Properties

Label 225.2.f.a.143.1
Level $225$
Weight $2$
Character 225.143
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 143.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 225.143
Dual form 225.2.f.a.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 2.00000i) q^{7} +(-2.12132 + 2.12132i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 2.00000i) q^{7} +(-2.12132 + 2.12132i) q^{8} -2.82843i q^{11} +(-1.00000 - 1.00000i) q^{13} -2.82843 q^{14} +1.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-2.00000 + 2.00000i) q^{22} +(2.82843 - 2.82843i) q^{23} +1.41421i q^{26} +(-2.00000 - 2.00000i) q^{28} +4.24264 q^{29} -4.00000 q^{31} +(3.53553 + 3.53553i) q^{32} +4.00000i q^{34} +(-1.00000 + 1.00000i) q^{37} +1.41421i q^{41} +(8.00000 + 8.00000i) q^{43} -2.82843 q^{44} -4.00000 q^{46} +(5.65685 + 5.65685i) q^{47} -1.00000i q^{49} +(-1.00000 + 1.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +8.48528i q^{56} +(-3.00000 - 3.00000i) q^{58} +8.48528 q^{59} +8.00000 q^{61} +(2.82843 + 2.82843i) q^{62} -7.00000i q^{64} +(-4.00000 + 4.00000i) q^{67} +(-2.82843 + 2.82843i) q^{68} +5.65685i q^{71} +(-1.00000 - 1.00000i) q^{73} +1.41421 q^{74} +(-5.65685 - 5.65685i) q^{77} +12.0000i q^{79} +(1.00000 - 1.00000i) q^{82} +(2.82843 - 2.82843i) q^{83} -11.3137i q^{86} +(6.00000 + 6.00000i) q^{88} -12.7279 q^{89} -4.00000 q^{91} +(-2.82843 - 2.82843i) q^{92} -8.00000i q^{94} +(11.0000 - 11.0000i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{7} - 4 q^{13} + 4 q^{16} - 8 q^{22} - 8 q^{28} - 16 q^{31} - 4 q^{37} + 32 q^{43} - 16 q^{46} - 4 q^{52} - 12 q^{58} + 32 q^{61} - 16 q^{67} - 4 q^{73} + 4 q^{82} + 24 q^{88} - 16 q^{91} + 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i 0.411438 0.911438i \(-0.365027\pi\)
−0.911438 + 0.411438i \(0.865027\pi\)
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.00000 2.00000i 0.755929 0.755929i −0.219650 0.975579i \(-0.570491\pi\)
0.975579 + 0.219650i \(0.0704915\pi\)
\(8\) −2.12132 + 2.12132i −0.750000 + 0.750000i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.82843i 0.852803i −0.904534 0.426401i \(-0.859781\pi\)
0.904534 0.426401i \(-0.140219\pi\)
\(12\) 0 0
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −2.82843 −0.755929
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.82843 2.82843i −0.685994 0.685994i 0.275350 0.961344i \(-0.411206\pi\)
−0.961344 + 0.275350i \(0.911206\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 + 2.00000i −0.426401 + 0.426401i
\(23\) 2.82843 2.82843i 0.589768 0.589768i −0.347801 0.937568i \(-0.613071\pi\)
0.937568 + 0.347801i \(0.113071\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.41421i 0.277350i
\(27\) 0 0
\(28\) −2.00000 2.00000i −0.377964 0.377964i
\(29\) 4.24264 0.787839 0.393919 0.919145i \(-0.371119\pi\)
0.393919 + 0.919145i \(0.371119\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 3.53553 + 3.53553i 0.625000 + 0.625000i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.00000i −0.164399 + 0.164399i −0.784512 0.620113i \(-0.787087\pi\)
0.620113 + 0.784512i \(0.287087\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.41421i 0.220863i 0.993884 + 0.110432i \(0.0352233\pi\)
−0.993884 + 0.110432i \(0.964777\pi\)
\(42\) 0 0
\(43\) 8.00000 + 8.00000i 1.21999 + 1.21999i 0.967635 + 0.252353i \(0.0812046\pi\)
0.252353 + 0.967635i \(0.418795\pi\)
\(44\) −2.82843 −0.426401
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 5.65685 + 5.65685i 0.825137 + 0.825137i 0.986840 0.161703i \(-0.0516985\pi\)
−0.161703 + 0.986840i \(0.551699\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 + 1.00000i −0.138675 + 0.138675i
\(53\) 2.82843 2.82843i 0.388514 0.388514i −0.485643 0.874157i \(-0.661414\pi\)
0.874157 + 0.485643i \(0.161414\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 8.48528i 1.13389i
\(57\) 0 0
\(58\) −3.00000 3.00000i −0.393919 0.393919i
\(59\) 8.48528 1.10469 0.552345 0.833616i \(-0.313733\pi\)
0.552345 + 0.833616i \(0.313733\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 2.82843 + 2.82843i 0.359211 + 0.359211i
\(63\) 0 0
\(64\) 7.00000i 0.875000i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 + 4.00000i −0.488678 + 0.488678i −0.907889 0.419211i \(-0.862307\pi\)
0.419211 + 0.907889i \(0.362307\pi\)
\(68\) −2.82843 + 2.82843i −0.342997 + 0.342997i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.65685i 0.671345i 0.941979 + 0.335673i \(0.108964\pi\)
−0.941979 + 0.335673i \(0.891036\pi\)
\(72\) 0 0
\(73\) −1.00000 1.00000i −0.117041 0.117041i 0.646160 0.763202i \(-0.276374\pi\)
−0.763202 + 0.646160i \(0.776374\pi\)
\(74\) 1.41421 0.164399
\(75\) 0 0
\(76\) 0 0
\(77\) −5.65685 5.65685i −0.644658 0.644658i
\(78\) 0 0
\(79\) 12.0000i 1.35011i 0.737769 + 0.675053i \(0.235879\pi\)
−0.737769 + 0.675053i \(0.764121\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1.00000 1.00000i 0.110432 0.110432i
\(83\) 2.82843 2.82843i 0.310460 0.310460i −0.534628 0.845088i \(-0.679548\pi\)
0.845088 + 0.534628i \(0.179548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 11.3137i 1.21999i
\(87\) 0 0
\(88\) 6.00000 + 6.00000i 0.639602 + 0.639602i
\(89\) −12.7279 −1.34916 −0.674579 0.738203i \(-0.735675\pi\)
−0.674579 + 0.738203i \(0.735675\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) −2.82843 2.82843i −0.294884 0.294884i
\(93\) 0 0
\(94\) 8.00000i 0.825137i
\(95\) 0 0
\(96\) 0 0
\(97\) 11.0000 11.0000i 1.11688 1.11688i 0.124684 0.992196i \(-0.460208\pi\)
0.992196 0.124684i \(-0.0397918\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 15.5563i 1.54791i −0.633238 0.773957i \(-0.718274\pi\)
0.633238 0.773957i \(-0.281726\pi\)
\(102\) 0 0
\(103\) −10.0000 10.0000i −0.985329 0.985329i 0.0145647 0.999894i \(-0.495364\pi\)
−0.999894 + 0.0145647i \(0.995364\pi\)
\(104\) 4.24264 0.416025
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) −2.82843 2.82843i −0.273434 0.273434i 0.557047 0.830481i \(-0.311934\pi\)
−0.830481 + 0.557047i \(0.811934\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 2.00000i 0.188982 0.188982i
\(113\) −9.89949 + 9.89949i −0.931266 + 0.931266i −0.997785 0.0665190i \(-0.978811\pi\)
0.0665190 + 0.997785i \(0.478811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.24264i 0.393919i
\(117\) 0 0
\(118\) −6.00000 6.00000i −0.552345 0.552345i
\(119\) −11.3137 −1.03713
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) −5.65685 5.65685i −0.512148 0.512148i
\(123\) 0 0
\(124\) 4.00000i 0.359211i
\(125\) 0 0
\(126\) 0 0
\(127\) −10.0000 + 10.0000i −0.887357 + 0.887357i −0.994268 0.106912i \(-0.965904\pi\)
0.106912 + 0.994268i \(0.465904\pi\)
\(128\) 2.12132 2.12132i 0.187500 0.187500i
\(129\) 0 0
\(130\) 0 0
\(131\) 14.1421i 1.23560i 0.786334 + 0.617802i \(0.211977\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 5.65685 0.488678
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) −7.07107 7.07107i −0.604122 0.604122i 0.337282 0.941404i \(-0.390493\pi\)
−0.941404 + 0.337282i \(0.890493\pi\)
\(138\) 0 0
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.00000 4.00000i 0.335673 0.335673i
\(143\) −2.82843 + 2.82843i −0.236525 + 0.236525i
\(144\) 0 0
\(145\) 0 0
\(146\) 1.41421i 0.117041i
\(147\) 0 0
\(148\) 1.00000 + 1.00000i 0.0821995 + 0.0821995i
\(149\) −4.24264 −0.347571 −0.173785 0.984784i \(-0.555600\pi\)
−0.173785 + 0.984784i \(0.555600\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 8.00000i 0.644658i
\(155\) 0 0
\(156\) 0 0
\(157\) 5.00000 5.00000i 0.399043 0.399043i −0.478852 0.877896i \(-0.658947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 8.48528 8.48528i 0.675053 0.675053i
\(159\) 0 0
\(160\) 0 0
\(161\) 11.3137i 0.891645i
\(162\) 0 0
\(163\) 8.00000 + 8.00000i 0.626608 + 0.626608i 0.947213 0.320605i \(-0.103886\pi\)
−0.320605 + 0.947213i \(0.603886\pi\)
\(164\) 1.41421 0.110432
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 14.1421 + 14.1421i 1.09435 + 1.09435i 0.995058 + 0.0992931i \(0.0316581\pi\)
0.0992931 + 0.995058i \(0.468342\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 8.00000i 0.609994 0.609994i
\(173\) −9.89949 + 9.89949i −0.752645 + 0.752645i −0.974972 0.222327i \(-0.928635\pi\)
0.222327 + 0.974972i \(0.428635\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.82843i 0.213201i
\(177\) 0 0
\(178\) 9.00000 + 9.00000i 0.674579 + 0.674579i
\(179\) 25.4558 1.90266 0.951330 0.308175i \(-0.0997184\pi\)
0.951330 + 0.308175i \(0.0997184\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.82843 + 2.82843i 0.209657 + 0.209657i
\(183\) 0 0
\(184\) 12.0000i 0.884652i
\(185\) 0 0
\(186\) 0 0
\(187\) −8.00000 + 8.00000i −0.585018 + 0.585018i
\(188\) 5.65685 5.65685i 0.412568 0.412568i
\(189\) 0 0
\(190\) 0 0
\(191\) 22.6274i 1.63726i 0.574320 + 0.818631i \(0.305267\pi\)
−0.574320 + 0.818631i \(0.694733\pi\)
\(192\) 0 0
\(193\) −1.00000 1.00000i −0.0719816 0.0719816i 0.670199 0.742181i \(-0.266209\pi\)
−0.742181 + 0.670199i \(0.766209\pi\)
\(194\) −15.5563 −1.11688
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) 9.89949 + 9.89949i 0.705310 + 0.705310i 0.965545 0.260235i \(-0.0838002\pi\)
−0.260235 + 0.965545i \(0.583800\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −11.0000 + 11.0000i −0.773957 + 0.773957i
\(203\) 8.48528 8.48528i 0.595550 0.595550i
\(204\) 0 0
\(205\) 0 0
\(206\) 14.1421i 0.985329i
\(207\) 0 0
\(208\) −1.00000 1.00000i −0.0693375 0.0693375i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −2.82843 2.82843i −0.194257 0.194257i
\(213\) 0 0
\(214\) 4.00000i 0.273434i
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 + 8.00000i −0.543075 + 0.543075i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.65685i 0.380521i
\(222\) 0 0
\(223\) −10.0000 10.0000i −0.669650 0.669650i 0.287985 0.957635i \(-0.407015\pi\)
−0.957635 + 0.287985i \(0.907015\pi\)
\(224\) 14.1421 0.944911
\(225\) 0 0
\(226\) 14.0000 0.931266
\(227\) 5.65685 + 5.65685i 0.375459 + 0.375459i 0.869461 0.494002i \(-0.164466\pi\)
−0.494002 + 0.869461i \(0.664466\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9.00000 + 9.00000i −0.590879 + 0.590879i
\(233\) 2.82843 2.82843i 0.185296 0.185296i −0.608363 0.793659i \(-0.708173\pi\)
0.793659 + 0.608363i \(0.208173\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.48528i 0.552345i
\(237\) 0 0
\(238\) 8.00000 + 8.00000i 0.518563 + 0.518563i
\(239\) −16.9706 −1.09773 −0.548867 0.835910i \(-0.684941\pi\)
−0.548867 + 0.835910i \(0.684941\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −2.12132 2.12132i −0.136364 0.136364i
\(243\) 0 0
\(244\) 8.00000i 0.512148i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 8.48528 8.48528i 0.538816 0.538816i
\(249\) 0 0
\(250\) 0 0
\(251\) 19.7990i 1.24970i −0.780744 0.624851i \(-0.785160\pi\)
0.780744 0.624851i \(-0.214840\pi\)
\(252\) 0 0
\(253\) −8.00000 8.00000i −0.502956 0.502956i
\(254\) 14.1421 0.887357
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 1.41421 + 1.41421i 0.0882162 + 0.0882162i 0.749838 0.661622i \(-0.230131\pi\)
−0.661622 + 0.749838i \(0.730131\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) 0 0
\(261\) 0 0
\(262\) 10.0000 10.0000i 0.617802 0.617802i
\(263\) 2.82843 2.82843i 0.174408 0.174408i −0.614505 0.788913i \(-0.710644\pi\)
0.788913 + 0.614505i \(0.210644\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000 + 4.00000i 0.244339 + 0.244339i
\(269\) −12.7279 −0.776035 −0.388018 0.921652i \(-0.626840\pi\)
−0.388018 + 0.921652i \(0.626840\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −2.82843 2.82843i −0.171499 0.171499i
\(273\) 0 0
\(274\) 10.0000i 0.604122i
\(275\) 0 0
\(276\) 0 0
\(277\) 11.0000 11.0000i 0.660926 0.660926i −0.294672 0.955598i \(-0.595211\pi\)
0.955598 + 0.294672i \(0.0952105\pi\)
\(278\) −8.48528 + 8.48528i −0.508913 + 0.508913i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.89949i 0.590554i 0.955412 + 0.295277i \(0.0954120\pi\)
−0.955412 + 0.295277i \(0.904588\pi\)
\(282\) 0 0
\(283\) 8.00000 + 8.00000i 0.475551 + 0.475551i 0.903705 0.428155i \(-0.140836\pi\)
−0.428155 + 0.903705i \(0.640836\pi\)
\(284\) 5.65685 0.335673
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 2.82843 + 2.82843i 0.166957 + 0.166957i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 + 1.00000i −0.0585206 + 0.0585206i
\(293\) −9.89949 + 9.89949i −0.578335 + 0.578335i −0.934444 0.356110i \(-0.884103\pi\)
0.356110 + 0.934444i \(0.384103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.24264i 0.246598i
\(297\) 0 0
\(298\) 3.00000 + 3.00000i 0.173785 + 0.173785i
\(299\) −5.65685 −0.327144
\(300\) 0 0
\(301\) 32.0000 1.84445
\(302\) −5.65685 5.65685i −0.325515 0.325515i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 8.00000 8.00000i 0.456584 0.456584i −0.440948 0.897532i \(-0.645358\pi\)
0.897532 + 0.440948i \(0.145358\pi\)
\(308\) −5.65685 + 5.65685i −0.322329 + 0.322329i
\(309\) 0 0
\(310\) 0 0
\(311\) 11.3137i 0.641542i −0.947157 0.320771i \(-0.896058\pi\)
0.947157 0.320771i \(-0.103942\pi\)
\(312\) 0 0
\(313\) −19.0000 19.0000i −1.07394 1.07394i −0.997038 0.0769051i \(-0.975496\pi\)
−0.0769051 0.997038i \(-0.524504\pi\)
\(314\) −7.07107 −0.399043
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) −19.7990 19.7990i −1.11202 1.11202i −0.992877 0.119145i \(-0.961985\pi\)
−0.119145 0.992877i \(-0.538015\pi\)
\(318\) 0 0
\(319\) 12.0000i 0.671871i
\(320\) 0 0
\(321\) 0 0
\(322\) −8.00000 + 8.00000i −0.445823 + 0.445823i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 11.3137i 0.626608i
\(327\) 0 0
\(328\) −3.00000 3.00000i −0.165647 0.165647i
\(329\) 22.6274 1.24749
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) −2.82843 2.82843i −0.155230 0.155230i
\(333\) 0 0
\(334\) 20.0000i 1.09435i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000 5.00000i 0.272367 0.272367i −0.557685 0.830053i \(-0.688310\pi\)
0.830053 + 0.557685i \(0.188310\pi\)
\(338\) −7.77817 + 7.77817i −0.423077 + 0.423077i
\(339\) 0 0
\(340\) 0 0
\(341\) 11.3137i 0.612672i
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −33.9411 −1.82998
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) −11.3137 11.3137i −0.607352 0.607352i 0.334901 0.942253i \(-0.391297\pi\)
−0.942253 + 0.334901i \(0.891297\pi\)
\(348\) 0 0
\(349\) 24.0000i 1.28469i −0.766415 0.642345i \(-0.777962\pi\)
0.766415 0.642345i \(-0.222038\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000 10.0000i 0.533002 0.533002i
\(353\) 2.82843 2.82843i 0.150542 0.150542i −0.627818 0.778360i \(-0.716052\pi\)
0.778360 + 0.627818i \(0.216052\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 12.7279i 0.674579i
\(357\) 0 0
\(358\) −18.0000 18.0000i −0.951330 0.951330i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 11.3137 + 11.3137i 0.594635 + 0.594635i
\(363\) 0 0
\(364\) 4.00000i 0.209657i
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000 2.00000i 0.104399 0.104399i −0.652978 0.757377i \(-0.726481\pi\)
0.757377 + 0.652978i \(0.226481\pi\)
\(368\) 2.82843 2.82843i 0.147442 0.147442i
\(369\) 0 0
\(370\) 0 0
\(371\) 11.3137i 0.587378i
\(372\) 0 0
\(373\) 17.0000 + 17.0000i 0.880227 + 0.880227i 0.993557 0.113331i \(-0.0361520\pi\)
−0.113331 + 0.993557i \(0.536152\pi\)
\(374\) 11.3137 0.585018
\(375\) 0 0
\(376\) −24.0000 −1.23771
\(377\) −4.24264 4.24264i −0.218507 0.218507i
\(378\) 0 0
\(379\) 36.0000i 1.84920i 0.380945 + 0.924598i \(0.375599\pi\)
−0.380945 + 0.924598i \(0.624401\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 16.0000 16.0000i 0.818631 0.818631i
\(383\) −22.6274 + 22.6274i −1.15621 + 1.15621i −0.170923 + 0.985284i \(0.554675\pi\)
−0.985284 + 0.170923i \(0.945325\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.41421i 0.0719816i
\(387\) 0 0
\(388\) −11.0000 11.0000i −0.558440 0.558440i
\(389\) 4.24264 0.215110 0.107555 0.994199i \(-0.465698\pi\)
0.107555 + 0.994199i \(0.465698\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 2.12132 + 2.12132i 0.107143 + 0.107143i
\(393\) 0 0
\(394\) 14.0000i 0.705310i
\(395\) 0 0
\(396\) 0 0
\(397\) −19.0000 + 19.0000i −0.953583 + 0.953583i −0.998969 0.0453868i \(-0.985548\pi\)
0.0453868 + 0.998969i \(0.485548\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 24.0416i 1.20058i −0.799782 0.600291i \(-0.795051\pi\)
0.799782 0.600291i \(-0.204949\pi\)
\(402\) 0 0
\(403\) 4.00000 + 4.00000i 0.199254 + 0.199254i
\(404\) −15.5563 −0.773957
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 2.82843 + 2.82843i 0.140200 + 0.140200i
\(408\) 0 0
\(409\) 24.0000i 1.18672i 0.804936 + 0.593362i \(0.202200\pi\)
−0.804936 + 0.593362i \(0.797800\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −10.0000 + 10.0000i −0.492665 + 0.492665i
\(413\) 16.9706 16.9706i 0.835067 0.835067i
\(414\) 0 0
\(415\) 0 0
\(416\) 7.07107i 0.346688i
\(417\) 0 0
\(418\) 0 0
\(419\) 8.48528 0.414533 0.207267 0.978285i \(-0.433543\pi\)
0.207267 + 0.978285i \(0.433543\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 2.82843 + 2.82843i 0.137686 + 0.137686i
\(423\) 0 0
\(424\) 12.0000i 0.582772i
\(425\) 0 0
\(426\) 0 0
\(427\) 16.0000 16.0000i 0.774294 0.774294i
\(428\) −2.82843 + 2.82843i −0.136717 + 0.136717i
\(429\) 0 0
\(430\) 0 0
\(431\) 5.65685i 0.272481i 0.990676 + 0.136241i \(0.0435020\pi\)
−0.990676 + 0.136241i \(0.956498\pi\)
\(432\) 0 0
\(433\) 17.0000 + 17.0000i 0.816968 + 0.816968i 0.985668 0.168700i \(-0.0539568\pi\)
−0.168700 + 0.985668i \(0.553957\pi\)
\(434\) 11.3137 0.543075
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 24.0000i 1.14546i −0.819745 0.572729i \(-0.805885\pi\)
0.819745 0.572729i \(-0.194115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000 4.00000i 0.190261 0.190261i
\(443\) 28.2843 28.2843i 1.34383 1.34383i 0.451612 0.892215i \(-0.350849\pi\)
0.892215 0.451612i \(-0.149151\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 14.1421i 0.669650i
\(447\) 0 0
\(448\) −14.0000 14.0000i −0.661438 0.661438i
\(449\) −12.7279 −0.600668 −0.300334 0.953834i \(-0.597098\pi\)
−0.300334 + 0.953834i \(0.597098\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 9.89949 + 9.89949i 0.465633 + 0.465633i
\(453\) 0 0
\(454\) 8.00000i 0.375459i
\(455\) 0 0
\(456\) 0 0
\(457\) −25.0000 + 25.0000i −1.16945 + 1.16945i −0.187112 + 0.982339i \(0.559913\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 4.24264 4.24264i 0.198246 0.198246i
\(459\) 0 0
\(460\) 0 0
\(461\) 9.89949i 0.461065i 0.973065 + 0.230533i \(0.0740469\pi\)
−0.973065 + 0.230533i \(0.925953\pi\)
\(462\) 0 0
\(463\) −10.0000 10.0000i −0.464739 0.464739i 0.435466 0.900205i \(-0.356584\pi\)
−0.900205 + 0.435466i \(0.856584\pi\)
\(464\) 4.24264 0.196960
\(465\) 0 0
\(466\) −4.00000 −0.185296
\(467\) −2.82843 2.82843i −0.130884 0.130884i 0.638630 0.769514i \(-0.279501\pi\)
−0.769514 + 0.638630i \(0.779501\pi\)
\(468\) 0 0
\(469\) 16.0000i 0.738811i
\(470\) 0 0
\(471\) 0 0
\(472\) −18.0000 + 18.0000i −0.828517 + 0.828517i
\(473\) 22.6274 22.6274i 1.04041 1.04041i
\(474\) 0 0
\(475\) 0 0
\(476\) 11.3137i 0.518563i
\(477\) 0 0
\(478\) 12.0000 + 12.0000i 0.548867 + 0.548867i
\(479\) 16.9706 0.775405 0.387702 0.921785i \(-0.373269\pi\)
0.387702 + 0.921785i \(0.373269\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) 7.07107 + 7.07107i 0.322078 + 0.322078i
\(483\) 0 0
\(484\) 3.00000i 0.136364i
\(485\) 0 0
\(486\) 0 0
\(487\) −10.0000 + 10.0000i −0.453143 + 0.453143i −0.896396 0.443253i \(-0.853824\pi\)
0.443253 + 0.896396i \(0.353824\pi\)
\(488\) −16.9706 + 16.9706i −0.768221 + 0.768221i
\(489\) 0 0
\(490\) 0 0
\(491\) 14.1421i 0.638226i 0.947717 + 0.319113i \(0.103385\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) −12.0000 12.0000i −0.540453 0.540453i
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 11.3137 + 11.3137i 0.507489 + 0.507489i
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −14.0000 + 14.0000i −0.624851 + 0.624851i
\(503\) −22.6274 + 22.6274i −1.00891 + 1.00891i −0.00894668 + 0.999960i \(0.502848\pi\)
−0.999960 + 0.00894668i \(0.997152\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 11.3137i 0.502956i
\(507\) 0 0
\(508\) 10.0000 + 10.0000i 0.443678 + 0.443678i
\(509\) −4.24264 −0.188052 −0.0940259 0.995570i \(-0.529974\pi\)
−0.0940259 + 0.995570i \(0.529974\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 7.77817 + 7.77817i 0.343750 + 0.343750i
\(513\) 0 0
\(514\) 2.00000i 0.0882162i
\(515\) 0 0
\(516\) 0 0
\(517\) 16.0000 16.0000i 0.703679 0.703679i
\(518\) 2.82843 2.82843i 0.124274 0.124274i
\(519\) 0 0
\(520\) 0 0
\(521\) 18.3848i 0.805452i 0.915321 + 0.402726i \(0.131937\pi\)
−0.915321 + 0.402726i \(0.868063\pi\)
\(522\) 0 0
\(523\) 8.00000 + 8.00000i 0.349816 + 0.349816i 0.860041 0.510225i \(-0.170438\pi\)
−0.510225 + 0.860041i \(0.670438\pi\)
\(524\) 14.1421 0.617802
\(525\) 0 0
\(526\) −4.00000 −0.174408
\(527\) 11.3137 + 11.3137i 0.492833 + 0.492833i
\(528\) 0 0
\(529\) 7.00000i 0.304348i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.41421 1.41421i 0.0612564 0.0612564i
\(534\) 0 0
\(535\) 0 0
\(536\) 16.9706i 0.733017i
\(537\) 0 0
\(538\) 9.00000 + 9.00000i 0.388018 + 0.388018i
\(539\) −2.82843 −0.121829
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 11.3137 + 11.3137i 0.485965 + 0.485965i
\(543\) 0 0
\(544\) 20.0000i 0.857493i
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 20.0000i 0.855138 0.855138i −0.135622 0.990761i \(-0.543303\pi\)
0.990761 + 0.135622i \(0.0433034\pi\)
\(548\) −7.07107 + 7.07107i −0.302061 + 0.302061i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 24.0000 + 24.0000i 1.02058 + 1.02058i
\(554\) −15.5563 −0.660926
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) −2.82843 2.82843i −0.119844 0.119844i 0.644641 0.764485i \(-0.277007\pi\)
−0.764485 + 0.644641i \(0.777007\pi\)
\(558\) 0 0
\(559\) 16.0000i 0.676728i
\(560\) 0 0
\(561\) 0 0
\(562\) 7.00000 7.00000i 0.295277 0.295277i
\(563\) 28.2843 28.2843i 1.19204 1.19204i 0.215546 0.976494i \(-0.430847\pi\)
0.976494 0.215546i \(-0.0691532\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 11.3137i 0.475551i
\(567\) 0 0
\(568\) −12.0000 12.0000i −0.503509 0.503509i
\(569\) 29.6985 1.24503 0.622513 0.782610i \(-0.286112\pi\)
0.622513 + 0.782610i \(0.286112\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 2.82843 + 2.82843i 0.118262 + 0.118262i
\(573\) 0 0
\(574\) 4.00000i 0.166957i
\(575\) 0 0
\(576\) 0 0
\(577\) 17.0000 17.0000i 0.707719 0.707719i −0.258336 0.966055i \(-0.583174\pi\)
0.966055 + 0.258336i \(0.0831741\pi\)
\(578\) −0.707107 + 0.707107i −0.0294118 + 0.0294118i
\(579\) 0 0
\(580\) 0 0
\(581\) 11.3137i 0.469372i
\(582\) 0 0
\(583\) −8.00000 8.00000i −0.331326 0.331326i
\(584\) 4.24264 0.175562
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −19.7990 19.7990i −0.817192 0.817192i 0.168508 0.985700i \(-0.446105\pi\)
−0.985700 + 0.168508i \(0.946105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 + 1.00000i −0.0410997 + 0.0410997i
\(593\) −9.89949 + 9.89949i −0.406524 + 0.406524i −0.880524 0.474001i \(-0.842809\pi\)
0.474001 + 0.880524i \(0.342809\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.24264i 0.173785i
\(597\) 0 0
\(598\) 4.00000 + 4.00000i 0.163572 + 0.163572i
\(599\) −16.9706 −0.693398 −0.346699 0.937976i \(-0.612698\pi\)
−0.346699 + 0.937976i \(0.612698\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) −22.6274 22.6274i −0.922225 0.922225i
\(603\) 0 0
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) 0 0
\(607\) −22.0000 + 22.0000i −0.892952 + 0.892952i −0.994800 0.101848i \(-0.967525\pi\)
0.101848 + 0.994800i \(0.467525\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.3137i 0.457704i
\(612\) 0 0
\(613\) −1.00000 1.00000i −0.0403896 0.0403896i 0.686624 0.727013i \(-0.259092\pi\)
−0.727013 + 0.686624i \(0.759092\pi\)
\(614\) −11.3137 −0.456584
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) 14.1421 + 14.1421i 0.569341 + 0.569341i 0.931944 0.362603i \(-0.118112\pi\)
−0.362603 + 0.931944i \(0.618112\pi\)
\(618\) 0 0
\(619\) 12.0000i 0.482321i 0.970485 + 0.241160i \(0.0775280\pi\)
−0.970485 + 0.241160i \(0.922472\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −8.00000 + 8.00000i −0.320771 + 0.320771i
\(623\) −25.4558 + 25.4558i −1.01987 + 1.01987i
\(624\) 0 0
\(625\) 0 0
\(626\) 26.8701i 1.07394i
\(627\) 0 0
\(628\) −5.00000 5.00000i −0.199522 0.199522i
\(629\) 5.65685 0.225554
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −25.4558 25.4558i −1.01258 1.01258i
\(633\) 0 0
\(634\) 28.0000i 1.11202i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 + 1.00000i −0.0396214 + 0.0396214i
\(638\) −8.48528 + 8.48528i −0.335936 + 0.335936i
\(639\) 0 0
\(640\) 0 0
\(641\) 15.5563i 0.614439i −0.951639 0.307219i \(-0.900601\pi\)
0.951639 0.307219i \(-0.0993986\pi\)
\(642\) 0 0
\(643\) −28.0000 28.0000i −1.10421 1.10421i −0.993897 0.110316i \(-0.964814\pi\)
−0.110316 0.993897i \(-0.535186\pi\)
\(644\) −11.3137 −0.445823
\(645\) 0 0
\(646\) 0 0
\(647\) −28.2843 28.2843i −1.11197 1.11197i −0.992884 0.119085i \(-0.962004\pi\)
−0.119085 0.992884i \(-0.537996\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 0 0
\(652\) 8.00000 8.00000i 0.313304 0.313304i
\(653\) 2.82843 2.82843i 0.110685 0.110685i −0.649595 0.760280i \(-0.725062\pi\)
0.760280 + 0.649595i \(0.225062\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.41421i 0.0552158i
\(657\) 0 0
\(658\) −16.0000 16.0000i −0.623745 0.623745i
\(659\) −8.48528 −0.330540 −0.165270 0.986248i \(-0.552849\pi\)
−0.165270 + 0.986248i \(0.552849\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) −5.65685 5.65685i −0.219860 0.219860i
\(663\) 0 0
\(664\) 12.0000i 0.465690i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 12.0000i 0.464642 0.464642i
\(668\) 14.1421 14.1421i 0.547176 0.547176i
\(669\) 0 0
\(670\) 0 0
\(671\) 22.6274i 0.873522i
\(672\) 0 0
\(673\) −1.00000 1.00000i −0.0385472 0.0385472i 0.687570 0.726118i \(-0.258677\pi\)
−0.726118 + 0.687570i \(0.758677\pi\)
\(674\) −7.07107 −0.272367
\(675\) 0 0
\(676\) −11.0000 −0.423077
\(677\) 31.1127 + 31.1127i 1.19576 + 1.19576i 0.975425 + 0.220334i \(0.0707146\pi\)
0.220334 + 0.975425i \(0.429285\pi\)
\(678\) 0 0
\(679\) 44.0000i 1.68857i
\(680\) 0 0
\(681\) 0 0
\(682\) 8.00000 8.00000i 0.306336 0.306336i
\(683\) 2.82843 2.82843i 0.108227 0.108227i −0.650920 0.759147i \(-0.725617\pi\)
0.759147 + 0.650920i \(0.225617\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 16.9706i 0.647939i
\(687\) 0 0
\(688\) 8.00000 + 8.00000i 0.304997 + 0.304997i
\(689\) −5.65685 −0.215509
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 9.89949 + 9.89949i 0.376322 + 0.376322i
\(693\) 0 0
\(694\) 16.0000i 0.607352i
\(695\) 0 0
\(696\) 0 0
\(697\) 4.00000 4.00000i 0.151511 0.151511i
\(698\) −16.9706 + 16.9706i −0.642345 + 0.642345i
\(699\) 0 0
\(700\) 0 0
\(701\) 7.07107i 0.267071i −0.991044 0.133535i \(-0.957367\pi\)
0.991044 0.133535i \(-0.0426329\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −19.7990 −0.746203
\(705\) 0 0
\(706\) −4.00000 −0.150542
\(707\) −31.1127 31.1127i −1.17011 1.17011i
\(708\) 0 0
\(709\) 6.00000i 0.225335i −0.993633 0.112667i \(-0.964061\pi\)
0.993633 0.112667i \(-0.0359394\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 27.0000 27.0000i 1.01187 1.01187i
\(713\) −11.3137 + 11.3137i −0.423702 + 0.423702i
\(714\) 0 0
\(715\) 0 0
\(716\) 25.4558i 0.951330i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −40.0000 −1.48968
\(722\) −13.4350 13.4350i −0.500000 0.500000i
\(723\) 0 0
\(724\) 16.0000i 0.594635i
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000 2.00000i 0.0741759 0.0741759i −0.669046 0.743221i \(-0.733297\pi\)
0.743221 + 0.669046i \(0.233297\pi\)
\(728\) 8.48528 8.48528i 0.314485 0.314485i
\(729\) 0 0
\(730\) 0 0
\(731\) 45.2548i 1.67381i
\(732\) 0 0
\(733\) −1.00000 1.00000i −0.0369358 0.0369358i 0.688398 0.725333i \(-0.258314\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(734\) −2.82843 −0.104399
\(735\) 0 0
\(736\) 20.0000 0.737210
\(737\) 11.3137 + 11.3137i 0.416746 + 0.416746i
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −8.00000 + 8.00000i −0.293689 + 0.293689i
\(743\) −22.6274 + 22.6274i −0.830119 + 0.830119i −0.987533 0.157413i \(-0.949684\pi\)
0.157413 + 0.987533i \(0.449684\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 24.0416i 0.880227i
\(747\) 0 0
\(748\) 8.00000 + 8.00000i 0.292509 + 0.292509i
\(749\) −11.3137 −0.413394
\(750\) 0 0
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 5.65685 + 5.65685i 0.206284 + 0.206284i
\(753\) 0 0
\(754\) 6.00000i 0.218507i
\(755\) 0 0
\(756\) 0 0
\(757\) −19.0000 + 19.0000i −0.690567 + 0.690567i −0.962357 0.271790i \(-0.912384\pi\)
0.271790 + 0.962357i \(0.412384\pi\)
\(758\) 25.4558 25.4558i 0.924598 0.924598i
\(759\) 0 0
\(760\) 0 0
\(761\) 52.3259i 1.89681i 0.317058 + 0.948406i \(0.397305\pi\)
−0.317058 + 0.948406i \(0.602695\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 22.6274 0.818631
\(765\) 0 0
\(766\) 32.0000 1.15621
\(767\) −8.48528 8.48528i −0.306386 0.306386i
\(768\) 0 0
\(769\) 24.0000i 0.865462i 0.901523 + 0.432731i \(0.142450\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 + 1.00000i −0.0359908 + 0.0359908i
\(773\) 2.82843 2.82843i 0.101731 0.101731i −0.654409 0.756141i \(-0.727083\pi\)
0.756141 + 0.654409i \(0.227083\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 46.6690i 1.67532i
\(777\) 0 0
\(778\) −3.00000 3.00000i −0.107555 0.107555i
\(779\) 0 0
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) 11.3137 + 11.3137i 0.404577 + 0.404577i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −4.00000 + 4.00000i −0.142585 + 0.142585i −0.774796 0.632211i \(-0.782147\pi\)
0.632211 + 0.774796i \(0.282147\pi\)
\(788\) 9.89949 9.89949i 0.352655 0.352655i
\(789\) 0 0
\(790\) 0 0
\(791\) 39.5980i 1.40794i
\(792\) 0 0
\(793\) −8.00000 8.00000i −0.284088 0.284088i
\(794\) 26.8701 0.953583
\(795\) 0 0
\(796\) 0 0
\(797\) 1.41421 + 1.41421i 0.0500940 + 0.0500940i 0.731710 0.681616i