Properties

Label 392.6.i.f.361.1
Level $392$
Weight $6$
Character 392.361
Analytic conductor $62.870$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,6,Mod(177,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.177");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.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: \(62.8704573667\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 392.361
Dual form 392.6.i.f.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(15.0000 - 25.9808i) q^{3} +(16.0000 + 27.7128i) q^{5} +(-328.500 - 568.979i) q^{9} +O(q^{10})\) \(q+(15.0000 - 25.9808i) q^{3} +(16.0000 + 27.7128i) q^{5} +(-328.500 - 568.979i) q^{9} +(312.000 - 540.400i) q^{11} +708.000 q^{13} +960.000 q^{15} +(467.000 - 808.868i) q^{17} +(929.000 + 1609.08i) q^{19} +(560.000 + 969.948i) q^{23} +(1050.50 - 1819.52i) q^{25} -12420.0 q^{27} -1174.00 q^{29} +(1454.00 - 2518.40i) q^{31} +(-9360.00 - 16212.0i) q^{33} +(6231.00 + 10792.4i) q^{37} +(10620.0 - 18394.4i) q^{39} -2662.00 q^{41} -7144.00 q^{43} +(10512.0 - 18207.3i) q^{45} +(-3734.00 - 6467.48i) q^{47} +(-14010.0 - 24266.0i) q^{51} +(13637.0 - 23620.0i) q^{53} +19968.0 q^{55} +55740.0 q^{57} +(1245.00 - 2156.40i) q^{59} +(-5548.00 - 9609.42i) q^{61} +(11328.0 + 19620.7i) q^{65} +(-19878.0 + 34429.7i) q^{67} +33600.0 q^{69} -69888.0 q^{71} +(8225.00 - 14246.1i) q^{73} +(-31515.0 - 54585.6i) q^{75} +(-39188.0 - 67875.6i) q^{79} +(-106474. + 184419. i) q^{81} -109818. q^{83} +29888.0 q^{85} +(-17610.0 + 30501.4i) q^{87} +(-28483.0 - 49334.0i) q^{89} +(-43620.0 - 75552.1i) q^{93} +(-29728.0 + 51490.4i) q^{95} +115946. q^{97} -409968. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 30 q^{3} + 32 q^{5} - 657 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 30 q^{3} + 32 q^{5} - 657 q^{9} + 624 q^{11} + 1416 q^{13} + 1920 q^{15} + 934 q^{17} + 1858 q^{19} + 1120 q^{23} + 2101 q^{25} - 24840 q^{27} - 2348 q^{29} + 2908 q^{31} - 18720 q^{33} + 12462 q^{37} + 21240 q^{39} - 5324 q^{41} - 14288 q^{43} + 21024 q^{45} - 7468 q^{47} - 28020 q^{51} + 27274 q^{53} + 39936 q^{55} + 111480 q^{57} + 2490 q^{59} - 11096 q^{61} + 22656 q^{65} - 39756 q^{67} + 67200 q^{69} - 139776 q^{71} + 16450 q^{73} - 63030 q^{75} - 78376 q^{79} - 212949 q^{81} - 219636 q^{83} + 59776 q^{85} - 35220 q^{87} - 56966 q^{89} - 87240 q^{93} - 59456 q^{95} + 231892 q^{97} - 819936 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 15.0000 25.9808i 0.962250 1.66667i 0.245423 0.969416i \(-0.421073\pi\)
0.716827 0.697251i \(-0.245594\pi\)
\(4\) 0 0
\(5\) 16.0000 + 27.7128i 0.286217 + 0.495742i 0.972904 0.231212i \(-0.0742689\pi\)
−0.686687 + 0.726953i \(0.740936\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −328.500 568.979i −1.35185 2.34148i
\(10\) 0 0
\(11\) 312.000 540.400i 0.777451 1.34658i −0.155956 0.987764i \(-0.549846\pi\)
0.933407 0.358820i \(-0.116821\pi\)
\(12\) 0 0
\(13\) 708.000 1.16192 0.580958 0.813933i \(-0.302678\pi\)
0.580958 + 0.813933i \(0.302678\pi\)
\(14\) 0 0
\(15\) 960.000 1.10165
\(16\) 0 0
\(17\) 467.000 808.868i 0.391917 0.678821i −0.600785 0.799411i \(-0.705145\pi\)
0.992702 + 0.120590i \(0.0384786\pi\)
\(18\) 0 0
\(19\) 929.000 + 1609.08i 0.590380 + 1.02257i 0.994181 + 0.107721i \(0.0343555\pi\)
−0.403801 + 0.914847i \(0.632311\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 560.000 + 969.948i 0.220734 + 0.382322i 0.955031 0.296506i \(-0.0958215\pi\)
−0.734297 + 0.678828i \(0.762488\pi\)
\(24\) 0 0
\(25\) 1050.50 1819.52i 0.336160 0.582246i
\(26\) 0 0
\(27\) −12420.0 −3.27878
\(28\) 0 0
\(29\) −1174.00 −0.259223 −0.129611 0.991565i \(-0.541373\pi\)
−0.129611 + 0.991565i \(0.541373\pi\)
\(30\) 0 0
\(31\) 1454.00 2518.40i 0.271744 0.470675i −0.697564 0.716522i \(-0.745733\pi\)
0.969309 + 0.245847i \(0.0790662\pi\)
\(32\) 0 0
\(33\) −9360.00 16212.0i −1.49620 2.59150i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6231.00 + 10792.4i 0.748262 + 1.29603i 0.948655 + 0.316312i \(0.102445\pi\)
−0.200394 + 0.979715i \(0.564222\pi\)
\(38\) 0 0
\(39\) 10620.0 18394.4i 1.11805 1.93653i
\(40\) 0 0
\(41\) −2662.00 −0.247314 −0.123657 0.992325i \(-0.539462\pi\)
−0.123657 + 0.992325i \(0.539462\pi\)
\(42\) 0 0
\(43\) −7144.00 −0.589210 −0.294605 0.955619i \(-0.595188\pi\)
−0.294605 + 0.955619i \(0.595188\pi\)
\(44\) 0 0
\(45\) 10512.0 18207.3i 0.773845 1.34034i
\(46\) 0 0
\(47\) −3734.00 6467.48i −0.246564 0.427061i 0.716006 0.698094i \(-0.245968\pi\)
−0.962570 + 0.271033i \(0.912635\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −14010.0 24266.0i −0.754245 1.30639i
\(52\) 0 0
\(53\) 13637.0 23620.0i 0.666852 1.15502i −0.311928 0.950106i \(-0.600975\pi\)
0.978780 0.204915i \(-0.0656918\pi\)
\(54\) 0 0
\(55\) 19968.0 0.890078
\(56\) 0 0
\(57\) 55740.0 2.27237
\(58\) 0 0
\(59\) 1245.00 2156.40i 0.0465628 0.0806492i −0.841805 0.539782i \(-0.818507\pi\)
0.888367 + 0.459133i \(0.151840\pi\)
\(60\) 0 0
\(61\) −5548.00 9609.42i −0.190903 0.330653i 0.754647 0.656131i \(-0.227808\pi\)
−0.945550 + 0.325478i \(0.894475\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11328.0 + 19620.7i 0.332560 + 0.576011i
\(66\) 0 0
\(67\) −19878.0 + 34429.7i −0.540986 + 0.937014i 0.457862 + 0.889023i \(0.348615\pi\)
−0.998848 + 0.0479913i \(0.984718\pi\)
\(68\) 0 0
\(69\) 33600.0 0.849604
\(70\) 0 0
\(71\) −69888.0 −1.64534 −0.822672 0.568516i \(-0.807518\pi\)
−0.822672 + 0.568516i \(0.807518\pi\)
\(72\) 0 0
\(73\) 8225.00 14246.1i 0.180646 0.312888i −0.761455 0.648218i \(-0.775514\pi\)
0.942101 + 0.335330i \(0.108848\pi\)
\(74\) 0 0
\(75\) −31515.0 54585.6i −0.646940 1.12053i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −39188.0 67875.6i −0.706456 1.22362i −0.966163 0.257931i \(-0.916959\pi\)
0.259707 0.965687i \(-0.416374\pi\)
\(80\) 0 0
\(81\) −106474. + 184419.i −1.80316 + 3.12316i
\(82\) 0 0
\(83\) −109818. −1.74976 −0.874880 0.484340i \(-0.839060\pi\)
−0.874880 + 0.484340i \(0.839060\pi\)
\(84\) 0 0
\(85\) 29888.0 0.448693
\(86\) 0 0
\(87\) −17610.0 + 30501.4i −0.249437 + 0.432038i
\(88\) 0 0
\(89\) −28483.0 49334.0i −0.381163 0.660194i 0.610066 0.792351i \(-0.291143\pi\)
−0.991229 + 0.132157i \(0.957810\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −43620.0 75552.1i −0.522972 0.905814i
\(94\) 0 0
\(95\) −29728.0 + 51490.4i −0.337953 + 0.585352i
\(96\) 0 0
\(97\) 115946. 1.25120 0.625600 0.780144i \(-0.284854\pi\)
0.625600 + 0.780144i \(0.284854\pi\)
\(98\) 0 0
\(99\) −409968. −4.20399
\(100\) 0 0
\(101\) 4176.00 7233.04i 0.0407340 0.0705534i −0.844940 0.534862i \(-0.820364\pi\)
0.885674 + 0.464308i \(0.153697\pi\)
\(102\) 0 0
\(103\) 89742.0 + 155438.i 0.833494 + 1.44365i 0.895250 + 0.445563i \(0.146997\pi\)
−0.0617560 + 0.998091i \(0.519670\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 26946.0 + 46671.8i 0.227528 + 0.394090i 0.957075 0.289841i \(-0.0936023\pi\)
−0.729547 + 0.683931i \(0.760269\pi\)
\(108\) 0 0
\(109\) −52985.0 + 91772.7i −0.427156 + 0.739856i −0.996619 0.0821608i \(-0.973818\pi\)
0.569463 + 0.822017i \(0.307151\pi\)
\(110\) 0 0
\(111\) 373860. 2.88006
\(112\) 0 0
\(113\) 2502.00 0.0184328 0.00921640 0.999958i \(-0.497066\pi\)
0.00921640 + 0.999958i \(0.497066\pi\)
\(114\) 0 0
\(115\) −17920.0 + 31038.4i −0.126355 + 0.218854i
\(116\) 0 0
\(117\) −232578. 402837.i −1.57074 2.72060i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −114162. 197735.i −0.708859 1.22778i
\(122\) 0 0
\(123\) −39930.0 + 69160.8i −0.237978 + 0.412190i
\(124\) 0 0
\(125\) 167232. 0.957292
\(126\) 0 0
\(127\) 287792. 1.58332 0.791661 0.610960i \(-0.209216\pi\)
0.791661 + 0.610960i \(0.209216\pi\)
\(128\) 0 0
\(129\) −107160. + 185607.i −0.566968 + 0.982017i
\(130\) 0 0
\(131\) −23831.0 41276.5i −0.121329 0.210148i 0.798963 0.601380i \(-0.205382\pi\)
−0.920292 + 0.391232i \(0.872049\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −198720. 344193.i −0.938441 1.62543i
\(136\) 0 0
\(137\) −111577. + 193257.i −0.507894 + 0.879699i 0.492064 + 0.870559i \(0.336243\pi\)
−0.999958 + 0.00913956i \(0.997091\pi\)
\(138\) 0 0
\(139\) −250542. −1.09988 −0.549938 0.835206i \(-0.685349\pi\)
−0.549938 + 0.835206i \(0.685349\pi\)
\(140\) 0 0
\(141\) −224040. −0.949025
\(142\) 0 0
\(143\) 220896. 382603.i 0.903333 1.56462i
\(144\) 0 0
\(145\) −18784.0 32534.8i −0.0741939 0.128508i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 243697. + 422096.i 0.899258 + 1.55756i 0.828444 + 0.560072i \(0.189226\pi\)
0.0708143 + 0.997490i \(0.477440\pi\)
\(150\) 0 0
\(151\) 27340.0 47354.3i 0.0975790 0.169012i −0.813103 0.582120i \(-0.802223\pi\)
0.910682 + 0.413108i \(0.135557\pi\)
\(152\) 0 0
\(153\) −613638. −2.11926
\(154\) 0 0
\(155\) 93056.0 0.311111
\(156\) 0 0
\(157\) 105534. 182790.i 0.341699 0.591839i −0.643050 0.765825i \(-0.722331\pi\)
0.984748 + 0.173985i \(0.0556644\pi\)
\(158\) 0 0
\(159\) −409110. 708599.i −1.28336 2.22284i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10096.0 + 17486.8i 0.0297632 + 0.0515515i 0.880523 0.474003i \(-0.157191\pi\)
−0.850760 + 0.525554i \(0.823858\pi\)
\(164\) 0 0
\(165\) 299520. 518784.i 0.856478 1.48346i
\(166\) 0 0
\(167\) 4524.00 0.0125525 0.00627627 0.999980i \(-0.498002\pi\)
0.00627627 + 0.999980i \(0.498002\pi\)
\(168\) 0 0
\(169\) 129971. 0.350050
\(170\) 0 0
\(171\) 610353. 1.05716e6i 1.59621 2.76472i
\(172\) 0 0
\(173\) −52166.0 90354.2i −0.132517 0.229527i 0.792129 0.610354i \(-0.208973\pi\)
−0.924646 + 0.380827i \(0.875639\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −37350.0 64692.1i −0.0896102 0.155209i
\(178\) 0 0
\(179\) 100862. 174698.i 0.235285 0.407526i −0.724070 0.689726i \(-0.757731\pi\)
0.959356 + 0.282200i \(0.0910642\pi\)
\(180\) 0 0
\(181\) −655700. −1.48768 −0.743839 0.668359i \(-0.766997\pi\)
−0.743839 + 0.668359i \(0.766997\pi\)
\(182\) 0 0
\(183\) −332880. −0.734784
\(184\) 0 0
\(185\) −199392. + 345357.i −0.428330 + 0.741889i
\(186\) 0 0
\(187\) −291408. 504733.i −0.609393 1.05550i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 75748.0 + 131199.i 0.150241 + 0.260225i 0.931316 0.364212i \(-0.118662\pi\)
−0.781075 + 0.624437i \(0.785328\pi\)
\(192\) 0 0
\(193\) −114663. + 198602.i −0.221580 + 0.383787i −0.955288 0.295677i \(-0.904455\pi\)
0.733708 + 0.679465i \(0.237788\pi\)
\(194\) 0 0
\(195\) 679680. 1.28002
\(196\) 0 0
\(197\) 421086. 0.773046 0.386523 0.922280i \(-0.373676\pi\)
0.386523 + 0.922280i \(0.373676\pi\)
\(198\) 0 0
\(199\) 98650.0 170867.i 0.176589 0.305862i −0.764121 0.645073i \(-0.776827\pi\)
0.940710 + 0.339211i \(0.110160\pi\)
\(200\) 0 0
\(201\) 596340. + 1.03289e6i 1.04113 + 1.80329i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −42592.0 73771.5i −0.0707853 0.122604i
\(206\) 0 0
\(207\) 367920. 637256.i 0.596798 1.03368i
\(208\) 0 0
\(209\) 1.15939e6 1.83597
\(210\) 0 0
\(211\) 679052. 1.05002 0.525009 0.851097i \(-0.324062\pi\)
0.525009 + 0.851097i \(0.324062\pi\)
\(212\) 0 0
\(213\) −1.04832e6 + 1.81574e6i −1.58323 + 2.74224i
\(214\) 0 0
\(215\) −114304. 197980.i −0.168642 0.292096i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −246750. 427384.i −0.347654 0.602154i
\(220\) 0 0
\(221\) 330636. 572678.i 0.455375 0.788733i
\(222\) 0 0
\(223\) 184440. 0.248366 0.124183 0.992259i \(-0.460369\pi\)
0.124183 + 0.992259i \(0.460369\pi\)
\(224\) 0 0
\(225\) −1.38036e6 −1.81775
\(226\) 0 0
\(227\) −434039. + 751778.i −0.559067 + 0.968333i 0.438507 + 0.898728i \(0.355507\pi\)
−0.997575 + 0.0696054i \(0.977826\pi\)
\(228\) 0 0
\(229\) −296930. 514298.i −0.374167 0.648076i 0.616035 0.787719i \(-0.288738\pi\)
−0.990202 + 0.139643i \(0.955405\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −24109.0 41758.0i −0.0290931 0.0503907i 0.851112 0.524984i \(-0.175929\pi\)
−0.880205 + 0.474593i \(0.842595\pi\)
\(234\) 0 0
\(235\) 119488. 206959.i 0.141141 0.244464i
\(236\) 0 0
\(237\) −2.35128e6 −2.71915
\(238\) 0 0
\(239\) 241688. 0.273691 0.136845 0.990592i \(-0.456304\pi\)
0.136845 + 0.990592i \(0.456304\pi\)
\(240\) 0 0
\(241\) 282635. 489538.i 0.313461 0.542930i −0.665648 0.746266i \(-0.731845\pi\)
0.979109 + 0.203335i \(0.0651782\pi\)
\(242\) 0 0
\(243\) 1.68520e6 + 2.91886e6i 1.83078 + 3.17101i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 657732. + 1.13923e6i 0.685972 + 1.18814i
\(248\) 0 0
\(249\) −1.64727e6 + 2.85316e6i −1.68371 + 2.91627i
\(250\) 0 0
\(251\) 1.43775e6 1.44045 0.720224 0.693741i \(-0.244039\pi\)
0.720224 + 0.693741i \(0.244039\pi\)
\(252\) 0 0
\(253\) 698880. 0.686438
\(254\) 0 0
\(255\) 448320. 776513.i 0.431755 0.747822i
\(256\) 0 0
\(257\) 247401. + 428511.i 0.233652 + 0.404696i 0.958880 0.283812i \(-0.0915992\pi\)
−0.725228 + 0.688508i \(0.758266\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 385659. + 667981.i 0.350431 + 0.606964i
\(262\) 0 0
\(263\) −778272. + 1.34801e6i −0.693812 + 1.20172i 0.276767 + 0.960937i \(0.410737\pi\)
−0.970579 + 0.240781i \(0.922596\pi\)
\(264\) 0 0
\(265\) 872768. 0.763456
\(266\) 0 0
\(267\) −1.70898e6 −1.46710
\(268\) 0 0
\(269\) 681018. 1.17956e6i 0.573823 0.993890i −0.422346 0.906435i \(-0.638793\pi\)
0.996168 0.0874555i \(-0.0278736\pi\)
\(270\) 0 0
\(271\) 279160. + 483519.i 0.230903 + 0.399936i 0.958074 0.286520i \(-0.0924986\pi\)
−0.727171 + 0.686456i \(0.759165\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −655512. 1.13538e6i −0.522696 0.905335i
\(276\) 0 0
\(277\) −293171. + 507787.i −0.229573 + 0.397633i −0.957682 0.287829i \(-0.907066\pi\)
0.728108 + 0.685462i \(0.240400\pi\)
\(278\) 0 0
\(279\) −1.91056e6 −1.46943
\(280\) 0 0
\(281\) 606234. 0.458010 0.229005 0.973425i \(-0.426453\pi\)
0.229005 + 0.973425i \(0.426453\pi\)
\(282\) 0 0
\(283\) −432587. + 749263.i −0.321076 + 0.556119i −0.980710 0.195467i \(-0.937378\pi\)
0.659635 + 0.751586i \(0.270711\pi\)
\(284\) 0 0
\(285\) 891840. + 1.54471e6i 0.650391 + 1.12651i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 273750. + 474150.i 0.192801 + 0.333942i
\(290\) 0 0
\(291\) 1.73919e6 3.01237e6i 1.20397 2.08533i
\(292\) 0 0
\(293\) 353352. 0.240458 0.120229 0.992746i \(-0.461637\pi\)
0.120229 + 0.992746i \(0.461637\pi\)
\(294\) 0 0
\(295\) 79680.0 0.0533082
\(296\) 0 0
\(297\) −3.87504e6 + 6.71177e6i −2.54909 + 4.41515i
\(298\) 0 0
\(299\) 396480. + 686724.i 0.256474 + 0.444226i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −125280. 216991.i −0.0783926 0.135780i
\(304\) 0 0
\(305\) 177536. 307501.i 0.109279 0.189277i
\(306\) 0 0
\(307\) 1.95904e6 1.18631 0.593153 0.805090i \(-0.297883\pi\)
0.593153 + 0.805090i \(0.297883\pi\)
\(308\) 0 0
\(309\) 5.38452e6 3.20812
\(310\) 0 0
\(311\) 1.53128e6 2.65226e6i 0.897749 1.55495i 0.0673832 0.997727i \(-0.478535\pi\)
0.830365 0.557219i \(-0.188132\pi\)
\(312\) 0 0
\(313\) −291317. 504576.i −0.168076 0.291116i 0.769668 0.638445i \(-0.220422\pi\)
−0.937743 + 0.347329i \(0.887089\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.54793e6 + 2.68108e6i 0.865171 + 1.49852i 0.866878 + 0.498521i \(0.166123\pi\)
−0.00170706 + 0.999999i \(0.500543\pi\)
\(318\) 0 0
\(319\) −366288. + 634429.i −0.201533 + 0.349065i
\(320\) 0 0
\(321\) 1.61676e6 0.875756
\(322\) 0 0
\(323\) 1.73537e6 0.925521
\(324\) 0 0
\(325\) 743754. 1.28822e6i 0.390590 0.676521i
\(326\) 0 0
\(327\) 1.58955e6 + 2.75318e6i 0.822062 + 1.42385i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −312748. 541695.i −0.156901 0.271760i 0.776849 0.629687i \(-0.216817\pi\)
−0.933749 + 0.357927i \(0.883484\pi\)
\(332\) 0 0
\(333\) 4.09377e6 7.09061e6i 2.02308 3.50407i
\(334\) 0 0
\(335\) −1.27219e6 −0.619356
\(336\) 0 0
\(337\) 2.32494e6 1.11516 0.557580 0.830123i \(-0.311730\pi\)
0.557580 + 0.830123i \(0.311730\pi\)
\(338\) 0 0
\(339\) 37530.0 65003.9i 0.0177370 0.0307213i
\(340\) 0 0
\(341\) −907296. 1.57148e6i −0.422535 0.731853i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 537600. + 931151.i 0.243171 + 0.421184i
\(346\) 0 0
\(347\) 390564. 676477.i 0.174128 0.301598i −0.765731 0.643161i \(-0.777623\pi\)
0.939859 + 0.341562i \(0.110956\pi\)
\(348\) 0 0
\(349\) −1.48586e6 −0.653002 −0.326501 0.945197i \(-0.605870\pi\)
−0.326501 + 0.945197i \(0.605870\pi\)
\(350\) 0 0
\(351\) −8.79336e6 −3.80967
\(352\) 0 0
\(353\) 722313. 1.25108e6i 0.308524 0.534379i −0.669516 0.742798i \(-0.733498\pi\)
0.978040 + 0.208419i \(0.0668317\pi\)
\(354\) 0 0
\(355\) −1.11821e6 1.93679e6i −0.470925 0.815666i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −202020. 349909.i −0.0827291 0.143291i 0.821692 0.569932i \(-0.193030\pi\)
−0.904421 + 0.426641i \(0.859697\pi\)
\(360\) 0 0
\(361\) −488032. + 845297.i −0.197097 + 0.341383i
\(362\) 0 0
\(363\) −6.84975e6 −2.72840
\(364\) 0 0
\(365\) 526400. 0.206816
\(366\) 0 0
\(367\) −1.35849e6 + 2.35298e6i −0.526492 + 0.911911i 0.473031 + 0.881046i \(0.343160\pi\)
−0.999524 + 0.0308656i \(0.990174\pi\)
\(368\) 0 0
\(369\) 874467. + 1.51462e6i 0.334332 + 0.579079i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 896993. + 1.55364e6i 0.333824 + 0.578199i 0.983258 0.182218i \(-0.0583277\pi\)
−0.649435 + 0.760417i \(0.724994\pi\)
\(374\) 0 0
\(375\) 2.50848e6 4.34481e6i 0.921154 1.59549i
\(376\) 0 0
\(377\) −831192. −0.301195
\(378\) 0 0
\(379\) −18624.0 −0.00666001 −0.00333001 0.999994i \(-0.501060\pi\)
−0.00333001 + 0.999994i \(0.501060\pi\)
\(380\) 0 0
\(381\) 4.31688e6 7.47706e6i 1.52355 2.63887i
\(382\) 0 0
\(383\) −665022. 1.15185e6i −0.231654 0.401236i 0.726641 0.687017i \(-0.241080\pi\)
−0.958295 + 0.285781i \(0.907747\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.34680e6 + 4.06478e6i 0.796525 + 1.37962i
\(388\) 0 0
\(389\) −1.13253e6 + 1.96160e6i −0.379468 + 0.657258i −0.990985 0.133973i \(-0.957226\pi\)
0.611517 + 0.791231i \(0.290560\pi\)
\(390\) 0 0
\(391\) 1.04608e6 0.346037
\(392\) 0 0
\(393\) −1.42986e6 −0.466995
\(394\) 0 0
\(395\) 1.25402e6 2.17202e6i 0.404399 0.700440i
\(396\) 0 0
\(397\) −2.24450e6 3.88759e6i −0.714733 1.23795i −0.963062 0.269278i \(-0.913215\pi\)
0.248330 0.968676i \(-0.420118\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 47721.0 + 82655.2i 0.0148200 + 0.0256690i 0.873340 0.487111i \(-0.161949\pi\)
−0.858520 + 0.512780i \(0.828616\pi\)
\(402\) 0 0
\(403\) 1.02943e6 1.78303e6i 0.315744 0.546885i
\(404\) 0 0
\(405\) −6.81437e6 −2.06437
\(406\) 0 0
\(407\) 7.77629e6 2.32695
\(408\) 0 0
\(409\) −1.49502e6 + 2.58945e6i −0.441914 + 0.765418i −0.997832 0.0658198i \(-0.979034\pi\)
0.555917 + 0.831238i \(0.312367\pi\)
\(410\) 0 0
\(411\) 3.34731e6 + 5.79771e6i 0.977443 + 1.69298i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.75709e6 3.04337e6i −0.500810 0.867429i
\(416\) 0 0
\(417\) −3.75813e6 + 6.50927e6i −1.05836 + 1.83313i
\(418\) 0 0
\(419\) −3.39037e6 −0.943436 −0.471718 0.881749i \(-0.656366\pi\)
−0.471718 + 0.881749i \(0.656366\pi\)
\(420\) 0 0
\(421\) 3.38397e6 0.930512 0.465256 0.885176i \(-0.345962\pi\)
0.465256 + 0.885176i \(0.345962\pi\)
\(422\) 0 0
\(423\) −2.45324e6 + 4.24913e6i −0.666636 + 1.15465i
\(424\) 0 0
\(425\) −981167. 1.69943e6i −0.263494 0.456385i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −6.62688e6 1.14781e7i −1.73846 3.01111i
\(430\) 0 0
\(431\) 991764. 1.71779e6i 0.257167 0.445426i −0.708315 0.705897i \(-0.750544\pi\)
0.965482 + 0.260470i \(0.0838776\pi\)
\(432\) 0 0
\(433\) 7.17581e6 1.83929 0.919647 0.392746i \(-0.128475\pi\)
0.919647 + 0.392746i \(0.128475\pi\)
\(434\) 0 0
\(435\) −1.12704e6 −0.285572
\(436\) 0 0
\(437\) −1.04048e6 + 1.80216e6i −0.260633 + 0.451430i
\(438\) 0 0
\(439\) −1.22195e6 2.11648e6i −0.302616 0.524146i 0.674112 0.738629i \(-0.264527\pi\)
−0.976728 + 0.214483i \(0.931193\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −115858. 200672.i −0.0280490 0.0485822i 0.851660 0.524094i \(-0.175596\pi\)
−0.879709 + 0.475512i \(0.842263\pi\)
\(444\) 0 0
\(445\) 911456. 1.57869e6i 0.218190 0.377917i
\(446\) 0 0
\(447\) 1.46218e7 3.46125
\(448\) 0 0
\(449\) −4.73637e6 −1.10874 −0.554370 0.832271i \(-0.687041\pi\)
−0.554370 + 0.832271i \(0.687041\pi\)
\(450\) 0 0
\(451\) −830544. + 1.43854e6i −0.192274 + 0.333029i
\(452\) 0 0
\(453\) −820200. 1.42063e6i −0.187791 0.325263i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.93743e6 + 6.81983e6i 0.881906 + 1.52751i 0.849219 + 0.528040i \(0.177073\pi\)
0.0326865 + 0.999466i \(0.489594\pi\)
\(458\) 0 0
\(459\) −5.80014e6 + 1.00461e7i −1.28501 + 2.22570i
\(460\) 0 0
\(461\) 8.23218e6 1.80411 0.902054 0.431623i \(-0.142059\pi\)
0.902054 + 0.431623i \(0.142059\pi\)
\(462\) 0 0
\(463\) 2.36038e6 0.511717 0.255859 0.966714i \(-0.417642\pi\)
0.255859 + 0.966714i \(0.417642\pi\)
\(464\) 0 0
\(465\) 1.39584e6 2.41767e6i 0.299367 0.518518i
\(466\) 0 0
\(467\) −3.15850e6 5.47068e6i −0.670175 1.16078i −0.977854 0.209288i \(-0.932885\pi\)
0.307679 0.951490i \(-0.400448\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −3.16602e6 5.48371e6i −0.657599 1.13900i
\(472\) 0 0
\(473\) −2.22893e6 + 3.86062e6i −0.458082 + 0.793421i
\(474\) 0 0
\(475\) 3.90366e6 0.793849
\(476\) 0 0
\(477\) −1.79190e7 −3.60594
\(478\) 0 0
\(479\) 729278. 1.26315e6i 0.145229 0.251545i −0.784229 0.620471i \(-0.786941\pi\)
0.929458 + 0.368927i \(0.120275\pi\)
\(480\) 0 0
\(481\) 4.41155e6 + 7.64103e6i 0.869417 + 1.50588i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.85514e6 + 3.21319e6i 0.358114 + 0.620272i
\(486\) 0 0
\(487\) −4.64391e6 + 8.04349e6i −0.887282 + 1.53682i −0.0442060 + 0.999022i \(0.514076\pi\)
−0.843076 + 0.537795i \(0.819258\pi\)
\(488\) 0 0
\(489\) 605760. 0.114559
\(490\) 0 0
\(491\) −234972. −0.0439858 −0.0219929 0.999758i \(-0.507001\pi\)
−0.0219929 + 0.999758i \(0.507001\pi\)
\(492\) 0 0
\(493\) −548258. + 949611.i −0.101594 + 0.175966i
\(494\) 0 0
\(495\) −6.55949e6 1.13614e7i −1.20325 2.08410i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.50396e6 + 6.06904e6i 0.629953 + 1.09111i 0.987561 + 0.157238i \(0.0502591\pi\)
−0.357608 + 0.933872i \(0.616408\pi\)
\(500\) 0 0
\(501\) 67860.0 117537.i 0.0120787 0.0209209i
\(502\) 0 0
\(503\) −4.94752e6 −0.871902 −0.435951 0.899970i \(-0.643588\pi\)
−0.435951 + 0.899970i \(0.643588\pi\)
\(504\) 0 0
\(505\) 267264. 0.0466350
\(506\) 0 0
\(507\) 1.94956e6 3.37675e6i 0.336835 0.583416i
\(508\) 0 0
\(509\) 2.75320e6 + 4.76869e6i 0.471025 + 0.815839i 0.999451 0.0331407i \(-0.0105510\pi\)
−0.528426 + 0.848979i \(0.677218\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.15382e7 1.99847e7i −1.93573 3.35278i
\(514\) 0 0
\(515\) −2.87174e6 + 4.97401e6i −0.477120 + 0.826396i
\(516\) 0 0
\(517\) −4.66003e6 −0.766765
\(518\) 0 0
\(519\) −3.12996e6 −0.510059
\(520\) 0 0
\(521\) 815379. 1.41228e6i 0.131603 0.227943i −0.792692 0.609623i \(-0.791321\pi\)
0.924295 + 0.381680i \(0.124654\pi\)
\(522\) 0 0
\(523\) −5.03827e6 8.72654e6i −0.805429 1.39504i −0.916001 0.401176i \(-0.868602\pi\)
0.110572 0.993868i \(-0.464732\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.35804e6 2.35219e6i −0.213003 0.368931i
\(528\) 0 0
\(529\) 2.59097e6 4.48769e6i 0.402553 0.697243i
\(530\) 0 0
\(531\) −1.63593e6 −0.251784
\(532\) 0 0
\(533\) −1.88470e6 −0.287358
\(534\) 0 0
\(535\) −862272. + 1.49350e6i −0.130245 + 0.225590i
\(536\) 0 0
\(537\) −3.02586e6 5.24094e6i −0.452807 0.784285i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 6.26125e6 + 1.08448e7i 0.919746 + 1.59305i 0.799800 + 0.600267i \(0.204939\pi\)
0.119947 + 0.992780i \(0.461728\pi\)
\(542\) 0 0
\(543\) −9.83550e6 + 1.70356e7i −1.43152 + 2.47946i
\(544\) 0 0
\(545\) −3.39104e6 −0.489037
\(546\) 0 0
\(547\) 6.67430e6 0.953756 0.476878 0.878970i \(-0.341768\pi\)
0.476878 + 0.878970i \(0.341768\pi\)
\(548\) 0 0
\(549\) −3.64504e6 + 6.31339e6i −0.516144 + 0.893988i
\(550\) 0 0
\(551\) −1.09065e6 1.88905e6i −0.153040 0.265073i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 5.98176e6 + 1.03607e7i 0.824321 + 1.42777i
\(556\) 0 0
\(557\) 2.30821e6 3.99794e6i 0.315238 0.546007i −0.664250 0.747510i \(-0.731249\pi\)
0.979488 + 0.201503i \(0.0645825\pi\)
\(558\) 0 0
\(559\) −5.05795e6 −0.684613
\(560\) 0 0
\(561\) −1.74845e7 −2.34555
\(562\) 0 0
\(563\) −4.42109e6 + 7.65755e6i −0.587839 + 1.01817i 0.406676 + 0.913572i \(0.366688\pi\)
−0.994515 + 0.104594i \(0.966646\pi\)
\(564\) 0 0
\(565\) 40032.0 + 69337.5i 0.00527577 + 0.00913791i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.78856e6 1.00261e7i −0.749532 1.29823i −0.948047 0.318129i \(-0.896945\pi\)
0.198515 0.980098i \(-0.436388\pi\)
\(570\) 0 0
\(571\) −2.24034e6 + 3.88039e6i −0.287557 + 0.498064i −0.973226 0.229850i \(-0.926177\pi\)
0.685669 + 0.727914i \(0.259510\pi\)
\(572\) 0 0
\(573\) 4.54488e6 0.578277
\(574\) 0 0
\(575\) 2.35312e6 0.296807
\(576\) 0 0
\(577\) 6.63939e6 1.14998e7i 0.830212 1.43797i −0.0676585 0.997709i \(-0.521553\pi\)
0.897870 0.440260i \(-0.145114\pi\)
\(578\) 0 0
\(579\) 3.43989e6 + 5.95806e6i 0.426430 + 0.738599i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −8.50949e6 1.47389e7i −1.03689 1.79594i
\(584\) 0 0
\(585\) 7.44250e6 1.28908e7i 0.899143 1.55736i
\(586\) 0 0
\(587\) 1.11188e7 1.33187 0.665936 0.746009i \(-0.268032\pi\)
0.665936 + 0.746009i \(0.268032\pi\)
\(588\) 0 0
\(589\) 5.40306e6 0.641729
\(590\) 0 0
\(591\) 6.31629e6 1.09401e7i 0.743864 1.28841i
\(592\) 0 0
\(593\) −1.96368e6 3.40120e6i −0.229316 0.397187i 0.728289 0.685270i \(-0.240316\pi\)
−0.957606 + 0.288082i \(0.906982\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.95950e6 5.12600e6i −0.339846 0.588631i
\(598\) 0 0
\(599\) 8.70497e6 1.50775e7i 0.991289 1.71696i 0.381585 0.924334i \(-0.375378\pi\)
0.609704 0.792630i \(-0.291288\pi\)
\(600\) 0 0
\(601\) −7.46243e6 −0.842740 −0.421370 0.906889i \(-0.638451\pi\)
−0.421370 + 0.906889i \(0.638451\pi\)
\(602\) 0 0
\(603\) 2.61197e7 2.92533
\(604\) 0 0
\(605\) 3.65320e6 6.32753e6i 0.405775 0.702822i
\(606\) 0 0
\(607\) 350576. + 607215.i 0.0386198 + 0.0668915i 0.884689 0.466181i \(-0.154371\pi\)
−0.846069 + 0.533073i \(0.821037\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.64367e6 4.57897e6i −0.286487 0.496210i
\(612\) 0 0
\(613\) −5.47876e6 + 9.48949e6i −0.588886 + 1.01998i 0.405493 + 0.914098i \(0.367100\pi\)
−0.994379 + 0.105882i \(0.966233\pi\)
\(614\) 0 0
\(615\) −2.55552e6 −0.272453
\(616\) 0 0
\(617\) 1.90666e6 0.201633 0.100816 0.994905i \(-0.467855\pi\)
0.100816 + 0.994905i \(0.467855\pi\)
\(618\) 0 0
\(619\) −1.11173e6 + 1.92557e6i −0.116620 + 0.201992i −0.918426 0.395592i \(-0.870539\pi\)
0.801806 + 0.597584i \(0.203873\pi\)
\(620\) 0 0
\(621\) −6.95520e6 1.20468e7i −0.723737 1.25355i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −607100. 1.05153e6i −0.0621671 0.107677i
\(626\) 0 0
\(627\) 1.73909e7 3.01219e7i 1.76666 3.05994i
\(628\) 0 0
\(629\) 1.16395e7 1.17303
\(630\) 0 0
\(631\) 752624. 0.0752497 0.0376248 0.999292i \(-0.488021\pi\)
0.0376248 + 0.999292i \(0.488021\pi\)
\(632\) 0 0
\(633\) 1.01858e7 1.76423e7i 1.01038 1.75003i
\(634\) 0 0
\(635\) 4.60467e6 + 7.97553e6i 0.453173 + 0.784919i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.29582e7 + 3.97648e7i 2.22426 + 3.85253i
\(640\) 0 0
\(641\) 1.22714e6 2.12548e6i 0.117964 0.204320i −0.800996 0.598669i \(-0.795696\pi\)
0.918961 + 0.394349i \(0.129030\pi\)
\(642\) 0 0
\(643\) −1.58237e7 −1.50932 −0.754660 0.656116i \(-0.772198\pi\)
−0.754660 + 0.656116i \(0.772198\pi\)
\(644\) 0 0
\(645\) −6.85824e6 −0.649103
\(646\) 0 0
\(647\) −1.32745e6 + 2.29920e6i −0.124668 + 0.215932i −0.921603 0.388133i \(-0.873120\pi\)
0.796935 + 0.604065i \(0.206453\pi\)
\(648\) 0 0
\(649\) −776880. 1.34560e6i −0.0724006 0.125402i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.63450e6 8.02718e6i −0.425324 0.736682i 0.571127 0.820862i \(-0.306506\pi\)
−0.996451 + 0.0841794i \(0.973173\pi\)
\(654\) 0 0
\(655\) 762592. 1.32085e6i 0.0694527 0.120296i
\(656\) 0 0
\(657\) −1.08076e7 −0.976827
\(658\) 0 0
\(659\) −1.68242e7 −1.50911 −0.754556 0.656235i \(-0.772148\pi\)
−0.754556 + 0.656235i \(0.772148\pi\)
\(660\) 0 0
\(661\) −3.38608e6 + 5.86487e6i −0.301435 + 0.522101i −0.976461 0.215693i \(-0.930799\pi\)
0.675026 + 0.737794i \(0.264132\pi\)
\(662\) 0 0
\(663\) −9.91908e6 1.71804e7i −0.876370 1.51792i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −657440. 1.13872e6i −0.0572192 0.0991065i
\(668\) 0 0
\(669\) 2.76660e6 4.79189e6i 0.238991 0.413944i
\(670\) 0 0
\(671\) −6.92390e6 −0.593669
\(672\) 0 0
\(673\) 7.61315e6 0.647928 0.323964 0.946069i \(-0.394984\pi\)
0.323964 + 0.946069i \(0.394984\pi\)
\(674\) 0 0
\(675\) −1.30472e7 + 2.25984e7i −1.10219 + 1.90906i
\(676\) 0 0
\(677\) 3.05836e6 + 5.29724e6i 0.256459 + 0.444199i 0.965291 0.261178i \(-0.0841109\pi\)
−0.708832 + 0.705377i \(0.750778\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.30212e7 + 2.25533e7i 1.07593 + 1.86356i
\(682\) 0 0
\(683\) 5.62942e6 9.75044e6i 0.461755 0.799784i −0.537293 0.843396i \(-0.680553\pi\)
0.999049 + 0.0436117i \(0.0138864\pi\)
\(684\) 0 0
\(685\) −7.14093e6 −0.581471
\(686\) 0 0
\(687\) −1.78158e7 −1.44017
\(688\) 0 0
\(689\) 9.65500e6 1.67229e7i 0.774826 1.34204i
\(690\) 0 0
\(691\) 4.75476e6 + 8.23549e6i 0.378821 + 0.656137i 0.990891 0.134667i \(-0.0429964\pi\)
−0.612070 + 0.790803i \(0.709663\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.00867e6 6.94322e6i −0.314803 0.545254i
\(696\) 0 0
\(697\) −1.24315e6 + 2.15321e6i −0.0969266 + 0.167882i
\(698\) 0 0
\(699\) −1.44654e6 −0.111979
\(700\) 0 0
\(701\) 1.53868e7 1.18264 0.591322 0.806436i \(-0.298606\pi\)
0.591322 + 0.806436i \(0.298606\pi\)
\(702\) 0 0
\(703\) −1.15772e7 + 2.00523e7i −0.883517 + 1.53030i
\(704\) 0 0
\(705\) −3.58464e6 6.20878e6i −0.271627 0.470472i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 606895. + 1.05117e6i 0.0453417 + 0.0785342i 0.887806 0.460219i \(-0.152229\pi\)
−0.842464 + 0.538753i \(0.818896\pi\)
\(710\) 0 0
\(711\) −2.57465e7 + 4.45943e7i −1.91005 + 3.30830i
\(712\) 0 0
\(713\) 3.25696e6 0.239932
\(714\) 0 0
\(715\) 1.41373e7 1.03420
\(716\) 0 0
\(717\) 3.62532e6 6.27924e6i 0.263359 0.456151i
\(718\) 0 0
\(719\) −5.00011e6 8.66044e6i −0.360709 0.624766i 0.627369 0.778722i \(-0.284132\pi\)
−0.988078 + 0.153956i \(0.950799\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −8.47905e6 1.46861e7i −0.603256 1.04487i
\(724\) 0 0
\(725\) −1.23329e6 + 2.13612e6i −0.0871403 + 0.150931i
\(726\) 0 0
\(727\) −1.33745e7 −0.938514 −0.469257 0.883062i \(-0.655478\pi\)
−0.469257 + 0.883062i \(0.655478\pi\)
\(728\) 0 0
\(729\) 4.93657e7 3.44038
\(730\) 0 0
\(731\) −3.33625e6 + 5.77855e6i −0.230922 + 0.399968i
\(732\) 0 0
\(733\) 8.06899e6 + 1.39759e7i 0.554701 + 0.960771i 0.997927 + 0.0643606i \(0.0205008\pi\)
−0.443225 + 0.896410i \(0.646166\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.24039e7 + 2.14841e7i 0.841179 + 1.45697i
\(738\) 0 0
\(739\) −4.30530e6 + 7.45699e6i −0.289996 + 0.502288i −0.973808 0.227370i \(-0.926987\pi\)
0.683812 + 0.729658i \(0.260321\pi\)
\(740\) 0 0
\(741\) 3.94639e7 2.64031
\(742\) 0 0
\(743\) −2.85027e7 −1.89415 −0.947075 0.321012i \(-0.895977\pi\)
−0.947075 + 0.321012i \(0.895977\pi\)
\(744\) 0 0
\(745\) −7.79830e6 + 1.35071e7i −0.514766 + 0.891600i
\(746\) 0 0
\(747\) 3.60752e7 + 6.24841e7i 2.36542 + 4.09702i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3.64360e6 + 6.31091e6i 0.235739 + 0.408312i 0.959487 0.281752i \(-0.0909156\pi\)
−0.723748 + 0.690064i \(0.757582\pi\)
\(752\) 0 0
\(753\) 2.15662e7 3.73537e7i 1.38607 2.40075i
\(754\) 0 0
\(755\) 1.74976e6 0.111715
\(756\) 0 0
\(757\) −2.77165e7 −1.75792 −0.878958 0.476899i \(-0.841761\pi\)
−0.878958 + 0.476899i \(0.841761\pi\)
\(758\) 0 0
\(759\) 1.04832e7 1.81574e7i 0.660525 1.14406i
\(760\) 0 0
\(761\) 1.53813e7 + 2.66411e7i 0.962787 + 1.66760i 0.715447 + 0.698667i \(0.246223\pi\)
0.247340 + 0.968929i \(0.420444\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −9.81821e6 1.70056e7i −0.606567 1.05060i
\(766\) 0 0
\(767\) 881460. 1.52673e6i 0.0541021 0.0937076i
\(768\) 0 0
\(769\) 1.83665e7 1.11998 0.559990 0.828499i \(-0.310805\pi\)
0.559990 + 0.828499i \(0.310805\pi\)
\(770\) 0 0
\(771\) 1.48441e7 0.899325
\(772\) 0 0
\(773\) −5.06986e6 + 8.78126e6i −0.305174 + 0.528577i −0.977300 0.211860i \(-0.932048\pi\)
0.672126 + 0.740437i \(0.265381\pi\)
\(774\) 0 0
\(775\) −3.05485e6 5.29116e6i −0.182699 0.316444i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.47300e6 4.28336e6i −0.146009 0.252895i
\(780\) 0 0
\(781\) −2.18051e7 + 3.77675e7i −1.27917 + 2.21559i
\(782\) 0 0
\(783\) 1.45811e7 0.849934
\(784\) 0 0
\(785\)