Properties

Label 128.4.g.a.17.10
Level $128$
Weight $4$
Character 128.17
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 17.10
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.10

$q$-expansion

\(f(q)\) \(=\) \(q+(3.21198 - 7.75440i) q^{3} +(-13.6472 + 5.65283i) q^{5} +(-9.07689 + 9.07689i) q^{7} +(-30.7220 - 30.7220i) q^{9} +O(q^{10})\) \(q+(3.21198 - 7.75440i) q^{3} +(-13.6472 + 5.65283i) q^{5} +(-9.07689 + 9.07689i) q^{7} +(-30.7220 - 30.7220i) q^{9} +(-16.7195 - 40.3646i) q^{11} +(-38.4266 - 15.9168i) q^{13} +123.982i q^{15} +92.5038i q^{17} +(16.6799 + 6.90905i) q^{19} +(41.2311 + 99.5406i) q^{21} +(-95.6008 - 95.6008i) q^{23} +(65.9018 - 65.9018i) q^{25} +(-127.540 + 52.8290i) q^{27} +(19.3621 - 46.7443i) q^{29} +38.1477 q^{31} -366.706 q^{33} +(72.5636 - 175.184i) q^{35} +(227.529 - 94.2456i) q^{37} +(-246.851 + 246.851i) q^{39} +(-279.334 - 279.334i) q^{41} +(-112.235 - 270.960i) q^{43} +(592.935 + 245.602i) q^{45} -321.955i q^{47} +178.220i q^{49} +(717.312 + 297.120i) q^{51} +(-52.5056 - 126.760i) q^{53} +(456.348 + 456.348i) q^{55} +(107.151 - 107.151i) q^{57} +(332.587 - 137.762i) q^{59} +(33.6815 - 81.3143i) q^{61} +557.721 q^{63} +614.389 q^{65} +(-108.572 + 262.117i) q^{67} +(-1048.39 + 434.259i) q^{69} +(-272.246 + 272.246i) q^{71} +(372.955 + 372.955i) q^{73} +(-299.354 - 722.704i) q^{75} +(518.146 + 214.623i) q^{77} -244.410i q^{79} -14.3973i q^{81} +(-1230.52 - 509.697i) q^{83} +(-522.909 - 1262.41i) q^{85} +(-300.283 - 300.283i) q^{87} +(216.134 - 216.134i) q^{89} +(493.270 - 204.319i) q^{91} +(122.529 - 295.812i) q^{93} -266.689 q^{95} +779.862 q^{97} +(-726.422 + 1753.74i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

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
\(3\) 3.21198 7.75440i 0.618145 1.49233i −0.235710 0.971824i \(-0.575741\pi\)
0.853855 0.520511i \(-0.174259\pi\)
\(4\) 0 0
\(5\) −13.6472 + 5.65283i −1.22064 + 0.505605i −0.897613 0.440785i \(-0.854700\pi\)
−0.323026 + 0.946390i \(0.604700\pi\)
\(6\) 0 0
\(7\) −9.07689 + 9.07689i −0.490106 + 0.490106i −0.908340 0.418233i \(-0.862649\pi\)
0.418233 + 0.908340i \(0.362649\pi\)
\(8\) 0 0
\(9\) −30.7220 30.7220i −1.13785 1.13785i
\(10\) 0 0
\(11\) −16.7195 40.3646i −0.458285 1.10640i −0.969091 0.246702i \(-0.920653\pi\)
0.510807 0.859696i \(-0.329347\pi\)
\(12\) 0 0
\(13\) −38.4266 15.9168i −0.819817 0.339580i −0.0669538 0.997756i \(-0.521328\pi\)
−0.752864 + 0.658177i \(0.771328\pi\)
\(14\) 0 0
\(15\) 123.982i 2.13414i
\(16\) 0 0
\(17\) 92.5038i 1.31973i 0.751383 + 0.659867i \(0.229387\pi\)
−0.751383 + 0.659867i \(0.770613\pi\)
\(18\) 0 0
\(19\) 16.6799 + 6.90905i 0.201402 + 0.0834235i 0.481104 0.876663i \(-0.340236\pi\)
−0.279702 + 0.960087i \(0.590236\pi\)
\(20\) 0 0
\(21\) 41.2311 + 99.5406i 0.428446 + 1.03436i
\(22\) 0 0
\(23\) −95.6008 95.6008i −0.866702 0.866702i 0.125404 0.992106i \(-0.459977\pi\)
−0.992106 + 0.125404i \(0.959977\pi\)
\(24\) 0 0
\(25\) 65.9018 65.9018i 0.527215 0.527215i
\(26\) 0 0
\(27\) −127.540 + 52.8290i −0.909081 + 0.376553i
\(28\) 0 0
\(29\) 19.3621 46.7443i 0.123981 0.299317i −0.849687 0.527288i \(-0.823209\pi\)
0.973668 + 0.227971i \(0.0732090\pi\)
\(30\) 0 0
\(31\) 38.1477 0.221017 0.110508 0.993875i \(-0.464752\pi\)
0.110508 + 0.993875i \(0.464752\pi\)
\(32\) 0 0
\(33\) −366.706 −1.93440
\(34\) 0 0
\(35\) 72.5636 175.184i 0.350442 0.846042i
\(36\) 0 0
\(37\) 227.529 94.2456i 1.01096 0.418754i 0.185156 0.982709i \(-0.440721\pi\)
0.825805 + 0.563955i \(0.190721\pi\)
\(38\) 0 0
\(39\) −246.851 + 246.851i −1.01353 + 1.01353i
\(40\) 0 0
\(41\) −279.334 279.334i −1.06401 1.06401i −0.997806 0.0662081i \(-0.978910\pi\)
−0.0662081 0.997806i \(-0.521090\pi\)
\(42\) 0 0
\(43\) −112.235 270.960i −0.398039 0.960952i −0.988131 0.153616i \(-0.950908\pi\)
0.590091 0.807337i \(-0.299092\pi\)
\(44\) 0 0
\(45\) 592.935 + 245.602i 1.96421 + 0.813603i
\(46\) 0 0
\(47\) 321.955i 0.999191i −0.866259 0.499596i \(-0.833482\pi\)
0.866259 0.499596i \(-0.166518\pi\)
\(48\) 0 0
\(49\) 178.220i 0.519592i
\(50\) 0 0
\(51\) 717.312 + 297.120i 1.96948 + 0.815787i
\(52\) 0 0
\(53\) −52.5056 126.760i −0.136079 0.328524i 0.841120 0.540848i \(-0.181897\pi\)
−0.977199 + 0.212324i \(0.931897\pi\)
\(54\) 0 0
\(55\) 456.348 + 456.348i 1.11880 + 1.11880i
\(56\) 0 0
\(57\) 107.151 107.151i 0.248991 0.248991i
\(58\) 0 0
\(59\) 332.587 137.762i 0.733884 0.303985i 0.0157369 0.999876i \(-0.494991\pi\)
0.718147 + 0.695892i \(0.244991\pi\)
\(60\) 0 0
\(61\) 33.6815 81.3143i 0.0706963 0.170676i −0.884582 0.466385i \(-0.845556\pi\)
0.955278 + 0.295709i \(0.0955560\pi\)
\(62\) 0 0
\(63\) 557.721 1.11534
\(64\) 0 0
\(65\) 614.389 1.17239
\(66\) 0 0
\(67\) −108.572 + 262.117i −0.197974 + 0.477951i −0.991424 0.130684i \(-0.958283\pi\)
0.793450 + 0.608635i \(0.208283\pi\)
\(68\) 0 0
\(69\) −1048.39 + 434.259i −1.82916 + 0.757661i
\(70\) 0 0
\(71\) −272.246 + 272.246i −0.455066 + 0.455066i −0.897032 0.441966i \(-0.854281\pi\)
0.441966 + 0.897032i \(0.354281\pi\)
\(72\) 0 0
\(73\) 372.955 + 372.955i 0.597960 + 0.597960i 0.939769 0.341809i \(-0.111040\pi\)
−0.341809 + 0.939769i \(0.611040\pi\)
\(74\) 0 0
\(75\) −299.354 722.704i −0.460885 1.11268i
\(76\) 0 0
\(77\) 518.146 + 214.623i 0.766860 + 0.317644i
\(78\) 0 0
\(79\) 244.410i 0.348080i −0.984739 0.174040i \(-0.944318\pi\)
0.984739 0.174040i \(-0.0556822\pi\)
\(80\) 0 0
\(81\) 14.3973i 0.0197494i
\(82\) 0 0
\(83\) −1230.52 509.697i −1.62731 0.674054i −0.632384 0.774655i \(-0.717924\pi\)
−0.994927 + 0.100600i \(0.967924\pi\)
\(84\) 0 0
\(85\) −522.909 1262.41i −0.667264 1.61092i
\(86\) 0 0
\(87\) −300.283 300.283i −0.370043 0.370043i
\(88\) 0 0
\(89\) 216.134 216.134i 0.257417 0.257417i −0.566586 0.824003i \(-0.691736\pi\)
0.824003 + 0.566586i \(0.191736\pi\)
\(90\) 0 0
\(91\) 493.270 204.319i 0.568228 0.235368i
\(92\) 0 0
\(93\) 122.529 295.812i 0.136621 0.329831i
\(94\) 0 0
\(95\) −266.689 −0.288018
\(96\) 0 0
\(97\) 779.862 0.816319 0.408160 0.912911i \(-0.366171\pi\)
0.408160 + 0.912911i \(0.366171\pi\)
\(98\) 0 0
\(99\) −726.422 + 1753.74i −0.737457 + 1.78038i
\(100\) 0 0
\(101\) −1046.60 + 433.515i −1.03109 + 0.427092i −0.833106 0.553113i \(-0.813440\pi\)
−0.197985 + 0.980205i \(0.563440\pi\)
\(102\) 0 0
\(103\) −683.721 + 683.721i −0.654069 + 0.654069i −0.953970 0.299901i \(-0.903046\pi\)
0.299901 + 0.953970i \(0.403046\pi\)
\(104\) 0 0
\(105\) −1125.37 1125.37i −1.04595 1.04595i
\(106\) 0 0
\(107\) 289.555 + 699.048i 0.261611 + 0.631584i 0.999038 0.0438418i \(-0.0139598\pi\)
−0.737428 + 0.675426i \(0.763960\pi\)
\(108\) 0 0
\(109\) 56.3510 + 23.3413i 0.0495179 + 0.0205110i 0.407305 0.913292i \(-0.366469\pi\)
−0.357787 + 0.933803i \(0.616469\pi\)
\(110\) 0 0
\(111\) 2067.07i 1.76754i
\(112\) 0 0
\(113\) 1567.46i 1.30491i 0.757828 + 0.652454i \(0.226260\pi\)
−0.757828 + 0.652454i \(0.773740\pi\)
\(114\) 0 0
\(115\) 1845.09 + 764.263i 1.49614 + 0.619720i
\(116\) 0 0
\(117\) 691.546 + 1669.54i 0.546440 + 1.31922i
\(118\) 0 0
\(119\) −839.647 839.647i −0.646810 0.646810i
\(120\) 0 0
\(121\) −408.595 + 408.595i −0.306983 + 0.306983i
\(122\) 0 0
\(123\) −3063.28 + 1268.85i −2.24558 + 0.930150i
\(124\) 0 0
\(125\) 179.764 433.989i 0.128629 0.310538i
\(126\) 0 0
\(127\) 1291.26 0.902209 0.451105 0.892471i \(-0.351030\pi\)
0.451105 + 0.892471i \(0.351030\pi\)
\(128\) 0 0
\(129\) −2461.63 −1.68011
\(130\) 0 0
\(131\) 326.012 787.064i 0.217434 0.524932i −0.777096 0.629382i \(-0.783308\pi\)
0.994530 + 0.104450i \(0.0333082\pi\)
\(132\) 0 0
\(133\) −214.115 + 88.6892i −0.139595 + 0.0578220i
\(134\) 0 0
\(135\) 1441.93 1441.93i 0.919271 0.919271i
\(136\) 0 0
\(137\) 1526.86 + 1526.86i 0.952177 + 0.952177i 0.998908 0.0467305i \(-0.0148802\pi\)
−0.0467305 + 0.998908i \(0.514880\pi\)
\(138\) 0 0
\(139\) 181.169 + 437.382i 0.110551 + 0.266894i 0.969467 0.245224i \(-0.0788614\pi\)
−0.858916 + 0.512117i \(0.828861\pi\)
\(140\) 0 0
\(141\) −2496.57 1034.11i −1.49113 0.617645i
\(142\) 0 0
\(143\) 1817.20i 1.06267i
\(144\) 0 0
\(145\) 747.377i 0.428043i
\(146\) 0 0
\(147\) 1381.99 + 572.439i 0.775405 + 0.321183i
\(148\) 0 0
\(149\) −1162.21 2805.81i −0.639004 1.54269i −0.828008 0.560716i \(-0.810526\pi\)
0.189004 0.981976i \(-0.439474\pi\)
\(150\) 0 0
\(151\) 262.518 + 262.518i 0.141479 + 0.141479i 0.774299 0.632820i \(-0.218103\pi\)
−0.632820 + 0.774299i \(0.718103\pi\)
\(152\) 0 0
\(153\) 2841.90 2841.90i 1.50166 1.50166i
\(154\) 0 0
\(155\) −520.607 + 215.642i −0.269782 + 0.111747i
\(156\) 0 0
\(157\) −1086.34 + 2622.67i −0.552227 + 1.33319i 0.363575 + 0.931565i \(0.381556\pi\)
−0.915802 + 0.401630i \(0.868444\pi\)
\(158\) 0 0
\(159\) −1151.59 −0.574385
\(160\) 0 0
\(161\) 1735.52 0.849552
\(162\) 0 0
\(163\) 380.057 917.540i 0.182628 0.440903i −0.805878 0.592081i \(-0.798307\pi\)
0.988507 + 0.151178i \(0.0483065\pi\)
\(164\) 0 0
\(165\) 5004.49 2072.93i 2.36120 0.978043i
\(166\) 0 0
\(167\) 1515.61 1515.61i 0.702283 0.702283i −0.262617 0.964900i \(-0.584586\pi\)
0.964900 + 0.262617i \(0.0845857\pi\)
\(168\) 0 0
\(169\) −330.254 330.254i −0.150320 0.150320i
\(170\) 0 0
\(171\) −300.181 724.701i −0.134242 0.324089i
\(172\) 0 0
\(173\) −1837.08 760.945i −0.807346 0.334414i −0.0594515 0.998231i \(-0.518935\pi\)
−0.747895 + 0.663817i \(0.768935\pi\)
\(174\) 0 0
\(175\) 1196.37i 0.516782i
\(176\) 0 0
\(177\) 3021.50i 1.28311i
\(178\) 0 0
\(179\) −2975.35 1232.43i −1.24239 0.514615i −0.337930 0.941171i \(-0.609727\pi\)
−0.904461 + 0.426556i \(0.859727\pi\)
\(180\) 0 0
\(181\) 1619.10 + 3908.85i 0.664899 + 1.60521i 0.790030 + 0.613068i \(0.210065\pi\)
−0.125132 + 0.992140i \(0.539935\pi\)
\(182\) 0 0
\(183\) −522.359 522.359i −0.211005 0.211005i
\(184\) 0 0
\(185\) −2572.37 + 2572.37i −1.02229 + 1.02229i
\(186\) 0 0
\(187\) 3733.88 1546.62i 1.46015 0.604814i
\(188\) 0 0
\(189\) 678.148 1637.19i 0.260995 0.630097i
\(190\) 0 0
\(191\) −697.265 −0.264148 −0.132074 0.991240i \(-0.542164\pi\)
−0.132074 + 0.991240i \(0.542164\pi\)
\(192\) 0 0
\(193\) 2386.61 0.890114 0.445057 0.895502i \(-0.353183\pi\)
0.445057 + 0.895502i \(0.353183\pi\)
\(194\) 0 0
\(195\) 1973.40 4764.22i 0.724710 1.74960i
\(196\) 0 0
\(197\) −2583.07 + 1069.94i −0.934194 + 0.386956i −0.797268 0.603625i \(-0.793722\pi\)
−0.136926 + 0.990581i \(0.543722\pi\)
\(198\) 0 0
\(199\) −2940.81 + 2940.81i −1.04758 + 1.04758i −0.0487695 + 0.998810i \(0.515530\pi\)
−0.998810 + 0.0487695i \(0.984470\pi\)
\(200\) 0 0
\(201\) 1683.83 + 1683.83i 0.590886 + 0.590886i
\(202\) 0 0
\(203\) 248.545 + 600.041i 0.0859332 + 0.207461i
\(204\) 0 0
\(205\) 5391.13 + 2233.08i 1.83675 + 0.760805i
\(206\) 0 0
\(207\) 5874.10i 1.97236i
\(208\) 0 0
\(209\) 788.794i 0.261062i
\(210\) 0 0
\(211\) −1399.25 579.589i −0.456533 0.189102i 0.142552 0.989787i \(-0.454469\pi\)
−0.599085 + 0.800685i \(0.704469\pi\)
\(212\) 0 0
\(213\) 1236.66 + 2985.55i 0.397814 + 0.960408i
\(214\) 0 0
\(215\) 3063.38 + 3063.38i 0.971724 + 0.971724i
\(216\) 0 0
\(217\) −346.262 + 346.262i −0.108322 + 0.108322i
\(218\) 0 0
\(219\) 4089.97 1694.12i 1.26198 0.522731i
\(220\) 0 0
\(221\) 1472.37 3554.61i 0.448155 1.08194i
\(222\) 0 0
\(223\) 1100.18 0.330374 0.165187 0.986262i \(-0.447177\pi\)
0.165187 + 0.986262i \(0.447177\pi\)
\(224\) 0 0
\(225\) −4049.27 −1.19979
\(226\) 0 0
\(227\) −1476.27 + 3564.04i −0.431647 + 1.04209i 0.547110 + 0.837061i \(0.315728\pi\)
−0.978756 + 0.205026i \(0.934272\pi\)
\(228\) 0 0
\(229\) 3573.95 1480.38i 1.03132 0.427188i 0.198134 0.980175i \(-0.436512\pi\)
0.833190 + 0.552986i \(0.186512\pi\)
\(230\) 0 0
\(231\) 3328.55 3328.55i 0.948062 0.948062i
\(232\) 0 0
\(233\) −3668.67 3668.67i −1.03151 1.03151i −0.999487 0.0320257i \(-0.989804\pi\)
−0.0320257 0.999487i \(-0.510196\pi\)
\(234\) 0 0
\(235\) 1819.96 + 4393.77i 0.505196 + 1.21965i
\(236\) 0 0
\(237\) −1895.25 785.040i −0.519451 0.215164i
\(238\) 0 0
\(239\) 5649.23i 1.52895i −0.644656 0.764473i \(-0.722999\pi\)
0.644656 0.764473i \(-0.277001\pi\)
\(240\) 0 0
\(241\) 5059.57i 1.35235i −0.736743 0.676173i \(-0.763637\pi\)
0.736743 0.676173i \(-0.236363\pi\)
\(242\) 0 0
\(243\) −3555.24 1472.63i −0.938553 0.388761i
\(244\) 0 0
\(245\) −1007.45 2432.20i −0.262708 0.634234i
\(246\) 0 0
\(247\) −530.983 530.983i −0.136784 0.136784i
\(248\) 0 0
\(249\) −7904.79 + 7904.79i −2.01183 + 2.01183i
\(250\) 0 0
\(251\) −980.968 + 406.330i −0.246686 + 0.102181i −0.502601 0.864519i \(-0.667623\pi\)
0.255915 + 0.966699i \(0.417623\pi\)
\(252\) 0 0
\(253\) −2260.48 + 5457.28i −0.561720 + 1.35611i
\(254\) 0 0
\(255\) −11468.8 −2.81649
\(256\) 0 0
\(257\) −1021.29 −0.247886 −0.123943 0.992289i \(-0.539554\pi\)
−0.123943 + 0.992289i \(0.539554\pi\)
\(258\) 0 0
\(259\) −1209.80 + 2920.72i −0.290244 + 0.700712i
\(260\) 0 0
\(261\) −2030.92 + 841.236i −0.481651 + 0.199506i
\(262\) 0 0
\(263\) 1134.88 1134.88i 0.266083 0.266083i −0.561437 0.827520i \(-0.689751\pi\)
0.827520 + 0.561437i \(0.189751\pi\)
\(264\) 0 0
\(265\) 1433.10 + 1433.10i 0.332207 + 0.332207i
\(266\) 0 0
\(267\) −981.770 2370.20i −0.225031 0.543273i
\(268\) 0 0
\(269\) −2221.12 920.017i −0.503435 0.208530i 0.116488 0.993192i \(-0.462836\pi\)
−0.619923 + 0.784663i \(0.712836\pi\)
\(270\) 0 0
\(271\) 1860.26i 0.416984i −0.978024 0.208492i \(-0.933144\pi\)
0.978024 0.208492i \(-0.0668555\pi\)
\(272\) 0 0
\(273\) 4481.28i 0.993477i
\(274\) 0 0
\(275\) −3761.95 1558.25i −0.824923 0.341694i
\(276\) 0 0
\(277\) −2311.55 5580.58i −0.501400 1.21049i −0.948721 0.316113i \(-0.897622\pi\)
0.447322 0.894373i \(-0.352378\pi\)
\(278\) 0 0
\(279\) −1171.97 1171.97i −0.251485 0.251485i
\(280\) 0 0
\(281\) −1740.45 + 1740.45i −0.369490 + 0.369490i −0.867291 0.497801i \(-0.834141\pi\)
0.497801 + 0.867291i \(0.334141\pi\)
\(282\) 0 0
\(283\) 2580.95 1069.06i 0.542125 0.224555i −0.0947795 0.995498i \(-0.530215\pi\)
0.636904 + 0.770943i \(0.280215\pi\)
\(284\) 0 0
\(285\) −856.600 + 2068.01i −0.178037 + 0.429820i
\(286\) 0 0
\(287\) 5070.96 1.04296
\(288\) 0 0
\(289\) −3643.96 −0.741697
\(290\) 0 0
\(291\) 2504.90 6047.36i 0.504604 1.21822i
\(292\) 0 0
\(293\) 6531.00 2705.23i 1.30220 0.539390i 0.379603 0.925149i \(-0.376061\pi\)
0.922599 + 0.385760i \(0.126061\pi\)
\(294\) 0 0
\(295\) −3760.12 + 3760.12i −0.742110 + 0.742110i
\(296\) 0 0
\(297\) 4264.84 + 4264.84i 0.833235 + 0.833235i
\(298\) 0 0
\(299\) 2151.95 + 5195.27i 0.416223 + 1.00485i
\(300\) 0 0
\(301\) 3478.22 + 1440.72i 0.666050 + 0.275887i
\(302\) 0 0
\(303\) 9508.17i 1.80274i
\(304\) 0 0
\(305\) 1300.10i 0.244078i
\(306\) 0 0
\(307\) 22.1910 + 9.19181i 0.00412543 + 0.00170881i 0.384745 0.923023i \(-0.374289\pi\)
−0.380620 + 0.924732i \(0.624289\pi\)
\(308\) 0 0
\(309\) 3105.75 + 7497.95i 0.571780 + 1.38040i
\(310\) 0 0
\(311\) 4220.58 + 4220.58i 0.769540 + 0.769540i 0.978026 0.208485i \(-0.0668533\pi\)
−0.208485 + 0.978026i \(0.566853\pi\)
\(312\) 0 0
\(313\) 6090.90 6090.90i 1.09993 1.09993i 0.105512 0.994418i \(-0.466352\pi\)
0.994418 0.105512i \(-0.0336481\pi\)
\(314\) 0 0
\(315\) −7611.30 + 3152.71i −1.36142 + 0.563920i
\(316\) 0 0
\(317\) −1660.86 + 4009.67i −0.294269 + 0.710428i 0.705729 + 0.708482i \(0.250620\pi\)
−0.999998 + 0.00194638i \(0.999380\pi\)
\(318\) 0 0
\(319\) −2210.54 −0.387982
\(320\) 0 0
\(321\) 6350.74 1.10425
\(322\) 0 0
\(323\) −639.114 + 1542.96i −0.110097 + 0.265797i
\(324\) 0 0
\(325\) −3581.33 + 1483.44i −0.611251 + 0.253188i
\(326\) 0 0
\(327\) 361.996 361.996i 0.0612185 0.0612185i
\(328\) 0 0
\(329\) 2922.35 + 2922.35i 0.489710 + 0.489710i
\(330\) 0 0
\(331\) −3722.12 8985.99i −0.618085 1.49219i −0.853924 0.520397i \(-0.825784\pi\)
0.235840 0.971792i \(-0.424216\pi\)
\(332\) 0 0
\(333\) −9885.57 4094.74i −1.62680 0.673845i
\(334\) 0 0
\(335\) 4190.90i 0.683502i
\(336\) 0 0
\(337\) 5211.97i 0.842475i 0.906950 + 0.421238i \(0.138404\pi\)
−0.906950 + 0.421238i \(0.861596\pi\)
\(338\) 0 0
\(339\) 12154.7 + 5034.66i 1.94736 + 0.806623i
\(340\) 0 0
\(341\) −637.812 1539.81i −0.101289 0.244532i
\(342\) 0 0
\(343\) −4731.06 4731.06i −0.744761 0.744761i
\(344\) 0 0
\(345\) 11852.8 11852.8i 1.84966 1.84966i
\(346\) 0 0
\(347\) −4987.20 + 2065.77i −0.771547 + 0.319585i −0.733499 0.679691i \(-0.762114\pi\)
−0.0380483 + 0.999276i \(0.512114\pi\)
\(348\) 0 0
\(349\) 3137.63 7574.92i 0.481243 1.16182i −0.477776 0.878481i \(-0.658557\pi\)
0.959019 0.283341i \(-0.0914429\pi\)
\(350\) 0 0
\(351\) 5741.82 0.873150
\(352\) 0 0
\(353\) 8999.28 1.35689 0.678446 0.734650i \(-0.262654\pi\)
0.678446 + 0.734650i \(0.262654\pi\)
\(354\) 0 0
\(355\) 2176.42 5254.35i 0.325387 0.785555i
\(356\) 0 0
\(357\) −9207.89 + 3814.03i −1.36508 + 0.565434i
\(358\) 0 0
\(359\) 4697.94 4697.94i 0.690662 0.690662i −0.271715 0.962378i \(-0.587591\pi\)
0.962378 + 0.271715i \(0.0875909\pi\)
\(360\) 0 0
\(361\) −4619.56 4619.56i −0.673503 0.673503i
\(362\) 0 0
\(363\) 1856.01 + 4480.80i 0.268361 + 0.647882i
\(364\) 0 0
\(365\) −7198.03 2981.52i −1.03222 0.427561i
\(366\) 0 0
\(367\) 5942.35i 0.845199i −0.906316 0.422600i \(-0.861118\pi\)
0.906316 0.422600i \(-0.138882\pi\)
\(368\) 0 0
\(369\) 17163.4i 2.42138i
\(370\) 0 0
\(371\) 1627.17 + 673.997i 0.227705 + 0.0943186i
\(372\) 0 0
\(373\) −611.014 1475.12i −0.0848180 0.204769i 0.875780 0.482711i \(-0.160348\pi\)
−0.960598 + 0.277942i \(0.910348\pi\)
\(374\) 0 0
\(375\) −2787.93 2787.93i −0.383915 0.383915i
\(376\) 0 0
\(377\) −1488.04 + 1488.04i −0.203284 + 0.203284i
\(378\) 0 0
\(379\) −3436.04 + 1423.25i −0.465692 + 0.192896i −0.603176 0.797608i \(-0.706098\pi\)
0.137484 + 0.990504i \(0.456098\pi\)
\(380\) 0 0
\(381\) 4147.49 10012.9i 0.557697 1.34640i
\(382\) 0 0
\(383\) 9327.55 1.24443 0.622213 0.782848i \(-0.286234\pi\)
0.622213 + 0.782848i \(0.286234\pi\)
\(384\) 0 0
\(385\) −8284.45 −1.09666
\(386\) 0 0
\(387\) −4876.34 + 11772.5i −0.640512 + 1.54633i
\(388\) 0 0
\(389\) 7840.37 3247.59i 1.02191 0.423288i 0.192123 0.981371i \(-0.438463\pi\)
0.829785 + 0.558083i \(0.188463\pi\)
\(390\) 0 0
\(391\) 8843.44 8843.44i 1.14382 1.14382i
\(392\) 0 0
\(393\) −5056.06 5056.06i −0.648968 0.648968i
\(394\) 0 0
\(395\) 1381.61 + 3335.50i 0.175991 + 0.424879i
\(396\) 0 0
\(397\) 6845.23 + 2835.39i 0.865370 + 0.358448i 0.770805 0.637071i \(-0.219854\pi\)
0.0945649 + 0.995519i \(0.469854\pi\)
\(398\) 0 0
\(399\) 1945.20i 0.244064i
\(400\) 0 0
\(401\) 5333.86i 0.664240i −0.943237 0.332120i \(-0.892236\pi\)
0.943237 0.332120i \(-0.107764\pi\)
\(402\) 0 0
\(403\) −1465.89 607.190i −0.181193 0.0750528i
\(404\) 0 0
\(405\) 81.3857 + 196.482i 0.00998540 + 0.0241069i
\(406\) 0 0
\(407\) −7608.37 7608.37i −0.926616 0.926616i
\(408\) 0 0
\(409\) −3906.82 + 3906.82i −0.472322 + 0.472322i −0.902665 0.430343i \(-0.858393\pi\)
0.430343 + 0.902665i \(0.358393\pi\)
\(410\) 0 0
\(411\) 16744.1 6935.63i 2.00955 0.832383i
\(412\) 0 0
\(413\) −1768.41 + 4269.31i −0.210696 + 0.508666i
\(414\) 0 0
\(415\) 19674.3 2.32716
\(416\) 0 0
\(417\) 3973.54 0.466631
\(418\) 0 0
\(419\) −510.706 + 1232.95i −0.0595456 + 0.143756i −0.950852 0.309646i \(-0.899790\pi\)
0.891306 + 0.453401i \(0.149790\pi\)
\(420\) 0 0
\(421\) −9078.42 + 3760.41i −1.05096 + 0.435323i −0.840235 0.542222i \(-0.817583\pi\)
−0.210727 + 0.977545i \(0.567583\pi\)
\(422\) 0 0
\(423\) −9891.11 + 9891.11i −1.13693 + 1.13693i
\(424\) 0 0
\(425\) 6096.17 + 6096.17i 0.695783 + 0.695783i
\(426\) 0 0
\(427\) 432.358 + 1043.80i 0.0490006 + 0.118298i
\(428\) 0 0
\(429\) 14091.3 + 5836.79i 1.58586 + 0.656883i
\(430\) 0 0
\(431\) 7684.54i 0.858820i −0.903110 0.429410i \(-0.858722\pi\)
0.903110 0.429410i \(-0.141278\pi\)
\(432\) 0 0
\(433\) 989.963i 0.109872i 0.998490 + 0.0549360i \(0.0174955\pi\)
−0.998490 + 0.0549360i \(0.982505\pi\)
\(434\) 0 0
\(435\) 5795.46 + 2400.56i 0.638784 + 0.264593i
\(436\) 0 0
\(437\) −934.103 2255.12i −0.102252 0.246859i
\(438\) 0 0
\(439\) −1705.59 1705.59i −0.185429 0.185429i 0.608287 0.793717i \(-0.291857\pi\)
−0.793717 + 0.608287i \(0.791857\pi\)
\(440\) 0 0
\(441\) 5475.28 5475.28i 0.591219 0.591219i
\(442\) 0 0
\(443\) −14875.4 + 6161.58i −1.59537 + 0.660826i −0.990752 0.135687i \(-0.956676\pi\)
−0.604622 + 0.796512i \(0.706676\pi\)
\(444\) 0 0
\(445\) −1727.84 + 4171.37i −0.184062 + 0.444364i
\(446\) 0 0
\(447\) −25490.4 −2.69721
\(448\) 0 0
\(449\) 1887.26 0.198364 0.0991819 0.995069i \(-0.468377\pi\)
0.0991819 + 0.995069i \(0.468377\pi\)
\(450\) 0 0
\(451\) −6604.84 + 15945.5i −0.689601 + 1.66484i
\(452\) 0 0
\(453\) 2878.87 1192.47i 0.298589 0.123680i
\(454\) 0 0
\(455\) −5576.74 + 5576.74i −0.574597 + 0.574597i
\(456\) 0 0
\(457\) −9275.37 9275.37i −0.949417 0.949417i 0.0493636 0.998781i \(-0.484281\pi\)
−0.998781 + 0.0493636i \(0.984281\pi\)
\(458\) 0 0
\(459\) −4886.88 11798.0i −0.496950 1.19974i
\(460\) 0 0
\(461\) 6867.75 + 2844.71i 0.693846 + 0.287400i 0.701601 0.712570i \(-0.252469\pi\)
−0.00775571 + 0.999970i \(0.502469\pi\)
\(462\) 0 0
\(463\) 7678.71i 0.770756i 0.922759 + 0.385378i \(0.125929\pi\)
−0.922759 + 0.385378i \(0.874071\pi\)
\(464\) 0 0
\(465\) 4729.63i 0.471681i
\(466\) 0 0
\(467\) 3867.05 + 1601.79i 0.383182 + 0.158719i 0.565955 0.824436i \(-0.308507\pi\)
−0.182773 + 0.983155i \(0.558507\pi\)
\(468\) 0 0
\(469\) −1393.71 3364.71i −0.137219 0.331275i
\(470\) 0 0
\(471\) 16847.9 + 16847.9i 1.64822 + 1.64822i
\(472\) 0 0
\(473\) −9060.64 + 9060.64i −0.880780 + 0.880780i
\(474\) 0 0
\(475\) 1554.56 643.919i 0.150164 0.0622000i
\(476\) 0 0
\(477\) −2281.24 + 5507.40i −0.218974 + 0.528651i
\(478\) 0 0
\(479\) −5602.73 −0.534436 −0.267218 0.963636i \(-0.586104\pi\)
−0.267218 + 0.963636i \(0.586104\pi\)
\(480\) 0 0
\(481\) −10243.3 −0.971004
\(482\) 0 0
\(483\) 5574.44 13457.9i 0.525146 1.26782i
\(484\) 0 0
\(485\) −10642.9 + 4408.43i −0.996431 + 0.412735i
\(486\) 0 0
\(487\) −13338.0 + 13338.0i −1.24107 + 1.24107i −0.281516 + 0.959556i \(0.590837\pi\)
−0.959556 + 0.281516i \(0.909163\pi\)
\(488\) 0 0
\(489\) −5894.23 5894.23i −0.545085 0.545085i
\(490\) 0 0
\(491\) −6069.18 14652.3i −0.557837 1.34674i −0.911475 0.411356i \(-0.865055\pi\)
0.353637 0.935383i \(-0.384945\pi\)
\(492\) 0 0
\(493\) 4324.03 + 1791.07i 0.395019 + 0.163622i
\(494\) 0 0
\(495\) 28039.9i 2.54606i
\(496\) 0 0
\(497\) 4942.30i 0.446061i
\(498\) 0 0
\(499\) −3108.34 1287.52i −0.278855 0.115505i 0.238873 0.971051i \(-0.423222\pi\)
−0.517728 + 0.855545i \(0.673222\pi\)
\(500\) 0 0
\(501\) −6884.53 16620.7i −0.613928 1.48215i
\(502\) 0 0
\(503\) 9569.65 + 9569.65i 0.848289 + 0.848289i 0.989920 0.141630i \(-0.0452344\pi\)
−0.141630 + 0.989920i \(0.545234\pi\)
\(504\) 0 0
\(505\) 11832.5 11832.5i 1.04265 1.04265i
\(506\) 0 0
\(507\) −3621.69 + 1500.15i −0.317248 + 0.131408i
\(508\) 0 0
\(509\) 4975.54 12012.0i 0.433275 1.04602i −0.544950 0.838469i \(-0.683451\pi\)
0.978225 0.207549i \(-0.0665487\pi\)
\(510\) 0 0
\(511\) −6770.55 −0.586128
\(512\) 0 0
\(513\) −2492.36 −0.214504
\(514\) 0 0
\(515\) 5465.89 13195.8i 0.467681 1.12908i
\(516\) 0 0
\(517\) −12995.6 + 5382.94i −1.10550 + 0.457914i
\(518\) 0 0
\(519\) −11801.3 + 11801.3i −0.998114 + 0.998114i
\(520\) 0 0
\(521\) 11056.5 + 11056.5i 0.929743 + 0.929743i 0.997689 0.0679465i \(-0.0216447\pi\)
−0.0679465 + 0.997689i \(0.521645\pi\)
\(522\) 0 0
\(523\) −7704.74 18600.9i −0.644178 1.55518i −0.820993 0.570938i \(-0.806580\pi\)
0.176815 0.984244i \(-0.443420\pi\)
\(524\) 0 0
\(525\) 9277.11 + 3842.71i 0.771212 + 0.319447i
\(526\) 0 0
\(527\) 3528.80i 0.291683i
\(528\) 0 0
\(529\) 6112.01i 0.502343i
\(530\) 0 0
\(531\) −14450.1 5985.42i −1.18094 0.489162i
\(532\) 0 0
\(533\) 6287.74 + 15179.9i 0.510980 + 1.23361i
\(534\) 0 0
\(535\) −7903.20 7903.20i −0.638664 0.638664i
\(536\) 0 0
\(537\) −19113.5 + 19113.5i −1.53596 + 1.53596i
\(538\) 0 0
\(539\) 7193.77 2979.76i 0.574875 0.238121i
\(540\) 0 0
\(541\) −3094.21 + 7470.07i −0.245897 + 0.593648i −0.997848 0.0655712i \(-0.979113\pi\)
0.751951 + 0.659219i \(0.229113\pi\)
\(542\) 0 0
\(543\) 35511.3 2.80651
\(544\) 0 0
\(545\) −900.975 −0.0708138
\(546\) 0 0
\(547\) −6470.84 + 15622.0i −0.505801 + 1.22111i 0.440479 + 0.897763i \(0.354809\pi\)
−0.946280 + 0.323349i \(0.895191\pi\)
\(548\) 0 0
\(549\) −3532.90 + 1463.38i −0.274646 + 0.113762i
\(550\) 0 0
\(551\) 645.918 645.918i 0.0499401 0.0499401i
\(552\) 0 0
\(553\) 2218.49 + 2218.49i 0.170596 + 0.170596i
\(554\) 0 0
\(555\) 11684.8 + 28209.6i 0.893678 + 2.15753i
\(556\) 0 0
\(557\) −10401.9 4308.63i −0.791283 0.327760i −0.0498238 0.998758i \(-0.515866\pi\)
−0.741459 + 0.670998i \(0.765866\pi\)
\(558\) 0 0
\(559\) 12198.5i 0.922971i
\(560\) 0 0
\(561\) 33921.7i 2.55290i
\(562\) 0 0
\(563\) 1760.24 + 729.116i 0.131768 + 0.0545801i 0.447593 0.894237i \(-0.352281\pi\)
−0.315825 + 0.948817i \(0.602281\pi\)
\(564\) 0 0
\(565\) −8860.61 21391.4i −0.659768 1.59282i
\(566\) 0 0
\(567\) 130.683 + 130.683i 0.00967931 + 0.00967931i
\(568\) 0 0
\(569\) 8079.71 8079.71i 0.595288 0.595288i −0.343767 0.939055i \(-0.611703\pi\)
0.939055 + 0.343767i \(0.111703\pi\)
\(570\) 0 0
\(571\) 16823.9 6968.69i 1.23303 0.510737i 0.331498 0.943456i \(-0.392446\pi\)
0.901529 + 0.432719i \(0.142446\pi\)
\(572\) 0 0
\(573\) −2239.60 + 5406.87i −0.163282 + 0.394198i
\(574\) 0 0
\(575\) −12600.5 −0.913875
\(576\) 0 0
\(577\) −4098.72 −0.295723 −0.147861 0.989008i \(-0.547239\pi\)
−0.147861 + 0.989008i \(0.547239\pi\)
\(578\) 0 0
\(579\) 7665.74 18506.7i 0.550220 1.32835i
\(580\) 0 0
\(581\) 15795.7 6542.81i 1.12791 0.467197i
\(582\) 0 0
\(583\) −4238.73 + 4238.73i −0.301115 + 0.301115i
\(584\) 0 0
\(585\) −18875.3 18875.3i −1.33401 1.33401i
\(586\) 0 0
\(587\) 437.187 + 1055.46i 0.0307404 + 0.0742139i 0.938504 0.345268i \(-0.112212\pi\)
−0.907764 + 0.419482i \(0.862212\pi\)
\(588\) 0 0
\(589\) 636.300 + 263.564i 0.0445132 + 0.0184380i
\(590\) 0 0
\(591\) 23466.8i 1.63332i
\(592\) 0 0
\(593\) 26161.0i 1.81164i 0.423661 + 0.905821i \(0.360745\pi\)
−0.423661 + 0.905821i \(0.639255\pi\)
\(594\) 0 0
\(595\) 16205.2 + 6712.41i 1.11655 + 0.462491i
\(596\) 0 0
\(597\) 13358.4 + 32250.0i 0.915783 + 2.21090i
\(598\) 0 0
\(599\) 12392.1 + 12392.1i 0.845288 + 0.845288i 0.989541 0.144253i \(-0.0460778\pi\)
−0.144253 + 0.989541i \(0.546078\pi\)
\(600\) 0 0
\(601\) 5696.78 5696.78i 0.386650 0.386650i −0.486841 0.873491i \(-0.661851\pi\)
0.873491 + 0.486841i \(0.161851\pi\)
\(602\) 0 0
\(603\) 11388.3 4717.20i 0.769103 0.318573i
\(604\) 0 0
\(605\) 3266.43 7885.87i 0.219503 0.529928i
\(606\) 0 0
\(607\) −19674.4 −1.31559 −0.657793 0.753199i \(-0.728510\pi\)
−0.657793 + 0.753199i \(0.728510\pi\)
\(608\) 0 0
\(609\) 5451.28 0.362721
\(610\) 0 0
\(611\) −5124.50 + 12371.6i −0.339305 + 0.819154i
\(612\) 0 0
\(613\) 25148.3 10416.7i 1.65698 0.686343i 0.659139 0.752021i \(-0.270921\pi\)
0.997841 + 0.0656781i \(0.0209210\pi\)
\(614\) 0 0
\(615\) 34632.4 34632.4i 2.27075 2.27075i
\(616\) 0 0
\(617\) 5951.82 + 5951.82i 0.388349 + 0.388349i 0.874098 0.485749i \(-0.161453\pi\)
−0.485749 + 0.874098i \(0.661453\pi\)
\(618\) 0 0
\(619\) −2222.03 5364.46i −0.144283 0.348329i 0.835173 0.549987i \(-0.185367\pi\)
−0.979456 + 0.201658i \(0.935367\pi\)
\(620\) 0 0
\(621\) 17243.5 + 7142.47i 1.11426 + 0.461542i
\(622\) 0 0
\(623\) 3923.64i 0.252323i
\(624\) 0 0
\(625\) 18588.8i 1.18968i
\(626\) 0 0
\(627\) −6116.62 2533.59i −0.389592 0.161374i
\(628\) 0 0
\(629\) 8718.08 + 21047.3i 0.552643 + 1.33420i
\(630\) 0 0
\(631\) −22236.1 22236.1i −1.40286 1.40286i −0.790837 0.612027i \(-0.790354\pi\)
−0.612027 0.790837i \(-0.709646\pi\)
\(632\) 0 0
\(633\) −8988.73 + 8988.73i −0.564407 + 0.564407i
\(634\) 0 0
\(635\) −17622.0 + 7299.27i −1.10127 + 0.456162i
\(636\) 0 0
\(637\) 2836.70 6848.39i 0.176443 0.425970i
\(638\) 0 0
\(639\) 16727.9 1.03560
\(640\) 0 0
\(641\) −3642.24 −0.224430 −0.112215 0.993684i \(-0.535795\pi\)
−0.112215 + 0.993684i \(0.535795\pi\)
\(642\) 0 0
\(643\) 7521.88 18159.4i 0.461328 1.11375i −0.506524 0.862226i \(-0.669070\pi\)
0.967852 0.251519i \(-0.0809302\pi\)
\(644\) 0 0
\(645\) 33594.2 13915.2i 2.05080 0.849471i
\(646\) 0 0
\(647\) 16784.8 16784.8i 1.01991 1.01991i 0.0201092 0.999798i \(-0.493599\pi\)
0.999798 0.0201092i \(-0.00640140\pi\)
\(648\) 0 0
\(649\) −11121.4 11121.4i −0.672655 0.672655i
\(650\) 0 0
\(651\) 1572.87 + 3797.24i 0.0946937 + 0.228611i
\(652\) 0 0
\(653\) −12553.7 5199.89i −0.752316 0.311620i −0.0266300 0.999645i \(-0.508478\pi\)
−0.725686 + 0.688026i \(0.758478\pi\)
\(654\) 0 0
\(655\) 12584.1i 0.750688i
\(656\) 0 0
\(657\) 22915.9i 1.36078i
\(658\) 0 0
\(659\) 7775.94 + 3220.90i 0.459647 + 0.190392i 0.600478 0.799642i \(-0.294977\pi\)
−0.140830 + 0.990034i \(0.544977\pi\)
\(660\) 0 0
\(661\) 1900.75 + 4588.81i 0.111847 + 0.270021i 0.969885 0.243564i \(-0.0783168\pi\)
−0.858038 + 0.513586i \(0.828317\pi\)
\(662\) 0 0
\(663\) −22834.6 22834.6i −1.33759 1.33759i
\(664\) 0 0
\(665\) 2420.71 2420.71i 0.141160 0.141160i
\(666\) 0 0
\(667\) −6319.82 + 2617.76i −0.366873 + 0.151964i
\(668\) 0 0
\(669\) 3533.75 8531.23i 0.204219 0.493029i
\(670\) 0 0
\(671\) −3845.36 −0.221234
\(672\) 0 0
\(673\) −9638.42 −0.552056 −0.276028 0.961150i \(-0.589018\pi\)
−0.276028 + 0.961150i \(0.589018\pi\)
\(674\) 0 0
\(675\) −4923.62 + 11886.7i −0.280756 + 0.677805i
\(676\) 0 0
\(677\) −27908.0 + 11559.9i −1.58433 + 0.656251i −0.989092 0.147297i \(-0.952943\pi\)
−0.595239 + 0.803549i \(0.702943\pi\)
\(678\) 0 0
\(679\) −7078.72 + 7078.72i −0.400083 + 0.400083i
\(680\) 0 0
\(681\) 22895.2 + 22895.2i 1.28832 + 1.28832i
\(682\) 0 0
\(683\) 11978.8 + 28919.3i 0.671090 + 1.62015i 0.779761 + 0.626077i \(0.215340\pi\)
−0.108671 + 0.994078i \(0.534660\pi\)
\(684\) 0 0
\(685\) −29468.3 12206.2i −1.64369 0.680838i
\(686\) 0 0
\(687\) 32468.8i 1.80315i
\(688\) 0 0
\(689\) 5706.67i 0.315540i
\(690\) 0 0
\(691\) 7238.99 + 2998.49i 0.398530 + 0.165076i 0.572941 0.819596i \(-0.305802\pi\)
−0.174412 + 0.984673i \(0.555802\pi\)
\(692\) 0 0
\(693\) −9324.84 22512.2i −0.511142 1.23401i
\(694\) 0 0
\(695\) −4944.89 4944.89i −0.269885 0.269885i
\(696\) 0 0
\(697\) 25839.4 25839.4i 1.40422 1.40422i
\(698\) 0 0
\(699\) −40232.0 + 16664.6i −2.17699 + 0.901738i
\(700\) 0 0
\(701\) 3609.66 8714.49i 0.194486 0.469532i −0.796311 0.604888i \(-0.793218\pi\)
0.990797 + 0.135356i \(0.0432179\pi\)
\(702\) 0 0
\(703\) 4446.32 0.238543
\(704\) 0 0
\(705\) 39916.7 2.13241
\(706\) 0 0
\(707\) 5564.88 13434.8i 0.296024 0.714665i
\(708\) 0 0
\(709\) −8921.05 + 3695.22i −0.472549 + 0.195736i −0.606232 0.795288i \(-0.707320\pi\)
0.133683 + 0.991024i \(0.457320\pi\)
\(710\) 0 0
\(711\) −7508.77 + 7508.77i −0.396063 + 0.396063i
\(712\) 0 0
\(713\) −3646.95 3646.95i −0.191556 0.191556i
\(714\) 0 0
\(715\) −10272.3 24799.5i −0.537290 1.29713i
\(716\) 0 0
\(717\) −43806.4 18145.2i −2.28170 0.945111i
\(718\) 0 0
\(719\) 36176.8i 1.87645i 0.346025 + 0.938225i \(0.387531\pi\)
−0.346025 + 0.938225i \(0.612469\pi\)
\(720\) 0 0
\(721\) 12412.1i 0.641126i
\(722\) 0 0
\(723\) −39233.9 16251.2i −2.01815 0.835947i
\(724\) 0 0
\(725\) −1804.54 4356.53i −0.0924397 0.223169i
\(726\) 0 0
\(727\) 25292.8 + 25292.8i 1.29031 + 1.29031i 0.934591 + 0.355723i \(0.115765\pi\)
0.355723 + 0.934591i \(0.384235\pi\)
\(728\) 0 0
\(729\) −22563.8 + 22563.8i −1.14636 + 1.14636i
\(730\) 0 0
\(731\) 25064.8 10382.2i 1.26820 0.525306i
\(732\) 0 0
\(733\) −11236.5 + 27127.4i −0.566208 + 1.36695i 0.338520 + 0.940959i \(0.390074\pi\)
−0.904729 + 0.425989i \(0.859926\pi\)
\(734\) 0 0
\(735\) −22096.1 −1.10888
\(736\) 0 0
\(737\) 12395.5 0.619532
\(738\) 0 0
\(739\) −2750.78 + 6640.98i −0.136927 + 0.330572i −0.977438 0.211224i \(-0.932255\pi\)
0.840510 + 0.541795i \(0.182255\pi\)
\(740\) 0 0
\(741\) −5822.96 + 2411.95i −0.288680 + 0.119575i
\(742\) 0 0
\(743\) 21298.6 21298.6i 1.05164 1.05164i 0.0530520 0.998592i \(-0.483105\pi\)
0.998592 0.0530520i \(-0.0168949\pi\)
\(744\) 0 0
\(745\) 31721.6 + 31721.6i 1.55999 + 1.55999i
\(746\) 0 0
\(747\) 22145.1 + 53462.9i 1.08467 + 2.61861i
\(748\) 0 0
\(749\) −8973.44 3716.92i −0.437760 0.181326i
\(750\) 0 0
\(751\) 33892.3i 1.64680i −0.567462 0.823400i \(-0.692075\pi\)
0.567462 0.823400i \(-0.307925\pi\)
\(752\) 0 0
\(753\) 8911.94i 0.431300i
\(754\) 0 0
\(755\) −5066.59 2098.65i −0.244228 0.101163i
\(756\) 0 0
\(757\) 1447.14 + 3493.72i 0.0694813 + 0.167743i 0.954805 0.297232i \(-0.0960634\pi\)
−0.885324 + 0.464975i \(0.846063\pi\)
\(758\) 0 0
\(759\) 35057.3 + 35057.3i 1.67655 + 1.67655i
\(760\) 0 0
\(761\) −8184.04 + 8184.04i −0.389844 + 0.389844i −0.874632 0.484788i \(-0.838897\pi\)
0.484788 + 0.874632i \(0.338897\pi\)
\(762\) 0 0
\(763\) −723.359 + 299.625i −0.0343216 + 0.0142165i
\(764\) 0 0
\(765\) −22719.1 + 54848.7i −1.07374 + 2.59223i
\(766\) 0 0
\(767\) −14972.9 −0.704878
\(768\) 0 0
\(769\) −29464.8 −1.38170 −0.690850 0.722998i \(-0.742763\pi\)
−0.690850 + 0.722998i \(0.742763\pi\)
\(770\) 0 0
\(771\) −3280.38 + 7919.53i −0.153229 + 0.369928i
\(772\) 0 0
\(773\) 24119.4 9990.57i 1.12227 0.464859i 0.257122 0.966379i \(-0.417226\pi\)
0.865146 + 0.501520i \(0.167226\pi\)
\(774\) 0 0
\(775\) 2514.00 2514.00i 0.116523 0.116523i
\(776\) 0 0
\(777\) 18762.5 + 18762.5i 0.866284 + 0.866284i
\(778\) 0 0
\(779\) −2729.33 6589.19i −0.125531 0.303058i
\(780\) 0 0
\(781\) 15540.9 + 6437.26i 0.712034 + 0.294934i
\(782\) 0 0
\(783\) 6984.67i 0.318789i
\(784\) 0 0
\(785\) 41932.8i 1.90656i
\(786\) 0 0