Properties

Label 1764.2.b.i.1567.3
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 1567.3
Root \(0.0777157 - 1.41208i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.i.1567.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0777157 - 1.41208i) q^{2} +(-1.98792 - 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 + 2.79004i) q^{8} +O(q^{10})\) \(q+(0.0777157 - 1.41208i) q^{2} +(-1.98792 - 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 + 2.79004i) q^{8} +(-0.619848 - 0.0341142i) q^{10} -2.11598i q^{11} +3.84803i q^{13} +(3.90366 + 0.872621i) q^{16} -5.64831i q^{17} -2.97584 q^{19} +(-0.0963438 + 0.872621i) q^{20} +(-2.98792 - 0.164445i) q^{22} -4.77038i q^{23} +4.80731 q^{25} +(5.43371 + 0.299052i) q^{26} -7.02285 q^{29} -7.42528 q^{31} +(1.53558 - 5.44445i) q^{32} +(-7.97584 - 0.438962i) q^{34} -5.28670 q^{37} +(-0.231269 + 4.20212i) q^{38} +(1.22472 + 0.203861i) q^{40} +6.81813i q^{41} -4.38646i q^{43} +(-0.464416 + 4.20639i) q^{44} +(-6.73615 - 0.370733i) q^{46} +1.68914 q^{47} +(0.373604 - 6.78829i) q^{50} +(0.844569 - 7.64957i) q^{52} -10.7120 q^{53} -0.928833 q^{55} +(-0.545785 + 9.91680i) q^{58} -8.11818 q^{59} +6.18674i q^{61} +(-0.577061 + 10.4851i) q^{62} +(-7.56863 - 2.59148i) q^{64} +1.68914 q^{65} -7.85056i q^{67} +(-1.23970 + 11.2284i) q^{68} -1.16982i q^{71} +10.0348i q^{73} +(-0.410860 + 7.46523i) q^{74} +(5.91574 + 0.653140i) q^{76} -15.5836i q^{79} +(0.383048 - 1.71356i) q^{80} +(9.62772 + 0.529876i) q^{82} +5.49645 q^{83} -2.47939 q^{85} +(-6.19401 - 0.340896i) q^{86} +(5.90366 + 0.982694i) q^{88} +10.4187i q^{89} +(-1.04701 + 9.48314i) q^{92} +(0.131272 - 2.38519i) q^{94} +1.30628i q^{95} -2.22605i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + O(q^{10}) \) \( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} - 8 q^{10} + 10 q^{16} + 12 q^{19} - 22 q^{20} - 6 q^{22} - 4 q^{25} + 6 q^{26} + 16 q^{29} - 12 q^{31} + 12 q^{32} - 28 q^{34} - 12 q^{37} + 2 q^{38} + 4 q^{40} - 4 q^{44} - 12 q^{46} + 8 q^{47} - 2 q^{50} + 4 q^{52} - 8 q^{53} - 8 q^{55} - 14 q^{58} - 28 q^{59} + 48 q^{62} + 2 q^{64} + 8 q^{65} - 16 q^{68} - 38 q^{74} + 44 q^{76} - 6 q^{80} - 4 q^{82} - 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} - 32 q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0777157 1.41208i 0.0549533 0.998489i
\(3\) 0 0
\(4\) −1.98792 0.219481i −0.993960 0.109740i
\(5\) 0.438962i 0.196310i −0.995171 0.0981549i \(-0.968706\pi\)
0.995171 0.0981549i \(-0.0312941\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −0.464416 + 2.79004i −0.164196 + 0.986428i
\(9\) 0 0
\(10\) −0.619848 0.0341142i −0.196013 0.0107879i
\(11\) 2.11598i 0.637991i −0.947756 0.318995i \(-0.896655\pi\)
0.947756 0.318995i \(-0.103345\pi\)
\(12\) 0 0
\(13\) 3.84803i 1.06725i 0.845721 + 0.533625i \(0.179171\pi\)
−0.845721 + 0.533625i \(0.820829\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.90366 + 0.872621i 0.975914 + 0.218155i
\(17\) 5.64831i 1.36992i −0.728583 0.684958i \(-0.759821\pi\)
0.728583 0.684958i \(-0.240179\pi\)
\(18\) 0 0
\(19\) −2.97584 −0.682705 −0.341352 0.939935i \(-0.610885\pi\)
−0.341352 + 0.939935i \(0.610885\pi\)
\(20\) −0.0963438 + 0.872621i −0.0215431 + 0.195124i
\(21\) 0 0
\(22\) −2.98792 0.164445i −0.637027 0.0350597i
\(23\) 4.77038i 0.994694i −0.867552 0.497347i \(-0.834308\pi\)
0.867552 0.497347i \(-0.165692\pi\)
\(24\) 0 0
\(25\) 4.80731 0.961462
\(26\) 5.43371 + 0.299052i 1.06564 + 0.0586489i
\(27\) 0 0
\(28\) 0 0
\(29\) −7.02285 −1.30411 −0.652055 0.758172i \(-0.726093\pi\)
−0.652055 + 0.758172i \(0.726093\pi\)
\(30\) 0 0
\(31\) −7.42528 −1.33362 −0.666810 0.745228i \(-0.732341\pi\)
−0.666810 + 0.745228i \(0.732341\pi\)
\(32\) 1.53558 5.44445i 0.271455 0.962451i
\(33\) 0 0
\(34\) −7.97584 0.438962i −1.36785 0.0752813i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.28670 −0.869129 −0.434564 0.900641i \(-0.643098\pi\)
−0.434564 + 0.900641i \(0.643098\pi\)
\(38\) −0.231269 + 4.20212i −0.0375169 + 0.681673i
\(39\) 0 0
\(40\) 1.22472 + 0.203861i 0.193645 + 0.0322333i
\(41\) 6.81813i 1.06481i 0.846489 + 0.532407i \(0.178712\pi\)
−0.846489 + 0.532407i \(0.821288\pi\)
\(42\) 0 0
\(43\) 4.38646i 0.668928i −0.942408 0.334464i \(-0.891445\pi\)
0.942408 0.334464i \(-0.108555\pi\)
\(44\) −0.464416 + 4.20639i −0.0700134 + 0.634138i
\(45\) 0 0
\(46\) −6.73615 0.370733i −0.993190 0.0546617i
\(47\) 1.68914 0.246386 0.123193 0.992383i \(-0.460687\pi\)
0.123193 + 0.992383i \(0.460687\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.373604 6.78829i 0.0528355 0.960010i
\(51\) 0 0
\(52\) 0.844569 7.64957i 0.117121 1.06080i
\(53\) −10.7120 −1.47140 −0.735702 0.677305i \(-0.763148\pi\)
−0.735702 + 0.677305i \(0.763148\pi\)
\(54\) 0 0
\(55\) −0.928833 −0.125244
\(56\) 0 0
\(57\) 0 0
\(58\) −0.545785 + 9.91680i −0.0716651 + 1.30214i
\(59\) −8.11818 −1.05690 −0.528448 0.848966i \(-0.677226\pi\)
−0.528448 + 0.848966i \(0.677226\pi\)
\(60\) 0 0
\(61\) 6.18674i 0.792130i 0.918222 + 0.396065i \(0.129625\pi\)
−0.918222 + 0.396065i \(0.870375\pi\)
\(62\) −0.577061 + 10.4851i −0.0732868 + 1.33160i
\(63\) 0 0
\(64\) −7.56863 2.59148i −0.946079 0.323935i
\(65\) 1.68914 0.209512
\(66\) 0 0
\(67\) 7.85056i 0.959098i −0.877515 0.479549i \(-0.840800\pi\)
0.877515 0.479549i \(-0.159200\pi\)
\(68\) −1.23970 + 11.2284i −0.150335 + 1.36164i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.16982i 0.138833i −0.997588 0.0694163i \(-0.977886\pi\)
0.997588 0.0694163i \(-0.0221137\pi\)
\(72\) 0 0
\(73\) 10.0348i 1.17448i 0.809413 + 0.587240i \(0.199786\pi\)
−0.809413 + 0.587240i \(0.800214\pi\)
\(74\) −0.410860 + 7.46523i −0.0477615 + 0.867815i
\(75\) 0 0
\(76\) 5.91574 + 0.653140i 0.678581 + 0.0749203i
\(77\) 0 0
\(78\) 0 0
\(79\) 15.5836i 1.75329i −0.481136 0.876646i \(-0.659776\pi\)
0.481136 0.876646i \(-0.340224\pi\)
\(80\) 0.383048 1.71356i 0.0428260 0.191581i
\(81\) 0 0
\(82\) 9.62772 + 0.529876i 1.06320 + 0.0585150i
\(83\) 5.49645 0.603314 0.301657 0.953417i \(-0.402460\pi\)
0.301657 + 0.953417i \(0.402460\pi\)
\(84\) 0 0
\(85\) −2.47939 −0.268928
\(86\) −6.19401 0.340896i −0.667918 0.0367598i
\(87\) 0 0
\(88\) 5.90366 + 0.982694i 0.629332 + 0.104756i
\(89\) 10.4187i 1.10438i 0.833719 + 0.552189i \(0.186207\pi\)
−0.833719 + 0.552189i \(0.813793\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.04701 + 9.48314i −0.109158 + 0.988686i
\(93\) 0 0
\(94\) 0.131272 2.38519i 0.0135397 0.246014i
\(95\) 1.30628i 0.134022i
\(96\) 0 0
\(97\) 2.22605i 0.226021i −0.993594 0.113011i \(-0.963951\pi\)
0.993594 0.113011i \(-0.0360494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −9.55656 1.05511i −0.955656 0.105511i
\(101\) 0.767851i 0.0764040i −0.999270 0.0382020i \(-0.987837\pi\)
0.999270 0.0382020i \(-0.0121630\pi\)
\(102\) 0 0
\(103\) −8.63878 −0.851205 −0.425602 0.904910i \(-0.639938\pi\)
−0.425602 + 0.904910i \(0.639938\pi\)
\(104\) −10.7361 1.78709i −1.05277 0.175238i
\(105\) 0 0
\(106\) −0.832489 + 15.1261i −0.0808585 + 1.46918i
\(107\) 2.54433i 0.245970i 0.992409 + 0.122985i \(0.0392467\pi\)
−0.992409 + 0.122985i \(0.960753\pi\)
\(108\) 0 0
\(109\) −6.80731 −0.652022 −0.326011 0.945366i \(-0.605705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(110\) −0.0721849 + 1.31158i −0.00688256 + 0.125055i
\(111\) 0 0
\(112\) 0 0
\(113\) −13.6408 −1.28322 −0.641610 0.767031i \(-0.721733\pi\)
−0.641610 + 0.767031i \(0.721733\pi\)
\(114\) 0 0
\(115\) −2.09402 −0.195268
\(116\) 13.9609 + 1.54138i 1.29623 + 0.143114i
\(117\) 0 0
\(118\) −0.630909 + 11.4635i −0.0580799 + 1.05530i
\(119\) 0 0
\(120\) 0 0
\(121\) 6.52264 0.592968
\(122\) 8.73615 + 0.480806i 0.790933 + 0.0435302i
\(123\) 0 0
\(124\) 14.7609 + 1.62971i 1.32557 + 0.146352i
\(125\) 4.30504i 0.385054i
\(126\) 0 0
\(127\) 3.51914i 0.312273i 0.987735 + 0.156137i \(0.0499040\pi\)
−0.987735 + 0.156137i \(0.950096\pi\)
\(128\) −4.24757 + 10.4861i −0.375436 + 0.926848i
\(129\) 0 0
\(130\) 0.131272 2.38519i 0.0115134 0.209195i
\(131\) −19.6167 −1.71392 −0.856958 0.515387i \(-0.827648\pi\)
−0.856958 + 0.515387i \(0.827648\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −11.0856 0.610111i −0.957649 0.0527056i
\(135\) 0 0
\(136\) 15.7590 + 2.62317i 1.35132 + 0.224935i
\(137\) 3.37827 0.288625 0.144313 0.989532i \(-0.453903\pi\)
0.144313 + 0.989532i \(0.453903\pi\)
\(138\) 0 0
\(139\) 16.4481 1.39511 0.697556 0.716530i \(-0.254271\pi\)
0.697556 + 0.716530i \(0.254271\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.65188 0.0909137i −0.138623 0.00762930i
\(143\) 8.14233 0.680896
\(144\) 0 0
\(145\) 3.08276i 0.256010i
\(146\) 14.1699 + 0.779858i 1.17271 + 0.0645415i
\(147\) 0 0
\(148\) 10.5095 + 1.16033i 0.863879 + 0.0953786i
\(149\) −6.47939 −0.530812 −0.265406 0.964137i \(-0.585506\pi\)
−0.265406 + 0.964137i \(0.585506\pi\)
\(150\) 0 0
\(151\) 7.76914i 0.632244i 0.948719 + 0.316122i \(0.102381\pi\)
−0.948719 + 0.316122i \(0.897619\pi\)
\(152\) 1.38203 8.30271i 0.112097 0.673439i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.25942i 0.261803i
\(156\) 0 0
\(157\) 8.46391i 0.675493i −0.941237 0.337747i \(-0.890335\pi\)
0.941237 0.337747i \(-0.109665\pi\)
\(158\) −22.0052 1.21109i −1.75064 0.0963492i
\(159\) 0 0
\(160\) −2.38990 0.674063i −0.188939 0.0532893i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.95459i 0.544725i −0.962195 0.272363i \(-0.912195\pi\)
0.962195 0.272363i \(-0.0878050\pi\)
\(164\) 1.49645 13.5539i 0.116853 1.05838i
\(165\) 0 0
\(166\) 0.427160 7.76141i 0.0331541 0.602402i
\(167\) −8.12021 −0.628361 −0.314180 0.949363i \(-0.601730\pi\)
−0.314180 + 0.949363i \(0.601730\pi\)
\(168\) 0 0
\(169\) −1.80731 −0.139024
\(170\) −0.192688 + 3.50109i −0.0147785 + 0.268521i
\(171\) 0 0
\(172\) −0.962744 + 8.71993i −0.0734085 + 0.664888i
\(173\) 1.41635i 0.107683i 0.998549 + 0.0538417i \(0.0171466\pi\)
−0.998549 + 0.0538417i \(0.982853\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.84645 8.26004i 0.139181 0.622624i
\(177\) 0 0
\(178\) 14.7120 + 0.809695i 1.10271 + 0.0606892i
\(179\) 10.7318i 0.802132i 0.916049 + 0.401066i \(0.131360\pi\)
−0.916049 + 0.401066i \(0.868640\pi\)
\(180\) 0 0
\(181\) 1.21426i 0.0902549i −0.998981 0.0451275i \(-0.985631\pi\)
0.998981 0.0451275i \(-0.0143694\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 13.3096 + 2.21544i 0.981193 + 0.163325i
\(185\) 2.32066i 0.170618i
\(186\) 0 0
\(187\) −11.9517 −0.873994
\(188\) −3.35787 0.370733i −0.244898 0.0270385i
\(189\) 0 0
\(190\) 1.84457 + 0.101518i 0.133819 + 0.00736493i
\(191\) 6.55261i 0.474131i −0.971494 0.237065i \(-0.923814\pi\)
0.971494 0.237065i \(-0.0761855\pi\)
\(192\) 0 0
\(193\) −3.23635 −0.232958 −0.116479 0.993193i \(-0.537161\pi\)
−0.116479 + 0.993193i \(0.537161\pi\)
\(194\) −3.14335 0.172999i −0.225680 0.0124206i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.2554 1.37189 0.685947 0.727652i \(-0.259388\pi\)
0.685947 + 0.727652i \(0.259388\pi\)
\(198\) 0 0
\(199\) −8.62173 −0.611178 −0.305589 0.952164i \(-0.598853\pi\)
−0.305589 + 0.952164i \(0.598853\pi\)
\(200\) −2.23260 + 13.4126i −0.157868 + 0.948413i
\(201\) 0 0
\(202\) −1.08426 0.0596741i −0.0762886 0.00419865i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.99290 0.209033
\(206\) −0.671369 + 12.1986i −0.0467765 + 0.849918i
\(207\) 0 0
\(208\) −3.35787 + 15.0214i −0.232826 + 1.04154i
\(209\) 6.29681i 0.435559i
\(210\) 0 0
\(211\) 6.09787i 0.419795i −0.977723 0.209897i \(-0.932687\pi\)
0.977723 0.209897i \(-0.0673130\pi\)
\(212\) 21.2946 + 2.35108i 1.46252 + 0.161473i
\(213\) 0 0
\(214\) 3.59279 + 0.197735i 0.245598 + 0.0135169i
\(215\) −1.92549 −0.131317
\(216\) 0 0
\(217\) 0 0
\(218\) −0.529035 + 9.61245i −0.0358308 + 0.651037i
\(219\) 0 0
\(220\) 1.84645 + 0.203861i 0.124487 + 0.0137443i
\(221\) 21.7348 1.46204
\(222\) 0 0
\(223\) 2.44944 0.164027 0.0820134 0.996631i \(-0.473865\pi\)
0.0820134 + 0.996631i \(0.473865\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.06011 + 19.2619i −0.0705172 + 1.28128i
\(227\) −23.2796 −1.54512 −0.772561 0.634941i \(-0.781024\pi\)
−0.772561 + 0.634941i \(0.781024\pi\)
\(228\) 0 0
\(229\) 11.7069i 0.773615i −0.922160 0.386808i \(-0.873578\pi\)
0.922160 0.386808i \(-0.126422\pi\)
\(230\) −0.162738 + 2.95691i −0.0107306 + 0.194973i
\(231\) 0 0
\(232\) 3.26153 19.5940i 0.214130 1.28641i
\(233\) 8.16853 0.535138 0.267569 0.963539i \(-0.413780\pi\)
0.267569 + 0.963539i \(0.413780\pi\)
\(234\) 0 0
\(235\) 0.741467i 0.0483680i
\(236\) 16.1383 + 1.78178i 1.05051 + 0.115984i
\(237\) 0 0
\(238\) 0 0
\(239\) 18.1984i 1.17716i −0.808439 0.588579i \(-0.799687\pi\)
0.808439 0.588579i \(-0.200313\pi\)
\(240\) 0 0
\(241\) 28.9148i 1.86256i −0.364299 0.931282i \(-0.618691\pi\)
0.364299 0.931282i \(-0.381309\pi\)
\(242\) 0.506912 9.21047i 0.0325855 0.592072i
\(243\) 0 0
\(244\) 1.35787 12.2987i 0.0869288 0.787346i
\(245\) 0 0
\(246\) 0 0
\(247\) 11.4511i 0.728617i
\(248\) 3.44842 20.7168i 0.218975 1.31552i
\(249\) 0 0
\(250\) −6.07904 0.334569i −0.384472 0.0211600i
\(251\) 20.3586 1.28502 0.642512 0.766276i \(-0.277892\pi\)
0.642512 + 0.766276i \(0.277892\pi\)
\(252\) 0 0
\(253\) −10.0940 −0.634605
\(254\) 4.96929 + 0.273492i 0.311801 + 0.0171604i
\(255\) 0 0
\(256\) 14.4771 + 6.81283i 0.904816 + 0.425802i
\(257\) 21.2869i 1.32784i −0.747802 0.663922i \(-0.768891\pi\)
0.747802 0.663922i \(-0.231109\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.35787 0.370733i −0.208246 0.0229919i
\(261\) 0 0
\(262\) −1.52452 + 27.7002i −0.0941853 + 1.71133i
\(263\) 20.1796i 1.24433i −0.782887 0.622164i \(-0.786254\pi\)
0.782887 0.622164i \(-0.213746\pi\)
\(264\) 0 0
\(265\) 4.70215i 0.288851i
\(266\) 0 0
\(267\) 0 0
\(268\) −1.72305 + 15.6063i −0.105252 + 0.953306i
\(269\) 16.3695i 0.998066i 0.866583 + 0.499033i \(0.166311\pi\)
−0.866583 + 0.499033i \(0.833689\pi\)
\(270\) 0 0
\(271\) −13.4539 −0.817268 −0.408634 0.912698i \(-0.633995\pi\)
−0.408634 + 0.912698i \(0.633995\pi\)
\(272\) 4.92883 22.0490i 0.298854 1.33692i
\(273\) 0 0
\(274\) 0.262545 4.77038i 0.0158609 0.288189i
\(275\) 10.1722i 0.613404i
\(276\) 0 0
\(277\) 2.80731 0.168675 0.0843375 0.996437i \(-0.473123\pi\)
0.0843375 + 0.996437i \(0.473123\pi\)
\(278\) 1.27828 23.2260i 0.0766660 1.39300i
\(279\) 0 0
\(280\) 0 0
\(281\) 25.4502 1.51823 0.759115 0.650957i \(-0.225632\pi\)
0.759115 + 0.650957i \(0.225632\pi\)
\(282\) 0 0
\(283\) 4.73949 0.281733 0.140867 0.990029i \(-0.455011\pi\)
0.140867 + 0.990029i \(0.455011\pi\)
\(284\) −0.256754 + 2.32552i −0.0152356 + 0.137994i
\(285\) 0 0
\(286\) 0.632787 11.4976i 0.0374175 0.679867i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.9034 −0.876668
\(290\) 4.35310 + 0.239579i 0.255623 + 0.0140686i
\(291\) 0 0
\(292\) 2.20244 19.9483i 0.128888 1.16739i
\(293\) 3.22818i 0.188592i 0.995544 + 0.0942960i \(0.0300600\pi\)
−0.995544 + 0.0942960i \(0.969940\pi\)
\(294\) 0 0
\(295\) 3.56357i 0.207479i
\(296\) 2.45523 14.7501i 0.142707 0.857333i
\(297\) 0 0
\(298\) −0.503550 + 9.14940i −0.0291699 + 0.530010i
\(299\) 18.3566 1.06159
\(300\) 0 0
\(301\) 0 0
\(302\) 10.9706 + 0.603784i 0.631288 + 0.0347439i
\(303\) 0 0
\(304\) −11.6167 2.59678i −0.666261 0.148936i
\(305\) 2.71574 0.155503
\(306\) 0 0
\(307\) 5.45523 0.311347 0.155673 0.987809i \(-0.450245\pi\)
0.155673 + 0.987809i \(0.450245\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.60255 + 0.253308i 0.261407 + 0.0143869i
\(311\) 30.5251 1.73092 0.865460 0.500979i \(-0.167027\pi\)
0.865460 + 0.500979i \(0.167027\pi\)
\(312\) 0 0
\(313\) 18.8324i 1.06447i −0.846596 0.532235i \(-0.821352\pi\)
0.846596 0.532235i \(-0.178648\pi\)
\(314\) −11.9517 0.657778i −0.674472 0.0371206i
\(315\) 0 0
\(316\) −3.42030 + 30.9790i −0.192407 + 1.74270i
\(317\) −17.1652 −0.964093 −0.482046 0.876146i \(-0.660106\pi\)
−0.482046 + 0.876146i \(0.660106\pi\)
\(318\) 0 0
\(319\) 14.8602i 0.832010i
\(320\) −1.13756 + 3.32234i −0.0635916 + 0.185725i
\(321\) 0 0
\(322\) 0 0
\(323\) 16.8085i 0.935248i
\(324\) 0 0
\(325\) 18.4987i 1.02612i
\(326\) −9.82041 0.540480i −0.543902 0.0299344i
\(327\) 0 0
\(328\) −19.0228 3.16645i −1.05036 0.174838i
\(329\) 0 0
\(330\) 0 0
\(331\) 21.4868i 1.18102i 0.807029 + 0.590511i \(0.201074\pi\)
−0.807029 + 0.590511i \(0.798926\pi\)
\(332\) −10.9265 1.20637i −0.599670 0.0662079i
\(333\) 0 0
\(334\) −0.631068 + 11.4664i −0.0345305 + 0.627411i
\(335\) −3.44610 −0.188280
\(336\) 0 0
\(337\) 5.91046 0.321964 0.160982 0.986957i \(-0.448534\pi\)
0.160982 + 0.986957i \(0.448534\pi\)
\(338\) −0.140456 + 2.55206i −0.00763983 + 0.138814i
\(339\) 0 0
\(340\) 4.92883 + 0.544179i 0.267303 + 0.0295123i
\(341\) 15.7117i 0.850837i
\(342\) 0 0
\(343\) 0 0
\(344\) 12.2384 + 2.03714i 0.659850 + 0.109835i
\(345\) 0 0
\(346\) 2.00000 + 0.110073i 0.107521 + 0.00591755i
\(347\) 2.81560i 0.151149i −0.997140 0.0755746i \(-0.975921\pi\)
0.997140 0.0755746i \(-0.0240791\pi\)
\(348\) 0 0
\(349\) 9.54077i 0.510705i −0.966848 0.255353i \(-0.917808\pi\)
0.966848 0.255353i \(-0.0821916\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −11.5203 3.24926i −0.614035 0.173186i
\(353\) 9.96912i 0.530603i 0.964166 + 0.265301i \(0.0854715\pi\)
−0.964166 + 0.265301i \(0.914529\pi\)
\(354\) 0 0
\(355\) −0.513508 −0.0272542
\(356\) 2.28670 20.7115i 0.121195 1.09771i
\(357\) 0 0
\(358\) 15.1541 + 0.834029i 0.800920 + 0.0440798i
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) 0 0
\(361\) −10.1444 −0.533914
\(362\) −1.71462 0.0943667i −0.0901185 0.00495980i
\(363\) 0 0
\(364\) 0 0
\(365\) 4.40488 0.230562
\(366\) 0 0
\(367\) −17.9047 −0.934616 −0.467308 0.884094i \(-0.654776\pi\)
−0.467308 + 0.884094i \(0.654776\pi\)
\(368\) 4.16274 18.6219i 0.216998 0.970735i
\(369\) 0 0
\(370\) 3.27695 + 0.180352i 0.170361 + 0.00937604i
\(371\) 0 0
\(372\) 0 0
\(373\) 14.4743 0.749452 0.374726 0.927136i \(-0.377737\pi\)
0.374726 + 0.927136i \(0.377737\pi\)
\(374\) −0.928833 + 16.8767i −0.0480288 + 0.872673i
\(375\) 0 0
\(376\) −0.784463 + 4.71276i −0.0404556 + 0.243042i
\(377\) 27.0241i 1.39181i
\(378\) 0 0
\(379\) 21.5969i 1.10936i −0.832064 0.554679i \(-0.812841\pi\)
0.832064 0.554679i \(-0.187159\pi\)
\(380\) 0.286704 2.59678i 0.0147076 0.133212i
\(381\) 0 0
\(382\) −9.25279 0.509241i −0.473414 0.0260550i
\(383\) −0.636338 −0.0325154 −0.0162577 0.999868i \(-0.505175\pi\)
−0.0162577 + 0.999868i \(0.505175\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.251515 + 4.56997i −0.0128018 + 0.232606i
\(387\) 0 0
\(388\) −0.488575 + 4.42521i −0.0248037 + 0.224656i
\(389\) 1.01909 0.0516701 0.0258351 0.999666i \(-0.491776\pi\)
0.0258351 + 0.999666i \(0.491776\pi\)
\(390\) 0 0
\(391\) −26.9446 −1.36265
\(392\) 0 0
\(393\) 0 0
\(394\) 1.49645 27.1902i 0.0753900 1.36982i
\(395\) −6.84061 −0.344188
\(396\) 0 0
\(397\) 29.7953i 1.49538i 0.664047 + 0.747691i \(0.268838\pi\)
−0.664047 + 0.747691i \(0.731162\pi\)
\(398\) −0.670043 + 12.1745i −0.0335862 + 0.610254i
\(399\) 0 0
\(400\) 18.7661 + 4.19496i 0.938305 + 0.209748i
\(401\) 6.79025 0.339089 0.169545 0.985523i \(-0.445770\pi\)
0.169545 + 0.985523i \(0.445770\pi\)
\(402\) 0 0
\(403\) 28.5727i 1.42331i
\(404\) −0.168529 + 1.52643i −0.00838461 + 0.0759426i
\(405\) 0 0
\(406\) 0 0
\(407\) 11.1865i 0.554496i
\(408\) 0 0
\(409\) 3.71322i 0.183607i −0.995777 0.0918034i \(-0.970737\pi\)
0.995777 0.0918034i \(-0.0292631\pi\)
\(410\) 0.232595 4.22620i 0.0114871 0.208717i
\(411\) 0 0
\(412\) 17.1732 + 1.89605i 0.846064 + 0.0934116i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.41273i 0.118436i
\(416\) 20.9504 + 5.90897i 1.02718 + 0.289711i
\(417\) 0 0
\(418\) 8.89158 + 0.489361i 0.434901 + 0.0239354i
\(419\) −20.7082 −1.01166 −0.505832 0.862632i \(-0.668814\pi\)
−0.505832 + 0.862632i \(0.668814\pi\)
\(420\) 0 0
\(421\) 15.6579 0.763118 0.381559 0.924344i \(-0.375387\pi\)
0.381559 + 0.924344i \(0.375387\pi\)
\(422\) −8.61066 0.473900i −0.419161 0.0230691i
\(423\) 0 0
\(424\) 4.97482 29.8869i 0.241599 1.45143i
\(425\) 27.1532i 1.31712i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.558433 5.05793i 0.0269929 0.244484i
\(429\) 0 0
\(430\) −0.149641 + 2.71894i −0.00721631 + 0.131119i
\(431\) 11.8614i 0.571345i 0.958327 + 0.285672i \(0.0922169\pi\)
−0.958327 + 0.285672i \(0.907783\pi\)
\(432\) 0 0
\(433\) 16.9269i 0.813454i −0.913550 0.406727i \(-0.866670\pi\)
0.913550 0.406727i \(-0.133330\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 13.5324 + 1.49408i 0.648084 + 0.0715532i
\(437\) 14.1959i 0.679082i
\(438\) 0 0
\(439\) 2.35281 0.112293 0.0561467 0.998423i \(-0.482119\pi\)
0.0561467 + 0.998423i \(0.482119\pi\)
\(440\) 0.431365 2.59148i 0.0205645 0.123544i
\(441\) 0 0
\(442\) 1.68914 30.6913i 0.0803441 1.45983i
\(443\) 1.60393i 0.0762050i 0.999274 + 0.0381025i \(0.0121313\pi\)
−0.999274 + 0.0381025i \(0.987869\pi\)
\(444\) 0 0
\(445\) 4.57341 0.216800
\(446\) 0.190360 3.45880i 0.00901381 0.163779i
\(447\) 0 0
\(448\) 0 0
\(449\) −1.35208 −0.0638086 −0.0319043 0.999491i \(-0.510157\pi\)
−0.0319043 + 0.999491i \(0.510157\pi\)
\(450\) 0 0
\(451\) 14.4270 0.679341
\(452\) 27.1169 + 2.99390i 1.27547 + 0.140821i
\(453\) 0 0
\(454\) −1.80919 + 32.8726i −0.0849095 + 1.54279i
\(455\) 0 0
\(456\) 0 0
\(457\) 22.1468 1.03598 0.517992 0.855385i \(-0.326680\pi\)
0.517992 + 0.855385i \(0.326680\pi\)
\(458\) −16.5311 0.909811i −0.772446 0.0425127i
\(459\) 0 0
\(460\) 4.16274 + 0.459597i 0.194089 + 0.0214288i
\(461\) 30.7842i 1.43376i −0.697195 0.716882i \(-0.745569\pi\)
0.697195 0.716882i \(-0.254431\pi\)
\(462\) 0 0
\(463\) 13.8120i 0.641897i 0.947097 + 0.320948i \(0.104002\pi\)
−0.947097 + 0.320948i \(0.895998\pi\)
\(464\) −27.4148 6.12829i −1.27270 0.284499i
\(465\) 0 0
\(466\) 0.634823 11.5346i 0.0294076 0.534329i
\(467\) −17.0266 −0.787897 −0.393949 0.919132i \(-0.628891\pi\)
−0.393949 + 0.919132i \(0.628891\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.04701 0.0576236i −0.0482949 0.00265798i
\(471\) 0 0
\(472\) 3.77021 22.6500i 0.173538 1.04255i
\(473\) −9.28164 −0.426770
\(474\) 0 0
\(475\) −14.3058 −0.656395
\(476\) 0 0
\(477\) 0 0
\(478\) −25.6976 1.41430i −1.17538 0.0646887i
\(479\) −31.7805 −1.45209 −0.726045 0.687647i \(-0.758644\pi\)
−0.726045 + 0.687647i \(0.758644\pi\)
\(480\) 0 0
\(481\) 20.3434i 0.927578i
\(482\) −40.8299 2.24713i −1.85975 0.102354i
\(483\) 0 0
\(484\) −12.9665 1.43160i −0.589386 0.0650726i
\(485\) −0.977151 −0.0443701
\(486\) 0 0
\(487\) 5.76992i 0.261460i 0.991418 + 0.130730i \(0.0417321\pi\)
−0.991418 + 0.130730i \(0.958268\pi\)
\(488\) −17.2612 2.87322i −0.781379 0.130065i
\(489\) 0 0
\(490\) 0 0
\(491\) 22.6443i 1.02192i −0.859603 0.510962i \(-0.829289\pi\)
0.859603 0.510962i \(-0.170711\pi\)
\(492\) 0 0
\(493\) 39.6672i 1.78652i
\(494\) −16.1699 0.889931i −0.727516 0.0400399i
\(495\) 0 0
\(496\) −28.9858 6.47946i −1.30150 0.290936i
\(497\) 0 0
\(498\) 0 0
\(499\) 19.4432i 0.870396i −0.900335 0.435198i \(-0.856678\pi\)
0.900335 0.435198i \(-0.143322\pi\)
\(500\) −0.944874 + 8.55807i −0.0422560 + 0.382729i
\(501\) 0 0
\(502\) 1.58218 28.7479i 0.0706162 1.28308i
\(503\) 11.7570 0.524217 0.262108 0.965038i \(-0.415582\pi\)
0.262108 + 0.965038i \(0.415582\pi\)
\(504\) 0 0
\(505\) −0.337057 −0.0149989
\(506\) −0.784463 + 14.2535i −0.0348736 + 0.633646i
\(507\) 0 0
\(508\) 0.772384 6.99577i 0.0342690 0.310387i
\(509\) 20.1467i 0.892987i 0.894787 + 0.446494i \(0.147327\pi\)
−0.894787 + 0.446494i \(0.852673\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 10.7453 19.9133i 0.474881 0.880050i
\(513\) 0 0
\(514\) −30.0588 1.65433i −1.32584 0.0729693i
\(515\) 3.79210i 0.167100i
\(516\) 0 0
\(517\) 3.57417i 0.157192i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.784463 + 4.71276i −0.0344010 + 0.206668i
\(521\) 35.9071i 1.57312i −0.617515 0.786559i \(-0.711860\pi\)
0.617515 0.786559i \(-0.288140\pi\)
\(522\) 0 0
\(523\) 45.2961 1.98066 0.990330 0.138735i \(-0.0443035\pi\)
0.990330 + 0.138735i \(0.0443035\pi\)
\(524\) 38.9964 + 4.30548i 1.70356 + 0.188086i
\(525\) 0 0
\(526\) −28.4951 1.56827i −1.24245 0.0683799i
\(527\) 41.9403i 1.82695i
\(528\) 0 0
\(529\) 0.243451 0.0105848
\(530\) 6.63980 + 0.365431i 0.288415 + 0.0158733i
\(531\) 0 0
\(532\) 0 0
\(533\) −26.2364 −1.13642
\(534\) 0 0
\(535\) 1.11687 0.0482863
\(536\) 21.9034 + 3.64593i 0.946081 + 0.157480i
\(537\) 0 0
\(538\) 23.1150 + 1.27217i 0.996558 + 0.0548470i
\(539\) 0 0
\(540\) 0 0
\(541\) −33.8983 −1.45740 −0.728701 0.684832i \(-0.759876\pi\)
−0.728701 + 0.684832i \(0.759876\pi\)
\(542\) −1.04558 + 18.9980i −0.0449115 + 0.816033i
\(543\) 0 0
\(544\) −30.7519 8.67345i −1.31848 0.371871i
\(545\) 2.98815i 0.127998i
\(546\) 0 0
\(547\) 7.83251i 0.334894i 0.985881 + 0.167447i \(0.0535523\pi\)
−0.985881 + 0.167447i \(0.946448\pi\)
\(548\) −6.71574 0.741467i −0.286882 0.0316739i
\(549\) 0 0
\(550\) −14.3639 0.790536i −0.612477 0.0337086i
\(551\) 20.8989 0.890322
\(552\) 0 0
\(553\) 0 0
\(554\) 0.218172 3.96414i 0.00926925 0.168420i
\(555\) 0 0
\(556\) −32.6976 3.61005i −1.38669 0.153100i
\(557\) −15.3940 −0.652266 −0.326133 0.945324i \(-0.605746\pi\)
−0.326133 + 0.945324i \(0.605746\pi\)
\(558\) 0 0
\(559\) 16.8792 0.713914
\(560\) 0 0
\(561\) 0 0
\(562\) 1.97788 35.9376i 0.0834317 1.51594i
\(563\) 16.4410 0.692907 0.346453 0.938067i \(-0.387386\pi\)
0.346453 + 0.938067i \(0.387386\pi\)
\(564\) 0 0
\(565\) 5.98780i 0.251909i
\(566\) 0.368333 6.69252i 0.0154822 0.281308i
\(567\) 0 0
\(568\) 3.26385 + 0.543286i 0.136948 + 0.0227958i
\(569\) 37.2292 1.56073 0.780366 0.625323i \(-0.215033\pi\)
0.780366 + 0.625323i \(0.215033\pi\)
\(570\) 0 0
\(571\) 20.7454i 0.868166i −0.900873 0.434083i \(-0.857072\pi\)
0.900873 0.434083i \(-0.142928\pi\)
\(572\) −16.1863 1.78709i −0.676784 0.0747219i
\(573\) 0 0
\(574\) 0 0
\(575\) 22.9327i 0.956361i
\(576\) 0 0
\(577\) 15.4211i 0.641988i 0.947081 + 0.320994i \(0.104017\pi\)
−0.947081 + 0.320994i \(0.895983\pi\)
\(578\) −1.15822 + 21.0447i −0.0481758 + 0.875344i
\(579\) 0 0
\(580\) 0.676608 6.12829i 0.0280946 0.254463i
\(581\) 0 0
\(582\) 0 0
\(583\) 22.6663i 0.938743i
\(584\) −27.9974 4.66031i −1.15854 0.192845i
\(585\) 0 0
\(586\) 4.55843 + 0.250880i 0.188307 + 0.0103638i
\(587\) −34.0410 −1.40502 −0.702512 0.711672i \(-0.747938\pi\)
−0.702512 + 0.711672i \(0.747938\pi\)
\(588\) 0 0
\(589\) 22.0965 0.910469
\(590\) 5.03203 + 0.276945i 0.207166 + 0.0114017i
\(591\) 0 0
\(592\) −20.6375 4.61329i −0.848195 0.189605i
\(593\) 31.8347i 1.30729i −0.756800 0.653647i \(-0.773238\pi\)
0.756800 0.653647i \(-0.226762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.8805 + 1.42210i 0.527606 + 0.0582516i
\(597\) 0 0
\(598\) 1.42659 25.9209i 0.0583377 1.05998i
\(599\) 20.7846i 0.849236i −0.905373 0.424618i \(-0.860408\pi\)
0.905373 0.424618i \(-0.139592\pi\)
\(600\) 0 0
\(601\) 15.8614i 0.646999i 0.946228 + 0.323499i \(0.104859\pi\)
−0.946228 + 0.323499i \(0.895141\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.70518 15.4444i 0.0693827 0.628425i
\(605\) 2.86319i 0.116405i
\(606\) 0 0
\(607\) 43.4302 1.76278 0.881388 0.472393i \(-0.156610\pi\)
0.881388 + 0.472393i \(0.156610\pi\)
\(608\) −4.56965 + 16.2018i −0.185324 + 0.657070i
\(609\) 0 0
\(610\) 0.211056 3.83484i 0.00854539 0.155268i
\(611\) 6.49985i 0.262956i
\(612\) 0 0
\(613\) 15.5206 0.626871 0.313436 0.949609i \(-0.398520\pi\)
0.313436 + 0.949609i \(0.398520\pi\)
\(614\) 0.423957 7.70321i 0.0171095 0.310876i
\(615\) 0 0
\(616\) 0 0
\(617\) 19.8053 0.797330 0.398665 0.917097i \(-0.369474\pi\)
0.398665 + 0.917097i \(0.369474\pi\)
\(618\) 0 0
\(619\) 16.3133 0.655687 0.327844 0.944732i \(-0.393678\pi\)
0.327844 + 0.944732i \(0.393678\pi\)
\(620\) 0.715380 6.47946i 0.0287303 0.260221i
\(621\) 0 0
\(622\) 2.37228 43.1038i 0.0951197 1.72830i
\(623\) 0 0
\(624\) 0 0
\(625\) 22.1468 0.885873
\(626\) −26.5928 1.46357i −1.06286 0.0584962i
\(627\) 0 0
\(628\) −1.85767 + 16.8256i −0.0741289 + 0.671413i
\(629\) 29.8609i 1.19063i
\(630\) 0 0
\(631\) 27.3095i 1.08717i 0.839353 + 0.543587i \(0.182934\pi\)
−0.839353 + 0.543587i \(0.817066\pi\)
\(632\) 43.4789 + 7.23728i 1.72950 + 0.287884i
\(633\) 0 0
\(634\) −1.33400 + 24.2386i −0.0529801 + 0.962636i
\(635\) 1.54477 0.0613022
\(636\) 0 0
\(637\) 0 0
\(638\) 20.9837 + 1.15487i 0.830753 + 0.0457217i
\(639\) 0 0
\(640\) 4.60300 + 1.86452i 0.181949 + 0.0737017i
\(641\) −9.79066 −0.386708 −0.193354 0.981129i \(-0.561937\pi\)
−0.193354 + 0.981129i \(0.561937\pi\)
\(642\) 0 0
\(643\) −7.26458 −0.286487 −0.143244 0.989687i \(-0.545753\pi\)
−0.143244 + 0.989687i \(0.545753\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 23.7348 + 1.30628i 0.933835 + 0.0513949i
\(647\) 46.0839 1.81174 0.905872 0.423551i \(-0.139217\pi\)
0.905872 + 0.423551i \(0.139217\pi\)
\(648\) 0 0
\(649\) 17.1779i 0.674290i
\(650\) 26.1215 + 1.43764i 1.02457 + 0.0563887i
\(651\) 0 0
\(652\) −1.52640 + 13.8252i −0.0597784 + 0.541435i
\(653\) 6.77981 0.265314 0.132657 0.991162i \(-0.457649\pi\)
0.132657 + 0.991162i \(0.457649\pi\)
\(654\) 0 0
\(655\) 8.61097i 0.336458i
\(656\) −5.94965 + 26.6156i −0.232295 + 1.03917i
\(657\) 0 0
\(658\) 0 0
\(659\) 29.3184i 1.14208i 0.820921 + 0.571041i \(0.193460\pi\)
−0.820921 + 0.571041i \(0.806540\pi\)
\(660\) 0 0
\(661\) 30.5780i 1.18935i −0.803967 0.594674i \(-0.797281\pi\)
0.803967 0.594674i \(-0.202719\pi\)
\(662\) 30.3410 + 1.66986i 1.17924 + 0.0649011i
\(663\) 0 0
\(664\) −2.55264 + 15.3353i −0.0990617 + 0.595125i
\(665\) 0 0
\(666\) 0 0
\(667\) 33.5017i 1.29719i
\(668\) 16.1423 + 1.78223i 0.624566 + 0.0689566i
\(669\) 0 0
\(670\) −0.267816 + 4.86615i −0.0103466 + 0.187996i
\(671\) 13.0910 0.505372
\(672\) 0 0
\(673\) −6.37827 −0.245864 −0.122932 0.992415i \(-0.539230\pi\)
−0.122932 + 0.992415i \(0.539230\pi\)
\(674\) 0.459336 8.34603i 0.0176930 0.321477i
\(675\) 0 0
\(676\) 3.59279 + 0.396671i 0.138184 + 0.0152566i
\(677\) 12.4960i 0.480261i 0.970741 + 0.240131i \(0.0771903\pi\)
−0.970741 + 0.240131i \(0.922810\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.15147 6.91760i 0.0441569 0.265278i
\(681\) 0 0
\(682\) 22.1862 + 1.22105i 0.849552 + 0.0467563i
\(683\) 45.2547i 1.73162i 0.500371 + 0.865811i \(0.333197\pi\)
−0.500371 + 0.865811i \(0.666803\pi\)
\(684\) 0 0
\(685\) 1.48293i 0.0566600i
\(686\) 0 0
\(687\) 0 0
\(688\) 3.82772 17.1232i 0.145930 0.652817i
\(689\) 41.2200i 1.57036i
\(690\) 0 0
\(691\) 10.5931 0.402980 0.201490 0.979491i \(-0.435422\pi\)
0.201490 + 0.979491i \(0.435422\pi\)
\(692\) 0.310863 2.81560i 0.0118172 0.107033i
\(693\) 0 0
\(694\) −3.97584 0.218816i −0.150921 0.00830615i
\(695\) 7.22010i 0.273874i
\(696\) 0 0
\(697\) 38.5109 1.45870
\(698\) −13.4723 0.741467i −0.509934 0.0280649i
\(699\) 0 0
\(700\) 0 0
\(701\) −29.6566 −1.12011 −0.560057 0.828454i \(-0.689221\pi\)
−0.560057 + 0.828454i \(0.689221\pi\)
\(702\) 0 0
\(703\) 15.7324 0.593358
\(704\) −5.48351 + 16.0151i −0.206668 + 0.603590i
\(705\) 0 0
\(706\) 14.0772 + 0.774757i 0.529801 + 0.0291584i
\(707\) 0 0
\(708\) 0 0
\(709\) −35.7011 −1.34078 −0.670392 0.742007i \(-0.733874\pi\)
−0.670392 + 0.742007i \(0.733874\pi\)
\(710\) −0.0399076 + 0.725113i −0.00149771 + 0.0272130i
\(711\) 0 0
\(712\) −29.0685 4.83861i −1.08939 0.181335i
\(713\) 35.4214i 1.32654i
\(714\) 0 0
\(715\) 3.57417i 0.133667i
\(716\) 2.35543 21.3340i 0.0880264 0.797288i
\(717\) 0 0
\(718\) −9.78315 0.538430i −0.365104 0.0200940i
\(719\) −12.8089 −0.477693 −0.238846 0.971057i \(-0.576769\pi\)
−0.238846 + 0.971057i \(0.576769\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.788376 + 14.3246i −0.0293403 + 0.533107i
\(723\) 0 0
\(724\) −0.266506 + 2.41384i −0.00990462 + 0.0897098i
\(725\) −33.7610 −1.25385
\(726\) 0 0
\(727\) 19.3286 0.716860 0.358430 0.933557i \(-0.383312\pi\)
0.358430 + 0.933557i \(0.383312\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.342328 6.22003i 0.0126701 0.230214i
\(731\) −24.7761 −0.916375
\(732\) 0 0
\(733\) 37.6903i 1.39212i −0.717983 0.696061i \(-0.754934\pi\)
0.717983 0.696061i \(-0.245066\pi\)
\(734\) −1.39147 + 25.2828i −0.0513602 + 0.933204i
\(735\) 0 0
\(736\) −25.9721 7.32532i −0.957344 0.270015i
\(737\) −16.6116 −0.611896
\(738\) 0 0
\(739\) 13.8647i 0.510023i 0.966938 + 0.255011i \(0.0820792\pi\)
−0.966938 + 0.255011i \(0.917921\pi\)
\(740\) 0.509341 4.61329i 0.0187237 0.169588i
\(741\) 0 0
\(742\) 0 0
\(743\) 18.9927i 0.696773i 0.937351 + 0.348387i \(0.113270\pi\)
−0.937351 + 0.348387i \(0.886730\pi\)
\(744\) 0 0
\(745\) 2.84421i 0.104204i
\(746\) 1.12488 20.4389i 0.0411849 0.748320i
\(747\) 0 0
\(748\) 23.7590 + 2.62317i 0.868715 + 0.0959125i
\(749\) 0 0
\(750\) 0 0
\(751\) 29.1987i 1.06547i 0.846281 + 0.532737i \(0.178836\pi\)
−0.846281 + 0.532737i \(0.821164\pi\)
\(752\) 6.59381 + 1.47398i 0.240452 + 0.0537504i
\(753\) 0 0
\(754\) −38.1601 2.10020i −1.38971 0.0764847i
\(755\) 3.41036 0.124116
\(756\) 0 0
\(757\) −10.8022 −0.392614 −0.196307 0.980542i \(-0.562895\pi\)
−0.196307 + 0.980542i \(0.562895\pi\)
\(758\) −30.4965 1.67842i −1.10768 0.0609628i
\(759\) 0 0
\(760\) −3.64457 0.606658i −0.132203 0.0220058i
\(761\) 0.234595i 0.00850407i 0.999991 + 0.00425204i \(0.00135347\pi\)
−0.999991 + 0.00425204i \(0.998647\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.43817 + 13.0261i −0.0520313 + 0.471267i
\(765\) 0 0
\(766\) −0.0494535 + 0.898559i −0.00178683 + 0.0324662i
\(767\) 31.2390i 1.12797i
\(768\) 0 0
\(769\) 34.8540i 1.25687i 0.777863 + 0.628434i \(0.216304\pi\)
−0.777863 + 0.628434i \(0.783696\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.43361 + 0.710317i 0.231551 + 0.0255649i
\(773\) 19.6717i 0.707540i 0.935332 + 0.353770i \(0.115100\pi\)
−0.935332 + 0.353770i \(0.884900\pi\)
\(774\) 0 0
\(775\) −35.6957 −1.28223
\(776\) 6.21076 + 1.03381i 0.222953 + 0.0371118i
\(777\) 0 0
\(778\) 0.0791996 1.43904i 0.00283944 0.0515920i
\(779\) 20.2897i 0.726953i
\(780\) 0 0
\(781\) −2.47532 −0.0885739
\(782\) −2.09402 + 38.0478i −0.0748819 + 1.36059i
\(783\) 0 0
\(784\) 0 0
\(785\) −3.71533 −0.132606
\(786\) 0 0
\(787\) 38.9562 1.38864 0.694319 0.719668i \(-0.255706\pi\)
0.694319 + 0.719668i \(0.255706\pi\)
\(788\) −38.2783 4.22620i −1.36361 0.150552i
\(789\) 0 0
\(790\) −0.531622 + 9.65946i −0.0189143 + 0.343668i
\(791\) 0 0
\(792\) 0 0
\(793\) −23.8067 −0.845402
\(794\) 42.0732 + 2.31556i 1.49312 + 0.0821762i
\(795\) 0 0
\(796\) 17.1393 + 1.89230i 0.607487 + 0.0670710i