Properties

Label 20.3.f.a.13.1
Level 20
Weight 3
Character 20.13
Analytic conductor 0.545
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.f (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.544960528721\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.1
Root \(-1.00000i\)
Character \(\chi\) = 20.13
Dual form 20.3.f.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +(-3.00000 - 4.00000i) q^{5} +(-7.00000 + 7.00000i) q^{7} -7.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +(-3.00000 - 4.00000i) q^{5} +(-7.00000 + 7.00000i) q^{7} -7.00000i q^{9} +10.0000 q^{11} +(9.00000 + 9.00000i) q^{13} +(1.00000 - 7.00000i) q^{15} +(1.00000 - 1.00000i) q^{17} +8.00000i q^{19} -14.0000 q^{21} +(-23.0000 - 23.0000i) q^{23} +(-7.00000 + 24.0000i) q^{25} +(16.0000 - 16.0000i) q^{27} +8.00000i q^{29} -14.0000 q^{31} +(10.0000 + 10.0000i) q^{33} +(49.0000 + 7.00000i) q^{35} +(33.0000 - 33.0000i) q^{37} +18.0000i q^{39} -14.0000 q^{41} +(-15.0000 - 15.0000i) q^{43} +(-28.0000 + 21.0000i) q^{45} +(-39.0000 + 39.0000i) q^{47} -49.0000i q^{49} +2.00000 q^{51} +(-7.00000 - 7.00000i) q^{53} +(-30.0000 - 40.0000i) q^{55} +(-8.00000 + 8.00000i) q^{57} +56.0000i q^{59} +42.0000 q^{61} +(49.0000 + 49.0000i) q^{63} +(9.00000 - 63.0000i) q^{65} +(-7.00000 + 7.00000i) q^{67} -46.0000i q^{69} +98.0000 q^{71} +(49.0000 + 49.0000i) q^{73} +(-31.0000 + 17.0000i) q^{75} +(-70.0000 + 70.0000i) q^{77} -96.0000i q^{79} -31.0000 q^{81} +(-63.0000 - 63.0000i) q^{83} +(-7.00000 - 1.00000i) q^{85} +(-8.00000 + 8.00000i) q^{87} +112.000i q^{89} -126.000 q^{91} +(-14.0000 - 14.0000i) q^{93} +(32.0000 - 24.0000i) q^{95} +(33.0000 - 33.0000i) q^{97} -70.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 6q^{5} - 14q^{7} + O(q^{10}) \) \( 2q + 2q^{3} - 6q^{5} - 14q^{7} + 20q^{11} + 18q^{13} + 2q^{15} + 2q^{17} - 28q^{21} - 46q^{23} - 14q^{25} + 32q^{27} - 28q^{31} + 20q^{33} + 98q^{35} + 66q^{37} - 28q^{41} - 30q^{43} - 56q^{45} - 78q^{47} + 4q^{51} - 14q^{53} - 60q^{55} - 16q^{57} + 84q^{61} + 98q^{63} + 18q^{65} - 14q^{67} + 196q^{71} + 98q^{73} - 62q^{75} - 140q^{77} - 62q^{81} - 126q^{83} - 14q^{85} - 16q^{87} - 252q^{91} - 28q^{93} + 64q^{95} + 66q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 1.00000 + 1.00000i 0.333333 + 0.333333i 0.853851 0.520518i \(-0.174261\pi\)
−0.520518 + 0.853851i \(0.674261\pi\)
\(4\) 0 0
\(5\) −3.00000 4.00000i −0.600000 0.800000i
\(6\) 0 0
\(7\) −7.00000 + 7.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) 7.00000i 0.777778i
\(10\) 0 0
\(11\) 10.0000 0.909091 0.454545 0.890724i \(-0.349802\pi\)
0.454545 + 0.890724i \(0.349802\pi\)
\(12\) 0 0
\(13\) 9.00000 + 9.00000i 0.692308 + 0.692308i 0.962739 0.270432i \(-0.0871664\pi\)
−0.270432 + 0.962739i \(0.587166\pi\)
\(14\) 0 0
\(15\) 1.00000 7.00000i 0.0666667 0.466667i
\(16\) 0 0
\(17\) 1.00000 1.00000i 0.0588235 0.0588235i −0.677083 0.735907i \(-0.736756\pi\)
0.735907 + 0.677083i \(0.236756\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i 0.977588 + 0.210526i \(0.0675178\pi\)
−0.977588 + 0.210526i \(0.932482\pi\)
\(20\) 0 0
\(21\) −14.0000 −0.666667
\(22\) 0 0
\(23\) −23.0000 23.0000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(26\) 0 0
\(27\) 16.0000 16.0000i 0.592593 0.592593i
\(28\) 0 0
\(29\) 8.00000i 0.275862i 0.990442 + 0.137931i \(0.0440452\pi\)
−0.990442 + 0.137931i \(0.955955\pi\)
\(30\) 0 0
\(31\) −14.0000 −0.451613 −0.225806 0.974172i \(-0.572502\pi\)
−0.225806 + 0.974172i \(0.572502\pi\)
\(32\) 0 0
\(33\) 10.0000 + 10.0000i 0.303030 + 0.303030i
\(34\) 0 0
\(35\) 49.0000 + 7.00000i 1.40000 + 0.200000i
\(36\) 0 0
\(37\) 33.0000 33.0000i 0.891892 0.891892i −0.102809 0.994701i \(-0.532783\pi\)
0.994701 + 0.102809i \(0.0327831\pi\)
\(38\) 0 0
\(39\) 18.0000i 0.461538i
\(40\) 0 0
\(41\) −14.0000 −0.341463 −0.170732 0.985318i \(-0.554613\pi\)
−0.170732 + 0.985318i \(0.554613\pi\)
\(42\) 0 0
\(43\) −15.0000 15.0000i −0.348837 0.348837i 0.510839 0.859676i \(-0.329335\pi\)
−0.859676 + 0.510839i \(0.829335\pi\)
\(44\) 0 0
\(45\) −28.0000 + 21.0000i −0.622222 + 0.466667i
\(46\) 0 0
\(47\) −39.0000 + 39.0000i −0.829787 + 0.829787i −0.987487 0.157700i \(-0.949592\pi\)
0.157700 + 0.987487i \(0.449592\pi\)
\(48\) 0 0
\(49\) 49.0000i 1.00000i
\(50\) 0 0
\(51\) 2.00000 0.0392157
\(52\) 0 0
\(53\) −7.00000 7.00000i −0.132075 0.132075i 0.637979 0.770054i \(-0.279771\pi\)
−0.770054 + 0.637979i \(0.779771\pi\)
\(54\) 0 0
\(55\) −30.0000 40.0000i −0.545455 0.727273i
\(56\) 0 0
\(57\) −8.00000 + 8.00000i −0.140351 + 0.140351i
\(58\) 0 0
\(59\) 56.0000i 0.949153i 0.880214 + 0.474576i \(0.157399\pi\)
−0.880214 + 0.474576i \(0.842601\pi\)
\(60\) 0 0
\(61\) 42.0000 0.688525 0.344262 0.938874i \(-0.388129\pi\)
0.344262 + 0.938874i \(0.388129\pi\)
\(62\) 0 0
\(63\) 49.0000 + 49.0000i 0.777778 + 0.777778i
\(64\) 0 0
\(65\) 9.00000 63.0000i 0.138462 0.969231i
\(66\) 0 0
\(67\) −7.00000 + 7.00000i −0.104478 + 0.104478i −0.757413 0.652936i \(-0.773537\pi\)
0.652936 + 0.757413i \(0.273537\pi\)
\(68\) 0 0
\(69\) 46.0000i 0.666667i
\(70\) 0 0
\(71\) 98.0000 1.38028 0.690141 0.723675i \(-0.257549\pi\)
0.690141 + 0.723675i \(0.257549\pi\)
\(72\) 0 0
\(73\) 49.0000 + 49.0000i 0.671233 + 0.671233i 0.958000 0.286767i \(-0.0925807\pi\)
−0.286767 + 0.958000i \(0.592581\pi\)
\(74\) 0 0
\(75\) −31.0000 + 17.0000i −0.413333 + 0.226667i
\(76\) 0 0
\(77\) −70.0000 + 70.0000i −0.909091 + 0.909091i
\(78\) 0 0
\(79\) 96.0000i 1.21519i −0.794247 0.607595i \(-0.792134\pi\)
0.794247 0.607595i \(-0.207866\pi\)
\(80\) 0 0
\(81\) −31.0000 −0.382716
\(82\) 0 0
\(83\) −63.0000 63.0000i −0.759036 0.759036i 0.217111 0.976147i \(-0.430337\pi\)
−0.976147 + 0.217111i \(0.930337\pi\)
\(84\) 0 0
\(85\) −7.00000 1.00000i −0.0823529 0.0117647i
\(86\) 0 0
\(87\) −8.00000 + 8.00000i −0.0919540 + 0.0919540i
\(88\) 0 0
\(89\) 112.000i 1.25843i 0.777233 + 0.629213i \(0.216623\pi\)
−0.777233 + 0.629213i \(0.783377\pi\)
\(90\) 0 0
\(91\) −126.000 −1.38462
\(92\) 0 0
\(93\) −14.0000 14.0000i −0.150538 0.150538i
\(94\) 0 0
\(95\) 32.0000 24.0000i 0.336842 0.252632i
\(96\) 0 0
\(97\) 33.0000 33.0000i 0.340206 0.340206i −0.516239 0.856445i \(-0.672668\pi\)
0.856445 + 0.516239i \(0.172668\pi\)
\(98\) 0 0
\(99\) 70.0000i 0.707071i
\(100\) 0 0
\(101\) 26.0000 0.257426 0.128713 0.991682i \(-0.458915\pi\)
0.128713 + 0.991682i \(0.458915\pi\)
\(102\) 0 0
\(103\) 73.0000 + 73.0000i 0.708738 + 0.708738i 0.966270 0.257532i \(-0.0829093\pi\)
−0.257532 + 0.966270i \(0.582909\pi\)
\(104\) 0 0
\(105\) 42.0000 + 56.0000i 0.400000 + 0.533333i
\(106\) 0 0
\(107\) 121.000 121.000i 1.13084 1.13084i 0.140804 0.990038i \(-0.455031\pi\)
0.990038 0.140804i \(-0.0449686\pi\)
\(108\) 0 0
\(109\) 136.000i 1.24771i 0.781542 + 0.623853i \(0.214434\pi\)
−0.781542 + 0.623853i \(0.785566\pi\)
\(110\) 0 0
\(111\) 66.0000 0.594595
\(112\) 0 0
\(113\) −127.000 127.000i −1.12389 1.12389i −0.991150 0.132743i \(-0.957621\pi\)
−0.132743 0.991150i \(-0.542379\pi\)
\(114\) 0 0
\(115\) −23.0000 + 161.000i −0.200000 + 1.40000i
\(116\) 0 0
\(117\) 63.0000 63.0000i 0.538462 0.538462i
\(118\) 0 0
\(119\) 14.0000i 0.117647i
\(120\) 0 0
\(121\) −21.0000 −0.173554
\(122\) 0 0
\(123\) −14.0000 14.0000i −0.113821 0.113821i
\(124\) 0 0
\(125\) 117.000 44.0000i 0.936000 0.352000i
\(126\) 0 0
\(127\) −7.00000 + 7.00000i −0.0551181 + 0.0551181i −0.734129 0.679010i \(-0.762409\pi\)
0.679010 + 0.734129i \(0.262409\pi\)
\(128\) 0 0
\(129\) 30.0000i 0.232558i
\(130\) 0 0
\(131\) −230.000 −1.75573 −0.877863 0.478913i \(-0.841031\pi\)
−0.877863 + 0.478913i \(0.841031\pi\)
\(132\) 0 0
\(133\) −56.0000 56.0000i −0.421053 0.421053i
\(134\) 0 0
\(135\) −112.000 16.0000i −0.829630 0.118519i
\(136\) 0 0
\(137\) −63.0000 + 63.0000i −0.459854 + 0.459854i −0.898607 0.438753i \(-0.855420\pi\)
0.438753 + 0.898607i \(0.355420\pi\)
\(138\) 0 0
\(139\) 88.0000i 0.633094i 0.948577 + 0.316547i \(0.102523\pi\)
−0.948577 + 0.316547i \(0.897477\pi\)
\(140\) 0 0
\(141\) −78.0000 −0.553191
\(142\) 0 0
\(143\) 90.0000 + 90.0000i 0.629371 + 0.629371i
\(144\) 0 0
\(145\) 32.0000 24.0000i 0.220690 0.165517i
\(146\) 0 0
\(147\) 49.0000 49.0000i 0.333333 0.333333i
\(148\) 0 0
\(149\) 168.000i 1.12752i −0.825940 0.563758i \(-0.809355\pi\)
0.825940 0.563758i \(-0.190645\pi\)
\(150\) 0 0
\(151\) 130.000 0.860927 0.430464 0.902608i \(-0.358350\pi\)
0.430464 + 0.902608i \(0.358350\pi\)
\(152\) 0 0
\(153\) −7.00000 7.00000i −0.0457516 0.0457516i
\(154\) 0 0
\(155\) 42.0000 + 56.0000i 0.270968 + 0.361290i
\(156\) 0 0
\(157\) −63.0000 + 63.0000i −0.401274 + 0.401274i −0.878682 0.477408i \(-0.841576\pi\)
0.477408 + 0.878682i \(0.341576\pi\)
\(158\) 0 0
\(159\) 14.0000i 0.0880503i
\(160\) 0 0
\(161\) 322.000 2.00000
\(162\) 0 0
\(163\) 65.0000 + 65.0000i 0.398773 + 0.398773i 0.877800 0.479027i \(-0.159010\pi\)
−0.479027 + 0.877800i \(0.659010\pi\)
\(164\) 0 0
\(165\) 10.0000 70.0000i 0.0606061 0.424242i
\(166\) 0 0
\(167\) −103.000 + 103.000i −0.616766 + 0.616766i −0.944701 0.327934i \(-0.893648\pi\)
0.327934 + 0.944701i \(0.393648\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.0414201i
\(170\) 0 0
\(171\) 56.0000 0.327485
\(172\) 0 0
\(173\) 73.0000 + 73.0000i 0.421965 + 0.421965i 0.885880 0.463915i \(-0.153556\pi\)
−0.463915 + 0.885880i \(0.653556\pi\)
\(174\) 0 0
\(175\) −119.000 217.000i −0.680000 1.24000i
\(176\) 0 0
\(177\) −56.0000 + 56.0000i −0.316384 + 0.316384i
\(178\) 0 0
\(179\) 56.0000i 0.312849i −0.987690 0.156425i \(-0.950003\pi\)
0.987690 0.156425i \(-0.0499968\pi\)
\(180\) 0 0
\(181\) −70.0000 −0.386740 −0.193370 0.981126i \(-0.561942\pi\)
−0.193370 + 0.981126i \(0.561942\pi\)
\(182\) 0 0
\(183\) 42.0000 + 42.0000i 0.229508 + 0.229508i
\(184\) 0 0
\(185\) −231.000 33.0000i −1.24865 0.178378i
\(186\) 0 0
\(187\) 10.0000 10.0000i 0.0534759 0.0534759i
\(188\) 0 0
\(189\) 224.000i 1.18519i
\(190\) 0 0
\(191\) −142.000 −0.743455 −0.371728 0.928342i \(-0.621235\pi\)
−0.371728 + 0.928342i \(0.621235\pi\)
\(192\) 0 0
\(193\) −63.0000 63.0000i −0.326425 0.326425i 0.524800 0.851225i \(-0.324140\pi\)
−0.851225 + 0.524800i \(0.824140\pi\)
\(194\) 0 0
\(195\) 72.0000 54.0000i 0.369231 0.276923i
\(196\) 0 0
\(197\) −63.0000 + 63.0000i −0.319797 + 0.319797i −0.848689 0.528892i \(-0.822608\pi\)
0.528892 + 0.848689i \(0.322608\pi\)
\(198\) 0 0
\(199\) 336.000i 1.68844i −0.535995 0.844221i \(-0.680063\pi\)
0.535995 0.844221i \(-0.319937\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.0696517
\(202\) 0 0
\(203\) −56.0000 56.0000i −0.275862 0.275862i
\(204\) 0 0
\(205\) 42.0000 + 56.0000i 0.204878 + 0.273171i
\(206\) 0 0
\(207\) −161.000 + 161.000i −0.777778 + 0.777778i
\(208\) 0 0
\(209\) 80.0000i 0.382775i
\(210\) 0 0
\(211\) 314.000 1.48815 0.744076 0.668095i \(-0.232890\pi\)
0.744076 + 0.668095i \(0.232890\pi\)
\(212\) 0 0
\(213\) 98.0000 + 98.0000i 0.460094 + 0.460094i
\(214\) 0 0
\(215\) −15.0000 + 105.000i −0.0697674 + 0.488372i
\(216\) 0 0
\(217\) 98.0000 98.0000i 0.451613 0.451613i
\(218\) 0 0
\(219\) 98.0000i 0.447489i
\(220\) 0 0
\(221\) 18.0000 0.0814480
\(222\) 0 0
\(223\) −135.000 135.000i −0.605381 0.605381i 0.336354 0.941736i \(-0.390806\pi\)
−0.941736 + 0.336354i \(0.890806\pi\)
\(224\) 0 0
\(225\) 168.000 + 49.0000i 0.746667 + 0.217778i
\(226\) 0 0
\(227\) 281.000 281.000i 1.23789 1.23789i 0.277022 0.960864i \(-0.410653\pi\)
0.960864 0.277022i \(-0.0893474\pi\)
\(228\) 0 0
\(229\) 168.000i 0.733624i −0.930295 0.366812i \(-0.880449\pi\)
0.930295 0.366812i \(-0.119551\pi\)
\(230\) 0 0
\(231\) −140.000 −0.606061
\(232\) 0 0
\(233\) 273.000 + 273.000i 1.17167 + 1.17167i 0.981811 + 0.189863i \(0.0608045\pi\)
0.189863 + 0.981811i \(0.439196\pi\)
\(234\) 0 0
\(235\) 273.000 + 39.0000i 1.16170 + 0.165957i
\(236\) 0 0
\(237\) 96.0000 96.0000i 0.405063 0.405063i
\(238\) 0 0
\(239\) 288.000i 1.20502i 0.798111 + 0.602510i \(0.205833\pi\)
−0.798111 + 0.602510i \(0.794167\pi\)
\(240\) 0 0
\(241\) −446.000 −1.85062 −0.925311 0.379209i \(-0.876196\pi\)
−0.925311 + 0.379209i \(0.876196\pi\)
\(242\) 0 0
\(243\) −175.000 175.000i −0.720165 0.720165i
\(244\) 0 0
\(245\) −196.000 + 147.000i −0.800000 + 0.600000i
\(246\) 0 0
\(247\) −72.0000 + 72.0000i −0.291498 + 0.291498i
\(248\) 0 0
\(249\) 126.000i 0.506024i
\(250\) 0 0
\(251\) −150.000 −0.597610 −0.298805 0.954314i \(-0.596588\pi\)
−0.298805 + 0.954314i \(0.596588\pi\)
\(252\) 0 0
\(253\) −230.000 230.000i −0.909091 0.909091i
\(254\) 0 0
\(255\) −6.00000 8.00000i −0.0235294 0.0313725i
\(256\) 0 0
\(257\) 161.000 161.000i 0.626459 0.626459i −0.320716 0.947175i \(-0.603924\pi\)
0.947175 + 0.320716i \(0.103924\pi\)
\(258\) 0 0
\(259\) 462.000i 1.78378i
\(260\) 0 0
\(261\) 56.0000 0.214559
\(262\) 0 0
\(263\) −151.000 151.000i −0.574144 0.574144i 0.359139 0.933284i \(-0.383070\pi\)
−0.933284 + 0.359139i \(0.883070\pi\)
\(264\) 0 0
\(265\) −7.00000 + 49.0000i −0.0264151 + 0.184906i
\(266\) 0 0
\(267\) −112.000 + 112.000i −0.419476 + 0.419476i
\(268\) 0 0
\(269\) 376.000i 1.39777i −0.715234 0.698885i \(-0.753680\pi\)
0.715234 0.698885i \(-0.246320\pi\)
\(270\) 0 0
\(271\) 210.000 0.774908 0.387454 0.921889i \(-0.373355\pi\)
0.387454 + 0.921889i \(0.373355\pi\)
\(272\) 0 0
\(273\) −126.000 126.000i −0.461538 0.461538i
\(274\) 0 0
\(275\) −70.0000 + 240.000i −0.254545 + 0.872727i
\(276\) 0 0
\(277\) 129.000 129.000i 0.465704 0.465704i −0.434816 0.900520i \(-0.643186\pi\)
0.900520 + 0.434816i \(0.143186\pi\)
\(278\) 0 0
\(279\) 98.0000i 0.351254i
\(280\) 0 0
\(281\) −174.000 −0.619217 −0.309609 0.950864i \(-0.600198\pi\)
−0.309609 + 0.950864i \(0.600198\pi\)
\(282\) 0 0
\(283\) 113.000 + 113.000i 0.399293 + 0.399293i 0.877984 0.478690i \(-0.158888\pi\)
−0.478690 + 0.877984i \(0.658888\pi\)
\(284\) 0 0
\(285\) 56.0000 + 8.00000i 0.196491 + 0.0280702i
\(286\) 0 0
\(287\) 98.0000 98.0000i 0.341463 0.341463i
\(288\) 0 0
\(289\) 287.000i 0.993080i
\(290\) 0 0
\(291\) 66.0000 0.226804
\(292\) 0 0
\(293\) 345.000 + 345.000i 1.17747 + 1.17747i 0.980386 + 0.197089i \(0.0631487\pi\)
0.197089 + 0.980386i \(0.436851\pi\)
\(294\) 0 0
\(295\) 224.000 168.000i 0.759322 0.569492i
\(296\) 0 0
\(297\) 160.000 160.000i 0.538721 0.538721i
\(298\) 0 0
\(299\) 414.000i 1.38462i
\(300\) 0 0
\(301\) 210.000 0.697674
\(302\) 0 0
\(303\) 26.0000 + 26.0000i 0.0858086 + 0.0858086i
\(304\) 0 0
\(305\) −126.000 168.000i −0.413115 0.550820i
\(306\) 0 0
\(307\) −327.000 + 327.000i −1.06515 + 1.06515i −0.0674220 + 0.997725i \(0.521477\pi\)
−0.997725 + 0.0674220i \(0.978523\pi\)
\(308\) 0 0
\(309\) 146.000i 0.472492i
\(310\) 0 0
\(311\) 2.00000 0.00643087 0.00321543 0.999995i \(-0.498976\pi\)
0.00321543 + 0.999995i \(0.498976\pi\)
\(312\) 0 0
\(313\) 81.0000 + 81.0000i 0.258786 + 0.258786i 0.824560 0.565774i \(-0.191423\pi\)
−0.565774 + 0.824560i \(0.691423\pi\)
\(314\) 0 0
\(315\) 49.0000 343.000i 0.155556 1.08889i
\(316\) 0 0
\(317\) −159.000 + 159.000i −0.501577 + 0.501577i −0.911928 0.410351i \(-0.865406\pi\)
0.410351 + 0.911928i \(0.365406\pi\)
\(318\) 0 0
\(319\) 80.0000i 0.250784i
\(320\) 0 0
\(321\) 242.000 0.753894
\(322\) 0 0
\(323\) 8.00000 + 8.00000i 0.0247678 + 0.0247678i
\(324\) 0 0
\(325\) −279.000 + 153.000i −0.858462 + 0.470769i
\(326\) 0 0
\(327\) −136.000 + 136.000i −0.415902 + 0.415902i
\(328\) 0 0
\(329\) 546.000i 1.65957i
\(330\) 0 0
\(331\) −182.000 −0.549849 −0.274924 0.961466i \(-0.588653\pi\)
−0.274924 + 0.961466i \(0.588653\pi\)
\(332\) 0 0
\(333\) −231.000 231.000i −0.693694 0.693694i
\(334\) 0 0
\(335\) 49.0000 + 7.00000i 0.146269 + 0.0208955i
\(336\) 0 0
\(337\) −447.000 + 447.000i −1.32641 + 1.32641i −0.417930 + 0.908479i \(0.637244\pi\)
−0.908479 + 0.417930i \(0.862756\pi\)
\(338\) 0 0
\(339\) 254.000i 0.749263i
\(340\) 0 0
\(341\) −140.000 −0.410557
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −184.000 + 138.000i −0.533333 + 0.400000i
\(346\) 0 0
\(347\) 25.0000 25.0000i 0.0720461 0.0720461i −0.670166 0.742212i \(-0.733777\pi\)
0.742212 + 0.670166i \(0.233777\pi\)
\(348\) 0 0
\(349\) 200.000i 0.573066i 0.958070 + 0.286533i \(0.0925028\pi\)
−0.958070 + 0.286533i \(0.907497\pi\)
\(350\) 0 0
\(351\) 288.000 0.820513
\(352\) 0 0
\(353\) 321.000 + 321.000i 0.909348 + 0.909348i 0.996220 0.0868711i \(-0.0276868\pi\)
−0.0868711 + 0.996220i \(0.527687\pi\)
\(354\) 0 0
\(355\) −294.000 392.000i −0.828169 1.10423i
\(356\) 0 0
\(357\) −14.0000 + 14.0000i −0.0392157 + 0.0392157i
\(358\) 0 0
\(359\) 112.000i 0.311978i 0.987759 + 0.155989i \(0.0498564\pi\)
−0.987759 + 0.155989i \(0.950144\pi\)
\(360\) 0 0
\(361\) 297.000 0.822715
\(362\) 0 0
\(363\) −21.0000 21.0000i −0.0578512 0.0578512i
\(364\) 0 0
\(365\) 49.0000 343.000i 0.134247 0.939726i
\(366\) 0 0
\(367\) 377.000 377.000i 1.02725 1.02725i 0.0276297 0.999618i \(-0.491204\pi\)
0.999618 0.0276297i \(-0.00879594\pi\)
\(368\) 0 0
\(369\) 98.0000i 0.265583i
\(370\) 0 0
\(371\) 98.0000 0.264151
\(372\) 0 0
\(373\) 217.000 + 217.000i 0.581769 + 0.581769i 0.935389 0.353620i \(-0.115049\pi\)
−0.353620 + 0.935389i \(0.615049\pi\)
\(374\) 0 0
\(375\) 161.000 + 73.0000i 0.429333 + 0.194667i
\(376\) 0 0
\(377\) −72.0000 + 72.0000i −0.190981 + 0.190981i
\(378\) 0 0
\(379\) 56.0000i 0.147757i 0.997267 + 0.0738786i \(0.0235377\pi\)
−0.997267 + 0.0738786i \(0.976462\pi\)
\(380\) 0 0
\(381\) −14.0000 −0.0367454
\(382\) 0 0
\(383\) 57.0000 + 57.0000i 0.148825 + 0.148825i 0.777593 0.628768i \(-0.216440\pi\)
−0.628768 + 0.777593i \(0.716440\pi\)
\(384\) 0 0
\(385\) 490.000 + 70.0000i 1.27273 + 0.181818i
\(386\) 0 0
\(387\) −105.000 + 105.000i −0.271318 + 0.271318i
\(388\) 0 0
\(389\) 312.000i 0.802057i 0.916066 + 0.401028i \(0.131347\pi\)
−0.916066 + 0.401028i \(0.868653\pi\)
\(390\) 0 0
\(391\) −46.0000 −0.117647
\(392\) 0 0
\(393\) −230.000 230.000i −0.585242 0.585242i
\(394\) 0 0
\(395\) −384.000 + 288.000i −0.972152 + 0.729114i
\(396\) 0 0
\(397\) 193.000 193.000i 0.486146 0.486146i −0.420942 0.907088i \(-0.638300\pi\)
0.907088 + 0.420942i \(0.138300\pi\)
\(398\) 0 0
\(399\) 112.000i 0.280702i
\(400\) 0 0
\(401\) −30.0000 −0.0748130 −0.0374065 0.999300i \(-0.511910\pi\)
−0.0374065 + 0.999300i \(0.511910\pi\)
\(402\) 0 0
\(403\) −126.000 126.000i −0.312655 0.312655i
\(404\) 0 0
\(405\) 93.0000 + 124.000i 0.229630 + 0.306173i
\(406\) 0 0
\(407\) 330.000 330.000i 0.810811 0.810811i
\(408\) 0 0
\(409\) 432.000i 1.05623i −0.849171 0.528117i \(-0.822898\pi\)
0.849171 0.528117i \(-0.177102\pi\)
\(410\) 0 0
\(411\) −126.000 −0.306569
\(412\) 0 0
\(413\) −392.000 392.000i −0.949153 0.949153i
\(414\) 0 0
\(415\) −63.0000 + 441.000i −0.151807 + 1.06265i
\(416\) 0 0
\(417\) −88.0000 + 88.0000i −0.211031 + 0.211031i
\(418\) 0 0
\(419\) 168.000i 0.400955i 0.979698 + 0.200477i \(0.0642493\pi\)
−0.979698 + 0.200477i \(0.935751\pi\)
\(420\) 0 0
\(421\) −454.000 −1.07838 −0.539192 0.842183i \(-0.681270\pi\)
−0.539192 + 0.842183i \(0.681270\pi\)
\(422\) 0 0
\(423\) 273.000 + 273.000i 0.645390 + 0.645390i
\(424\) 0 0
\(425\) 17.0000 + 31.0000i 0.0400000 + 0.0729412i
\(426\) 0 0
\(427\) −294.000 + 294.000i −0.688525 + 0.688525i
\(428\) 0 0
\(429\) 180.000i 0.419580i
\(430\) 0 0
\(431\) −494.000 −1.14617 −0.573086 0.819495i \(-0.694254\pi\)
−0.573086 + 0.819495i \(0.694254\pi\)
\(432\) 0 0
\(433\) −511.000 511.000i −1.18014 1.18014i −0.979708 0.200431i \(-0.935766\pi\)
−0.200431 0.979708i \(-0.564234\pi\)
\(434\) 0 0
\(435\) 56.0000 + 8.00000i 0.128736 + 0.0183908i
\(436\) 0 0
\(437\) 184.000 184.000i 0.421053 0.421053i
\(438\) 0 0
\(439\) 176.000i 0.400911i −0.979703 0.200456i \(-0.935758\pi\)
0.979703 0.200456i \(-0.0642422\pi\)
\(440\) 0 0
\(441\) −343.000 −0.777778
\(442\) 0 0
\(443\) 177.000 + 177.000i 0.399549 + 0.399549i 0.878074 0.478525i \(-0.158828\pi\)
−0.478525 + 0.878074i \(0.658828\pi\)
\(444\) 0 0
\(445\) 448.000 336.000i 1.00674 0.755056i
\(446\) 0 0
\(447\) 168.000 168.000i 0.375839 0.375839i
\(448\) 0 0
\(449\) 608.000i 1.35412i 0.735928 + 0.677060i \(0.236746\pi\)
−0.735928 + 0.677060i \(0.763254\pi\)
\(450\) 0 0
\(451\) −140.000 −0.310421
\(452\) 0 0
\(453\) 130.000 + 130.000i 0.286976 + 0.286976i
\(454\) 0 0
\(455\) 378.000 + 504.000i 0.830769 + 1.10769i
\(456\) 0 0
\(457\) 609.000 609.000i 1.33260 1.33260i 0.429571 0.903033i \(-0.358665\pi\)
0.903033 0.429571i \(-0.141335\pi\)
\(458\) 0 0
\(459\) 32.0000i 0.0697168i
\(460\) 0 0
\(461\) 490.000 1.06291 0.531453 0.847088i \(-0.321646\pi\)
0.531453 + 0.847088i \(0.321646\pi\)
\(462\) 0 0
\(463\) −7.00000 7.00000i −0.0151188 0.0151188i 0.699507 0.714626i \(-0.253403\pi\)
−0.714626 + 0.699507i \(0.753403\pi\)
\(464\) 0 0
\(465\) −14.0000 + 98.0000i −0.0301075 + 0.210753i
\(466\) 0 0
\(467\) 25.0000 25.0000i 0.0535332 0.0535332i −0.679833 0.733367i \(-0.737948\pi\)
0.733367 + 0.679833i \(0.237948\pi\)
\(468\) 0 0
\(469\) 98.0000i 0.208955i
\(470\) 0 0
\(471\) −126.000 −0.267516
\(472\) 0 0
\(473\) −150.000 150.000i −0.317125 0.317125i
\(474\) 0 0
\(475\) −192.000 56.0000i −0.404211 0.117895i
\(476\) 0 0
\(477\) −49.0000 + 49.0000i −0.102725 + 0.102725i
\(478\) 0 0
\(479\) 128.000i 0.267223i 0.991034 + 0.133612i \(0.0426575\pi\)
−0.991034 + 0.133612i \(0.957343\pi\)
\(480\) 0 0
\(481\) 594.000 1.23493
\(482\) 0 0
\(483\) 322.000 + 322.000i 0.666667 + 0.666667i
\(484\) 0 0
\(485\) −231.000 33.0000i −0.476289 0.0680412i
\(486\) 0 0
\(487\) 249.000 249.000i 0.511294 0.511294i −0.403629 0.914923i \(-0.632251\pi\)
0.914923 + 0.403629i \(0.132251\pi\)
\(488\) 0 0
\(489\) 130.000i 0.265849i
\(490\) 0 0
\(491\) 650.000 1.32383 0.661914 0.749579i \(-0.269744\pi\)
0.661914 + 0.749579i \(0.269744\pi\)
\(492\) 0 0
\(493\) 8.00000 + 8.00000i 0.0162272 + 0.0162272i
\(494\) 0 0
\(495\) −280.000 + 210.000i −0.565657 + 0.424242i
\(496\) 0 0
\(497\) −686.000 + 686.000i −1.38028 + 1.38028i
\(498\) 0 0
\(499\) 632.000i 1.26653i −0.773934 0.633267i \(-0.781714\pi\)
0.773934 0.633267i \(-0.218286\pi\)
\(500\) 0 0
\(501\) −206.000 −0.411178
\(502\) 0 0
\(503\) −471.000 471.000i −0.936382 0.936382i 0.0617123 0.998094i \(-0.480344\pi\)
−0.998094 + 0.0617123i \(0.980344\pi\)
\(504\) 0 0
\(505\) −78.0000 104.000i −0.154455 0.205941i
\(506\) 0 0
\(507\) 7.00000 7.00000i 0.0138067 0.0138067i
\(508\) 0 0
\(509\) 8.00000i 0.0157171i 0.999969 + 0.00785855i \(0.00250148\pi\)
−0.999969 + 0.00785855i \(0.997499\pi\)
\(510\) 0 0
\(511\) −686.000 −1.34247
\(512\) 0 0
\(513\) 128.000 + 128.000i 0.249513 + 0.249513i
\(514\) 0 0
\(515\) 73.0000 511.000i 0.141748 0.992233i
\(516\) 0 0
\(517\) −390.000 + 390.000i −0.754352 + 0.754352i
\(518\) 0 0
\(519\) 146.000i 0.281310i
\(520\) 0 0
\(521\) −366.000 −0.702495 −0.351248 0.936283i \(-0.614242\pi\)
−0.351248 + 0.936283i \(0.614242\pi\)
\(522\) 0 0
\(523\) 273.000 + 273.000i 0.521989 + 0.521989i 0.918172 0.396183i \(-0.129665\pi\)
−0.396183 + 0.918172i \(0.629665\pi\)
\(524\) 0 0
\(525\) 98.0000 336.000i 0.186667 0.640000i
\(526\) 0 0
\(527\) −14.0000 + 14.0000i −0.0265655 + 0.0265655i
\(528\) 0 0
\(529\) 529.000i 1.00000i
\(530\) 0 0
\(531\) 392.000 0.738230
\(532\) 0 0
\(533\) −126.000 126.000i −0.236398 0.236398i
\(534\) 0 0
\(535\) −847.000 121.000i −1.58318 0.226168i
\(536\) 0 0
\(537\) 56.0000 56.0000i 0.104283 0.104283i
\(538\) 0 0
\(539\) 490.000i 0.909091i
\(540\) 0 0
\(541\) 394.000 0.728281 0.364140 0.931344i \(-0.381363\pi\)
0.364140 + 0.931344i \(0.381363\pi\)
\(542\) 0 0
\(543\) −70.0000 70.0000i −0.128913 0.128913i
\(544\) 0 0
\(545\) 544.000 408.000i 0.998165 0.748624i
\(546\) 0 0
\(547\) −231.000 + 231.000i −0.422303 + 0.422303i −0.885996 0.463693i \(-0.846524\pi\)
0.463693 + 0.885996i \(0.346524\pi\)
\(548\) 0 0
\(549\) 294.000i 0.535519i
\(550\) 0 0
\(551\) −64.0000 −0.116152
\(552\) 0 0
\(553\) 672.000 + 672.000i 1.21519 + 1.21519i
\(554\) 0 0
\(555\) −198.000 264.000i −0.356757 0.475676i
\(556\) 0 0
\(557\) −735.000 + 735.000i −1.31957 + 1.31957i −0.405453 + 0.914116i \(0.632886\pi\)
−0.914116 + 0.405453i \(0.867114\pi\)
\(558\) 0 0
\(559\) 270.000i 0.483005i
\(560\) 0 0
\(561\) 20.0000 0.0356506
\(562\) 0 0
\(563\) 609.000 + 609.000i 1.08171 + 1.08171i 0.996351 + 0.0853545i \(0.0272023\pi\)
0.0853545 + 0.996351i \(0.472798\pi\)
\(564\) 0 0
\(565\) −127.000 + 889.000i −0.224779 + 1.57345i
\(566\) 0 0
\(567\) 217.000 217.000i 0.382716 0.382716i
\(568\) 0 0
\(569\) 560.000i 0.984183i −0.870544 0.492091i \(-0.836233\pi\)
0.870544 0.492091i \(-0.163767\pi\)
\(570\) 0 0
\(571\) 938.000 1.64273 0.821366 0.570401i \(-0.193212\pi\)
0.821366 + 0.570401i \(0.193212\pi\)
\(572\) 0 0
\(573\) −142.000 142.000i −0.247818 0.247818i
\(574\) 0 0
\(575\) 713.000 391.000i 1.24000 0.680000i
\(576\) 0 0
\(577\) 97.0000 97.0000i 0.168111 0.168111i −0.618038 0.786149i \(-0.712072\pi\)
0.786149 + 0.618038i \(0.212072\pi\)
\(578\) 0 0
\(579\) 126.000i 0.217617i
\(580\) 0 0
\(581\) 882.000 1.51807
\(582\) 0 0
\(583\) −70.0000 70.0000i −0.120069 0.120069i
\(584\) 0 0
\(585\) −441.000 63.0000i −0.753846 0.107692i
\(586\) 0 0
\(587\) −39.0000 + 39.0000i −0.0664395 + 0.0664395i −0.739546 0.673106i \(-0.764960\pi\)
0.673106 + 0.739546i \(0.264960\pi\)
\(588\) 0 0
\(589\) 112.000i 0.190153i
\(590\) 0 0
\(591\) −126.000 −0.213198
\(592\) 0 0
\(593\) −479.000 479.000i −0.807757 0.807757i 0.176537 0.984294i \(-0.443511\pi\)
−0.984294 + 0.176537i \(0.943511\pi\)
\(594\) 0 0
\(595\) 56.0000 42.0000i 0.0941176 0.0705882i
\(596\) 0 0
\(597\) 336.000 336.000i 0.562814 0.562814i
\(598\) 0 0
\(599\) 1040.00i 1.73623i 0.496366 + 0.868114i \(0.334668\pi\)
−0.496366 + 0.868114i \(0.665332\pi\)
\(600\) 0 0
\(601\) −430.000 −0.715474 −0.357737 0.933822i \(-0.616452\pi\)
−0.357737 + 0.933822i \(0.616452\pi\)
\(602\) 0 0
\(603\) 49.0000 + 49.0000i 0.0812604 + 0.0812604i
\(604\) 0 0
\(605\) 63.0000 + 84.0000i 0.104132 + 0.138843i
\(606\) 0 0
\(607\) −423.000 + 423.000i −0.696870 + 0.696870i −0.963734 0.266864i \(-0.914012\pi\)
0.266864 + 0.963734i \(0.414012\pi\)
\(608\) 0 0
\(609\) 112.000i 0.183908i
\(610\) 0 0
\(611\) −702.000 −1.14894
\(612\) 0 0
\(613\) 249.000 + 249.000i 0.406199 + 0.406199i 0.880411 0.474212i \(-0.157267\pi\)
−0.474212 + 0.880411i \(0.657267\pi\)
\(614\) 0 0
\(615\) −14.0000 + 98.0000i −0.0227642 + 0.159350i
\(616\) 0 0
\(617\) 321.000 321.000i 0.520259 0.520259i −0.397390 0.917650i \(-0.630084\pi\)
0.917650 + 0.397390i \(0.130084\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i 0.874707 + 0.484653i \(0.161054\pi\)
−0.874707 + 0.484653i \(0.838946\pi\)
\(620\) 0 0
\(621\) −736.000 −1.18519
\(622\) 0 0
\(623\) −784.000 784.000i −1.25843 1.25843i
\(624\) 0 0
\(625\) −527.000 336.000i −0.843200 0.537600i
\(626\) 0 0
\(627\) −80.0000 + 80.0000i −0.127592 + 0.127592i
\(628\) 0 0
\(629\) 66.0000i 0.104928i
\(630\) 0 0
\(631\) −638.000 −1.01109 −0.505547 0.862799i \(-0.668709\pi\)
−0.505547 + 0.862799i \(0.668709\pi\)
\(632\) 0 0
\(633\) 314.000 + 314.000i 0.496051 + 0.496051i
\(634\) 0 0
\(635\) 49.0000 + 7.00000i 0.0771654 + 0.0110236i
\(636\) 0 0
\(637\) 441.000 441.000i 0.692308 0.692308i
\(638\) 0 0
\(639\) 686.000i 1.07355i
\(640\) 0 0
\(641\) 482.000 0.751950 0.375975 0.926630i \(-0.377308\pi\)
0.375975 + 0.926630i \(0.377308\pi\)
\(642\) 0 0
\(643\) 33.0000 + 33.0000i 0.0513219 + 0.0513219i 0.732302 0.680980i \(-0.238446\pi\)
−0.680980 + 0.732302i \(0.738446\pi\)
\(644\) 0 0
\(645\) −120.000 + 90.0000i −0.186047 + 0.139535i
\(646\) 0 0
\(647\) −7.00000 + 7.00000i −0.0108192 + 0.0108192i −0.712496 0.701677i \(-0.752435\pi\)
0.701677 + 0.712496i \(0.252435\pi\)
\(648\) 0 0
\(649\) 560.000i 0.862866i
\(650\) 0 0
\(651\) 196.000 0.301075
\(652\) 0 0
\(653\) −471.000 471.000i −0.721286 0.721286i 0.247581 0.968867i \(-0.420364\pi\)
−0.968867 + 0.247581i \(0.920364\pi\)
\(654\) 0 0
\(655\) 690.000 + 920.000i 1.05344 + 1.40458i
\(656\) 0 0
\(657\) 343.000 343.000i 0.522070 0.522070i
\(658\) 0 0
\(659\) 328.000i 0.497724i 0.968539 + 0.248862i \(0.0800565\pi\)
−0.968539 + 0.248862i \(0.919943\pi\)
\(660\) 0 0
\(661\) −742.000 −1.12254 −0.561271 0.827632i \(-0.689687\pi\)
−0.561271 + 0.827632i \(0.689687\pi\)
\(662\) 0 0
\(663\) 18.0000 + 18.0000i 0.0271493 + 0.0271493i
\(664\) 0 0
\(665\) −56.0000 + 392.000i −0.0842105 + 0.589474i
\(666\) 0 0
\(667\) 184.000 184.000i 0.275862 0.275862i
\(668\) 0 0
\(669\) 270.000i 0.403587i
\(670\) 0 0
\(671\) 420.000 0.625931
\(672\) 0 0
\(673\) −287.000 287.000i −0.426449 0.426449i 0.460968 0.887417i \(-0.347502\pi\)
−0.887417 + 0.460968i \(0.847502\pi\)
\(674\) 0 0
\(675\) 272.000 + 496.000i 0.402963 + 0.734815i
\(676\) 0 0
\(677\) 577.000 577.000i 0.852290 0.852290i −0.138125 0.990415i \(-0.544108\pi\)
0.990415 + 0.138125i \(0.0441077\pi\)
\(678\) 0 0
\(679\) 462.000i 0.680412i
\(680\) 0 0
\(681\) 562.000 0.825257
\(682\) 0 0
\(683\) −399.000 399.000i −0.584187 0.584187i 0.351864 0.936051i \(-0.385548\pi\)
−0.936051 + 0.351864i \(0.885548\pi\)
\(684\) 0 0
\(685\) 441.000 + 63.0000i 0.643796 + 0.0919708i
\(686\) 0 0
\(687\) 168.000 168.000i 0.244541 0.244541i
\(688\) 0 0
\(689\) 126.000i 0.182874i
\(690\) 0 0
\(691\) 378.000 0.547033 0.273517 0.961867i \(-0.411813\pi\)
0.273517 + 0.961867i \(0.411813\pi\)
\(692\) 0 0
\(693\) 490.000 + 490.000i 0.707071 + 0.707071i
\(694\) 0 0
\(695\) 352.000 264.000i 0.506475 0.379856i
\(696\) 0 0
\(697\) −14.0000 + 14.0000i −0.0200861 + 0.0200861i
\(698\) 0 0
\(699\) 546.000i 0.781116i
\(700\) 0 0
\(701\) −470.000 −0.670471 −0.335235 0.942134i \(-0.608816\pi\)
−0.335235 + 0.942134i \(0.608816\pi\)
\(702\) 0 0
\(703\) 264.000 + 264.000i 0.375533 + 0.375533i
\(704\) 0 0
\(705\) 234.000 + 312.000i 0.331915 + 0.442553i
\(706\) 0 0
\(707\) −182.000 + 182.000i −0.257426 + 0.257426i
\(708\) 0 0
\(709\) 1192.00i 1.68124i −0.541624 0.840621i \(-0.682190\pi\)
0.541624 0.840621i \(-0.317810\pi\)
\(710\) 0 0
\(711\) −672.000 −0.945148
\(712\) 0 0
\(713\) 322.000 + 322.000i 0.451613 + 0.451613i
\(714\) 0 0
\(715\) 90.0000 630.000i 0.125874 0.881119i
\(716\) 0 0
\(717\) −288.000 + 288.000i −0.401674 + 0.401674i
\(718\) 0 0
\(719\) 608.000i 0.845619i 0.906219 + 0.422809i \(0.138956\pi\)
−0.906219 + 0.422809i \(0.861044\pi\)
\(720\) 0 0
\(721\) −1022.00 −1.41748
\(722\) 0 0
\(723\) −446.000 446.000i −0.616874 0.616874i
\(724\) 0 0
\(725\) −192.000 56.0000i −0.264828 0.0772414i
\(726\) 0 0
\(727\) 441.000 441.000i 0.606602 0.606602i −0.335454 0.942057i \(-0.608890\pi\)
0.942057 + 0.335454i \(0.108890\pi\)
\(728\) 0 0
\(729\) 71.0000i 0.0973937i
\(730\) 0 0
\(731\) −30.0000 −0.0410397
\(732\) 0 0
\(733\) 361.000 + 361.000i 0.492497 + 0.492497i 0.909092 0.416595i \(-0.136777\pi\)
−0.416595 + 0.909092i \(0.636777\pi\)
\(734\) 0 0
\(735\) −343.000 49.0000i −0.466667 0.0666667i
\(736\) 0 0
\(737\) −70.0000 + 70.0000i −0.0949796 + 0.0949796i
\(738\) 0 0
\(739\) 920.000i 1.24493i −0.782649 0.622463i \(-0.786132\pi\)
0.782649 0.622463i \(-0.213868\pi\)
\(740\) 0 0
\(741\) −144.000 −0.194332
\(742\) 0 0
\(743\) −343.000 343.000i −0.461642 0.461642i 0.437551 0.899193i \(-0.355846\pi\)
−0.899193 + 0.437551i \(0.855846\pi\)
\(744\) 0 0
\(745\) −672.000 + 504.000i −0.902013 + 0.676510i
\(746\) 0 0
\(747\) −441.000 + 441.000i −0.590361 + 0.590361i
\(748\) 0 0
\(749\) 1694.00i 2.26168i
\(750\) 0 0
\(751\) 786.000 1.04660 0.523302 0.852147i \(-0.324700\pi\)
0.523302 + 0.852147i \(0.324700\pi\)
\(752\) 0 0
\(753\) −150.000 150.000i −0.199203 0.199203i
\(754\) 0 0
\(755\) −390.000 520.000i −0.516556 0.688742i
\(756\) 0 0
\(757\) −63.0000 + 63.0000i −0.0832232 + 0.0832232i −0.747493 0.664270i \(-0.768743\pi\)
0.664270 + 0.747493i \(0.268743\pi\)
\(758\) 0 0
\(759\) 460.000i 0.606061i
\(760\) 0 0
\(761\) −398.000 −0.522996 −0.261498 0.965204i \(-0.584216\pi\)
−0.261498 + 0.965204i \(0.584216\pi\)
\(762\) 0 0
\(763\) −952.000 952.000i −1.24771 1.24771i
\(764\) 0 0
\(765\) −7.00000 + 49.0000i −0.00915033 + 0.0640523i
\(766\) 0 0
\(767\) −504.000 + 504.000i −0.657106 + 0.657106i
\(768\) 0 0
\(769\) 704.000i 0.915475i −0.889087 0.457737i \(-0.848660\pi\)
0.889087 0.457737i \(-0.151340\pi\)
\(770\) 0 0
\(771\) 322.000 0.417639
\(772\) 0 0
\(773\) 825.000 + 825.000i 1.06727 + 1.06727i 0.997568 + 0.0697026i \(0.0222050\pi\)
0.0697026 + 0.997568i \(0.477795\pi\)
\(774\) 0 0
\(775\) 98.0000 336.000i 0.126452 0.433548i
\(776\) 0 0
\(777\) −462.000 + 462.000i −0.594595 + 0.594595i
\(778\) 0 0
\(779\) 112.000i 0.143774i
\(780\) 0 0
\(781\) 980.000 1.25480
\(782\) 0 0
\(783\) 128.000 + 128.000i 0.163474 + 0.163474i
\(784\) 0 0
\(785\) 441.000 + 63.0000i 0.561783 + 0.0802548i
\(786\) 0 0
\(787\) −71.0000 + 71.0000i −0.0902160 + 0.0902160i −0.750775 0.660559i \(-0.770320\pi\)
0.660559 + 0.750775i \(0.270320\pi\)
\(788\) 0 0
\(789\) 302.000i 0.382763i
\(790\) 0 0
\(791\) 1778.00 2.24779
\(792\) 0 0
\(793\) 378.000 + 378.000i 0.476671 + 0.476671i
\(794\) 0 0
\(795\) −56.0000 + 42.0000i −0.0704403 + 0.0528302i
\(796\) 0 0
\(797\) 33.0000 33.0000i 0.0414053 0.0414053i −0.686101 0.727506i \(-0.740679\pi\)
0.727506 + 0.686101i \(0.240679\pi\)
\(798\) 0 0
\(799\) 78.0000i 0.0976220i
\(800\) 0 0
\(801\) 784.000 0.978777
\(802\) 0 0
\(803\) 490.000 + 490.000i 0.610212 + 0.610212i
\(804\) 0 0
\(805\) −966.000 1288.00i −1.20000 1.60000i
\(806\) 0 0
\(807\) 376.000 376.000i 0.465923 0.465923i
\(808\) 0 0
\(809\) 368.000i