Properties

Label 588.6.i.o.373.2
Level $588$
Weight $6$
Character 588.373
Analytic conductor $94.306$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,6,Mod(361,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.361");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 588.i (of order \(3\), degree \(2\), not 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: \(94.3056860500\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 703x^{6} + 2770x^{5} + 427565x^{4} + 718170x^{3} + 42175732x^{2} - 40929504x + 3559792896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{4}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(13.1471 + 22.7714i\) of defining polynomial
Character \(\chi\) \(=\) 588.373
Dual form 588.6.i.o.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{3} +(-15.9808 + 27.6796i) q^{5} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{3} +(-15.9808 + 27.6796i) q^{5} +(-40.5000 + 70.1481i) q^{9} +(-130.442 - 225.932i) q^{11} -769.735 q^{13} +287.654 q^{15} +(-776.659 - 1345.21i) q^{17} +(375.024 - 649.561i) q^{19} +(-377.427 + 653.723i) q^{23} +(1051.73 + 1821.65i) q^{25} +729.000 q^{27} +6008.93 q^{29} +(-3210.02 - 5559.92i) q^{31} +(-1173.98 + 2033.39i) q^{33} +(2387.86 - 4135.90i) q^{37} +(3463.81 + 5999.49i) q^{39} +5423.27 q^{41} -11896.4 q^{43} +(-1294.44 - 2242.04i) q^{45} +(-8714.00 + 15093.1i) q^{47} +(-6989.93 + 12106.9i) q^{51} +(-18825.3 - 32606.4i) q^{53} +8338.26 q^{55} -6750.44 q^{57} +(11039.0 + 19120.2i) q^{59} +(-4086.69 + 7078.36i) q^{61} +(12301.0 - 21305.9i) q^{65} +(-6500.87 - 11259.8i) q^{67} +6793.69 q^{69} -12349.6 q^{71} +(21800.2 + 37759.0i) q^{73} +(9465.55 - 16394.8i) q^{75} +(-38374.7 + 66467.0i) q^{79} +(-3280.50 - 5681.99i) q^{81} -21893.6 q^{83} +49646.5 q^{85} +(-27040.2 - 46835.0i) q^{87} +(-68483.5 + 118617. i) q^{89} +(-28890.2 + 50039.3i) q^{93} +(11986.4 + 20761.0i) q^{95} +93050.1 q^{97} +21131.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 36 q^{3} - 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 36 q^{3} - 324 q^{9} - 462 q^{11} + 1204 q^{13} - 228 q^{17} - 358 q^{19} - 2148 q^{23} - 5454 q^{25} + 5832 q^{27} - 11064 q^{29} - 830 q^{31} - 4158 q^{33} - 3914 q^{37} - 5418 q^{39} + 16632 q^{41} - 29036 q^{43} - 41700 q^{47} - 2052 q^{51} + 22164 q^{53} - 7784 q^{55} + 6444 q^{57} - 32886 q^{59} - 83732 q^{61} - 93192 q^{65} - 80034 q^{67} + 38664 q^{69} + 89544 q^{71} + 22470 q^{73} - 49086 q^{75} - 75286 q^{79} - 26244 q^{81} + 34836 q^{83} + 278504 q^{85} + 49788 q^{87} - 28944 q^{89} - 7470 q^{93} - 144120 q^{95} + 433356 q^{97} + 74844 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 0 0
\(5\) −15.9808 + 27.6796i −0.285873 + 0.495147i −0.972821 0.231560i \(-0.925617\pi\)
0.686947 + 0.726707i \(0.258950\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −130.442 225.932i −0.325039 0.562984i 0.656481 0.754342i \(-0.272044\pi\)
−0.981520 + 0.191359i \(0.938711\pi\)
\(12\) 0 0
\(13\) −769.735 −1.26323 −0.631616 0.775281i \(-0.717608\pi\)
−0.631616 + 0.775281i \(0.717608\pi\)
\(14\) 0 0
\(15\) 287.654 0.330098
\(16\) 0 0
\(17\) −776.659 1345.21i −0.651791 1.12893i −0.982688 0.185268i \(-0.940685\pi\)
0.330898 0.943667i \(-0.392649\pi\)
\(18\) 0 0
\(19\) 375.024 649.561i 0.238328 0.412797i −0.721906 0.691991i \(-0.756734\pi\)
0.960235 + 0.279194i \(0.0900673\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −377.427 + 653.723i −0.148769 + 0.257676i −0.930773 0.365598i \(-0.880865\pi\)
0.782004 + 0.623274i \(0.214198\pi\)
\(24\) 0 0
\(25\) 1051.73 + 1821.65i 0.336553 + 0.582927i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 6008.93 1.32679 0.663395 0.748269i \(-0.269115\pi\)
0.663395 + 0.748269i \(0.269115\pi\)
\(30\) 0 0
\(31\) −3210.02 5559.92i −0.599934 1.03912i −0.992830 0.119533i \(-0.961860\pi\)
0.392896 0.919583i \(-0.371473\pi\)
\(32\) 0 0
\(33\) −1173.98 + 2033.39i −0.187661 + 0.325039i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2387.86 4135.90i 0.286751 0.496668i −0.686281 0.727336i \(-0.740758\pi\)
0.973032 + 0.230669i \(0.0740914\pi\)
\(38\) 0 0
\(39\) 3463.81 + 5999.49i 0.364664 + 0.631616i
\(40\) 0 0
\(41\) 5423.27 0.503850 0.251925 0.967747i \(-0.418936\pi\)
0.251925 + 0.967747i \(0.418936\pi\)
\(42\) 0 0
\(43\) −11896.4 −0.981171 −0.490585 0.871393i \(-0.663217\pi\)
−0.490585 + 0.871393i \(0.663217\pi\)
\(44\) 0 0
\(45\) −1294.44 2242.04i −0.0952911 0.165049i
\(46\) 0 0
\(47\) −8714.00 + 15093.1i −0.575404 + 0.996629i 0.420594 + 0.907249i \(0.361822\pi\)
−0.995998 + 0.0893798i \(0.971512\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −6989.93 + 12106.9i −0.376311 + 0.651791i
\(52\) 0 0
\(53\) −18825.3 32606.4i −0.920561 1.59446i −0.798549 0.601930i \(-0.794399\pi\)
−0.122012 0.992529i \(-0.538935\pi\)
\(54\) 0 0
\(55\) 8338.26 0.371679
\(56\) 0 0
\(57\) −6750.44 −0.275198
\(58\) 0 0
\(59\) 11039.0 + 19120.2i 0.412859 + 0.715092i 0.995201 0.0978516i \(-0.0311971\pi\)
−0.582342 + 0.812944i \(0.697864\pi\)
\(60\) 0 0
\(61\) −4086.69 + 7078.36i −0.140620 + 0.243561i −0.927730 0.373251i \(-0.878243\pi\)
0.787110 + 0.616812i \(0.211576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12301.0 21305.9i 0.361124 0.625485i
\(66\) 0 0
\(67\) −6500.87 11259.8i −0.176923 0.306440i 0.763902 0.645332i \(-0.223281\pi\)
−0.940825 + 0.338892i \(0.889948\pi\)
\(68\) 0 0
\(69\) 6793.69 0.171784
\(70\) 0 0
\(71\) −12349.6 −0.290742 −0.145371 0.989377i \(-0.546438\pi\)
−0.145371 + 0.989377i \(0.546438\pi\)
\(72\) 0 0
\(73\) 21800.2 + 37759.0i 0.478798 + 0.829303i 0.999704 0.0243110i \(-0.00773921\pi\)
−0.520906 + 0.853614i \(0.674406\pi\)
\(74\) 0 0
\(75\) 9465.55 16394.8i 0.194309 0.336553i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −38374.7 + 66467.0i −0.691796 + 1.19823i 0.279453 + 0.960159i \(0.409847\pi\)
−0.971249 + 0.238066i \(0.923487\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −21893.6 −0.348836 −0.174418 0.984672i \(-0.555804\pi\)
−0.174418 + 0.984672i \(0.555804\pi\)
\(84\) 0 0
\(85\) 49646.5 0.745318
\(86\) 0 0
\(87\) −27040.2 46835.0i −0.383011 0.663395i
\(88\) 0 0
\(89\) −68483.5 + 118617.i −0.916454 + 1.58735i −0.111696 + 0.993742i \(0.535628\pi\)
−0.804758 + 0.593603i \(0.797705\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −28890.2 + 50039.3i −0.346372 + 0.599934i
\(94\) 0 0
\(95\) 11986.4 + 20761.0i 0.136263 + 0.236015i
\(96\) 0 0
\(97\) 93050.1 1.00412 0.502062 0.864832i \(-0.332575\pi\)
0.502062 + 0.864832i \(0.332575\pi\)
\(98\) 0 0
\(99\) 21131.6 0.216692
\(100\) 0 0
\(101\) 61150.8 + 105916.i 0.596484 + 1.03314i 0.993336 + 0.115258i \(0.0367693\pi\)
−0.396852 + 0.917883i \(0.629897\pi\)
\(102\) 0 0
\(103\) 37400.6 64779.8i 0.347365 0.601654i −0.638415 0.769692i \(-0.720410\pi\)
0.985781 + 0.168038i \(0.0537432\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −35386.2 + 61290.7i −0.298796 + 0.517530i −0.975861 0.218394i \(-0.929918\pi\)
0.677065 + 0.735923i \(0.263252\pi\)
\(108\) 0 0
\(109\) 71131.0 + 123202.i 0.573446 + 0.993238i 0.996209 + 0.0869972i \(0.0277271\pi\)
−0.422762 + 0.906241i \(0.638940\pi\)
\(110\) 0 0
\(111\) −42981.5 −0.331112
\(112\) 0 0
\(113\) 198899. 1.46533 0.732667 0.680588i \(-0.238275\pi\)
0.732667 + 0.680588i \(0.238275\pi\)
\(114\) 0 0
\(115\) −12063.2 20894.0i −0.0850583 0.147325i
\(116\) 0 0
\(117\) 31174.3 53995.4i 0.210539 0.364664i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 46495.4 80532.3i 0.288700 0.500042i
\(122\) 0 0
\(123\) −24404.7 42270.2i −0.145449 0.251925i
\(124\) 0 0
\(125\) −167110. −0.956592
\(126\) 0 0
\(127\) 219619. 1.20826 0.604131 0.796885i \(-0.293521\pi\)
0.604131 + 0.796885i \(0.293521\pi\)
\(128\) 0 0
\(129\) 53533.8 + 92723.3i 0.283240 + 0.490585i
\(130\) 0 0
\(131\) 27311.1 47304.1i 0.139047 0.240836i −0.788089 0.615561i \(-0.788930\pi\)
0.927136 + 0.374725i \(0.122263\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −11650.0 + 20178.4i −0.0550163 + 0.0952911i
\(136\) 0 0
\(137\) −36471.4 63170.4i −0.166017 0.287549i 0.770999 0.636836i \(-0.219757\pi\)
−0.937016 + 0.349287i \(0.886424\pi\)
\(138\) 0 0
\(139\) 110668. 0.485831 0.242915 0.970047i \(-0.421896\pi\)
0.242915 + 0.970047i \(0.421896\pi\)
\(140\) 0 0
\(141\) 156852. 0.664419
\(142\) 0 0
\(143\) 100406. + 173908.i 0.410599 + 0.711179i
\(144\) 0 0
\(145\) −96027.5 + 166325.i −0.379294 + 0.656956i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −163513. + 283212.i −0.603373 + 1.04507i 0.388933 + 0.921266i \(0.372844\pi\)
−0.992306 + 0.123807i \(0.960490\pi\)
\(150\) 0 0
\(151\) −87245.1 151113.i −0.311386 0.539336i 0.667277 0.744810i \(-0.267460\pi\)
−0.978663 + 0.205474i \(0.934126\pi\)
\(152\) 0 0
\(153\) 125819. 0.434527
\(154\) 0 0
\(155\) 205195. 0.686020
\(156\) 0 0
\(157\) 220146. + 381304.i 0.712790 + 1.23459i 0.963806 + 0.266606i \(0.0859022\pi\)
−0.251016 + 0.967983i \(0.580765\pi\)
\(158\) 0 0
\(159\) −169428. + 293458.i −0.531486 + 0.920561i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −28246.0 + 48923.5i −0.0832698 + 0.144228i −0.904653 0.426150i \(-0.859870\pi\)
0.821383 + 0.570377i \(0.193203\pi\)
\(164\) 0 0
\(165\) −37522.2 64990.3i −0.107295 0.185840i
\(166\) 0 0
\(167\) 688014. 1.90900 0.954501 0.298209i \(-0.0963891\pi\)
0.954501 + 0.298209i \(0.0963891\pi\)
\(168\) 0 0
\(169\) 221200. 0.595755
\(170\) 0 0
\(171\) 30377.0 + 52614.5i 0.0794427 + 0.137599i
\(172\) 0 0
\(173\) 141279. 244703.i 0.358891 0.621618i −0.628885 0.777499i \(-0.716488\pi\)
0.987776 + 0.155881i \(0.0498216\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 99351.4 172082.i 0.238364 0.412859i
\(178\) 0 0
\(179\) −75890.9 131447.i −0.177034 0.306632i 0.763829 0.645419i \(-0.223317\pi\)
−0.940863 + 0.338786i \(0.889984\pi\)
\(180\) 0 0
\(181\) 322258. 0.731151 0.365575 0.930782i \(-0.380872\pi\)
0.365575 + 0.930782i \(0.380872\pi\)
\(182\) 0 0
\(183\) 73560.4 0.162374
\(184\) 0 0
\(185\) 76319.9 + 132190.i 0.163949 + 0.283968i
\(186\) 0 0
\(187\) −202618. + 350944.i −0.423714 + 0.733895i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −269260. + 466373.i −0.534059 + 0.925017i 0.465150 + 0.885232i \(0.346001\pi\)
−0.999208 + 0.0397847i \(0.987333\pi\)
\(192\) 0 0
\(193\) −151720. 262786.i −0.293190 0.507820i 0.681372 0.731937i \(-0.261383\pi\)
−0.974562 + 0.224117i \(0.928050\pi\)
\(194\) 0 0
\(195\) −221418. −0.416990
\(196\) 0 0
\(197\) 656475. 1.20518 0.602591 0.798050i \(-0.294135\pi\)
0.602591 + 0.798050i \(0.294135\pi\)
\(198\) 0 0
\(199\) 421102. + 729370.i 0.753797 + 1.30562i 0.945970 + 0.324254i \(0.105113\pi\)
−0.192173 + 0.981361i \(0.561553\pi\)
\(200\) 0 0
\(201\) −58507.8 + 101339.i −0.102147 + 0.176923i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −86668.1 + 150114.i −0.144037 + 0.249480i
\(206\) 0 0
\(207\) −30571.6 52951.6i −0.0495898 0.0858920i
\(208\) 0 0
\(209\) −195675. −0.309864
\(210\) 0 0
\(211\) 1.01133e6 1.56382 0.781908 0.623394i \(-0.214247\pi\)
0.781908 + 0.623394i \(0.214247\pi\)
\(212\) 0 0
\(213\) 55573.3 + 96255.8i 0.0839300 + 0.145371i
\(214\) 0 0
\(215\) 190114. 329287.i 0.280490 0.485824i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 196201. 339831.i 0.276434 0.478798i
\(220\) 0 0
\(221\) 597822. + 1.03546e6i 0.823363 + 1.42611i
\(222\) 0 0
\(223\) −957124. −1.28886 −0.644431 0.764663i \(-0.722906\pi\)
−0.644431 + 0.764663i \(0.722906\pi\)
\(224\) 0 0
\(225\) −170380. −0.224369
\(226\) 0 0
\(227\) 235740. + 408313.i 0.303647 + 0.525931i 0.976959 0.213427i \(-0.0684624\pi\)
−0.673312 + 0.739358i \(0.735129\pi\)
\(228\) 0 0
\(229\) −134098. + 232265.i −0.168980 + 0.292681i −0.938061 0.346469i \(-0.887381\pi\)
0.769082 + 0.639150i \(0.220714\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −773610. + 1.33993e6i −0.933538 + 1.61694i −0.156318 + 0.987707i \(0.549962\pi\)
−0.777220 + 0.629229i \(0.783371\pi\)
\(234\) 0 0
\(235\) −278513. 482399.i −0.328985 0.569819i
\(236\) 0 0
\(237\) 690745. 0.798817
\(238\) 0 0
\(239\) −937542. −1.06169 −0.530843 0.847470i \(-0.678125\pi\)
−0.530843 + 0.847470i \(0.678125\pi\)
\(240\) 0 0
\(241\) −642430. 1.11272e6i −0.712497 1.23408i −0.963917 0.266203i \(-0.914231\pi\)
0.251420 0.967878i \(-0.419103\pi\)
\(242\) 0 0
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −288670. + 499990.i −0.301064 + 0.521458i
\(248\) 0 0
\(249\) 98521.1 + 170644.i 0.100700 + 0.174418i
\(250\) 0 0
\(251\) −709769. −0.711103 −0.355552 0.934657i \(-0.615707\pi\)
−0.355552 + 0.934657i \(0.615707\pi\)
\(252\) 0 0
\(253\) 196929. 0.193423
\(254\) 0 0
\(255\) −223409. 386956.i −0.215155 0.372659i
\(256\) 0 0
\(257\) −910080. + 1.57631e6i −0.859502 + 1.48870i 0.0129024 + 0.999917i \(0.495893\pi\)
−0.872405 + 0.488785i \(0.837440\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −243362. + 421515.i −0.221132 + 0.383011i
\(262\) 0 0
\(263\) −179594. 311065.i −0.160104 0.277308i 0.774802 0.632204i \(-0.217850\pi\)
−0.934906 + 0.354896i \(0.884516\pi\)
\(264\) 0 0
\(265\) 1.20337e6 1.05265
\(266\) 0 0
\(267\) 1.23270e6 1.05823
\(268\) 0 0
\(269\) 578834. + 1.00257e6i 0.487723 + 0.844761i 0.999900 0.0141188i \(-0.00449429\pi\)
−0.512177 + 0.858880i \(0.671161\pi\)
\(270\) 0 0
\(271\) −390088. + 675652.i −0.322655 + 0.558856i −0.981035 0.193830i \(-0.937909\pi\)
0.658380 + 0.752686i \(0.271242\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 274379. 475238.i 0.218786 0.378948i
\(276\) 0 0
\(277\) 163165. + 282611.i 0.127770 + 0.221304i 0.922812 0.385250i \(-0.125885\pi\)
−0.795042 + 0.606554i \(0.792551\pi\)
\(278\) 0 0
\(279\) 520023. 0.399956
\(280\) 0 0
\(281\) 364094. 0.275073 0.137536 0.990497i \(-0.456082\pi\)
0.137536 + 0.990497i \(0.456082\pi\)
\(282\) 0 0
\(283\) −32009.6 55442.3i −0.0237582 0.0411505i 0.853902 0.520434i \(-0.174230\pi\)
−0.877660 + 0.479284i \(0.840897\pi\)
\(284\) 0 0
\(285\) 107877. 186849.i 0.0786717 0.136263i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −496470. + 859911.i −0.349662 + 0.605632i
\(290\) 0 0
\(291\) −418725. 725254.i −0.289866 0.502062i
\(292\) 0 0
\(293\) −398020. −0.270855 −0.135427 0.990787i \(-0.543241\pi\)
−0.135427 + 0.990787i \(0.543241\pi\)
\(294\) 0 0
\(295\) −705651. −0.472101
\(296\) 0 0
\(297\) −95092.1 164704.i −0.0625537 0.108346i
\(298\) 0 0
\(299\) 290519. 503194.i 0.187930 0.325505i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 550357. 953247.i 0.344380 0.596484i
\(304\) 0 0
\(305\) −130617. 226236.i −0.0803990 0.139255i
\(306\) 0 0
\(307\) 638841. 0.386854 0.193427 0.981115i \(-0.438040\pi\)
0.193427 + 0.981115i \(0.438040\pi\)
\(308\) 0 0
\(309\) −673212. −0.401103
\(310\) 0 0
\(311\) 1.24094e6 + 2.14937e6i 0.727529 + 1.26012i 0.957924 + 0.287020i \(0.0926648\pi\)
−0.230395 + 0.973097i \(0.574002\pi\)
\(312\) 0 0
\(313\) 738267. 1.27872e6i 0.425944 0.737757i −0.570564 0.821253i \(-0.693275\pi\)
0.996508 + 0.0834961i \(0.0266086\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.11563e6 1.93233e6i 0.623551 1.08002i −0.365269 0.930902i \(-0.619023\pi\)
0.988819 0.149119i \(-0.0476438\pi\)
\(318\) 0 0
\(319\) −783816. 1.35761e6i −0.431258 0.746961i
\(320\) 0 0
\(321\) 636952. 0.345020
\(322\) 0 0
\(323\) −1.16506e6 −0.621360
\(324\) 0 0
\(325\) −809552. 1.40219e6i −0.425145 0.736372i
\(326\) 0 0
\(327\) 640179. 1.10882e6i 0.331079 0.573446i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.20561e6 2.08818e6i 0.604836 1.04761i −0.387242 0.921978i \(-0.626572\pi\)
0.992077 0.125628i \(-0.0400946\pi\)
\(332\) 0 0
\(333\) 193417. + 335008.i 0.0955837 + 0.165556i
\(334\) 0 0
\(335\) 415556. 0.202310
\(336\) 0 0
\(337\) −1.79586e6 −0.861388 −0.430694 0.902498i \(-0.641731\pi\)
−0.430694 + 0.902498i \(0.641731\pi\)
\(338\) 0 0
\(339\) −895045. 1.55026e6i −0.423005 0.732667i
\(340\) 0 0
\(341\) −837442. + 1.45049e6i −0.390004 + 0.675506i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −108569. + 188046.i −0.0491085 + 0.0850583i
\(346\) 0 0
\(347\) −1.10366e6 1.91159e6i −0.492051 0.852258i 0.507907 0.861412i \(-0.330419\pi\)
−0.999958 + 0.00915399i \(0.997086\pi\)
\(348\) 0 0
\(349\) −148188. −0.0651252 −0.0325626 0.999470i \(-0.510367\pi\)
−0.0325626 + 0.999470i \(0.510367\pi\)
\(350\) 0 0
\(351\) −561137. −0.243109
\(352\) 0 0
\(353\) 985200. + 1.70642e6i 0.420811 + 0.728867i 0.996019 0.0891407i \(-0.0284121\pi\)
−0.575208 + 0.818007i \(0.695079\pi\)
\(354\) 0 0
\(355\) 197357. 341832.i 0.0831154 0.143960i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.21697e6 + 2.10786e6i −0.498362 + 0.863188i −0.999998 0.00189067i \(-0.999398\pi\)
0.501636 + 0.865079i \(0.332732\pi\)
\(360\) 0 0
\(361\) 956763. + 1.65716e6i 0.386399 + 0.669263i
\(362\) 0 0
\(363\) −836917. −0.333362
\(364\) 0 0
\(365\) −1.39354e6 −0.547502
\(366\) 0 0
\(367\) −2.15174e6 3.72692e6i −0.833920 1.44439i −0.894907 0.446253i \(-0.852758\pi\)
0.0609873 0.998139i \(-0.480575\pi\)
\(368\) 0 0
\(369\) −219642. + 380432.i −0.0839750 + 0.145449i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 601526. 1.04187e6i 0.223863 0.387742i −0.732115 0.681181i \(-0.761467\pi\)
0.955978 + 0.293439i \(0.0947999\pi\)
\(374\) 0 0
\(375\) 751994. + 1.30249e6i 0.276144 + 0.478296i
\(376\) 0 0
\(377\) −4.62529e6 −1.67604
\(378\) 0 0
\(379\) 5.11488e6 1.82910 0.914550 0.404473i \(-0.132545\pi\)
0.914550 + 0.404473i \(0.132545\pi\)
\(380\) 0 0
\(381\) −988286. 1.71176e6i −0.348795 0.604131i
\(382\) 0 0
\(383\) 2.50528e6 4.33926e6i 0.872687 1.51154i 0.0134808 0.999909i \(-0.495709\pi\)
0.859206 0.511629i \(-0.170958\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 481804. 834510.i 0.163528 0.283240i
\(388\) 0 0
\(389\) 2.04163e6 + 3.53620e6i 0.684073 + 1.18485i 0.973727 + 0.227718i \(0.0731265\pi\)
−0.289654 + 0.957131i \(0.593540\pi\)
\(390\) 0 0
\(391\) 1.17253e6 0.387866
\(392\) 0 0
\(393\) −491599. −0.160557
\(394\) 0 0
\(395\) −1.22652e6 2.12439e6i −0.395532 0.685081i
\(396\) 0 0
\(397\) −536498. + 929242.i −0.170841 + 0.295905i −0.938714 0.344697i \(-0.887982\pi\)
0.767873 + 0.640602i \(0.221315\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 949741. 1.64500e6i 0.294947 0.510863i −0.680026 0.733188i \(-0.738031\pi\)
0.974973 + 0.222325i \(0.0713647\pi\)
\(402\) 0 0
\(403\) 2.47087e6 + 4.27967e6i 0.757856 + 1.31264i
\(404\) 0 0
\(405\) 209700. 0.0635274
\(406\) 0 0
\(407\) −1.24591e6 −0.372821
\(408\) 0 0
\(409\) 967887. + 1.67643e6i 0.286099 + 0.495538i 0.972875 0.231331i \(-0.0743081\pi\)
−0.686776 + 0.726869i \(0.740975\pi\)
\(410\) 0 0
\(411\) −328243. + 568533.i −0.0958497 + 0.166017i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 349877. 606004.i 0.0997229 0.172725i
\(416\) 0 0
\(417\) −498006. 862572.i −0.140247 0.242915i
\(418\) 0 0
\(419\) −3.93448e6 −1.09484 −0.547422 0.836856i \(-0.684391\pi\)
−0.547422 + 0.836856i \(0.684391\pi\)
\(420\) 0 0
\(421\) −5.16927e6 −1.42142 −0.710712 0.703483i \(-0.751627\pi\)
−0.710712 + 0.703483i \(0.751627\pi\)
\(422\) 0 0
\(423\) −705834. 1.22254e6i −0.191801 0.332210i
\(424\) 0 0
\(425\) 1.63367e6 2.82960e6i 0.438724 0.759893i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 903651. 1.56517e6i 0.237060 0.410599i
\(430\) 0 0
\(431\) 1.06475e6 + 1.84421e6i 0.276093 + 0.478208i 0.970410 0.241462i \(-0.0776268\pi\)
−0.694317 + 0.719669i \(0.744293\pi\)
\(432\) 0 0
\(433\) −3.20879e6 −0.822473 −0.411237 0.911529i \(-0.634903\pi\)
−0.411237 + 0.911529i \(0.634903\pi\)
\(434\) 0 0
\(435\) 1.72849e6 0.437971
\(436\) 0 0
\(437\) 283089. + 490324.i 0.0709119 + 0.122823i
\(438\) 0 0
\(439\) 3.49538e6 6.05418e6i 0.865632 1.49932i −0.000785585 1.00000i \(-0.500250\pi\)
0.866418 0.499320i \(-0.166417\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.73004e6 + 6.46062e6i −0.903034 + 1.56410i −0.0795000 + 0.996835i \(0.525332\pi\)
−0.823534 + 0.567266i \(0.808001\pi\)
\(444\) 0 0
\(445\) −2.18884e6 3.79118e6i −0.523979 0.907559i
\(446\) 0 0
\(447\) 2.94323e6 0.696715
\(448\) 0 0
\(449\) −5.61620e6 −1.31470 −0.657350 0.753586i \(-0.728323\pi\)
−0.657350 + 0.753586i \(0.728323\pi\)
\(450\) 0 0
\(451\) −707421. 1.22529e6i −0.163771 0.283659i
\(452\) 0 0
\(453\) −785206. + 1.36002e6i −0.179779 + 0.311386i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.40636e6 7.63203e6i 0.986936 1.70942i 0.353942 0.935267i \(-0.384841\pi\)
0.632994 0.774156i \(-0.281826\pi\)
\(458\) 0 0
\(459\) −566184. 980660.i −0.125437 0.217264i
\(460\) 0 0
\(461\) −3.24339e6 −0.710798 −0.355399 0.934715i \(-0.615655\pi\)
−0.355399 + 0.934715i \(0.615655\pi\)
\(462\) 0 0
\(463\) −5.70039e6 −1.23581 −0.617906 0.786252i \(-0.712019\pi\)
−0.617906 + 0.786252i \(0.712019\pi\)
\(464\) 0 0
\(465\) −923376. 1.59933e6i −0.198037 0.343010i
\(466\) 0 0
\(467\) 1.09007e6 1.88805e6i 0.231292 0.400610i −0.726896 0.686747i \(-0.759038\pi\)
0.958189 + 0.286137i \(0.0923712\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.98131e6 3.43174e6i 0.411530 0.712790i
\(472\) 0 0
\(473\) 1.55179e6 + 2.68778e6i 0.318918 + 0.552383i
\(474\) 0 0
\(475\) 1.57770e6 0.320840
\(476\) 0 0
\(477\) 3.04970e6 0.613707
\(478\) 0 0
\(479\) 1.96808e6 + 3.40881e6i 0.391926 + 0.678835i 0.992704 0.120581i \(-0.0384757\pi\)
−0.600778 + 0.799416i \(0.705142\pi\)
\(480\) 0 0
\(481\) −1.83802e6 + 3.18355e6i −0.362233 + 0.627406i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.48701e6 + 2.57558e6i −0.287052 + 0.497189i
\(486\) 0 0
\(487\) −3.50088e6 6.06370e6i −0.668890 1.15855i −0.978215 0.207595i \(-0.933436\pi\)
0.309325 0.950956i \(-0.399897\pi\)
\(488\) 0 0
\(489\) 508428. 0.0961517
\(490\) 0 0
\(491\) −9.37114e6 −1.75424 −0.877119 0.480273i \(-0.840537\pi\)
−0.877119 + 0.480273i \(0.840537\pi\)
\(492\) 0 0
\(493\) −4.66689e6 8.08329e6i −0.864789 1.49786i
\(494\) 0 0
\(495\) −337699. + 584912.i −0.0619466 + 0.107295i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.87966e6 8.45182e6i 0.877280 1.51949i 0.0229668 0.999736i \(-0.492689\pi\)
0.854314 0.519758i \(-0.173978\pi\)
\(500\) 0 0
\(501\) −3.09606e6 5.36254e6i −0.551081 0.954501i
\(502\) 0 0
\(503\) 1.69667e6 0.299004 0.149502 0.988761i \(-0.452233\pi\)
0.149502 + 0.988761i \(0.452233\pi\)
\(504\) 0 0
\(505\) −3.90895e6 −0.682075
\(506\) 0 0
\(507\) −995398. 1.72408e6i −0.171980 0.297877i
\(508\) 0 0
\(509\) −1.86783e6 + 3.23518e6i −0.319553 + 0.553482i −0.980395 0.197043i \(-0.936866\pi\)
0.660842 + 0.750525i \(0.270199\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 273393. 473530.i 0.0458663 0.0794427i
\(514\) 0 0
\(515\) 1.19538e6 + 2.07047e6i 0.198605 + 0.343993i
\(516\) 0 0
\(517\) 4.54668e6 0.748114
\(518\) 0 0
\(519\) −2.54302e6 −0.414412
\(520\) 0 0
\(521\) 3.66359e6 + 6.34552e6i 0.591306 + 1.02417i 0.994057 + 0.108863i \(0.0347209\pi\)
−0.402750 + 0.915310i \(0.631946\pi\)
\(522\) 0 0
\(523\) −4795.71 + 8306.42i −0.000766653 + 0.00132788i −0.866408 0.499336i \(-0.833577\pi\)
0.865642 + 0.500664i \(0.166911\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.98618e6 + 8.63632e6i −0.782063 + 1.35457i
\(528\) 0 0
\(529\) 2.93327e6 + 5.08057e6i 0.455735 + 0.789357i
\(530\) 0 0
\(531\) −1.78832e6 −0.275239
\(532\) 0 0
\(533\) −4.17448e6 −0.636479
\(534\) 0 0
\(535\) −1.13100e6 1.95895e6i −0.170836 0.295896i
\(536\) 0 0
\(537\) −683018. + 1.18302e6i −0.102211 + 0.177034i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.87846e6 3.25359e6i 0.275936 0.477935i −0.694435 0.719556i \(-0.744346\pi\)
0.970371 + 0.241620i \(0.0776788\pi\)
\(542\) 0 0
\(543\) −1.45016e6 2.51175e6i −0.211065 0.365575i
\(544\) 0 0
\(545\) −4.54692e6 −0.655731
\(546\) 0 0
\(547\) 1.03391e7 1.47746 0.738729 0.674002i \(-0.235426\pi\)
0.738729 + 0.674002i \(0.235426\pi\)
\(548\) 0 0
\(549\) −331022. 573347.i −0.0468734 0.0811870i
\(550\) 0 0
\(551\) 2.25350e6 3.90317e6i 0.316212 0.547694i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 686879. 1.18971e6i 0.0946560 0.163949i
\(556\) 0 0
\(557\) 5.02378e6 + 8.70144e6i 0.686108 + 1.18837i 0.973087 + 0.230437i \(0.0740156\pi\)
−0.286979 + 0.957937i \(0.592651\pi\)
\(558\) 0 0
\(559\) 9.15708e6 1.23945
\(560\) 0 0
\(561\) 3.64712e6 0.489263
\(562\) 0 0
\(563\) −4.24690e6 7.35585e6i −0.564678 0.978052i −0.997080 0.0763704i \(-0.975667\pi\)
0.432401 0.901681i \(-0.357666\pi\)
\(564\) 0 0
\(565\) −3.17856e6 + 5.50543e6i −0.418899 + 0.725555i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.90765e6 + 3.30415e6i −0.247012 + 0.427838i −0.962695 0.270587i \(-0.912782\pi\)
0.715683 + 0.698425i \(0.246115\pi\)
\(570\) 0 0
\(571\) −6.10664e6 1.05770e7i −0.783812 1.35760i −0.929706 0.368302i \(-0.879939\pi\)
0.145894 0.989300i \(-0.453394\pi\)
\(572\) 0 0
\(573\) 4.84669e6 0.616678
\(574\) 0 0
\(575\) −1.58780e6 −0.200275
\(576\) 0 0
\(577\) −1.14735e6 1.98727e6i −0.143469 0.248495i 0.785332 0.619075i \(-0.212492\pi\)
−0.928801 + 0.370580i \(0.879159\pi\)
\(578\) 0 0
\(579\) −1.36548e6 + 2.36508e6i −0.169273 + 0.293190i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4.91122e6 + 8.50648e6i −0.598436 + 1.03652i
\(584\) 0 0
\(585\) 996380. + 1.72578e6i 0.120375 + 0.208495i
\(586\) 0 0
\(587\) −7.53391e6 −0.902454 −0.451227 0.892409i \(-0.649014\pi\)
−0.451227 + 0.892409i \(0.649014\pi\)
\(588\) 0 0
\(589\) −4.81534e6 −0.571925
\(590\) 0 0
\(591\) −2.95414e6 5.11671e6i −0.347906 0.602591i
\(592\) 0 0
\(593\) 3.61760e6 6.26588e6i 0.422459 0.731720i −0.573721 0.819051i \(-0.694500\pi\)
0.996179 + 0.0873310i \(0.0278338\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.78992e6 6.56433e6i 0.435205 0.753797i
\(598\) 0 0
\(599\) −1.66928e6 2.89128e6i −0.190091 0.329247i 0.755189 0.655507i \(-0.227545\pi\)
−0.945280 + 0.326259i \(0.894212\pi\)
\(600\) 0 0
\(601\) −1.48297e7 −1.67474 −0.837370 0.546636i \(-0.815908\pi\)
−0.837370 + 0.546636i \(0.815908\pi\)
\(602\) 0 0
\(603\) 1.05314e6 0.117949
\(604\) 0 0
\(605\) 1.48607e6 + 2.57394e6i 0.165063 + 0.285897i
\(606\) 0 0
\(607\) −3.18737e6 + 5.52068e6i −0.351124 + 0.608164i −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772247i \(0.280867\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.70747e6 1.16177e7i 0.726869 1.25897i
\(612\) 0 0
\(613\) 7.74344e6 + 1.34120e7i 0.832306 + 1.44160i 0.896205 + 0.443639i \(0.146313\pi\)
−0.0638996 + 0.997956i \(0.520354\pi\)
\(614\) 0 0
\(615\) 1.56003e6 0.166320
\(616\) 0 0
\(617\) −4.55324e6 −0.481513 −0.240756 0.970586i \(-0.577396\pi\)
−0.240756 + 0.970586i \(0.577396\pi\)
\(618\) 0 0
\(619\) −5.82108e6 1.00824e7i −0.610628 1.05764i −0.991135 0.132861i \(-0.957584\pi\)
0.380507 0.924778i \(-0.375750\pi\)
\(620\) 0 0
\(621\) −275144. + 476564.i −0.0286307 + 0.0495898i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −616103. + 1.06712e6i −0.0630890 + 0.109273i
\(626\) 0 0
\(627\) 880539. + 1.52514e6i 0.0894499 + 0.154932i
\(628\) 0 0
\(629\) −7.41822e6 −0.747607
\(630\) 0 0
\(631\) 1.07436e7 1.07417 0.537087 0.843527i \(-0.319525\pi\)
0.537087 + 0.843527i \(0.319525\pi\)
\(632\) 0 0
\(633\) −4.55097e6 7.88252e6i −0.451435 0.781908i
\(634\) 0 0
\(635\) −3.50969e6 + 6.07896e6i −0.345409 + 0.598267i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 500160. 866302.i 0.0484570 0.0839300i
\(640\) 0 0
\(641\) −6.15689e6 1.06641e7i −0.591857 1.02513i −0.993982 0.109541i \(-0.965062\pi\)
0.402126 0.915585i \(-0.368272\pi\)
\(642\) 0 0
\(643\) 1.67944e7 1.60191 0.800955 0.598724i \(-0.204325\pi\)
0.800955 + 0.598724i \(0.204325\pi\)
\(644\) 0 0
\(645\) −3.42205e6 −0.323882
\(646\) 0 0
\(647\) 9.95539e6 + 1.72432e7i 0.934970 + 1.61942i 0.774687 + 0.632345i \(0.217907\pi\)
0.160283 + 0.987071i \(0.448759\pi\)
\(648\) 0 0
\(649\) 2.87990e6 4.98814e6i 0.268390 0.464865i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.05495e7 + 1.82723e7i −0.968163 + 1.67691i −0.267299 + 0.963614i \(0.586131\pi\)
−0.700864 + 0.713295i \(0.747202\pi\)
\(654\) 0 0
\(655\) 872905. + 1.51192e6i 0.0794994 + 0.137697i
\(656\) 0 0
\(657\) −3.53163e6 −0.319199
\(658\) 0 0
\(659\) 1.75070e7 1.57035 0.785177 0.619271i \(-0.212572\pi\)
0.785177 + 0.619271i \(0.212572\pi\)
\(660\) 0 0
\(661\) 9.00844e6 + 1.56031e7i 0.801947 + 1.38901i 0.918333 + 0.395810i \(0.129536\pi\)
−0.116385 + 0.993204i \(0.537131\pi\)
\(662\) 0 0
\(663\) 5.38040e6 9.31912e6i 0.475369 0.823363i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.26793e6 + 3.92818e6i −0.197386 + 0.341882i
\(668\) 0 0
\(669\) 4.30706e6 + 7.46004e6i 0.372062 + 0.644431i
\(670\) 0 0
\(671\) 2.13230e6 0.182828
\(672\) 0 0
\(673\) 1.48593e7 1.26462 0.632312 0.774714i \(-0.282106\pi\)
0.632312 + 0.774714i \(0.282106\pi\)
\(674\) 0 0
\(675\) 766710. + 1.32798e6i 0.0647697 + 0.112184i
\(676\) 0 0
\(677\) 3.59160e6 6.22084e6i 0.301173 0.521648i −0.675229 0.737609i \(-0.735955\pi\)
0.976402 + 0.215961i \(0.0692884\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.12166e6 3.67482e6i 0.175310 0.303647i
\(682\) 0 0
\(683\) −825461. 1.42974e6i −0.0677087 0.117275i 0.830184 0.557490i \(-0.188236\pi\)
−0.897892 + 0.440215i \(0.854902\pi\)
\(684\) 0 0
\(685\) 2.33137e6 0.189839
\(686\) 0 0
\(687\) 2.41377e6 0.195121
\(688\) 0 0
\(689\) 1.44905e7 + 2.50983e7i 1.16288 + 2.01417i
\(690\) 0 0
\(691\) 388722. 673286.i 0.0309702 0.0536419i −0.850125 0.526581i \(-0.823474\pi\)
0.881095 + 0.472939i \(0.156807\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.76856e6 + 3.06324e6i −0.138886 + 0.240558i
\(696\) 0 0
\(697\) −4.21203e6 7.29545e6i −0.328405 0.568814i
\(698\) 0 0
\(699\) 1.39250e7 1.07796
\(700\) 0 0
\(701\) 1.65671e6 0.127336 0.0636681 0.997971i \(-0.479720\pi\)
0.0636681 + 0.997971i \(0.479720\pi\)
\(702\) 0 0
\(703\) −1.79101e6 3.10213e6i −0.136682 0.236740i
\(704\) 0 0
\(705\) −2.50662e6 + 4.34159e6i −0.189940 + 0.328985i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.49950e6 + 4.32927e6i −0.186740 + 0.323444i −0.944162 0.329483i \(-0.893126\pi\)
0.757421 + 0.652927i \(0.226459\pi\)
\(710\) 0 0
\(711\) −3.10835e6 5.38383e6i −0.230599 0.399408i
\(712\) 0 0
\(713\) 4.84619e6 0.357007
\(714\) 0 0
\(715\) −6.41825e6 −0.469517
\(716\) 0 0
\(717\) 4.21894e6 + 7.30742e6i 0.306482 + 0.530843i
\(718\) 0 0
\(719\) −9.06918e6 + 1.57083e7i −0.654253 + 1.13320i 0.327828 + 0.944738i \(0.393683\pi\)
−0.982081 + 0.188462i \(0.939650\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −5.78187e6 + 1.00145e7i −0.411360 + 0.712497i
\(724\) 0 0
\(725\) 6.31976e6 + 1.09461e7i 0.446535 + 0.773422i
\(726\) 0 0
\(727\) −1.17918e7 −0.827454 −0.413727 0.910401i \(-0.635773\pi\)
−0.413727 + 0.910401i \(0.635773\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 9.23945e6 + 1.60032e7i 0.639518 + 1.10768i
\(732\) 0 0
\(733\) −2.48235e6 + 4.29955e6i −0.170648 + 0.295572i −0.938647 0.344880i \(-0.887920\pi\)
0.767998 + 0.640452i \(0.221253\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.69597e6 + 2.93751e6i −0.115014 + 0.199210i
\(738\) 0 0
\(739\) −9.31461e6 1.61334e7i −0.627413 1.08671i −0.988069 0.154013i \(-0.950780\pi\)
0.360656 0.932699i \(-0.382553\pi\)
\(740\) 0 0
\(741\) 5.19605e6 0.347639
\(742\) 0 0
\(743\) 1.77727e7 1.18109 0.590544 0.807006i \(-0.298913\pi\)
0.590544 + 0.807006i \(0.298913\pi\)
\(744\) 0 0
\(745\) −5.22613e6 9.05192e6i −0.344976 0.597516i
\(746\) 0 0
\(747\) 886690. 1.53579e6i 0.0581394 0.100700i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.33030e6 + 4.03619e6i −0.150769 + 0.261139i −0.931510 0.363715i \(-0.881508\pi\)
0.780742 + 0.624854i \(0.214842\pi\)
\(752\) 0 0
\(753\) 3.19396e6 + 5.53210e6i 0.205278 + 0.355552i
\(754\) 0 0
\(755\) 5.57699e6 0.356067
\(756\) 0 0
\(757\) −2.36520e6 −0.150013 −0.0750064 0.997183i \(-0.523898\pi\)
−0.0750064 + 0.997183i \(0.523898\pi\)
\(758\) 0 0
\(759\) −886181. 1.53491e6i −0.0558365 0.0967116i
\(760\) 0 0
\(761\) −8.84728e6 + 1.53239e7i −0.553794 + 0.959199i 0.444202 + 0.895926i \(0.353487\pi\)
−0.997996 + 0.0632726i \(0.979846\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.01068e6 + 3.48261e6i −0.124220 + 0.215155i
\(766\) 0 0
\(767\) −8.49714e6 1.47175e7i −0.521536 0.903327i
\(768\) 0 0
\(769\) 7.90324e6 0.481936 0.240968 0.970533i \(-0.422535\pi\)
0.240968 + 0.970533i \(0.422535\pi\)
\(770\) 0 0
\(771\) 1.63814e7 0.992468
\(772\) 0 0
\(773\) 1.11230e7 + 1.92656e7i 0.669534 + 1.15967i 0.978035 + 0.208442i \(0.0668393\pi\)
−0.308501 + 0.951224i \(0.599827\pi\)
\(774\) 0 0
\(775\) 6.75214e6 1.16950e7i 0.403819 0.699436i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.03386e6 3.52274e6i 0.120082 0.207988i
\(780\) 0 0
\(781\) 1.61091e6 + 2.79017e6i 0.0945024 + 0.163683i
\(782\) 0 0
\(783\) 4.38051e6 0.255341
\(784\) 0 0
\(785\) −1.40724e7 −0.815070