Properties

Label 80.6.n.d.47.2
Level $80$
Weight $6$
Character 80.47
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Root \(3.75557 + 3.81117i\) of defining polynomial
Character \(\chi\) \(=\) 80.47
Dual form 80.6.n.d.63.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-17.2921 - 17.2921i) q^{3} +(46.1930 + 31.4834i) q^{5} +(154.079 - 154.079i) q^{7} +355.037i q^{9} +O(q^{10})\) \(q+(-17.2921 - 17.2921i) q^{3} +(46.1930 + 31.4834i) q^{5} +(154.079 - 154.079i) q^{7} +355.037i q^{9} +127.489i q^{11} +(335.067 - 335.067i) q^{13} +(-254.362 - 1343.19i) q^{15} +(-1155.01 - 1155.01i) q^{17} +28.2166 q^{19} -5328.70 q^{21} +(-2783.04 - 2783.04i) q^{23} +(1142.60 + 2908.63i) q^{25} +(1937.35 - 1937.35i) q^{27} -3388.31i q^{29} -5384.41i q^{31} +(2204.56 - 2204.56i) q^{33} +(11968.3 - 2266.45i) q^{35} +(11534.0 + 11534.0i) q^{37} -11588.1 q^{39} -11147.8 q^{41} +(-1437.07 - 1437.07i) q^{43} +(-11177.7 + 16400.2i) q^{45} +(-219.040 + 219.040i) q^{47} -30673.4i q^{49} +39945.1i q^{51} +(22745.6 - 22745.6i) q^{53} +(-4013.79 + 5889.12i) q^{55} +(-487.926 - 487.926i) q^{57} -22196.6 q^{59} -1431.25 q^{61} +(54703.5 + 54703.5i) q^{63} +(26026.8 - 4928.73i) q^{65} +(-28948.2 + 28948.2i) q^{67} +96249.3i q^{69} -24188.3i q^{71} +(28574.8 - 28574.8i) q^{73} +(30538.4 - 70054.3i) q^{75} +(19643.4 + 19643.4i) q^{77} +23417.0 q^{79} +19271.9 q^{81} +(-18919.5 - 18919.5i) q^{83} +(-16989.8 - 89716.9i) q^{85} +(-58591.1 + 58591.1i) q^{87} +8179.53i q^{89} -103253. i q^{91} +(-93107.9 + 93107.9i) q^{93} +(1303.41 + 888.354i) q^{95} +(-76747.2 - 76747.2i) q^{97} -45263.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −17.2921 17.2921i −1.10929 1.10929i −0.993244 0.116048i \(-0.962977\pi\)
−0.116048 0.993244i \(1.46298\pi\)
\(4\) 0 0
\(5\) 46.1930 + 31.4834i 0.826326 + 0.563192i
\(6\) 0 0
\(7\) 154.079 154.079i 1.18849 1.18849i 0.211011 0.977484i \(-0.432324\pi\)
0.977484 0.211011i \(-0.0676755\pi\)
\(8\) 0 0
\(9\) 355.037i 1.46106i
\(10\) 0 0
\(11\) 127.489i 0.317682i 0.987304 + 0.158841i \(0.0507757\pi\)
−0.987304 + 0.158841i \(0.949224\pi\)
\(12\) 0 0
\(13\) 335.067 335.067i 0.549887 0.549887i −0.376521 0.926408i \(-0.622880\pi\)
0.926408 + 0.376521i \(0.122880\pi\)
\(14\) 0 0
\(15\) −254.362 1343.19i −0.291893 1.54138i
\(16\) 0 0
\(17\) −1155.01 1155.01i −0.969310 0.969310i 0.0302331 0.999543i \(-0.490375\pi\)
−0.999543 + 0.0302331i \(0.990375\pi\)
\(18\) 0 0
\(19\) 28.2166 0.0179317 0.00896584 0.999960i \(-0.497146\pi\)
0.00896584 + 0.999960i \(0.497146\pi\)
\(20\) 0 0
\(21\) −5328.70 −2.63677
\(22\) 0 0
\(23\) −2783.04 2783.04i −1.09698 1.09698i −0.994762 0.102219i \(-0.967406\pi\)
−0.102219 0.994762i \(1.46741\pi\)
\(24\) 0 0
\(25\) 1142.60 + 2908.63i 0.365631 + 0.930760i
\(26\) 0 0
\(27\) 1937.35 1937.35i 0.511446 0.511446i
\(28\) 0 0
\(29\) 3388.31i 0.748149i −0.927399 0.374074i \(-0.877960\pi\)
0.927399 0.374074i \(-0.122040\pi\)
\(30\) 0 0
\(31\) 5384.41i 1.00631i −0.864195 0.503157i \(-0.832172\pi\)
0.864195 0.503157i \(-0.167828\pi\)
\(32\) 0 0
\(33\) 2204.56 2204.56i 0.352402 0.352402i
\(34\) 0 0
\(35\) 11968.3 2266.45i 1.65143 0.312734i
\(36\) 0 0
\(37\) 11534.0 + 11534.0i 1.38508 + 1.38508i 0.835324 + 0.549757i \(0.185280\pi\)
0.549757 + 0.835324i \(0.314720\pi\)
\(38\) 0 0
\(39\) −11588.1 −1.21997
\(40\) 0 0
\(41\) −11147.8 −1.03569 −0.517844 0.855475i \(-0.673265\pi\)
−0.517844 + 0.855475i \(0.673265\pi\)
\(42\) 0 0
\(43\) −1437.07 1437.07i −0.118524 0.118524i 0.645357 0.763881i \(-0.276709\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(44\) 0 0
\(45\) −11177.7 + 16400.2i −0.822855 + 1.20731i
\(46\) 0 0
\(47\) −219.040 + 219.040i −0.0144637 + 0.0144637i −0.714302 0.699838i \(-0.753256\pi\)
0.699838 + 0.714302i \(0.253256\pi\)
\(48\) 0 0
\(49\) 30673.4i 1.82504i
\(50\) 0 0
\(51\) 39945.1i 2.15049i
\(52\) 0 0
\(53\) 22745.6 22745.6i 1.11226 1.11226i 0.119421 0.992844i \(-0.461896\pi\)
0.992844 0.119421i \(-0.0381037\pi\)
\(54\) 0 0
\(55\) −4013.79 + 5889.12i −0.178916 + 0.262509i
\(56\) 0 0
\(57\) −487.926 487.926i −0.0198915 0.0198915i
\(58\) 0 0
\(59\) −22196.6 −0.830149 −0.415074 0.909787i \(-0.636244\pi\)
−0.415074 + 0.909787i \(0.636244\pi\)
\(60\) 0 0
\(61\) −1431.25 −0.0492484 −0.0246242 0.999697i \(-0.507839\pi\)
−0.0246242 + 0.999697i \(0.507839\pi\)
\(62\) 0 0
\(63\) 54703.5 + 54703.5i 1.73646 + 1.73646i
\(64\) 0 0
\(65\) 26026.8 4928.73i 0.764078 0.144694i
\(66\) 0 0
\(67\) −28948.2 + 28948.2i −0.787835 + 0.787835i −0.981139 0.193304i \(-0.938080\pi\)
0.193304 + 0.981139i \(0.438080\pi\)
\(68\) 0 0
\(69\) 96249.3i 2.43374i
\(70\) 0 0
\(71\) 24188.3i 0.569456i −0.958608 0.284728i \(-0.908097\pi\)
0.958608 0.284728i \(-0.0919032\pi\)
\(72\) 0 0
\(73\) 28574.8 28574.8i 0.627591 0.627591i −0.319871 0.947461i \(-0.603639\pi\)
0.947461 + 0.319871i \(0.103639\pi\)
\(74\) 0 0
\(75\) 30538.4 70054.3i 0.626894 1.43808i
\(76\) 0 0
\(77\) 19643.4 + 19643.4i 0.377563 + 0.377563i
\(78\) 0 0
\(79\) 23417.0 0.422147 0.211073 0.977470i \(-0.432304\pi\)
0.211073 + 0.977470i \(0.432304\pi\)
\(80\) 0 0
\(81\) 19271.9 0.326371
\(82\) 0 0
\(83\) −18919.5 18919.5i −0.301450 0.301450i 0.540131 0.841581i \(-0.318375\pi\)
−0.841581 + 0.540131i \(0.818375\pi\)
\(84\) 0 0
\(85\) −16989.8 89716.9i −0.255059 1.34687i
\(86\) 0 0
\(87\) −58591.1 + 58591.1i −0.829915 + 0.829915i
\(88\) 0 0
\(89\) 8179.53i 0.109459i 0.998501 + 0.0547297i \(0.0174297\pi\)
−0.998501 + 0.0547297i \(0.982570\pi\)
\(90\) 0 0
\(91\) 103253.i 1.30708i
\(92\) 0 0
\(93\) −93107.9 + 93107.9i −1.11630 + 1.11630i
\(94\) 0 0
\(95\) 1303.41 + 888.354i 0.0148174 + 0.0100990i
\(96\) 0 0
\(97\) −76747.2 76747.2i −0.828196 0.828196i 0.159071 0.987267i \(-0.449150\pi\)
−0.987267 + 0.159071i \(0.949150\pi\)
\(98\) 0 0
\(99\) −45263.4 −0.464151
\(100\) 0 0
\(101\) −1379.60 −0.0134570 −0.00672851 0.999977i \(-0.502142\pi\)
−0.00672851 + 0.999977i \(0.502142\pi\)
\(102\) 0 0
\(103\) 127370. + 127370.i 1.18297 + 1.18297i 0.978972 + 0.203994i \(0.0653924\pi\)
0.203994 + 0.978972i \(0.434608\pi\)
\(104\) 0 0
\(105\) −246149. 167765.i −2.17884 1.48501i
\(106\) 0 0
\(107\) −17327.3 + 17327.3i −0.146309 + 0.146309i −0.776467 0.630158i \(-0.782990\pi\)
0.630158 + 0.776467i \(0.282990\pi\)
\(108\) 0 0
\(109\) 105777.i 0.852759i 0.904544 + 0.426379i \(0.140211\pi\)
−0.904544 + 0.426379i \(0.859789\pi\)
\(110\) 0 0
\(111\) 398895.i 3.07292i
\(112\) 0 0
\(113\) 63449.7 63449.7i 0.467449 0.467449i −0.433638 0.901087i \(-0.642770\pi\)
0.901087 + 0.433638i \(0.142770\pi\)
\(114\) 0 0
\(115\) −40937.6 216176.i −0.288654 1.52428i
\(116\) 0 0
\(117\) 118961. + 118961.i 0.803416 + 0.803416i
\(118\) 0 0
\(119\) −355924. −2.30404
\(120\) 0 0
\(121\) 144797. 0.899078
\(122\) 0 0
\(123\) 192769. + 192769.i 1.14888 + 1.14888i
\(124\) 0 0
\(125\) −38793.3 + 170331.i −0.222066 + 0.975032i
\(126\) 0 0
\(127\) 150685. 150685.i 0.829009 0.829009i −0.158370 0.987380i \(-0.550624\pi\)
0.987380 + 0.158370i \(0.0506240\pi\)
\(128\) 0 0
\(129\) 49700.1i 0.262956i
\(130\) 0 0
\(131\) 218406.i 1.11195i 0.831199 + 0.555976i \(0.187655\pi\)
−0.831199 + 0.555976i \(0.812345\pi\)
\(132\) 0 0
\(133\) 4347.58 4347.58i 0.0213117 0.0213117i
\(134\) 0 0
\(135\) 150487. 28497.9i 0.710663 0.134579i
\(136\) 0 0
\(137\) 48858.6 + 48858.6i 0.222403 + 0.222403i 0.809509 0.587107i \(-0.199733\pi\)
−0.587107 + 0.809509i \(0.699733\pi\)
\(138\) 0 0
\(139\) 356608. 1.56550 0.782752 0.622334i \(-0.213815\pi\)
0.782752 + 0.622334i \(0.213815\pi\)
\(140\) 0 0
\(141\) 7575.36 0.0320889
\(142\) 0 0
\(143\) 42717.5 + 42717.5i 0.174689 + 0.174689i
\(144\) 0 0
\(145\) 106675. 156516.i 0.421351 0.618215i
\(146\) 0 0
\(147\) −530409. + 530409.i −2.02450 + 2.02450i
\(148\) 0 0
\(149\) 39079.0i 0.144204i 0.997397 + 0.0721022i \(0.0229708\pi\)
−0.997397 + 0.0721022i \(0.977029\pi\)
\(150\) 0 0
\(151\) 355671.i 1.26942i 0.772750 + 0.634711i \(0.218881\pi\)
−0.772750 + 0.634711i \(0.781119\pi\)
\(152\) 0 0
\(153\) 410070. 410070.i 1.41622 1.41622i
\(154\) 0 0
\(155\) 169519. 248722.i 0.566748 0.831544i
\(156\) 0 0
\(157\) −37305.0 37305.0i −0.120786 0.120786i 0.644130 0.764916i \(-0.277220\pi\)
−0.764916 + 0.644130i \(0.777220\pi\)
\(158\) 0 0
\(159\) −786641. −2.46765
\(160\) 0 0
\(161\) −857612. −2.60751
\(162\) 0 0
\(163\) 180954. + 180954.i 0.533458 + 0.533458i 0.921600 0.388142i \(-0.126883\pi\)
−0.388142 + 0.921600i \(0.626883\pi\)
\(164\) 0 0
\(165\) 171243. 32428.4i 0.489668 0.0927291i
\(166\) 0 0
\(167\) −174882. + 174882.i −0.485236 + 0.485236i −0.906799 0.421563i \(-0.861482\pi\)
0.421563 + 0.906799i \(0.361482\pi\)
\(168\) 0 0
\(169\) 146753.i 0.395249i
\(170\) 0 0
\(171\) 10017.9i 0.0261992i
\(172\) 0 0
\(173\) 376164. 376164.i 0.955568 0.955568i −0.0434856 0.999054i \(-0.513846\pi\)
0.999054 + 0.0434856i \(0.0138463\pi\)
\(174\) 0 0
\(175\) 624206. + 272107.i 1.54075 + 0.671653i
\(176\) 0 0
\(177\) 383826. + 383826.i 0.920877 + 0.920877i
\(178\) 0 0
\(179\) 384984. 0.898070 0.449035 0.893514i \(-0.351768\pi\)
0.449035 + 0.893514i \(0.351768\pi\)
\(180\) 0 0
\(181\) −332337. −0.754020 −0.377010 0.926209i \(-0.623048\pi\)
−0.377010 + 0.926209i \(0.623048\pi\)
\(182\) 0 0
\(183\) 24749.5 + 24749.5i 0.0546308 + 0.0546308i
\(184\) 0 0
\(185\) 169661. + 895919.i 0.364463 + 1.92460i
\(186\) 0 0
\(187\) 147251. 147251.i 0.307932 0.307932i
\(188\) 0 0
\(189\) 597010.i 1.21570i
\(190\) 0 0
\(191\) 164553.i 0.326378i 0.986595 + 0.163189i \(0.0521781\pi\)
−0.986595 + 0.163189i \(0.947822\pi\)
\(192\) 0 0
\(193\) −58078.0 + 58078.0i −0.112232 + 0.112232i −0.760993 0.648760i \(-0.775288\pi\)
0.648760 + 0.760993i \(0.275288\pi\)
\(194\) 0 0
\(195\) −535288. 364831.i −1.00809 0.687077i
\(196\) 0 0
\(197\) 386719. + 386719.i 0.709954 + 0.709954i 0.966525 0.256571i \(-0.0825929\pi\)
−0.256571 + 0.966525i \(0.582593\pi\)
\(198\) 0 0
\(199\) 14055.2 0.0251596 0.0125798 0.999921i \(-0.495996\pi\)
0.0125798 + 0.999921i \(0.495996\pi\)
\(200\) 0 0
\(201\) 1.00115e6 1.74788
\(202\) 0 0
\(203\) −522066. 522066.i −0.889171 0.889171i
\(204\) 0 0
\(205\) −514950. 350970.i −0.855816 0.583291i
\(206\) 0 0
\(207\) 988080. 988080.i 1.60275 1.60275i
\(208\) 0 0
\(209\) 3597.32i 0.00569657i
\(210\) 0 0
\(211\) 438963.i 0.678768i −0.940648 0.339384i \(-0.889781\pi\)
0.940648 0.339384i \(-0.110219\pi\)
\(212\) 0 0
\(213\) −418268. + 418268.i −0.631692 + 0.631692i
\(214\) 0 0
\(215\) −21138.9 111627.i −0.0311878 0.164691i
\(216\) 0 0
\(217\) −829622. 829622.i −1.19600 1.19600i
\(218\) 0 0
\(219\) −988240. −1.39236
\(220\) 0 0
\(221\) −774010. −1.06602
\(222\) 0 0
\(223\) 413890. + 413890.i 0.557343 + 0.557343i 0.928550 0.371207i \(-0.121056\pi\)
−0.371207 + 0.928550i \(0.621056\pi\)
\(224\) 0 0
\(225\) −1.03267e6 + 405663.i −1.35989 + 0.534207i
\(226\) 0 0
\(227\) −165742. + 165742.i −0.213485 + 0.213485i −0.805746 0.592261i \(-0.798235\pi\)
0.592261 + 0.805746i \(0.298235\pi\)
\(228\) 0 0
\(229\) 590717.i 0.744373i −0.928158 0.372187i \(-0.878608\pi\)
0.928158 0.372187i \(-0.121392\pi\)
\(230\) 0 0
\(231\) 679352.i 0.837655i
\(232\) 0 0
\(233\) −849795. + 849795.i −1.02547 + 1.02547i −0.0258063 + 0.999667i \(0.508215\pi\)
−0.999667 + 0.0258063i \(0.991785\pi\)
\(234\) 0 0
\(235\) −17014.3 + 3222.02i −0.0200976 + 0.00380591i
\(236\) 0 0
\(237\) −404930. 404930.i −0.468284 0.468284i
\(238\) 0 0
\(239\) 72025.5 0.0815627 0.0407814 0.999168i \(-0.487015\pi\)
0.0407814 + 0.999168i \(0.487015\pi\)
\(240\) 0 0
\(241\) 358847. 0.397985 0.198992 0.980001i \(-0.436233\pi\)
0.198992 + 0.980001i \(0.436233\pi\)
\(242\) 0 0
\(243\) −804029. 804029.i −0.873486 0.873486i
\(244\) 0 0
\(245\) 965703. 1.41690e6i 1.02785 1.50808i
\(246\) 0 0
\(247\) 9454.46 9454.46i 0.00986040 0.00986040i
\(248\) 0 0
\(249\) 654318.i 0.668791i
\(250\) 0 0
\(251\) 209249.i 0.209642i 0.994491 + 0.104821i \(0.0334270\pi\)
−0.994491 + 0.104821i \(0.966573\pi\)
\(252\) 0 0
\(253\) 354807. 354807.i 0.348491 0.348491i
\(254\) 0 0
\(255\) −1.25761e6 + 1.84519e6i −1.21114 + 1.77701i
\(256\) 0 0
\(257\) −228218. 228218.i −0.215535 0.215535i 0.591079 0.806614i \(-0.298702\pi\)
−0.806614 + 0.591079i \(0.798702\pi\)
\(258\) 0 0
\(259\) 3.55428e6 3.29232
\(260\) 0 0
\(261\) 1.20297e6 1.09309
\(262\) 0 0
\(263\) −945242. 945242.i −0.842663 0.842663i 0.146542 0.989204i \(-0.453186\pi\)
−0.989204 + 0.146542i \(0.953186\pi\)
\(264\) 0 0
\(265\) 1.76680e6 334581.i 1.54551 0.292675i
\(266\) 0 0
\(267\) 141442. 141442.i 0.121422 0.121422i
\(268\) 0 0
\(269\) 1.56559e6i 1.31916i 0.751635 + 0.659579i \(0.229265\pi\)
−0.751635 + 0.659579i \(0.770735\pi\)
\(270\) 0 0
\(271\) 990821.i 0.819543i −0.912188 0.409772i \(-0.865608\pi\)
0.912188 0.409772i \(-0.134392\pi\)
\(272\) 0 0
\(273\) −1.78547e6 + 1.78547e6i −1.44993 + 1.44993i
\(274\) 0 0
\(275\) −370819. + 145669.i −0.295685 + 0.116154i
\(276\) 0 0
\(277\) −174283. 174283.i −0.136476 0.136476i 0.635569 0.772044i \(-0.280766\pi\)
−0.772044 + 0.635569i \(0.780766\pi\)
\(278\) 0 0
\(279\) 1.91166e6 1.47028
\(280\) 0 0
\(281\) 2.17766e6 1.64522 0.822609 0.568607i \(-0.192517\pi\)
0.822609 + 0.568607i \(0.192517\pi\)
\(282\) 0 0
\(283\) 502126. + 502126.i 0.372689 + 0.372689i 0.868456 0.495767i \(-0.165113\pi\)
−0.495767 + 0.868456i \(0.665113\pi\)
\(284\) 0 0
\(285\) −7177.24 37900.3i −0.00523414 0.0276396i
\(286\) 0 0
\(287\) −1.71763e6 + 1.71763e6i −1.23091 + 1.23091i
\(288\) 0 0
\(289\) 1.24823e6i 0.879123i
\(290\) 0 0
\(291\) 2.65425e6i 1.83742i
\(292\) 0 0
\(293\) 45772.5 45772.5i 0.0311484 0.0311484i −0.691361 0.722509i \(-0.742989\pi\)
0.722509 + 0.691361i \(0.242989\pi\)
\(294\) 0 0
\(295\) −1.02533e6 698823.i −0.685974 0.467533i
\(296\) 0 0
\(297\) 246992. + 246992.i 0.162477 + 0.162477i
\(298\) 0 0
\(299\) −1.86501e6 −1.20643
\(300\) 0 0
\(301\) −442844. −0.281731
\(302\) 0 0
\(303\) 23856.2 + 23856.2i 0.0149277 + 0.0149277i
\(304\) 0 0
\(305\) −66114.0 45060.7i −0.0406953 0.0277363i
\(306\) 0 0
\(307\) 1.39565e6 1.39565e6i 0.845144 0.845144i −0.144379 0.989523i \(-0.546118\pi\)
0.989523 + 0.144379i \(0.0461183\pi\)
\(308\) 0 0
\(309\) 4.40498e6i 2.62451i
\(310\) 0 0
\(311\) 1.84115e6i 1.07942i 0.841852 + 0.539709i \(0.181466\pi\)
−0.841852 + 0.539709i \(0.818534\pi\)
\(312\) 0 0
\(313\) 2.22340e6 2.22340e6i 1.28279 1.28279i 0.343718 0.939073i \(-0.388314\pi\)
0.939073 0.343718i \(-0.111686\pi\)
\(314\) 0 0
\(315\) 804672. + 4.24918e6i 0.456922 + 2.41284i
\(316\) 0 0
\(317\) −1.35501e6 1.35501e6i −0.757344 0.757344i 0.218495 0.975838i \(-0.429885\pi\)
−0.975838 + 0.218495i \(0.929885\pi\)
\(318\) 0 0
\(319\) 431973. 0.237673
\(320\) 0 0
\(321\) 599254. 0.324600
\(322\) 0 0
\(323\) −32590.4 32590.4i −0.0173814 0.0173814i
\(324\) 0 0
\(325\) 1.35743e6 + 591738.i 0.712868 + 0.310757i
\(326\) 0 0
\(327\) 1.82912e6 1.82912e6i 0.945958 0.945958i
\(328\) 0 0
\(329\) 67498.9i 0.0343801i
\(330\) 0 0
\(331\) 2.40493e6i 1.20652i 0.797546 + 0.603258i \(0.206131\pi\)
−0.797546 + 0.603258i \(0.793869\pi\)
\(332\) 0 0
\(333\) −4.09499e6 + 4.09499e6i −2.02368 + 2.02368i
\(334\) 0 0
\(335\) −2.24859e6 + 425819.i −1.09471 + 0.207307i
\(336\) 0 0
\(337\) −1.72476e6 1.72476e6i −0.827284 0.827284i 0.159856 0.987140i \(-0.448897\pi\)
−0.987140 + 0.159856i \(0.948897\pi\)
\(338\) 0 0
\(339\) −2.19436e6 −1.03707
\(340\) 0 0
\(341\) 686454. 0.319687
\(342\) 0 0
\(343\) −2.13652e6 2.13652e6i −0.980554 0.980554i
\(344\) 0 0
\(345\) −3.03025e6 + 4.44605e6i −1.37066 + 2.01107i
\(346\) 0 0
\(347\) 2.06948e6 2.06948e6i 0.922653 0.922653i −0.0745635 0.997216i \(-0.523756\pi\)
0.997216 + 0.0745635i \(0.0237563\pi\)
\(348\) 0 0
\(349\) 1.88338e6i 0.827702i −0.910345 0.413851i \(-0.864183\pi\)
0.910345 0.413851i \(-0.135817\pi\)
\(350\) 0 0
\(351\) 1.29829e6i 0.562475i
\(352\) 0 0
\(353\) 1.77943e6 1.77943e6i 0.760054 0.760054i −0.216278 0.976332i \(-0.569392\pi\)
0.976332 + 0.216278i \(0.0693916\pi\)
\(354\) 0 0
\(355\) 761530. 1.11733e6i 0.320713 0.470556i
\(356\) 0 0
\(357\) 6.15469e6 + 6.15469e6i 2.55585 + 2.55585i
\(358\) 0 0
\(359\) 4.50238e6 1.84377 0.921884 0.387466i \(-0.126650\pi\)
0.921884 + 0.387466i \(0.126650\pi\)
\(360\) 0 0
\(361\) −2.47530e6 −0.999678
\(362\) 0 0
\(363\) −2.50386e6 2.50386e6i −0.997340 0.997340i
\(364\) 0 0
\(365\) 2.21959e6 420327.i 0.872049 0.165141i
\(366\) 0 0
\(367\) −604369. + 604369.i −0.234227 + 0.234227i −0.814455 0.580227i \(-0.802964\pi\)
0.580227 + 0.814455i \(0.302964\pi\)
\(368\) 0 0
\(369\) 3.95787e6i 1.51320i
\(370\) 0 0
\(371\) 7.00922e6i 2.64384i
\(372\) 0 0
\(373\) 87601.5 87601.5i 0.0326016 0.0326016i −0.690618 0.723220i \(-0.742661\pi\)
0.723220 + 0.690618i \(0.242661\pi\)
\(374\) 0 0
\(375\) 3.61621e6 2.27457e6i 1.32793 0.835258i
\(376\) 0 0
\(377\) −1.13531e6 1.13531e6i −0.411397 0.411397i
\(378\) 0 0
\(379\) −2.48550e6 −0.888824 −0.444412 0.895823i \(-0.646587\pi\)
−0.444412 + 0.895823i \(0.646587\pi\)
\(380\) 0 0
\(381\) −5.21132e6 −1.83923
\(382\) 0 0
\(383\) −601337. 601337.i −0.209470 0.209470i 0.594572 0.804042i \(-0.297321\pi\)
−0.804042 + 0.594572i \(0.797321\pi\)
\(384\) 0 0
\(385\) 288948. + 1.52583e6i 0.0993499 + 0.524630i
\(386\) 0 0
\(387\) 510213. 510213.i 0.173171 0.173171i
\(388\) 0 0
\(389\) 3.73874e6i 1.25271i 0.779537 + 0.626356i \(0.215454\pi\)
−0.779537 + 0.626356i \(0.784546\pi\)
\(390\) 0 0
\(391\) 6.42886e6i 2.12663i
\(392\) 0 0
\(393\) 3.77670e6 3.77670e6i 1.23348 1.23348i
\(394\) 0 0
\(395\) 1.08170e6 + 737246.i 0.348831 + 0.237750i
\(396\) 0 0
\(397\) −209001. 209001.i −0.0665538 0.0665538i 0.673046 0.739600i \(-0.264985\pi\)
−0.739600 + 0.673046i \(0.764985\pi\)
\(398\) 0 0
\(399\) −150358. −0.0472818
\(400\) 0 0
\(401\) −3.88404e6 −1.20621 −0.603104 0.797662i \(-0.706070\pi\)
−0.603104 + 0.797662i \(0.706070\pi\)
\(402\) 0 0
\(403\) −1.80414e6 1.80414e6i −0.553359 0.553359i
\(404\) 0 0
\(405\) 890227. + 606743.i 0.269689 + 0.183809i
\(406\) 0 0
\(407\) −1.47046e6 + 1.47046e6i −0.440015 + 0.440015i
\(408\) 0 0
\(409\) 1.17358e6i 0.346899i 0.984843 + 0.173450i \(0.0554913\pi\)
−0.984843 + 0.173450i \(0.944509\pi\)
\(410\) 0 0
\(411\) 1.68974e6i 0.493419i
\(412\) 0 0
\(413\) −3.42002e6 + 3.42002e6i −0.986627 + 0.986627i
\(414\) 0 0
\(415\) −278300. 1.46960e6i −0.0793219 0.418870i
\(416\) 0 0
\(417\) −6.16652e6 6.16652e6i −1.73660 1.73660i
\(418\) 0 0
\(419\) 1.60340e6 0.446177 0.223089 0.974798i \(-0.428386\pi\)
0.223089 + 0.974798i \(0.428386\pi\)
\(420\) 0 0
\(421\) −3.71020e6 −1.02022 −0.510108 0.860111i \(-0.670394\pi\)
−0.510108 + 0.860111i \(0.670394\pi\)
\(422\) 0 0
\(423\) −77767.4 77767.4i −0.0211323 0.0211323i
\(424\) 0 0
\(425\) 2.03978e6 4.67919e6i 0.547786 1.25660i
\(426\) 0 0
\(427\) −220526. + 220526.i −0.0585315 + 0.0585315i
\(428\) 0 0
\(429\) 1.47735e6i 0.387562i
\(430\) 0 0
\(431\) 2.29101e6i 0.594065i 0.954867 + 0.297033i \(0.0959971\pi\)
−0.954867 + 0.297033i \(0.904003\pi\)
\(432\) 0 0
\(433\) −972567. + 972567.i −0.249287 + 0.249287i −0.820678 0.571391i \(-0.806404\pi\)
0.571391 + 0.820678i \(0.306404\pi\)
\(434\) 0 0
\(435\) −4.55115e6 + 861857.i −1.15318 + 0.218380i
\(436\) 0 0
\(437\) −78527.9 78527.9i −0.0196707 0.0196707i
\(438\) 0 0
\(439\) −3.49284e6 −0.865002 −0.432501 0.901633i \(-0.642369\pi\)
−0.432501 + 0.901633i \(0.642369\pi\)
\(440\) 0 0
\(441\) 1.08902e7 2.66648
\(442\) 0 0
\(443\) 4.91464e6 + 4.91464e6i 1.18982 + 1.18982i 0.977116 + 0.212707i \(0.0682281\pi\)
0.212707 + 0.977116i \(0.431772\pi\)
\(444\) 0 0
\(445\) −257519. + 377837.i −0.0616466 + 0.0904492i
\(446\) 0 0
\(447\) 675761. 675761.i 0.159965 0.159965i
\(448\) 0 0
\(449\) 3.79845e6i 0.889182i 0.895734 + 0.444591i \(0.146651\pi\)
−0.895734 + 0.444591i \(0.853349\pi\)
\(450\) 0 0
\(451\) 1.42122e6i 0.329019i
\(452\) 0 0
\(453\) 6.15031e6 6.15031e6i 1.40816 1.40816i
\(454\) 0 0
\(455\) 3.25076e6 4.76959e6i 0.736134 1.08007i
\(456\) 0 0
\(457\) 4.14446e6 + 4.14446e6i 0.928276 + 0.928276i 0.997595 0.0693189i \(-0.0220826\pi\)
−0.0693189 + 0.997595i \(0.522083\pi\)
\(458\) 0 0
\(459\) −4.47532e6 −0.991499
\(460\) 0 0
\(461\) 1.33612e6 0.292815 0.146407 0.989224i \(-0.453229\pi\)
0.146407 + 0.989224i \(0.453229\pi\)
\(462\) 0 0
\(463\) 3.66263e6 + 3.66263e6i 0.794036 + 0.794036i 0.982148 0.188112i \(-0.0602367\pi\)
−0.188112 + 0.982148i \(0.560237\pi\)
\(464\) 0 0
\(465\) −7.23229e6 + 1.36959e6i −1.55111 + 0.293736i
\(466\) 0 0
\(467\) −4.58287e6 + 4.58287e6i −0.972401 + 0.972401i −0.999629 0.0272279i \(-0.991332\pi\)
0.0272279 + 0.999629i \(0.491332\pi\)
\(468\) 0 0
\(469\) 8.92061e6i 1.87267i
\(470\) 0 0
\(471\) 1.29017e6i 0.267975i
\(472\) 0 0
\(473\) 183211. 183211.i 0.0376530 0.0376530i
\(474\) 0 0
\(475\) 32240.2 + 82071.6i 0.00655637 + 0.0166901i
\(476\) 0 0
\(477\) 8.07553e6 + 8.07553e6i 1.62508 + 1.62508i
\(478\) 0 0
\(479\) 7.00075e6 1.39414 0.697069 0.717004i \(-0.254487\pi\)
0.697069 + 0.717004i \(0.254487\pi\)
\(480\) 0 0
\(481\) 7.72932e6 1.52328
\(482\) 0 0
\(483\) 1.48300e7 + 1.48300e7i 2.89249 + 2.89249i
\(484\) 0 0
\(485\) −1.12893e6 5.96145e6i −0.217927 1.15079i
\(486\) 0 0
\(487\) −3.98892e6 + 3.98892e6i −0.762137 + 0.762137i −0.976708 0.214571i \(-0.931165\pi\)
0.214571 + 0.976708i \(0.431165\pi\)
\(488\) 0 0
\(489\) 6.25818e6i 1.18352i
\(490\) 0 0
\(491\) 2.30379e6i 0.431260i −0.976475 0.215630i \(-0.930819\pi\)
0.976475 0.215630i \(-0.0691805\pi\)
\(492\) 0 0
\(493\) −3.91352e6 + 3.91352e6i −0.725188 + 0.725188i
\(494\) 0 0
\(495\) −2.09085e6 1.42504e6i −0.383540 0.261406i
\(496\) 0 0
\(497\) −3.72690e6 3.72690e6i −0.676795 0.676795i
\(498\) 0 0
\(499\) −2.47982e6 −0.445829 −0.222914 0.974838i \(-0.571557\pi\)
−0.222914 + 0.974838i \(0.571557\pi\)
\(500\) 0 0
\(501\) 6.04816e6 1.07654
\(502\) 0 0
\(503\) −4.08077e6 4.08077e6i −0.719154 0.719154i 0.249278 0.968432i \(-0.419807\pi\)
−0.968432 + 0.249278i \(0.919807\pi\)
\(504\) 0 0
\(505\) −63727.8 43434.3i −0.0111199 0.00757887i
\(506\) 0 0
\(507\) 2.53768e6 2.53768e6i 0.438446 0.438446i
\(508\) 0 0
\(509\) 2.80205e6i 0.479382i −0.970849 0.239691i \(-0.922954\pi\)
0.970849 0.239691i \(-0.0770461\pi\)
\(510\) 0 0
\(511\) 8.80554e6i 1.49178i
\(512\) 0 0
\(513\) 54665.6 54665.6i 0.00917109 0.00917109i
\(514\) 0 0
\(515\) 1.87357e6 + 9.89361e6i 0.311280 + 1.64375i
\(516\) 0 0
\(517\) −27925.3 27925.3i −0.00459485 0.00459485i
\(518\) 0 0
\(519\) −1.30094e7 −2.12001
\(520\) 0 0
\(521\) 144765. 0.0233652 0.0116826 0.999932i \(-0.496281\pi\)
0.0116826 + 0.999932i \(0.496281\pi\)
\(522\) 0 0
\(523\) −3.79906e6 3.79906e6i −0.607327 0.607327i 0.334920 0.942247i \(-0.391291\pi\)
−0.942247 + 0.334920i \(0.891291\pi\)
\(524\) 0 0
\(525\) −6.08855e6 1.54992e7i −0.964085 2.45420i
\(526\) 0 0
\(527\) −6.21903e6 + 6.21903e6i −0.975430 + 0.975430i
\(528\) 0 0
\(529\) 9.05423e6i 1.40674i
\(530\) 0 0
\(531\) 7.88060e6i 1.21289i
\(532\) 0 0
\(533\) −3.73526e6 + 3.73526e6i −0.569511 + 0.569511i
\(534\) 0 0
\(535\) −1.34593e6 + 254880.i −0.203300 + 0.0384991i
\(536\) 0 0
\(537\) −6.65720e6 6.65720e6i −0.996221 0.996221i
\(538\) 0 0
\(539\) 3.91053e6 0.579781
\(540\) 0 0
\(541\) −1.17321e7 −1.72339 −0.861695 0.507426i \(-0.830597\pi\)
−0.861695 + 0.507426i \(0.830597\pi\)
\(542\) 0 0
\(543\) 5.74683e6 + 5.74683e6i 0.836428 + 0.836428i
\(544\) 0 0
\(545\) −3.33023e6 + 4.88618e6i −0.480267 + 0.704657i
\(546\) 0 0
\(547\) −5.24186e6 + 5.24186e6i −0.749060 + 0.749060i −0.974303 0.225243i \(-0.927683\pi\)
0.225243 + 0.974303i \(0.427683\pi\)
\(548\) 0 0
\(549\) 508148.i 0.0719547i
\(550\) 0 0
\(551\) 95606.6i 0.0134156i
\(552\) 0 0
\(553\) 3.60806e6 3.60806e6i 0.501719 0.501719i
\(554\) 0 0
\(555\) 1.25586e7 1.84262e7i 1.73064 2.53923i
\(556\) 0 0
\(557\) 7.61782e6 + 7.61782e6i 1.04038 + 1.04038i 0.999150 + 0.0412325i \(0.0131284\pi\)
0.0412325 + 0.999150i \(0.486872\pi\)
\(558\) 0 0
\(559\) −963030. −0.130350
\(560\) 0 0
\(561\) −5.09258e6 −0.683173
\(562\) 0 0
\(563\) −86277.5 86277.5i −0.0114717 0.0114717i 0.701348 0.712819i \(-0.252582\pi\)
−0.712819 + 0.701348i \(0.752582\pi\)
\(564\) 0 0
\(565\) 4.92855e6 933326.i 0.649528 0.123002i
\(566\) 0 0
\(567\) 2.96938e6 2.96938e6i 0.387890 0.387890i
\(568\) 0 0
\(569\) 5.02097e6i 0.650140i 0.945690 + 0.325070i \(0.105388\pi\)
−0.945690 + 0.325070i \(0.894612\pi\)
\(570\) 0 0
\(571\) 8.08321e6i 1.03751i 0.854922 + 0.518756i \(0.173605\pi\)
−0.854922 + 0.518756i \(0.826395\pi\)
\(572\) 0 0
\(573\) 2.84547e6 2.84547e6i 0.362049 0.362049i
\(574\) 0 0
\(575\) 4.91492e6 1.12747e7i 0.619936 1.42212i
\(576\) 0 0
\(577\) −3.25025e6 3.25025e6i −0.406422 0.406422i 0.474067 0.880489i \(-0.342786\pi\)
−0.880489 + 0.474067i \(0.842786\pi\)
\(578\) 0 0
\(579\) 2.00859e6 0.248997
\(580\) 0 0
\(581\) −5.83018e6 −0.716542
\(582\) 0 0
\(583\) 2.89982e6 + 2.89982e6i 0.353346 + 0.353346i
\(584\) 0 0
\(585\) 1.74988e6 + 9.24047e6i 0.211407 + 1.11636i
\(586\) 0 0
\(587\) 3.79350e6 3.79350e6i 0.454407 0.454407i −0.442407 0.896814i \(-0.645875\pi\)
0.896814 + 0.442407i \(0.145875\pi\)
\(588\) 0 0
\(589\) 151930.i 0.0180449i
\(590\) 0 0
\(591\) 1.33744e7i 1.57509i
\(592\) 0 0
\(593\) 1.01322e7 1.01322e7i 1.18323 1.18323i 0.204321 0.978904i \(-0.434501\pi\)
0.978904 0.204321i \(-0.0654987\pi\)
\(594\) 0 0
\(595\) −1.64412e7 1.12057e7i −1.90389 1.29762i
\(596\) 0 0
\(597\) −243044. 243044.i −0.0279093 0.0279093i
\(598\) 0 0
\(599\) −1.84016e6 −0.209550 −0.104775 0.994496i \(-0.533412\pi\)
−0.104775 + 0.994496i \(0.533412\pi\)
\(600\) 0 0
\(601\) 2.07660e6 0.234513 0.117257 0.993102i \(-0.462590\pi\)
0.117257 + 0.993102i \(0.462590\pi\)
\(602\) 0 0
\(603\) −1.02777e7 1.02777e7i −1.15107 1.15107i
\(604\) 0 0
\(605\) 6.68864e6 + 4.55871e6i 0.742932 + 0.506353i
\(606\) 0 0
\(607\) 7.47671e6 7.47671e6i 0.823643 0.823643i −0.162986 0.986628i \(-0.552112\pi\)
0.986628 + 0.162986i \(0.0521125\pi\)
\(608\) 0 0
\(609\) 1.80553e7i 1.97270i
\(610\) 0 0
\(611\) 146786.i 0.0159068i
\(612\) 0 0
\(613\) 421185. 421185.i 0.0452712 0.0452712i −0.684109 0.729380i \(-0.739809\pi\)
0.729380 + 0.684109i \(0.239809\pi\)
\(614\) 0 0
\(615\) 2.83557e6 + 1.49736e7i 0.302310 + 1.59639i
\(616\) 0 0
\(617\) 4.79146e6 + 4.79146e6i 0.506705 + 0.506705i 0.913514 0.406808i \(-0.133358\pi\)
−0.406808 + 0.913514i \(0.633358\pi\)
\(618\) 0 0
\(619\) −8.81805e6 −0.925009 −0.462505 0.886617i \(-0.653049\pi\)
−0.462505 + 0.886617i \(0.653049\pi\)
\(620\) 0 0
\(621\) −1.07835e7 −1.12209
\(622\) 0 0
\(623\) 1.26029e6 + 1.26029e6i 0.130092 + 0.130092i
\(624\) 0 0
\(625\) −7.15458e6 + 6.64676e6i −0.732629 + 0.680629i
\(626\) 0 0
\(627\) 62205.4 62205.4i 0.00631915 0.00631915i
\(628\) 0 0
\(629\) 2.66437e7i 2.68515i
\(630\) 0 0
\(631\) 4.57807e6i 0.457730i 0.973458 + 0.228865i \(0.0735014\pi\)
−0.973458 + 0.228865i \(0.926499\pi\)
\(632\) 0 0
\(633\) −7.59061e6 + 7.59061e6i −0.752952 + 0.752952i
\(634\) 0 0
\(635\) 1.17046e7 2.21652e6i 1.15192 0.218141i
\(636\) 0 0
\(637\) −1.02777e7 1.02777e7i −1.00356 1.00356i
\(638\) 0 0
\(639\) 8.58774e6 0.832007
\(640\) 0 0
\(641\) −1.62758e7 −1.56458 −0.782288 0.622917i \(-0.785947\pi\)
−0.782288 + 0.622917i \(0.785947\pi\)
\(642\) 0 0
\(643\) −2.99416e6 2.99416e6i −0.285593 0.285593i 0.549742 0.835335i \(-0.314726\pi\)
−0.835335 + 0.549742i \(0.814726\pi\)
\(644\) 0 0
\(645\) −1.56473e6 + 2.29580e6i −0.148094 + 0.217287i
\(646\) 0 0
\(647\) 4.92387e6 4.92387e6i 0.462430 0.462430i −0.437021 0.899451i \(-0.643967\pi\)
0.899451 + 0.437021i \(0.143967\pi\)
\(648\) 0 0
\(649\) 2.82983e6i 0.263723i
\(650\) 0 0
\(651\) 2.86919e7i 2.65342i
\(652\) 0 0
\(653\) 1.05307e7 1.05307e7i 0.966441 0.966441i −0.0330138 0.999455i \(-0.510511\pi\)
0.999455 + 0.0330138i \(0.0105105\pi\)
\(654\) 0 0
\(655\) −6.87615e6 + 1.00888e7i −0.626241 + 0.918835i
\(656\) 0 0
\(657\) 1.01451e7 + 1.01451e7i 0.916945 + 0.916945i
\(658\) 0 0
\(659\) −1.29023e7 −1.15732 −0.578659 0.815570i \(-0.696424\pi\)
−0.578659 + 0.815570i \(0.696424\pi\)
\(660\) 0 0
\(661\) 6.60437e6 0.587933 0.293967 0.955816i \(-0.405025\pi\)
0.293967 + 0.955816i \(0.405025\pi\)
\(662\) 0 0
\(663\) 1.33843e7 + 1.33843e7i 1.18253 + 1.18253i
\(664\) 0 0
\(665\) 337704. 63951.5i 0.0296130 0.00560785i
\(666\) 0 0
\(667\) −9.42978e6 + 9.42978e6i −0.820705 + 0.820705i
\(668\) 0 0
\(669\) 1.43141e7i 1.23651i
\(670\) 0 0
\(671\) 182470.i 0.0156453i
\(672\) 0 0
\(673\) 1.01077e7 1.01077e7i 0.860230 0.860230i −0.131135 0.991365i \(-0.541862\pi\)
0.991365 + 0.131135i \(0.0418621\pi\)
\(674\) 0 0
\(675\) 7.84865e6 + 3.42143e6i 0.663034 + 0.289033i
\(676\) 0 0
\(677\) 5.24850e6 + 5.24850e6i 0.440112 + 0.440112i 0.892050 0.451938i \(-0.149267\pi\)
−0.451938 + 0.892050i \(0.649267\pi\)
\(678\) 0 0
\(679\) −2.36502e7 −1.96861
\(680\) 0 0
\(681\) 5.73207e6 0.473635
\(682\) 0 0
\(683\) −1.03798e7 1.03798e7i −0.851407 0.851407i 0.138900 0.990306i \(-0.455643\pi\)
−0.990306 + 0.138900i \(0.955643\pi\)
\(684\) 0 0
\(685\) 718695. + 3.79516e6i 0.0585218 + 0.309032i
\(686\) 0 0
\(687\) −1.02148e7 + 1.02148e7i −0.825727 + 0.825727i
\(688\) 0 0
\(689\) 1.52426e7i 1.22324i
\(690\) 0 0
\(691\) 6.06155e6i 0.482935i −0.970409 0.241468i \(-0.922371\pi\)
0.970409 0.241468i \(-0.0776288\pi\)
\(692\) 0 0
\(693\) −6.97412e6 + 6.97412e6i −0.551641 + 0.551641i
\(694\) 0 0
\(695\) 1.64728e7 + 1.12272e7i 1.29362 + 0.881679i
\(696\) 0 0
\(697\) 1.28758e7 + 1.28758e7i 1.00390 + 1.00390i
\(698\) 0 0
\(699\) 2.93896e7 2.27510
\(700\) 0 0
\(701\) 2.87503e6 0.220977 0.110489 0.993877i \(-0.464758\pi\)
0.110489 + 0.993877i \(0.464758\pi\)
\(702\) 0 0
\(703\) 325450. + 325450.i 0.0248368 + 0.0248368i
\(704\) 0 0
\(705\) 349929. + 238498.i 0.0265159 + 0.0180722i
\(706\) 0 0
\(707\) −212566. + 212566.i −0.0159936 + 0.0159936i
\(708\) 0 0
\(709\) 528547.i 0.0394883i −0.999805 0.0197441i \(-0.993715\pi\)
0.999805 0.0197441i \(-0.00628516\pi\)
\(710\) 0 0
\(711\) 8.31390e6i 0.616780i
\(712\) 0 0
\(713\) −1.49850e7 + 1.49850e7i −1.10391 + 1.10391i
\(714\) 0 0
\(715\) 628360. + 3.31814e6i 0.0459667 + 0.242733i
\(716\) 0 0
\(717\) −1.24548e6 1.24548e6i −0.0904769 0.0904769i
\(718\) 0 0
\(719\) 1.66055e7 1.19793 0.598963 0.800777i \(-0.295580\pi\)
0.598963 + 0.800777i \(0.295580\pi\)
\(720\) 0 0
\(721\) 3.92498e7 2.81190
\(722\) 0 0
\(723\) −6.20523e6 6.20523e6i −0.441481 0.441481i
\(724\) 0 0
\(725\) 9.85532e6 3.87147e6i 0.696347 0.273546i
\(726\) 0 0
\(727\) 1.54075e7 1.54075e7i 1.08118 1.08118i 0.0847783 0.996400i \(-0.472982\pi\)
0.996400 0.0847783i \(-0.0270182\pi\)
\(728\) 0 0
\(729\) 2.31237e7i 1.61153i
\(730\) 0 0
\(731\) 3.31966e6i 0.229773i
\(732\) 0 0
\(733\) −1.69113e7 + 1.69113e7i −1.16256 + 1.16256i −0.178650 + 0.983913i \(0.557173\pi\)
−0.983913 + 0.178650i \(0.942827\pi\)
\(734\) 0 0
\(735\) −4.12003e7 + 7.80215e6i −2.81308 + 0.532716i
\(736\) 0 0
\(737\) −3.69059e6 3.69059e6i −0.250281 0.250281i
\(738\) 0 0
\(739\) 2.76180e7 1.86029 0.930147 0.367187i \(-0.119679\pi\)
0.930147 + 0.367187i \(0.119679\pi\)
\(740\) 0 0
\(741\) −326976. −0.0218761
\(742\) 0 0
\(743\) −1.71922e7 1.71922e7i −1.14251 1.14251i −0.987990 0.154521i \(-0.950617\pi\)
−0.154521 0.987990i \(1.45062\pi\)
\(744\) 0 0
\(745\) −1.23034e6 + 1.80518e6i −0.0812147 + 0.119160i
\(746\) 0 0
\(747\) 6.71712e6 6.71712e6i 0.440435 0.440435i
\(748\) 0 0
\(749\) 5.33954e6i 0.347776i
\(750\) 0 0
\(751\) 1.11896e7i 0.723961i −0.932186 0.361981i \(-0.882101\pi\)
0.932186 0.361981i \(-0.117899\pi\)
\(752\) 0 0
\(753\) 3.61836e6 3.61836e6i 0.232554 0.232554i
\(754\) 0 0
\(755\) −1.11977e7 + 1.64295e7i −0.714928 + 1.04896i
\(756\) 0 0
\(757\) −1.17247e6 1.17247e6i −0.0743637 0.0743637i 0.668947 0.743310i \(-0.266745\pi\)
−0.743310 + 0.668947i \(0.766745\pi\)
\(758\) 0 0
\(759\) −1.22708e7 −0.773156
\(760\) 0 0
\(761\) −9.79138e6 −0.612890 −0.306445 0.951888i \(-0.599140\pi\)
−0.306445 + 0.951888i \(0.599140\pi\)
\(762\) 0 0
\(763\) 1.62980e7 + 1.62980e7i 1.01350 + 1.01350i
\(764\) 0 0
\(765\) 3.18528e7 6.03200e6i 1.96786 0.372656i
\(766\) 0 0
\(767\) −7.43734e6 + 7.43734e6i −0.456488 + 0.456488i
\(768\) 0 0
\(769\) 1.10059e7i 0.671138i −0.942016 0.335569i \(-0.891071\pi\)
0.942016 0.335569i \(-0.108929\pi\)
\(770\) 0 0
\(771\) 7.89277e6i 0.478182i
\(772\) 0 0
\(773\) 8.90959e6 8.90959e6i 0.536302 0.536302i −0.386139 0.922441i \(-0.626191\pi\)
0.922441 + 0.386139i \(0.126191\pi\)
\(774\) 0 0
\(775\) 1.56612e7 6.15220e6i 0.936637 0.367939i
\(776\) 0 0
\(777\) −6.14612e7 6.14612e7i −3.65215 3.65215i
\(778\) 0 0
\(779\) −314553. −0.0185716
\(780\) 0 0
\(781\) 3.08375e6 0.180906
\(782\) 0 0
\(783\) −6.56435e6 6.56435e6i −0.382638 0.382638i
\(784\) 0 0
\(785\) −548745. 2.89772e6i −0.0317831 0.167835i
\(786\) 0 0
\(787\) 4.88094e6 4.88094e6i 0.280910 0.280910i −0.552562 0.833472i \(-0.686350\pi\)
0.833472 + 0.552562i \(0.186350\pi\)
\(788\) 0 0
\(789\) 3.26905e7i 1.86952i
\(790\) 0 0