Properties

Label 72.3.h.a.53.2
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 53.2
Root \(-0.651388 + 2.66948i\) of defining polynomial
Character \(\chi\) \(=\) 72.53
Dual form 72.3.h.a.53.1

$q$-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 \(-0.465716\pi\)
0.107498 + 0.994205i \(0.465716\pi\)
\(6\) 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 \(-0.233279\pi\)
0.743258 + 0.669004i \(0.233279\pi\)
\(12\) 0 0
\(13\) 21.6045i 1.66189i 0.556357 + 0.830943i \(0.312199\pi\)
−0.556357 + 0.830943i \(0.687801\pi\)
\(14\) −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 \(-0.851951\pi\)
0.893773 0.448520i \(-0.148049\pi\)
\(20\) 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 \(-0.669707\pi\)
−0.508249 + 0.861210i \(0.669707\pi\)
\(30\) 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 \(0.0739776\pi\)
−0.973115 + 0.230321i \(0.926022\pi\)
\(38\) 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 \(-0.791774\pi\)
0.793558 0.608495i \(-0.208226\pi\)
\(44\) 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 \(-0.610071\pi\)
−0.338946 + 0.940806i \(0.610071\pi\)
\(54\) 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 \(-0.659877\pi\)
−0.481414 + 0.876493i \(0.659877\pi\)
\(60\) 0 0
\(61\) 69.3743i 1.13728i −0.822585 0.568642i \(-0.807469\pi\)
0.822585 0.568642i \(-0.192531\pi\)
\(62\) −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 \(0.173219\pi\)
−0.855551 + 0.517719i \(0.826781\pi\)
\(68\) −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 \(-0.514870\pi\)
−0.0466977 + 0.998909i \(0.514870\pi\)
\(84\) 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 \(-0.324833\pi\)
0.522946 + 0.852366i \(0.324833\pi\)
\(102\) 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 \(-0.401130\pi\)
0.305639 + 0.952147i \(0.401130\pi\)
\(108\) 0 0
\(109\) 3.36144i 0.0308389i −0.999881 0.0154195i \(-0.995092\pi\)
0.999881 0.0154195i \(-0.00490836\pi\)
\(110\) −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 \(-0.664032\pi\)
−0.492814 + 0.870134i \(0.664032\pi\)
\(132\) 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 \(0.00137323\pi\)
−0.999991 + 0.00431412i \(0.998627\pi\)
\(140\) 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 \(-0.467974\pi\)
0.100444 + 0.994943i \(0.467974\pi\)
\(150\) 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 \(0.144333\pi\)
−0.898948 + 0.438055i \(0.855667\pi\)
\(158\) 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 \(-0.800650\pi\)
0.810215 0.586133i \(-0.199350\pi\)
\(164\) 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 \(-0.885378\pi\)
−0.935864 + 0.352363i \(0.885378\pi\)
\(174\) 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 \(-0.326177\pi\)
0.519342 + 0.854567i \(0.326177\pi\)
\(180\) 0 0
\(181\) 126.266i 0.697600i 0.937197 + 0.348800i \(0.113411\pi\)
−0.937197 + 0.348800i \(0.886589\pi\)
\(182\) −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 \(-0.770941\pi\)
−0.752064 + 0.659091i \(0.770941\pi\)
\(198\) 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 \(0.0266476\pi\)
−0.996498 + 0.0836181i \(0.973352\pi\)
\(212\) −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 \(-0.236047\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(228\) 0 0
\(229\) 219.407i 0.958108i 0.877786 + 0.479054i \(0.159020\pi\)
−0.877786 + 0.479054i \(0.840980\pi\)
\(230\) 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 \(-0.243372\pi\)
0.721676 + 0.692231i \(0.243372\pi\)
\(252\) 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 \(-0.498360\pi\)
0.00515072 + 0.999987i \(0.498360\pi\)
\(270\) 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 \(0.0949119\pi\)
−0.955874 + 0.293776i \(0.905088\pi\)
\(278\) −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 \(0.0178307\pi\)
−0.998431 + 0.0559874i \(0.982169\pi\)
\(284\) −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 \(-0.325809\pi\)
0.520329 + 0.853966i \(0.325809\pi\)
\(294\) 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 \(0.0551558\pi\)
−0.985025 + 0.172411i \(0.944844\pi\)
\(308\) 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 \(-0.548910\pi\)
−0.153052 + 0.988218i \(0.548910\pi\)
\(318\) 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 \(0.385419\pi\)
−0.352242 + 0.935909i \(0.614581\pi\)
\(332\) −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 \(-0.642486\pi\)
−0.432833 + 0.901474i \(0.642486\pi\)
\(348\) 0 0
\(349\) 53.5299i 0.153381i 0.997055 + 0.0766904i \(0.0244353\pi\)
−0.997055 + 0.0766904i \(0.975565\pi\)
\(350\) 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 \(-0.682455\pi\)
0.542321 0.840171i \(-0.317545\pi\)
\(374\) 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 \(-0.856143\pi\)
0.899602 0.436711i \(-0.143857\pi\)
\(380\) −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 \(-0.521940\pi\)
−0.0688714 + 0.997626i \(0.521940\pi\)
\(390\) 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 \(0.118902\pi\)
−0.931040 + 0.364917i \(0.881098\pi\)
\(398\) −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 \(-0.368479\pi\)
0.401529 + 0.915846i \(0.368479\pi\)
\(420\) 0 0
\(421\) 217.481i 0.516582i 0.966067 + 0.258291i \(0.0831594\pi\)
−0.966067 + 0.258291i \(0.916841\pi\)
\(422\) −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 \(-0.521950\pi\)
−0.0689020 + 0.997623i \(0.521950\pi\)
\(444\) 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 \(-0.210159\pi\)
0.789850 + 0.613301i \(0.210159\pi\)
\(462\) 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 \(-0.158738\pi\)
0.878210 + 0.478276i \(0.158738\pi\)
\(468\) 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 \(-0.372769\pi\)
0.389149 + 0.921175i \(0.372769\pi\)
\(492\) 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 \(-0.812295\pi\)
0.831111 0.556107i \(-0.187705\pi\)
\(500\) −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 \(-0.668816\pi\)
−0.505836 + 0.862630i \(0.668816\pi\)
\(510\) 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 \(-0.734769\pi\)
0.672476 0.740119i \(-0.265231\pi\)
\(524\) −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 \(-0.816405\pi\)
0.838223 0.545328i \(-0.183595\pi\)
\(542\) 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 \(-0.776263\pi\)
0.762977 0.646425i \(-0.223737\pi\)
\(548\) 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 \(-0.478530\pi\)
0.0673982 + 0.997726i \(0.478530\pi\)
\(558\) 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 \(-0.467587\pi\)
0.101653 + 0.994820i \(0.467587\pi\)
\(564\) 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 \(0.259029\pi\)
−0.686768 + 0.726877i \(0.740971\pi\)
\(572\) 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 \(-0.381027\pi\)
0.365124 + 0.930959i \(0.381027\pi\)
\(588\) 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 \(-0.887014\pi\)
0.937662 0.347548i \(-0.112986\pi\)
\(614\) −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 \(-0.954792\pi\)
0.989932 0.141547i \(-0.0452075\pi\)
\(620\) 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 \(0.0214063\pi\)
−0.997740 + 0.0671991i \(0.978594\pi\)
\(644\) −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 \(-0.737552\pi\)
−0.678920 + 0.734212i \(0.737552\pi\)
\(654\) 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 \(-0.586265\pi\)
−0.267704 + 0.963501i \(0.586265\pi\)
\(660\) 0 0
\(661\) 1206.26i 1.82489i −0.409195 0.912447i \(-0.634190\pi\)
0.409195 0.912447i \(-0.365810\pi\)
\(662\) −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 \(-0.600531\pi\)
−0.310604 + 0.950540i \(0.600531\pi\)
\(678\) 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 \(-0.629295\pi\)
−0.395113 + 0.918632i \(0.629295\pi\)
\(684\) 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 \(0.101219\pi\)
−0.949866 + 0.312656i \(0.898781\pi\)
\(692\) −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 \(-0.283908\pi\)
0.627917 + 0.778280i \(0.283908\pi\)
\(702\) 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 \(-0.809366\pi\)
0.825960 0.563729i \(-0.190634\pi\)
\(710\) 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 \(0.212841\pi\)
−0.784653 + 0.619936i \(0.787159\pi\)
\(734\) −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 \(0.271215\pi\)
−0.658443 + 0.752631i \(0.728785\pi\)
\(740\) 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 \(0.0892869\pi\)
−0.960916 + 0.276839i \(0.910713\pi\)
\(758\) 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 \(-0.128813\pi\)
0.919229 + 0.393724i \(0.128813\pi\)
\(774\) 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 \(0.135463\pi\)
−0.910804 + 0.412839i \(0.864537\pi\)
\(788\) −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