\(632\) −30.2866 + 24.7351i −1.20474 + 0.983911i
\(633\) 0 0
\(634\) 4.09808 + 4.38244i 0.162755 + 0.174049i
\(635\) 10.1208 0.401632
\(636\) 0 0
\(637\) 0 0
\(638\) −2.06590 2.20925i −0.0817898 0.0874652i
\(639\) 0 0
\(640\) −26.3388 + 16.1763i −1.04113 + 0.639423i
\(641\) 18.6622i 0.737112i −0.929606 0.368556i \(-0.879852\pi\)
0.929606 0.368556i \(-0.120148\pi\)
\(642\) 0 0
\(643\) 26.7084i 1.05328i 0.850090 + 0.526638i \(0.176548\pi\)
−0.850090 + 0.526638i \(0.823452\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 26.4449 24.7289i 1.04046 0.972947i
\(647\) 5.27017 0.207192 0.103596 0.994619i \(-0.466965\pi\)
0.103596 + 0.994619i \(0.466965\pi\)
\(648\) 0 0
\(649\) 78.0319 3.06302
\(650\) 3.59959 3.36603i 0.141188 0.132026i
\(651\) 0 0
\(652\) 24.4641 + 1.64247i 0.958088 + 0.0643242i
\(653\) 34.3201i 1.34305i 0.740983 + 0.671524i \(0.234360\pi\)
−0.740983 + 0.671524i \(0.765640\pi\)
\(654\) 0 0
\(655\) 31.9281i 1.24753i
\(656\) −2.81674 + 20.8827i −0.109975 + 0.815332i
\(657\) 0 0
\(658\) 0 0
\(659\) −14.7182 −0.573340 −0.286670 0.958029i \(-0.592548\pi\)
−0.286670 + 0.958029i \(0.592548\pi\)
\(660\) 0 0
\(661\) 25.8348 1.00486 0.502428 0.864619i \(-0.332440\pi\)
0.502428 + 0.864619i \(0.332440\pi\)
\(662\) −30.8402 32.9802i −1.19864 1.28181i
\(663\) 0 0
\(664\) −18.1074 22.1714i −0.702702 0.860416i
\(665\) 0 0
\(666\) 0 0
\(667\) 2.13878i 0.0828138i
\(668\) 0.286542 4.26795i 0.0110866 0.165132i
\(669\) 0 0
\(670\) −22.5259 + 21.0642i −0.870251 + 0.813783i
\(671\) 85.0905 3.28488
\(672\) 0 0
\(673\) −42.0000 −1.61898 −0.809491 0.587133i \(-0.800257\pi\)
−0.809491 + 0.587133i \(0.800257\pi\)
\(674\) −23.1301 + 21.6293i −0.890940 + 0.833130i
\(675\) 0 0
\(676\) −1.47372 + 21.9506i −0.0566816 + 0.844253i
\(677\) 49.1244i 1.88800i −0.329942 0.944001i \(-0.607029\pi\)
0.329942 0.944001i \(-0.392971\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −30.2866 37.0841i −1.16144 1.42211i
\(681\) 0 0
\(682\) −39.0160 41.7233i −1.49400 1.59767i
\(683\) −10.8831 −0.416429 −0.208214 0.978083i \(-0.566765\pi\)
−0.208214 + 0.978083i \(0.566765\pi\)
\(684\) 0 0
\(685\) −1.03528 −0.0395559
\(686\) 0 0
\(687\) 0 0
\(688\) −3.12436 + 23.1632i −0.119115 + 0.883090i
\(689\) 0.928203i 0.0353617i
\(690\) 0 0
\(691\) 13.5025i 0.513660i −0.966457 0.256830i \(-0.917322\pi\)
0.966457 0.256830i \(-0.0826781\pi\)
\(692\) 15.2861 + 1.02628i 0.581090 + 0.0390133i
\(693\) 0 0
\(694\) 22.9019 21.4159i 0.869345 0.812936i
\(695\) 22.5766 0.856379
\(696\) 0 0
\(697\) −32.6410 −1.23637
\(698\) −23.5547 + 22.0263i −0.891557 + 0.833707i
\(699\) 0 0
\(700\) 0 0
\(701\) 13.9663i 0.527499i 0.964591 + 0.263749i \(0.0849592\pi\)
−0.964591 + 0.263749i \(0.915041\pi\)
\(702\) 0 0
\(703\) 14.3130i 0.539824i
\(704\) 9.01978 44.2431i 0.339946 1.66748i
\(705\) 0 0
\(706\) −17.1972 18.3905i −0.647225 0.692136i
\(707\) 0 0
\(708\) 0 0
\(709\) 12.9282 0.485529 0.242764 0.970085i \(-0.421946\pi\)
0.242764 + 0.970085i \(0.421946\pi\)
\(710\) −36.7020 39.2487i −1.37740 1.47298i
\(711\) 0 0
\(712\) 11.5403 9.42501i 0.432493 0.353217i
\(713\) 40.3923i 1.51270i
\(714\) 0 0
\(715\) 21.8073i 0.815547i
\(716\) 1.16140 17.2987i 0.0434037 0.646484i
\(717\) 0 0
\(718\) −14.3660 + 13.4339i −0.536135 + 0.501347i
\(719\) −19.0955 −0.712140 −0.356070 0.934459i \(-0.615884\pi\)
−0.356070 + 0.934459i \(0.615884\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.99174 1.86250i 0.0741249 0.0693151i
\(723\) 0 0
\(724\) 1.98262 29.5305i 0.0736835 1.09749i
\(725\) 0.933740i 0.0346782i
\(726\) 0 0
\(727\) 49.2850i 1.82788i −0.405850 0.913939i \(-0.633025\pi\)
0.405850 0.913939i \(-0.366975\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 34.3205 + 36.7020i 1.27026 + 1.35840i
\(731\) −36.2057 −1.33912
\(732\) 0 0
\(733\) −28.9406 −1.06895 −0.534473 0.845186i \(-0.679490\pi\)
−0.534473 + 0.845186i \(0.679490\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 26.0263 18.4943i 0.959341 0.681708i
\(737\) 45.0518i 1.65950i
\(738\) 0 0
\(739\) 19.6685i 0.723519i 0.932272 + 0.361759i \(0.117824\pi\)
−0.932272 + 0.361759i \(0.882176\pi\)
\(740\) −18.8857 1.26795i −0.694252 0.0466107i
\(741\) 0 0
\(742\) 0 0
\(743\) −31.2454 −1.14628 −0.573142 0.819456i \(-0.694276\pi\)
−0.573142 + 0.819456i \(0.694276\pi\)
\(744\) 0 0
\(745\) −11.5911 −0.424665
\(746\) 3.17301 2.96713i 0.116172 0.108634i
\(747\) 0 0
\(748\) 69.7869 + 4.68536i 2.55166 + 0.171314i
\(749\) 0 0
\(750\) 0 0
\(751\) 36.2057i 1.32116i 0.750754 + 0.660582i \(0.229690\pi\)
−0.750754 + 0.660582i \(0.770310\pi\)
\(752\) 8.47834 + 1.14359i 0.309173 + 0.0417026i
\(753\) 0 0
\(754\) −0.517638 0.553557i −0.0188513 0.0201593i
\(755\) 15.9641 0.580992
\(756\) 0 0
\(757\) −28.6410 −1.04098 −0.520488 0.853869i \(-0.674250\pi\)
−0.520488 + 0.853869i \(0.674250\pi\)
\(758\) −19.5519 20.9086i −0.710157 0.759434i
\(759\) 0 0
\(760\) 20.1962 + 24.7289i 0.732591 + 0.897013i
\(761\) 12.8756i 0.466742i 0.972388 + 0.233371i \(0.0749756\pi\)
−0.972388 + 0.233371i \(0.925024\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.350941 + 5.22715i −0.0126966 + 0.189112i
\(765\) 0 0
\(766\) −4.41851 + 4.13180i −0.159647 + 0.149288i
\(767\) 19.5519 0.705978
\(768\) 0 0
\(769\) −16.8690 −0.608313 −0.304156 0.952622i \(-0.598375\pi\)
−0.304156 + 0.952622i \(0.598375\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.39230 35.6326i 0.0861009 1.28245i
\(773\) 33.5167i 1.20551i 0.797926 + 0.602755i \(0.205930\pi\)
−0.797926 + 0.602755i \(0.794070\pi\)
\(774\) 0 0
\(775\) 17.6343i 0.633444i
\(776\) −16.8518 20.6340i −0.604944 0.740717i
\(777\) 0 0
\(778\) 20.5622 + 21.9890i 0.737190 + 0.788343i
\(779\) 21.7661 0.779852
\(780\) 0 0
\(781\) 78.4974 2.80886
\(782\) 33.7804 + 36.1244i 1.20798 + 1.29180i
\(783\) 0 0
\(784\) 0 0
\(785\) 25.7332i 0.918459i
\(786\) 0 0
\(787\) 36.0791i 1.28608i 0.765832 + 0.643041i \(0.222327\pi\)
−0.765832 + 0.643041i \(0.777673\pi\)
\(788\) −47.5700 3.19376i −1.69461 0.113773i
\(789\) 0 0
\(790\) 39.0160 36.4843i 1.38813 1.29805i
\(791\) 0 0
\(792\) 0 0
\(793\) 21.3205 0.757113
\(794\) −22.9816 + 21.4904i −0.815586 + 0.762665i
\(795\) 0