Properties

Label 405.2.e.a.271.1
Level $405$
Weight $2$
Character 405.271
Analytic conductor $3.234$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.2.e.a.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.00000 q^{10} +(-2.50000 - 4.33013i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(2.00000 + 3.46410i) q^{16} -4.00000 q^{17} -5.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(-5.00000 + 8.66025i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +8.00000 q^{26} +(2.50000 + 4.33013i) q^{29} +(4.50000 - 7.79423i) q^{31} +(4.00000 - 6.92820i) q^{32} +(4.00000 + 6.92820i) q^{34} -10.0000 q^{37} +(5.00000 + 8.66025i) q^{38} +(-3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{43} +10.0000 q^{44} +12.0000 q^{46} +(-1.00000 - 1.73205i) q^{47} +(3.50000 - 6.06218i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(-4.00000 - 6.92820i) q^{52} +8.00000 q^{53} +5.00000 q^{55} +(5.00000 - 8.66025i) q^{58} +(0.500000 - 0.866025i) q^{59} +(1.00000 + 1.73205i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(4.00000 - 6.92820i) q^{68} +1.00000 q^{71} -8.00000 q^{73} +(10.0000 + 17.3205i) q^{74} +(5.00000 - 8.66025i) q^{76} +(-6.00000 - 10.3923i) q^{79} -4.00000 q^{80} +14.0000 q^{82} +(-3.00000 - 5.19615i) q^{83} +(2.00000 - 3.46410i) q^{85} +(2.00000 - 3.46410i) q^{86} -9.00000 q^{89} +(-6.00000 - 10.3923i) q^{92} +(-2.00000 + 3.46410i) q^{94} +(2.50000 - 4.33013i) q^{95} +(-7.00000 - 12.1244i) q^{97} -14.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{4} - q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 2 q^{4} - q^{5} + 4 q^{10} - 5 q^{11} - 4 q^{13} + 4 q^{16} - 8 q^{17} - 10 q^{19} - 2 q^{20} - 10 q^{22} - 6 q^{23} - q^{25} + 16 q^{26} + 5 q^{29} + 9 q^{31} + 8 q^{32} + 8 q^{34} - 20 q^{37} + 10 q^{38} - 7 q^{41} + 2 q^{43} + 20 q^{44} + 24 q^{46} - 2 q^{47} + 7 q^{49} - 2 q^{50} - 8 q^{52} + 16 q^{53} + 10 q^{55} + 10 q^{58} + q^{59} + 2 q^{61} - 36 q^{62} - 16 q^{64} - 4 q^{65} - 6 q^{67} + 8 q^{68} + 2 q^{71} - 16 q^{73} + 20 q^{74} + 10 q^{76} - 12 q^{79} - 8 q^{80} + 28 q^{82} - 6 q^{83} + 4 q^{85} + 4 q^{86} - 18 q^{89} - 12 q^{92} - 4 q^{94} + 5 q^{95} - 14 q^{97} - 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 0 0
\(22\) −5.00000 + 8.66025i −1.06600 + 1.84637i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 8.00000 1.56893
\(27\) 0 0
\(28\) 0 0
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 0 0
\(31\) 4.50000 7.79423i 0.808224 1.39988i −0.105869 0.994380i \(-0.533762\pi\)
0.914093 0.405505i \(-0.132904\pi\)
\(32\) 4.00000 6.92820i 0.707107 1.22474i
\(33\) 0 0
\(34\) 4.00000 + 6.92820i 0.685994 + 1.18818i
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 5.00000 + 8.66025i 0.811107 + 1.40488i
\(39\) 0 0
\(40\) 0 0
\(41\) −3.50000 + 6.06218i −0.546608 + 0.946753i 0.451896 + 0.892071i \(0.350748\pi\)
−0.998504 + 0.0546823i \(0.982585\pi\)
\(42\) 0 0
\(43\) 1.00000 + 1.73205i 0.152499 + 0.264135i 0.932145 0.362084i \(-0.117935\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(44\) 10.0000 1.50756
\(45\) 0 0
\(46\) 12.0000 1.76930
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 0 0
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) −1.00000 + 1.73205i −0.141421 + 0.244949i
\(51\) 0 0
\(52\) −4.00000 6.92820i −0.554700 0.960769i
\(53\) 8.00000 1.09888 0.549442 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 5.00000 8.66025i 0.656532 1.13715i
\(59\) 0.500000 0.866025i 0.0650945 0.112747i −0.831641 0.555313i \(-0.812598\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −18.0000 −2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) −3.00000 + 5.19615i −0.366508 + 0.634811i −0.989017 0.147802i \(-0.952780\pi\)
0.622509 + 0.782613i \(0.286114\pi\)
\(68\) 4.00000 6.92820i 0.485071 0.840168i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.00000 0.118678 0.0593391 0.998238i \(-0.481101\pi\)
0.0593391 + 0.998238i \(0.481101\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) 10.0000 + 17.3205i 1.16248 + 2.01347i
\(75\) 0 0
\(76\) 5.00000 8.66025i 0.573539 0.993399i
\(77\) 0 0
\(78\) 0 0
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) 14.0000 1.54604
\(83\) −3.00000 5.19615i −0.329293 0.570352i 0.653079 0.757290i \(-0.273477\pi\)
−0.982372 + 0.186938i \(0.940144\pi\)
\(84\) 0 0
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 0 0
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 10.3923i −0.625543 1.08347i
\(93\) 0 0
\(94\) −2.00000 + 3.46410i −0.206284 + 0.357295i
\(95\) 2.50000 4.33013i 0.256495 0.444262i
\(96\) 0 0
\(97\) −7.00000 12.1244i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) −14.0000 −1.41421
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) 0 0
\(103\) −1.00000 + 1.73205i −0.0985329 + 0.170664i −0.911078 0.412235i \(-0.864748\pi\)
0.812545 + 0.582899i \(0.198082\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.00000 13.8564i −0.777029 1.34585i
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) −5.00000 8.66025i −0.476731 0.825723i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.00000 13.8564i 0.752577 1.30350i −0.193993 0.981003i \(-0.562144\pi\)
0.946570 0.322498i \(-0.104523\pi\)
\(114\) 0 0
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) −10.0000 −0.928477
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 2.00000 3.46410i 0.181071 0.313625i
\(123\) 0 0
\(124\) 9.00000 + 15.5885i 0.808224 + 1.39988i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) −4.00000 + 6.92820i −0.350823 + 0.607644i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i \(-0.535080\pi\)
0.915764 0.401718i \(-0.131587\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) 20.0000 1.67248
\(144\) 0 0
\(145\) −5.00000 −0.415227
\(146\) 8.00000 + 13.8564i 0.662085 + 1.14676i
\(147\) 0 0
\(148\) 10.0000 17.3205i 0.821995 1.42374i
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0 0
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.50000 + 7.79423i 0.361449 + 0.626048i
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) −12.0000 + 20.7846i −0.954669 + 1.65353i
\(159\) 0 0
\(160\) 4.00000 + 6.92820i 0.316228 + 0.547723i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) −7.00000 12.1244i −0.546608 0.946753i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) −8.00000 −0.613572
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 10.0000 17.3205i 0.753778 1.30558i
\(177\) 0 0
\(178\) 9.00000 + 15.5885i 0.674579 + 1.16840i
\(179\) 23.0000 1.71910 0.859550 0.511051i \(-0.170744\pi\)
0.859550 + 0.511051i \(0.170744\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.00000 8.66025i 0.367607 0.636715i
\(186\) 0 0
\(187\) 10.0000 + 17.3205i 0.731272 + 1.26660i
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) −10.0000 −0.725476
\(191\) −0.500000 0.866025i −0.0361787 0.0626634i 0.847369 0.531004i \(-0.178185\pi\)
−0.883548 + 0.468341i \(0.844852\pi\)
\(192\) 0 0
\(193\) −13.0000 + 22.5167i −0.935760 + 1.62078i −0.162488 + 0.986710i \(0.551952\pi\)
−0.773272 + 0.634074i \(0.781381\pi\)
\(194\) −14.0000 + 24.2487i −1.00514 + 1.74096i
\(195\) 0 0
\(196\) 7.00000 + 12.1244i 0.500000 + 0.866025i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.00000 5.19615i 0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.50000 6.06218i −0.244451 0.423401i
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) −16.0000 −1.10940
\(209\) 12.5000 + 21.6506i 0.864643 + 1.49761i
\(210\) 0 0
\(211\) −5.50000 + 9.52628i −0.378636 + 0.655816i −0.990864 0.134865i \(-0.956940\pi\)
0.612228 + 0.790681i \(0.290273\pi\)
\(212\) −8.00000 + 13.8564i −0.549442 + 0.951662i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) 0 0
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 0 0
\(220\) −5.00000 + 8.66025i −0.337100 + 0.583874i
\(221\) 8.00000 13.8564i 0.538138 0.932083i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −32.0000 −2.12861
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) 0 0
\(229\) −3.00000 + 5.19615i −0.198246 + 0.343371i −0.947960 0.318390i \(-0.896858\pi\)
0.749714 + 0.661762i \(0.230191\pi\)
\(230\) −6.00000 + 10.3923i −0.395628 + 0.685248i
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 2.00000 0.130466
\(236\) 1.00000 + 1.73205i 0.0650945 + 0.112747i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.00000 13.8564i 0.517477 0.896296i −0.482317 0.875997i \(-0.660205\pi\)
0.999794 0.0202996i \(-0.00646202\pi\)
\(240\) 0 0
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) 28.0000 1.79991
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) 3.50000 + 6.06218i 0.223607 + 0.387298i
\(246\) 0 0
\(247\) 10.0000 17.3205i 0.636285 1.10208i
\(248\) 0 0
\(249\) 0 0
\(250\) −1.00000 1.73205i −0.0632456 0.109545i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 30.0000 1.88608
\(254\) −16.0000 27.7128i −1.00393 1.73886i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.00000 0.496139
\(261\) 0 0
\(262\) 30.0000 1.85341
\(263\) −5.00000 8.66025i −0.308313 0.534014i 0.669680 0.742650i \(-0.266431\pi\)
−0.977993 + 0.208635i \(0.933098\pi\)
\(264\) 0 0
\(265\) −4.00000 + 6.92820i −0.245718 + 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) −31.0000 −1.89010 −0.945052 0.326921i \(-0.893989\pi\)
−0.945052 + 0.326921i \(0.893989\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −8.00000 13.8564i −0.485071 0.840168i
\(273\) 0 0
\(274\) −12.0000 + 20.7846i −0.724947 + 1.25564i
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) 9.00000 + 15.5885i 0.540758 + 0.936620i 0.998861 + 0.0477206i \(0.0151957\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) −38.0000 −2.27909
\(279\) 0 0
\(280\) 0 0
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) −3.00000 + 5.19615i −0.178331 + 0.308879i −0.941309 0.337546i \(-0.890403\pi\)
0.762978 + 0.646425i \(0.223737\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −20.0000 34.6410i −1.18262 2.04837i
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 5.00000 + 8.66025i 0.293610 + 0.508548i
\(291\) 0 0
\(292\) 8.00000 13.8564i 0.468165 0.810885i
\(293\) −9.00000 + 15.5885i −0.525786 + 0.910687i 0.473763 + 0.880652i \(0.342895\pi\)
−0.999549 + 0.0300351i \(0.990438\pi\)
\(294\) 0 0
\(295\) 0.500000 + 0.866025i 0.0291111 + 0.0504219i
\(296\) 0 0
\(297\) 0 0
\(298\) −4.00000 −0.231714
\(299\) −12.0000 20.7846i −0.693978 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 0 0
\(304\) −10.0000 17.3205i −0.573539 0.993399i
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.00000 15.5885i 0.511166 0.885365i
\(311\) 4.50000 7.79423i 0.255172 0.441970i −0.709771 0.704433i \(-0.751201\pi\)
0.964942 + 0.262463i \(0.0845347\pi\)
\(312\) 0 0
\(313\) 2.00000 + 3.46410i 0.113047 + 0.195803i 0.916997 0.398894i \(-0.130606\pi\)
−0.803951 + 0.594696i \(0.797272\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 24.0000 1.35011
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 0 0
\(319\) 12.5000 21.6506i 0.699866 1.21220i
\(320\) 4.00000 6.92820i 0.223607 0.387298i
\(321\) 0 0
\(322\) 0 0
\(323\) 20.0000 1.11283
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.5000 + 18.1865i 0.577132 + 0.999622i 0.995806 + 0.0914858i \(0.0291616\pi\)
−0.418674 + 0.908137i \(0.637505\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) 24.0000 1.31322
\(335\) −3.00000 5.19615i −0.163908 0.283896i
\(336\) 0 0
\(337\) 4.00000 6.92820i 0.217894 0.377403i −0.736270 0.676688i \(-0.763415\pi\)
0.954164 + 0.299285i \(0.0967480\pi\)
\(338\) −3.00000 + 5.19615i −0.163178 + 0.282633i
\(339\) 0 0
\(340\) 4.00000 + 6.92820i 0.216930 + 0.375735i
\(341\) −45.0000 −2.43689
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) 0 0
\(349\) −6.50000 11.2583i −0.347937 0.602645i 0.637946 0.770081i \(-0.279784\pi\)
−0.985883 + 0.167437i \(0.946451\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −40.0000 −2.13201
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 0 0
\(355\) −0.500000 + 0.866025i −0.0265372 + 0.0459639i
\(356\) 9.00000 15.5885i 0.476999 0.826187i
\(357\) 0 0
\(358\) −23.0000 39.8372i −1.21559 2.10546i
\(359\) −27.0000 −1.42501 −0.712503 0.701669i \(-0.752438\pi\)
−0.712503 + 0.701669i \(0.752438\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 25.0000 + 43.3013i 1.31397 + 2.27586i
\(363\) 0 0
\(364\) 0 0
\(365\) 4.00000 6.92820i 0.209370 0.362639i
\(366\) 0 0
\(367\) −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i \(-0.322339\pi\)
−0.999404 + 0.0345320i \(0.989006\pi\)
\(368\) −24.0000 −1.25109
\(369\) 0 0
\(370\) −20.0000 −1.03975
\(371\) 0 0
\(372\) 0 0
\(373\) −8.00000 + 13.8564i −0.414224 + 0.717458i −0.995347 0.0963587i \(-0.969280\pi\)
0.581122 + 0.813816i \(0.302614\pi\)
\(374\) 20.0000 34.6410i 1.03418 1.79124i
\(375\) 0 0
\(376\) 0 0
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 5.00000 + 8.66025i 0.256495 + 0.444262i
\(381\) 0 0
\(382\) −1.00000 + 1.73205i −0.0511645 + 0.0886194i
\(383\) 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i \(-0.461719\pi\)
0.799783 0.600289i \(-0.204948\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 52.0000 2.64673
\(387\) 0 0
\(388\) 28.0000 1.42148
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 12.0000 20.7846i 0.606866 1.05112i
\(392\) 0 0
\(393\) 0 0
\(394\) −12.0000 20.7846i −0.604551 1.04711i
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) −38.0000 −1.90717 −0.953583 0.301131i \(-0.902636\pi\)
−0.953583 + 0.301131i \(0.902636\pi\)
\(398\) −16.0000 27.7128i −0.802008 1.38912i
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) 18.0000 + 31.1769i 0.896644 + 1.55303i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) 25.0000 + 43.3013i 1.23920 + 2.14636i
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −7.00000 + 12.1244i −0.345705 + 0.598779i
\(411\) 0 0
\(412\) −2.00000 3.46410i −0.0985329 0.170664i
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 16.0000 + 27.7128i 0.784465 + 1.35873i
\(417\) 0 0
\(418\) 25.0000 43.3013i 1.22279 2.11793i
\(419\) −8.00000 + 13.8564i −0.390826 + 0.676930i −0.992559 0.121768i \(-0.961144\pi\)
0.601733 + 0.798697i \(0.294477\pi\)
\(420\) 0 0
\(421\) −6.50000 11.2583i −0.316791 0.548697i 0.663026 0.748596i \(-0.269272\pi\)
−0.979817 + 0.199899i \(0.935939\pi\)
\(422\) 22.0000 1.07094
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) 2.00000 + 3.46410i 0.0964486 + 0.167054i
\(431\) 3.00000 0.144505 0.0722525 0.997386i \(-0.476981\pi\)
0.0722525 + 0.997386i \(0.476981\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 15.0000 25.9808i 0.717547 1.24283i
\(438\) 0 0
\(439\) 14.5000 + 25.1147i 0.692047 + 1.19866i 0.971166 + 0.238404i \(0.0766244\pi\)
−0.279119 + 0.960257i \(0.590042\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −32.0000 −1.52208
\(443\) −3.00000 5.19615i −0.142534 0.246877i 0.785916 0.618333i \(-0.212192\pi\)
−0.928450 + 0.371457i \(0.878858\pi\)
\(444\) 0 0
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) 0 0
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) 0 0
\(451\) 35.0000 1.64809
\(452\) 16.0000 + 27.7128i 0.752577 + 1.30350i
\(453\) 0 0
\(454\) −4.00000 + 6.92820i −0.187729 + 0.325157i
\(455\) 0 0
\(456\) 0 0
\(457\) 19.0000 + 32.9090i 0.888783 + 1.53942i 0.841316 + 0.540544i \(0.181781\pi\)
0.0474665 + 0.998873i \(0.484885\pi\)
\(458\) 12.0000 0.560723
\(459\) 0 0
\(460\) 12.0000 0.559503
\(461\) 7.50000 + 12.9904i 0.349310 + 0.605022i 0.986127 0.165992i \(-0.0530827\pi\)
−0.636817 + 0.771015i \(0.719749\pi\)
\(462\) 0 0
\(463\) 3.00000 5.19615i 0.139422 0.241486i −0.787856 0.615859i \(-0.788809\pi\)
0.927278 + 0.374374i \(0.122142\pi\)
\(464\) −10.0000 + 17.3205i −0.464238 + 0.804084i
\(465\) 0 0
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.00000 3.46410i −0.0922531 0.159787i
\(471\) 0 0
\(472\) 0 0
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) 0 0
\(475\) 2.50000 + 4.33013i 0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) −32.0000 −1.46365
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) 20.0000 34.6410i 0.911922 1.57949i
\(482\) 11.0000 19.0526i 0.501036 0.867820i
\(483\) 0 0
\(484\) −14.0000 24.2487i −0.636364 1.10221i
\(485\) 14.0000 0.635707
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 7.00000 12.1244i 0.316228 0.547723i
\(491\) −21.5000 + 37.2391i −0.970281 + 1.68058i −0.275581 + 0.961278i \(0.588870\pi\)
−0.694701 + 0.719299i \(0.744463\pi\)
\(492\) 0 0
\(493\) −10.0000 17.3205i −0.450377 0.780076i
\(494\) −40.0000 −1.79969
\(495\) 0 0
\(496\) 36.0000 1.61645
\(497\) 0 0
\(498\) 0 0
\(499\) −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i \(-0.883413\pi\)
0.776989 + 0.629515i \(0.216746\pi\)
\(500\) −1.00000 + 1.73205i −0.0447214 + 0.0774597i
\(501\) 0 0
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) −20.0000 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) −30.0000 51.9615i −1.33366 2.30997i
\(507\) 0 0
\(508\) −16.0000 + 27.7128i −0.709885 + 1.22956i
\(509\) −1.00000 + 1.73205i −0.0443242 + 0.0767718i −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) −1.00000 1.73205i −0.0440653 0.0763233i
\(516\) 0 0
\(517\) −5.00000 + 8.66025i −0.219900 + 0.380878i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) −15.0000 25.9808i −0.655278 1.13497i
\(525\) 0 0
\(526\) −10.0000 + 17.3205i −0.436021 + 0.755210i
\(527\) −18.0000 + 31.1769i −0.784092 + 1.35809i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 16.0000 0.694996
\(531\) 0 0
\(532\) 0 0
\(533\) −14.0000 24.2487i −0.606407 1.05033i
\(534\) 0 0
\(535\) 3.00000 5.19615i 0.129701 0.224649i
\(536\) 0 0
\(537\) 0 0
\(538\) 31.0000 + 53.6936i 1.33650 + 2.31489i
\(539\) −35.0000 −1.50756
\(540\) 0 0
\(541\) 3.00000 0.128980 0.0644900 0.997918i \(-0.479458\pi\)
0.0644900 + 0.997918i \(0.479458\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) −16.0000 + 27.7128i −0.685994 + 1.18818i
\(545\) 0.500000 0.866025i 0.0214176 0.0370965i
\(546\) 0 0
\(547\) −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i \(-0.962392\pi\)
0.394432 0.918925i \(-0.370941\pi\)
\(548\) 24.0000 1.02523
\(549\) 0 0
\(550\) 10.0000 0.426401
\(551\) −12.5000 21.6506i −0.532518 0.922348i
\(552\) 0 0
\(553\) 0 0
\(554\) 18.0000 31.1769i 0.764747 1.32458i
\(555\) 0 0
\(556\) 19.0000 + 32.9090i 0.805779 + 1.39565i
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 + 10.3923i −0.253095 + 0.438373i
\(563\) 9.00000 15.5885i 0.379305 0.656975i −0.611656 0.791123i \(-0.709497\pi\)
0.990961 + 0.134148i \(0.0428299\pi\)
\(564\) 0 0
\(565\) 8.00000 + 13.8564i 0.336563 + 0.582943i
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 0 0
\(569\) 1.50000 + 2.59808i 0.0628833 + 0.108917i 0.895753 0.444552i \(-0.146637\pi\)
−0.832870 + 0.553469i \(0.813304\pi\)
\(570\) 0 0
\(571\) −2.50000 + 4.33013i −0.104622 + 0.181210i −0.913584 0.406651i \(-0.866697\pi\)
0.808962 + 0.587861i \(0.200030\pi\)
\(572\) −20.0000 + 34.6410i −0.836242 + 1.44841i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.00000 0.250217
\(576\) 0 0
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 1.00000 + 1.73205i 0.0415945 + 0.0720438i
\(579\) 0 0
\(580\) 5.00000 8.66025i 0.207614 0.359597i
\(581\) 0 0
\(582\) 0 0
\(583\) −20.0000 34.6410i −0.828315 1.43468i
\(584\) 0 0
\(585\) 0 0
\(586\) 36.0000 1.48715
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) 0 0
\(589\) −22.5000 + 38.9711i −0.927096 + 1.60578i
\(590\) 1.00000 1.73205i 0.0411693 0.0713074i
\(591\) 0 0
\(592\) −20.0000 34.6410i −0.821995 1.42374i
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.00000 + 3.46410i 0.0819232 + 0.141895i
\(597\) 0 0
\(598\) −24.0000 + 41.5692i −0.981433 + 1.69989i
\(599\) 8.50000 14.7224i 0.347301 0.601542i −0.638468 0.769648i \(-0.720432\pi\)
0.985769 + 0.168106i \(0.0537650\pi\)
\(600\) 0 0
\(601\) 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i \(-0.0400009\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) −17.0000 + 29.4449i −0.690009 + 1.19513i 0.281826 + 0.959466i \(0.409060\pi\)
−0.971834 + 0.235665i \(0.924273\pi\)
\(608\) −20.0000 + 34.6410i −0.811107 + 1.40488i
\(609\) 0 0
\(610\) 2.00000 + 3.46410i 0.0809776 + 0.140257i
\(611\) 8.00000 0.323645
\(612\) 0 0
\(613\) 4.00000 0.161558 0.0807792 0.996732i \(-0.474259\pi\)
0.0807792 + 0.996732i \(0.474259\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 20.7846i 0.483102 0.836757i −0.516710 0.856161i \(-0.672843\pi\)
0.999812 + 0.0194037i \(0.00617676\pi\)
\(618\) 0 0
\(619\) 14.0000 + 24.2487i 0.562708 + 0.974638i 0.997259 + 0.0739910i \(0.0235736\pi\)
−0.434551 + 0.900647i \(0.643093\pi\)
\(620\) −18.0000 −0.722897
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 4.00000 6.92820i 0.159872 0.276907i
\(627\) 0 0
\(628\) −2.00000 3.46410i −0.0798087 0.138233i
\(629\) 40.0000 1.59490
\(630\) 0 0
\(631\) −17.0000 −0.676759 −0.338380 0.941010i \(-0.609879\pi\)
−0.338380 + 0.941010i \(0.609879\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2.00000 3.46410i 0.0794301 0.137577i
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) 14.0000 + 24.2487i 0.554700 + 0.960769i
\(638\) −50.0000 −1.97952
\(639\) 0 0
\(640\) 0 0
\(641\) −1.50000 2.59808i −0.0592464 0.102618i 0.834881 0.550431i \(-0.185536\pi\)
−0.894127 + 0.447813i \(0.852203\pi\)
\(642\) 0 0
\(643\) −3.00000 + 5.19615i −0.118308 + 0.204916i −0.919097 0.394030i \(-0.871080\pi\)
0.800789 + 0.598947i \(0.204414\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −20.0000 34.6410i −0.786889 1.36293i
\(647\) −10.0000 −0.393141 −0.196570 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(648\) 0 0
\(649\) −5.00000 −0.196267
\(650\) −4.00000 6.92820i −0.156893 0.271746i
\(651\) 0 0
\(652\) −8.00000 + 13.8564i −0.313304 + 0.542659i
\(653\) 4.00000 6.92820i 0.156532 0.271122i −0.777084 0.629397i \(-0.783302\pi\)
0.933616 + 0.358276i \(0.116635\pi\)
\(654\) 0 0
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) −28.0000 −1.09322
\(657\) 0 0
\(658\) 0 0
\(659\) −22.0000 38.1051i −0.856998 1.48436i −0.874779 0.484523i \(-0.838993\pi\)
0.0177803 0.999842i \(-0.494340\pi\)
\(660\) 0 0
\(661\) −12.5000 + 21.6506i −0.486194 + 0.842112i −0.999874 0.0158695i \(-0.994948\pi\)
0.513680 + 0.857982i \(0.328282\pi\)
\(662\) 21.0000 36.3731i 0.816188 1.41368i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −30.0000 −1.16160
\(668\) −12.0000 20.7846i −0.464294 0.804181i
\(669\) 0 0
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) 5.00000 8.66025i 0.193023 0.334325i
\(672\) 0 0
\(673\) −21.0000 36.3731i −0.809491 1.40208i −0.913217 0.407473i \(-0.866410\pi\)
0.103727 0.994606i \(-0.466923\pi\)
\(674\) −16.0000 −0.616297
\(675\) 0 0
\(676\) 6.00000 0.230769
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 45.0000 + 77.9423i 1.72314 + 2.98456i
\(683\) 48.0000 1.83667 0.918334 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −16.0000 + 27.7128i −0.609551 + 1.05577i
\(690\) 0 0
\(691\) −2.00000 3.46410i −0.0760836 0.131781i 0.825473 0.564441i \(-0.190908\pi\)
−0.901557 + 0.432660i \(0.857575\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 40.0000 1.51838
\(695\) 9.50000 + 16.4545i 0.360356 + 0.624154i
\(696\) 0 0
\(697\) 14.0000 24.2487i 0.530288 0.918485i
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.0000 0.717620 0.358810 0.933411i \(-0.383183\pi\)
0.358810 + 0.933411i \(0.383183\pi\)
\(702\) 0 0
\(703\) 50.0000 1.88579
\(704\) 20.0000 + 34.6410i 0.753778 + 1.30558i
\(705\) 0 0
\(706\) 18.0000 31.1769i 0.677439 1.17336i
\(707\) 0 0
\(708\) 0 0
\(709\) −11.0000 19.0526i −0.413114 0.715534i 0.582115 0.813107i \(-0.302225\pi\)
−0.995228 + 0.0975728i \(0.968892\pi\)
\(710\) 2.00000 0.0750587
\(711\) 0 0
\(712\) 0 0
\(713\) 27.0000 + 46.7654i 1.01116 + 1.75138i
\(714\) 0 0
\(715\) −10.0000 + 17.3205i −0.373979 + 0.647750i
\(716\) −23.0000 + 39.8372i −0.859550 + 1.48878i
\(717\) 0 0
\(718\) 27.0000 + 46.7654i 1.00763 + 1.74527i
\(719\) 27.0000 1.00693 0.503465 0.864016i \(-0.332058\pi\)
0.503465 + 0.864016i \(0.332058\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −6.00000 10.3923i −0.223297 0.386762i
\(723\) 0 0
\(724\) 25.0000 43.3013i 0.929118 1.60928i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) −22.0000 38.1051i −0.815935 1.41324i −0.908655 0.417548i \(-0.862889\pi\)
0.0927199 0.995692i \(-0.470444\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.0000 −0.592187
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) 0 0
\(733\) 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i \(-0.510222\pi\)
0.881633 0.471935i \(-0.156444\pi\)
\(734\) −18.0000 + 31.1769i −0.664392 + 1.15076i
\(735\) 0 0
\(736\) 24.0000 + 41.5692i 0.884652 + 1.53226i
\(737\) 30.0000 1.10506
\(738\) 0 0
\(739\) −35.0000 −1.28750 −0.643748 0.765238i \(-0.722621\pi\)
−0.643748 + 0.765238i \(0.722621\pi\)
\(740\) 10.0000 + 17.3205i 0.367607 + 0.636715i
\(741\) 0 0
\(742\) 0 0
\(743\) 2.00000 3.46410i 0.0733729 0.127086i −0.827005 0.562195i \(-0.809957\pi\)
0.900378 + 0.435110i \(0.143290\pi\)
\(744\) 0 0
\(745\) 1.00000 + 1.73205i 0.0366372 + 0.0634574i
\(746\) 32.0000 1.17160
\(747\) 0 0
\(748\) −40.0000 −1.46254
\(749\) 0 0
\(750\) 0 0
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 4.00000 6.92820i 0.145865 0.252646i
\(753\) 0 0
\(754\) 20.0000 + 34.6410i 0.728357 + 1.26155i
\(755\) −5.00000 −0.181969
\(756\) 0 0
\(757\) 28.0000 1.01768 0.508839 0.860862i \(-0.330075\pi\)
0.508839 + 0.860862i \(0.330075\pi\)
\(758\) −4.00000 6.92820i −0.145287 0.251644i
\(759\) 0 0
\(760\) 0 0
\(761\) 13.5000 23.3827i 0.489375 0.847622i −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.00000 0.0723575
\(765\) 0 0
\(766\) −72.0000 −2.60147
\(767\) 2.00000 + 3.46410i 0.0722158 + 0.125081i
\(768\) 0 0
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −26.0000 45.0333i −0.935760 1.62078i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) −9.00000 −0.323290
\(776\) 0 0
\(777\) 0 0
\(778\) −6.00000 + 10.3923i −0.215110 + 0.372582i
\(779\) 17.5000 30.3109i 0.627003 1.08600i
\(780\) 0 0
\(781\) −2.50000 4.33013i −0.0894570 0.154944i
\(782\) −48.0000 −1.71648
\(783\) 0 0
\(784\) 28.0000 1.00000
\(785\) −1.00000 1.73205i −0.0356915 0.0618195i
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) −12.0000 + 20.7846i −0.427482 + 0.740421i
\(789\) 0 0
\(790\) −12.0000 20.7846i −0.426941 0.739483i
\(791\) 0 0
\(792\) 0 0
\(793\) −8.00000