Properties

Label 588.6.i.i.373.1
Level $588$
Weight $6$
Character 588.373
Analytic conductor $94.306$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5569})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 1393x^{2} + 1392x + 1937664 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(18.9064 + 32.7469i\) of defining polynomial
Character \(\chi\) \(=\) 588.373
Dual form 588.6.i.i.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{3} +(-38.8129 + 67.2259i) q^{5} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{3} +(-38.8129 + 67.2259i) q^{5} +(-40.5000 + 70.1481i) q^{9} +(-238.690 - 413.423i) q^{11} +63.7544 q^{13} +698.632 q^{15} +(518.813 + 898.610i) q^{17} +(-333.509 + 577.654i) q^{19} +(-1625.81 + 2815.99i) q^{23} +(-1450.38 - 2512.13i) q^{25} +729.000 q^{27} +2300.97 q^{29} +(1858.53 + 3219.06i) q^{31} +(-2148.21 + 3720.81i) q^{33} +(-6122.93 + 10605.2i) q^{37} +(-286.895 - 496.916i) q^{39} +1829.65 q^{41} -20794.2 q^{43} +(-3143.84 - 5445.29i) q^{45} +(-2141.68 + 3709.51i) q^{47} +(4669.32 - 8087.49i) q^{51} +(-12859.2 - 22272.8i) q^{53} +37057.0 q^{55} +6003.16 q^{57} +(-1419.36 - 2458.40i) q^{59} +(8401.60 - 14552.0i) q^{61} +(-2474.49 + 4285.94i) q^{65} +(31267.5 + 54157.0i) q^{67} +29264.6 q^{69} +72301.0 q^{71} +(-27838.4 - 48217.6i) q^{73} +(-13053.4 + 22609.1i) q^{75} +(1994.60 - 3454.74i) q^{79} +(-3280.50 - 5681.99i) q^{81} +46092.2 q^{83} -80546.5 q^{85} +(-10354.4 - 17934.3i) q^{87} +(67692.3 - 117247. i) q^{89} +(16726.7 - 28971.6i) q^{93} +(-25888.9 - 44840.8i) q^{95} -142878. q^{97} +38667.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} - 6 q^{5} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} - 6 q^{5} - 162 q^{9} + 90 q^{11} - 1536 q^{13} + 108 q^{15} + 1926 q^{17} + 2248 q^{19} - 6354 q^{23} - 4906 q^{25} + 2916 q^{27} + 21144 q^{29} - 3312 q^{31} + 810 q^{33} - 2104 q^{37} + 6912 q^{39} - 2532 q^{41} - 11536 q^{43} - 486 q^{45} + 15612 q^{47} + 17334 q^{51} - 16512 q^{53} + 155392 q^{55} - 40464 q^{57} - 13140 q^{59} - 5796 q^{61} - 64524 q^{65} + 56116 q^{67} + 114372 q^{69} + 22044 q^{71} - 85384 q^{73} - 44154 q^{75} + 19620 q^{79} - 13122 q^{81} + 88848 q^{83} - 33832 q^{85} - 95148 q^{87} + 211218 q^{89} - 29808 q^{93} - 260568 q^{95} - 89728 q^{97} - 14580 q^{99}+O(q^{100}) \) 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
\(5\) −38.8129 + 67.2259i −0.694306 + 1.20257i 0.276109 + 0.961126i \(0.410955\pi\)
−0.970414 + 0.241446i \(0.922378\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −238.690 413.423i −0.594775 1.03018i −0.993579 0.113144i \(-0.963908\pi\)
0.398804 0.917036i \(-0.369425\pi\)
\(12\) 0 0
\(13\) 63.7544 0.104629 0.0523145 0.998631i \(-0.483340\pi\)
0.0523145 + 0.998631i \(0.483340\pi\)
\(14\) 0 0
\(15\) 698.632 0.801715
\(16\) 0 0
\(17\) 518.813 + 898.610i 0.435400 + 0.754135i 0.997328 0.0730511i \(-0.0232736\pi\)
−0.561928 + 0.827186i \(0.689940\pi\)
\(18\) 0 0
\(19\) −333.509 + 577.654i −0.211945 + 0.367100i −0.952323 0.305091i \(-0.901313\pi\)
0.740378 + 0.672191i \(0.234646\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1625.81 + 2815.99i −0.640842 + 1.10997i 0.344403 + 0.938822i \(0.388081\pi\)
−0.985245 + 0.171149i \(0.945252\pi\)
\(24\) 0 0
\(25\) −1450.38 2512.13i −0.464121 0.803881i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 2300.97 0.508061 0.254031 0.967196i \(-0.418244\pi\)
0.254031 + 0.967196i \(0.418244\pi\)
\(30\) 0 0
\(31\) 1858.53 + 3219.06i 0.347348 + 0.601624i 0.985777 0.168056i \(-0.0537490\pi\)
−0.638430 + 0.769680i \(0.720416\pi\)
\(32\) 0 0
\(33\) −2148.21 + 3720.81i −0.343393 + 0.594775i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6122.93 + 10605.2i −0.735284 + 1.27355i 0.219315 + 0.975654i \(0.429618\pi\)
−0.954599 + 0.297895i \(0.903716\pi\)
\(38\) 0 0
\(39\) −286.895 496.916i −0.0302038 0.0523145i
\(40\) 0 0
\(41\) 1829.65 0.169984 0.0849920 0.996382i \(-0.472914\pi\)
0.0849920 + 0.996382i \(0.472914\pi\)
\(42\) 0 0
\(43\) −20794.2 −1.71503 −0.857513 0.514463i \(-0.827991\pi\)
−0.857513 + 0.514463i \(0.827991\pi\)
\(44\) 0 0
\(45\) −3143.84 5445.29i −0.231435 0.400858i
\(46\) 0 0
\(47\) −2141.68 + 3709.51i −0.141420 + 0.244947i −0.928032 0.372502i \(-0.878500\pi\)
0.786612 + 0.617448i \(0.211833\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4669.32 8087.49i 0.251378 0.435400i
\(52\) 0 0
\(53\) −12859.2 22272.8i −0.628818 1.08914i −0.987789 0.155796i \(-0.950206\pi\)
0.358972 0.933348i \(-0.383127\pi\)
\(54\) 0 0
\(55\) 37057.0 1.65182
\(56\) 0 0
\(57\) 6003.16 0.244733
\(58\) 0 0
\(59\) −1419.36 2458.40i −0.0530837 0.0919437i 0.838262 0.545267i \(-0.183572\pi\)
−0.891346 + 0.453323i \(0.850238\pi\)
\(60\) 0 0
\(61\) 8401.60 14552.0i 0.289093 0.500723i −0.684501 0.729012i \(-0.739980\pi\)
0.973593 + 0.228289i \(0.0733131\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2474.49 + 4285.94i −0.0726445 + 0.125824i
\(66\) 0 0
\(67\) 31267.5 + 54157.0i 0.850955 + 1.47390i 0.880347 + 0.474330i \(0.157310\pi\)
−0.0293918 + 0.999568i \(0.509357\pi\)
\(68\) 0 0
\(69\) 29264.6 0.739981
\(70\) 0 0
\(71\) 72301.0 1.70215 0.851077 0.525042i \(-0.175950\pi\)
0.851077 + 0.525042i \(0.175950\pi\)
\(72\) 0 0
\(73\) −27838.4 48217.6i −0.611417 1.05901i −0.991002 0.133849i \(-0.957266\pi\)
0.379584 0.925157i \(-0.376067\pi\)
\(74\) 0 0
\(75\) −13053.4 + 22609.1i −0.267960 + 0.464121i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1994.60 3454.74i 0.0359573 0.0622799i −0.847487 0.530817i \(-0.821885\pi\)
0.883444 + 0.468537i \(0.155219\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 46092.2 0.734400 0.367200 0.930142i \(-0.380316\pi\)
0.367200 + 0.930142i \(0.380316\pi\)
\(84\) 0 0
\(85\) −80546.5 −1.20920
\(86\) 0 0
\(87\) −10354.4 17934.3i −0.146665 0.254031i
\(88\) 0 0
\(89\) 67692.3 117247.i 0.905867 1.56901i 0.0861180 0.996285i \(-0.472554\pi\)
0.819749 0.572723i \(-0.194113\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 16726.7 28971.6i 0.200541 0.347348i
\(94\) 0 0
\(95\) −25888.9 44840.8i −0.294309 0.509759i
\(96\) 0 0
\(97\) −142878. −1.54183 −0.770914 0.636939i \(-0.780200\pi\)
−0.770914 + 0.636939i \(0.780200\pi\)
\(98\) 0 0
\(99\) 38667.8 0.396517
\(100\) 0 0
\(101\) 22233.5 + 38509.6i 0.216873 + 0.375635i 0.953850 0.300283i \(-0.0970810\pi\)
−0.736977 + 0.675917i \(0.763748\pi\)
\(102\) 0 0
\(103\) 101310. 175474.i 0.940931 1.62974i 0.177232 0.984169i \(-0.443286\pi\)
0.763700 0.645572i \(-0.223381\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −49762.9 + 86192.0i −0.420191 + 0.727792i −0.995958 0.0898219i \(-0.971370\pi\)
0.575767 + 0.817614i \(0.304704\pi\)
\(108\) 0 0
\(109\) −110465. 191331.i −0.890551 1.54248i −0.839216 0.543798i \(-0.816986\pi\)
−0.0513352 0.998681i \(-0.516348\pi\)
\(110\) 0 0
\(111\) 110213. 0.849033
\(112\) 0 0
\(113\) 29623.1 0.218240 0.109120 0.994029i \(-0.465197\pi\)
0.109120 + 0.994029i \(0.465197\pi\)
\(114\) 0 0
\(115\) −126205. 218593.i −0.889880 1.54132i
\(116\) 0 0
\(117\) −2582.05 + 4472.25i −0.0174382 + 0.0302038i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −33420.4 + 57885.8i −0.207514 + 0.359425i
\(122\) 0 0
\(123\) −8233.42 14260.7i −0.0490702 0.0849920i
\(124\) 0 0
\(125\) −17407.2 −0.0996448
\(126\) 0 0
\(127\) −264132. −1.45315 −0.726577 0.687086i \(-0.758890\pi\)
−0.726577 + 0.687086i \(0.758890\pi\)
\(128\) 0 0
\(129\) 93573.8 + 162075.i 0.495085 + 0.857513i
\(130\) 0 0
\(131\) −38925.0 + 67420.2i −0.198176 + 0.343251i −0.947937 0.318458i \(-0.896835\pi\)
0.749761 + 0.661709i \(0.230168\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −28294.6 + 49007.6i −0.133619 + 0.231435i
\(136\) 0 0
\(137\) −186201. 322510.i −0.847581 1.46805i −0.883361 0.468694i \(-0.844725\pi\)
0.0357792 0.999360i \(-0.488609\pi\)
\(138\) 0 0
\(139\) 274550. 1.20527 0.602636 0.798016i \(-0.294117\pi\)
0.602636 + 0.798016i \(0.294117\pi\)
\(140\) 0 0
\(141\) 38550.3 0.163298
\(142\) 0 0
\(143\) −15217.5 26357.6i −0.0622307 0.107787i
\(144\) 0 0
\(145\) −89307.3 + 154685.i −0.352750 + 0.610981i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 156491. 271050.i 0.577462 1.00019i −0.418307 0.908306i \(-0.637376\pi\)
0.995769 0.0918883i \(-0.0292903\pi\)
\(150\) 0 0
\(151\) −216047. 374205.i −0.771093 1.33557i −0.936965 0.349424i \(-0.886377\pi\)
0.165872 0.986147i \(-0.446956\pi\)
\(152\) 0 0
\(153\) −84047.7 −0.290267
\(154\) 0 0
\(155\) −288539. −0.964662
\(156\) 0 0
\(157\) −42301.8 73268.9i −0.136965 0.237231i 0.789381 0.613903i \(-0.210402\pi\)
−0.926346 + 0.376673i \(0.877068\pi\)
\(158\) 0 0
\(159\) −115733. + 200455.i −0.363048 + 0.628818i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −153152. + 265266.i −0.451494 + 0.782011i −0.998479 0.0551313i \(-0.982442\pi\)
0.546985 + 0.837143i \(0.315776\pi\)
\(164\) 0 0
\(165\) −166756. 288831.i −0.476840 0.825911i
\(166\) 0 0
\(167\) 606514. 1.68287 0.841433 0.540362i \(-0.181713\pi\)
0.841433 + 0.540362i \(0.181713\pi\)
\(168\) 0 0
\(169\) −367228. −0.989053
\(170\) 0 0
\(171\) −27014.2 46790.0i −0.0706484 0.122367i
\(172\) 0 0
\(173\) −144240. + 249832.i −0.366414 + 0.634648i −0.989002 0.147902i \(-0.952748\pi\)
0.622588 + 0.782550i \(0.286081\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12774.2 + 22125.6i −0.0306479 + 0.0530837i
\(178\) 0 0
\(179\) −74429.1 128915.i −0.173624 0.300726i 0.766060 0.642769i \(-0.222214\pi\)
−0.939684 + 0.342043i \(0.888881\pi\)
\(180\) 0 0
\(181\) −93377.8 −0.211859 −0.105930 0.994374i \(-0.533782\pi\)
−0.105930 + 0.994374i \(0.533782\pi\)
\(182\) 0 0
\(183\) −151229. −0.333816
\(184\) 0 0
\(185\) −475297. 823238.i −1.02102 1.76846i
\(186\) 0 0
\(187\) 247671. 428979.i 0.517930 0.897081i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −123457. + 213835.i −0.244869 + 0.424126i −0.962095 0.272715i \(-0.912078\pi\)
0.717226 + 0.696841i \(0.245412\pi\)
\(192\) 0 0
\(193\) −240718. 416937.i −0.465175 0.805706i 0.534035 0.845463i \(-0.320675\pi\)
−0.999209 + 0.0397564i \(0.987342\pi\)
\(194\) 0 0
\(195\) 44540.8 0.0838826
\(196\) 0 0
\(197\) −548236. −1.00647 −0.503237 0.864149i \(-0.667858\pi\)
−0.503237 + 0.864149i \(0.667858\pi\)
\(198\) 0 0
\(199\) 79089.6 + 136987.i 0.141575 + 0.245215i 0.928090 0.372356i \(-0.121450\pi\)
−0.786515 + 0.617571i \(0.788117\pi\)
\(200\) 0 0
\(201\) 281408. 487413.i 0.491299 0.850955i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −71013.9 + 123000.i −0.118021 + 0.204418i
\(206\) 0 0
\(207\) −131691. 228095.i −0.213614 0.369990i
\(208\) 0 0
\(209\) 318421. 0.504238
\(210\) 0 0
\(211\) 283510. 0.438392 0.219196 0.975681i \(-0.429657\pi\)
0.219196 + 0.975681i \(0.429657\pi\)
\(212\) 0 0
\(213\) −325355. 563531.i −0.491369 0.851077i
\(214\) 0 0
\(215\) 807082. 1.39791e6i 1.19075 2.06244i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −250546. + 433958.i −0.353002 + 0.611417i
\(220\) 0 0
\(221\) 33076.6 + 57290.4i 0.0455554 + 0.0789043i
\(222\) 0 0
\(223\) 651135. 0.876817 0.438409 0.898776i \(-0.355542\pi\)
0.438409 + 0.898776i \(0.355542\pi\)
\(224\) 0 0
\(225\) 234961. 0.309414
\(226\) 0 0
\(227\) −189147. 327612.i −0.243632 0.421983i 0.718114 0.695925i \(-0.245006\pi\)
−0.961746 + 0.273942i \(0.911672\pi\)
\(228\) 0 0
\(229\) −11166.4 + 19340.8i −0.0140710 + 0.0243717i −0.872975 0.487765i \(-0.837812\pi\)
0.858904 + 0.512136i \(0.171146\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 454470. 787165.i 0.548423 0.949896i −0.449960 0.893049i \(-0.648562\pi\)
0.998383 0.0568472i \(-0.0181048\pi\)
\(234\) 0 0
\(235\) −166250. 287953.i −0.196377 0.340136i
\(236\) 0 0
\(237\) −35902.7 −0.0415199
\(238\) 0 0
\(239\) 1.05363e6 1.19315 0.596573 0.802559i \(-0.296529\pi\)
0.596573 + 0.802559i \(0.296529\pi\)
\(240\) 0 0
\(241\) 526164. + 911342.i 0.583550 + 1.01074i 0.995054 + 0.0993307i \(0.0316702\pi\)
−0.411504 + 0.911408i \(0.634996\pi\)
\(242\) 0 0
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −21262.7 + 36828.0i −0.0221756 + 0.0384092i
\(248\) 0 0
\(249\) −207415. 359253.i −0.212003 0.367200i
\(250\) 0 0
\(251\) −972876. −0.974705 −0.487352 0.873205i \(-0.662037\pi\)
−0.487352 + 0.873205i \(0.662037\pi\)
\(252\) 0 0
\(253\) 1.55226e6 1.52463
\(254\) 0 0
\(255\) 362459. + 627798.i 0.349067 + 0.604601i
\(256\) 0 0
\(257\) 889738. 1.54107e6i 0.840290 1.45542i −0.0493598 0.998781i \(-0.515718\pi\)
0.889650 0.456644i \(-0.150949\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −93189.3 + 161409.i −0.0846769 + 0.146665i
\(262\) 0 0
\(263\) −10979.8 19017.6i −0.00978827 0.0169538i 0.861090 0.508453i \(-0.169782\pi\)
−0.870878 + 0.491499i \(0.836449\pi\)
\(264\) 0 0
\(265\) 1.99641e6 1.74637
\(266\) 0 0
\(267\) −1.21846e6 −1.04601
\(268\) 0 0
\(269\) −845555. 1.46454e6i −0.712461 1.23402i −0.963931 0.266153i \(-0.914247\pi\)
0.251470 0.967865i \(-0.419086\pi\)
\(270\) 0 0
\(271\) −233932. + 405182.i −0.193493 + 0.335140i −0.946406 0.322981i \(-0.895315\pi\)
0.752912 + 0.658121i \(0.228648\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −692381. + 1.19924e6i −0.552095 + 0.956256i
\(276\) 0 0
\(277\) −453084. 784765.i −0.354797 0.614526i 0.632286 0.774735i \(-0.282117\pi\)
−0.987083 + 0.160209i \(0.948783\pi\)
\(278\) 0 0
\(279\) −301081. −0.231565
\(280\) 0 0
\(281\) −781388. −0.590338 −0.295169 0.955445i \(-0.595376\pi\)
−0.295169 + 0.955445i \(0.595376\pi\)
\(282\) 0 0
\(283\) −749216. 1.29768e6i −0.556085 0.963167i −0.997818 0.0660209i \(-0.978970\pi\)
0.441733 0.897146i \(-0.354364\pi\)
\(284\) 0 0
\(285\) −233000. + 403567.i −0.169920 + 0.294309i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 171595. 297211.i 0.120854 0.209325i
\(290\) 0 0
\(291\) 642951. + 1.11362e6i 0.445087 + 0.770914i
\(292\) 0 0
\(293\) 1.56070e6 1.06206 0.531031 0.847352i \(-0.321805\pi\)
0.531031 + 0.847352i \(0.321805\pi\)
\(294\) 0 0
\(295\) 220357. 0.147425
\(296\) 0 0
\(297\) −174005. 301386.i −0.114464 0.198258i
\(298\) 0 0
\(299\) −103653. + 179532.i −0.0670506 + 0.116135i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 200102. 346587.i 0.125212 0.216873i
\(304\) 0 0
\(305\) 652180. + 1.12961e6i 0.401438 + 0.695310i
\(306\) 0 0
\(307\) 889308. 0.538525 0.269263 0.963067i \(-0.413220\pi\)
0.269263 + 0.963067i \(0.413220\pi\)
\(308\) 0 0
\(309\) −1.82357e6 −1.08649
\(310\) 0 0
\(311\) 1.22413e6 + 2.12026e6i 0.717674 + 1.24305i 0.961919 + 0.273334i \(0.0881263\pi\)
−0.244246 + 0.969713i \(0.578540\pi\)
\(312\) 0 0
\(313\) −1.36551e6 + 2.36514e6i −0.787834 + 1.36457i 0.139457 + 0.990228i \(0.455464\pi\)
−0.927291 + 0.374341i \(0.877869\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 124802. 216163.i 0.0697545 0.120818i −0.829039 0.559191i \(-0.811112\pi\)
0.898793 + 0.438373i \(0.144445\pi\)
\(318\) 0 0
\(319\) −549219. 951275.i −0.302182 0.523395i
\(320\) 0 0
\(321\) 895733. 0.485195
\(322\) 0 0
\(323\) −692115. −0.369124
\(324\) 0 0
\(325\) −92467.9 160159.i −0.0485605 0.0841092i
\(326\) 0 0
\(327\) −994186. + 1.72198e6i −0.514160 + 0.890551i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −323308. + 559986.i −0.162199 + 0.280936i −0.935657 0.352911i \(-0.885192\pi\)
0.773458 + 0.633847i \(0.218525\pi\)
\(332\) 0 0
\(333\) −495957. 859023.i −0.245095 0.424516i
\(334\) 0 0
\(335\) −4.85433e6 −2.36329
\(336\) 0 0
\(337\) −1.02782e6 −0.492994 −0.246497 0.969144i \(-0.579280\pi\)
−0.246497 + 0.969144i \(0.579280\pi\)
\(338\) 0 0
\(339\) −133304. 230890.i −0.0630006 0.109120i
\(340\) 0 0
\(341\) 887224. 1.53672e6i 0.413187 0.715662i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.13584e6 + 1.96734e6i −0.513773 + 0.889880i
\(346\) 0 0
\(347\) 824579. + 1.42821e6i 0.367628 + 0.636750i 0.989194 0.146611i \(-0.0468367\pi\)
−0.621566 + 0.783362i \(0.713503\pi\)
\(348\) 0 0
\(349\) −2.21201e6 −0.972128 −0.486064 0.873923i \(-0.661568\pi\)
−0.486064 + 0.873923i \(0.661568\pi\)
\(350\) 0 0
\(351\) 46477.0 0.0201358
\(352\) 0 0
\(353\) 550789. + 953995.i 0.235260 + 0.407483i 0.959348 0.282225i \(-0.0910724\pi\)
−0.724088 + 0.689708i \(0.757739\pi\)
\(354\) 0 0
\(355\) −2.80621e6 + 4.86050e6i −1.18181 + 2.04696i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 649699. 1.12531e6i 0.266058 0.460826i −0.701782 0.712391i \(-0.747612\pi\)
0.967840 + 0.251566i \(0.0809455\pi\)
\(360\) 0 0
\(361\) 1.01559e6 + 1.75906e6i 0.410159 + 0.710416i
\(362\) 0 0
\(363\) 601567. 0.239617
\(364\) 0 0
\(365\) 4.32196e6 1.69804
\(366\) 0 0
\(367\) 778345. + 1.34813e6i 0.301652 + 0.522477i 0.976510 0.215470i \(-0.0691285\pi\)
−0.674858 + 0.737948i \(0.735795\pi\)
\(368\) 0 0
\(369\) −74100.8 + 128346.i −0.0283307 + 0.0490702i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.56330e6 2.70772e6i 0.581796 1.00770i −0.413471 0.910517i \(-0.635684\pi\)
0.995267 0.0971823i \(-0.0309830\pi\)
\(374\) 0 0
\(375\) 78332.5 + 135676.i 0.0287650 + 0.0498224i
\(376\) 0 0
\(377\) 146697. 0.0531579
\(378\) 0 0
\(379\) −2.96497e6 −1.06029 −0.530143 0.847908i \(-0.677862\pi\)
−0.530143 + 0.847908i \(0.677862\pi\)
\(380\) 0 0
\(381\) 1.18859e6 + 2.05870e6i 0.419489 + 0.726577i
\(382\) 0 0
\(383\) 1.37387e6 2.37962e6i 0.478574 0.828915i −0.521124 0.853481i \(-0.674487\pi\)
0.999698 + 0.0245659i \(0.00782036\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 842164. 1.45867e6i 0.285838 0.495085i
\(388\) 0 0
\(389\) 305671. + 529438.i 0.102419 + 0.177395i 0.912681 0.408673i \(-0.134008\pi\)
−0.810262 + 0.586068i \(0.800675\pi\)
\(390\) 0 0
\(391\) −3.37397e6 −1.11609
\(392\) 0 0
\(393\) 700651. 0.228834
\(394\) 0 0
\(395\) 154832. + 268177.i 0.0499307 + 0.0864826i
\(396\) 0 0
\(397\) 1.08397e6 1.87749e6i 0.345176 0.597862i −0.640210 0.768200i \(-0.721153\pi\)
0.985386 + 0.170338i \(0.0544859\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.57322e6 2.72489e6i 0.488572 0.846231i −0.511342 0.859377i \(-0.670851\pi\)
0.999914 + 0.0131465i \(0.00418480\pi\)
\(402\) 0 0
\(403\) 118489. + 205229.i 0.0363426 + 0.0629473i
\(404\) 0 0
\(405\) 509302. 0.154290
\(406\) 0 0
\(407\) 5.84593e6 1.74931
\(408\) 0 0
\(409\) 2.79082e6 + 4.83385e6i 0.824943 + 1.42884i 0.901963 + 0.431814i \(0.142126\pi\)
−0.0770193 + 0.997030i \(0.524540\pi\)
\(410\) 0 0
\(411\) −1.67581e6 + 2.90259e6i −0.489351 + 0.847581i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.78897e6 + 3.09859e6i −0.509898 + 0.883169i
\(416\) 0 0
\(417\) −1.23548e6 2.13991e6i −0.347932 0.602636i
\(418\) 0 0
\(419\) −2.25054e6 −0.626257 −0.313128 0.949711i \(-0.601377\pi\)
−0.313128 + 0.949711i \(0.601377\pi\)
\(420\) 0 0
\(421\) 3.45914e6 0.951180 0.475590 0.879667i \(-0.342235\pi\)
0.475590 + 0.879667i \(0.342235\pi\)
\(422\) 0 0
\(423\) −173476. 300470.i −0.0471400 0.0816489i
\(424\) 0 0
\(425\) 1.50495e6 2.60665e6i 0.404156 0.700019i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −136958. + 237218.i −0.0359289 + 0.0622307i
\(430\) 0 0
\(431\) 3.27963e6 + 5.68049e6i 0.850417 + 1.47297i 0.880833 + 0.473428i \(0.156984\pi\)
−0.0304157 + 0.999537i \(0.509683\pi\)
\(432\) 0 0
\(433\) −5.05669e6 −1.29612 −0.648062 0.761587i \(-0.724420\pi\)
−0.648062 + 0.761587i \(0.724420\pi\)
\(434\) 0 0
\(435\) 1.60753e6 0.407320
\(436\) 0 0
\(437\) −1.08445e6 1.87832e6i −0.271647 0.470506i
\(438\) 0 0
\(439\) 2.11613e6 3.66524e6i 0.524059 0.907697i −0.475549 0.879689i \(-0.657750\pi\)
0.999608 0.0280074i \(-0.00891619\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.02763e6 5.24400e6i 0.732981 1.26956i −0.222622 0.974905i \(-0.571462\pi\)
0.955603 0.294656i \(-0.0952050\pi\)
\(444\) 0 0
\(445\) 5.25467e6 + 9.10135e6i 1.25790 + 2.17874i
\(446\) 0 0
\(447\) −2.81684e6 −0.666796
\(448\) 0 0
\(449\) −299186. −0.0700368 −0.0350184 0.999387i \(-0.511149\pi\)
−0.0350184 + 0.999387i \(0.511149\pi\)
\(450\) 0 0
\(451\) −436719. 756420.i −0.101102 0.175114i
\(452\) 0 0
\(453\) −1.94443e6 + 3.36785e6i −0.445191 + 0.771093i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.87589e6 + 3.24913e6i −0.420161 + 0.727740i −0.995955 0.0898545i \(-0.971360\pi\)
0.575794 + 0.817595i \(0.304693\pi\)
\(458\) 0 0
\(459\) 378215. + 655087.i 0.0837928 + 0.145133i
\(460\) 0 0
\(461\) −6.94525e6 −1.52207 −0.761036 0.648709i \(-0.775309\pi\)
−0.761036 + 0.648709i \(0.775309\pi\)
\(462\) 0 0
\(463\) −9.13226e6 −1.97982 −0.989910 0.141697i \(-0.954744\pi\)
−0.989910 + 0.141697i \(0.954744\pi\)
\(464\) 0 0
\(465\) 1.29843e6 + 2.24894e6i 0.278474 + 0.482331i
\(466\) 0 0
\(467\) −212068. + 367313.i −0.0449970 + 0.0779371i −0.887647 0.460525i \(-0.847661\pi\)
0.842650 + 0.538462i \(0.180994\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −380717. + 659420.i −0.0790769 + 0.136965i
\(472\) 0 0
\(473\) 4.96336e6 + 8.59680e6i 1.02005 + 1.76679i
\(474\) 0 0
\(475\) 1.93485e6 0.393472
\(476\) 0 0
\(477\) 2.08319e6 0.419212
\(478\) 0 0
\(479\) −3.89303e6 6.74292e6i −0.775262 1.34279i −0.934647 0.355577i \(-0.884285\pi\)
0.159385 0.987216i \(-0.449049\pi\)
\(480\) 0 0
\(481\) −390364. + 676130.i −0.0769320 + 0.133250i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.54550e6 9.60509e6i 1.07050 1.85416i
\(486\) 0 0
\(487\) −1.16130e6 2.01143e6i −0.221881 0.384310i 0.733498 0.679692i \(-0.237886\pi\)
−0.955379 + 0.295382i \(0.904553\pi\)
\(488\) 0 0
\(489\) 2.75673e6 0.521341
\(490\) 0 0
\(491\) 6.01036e6 1.12512 0.562558 0.826758i \(-0.309817\pi\)
0.562558 + 0.826758i \(0.309817\pi\)
\(492\) 0 0
\(493\) 1.19377e6 + 2.06768e6i 0.221210 + 0.383147i
\(494\) 0 0
\(495\) −1.50081e6 + 2.59948e6i −0.275304 + 0.476840i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.68693e6 + 2.92184e6i −0.303281 + 0.525298i −0.976877 0.213802i \(-0.931415\pi\)
0.673596 + 0.739100i \(0.264749\pi\)
\(500\) 0 0
\(501\) −2.72931e6 4.72731e6i −0.485801 0.841433i
\(502\) 0 0
\(503\) 1.22068e6 0.215120 0.107560 0.994199i \(-0.465696\pi\)
0.107560 + 0.994199i \(0.465696\pi\)
\(504\) 0 0
\(505\) −3.45179e6 −0.602304
\(506\) 0 0
\(507\) 1.65253e6 + 2.86226e6i 0.285515 + 0.494526i
\(508\) 0 0
\(509\) 784485. 1.35877e6i 0.134212 0.232461i −0.791084 0.611707i \(-0.790483\pi\)
0.925296 + 0.379246i \(0.123816\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −243128. + 421110.i −0.0407888 + 0.0706484i
\(514\) 0 0
\(515\) 7.86424e6 + 1.36213e7i 1.30659 + 2.26308i
\(516\) 0 0
\(517\) 2.04480e6 0.336452
\(518\) 0 0
\(519\) 2.59633e6 0.423098
\(520\) 0 0
\(521\) 5.33893e6 + 9.24730e6i 0.861708 + 1.49252i 0.870279 + 0.492559i \(0.163938\pi\)
−0.00857106 + 0.999963i \(0.502728\pi\)
\(522\) 0 0
\(523\) −6.05033e6 + 1.04795e7i −0.967219 + 1.67527i −0.263689 + 0.964608i \(0.584939\pi\)
−0.703531 + 0.710665i \(0.748394\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.92845e6 + 3.34018e6i −0.302470 + 0.523894i
\(528\) 0 0
\(529\) −2.06836e6 3.58251e6i −0.321357 0.556607i
\(530\) 0 0
\(531\) 229936. 0.0353892
\(532\) 0 0
\(533\) 116648. 0.0177852
\(534\) 0 0
\(535\) −3.86289e6 6.69071e6i −0.583482 1.01062i
\(536\) 0 0
\(537\) −669861. + 1.16023e6i −0.100242 + 0.173624i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.59903e6 2.76959e6i 0.234889 0.406839i −0.724352 0.689431i \(-0.757861\pi\)
0.959240 + 0.282591i \(0.0911941\pi\)
\(542\) 0 0
\(543\) 420200. + 727808.i 0.0611585 + 0.105930i
\(544\) 0 0
\(545\) 1.71499e7 2.47326
\(546\) 0 0
\(547\) 3.97811e6 0.568471 0.284235 0.958755i \(-0.408260\pi\)
0.284235 + 0.958755i \(0.408260\pi\)
\(548\) 0 0
\(549\) 680529. + 1.17871e6i 0.0963643 + 0.166908i
\(550\) 0 0
\(551\) −767394. + 1.32917e6i −0.107681 + 0.186509i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −4.27767e6 + 7.40915e6i −0.589488 + 1.02102i
\(556\) 0 0
\(557\) −5.70567e6 9.88251e6i −0.779236 1.34968i −0.932383 0.361472i \(-0.882274\pi\)
0.153147 0.988203i \(-0.451059\pi\)
\(558\) 0 0
\(559\) −1.32572e6 −0.179441
\(560\) 0 0
\(561\) −4.45808e6 −0.598054
\(562\) 0 0
\(563\) −3.23486e6 5.60295e6i −0.430115 0.744982i 0.566768 0.823878i \(-0.308194\pi\)
−0.996883 + 0.0788962i \(0.974860\pi\)
\(564\) 0 0
\(565\) −1.14976e6 + 1.99144e6i −0.151526 + 0.262450i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −358514. + 620965.i −0.0464222 + 0.0804056i −0.888303 0.459258i \(-0.848115\pi\)
0.841881 + 0.539664i \(0.181449\pi\)
\(570\) 0 0
\(571\) −3.00143e6 5.19863e6i −0.385246 0.667265i 0.606558 0.795040i \(-0.292550\pi\)
−0.991803 + 0.127774i \(0.959217\pi\)
\(572\) 0 0
\(573\) 2.22223e6 0.282750
\(574\) 0 0
\(575\) 9.43217e6 1.18971
\(576\) 0 0
\(577\) 7.78560e6 + 1.34850e7i 0.973537 + 1.68621i 0.684682 + 0.728842i \(0.259941\pi\)
0.288855 + 0.957373i \(0.406726\pi\)
\(578\) 0 0
\(579\) −2.16647e6 + 3.75243e6i −0.268569 + 0.465175i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.13873e6 + 1.06326e7i −0.748010 + 1.29559i
\(584\) 0 0
\(585\) −200434. 347161.i −0.0242148 0.0419413i
\(586\) 0 0
\(587\) −7.84621e6 −0.939863 −0.469931 0.882703i \(-0.655721\pi\)
−0.469931 + 0.882703i \(0.655721\pi\)
\(588\) 0 0
\(589\) −2.47934e6 −0.294475
\(590\) 0 0
\(591\) 2.46706e6 + 4.27308e6i 0.290544 + 0.503237i
\(592\) 0 0
\(593\) 6.66240e6 1.15396e7i 0.778026 1.34758i −0.155052 0.987906i \(-0.549555\pi\)
0.933078 0.359674i \(-0.117112\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 711807. 1.23289e6i 0.0817384 0.141575i
\(598\) 0 0
\(599\) 3.88958e6 + 6.73695e6i 0.442930 + 0.767178i 0.997905 0.0646890i \(-0.0206055\pi\)
−0.554975 + 0.831867i \(0.687272\pi\)
\(600\) 0 0
\(601\) −8.62898e6 −0.974480 −0.487240 0.873268i \(-0.661996\pi\)
−0.487240 + 0.873268i \(0.661996\pi\)
\(602\) 0 0
\(603\) −5.06534e6 −0.567304
\(604\) 0 0
\(605\) −2.59428e6 4.49343e6i −0.288157 0.499102i
\(606\) 0 0
\(607\) −3.54676e6 + 6.14317e6i −0.390715 + 0.676739i −0.992544 0.121886i \(-0.961106\pi\)
0.601829 + 0.798625i \(0.294439\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −136542. + 236497.i −0.0147966 + 0.0256285i
\(612\) 0 0
\(613\) −2.26320e6 3.91998e6i −0.243261 0.421340i 0.718381 0.695650i \(-0.244884\pi\)
−0.961641 + 0.274311i \(0.911550\pi\)
\(614\) 0 0
\(615\) 1.27825e6 0.136279
\(616\) 0 0
\(617\) −8.38009e6 −0.886208 −0.443104 0.896470i \(-0.646123\pi\)
−0.443104 + 0.896470i \(0.646123\pi\)
\(618\) 0 0
\(619\) −84171.0 145788.i −0.00882949 0.0152931i 0.861577 0.507627i \(-0.169477\pi\)
−0.870406 + 0.492334i \(0.836144\pi\)
\(620\) 0 0
\(621\) −1.18522e6 + 2.05286e6i −0.123330 + 0.213614i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 5.20805e6 9.02061e6i 0.533305 0.923711i
\(626\) 0 0
\(627\) −1.43289e6 2.48185e6i −0.145561 0.252119i
\(628\) 0 0
\(629\) −1.27066e7 −1.28057
\(630\) 0 0
\(631\) 1.66208e7 1.66180 0.830899 0.556423i \(-0.187826\pi\)
0.830899 + 0.556423i \(0.187826\pi\)
\(632\) 0 0
\(633\) −1.27580e6 2.20974e6i −0.126553 0.219196i
\(634\) 0 0
\(635\) 1.02517e7 1.77565e7i 1.00893 1.74752i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.92819e6 + 5.07178e6i −0.283692 + 0.491369i
\(640\) 0 0
\(641\) −512367. 887446.i −0.0492534 0.0853094i 0.840348 0.542048i \(-0.182351\pi\)
−0.889601 + 0.456738i \(0.849018\pi\)
\(642\) 0 0
\(643\) 1.22962e7 1.17286 0.586428 0.810001i \(-0.300534\pi\)
0.586428 + 0.810001i \(0.300534\pi\)
\(644\) 0 0
\(645\) −1.45275e7 −1.37496
\(646\) 0 0
\(647\) −1.08269e6 1.87527e6i −0.101682 0.176118i 0.810696 0.585467i \(-0.199089\pi\)
−0.912378 + 0.409350i \(0.865756\pi\)
\(648\) 0 0
\(649\) −677573. + 1.17359e6i −0.0631458 + 0.109372i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.12507e6 1.06089e7i 0.562119 0.973619i −0.435192 0.900338i \(-0.643320\pi\)
0.997311 0.0732814i \(-0.0233471\pi\)
\(654\) 0 0
\(655\) −3.02158e6 5.23354e6i −0.275189 0.476642i
\(656\) 0 0
\(657\) 4.50983e6 0.407612
\(658\) 0 0
\(659\) 1.18607e6 0.106389 0.0531944 0.998584i \(-0.483060\pi\)
0.0531944 + 0.998584i \(0.483060\pi\)
\(660\) 0 0
\(661\) −7.26909e6 1.25904e7i −0.647107 1.12082i −0.983811 0.179212i \(-0.942645\pi\)
0.336703 0.941611i \(-0.390688\pi\)
\(662\) 0 0
\(663\) 297689. 515613.i 0.0263014 0.0455554i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.74095e6 + 6.47951e6i −0.325587 + 0.563933i
\(668\) 0 0
\(669\) −2.93011e6 5.07510e6i −0.253115 0.438409i
\(670\) 0 0
\(671\) −8.02151e6 −0.687781
\(672\) 0 0
\(673\) −5.99405e6 −0.510132 −0.255066 0.966924i \(-0.582097\pi\)
−0.255066 + 0.966924i \(0.582097\pi\)
\(674\) 0 0
\(675\) −1.05732e6 1.83134e6i −0.0893201 0.154707i
\(676\) 0 0
\(677\) 1.04194e7 1.80470e7i 0.873721 1.51333i 0.0156016 0.999878i \(-0.495034\pi\)
0.858119 0.513451i \(-0.171633\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.70232e6 + 2.94851e6i −0.140661 + 0.243632i
\(682\) 0 0
\(683\) −2.27783e6 3.94531e6i −0.186840 0.323616i 0.757355 0.653003i \(-0.226491\pi\)
−0.944195 + 0.329387i \(0.893158\pi\)
\(684\) 0 0
\(685\) 2.89080e7 2.35392
\(686\) 0 0
\(687\) 200995. 0.0162478
\(688\) 0 0
\(689\) −819831. 1.41999e6i −0.0657925 0.113956i
\(690\) 0 0
\(691\) 842712. 1.45962e6i 0.0671404 0.116291i −0.830501 0.557017i \(-0.811946\pi\)
0.897641 + 0.440726i \(0.145279\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.06561e7 + 1.84569e7i −0.836827 + 1.44943i
\(696\) 0 0
\(697\) 949246. + 1.64414e6i 0.0740111 + 0.128191i
\(698\) 0 0
\(699\) −8.18046e6 −0.633264
\(700\) 0 0
\(701\) 2.45349e6 0.188577 0.0942887 0.995545i \(-0.469942\pi\)
0.0942887 + 0.995545i \(0.469942\pi\)
\(702\) 0 0
\(703\) −4.08410e6 7.07387e6i −0.311680 0.539845i
\(704\) 0 0
\(705\) −1.49625e6 + 2.59158e6i −0.113379 + 0.196377i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6.61569e6 1.14587e7i 0.494265 0.856092i −0.505713 0.862702i \(-0.668771\pi\)
0.999978 + 0.00660968i \(0.00210394\pi\)
\(710\) 0 0
\(711\) 161562. + 279834.i 0.0119858 + 0.0207600i
\(712\) 0 0
\(713\) −1.20865e7 −0.890380
\(714\) 0 0
\(715\) 2.36255e6 0.172828
\(716\) 0 0
\(717\) −4.74134e6 8.21224e6i −0.344432 0.596573i
\(718\) 0 0
\(719\) 6.76685e6 1.17205e7i 0.488162 0.845522i −0.511745 0.859137i \(-0.671001\pi\)
0.999907 + 0.0136156i \(0.00433413\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 4.73547e6 8.20208e6i 0.336913 0.583550i
\(724\) 0 0
\(725\) −3.33728e6 5.78033e6i −0.235802 0.408421i
\(726\) 0 0
\(727\) −5.29416e6 −0.371502 −0.185751 0.982597i \(-0.559472\pi\)
−0.185751 + 0.982597i \(0.559472\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −1.07883e7 1.86859e7i −0.746722 1.29336i
\(732\) 0 0
\(733\) −1.12507e7 + 1.94868e7i −0.773426 + 1.33961i 0.162249 + 0.986750i \(0.448125\pi\)
−0.935675 + 0.352863i \(0.885208\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.49265e7 2.58535e7i 1.01225 1.75327i
\(738\) 0 0
\(739\) −8.03696e6 1.39204e7i −0.541353 0.937652i −0.998827 0.0484282i \(-0.984579\pi\)
0.457473 0.889223i \(-0.348755\pi\)
\(740\) 0 0
\(741\) 382728. 0.0256062
\(742\) 0 0
\(743\) −2.31604e6 −0.153913 −0.0769563 0.997034i \(-0.524520\pi\)
−0.0769563 + 0.997034i \(0.524520\pi\)
\(744\) 0 0
\(745\) 1.21477e7 + 2.10405e7i 0.801871 + 1.38888i
\(746\) 0 0
\(747\) −1.86674e6 + 3.23328e6i −0.122400 + 0.212003i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3.88632e6 6.73130e6i 0.251442 0.435511i −0.712481 0.701692i \(-0.752428\pi\)
0.963923 + 0.266181i \(0.0857618\pi\)
\(752\) 0 0
\(753\) 4.37794e6 + 7.58282e6i 0.281373 + 0.487352i
\(754\) 0 0
\(755\) 3.35417e7 2.14150
\(756\) 0 0
\(757\) −1.59716e7 −1.01300 −0.506498 0.862241i \(-0.669060\pi\)
−0.506498 + 0.862241i \(0.669060\pi\)
\(758\) 0 0
\(759\) −6.98518e6 1.20987e7i −0.440122 0.762313i
\(760\) 0 0
\(761\) 9.24701e6 1.60163e7i 0.578815 1.00254i −0.416801 0.908998i \(-0.636849\pi\)
0.995616 0.0935391i \(-0.0298180\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3.26213e6 5.65018e6i 0.201534 0.349067i
\(766\) 0 0
\(767\) −90490.2 156734.i −0.00555409 0.00961997i
\(768\) 0 0
\(769\) 2.33524e7 1.42402 0.712009 0.702170i \(-0.247786\pi\)
0.712009 + 0.702170i \(0.247786\pi\)
\(770\) 0 0
\(771\) −1.60153e7 −0.970283
\(772\) 0 0
\(773\) 3.62631e6 + 6.28095e6i 0.218281 + 0.378074i 0.954283 0.298906i \(-0.0966217\pi\)
−0.736001 + 0.676980i \(0.763288\pi\)
\(774\) 0 0
\(775\) 5.39113e6 9.33771e6i 0.322423 0.558452i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −610204. + 1.05690e6i −0.0360273 + 0.0624011i
\(780\) 0 0
\(781\) −1.72575e7 2.98909e7i −1.01240 1.75352i
\(782\) 0 0
\(783\) 1.67741e6 0.0977764
\(784\) 0 0
\(785\) 6.56742e6 0.380383