Properties

Label 3330.2.d.c.1999.2
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.c.1999.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(-2.00000 - 1.00000i) q^{10} +3.00000 q^{11} -4.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} +(1.00000 - 2.00000i) q^{20} +3.00000i q^{22} +8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +1.00000i q^{28} -3.00000 q^{29} -7.00000 q^{31} +1.00000i q^{32} +3.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +1.00000i q^{37} +(2.00000 + 1.00000i) q^{40} -11.0000 q^{41} +11.0000i q^{43} -3.00000 q^{44} -8.00000 q^{46} +4.00000i q^{47} +6.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +4.00000i q^{52} -11.0000i q^{53} +(-3.00000 + 6.00000i) q^{55} -1.00000 q^{56} -3.00000i q^{58} -12.0000 q^{59} -15.0000 q^{61} -7.00000i q^{62} -1.00000 q^{64} +(8.00000 + 4.00000i) q^{65} +4.00000i q^{67} +3.00000i q^{68} +(-1.00000 + 2.00000i) q^{70} -6.00000 q^{71} +2.00000i q^{73} -1.00000 q^{74} -3.00000i q^{77} +8.00000 q^{79} +(-1.00000 + 2.00000i) q^{80} -11.0000i q^{82} -12.0000i q^{83} +(6.00000 + 3.00000i) q^{85} -11.0000 q^{86} -3.00000i q^{88} -4.00000 q^{91} -8.00000i q^{92} -4.00000 q^{94} +1.00000i q^{97} +6.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 2 q^{5} - 4 q^{10} + 6 q^{11} + 2 q^{14} + 2 q^{16} + 2 q^{20} - 6 q^{25} + 8 q^{26} - 6 q^{29} - 14 q^{31} + 6 q^{34} + 4 q^{35} + 4 q^{40} - 22 q^{41} - 6 q^{44} - 16 q^{46} + 12 q^{49} + 8 q^{50} - 6 q^{55} - 2 q^{56} - 24 q^{59} - 30 q^{61} - 2 q^{64} + 16 q^{65} - 2 q^{70} - 12 q^{71} - 2 q^{74} + 16 q^{79} - 2 q^{80} + 12 q^{85} - 22 q^{86} - 8 q^{91} - 8 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 1.00000i 0.377964i −0.981981 0.188982i \(-0.939481\pi\)
0.981981 0.188982i \(-0.0605189\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000i 0.727607i −0.931476 0.363803i \(-0.881478\pi\)
0.931476 0.363803i \(-0.118522\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) 8.00000i 1.66812i 0.551677 + 0.834058i \(0.313988\pi\)
−0.551677 + 0.834058i \(0.686012\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 2.00000 + 1.00000i 0.338062 + 0.169031i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 0 0
\(39\) 0 0
\(40\) 2.00000 + 1.00000i 0.316228 + 0.158114i
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 0 0
\(43\) 11.0000i 1.67748i 0.544529 + 0.838742i \(0.316708\pi\)
−0.544529 + 0.838742i \(0.683292\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −8.00000 −1.17954
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 0 0
\(49\) 6.00000 0.857143
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 11.0000i 1.51097i −0.655168 0.755483i \(-0.727402\pi\)
0.655168 0.755483i \(-0.272598\pi\)
\(54\) 0 0
\(55\) −3.00000 + 6.00000i −0.404520 + 0.809040i
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 3.00000i 0.393919i
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −15.0000 −1.92055 −0.960277 0.279050i \(-0.909981\pi\)
−0.960277 + 0.279050i \(0.909981\pi\)
\(62\) 7.00000i 0.889001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.00000 + 4.00000i 0.992278 + 0.496139i
\(66\) 0 0
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 3.00000i 0.363803i
\(69\) 0 0
\(70\) −1.00000 + 2.00000i −0.119523 + 0.239046i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 0 0
\(77\) 3.00000i 0.341882i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) 0 0
\(82\) 11.0000i 1.21475i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 6.00000 + 3.00000i 0.650791 + 0.325396i
\(86\) −11.0000 −1.18616
\(87\) 0 0
\(88\) 3.00000i 0.319801i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 8.00000i 0.834058i
\(93\) 0 0
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) 0 0
\(97\) 1.00000i 0.101535i 0.998711 + 0.0507673i \(0.0161667\pi\)
−0.998711 + 0.0507673i \(0.983833\pi\)
\(98\) 6.00000i 0.606092i
\(99\) 0 0
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 11.0000 1.06841
\(107\) 10.0000i 0.966736i −0.875417 0.483368i \(-0.839413\pi\)
0.875417 0.483368i \(-0.160587\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) −6.00000 3.00000i −0.572078 0.286039i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 1.00000i 0.0940721i 0.998893 + 0.0470360i \(0.0149776\pi\)
−0.998893 + 0.0470360i \(0.985022\pi\)
\(114\) 0 0
\(115\) −16.0000 8.00000i −1.49201 0.746004i
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) 12.0000i 1.10469i
\(119\) −3.00000 −0.275010
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 15.0000i 1.35804i
\(123\) 0 0
\(124\) 7.00000 0.628619
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 16.0000i 1.41977i −0.704317 0.709885i \(-0.748747\pi\)
0.704317 0.709885i \(-0.251253\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −4.00000 + 8.00000i −0.350823 + 0.701646i
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) −1.00000 −0.0848189 −0.0424094 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) −2.00000 1.00000i −0.169031 0.0845154i
\(141\) 0 0
\(142\) 6.00000i 0.503509i
\(143\) 12.0000i 1.00349i
\(144\) 0 0
\(145\) 3.00000 6.00000i 0.249136 0.498273i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 0 0
\(151\) −14.0000 −1.13930 −0.569652 0.821886i \(-0.692922\pi\)
−0.569652 + 0.821886i \(0.692922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 3.00000 0.241747
\(155\) 7.00000 14.0000i 0.562254 1.12451i
\(156\) 0 0
\(157\) 5.00000i 0.399043i 0.979893 + 0.199522i \(0.0639388\pi\)
−0.979893 + 0.199522i \(0.936061\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 0 0
\(160\) −2.00000 1.00000i −0.158114 0.0790569i
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 3.00000i 0.234978i 0.993074 + 0.117489i \(0.0374845\pi\)
−0.993074 + 0.117489i \(0.962515\pi\)
\(164\) 11.0000 0.858956
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 14.0000i 1.08335i −0.840587 0.541676i \(-0.817790\pi\)
0.840587 0.541676i \(-0.182210\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) −3.00000 + 6.00000i −0.230089 + 0.460179i
\(171\) 0 0
\(172\) 11.0000i 0.838742i
\(173\) 13.0000i 0.988372i 0.869356 + 0.494186i \(0.164534\pi\)
−0.869356 + 0.494186i \(0.835466\pi\)
\(174\) 0 0
\(175\) −4.00000 + 3.00000i −0.302372 + 0.226779i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) −2.00000 1.00000i −0.147043 0.0735215i
\(186\) 0 0
\(187\) 9.00000i 0.658145i
\(188\) 4.00000i 0.291730i
\(189\) 0 0
\(190\) 0 0
\(191\) 17.0000 1.23008 0.615038 0.788497i \(-0.289140\pi\)
0.615038 + 0.788497i \(0.289140\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) 0 0
\(202\) 14.0000i 0.985037i
\(203\) 3.00000i 0.210559i
\(204\) 0 0
\(205\) 11.0000 22.0000i 0.768273 1.53655i
\(206\) 0 0
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 11.0000i 0.755483i
\(213\) 0 0
\(214\) 10.0000 0.683586
\(215\) −22.0000 11.0000i −1.50039 0.750194i
\(216\) 0 0
\(217\) 7.00000i 0.475191i
\(218\) 11.0000i 0.745014i
\(219\) 0 0
\(220\) 3.00000 6.00000i 0.202260 0.404520i
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 11.0000i 0.736614i 0.929704 + 0.368307i \(0.120063\pi\)
−0.929704 + 0.368307i \(0.879937\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −1.00000 −0.0665190
\(227\) 17.0000i 1.12833i 0.825662 + 0.564165i \(0.190802\pi\)
−0.825662 + 0.564165i \(0.809198\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 8.00000 16.0000i 0.527504 1.05501i
\(231\) 0 0
\(232\) 3.00000i 0.196960i
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 0 0
\(235\) −8.00000 4.00000i −0.521862 0.260931i
\(236\) 12.0000 0.781133
\(237\) 0 0
\(238\) 3.00000i 0.194461i
\(239\) −17.0000 −1.09964 −0.549819 0.835284i \(-0.685303\pi\)
−0.549819 + 0.835284i \(0.685303\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 15.0000 0.960277
\(245\) −6.00000 + 12.0000i −0.383326 + 0.766652i
\(246\) 0 0
\(247\) 0 0
\(248\) 7.00000i 0.444500i
\(249\) 0 0
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 24.0000i 1.50887i
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) −8.00000 4.00000i −0.496139 0.248069i
\(261\) 0 0
\(262\) 10.0000i 0.617802i
\(263\) 31.0000i 1.91154i −0.294112 0.955771i \(-0.595024\pi\)
0.294112 0.955771i \(-0.404976\pi\)
\(264\) 0 0
\(265\) 22.0000 + 11.0000i 1.35145 + 0.675725i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) −16.0000 −0.975537 −0.487769 0.872973i \(-0.662189\pi\)
−0.487769 + 0.872973i \(0.662189\pi\)
\(270\) 0 0
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 3.00000i 0.181902i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −9.00000 12.0000i −0.542720 0.723627i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 1.00000i 0.0599760i
\(279\) 0 0
\(280\) 1.00000 2.00000i 0.0597614 0.119523i
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 8.00000i 0.475551i −0.971320 0.237775i \(-0.923582\pi\)
0.971320 0.237775i \(-0.0764182\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 11.0000i 0.649309i
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 6.00000 + 3.00000i 0.352332 + 0.176166i
\(291\) 0 0
\(292\) 2.00000i 0.117041i
\(293\) 15.0000i 0.876309i 0.898900 + 0.438155i \(0.144368\pi\)
−0.898900 + 0.438155i \(0.855632\pi\)
\(294\) 0 0
\(295\) 12.0000 24.0000i 0.698667 1.39733i
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) 4.00000i 0.231714i
\(299\) 32.0000 1.85061
\(300\) 0 0
\(301\) 11.0000 0.634029
\(302\) 14.0000i 0.805609i
\(303\) 0 0
\(304\) 0 0
\(305\) 15.0000 30.0000i 0.858898 1.71780i
\(306\) 0 0
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) 3.00000i 0.170941i
\(309\) 0 0
\(310\) 14.0000 + 7.00000i 0.795147 + 0.397573i
\(311\) −3.00000 −0.170114 −0.0850572 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 0 0
\(313\) 14.0000i 0.791327i −0.918396 0.395663i \(-0.870515\pi\)
0.918396 0.395663i \(-0.129485\pi\)
\(314\) −5.00000 −0.282166
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 21.0000i 1.17948i −0.807594 0.589739i \(-0.799231\pi\)
0.807594 0.589739i \(-0.200769\pi\)
\(318\) 0 0
\(319\) −9.00000 −0.503903
\(320\) 1.00000 2.00000i 0.0559017 0.111803i
\(321\) 0 0
\(322\) 8.00000i 0.445823i
\(323\) 0 0
\(324\) 0 0
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) −3.00000 −0.166155
\(327\) 0 0
\(328\) 11.0000i 0.607373i
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) 2.00000 0.109930 0.0549650 0.998488i \(-0.482495\pi\)
0.0549650 + 0.998488i \(0.482495\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 0 0
\(334\) 14.0000 0.766046
\(335\) −8.00000 4.00000i −0.437087 0.218543i
\(336\) 0 0
\(337\) 28.0000i 1.52526i 0.646837 + 0.762629i \(0.276092\pi\)
−0.646837 + 0.762629i \(0.723908\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 0 0
\(340\) −6.00000 3.00000i −0.325396 0.162698i
\(341\) −21.0000 −1.13721
\(342\) 0 0
\(343\) 13.0000i 0.701934i
\(344\) 11.0000 0.593080
\(345\) 0 0
\(346\) −13.0000 −0.698884
\(347\) 12.0000i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) −3.00000 4.00000i −0.160357 0.213809i
\(351\) 0 0
\(352\) 3.00000i 0.159901i
\(353\) 3.00000i 0.159674i 0.996808 + 0.0798369i \(0.0254400\pi\)
−0.996808 + 0.0798369i \(0.974560\pi\)
\(354\) 0 0
\(355\) 6.00000 12.0000i 0.318447 0.636894i
\(356\) 0 0
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) −14.0000 −0.738892 −0.369446 0.929252i \(-0.620452\pi\)
−0.369446 + 0.929252i \(0.620452\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 16.0000i 0.840941i
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) −4.00000 2.00000i −0.209370 0.104685i
\(366\) 0 0
\(367\) 13.0000i 0.678594i −0.940679 0.339297i \(-0.889811\pi\)
0.940679 0.339297i \(-0.110189\pi\)
\(368\) 8.00000i 0.417029i
\(369\) 0 0
\(370\) 1.00000 2.00000i 0.0519875 0.103975i
\(371\) −11.0000 −0.571092
\(372\) 0 0
\(373\) 38.0000i 1.96757i 0.179364 + 0.983783i \(0.442596\pi\)
−0.179364 + 0.983783i \(0.557404\pi\)
\(374\) 9.00000 0.465379
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 17.0000i 0.869796i
\(383\) 16.0000i 0.817562i 0.912633 + 0.408781i \(0.134046\pi\)
−0.912633 + 0.408781i \(0.865954\pi\)
\(384\) 0 0
\(385\) 6.00000 + 3.00000i 0.305788 + 0.152894i
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 1.00000i 0.0507673i
\(389\) 23.0000 1.16615 0.583073 0.812420i \(-0.301850\pi\)
0.583073 + 0.812420i \(0.301850\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 6.00000i 0.303046i
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) −8.00000 + 16.0000i −0.402524 + 0.805047i
\(396\) 0 0
\(397\) 14.0000i 0.702640i −0.936255 0.351320i \(-0.885733\pi\)
0.936255 0.351320i \(-0.114267\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 0 0
\(403\) 28.0000i 1.39478i
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 4.00000 0.197787 0.0988936 0.995098i \(-0.468470\pi\)
0.0988936 + 0.995098i \(0.468470\pi\)
\(410\) 22.0000 + 11.0000i 1.08650 + 0.543251i
\(411\) 0 0
\(412\) 0 0
\(413\) 12.0000i 0.590481i
\(414\) 0 0
\(415\) 24.0000 + 12.0000i 1.17811 + 0.589057i
\(416\) 4.00000 0.196116
\(417\) 0 0
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 1.00000i 0.0486792i
\(423\) 0 0
\(424\) −11.0000 −0.534207
\(425\) −12.0000 + 9.00000i −0.582086 + 0.436564i
\(426\) 0 0
\(427\) 15.0000i 0.725901i
\(428\) 10.0000i 0.483368i
\(429\) 0 0
\(430\) 11.0000 22.0000i 0.530467 1.06093i
\(431\) −23.0000 −1.10787 −0.553936 0.832560i \(-0.686875\pi\)
−0.553936 + 0.832560i \(0.686875\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.768911i −0.923144 0.384455i \(-0.874389\pi\)
0.923144 0.384455i \(-0.125611\pi\)
\(434\) −7.00000 −0.336011
\(435\) 0 0
\(436\) −11.0000 −0.526804
\(437\) 0 0
\(438\) 0 0
\(439\) −7.00000 −0.334092 −0.167046 0.985949i \(-0.553423\pi\)
−0.167046 + 0.985949i \(0.553423\pi\)
\(440\) 6.00000 + 3.00000i 0.286039 + 0.143019i
\(441\) 0 0
\(442\) 12.0000i 0.570782i
\(443\) 34.0000i 1.61539i −0.589601 0.807694i \(-0.700715\pi\)
0.589601 0.807694i \(-0.299285\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.0000 −0.520865
\(447\) 0 0
\(448\) 1.00000i 0.0472456i
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) −33.0000 −1.55391
\(452\) 1.00000i 0.0470360i
\(453\) 0 0
\(454\) −17.0000 −0.797850
\(455\) 4.00000 8.00000i 0.187523 0.375046i
\(456\) 0 0
\(457\) 37.0000i 1.73079i 0.501093 + 0.865393i \(0.332931\pi\)
−0.501093 + 0.865393i \(0.667069\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 0 0
\(460\) 16.0000 + 8.00000i 0.746004 + 0.373002i
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 3.00000i 0.138823i 0.997588 + 0.0694117i \(0.0221122\pi\)
−0.997588 + 0.0694117i \(0.977888\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 4.00000 8.00000i 0.184506 0.369012i
\(471\) 0 0
\(472\) 12.0000i 0.552345i
\(473\) 33.0000i 1.51734i
\(474\) 0 0
\(475\) 0 0
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) 17.0000i 0.777562i
\(479\) −36.0000 −1.64488 −0.822441 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 14.0000i 0.637683i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) −2.00000 1.00000i −0.0908153 0.0454077i
\(486\) 0 0
\(487\) 36.0000i 1.63132i −0.578535 0.815658i \(-0.696375\pi\)
0.578535 0.815658i \(-0.303625\pi\)
\(488\) 15.0000i 0.679018i
\(489\) 0 0
\(490\) −12.0000 6.00000i −0.542105 0.271052i
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 9.00000i 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) 6.00000i 0.269137i
\(498\) 0 0
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) −11.0000 + 2.00000i −0.491935 + 0.0894427i
\(501\) 0 0
\(502\) 20.0000i 0.892644i
\(503\) 26.0000i 1.15928i 0.814872 + 0.579641i \(0.196807\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(504\) 0 0
\(505\) 14.0000 28.0000i 0.622992 1.24598i
\(506\) −24.0000 −1.06693
\(507\) 0 0
\(508\) 16.0000i 0.709885i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) 12.0000i 0.527759i
\(518\) 1.00000i 0.0439375i
\(519\) 0 0
\(520\) 4.00000 8.00000i 0.175412 0.350823i
\(521\) 7.00000 0.306676 0.153338 0.988174i \(-0.450998\pi\)
0.153338 + 0.988174i \(0.450998\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) −10.0000 −0.436852
\(525\) 0 0
\(526\) 31.0000 1.35166
\(527\) 21.0000i 0.914774i
\(528\) 0 0
\(529\) −41.0000 −1.78261
\(530\) −11.0000 + 22.0000i −0.477809 + 0.955619i
\(531\) 0 0
\(532\) 0 0
\(533\) 44.0000i 1.90585i
\(534\) 0 0
\(535\) 20.0000 + 10.0000i 0.864675 + 0.432338i
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) 16.0000i 0.689809i
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 26.0000 1.11783 0.558914 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 22.0000i 0.944981i
\(543\) 0 0
\(544\) 3.00000 0.128624
\(545\) −11.0000 + 22.0000i −0.471188 + 0.942376i
\(546\) 0 0
\(547\) 35.0000i 1.49649i −0.663421 0.748246i \(-0.730896\pi\)
0.663421 0.748246i \(-0.269104\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 0 0
\(550\) 12.0000 9.00000i 0.511682 0.383761i
\(551\) 0 0
\(552\) 0 0
\(553\) 8.00000i 0.340195i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.00000 0.0424094
\(557\) 6.00000i 0.254228i −0.991888 0.127114i \(-0.959429\pi\)
0.991888 0.127114i \(-0.0405714\pi\)
\(558\) 0 0
\(559\) 44.0000 1.86100
\(560\) 2.00000 + 1.00000i 0.0845154 + 0.0422577i
\(561\) 0 0
\(562\) 6.00000i 0.253095i
\(563\) 19.0000i 0.800755i 0.916350 + 0.400377i \(0.131121\pi\)
−0.916350 + 0.400377i \(0.868879\pi\)
\(564\) 0 0
\(565\) −2.00000 1.00000i −0.0841406 0.0420703i
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 14.0000 0.586911 0.293455 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 0 0
\(574\) −11.0000 −0.459131
\(575\) 32.0000 24.0000i 1.33449 1.00087i
\(576\) 0 0
\(577\) 2.00000i 0.0832611i 0.999133 + 0.0416305i \(0.0132552\pi\)
−0.999133 + 0.0416305i \(0.986745\pi\)
\(578\) 8.00000i 0.332756i
\(579\) 0 0
\(580\) −3.00000 + 6.00000i −0.124568 + 0.249136i
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 33.0000i 1.36672i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −15.0000 −0.619644
\(587\) 15.0000i 0.619116i 0.950881 + 0.309558i \(0.100181\pi\)
−0.950881 + 0.309558i \(0.899819\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 24.0000 + 12.0000i 0.988064 + 0.494032i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 36.0000i 1.47834i 0.673517 + 0.739171i \(0.264783\pi\)
−0.673517 + 0.739171i \(0.735217\pi\)
\(594\) 0 0
\(595\) 3.00000 6.00000i 0.122988 0.245976i
\(596\) 4.00000 0.163846
\(597\) 0 0
\(598\) 32.0000i 1.30858i
\(599\) −32.0000 −1.30748 −0.653742 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) −47.0000 −1.91717 −0.958585 0.284807i \(-0.908071\pi\)
−0.958585 + 0.284807i \(0.908071\pi\)
\(602\) 11.0000i 0.448327i
\(603\) 0 0
\(604\) 14.0000 0.569652
\(605\) 2.00000 4.00000i 0.0813116 0.162623i
\(606\) 0 0
\(607\) 42.0000i 1.70473i 0.522949 + 0.852364i \(0.324832\pi\)
−0.522949 + 0.852364i \(0.675168\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 30.0000 + 15.0000i 1.21466 + 0.607332i
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) 15.0000i 0.605844i −0.953015 0.302922i \(-0.902038\pi\)
0.953015 0.302922i \(-0.0979622\pi\)
\(614\) −8.00000 −0.322854
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) 42.0000i 1.69086i −0.534089 0.845428i \(-0.679345\pi\)
0.534089 0.845428i \(-0.320655\pi\)
\(618\) 0 0
\(619\) 35.0000 1.40677 0.703384 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) −7.00000 + 14.0000i −0.281127 + 0.562254i
\(621\) 0 0
\(622\) 3.00000i 0.120289i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) 5.00000i 0.199522i
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 0 0
\(634\) 21.0000 0.834017
\(635\) 32.0000 + 16.0000i 1.26988 + 0.634941i
\(636\) 0 0
\(637\) 24.0000i 0.950915i
\(638\) 9.00000i 0.356313i
\(639\) 0 0
\(640\) 2.00000 + 1.00000i 0.0790569 + 0.0395285i
\(641\) 25.0000 0.987441 0.493720 0.869621i \(-0.335637\pi\)
0.493720 + 0.869621i \(0.335637\pi\)
\(642\) 0 0
\(643\) 7.00000i 0.276053i 0.990429 + 0.138027i \(0.0440759\pi\)
−0.990429 + 0.138027i \(0.955924\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) 0 0
\(647\) 2.00000i 0.0786281i 0.999227 + 0.0393141i \(0.0125173\pi\)
−0.999227 + 0.0393141i \(0.987483\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) −12.0000 16.0000i −0.470679 0.627572i
\(651\) 0 0
\(652\) 3.00000i 0.117489i
\(653\) 38.0000i 1.48705i −0.668705 0.743527i \(-0.733151\pi\)
0.668705 0.743527i \(-0.266849\pi\)
\(654\) 0 0
\(655\) −10.0000 + 20.0000i −0.390732 + 0.781465i
\(656\) −11.0000 −0.429478
\(657\) 0 0
\(658\) 4.00000i 0.155936i
\(659\) 48.0000 1.86981 0.934907 0.354892i \(-0.115482\pi\)
0.934907 + 0.354892i \(0.115482\pi\)
\(660\) 0 0
\(661\) −25.0000 −0.972387 −0.486194 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) 2.00000i 0.0777322i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0000i 0.929284i
\(668\) 14.0000i 0.541676i
\(669\) 0 0
\(670\) 4.00000 8.00000i 0.154533 0.309067i
\(671\) −45.0000 −1.73721
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −28.0000 −1.07852
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 42.0000i 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 0 0
\(679\) 1.00000 0.0383765
\(680\) 3.00000 6.00000i 0.115045 0.230089i
\(681\) 0 0
\(682\) 21.0000i 0.804132i
\(683\) 13.0000i 0.497431i −0.968577 0.248716i \(-0.919992\pi\)
0.968577 0.248716i \(-0.0800084\pi\)
\(684\) 0 0
\(685\) −12.0000 6.00000i −0.458496 0.229248i
\(686\) 13.0000 0.496342
\(687\) 0 0
\(688\) 11.0000i 0.419371i
\(689\) −44.0000 −1.67627
\(690\) 0 0
\(691\) −41.0000 −1.55971 −0.779857 0.625958i \(-0.784708\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 13.0000i 0.494186i
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 1.00000 2.00000i 0.0379322 0.0758643i
\(696\) 0 0
\(697\) 33.0000i 1.24996i
\(698\) 6.00000i 0.227103i
\(699\) 0 0
\(700\) 4.00000 3.00000i 0.151186 0.113389i
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) −3.00000 −0.112906
\(707\) 14.0000i 0.526524i
\(708\) 0 0
\(709\) −29.0000 −1.08912 −0.544559 0.838723i \(-0.683303\pi\)
−0.544559 + 0.838723i \(0.683303\pi\)
\(710\) 12.0000 + 6.00000i 0.450352 + 0.225176i
\(711\) 0 0
\(712\) 0 0
\(713\) 56.0000i 2.09722i
\(714\) 0 0
\(715\) 24.0000 + 12.0000i 0.897549 + 0.448775i
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) 14.0000i 0.522475i
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 19.0000i 0.707107i
\(723\) 0 0
\(724\) 16.0000 0.594635
\(725\) 9.00000 + 12.0000i 0.334252 + 0.445669i
\(726\) 0 0
\(727\) 14.0000i 0.519231i 0.965712 + 0.259616i \(0.0835959\pi\)
−0.965712 + 0.259616i \(0.916404\pi\)
\(728\) 4.00000i 0.148250i
\(729\) 0 0
\(730\) 2.00000 4.00000i 0.0740233 0.148047i
\(731\) 33.0000 1.22055
\(732\) 0 0
\(733\) 1.00000i 0.0369358i 0.999829 + 0.0184679i \(0.00587886\pi\)
−0.999829 + 0.0184679i \(0.994121\pi\)
\(734\) 13.0000 0.479839
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 12.0000i 0.442026i
\(738\) 0 0
\(739\) 15.0000 0.551784 0.275892 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(740\) 2.00000 + 1.00000i 0.0735215 + 0.0367607i
\(741\) 0 0
\(742\) 11.0000i 0.403823i
\(743\) 13.0000i 0.476924i 0.971152 + 0.238462i \(0.0766432\pi\)
−0.971152 + 0.238462i \(0.923357\pi\)
\(744\) 0 0
\(745\) 4.00000 8.00000i 0.146549 0.293097i
\(746\) −38.0000 −1.39128
\(747\) 0 0
\(748\) 9.00000i 0.329073i
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 4.00000i 0.145865i
\(753\) 0 0
\(754\) −12.0000 −0.437014
\(755\) 14.0000 28.0000i 0.509512 1.01902i
\(756\) 0 0
\(757\) 28.0000i 1.01768i 0.860862 + 0.508839i \(0.169925\pi\)
−0.860862 + 0.508839i \(0.830075\pi\)
\(758\) 12.0000i 0.435860i
\(759\) 0 0
\(760\) 0 0
\(761\) −7.00000 −0.253750 −0.126875 0.991919i \(-0.540495\pi\)
−0.126875 + 0.991919i \(0.540495\pi\)
\(762\) 0 0
\(763\) 11.0000i 0.398227i
\(764\) −17.0000 −0.615038
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 48.0000i 1.73318i
\(768\) 0 0
\(769\) 44.0000 1.58668 0.793340 0.608778i \(-0.208340\pi\)
0.793340 + 0.608778i \(0.208340\pi\)
\(770\) −3.00000 + 6.00000i −0.108112 + 0.216225i
\(771\) 0 0
\(772\) 14.0000i 0.503871i
\(773\) 51.0000i 1.83434i 0.398493 + 0.917171i \(0.369533\pi\)
−0.398493 + 0.917171i \(0.630467\pi\)
\(774\) 0 0
\(775\) 21.0000 + 28.0000i 0.754342 + 1.00579i
\(776\) 1.00000 0.0358979
\(777\) 0 0
\(778\) 23.0000i 0.824590i
\(779\) 0 0
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 24.0000i 0.858238i
\(783\) 0 0
\(784\) 6.00000 0.214286
\(785\) −10.0000 5.00000i −0.356915 0.178458i
\(786\) 0 0
\(787\) 22.0000i 0.784215i −0.919919 0.392108i \(-0.871746\pi\)
0.919919 0.392108i \(-0.128254\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 0 0
\(790\) −16.0000 8.00000i −0.569254 0.284627i
\(791\) 1.00000 0.0355559
\(792\) 0 0
\(793\) 60.0000i 2.13066i
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 12.0000i