Properties

Label 1134.2.d.a.1133.4
Level $1134$
Weight $2$
Character 1134.1133
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1133.4
Root \(-0.0967785 - 1.72934i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.a.1133.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} -0.366598 q^{5} +(-1.91449 + 1.82612i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} -0.366598 q^{5} +(-1.91449 + 1.82612i) q^{7} +1.00000i q^{8} +0.366598i q^{10} -0.669453i q^{11} +1.00156i q^{13} +(1.82612 + 1.91449i) q^{14} +1.00000 q^{16} +4.98906 q^{17} -6.35722i q^{19} +0.366598 q^{20} -0.669453 q^{22} -7.69459i q^{23} -4.86561 q^{25} +1.00156 q^{26} +(1.91449 - 1.82612i) q^{28} -1.82898i q^{29} -6.32588i q^{31} -1.00000i q^{32} -4.98906i q^{34} +(0.701849 - 0.669453i) q^{35} -5.16789 q^{37} -6.35722 q^{38} -0.366598i q^{40} -4.31856 q^{41} -4.49843 q^{43} +0.669453i q^{44} -7.69459 q^{46} +8.32901 q^{47} +(0.330547 - 6.99219i) q^{49} +4.86561i q^{50} -1.00156i q^{52} +0.245420i q^{55} +(-1.82612 - 1.91449i) q^{56} -1.82898 q^{58} +8.72695 q^{59} -4.95771i q^{61} -6.32588 q^{62} -1.00000 q^{64} -0.367172i q^{65} -10.8907 q^{67} -4.98906 q^{68} +(-0.669453 - 0.701849i) q^{70} -5.49843i q^{71} +4.07314i q^{73} +5.16789i q^{74} +6.35722i q^{76} +(1.22250 + 1.28166i) q^{77} +8.35568 q^{79} -0.366598 q^{80} +4.31856i q^{82} +17.0142 q^{83} -1.82898 q^{85} +4.49843i q^{86} +0.669453 q^{88} -10.7113 q^{89} +(-1.82898 - 1.91749i) q^{91} +7.69459i q^{92} -8.32901i q^{94} +2.33055i q^{95} -17.2157i q^{97} +(-6.99219 - 0.330547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 4 q^{7} + O(q^{10}) \) \( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(5\) −0.366598 −0.163948 −0.0819738 0.996634i \(-0.526122\pi\)
−0.0819738 + 0.996634i \(0.526122\pi\)
\(6\) 0 0
\(7\) −1.91449 + 1.82612i −0.723609 + 0.690210i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.366598i 0.115929i
\(11\) 0.669453i 0.201848i −0.994894 0.100924i \(-0.967820\pi\)
0.994894 0.100924i \(-0.0321799\pi\)
\(12\) 0 0
\(13\) 1.00156i 0.277784i 0.990308 + 0.138892i \(0.0443541\pi\)
−0.990308 + 0.138892i \(0.955646\pi\)
\(14\) 1.82612 + 1.91449i 0.488052 + 0.511669i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.98906 1.21003 0.605013 0.796216i \(-0.293168\pi\)
0.605013 + 0.796216i \(0.293168\pi\)
\(18\) 0 0
\(19\) 6.35722i 1.45845i −0.684275 0.729224i \(-0.739881\pi\)
0.684275 0.729224i \(-0.260119\pi\)
\(20\) 0.366598 0.0819738
\(21\) 0 0
\(22\) −0.669453 −0.142728
\(23\) 7.69459i 1.60443i −0.597034 0.802216i \(-0.703654\pi\)
0.597034 0.802216i \(-0.296346\pi\)
\(24\) 0 0
\(25\) −4.86561 −0.973121
\(26\) 1.00156 0.196423
\(27\) 0 0
\(28\) 1.91449 1.82612i 0.361805 0.345105i
\(29\) 1.82898i 0.339633i −0.985476 0.169817i \(-0.945682\pi\)
0.985476 0.169817i \(-0.0543175\pi\)
\(30\) 0 0
\(31\) 6.32588i 1.13616i −0.822973 0.568081i \(-0.807686\pi\)
0.822973 0.568081i \(-0.192314\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 4.98906i 0.855617i
\(35\) 0.701849 0.669453i 0.118634 0.113158i
\(36\) 0 0
\(37\) −5.16789 −0.849595 −0.424798 0.905288i \(-0.639655\pi\)
−0.424798 + 0.905288i \(0.639655\pi\)
\(38\) −6.35722 −1.03128
\(39\) 0 0
\(40\) 0.366598i 0.0579643i
\(41\) −4.31856 −0.674446 −0.337223 0.941425i \(-0.609488\pi\)
−0.337223 + 0.941425i \(0.609488\pi\)
\(42\) 0 0
\(43\) −4.49843 −0.686005 −0.343002 0.939335i \(-0.611444\pi\)
−0.343002 + 0.939335i \(0.611444\pi\)
\(44\) 0.669453i 0.100924i
\(45\) 0 0
\(46\) −7.69459 −1.13450
\(47\) 8.32901 1.21491 0.607455 0.794354i \(-0.292190\pi\)
0.607455 + 0.794354i \(0.292190\pi\)
\(48\) 0 0
\(49\) 0.330547 6.99219i 0.0472209 0.998884i
\(50\) 4.86561i 0.688101i
\(51\) 0 0
\(52\) 1.00156i 0.138892i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0.245420i 0.0330925i
\(56\) −1.82612 1.91449i −0.244026 0.255835i
\(57\) 0 0
\(58\) −1.82898 −0.240157
\(59\) 8.72695 1.13615 0.568076 0.822976i \(-0.307688\pi\)
0.568076 + 0.822976i \(0.307688\pi\)
\(60\) 0 0
\(61\) 4.95771i 0.634770i −0.948297 0.317385i \(-0.897195\pi\)
0.948297 0.317385i \(-0.102805\pi\)
\(62\) −6.32588 −0.803387
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.367172i 0.0455420i
\(66\) 0 0
\(67\) −10.8907 −1.33052 −0.665258 0.746614i \(-0.731678\pi\)
−0.665258 + 0.746614i \(0.731678\pi\)
\(68\) −4.98906 −0.605013
\(69\) 0 0
\(70\) −0.669453 0.701849i −0.0800150 0.0838869i
\(71\) 5.49843i 0.652544i −0.945276 0.326272i \(-0.894207\pi\)
0.945276 0.326272i \(-0.105793\pi\)
\(72\) 0 0
\(73\) 4.07314i 0.476725i 0.971176 + 0.238363i \(0.0766106\pi\)
−0.971176 + 0.238363i \(0.923389\pi\)
\(74\) 5.16789i 0.600755i
\(75\) 0 0
\(76\) 6.35722i 0.729224i
\(77\) 1.22250 + 1.28166i 0.139317 + 0.146059i
\(78\) 0 0
\(79\) 8.35568 0.940087 0.470044 0.882643i \(-0.344238\pi\)
0.470044 + 0.882643i \(0.344238\pi\)
\(80\) −0.366598 −0.0409869
\(81\) 0 0
\(82\) 4.31856i 0.476905i
\(83\) 17.0142 1.86756 0.933778 0.357852i \(-0.116491\pi\)
0.933778 + 0.357852i \(0.116491\pi\)
\(84\) 0 0
\(85\) −1.82898 −0.198381
\(86\) 4.49843i 0.485079i
\(87\) 0 0
\(88\) 0.669453 0.0713640
\(89\) −10.7113 −1.13540 −0.567699 0.823236i \(-0.692166\pi\)
−0.567699 + 0.823236i \(0.692166\pi\)
\(90\) 0 0
\(91\) −1.82898 1.91749i −0.191729 0.201007i
\(92\) 7.69459i 0.802216i
\(93\) 0 0
\(94\) 8.32901i 0.859071i
\(95\) 2.33055i 0.239109i
\(96\) 0 0
\(97\) 17.2157i 1.74799i −0.485932 0.873997i \(-0.661520\pi\)
0.485932 0.873997i \(-0.338480\pi\)
\(98\) −6.99219 0.330547i −0.706318 0.0333902i
\(99\) 0 0
\(100\) 4.86561 0.486561
\(101\) −15.7317 −1.56537 −0.782683 0.622421i \(-0.786149\pi\)
−0.782683 + 0.622421i \(0.786149\pi\)
\(102\) 0 0
\(103\) 11.4445i 1.12766i 0.825890 + 0.563831i \(0.190673\pi\)
−0.825890 + 0.563831i \(0.809327\pi\)
\(104\) −1.00156 −0.0982115
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0618i 1.06938i −0.845048 0.534690i \(-0.820428\pi\)
0.845048 0.534690i \(-0.179572\pi\)
\(108\) 0 0
\(109\) −10.5633 −1.01178 −0.505891 0.862597i \(-0.668836\pi\)
−0.505891 + 0.862597i \(0.668836\pi\)
\(110\) 0.245420 0.0233999
\(111\) 0 0
\(112\) −1.91449 + 1.82612i −0.180902 + 0.172552i
\(113\) 4.15953i 0.391295i 0.980674 + 0.195648i \(0.0626809\pi\)
−0.980674 + 0.195648i \(0.937319\pi\)
\(114\) 0 0
\(115\) 2.82082i 0.263043i
\(116\) 1.82898i 0.169817i
\(117\) 0 0
\(118\) 8.72695i 0.803381i
\(119\) −9.55151 + 9.11064i −0.875586 + 0.835171i
\(120\) 0 0
\(121\) 10.5518 0.959257
\(122\) −4.95771 −0.448850
\(123\) 0 0
\(124\) 6.32588i 0.568081i
\(125\) 3.61671 0.323489
\(126\) 0 0
\(127\) −1.66945 −0.148140 −0.0740700 0.997253i \(-0.523599\pi\)
−0.0740700 + 0.997253i \(0.523599\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −0.367172 −0.0322031
\(131\) 13.5321 1.18231 0.591154 0.806558i \(-0.298672\pi\)
0.591154 + 0.806558i \(0.298672\pi\)
\(132\) 0 0
\(133\) 11.6091 + 12.1708i 1.00663 + 1.05535i
\(134\) 10.8907i 0.940817i
\(135\) 0 0
\(136\) 4.98906i 0.427809i
\(137\) 8.98851i 0.767940i −0.923346 0.383970i \(-0.874557\pi\)
0.923346 0.383970i \(-0.125443\pi\)
\(138\) 0 0
\(139\) 9.29922i 0.788750i 0.918950 + 0.394375i \(0.129039\pi\)
−0.918950 + 0.394375i \(0.870961\pi\)
\(140\) −0.701849 + 0.669453i −0.0593170 + 0.0565791i
\(141\) 0 0
\(142\) −5.49843 −0.461418
\(143\) 0.670501 0.0560701
\(144\) 0 0
\(145\) 0.670501i 0.0556821i
\(146\) 4.07314 0.337096
\(147\) 0 0
\(148\) 5.16789 0.424798
\(149\) 2.83211i 0.232016i −0.993248 0.116008i \(-0.962990\pi\)
0.993248 0.116008i \(-0.0370098\pi\)
\(150\) 0 0
\(151\) −16.5518 −1.34697 −0.673484 0.739201i \(-0.735203\pi\)
−0.673484 + 0.739201i \(0.735203\pi\)
\(152\) 6.35722 0.515639
\(153\) 0 0
\(154\) 1.28166 1.22250i 0.103279 0.0985122i
\(155\) 2.31905i 0.186271i
\(156\) 0 0
\(157\) 2.83456i 0.226222i −0.993582 0.113111i \(-0.963918\pi\)
0.993582 0.113111i \(-0.0360816\pi\)
\(158\) 8.35568i 0.664742i
\(159\) 0 0
\(160\) 0.366598i 0.0289821i
\(161\) 14.0513 + 14.7312i 1.10739 + 1.16098i
\(162\) 0 0
\(163\) 24.7281 1.93685 0.968426 0.249300i \(-0.0802005\pi\)
0.968426 + 0.249300i \(0.0802005\pi\)
\(164\) 4.31856 0.337223
\(165\) 0 0
\(166\) 17.0142i 1.32056i
\(167\) −19.3484 −1.49723 −0.748614 0.663006i \(-0.769280\pi\)
−0.748614 + 0.663006i \(0.769280\pi\)
\(168\) 0 0
\(169\) 11.9969 0.922836
\(170\) 1.82898i 0.140276i
\(171\) 0 0
\(172\) 4.49843 0.343002
\(173\) −4.83654 −0.367715 −0.183858 0.982953i \(-0.558859\pi\)
−0.183858 + 0.982953i \(0.558859\pi\)
\(174\) 0 0
\(175\) 9.31516 8.88520i 0.704160 0.671658i
\(176\) 0.669453i 0.0504619i
\(177\) 0 0
\(178\) 10.7113i 0.802847i
\(179\) 3.65796i 0.273409i −0.990612 0.136704i \(-0.956349\pi\)
0.990612 0.136704i \(-0.0436511\pi\)
\(180\) 0 0
\(181\) 5.66796i 0.421296i 0.977562 + 0.210648i \(0.0675574\pi\)
−0.977562 + 0.210648i \(0.932443\pi\)
\(182\) −1.91749 + 1.82898i −0.142134 + 0.135573i
\(183\) 0 0
\(184\) 7.69459 0.567252
\(185\) 1.89454 0.139289
\(186\) 0 0
\(187\) 3.33994i 0.244241i
\(188\) −8.32901 −0.607455
\(189\) 0 0
\(190\) 2.33055 0.169076
\(191\) 27.3777i 1.98098i −0.137587 0.990490i \(-0.543935\pi\)
0.137587 0.990490i \(-0.456065\pi\)
\(192\) 0 0
\(193\) −10.0283 −0.721850 −0.360925 0.932595i \(-0.617539\pi\)
−0.360925 + 0.932595i \(0.617539\pi\)
\(194\) −17.2157 −1.23602
\(195\) 0 0
\(196\) −0.330547 + 6.99219i −0.0236105 + 0.499442i
\(197\) 18.8258i 1.34129i 0.741780 + 0.670643i \(0.233982\pi\)
−0.741780 + 0.670643i \(0.766018\pi\)
\(198\) 0 0
\(199\) 5.36406i 0.380248i −0.981760 0.190124i \(-0.939111\pi\)
0.981760 0.190124i \(-0.0608890\pi\)
\(200\) 4.86561i 0.344050i
\(201\) 0 0
\(202\) 15.7317i 1.10688i
\(203\) 3.33994 + 3.50157i 0.234418 + 0.245762i
\(204\) 0 0
\(205\) 1.58318 0.110574
\(206\) 11.4445 0.797377
\(207\) 0 0
\(208\) 1.00156i 0.0694460i
\(209\) −4.25587 −0.294384
\(210\) 0 0
\(211\) 1.65796 0.114139 0.0570694 0.998370i \(-0.481824\pi\)
0.0570694 + 0.998370i \(0.481824\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −11.0618 −0.756166
\(215\) 1.64912 0.112469
\(216\) 0 0
\(217\) 11.5518 + 12.1108i 0.784189 + 0.822137i
\(218\) 10.5633i 0.715439i
\(219\) 0 0
\(220\) 0.245420i 0.0165462i
\(221\) 4.99687i 0.336126i
\(222\) 0 0
\(223\) 17.0372i 1.14090i 0.821334 + 0.570448i \(0.193230\pi\)
−0.821334 + 0.570448i \(0.806770\pi\)
\(224\) 1.82612 + 1.91449i 0.122013 + 0.127917i
\(225\) 0 0
\(226\) 4.15953 0.276688
\(227\) 5.11024 0.339179 0.169589 0.985515i \(-0.445756\pi\)
0.169589 + 0.985515i \(0.445756\pi\)
\(228\) 0 0
\(229\) 15.2669i 1.00887i 0.863451 + 0.504433i \(0.168298\pi\)
−0.863451 + 0.504433i \(0.831702\pi\)
\(230\) 2.82082 0.185999
\(231\) 0 0
\(232\) 1.82898 0.120078
\(233\) 10.1930i 0.667767i −0.942614 0.333883i \(-0.891641\pi\)
0.942614 0.333883i \(-0.108359\pi\)
\(234\) 0 0
\(235\) −3.05340 −0.199182
\(236\) −8.72695 −0.568076
\(237\) 0 0
\(238\) 9.11064 + 9.55151i 0.590555 + 0.619132i
\(239\) 19.1815i 1.24075i −0.784305 0.620375i \(-0.786980\pi\)
0.784305 0.620375i \(-0.213020\pi\)
\(240\) 0 0
\(241\) 20.6853i 1.33245i 0.745749 + 0.666227i \(0.232092\pi\)
−0.745749 + 0.666227i \(0.767908\pi\)
\(242\) 10.5518i 0.678297i
\(243\) 0 0
\(244\) 4.95771i 0.317385i
\(245\) −0.121178 + 2.56332i −0.00774176 + 0.163765i
\(246\) 0 0
\(247\) 6.36717 0.405133
\(248\) 6.32588 0.401694
\(249\) 0 0
\(250\) 3.61671i 0.228741i
\(251\) 1.81200 0.114373 0.0571864 0.998364i \(-0.481787\pi\)
0.0571864 + 0.998364i \(0.481787\pi\)
\(252\) 0 0
\(253\) −5.15117 −0.323851
\(254\) 1.66945i 0.104751i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.45545 0.402680 0.201340 0.979521i \(-0.435470\pi\)
0.201340 + 0.979521i \(0.435470\pi\)
\(258\) 0 0
\(259\) 9.89387 9.43720i 0.614775 0.586399i
\(260\) 0.367172i 0.0227710i
\(261\) 0 0
\(262\) 13.5321i 0.836018i
\(263\) 8.82062i 0.543903i 0.962311 + 0.271951i \(0.0876690\pi\)
−0.962311 + 0.271951i \(0.912331\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 12.1708 11.6091i 0.746242 0.711798i
\(267\) 0 0
\(268\) 10.8907 0.665258
\(269\) −14.2653 −0.869773 −0.434886 0.900485i \(-0.643212\pi\)
−0.434886 + 0.900485i \(0.643212\pi\)
\(270\) 0 0
\(271\) 3.05281i 0.185445i 0.995692 + 0.0927226i \(0.0295570\pi\)
−0.995692 + 0.0927226i \(0.970443\pi\)
\(272\) 4.98906 0.302506
\(273\) 0 0
\(274\) −8.98851 −0.543016
\(275\) 3.25730i 0.196422i
\(276\) 0 0
\(277\) 1.26566 0.0760459 0.0380230 0.999277i \(-0.487894\pi\)
0.0380230 + 0.999277i \(0.487894\pi\)
\(278\) 9.29922 0.557730
\(279\) 0 0
\(280\) 0.669453 + 0.701849i 0.0400075 + 0.0419435i
\(281\) 10.5267i 0.627970i −0.949428 0.313985i \(-0.898336\pi\)
0.949428 0.313985i \(-0.101664\pi\)
\(282\) 0 0
\(283\) 19.8718i 1.18125i 0.806945 + 0.590627i \(0.201119\pi\)
−0.806945 + 0.590627i \(0.798881\pi\)
\(284\) 5.49843i 0.326272i
\(285\) 0 0
\(286\) 0.670501i 0.0396475i
\(287\) 8.26784 7.88623i 0.488035 0.465509i
\(288\) 0 0
\(289\) 7.89074 0.464161
\(290\) 0.670501 0.0393732
\(291\) 0 0
\(292\) 4.07314i 0.238363i
\(293\) 13.4121 0.783544 0.391772 0.920062i \(-0.371862\pi\)
0.391772 + 0.920062i \(0.371862\pi\)
\(294\) 0 0
\(295\) −3.19928 −0.186270
\(296\) 5.16789i 0.300377i
\(297\) 0 0
\(298\) −2.83211 −0.164060
\(299\) 7.70663 0.445686
\(300\) 0 0
\(301\) 8.61221 8.21470i 0.496399 0.473487i
\(302\) 16.5518i 0.952451i
\(303\) 0 0
\(304\) 6.35722i 0.364612i
\(305\) 1.81749i 0.104069i
\(306\) 0 0
\(307\) 0.653728i 0.0373102i 0.999826 + 0.0186551i \(0.00593845\pi\)
−0.999826 + 0.0186551i \(0.994062\pi\)
\(308\) −1.22250 1.28166i −0.0696587 0.0730295i
\(309\) 0 0
\(310\) 2.31905 0.131713
\(311\) 9.24493 0.524232 0.262116 0.965036i \(-0.415580\pi\)
0.262116 + 0.965036i \(0.415580\pi\)
\(312\) 0 0
\(313\) 6.16414i 0.348418i −0.984709 0.174209i \(-0.944263\pi\)
0.984709 0.174209i \(-0.0557368\pi\)
\(314\) −2.83456 −0.159963
\(315\) 0 0
\(316\) −8.35568 −0.470044
\(317\) 20.6548i 1.16009i 0.814584 + 0.580045i \(0.196965\pi\)
−0.814584 + 0.580045i \(0.803035\pi\)
\(318\) 0 0
\(319\) −1.22442 −0.0685542
\(320\) 0.366598 0.0204935
\(321\) 0 0
\(322\) 14.7312 14.0513i 0.820938 0.783046i
\(323\) 31.7166i 1.76476i
\(324\) 0 0
\(325\) 4.87322i 0.270318i
\(326\) 24.7281i 1.36956i
\(327\) 0 0
\(328\) 4.31856i 0.238453i
\(329\) −15.9458 + 15.2098i −0.879121 + 0.838543i
\(330\) 0 0
\(331\) 10.7114 0.588750 0.294375 0.955690i \(-0.404889\pi\)
0.294375 + 0.955690i \(0.404889\pi\)
\(332\) −17.0142 −0.933778
\(333\) 0 0
\(334\) 19.3484i 1.05870i
\(335\) 3.99252 0.218135
\(336\) 0 0
\(337\) −7.55183 −0.411375 −0.205687 0.978618i \(-0.565943\pi\)
−0.205687 + 0.978618i \(0.565943\pi\)
\(338\) 11.9969i 0.652544i
\(339\) 0 0
\(340\) 1.82898 0.0991904
\(341\) −4.23488 −0.229332
\(342\) 0 0
\(343\) 12.1358 + 13.9901i 0.655270 + 0.755394i
\(344\) 4.49843i 0.242539i
\(345\) 0 0
\(346\) 4.83654i 0.260014i
\(347\) 10.9320i 0.586859i −0.955981 0.293430i \(-0.905203\pi\)
0.955981 0.293430i \(-0.0947967\pi\)
\(348\) 0 0
\(349\) 1.18429i 0.0633936i 0.999498 + 0.0316968i \(0.0100911\pi\)
−0.999498 + 0.0316968i \(0.989909\pi\)
\(350\) −8.88520 9.31516i −0.474934 0.497916i
\(351\) 0 0
\(352\) −0.669453 −0.0356820
\(353\) 33.5824 1.78741 0.893706 0.448653i \(-0.148096\pi\)
0.893706 + 0.448653i \(0.148096\pi\)
\(354\) 0 0
\(355\) 2.01572i 0.106983i
\(356\) 10.7113 0.567699
\(357\) 0 0
\(358\) −3.65796 −0.193329
\(359\) 10.1281i 0.534542i 0.963621 + 0.267271i \(0.0861219\pi\)
−0.963621 + 0.267271i \(0.913878\pi\)
\(360\) 0 0
\(361\) −21.4143 −1.12707
\(362\) 5.66796 0.297901
\(363\) 0 0
\(364\) 1.82898 + 1.91749i 0.0958646 + 0.100504i
\(365\) 1.49321i 0.0781580i
\(366\) 0 0
\(367\) 18.0021i 0.939701i −0.882746 0.469850i \(-0.844308\pi\)
0.882746 0.469850i \(-0.155692\pi\)
\(368\) 7.69459i 0.401108i
\(369\) 0 0
\(370\) 1.89454i 0.0984923i
\(371\) 0 0
\(372\) 0 0
\(373\) 16.4090 0.849627 0.424814 0.905281i \(-0.360340\pi\)
0.424814 + 0.905281i \(0.360340\pi\)
\(374\) −3.33994 −0.172704
\(375\) 0 0
\(376\) 8.32901i 0.429536i
\(377\) 1.83184 0.0943447
\(378\) 0 0
\(379\) −2.91372 −0.149668 −0.0748339 0.997196i \(-0.523843\pi\)
−0.0748339 + 0.997196i \(0.523843\pi\)
\(380\) 2.33055i 0.119555i
\(381\) 0 0
\(382\) −27.3777 −1.40076
\(383\) −8.57443 −0.438133 −0.219066 0.975710i \(-0.570301\pi\)
−0.219066 + 0.975710i \(0.570301\pi\)
\(384\) 0 0
\(385\) −0.448168 0.469855i −0.0228407 0.0239460i
\(386\) 10.0283i 0.510425i
\(387\) 0 0
\(388\) 17.2157i 0.873997i
\(389\) 35.5539i 1.80266i 0.433137 + 0.901328i \(0.357406\pi\)
−0.433137 + 0.901328i \(0.642594\pi\)
\(390\) 0 0
\(391\) 38.3888i 1.94140i
\(392\) 6.99219 + 0.330547i 0.353159 + 0.0166951i
\(393\) 0 0
\(394\) 18.8258 0.948433
\(395\) −3.06318 −0.154125
\(396\) 0 0
\(397\) 3.58034i 0.179692i −0.995956 0.0898460i \(-0.971363\pi\)
0.995956 0.0898460i \(-0.0286375\pi\)
\(398\) −5.36406 −0.268876
\(399\) 0 0
\(400\) −4.86561 −0.243280
\(401\) 0.190871i 0.00953167i 0.999989 + 0.00476583i \(0.00151702\pi\)
−0.999989 + 0.00476583i \(0.998483\pi\)
\(402\) 0 0
\(403\) 6.33577 0.315607
\(404\) 15.7317 0.782683
\(405\) 0 0
\(406\) 3.50157 3.33994i 0.173780 0.165759i
\(407\) 3.45966i 0.171489i
\(408\) 0 0
\(409\) 3.47371i 0.171764i 0.996305 + 0.0858819i \(0.0273708\pi\)
−0.996305 + 0.0858819i \(0.972629\pi\)
\(410\) 1.58318i 0.0781875i
\(411\) 0 0
\(412\) 11.4445i 0.563831i
\(413\) −16.7077 + 15.9365i −0.822130 + 0.784183i
\(414\) 0 0
\(415\) −6.23739 −0.306182
\(416\) 1.00156 0.0491057
\(417\) 0 0
\(418\) 4.25587i 0.208161i
\(419\) 1.40791 0.0687809 0.0343905 0.999408i \(-0.489051\pi\)
0.0343905 + 0.999408i \(0.489051\pi\)
\(420\) 0 0
\(421\) −30.3860 −1.48093 −0.740463 0.672098i \(-0.765393\pi\)
−0.740463 + 0.672098i \(0.765393\pi\)
\(422\) 1.65796i 0.0807083i
\(423\) 0 0
\(424\) 0 0
\(425\) −24.2748 −1.17750
\(426\) 0 0
\(427\) 9.05340 + 9.49150i 0.438125 + 0.459326i
\(428\) 11.0618i 0.534690i
\(429\) 0 0
\(430\) 1.64912i 0.0795275i
\(431\) 27.2747i 1.31378i 0.753988 + 0.656888i \(0.228127\pi\)
−0.753988 + 0.656888i \(0.771873\pi\)
\(432\) 0 0
\(433\) 8.15047i 0.391686i 0.980635 + 0.195843i \(0.0627444\pi\)
−0.980635 + 0.195843i \(0.937256\pi\)
\(434\) 12.1108 11.5518i 0.581338 0.554506i
\(435\) 0 0
\(436\) 10.5633 0.505891
\(437\) −48.9162 −2.33998
\(438\) 0 0
\(439\) 12.2404i 0.584203i 0.956387 + 0.292101i \(0.0943545\pi\)
−0.956387 + 0.292101i \(0.905646\pi\)
\(440\) −0.245420 −0.0117000
\(441\) 0 0
\(442\) 4.99687 0.237677
\(443\) 8.00836i 0.380489i −0.981737 0.190244i \(-0.939072\pi\)
0.981737 0.190244i \(-0.0609280\pi\)
\(444\) 0 0
\(445\) 3.92675 0.186146
\(446\) 17.0372 0.806735
\(447\) 0 0
\(448\) 1.91449 1.82612i 0.0904512 0.0862762i
\(449\) 14.5183i 0.685163i −0.939488 0.342581i \(-0.888699\pi\)
0.939488 0.342581i \(-0.111301\pi\)
\(450\) 0 0
\(451\) 2.89108i 0.136135i
\(452\) 4.15953i 0.195648i
\(453\) 0 0
\(454\) 5.11024i 0.239835i
\(455\) 0.670501 + 0.702947i 0.0314336 + 0.0329547i
\(456\) 0 0
\(457\) 9.95501 0.465676 0.232838 0.972516i \(-0.425199\pi\)
0.232838 + 0.972516i \(0.425199\pi\)
\(458\) 15.2669 0.713375
\(459\) 0 0
\(460\) 2.82082i 0.131521i
\(461\) −32.3270 −1.50562 −0.752810 0.658237i \(-0.771302\pi\)
−0.752810 + 0.658237i \(0.771302\pi\)
\(462\) 0 0
\(463\) 9.45032 0.439193 0.219597 0.975591i \(-0.429526\pi\)
0.219597 + 0.975591i \(0.429526\pi\)
\(464\) 1.82898i 0.0849083i
\(465\) 0 0
\(466\) −10.1930 −0.472183
\(467\) −20.6623 −0.956138 −0.478069 0.878322i \(-0.658663\pi\)
−0.478069 + 0.878322i \(0.658663\pi\)
\(468\) 0 0
\(469\) 20.8502 19.8878i 0.962773 0.918335i
\(470\) 3.05340i 0.140843i
\(471\) 0 0
\(472\) 8.72695i 0.401691i
\(473\) 3.01149i 0.138469i
\(474\) 0 0
\(475\) 30.9317i 1.41925i
\(476\) 9.55151 9.11064i 0.437793 0.417586i
\(477\) 0 0
\(478\) −19.1815 −0.877343
\(479\) −10.1608 −0.464261 −0.232131 0.972685i \(-0.574570\pi\)
−0.232131 + 0.972685i \(0.574570\pi\)
\(480\) 0 0
\(481\) 5.17597i 0.236004i
\(482\) 20.6853 0.942188
\(483\) 0 0
\(484\) −10.5518 −0.479629
\(485\) 6.31126i 0.286579i
\(486\) 0 0
\(487\) −31.2296 −1.41515 −0.707575 0.706638i \(-0.750211\pi\)
−0.707575 + 0.706638i \(0.750211\pi\)
\(488\) 4.95771 0.224425
\(489\) 0 0
\(490\) 2.56332 + 0.121178i 0.115799 + 0.00547425i
\(491\) 20.5899i 0.929211i 0.885518 + 0.464605i \(0.153804\pi\)
−0.885518 + 0.464605i \(0.846196\pi\)
\(492\) 0 0
\(493\) 9.12490i 0.410965i
\(494\) 6.36717i 0.286473i
\(495\) 0 0
\(496\) 6.32588i 0.284040i
\(497\) 10.0408 + 10.5267i 0.450392 + 0.472187i
\(498\) 0 0
\(499\) −25.1533 −1.12601 −0.563007 0.826452i \(-0.690356\pi\)
−0.563007 + 0.826452i \(0.690356\pi\)
\(500\) −3.61671 −0.161744
\(501\) 0 0
\(502\) 1.81200i 0.0808737i
\(503\) 31.1553 1.38915 0.694574 0.719421i \(-0.255593\pi\)
0.694574 + 0.719421i \(0.255593\pi\)
\(504\) 0 0
\(505\) 5.76722 0.256638
\(506\) 5.15117i 0.228997i
\(507\) 0 0
\(508\) 1.66945 0.0740700
\(509\) −4.83347 −0.214240 −0.107120 0.994246i \(-0.534163\pi\)
−0.107120 + 0.994246i \(0.534163\pi\)
\(510\) 0 0
\(511\) −7.43806 7.79799i −0.329040 0.344963i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 6.45545i 0.284738i
\(515\) 4.19554i 0.184877i
\(516\) 0 0
\(517\) 5.57588i 0.245227i
\(518\) −9.43720 9.89387i −0.414647 0.434712i
\(519\) 0 0
\(520\) 0.367172 0.0161015
\(521\) −17.5322 −0.768101 −0.384050 0.923312i \(-0.625471\pi\)
−0.384050 + 0.923312i \(0.625471\pi\)
\(522\) 0 0
\(523\) 19.1019i 0.835267i −0.908616 0.417633i \(-0.862860\pi\)
0.908616 0.417633i \(-0.137140\pi\)
\(524\) −13.5321 −0.591154
\(525\) 0 0
\(526\) 8.82062 0.384597
\(527\) 31.5602i 1.37478i
\(528\) 0 0
\(529\) −36.2067 −1.57420
\(530\) 0 0
\(531\) 0 0
\(532\) −11.6091 12.1708i −0.503317 0.527673i
\(533\) 4.32532i 0.187350i
\(534\) 0 0
\(535\) 4.05522i 0.175322i
\(536\) 10.8907i 0.470408i
\(537\) 0 0
\(538\) 14.2653i 0.615022i
\(539\) −4.68095 0.221286i −0.201623 0.00953144i
\(540\) 0 0
\(541\) 13.6642 0.587471 0.293735 0.955887i \(-0.405102\pi\)
0.293735 + 0.955887i \(0.405102\pi\)
\(542\) 3.05281 0.131130
\(543\) 0 0
\(544\) 4.98906i 0.213904i
\(545\) 3.87249 0.165879
\(546\) 0 0
\(547\) −9.88761 −0.422764 −0.211382 0.977404i \(-0.567796\pi\)
−0.211382 + 0.977404i \(0.567796\pi\)
\(548\) 8.98851i 0.383970i
\(549\) 0 0
\(550\) 3.25730 0.138892
\(551\) −11.6272 −0.495337
\(552\) 0 0
\(553\) −15.9969 + 15.2585i −0.680256 + 0.648858i
\(554\) 1.26566i 0.0537726i
\(555\) 0 0
\(556\) 9.29922i 0.394375i
\(557\) 12.5800i 0.533034i 0.963830 + 0.266517i \(0.0858728\pi\)
−0.963830 + 0.266517i \(0.914127\pi\)
\(558\) 0 0
\(559\) 4.50547i 0.190561i
\(560\) 0.701849 0.669453i 0.0296585 0.0282896i
\(561\) 0 0
\(562\) −10.5267 −0.444042
\(563\) 24.3333 1.02553 0.512763 0.858530i \(-0.328622\pi\)
0.512763 + 0.858530i \(0.328622\pi\)
\(564\) 0 0
\(565\) 1.52487i 0.0641520i
\(566\) 19.8718 0.835272
\(567\) 0 0
\(568\) 5.49843 0.230709
\(569\) 9.45406i 0.396335i 0.980168 + 0.198167i \(0.0634990\pi\)
−0.980168 + 0.198167i \(0.936501\pi\)
\(570\) 0 0
\(571\) −31.5686 −1.32110 −0.660551 0.750781i \(-0.729677\pi\)
−0.660551 + 0.750781i \(0.729677\pi\)
\(572\) −0.670501 −0.0280351
\(573\) 0 0
\(574\) −7.88623 8.26784i −0.329165 0.345093i
\(575\) 37.4388i 1.56131i
\(576\) 0 0
\(577\) 33.5794i 1.39793i −0.715157 0.698964i \(-0.753645\pi\)
0.715157 0.698964i \(-0.246355\pi\)
\(578\) 7.89074i 0.328211i
\(579\) 0 0
\(580\) 0.670501i 0.0278410i
\(581\) −32.5736 + 31.0701i −1.35138 + 1.28901i
\(582\) 0 0
\(583\) 0 0
\(584\) −4.07314 −0.168548
\(585\) 0 0
\(586\) 13.4121i 0.554049i
\(587\) −19.3171 −0.797302 −0.398651 0.917103i \(-0.630521\pi\)
−0.398651 + 0.917103i \(0.630521\pi\)
\(588\) 0 0
\(589\) −40.2150 −1.65703
\(590\) 3.19928i 0.131712i
\(591\) 0 0
\(592\) −5.16789 −0.212399
\(593\) −0.733196 −0.0301088 −0.0150544 0.999887i \(-0.504792\pi\)
−0.0150544 + 0.999887i \(0.504792\pi\)
\(594\) 0 0
\(595\) 3.50157 3.33994i 0.143550 0.136924i
\(596\) 2.83211i 0.116008i
\(597\) 0 0
\(598\) 7.70663i 0.315147i
\(599\) 30.7783i 1.25757i 0.777580 + 0.628785i \(0.216447\pi\)
−0.777580 + 0.628785i \(0.783553\pi\)
\(600\) 0 0
\(601\) 0.908670i 0.0370654i −0.999828 0.0185327i \(-0.994101\pi\)
0.999828 0.0185327i \(-0.00589948\pi\)
\(602\) −8.21470 8.61221i −0.334806 0.351007i
\(603\) 0 0
\(604\) 16.5518 0.673484
\(605\) −3.86828 −0.157268
\(606\) 0 0
\(607\) 44.7773i 1.81746i −0.417389 0.908728i \(-0.637055\pi\)
0.417389 0.908728i \(-0.362945\pi\)
\(608\) −6.35722 −0.257820
\(609\) 0 0
\(610\) 1.81749 0.0735880
\(611\) 8.34204i 0.337483i
\(612\) 0 0
\(613\) 18.1480 0.732992 0.366496 0.930420i \(-0.380557\pi\)
0.366496 + 0.930420i \(0.380557\pi\)
\(614\) 0.653728 0.0263823
\(615\) 0 0
\(616\) −1.28166 + 1.22250i −0.0516396 + 0.0492561i
\(617\) 22.7930i 0.917610i −0.888537 0.458805i \(-0.848278\pi\)
0.888537 0.458805i \(-0.151722\pi\)
\(618\) 0 0
\(619\) 44.3668i 1.78325i −0.452772 0.891626i \(-0.649565\pi\)
0.452772 0.891626i \(-0.350435\pi\)
\(620\) 2.31905i 0.0931355i
\(621\) 0 0
\(622\) 9.24493i 0.370688i
\(623\) 20.5067 19.5602i 0.821584 0.783663i
\(624\) 0 0
\(625\) 23.0021 0.920086
\(626\) −6.16414 −0.246368
\(627\) 0 0
\(628\) 2.83456i 0.113111i
\(629\) −25.7829 −1.02803
\(630\) 0 0
\(631\) −32.5707 −1.29662 −0.648310 0.761377i \(-0.724524\pi\)
−0.648310 + 0.761377i \(0.724524\pi\)
\(632\) 8.35568i 0.332371i
\(633\) 0 0
\(634\) 20.6548 0.820308
\(635\) 0.612018 0.0242872
\(636\) 0 0
\(637\) 7.00313 + 0.331064i 0.277474 + 0.0131172i
\(638\) 1.22442i 0.0484751i
\(639\) 0 0
\(640\) 0.366598i 0.0144911i
\(641\) 11.8091i 0.466433i 0.972425 + 0.233216i \(0.0749250\pi\)
−0.972425 + 0.233216i \(0.925075\pi\)
\(642\) 0 0
\(643\) 29.2964i 1.15534i −0.816272 0.577668i \(-0.803963\pi\)
0.816272 0.577668i \(-0.196037\pi\)
\(644\) −14.0513 14.7312i −0.553697 0.580491i
\(645\) 0 0
\(646\) −31.7166 −1.24787
\(647\) 28.1683 1.10741 0.553705 0.832713i \(-0.313214\pi\)
0.553705 + 0.832713i \(0.313214\pi\)
\(648\) 0 0
\(649\) 5.84229i 0.229330i
\(650\) −4.87322 −0.191143
\(651\) 0 0
\(652\) −24.7281 −0.968426
\(653\) 45.0974i 1.76480i 0.470502 + 0.882399i \(0.344073\pi\)
−0.470502 + 0.882399i \(0.655927\pi\)
\(654\) 0 0
\(655\) −4.96086 −0.193837
\(656\) −4.31856 −0.168611
\(657\) 0 0
\(658\) 15.2098 + 15.9458i 0.592939 + 0.621632i
\(659\) 31.8045i 1.23893i −0.785026 0.619463i \(-0.787350\pi\)
0.785026 0.619463i \(-0.212650\pi\)
\(660\) 0 0
\(661\) 19.7724i 0.769056i −0.923113 0.384528i \(-0.874364\pi\)
0.923113 0.384528i \(-0.125636\pi\)
\(662\) 10.7114i 0.416309i
\(663\) 0 0
\(664\) 17.0142i 0.660281i
\(665\) −4.25587 4.46181i −0.165035 0.173022i
\(666\) 0 0
\(667\) −14.0733 −0.544918
\(668\) 19.3484 0.748614
\(669\) 0 0
\(670\) 3.99252i 0.154245i
\(671\) −3.31896 −0.128127
\(672\) 0 0
\(673\) 1.89074 0.0728826 0.0364413 0.999336i \(-0.488398\pi\)
0.0364413 + 0.999336i \(0.488398\pi\)
\(674\) 7.55183i 0.290886i
\(675\) 0 0
\(676\) −11.9969 −0.461418
\(677\) 21.1322 0.812175 0.406088 0.913834i \(-0.366893\pi\)
0.406088 + 0.913834i \(0.366893\pi\)
\(678\) 0 0
\(679\) 31.4381 + 32.9594i 1.20648 + 1.26486i
\(680\) 1.82898i 0.0701382i
\(681\) 0 0
\(682\) 4.23488i 0.162162i
\(683\) 8.71972i 0.333651i 0.985986 + 0.166825i \(0.0533516\pi\)
−0.985986 + 0.166825i \(0.946648\pi\)
\(684\) 0 0
\(685\) 3.29517i 0.125902i
\(686\) 13.9901 12.1358i 0.534145 0.463346i
\(687\) 0 0
\(688\) −4.49843 −0.171501
\(689\) 0 0
\(690\) 0 0
\(691\) 18.1370i 0.689964i −0.938609 0.344982i \(-0.887885\pi\)
0.938609 0.344982i \(-0.112115\pi\)
\(692\) 4.83654 0.183858
\(693\) 0 0
\(694\) −10.9320 −0.414972
\(695\) 3.40908i 0.129314i
\(696\) 0 0
\(697\) −21.5456 −0.816097
\(698\) 1.18429 0.0448260
\(699\) 0 0
\(700\) −9.31516 + 8.88520i −0.352080 + 0.335829i
\(701\) 35.6167i 1.34523i −0.739995 0.672613i \(-0.765172\pi\)
0.739995 0.672613i \(-0.234828\pi\)
\(702\) 0 0
\(703\) 32.8534i 1.23909i
\(704\) 0.669453i 0.0252310i
\(705\) 0 0
\(706\) 33.5824i 1.26389i
\(707\) 30.1182 28.7281i 1.13271 1.08043i
\(708\) 0 0
\(709\) −3.60770 −0.135490 −0.0677449 0.997703i \(-0.521580\pi\)
−0.0677449 + 0.997703i \(0.521580\pi\)
\(710\) 2.01572 0.0756485
\(711\) 0 0
\(712\) 10.7113i 0.401424i
\(713\) −48.6750 −1.82289
\(714\) 0 0
\(715\) −0.245804 −0.00919256
\(716\) 3.65796i 0.136704i
\(717\) 0 0
\(718\) 10.1281 0.377978
\(719\) 25.7829 0.961540 0.480770 0.876847i \(-0.340357\pi\)
0.480770 + 0.876847i \(0.340357\pi\)
\(720\) 0 0
\(721\) −20.8991 21.9104i −0.778323 0.815987i
\(722\) 21.4143i 0.796958i
\(723\) 0 0
\(724\) 5.66796i 0.210648i
\(725\) 8.89910i 0.330504i
\(726\) 0 0
\(727\) 1.52909i 0.0567107i 0.999598 + 0.0283554i \(0.00902700\pi\)
−0.999598 + 0.0283554i \(0.990973\pi\)
\(728\) 1.91749 1.82898i 0.0710668 0.0677865i
\(729\) 0 0
\(730\) −1.49321 −0.0552660
\(731\) −22.4430 −0.830083
\(732\) 0 0
\(733\) 20.7739i 0.767303i 0.923478 + 0.383651i \(0.125334\pi\)
−0.923478 + 0.383651i \(0.874666\pi\)
\(734\) −18.0021 −0.664469
\(735\) 0 0
\(736\) −7.69459 −0.283626
\(737\) 7.29084i 0.268562i
\(738\) 0 0
\(739\) −11.8709 −0.436678 −0.218339 0.975873i \(-0.570064\pi\)
−0.218339 + 0.975873i \(0.570064\pi\)
\(740\) −1.89454 −0.0696446
\(741\) 0 0
\(742\) 0 0
\(743\) 43.4059i 1.59241i −0.605028 0.796204i \(-0.706838\pi\)
0.605028 0.796204i \(-0.293162\pi\)
\(744\) 0 0
\(745\) 1.03825i 0.0380384i
\(746\) 16.4090i 0.600777i
\(747\) 0 0
\(748\) 3.33994i 0.122120i
\(749\) 20.2001 + 21.1776i 0.738097 + 0.773814i
\(750\) 0 0
\(751\) 2.31383 0.0844327 0.0422164 0.999108i \(-0.486558\pi\)
0.0422164 + 0.999108i \(0.486558\pi\)
\(752\) 8.32901 0.303728
\(753\) 0 0
\(754\) 1.83184i 0.0667118i
\(755\) 6.06787 0.220832
\(756\) 0 0
\(757\) −15.0946 −0.548624 −0.274312 0.961641i \(-0.588450\pi\)
−0.274312 + 0.961641i \(0.588450\pi\)
\(758\) 2.91372i 0.105831i
\(759\) 0 0
\(760\) −2.33055 −0.0845378
\(761\) 23.3379 0.845998 0.422999 0.906130i \(-0.360977\pi\)
0.422999 + 0.906130i \(0.360977\pi\)
\(762\) 0 0
\(763\) 20.2234 19.2899i 0.732136 0.698342i
\(764\) 27.3777i 0.990490i
\(765\) 0 0
\(766\) 8.57443i 0.309807i
\(767\) 8.74061i 0.315605i
\(768\) 0 0
\(769\) 18.2750i 0.659012i 0.944153 + 0.329506i \(0.106882\pi\)
−0.944153 + 0.329506i \(0.893118\pi\)
\(770\) −0.469855 + 0.448168i −0.0169324 + 0.0161508i
\(771\) 0 0
\(772\) 10.0283 0.360925
\(773\) 0.438507 0.0157720 0.00788600 0.999969i \(-0.497490\pi\)
0.00788600 + 0.999969i \(0.497490\pi\)
\(774\) 0 0
\(775\) 30.7792i 1.10562i
\(776\) 17.2157 0.618009
\(777\) 0 0
\(778\) 35.5539 1.27467
\(779\) 27.4541i 0.983644i
\(780\) 0 0
\(781\) −3.68095 −0.131715
\(782\) −38.3888 −1.37278
\(783\) 0 0
\(784\) 0.330547 6.99219i 0.0118052 0.249721i
\(785\) 1.03914i 0.0370886i
\(786\) 0 0
\(787\) 38.2572i 1.36372i 0.731481 + 0.681861i \(0.238829\pi\)
−0.731481 + 0.681861i \(0.761171\pi\)
\(788\) 18.8258i 0.670643i
\(789\) 0 0
\(790\) 3.06318i 0.108983i
\(791\) −7.59581 7.96337i −0.270076 0.283145i
\(792\) 0 0
\(793\) 4.96547 0.176329
\(794\) −3.58034 −0.127061
\(795\) 0 0
\(796\) 5.36406i 0.190124i
\(797\) 35.3225 1.25119 0.625594 0.780149i \(-0.284857\pi\)
0.625594 + 0.780149i \(0.284857\pi\)
\(798\) 0 0
\(799\) 41.5539 1.47007