Properties

Label 75.3.d.b.74.2
Level $75$
Weight $3$
Character 75.74
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.2
Root \(0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.3.d.b.74.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23607 q^{2} +(-2.23607 + 2.00000i) q^{3} +1.00000 q^{4} +(5.00000 - 4.47214i) q^{6} -6.00000i q^{7} +6.70820 q^{8} +(1.00000 - 8.94427i) q^{9} +O(q^{10})\) \(q-2.23607 q^{2} +(-2.23607 + 2.00000i) q^{3} +1.00000 q^{4} +(5.00000 - 4.47214i) q^{6} -6.00000i q^{7} +6.70820 q^{8} +(1.00000 - 8.94427i) q^{9} -4.47214i q^{11} +(-2.23607 + 2.00000i) q^{12} -16.0000i q^{13} +13.4164i q^{14} -19.0000 q^{16} +4.47214 q^{17} +(-2.23607 + 20.0000i) q^{18} +2.00000 q^{19} +(12.0000 + 13.4164i) q^{21} +10.0000i q^{22} -13.4164 q^{23} +(-15.0000 + 13.4164i) q^{24} +35.7771i q^{26} +(15.6525 + 22.0000i) q^{27} -6.00000i q^{28} -31.3050i q^{29} -18.0000 q^{31} +15.6525 q^{32} +(8.94427 + 10.0000i) q^{33} -10.0000 q^{34} +(1.00000 - 8.94427i) q^{36} -16.0000i q^{37} -4.47214 q^{38} +(32.0000 + 35.7771i) q^{39} -62.6099i q^{41} +(-26.8328 - 30.0000i) q^{42} -16.0000i q^{43} -4.47214i q^{44} +30.0000 q^{46} -49.1935 q^{47} +(42.4853 - 38.0000i) q^{48} +13.0000 q^{49} +(-10.0000 + 8.94427i) q^{51} -16.0000i q^{52} -4.47214 q^{53} +(-35.0000 - 49.1935i) q^{54} -40.2492i q^{56} +(-4.47214 + 4.00000i) q^{57} +70.0000i q^{58} +4.47214i q^{59} +82.0000 q^{61} +40.2492 q^{62} +(-53.6656 - 6.00000i) q^{63} +41.0000 q^{64} +(-20.0000 - 22.3607i) q^{66} +24.0000i q^{67} +4.47214 q^{68} +(30.0000 - 26.8328i) q^{69} +125.220i q^{71} +(6.70820 - 60.0000i) q^{72} +74.0000i q^{73} +35.7771i q^{74} +2.00000 q^{76} -26.8328 q^{77} +(-71.5542 - 80.0000i) q^{78} -138.000 q^{79} +(-79.0000 - 17.8885i) q^{81} +140.000i q^{82} +93.9149 q^{83} +(12.0000 + 13.4164i) q^{84} +35.7771i q^{86} +(62.6099 + 70.0000i) q^{87} -30.0000i q^{88} +107.331i q^{89} -96.0000 q^{91} -13.4164 q^{92} +(40.2492 - 36.0000i) q^{93} +110.000 q^{94} +(-35.0000 + 31.3050i) q^{96} -166.000i q^{97} -29.0689 q^{98} +(-40.0000 - 4.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + 20q^{6} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{4} + 20q^{6} + 4q^{9} - 76q^{16} + 8q^{19} + 48q^{21} - 60q^{24} - 72q^{31} - 40q^{34} + 4q^{36} + 128q^{39} + 120q^{46} + 52q^{49} - 40q^{51} - 140q^{54} + 328q^{61} + 164q^{64} - 80q^{66} + 120q^{69} + 8q^{76} - 552q^{79} - 316q^{81} + 48q^{84} - 384q^{91} + 440q^{94} - 140q^{96} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23607 −1.11803 −0.559017 0.829156i \(-0.688821\pi\)
−0.559017 + 0.829156i \(0.688821\pi\)
\(3\) −2.23607 + 2.00000i −0.745356 + 0.666667i
\(4\) 1.00000 0.250000
\(5\) 0 0
\(6\) 5.00000 4.47214i 0.833333 0.745356i
\(7\) 6.00000i 0.857143i −0.903508 0.428571i \(-0.859017\pi\)
0.903508 0.428571i \(-0.140983\pi\)
\(8\) 6.70820 0.838525
\(9\) 1.00000 8.94427i 0.111111 0.993808i
\(10\) 0 0
\(11\) 4.47214i 0.406558i −0.979121 0.203279i \(-0.934840\pi\)
0.979121 0.203279i \(-0.0651598\pi\)
\(12\) −2.23607 + 2.00000i −0.186339 + 0.166667i
\(13\) 16.0000i 1.23077i −0.788227 0.615385i \(-0.789001\pi\)
0.788227 0.615385i \(-0.210999\pi\)
\(14\) 13.4164i 0.958315i
\(15\) 0 0
\(16\) −19.0000 −1.18750
\(17\) 4.47214 0.263067 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(18\) −2.23607 + 20.0000i −0.124226 + 1.11111i
\(19\) 2.00000 0.105263 0.0526316 0.998614i \(-0.483239\pi\)
0.0526316 + 0.998614i \(0.483239\pi\)
\(20\) 0 0
\(21\) 12.0000 + 13.4164i 0.571429 + 0.638877i
\(22\) 10.0000i 0.454545i
\(23\) −13.4164 −0.583322 −0.291661 0.956522i \(-0.594208\pi\)
−0.291661 + 0.956522i \(0.594208\pi\)
\(24\) −15.0000 + 13.4164i −0.625000 + 0.559017i
\(25\) 0 0
\(26\) 35.7771i 1.37604i
\(27\) 15.6525 + 22.0000i 0.579721 + 0.814815i
\(28\) 6.00000i 0.214286i
\(29\) 31.3050i 1.07948i −0.841831 0.539741i \(-0.818522\pi\)
0.841831 0.539741i \(-0.181478\pi\)
\(30\) 0 0
\(31\) −18.0000 −0.580645 −0.290323 0.956929i \(-0.593763\pi\)
−0.290323 + 0.956929i \(0.593763\pi\)
\(32\) 15.6525 0.489140
\(33\) 8.94427 + 10.0000i 0.271039 + 0.303030i
\(34\) −10.0000 −0.294118
\(35\) 0 0
\(36\) 1.00000 8.94427i 0.0277778 0.248452i
\(37\) 16.0000i 0.432432i −0.976346 0.216216i \(-0.930628\pi\)
0.976346 0.216216i \(-0.0693716\pi\)
\(38\) −4.47214 −0.117688
\(39\) 32.0000 + 35.7771i 0.820513 + 0.917361i
\(40\) 0 0
\(41\) 62.6099i 1.52707i −0.645766 0.763535i \(-0.723462\pi\)
0.645766 0.763535i \(-0.276538\pi\)
\(42\) −26.8328 30.0000i −0.638877 0.714286i
\(43\) 16.0000i 0.372093i −0.982541 0.186047i \(-0.940432\pi\)
0.982541 0.186047i \(-0.0595675\pi\)
\(44\) 4.47214i 0.101639i
\(45\) 0 0
\(46\) 30.0000 0.652174
\(47\) −49.1935 −1.04667 −0.523335 0.852127i \(-0.675312\pi\)
−0.523335 + 0.852127i \(0.675312\pi\)
\(48\) 42.4853 38.0000i 0.885110 0.791667i
\(49\) 13.0000 0.265306
\(50\) 0 0
\(51\) −10.0000 + 8.94427i −0.196078 + 0.175378i
\(52\) 16.0000i 0.307692i
\(53\) −4.47214 −0.0843799 −0.0421900 0.999110i \(-0.513433\pi\)
−0.0421900 + 0.999110i \(0.513433\pi\)
\(54\) −35.0000 49.1935i −0.648148 0.910991i
\(55\) 0 0
\(56\) 40.2492i 0.718736i
\(57\) −4.47214 + 4.00000i −0.0784585 + 0.0701754i
\(58\) 70.0000i 1.20690i
\(59\) 4.47214i 0.0757989i 0.999282 + 0.0378995i \(0.0120667\pi\)
−0.999282 + 0.0378995i \(0.987933\pi\)
\(60\) 0 0
\(61\) 82.0000 1.34426 0.672131 0.740432i \(-0.265379\pi\)
0.672131 + 0.740432i \(0.265379\pi\)
\(62\) 40.2492 0.649181
\(63\) −53.6656 6.00000i −0.851835 0.0952381i
\(64\) 41.0000 0.640625
\(65\) 0 0
\(66\) −20.0000 22.3607i −0.303030 0.338798i
\(67\) 24.0000i 0.358209i 0.983830 + 0.179104i \(0.0573200\pi\)
−0.983830 + 0.179104i \(0.942680\pi\)
\(68\) 4.47214 0.0657667
\(69\) 30.0000 26.8328i 0.434783 0.388881i
\(70\) 0 0
\(71\) 125.220i 1.76366i 0.471568 + 0.881830i \(0.343688\pi\)
−0.471568 + 0.881830i \(0.656312\pi\)
\(72\) 6.70820 60.0000i 0.0931695 0.833333i
\(73\) 74.0000i 1.01370i 0.862035 + 0.506849i \(0.169190\pi\)
−0.862035 + 0.506849i \(0.830810\pi\)
\(74\) 35.7771i 0.483474i
\(75\) 0 0
\(76\) 2.00000 0.0263158
\(77\) −26.8328 −0.348478
\(78\) −71.5542 80.0000i −0.917361 1.02564i
\(79\) −138.000 −1.74684 −0.873418 0.486972i \(-0.838101\pi\)
−0.873418 + 0.486972i \(0.838101\pi\)
\(80\) 0 0
\(81\) −79.0000 17.8885i −0.975309 0.220846i
\(82\) 140.000i 1.70732i
\(83\) 93.9149 1.13150 0.565752 0.824575i \(-0.308586\pi\)
0.565752 + 0.824575i \(0.308586\pi\)
\(84\) 12.0000 + 13.4164i 0.142857 + 0.159719i
\(85\) 0 0
\(86\) 35.7771i 0.416013i
\(87\) 62.6099 + 70.0000i 0.719654 + 0.804598i
\(88\) 30.0000i 0.340909i
\(89\) 107.331i 1.20597i 0.797753 + 0.602985i \(0.206022\pi\)
−0.797753 + 0.602985i \(0.793978\pi\)
\(90\) 0 0
\(91\) −96.0000 −1.05495
\(92\) −13.4164 −0.145831
\(93\) 40.2492 36.0000i 0.432787 0.387097i
\(94\) 110.000 1.17021
\(95\) 0 0
\(96\) −35.0000 + 31.3050i −0.364583 + 0.326093i
\(97\) 166.000i 1.71134i −0.517522 0.855670i \(-0.673145\pi\)
0.517522 0.855670i \(-0.326855\pi\)
\(98\) −29.0689 −0.296621
\(99\) −40.0000 4.47214i −0.404040 0.0451731i
\(100\) 0 0
\(101\) 67.0820i 0.664179i −0.943248 0.332089i \(-0.892246\pi\)
0.943248 0.332089i \(-0.107754\pi\)
\(102\) 22.3607 20.0000i 0.219222 0.196078i
\(103\) 26.0000i 0.252427i −0.992003 0.126214i \(-0.959718\pi\)
0.992003 0.126214i \(-0.0402825\pi\)
\(104\) 107.331i 1.03203i
\(105\) 0 0
\(106\) 10.0000 0.0943396
\(107\) 201.246 1.88080 0.940402 0.340064i \(-0.110449\pi\)
0.940402 + 0.340064i \(0.110449\pi\)
\(108\) 15.6525 + 22.0000i 0.144930 + 0.203704i
\(109\) −38.0000 −0.348624 −0.174312 0.984690i \(-0.555770\pi\)
−0.174312 + 0.984690i \(0.555770\pi\)
\(110\) 0 0
\(111\) 32.0000 + 35.7771i 0.288288 + 0.322316i
\(112\) 114.000i 1.01786i
\(113\) −31.3050 −0.277035 −0.138517 0.990360i \(-0.544234\pi\)
−0.138517 + 0.990360i \(0.544234\pi\)
\(114\) 10.0000 8.94427i 0.0877193 0.0784585i
\(115\) 0 0
\(116\) 31.3050i 0.269870i
\(117\) −143.108 16.0000i −1.22315 0.136752i
\(118\) 10.0000i 0.0847458i
\(119\) 26.8328i 0.225486i
\(120\) 0 0
\(121\) 101.000 0.834711
\(122\) −183.358 −1.50293
\(123\) 125.220 + 140.000i 1.01805 + 1.13821i
\(124\) −18.0000 −0.145161
\(125\) 0 0
\(126\) 120.000 + 13.4164i 0.952381 + 0.106479i
\(127\) 26.0000i 0.204724i −0.994747 0.102362i \(-0.967360\pi\)
0.994747 0.102362i \(-0.0326401\pi\)
\(128\) −154.289 −1.20538
\(129\) 32.0000 + 35.7771i 0.248062 + 0.277342i
\(130\) 0 0
\(131\) 13.4164i 0.102415i −0.998688 0.0512077i \(-0.983693\pi\)
0.998688 0.0512077i \(-0.0163070\pi\)
\(132\) 8.94427 + 10.0000i 0.0677596 + 0.0757576i
\(133\) 12.0000i 0.0902256i
\(134\) 53.6656i 0.400490i
\(135\) 0 0
\(136\) 30.0000 0.220588
\(137\) −120.748 −0.881370 −0.440685 0.897662i \(-0.645264\pi\)
−0.440685 + 0.897662i \(0.645264\pi\)
\(138\) −67.0820 + 60.0000i −0.486102 + 0.434783i
\(139\) 82.0000 0.589928 0.294964 0.955508i \(-0.404692\pi\)
0.294964 + 0.955508i \(0.404692\pi\)
\(140\) 0 0
\(141\) 110.000 98.3870i 0.780142 0.697780i
\(142\) 280.000i 1.97183i
\(143\) −71.5542 −0.500379
\(144\) −19.0000 + 169.941i −0.131944 + 1.18015i
\(145\) 0 0
\(146\) 165.469i 1.13335i
\(147\) −29.0689 + 26.0000i −0.197748 + 0.176871i
\(148\) 16.0000i 0.108108i
\(149\) 111.803i 0.750358i −0.926952 0.375179i \(-0.877581\pi\)
0.926952 0.375179i \(-0.122419\pi\)
\(150\) 0 0
\(151\) −158.000 −1.04636 −0.523179 0.852223i \(-0.675254\pi\)
−0.523179 + 0.852223i \(0.675254\pi\)
\(152\) 13.4164 0.0882658
\(153\) 4.47214 40.0000i 0.0292296 0.261438i
\(154\) 60.0000 0.389610
\(155\) 0 0
\(156\) 32.0000 + 35.7771i 0.205128 + 0.229340i
\(157\) 164.000i 1.04459i 0.852766 + 0.522293i \(0.174923\pi\)
−0.852766 + 0.522293i \(0.825077\pi\)
\(158\) 308.577 1.95302
\(159\) 10.0000 8.94427i 0.0628931 0.0562533i
\(160\) 0 0
\(161\) 80.4984i 0.499990i
\(162\) 176.649 + 40.0000i 1.09043 + 0.246914i
\(163\) 236.000i 1.44785i −0.689877 0.723926i \(-0.742336\pi\)
0.689877 0.723926i \(-0.257664\pi\)
\(164\) 62.6099i 0.381768i
\(165\) 0 0
\(166\) −210.000 −1.26506
\(167\) 93.9149 0.562364 0.281182 0.959654i \(-0.409273\pi\)
0.281182 + 0.959654i \(0.409273\pi\)
\(168\) 80.4984 + 90.0000i 0.479157 + 0.535714i
\(169\) −87.0000 −0.514793
\(170\) 0 0
\(171\) 2.00000 17.8885i 0.0116959 0.104611i
\(172\) 16.0000i 0.0930233i
\(173\) −13.4164 −0.0775515 −0.0387757 0.999248i \(-0.512346\pi\)
−0.0387757 + 0.999248i \(0.512346\pi\)
\(174\) −140.000 156.525i −0.804598 0.899568i
\(175\) 0 0
\(176\) 84.9706i 0.482787i
\(177\) −8.94427 10.0000i −0.0505326 0.0564972i
\(178\) 240.000i 1.34831i
\(179\) 192.302i 1.07431i 0.843483 + 0.537156i \(0.180501\pi\)
−0.843483 + 0.537156i \(0.819499\pi\)
\(180\) 0 0
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) 214.663 1.17946
\(183\) −183.358 + 164.000i −1.00195 + 0.896175i
\(184\) −90.0000 −0.489130
\(185\) 0 0
\(186\) −90.0000 + 80.4984i −0.483871 + 0.432787i
\(187\) 20.0000i 0.106952i
\(188\) −49.1935 −0.261668
\(189\) 132.000 93.9149i 0.698413 0.496904i
\(190\) 0 0
\(191\) 205.718i 1.07706i 0.842607 + 0.538529i \(0.181020\pi\)
−0.842607 + 0.538529i \(0.818980\pi\)
\(192\) −91.6788 + 82.0000i −0.477494 + 0.427083i
\(193\) 214.000i 1.10881i 0.832248 + 0.554404i \(0.187054\pi\)
−0.832248 + 0.554404i \(0.812946\pi\)
\(194\) 371.187i 1.91334i
\(195\) 0 0
\(196\) 13.0000 0.0663265
\(197\) −93.9149 −0.476725 −0.238363 0.971176i \(-0.576611\pi\)
−0.238363 + 0.971176i \(0.576611\pi\)
\(198\) 89.4427 + 10.0000i 0.451731 + 0.0505051i
\(199\) 242.000 1.21608 0.608040 0.793906i \(-0.291956\pi\)
0.608040 + 0.793906i \(0.291956\pi\)
\(200\) 0 0
\(201\) −48.0000 53.6656i −0.238806 0.266993i
\(202\) 150.000i 0.742574i
\(203\) −187.830 −0.925270
\(204\) −10.0000 + 8.94427i −0.0490196 + 0.0438445i
\(205\) 0 0
\(206\) 58.1378i 0.282222i
\(207\) −13.4164 + 120.000i −0.0648136 + 0.579710i
\(208\) 304.000i 1.46154i
\(209\) 8.94427i 0.0427956i
\(210\) 0 0
\(211\) 2.00000 0.00947867 0.00473934 0.999989i \(-0.498491\pi\)
0.00473934 + 0.999989i \(0.498491\pi\)
\(212\) −4.47214 −0.0210950
\(213\) −250.440 280.000i −1.17577 1.31455i
\(214\) −450.000 −2.10280
\(215\) 0 0
\(216\) 105.000 + 147.580i 0.486111 + 0.683243i
\(217\) 108.000i 0.497696i
\(218\) 84.9706 0.389773
\(219\) −148.000 165.469i −0.675799 0.755566i
\(220\) 0 0
\(221\) 71.5542i 0.323775i
\(222\) −71.5542 80.0000i −0.322316 0.360360i
\(223\) 86.0000i 0.385650i −0.981233 0.192825i \(-0.938235\pi\)
0.981233 0.192825i \(-0.0617650\pi\)
\(224\) 93.9149i 0.419263i
\(225\) 0 0
\(226\) 70.0000 0.309735
\(227\) −58.1378 −0.256114 −0.128057 0.991767i \(-0.540874\pi\)
−0.128057 + 0.991767i \(0.540874\pi\)
\(228\) −4.47214 + 4.00000i −0.0196146 + 0.0175439i
\(229\) 282.000 1.23144 0.615721 0.787965i \(-0.288865\pi\)
0.615721 + 0.787965i \(0.288865\pi\)
\(230\) 0 0
\(231\) 60.0000 53.6656i 0.259740 0.232319i
\(232\) 210.000i 0.905172i
\(233\) 362.243 1.55469 0.777346 0.629074i \(-0.216566\pi\)
0.777346 + 0.629074i \(0.216566\pi\)
\(234\) 320.000 + 35.7771i 1.36752 + 0.152894i
\(235\) 0 0
\(236\) 4.47214i 0.0189497i
\(237\) 308.577 276.000i 1.30201 1.16456i
\(238\) 60.0000i 0.252101i
\(239\) 250.440i 1.04786i −0.851760 0.523932i \(-0.824464\pi\)
0.851760 0.523932i \(-0.175536\pi\)
\(240\) 0 0
\(241\) 262.000 1.08714 0.543568 0.839365i \(-0.317073\pi\)
0.543568 + 0.839365i \(0.317073\pi\)
\(242\) −225.843 −0.933235
\(243\) 212.426 118.000i 0.874183 0.485597i
\(244\) 82.0000 0.336066
\(245\) 0 0
\(246\) −280.000 313.050i −1.13821 1.27256i
\(247\) 32.0000i 0.129555i
\(248\) −120.748 −0.486886
\(249\) −210.000 + 187.830i −0.843373 + 0.754336i
\(250\) 0 0
\(251\) 469.574i 1.87081i −0.353573 0.935407i \(-0.615033\pi\)
0.353573 0.935407i \(-0.384967\pi\)
\(252\) −53.6656 6.00000i −0.212959 0.0238095i
\(253\) 60.0000i 0.237154i
\(254\) 58.1378i 0.228889i
\(255\) 0 0
\(256\) 181.000 0.707031
\(257\) 201.246 0.783059 0.391529 0.920166i \(-0.371946\pi\)
0.391529 + 0.920166i \(0.371946\pi\)
\(258\) −71.5542 80.0000i −0.277342 0.310078i
\(259\) −96.0000 −0.370656
\(260\) 0 0
\(261\) −280.000 31.3050i −1.07280 0.119942i
\(262\) 30.0000i 0.114504i
\(263\) 58.1378 0.221056 0.110528 0.993873i \(-0.464746\pi\)
0.110528 + 0.993873i \(0.464746\pi\)
\(264\) 60.0000 + 67.0820i 0.227273 + 0.254099i
\(265\) 0 0
\(266\) 26.8328i 0.100875i
\(267\) −214.663 240.000i −0.803979 0.898876i
\(268\) 24.0000i 0.0895522i
\(269\) 371.187i 1.37988i −0.723867 0.689939i \(-0.757637\pi\)
0.723867 0.689939i \(-0.242363\pi\)
\(270\) 0 0
\(271\) 82.0000 0.302583 0.151292 0.988489i \(-0.451657\pi\)
0.151292 + 0.988489i \(0.451657\pi\)
\(272\) −84.9706 −0.312392
\(273\) 214.663 192.000i 0.786310 0.703297i
\(274\) 270.000 0.985401
\(275\) 0 0
\(276\) 30.0000 26.8328i 0.108696 0.0972203i
\(277\) 24.0000i 0.0866426i 0.999061 + 0.0433213i \(0.0137939\pi\)
−0.999061 + 0.0433213i \(0.986206\pi\)
\(278\) −183.358 −0.659560
\(279\) −18.0000 + 160.997i −0.0645161 + 0.577050i
\(280\) 0 0
\(281\) 187.830i 0.668433i 0.942496 + 0.334217i \(0.108472\pi\)
−0.942496 + 0.334217i \(0.891528\pi\)
\(282\) −245.967 + 220.000i −0.872225 + 0.780142i
\(283\) 144.000i 0.508834i 0.967095 + 0.254417i \(0.0818836\pi\)
−0.967095 + 0.254417i \(0.918116\pi\)
\(284\) 125.220i 0.440915i
\(285\) 0 0
\(286\) 160.000 0.559441
\(287\) −375.659 −1.30892
\(288\) 15.6525 140.000i 0.0543489 0.486111i
\(289\) −269.000 −0.930796
\(290\) 0 0
\(291\) 332.000 + 371.187i 1.14089 + 1.27556i
\(292\) 74.0000i 0.253425i
\(293\) −469.574 −1.60264 −0.801321 0.598234i \(-0.795869\pi\)
−0.801321 + 0.598234i \(0.795869\pi\)
\(294\) 65.0000 58.1378i 0.221088 0.197748i
\(295\) 0 0
\(296\) 107.331i 0.362606i
\(297\) 98.3870 70.0000i 0.331269 0.235690i
\(298\) 250.000i 0.838926i
\(299\) 214.663i 0.717935i
\(300\) 0 0
\(301\) −96.0000 −0.318937
\(302\) 353.299 1.16986
\(303\) 134.164 + 150.000i 0.442786 + 0.495050i
\(304\) −38.0000 −0.125000
\(305\) 0 0
\(306\) −10.0000 + 89.4427i −0.0326797 + 0.292296i
\(307\) 184.000i 0.599349i 0.954042 + 0.299674i \(0.0968780\pi\)
−0.954042 + 0.299674i \(0.903122\pi\)
\(308\) −26.8328 −0.0871195
\(309\) 52.0000 + 58.1378i 0.168285 + 0.188148i
\(310\) 0 0
\(311\) 160.997i 0.517675i −0.965921 0.258837i \(-0.916661\pi\)
0.965921 0.258837i \(-0.0833394\pi\)
\(312\) 214.663 + 240.000i 0.688021 + 0.769231i
\(313\) 394.000i 1.25879i 0.777087 + 0.629393i \(0.216696\pi\)
−0.777087 + 0.629393i \(0.783304\pi\)
\(314\) 366.715i 1.16788i
\(315\) 0 0
\(316\) −138.000 −0.436709
\(317\) 451.686 1.42488 0.712438 0.701735i \(-0.247591\pi\)
0.712438 + 0.701735i \(0.247591\pi\)
\(318\) −22.3607 + 20.0000i −0.0703166 + 0.0628931i
\(319\) −140.000 −0.438871
\(320\) 0 0
\(321\) −450.000 + 402.492i −1.40187 + 1.25387i
\(322\) 180.000i 0.559006i
\(323\) 8.94427 0.0276912
\(324\) −79.0000 17.8885i −0.243827 0.0552116i
\(325\) 0 0
\(326\) 527.712i 1.61875i
\(327\) 84.9706 76.0000i 0.259849 0.232416i
\(328\) 420.000i 1.28049i
\(329\) 295.161i 0.897146i
\(330\) 0 0
\(331\) −198.000 −0.598187 −0.299094 0.954224i \(-0.596684\pi\)
−0.299094 + 0.954224i \(0.596684\pi\)
\(332\) 93.9149 0.282876
\(333\) −143.108 16.0000i −0.429755 0.0480480i
\(334\) −210.000 −0.628743
\(335\) 0 0
\(336\) −228.000 254.912i −0.678571 0.758666i
\(337\) 394.000i 1.16914i 0.811343 + 0.584570i \(0.198737\pi\)
−0.811343 + 0.584570i \(0.801263\pi\)
\(338\) 194.538 0.575556
\(339\) 70.0000 62.6099i 0.206490 0.184690i
\(340\) 0 0
\(341\) 80.4984i 0.236066i
\(342\) −4.47214 + 40.0000i −0.0130764 + 0.116959i
\(343\) 372.000i 1.08455i
\(344\) 107.331i 0.312009i
\(345\) 0 0
\(346\) 30.0000 0.0867052
\(347\) −183.358 −0.528408 −0.264204 0.964467i \(-0.585109\pi\)
−0.264204 + 0.964467i \(0.585109\pi\)
\(348\) 62.6099 + 70.0000i 0.179914 + 0.201149i
\(349\) 362.000 1.03725 0.518625 0.855002i \(-0.326444\pi\)
0.518625 + 0.855002i \(0.326444\pi\)
\(350\) 0 0
\(351\) 352.000 250.440i 1.00285 0.713503i
\(352\) 70.0000i 0.198864i
\(353\) 308.577 0.874157 0.437078 0.899423i \(-0.356013\pi\)
0.437078 + 0.899423i \(0.356013\pi\)
\(354\) 20.0000 + 22.3607i 0.0564972 + 0.0631658i
\(355\) 0 0
\(356\) 107.331i 0.301492i
\(357\) 53.6656 + 60.0000i 0.150324 + 0.168067i
\(358\) 430.000i 1.20112i
\(359\) 295.161i 0.822175i 0.911596 + 0.411088i \(0.134851\pi\)
−0.911596 + 0.411088i \(0.865149\pi\)
\(360\) 0 0
\(361\) −357.000 −0.988920
\(362\) −4.47214 −0.0123540
\(363\) −225.843 + 202.000i −0.622157 + 0.556474i
\(364\) −96.0000 −0.263736
\(365\) 0 0
\(366\) 410.000 366.715i 1.12022 1.00195i
\(367\) 186.000i 0.506812i −0.967360 0.253406i \(-0.918449\pi\)
0.967360 0.253406i \(-0.0815509\pi\)
\(368\) 254.912 0.692695
\(369\) −560.000 62.6099i −1.51762 0.169675i
\(370\) 0 0
\(371\) 26.8328i 0.0723256i
\(372\) 40.2492 36.0000i 0.108197 0.0967742i
\(373\) 44.0000i 0.117962i 0.998259 + 0.0589812i \(0.0187852\pi\)
−0.998259 + 0.0589812i \(0.981215\pi\)
\(374\) 44.7214i 0.119576i
\(375\) 0 0
\(376\) −330.000 −0.877660
\(377\) −500.879 −1.32859
\(378\) −295.161 + 210.000i −0.780849 + 0.555556i
\(379\) 362.000 0.955145 0.477573 0.878592i \(-0.341517\pi\)
0.477573 + 0.878592i \(0.341517\pi\)
\(380\) 0 0
\(381\) 52.0000 + 58.1378i 0.136483 + 0.152593i
\(382\) 460.000i 1.20419i
\(383\) 362.243 0.945804 0.472902 0.881115i \(-0.343206\pi\)
0.472902 + 0.881115i \(0.343206\pi\)
\(384\) 345.000 308.577i 0.898438 0.803587i
\(385\) 0 0
\(386\) 478.519i 1.23969i
\(387\) −143.108 16.0000i −0.369789 0.0413437i
\(388\) 166.000i 0.427835i
\(389\) 442.741i 1.13815i 0.822285 + 0.569076i \(0.192699\pi\)
−0.822285 + 0.569076i \(0.807301\pi\)
\(390\) 0 0
\(391\) −60.0000 −0.153453
\(392\) 87.2067 0.222466
\(393\) 26.8328 + 30.0000i 0.0682769 + 0.0763359i
\(394\) 210.000 0.532995
\(395\) 0 0
\(396\) −40.0000 4.47214i −0.101010 0.0112933i
\(397\) 124.000i 0.312343i 0.987730 + 0.156171i \(0.0499152\pi\)
−0.987730 + 0.156171i \(0.950085\pi\)
\(398\) −541.128 −1.35962
\(399\) 24.0000 + 26.8328i 0.0601504 + 0.0672502i
\(400\) 0 0
\(401\) 268.328i 0.669148i 0.942370 + 0.334574i \(0.108592\pi\)
−0.942370 + 0.334574i \(0.891408\pi\)
\(402\) 107.331 + 120.000i 0.266993 + 0.298507i
\(403\) 288.000i 0.714640i
\(404\) 67.0820i 0.166045i
\(405\) 0 0
\(406\) 420.000 1.03448
\(407\) −71.5542 −0.175809
\(408\) −67.0820 + 60.0000i −0.164417 + 0.147059i
\(409\) −458.000 −1.11980 −0.559902 0.828559i \(-0.689161\pi\)
−0.559902 + 0.828559i \(0.689161\pi\)
\(410\) 0 0
\(411\) 270.000 241.495i 0.656934 0.587580i
\(412\) 26.0000i 0.0631068i
\(413\) 26.8328 0.0649705
\(414\) 30.0000 268.328i 0.0724638 0.648136i
\(415\) 0 0
\(416\) 250.440i 0.602018i
\(417\) −183.358 + 164.000i −0.439706 + 0.393285i
\(418\) 20.0000i 0.0478469i
\(419\) 594.794i 1.41956i −0.704425 0.709778i \(-0.748795\pi\)
0.704425 0.709778i \(-0.251205\pi\)
\(420\) 0 0
\(421\) 562.000 1.33492 0.667458 0.744647i \(-0.267382\pi\)
0.667458 + 0.744647i \(0.267382\pi\)
\(422\) −4.47214 −0.0105975
\(423\) −49.1935 + 440.000i −0.116297 + 1.04019i
\(424\) −30.0000 −0.0707547
\(425\) 0 0
\(426\) 560.000 + 626.099i 1.31455 + 1.46972i
\(427\) 492.000i 1.15222i
\(428\) 201.246 0.470201
\(429\) 160.000 143.108i 0.372960 0.333586i
\(430\) 0 0
\(431\) 348.827i 0.809342i −0.914462 0.404671i \(-0.867386\pi\)
0.914462 0.404671i \(-0.132614\pi\)
\(432\) −297.397 418.000i −0.688419 0.967593i
\(433\) 226.000i 0.521940i −0.965347 0.260970i \(-0.915958\pi\)
0.965347 0.260970i \(-0.0840424\pi\)
\(434\) 241.495i 0.556441i
\(435\) 0 0
\(436\) −38.0000 −0.0871560
\(437\) −26.8328 −0.0614023
\(438\) 330.938 + 370.000i 0.755566 + 0.844749i
\(439\) 2.00000 0.00455581 0.00227790 0.999997i \(-0.499275\pi\)
0.00227790 + 0.999997i \(0.499275\pi\)
\(440\) 0 0
\(441\) 13.0000 116.276i 0.0294785 0.263663i
\(442\) 160.000i 0.361991i
\(443\) −201.246 −0.454280 −0.227140 0.973862i \(-0.572938\pi\)
−0.227140 + 0.973862i \(0.572938\pi\)
\(444\) 32.0000 + 35.7771i 0.0720721 + 0.0805790i
\(445\) 0 0
\(446\) 192.302i 0.431170i
\(447\) 223.607 + 250.000i 0.500239 + 0.559284i
\(448\) 246.000i 0.549107i
\(449\) 313.050i 0.697215i 0.937269 + 0.348607i \(0.113345\pi\)
−0.937269 + 0.348607i \(0.886655\pi\)
\(450\) 0 0
\(451\) −280.000 −0.620843
\(452\) −31.3050 −0.0692587
\(453\) 353.299 316.000i 0.779909 0.697572i
\(454\) 130.000 0.286344
\(455\) 0 0
\(456\) −30.0000 + 26.8328i −0.0657895 + 0.0588439i
\(457\) 334.000i 0.730853i 0.930840 + 0.365427i \(0.119077\pi\)
−0.930840 + 0.365427i \(0.880923\pi\)
\(458\) −630.571 −1.37679
\(459\) 70.0000 + 98.3870i 0.152505 + 0.214351i
\(460\) 0 0
\(461\) 93.9149i 0.203720i −0.994799 0.101860i \(-0.967521\pi\)
0.994799 0.101860i \(-0.0324794\pi\)
\(462\) −134.164 + 120.000i −0.290398 + 0.259740i
\(463\) 366.000i 0.790497i −0.918574 0.395248i \(-0.870659\pi\)
0.918574 0.395248i \(-0.129341\pi\)
\(464\) 594.794i 1.28188i
\(465\) 0 0
\(466\) −810.000 −1.73820
\(467\) 451.686 0.967207 0.483604 0.875287i \(-0.339328\pi\)
0.483604 + 0.875287i \(0.339328\pi\)
\(468\) −143.108 16.0000i −0.305787 0.0341880i
\(469\) 144.000 0.307036
\(470\) 0 0
\(471\) −328.000 366.715i −0.696391 0.778588i
\(472\) 30.0000i 0.0635593i
\(473\) −71.5542 −0.151277
\(474\) −690.000 + 617.155i −1.45570 + 1.30201i
\(475\) 0 0
\(476\) 26.8328i 0.0563715i
\(477\) −4.47214 + 40.0000i −0.00937555 + 0.0838574i
\(478\) 560.000i 1.17155i
\(479\) 590.322i 1.23240i −0.787588 0.616202i \(-0.788670\pi\)
0.787588 0.616202i \(-0.211330\pi\)
\(480\) 0 0
\(481\) −256.000 −0.532225
\(482\) −585.850 −1.21546
\(483\) −160.997 180.000i −0.333327 0.372671i
\(484\) 101.000 0.208678
\(485\) 0 0
\(486\) −475.000 + 263.856i −0.977366 + 0.542914i
\(487\) 886.000i 1.81930i −0.415374 0.909651i \(-0.636349\pi\)
0.415374 0.909651i \(-0.363651\pi\)
\(488\) 550.073 1.12720
\(489\) 472.000 + 527.712i 0.965235 + 1.07917i
\(490\) 0 0
\(491\) 406.964i 0.828848i 0.910084 + 0.414424i \(0.136017\pi\)
−0.910084 + 0.414424i \(0.863983\pi\)
\(492\) 125.220 + 140.000i 0.254512 + 0.284553i
\(493\) 140.000i 0.283976i
\(494\) 71.5542i 0.144847i
\(495\) 0 0
\(496\) 342.000 0.689516
\(497\) 751.319 1.51171
\(498\) 469.574 420.000i 0.942920 0.843373i
\(499\) 2.00000 0.00400802 0.00200401 0.999998i \(-0.499362\pi\)
0.00200401 + 0.999998i \(0.499362\pi\)
\(500\) 0 0
\(501\) −210.000 + 187.830i −0.419162 + 0.374910i
\(502\) 1050.00i 2.09163i
\(503\) 219.135 0.435655 0.217828 0.975987i \(-0.430103\pi\)
0.217828 + 0.975987i \(0.430103\pi\)
\(504\) −360.000 40.2492i −0.714286 0.0798596i
\(505\) 0 0
\(506\) 134.164i 0.265146i
\(507\) 194.538 174.000i 0.383704 0.343195i
\(508\) 26.0000i 0.0511811i
\(509\) 800.512i 1.57272i −0.617771 0.786358i \(-0.711964\pi\)
0.617771 0.786358i \(-0.288036\pi\)
\(510\) 0 0
\(511\) 444.000 0.868885
\(512\) 212.426 0.414895
\(513\) 31.3050 + 44.0000i 0.0610233 + 0.0857700i
\(514\) −450.000 −0.875486
\(515\) 0 0
\(516\) 32.0000 + 35.7771i 0.0620155 + 0.0693354i
\(517\) 220.000i 0.425532i
\(518\) 214.663 0.414406
\(519\) 30.0000 26.8328i 0.0578035 0.0517010i
\(520\) 0 0
\(521\) 527.712i 1.01288i 0.862274 + 0.506441i \(0.169039\pi\)
−0.862274 + 0.506441i \(0.830961\pi\)
\(522\) 626.099 + 70.0000i 1.19942 + 0.134100i
\(523\) 376.000i 0.718929i −0.933159 0.359465i \(-0.882959\pi\)
0.933159 0.359465i \(-0.117041\pi\)
\(524\) 13.4164i 0.0256038i
\(525\) 0 0
\(526\) −130.000 −0.247148
\(527\) −80.4984 −0.152748
\(528\) −169.941 190.000i −0.321858 0.359848i
\(529\) −349.000 −0.659735
\(530\) 0 0
\(531\) 40.0000 + 4.47214i 0.0753296 + 0.00842210i
\(532\) 12.0000i 0.0225564i
\(533\) −1001.76 −1.87947
\(534\) 480.000 + 536.656i 0.898876 + 1.00497i
\(535\) 0 0
\(536\) 160.997i 0.300367i
\(537\) −384.604 430.000i −0.716208 0.800745i
\(538\) 830.000i 1.54275i
\(539\) 58.1378i 0.107862i
\(540\) 0 0
\(541\) −198.000 −0.365989 −0.182994 0.983114i \(-0.558579\pi\)
−0.182994 + 0.983114i \(0.558579\pi\)
\(542\) −183.358 −0.338298
\(543\) −4.47214 + 4.00000i −0.00823598 + 0.00736648i
\(544\) 70.0000 0.128676
\(545\) 0 0
\(546\) −480.000 + 429.325i −0.879121 + 0.786310i
\(547\) 1024.00i 1.87203i 0.351961 + 0.936015i \(0.385515\pi\)
−0.351961 + 0.936015i \(0.614485\pi\)
\(548\) −120.748 −0.220342
\(549\) 82.0000 733.430i 0.149362 1.33594i
\(550\) 0 0
\(551\) 62.6099i 0.113630i
\(552\) 201.246 180.000i 0.364576 0.326087i
\(553\) 828.000i 1.49729i
\(554\) 53.6656i 0.0968694i
\(555\) 0 0
\(556\) 82.0000 0.147482
\(557\) 67.0820 0.120435 0.0602173 0.998185i \(-0.480821\pi\)
0.0602173 + 0.998185i \(0.480821\pi\)
\(558\) 40.2492 360.000i 0.0721312 0.645161i
\(559\) −256.000 −0.457961
\(560\) 0 0
\(561\) 40.0000 + 44.7214i 0.0713012 + 0.0797172i
\(562\) 420.000i 0.747331i
\(563\) −254.912 −0.452774 −0.226387 0.974037i \(-0.572691\pi\)
−0.226387 + 0.974037i \(0.572691\pi\)
\(564\) 110.000 98.3870i 0.195035 0.174445i
\(565\) 0 0
\(566\) 321.994i 0.568894i
\(567\) −107.331 + 474.000i −0.189297 + 0.835979i
\(568\) 840.000i 1.47887i
\(569\) 858.650i 1.50905i 0.656271 + 0.754526i \(0.272133\pi\)
−0.656271 + 0.754526i \(0.727867\pi\)
\(570\) 0 0
\(571\) 962.000 1.68476 0.842382 0.538881i \(-0.181153\pi\)
0.842382 + 0.538881i \(0.181153\pi\)
\(572\) −71.5542 −0.125095
\(573\) −411.437 460.000i −0.718039 0.802792i
\(574\) 840.000 1.46341
\(575\) 0 0
\(576\) 41.0000 366.715i 0.0711806 0.636658i
\(577\) 886.000i 1.53553i −0.640732 0.767764i \(-0.721369\pi\)
0.640732 0.767764i \(-0.278631\pi\)
\(578\) 601.502 1.04066
\(579\) −428.000 478.519i −0.739206 0.826457i
\(580\) 0 0
\(581\) 563.489i 0.969861i
\(582\) −742.375 830.000i −1.27556 1.42612i
\(583\) 20.0000i 0.0343053i
\(584\) 496.407i 0.850012i
\(585\) 0 0
\(586\) 1050.00 1.79181
\(587\) −657.404 −1.11994 −0.559969 0.828513i \(-0.689187\pi\)
−0.559969 + 0.828513i \(0.689187\pi\)
\(588\) −29.0689 + 26.0000i −0.0494369 + 0.0442177i
\(589\) −36.0000 −0.0611205
\(590\) 0 0
\(591\) 210.000 187.830i 0.355330 0.317817i
\(592\) 304.000i 0.513514i
\(593\) 111.803 0.188539 0.0942693 0.995547i \(-0.469949\pi\)
0.0942693 + 0.995547i \(0.469949\pi\)
\(594\) −220.000 + 156.525i −0.370370 + 0.263510i
\(595\) 0 0
\(596\) 111.803i 0.187590i
\(597\) −541.128 + 484.000i −0.906413 + 0.810720i
\(598\) 480.000i 0.802676i
\(599\) 223.607i 0.373300i 0.982426 + 0.186650i \(0.0597631\pi\)
−0.982426 + 0.186650i \(0.940237\pi\)
\(600\) 0 0
\(601\) 2.00000 0.00332779 0.00166389 0.999999i \(-0.499470\pi\)
0.00166389 + 0.999999i \(0.499470\pi\)
\(602\) 214.663 0.356582
\(603\) 214.663 + 24.0000i 0.355991 + 0.0398010i
\(604\) −158.000 −0.261589
\(605\) 0 0
\(606\) −300.000 335.410i −0.495050 0.553482i
\(607\) 506.000i 0.833608i −0.908996 0.416804i \(-0.863150\pi\)
0.908996 0.416804i \(-0.136850\pi\)
\(608\) 31.3050 0.0514884
\(609\) 420.000 375.659i 0.689655 0.616846i
\(610\) 0 0
\(611\) 787.096i 1.28821i
\(612\) 4.47214 40.0000i 0.00730741 0.0653595i
\(613\) 556.000i 0.907015i −0.891253 0.453507i \(-0.850173\pi\)
0.891253 0.453507i \(-0.149827\pi\)
\(614\) 411.437i 0.670092i
\(615\) 0 0
\(616\) −180.000 −0.292208
\(617\) 93.9149 0.152212 0.0761060 0.997100i \(-0.475751\pi\)
0.0761060 + 0.997100i \(0.475751\pi\)
\(618\) −116.276 130.000i −0.188148 0.210356i
\(619\) 802.000 1.29564 0.647819 0.761794i \(-0.275681\pi\)
0.647819 + 0.761794i \(0.275681\pi\)
\(620\) 0 0
\(621\) −210.000 295.161i −0.338164 0.475299i
\(622\) 360.000i 0.578778i
\(623\) 643.988 1.03369
\(624\) −608.000 679.765i −0.974359 1.08937i
\(625\) 0 0
\(626\) 881.011i 1.40737i
\(627\) 17.8885 + 20.0000i 0.0285304 + 0.0318979i
\(628\) 164.000i 0.261146i
\(629\) 71.5542i 0.113759i
\(630\) 0 0
\(631\) −698.000 −1.10618 −0.553090 0.833121i \(-0.686552\pi\)
−0.553090 + 0.833121i \(0.686552\pi\)
\(632\) −925.732 −1.46477
\(633\) −4.47214 + 4.00000i −0.00706499 + 0.00631912i
\(634\) −1010.00 −1.59306
\(635\) 0 0
\(636\) 10.0000 8.94427i 0.0157233 0.0140633i
\(637\) 208.000i 0.326531i
\(638\) 313.050 0.490673
\(639\) 1120.00 + 125.220i 1.75274 + 0.195962i
\(640\) 0 0
\(641\) 912.316i 1.42327i −0.702550 0.711635i \(-0.747955\pi\)
0.702550 0.711635i \(-0.252045\pi\)
\(642\) 1006.23 900.000i 1.56734 1.40187i
\(643\) 156.000i 0.242613i −0.992615 0.121306i \(-0.961292\pi\)
0.992615 0.121306i \(-0.0387084\pi\)
\(644\) 80.4984i 0.124998i
\(645\) 0 0
\(646\) −20.0000 −0.0309598
\(647\) 755.791 1.16815 0.584073 0.811701i \(-0.301458\pi\)
0.584073 + 0.811701i \(0.301458\pi\)
\(648\) −529.948 120.000i −0.817821 0.185185i
\(649\) 20.0000 0.0308166
\(650\) 0 0
\(651\) −216.000 241.495i −0.331797 0.370961i
\(652\) 236.000i 0.361963i
\(653\) 487.463 0.746497 0.373249 0.927731i \(-0.378244\pi\)
0.373249 + 0.927731i \(0.378244\pi\)
\(654\) −190.000 + 169.941i −0.290520 + 0.259849i
\(655\) 0 0
\(656\) 1189.59i 1.81340i
\(657\) 661.876 + 74.0000i 1.00742 + 0.112633i
\(658\) 660.000i 1.00304i
\(659\) 406.964i 0.617548i 0.951135 + 0.308774i \(0.0999187\pi\)
−0.951135 + 0.308774i \(0.900081\pi\)
\(660\) 0 0
\(661\) 682.000 1.03177 0.515885 0.856658i \(-0.327463\pi\)
0.515885 + 0.856658i \(0.327463\pi\)
\(662\) 442.741 0.668794
\(663\) 143.108 + 160.000i 0.215850 + 0.241327i
\(664\) 630.000 0.948795
\(665\) 0 0
\(666\) 320.000 + 35.7771i 0.480480 + 0.0537194i
\(667\) 420.000i 0.629685i
\(668\) 93.9149 0.140591
\(669\) 172.000 + 192.302i 0.257100 + 0.287447i
\(670\) 0 0
\(671\) 366.715i 0.546520i
\(672\) 187.830 + 210.000i 0.279508 + 0.312500i
\(673\) 894.000i 1.32838i 0.747564 + 0.664190i \(0.231223\pi\)
−0.747564 + 0.664190i \(0.768777\pi\)
\(674\) 881.011i 1.30714i
\(675\) 0 0
\(676\) −87.0000 −0.128698
\(677\) −550.073 −0.812515 −0.406258 0.913759i \(-0.633166\pi\)
−0.406258 + 0.913759i \(0.633166\pi\)
\(678\) −156.525 + 140.000i −0.230862 + 0.206490i
\(679\) −996.000 −1.46686
\(680\) 0 0
\(681\) 130.000 116.276i 0.190896 0.170742i
\(682\) 180.000i 0.263930i
\(683\) −442.741 −0.648231 −0.324115 0.946018i \(-0.605067\pi\)
−0.324115 + 0.946018i \(0.605067\pi\)
\(684\) 2.00000 17.8885i 0.00292398 0.0261528i
\(685\) 0 0
\(686\) 831.817i 1.21256i
\(687\) −630.571 + 564.000i −0.917862 + 0.820961i
\(688\) 304.000i 0.441860i
\(689\) 71.5542i 0.103852i
\(690\) 0 0
\(691\) −758.000 −1.09696 −0.548480 0.836163i \(-0.684793\pi\)
−0.548480 + 0.836163i \(0.684793\pi\)
\(692\) −13.4164 −0.0193879
\(693\) −26.8328 + 240.000i −0.0387198 + 0.346320i
\(694\) 410.000 0.590778
\(695\) 0 0
\(696\) 420.000 + 469.574i 0.603448 + 0.674676i
\(697\) 280.000i 0.401722i
\(698\) −809.457 −1.15968
\(699\) −810.000 + 724.486i −1.15880 + 1.03646i
\(700\) 0 0
\(701\) 782.624i 1.11644i 0.829693 + 0.558220i \(0.188515\pi\)
−0.829693 + 0.558220i \(0.811485\pi\)
\(702\) −787.096 + 560.000i −1.12122 + 0.797721i
\(703\) 32.0000i 0.0455192i
\(704\) 183.358i 0.260451i
\(705\) 0 0
\(706\) −690.000 −0.977337
\(707\) −402.492 −0.569296
\(708\) −8.94427 10.0000i −0.0126332 0.0141243i
\(709\) 2.00000 0.00282087 0.00141044 0.999999i \(-0.499551\pi\)
0.00141044 + 0.999999i \(0.499551\pi\)
\(710\) 0 0
\(711\) −138.000 + 1234.31i −0.194093 + 1.73602i
\(712\) 720.000i 1.01124i
\(713\) 241.495 0.338703
\(714\) −120.000 134.164i −0.168067 0.187905i
\(715\) 0 0
\(716\) 192.302i 0.268578i
\(717\) 500.879 + 560.000i 0.698576 + 0.781032i
\(718\) 660.000i 0.919220i
\(719\) 858.650i 1.19423i 0.802156 + 0.597114i \(0.203686\pi\)
−0.802156 + 0.597114i \(0.796314\pi\)
\(720\) 0 0
\(721\) −156.000 −0.216366
\(722\) 798.276 1.10565
\(723\) −585.850 + 524.000i −0.810304 + 0.724758i
\(724\) 2.00000 0.00276243
\(725\) 0 0
\(726\) 505.000 451.686i 0.695592 0.622157i
\(727\) 674.000i 0.927098i 0.886071 + 0.463549i \(0.153424\pi\)
−0.886071 + 0.463549i \(0.846576\pi\)
\(728\) −643.988 −0.884598
\(729\) −239.000 + 688.709i −0.327846 + 0.944731i
\(730\) 0 0
\(731\) 71.5542i 0.0978853i
\(732\) −183.358 + 164.000i −0.250488 + 0.224044i
\(733\) 656.000i 0.894952i −0.894296 0.447476i \(-0.852323\pi\)
0.894296 0.447476i \(-0.147677\pi\)
\(734\) 415.909i 0.566633i
\(735\) 0 0
\(736\) −210.000 −0.285326
\(737\) 107.331 0.145633
\(738\) 1252.20 + 140.000i 1.69675 + 0.189702i
\(739\) −598.000 −0.809202 −0.404601 0.914493i \(-0.632590\pi\)
−0.404601 + 0.914493i \(0.632590\pi\)
\(740\) 0 0
\(741\) 64.0000 + 71.5542i 0.0863698 + 0.0965643i
\(742\) 60.0000i 0.0808625i
\(743\) −782.624 −1.05333 −0.526665 0.850073i \(-0.676558\pi\)
−0.526665 + 0.850073i \(0.676558\pi\)
\(744\) 270.000 241.495i 0.362903 0.324591i
\(745\) 0 0
\(746\) 98.3870i 0.131886i
\(747\) 93.9149 840.000i 0.125723 1.12450i
\(748\) 20.0000i 0.0267380i
\(749\) 1207.48i 1.61212i
\(750\) 0 0
\(751\) −338.000 −0.450067 −0.225033 0.974351i \(-0.572249\pi\)
−0.225033 + 0.974351i \(0.572249\pi\)
\(752\) 934.676 1.24292
\(753\) 939.149 + 1050.00i 1.24721 + 1.39442i
\(754\) 1120.00 1.48541
\(755\) 0 0
\(756\) 132.000 93.9149i 0.174603 0.124226i
\(757\) 656.000i 0.866579i −0.901255 0.433289i \(-0.857353\pi\)
0.901255 0.433289i \(-0.142647\pi\)
\(758\) −809.457 −1.06788
\(759\) −120.000 134.164i −0.158103 0.176764i
\(760\) 0 0
\(761\) 295.161i 0.387859i −0.981015 0.193930i \(-0.937877\pi\)
0.981015 0.193930i \(-0.0621234\pi\)
\(762\) −116.276 130.000i −0.152593 0.170604i
\(763\) 228.000i 0.298820i
\(764\) 205.718i 0.269265i
\(765\) 0 0
\(766\) −810.000 −1.05744
\(767\) 71.5542 0.0932910
\(768\) −404.728 + 362.000i −0.526990 + 0.471354i
\(769\) 82.0000 0.106632 0.0533160 0.998578i \(-0.483021\pi\)
0.0533160 + 0.998578i \(0.483021\pi\)
\(770\) 0 0
\(771\) −450.000 + 402.492i −0.583658 + 0.522039i
\(772\) 214.000i 0.277202i
\(773\) 1059.90 1.37115 0.685573 0.728004i \(-0.259552\pi\)
0.685573 + 0.728004i \(0.259552\pi\)
\(774\) 320.000 + 35.7771i 0.413437 + 0.0462236i
\(775\) 0 0
\(776\) 1113.56i 1.43500i
\(777\) 214.663 192.000i 0.276271 0.247104i
\(778\) 990.000i 1.27249i
\(779\) 125.220i 0.160744i
\(780\) 0 0
\(781\) 560.000 0.717029
\(782\) 134.164 0.171565
\(783\) 688.709 490.000i 0.879577 0.625798i
\(784\) −247.000 −0.315051
\(785\) 0 0
\(786\) −60.0000 67.0820i −0.0763359 0.0853461i
\(787\) 536.000i 0.681067i −0.940232 0.340534i \(-0.889392\pi\)
0.940232 0.340534i \(-0.110608\pi\)
\(788\) −93.9149 −0.119181