Properties

Label 588.3.m.f.313.2
Level $588$
Weight $3$
Character 588.313
Analytic conductor $16.022$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.0218395444\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 313.2
Root \(-0.662827 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 588.313
Dual form 588.3.m.f.325.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.416265 - 0.240331i) q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.416265 - 0.240331i) q^{5} +(1.50000 - 2.59808i) q^{9} +(-2.88158 - 4.99104i) q^{11} -1.41991i q^{13} -0.832530 q^{15} +(19.9767 - 11.5336i) q^{17} +(-9.24384 - 5.33693i) q^{19} +(3.29990 - 5.71559i) q^{23} +(-12.3845 - 21.4506i) q^{25} -5.19615i q^{27} -6.20258 q^{29} +(36.3142 - 20.9660i) q^{31} +(-8.64474 - 4.99104i) q^{33} +(30.0464 - 52.0419i) q^{37} +(-1.22968 - 2.12987i) q^{39} +48.8250i q^{41} -51.5603 q^{43} +(-1.24880 + 0.720992i) q^{45} +(16.6641 + 9.62104i) q^{47} +(19.9767 - 34.6007i) q^{51} +(-41.0672 - 71.1306i) q^{53} +2.77013i q^{55} -18.4877 q^{57} +(80.1766 - 46.2900i) q^{59} +(-4.32309 - 2.49594i) q^{61} +(-0.341248 + 0.591060i) q^{65} +(1.10350 + 1.91131i) q^{67} -11.4312i q^{69} -80.5899 q^{71} +(-12.0454 + 6.95439i) q^{73} +(-37.1534 - 21.4506i) q^{75} +(32.4442 - 56.1951i) q^{79} +(-4.50000 - 7.79423i) q^{81} +118.005i q^{83} -11.0875 q^{85} +(-9.30387 + 5.37159i) q^{87} +(90.2959 + 52.1324i) q^{89} +(36.3142 - 62.8981i) q^{93} +(2.56526 + 4.44316i) q^{95} -31.7875i q^{97} -17.2895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{3} + 12 q^{9} + O(q^{10}) \) \( 8 q + 12 q^{3} + 12 q^{9} + 48 q^{17} - 96 q^{19} + 8 q^{23} - 36 q^{25} + 80 q^{29} + 48 q^{31} - 64 q^{37} - 112 q^{43} - 264 q^{47} + 48 q^{51} + 72 q^{53} - 192 q^{57} + 168 q^{59} - 144 q^{61} - 120 q^{65} + 32 q^{67} + 224 q^{71} + 336 q^{73} - 108 q^{75} + 216 q^{79} - 36 q^{81} - 96 q^{85} + 120 q^{87} + 96 q^{89} + 48 q^{93} + 136 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) 0 0
\(5\) −0.416265 0.240331i −0.0832530 0.0480662i 0.457796 0.889057i \(-0.348639\pi\)
−0.541049 + 0.840991i \(0.681972\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 0 0
\(11\) −2.88158 4.99104i −0.261962 0.453731i 0.704801 0.709405i \(-0.251036\pi\)
−0.966763 + 0.255673i \(0.917703\pi\)
\(12\) 0 0
\(13\) 1.41991i 0.109224i −0.998508 0.0546120i \(-0.982608\pi\)
0.998508 0.0546120i \(-0.0173922\pi\)
\(14\) 0 0
\(15\) −0.832530 −0.0555020
\(16\) 0 0
\(17\) 19.9767 11.5336i 1.17510 0.678445i 0.220225 0.975449i \(-0.429321\pi\)
0.954876 + 0.297004i \(0.0959876\pi\)
\(18\) 0 0
\(19\) −9.24384 5.33693i −0.486518 0.280891i 0.236611 0.971605i \(-0.423963\pi\)
−0.723129 + 0.690713i \(0.757297\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.29990 5.71559i 0.143474 0.248504i −0.785329 0.619079i \(-0.787506\pi\)
0.928803 + 0.370575i \(0.120839\pi\)
\(24\) 0 0
\(25\) −12.3845 21.4506i −0.495379 0.858022i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) −6.20258 −0.213882 −0.106941 0.994265i \(-0.534106\pi\)
−0.106941 + 0.994265i \(0.534106\pi\)
\(30\) 0 0
\(31\) 36.3142 20.9660i 1.17143 0.676323i 0.217410 0.976080i \(-0.430239\pi\)
0.954016 + 0.299757i \(0.0969057\pi\)
\(32\) 0 0
\(33\) −8.64474 4.99104i −0.261962 0.151244i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 30.0464 52.0419i 0.812066 1.40654i −0.0993502 0.995053i \(-0.531676\pi\)
0.911416 0.411486i \(-0.134990\pi\)
\(38\) 0 0
\(39\) −1.22968 2.12987i −0.0315302 0.0546120i
\(40\) 0 0
\(41\) 48.8250i 1.19085i 0.803409 + 0.595427i \(0.203017\pi\)
−0.803409 + 0.595427i \(0.796983\pi\)
\(42\) 0 0
\(43\) −51.5603 −1.19908 −0.599539 0.800346i \(-0.704649\pi\)
−0.599539 + 0.800346i \(0.704649\pi\)
\(44\) 0 0
\(45\) −1.24880 + 0.720992i −0.0277510 + 0.0160221i
\(46\) 0 0
\(47\) 16.6641 + 9.62104i 0.354556 + 0.204703i 0.666690 0.745335i \(-0.267710\pi\)
−0.312134 + 0.950038i \(0.601044\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 19.9767 34.6007i 0.391700 0.678445i
\(52\) 0 0
\(53\) −41.0672 71.1306i −0.774854 1.34209i −0.934877 0.354973i \(-0.884490\pi\)
0.160023 0.987113i \(-0.448843\pi\)
\(54\) 0 0
\(55\) 2.77013i 0.0503660i
\(56\) 0 0
\(57\) −18.4877 −0.324345
\(58\) 0 0
\(59\) 80.1766 46.2900i 1.35893 0.784576i 0.369447 0.929252i \(-0.379547\pi\)
0.989479 + 0.144676i \(0.0462138\pi\)
\(60\) 0 0
\(61\) −4.32309 2.49594i −0.0708703 0.0409170i 0.464146 0.885759i \(-0.346361\pi\)
−0.535016 + 0.844842i \(0.679695\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.341248 + 0.591060i −0.00524998 + 0.00909323i
\(66\) 0 0
\(67\) 1.10350 + 1.91131i 0.0164701 + 0.0285270i 0.874143 0.485669i \(-0.161424\pi\)
−0.857673 + 0.514196i \(0.828091\pi\)
\(68\) 0 0
\(69\) 11.4312i 0.165669i
\(70\) 0 0
\(71\) −80.5899 −1.13507 −0.567535 0.823349i \(-0.692103\pi\)
−0.567535 + 0.823349i \(0.692103\pi\)
\(72\) 0 0
\(73\) −12.0454 + 6.95439i −0.165005 + 0.0952657i −0.580228 0.814454i \(-0.697037\pi\)
0.415223 + 0.909719i \(0.363703\pi\)
\(74\) 0 0
\(75\) −37.1534 21.4506i −0.495379 0.286007i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 32.4442 56.1951i 0.410687 0.711330i −0.584278 0.811553i \(-0.698622\pi\)
0.994965 + 0.100223i \(0.0319557\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 118.005i 1.42174i 0.703322 + 0.710872i \(0.251699\pi\)
−0.703322 + 0.710872i \(0.748301\pi\)
\(84\) 0 0
\(85\) −11.0875 −0.130441
\(86\) 0 0
\(87\) −9.30387 + 5.37159i −0.106941 + 0.0617425i
\(88\) 0 0
\(89\) 90.2959 + 52.1324i 1.01456 + 0.585757i 0.912524 0.409024i \(-0.134131\pi\)
0.102037 + 0.994781i \(0.467464\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 36.3142 62.8981i 0.390475 0.676323i
\(94\) 0 0
\(95\) 2.56526 + 4.44316i 0.0270027 + 0.0467701i
\(96\) 0 0
\(97\) 31.7875i 0.327706i −0.986485 0.163853i \(-0.947608\pi\)
0.986485 0.163853i \(-0.0523923\pi\)
\(98\) 0 0
\(99\) −17.2895 −0.174641
\(100\) 0 0
\(101\) 62.7901 36.2519i 0.621684 0.358929i −0.155840 0.987782i \(-0.549809\pi\)
0.777524 + 0.628853i \(0.216475\pi\)
\(102\) 0 0
\(103\) −92.6323 53.4813i −0.899343 0.519236i −0.0223558 0.999750i \(-0.507117\pi\)
−0.876987 + 0.480514i \(0.840450\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −98.3097 + 170.277i −0.918782 + 1.59138i −0.117515 + 0.993071i \(0.537493\pi\)
−0.801268 + 0.598306i \(0.795841\pi\)
\(108\) 0 0
\(109\) −21.3461 36.9726i −0.195836 0.339198i 0.751338 0.659917i \(-0.229409\pi\)
−0.947174 + 0.320719i \(0.896075\pi\)
\(110\) 0 0
\(111\) 104.084i 0.937693i
\(112\) 0 0
\(113\) 175.501 1.55310 0.776552 0.630053i \(-0.216967\pi\)
0.776552 + 0.630053i \(0.216967\pi\)
\(114\) 0 0
\(115\) −2.74726 + 1.58613i −0.0238893 + 0.0137925i
\(116\) 0 0
\(117\) −3.68904 2.12987i −0.0315302 0.0182040i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 43.8930 76.0249i 0.362752 0.628305i
\(122\) 0 0
\(123\) 42.2837 + 73.2375i 0.343770 + 0.595427i
\(124\) 0 0
\(125\) 23.9220i 0.191376i
\(126\) 0 0
\(127\) 31.0434 0.244436 0.122218 0.992503i \(-0.460999\pi\)
0.122218 + 0.992503i \(0.460999\pi\)
\(128\) 0 0
\(129\) −77.3405 + 44.6526i −0.599539 + 0.346144i
\(130\) 0 0
\(131\) 40.2784 + 23.2547i 0.307469 + 0.177517i 0.645793 0.763512i \(-0.276527\pi\)
−0.338325 + 0.941029i \(0.609860\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.24880 + 2.16298i −0.00925034 + 0.0160221i
\(136\) 0 0
\(137\) −22.7327 39.3742i −0.165932 0.287403i 0.771054 0.636770i \(-0.219730\pi\)
−0.936986 + 0.349367i \(0.886397\pi\)
\(138\) 0 0
\(139\) 138.075i 0.993343i −0.867939 0.496672i \(-0.834555\pi\)
0.867939 0.496672i \(-0.165445\pi\)
\(140\) 0 0
\(141\) 33.3283 0.236371
\(142\) 0 0
\(143\) −7.08684 + 4.09159i −0.0495583 + 0.0286125i
\(144\) 0 0
\(145\) 2.58192 + 1.49067i 0.0178063 + 0.0102805i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −119.614 + 207.178i −0.802780 + 1.39045i 0.115000 + 0.993365i \(0.463313\pi\)
−0.917780 + 0.397089i \(0.870020\pi\)
\(150\) 0 0
\(151\) 94.0732 + 162.940i 0.623001 + 1.07907i 0.988924 + 0.148425i \(0.0474202\pi\)
−0.365922 + 0.930645i \(0.619246\pi\)
\(152\) 0 0
\(153\) 69.2014i 0.452297i
\(154\) 0 0
\(155\) −20.1551 −0.130033
\(156\) 0 0
\(157\) −186.402 + 107.619i −1.18728 + 0.685474i −0.957686 0.287814i \(-0.907072\pi\)
−0.229589 + 0.973288i \(0.573738\pi\)
\(158\) 0 0
\(159\) −123.202 71.1306i −0.774854 0.447362i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −74.9053 + 129.740i −0.459542 + 0.795949i −0.998937 0.0461035i \(-0.985320\pi\)
0.539395 + 0.842053i \(0.318653\pi\)
\(164\) 0 0
\(165\) 2.39900 + 4.15520i 0.0145394 + 0.0251830i
\(166\) 0 0
\(167\) 137.195i 0.821528i 0.911742 + 0.410764i \(0.134738\pi\)
−0.911742 + 0.410764i \(0.865262\pi\)
\(168\) 0 0
\(169\) 166.984 0.988070
\(170\) 0 0
\(171\) −27.7315 + 16.0108i −0.162173 + 0.0936304i
\(172\) 0 0
\(173\) 217.529 + 125.591i 1.25739 + 0.725957i 0.972567 0.232621i \(-0.0747303\pi\)
0.284828 + 0.958579i \(0.408064\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 80.1766 138.870i 0.452975 0.784576i
\(178\) 0 0
\(179\) 58.3967 + 101.146i 0.326239 + 0.565062i 0.981762 0.190113i \(-0.0608854\pi\)
−0.655524 + 0.755175i \(0.727552\pi\)
\(180\) 0 0
\(181\) 117.148i 0.647228i −0.946189 0.323614i \(-0.895102\pi\)
0.946189 0.323614i \(-0.104898\pi\)
\(182\) 0 0
\(183\) −8.64618 −0.0472469
\(184\) 0 0
\(185\) −25.0146 + 14.4422i −0.135214 + 0.0780657i
\(186\) 0 0
\(187\) −115.129 66.4698i −0.615663 0.355453i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −170.909 + 296.023i −0.894812 + 1.54986i −0.0607755 + 0.998151i \(0.519357\pi\)
−0.834037 + 0.551709i \(0.813976\pi\)
\(192\) 0 0
\(193\) 112.275 + 194.467i 0.581738 + 1.00760i 0.995273 + 0.0971119i \(0.0309605\pi\)
−0.413535 + 0.910488i \(0.635706\pi\)
\(194\) 0 0
\(195\) 1.18212i 0.00606215i
\(196\) 0 0
\(197\) 257.109 1.30512 0.652560 0.757737i \(-0.273695\pi\)
0.652560 + 0.757737i \(0.273695\pi\)
\(198\) 0 0
\(199\) −212.591 + 122.740i −1.06830 + 0.616782i −0.927716 0.373287i \(-0.878231\pi\)
−0.140582 + 0.990069i \(0.544897\pi\)
\(200\) 0 0
\(201\) 3.31049 + 1.91131i 0.0164701 + 0.00950902i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 11.7342 20.3241i 0.0572398 0.0991422i
\(206\) 0 0
\(207\) −9.89969 17.1468i −0.0478246 0.0828346i
\(208\) 0 0
\(209\) 61.5152i 0.294331i
\(210\) 0 0
\(211\) −95.8210 −0.454128 −0.227064 0.973880i \(-0.572913\pi\)
−0.227064 + 0.973880i \(0.572913\pi\)
\(212\) 0 0
\(213\) −120.885 + 69.7929i −0.567535 + 0.327666i
\(214\) 0 0
\(215\) 21.4628 + 12.3915i 0.0998268 + 0.0576350i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −12.0454 + 20.8632i −0.0550016 + 0.0952657i
\(220\) 0 0
\(221\) −16.3766 28.3652i −0.0741024 0.128349i
\(222\) 0 0
\(223\) 94.2091i 0.422462i −0.977436 0.211231i \(-0.932253\pi\)
0.977436 0.211231i \(-0.0677473\pi\)
\(224\) 0 0
\(225\) −74.3069 −0.330253
\(226\) 0 0
\(227\) −194.209 + 112.127i −0.855545 + 0.493949i −0.862518 0.506026i \(-0.831114\pi\)
0.00697266 + 0.999976i \(0.497781\pi\)
\(228\) 0 0
\(229\) 317.592 + 183.362i 1.38687 + 0.800708i 0.992961 0.118443i \(-0.0377902\pi\)
0.393906 + 0.919151i \(0.371124\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −34.8370 + 60.3395i −0.149515 + 0.258968i −0.931048 0.364896i \(-0.881105\pi\)
0.781533 + 0.623864i \(0.214438\pi\)
\(234\) 0 0
\(235\) −4.62447 8.00981i −0.0196786 0.0340843i
\(236\) 0 0
\(237\) 112.390i 0.474220i
\(238\) 0 0
\(239\) −214.544 −0.897674 −0.448837 0.893614i \(-0.648162\pi\)
−0.448837 + 0.893614i \(0.648162\pi\)
\(240\) 0 0
\(241\) −141.504 + 81.6976i −0.587155 + 0.338994i −0.763972 0.645250i \(-0.776753\pi\)
0.176817 + 0.984244i \(0.443420\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.57798 + 13.1254i −0.0306801 + 0.0531394i
\(248\) 0 0
\(249\) 102.195 + 177.007i 0.410422 + 0.710872i
\(250\) 0 0
\(251\) 330.546i 1.31692i 0.752617 + 0.658458i \(0.228791\pi\)
−0.752617 + 0.658458i \(0.771209\pi\)
\(252\) 0 0
\(253\) −38.0357 −0.150339
\(254\) 0 0
\(255\) −16.6312 + 9.60204i −0.0652205 + 0.0376551i
\(256\) 0 0
\(257\) 139.022 + 80.2644i 0.540942 + 0.312313i 0.745461 0.666550i \(-0.232230\pi\)
−0.204519 + 0.978863i \(0.565563\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −9.30387 + 16.1148i −0.0356470 + 0.0617425i
\(262\) 0 0
\(263\) 53.2577 + 92.2451i 0.202501 + 0.350742i 0.949334 0.314270i \(-0.101760\pi\)
−0.746833 + 0.665012i \(0.768426\pi\)
\(264\) 0 0
\(265\) 39.4789i 0.148977i
\(266\) 0 0
\(267\) 180.592 0.676374
\(268\) 0 0
\(269\) 134.627 77.7268i 0.500471 0.288947i −0.228437 0.973559i \(-0.573361\pi\)
0.728908 + 0.684611i \(0.240028\pi\)
\(270\) 0 0
\(271\) −446.938 258.040i −1.64922 0.952176i −0.977383 0.211475i \(-0.932173\pi\)
−0.671834 0.740702i \(-0.734493\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −71.3738 + 123.623i −0.259541 + 0.449538i
\(276\) 0 0
\(277\) −100.101 173.380i −0.361375 0.625919i 0.626813 0.779170i \(-0.284359\pi\)
−0.988187 + 0.153251i \(0.951026\pi\)
\(278\) 0 0
\(279\) 125.796i 0.450882i
\(280\) 0 0
\(281\) 228.093 0.811720 0.405860 0.913935i \(-0.366972\pi\)
0.405860 + 0.913935i \(0.366972\pi\)
\(282\) 0 0
\(283\) 225.781 130.355i 0.797814 0.460618i −0.0448922 0.998992i \(-0.514294\pi\)
0.842706 + 0.538374i \(0.180961\pi\)
\(284\) 0 0
\(285\) 7.69578 + 4.44316i 0.0270027 + 0.0155900i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 121.546 210.524i 0.420575 0.728457i
\(290\) 0 0
\(291\) −27.5288 47.6813i −0.0946007 0.163853i
\(292\) 0 0
\(293\) 349.885i 1.19415i −0.802186 0.597074i \(-0.796330\pi\)
0.802186 0.597074i \(-0.203670\pi\)
\(294\) 0 0
\(295\) −44.4996 −0.150846
\(296\) 0 0
\(297\) −25.9342 + 14.9731i −0.0873206 + 0.0504146i
\(298\) 0 0
\(299\) −8.11563 4.68556i −0.0271426 0.0156708i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 62.7901 108.756i 0.207228 0.358929i
\(304\) 0 0
\(305\) 1.19970 + 2.07794i 0.00393345 + 0.00681293i
\(306\) 0 0
\(307\) 146.898i 0.478495i 0.970959 + 0.239247i \(0.0769007\pi\)
−0.970959 + 0.239247i \(0.923099\pi\)
\(308\) 0 0
\(309\) −185.265 −0.599562
\(310\) 0 0
\(311\) 69.9177 40.3670i 0.224816 0.129797i −0.383362 0.923598i \(-0.625234\pi\)
0.608178 + 0.793801i \(0.291901\pi\)
\(312\) 0 0
\(313\) 133.661 + 77.1695i 0.427033 + 0.246548i 0.698082 0.716018i \(-0.254037\pi\)
−0.271049 + 0.962566i \(0.587370\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 94.2726 163.285i 0.297390 0.515094i −0.678148 0.734925i \(-0.737217\pi\)
0.975538 + 0.219831i \(0.0705505\pi\)
\(318\) 0 0
\(319\) 17.8732 + 30.9574i 0.0560290 + 0.0970450i
\(320\) 0 0
\(321\) 340.555i 1.06092i
\(322\) 0 0
\(323\) −246.216 −0.762277
\(324\) 0 0
\(325\) −30.4579 + 17.5849i −0.0937166 + 0.0541073i
\(326\) 0 0
\(327\) −64.0384 36.9726i −0.195836 0.113066i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −73.3936 + 127.121i −0.221733 + 0.384053i −0.955334 0.295527i \(-0.904505\pi\)
0.733601 + 0.679580i \(0.237838\pi\)
\(332\) 0 0
\(333\) −90.1393 156.126i −0.270689 0.468846i
\(334\) 0 0
\(335\) 1.06082i 0.00316662i
\(336\) 0 0
\(337\) 101.231 0.300388 0.150194 0.988657i \(-0.452010\pi\)
0.150194 + 0.988657i \(0.452010\pi\)
\(338\) 0 0
\(339\) 263.251 151.988i 0.776552 0.448343i
\(340\) 0 0
\(341\) −209.285 120.831i −0.613738 0.354342i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.74726 + 4.75840i −0.00796308 + 0.0137925i
\(346\) 0 0
\(347\) −175.844 304.571i −0.506756 0.877727i −0.999969 0.00781897i \(-0.997511\pi\)
0.493213 0.869908i \(-0.335822\pi\)
\(348\) 0 0
\(349\) 88.3780i 0.253232i −0.991952 0.126616i \(-0.959588\pi\)
0.991952 0.126616i \(-0.0404116\pi\)
\(350\) 0 0
\(351\) −7.37808 −0.0210202
\(352\) 0 0
\(353\) 450.803 260.271i 1.27706 0.737312i 0.300755 0.953702i \(-0.402761\pi\)
0.976307 + 0.216390i \(0.0694281\pi\)
\(354\) 0 0
\(355\) 33.5468 + 19.3682i 0.0944980 + 0.0545584i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 257.132 445.366i 0.716246 1.24058i −0.246231 0.969211i \(-0.579192\pi\)
0.962477 0.271364i \(-0.0874746\pi\)
\(360\) 0 0
\(361\) −123.534 213.968i −0.342200 0.592708i
\(362\) 0 0
\(363\) 152.050i 0.418870i
\(364\) 0 0
\(365\) 6.68542 0.0183162
\(366\) 0 0
\(367\) 361.726 208.843i 0.985630 0.569054i 0.0816651 0.996660i \(-0.473976\pi\)
0.903965 + 0.427606i \(0.140643\pi\)
\(368\) 0 0
\(369\) 126.851 + 73.2375i 0.343770 + 0.198476i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 70.1568 121.515i 0.188088 0.325778i −0.756525 0.653965i \(-0.773104\pi\)
0.944613 + 0.328187i \(0.106438\pi\)
\(374\) 0 0
\(375\) 20.7171 + 35.8830i 0.0552456 + 0.0956881i
\(376\) 0 0
\(377\) 8.80712i 0.0233611i
\(378\) 0 0
\(379\) 153.298 0.404480 0.202240 0.979336i \(-0.435178\pi\)
0.202240 + 0.979336i \(0.435178\pi\)
\(380\) 0 0
\(381\) 46.5651 26.8844i 0.122218 0.0705626i
\(382\) 0 0
\(383\) −105.410 60.8586i −0.275222 0.158900i 0.356036 0.934472i \(-0.384128\pi\)
−0.631258 + 0.775573i \(0.717461\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −77.3405 + 133.958i −0.199846 + 0.346144i
\(388\) 0 0
\(389\) −200.636 347.511i −0.515773 0.893345i −0.999832 0.0183096i \(-0.994172\pi\)
0.484060 0.875035i \(-0.339162\pi\)
\(390\) 0 0
\(391\) 152.238i 0.389356i
\(392\) 0 0
\(393\) 80.5568 0.204979
\(394\) 0 0
\(395\) −27.0108 + 15.5947i −0.0683818 + 0.0394802i
\(396\) 0 0
\(397\) −52.1564 30.1125i −0.131376 0.0758502i 0.432871 0.901456i \(-0.357500\pi\)
−0.564248 + 0.825605i \(0.690834\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 187.154 324.160i 0.466718 0.808380i −0.532559 0.846393i \(-0.678770\pi\)
0.999277 + 0.0380132i \(0.0121029\pi\)
\(402\) 0 0
\(403\) −29.7699 51.5630i −0.0738707 0.127948i
\(404\) 0 0
\(405\) 4.32595i 0.0106814i
\(406\) 0 0
\(407\) −346.325 −0.850921
\(408\) 0 0
\(409\) 532.267 307.305i 1.30139 0.751356i 0.320745 0.947166i \(-0.396067\pi\)
0.980642 + 0.195810i \(0.0627335\pi\)
\(410\) 0 0
\(411\) −68.1981 39.3742i −0.165932 0.0958010i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 28.3602 49.1212i 0.0683377 0.118364i
\(416\) 0 0
\(417\) −119.576 207.112i −0.286753 0.496672i
\(418\) 0 0
\(419\) 129.067i 0.308035i 0.988068 + 0.154017i \(0.0492212\pi\)
−0.988068 + 0.154017i \(0.950779\pi\)
\(420\) 0 0
\(421\) −697.880 −1.65767 −0.828836 0.559492i \(-0.810996\pi\)
−0.828836 + 0.559492i \(0.810996\pi\)
\(422\) 0 0
\(423\) 49.9924 28.8631i 0.118185 0.0682344i
\(424\) 0 0
\(425\) −494.803 285.674i −1.16424 0.672175i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −7.08684 + 12.2748i −0.0165194 + 0.0286125i
\(430\) 0 0
\(431\) 138.546 + 239.969i 0.321453 + 0.556773i 0.980788 0.195076i \(-0.0624955\pi\)
−0.659335 + 0.751849i \(0.729162\pi\)
\(432\) 0 0
\(433\) 822.794i 1.90022i 0.311919 + 0.950109i \(0.399028\pi\)
−0.311919 + 0.950109i \(0.600972\pi\)
\(434\) 0 0
\(435\) 5.16384 0.0118709
\(436\) 0 0
\(437\) −61.0075 + 35.2227i −0.139605 + 0.0806011i
\(438\) 0 0
\(439\) 316.816 + 182.914i 0.721676 + 0.416660i 0.815369 0.578941i \(-0.196534\pi\)
−0.0936932 + 0.995601i \(0.529867\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 286.696 496.572i 0.647169 1.12093i −0.336626 0.941638i \(-0.609286\pi\)
0.983796 0.179292i \(-0.0573807\pi\)
\(444\) 0 0
\(445\) −25.0580 43.4018i −0.0563102 0.0975321i
\(446\) 0 0
\(447\) 414.356i 0.926970i
\(448\) 0 0
\(449\) 227.961 0.507708 0.253854 0.967243i \(-0.418302\pi\)
0.253854 + 0.967243i \(0.418302\pi\)
\(450\) 0 0
\(451\) 243.688 140.693i 0.540328 0.311958i
\(452\) 0 0
\(453\) 282.220 + 162.940i 0.623001 + 0.359690i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 171.562 297.154i 0.375409 0.650228i −0.614979 0.788544i \(-0.710836\pi\)
0.990388 + 0.138316i \(0.0441688\pi\)
\(458\) 0 0
\(459\) −59.9302 103.802i −0.130567 0.226148i
\(460\) 0 0
\(461\) 611.314i 1.32606i −0.748593 0.663030i \(-0.769270\pi\)
0.748593 0.663030i \(-0.230730\pi\)
\(462\) 0 0
\(463\) −67.2682 −0.145288 −0.0726439 0.997358i \(-0.523144\pi\)
−0.0726439 + 0.997358i \(0.523144\pi\)
\(464\) 0 0
\(465\) −30.2327 + 17.4548i −0.0650165 + 0.0375373i
\(466\) 0 0
\(467\) 81.1897 + 46.8749i 0.173854 + 0.100375i 0.584402 0.811464i \(-0.301329\pi\)
−0.410548 + 0.911839i \(0.634663\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −186.402 + 322.858i −0.395758 + 0.685474i
\(472\) 0 0
\(473\) 148.575 + 257.340i 0.314113 + 0.544059i
\(474\) 0 0
\(475\) 264.381i 0.556591i
\(476\) 0 0
\(477\) −246.403 −0.516569
\(478\) 0 0
\(479\) −306.396 + 176.898i −0.639658 + 0.369306i −0.784483 0.620151i \(-0.787071\pi\)
0.144825 + 0.989457i \(0.453738\pi\)
\(480\) 0 0
\(481\) −73.8950 42.6633i −0.153628 0.0886970i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.63952 + 13.2320i −0.0157516 + 0.0272825i
\(486\) 0 0
\(487\) −476.338 825.042i −0.978107 1.69413i −0.669274 0.743016i \(-0.733395\pi\)
−0.308833 0.951116i \(-0.599939\pi\)
\(488\) 0 0
\(489\) 259.479i 0.530633i
\(490\) 0 0
\(491\) −818.649 −1.66731 −0.833655 0.552286i \(-0.813756\pi\)
−0.833655 + 0.552286i \(0.813756\pi\)
\(492\) 0 0
\(493\) −123.907 + 71.5379i −0.251333 + 0.145107i
\(494\) 0 0
\(495\) 7.19701 + 4.15520i 0.0145394 + 0.00839433i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.0411 20.8557i 0.0241304 0.0417950i −0.853708 0.520752i \(-0.825652\pi\)
0.877838 + 0.478957i \(0.158985\pi\)
\(500\) 0 0
\(501\) 118.815 + 205.793i 0.237155 + 0.410764i
\(502\) 0 0
\(503\) 420.445i 0.835874i −0.908476 0.417937i \(-0.862753\pi\)
0.908476 0.417937i \(-0.137247\pi\)
\(504\) 0 0
\(505\) −34.8498 −0.0690094
\(506\) 0 0
\(507\) 250.476 144.612i 0.494035 0.285231i
\(508\) 0 0
\(509\) −207.732 119.934i −0.408119 0.235627i 0.281862 0.959455i \(-0.409048\pi\)
−0.689981 + 0.723827i \(0.742381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −27.7315 + 48.0324i −0.0540576 + 0.0936304i
\(514\) 0 0
\(515\) 25.7064 + 44.5248i 0.0499153 + 0.0864559i
\(516\) 0 0
\(517\) 110.895i 0.214498i
\(518\) 0 0
\(519\) 435.059 0.838263
\(520\) 0 0
\(521\) −23.2584 + 13.4282i −0.0446418 + 0.0257739i −0.522155 0.852851i \(-0.674872\pi\)
0.477513 + 0.878625i \(0.341538\pi\)
\(522\) 0 0
\(523\) 193.762 + 111.869i 0.370482 + 0.213898i 0.673669 0.739033i \(-0.264717\pi\)
−0.303187 + 0.952931i \(0.598051\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 483.626 837.664i 0.917696 1.58950i
\(528\) 0 0
\(529\) 242.721 + 420.406i 0.458831 + 0.794718i
\(530\) 0 0
\(531\) 277.740i 0.523051i
\(532\) 0 0
\(533\) 69.3272 0.130070
\(534\) 0 0
\(535\) 81.8458 47.2537i 0.152983 0.0883246i
\(536\) 0 0
\(537\) 175.190 + 101.146i 0.326239 + 0.188354i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −493.095 + 854.065i −0.911451 + 1.57868i −0.0994342 + 0.995044i \(0.531703\pi\)
−0.812016 + 0.583635i \(0.801630\pi\)
\(542\) 0 0
\(543\) −101.453 175.723i −0.186839 0.323614i
\(544\) 0 0
\(545\) 20.5205i 0.0376523i
\(546\) 0 0
\(547\) 735.369 1.34437 0.672183 0.740385i \(-0.265357\pi\)
0.672183 + 0.740385i \(0.265357\pi\)
\(548\) 0 0
\(549\) −12.9693 + 7.48781i −0.0236234 + 0.0136390i
\(550\) 0 0
\(551\) 57.3357 + 33.1028i 0.104058 + 0.0600776i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −25.0146 + 43.3265i −0.0450713 + 0.0780657i
\(556\) 0 0
\(557\) −209.284 362.491i −0.375735 0.650791i 0.614702 0.788759i \(-0.289276\pi\)
−0.990437 + 0.137968i \(0.955943\pi\)
\(558\) 0 0
\(559\) 73.2111i 0.130968i
\(560\) 0 0
\(561\) −230.258 −0.410442
\(562\) 0 0
\(563\) −646.694 + 373.369i −1.14866 + 0.663177i −0.948560 0.316599i \(-0.897459\pi\)
−0.200097 + 0.979776i \(0.564126\pi\)
\(564\) 0 0
\(565\) −73.0549 42.1782i −0.129301 0.0746518i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 144.355 250.030i 0.253699 0.439420i −0.710842 0.703351i \(-0.751686\pi\)
0.964541 + 0.263932i \(0.0850194\pi\)
\(570\) 0 0
\(571\) 458.104 + 793.459i 0.802283 + 1.38960i 0.918110 + 0.396326i \(0.129715\pi\)
−0.115827 + 0.993269i \(0.536952\pi\)
\(572\) 0 0
\(573\) 592.047i 1.03324i
\(574\) 0 0
\(575\) −163.470 −0.284296
\(576\) 0 0
\(577\) −859.156 + 496.034i −1.48901 + 0.859678i −0.999921 0.0125584i \(-0.996002\pi\)
−0.489085 + 0.872236i \(0.662669\pi\)
\(578\) 0 0
\(579\) 336.826 + 194.467i 0.581738 + 0.335867i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −236.677 + 409.937i −0.405964 + 0.703151i
\(584\) 0 0
\(585\) 1.02375 + 1.77318i 0.00174999 + 0.00303108i
\(586\) 0 0
\(587\) 154.965i 0.263996i −0.991250 0.131998i \(-0.957861\pi\)
0.991250 0.131998i \(-0.0421392\pi\)
\(588\) 0 0
\(589\) −447.577 −0.759893
\(590\) 0 0
\(591\) 385.663 222.663i 0.652560 0.376756i
\(592\) 0 0
\(593\) −869.636 502.084i −1.46650 0.846685i −0.467204 0.884149i \(-0.654739\pi\)
−0.999298 + 0.0374640i \(0.988072\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −212.591 + 368.219i −0.356099 + 0.616782i
\(598\) 0 0
\(599\) 398.459 + 690.150i 0.665206 + 1.15217i 0.979229 + 0.202756i \(0.0649897\pi\)
−0.314023 + 0.949415i \(0.601677\pi\)
\(600\) 0 0
\(601\) 467.002i 0.777041i 0.921440 + 0.388521i \(0.127014\pi\)
−0.921440 + 0.388521i \(0.872986\pi\)
\(602\) 0 0
\(603\) 6.62098 0.0109801
\(604\) 0 0
\(605\) −36.5422 + 21.0977i −0.0604004 + 0.0348722i
\(606\) 0 0
\(607\) 788.270 + 455.108i 1.29863 + 0.749766i 0.980168 0.198169i \(-0.0634993\pi\)
0.318465 + 0.947935i \(0.396833\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13.6610 23.6616i 0.0223585 0.0387260i
\(612\) 0 0
\(613\) −387.900 671.863i −0.632790 1.09602i −0.986979 0.160850i \(-0.948576\pi\)
0.354189 0.935174i \(-0.384757\pi\)
\(614\) 0 0
\(615\) 40.6483i 0.0660948i
\(616\) 0 0
\(617\) 974.803 1.57991 0.789954 0.613166i \(-0.210104\pi\)
0.789954 + 0.613166i \(0.210104\pi\)
\(618\) 0 0
\(619\) 172.564 99.6300i 0.278779 0.160953i −0.354092 0.935211i \(-0.615210\pi\)
0.632870 + 0.774258i \(0.281877\pi\)
\(620\) 0 0
\(621\) −29.6991 17.1468i −0.0478246 0.0276115i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −303.863 + 526.306i −0.486181 + 0.842089i
\(626\) 0 0
\(627\) 53.2738 + 92.2729i 0.0849661 + 0.147166i
\(628\) 0 0
\(629\) 1386.17i 2.20377i
\(630\) 0 0
\(631\) 751.062 1.19027 0.595136 0.803625i \(-0.297098\pi\)
0.595136 + 0.803625i \(0.297098\pi\)
\(632\) 0 0
\(633\) −143.732 + 82.9835i −0.227064 + 0.131096i
\(634\) 0 0
\(635\) −12.9223 7.46068i −0.0203500 0.0117491i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −120.885 + 209.379i −0.189178 + 0.327666i
\(640\) 0 0
\(641\) 569.138 + 985.776i 0.887891 + 1.53787i 0.842364 + 0.538910i \(0.181164\pi\)
0.0455278 + 0.998963i \(0.485503\pi\)
\(642\) 0 0
\(643\) 647.823i 1.00750i −0.863849 0.503751i \(-0.831953\pi\)
0.863849 0.503751i \(-0.168047\pi\)
\(644\) 0 0
\(645\) 42.9255 0.0665512
\(646\) 0 0
\(647\) −764.651 + 441.471i −1.18184 + 0.682336i −0.956440 0.291930i \(-0.905703\pi\)
−0.225401 + 0.974266i \(0.572369\pi\)
\(648\) 0 0
\(649\) −462.071 266.777i −0.711974 0.411058i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −272.558 + 472.085i −0.417394 + 0.722948i −0.995676 0.0928890i \(-0.970390\pi\)
0.578282 + 0.815837i \(0.303723\pi\)
\(654\) 0 0
\(655\) −11.1777 19.3603i −0.0170651 0.0295577i
\(656\) 0 0
\(657\) 41.7264i 0.0635104i
\(658\) 0 0
\(659\) 698.290 1.05962 0.529810 0.848116i \(-0.322263\pi\)
0.529810 + 0.848116i \(0.322263\pi\)
\(660\) 0 0
\(661\) 495.128 285.863i 0.749060 0.432470i −0.0762943 0.997085i \(-0.524309\pi\)
0.825354 + 0.564616i \(0.190976\pi\)
\(662\) 0 0
\(663\) −49.1299 28.3652i −0.0741024 0.0427831i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −20.4679 + 35.4514i −0.0306865 + 0.0531505i
\(668\) 0 0
\(669\) −81.5875 141.314i −0.121954 0.211231i
\(670\) 0 0
\(671\) 28.7690i 0.0428748i
\(672\) 0 0
\(673\) 221.015 0.328403 0.164202 0.986427i \(-0.447495\pi\)
0.164202 + 0.986427i \(0.447495\pi\)
\(674\) 0 0
\(675\) −111.460 + 64.3517i −0.165126 + 0.0953358i
\(676\) 0 0
\(677\) −407.608 235.333i −0.602080 0.347611i 0.167779 0.985825i \(-0.446340\pi\)
−0.769860 + 0.638213i \(0.779674\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −194.209 + 336.380i −0.285182 + 0.493949i
\(682\) 0 0
\(683\) −107.980 187.027i −0.158097 0.273831i 0.776086 0.630628i \(-0.217202\pi\)
−0.934182 + 0.356796i \(0.883869\pi\)
\(684\) 0 0
\(685\) 21.8535i 0.0319029i
\(686\) 0 0
\(687\) 635.185 0.924578
\(688\) 0 0
\(689\) −100.999 + 58.3119i −0.146588 + 0.0846326i
\(690\) 0 0
\(691\) −69.3808 40.0570i −0.100406 0.0579697i 0.448956 0.893554i \(-0.351796\pi\)
−0.549362 + 0.835584i \(0.685129\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −33.1836 + 57.4757i −0.0477462 + 0.0826988i
\(696\) 0 0
\(697\) 563.126 + 975.363i 0.807929 + 1.39937i
\(698\) 0 0
\(699\) 120.679i 0.172645i
\(700\) 0 0
\(701\) −821.973 −1.17257 −0.586286 0.810104i \(-0.699411\pi\)
−0.586286 + 0.810104i \(0.699411\pi\)
\(702\) 0 0
\(703\) −555.489 + 320.712i −0.790169 + 0.456204i
\(704\) 0 0
\(705\) −13.8734 8.00981i −0.0196786 0.0113614i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −287.728 + 498.359i −0.405822 + 0.702904i −0.994417 0.105524i \(-0.966348\pi\)
0.588595 + 0.808428i \(0.299681\pi\)
\(710\) 0 0
\(711\) −97.3327 168.585i −0.136896 0.237110i
\(712\) 0 0
\(713\) 276.743i 0.388139i
\(714\) 0 0
\(715\) 3.93334 0.00550117
\(716\) 0 0
\(717\) −321.816 + 185.801i −0.448837 + 0.259136i
\(718\) 0 0
\(719\) 1051.29 + 606.964i 1.46216 + 0.844178i 0.999111 0.0421556i \(-0.0134225\pi\)
0.463048 + 0.886333i \(0.346756\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −141.504 + 245.093i −0.195718 + 0.338994i
\(724\) 0 0
\(725\) 76.8158 + 133.049i 0.105953 + 0.183516i
\(726\) 0 0
\(727\) 379.498i 0.522005i −0.965338 0.261003i \(-0.915947\pi\)
0.965338 0.261003i \(-0.0840532\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −1030.01 + 594.674i −1.40904 + 0.813508i
\(732\) 0 0
\(733\) 1082.93 + 625.230i 1.47739 + 0.852973i 0.999674 0.0255391i \(-0.00813022\pi\)
0.477719 + 0.878512i \(0.341464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.35963 11.0152i 0.00862908 0.0149460i
\(738\) 0 0
\(739\) −250.617 434.081i −0.339130 0.587390i 0.645139 0.764065i \(-0.276799\pi\)
−0.984269 + 0.176675i \(0.943466\pi\)
\(740\) 0 0
\(741\) 26.2509i 0.0354263i
\(742\) 0 0
\(743\) 444.584 0.598363 0.299181 0.954196i \(-0.403286\pi\)
0.299181 + 0.954196i \(0.403286\pi\)
\(744\) 0 0
\(745\) 99.5824 57.4939i 0.133668 0.0771730i
\(746\) 0 0
\(747\) 306.585 + 177.007i 0.410422 + 0.236957i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −119.667 + 207.270i −0.159344 + 0.275992i −0.934632 0.355616i \(-0.884271\pi\)
0.775288 + 0.631608i \(0.217605\pi\)
\(752\) 0 0
\(753\) 286.261 + 495.819i 0.380161 + 0.658458i
\(754\) 0 0
\(755\) 90.4347i 0.119781i
\(756\) 0 0
\(757\) 249.486 0.329572 0.164786 0.986329i \(-0.447307\pi\)
0.164786 + 0.986329i \(0.447307\pi\)
\(758\) 0 0
\(759\) −57.0535 + 32.9399i −0.0751693 + 0.0433990i
\(760\) 0 0
\(761\) −1191.37 687.840i −1.56554 0.903864i −0.996679 0.0814280i \(-0.974052\pi\)
−0.568858 0.822436i \(-0.692615\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −16.6312 + 28.8061i −0.0217402 + 0.0376551i
\(766\) 0 0
\(767\) −65.7277 113.844i −0.0856945 0.148427i
\(768\) 0 0
\(769\) 528.594i 0.687379i 0.939083 + 0.343689i \(0.111677\pi\)
−0.939083 + 0.343689i \(0.888323\pi\)
\(770\) 0 0
\(771\) 278.044 0.360628
\(772\) 0 0
\(773\) 53.6879 30.9967i 0.0694539 0.0400992i −0.464871 0.885378i \(-0.653899\pi\)
0.534325 + 0.845279i \(0.320566\pi\)
\(774\) 0 0
\(775\) −899.465 519.307i −1.16060 0.670073i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 260.576 451.331i 0.334501 0.579372i
\(780\) 0 0
\(781\) 232.226 + 402.228i 0.297345 + 0.515017i
\(782\) 0 0
\(783\) 32.2296i 0.0411616i
\(784\) 0 0
\(785\) 103.457 0.131792
\(786\) 0 0
\(787\) −141.654 + 81.7839i −0.179992 + 0.103919i −0.587289 0.809377i \(-0.699805\pi\)
0.407297 + 0.913296i \(0.366471\pi\)
\(788\) 0 0
\(789\) 159.773 + 92.2451i 0.202501 + 0.116914i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −3.54401 + 6.13841i −0.00446912 + 0.00774074i
\(794\) 0 0
\(795\) 34.1897 + 59.2183i 0.0430059 + 0.0744885i
\(796\) 0 0
\(797\) 533.394i 0.669253i −0.942351 0.334626i \(-0.891390\pi\)
0.942351 0.334626i \(-0.108610\pi\)