Properties

Label 690.3.c.a.91.8
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.8
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949 q^{6} +12.6313i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949 q^{6} +12.6313i q^{7} -2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} +6.64640i q^{11} -3.46410 q^{12} -21.6127 q^{13} -17.8634i q^{14} -3.87298i q^{15} +4.00000 q^{16} +26.9012i q^{17} -4.24264 q^{18} +5.80470i q^{19} +4.47214i q^{20} -21.8781i q^{21} -9.39943i q^{22} +(-11.1853 - 20.0970i) q^{23} +4.89898 q^{24} -5.00000 q^{25} +30.5649 q^{26} -5.19615 q^{27} +25.2627i q^{28} +50.7850 q^{29} +5.47723i q^{30} +0.790554 q^{31} -5.65685 q^{32} -11.5119i q^{33} -38.0440i q^{34} -28.2445 q^{35} +6.00000 q^{36} +11.7874i q^{37} -8.20908i q^{38} +37.4342 q^{39} -6.32456i q^{40} -0.0875420 q^{41} +30.9403i q^{42} -78.4553i q^{43} +13.2928i q^{44} +6.70820i q^{45} +(15.8184 + 28.4214i) q^{46} +65.2980 q^{47} -6.92820 q^{48} -110.551 q^{49} +7.07107 q^{50} -46.5942i q^{51} -43.2253 q^{52} +35.8320i q^{53} +7.34847 q^{54} -14.8618 q^{55} -35.7268i q^{56} -10.0540i q^{57} -71.8208 q^{58} -28.0844 q^{59} -7.74597i q^{60} -18.6748i q^{61} -1.11801 q^{62} +37.8940i q^{63} +8.00000 q^{64} -48.3274i q^{65} +16.2803i q^{66} +23.9607i q^{67} +53.8024i q^{68} +(19.3736 + 34.8090i) q^{69} +39.9438 q^{70} -101.896 q^{71} -8.48528 q^{72} -111.078 q^{73} -16.6699i q^{74} +8.66025 q^{75} +11.6094i q^{76} -83.9530 q^{77} -52.9400 q^{78} -84.0979i q^{79} +8.94427i q^{80} +9.00000 q^{81} +0.123803 q^{82} +137.812i q^{83} -43.7563i q^{84} -60.1529 q^{85} +110.953i q^{86} -87.9622 q^{87} -18.7989i q^{88} -46.7519i q^{89} -9.48683i q^{90} -272.997i q^{91} +(-22.3707 - 40.1940i) q^{92} -1.36928 q^{93} -92.3454 q^{94} -12.9797 q^{95} +9.79796 q^{96} -20.6627i q^{97} +156.343 q^{98} +19.9392i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.73205 −0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 2.44949 0.408248
\(7\) 12.6313i 1.80448i 0.431237 + 0.902239i \(0.358077\pi\)
−0.431237 + 0.902239i \(0.641923\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 6.64640i 0.604218i 0.953273 + 0.302109i \(0.0976907\pi\)
−0.953273 + 0.302109i \(0.902309\pi\)
\(12\) −3.46410 −0.288675
\(13\) −21.6127 −1.66251 −0.831256 0.555890i \(-0.812378\pi\)
−0.831256 + 0.555890i \(0.812378\pi\)
\(14\) 17.8634i 1.27596i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 26.9012i 1.58242i 0.611543 + 0.791211i \(0.290549\pi\)
−0.611543 + 0.791211i \(0.709451\pi\)
\(18\) −4.24264 −0.235702
\(19\) 5.80470i 0.305510i 0.988264 + 0.152755i \(0.0488146\pi\)
−0.988264 + 0.152755i \(0.951185\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 21.8781i 1.04182i
\(22\) 9.39943i 0.427247i
\(23\) −11.1853 20.0970i −0.486319 0.873782i
\(24\) 4.89898 0.204124
\(25\) −5.00000 −0.200000
\(26\) 30.5649 1.17557
\(27\) −5.19615 −0.192450
\(28\) 25.2627i 0.902239i
\(29\) 50.7850 1.75121 0.875604 0.483031i \(-0.160464\pi\)
0.875604 + 0.483031i \(0.160464\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 0.790554 0.0255017 0.0127509 0.999919i \(-0.495941\pi\)
0.0127509 + 0.999919i \(0.495941\pi\)
\(32\) −5.65685 −0.176777
\(33\) 11.5119i 0.348846i
\(34\) 38.0440i 1.11894i
\(35\) −28.2445 −0.806987
\(36\) 6.00000 0.166667
\(37\) 11.7874i 0.318578i 0.987232 + 0.159289i \(0.0509202\pi\)
−0.987232 + 0.159289i \(0.949080\pi\)
\(38\) 8.20908i 0.216028i
\(39\) 37.4342 0.959852
\(40\) 6.32456i 0.158114i
\(41\) −0.0875420 −0.00213517 −0.00106759 0.999999i \(-0.500340\pi\)
−0.00106759 + 0.999999i \(0.500340\pi\)
\(42\) 30.9403i 0.736675i
\(43\) 78.4553i 1.82454i −0.409588 0.912271i \(-0.634327\pi\)
0.409588 0.912271i \(-0.365673\pi\)
\(44\) 13.2928i 0.302109i
\(45\) 6.70820i 0.149071i
\(46\) 15.8184 + 28.4214i 0.343879 + 0.617857i
\(47\) 65.2980 1.38932 0.694660 0.719338i \(-0.255555\pi\)
0.694660 + 0.719338i \(0.255555\pi\)
\(48\) −6.92820 −0.144338
\(49\) −110.551 −2.25614
\(50\) 7.07107 0.141421
\(51\) 46.5942i 0.913612i
\(52\) −43.2253 −0.831256
\(53\) 35.8320i 0.676076i 0.941132 + 0.338038i \(0.109763\pi\)
−0.941132 + 0.338038i \(0.890237\pi\)
\(54\) 7.34847 0.136083
\(55\) −14.8618 −0.270215
\(56\) 35.7268i 0.637979i
\(57\) 10.0540i 0.176387i
\(58\) −71.8208 −1.23829
\(59\) −28.0844 −0.476006 −0.238003 0.971264i \(-0.576493\pi\)
−0.238003 + 0.971264i \(0.576493\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 18.6748i 0.306145i −0.988215 0.153072i \(-0.951083\pi\)
0.988215 0.153072i \(-0.0489168\pi\)
\(62\) −1.11801 −0.0180324
\(63\) 37.8940i 0.601493i
\(64\) 8.00000 0.125000
\(65\) 48.3274i 0.743498i
\(66\) 16.2803i 0.246671i
\(67\) 23.9607i 0.357622i 0.983883 + 0.178811i \(0.0572250\pi\)
−0.983883 + 0.178811i \(0.942775\pi\)
\(68\) 53.8024i 0.791211i
\(69\) 19.3736 + 34.8090i 0.280776 + 0.504478i
\(70\) 39.9438 0.570626
\(71\) −101.896 −1.43515 −0.717576 0.696481i \(-0.754748\pi\)
−0.717576 + 0.696481i \(0.754748\pi\)
\(72\) −8.48528 −0.117851
\(73\) −111.078 −1.52162 −0.760811 0.648973i \(-0.775199\pi\)
−0.760811 + 0.648973i \(0.775199\pi\)
\(74\) 16.6699i 0.225269i
\(75\) 8.66025 0.115470
\(76\) 11.6094i 0.152755i
\(77\) −83.9530 −1.09030
\(78\) −52.9400 −0.678718
\(79\) 84.0979i 1.06453i −0.846578 0.532265i \(-0.821341\pi\)
0.846578 0.532265i \(-0.178659\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 0.123803 0.00150979
\(83\) 137.812i 1.66039i 0.557476 + 0.830193i \(0.311770\pi\)
−0.557476 + 0.830193i \(0.688230\pi\)
\(84\) 43.7563i 0.520908i
\(85\) −60.1529 −0.707681
\(86\) 110.953i 1.29015i
\(87\) −87.9622 −1.01106
\(88\) 18.7989i 0.213623i
\(89\) 46.7519i 0.525302i −0.964891 0.262651i \(-0.915403\pi\)
0.964891 0.262651i \(-0.0845967\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 272.997i 2.99997i
\(92\) −22.3707 40.1940i −0.243159 0.436891i
\(93\) −1.36928 −0.0147234
\(94\) −92.3454 −0.982398
\(95\) −12.9797 −0.136628
\(96\) 9.79796 0.102062
\(97\) 20.6627i 0.213018i −0.994312 0.106509i \(-0.966033\pi\)
0.994312 0.106509i \(-0.0339673\pi\)
\(98\) 156.343 1.59533
\(99\) 19.9392i 0.201406i
\(100\) −10.0000 −0.100000
\(101\) 109.820 1.08733 0.543665 0.839303i \(-0.317036\pi\)
0.543665 + 0.839303i \(0.317036\pi\)
\(102\) 65.8942i 0.646021i
\(103\) 9.00887i 0.0874647i 0.999043 + 0.0437324i \(0.0139249\pi\)
−0.999043 + 0.0437324i \(0.986075\pi\)
\(104\) 61.1298 0.587787
\(105\) 48.9210 0.465914
\(106\) 50.6742i 0.478058i
\(107\) 168.462i 1.57441i −0.616689 0.787207i \(-0.711526\pi\)
0.616689 0.787207i \(-0.288474\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 32.8697i 0.301557i −0.988568 0.150778i \(-0.951822\pi\)
0.988568 0.150778i \(-0.0481780\pi\)
\(110\) 21.0178 0.191071
\(111\) 20.4164i 0.183931i
\(112\) 50.5254i 0.451119i
\(113\) 40.3701i 0.357257i −0.983917 0.178629i \(-0.942834\pi\)
0.983917 0.178629i \(-0.0571661\pi\)
\(114\) 14.2185i 0.124724i
\(115\) 44.9382 25.0112i 0.390767 0.217488i
\(116\) 101.570 0.875604
\(117\) −64.8380 −0.554171
\(118\) 39.7173 0.336587
\(119\) −339.798 −2.85545
\(120\) 10.9545i 0.0912871i
\(121\) 76.8254 0.634920
\(122\) 26.4102i 0.216477i
\(123\) 0.151627 0.00123274
\(124\) 1.58111 0.0127509
\(125\) 11.1803i 0.0894427i
\(126\) 53.5903i 0.425319i
\(127\) −222.002 −1.74805 −0.874023 0.485884i \(-0.838498\pi\)
−0.874023 + 0.485884i \(0.838498\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 135.889i 1.05340i
\(130\) 68.3452i 0.525733i
\(131\) −104.077 −0.794482 −0.397241 0.917714i \(-0.630032\pi\)
−0.397241 + 0.917714i \(0.630032\pi\)
\(132\) 23.0238i 0.174423i
\(133\) −73.3211 −0.551287
\(134\) 33.8855i 0.252877i
\(135\) 11.6190i 0.0860663i
\(136\) 76.0880i 0.559471i
\(137\) 153.744i 1.12222i 0.827741 + 0.561110i \(0.189625\pi\)
−0.827741 + 0.561110i \(0.810375\pi\)
\(138\) −27.3983 49.2273i −0.198539 0.356720i
\(139\) 35.8886 0.258191 0.129096 0.991632i \(-0.458793\pi\)
0.129096 + 0.991632i \(0.458793\pi\)
\(140\) −56.4891 −0.403493
\(141\) −113.100 −0.802124
\(142\) 144.102 1.01481
\(143\) 143.646i 1.00452i
\(144\) 12.0000 0.0833333
\(145\) 113.559i 0.783164i
\(146\) 157.089 1.07595
\(147\) 191.480 1.30258
\(148\) 23.5748i 0.159289i
\(149\) 5.22632i 0.0350760i 0.999846 + 0.0175380i \(0.00558280\pi\)
−0.999846 + 0.0175380i \(0.994417\pi\)
\(150\) −12.2474 −0.0816497
\(151\) −277.637 −1.83865 −0.919326 0.393496i \(-0.871266\pi\)
−0.919326 + 0.393496i \(0.871266\pi\)
\(152\) 16.4182i 0.108014i
\(153\) 80.7035i 0.527474i
\(154\) 118.727 0.770957
\(155\) 1.76773i 0.0114047i
\(156\) 74.8684 0.479926
\(157\) 188.330i 1.19955i 0.800168 + 0.599776i \(0.204743\pi\)
−0.800168 + 0.599776i \(0.795257\pi\)
\(158\) 118.932i 0.752737i
\(159\) 62.0629i 0.390333i
\(160\) 12.6491i 0.0790569i
\(161\) 253.852 141.286i 1.57672 0.877551i
\(162\) −12.7279 −0.0785674
\(163\) −119.568 −0.733543 −0.366772 0.930311i \(-0.619537\pi\)
−0.366772 + 0.930311i \(0.619537\pi\)
\(164\) −0.175084 −0.00106759
\(165\) 25.7414 0.156008
\(166\) 194.896i 1.17407i
\(167\) 106.259 0.636281 0.318140 0.948044i \(-0.396942\pi\)
0.318140 + 0.948044i \(0.396942\pi\)
\(168\) 61.8807i 0.368337i
\(169\) 298.107 1.76395
\(170\) 85.0690 0.500406
\(171\) 17.4141i 0.101837i
\(172\) 156.911i 0.912271i
\(173\) 343.403 1.98499 0.992494 0.122293i \(-0.0390249\pi\)
0.992494 + 0.122293i \(0.0390249\pi\)
\(174\) 124.397 0.714927
\(175\) 63.1567i 0.360896i
\(176\) 26.5856i 0.151055i
\(177\) 48.6435 0.274822
\(178\) 66.1171i 0.371444i
\(179\) 172.782 0.965260 0.482630 0.875824i \(-0.339682\pi\)
0.482630 + 0.875824i \(0.339682\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 20.5336i 0.113445i −0.998390 0.0567226i \(-0.981935\pi\)
0.998390 0.0567226i \(-0.0180651\pi\)
\(182\) 386.076i 2.12130i
\(183\) 32.3457i 0.176753i
\(184\) 31.6369 + 56.8428i 0.171940 + 0.308928i
\(185\) −26.3574 −0.142473
\(186\) 1.93645 0.0104110
\(187\) −178.796 −0.956129
\(188\) 130.596 0.694660
\(189\) 65.6344i 0.347272i
\(190\) 18.3561 0.0966109
\(191\) 126.392i 0.661741i 0.943676 + 0.330870i \(0.107342\pi\)
−0.943676 + 0.330870i \(0.892658\pi\)
\(192\) −13.8564 −0.0721688
\(193\) −119.288 −0.618073 −0.309037 0.951050i \(-0.600007\pi\)
−0.309037 + 0.951050i \(0.600007\pi\)
\(194\) 29.2215i 0.150626i
\(195\) 83.7055i 0.429259i
\(196\) −221.102 −1.12807
\(197\) 32.0842 0.162864 0.0814319 0.996679i \(-0.474051\pi\)
0.0814319 + 0.996679i \(0.474051\pi\)
\(198\) 28.1983i 0.142416i
\(199\) 308.976i 1.55264i 0.630336 + 0.776322i \(0.282917\pi\)
−0.630336 + 0.776322i \(0.717083\pi\)
\(200\) 14.1421 0.0707107
\(201\) 41.5011i 0.206473i
\(202\) −155.309 −0.768858
\(203\) 641.483i 3.16001i
\(204\) 93.1884i 0.456806i
\(205\) 0.195750i 0.000954878i
\(206\) 12.7405i 0.0618469i
\(207\) −33.5560 60.2909i −0.162106 0.291261i
\(208\) −86.4506 −0.415628
\(209\) −38.5803 −0.184595
\(210\) −69.1847 −0.329451
\(211\) 284.915 1.35031 0.675153 0.737678i \(-0.264078\pi\)
0.675153 + 0.737678i \(0.264078\pi\)
\(212\) 71.6641i 0.338038i
\(213\) 176.489 0.828585
\(214\) 238.242i 1.11328i
\(215\) 175.431 0.815960
\(216\) 14.6969 0.0680414
\(217\) 9.98576i 0.0460173i
\(218\) 46.4848i 0.213233i
\(219\) 192.394 0.878509
\(220\) −29.7236 −0.135107
\(221\) 581.406i 2.63080i
\(222\) 28.8731i 0.130059i
\(223\) −58.1222 −0.260638 −0.130319 0.991472i \(-0.541600\pi\)
−0.130319 + 0.991472i \(0.541600\pi\)
\(224\) 71.4537i 0.318990i
\(225\) −15.0000 −0.0666667
\(226\) 57.0919i 0.252619i
\(227\) 61.9517i 0.272915i 0.990646 + 0.136458i \(0.0435717\pi\)
−0.990646 + 0.136458i \(0.956428\pi\)
\(228\) 20.1081i 0.0881933i
\(229\) 274.171i 1.19725i 0.801029 + 0.598626i \(0.204286\pi\)
−0.801029 + 0.598626i \(0.795714\pi\)
\(230\) −63.5522 + 35.3711i −0.276314 + 0.153787i
\(231\) 145.411 0.629484
\(232\) −143.642 −0.619145
\(233\) −12.4541 −0.0534511 −0.0267255 0.999643i \(-0.508508\pi\)
−0.0267255 + 0.999643i \(0.508508\pi\)
\(234\) 91.6947 0.391858
\(235\) 146.011i 0.621323i
\(236\) −56.1687 −0.238003
\(237\) 145.662i 0.614607i
\(238\) 480.547 2.01911
\(239\) −348.698 −1.45899 −0.729494 0.683987i \(-0.760244\pi\)
−0.729494 + 0.683987i \(0.760244\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 333.130i 1.38228i −0.722719 0.691142i \(-0.757108\pi\)
0.722719 0.691142i \(-0.242892\pi\)
\(242\) −108.647 −0.448956
\(243\) −15.5885 −0.0641500
\(244\) 37.3497i 0.153072i
\(245\) 247.199i 1.00898i
\(246\) −0.214433 −0.000871680
\(247\) 125.455i 0.507915i
\(248\) −2.23602 −0.00901622
\(249\) 238.697i 0.958624i
\(250\) 15.8114i 0.0632456i
\(251\) 218.644i 0.871093i −0.900166 0.435546i \(-0.856555\pi\)
0.900166 0.435546i \(-0.143445\pi\)
\(252\) 75.7881i 0.300746i
\(253\) 133.573 74.3422i 0.527955 0.293843i
\(254\) 313.958 1.23606
\(255\) 104.188 0.408580
\(256\) 16.0000 0.0625000
\(257\) 436.402 1.69806 0.849032 0.528342i \(-0.177186\pi\)
0.849032 + 0.528342i \(0.177186\pi\)
\(258\) 192.175i 0.744866i
\(259\) −148.891 −0.574867
\(260\) 96.6548i 0.371749i
\(261\) 152.355 0.583736
\(262\) 147.187 0.561784
\(263\) 431.615i 1.64112i −0.571558 0.820562i \(-0.693661\pi\)
0.571558 0.820562i \(-0.306339\pi\)
\(264\) 32.5606i 0.123336i
\(265\) −80.1229 −0.302351
\(266\) 103.692 0.389819
\(267\) 80.9766i 0.303283i
\(268\) 47.9213i 0.178811i
\(269\) −312.123 −1.16031 −0.580155 0.814506i \(-0.697008\pi\)
−0.580155 + 0.814506i \(0.697008\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −70.7048 −0.260903 −0.130452 0.991455i \(-0.541643\pi\)
−0.130452 + 0.991455i \(0.541643\pi\)
\(272\) 107.605i 0.395606i
\(273\) 472.845i 1.73203i
\(274\) 217.427i 0.793529i
\(275\) 33.2320i 0.120844i
\(276\) 38.7471 + 69.6180i 0.140388 + 0.252239i
\(277\) 344.720 1.24448 0.622239 0.782827i \(-0.286223\pi\)
0.622239 + 0.782827i \(0.286223\pi\)
\(278\) −50.7541 −0.182569
\(279\) 2.37166 0.00850058
\(280\) 79.8876 0.285313
\(281\) 299.210i 1.06481i 0.846491 + 0.532403i \(0.178711\pi\)
−0.846491 + 0.532403i \(0.821289\pi\)
\(282\) 159.947 0.567188
\(283\) 49.7476i 0.175787i −0.996130 0.0878933i \(-0.971987\pi\)
0.996130 0.0878933i \(-0.0280135\pi\)
\(284\) −203.791 −0.717576
\(285\) 22.4815 0.0788824
\(286\) 203.147i 0.710303i
\(287\) 1.10577i 0.00385287i
\(288\) −16.9706 −0.0589256
\(289\) −434.674 −1.50406
\(290\) 160.596i 0.553780i
\(291\) 35.7889i 0.122986i
\(292\) −222.157 −0.760811
\(293\) 37.1215i 0.126695i −0.997992 0.0633473i \(-0.979822\pi\)
0.997992 0.0633473i \(-0.0201776\pi\)
\(294\) −270.793 −0.921065
\(295\) 62.7985i 0.212876i
\(296\) 33.3398i 0.112634i
\(297\) 34.5357i 0.116282i
\(298\) 7.39113i 0.0248025i
\(299\) 241.745 + 434.349i 0.808511 + 1.45267i
\(300\) 17.3205 0.0577350
\(301\) 990.996 3.29234
\(302\) 392.637 1.30012
\(303\) −190.214 −0.627770
\(304\) 23.2188i 0.0763776i
\(305\) 41.7582 0.136912
\(306\) 114.132i 0.372981i
\(307\) −0.623436 −0.00203074 −0.00101537 0.999999i \(-0.500323\pi\)
−0.00101537 + 0.999999i \(0.500323\pi\)
\(308\) −167.906 −0.545149
\(309\) 15.6038i 0.0504978i
\(310\) 2.49995i 0.00806436i
\(311\) 118.290 0.380352 0.190176 0.981750i \(-0.439094\pi\)
0.190176 + 0.981750i \(0.439094\pi\)
\(312\) −105.880 −0.339359
\(313\) 318.068i 1.01619i 0.861300 + 0.508096i \(0.169651\pi\)
−0.861300 + 0.508096i \(0.830349\pi\)
\(314\) 266.338i 0.848211i
\(315\) −84.7336 −0.268996
\(316\) 168.196i 0.532265i
\(317\) −291.589 −0.919839 −0.459919 0.887961i \(-0.652122\pi\)
−0.459919 + 0.887961i \(0.652122\pi\)
\(318\) 87.7702i 0.276007i
\(319\) 337.537i 1.05811i
\(320\) 17.8885i 0.0559017i
\(321\) 291.785i 0.908988i
\(322\) −359.001 + 199.808i −1.11491 + 0.620522i
\(323\) −156.153 −0.483447
\(324\) 18.0000 0.0555556
\(325\) 108.063 0.332502
\(326\) 169.094 0.518693
\(327\) 56.9320i 0.174104i
\(328\) 0.247606 0.000754897
\(329\) 824.802i 2.50700i
\(330\) −36.4038 −0.110315
\(331\) 64.2594 0.194137 0.0970686 0.995278i \(-0.469053\pi\)
0.0970686 + 0.995278i \(0.469053\pi\)
\(332\) 275.624i 0.830193i
\(333\) 35.3622i 0.106193i
\(334\) −150.273 −0.449919
\(335\) −53.5777 −0.159933
\(336\) 87.5125i 0.260454i
\(337\) 353.359i 1.04854i −0.851552 0.524271i \(-0.824338\pi\)
0.851552 0.524271i \(-0.175662\pi\)
\(338\) −421.587 −1.24730
\(339\) 69.9230i 0.206263i
\(340\) −120.306 −0.353840
\(341\) 5.25434i 0.0154086i
\(342\) 24.6272i 0.0720095i
\(343\) 777.470i 2.26668i
\(344\) 221.905i 0.645073i
\(345\) −77.8352 + 43.3206i −0.225609 + 0.125567i
\(346\) −485.645 −1.40360
\(347\) −424.699 −1.22392 −0.611958 0.790890i \(-0.709618\pi\)
−0.611958 + 0.790890i \(0.709618\pi\)
\(348\) −175.924 −0.505530
\(349\) −111.111 −0.318370 −0.159185 0.987249i \(-0.550887\pi\)
−0.159185 + 0.987249i \(0.550887\pi\)
\(350\) 89.3171i 0.255192i
\(351\) 112.303 0.319951
\(352\) 37.5977i 0.106812i
\(353\) −306.094 −0.867121 −0.433561 0.901124i \(-0.642743\pi\)
−0.433561 + 0.901124i \(0.642743\pi\)
\(354\) −68.7924 −0.194329
\(355\) 227.846i 0.641819i
\(356\) 93.5037i 0.262651i
\(357\) 588.548 1.64859
\(358\) −244.350 −0.682542
\(359\) 77.5601i 0.216045i −0.994148 0.108022i \(-0.965548\pi\)
0.994148 0.108022i \(-0.0344518\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 327.305 0.906663
\(362\) 29.0389i 0.0802178i
\(363\) −133.065 −0.366571
\(364\) 545.994i 1.49998i
\(365\) 248.379i 0.680490i
\(366\) 45.7438i 0.124983i
\(367\) 85.7495i 0.233650i 0.993153 + 0.116825i \(0.0372717\pi\)
−0.993153 + 0.116825i \(0.962728\pi\)
\(368\) −44.7413 80.3879i −0.121580 0.218445i
\(369\) −0.262626 −0.000711724
\(370\) 37.2750 0.100743
\(371\) −452.607 −1.21996
\(372\) −2.73856 −0.00736172
\(373\) 144.680i 0.387882i −0.981013 0.193941i \(-0.937873\pi\)
0.981013 0.193941i \(-0.0621271\pi\)
\(374\) 252.856 0.676085
\(375\) 19.3649i 0.0516398i
\(376\) −184.691 −0.491199
\(377\) −1097.60 −2.91140
\(378\) 92.8210i 0.245558i
\(379\) 303.886i 0.801810i 0.916120 + 0.400905i \(0.131304\pi\)
−0.916120 + 0.400905i \(0.868696\pi\)
\(380\) −25.9594 −0.0683142
\(381\) 384.518 1.00923
\(382\) 178.746i 0.467921i
\(383\) 215.968i 0.563884i −0.959431 0.281942i \(-0.909021\pi\)
0.959431 0.281942i \(-0.0909785\pi\)
\(384\) 19.5959 0.0510310
\(385\) 187.725i 0.487596i
\(386\) 168.699 0.437044
\(387\) 235.366i 0.608180i
\(388\) 41.3254i 0.106509i
\(389\) 41.3140i 0.106206i −0.998589 0.0531028i \(-0.983089\pi\)
0.998589 0.0531028i \(-0.0169111\pi\)
\(390\) 118.377i 0.303532i
\(391\) 540.632 300.899i 1.38269 0.769562i
\(392\) 312.685 0.797666
\(393\) 180.267 0.458694
\(394\) −45.3739 −0.115162
\(395\) 188.049 0.476072
\(396\) 39.8784i 0.100703i
\(397\) 400.330 1.00839 0.504194 0.863590i \(-0.331790\pi\)
0.504194 + 0.863590i \(0.331790\pi\)
\(398\) 436.958i 1.09789i
\(399\) 126.996 0.318286
\(400\) −20.0000 −0.0500000
\(401\) 442.777i 1.10418i 0.833784 + 0.552091i \(0.186170\pi\)
−0.833784 + 0.552091i \(0.813830\pi\)
\(402\) 58.6914i 0.145998i
\(403\) −17.0860 −0.0423969
\(404\) 219.641 0.543665
\(405\) 20.1246i 0.0496904i
\(406\) 907.194i 2.23447i
\(407\) −78.3438 −0.192491
\(408\) 131.788i 0.323011i
\(409\) −781.825 −1.91155 −0.955776 0.294096i \(-0.904981\pi\)
−0.955776 + 0.294096i \(0.904981\pi\)
\(410\) 0.276832i 0.000675200i
\(411\) 266.293i 0.647914i
\(412\) 18.0177i 0.0437324i
\(413\) 354.743i 0.858943i
\(414\) 47.4553 + 85.2642i 0.114626 + 0.205952i
\(415\) −308.157 −0.742547
\(416\) 122.260 0.293893
\(417\) −62.1608 −0.149067
\(418\) 54.5609 0.130528
\(419\) 417.722i 0.996950i 0.866904 + 0.498475i \(0.166106\pi\)
−0.866904 + 0.498475i \(0.833894\pi\)
\(420\) 97.8420 0.232957
\(421\) 140.248i 0.333131i 0.986030 + 0.166566i \(0.0532678\pi\)
−0.986030 + 0.166566i \(0.946732\pi\)
\(422\) −402.930 −0.954811
\(423\) 195.894 0.463107
\(424\) 101.348i 0.239029i
\(425\) 134.506i 0.316484i
\(426\) −249.593 −0.585898
\(427\) 235.888 0.552431
\(428\) 336.925i 0.787207i
\(429\) 248.803i 0.579960i
\(430\) −248.097 −0.576971
\(431\) 3.48703i 0.00809055i −0.999992 0.00404528i \(-0.998712\pi\)
0.999992 0.00404528i \(-0.00128765\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 372.607i 0.860523i 0.902704 + 0.430262i \(0.141579\pi\)
−0.902704 + 0.430262i \(0.858421\pi\)
\(434\) 14.1220i 0.0325391i
\(435\) 196.689i 0.452160i
\(436\) 65.7394i 0.150778i
\(437\) 116.657 64.9275i 0.266949 0.148575i
\(438\) −272.086 −0.621200
\(439\) 103.728 0.236283 0.118142 0.992997i \(-0.462306\pi\)
0.118142 + 0.992997i \(0.462306\pi\)
\(440\) 42.0355 0.0955353
\(441\) −331.653 −0.752047
\(442\) 822.232i 1.86025i
\(443\) −693.747 −1.56602 −0.783010 0.622009i \(-0.786317\pi\)
−0.783010 + 0.622009i \(0.786317\pi\)
\(444\) 40.8327i 0.0919656i
\(445\) 104.540 0.234922
\(446\) 82.1972 0.184299
\(447\) 9.05225i 0.0202511i
\(448\) 101.051i 0.225560i
\(449\) 274.366 0.611061 0.305531 0.952182i \(-0.401166\pi\)
0.305531 + 0.952182i \(0.401166\pi\)
\(450\) 21.2132 0.0471405
\(451\) 0.581839i 0.00129011i
\(452\) 80.7401i 0.178629i
\(453\) 480.881 1.06155
\(454\) 87.6130i 0.192980i
\(455\) 610.440 1.34163
\(456\) 28.4371i 0.0623621i
\(457\) 588.108i 1.28689i 0.765493 + 0.643444i \(0.222495\pi\)
−0.765493 + 0.643444i \(0.777505\pi\)
\(458\) 387.736i 0.846585i
\(459\) 139.783i 0.304537i
\(460\) 89.8764 50.0223i 0.195383 0.108744i
\(461\) −219.244 −0.475584 −0.237792 0.971316i \(-0.576424\pi\)
−0.237792 + 0.971316i \(0.576424\pi\)
\(462\) −205.642 −0.445112
\(463\) −105.290 −0.227409 −0.113705 0.993515i \(-0.536272\pi\)
−0.113705 + 0.993515i \(0.536272\pi\)
\(464\) 203.140 0.437802
\(465\) 3.06180i 0.00658452i
\(466\) 17.6128 0.0377956
\(467\) 297.818i 0.637727i 0.947801 + 0.318863i \(0.103301\pi\)
−0.947801 + 0.318863i \(0.896699\pi\)
\(468\) −129.676 −0.277085
\(469\) −302.655 −0.645321
\(470\) 206.491i 0.439342i
\(471\) 326.196i 0.692561i
\(472\) 79.4346 0.168294
\(473\) 521.445 1.10242
\(474\) 205.997i 0.434593i
\(475\) 29.0235i 0.0611021i
\(476\) −679.596 −1.42772
\(477\) 107.496i 0.225359i
\(478\) 493.134 1.03166
\(479\) 573.980i 1.19829i −0.800641 0.599144i \(-0.795508\pi\)
0.800641 0.599144i \(-0.204492\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 254.757i 0.529640i
\(482\) 471.117i 0.977422i
\(483\) −439.684 + 244.714i −0.910319 + 0.506654i
\(484\) 153.651 0.317460
\(485\) 46.2033 0.0952644
\(486\) 22.0454 0.0453609
\(487\) −934.765 −1.91944 −0.959718 0.280965i \(-0.909346\pi\)
−0.959718 + 0.280965i \(0.909346\pi\)
\(488\) 52.8204i 0.108238i
\(489\) 207.097 0.423511
\(490\) 349.592i 0.713454i
\(491\) −285.271 −0.581001 −0.290500 0.956875i \(-0.593822\pi\)
−0.290500 + 0.956875i \(0.593822\pi\)
\(492\) 0.303254 0.000616371
\(493\) 1366.18i 2.77115i
\(494\) 177.420i 0.359150i
\(495\) −44.5854 −0.0900715
\(496\) 3.16221 0.00637543
\(497\) 1287.08i 2.58970i
\(498\) 337.569i 0.677850i
\(499\) 225.862 0.452628 0.226314 0.974054i \(-0.427332\pi\)
0.226314 + 0.974054i \(0.427332\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −184.046 −0.367357
\(502\) 309.210i 0.615956i
\(503\) 689.412i 1.37060i −0.728261 0.685300i \(-0.759671\pi\)
0.728261 0.685300i \(-0.240329\pi\)
\(504\) 107.181i 0.212660i
\(505\) 245.566i 0.486268i
\(506\) −188.900 + 105.136i −0.373320 + 0.207778i
\(507\) −516.337 −1.01842
\(508\) −444.004 −0.874023
\(509\) 203.484 0.399772 0.199886 0.979819i \(-0.435943\pi\)
0.199886 + 0.979819i \(0.435943\pi\)
\(510\) −147.344 −0.288909
\(511\) 1403.07i 2.74573i
\(512\) −22.6274 −0.0441942
\(513\) 30.1621i 0.0587955i
\(514\) −617.166 −1.20071
\(515\) −20.1444 −0.0391154
\(516\) 271.777i 0.526700i
\(517\) 433.997i 0.839453i
\(518\) 210.563 0.406493
\(519\) −594.791 −1.14603
\(520\) 136.690i 0.262866i
\(521\) 427.253i 0.820063i 0.912071 + 0.410031i \(0.134482\pi\)
−0.912071 + 0.410031i \(0.865518\pi\)
\(522\) −215.463 −0.412763
\(523\) 824.411i 1.57631i −0.615476 0.788156i \(-0.711036\pi\)
0.615476 0.788156i \(-0.288964\pi\)
\(524\) −208.154 −0.397241
\(525\) 109.391i 0.208363i
\(526\) 610.396i 1.16045i
\(527\) 21.2668i 0.0403545i
\(528\) 46.0476i 0.0872114i
\(529\) −278.777 + 449.583i −0.526988 + 0.849873i
\(530\) 113.311 0.213794
\(531\) −84.2531 −0.158669
\(532\) −146.642 −0.275643
\(533\) 1.89202 0.00354975
\(534\) 114.518i 0.214454i
\(535\) 376.693 0.704099
\(536\) 67.7710i 0.126438i
\(537\) −299.266 −0.557293
\(538\) 441.409 0.820462
\(539\) 734.765i 1.36320i
\(540\) 23.2379i 0.0430331i
\(541\) −628.584 −1.16189 −0.580947 0.813942i \(-0.697318\pi\)
−0.580947 + 0.813942i \(0.697318\pi\)
\(542\) 99.9917 0.184487
\(543\) 35.5652i 0.0654976i
\(544\) 152.176i 0.279735i
\(545\) 73.4989 0.134860
\(546\) 668.703i 1.22473i
\(547\) 419.610 0.767112 0.383556 0.923518i \(-0.374699\pi\)
0.383556 + 0.923518i \(0.374699\pi\)
\(548\) 307.488i 0.561110i
\(549\) 56.0245i 0.102048i
\(550\) 46.9972i 0.0854494i
\(551\) 294.792i 0.535012i
\(552\) −54.7967 98.4547i −0.0992694 0.178360i
\(553\) 1062.27 1.92092
\(554\) −487.508 −0.879979
\(555\) 45.6524 0.0822566
\(556\) 71.7771 0.129096
\(557\) 573.400i 1.02944i −0.857357 0.514722i \(-0.827895\pi\)
0.857357 0.514722i \(-0.172105\pi\)
\(558\) −3.35404 −0.00601082
\(559\) 1695.63i 3.03332i
\(560\) −112.978 −0.201747
\(561\) 309.684 0.552021
\(562\) 423.147i 0.752931i
\(563\) 38.6963i 0.0687323i −0.999409 0.0343661i \(-0.989059\pi\)
0.999409 0.0343661i \(-0.0109412\pi\)
\(564\) −226.199 −0.401062
\(565\) 90.2702 0.159770
\(566\) 70.3537i 0.124300i
\(567\) 113.682i 0.200498i
\(568\) 288.205 0.507403
\(569\) 426.562i 0.749670i −0.927092 0.374835i \(-0.877699\pi\)
0.927092 0.374835i \(-0.122301\pi\)
\(570\) −31.7936 −0.0557783
\(571\) 761.099i 1.33292i 0.745539 + 0.666462i \(0.232192\pi\)
−0.745539 + 0.666462i \(0.767808\pi\)
\(572\) 287.293i 0.502260i
\(573\) 218.918i 0.382056i
\(574\) 1.56380i 0.00272439i
\(575\) 55.9266 + 100.485i 0.0972637 + 0.174756i
\(576\) 24.0000 0.0416667
\(577\) 194.028 0.336270 0.168135 0.985764i \(-0.446226\pi\)
0.168135 + 0.985764i \(0.446226\pi\)
\(578\) 614.721 1.06353
\(579\) 206.613 0.356845
\(580\) 227.117i 0.391582i
\(581\) −1740.75 −2.99613
\(582\) 50.6131i 0.0869641i
\(583\) −238.154 −0.408498
\(584\) 314.177 0.537975
\(585\) 144.982i 0.247833i
\(586\) 52.4978i 0.0895867i
\(587\) 575.615 0.980605 0.490302 0.871552i \(-0.336886\pi\)
0.490302 + 0.871552i \(0.336886\pi\)
\(588\) 382.959 0.651291
\(589\) 4.58893i 0.00779104i
\(590\) 88.8106i 0.150526i
\(591\) −55.5714 −0.0940295
\(592\) 47.1496i 0.0796446i
\(593\) 270.936 0.456890 0.228445 0.973557i \(-0.426636\pi\)
0.228445 + 0.973557i \(0.426636\pi\)
\(594\) 48.8409i 0.0822237i
\(595\) 759.812i 1.27699i
\(596\) 10.4526i 0.0175380i
\(597\) 535.163i 0.896420i
\(598\) −341.879 614.262i −0.571703 1.02719i
\(599\) 421.554 0.703762 0.351881 0.936045i \(-0.385542\pi\)
0.351881 + 0.936045i \(0.385542\pi\)
\(600\) −24.4949 −0.0408248
\(601\) 732.875 1.21943 0.609713 0.792622i \(-0.291285\pi\)
0.609713 + 0.792622i \(0.291285\pi\)
\(602\) −1401.48 −2.32804
\(603\) 71.8820i 0.119207i
\(604\) −555.273 −0.919326
\(605\) 171.787i 0.283945i
\(606\) 269.004 0.443900
\(607\) −128.402 −0.211536 −0.105768 0.994391i \(-0.533730\pi\)
−0.105768 + 0.994391i \(0.533730\pi\)
\(608\) 32.8363i 0.0540071i
\(609\) 1111.08i 1.82443i
\(610\) −59.0550 −0.0968115
\(611\) −1411.26 −2.30976
\(612\) 161.407i 0.263737i
\(613\) 863.292i 1.40831i 0.710048 + 0.704153i \(0.248673\pi\)
−0.710048 + 0.704153i \(0.751327\pi\)
\(614\) 0.881672 0.00143595
\(615\) 0.339049i 0.000551299i
\(616\) 237.455 0.385479
\(617\) 883.691i 1.43224i 0.697978 + 0.716119i \(0.254083\pi\)
−0.697978 + 0.716119i \(0.745917\pi\)
\(618\) 22.0671i 0.0357073i
\(619\) 265.802i 0.429405i −0.976680 0.214702i \(-0.931122\pi\)
0.976680 0.214702i \(-0.0688782\pi\)
\(620\) 3.53546i 0.00570236i
\(621\) 58.1207 + 104.427i 0.0935921 + 0.168159i
\(622\) −167.287 −0.268950
\(623\) 590.539 0.947895
\(624\) 149.737 0.239963
\(625\) 25.0000 0.0400000
\(626\) 449.816i 0.718556i
\(627\) 66.8231 0.106576
\(628\) 376.659i 0.599776i
\(629\) −317.095 −0.504125
\(630\) 119.831 0.190209
\(631\) 610.986i 0.968283i 0.874990 + 0.484141i \(0.160868\pi\)
−0.874990 + 0.484141i \(0.839132\pi\)
\(632\) 237.865i 0.376368i
\(633\) −493.487 −0.779600
\(634\) 412.369 0.650424
\(635\) 496.411i 0.781750i
\(636\) 124.126i 0.195166i
\(637\) 2389.30 3.75086
\(638\) 477.350i 0.748198i
\(639\) −305.687 −0.478384
\(640\) 25.2982i 0.0395285i
\(641\) 722.476i 1.12711i 0.826079 + 0.563554i \(0.190566\pi\)
−0.826079 + 0.563554i \(0.809434\pi\)
\(642\) 412.647i 0.642752i
\(643\) 912.834i 1.41965i 0.704379 + 0.709824i \(0.251226\pi\)
−0.704379 + 0.709824i \(0.748774\pi\)
\(644\) 507.704 282.571i 0.788360 0.438776i
\(645\) −303.856 −0.471095
\(646\) 220.834 0.341848
\(647\) 378.045 0.584305 0.292153 0.956372i \(-0.405628\pi\)
0.292153 + 0.956372i \(0.405628\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 186.660i 0.287612i
\(650\) −152.825 −0.235115
\(651\) 17.2958i 0.0265681i
\(652\) −239.135 −0.366772
\(653\) −165.523 −0.253481 −0.126740 0.991936i \(-0.540451\pi\)
−0.126740 + 0.991936i \(0.540451\pi\)
\(654\) 80.5140i 0.123110i
\(655\) 232.724i 0.355303i
\(656\) −0.350168 −0.000533793
\(657\) −333.235 −0.507208
\(658\) 1166.45i 1.77271i
\(659\) 396.351i 0.601443i 0.953712 + 0.300721i \(0.0972274\pi\)
−0.953712 + 0.300721i \(0.902773\pi\)
\(660\) 51.4828 0.0780042
\(661\) 631.845i 0.955893i −0.878389 0.477946i \(-0.841381\pi\)
0.878389 0.477946i \(-0.158619\pi\)
\(662\) −90.8765 −0.137276
\(663\) 1007.02i 1.51889i
\(664\) 389.791i 0.587035i
\(665\) 163.951i 0.246543i
\(666\) 50.0097i 0.0750896i
\(667\) −568.047 1020.62i −0.851645 1.53017i
\(668\) 212.518 0.318140
\(669\) 100.671 0.150479
\(670\) 75.7703 0.113090
\(671\) 124.120 0.184978
\(672\) 123.761i 0.184169i
\(673\) 197.566 0.293560 0.146780 0.989169i \(-0.453109\pi\)
0.146780 + 0.989169i \(0.453109\pi\)
\(674\) 499.724i 0.741431i
\(675\) 25.9808 0.0384900
\(676\) 596.214 0.881974
\(677\) 493.179i 0.728478i 0.931306 + 0.364239i \(0.118671\pi\)
−0.931306 + 0.364239i \(0.881329\pi\)
\(678\) 98.8861i 0.145850i
\(679\) 260.998 0.384386
\(680\) 170.138 0.250203
\(681\) 107.304i 0.157568i
\(682\) 7.43075i 0.0108955i
\(683\) 13.6542 0.0199914 0.00999572 0.999950i \(-0.496818\pi\)
0.00999572 + 0.999950i \(0.496818\pi\)
\(684\) 34.8282i 0.0509184i
\(685\) −343.782 −0.501872
\(686\) 1099.51i 1.60278i
\(687\) 474.877i 0.691233i
\(688\) 313.821i 0.456135i
\(689\) 774.426i 1.12399i
\(690\) 110.076 61.2646i 0.159530 0.0887892i
\(691\) −753.863 −1.09097 −0.545487 0.838119i \(-0.683655\pi\)
−0.545487 + 0.838119i \(0.683655\pi\)
\(692\) 686.806 0.992494
\(693\) −251.859 −0.363433
\(694\) 600.615 0.865440
\(695\) 80.2492i 0.115467i
\(696\) 248.795 0.357464
\(697\) 2.35498i 0.00337874i
\(698\) 157.135 0.225122
\(699\) 21.5711 0.0308600
\(700\) 126.313i 0.180448i
\(701\) 1093.76i 1.56029i 0.625601 + 0.780143i \(0.284854\pi\)
−0.625601 + 0.780143i \(0.715146\pi\)
\(702\) −158.820 −0.226239
\(703\) −68.4223 −0.0973290
\(704\) 53.1712i 0.0755273i
\(705\) 252.898i 0.358721i
\(706\) 432.882 0.613147
\(707\) 1387.18i 1.96206i
\(708\) 97.2871 0.137411
\(709\) 968.137i 1.36550i −0.730654 0.682748i \(-0.760785\pi\)
0.730654 0.682748i \(-0.239215\pi\)
\(710\) 322.223i 0.453835i
\(711\) 252.294i 0.354843i
\(712\) 132.234i 0.185722i
\(713\) −8.84260 15.8877i −0.0124020 0.0222829i
\(714\) −832.332 −1.16573
\(715\) 321.203 0.449235
\(716\) 345.563 0.482630
\(717\) 603.963 0.842347
\(718\) 109.687i 0.152767i
\(719\) −831.863 −1.15697 −0.578486 0.815692i \(-0.696356\pi\)
−0.578486 + 0.815692i \(0.696356\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −113.794 −0.157828
\(722\) −462.880 −0.641108
\(723\) 576.999i 0.798062i
\(724\) 41.0671i 0.0567226i
\(725\) −253.925 −0.350241
\(726\) 188.183 0.259205
\(727\) 961.589i 1.32268i −0.750086 0.661340i \(-0.769988\pi\)
0.750086 0.661340i \(-0.230012\pi\)
\(728\) 772.152i 1.06065i
\(729\) 27.0000 0.0370370
\(730\) 351.261i 0.481179i
\(731\) 2110.54 2.88720
\(732\) 64.6915i 0.0883764i
\(733\) 817.386i 1.11512i −0.830135 0.557562i \(-0.811737\pi\)
0.830135 0.557562i \(-0.188263\pi\)
\(734\) 121.268i 0.165215i
\(735\) 428.162i 0.582533i
\(736\) 63.2738 + 113.686i 0.0859698 + 0.154464i
\(737\) −159.252 −0.216082
\(738\) 0.371409 0.000503265
\(739\) 1419.01 1.92018 0.960088 0.279698i \(-0.0902343\pi\)
0.960088 + 0.279698i \(0.0902343\pi\)
\(740\) −52.7148 −0.0712363
\(741\) 217.294i 0.293245i
\(742\) 640.083 0.862645
\(743\) 406.342i 0.546894i −0.961887 0.273447i \(-0.911836\pi\)
0.961887 0.273447i \(-0.0881638\pi\)
\(744\) 3.87291 0.00520552
\(745\) −11.6864 −0.0156865
\(746\) 204.608i 0.274274i
\(747\) 413.436i 0.553462i
\(748\) −357.592 −0.478064
\(749\) 2127.91 2.84099
\(750\) 27.3861i 0.0365148i
\(751\) 1221.72i 1.62679i 0.581713 + 0.813394i \(0.302383\pi\)
−0.581713 + 0.813394i \(0.697617\pi\)
\(752\) 261.192 0.347330
\(753\) 378.703i 0.502926i
\(754\) 1552.24 2.05867
\(755\) 620.814i 0.822271i
\(756\) 131.269i 0.173636i
\(757\) 113.386i 0.149784i −0.997192 0.0748919i \(-0.976139\pi\)
0.997192 0.0748919i \(-0.0238612\pi\)
\(758\) 429.760i 0.566965i
\(759\) −231.354 + 128.764i −0.304815 + 0.169650i
\(760\) 36.7121 0.0483054
\(761\) −224.399 −0.294874 −0.147437 0.989071i \(-0.547102\pi\)
−0.147437 + 0.989071i \(0.547102\pi\)
\(762\) −543.791 −0.713637
\(763\) 415.188 0.544153
\(764\) 252.785i 0.330870i
\(765\) −180.459 −0.235894
\(766\) 305.424i 0.398726i
\(767\) 606.978 0.791366
\(768\) −27.7128 −0.0360844
\(769\) 1448.92i 1.88417i 0.335379 + 0.942083i \(0.391135\pi\)
−0.335379 + 0.942083i \(0.608865\pi\)
\(770\) 265.483i 0.344783i
\(771\) −755.871 −0.980377
\(772\) −238.576 −0.309037
\(773\) 422.972i 0.547182i 0.961846 + 0.273591i \(0.0882115\pi\)
−0.961846 + 0.273591i \(0.911789\pi\)
\(774\) 332.858i 0.430049i
\(775\) −3.95277 −0.00510035
\(776\) 58.4430i 0.0753132i
\(777\) 257.886 0.331900
\(778\) 58.4268i 0.0750987i
\(779\) 0.508155i 0.000652317i
\(780\) 167.411i 0.214629i
\(781\) 677.240i 0.867145i
\(782\) −764.570 + 425.535i −0.977711 + 0.544162i
\(783\) −263.887 −0.337020
\(784\) −442.203 −0.564035
\(785\) −421.118 −0.536456
\(786\) −254.936 −0.324346
\(787\) 588.517i 0.747798i 0.927469 + 0.373899i \(0.121979\pi\)
−0.927469 + 0.373899i \(0.878021\pi\)
\(788\) 64.1683 0.0814319
\(789\) 747.580i 0.947503i
\(790\) −265.941 −0.336634
\(791\) 509.928 0.644663
\(792\) 56.3966i