Properties

Label 128.3.h.a.15.7
Level $128$
Weight $3$
Character 128.15
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 15.7
Character \(\chi\) \(=\) 128.15
Dual form 128.3.h.a.111.7

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 0.576758 0.816915i \(-0.304318\pi\)
0.985476 + 0.169817i \(0.0543176\pi\)
\(4\) 0 0
\(5\) −4.51028 1.86822i −0.902055 0.373644i −0.117045 0.993127i \(-0.537342\pi\)
−0.785010 + 0.619483i \(0.787342\pi\)
\(6\) 0 0
\(7\) 3.85317 3.85317i 0.550453 0.550453i −0.376119 0.926571i \(-0.622742\pi\)
0.926571 + 0.376119i \(0.122742\pi\)
\(8\) 0 0
\(9\) 11.8326 11.8326i 1.31473 1.31473i
\(10\) 0 0
\(11\) 4.56441 + 1.89064i 0.414946 + 0.171876i 0.580382 0.814344i \(-0.302903\pi\)
−0.165436 + 0.986221i \(0.552903\pi\)
\(12\) 0 0
\(13\) −5.58307 + 2.31258i −0.429467 + 0.177891i −0.586937 0.809633i \(-0.699666\pi\)
0.157470 + 0.987524i \(0.449666\pi\)
\(14\) 0 0
\(15\) −24.7651 −1.65101
\(16\) 0 0
\(17\) 25.0539i 1.47376i 0.676025 + 0.736879i \(0.263701\pi\)
−0.676025 + 0.736879i \(0.736299\pi\)
\(18\) 0 0
\(19\) −6.43433 15.5338i −0.338649 0.817571i −0.997846 0.0656005i \(-0.979104\pi\)
0.659197 0.751970i \(-0.270896\pi\)
\(20\) 0 0
\(21\) 10.5785 25.5388i 0.503739 1.21613i
\(22\) 0 0
\(23\) 26.9024 + 26.9024i 1.16967 + 1.16967i 0.982287 + 0.187381i \(0.0600000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(24\) 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 0.920217 0.391409i \(-0.128012\pi\)
−0.927459 + 0.373924i \(0.878012\pi\)
\(30\) 0 0
\(31\) 15.8372i 0.510877i 0.966825 + 0.255438i \(0.0822198\pi\)
−0.966825 + 0.255438i \(0.917780\pi\)
\(32\) 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 0.352946 0.935644i \(-0.385180\pi\)
−0.412029 + 0.911171i \(0.635180\pi\)
\(38\) 0 0
\(39\) −21.6768 + 21.6768i −0.555814 + 0.555814i
\(40\) 0 0
\(41\) −31.1517 + 31.1517i −0.759798 + 0.759798i −0.976285 0.216488i \(-0.930540\pi\)
0.216488 + 0.976285i \(0.430540\pi\)
\(42\) 0 0
\(43\) −12.9078 5.34659i −0.300182 0.124339i 0.227509 0.973776i \(-0.426942\pi\)
−0.527691 + 0.849437i \(0.676942\pi\)
\(44\) 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 −0.999998 0.00219873i \(-0.999300\pi\)
0.708660 + 0.705550i \(0.249300\pi\)
\(54\) 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 −0.748605 0.663016i \(-0.769276\pi\)
0.998167 + 0.0605202i \(0.0192760\pi\)
\(60\) 0 0
\(61\) −15.4603 37.3243i −0.253447 0.611875i 0.745031 0.667030i \(-0.232435\pi\)
−0.998478 + 0.0551552i \(0.982435\pi\)
\(62\) 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 −0.790281 0.612745i \(-0.790065\pi\)
−0.125537 + 0.992089i \(0.540065\pi\)
\(68\) 0 0
\(69\) 178.309 + 73.8579i 2.58419 + 1.07040i
\(70\) 0 0
\(71\) 51.7789 51.7789i 0.729281 0.729281i −0.241196 0.970477i \(-0.577540\pi\)
0.970477 + 0.241196i \(0.0775395\pi\)
\(72\) 0 0
\(73\) 64.9440 64.9440i 0.889643 0.889643i −0.104845 0.994489i \(-0.533435\pi\)
0.994489 + 0.104845i \(0.0334347\pi\)
\(74\) 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 0.797923 0.602759i \(-0.205932\pi\)
−0.990432 + 0.138002i \(0.955932\pi\)
\(84\) 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 0.827906 0.560866i \(-0.189532\pi\)
−0.560866 + 0.827906i \(0.689532\pi\)
\(90\) 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 −0.984652 0.174529i \(-0.944160\pi\)
−0.819665 0.572844i \(-0.805840\pi\)
\(102\) 0 0
\(103\) 80.3171 80.3171i 0.779777 0.779777i −0.200016 0.979793i \(-0.564099\pi\)
0.979793 + 0.200016i \(0.0640993\pi\)
\(104\) 0 0
\(105\) −95.4240 + 95.4240i −0.908800 + 0.908800i
\(106\) 0 0
\(107\) −22.6854 9.39659i −0.212013 0.0878186i 0.274150 0.961687i \(-0.411604\pi\)
−0.486162 + 0.873868i \(0.661604\pi\)
\(108\) 0 0
\(109\) 181.428 75.1501i 1.66448 0.689450i 0.666074 0.745886i \(-0.267974\pi\)
0.998406 + 0.0564360i \(0.0179737\pi\)
\(110\) 0 0
\(111\) −12.0033 −0.108138
\(112\) 0 0
\(113\) 32.7876i 0.290156i 0.989420 + 0.145078i \(0.0463433\pi\)
−0.989420 + 0.145078i \(0.953657\pi\)
\(114\) 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 \(-0.828734\pi\)
0.858710 0.512462i \(-0.171266\pi\)
\(128\) 0 0
\(129\) −70.8744 −0.549414
\(130\) 0 0
\(131\) −24.3356 + 10.0801i −0.185768 + 0.0769476i −0.473628 0.880725i \(-0.657056\pi\)
0.287861 + 0.957672i \(0.407056\pi\)
\(132\) 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 0.0829047 0.996557i \(-0.473580\pi\)
0.996557 0.0829047i \(-0.0264197\pi\)
\(138\) 0 0
\(139\) 206.929 + 85.7129i 1.48870 + 0.616639i 0.971033 0.238944i \(-0.0768011\pi\)
0.517666 + 0.855583i \(0.326801\pi\)
\(140\) 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 −0.977480 0.211028i \(-0.932319\pi\)
0.840402 + 0.541964i \(0.182319\pi\)
\(150\) 0 0
\(151\) −180.137 180.137i −1.19296 1.19296i −0.976232 0.216726i \(-0.930462\pi\)
−0.216726 0.976232i \(-0.569538\pi\)
\(152\) 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 −0.991040 0.133564i \(-0.957358\pi\)
0.606327 0.795215i \(-0.292642\pi\)
\(158\) 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 0.136502 0.990640i \(-0.456414\pi\)
0.797010 + 0.603966i \(0.206414\pi\)
\(164\) 0 0
\(165\) −113.038 46.8218i −0.685078 0.283769i
\(166\) 0 0
\(167\) −94.8188 + 94.8188i −0.567777 + 0.567777i −0.931505 0.363728i \(-0.881504\pi\)
0.363728 + 0.931505i \(0.381504\pi\)
\(168\) 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 −0.670881 0.741565i \(-0.734084\pi\)
0.0499813 + 0.998750i \(0.484084\pi\)
\(174\) 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 −0.999835 0.0181410i \(-0.994225\pi\)
0.694163 0.719818i \(-0.255775\pi\)
\(180\) 0 0
\(181\) −128.496 + 310.218i −0.709925 + 1.71391i −0.00973575 + 0.999953i \(0.503099\pi\)
−0.700189 + 0.713957i \(0.746901\pi\)
\(182\) 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 \(0.305396\pi\)
−0.573986 + 0.818865i \(0.694604\pi\)
\(192\) 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 0.579996 0.814619i \(-0.303054\pi\)
−0.165904 + 0.986142i \(0.553054\pi\)
\(198\) 0 0
\(199\) −102.666 + 102.666i −0.515910 + 0.515910i −0.916331 0.400421i \(-0.868864\pi\)
0.400421 + 0.916331i \(0.368864\pi\)
\(200\) 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 0.902853 0.429950i \(-0.141469\pi\)
−0.942434 + 0.334393i \(0.891469\pi\)
\(212\) 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 \(-0.904594\pi\)
0.955418 0.295258i \(-0.0954056\pi\)
\(224\) 0 0
\(225\) −19.5312 −0.0868054
\(226\) 0 0
\(227\) −60.7552 + 25.1656i −0.267644 + 0.110862i −0.512470 0.858705i \(-0.671269\pi\)
0.244825 + 0.969567i \(0.421269\pi\)
\(228\) 0 0
\(229\) 123.210 + 51.0352i 0.538035 + 0.222861i 0.635118 0.772415i \(-0.280951\pi\)
−0.0970835 + 0.995276i \(0.530951\pi\)
\(230\) 0 0
\(231\) 96.5693 96.5693i 0.418049 0.418049i
\(232\) 0 0
\(233\) 110.005 110.005i 0.472124 0.472124i −0.430477 0.902601i \(-0.641655\pi\)
0.902601 + 0.430477i \(0.141655\pi\)
\(234\) 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 \(-0.965592\pi\)
0.994163 0.107885i \(-0.0344079\pi\)
\(242\) 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 −0.970798 0.239899i \(-0.922886\pi\)
0.856092 + 0.516823i \(0.172886\pi\)
\(252\) 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 −0.444626 0.895716i \(-0.646664\pi\)
0.895716 + 0.444626i \(0.146664\pi\)
\(264\) 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 −0.768496 0.639855i \(-0.778994\pi\)
−0.0909629 + 0.995854i \(0.528994\pi\)
\(270\) 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 0.183296 + 0.983058i \(0.441323\pi\)
−0.824737 + 0.565517i \(0.808677\pi\)
\(278\) 0 0
\(279\) 187.395 + 187.395i 0.671665 + 0.671665i
\(280\) 0 0
\(281\) −261.664 261.664i −0.931188 0.931188i 0.0665922 0.997780i \(-0.478787\pi\)
−0.997780 + 0.0665922i \(0.978787\pi\)
\(282\) 0 0
\(283\) −160.904 + 388.456i −0.568564 + 1.37264i 0.334201 + 0.942502i \(0.391534\pi\)
−0.902765 + 0.430134i \(0.858466\pi\)
\(284\) 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 0.127164 0.991882i \(-0.459413\pi\)
−0.611448 + 0.791285i \(0.709413\pi\)
\(294\) 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 0.971787 0.235860i \(-0.0757905\pi\)
−0.853935 + 0.520379i \(0.825791\pi\)
\(308\) 0 0
\(309\) 220.503 532.341i 0.713602 1.72279i
\(310\) 0 0
\(311\) −221.462 221.462i −0.712098 0.712098i 0.254876 0.966974i \(-0.417965\pi\)
−0.966974 + 0.254876i \(0.917965\pi\)
\(312\) 0 0
\(313\) 280.384 + 280.384i 0.895795 + 0.895795i 0.995061 0.0992662i \(-0.0316495\pi\)
−0.0992662 + 0.995061i \(0.531650\pi\)
\(314\) 0 0
\(315\) −170.355 + 411.273i −0.540809 + 1.30563i
\(316\) 0 0
\(317\) 155.972 + 376.549i 0.492024 + 1.18785i 0.953688 + 0.300796i \(0.0972524\pi\)
−0.461665 + 0.887055i \(0.652748\pi\)
\(318\) 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 0.910917 0.412591i \(-0.135376\pi\)
0.352370 + 0.935861i \(0.385376\pi\)
\(332\) 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 \(0.0180127\pi\)
−0.998399 + 0.0565582i \(0.981987\pi\)
\(338\) 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 −0.311760 0.950161i \(-0.600918\pi\)
0.892313 0.451418i \(-0.149082\pi\)
\(348\) 0 0
\(349\) −53.2160 128.475i −0.152481 0.368122i 0.829118 0.559073i \(-0.188843\pi\)
−0.981600 + 0.190951i \(0.938843\pi\)
\(350\) 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 −0.642309 0.766446i \(-0.722023\pi\)
0.766446 + 0.642309i \(0.222023\pi\)
\(360\) 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 −0.740094 0.672504i \(-0.765219\pi\)
0.998857 + 0.0477936i \(0.0152190\pi\)
\(374\) 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 −0.803804 0.594894i \(-0.797194\pi\)
0.989029 + 0.147722i \(0.0471941\pi\)
\(380\) 0 0
\(381\) −252.689 610.046i −0.663227 1.60117i
\(382\) 0 0
\(383\) 519.043i 1.35520i −0.735429 0.677602i \(-0.763019\pi\)
0.735429 0.677602i \(-0.236981\pi\)
\(384\) 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 0.448534 0.893766i \(-0.351946\pi\)
−0.314827 + 0.949149i \(0.601946\pi\)
\(390\) 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 −0.201322 0.979525i \(-0.564524\pi\)
0.550272 + 0.834985i \(0.314524\pi\)
\(398\) 0 0
\(399\) −464.781 −1.16487
\(400\) 0 0
\(401\) 11.3014i 0.0281830i 0.999901 + 0.0140915i \(0.00448560\pi\)
−0.999901 + 0.0140915i \(0.995514\pi\)
\(402\) 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 0.899311 0.437310i \(-0.144069\pi\)
−0.437310 + 0.899311i \(0.644069\pi\)
\(410\) 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 −0.0801080 0.996786i \(-0.525527\pi\)
0.648189 + 0.761479i \(0.275527\pi\)
\(420\) 0 0
\(421\) 324.923 + 134.588i 0.771790 + 0.319686i 0.733597 0.679585i \(-0.237840\pi\)
0.0381925 + 0.999270i \(0.487840\pi\)
\(422\) 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 \(-0.678905\pi\)
0.532918 0.846167i \(-0.321095\pi\)
\(434\) 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 −0.998722 0.0505487i \(-0.983903\pi\)
−0.0505487 0.998722i \(-0.516097\pi\)
\(440\) 0 0
\(441\) 228.442 + 228.442i 0.518009 + 0.518009i
\(442\) 0 0
\(443\) 55.5453 134.098i 0.125384 0.302705i −0.848705 0.528866i \(-0.822618\pi\)
0.974090 + 0.226161i \(0.0726175\pi\)
\(444\) 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 −0.970298 0.241911i \(-0.922226\pi\)
0.241911 + 0.970298i \(0.422226\pi\)
\(458\) 0 0
\(459\) 908.102 + 376.148i 1.97844 + 0.819495i
\(460\) 0 0
\(461\) −132.650 + 54.9455i −0.287744 + 0.119188i −0.521887 0.853015i \(-0.674772\pi\)
0.234143 + 0.972202i \(0.424772\pi\)
\(462\) 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 0.999993 0.00372448i \(-0.00118554\pi\)
−0.709735 + 0.704468i \(0.751186\pi\)
\(468\) 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 \(-0.900002\pi\)
0.951059 0.309011i \(-0.0999979\pi\)
\(480\) 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 −0.426707 0.904390i \(-0.640326\pi\)
0.904390 + 0.426707i \(0.140326\pi\)
\(488\) 0 0
\(489\) 590.784 590.784i 1.20815 1.20815i
\(490\) 0 0
\(491\) −217.435 90.0644i −0.442840 0.183430i 0.150110 0.988669i \(-0.452037\pi\)
−0.592951 + 0.805239i \(0.702037\pi\)
\(492\) 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 0.845597 0.533822i \(-0.179245\pi\)
−0.975396 + 0.220458i \(0.929245\pi\)
\(500\) 0 0
\(501\) −260.316 + 628.458i −0.519593 + 1.25441i
\(502\) 0 0
\(503\) 612.203 + 612.203i 1.21710 + 1.21710i 0.968642 + 0.248460i \(0.0799246\pi\)
0.248460 + 0.968642i \(0.420075\pi\)
\(504\) 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 −0.926078 0.377332i \(-0.876842\pi\)
0.388022 0.921650i \(-0.373158\pi\)
\(510\) 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 −0.0131690 + 0.999913i \(0.504192\pi\)
−0.999913 + 0.0131690i \(0.995808\pi\)
\(522\) 0 0
\(523\) −5.01268 2.07632i −0.00958447 0.00397002i 0.377886 0.925852i \(-0.376651\pi\)
−0.387471 + 0.921882i \(0.626651\pi\)
\(524\) 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 −0.981215 0.192919i \(-0.938204\pi\)
0.557409 0.830238i \(-0.311796\pi\)
\(542\) 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 0.00492387 0.999988i \(-0.498433\pi\)
0.710580 + 0.703617i \(0.248433\pi\)
\(548\) 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 −0.0306953 0.999529i \(-0.509772\pi\)
0.685069 + 0.728478i \(0.259772\pi\)
\(558\) 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 0.788591 0.614918i \(-0.210811\pi\)
−0.992431 + 0.122805i \(0.960811\pi\)
\(564\) 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 0.842198 0.539169i \(-0.181261\pi\)
−0.539169 + 0.842198i \(0.681261\pi\)
\(570\) 0 0
\(571\) −295.206 + 712.690i −0.516998 + 1.24814i 0.422740 + 0.906251i \(0.361068\pi\)
−0.939739 + 0.341894i \(0.888932\pi\)
\(572\) 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 −0.346670 0.937987i \(-0.612688\pi\)
−0.908390 + 0.418125i \(0.862688\pi\)
\(588\) 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 \(-0.979400\pi\)
0.997907 0.0646714i \(-0.0205999\pi\)
\(594\) 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 0.678048 0.735018i \(-0.262826\pi\)
−0.735018 + 0.678048i \(0.762826\pi\)
\(600\) 0 0
\(601\) 212.552 + 212.552i 0.353664 + 0.353664i 0.861471 0.507807i \(-0.169544\pi\)
−0.507807 + 0.861471i \(0.669544\pi\)
\(602\) 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 \(0.0149083\pi\)
−0.998903 + 0.0468186i \(0.985092\pi\)
\(608\) 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 0.376596 0.926378i \(-0.377095\pi\)
−0.388754 + 0.921341i \(0.627095\pi\)
\(614\) 0 0
\(615\) 771.474 771.474i 1.25443 1.25443i
\(616\) 0 0
\(617\) −325.733 + 325.733i −0.527931 + 0.527931i −0.919955 0.392024i \(-0.871775\pi\)
0.392024 + 0.919955i \(0.371775\pi\)
\(618\) 0 0
\(619\) −76.1643 31.5483i −0.123044 0.0509665i 0.320312 0.947312i \(-0.396212\pi\)
−0.443356 + 0.896346i \(0.646212\pi\)
\(620\) 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 0.649349 0.760490i \(-0.275041\pi\)
−0.760490 + 0.649349i \(0.775041\pi\)
\(632\) 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 0.429950 0.902853i \(-0.358531\pi\)
0.942434 + 0.334393i \(0.108531\pi\)
\(644\) 0 0
\(645\) 319.663 + 132.409i 0.495602 + 0.205285i
\(646\) 0 0
\(647\) 130.433 130.433i 0.201597 0.201597i −0.599087 0.800684i \(-0.704470\pi\)
0.800684 + 0.599087i \(0.204470\pi\)
\(648\) 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 0.539047 0.842275i \(-0.318784\pi\)
0.976743 + 0.214415i \(0.0687844\pi\)
\(654\) 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 0.735289 + 0.677753i \(0.237046\pi\)
−0.0406841 + 0.999172i \(0.512954\pi\)
\(660\) 0 0
\(661\) −96.2729 + 232.423i −0.145647 + 0.351624i −0.979821 0.199879i \(-0.935945\pi\)
0.834173 + 0.551502i \(0.185945\pi\)
\(662\) 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 0.110399 0.993887i \(-0.464787\pi\)
−0.624721 + 0.780848i \(0.714787\pi\)
\(678\) 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 0.887836 0.460159i \(-0.152208\pi\)
0.302413 + 0.953177i \(0.402208\pi\)
\(684\) 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 0.970396 0.241518i \(-0.0776454\pi\)
−0.856953 + 0.515395i \(0.827645\pi\)
\(692\) 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 0.855785 + 0.517332i \(0.173075\pi\)
−0.239322 + 0.970940i \(0.576925\pi\)
\(702\) 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 0.626490 0.779430i \(-0.284491\pi\)
−0.108145 + 0.994135i \(0.534491\pi\)
\(710\) 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 0.897743 0.440519i \(-0.145206\pi\)
−0.440519 + 0.897743i \(0.645206\pi\)
\(728\) 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 0.769051 0.639187i \(-0.220729\pi\)
−0.995775 + 0.0918276i \(0.970729\pi\)
\(734\) 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 −0.941355 0.337417i \(-0.890447\pi\)
−0.427049 + 0.904229i \(0.640447\pi\)
\(740\) 0 0
\(741\) 476.199 + 197.248i 0.642643 + 0.266192i
\(742\) 0 0
\(743\) −458.897 + 458.897i −0.617627 + 0.617627i −0.944922 0.327295i \(-0.893863\pi\)
0.327295 + 0.944922i \(0.393863\pi\)
\(744\) 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 0.371038 + 0.928618i \(0.379002\pi\)
−0.918995 + 0.394269i \(0.870998\pi\)
\(758\) 0 0
\(759\) 674.236 + 674.236i 0.888321 + 0.888321i
\(760\) 0 0
\(761\) −520.779 520.779i −0.684334 0.684334i 0.276639 0.960974i \(-0.410779\pi\)
−0.960974 + 0.276639i \(0.910779\pi\)
\(762\) 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 0.904142 0.427232i \(-0.140511\pi\)
0.337227 + 0.941423i \(0.390511\pi\)
\(774\) 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 −0.935219 0.354070i \(-0.884798\pi\)
0.410935 0.911665i \(-0.365202\pi\)
\(788\) 0 0