Properties

Label 804.2.y.b.121.3
Level 804
Weight 2
Character 804.121
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 121.3
Character \(\chi\) = 804.121
Dual form 804.2.y.b.505.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(-1.40224 + 0.901162i) q^{5} +(-1.99913 - 0.800331i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(-1.40224 + 0.901162i) q^{5} +(-1.99913 - 0.800331i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-0.208373 - 4.37429i) q^{11} +(-0.464734 + 0.0443767i) q^{13} +(-0.237216 + 1.64987i) q^{15} +(0.912776 + 3.76251i) q^{17} +(-6.15541 + 2.46425i) q^{19} +(-1.91400 + 0.986737i) q^{21} +(-4.51419 - 0.870038i) q^{23} +(-0.922904 + 2.02088i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(2.53756 - 4.39519i) q^{29} +(-5.39342 - 0.515009i) q^{31} +(-3.44232 - 2.70707i) q^{33} +(3.52448 - 0.679288i) q^{35} +(-5.22914 - 9.05714i) q^{37} +(-0.270798 + 0.380283i) q^{39} +(-4.28708 + 4.08773i) q^{41} +(-2.06844 - 0.607347i) q^{43} +(1.09155 + 1.25971i) q^{45} +(-3.61162 - 10.4351i) q^{47} +(-1.71014 - 1.63062i) q^{49} +(3.44126 + 1.77409i) q^{51} +(10.1057 - 2.96731i) q^{53} +(4.23413 + 5.94601i) q^{55} +(-2.16858 + 6.26569i) q^{57} +(1.79019 + 3.91998i) q^{59} +(-0.277619 + 5.82794i) q^{61} +(-0.507679 + 2.09268i) q^{63} +(0.611676 - 0.481027i) q^{65} +(1.49050 + 8.04850i) q^{67} +(-3.61370 + 2.84184i) q^{69} +(2.29558 - 9.46250i) q^{71} +(-0.234379 + 4.92022i) q^{73} +(0.922904 + 2.02088i) q^{75} +(-3.08432 + 8.91155i) q^{77} +(-5.30590 - 7.45109i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(7.34299 + 3.78558i) q^{83} +(-4.67056 - 4.45337i) q^{85} +(-1.65991 - 4.79600i) q^{87} +(2.01751 + 2.32833i) q^{89} +(0.964580 + 0.283226i) q^{91} +(-3.92116 + 3.73881i) q^{93} +(6.41064 - 9.00249i) q^{95} +(5.10144 + 8.83595i) q^{97} +(-4.30011 + 0.828779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{26}{33}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) −1.40224 + 0.901162i −0.627099 + 0.403012i −0.815234 0.579131i \(-0.803392\pi\)
0.188136 + 0.982143i \(0.439756\pi\)
\(6\) 0 0
\(7\) −1.99913 0.800331i −0.755600 0.302497i −0.0383051 0.999266i \(-0.512196\pi\)
−0.717295 + 0.696769i \(0.754620\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) −0.208373 4.37429i −0.0628269 1.31890i −0.781655 0.623711i \(-0.785624\pi\)
0.718828 0.695188i \(-0.244679\pi\)
\(12\) 0 0
\(13\) −0.464734 + 0.0443767i −0.128894 + 0.0123079i −0.159304 0.987230i \(-0.550925\pi\)
0.0304096 + 0.999538i \(0.490319\pi\)
\(14\) 0 0
\(15\) −0.237216 + 1.64987i −0.0612489 + 0.425996i
\(16\) 0 0
\(17\) 0.912776 + 3.76251i 0.221381 + 0.912544i 0.968731 + 0.248113i \(0.0798106\pi\)
−0.747350 + 0.664430i \(0.768674\pi\)
\(18\) 0 0
\(19\) −6.15541 + 2.46425i −1.41215 + 0.565339i −0.947385 0.320096i \(-0.896285\pi\)
−0.464763 + 0.885435i \(0.653861\pi\)
\(20\) 0 0
\(21\) −1.91400 + 0.986737i −0.417670 + 0.215324i
\(22\) 0 0
\(23\) −4.51419 0.870038i −0.941273 0.181416i −0.304540 0.952500i \(-0.598503\pi\)
−0.636733 + 0.771084i \(0.719715\pi\)
\(24\) 0 0
\(25\) −0.922904 + 2.02088i −0.184581 + 0.404176i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) 2.53756 4.39519i 0.471214 0.816166i −0.528244 0.849093i \(-0.677149\pi\)
0.999458 + 0.0329265i \(0.0104827\pi\)
\(30\) 0 0
\(31\) −5.39342 0.515009i −0.968686 0.0924983i −0.401297 0.915948i \(-0.631440\pi\)
−0.567389 + 0.823450i \(0.692047\pi\)
\(32\) 0 0
\(33\) −3.44232 2.70707i −0.599232 0.471241i
\(34\) 0 0
\(35\) 3.52448 0.679288i 0.595746 0.114821i
\(36\) 0 0
\(37\) −5.22914 9.05714i −0.859666 1.48898i −0.872248 0.489064i \(-0.837339\pi\)
0.0125824 0.999921i \(-0.495995\pi\)
\(38\) 0 0
\(39\) −0.270798 + 0.380283i −0.0433625 + 0.0608940i
\(40\) 0 0
\(41\) −4.28708 + 4.08773i −0.669530 + 0.638396i −0.946583 0.322459i \(-0.895491\pi\)
0.277053 + 0.960855i \(0.410642\pi\)
\(42\) 0 0
\(43\) −2.06844 0.607347i −0.315433 0.0926196i 0.120184 0.992752i \(-0.461652\pi\)
−0.435617 + 0.900132i \(0.643470\pi\)
\(44\) 0 0
\(45\) 1.09155 + 1.25971i 0.162718 + 0.187787i
\(46\) 0 0
\(47\) −3.61162 10.4351i −0.526809 1.52211i −0.823599 0.567172i \(-0.808037\pi\)
0.296790 0.954943i \(-0.404084\pi\)
\(48\) 0 0
\(49\) −1.71014 1.63062i −0.244306 0.232946i
\(50\) 0 0
\(51\) 3.44126 + 1.77409i 0.481873 + 0.248423i
\(52\) 0 0
\(53\) 10.1057 2.96731i 1.38813 0.407591i 0.499536 0.866293i \(-0.333504\pi\)
0.888590 + 0.458702i \(0.151685\pi\)
\(54\) 0 0
\(55\) 4.23413 + 5.94601i 0.570930 + 0.801759i
\(56\) 0 0
\(57\) −2.16858 + 6.26569i −0.287235 + 0.829911i
\(58\) 0 0
\(59\) 1.79019 + 3.91998i 0.233063 + 0.510338i 0.989641 0.143567i \(-0.0458572\pi\)
−0.756577 + 0.653904i \(0.773130\pi\)
\(60\) 0 0
\(61\) −0.277619 + 5.82794i −0.0355455 + 0.746191i 0.908799 + 0.417234i \(0.137000\pi\)
−0.944345 + 0.328957i \(0.893303\pi\)
\(62\) 0 0
\(63\) −0.507679 + 2.09268i −0.0639615 + 0.263653i
\(64\) 0 0
\(65\) 0.611676 0.481027i 0.0758691 0.0596641i
\(66\) 0 0
\(67\) 1.49050 + 8.04850i 0.182093 + 0.983281i
\(68\) 0 0
\(69\) −3.61370 + 2.84184i −0.435038 + 0.342118i
\(70\) 0 0
\(71\) 2.29558 9.46250i 0.272435 1.12299i −0.656966 0.753920i \(-0.728160\pi\)
0.929401 0.369072i \(-0.120324\pi\)
\(72\) 0 0
\(73\) −0.234379 + 4.92022i −0.0274320 + 0.575868i 0.942751 + 0.333496i \(0.108228\pi\)
−0.970183 + 0.242372i \(0.922075\pi\)
\(74\) 0 0
\(75\) 0.922904 + 2.02088i 0.106568 + 0.233351i
\(76\) 0 0
\(77\) −3.08432 + 8.91155i −0.351491 + 1.01557i
\(78\) 0 0
\(79\) −5.30590 7.45109i −0.596960 0.838313i 0.399977 0.916525i \(-0.369018\pi\)
−0.996937 + 0.0782124i \(0.975079\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) 7.34299 + 3.78558i 0.805998 + 0.415521i 0.811419 0.584464i \(-0.198695\pi\)
−0.00542115 + 0.999985i \(0.501726\pi\)
\(84\) 0 0
\(85\) −4.67056 4.45337i −0.506593 0.483036i
\(86\) 0 0
\(87\) −1.65991 4.79600i −0.177961 0.514185i
\(88\) 0 0
\(89\) 2.01751 + 2.32833i 0.213855 + 0.246802i 0.852535 0.522671i \(-0.175064\pi\)
−0.638679 + 0.769473i \(0.720519\pi\)
\(90\) 0 0
\(91\) 0.964580 + 0.283226i 0.101115 + 0.0296902i
\(92\) 0 0
\(93\) −3.92116 + 3.73881i −0.406605 + 0.387697i
\(94\) 0 0
\(95\) 6.41064 9.00249i 0.657718 0.923636i
\(96\) 0 0
\(97\) 5.10144 + 8.83595i 0.517973 + 0.897155i 0.999782 + 0.0208788i \(0.00664642\pi\)
−0.481809 + 0.876276i \(0.660020\pi\)
\(98\) 0 0
\(99\) −4.30011 + 0.828779i −0.432178 + 0.0832954i
\(100\) 0 0
\(101\) 1.05593 + 0.830391i 0.105069 + 0.0826270i 0.669311 0.742982i \(-0.266589\pi\)
−0.564243 + 0.825609i \(0.690832\pi\)
\(102\) 0 0
\(103\) 6.76119 + 0.645615i 0.666199 + 0.0636143i 0.422676 0.906281i \(-0.361091\pi\)
0.243523 + 0.969895i \(0.421697\pi\)
\(104\) 0 0
\(105\) 1.79467 3.10846i 0.175142 0.303355i
\(106\) 0 0
\(107\) −6.31699 4.05969i −0.610687 0.392465i 0.198428 0.980116i \(-0.436416\pi\)
−0.809115 + 0.587651i \(0.800053\pi\)
\(108\) 0 0
\(109\) 1.81460 3.97343i 0.173808 0.380585i −0.802601 0.596516i \(-0.796551\pi\)
0.976409 + 0.215931i \(0.0692785\pi\)
\(110\) 0 0
\(111\) −10.2693 1.97924i −0.974718 0.187861i
\(112\) 0 0
\(113\) 10.3027 5.31141i 0.969197 0.499656i 0.100466 0.994940i \(-0.467967\pi\)
0.868731 + 0.495285i \(0.164936\pi\)
\(114\) 0 0
\(115\) 7.11400 2.84802i 0.663384 0.265579i
\(116\) 0 0
\(117\) 0.110064 + 0.453688i 0.0101754 + 0.0419435i
\(118\) 0 0
\(119\) 1.18650 8.25228i 0.108766 0.756485i
\(120\) 0 0
\(121\) −8.14081 + 0.777353i −0.740074 + 0.0706685i
\(122\) 0 0
\(123\) 0.281855 + 5.91685i 0.0254140 + 0.533505i
\(124\) 0 0
\(125\) −1.71309 11.9148i −0.153223 1.06569i
\(126\) 0 0
\(127\) 12.5019 + 5.00501i 1.10937 + 0.444123i 0.852713 0.522380i \(-0.174956\pi\)
0.256653 + 0.966504i \(0.417380\pi\)
\(128\) 0 0
\(129\) −1.81354 + 1.16549i −0.159673 + 0.102616i
\(130\) 0 0
\(131\) 7.14097 8.24112i 0.623910 0.720030i −0.352535 0.935799i \(-0.614680\pi\)
0.976445 + 0.215769i \(0.0692257\pi\)
\(132\) 0 0
\(133\) 14.2777 1.23803
\(134\) 0 0
\(135\) 1.66684 0.143459
\(136\) 0 0
\(137\) −4.29690 + 4.95889i −0.367109 + 0.423667i −0.909009 0.416777i \(-0.863160\pi\)
0.541900 + 0.840443i \(0.317705\pi\)
\(138\) 0 0
\(139\) −9.56530 + 6.14725i −0.811318 + 0.521403i −0.879291 0.476284i \(-0.841983\pi\)
0.0679728 + 0.997687i \(0.478347\pi\)
\(140\) 0 0
\(141\) −10.2514 4.10405i −0.863326 0.345624i
\(142\) 0 0
\(143\) 0.290955 + 2.02364i 0.0243309 + 0.169225i
\(144\) 0 0
\(145\) 0.402516 + 8.44984i 0.0334271 + 0.701721i
\(146\) 0 0
\(147\) −2.35225 + 0.224612i −0.194010 + 0.0185257i
\(148\) 0 0
\(149\) −1.35469 + 9.42205i −0.110980 + 0.771884i 0.855990 + 0.516993i \(0.172949\pi\)
−0.966970 + 0.254891i \(0.917960\pi\)
\(150\) 0 0
\(151\) 3.28306 + 13.5329i 0.267171 + 1.10129i 0.934338 + 0.356387i \(0.115991\pi\)
−0.667167 + 0.744908i \(0.732493\pi\)
\(152\) 0 0
\(153\) 3.59432 1.43895i 0.290583 0.116332i
\(154\) 0 0
\(155\) 8.02695 4.13818i 0.644740 0.332387i
\(156\) 0 0
\(157\) −20.3787 3.92767i −1.62640 0.313462i −0.707126 0.707088i \(-0.750009\pi\)
−0.919271 + 0.393625i \(0.871221\pi\)
\(158\) 0 0
\(159\) 4.37530 9.58056i 0.346984 0.759788i
\(160\) 0 0
\(161\) 8.32813 + 5.35217i 0.656349 + 0.421810i
\(162\) 0 0
\(163\) 10.9953 19.0444i 0.861219 1.49167i −0.00953503 0.999955i \(-0.503035\pi\)
0.870754 0.491720i \(-0.163632\pi\)
\(164\) 0 0
\(165\) 7.26646 + 0.693863i 0.565693 + 0.0540171i
\(166\) 0 0
\(167\) −10.3502 8.13949i −0.800923 0.629853i 0.131461 0.991321i \(-0.458033\pi\)
−0.932384 + 0.361468i \(0.882276\pi\)
\(168\) 0 0
\(169\) −12.5511 + 2.41902i −0.965467 + 0.186078i
\(170\) 0 0
\(171\) 3.31518 + 5.74206i 0.253518 + 0.439106i
\(172\) 0 0
\(173\) 8.67550 12.1830i 0.659586 0.926259i −0.340315 0.940311i \(-0.610534\pi\)
0.999901 + 0.0140527i \(0.00447326\pi\)
\(174\) 0 0
\(175\) 3.46238 3.30137i 0.261731 0.249560i
\(176\) 0 0
\(177\) 4.13485 + 1.21410i 0.310794 + 0.0912574i
\(178\) 0 0
\(179\) 10.7078 + 12.3575i 0.800339 + 0.923640i 0.998400 0.0565493i \(-0.0180098\pi\)
−0.198061 + 0.980190i \(0.563464\pi\)
\(180\) 0 0
\(181\) 5.22962 + 15.1100i 0.388715 + 1.12312i 0.954409 + 0.298503i \(0.0964872\pi\)
−0.565694 + 0.824615i \(0.691392\pi\)
\(182\) 0 0
\(183\) 4.22266 + 4.02630i 0.312148 + 0.297633i
\(184\) 0 0
\(185\) 15.4944 + 7.98794i 1.13917 + 0.587285i
\(186\) 0 0
\(187\) 16.2681 4.77675i 1.18964 0.349311i
\(188\) 0 0
\(189\) 1.24908 + 1.75409i 0.0908575 + 0.127592i
\(190\) 0 0
\(191\) 7.61105 21.9907i 0.550716 1.59119i −0.234598 0.972093i \(-0.575377\pi\)
0.785314 0.619098i \(-0.212502\pi\)
\(192\) 0 0
\(193\) −7.83873 17.1644i −0.564244 1.23552i −0.949806 0.312840i \(-0.898720\pi\)
0.385562 0.922682i \(-0.374008\pi\)
\(194\) 0 0
\(195\) 0.0370264 0.777280i 0.00265152 0.0556622i
\(196\) 0 0
\(197\) −6.08682 + 25.0902i −0.433668 + 1.78760i 0.164658 + 0.986351i \(0.447348\pi\)
−0.598326 + 0.801253i \(0.704167\pi\)
\(198\) 0 0
\(199\) −4.97296 + 3.91078i −0.352524 + 0.277228i −0.778679 0.627422i \(-0.784110\pi\)
0.426155 + 0.904650i \(0.359868\pi\)
\(200\) 0 0
\(201\) 7.05872 + 4.14421i 0.497884 + 0.292310i
\(202\) 0 0
\(203\) −8.59053 + 6.75567i −0.602937 + 0.474155i
\(204\) 0 0
\(205\) 2.32780 9.59531i 0.162580 0.670166i
\(206\) 0 0
\(207\) −0.218747 + 4.59206i −0.0152040 + 0.319170i
\(208\) 0 0
\(209\) 12.0620 + 26.4121i 0.834345 + 1.82696i
\(210\) 0 0
\(211\) 7.91698 22.8746i 0.545028 1.57475i −0.250042 0.968235i \(-0.580444\pi\)
0.795069 0.606519i \(-0.207434\pi\)
\(212\) 0 0
\(213\) −5.64800 7.93150i −0.386994 0.543458i
\(214\) 0 0
\(215\) 3.44775 1.01235i 0.235135 0.0690418i
\(216\) 0 0
\(217\) 10.3700 + 5.34609i 0.703959 + 0.362916i
\(218\) 0 0
\(219\) 3.56497 + 3.39919i 0.240898 + 0.229696i
\(220\) 0 0
\(221\) −0.591166 1.70806i −0.0397661 0.114897i
\(222\) 0 0
\(223\) −16.6812 19.2511i −1.11706 1.28915i −0.953090 0.302686i \(-0.902117\pi\)
−0.163966 0.986466i \(-0.552429\pi\)
\(224\) 0 0
\(225\) 2.13165 + 0.625909i 0.142110 + 0.0417273i
\(226\) 0 0
\(227\) 2.39743 2.28595i 0.159123 0.151724i −0.606335 0.795209i \(-0.707361\pi\)
0.765458 + 0.643486i \(0.222512\pi\)
\(228\) 0 0
\(229\) −6.69342 + 9.39959i −0.442314 + 0.621143i −0.974204 0.225671i \(-0.927543\pi\)
0.531890 + 0.846813i \(0.321482\pi\)
\(230\) 0 0
\(231\) 4.71510 + 8.16679i 0.310231 + 0.537336i
\(232\) 0 0
\(233\) −7.14497 + 1.37708i −0.468083 + 0.0902155i −0.417838 0.908521i \(-0.637212\pi\)
−0.0502443 + 0.998737i \(0.516000\pi\)
\(234\) 0 0
\(235\) 14.4681 + 11.3778i 0.943792 + 0.742206i
\(236\) 0 0
\(237\) −9.10578 0.869496i −0.591484 0.0564799i
\(238\) 0 0
\(239\) 2.43080 4.21027i 0.157236 0.272340i −0.776635 0.629951i \(-0.783075\pi\)
0.933871 + 0.357611i \(0.116408\pi\)
\(240\) 0 0
\(241\) 1.44414 + 0.928095i 0.0930255 + 0.0597838i 0.586327 0.810075i \(-0.300574\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 3.86748 + 0.745395i 0.247084 + 0.0476215i
\(246\) 0 0
\(247\) 2.75127 1.41838i 0.175059 0.0902494i
\(248\) 0 0
\(249\) 7.66959 3.07044i 0.486040 0.194581i
\(250\) 0 0
\(251\) 2.20886 + 9.10506i 0.139422 + 0.574706i 0.998068 + 0.0621363i \(0.0197913\pi\)
−0.858645 + 0.512570i \(0.828694\pi\)
\(252\) 0 0
\(253\) −2.86517 + 19.9277i −0.180131 + 1.25284i
\(254\) 0 0
\(255\) −6.42420 + 0.613437i −0.402299 + 0.0384149i
\(256\) 0 0
\(257\) −1.12339 23.5828i −0.0700750 1.47106i −0.710859 0.703334i \(-0.751694\pi\)
0.640784 0.767721i \(-0.278609\pi\)
\(258\) 0 0
\(259\) 3.20503 + 22.2915i 0.199151 + 1.38512i
\(260\) 0 0
\(261\) −4.71159 1.88623i −0.291640 0.116755i
\(262\) 0 0
\(263\) 0.455108 0.292480i 0.0280632 0.0180351i −0.526534 0.850154i \(-0.676509\pi\)
0.554597 + 0.832119i \(0.312872\pi\)
\(264\) 0 0
\(265\) −11.4966 + 13.2677i −0.706228 + 0.815031i
\(266\) 0 0
\(267\) 3.08082 0.188543
\(268\) 0 0
\(269\) −3.36580 −0.205216 −0.102608 0.994722i \(-0.532719\pi\)
−0.102608 + 0.994722i \(0.532719\pi\)
\(270\) 0 0
\(271\) −9.20589 + 10.6242i −0.559218 + 0.645372i −0.963006 0.269481i \(-0.913148\pi\)
0.403788 + 0.914853i \(0.367693\pi\)
\(272\) 0 0
\(273\) 0.845714 0.543507i 0.0511849 0.0328946i
\(274\) 0 0
\(275\) 9.03222 + 3.61595i 0.544663 + 0.218050i
\(276\) 0 0
\(277\) 0.504782 + 3.51084i 0.0303294 + 0.210946i 0.999351 0.0360316i \(-0.0114717\pi\)
−0.969021 + 0.246978i \(0.920563\pi\)
\(278\) 0 0
\(279\) 0.257796 + 5.41181i 0.0154339 + 0.323997i
\(280\) 0 0
\(281\) −13.1280 + 1.25357i −0.783150 + 0.0747818i −0.478968 0.877832i \(-0.658989\pi\)
−0.304182 + 0.952614i \(0.598383\pi\)
\(282\) 0 0
\(283\) 2.14555 14.9227i 0.127540 0.887060i −0.821119 0.570758i \(-0.806650\pi\)
0.948659 0.316302i \(-0.102441\pi\)
\(284\) 0 0
\(285\) −2.60555 10.7402i −0.154339 0.636195i
\(286\) 0 0
\(287\) 11.8420 4.74081i 0.699010 0.279841i
\(288\) 0 0
\(289\) 1.78685 0.921187i 0.105109 0.0541874i
\(290\) 0 0
\(291\) 10.0185 + 1.93091i 0.587295 + 0.113192i
\(292\) 0 0
\(293\) 0.650445 1.42428i 0.0379994 0.0832071i −0.889680 0.456584i \(-0.849073\pi\)
0.927680 + 0.373377i \(0.121800\pi\)
\(294\) 0 0
\(295\) −6.04281 3.88348i −0.351826 0.226105i
\(296\) 0 0
\(297\) −2.18963 + 3.79254i −0.127055 + 0.220066i
\(298\) 0 0
\(299\) 2.13651 + 0.204012i 0.123557 + 0.0117983i
\(300\) 0 0
\(301\) 3.64899 + 2.86960i 0.210325 + 0.165401i
\(302\) 0 0
\(303\) 1.31905 0.254227i 0.0757776 0.0146049i
\(304\) 0 0
\(305\) −4.86263 8.42232i −0.278433 0.482261i
\(306\) 0 0
\(307\) −4.91933 + 6.90823i −0.280761 + 0.394273i −0.930742 0.365677i \(-0.880837\pi\)
0.649981 + 0.759951i \(0.274777\pi\)
\(308\) 0 0
\(309\) 4.91556 4.68698i 0.279636 0.266633i
\(310\) 0 0
\(311\) 10.2291 + 3.00354i 0.580040 + 0.170315i 0.558574 0.829455i \(-0.311349\pi\)
0.0214655 + 0.999770i \(0.493167\pi\)
\(312\) 0 0
\(313\) −11.6831 13.4830i −0.660367 0.762104i 0.322470 0.946580i \(-0.395487\pi\)
−0.982837 + 0.184475i \(0.940941\pi\)
\(314\) 0 0
\(315\) −1.17396 3.39193i −0.0661451 0.191114i
\(316\) 0 0
\(317\) 6.90071 + 6.57981i 0.387582 + 0.369559i 0.858671 0.512527i \(-0.171290\pi\)
−0.471089 + 0.882086i \(0.656139\pi\)
\(318\) 0 0
\(319\) −19.7546 10.1842i −1.10605 0.570206i
\(320\) 0 0
\(321\) −7.20486 + 2.11554i −0.402136 + 0.118078i
\(322\) 0 0
\(323\) −14.8903 20.9105i −0.828519 1.16349i
\(324\) 0 0
\(325\) 0.339225 0.980126i 0.0188168 0.0543676i
\(326\) 0 0
\(327\) −1.81460 3.97343i −0.100348 0.219731i
\(328\) 0 0
\(329\) −1.13143 + 23.7516i −0.0623777 + 1.30947i
\(330\) 0 0
\(331\) −3.82407 + 15.7630i −0.210190 + 0.866413i 0.764819 + 0.644245i \(0.222828\pi\)
−0.975008 + 0.222168i \(0.928687\pi\)
\(332\) 0 0
\(333\) −8.22077 + 6.46488i −0.450495 + 0.354273i
\(334\) 0 0
\(335\) −9.34303 9.94272i −0.510464 0.543229i
\(336\) 0 0
\(337\) 9.58393 7.53688i 0.522070 0.410560i −0.322044 0.946725i \(-0.604370\pi\)
0.844113 + 0.536165i \(0.180127\pi\)
\(338\) 0 0
\(339\) 2.73274 11.2645i 0.148422 0.611804i
\(340\) 0 0
\(341\) −1.12896 + 23.6997i −0.0611364 + 1.28341i
\(342\) 0 0
\(343\) 8.37560 + 18.3400i 0.452240 + 0.990267i
\(344\) 0 0
\(345\) 2.50629 7.24146i 0.134934 0.389867i
\(346\) 0 0
\(347\) −8.95448 12.5748i −0.480701 0.675051i 0.501007 0.865444i \(-0.332963\pi\)
−0.981708 + 0.190393i \(0.939024\pi\)
\(348\) 0 0
\(349\) 18.1578 5.33160i 0.971963 0.285394i 0.243060 0.970011i \(-0.421849\pi\)
0.728903 + 0.684617i \(0.240031\pi\)
\(350\) 0 0
\(351\) 0.414951 + 0.213922i 0.0221485 + 0.0114183i
\(352\) 0 0
\(353\) −24.3642 23.2312i −1.29678 1.23647i −0.954970 0.296702i \(-0.904113\pi\)
−0.341805 0.939771i \(-0.611038\pi\)
\(354\) 0 0
\(355\) 5.30831 + 15.3373i 0.281736 + 0.814022i
\(356\) 0 0
\(357\) −5.45967 6.30079i −0.288956 0.333473i
\(358\) 0 0
\(359\) −27.4354 8.05575i −1.44798 0.425166i −0.539109 0.842236i \(-0.681239\pi\)
−0.908874 + 0.417070i \(0.863057\pi\)
\(360\) 0 0
\(361\) 18.0656 17.2255i 0.950820 0.906605i
\(362\) 0 0
\(363\) −4.74361 + 6.66147i −0.248975 + 0.349637i
\(364\) 0 0
\(365\) −4.10526 7.11052i −0.214879 0.372182i
\(366\) 0 0
\(367\) −9.65430 + 1.86071i −0.503950 + 0.0971285i −0.434889 0.900484i \(-0.643212\pi\)
−0.0690612 + 0.997612i \(0.522000\pi\)
\(368\) 0 0
\(369\) 4.65624 + 3.66170i 0.242394 + 0.190621i
\(370\) 0 0
\(371\) −22.5775 2.15589i −1.17216 0.111928i
\(372\) 0 0
\(373\) 14.2631 24.7045i 0.738518 1.27915i −0.214645 0.976692i \(-0.568859\pi\)
0.953163 0.302458i \(-0.0978073\pi\)
\(374\) 0 0
\(375\) −10.1264 6.50787i −0.522927 0.336065i
\(376\) 0 0
\(377\) −0.984248 + 2.15520i −0.0506914 + 0.110999i
\(378\) 0 0
\(379\) −14.1586 2.72884i −0.727277 0.140171i −0.187843 0.982199i \(-0.560150\pi\)
−0.539434 + 0.842028i \(0.681362\pi\)
\(380\) 0 0
\(381\) 11.9696 6.17073i 0.613219 0.316136i
\(382\) 0 0
\(383\) 3.78344 1.51466i 0.193325 0.0773956i −0.272980 0.962020i \(-0.588009\pi\)
0.466305 + 0.884624i \(0.345585\pi\)
\(384\) 0 0
\(385\) −3.70581 15.2756i −0.188866 0.778514i
\(386\) 0 0
\(387\) −0.306796 + 2.13382i −0.0155953 + 0.108468i
\(388\) 0 0
\(389\) −7.49919 + 0.716086i −0.380224 + 0.0363070i −0.283418 0.958996i \(-0.591469\pi\)
−0.0968055 + 0.995303i \(0.530862\pi\)
\(390\) 0 0
\(391\) −0.846911 17.7788i −0.0428301 0.899115i
\(392\) 0 0
\(393\) −1.55188 10.7936i −0.0782821 0.544464i
\(394\) 0 0
\(395\) 14.1547 + 5.66671i 0.712203 + 0.285123i
\(396\) 0 0
\(397\) −6.62823 + 4.25971i −0.332661 + 0.213789i −0.696299 0.717752i \(-0.745171\pi\)
0.363637 + 0.931541i \(0.381535\pi\)
\(398\) 0 0
\(399\) 9.34990 10.7904i 0.468080 0.540194i
\(400\) 0 0
\(401\) −26.3539 −1.31605 −0.658026 0.752995i \(-0.728608\pi\)
−0.658026 + 0.752995i \(0.728608\pi\)
\(402\) 0 0
\(403\) 2.52936 0.125996
\(404\) 0 0
\(405\) 1.09155 1.25971i 0.0542395 0.0625957i
\(406\) 0 0
\(407\) −38.5290 + 24.7611i −1.90981 + 1.22736i
\(408\) 0 0
\(409\) −23.1960 9.28630i −1.14697 0.459178i −0.281215 0.959645i \(-0.590737\pi\)
−0.865756 + 0.500467i \(0.833162\pi\)
\(410\) 0 0
\(411\) 0.933806 + 6.49476i 0.0460613 + 0.320363i
\(412\) 0 0
\(413\) −0.441551 9.26929i −0.0217273 0.456112i
\(414\) 0 0
\(415\) −13.7080 + 1.30896i −0.672900 + 0.0642542i
\(416\) 0 0
\(417\) −1.61816 + 11.2546i −0.0792417 + 0.551138i
\(418\) 0 0
\(419\) 0.678308 + 2.79602i 0.0331375 + 0.136595i 0.985977 0.166879i \(-0.0533688\pi\)
−0.952840 + 0.303473i \(0.901854\pi\)
\(420\) 0 0
\(421\) −12.3820 + 4.95701i −0.603463 + 0.241590i −0.653216 0.757172i \(-0.726581\pi\)
0.0497534 + 0.998762i \(0.484156\pi\)
\(422\) 0 0
\(423\) −9.81489 + 5.05993i −0.477216 + 0.246022i
\(424\) 0 0
\(425\) −8.44599 1.62783i −0.409691 0.0789614i
\(426\) 0 0
\(427\) 5.21928 11.4286i 0.252579 0.553070i
\(428\) 0 0
\(429\) 1.71990 + 1.10531i 0.0830374 + 0.0533649i
\(430\) 0 0
\(431\) −18.9487 + 32.8201i −0.912727 + 1.58089i −0.102532 + 0.994730i \(0.532694\pi\)
−0.810195 + 0.586160i \(0.800639\pi\)
\(432\) 0 0
\(433\) 26.2086 + 2.50261i 1.25950 + 0.120268i 0.703369 0.710825i \(-0.251678\pi\)
0.556134 + 0.831093i \(0.312284\pi\)
\(434\) 0 0
\(435\) 6.64956 + 5.22927i 0.318822 + 0.250724i
\(436\) 0 0
\(437\) 29.9307 5.76867i 1.43178 0.275953i
\(438\) 0 0
\(439\) −11.0246 19.0952i −0.526177 0.911365i −0.999535 0.0304946i \(-0.990292\pi\)
0.473358 0.880870i \(-0.343042\pi\)
\(440\) 0 0
\(441\) −1.37064 + 1.92480i −0.0652687 + 0.0916571i
\(442\) 0 0
\(443\) −10.0086 + 9.54317i −0.475522 + 0.453410i −0.889539 0.456860i \(-0.848974\pi\)
0.414016 + 0.910269i \(0.364126\pi\)
\(444\) 0 0
\(445\) −4.92722 1.44676i −0.233573 0.0685831i
\(446\) 0 0
\(447\) 6.23358 + 7.19393i 0.294838 + 0.340261i
\(448\) 0 0
\(449\) 2.29173 + 6.62151i 0.108153 + 0.312488i 0.986071 0.166322i \(-0.0531893\pi\)
−0.877918 + 0.478811i \(0.841068\pi\)
\(450\) 0 0
\(451\) 18.7742 + 17.9012i 0.884044 + 0.842934i
\(452\) 0 0
\(453\) 12.3775 + 6.38102i 0.581544 + 0.299807i
\(454\) 0 0
\(455\) −1.60780 + 0.472093i −0.0753749 + 0.0221321i
\(456\) 0 0
\(457\) −11.4709 16.1086i −0.536585 0.753528i 0.453914 0.891045i \(-0.350027\pi\)
−0.990499 + 0.137517i \(0.956088\pi\)
\(458\) 0 0
\(459\) 1.26629 3.65871i 0.0591055 0.170774i
\(460\) 0 0
\(461\) 5.77843 + 12.6530i 0.269128 + 0.589309i 0.995151 0.0983621i \(-0.0313603\pi\)
−0.726022 + 0.687671i \(0.758633\pi\)
\(462\) 0 0
\(463\) −1.20309 + 25.2560i −0.0559124 + 1.17374i 0.780324 + 0.625376i \(0.215054\pi\)
−0.836236 + 0.548369i \(0.815249\pi\)
\(464\) 0 0
\(465\) 2.12911 8.77629i 0.0987349 0.406991i
\(466\) 0 0
\(467\) −16.6830 + 13.1197i −0.771998 + 0.607106i −0.924493 0.381199i \(-0.875511\pi\)
0.152496 + 0.988304i \(0.451269\pi\)
\(468\) 0 0
\(469\) 3.46177 17.2829i 0.159850 0.798050i
\(470\) 0 0
\(471\) −16.3135 + 12.8291i −0.751688 + 0.591134i
\(472\) 0 0
\(473\) −2.22571 + 9.17449i −0.102338 + 0.421844i
\(474\) 0 0
\(475\) 0.700896 14.7136i 0.0321593 0.675107i
\(476\) 0 0
\(477\) −4.37530 9.58056i −0.200331 0.438664i
\(478\) 0 0
\(479\) 3.76807 10.8871i 0.172168 0.497445i −0.825598 0.564259i \(-0.809162\pi\)
0.997765 + 0.0668134i \(0.0212832\pi\)
\(480\) 0 0
\(481\) 2.83209 + 3.97711i 0.129132 + 0.181341i
\(482\) 0 0
\(483\) 9.49867 2.78906i 0.432204 0.126907i
\(484\) 0 0
\(485\) −15.1160 7.79286i −0.686384 0.353856i
\(486\) 0 0
\(487\) −6.96417 6.64032i −0.315577 0.300902i 0.515690 0.856775i \(-0.327535\pi\)
−0.831267 + 0.555873i \(0.812384\pi\)
\(488\) 0 0
\(489\) −7.19242 20.7811i −0.325253 0.939756i
\(490\) 0 0
\(491\) 6.67958 + 7.70864i 0.301445 + 0.347886i 0.886182 0.463336i \(-0.153348\pi\)
−0.584737 + 0.811223i \(0.698802\pi\)
\(492\) 0 0
\(493\) 18.8532 + 5.53579i 0.849105 + 0.249320i
\(494\) 0 0
\(495\) 5.28291 5.03724i 0.237449 0.226407i
\(496\) 0 0
\(497\) −12.1623 + 17.0796i −0.545554 + 0.766123i
\(498\) 0 0
\(499\) −13.2742 22.9915i −0.594233 1.02924i −0.993655 0.112474i \(-0.964122\pi\)
0.399422 0.916767i \(-0.369211\pi\)
\(500\) 0 0
\(501\) −12.9294 + 2.49193i −0.577641 + 0.111331i
\(502\) 0 0
\(503\) −3.54014 2.78400i −0.157847 0.124132i 0.536112 0.844147i \(-0.319893\pi\)
−0.693959 + 0.720015i \(0.744135\pi\)
\(504\) 0 0
\(505\) −2.22898 0.212841i −0.0991881 0.00947132i
\(506\) 0 0
\(507\) −6.39103 + 11.0696i −0.283835 + 0.491617i
\(508\) 0 0
\(509\) 8.78303 + 5.64451i 0.389301 + 0.250189i 0.720620 0.693330i \(-0.243857\pi\)
−0.331319 + 0.943519i \(0.607494\pi\)
\(510\) 0 0
\(511\) 4.40636 9.64858i 0.194926 0.426828i
\(512\) 0 0
\(513\) 6.51054 + 1.25480i 0.287447 + 0.0554009i
\(514\) 0 0
\(515\) −10.0626 + 5.18762i −0.443410 + 0.228594i
\(516\) 0 0
\(517\) −44.8936 + 17.9727i −1.97442 + 0.790437i
\(518\) 0 0
\(519\) −3.52608 14.5347i −0.154778 0.638002i
\(520\) 0 0
\(521\) −1.56980 + 10.9182i −0.0687740 + 0.478334i 0.926105 + 0.377265i \(0.123135\pi\)
−0.994879 + 0.101069i \(0.967774\pi\)
\(522\) 0 0
\(523\) 19.8278 1.89332i 0.867008 0.0827893i 0.347935 0.937519i \(-0.386883\pi\)
0.519074 + 0.854730i \(0.326277\pi\)
\(524\) 0 0
\(525\) −0.227634 4.77863i −0.00993477 0.208556i
\(526\) 0 0
\(527\) −2.98525 20.7629i −0.130040 0.904446i
\(528\) 0 0
\(529\) −1.73153 0.693202i −0.0752841 0.0301392i
\(530\) 0 0
\(531\) 3.62531 2.32984i 0.157325 0.101107i
\(532\) 0 0
\(533\) 1.81095 2.08995i 0.0784412 0.0905259i
\(534\) 0 0
\(535\) 12.5163 0.541129
\(536\) 0 0
\(537\) 16.3513 0.705609
\(538\) 0 0
\(539\) −6.77646 + 7.82045i −0.291883 + 0.336851i
\(540\) 0 0
\(541\) 29.8403 19.1772i 1.28293 0.824491i 0.291686 0.956514i \(-0.405784\pi\)
0.991247 + 0.132023i \(0.0421473\pi\)
\(542\) 0 0
\(543\) 14.8441 + 5.94266i 0.637019 + 0.255024i
\(544\) 0 0
\(545\) 1.03620 + 7.20693i 0.0443859 + 0.308711i
\(546\) 0 0
\(547\) 1.77333 + 37.2267i 0.0758220 + 1.59170i 0.641532 + 0.767096i \(0.278299\pi\)
−0.565710 + 0.824604i \(0.691398\pi\)
\(548\) 0 0
\(549\) 5.80813 0.554609i 0.247885 0.0236701i
\(550\) 0 0
\(551\) −4.78888 + 33.3074i −0.204013 + 1.41894i
\(552\) 0 0
\(553\) 4.64384 + 19.1422i 0.197476 + 0.814008i
\(554\) 0 0
\(555\) 16.1836 6.47893i 0.686955 0.275015i
\(556\) 0 0
\(557\) 9.81758 5.06132i 0.415984 0.214455i −0.237512 0.971385i \(-0.576332\pi\)
0.653496 + 0.756930i \(0.273302\pi\)
\(558\) 0 0
\(559\) 0.988225 + 0.190465i 0.0417974 + 0.00805580i
\(560\) 0 0
\(561\) 7.04333 15.4227i 0.297370 0.651149i
\(562\) 0 0
\(563\) −19.9716 12.8350i −0.841703 0.540930i 0.0472736 0.998882i \(-0.484947\pi\)
−0.888977 + 0.457952i \(0.848583\pi\)
\(564\) 0 0
\(565\) −9.66037 + 16.7323i −0.406415 + 0.703931i
\(566\) 0 0
\(567\) 2.14363 + 0.204692i 0.0900241 + 0.00859625i
\(568\) 0 0
\(569\) 21.0675 + 16.5677i 0.883195 + 0.694552i 0.952988 0.303009i \(-0.0979914\pi\)
−0.0697928 + 0.997562i \(0.522234\pi\)
\(570\) 0 0
\(571\) 35.9896 6.93643i 1.50612 0.290280i 0.631608 0.775288i \(-0.282395\pi\)
0.874510 + 0.485007i \(0.161183\pi\)
\(572\) 0 0
\(573\) −11.6353 20.1529i −0.486071 0.841899i
\(574\) 0 0
\(575\) 5.92440 8.31966i 0.247065 0.346954i
\(576\) 0 0
\(577\) 7.23841 6.90181i 0.301339 0.287326i −0.524290 0.851540i \(-0.675669\pi\)
0.825629 + 0.564214i \(0.190821\pi\)
\(578\) 0 0
\(579\) −18.1053 5.31619i −0.752429 0.220933i
\(580\) 0 0
\(581\) −11.6499 13.4447i −0.483319 0.557780i
\(582\) 0 0
\(583\) −15.0856 43.5870i −0.624782 1.80519i
\(584\) 0 0
\(585\) −0.563182 0.536993i −0.0232847 0.0222019i
\(586\) 0 0
\(587\) −6.85925 3.53619i −0.283111 0.145954i 0.310822 0.950468i \(-0.399396\pi\)
−0.593934 + 0.804514i \(0.702426\pi\)
\(588\) 0 0
\(589\) 34.4678 10.1207i 1.42022 0.417015i
\(590\) 0 0
\(591\) 14.9759 + 21.0307i 0.616026 + 0.865088i
\(592\) 0 0
\(593\) 6.56263 18.9615i 0.269495 0.778654i −0.726328 0.687348i \(-0.758775\pi\)
0.995823 0.0913059i \(-0.0291041\pi\)
\(594\) 0 0
\(595\) 5.77289 + 12.6409i 0.236665 + 0.518225i
\(596\) 0 0
\(597\) −0.301027 + 6.31933i −0.0123202 + 0.258633i
\(598\) 0 0
\(599\) −8.59216 + 35.4174i −0.351066 + 1.44711i 0.473222 + 0.880943i \(0.343091\pi\)
−0.824288 + 0.566171i \(0.808424\pi\)
\(600\) 0 0
\(601\) −14.1426 + 11.1219i −0.576890 + 0.453671i −0.863481 0.504382i \(-0.831720\pi\)
0.286591 + 0.958053i \(0.407478\pi\)
\(602\) 0 0
\(603\) 7.75446 2.62075i 0.315786 0.106725i
\(604\) 0 0
\(605\) 10.7148 8.42622i 0.435619 0.342575i
\(606\) 0 0
\(607\) −1.98390 + 8.17773i −0.0805238 + 0.331924i −0.997797 0.0663337i \(-0.978870\pi\)
0.917274 + 0.398257i \(0.130385\pi\)
\(608\) 0 0
\(609\) −0.520008 + 10.9163i −0.0210718 + 0.442351i
\(610\) 0 0
\(611\) 2.14152 + 4.68927i 0.0866366 + 0.189708i
\(612\) 0 0
\(613\) 3.29936 9.53287i 0.133260 0.385029i −0.858554 0.512724i \(-0.828637\pi\)
0.991814 + 0.127695i \(0.0407578\pi\)
\(614\) 0 0
\(615\) −5.72727 8.04283i −0.230946 0.324318i
\(616\) 0 0
\(617\) −36.7903 + 10.8026i −1.48112 + 0.434896i −0.919696 0.392631i \(-0.871565\pi\)
−0.561425 + 0.827528i \(0.689747\pi\)
\(618\) 0 0
\(619\) 38.0670 + 19.6249i 1.53004 + 0.788792i 0.998310 0.0581208i \(-0.0185109\pi\)
0.531733 + 0.846912i \(0.321541\pi\)
\(620\) 0 0
\(621\) 3.32720 + 3.17248i 0.133516 + 0.127307i
\(622\) 0 0
\(623\) −2.16983 6.26931i −0.0869323 0.251175i
\(624\) 0 0
\(625\) 5.86499 + 6.76855i 0.234599 + 0.270742i
\(626\) 0 0
\(627\) 27.8598 + 8.18039i 1.11261 + 0.326693i
\(628\) 0 0
\(629\) 29.3046 27.9419i 1.16845 1.11411i
\(630\) 0 0
\(631\) −9.68347 + 13.5985i −0.385493 + 0.541349i −0.961036 0.276422i \(-0.910851\pi\)
0.575543 + 0.817771i \(0.304791\pi\)
\(632\) 0 0
\(633\) −12.1030 20.9629i −0.481050 0.833202i
\(634\) 0 0
\(635\) −22.0410 + 4.24805i −0.874669 + 0.168579i
\(636\) 0 0
\(637\) 0.867124 + 0.681914i 0.0343567 + 0.0270184i
\(638\) 0 0
\(639\) −9.69288 0.925558i −0.383444 0.0366145i
\(640\) 0 0
\(641\) −19.2918 + 33.4144i −0.761981 + 1.31979i 0.179847 + 0.983695i \(0.442440\pi\)
−0.941828 + 0.336095i \(0.890894\pi\)
\(642\) 0 0
\(643\) −13.3501 8.57960i −0.526477 0.338346i 0.250252 0.968181i \(-0.419486\pi\)
−0.776730 + 0.629834i \(0.783123\pi\)
\(644\) 0 0
\(645\) 1.49271 3.26859i 0.0587755 0.128700i
\(646\) 0 0
\(647\) −3.42780 0.660654i −0.134761 0.0259730i 0.121425 0.992601i \(-0.461254\pi\)
−0.256185 + 0.966628i \(0.582466\pi\)
\(648\) 0 0
\(649\) 16.7741 8.64765i 0.658441 0.339450i
\(650\) 0 0
\(651\) 10.8312 4.33616i 0.424508 0.169947i
\(652\) 0 0
\(653\) 2.53736 + 10.4591i 0.0992946 + 0.409298i 0.999667 0.0258232i \(-0.00822068\pi\)
−0.900372 + 0.435121i \(0.856706\pi\)
\(654\) 0 0
\(655\) −2.58674 + 17.9912i −0.101072 + 0.702973i
\(656\) 0 0
\(657\) 4.90350 0.468227i 0.191304 0.0182673i
\(658\) 0 0
\(659\) 0.621064 + 13.0377i 0.0241932 + 0.507878i 0.978146 + 0.207920i \(0.0666695\pi\)
−0.953953 + 0.299958i \(0.903027\pi\)
\(660\) 0 0
\(661\) −2.76495 19.2306i −0.107544 0.747985i −0.970220 0.242227i \(-0.922122\pi\)
0.862675 0.505758i \(-0.168787\pi\)
\(662\) 0 0
\(663\) −1.67800 0.671769i −0.0651681 0.0260894i
\(664\) 0 0
\(665\) −20.0207 + 12.8665i −0.776369 + 0.498942i
\(666\) 0 0
\(667\) −15.2790 + 17.6329i −0.591606 + 0.682750i
\(668\) 0 0
\(669\) −25.4729 −0.984840
\(670\) 0 0
\(671\) 25.5509 0.986383
\(672\) 0 0
\(673\) 22.4025 25.8539i 0.863554 0.996595i −0.136428 0.990650i \(-0.543562\pi\)
0.999982 0.00594457i \(-0.00189223\pi\)
\(674\) 0 0
\(675\) 1.86897 1.20111i 0.0719365 0.0462308i
\(676\) 0 0
\(677\) −8.69984 3.48289i −0.334362 0.133858i 0.198405 0.980120i \(-0.436424\pi\)
−0.532767 + 0.846262i \(0.678848\pi\)
\(678\) 0 0
\(679\) −3.12676 21.7471i −0.119994 0.834576i
\(680\) 0 0
\(681\) −0.157619 3.30884i −0.00603999 0.126795i
\(682\) 0 0
\(683\) 25.2393 2.41006i 0.965753 0.0922182i 0.399753 0.916623i \(-0.369096\pi\)
0.566001 + 0.824405i \(0.308490\pi\)
\(684\) 0 0
\(685\) 1.55651 10.8257i 0.0594710 0.413630i
\(686\) 0 0
\(687\) 2.72048 + 11.2140i 0.103793 + 0.427840i
\(688\) 0 0
\(689\) −4.56479 + 1.82747i −0.173905 + 0.0696209i
\(690\) 0 0
\(691\) −40.1633 + 20.7056i −1.52788 + 0.787679i −0.998168 0.0604955i \(-0.980732\pi\)
−0.529716 + 0.848175i \(0.677702\pi\)
\(692\) 0 0
\(693\) 9.25979 + 1.78468i 0.351750 + 0.0677943i
\(694\) 0 0
\(695\) 7.87314 17.2398i 0.298645 0.653942i
\(696\) 0 0
\(697\) −19.2933 12.3990i −0.730785 0.469647i
\(698\) 0 0
\(699\) −3.63823 + 6.30160i −0.137611 + 0.238349i
\(700\) 0 0
\(701\) 6.68903 + 0.638725i 0.252641 + 0.0241243i 0.220608 0.975362i \(-0.429196\pi\)
0.0320331 + 0.999487i \(0.489802\pi\)
\(702\) 0 0
\(703\) 54.5066 + 42.8645i 2.05576 + 1.61666i
\(704\) 0 0
\(705\) 18.0733 3.48335i 0.680681 0.131190i
\(706\) 0 0
\(707\) −1.44635 2.50515i −0.0543956 0.0942159i
\(708\) 0 0
\(709\) 8.26091 11.6008i 0.310245 0.435678i −0.629785 0.776769i \(-0.716857\pi\)
0.940030 + 0.341091i \(0.110796\pi\)
\(710\) 0 0
\(711\) −6.62014 + 6.31229i −0.248275 + 0.236729i
\(712\) 0 0
\(713\) 23.8988 + 7.01733i 0.895018 + 0.262801i
\(714\) 0 0
\(715\) −2.23161 2.57542i −0.0834575 0.0963151i
\(716\) 0 0
\(717\) −1.59008 4.59422i −0.0593825 0.171574i
\(718\) 0 0
\(719\) −6.82534 6.50795i −0.254542 0.242706i 0.552054 0.833808i \(-0.313844\pi\)
−0.806596 + 0.591103i \(0.798693\pi\)
\(720\) 0 0
\(721\) −12.9998 6.70186i −0.484137 0.249590i
\(722\) 0 0
\(723\) 1.64712 0.483638i 0.0612570 0.0179867i
\(724\) 0 0
\(725\) 6.54021 + 9.18444i 0.242897 + 0.341102i
\(726\) 0 0
\(727\) −3.22228 + 9.31016i −0.119508 + 0.345295i −0.988850 0.148916i \(-0.952422\pi\)
0.869342 + 0.494211i \(0.164543\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) 0.397135 8.33689i 0.0146886 0.308351i
\(732\) 0 0
\(733\) −9.24938 + 38.1265i −0.341634 + 1.40823i 0.498987 + 0.866609i \(0.333706\pi\)
−0.840621 + 0.541624i \(0.817810\pi\)
\(734\) 0 0
\(735\) 3.09599 2.43471i 0.114197 0.0898058i
\(736\) 0 0
\(737\) 34.8959 8.19695i 1.28541 0.301939i
\(738\) 0 0
\(739\) −2.94814 + 2.31845i −0.108449 + 0.0852854i −0.670911 0.741538i \(-0.734097\pi\)
0.562462 + 0.826823i \(0.309854\pi\)
\(740\) 0 0
\(741\) 0.729761 3.00812i 0.0268084 0.110506i
\(742\) 0 0
\(743\) 2.16539 45.4571i 0.0794404 1.66766i −0.510248 0.860028i \(-0.670446\pi\)
0.589688 0.807631i \(-0.299251\pi\)
\(744\) 0 0
\(745\) −6.59120 14.4327i −0.241483 0.528774i
\(746\) 0 0
\(747\) 2.70203 7.80700i 0.0988620 0.285643i
\(748\) 0 0
\(749\) 9.37940 + 13.1715i 0.342716 + 0.481277i
\(750\) 0 0
\(751\) −4.73690 + 1.39088i −0.172852 + 0.0507539i −0.367013 0.930216i \(-0.619620\pi\)
0.194161 + 0.980970i \(0.437801\pi\)
\(752\) 0 0
\(753\) 8.32764 + 4.29320i 0.303476 + 0.156453i
\(754\) 0 0
\(755\) −16.7990 16.0178i −0.611378 0.582947i
\(756\) 0 0
\(757\) 0.0525275 + 0.151768i 0.00190914 + 0.00551611i 0.945951 0.324309i \(-0.105132\pi\)
−0.944042 + 0.329825i \(0.893010\pi\)
\(758\) 0 0
\(759\) 13.1840 + 15.2152i 0.478550 + 0.552277i
\(760\) 0 0
\(761\) 28.2495 + 8.29479i 1.02404 + 0.300686i 0.750286 0.661113i \(-0.229916\pi\)
0.273756 + 0.961799i \(0.411734\pi\)
\(762\) 0 0
\(763\) −6.80769 + 6.49112i −0.246455 + 0.234994i
\(764\) 0 0
\(765\) −3.74335 + 5.25680i −0.135341 + 0.190060i
\(766\) 0 0
\(767\) −1.00592 1.74230i −0.0363217 0.0629110i
\(768\) 0 0
\(769\) 45.1761 8.70698i 1.62909 0.313982i 0.708858 0.705351i \(-0.249211\pi\)
0.920234 + 0.391369i \(0.127998\pi\)
\(770\) 0 0
\(771\) −18.5584 14.5945i −0.668363 0.525607i
\(772\) 0 0
\(773\) 47.1550 + 4.50275i 1.69605 + 0.161953i 0.897808 0.440388i \(-0.145159\pi\)
0.798239 + 0.602341i \(0.205765\pi\)
\(774\) 0 0
\(775\) 6.01838 10.4241i 0.216187 0.374446i
\(776\) 0 0
\(777\) 18.9456 + 12.1756i 0.679670 + 0.436797i
\(778\) 0