Properties

Label 320.2.n.f.127.1
Level $320$
Weight $2$
Character 320.127
Analytic conductor $2.555$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.n (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 320.127
Dual form 320.2.n.f.63.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +6.00000i q^{11} +(1.00000 - 1.00000i) q^{13} +(-3.00000 + 1.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} -4.00000 q^{19} -2.00000 q^{21} +(5.00000 + 5.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -8.00000i q^{29} +2.00000i q^{31} +(-6.00000 + 6.00000i) q^{33} +(-1.00000 - 3.00000i) q^{35} +(5.00000 + 5.00000i) q^{37} +2.00000 q^{39} +6.00000 q^{41} +(-3.00000 - 3.00000i) q^{43} +(2.00000 + 1.00000i) q^{45} +(7.00000 - 7.00000i) q^{47} +5.00000i q^{49} +2.00000i q^{51} +(1.00000 - 1.00000i) q^{53} +(-12.0000 - 6.00000i) q^{55} +(-4.00000 - 4.00000i) q^{57} -4.00000 q^{59} -2.00000 q^{61} +(1.00000 + 1.00000i) q^{63} +(1.00000 + 3.00000i) q^{65} +(7.00000 - 7.00000i) q^{67} +10.0000i q^{69} -6.00000i q^{71} +(9.00000 - 9.00000i) q^{73} +(1.00000 - 7.00000i) q^{75} +(-6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(5.00000 + 5.00000i) q^{83} +(-3.00000 + 1.00000i) q^{85} +(8.00000 - 8.00000i) q^{87} +2.00000i q^{91} +(-2.00000 + 2.00000i) q^{93} +(4.00000 - 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 2 q^{5} - 2 q^{7} + 2 q^{13} - 6 q^{15} + 2 q^{17} - 8 q^{19} - 4 q^{21} + 10 q^{23} - 6 q^{25} + 8 q^{27} - 12 q^{33} - 2 q^{35} + 10 q^{37} + 4 q^{39} + 12 q^{41} - 6 q^{43} + 4 q^{45} + 14 q^{47} + 2 q^{53} - 24 q^{55} - 8 q^{57} - 8 q^{59} - 4 q^{61} + 2 q^{63} + 2 q^{65} + 14 q^{67} + 18 q^{73} + 2 q^{75} - 12 q^{77} - 16 q^{79} + 10 q^{81} + 10 q^{83} - 6 q^{85} + 16 q^{87} - 4 q^{93} + 8 q^{95} - 6 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 6.00000i 1.80907i 0.426401 + 0.904534i \(0.359781\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) −3.00000 + 1.00000i −0.774597 + 0.258199i
\(16\) 0 0
\(17\) 1.00000 + 1.00000i 0.242536 + 0.242536i 0.817898 0.575363i \(-0.195139\pi\)
−0.575363 + 0.817898i \(0.695139\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 5.00000 + 5.00000i 1.04257 + 1.04257i 0.999053 + 0.0435195i \(0.0138571\pi\)
0.0435195 + 0.999053i \(0.486143\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 0 0
\(29\) 8.00000i 1.48556i −0.669534 0.742781i \(-0.733506\pi\)
0.669534 0.742781i \(-0.266494\pi\)
\(30\) 0 0
\(31\) 2.00000i 0.359211i 0.983739 + 0.179605i \(0.0574821\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(32\) 0 0
\(33\) −6.00000 + 6.00000i −1.04447 + 1.04447i
\(34\) 0 0
\(35\) −1.00000 3.00000i −0.169031 0.507093i
\(36\) 0 0
\(37\) 5.00000 + 5.00000i 0.821995 + 0.821995i 0.986394 0.164399i \(-0.0525685\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −3.00000 3.00000i −0.457496 0.457496i 0.440337 0.897833i \(-0.354859\pi\)
−0.897833 + 0.440337i \(0.854859\pi\)
\(44\) 0 0
\(45\) 2.00000 + 1.00000i 0.298142 + 0.149071i
\(46\) 0 0
\(47\) 7.00000 7.00000i 1.02105 1.02105i 0.0212814 0.999774i \(-0.493225\pi\)
0.999774 0.0212814i \(-0.00677460\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 2.00000i 0.280056i
\(52\) 0 0
\(53\) 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) 0 0
\(55\) −12.0000 6.00000i −1.61808 0.809040i
\(56\) 0 0
\(57\) −4.00000 4.00000i −0.529813 0.529813i
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 1.00000 + 1.00000i 0.125988 + 0.125988i
\(64\) 0 0
\(65\) 1.00000 + 3.00000i 0.124035 + 0.372104i
\(66\) 0 0
\(67\) 7.00000 7.00000i 0.855186 0.855186i −0.135580 0.990766i \(-0.543290\pi\)
0.990766 + 0.135580i \(0.0432899\pi\)
\(68\) 0 0
\(69\) 10.0000i 1.20386i
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) 9.00000 9.00000i 1.05337 1.05337i 0.0548772 0.998493i \(-0.482523\pi\)
0.998493 0.0548772i \(-0.0174767\pi\)
\(74\) 0 0
\(75\) 1.00000 7.00000i 0.115470 0.808290i
\(76\) 0 0
\(77\) −6.00000 6.00000i −0.683763 0.683763i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 5.00000 + 5.00000i 0.548821 + 0.548821i 0.926100 0.377279i \(-0.123140\pi\)
−0.377279 + 0.926100i \(0.623140\pi\)
\(84\) 0 0
\(85\) −3.00000 + 1.00000i −0.325396 + 0.108465i
\(86\) 0 0
\(87\) 8.00000 8.00000i 0.857690 0.857690i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 2.00000i 0.209657i
\(92\) 0 0
\(93\) −2.00000 + 2.00000i −0.207390 + 0.207390i
\(94\) 0 0
\(95\) 4.00000 8.00000i 0.410391 0.820783i
\(96\) 0 0
\(97\) −3.00000 3.00000i −0.304604 0.304604i 0.538208 0.842812i \(-0.319101\pi\)
−0.842812 + 0.538208i \(0.819101\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −3.00000 3.00000i −0.295599 0.295599i 0.543688 0.839287i \(-0.317027\pi\)
−0.839287 + 0.543688i \(0.817027\pi\)
\(104\) 0 0
\(105\) 2.00000 4.00000i 0.195180 0.390360i
\(106\) 0 0
\(107\) 3.00000 3.00000i 0.290021 0.290021i −0.547068 0.837088i \(-0.684256\pi\)
0.837088 + 0.547068i \(0.184256\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 10.0000i 0.949158i
\(112\) 0 0
\(113\) −3.00000 + 3.00000i −0.282216 + 0.282216i −0.833992 0.551776i \(-0.813950\pi\)
0.551776 + 0.833992i \(0.313950\pi\)
\(114\) 0 0
\(115\) −15.0000 + 5.00000i −1.39876 + 0.466252i
\(116\) 0 0
\(117\) −1.00000 1.00000i −0.0924500 0.0924500i
\(118\) 0 0
\(119\) −2.00000 −0.183340
\(120\) 0 0
\(121\) −25.0000 −2.27273
\(122\) 0 0
\(123\) 6.00000 + 6.00000i 0.541002 + 0.541002i
\(124\) 0 0
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) −5.00000 + 5.00000i −0.443678 + 0.443678i −0.893246 0.449568i \(-0.851578\pi\)
0.449568 + 0.893246i \(0.351578\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 2.00000i 0.174741i −0.996176 0.0873704i \(-0.972154\pi\)
0.996176 0.0873704i \(-0.0278464\pi\)
\(132\) 0 0
\(133\) 4.00000 4.00000i 0.346844 0.346844i
\(134\) 0 0
\(135\) 4.00000 + 12.0000i 0.344265 + 1.03280i
\(136\) 0 0
\(137\) 13.0000 + 13.0000i 1.11066 + 1.11066i 0.993061 + 0.117604i \(0.0375215\pi\)
0.117604 + 0.993061i \(0.462479\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 14.0000 1.17901
\(142\) 0 0
\(143\) 6.00000 + 6.00000i 0.501745 + 0.501745i
\(144\) 0 0
\(145\) 16.0000 + 8.00000i 1.32873 + 0.664364i
\(146\) 0 0
\(147\) −5.00000 + 5.00000i −0.412393 + 0.412393i
\(148\) 0 0
\(149\) 12.0000i 0.983078i 0.870855 + 0.491539i \(0.163566\pi\)
−0.870855 + 0.491539i \(0.836434\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 0 0
\(153\) 1.00000 1.00000i 0.0808452 0.0808452i
\(154\) 0 0
\(155\) −4.00000 2.00000i −0.321288 0.160644i
\(156\) 0 0
\(157\) −3.00000 3.00000i −0.239426 0.239426i 0.577186 0.816612i \(-0.304151\pi\)
−0.816612 + 0.577186i \(0.804151\pi\)
\(158\) 0 0
\(159\) 2.00000 0.158610
\(160\) 0 0
\(161\) −10.0000 −0.788110
\(162\) 0 0
\(163\) 1.00000 + 1.00000i 0.0783260 + 0.0783260i 0.745184 0.666858i \(-0.232361\pi\)
−0.666858 + 0.745184i \(0.732361\pi\)
\(164\) 0 0
\(165\) −6.00000 18.0000i −0.467099 1.40130i
\(166\) 0 0
\(167\) −5.00000 + 5.00000i −0.386912 + 0.386912i −0.873584 0.486673i \(-0.838210\pi\)
0.486673 + 0.873584i \(0.338210\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 0 0
\(173\) −7.00000 + 7.00000i −0.532200 + 0.532200i −0.921227 0.389026i \(-0.872811\pi\)
0.389026 + 0.921227i \(0.372811\pi\)
\(174\) 0 0
\(175\) 7.00000 + 1.00000i 0.529150 + 0.0755929i
\(176\) 0 0
\(177\) −4.00000 4.00000i −0.300658 0.300658i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −2.00000 2.00000i −0.147844 0.147844i
\(184\) 0 0
\(185\) −15.0000 + 5.00000i −1.10282 + 0.367607i
\(186\) 0 0
\(187\) −6.00000 + 6.00000i −0.438763 + 0.438763i
\(188\) 0 0
\(189\) 8.00000i 0.581914i
\(190\) 0 0
\(191\) 10.0000i 0.723575i 0.932261 + 0.361787i \(0.117833\pi\)
−0.932261 + 0.361787i \(0.882167\pi\)
\(192\) 0 0
\(193\) 1.00000 1.00000i 0.0719816 0.0719816i −0.670199 0.742181i \(-0.733791\pi\)
0.742181 + 0.670199i \(0.233791\pi\)
\(194\) 0 0
\(195\) −2.00000 + 4.00000i −0.143223 + 0.286446i
\(196\) 0 0
\(197\) 1.00000 + 1.00000i 0.0712470 + 0.0712470i 0.741832 0.670585i \(-0.233957\pi\)
−0.670585 + 0.741832i \(0.733957\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 14.0000 0.987484
\(202\) 0 0
\(203\) 8.00000 + 8.00000i 0.561490 + 0.561490i
\(204\) 0 0
\(205\) −6.00000 + 12.0000i −0.419058 + 0.838116i
\(206\) 0 0
\(207\) 5.00000 5.00000i 0.347524 0.347524i
\(208\) 0 0
\(209\) 24.0000i 1.66011i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 0 0
\(213\) 6.00000 6.00000i 0.411113 0.411113i
\(214\) 0 0
\(215\) 9.00000 3.00000i 0.613795 0.204598i
\(216\) 0 0
\(217\) −2.00000 2.00000i −0.135769 0.135769i
\(218\) 0 0
\(219\) 18.0000 1.21633
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) −19.0000 19.0000i −1.27233 1.27233i −0.944860 0.327474i \(-0.893803\pi\)
−0.327474 0.944860i \(-0.606197\pi\)
\(224\) 0 0
\(225\) −4.00000 + 3.00000i −0.266667 + 0.200000i
\(226\) 0 0
\(227\) −13.0000 + 13.0000i −0.862840 + 0.862840i −0.991667 0.128827i \(-0.958879\pi\)
0.128827 + 0.991667i \(0.458879\pi\)
\(228\) 0 0
\(229\) 16.0000i 1.05731i −0.848837 0.528655i \(-0.822697\pi\)
0.848837 0.528655i \(-0.177303\pi\)
\(230\) 0 0
\(231\) 12.0000i 0.789542i
\(232\) 0 0
\(233\) 13.0000 13.0000i 0.851658 0.851658i −0.138679 0.990337i \(-0.544286\pi\)
0.990337 + 0.138679i \(0.0442856\pi\)
\(234\) 0 0
\(235\) 7.00000 + 21.0000i 0.456630 + 1.36989i
\(236\) 0 0
\(237\) −8.00000 8.00000i −0.519656 0.519656i
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) 0 0
\(245\) −10.0000 5.00000i −0.638877 0.319438i
\(246\) 0 0
\(247\) −4.00000 + 4.00000i −0.254514 + 0.254514i
\(248\) 0 0
\(249\) 10.0000i 0.633724i
\(250\) 0 0
\(251\) 18.0000i 1.13615i −0.822977 0.568075i \(-0.807688\pi\)
0.822977 0.568075i \(-0.192312\pi\)
\(252\) 0 0
\(253\) −30.0000 + 30.0000i −1.88608 + 1.88608i
\(254\) 0 0
\(255\) −4.00000 2.00000i −0.250490 0.125245i
\(256\) 0 0
\(257\) −11.0000 11.0000i −0.686161 0.686161i 0.275220 0.961381i \(-0.411249\pi\)
−0.961381 + 0.275220i \(0.911249\pi\)
\(258\) 0 0
\(259\) −10.0000 −0.621370
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) 0 0
\(263\) 9.00000 + 9.00000i 0.554964 + 0.554964i 0.927869 0.372906i \(-0.121638\pi\)
−0.372906 + 0.927869i \(0.621638\pi\)
\(264\) 0 0
\(265\) 1.00000 + 3.00000i 0.0614295 + 0.184289i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.00000i 0.243884i 0.992537 + 0.121942i \(0.0389122\pi\)
−0.992537 + 0.121942i \(0.961088\pi\)
\(270\) 0 0
\(271\) 22.0000i 1.33640i −0.743980 0.668202i \(-0.767064\pi\)
0.743980 0.668202i \(-0.232936\pi\)
\(272\) 0 0
\(273\) −2.00000 + 2.00000i −0.121046 + 0.121046i
\(274\) 0 0
\(275\) 24.0000 18.0000i 1.44725 1.08544i
\(276\) 0 0
\(277\) 9.00000 + 9.00000i 0.540758 + 0.540758i 0.923751 0.382993i \(-0.125107\pi\)
−0.382993 + 0.923751i \(0.625107\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −15.0000 15.0000i −0.891657 0.891657i 0.103022 0.994679i \(-0.467149\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(284\) 0 0
\(285\) 12.0000 4.00000i 0.710819 0.236940i
\(286\) 0 0
\(287\) −6.00000 + 6.00000i −0.354169 + 0.354169i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 0 0
\(293\) 17.0000 17.0000i 0.993151 0.993151i −0.00682610 0.999977i \(-0.502173\pi\)
0.999977 + 0.00682610i \(0.00217283\pi\)
\(294\) 0 0
\(295\) 4.00000 8.00000i 0.232889 0.465778i
\(296\) 0 0
\(297\) 24.0000 + 24.0000i 1.39262 + 1.39262i
\(298\) 0 0
\(299\) 10.0000 0.578315
\(300\) 0 0
\(301\) 6.00000 0.345834
\(302\) 0 0
\(303\) −6.00000 6.00000i −0.344691 0.344691i
\(304\) 0 0
\(305\) 2.00000 4.00000i 0.114520 0.229039i
\(306\) 0 0
\(307\) 7.00000 7.00000i 0.399511 0.399511i −0.478549 0.878061i \(-0.658837\pi\)
0.878061 + 0.478549i \(0.158837\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 22.0000i 1.24751i −0.781622 0.623753i \(-0.785607\pi\)
0.781622 0.623753i \(-0.214393\pi\)
\(312\) 0 0
\(313\) −15.0000 + 15.0000i −0.847850 + 0.847850i −0.989865 0.142014i \(-0.954642\pi\)
0.142014 + 0.989865i \(0.454642\pi\)
\(314\) 0 0
\(315\) −3.00000 + 1.00000i −0.169031 + 0.0563436i
\(316\) 0 0
\(317\) 25.0000 + 25.0000i 1.40414 + 1.40414i 0.786318 + 0.617822i \(0.211985\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 0 0
\(319\) 48.0000 2.68748
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −4.00000 4.00000i −0.222566 0.222566i
\(324\) 0 0
\(325\) −7.00000 1.00000i −0.388290 0.0554700i
\(326\) 0 0
\(327\) 4.00000 4.00000i 0.221201 0.221201i
\(328\) 0 0
\(329\) 14.0000i 0.771845i
\(330\) 0 0
\(331\) 18.0000i 0.989369i −0.869072 0.494685i \(-0.835284\pi\)
0.869072 0.494685i \(-0.164716\pi\)
\(332\) 0 0
\(333\) 5.00000 5.00000i 0.273998 0.273998i
\(334\) 0 0
\(335\) 7.00000 + 21.0000i 0.382451 + 1.14735i
\(336\) 0 0
\(337\) 1.00000 + 1.00000i 0.0544735 + 0.0544735i 0.733819 0.679345i \(-0.237736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) −20.0000 10.0000i −1.07676 0.538382i
\(346\) 0 0
\(347\) −9.00000 + 9.00000i −0.483145 + 0.483145i −0.906135 0.422989i \(-0.860981\pi\)
0.422989 + 0.906135i \(0.360981\pi\)
\(348\) 0 0
\(349\) 32.0000i 1.71292i −0.516213 0.856460i \(-0.672659\pi\)
0.516213 0.856460i \(-0.327341\pi\)
\(350\) 0 0
\(351\) 8.00000i 0.427008i
\(352\) 0 0
\(353\) −15.0000 + 15.0000i −0.798369 + 0.798369i −0.982838 0.184469i \(-0.940943\pi\)
0.184469 + 0.982838i \(0.440943\pi\)
\(354\) 0 0
\(355\) 12.0000 + 6.00000i 0.636894 + 0.318447i
\(356\) 0 0
\(357\) −2.00000 2.00000i −0.105851 0.105851i
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −25.0000 25.0000i −1.31216 1.31216i
\(364\) 0 0
\(365\) 9.00000 + 27.0000i 0.471082 + 1.41324i
\(366\) 0 0
\(367\) −13.0000 + 13.0000i −0.678594 + 0.678594i −0.959682 0.281088i \(-0.909305\pi\)
0.281088 + 0.959682i \(0.409305\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 2.00000i 0.103835i
\(372\) 0 0
\(373\) 21.0000 21.0000i 1.08734 1.08734i 0.0915371 0.995802i \(-0.470822\pi\)
0.995802 0.0915371i \(-0.0291780\pi\)
\(374\) 0 0
\(375\) 13.0000 + 9.00000i 0.671317 + 0.464758i
\(376\) 0 0
\(377\) −8.00000 8.00000i −0.412021 0.412021i
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −10.0000 −0.512316
\(382\) 0 0
\(383\) 13.0000 + 13.0000i 0.664269 + 0.664269i 0.956383 0.292114i \(-0.0943588\pi\)
−0.292114 + 0.956383i \(0.594359\pi\)
\(384\) 0 0
\(385\) 18.0000 6.00000i 0.917365 0.305788i
\(386\) 0 0
\(387\) −3.00000 + 3.00000i −0.152499 + 0.152499i
\(388\) 0 0
\(389\) 12.0000i 0.608424i 0.952604 + 0.304212i \(0.0983931\pi\)
−0.952604 + 0.304212i \(0.901607\pi\)
\(390\) 0 0
\(391\) 10.0000i 0.505722i
\(392\) 0 0
\(393\) 2.00000 2.00000i 0.100887 0.100887i
\(394\) 0 0
\(395\) 8.00000 16.0000i 0.402524 0.805047i
\(396\) 0 0
\(397\) −19.0000 19.0000i −0.953583 0.953583i 0.0453868 0.998969i \(-0.485548\pi\)
−0.998969 + 0.0453868i \(0.985548\pi\)
\(398\) 0 0
\(399\) 8.00000 0.400501
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 0 0
\(403\) 2.00000 + 2.00000i 0.0996271 + 0.0996271i
\(404\) 0 0
\(405\) −5.00000 + 10.0000i −0.248452 + 0.496904i
\(406\) 0 0
\(407\) −30.0000 + 30.0000i −1.48704 + 1.48704i
\(408\) 0 0
\(409\) 20.0000i 0.988936i 0.869196 + 0.494468i \(0.164637\pi\)
−0.869196 + 0.494468i \(0.835363\pi\)
\(410\) 0 0
\(411\) 26.0000i 1.28249i
\(412\) 0 0
\(413\) 4.00000 4.00000i 0.196827 0.196827i
\(414\) 0 0
\(415\) −15.0000 + 5.00000i −0.736321 + 0.245440i
\(416\) 0 0
\(417\) −12.0000 12.0000i −0.587643 0.587643i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) −7.00000 7.00000i −0.340352 0.340352i
\(424\) 0 0
\(425\) 1.00000 7.00000i 0.0485071 0.339550i
\(426\) 0 0
\(427\) 2.00000 2.00000i 0.0967868 0.0967868i
\(428\) 0 0
\(429\) 12.0000i 0.579365i
\(430\) 0 0
\(431\) 38.0000i 1.83040i −0.403005 0.915198i \(-0.632034\pi\)
0.403005 0.915198i \(-0.367966\pi\)
\(432\) 0 0
\(433\) 5.00000 5.00000i 0.240285 0.240285i −0.576683 0.816968i \(-0.695653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 8.00000 + 24.0000i 0.383571 + 1.15071i
\(436\) 0 0
\(437\) −20.0000 20.0000i −0.956730 0.956730i
\(438\) 0 0
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) 17.0000 + 17.0000i 0.807694 + 0.807694i 0.984284 0.176590i \(-0.0565067\pi\)
−0.176590 + 0.984284i \(0.556507\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −12.0000 + 12.0000i −0.567581 + 0.567581i
\(448\) 0 0
\(449\) 4.00000i 0.188772i 0.995536 + 0.0943858i \(0.0300887\pi\)
−0.995536 + 0.0943858i \(0.969911\pi\)
\(450\) 0 0
\(451\) 36.0000i 1.69517i
\(452\) 0 0
\(453\) −18.0000 + 18.0000i −0.845714 + 0.845714i
\(454\) 0 0
\(455\) −4.00000 2.00000i −0.187523 0.0937614i
\(456\) 0 0
\(457\) −15.0000 15.0000i −0.701670 0.701670i 0.263099 0.964769i \(-0.415256\pi\)
−0.964769 + 0.263099i \(0.915256\pi\)
\(458\) 0 0
\(459\) 8.00000 0.373408
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 17.0000 + 17.0000i 0.790057 + 0.790057i 0.981503 0.191446i \(-0.0613177\pi\)
−0.191446 + 0.981503i \(0.561318\pi\)
\(464\) 0 0
\(465\) −2.00000 6.00000i −0.0927478 0.278243i
\(466\) 0 0
\(467\) −5.00000 + 5.00000i −0.231372 + 0.231372i −0.813265 0.581893i \(-0.802312\pi\)
0.581893 + 0.813265i \(0.302312\pi\)
\(468\) 0 0
\(469\) 14.0000i 0.646460i
\(470\) 0 0
\(471\) 6.00000i 0.276465i
\(472\) 0 0
\(473\) 18.0000 18.0000i 0.827641 0.827641i
\(474\) 0 0
\(475\) 12.0000 + 16.0000i 0.550598 + 0.734130i
\(476\) 0 0
\(477\) −1.00000 1.00000i −0.0457869 0.0457869i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 0 0
\(483\) −10.0000 10.0000i −0.455016 0.455016i
\(484\) 0 0
\(485\) 9.00000 3.00000i 0.408669 0.136223i
\(486\) 0 0
\(487\) 15.0000 15.0000i 0.679715 0.679715i −0.280221 0.959936i \(-0.590408\pi\)
0.959936 + 0.280221i \(0.0904077\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 2.00000i 0.0902587i −0.998981 0.0451294i \(-0.985630\pi\)
0.998981 0.0451294i \(-0.0143700\pi\)
\(492\) 0 0
\(493\) 8.00000 8.00000i 0.360302 0.360302i
\(494\) 0 0
\(495\) −6.00000 + 12.0000i −0.269680 + 0.539360i
\(496\) 0 0
\(497\) 6.00000 + 6.00000i 0.269137 + 0.269137i
\(498\) 0 0
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) −10.0000 −0.446767
\(502\) 0 0
\(503\) −11.0000 11.0000i −0.490466 0.490466i 0.417987 0.908453i \(-0.362736\pi\)
−0.908453 + 0.417987i \(0.862736\pi\)
\(504\) 0 0
\(505\) 6.00000 12.0000i 0.266996 0.533993i
\(506\) 0 0
\(507\) −11.0000 + 11.0000i −0.488527 + 0.488527i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 18.0000i 0.796273i
\(512\) 0 0
\(513\) −16.0000 + 16.0000i −0.706417 + 0.706417i
\(514\) 0 0
\(515\) 9.00000 3.00000i 0.396587 0.132196i
\(516\) 0 0
\(517\) 42.0000 + 42.0000i 1.84716 + 1.84716i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 25.0000 + 25.0000i 1.09317 + 1.09317i 0.995188 + 0.0979859i \(0.0312400\pi\)
0.0979859 + 0.995188i \(0.468760\pi\)
\(524\) 0 0
\(525\) 6.00000 + 8.00000i 0.261861 + 0.349149i
\(526\) 0 0
\(527\) −2.00000 + 2.00000i −0.0871214 + 0.0871214i
\(528\) 0 0
\(529\) 27.0000i 1.17391i
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 0 0
\(533\) 6.00000 6.00000i 0.259889 0.259889i
\(534\) 0 0
\(535\) 3.00000 + 9.00000i 0.129701 + 0.389104i
\(536\) 0 0
\(537\) 12.0000 + 12.0000i 0.517838 + 0.517838i
\(538\) 0 0
\(539\) −30.0000 −1.29219
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) 10.0000 + 10.0000i 0.429141 + 0.429141i
\(544\) 0 0
\(545\) 8.00000 + 4.00000i 0.342682 + 0.171341i
\(546\) 0 0
\(547\) 3.00000 3.00000i 0.128271 0.128271i −0.640057 0.768328i \(-0.721089\pi\)
0.768328 + 0.640057i \(0.221089\pi\)
\(548\) 0 0
\(549\) 2.00000i 0.0853579i
\(550\) 0 0
\(551\) 32.0000i 1.36325i
\(552\) 0 0
\(553\) 8.00000 8.00000i 0.340195 0.340195i
\(554\) 0 0
\(555\) −20.0000 10.0000i −0.848953 0.424476i
\(556\) 0 0
\(557\) −15.0000 15.0000i −0.635570 0.635570i 0.313889 0.949460i \(-0.398368\pi\)
−0.949460 + 0.313889i \(0.898368\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) −15.0000 15.0000i −0.632175 0.632175i 0.316438 0.948613i \(-0.397513\pi\)
−0.948613 + 0.316438i \(0.897513\pi\)
\(564\) 0 0
\(565\) −3.00000 9.00000i −0.126211 0.378633i
\(566\) 0 0
\(567\) −5.00000 + 5.00000i −0.209980 + 0.209980i
\(568\) 0 0
\(569\) 20.0000i 0.838444i −0.907884 0.419222i \(-0.862303\pi\)
0.907884 0.419222i \(-0.137697\pi\)
\(570\) 0 0
\(571\) 26.0000i 1.08807i −0.839064 0.544033i \(-0.816897\pi\)
0.839064 0.544033i \(-0.183103\pi\)
\(572\) 0 0
\(573\) −10.0000 + 10.0000i −0.417756 + 0.417756i
\(574\) 0 0
\(575\) 5.00000 35.0000i 0.208514 1.45960i
\(576\) 0 0
\(577\) −3.00000 3.00000i −0.124892 0.124892i 0.641898 0.766790i \(-0.278147\pi\)
−0.766790 + 0.641898i \(0.778147\pi\)
\(578\) 0 0
\(579\) 2.00000 0.0831172
\(580\) 0 0
\(581\) −10.0000 −0.414870
\(582\) 0 0
\(583\) 6.00000 + 6.00000i 0.248495 + 0.248495i
\(584\) 0 0
\(585\) 3.00000 1.00000i 0.124035 0.0413449i
\(586\) 0 0
\(587\) −25.0000 + 25.0000i −1.03186 + 1.03186i −0.0323850 + 0.999475i \(0.510310\pi\)
−0.999475 + 0.0323850i \(0.989690\pi\)
\(588\) 0 0
\(589\) 8.00000i 0.329634i
\(590\) 0 0
\(591\) 2.00000i 0.0822690i
\(592\) 0 0
\(593\) −23.0000 + 23.0000i −0.944497 + 0.944497i −0.998539 0.0540419i \(-0.982790\pi\)
0.0540419 + 0.998539i \(0.482790\pi\)
\(594\) 0 0
\(595\) 2.00000 4.00000i 0.0819920 0.163984i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) −7.00000 7.00000i −0.285062 0.285062i
\(604\) 0 0
\(605\) 25.0000 50.0000i 1.01639 2.03279i
\(606\) 0 0
\(607\) 15.0000 15.0000i 0.608831 0.608831i −0.333809 0.942641i \(-0.608334\pi\)
0.942641 + 0.333809i \(0.108334\pi\)
\(608\) 0 0
\(609\) 16.0000i 0.648353i
\(610\) 0 0
\(611\) 14.0000i 0.566379i
\(612\) 0 0
\(613\) −3.00000 + 3.00000i −0.121169 + 0.121169i −0.765091 0.643922i \(-0.777306\pi\)
0.643922 + 0.765091i \(0.277306\pi\)
\(614\) 0 0
\(615\) −18.0000 + 6.00000i −0.725830 + 0.241943i
\(616\) 0 0
\(617\) −11.0000 11.0000i −0.442843 0.442843i 0.450123 0.892966i \(-0.351380\pi\)
−0.892966 + 0.450123i \(0.851380\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 40.0000 1.60514
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 24.0000 24.0000i 0.958468 0.958468i
\(628\) 0 0
\(629\) 10.0000i 0.398726i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 10.0000 10.0000i 0.397464 0.397464i
\(634\) 0 0
\(635\) −5.00000 15.0000i −0.198419 0.595257i
\(636\) 0 0
\(637\) 5.00000 + 5.00000i 0.198107 + 0.198107i
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −11.0000 11.0000i −0.433798 0.433798i 0.456120 0.889918i \(-0.349239\pi\)
−0.889918 + 0.456120i \(0.849239\pi\)
\(644\) 0 0
\(645\) 12.0000 + 6.00000i 0.472500 + 0.236250i
\(646\) 0 0
\(647\) 31.0000 31.0000i 1.21874 1.21874i 0.250661 0.968075i \(-0.419352\pi\)
0.968075 0.250661i \(-0.0806479\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 4.00000i 0.156772i
\(652\) 0 0
\(653\) 5.00000 5.00000i 0.195665 0.195665i −0.602474 0.798139i \(-0.705818\pi\)
0.798139 + 0.602474i \(0.205818\pi\)
\(654\) 0 0
\(655\) 4.00000 + 2.00000i 0.156293 + 0.0781465i
\(656\) 0 0
\(657\) −9.00000 9.00000i −0.351123 0.351123i
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 0 0
\(663\) 2.00000 + 2.00000i 0.0776736 + 0.0776736i
\(664\) 0 0
\(665\) 4.00000 + 12.0000i 0.155113 + 0.465340i
\(666\) 0 0
\(667\) 40.0000 40.0000i 1.54881 1.54881i
\(668\) 0 0
\(669\) 38.0000i 1.46916i
\(670\) 0 0
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) 29.0000 29.0000i 1.11787 1.11787i 0.125814 0.992054i \(-0.459846\pi\)
0.992054 0.125814i \(-0.0401543\pi\)
\(674\) 0 0
\(675\) −28.0000 4.00000i −1.07772 0.153960i
\(676\) 0 0
\(677\) −15.0000 15.0000i −0.576497 0.576497i 0.357439 0.933936i \(-0.383650\pi\)
−0.933936 + 0.357439i \(0.883650\pi\)
\(678\) 0 0
\(679\) 6.00000 0.230259
\(680\) 0 0
\(681\) −26.0000 −0.996322
\(682\) 0 0
\(683\) 13.0000 + 13.0000i 0.497431 + 0.497431i 0.910637 0.413206i \(-0.135591\pi\)
−0.413206 + 0.910637i \(0.635591\pi\)
\(684\) 0 0
\(685\) −39.0000 + 13.0000i −1.49011 + 0.496704i
\(686\) 0 0
\(687\) 16.0000 16.0000i 0.610438 0.610438i
\(688\) 0 0
\(689\) 2.00000i 0.0761939i
\(690\) 0 0
\(691\) 10.0000i 0.380418i −0.981744 0.190209i \(-0.939083\pi\)
0.981744 0.190209i \(-0.0609166\pi\)
\(692\) 0 0
\(693\) −6.00000 + 6.00000i −0.227921 + 0.227921i
\(694\) 0 0
\(695\) 12.0000 24.0000i 0.455186 0.910372i
\(696\) 0 0
\(697\) 6.00000 + 6.00000i 0.227266 + 0.227266i
\(698\) 0 0
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −20.0000 20.0000i −0.754314 0.754314i
\(704\) 0 0
\(705\) −14.0000 + 28.0000i −0.527271 + 1.05454i
\(706\) 0 0
\(707\) 6.00000 6.00000i 0.225653 0.225653i
\(708\) 0 0
\(709\) 24.0000i 0.901339i 0.892691 + 0.450669i \(0.148815\pi\)
−0.892691 + 0.450669i \(0.851185\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) −10.0000 + 10.0000i −0.374503 + 0.374503i
\(714\) 0 0
\(715\) −18.0000 + 6.00000i −0.673162 + 0.224387i
\(716\) 0 0
\(717\) −16.0000 16.0000i −0.597531 0.597531i
\(718\) 0 0
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 14.0000 + 14.0000i 0.520666 + 0.520666i
\(724\) 0 0
\(725\) −32.0000 + 24.0000i −1.18845 + 0.891338i
\(726\) 0 0
\(727\) 15.0000 15.0000i 0.556319 0.556319i −0.371938 0.928257i \(-0.621307\pi\)
0.928257 + 0.371938i \(0.121307\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 6.00000i 0.221918i
\(732\) 0 0
\(733\) 9.00000 9.00000i 0.332423 0.332423i −0.521083 0.853506i \(-0.674472\pi\)
0.853506 + 0.521083i \(0.174472\pi\)
\(734\) 0 0
\(735\) −5.00000 15.0000i −0.184428 0.553283i
\(736\) 0 0
\(737\) 42.0000 + 42.0000i 1.54709 + 1.54709i
\(738\) 0 0
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 9.00000 + 9.00000i 0.330178 + 0.330178i 0.852654 0.522476i \(-0.174992\pi\)
−0.522476 + 0.852654i \(0.674992\pi\)
\(744\) 0 0
\(745\) −24.0000 12.0000i −0.879292 0.439646i
\(746\) 0 0
\(747\) 5.00000 5.00000i 0.182940 0.182940i
\(748\) 0 0
\(749\) 6.00000i 0.219235i
\(750\) 0 0
\(751\) 26.0000i 0.948753i 0.880322 + 0.474377i \(0.157327\pi\)
−0.880322 + 0.474377i \(0.842673\pi\)
\(752\) 0 0
\(753\) 18.0000 18.0000i 0.655956 0.655956i
\(754\) 0 0
\(755\) −36.0000 18.0000i −1.31017 0.655087i
\(756\) 0 0
\(757\) 1.00000 + 1.00000i 0.0363456 + 0.0363456i 0.725046 0.688700i \(-0.241818\pi\)
−0.688700 + 0.725046i \(0.741818\pi\)
\(758\) 0 0
\(759\) −60.0000 −2.17786
\(760\) 0 0
\(761\) 50.0000 1.81250 0.906249 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) 0 0
\(763\) 4.00000 + 4.00000i 0.144810 + 0.144810i
\(764\) 0 0
\(765\) 1.00000 + 3.00000i 0.0361551 + 0.108465i
\(766\) 0 0
\(767\) −4.00000 + 4.00000i −0.144432 + 0.144432i
\(768\) 0 0
\(769\) 8.00000i 0.288487i −0.989542 0.144244i \(-0.953925\pi\)
0.989542 0.144244i \(-0.0460749\pi\)
\(770\) 0 0
\(771\) 22.0000i 0.792311i
\(772\) 0 0
\(773\) −35.0000 + 35.0000i −1.25886 + 1.25886i −0.307226 + 0.951637i \(0.599401\pi\)
−0.951637 + 0.307226i \(0.900599\pi\)
\(774\) 0 0
\(775\) 8.00000 6.00000i 0.287368 0.215526i
\(776\) 0 0
\(777\) −10.0000 10.0000i −0.358748 0.358748i
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 0 0
\(783\) −32.0000 32.0000i −1.14359 1.14359i
\(784\) 0 0
\(785\) 9.00000 3.00000i 0.321224 0.107075i
\(786\) 0 0
\(787\) −9.00000 + 9.00000i −0.320815 + 0.320815i −0.849080 0.528265i \(-0.822843\pi\)
0.528265 + 0.849080i \(0.322843\pi\)
\(788\) 0 0
\(789\) 18.0000i 0.640817i
\(790\) 0 0
\(791\) 6.00000i 0.213335i
\(792\) 0 0
\(793\) −2.00000 + 2.00000i −0.0710221 + 0.0710221i
\(794\) 0 0
\(795\) −2.00000 + 4.00000i −0.0709327 + 0.141865i