Properties

Label 768.2.n.b.481.3
Level $768$
Weight $2$
Character 768.481
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 481.3
Character \(\chi\) \(=\) 768.481
Dual form 768.2.n.b.289.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.32741 + 3.20465i) q^{11} +(5.55375 - 2.30044i) q^{13} -2.72085i q^{15} -4.16447i q^{17} +(4.49866 - 1.86340i) q^{19} +(-1.08795 + 2.62654i) q^{21} +(1.94282 - 1.94282i) q^{23} +(1.69919 + 1.69919i) q^{25} +(0.923880 + 0.382683i) q^{27} +(1.96103 + 4.73434i) q^{29} +2.87015 q^{31} +3.46869 q^{33} +(-2.96015 - 7.14642i) q^{35} +(-6.31049 - 2.61389i) q^{37} +(-4.25066 - 4.25066i) q^{39} +(0.756366 - 0.756366i) q^{41} +(1.53775 - 3.71245i) q^{43} +(-2.51374 + 1.04122i) q^{45} +1.08220i q^{47} +1.08236i q^{49} +(-3.84747 + 1.59367i) q^{51} +(2.90450 - 7.01208i) q^{53} +(-6.67351 + 6.67351i) q^{55} +(-3.44312 - 3.44312i) q^{57} +(10.3425 + 4.28402i) q^{59} +(2.97711 + 7.18739i) q^{61} +2.84295 q^{63} +16.3559 q^{65} +(-3.88805 - 9.38659i) q^{67} +(-2.53841 - 1.05145i) q^{69} +(1.88924 + 1.88924i) q^{71} +(-7.00727 + 7.00727i) q^{73} +(0.919594 - 2.22010i) q^{75} +(9.11066 - 3.77376i) q^{77} -11.0255i q^{79} -1.00000i q^{81} +(-2.30515 + 0.954824i) q^{83} +(4.33615 - 10.4684i) q^{85} +(3.62351 - 3.62351i) q^{87} +(7.65800 + 7.65800i) q^{89} +(-15.7890 - 6.54003i) q^{91} +(-1.09836 - 2.65168i) q^{93} +13.2487 q^{95} -11.3029 q^{97} +(-1.32741 - 3.20465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} - 48q^{35} - 16q^{43} + 16q^{51} + 32q^{53} - 32q^{55} + 64q^{59} + 32q^{61} - 16q^{63} + 16q^{67} + 32q^{69} - 64q^{71} + 32q^{75} + 32q^{77} - 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\)

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
\(3\) −0.382683 0.923880i −0.220942 0.533402i
\(4\) 0 0
\(5\) 2.51374 + 1.04122i 1.12418 + 0.465649i 0.865798 0.500394i \(-0.166812\pi\)
0.258379 + 0.966044i \(0.416812\pi\)
\(6\) 0 0
\(7\) −2.01027 2.01027i −0.759810 0.759810i 0.216477 0.976288i \(-0.430543\pi\)
−0.976288 + 0.216477i \(0.930543\pi\)
\(8\) 0 0
\(9\) −0.707107 + 0.707107i −0.235702 + 0.235702i
\(10\) 0 0
\(11\) −1.32741 + 3.20465i −0.400229 + 0.966238i 0.587381 + 0.809310i \(0.300159\pi\)
−0.987610 + 0.156928i \(0.949841\pi\)
\(12\) 0 0
\(13\) 5.55375 2.30044i 1.54033 0.638027i 0.558798 0.829304i \(-0.311263\pi\)
0.981536 + 0.191277i \(0.0612628\pi\)
\(14\) 0 0
\(15\) 2.72085i 0.702520i
\(16\) 0 0
\(17\) 4.16447i 1.01003i −0.863110 0.505016i \(-0.831486\pi\)
0.863110 0.505016i \(-0.168514\pi\)
\(18\) 0 0
\(19\) 4.49866 1.86340i 1.03206 0.427494i 0.198606 0.980079i \(-0.436359\pi\)
0.833456 + 0.552585i \(0.186359\pi\)
\(20\) 0 0
\(21\) −1.08795 + 2.62654i −0.237410 + 0.573159i
\(22\) 0 0
\(23\) 1.94282 1.94282i 0.405106 0.405106i −0.474922 0.880028i \(-0.657524\pi\)
0.880028 + 0.474922i \(0.157524\pi\)
\(24\) 0 0
\(25\) 1.69919 + 1.69919i 0.339838 + 0.339838i
\(26\) 0 0
\(27\) 0.923880 + 0.382683i 0.177801 + 0.0736475i
\(28\) 0 0
\(29\) 1.96103 + 4.73434i 0.364154 + 0.879145i 0.994683 + 0.102980i \(0.0328377\pi\)
−0.630530 + 0.776165i \(0.717162\pi\)
\(30\) 0 0
\(31\) 2.87015 0.515495 0.257747 0.966212i \(-0.417020\pi\)
0.257747 + 0.966212i \(0.417020\pi\)
\(32\) 0 0
\(33\) 3.46869 0.603821
\(34\) 0 0
\(35\) −2.96015 7.14642i −0.500356 1.20797i
\(36\) 0 0
\(37\) −6.31049 2.61389i −1.03744 0.429721i −0.202046 0.979376i \(-0.564759\pi\)
−0.835392 + 0.549655i \(0.814759\pi\)
\(38\) 0 0
\(39\) −4.25066 4.25066i −0.680650 0.680650i
\(40\) 0 0
\(41\) 0.756366 0.756366i 0.118125 0.118125i −0.645574 0.763698i \(-0.723382\pi\)
0.763698 + 0.645574i \(0.223382\pi\)
\(42\) 0 0
\(43\) 1.53775 3.71245i 0.234504 0.566143i −0.762193 0.647350i \(-0.775877\pi\)
0.996697 + 0.0812067i \(0.0258774\pi\)
\(44\) 0 0
\(45\) −2.51374 + 1.04122i −0.374726 + 0.155216i
\(46\) 0 0
\(47\) 1.08220i 0.157855i 0.996880 + 0.0789273i \(0.0251495\pi\)
−0.996880 + 0.0789273i \(0.974851\pi\)
\(48\) 0 0
\(49\) 1.08236i 0.154623i
\(50\) 0 0
\(51\) −3.84747 + 1.59367i −0.538754 + 0.223159i
\(52\) 0 0
\(53\) 2.90450 7.01208i 0.398963 0.963183i −0.588949 0.808170i \(-0.700458\pi\)
0.987912 0.155013i \(-0.0495418\pi\)
\(54\) 0 0
\(55\) −6.67351 + 6.67351i −0.899856 + 0.899856i
\(56\) 0 0
\(57\) −3.44312 3.44312i −0.456053 0.456053i
\(58\) 0 0
\(59\) 10.3425 + 4.28402i 1.34648 + 0.557732i 0.935311 0.353826i \(-0.115120\pi\)
0.411172 + 0.911558i \(0.365120\pi\)
\(60\) 0 0
\(61\) 2.97711 + 7.18739i 0.381180 + 0.920251i 0.991738 + 0.128279i \(0.0409454\pi\)
−0.610558 + 0.791972i \(0.709055\pi\)
\(62\) 0 0
\(63\) 2.84295 0.358178
\(64\) 0 0
\(65\) 16.3559 2.02870
\(66\) 0 0
\(67\) −3.88805 9.38659i −0.475001 1.14676i −0.961926 0.273311i \(-0.911881\pi\)
0.486924 0.873444i \(-0.338119\pi\)
\(68\) 0 0
\(69\) −2.53841 1.05145i −0.305589 0.126579i
\(70\) 0 0
\(71\) 1.88924 + 1.88924i 0.224211 + 0.224211i 0.810269 0.586058i \(-0.199321\pi\)
−0.586058 + 0.810269i \(0.699321\pi\)
\(72\) 0 0
\(73\) −7.00727 + 7.00727i −0.820139 + 0.820139i −0.986128 0.165989i \(-0.946918\pi\)
0.165989 + 0.986128i \(0.446918\pi\)
\(74\) 0 0
\(75\) 0.919594 2.22010i 0.106186 0.256355i
\(76\) 0 0
\(77\) 9.11066 3.77376i 1.03826 0.430060i
\(78\) 0 0
\(79\) 11.0255i 1.24047i −0.784417 0.620234i \(-0.787038\pi\)
0.784417 0.620234i \(-0.212962\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −2.30515 + 0.954824i −0.253023 + 0.104806i −0.505590 0.862774i \(-0.668725\pi\)
0.252567 + 0.967579i \(0.418725\pi\)
\(84\) 0 0
\(85\) 4.33615 10.4684i 0.470321 1.13546i
\(86\) 0 0
\(87\) 3.62351 3.62351i 0.388481 0.388481i
\(88\) 0 0
\(89\) 7.65800 + 7.65800i 0.811747 + 0.811747i 0.984896 0.173149i \(-0.0553943\pi\)
−0.173149 + 0.984896i \(0.555394\pi\)
\(90\) 0 0
\(91\) −15.7890 6.54003i −1.65514 0.685582i
\(92\) 0 0
\(93\) −1.09836 2.65168i −0.113895 0.274966i
\(94\) 0 0
\(95\) 13.2487 1.35928
\(96\) 0 0
\(97\) −11.3029 −1.14764 −0.573819 0.818982i \(-0.694539\pi\)
−0.573819 + 0.818982i \(0.694539\pi\)
\(98\) 0 0
\(99\) −1.32741 3.20465i −0.133410 0.322079i
\(100\) 0 0
\(101\) −3.56392 1.47622i −0.354623 0.146890i 0.198258 0.980150i \(-0.436472\pi\)
−0.552881 + 0.833260i \(0.686472\pi\)
\(102\) 0 0
\(103\) 1.94329 + 1.94329i 0.191478 + 0.191478i 0.796335 0.604856i \(-0.206769\pi\)
−0.604856 + 0.796335i \(0.706769\pi\)
\(104\) 0 0
\(105\) −5.46964 + 5.46964i −0.533782 + 0.533782i
\(106\) 0 0
\(107\) −5.35190 + 12.9206i −0.517388 + 1.24908i 0.422114 + 0.906543i \(0.361288\pi\)
−0.939502 + 0.342542i \(0.888712\pi\)
\(108\) 0 0
\(109\) −12.1425 + 5.02958i −1.16304 + 0.481747i −0.878886 0.477032i \(-0.841713\pi\)
−0.284154 + 0.958779i \(0.591713\pi\)
\(110\) 0 0
\(111\) 6.83043i 0.648315i
\(112\) 0 0
\(113\) 13.8394i 1.30190i −0.759121 0.650950i \(-0.774371\pi\)
0.759121 0.650950i \(-0.225629\pi\)
\(114\) 0 0
\(115\) 6.90664 2.86082i 0.644048 0.266773i
\(116\) 0 0
\(117\) −2.30044 + 5.55375i −0.212676 + 0.513445i
\(118\) 0 0
\(119\) −8.37171 + 8.37171i −0.767433 + 0.767433i
\(120\) 0 0
\(121\) −0.729588 0.729588i −0.0663262 0.0663262i
\(122\) 0 0
\(123\) −0.988240 0.409342i −0.0891066 0.0369092i
\(124\) 0 0
\(125\) −2.70404 6.52814i −0.241857 0.583894i
\(126\) 0 0
\(127\) 5.47542 0.485865 0.242932 0.970043i \(-0.421891\pi\)
0.242932 + 0.970043i \(0.421891\pi\)
\(128\) 0 0
\(129\) −4.01832 −0.353794
\(130\) 0 0
\(131\) 8.03254 + 19.3923i 0.701806 + 1.69431i 0.719525 + 0.694466i \(0.244359\pi\)
−0.0177195 + 0.999843i \(0.505641\pi\)
\(132\) 0 0
\(133\) −12.7894 5.29756i −1.10899 0.459357i
\(134\) 0 0
\(135\) 1.92393 + 1.92393i 0.165586 + 0.165586i
\(136\) 0 0
\(137\) −3.73965 + 3.73965i −0.319500 + 0.319500i −0.848575 0.529075i \(-0.822539\pi\)
0.529075 + 0.848575i \(0.322539\pi\)
\(138\) 0 0
\(139\) −4.05949 + 9.80047i −0.344321 + 0.831265i 0.652947 + 0.757403i \(0.273532\pi\)
−0.997268 + 0.0738616i \(0.976468\pi\)
\(140\) 0 0
\(141\) 0.999819 0.414139i 0.0841999 0.0348768i
\(142\) 0 0
\(143\) 20.8515i 1.74369i
\(144\) 0 0
\(145\) 13.9427i 1.15788i
\(146\) 0 0
\(147\) 0.999970 0.414201i 0.0824761 0.0341627i
\(148\) 0 0
\(149\) −4.32999 + 10.4535i −0.354727 + 0.856386i 0.641297 + 0.767293i \(0.278397\pi\)
−0.996023 + 0.0890929i \(0.971603\pi\)
\(150\) 0 0
\(151\) −12.1795 + 12.1795i −0.991157 + 0.991157i −0.999961 0.00880460i \(-0.997197\pi\)
0.00880460 + 0.999961i \(0.497197\pi\)
\(152\) 0 0
\(153\) 2.94473 + 2.94473i 0.238067 + 0.238067i
\(154\) 0 0
\(155\) 7.21481 + 2.98847i 0.579507 + 0.240040i
\(156\) 0 0
\(157\) 5.53996 + 13.3746i 0.442137 + 1.06741i 0.975198 + 0.221336i \(0.0710417\pi\)
−0.533061 + 0.846077i \(0.678958\pi\)
\(158\) 0 0
\(159\) −7.58982 −0.601912
\(160\) 0 0
\(161\) −7.81117 −0.615607
\(162\) 0 0
\(163\) 5.79233 + 13.9839i 0.453690 + 1.09530i 0.970908 + 0.239451i \(0.0769675\pi\)
−0.517218 + 0.855854i \(0.673032\pi\)
\(164\) 0 0
\(165\) 8.71936 + 3.61168i 0.678802 + 0.281169i
\(166\) 0 0
\(167\) −4.07626 4.07626i −0.315430 0.315430i 0.531579 0.847009i \(-0.321599\pi\)
−0.847009 + 0.531579i \(0.821599\pi\)
\(168\) 0 0
\(169\) 16.3598 16.3598i 1.25844 1.25844i
\(170\) 0 0
\(171\) −1.86340 + 4.49866i −0.142498 + 0.344021i
\(172\) 0 0
\(173\) −4.29724 + 1.77998i −0.326713 + 0.135329i −0.540010 0.841658i \(-0.681580\pi\)
0.213297 + 0.976987i \(0.431580\pi\)
\(174\) 0 0
\(175\) 6.83165i 0.516424i
\(176\) 0 0
\(177\) 11.1947i 0.841443i
\(178\) 0 0
\(179\) −0.273384 + 0.113240i −0.0204337 + 0.00846392i −0.392877 0.919591i \(-0.628520\pi\)
0.372443 + 0.928055i \(0.378520\pi\)
\(180\) 0 0
\(181\) −4.00336 + 9.66497i −0.297567 + 0.718391i 0.702411 + 0.711772i \(0.252107\pi\)
−0.999978 + 0.00661937i \(0.997893\pi\)
\(182\) 0 0
\(183\) 5.50099 5.50099i 0.406645 0.406645i
\(184\) 0 0
\(185\) −13.1413 13.1413i −0.966165 0.966165i
\(186\) 0 0
\(187\) 13.3457 + 5.52796i 0.975932 + 0.404244i
\(188\) 0 0
\(189\) −1.08795 2.62654i −0.0791367 0.191053i
\(190\) 0 0
\(191\) −15.1625 −1.09712 −0.548561 0.836110i \(-0.684824\pi\)
−0.548561 + 0.836110i \(0.684824\pi\)
\(192\) 0 0
\(193\) −18.3549 −1.32122 −0.660608 0.750731i \(-0.729701\pi\)
−0.660608 + 0.750731i \(0.729701\pi\)
\(194\) 0 0
\(195\) −6.25915 15.1109i −0.448227 1.08212i
\(196\) 0 0
\(197\) 6.65334 + 2.75590i 0.474031 + 0.196350i 0.606891 0.794785i \(-0.292416\pi\)
−0.132861 + 0.991135i \(0.542416\pi\)
\(198\) 0 0
\(199\) 0.849057 + 0.849057i 0.0601880 + 0.0601880i 0.736560 0.676372i \(-0.236449\pi\)
−0.676372 + 0.736560i \(0.736449\pi\)
\(200\) 0 0
\(201\) −7.18419 + 7.18419i −0.506734 + 0.506734i
\(202\) 0 0
\(203\) 5.57510 13.4595i 0.391295 0.944671i
\(204\) 0 0
\(205\) 2.68885 1.11376i 0.187797 0.0777883i
\(206\) 0 0
\(207\) 2.74756i 0.190969i
\(208\) 0 0
\(209\) 16.8901i 1.16831i
\(210\) 0 0
\(211\) −7.40729 + 3.06820i −0.509939 + 0.211224i −0.622791 0.782388i \(-0.714001\pi\)
0.112852 + 0.993612i \(0.464001\pi\)
\(212\) 0 0
\(213\) 1.02245 2.46841i 0.0700570 0.169133i
\(214\) 0 0
\(215\) 7.73098 7.73098i 0.527248 0.527248i
\(216\) 0 0
\(217\) −5.76978 5.76978i −0.391678 0.391678i
\(218\) 0 0
\(219\) 9.15544 + 3.79231i 0.618667 + 0.256260i
\(220\) 0 0
\(221\) −9.58012 23.1285i −0.644429 1.55579i
\(222\) 0 0
\(223\) −0.188370 −0.0126142 −0.00630710 0.999980i \(-0.502008\pi\)
−0.00630710 + 0.999980i \(0.502008\pi\)
\(224\) 0 0
\(225\) −2.40301 −0.160201
\(226\) 0 0
\(227\) −0.106761 0.257744i −0.00708599 0.0171071i 0.920297 0.391221i \(-0.127947\pi\)
−0.927383 + 0.374113i \(0.877947\pi\)
\(228\) 0 0
\(229\) −2.03685 0.843689i −0.134599 0.0557526i 0.314367 0.949301i \(-0.398208\pi\)
−0.448966 + 0.893549i \(0.648208\pi\)
\(230\) 0 0
\(231\) −6.97299 6.97299i −0.458789 0.458789i
\(232\) 0 0
\(233\) −4.32675 + 4.32675i −0.283455 + 0.283455i −0.834485 0.551030i \(-0.814235\pi\)
0.551030 + 0.834485i \(0.314235\pi\)
\(234\) 0 0
\(235\) −1.12681 + 2.72036i −0.0735049 + 0.177456i
\(236\) 0 0
\(237\) −10.1863 + 4.21928i −0.661668 + 0.274072i
\(238\) 0 0
\(239\) 8.26905i 0.534880i 0.963575 + 0.267440i \(0.0861777\pi\)
−0.963575 + 0.267440i \(0.913822\pi\)
\(240\) 0 0
\(241\) 22.7291i 1.46411i −0.681244 0.732057i \(-0.738561\pi\)
0.681244 0.732057i \(-0.261439\pi\)
\(242\) 0 0
\(243\) −0.923880 + 0.382683i −0.0592669 + 0.0245492i
\(244\) 0 0
\(245\) −1.12698 + 2.72077i −0.0720000 + 0.173823i
\(246\) 0 0
\(247\) 20.6978 20.6978i 1.31697 1.31697i
\(248\) 0 0
\(249\) 1.76429 + 1.76429i 0.111807 + 0.111807i
\(250\) 0 0
\(251\) −12.3335 5.10871i −0.778485 0.322459i −0.0421812 0.999110i \(-0.513431\pi\)
−0.736304 + 0.676651i \(0.763431\pi\)
\(252\) 0 0
\(253\) 3.64714 + 8.80497i 0.229294 + 0.553564i
\(254\) 0 0
\(255\) −11.3309 −0.709568
\(256\) 0 0
\(257\) 15.9974 0.997893 0.498947 0.866633i \(-0.333720\pi\)
0.498947 + 0.866633i \(0.333720\pi\)
\(258\) 0 0
\(259\) 7.43116 + 17.9404i 0.461750 + 1.11476i
\(260\) 0 0
\(261\) −4.73434 1.96103i −0.293048 0.121385i
\(262\) 0 0
\(263\) 4.44583 + 4.44583i 0.274141 + 0.274141i 0.830765 0.556623i \(-0.187903\pi\)
−0.556623 + 0.830765i \(0.687903\pi\)
\(264\) 0 0
\(265\) 14.6023 14.6023i 0.897011 0.897011i
\(266\) 0 0
\(267\) 4.14448 10.0057i 0.253638 0.612336i
\(268\) 0 0
\(269\) 11.1204 4.60621i 0.678021 0.280846i −0.0169781 0.999856i \(-0.505405\pi\)
0.695000 + 0.719010i \(0.255405\pi\)
\(270\) 0 0
\(271\) 18.7073i 1.13638i −0.822896 0.568192i \(-0.807643\pi\)
0.822896 0.568192i \(-0.192357\pi\)
\(272\) 0 0
\(273\) 17.0899i 1.03433i
\(274\) 0 0
\(275\) −7.70082 + 3.18978i −0.464377 + 0.192351i
\(276\) 0 0
\(277\) 4.13646 9.98630i 0.248536 0.600019i −0.749544 0.661954i \(-0.769727\pi\)
0.998080 + 0.0619354i \(0.0197273\pi\)
\(278\) 0 0
\(279\) −2.02950 + 2.02950i −0.121503 + 0.121503i
\(280\) 0 0
\(281\) −13.2105 13.2105i −0.788071 0.788071i 0.193106 0.981178i \(-0.438144\pi\)
−0.981178 + 0.193106i \(0.938144\pi\)
\(282\) 0 0
\(283\) −21.9884 9.10789i −1.30707 0.541408i −0.383045 0.923730i \(-0.625125\pi\)
−0.924029 + 0.382321i \(0.875125\pi\)
\(284\) 0 0
\(285\) −5.07004 12.2402i −0.300323 0.725044i
\(286\) 0 0
\(287\) −3.04100 −0.179504
\(288\) 0 0
\(289\) −0.342832 −0.0201666
\(290\) 0 0
\(291\) 4.32544 + 10.4425i 0.253562 + 0.612152i
\(292\) 0 0
\(293\) 18.8878 + 7.82359i 1.10344 + 0.457059i 0.858673 0.512524i \(-0.171289\pi\)
0.244764 + 0.969583i \(0.421289\pi\)
\(294\) 0 0
\(295\) 21.5378 + 21.5378i 1.25398 + 1.25398i
\(296\) 0 0
\(297\) −2.45273 + 2.45273i −0.142322 + 0.142322i
\(298\) 0 0
\(299\) 6.32060 15.2593i 0.365530 0.882466i
\(300\) 0 0
\(301\) −10.5543 + 4.37173i −0.608340 + 0.251983i
\(302\) 0 0
\(303\) 3.85756i 0.221611i
\(304\) 0 0
\(305\) 21.1670i 1.21202i
\(306\) 0 0
\(307\) 10.7709 4.46145i 0.614728 0.254629i −0.0535206 0.998567i \(-0.517044\pi\)
0.668249 + 0.743938i \(0.267044\pi\)
\(308\) 0 0
\(309\) 1.05170 2.53903i 0.0598292 0.144440i
\(310\) 0 0
\(311\) 6.79085 6.79085i 0.385074 0.385074i −0.487852 0.872926i \(-0.662220\pi\)
0.872926 + 0.487852i \(0.162220\pi\)
\(312\) 0 0
\(313\) 12.7080 + 12.7080i 0.718300 + 0.718300i 0.968257 0.249957i \(-0.0804166\pi\)
−0.249957 + 0.968257i \(0.580417\pi\)
\(314\) 0 0
\(315\) 7.14642 + 2.96015i 0.402655 + 0.166785i
\(316\) 0 0
\(317\) 6.89303 + 16.6412i 0.387151 + 0.934665i 0.990541 + 0.137219i \(0.0438163\pi\)
−0.603390 + 0.797446i \(0.706184\pi\)
\(318\) 0 0
\(319\) −17.7750 −0.995208
\(320\) 0 0
\(321\) 13.9852 0.780577
\(322\) 0 0
\(323\) −7.76010 18.7345i −0.431783 1.04242i
\(324\) 0 0
\(325\) 13.3457 + 5.52799i 0.740289 + 0.306638i
\(326\) 0 0
\(327\) 9.29346 + 9.29346i 0.513930 + 0.513930i
\(328\) 0 0
\(329\) 2.17550 2.17550i 0.119939 0.119939i
\(330\) 0 0
\(331\) 0.259261 0.625913i 0.0142503 0.0344033i −0.916594 0.399819i \(-0.869073\pi\)
0.930845 + 0.365415i \(0.119073\pi\)
\(332\) 0 0
\(333\) 6.31049 2.61389i 0.345813 0.143240i
\(334\) 0 0
\(335\) 27.6438i 1.51034i
\(336\) 0 0
\(337\) 24.3244i 1.32504i 0.749046 + 0.662518i \(0.230512\pi\)
−0.749046 + 0.662518i \(0.769488\pi\)
\(338\) 0 0
\(339\) −12.7859 + 5.29611i −0.694436 + 0.287645i
\(340\) 0 0
\(341\) −3.80987 + 9.19783i −0.206316 + 0.498091i
\(342\) 0 0
\(343\) −11.8960 + 11.8960i −0.642326 + 0.642326i
\(344\) 0 0
\(345\) −5.28611 5.28611i −0.284595 0.284595i
\(346\) 0 0
\(347\) 6.95491 + 2.88082i 0.373359 + 0.154650i 0.561469 0.827498i \(-0.310236\pi\)
−0.188110 + 0.982148i \(0.560236\pi\)
\(348\) 0 0
\(349\) −11.9159 28.7676i −0.637845 1.53989i −0.829545 0.558440i \(-0.811400\pi\)
0.191700 0.981454i \(-0.438600\pi\)
\(350\) 0 0
\(351\) 6.01134 0.320862
\(352\) 0 0
\(353\) −22.1334 −1.17804 −0.589021 0.808118i \(-0.700486\pi\)
−0.589021 + 0.808118i \(0.700486\pi\)
\(354\) 0 0
\(355\) 2.78193 + 6.71616i 0.147649 + 0.356457i
\(356\) 0 0
\(357\) 10.9382 + 4.53074i 0.578909 + 0.239792i
\(358\) 0 0
\(359\) 10.1669 + 10.1669i 0.536586 + 0.536586i 0.922524 0.385939i \(-0.126122\pi\)
−0.385939 + 0.922524i \(0.626122\pi\)
\(360\) 0 0
\(361\) 3.33060 3.33060i 0.175295 0.175295i
\(362\) 0 0
\(363\) −0.394850 + 0.953252i −0.0207243 + 0.0500328i
\(364\) 0 0
\(365\) −24.9106 + 10.3183i −1.30388 + 0.540084i
\(366\) 0 0
\(367\) 9.77761i 0.510387i 0.966890 + 0.255194i \(0.0821392\pi\)
−0.966890 + 0.255194i \(0.917861\pi\)
\(368\) 0 0
\(369\) 1.06966i 0.0556844i
\(370\) 0 0
\(371\) −19.9350 + 8.25734i −1.03497 + 0.428700i
\(372\) 0 0
\(373\) 2.04735 4.94275i 0.106008 0.255926i −0.861971 0.506958i \(-0.830770\pi\)
0.967979 + 0.251032i \(0.0807700\pi\)
\(374\) 0 0
\(375\) −4.99642 + 4.99642i −0.258014 + 0.258014i
\(376\) 0 0
\(377\) 21.7821 + 21.7821i 1.12184 + 1.12184i
\(378\) 0 0
\(379\) −29.0333 12.0260i −1.49134 0.617733i −0.519732 0.854329i \(-0.673968\pi\)
−0.971608 + 0.236596i \(0.923968\pi\)
\(380\) 0 0
\(381\) −2.09535 5.05863i −0.107348 0.259161i
\(382\) 0 0
\(383\) −2.47568 −0.126501 −0.0632507 0.997998i \(-0.520147\pi\)
−0.0632507 + 0.997998i \(0.520147\pi\)
\(384\) 0 0
\(385\) 26.8311 1.36744
\(386\) 0 0
\(387\) 1.53775 + 3.71245i 0.0781680 + 0.188714i
\(388\) 0 0
\(389\) 9.49742 + 3.93396i 0.481538 + 0.199460i 0.610229 0.792225i \(-0.291077\pi\)
−0.128691 + 0.991685i \(0.541077\pi\)
\(390\) 0 0
\(391\) −8.09081 8.09081i −0.409170 0.409170i
\(392\) 0 0
\(393\) 14.8422 14.8422i 0.748689 0.748689i
\(394\) 0 0
\(395\) 11.4800 27.7153i 0.577623 1.39451i
\(396\) 0 0
\(397\) 13.8666 5.74373i 0.695944 0.288269i −0.00653022 0.999979i \(-0.502079\pi\)
0.702474 + 0.711709i \(0.252079\pi\)
\(398\) 0 0
\(399\) 13.8432i 0.693027i
\(400\) 0 0
\(401\) 21.9112i 1.09419i −0.837069 0.547097i \(-0.815733\pi\)
0.837069 0.547097i \(-0.184267\pi\)
\(402\) 0 0
\(403\) 15.9401 6.60262i 0.794034 0.328900i
\(404\) 0 0
\(405\) 1.04122 2.51374i 0.0517388 0.124909i
\(406\) 0 0
\(407\) 16.7532 16.7532i 0.830426 0.830426i
\(408\) 0 0
\(409\) 13.0005 + 13.0005i 0.642835 + 0.642835i 0.951251 0.308417i \(-0.0997991\pi\)
−0.308417 + 0.951251i \(0.599799\pi\)
\(410\) 0 0
\(411\) 4.88609 + 2.02388i 0.241013 + 0.0998308i
\(412\) 0 0
\(413\) −12.1792 29.4033i −0.599301 1.44684i
\(414\) 0 0
\(415\) −6.78872 −0.333245
\(416\) 0 0
\(417\) 10.6080 0.519474
\(418\) 0 0
\(419\) −7.98199 19.2702i −0.389946 0.941412i −0.989950 0.141416i \(-0.954835\pi\)
0.600005 0.799997i \(-0.295165\pi\)
\(420\) 0 0
\(421\) 5.11481 + 2.11863i 0.249281 + 0.103255i 0.503825 0.863806i \(-0.331926\pi\)
−0.254545 + 0.967061i \(0.581926\pi\)
\(422\) 0 0
\(423\) −0.765228 0.765228i −0.0372067 0.0372067i
\(424\) 0 0
\(425\) 7.07622 7.07622i 0.343247 0.343247i
\(426\) 0 0
\(427\) 8.46379 20.4334i 0.409591 0.988841i
\(428\) 0 0
\(429\) 19.2642 7.97951i 0.930086 0.385254i
\(430\) 0 0
\(431\) 5.20156i 0.250551i 0.992122 + 0.125275i \(0.0399814\pi\)
−0.992122 + 0.125275i \(0.960019\pi\)
\(432\) 0 0
\(433\) 6.44939i 0.309938i 0.987919 + 0.154969i \(0.0495278\pi\)
−0.987919 + 0.154969i \(0.950472\pi\)
\(434\) 0 0
\(435\) 12.8814 5.33566i 0.617617 0.255825i
\(436\) 0 0
\(437\) 5.11982 12.3603i 0.244914 0.591275i
\(438\) 0 0
\(439\) 20.5461 20.5461i 0.980610 0.980610i −0.0192051 0.999816i \(-0.506114\pi\)
0.999816 + 0.0192051i \(0.00611355\pi\)
\(440\) 0 0
\(441\) −0.765344 0.765344i −0.0364450 0.0364450i
\(442\) 0 0
\(443\) −16.1487 6.68902i −0.767249 0.317805i −0.0354912 0.999370i \(-0.511300\pi\)
−0.731757 + 0.681565i \(0.761300\pi\)
\(444\) 0 0
\(445\) 11.2765 + 27.2239i 0.534557 + 1.29054i
\(446\) 0 0
\(447\) 11.3148 0.535172
\(448\) 0 0
\(449\) −0.794308 −0.0374857 −0.0187428 0.999824i \(-0.505966\pi\)
−0.0187428 + 0.999824i \(0.505966\pi\)
\(450\) 0 0
\(451\) 1.41988 + 3.42790i 0.0668596 + 0.161413i
\(452\) 0 0
\(453\) 15.9133 + 6.59152i 0.747674 + 0.309697i
\(454\) 0 0
\(455\) −32.8798 32.8798i −1.54143 1.54143i
\(456\) 0 0
\(457\) 21.2796 21.2796i 0.995420 0.995420i −0.00456968 0.999990i \(-0.501455\pi\)
0.999990 + 0.00456968i \(0.00145458\pi\)
\(458\) 0 0
\(459\) 1.59367 3.84747i 0.0743864 0.179585i
\(460\) 0 0
\(461\) 0.541763 0.224405i 0.0252324 0.0104516i −0.370032 0.929019i \(-0.620653\pi\)
0.395264 + 0.918568i \(0.370653\pi\)
\(462\) 0 0
\(463\) 13.0365i 0.605859i 0.953013 + 0.302929i \(0.0979646\pi\)
−0.953013 + 0.302929i \(0.902035\pi\)
\(464\) 0 0
\(465\) 7.80925i 0.362145i
\(466\) 0 0
\(467\) 36.1793 14.9860i 1.67418 0.693467i 0.675156 0.737675i \(-0.264076\pi\)
0.999022 + 0.0442081i \(0.0140765\pi\)
\(468\) 0 0
\(469\) −11.0535 + 26.6856i −0.510405 + 1.23223i
\(470\) 0 0
\(471\) 10.2365 10.2365i 0.471674 0.471674i
\(472\) 0 0
\(473\) 9.85587 + 9.85587i 0.453174 + 0.453174i
\(474\) 0 0
\(475\) 10.8103 + 4.47779i 0.496012 + 0.205455i
\(476\) 0 0
\(477\) 2.90450 + 7.01208i 0.132988 + 0.321061i
\(478\) 0 0
\(479\) −27.6976 −1.26554 −0.632768 0.774341i \(-0.718081\pi\)
−0.632768 + 0.774341i \(0.718081\pi\)
\(480\) 0 0
\(481\) −41.0600 −1.87217
\(482\) 0 0
\(483\) 2.98921 + 7.21658i 0.136014 + 0.328366i
\(484\) 0 0
\(485\) −28.4125 11.7689i −1.29015 0.534396i
\(486\) 0 0
\(487\) −22.8658 22.8658i −1.03615 1.03615i −0.999322 0.0368273i \(-0.988275\pi\)
−0.0368273 0.999322i \(-0.511725\pi\)
\(488\) 0 0
\(489\) 10.7028 10.7028i 0.483999 0.483999i
\(490\) 0 0
\(491\) −10.1610 + 24.5308i −0.458559 + 1.10706i 0.510423 + 0.859924i \(0.329489\pi\)
−0.968981 + 0.247135i \(0.920511\pi\)
\(492\) 0 0
\(493\) 19.7160 8.16665i 0.887965 0.367807i
\(494\) 0 0
\(495\) 9.43777i 0.424196i
\(496\) 0 0
\(497\) 7.59575i 0.340716i
\(498\) 0 0
\(499\) −11.6135 + 4.81046i −0.519890 + 0.215346i −0.627169 0.778883i \(-0.715786\pi\)
0.107278 + 0.994229i \(0.465786\pi\)
\(500\) 0 0
\(501\) −2.20606 + 5.32589i −0.0985593 + 0.237943i
\(502\) 0 0
\(503\) −12.9948 + 12.9948i −0.579412 + 0.579412i −0.934741 0.355330i \(-0.884369\pi\)
0.355330 + 0.934741i \(0.384369\pi\)
\(504\) 0 0
\(505\) −7.42167 7.42167i −0.330260 0.330260i
\(506\) 0 0
\(507\) −21.3751 8.85384i −0.949300 0.393213i
\(508\) 0 0
\(509\) 13.3636 + 32.2627i 0.592333 + 1.43002i 0.881244 + 0.472662i \(0.156707\pi\)
−0.288911 + 0.957356i \(0.593293\pi\)
\(510\) 0 0
\(511\) 28.1730 1.24630
\(512\) 0 0
\(513\) 4.86931 0.214985
\(514\) 0 0
\(515\) 2.86152 + 6.90832i 0.126094 + 0.304417i
\(516\) 0 0
\(517\) −3.46806 1.43652i −0.152525 0.0631780i
\(518\) 0 0
\(519\) 3.28896 + 3.28896i 0.144370 + 0.144370i
\(520\) 0 0
\(521\) 1.74966 1.74966i 0.0766541 0.0766541i −0.667740 0.744394i \(-0.732738\pi\)
0.744394 + 0.667740i \(0.232738\pi\)
\(522\) 0 0
\(523\) 7.05117 17.0230i 0.308326 0.744366i −0.691433 0.722440i \(-0.743020\pi\)
0.999760 0.0219253i \(-0.00697960\pi\)
\(524\) 0 0
\(525\) −6.31162 + 2.61436i −0.275462 + 0.114100i
\(526\) 0 0
\(527\) 11.9527i 0.520667i
\(528\) 0 0
\(529\) 15.4509i 0.671779i
\(530\) 0 0
\(531\) −10.3425 + 4.28402i −0.448828 + 0.185911i
\(532\) 0 0
\(533\) 2.46070 5.94064i 0.106585 0.257318i
\(534\) 0 0
\(535\) −26.9065 + 26.9065i −1.16327 + 1.16327i
\(536\) 0 0
\(537\) 0.209239 + 0.209239i 0.00902935 + 0.00902935i
\(538\) 0 0
\(539\) −3.46858 1.43673i −0.149402 0.0618845i
\(540\) 0 0
\(541\) −7.86315 18.9833i −0.338063 0.816157i −0.997902 0.0647494i \(-0.979375\pi\)
0.659838 0.751408i \(-0.270625\pi\)
\(542\) 0 0
\(543\) 10.4613 0.448937
\(544\) 0 0
\(545\) −35.7599 −1.53179
\(546\) 0 0
\(547\) −0.832145 2.00898i −0.0355799 0.0858976i 0.905091 0.425219i \(-0.139803\pi\)
−0.940671 + 0.339321i \(0.889803\pi\)
\(548\) 0 0
\(549\) −7.18739 2.97711i −0.306750 0.127060i
\(550\) 0 0
\(551\) 17.6440 + 17.6440i 0.751659 + 0.751659i
\(552\) 0 0
\(553\) −22.1643 + 22.1643i −0.942520 + 0.942520i
\(554\) 0 0
\(555\) −7.11200 + 17.1699i −0.301888 + 0.728821i
\(556\) 0 0
\(557\) −27.8685 + 11.5435i −1.18083 + 0.489115i −0.884758 0.466051i \(-0.845676\pi\)
−0.296070 + 0.955166i \(0.595676\pi\)
\(558\) 0 0
\(559\) 24.1555i 1.02167i
\(560\) 0 0
\(561\) 14.4453i 0.609879i
\(562\) 0 0
\(563\) −17.3847 + 7.20096i −0.732676 + 0.303484i −0.717651 0.696403i \(-0.754783\pi\)
−0.0150247 + 0.999887i \(0.504783\pi\)
\(564\) 0 0
\(565\) 14.4099 34.7886i 0.606229 1.46357i
\(566\) 0 0
\(567\) −2.01027 + 2.01027i −0.0844233 + 0.0844233i
\(568\) 0 0
\(569\) −5.37251 5.37251i −0.225227 0.225227i 0.585468 0.810695i \(-0.300911\pi\)
−0.810695 + 0.585468i \(0.800911\pi\)
\(570\) 0 0
\(571\) 37.6829 + 15.6087i 1.57698 + 0.653206i 0.987931 0.154893i \(-0.0495033\pi\)
0.589047 + 0.808099i \(0.299503\pi\)
\(572\) 0 0
\(573\) 5.80245 + 14.0084i 0.242401 + 0.585207i
\(574\) 0 0
\(575\) 6.60243 0.275340
\(576\) 0 0
\(577\) 28.6100 1.19105 0.595525 0.803337i \(-0.296944\pi\)
0.595525 + 0.803337i \(0.296944\pi\)
\(578\) 0 0
\(579\) 7.02413 + 16.9577i 0.291913 + 0.704740i
\(580\) 0 0
\(581\) 6.55342 + 2.71452i 0.271882 + 0.112617i
\(582\) 0 0
\(583\) 18.6158 + 18.6158i 0.770987 + 0.770987i
\(584\) 0 0
\(585\) −11.5654 + 11.5654i −0.478170 + 0.478170i
\(586\) 0 0
\(587\) −14.0646 + 33.9550i −0.580509 + 1.40147i 0.311844 + 0.950133i \(0.399053\pi\)
−0.892353 + 0.451339i \(0.850947\pi\)
\(588\) 0 0
\(589\) 12.9118 5.34826i 0.532023 0.220371i
\(590\) 0 0
\(591\) 7.20152i 0.296231i
\(592\) 0 0
\(593\) 28.6736i 1.17749i 0.808321 + 0.588743i \(0.200377\pi\)
−0.808321 + 0.588743i \(0.799623\pi\)
\(594\) 0 0
\(595\) −29.7611 + 12.3274i −1.22009 + 0.505376i
\(596\) 0 0
\(597\) 0.459506 1.10935i 0.0188063 0.0454025i
\(598\) 0 0
\(599\) 28.5413 28.5413i 1.16617 1.16617i 0.183067 0.983100i \(-0.441397\pi\)
0.983100 0.183067i \(-0.0586027\pi\)
\(600\) 0 0
\(601\) −29.9824 29.9824i −1.22301 1.22301i −0.966558 0.256448i \(-0.917448\pi\)
−0.256448 0.966558i \(-0.582552\pi\)
\(602\) 0 0
\(603\) 9.38659 + 3.88805i 0.382252 + 0.158334i
\(604\) 0 0
\(605\) −1.07433 2.59365i −0.0436776 0.105447i
\(606\) 0 0
\(607\) 20.2791 0.823105 0.411552 0.911386i \(-0.364987\pi\)
0.411552 + 0.911386i \(0.364987\pi\)
\(608\) 0 0
\(609\) −14.5684 −0.590343
\(610\) 0 0
\(611\) 2.48953 + 6.01025i 0.100715 + 0.243149i
\(612\) 0 0
\(613\) 22.4278 + 9.28988i 0.905849 + 0.375215i 0.786466 0.617633i \(-0.211908\pi\)
0.119383 + 0.992848i \(0.461908\pi\)
\(614\) 0 0
\(615\) −2.05796 2.05796i −0.0829848 0.0829848i
\(616\) 0 0
\(617\) −28.6181 + 28.6181i −1.15212 + 1.15212i −0.165993 + 0.986127i \(0.553083\pi\)
−0.986127 + 0.165993i \(0.946917\pi\)
\(618\) 0 0
\(619\) −0.706861 + 1.70651i −0.0284111 + 0.0685905i −0.937448 0.348124i \(-0.886819\pi\)
0.909037 + 0.416715i \(0.136819\pi\)
\(620\) 0 0
\(621\) 2.53841 1.05145i 0.101863 0.0421931i
\(622\) 0 0
\(623\) 30.7893i 1.23355i
\(624\) 0 0
\(625\) 31.2406i 1.24962i
\(626\) 0 0
\(627\) 15.6044 6.46357i 0.623181 0.258130i
\(628\) 0 0
\(629\) −10.8855 + 26.2799i −0.434032 + 1.04785i
\(630\) 0 0
\(631\) −24.6361 + 24.6361i −0.980748 + 0.980748i −0.999818 0.0190703i \(-0.993929\pi\)
0.0190703 + 0.999818i \(0.493929\pi\)
\(632\) 0 0
\(633\) 5.66930 + 5.66930i 0.225334 + 0.225334i
\(634\) 0 0
\(635\) 13.7638 + 5.70114i 0.546198 + 0.226243i
\(636\) 0 0
\(637\) 2.48990 + 6.01116i 0.0986536 + 0.238171i
\(638\) 0 0
\(639\) −2.67179 −0.105694
\(640\) 0 0
\(641\) 0.278463 0.0109986 0.00549931 0.999985i \(-0.498250\pi\)
0.00549931 + 0.999985i \(0.498250\pi\)
\(642\) 0 0
\(643\) −5.39050 13.0138i −0.212581 0.513215i 0.781238 0.624234i \(-0.214589\pi\)
−0.993818 + 0.111019i \(0.964589\pi\)
\(644\) 0 0
\(645\) −10.1010 4.18397i −0.397727 0.164744i
\(646\) 0 0
\(647\) −17.8303 17.8303i −0.700980 0.700980i 0.263641 0.964621i \(-0.415077\pi\)
−0.964621 + 0.263641i \(0.915077\pi\)
\(648\) 0 0
\(649\) −27.4575 + 27.4575i −1.07780 + 1.07780i
\(650\) 0 0
\(651\) −3.12258 + 7.53858i −0.122384 + 0.295460i
\(652\) 0 0
\(653\) −31.3223 + 12.9741i −1.22574 + 0.507716i −0.899229 0.437478i \(-0.855872\pi\)
−0.326507 + 0.945195i \(0.605872\pi\)
\(654\) 0 0
\(655\) 57.1107i 2.23150i
\(656\) 0 0
\(657\) 9.90978i 0.386617i
\(658\) 0 0
\(659\) 38.2358 15.8378i 1.48946 0.616953i 0.518258 0.855224i \(-0.326581\pi\)
0.971199 + 0.238271i \(0.0765807\pi\)
\(660\) 0 0
\(661\) 7.49776 18.1012i 0.291629 0.704055i −0.708369 0.705842i \(-0.750569\pi\)
0.999998 + 0.00178728i \(0.000568910\pi\)
\(662\) 0 0
\(663\) −17.7018 + 17.7018i −0.687479 + 0.687479i
\(664\) 0 0
\(665\) −26.6334 26.6334i −1.03280 1.03280i
\(666\) 0 0
\(667\) 13.0079 + 5.38804i 0.503667 + 0.208626i
\(668\) 0 0
\(669\) 0.0720861 + 0.174031i 0.00278701 + 0.00672844i
\(670\) 0 0
\(671\) −26.9849 −1.04174
\(672\) 0 0
\(673\) 18.3856 0.708711 0.354356 0.935111i \(-0.384700\pi\)
0.354356 + 0.935111i \(0.384700\pi\)
\(674\) 0 0
\(675\) 0.919594 + 2.22010i 0.0353952 + 0.0854515i
\(676\) 0 0
\(677\) −34.2111 14.1707i −1.31484 0.544624i −0.388546 0.921429i \(-0.627023\pi\)
−0.926293 + 0.376805i \(0.877023\pi\)
\(678\) 0 0
\(679\) 22.7219 + 22.7219i 0.871986 + 0.871986i
\(680\) 0 0
\(681\) −0.197269 + 0.197269i −0.00755936 + 0.00755936i
\(682\) 0 0
\(683\) 9.51662 22.9752i 0.364143 0.879120i −0.630542 0.776155i \(-0.717167\pi\)
0.994685 0.102964i \(-0.0328328\pi\)
\(684\) 0 0
\(685\) −13.2943 + 5.50668i −0.507949 + 0.210399i
\(686\) 0 0
\(687\) 2.20467i 0.0841133i
\(688\) 0 0
\(689\) 45.6250i 1.73817i
\(690\) 0 0
\(691\) 18.8902 7.82459i 0.718618 0.297661i 0.00675270 0.999977i \(-0.497851\pi\)
0.711866 + 0.702316i \(0.247851\pi\)
\(692\) 0 0
\(693\) −3.77376 + 9.11066i −0.143353 + 0.346085i
\(694\) 0 0
\(695\) −20.4090 + 20.4090i −0.774156 + 0.774156i
\(696\) 0 0
\(697\) −3.14987 3.14987i −0.119310 0.119310i
\(698\) 0 0
\(699\) 5.65317 + 2.34162i 0.213823 + 0.0885683i
\(700\) 0 0
\(701\) 5.48707 + 13.2470i 0.207244 + 0.500331i 0.992987 0.118222i \(-0.0377194\pi\)
−0.785743 + 0.618552i \(0.787719\pi\)
\(702\) 0 0
\(703\) −33.2595 −1.25440
\(704\) 0 0
\(705\) 2.94449 0.110896
\(706\) 0 0
\(707\) 4.19683 + 10.1320i 0.157838 + 0.381055i
\(708\) 0 0
\(709\) −3.85647 1.59740i −0.144833 0.0599917i 0.309090 0.951033i \(-0.399976\pi\)
−0.453922 + 0.891041i \(0.649976\pi\)
\(710\) 0 0
\(711\) 7.79622 + 7.79622i 0.292381 + 0.292381i
\(712\) 0 0
\(713\) 5.57619 5.57619i 0.208830 0.208830i
\(714\) 0 0
\(715\) −21.7110 + 52.4151i −0.811946 + 1.96021i
\(716\) 0 0
\(717\) 7.63960 3.16443i 0.285306 0.118178i
\(718\) 0 0
\(719\) 8.78550i 0.327644i −0.986490 0.163822i \(-0.947618\pi\)
0.986490 0.163822i \(-0.0523823\pi\)
\(720\) 0 0
\(721\) 7.81307i 0.290974i
\(722\) 0 0
\(723\) −20.9990 + 8.69807i −0.780961 + 0.323485i
\(724\) 0 0
\(725\) −4.71238 + 11.3767i −0.175013 + 0.422520i
\(726\) 0 0
\(727\) 10.0533 10.0533i 0.372858 0.372858i −0.495659 0.868517i \(-0.665073\pi\)
0.868517 + 0.495659i \(0.165073\pi\)
\(728\) 0 0
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) −15.4604 6.40390i −0.571823 0.236857i
\(732\) 0 0
\(733\) −10.3759 25.0496i −0.383242 0.925228i −0.991334 0.131362i \(-0.958065\pi\)
0.608093 0.793866i \(-0.291935\pi\)
\(734\) 0 0
\(735\) 2.94494 0.108626
\(736\) 0 0
\(737\) 35.2418 1.29815
\(738\) 0 0
\(739\) −12.3459 29.8057i −0.454153 1.09642i −0.970728 0.240180i \(-0.922793\pi\)
0.516575 0.856242i \(-0.327207\pi\)
\(740\) 0 0
\(741\) −27.0429 11.2016i −0.993447 0.411499i
\(742\) 0 0
\(743\) −16.0222 16.0222i −0.587799 0.587799i 0.349236 0.937035i \(-0.386441\pi\)
−0.937035 + 0.349236i \(0.886441\pi\)
\(744\) 0 0
\(745\) −21.7689 + 21.7689i −0.797551 + 0.797551i
\(746\) 0 0
\(747\) 0.954824 2.30515i 0.0349352 0.0843410i
\(748\) 0 0
\(749\) 36.7327 15.2152i 1.34218 0.555951i
\(750\) 0 0
\(751\) 26.5917i 0.970346i 0.874418 + 0.485173i \(0.161243\pi\)
−0.874418 + 0.485173i \(0.838757\pi\)
\(752\) 0 0
\(753\) 13.3497i 0.486491i
\(754\) 0 0
\(755\) −43.2978 + 17.9345i −1.57577 + 0.652704i
\(756\) 0 0
\(757\) −5.33084 + 12.8698i −0.193753 + 0.467760i −0.990662 0.136338i \(-0.956467\pi\)
0.796910 + 0.604098i \(0.206467\pi\)
\(758\) 0 0
\(759\) 6.73903 6.73903i 0.244611 0.244611i
\(760\) 0 0
\(761\) 11.8263 + 11.8263i 0.428704 + 0.428704i 0.888187 0.459483i \(-0.151965\pi\)
−0.459483 + 0.888187i \(0.651965\pi\)
\(762\) 0 0
\(763\) 34.5205 + 14.2989i 1.24973 + 0.517653i
\(764\) 0 0
\(765\) 4.33615 + 10.4684i 0.156774 + 0.378485i
\(766\) 0 0
\(767\) 67.2950 2.42988
\(768\) 0 0
\(769\) 39.2000 1.41359 0.706795 0.707419i \(-0.250140\pi\)
0.706795 + 0.707419i \(0.250140\pi\)
\(770\) 0 0
\(771\) −6.12196 14.7797i −0.220477 0.532278i
\(772\) 0 0
\(773\) −39.7946 16.4834i −1.43131 0.592868i −0.473636 0.880721i \(-0.657059\pi\)
−0.957675 + 0.287852i \(0.907059\pi\)
\(774\) 0 0
\(775\) 4.87693 + 4.87693i 0.175184 + 0.175184i
\(776\) 0 0
\(777\) 13.7310 13.7310i 0.492596 0.492596i
\(778\) 0 0
\(779\) 1.99321 4.81205i 0.0714143 0.172409i
\(780\) 0 0
\(781\) −8.56214 + 3.54655i −0.306377 + 0.126906i
\(782\) 0 0
\(783\) 5.12441i 0.183132i
\(784\) 0 0
\(785\) 39.3887i 1.40584i
\(786\) 0 0
\(787\) 3.18736 1.32025i 0.113617 0.0470618i −0.325151 0.945662i \(-0.605415\pi\)
0.438768 + 0.898600i \(0.355415\pi\)
\(788\) 0 0
\(789\) 2.40606 5.80875i 0.0856581 0.206797i
\(790\) 0 0
\(791\) −27.8209 + 27.8209i −0.989197 + 0.989197i
\(792\) 0 0
\(793\) 33.0683 + 33.0683i 1.17429 + 1.17429i
\(794\) 0 0
\(795\) −19.0788 7.90269i −0.676655 0.280280i
\(796\) 0 0
\(797\) 9.15542 + 22.1031i 0.324302 + 0.782934i 0.998994 + 0.0448349i \(0.0142762\pi\)
−0.674693 + 0.738099i \(0.735724\pi\)
\(798\) 0 0