Properties

Label 1512.2.c.e.757.7
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.7
Root \(-0.725842 - 1.21374i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.725842 - 1.21374i) q^{2} +(-0.946308 + 1.76196i) q^{4} -3.06888i q^{5} -1.00000 q^{7} +(2.82542 - 0.130337i) q^{8} +O(q^{10})\) \(q+(-0.725842 - 1.21374i) q^{2} +(-0.946308 + 1.76196i) q^{4} -3.06888i q^{5} -1.00000 q^{7} +(2.82542 - 0.130337i) q^{8} +(-3.72481 + 2.22752i) q^{10} +5.80820i q^{11} -3.52392i q^{13} +(0.725842 + 1.21374i) q^{14} +(-2.20900 - 3.33471i) q^{16} +6.79736 q^{17} +5.28617i q^{19} +(5.40724 + 2.90410i) q^{20} +(7.04962 - 4.21584i) q^{22} +5.65085 q^{23} -4.41801 q^{25} +(-4.27711 + 2.55781i) q^{26} +(0.946308 - 1.76196i) q^{28} -1.21394i q^{29} +0.107385 q^{31} +(-2.44407 + 5.10162i) q^{32} +(-4.93381 - 8.25020i) q^{34} +3.06888i q^{35} -4.90235i q^{37} +(6.41601 - 3.83692i) q^{38} +(-0.399987 - 8.67087i) q^{40} +11.6855 q^{41} -1.85684i q^{43} +(-10.2338 - 5.49635i) q^{44} +(-4.10162 - 6.85863i) q^{46} -6.76459 q^{47} +1.00000 q^{49} +(3.20677 + 5.36229i) q^{50} +(6.20900 + 3.33471i) q^{52} -11.4861i q^{53} +17.8247 q^{55} +(-2.82542 + 0.130337i) q^{56} +(-1.47340 + 0.881125i) q^{58} +7.85494i q^{59} +12.0556i q^{61} +(-0.0779442 - 0.130337i) q^{62} +(7.96602 - 0.736512i) q^{64} -10.8145 q^{65} -6.66942i q^{67} +(-6.43240 + 11.9767i) q^{68} +(3.72481 - 2.22752i) q^{70} -1.98478 q^{71} -6.52879 q^{73} +(-5.95016 + 3.55833i) q^{74} +(-9.31402 - 5.00234i) q^{76} -5.80820i q^{77} +2.30741 q^{79} +(-10.2338 + 6.77916i) q^{80} +(-8.48183 - 14.1831i) q^{82} -12.5795i q^{83} -20.8603i q^{85} +(-2.25371 + 1.34777i) q^{86} +(0.757021 + 16.4106i) q^{88} +7.79151 q^{89} +3.52392i q^{91} +(-5.34744 + 9.95656i) q^{92} +(4.91002 + 8.21043i) q^{94} +16.2226 q^{95} +4.05981 q^{97} +(-0.725842 - 1.21374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{4} - 20q^{7} + O(q^{10}) \) \( 20q - 2q^{4} - 20q^{7} - 12q^{10} - 14q^{16} + 8q^{22} - 28q^{25} + 2q^{28} + 36q^{31} - 6q^{34} - 16q^{40} - 18q^{46} + 20q^{49} + 94q^{52} + 48q^{55} + 66q^{58} + 22q^{64} + 12q^{70} + 12q^{76} + 64q^{79} - 92q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.725842 1.21374i −0.513248 0.858241i
\(3\) 0 0
\(4\) −0.946308 + 1.76196i −0.473154 + 0.880980i
\(5\) 3.06888i 1.37244i −0.727392 0.686222i \(-0.759268\pi\)
0.727392 0.686222i \(-0.240732\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.82542 0.130337i 0.998938 0.0460809i
\(9\) 0 0
\(10\) −3.72481 + 2.22752i −1.17789 + 0.704403i
\(11\) 5.80820i 1.75124i 0.483001 + 0.875620i \(0.339547\pi\)
−0.483001 + 0.875620i \(0.660453\pi\)
\(12\) 0 0
\(13\) 3.52392i 0.977359i −0.872463 0.488680i \(-0.837479\pi\)
0.872463 0.488680i \(-0.162521\pi\)
\(14\) 0.725842 + 1.21374i 0.193989 + 0.324384i
\(15\) 0 0
\(16\) −2.20900 3.33471i −0.552251 0.833678i
\(17\) 6.79736 1.64860 0.824301 0.566151i \(-0.191568\pi\)
0.824301 + 0.566151i \(0.191568\pi\)
\(18\) 0 0
\(19\) 5.28617i 1.21273i 0.795186 + 0.606365i \(0.207373\pi\)
−0.795186 + 0.606365i \(0.792627\pi\)
\(20\) 5.40724 + 2.90410i 1.20910 + 0.649377i
\(21\) 0 0
\(22\) 7.04962 4.21584i 1.50298 0.898819i
\(23\) 5.65085 1.17828 0.589141 0.808030i \(-0.299466\pi\)
0.589141 + 0.808030i \(0.299466\pi\)
\(24\) 0 0
\(25\) −4.41801 −0.883601
\(26\) −4.27711 + 2.55781i −0.838809 + 0.501627i
\(27\) 0 0
\(28\) 0.946308 1.76196i 0.178835 0.332979i
\(29\) 1.21394i 0.225422i −0.993628 0.112711i \(-0.964047\pi\)
0.993628 0.112711i \(-0.0359534\pi\)
\(30\) 0 0
\(31\) 0.107385 0.0192868 0.00964342 0.999954i \(-0.496930\pi\)
0.00964342 + 0.999954i \(0.496930\pi\)
\(32\) −2.44407 + 5.10162i −0.432055 + 0.901847i
\(33\) 0 0
\(34\) −4.93381 8.25020i −0.846141 1.41490i
\(35\) 3.06888i 0.518735i
\(36\) 0 0
\(37\) 4.90235i 0.805942i −0.915213 0.402971i \(-0.867978\pi\)
0.915213 0.402971i \(-0.132022\pi\)
\(38\) 6.41601 3.83692i 1.04081 0.622431i
\(39\) 0 0
\(40\) −0.399987 8.67087i −0.0632435 1.37099i
\(41\) 11.6855 1.82497 0.912485 0.409111i \(-0.134161\pi\)
0.912485 + 0.409111i \(0.134161\pi\)
\(42\) 0 0
\(43\) 1.85684i 0.283165i −0.989926 0.141583i \(-0.954781\pi\)
0.989926 0.141583i \(-0.0452191\pi\)
\(44\) −10.2338 5.49635i −1.54281 0.828606i
\(45\) 0 0
\(46\) −4.10162 6.85863i −0.604751 1.01125i
\(47\) −6.76459 −0.986717 −0.493359 0.869826i \(-0.664231\pi\)
−0.493359 + 0.869826i \(0.664231\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 3.20677 + 5.36229i 0.453506 + 0.758343i
\(51\) 0 0
\(52\) 6.20900 + 3.33471i 0.861034 + 0.462441i
\(53\) 11.4861i 1.57773i −0.614566 0.788865i \(-0.710669\pi\)
0.614566 0.788865i \(-0.289331\pi\)
\(54\) 0 0
\(55\) 17.8247 2.40348
\(56\) −2.82542 + 0.130337i −0.377563 + 0.0174170i
\(57\) 0 0
\(58\) −1.47340 + 0.881125i −0.193466 + 0.115697i
\(59\) 7.85494i 1.02263i 0.859394 + 0.511313i \(0.170841\pi\)
−0.859394 + 0.511313i \(0.829159\pi\)
\(60\) 0 0
\(61\) 12.0556i 1.54356i 0.635890 + 0.771779i \(0.280633\pi\)
−0.635890 + 0.771779i \(0.719367\pi\)
\(62\) −0.0779442 0.130337i −0.00989893 0.0165528i
\(63\) 0 0
\(64\) 7.96602 0.736512i 0.995753 0.0920639i
\(65\) −10.8145 −1.34137
\(66\) 0 0
\(67\) 6.66942i 0.814800i −0.913250 0.407400i \(-0.866436\pi\)
0.913250 0.407400i \(-0.133564\pi\)
\(68\) −6.43240 + 11.9767i −0.780043 + 1.45239i
\(69\) 0 0
\(70\) 3.72481 2.22752i 0.445199 0.266239i
\(71\) −1.98478 −0.235550 −0.117775 0.993040i \(-0.537576\pi\)
−0.117775 + 0.993040i \(0.537576\pi\)
\(72\) 0 0
\(73\) −6.52879 −0.764137 −0.382068 0.924134i \(-0.624788\pi\)
−0.382068 + 0.924134i \(0.624788\pi\)
\(74\) −5.95016 + 3.55833i −0.691692 + 0.413648i
\(75\) 0 0
\(76\) −9.31402 5.00234i −1.06839 0.573808i
\(77\) 5.80820i 0.661906i
\(78\) 0 0
\(79\) 2.30741 0.259604 0.129802 0.991540i \(-0.458566\pi\)
0.129802 + 0.991540i \(0.458566\pi\)
\(80\) −10.2338 + 6.77916i −1.14418 + 0.757933i
\(81\) 0 0
\(82\) −8.48183 14.1831i −0.936661 1.56626i
\(83\) 12.5795i 1.38078i −0.723436 0.690391i \(-0.757438\pi\)
0.723436 0.690391i \(-0.242562\pi\)
\(84\) 0 0
\(85\) 20.8603i 2.26261i
\(86\) −2.25371 + 1.34777i −0.243024 + 0.145334i
\(87\) 0 0
\(88\) 0.757021 + 16.4106i 0.0806987 + 1.74938i
\(89\) 7.79151 0.825898 0.412949 0.910754i \(-0.364499\pi\)
0.412949 + 0.910754i \(0.364499\pi\)
\(90\) 0 0
\(91\) 3.52392i 0.369407i
\(92\) −5.34744 + 9.95656i −0.557509 + 1.03804i
\(93\) 0 0
\(94\) 4.91002 + 8.21043i 0.506430 + 0.846841i
\(95\) 16.2226 1.66440
\(96\) 0 0
\(97\) 4.05981 0.412212 0.206106 0.978530i \(-0.433921\pi\)
0.206106 + 0.978530i \(0.433921\pi\)
\(98\) −0.725842 1.21374i −0.0733211 0.122606i
\(99\) 0 0
\(100\) 4.18079 7.78435i 0.418079 0.778435i
\(101\) 10.3336i 1.02823i 0.857721 + 0.514116i \(0.171880\pi\)
−0.857721 + 0.514116i \(0.828120\pi\)
\(102\) 0 0
\(103\) 8.94679 0.881554 0.440777 0.897617i \(-0.354703\pi\)
0.440777 + 0.897617i \(0.354703\pi\)
\(104\) −0.459295 9.95656i −0.0450376 0.976321i
\(105\) 0 0
\(106\) −13.9410 + 8.33705i −1.35407 + 0.809766i
\(107\) 17.8845i 1.72896i −0.502669 0.864479i \(-0.667649\pi\)
0.502669 0.864479i \(-0.332351\pi\)
\(108\) 0 0
\(109\) 11.9610i 1.14566i −0.819676 0.572828i \(-0.805846\pi\)
0.819676 0.572828i \(-0.194154\pi\)
\(110\) −12.9379 21.6344i −1.23358 2.06276i
\(111\) 0 0
\(112\) 2.20900 + 3.33471i 0.208731 + 0.315101i
\(113\) 13.3192 1.25297 0.626484 0.779434i \(-0.284493\pi\)
0.626484 + 0.779434i \(0.284493\pi\)
\(114\) 0 0
\(115\) 17.3417i 1.61713i
\(116\) 2.13890 + 1.14876i 0.198592 + 0.106659i
\(117\) 0 0
\(118\) 9.53382 5.70144i 0.877659 0.524860i
\(119\) −6.79736 −0.623113
\(120\) 0 0
\(121\) −22.7352 −2.06684
\(122\) 14.6323 8.75044i 1.32474 0.792228i
\(123\) 0 0
\(124\) −0.101619 + 0.189207i −0.00912565 + 0.0169913i
\(125\) 1.78606i 0.159750i
\(126\) 0 0
\(127\) −7.42140 −0.658543 −0.329271 0.944235i \(-0.606803\pi\)
−0.329271 + 0.944235i \(0.606803\pi\)
\(128\) −6.67600 9.13406i −0.590081 0.807344i
\(129\) 0 0
\(130\) 7.84960 + 13.1259i 0.688455 + 1.15122i
\(131\) 4.82695i 0.421733i −0.977515 0.210866i \(-0.932372\pi\)
0.977515 0.210866i \(-0.0676285\pi\)
\(132\) 0 0
\(133\) 5.28617i 0.458369i
\(134\) −8.09492 + 4.84095i −0.699294 + 0.418194i
\(135\) 0 0
\(136\) 19.2054 0.885945i 1.64685 0.0759691i
\(137\) 14.8496 1.26868 0.634342 0.773052i \(-0.281271\pi\)
0.634342 + 0.773052i \(0.281271\pi\)
\(138\) 0 0
\(139\) 4.99694i 0.423835i −0.977288 0.211918i \(-0.932029\pi\)
0.977288 0.211918i \(-0.0679708\pi\)
\(140\) −5.40724 2.90410i −0.456995 0.245441i
\(141\) 0 0
\(142\) 1.44063 + 2.40899i 0.120895 + 0.202158i
\(143\) 20.4676 1.71159
\(144\) 0 0
\(145\) −3.72542 −0.309379
\(146\) 4.73886 + 7.92422i 0.392191 + 0.655813i
\(147\) 0 0
\(148\) 8.63775 + 4.63914i 0.710019 + 0.381335i
\(149\) 9.54688i 0.782111i 0.920367 + 0.391055i \(0.127890\pi\)
−0.920367 + 0.391055i \(0.872110\pi\)
\(150\) 0 0
\(151\) −11.4778 −0.934052 −0.467026 0.884244i \(-0.654675\pi\)
−0.467026 + 0.884244i \(0.654675\pi\)
\(152\) 0.688981 + 14.9357i 0.0558837 + 1.21144i
\(153\) 0 0
\(154\) −7.04962 + 4.21584i −0.568075 + 0.339722i
\(155\) 0.329550i 0.0264701i
\(156\) 0 0
\(157\) 1.38325i 0.110396i 0.998475 + 0.0551979i \(0.0175790\pi\)
−0.998475 + 0.0551979i \(0.982421\pi\)
\(158\) −1.67482 2.80059i −0.133241 0.222803i
\(159\) 0 0
\(160\) 15.6562 + 7.50055i 1.23773 + 0.592971i
\(161\) −5.65085 −0.445349
\(162\) 0 0
\(163\) 10.0101i 0.784050i −0.919955 0.392025i \(-0.871775\pi\)
0.919955 0.392025i \(-0.128225\pi\)
\(164\) −11.0581 + 20.5894i −0.863491 + 1.60776i
\(165\) 0 0
\(166\) −15.2682 + 9.13074i −1.18504 + 0.708683i
\(167\) −1.63373 −0.126422 −0.0632110 0.998000i \(-0.520134\pi\)
−0.0632110 + 0.998000i \(0.520134\pi\)
\(168\) 0 0
\(169\) 0.581993 0.0447687
\(170\) −25.3188 + 15.1413i −1.94187 + 1.16128i
\(171\) 0 0
\(172\) 3.27167 + 1.75714i 0.249463 + 0.133981i
\(173\) 3.93513i 0.299182i −0.988748 0.149591i \(-0.952204\pi\)
0.988748 0.149591i \(-0.0477957\pi\)
\(174\) 0 0
\(175\) 4.41801 0.333970
\(176\) 19.3687 12.8303i 1.45997 0.967124i
\(177\) 0 0
\(178\) −5.65540 9.45683i −0.423890 0.708819i
\(179\) 0.199235i 0.0148915i 0.999972 + 0.00744577i \(0.00237008\pi\)
−0.999972 + 0.00744577i \(0.997630\pi\)
\(180\) 0 0
\(181\) 7.14783i 0.531294i 0.964070 + 0.265647i \(0.0855855\pi\)
−0.964070 + 0.265647i \(0.914414\pi\)
\(182\) 4.27711 2.55781i 0.317040 0.189597i
\(183\) 0 0
\(184\) 15.9660 0.736512i 1.17703 0.0542964i
\(185\) −15.0447 −1.10611
\(186\) 0 0
\(187\) 39.4805i 2.88710i
\(188\) 6.40139 11.9189i 0.466869 0.869278i
\(189\) 0 0
\(190\) −11.7750 19.6899i −0.854251 1.42846i
\(191\) 17.8761 1.29347 0.646733 0.762717i \(-0.276135\pi\)
0.646733 + 0.762717i \(0.276135\pi\)
\(192\) 0 0
\(193\) −14.2993 −1.02928 −0.514642 0.857405i \(-0.672075\pi\)
−0.514642 + 0.857405i \(0.672075\pi\)
\(194\) −2.94678 4.92754i −0.211567 0.353777i
\(195\) 0 0
\(196\) −0.946308 + 1.76196i −0.0675934 + 0.125854i
\(197\) 4.13436i 0.294561i 0.989095 + 0.147280i \(0.0470520\pi\)
−0.989095 + 0.147280i \(0.952948\pi\)
\(198\) 0 0
\(199\) 14.5173 1.02910 0.514550 0.857460i \(-0.327959\pi\)
0.514550 + 0.857460i \(0.327959\pi\)
\(200\) −12.4827 + 0.575828i −0.882663 + 0.0407172i
\(201\) 0 0
\(202\) 12.5423 7.50055i 0.882470 0.527737i
\(203\) 1.21394i 0.0852015i
\(204\) 0 0
\(205\) 35.8614i 2.50467i
\(206\) −6.49395 10.8590i −0.452455 0.756585i
\(207\) 0 0
\(208\) −11.7513 + 7.78435i −0.814803 + 0.539748i
\(209\) −30.7031 −2.12378
\(210\) 0 0
\(211\) 13.9076i 0.957439i 0.877968 + 0.478719i \(0.158899\pi\)
−0.877968 + 0.478719i \(0.841101\pi\)
\(212\) 20.2380 + 10.8693i 1.38995 + 0.746509i
\(213\) 0 0
\(214\) −21.7070 + 12.9813i −1.48386 + 0.887383i
\(215\) −5.69841 −0.388628
\(216\) 0 0
\(217\) −0.107385 −0.00728974
\(218\) −14.5175 + 8.68179i −0.983248 + 0.588005i
\(219\) 0 0
\(220\) −16.8676 + 31.4063i −1.13721 + 2.11742i
\(221\) 23.9534i 1.61128i
\(222\) 0 0
\(223\) −12.1591 −0.814231 −0.407115 0.913377i \(-0.633465\pi\)
−0.407115 + 0.913377i \(0.633465\pi\)
\(224\) 2.44407 5.10162i 0.163301 0.340866i
\(225\) 0 0
\(226\) −9.66766 16.1660i −0.643083 1.07535i
\(227\) 24.4059i 1.61987i −0.586517 0.809937i \(-0.699501\pi\)
0.586517 0.809937i \(-0.300499\pi\)
\(228\) 0 0
\(229\) 1.95033i 0.128881i −0.997922 0.0644407i \(-0.979474\pi\)
0.997922 0.0644407i \(-0.0205263\pi\)
\(230\) −21.0483 + 12.5874i −1.38788 + 0.829986i
\(231\) 0 0
\(232\) −0.158220 3.42988i −0.0103877 0.225183i
\(233\) −16.3094 −1.06847 −0.534233 0.845337i \(-0.679400\pi\)
−0.534233 + 0.845337i \(0.679400\pi\)
\(234\) 0 0
\(235\) 20.7597i 1.35421i
\(236\) −13.8401 7.43319i −0.900913 0.483860i
\(237\) 0 0
\(238\) 4.93381 + 8.25020i 0.319811 + 0.534781i
\(239\) −1.65345 −0.106953 −0.0534764 0.998569i \(-0.517030\pi\)
−0.0534764 + 0.998569i \(0.517030\pi\)
\(240\) 0 0
\(241\) 3.63938 0.234433 0.117217 0.993106i \(-0.462603\pi\)
0.117217 + 0.993106i \(0.462603\pi\)
\(242\) 16.5022 + 27.5946i 1.06080 + 1.77385i
\(243\) 0 0
\(244\) −21.2414 11.4083i −1.35984 0.730341i
\(245\) 3.06888i 0.196063i
\(246\) 0 0
\(247\) 18.6280 1.18527
\(248\) 0.303407 0.0139961i 0.0192664 0.000888756i
\(249\) 0 0
\(250\) −2.16781 + 1.29640i −0.137104 + 0.0819916i
\(251\) 25.2386i 1.59305i 0.604607 + 0.796524i \(0.293330\pi\)
−0.604607 + 0.796524i \(0.706670\pi\)
\(252\) 0 0
\(253\) 32.8213i 2.06346i
\(254\) 5.38676 + 9.00762i 0.337996 + 0.565188i
\(255\) 0 0
\(256\) −6.24061 + 14.7328i −0.390038 + 0.920799i
\(257\) 14.2051 0.886087 0.443044 0.896500i \(-0.353899\pi\)
0.443044 + 0.896500i \(0.353899\pi\)
\(258\) 0 0
\(259\) 4.90235i 0.304617i
\(260\) 10.2338 19.0547i 0.634675 1.18172i
\(261\) 0 0
\(262\) −5.85864 + 3.50360i −0.361948 + 0.216453i
\(263\) 16.3785 1.00994 0.504971 0.863137i \(-0.331503\pi\)
0.504971 + 0.863137i \(0.331503\pi\)
\(264\) 0 0
\(265\) −35.2493 −2.16535
\(266\) −6.41601 + 3.83692i −0.393391 + 0.235257i
\(267\) 0 0
\(268\) 11.7513 + 6.31133i 0.717822 + 0.385526i
\(269\) 4.73448i 0.288666i −0.989529 0.144333i \(-0.953896\pi\)
0.989529 0.144333i \(-0.0461037\pi\)
\(270\) 0 0
\(271\) 20.3680 1.23727 0.618634 0.785679i \(-0.287686\pi\)
0.618634 + 0.785679i \(0.287686\pi\)
\(272\) −15.0154 22.6672i −0.910442 1.37440i
\(273\) 0 0
\(274\) −10.7784 18.0234i −0.651149 1.08884i
\(275\) 25.6607i 1.54740i
\(276\) 0 0
\(277\) 29.0135i 1.74325i 0.490170 + 0.871627i \(0.336935\pi\)
−0.490170 + 0.871627i \(0.663065\pi\)
\(278\) −6.06497 + 3.62699i −0.363753 + 0.217532i
\(279\) 0 0
\(280\) 0.399987 + 8.67087i 0.0239038 + 0.518184i
\(281\) 16.5849 0.989373 0.494687 0.869071i \(-0.335283\pi\)
0.494687 + 0.869071i \(0.335283\pi\)
\(282\) 0 0
\(283\) 21.8603i 1.29946i 0.760165 + 0.649730i \(0.225118\pi\)
−0.760165 + 0.649730i \(0.774882\pi\)
\(284\) 1.87821 3.49709i 0.111451 0.207514i
\(285\) 0 0
\(286\) −14.8563 24.8423i −0.878470 1.46896i
\(287\) −11.6855 −0.689774
\(288\) 0 0
\(289\) 29.2041 1.71789
\(290\) 2.70406 + 4.52167i 0.158788 + 0.265522i
\(291\) 0 0
\(292\) 6.17824 11.5035i 0.361554 0.673189i
\(293\) 3.59022i 0.209743i 0.994486 + 0.104872i \(0.0334431\pi\)
−0.994486 + 0.104872i \(0.966557\pi\)
\(294\) 0 0
\(295\) 24.1059 1.40350
\(296\) −0.638956 13.8512i −0.0371386 0.805086i
\(297\) 0 0
\(298\) 11.5874 6.92952i 0.671239 0.401416i
\(299\) 19.9131i 1.15161i
\(300\) 0 0
\(301\) 1.85684i 0.107026i
\(302\) 8.33108 + 13.9310i 0.479400 + 0.801641i
\(303\) 0 0
\(304\) 17.6279 11.6772i 1.01103 0.669731i
\(305\) 36.9971 2.11845
\(306\) 0 0
\(307\) 17.1418i 0.978333i 0.872191 + 0.489166i \(0.162699\pi\)
−0.872191 + 0.489166i \(0.837301\pi\)
\(308\) 10.2338 + 5.49635i 0.583126 + 0.313184i
\(309\) 0 0
\(310\) −0.399987 + 0.239201i −0.0227177 + 0.0135857i
\(311\) −21.2814 −1.20676 −0.603379 0.797454i \(-0.706180\pi\)
−0.603379 + 0.797454i \(0.706180\pi\)
\(312\) 0 0
\(313\) −7.14361 −0.403781 −0.201890 0.979408i \(-0.564708\pi\)
−0.201890 + 0.979408i \(0.564708\pi\)
\(314\) 1.67891 1.00402i 0.0947461 0.0566604i
\(315\) 0 0
\(316\) −2.18352 + 4.06556i −0.122833 + 0.228706i
\(317\) 31.4066i 1.76397i 0.471277 + 0.881986i \(0.343793\pi\)
−0.471277 + 0.881986i \(0.656207\pi\)
\(318\) 0 0
\(319\) 7.05078 0.394768
\(320\) −2.26026 24.4468i −0.126353 1.36661i
\(321\) 0 0
\(322\) 4.10162 + 6.85863i 0.228574 + 0.382217i
\(323\) 35.9320i 1.99931i
\(324\) 0 0
\(325\) 15.5687i 0.863596i
\(326\) −12.1496 + 7.26574i −0.672904 + 0.402412i
\(327\) 0 0
\(328\) 33.0165 1.52305i 1.82303 0.0840963i
\(329\) 6.76459 0.372944
\(330\) 0 0
\(331\) 11.6712i 0.641506i −0.947163 0.320753i \(-0.896064\pi\)
0.947163 0.320753i \(-0.103936\pi\)
\(332\) 22.1646 + 11.9041i 1.21644 + 0.653322i
\(333\) 0 0
\(334\) 1.18583 + 1.98292i 0.0648858 + 0.108500i
\(335\) −20.4676 −1.11827
\(336\) 0 0
\(337\) 20.4008 1.11130 0.555652 0.831415i \(-0.312469\pi\)
0.555652 + 0.831415i \(0.312469\pi\)
\(338\) −0.422435 0.706385i −0.0229774 0.0384223i
\(339\) 0 0
\(340\) 36.7550 + 19.7402i 1.99332 + 1.07056i
\(341\) 0.623712i 0.0337759i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −0.242014 5.24635i −0.0130485 0.282864i
\(345\) 0 0
\(346\) −4.77620 + 2.85628i −0.256770 + 0.153554i
\(347\) 12.5903i 0.675881i 0.941167 + 0.337940i \(0.109730\pi\)
−0.941167 + 0.337940i \(0.890270\pi\)
\(348\) 0 0
\(349\) 12.8022i 0.685286i −0.939466 0.342643i \(-0.888678\pi\)
0.939466 0.342643i \(-0.111322\pi\)
\(350\) −3.20677 5.36229i −0.171409 0.286627i
\(351\) 0 0
\(352\) −29.6312 14.1957i −1.57935 0.756631i
\(353\) −17.2495 −0.918099 −0.459050 0.888411i \(-0.651810\pi\)
−0.459050 + 0.888411i \(0.651810\pi\)
\(354\) 0 0
\(355\) 6.09103i 0.323278i
\(356\) −7.37317 + 13.7283i −0.390777 + 0.727600i
\(357\) 0 0
\(358\) 0.241819 0.144613i 0.0127805 0.00764304i
\(359\) −1.52892 −0.0806935 −0.0403468 0.999186i \(-0.512846\pi\)
−0.0403468 + 0.999186i \(0.512846\pi\)
\(360\) 0 0
\(361\) −8.94358 −0.470715
\(362\) 8.67557 5.18819i 0.455978 0.272685i
\(363\) 0 0
\(364\) −6.20900 3.33471i −0.325440 0.174786i
\(365\) 20.0360i 1.04873i
\(366\) 0 0
\(367\) −4.04525 −0.211160 −0.105580 0.994411i \(-0.533670\pi\)
−0.105580 + 0.994411i \(0.533670\pi\)
\(368\) −12.4827 18.8439i −0.650708 0.982308i
\(369\) 0 0
\(370\) 10.9201 + 18.2603i 0.567708 + 0.949309i
\(371\) 11.4861i 0.596326i
\(372\) 0 0
\(373\) 25.1416i 1.30178i −0.759171 0.650891i \(-0.774395\pi\)
0.759171 0.650891i \(-0.225605\pi\)
\(374\) 47.9188 28.6566i 2.47782 1.48180i
\(375\) 0 0
\(376\) −19.1128 + 0.881673i −0.985669 + 0.0454688i
\(377\) −4.27781 −0.220318
\(378\) 0 0
\(379\) 10.1885i 0.523349i −0.965156 0.261675i \(-0.915725\pi\)
0.965156 0.261675i \(-0.0842747\pi\)
\(380\) −15.3516 + 28.5836i −0.787519 + 1.46631i
\(381\) 0 0
\(382\) −12.9752 21.6968i −0.663868 1.11010i
\(383\) 35.9423 1.83657 0.918284 0.395923i \(-0.129575\pi\)
0.918284 + 0.395923i \(0.129575\pi\)
\(384\) 0 0
\(385\) −17.8247 −0.908429
\(386\) 10.3790 + 17.3555i 0.528278 + 0.883373i
\(387\) 0 0
\(388\) −3.84183 + 7.15323i −0.195039 + 0.363150i
\(389\) 6.81471i 0.345519i 0.984964 + 0.172760i \(0.0552684\pi\)
−0.984964 + 0.172760i \(0.944732\pi\)
\(390\) 0 0
\(391\) 38.4108 1.94252
\(392\) 2.82542 0.130337i 0.142705 0.00658299i
\(393\) 0 0
\(394\) 5.01802 3.00089i 0.252804 0.151183i
\(395\) 7.08116i 0.356292i
\(396\) 0 0
\(397\) 11.1982i 0.562021i 0.959705 + 0.281010i \(0.0906695\pi\)
−0.959705 + 0.281010i \(0.909330\pi\)
\(398\) −10.5372 17.6201i −0.528184 0.883216i
\(399\) 0 0
\(400\) 9.75939 + 14.7328i 0.487970 + 0.736639i
\(401\) 29.9404 1.49515 0.747577 0.664175i \(-0.231217\pi\)
0.747577 + 0.664175i \(0.231217\pi\)
\(402\) 0 0
\(403\) 0.378415i 0.0188502i
\(404\) −18.2074 9.77876i −0.905851 0.486512i
\(405\) 0 0
\(406\) 1.47340 0.881125i 0.0731234 0.0437295i
\(407\) 28.4739 1.41140
\(408\) 0 0
\(409\) −11.0213 −0.544968 −0.272484 0.962160i \(-0.587845\pi\)
−0.272484 + 0.962160i \(0.587845\pi\)
\(410\) −43.5262 + 26.0297i −2.14961 + 1.28551i
\(411\) 0 0
\(412\) −8.46642 + 15.7639i −0.417110 + 0.776631i
\(413\) 7.85494i 0.386516i
\(414\) 0 0
\(415\) −38.6050 −1.89505
\(416\) 17.9777 + 8.61271i 0.881429 + 0.422273i
\(417\) 0 0
\(418\) 22.2856 + 37.2655i 1.09003 + 1.82272i
\(419\) 14.0133i 0.684594i −0.939592 0.342297i \(-0.888795\pi\)
0.939592 0.342297i \(-0.111205\pi\)
\(420\) 0 0
\(421\) 19.4716i 0.948988i 0.880259 + 0.474494i \(0.157369\pi\)
−0.880259 + 0.474494i \(0.842631\pi\)
\(422\) 16.8801 10.0947i 0.821713 0.491403i
\(423\) 0 0
\(424\) −1.49705 32.4529i −0.0727033 1.57605i
\(425\) −30.0308 −1.45671
\(426\) 0 0
\(427\) 12.0556i 0.583410i
\(428\) 31.5117 + 16.9242i 1.52318 + 0.818063i
\(429\) 0 0
\(430\) 4.13614 + 6.91636i 0.199462 + 0.333536i
\(431\) −37.2120 −1.79244 −0.896219 0.443612i \(-0.853697\pi\)
−0.896219 + 0.443612i \(0.853697\pi\)
\(432\) 0 0
\(433\) −23.4042 −1.12474 −0.562368 0.826887i \(-0.690109\pi\)
−0.562368 + 0.826887i \(0.690109\pi\)
\(434\) 0.0779442 + 0.130337i 0.00374144 + 0.00625635i
\(435\) 0 0
\(436\) 21.0748 + 11.3188i 1.00930 + 0.542071i
\(437\) 29.8713i 1.42894i
\(438\) 0 0
\(439\) 21.7533 1.03823 0.519115 0.854705i \(-0.326262\pi\)
0.519115 + 0.854705i \(0.326262\pi\)
\(440\) 50.3622 2.32321i 2.40092 0.110754i
\(441\) 0 0
\(442\) −29.0730 + 17.3863i −1.38286 + 0.826984i
\(443\) 12.8369i 0.609901i −0.952368 0.304951i \(-0.901360\pi\)
0.952368 0.304951i \(-0.0986400\pi\)
\(444\) 0 0
\(445\) 23.9112i 1.13350i
\(446\) 8.82555 + 14.7579i 0.417902 + 0.698806i
\(447\) 0 0
\(448\) −7.96602 + 0.736512i −0.376359 + 0.0347969i
\(449\) −11.7889 −0.556353 −0.278176 0.960530i \(-0.589730\pi\)
−0.278176 + 0.960530i \(0.589730\pi\)
\(450\) 0 0
\(451\) 67.8718i 3.19596i
\(452\) −12.6041 + 23.4680i −0.592847 + 1.10384i
\(453\) 0 0
\(454\) −29.6223 + 17.7148i −1.39024 + 0.831397i
\(455\) 10.8145 0.506990
\(456\) 0 0
\(457\) −33.5157 −1.56780 −0.783900 0.620888i \(-0.786772\pi\)
−0.783900 + 0.620888i \(0.786772\pi\)
\(458\) −2.36718 + 1.41563i −0.110611 + 0.0661480i
\(459\) 0 0
\(460\) 30.5555 + 16.4106i 1.42466 + 0.765150i
\(461\) 10.0902i 0.469946i 0.972002 + 0.234973i \(0.0755002\pi\)
−0.972002 + 0.234973i \(0.924500\pi\)
\(462\) 0 0
\(463\) −23.6131 −1.09739 −0.548697 0.836021i \(-0.684876\pi\)
−0.548697 + 0.836021i \(0.684876\pi\)
\(464\) −4.04812 + 2.68159i −0.187929 + 0.124490i
\(465\) 0 0
\(466\) 11.8381 + 19.7953i 0.548388 + 0.917001i
\(467\) 2.52944i 0.117048i 0.998286 + 0.0585242i \(0.0186395\pi\)
−0.998286 + 0.0585242i \(0.981361\pi\)
\(468\) 0 0
\(469\) 6.66942i 0.307965i
\(470\) 25.1968 15.0683i 1.16224 0.695047i
\(471\) 0 0
\(472\) 1.02379 + 22.1935i 0.0471236 + 1.02154i
\(473\) 10.7849 0.495890
\(474\) 0 0
\(475\) 23.3543i 1.07157i
\(476\) 6.43240 11.9767i 0.294828 0.548950i
\(477\) 0 0
\(478\) 1.20014 + 2.00685i 0.0548933 + 0.0917912i
\(479\) 15.1106 0.690421 0.345210 0.938525i \(-0.387808\pi\)
0.345210 + 0.938525i \(0.387808\pi\)
\(480\) 0 0
\(481\) −17.2755 −0.787695
\(482\) −2.64161 4.41725i −0.120322 0.201200i
\(483\) 0 0
\(484\) 21.5145 40.0586i 0.977933 1.82084i
\(485\) 12.4591i 0.565737i
\(486\) 0 0
\(487\) 41.1541 1.86487 0.932436 0.361335i \(-0.117679\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(488\) 1.57128 + 34.0621i 0.0711286 + 1.54192i
\(489\) 0 0
\(490\) −3.72481 + 2.22752i −0.168270 + 0.100629i
\(491\) 36.6868i 1.65565i 0.560984 + 0.827827i \(0.310423\pi\)
−0.560984 + 0.827827i \(0.689577\pi\)
\(492\) 0 0
\(493\) 8.25156i 0.371631i
\(494\) −13.5210 22.6095i −0.608339 1.01725i
\(495\) 0 0
\(496\) −0.237213 0.358097i −0.0106512 0.0160790i
\(497\) 1.98478 0.0890294
\(498\) 0 0
\(499\) 20.1824i 0.903489i −0.892147 0.451744i \(-0.850802\pi\)
0.892147 0.451744i \(-0.149198\pi\)
\(500\) 3.14697 + 1.69017i 0.140737 + 0.0755866i
\(501\) 0 0
\(502\) 30.6330 18.3192i 1.36722 0.817628i
\(503\) −10.5011 −0.468222 −0.234111 0.972210i \(-0.575218\pi\)
−0.234111 + 0.972210i \(0.575218\pi\)
\(504\) 0 0
\(505\) 31.7125 1.41119
\(506\) 39.8363 23.8230i 1.77094 1.05906i
\(507\) 0 0
\(508\) 7.02293 13.0762i 0.311592 0.580163i
\(509\) 28.5910i 1.26727i −0.773630 0.633637i \(-0.781561\pi\)
0.773630 0.633637i \(-0.218439\pi\)
\(510\) 0 0
\(511\) 6.52879 0.288816
\(512\) 22.4114 3.11922i 0.990453 0.137851i
\(513\) 0 0
\(514\) −10.3106 17.2412i −0.454782 0.760476i
\(515\) 27.4566i 1.20988i
\(516\) 0 0
\(517\) 39.2901i 1.72798i
\(518\) 5.95016 3.55833i 0.261435 0.156344i
\(519\) 0 0
\(520\) −30.5555 + 1.40952i −1.33995 + 0.0618116i
\(521\) −10.8325 −0.474578 −0.237289 0.971439i \(-0.576259\pi\)
−0.237289 + 0.971439i \(0.576259\pi\)
\(522\) 0 0
\(523\) 1.77247i 0.0775047i −0.999249 0.0387523i \(-0.987662\pi\)
0.999249 0.0387523i \(-0.0123383\pi\)
\(524\) 8.50489 + 4.56778i 0.371538 + 0.199544i
\(525\) 0 0
\(526\) −11.8882 19.8792i −0.518350 0.866772i
\(527\) 0.729932 0.0317963
\(528\) 0 0
\(529\) 8.93205 0.388350
\(530\) 25.5854 + 42.7833i 1.11136 + 1.85839i
\(531\) 0 0
\(532\) 9.31402 + 5.00234i 0.403814 + 0.216879i
\(533\) 41.1788i 1.78365i
\(534\) 0 0
\(535\) −54.8853 −2.37290
\(536\) −0.869270 18.8439i −0.0375467 0.813934i
\(537\) 0 0
\(538\) −5.74641 + 3.43648i −0.247745 + 0.148157i
\(539\) 5.80820i 0.250177i
\(540\) 0 0
\(541\) 11.0556i 0.475316i 0.971349 + 0.237658i \(0.0763797\pi\)
−0.971349 + 0.237658i \(0.923620\pi\)
\(542\) −14.7840 24.7214i −0.635025 1.06187i
\(543\) 0 0
\(544\) −16.6132 + 34.6776i −0.712287 + 1.48679i
\(545\) −36.7068 −1.57235
\(546\) 0 0
\(547\) 5.55978i 0.237719i −0.992911 0.118859i \(-0.962076\pi\)
0.992911 0.118859i \(-0.0379238\pi\)
\(548\) −14.0523 + 26.1643i −0.600283 + 1.11769i
\(549\) 0 0
\(550\) −31.1453 + 18.6256i −1.32804 + 0.794198i
\(551\) 6.41707 0.273376
\(552\) 0 0
\(553\) −2.30741 −0.0981211
\(554\) 35.2147 21.0592i 1.49613 0.894720i
\(555\) 0 0
\(556\) 8.80441 + 4.72865i 0.373390 + 0.200539i
\(557\) 4.30560i 0.182434i −0.995831 0.0912171i \(-0.970924\pi\)
0.995831 0.0912171i \(-0.0290757\pi\)
\(558\) 0 0
\(559\) −6.54335 −0.276754
\(560\) 10.2338 6.77916i 0.432458 0.286472i
\(561\) 0 0
\(562\) −12.0380 20.1297i −0.507793 0.849120i
\(563\) 2.43447i 0.102601i 0.998683 + 0.0513003i \(0.0163366\pi\)
−0.998683 + 0.0513003i \(0.983663\pi\)
\(564\) 0 0
\(565\) 40.8751i 1.71963i
\(566\) 26.5326 15.8671i 1.11525 0.666944i
\(567\) 0 0
\(568\) −5.60783 + 0.258689i −0.235299 + 0.0108543i
\(569\) −10.9163 −0.457635 −0.228818 0.973469i \(-0.573486\pi\)
−0.228818 + 0.973469i \(0.573486\pi\)
\(570\) 0 0
\(571\) 11.3442i 0.474740i −0.971419 0.237370i \(-0.923715\pi\)
0.971419 0.237370i \(-0.0762854\pi\)
\(572\) −19.3687 + 36.0632i −0.809845 + 1.50788i
\(573\) 0 0
\(574\) 8.48183 + 14.1831i 0.354025 + 0.591992i
\(575\) −24.9655 −1.04113
\(576\) 0 0
\(577\) 7.97962 0.332196 0.166098 0.986109i \(-0.446883\pi\)
0.166098 + 0.986109i \(0.446883\pi\)
\(578\) −21.1976 35.4461i −0.881703 1.47436i
\(579\) 0 0
\(580\) 3.52539 6.56404i 0.146384 0.272557i
\(581\) 12.5795i 0.521887i
\(582\) 0 0
\(583\) 66.7133 2.76298
\(584\) −18.4466 + 0.850939i −0.763325 + 0.0352121i
\(585\) 0 0
\(586\) 4.35758 2.60593i 0.180010 0.107650i
\(587\) 41.7410i 1.72283i 0.507898 + 0.861417i \(0.330423\pi\)
−0.507898 + 0.861417i \(0.669577\pi\)
\(588\) 0 0
\(589\) 0.567653i 0.0233897i
\(590\) −17.4970 29.2581i −0.720341 1.20454i
\(591\) 0 0
\(592\) −16.3479 + 10.8293i −0.671896 + 0.445082i
\(593\) −4.43527 −0.182135 −0.0910673 0.995845i \(-0.529028\pi\)
−0.0910673 + 0.995845i \(0.529028\pi\)
\(594\) 0 0
\(595\) 20.8603i 0.855188i
\(596\) −16.8212 9.03429i −0.689024 0.370059i
\(597\) 0 0
\(598\) −24.1693 + 14.4538i −0.988355 + 0.591059i
\(599\) −12.4875 −0.510224 −0.255112 0.966911i \(-0.582112\pi\)
−0.255112 + 0.966911i \(0.582112\pi\)
\(600\) 0 0
\(601\) 37.1871 1.51690 0.758448 0.651734i \(-0.225958\pi\)
0.758448 + 0.651734i \(0.225958\pi\)
\(602\) 2.25371 1.34777i 0.0918544 0.0549310i
\(603\) 0 0
\(604\) 10.8615 20.2235i 0.441950 0.822881i
\(605\) 69.7716i 2.83662i
\(606\) 0 0
\(607\) −21.8403 −0.886470 −0.443235 0.896405i \(-0.646169\pi\)
−0.443235 + 0.896405i \(0.646169\pi\)
\(608\) −26.9680 12.9198i −1.09370 0.523966i
\(609\) 0 0
\(610\) −26.8540 44.9047i −1.08729 1.81814i
\(611\) 23.8379i 0.964377i
\(612\) 0 0
\(613\) 30.7687i 1.24274i 0.783519 + 0.621368i \(0.213423\pi\)
−0.783519 + 0.621368i \(0.786577\pi\)
\(614\) 20.8056 12.4422i 0.839645 0.502127i
\(615\) 0 0
\(616\) −0.757021 16.4106i −0.0305013 0.661203i
\(617\) −38.0402 −1.53144 −0.765721 0.643173i \(-0.777617\pi\)
−0.765721 + 0.643173i \(0.777617\pi\)
\(618\) 0 0
\(619\) 14.9005i 0.598903i −0.954111 0.299452i \(-0.903196\pi\)
0.954111 0.299452i \(-0.0968037\pi\)
\(620\) 0.580654 + 0.311856i 0.0233196 + 0.0125244i
\(621\) 0 0
\(622\) 15.4469 + 25.8300i 0.619366 + 1.03569i
\(623\) −7.79151 −0.312160
\(624\) 0 0
\(625\) −27.5712 −1.10285
\(626\) 5.18513 + 8.67045i 0.207239 + 0.346541i
\(627\) 0 0
\(628\) −2.43724 1.30898i −0.0972564 0.0522342i
\(629\) 33.3231i 1.32868i
\(630\) 0 0
\(631\) −26.8787 −1.07002 −0.535011 0.844845i \(-0.679693\pi\)
−0.535011 + 0.844845i \(0.679693\pi\)
\(632\) 6.51941 0.300740i 0.259328 0.0119628i
\(633\) 0 0
\(634\) 38.1193 22.7962i 1.51391 0.905354i
\(635\) 22.7754i 0.903813i
\(636\) 0 0
\(637\) 3.52392i 0.139623i
\(638\) −5.11775 8.55779i −0.202614 0.338806i
\(639\) 0 0
\(640\) −28.0313 + 20.4878i −1.10803 + 0.809853i
\(641\) 12.4910 0.493365 0.246682 0.969096i \(-0.420660\pi\)
0.246682 + 0.969096i \(0.420660\pi\)
\(642\) 0 0
\(643\) 3.53414i 0.139373i −0.997569 0.0696864i \(-0.977800\pi\)
0.997569 0.0696864i \(-0.0221999\pi\)
\(644\) 5.34744 9.95656i 0.210719 0.392343i
\(645\) 0 0
\(646\) 43.6119 26.0809i 1.71589 1.02614i
\(647\) −28.3282 −1.11370 −0.556848 0.830614i \(-0.687990\pi\)
−0.556848 + 0.830614i \(0.687990\pi\)
\(648\) 0 0
\(649\) −45.6231 −1.79086
\(650\) 18.8963 11.3004i 0.741173 0.443239i
\(651\) 0 0
\(652\) 17.6374 + 9.47262i 0.690732 + 0.370976i
\(653\) 29.9962i 1.17384i −0.809644 0.586921i \(-0.800340\pi\)
0.809644 0.586921i \(-0.199660\pi\)
\(654\) 0 0
\(655\) −14.8133 −0.578804
\(656\) −25.8133 38.9678i −1.00784 1.52144i
\(657\) 0 0
\(658\) −4.91002 8.21043i −0.191413 0.320076i
\(659\) 16.0647i 0.625793i −0.949787 0.312896i \(-0.898701\pi\)
0.949787 0.312896i \(-0.101299\pi\)
\(660\) 0 0
\(661\) 44.3984i 1.72690i 0.504435 + 0.863450i \(0.331701\pi\)
−0.504435 + 0.863450i \(0.668299\pi\)
\(662\) −14.1657 + 8.47143i −0.550567 + 0.329252i
\(663\) 0 0
\(664\) −1.63957 35.5425i −0.0636277 1.37932i
\(665\) −16.2226 −0.629086
\(666\) 0 0
\(667\) 6.85976i 0.265611i
\(668\) 1.54601 2.87857i 0.0598170 0.111375i
\(669\) 0 0
\(670\) 14.8563 + 24.8423i 0.573948 + 0.959742i
\(671\) −70.0213 −2.70314
\(672\) 0 0
\(673\) −50.0649 −1.92986 −0.964930 0.262508i \(-0.915450\pi\)
−0.964930 + 0.262508i \(0.915450\pi\)
\(674\) −14.8078 24.7612i −0.570374 0.953767i
\(675\) 0 0
\(676\) −0.550744 + 1.02545i −0.0211825 + 0.0394403i
\(677\) 30.1370i 1.15826i 0.815236 + 0.579129i \(0.196607\pi\)
−0.815236 + 0.579129i \(0.803393\pi\)
\(678\) 0 0
\(679\) −4.05981 −0.155801
\(680\) −2.71886 58.9391i −0.104263 2.26021i
\(681\) 0 0
\(682\) 0.757021 0.452716i 0.0289878 0.0173354i
\(683\) 1.49520i 0.0572124i 0.999591 + 0.0286062i \(0.00910688\pi\)
−0.999591 + 0.0286062i \(0.990893\pi\)
\(684\) 0 0
\(685\) 45.5715i 1.74120i
\(686\) 0.725842 + 1.21374i 0.0277128 + 0.0463406i
\(687\) 0 0
\(688\) −6.19202 + 4.10176i −0.236069 + 0.156378i
\(689\) −40.4759 −1.54201
\(690\) 0 0
\(691\) 0.438347i 0.0166755i −0.999965 0.00833774i \(-0.997346\pi\)
0.999965 0.00833774i \(-0.00265402\pi\)
\(692\) 6.93353 + 3.72384i 0.263573 + 0.141559i
\(693\) 0 0
\(694\) 15.2813 9.13854i 0.580068 0.346894i
\(695\) −15.3350 −0.581690
\(696\) 0 0
\(697\) 79.4306 3.00865
\(698\) −15.5385 + 9.29236i −0.588140 + 0.351721i
\(699\) 0 0
\(700\) −4.18079 + 7.78435i −0.158019 + 0.294221i
\(701\) 43.1330i 1.62911i −0.580084 0.814556i \(-0.696980\pi\)
0.580084 0.814556i \(-0.303020\pi\)
\(702\) 0 0
\(703\) 25.9147 0.977390
\(704\) 4.27781 + 46.2683i 0.161226 + 1.74380i
\(705\) 0 0
\(706\) 12.5204 + 20.9364i 0.471212 + 0.787950i
\(707\) 10.3336i 0.388635i
\(708\) 0 0
\(709\) 30.8542i 1.15875i −0.815060 0.579376i \(-0.803296\pi\)
0.815060 0.579376i \(-0.196704\pi\)
\(710\) 7.39290 4.42113i 0.277451 0.165922i
\(711\) 0 0
\(712\) 22.0143 1.01552i 0.825021 0.0380582i
\(713\) 0.606814 0.0227254
\(714\) 0 0
\(715\) 62.8127i 2.34906i
\(716\) −0.351044 0.188538i −0.0131191 0.00704599i
\(717\) 0 0
\(718\) 1.10976 + 1.85571i 0.0414158 + 0.0692544i
\(719\) −2.24406 −0.0836895 −0.0418447 0.999124i \(-0.513323\pi\)
−0.0418447 + 0.999124i \(0.513323\pi\)
\(720\) 0 0
\(721\) −8.94679 −0.333196
\(722\) 6.49162 + 10.8551i 0.241593 + 0.403987i
\(723\) 0 0
\(724\) −12.5942 6.76404i −0.468059 0.251384i
\(725\) 5.36317i 0.199183i
\(726\) 0 0
\(727\) −16.9794 −0.629733 −0.314866 0.949136i \(-0.601960\pi\)
−0.314866 + 0.949136i \(0.601960\pi\)
\(728\) 0.459295 + 9.95656i 0.0170226 + 0.369015i
\(729\) 0 0
\(730\) 24.3185 14.5430i 0.900066 0.538260i
\(731\) 12.6216i 0.466827i
\(732\) 0 0
\(733\) 34.0255i 1.25676i 0.777906 + 0.628380i \(0.216282\pi\)
−0.777906 + 0.628380i \(0.783718\pi\)
\(734\) 2.93621 + 4.90987i 0.108378 + 0.181226i
\(735\) 0 0
\(736\) −13.8111 + 28.8285i −0.509083 + 1.06263i
\(737\) 38.7374 1.42691
\(738\) 0 0
\(739\) 0.0107994i 0.000397263i 1.00000 0.000198632i \(6.32264e-5\pi\)
−1.00000 0.000198632i \(0.999937\pi\)
\(740\) 14.2369 26.5082i 0.523360 0.974461i
\(741\) 0 0
\(742\) 13.9410 8.33705i 0.511791 0.306063i
\(743\) −45.6360 −1.67422 −0.837112 0.547032i \(-0.815758\pi\)
−0.837112 + 0.547032i \(0.815758\pi\)
\(744\) 0 0
\(745\) 29.2982 1.07340
\(746\) −30.5152 + 18.2488i −1.11724 + 0.668137i
\(747\) 0 0
\(748\) −69.5630 37.3607i −2.54347 1.36604i
\(749\) 17.8845i 0.653485i
\(750\) 0 0
\(751\) −3.95000 −0.144138 −0.0720688 0.997400i \(-0.522960\pi\)
−0.0720688 + 0.997400i \(0.522960\pi\)
\(752\) 14.9430 + 22.5580i 0.544915 + 0.822604i
\(753\) 0 0
\(754\) 3.10501 + 5.19213i 0.113078 + 0.189086i
\(755\) 35.2240i 1.28193i
\(756\) 0 0
\(757\) 18.6412i 0.677524i −0.940872 0.338762i \(-0.889992\pi\)
0.940872 0.338762i \(-0.110008\pi\)
\(758\) −12.3662 + 7.39525i −0.449160 + 0.268608i
\(759\) 0 0
\(760\) 45.8357 2.11440i 1.66264 0.0766973i
\(761\) −4.86842 −0.176480 −0.0882401 0.996099i \(-0.528124\pi\)
−0.0882401 + 0.996099i \(0.528124\pi\)
\(762\) 0 0
\(763\) 11.9610i 0.433017i
\(764\) −16.9162 + 31.4969i −0.612008 + 1.13952i
\(765\) 0 0
\(766\) −26.0884 43.6245i −0.942614 1.57622i
\(767\) 27.6802 0.999473
\(768\) 0 0
\(769\) −1.48442 −0.0535297 −0.0267649 0.999642i \(-0.508521\pi\)
−0.0267649 + 0.999642i \(0.508521\pi\)
\(770\) 12.9379 + 21.6344i 0.466249 + 0.779651i
\(771\) 0 0
\(772\) 13.5315 25.1947i 0.487010 0.906779i
\(773\) 14.2868i 0.513861i 0.966430 + 0.256931i \(0.0827112\pi\)
−0.966430 + 0.256931i \(0.917289\pi\)
\(774\) 0 0
\(775\) −0.474426 −0.0170419
\(776\) 11.4707 0.529142i 0.411774 0.0189951i
\(777\) 0 0
\(778\) 8.27125 4.94640i 0.296539 0.177337i
\(779\) 61.7716i 2.21320i
\(780\) 0 0
\(781\) 11.5280i 0.412504i
\(782\) −27.8802 46.6206i −0.996993 1.66715i
\(783\) 0 0
\(784\) −2.20900 3.33471i −0.0788930 0.119097i
\(785\) 4.24504 0.151512
\(786\) 0 0
\(78