Properties

Label 320.2.n.g.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: \(x^{2} + 1\)
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.g.63.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(3.00000 - 3.00000i) q^{7} -1.00000i q^{9} -2.00000i q^{11} +(-3.00000 + 3.00000i) q^{13} +(1.00000 - 3.00000i) q^{15} +(1.00000 + 1.00000i) q^{17} +4.00000 q^{19} +6.00000 q^{21} +(1.00000 + 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} +10.0000i q^{31} +(2.00000 - 2.00000i) q^{33} +(-9.00000 - 3.00000i) q^{35} +(1.00000 + 1.00000i) q^{37} -6.00000 q^{39} -10.0000 q^{41} +(5.00000 + 5.00000i) q^{43} +(-2.00000 + 1.00000i) q^{45} +(3.00000 - 3.00000i) q^{47} -11.0000i q^{49} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-4.00000 + 2.00000i) q^{55} +(4.00000 + 4.00000i) q^{57} -12.0000 q^{59} -2.00000 q^{61} +(-3.00000 - 3.00000i) q^{63} +(9.00000 + 3.00000i) q^{65} +(-1.00000 + 1.00000i) q^{67} +2.00000i q^{69} +2.00000i q^{71} +(1.00000 - 1.00000i) q^{73} +(-7.00000 + 1.00000i) q^{75} +(-6.00000 - 6.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(5.00000 + 5.00000i) q^{83} +(1.00000 - 3.00000i) q^{85} +16.0000i q^{89} +18.0000i q^{91} +(-10.0000 + 10.0000i) q^{93} +(-4.00000 - 8.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{5} + 6q^{7} - 6q^{13} + 2q^{15} + 2q^{17} + 8q^{19} + 12q^{21} + 2q^{23} - 6q^{25} + 8q^{27} + 4q^{33} - 18q^{35} + 2q^{37} - 12q^{39} - 20q^{41} + 10q^{43} - 4q^{45} + 6q^{47} + 10q^{53} - 8q^{55} + 8q^{57} - 24q^{59} - 4q^{61} - 6q^{63} + 18q^{65} - 2q^{67} + 2q^{73} - 14q^{75} - 12q^{77} - 16q^{79} + 10q^{81} + 10q^{83} + 2q^{85} - 20q^{93} - 8q^{95} - 6q^{97} - 4q^{99} + O(q^{100}) \)

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
\(7\) 3.00000 3.00000i 1.13389 1.13389i 0.144370 0.989524i \(-0.453885\pi\)
0.989524 0.144370i \(-0.0461154\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 0 0
\(13\) −3.00000 + 3.00000i −0.832050 + 0.832050i −0.987797 0.155747i \(-0.950222\pi\)
0.155747 + 0.987797i \(0.450222\pi\)
\(14\) 0 0
\(15\) 1.00000 3.00000i 0.258199 0.774597i
\(16\) 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 \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 6.00000 1.30931
\(22\) 0 0
\(23\) 1.00000 + 1.00000i 0.208514 + 0.208514i 0.803636 0.595121i \(-0.202896\pi\)
−0.595121 + 0.803636i \(0.702896\pi\)
\(24\) 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
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 10.0000i 1.79605i 0.439941 + 0.898027i \(0.354999\pi\)
−0.439941 + 0.898027i \(0.645001\pi\)
\(32\) 0 0
\(33\) 2.00000 2.00000i 0.348155 0.348155i
\(34\) 0 0
\(35\) −9.00000 3.00000i −1.52128 0.507093i
\(36\) 0 0
\(37\) 1.00000 + 1.00000i 0.164399 + 0.164399i 0.784512 0.620113i \(-0.212913\pi\)
−0.620113 + 0.784512i \(0.712913\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 5.00000 + 5.00000i 0.762493 + 0.762493i 0.976772 0.214280i \(-0.0687403\pi\)
−0.214280 + 0.976772i \(0.568740\pi\)
\(44\) 0 0
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 0 0
\(47\) 3.00000 3.00000i 0.437595 0.437595i −0.453607 0.891202i \(-0.649863\pi\)
0.891202 + 0.453607i \(0.149863\pi\)
\(48\) 0 0
\(49\) 11.0000i 1.57143i
\(50\) 0 0
\(51\) 2.00000i 0.280056i
\(52\) 0 0
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 0 0
\(55\) −4.00000 + 2.00000i −0.539360 + 0.269680i
\(56\) 0 0
\(57\) 4.00000 + 4.00000i 0.529813 + 0.529813i
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −3.00000 3.00000i −0.377964 0.377964i
\(64\) 0 0
\(65\) 9.00000 + 3.00000i 1.11631 + 0.372104i
\(66\) 0 0
\(67\) −1.00000 + 1.00000i −0.122169 + 0.122169i −0.765548 0.643379i \(-0.777532\pi\)
0.643379 + 0.765548i \(0.277532\pi\)
\(68\) 0 0
\(69\) 2.00000i 0.240772i
\(70\) 0 0
\(71\) 2.00000i 0.237356i 0.992933 + 0.118678i \(0.0378657\pi\)
−0.992933 + 0.118678i \(0.962134\pi\)
\(72\) 0 0
\(73\) 1.00000 1.00000i 0.117041 0.117041i −0.646160 0.763202i \(-0.723626\pi\)
0.763202 + 0.646160i \(0.223626\pi\)
\(74\) 0 0
\(75\) −7.00000 + 1.00000i −0.808290 + 0.115470i
\(76\) 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
\(85\) 1.00000 3.00000i 0.108465 0.325396i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.0000i 1.69600i 0.529999 + 0.847998i \(0.322192\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 18.0000i 1.88691i
\(92\) 0 0
\(93\) −10.0000 + 10.0000i −1.03695 + 1.03695i
\(94\) 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
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 9.00000 + 9.00000i 0.886796 + 0.886796i 0.994214 0.107418i \(-0.0342582\pi\)
−0.107418 + 0.994214i \(0.534258\pi\)
\(104\) 0 0
\(105\) −6.00000 12.0000i −0.585540 1.17108i
\(106\) 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 \(0.0613564\pi\)
−0.981480 + 0.191565i \(0.938644\pi\)
\(110\) 0 0
\(111\) 2.00000i 0.189832i
\(112\) 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
\(115\) 1.00000 3.00000i 0.0932505 0.279751i
\(116\) 0 0
\(117\) 3.00000 + 3.00000i 0.277350 + 0.277350i
\(118\) 0 0
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) −10.0000 10.0000i −0.901670 0.901670i
\(124\) 0 0
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 7.00000 7.00000i 0.621150 0.621150i −0.324676 0.945825i \(-0.605255\pi\)
0.945825 + 0.324676i \(0.105255\pi\)
\(128\) 0 0
\(129\) 10.0000i 0.880451i
\(130\) 0 0
\(131\) 10.0000i 0.873704i −0.899533 0.436852i \(-0.856093\pi\)
0.899533 0.436852i \(-0.143907\pi\)
\(132\) 0 0
\(133\) 12.0000 12.0000i 1.04053 1.04053i
\(134\) 0 0
\(135\) −12.0000 4.00000i −1.03280 0.344265i
\(136\) 0 0
\(137\) −11.0000 11.0000i −0.939793 0.939793i 0.0584943 0.998288i \(-0.481370\pi\)
−0.998288 + 0.0584943i \(0.981370\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 6.00000 + 6.00000i 0.501745 + 0.501745i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 11.0000 11.0000i 0.907265 0.907265i
\(148\) 0 0
\(149\) 4.00000i 0.327693i 0.986486 + 0.163846i \(0.0523901\pi\)
−0.986486 + 0.163846i \(0.947610\pi\)
\(150\) 0 0
\(151\) 6.00000i 0.488273i −0.969741 0.244137i \(-0.921495\pi\)
0.969741 0.244137i \(-0.0785045\pi\)
\(152\) 0 0
\(153\) 1.00000 1.00000i 0.0808452 0.0808452i
\(154\) 0 0
\(155\) 20.0000 10.0000i 1.60644 0.803219i
\(156\) 0 0
\(157\) 1.00000 + 1.00000i 0.0798087 + 0.0798087i 0.745884 0.666076i \(-0.232027\pi\)
−0.666076 + 0.745884i \(0.732027\pi\)
\(158\) 0 0
\(159\) 10.0000 0.793052
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 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 2.00000i −0.467099 0.155700i
\(166\) 0 0
\(167\) −1.00000 + 1.00000i −0.0773823 + 0.0773823i −0.744739 0.667356i \(-0.767426\pi\)
0.667356 + 0.744739i \(0.267426\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 0 0
\(173\) 5.00000 5.00000i 0.380143 0.380143i −0.491011 0.871154i \(-0.663372\pi\)
0.871154 + 0.491011i \(0.163372\pi\)
\(174\) 0 0
\(175\) 3.00000 + 21.0000i 0.226779 + 1.58745i
\(176\) 0 0
\(177\) −12.0000 12.0000i −0.901975 0.901975i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −2.00000 2.00000i −0.147844 0.147844i
\(184\) 0 0
\(185\) 1.00000 3.00000i 0.0735215 0.220564i
\(186\) 0 0
\(187\) 2.00000 2.00000i 0.146254 0.146254i
\(188\) 0 0
\(189\) 24.0000i 1.74574i
\(190\) 0 0
\(191\) 14.0000i 1.01300i −0.862239 0.506502i \(-0.830938\pi\)
0.862239 0.506502i \(-0.169062\pi\)
\(192\) 0 0
\(193\) −15.0000 + 15.0000i −1.07972 + 1.07972i −0.0831899 + 0.996534i \(0.526511\pi\)
−0.996534 + 0.0831899i \(0.973489\pi\)
\(194\) 0 0
\(195\) 6.00000 + 12.0000i 0.429669 + 0.859338i
\(196\) 0 0
\(197\) 13.0000 + 13.0000i 0.926212 + 0.926212i 0.997459 0.0712470i \(-0.0226979\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −2.00000 −0.141069
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 10.0000 + 20.0000i 0.698430 + 1.39686i
\(206\) 0 0
\(207\) 1.00000 1.00000i 0.0695048 0.0695048i
\(208\) 0 0
\(209\) 8.00000i 0.553372i
\(210\) 0 0
\(211\) 14.0000i 0.963800i 0.876226 + 0.481900i \(0.160053\pi\)
−0.876226 + 0.481900i \(0.839947\pi\)
\(212\) 0 0
\(213\) −2.00000 + 2.00000i −0.137038 + 0.137038i
\(214\) 0 0
\(215\) 5.00000 15.0000i 0.340997 1.02299i
\(216\) 0 0
\(217\) 30.0000 + 30.0000i 2.03653 + 2.03653i
\(218\) 0 0
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) 1.00000 + 1.00000i 0.0669650 + 0.0669650i 0.739796 0.672831i \(-0.234922\pi\)
−0.672831 + 0.739796i \(0.734922\pi\)
\(224\) 0 0
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 0 0
\(227\) −5.00000 + 5.00000i −0.331862 + 0.331862i −0.853293 0.521431i \(-0.825398\pi\)
0.521431 + 0.853293i \(0.325398\pi\)
\(228\) 0 0
\(229\) 8.00000i 0.528655i 0.964433 + 0.264327i \(0.0851500\pi\)
−0.964433 + 0.264327i \(0.914850\pi\)
\(230\) 0 0
\(231\) 12.0000i 0.789542i
\(232\) 0 0
\(233\) 21.0000 21.0000i 1.37576 1.37576i 0.524097 0.851658i \(-0.324403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 0 0
\(235\) −9.00000 3.00000i −0.587095 0.195698i
\(236\) 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
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) 0 0
\(245\) −22.0000 + 11.0000i −1.40553 + 0.702764i
\(246\) 0 0
\(247\) −12.0000 + 12.0000i −0.763542 + 0.763542i
\(248\) 0 0
\(249\) 10.0000i 0.633724i
\(250\) 0 0
\(251\) 6.00000i 0.378717i 0.981908 + 0.189358i \(0.0606408\pi\)
−0.981908 + 0.189358i \(0.939359\pi\)
\(252\) 0 0
\(253\) 2.00000 2.00000i 0.125739 0.125739i
\(254\) 0 0
\(255\) 4.00000 2.00000i 0.250490 0.125245i
\(256\) 0 0
\(257\) 5.00000 + 5.00000i 0.311891 + 0.311891i 0.845642 0.533751i \(-0.179218\pi\)
−0.533751 + 0.845642i \(0.679218\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.0000 11.0000i −0.678289 0.678289i 0.281324 0.959613i \(-0.409226\pi\)
−0.959613 + 0.281324i \(0.909226\pi\)
\(264\) 0 0
\(265\) −15.0000 5.00000i −0.921443 0.307148i
\(266\) 0 0
\(267\) −16.0000 + 16.0000i −0.979184 + 0.979184i
\(268\) 0 0
\(269\) 20.0000i 1.21942i −0.792624 0.609711i \(-0.791286\pi\)
0.792624 0.609711i \(-0.208714\pi\)
\(270\) 0 0
\(271\) 14.0000i 0.850439i −0.905090 0.425220i \(-0.860197\pi\)
0.905090 0.425220i \(-0.139803\pi\)
\(272\) 0 0
\(273\) −18.0000 + 18.0000i −1.08941 + 1.08941i
\(274\) 0 0
\(275\) 8.00000 + 6.00000i 0.482418 + 0.361814i
\(276\) 0 0
\(277\) −11.0000 11.0000i −0.660926 0.660926i 0.294672 0.955598i \(-0.404789\pi\)
−0.955598 + 0.294672i \(0.904789\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −7.00000 7.00000i −0.416107 0.416107i 0.467753 0.883859i \(-0.345064\pi\)
−0.883859 + 0.467753i \(0.845064\pi\)
\(284\) 0 0
\(285\) 4.00000 12.0000i 0.236940 0.710819i
\(286\) 0 0
\(287\) −30.0000 + 30.0000i −1.77084 + 1.77084i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 0 0
\(293\) −11.0000 + 11.0000i −0.642627 + 0.642627i −0.951200 0.308574i \(-0.900148\pi\)
0.308574 + 0.951200i \(0.400148\pi\)
\(294\) 0 0
\(295\) 12.0000 + 24.0000i 0.698667 + 1.39733i
\(296\) 0 0
\(297\) −8.00000 8.00000i −0.464207 0.464207i
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 30.0000 1.72917
\(302\) 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
\(307\) −17.0000 + 17.0000i −0.970241 + 0.970241i −0.999570 0.0293286i \(-0.990663\pi\)
0.0293286 + 0.999570i \(0.490663\pi\)
\(308\) 0 0
\(309\) 18.0000i 1.02398i
\(310\) 0 0
\(311\) 18.0000i 1.02069i 0.859971 + 0.510343i \(0.170482\pi\)
−0.859971 + 0.510343i \(0.829518\pi\)
\(312\) 0 0
\(313\) 9.00000 9.00000i 0.508710 0.508710i −0.405420 0.914130i \(-0.632875\pi\)
0.914130 + 0.405420i \(0.132875\pi\)
\(314\) 0 0
\(315\) −3.00000 + 9.00000i −0.169031 + 0.507093i
\(316\) 0 0
\(317\) 13.0000 + 13.0000i 0.730153 + 0.730153i 0.970650 0.240497i \(-0.0773105\pi\)
−0.240497 + 0.970650i \(0.577310\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 4.00000 + 4.00000i 0.222566 + 0.222566i
\(324\) 0 0
\(325\) −3.00000 21.0000i −0.166410 1.16487i
\(326\) 0 0
\(327\) −4.00000 + 4.00000i −0.221201 + 0.221201i
\(328\) 0 0
\(329\) 18.0000i 0.992372i
\(330\) 0 0
\(331\) 26.0000i 1.42909i −0.699590 0.714545i \(-0.746634\pi\)
0.699590 0.714545i \(-0.253366\pi\)
\(332\) 0 0
\(333\) 1.00000 1.00000i 0.0547997 0.0547997i
\(334\) 0 0
\(335\) 3.00000 + 1.00000i 0.163908 + 0.0546358i
\(336\) 0 0
\(337\) −15.0000 15.0000i −0.817102 0.817102i 0.168585 0.985687i \(-0.446080\pi\)
−0.985687 + 0.168585i \(0.946080\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 20.0000 1.08306
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) 4.00000 2.00000i 0.215353 0.107676i
\(346\) 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
\(349\) 8.00000i 0.428230i 0.976808 + 0.214115i \(0.0686868\pi\)
−0.976808 + 0.214115i \(0.931313\pi\)
\(350\) 0 0
\(351\) 24.0000i 1.28103i
\(352\) 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
\(355\) 4.00000 2.00000i 0.212298 0.106149i
\(356\) 0 0
\(357\) 6.00000 + 6.00000i 0.317554 + 0.317554i
\(358\) 0 0
\(359\) −32.0000 −1.68890 −0.844448 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 7.00000 + 7.00000i 0.367405 + 0.367405i
\(364\) 0 0
\(365\) −3.00000 1.00000i −0.157027 0.0523424i
\(366\) 0 0
\(367\) 15.0000 15.0000i 0.782994 0.782994i −0.197341 0.980335i \(-0.563231\pi\)
0.980335 + 0.197341i \(0.0632307\pi\)
\(368\) 0 0
\(369\) 10.0000i 0.520579i
\(370\) 0 0
\(371\) 30.0000i 1.55752i
\(372\) 0 0
\(373\) 9.00000 9.00000i 0.466002 0.466002i −0.434614 0.900617i \(-0.643115\pi\)
0.900617 + 0.434614i \(0.143115\pi\)
\(374\) 0 0
\(375\) 9.00000 + 13.0000i 0.464758 + 0.671317i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 14.0000 0.717242
\(382\) 0 0
\(383\) 1.00000 + 1.00000i 0.0510976 + 0.0510976i 0.732194 0.681096i \(-0.238496\pi\)
−0.681096 + 0.732194i \(0.738496\pi\)
\(384\) 0 0
\(385\) −6.00000 + 18.0000i −0.305788 + 0.917365i
\(386\) 0 0
\(387\) 5.00000 5.00000i 0.254164 0.254164i
\(388\) 0 0
\(389\) 4.00000i 0.202808i 0.994845 + 0.101404i \(0.0323335\pi\)
−0.994845 + 0.101404i \(0.967667\pi\)
\(390\) 0 0
\(391\) 2.00000i 0.101144i
\(392\) 0 0
\(393\) 10.0000 10.0000i 0.504433 0.504433i
\(394\) 0 0
\(395\) 8.00000 + 16.0000i 0.402524 + 0.805047i
\(396\) 0 0
\(397\) −15.0000 15.0000i −0.752828 0.752828i 0.222178 0.975006i \(-0.428683\pi\)
−0.975006 + 0.222178i \(0.928683\pi\)
\(398\) 0 0
\(399\) 24.0000 1.20150
\(400\) 0 0
\(401\) −22.0000 −1.09863 −0.549314 0.835616i \(-0.685111\pi\)
−0.549314 + 0.835616i \(0.685111\pi\)
\(402\) 0 0
\(403\) −30.0000 30.0000i −1.49441 1.49441i
\(404\) 0 0
\(405\) −5.00000 10.0000i −0.248452 0.496904i
\(406\) 0 0
\(407\) 2.00000 2.00000i 0.0991363 0.0991363i
\(408\) 0 0
\(409\) 20.0000i 0.988936i 0.869196 + 0.494468i \(0.164637\pi\)
−0.869196 + 0.494468i \(0.835363\pi\)
\(410\) 0 0
\(411\) 22.0000i 1.08518i
\(412\) 0 0
\(413\) −36.0000 + 36.0000i −1.77144 + 1.77144i
\(414\) 0 0
\(415\) 5.00000 15.0000i 0.245440 0.736321i
\(416\) 0 0
\(417\) 12.0000 + 12.0000i 0.587643 + 0.587643i
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) −3.00000 3.00000i −0.145865 0.145865i
\(424\) 0 0
\(425\) −7.00000 + 1.00000i −0.339550 + 0.0485071i
\(426\) 0 0
\(427\) −6.00000 + 6.00000i −0.290360 + 0.290360i
\(428\) 0 0
\(429\) 12.0000i 0.579365i
\(430\) 0 0
\(431\) 30.0000i 1.44505i −0.691345 0.722525i \(-0.742982\pi\)
0.691345 0.722525i \(-0.257018\pi\)
\(432\) 0 0
\(433\) 21.0000 21.0000i 1.00920 1.00920i 0.00923827 0.999957i \(-0.497059\pi\)
0.999957 0.00923827i \(-0.00294067\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.00000 + 4.00000i 0.191346 + 0.191346i
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) −11.0000 −0.523810
\(442\) 0 0
\(443\) 25.0000 + 25.0000i 1.18779 + 1.18779i 0.977678 + 0.210108i \(0.0673814\pi\)
0.210108 + 0.977678i \(0.432619\pi\)
\(444\) 0 0
\(445\) 32.0000 16.0000i 1.51695 0.758473i
\(446\) 0 0
\(447\) −4.00000 + 4.00000i −0.189194 + 0.189194i
\(448\) 0 0
\(449\) 12.0000i 0.566315i −0.959073 0.283158i \(-0.908618\pi\)
0.959073 0.283158i \(-0.0913819\pi\)
\(450\) 0 0
\(451\) 20.0000i 0.941763i
\(452\) 0 0
\(453\) 6.00000 6.00000i 0.281905 0.281905i
\(454\) 0 0
\(455\) 36.0000 18.0000i 1.68771 0.843853i
\(456\) 0 0
\(457\) 9.00000 + 9.00000i 0.421002 + 0.421002i 0.885549 0.464546i \(-0.153783\pi\)
−0.464546 + 0.885549i \(0.653783\pi\)
\(458\) 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
\(463\) −11.0000 11.0000i −0.511213 0.511213i 0.403685 0.914898i \(-0.367729\pi\)
−0.914898 + 0.403685i \(0.867729\pi\)
\(464\) 0 0
\(465\) 30.0000 + 10.0000i 1.39122 + 0.463739i
\(466\) 0 0
\(467\) −13.0000 + 13.0000i −0.601568 + 0.601568i −0.940729 0.339160i \(-0.889857\pi\)
0.339160 + 0.940729i \(0.389857\pi\)
\(468\) 0 0
\(469\) 6.00000i 0.277054i
\(470\) 0 0
\(471\) 2.00000i 0.0921551i
\(472\) 0 0
\(473\) 10.0000 10.0000i 0.459800 0.459800i
\(474\) 0 0
\(475\) −12.0000 + 16.0000i −0.550598 + 0.734130i
\(476\) 0 0
\(477\) −5.00000 5.00000i −0.228934 0.228934i
\(478\) 0 0
\(479\) 40.0000 1.82765 0.913823 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) 6.00000 + 6.00000i 0.273009 + 0.273009i
\(484\) 0 0
\(485\) −3.00000 + 9.00000i −0.136223 + 0.408669i
\(486\) 0 0
\(487\) 19.0000 19.0000i 0.860972 0.860972i −0.130479 0.991451i \(-0.541651\pi\)
0.991451 + 0.130479i \(0.0416515\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 10.0000i 0.451294i −0.974209 0.225647i \(-0.927550\pi\)
0.974209 0.225647i \(-0.0724495\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.00000 + 4.00000i 0.0898933 + 0.179787i
\(496\) 0 0
\(497\) 6.00000 + 6.00000i 0.269137 + 0.269137i
\(498\) 0 0
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) −2.00000 −0.0893534
\(502\) 0 0
\(503\) 17.0000 + 17.0000i 0.757993 + 0.757993i 0.975957 0.217964i \(-0.0699416\pi\)
−0.217964 + 0.975957i \(0.569942\pi\)
\(504\) 0 0
\(505\) 6.00000 + 12.0000i 0.266996 + 0.533993i
\(506\) 0 0
\(507\) 5.00000 5.00000i 0.222058 0.222058i
\(508\) 0 0
\(509\) 24.0000i 1.06378i −0.846813 0.531891i \(-0.821482\pi\)
0.846813 0.531891i \(-0.178518\pi\)
\(510\) 0 0
\(511\) 6.00000i 0.265424i
\(512\) 0 0
\(513\) 16.0000 16.0000i 0.706417 0.706417i
\(514\) 0 0
\(515\) 9.00000 27.0000i 0.396587 1.18976i
\(516\) 0 0
\(517\) −6.00000 6.00000i −0.263880 0.263880i
\(518\) 0 0
\(519\) 10.0000 0.438951
\(520\) 0 0
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 0 0
\(523\) −15.0000 15.0000i −0.655904 0.655904i 0.298504 0.954408i \(-0.403512\pi\)
−0.954408 + 0.298504i \(0.903512\pi\)
\(524\) 0 0
\(525\) −18.0000 + 24.0000i −0.785584 + 1.04745i
\(526\) 0 0
\(527\) −10.0000 + 10.0000i −0.435607 + 0.435607i
\(528\) 0 0
\(529\) 21.0000i 0.913043i
\(530\) 0 0
\(531\) 12.0000i 0.520756i
\(532\) 0 0
\(533\) 30.0000 30.0000i 1.29944 1.29944i
\(534\) 0 0
\(535\) −9.00000 3.00000i −0.389104 0.129701i
\(536\) 0 0
\(537\) −12.0000 12.0000i −0.517838 0.517838i
\(538\) 0 0
\(539\) −22.0000 −0.947607
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) −22.0000 22.0000i −0.944110 0.944110i
\(544\) 0 0
\(545\) 8.00000 4.00000i 0.342682 0.171341i
\(546\) 0 0
\(547\) 11.0000 11.0000i 0.470326 0.470326i −0.431694 0.902020i \(-0.642084\pi\)
0.902020 + 0.431694i \(0.142084\pi\)
\(548\) 0 0
\(549\) 2.00000i 0.0853579i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −24.0000 + 24.0000i −1.02058 + 1.02058i
\(554\) 0 0
\(555\) 4.00000 2.00000i 0.169791 0.0848953i
\(556\) 0 0
\(557\) −27.0000 27.0000i −1.14403 1.14403i −0.987706 0.156320i \(-0.950037\pi\)
−0.156320 0.987706i \(-0.549963\pi\)
\(558\) 0 0
\(559\) −30.0000 −1.26886
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) 33.0000 + 33.0000i 1.39078 + 1.39078i 0.823571 + 0.567213i \(0.191978\pi\)
0.567213 + 0.823571i \(0.308022\pi\)
\(564\) 0 0
\(565\) 9.00000 + 3.00000i 0.378633 + 0.126211i
\(566\) 0 0
\(567\) 15.0000 15.0000i 0.629941 0.629941i
\(568\) 0 0
\(569\) 12.0000i 0.503066i 0.967849 + 0.251533i \(0.0809347\pi\)
−0.967849 + 0.251533i \(0.919065\pi\)
\(570\) 0 0
\(571\) 34.0000i 1.42286i −0.702759 0.711428i \(-0.748049\pi\)
0.702759 0.711428i \(-0.251951\pi\)
\(572\) 0 0
\(573\) 14.0000 14.0000i 0.584858 0.584858i
\(574\) 0 0
\(575\) −7.00000 + 1.00000i −0.291920 + 0.0417029i
\(576\) 0 0
\(577\) −19.0000 19.0000i −0.790980 0.790980i 0.190673 0.981654i \(-0.438933\pi\)
−0.981654 + 0.190673i \(0.938933\pi\)
\(578\) 0 0
\(579\) −30.0000 −1.24676
\(580\) 0 0
\(581\) 30.0000 1.24461
\(582\) 0 0
\(583\) −10.0000 10.0000i −0.414158 0.414158i
\(584\) 0 0
\(585\) 3.00000 9.00000i 0.124035 0.372104i
\(586\) 0 0
\(587\) 23.0000 23.0000i 0.949312 0.949312i −0.0494643 0.998776i \(-0.515751\pi\)
0.998776 + 0.0494643i \(0.0157514\pi\)
\(588\) 0 0
\(589\) 40.0000i 1.64817i
\(590\) 0 0
\(591\) 26.0000i 1.06950i
\(592\) 0 0
\(593\) −7.00000 + 7.00000i −0.287456 + 0.287456i −0.836073 0.548618i \(-0.815154\pi\)
0.548618 + 0.836073i \(0.315154\pi\)
\(594\) 0 0
\(595\) −6.00000 12.0000i −0.245976 0.491952i
\(596\) 0 0
\(597\) 16.0000 + 16.0000i 0.654836 + 0.654836i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 1.00000 + 1.00000i 0.0407231 + 0.0407231i
\(604\) 0 0
\(605\) −7.00000 14.0000i −0.284590 0.569181i
\(606\) 0 0
\(607\) −5.00000 + 5.00000i −0.202944 + 0.202944i −0.801260 0.598316i \(-0.795837\pi\)
0.598316 + 0.801260i \(0.295837\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0000i 0.728202i
\(612\) 0 0
\(613\) −15.0000 + 15.0000i −0.605844 + 0.605844i −0.941857 0.336013i \(-0.890921\pi\)
0.336013 + 0.941857i \(0.390921\pi\)
\(614\) 0 0
\(615\) −10.0000 + 30.0000i −0.403239 + 1.20972i
\(616\) 0 0
\(617\) 13.0000 + 13.0000i 0.523360 + 0.523360i 0.918585 0.395224i \(-0.129333\pi\)
−0.395224 + 0.918585i \(0.629333\pi\)
\(618\) 0 0
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 0 0
\(621\) 8.00000 0.321029
\(622\) 0 0
\(623\) 48.0000 + 48.0000i 1.92308 + 1.92308i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) 8.00000 8.00000i 0.319489 0.319489i
\(628\) 0 0
\(629\) 2.00000i 0.0797452i
\(630\) 0 0
\(631\) 14.0000i 0.557331i −0.960388 0.278666i \(-0.910108\pi\)
0.960388 0.278666i \(-0.0898921\pi\)
\(632\) 0 0
\(633\) −14.0000 + 14.0000i −0.556450 + 0.556450i
\(634\) 0 0
\(635\) −21.0000 7.00000i −0.833360 0.277787i
\(636\) 0 0
\(637\) 33.0000 + 33.0000i 1.30751 + 1.30751i
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −27.0000 27.0000i −1.06478 1.06478i −0.997751 0.0670247i \(-0.978649\pi\)
−0.0670247 0.997751i \(-0.521351\pi\)
\(644\) 0 0
\(645\) 20.0000 10.0000i 0.787499 0.393750i
\(646\) 0 0
\(647\) −29.0000 + 29.0000i −1.14011 + 1.14011i −0.151678 + 0.988430i \(0.548468\pi\)
−0.988430 + 0.151678i \(0.951532\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 60.0000i 2.35159i
\(652\) 0 0
\(653\) 1.00000 1.00000i 0.0391330 0.0391330i −0.687270 0.726403i \(-0.741191\pi\)
0.726403 + 0.687270i \(0.241191\pi\)
\(654\) 0 0
\(655\) −20.0000 + 10.0000i −0.781465 + 0.390732i
\(656\) 0 0
\(657\) −1.00000 1.00000i −0.0390137 0.0390137i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 0 0
\(663\) −6.00000 6.00000i −0.233021 0.233021i
\(664\) 0 0
\(665\) −36.0000 12.0000i −1.39602 0.465340i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 2.00000i 0.0773245i
\(670\) 0 0
\(671\) 4.00000i 0.154418i
\(672\) 0 0
\(673\) −3.00000 + 3.00000i −0.115642 + 0.115642i −0.762560 0.646918i \(-0.776058\pi\)
0.646918 + 0.762560i \(0.276058\pi\)
\(674\) 0 0
\(675\) 4.00000 + 28.0000i 0.153960 + 1.07772i
\(676\) 0 0
\(677\) −3.00000 3.00000i −0.115299 0.115299i 0.647103 0.762402i \(-0.275980\pi\)
−0.762402 + 0.647103i \(0.775980\pi\)
\(678\) 0 0
\(679\) −18.0000 −0.690777
\(680\) 0 0
\(681\) −10.0000 −0.383201
\(682\) 0 0
\(683\) −11.0000 11.0000i −0.420903 0.420903i 0.464611 0.885515i \(-0.346194\pi\)
−0.885515 + 0.464611i \(0.846194\pi\)
\(684\) 0 0
\(685\) −11.0000 + 33.0000i −0.420288 + 1.26087i
\(686\) 0 0
\(687\) −8.00000 + 8.00000i −0.305219 + 0.305219i
\(688\) 0 0
\(689\) 30.0000i 1.14291i
\(690\) 0 0
\(691\) 14.0000i 0.532585i 0.963892 + 0.266293i \(0.0857987\pi\)
−0.963892 + 0.266293i \(0.914201\pi\)
\(692\) 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
\(697\) −10.0000 10.0000i −0.378777 0.378777i
\(698\) 0 0
\(699\) 42.0000 1.58859
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 0 0
\(703\) 4.00000 + 4.00000i 0.150863 + 0.150863i
\(704\) 0 0
\(705\) −6.00000 12.0000i −0.225973 0.451946i
\(706\) 0 0
\(707\) −18.0000 + 18.0000i −0.676960 + 0.676960i
\(708\) 0 0
\(709\) 48.0000i 1.80268i −0.433114 0.901339i \(-0.642585\pi\)
0.433114 0.901339i \(-0.357415\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) −10.0000 + 10.0000i −0.374503 + 0.374503i
\(714\) 0 0
\(715\) 6.00000 18.0000i 0.224387 0.673162i
\(716\) 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
\(721\) 54.0000 2.01107
\(722\) 0 0
\(723\) −2.00000 2.00000i −0.0743808 0.0743808i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.00000 3.00000i 0.111264 0.111264i −0.649283 0.760547i \(-0.724931\pi\)
0.760547 + 0.649283i \(0.224931\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 10.0000i 0.369863i
\(732\) 0 0
\(733\) −27.0000 + 27.0000i −0.997268 + 0.997268i −0.999996 0.00272852i \(-0.999131\pi\)
0.00272852 + 0.999996i \(0.499131\pi\)
\(734\) 0 0
\(735\) −33.0000 11.0000i −1.21722 0.405741i
\(736\) 0 0
\(737\) 2.00000 + 2.00000i 0.0736709 + 0.0736709i
\(738\) 0 0
\(739\) −28.0000 −1.03000 −0.514998 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 0 0
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) 21.0000 + 21.0000i 0.770415 + 0.770415i 0.978179 0.207764i \(-0.0666185\pi\)
−0.207764 + 0.978179i \(0.566619\pi\)
\(744\) 0 0
\(745\) 8.00000 4.00000i 0.293097 0.146549i
\(746\) 0 0
\(747\) 5.00000 5.00000i 0.182940 0.182940i
\(748\) 0 0
\(749\) 18.0000i 0.657706i
\(750\) 0 0
\(751\) 2.00000i 0.0729810i 0.999334 + 0.0364905i \(0.0116179\pi\)
−0.999334 + 0.0364905i \(0.988382\pi\)
\(752\) 0 0
\(753\) −6.00000 + 6.00000i −0.218652 + 0.218652i
\(754\) 0 0
\(755\) −12.0000 + 6.00000i −0.436725 + 0.218362i
\(756\) 0 0
\(757\) −19.0000 19.0000i −0.690567 0.690567i 0.271790 0.962357i \(-0.412384\pi\)
−0.962357 + 0.271790i \(0.912384\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 0 0
\(763\) 12.0000 + 12.0000i 0.434429 + 0.434429i
\(764\) 0 0
\(765\) −3.00000 1.00000i −0.108465 0.0361551i
\(766\) 0 0
\(767\) 36.0000 36.0000i 1.29988 1.29988i
\(768\) 0 0
\(769\) 8.00000i 0.288487i −0.989542 0.144244i \(-0.953925\pi\)
0.989542 0.144244i \(-0.0460749\pi\)
\(770\) 0 0
\(771\) 10.0000i 0.360141i
\(772\) 0 0
\(773\) 17.0000 17.0000i 0.611448 0.611448i −0.331876 0.943323i \(-0.607681\pi\)
0.943323 + 0.331876i \(0.107681\pi\)
\(774\) 0 0
\(775\) −40.0000 30.0000i −1.43684 1.07763i
\(776\) 0 0
\(777\) 6.00000 + 6.00000i 0.215249 + 0.215249i
\(778\) 0 0
\(779\) −40.0000 −1.43315
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.00000 3.00000i 0.0356915 0.107075i
\(786\) 0 0
\(787\) 31.0000 31.0000i 1.10503 1.10503i 0.111237 0.993794i \(-0.464519\pi\)
0.993794 0.111237i \(-0.0354812\pi\)
\(788\) 0 0
\(789\) 22.0000i 0.783221i
\(790\) 0 0
\(791\) 18.0000i 0.640006i
\(792\) 0 0
\(793\) 6.00000 6.00000i 0.213066 0.213066i
\(794\) 0 0
\(795\) −10.0000 20.0000i −0.354663 0.709327i
\(796\) 0 0
\(797\) 37.0000 + 37.0000i 1.31061 + 1.31061i 0.920967 + 0.389640i \(0.