Properties

Label 72.3.h.a.53.8
Level $72$
Weight $3$
Character 72.53
Analytic conductor $1.962$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.33808912384.2
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 18 x^{5} + 47 x^{4} - 28 x^{3} - 44 x^{2} + 48 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 53.8
Root \(-0.651388 + 0.158947i\) of defining polynomial
Character \(\chi\) \(=\) 72.53
Dual form 72.3.h.a.53.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.77521 + 0.921201i) q^{2} +(2.30278 + 3.27066i) q^{4} -1.07498 q^{5} +7.21110 q^{7} +(1.07498 + 7.92745i) q^{8} +O(q^{10})\) \(q+(1.77521 + 0.921201i) q^{2} +(2.30278 + 3.27066i) q^{4} -1.07498 q^{5} +7.21110 q^{7} +(1.07498 + 7.92745i) q^{8} +(-1.90833 - 0.990277i) q^{10} -16.3517 q^{11} -21.6045i q^{13} +(12.8013 + 6.64288i) q^{14} +(-5.39445 + 15.0632i) q^{16} -18.9819i q^{17} +17.0438i q^{19} +(-2.47545 - 3.51591i) q^{20} +(-29.0278 - 15.0632i) q^{22} -1.11567i q^{23} -23.8444 q^{25} +(19.9021 - 38.3527i) q^{26} +(16.6056 + 23.5851i) q^{28} +29.4784 q^{29} +5.63331 q^{31} +(-23.4525 + 21.7710i) q^{32} +(17.4861 - 33.6969i) q^{34} -7.75182 q^{35} -17.0438i q^{37} +(-15.7007 + 30.2563i) q^{38} +(-1.15559 - 8.52188i) q^{40} +27.4671i q^{41} +52.3306i q^{43} +(-37.6543 - 53.4808i) q^{44} +(1.02776 - 1.98055i) q^{46} +64.5352i q^{47} +3.00000 q^{49} +(-42.3290 - 21.9655i) q^{50} +(70.6611 - 49.7504i) q^{52} +35.9283 q^{53} +17.5778 q^{55} +(7.75182 + 57.1656i) q^{56} +(52.3305 + 27.1556i) q^{58} +56.8069 q^{59} +69.3743i q^{61} +(10.0003 + 5.18941i) q^{62} +(-61.6888 + 17.0438i) q^{64} +23.2245i q^{65} -69.3743i q^{67} +(62.0832 - 43.7110i) q^{68} +(-13.7611 - 7.14099i) q^{70} -98.4764i q^{71} +37.6888 q^{73} +(15.7007 - 30.2563i) q^{74} +(-55.7443 + 39.2479i) q^{76} -117.914 q^{77} -127.322 q^{79} +(5.79894 - 16.1927i) q^{80} +(-25.3028 + 48.7601i) q^{82} +7.75182 q^{83} +20.4052i q^{85} +(-48.2070 + 92.8980i) q^{86} +(-17.5778 - 129.627i) q^{88} -76.1475i q^{89} -155.792i q^{91} +(3.64898 - 2.56914i) q^{92} +(-59.4500 + 114.564i) q^{94} -18.3218i q^{95} +4.84441 q^{97} +(5.32564 + 2.76360i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} + 28q^{10} - 72q^{16} - 88q^{22} + 40q^{25} + 104q^{28} - 128q^{31} + 212q^{34} - 240q^{40} - 136q^{46} + 24q^{49} + 248q^{52} + 256q^{55} + 260q^{58} - 32q^{64} - 312q^{70} - 160q^{73} + 304q^{76} - 384q^{79} - 188q^{82} - 256q^{88} - 216q^{94} - 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.77521 + 0.921201i 0.887607 + 0.460601i
\(3\) 0 0
\(4\) 2.30278 + 3.27066i 0.575694 + 0.817665i
\(5\) −1.07498 −0.214997 −0.107498 0.994205i \(-0.534284\pi\)
−0.107498 + 0.994205i \(0.534284\pi\)
\(6\) 0 0
\(7\) 7.21110 1.03016 0.515079 0.857143i \(-0.327763\pi\)
0.515079 + 0.857143i \(0.327763\pi\)
\(8\) 1.07498 + 7.92745i 0.134373 + 0.990931i
\(9\) 0 0
\(10\) −1.90833 0.990277i −0.190833 0.0990277i
\(11\) −16.3517 −1.48652 −0.743258 0.669004i \(-0.766721\pi\)
−0.743258 + 0.669004i \(0.766721\pi\)
\(12\) 0 0
\(13\) 21.6045i 1.66189i −0.556357 0.830943i \(-0.687801\pi\)
0.556357 0.830943i \(-0.312199\pi\)
\(14\) 12.8013 + 6.64288i 0.914375 + 0.474491i
\(15\) 0 0
\(16\) −5.39445 + 15.0632i −0.337153 + 0.941450i
\(17\) 18.9819i 1.11658i −0.829646 0.558290i \(-0.811458\pi\)
0.829646 0.558290i \(-0.188542\pi\)
\(18\) 0 0
\(19\) 17.0438i 0.897040i 0.893773 + 0.448520i \(0.148049\pi\)
−0.893773 + 0.448520i \(0.851951\pi\)
\(20\) −2.47545 3.51591i −0.123772 0.175795i
\(21\) 0 0
\(22\) −29.0278 15.0632i −1.31944 0.684691i
\(23\) 1.11567i 0.0485074i −0.999706 0.0242537i \(-0.992279\pi\)
0.999706 0.0242537i \(-0.00772094\pi\)
\(24\) 0 0
\(25\) −23.8444 −0.953776
\(26\) 19.9021 38.3527i 0.765466 1.47510i
\(27\) 0 0
\(28\) 16.6056 + 23.5851i 0.593055 + 0.842324i
\(29\) 29.4784 1.01650 0.508249 0.861210i \(-0.330293\pi\)
0.508249 + 0.861210i \(0.330293\pi\)
\(30\) 0 0
\(31\) 5.63331 0.181720 0.0908598 0.995864i \(-0.471038\pi\)
0.0908598 + 0.995864i \(0.471038\pi\)
\(32\) −23.4525 + 21.7710i −0.732892 + 0.680345i
\(33\) 0 0
\(34\) 17.4861 33.6969i 0.514298 0.991085i
\(35\) −7.75182 −0.221480
\(36\) 0 0
\(37\) 17.0438i 0.460642i −0.973115 0.230321i \(-0.926022\pi\)
0.973115 0.230321i \(-0.0739776\pi\)
\(38\) −15.7007 + 30.2563i −0.413177 + 0.796219i
\(39\) 0 0
\(40\) −1.15559 8.52188i −0.0288897 0.213047i
\(41\) 27.4671i 0.669930i 0.942231 + 0.334965i \(0.108725\pi\)
−0.942231 + 0.334965i \(0.891275\pi\)
\(42\) 0 0
\(43\) 52.3306i 1.21699i 0.793558 + 0.608495i \(0.208226\pi\)
−0.793558 + 0.608495i \(0.791774\pi\)
\(44\) −37.6543 53.4808i −0.855779 1.21547i
\(45\) 0 0
\(46\) 1.02776 1.98055i 0.0223425 0.0430555i
\(47\) 64.5352i 1.37309i 0.727087 + 0.686545i \(0.240874\pi\)
−0.727087 + 0.686545i \(0.759126\pi\)
\(48\) 0 0
\(49\) 3.00000 0.0612245
\(50\) −42.3290 21.9655i −0.846579 0.439310i
\(51\) 0 0
\(52\) 70.6611 49.7504i 1.35887 0.956738i
\(53\) 35.9283 0.677893 0.338946 0.940806i \(-0.389929\pi\)
0.338946 + 0.940806i \(0.389929\pi\)
\(54\) 0 0
\(55\) 17.5778 0.319596
\(56\) 7.75182 + 57.1656i 0.138425 + 1.02081i
\(57\) 0 0
\(58\) 52.3305 + 27.1556i 0.902251 + 0.468199i
\(59\) 56.8069 0.962828 0.481414 0.876493i \(-0.340123\pi\)
0.481414 + 0.876493i \(0.340123\pi\)
\(60\) 0 0
\(61\) 69.3743i 1.13728i 0.822585 + 0.568642i \(0.192531\pi\)
−0.822585 + 0.568642i \(0.807469\pi\)
\(62\) 10.0003 + 5.18941i 0.161296 + 0.0837002i
\(63\) 0 0
\(64\) −61.6888 + 17.0438i −0.963888 + 0.266309i
\(65\) 23.2245i 0.357300i
\(66\) 0 0
\(67\) 69.3743i 1.03544i −0.855551 0.517719i \(-0.826781\pi\)
0.855551 0.517719i \(-0.173219\pi\)
\(68\) 62.0832 43.7110i 0.912989 0.642808i
\(69\) 0 0
\(70\) −13.7611 7.14099i −0.196588 0.102014i
\(71\) 98.4764i 1.38699i −0.720461 0.693496i \(-0.756070\pi\)
0.720461 0.693496i \(-0.243930\pi\)
\(72\) 0 0
\(73\) 37.6888 0.516285 0.258143 0.966107i \(-0.416890\pi\)
0.258143 + 0.966107i \(0.416890\pi\)
\(74\) 15.7007 30.2563i 0.212172 0.408869i
\(75\) 0 0
\(76\) −55.7443 + 39.2479i −0.733478 + 0.516420i
\(77\) −117.914 −1.53135
\(78\) 0 0
\(79\) −127.322 −1.61167 −0.805836 0.592138i \(-0.798284\pi\)
−0.805836 + 0.592138i \(0.798284\pi\)
\(80\) 5.79894 16.1927i 0.0724868 0.202409i
\(81\) 0 0
\(82\) −25.3028 + 48.7601i −0.308570 + 0.594635i
\(83\) 7.75182 0.0933954 0.0466977 0.998909i \(-0.485130\pi\)
0.0466977 + 0.998909i \(0.485130\pi\)
\(84\) 0 0
\(85\) 20.4052i 0.240061i
\(86\) −48.2070 + 92.8980i −0.560547 + 1.08021i
\(87\) 0 0
\(88\) −17.5778 129.627i −0.199748 1.47304i
\(89\) 76.1475i 0.855590i −0.903876 0.427795i \(-0.859291\pi\)
0.903876 0.427795i \(-0.140709\pi\)
\(90\) 0 0
\(91\) 155.792i 1.71200i
\(92\) 3.64898 2.56914i 0.0396628 0.0279254i
\(93\) 0 0
\(94\) −59.4500 + 114.564i −0.632446 + 1.21877i
\(95\) 18.3218i 0.192861i
\(96\) 0 0
\(97\) 4.84441 0.0499424 0.0249712 0.999688i \(-0.492051\pi\)
0.0249712 + 0.999688i \(0.492051\pi\)
\(98\) 5.32564 + 2.76360i 0.0543433 + 0.0282000i
\(99\) 0 0
\(100\) −54.9083 77.9870i −0.549083 0.779870i
\(101\) −105.635 −1.04589 −0.522946 0.852366i \(-0.675167\pi\)
−0.522946 + 0.852366i \(0.675167\pi\)
\(102\) 0 0
\(103\) 104.789 1.01737 0.508684 0.860953i \(-0.330132\pi\)
0.508684 + 0.860953i \(0.330132\pi\)
\(104\) 171.269 23.2245i 1.64681 0.223313i
\(105\) 0 0
\(106\) 63.7805 + 33.0972i 0.601703 + 0.312238i
\(107\) −65.4067 −0.611278 −0.305639 0.952147i \(-0.598870\pi\)
−0.305639 + 0.952147i \(0.598870\pi\)
\(108\) 0 0
\(109\) 3.36144i 0.0308389i 0.999881 + 0.0154195i \(0.00490836\pi\)
−0.999881 + 0.0154195i \(0.995092\pi\)
\(110\) 31.2044 + 16.1927i 0.283676 + 0.147206i
\(111\) 0 0
\(112\) −38.8999 + 108.622i −0.347321 + 0.969842i
\(113\) 84.1927i 0.745068i 0.928019 + 0.372534i \(0.121511\pi\)
−0.928019 + 0.372534i \(0.878489\pi\)
\(114\) 0 0
\(115\) 1.19933i 0.0104289i
\(116\) 67.8822 + 96.4139i 0.585191 + 0.831155i
\(117\) 0 0
\(118\) 100.844 + 52.3306i 0.854614 + 0.443479i
\(119\) 136.880i 1.15025i
\(120\) 0 0
\(121\) 146.378 1.20973
\(122\) −63.9077 + 123.154i −0.523834 + 1.00946i
\(123\) 0 0
\(124\) 12.9722 + 18.4246i 0.104615 + 0.148586i
\(125\) 52.5069 0.420056
\(126\) 0 0
\(127\) −45.5223 −0.358443 −0.179222 0.983809i \(-0.557358\pi\)
−0.179222 + 0.983809i \(0.557358\pi\)
\(128\) −125.212 26.5715i −0.978216 0.207590i
\(129\) 0 0
\(130\) −21.3944 + 41.2285i −0.164573 + 0.317142i
\(131\) 129.117 0.985629 0.492814 0.870134i \(-0.335968\pi\)
0.492814 + 0.870134i \(0.335968\pi\)
\(132\) 0 0
\(133\) 122.904i 0.924092i
\(134\) 63.9077 123.154i 0.476923 0.919062i
\(135\) 0 0
\(136\) 150.478 20.4052i 1.10645 0.150038i
\(137\) 10.9367i 0.0798296i 0.999203 + 0.0399148i \(0.0127087\pi\)
−0.999203 + 0.0399148i \(0.987291\pi\)
\(138\) 0 0
\(139\) 1.19933i 0.00862825i −0.999991 0.00431412i \(-0.998627\pi\)
0.999991 0.00431412i \(-0.00137323\pi\)
\(140\) −17.8507 25.3536i −0.127505 0.181097i
\(141\) 0 0
\(142\) 90.7166 174.817i 0.638849 1.23110i
\(143\) 353.270i 2.47042i
\(144\) 0 0
\(145\) −31.6888 −0.218544
\(146\) 66.9058 + 34.7190i 0.458259 + 0.237801i
\(147\) 0 0
\(148\) 55.7443 39.2479i 0.376651 0.265189i
\(149\) −29.9323 −0.200888 −0.100444 0.994943i \(-0.532026\pi\)
−0.100444 + 0.994943i \(0.532026\pi\)
\(150\) 0 0
\(151\) 61.5223 0.407432 0.203716 0.979030i \(-0.434698\pi\)
0.203716 + 0.979030i \(0.434698\pi\)
\(152\) −135.113 + 18.3218i −0.888904 + 0.120538i
\(153\) 0 0
\(154\) −209.322 108.622i −1.35923 0.705339i
\(155\) −6.05571 −0.0390691
\(156\) 0 0
\(157\) 137.549i 0.876110i −0.898948 0.438055i \(-0.855667\pi\)
0.898948 0.438055i \(-0.144333\pi\)
\(158\) −226.024 117.289i −1.43053 0.742338i
\(159\) 0 0
\(160\) 25.2111 23.4035i 0.157569 0.146272i
\(161\) 8.04521i 0.0499702i
\(162\) 0 0
\(163\) 191.079i 1.17227i 0.810215 + 0.586133i \(0.199350\pi\)
−0.810215 + 0.586133i \(0.800650\pi\)
\(164\) −89.8357 + 63.2507i −0.547779 + 0.385675i
\(165\) 0 0
\(166\) 13.7611 + 7.14099i 0.0828984 + 0.0430180i
\(167\) 233.125i 1.39596i −0.716118 0.697980i \(-0.754083\pi\)
0.716118 0.697980i \(-0.245917\pi\)
\(168\) 0 0
\(169\) −297.755 −1.76187
\(170\) −18.7973 + 36.2236i −0.110572 + 0.213080i
\(171\) 0 0
\(172\) −171.156 + 120.506i −0.995091 + 0.700614i
\(173\) 323.809 1.87173 0.935864 0.352363i \(-0.114622\pi\)
0.935864 + 0.352363i \(0.114622\pi\)
\(174\) 0 0
\(175\) −171.944 −0.982540
\(176\) 88.2083 246.309i 0.501184 1.39948i
\(177\) 0 0
\(178\) 70.1472 135.178i 0.394085 0.759428i
\(179\) −185.924 −1.03868 −0.519342 0.854567i \(-0.673823\pi\)
−0.519342 + 0.854567i \(0.673823\pi\)
\(180\) 0 0
\(181\) 126.266i 0.697600i −0.937197 0.348800i \(-0.886589\pi\)
0.937197 0.348800i \(-0.113411\pi\)
\(182\) 143.516 276.565i 0.788551 1.51959i
\(183\) 0 0
\(184\) 8.84441 1.19933i 0.0480674 0.00651808i
\(185\) 18.3218i 0.0990365i
\(186\) 0 0
\(187\) 310.385i 1.65982i
\(188\) −211.073 + 148.610i −1.12273 + 0.790480i
\(189\) 0 0
\(190\) 16.8780 32.5250i 0.0888317 0.171184i
\(191\) 233.125i 1.22055i 0.792189 + 0.610275i \(0.208941\pi\)
−0.792189 + 0.610275i \(0.791059\pi\)
\(192\) 0 0
\(193\) −117.378 −0.608174 −0.304087 0.952644i \(-0.598351\pi\)
−0.304087 + 0.952644i \(0.598351\pi\)
\(194\) 8.59987 + 4.46268i 0.0443292 + 0.0230035i
\(195\) 0 0
\(196\) 6.90833 + 9.81198i 0.0352466 + 0.0500611i
\(197\) 296.313 1.50413 0.752064 0.659091i \(-0.229059\pi\)
0.752064 + 0.659091i \(0.229059\pi\)
\(198\) 0 0
\(199\) 233.011 1.17091 0.585455 0.810705i \(-0.300916\pi\)
0.585455 + 0.810705i \(0.300916\pi\)
\(200\) −25.6324 189.025i −0.128162 0.945126i
\(201\) 0 0
\(202\) −187.525 97.3111i −0.928341 0.481738i
\(203\) 212.572 1.04715
\(204\) 0 0
\(205\) 29.5267i 0.144033i
\(206\) 186.023 + 96.5317i 0.903023 + 0.468600i
\(207\) 0 0
\(208\) 325.433 + 116.544i 1.56458 + 0.560310i
\(209\) 278.694i 1.33346i
\(210\) 0 0
\(211\) 35.2868i 0.167236i −0.996498 0.0836181i \(-0.973352\pi\)
0.996498 0.0836181i \(-0.0266476\pi\)
\(212\) 82.7349 + 117.509i 0.390259 + 0.554289i
\(213\) 0 0
\(214\) −116.111 60.2528i −0.542575 0.281555i
\(215\) 56.2545i 0.261649i
\(216\) 0 0
\(217\) 40.6224 0.187200
\(218\) −3.09657 + 5.96728i −0.0142044 + 0.0273729i
\(219\) 0 0
\(220\) 40.4777 + 57.4910i 0.183990 + 0.261323i
\(221\) −410.094 −1.85563
\(222\) 0 0
\(223\) −51.8335 −0.232437 −0.116219 0.993224i \(-0.537077\pi\)
−0.116219 + 0.993224i \(0.537077\pi\)
\(224\) −169.119 + 156.993i −0.754994 + 0.700862i
\(225\) 0 0
\(226\) −77.5584 + 149.460i −0.343179 + 0.661328i
\(227\) −334.786 −1.47483 −0.737413 0.675442i \(-0.763953\pi\)
−0.737413 + 0.675442i \(0.763953\pi\)
\(228\) 0 0
\(229\) 219.407i 0.958108i −0.877786 0.479054i \(-0.840980\pi\)
0.877786 0.479054i \(-0.159020\pi\)
\(230\) −1.10482 + 2.12906i −0.00480357 + 0.00925679i
\(231\) 0 0
\(232\) 31.6888 + 233.689i 0.136590 + 1.00728i
\(233\) 203.867i 0.874965i 0.899227 + 0.437482i \(0.144130\pi\)
−0.899227 + 0.437482i \(0.855870\pi\)
\(234\) 0 0
\(235\) 69.3743i 0.295210i
\(236\) 130.813 + 185.796i 0.554294 + 0.787271i
\(237\) 0 0
\(238\) 126.094 242.992i 0.529808 1.02097i
\(239\) 54.0232i 0.226038i 0.993593 + 0.113019i \(0.0360522\pi\)
−0.993593 + 0.113019i \(0.963948\pi\)
\(240\) 0 0
\(241\) 327.600 1.35933 0.679667 0.733520i \(-0.262124\pi\)
0.679667 + 0.733520i \(0.262124\pi\)
\(242\) 259.852 + 134.843i 1.07377 + 0.557204i
\(243\) 0 0
\(244\) −226.900 + 159.754i −0.929918 + 0.654728i
\(245\) −3.22495 −0.0131631
\(246\) 0 0
\(247\) 368.222 1.49078
\(248\) 6.05571 + 44.6577i 0.0244182 + 0.180072i
\(249\) 0 0
\(250\) 93.2111 + 48.3695i 0.372844 + 0.193478i
\(251\) −362.281 −1.44335 −0.721676 0.692231i \(-0.756628\pi\)
−0.721676 + 0.692231i \(0.756628\pi\)
\(252\) 0 0
\(253\) 18.2431i 0.0721070i
\(254\) −80.8118 41.9352i −0.318157 0.165099i
\(255\) 0 0
\(256\) −197.800 162.515i −0.772656 0.634825i
\(257\) 21.2132i 0.0825416i 0.999148 + 0.0412708i \(0.0131406\pi\)
−0.999148 + 0.0412708i \(0.986859\pi\)
\(258\) 0 0
\(259\) 122.904i 0.474534i
\(260\) −75.9595 + 53.4808i −0.292152 + 0.205695i
\(261\) 0 0
\(262\) 229.211 + 118.943i 0.874852 + 0.453981i
\(263\) 205.878i 0.782806i −0.920219 0.391403i \(-0.871990\pi\)
0.920219 0.391403i \(-0.128010\pi\)
\(264\) 0 0
\(265\) −38.6224 −0.145745
\(266\) −113.220 + 218.181i −0.425637 + 0.820231i
\(267\) 0 0
\(268\) 226.900 159.754i 0.846642 0.596095i
\(269\) −2.77109 −0.0103014 −0.00515072 0.999987i \(-0.501640\pi\)
−0.00515072 + 0.999987i \(0.501640\pi\)
\(270\) 0 0
\(271\) −125.744 −0.464001 −0.232001 0.972716i \(-0.574527\pi\)
−0.232001 + 0.972716i \(0.574527\pi\)
\(272\) 285.928 + 102.397i 1.05120 + 0.376458i
\(273\) 0 0
\(274\) −10.0749 + 19.4149i −0.0367696 + 0.0708574i
\(275\) 389.896 1.41780
\(276\) 0 0
\(277\) 162.752i 0.587552i −0.955874 0.293776i \(-0.905088\pi\)
0.955874 0.293776i \(-0.0949119\pi\)
\(278\) 1.10482 2.12906i 0.00397418 0.00765850i
\(279\) 0 0
\(280\) −8.33308 61.4521i −0.0297610 0.219472i
\(281\) 301.227i 1.07198i −0.844223 0.535992i \(-0.819938\pi\)
0.844223 0.535992i \(-0.180062\pi\)
\(282\) 0 0
\(283\) 31.6888i 0.111975i −0.998431 0.0559874i \(-0.982169\pi\)
0.998431 0.0559874i \(-0.0178307\pi\)
\(284\) 322.083 226.769i 1.13409 0.798482i
\(285\) 0 0
\(286\) −325.433 + 627.131i −1.13788 + 2.19276i
\(287\) 198.068i 0.690134i
\(288\) 0 0
\(289\) −71.3112 −0.246751
\(290\) −56.2545 29.1918i −0.193981 0.100661i
\(291\) 0 0
\(292\) 86.7889 + 123.267i 0.297222 + 0.422148i
\(293\) −304.913 −1.04066 −0.520329 0.853966i \(-0.674191\pi\)
−0.520329 + 0.853966i \(0.674191\pi\)
\(294\) 0 0
\(295\) −61.0665 −0.207005
\(296\) 135.113 18.3218i 0.456464 0.0618978i
\(297\) 0 0
\(298\) −53.1362 27.5737i −0.178310 0.0925291i
\(299\) −24.1035 −0.0806137
\(300\) 0 0
\(301\) 377.361i 1.25369i
\(302\) 109.215 + 56.6744i 0.361640 + 0.187664i
\(303\) 0 0
\(304\) −256.733 91.9416i −0.844518 0.302440i
\(305\) 74.5763i 0.244512i
\(306\) 0 0
\(307\) 105.860i 0.344822i −0.985025 0.172411i \(-0.944844\pi\)
0.985025 0.172411i \(-0.0551558\pi\)
\(308\) −271.529 385.656i −0.881587 1.25213i
\(309\) 0 0
\(310\) −10.7502 5.57853i −0.0346780 0.0179953i
\(311\) 555.157i 1.78507i −0.450978 0.892535i \(-0.648925\pi\)
0.450978 0.892535i \(-0.351075\pi\)
\(312\) 0 0
\(313\) 158.000 0.504792 0.252396 0.967624i \(-0.418781\pi\)
0.252396 + 0.967624i \(0.418781\pi\)
\(314\) 126.711 244.180i 0.403537 0.777642i
\(315\) 0 0
\(316\) −293.194 416.428i −0.927830 1.31781i
\(317\) 97.0351 0.306105 0.153052 0.988218i \(-0.451090\pi\)
0.153052 + 0.988218i \(0.451090\pi\)
\(318\) 0 0
\(319\) −482.022 −1.51104
\(320\) 66.3145 18.3218i 0.207233 0.0572555i
\(321\) 0 0
\(322\) 7.41126 14.2820i 0.0230163 0.0443539i
\(323\) 323.522 1.00162
\(324\) 0 0
\(325\) 515.147i 1.58507i
\(326\) −176.022 + 339.207i −0.539946 + 1.04051i
\(327\) 0 0
\(328\) −217.744 + 29.5267i −0.663855 + 0.0900205i
\(329\) 465.370i 1.41450i
\(330\) 0 0
\(331\) 619.572i 1.87182i −0.352242 0.935909i \(-0.614581\pi\)
0.352242 0.935909i \(-0.385419\pi\)
\(332\) 17.8507 + 25.3536i 0.0537672 + 0.0763662i
\(333\) 0 0
\(334\) 214.755 413.847i 0.642980 1.23906i
\(335\) 74.5763i 0.222616i
\(336\) 0 0
\(337\) −170.755 −0.506692 −0.253346 0.967376i \(-0.581531\pi\)
−0.253346 + 0.967376i \(0.581531\pi\)
\(338\) −528.580 274.293i −1.56384 0.811517i
\(339\) 0 0
\(340\) −66.7385 + 46.9886i −0.196290 + 0.138202i
\(341\) −92.1141 −0.270129
\(342\) 0 0
\(343\) −331.711 −0.967087
\(344\) −414.848 + 56.2545i −1.20595 + 0.163531i
\(345\) 0 0
\(346\) 574.830 + 298.293i 1.66136 + 0.862119i
\(347\) 300.386 0.865666 0.432833 0.901474i \(-0.357514\pi\)
0.432833 + 0.901474i \(0.357514\pi\)
\(348\) 0 0
\(349\) 53.5299i 0.153381i −0.997055 0.0766904i \(-0.975565\pi\)
0.997055 0.0766904i \(-0.0244353\pi\)
\(350\) −305.238 158.396i −0.872110 0.452559i
\(351\) 0 0
\(352\) 383.489 355.993i 1.08946 1.01134i
\(353\) 600.475i 1.70106i 0.525925 + 0.850531i \(0.323719\pi\)
−0.525925 + 0.850531i \(0.676281\pi\)
\(354\) 0 0
\(355\) 105.860i 0.298199i
\(356\) 249.053 175.351i 0.699586 0.492558i
\(357\) 0 0
\(358\) −330.056 171.274i −0.921943 0.478418i
\(359\) 148.508i 0.413671i 0.978376 + 0.206836i \(0.0663165\pi\)
−0.978376 + 0.206836i \(0.933683\pi\)
\(360\) 0 0
\(361\) 70.5106 0.195320
\(362\) 116.316 224.149i 0.321315 0.619195i
\(363\) 0 0
\(364\) 509.544 358.755i 1.39985 0.985591i
\(365\) −40.5149 −0.111000
\(366\) 0 0
\(367\) 316.389 0.862094 0.431047 0.902329i \(-0.358144\pi\)
0.431047 + 0.902329i \(0.358144\pi\)
\(368\) 16.8055 + 6.01842i 0.0456673 + 0.0163544i
\(369\) 0 0
\(370\) −16.8780 + 32.5250i −0.0456163 + 0.0879055i
\(371\) 259.083 0.698336
\(372\) 0 0
\(373\) 626.768i 1.68034i 0.542321 + 0.840171i \(0.317545\pi\)
−0.542321 + 0.840171i \(0.682455\pi\)
\(374\) −285.928 + 551.001i −0.764512 + 1.47326i
\(375\) 0 0
\(376\) −511.600 + 69.3743i −1.36064 + 0.184506i
\(377\) 636.867i 1.68930i
\(378\) 0 0
\(379\) 331.027i 0.873423i 0.899602 + 0.436711i \(0.143857\pi\)
−0.899602 + 0.436711i \(0.856143\pi\)
\(380\) 59.9242 42.1909i 0.157695 0.111029i
\(381\) 0 0
\(382\) −214.755 + 413.847i −0.562187 + 1.08337i
\(383\) 407.765i 1.06466i 0.846537 + 0.532330i \(0.178683\pi\)
−0.846537 + 0.532330i \(0.821317\pi\)
\(384\) 0 0
\(385\) 126.755 0.329234
\(386\) −208.371 108.128i −0.539820 0.280126i
\(387\) 0 0
\(388\) 11.1556 + 15.8444i 0.0287515 + 0.0408361i
\(389\) 53.5819 0.137743 0.0688714 0.997626i \(-0.478060\pi\)
0.0688714 + 0.997626i \(0.478060\pi\)
\(390\) 0 0
\(391\) −21.1775 −0.0541624
\(392\) 3.22495 + 23.7823i 0.00822692 + 0.0606692i
\(393\) 0 0
\(394\) 526.019 + 272.964i 1.33507 + 0.692802i
\(395\) 136.869 0.346504
\(396\) 0 0
\(397\) 289.744i 0.729833i −0.931040 0.364917i \(-0.881098\pi\)
0.931040 0.364917i \(-0.118902\pi\)
\(398\) 413.644 + 214.650i 1.03931 + 0.539322i
\(399\) 0 0
\(400\) 128.627 359.173i 0.321569 0.897933i
\(401\) 203.458i 0.507376i 0.967286 + 0.253688i \(0.0816436\pi\)
−0.967286 + 0.253688i \(0.918356\pi\)
\(402\) 0 0
\(403\) 121.705i 0.301997i
\(404\) −243.254 345.496i −0.602113 0.855189i
\(405\) 0 0
\(406\) 377.361 + 195.822i 0.929460 + 0.482319i
\(407\) 278.694i 0.684752i
\(408\) 0 0
\(409\) 412.844 1.00940 0.504700 0.863295i \(-0.331603\pi\)
0.504700 + 0.863295i \(0.331603\pi\)
\(410\) 27.2001 52.4163i 0.0663416 0.127845i
\(411\) 0 0
\(412\) 241.305 + 342.729i 0.585693 + 0.831866i
\(413\) 409.640 0.991865
\(414\) 0 0
\(415\) −8.33308 −0.0200797
\(416\) 470.353 + 506.681i 1.13066 + 1.21798i
\(417\) 0 0
\(418\) 256.733 494.742i 0.614195 1.18359i
\(419\) −336.482 −0.803059 −0.401529 0.915846i \(-0.631521\pi\)
−0.401529 + 0.915846i \(0.631521\pi\)
\(420\) 0 0
\(421\) 217.481i 0.516582i −0.966067 0.258291i \(-0.916841\pi\)
0.966067 0.258291i \(-0.0831594\pi\)
\(422\) 32.5063 62.6417i 0.0770291 0.148440i
\(423\) 0 0
\(424\) 38.6224 + 284.820i 0.0910905 + 0.671745i
\(425\) 452.611i 1.06497i
\(426\) 0 0
\(427\) 500.265i 1.17158i
\(428\) −150.617 213.923i −0.351909 0.499821i
\(429\) 0 0
\(430\) 51.8217 99.8639i 0.120516 0.232242i
\(431\) 750.994i 1.74245i −0.490888 0.871223i \(-0.663328\pi\)
0.490888 0.871223i \(-0.336672\pi\)
\(432\) 0 0
\(433\) −176.133 −0.406773 −0.203387 0.979098i \(-0.565195\pi\)
−0.203387 + 0.979098i \(0.565195\pi\)
\(434\) 72.1134 + 37.4214i 0.166160 + 0.0862244i
\(435\) 0 0
\(436\) −10.9941 + 7.74065i −0.0252159 + 0.0177538i
\(437\) 19.0152 0.0435130
\(438\) 0 0
\(439\) 417.788 0.951681 0.475841 0.879531i \(-0.342144\pi\)
0.475841 + 0.879531i \(0.342144\pi\)
\(440\) 18.8958 + 139.347i 0.0429451 + 0.316698i
\(441\) 0 0
\(442\) −728.005 377.779i −1.64707 0.854704i
\(443\) 61.0471 0.137804 0.0689020 0.997623i \(-0.478050\pi\)
0.0689020 + 0.997623i \(0.478050\pi\)
\(444\) 0 0
\(445\) 81.8573i 0.183949i
\(446\) −92.0155 47.7491i −0.206313 0.107061i
\(447\) 0 0
\(448\) −444.844 + 122.904i −0.992956 + 0.274340i
\(449\) 182.905i 0.407360i −0.979038 0.203680i \(-0.934710\pi\)
0.979038 0.203680i \(-0.0652902\pi\)
\(450\) 0 0
\(451\) 449.134i 0.995863i
\(452\) −275.366 + 193.877i −0.609216 + 0.428931i
\(453\) 0 0
\(454\) −594.316 308.405i −1.30907 0.679306i
\(455\) 167.474i 0.368075i
\(456\) 0 0
\(457\) −443.600 −0.970678 −0.485339 0.874326i \(-0.661304\pi\)
−0.485339 + 0.874326i \(0.661304\pi\)
\(458\) 202.118 389.494i 0.441305 0.850423i
\(459\) 0 0
\(460\) −3.92259 + 2.76178i −0.00852737 + 0.00600387i
\(461\) −728.241 −1.57970 −0.789850 0.613301i \(-0.789841\pi\)
−0.789850 + 0.613301i \(0.789841\pi\)
\(462\) 0 0
\(463\) −107.722 −0.232662 −0.116331 0.993211i \(-0.537113\pi\)
−0.116331 + 0.993211i \(0.537113\pi\)
\(464\) −159.020 + 444.039i −0.342715 + 0.956981i
\(465\) 0 0
\(466\) −187.802 + 361.907i −0.403009 + 0.776625i
\(467\) −820.248 −1.75642 −0.878210 0.478276i \(-0.841262\pi\)
−0.878210 + 0.478276i \(0.841262\pi\)
\(468\) 0 0
\(469\) 500.265i 1.06666i
\(470\) 63.9077 123.154i 0.135974 0.262031i
\(471\) 0 0
\(472\) 61.0665 + 450.333i 0.129378 + 0.954096i
\(473\) 855.693i 1.80908i
\(474\) 0 0
\(475\) 406.398i 0.855575i
\(476\) 447.689 315.204i 0.940522 0.662194i
\(477\) 0 0
\(478\) −49.7662 + 95.9027i −0.104113 + 0.200633i
\(479\) 120.790i 0.252171i −0.992019 0.126085i \(-0.959759\pi\)
0.992019 0.126085i \(-0.0402413\pi\)
\(480\) 0 0
\(481\) −368.222 −0.765534
\(482\) 581.560 + 301.785i 1.20656 + 0.626111i
\(483\) 0 0
\(484\) 337.075 + 478.752i 0.696436 + 0.989156i
\(485\) −5.20766 −0.0107374
\(486\) 0 0
\(487\) −128.234 −0.263314 −0.131657 0.991295i \(-0.542030\pi\)
−0.131657 + 0.991295i \(0.542030\pi\)
\(488\) −549.961 + 74.5763i −1.12697 + 0.152820i
\(489\) 0 0
\(490\) −5.72498 2.97083i −0.0116836 0.00606292i
\(491\) −382.144 −0.778298 −0.389149 0.921175i \(-0.627231\pi\)
−0.389149 + 0.921175i \(0.627231\pi\)
\(492\) 0 0
\(493\) 559.555i 1.13500i
\(494\) 653.673 + 339.207i 1.32323 + 0.686653i
\(495\) 0 0
\(496\) −30.3886 + 84.8556i −0.0612673 + 0.171080i
\(497\) 710.123i 1.42882i
\(498\) 0 0
\(499\) 554.995i 1.11221i 0.831111 + 0.556107i \(0.187705\pi\)
−0.831111 + 0.556107i \(0.812295\pi\)
\(500\) 120.912 + 171.732i 0.241823 + 0.343465i
\(501\) 0 0
\(502\) −643.127 333.734i −1.28113 0.664809i
\(503\) 78.3943i 0.155854i −0.996959 0.0779268i \(-0.975170\pi\)
0.996959 0.0779268i \(-0.0248300\pi\)
\(504\) 0 0
\(505\) 113.556 0.224863
\(506\) −16.8055 + 32.3854i −0.0332125 + 0.0640027i
\(507\) 0 0
\(508\) −104.828 148.888i −0.206354 0.293087i
\(509\) 514.941 1.01167 0.505836 0.862630i \(-0.331184\pi\)
0.505836 + 0.862630i \(0.331184\pi\)
\(510\) 0 0
\(511\) 271.778 0.531855
\(512\) −201.428 470.713i −0.393414 0.919361i
\(513\) 0 0
\(514\) −19.5416 + 37.6580i −0.0380187 + 0.0732646i
\(515\) −112.646 −0.218731
\(516\) 0 0
\(517\) 1055.26i 2.04112i
\(518\) 113.220 218.181i 0.218571 0.421200i
\(519\) 0 0
\(520\) −184.111 + 24.9660i −0.354060 + 0.0480115i
\(521\) 489.695i 0.939914i 0.882689 + 0.469957i \(0.155730\pi\)
−0.882689 + 0.469957i \(0.844270\pi\)
\(522\) 0 0
\(523\) 774.165i 1.48024i 0.672476 + 0.740119i \(0.265231\pi\)
−0.672476 + 0.740119i \(0.734769\pi\)
\(524\) 297.328 + 422.299i 0.567421 + 0.805915i
\(525\) 0 0
\(526\) 189.655 365.478i 0.360561 0.694825i
\(527\) 106.931i 0.202905i
\(528\) 0 0
\(529\) 527.755 0.997647
\(530\) −68.5630 35.5790i −0.129364 0.0671301i
\(531\) 0 0
\(532\) −401.978 + 283.021i −0.755598 + 0.531994i
\(533\) 593.415 1.11335
\(534\) 0 0
\(535\) 70.3112 0.131423
\(536\) 549.961 74.5763i 1.02605 0.139135i
\(537\) 0 0
\(538\) −4.91928 2.55273i −0.00914363 0.00474485i
\(539\) −49.0551 −0.0910112
\(540\) 0 0
\(541\) 590.045i 1.09066i 0.838223 + 0.545328i \(0.183595\pi\)
−0.838223 + 0.545328i \(0.816405\pi\)
\(542\) −223.223 115.836i −0.411851 0.213719i
\(543\) 0 0
\(544\) 413.255 + 445.173i 0.759660 + 0.818333i
\(545\) 3.61350i 0.00663027i
\(546\) 0 0
\(547\) 707.189i 1.29285i 0.762977 + 0.646425i \(0.223737\pi\)
−0.762977 + 0.646425i \(0.776263\pi\)
\(548\) −35.7701 + 25.1847i −0.0652739 + 0.0459574i
\(549\) 0 0
\(550\) 692.150 + 359.173i 1.25845 + 0.653042i
\(551\) 502.423i 0.911838i
\(552\) 0 0
\(553\) −918.133 −1.66028
\(554\) 149.927 288.919i 0.270627 0.521515i
\(555\) 0 0
\(556\) 3.92259 2.76178i 0.00705502 0.00496723i
\(557\) −75.0816 −0.134796 −0.0673982 0.997726i \(-0.521470\pi\)
−0.0673982 + 0.997726i \(0.521470\pi\)
\(558\) 0 0
\(559\) 1130.58 2.02250
\(560\) 41.8168 116.767i 0.0746728 0.208513i
\(561\) 0 0
\(562\) 277.491 534.744i 0.493757 0.951501i
\(563\) −114.462 −0.203307 −0.101653 0.994820i \(-0.532413\pi\)
−0.101653 + 0.994820i \(0.532413\pi\)
\(564\) 0 0
\(565\) 90.5058i 0.160187i
\(566\) 29.1918 56.2545i 0.0515756 0.0993896i
\(567\) 0 0
\(568\) 780.666 105.860i 1.37441 0.186374i
\(569\) 45.8199i 0.0805270i 0.999189 + 0.0402635i \(0.0128197\pi\)
−0.999189 + 0.0402635i \(0.987180\pi\)
\(570\) 0 0
\(571\) 830.093i 1.45375i −0.686768 0.726877i \(-0.740971\pi\)
0.686768 0.726877i \(-0.259029\pi\)
\(572\) −1155.43 + 813.502i −2.01998 + 1.42221i
\(573\) 0 0
\(574\) −182.461 + 351.614i −0.317876 + 0.612568i
\(575\) 26.6025i 0.0462652i
\(576\) 0 0
\(577\) −69.3776 −0.120239 −0.0601193 0.998191i \(-0.519148\pi\)
−0.0601193 + 0.998191i \(0.519148\pi\)
\(578\) −126.593 65.6920i −0.219018 0.113654i
\(579\) 0 0
\(580\) −72.9722 103.643i −0.125814 0.178696i
\(581\) 55.8991 0.0962120
\(582\) 0 0
\(583\) −587.489 −1.00770
\(584\) 40.5149 + 298.776i 0.0693748 + 0.511603i
\(585\) 0 0
\(586\) −541.286 280.886i −0.923696 0.479328i
\(587\) −428.655 −0.730248 −0.365124 0.930959i \(-0.618973\pi\)
−0.365124 + 0.930959i \(0.618973\pi\)
\(588\) 0 0
\(589\) 96.0127i 0.163010i
\(590\) −108.406 56.2545i −0.183739 0.0953466i
\(591\) 0 0
\(592\) 256.733 + 91.9416i 0.433671 + 0.155307i
\(593\) 77.0276i 0.129895i −0.997889 0.0649474i \(-0.979312\pi\)
0.997889 0.0649474i \(-0.0206880\pi\)
\(594\) 0 0
\(595\) 147.144i 0.247301i
\(596\) −68.9273 97.8984i −0.115650 0.164259i
\(597\) 0 0
\(598\) −42.7889 22.2042i −0.0715533 0.0371307i
\(599\) 963.566i 1.60862i 0.594207 + 0.804312i \(0.297466\pi\)
−0.594207 + 0.804312i \(0.702534\pi\)
\(600\) 0 0
\(601\) 840.133 1.39789 0.698946 0.715175i \(-0.253653\pi\)
0.698946 + 0.715175i \(0.253653\pi\)
\(602\) −347.626 + 669.897i −0.577451 + 1.11279i
\(603\) 0 0
\(604\) 141.672 + 201.219i 0.234556 + 0.333143i
\(605\) −157.354 −0.260089
\(606\) 0 0
\(607\) 156.611 0.258008 0.129004 0.991644i \(-0.458822\pi\)
0.129004 + 0.991644i \(0.458822\pi\)
\(608\) −371.060 399.719i −0.610296 0.657433i
\(609\) 0 0
\(610\) 68.6998 132.389i 0.112623 0.217031i
\(611\) 1394.25 2.28192
\(612\) 0 0
\(613\) 426.094i 0.695096i 0.937662 + 0.347548i \(0.112986\pi\)
−0.937662 + 0.347548i \(0.887014\pi\)
\(614\) 97.5188 187.925i 0.158825 0.306067i
\(615\) 0 0
\(616\) −126.755 934.754i −0.205772 1.51746i
\(617\) 963.520i 1.56162i 0.624769 + 0.780810i \(0.285193\pi\)
−0.624769 + 0.780810i \(0.714807\pi\)
\(618\) 0 0
\(619\) 175.235i 0.283093i 0.989932 + 0.141547i \(0.0452075\pi\)
−0.989932 + 0.141547i \(0.954792\pi\)
\(620\) −13.9449 19.8062i −0.0224919 0.0319455i
\(621\) 0 0
\(622\) 511.411 985.523i 0.822205 1.58444i
\(623\) 549.107i 0.881392i
\(624\) 0 0
\(625\) 539.666 0.863466
\(626\) 280.484 + 145.550i 0.448057 + 0.232508i
\(627\) 0 0
\(628\) 449.877 316.745i 0.716365 0.504371i
\(629\) −323.522 −0.514344
\(630\) 0 0
\(631\) −1140.72 −1.80780 −0.903900 0.427744i \(-0.859308\pi\)
−0.903900 + 0.427744i \(0.859308\pi\)
\(632\) −136.869 1009.34i −0.216565 1.59706i
\(633\) 0 0
\(634\) 172.258 + 89.3889i 0.271701 + 0.140992i
\(635\) 48.9357 0.0770641
\(636\) 0 0
\(637\) 64.8136i 0.101748i
\(638\) −855.692 444.039i −1.34121 0.695986i
\(639\) 0 0
\(640\) 134.600 + 28.5639i 0.210313 + 0.0446312i
\(641\) 351.730i 0.548721i 0.961627 + 0.274360i \(0.0884661\pi\)
−0.961627 + 0.274360i \(0.911534\pi\)
\(642\) 0 0
\(643\) 86.4181i 0.134398i −0.997740 0.0671991i \(-0.978594\pi\)
0.997740 0.0671991i \(-0.0214063\pi\)
\(644\) 26.3131 18.5263i 0.0408589 0.0287676i
\(645\) 0 0
\(646\) 574.321 + 298.029i 0.889042 + 0.461345i
\(647\) 430.723i 0.665723i 0.942976 + 0.332861i \(0.108014\pi\)
−0.942976 + 0.332861i \(0.891986\pi\)
\(648\) 0 0
\(649\) −928.888 −1.43126
\(650\) −474.554 + 914.497i −0.730083 + 1.40692i
\(651\) 0 0
\(652\) −624.955 + 440.013i −0.958521 + 0.674866i
\(653\) 886.670 1.35784 0.678920 0.734212i \(-0.262448\pi\)
0.678920 + 0.734212i \(0.262448\pi\)
\(654\) 0 0
\(655\) −138.799 −0.211907
\(656\) −413.743 148.170i −0.630706 0.225869i
\(657\) 0 0
\(658\) −428.700 + 826.132i −0.651519 + 1.25552i
\(659\) 352.833 0.535407 0.267704 0.963501i \(-0.413735\pi\)
0.267704 + 0.963501i \(0.413735\pi\)
\(660\) 0 0
\(661\) 1206.26i 1.82489i 0.409195 + 0.912447i \(0.365810\pi\)
−0.409195 + 0.912447i \(0.634190\pi\)
\(662\) 570.750 1099.87i 0.862161 1.66144i
\(663\) 0 0
\(664\) 8.33308 + 61.4521i 0.0125498 + 0.0925484i
\(665\) 132.120i 0.198677i
\(666\) 0 0
\(667\) 32.8882i 0.0493076i
\(668\) 762.474 536.835i 1.14143 0.803645i
\(669\) 0 0
\(670\) −68.6998 + 132.389i −0.102537 + 0.197595i
\(671\) 1134.39i 1.69059i
\(672\) 0 0
\(673\) −956.133 −1.42070 −0.710351 0.703847i \(-0.751464\pi\)
−0.710351 + 0.703847i \(0.751464\pi\)
\(674\) −303.127 157.300i −0.449744 0.233383i
\(675\) 0 0
\(676\) −685.664 973.857i −1.01430 1.44062i
\(677\) 420.557 0.621207 0.310604 0.950540i \(-0.399469\pi\)
0.310604 + 0.950540i \(0.399469\pi\)
\(678\) 0 0
\(679\) 34.9335 0.0514485
\(680\) −161.761 + 21.9352i −0.237884 + 0.0322577i
\(681\) 0 0
\(682\) −163.522 84.8556i −0.239769 0.124422i
\(683\) 539.725 0.790227 0.395113 0.918632i \(-0.370705\pi\)
0.395113 + 0.918632i \(0.370705\pi\)
\(684\) 0 0
\(685\) 11.7567i 0.0171631i
\(686\) −588.858 305.572i −0.858393 0.445441i
\(687\) 0 0
\(688\) −788.266 282.295i −1.14574 0.410312i
\(689\) 776.214i 1.12658i
\(690\) 0 0
\(691\) 432.090i 0.625312i −0.949866 0.312656i \(-0.898781\pi\)
0.949866 0.312656i \(-0.101219\pi\)
\(692\) 745.659 + 1059.07i 1.07754 + 1.53045i
\(693\) 0 0
\(694\) 533.250 + 276.716i 0.768371 + 0.398726i
\(695\) 1.28926i 0.00185504i
\(696\) 0 0
\(697\) 521.378 0.748031
\(698\) 49.3118 95.0271i 0.0706473 0.136142i
\(699\) 0 0
\(700\) −395.950 562.372i −0.565642 0.803389i
\(701\) −880.339 −1.25583 −0.627917 0.778280i \(-0.716092\pi\)
−0.627917 + 0.778280i \(0.716092\pi\)
\(702\) 0 0
\(703\) 290.489 0.413214
\(704\) 1008.72 278.694i 1.43284 0.395872i
\(705\) 0 0
\(706\) −553.158 + 1065.97i −0.783510 + 1.50987i
\(707\) −761.745 −1.07743
\(708\) 0 0
\(709\) 799.367i 1.12746i 0.825960 + 0.563729i \(0.190634\pi\)
−0.825960 + 0.563729i \(0.809366\pi\)
\(710\) −97.5188 + 187.925i −0.137350 + 0.264683i
\(711\) 0 0
\(712\) 603.655 81.8573i 0.847830 0.114968i
\(713\) 6.28491i 0.00881474i
\(714\) 0 0
\(715\) 379.760i 0.531133i
\(716\) −428.142 608.095i −0.597963 0.849295i
\(717\) 0 0
\(718\) −136.806 + 263.633i −0.190537 + 0.367178i
\(719\) 258.786i 0.359924i −0.983674 0.179962i \(-0.942402\pi\)
0.983674 0.179962i \(-0.0575975\pi\)
\(720\) 0 0
\(721\) 755.643 1.04805
\(722\) 125.171 + 64.9544i 0.173368 + 0.0899646i
\(723\) 0 0
\(724\) 412.972 290.762i 0.570404 0.401604i
\(725\) −702.896 −0.969511
\(726\) 0 0
\(727\) −663.211 −0.912257 −0.456129 0.889914i \(-0.650764\pi\)
−0.456129 + 0.889914i \(0.650764\pi\)
\(728\) 1235.04 167.474i 1.69648 0.230047i
\(729\) 0 0
\(730\) −71.9226 37.3224i −0.0985241 0.0511265i
\(731\) 993.332 1.35887
\(732\) 0 0
\(733\) 908.826i 1.23987i −0.784653 0.619936i \(-0.787159\pi\)
0.784653 0.619936i \(-0.212841\pi\)
\(734\) 561.658 + 291.458i 0.765201 + 0.397081i
\(735\) 0 0
\(736\) 24.2893 + 26.1653i 0.0330017 + 0.0355507i
\(737\) 1134.39i 1.53920i
\(738\) 0 0
\(739\) 1112.39i 1.50526i −0.658443 0.752631i \(-0.728785\pi\)
0.658443 0.752631i \(-0.271215\pi\)
\(740\) −59.9242 + 42.1909i −0.0809787 + 0.0570147i
\(741\) 0 0
\(742\) 459.928 + 238.667i 0.619849 + 0.321654i
\(743\) 541.298i 0.728530i 0.931295 + 0.364265i \(0.118680\pi\)
−0.931295 + 0.364265i \(0.881320\pi\)
\(744\) 0 0
\(745\) 32.1767 0.0431902
\(746\) −577.379 + 1112.65i −0.773967 + 1.49148i
\(747\) 0 0
\(748\) −1015.17 + 714.748i −1.35717 + 0.955546i
\(749\) −471.655 −0.629713
\(750\) 0 0
\(751\) −763.699 −1.01691 −0.508455 0.861089i \(-0.669783\pi\)
−0.508455 + 0.861089i \(0.669783\pi\)
\(752\) −972.107 348.132i −1.29270 0.462942i
\(753\) 0 0
\(754\) 586.683 1130.58i 0.778094 1.49944i
\(755\) −66.1354 −0.0875966
\(756\) 0 0
\(757\) 419.134i 0.553678i −0.960916 0.276839i \(-0.910713\pi\)
0.960916 0.276839i \(-0.0892869\pi\)
\(758\) −304.943 + 587.644i −0.402299 + 0.775257i
\(759\) 0 0
\(760\) 145.245 19.6956i 0.191111 0.0259152i
\(761\) 1330.24i 1.74802i −0.485912 0.874008i \(-0.661512\pi\)
0.485912 0.874008i \(-0.338488\pi\)
\(762\) 0 0
\(763\) 24.2397i 0.0317690i
\(764\) −762.474 + 536.835i −0.998002 + 0.702664i
\(765\) 0 0
\(766\) −375.633 + 723.870i −0.490383 + 0.945000i
\(767\) 1227.29i 1.60011i
\(768\) 0 0
\(769\) 671.511 0.873226 0.436613 0.899649i \(-0.356178\pi\)
0.436613 + 0.899649i \(0.356178\pi\)
\(770\) 225.018 + 116.767i 0.292231 + 0.151646i
\(771\) 0 0
\(772\) −270.294 383.902i −0.350122 0.497283i
\(773\) −1421.13 −1.83846 −0.919229 0.393724i \(-0.871187\pi\)
−0.919229 + 0.393724i \(0.871187\pi\)
\(774\) 0 0
\(775\) −134.323 −0.173320
\(776\) 5.20766 + 38.4038i 0.00671090 + 0.0494894i
\(777\) 0 0
\(778\) 95.1194 + 49.3597i 0.122261 + 0.0634444i
\(779\) −468.143 −0.600954
\(780\) 0 0
\(781\) 1610.25i 2.06179i
\(782\) −37.5946 19.5087i −0.0480749 0.0249472i
\(783\) 0 0
\(784\) −16.1833 + 45.1896i −0.0206420 + 0.0576398i
\(785\) 147.863i 0.188361i
\(786\) 0 0
\(787\) 649.808i 0.825677i −0.910804 0.412839i \(-0.864537\pi\)
0.910804 0.412839i \(-0.135463\pi\)
\(788\) 682.343 + 969.140i 0.865917 + 1.22987i
\(789\) 0 0
\(790\) 242.972 + 126.084i 0.307560 + 0.159600i
\(791\) 607.122i 0.767538i