Properties

Label 128.3.h.a.111.7
Level $128$
Weight $3$
Character 128.111
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 111.7
Character \(\chi\) \(=\) 128.111
Dual form 128.3.h.a.15.7

$q$-expansion

\(f(q)\) \(=\) \(q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +O(q^{10})\) \(q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +(4.56441 - 1.89064i) q^{11} +(-5.58307 - 2.31258i) q^{13} -24.7651 q^{15} -25.0539i q^{17} +(-6.43433 + 15.5338i) q^{19} +(10.5785 + 25.5388i) q^{21} +(26.9024 - 26.9024i) q^{23} +(-0.825315 + 0.825315i) q^{25} +(15.0136 + 36.2460i) q^{27} +(-0.210028 + 0.507052i) q^{29} -15.8372i q^{31} +25.0623 q^{33} +(-24.5774 - 10.1803i) q^{35} +(-2.18606 + 0.905498i) q^{37} +(-21.6768 - 21.6768i) q^{39} +(-31.1517 - 31.1517i) q^{41} +(-12.9078 + 5.34659i) q^{43} +(-75.4740 - 31.2624i) q^{45} -15.0033 q^{47} -19.3062i q^{49} +(48.6370 - 117.420i) q^{51} +(-15.4409 - 37.2776i) q^{53} +(-17.0546 + 17.0546i) q^{55} +(-60.3115 + 60.3115i) q^{57} +(14.7242 + 35.5473i) q^{59} +(-15.4603 + 37.3243i) q^{61} +91.1858i q^{63} +29.5016 q^{65} +(-61.3598 - 25.4161i) q^{67} +(178.309 - 73.8579i) q^{69} +(51.7789 + 51.7789i) q^{71} +(64.9440 + 64.9440i) q^{73} +(-5.47018 + 2.26582i) q^{75} +(24.8724 + 10.3025i) q^{77} +38.1202 q^{79} +48.4156i q^{81} +(-15.9782 + 38.5748i) q^{83} +(46.8061 + 113.000i) q^{85} +(-1.96868 + 1.96868i) q^{87} +(23.7666 - 23.7666i) q^{89} +(-12.6017 - 30.4233i) q^{91} +(30.7446 - 74.2241i) q^{93} -82.0827i q^{95} -118.710 q^{97} +(76.3798 + 31.6376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.68670 + 1.94129i 1.56223 + 0.647098i 0.985476 0.169817i \(-0.0543176\pi\)
0.576758 + 0.816915i \(0.304318\pi\)
\(4\) 0 0
\(5\) −4.51028 + 1.86822i −0.902055 + 0.373644i −0.785010 0.619483i \(-0.787342\pi\)
−0.117045 + 0.993127i \(0.537342\pi\)
\(6\) 0 0
\(7\) 3.85317 + 3.85317i 0.550453 + 0.550453i 0.926571 0.376119i \(-0.122742\pi\)
−0.376119 + 0.926571i \(0.622742\pi\)
\(8\) 0 0
\(9\) 11.8326 + 11.8326i 1.31473 + 1.31473i
\(10\) 0 0
\(11\) 4.56441 1.89064i 0.414946 0.171876i −0.165436 0.986221i \(-0.552903\pi\)
0.580382 + 0.814344i \(0.302903\pi\)
\(12\) 0 0
\(13\) −5.58307 2.31258i −0.429467 0.177891i 0.157470 0.987524i \(-0.449666\pi\)
−0.586937 + 0.809633i \(0.699666\pi\)
\(14\) 0 0
\(15\) −24.7651 −1.65101
\(16\) 0 0
\(17\) 25.0539i 1.47376i −0.676025 0.736879i \(-0.736299\pi\)
0.676025 0.736879i \(-0.263701\pi\)
\(18\) 0 0
\(19\) −6.43433 + 15.5338i −0.338649 + 0.817571i 0.659197 + 0.751970i \(0.270896\pi\)
−0.997846 + 0.0656005i \(0.979104\pi\)
\(20\) 0 0
\(21\) 10.5785 + 25.5388i 0.503739 + 1.21613i
\(22\) 0 0
\(23\) 26.9024 26.9024i 1.16967 1.16967i 0.187381 0.982287i \(-0.440000\pi\)
0.982287 0.187381i \(-0.0600000\pi\)
\(24\) 0 0
\(25\) −0.825315 + 0.825315i −0.0330126 + 0.0330126i
\(26\) 0 0
\(27\) 15.0136 + 36.2460i 0.556058 + 1.34244i
\(28\) 0 0
\(29\) −0.210028 + 0.507052i −0.00724234 + 0.0174846i −0.927459 0.373924i \(-0.878012\pi\)
0.920217 + 0.391409i \(0.128012\pi\)
\(30\) 0 0
\(31\) 15.8372i 0.510877i −0.966825 0.255438i \(-0.917780\pi\)
0.966825 0.255438i \(-0.0822198\pi\)
\(32\) 0 0
\(33\) 25.0623 0.759464
\(34\) 0 0
\(35\) −24.5774 10.1803i −0.702212 0.290866i
\(36\) 0 0
\(37\) −2.18606 + 0.905498i −0.0590828 + 0.0244729i −0.412029 0.911171i \(-0.635180\pi\)
0.352946 + 0.935644i \(0.385180\pi\)
\(38\) 0 0
\(39\) −21.6768 21.6768i −0.555814 0.555814i
\(40\) 0 0
\(41\) −31.1517 31.1517i −0.759798 0.759798i 0.216488 0.976285i \(-0.430540\pi\)
−0.976285 + 0.216488i \(0.930540\pi\)
\(42\) 0 0
\(43\) −12.9078 + 5.34659i −0.300182 + 0.124339i −0.527691 0.849437i \(-0.676942\pi\)
0.227509 + 0.973776i \(0.426942\pi\)
\(44\) 0 0
\(45\) −75.4740 31.2624i −1.67720 0.694719i
\(46\) 0 0
\(47\) −15.0033 −0.319220 −0.159610 0.987180i \(-0.551024\pi\)
−0.159610 + 0.987180i \(0.551024\pi\)
\(48\) 0 0
\(49\) 19.3062i 0.394004i
\(50\) 0 0
\(51\) 48.6370 117.420i 0.953666 2.30235i
\(52\) 0 0
\(53\) −15.4409 37.2776i −0.291338 0.703352i 0.708660 0.705550i \(-0.249300\pi\)
−0.999998 + 0.00219873i \(0.999300\pi\)
\(54\) 0 0
\(55\) −17.0546 + 17.0546i −0.310084 + 0.310084i
\(56\) 0 0
\(57\) −60.3115 + 60.3115i −1.05810 + 1.05810i
\(58\) 0 0
\(59\) 14.7242 + 35.5473i 0.249562 + 0.602496i 0.998167 0.0605202i \(-0.0192760\pi\)
−0.748605 + 0.663016i \(0.769276\pi\)
\(60\) 0 0
\(61\) −15.4603 + 37.3243i −0.253447 + 0.611875i −0.998478 0.0551552i \(-0.982435\pi\)
0.745031 + 0.667030i \(0.232435\pi\)
\(62\) 0 0
\(63\) 91.1858i 1.44739i
\(64\) 0 0
\(65\) 29.5016 0.453870
\(66\) 0 0
\(67\) −61.3598 25.4161i −0.915818 0.379344i −0.125537 0.992089i \(-0.540065\pi\)
−0.790281 + 0.612745i \(0.790065\pi\)
\(68\) 0 0
\(69\) 178.309 73.8579i 2.58419 1.07040i
\(70\) 0 0
\(71\) 51.7789 + 51.7789i 0.729281 + 0.729281i 0.970477 0.241196i \(-0.0775395\pi\)
−0.241196 + 0.970477i \(0.577540\pi\)
\(72\) 0 0
\(73\) 64.9440 + 64.9440i 0.889643 + 0.889643i 0.994489 0.104845i \(-0.0334347\pi\)
−0.104845 + 0.994489i \(0.533435\pi\)
\(74\) 0 0
\(75\) −5.47018 + 2.26582i −0.0729358 + 0.0302110i
\(76\) 0 0
\(77\) 24.8724 + 10.3025i 0.323018 + 0.133798i
\(78\) 0 0
\(79\) 38.1202 0.482535 0.241267 0.970459i \(-0.422437\pi\)
0.241267 + 0.970459i \(0.422437\pi\)
\(80\) 0 0
\(81\) 48.4156i 0.597724i
\(82\) 0 0
\(83\) −15.9782 + 38.5748i −0.192509 + 0.464757i −0.990432 0.138002i \(-0.955932\pi\)
0.797923 + 0.602759i \(0.205932\pi\)
\(84\) 0 0
\(85\) 46.8061 + 113.000i 0.550660 + 1.32941i
\(86\) 0 0
\(87\) −1.96868 + 1.96868i −0.0226285 + 0.0226285i
\(88\) 0 0
\(89\) 23.7666 23.7666i 0.267040 0.267040i −0.560866 0.827906i \(-0.689532\pi\)
0.827906 + 0.560866i \(0.189532\pi\)
\(90\) 0 0
\(91\) −12.6017 30.4233i −0.138481 0.334322i
\(92\) 0 0
\(93\) 30.7446 74.2241i 0.330587 0.798109i
\(94\) 0 0
\(95\) 82.0827i 0.864028i
\(96\) 0 0
\(97\) −118.710 −1.22382 −0.611908 0.790929i \(-0.709598\pi\)
−0.611908 + 0.790929i \(0.709598\pi\)
\(98\) 0 0
\(99\) 76.3798 + 31.6376i 0.771514 + 0.319571i
\(100\) 0 0
\(101\) −182.236 + 75.4846i −1.80432 + 0.747372i −0.819665 + 0.572844i \(0.805840\pi\)
−0.984652 + 0.174529i \(0.944160\pi\)
\(102\) 0 0
\(103\) 80.3171 + 80.3171i 0.779777 + 0.779777i 0.979793 0.200016i \(-0.0640993\pi\)
−0.200016 + 0.979793i \(0.564099\pi\)
\(104\) 0 0
\(105\) −95.4240 95.4240i −0.908800 0.908800i
\(106\) 0 0
\(107\) −22.6854 + 9.39659i −0.212013 + 0.0878186i −0.486162 0.873868i \(-0.661604\pi\)
0.274150 + 0.961687i \(0.411604\pi\)
\(108\) 0 0
\(109\) 181.428 + 75.1501i 1.66448 + 0.689450i 0.998406 0.0564360i \(-0.0179737\pi\)
0.666074 + 0.745886i \(0.267974\pi\)
\(110\) 0 0
\(111\) −12.0033 −0.108138
\(112\) 0 0
\(113\) 32.7876i 0.290156i −0.989420 0.145078i \(-0.953657\pi\)
0.989420 0.145078i \(-0.0463433\pi\)
\(114\) 0 0
\(115\) −71.0777 + 171.597i −0.618067 + 1.49214i
\(116\) 0 0
\(117\) −38.6983 93.4259i −0.330754 0.798512i
\(118\) 0 0
\(119\) 96.5368 96.5368i 0.811234 0.811234i
\(120\) 0 0
\(121\) −68.3006 + 68.3006i −0.564468 + 0.564468i
\(122\) 0 0
\(123\) −85.5241 206.473i −0.695318 1.67865i
\(124\) 0 0
\(125\) 48.8860 118.021i 0.391088 0.944169i
\(126\) 0 0
\(127\) 130.165i 1.02492i 0.858710 + 0.512462i \(0.171266\pi\)
−0.858710 + 0.512462i \(0.828734\pi\)
\(128\) 0 0
\(129\) −70.8744 −0.549414
\(130\) 0 0
\(131\) −24.3356 10.0801i −0.185768 0.0769476i 0.287861 0.957672i \(-0.407056\pi\)
−0.473628 + 0.880725i \(0.657056\pi\)
\(132\) 0 0
\(133\) −84.6471 + 35.0620i −0.636444 + 0.263624i
\(134\) 0 0
\(135\) −135.431 135.431i −1.00319 1.00319i
\(136\) 0 0
\(137\) 147.886 + 147.886i 1.07946 + 1.07946i 0.996557 + 0.0829047i \(0.0264197\pi\)
0.0829047 + 0.996557i \(0.473580\pi\)
\(138\) 0 0
\(139\) 206.929 85.7129i 1.48870 0.616639i 0.517666 0.855583i \(-0.326801\pi\)
0.971033 + 0.238944i \(0.0768011\pi\)
\(140\) 0 0
\(141\) −70.3162 29.1259i −0.498696 0.206567i
\(142\) 0 0
\(143\) −29.8556 −0.208781
\(144\) 0 0
\(145\) 2.67932i 0.0184781i
\(146\) 0 0
\(147\) 37.4790 90.4823i 0.254959 0.615526i
\(148\) 0 0
\(149\) −20.4247 49.3095i −0.137078 0.330936i 0.840402 0.541964i \(-0.182319\pi\)
−0.977480 + 0.211028i \(0.932319\pi\)
\(150\) 0 0
\(151\) −180.137 + 180.137i −1.19296 + 1.19296i −0.216726 + 0.976232i \(0.569538\pi\)
−0.976232 + 0.216726i \(0.930462\pi\)
\(152\) 0 0
\(153\) 296.452 296.452i 1.93759 1.93759i
\(154\) 0 0
\(155\) 29.5873 + 71.4300i 0.190886 + 0.460839i
\(156\) 0 0
\(157\) −60.3999 + 145.818i −0.384713 + 0.928779i 0.606327 + 0.795215i \(0.292642\pi\)
−0.991040 + 0.133564i \(0.957358\pi\)
\(158\) 0 0
\(159\) 204.684i 1.28732i
\(160\) 0 0
\(161\) 207.319 1.28769
\(162\) 0 0
\(163\) 152.162 + 63.0277i 0.933512 + 0.386673i 0.797010 0.603966i \(-0.206414\pi\)
0.136502 + 0.990640i \(0.456414\pi\)
\(164\) 0 0
\(165\) −113.038 + 46.8218i −0.685078 + 0.283769i
\(166\) 0 0
\(167\) −94.8188 94.8188i −0.567777 0.567777i 0.363728 0.931505i \(-0.381504\pi\)
−0.931505 + 0.363728i \(0.881504\pi\)
\(168\) 0 0
\(169\) −93.6785 93.6785i −0.554310 0.554310i
\(170\) 0 0
\(171\) −259.940 + 107.671i −1.52012 + 0.629653i
\(172\) 0 0
\(173\) −107.416 44.4930i −0.620900 0.257185i 0.0499813 0.998750i \(-0.484084\pi\)
−0.670881 + 0.741565i \(0.734084\pi\)
\(174\) 0 0
\(175\) −6.36016 −0.0363437
\(176\) 0 0
\(177\) 195.183i 1.10273i
\(178\) 0 0
\(179\) −54.7154 + 132.095i −0.305673 + 0.737959i 0.694163 + 0.719818i \(0.255775\pi\)
−0.999835 + 0.0181410i \(0.994225\pi\)
\(180\) 0 0
\(181\) −128.496 310.218i −0.709925 1.71391i −0.700189 0.713957i \(-0.746901\pi\)
−0.00973575 0.999953i \(-0.503099\pi\)
\(182\) 0 0
\(183\) −144.915 + 144.915i −0.791886 + 0.791886i
\(184\) 0 0
\(185\) 8.16809 8.16809i 0.0441518 0.0441518i
\(186\) 0 0
\(187\) −47.3678 114.356i −0.253304 0.611530i
\(188\) 0 0
\(189\) −81.8120 + 197.512i −0.432868 + 1.04503i
\(190\) 0 0
\(191\) 312.806i 1.63773i −0.573986 0.818865i \(-0.694604\pi\)
0.573986 0.818865i \(-0.305396\pi\)
\(192\) 0 0
\(193\) −70.6708 −0.366170 −0.183085 0.983097i \(-0.558608\pi\)
−0.183085 + 0.983097i \(0.558608\pi\)
\(194\) 0 0
\(195\) 138.265 + 57.2713i 0.709052 + 0.293699i
\(196\) 0 0
\(197\) 81.5762 33.7900i 0.414092 0.171523i −0.165904 0.986142i \(-0.553054\pi\)
0.579996 + 0.814619i \(0.303054\pi\)
\(198\) 0 0
\(199\) −102.666 102.666i −0.515910 0.515910i 0.400421 0.916331i \(-0.368864\pi\)
−0.916331 + 0.400421i \(0.868864\pi\)
\(200\) 0 0
\(201\) −238.235 238.235i −1.18525 1.18525i
\(202\) 0 0
\(203\) −2.76303 + 1.14449i −0.0136110 + 0.00563786i
\(204\) 0 0
\(205\) 198.701 + 82.3046i 0.969273 + 0.401486i
\(206\) 0 0
\(207\) 636.649 3.07560
\(208\) 0 0
\(209\) 83.0678i 0.397454i
\(210\) 0 0
\(211\) −8.35160 + 20.1625i −0.0395810 + 0.0955571i −0.942434 0.334393i \(-0.891469\pi\)
0.902853 + 0.429950i \(0.141469\pi\)
\(212\) 0 0
\(213\) 142.154 + 343.191i 0.667391 + 1.61122i
\(214\) 0 0
\(215\) 48.2292 48.2292i 0.224322 0.224322i
\(216\) 0 0
\(217\) 61.0233 61.0233i 0.281213 0.281213i
\(218\) 0 0
\(219\) 178.298 + 430.448i 0.814144 + 1.96552i
\(220\) 0 0
\(221\) −57.9391 + 139.877i −0.262168 + 0.632930i
\(222\) 0 0
\(223\) 131.685i 0.590516i 0.955418 + 0.295258i \(0.0954056\pi\)
−0.955418 + 0.295258i \(0.904594\pi\)
\(224\) 0 0
\(225\) −19.5312 −0.0868054
\(226\) 0 0
\(227\) −60.7552 25.1656i −0.267644 0.110862i 0.244825 0.969567i \(-0.421269\pi\)
−0.512470 + 0.858705i \(0.671269\pi\)
\(228\) 0 0
\(229\) 123.210 51.0352i 0.538035 0.222861i −0.0970835 0.995276i \(-0.530951\pi\)
0.635118 + 0.772415i \(0.280951\pi\)
\(230\) 0 0
\(231\) 96.5693 + 96.5693i 0.418049 + 0.418049i
\(232\) 0 0
\(233\) 110.005 + 110.005i 0.472124 + 0.472124i 0.902601 0.430477i \(-0.141655\pi\)
−0.430477 + 0.902601i \(0.641655\pi\)
\(234\) 0 0
\(235\) 67.6692 28.0295i 0.287954 0.119274i
\(236\) 0 0
\(237\) 178.658 + 74.0026i 0.753832 + 0.312247i
\(238\) 0 0
\(239\) −277.831 −1.16247 −0.581236 0.813735i \(-0.697431\pi\)
−0.581236 + 0.813735i \(0.697431\pi\)
\(240\) 0 0
\(241\) 52.0006i 0.215770i 0.994163 + 0.107885i \(0.0344079\pi\)
−0.994163 + 0.107885i \(0.965592\pi\)
\(242\) 0 0
\(243\) 41.1331 99.3041i 0.169272 0.408659i
\(244\) 0 0
\(245\) 36.0681 + 87.0762i 0.147217 + 0.355413i
\(246\) 0 0
\(247\) 71.8466 71.8466i 0.290877 0.290877i
\(248\) 0 0
\(249\) −149.770 + 149.770i −0.601487 + 0.601487i
\(250\) 0 0
\(251\) −28.7912 69.5080i −0.114706 0.276924i 0.856092 0.516823i \(-0.172886\pi\)
−0.970798 + 0.239899i \(0.922886\pi\)
\(252\) 0 0
\(253\) 71.9307 173.656i 0.284311 0.686388i
\(254\) 0 0
\(255\) 620.461i 2.43318i
\(256\) 0 0
\(257\) 241.501 0.939692 0.469846 0.882748i \(-0.344309\pi\)
0.469846 + 0.882748i \(0.344309\pi\)
\(258\) 0 0
\(259\) −11.9123 4.93424i −0.0459935 0.0190511i
\(260\) 0 0
\(261\) −8.48491 + 3.51456i −0.0325092 + 0.0134658i
\(262\) 0 0
\(263\) 118.637 + 118.637i 0.451090 + 0.451090i 0.895716 0.444626i \(-0.146664\pi\)
−0.444626 + 0.895716i \(0.646664\pi\)
\(264\) 0 0
\(265\) 139.285 + 139.285i 0.525606 + 0.525606i
\(266\) 0 0
\(267\) 157.525 65.2489i 0.589981 0.244378i
\(268\) 0 0
\(269\) −231.194 95.7638i −0.859459 0.355999i −0.0909629 0.995854i \(-0.528994\pi\)
−0.768496 + 0.639855i \(0.778994\pi\)
\(270\) 0 0
\(271\) 2.13724 0.00788650 0.00394325 0.999992i \(-0.498745\pi\)
0.00394325 + 0.999992i \(0.498745\pi\)
\(272\) 0 0
\(273\) 167.048i 0.611899i
\(274\) 0 0
\(275\) −2.20670 + 5.32745i −0.00802437 + 0.0193725i
\(276\) 0 0
\(277\) −177.679 428.955i −0.641441 1.54857i −0.824737 0.565517i \(-0.808677\pi\)
0.183296 0.983058i \(-0.441323\pi\)
\(278\) 0 0
\(279\) 187.395 187.395i 0.671665 0.671665i
\(280\) 0 0
\(281\) −261.664 + 261.664i −0.931188 + 0.931188i −0.997780 0.0665922i \(-0.978787\pi\)
0.0665922 + 0.997780i \(0.478787\pi\)
\(282\) 0 0
\(283\) −160.904 388.456i −0.568564 1.37264i −0.902765 0.430134i \(-0.858466\pi\)
0.334201 0.942502i \(-0.391534\pi\)
\(284\) 0 0
\(285\) 159.347 384.697i 0.559111 1.34981i
\(286\) 0 0
\(287\) 240.066i 0.836465i
\(288\) 0 0
\(289\) −338.697 −1.17196
\(290\) 0 0
\(291\) −556.359 230.452i −1.91189 0.791930i
\(292\) 0 0
\(293\) −141.895 + 58.7749i −0.484284 + 0.200597i −0.611448 0.791285i \(-0.709413\pi\)
0.127164 + 0.991882i \(0.459413\pi\)
\(294\) 0 0
\(295\) −132.820 132.820i −0.450238 0.450238i
\(296\) 0 0
\(297\) 137.056 + 137.056i 0.461468 + 0.461468i
\(298\) 0 0
\(299\) −212.412 + 87.9838i −0.710407 + 0.294260i
\(300\) 0 0
\(301\) −70.3373 29.1347i −0.233679 0.0967929i
\(302\) 0 0
\(303\) −1000.62 −3.30239
\(304\) 0 0
\(305\) 197.226i 0.646643i
\(306\) 0 0
\(307\) 36.1806 87.3476i 0.117852 0.284520i −0.853935 0.520379i \(-0.825791\pi\)
0.971787 + 0.235860i \(0.0757905\pi\)
\(308\) 0 0
\(309\) 220.503 + 532.341i 0.713602 + 1.72279i
\(310\) 0 0
\(311\) −221.462 + 221.462i −0.712098 + 0.712098i −0.966974 0.254876i \(-0.917965\pi\)
0.254876 + 0.966974i \(0.417965\pi\)
\(312\) 0 0
\(313\) 280.384 280.384i 0.895795 0.895795i −0.0992662 0.995061i \(-0.531650\pi\)
0.995061 + 0.0992662i \(0.0316495\pi\)
\(314\) 0 0
\(315\) −170.355 411.273i −0.540809 1.30563i
\(316\) 0 0
\(317\) 155.972 376.549i 0.492024 1.18785i −0.461665 0.887055i \(-0.652748\pi\)
0.953688 0.300796i \(-0.0972524\pi\)
\(318\) 0 0
\(319\) 2.71148i 0.00849994i
\(320\) 0 0
\(321\) −124.561 −0.388041
\(322\) 0 0
\(323\) 389.183 + 161.205i 1.20490 + 0.499086i
\(324\) 0 0
\(325\) 6.51640 2.69918i 0.0200505 0.00830517i
\(326\) 0 0
\(327\) 704.412 + 704.412i 2.15416 + 2.15416i
\(328\) 0 0
\(329\) −57.8104 57.8104i −0.175715 0.175715i
\(330\) 0 0
\(331\) 418.148 173.202i 1.26329 0.523270i 0.352370 0.935861i \(-0.385376\pi\)
0.910917 + 0.412591i \(0.135376\pi\)
\(332\) 0 0
\(333\) −36.5812 15.1524i −0.109853 0.0455027i
\(334\) 0 0
\(335\) 324.232 0.967857
\(336\) 0 0
\(337\) 38.1203i 0.113116i −0.998399 0.0565582i \(-0.981987\pi\)
0.998399 0.0565582i \(-0.0180127\pi\)
\(338\) 0 0
\(339\) 63.6504 153.666i 0.187759 0.453291i
\(340\) 0 0
\(341\) −29.9424 72.2873i −0.0878076 0.211986i
\(342\) 0 0
\(343\) 263.195 263.195i 0.767333 0.767333i
\(344\) 0 0
\(345\) −666.239 + 666.239i −1.93113 + 1.93113i
\(346\) 0 0
\(347\) 201.452 + 486.348i 0.580553 + 1.40158i 0.892313 + 0.451418i \(0.149082\pi\)
−0.311760 + 0.950161i \(0.600918\pi\)
\(348\) 0 0
\(349\) −53.2160 + 128.475i −0.152481 + 0.368122i −0.981600 0.190951i \(-0.938843\pi\)
0.829118 + 0.559073i \(0.188843\pi\)
\(350\) 0 0
\(351\) 237.084i 0.675452i
\(352\) 0 0
\(353\) −223.875 −0.634208 −0.317104 0.948391i \(-0.602710\pi\)
−0.317104 + 0.948391i \(0.602710\pi\)
\(354\) 0 0
\(355\) −330.272 136.803i −0.930343 0.385361i
\(356\) 0 0
\(357\) 639.846 265.033i 1.79228 0.742389i
\(358\) 0 0
\(359\) 44.5652 + 44.5652i 0.124137 + 0.124137i 0.766446 0.642309i \(-0.222023\pi\)
−0.642309 + 0.766446i \(0.722023\pi\)
\(360\) 0 0
\(361\) 55.3658 + 55.3658i 0.153368 + 0.153368i
\(362\) 0 0
\(363\) −452.696 + 187.513i −1.24710 + 0.516565i
\(364\) 0 0
\(365\) −414.245 171.586i −1.13492 0.470098i
\(366\) 0 0
\(367\) 294.972 0.803739 0.401869 0.915697i \(-0.368361\pi\)
0.401869 + 0.915697i \(0.368361\pi\)
\(368\) 0 0
\(369\) 737.210i 1.99786i
\(370\) 0 0
\(371\) 84.1406 203.133i 0.226794 0.547529i
\(372\) 0 0
\(373\) 96.5187 + 233.017i 0.258763 + 0.624710i 0.998857 0.0477936i \(-0.0152190\pi\)
−0.740094 + 0.672504i \(0.765219\pi\)
\(374\) 0 0
\(375\) 458.228 458.228i 1.22194 1.22194i
\(376\) 0 0
\(377\) 2.34520 2.34520i 0.00622069 0.00622069i
\(378\) 0 0
\(379\) 70.2002 + 169.478i 0.185225 + 0.447172i 0.989029 0.147722i \(-0.0471941\pi\)
−0.803804 + 0.594894i \(0.797194\pi\)
\(380\) 0 0
\(381\) −252.689 + 610.046i −0.663227 + 1.60117i
\(382\) 0 0
\(383\) 519.043i 1.35520i 0.735429 + 0.677602i \(0.236981\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(384\) 0 0
\(385\) −131.429 −0.341373
\(386\) 0 0
\(387\) −215.997 89.4688i −0.558131 0.231185i
\(388\) 0 0
\(389\) 52.0121 21.5441i 0.133707 0.0553834i −0.314827 0.949149i \(-0.601946\pi\)
0.448534 + 0.893766i \(0.351946\pi\)
\(390\) 0 0
\(391\) −674.009 674.009i −1.72381 1.72381i
\(392\) 0 0
\(393\) −94.4851 94.4851i −0.240420 0.240420i
\(394\) 0 0
\(395\) −171.933 + 71.2169i −0.435273 + 0.180296i
\(396\) 0 0
\(397\) 138.533 + 57.3823i 0.348950 + 0.144540i 0.550272 0.834985i \(-0.314524\pi\)
−0.201322 + 0.979525i \(0.564524\pi\)
\(398\) 0 0
\(399\) −464.781 −1.16487
\(400\) 0 0
\(401\) 11.3014i 0.0281830i −0.999901 0.0140915i \(-0.995514\pi\)
0.999901 0.0140915i \(-0.00448560\pi\)
\(402\) 0 0
\(403\) −36.6248 + 88.4200i −0.0908803 + 0.219404i
\(404\) 0 0
\(405\) −90.4509 218.368i −0.223336 0.539180i
\(406\) 0 0
\(407\) −8.26612 + 8.26612i −0.0203099 + 0.0203099i
\(408\) 0 0
\(409\) 188.958 188.958i 0.462001 0.462001i −0.437310 0.899311i \(-0.644069\pi\)
0.899311 + 0.437310i \(0.144069\pi\)
\(410\) 0 0
\(411\) 406.008 + 980.190i 0.987854 + 2.38489i
\(412\) 0 0
\(413\) −80.2350 + 193.704i −0.194274 + 0.469018i
\(414\) 0 0
\(415\) 203.834i 0.491166i
\(416\) 0 0
\(417\) 1136.21 2.72472
\(418\) 0 0
\(419\) 238.026 + 98.5936i 0.568081 + 0.235307i 0.648189 0.761479i \(-0.275527\pi\)
−0.0801080 + 0.996786i \(0.525527\pi\)
\(420\) 0 0
\(421\) 324.923 134.588i 0.771790 0.319686i 0.0381925 0.999270i \(-0.487840\pi\)
0.733597 + 0.679585i \(0.237840\pi\)
\(422\) 0 0
\(423\) −177.528 177.528i −0.419688 0.419688i
\(424\) 0 0
\(425\) 20.6773 + 20.6773i 0.0486526 + 0.0486526i
\(426\) 0 0
\(427\) −203.388 + 84.2461i −0.476318 + 0.197298i
\(428\) 0 0
\(429\) −139.924 57.9586i −0.326164 0.135102i
\(430\) 0 0
\(431\) 16.1400 0.0374479 0.0187239 0.999825i \(-0.494040\pi\)
0.0187239 + 0.999825i \(0.494040\pi\)
\(432\) 0 0
\(433\) 732.781i 1.69233i 0.532918 + 0.846167i \(0.321095\pi\)
−0.532918 + 0.846167i \(0.678905\pi\)
\(434\) 0 0
\(435\) 5.20136 12.5572i 0.0119571 0.0288671i
\(436\) 0 0
\(437\) 244.799 + 590.996i 0.560180 + 1.35239i
\(438\) 0 0
\(439\) −460.630 + 460.630i −1.04927 + 1.04927i −0.0505487 + 0.998722i \(0.516097\pi\)
−0.998722 + 0.0505487i \(0.983903\pi\)
\(440\) 0 0
\(441\) 228.442 228.442i 0.518009 0.518009i
\(442\) 0 0
\(443\) 55.5453 + 134.098i 0.125384 + 0.302705i 0.974090 0.226161i \(-0.0726175\pi\)
−0.848705 + 0.528866i \(0.822618\pi\)
\(444\) 0 0
\(445\) −62.7927 + 151.595i −0.141107 + 0.340663i
\(446\) 0 0
\(447\) 270.749i 0.605703i
\(448\) 0 0
\(449\) 731.262 1.62865 0.814323 0.580412i \(-0.197108\pi\)
0.814323 + 0.580412i \(0.197108\pi\)
\(450\) 0 0
\(451\) −201.086 83.2924i −0.445866 0.184684i
\(452\) 0 0
\(453\) −1193.95 + 494.549i −2.63564 + 1.09172i
\(454\) 0 0
\(455\) 113.675 + 113.675i 0.249834 + 0.249834i
\(456\) 0 0
\(457\) −332.873 332.873i −0.728388 0.728388i 0.241911 0.970298i \(-0.422226\pi\)
−0.970298 + 0.241911i \(0.922226\pi\)
\(458\) 0 0
\(459\) 908.102 376.148i 1.97844 0.819495i
\(460\) 0 0
\(461\) −132.650 54.9455i −0.287744 0.119188i 0.234143 0.972202i \(-0.424772\pi\)
−0.521887 + 0.853015i \(0.674772\pi\)
\(462\) 0 0
\(463\) 873.591 1.88680 0.943402 0.331650i \(-0.107605\pi\)
0.943402 + 0.331650i \(0.107605\pi\)
\(464\) 0 0
\(465\) 392.209i 0.843460i
\(466\) 0 0
\(467\) 135.550 327.247i 0.290258 0.700744i −0.709735 0.704468i \(-0.751186\pi\)
0.999993 + 0.00372448i \(0.00118554\pi\)
\(468\) 0 0
\(469\) −138.497 334.362i −0.295303 0.712925i
\(470\) 0 0
\(471\) −566.153 + 566.153i −1.20202 + 1.20202i
\(472\) 0 0
\(473\) −48.8081 + 48.8081i −0.103188 + 0.103188i
\(474\) 0 0
\(475\) −7.50997 18.1307i −0.0158105 0.0381698i
\(476\) 0 0
\(477\) 258.385 623.796i 0.541687 1.30775i
\(478\) 0 0
\(479\) 296.032i 0.618021i 0.951059 + 0.309011i \(0.0999979\pi\)
−0.951059 + 0.309011i \(0.900002\pi\)
\(480\) 0 0
\(481\) 14.2990 0.0297276
\(482\) 0 0
\(483\) 971.641 + 402.467i 2.01168 + 0.833265i
\(484\) 0 0
\(485\) 535.416 221.777i 1.10395 0.457271i
\(486\) 0 0
\(487\) 232.632 + 232.632i 0.477683 + 0.477683i 0.904390 0.426707i \(-0.140326\pi\)
−0.426707 + 0.904390i \(0.640326\pi\)
\(488\) 0 0
\(489\) 590.784 + 590.784i 1.20815 + 1.20815i
\(490\) 0 0
\(491\) −217.435 + 90.0644i −0.442840 + 0.183430i −0.592951 0.805239i \(-0.702037\pi\)
0.150110 + 0.988669i \(0.452037\pi\)
\(492\) 0 0
\(493\) 12.7036 + 5.26201i 0.0257680 + 0.0106735i
\(494\) 0 0
\(495\) −403.600 −0.815354
\(496\) 0 0
\(497\) 399.026i 0.802869i
\(498\) 0 0
\(499\) −64.7699 + 156.368i −0.129799 + 0.313364i −0.975396 0.220458i \(-0.929245\pi\)
0.845597 + 0.533822i \(0.179245\pi\)
\(500\) 0 0
\(501\) −260.316 628.458i −0.519593 1.25441i
\(502\) 0 0
\(503\) 612.203 612.203i 1.21710 1.21710i 0.248460 0.968642i \(-0.420075\pi\)
0.968642 0.248460i \(-0.0799246\pi\)
\(504\) 0 0
\(505\) 680.913 680.913i 1.34834 1.34834i
\(506\) 0 0
\(507\) −257.185 620.900i −0.507269 1.22466i
\(508\) 0 0
\(509\) −273.870 + 661.182i −0.538056 + 1.29898i 0.388022 + 0.921650i \(0.373158\pi\)
−0.926078 + 0.377332i \(0.876842\pi\)
\(510\) 0 0
\(511\) 500.480i 0.979413i
\(512\) 0 0
\(513\) −659.641 −1.28585
\(514\) 0 0
\(515\) −512.302 212.202i −0.994761 0.412043i
\(516\) 0 0
\(517\) −68.4813 + 28.3659i −0.132459 + 0.0548663i
\(518\) 0 0
\(519\) −417.051 417.051i −0.803566 0.803566i
\(520\) 0 0
\(521\) −527.816 527.816i −1.01308 1.01308i −0.999913 0.0131690i \(-0.995808\pi\)
−0.0131690 0.999913i \(-0.504192\pi\)
\(522\) 0 0
\(523\) −5.01268 + 2.07632i −0.00958447 + 0.00397002i −0.387471 0.921882i \(-0.626651\pi\)
0.377886 + 0.925852i \(0.376651\pi\)
\(524\) 0 0
\(525\) −29.8081 12.3469i −0.0567774 0.0235180i
\(526\) 0 0
\(527\) −396.783 −0.752908
\(528\) 0 0
\(529\) 918.476i 1.73625i
\(530\) 0 0
\(531\) −246.391 + 594.841i −0.464013 + 1.12023i
\(532\) 0 0
\(533\) 101.881 + 245.963i 0.191147 + 0.461469i
\(534\) 0 0
\(535\) 84.7624 84.7624i 0.158434 0.158434i
\(536\) 0 0
\(537\) −512.869 + 512.869i −0.955064 + 0.955064i
\(538\) 0 0
\(539\) −36.5010 88.1213i −0.0677199 0.163490i
\(540\) 0 0
\(541\) −229.279 + 553.528i −0.423806 + 1.02316i 0.557409 + 0.830238i \(0.311796\pi\)
−0.981215 + 0.192919i \(0.938204\pi\)
\(542\) 0 0
\(543\) 1703.35i 3.13692i
\(544\) 0 0
\(545\) −958.688 −1.75906
\(546\) 0 0
\(547\) 391.381 + 162.115i 0.715504 + 0.296371i 0.710580 0.703617i \(-0.248433\pi\)
0.00492387 + 0.999988i \(0.498433\pi\)
\(548\) 0 0
\(549\) −624.578 + 258.709i −1.13766 + 0.471236i
\(550\) 0 0
\(551\) −6.52508 6.52508i −0.0118423 0.0118423i
\(552\) 0 0
\(553\) 146.884 + 146.884i 0.265613 + 0.265613i
\(554\) 0 0
\(555\) 54.1381 22.4247i 0.0975461 0.0404049i
\(556\) 0 0
\(557\) 364.486 + 150.975i 0.654374 + 0.271050i 0.685069 0.728478i \(-0.259772\pi\)
−0.0306953 + 0.999529i \(0.509772\pi\)
\(558\) 0 0
\(559\) 84.4296 0.151037
\(560\) 0 0
\(561\) 627.908i 1.11927i
\(562\) 0 0
\(563\) −114.762 + 277.059i −0.203840 + 0.492113i −0.992431 0.122805i \(-0.960811\pi\)
0.788591 + 0.614918i \(0.210811\pi\)
\(564\) 0 0
\(565\) 61.2544 + 147.881i 0.108415 + 0.261736i
\(566\) 0 0
\(567\) −186.554 + 186.554i −0.329019 + 0.329019i
\(568\) 0 0
\(569\) 172.424 172.424i 0.303029 0.303029i −0.539169 0.842198i \(-0.681261\pi\)
0.842198 + 0.539169i \(0.181261\pi\)
\(570\) 0 0
\(571\) −295.206 712.690i −0.516998 1.24814i −0.939739 0.341894i \(-0.888932\pi\)
0.422740 0.906251i \(-0.361068\pi\)
\(572\) 0 0
\(573\) 607.250 1466.03i 1.05977 2.55852i
\(574\) 0 0
\(575\) 44.4059i 0.0772276i
\(576\) 0 0
\(577\) −756.330 −1.31080 −0.655398 0.755283i \(-0.727499\pi\)
−0.655398 + 0.755283i \(0.727499\pi\)
\(578\) 0 0
\(579\) −331.213 137.193i −0.572043 0.236948i
\(580\) 0 0
\(581\) −210.202 + 87.0686i −0.361794 + 0.149860i
\(582\) 0 0
\(583\) −140.957 140.957i −0.241779 0.241779i
\(584\) 0 0
\(585\) 349.080 + 349.080i 0.596717 + 0.596717i
\(586\) 0 0
\(587\) −736.720 + 305.159i −1.25506 + 0.519863i −0.908390 0.418125i \(-0.862688\pi\)
−0.346670 + 0.937987i \(0.612688\pi\)
\(588\) 0 0
\(589\) 246.012 + 101.902i 0.417678 + 0.173008i
\(590\) 0 0
\(591\) 447.919 0.757901
\(592\) 0 0
\(593\) 76.7003i 0.129343i 0.997907 + 0.0646714i \(0.0205999\pi\)
−0.997907 + 0.0646714i \(0.979400\pi\)
\(594\) 0 0
\(595\) −255.056 + 615.759i −0.428665 + 1.03489i
\(596\) 0 0
\(597\) −281.860 680.470i −0.472127 1.13982i
\(598\) 0 0
\(599\) −34.1251 + 34.1251i −0.0569702 + 0.0569702i −0.735018 0.678048i \(-0.762826\pi\)
0.678048 + 0.735018i \(0.262826\pi\)
\(600\) 0 0
\(601\) 212.552 212.552i 0.353664 0.353664i −0.507807 0.861471i \(-0.669544\pi\)
0.861471 + 0.507807i \(0.169544\pi\)
\(602\) 0 0
\(603\) −425.307 1026.78i −0.705318 1.70279i
\(604\) 0 0
\(605\) 180.454 435.655i 0.298271 0.720091i
\(606\) 0 0
\(607\) 56.8377i 0.0936371i −0.998903 0.0468186i \(-0.985092\pi\)
0.998903 0.0468186i \(-0.0149083\pi\)
\(608\) 0 0
\(609\) −15.1713 −0.0249118
\(610\) 0 0
\(611\) 83.7646 + 34.6964i 0.137094 + 0.0567863i
\(612\) 0 0
\(613\) −7.45320 + 3.08722i −0.0121586 + 0.00503624i −0.388754 0.921341i \(-0.627095\pi\)
0.376596 + 0.926378i \(0.377095\pi\)
\(614\) 0 0
\(615\) 771.474 + 771.474i 1.25443 + 1.25443i
\(616\) 0 0
\(617\) −325.733 325.733i −0.527931 0.527931i 0.392024 0.919955i \(-0.371775\pi\)
−0.919955 + 0.392024i \(0.871775\pi\)
\(618\) 0 0
\(619\) −76.1643 + 31.5483i −0.123044 + 0.0509665i −0.443356 0.896346i \(-0.646212\pi\)
0.320312 + 0.947312i \(0.396212\pi\)
\(620\) 0 0
\(621\) 1379.00 + 571.202i 2.22062 + 0.919810i
\(622\) 0 0
\(623\) 183.153 0.293986
\(624\) 0 0
\(625\) 594.458i 0.951133i
\(626\) 0 0
\(627\) −161.259 + 389.314i −0.257192 + 0.620915i
\(628\) 0 0
\(629\) 22.6862 + 54.7694i 0.0360671 + 0.0870738i
\(630\) 0 0
\(631\) −70.1301 + 70.1301i −0.111141 + 0.111141i −0.760490 0.649349i \(-0.775041\pi\)
0.649349 + 0.760490i \(0.275041\pi\)
\(632\) 0 0
\(633\) −78.2829 + 78.2829i −0.123670 + 0.123670i
\(634\) 0 0
\(635\) −243.177 587.082i −0.382956 0.924538i
\(636\) 0 0
\(637\) −44.6471 + 107.788i −0.0700897 + 0.169211i
\(638\) 0 0
\(639\) 1225.36i 1.91762i
\(640\) 0 0
\(641\) 458.396 0.715126 0.357563 0.933889i \(-0.383608\pi\)
0.357563 + 0.933889i \(0.383608\pi\)
\(642\) 0 0
\(643\) 882.443 + 365.520i 1.37238 + 0.568460i 0.942434 0.334393i \(-0.108531\pi\)
0.429950 + 0.902853i \(0.358531\pi\)
\(644\) 0 0
\(645\) 319.663 132.409i 0.495602 0.205285i
\(646\) 0 0
\(647\) 130.433 + 130.433i 0.201597 + 0.201597i 0.800684 0.599087i \(-0.204470\pi\)
−0.599087 + 0.800684i \(0.704470\pi\)
\(648\) 0 0
\(649\) 134.414 + 134.414i 0.207110 + 0.207110i
\(650\) 0 0
\(651\) 404.462 167.534i 0.621294 0.257348i
\(652\) 0 0
\(653\) 989.811 + 409.993i 1.51579 + 0.627861i 0.976743 0.214415i \(-0.0687844\pi\)
0.539047 + 0.842275i \(0.318784\pi\)
\(654\) 0 0
\(655\) 128.592 0.196324
\(656\) 0 0
\(657\) 1536.91i 2.33928i
\(658\) 0 0
\(659\) 457.745 1105.09i 0.694605 1.67693i −0.0406841 0.999172i \(-0.512954\pi\)
0.735289 0.677753i \(-0.237046\pi\)
\(660\) 0 0
\(661\) −96.2729 232.423i −0.145647 0.351624i 0.834173 0.551502i \(-0.185945\pi\)
−0.979821 + 0.199879i \(0.935945\pi\)
\(662\) 0 0
\(663\) −543.087 + 543.087i −0.819135 + 0.819135i
\(664\) 0 0
\(665\) 316.278 316.278i 0.475607 0.475607i
\(666\) 0 0
\(667\) 7.99066 + 19.2912i 0.0119800 + 0.0289223i
\(668\) 0 0
\(669\) −255.640 + 617.168i −0.382122 + 0.922524i
\(670\) 0 0
\(671\) 199.593i 0.297456i
\(672\) 0 0
\(673\) −135.640 −0.201545 −0.100772 0.994910i \(-0.532131\pi\)
−0.100772 + 0.994910i \(0.532131\pi\)
\(674\) 0 0
\(675\) −42.3053 17.5234i −0.0626745 0.0259606i
\(676\) 0 0
\(677\) −348.196 + 144.228i −0.514322 + 0.213039i −0.624721 0.780848i \(-0.714787\pi\)
0.110399 + 0.993887i \(0.464787\pi\)
\(678\) 0 0
\(679\) −457.411 457.411i −0.673653 0.673653i
\(680\) 0 0
\(681\) −235.888 235.888i −0.346384 0.346384i
\(682\) 0 0
\(683\) 812.940 336.731i 1.19025 0.493017i 0.302413 0.953177i \(-0.402208\pi\)
0.887836 + 0.460159i \(0.152208\pi\)
\(684\) 0 0
\(685\) −943.292 390.724i −1.37707 0.570400i
\(686\) 0 0
\(687\) 676.523 0.984749
\(688\) 0 0
\(689\) 243.832i 0.353892i
\(690\) 0 0
\(691\) 78.3893 189.249i 0.113443 0.273876i −0.856953 0.515395i \(-0.827645\pi\)
0.970396 + 0.241518i \(0.0776454\pi\)
\(692\) 0 0
\(693\) 172.400 + 416.209i 0.248773 + 0.600591i
\(694\) 0 0
\(695\) −773.177 + 773.177i −1.11249 + 1.11249i
\(696\) 0 0
\(697\) −780.471 + 780.471i −1.11976 + 1.11976i
\(698\) 0 0
\(699\) 302.008 + 729.112i 0.432057 + 1.04308i
\(700\) 0 0
\(701\) 432.140 1043.28i 0.616463 1.48827i −0.239322 0.970940i \(-0.576925\pi\)
0.855785 0.517332i \(-0.173075\pi\)
\(702\) 0 0
\(703\) 39.7843i 0.0565921i
\(704\) 0 0
\(705\) 371.559 0.527034
\(706\) 0 0
\(707\) −993.041 411.331i −1.40458 0.581798i
\(708\) 0 0
\(709\) 367.507 152.226i 0.518345 0.214706i −0.108145 0.994135i \(-0.534491\pi\)
0.626490 + 0.779430i \(0.284491\pi\)
\(710\) 0 0
\(711\) 451.061 + 451.061i 0.634403 + 0.634403i
\(712\) 0 0
\(713\) −426.058 426.058i −0.597556 0.597556i
\(714\) 0 0
\(715\) 134.657 55.7768i 0.188332 0.0780096i
\(716\) 0 0
\(717\) −1302.11 539.352i −1.81605 0.752234i
\(718\) 0 0
\(719\) 100.566 0.139869 0.0699344 0.997552i \(-0.477721\pi\)
0.0699344 + 0.997552i \(0.477721\pi\)
\(720\) 0 0
\(721\) 618.950i 0.858461i
\(722\) 0 0
\(723\) −100.949 + 243.711i −0.139625 + 0.337084i
\(724\) 0 0
\(725\) −0.245139 0.591817i −0.000338122 0.000816300i
\(726\) 0 0
\(727\) 332.402 332.402i 0.457224 0.457224i −0.440519 0.897743i \(-0.645206\pi\)
0.897743 + 0.440519i \(0.145206\pi\)
\(728\) 0 0
\(729\) 693.672 693.672i 0.951540 0.951540i
\(730\) 0 0
\(731\) 133.953 + 323.391i 0.183246 + 0.442395i
\(732\) 0 0
\(733\) −166.189 + 401.215i −0.226724 + 0.547360i −0.995775 0.0918276i \(-0.970729\pi\)
0.769051 + 0.639187i \(0.220729\pi\)
\(734\) 0 0
\(735\) 478.119i 0.650502i
\(736\) 0 0
\(737\) −328.124 −0.445215
\(738\) 0 0
\(739\) −1011.25 418.874i −1.36840 0.566812i −0.427049 0.904229i \(-0.640447\pi\)
−0.941355 + 0.337417i \(0.890447\pi\)
\(740\) 0 0
\(741\) 476.199 197.248i 0.642643 0.266192i
\(742\) 0 0
\(743\) −458.897 458.897i −0.617627 0.617627i 0.327295 0.944922i \(-0.393863\pi\)
−0.944922 + 0.327295i \(0.893863\pi\)
\(744\) 0 0
\(745\) 184.242 + 184.242i 0.247304 + 0.247304i
\(746\) 0 0
\(747\) −645.503 + 267.376i −0.864128 + 0.357933i
\(748\) 0 0
\(749\) −123.617 51.2039i −0.165043 0.0683630i
\(750\) 0 0
\(751\) 636.920 0.848096 0.424048 0.905640i \(-0.360609\pi\)
0.424048 + 0.905640i \(0.360609\pi\)
\(752\) 0 0
\(753\) 381.656i 0.506847i
\(754\) 0 0
\(755\) 475.932 1149.00i 0.630373 1.52186i
\(756\) 0 0
\(757\) −414.804 1001.43i −0.547958 1.32289i −0.918995 0.394269i \(-0.870998\pi\)
0.371038 0.928618i \(-0.379002\pi\)
\(758\) 0 0
\(759\) 674.236 674.236i 0.888321 0.888321i
\(760\) 0 0
\(761\) −520.779 + 520.779i −0.684334 + 0.684334i −0.960974 0.276639i \(-0.910779\pi\)
0.276639 + 0.960974i \(0.410779\pi\)
\(762\) 0 0
\(763\) 409.508 + 988.640i 0.536708 + 1.29573i
\(764\) 0 0
\(765\) −783.243 + 1890.92i −1.02385 + 2.47179i
\(766\) 0 0
\(767\) 232.514i 0.303147i
\(768\) 0 0
\(769\) 973.035 1.26533 0.632663 0.774427i \(-0.281962\pi\)
0.632663 + 0.774427i \(0.281962\pi\)
\(770\) 0 0
\(771\) 1131.84 + 468.825i 1.46802 + 0.608073i
\(772\) 0 0
\(773\) 959.578 397.470i 1.24137 0.514192i 0.337227 0.941423i \(-0.390511\pi\)
0.904142 + 0.427232i \(0.140511\pi\)
\(774\) 0 0
\(775\) 13.0707 + 13.0707i 0.0168654 + 0.0168654i
\(776\) 0 0
\(777\) −46.2506 46.2506i −0.0595246 0.0595246i
\(778\) 0 0
\(779\) 684.346 283.465i 0.878493 0.363884i
\(780\) 0 0
\(781\) 334.236 + 138.445i 0.427958 + 0.177266i
\(782\) 0 0
\(783\) −21.5319 −0.0274992
\(784\) 0 0
\(785\) 770.521i 0.981556i
\(786\) 0 0
\(787\) −412.612 + 996.133i −0.524284 + 1.26573i 0.410935 + 0.911665i \(0.365202\pi\)
−0.935219 + 0.354070i \(0.884798\pi\)
\(788\) 0 0
\(789\) 325.706 + 786.323i 0.412808 + 0.996607i
\(790\) 0 0
\(791\) 126.336 126.336i 0.159717 0.159717i
\(792\) 0 0
\(793\) 172.631 172.631i 0.217694 0.217694i
\(794\) 0 0
\(795\) 382.395 + 923.183i 0.481000 + 1.16124i
\(796\) 0 0
\(797\) −46.5600 + 112.406i −0.0584191 + 0.141036i −0.950394 0.311049i \(-0.899320\pi\)
0.891975