Properties

Label 72.3.m.b.41.2
Level $72$
Weight $3$
Character 72.41
Analytic conductor $1.962$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19269881856.9
Defining polynomial: \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.2
Root \(0.831167 - 1.43962i\) of defining polynomial
Character \(\chi\) \(=\) 72.41
Dual form 72.3.m.b.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.668833 + 2.92449i) q^{3} +(-0.0440114 - 0.0254100i) q^{5} +(4.52944 + 7.84521i) q^{7} +(-8.10532 + 3.91200i) q^{9} +O(q^{10})\) \(q+(0.668833 + 2.92449i) q^{3} +(-0.0440114 - 0.0254100i) q^{5} +(4.52944 + 7.84521i) q^{7} +(-8.10532 + 3.91200i) q^{9} +(3.29117 - 1.90016i) q^{11} +(0.216902 - 0.375686i) q^{13} +(0.0448751 - 0.145706i) q^{15} -26.2355i q^{17} +34.2225 q^{19} +(-19.9138 + 18.4934i) q^{21} +(-29.9930 - 17.3164i) q^{23} +(-12.4987 - 21.6484i) q^{25} +(-16.8617 - 21.0875i) q^{27} +(14.0316 - 8.10114i) q^{29} +(-17.1675 + 29.7350i) q^{31} +(7.75825 + 8.35413i) q^{33} -0.460372i q^{35} +29.2761 q^{37} +(1.24376 + 0.383058i) q^{39} +(48.7026 + 28.1185i) q^{41} +(-3.94539 - 6.83362i) q^{43} +(0.456130 + 0.0337838i) q^{45} +(-33.4489 + 19.3117i) q^{47} +(-16.5316 + 28.6335i) q^{49} +(76.7256 - 17.5472i) q^{51} +50.5273i q^{53} -0.193132 q^{55} +(22.8891 + 100.083i) q^{57} +(-8.54743 - 4.93486i) q^{59} +(-36.5718 - 63.3442i) q^{61} +(-67.4030 - 45.8689i) q^{63} +(-0.0190923 + 0.0110230i) q^{65} +(-12.6797 + 21.9618i) q^{67} +(30.5815 - 99.2960i) q^{69} +97.8262i q^{71} -77.0599 q^{73} +(54.9511 - 51.0316i) q^{75} +(29.8143 + 17.2133i) q^{77} +(-42.1389 - 72.9868i) q^{79} +(50.3926 - 63.4160i) q^{81} +(40.6763 - 23.4845i) q^{83} +(-0.666644 + 1.15466i) q^{85} +(33.0765 + 35.6170i) q^{87} -108.587i q^{89} +3.92978 q^{91} +(-98.4420 - 30.3185i) q^{93} +(-1.50618 - 0.869593i) q^{95} +(-32.4021 - 56.1221i) q^{97} +(-19.2426 + 28.2765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) 0.668833 + 2.92449i 0.222944 + 0.974831i
\(4\) 0 0
\(5\) −0.0440114 0.0254100i −0.00880228 0.00508200i 0.495592 0.868555i \(-0.334951\pi\)
−0.504395 + 0.863473i \(0.668284\pi\)
\(6\) 0 0
\(7\) 4.52944 + 7.84521i 0.647062 + 1.12074i 0.983821 + 0.179154i \(0.0573360\pi\)
−0.336759 + 0.941591i \(0.609331\pi\)
\(8\) 0 0
\(9\) −8.10532 + 3.91200i −0.900592 + 0.434666i
\(10\) 0 0
\(11\) 3.29117 1.90016i 0.299198 0.172742i −0.342885 0.939377i \(-0.611404\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(12\) 0 0
\(13\) 0.216902 0.375686i 0.0166848 0.0288989i −0.857562 0.514380i \(-0.828022\pi\)
0.874247 + 0.485481i \(0.161355\pi\)
\(14\) 0 0
\(15\) 0.0448751 0.145706i 0.00299167 0.00971373i
\(16\) 0 0
\(17\) 26.2355i 1.54327i −0.636068 0.771633i \(-0.719440\pi\)
0.636068 0.771633i \(-0.280560\pi\)
\(18\) 0 0
\(19\) 34.2225 1.80118 0.900592 0.434666i \(-0.143133\pi\)
0.900592 + 0.434666i \(0.143133\pi\)
\(20\) 0 0
\(21\) −19.9138 + 18.4934i −0.948278 + 0.880640i
\(22\) 0 0
\(23\) −29.9930 17.3164i −1.30404 0.752889i −0.322947 0.946417i \(-0.604674\pi\)
−0.981095 + 0.193528i \(0.938007\pi\)
\(24\) 0 0
\(25\) −12.4987 21.6484i −0.499948 0.865936i
\(26\) 0 0
\(27\) −16.8617 21.0875i −0.624508 0.781018i
\(28\) 0 0
\(29\) 14.0316 8.10114i 0.483848 0.279350i −0.238171 0.971223i \(-0.576548\pi\)
0.722019 + 0.691874i \(0.243214\pi\)
\(30\) 0 0
\(31\) −17.1675 + 29.7350i −0.553790 + 0.959193i 0.444206 + 0.895925i \(0.353486\pi\)
−0.997997 + 0.0632685i \(0.979848\pi\)
\(32\) 0 0
\(33\) 7.75825 + 8.35413i 0.235099 + 0.253155i
\(34\) 0 0
\(35\) 0.460372i 0.0131535i
\(36\) 0 0
\(37\) 29.2761 0.791247 0.395623 0.918413i \(-0.370529\pi\)
0.395623 + 0.918413i \(0.370529\pi\)
\(38\) 0 0
\(39\) 1.24376 + 0.383058i 0.0318913 + 0.00982200i
\(40\) 0 0
\(41\) 48.7026 + 28.1185i 1.18787 + 0.685816i 0.957822 0.287363i \(-0.0927787\pi\)
0.230047 + 0.973180i \(0.426112\pi\)
\(42\) 0 0
\(43\) −3.94539 6.83362i −0.0917533 0.158921i 0.816496 0.577352i \(-0.195914\pi\)
−0.908249 + 0.418430i \(0.862580\pi\)
\(44\) 0 0
\(45\) 0.456130 + 0.0337838i 0.0101362 + 0.000750752i
\(46\) 0 0
\(47\) −33.4489 + 19.3117i −0.711678 + 0.410887i −0.811682 0.584100i \(-0.801448\pi\)
0.100004 + 0.994987i \(0.468114\pi\)
\(48\) 0 0
\(49\) −16.5316 + 28.6335i −0.337379 + 0.584358i
\(50\) 0 0
\(51\) 76.7256 17.5472i 1.50442 0.344062i
\(52\) 0 0
\(53\) 50.5273i 0.953344i 0.879081 + 0.476672i \(0.158157\pi\)
−0.879081 + 0.476672i \(0.841843\pi\)
\(54\) 0 0
\(55\) −0.193132 −0.00351149
\(56\) 0 0
\(57\) 22.8891 + 100.083i 0.401564 + 1.75585i
\(58\) 0 0
\(59\) −8.54743 4.93486i −0.144872 0.0836417i 0.425812 0.904812i \(-0.359988\pi\)
−0.570684 + 0.821170i \(0.693322\pi\)
\(60\) 0 0
\(61\) −36.5718 63.3442i −0.599537 1.03843i −0.992889 0.119041i \(-0.962018\pi\)
0.393352 0.919388i \(-0.371315\pi\)
\(62\) 0 0
\(63\) −67.4030 45.8689i −1.06989 0.728077i
\(64\) 0 0
\(65\) −0.0190923 + 0.0110230i −0.000293728 + 0.000169584i
\(66\) 0 0
\(67\) −12.6797 + 21.9618i −0.189249 + 0.327789i −0.945000 0.327070i \(-0.893939\pi\)
0.755751 + 0.654859i \(0.227272\pi\)
\(68\) 0 0
\(69\) 30.5815 99.2960i 0.443211 1.43907i
\(70\) 0 0
\(71\) 97.8262i 1.37783i 0.724840 + 0.688917i \(0.241914\pi\)
−0.724840 + 0.688917i \(0.758086\pi\)
\(72\) 0 0
\(73\) −77.0599 −1.05561 −0.527807 0.849364i \(-0.676986\pi\)
−0.527807 + 0.849364i \(0.676986\pi\)
\(74\) 0 0
\(75\) 54.9511 51.0316i 0.732681 0.680421i
\(76\) 0 0
\(77\) 29.8143 + 17.2133i 0.387199 + 0.223549i
\(78\) 0 0
\(79\) −42.1389 72.9868i −0.533404 0.923883i −0.999239 0.0390112i \(-0.987579\pi\)
0.465835 0.884872i \(-0.345754\pi\)
\(80\) 0 0
\(81\) 50.3926 63.4160i 0.622131 0.782913i
\(82\) 0 0
\(83\) 40.6763 23.4845i 0.490076 0.282946i −0.234530 0.972109i \(-0.575355\pi\)
0.724606 + 0.689163i \(0.242022\pi\)
\(84\) 0 0
\(85\) −0.666644 + 1.15466i −0.00784287 + 0.0135843i
\(86\) 0 0
\(87\) 33.0765 + 35.6170i 0.380190 + 0.409390i
\(88\) 0 0
\(89\) 108.587i 1.22008i −0.792371 0.610039i \(-0.791154\pi\)
0.792371 0.610039i \(-0.208846\pi\)
\(90\) 0 0
\(91\) 3.92978 0.0431844
\(92\) 0 0
\(93\) −98.4420 30.3185i −1.05852 0.326005i
\(94\) 0 0
\(95\) −1.50618 0.869593i −0.0158545 0.00915361i
\(96\) 0 0
\(97\) −32.4021 56.1221i −0.334043 0.578579i 0.649258 0.760568i \(-0.275080\pi\)
−0.983300 + 0.181990i \(0.941746\pi\)
\(98\) 0 0
\(99\) −19.2426 + 28.2765i −0.194370 + 0.285621i
\(100\) 0 0
\(101\) −168.478 + 97.2705i −1.66809 + 0.963075i −0.699430 + 0.714701i \(0.746563\pi\)
−0.968664 + 0.248373i \(0.920104\pi\)
\(102\) 0 0
\(103\) −12.4420 + 21.5502i −0.120796 + 0.209225i −0.920082 0.391726i \(-0.871878\pi\)
0.799286 + 0.600951i \(0.205211\pi\)
\(104\) 0 0
\(105\) 1.34635 0.307912i 0.0128224 0.00293249i
\(106\) 0 0
\(107\) 23.2306i 0.217108i 0.994091 + 0.108554i \(0.0346221\pi\)
−0.994091 + 0.108554i \(0.965378\pi\)
\(108\) 0 0
\(109\) 157.077 1.44108 0.720538 0.693416i \(-0.243895\pi\)
0.720538 + 0.693416i \(0.243895\pi\)
\(110\) 0 0
\(111\) 19.5808 + 85.6179i 0.176404 + 0.771332i
\(112\) 0 0
\(113\) −32.5614 18.7994i −0.288154 0.166366i 0.348955 0.937140i \(-0.386537\pi\)
−0.637109 + 0.770774i \(0.719870\pi\)
\(114\) 0 0
\(115\) 0.880021 + 1.52424i 0.00765236 + 0.0132543i
\(116\) 0 0
\(117\) −0.288382 + 3.89357i −0.00246481 + 0.0332784i
\(118\) 0 0
\(119\) 205.823 118.832i 1.72961 0.998589i
\(120\) 0 0
\(121\) −53.2788 + 92.2816i −0.440321 + 0.762658i
\(122\) 0 0
\(123\) −49.6584 + 161.237i −0.403727 + 1.31087i
\(124\) 0 0
\(125\) 2.54087i 0.0203269i
\(126\) 0 0
\(127\) 48.4364 0.381389 0.190694 0.981649i \(-0.438926\pi\)
0.190694 + 0.981649i \(0.438926\pi\)
\(128\) 0 0
\(129\) 17.3461 16.1088i 0.134466 0.124875i
\(130\) 0 0
\(131\) 0.0274376 + 0.0158411i 0.000209447 + 0.000120924i 0.500105 0.865965i \(-0.333295\pi\)
−0.499895 + 0.866086i \(0.666628\pi\)
\(132\) 0 0
\(133\) 155.009 + 268.483i 1.16548 + 2.01867i
\(134\) 0 0
\(135\) 0.206274 + 1.35655i 0.00152796 + 0.0100485i
\(136\) 0 0
\(137\) 0.913705 0.527528i 0.00666938 0.00385057i −0.496662 0.867944i \(-0.665441\pi\)
0.503331 + 0.864094i \(0.332108\pi\)
\(138\) 0 0
\(139\) 45.3655 78.5754i 0.326371 0.565290i −0.655418 0.755266i \(-0.727508\pi\)
0.981789 + 0.189976i \(0.0608410\pi\)
\(140\) 0 0
\(141\) −78.8487 84.9047i −0.559211 0.602161i
\(142\) 0 0
\(143\) 1.64860i 0.0115286i
\(144\) 0 0
\(145\) −0.823399 −0.00567862
\(146\) 0 0
\(147\) −94.7955 29.1955i −0.644867 0.198609i
\(148\) 0 0
\(149\) 15.1086 + 8.72295i 0.101400 + 0.0585433i 0.549842 0.835268i \(-0.314688\pi\)
−0.448442 + 0.893812i \(0.648021\pi\)
\(150\) 0 0
\(151\) 40.8713 + 70.7912i 0.270671 + 0.468816i 0.969034 0.246928i \(-0.0794211\pi\)
−0.698363 + 0.715744i \(0.746088\pi\)
\(152\) 0 0
\(153\) 102.633 + 212.647i 0.670806 + 1.38985i
\(154\) 0 0
\(155\) 1.51113 0.872452i 0.00974923 0.00562872i
\(156\) 0 0
\(157\) 96.4835 167.114i 0.614544 1.06442i −0.375920 0.926652i \(-0.622673\pi\)
0.990464 0.137770i \(-0.0439934\pi\)
\(158\) 0 0
\(159\) −147.767 + 33.7943i −0.929350 + 0.212543i
\(160\) 0 0
\(161\) 313.735i 1.94866i
\(162\) 0 0
\(163\) −165.401 −1.01473 −0.507364 0.861732i \(-0.669380\pi\)
−0.507364 + 0.861732i \(0.669380\pi\)
\(164\) 0 0
\(165\) −0.129173 0.564814i −0.000782868 0.00342311i
\(166\) 0 0
\(167\) −215.643 124.502i −1.29128 0.745520i −0.312398 0.949951i \(-0.601132\pi\)
−0.978881 + 0.204432i \(0.934465\pi\)
\(168\) 0 0
\(169\) 84.4059 + 146.195i 0.499443 + 0.865061i
\(170\) 0 0
\(171\) −277.384 + 133.878i −1.62213 + 0.782914i
\(172\) 0 0
\(173\) −117.476 + 67.8248i −0.679052 + 0.392051i −0.799498 0.600669i \(-0.794901\pi\)
0.120446 + 0.992720i \(0.461568\pi\)
\(174\) 0 0
\(175\) 113.224 196.110i 0.646995 1.12063i
\(176\) 0 0
\(177\) 8.71516 28.2975i 0.0492382 0.159873i
\(178\) 0 0
\(179\) 95.4526i 0.533255i −0.963800 0.266627i \(-0.914091\pi\)
0.963800 0.266627i \(-0.0859093\pi\)
\(180\) 0 0
\(181\) 58.9249 0.325552 0.162776 0.986663i \(-0.447955\pi\)
0.162776 + 0.986663i \(0.447955\pi\)
\(182\) 0 0
\(183\) 160.789 149.321i 0.878630 0.815960i
\(184\) 0 0
\(185\) −1.28848 0.743906i −0.00696477 0.00402111i
\(186\) 0 0
\(187\) −49.8517 86.3457i −0.266587 0.461742i
\(188\) 0 0
\(189\) 89.0619 227.798i 0.471227 1.20528i
\(190\) 0 0
\(191\) 164.852 95.1775i 0.863101 0.498311i −0.00194880 0.999998i \(-0.500620\pi\)
0.865049 + 0.501687i \(0.167287\pi\)
\(192\) 0 0
\(193\) 5.29645 9.17373i 0.0274428 0.0475323i −0.851978 0.523578i \(-0.824597\pi\)
0.879421 + 0.476046i \(0.157930\pi\)
\(194\) 0 0
\(195\) −0.0450062 0.0484629i −0.000230801 0.000248528i
\(196\) 0 0
\(197\) 215.874i 1.09581i 0.836541 + 0.547904i \(0.184574\pi\)
−0.836541 + 0.547904i \(0.815426\pi\)
\(198\) 0 0
\(199\) −146.668 −0.737026 −0.368513 0.929623i \(-0.620133\pi\)
−0.368513 + 0.929623i \(0.620133\pi\)
\(200\) 0 0
\(201\) −72.7079 22.3928i −0.361731 0.111407i
\(202\) 0 0
\(203\) 127.110 + 73.3872i 0.626159 + 0.361513i
\(204\) 0 0
\(205\) −1.42898 2.47506i −0.00697063 0.0120735i
\(206\) 0 0
\(207\) 310.845 + 23.0231i 1.50166 + 0.111223i
\(208\) 0 0
\(209\) 112.632 65.0282i 0.538910 0.311140i
\(210\) 0 0
\(211\) −54.8335 + 94.9744i −0.259874 + 0.450116i −0.966208 0.257763i \(-0.917014\pi\)
0.706334 + 0.707879i \(0.250348\pi\)
\(212\) 0 0
\(213\) −286.092 + 65.4294i −1.34316 + 0.307180i
\(214\) 0 0
\(215\) 0.401009i 0.00186516i
\(216\) 0 0
\(217\) −311.036 −1.43335
\(218\) 0 0
\(219\) −51.5402 225.361i −0.235343 1.02905i
\(220\) 0 0
\(221\) −9.85631 5.69054i −0.0445987 0.0257491i
\(222\) 0 0
\(223\) 73.8403 + 127.895i 0.331123 + 0.573521i 0.982732 0.185033i \(-0.0592393\pi\)
−0.651610 + 0.758554i \(0.725906\pi\)
\(224\) 0 0
\(225\) 185.995 + 126.572i 0.826642 + 0.562544i
\(226\) 0 0
\(227\) −346.255 + 199.911i −1.52535 + 0.880664i −0.525806 + 0.850605i \(0.676236\pi\)
−0.999548 + 0.0300589i \(0.990431\pi\)
\(228\) 0 0
\(229\) 39.1692 67.8430i 0.171044 0.296258i −0.767741 0.640760i \(-0.778619\pi\)
0.938785 + 0.344503i \(0.111953\pi\)
\(230\) 0 0
\(231\) −30.3994 + 98.7046i −0.131599 + 0.427293i
\(232\) 0 0
\(233\) 352.995i 1.51500i 0.652835 + 0.757500i \(0.273580\pi\)
−0.652835 + 0.757500i \(0.726420\pi\)
\(234\) 0 0
\(235\) 1.96284 0.00835251
\(236\) 0 0
\(237\) 185.265 172.051i 0.781711 0.725953i
\(238\) 0 0
\(239\) 279.549 + 161.397i 1.16966 + 0.675303i 0.953600 0.301077i \(-0.0973461\pi\)
0.216060 + 0.976380i \(0.430679\pi\)
\(240\) 0 0
\(241\) −105.601 182.907i −0.438180 0.758949i 0.559370 0.828918i \(-0.311043\pi\)
−0.997549 + 0.0699691i \(0.977710\pi\)
\(242\) 0 0
\(243\) 219.164 + 104.958i 0.901909 + 0.431926i
\(244\) 0 0
\(245\) 1.45516 0.840135i 0.00593941 0.00342912i
\(246\) 0 0
\(247\) 7.42293 12.8569i 0.0300524 0.0520522i
\(248\) 0 0
\(249\) 95.8859 + 103.250i 0.385084 + 0.414661i
\(250\) 0 0
\(251\) 206.824i 0.824001i 0.911184 + 0.412001i \(0.135170\pi\)
−0.911184 + 0.412001i \(0.864830\pi\)
\(252\) 0 0
\(253\) −131.616 −0.520222
\(254\) 0 0
\(255\) −3.82267 1.17732i −0.0149909 0.00461694i
\(256\) 0 0
\(257\) 20.7432 + 11.9761i 0.0807127 + 0.0465995i 0.539813 0.841785i \(-0.318495\pi\)
−0.459100 + 0.888384i \(0.651828\pi\)
\(258\) 0 0
\(259\) 132.604 + 229.678i 0.511986 + 0.886786i
\(260\) 0 0
\(261\) −82.0389 + 120.554i −0.314325 + 0.461892i
\(262\) 0 0
\(263\) −119.369 + 68.9175i −0.453873 + 0.262044i −0.709464 0.704741i \(-0.751063\pi\)
0.255592 + 0.966785i \(0.417730\pi\)
\(264\) 0 0
\(265\) 1.28390 2.22377i 0.00484489 0.00839160i
\(266\) 0 0
\(267\) 317.562 72.6265i 1.18937 0.272009i
\(268\) 0 0
\(269\) 249.461i 0.927366i −0.886001 0.463683i \(-0.846528\pi\)
0.886001 0.463683i \(-0.153472\pi\)
\(270\) 0 0
\(271\) 72.6700 0.268155 0.134078 0.990971i \(-0.457193\pi\)
0.134078 + 0.990971i \(0.457193\pi\)
\(272\) 0 0
\(273\) 2.62837 + 11.4926i 0.00962771 + 0.0420975i
\(274\) 0 0
\(275\) −82.2709 47.4991i −0.299167 0.172724i
\(276\) 0 0
\(277\) −182.021 315.270i −0.657117 1.13816i −0.981359 0.192185i \(-0.938443\pi\)
0.324242 0.945974i \(-0.394891\pi\)
\(278\) 0 0
\(279\) 22.8251 308.171i 0.0818102 1.10456i
\(280\) 0 0
\(281\) 241.120 139.211i 0.858077 0.495411i −0.00529060 0.999986i \(-0.501684\pi\)
0.863368 + 0.504575i \(0.168351\pi\)
\(282\) 0 0
\(283\) −13.7745 + 23.8581i −0.0486732 + 0.0843044i −0.889336 0.457255i \(-0.848833\pi\)
0.840662 + 0.541560i \(0.182166\pi\)
\(284\) 0 0
\(285\) 1.53574 4.98642i 0.00538855 0.0174962i
\(286\) 0 0
\(287\) 509.443i 1.77506i
\(288\) 0 0
\(289\) −399.303 −1.38167
\(290\) 0 0
\(291\) 142.457 132.296i 0.489544 0.454626i
\(292\) 0 0
\(293\) 342.145 + 197.537i 1.16773 + 0.674189i 0.953144 0.302517i \(-0.0978267\pi\)
0.214585 + 0.976705i \(0.431160\pi\)
\(294\) 0 0
\(295\) 0.250789 + 0.434380i 0.000850133 + 0.00147247i
\(296\) 0 0
\(297\) −95.5645 37.3627i −0.321766 0.125800i
\(298\) 0 0
\(299\) −13.0111 + 7.51195i −0.0435153 + 0.0251236i
\(300\) 0 0
\(301\) 35.7408 61.9049i 0.118740 0.205664i
\(302\) 0 0
\(303\) −397.150 427.654i −1.31073 1.41140i
\(304\) 0 0
\(305\) 3.71715i 0.0121874i
\(306\) 0 0
\(307\) −122.443 −0.398836 −0.199418 0.979915i \(-0.563905\pi\)
−0.199418 + 0.979915i \(0.563905\pi\)
\(308\) 0 0
\(309\) −71.3449 21.9731i −0.230890 0.0711102i
\(310\) 0 0
\(311\) −420.591 242.829i −1.35238 0.780799i −0.363801 0.931477i \(-0.618521\pi\)
−0.988583 + 0.150677i \(0.951855\pi\)
\(312\) 0 0
\(313\) 5.15434 + 8.92759i 0.0164676 + 0.0285226i 0.874142 0.485671i \(-0.161425\pi\)
−0.857674 + 0.514194i \(0.828091\pi\)
\(314\) 0 0
\(315\) 1.80097 + 3.73146i 0.00571737 + 0.0118459i
\(316\) 0 0
\(317\) −144.879 + 83.6462i −0.457033 + 0.263868i −0.710796 0.703398i \(-0.751665\pi\)
0.253763 + 0.967266i \(0.418332\pi\)
\(318\) 0 0
\(319\) 30.7869 53.3245i 0.0965107 0.167162i
\(320\) 0 0
\(321\) −67.9378 + 15.5374i −0.211644 + 0.0484031i
\(322\) 0 0
\(323\) 897.845i 2.77971i
\(324\) 0 0
\(325\) −10.8440 −0.0333661
\(326\) 0 0
\(327\) 105.058 + 459.371i 0.321280 + 1.40481i
\(328\) 0 0
\(329\) −303.009 174.942i −0.921000 0.531740i
\(330\) 0 0
\(331\) 52.2422 + 90.4861i 0.157831 + 0.273372i 0.934086 0.357047i \(-0.116216\pi\)
−0.776255 + 0.630419i \(0.782883\pi\)
\(332\) 0 0
\(333\) −237.293 + 114.528i −0.712590 + 0.343928i
\(334\) 0 0
\(335\) 1.11610 0.644381i 0.00333164 0.00192352i
\(336\) 0 0
\(337\) 196.086 339.631i 0.581858 1.00781i −0.413401 0.910549i \(-0.635659\pi\)
0.995259 0.0972586i \(-0.0310074\pi\)
\(338\) 0 0
\(339\) 33.2004 107.799i 0.0979364 0.317992i
\(340\) 0 0
\(341\) 130.484i 0.382651i
\(342\) 0 0
\(343\) 144.370 0.420903
\(344\) 0 0
\(345\) −3.86905 + 3.59308i −0.0112146 + 0.0104147i
\(346\) 0 0
\(347\) 247.220 + 142.732i 0.712449 + 0.411333i 0.811967 0.583703i \(-0.198397\pi\)
−0.0995180 + 0.995036i \(0.531730\pi\)
\(348\) 0 0
\(349\) 151.562 + 262.514i 0.434276 + 0.752189i 0.997236 0.0742956i \(-0.0236708\pi\)
−0.562960 + 0.826484i \(0.690337\pi\)
\(350\) 0 0
\(351\) −11.5796 + 1.76078i −0.0329903 + 0.00501646i
\(352\) 0 0
\(353\) 308.183 177.929i 0.873039 0.504049i 0.00468222 0.999989i \(-0.498510\pi\)
0.868357 + 0.495940i \(0.165176\pi\)
\(354\) 0 0
\(355\) 2.48576 4.30547i 0.00700215 0.0121281i
\(356\) 0 0
\(357\) 485.185 + 522.450i 1.35906 + 1.46345i
\(358\) 0 0
\(359\) 148.171i 0.412733i −0.978475 0.206367i \(-0.933836\pi\)
0.978475 0.206367i \(-0.0661639\pi\)
\(360\) 0 0
\(361\) 810.179 2.24426
\(362\) 0 0
\(363\) −305.511 94.0925i −0.841629 0.259208i
\(364\) 0 0
\(365\) 3.39151 + 1.95809i 0.00929181 + 0.00536463i
\(366\) 0 0
\(367\) −123.772 214.380i −0.337254 0.584141i 0.646661 0.762777i \(-0.276165\pi\)
−0.983915 + 0.178636i \(0.942831\pi\)
\(368\) 0 0
\(369\) −504.750 37.3849i −1.36789 0.101314i
\(370\) 0 0
\(371\) −396.397 + 228.860i −1.06846 + 0.616873i
\(372\) 0 0
\(373\) −224.520 + 388.881i −0.601931 + 1.04258i 0.390597 + 0.920562i \(0.372269\pi\)
−0.992528 + 0.122014i \(0.961065\pi\)
\(374\) 0 0
\(375\) −7.43075 + 1.69942i −0.0198153 + 0.00453177i
\(376\) 0 0
\(377\) 7.02862i 0.0186436i
\(378\) 0 0
\(379\) 618.282 1.63135 0.815675 0.578510i \(-0.196366\pi\)
0.815675 + 0.578510i \(0.196366\pi\)
\(380\) 0 0
\(381\) 32.3959 + 141.652i 0.0850285 + 0.371790i
\(382\) 0 0
\(383\) −370.803 214.083i −0.968155 0.558965i −0.0694818 0.997583i \(-0.522135\pi\)
−0.898673 + 0.438619i \(0.855468\pi\)
\(384\) 0 0
\(385\) −0.874780 1.51516i −0.00227216 0.00393549i
\(386\) 0 0
\(387\) 58.7118 + 39.9544i 0.151710 + 0.103241i
\(388\) 0 0
\(389\) 585.313 337.930i 1.50466 0.868716i 0.504674 0.863310i \(-0.331613\pi\)
0.999985 0.00540555i \(-0.00172065\pi\)
\(390\) 0 0
\(391\) −454.306 + 786.881i −1.16191 + 2.01248i
\(392\) 0 0
\(393\) −0.0279760 + 0.0908360i −7.11857e−5 + 0.000231135i
\(394\) 0 0
\(395\) 4.28300i 0.0108430i
\(396\) 0 0
\(397\) 209.902 0.528721 0.264361 0.964424i \(-0.414839\pi\)
0.264361 + 0.964424i \(0.414839\pi\)
\(398\) 0 0
\(399\) −681.501 + 632.892i −1.70802 + 1.58619i
\(400\) 0 0
\(401\) 175.023 + 101.050i 0.436467 + 0.251994i 0.702098 0.712080i \(-0.252247\pi\)
−0.265631 + 0.964075i \(0.585580\pi\)
\(402\) 0 0
\(403\) 7.44734 + 12.8992i 0.0184797 + 0.0320079i
\(404\) 0 0
\(405\) −3.82925 + 1.51055i −0.00945493 + 0.00372975i
\(406\) 0 0
\(407\) 96.3528 55.6293i 0.236739 0.136681i
\(408\) 0 0
\(409\) −291.252 + 504.464i −0.712108 + 1.23341i 0.251957 + 0.967739i \(0.418926\pi\)
−0.964064 + 0.265669i \(0.914407\pi\)
\(410\) 0 0
\(411\) 2.15387 + 2.31930i 0.00524056 + 0.00564306i
\(412\) 0 0
\(413\) 89.4085i 0.216486i
\(414\) 0 0
\(415\) −2.38696 −0.00575172
\(416\) 0 0
\(417\) 260.135 + 80.1173i 0.623825 + 0.192128i
\(418\) 0 0
\(419\) 675.460 + 389.977i 1.61208 + 0.930733i 0.988888 + 0.148662i \(0.0474968\pi\)
0.623189 + 0.782071i \(0.285837\pi\)
\(420\) 0 0
\(421\) −84.1068 145.677i −0.199779 0.346027i 0.748678 0.662934i \(-0.230689\pi\)
−0.948457 + 0.316907i \(0.897356\pi\)
\(422\) 0 0
\(423\) 195.567 287.380i 0.462332 0.679384i
\(424\) 0 0
\(425\) −567.957 + 327.910i −1.33637 + 0.771553i
\(426\) 0 0
\(427\) 331.299 573.827i 0.775876 1.34386i
\(428\) 0 0
\(429\) 4.82131 1.10264i 0.0112385 0.00257024i
\(430\) 0 0
\(431\) 182.732i 0.423973i −0.977273 0.211986i \(-0.932007\pi\)
0.977273 0.211986i \(-0.0679933\pi\)
\(432\) 0 0
\(433\) 447.193 1.03278 0.516389 0.856354i \(-0.327276\pi\)
0.516389 + 0.856354i \(0.327276\pi\)
\(434\) 0 0
\(435\) −0.550717 2.40803i −0.00126602 0.00553569i
\(436\) 0 0
\(437\) −1026.43 592.612i −2.34882 1.35609i
\(438\) 0 0
\(439\) 98.6108 + 170.799i 0.224626 + 0.389063i 0.956207 0.292691i \(-0.0945507\pi\)
−0.731581 + 0.681754i \(0.761217\pi\)
\(440\) 0 0
\(441\) 21.9796 296.756i 0.0498403 0.672915i
\(442\) 0 0
\(443\) 244.803 141.337i 0.552603 0.319045i −0.197568 0.980289i \(-0.563304\pi\)
0.750171 + 0.661244i \(0.229971\pi\)
\(444\) 0 0
\(445\) −2.75919 + 4.77906i −0.00620043 + 0.0107395i
\(446\) 0 0
\(447\) −15.4051 + 50.0192i −0.0344633 + 0.111900i
\(448\) 0 0
\(449\) 349.046i 0.777386i 0.921367 + 0.388693i \(0.127073\pi\)
−0.921367 + 0.388693i \(0.872927\pi\)
\(450\) 0 0
\(451\) 213.718 0.473877
\(452\) 0 0
\(453\) −179.692 + 166.875i −0.396672 + 0.368378i
\(454\) 0 0
\(455\) −0.172955 0.0998556i −0.000380121 0.000219463i
\(456\) 0 0
\(457\) −40.2987 69.7995i −0.0881811 0.152734i 0.818561 0.574419i \(-0.194772\pi\)
−0.906742 + 0.421685i \(0.861439\pi\)
\(458\) 0 0
\(459\) −553.242 + 442.376i −1.20532 + 0.963782i
\(460\) 0 0
\(461\) 495.135 285.866i 1.07405 0.620100i 0.144761 0.989467i \(-0.453759\pi\)
0.929284 + 0.369366i \(0.120425\pi\)
\(462\) 0 0
\(463\) 139.837 242.205i 0.302024 0.523120i −0.674571 0.738210i \(-0.735671\pi\)
0.976594 + 0.215090i \(0.0690045\pi\)
\(464\) 0 0
\(465\) 3.56217 + 3.83577i 0.00766059 + 0.00824896i
\(466\) 0 0
\(467\) 506.702i 1.08501i −0.840051 0.542507i \(-0.817475\pi\)
0.840051 0.542507i \(-0.182525\pi\)
\(468\) 0 0
\(469\) −229.727 −0.489823
\(470\) 0 0
\(471\) 553.256 + 170.394i 1.17464 + 0.361770i
\(472\) 0 0
\(473\) −25.9699 14.9938i −0.0549048 0.0316993i
\(474\) 0 0
\(475\) −427.737 740.862i −0.900499 1.55971i
\(476\) 0 0
\(477\) −197.662 409.540i −0.414387 0.858574i
\(478\) 0 0
\(479\) −217.596 + 125.629i −0.454271 + 0.262274i −0.709632 0.704572i \(-0.751139\pi\)
0.255361 + 0.966846i \(0.417806\pi\)
\(480\) 0 0
\(481\) 6.35006 10.9986i 0.0132018 0.0228662i
\(482\) 0 0
\(483\) 917.516 209.836i 1.89962 0.434444i
\(484\) 0 0
\(485\) 3.29335i 0.00679041i
\(486\) 0 0
\(487\) −313.224 −0.643170 −0.321585 0.946881i \(-0.604216\pi\)
−0.321585 + 0.946881i \(0.604216\pi\)
\(488\) 0 0
\(489\) −110.625 483.713i −0.226228 0.989188i
\(490\) 0 0
\(491\) 533.397 + 307.957i 1.08635 + 0.627204i 0.932602 0.360906i \(-0.117533\pi\)
0.153747 + 0.988110i \(0.450866\pi\)
\(492\) 0 0
\(493\) −212.538 368.126i −0.431111 0.746706i
\(494\) 0 0
\(495\) 1.56540 0.755532i 0.00316242 0.00152633i
\(496\) 0 0
\(497\) −767.467 + 443.098i −1.54420 + 0.891544i
\(498\) 0 0
\(499\) −412.029 + 713.654i −0.825709 + 1.43017i 0.0756679 + 0.997133i \(0.475891\pi\)
−0.901377 + 0.433036i \(0.857442\pi\)
\(500\) 0 0
\(501\) 219.875 713.919i 0.438873 1.42499i
\(502\) 0 0
\(503\) 175.718i 0.349340i 0.984627 + 0.174670i \(0.0558858\pi\)
−0.984627 + 0.174670i \(0.944114\pi\)
\(504\) 0 0
\(505\) 9.88657 0.0195774
\(506\) 0 0
\(507\) −371.094 + 344.625i −0.731940 + 0.679733i
\(508\) 0 0
\(509\) −314.934 181.827i −0.618730 0.357224i 0.157644 0.987496i \(-0.449610\pi\)
−0.776374 + 0.630272i \(0.782943\pi\)
\(510\) 0 0
\(511\) −349.038 604.551i −0.683049 1.18307i
\(512\) 0 0
\(513\) −577.050 721.667i −1.12485 1.40676i
\(514\) 0 0
\(515\) 1.09518 0.632301i 0.00212656 0.00122777i
\(516\) 0 0
\(517\) −73.3907 + 127.116i −0.141955 + 0.245873i
\(518\) 0 0
\(519\) −276.925 298.194i −0.533574 0.574556i
\(520\) 0 0
\(521\) 458.709i 0.880440i 0.897890 + 0.440220i \(0.145099\pi\)
−0.897890 + 0.440220i \(0.854901\pi\)
\(522\) 0 0
\(523\) −458.289 −0.876270 −0.438135 0.898909i \(-0.644361\pi\)
−0.438135 + 0.898909i \(0.644361\pi\)
\(524\) 0 0
\(525\) 649.251 + 199.959i 1.23667 + 0.380873i
\(526\) 0 0
\(527\) 780.113 + 450.398i 1.48029 + 0.854646i
\(528\) 0 0
\(529\) 335.219 + 580.616i 0.633683 + 1.09757i
\(530\) 0 0
\(531\) 88.5848 + 6.56114i 0.166826 + 0.0123562i
\(532\) 0 0
\(533\) 21.1274 12.1979i 0.0396387 0.0228854i
\(534\) 0 0
\(535\) 0.590289 1.02241i 0.00110334 0.00191105i
\(536\) 0 0
\(537\) 279.150 63.8418i 0.519833 0.118886i
\(538\) 0 0
\(539\) 125.651i 0.233118i
\(540\) 0 0
\(541\) −824.876 −1.52472 −0.762362 0.647150i \(-0.775961\pi\)
−0.762362 + 0.647150i \(0.775961\pi\)
\(542\) 0 0
\(543\) 39.4109 + 172.325i 0.0725800 + 0.317358i
\(544\) 0 0
\(545\) −6.91319 3.99133i −0.0126847 0.00732354i
\(546\) 0 0
\(547\) −16.8719 29.2230i −0.0308444 0.0534241i 0.850191 0.526474i \(-0.176486\pi\)
−0.881036 + 0.473050i \(0.843153\pi\)
\(548\) 0 0
\(549\) 544.228 + 370.357i 0.991309 + 0.674602i
\(550\) 0 0
\(551\) 480.196 277.241i 0.871499 0.503160i
\(552\) 0 0
\(553\) 381.731 661.178i 0.690291 1.19562i
\(554\) 0 0
\(555\) 1.31377 4.26571i 0.00236715 0.00768596i
\(556\) 0 0
\(557\) 541.032i 0.971332i 0.874145 + 0.485666i \(0.161423\pi\)
−0.874145 + 0.485666i \(0.838577\pi\)
\(558\) 0 0
\(559\) −3.42306 −0.00612354
\(560\) 0 0
\(561\) 219.175 203.542i 0.390686 0.362820i
\(562\) 0 0
\(563\) −97.8909 56.5173i −0.173874 0.100386i 0.410537 0.911844i \(-0.365341\pi\)
−0.584411 + 0.811458i \(0.698674\pi\)
\(564\) 0 0
\(565\) 0.955383 + 1.65477i 0.00169094 + 0.00292880i
\(566\) 0 0
\(567\) 725.762 + 108.102i 1.28000 + 0.190656i
\(568\) 0 0
\(569\) 236.524 136.557i 0.415684 0.239995i −0.277545 0.960713i \(-0.589521\pi\)
0.693229 + 0.720717i \(0.256187\pi\)
\(570\) 0 0
\(571\) 122.654 212.443i 0.214806 0.372054i −0.738407 0.674356i \(-0.764421\pi\)
0.953212 + 0.302301i \(0.0977548\pi\)
\(572\) 0 0
\(573\) 388.604 + 418.451i 0.678193 + 0.730282i
\(574\) 0 0
\(575\) 865.733i 1.50562i
\(576\) 0 0
\(577\) 632.666 1.09648 0.548238 0.836323i \(-0.315299\pi\)
0.548238 + 0.836323i \(0.315299\pi\)
\(578\) 0 0
\(579\) 30.3709 + 9.35375i 0.0524541 + 0.0161550i
\(580\) 0 0
\(581\) 368.482 + 212.743i 0.634220 + 0.366167i
\(582\) 0 0
\(583\) 96.0099 + 166.294i 0.164682 + 0.285238i
\(584\) 0 0
\(585\) 0.111628 0.164034i 0.000190817 0.000280400i
\(586\) 0 0
\(587\) −980.129 + 565.878i −1.66973 + 0.964017i −0.701942 + 0.712234i \(0.747683\pi\)
−0.967784 + 0.251782i \(0.918983\pi\)
\(588\) 0 0
\(589\) −587.515 + 1017.61i −0.997478 + 1.72768i
\(590\) 0 0
\(591\) −631.322 + 144.384i −1.06823 + 0.244304i
\(592\) 0 0
\(593\) 180.213i 0.303900i 0.988388 + 0.151950i \(0.0485553\pi\)
−0.988388 + 0.151950i \(0.951445\pi\)
\(594\) 0 0
\(595\) −12.0781 −0.0202993
\(596\) 0 0
\(597\) −98.0965 428.930i −0.164316 0.718476i
\(598\) 0 0
\(599\) −566.086 326.830i −0.945052 0.545626i −0.0535119 0.998567i \(-0.517041\pi\)
−0.891541 + 0.452941i \(0.850375\pi\)
\(600\) 0 0
\(601\) −178.947 309.945i −0.297749 0.515716i 0.677872 0.735180i \(-0.262902\pi\)
−0.975621 + 0.219464i \(0.929569\pi\)
\(602\) 0 0
\(603\) 16.8583 227.611i 0.0279573 0.377464i
\(604\) 0 0
\(605\) 4.68975 2.70763i 0.00775164 0.00447541i
\(606\) 0 0
\(607\) 320.064 554.367i 0.527288 0.913290i −0.472206 0.881488i \(-0.656542\pi\)
0.999494 0.0318015i \(-0.0101245\pi\)
\(608\) 0 0
\(609\) −129.605 + 420.817i −0.212816 + 0.690997i
\(610\) 0 0
\(611\) 16.7550i 0.0274223i
\(612\) 0 0
\(613\) 246.093 0.401457 0.200729 0.979647i \(-0.435669\pi\)
0.200729 + 0.979647i \(0.435669\pi\)
\(614\) 0 0
\(615\) 6.28256 5.83445i 0.0102155 0.00948690i
\(616\) 0 0
\(617\) 309.912 + 178.928i 0.502289 + 0.289997i 0.729658 0.683812i \(-0.239679\pi\)
−0.227369 + 0.973809i \(0.573013\pi\)
\(618\) 0 0
\(619\) −40.5053 70.1573i −0.0654368 0.113340i 0.831451 0.555598i \(-0.187511\pi\)
−0.896888 + 0.442258i \(0.854177\pi\)
\(620\) 0 0
\(621\) 140.572 + 924.462i 0.226364 + 1.48867i
\(622\) 0 0
\(623\) 851.888 491.838i 1.36740 0.789467i
\(624\) 0 0
\(625\) −312.403 + 541.098i −0.499845 + 0.865757i
\(626\) 0 0
\(627\) 265.507 + 285.899i 0.423456 + 0.455979i
\(628\) 0 0
\(629\) 768.075i 1.22110i
\(630\) 0 0
\(631\) −252.241 −0.399748 −0.199874 0.979822i \(-0.564053\pi\)
−0.199874 + 0.979822i \(0.564053\pi\)
\(632\) 0 0
\(633\) −314.426 96.8382i −0.496724 0.152983i
\(634\) 0 0
\(635\) −2.13175 1.23077i −0.00335709 0.00193822i
\(636\) 0 0
\(637\) 7.17147 + 12.4214i 0.0112582 + 0.0194998i
\(638\) 0 0
\(639\) −382.696 792.913i −0.598898 1.24087i
\(640\) 0 0
\(641\) −843.278 + 486.867i −1.31557 + 0.759542i −0.983012 0.183542i \(-0.941244\pi\)
−0.332554 + 0.943084i \(0.607910\pi\)
\(642\) 0 0
\(643\) −341.530 + 591.547i −0.531151 + 0.919980i 0.468188 + 0.883629i \(0.344907\pi\)
−0.999339 + 0.0363512i \(0.988426\pi\)
\(644\) 0 0
\(645\) −1.17275 + 0.268208i −0.00181822 + 0.000415827i
\(646\) 0 0
\(647\) 390.640i 0.603771i −0.953344 0.301885i \(-0.902384\pi\)
0.953344 0.301885i \(-0.0976160\pi\)
\(648\) 0 0
\(649\) −37.5081 −0.0577937
\(650\) 0 0
\(651\) −208.031 909.624i −0.319557 1.39727i
\(652\) 0 0
\(653\) 542.529 + 313.230i 0.830826 + 0.479678i 0.854135 0.520051i \(-0.174087\pi\)
−0.0233093 + 0.999728i \(0.507420\pi\)
\(654\) 0 0
\(655\) −0.000805043 0.00139438i −1.22907e−6 2.12882e-6i
\(656\) 0 0
\(657\) 624.595 301.458i 0.950678 0.458840i
\(658\) 0 0
\(659\) 51.4518 29.7057i 0.0780755 0.0450769i −0.460454 0.887684i \(-0.652313\pi\)
0.538530 + 0.842607i \(0.318980\pi\)
\(660\) 0 0
\(661\) 425.950 737.767i 0.644402 1.11614i −0.340037 0.940412i \(-0.610440\pi\)
0.984439 0.175725i \(-0.0562270\pi\)
\(662\) 0 0
\(663\) 10.0497 32.6307i 0.0151580 0.0492168i
\(664\) 0 0
\(665\) 15.7551i 0.0236918i
\(666\) 0 0
\(667\) −561.132 −0.841277
\(668\) 0 0
\(669\) −324.642 + 301.486i −0.485264 + 0.450652i
\(670\) 0 0
\(671\) −240.728 138.985i −0.358760 0.207130i
\(672\) 0 0
\(673\) 210.489 + 364.577i 0.312762 + 0.541720i 0.978959 0.204056i \(-0.0654124\pi\)
−0.666197 + 0.745776i \(0.732079\pi\)
\(674\) 0 0
\(675\) −245.761 + 628.596i −0.364090 + 0.931253i
\(676\) 0 0
\(677\) 313.326 180.899i 0.462816 0.267207i −0.250412 0.968139i \(-0.580566\pi\)
0.713227 + 0.700933i \(0.247233\pi\)
\(678\) 0 0
\(679\) 293.527 508.403i 0.432293 0.748753i
\(680\) 0 0
\(681\) −816.224 878.915i −1.19857 1.29062i
\(682\) 0 0
\(683\) 705.769i 1.03334i −0.856186 0.516668i \(-0.827172\pi\)
0.856186 0.516668i \(-0.172828\pi\)
\(684\) 0 0
\(685\) −0.0536179 −7.82743e−5
\(686\) 0 0
\(687\) 224.604 + 69.1743i 0.326934 + 0.100690i
\(688\) 0 0
\(689\) 18.9824 + 10.9595i 0.0275506 + 0.0159063i
\(690\) 0 0
\(691\) 345.384 + 598.222i 0.499832 + 0.865734i 1.00000 0.000194148i \(-6.17992e-5\pi\)
−0.500168 + 0.865928i \(0.666728\pi\)
\(692\) 0 0
\(693\) −308.993 22.8860i −0.445878 0.0330245i
\(694\) 0 0
\(695\) −3.99320 + 2.30547i −0.00574561 + 0.00331723i
\(696\) 0 0
\(697\) 737.703 1277.74i 1.05840 1.83320i
\(698\) 0 0
\(699\) −1032.33 + 236.095i −1.47687 + 0.337761i
\(700\) 0 0
\(701\) 1213.04i 1.73045i −0.501384 0.865225i \(-0.667176\pi\)
0.501384 0.865225i \(-0.332824\pi\)
\(702\) 0 0
\(703\) 1001.90 1.42518
\(704\) 0 0
\(705\) 1.31281 + 5.74032i 0.00186215 + 0.00814229i
\(706\) 0 0
\(707\) −1526.22 881.161i −2.15872 1.24634i
\(708\) 0 0
\(709\) 226.667 + 392.598i 0.319699 + 0.553735i 0.980425 0.196892i \(-0.0630848\pi\)
−0.660726 + 0.750627i \(0.729751\pi\)
\(710\) 0 0
\(711\) 627.074 + 426.734i 0.881960 + 0.600189i
\(712\) 0 0
\(713\) 1029.81 594.560i 1.44433 0.833885i
\(714\) 0 0
\(715\) −0.0418908 + 0.0725570i −5.85885e−5 + 0.000101478i
\(716\) 0 0
\(717\) −285.035 + 925.486i −0.397538 + 1.29078i
\(718\) 0 0
\(719\) 418.833i 0.582522i 0.956644 + 0.291261i \(0.0940748\pi\)
−0.956644 + 0.291261i \(0.905925\pi\)
\(720\) 0 0
\(721\) −225.421 −0.312650
\(722\) 0 0
\(723\) 464.280 431.164i 0.642158 0.596355i
\(724\) 0 0
\(725\) −350.753 202.508i −0.483798 0.279321i
\(726\) 0 0
\(727\) 376.166 + 651.539i 0.517423 + 0.896203i 0.999795 + 0.0202365i \(0.00644191\pi\)
−0.482372 + 0.875966i \(0.660225\pi\)
\(728\) 0 0
\(729\) −160.365 + 711.143i −0.219980 + 0.975504i
\(730\) 0 0
\(731\) −179.284 + 103.509i −0.245258 + 0.141600i
\(732\) 0 0
\(733\) 255.863 443.168i 0.349063 0.604595i −0.637020 0.770847i \(-0.719833\pi\)
0.986083 + 0.166252i \(0.0531665\pi\)
\(734\) 0 0
\(735\) 3.43022 + 3.69368i 0.00466697 + 0.00502542i
\(736\) 0 0
\(737\) 96.3737i 0.130765i
\(738\) 0 0
\(739\) −466.830 −0.631705 −0.315853 0.948808i \(-0.602290\pi\)
−0.315853 + 0.948808i \(0.602290\pi\)
\(740\) 0 0
\(741\) 42.5646 + 13.1092i 0.0574421 + 0.0176912i
\(742\) 0 0
\(743\) −546.320 315.418i −0.735290 0.424520i 0.0850643 0.996375i \(-0.472890\pi\)
−0.820354 + 0.571856i \(0.806224\pi\)
\(744\) 0 0
\(745\) −0.443300 0.767818i −0.000595034 0.00103063i
\(746\) 0 0
\(747\) −237.824 + 349.475i −0.318372 + 0.467838i
\(748\) 0 0
\(749\) −182.249 + 105.222i −0.243323 + 0.140483i
\(750\) 0 0
\(751\) 90.7172 157.127i 0.120795 0.209223i −0.799286 0.600950i \(-0.794789\pi\)
0.920081 + 0.391727i \(0.128122\pi\)
\(752\) 0 0
\(753\) −604.856 + 138.331i −0.803262 + 0.183706i
\(754\) 0 0
\(755\) 4.15416i 0.00550220i
\(756\) 0 0
\(757\) −1381.82 −1.82539 −0.912696 0.408640i \(-0.866003\pi\)
−0.912696 + 0.408640i \(0.866003\pi\)
\(758\) 0 0
\(759\) −88.0292 384.910i −0.115980 0.507128i
\(760\) 0 0
\(761\) −590.093 340.690i −0.775418 0.447688i 0.0593862 0.998235i \(-0.481086\pi\)
−0.834804 + 0.550548i \(0.814419\pi\)
\(762\) 0 0
\(763\) 711.471 + 1232.30i 0.932466 + 1.61508i
\(764\) 0 0
\(765\) 0.886337 11.9668i 0.00115861 0.0156429i
\(766\) 0 0
\(767\) −3.70791 + 2.14076i −0.00483430 + 0.00279109i
\(768\) 0 0
\(769\) −45.1754 + 78.2461i −0.0587457 + 0.101750i −0.893903 0.448261i \(-0.852043\pi\)
0.835157 + 0.550012i \(0.185377\pi\)
\(770\) 0 0
\(771\) −21.1502 + 68.6732i −0.0274322 + 0.0890703i
\(772\) 0 0
\(773\) 87.4025i 0.113069i −0.998401 0.0565346i \(-0.981995\pi\)
0.998401 0.0565346i \(-0.0180051\pi\)
\(774\) 0 0
\(775\) 858.286 1.10747
\(776\) 0 0
\(777\) −583.000 + 541.417i −0.750322 + 0.696804i
\(778\) 0 0
\(779\) 1666.72 + 962.284i 2.13957 + 1.23528i
\(780\) 0 0
\(781\) 185.885 + 321.963i 0.238010 + 0.412245i
\(782\) 0 0
\(783\) −407.429 159.292i −0.520344 0.203438i
\(784\) 0 0
\(785\) −8.49274 + 4.90329i −0.0108188 + 0.00624622i
\(786\) 0 0
\(787\) 366.731 635.196i 0.465986 0.807111i −0.533260 0.845951i \(-0.679033\pi\)
0.999245 + 0.0388408i \(0.0123665\pi\)
\(788\) 0 0
\(789\) −281.386 302.998i −0.356637 0.384028i
\(790\) 0 0
\(791\) 340.602i 0.430597i