Properties

Label 15.3.c.a.11.1
Level $15$
Weight $3$
Character 15.11
Analytic conductor $0.409$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 15.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.408720396540\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-5}) \)
Defining polynomial: \(x^{2} + 5\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.1
Root \(-2.23607i\) of defining polynomial
Character \(\chi\) \(=\) 15.11
Dual form 15.3.c.a.11.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +O(q^{10})\) \(q-2.23607i q^{2} +(-2.00000 + 2.23607i) q^{3} -1.00000 q^{4} +2.23607i q^{5} +(5.00000 + 4.47214i) q^{6} -6.00000 q^{7} -6.70820i q^{8} +(-1.00000 - 8.94427i) q^{9} +5.00000 q^{10} +4.47214i q^{11} +(2.00000 - 2.23607i) q^{12} +16.0000 q^{13} +13.4164i q^{14} +(-5.00000 - 4.47214i) q^{15} -19.0000 q^{16} +4.47214i q^{17} +(-20.0000 + 2.23607i) q^{18} -2.00000 q^{19} -2.23607i q^{20} +(12.0000 - 13.4164i) q^{21} +10.0000 q^{22} +13.4164i q^{23} +(15.0000 + 13.4164i) q^{24} -5.00000 q^{25} -35.7771i q^{26} +(22.0000 + 15.6525i) q^{27} +6.00000 q^{28} -31.3050i q^{29} +(-10.0000 + 11.1803i) q^{30} -18.0000 q^{31} +15.6525i q^{32} +(-10.0000 - 8.94427i) q^{33} +10.0000 q^{34} -13.4164i q^{35} +(1.00000 + 8.94427i) q^{36} -16.0000 q^{37} +4.47214i q^{38} +(-32.0000 + 35.7771i) q^{39} +15.0000 q^{40} +62.6099i q^{41} +(-30.0000 - 26.8328i) q^{42} +16.0000 q^{43} -4.47214i q^{44} +(20.0000 - 2.23607i) q^{45} +30.0000 q^{46} -49.1935i q^{47} +(38.0000 - 42.4853i) q^{48} -13.0000 q^{49} +11.1803i q^{50} +(-10.0000 - 8.94427i) q^{51} -16.0000 q^{52} +4.47214i q^{53} +(35.0000 - 49.1935i) q^{54} -10.0000 q^{55} +40.2492i q^{56} +(4.00000 - 4.47214i) q^{57} -70.0000 q^{58} +4.47214i q^{59} +(5.00000 + 4.47214i) q^{60} +82.0000 q^{61} +40.2492i q^{62} +(6.00000 + 53.6656i) q^{63} -41.0000 q^{64} +35.7771i q^{65} +(-20.0000 + 22.3607i) q^{66} +24.0000 q^{67} -4.47214i q^{68} +(-30.0000 - 26.8328i) q^{69} -30.0000 q^{70} -125.220i q^{71} +(-60.0000 + 6.70820i) q^{72} -74.0000 q^{73} +35.7771i q^{74} +(10.0000 - 11.1803i) q^{75} +2.00000 q^{76} -26.8328i q^{77} +(80.0000 + 71.5542i) q^{78} +138.000 q^{79} -42.4853i q^{80} +(-79.0000 + 17.8885i) q^{81} +140.000 q^{82} -93.9149i q^{83} +(-12.0000 + 13.4164i) q^{84} -10.0000 q^{85} -35.7771i q^{86} +(70.0000 + 62.6099i) q^{87} +30.0000 q^{88} +107.331i q^{89} +(-5.00000 - 44.7214i) q^{90} -96.0000 q^{91} -13.4164i q^{92} +(36.0000 - 40.2492i) q^{93} -110.000 q^{94} -4.47214i q^{95} +(-35.0000 - 31.3050i) q^{96} -166.000 q^{97} +29.0689i q^{98} +(40.0000 - 4.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{3} - 2q^{4} + 10q^{6} - 12q^{7} - 2q^{9} + O(q^{10}) \) \( 2q - 4q^{3} - 2q^{4} + 10q^{6} - 12q^{7} - 2q^{9} + 10q^{10} + 4q^{12} + 32q^{13} - 10q^{15} - 38q^{16} - 40q^{18} - 4q^{19} + 24q^{21} + 20q^{22} + 30q^{24} - 10q^{25} + 44q^{27} + 12q^{28} - 20q^{30} - 36q^{31} - 20q^{33} + 20q^{34} + 2q^{36} - 32q^{37} - 64q^{39} + 30q^{40} - 60q^{42} + 32q^{43} + 40q^{45} + 60q^{46} + 76q^{48} - 26q^{49} - 20q^{51} - 32q^{52} + 70q^{54} - 20q^{55} + 8q^{57} - 140q^{58} + 10q^{60} + 164q^{61} + 12q^{63} - 82q^{64} - 40q^{66} + 48q^{67} - 60q^{69} - 60q^{70} - 120q^{72} - 148q^{73} + 20q^{75} + 4q^{76} + 160q^{78} + 276q^{79} - 158q^{81} + 280q^{82} - 24q^{84} - 20q^{85} + 140q^{87} + 60q^{88} - 10q^{90} - 192q^{91} + 72q^{93} - 220q^{94} - 70q^{96} - 332q^{97} + 80q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607i 1.11803i −0.829156 0.559017i \(-0.811179\pi\)
0.829156 0.559017i \(-0.188821\pi\)
\(3\) −2.00000 + 2.23607i −0.666667 + 0.745356i
\(4\) −1.00000 −0.250000
\(5\) 2.23607i 0.447214i
\(6\) 5.00000 + 4.47214i 0.833333 + 0.745356i
\(7\) −6.00000 −0.857143 −0.428571 0.903508i \(-0.640983\pi\)
−0.428571 + 0.903508i \(0.640983\pi\)
\(8\) 6.70820i 0.838525i
\(9\) −1.00000 8.94427i −0.111111 0.993808i
\(10\) 5.00000 0.500000
\(11\) 4.47214i 0.406558i 0.979121 + 0.203279i \(0.0651598\pi\)
−0.979121 + 0.203279i \(0.934840\pi\)
\(12\) 2.00000 2.23607i 0.166667 0.186339i
\(13\) 16.0000 1.23077 0.615385 0.788227i \(-0.289001\pi\)
0.615385 + 0.788227i \(0.289001\pi\)
\(14\) 13.4164i 0.958315i
\(15\) −5.00000 4.47214i −0.333333 0.298142i
\(16\) −19.0000 −1.18750
\(17\) 4.47214i 0.263067i 0.991312 + 0.131533i \(0.0419901\pi\)
−0.991312 + 0.131533i \(0.958010\pi\)
\(18\) −20.0000 + 2.23607i −1.11111 + 0.124226i
\(19\) −2.00000 −0.105263 −0.0526316 0.998614i \(-0.516761\pi\)
−0.0526316 + 0.998614i \(0.516761\pi\)
\(20\) 2.23607i 0.111803i
\(21\) 12.0000 13.4164i 0.571429 0.638877i
\(22\) 10.0000 0.454545
\(23\) 13.4164i 0.583322i 0.956522 + 0.291661i \(0.0942079\pi\)
−0.956522 + 0.291661i \(0.905792\pi\)
\(24\) 15.0000 + 13.4164i 0.625000 + 0.559017i
\(25\) −5.00000 −0.200000
\(26\) 35.7771i 1.37604i
\(27\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(28\) 6.00000 0.214286
\(29\) 31.3050i 1.07948i −0.841831 0.539741i \(-0.818522\pi\)
0.841831 0.539741i \(-0.181478\pi\)
\(30\) −10.0000 + 11.1803i −0.333333 + 0.372678i
\(31\) −18.0000 −0.580645 −0.290323 0.956929i \(-0.593763\pi\)
−0.290323 + 0.956929i \(0.593763\pi\)
\(32\) 15.6525i 0.489140i
\(33\) −10.0000 8.94427i −0.303030 0.271039i
\(34\) 10.0000 0.294118
\(35\) 13.4164i 0.383326i
\(36\) 1.00000 + 8.94427i 0.0277778 + 0.248452i
\(37\) −16.0000 −0.432432 −0.216216 0.976346i \(-0.569372\pi\)
−0.216216 + 0.976346i \(0.569372\pi\)
\(38\) 4.47214i 0.117688i
\(39\) −32.0000 + 35.7771i −0.820513 + 0.917361i
\(40\) 15.0000 0.375000
\(41\) 62.6099i 1.52707i 0.645766 + 0.763535i \(0.276538\pi\)
−0.645766 + 0.763535i \(0.723462\pi\)
\(42\) −30.0000 26.8328i −0.714286 0.638877i
\(43\) 16.0000 0.372093 0.186047 0.982541i \(-0.440432\pi\)
0.186047 + 0.982541i \(0.440432\pi\)
\(44\) 4.47214i 0.101639i
\(45\) 20.0000 2.23607i 0.444444 0.0496904i
\(46\) 30.0000 0.652174
\(47\) 49.1935i 1.04667i −0.852127 0.523335i \(-0.824688\pi\)
0.852127 0.523335i \(-0.175312\pi\)
\(48\) 38.0000 42.4853i 0.791667 0.885110i
\(49\) −13.0000 −0.265306
\(50\) 11.1803i 0.223607i
\(51\) −10.0000 8.94427i −0.196078 0.175378i
\(52\) −16.0000 −0.307692
\(53\) 4.47214i 0.0843799i 0.999110 + 0.0421900i \(0.0134335\pi\)
−0.999110 + 0.0421900i \(0.986567\pi\)
\(54\) 35.0000 49.1935i 0.648148 0.910991i
\(55\) −10.0000 −0.181818
\(56\) 40.2492i 0.718736i
\(57\) 4.00000 4.47214i 0.0701754 0.0784585i
\(58\) −70.0000 −1.20690
\(59\) 4.47214i 0.0757989i 0.999282 + 0.0378995i \(0.0120667\pi\)
−0.999282 + 0.0378995i \(0.987933\pi\)
\(60\) 5.00000 + 4.47214i 0.0833333 + 0.0745356i
\(61\) 82.0000 1.34426 0.672131 0.740432i \(-0.265379\pi\)
0.672131 + 0.740432i \(0.265379\pi\)
\(62\) 40.2492i 0.649181i
\(63\) 6.00000 + 53.6656i 0.0952381 + 0.851835i
\(64\) −41.0000 −0.640625
\(65\) 35.7771i 0.550417i
\(66\) −20.0000 + 22.3607i −0.303030 + 0.338798i
\(67\) 24.0000 0.358209 0.179104 0.983830i \(-0.442680\pi\)
0.179104 + 0.983830i \(0.442680\pi\)
\(68\) 4.47214i 0.0657667i
\(69\) −30.0000 26.8328i −0.434783 0.388881i
\(70\) −30.0000 −0.428571
\(71\) 125.220i 1.76366i −0.471568 0.881830i \(-0.656312\pi\)
0.471568 0.881830i \(-0.343688\pi\)
\(72\) −60.0000 + 6.70820i −0.833333 + 0.0931695i
\(73\) −74.0000 −1.01370 −0.506849 0.862035i \(-0.669190\pi\)
−0.506849 + 0.862035i \(0.669190\pi\)
\(74\) 35.7771i 0.483474i
\(75\) 10.0000 11.1803i 0.133333 0.149071i
\(76\) 2.00000 0.0263158
\(77\) 26.8328i 0.348478i
\(78\) 80.0000 + 71.5542i 1.02564 + 0.917361i
\(79\) 138.000 1.74684 0.873418 0.486972i \(-0.161899\pi\)
0.873418 + 0.486972i \(0.161899\pi\)
\(80\) 42.4853i 0.531066i
\(81\) −79.0000 + 17.8885i −0.975309 + 0.220846i
\(82\) 140.000 1.70732
\(83\) 93.9149i 1.13150i −0.824575 0.565752i \(-0.808586\pi\)
0.824575 0.565752i \(-0.191414\pi\)
\(84\) −12.0000 + 13.4164i −0.142857 + 0.159719i
\(85\) −10.0000 −0.117647
\(86\) 35.7771i 0.416013i
\(87\) 70.0000 + 62.6099i 0.804598 + 0.719654i
\(88\) 30.0000 0.340909
\(89\) 107.331i 1.20597i 0.797753 + 0.602985i \(0.206022\pi\)
−0.797753 + 0.602985i \(0.793978\pi\)
\(90\) −5.00000 44.7214i −0.0555556 0.496904i
\(91\) −96.0000 −1.05495
\(92\) 13.4164i 0.145831i
\(93\) 36.0000 40.2492i 0.387097 0.432787i
\(94\) −110.000 −1.17021
\(95\) 4.47214i 0.0470751i
\(96\) −35.0000 31.3050i −0.364583 0.326093i
\(97\) −166.000 −1.71134 −0.855670 0.517522i \(-0.826855\pi\)
−0.855670 + 0.517522i \(0.826855\pi\)
\(98\) 29.0689i 0.296621i
\(99\) 40.0000 4.47214i 0.404040 0.0451731i
\(100\) 5.00000 0.0500000
\(101\) 67.0820i 0.664179i 0.943248 + 0.332089i \(0.107754\pi\)
−0.943248 + 0.332089i \(0.892246\pi\)
\(102\) −20.0000 + 22.3607i −0.196078 + 0.219222i
\(103\) 26.0000 0.252427 0.126214 0.992003i \(-0.459718\pi\)
0.126214 + 0.992003i \(0.459718\pi\)
\(104\) 107.331i 1.03203i
\(105\) 30.0000 + 26.8328i 0.285714 + 0.255551i
\(106\) 10.0000 0.0943396
\(107\) 201.246i 1.88080i 0.340064 + 0.940402i \(0.389551\pi\)
−0.340064 + 0.940402i \(0.610449\pi\)
\(108\) −22.0000 15.6525i −0.203704 0.144930i
\(109\) 38.0000 0.348624 0.174312 0.984690i \(-0.444230\pi\)
0.174312 + 0.984690i \(0.444230\pi\)
\(110\) 22.3607i 0.203279i
\(111\) 32.0000 35.7771i 0.288288 0.322316i
\(112\) 114.000 1.01786
\(113\) 31.3050i 0.277035i 0.990360 + 0.138517i \(0.0442337\pi\)
−0.990360 + 0.138517i \(0.955766\pi\)
\(114\) −10.0000 8.94427i −0.0877193 0.0784585i
\(115\) −30.0000 −0.260870
\(116\) 31.3050i 0.269870i
\(117\) −16.0000 143.108i −0.136752 1.22315i
\(118\) 10.0000 0.0847458
\(119\) 26.8328i 0.225486i
\(120\) −30.0000 + 33.5410i −0.250000 + 0.279508i
\(121\) 101.000 0.834711
\(122\) 183.358i 1.50293i
\(123\) −140.000 125.220i −1.13821 1.01805i
\(124\) 18.0000 0.145161
\(125\) 11.1803i 0.0894427i
\(126\) 120.000 13.4164i 0.952381 0.106479i
\(127\) −26.0000 −0.204724 −0.102362 0.994747i \(-0.532640\pi\)
−0.102362 + 0.994747i \(0.532640\pi\)
\(128\) 154.289i 1.20538i
\(129\) −32.0000 + 35.7771i −0.248062 + 0.277342i
\(130\) 80.0000 0.615385
\(131\) 13.4164i 0.102415i 0.998688 + 0.0512077i \(0.0163070\pi\)
−0.998688 + 0.0512077i \(0.983693\pi\)
\(132\) 10.0000 + 8.94427i 0.0757576 + 0.0677596i
\(133\) 12.0000 0.0902256
\(134\) 53.6656i 0.400490i
\(135\) −35.0000 + 49.1935i −0.259259 + 0.364396i
\(136\) 30.0000 0.220588
\(137\) 120.748i 0.881370i −0.897662 0.440685i \(-0.854736\pi\)
0.897662 0.440685i \(-0.145264\pi\)
\(138\) −60.0000 + 67.0820i −0.434783 + 0.486102i
\(139\) −82.0000 −0.589928 −0.294964 0.955508i \(-0.595308\pi\)
−0.294964 + 0.955508i \(0.595308\pi\)
\(140\) 13.4164i 0.0958315i
\(141\) 110.000 + 98.3870i 0.780142 + 0.697780i
\(142\) −280.000 −1.97183
\(143\) 71.5542i 0.500379i
\(144\) 19.0000 + 169.941i 0.131944 + 1.18015i
\(145\) 70.0000 0.482759
\(146\) 165.469i 1.13335i
\(147\) 26.0000 29.0689i 0.176871 0.197748i
\(148\) 16.0000 0.108108
\(149\) 111.803i 0.750358i −0.926952 0.375179i \(-0.877581\pi\)
0.926952 0.375179i \(-0.122419\pi\)
\(150\) −25.0000 22.3607i −0.166667 0.149071i
\(151\) −158.000 −1.04636 −0.523179 0.852223i \(-0.675254\pi\)
−0.523179 + 0.852223i \(0.675254\pi\)
\(152\) 13.4164i 0.0882658i
\(153\) 40.0000 4.47214i 0.261438 0.0292296i
\(154\) −60.0000 −0.389610
\(155\) 40.2492i 0.259672i
\(156\) 32.0000 35.7771i 0.205128 0.229340i
\(157\) 164.000 1.04459 0.522293 0.852766i \(-0.325077\pi\)
0.522293 + 0.852766i \(0.325077\pi\)
\(158\) 308.577i 1.95302i
\(159\) −10.0000 8.94427i −0.0628931 0.0562533i
\(160\) −35.0000 −0.218750
\(161\) 80.4984i 0.499990i
\(162\) 40.0000 + 176.649i 0.246914 + 1.09043i
\(163\) 236.000 1.44785 0.723926 0.689877i \(-0.242336\pi\)
0.723926 + 0.689877i \(0.242336\pi\)
\(164\) 62.6099i 0.381768i
\(165\) 20.0000 22.3607i 0.121212 0.135519i
\(166\) −210.000 −1.26506
\(167\) 93.9149i 0.562364i 0.959654 + 0.281182i \(0.0907265\pi\)
−0.959654 + 0.281182i \(0.909273\pi\)
\(168\) −90.0000 80.4984i −0.535714 0.479157i
\(169\) 87.0000 0.514793
\(170\) 22.3607i 0.131533i
\(171\) 2.00000 + 17.8885i 0.0116959 + 0.104611i
\(172\) −16.0000 −0.0930233
\(173\) 13.4164i 0.0775515i 0.999248 + 0.0387757i \(0.0123458\pi\)
−0.999248 + 0.0387757i \(0.987654\pi\)
\(174\) 140.000 156.525i 0.804598 0.899568i
\(175\) 30.0000 0.171429
\(176\) 84.9706i 0.482787i
\(177\) −10.0000 8.94427i −0.0564972 0.0505326i
\(178\) 240.000 1.34831
\(179\) 192.302i 1.07431i 0.843483 + 0.537156i \(0.180501\pi\)
−0.843483 + 0.537156i \(0.819499\pi\)
\(180\) −20.0000 + 2.23607i −0.111111 + 0.0124226i
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) 214.663i 1.17946i
\(183\) −164.000 + 183.358i −0.896175 + 1.00195i
\(184\) 90.0000 0.489130
\(185\) 35.7771i 0.193390i
\(186\) −90.0000 80.4984i −0.483871 0.432787i
\(187\) −20.0000 −0.106952
\(188\) 49.1935i 0.261668i
\(189\) −132.000 93.9149i −0.698413 0.496904i
\(190\) −10.0000 −0.0526316
\(191\) 205.718i 1.07706i −0.842607 0.538529i \(-0.818980\pi\)
0.842607 0.538529i \(-0.181020\pi\)
\(192\) 82.0000 91.6788i 0.427083 0.477494i
\(193\) −214.000 −1.10881 −0.554404 0.832248i \(-0.687054\pi\)
−0.554404 + 0.832248i \(0.687054\pi\)
\(194\) 371.187i 1.91334i
\(195\) −80.0000 71.5542i −0.410256 0.366944i
\(196\) 13.0000 0.0663265
\(197\) 93.9149i 0.476725i −0.971176 0.238363i \(-0.923389\pi\)
0.971176 0.238363i \(-0.0766107\pi\)
\(198\) −10.0000 89.4427i −0.0505051 0.451731i
\(199\) −242.000 −1.21608 −0.608040 0.793906i \(-0.708044\pi\)
−0.608040 + 0.793906i \(0.708044\pi\)
\(200\) 33.5410i 0.167705i
\(201\) −48.0000 + 53.6656i −0.238806 + 0.266993i
\(202\) 150.000 0.742574
\(203\) 187.830i 0.925270i
\(204\) 10.0000 + 8.94427i 0.0490196 + 0.0438445i
\(205\) −140.000 −0.682927
\(206\) 58.1378i 0.282222i
\(207\) 120.000 13.4164i 0.579710 0.0648136i
\(208\) −304.000 −1.46154
\(209\) 8.94427i 0.0427956i
\(210\) 60.0000 67.0820i 0.285714 0.319438i
\(211\) 2.00000 0.00947867 0.00473934 0.999989i \(-0.498491\pi\)
0.00473934 + 0.999989i \(0.498491\pi\)
\(212\) 4.47214i 0.0210950i
\(213\) 280.000 + 250.440i 1.31455 + 1.17577i
\(214\) 450.000 2.10280
\(215\) 35.7771i 0.166405i
\(216\) 105.000 147.580i 0.486111 0.683243i
\(217\) 108.000 0.497696
\(218\) 84.9706i 0.389773i
\(219\) 148.000 165.469i 0.675799 0.755566i
\(220\) 10.0000 0.0454545
\(221\) 71.5542i 0.323775i
\(222\) −80.0000 71.5542i −0.360360 0.322316i
\(223\) 86.0000 0.385650 0.192825 0.981233i \(-0.438235\pi\)
0.192825 + 0.981233i \(0.438235\pi\)
\(224\) 93.9149i 0.419263i
\(225\) 5.00000 + 44.7214i 0.0222222 + 0.198762i
\(226\) 70.0000 0.309735
\(227\) 58.1378i 0.256114i −0.991767 0.128057i \(-0.959126\pi\)
0.991767 0.128057i \(-0.0408740\pi\)
\(228\) −4.00000 + 4.47214i −0.0175439 + 0.0196146i
\(229\) −282.000 −1.23144 −0.615721 0.787965i \(-0.711135\pi\)
−0.615721 + 0.787965i \(0.711135\pi\)
\(230\) 67.0820i 0.291661i
\(231\) 60.0000 + 53.6656i 0.259740 + 0.232319i
\(232\) −210.000 −0.905172
\(233\) 362.243i 1.55469i −0.629074 0.777346i \(-0.716566\pi\)
0.629074 0.777346i \(-0.283434\pi\)
\(234\) −320.000 + 35.7771i −1.36752 + 0.152894i
\(235\) 110.000 0.468085
\(236\) 4.47214i 0.0189497i
\(237\) −276.000 + 308.577i −1.16456 + 1.30201i
\(238\) −60.0000 −0.252101
\(239\) 250.440i 1.04786i −0.851760 0.523932i \(-0.824464\pi\)
0.851760 0.523932i \(-0.175536\pi\)
\(240\) 95.0000 + 84.9706i 0.395833 + 0.354044i
\(241\) 262.000 1.08714 0.543568 0.839365i \(-0.317073\pi\)
0.543568 + 0.839365i \(0.317073\pi\)
\(242\) 225.843i 0.933235i
\(243\) 118.000 212.426i 0.485597 0.874183i
\(244\) −82.0000 −0.336066
\(245\) 29.0689i 0.118649i
\(246\) −280.000 + 313.050i −1.13821 + 1.27256i
\(247\) −32.0000 −0.129555
\(248\) 120.748i 0.486886i
\(249\) 210.000 + 187.830i 0.843373 + 0.754336i
\(250\) −25.0000 −0.100000
\(251\) 469.574i 1.87081i 0.353573 + 0.935407i \(0.384967\pi\)
−0.353573 + 0.935407i \(0.615033\pi\)
\(252\) −6.00000 53.6656i −0.0238095 0.212959i
\(253\) −60.0000 −0.237154
\(254\) 58.1378i 0.228889i
\(255\) 20.0000 22.3607i 0.0784314 0.0876889i
\(256\) 181.000 0.707031
\(257\) 201.246i 0.783059i 0.920166 + 0.391529i \(0.128054\pi\)
−0.920166 + 0.391529i \(0.871946\pi\)
\(258\) 80.0000 + 71.5542i 0.310078 + 0.277342i
\(259\) 96.0000 0.370656
\(260\) 35.7771i 0.137604i
\(261\) −280.000 + 31.3050i −1.07280 + 0.119942i
\(262\) 30.0000 0.114504
\(263\) 58.1378i 0.221056i −0.993873 0.110528i \(-0.964746\pi\)
0.993873 0.110528i \(-0.0352542\pi\)
\(264\) −60.0000 + 67.0820i −0.227273 + 0.254099i
\(265\) −10.0000 −0.0377358
\(266\) 26.8328i 0.100875i
\(267\) −240.000 214.663i −0.898876 0.803979i
\(268\) −24.0000 −0.0895522
\(269\) 371.187i 1.37988i −0.723867 0.689939i \(-0.757637\pi\)
0.723867 0.689939i \(-0.242363\pi\)
\(270\) 110.000 + 78.2624i 0.407407 + 0.289861i
\(271\) 82.0000 0.302583 0.151292 0.988489i \(-0.451657\pi\)
0.151292 + 0.988489i \(0.451657\pi\)
\(272\) 84.9706i 0.312392i
\(273\) 192.000 214.663i 0.703297 0.786310i
\(274\) −270.000 −0.985401
\(275\) 22.3607i 0.0813116i
\(276\) 30.0000 + 26.8328i 0.108696 + 0.0972203i
\(277\) 24.0000 0.0866426 0.0433213 0.999061i \(-0.486206\pi\)
0.0433213 + 0.999061i \(0.486206\pi\)
\(278\) 183.358i 0.659560i
\(279\) 18.0000 + 160.997i 0.0645161 + 0.577050i
\(280\) −90.0000 −0.321429
\(281\) 187.830i 0.668433i −0.942496 0.334217i \(-0.891528\pi\)
0.942496 0.334217i \(-0.108472\pi\)
\(282\) 220.000 245.967i 0.780142 0.872225i
\(283\) −144.000 −0.508834 −0.254417 0.967095i \(-0.581884\pi\)
−0.254417 + 0.967095i \(0.581884\pi\)
\(284\) 125.220i 0.440915i
\(285\) 10.0000 + 8.94427i 0.0350877 + 0.0313834i
\(286\) 160.000 0.559441
\(287\) 375.659i 1.30892i
\(288\) 140.000 15.6525i 0.486111 0.0543489i
\(289\) 269.000 0.930796
\(290\) 156.525i 0.539741i
\(291\) 332.000 371.187i 1.14089 1.27556i
\(292\) 74.0000 0.253425
\(293\) 469.574i 1.60264i 0.598234 + 0.801321i \(0.295869\pi\)
−0.598234 + 0.801321i \(0.704131\pi\)
\(294\) −65.0000 58.1378i −0.221088 0.197748i
\(295\) −10.0000 −0.0338983
\(296\) 107.331i 0.362606i
\(297\) −70.0000 + 98.3870i −0.235690 + 0.331269i
\(298\) −250.000 −0.838926
\(299\) 214.663i 0.717935i
\(300\) −10.0000 + 11.1803i −0.0333333 + 0.0372678i
\(301\) −96.0000 −0.318937
\(302\) 353.299i 1.16986i
\(303\) −150.000 134.164i −0.495050 0.442786i
\(304\) 38.0000 0.125000
\(305\) 183.358i 0.601172i
\(306\) −10.0000 89.4427i −0.0326797 0.292296i
\(307\) 184.000 0.599349 0.299674 0.954042i \(-0.403122\pi\)
0.299674 + 0.954042i \(0.403122\pi\)
\(308\) 26.8328i 0.0871195i
\(309\) −52.0000 + 58.1378i −0.168285 + 0.188148i
\(310\) −90.0000 −0.290323
\(311\) 160.997i 0.517675i 0.965921 + 0.258837i \(0.0833394\pi\)
−0.965921 + 0.258837i \(0.916661\pi\)
\(312\) 240.000 + 214.663i 0.769231 + 0.688021i
\(313\) −394.000 −1.25879 −0.629393 0.777087i \(-0.716696\pi\)
−0.629393 + 0.777087i \(0.716696\pi\)
\(314\) 366.715i 1.16788i
\(315\) −120.000 + 13.4164i −0.380952 + 0.0425918i
\(316\) −138.000 −0.436709
\(317\) 451.686i 1.42488i 0.701735 + 0.712438i \(0.252409\pi\)
−0.701735 + 0.712438i \(0.747591\pi\)
\(318\) −20.0000 + 22.3607i −0.0628931 + 0.0703166i
\(319\) 140.000 0.438871
\(320\) 91.6788i 0.286496i
\(321\) −450.000 402.492i −1.40187 1.25387i
\(322\) −180.000 −0.559006
\(323\) 8.94427i 0.0276912i
\(324\) 79.0000 17.8885i 0.243827 0.0552116i
\(325\) −80.0000 −0.246154
\(326\) 527.712i 1.61875i
\(327\) −76.0000 + 84.9706i −0.232416 + 0.259849i
\(328\) 420.000 1.28049
\(329\) 295.161i 0.897146i
\(330\) −50.0000 44.7214i −0.151515 0.135519i
\(331\) −198.000 −0.598187 −0.299094 0.954224i \(-0.596684\pi\)
−0.299094 + 0.954224i \(0.596684\pi\)
\(332\) 93.9149i 0.282876i
\(333\) 16.0000 + 143.108i 0.0480480 + 0.429755i
\(334\) 210.000 0.628743
\(335\) 53.6656i 0.160196i
\(336\) −228.000 + 254.912i −0.678571 + 0.758666i
\(337\) 394.000 1.16914 0.584570 0.811343i \(-0.301263\pi\)
0.584570 + 0.811343i \(0.301263\pi\)
\(338\) 194.538i 0.575556i
\(339\) −70.0000 62.6099i −0.206490 0.184690i
\(340\) 10.0000 0.0294118
\(341\) 80.4984i 0.236066i
\(342\) 40.0000 4.47214i 0.116959 0.0130764i
\(343\) 372.000 1.08455
\(344\) 107.331i 0.312009i
\(345\) 60.0000 67.0820i 0.173913 0.194441i
\(346\) 30.0000 0.0867052
\(347\) 183.358i 0.528408i −0.964467 0.264204i \(-0.914891\pi\)
0.964467 0.264204i \(-0.0851092\pi\)
\(348\) −70.0000 62.6099i −0.201149 0.179914i
\(349\) −362.000 −1.03725 −0.518625 0.855002i \(-0.673556\pi\)
−0.518625 + 0.855002i \(0.673556\pi\)
\(350\) 67.0820i 0.191663i
\(351\) 352.000 + 250.440i 1.00285 + 0.713503i
\(352\) −70.0000 −0.198864
\(353\) 308.577i 0.874157i −0.899423 0.437078i \(-0.856013\pi\)
0.899423 0.437078i \(-0.143987\pi\)
\(354\) −20.0000 + 22.3607i −0.0564972 + 0.0631658i
\(355\) 280.000 0.788732
\(356\) 107.331i 0.301492i
\(357\) 60.0000 + 53.6656i 0.168067 + 0.150324i
\(358\) 430.000 1.20112
\(359\) 295.161i 0.822175i 0.911596 + 0.411088i \(0.134851\pi\)
−0.911596 + 0.411088i \(0.865149\pi\)
\(360\) −15.0000 134.164i −0.0416667 0.372678i
\(361\) −357.000 −0.988920
\(362\) 4.47214i 0.0123540i
\(363\) −202.000 + 225.843i −0.556474 + 0.622157i
\(364\) 96.0000 0.263736
\(365\) 165.469i 0.453340i
\(366\) 410.000 + 366.715i 1.12022 + 1.00195i
\(367\) −186.000 −0.506812 −0.253406 0.967360i \(-0.581551\pi\)
−0.253406 + 0.967360i \(0.581551\pi\)
\(368\) 254.912i 0.692695i
\(369\) 560.000 62.6099i 1.51762 0.169675i
\(370\) −80.0000 −0.216216
\(371\) 26.8328i 0.0723256i
\(372\) −36.0000 + 40.2492i −0.0967742 + 0.108197i
\(373\) −44.0000 −0.117962 −0.0589812 0.998259i \(-0.518785\pi\)
−0.0589812 + 0.998259i \(0.518785\pi\)
\(374\) 44.7214i 0.119576i
\(375\) 25.0000 + 22.3607i 0.0666667 + 0.0596285i
\(376\) −330.000 −0.877660
\(377\) 500.879i 1.32859i
\(378\) −210.000 + 295.161i −0.555556 + 0.780849i
\(379\) −362.000 −0.955145 −0.477573 0.878592i \(-0.658483\pi\)
−0.477573 + 0.878592i \(0.658483\pi\)
\(380\) 4.47214i 0.0117688i
\(381\) 52.0000 58.1378i 0.136483 0.152593i
\(382\) −460.000 −1.20419
\(383\) 362.243i 0.945804i −0.881115 0.472902i \(-0.843206\pi\)
0.881115 0.472902i \(-0.156794\pi\)
\(384\) −345.000 308.577i −0.898438 0.803587i
\(385\) 60.0000 0.155844
\(386\) 478.519i 1.23969i
\(387\) −16.0000 143.108i −0.0413437 0.369789i
\(388\) 166.000 0.427835
\(389\) 442.741i 1.13815i 0.822285 + 0.569076i \(0.192699\pi\)
−0.822285 + 0.569076i \(0.807301\pi\)
\(390\) −160.000 + 178.885i −0.410256 + 0.458681i
\(391\) −60.0000 −0.153453
\(392\) 87.2067i 0.222466i
\(393\) −30.0000 26.8328i −0.0763359 0.0682769i
\(394\) −210.000 −0.532995
\(395\) 308.577i 0.781209i
\(396\) −40.0000 + 4.47214i −0.101010 + 0.0112933i
\(397\) 124.000 0.312343 0.156171 0.987730i \(-0.450085\pi\)
0.156171 + 0.987730i \(0.450085\pi\)
\(398\) 541.128i 1.35962i
\(399\) −24.0000 + 26.8328i −0.0601504 + 0.0672502i
\(400\) 95.0000 0.237500
\(401\) 268.328i 0.669148i −0.942370 0.334574i \(-0.891408\pi\)
0.942370 0.334574i \(-0.108592\pi\)
\(402\) 120.000 + 107.331i 0.298507 + 0.266993i
\(403\) −288.000 −0.714640
\(404\) 67.0820i 0.166045i
\(405\) −40.0000 176.649i −0.0987654 0.436171i
\(406\) 420.000 1.03448
\(407\) 71.5542i 0.175809i
\(408\) −60.0000 + 67.0820i −0.147059 + 0.164417i
\(409\) 458.000 1.11980 0.559902 0.828559i \(-0.310839\pi\)
0.559902 + 0.828559i \(0.310839\pi\)
\(410\) 313.050i 0.763535i
\(411\) 270.000 + 241.495i 0.656934 + 0.587580i
\(412\) −26.0000 −0.0631068
\(413\) 26.8328i 0.0649705i
\(414\) −30.0000 268.328i −0.0724638 0.648136i
\(415\) 210.000 0.506024
\(416\) 250.440i 0.602018i
\(417\) 164.000 183.358i 0.393285 0.439706i
\(418\) −20.0000 −0.0478469
\(419\) 594.794i 1.41956i −0.704425 0.709778i \(-0.748795\pi\)
0.704425 0.709778i \(-0.251205\pi\)
\(420\) −30.0000 26.8328i −0.0714286 0.0638877i
\(421\) 562.000 1.33492 0.667458 0.744647i \(-0.267382\pi\)
0.667458 + 0.744647i \(0.267382\pi\)
\(422\) 4.47214i 0.0105975i
\(423\) −440.000 + 49.1935i −1.04019 + 0.116297i
\(424\) 30.0000 0.0707547
\(425\) 22.3607i 0.0526134i
\(426\) 560.000 626.099i 1.31455 1.46972i
\(427\) −492.000 −1.15222
\(428\) 201.246i 0.470201i
\(429\) −160.000 143.108i −0.372960 0.333586i
\(430\) 80.0000 0.186047
\(431\) 348.827i 0.809342i 0.914462 + 0.404671i \(0.132614\pi\)
−0.914462 + 0.404671i \(0.867386\pi\)
\(432\) −418.000 297.397i −0.967593 0.688419i
\(433\) 226.000 0.521940 0.260970 0.965347i \(-0.415958\pi\)
0.260970 + 0.965347i \(0.415958\pi\)
\(434\) 241.495i 0.556441i
\(435\) −140.000 + 156.525i −0.321839 + 0.359827i
\(436\) −38.0000 −0.0871560
\(437\) 26.8328i 0.0614023i
\(438\) −370.000 330.938i −0.844749 0.755566i
\(439\) −2.00000 −0.00455581 −0.00227790 0.999997i \(-0.500725\pi\)
−0.00227790 + 0.999997i \(0.500725\pi\)
\(440\) 67.0820i 0.152459i
\(441\) 13.0000 + 116.276i 0.0294785 + 0.263663i
\(442\) 160.000 0.361991
\(443\) 201.246i 0.454280i 0.973862 + 0.227140i \(0.0729375\pi\)
−0.973862 + 0.227140i \(0.927062\pi\)
\(444\) −32.0000 + 35.7771i −0.0720721 + 0.0805790i
\(445\) −240.000 −0.539326
\(446\) 192.302i 0.431170i
\(447\) 250.000 + 223.607i 0.559284 + 0.500239i
\(448\) 246.000 0.549107
\(449\) 313.050i 0.697215i 0.937269 + 0.348607i \(0.113345\pi\)
−0.937269 + 0.348607i \(0.886655\pi\)
\(450\) 100.000 11.1803i 0.222222 0.0248452i
\(451\) −280.000 −0.620843
\(452\) 31.3050i 0.0692587i
\(453\) 316.000 353.299i 0.697572 0.779909i
\(454\) −130.000 −0.286344
\(455\) 214.663i 0.471786i
\(456\) −30.0000 26.8328i −0.0657895 0.0588439i
\(457\) 334.000 0.730853 0.365427 0.930840i \(-0.380923\pi\)
0.365427 + 0.930840i \(0.380923\pi\)
\(458\) 630.571i 1.37679i
\(459\) −70.0000 + 98.3870i −0.152505 + 0.214351i
\(460\) 30.0000 0.0652174
\(461\) 93.9149i 0.203720i 0.994799 + 0.101860i \(0.0324794\pi\)
−0.994799 + 0.101860i \(0.967521\pi\)
\(462\) 120.000 134.164i 0.259740 0.290398i
\(463\) 366.000 0.790497 0.395248 0.918574i \(-0.370659\pi\)
0.395248 + 0.918574i \(0.370659\pi\)
\(464\) 594.794i 1.28188i
\(465\) 90.0000 + 80.4984i 0.193548 + 0.173115i
\(466\) −810.000 −1.73820
\(467\) 451.686i 0.967207i 0.875287 + 0.483604i \(0.160672\pi\)
−0.875287 + 0.483604i \(0.839328\pi\)
\(468\) 16.0000 + 143.108i 0.0341880 + 0.305787i
\(469\) −144.000 −0.307036
\(470\) 245.967i 0.523335i
\(471\) −328.000 + 366.715i −0.696391 + 0.778588i
\(472\) 30.0000 0.0635593
\(473\) 71.5542i 0.151277i
\(474\) 690.000 + 617.155i 1.45570 + 1.30201i
\(475\) 10.0000 0.0210526
\(476\) 26.8328i 0.0563715i
\(477\) 40.0000 4.47214i 0.0838574 0.00937555i
\(478\) −560.000 −1.17155
\(479\) 590.322i 1.23240i −0.787588 0.616202i \(-0.788670\pi\)
0.787588 0.616202i \(-0.211330\pi\)
\(480\) 70.0000 78.2624i 0.145833 0.163047i
\(481\) −256.000 −0.532225
\(482\) 585.850i 1.21546i
\(483\) 180.000 + 160.997i 0.372671 + 0.333327i
\(484\) −101.000 −0.208678
\(485\) 371.187i 0.765335i
\(486\) −475.000 263.856i −0.977366 0.542914i
\(487\) −886.000 −1.81930 −0.909651 0.415374i \(-0.863651\pi\)
−0.909651 + 0.415374i \(0.863651\pi\)
\(488\) 550.073i 1.12720i
\(489\) −472.000 + 527.712i −0.965235 + 1.07917i
\(490\) −65.0000 −0.132653
\(491\) 406.964i 0.828848i −0.910084 0.414424i \(-0.863983\pi\)
0.910084 0.414424i \(-0.136017\pi\)
\(492\) 140.000 + 125.220i 0.284553 + 0.254512i
\(493\) 140.000 0.283976
\(494\) 71.5542i 0.144847i
\(495\) 10.0000 + 89.4427i 0.0202020 + 0.180692i
\(496\) 342.000 0.689516
\(497\) 751.319i 1.51171i
\(498\) 420.000 469.574i 0.843373 0.942920i
\(499\) −2.00000 −0.00400802 −0.00200401 0.999998i \(-0.500638\pi\)
−0.00200401 + 0.999998i \(0.500638\pi\)
\(500\) 11.1803i 0.0223607i
\(501\) −210.000 187.830i −0.419162 0.374910i
\(502\) 1050.00 2.09163
\(503\) 219.135i 0.435655i −0.975987 0.217828i \(-0.930103\pi\)
0.975987 0.217828i \(-0.0698971\pi\)
\(504\) 360.000 40.2492i 0.714286 0.0798596i
\(505\) −150.000 −0.297030
\(506\) 134.164i 0.265146i
\(507\) −174.000 + 194.538i −0.343195 + 0.383704i
\(508\) 26.0000 0.0511811
\(509\) 800.512i 1.57272i −0.617771 0.786358i \(-0.711964\pi\)
0.617771 0.786358i \(-0.288036\pi\)
\(510\) −50.0000 44.7214i −0.0980392 0.0876889i
\(511\) 444.000 0.868885
\(512\) 212.426i 0.414895i
\(513\) −44.0000 31.3050i −0.0857700 0.0610233i
\(514\) 450.000 0.875486
\(515\) 58.1378i 0.112889i
\(516\) 32.0000 35.7771i 0.0620155 0.0693354i
\(517\) 220.000 0.425532
\(518\) 214.663i 0.414406i
\(519\) −30.0000 26.8328i −0.0578035 0.0517010i
\(520\) 240.000 0.461538
\(521\) 527.712i 1.01288i −0.862274 0.506441i \(-0.830961\pi\)
0.862274 0.506441i \(-0.169039\pi\)
\(522\) 70.0000 + 626.099i 0.134100 + 1.19942i
\(523\) 376.000 0.718929 0.359465 0.933159i \(-0.382959\pi\)
0.359465 + 0.933159i \(0.382959\pi\)
\(524\) 13.4164i 0.0256038i
\(525\) −60.0000 + 67.0820i −0.114286 + 0.127775i
\(526\) −130.000 −0.247148
\(527\) 80.4984i 0.152748i
\(528\) 190.000 + 169.941i 0.359848 + 0.321858i
\(529\) 349.000 0.659735
\(530\) 22.3607i 0.0421900i
\(531\) 40.0000 4.47214i 0.0753296 0.00842210i
\(532\) −12.0000 −0.0225564
\(533\) 1001.76i 1.87947i
\(534\) −480.000 + 536.656i −0.898876 + 1.00497i
\(535\) −450.000 −0.841121
\(536\) 160.997i 0.300367i
\(537\) −430.000 384.604i −0.800745 0.716208i
\(538\) −830.000 −1.54275
\(539\) 58.1378i 0.107862i
\(540\) 35.0000 49.1935i 0.0648148 0.0910991i
\(541\) −198.000 −0.365989 −0.182994 0.983114i \(-0.558579\pi\)
−0.182994 + 0.983114i \(0.558579\pi\)
\(542\) 183.358i 0.338298i
\(543\) −4.00000 + 4.47214i −0.00736648 + 0.00823598i
\(544\) −70.0000 −0.128676
\(545\) 84.9706i 0.155909i
\(546\) −480.000 429.325i −0.879121 0.786310i
\(547\) 1024.00 1.87203 0.936015 0.351961i \(-0.114485\pi\)
0.936015 + 0.351961i \(0.114485\pi\)
\(548\) 120.748i 0.220342i
\(549\) −82.0000 733.430i −0.149362 1.33594i
\(550\) −50.0000 −0.0909091
\(551\) 62.6099i 0.113630i
\(552\) −180.000 + 201.246i −0.326087 + 0.364576i
\(553\) −828.000 −1.49729
\(554\) 53.6656i 0.0968694i
\(555\) 80.0000 + 71.5542i 0.144144 + 0.128926i
\(556\) 82.0000 0.147482
\(557\) 67.0820i 0.120435i 0.998185 + 0.0602173i \(0.0191794\pi\)
−0.998185 + 0.0602173i \(0.980821\pi\)
\(558\) 360.000 40.2492i 0.645161 0.0721312i
\(559\) 256.000 0.457961
\(560\) 254.912i 0.455200i
\(561\) 40.0000 44.7214i 0.0713012 0.0797172i
\(562\) −420.000 −0.747331
\(563\) 254.912i 0.452774i 0.974037 + 0.226387i \(0.0726914\pi\)
−0.974037 + 0.226387i \(0.927309\pi\)
\(564\) −110.000 98.3870i −0.195035 0.174445i
\(565\) −70.0000 −0.123894
\(566\) 321.994i 0.568894i
\(567\) 474.000 107.331i 0.835979 0.189297i
\(568\) −840.000 −1.47887
\(569\) 858.650i 1.50905i 0.656271 + 0.754526i \(0.272133\pi\)
−0.656271 + 0.754526i \(0.727867\pi\)
\(570\) 20.0000 22.3607i 0.0350877 0.0392293i
\(571\) 962.000 1.68476 0.842382 0.538881i \(-0.181153\pi\)
0.842382 + 0.538881i \(0.181153\pi\)
\(572\) 71.5542i 0.125095i
\(573\) 460.000 + 411.437i 0.802792 + 0.718039i
\(574\) −840.000 −1.46341
\(575\) 67.0820i 0.116664i
\(576\) 41.0000 + 366.715i 0.0711806 + 0.636658i
\(577\) −886.000 −1.53553 −0.767764 0.640732i \(-0.778631\pi\)
−0.767764 + 0.640732i \(0.778631\pi\)
\(578\) 601.502i 1.04066i
\(579\) 428.000 478.519i 0.739206 0.826457i
\(580\) −70.0000 −0.120690
\(581\) 563.489i 0.969861i
\(582\) −830.000 742.375i −1.42612 1.27556i
\(583\) −20.0000 −0.0343053
\(584\) 496.407i 0.850012i
\(585\) 320.000 35.7771i 0.547009 0.0611574i
\(586\) 1050.00 1.79181
\(587\) 657.404i 1.11994i −0.828513 0.559969i \(-0.810813\pi\)
0.828513 0.559969i \(-0.189187\pi\)
\(588\) −26.0000 + 29.0689i −0.0442177 + 0.0494369i
\(589\) 36.0000 0.0611205
\(590\) 22.3607i 0.0378995i
\(591\) 210.000 + 187.830i 0.355330 + 0.317817i
\(592\) 304.000 0.513514
\(593\) 111.803i 0.188539i −0.995547 0.0942693i \(-0.969949\pi\)
0.995547 0.0942693i \(-0.0300515\pi\)
\(594\) 220.000 + 156.525i 0.370370 + 0.263510i
\(595\) 60.0000 0.100840
\(596\) 111.803i 0.187590i
\(597\) 484.000 541.128i 0.810720 0.906413i
\(598\) 480.000 0.802676
\(599\) 223.607i 0.373300i 0.982426 + 0.186650i \(0.0597631\pi\)
−0.982426 + 0.186650i \(0.940237\pi\)
\(600\) −75.0000 67.0820i −0.125000 0.111803i
\(601\) 2.00000 0.00332779 0.00166389 0.999999i \(-0.499470\pi\)
0.00166389 + 0.999999i \(0.499470\pi\)
\(602\) 214.663i 0.356582i
\(603\) −24.0000 214.663i −0.0398010 0.355991i
\(604\) 158.000 0.261589
\(605\) 225.843i 0.373294i
\(606\) −300.000 + 335.410i −0.495050 + 0.553482i
\(607\) −506.000 −0.833608 −0.416804 0.908996i \(-0.636850\pi\)
−0.416804 + 0.908996i \(0.636850\pi\)
\(608\) 31.3050i 0.0514884i
\(609\) −420.000 375.659i −0.689655 0.616846i
\(610\) 410.000 0.672131
\(611\) 787.096i 1.28821i
\(612\) −40.0000 + 4.47214i −0.0653595 + 0.00730741i
\(613\) 556.000 0.907015 0.453507 0.891253i \(-0.350173\pi\)
0.453507 + 0.891253i \(0.350173\pi\)
\(614\) 411.437i 0.670092i
\(615\) 280.000 313.050i 0.455285 0.509024i
\(616\) −180.000 −0.292208
\(617\) 93.9149i 0.152212i 0.997100 + 0.0761060i \(0.0242488\pi\)
−0.997100 + 0.0761060i \(0.975751\pi\)
\(618\) 130.000 + 116.276i 0.210356 + 0.188148i
\(619\) −802.000 −1.29564 −0.647819 0.761794i \(-0.724319\pi\)
−0.647819 + 0.761794i \(0.724319\pi\)
\(620\) 40.2492i 0.0649181i
\(621\) −210.000 + 295.161i −0.338164 + 0.475299i
\(622\) 360.000 0.578778
\(623\) 643.988i 1.03369i
\(624\) 608.000 679.765i 0.974359 1.08937i
\(625\) 25.0000 0.0400000
\(626\) 881.011i 1.40737i
\(627\) 20.0000 + 17.8885i 0.0318979 + 0.0285304i
\(628\) −164.000 −0.261146
\(629\) 71.5542i 0.113759i
\(630\) 30.0000 + 268.328i 0.0476190 + 0.425918i
\(631\) −698.000 −1.10618 −0.553090 0.833121i \(-0.686552\pi\)
−0.553090 + 0.833121i \(0.686552\pi\)
\(632\) 925.732i 1.46477i
\(633\) −4.00000 + 4.47214i −0.00631912 + 0.00706499i
\(634\) 1010.00 1.59306
\(635\) 58.1378i 0.0915555i
\(636\) 10.0000 + 8.94427i 0.0157233 + 0.0140633i
\(637\) −208.000 −0.326531
\(638\) 313.050i 0.490673i
\(639\) −1120.00 + 125.220i −1.75274 + 0.195962i
\(640\) −345.000 −0.539062
\(641\) 912.316i 1.42327i 0.702550 + 0.711635i \(0.252045\pi\)
−0.702550 + 0.711635i \(0.747955\pi\)
\(642\) −900.000 + 1006.23i −1.40187 + 1.56734i
\(643\) 156.000 0.242613 0.121306 0.992615i \(-0.461292\pi\)
0.121306 + 0.992615i \(0.461292\pi\)
\(644\) 80.4984i 0.124998i
\(645\) −80.0000 71.5542i −0.124031 0.110937i
\(646\) −20.0000 −0.0309598
\(647\) 755.791i 1.16815i 0.811701 + 0.584073i \(0.198542\pi\)
−0.811701 + 0.584073i \(0.801458\pi\)
\(648\) 120.000 + 529.948i 0.185185 + 0.817821i
\(649\) −20.0000 −0.0308166
\(650\) 178.885i 0.275208i
\(651\) −216.000 + 241.495i −0.331797 + 0.370961i
\(652\) −236.000 −0.361963
\(653\) 487.463i 0.746497i −0.927731 0.373249i \(-0.878244\pi\)
0.927731 0.373249i \(-0.121756\pi\)
\(654\) 190.000 + 169.941i 0.290520 + 0.259849i
\(655\) −30.0000 −0.0458015
\(656\) 1189.59i 1.81340i
\(657\) 74.0000 + 661.876i 0.112633 + 1.00742i
\(658\) 660.000 1.00304
\(659\) 406.964i 0.617548i 0.951135 + 0.308774i \(0.0999187\pi\)
−0.951135 + 0.308774i \(0.900081\pi\)
\(660\) −20.0000 + 22.3607i −0.0303030 + 0.0338798i
\(661\) 682.000 1.03177 0.515885 0.856658i \(-0.327463\pi\)
0.515885 + 0.856658i \(0.327463\pi\)
\(662\) 442.741i 0.668794i
\(663\) −160.000 143.108i −0.241327 0.215850i
\(664\) −630.000 −0.948795
\(665\) 26.8328i 0.0403501i
\(666\) 320.000 35.7771i 0.480480 0.0537194i
\(667\) 420.000 0.629685
\(668\) 93.9149i 0.140591i
\(669\) −172.000 + 192.302i −0.257100 + 0.287447i
\(670\) 120.000 0.179104
\(671\) 366.715i 0.546520i
\(672\) 210.000 + 187.830i 0.312500 + 0.279508i
\(673\) −894.000 −1.32838 −0.664190 0.747564i \(-0.731223\pi\)
−0.664190 + 0.747564i \(0.731223\pi\)
\(674\) 881.011i 1.30714i
\(675\) −110.000 78.2624i −0.162963 0.115944i
\(676\) −87.0000 −0.128698
\(677\) 550.073i 0.812515i −0.913759 0.406258i \(-0.866834\pi\)
0.913759 0.406258i \(-0.133166\pi\)
\(678\) −140.000 + 156.525i −0.206490 + 0.230862i
\(679\) 996.000 1.46686
\(680\) 67.0820i 0.0986501i
\(681\) 130.000 + 116.276i 0.190896 + 0.170742i
\(682\) −180.000 −0.263930
\(683\) 442.741i 0.648231i 0.946018 + 0.324115i \(0.105067\pi\)
−0.946018 + 0.324115i \(0.894933\pi\)
\(684\) −2.00000 17.8885i −0.00292398 0.0261528i
\(685\) 270.000 0.394161
\(686\) 831.817i 1.21256i
\(687\) 564.000 630.571i 0.820961 0.917862i
\(688\) −304.000 −0.441860
\(689\) 71.5542i 0.103852i
\(690\) −150.000 134.164i −0.217391 0.194441i
\(691\) −758.000 −1.09696 −0.548480 0.836163i \(-0.684793\pi\)
−0.548480 + 0.836163i \(0.684793\pi\)
\(692\) 13.4164i 0.0193879i
\(693\) −240.000 + 26.8328i −0.346320 + 0.0387198i
\(694\) −410.000 −0.590778
\(695\) 183.358i 0.263824i
\(696\) 420.000 469.574i 0.603448 0.674676i
\(697\) −280.000 −0.401722
\(698\) 809.457i 1.15968i
\(699\) 810.000 + 724.486i 1.15880 + 1.03646i
\(700\) −30.0000 −0.0428571
\(701\) 782.624i 1.11644i −0.829693 0.558220i \(-0.811485\pi\)
0.829693 0.558220i \(-0.188515\pi\)
\(702\) 560.000 787.096i 0.797721 1.12122i
\(703\) 32.0000 0.0455192
\(704\) 183.358i 0.260451i
\(705\) −220.000 + 245.967i −0.312057 + 0.348890i
\(706\) −690.000 −0.977337
\(707\) 402.492i 0.569296i
\(708\) 10.0000 + 8.94427i 0.0141243 + 0.0126332i
\(709\) −2.00000 −0.00282087 −0.00141044 0.999999i \(-0.500449\pi\)
−0.00141044 + 0.999999i \(0.500449\pi\)
\(710\) 626.099i 0.881830i
\(711\) −138.000 1234.31i −0.194093 1.73602i
\(712\) 720.000 1.01124
\(713\) 241.495i 0.338703i
\(714\) 120.000 134.164i 0.168067 0.187905i
\(715\) −160.000 −0.223776
\(716\) 192.302i 0.268578i
\(717\) 560.000 + 500.879i 0.781032 + 0.698576i
\(718\) 660.000 0.919220
\(719\) 858.650i 1.19423i 0.802156 + 0.597114i \(0.203686\pi\)
−0.802156 + 0.597114i \(0.796314\pi\)
\(720\) −380.000 + 42.4853i −0.527778 + 0.0590073i
\(721\) −156.000 −0.216366
\(722\) 798.276i 1.10565i
\(723\) −524.000 + 585.850i −0.724758 + 0.810304i
\(724\) −2.00000 −0.00276243
\(725\) 156.525i 0.215896i
\(726\) 505.000 + 451.686i 0.695592 + 0.622157i
\(727\) 674.000 0.927098 0.463549 0.886071i \(-0.346576\pi\)
0.463549 + 0.886071i \(0.346576\pi\)
\(728\) 643.988i 0.884598i
\(729\) 239.000 + 688.709i 0.327846 + 0.944731i
\(730\) −370.000 −0.506849
\(731\) 71.5542i 0.0978853i
\(732\) 164.000 183.358i 0.224044 0.250488i
\(733\) 656.000 0.894952 0.447476 0.894296i \(-0.352323\pi\)
0.447476 + 0.894296i \(0.352323\pi\)
\(734\) 415.909i 0.566633i
\(735\) 65.0000 + 58.1378i 0.0884354 + 0.0790990i
\(736\) −210.000 −0.285326
\(737\) 107.331i 0.145633i
\(738\) −140.000 1252.20i −0.189702 1.69675i
\(739\) 598.000 0.809202 0.404601 0.914493i \(-0.367410\pi\)
0.404601 + 0.914493i \(0.367410\pi\)
\(740\) 35.7771i 0.0483474i
\(741\) 64.0000 71.5542i 0.0863698 0.0965643i
\(742\) −60.0000 −0.0808625
\(743\) 782.624i 1.05333i 0.850073 + 0.526665i \(0.176558\pi\)
−0.850073 + 0.526665i \(0.823442\pi\)
\(744\) −270.000 241.495i −0.362903 0.324591i
\(745\) 250.000 0.335570
\(746\) 98.3870i 0.131886i
\(747\) −840.000 + 93.9149i −1.12450 + 0.125723i
\(748\) 20.0000 0.0267380
\(749\) 1207.48i 1.61212i
\(750\) 50.0000 55.9017i 0.0666667 0.0745356i
\(751\) −338.000 −0.450067 −0.225033 0.974351i \(-0.572249\pi\)
−0.225033 + 0.974351i \(0.572249\pi\)
\(752\) 934.676i 1.24292i
\(753\) −1050.00 939.149i −1.39442 1.24721i
\(754\) −1120.00 −1.48541
\(755\) 353.299i 0.467945i
\(756\) 132.000 + 93.9149i 0.174603 + 0.124226i
\(757\) −656.000 −0.866579 −0.433289 0.901255i \(-0.642647\pi\)
−0.433289 + 0.901255i \(0.642647\pi\)
\(758\) 809.457i 1.06788i
\(759\) 120.000 134.164i 0.158103 0.176764i
\(760\) −30.0000 −0.0394737
\(761\) 295.161i 0.387859i 0.981015 + 0.193930i \(0.0621234\pi\)
−0.981015 + 0.193930i \(0.937877\pi\)
\(762\) −130.000 116.276i −0.170604 0.152593i
\(763\) −228.000 −0.298820
\(764\) 205.718i 0.269265i
\(765\) 10.0000 + 89.4427i 0.0130719 + 0.116919i
\(766\) −810.000 −1.05744
\(767\) 71.5542i 0.0932910i
\(768\) −362.000 + 404.728i −0.471354 + 0.526990i
\(769\) −82.0000 −0.106632 −0.0533160 0.998578i \(-0.516979\pi\)
−0.0533160 + 0.998578i \(0.516979\pi\)
\(770\) 134.164i 0.174239i
\(771\) −450.000 402.492i −0.583658 0.522039i
\(772\) 214.000 0.277202
\(773\) 1059.90i 1.37115i −0.728004 0.685573i \(-0.759552\pi\)
0.728004 0.685573i \(-0.240448\pi\)
\(774\) −320.000 + 35.7771i −0.413437 + 0.0462236i
\(775\) 90.0000 0.116129
\(776\) 1113.56i 1.43500i
\(777\) −192.000 + 214.663i −0.247104 + 0.276271i
\(778\) 990.000 1.27249
\(779\) 125.220i 0.160744i
\(780\) 80.0000 + 71.5542i 0.102564 + 0.0917361i
\(781\) 560.000 0.717029