Properties

Label 1764.2.b.n.1567.16
Level $1764$
Weight $2$
Character 1764.1567
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.b (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: \(x^{16} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + 4132 x^{6} - 16824 x^{5} + 27780 x^{4} - 26200 x^{3} + 14608 x^{2} - 4784 x + 782\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.16
Root \(1.14224 - 1.48800i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.n.1567.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.05050 + 0.946809i) q^{2} +(0.207107 + 1.98925i) q^{4} +1.60804i q^{5} +(-1.66587 + 2.28580i) q^{8} +O(q^{10})\) \(q+(1.05050 + 0.946809i) q^{2} +(0.207107 + 1.98925i) q^{4} +1.60804i q^{5} +(-1.66587 + 2.28580i) q^{8} +(-1.52250 + 1.68925i) q^{10} -2.67798i q^{11} +3.37849i q^{13} +(-3.91421 + 0.823973i) q^{16} +1.60804i q^{17} -4.30629 q^{19} +(-3.19879 + 0.333036i) q^{20} +(2.53553 - 2.81322i) q^{22} +6.46521i q^{23} +2.41421 q^{25} +(-3.19879 + 3.54911i) q^{26} +4.71179 q^{29} -10.3963 q^{31} +(-4.89203 - 2.84043i) q^{32} +(-1.52250 + 1.68925i) q^{34} +0.242641 q^{37} +(-4.52377 - 4.07724i) q^{38} +(-3.67565 - 2.67878i) q^{40} +11.6464i q^{41} -7.95699i q^{43} +(5.32716 - 0.554628i) q^{44} +(-6.12132 + 6.79172i) q^{46} -9.04753 q^{47} +(2.53613 + 2.28580i) q^{50} +(-6.72066 + 0.699709i) q^{52} -2.46148 q^{53} +4.30629 q^{55} +(4.94975 + 4.46117i) q^{58} +9.04753 q^{59} -3.37849i q^{61} +(-10.9213 - 9.84332i) q^{62} +(-2.44975 - 7.61569i) q^{64} -5.43275 q^{65} +11.2529i q^{67} +(-3.19879 + 0.333036i) q^{68} -8.03394i q^{71} -6.17733i q^{73} +(0.254894 + 0.229734i) q^{74} +(-0.891862 - 8.56628i) q^{76} +3.29589i q^{79} +(-1.32498 - 6.29420i) q^{80} +(-11.0270 + 12.2346i) q^{82} +12.7951 q^{83} -2.58579 q^{85} +(7.53375 - 8.35883i) q^{86} +(6.12132 + 4.46117i) q^{88} +0.275896i q^{89} +(-12.8609 + 1.33899i) q^{92} +(-9.50445 - 8.56628i) q^{94} -6.92468i q^{95} -12.9343i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{4} + O(q^{10}) \) \( 16q - 8q^{4} - 40q^{16} - 16q^{22} + 16q^{25} - 64q^{37} - 64q^{46} + 40q^{64} - 64q^{85} + 64q^{88} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05050 + 0.946809i 0.742817 + 0.669495i
\(3\) 0 0
\(4\) 0.207107 + 1.98925i 0.103553 + 0.994624i
\(5\) 1.60804i 0.719136i 0.933119 + 0.359568i \(0.117076\pi\)
−0.933119 + 0.359568i \(0.882924\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.66587 + 2.28580i −0.588974 + 0.808152i
\(9\) 0 0
\(10\) −1.52250 + 1.68925i −0.481458 + 0.534187i
\(11\) 2.67798i 0.807441i −0.914882 0.403721i \(-0.867717\pi\)
0.914882 0.403721i \(-0.132283\pi\)
\(12\) 0 0
\(13\) 3.37849i 0.937025i 0.883457 + 0.468513i \(0.155210\pi\)
−0.883457 + 0.468513i \(0.844790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.91421 + 0.823973i −0.978553 + 0.205993i
\(17\) 1.60804i 0.390007i 0.980803 + 0.195003i \(0.0624717\pi\)
−0.980803 + 0.195003i \(0.937528\pi\)
\(18\) 0 0
\(19\) −4.30629 −0.987931 −0.493966 0.869481i \(-0.664453\pi\)
−0.493966 + 0.869481i \(0.664453\pi\)
\(20\) −3.19879 + 0.333036i −0.715270 + 0.0744690i
\(21\) 0 0
\(22\) 2.53553 2.81322i 0.540578 0.599781i
\(23\) 6.46521i 1.34809i 0.738690 + 0.674045i \(0.235445\pi\)
−0.738690 + 0.674045i \(0.764555\pi\)
\(24\) 0 0
\(25\) 2.41421 0.482843
\(26\) −3.19879 + 3.54911i −0.627334 + 0.696038i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.71179 0.874958 0.437479 0.899229i \(-0.355871\pi\)
0.437479 + 0.899229i \(0.355871\pi\)
\(30\) 0 0
\(31\) −10.3963 −1.86723 −0.933616 0.358275i \(-0.883365\pi\)
−0.933616 + 0.358275i \(0.883365\pi\)
\(32\) −4.89203 2.84043i −0.864797 0.502121i
\(33\) 0 0
\(34\) −1.52250 + 1.68925i −0.261107 + 0.289703i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.242641 0.0398899 0.0199449 0.999801i \(-0.493651\pi\)
0.0199449 + 0.999801i \(0.493651\pi\)
\(38\) −4.52377 4.07724i −0.733852 0.661415i
\(39\) 0 0
\(40\) −3.67565 2.67878i −0.581171 0.423553i
\(41\) 11.6464i 1.81887i 0.415848 + 0.909434i \(0.363485\pi\)
−0.415848 + 0.909434i \(0.636515\pi\)
\(42\) 0 0
\(43\) 7.95699i 1.21343i −0.794920 0.606715i \(-0.792487\pi\)
0.794920 0.606715i \(-0.207513\pi\)
\(44\) 5.32716 0.554628i 0.803100 0.0836133i
\(45\) 0 0
\(46\) −6.12132 + 6.79172i −0.902539 + 1.00138i
\(47\) −9.04753 −1.31972 −0.659859 0.751389i \(-0.729384\pi\)
−0.659859 + 0.751389i \(0.729384\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.53613 + 2.28580i 0.358664 + 0.323261i
\(51\) 0 0
\(52\) −6.72066 + 0.699709i −0.931988 + 0.0970321i
\(53\) −2.46148 −0.338110 −0.169055 0.985607i \(-0.554072\pi\)
−0.169055 + 0.985607i \(0.554072\pi\)
\(54\) 0 0
\(55\) 4.30629 0.580660
\(56\) 0 0
\(57\) 0 0
\(58\) 4.94975 + 4.46117i 0.649934 + 0.585780i
\(59\) 9.04753 1.17789 0.588944 0.808174i \(-0.299544\pi\)
0.588944 + 0.808174i \(0.299544\pi\)
\(60\) 0 0
\(61\) 3.37849i 0.432572i −0.976330 0.216286i \(-0.930606\pi\)
0.976330 0.216286i \(-0.0693943\pi\)
\(62\) −10.9213 9.84332i −1.38701 1.25010i
\(63\) 0 0
\(64\) −2.44975 7.61569i −0.306218 0.951961i
\(65\) −5.43275 −0.673849
\(66\) 0 0
\(67\) 11.2529i 1.37476i 0.726299 + 0.687379i \(0.241239\pi\)
−0.726299 + 0.687379i \(0.758761\pi\)
\(68\) −3.19879 + 0.333036i −0.387910 + 0.0403865i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.03394i 0.953453i −0.879052 0.476726i \(-0.841823\pi\)
0.879052 0.476726i \(-0.158177\pi\)
\(72\) 0 0
\(73\) 6.17733i 0.723002i −0.932372 0.361501i \(-0.882264\pi\)
0.932372 0.361501i \(-0.117736\pi\)
\(74\) 0.254894 + 0.229734i 0.0296309 + 0.0267061i
\(75\) 0 0
\(76\) −0.891862 8.56628i −0.102304 0.982620i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.29589i 0.370817i 0.982662 + 0.185409i \(0.0593608\pi\)
−0.982662 + 0.185409i \(0.940639\pi\)
\(80\) −1.32498 6.29420i −0.148137 0.703713i
\(81\) 0 0
\(82\) −11.0270 + 12.2346i −1.21772 + 1.35109i
\(83\) 12.7951 1.40445 0.702225 0.711955i \(-0.252190\pi\)
0.702225 + 0.711955i \(0.252190\pi\)
\(84\) 0 0
\(85\) −2.58579 −0.280468
\(86\) 7.53375 8.35883i 0.812385 0.901356i
\(87\) 0 0
\(88\) 6.12132 + 4.46117i 0.652535 + 0.475562i
\(89\) 0.275896i 0.0292449i 0.999893 + 0.0146224i \(0.00465463\pi\)
−0.999893 + 0.0146224i \(0.995345\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −12.8609 + 1.33899i −1.34084 + 0.139599i
\(93\) 0 0
\(94\) −9.50445 8.56628i −0.980309 0.883545i
\(95\) 6.92468i 0.710457i
\(96\) 0 0
\(97\) 12.9343i 1.31328i −0.754204 0.656640i \(-0.771977\pi\)
0.754204 0.656640i \(-0.228023\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 + 4.80247i 0.0500000 + 0.480247i
\(101\) 16.1947i 1.61143i 0.592304 + 0.805714i \(0.298218\pi\)
−0.592304 + 0.805714i \(0.701782\pi\)
\(102\) 0 0
\(103\) −10.3963 −1.02438 −0.512189 0.858873i \(-0.671165\pi\)
−0.512189 + 0.858873i \(0.671165\pi\)
\(104\) −7.72255 5.62813i −0.757259 0.551884i
\(105\) 0 0
\(106\) −2.58579 2.33055i −0.251154 0.226363i
\(107\) 6.46521i 0.625016i 0.949915 + 0.312508i \(0.101169\pi\)
−0.949915 + 0.312508i \(0.898831\pi\)
\(108\) 0 0
\(109\) −7.41421 −0.710153 −0.355076 0.934837i \(-0.615545\pi\)
−0.355076 + 0.934837i \(0.615545\pi\)
\(110\) 4.52377 + 4.07724i 0.431324 + 0.388749i
\(111\) 0 0
\(112\) 0 0
\(113\) 12.6060 1.18587 0.592937 0.805249i \(-0.297968\pi\)
0.592937 + 0.805249i \(0.297968\pi\)
\(114\) 0 0
\(115\) −10.3963 −0.969461
\(116\) 0.975845 + 9.37293i 0.0906049 + 0.870254i
\(117\) 0 0
\(118\) 9.50445 + 8.56628i 0.874955 + 0.788590i
\(119\) 0 0
\(120\) 0 0
\(121\) 3.82843 0.348039
\(122\) 3.19879 3.54911i 0.289604 0.321321i
\(123\) 0 0
\(124\) −2.15315 20.6808i −0.193358 1.85719i
\(125\) 11.9223i 1.06637i
\(126\) 0 0
\(127\) 11.2529i 0.998532i −0.866449 0.499266i \(-0.833603\pi\)
0.866449 0.499266i \(-0.166397\pi\)
\(128\) 4.63714 10.3197i 0.409869 0.912144i
\(129\) 0 0
\(130\) −5.70711 5.14377i −0.500546 0.451138i
\(131\) 12.7951 1.11792 0.558958 0.829196i \(-0.311201\pi\)
0.558958 + 0.829196i \(0.311201\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −10.6543 + 11.8212i −0.920394 + 1.02119i
\(135\) 0 0
\(136\) −3.67565 2.67878i −0.315184 0.229704i
\(137\) 19.0583 1.62826 0.814132 0.580680i \(-0.197213\pi\)
0.814132 + 0.580680i \(0.197213\pi\)
\(138\) 0 0
\(139\) −6.09002 −0.516549 −0.258274 0.966072i \(-0.583154\pi\)
−0.258274 + 0.966072i \(0.583154\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.60660 8.43966i 0.638332 0.708241i
\(143\) 9.04753 0.756593
\(144\) 0 0
\(145\) 7.57675i 0.629214i
\(146\) 5.84875 6.48929i 0.484046 0.537058i
\(147\) 0 0
\(148\) 0.0502525 + 0.482672i 0.00413073 + 0.0396754i
\(149\) −23.7701 −1.94733 −0.973663 0.227993i \(-0.926784\pi\)
−0.973663 + 0.227993i \(0.926784\pi\)
\(150\) 0 0
\(151\) 7.95699i 0.647531i 0.946137 + 0.323765i \(0.104949\pi\)
−0.946137 + 0.323765i \(0.895051\pi\)
\(152\) 7.17373 9.84332i 0.581866 0.798398i
\(153\) 0 0
\(154\) 0 0
\(155\) 16.7177i 1.34279i
\(156\) 0 0
\(157\) 10.9552i 0.874323i 0.899383 + 0.437162i \(0.144016\pi\)
−0.899383 + 0.437162i \(0.855984\pi\)
\(158\) −3.12058 + 3.46234i −0.248260 + 0.275449i
\(159\) 0 0
\(160\) 4.56751 7.86657i 0.361094 0.621907i
\(161\) 0 0
\(162\) 0 0
\(163\) 11.2529i 0.881394i 0.897656 + 0.440697i \(0.145269\pi\)
−0.897656 + 0.440697i \(0.854731\pi\)
\(164\) −23.1677 + 2.41206i −1.80909 + 0.188350i
\(165\) 0 0
\(166\) 13.4413 + 12.1146i 1.04325 + 0.940272i
\(167\) 21.8427 1.69024 0.845119 0.534579i \(-0.179530\pi\)
0.845119 + 0.534579i \(0.179530\pi\)
\(168\) 0 0
\(169\) 1.58579 0.121984
\(170\) −2.71637 2.44824i −0.208336 0.187772i
\(171\) 0 0
\(172\) 15.8284 1.64795i 1.20691 0.125655i
\(173\) 11.2563i 0.855798i −0.903827 0.427899i \(-0.859254\pi\)
0.903827 0.427899i \(-0.140746\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.20658 + 10.4822i 0.166328 + 0.790124i
\(177\) 0 0
\(178\) −0.261220 + 0.289829i −0.0195793 + 0.0217236i
\(179\) 12.4710i 0.932123i 0.884752 + 0.466062i \(0.154328\pi\)
−0.884752 + 0.466062i \(0.845672\pi\)
\(180\) 0 0
\(181\) 14.9134i 1.10850i 0.832349 + 0.554252i \(0.186996\pi\)
−0.832349 + 0.554252i \(0.813004\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −14.7782 10.7702i −1.08946 0.793991i
\(185\) 0.390175i 0.0286863i
\(186\) 0 0
\(187\) 4.30629 0.314907
\(188\) −1.87381 17.9978i −0.136661 1.31262i
\(189\) 0 0
\(190\) 6.55635 7.27439i 0.475648 0.527740i
\(191\) 10.2524i 0.741841i 0.928665 + 0.370921i \(0.120958\pi\)
−0.928665 + 0.370921i \(0.879042\pi\)
\(192\) 0 0
\(193\) −7.65685 −0.551152 −0.275576 0.961279i \(-0.588869\pi\)
−0.275576 + 0.961279i \(0.588869\pi\)
\(194\) 12.2463 13.5875i 0.879235 0.975527i
\(195\) 0 0
\(196\) 0 0
\(197\) 10.1445 0.722769 0.361384 0.932417i \(-0.382304\pi\)
0.361384 + 0.932417i \(0.382304\pi\)
\(198\) 0 0
\(199\) 14.7026 1.04224 0.521120 0.853483i \(-0.325514\pi\)
0.521120 + 0.853483i \(0.325514\pi\)
\(200\) −4.02177 + 5.51841i −0.284382 + 0.390210i
\(201\) 0 0
\(202\) −15.3332 + 17.0125i −1.07884 + 1.19700i
\(203\) 0 0
\(204\) 0 0
\(205\) −18.7279 −1.30801
\(206\) −10.9213 9.84332i −0.760926 0.685816i
\(207\) 0 0
\(208\) −2.78379 13.2241i −0.193021 0.916929i
\(209\) 11.5322i 0.797696i
\(210\) 0 0
\(211\) 15.9140i 1.09556i 0.836621 + 0.547782i \(0.184528\pi\)
−0.836621 + 0.547782i \(0.815472\pi\)
\(212\) −0.509789 4.89649i −0.0350124 0.336292i
\(213\) 0 0
\(214\) −6.12132 + 6.79172i −0.418445 + 0.464272i
\(215\) 12.7951 0.872622
\(216\) 0 0
\(217\) 0 0
\(218\) −7.78864 7.01984i −0.527513 0.475444i
\(219\) 0 0
\(220\) 0.891862 + 8.56628i 0.0601294 + 0.577539i
\(221\) −5.43275 −0.365446
\(222\) 0 0
\(223\) −8.61259 −0.576741 −0.288371 0.957519i \(-0.593114\pi\)
−0.288371 + 0.957519i \(0.593114\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 13.2426 + 11.9355i 0.880887 + 0.793937i
\(227\) −3.74761 −0.248738 −0.124369 0.992236i \(-0.539691\pi\)
−0.124369 + 0.992236i \(0.539691\pi\)
\(228\) 0 0
\(229\) 4.19825i 0.277428i −0.990332 0.138714i \(-0.955703\pi\)
0.990332 0.138714i \(-0.0442969\pi\)
\(230\) −10.9213 9.84332i −0.720132 0.649049i
\(231\) 0 0
\(232\) −7.84924 + 10.7702i −0.515328 + 0.707099i
\(233\) −3.69222 −0.241885 −0.120943 0.992660i \(-0.538592\pi\)
−0.120943 + 0.992660i \(0.538592\pi\)
\(234\) 0 0
\(235\) 14.5488i 0.949058i
\(236\) 1.87381 + 17.9978i 0.121974 + 1.17156i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.10926i 0.0717518i 0.999356 + 0.0358759i \(0.0114221\pi\)
−0.999356 + 0.0358759i \(0.988578\pi\)
\(240\) 0 0
\(241\) 1.39942i 0.0901444i −0.998984 0.0450722i \(-0.985648\pi\)
0.998984 0.0450722i \(-0.0143518\pi\)
\(242\) 4.02177 + 3.62479i 0.258529 + 0.233010i
\(243\) 0 0
\(244\) 6.72066 0.699709i 0.430246 0.0447943i
\(245\) 0 0
\(246\) 0 0
\(247\) 14.5488i 0.925717i
\(248\) 17.3189 23.7639i 1.09975 1.50901i
\(249\) 0 0
\(250\) −11.2882 + 12.5244i −0.713927 + 0.792115i
\(251\) 21.8427 1.37870 0.689349 0.724430i \(-0.257897\pi\)
0.689349 + 0.724430i \(0.257897\pi\)
\(252\) 0 0
\(253\) 17.3137 1.08850
\(254\) 10.6543 11.8212i 0.668512 0.741726i
\(255\) 0 0
\(256\) 14.6421 6.45042i 0.915133 0.403151i
\(257\) 14.3107i 0.892679i −0.894864 0.446339i \(-0.852727\pi\)
0.894864 0.446339i \(-0.147273\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.12516 10.8071i −0.0697794 0.670226i
\(261\) 0 0
\(262\) 13.4413 + 12.1146i 0.830407 + 0.748440i
\(263\) 2.67798i 0.165131i −0.996586 0.0825656i \(-0.973689\pi\)
0.996586 0.0825656i \(-0.0263114\pi\)
\(264\) 0 0
\(265\) 3.95815i 0.243147i
\(266\) 0 0
\(267\) 0 0
\(268\) −22.3848 + 2.33055i −1.36737 + 0.142361i
\(269\) 16.1947i 0.987406i 0.869631 + 0.493703i \(0.164357\pi\)
−0.869631 + 0.493703i \(0.835643\pi\)
\(270\) 0 0
\(271\) 16.4863 1.00147 0.500737 0.865600i \(-0.333063\pi\)
0.500737 + 0.865600i \(0.333063\pi\)
\(272\) −1.32498 6.29420i −0.0803388 0.381642i
\(273\) 0 0
\(274\) 20.0208 + 18.0446i 1.20950 + 1.09011i
\(275\) 6.46521i 0.389867i
\(276\) 0 0
\(277\) 23.7990 1.42994 0.714971 0.699154i \(-0.246440\pi\)
0.714971 + 0.699154i \(0.246440\pi\)
\(278\) −6.39757 5.76608i −0.383701 0.345827i
\(279\) 0 0
\(280\) 0 0
\(281\) −8.19285 −0.488744 −0.244372 0.969681i \(-0.578582\pi\)
−0.244372 + 0.969681i \(0.578582\pi\)
\(282\) 0 0
\(283\) 10.3963 0.617996 0.308998 0.951063i \(-0.400006\pi\)
0.308998 + 0.951063i \(0.400006\pi\)
\(284\) 15.9815 1.66388i 0.948327 0.0987333i
\(285\) 0 0
\(286\) 9.50445 + 8.56628i 0.562010 + 0.506535i
\(287\) 0 0
\(288\) 0 0
\(289\) 14.4142 0.847895
\(290\) −7.17373 + 7.95938i −0.421256 + 0.467391i
\(291\) 0 0
\(292\) 12.2882 1.27937i 0.719115 0.0748693i
\(293\) 1.21786i 0.0711483i −0.999367 0.0355741i \(-0.988674\pi\)
0.999367 0.0355741i \(-0.0113260\pi\)
\(294\) 0 0
\(295\) 14.5488i 0.847063i
\(296\) −0.404208 + 0.554628i −0.0234941 + 0.0322371i
\(297\) 0 0
\(298\) −24.9706 22.5058i −1.44651 1.30372i
\(299\) −21.8427 −1.26319
\(300\) 0 0
\(301\) 0 0
\(302\) −7.53375 + 8.35883i −0.433518 + 0.480997i
\(303\) 0 0
\(304\) 16.8557 3.54827i 0.966743 0.203507i
\(305\) 5.43275 0.311078
\(306\) 0 0
\(307\) 22.5763 1.28850 0.644250 0.764815i \(-0.277170\pi\)
0.644250 + 0.764815i \(0.277170\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 15.8284 17.5619i 0.898994 0.997451i
\(311\) 21.8427 1.23858 0.619292 0.785161i \(-0.287420\pi\)
0.619292 + 0.785161i \(0.287420\pi\)
\(312\) 0 0
\(313\) 6.17733i 0.349163i −0.984643 0.174582i \(-0.944143\pi\)
0.984643 0.174582i \(-0.0558573\pi\)
\(314\) −10.3725 + 11.5085i −0.585355 + 0.649462i
\(315\) 0 0
\(316\) −6.55635 + 0.682602i −0.368823 + 0.0383994i
\(317\) −10.1445 −0.569774 −0.284887 0.958561i \(-0.591956\pi\)
−0.284887 + 0.958561i \(0.591956\pi\)
\(318\) 0 0
\(319\) 12.6181i 0.706477i
\(320\) 12.2463 3.93929i 0.684590 0.220213i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.92468i 0.385300i
\(324\) 0 0
\(325\) 8.15640i 0.452436i
\(326\) −10.6543 + 11.8212i −0.590089 + 0.654714i
\(327\) 0 0
\(328\) −26.6214 19.4015i −1.46992 1.07127i
\(329\) 0 0
\(330\) 0 0
\(331\) 22.5058i 1.23703i −0.785773 0.618514i \(-0.787735\pi\)
0.785773 0.618514i \(-0.212265\pi\)
\(332\) 2.64996 + 25.4527i 0.145436 + 1.39690i
\(333\) 0 0
\(334\) 22.9458 + 20.6808i 1.25554 + 1.13161i
\(335\) −18.0951 −0.988639
\(336\) 0 0
\(337\) −34.3848 −1.87306 −0.936529 0.350590i \(-0.885981\pi\)
−0.936529 + 0.350590i \(0.885981\pi\)
\(338\) 1.66587 + 1.50144i 0.0906114 + 0.0816674i
\(339\) 0 0
\(340\) −0.535534 5.14377i −0.0290434 0.278960i
\(341\) 27.8411i 1.50768i
\(342\) 0 0
\(343\) 0 0
\(344\) 18.1881 + 13.2553i 0.980635 + 0.714679i
\(345\) 0 0
\(346\) 10.6575 11.8247i 0.572952 0.635701i
\(347\) 14.0397i 0.753690i −0.926276 0.376845i \(-0.877009\pi\)
0.926276 0.376845i \(-0.122991\pi\)
\(348\) 0 0
\(349\) 8.15640i 0.436602i 0.975881 + 0.218301i \(0.0700515\pi\)
−0.975881 + 0.218301i \(0.929949\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −7.60660 + 13.1008i −0.405433 + 0.698273i
\(353\) 1.21786i 0.0648203i 0.999475 + 0.0324101i \(0.0103183\pi\)
−0.999475 + 0.0324101i \(0.989682\pi\)
\(354\) 0 0
\(355\) 12.9189 0.685663
\(356\) −0.548825 + 0.0571399i −0.0290877 + 0.00302841i
\(357\) 0 0
\(358\) −11.8076 + 13.1008i −0.624052 + 0.692397i
\(359\) 6.46521i 0.341221i −0.985339 0.170610i \(-0.945426\pi\)
0.985339 0.170610i \(-0.0545740\pi\)
\(360\) 0 0
\(361\) −0.455844 −0.0239918
\(362\) −14.1201 + 15.6665i −0.742137 + 0.823415i
\(363\) 0 0
\(364\) 0 0
\(365\) 9.93338 0.519937
\(366\) 0 0
\(367\) 18.2701 0.953689 0.476844 0.878988i \(-0.341780\pi\)
0.476844 + 0.878988i \(0.341780\pi\)
\(368\) −5.32716 25.3062i −0.277698 1.31918i
\(369\) 0 0
\(370\) −0.369422 + 0.409880i −0.0192053 + 0.0213086i
\(371\) 0 0
\(372\) 0 0
\(373\) 2.82843 0.146450 0.0732252 0.997315i \(-0.476671\pi\)
0.0732252 + 0.997315i \(0.476671\pi\)
\(374\) 4.52377 + 4.07724i 0.233918 + 0.210829i
\(375\) 0 0
\(376\) 15.0720 20.6808i 0.777280 1.06653i
\(377\) 15.9188i 0.819858i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 13.7749 1.43415i 0.706638 0.0735703i
\(381\) 0 0
\(382\) −9.70711 + 10.7702i −0.496659 + 0.551052i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.04354 7.24958i −0.409405 0.368994i
\(387\) 0 0
\(388\) 25.7296 2.67878i 1.30622 0.135995i
\(389\) −0.211161 −0.0107063 −0.00535315 0.999986i \(-0.501704\pi\)
−0.00535315 + 0.999986i \(0.501704\pi\)
\(390\) 0 0
\(391\) −10.3963 −0.525764
\(392\) 0 0
\(393\) 0 0
\(394\) 10.6569 + 9.60494i 0.536885 + 0.483890i
\(395\) −5.29992 −0.266668
\(396\) 0 0
\(397\) 7.33664i 0.368216i 0.982906 + 0.184108i \(0.0589395\pi\)
−0.982906 + 0.184108i \(0.941060\pi\)
\(398\) 15.4451 + 13.9206i 0.774193 + 0.697774i
\(399\) 0 0
\(400\) −9.44975 + 1.98925i −0.472487 + 0.0994624i
\(401\) 29.9238 1.49432 0.747162 0.664642i \(-0.231416\pi\)
0.747162 + 0.664642i \(0.231416\pi\)
\(402\) 0 0
\(403\) 35.1239i 1.74964i
\(404\) −32.2152 + 3.35402i −1.60277 + 0.166869i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.649787i 0.0322087i
\(408\) 0 0
\(409\) 33.2053i 1.64189i −0.571004 0.820947i \(-0.693446\pi\)
0.571004 0.820947i \(-0.306554\pi\)
\(410\) −19.6737 17.7318i −0.971615 0.875709i
\(411\) 0 0
\(412\) −2.15315 20.6808i −0.106078 1.01887i
\(413\) 0 0
\(414\) 0 0
\(415\) 20.5751i 1.00999i
\(416\) 9.59636 16.5277i 0.470500 0.810337i
\(417\) 0 0
\(418\) −10.9188 + 12.1146i −0.534054 + 0.592542i
\(419\) −34.6378 −1.69217 −0.846084 0.533049i \(-0.821046\pi\)
−0.846084 + 0.533049i \(0.821046\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) −15.0675 + 16.7177i −0.733474 + 0.813803i
\(423\) 0 0
\(424\) 4.10051 5.62644i 0.199138 0.273244i
\(425\) 3.88215i 0.188312i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.8609 + 1.33899i −0.621656 + 0.0647225i
\(429\) 0 0
\(430\) 13.4413 + 12.1146i 0.648198 + 0.584216i
\(431\) 2.67798i 0.128994i 0.997918 + 0.0644969i \(0.0205442\pi\)
−0.997918 + 0.0644969i \(0.979456\pi\)
\(432\) 0 0
\(433\) 25.6285i 1.23163i −0.787891 0.615814i \(-0.788827\pi\)
0.787891 0.615814i \(-0.211173\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.53553 14.7487i −0.0735387 0.706335i
\(437\) 27.8411i 1.33182i
\(438\) 0 0
\(439\) 14.7026 0.701717 0.350858 0.936429i \(-0.385890\pi\)
0.350858 + 0.936429i \(0.385890\pi\)
\(440\) −7.17373 + 9.84332i −0.341994 + 0.469262i
\(441\) 0 0
\(442\) −5.70711 5.14377i −0.271459 0.244664i
\(443\) 33.8948i 1.61039i 0.593010 + 0.805195i \(0.297939\pi\)
−0.593010 + 0.805195i \(0.702061\pi\)
\(444\) 0 0
\(445\) −0.443651 −0.0210311
\(446\) −9.04753 8.15447i −0.428413 0.386125i
\(447\) 0 0
\(448\) 0 0
\(449\) 8.70264 0.410703 0.205351 0.978688i \(-0.434166\pi\)
0.205351 + 0.978688i \(0.434166\pi\)
\(450\) 0 0
\(451\) 31.1889 1.46863
\(452\) 2.61079 + 25.0765i 0.122801 + 1.17950i
\(453\) 0 0
\(454\) −3.93687 3.54827i −0.184767 0.166529i
\(455\) 0 0
\(456\) 0 0
\(457\) 32.4853 1.51960 0.759799 0.650158i \(-0.225297\pi\)
0.759799 + 0.650158i \(0.225297\pi\)
\(458\) 3.97494 4.41027i 0.185737 0.206078i
\(459\) 0 0
\(460\) −2.15315 20.6808i −0.100391 0.964249i
\(461\) 29.4491i 1.37158i −0.727798 0.685792i \(-0.759456\pi\)
0.727798 0.685792i \(-0.240544\pi\)
\(462\) 0 0
\(463\) 38.4198i 1.78552i 0.450535 + 0.892759i \(0.351233\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(464\) −18.4430 + 3.88239i −0.856193 + 0.180236i
\(465\) 0 0
\(466\) −3.87868 3.49582i −0.179676 0.161941i
\(467\) −9.04753 −0.418670 −0.209335 0.977844i \(-0.567130\pi\)
−0.209335 + 0.977844i \(0.567130\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 13.7749 15.2835i 0.635389 0.704976i
\(471\) 0 0
\(472\) −15.0720 + 20.6808i −0.693746 + 0.951913i
\(473\) −21.3087 −0.979773
\(474\) 0 0
\(475\) −10.3963 −0.477015
\(476\) 0 0
\(477\) 0 0
\(478\) −1.05025 + 1.16527i −0.0480374 + 0.0532984i
\(479\) −34.6378 −1.58264 −0.791321 0.611401i \(-0.790606\pi\)
−0.791321 + 0.611401i \(0.790606\pi\)
\(480\) 0 0
\(481\) 0.819760i 0.0373778i
\(482\) 1.32498 1.47009i 0.0603512 0.0669608i
\(483\) 0 0
\(484\) 0.792893 + 7.61569i 0.0360406 + 0.346168i
\(485\) 20.7989 0.944428
\(486\) 0 0
\(487\) 14.5488i 0.659268i −0.944109 0.329634i \(-0.893075\pi\)
0.944109 0.329634i \(-0.106925\pi\)
\(488\) 7.72255 + 5.62813i 0.349584 + 0.254774i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.3261i 1.45886i 0.684058 + 0.729428i \(0.260213\pi\)
−0.684058 + 0.729428i \(0.739787\pi\)
\(492\) 0 0
\(493\) 7.57675i 0.341239i
\(494\) 13.7749 15.2835i 0.619762 0.687638i
\(495\) 0 0
\(496\) 40.6934 8.56628i 1.82719 0.384637i
\(497\) 0 0
\(498\) 0 0
\(499\) 19.2099i 0.859952i −0.902840 0.429976i \(-0.858522\pi\)
0.902840 0.429976i \(-0.141478\pi\)
\(500\) −23.7165 + 2.46920i −1.06063 + 0.110426i
\(501\) 0 0
\(502\) 22.9458 + 20.6808i 1.02412 + 0.923031i
\(503\) 5.29992 0.236312 0.118156 0.992995i \(-0.462302\pi\)
0.118156 + 0.992995i \(0.462302\pi\)
\(504\) 0 0
\(505\) −26.0416 −1.15884
\(506\) 18.1881 + 16.3928i 0.808559 + 0.728747i
\(507\) 0 0
\(508\) 22.3848 2.33055i 0.993164 0.103401i
\(509\) 1.21786i 0.0539808i 0.999636 + 0.0269904i \(0.00859236\pi\)
−0.999636 + 0.0269904i \(0.991408\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 21.4889 + 7.08713i 0.949684 + 0.313210i
\(513\) 0 0
\(514\) 13.5495 15.0334i 0.597644 0.663097i
\(515\) 16.7177i 0.736668i
\(516\) 0 0
\(517\) 24.2291i 1.06559i
\(518\) 0 0
\(519\) 0 0
\(520\) 9.05025 12.4182i 0.396880 0.544572i
\(521\) 15.6429i 0.685327i −0.939458 0.342663i \(-0.888671\pi\)
0.939458 0.342663i \(-0.111329\pi\)
\(522\) 0 0
\(523\) −14.7026 −0.642900 −0.321450 0.946927i \(-0.604170\pi\)
−0.321450 + 0.946927i \(0.604170\pi\)
\(524\) 2.64996 + 25.4527i 0.115764 + 1.11191i
\(525\) 0 0
\(526\) 2.53553 2.81322i 0.110555 0.122662i
\(527\) 16.7177i 0.728233i
\(528\) 0 0
\(529\) −18.7990 −0.817347
\(530\) 3.74761 4.15804i 0.162786 0.180614i
\(531\) 0 0
\(532\) 0 0
\(533\) −39.3474 −1.70433
\(534\) 0 0
\(535\) −10.3963 −0.449472
\(536\) −25.7218 18.7459i −1.11101 0.809698i
\(537\) 0 0
\(538\) −15.3332 + 17.0125i −0.661063 + 0.733462i
\(539\) 0 0
\(540\) 0 0
\(541\) −33.1127 −1.42363 −0.711813 0.702369i \(-0.752126\pi\)
−0.711813 + 0.702369i \(0.752126\pi\)
\(542\) 17.3189 + 15.6094i 0.743911 + 0.670481i
\(543\) 0 0
\(544\) 4.56751 7.86657i 0.195831 0.337277i
\(545\) 11.9223i 0.510697i
\(546\) 0 0
\(547\) 3.29589i 0.140922i −0.997515 0.0704611i \(-0.977553\pi\)
0.997515 0.0704611i \(-0.0224471\pi\)
\(548\) 3.94711 + 37.9118i 0.168612 + 1.61951i
\(549\) 0 0
\(550\) 6.12132 6.79172i 0.261014 0.289600i
\(551\) −20.2904 −0.864399
\(552\) 0 0
\(553\) 0 0
\(554\) 25.0009 + 22.5331i 1.06219 + 0.957339i
\(555\) 0 0
\(556\) −1.26128 12.1146i −0.0534904 0.513772i
\(557\) −31.4532 −1.33271 −0.666357 0.745633i \(-0.732147\pi\)
−0.666357 + 0.745633i \(0.732147\pi\)
\(558\) 0 0
\(559\) 26.8826 1.13701
\(560\) 0 0
\(561\) 0 0
\(562\) −8.60660 7.75706i −0.363048 0.327212i
\(563\) 3.74761 0.157943 0.0789715 0.996877i \(-0.474836\pi\)
0.0789715 + 0.996877i \(0.474836\pi\)
\(564\) 0 0
\(565\) 20.2710i 0.852806i
\(566\) 10.9213 + 9.84332i 0.459058 + 0.413745i
\(567\) 0 0
\(568\) 18.3640 + 13.3835i 0.770535 + 0.561559i
\(569\) −12.0962 −0.507100 −0.253550 0.967322i \(-0.581598\pi\)
−0.253550 + 0.967322i \(0.581598\pi\)
\(570\) 0 0
\(571\) 30.4628i 1.27483i 0.770522 + 0.637413i \(0.219996\pi\)
−0.770522 + 0.637413i \(0.780004\pi\)
\(572\) 1.87381 + 17.9978i 0.0783477 + 0.752525i
\(573\) 0 0
\(574\) 0 0
\(575\) 15.6084i 0.650916i
\(576\) 0 0
\(577\) 18.8715i 0.785632i 0.919617 + 0.392816i \(0.128499\pi\)
−0.919617 + 0.392816i \(0.871501\pi\)
\(578\) 15.1422 + 13.6475i 0.629831 + 0.567661i
\(579\) 0 0
\(580\) −15.0720 + 1.56920i −0.625832 + 0.0651573i
\(581\) 0 0
\(582\) 0 0
\(583\) 6.59179i 0.273004i
\(584\) 14.1201 + 10.2906i 0.584295 + 0.425829i
\(585\) 0 0
\(586\) 1.15308 1.27937i 0.0476334 0.0528501i
\(587\) −34.6378 −1.42966 −0.714828 0.699300i \(-0.753495\pi\)
−0.714828 + 0.699300i \(0.753495\pi\)
\(588\) 0 0
\(589\) 44.7696 1.84470
\(590\) −13.7749 + 15.2835i −0.567104 + 0.629212i
\(591\) 0 0
\(592\) −0.949747 + 0.199929i −0.0390344 + 0.00821705i
\(593\) 18.4688i 0.758421i 0.925310 + 0.379211i \(0.123804\pi\)
−0.925310 + 0.379211i \(0.876196\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.92296 47.2847i −0.201652 1.93686i
\(597\) 0 0
\(598\) −22.9458 20.6808i −0.938322 0.845702i
\(599\) 16.5273i 0.675289i 0.941274 + 0.337644i \(0.109630\pi\)
−0.941274 + 0.337644i \(0.890370\pi\)
\(600\) 0 0
\(601\) 16.8925i 0.689058i −0.938776 0.344529i \(-0.888039\pi\)
0.938776 0.344529i \(-0.111961\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −15.8284 + 1.64795i −0.644050 + 0.0670540i
\(605\) 6.15626i 0.250287i
\(606\) 0 0
\(607\) 2.52257 0.102388 0.0511939 0.998689i \(-0.483697\pi\)
0.0511939 + 0.998689i \(0.483697\pi\)
\(608\) 21.0665 + 12.2317i 0.854360 + 0.496061i
\(609\) 0 0
\(610\) 5.70711 + 5.14377i 0.231074 + 0.208265i
\(611\) 30.5670i 1.23661i
\(612\) 0 0
\(613\) 22.0416 0.890253 0.445127 0.895468i \(-0.353159\pi\)
0.445127 + 0.895468i \(0.353159\pi\)
\(614\) 23.7165 + 21.3755i 0.957119 + 0.862644i
\(615\) 0 0
\(616\) 0 0
\(617\) −16.5969 −0.668165 −0.334082 0.942544i \(-0.608426\pi\)
−0.334082 + 0.942544i \(0.608426\pi\)
\(618\) 0 0
\(619\) −6.09002 −0.244778 −0.122389 0.992482i \(-0.539056\pi\)
−0.122389 + 0.992482i \(0.539056\pi\)
\(620\) 33.2556 3.46234i 1.33558 0.139051i
\(621\) 0 0
\(622\) 22.9458 + 20.6808i 0.920041 + 0.829226i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.10051 −0.284020
\(626\) 5.84875 6.48929i 0.233763 0.259364i
\(627\) 0 0
\(628\) −21.7927 + 2.26890i −0.869623 + 0.0905391i
\(629\) 0.390175i 0.0155573i
\(630\) 0 0
\(631\) 45.0115i 1.79188i −0.444174 0.895941i \(-0.646503\pi\)
0.444174 0.895941i \(-0.353497\pi\)
\(632\) −7.53375 5.49053i −0.299676 0.218402i
\(633\) 0 0
\(634\) −10.6569 9.60494i −0.423238 0.381461i
\(635\) 18.0951 0.718081
\(636\) 0 0
\(637\) 0 0
\(638\) 11.9469 13.2553i 0.472983 0.524783i
\(639\) 0 0
\(640\) 16.5945 + 7.45669i 0.655956 + 0.294752i
\(641\) 28.9043 1.14165 0.570825 0.821072i \(-0.306624\pi\)
0.570825 + 0.821072i \(0.306624\pi\)
\(642\) 0 0
\(643\) −45.8915 −1.80979 −0.904893 0.425640i \(-0.860049\pi\)
−0.904893 + 0.425640i \(0.860049\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.55635 7.27439i 0.257956 0.286207i
\(647\) −27.1426 −1.06709 −0.533543 0.845773i \(-0.679140\pi\)
−0.533543 + 0.845773i \(0.679140\pi\)
\(648\) 0 0
\(649\) 24.2291i 0.951076i
\(650\) −7.72255 + 8.56831i −0.302903 + 0.336077i
\(651\) 0 0
\(652\) −22.3848 + 2.33055i −0.876655 + 0.0912713i
\(653\) 37.3083 1.45999 0.729993 0.683455i \(-0.239523\pi\)
0.729993 + 0.683455i \(0.239523\pi\)
\(654\) 0 0
\(655\) 20.5751i 0.803935i
\(656\) −9.59636 45.5867i −0.374675 1.77986i
\(657\) 0 0
\(658\) 0 0
\(659\) 31.6763i 1.23393i 0.786990 + 0.616966i \(0.211639\pi\)
−0.786990 + 0.616966i \(0.788361\pi\)
\(660\) 0 0
\(661\) 43.5809i 1.69510i 0.530717 + 0.847549i \(0.321923\pi\)
−0.530717 + 0.847549i \(0.678077\pi\)
\(662\) 21.3087 23.6423i 0.828184 0.918886i
\(663\) 0 0
\(664\) −21.3151 + 29.2471i −0.827185 + 1.13501i
\(665\) 0 0
\(666\) 0 0
\(667\) 30.4628i 1.17952i
\(668\) 4.52377 + 43.4505i 0.175030 + 1.68115i
\(669\) 0 0
\(670\) −19.0089 17.1326i −0.734378 0.661889i
\(671\) −9.04753 −0.349276
\(672\) 0 0
\(673\) −16.1005 −0.620629 −0.310314 0.950634i \(-0.600434\pi\)
−0.310314 + 0.950634i \(0.600434\pi\)
\(674\) −36.1213 32.5558i −1.39134 1.25400i
\(675\) 0 0
\(676\) 0.328427 + 3.15452i 0.0126318 + 0.121328i
\(677\) 31.8849i 1.22543i −0.790302 0.612717i \(-0.790076\pi\)
0.790302 0.612717i \(-0.209924\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.30759 5.91059i 0.165188 0.226661i
\(681\) 0 0
\(682\) −26.3602 + 29.2471i −1.00938 + 1.11993i
\(683\) 16.5273i 0.632401i 0.948692 + 0.316201i \(0.102407\pi\)
−0.948692 + 0.316201i \(0.897593\pi\)
\(684\) 0 0
\(685\) 30.6465i 1.17094i
\(686\) 0 0
\(687\) 0 0
\(688\) 6.55635 + 31.1454i 0.249958 + 1.18741i
\(689\) 8.31609i 0.316818i
\(690\) 0 0
\(691\) 12.1800 0.463350 0.231675 0.972793i \(-0.425579\pi\)
0.231675 + 0.972793i \(0.425579\pi\)
\(692\) 22.3915 2.33125i 0.851197 0.0886208i
\(693\) 0 0
\(694\) 13.2929 14.7487i 0.504591 0.559853i
\(695\) 9.79298i 0.371469i
\(696\) 0 0
\(697\) −18.7279 −0.709371
\(698\) −7.72255 + 8.56831i −0.292303 + 0.324315i
\(699\) 0 0
\(700\) 0 0
\(701\) −19.0583 −0.719824 −0.359912 0.932986i \(-0.617193\pi\)
−0.359912 + 0.932986i \(0.617193\pi\)
\(702\) 0 0
\(703\) −1.04488 −0.0394085
\(704\) −20.3947 + 6.56037i −0.768653 + 0.247253i
\(705\) 0 0
\(706\) −1.15308 + 1.27937i −0.0433968 + 0.0481496i
\(707\) 0 0
\(708\) 0 0
\(709\) −31.4142 −1.17979 −0.589893 0.807482i \(-0.700830\pi\)
−0.589893 + 0.807482i \(0.700830\pi\)
\(710\) 13.5713 + 12.2317i 0.509322 + 0.459048i
\(711\) 0 0
\(712\) −0.630642 0.459607i −0.0236343 0.0172245i
\(713\) 67.2144i 2.51720i
\(714\) 0 0
\(715\) 14.5488i 0.544093i
\(716\) −24.8078 + 2.58282i −0.927112 + 0.0965245i
\(717\) 0 0
\(718\) 6.12132 6.79172i 0.228446 0.253465i
\(719\) 43.6854 1.62919 0.814594 0.580031i \(-0.196960\pi\)
0.814594 + 0.580031i \(0.196960\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.478865 0.431597i −0.0178215 0.0160624i
\(723\) 0 0
\(724\) −29.6664 + 3.08866i −1.10254 + 0.114789i
\(725\) 11.3753 0.422467
\(726\) 0 0
\(727\) −1.78372 −0.0661547 −0.0330773 0.999453i \(-0.510531\pi\)
−0.0330773 + 0.999453i \(0.510531\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 10.4350 + 9.40501i 0.386218 + 0.348095i
\(731\) 12.7951 0.473246
\(732\) 0 0
\(733\) 23.3099i 0.860971i −0.902598 0.430485i \(-0.858342\pi\)
0.902598 0.430485i \(-0.141658\pi\)
\(734\) 19.1927 + 17.2982i 0.708416 + 0.638490i
\(735\) 0 0
\(736\) 18.3640 31.6280i 0.676905 1.16582i
\(737\) 30.1350 1.11004
\(738\) 0 0
\(739\) 31.8280i 1.17081i 0.810741 + 0.585405i \(0.199065\pi\)
−0.810741 + 0.585405i \(0.800935\pi\)
\(740\) −0.776156 + 0.0808080i −0.0285321 + 0.00297056i
\(741\) 0 0
\(742\) 0 0
\(743\) 17.8269i 0.654006i −0.945023 0.327003i \(-0.893961\pi\)
0.945023 0.327003i \(-0.106039\pi\)
\(744\) 0 0
\(745\) 38.2233i 1.40039i
\(746\) 2.97127 + 2.67798i 0.108786 + 0.0980478i
\(747\) 0 0
\(748\) 0.891862 + 8.56628i 0.0326097 + 0.313214i
\(749\) 0 0
\(750\) 0 0
\(751\) 36.4891i 1.33150i −0.746173 0.665752i \(-0.768111\pi\)
0.746173 0.665752i \(-0.231889\pi\)
\(752\) 35.4140 7.45493i 1.29141 0.271853i
\(753\) 0 0
\(754\) −15.0720 + 16.7227i −0.548891 + 0.609004i
\(755\) −12.7951 −0.465663
\(756\) 0 0
\(757\) 11.8995 0.432494 0.216247 0.976339i \(-0.430618\pi\)
0.216247 + 0.976339i \(0.430618\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 15.8284 + 11.5356i 0.574157 + 0.418441i
\(761\) 8.26875i 0.299742i 0.988706 + 0.149871i \(0.0478858\pi\)
−0.988706 + 0.149871i \(0.952114\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.3947 + 2.12335i −0.737853 + 0.0768202i
\(765\) 0 0
\(766\) 0 0
\(767\) 30.5670i 1.10371i
\(768\) 0 0
\(769\) 43.5809i 1.57157i −0.618502 0.785783i \(-0.712260\pi\)
0.618502 0.785783i \(-0.287740\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.58579 15.2314i −0.0570737 0.548189i
\(773\) 41.7617i 1.50206i −0.660267 0.751031i \(-0.729557\pi\)
0.660267 0.751031i \(-0.270443\pi\)
\(774\) 0 0
\(775\) −25.0989 −0.901580
\(776\) 29.5652 + 21.5469i 1.06133 + 0.773489i
\(777\) 0 0
\(778\) −0.221825 0.199929i −0.00795283 0.00716782i
\(779\) 50.1530i 1.79692i
\(780\) 0 0
\(781\) −21.5147 −0.769857
\(782\) −10.9213 9.84332i −0.390546 0.351996i
\(783\) 0 0
\(784\) 0 0
\(785\) −17.6164 −0.628758
\(786\) 0 0
\(787\) −44.1078 −1.57227 −0.786137 0.618053i \(-0.787922\pi\)
−0.786137 + 0.618053i \(0.787922\pi\)
\(788\) 2.10100 + 20.1800i 0.0748451 + 0.718883i
\(789\) 0 0
\(790\) −5.56758 5.01801i −0.198085 0.178533i
\(791\) 0 0
\(792\) 0 0
\(793\)