Properties

Label 1764.2.b.i.1567.7
Level $1764$
Weight $2$
Character 1764.1567
Analytic conductor $14.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.562828176.1
Defining polynomial: \(x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 6 x^{4} + 4 x^{3} + 4 x^{2} - 16 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.7
Root \(1.40376 - 0.171630i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.i.1567.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40376 - 0.171630i) q^{2} +(1.94109 - 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 - 1.00956i) q^{8} +O(q^{10})\) \(q+(1.40376 - 0.171630i) q^{2} +(1.94109 - 0.481855i) q^{4} -0.963711i q^{5} +(2.64212 - 1.00956i) q^{8} +(-0.165402 - 1.35282i) q^{10} +5.48322i q^{11} -3.75117i q^{13} +(3.53563 - 1.87065i) q^{16} -0.686521i q^{17} +4.88217 q^{19} +(-0.464369 - 1.87065i) q^{20} +(0.941086 + 7.69713i) q^{22} +1.24090i q^{23} +4.07126 q^{25} +(-0.643814 - 5.26574i) q^{26} +2.48011 q^{29} +4.82802 q^{31} +(4.64212 - 3.23276i) q^{32} +(-0.117828 - 0.963711i) q^{34} -2.73287 q^{37} +(6.85340 - 0.837928i) q^{38} +(-0.972923 - 2.54624i) q^{40} -9.42976i q^{41} -5.97437i q^{43} +(2.64212 + 10.6434i) q^{44} +(0.212976 + 1.74193i) q^{46} -3.61504 q^{47} +(5.71508 - 0.698752i) q^{50} +(-1.80752 - 7.28134i) q^{52} +4.09515 q^{53} +5.28424 q^{55} +(3.48148 - 0.425661i) q^{58} -12.6863 q^{59} +10.4121i q^{61} +(6.77738 - 0.828634i) q^{62} +(5.96158 - 5.33475i) q^{64} -3.61504 q^{65} -9.43847i q^{67} +(-0.330804 - 1.33260i) q^{68} +10.1163i q^{71} +6.66089i q^{73} +(-3.83629 + 0.469043i) q^{74} +(9.47672 - 2.35250i) q^{76} +1.41442i q^{79} +(-1.80276 - 3.40733i) q^{80} +(-1.61843 - 13.2371i) q^{82} -0.543780 q^{83} -0.661608 q^{85} +(-1.02538 - 8.38658i) q^{86} +(5.53563 + 14.4873i) q^{88} -0.554380i q^{89} +(0.597935 + 2.40870i) q^{92} +(-5.07465 + 0.620450i) q^{94} -4.70500i q^{95} -10.8747i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} + O(q^{10}) \) \( 8q + 2q^{2} + 2q^{4} - 4q^{8} - 8q^{10} + 10q^{16} + 12q^{19} - 22q^{20} - 6q^{22} - 4q^{25} + 6q^{26} + 16q^{29} - 12q^{31} + 12q^{32} - 28q^{34} - 12q^{37} + 2q^{38} + 4q^{40} - 4q^{44} - 12q^{46} + 8q^{47} - 2q^{50} + 4q^{52} - 8q^{53} - 8q^{55} - 14q^{58} - 28q^{59} + 48q^{62} + 2q^{64} + 8q^{65} - 16q^{68} - 38q^{74} + 44q^{76} - 6q^{80} - 4q^{82} - 4q^{83} - 32q^{85} - 6q^{86} + 26q^{88} + 28q^{92} - 32q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40376 0.171630i 0.992608 0.121361i
\(3\) 0 0
\(4\) 1.94109 0.481855i 0.970543 0.240928i
\(5\) 0.963711i 0.430985i −0.976506 0.215492i \(-0.930864\pi\)
0.976506 0.215492i \(-0.0691356\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.64212 1.00956i 0.934130 0.356933i
\(9\) 0 0
\(10\) −0.165402 1.35282i −0.0523047 0.427799i
\(11\) 5.48322i 1.65325i 0.562751 + 0.826626i \(0.309743\pi\)
−0.562751 + 0.826626i \(0.690257\pi\)
\(12\) 0 0
\(13\) 3.75117i 1.04039i −0.854048 0.520193i \(-0.825860\pi\)
0.854048 0.520193i \(-0.174140\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.53563 1.87065i 0.883908 0.467661i
\(17\) 0.686521i 0.166506i −0.996528 0.0832529i \(-0.973469\pi\)
0.996528 0.0832529i \(-0.0265309\pi\)
\(18\) 0 0
\(19\) 4.88217 1.12005 0.560024 0.828477i \(-0.310792\pi\)
0.560024 + 0.828477i \(0.310792\pi\)
\(20\) −0.464369 1.87065i −0.103836 0.418289i
\(21\) 0 0
\(22\) 0.941086 + 7.69713i 0.200640 + 1.64103i
\(23\) 1.24090i 0.258746i 0.991596 + 0.129373i \(0.0412964\pi\)
−0.991596 + 0.129373i \(0.958704\pi\)
\(24\) 0 0
\(25\) 4.07126 0.814252
\(26\) −0.643814 5.26574i −0.126262 1.03270i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.48011 0.460544 0.230272 0.973126i \(-0.426038\pi\)
0.230272 + 0.973126i \(0.426038\pi\)
\(30\) 0 0
\(31\) 4.82802 0.867138 0.433569 0.901120i \(-0.357254\pi\)
0.433569 + 0.901120i \(0.357254\pi\)
\(32\) 4.64212 3.23276i 0.820618 0.571477i
\(33\) 0 0
\(34\) −0.117828 0.963711i −0.0202073 0.165275i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.73287 −0.449281 −0.224640 0.974442i \(-0.572121\pi\)
−0.224640 + 0.974442i \(0.572121\pi\)
\(38\) 6.85340 0.837928i 1.11177 0.135930i
\(39\) 0 0
\(40\) −0.972923 2.54624i −0.153833 0.402596i
\(41\) 9.42976i 1.47268i −0.676611 0.736340i \(-0.736552\pi\)
0.676611 0.736340i \(-0.263448\pi\)
\(42\) 0 0
\(43\) 5.97437i 0.911083i −0.890215 0.455541i \(-0.849446\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(44\) 2.64212 + 10.6434i 0.398314 + 1.60455i
\(45\) 0 0
\(46\) 0.212976 + 1.74193i 0.0314016 + 0.256833i
\(47\) −3.61504 −0.527308 −0.263654 0.964617i \(-0.584928\pi\)
−0.263654 + 0.964617i \(0.584928\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 5.71508 0.698752i 0.808234 0.0988184i
\(51\) 0 0
\(52\) −1.80752 7.28134i −0.250658 1.00974i
\(53\) 4.09515 0.562512 0.281256 0.959633i \(-0.409249\pi\)
0.281256 + 0.959633i \(0.409249\pi\)
\(54\) 0 0
\(55\) 5.28424 0.712526
\(56\) 0 0
\(57\) 0 0
\(58\) 3.48148 0.425661i 0.457140 0.0558921i
\(59\) −12.6863 −1.65162 −0.825808 0.563951i \(-0.809281\pi\)
−0.825808 + 0.563951i \(0.809281\pi\)
\(60\) 0 0
\(61\) 10.4121i 1.33313i 0.745448 + 0.666564i \(0.232236\pi\)
−0.745448 + 0.666564i \(0.767764\pi\)
\(62\) 6.77738 0.828634i 0.860728 0.105237i
\(63\) 0 0
\(64\) 5.96158 5.33475i 0.745198 0.666843i
\(65\) −3.61504 −0.448391
\(66\) 0 0
\(67\) 9.43847i 1.15309i −0.817064 0.576546i \(-0.804400\pi\)
0.817064 0.576546i \(-0.195600\pi\)
\(68\) −0.330804 1.33260i −0.0401159 0.161601i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.1163i 1.20058i 0.799782 + 0.600291i \(0.204948\pi\)
−0.799782 + 0.600291i \(0.795052\pi\)
\(72\) 0 0
\(73\) 6.66089i 0.779598i 0.920900 + 0.389799i \(0.127456\pi\)
−0.920900 + 0.389799i \(0.872544\pi\)
\(74\) −3.83629 + 0.469043i −0.445960 + 0.0545251i
\(75\) 0 0
\(76\) 9.47672 2.35250i 1.08705 0.269850i
\(77\) 0 0
\(78\) 0 0
\(79\) 1.41442i 0.159134i 0.996830 + 0.0795671i \(0.0253538\pi\)
−0.996830 + 0.0795671i \(0.974646\pi\)
\(80\) −1.80276 3.40733i −0.201555 0.380951i
\(81\) 0 0
\(82\) −1.61843 13.2371i −0.178726 1.46180i
\(83\) −0.543780 −0.0596876 −0.0298438 0.999555i \(-0.509501\pi\)
−0.0298438 + 0.999555i \(0.509501\pi\)
\(84\) 0 0
\(85\) −0.661608 −0.0717614
\(86\) −1.02538 8.38658i −0.110570 0.904348i
\(87\) 0 0
\(88\) 5.53563 + 14.4873i 0.590100 + 1.54435i
\(89\) 0.554380i 0.0587641i −0.999568 0.0293821i \(-0.990646\pi\)
0.999568 0.0293821i \(-0.00935395\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.597935 + 2.40870i 0.0623390 + 0.251124i
\(93\) 0 0
\(94\) −5.07465 + 0.620450i −0.523410 + 0.0639946i
\(95\) 4.70500i 0.482723i
\(96\) 0 0
\(97\) 10.8747i 1.10416i −0.833790 0.552081i \(-0.813834\pi\)
0.833790 0.552081i \(-0.186166\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 7.90267 1.96176i 0.790267 0.196176i
\(101\) 14.4305i 1.43589i 0.696099 + 0.717946i \(0.254918\pi\)
−0.696099 + 0.717946i \(0.745082\pi\)
\(102\) 0 0
\(103\) −15.0247 −1.48043 −0.740214 0.672372i \(-0.765276\pi\)
−0.740214 + 0.672372i \(0.765276\pi\)
\(104\) −3.78702 9.91103i −0.371348 0.971857i
\(105\) 0 0
\(106\) 5.74861 0.702851i 0.558354 0.0682669i
\(107\) 12.1156i 1.17126i −0.810577 0.585632i \(-0.800847\pi\)
0.810577 0.585632i \(-0.199153\pi\)
\(108\) 0 0
\(109\) −6.07126 −0.581521 −0.290761 0.956796i \(-0.593908\pi\)
−0.290761 + 0.956796i \(0.593908\pi\)
\(110\) 7.41780 0.906935i 0.707260 0.0864729i
\(111\) 0 0
\(112\) 0 0
\(113\) 7.37939 0.694194 0.347097 0.937829i \(-0.387167\pi\)
0.347097 + 0.937829i \(0.387167\pi\)
\(114\) 0 0
\(115\) 1.19587 0.111515
\(116\) 4.81410 1.19505i 0.446978 0.110958i
\(117\) 0 0
\(118\) −17.8085 + 2.17735i −1.63941 + 0.200442i
\(119\) 0 0
\(120\) 0 0
\(121\) −19.0657 −1.73324
\(122\) 1.78702 + 14.6160i 0.161790 + 1.32327i
\(123\) 0 0
\(124\) 9.37160 2.32641i 0.841594 0.208917i
\(125\) 8.74207i 0.781915i
\(126\) 0 0
\(127\) 11.6431i 1.03316i 0.856240 + 0.516578i \(0.172794\pi\)
−0.856240 + 0.516578i \(0.827206\pi\)
\(128\) 7.45303 8.51189i 0.658761 0.752352i
\(129\) 0 0
\(130\) −5.07465 + 0.620450i −0.445076 + 0.0544171i
\(131\) 9.26156 0.809186 0.404593 0.914497i \(-0.367413\pi\)
0.404593 + 0.914497i \(0.367413\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.61993 13.2494i −0.139940 1.14457i
\(135\) 0 0
\(136\) −0.693083 1.81387i −0.0594314 0.155538i
\(137\) −7.23008 −0.617708 −0.308854 0.951110i \(-0.599945\pi\)
−0.308854 + 0.951110i \(0.599945\pi\)
\(138\) 0 0
\(139\) −5.30812 −0.450229 −0.225115 0.974332i \(-0.572276\pi\)
−0.225115 + 0.974332i \(0.572276\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.73626 + 14.2008i 0.145704 + 1.19171i
\(143\) 20.5685 1.72002
\(144\) 0 0
\(145\) 2.39011i 0.198488i
\(146\) 1.14321 + 9.35029i 0.0946127 + 0.773836i
\(147\) 0 0
\(148\) −5.30473 + 1.31685i −0.436046 + 0.108244i
\(149\) −4.66161 −0.381894 −0.190947 0.981600i \(-0.561156\pi\)
−0.190947 + 0.981600i \(0.561156\pi\)
\(150\) 0 0
\(151\) 12.2062i 0.993324i 0.867944 + 0.496662i \(0.165441\pi\)
−0.867944 + 0.496662i \(0.834559\pi\)
\(152\) 12.8993 4.92884i 1.04627 0.399782i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.65281i 0.373723i
\(156\) 0 0
\(157\) 21.9329i 1.75043i 0.483731 + 0.875217i \(0.339281\pi\)
−0.483731 + 0.875217i \(0.660719\pi\)
\(158\) 0.242756 + 1.98550i 0.0193127 + 0.157958i
\(159\) 0 0
\(160\) −3.11545 4.47366i −0.246298 0.353674i
\(161\) 0 0
\(162\) 0 0
\(163\) 4.01848i 0.314752i 0.987539 + 0.157376i \(0.0503034\pi\)
−0.987539 + 0.157376i \(0.949697\pi\)
\(164\) −4.54378 18.3040i −0.354810 1.42930i
\(165\) 0 0
\(166\) −0.763337 + 0.0933291i −0.0592464 + 0.00724374i
\(167\) 14.7178 1.13890 0.569448 0.822027i \(-0.307157\pi\)
0.569448 + 0.822027i \(0.307157\pi\)
\(168\) 0 0
\(169\) −1.07126 −0.0824047
\(170\) −0.928739 + 0.113552i −0.0712310 + 0.00870903i
\(171\) 0 0
\(172\) −2.87878 11.5968i −0.219505 0.884245i
\(173\) 11.6530i 0.885958i 0.896532 + 0.442979i \(0.146078\pi\)
−0.896532 + 0.442979i \(0.853922\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 10.2572 + 19.3866i 0.773163 + 1.46132i
\(177\) 0 0
\(178\) −0.0951483 0.778216i −0.00713167 0.0583298i
\(179\) 2.59419i 0.193899i 0.995289 + 0.0969494i \(0.0309085\pi\)
−0.995289 + 0.0969494i \(0.969091\pi\)
\(180\) 0 0
\(181\) 9.53343i 0.708615i 0.935129 + 0.354307i \(0.115283\pi\)
−0.935129 + 0.354307i \(0.884717\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.25276 + 3.27861i 0.0923548 + 0.241702i
\(185\) 2.63370i 0.193633i
\(186\) 0 0
\(187\) 3.76434 0.275276
\(188\) −7.01711 + 1.74193i −0.511775 + 0.127043i
\(189\) 0 0
\(190\) −0.807521 6.60470i −0.0585837 0.479155i
\(191\) 8.33274i 0.602936i 0.953476 + 0.301468i \(0.0974767\pi\)
−0.953476 + 0.301468i \(0.902523\pi\)
\(192\) 0 0
\(193\) −12.3726 −0.890600 −0.445300 0.895382i \(-0.646903\pi\)
−0.445300 + 0.895382i \(0.646903\pi\)
\(194\) −1.86643 15.2655i −0.134002 1.09600i
\(195\) 0 0
\(196\) 0 0
\(197\) −3.23686 −0.230617 −0.115308 0.993330i \(-0.536786\pi\)
−0.115308 + 0.993330i \(0.536786\pi\)
\(198\) 0 0
\(199\) −19.2301 −1.36318 −0.681592 0.731732i \(-0.738712\pi\)
−0.681592 + 0.731732i \(0.738712\pi\)
\(200\) 10.7568 4.11018i 0.760618 0.290633i
\(201\) 0 0
\(202\) 2.47672 + 20.2570i 0.174261 + 1.42528i
\(203\) 0 0
\(204\) 0 0
\(205\) −9.08756 −0.634703
\(206\) −21.0911 + 2.57869i −1.46948 + 0.179666i
\(207\) 0 0
\(208\) −7.01711 13.2627i −0.486549 0.919606i
\(209\) 26.7700i 1.85172i
\(210\) 0 0
\(211\) 9.24637i 0.636546i −0.947999 0.318273i \(-0.896897\pi\)
0.947999 0.318273i \(-0.103103\pi\)
\(212\) 7.94904 1.97327i 0.545942 0.135525i
\(213\) 0 0
\(214\) −2.07941 17.0075i −0.142146 1.16261i
\(215\) −5.75756 −0.392663
\(216\) 0 0
\(217\) 0 0
\(218\) −8.52260 + 1.04201i −0.577223 + 0.0705740i
\(219\) 0 0
\(220\) 10.2572 2.54624i 0.691538 0.171667i
\(221\) −2.57526 −0.173230
\(222\) 0 0
\(223\) −1.94585 −0.130303 −0.0651517 0.997875i \(-0.520753\pi\)
−0.0651517 + 0.997875i \(0.520753\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 10.3589 1.26653i 0.689063 0.0842480i
\(227\) −8.64531 −0.573809 −0.286905 0.957959i \(-0.592626\pi\)
−0.286905 + 0.957959i \(0.592626\pi\)
\(228\) 0 0
\(229\) 16.7889i 1.10944i 0.832036 + 0.554721i \(0.187175\pi\)
−0.832036 + 0.554721i \(0.812825\pi\)
\(230\) 1.67871 0.205247i 0.110691 0.0135336i
\(231\) 0 0
\(232\) 6.55274 2.50381i 0.430208 0.164383i
\(233\) 1.04657 0.0685628 0.0342814 0.999412i \(-0.489086\pi\)
0.0342814 + 0.999412i \(0.489086\pi\)
\(234\) 0 0
\(235\) 3.48385i 0.227262i
\(236\) −24.6252 + 6.11296i −1.60296 + 0.397920i
\(237\) 0 0
\(238\) 0 0
\(239\) 19.2479i 1.24505i −0.782602 0.622523i \(-0.786108\pi\)
0.782602 0.622523i \(-0.213892\pi\)
\(240\) 0 0
\(241\) 2.75689i 0.177587i 0.996050 + 0.0887934i \(0.0283011\pi\)
−0.996050 + 0.0887934i \(0.971699\pi\)
\(242\) −26.7637 + 3.27225i −1.72043 + 0.210348i
\(243\) 0 0
\(244\) 5.01711 + 20.2107i 0.321187 + 1.29386i
\(245\) 0 0
\(246\) 0 0
\(247\) 18.3138i 1.16528i
\(248\) 12.7562 4.87417i 0.810019 0.309510i
\(249\) 0 0
\(250\) −1.50040 12.2718i −0.0948939 0.776135i
\(251\) −20.7493 −1.30968 −0.654841 0.755767i \(-0.727264\pi\)
−0.654841 + 0.755767i \(0.727264\pi\)
\(252\) 0 0
\(253\) −6.80413 −0.427772
\(254\) 1.99830 + 16.3441i 0.125385 + 1.02552i
\(255\) 0 0
\(256\) 9.00137 13.2278i 0.562586 0.826739i
\(257\) 7.45109i 0.464786i −0.972622 0.232393i \(-0.925344\pi\)
0.972622 0.232393i \(-0.0746555\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7.01711 + 1.74193i −0.435182 + 0.108030i
\(261\) 0 0
\(262\) 13.0010 1.58956i 0.803205 0.0982036i
\(263\) 29.6797i 1.83013i −0.403305 0.915066i \(-0.632139\pi\)
0.403305 0.915066i \(-0.367861\pi\)
\(264\) 0 0
\(265\) 3.94654i 0.242434i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.54798 18.3209i −0.277812 1.11913i
\(269\) 4.31542i 0.263116i −0.991308 0.131558i \(-0.958002\pi\)
0.991308 0.131558i \(-0.0419980\pi\)
\(270\) 0 0
\(271\) 13.5828 0.825099 0.412550 0.910935i \(-0.364638\pi\)
0.412550 + 0.910935i \(0.364638\pi\)
\(272\) −1.28424 2.42728i −0.0778683 0.147176i
\(273\) 0 0
\(274\) −10.1493 + 1.24090i −0.613142 + 0.0749656i
\(275\) 22.3236i 1.34616i
\(276\) 0 0
\(277\) 2.07126 0.124450 0.0622250 0.998062i \(-0.480180\pi\)
0.0622250 + 0.998062i \(0.480180\pi\)
\(278\) −7.45133 + 0.911035i −0.446901 + 0.0546402i
\(279\) 0 0
\(280\) 0 0
\(281\) −23.7122 −1.41455 −0.707276 0.706938i \(-0.750076\pi\)
−0.707276 + 0.706938i \(0.750076\pi\)
\(282\) 0 0
\(283\) −12.2548 −0.728471 −0.364235 0.931307i \(-0.618670\pi\)
−0.364235 + 0.931307i \(0.618670\pi\)
\(284\) 4.87458 + 19.6366i 0.289253 + 1.16522i
\(285\) 0 0
\(286\) 28.8732 3.53017i 1.70731 0.208743i
\(287\) 0 0
\(288\) 0 0
\(289\) 16.5287 0.972276
\(290\) −0.410214 3.35514i −0.0240886 0.197020i
\(291\) 0 0
\(292\) 3.20959 + 12.9294i 0.187827 + 0.756634i
\(293\) 10.7090i 0.625626i −0.949815 0.312813i \(-0.898729\pi\)
0.949815 0.312813i \(-0.101271\pi\)
\(294\) 0 0
\(295\) 12.2259i 0.711821i
\(296\) −7.22056 + 2.75899i −0.419687 + 0.160363i
\(297\) 0 0
\(298\) −6.54378 + 0.800073i −0.379071 + 0.0463470i
\(299\) 4.65483 0.269196
\(300\) 0 0
\(301\) 0 0
\(302\) 2.09495 + 17.1345i 0.120551 + 0.985982i
\(303\) 0 0
\(304\) 17.2616 9.13281i 0.990018 0.523803i
\(305\) 10.0342 0.574557
\(306\) 0 0
\(307\) −4.22056 −0.240880 −0.120440 0.992721i \(-0.538431\pi\)
−0.120440 + 0.992721i \(0.538431\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.798563 6.53143i −0.0453554 0.370961i
\(311\) 9.70139 0.550116 0.275058 0.961428i \(-0.411303\pi\)
0.275058 + 0.961428i \(0.411303\pi\)
\(312\) 0 0
\(313\) 13.6634i 0.772299i 0.922436 + 0.386149i \(0.126195\pi\)
−0.922436 + 0.386149i \(0.873805\pi\)
\(314\) 3.76434 + 30.7885i 0.212434 + 1.73750i
\(315\) 0 0
\(316\) 0.681544 + 2.74550i 0.0383398 + 0.154447i
\(317\) −20.0884 −1.12828 −0.564138 0.825681i \(-0.690791\pi\)
−0.564138 + 0.825681i \(0.690791\pi\)
\(318\) 0 0
\(319\) 13.5990i 0.761396i
\(320\) −5.14115 5.74524i −0.287399 0.321169i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.35171i 0.186494i
\(324\) 0 0
\(325\) 15.2720i 0.847137i
\(326\) 0.689693 + 5.64098i 0.0381986 + 0.312425i
\(327\) 0 0
\(328\) −9.51989 24.9145i −0.525648 1.37568i
\(329\) 0 0
\(330\) 0 0
\(331\) 9.42104i 0.517827i −0.965900 0.258914i \(-0.916635\pi\)
0.965900 0.258914i \(-0.0833645\pi\)
\(332\) −1.05552 + 0.262023i −0.0579294 + 0.0143804i
\(333\) 0 0
\(334\) 20.6602 2.52602i 1.13048 0.138217i
\(335\) −9.09596 −0.496965
\(336\) 0 0
\(337\) −13.4411 −0.732185 −0.366092 0.930578i \(-0.619305\pi\)
−0.366092 + 0.930578i \(0.619305\pi\)
\(338\) −1.50379 + 0.183861i −0.0817956 + 0.0100007i
\(339\) 0 0
\(340\) −1.28424 + 0.318799i −0.0696476 + 0.0172893i
\(341\) 26.4731i 1.43360i
\(342\) 0 0
\(343\) 0 0
\(344\) −6.03148 15.7850i −0.325195 0.851070i
\(345\) 0 0
\(346\) 2.00000 + 16.3580i 0.107521 + 0.879409i
\(347\) 22.6194i 1.21427i 0.794598 + 0.607136i \(0.207682\pi\)
−0.794598 + 0.607136i \(0.792318\pi\)
\(348\) 0 0
\(349\) 2.48180i 0.132848i 0.997791 + 0.0664239i \(0.0211590\pi\)
−0.997791 + 0.0664239i \(0.978841\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 17.7259 + 25.4538i 0.944795 + 1.35669i
\(353\) 9.11423i 0.485101i −0.970139 0.242551i \(-0.922016\pi\)
0.970139 0.242551i \(-0.0779841\pi\)
\(354\) 0 0
\(355\) 9.74917 0.517432
\(356\) −0.267131 1.07610i −0.0141579 0.0570331i
\(357\) 0 0
\(358\) 0.445241 + 3.64162i 0.0235317 + 0.192466i
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) 0 0
\(361\) 4.83561 0.254506
\(362\) 1.63623 + 13.3827i 0.0859981 + 0.703377i
\(363\) 0 0
\(364\) 0 0
\(365\) 6.41917 0.335995
\(366\) 0 0
\(367\) −3.83359 −0.200112 −0.100056 0.994982i \(-0.531902\pi\)
−0.100056 + 0.994982i \(0.531902\pi\)
\(368\) 2.32129 + 4.38737i 0.121005 + 0.228707i
\(369\) 0 0
\(370\) 0.452022 + 3.69708i 0.0234995 + 0.192202i
\(371\) 0 0
\(372\) 0 0
\(373\) −26.8300 −1.38921 −0.694603 0.719393i \(-0.744420\pi\)
−0.694603 + 0.719393i \(0.744420\pi\)
\(374\) 5.28424 0.646075i 0.273241 0.0334078i
\(375\) 0 0
\(376\) −9.55137 + 3.64960i −0.492574 + 0.188214i
\(377\) 9.30330i 0.479144i
\(378\) 0 0
\(379\) 6.93692i 0.356325i −0.984001 0.178163i \(-0.942985\pi\)
0.984001 0.178163i \(-0.0570153\pi\)
\(380\) −2.26713 9.13281i −0.116301 0.468504i
\(381\) 0 0
\(382\) 1.43015 + 11.6972i 0.0731729 + 0.598479i
\(383\) −2.25761 −0.115359 −0.0576793 0.998335i \(-0.518370\pi\)
−0.0576793 + 0.998335i \(0.518370\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −17.3682 + 2.12351i −0.884017 + 0.108084i
\(387\) 0 0
\(388\) −5.24005 21.1088i −0.266023 1.07164i
\(389\) −30.6095 −1.55196 −0.775981 0.630756i \(-0.782745\pi\)
−0.775981 + 0.630756i \(0.782745\pi\)
\(390\) 0 0
\(391\) 0.851904 0.0430827
\(392\) 0 0
\(393\) 0 0
\(394\) −4.54378 + 0.555544i −0.228912 + 0.0279879i
\(395\) 1.36309 0.0685844
\(396\) 0 0
\(397\) 13.8989i 0.697568i −0.937203 0.348784i \(-0.886595\pi\)
0.937203 0.348784i \(-0.113405\pi\)
\(398\) −26.9944 + 3.30046i −1.35311 + 0.165437i
\(399\) 0 0
\(400\) 14.3945 7.61589i 0.719724 0.380794i
\(401\) 10.2766 0.513191 0.256596 0.966519i \(-0.417399\pi\)
0.256596 + 0.966519i \(0.417399\pi\)
\(402\) 0 0
\(403\) 18.1107i 0.902158i
\(404\) 6.95343 + 28.0109i 0.345946 + 1.39360i
\(405\) 0 0
\(406\) 0 0
\(407\) 14.9849i 0.742775i
\(408\) 0 0
\(409\) 12.1639i 0.601464i −0.953709 0.300732i \(-0.902769\pi\)
0.953709 0.300732i \(-0.0972310\pi\)
\(410\) −12.7568 + 1.55970i −0.630011 + 0.0770281i
\(411\) 0 0
\(412\) −29.1642 + 7.23973i −1.43682 + 0.356676i
\(413\) 0 0
\(414\) 0 0
\(415\) 0.524047i 0.0257244i
\(416\) −12.1266 17.4134i −0.594557 0.853761i
\(417\) 0 0
\(418\) 4.59454 + 37.5787i 0.224727 + 1.83803i
\(419\) 16.2245 0.792619 0.396310 0.918117i \(-0.370291\pi\)
0.396310 + 0.918117i \(0.370291\pi\)
\(420\) 0 0
\(421\) −9.58477 −0.467133 −0.233567 0.972341i \(-0.575040\pi\)
−0.233567 + 0.972341i \(0.575040\pi\)
\(422\) −1.58696 12.9797i −0.0772518 0.631841i
\(423\) 0 0
\(424\) 10.8199 4.13429i 0.525459 0.200779i
\(425\) 2.79501i 0.135578i
\(426\) 0 0
\(427\) 0 0
\(428\) −5.83799 23.5175i −0.282190 1.13676i
\(429\) 0 0
\(430\) −8.08224 + 0.988172i −0.389760 + 0.0476539i
\(431\) 0.151894i 0.00731648i 0.999993 + 0.00365824i \(0.00116446\pi\)
−0.999993 + 0.00365824i \(0.998836\pi\)
\(432\) 0 0
\(433\) 9.46997i 0.455098i 0.973767 + 0.227549i \(0.0730711\pi\)
−0.973767 + 0.227549i \(0.926929\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.7848 + 2.92547i −0.564392 + 0.140105i
\(437\) 6.05829i 0.289807i
\(438\) 0 0
\(439\) −33.4745 −1.59765 −0.798826 0.601562i \(-0.794545\pi\)
−0.798826 + 0.601562i \(0.794545\pi\)
\(440\) 13.9616 5.33475i 0.665592 0.254324i
\(441\) 0 0
\(442\) −3.61504 + 0.441992i −0.171950 + 0.0210234i
\(443\) 26.1554i 1.24268i −0.783540 0.621341i \(-0.786588\pi\)
0.783540 0.621341i \(-0.213412\pi\)
\(444\) 0 0
\(445\) −0.534262 −0.0253264
\(446\) −2.73150 + 0.333966i −0.129340 + 0.0158137i
\(447\) 0 0
\(448\) 0 0
\(449\) −10.2918 −0.485701 −0.242851 0.970064i \(-0.578082\pi\)
−0.242851 + 0.970064i \(0.578082\pi\)
\(450\) 0 0
\(451\) 51.7054 2.43471
\(452\) 14.3240 3.55580i 0.673745 0.167251i
\(453\) 0 0
\(454\) −12.1359 + 1.48380i −0.569568 + 0.0696380i
\(455\) 0 0
\(456\) 0 0
\(457\) 11.9315 0.558131 0.279065 0.960272i \(-0.409975\pi\)
0.279065 + 0.960272i \(0.409975\pi\)
\(458\) 2.88148 + 23.5676i 0.134643 + 1.10124i
\(459\) 0 0
\(460\) 2.32129 0.576236i 0.108231 0.0268672i
\(461\) 30.0093i 1.39767i 0.715281 + 0.698837i \(0.246299\pi\)
−0.715281 + 0.698837i \(0.753701\pi\)
\(462\) 0 0
\(463\) 13.2736i 0.616875i 0.951245 + 0.308437i \(0.0998060\pi\)
−0.951245 + 0.308437i \(0.900194\pi\)
\(464\) 8.76874 4.63940i 0.407079 0.215379i
\(465\) 0 0
\(466\) 1.46913 0.179622i 0.0680561 0.00832085i
\(467\) −29.6493 −1.37200 −0.686002 0.727600i \(-0.740636\pi\)
−0.686002 + 0.727600i \(0.740636\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.597935 + 4.89050i 0.0275807 + 0.225582i
\(471\) 0 0
\(472\) −33.5187 + 12.8076i −1.54282 + 0.589516i
\(473\) 32.7588 1.50625
\(474\) 0 0
\(475\) 19.8766 0.912001
\(476\) 0 0
\(477\) 0 0
\(478\) −3.30353 27.0195i −0.151100 1.23584i
\(479\) 11.5355 0.527069 0.263535 0.964650i \(-0.415112\pi\)
0.263535 + 0.964650i \(0.415112\pi\)
\(480\) 0 0
\(481\) 10.2515i 0.467426i
\(482\) 0.473165 + 3.87001i 0.0215521 + 0.176274i
\(483\) 0 0
\(484\) −37.0081 + 9.18691i −1.68219 + 0.417587i
\(485\) −10.4801 −0.475877
\(486\) 0 0
\(487\) 9.75517i 0.442049i −0.975268 0.221024i \(-0.929060\pi\)
0.975268 0.221024i \(-0.0709400\pi\)
\(488\) 10.5116 + 27.5099i 0.475837 + 1.24531i
\(489\) 0 0
\(490\) 0 0
\(491\) 40.4736i 1.82655i 0.407346 + 0.913274i \(0.366454\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(492\) 0 0
\(493\) 1.70265i 0.0766833i
\(494\) −3.14321 25.7083i −0.141420 1.15667i
\(495\) 0 0
\(496\) 17.0701 9.03151i 0.766470 0.405527i
\(497\) 0 0
\(498\) 0 0
\(499\) 31.9652i 1.43096i 0.698633 + 0.715480i \(0.253792\pi\)
−0.698633 + 0.715480i \(0.746208\pi\)
\(500\) −4.21242 16.9691i −0.188385 0.758882i
\(501\) 0 0
\(502\) −29.1270 + 3.56120i −1.30000 + 0.158944i
\(503\) 22.7110 1.01263 0.506317 0.862348i \(-0.331007\pi\)
0.506317 + 0.862348i \(0.331007\pi\)
\(504\) 0 0
\(505\) 13.9069 0.618847
\(506\) −9.55137 + 1.16779i −0.424610 + 0.0519148i
\(507\) 0 0
\(508\) 5.61028 + 22.6002i 0.248916 + 1.00272i
\(509\) 2.29725i 0.101824i 0.998703 + 0.0509118i \(0.0162128\pi\)
−0.998703 + 0.0509118i \(0.983787\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 10.3655 20.1136i 0.458093 0.888904i
\(513\) 0 0
\(514\) −1.27883 10.4595i −0.0564068 0.461350i
\(515\) 14.4795i 0.638041i
\(516\) 0 0
\(517\) 19.8221i 0.871773i
\(518\) 0 0
\(519\) 0 0
\(520\) −9.55137 + 3.64960i −0.418855 + 0.160045i
\(521\) 37.6100i 1.64772i −0.566791 0.823862i \(-0.691815\pi\)
0.566791 0.823862i \(-0.308185\pi\)
\(522\) 0 0
\(523\) −35.6887 −1.56056 −0.780279 0.625431i \(-0.784923\pi\)
−0.780279 + 0.625431i \(0.784923\pi\)
\(524\) 17.9775 4.46273i 0.785350 0.194955i
\(525\) 0 0
\(526\) −5.09394 41.6632i −0.222106 1.81660i
\(527\) 3.31454i 0.144383i
\(528\) 0 0
\(529\) 21.4602 0.933051
\(530\) −0.677345 5.53999i −0.0294220 0.240642i
\(531\) 0 0
\(532\) 0 0
\(533\) −35.3726 −1.53216
\(534\) 0 0
\(535\) −11.6760 −0.504796
\(536\) −9.52869 24.9376i −0.411577 1.07714i
\(537\) 0 0
\(538\) −0.740657 6.05782i −0.0319320 0.261171i
\(539\) 0 0
\(540\) 0 0
\(541\) 37.0203 1.59163 0.795814 0.605541i \(-0.207043\pi\)
0.795814 + 0.605541i \(0.207043\pi\)
\(542\) 19.0671 2.33123i 0.819000 0.100135i
\(543\) 0 0
\(544\) −2.21936 3.18691i −0.0951541 0.136638i
\(545\) 5.85094i 0.250627i
\(546\) 0 0
\(547\) 2.09106i 0.0894073i −0.999000 0.0447036i \(-0.985766\pi\)
0.999000 0.0447036i \(-0.0142344\pi\)
\(548\) −14.0342 + 3.48385i −0.599512 + 0.148823i
\(549\) 0 0
\(550\) 3.83141 + 31.3370i 0.163372 + 1.33621i
\(551\) 12.1083 0.515831
\(552\) 0 0
\(553\) 0 0
\(554\) 2.90755 0.355491i 0.123530 0.0151034i
\(555\) 0 0
\(556\) −10.3035 + 2.55775i −0.436967 + 0.108473i
\(557\) 16.7977 0.711743 0.355872 0.934535i \(-0.384184\pi\)
0.355872 + 0.934535i \(0.384184\pi\)
\(558\) 0 0
\(559\) −22.4109 −0.947878
\(560\) 0 0
\(561\) 0 0
\(562\) −33.2863 + 4.06973i −1.40410 + 0.171671i
\(563\) −17.3957 −0.733141 −0.366570 0.930390i \(-0.619468\pi\)
−0.366570 + 0.930390i \(0.619468\pi\)
\(564\) 0 0
\(565\) 7.11159i 0.299187i
\(566\) −17.2028 + 2.10329i −0.723086 + 0.0884079i
\(567\) 0 0
\(568\) 10.2130 + 26.7284i 0.428527 + 1.12150i
\(569\) 34.2850 1.43730 0.718652 0.695370i \(-0.244759\pi\)
0.718652 + 0.695370i \(0.244759\pi\)
\(570\) 0 0
\(571\) 5.93719i 0.248464i 0.992253 + 0.124232i \(0.0396467\pi\)
−0.992253 + 0.124232i \(0.960353\pi\)
\(572\) 39.9252 9.91103i 1.66936 0.414401i
\(573\) 0 0
\(574\) 0 0
\(575\) 5.05203i 0.210684i
\(576\) 0 0
\(577\) 39.0208i 1.62446i −0.583338 0.812229i \(-0.698254\pi\)
0.583338 0.812229i \(-0.301746\pi\)
\(578\) 23.2023 2.83682i 0.965089 0.117996i
\(579\) 0 0
\(580\) −1.15169 4.63940i −0.0478211 0.192641i
\(581\) 0 0
\(582\) 0 0
\(583\) 22.4546i 0.929974i
\(584\) 6.72456 + 17.5989i 0.278264 + 0.728246i
\(585\) 0 0
\(586\) −1.83799 15.0329i −0.0759266 0.621002i
\(587\) −7.71931 −0.318610 −0.159305 0.987229i \(-0.550925\pi\)
−0.159305 + 0.987229i \(0.550925\pi\)
\(588\) 0 0
\(589\) 23.5712 0.971235
\(590\) 2.09834 + 17.1623i 0.0863872 + 0.706560i
\(591\) 0 0
\(592\) −9.66242 + 5.11223i −0.397123 + 0.210111i
\(593\) 0.388414i 0.0159503i −0.999968 0.00797513i \(-0.997461\pi\)
0.999968 0.00797513i \(-0.00253859\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.04858 + 2.24622i −0.370644 + 0.0920088i
\(597\) 0 0
\(598\) 6.53426 0.798909i 0.267206 0.0326698i
\(599\) 20.7846i 0.849236i −0.905373 0.424618i \(-0.860408\pi\)
0.905373 0.424618i \(-0.139592\pi\)
\(600\) 0 0
\(601\) 26.4110i 1.07733i 0.842521 + 0.538664i \(0.181071\pi\)
−0.842521 + 0.538664i \(0.818929\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.88161 + 23.6932i 0.239319 + 0.964064i
\(605\) 18.3738i 0.747002i
\(606\) 0 0
\(607\) 40.7061 1.65221 0.826106 0.563515i \(-0.190551\pi\)
0.826106 + 0.563515i \(0.190551\pi\)
\(608\) 22.6636 15.7829i 0.919131 0.640081i
\(609\) 0 0
\(610\) 14.0856 1.72217i 0.570310 0.0697288i
\(611\) 13.5606i 0.548604i
\(612\) 0 0
\(613\) 17.3384 0.700291 0.350146 0.936695i \(-0.386132\pi\)
0.350146 + 0.936695i \(0.386132\pi\)
\(614\) −5.92466 + 0.724376i −0.239100 + 0.0292335i
\(615\) 0 0
\(616\) 0 0
\(617\) 46.4753 1.87103 0.935513 0.353291i \(-0.114938\pi\)
0.935513 + 0.353291i \(0.114938\pi\)
\(618\) 0 0
\(619\) 26.3821 1.06039 0.530194 0.847877i \(-0.322119\pi\)
0.530194 + 0.847877i \(0.322119\pi\)
\(620\) −2.24198 9.03151i −0.0900402 0.362714i
\(621\) 0 0
\(622\) 13.6184 1.66505i 0.546049 0.0667625i
\(623\) 0 0
\(624\) 0 0
\(625\) 11.9315 0.477259
\(626\) 2.34505 + 19.1801i 0.0937269 + 0.766590i
\(627\) 0 0
\(628\) 10.5685 + 42.5736i 0.421728 + 1.69887i
\(629\) 1.87617i 0.0748079i
\(630\) 0 0
\(631\) 41.0696i 1.63495i −0.575961 0.817477i \(-0.695372\pi\)
0.575961 0.817477i \(-0.304628\pi\)
\(632\) 1.42794 + 3.73705i 0.0568002 + 0.148652i
\(633\) 0 0
\(634\) −28.1993 + 3.44777i −1.11994 + 0.136928i
\(635\) 11.2206 0.445275
\(636\) 0 0
\(637\) 0 0
\(638\) 2.33399 + 19.0897i 0.0924037 + 0.755768i
\(639\) 0 0
\(640\) −8.20301 7.18257i −0.324252 0.283916i
\(641\) −45.4478 −1.79508 −0.897540 0.440932i \(-0.854648\pi\)
−0.897540 + 0.440932i \(0.854648\pi\)
\(642\) 0 0
\(643\) 30.5534 1.20491 0.602454 0.798154i \(-0.294190\pi\)
0.602454 + 0.798154i \(0.294190\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.575255 4.70500i −0.0226331 0.185116i
\(647\) −36.1792 −1.42235 −0.711175 0.703015i \(-0.751836\pi\)
−0.711175 + 0.703015i \(0.751836\pi\)
\(648\) 0 0
\(649\) 69.5618i 2.73054i
\(650\) −2.62113 21.4382i −0.102809 0.840876i
\(651\) 0 0
\(652\) 1.93633 + 7.80022i 0.0758324 + 0.305480i
\(653\) 8.23089 0.322100 0.161050 0.986946i \(-0.448512\pi\)
0.161050 + 0.986946i \(0.448512\pi\)
\(654\) 0 0
\(655\) 8.92546i 0.348747i
\(656\) −17.6397 33.3401i −0.688716 1.30171i
\(657\) 0 0
\(658\) 0 0
\(659\) 22.8837i 0.891422i 0.895177 + 0.445711i \(0.147049\pi\)
−0.895177 + 0.445711i \(0.852951\pi\)
\(660\) 0 0
\(661\) 20.4627i 0.795906i 0.917406 + 0.397953i \(0.130279\pi\)
−0.917406 + 0.397953i \(0.869721\pi\)
\(662\) −1.61694 13.2249i −0.0628440 0.514000i
\(663\) 0 0
\(664\) −1.43673 + 0.548978i −0.0557560 + 0.0213045i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.07757i 0.119164i
\(668\) 28.5685 7.09184i 1.10535 0.274392i
\(669\) 0 0
\(670\) −12.7685 + 1.56114i −0.493292 + 0.0603121i
\(671\) −57.0916 −2.20400
\(672\) 0 0
\(673\) 4.23008 0.163058 0.0815289 0.996671i \(-0.474020\pi\)
0.0815289 + 0.996671i \(0.474020\pi\)
\(674\) −18.8681 + 2.30690i −0.726773 + 0.0888586i
\(675\) 0 0
\(676\) −2.07941 + 0.516193i −0.0799773 + 0.0198536i
\(677\) 24.0134i 0.922908i −0.887164 0.461454i \(-0.847328\pi\)
0.887164 0.461454i \(-0.152672\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.74805 + 0.667932i −0.0670345 + 0.0256140i
\(681\) 0 0
\(682\) 4.54358 + 37.1619i 0.173983 + 1.42300i
\(683\) 8.19781i 0.313680i 0.987624 + 0.156840i \(0.0501307\pi\)
−0.987624 + 0.156840i \(0.949869\pi\)
\(684\) 0 0
\(685\) 6.96771i 0.266222i
\(686\) 0 0
\(687\) 0 0
\(688\) −11.1759 21.1232i −0.426078 0.805313i
\(689\) 15.3616i 0.585230i
\(690\) 0 0
\(691\) 35.9849 1.36893 0.684465 0.729046i \(-0.260036\pi\)
0.684465 + 0.729046i \(0.260036\pi\)
\(692\) 5.61504 + 22.6194i 0.213452 + 0.859860i
\(693\) 0 0
\(694\) 3.88217 + 31.7522i 0.147365 + 1.20530i
\(695\) 5.11550i 0.194042i
\(696\) 0 0
\(697\) −6.47373 −0.245210
\(698\) 0.425952 + 3.48385i 0.0161225 + 0.131866i
\(699\) 0 0
\(700\) 0 0
\(701\) 12.9471 0.489003 0.244502 0.969649i \(-0.421376\pi\)
0.244502 + 0.969649i \(0.421376\pi\)
\(702\) 0 0
\(703\) −13.3423 −0.503216
\(704\) 29.2516 + 32.6887i 1.10246 + 1.23200i
\(705\) 0 0
\(706\) −1.56428 12.7942i −0.0588723 0.481516i
\(707\) 0 0
\(708\) 0 0
\(709\) 13.3121 0.499945 0.249973 0.968253i \(-0.419578\pi\)
0.249973 + 0.968253i \(0.419578\pi\)
\(710\) 13.6855 1.67325i 0.513607 0.0627960i
\(711\) 0 0
\(712\) −0.559679 1.46474i −0.0209749 0.0548934i
\(713\) 5.99109i 0.224368i
\(714\) 0 0
\(715\) 19.8221i 0.741303i
\(716\) 1.25002 + 5.03555i 0.0467156 + 0.188187i
\(717\) 0 0
\(718\) −1.18909 9.72554i −0.0443764 0.362954i
\(719\) 47.5040 1.77160 0.885800 0.464068i \(-0.153611\pi\)
0.885800 + 0.464068i \(0.153611\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.78803 0.829936i 0.252624 0.0308870i
\(723\) 0 0
\(724\) 4.59374 + 18.5052i 0.170725 + 0.687741i
\(725\) 10.0972 0.374999
\(726\) 0 0
\(727\) −24.3567 −0.903340 −0.451670 0.892185i \(-0.649172\pi\)
−0.451670 + 0.892185i \(0.649172\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 9.01098 1.10172i 0.333511 0.0407766i
\(731\) −4.10153 −0.151701
\(732\) 0 0
\(733\) 3.87763i 0.143223i 0.997433 + 0.0716117i \(0.0228142\pi\)
−0.997433 + 0.0716117i \(0.977186\pi\)
\(734\) −5.38144 + 0.657960i −0.198633 + 0.0242857i
\(735\) 0 0
\(736\) 4.01153 + 5.76041i 0.147867 + 0.212331i
\(737\) 51.7532 1.90635
\(738\) 0 0
\(739\) 8.61981i 0.317085i −0.987352 0.158542i \(-0.949321\pi\)
0.987352 0.158542i \(-0.0506795\pi\)
\(740\) 1.26906 + 5.11223i 0.0466516 + 0.187929i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.12929i 0.224862i −0.993660 0.112431i \(-0.964136\pi\)
0.993660 0.112431i \(-0.0358637\pi\)
\(744\) 0 0
\(745\) 4.49244i 0.164590i
\(746\) −37.6629 + 4.60484i −1.37894 + 0.168595i
\(747\) 0 0
\(748\) 7.30692 1.81387i 0.267167 0.0663216i
\(749\) 0 0
\(750\) 0 0
\(751\) 35.4662i 1.29418i −0.762414 0.647090i \(-0.775986\pi\)
0.762414 0.647090i \(-0.224014\pi\)
\(752\) −12.7815 + 6.76246i −0.466092 + 0.246602i
\(753\) 0 0
\(754\) −1.59673 13.0596i −0.0581494 0.475603i
\(755\) 11.7632 0.428108
\(756\) 0 0
\(757\) 29.4204 1.06930 0.534651 0.845073i \(-0.320443\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(758\) −1.19058 9.73777i −0.0432440 0.353692i
\(759\) 0 0
\(760\) −4.74998 12.4312i −0.172300 0.450926i
\(761\) 50.2950i 1.82319i −0.411086 0.911597i \(-0.634850\pi\)
0.411086 0.911597i \(-0.365150\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.01518 + 16.1746i 0.145264 + 0.585175i
\(765\) 0 0
\(766\) −3.16915 + 0.387475i −0.114506 + 0.0140000i
\(767\) 47.5885i 1.71832i
\(768\) 0 0
\(769\) 20.2817i 0.731377i 0.930737 + 0.365689i \(0.119167\pi\)
−0.930737 + 0.365689i \(0.880833\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −24.0163 + 5.96181i −0.864365 + 0.214570i
\(773\) 21.7255i 0.781413i −0.920515 0.390706i \(-0.872231\pi\)
0.920515 0.390706i \(-0.127769\pi\)
\(774\) 0 0
\(775\) 19.6561 0.706069
\(776\) −10.9787 28.7324i −0.394112 1.03143i
\(777\) 0 0
\(778\) −42.9684 + 5.25351i −1.54049 + 0.188347i
\(779\) 46.0377i 1.64947i
\(780\) 0 0
\(781\) −55.4698 −1.98486
\(782\) 1.19587 0.146213i 0.0427642 0.00522855i
\(783\) 0 0
\(784\) 0 0
\(785\) 21.1369 0.754410
\(786\) 0 0
\(787\) 0.598657 0.0213398 0.0106699 0.999943i \(-0.496604\pi\)
0.0106699 + 0.999943i \(0.496604\pi\)
\(788\) −6.28303 + 1.55970i −0.223824 + 0.0555620i
\(789\) 0 0
\(790\) 1.91345 0.233947i 0.0680774 0.00832346i
\(791\) 0 0
\(792\) 0 0
\(793\) 39.0574 1.38697
\(794\) −2.38548 19.5108i −0.0846575 0.692412i
\(795\) 0 0
\(796\) −37.3272 + 9.26612i −1.32303 + 0.328429i
\(797\)