Properties

Label 768.2.n.b.289.3
Level $768$
Weight $2$
Character 768.289
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 289.3
Character \(\chi\) \(=\) 768.289
Dual form 768.2.n.b.481.3

$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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 0.258379 0.966044i \(-0.416812\pi\)
0.865798 + 0.500394i \(0.166812\pi\)
\(6\) 0 0
\(7\) −2.01027 + 2.01027i −0.759810 + 0.759810i −0.976288 0.216477i \(-0.930543\pi\)
0.216477 + 0.976288i \(0.430543\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −1.32741 3.20465i −0.400229 0.966238i −0.987610 0.156928i \(-0.949841\pi\)
0.587381 0.809310i \(-0.300159\pi\)
\(12\) 0 0
\(13\) 5.55375 + 2.30044i 1.54033 + 0.638027i 0.981536 0.191277i \(-0.0612628\pi\)
0.558798 + 0.829304i \(0.311263\pi\)
\(14\) 0 0
\(15\) 2.72085i 0.702520i
\(16\) 0 0
\(17\) 4.16447i 1.01003i 0.863110 + 0.505016i \(0.168514\pi\)
−0.863110 + 0.505016i \(0.831486\pi\)
\(18\) 0 0
\(19\) 4.49866 + 1.86340i 1.03206 + 0.427494i 0.833456 0.552585i \(-0.186359\pi\)
0.198606 + 0.980079i \(0.436359\pi\)
\(20\) 0 0
\(21\) −1.08795 2.62654i −0.237410 0.573159i
\(22\) 0 0
\(23\) 1.94282 + 1.94282i 0.405106 + 0.405106i 0.880028 0.474922i \(-0.157524\pi\)
−0.474922 + 0.880028i \(0.657524\pi\)
\(24\) 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 −0.630530 0.776165i \(-0.717162\pi\)
0.994683 0.102980i \(-0.0328377\pi\)
\(30\) 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 −0.835392 0.549655i \(-0.814759\pi\)
−0.202046 + 0.979376i \(0.564759\pi\)
\(38\) 0 0
\(39\) −4.25066 + 4.25066i −0.680650 + 0.680650i
\(40\) 0 0
\(41\) 0.756366 + 0.756366i 0.118125 + 0.118125i 0.763698 0.645574i \(-0.223382\pi\)
−0.645574 + 0.763698i \(0.723382\pi\)
\(42\) 0 0
\(43\) 1.53775 + 3.71245i 0.234504 + 0.566143i 0.996697 0.0812067i \(-0.0258774\pi\)
−0.762193 + 0.647350i \(0.775877\pi\)
\(44\) 0 0
\(45\) −2.51374 1.04122i −0.374726 0.155216i
\(46\) 0 0
\(47\) 1.08220i 0.157855i −0.996880 0.0789273i \(-0.974851\pi\)
0.996880 0.0789273i \(-0.0251495\pi\)
\(48\) 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 0.987912 + 0.155013i \(0.0495418\pi\)
−0.588949 + 0.808170i \(0.700458\pi\)
\(54\) 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 0.411172 0.911558i \(-0.365120\pi\)
0.935311 + 0.353826i \(0.115120\pi\)
\(60\) 0 0
\(61\) 2.97711 7.18739i 0.381180 0.920251i −0.610558 0.791972i \(-0.709055\pi\)
0.991738 0.128279i \(-0.0409454\pi\)
\(62\) 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 0.486924 + 0.873444i \(0.338119\pi\)
−0.961926 + 0.273311i \(0.911881\pi\)
\(68\) 0 0
\(69\) −2.53841 + 1.05145i −0.305589 + 0.126579i
\(70\) 0 0
\(71\) 1.88924 1.88924i 0.224211 0.224211i −0.586058 0.810269i \(-0.699321\pi\)
0.810269 + 0.586058i \(0.199321\pi\)
\(72\) 0 0
\(73\) −7.00727 7.00727i −0.820139 0.820139i 0.165989 0.986128i \(-0.446918\pi\)
−0.986128 + 0.165989i \(0.946918\pi\)
\(74\) 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 \(0.212962\pi\)
−0.784417 + 0.620234i \(0.787038\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −2.30515 0.954824i −0.253023 0.104806i 0.252567 0.967579i \(-0.418725\pi\)
−0.505590 + 0.862774i \(0.668725\pi\)
\(84\) 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 −0.173149 0.984896i \(-0.555394\pi\)
0.984896 + 0.173149i \(0.0553943\pi\)
\(90\) 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 −0.552881 0.833260i \(-0.686472\pi\)
0.198258 + 0.980150i \(0.436472\pi\)
\(102\) 0 0
\(103\) 1.94329 1.94329i 0.191478 0.191478i −0.604856 0.796335i \(-0.706769\pi\)
0.796335 + 0.604856i \(0.206769\pi\)
\(104\) 0 0
\(105\) −5.46964 5.46964i −0.533782 0.533782i
\(106\) 0 0
\(107\) −5.35190 12.9206i −0.517388 1.24908i −0.939502 0.342542i \(-0.888712\pi\)
0.422114 0.906543i \(-0.361288\pi\)
\(108\) 0 0
\(109\) −12.1425 5.02958i −1.16304 0.481747i −0.284154 0.958779i \(-0.591713\pi\)
−0.878886 + 0.477032i \(0.841713\pi\)
\(110\) 0 0
\(111\) 6.83043i 0.648315i
\(112\) 0 0
\(113\) 13.8394i 1.30190i 0.759121 + 0.650950i \(0.225629\pi\)
−0.759121 + 0.650950i \(0.774371\pi\)
\(114\) 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 −0.0177195 0.999843i \(-0.505641\pi\)
0.719525 0.694466i \(-0.244359\pi\)
\(132\) 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 0.529075 0.848575i \(-0.322539\pi\)
−0.848575 + 0.529075i \(0.822539\pi\)
\(138\) 0 0
\(139\) −4.05949 9.80047i −0.344321 0.831265i −0.997268 0.0738616i \(-0.976468\pi\)
0.652947 0.757403i \(-0.273532\pi\)
\(140\) 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 −0.996023 0.0890929i \(-0.971603\pi\)
0.641297 0.767293i \(-0.278397\pi\)
\(150\) 0 0
\(151\) −12.1795 12.1795i −0.991157 0.991157i 0.00880460 0.999961i \(-0.497197\pi\)
−0.999961 + 0.00880460i \(0.997197\pi\)
\(152\) 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 −0.533061 0.846077i \(-0.678958\pi\)
0.975198 0.221336i \(-0.0710417\pi\)
\(158\) 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 −0.517218 0.855854i \(-0.673032\pi\)
0.970908 0.239451i \(-0.0769675\pi\)
\(164\) 0 0
\(165\) 8.71936 3.61168i 0.678802 0.281169i
\(166\) 0 0
\(167\) −4.07626 + 4.07626i −0.315430 + 0.315430i −0.847009 0.531579i \(-0.821599\pi\)
0.531579 + 0.847009i \(0.321599\pi\)
\(168\) 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 0.213297 0.976987i \(-0.431580\pi\)
−0.540010 + 0.841658i \(0.681580\pi\)
\(174\) 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 0.372443 0.928055i \(-0.378520\pi\)
−0.392877 + 0.919591i \(0.628520\pi\)
\(180\) 0 0
\(181\) −4.00336 9.66497i −0.297567 0.718391i −0.999978 0.00661937i \(-0.997893\pi\)
0.702411 0.711772i \(-0.252107\pi\)
\(182\) 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 −0.132861 0.991135i \(-0.542416\pi\)
0.606891 + 0.794785i \(0.292416\pi\)
\(198\) 0 0
\(199\) 0.849057 0.849057i 0.0601880 0.0601880i −0.676372 0.736560i \(-0.736449\pi\)
0.736560 + 0.676372i \(0.236449\pi\)
\(200\) 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 0.112852 0.993612i \(-0.464001\pi\)
−0.622791 + 0.782388i \(0.714001\pi\)
\(212\) 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 −0.927383 0.374113i \(-0.877947\pi\)
0.920297 + 0.391221i \(0.127947\pi\)
\(228\) 0 0
\(229\) −2.03685 + 0.843689i −0.134599 + 0.0557526i −0.448966 0.893549i \(-0.648208\pi\)
0.314367 + 0.949301i \(0.398208\pi\)
\(230\) 0 0
\(231\) −6.97299 + 6.97299i −0.458789 + 0.458789i
\(232\) 0 0
\(233\) −4.32675 4.32675i −0.283455 0.283455i 0.551030 0.834485i \(-0.314235\pi\)
−0.834485 + 0.551030i \(0.814235\pi\)
\(234\) 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 \(-0.913822\pi\)
0.963575 0.267440i \(-0.0861777\pi\)
\(240\) 0 0
\(241\) 22.7291i 1.46411i 0.681244 + 0.732057i \(0.261439\pi\)
−0.681244 + 0.732057i \(0.738561\pi\)
\(242\) 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 −0.736304 0.676651i \(-0.763431\pi\)
−0.0421812 + 0.999110i \(0.513431\pi\)
\(252\) 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 −0.556623 0.830765i \(-0.687903\pi\)
0.830765 + 0.556623i \(0.187903\pi\)
\(264\) 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 0.695000 0.719010i \(-0.255405\pi\)
−0.0169781 + 0.999856i \(0.505405\pi\)
\(270\) 0 0
\(271\) 18.7073i 1.13638i 0.822896 + 0.568192i \(0.192357\pi\)
−0.822896 + 0.568192i \(0.807643\pi\)
\(272\) 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 0.998080 0.0619354i \(-0.0197273\pi\)
−0.749544 + 0.661954i \(0.769727\pi\)
\(278\) 0 0
\(279\) −2.02950 2.02950i −0.121503 0.121503i
\(280\) 0 0
\(281\) −13.2105 + 13.2105i −0.788071 + 0.788071i −0.981178 0.193106i \(-0.938144\pi\)
0.193106 + 0.981178i \(0.438144\pi\)
\(282\) 0 0
\(283\) −21.9884 + 9.10789i −1.30707 + 0.541408i −0.924029 0.382321i \(-0.875125\pi\)
−0.383045 + 0.923730i \(0.625125\pi\)
\(284\) 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 0.244764 0.969583i \(-0.421289\pi\)
0.858673 + 0.512524i \(0.171289\pi\)
\(294\) 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 0.668249 0.743938i \(-0.267044\pi\)
−0.0535206 + 0.998567i \(0.517044\pi\)
\(308\) 0 0
\(309\) 1.05170 + 2.53903i 0.0598292 + 0.144440i
\(310\) 0 0
\(311\) 6.79085 + 6.79085i 0.385074 + 0.385074i 0.872926 0.487852i \(-0.162220\pi\)
−0.487852 + 0.872926i \(0.662220\pi\)
\(312\) 0 0
\(313\) 12.7080 12.7080i 0.718300 0.718300i −0.249957 0.968257i \(-0.580417\pi\)
0.968257 + 0.249957i \(0.0804166\pi\)
\(314\) 0 0
\(315\) 7.14642 2.96015i 0.402655 0.166785i
\(316\) 0 0
\(317\) 6.89303 16.6412i 0.387151 0.934665i −0.603390 0.797446i \(-0.706184\pi\)
0.990541 0.137219i \(-0.0438163\pi\)
\(318\) 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 0.930845 0.365415i \(-0.119073\pi\)
−0.916594 + 0.399819i \(0.869073\pi\)
\(332\) 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 \(-0.769488\pi\)
0.749046 0.662518i \(-0.230512\pi\)
\(338\) 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 −0.188110 0.982148i \(-0.560236\pi\)
0.561469 + 0.827498i \(0.310236\pi\)
\(348\) 0 0
\(349\) −11.9159 + 28.7676i −0.637845 + 1.53989i 0.191700 + 0.981454i \(0.438600\pi\)
−0.829545 + 0.558440i \(0.811400\pi\)
\(350\) 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 −0.385939 0.922524i \(-0.626122\pi\)
0.922524 + 0.385939i \(0.126122\pi\)
\(360\) 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 \(-0.917861\pi\)
0.966890 0.255194i \(-0.0821392\pi\)
\(368\) 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 0.967979 0.251032i \(-0.0807700\pi\)
−0.861971 + 0.506958i \(0.830770\pi\)
\(374\) 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 −0.971608 0.236596i \(-0.923968\pi\)
−0.519732 + 0.854329i \(0.673968\pi\)
\(380\) 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 −0.128691 0.991685i \(-0.541077\pi\)
0.610229 + 0.792225i \(0.291077\pi\)
\(390\) 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 0.702474 0.711709i \(-0.252079\pi\)
−0.00653022 + 0.999979i \(0.502079\pi\)
\(398\) 0 0
\(399\) 13.8432i 0.693027i
\(400\) 0 0
\(401\) 21.9112i 1.09419i 0.837069 + 0.547097i \(0.184267\pi\)
−0.837069 + 0.547097i \(0.815733\pi\)
\(402\) 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 −0.308417 0.951251i \(-0.599799\pi\)
0.951251 + 0.308417i \(0.0997991\pi\)
\(410\) 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 0.600005 + 0.799997i \(0.295165\pi\)
−0.989950 + 0.141416i \(0.954835\pi\)
\(420\) 0 0
\(421\) 5.11481 2.11863i 0.249281 0.103255i −0.254545 0.967061i \(-0.581926\pi\)
0.503825 + 0.863806i \(0.331926\pi\)
\(422\) 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 \(-0.960019\pi\)
0.992122 0.125275i \(-0.0399814\pi\)
\(432\) 0 0
\(433\) 6.44939i 0.309938i −0.987919 0.154969i \(-0.950472\pi\)
0.987919 0.154969i \(-0.0495278\pi\)
\(434\) 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 0.999816 0.0192051i \(-0.00611355\pi\)
−0.0192051 + 0.999816i \(0.506114\pi\)
\(440\) 0 0
\(441\) −0.765344 + 0.765344i −0.0364450 + 0.0364450i
\(442\) 0 0
\(443\) −16.1487 + 6.68902i −0.767249 + 0.317805i −0.731757 0.681565i \(-0.761300\pi\)
−0.0354912 + 0.999370i \(0.511300\pi\)
\(444\) 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 0.999990 0.00456968i \(-0.00145458\pi\)
−0.00456968 + 0.999990i \(0.501455\pi\)
\(458\) 0 0
\(459\) 1.59367 + 3.84747i 0.0743864 + 0.179585i
\(460\) 0 0
\(461\) 0.541763 + 0.224405i 0.0252324 + 0.0104516i 0.395264 0.918568i \(-0.370653\pi\)
−0.370032 + 0.929019i \(0.620653\pi\)
\(462\) 0 0
\(463\) 13.0365i 0.605859i −0.953013 0.302929i \(-0.902035\pi\)
0.953013 0.302929i \(-0.0979646\pi\)
\(464\) 0 0
\(465\) 7.80925i 0.362145i
\(466\) 0 0
\(467\) 36.1793 + 14.9860i 1.67418 + 0.693467i 0.999022 0.0442081i \(-0.0140765\pi\)
0.675156 + 0.737675i \(0.264076\pi\)
\(468\) 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 −0.0368273 + 0.999322i \(0.511725\pi\)
−0.999322 + 0.0368273i \(0.988275\pi\)
\(488\) 0 0
\(489\) 10.7028 + 10.7028i 0.483999 + 0.483999i
\(490\) 0 0
\(491\) −10.1610 24.5308i −0.458559 1.10706i −0.968981 0.247135i \(-0.920511\pi\)
0.510423 0.859924i \(-0.329489\pi\)
\(492\) 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 0.107278 0.994229i \(-0.465786\pi\)
−0.627169 + 0.778883i \(0.715786\pi\)
\(500\) 0 0
\(501\) −2.20606 5.32589i −0.0985593 0.237943i
\(502\) 0 0
\(503\) −12.9948 12.9948i −0.579412 0.579412i 0.355330 0.934741i \(-0.384369\pi\)
−0.934741 + 0.355330i \(0.884369\pi\)
\(504\) 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 −0.288911 0.957356i \(-0.593293\pi\)
0.881244 0.472662i \(-0.156707\pi\)
\(510\) 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 0.744394 0.667740i \(-0.232738\pi\)
−0.667740 + 0.744394i \(0.732738\pi\)
\(522\) 0 0
\(523\) 7.05117 + 17.0230i 0.308326 + 0.744366i 0.999760 + 0.0219253i \(0.00697960\pi\)
−0.691433 + 0.722440i \(0.743020\pi\)
\(524\) 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 0.659838 + 0.751408i \(0.270625\pi\)
−0.997902 + 0.0647494i \(0.979375\pi\)
\(542\) 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 −0.940671 0.339321i \(-0.889803\pi\)
0.905091 + 0.425219i \(0.139803\pi\)
\(548\) 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 −0.296070 0.955166i \(-0.595676\pi\)
−0.884758 + 0.466051i \(0.845676\pi\)
\(558\) 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 −0.0150247 0.999887i \(-0.504783\pi\)
−0.717651 + 0.696403i \(0.754783\pi\)
\(564\) 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 −0.810695 0.585468i \(-0.800911\pi\)
0.585468 + 0.810695i \(0.300911\pi\)
\(570\) 0 0
\(571\) 37.6829 15.6087i 1.57698 0.653206i 0.589047 0.808099i \(-0.299503\pi\)
0.987931 + 0.154893i \(0.0495033\pi\)
\(572\) 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 −0.892353 0.451339i \(-0.850947\pi\)
0.311844 0.950133i \(-0.399053\pi\)
\(588\) 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 \(-0.799623\pi\)
0.808321 0.588743i \(-0.200377\pi\)
\(594\) 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 0.983100 + 0.183067i \(0.0586027\pi\)
0.183067 + 0.983100i \(0.441397\pi\)
\(600\) 0 0
\(601\) −29.9824 + 29.9824i −1.22301 + 1.22301i −0.256448 + 0.966558i \(0.582552\pi\)
−0.966558 + 0.256448i \(0.917448\pi\)
\(602\) 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 0.119383 0.992848i \(-0.461908\pi\)
0.786466 + 0.617633i \(0.211908\pi\)
\(614\) 0 0
\(615\) −2.05796 + 2.05796i −0.0829848 + 0.0829848i
\(616\) 0 0
\(617\) −28.6181 28.6181i −1.15212 1.15212i −0.986127 0.165993i \(-0.946917\pi\)
−0.165993 0.986127i \(-0.553083\pi\)
\(618\) 0 0
\(619\) −0.706861 1.70651i −0.0284111 0.0685905i 0.909037 0.416715i \(-0.136819\pi\)
−0.937448 + 0.348124i \(0.886819\pi\)
\(620\) 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 0.0190703 0.999818i \(-0.493929\pi\)
−0.999818 + 0.0190703i \(0.993929\pi\)
\(632\) 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 −0.993818 0.111019i \(-0.964589\pi\)
0.781238 + 0.624234i \(0.214589\pi\)
\(644\) 0 0
\(645\) −10.1010 + 4.18397i −0.397727 + 0.164744i
\(646\) 0 0
\(647\) −17.8303 + 17.8303i −0.700980 + 0.700980i −0.964621 0.263641i \(-0.915077\pi\)
0.263641 + 0.964621i \(0.415077\pi\)
\(648\) 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 −0.326507 0.945195i \(-0.605872\pi\)
−0.899229 + 0.437478i \(0.855872\pi\)
\(654\) 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 0.971199 0.238271i \(-0.0765807\pi\)
0.518258 + 0.855224i \(0.326581\pi\)
\(660\) 0 0
\(661\) 7.49776 + 18.1012i 0.291629 + 0.704055i 0.999998 0.00178728i \(-0.000568910\pi\)
−0.708369 + 0.705842i \(0.750569\pi\)
\(662\) 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 −0.926293 0.376805i \(-0.877023\pi\)
−0.388546 + 0.921429i \(0.627023\pi\)
\(678\) 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 0.994685 + 0.102964i \(0.0328328\pi\)
−0.630542 + 0.776155i \(0.717167\pi\)
\(684\) 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 0.711866 0.702316i \(-0.247851\pi\)
0.00675270 + 0.999977i \(0.497851\pi\)
\(692\) 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 −0.785743 0.618552i \(-0.787719\pi\)
0.992987 + 0.118222i \(0.0377194\pi\)
\(702\) 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 −0.453922 0.891041i \(-0.649976\pi\)
0.309090 + 0.951033i \(0.399976\pi\)
\(710\) 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 \(0.0523823\pi\)
−0.986490 + 0.163822i \(0.947618\pi\)
\(720\) 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 0.868517 0.495659i \(-0.165073\pi\)
−0.495659 + 0.868517i \(0.665073\pi\)
\(728\) 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 0.608093 + 0.793866i \(0.291935\pi\)
−0.991334 + 0.131362i \(0.958065\pi\)
\(734\) 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 0.516575 + 0.856242i \(0.327207\pi\)
−0.970728 + 0.240180i \(0.922793\pi\)
\(740\) 0 0
\(741\) −27.0429 + 11.2016i −0.993447 + 0.411499i
\(742\) 0 0
\(743\) −16.0222 + 16.0222i −0.587799 + 0.587799i −0.937035 0.349236i \(-0.886441\pi\)
0.349236 + 0.937035i \(0.386441\pi\)
\(744\) 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 \(-0.838757\pi\)
0.874418 0.485173i \(-0.161243\pi\)
\(752\) 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 0.796910 0.604098i \(-0.206467\pi\)
−0.990662 + 0.136338i \(0.956467\pi\)
\(758\) 0 0
\(759\) 6.73903 + 6.73903i 0.244611 + 0.244611i
\(760\) 0 0
\(761\) 11.8263 11.8263i 0.428704 0.428704i −0.459483 0.888187i \(-0.651965\pi\)
0.888187 + 0.459483i \(0.151965\pi\)
\(762\) 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 −0.957675 0.287852i \(-0.907059\pi\)
−0.473636 + 0.880721i \(0.657059\pi\)
\(774\) 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 0.438768 0.898600i \(-0.355415\pi\)
−0.325151 + 0.945662i \(0.605415\pi\)
\(788\) 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 −0.674693 0.738099i \(-0.735724\pi\)
0.998994 0.0448349i \(-0.0142762\pi\)
\(798\) 0