Properties

Label 336.6.q.c.289.1
Level $336$
Weight $6$
Character 336.289
Analytic conductor $53.889$
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] = [336,6,Mod(193,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("336.193");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.q (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: \(53.8889634572\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.6.q.c.193.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.50000 + 7.79423i) q^{3} +(3.00000 - 5.19615i) q^{5} +(-59.5000 - 115.181i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(4.50000 + 7.79423i) q^{3} +(3.00000 - 5.19615i) q^{5} +(-59.5000 - 115.181i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-333.000 - 576.773i) q^{11} -559.000 q^{13} +54.0000 q^{15} +(870.000 + 1506.88i) q^{17} +(578.500 - 1001.99i) q^{19} +(630.000 - 982.073i) q^{21} +(-1734.00 + 3003.38i) q^{23} +(1544.50 + 2675.15i) q^{25} -729.000 q^{27} +3372.00 q^{29} +(3146.50 + 5449.90i) q^{31} +(2997.00 - 5190.96i) q^{33} +(-777.000 - 36.3731i) q^{35} +(-1565.50 + 2711.53i) q^{37} +(-2515.50 - 4356.97i) q^{39} -4866.00 q^{41} +11407.0 q^{43} +(243.000 + 420.888i) q^{45} +(1155.00 - 2000.52i) q^{47} +(-9726.50 + 13706.6i) q^{49} +(-7830.00 + 13562.0i) q^{51} +(14148.0 + 24505.1i) q^{53} -3996.00 q^{55} +10413.0 q^{57} +(10272.0 + 17791.6i) q^{59} +(2315.00 - 4009.70i) q^{61} +(10489.5 + 491.036i) q^{63} +(-1677.00 + 2904.65i) q^{65} +(-9372.50 - 16233.6i) q^{67} -31212.0 q^{69} +38226.0 q^{71} +(-35294.5 - 61131.9i) q^{73} +(-13900.5 + 24076.4i) q^{75} +(-46620.0 + 72673.4i) q^{77} +(-31146.5 + 53947.3i) q^{79} +(-3280.50 - 5681.99i) q^{81} -79818.0 q^{83} +10440.0 q^{85} +(15174.0 + 26282.1i) q^{87} +(9060.00 - 15692.4i) q^{89} +(33260.5 + 64386.4i) q^{91} +(-28318.5 + 49049.1i) q^{93} +(-3471.00 - 6011.95i) q^{95} +124754. q^{97} +53946.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 9 q^{3} + 6 q^{5} - 119 q^{7} - 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 9 q^{3} + 6 q^{5} - 119 q^{7} - 81 q^{9} - 666 q^{11} - 1118 q^{13} + 108 q^{15} + 1740 q^{17} + 1157 q^{19} + 1260 q^{21} - 3468 q^{23} + 3089 q^{25} - 1458 q^{27} + 6744 q^{29} + 6293 q^{31} + 5994 q^{33} - 1554 q^{35} - 3131 q^{37} - 5031 q^{39} - 9732 q^{41} + 22814 q^{43} + 486 q^{45} + 2310 q^{47} - 19453 q^{49} - 15660 q^{51} + 28296 q^{53} - 7992 q^{55} + 20826 q^{57} + 20544 q^{59} + 4630 q^{61} + 20979 q^{63} - 3354 q^{65} - 18745 q^{67} - 62424 q^{69} + 76452 q^{71} - 70589 q^{73} - 27801 q^{75} - 93240 q^{77} - 62293 q^{79} - 6561 q^{81} - 159636 q^{83} + 20880 q^{85} + 30348 q^{87} + 18120 q^{89} + 66521 q^{91} - 56637 q^{93} - 6942 q^{95} + 249508 q^{97} + 107892 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 3.00000 5.19615i 0.0536656 0.0929516i −0.837945 0.545755i \(-0.816243\pi\)
0.891610 + 0.452804i \(0.149576\pi\)
\(6\) 0 0
\(7\) −59.5000 115.181i −0.458957 0.888459i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −333.000 576.773i −0.829779 1.43722i −0.898211 0.439564i \(-0.855133\pi\)
0.0684322 0.997656i \(-0.478200\pi\)
\(12\) 0 0
\(13\) −559.000 −0.917389 −0.458694 0.888594i \(-0.651683\pi\)
−0.458694 + 0.888594i \(0.651683\pi\)
\(14\) 0 0
\(15\) 54.0000 0.0619677
\(16\) 0 0
\(17\) 870.000 + 1506.88i 0.730125 + 1.26461i 0.956830 + 0.290649i \(0.0938713\pi\)
−0.226705 + 0.973963i \(0.572795\pi\)
\(18\) 0 0
\(19\) 578.500 1001.99i 0.367637 0.636766i −0.621558 0.783368i \(-0.713500\pi\)
0.989196 + 0.146602i \(0.0468335\pi\)
\(20\) 0 0
\(21\) 630.000 982.073i 0.311740 0.485954i
\(22\) 0 0
\(23\) −1734.00 + 3003.38i −0.683486 + 1.18383i 0.290424 + 0.956898i \(0.406204\pi\)
−0.973910 + 0.226934i \(0.927130\pi\)
\(24\) 0 0
\(25\) 1544.50 + 2675.15i 0.494240 + 0.856049i
\(26\) 0 0
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) 3372.00 0.744548 0.372274 0.928123i \(-0.378578\pi\)
0.372274 + 0.928123i \(0.378578\pi\)
\(30\) 0 0
\(31\) 3146.50 + 5449.90i 0.588063 + 1.01855i 0.994486 + 0.104869i \(0.0334424\pi\)
−0.406423 + 0.913685i \(0.633224\pi\)
\(32\) 0 0
\(33\) 2997.00 5190.96i 0.479073 0.829779i
\(34\) 0 0
\(35\) −777.000 36.3731i −0.107214 0.00501891i
\(36\) 0 0
\(37\) −1565.50 + 2711.53i −0.187996 + 0.325619i −0.944582 0.328276i \(-0.893533\pi\)
0.756586 + 0.653894i \(0.226866\pi\)
\(38\) 0 0
\(39\) −2515.50 4356.97i −0.264827 0.458694i
\(40\) 0 0
\(41\) −4866.00 −0.452077 −0.226039 0.974118i \(-0.572578\pi\)
−0.226039 + 0.974118i \(0.572578\pi\)
\(42\) 0 0
\(43\) 11407.0 0.940806 0.470403 0.882452i \(-0.344108\pi\)
0.470403 + 0.882452i \(0.344108\pi\)
\(44\) 0 0
\(45\) 243.000 + 420.888i 0.0178885 + 0.0309839i
\(46\) 0 0
\(47\) 1155.00 2000.52i 0.0762671 0.132099i −0.825369 0.564593i \(-0.809033\pi\)
0.901637 + 0.432494i \(0.142366\pi\)
\(48\) 0 0
\(49\) −9726.50 + 13706.6i −0.578717 + 0.815528i
\(50\) 0 0
\(51\) −7830.00 + 13562.0i −0.421538 + 0.730125i
\(52\) 0 0
\(53\) 14148.0 + 24505.1i 0.691840 + 1.19830i 0.971235 + 0.238125i \(0.0765328\pi\)
−0.279395 + 0.960176i \(0.590134\pi\)
\(54\) 0 0
\(55\) −3996.00 −0.178122
\(56\) 0 0
\(57\) 10413.0 0.424511
\(58\) 0 0
\(59\) 10272.0 + 17791.6i 0.384171 + 0.665404i 0.991654 0.128929i \(-0.0411539\pi\)
−0.607483 + 0.794333i \(0.707821\pi\)
\(60\) 0 0
\(61\) 2315.00 4009.70i 0.0796575 0.137971i −0.823445 0.567397i \(-0.807951\pi\)
0.903102 + 0.429426i \(0.141284\pi\)
\(62\) 0 0
\(63\) 10489.5 + 491.036i 0.332969 + 0.0155870i
\(64\) 0 0
\(65\) −1677.00 + 2904.65i −0.0492322 + 0.0852728i
\(66\) 0 0
\(67\) −9372.50 16233.6i −0.255075 0.441803i 0.709841 0.704362i \(-0.248767\pi\)
−0.964916 + 0.262559i \(0.915434\pi\)
\(68\) 0 0
\(69\) −31212.0 −0.789221
\(70\) 0 0
\(71\) 38226.0 0.899939 0.449969 0.893044i \(-0.351435\pi\)
0.449969 + 0.893044i \(0.351435\pi\)
\(72\) 0 0
\(73\) −35294.5 61131.9i −0.775175 1.34264i −0.934696 0.355448i \(-0.884328\pi\)
0.159521 0.987195i \(-0.449005\pi\)
\(74\) 0 0
\(75\) −13900.5 + 24076.4i −0.285350 + 0.494240i
\(76\) 0 0
\(77\) −46620.0 + 72673.4i −0.896077 + 1.39685i
\(78\) 0 0
\(79\) −31146.5 + 53947.3i −0.561489 + 0.972528i 0.435877 + 0.900006i \(0.356438\pi\)
−0.997367 + 0.0725221i \(0.976895\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −79818.0 −1.27176 −0.635881 0.771787i \(-0.719363\pi\)
−0.635881 + 0.771787i \(0.719363\pi\)
\(84\) 0 0
\(85\) 10440.0 0.156730
\(86\) 0 0
\(87\) 15174.0 + 26282.1i 0.214932 + 0.372274i
\(88\) 0 0
\(89\) 9060.00 15692.4i 0.121242 0.209997i −0.799016 0.601310i \(-0.794646\pi\)
0.920258 + 0.391313i \(0.127979\pi\)
\(90\) 0 0
\(91\) 33260.5 + 64386.4i 0.421042 + 0.815062i
\(92\) 0 0
\(93\) −28318.5 + 49049.1i −0.339518 + 0.588063i
\(94\) 0 0
\(95\) −3471.00 6011.95i −0.0394590 0.0683449i
\(96\) 0 0
\(97\) 124754. 1.34625 0.673124 0.739530i \(-0.264952\pi\)
0.673124 + 0.739530i \(0.264952\pi\)
\(98\) 0 0
\(99\) 53946.0 0.553186
\(100\) 0 0
\(101\) 46695.0 + 80878.1i 0.455478 + 0.788910i 0.998716 0.0506685i \(-0.0161352\pi\)
−0.543238 + 0.839579i \(0.682802\pi\)
\(102\) 0 0
\(103\) −83865.5 + 145259.i −0.778915 + 1.34912i 0.153652 + 0.988125i \(0.450897\pi\)
−0.932567 + 0.360996i \(0.882437\pi\)
\(104\) 0 0
\(105\) −3213.00 6219.79i −0.0284405 0.0550558i
\(106\) 0 0
\(107\) 34590.0 59911.6i 0.292073 0.505885i −0.682227 0.731141i \(-0.738988\pi\)
0.974300 + 0.225256i \(0.0723217\pi\)
\(108\) 0 0
\(109\) 109779. + 190144.i 0.885024 + 1.53291i 0.845686 + 0.533680i \(0.179191\pi\)
0.0393377 + 0.999226i \(0.487475\pi\)
\(110\) 0 0
\(111\) −28179.0 −0.217079
\(112\) 0 0
\(113\) −39354.0 −0.289930 −0.144965 0.989437i \(-0.546307\pi\)
−0.144965 + 0.989437i \(0.546307\pi\)
\(114\) 0 0
\(115\) 10404.0 + 18020.3i 0.0733594 + 0.127062i
\(116\) 0 0
\(117\) 22639.5 39212.8i 0.152898 0.264827i
\(118\) 0 0
\(119\) 121800. 189867.i 0.788460 1.22909i
\(120\) 0 0
\(121\) −141252. + 244657.i −0.877067 + 1.51912i
\(122\) 0 0
\(123\) −21897.0 37926.7i −0.130503 0.226039i
\(124\) 0 0
\(125\) 37284.0 0.213426
\(126\) 0 0
\(127\) −317093. −1.74453 −0.872263 0.489037i \(-0.837348\pi\)
−0.872263 + 0.489037i \(0.837348\pi\)
\(128\) 0 0
\(129\) 51331.5 + 88908.8i 0.271587 + 0.470403i
\(130\) 0 0
\(131\) −77415.0 + 134087.i −0.394137 + 0.682665i −0.992991 0.118194i \(-0.962290\pi\)
0.598854 + 0.800858i \(0.295623\pi\)
\(132\) 0 0
\(133\) −149832. 7013.94i −0.734470 0.0343821i
\(134\) 0 0
\(135\) −2187.00 + 3788.00i −0.0103280 + 0.0178885i
\(136\) 0 0
\(137\) −33666.0 58311.2i −0.153246 0.265430i 0.779173 0.626809i \(-0.215639\pi\)
−0.932419 + 0.361379i \(0.882306\pi\)
\(138\) 0 0
\(139\) 365215. 1.60329 0.801644 0.597802i \(-0.203959\pi\)
0.801644 + 0.597802i \(0.203959\pi\)
\(140\) 0 0
\(141\) 20790.0 0.0880657
\(142\) 0 0
\(143\) 186147. + 322416.i 0.761230 + 1.31849i
\(144\) 0 0
\(145\) 10116.0 17521.4i 0.0399566 0.0692069i
\(146\) 0 0
\(147\) −150602. 14130.9i −0.574825 0.0539359i
\(148\) 0 0
\(149\) 84030.0 145544.i 0.310076 0.537068i −0.668302 0.743890i \(-0.732979\pi\)
0.978379 + 0.206822i \(0.0663120\pi\)
\(150\) 0 0
\(151\) 76768.0 + 132966.i 0.273992 + 0.474568i 0.969880 0.243582i \(-0.0783225\pi\)
−0.695888 + 0.718150i \(0.744989\pi\)
\(152\) 0 0
\(153\) −140940. −0.486750
\(154\) 0 0
\(155\) 37758.0 0.126235
\(156\) 0 0
\(157\) −101209. 175299.i −0.327695 0.567585i 0.654359 0.756184i \(-0.272939\pi\)
−0.982054 + 0.188599i \(0.939605\pi\)
\(158\) 0 0
\(159\) −127332. + 220545.i −0.399434 + 0.691840i
\(160\) 0 0
\(161\) 449106. + 21023.6i 1.36548 + 0.0639209i
\(162\) 0 0
\(163\) −89882.0 + 155680.i −0.264974 + 0.458949i −0.967557 0.252653i \(-0.918697\pi\)
0.702583 + 0.711602i \(0.252030\pi\)
\(164\) 0 0
\(165\) −17982.0 31145.7i −0.0514195 0.0890612i
\(166\) 0 0
\(167\) −217302. −0.602938 −0.301469 0.953476i \(-0.597477\pi\)
−0.301469 + 0.953476i \(0.597477\pi\)
\(168\) 0 0
\(169\) −58812.0 −0.158398
\(170\) 0 0
\(171\) 46858.5 + 81161.3i 0.122546 + 0.212255i
\(172\) 0 0
\(173\) 36990.0 64068.6i 0.0939656 0.162753i −0.815211 0.579164i \(-0.803379\pi\)
0.909176 + 0.416411i \(0.136712\pi\)
\(174\) 0 0
\(175\) 216230. 337069.i 0.533729 0.832001i
\(176\) 0 0
\(177\) −92448.0 + 160125.i −0.221801 + 0.384171i
\(178\) 0 0
\(179\) 394683. + 683611.i 0.920695 + 1.59469i 0.798342 + 0.602204i \(0.205711\pi\)
0.122353 + 0.992487i \(0.460956\pi\)
\(180\) 0 0
\(181\) −477739. −1.08391 −0.541956 0.840407i \(-0.682316\pi\)
−0.541956 + 0.840407i \(0.682316\pi\)
\(182\) 0 0
\(183\) 41670.0 0.0919805
\(184\) 0 0
\(185\) 9393.00 + 16269.2i 0.0201779 + 0.0349491i
\(186\) 0 0
\(187\) 579420. 1.00358e6i 1.21168 2.09870i
\(188\) 0 0
\(189\) 43375.5 + 83967.2i 0.0883263 + 0.170984i
\(190\) 0 0
\(191\) 179487. 310881.i 0.356000 0.616609i −0.631289 0.775548i \(-0.717474\pi\)
0.987289 + 0.158938i \(0.0508071\pi\)
\(192\) 0 0
\(193\) 90966.5 + 157559.i 0.175788 + 0.304473i 0.940434 0.339978i \(-0.110419\pi\)
−0.764646 + 0.644451i \(0.777086\pi\)
\(194\) 0 0
\(195\) −30186.0 −0.0568485
\(196\) 0 0
\(197\) 717924. 1.31799 0.658996 0.752146i \(-0.270981\pi\)
0.658996 + 0.752146i \(0.270981\pi\)
\(198\) 0 0
\(199\) 101548. + 175886.i 0.181777 + 0.314847i 0.942486 0.334246i \(-0.108482\pi\)
−0.760709 + 0.649093i \(0.775148\pi\)
\(200\) 0 0
\(201\) 84352.5 146103.i 0.147268 0.255075i
\(202\) 0 0
\(203\) −200634. 388392.i −0.341715 0.661500i
\(204\) 0 0
\(205\) −14598.0 + 25284.5i −0.0242610 + 0.0420213i
\(206\) 0 0
\(207\) −140454. 243273.i −0.227829 0.394611i
\(208\) 0 0
\(209\) −770562. −1.22023
\(210\) 0 0
\(211\) −1.17098e6 −1.81069 −0.905343 0.424680i \(-0.860387\pi\)
−0.905343 + 0.424680i \(0.860387\pi\)
\(212\) 0 0
\(213\) 172017. + 297942.i 0.259790 + 0.449969i
\(214\) 0 0
\(215\) 34221.0 59272.5i 0.0504890 0.0874495i
\(216\) 0 0
\(217\) 440510. 686687.i 0.635048 0.989942i
\(218\) 0 0
\(219\) 317651. 550187.i 0.447548 0.775175i
\(220\) 0 0
\(221\) −486330. 842348.i −0.669808 1.16014i
\(222\) 0 0
\(223\) −1.24635e6 −1.67833 −0.839167 0.543873i \(-0.816957\pi\)
−0.839167 + 0.543873i \(0.816957\pi\)
\(224\) 0 0
\(225\) −250209. −0.329493
\(226\) 0 0
\(227\) −459471. 795827.i −0.591825 1.02507i −0.993987 0.109503i \(-0.965074\pi\)
0.402161 0.915569i \(-0.368259\pi\)
\(228\) 0 0
\(229\) −601874. + 1.04248e6i −0.758433 + 1.31364i 0.185216 + 0.982698i \(0.440701\pi\)
−0.943649 + 0.330947i \(0.892632\pi\)
\(230\) 0 0
\(231\) −776223. 36336.7i −0.957098 0.0448039i
\(232\) 0 0
\(233\) 459531. 795931.i 0.554530 0.960474i −0.443410 0.896319i \(-0.646231\pi\)
0.997940 0.0641551i \(-0.0204353\pi\)
\(234\) 0 0
\(235\) −6930.00 12003.1i −0.00818585 0.0141783i
\(236\) 0 0
\(237\) −560637. −0.648352
\(238\) 0 0
\(239\) 625338. 0.708142 0.354071 0.935219i \(-0.384797\pi\)
0.354071 + 0.935219i \(0.384797\pi\)
\(240\) 0 0
\(241\) −626911. 1.08584e6i −0.695286 1.20427i −0.970084 0.242768i \(-0.921945\pi\)
0.274799 0.961502i \(-0.411389\pi\)
\(242\) 0 0
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 42042.0 + 91660.1i 0.0447474 + 0.0975585i
\(246\) 0 0
\(247\) −323382. + 560113.i −0.337266 + 0.584162i
\(248\) 0 0
\(249\) −359181. 622120.i −0.367126 0.635881i
\(250\) 0 0
\(251\) 1.51333e6 1.51618 0.758089 0.652152i \(-0.226133\pi\)
0.758089 + 0.652152i \(0.226133\pi\)
\(252\) 0 0
\(253\) 2.30969e6 2.26857
\(254\) 0 0
\(255\) 46980.0 + 81371.7i 0.0452442 + 0.0783652i
\(256\) 0 0
\(257\) 777465. 1.34661e6i 0.734257 1.27177i −0.220792 0.975321i \(-0.570864\pi\)
0.955049 0.296449i \(-0.0958026\pi\)
\(258\) 0 0
\(259\) 405464. + 18980.7i 0.375581 + 0.0175818i
\(260\) 0 0
\(261\) −136566. + 236539.i −0.124091 + 0.214932i
\(262\) 0 0
\(263\) −557658. 965892.i −0.497140 0.861071i 0.502855 0.864371i \(-0.332283\pi\)
−0.999995 + 0.00329949i \(0.998950\pi\)
\(264\) 0 0
\(265\) 169776. 0.148512
\(266\) 0 0
\(267\) 163080. 0.139998
\(268\) 0 0
\(269\) −17835.0 30891.1i −0.0150277 0.0260287i 0.858414 0.512958i \(-0.171450\pi\)
−0.873441 + 0.486929i \(0.838117\pi\)
\(270\) 0 0
\(271\) −146384. + 253545.i −0.121079 + 0.209716i −0.920194 0.391464i \(-0.871969\pi\)
0.799114 + 0.601179i \(0.205302\pi\)
\(272\) 0 0
\(273\) −352170. + 548979.i −0.285987 + 0.445809i
\(274\) 0 0
\(275\) 1.02864e6 1.78165e6i 0.820220 1.42066i
\(276\) 0 0
\(277\) −431607. 747564.i −0.337978 0.585395i 0.646074 0.763275i \(-0.276410\pi\)
−0.984052 + 0.177879i \(0.943076\pi\)
\(278\) 0 0
\(279\) −509733. −0.392042
\(280\) 0 0
\(281\) 1.47110e6 1.11142 0.555709 0.831377i \(-0.312447\pi\)
0.555709 + 0.831377i \(0.312447\pi\)
\(282\) 0 0
\(283\) 344420. + 596554.i 0.255637 + 0.442775i 0.965068 0.261999i \(-0.0843816\pi\)
−0.709432 + 0.704774i \(0.751048\pi\)
\(284\) 0 0
\(285\) 31239.0 54107.5i 0.0227816 0.0394590i
\(286\) 0 0
\(287\) 289527. + 560473.i 0.207484 + 0.401652i
\(288\) 0 0
\(289\) −803872. + 1.39235e6i −0.566164 + 0.980624i
\(290\) 0 0
\(291\) 561393. + 972361.i 0.388628 + 0.673124i
\(292\) 0 0
\(293\) 722832. 0.491890 0.245945 0.969284i \(-0.420902\pi\)
0.245945 + 0.969284i \(0.420902\pi\)
\(294\) 0 0
\(295\) 123264. 0.0824672
\(296\) 0 0
\(297\) 242757. + 420467.i 0.159691 + 0.276593i
\(298\) 0 0
\(299\) 969306. 1.67889e6i 0.627022 1.08603i
\(300\) 0 0
\(301\) −678716. 1.31387e6i −0.431790 0.835868i
\(302\) 0 0
\(303\) −420255. + 727903.i −0.262970 + 0.455478i
\(304\) 0 0
\(305\) −13890.0 24058.2i −0.00854973 0.0148086i
\(306\) 0 0
\(307\) 20125.0 0.0121868 0.00609340 0.999981i \(-0.498060\pi\)
0.00609340 + 0.999981i \(0.498060\pi\)
\(308\) 0 0
\(309\) −1.50958e6 −0.899414
\(310\) 0 0
\(311\) −871779. 1.50997e6i −0.511099 0.885250i −0.999917 0.0128643i \(-0.995905\pi\)
0.488818 0.872386i \(-0.337428\pi\)
\(312\) 0 0
\(313\) −904272. + 1.56624e6i −0.521721 + 0.903647i 0.477960 + 0.878382i \(0.341376\pi\)
−0.999681 + 0.0252651i \(0.991957\pi\)
\(314\) 0 0
\(315\) 34020.0 53031.9i 0.0193178 0.0301135i
\(316\) 0 0
\(317\) −511776. + 886422.i −0.286043 + 0.495442i −0.972862 0.231388i \(-0.925673\pi\)
0.686818 + 0.726829i \(0.259007\pi\)
\(318\) 0 0
\(319\) −1.12288e6 1.94488e6i −0.617810 1.07008i
\(320\) 0 0
\(321\) 622620. 0.337257
\(322\) 0 0
\(323\) 2.01318e6 1.07368
\(324\) 0 0
\(325\) −863376. 1.49541e6i −0.453410 0.785330i
\(326\) 0 0
\(327\) −988016. + 1.71129e6i −0.510969 + 0.885024i
\(328\) 0 0
\(329\) −299145. 14003.6i −0.152367 0.00713265i
\(330\) 0 0
\(331\) −503766. + 872549.i −0.252731 + 0.437744i −0.964277 0.264896i \(-0.914662\pi\)
0.711545 + 0.702640i \(0.247996\pi\)
\(332\) 0 0
\(333\) −126806. 219634.i −0.0626654 0.108540i
\(334\) 0 0
\(335\) −112470. −0.0547551
\(336\) 0 0
\(337\) −1.56571e6 −0.750993 −0.375496 0.926824i \(-0.622528\pi\)
−0.375496 + 0.926824i \(0.622528\pi\)
\(338\) 0 0
\(339\) −177093. 306734.i −0.0836955 0.144965i
\(340\) 0 0
\(341\) 2.09557e6 3.62963e6i 0.975924 1.69035i
\(342\) 0 0
\(343\) 2.15747e6 + 304770.i 0.990169 + 0.139874i
\(344\) 0 0
\(345\) −93636.0 + 162182.i −0.0423541 + 0.0733594i
\(346\) 0 0
\(347\) 378642. + 655827.i 0.168813 + 0.292392i 0.938003 0.346628i \(-0.112673\pi\)
−0.769190 + 0.639020i \(0.779340\pi\)
\(348\) 0 0
\(349\) −455638. −0.200243 −0.100121 0.994975i \(-0.531923\pi\)
−0.100121 + 0.994975i \(0.531923\pi\)
\(350\) 0 0
\(351\) 407511. 0.176552
\(352\) 0 0
\(353\) 1.81569e6 + 3.14487e6i 0.775543 + 1.34328i 0.934489 + 0.355992i \(0.115857\pi\)
−0.158946 + 0.987287i \(0.550810\pi\)
\(354\) 0 0
\(355\) 114678. 198628.i 0.0482958 0.0836508i
\(356\) 0 0
\(357\) 2.02797e6 + 94933.7i 0.842153 + 0.0394230i
\(358\) 0 0
\(359\) −2.01242e6 + 3.48561e6i −0.824104 + 1.42739i 0.0784980 + 0.996914i \(0.474988\pi\)
−0.902602 + 0.430476i \(0.858346\pi\)
\(360\) 0 0
\(361\) 568725. + 985061.i 0.229686 + 0.397828i
\(362\) 0 0
\(363\) −2.54254e6 −1.01275
\(364\) 0 0
\(365\) −423534. −0.166401
\(366\) 0 0
\(367\) 1.28894e6 + 2.23251e6i 0.499536 + 0.865222i 1.00000 0.000535822i \(-0.000170558\pi\)
−0.500464 + 0.865757i \(0.666837\pi\)
\(368\) 0 0
\(369\) 197073. 341340.i 0.0753462 0.130503i
\(370\) 0 0
\(371\) 1.98072e6 3.08764e6i 0.747116 1.16464i
\(372\) 0 0
\(373\) 1.26566e6 2.19220e6i 0.471028 0.815844i −0.528423 0.848981i \(-0.677216\pi\)
0.999451 + 0.0331372i \(0.0105498\pi\)
\(374\) 0 0
\(375\) 167778. + 290600.i 0.0616108 + 0.106713i
\(376\) 0 0
\(377\) −1.88495e6 −0.683040
\(378\) 0 0
\(379\) 3.06677e6 1.09669 0.548344 0.836253i \(-0.315258\pi\)
0.548344 + 0.836253i \(0.315258\pi\)
\(380\) 0 0
\(381\) −1.42692e6 2.47150e6i −0.503601 0.872263i
\(382\) 0 0
\(383\) −1.96260e6 + 3.39932e6i −0.683652 + 1.18412i 0.290207 + 0.956964i \(0.406276\pi\)
−0.973859 + 0.227155i \(0.927057\pi\)
\(384\) 0 0
\(385\) 237762. + 460265.i 0.0817505 + 0.158254i
\(386\) 0 0
\(387\) −461984. + 800179.i −0.156801 + 0.271587i
\(388\) 0 0
\(389\) 2.01334e6 + 3.48722e6i 0.674597 + 1.16844i 0.976587 + 0.215125i \(0.0690158\pi\)
−0.301990 + 0.953311i \(0.597651\pi\)
\(390\) 0 0
\(391\) −6.03432e6 −1.99612
\(392\) 0 0
\(393\) −1.39347e6 −0.455110
\(394\) 0 0
\(395\) 186879. + 323684.i 0.0602654 + 0.104383i
\(396\) 0 0
\(397\) −2.28720e6 + 3.96155e6i −0.728329 + 1.26150i 0.229260 + 0.973365i \(0.426370\pi\)
−0.957589 + 0.288138i \(0.906964\pi\)
\(398\) 0 0
\(399\) −619574. 1.19938e6i −0.194832 0.377160i
\(400\) 0 0
\(401\) 1.13472e6 1.96539e6i 0.352393 0.610363i −0.634275 0.773108i \(-0.718701\pi\)
0.986668 + 0.162744i \(0.0520346\pi\)
\(402\) 0 0
\(403\) −1.75889e6 3.04649e6i −0.539482 0.934410i
\(404\) 0 0
\(405\) −39366.0 −0.0119257
\(406\) 0 0
\(407\) 2.08525e6 0.623981
\(408\) 0 0
\(409\) 2.02298e6 + 3.50391e6i 0.597976 + 1.03572i 0.993120 + 0.117105i \(0.0373615\pi\)
−0.395144 + 0.918619i \(0.629305\pi\)
\(410\) 0 0
\(411\) 302994. 524801.i 0.0884768 0.153246i
\(412\) 0 0
\(413\) 1.43808e6 2.24174e6i 0.414866 0.646712i
\(414\) 0 0
\(415\) −239454. + 414746.i −0.0682499 + 0.118212i
\(416\) 0 0
\(417\) 1.64347e6 + 2.84657e6i 0.462829 + 0.801644i
\(418\) 0 0
\(419\) 3.91281e6 1.08881 0.544407 0.838821i \(-0.316755\pi\)
0.544407 + 0.838821i \(0.316755\pi\)
\(420\) 0 0
\(421\) −2.78086e6 −0.764671 −0.382335 0.924024i \(-0.624880\pi\)
−0.382335 + 0.924024i \(0.624880\pi\)
\(422\) 0 0
\(423\) 93555.0 + 162042.i 0.0254224 + 0.0440328i
\(424\) 0 0
\(425\) −2.68743e6 + 4.65477e6i −0.721714 + 1.25004i
\(426\) 0 0
\(427\) −599585. 28067.9i −0.159141 0.00744972i
\(428\) 0 0
\(429\) −1.67532e6 + 2.90174e6i −0.439496 + 0.761230i
\(430\) 0 0
\(431\) −2.19104e6 3.79498e6i −0.568141 0.984049i −0.996750 0.0805589i \(-0.974329\pi\)
0.428609 0.903490i \(-0.359004\pi\)
\(432\) 0 0
\(433\) 1.24946e6 0.320261 0.160130 0.987096i \(-0.448809\pi\)
0.160130 + 0.987096i \(0.448809\pi\)
\(434\) 0 0
\(435\) 182088. 0.0461379
\(436\) 0 0
\(437\) 2.00624e6 + 3.47491e6i 0.502550 + 0.870441i
\(438\) 0 0
\(439\) −3.37210e6 + 5.84066e6i −0.835102 + 1.44644i 0.0588449 + 0.998267i \(0.481258\pi\)
−0.893947 + 0.448172i \(0.852075\pi\)
\(440\) 0 0
\(441\) −567567. 1.23741e6i −0.138970 0.302983i
\(442\) 0 0
\(443\) 239448. 414736.i 0.0579698 0.100407i −0.835584 0.549362i \(-0.814871\pi\)
0.893554 + 0.448956i \(0.148204\pi\)
\(444\) 0 0
\(445\) −54360.0 94154.3i −0.0130131 0.0225393i
\(446\) 0 0
\(447\) 1.51254e6 0.358045
\(448\) 0 0
\(449\) 724506. 0.169600 0.0848001 0.996398i \(-0.472975\pi\)
0.0848001 + 0.996398i \(0.472975\pi\)
\(450\) 0 0
\(451\) 1.62038e6 + 2.80658e6i 0.375124 + 0.649734i
\(452\) 0 0
\(453\) −690912. + 1.19669e6i −0.158189 + 0.273992i
\(454\) 0 0
\(455\) 434343. + 20332.5i 0.0983568 + 0.00460430i
\(456\) 0 0
\(457\) 1.16978e6 2.02612e6i 0.262008 0.453811i −0.704768 0.709438i \(-0.748949\pi\)
0.966775 + 0.255627i \(0.0822820\pi\)
\(458\) 0 0
\(459\) −634230. 1.09852e6i −0.140513 0.243375i
\(460\) 0 0
\(461\) 2.98247e6 0.653617 0.326809 0.945091i \(-0.394027\pi\)
0.326809 + 0.945091i \(0.394027\pi\)
\(462\) 0 0
\(463\) −4.28423e6 −0.928795 −0.464398 0.885627i \(-0.653729\pi\)
−0.464398 + 0.885627i \(0.653729\pi\)
\(464\) 0 0
\(465\) 169911. + 294294.i 0.0364409 + 0.0631175i
\(466\) 0 0
\(467\) −2.87018e6 + 4.97129e6i −0.608998 + 1.05482i 0.382407 + 0.923994i \(0.375095\pi\)
−0.991406 + 0.130822i \(0.958238\pi\)
\(468\) 0 0
\(469\) −1.31215e6 + 2.04544e6i −0.275455 + 0.429393i
\(470\) 0 0
\(471\) 910881. 1.57769e6i 0.189195 0.327695i
\(472\) 0 0
\(473\) −3.79853e6 6.57925e6i −0.780662 1.35215i
\(474\) 0 0
\(475\) 3.57397e6 0.726804
\(476\) 0 0
\(477\) −2.29198e6 −0.461226
\(478\) 0 0
\(479\) 1.32526e6 + 2.29541e6i 0.263913 + 0.457111i 0.967278 0.253718i \(-0.0816534\pi\)
−0.703365 + 0.710829i \(0.748320\pi\)
\(480\) 0 0
\(481\) 875114. 1.51574e6i 0.172465 0.298719i
\(482\) 0 0
\(483\) 1.85711e6 + 3.59504e6i 0.362219 + 0.701191i
\(484\) 0 0
\(485\) 374262. 648241.i 0.0722473 0.125136i
\(486\) 0 0
\(487\) 1.40277e6 + 2.42967e6i 0.268018 + 0.464221i 0.968350 0.249597i \(-0.0802980\pi\)
−0.700332 + 0.713817i \(0.746965\pi\)
\(488\) 0 0
\(489\) −1.61788e6 −0.305966
\(490\) 0 0
\(491\) 4.68450e6 0.876919 0.438460 0.898751i \(-0.355524\pi\)
0.438460 + 0.898751i \(0.355524\pi\)
\(492\) 0 0
\(493\) 2.93364e6 + 5.08121e6i 0.543613 + 0.941565i
\(494\) 0 0
\(495\) 161838. 280312.i 0.0296871 0.0514195i
\(496\) 0 0
\(497\) −2.27445e6 4.40292e6i −0.413033 0.799558i
\(498\) 0 0
\(499\) 737876. 1.27804e6i 0.132658 0.229770i −0.792043 0.610466i \(-0.790982\pi\)
0.924700 + 0.380696i \(0.124316\pi\)
\(500\) 0 0
\(501\) −977859. 1.69370e6i −0.174053 0.301469i
\(502\) 0 0
\(503\) −63606.0 −0.0112093 −0.00560465 0.999984i \(-0.501784\pi\)
−0.00560465 + 0.999984i \(0.501784\pi\)
\(504\) 0 0
\(505\) 560340. 0.0977740
\(506\) 0 0
\(507\) −264654. 458394.i −0.0457255 0.0791989i
\(508\) 0 0
\(509\) −3.10578e6 + 5.37937e6i −0.531345 + 0.920317i 0.467986 + 0.883736i \(0.344980\pi\)
−0.999331 + 0.0365806i \(0.988353\pi\)
\(510\) 0 0
\(511\) −4.94123e6 + 7.70262e6i −0.837111 + 1.30493i
\(512\) 0 0
\(513\) −421726. + 730452.i −0.0707518 + 0.122546i
\(514\) 0 0
\(515\) 503193. + 871556.i 0.0836020 + 0.144803i
\(516\) 0 0
\(517\) −1.53846e6 −0.253139
\(518\) 0 0
\(519\) 665820. 0.108502
\(520\) 0 0
\(521\) −706026. 1.22287e6i −0.113953 0.197373i 0.803408 0.595429i \(-0.203018\pi\)
−0.917361 + 0.398057i \(0.869685\pi\)
\(522\) 0 0
\(523\) 2.61467e6 4.52875e6i 0.417987 0.723976i −0.577749 0.816214i \(-0.696069\pi\)
0.995737 + 0.0922386i \(0.0294023\pi\)
\(524\) 0 0
\(525\) 3.60023e6 + 168535.i 0.570075 + 0.0266865i
\(526\) 0 0
\(527\) −5.47491e6 + 9.48282e6i −0.858718 + 1.48734i
\(528\) 0 0
\(529\) −2.79534e6 4.84167e6i −0.434306 0.752240i
\(530\) 0 0
\(531\) −1.66406e6 −0.256114
\(532\) 0 0
\(533\) 2.72009e6 0.414730
\(534\) 0 0
\(535\) −207540. 359470.i −0.0313485 0.0542973i
\(536\) 0 0
\(537\) −3.55215e6 + 6.15250e6i −0.531564 + 0.920695i
\(538\) 0 0
\(539\) 1.11445e7 + 1.04569e6i 1.65230 + 0.155035i
\(540\) 0 0
\(541\) −2.20686e6 + 3.82240e6i −0.324177 + 0.561491i −0.981345 0.192253i \(-0.938421\pi\)
0.657169 + 0.753744i \(0.271754\pi\)
\(542\) 0 0
\(543\) −2.14983e6 3.72361e6i −0.312899 0.541956i
\(544\) 0 0
\(545\) 1.31735e6 0.189981
\(546\) 0 0
\(547\) 1.19038e7 1.70105 0.850523 0.525938i \(-0.176286\pi\)
0.850523 + 0.525938i \(0.176286\pi\)
\(548\) 0 0
\(549\) 187515. + 324786.i 0.0265525 + 0.0459903i
\(550\) 0 0
\(551\) 1.95070e6 3.37871e6i 0.273723 0.474103i
\(552\) 0 0
\(553\) 8.06694e6 + 377631.i 1.12175 + 0.0525116i
\(554\) 0 0
\(555\) −84537.0 + 146422.i −0.0116497 + 0.0201779i
\(556\) 0 0
\(557\) −6.45665e6 1.11832e7i −0.881798 1.52732i −0.849340 0.527847i \(-0.823000\pi\)
−0.0324587 0.999473i \(-0.510334\pi\)
\(558\) 0 0
\(559\) −6.37651e6 −0.863085
\(560\) 0 0
\(561\) 1.04296e7 1.39913
\(562\) 0 0
\(563\) −5.68492e6 9.84657e6i −0.755881 1.30922i −0.944935 0.327257i \(-0.893876\pi\)
0.189055 0.981967i \(-0.439458\pi\)
\(564\) 0 0
\(565\) −118062. + 204489.i −0.0155593 + 0.0269494i
\(566\) 0 0
\(567\) −459270. + 715931.i −0.0599944 + 0.0935220i
\(568\) 0 0
\(569\) 2.84898e6 4.93457e6i 0.368900 0.638953i −0.620494 0.784211i \(-0.713068\pi\)
0.989394 + 0.145258i \(0.0464013\pi\)
\(570\) 0 0
\(571\) −3.52110e6 6.09873e6i −0.451948 0.782797i 0.546559 0.837421i \(-0.315937\pi\)
−0.998507 + 0.0546236i \(0.982604\pi\)
\(572\) 0 0
\(573\) 3.23077e6 0.411073
\(574\) 0 0
\(575\) −1.07127e7 −1.35122
\(576\) 0 0
\(577\) 1.29098e6 + 2.23605e6i 0.161429 + 0.279603i 0.935381 0.353641i \(-0.115056\pi\)
−0.773952 + 0.633244i \(0.781723\pi\)
\(578\) 0 0
\(579\) −818698. + 1.41803e6i −0.101491 + 0.175788i
\(580\) 0 0
\(581\) 4.74917e6 + 9.19355e6i 0.583684 + 1.12991i
\(582\) 0 0
\(583\) 9.42257e6 1.63204e7i 1.14815 1.98865i
\(584\) 0 0
\(585\) −135837. 235277.i −0.0164107 0.0284243i
\(586\) 0 0
\(587\) −4.69459e6 −0.562345 −0.281172 0.959657i \(-0.590723\pi\)
−0.281172 + 0.959657i \(0.590723\pi\)
\(588\) 0 0
\(589\) 7.28100e6 0.864774
\(590\) 0 0
\(591\) 3.23066e6 + 5.59566e6i 0.380472 + 0.658996i
\(592\) 0 0
\(593\) −6.71175e6 + 1.16251e7i −0.783789 + 1.35756i 0.145931 + 0.989295i \(0.453382\pi\)
−0.929720 + 0.368268i \(0.879951\pi\)
\(594\) 0 0
\(595\) −621180. 1.20249e6i −0.0719325 0.139248i
\(596\) 0 0
\(597\) −913932. + 1.58298e6i −0.104949 + 0.181777i
\(598\) 0 0
\(599\) 2.52301e6 + 4.36997e6i 0.287310 + 0.497636i 0.973167 0.230101i \(-0.0739056\pi\)
−0.685856 + 0.727737i \(0.740572\pi\)
\(600\) 0 0
\(601\) −1.06391e7 −1.20148 −0.600742 0.799443i \(-0.705128\pi\)
−0.600742 + 0.799443i \(0.705128\pi\)
\(602\) 0 0
\(603\) 1.51834e6 0.170050
\(604\) 0 0
\(605\) 847515. + 1.46794e6i 0.0941367 + 0.163050i
\(606\) 0 0
\(607\) 708041. 1.22636e6i 0.0779986 0.135098i −0.824388 0.566026i \(-0.808480\pi\)
0.902386 + 0.430928i \(0.141814\pi\)
\(608\) 0 0
\(609\) 2.12436e6 3.31155e6i 0.232105 0.361816i
\(610\) 0 0
\(611\) −645645. + 1.11829e6i −0.0699666 + 0.121186i
\(612\) 0 0
\(613\) −4.73152e6 8.19523e6i −0.508568 0.880866i −0.999951 0.00992215i \(-0.996842\pi\)
0.491383 0.870944i \(-0.336492\pi\)
\(614\) 0 0
\(615\) −262764. −0.0280142
\(616\) 0 0
\(617\) 1.29388e7 1.36830 0.684148 0.729343i \(-0.260174\pi\)
0.684148 + 0.729343i \(0.260174\pi\)
\(618\) 0 0
\(619\) −1.90188e6 3.29415e6i −0.199506 0.345555i 0.748862 0.662726i \(-0.230600\pi\)
−0.948368 + 0.317171i \(0.897267\pi\)
\(620\) 0 0
\(621\) 1.26409e6 2.18946e6i 0.131537 0.227829i
\(622\) 0 0
\(623\) −2.34654e6 109847.i −0.242219 0.0113388i
\(624\) 0 0
\(625\) −4.71471e6 + 8.16612e6i −0.482786 + 0.836210i
\(626\) 0 0
\(627\) −3.46753e6 6.00594e6i −0.352250 0.610115i
\(628\) 0 0
\(629\) −5.44794e6 −0.549042
\(630\) 0 0
\(631\) 9.17498e6 0.917343 0.458671 0.888606i \(-0.348326\pi\)
0.458671 + 0.888606i \(0.348326\pi\)
\(632\) 0 0
\(633\) −5.26941e6 9.12689e6i −0.522700 0.905343i
\(634\) 0 0
\(635\) −951279. + 1.64766e6i −0.0936211 + 0.162156i
\(636\) 0 0
\(637\) 5.43711e6 7.66198e6i 0.530909 0.748157i
\(638\) 0 0
\(639\) −1.54815e6 + 2.68148e6i −0.149990 + 0.259790i
\(640\) 0 0
\(641\) −5.12269e6 8.87275e6i −0.492439 0.852930i 0.507523 0.861638i \(-0.330561\pi\)
−0.999962 + 0.00870851i \(0.997228\pi\)
\(642\) 0 0
\(643\) 5.72346e6 0.545922 0.272961 0.962025i \(-0.411997\pi\)
0.272961 + 0.962025i \(0.411997\pi\)
\(644\) 0 0
\(645\) 615978. 0.0582996
\(646\) 0 0
\(647\) −4.99397e6 8.64981e6i −0.469013 0.812355i 0.530359 0.847773i \(-0.322057\pi\)
−0.999373 + 0.0354179i \(0.988724\pi\)
\(648\) 0 0
\(649\) 6.84115e6 1.18492e7i 0.637555 1.10428i
\(650\) 0 0
\(651\) 7.33449e6 + 343344.i 0.678293 + 0.0317524i
\(652\) 0 0
\(653\) 599439. 1.03826e6i 0.0550126 0.0952846i −0.837208 0.546885i \(-0.815813\pi\)
0.892220 + 0.451601i \(0.149147\pi\)
\(654\) 0 0
\(655\) 464490. + 804520.i 0.0423032 + 0.0732713i
\(656\) 0 0
\(657\) 5.71771e6 0.516783
\(658\) 0 0
\(659\) −1.18065e7 −1.05903 −0.529516 0.848300i \(-0.677626\pi\)
−0.529516 + 0.848300i \(0.677626\pi\)
\(660\) 0 0
\(661\) −2.36020e6 4.08798e6i −0.210109 0.363919i 0.741640 0.670799i \(-0.234049\pi\)
−0.951748 + 0.306879i \(0.900715\pi\)
\(662\) 0 0
\(663\) 4.37697e6 7.58113e6i 0.386714 0.669808i
\(664\) 0 0
\(665\) −485940. + 757505.i −0.0426117 + 0.0664250i
\(666\) 0 0
\(667\) −5.84705e6 + 1.01274e7i −0.508888 + 0.881420i
\(668\) 0 0
\(669\) −5.60858e6 9.71435e6i −0.484493 0.839167i
\(670\) 0 0
\(671\) −3.08358e6 −0.264392
\(672\) 0 0
\(673\) −8.70826e6 −0.741129 −0.370564 0.928807i \(-0.620836\pi\)
−0.370564 + 0.928807i \(0.620836\pi\)
\(674\) 0 0
\(675\) −1.12594e6 1.95019e6i −0.0951165 0.164747i
\(676\) 0 0
\(677\) −2.55553e6 + 4.42630e6i −0.214293 + 0.371167i −0.953054 0.302801i \(-0.902078\pi\)
0.738760 + 0.673968i \(0.235412\pi\)
\(678\) 0 0
\(679\) −7.42286e6 1.43693e7i −0.617870 1.19609i
\(680\) 0 0
\(681\) 4.13524e6 7.16244e6i 0.341690 0.591825i
\(682\) 0 0
\(683\) −8.85989e6 1.53458e7i −0.726736 1.25874i −0.958256 0.285913i \(-0.907703\pi\)
0.231520 0.972830i \(-0.425630\pi\)
\(684\) 0 0
\(685\) −403992. −0.0328962
\(686\) 0 0
\(687\) −1.08337e7 −0.875763
\(688\) 0 0
\(689\) −7.90873e6 1.36983e7i −0.634686 1.09931i
\(690\) 0 0
\(691\) −1.12997e7 + 1.95716e7i −0.900265 + 1.55931i −0.0731160 + 0.997323i \(0.523294\pi\)
−0.827149 + 0.561982i \(0.810039\pi\)
\(692\) 0 0
\(693\) −3.20979e6 6.21357e6i −0.253889 0.491483i
\(694\) 0 0
\(695\) 1.09564e6 1.89771e6i 0.0860415 0.149028i
\(696\) 0 0
\(697\) −4.23342e6 7.33250e6i −0.330073 0.571702i
\(698\) 0 0
\(699\) 8.27156e6 0.640316
\(700\) 0 0
\(701\) −818148. −0.0628835 −0.0314418 0.999506i \(-0.510010\pi\)
−0.0314418 + 0.999506i \(0.510010\pi\)
\(702\) 0 0
\(703\) 1.81128e6 + 3.13724e6i 0.138229 + 0.239419i
\(704\) 0 0
\(705\) 62370.0 108028.i 0.00472610 0.00818585i
\(706\) 0 0
\(707\) 6.53730e6 1.01906e7i 0.491869 0.766749i
\(708\) 0 0
\(709\) 2.54591e6 4.40965e6i 0.190208 0.329449i −0.755111 0.655597i \(-0.772417\pi\)
0.945319 + 0.326147i \(0.105751\pi\)
\(710\) 0 0
\(711\) −2.52287e6 4.36973e6i −0.187163 0.324176i
\(712\) 0 0
\(713\) −2.18241e7 −1.60773
\(714\) 0 0
\(715\) 2.23376e6 0.163408
\(716\) 0 0
\(717\) 2.81402e6 + 4.87403e6i 0.204423 + 0.354071i
\(718\) 0 0
\(719\) −240429. + 416435.i −0.0173446 + 0.0300418i −0.874567 0.484904i \(-0.838855\pi\)
0.857223 + 0.514946i \(0.172188\pi\)
\(720\) 0 0
\(721\) 2.17212e7 + 1.01682e6i 1.55613 + 0.0728457i
\(722\) 0 0
\(723\) 5.64220e6 9.77258e6i 0.401423 0.695286i
\(724\) 0 0
\(725\) 5.20805e6 + 9.02061e6i 0.367985 + 0.637369i
\(726\) 0 0
\(727\) 1.40783e7 0.987905 0.493952 0.869489i \(-0.335552\pi\)
0.493952 + 0.869489i \(0.335552\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 9.92409e6 + 1.71890e7i 0.686906 + 1.18976i
\(732\) 0 0
\(733\) −1.01966e6 + 1.76610e6i −0.0700964 + 0.121411i −0.898943 0.438065i \(-0.855664\pi\)
0.828847 + 0.559475i \(0.188997\pi\)
\(734\) 0 0
\(735\) −525231. + 740156.i −0.0358618 + 0.0505364i
\(736\) 0 0
\(737\) −6.24209e6 + 1.08116e7i −0.423312 + 0.733199i
\(738\) 0 0
\(739\) −8.24785e6 1.42857e7i −0.555558 0.962255i −0.997860 0.0653888i \(-0.979171\pi\)
0.442302 0.896866i \(-0.354162\pi\)
\(740\) 0 0
\(741\) −5.82087e6 −0.389441
\(742\) 0 0
\(743\) 2.38121e7 1.58243 0.791217 0.611536i \(-0.209448\pi\)
0.791217 + 0.611536i \(0.209448\pi\)
\(744\) 0 0
\(745\) −504180. 873265.i −0.0332809 0.0576442i
\(746\) 0 0
\(747\) 3.23263e6 5.59908e6i 0.211960 0.367126i
\(748\) 0 0
\(749\) −8.95881e6 419381.i −0.583507 0.0273152i
\(750\) 0 0
\(751\) 962480. 1.66707e6i 0.0622719 0.107858i −0.833209 0.552959i \(-0.813499\pi\)
0.895481 + 0.445101i \(0.146832\pi\)
\(752\) 0 0
\(753\) 6.80999e6 + 1.17953e7i 0.437683 + 0.758089i
\(754\) 0 0
\(755\) 921216. 0.0588158
\(756\) 0 0
\(757\) 8.98092e6 0.569615 0.284807 0.958585i \(-0.408070\pi\)
0.284807 + 0.958585i \(0.408070\pi\)
\(758\) 0 0
\(759\) 1.03936e7 + 1.80022e7i 0.654879 + 1.13428i
\(760\) 0 0
\(761\) −7.29955e6 + 1.26432e7i −0.456914 + 0.791398i −0.998796 0.0490566i \(-0.984379\pi\)
0.541882 + 0.840454i \(0.317712\pi\)
\(762\) 0 0
\(763\) 1.53691e7 2.39581e7i 0.955736 1.48984i
\(764\) 0 0
\(765\) −422820. + 732346.i −0.0261217 + 0.0452442i
\(766\) 0 0
\(767\) −5.74205e6 9.94552e6i −0.352434 0.610434i
\(768\) 0 0
\(769\) 2.78381e7 1.69755 0.848776 0.528753i \(-0.177340\pi\)
0.848776 + 0.528753i \(0.177340\pi\)
\(770\) 0 0
\(771\) 1.39944e7 0.847847
\(772\) 0 0
\(773\) 1.41429e7 + 2.44962e7i 0.851312 + 1.47451i 0.880025 + 0.474927i \(0.157526\pi\)
−0.0287135 + 0.999588i \(0.509141\pi\)
\(774\) 0 0
\(775\) −9.71954e6 + 1.68347e7i −0.581288 + 1.00682i
\(776\) 0 0
\(777\) 1.67665e6 + 3.24570e6i 0.0996300 + 0.192866i
\(778\) 0 0
\(779\) −2.81498e6 + 4.87569e6i −0.166200 + 0.287867i
\(780\) 0 0
\(781\) −1.27293e7 2.20477e7i −0.746750 1.29341i
\(782\) 0 0