Properties

Label 1710.2.d.d.1369.6
Level $1710$
Weight $2$
Character 1710.1369
Analytic conductor $13.654$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1369.6
Root \(0.432320 - 0.432320i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1369
Dual form 1710.2.d.d.1369.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -1.00000i q^{8} +(0.432320 + 2.19388i) q^{10} +0.864641 q^{11} +5.62620i q^{13} -0.761557 q^{14} +1.00000 q^{16} -3.62620i q^{17} -1.00000 q^{19} +(-2.19388 + 0.432320i) q^{20} +0.864641i q^{22} +8.01395i q^{23} +(4.62620 - 1.89692i) q^{25} -5.62620 q^{26} -0.761557i q^{28} -7.35548 q^{29} +8.11704 q^{31} +1.00000i q^{32} +3.62620 q^{34} +(0.329237 + 1.67076i) q^{35} -0.476886i q^{37} -1.00000i q^{38} +(-0.432320 - 2.19388i) q^{40} +2.65847 q^{41} +6.86464i q^{43} -0.864641 q^{44} -8.01395 q^{46} +1.25240i q^{47} +6.42003 q^{49} +(1.89692 + 4.62620i) q^{50} -5.62620i q^{52} -2.37380i q^{53} +(1.89692 - 0.373802i) q^{55} +0.761557 q^{56} -7.35548i q^{58} +4.49084 q^{59} -10.8646 q^{61} +8.11704i q^{62} -1.00000 q^{64} +(2.43232 + 12.3432i) q^{65} -1.03228i q^{67} +3.62620i q^{68} +(-1.67076 + 0.329237i) q^{70} +10.1816 q^{71} +16.4017i q^{73} +0.476886 q^{74} +1.00000 q^{76} +0.658473i q^{77} +12.5693 q^{79} +(2.19388 - 0.432320i) q^{80} +2.65847i q^{82} +0.270718i q^{83} +(-1.56768 - 7.95543i) q^{85} -6.86464 q^{86} -0.864641i q^{88} +0.387755 q^{89} -4.28467 q^{91} -8.01395i q^{92} -1.25240 q^{94} +(-2.19388 + 0.432320i) q^{95} +8.50479i q^{97} +6.42003i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 2q^{5} + O(q^{10}) \) \( 6q - 6q^{4} - 2q^{5} + 8q^{14} + 6q^{16} - 6q^{19} + 2q^{20} + 10q^{25} - 16q^{26} - 16q^{29} + 8q^{31} + 4q^{34} - 8q^{35} - 4q^{41} + 6q^{49} + 4q^{50} + 4q^{55} - 8q^{56} + 4q^{59} - 60q^{61} - 6q^{64} + 12q^{65} - 20q^{70} + 16q^{71} + 28q^{74} + 6q^{76} - 2q^{80} - 12q^{85} - 36q^{86} - 28q^{89} + 12q^{91} + 28q^{94} + 2q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(5\) 2.19388 0.432320i 0.981132 0.193340i
\(6\) 0 0
\(7\) 0.761557i 0.287842i 0.989589 + 0.143921i \(0.0459710\pi\)
−0.989589 + 0.143921i \(0.954029\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.432320 + 2.19388i 0.136712 + 0.693765i
\(11\) 0.864641 0.260699 0.130350 0.991468i \(-0.458390\pi\)
0.130350 + 0.991468i \(0.458390\pi\)
\(12\) 0 0
\(13\) 5.62620i 1.56043i 0.625514 + 0.780213i \(0.284889\pi\)
−0.625514 + 0.780213i \(0.715111\pi\)
\(14\) −0.761557 −0.203535
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.62620i 0.879482i −0.898125 0.439741i \(-0.855070\pi\)
0.898125 0.439741i \(-0.144930\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) −2.19388 + 0.432320i −0.490566 + 0.0966698i
\(21\) 0 0
\(22\) 0.864641i 0.184342i
\(23\) 8.01395i 1.67102i 0.549472 + 0.835512i \(0.314829\pi\)
−0.549472 + 0.835512i \(0.685171\pi\)
\(24\) 0 0
\(25\) 4.62620 1.89692i 0.925240 0.379383i
\(26\) −5.62620 −1.10339
\(27\) 0 0
\(28\) 0.761557i 0.143921i
\(29\) −7.35548 −1.36588 −0.682939 0.730475i \(-0.739299\pi\)
−0.682939 + 0.730475i \(0.739299\pi\)
\(30\) 0 0
\(31\) 8.11704 1.45786 0.728931 0.684587i \(-0.240017\pi\)
0.728931 + 0.684587i \(0.240017\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.62620 0.621888
\(35\) 0.329237 + 1.67076i 0.0556512 + 0.282411i
\(36\) 0 0
\(37\) 0.476886i 0.0783995i −0.999231 0.0391998i \(-0.987519\pi\)
0.999231 0.0391998i \(-0.0124809\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 0 0
\(40\) −0.432320 2.19388i −0.0683559 0.346883i
\(41\) 2.65847 0.415184 0.207592 0.978216i \(-0.433437\pi\)
0.207592 + 0.978216i \(0.433437\pi\)
\(42\) 0 0
\(43\) 6.86464i 1.04685i 0.852072 + 0.523424i \(0.175346\pi\)
−0.852072 + 0.523424i \(0.824654\pi\)
\(44\) −0.864641 −0.130350
\(45\) 0 0
\(46\) −8.01395 −1.18159
\(47\) 1.25240i 0.182681i 0.995820 + 0.0913404i \(0.0291151\pi\)
−0.995820 + 0.0913404i \(0.970885\pi\)
\(48\) 0 0
\(49\) 6.42003 0.917147
\(50\) 1.89692 + 4.62620i 0.268264 + 0.654243i
\(51\) 0 0
\(52\) 5.62620i 0.780213i
\(53\) 2.37380i 0.326067i −0.986621 0.163033i \(-0.947872\pi\)
0.986621 0.163033i \(-0.0521278\pi\)
\(54\) 0 0
\(55\) 1.89692 0.373802i 0.255780 0.0504034i
\(56\) 0.761557 0.101767
\(57\) 0 0
\(58\) 7.35548i 0.965822i
\(59\) 4.49084 0.584657 0.292329 0.956318i \(-0.405570\pi\)
0.292329 + 0.956318i \(0.405570\pi\)
\(60\) 0 0
\(61\) −10.8646 −1.39107 −0.695537 0.718490i \(-0.744834\pi\)
−0.695537 + 0.718490i \(0.744834\pi\)
\(62\) 8.11704i 1.03086i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.43232 + 12.3432i 0.301692 + 1.53098i
\(66\) 0 0
\(67\) 1.03228i 0.126113i −0.998010 0.0630563i \(-0.979915\pi\)
0.998010 0.0630563i \(-0.0200848\pi\)
\(68\) 3.62620i 0.439741i
\(69\) 0 0
\(70\) −1.67076 + 0.329237i −0.199694 + 0.0393513i
\(71\) 10.1816 1.20833 0.604166 0.796858i \(-0.293506\pi\)
0.604166 + 0.796858i \(0.293506\pi\)
\(72\) 0 0
\(73\) 16.4017i 1.91967i 0.280557 + 0.959837i \(0.409481\pi\)
−0.280557 + 0.959837i \(0.590519\pi\)
\(74\) 0.476886 0.0554368
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 0.658473i 0.0750400i
\(78\) 0 0
\(79\) 12.5693 1.41416 0.707081 0.707133i \(-0.250012\pi\)
0.707081 + 0.707133i \(0.250012\pi\)
\(80\) 2.19388 0.432320i 0.245283 0.0483349i
\(81\) 0 0
\(82\) 2.65847i 0.293579i
\(83\) 0.270718i 0.0297152i 0.999890 + 0.0148576i \(0.00472949\pi\)
−0.999890 + 0.0148576i \(0.995271\pi\)
\(84\) 0 0
\(85\) −1.56768 7.95543i −0.170039 0.862888i
\(86\) −6.86464 −0.740233
\(87\) 0 0
\(88\) 0.864641i 0.0921710i
\(89\) 0.387755 0.0411020 0.0205510 0.999789i \(-0.493458\pi\)
0.0205510 + 0.999789i \(0.493458\pi\)
\(90\) 0 0
\(91\) −4.28467 −0.449156
\(92\) 8.01395i 0.835512i
\(93\) 0 0
\(94\) −1.25240 −0.129175
\(95\) −2.19388 + 0.432320i −0.225087 + 0.0443551i
\(96\) 0 0
\(97\) 8.50479i 0.863531i 0.901986 + 0.431765i \(0.142109\pi\)
−0.901986 + 0.431765i \(0.857891\pi\)
\(98\) 6.42003i 0.648521i
\(99\) 0 0
\(100\) −4.62620 + 1.89692i −0.462620 + 0.189692i
\(101\) −16.4157 −1.63342 −0.816710 0.577049i \(-0.804204\pi\)
−0.816710 + 0.577049i \(0.804204\pi\)
\(102\) 0 0
\(103\) 9.64015i 0.949872i −0.880020 0.474936i \(-0.842471\pi\)
0.880020 0.474936i \(-0.157529\pi\)
\(104\) 5.62620 0.551694
\(105\) 0 0
\(106\) 2.37380 0.230564
\(107\) 4.28467i 0.414215i 0.978318 + 0.207107i \(0.0664050\pi\)
−0.978318 + 0.207107i \(0.933595\pi\)
\(108\) 0 0
\(109\) 13.4200 1.28541 0.642703 0.766116i \(-0.277813\pi\)
0.642703 + 0.766116i \(0.277813\pi\)
\(110\) 0.373802 + 1.89692i 0.0356406 + 0.180864i
\(111\) 0 0
\(112\) 0.761557i 0.0719604i
\(113\) 10.3232i 0.971125i 0.874202 + 0.485563i \(0.161385\pi\)
−0.874202 + 0.485563i \(0.838615\pi\)
\(114\) 0 0
\(115\) 3.46460 + 17.5816i 0.323075 + 1.63950i
\(116\) 7.35548 0.682939
\(117\) 0 0
\(118\) 4.49084i 0.413415i
\(119\) 2.76156 0.253152
\(120\) 0 0
\(121\) −10.2524 −0.932036
\(122\) 10.8646i 0.983638i
\(123\) 0 0
\(124\) −8.11704 −0.728931
\(125\) 9.32924 6.16160i 0.834432 0.551110i
\(126\) 0 0
\(127\) 16.9817i 1.50688i −0.657517 0.753440i \(-0.728393\pi\)
0.657517 0.753440i \(-0.271607\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −12.3432 + 2.43232i −1.08257 + 0.213329i
\(131\) −0.541436 −0.0473055 −0.0236528 0.999720i \(-0.507530\pi\)
−0.0236528 + 0.999720i \(0.507530\pi\)
\(132\) 0 0
\(133\) 0.761557i 0.0660354i
\(134\) 1.03228 0.0891750
\(135\) 0 0
\(136\) −3.62620 −0.310944
\(137\) 2.87859i 0.245935i 0.992411 + 0.122967i \(0.0392411\pi\)
−0.992411 + 0.122967i \(0.960759\pi\)
\(138\) 0 0
\(139\) −3.58767 −0.304302 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(140\) −0.329237 1.67076i −0.0278256 0.141205i
\(141\) 0 0
\(142\) 10.1816i 0.854420i
\(143\) 4.86464i 0.406802i
\(144\) 0 0
\(145\) −16.1370 + 3.17992i −1.34011 + 0.264078i
\(146\) −16.4017 −1.35742
\(147\) 0 0
\(148\) 0.476886i 0.0391998i
\(149\) −16.8401 −1.37959 −0.689796 0.724004i \(-0.742300\pi\)
−0.689796 + 0.724004i \(0.742300\pi\)
\(150\) 0 0
\(151\) −16.9817 −1.38195 −0.690975 0.722879i \(-0.742818\pi\)
−0.690975 + 0.722879i \(0.742818\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0 0
\(154\) −0.658473 −0.0530613
\(155\) 17.8078 3.50916i 1.43036 0.281863i
\(156\) 0 0
\(157\) 14.8401i 1.18437i −0.805804 0.592183i \(-0.798266\pi\)
0.805804 0.592183i \(-0.201734\pi\)
\(158\) 12.5693i 0.999963i
\(159\) 0 0
\(160\) 0.432320 + 2.19388i 0.0341779 + 0.173441i
\(161\) −6.10308 −0.480990
\(162\) 0 0
\(163\) 13.3694i 1.04717i 0.851972 + 0.523587i \(0.175407\pi\)
−0.851972 + 0.523587i \(0.824593\pi\)
\(164\) −2.65847 −0.207592
\(165\) 0 0
\(166\) −0.270718 −0.0210118
\(167\) 9.84632i 0.761931i 0.924589 + 0.380966i \(0.124408\pi\)
−0.924589 + 0.380966i \(0.875592\pi\)
\(168\) 0 0
\(169\) −18.6541 −1.43493
\(170\) 7.95543 1.56768i 0.610154 0.120236i
\(171\) 0 0
\(172\) 6.86464i 0.523424i
\(173\) 2.98168i 0.226693i −0.993556 0.113346i \(-0.963843\pi\)
0.993556 0.113346i \(-0.0361570\pi\)
\(174\) 0 0
\(175\) 1.44461 + 3.52311i 0.109202 + 0.266322i
\(176\) 0.864641 0.0651748
\(177\) 0 0
\(178\) 0.387755i 0.0290635i
\(179\) 11.7938 0.881512 0.440756 0.897627i \(-0.354710\pi\)
0.440756 + 0.897627i \(0.354710\pi\)
\(180\) 0 0
\(181\) 14.5693 1.08293 0.541465 0.840723i \(-0.317870\pi\)
0.541465 + 0.840723i \(0.317870\pi\)
\(182\) 4.28467i 0.317601i
\(183\) 0 0
\(184\) 8.01395 0.590796
\(185\) −0.206167 1.04623i −0.0151577 0.0769203i
\(186\) 0 0
\(187\) 3.13536i 0.229280i
\(188\) 1.25240i 0.0913404i
\(189\) 0 0
\(190\) −0.432320 2.19388i −0.0313638 0.159161i
\(191\) −13.2384 −0.957900 −0.478950 0.877842i \(-0.658983\pi\)
−0.478950 + 0.877842i \(0.658983\pi\)
\(192\) 0 0
\(193\) 2.54144i 0.182937i 0.995808 + 0.0914683i \(0.0291560\pi\)
−0.995808 + 0.0914683i \(0.970844\pi\)
\(194\) −8.50479 −0.610609
\(195\) 0 0
\(196\) −6.42003 −0.458574
\(197\) 19.9109i 1.41859i −0.704911 0.709295i \(-0.749013\pi\)
0.704911 0.709295i \(-0.250987\pi\)
\(198\) 0 0
\(199\) 20.3126 1.43992 0.719960 0.694015i \(-0.244160\pi\)
0.719960 + 0.694015i \(0.244160\pi\)
\(200\) −1.89692 4.62620i −0.134132 0.327122i
\(201\) 0 0
\(202\) 16.4157i 1.15500i
\(203\) 5.60162i 0.393157i
\(204\) 0 0
\(205\) 5.83237 1.14931i 0.407350 0.0802715i
\(206\) 9.64015 0.671661
\(207\) 0 0
\(208\) 5.62620i 0.390107i
\(209\) −0.864641 −0.0598085
\(210\) 0 0
\(211\) 18.0419 1.24205 0.621026 0.783790i \(-0.286716\pi\)
0.621026 + 0.783790i \(0.286716\pi\)
\(212\) 2.37380i 0.163033i
\(213\) 0 0
\(214\) −4.28467 −0.292894
\(215\) 2.96772 + 15.0602i 0.202397 + 1.02710i
\(216\) 0 0
\(217\) 6.18159i 0.419634i
\(218\) 13.4200i 0.908919i
\(219\) 0 0
\(220\) −1.89692 + 0.373802i −0.127890 + 0.0252017i
\(221\) 20.4017 1.37237
\(222\) 0 0
\(223\) 13.5231i 0.905575i −0.891619 0.452787i \(-0.850430\pi\)
0.891619 0.452787i \(-0.149570\pi\)
\(224\) −0.761557 −0.0508837
\(225\) 0 0
\(226\) −10.3232 −0.686689
\(227\) 13.6016i 0.902771i 0.892329 + 0.451386i \(0.149070\pi\)
−0.892329 + 0.451386i \(0.850930\pi\)
\(228\) 0 0
\(229\) −13.5877 −0.897898 −0.448949 0.893557i \(-0.648202\pi\)
−0.448949 + 0.893557i \(0.648202\pi\)
\(230\) −17.5816 + 3.46460i −1.15930 + 0.228449i
\(231\) 0 0
\(232\) 7.35548i 0.482911i
\(233\) 25.5510i 1.67390i −0.547277 0.836952i \(-0.684336\pi\)
0.547277 0.836952i \(-0.315664\pi\)
\(234\) 0 0
\(235\) 0.541436 + 2.74760i 0.0353194 + 0.179234i
\(236\) −4.49084 −0.292329
\(237\) 0 0
\(238\) 2.76156i 0.179005i
\(239\) −11.3309 −0.732935 −0.366468 0.930431i \(-0.619433\pi\)
−0.366468 + 0.930431i \(0.619433\pi\)
\(240\) 0 0
\(241\) −1.25240 −0.0806739 −0.0403370 0.999186i \(-0.512843\pi\)
−0.0403370 + 0.999186i \(0.512843\pi\)
\(242\) 10.2524i 0.659049i
\(243\) 0 0
\(244\) 10.8646 0.695537
\(245\) 14.0848 2.77551i 0.899842 0.177321i
\(246\) 0 0
\(247\) 5.62620i 0.357986i
\(248\) 8.11704i 0.515432i
\(249\) 0 0
\(250\) 6.16160 + 9.32924i 0.389694 + 0.590033i
\(251\) −10.5939 −0.668682 −0.334341 0.942452i \(-0.608514\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(252\) 0 0
\(253\) 6.92919i 0.435635i
\(254\) 16.9817 1.06553
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 0.153681i 0.00958637i −0.999989 0.00479319i \(-0.998474\pi\)
0.999989 0.00479319i \(-0.00152572\pi\)
\(258\) 0 0
\(259\) 0.363176 0.0225666
\(260\) −2.43232 12.3432i −0.150846 0.765492i
\(261\) 0 0
\(262\) 0.541436i 0.0334501i
\(263\) 0.504792i 0.0311268i −0.999879 0.0155634i \(-0.995046\pi\)
0.999879 0.0155634i \(-0.00495419\pi\)
\(264\) 0 0
\(265\) −1.02624 5.20783i −0.0630416 0.319915i
\(266\) 0.761557 0.0466941
\(267\) 0 0
\(268\) 1.03228i 0.0630563i
\(269\) −3.49521 −0.213107 −0.106553 0.994307i \(-0.533981\pi\)
−0.106553 + 0.994307i \(0.533981\pi\)
\(270\) 0 0
\(271\) 5.47252 0.332432 0.166216 0.986089i \(-0.446845\pi\)
0.166216 + 0.986089i \(0.446845\pi\)
\(272\) 3.62620i 0.219871i
\(273\) 0 0
\(274\) −2.87859 −0.173902
\(275\) 4.00000 1.64015i 0.241209 0.0989049i
\(276\) 0 0
\(277\) 12.9538i 0.778317i −0.921171 0.389158i \(-0.872766\pi\)
0.921171 0.389158i \(-0.127234\pi\)
\(278\) 3.58767i 0.215174i
\(279\) 0 0
\(280\) 1.67076 0.329237i 0.0998472 0.0196757i
\(281\) −0.153681 −0.00916785 −0.00458393 0.999989i \(-0.501459\pi\)
−0.00458393 + 0.999989i \(0.501459\pi\)
\(282\) 0 0
\(283\) 18.2341i 1.08390i −0.840410 0.541952i \(-0.817686\pi\)
0.840410 0.541952i \(-0.182314\pi\)
\(284\) −10.1816 −0.604166
\(285\) 0 0
\(286\) −4.86464 −0.287652
\(287\) 2.02458i 0.119507i
\(288\) 0 0
\(289\) 3.85069 0.226511
\(290\) −3.17992 16.1370i −0.186732 0.947599i
\(291\) 0 0
\(292\) 16.4017i 0.959837i
\(293\) 2.03853i 0.119092i −0.998226 0.0595462i \(-0.981035\pi\)
0.998226 0.0595462i \(-0.0189654\pi\)
\(294\) 0 0
\(295\) 9.85235 1.94148i 0.573626 0.113037i
\(296\) −0.476886 −0.0277184
\(297\) 0 0
\(298\) 16.8401i 0.975519i
\(299\) −45.0881 −2.60751
\(300\) 0 0
\(301\) −5.22782 −0.301326
\(302\) 16.9817i 0.977186i
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) −23.8357 + 4.69701i −1.36483 + 0.268950i
\(306\) 0 0
\(307\) 16.5414i 0.944070i −0.881580 0.472035i \(-0.843520\pi\)
0.881580 0.472035i \(-0.156480\pi\)
\(308\) 0.658473i 0.0375200i
\(309\) 0 0
\(310\) 3.50916 + 17.8078i 0.199307 + 1.01141i
\(311\) 21.4725 1.21759 0.608797 0.793326i \(-0.291652\pi\)
0.608797 + 0.793326i \(0.291652\pi\)
\(312\) 0 0
\(313\) 1.12141i 0.0633856i −0.999498 0.0316928i \(-0.989910\pi\)
0.999498 0.0316928i \(-0.0100898\pi\)
\(314\) 14.8401 0.837473
\(315\) 0 0
\(316\) −12.5693 −0.707081
\(317\) 29.8882i 1.67869i −0.543601 0.839344i \(-0.682940\pi\)
0.543601 0.839344i \(-0.317060\pi\)
\(318\) 0 0
\(319\) −6.35985 −0.356083
\(320\) −2.19388 + 0.432320i −0.122641 + 0.0241674i
\(321\) 0 0
\(322\) 6.10308i 0.340112i
\(323\) 3.62620i 0.201767i
\(324\) 0 0
\(325\) 10.6724 + 26.0279i 0.592000 + 1.44377i
\(326\) −13.3694 −0.740464
\(327\) 0 0
\(328\) 2.65847i 0.146790i
\(329\) −0.953771 −0.0525831
\(330\) 0 0
\(331\) 32.3126 1.77606 0.888030 0.459786i \(-0.152074\pi\)
0.888030 + 0.459786i \(0.152074\pi\)
\(332\) 0.270718i 0.0148576i
\(333\) 0 0
\(334\) −9.84632 −0.538767
\(335\) −0.446274 2.26469i −0.0243825 0.123733i
\(336\) 0 0
\(337\) 26.3511i 1.43544i −0.696334 0.717718i \(-0.745187\pi\)
0.696334 0.717718i \(-0.254813\pi\)
\(338\) 18.6541i 1.01465i
\(339\) 0 0
\(340\) 1.56768 + 7.95543i 0.0850194 + 0.431444i
\(341\) 7.01832 0.380063
\(342\) 0 0
\(343\) 10.2201i 0.551835i
\(344\) 6.86464 0.370117
\(345\) 0 0
\(346\) 2.98168 0.160296
\(347\) 2.77551i 0.148997i −0.997221 0.0744986i \(-0.976264\pi\)
0.997221 0.0744986i \(-0.0237356\pi\)
\(348\) 0 0
\(349\) −11.5510 −0.618312 −0.309156 0.951011i \(-0.600047\pi\)
−0.309156 + 0.951011i \(0.600047\pi\)
\(350\) −3.52311 + 1.44461i −0.188318 + 0.0772177i
\(351\) 0 0
\(352\) 0.864641i 0.0460855i
\(353\) 8.40171i 0.447178i 0.974684 + 0.223589i \(0.0717773\pi\)
−0.974684 + 0.223589i \(0.928223\pi\)
\(354\) 0 0
\(355\) 22.3372 4.40171i 1.18553 0.233618i
\(356\) −0.387755 −0.0205510
\(357\) 0 0
\(358\) 11.7938i 0.623323i
\(359\) 22.7895 1.20278 0.601391 0.798955i \(-0.294613\pi\)
0.601391 + 0.798955i \(0.294613\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 14.5693i 0.765748i
\(363\) 0 0
\(364\) 4.28467 0.224578
\(365\) 7.09079 + 35.9833i 0.371149 + 1.88345i
\(366\) 0 0
\(367\) 4.06455i 0.212168i −0.994357 0.106084i \(-0.966169\pi\)
0.994357 0.106084i \(-0.0338312\pi\)
\(368\) 8.01395i 0.417756i
\(369\) 0 0
\(370\) 1.04623 0.206167i 0.0543908 0.0107181i
\(371\) 1.80779 0.0938556
\(372\) 0 0
\(373\) 18.4017i 0.952804i −0.879227 0.476402i \(-0.841941\pi\)
0.879227 0.476402i \(-0.158059\pi\)
\(374\) 3.13536 0.162126
\(375\) 0 0
\(376\) 1.25240 0.0645874
\(377\) 41.3834i 2.13135i
\(378\) 0 0
\(379\) −1.23844 −0.0636145 −0.0318073 0.999494i \(-0.510126\pi\)
−0.0318073 + 0.999494i \(0.510126\pi\)
\(380\) 2.19388 0.432320i 0.112544 0.0221776i
\(381\) 0 0
\(382\) 13.2384i 0.677338i
\(383\) 16.8646i 0.861743i −0.902413 0.430871i \(-0.858206\pi\)
0.902413 0.430871i \(-0.141794\pi\)
\(384\) 0 0
\(385\) 0.284672 + 1.44461i 0.0145082 + 0.0736242i
\(386\) −2.54144 −0.129356
\(387\) 0 0
\(388\) 8.50479i 0.431765i
\(389\) 8.59392 0.435729 0.217865 0.975979i \(-0.430091\pi\)
0.217865 + 0.975979i \(0.430091\pi\)
\(390\) 0 0
\(391\) 29.0602 1.46964
\(392\) 6.42003i 0.324261i
\(393\) 0 0
\(394\) 19.9109 1.00310
\(395\) 27.5756 5.43398i 1.38748 0.273413i
\(396\) 0 0
\(397\) 16.0558i 0.805818i −0.915240 0.402909i \(-0.867999\pi\)
0.915240 0.402909i \(-0.132001\pi\)
\(398\) 20.3126i 1.01818i
\(399\) 0 0
\(400\) 4.62620 1.89692i 0.231310 0.0948458i
\(401\) 14.8925 0.743698 0.371849 0.928293i \(-0.378724\pi\)
0.371849 + 0.928293i \(0.378724\pi\)
\(402\) 0 0
\(403\) 45.6681i 2.27489i
\(404\) 16.4157 0.816710
\(405\) 0 0
\(406\) 5.60162 0.278004
\(407\) 0.412335i 0.0204387i
\(408\) 0 0
\(409\) 18.3511 0.907404 0.453702 0.891153i \(-0.350103\pi\)
0.453702 + 0.891153i \(0.350103\pi\)
\(410\) 1.14931 + 5.83237i 0.0567605 + 0.288040i
\(411\) 0 0
\(412\) 9.64015i 0.474936i
\(413\) 3.42003i 0.168289i
\(414\) 0 0
\(415\) 0.117037 + 0.593923i 0.00574512 + 0.0291545i
\(416\) −5.62620 −0.275847
\(417\) 0 0
\(418\) 0.864641i 0.0422910i
\(419\) 34.7509 1.69769 0.848847 0.528639i \(-0.177297\pi\)
0.848847 + 0.528639i \(0.177297\pi\)
\(420\) 0 0
\(421\) −40.1589 −1.95722 −0.978612 0.205713i \(-0.934049\pi\)
−0.978612 + 0.205713i \(0.934049\pi\)
\(422\) 18.0419i 0.878264i
\(423\) 0 0
\(424\) −2.37380 −0.115282
\(425\) −6.87859 16.7755i −0.333661 0.813732i
\(426\) 0 0
\(427\) 8.27405i 0.400409i
\(428\) 4.28467i 0.207107i
\(429\) 0 0
\(430\) −15.0602 + 2.96772i −0.726266 + 0.143116i
\(431\) −34.9571 −1.68382 −0.841912 0.539615i \(-0.818570\pi\)
−0.841912 + 0.539615i \(0.818570\pi\)
\(432\) 0 0
\(433\) 1.13536i 0.0545619i 0.999628 + 0.0272809i \(0.00868487\pi\)
−0.999628 + 0.0272809i \(0.991315\pi\)
\(434\) −6.18159 −0.296726
\(435\) 0 0
\(436\) −13.4200 −0.642703
\(437\) 8.01395i 0.383359i
\(438\) 0 0
\(439\) 6.80009 0.324551 0.162275 0.986746i \(-0.448117\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(440\) −0.373802 1.89692i −0.0178203 0.0904319i
\(441\) 0 0
\(442\) 20.4017i 0.970410i
\(443\) 38.0679i 1.80866i −0.426835 0.904330i \(-0.640371\pi\)
0.426835 0.904330i \(-0.359629\pi\)
\(444\) 0 0
\(445\) 0.850688 0.167635i 0.0403265 0.00794664i
\(446\) 13.5231 0.640338
\(447\) 0 0
\(448\) 0.761557i 0.0359802i
\(449\) −18.5414 −0.875024 −0.437512 0.899212i \(-0.644140\pi\)
−0.437512 + 0.899212i \(0.644140\pi\)
\(450\) 0 0
\(451\) 2.29862 0.108238
\(452\) 10.3232i 0.485563i
\(453\) 0 0
\(454\) −13.6016 −0.638356
\(455\) −9.40005 + 1.85235i −0.440681 + 0.0868396i
\(456\) 0 0
\(457\) 16.3738i 0.765934i −0.923762 0.382967i \(-0.874902\pi\)
0.923762 0.382967i \(-0.125098\pi\)
\(458\) 13.5877i 0.634910i
\(459\) 0 0
\(460\) −3.46460 17.5816i −0.161538 0.819748i
\(461\) −1.70470 −0.0793959 −0.0396979 0.999212i \(-0.512640\pi\)
−0.0396979 + 0.999212i \(0.512640\pi\)
\(462\) 0 0
\(463\) 10.0279i 0.466036i −0.972472 0.233018i \(-0.925140\pi\)
0.972472 0.233018i \(-0.0748602\pi\)
\(464\) −7.35548 −0.341470
\(465\) 0 0
\(466\) 25.5510 1.18363
\(467\) 32.7509i 1.51553i 0.652526 + 0.757766i \(0.273709\pi\)
−0.652526 + 0.757766i \(0.726291\pi\)
\(468\) 0 0
\(469\) 0.786137 0.0363004
\(470\) −2.74760 + 0.541436i −0.126738 + 0.0249746i
\(471\) 0 0
\(472\) 4.49084i 0.206708i
\(473\) 5.93545i 0.272912i
\(474\) 0 0
\(475\) −4.62620 + 1.89692i −0.212265 + 0.0870365i
\(476\) −2.76156 −0.126576
\(477\) 0 0
\(478\) 11.3309i 0.518263i
\(479\) 27.2803 1.24647 0.623234 0.782035i \(-0.285818\pi\)
0.623234 + 0.782035i \(0.285818\pi\)
\(480\) 0 0
\(481\) 2.68305 0.122337
\(482\) 1.25240i 0.0570451i
\(483\) 0 0
\(484\) 10.2524 0.466018
\(485\) 3.67680 + 18.6585i 0.166955 + 0.847238i
\(486\) 0 0
\(487\) 11.0741i 0.501817i 0.968011 + 0.250908i \(0.0807293\pi\)
−0.968011 + 0.250908i \(0.919271\pi\)
\(488\) 10.8646i 0.491819i
\(489\) 0 0
\(490\) 2.77551 + 14.0848i 0.125385 + 0.636285i
\(491\) −8.11704 −0.366317 −0.183158 0.983083i \(-0.558632\pi\)
−0.183158 + 0.983083i \(0.558632\pi\)
\(492\) 0 0
\(493\) 26.6724i 1.20127i
\(494\) 5.62620 0.253135
\(495\) 0 0
\(496\) 8.11704 0.364466
\(497\) 7.75386i 0.347808i
\(498\) 0 0
\(499\) −0.295298 −0.0132193 −0.00660967 0.999978i \(-0.502104\pi\)
−0.00660967 + 0.999978i \(0.502104\pi\)
\(500\) −9.32924 + 6.16160i −0.417216 + 0.275555i
\(501\) 0 0
\(502\) 10.5939i 0.472830i
\(503\) 19.6016i 0.873993i −0.899463 0.436996i \(-0.856042\pi\)
0.899463 0.436996i \(-0.143958\pi\)
\(504\) 0 0
\(505\) −36.0140 + 7.09683i −1.60260 + 0.315805i
\(506\) −6.92919 −0.308040
\(507\) 0 0
\(508\) 16.9817i 0.753440i
\(509\) −1.79383 −0.0795102 −0.0397551 0.999209i \(-0.512658\pi\)
−0.0397551 + 0.999209i \(0.512658\pi\)
\(510\) 0 0
\(511\) −12.4908 −0.552562
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0.153681 0.00677859
\(515\) −4.16763 21.1493i −0.183648 0.931950i
\(516\) 0 0
\(517\) 1.08287i 0.0476247i
\(518\) 0.363176i 0.0159570i
\(519\) 0 0
\(520\) 12.3432 2.43232i 0.541285 0.106664i
\(521\) 2.61850 0.114719 0.0573593 0.998354i \(-0.481732\pi\)
0.0573593 + 0.998354i \(0.481732\pi\)
\(522\) 0 0
\(523\) 14.9956i 0.655713i 0.944728 + 0.327857i \(0.106326\pi\)
−0.944728 + 0.327857i \(0.893674\pi\)
\(524\) 0.541436 0.0236528
\(525\) 0 0
\(526\) 0.504792 0.0220100
\(527\) 29.4340i 1.28216i
\(528\) 0 0
\(529\) −41.2234 −1.79232
\(530\) 5.20783 1.02624i 0.226214 0.0445772i
\(531\) 0 0
\(532\) 0.761557i 0.0330177i
\(533\) 14.9571i 0.647864i
\(534\) 0 0
\(535\) 1.85235 + 9.40005i 0.0800841 + 0.406399i
\(536\) −1.03228 −0.0445875
\(537\) 0 0
\(538\) 3.49521i 0.150689i
\(539\) 5.55102 0.239099
\(540\) 0 0
\(541\) 3.40608 0.146439 0.0732194 0.997316i \(-0.476673\pi\)
0.0732194 + 0.997316i \(0.476673\pi\)
\(542\) 5.47252i 0.235065i
\(543\) 0 0
\(544\) 3.62620 0.155472
\(545\) 29.4419 5.80175i 1.26115 0.248520i
\(546\) 0 0
\(547\) 4.74760i 0.202993i −0.994836 0.101496i \(-0.967637\pi\)
0.994836 0.101496i \(-0.0323630\pi\)
\(548\) 2.87859i 0.122967i
\(549\) 0 0
\(550\) 1.64015 + 4.00000i 0.0699363 + 0.170561i
\(551\) 7.35548 0.313354
\(552\) 0 0
\(553\) 9.57227i 0.407054i
\(554\) 12.9538 0.550353
\(555\) 0 0
\(556\) 3.58767 0.152151
\(557\) 43.0462i 1.82393i 0.410271 + 0.911964i \(0.365434\pi\)
−0.410271 + 0.911964i \(0.634566\pi\)
\(558\) 0 0
\(559\) −38.6218 −1.63353
\(560\) 0.329237 + 1.67076i 0.0139128 + 0.0706026i
\(561\) 0 0
\(562\) 0.153681i 0.00648265i
\(563\) 17.0096i 0.716869i −0.933555 0.358434i \(-0.883311\pi\)
0.933555 0.358434i \(-0.116689\pi\)
\(564\) 0 0
\(565\) 4.46293 + 22.6478i 0.187757 + 0.952802i
\(566\) 18.2341 0.766435
\(567\) 0 0
\(568\) 10.1816i 0.427210i
\(569\) −19.7572 −0.828264 −0.414132 0.910217i \(-0.635915\pi\)
−0.414132 + 0.910217i \(0.635915\pi\)
\(570\) 0 0
\(571\) −11.3973 −0.476964 −0.238482 0.971147i \(-0.576650\pi\)
−0.238482 + 0.971147i \(0.576650\pi\)
\(572\) 4.86464i 0.203401i
\(573\) 0 0
\(574\) −2.02458 −0.0845043
\(575\) 15.2018 + 37.0741i 0.633959 + 1.54610i
\(576\) 0 0
\(577\) 18.3372i 0.763386i 0.924289 + 0.381693i \(0.124659\pi\)
−0.924289 + 0.381693i \(0.875341\pi\)
\(578\) 3.85069i 0.160167i
\(579\) 0 0
\(580\) 16.1370 3.17992i 0.670053 0.132039i
\(581\) −0.206167 −0.00855327
\(582\) 0 0
\(583\) 2.05249i 0.0850053i
\(584\) 16.4017 0.678708
\(585\) 0 0
\(586\) 2.03853 0.0842110
\(587\) 11.9475i 0.493127i −0.969127 0.246563i \(-0.920699\pi\)
0.969127 0.246563i \(-0.0793013\pi\)
\(588\) 0 0
\(589\) −8.11704 −0.334457
\(590\) 1.94148 + 9.85235i 0.0799295 + 0.405615i
\(591\) 0 0
\(592\) 0.476886i 0.0195999i
\(593\) 24.3911i 1.00162i 0.865557 + 0.500811i \(0.166965\pi\)
−0.865557 + 0.500811i \(0.833035\pi\)
\(594\) 0 0
\(595\) 6.05852 1.19388i 0.248375 0.0489442i
\(596\) 16.8401 0.689796
\(597\) 0 0
\(598\) 45.0881i 1.84379i
\(599\) −21.0708 −0.860930 −0.430465 0.902607i \(-0.641650\pi\)
−0.430465 + 0.902607i \(0.641650\pi\)
\(600\) 0 0
\(601\) 32.3878 1.32112 0.660562 0.750771i \(-0.270318\pi\)
0.660562 + 0.750771i \(0.270318\pi\)
\(602\) 5.22782i 0.213070i
\(603\) 0 0
\(604\) 16.9817 0.690975
\(605\) −22.4925 + 4.43232i −0.914450 + 0.180199i
\(606\) 0 0
\(607\) 19.0183i 0.771930i −0.922513 0.385965i \(-0.873869\pi\)
0.922513 0.385965i \(-0.126131\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) −4.69701 23.8357i −0.190176 0.965079i
\(611\) −7.04623 −0.285060
\(612\) 0 0
\(613\) 23.5756i 0.952210i −0.879389 0.476105i \(-0.842048\pi\)
0.879389 0.476105i \(-0.157952\pi\)
\(614\) 16.5414 0.667558
\(615\) 0 0
\(616\) 0.658473 0.0265307
\(617\) 26.2707i 1.05762i −0.848740 0.528810i \(-0.822639\pi\)
0.848740 0.528810i \(-0.177361\pi\)
\(618\) 0 0
\(619\) −11.4985 −0.462165 −0.231083 0.972934i \(-0.574227\pi\)
−0.231083 + 0.972934i \(0.574227\pi\)
\(620\) −17.8078 + 3.50916i −0.715178 + 0.140931i
\(621\) 0 0
\(622\) 21.4725i 0.860969i
\(623\) 0.295298i 0.0118309i
\(624\) 0 0
\(625\) 17.8034 17.5510i 0.712137 0.702041i
\(626\) 1.12141 0.0448204
\(627\) 0 0
\(628\) 14.8401i 0.592183i
\(629\) −1.72928 −0.0689510
\(630\) 0 0
\(631\) −45.8130 −1.82379 −0.911893 0.410427i \(-0.865380\pi\)
−0.911893 + 0.410427i \(0.865380\pi\)
\(632\) 12.5693i 0.499982i
\(633\) 0 0
\(634\) 29.8882 1.18701
\(635\) −7.34153 37.2557i −0.291340 1.47845i
\(636\) 0 0
\(637\) 36.1204i 1.43114i
\(638\) 6.35985i 0.251789i
\(639\) 0 0
\(640\) −0.432320 2.19388i −0.0170890 0.0867206i
\(641\) −1.36943 −0.0540894 −0.0270447 0.999634i \(-0.508610\pi\)
−0.0270447 + 0.999634i \(0.508610\pi\)
\(642\) 0 0
\(643\) 24.7389i 0.975606i −0.872954 0.487803i \(-0.837799\pi\)
0.872954 0.487803i \(-0.162201\pi\)
\(644\) 6.10308 0.240495
\(645\) 0 0
\(646\) −3.62620 −0.142671
\(647\) 6.82611i 0.268362i −0.990957 0.134181i \(-0.957160\pi\)
0.990957 0.134181i \(-0.0428404\pi\)
\(648\) 0 0
\(649\) 3.88296 0.152420
\(650\) −26.0279 + 10.6724i −1.02090 + 0.418607i
\(651\) 0 0
\(652\) 13.3694i 0.523587i
\(653\) 6.91713i 0.270688i −0.990799 0.135344i \(-0.956786\pi\)
0.990799 0.135344i \(-0.0432140\pi\)
\(654\) 0 0
\(655\) −1.18785 + 0.234074i −0.0464130 + 0.00914603i
\(656\) 2.65847 0.103796
\(657\) 0 0
\(658\) 0.953771i 0.0371819i
\(659\) 9.44461 0.367910 0.183955 0.982935i \(-0.441110\pi\)
0.183955 + 0.982935i \(0.441110\pi\)
\(660\) 0 0
\(661\) −22.1955 −0.863306 −0.431653 0.902040i \(-0.642070\pi\)
−0.431653 + 0.902040i \(0.642070\pi\)
\(662\) 32.3126i 1.25586i
\(663\) 0 0
\(664\) 0.270718 0.0105059
\(665\) −0.329237 1.67076i −0.0127673 0.0647894i
\(666\) 0 0
\(667\) 58.9465i 2.28242i
\(668\) 9.84632i 0.380966i
\(669\) 0 0
\(670\) 2.26469 0.446274i 0.0874925 0.0172411i
\(671\) −9.39401 −0.362652
\(672\) 0 0
\(673\) 12.2986i 0.474077i 0.971500 + 0.237039i \(0.0761768\pi\)
−0.971500 + 0.237039i \(0.923823\pi\)
\(674\) 26.3511 1.01501
\(675\) 0 0
\(676\) 18.6541 0.717466
\(677\) 35.9527i 1.38178i −0.722962 0.690888i \(-0.757220\pi\)
0.722962 0.690888i \(-0.242780\pi\)
\(678\) 0 0
\(679\) −6.47689 −0.248560
\(680\) −7.95543 + 1.56768i −0.305077 + 0.0601178i
\(681\) 0 0
\(682\) 7.01832i 0.268745i
\(683\) 9.00958i 0.344742i 0.985032 + 0.172371i \(0.0551428\pi\)
−0.985032 + 0.172371i \(0.944857\pi\)
\(684\) 0 0
\(685\) 1.24448 + 6.31528i 0.0475490 + 0.241295i
\(686\) −10.2201 −0.390206
\(687\) 0 0
\(688\) 6.86464i 0.261712i
\(689\) 13.3555 0.508803
\(690\) 0 0
\(691\) −9.11078 −0.346590 −0.173295 0.984870i \(-0.555441\pi\)
−0.173295 + 0.984870i \(0.555441\pi\)
\(692\) 2.98168i 0.113346i
\(693\) 0 0
\(694\) 2.77551 0.105357
\(695\) −7.87090 + 1.55102i −0.298560 + 0.0588336i
\(696\) 0 0
\(697\) 9.64015i 0.365147i
\(698\) 11.5510i 0.437213i
\(699\) 0 0
\(700\) −1.44461 3.52311i −0.0546011 0.133161i
\(701\) 14.7476 0.557009 0.278505 0.960435i \(-0.410161\pi\)
0.278505 + 0.960435i \(0.410161\pi\)
\(702\) 0 0
\(703\) 0.476886i 0.0179861i
\(704\) −0.864641 −0.0325874
\(705\) 0 0
\(706\) −8.40171 −0.316202
\(707\) 12.5015i 0.470166i
\(708\) 0 0
\(709\) 8.63389 0.324253 0.162126 0.986770i \(-0.448165\pi\)
0.162126 + 0.986770i \(0.448165\pi\)
\(710\) 4.40171 + 22.3372i 0.165193 + 0.838299i
\(711\) 0 0
\(712\) 0.387755i 0.0145317i
\(713\) 65.0496i 2.43613i
\(714\) 0 0
\(715\) 2.10308 + 10.6724i 0.0786509 + 0.399126i
\(716\) −11.7938 −0.440756
\(717\) 0 0
\(718\) 22.7895i 0.850495i
\(719\) −38.2759 −1.42745 −0.713726 0.700425i \(-0.752994\pi\)
−0.713726 + 0.700425i \(0.752994\pi\)
\(720\) 0 0
\(721\) 7.34153 0.273413
\(722\) 1.00000i 0.0372161i
\(723\) 0 0
\(724\) −14.5693 −0.541465
\(725\) −34.0279 + 13.9527i −1.26376 + 0.518191i
\(726\) 0 0
\(727\) 31.1893i 1.15675i 0.815772 + 0.578373i \(0.196312\pi\)
−0.815772 + 0.578373i \(0.803688\pi\)
\(728\) 4.28467i 0.158800i
\(729\) 0 0
\(730\) −35.9833 + 7.09079i −1.33180 + 0.262442i
\(731\) 24.8925 0.920684
\(732\) 0 0
\(733\) 13.9634i 0.515748i −0.966179 0.257874i \(-0.916978\pi\)
0.966179 0.257874i \(-0.0830220\pi\)
\(734\) 4.06455 0.150025
\(735\) 0 0
\(736\) −8.01395 −0.295398
\(737\) 0.892548i 0.0328774i
\(738\) 0 0
\(739\) −9.02165 −0.331867 −0.165933 0.986137i \(-0.553064\pi\)
−0.165933 + 0.986137i \(0.553064\pi\)
\(740\) 0.206167 + 1.04623i 0.00757886 + 0.0384601i
\(741\) 0 0
\(742\) 1.80779i 0.0663659i
\(743\) 15.0342i 0.551550i 0.961222 + 0.275775i \(0.0889345\pi\)
−0.961222 + 0.275775i \(0.911066\pi\)
\(744\) 0 0
\(745\) −36.9450 + 7.28030i −1.35356 + 0.266730i
\(746\) 18.4017 0.673734
\(747\) 0 0
\(748\) 3.13536i 0.114640i
\(749\) −3.26302 −0.119228
\(750\) 0 0
\(751\) 29.6681 1.08260 0.541301 0.840829i \(-0.317932\pi\)
0.541301 + 0.840829i \(0.317932\pi\)
\(752\) 1.25240i 0.0456702i
\(753\) 0 0
\(754\) 41.3834 1.50709
\(755\) −37.2557 + 7.34153i −1.35587 + 0.267186i
\(756\) 0 0
\(757\) 10.5819i 0.384604i −0.981336 0.192302i \(-0.938405\pi\)
0.981336 0.192302i \(-0.0615953\pi\)
\(758\) 1.23844i 0.0449823i
\(759\) 0 0
\(760\) 0.432320 + 2.19388i 0.0156819 + 0.0795803i
\(761\) 0.979789 0.0355173 0.0177587 0.999842i \(-0.494347\pi\)
0.0177587 + 0.999842i \(0.494347\pi\)
\(762\) 0 0
\(763\) 10.2201i 0.369993i
\(764\) 13.2384 0.478950
\(765\) 0 0
\(766\) 16.8646 0.609344
\(767\) 25.2663i 0.912315i
\(768\) 0 0
\(769\) −43.1772 −1.55701 −0.778505 0.627638i \(-0.784022\pi\)
−0.778505 + 0.627638i \(0.784022\pi\)
\(770\) −1.44461 + 0.284672i −0.0520601 + 0.0102589i
\(771\) 0 0
\(772\) 2.54144i 0.0914683i
\(773\) 37.5250i 1.34968i −0.737964 0.674840i \(-0.764213\pi\)
0.737964 0.674840i \(-0.235787\pi\)
\(774\) 0 0
\(775\) 37.5510 15.3973i 1.34887 0.553089i
\(776\) 8.50479 0.305304
\(777\) 0 0
\(778\) 8.59392i 0.308107i
\(779\) −2.65847 −0.0952497
\(780\) 0 0
\(781\) 8.80342 0.315011
\(782\) 29.0602i 1.03919i
\(783\) 0 0
\(784\) 6.42003 0.229287
\(785\) −6.41566 32.5573i −0.228985 1.16202i
\(786\) 0 0
\(787\) 22.5833i 0.805008i −0.915418 0.402504i \(-0.868140\pi\)
0.915418 0.402504i \(-0.131860\pi\)
\(788\) 19.9109i 0.709295i
\(789\) 0 0
\(790\) 5.43398 + 27.5756i 0.193332 + 0.981096i
\(791\) −7.86171 −0.279530
\(792\) 0 0
\(793\) 61.1266i 2.17067i
\(794\) 16.0558 0.569799
\(795\) 0 0
\(796\) −20.3126 −0.719960
\(797\) 35.9806i 1.27450i 0.770657 + 0.637250i \(0.219928\pi\)
−0.770657 + 0.637250i \(0.780072\pi\)