Properties

Label 72.4.d.c.37.1
Level $72$
Weight $4$
Character 72.37
Analytic conductor $4.248$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,4,Mod(37,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 72.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.24813752041\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-10}, \sqrt{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 6x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.1
Root \(-2.34521 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 72.37
Dual form 72.4.d.c.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.34521 - 1.58114i) q^{2} +(3.00000 + 7.41620i) q^{4} -6.32456i q^{5} +10.0000 q^{7} +(4.69042 - 22.1359i) q^{8} +O(q^{10})\) \(q+(-2.34521 - 1.58114i) q^{2} +(3.00000 + 7.41620i) q^{4} -6.32456i q^{5} +10.0000 q^{7} +(4.69042 - 22.1359i) q^{8} +(-10.0000 + 14.8324i) q^{10} -37.9473i q^{11} -59.3296i q^{13} +(-23.4521 - 15.8114i) q^{14} +(-46.0000 + 44.4972i) q^{16} -75.0467 q^{17} -118.659i q^{19} +(46.9042 - 18.9737i) q^{20} +(-60.0000 + 88.9944i) q^{22} +150.093 q^{23} +85.0000 q^{25} +(-93.8083 + 139.140i) q^{26} +(30.0000 + 74.1620i) q^{28} +246.658i q^{29} +62.0000 q^{31} +(178.236 - 31.6228i) q^{32} +(176.000 + 118.659i) q^{34} -63.2456i q^{35} -59.3296i q^{37} +(-187.617 + 278.280i) q^{38} +(-140.000 - 29.6648i) q^{40} -375.233 q^{41} +118.659i q^{43} +(281.425 - 113.842i) q^{44} +(-352.000 - 237.318i) q^{46} +450.280 q^{47} -243.000 q^{49} +(-199.343 - 134.397i) q^{50} +(440.000 - 177.989i) q^{52} +132.816i q^{53} -240.000 q^{55} +(46.9042 - 221.359i) q^{56} +(390.000 - 578.463i) q^{58} -733.648i q^{59} +533.966i q^{61} +(-145.403 - 98.0306i) q^{62} +(-468.000 - 207.654i) q^{64} -375.233 q^{65} +711.955i q^{67} +(-225.140 - 556.561i) q^{68} +(-100.000 + 148.324i) q^{70} +30.0000 q^{73} +(-93.8083 + 139.140i) q^{74} +(880.000 - 355.978i) q^{76} -379.473i q^{77} +94.0000 q^{79} +(281.425 + 290.930i) q^{80} +(880.000 + 593.296i) q^{82} +670.403i q^{83} +474.637i q^{85} +(187.617 - 278.280i) q^{86} +(-840.000 - 177.989i) q^{88} +750.467 q^{89} -593.296i q^{91} +(450.280 + 1113.12i) q^{92} +(-1056.00 - 711.955i) q^{94} -750.467 q^{95} +130.000 q^{97} +(569.886 + 384.217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{4} + 40 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{4} + 40 q^{7} - 40 q^{10} - 184 q^{16} - 240 q^{22} + 340 q^{25} + 120 q^{28} + 248 q^{31} + 704 q^{34} - 560 q^{40} - 1408 q^{46} - 972 q^{49} + 1760 q^{52} - 960 q^{55} + 1560 q^{58} - 1872 q^{64} - 400 q^{70} + 120 q^{73} + 3520 q^{76} + 376 q^{79} + 3520 q^{82} - 3360 q^{88} - 4224 q^{94} + 520 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34521 1.58114i −0.829156 0.559017i
\(3\) 0 0
\(4\) 3.00000 + 7.41620i 0.375000 + 0.927025i
\(5\) 6.32456i 0.565685i −0.959166 0.282843i \(-0.908723\pi\)
0.959166 0.282843i \(-0.0912774\pi\)
\(6\) 0 0
\(7\) 10.0000 0.539949 0.269975 0.962867i \(-0.412985\pi\)
0.269975 + 0.962867i \(0.412985\pi\)
\(8\) 4.69042 22.1359i 0.207289 0.978280i
\(9\) 0 0
\(10\) −10.0000 + 14.8324i −0.316228 + 0.469042i
\(11\) 37.9473i 1.04014i −0.854123 0.520071i \(-0.825906\pi\)
0.854123 0.520071i \(-0.174094\pi\)
\(12\) 0 0
\(13\) 59.3296i 1.26577i −0.774244 0.632887i \(-0.781870\pi\)
0.774244 0.632887i \(-0.218130\pi\)
\(14\) −23.4521 15.8114i −0.447702 0.301841i
\(15\) 0 0
\(16\) −46.0000 + 44.4972i −0.718750 + 0.695269i
\(17\) −75.0467 −1.07068 −0.535338 0.844638i \(-0.679816\pi\)
−0.535338 + 0.844638i \(0.679816\pi\)
\(18\) 0 0
\(19\) 118.659i 1.43275i −0.697715 0.716376i \(-0.745800\pi\)
0.697715 0.716376i \(-0.254200\pi\)
\(20\) 46.9042 18.9737i 0.524404 0.212132i
\(21\) 0 0
\(22\) −60.0000 + 88.9944i −0.581456 + 0.862439i
\(23\) 150.093 1.36072 0.680361 0.732877i \(-0.261823\pi\)
0.680361 + 0.732877i \(0.261823\pi\)
\(24\) 0 0
\(25\) 85.0000 0.680000
\(26\) −93.8083 + 139.140i −0.707589 + 1.04952i
\(27\) 0 0
\(28\) 30.0000 + 74.1620i 0.202481 + 0.500546i
\(29\) 246.658i 1.57942i 0.613480 + 0.789710i \(0.289769\pi\)
−0.613480 + 0.789710i \(0.710231\pi\)
\(30\) 0 0
\(31\) 62.0000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 178.236 31.6228i 0.984623 0.174693i
\(33\) 0 0
\(34\) 176.000 + 118.659i 0.887757 + 0.598526i
\(35\) 63.2456i 0.305441i
\(36\) 0 0
\(37\) 59.3296i 0.263614i −0.991275 0.131807i \(-0.957922\pi\)
0.991275 0.131807i \(-0.0420779\pi\)
\(38\) −187.617 + 278.280i −0.800933 + 1.18797i
\(39\) 0 0
\(40\) −140.000 29.6648i −0.553399 0.117260i
\(41\) −375.233 −1.42931 −0.714654 0.699479i \(-0.753416\pi\)
−0.714654 + 0.699479i \(0.753416\pi\)
\(42\) 0 0
\(43\) 118.659i 0.420822i 0.977613 + 0.210411i \(0.0674802\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(44\) 281.425 113.842i 0.964237 0.390053i
\(45\) 0 0
\(46\) −352.000 237.318i −1.12825 0.760667i
\(47\) 450.280 1.39745 0.698724 0.715391i \(-0.253751\pi\)
0.698724 + 0.715391i \(0.253751\pi\)
\(48\) 0 0
\(49\) −243.000 −0.708455
\(50\) −199.343 134.397i −0.563826 0.380132i
\(51\) 0 0
\(52\) 440.000 177.989i 1.17340 0.474665i
\(53\) 132.816i 0.344220i 0.985078 + 0.172110i \(0.0550584\pi\)
−0.985078 + 0.172110i \(0.944942\pi\)
\(54\) 0 0
\(55\) −240.000 −0.588393
\(56\) 46.9042 221.359i 0.111926 0.528221i
\(57\) 0 0
\(58\) 390.000 578.463i 0.882923 1.30959i
\(59\) 733.648i 1.61886i −0.587215 0.809431i \(-0.699776\pi\)
0.587215 0.809431i \(-0.300224\pi\)
\(60\) 0 0
\(61\) 533.966i 1.12078i 0.828230 + 0.560388i \(0.189348\pi\)
−0.828230 + 0.560388i \(0.810652\pi\)
\(62\) −145.403 98.0306i −0.297842 0.200805i
\(63\) 0 0
\(64\) −468.000 207.654i −0.914062 0.405573i
\(65\) −375.233 −0.716030
\(66\) 0 0
\(67\) 711.955i 1.29820i 0.760705 + 0.649098i \(0.224854\pi\)
−0.760705 + 0.649098i \(0.775146\pi\)
\(68\) −225.140 556.561i −0.401503 0.992543i
\(69\) 0 0
\(70\) −100.000 + 148.324i −0.170747 + 0.253259i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 30.0000 0.0480991 0.0240496 0.999711i \(-0.492344\pi\)
0.0240496 + 0.999711i \(0.492344\pi\)
\(74\) −93.8083 + 139.140i −0.147365 + 0.218577i
\(75\) 0 0
\(76\) 880.000 355.978i 1.32820 0.537282i
\(77\) 379.473i 0.561623i
\(78\) 0 0
\(79\) 94.0000 0.133871 0.0669356 0.997757i \(-0.478678\pi\)
0.0669356 + 0.997757i \(0.478678\pi\)
\(80\) 281.425 + 290.930i 0.393303 + 0.406586i
\(81\) 0 0
\(82\) 880.000 + 593.296i 1.18512 + 0.799007i
\(83\) 670.403i 0.886582i 0.896378 + 0.443291i \(0.146189\pi\)
−0.896378 + 0.443291i \(0.853811\pi\)
\(84\) 0 0
\(85\) 474.637i 0.605666i
\(86\) 187.617 278.280i 0.235247 0.348927i
\(87\) 0 0
\(88\) −840.000 177.989i −1.01755 0.215610i
\(89\) 750.467 0.893812 0.446906 0.894581i \(-0.352526\pi\)
0.446906 + 0.894581i \(0.352526\pi\)
\(90\) 0 0
\(91\) 593.296i 0.683454i
\(92\) 450.280 + 1113.12i 0.510271 + 1.26142i
\(93\) 0 0
\(94\) −1056.00 711.955i −1.15870 0.781197i
\(95\) −750.467 −0.810487
\(96\) 0 0
\(97\) 130.000 0.136077 0.0680387 0.997683i \(-0.478326\pi\)
0.0680387 + 0.997683i \(0.478326\pi\)
\(98\) 569.886 + 384.217i 0.587420 + 0.396038i
\(99\) 0 0
\(100\) 255.000 + 630.377i 0.255000 + 0.630377i
\(101\) 562.885i 0.554546i 0.960791 + 0.277273i \(0.0894307\pi\)
−0.960791 + 0.277273i \(0.910569\pi\)
\(102\) 0 0
\(103\) −570.000 −0.545279 −0.272640 0.962116i \(-0.587897\pi\)
−0.272640 + 0.962116i \(0.587897\pi\)
\(104\) −1313.32 278.280i −1.23828 0.262381i
\(105\) 0 0
\(106\) 210.000 311.480i 0.192425 0.285412i
\(107\) 1290.21i 1.16569i 0.812582 + 0.582847i \(0.198061\pi\)
−0.812582 + 0.582847i \(0.801939\pi\)
\(108\) 0 0
\(109\) 1720.56i 1.51192i −0.654616 0.755961i \(-0.727170\pi\)
0.654616 0.755961i \(-0.272830\pi\)
\(110\) 562.850 + 379.473i 0.487869 + 0.328921i
\(111\) 0 0
\(112\) −460.000 + 444.972i −0.388089 + 0.375410i
\(113\) 1350.84 1.12457 0.562285 0.826944i \(-0.309923\pi\)
0.562285 + 0.826944i \(0.309923\pi\)
\(114\) 0 0
\(115\) 949.273i 0.769741i
\(116\) −1829.26 + 739.973i −1.46416 + 0.592282i
\(117\) 0 0
\(118\) −1160.00 + 1720.56i −0.904972 + 1.34229i
\(119\) −750.467 −0.578111
\(120\) 0 0
\(121\) −109.000 −0.0818933
\(122\) 844.275 1252.26i 0.626533 0.929299i
\(123\) 0 0
\(124\) 186.000 + 459.804i 0.134704 + 0.332997i
\(125\) 1328.16i 0.950352i
\(126\) 0 0
\(127\) 2530.00 1.76773 0.883863 0.467746i \(-0.154934\pi\)
0.883863 + 0.467746i \(0.154934\pi\)
\(128\) 769.228 + 1226.96i 0.531178 + 0.847260i
\(129\) 0 0
\(130\) 880.000 + 593.296i 0.593701 + 0.400273i
\(131\) 252.982i 0.168726i 0.996435 + 0.0843632i \(0.0268856\pi\)
−0.996435 + 0.0843632i \(0.973114\pi\)
\(132\) 0 0
\(133\) 1186.59i 0.773613i
\(134\) 1125.70 1669.68i 0.725714 1.07641i
\(135\) 0 0
\(136\) −352.000 + 1661.23i −0.221939 + 1.04742i
\(137\) 675.420 0.421204 0.210602 0.977572i \(-0.432458\pi\)
0.210602 + 0.977572i \(0.432458\pi\)
\(138\) 0 0
\(139\) 237.318i 0.144814i 0.997375 + 0.0724068i \(0.0230680\pi\)
−0.997375 + 0.0724068i \(0.976932\pi\)
\(140\) 469.042 189.737i 0.283152 0.114541i
\(141\) 0 0
\(142\) 0 0
\(143\) −2251.40 −1.31658
\(144\) 0 0
\(145\) 1560.00 0.893455
\(146\) −70.3562 47.4342i −0.0398817 0.0268882i
\(147\) 0 0
\(148\) 440.000 177.989i 0.244377 0.0988553i
\(149\) 2940.92i 1.61698i −0.588513 0.808488i \(-0.700286\pi\)
0.588513 0.808488i \(-0.299714\pi\)
\(150\) 0 0
\(151\) −2262.00 −1.21907 −0.609533 0.792761i \(-0.708643\pi\)
−0.609533 + 0.792761i \(0.708643\pi\)
\(152\) −2626.63 556.561i −1.40163 0.296994i
\(153\) 0 0
\(154\) −600.000 + 889.944i −0.313957 + 0.465673i
\(155\) 392.122i 0.203200i
\(156\) 0 0
\(157\) 1720.56i 0.874621i 0.899311 + 0.437310i \(0.144069\pi\)
−0.899311 + 0.437310i \(0.855931\pi\)
\(158\) −220.450 148.627i −0.111000 0.0748363i
\(159\) 0 0
\(160\) −200.000 1127.26i −0.0988212 0.556987i
\(161\) 1500.93 0.734721
\(162\) 0 0
\(163\) 2017.21i 0.969324i −0.874702 0.484662i \(-0.838943\pi\)
0.874702 0.484662i \(-0.161057\pi\)
\(164\) −1125.70 2782.80i −0.535990 1.32500i
\(165\) 0 0
\(166\) 1060.00 1572.23i 0.495614 0.735115i
\(167\) −1050.65 −0.486838 −0.243419 0.969921i \(-0.578269\pi\)
−0.243419 + 0.969921i \(0.578269\pi\)
\(168\) 0 0
\(169\) −1323.00 −0.602185
\(170\) 750.467 1113.12i 0.338577 0.502191i
\(171\) 0 0
\(172\) −880.000 + 355.978i −0.390113 + 0.157808i
\(173\) 1423.02i 0.625379i 0.949855 + 0.312690i \(0.101230\pi\)
−0.949855 + 0.312690i \(0.898770\pi\)
\(174\) 0 0
\(175\) 850.000 0.367165
\(176\) 1688.55 + 1745.58i 0.723177 + 0.747601i
\(177\) 0 0
\(178\) −1760.00 1186.59i −0.741110 0.499656i
\(179\) 126.491i 0.0528178i −0.999651 0.0264089i \(-0.991593\pi\)
0.999651 0.0264089i \(-0.00840719\pi\)
\(180\) 0 0
\(181\) 59.3296i 0.0243643i 0.999926 + 0.0121821i \(0.00387779\pi\)
−0.999926 + 0.0121821i \(0.996122\pi\)
\(182\) −938.083 + 1391.40i −0.382062 + 0.566690i
\(183\) 0 0
\(184\) 704.000 3322.46i 0.282063 1.33117i
\(185\) −375.233 −0.149123
\(186\) 0 0
\(187\) 2847.82i 1.11365i
\(188\) 1350.84 + 3339.37i 0.524043 + 1.29547i
\(189\) 0 0
\(190\) 1760.00 + 1186.59i 0.672020 + 0.453076i
\(191\) 3752.33 1.42151 0.710757 0.703437i \(-0.248352\pi\)
0.710757 + 0.703437i \(0.248352\pi\)
\(192\) 0 0
\(193\) −1350.00 −0.503498 −0.251749 0.967793i \(-0.581006\pi\)
−0.251749 + 0.967793i \(0.581006\pi\)
\(194\) −304.877 205.548i −0.112829 0.0760695i
\(195\) 0 0
\(196\) −729.000 1802.14i −0.265671 0.656755i
\(197\) 1448.32i 0.523801i 0.965095 + 0.261900i \(0.0843492\pi\)
−0.965095 + 0.261900i \(0.915651\pi\)
\(198\) 0 0
\(199\) −3194.00 −1.13777 −0.568886 0.822416i \(-0.692625\pi\)
−0.568886 + 0.822416i \(0.692625\pi\)
\(200\) 398.685 1881.56i 0.140957 0.665230i
\(201\) 0 0
\(202\) 890.000 1320.08i 0.310001 0.459806i
\(203\) 2466.58i 0.852807i
\(204\) 0 0
\(205\) 2373.18i 0.808538i
\(206\) 1336.77 + 901.249i 0.452122 + 0.304820i
\(207\) 0 0
\(208\) 2640.00 + 2729.16i 0.880053 + 0.909775i
\(209\) −4502.80 −1.49026
\(210\) 0 0
\(211\) 5458.32i 1.78088i 0.455097 + 0.890442i \(0.349604\pi\)
−0.455097 + 0.890442i \(0.650396\pi\)
\(212\) −984.987 + 398.447i −0.319100 + 0.129082i
\(213\) 0 0
\(214\) 2040.00 3025.81i 0.651643 0.966542i
\(215\) 750.467 0.238053
\(216\) 0 0
\(217\) 620.000 0.193955
\(218\) −2720.44 + 4035.07i −0.845190 + 1.25362i
\(219\) 0 0
\(220\) −720.000 1779.89i −0.220647 0.545455i
\(221\) 4452.49i 1.35523i
\(222\) 0 0
\(223\) 5330.00 1.60055 0.800276 0.599632i \(-0.204686\pi\)
0.800276 + 0.599632i \(0.204686\pi\)
\(224\) 1782.36 316.228i 0.531646 0.0943253i
\(225\) 0 0
\(226\) −3168.00 2135.87i −0.932443 0.628653i
\(227\) 4768.71i 1.39432i −0.716915 0.697160i \(-0.754447\pi\)
0.716915 0.697160i \(-0.245553\pi\)
\(228\) 0 0
\(229\) 3619.10i 1.04435i 0.852837 + 0.522177i \(0.174880\pi\)
−0.852837 + 0.522177i \(0.825120\pi\)
\(230\) −1500.93 + 2226.24i −0.430298 + 0.638235i
\(231\) 0 0
\(232\) 5460.00 + 1156.93i 1.54511 + 0.327396i
\(233\) −150.093 −0.0422015 −0.0211007 0.999777i \(-0.506717\pi\)
−0.0211007 + 0.999777i \(0.506717\pi\)
\(234\) 0 0
\(235\) 2847.82i 0.790516i
\(236\) 5440.88 2200.95i 1.50073 0.607073i
\(237\) 0 0
\(238\) 1760.00 + 1186.59i 0.479344 + 0.323174i
\(239\) 2251.40 0.609334 0.304667 0.952459i \(-0.401455\pi\)
0.304667 + 0.952459i \(0.401455\pi\)
\(240\) 0 0
\(241\) −1162.00 −0.310585 −0.155293 0.987869i \(-0.549632\pi\)
−0.155293 + 0.987869i \(0.549632\pi\)
\(242\) 255.628 + 172.344i 0.0679023 + 0.0457798i
\(243\) 0 0
\(244\) −3960.00 + 1601.90i −1.03899 + 0.420291i
\(245\) 1536.87i 0.400763i
\(246\) 0 0
\(247\) −7040.00 −1.81354
\(248\) 290.806 1372.43i 0.0744604 0.351408i
\(249\) 0 0
\(250\) −2100.00 + 3114.80i −0.531263 + 0.787990i
\(251\) 645.105i 0.162226i −0.996705 0.0811128i \(-0.974153\pi\)
0.996705 0.0811128i \(-0.0258474\pi\)
\(252\) 0 0
\(253\) 5695.64i 1.41534i
\(254\) −5933.38 4000.28i −1.46572 0.988189i
\(255\) 0 0
\(256\) 136.000 4093.74i 0.0332031 0.999449i
\(257\) −1801.12 −0.437162 −0.218581 0.975819i \(-0.570143\pi\)
−0.218581 + 0.975819i \(0.570143\pi\)
\(258\) 0 0
\(259\) 593.296i 0.142338i
\(260\) −1125.70 2782.80i −0.268511 0.663778i
\(261\) 0 0
\(262\) 400.000 593.296i 0.0943209 0.139901i
\(263\) 6604.11 1.54839 0.774195 0.632947i \(-0.218155\pi\)
0.774195 + 0.632947i \(0.218155\pi\)
\(264\) 0 0
\(265\) 840.000 0.194720
\(266\) −1876.17 + 2782.80i −0.432463 + 0.641446i
\(267\) 0 0
\(268\) −5280.00 + 2135.87i −1.20346 + 0.486824i
\(269\) 6052.60i 1.37187i −0.727662 0.685936i \(-0.759393\pi\)
0.727662 0.685936i \(-0.240607\pi\)
\(270\) 0 0
\(271\) 6402.00 1.43503 0.717516 0.696542i \(-0.245279\pi\)
0.717516 + 0.696542i \(0.245279\pi\)
\(272\) 3452.15 3339.37i 0.769548 0.744407i
\(273\) 0 0
\(274\) −1584.00 1067.93i −0.349244 0.235460i
\(275\) 3225.52i 0.707296i
\(276\) 0 0
\(277\) 2076.54i 0.450422i −0.974310 0.225211i \(-0.927693\pi\)
0.974310 0.225211i \(-0.0723072\pi\)
\(278\) 375.233 556.561i 0.0809532 0.120073i
\(279\) 0 0
\(280\) −1400.00 296.648i −0.298807 0.0633147i
\(281\) −9005.60 −1.91185 −0.955923 0.293616i \(-0.905141\pi\)
−0.955923 + 0.293616i \(0.905141\pi\)
\(282\) 0 0
\(283\) 5221.00i 1.09667i −0.836260 0.548333i \(-0.815263\pi\)
0.836260 0.548333i \(-0.184737\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 5280.00 + 3559.78i 1.09165 + 0.735993i
\(287\) −3752.33 −0.771753
\(288\) 0 0
\(289\) 719.000 0.146346
\(290\) −3658.52 2466.58i −0.740814 0.499456i
\(291\) 0 0
\(292\) 90.0000 + 222.486i 0.0180372 + 0.0445891i
\(293\) 5293.65i 1.05549i 0.849403 + 0.527745i \(0.176962\pi\)
−0.849403 + 0.527745i \(0.823038\pi\)
\(294\) 0 0
\(295\) −4640.00 −0.915767
\(296\) −1313.32 278.280i −0.257888 0.0546443i
\(297\) 0 0
\(298\) −4650.00 + 6897.06i −0.903917 + 1.34073i
\(299\) 8904.97i 1.72237i
\(300\) 0 0
\(301\) 1186.59i 0.227223i
\(302\) 5304.86 + 3576.54i 1.01080 + 0.681479i
\(303\) 0 0
\(304\) 5280.00 + 5458.32i 0.996147 + 1.02979i
\(305\) 3377.10 0.634007
\(306\) 0 0
\(307\) 4983.69i 0.926495i −0.886229 0.463247i \(-0.846684\pi\)
0.886229 0.463247i \(-0.153316\pi\)
\(308\) 2814.25 1138.42i 0.520639 0.210609i
\(309\) 0 0
\(310\) −620.000 + 919.609i −0.113592 + 0.168485i
\(311\) 1500.93 0.273666 0.136833 0.990594i \(-0.456308\pi\)
0.136833 + 0.990594i \(0.456308\pi\)
\(312\) 0 0
\(313\) 6350.00 1.14672 0.573360 0.819304i \(-0.305640\pi\)
0.573360 + 0.819304i \(0.305640\pi\)
\(314\) 2720.44 4035.07i 0.488928 0.725197i
\(315\) 0 0
\(316\) 282.000 + 697.123i 0.0502017 + 0.124102i
\(317\) 1739.25i 0.308158i 0.988059 + 0.154079i \(0.0492411\pi\)
−0.988059 + 0.154079i \(0.950759\pi\)
\(318\) 0 0
\(319\) 9360.00 1.64282
\(320\) −1313.32 + 2959.89i −0.229427 + 0.517072i
\(321\) 0 0
\(322\) −3520.00 2373.18i −0.609199 0.410722i
\(323\) 8904.97i 1.53401i
\(324\) 0 0
\(325\) 5043.01i 0.860727i
\(326\) −3189.48 + 4730.77i −0.541868 + 0.803721i
\(327\) 0 0
\(328\) −1760.00 + 8306.14i −0.296280 + 1.39826i
\(329\) 4502.80 0.754551
\(330\) 0 0
\(331\) 3322.46i 0.551718i 0.961198 + 0.275859i \(0.0889623\pi\)
−0.961198 + 0.275859i \(0.911038\pi\)
\(332\) −4971.84 + 2011.21i −0.821883 + 0.332468i
\(333\) 0 0
\(334\) 2464.00 + 1661.23i 0.403665 + 0.272151i
\(335\) 4502.80 0.734371
\(336\) 0 0
\(337\) −1430.00 −0.231149 −0.115574 0.993299i \(-0.536871\pi\)
−0.115574 + 0.993299i \(0.536871\pi\)
\(338\) 3102.71 + 2091.85i 0.499305 + 0.336632i
\(339\) 0 0
\(340\) −3520.00 + 1423.91i −0.561467 + 0.227125i
\(341\) 2352.73i 0.373630i
\(342\) 0 0
\(343\) −5860.00 −0.922479
\(344\) 2626.63 + 556.561i 0.411682 + 0.0872318i
\(345\) 0 0
\(346\) 2250.00 3337.29i 0.349598 0.518537i
\(347\) 10106.6i 1.56355i 0.623559 + 0.781776i \(0.285686\pi\)
−0.623559 + 0.781776i \(0.714314\pi\)
\(348\) 0 0
\(349\) 1127.26i 0.172897i −0.996256 0.0864484i \(-0.972448\pi\)
0.996256 0.0864484i \(-0.0275518\pi\)
\(350\) −1993.43 1343.97i −0.304438 0.205252i
\(351\) 0 0
\(352\) −1200.00 6763.57i −0.181705 1.02415i
\(353\) −1350.84 −0.203677 −0.101838 0.994801i \(-0.532472\pi\)
−0.101838 + 0.994801i \(0.532472\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2251.40 + 5565.61i 0.335180 + 0.828586i
\(357\) 0 0
\(358\) −200.000 + 296.648i −0.0295261 + 0.0437942i
\(359\) −12007.5 −1.76526 −0.882632 0.470065i \(-0.844231\pi\)
−0.882632 + 0.470065i \(0.844231\pi\)
\(360\) 0 0
\(361\) −7221.00 −1.05278
\(362\) 93.8083 139.140i 0.0136200 0.0202018i
\(363\) 0 0
\(364\) 4400.00 1779.89i 0.633579 0.256295i
\(365\) 189.737i 0.0272090i
\(366\) 0 0
\(367\) 5070.00 0.721122 0.360561 0.932736i \(-0.382585\pi\)
0.360561 + 0.932736i \(0.382585\pi\)
\(368\) −6904.29 + 6678.73i −0.978019 + 0.946068i
\(369\) 0 0
\(370\) 880.000 + 593.296i 0.123646 + 0.0833621i
\(371\) 1328.16i 0.185861i
\(372\) 0 0
\(373\) 2432.51i 0.337670i −0.985644 0.168835i \(-0.946000\pi\)
0.985644 0.168835i \(-0.0540004\pi\)
\(374\) 4502.80 6678.73i 0.622551 0.923393i
\(375\) 0 0
\(376\) 2112.00 9967.37i 0.289676 1.36710i
\(377\) 14634.1 1.99919
\(378\) 0 0
\(379\) 7712.85i 1.04534i 0.852536 + 0.522668i \(0.175063\pi\)
−0.852536 + 0.522668i \(0.824937\pi\)
\(380\) −2251.40 5565.61i −0.303933 0.751341i
\(381\) 0 0
\(382\) −8800.00 5932.96i −1.17866 0.794651i
\(383\) −5853.64 −0.780958 −0.390479 0.920612i \(-0.627691\pi\)
−0.390479 + 0.920612i \(0.627691\pi\)
\(384\) 0 0
\(385\) −2400.00 −0.317702
\(386\) 3166.03 + 2134.54i 0.417479 + 0.281464i
\(387\) 0 0
\(388\) 390.000 + 964.106i 0.0510290 + 0.126147i
\(389\) 2156.67i 0.281099i −0.990074 0.140550i \(-0.955113\pi\)
0.990074 0.140550i \(-0.0448870\pi\)
\(390\) 0 0
\(391\) −11264.0 −1.45689
\(392\) −1139.77 + 5379.03i −0.146855 + 0.693067i
\(393\) 0 0
\(394\) 2290.00 3396.62i 0.292814 0.434313i
\(395\) 594.508i 0.0757290i
\(396\) 0 0
\(397\) 12162.6i 1.53759i 0.639498 + 0.768793i \(0.279142\pi\)
−0.639498 + 0.768793i \(0.720858\pi\)
\(398\) 7490.59 + 5050.16i 0.943391 + 0.636034i
\(399\) 0 0
\(400\) −3910.00 + 3782.26i −0.488750 + 0.472783i
\(401\) 3377.10 0.420559 0.210280 0.977641i \(-0.432563\pi\)
0.210280 + 0.977641i \(0.432563\pi\)
\(402\) 0 0
\(403\) 3678.43i 0.454680i
\(404\) −4174.47 + 1688.66i −0.514078 + 0.207955i
\(405\) 0 0
\(406\) 3900.00 5784.63i 0.476733 0.707110i
\(407\) −2251.40 −0.274196
\(408\) 0 0
\(409\) 3526.00 0.426282 0.213141 0.977021i \(-0.431631\pi\)
0.213141 + 0.977021i \(0.431631\pi\)
\(410\) 3752.33 5565.61i 0.451987 0.670404i
\(411\) 0 0
\(412\) −1710.00 4227.23i −0.204480 0.505487i
\(413\) 7336.48i 0.874104i
\(414\) 0 0
\(415\) 4240.00 0.501526
\(416\) −1876.17 10574.7i −0.221122 1.24631i
\(417\) 0 0
\(418\) 10560.0 + 7119.55i 1.23566 + 0.833083i
\(419\) 2466.58i 0.287590i 0.989608 + 0.143795i \(0.0459306\pi\)
−0.989608 + 0.143795i \(0.954069\pi\)
\(420\) 0 0
\(421\) 13586.5i 1.57284i 0.617694 + 0.786418i \(0.288067\pi\)
−0.617694 + 0.786418i \(0.711933\pi\)
\(422\) 8630.36 12800.9i 0.995544 1.47663i
\(423\) 0 0
\(424\) 2940.00 + 622.961i 0.336743 + 0.0713529i
\(425\) −6378.97 −0.728059
\(426\) 0 0
\(427\) 5339.66i 0.605163i
\(428\) −9568.45 + 3870.63i −1.08063 + 0.437135i
\(429\) 0 0
\(430\) −1760.00 1186.59i −0.197383 0.133076i
\(431\) −6754.20 −0.754845 −0.377423 0.926041i \(-0.623190\pi\)
−0.377423 + 0.926041i \(0.623190\pi\)
\(432\) 0 0
\(433\) 7790.00 0.864581 0.432290 0.901734i \(-0.357706\pi\)
0.432290 + 0.901734i \(0.357706\pi\)
\(434\) −1454.03 980.306i −0.160819 0.108424i
\(435\) 0 0
\(436\) 12760.0 5161.67i 1.40159 0.566971i
\(437\) 17809.9i 1.94958i
\(438\) 0 0
\(439\) −9354.00 −1.01695 −0.508476 0.861076i \(-0.669791\pi\)
−0.508476 + 0.861076i \(0.669791\pi\)
\(440\) −1125.70 + 5312.63i −0.121967 + 0.575613i
\(441\) 0 0
\(442\) 7040.00 10442.0i 0.757599 1.12370i
\(443\) 6488.99i 0.695940i −0.937506 0.347970i \(-0.886871\pi\)
0.937506 0.347970i \(-0.113129\pi\)
\(444\) 0 0
\(445\) 4746.37i 0.505617i
\(446\) −12500.0 8427.47i −1.32711 0.894736i
\(447\) 0 0
\(448\) −4680.00 2076.54i −0.493547 0.218989i
\(449\) 10131.3 1.06487 0.532434 0.846472i \(-0.321278\pi\)
0.532434 + 0.846472i \(0.321278\pi\)
\(450\) 0 0
\(451\) 14239.1i 1.48668i
\(452\) 4052.52 + 10018.1i 0.421713 + 1.04250i
\(453\) 0 0
\(454\) −7540.00 + 11183.6i −0.779449 + 1.15611i
\(455\) −3752.33 −0.386620
\(456\) 0 0
\(457\) −12010.0 −1.22933 −0.614665 0.788788i \(-0.710709\pi\)
−0.614665 + 0.788788i \(0.710709\pi\)
\(458\) 5722.31 8487.55i 0.583812 0.865933i
\(459\) 0 0
\(460\) 7040.00 2847.82i 0.713569 0.288653i
\(461\) 9316.07i 0.941199i 0.882347 + 0.470599i \(0.155962\pi\)
−0.882347 + 0.470599i \(0.844038\pi\)
\(462\) 0 0
\(463\) 14770.0 1.48255 0.741274 0.671202i \(-0.234222\pi\)
0.741274 + 0.671202i \(0.234222\pi\)
\(464\) −10975.6 11346.3i −1.09812 1.13521i
\(465\) 0 0
\(466\) 352.000 + 237.318i 0.0349916 + 0.0235913i
\(467\) 8740.54i 0.866089i 0.901372 + 0.433045i \(0.142561\pi\)
−0.901372 + 0.433045i \(0.857439\pi\)
\(468\) 0 0
\(469\) 7119.55i 0.700960i
\(470\) −4502.80 + 6678.73i −0.441912 + 0.655461i
\(471\) 0 0
\(472\) −16240.0 3441.12i −1.58370 0.335572i
\(473\) 4502.80 0.437714
\(474\) 0 0
\(475\) 10086.0i 0.974271i
\(476\) −2251.40 5565.61i −0.216791 0.535923i
\(477\) 0 0
\(478\) −5280.00 3559.78i −0.505233 0.340628i
\(479\) 3001.87 0.286344 0.143172 0.989698i \(-0.454270\pi\)
0.143172 + 0.989698i \(0.454270\pi\)
\(480\) 0 0
\(481\) −3520.00 −0.333676
\(482\) 2725.13 + 1837.28i 0.257524 + 0.173622i
\(483\) 0 0
\(484\) −327.000 808.366i −0.0307100 0.0759171i
\(485\) 822.192i 0.0769770i
\(486\) 0 0
\(487\) −9910.00 −0.922105 −0.461052 0.887373i \(-0.652528\pi\)
−0.461052 + 0.887373i \(0.652528\pi\)
\(488\) 11819.8 + 2504.52i 1.09643 + 0.232325i
\(489\) 0 0
\(490\) 2430.00 3604.27i 0.224033 0.332295i
\(491\) 3389.96i 0.311582i −0.987790 0.155791i \(-0.950207\pi\)
0.987790 0.155791i \(-0.0497927\pi\)
\(492\) 0 0
\(493\) 18510.8i 1.69105i
\(494\) 16510.3 + 11131.2i 1.50371 + 1.01380i
\(495\) 0 0
\(496\) −2852.00 + 2758.83i −0.258183 + 0.249748i
\(497\) 0 0
\(498\) 0 0
\(499\) 4271.73i 0.383224i −0.981471 0.191612i \(-0.938628\pi\)
0.981471 0.191612i \(-0.0613716\pi\)
\(500\) 9849.87 3984.47i 0.880999 0.356382i
\(501\) 0 0
\(502\) −1020.00 + 1512.90i −0.0906869 + 0.134510i
\(503\) −900.560 −0.0798290 −0.0399145 0.999203i \(-0.512709\pi\)
−0.0399145 + 0.999203i \(0.512709\pi\)
\(504\) 0 0
\(505\) 3560.00 0.313699
\(506\) −9005.60 + 13357.5i −0.791201 + 1.17354i
\(507\) 0 0
\(508\) 7590.00 + 18763.0i 0.662897 + 1.63873i
\(509\) 853.815i 0.0743510i 0.999309 + 0.0371755i \(0.0118361\pi\)
−0.999309 + 0.0371755i \(0.988164\pi\)
\(510\) 0 0
\(511\) 300.000 0.0259711
\(512\) −6791.72 + 9385.64i −0.586239 + 0.810138i
\(513\) 0 0
\(514\) 4224.00 + 2847.82i 0.362476 + 0.244381i
\(515\) 3605.00i 0.308457i
\(516\) 0 0
\(517\) 17086.9i 1.45354i
\(518\) −938.083 + 1391.40i −0.0795695 + 0.118021i
\(519\) 0 0
\(520\) −1760.00 + 8306.14i −0.148425 + 0.700478i
\(521\) −7879.90 −0.662619 −0.331310 0.943522i \(-0.607490\pi\)
−0.331310 + 0.943522i \(0.607490\pi\)
\(522\) 0 0
\(523\) 10323.3i 0.863114i −0.902086 0.431557i \(-0.857964\pi\)
0.902086 0.431557i \(-0.142036\pi\)
\(524\) −1876.17 + 758.947i −0.156414 + 0.0632724i
\(525\) 0 0
\(526\) −15488.0 10442.0i −1.28386 0.865576i
\(527\) −4652.89 −0.384598
\(528\) 0 0
\(529\) 10361.0 0.851566
\(530\) −1969.97 1328.16i −0.161453 0.108852i
\(531\) 0 0
\(532\) 8800.00 3559.78i 0.717159 0.290105i
\(533\) 22262.4i 1.80918i
\(534\) 0 0
\(535\) 8160.00 0.659416
\(536\) 15759.8 + 3339.37i 1.27000 + 0.269102i
\(537\) 0 0
\(538\) −9570.00 + 14194.6i −0.766900 + 1.13750i
\(539\) 9221.20i 0.736893i
\(540\) 0 0
\(541\) 15603.7i 1.24003i 0.784591 + 0.620014i \(0.212873\pi\)
−0.784591 + 0.620014i \(0.787127\pi\)
\(542\) −15014.0 10122.5i −1.18987 0.802208i
\(543\) 0 0
\(544\) −13376.0 + 2373.18i −1.05421 + 0.187039i
\(545\) −10881.8 −0.855273
\(546\) 0 0
\(547\) 2254.52i 0.176228i −0.996110 0.0881138i \(-0.971916\pi\)
0.996110 0.0881138i \(-0.0280839\pi\)
\(548\) 2026.26 + 5009.05i 0.157952 + 0.390467i
\(549\) 0 0
\(550\) −5100.00 + 7564.52i −0.395390 + 0.586459i
\(551\) 29268.2 2.26292
\(552\) 0 0
\(553\) 940.000 0.0722837
\(554\) −3283.29 + 4869.91i −0.251794 + 0.373470i
\(555\) 0 0
\(556\) −1760.00 + 711.955i −0.134246 + 0.0543051i
\(557\) 284.605i 0.0216501i 0.999941 + 0.0108250i \(0.00344579\pi\)
−0.999941 + 0.0108250i \(0.996554\pi\)
\(558\) 0 0
\(559\) 7040.00 0.532666
\(560\) 2814.25 + 2909.30i 0.212364 + 0.219536i
\(561\) 0 0
\(562\) 21120.0 + 14239.1i 1.58522 + 1.06875i
\(563\) 18328.6i 1.37204i −0.727584 0.686018i \(-0.759357\pi\)
0.727584 0.686018i \(-0.240643\pi\)
\(564\) 0 0
\(565\) 8543.46i 0.636152i
\(566\) −8255.13 + 12244.3i −0.613055 + 0.909307i
\(567\) 0 0
\(568\) 0 0
\(569\) −7879.90 −0.580567 −0.290283 0.956941i \(-0.593750\pi\)
−0.290283 + 0.956941i \(0.593750\pi\)
\(570\) 0 0
\(571\) 8306.14i 0.608759i −0.952551 0.304379i \(-0.901551\pi\)
0.952551 0.304379i \(-0.0984491\pi\)
\(572\) −6754.20 16696.8i −0.493719 1.22051i
\(573\) 0 0
\(574\) 8800.00 + 5932.96i 0.639904 + 0.431423i
\(575\) 12757.9 0.925291
\(576\) 0 0
\(577\) −6330.00 −0.456709 −0.228355 0.973578i \(-0.573335\pi\)
−0.228355 + 0.973578i \(0.573335\pi\)
\(578\) −1686.20 1136.84i −0.121344 0.0818101i
\(579\) 0 0
\(580\) 4680.00 + 11569.3i 0.335046 + 0.828255i
\(581\) 6704.03i 0.478709i
\(582\) 0 0
\(583\) 5040.00 0.358037
\(584\) 140.712 664.078i 0.00997042 0.0470544i
\(585\) 0 0
\(586\) 8370.00 12414.7i 0.590037 0.875166i
\(587\) 1922.66i 0.135191i 0.997713 + 0.0675953i \(0.0215327\pi\)
−0.997713 + 0.0675953i \(0.978467\pi\)
\(588\) 0 0
\(589\) 7356.87i 0.514660i
\(590\) 10881.8 + 7336.48i 0.759314 + 0.511929i
\(591\) 0 0
\(592\) 2640.00 + 2729.16i 0.183283 + 0.189473i
\(593\) −10356.4 −0.717180 −0.358590 0.933495i \(-0.616742\pi\)
−0.358590 + 0.933495i \(0.616742\pi\)
\(594\) 0 0
\(595\) 4746.37i 0.327029i
\(596\) 21810.4 8822.75i 1.49898 0.606366i
\(597\) 0 0
\(598\) −14080.0 + 20884.0i −0.962833 + 1.42811i
\(599\) −750.467 −0.0511907 −0.0255954 0.999672i \(-0.508148\pi\)
−0.0255954 + 0.999672i \(0.508148\pi\)
\(600\) 0 0
\(601\) 18578.0 1.26092 0.630460 0.776222i \(-0.282866\pi\)
0.630460 + 0.776222i \(0.282866\pi\)
\(602\) 1876.17 2782.80i 0.127021 0.188403i
\(603\) 0 0
\(604\) −6786.00 16775.4i −0.457150 1.13010i
\(605\) 689.377i 0.0463259i
\(606\) 0 0
\(607\) −8030.00 −0.536948 −0.268474 0.963287i \(-0.586519\pi\)
−0.268474 + 0.963287i \(0.586519\pi\)
\(608\) −3752.33 21149.3i −0.250291 1.41072i
\(609\) 0 0
\(610\) −7920.00 5339.66i −0.525691 0.354421i
\(611\) 26714.9i 1.76885i
\(612\) 0 0
\(613\) 3856.42i 0.254094i −0.991897 0.127047i \(-0.959450\pi\)
0.991897 0.127047i \(-0.0405499\pi\)
\(614\) −7879.90 + 11687.8i −0.517926 + 0.768209i
\(615\) 0 0
\(616\) −8400.00 1779.89i −0.549425 0.116418i
\(617\) −300.187 −0.0195868 −0.00979340 0.999952i \(-0.503117\pi\)
−0.00979340 + 0.999952i \(0.503117\pi\)
\(618\) 0 0
\(619\) 1423.91i 0.0924584i 0.998931 + 0.0462292i \(0.0147205\pi\)
−0.998931 + 0.0462292i \(0.985280\pi\)
\(620\) 2908.06 1176.37i 0.188372 0.0762001i
\(621\) 0 0
\(622\) −3520.00 2373.18i −0.226912 0.152984i
\(623\) 7504.67 0.482613
\(624\) 0 0
\(625\) 2225.00 0.142400
\(626\) −14892.1 10040.2i −0.950810 0.641036i
\(627\) 0 0
\(628\) −12760.0 + 5161.67i −0.810795 + 0.327983i
\(629\) 4452.49i 0.282245i
\(630\) 0 0
\(631\) −12902.0 −0.813979 −0.406989 0.913433i \(-0.633421\pi\)
−0.406989 + 0.913433i \(0.633421\pi\)
\(632\) 440.899 2080.78i 0.0277500 0.130964i
\(633\) 0 0
\(634\) 2750.00 4078.91i 0.172266 0.255511i
\(635\) 16001.1i 0.999977i
\(636\) 0 0
\(637\) 14417.1i 0.896744i
\(638\) −21951.1 14799.5i −1.36215 0.918364i
\(639\) 0 0
\(640\) 7760.00 4865.03i 0.479283 0.300480i
\(641\) −19887.4 −1.22543 −0.612717 0.790302i \(-0.709924\pi\)
−0.612717 + 0.790302i \(0.709924\pi\)
\(642\) 0 0
\(643\) 29783.5i 1.82666i −0.407216 0.913332i \(-0.633500\pi\)
0.407216 0.913332i \(-0.366500\pi\)
\(644\) 4502.80 + 11131.2i 0.275520 + 0.681105i
\(645\) 0 0
\(646\) 14080.0 20884.0i 0.857539 1.27194i
\(647\) −13958.7 −0.848180 −0.424090 0.905620i \(-0.639406\pi\)
−0.424090 + 0.905620i \(0.639406\pi\)
\(648\) 0 0
\(649\) −27840.0 −1.68385
\(650\) −7973.71 + 11826.9i −0.481161 + 0.713677i
\(651\) 0 0
\(652\) 14960.0 6051.62i 0.898587 0.363496i
\(653\) 18461.4i 1.10635i −0.833064 0.553177i \(-0.813415\pi\)
0.833064 0.553177i \(-0.186585\pi\)
\(654\) 0 0
\(655\) 1600.00 0.0954461
\(656\) 17260.7 16696.8i 1.02731 0.993752i
\(657\) 0 0
\(658\) −10560.0 7119.55i −0.625641 0.421807i
\(659\) 5160.84i 0.305065i 0.988298 + 0.152532i \(0.0487428\pi\)
−0.988298 + 0.152532i \(0.951257\pi\)
\(660\) 0 0
\(661\) 13467.8i 0.792492i 0.918144 + 0.396246i \(0.129687\pi\)
−0.918144 + 0.396246i \(0.870313\pi\)
\(662\) 5253.27 7791.85i 0.308420 0.457461i
\(663\) 0 0
\(664\) 14840.0 + 3144.47i 0.867325 + 0.183779i
\(665\) −7504.67 −0.437622
\(666\) 0 0
\(667\) 37021.7i 2.14915i
\(668\) −3151.96 7791.85i −0.182564 0.451311i
\(669\) 0 0
\(670\) −10560.0 7119.55i −0.608908 0.410526i
\(671\) 20262.6 1.16577
\(672\) 0 0
\(673\) −15010.0 −0.859722 −0.429861 0.902895i \(-0.641437\pi\)
−0.429861 + 0.902895i \(0.641437\pi\)
\(674\) 3353.65 + 2261.03i 0.191658 + 0.129216i
\(675\) 0 0
\(676\) −3969.00 9811.63i −0.225819 0.558240i
\(677\) 6280.28i 0.356530i −0.983983 0.178265i \(-0.942952\pi\)
0.983983 0.178265i \(-0.0570485\pi\)
\(678\) 0 0
\(679\) 1300.00 0.0734748
\(680\) 10506.5 + 2226.24i 0.592510 + 0.125548i
\(681\) 0 0
\(682\) −3720.00 + 5517.65i −0.208865 + 0.309797i
\(683\) 12510.0i 0.700850i 0.936591 + 0.350425i \(0.113963\pi\)
−0.936591 + 0.350425i \(0.886037\pi\)
\(684\) 0 0
\(685\) 4271.73i 0.238269i
\(686\) 13742.9 + 9265.47i 0.764879 + 0.515681i
\(687\) 0 0
\(688\) −5280.00 5458.32i −0.292584 0.302466i
\(689\) 7879.90 0.435704
\(690\) 0 0
\(691\) 28359.5i 1.56128i 0.624978 + 0.780642i \(0.285108\pi\)
−0.624978 + 0.780642i \(0.714892\pi\)
\(692\) −10553.4 + 4269.07i −0.579742 + 0.234517i
\(693\) 0 0
\(694\) 15980.0 23702.2i 0.874053 1.29643i
\(695\) 1500.93 0.0819189
\(696\) 0 0
\(697\) 28160.0 1.53032
\(698\) −1782.36 + 2643.66i −0.0966522 + 0.143358i
\(699\) 0 0
\(700\) 2550.00 + 6303.77i 0.137687 + 0.340372i
\(701\) 19802.2i 1.06693i 0.845822 + 0.533465i \(0.179110\pi\)
−0.845822 + 0.533465i \(0.820890\pi\)
\(702\) 0 0
\(703\) −7040.00 −0.377694
\(704\) −7879.90 + 17759.4i −0.421853 + 0.950754i
\(705\) 0 0
\(706\) 3168.00 + 2135.87i 0.168880 + 0.113859i
\(707\) 5628.85i 0.299427i
\(708\) 0 0
\(709\) 12874.5i 0.681964i 0.940070 + 0.340982i \(0.110760\pi\)
−0.940070 + 0.340982i \(0.889240\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3520.00 16612.3i 0.185277 0.874398i
\(713\) 9305.78 0.488786
\(714\) 0 0
\(715\) 14239.1i 0.744772i
\(716\) 938.083 379.473i 0.0489634 0.0198067i
\(717\) 0 0
\(718\) 28160.0 + 18985.5i 1.46368 + 0.986813i
\(719\) 1500.93 0.0778517 0.0389258 0.999242i \(-0.487606\pi\)
0.0389258 + 0.999242i \(0.487606\pi\)
\(720\) 0 0
\(721\) −5700.00 −0.294423
\(722\) 16934.7 + 11417.4i 0.872917 + 0.588520i
\(723\) 0 0
\(724\) −440.000 + 177.989i −0.0225863 + 0.00913660i
\(725\) 20965.9i 1.07401i
\(726\) 0 0
\(727\) 23850.0 1.21671 0.608355 0.793665i \(-0.291830\pi\)
0.608355 + 0.793665i \(0.291830\pi\)
\(728\) −13133.2 2782.80i −0.668609 0.141673i
\(729\) 0 0
\(730\) −300.000 + 444.972i −0.0152103 + 0.0225605i
\(731\) 8904.97i 0.450564i
\(732\) 0 0
\(733\) 2195.19i 0.110616i −0.998469 0.0553079i \(-0.982386\pi\)
0.998469 0.0553079i \(-0.0176140\pi\)
\(734\) −11890.2 8016.37i −0.597923 0.403120i
\(735\) 0 0
\(736\) 26752.0 4746.37i 1.33980 0.237708i
\(737\) 27016.8 1.35031
\(738\) 0 0
\(739\) 2610.50i 0.129944i 0.997887 + 0.0649722i \(0.0206959\pi\)
−0.997887 + 0.0649722i \(0.979304\pi\)
\(740\) −1125.70 2782.80i −0.0559210 0.138240i
\(741\) 0 0
\(742\) 2100.00 3114.80i 0.103899 0.154108i
\(743\) −2851.77 −0.140809 −0.0704047 0.997519i \(-0.522429\pi\)
−0.0704047 + 0.997519i \(0.522429\pi\)
\(744\) 0 0
\(745\) −18600.0 −0.914700
\(746\) −3846.14 + 5704.75i −0.188763 + 0.279981i
\(747\) 0 0
\(748\) −21120.0 + 8543.46i −1.03238 + 0.417620i
\(749\) 12902.1i 0.629416i
\(750\) 0 0
\(751\) −20578.0 −0.999869 −0.499935 0.866063i \(-0.666643\pi\)
−0.499935 + 0.866063i \(0.666643\pi\)
\(752\) −20712.9 + 20036.2i −1.00442 + 0.971602i
\(753\) 0 0
\(754\) −34320.0 23138.5i −1.65764 1.11758i
\(755\) 14306.1i 0.689608i
\(756\) 0 0
\(757\) 20468.7i 0.982758i 0.870946 + 0.491379i \(0.163507\pi\)
−0.870946 + 0.491379i \(0.836493\pi\)
\(758\) 12195.1 18088.2i 0.584361 0.866747i
\(759\) 0 0
\(760\) −3520.00 + 16612.3i −0.168005 + 0.792883i
\(761\) −22138.8 −1.05457 −0.527286 0.849688i \(-0.676790\pi\)
−0.527286 + 0.849688i \(0.676790\pi\)
\(762\) 0 0
\(763\) 17205.6i 0.816362i
\(764\) 11257.0 + 27828.0i 0.533068 + 1.31778i
\(765\) 0 0
\(766\) 13728.0 + 9255.42i 0.647536 + 0.436569i
\(767\) −43527.1 −2.04911
\(768\) 0 0
\(769\) −6854.00 −0.321406 −0.160703 0.987003i \(-0.551376\pi\)
−0.160703 + 0.987003i \(0.551376\pi\)
\(770\) 5628.50 + 3794.73i 0.263425 + 0.177601i
\(771\) 0 0
\(772\) −4050.00 10011.9i −0.188812 0.466755i
\(773\) 38902.3i 1.81012i −0.425288 0.905058i \(-0.639827\pi\)
0.425288 0.905058i \(-0.360173\pi\)
\(774\) 0 0
\(775\) 5270.00 0.244263
\(776\) 609.754 2877.67i 0.0282073 0.133122i
\(777\) 0 0
\(778\) −3410.00 + 5057.85i −0.157139 + 0.233075i
\(779\) 44524.9i 2.04784i
\(780\) 0 0
\(781\) 0 0
\(782\) 26416.4 + 17809.9i 1.20799 + 0.814428i
\(783\)