Properties

Label 1040.2.da.f.641.7
Level $1040$
Weight $2$
Character 1040.641
Analytic conductor $8.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(641,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1040.641");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), 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: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 520)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 641.7
Root \(0.956612i\) of defining polynomial
Character \(\chi\) \(=\) 1040.641
Dual form 1040.2.da.f.881.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.52075 - 2.63402i) q^{3} +1.00000i q^{5} +(2.67664 - 1.54536i) q^{7} +(-3.12538 - 5.41331i) q^{9} +O(q^{10})\) \(q+(1.52075 - 2.63402i) q^{3} +1.00000i q^{5} +(2.67664 - 1.54536i) q^{7} +(-3.12538 - 5.41331i) q^{9} +(5.36505 + 3.09751i) q^{11} +(2.54049 - 2.55850i) q^{13} +(2.63402 + 1.52075i) q^{15} +(3.24262 + 5.61638i) q^{17} +(-2.65678 + 1.53389i) q^{19} -9.40042i q^{21} +(-0.896274 + 1.55239i) q^{23} -1.00000 q^{25} -9.88720 q^{27} +(-1.49128 + 2.58297i) q^{29} -4.34508i q^{31} +(16.3178 - 9.42110i) q^{33} +(1.54536 + 2.67664i) q^{35} +(-8.31867 - 4.80279i) q^{37} +(-2.87569 - 10.5825i) q^{39} +(-6.40038 - 3.69526i) q^{41} +(2.64990 + 4.58977i) q^{43} +(5.41331 - 3.12538i) q^{45} +3.46118i q^{47} +(1.27625 - 2.21053i) q^{49} +19.7249 q^{51} -7.82172 q^{53} +(-3.09751 + 5.36505i) q^{55} +9.33068i q^{57} +(-1.21101 + 0.699176i) q^{59} +(-4.92252 - 8.52605i) q^{61} +(-16.7310 - 9.65965i) q^{63} +(2.55850 + 2.54049i) q^{65} +(1.52639 + 0.881260i) q^{67} +(2.72602 + 4.72161i) q^{69} +(3.60493 - 2.08131i) q^{71} +11.7104i q^{73} +(-1.52075 + 2.63402i) q^{75} +19.1470 q^{77} -6.58127 q^{79} +(-5.65985 + 9.80314i) q^{81} -4.46298i q^{83} +(-5.61638 + 3.24262i) q^{85} +(4.53573 + 7.85612i) q^{87} +(-10.0616 - 5.80904i) q^{89} +(2.84617 - 10.7741i) q^{91} +(-11.4450 - 6.60779i) q^{93} +(-1.53389 - 2.65678i) q^{95} +(-10.6392 + 6.14254i) q^{97} -38.7236i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.52075 2.63402i 0.878007 1.52075i 0.0244825 0.999700i \(-0.492206\pi\)
0.853525 0.521053i \(-0.174460\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.67664 1.54536i 1.01167 0.584090i 0.0999920 0.994988i \(-0.468118\pi\)
0.911681 + 0.410898i \(0.134785\pi\)
\(8\) 0 0
\(9\) −3.12538 5.41331i −1.04179 1.80444i
\(10\) 0 0
\(11\) 5.36505 + 3.09751i 1.61762 + 0.933935i 0.987533 + 0.157414i \(0.0503157\pi\)
0.630091 + 0.776521i \(0.283018\pi\)
\(12\) 0 0
\(13\) 2.54049 2.55850i 0.704605 0.709600i
\(14\) 0 0
\(15\) 2.63402 + 1.52075i 0.680101 + 0.392657i
\(16\) 0 0
\(17\) 3.24262 + 5.61638i 0.786450 + 1.36217i 0.928129 + 0.372259i \(0.121417\pi\)
−0.141678 + 0.989913i \(0.545250\pi\)
\(18\) 0 0
\(19\) −2.65678 + 1.53389i −0.609507 + 0.351899i −0.772772 0.634683i \(-0.781131\pi\)
0.163266 + 0.986582i \(0.447797\pi\)
\(20\) 0 0
\(21\) 9.40042i 2.05134i
\(22\) 0 0
\(23\) −0.896274 + 1.55239i −0.186886 + 0.323696i −0.944210 0.329343i \(-0.893173\pi\)
0.757324 + 0.653039i \(0.226506\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −9.88720 −1.90279
\(28\) 0 0
\(29\) −1.49128 + 2.58297i −0.276923 + 0.479645i −0.970619 0.240623i \(-0.922648\pi\)
0.693695 + 0.720269i \(0.255981\pi\)
\(30\) 0 0
\(31\) 4.34508i 0.780399i −0.920730 0.390199i \(-0.872406\pi\)
0.920730 0.390199i \(-0.127594\pi\)
\(32\) 0 0
\(33\) 16.3178 9.42110i 2.84057 1.64000i
\(34\) 0 0
\(35\) 1.54536 + 2.67664i 0.261213 + 0.452434i
\(36\) 0 0
\(37\) −8.31867 4.80279i −1.36758 0.789574i −0.376963 0.926228i \(-0.623032\pi\)
−0.990619 + 0.136655i \(0.956365\pi\)
\(38\) 0 0
\(39\) −2.87569 10.5825i −0.460478 1.69456i
\(40\) 0 0
\(41\) −6.40038 3.69526i −0.999571 0.577102i −0.0914495 0.995810i \(-0.529150\pi\)
−0.908121 + 0.418707i \(0.862483\pi\)
\(42\) 0 0
\(43\) 2.64990 + 4.58977i 0.404106 + 0.699933i 0.994217 0.107390i \(-0.0342492\pi\)
−0.590111 + 0.807322i \(0.700916\pi\)
\(44\) 0 0
\(45\) 5.41331 3.12538i 0.806969 0.465904i
\(46\) 0 0
\(47\) 3.46118i 0.504864i 0.967615 + 0.252432i \(0.0812305\pi\)
−0.967615 + 0.252432i \(0.918770\pi\)
\(48\) 0 0
\(49\) 1.27625 2.21053i 0.182322 0.315790i
\(50\) 0 0
\(51\) 19.7249 2.76204
\(52\) 0 0
\(53\) −7.82172 −1.07440 −0.537198 0.843456i \(-0.680517\pi\)
−0.537198 + 0.843456i \(0.680517\pi\)
\(54\) 0 0
\(55\) −3.09751 + 5.36505i −0.417669 + 0.723423i
\(56\) 0 0
\(57\) 9.33068i 1.23588i
\(58\) 0 0
\(59\) −1.21101 + 0.699176i −0.157660 + 0.0910250i −0.576754 0.816918i \(-0.695681\pi\)
0.419094 + 0.907943i \(0.362348\pi\)
\(60\) 0 0
\(61\) −4.92252 8.52605i −0.630264 1.09165i −0.987498 0.157634i \(-0.949613\pi\)
0.357234 0.934015i \(-0.383720\pi\)
\(62\) 0 0
\(63\) −16.7310 9.65965i −2.10791 1.21700i
\(64\) 0 0
\(65\) 2.55850 + 2.54049i 0.317343 + 0.315109i
\(66\) 0 0
\(67\) 1.52639 + 0.881260i 0.186478 + 0.107663i 0.590333 0.807160i \(-0.298997\pi\)
−0.403855 + 0.914823i \(0.632330\pi\)
\(68\) 0 0
\(69\) 2.72602 + 4.72161i 0.328175 + 0.568415i
\(70\) 0 0
\(71\) 3.60493 2.08131i 0.427826 0.247005i −0.270594 0.962694i \(-0.587220\pi\)
0.698420 + 0.715688i \(0.253887\pi\)
\(72\) 0 0
\(73\) 11.7104i 1.37060i 0.728263 + 0.685298i \(0.240328\pi\)
−0.728263 + 0.685298i \(0.759672\pi\)
\(74\) 0 0
\(75\) −1.52075 + 2.63402i −0.175601 + 0.304151i
\(76\) 0 0
\(77\) 19.1470 2.18201
\(78\) 0 0
\(79\) −6.58127 −0.740451 −0.370225 0.928942i \(-0.620720\pi\)
−0.370225 + 0.928942i \(0.620720\pi\)
\(80\) 0 0
\(81\) −5.65985 + 9.80314i −0.628872 + 1.08924i
\(82\) 0 0
\(83\) 4.46298i 0.489875i −0.969539 0.244938i \(-0.921233\pi\)
0.969539 0.244938i \(-0.0787675\pi\)
\(84\) 0 0
\(85\) −5.61638 + 3.24262i −0.609182 + 0.351711i
\(86\) 0 0
\(87\) 4.53573 + 7.85612i 0.486281 + 0.842264i
\(88\) 0 0
\(89\) −10.0616 5.80904i −1.06652 0.615757i −0.139294 0.990251i \(-0.544483\pi\)
−0.927229 + 0.374494i \(0.877816\pi\)
\(90\) 0 0
\(91\) 2.84617 10.7741i 0.298360 1.12944i
\(92\) 0 0
\(93\) −11.4450 6.60779i −1.18679 0.685196i
\(94\) 0 0
\(95\) −1.53389 2.65678i −0.157374 0.272580i
\(96\) 0 0
\(97\) −10.6392 + 6.14254i −1.08025 + 0.623681i −0.930963 0.365114i \(-0.881030\pi\)
−0.149284 + 0.988794i \(0.547697\pi\)
\(98\) 0 0
\(99\) 38.7236i 3.89187i
\(100\) 0 0
\(101\) −5.08529 + 8.80797i −0.506005 + 0.876426i 0.493971 + 0.869478i \(0.335545\pi\)
−0.999976 + 0.00694776i \(0.997788\pi\)
\(102\) 0 0
\(103\) −6.53156 −0.643573 −0.321787 0.946812i \(-0.604283\pi\)
−0.321787 + 0.946812i \(0.604283\pi\)
\(104\) 0 0
\(105\) 9.40042 0.917387
\(106\) 0 0
\(107\) 9.10227 15.7656i 0.879949 1.52412i 0.0285544 0.999592i \(-0.490910\pi\)
0.851395 0.524525i \(-0.175757\pi\)
\(108\) 0 0
\(109\) 14.6401i 1.40227i −0.713028 0.701135i \(-0.752677\pi\)
0.713028 0.701135i \(-0.247323\pi\)
\(110\) 0 0
\(111\) −25.3013 + 14.6077i −2.40149 + 1.38650i
\(112\) 0 0
\(113\) 1.36006 + 2.35569i 0.127943 + 0.221604i 0.922880 0.385089i \(-0.125829\pi\)
−0.794936 + 0.606693i \(0.792496\pi\)
\(114\) 0 0
\(115\) −1.55239 0.896274i −0.144761 0.0835780i
\(116\) 0 0
\(117\) −21.7900 5.75618i −2.01448 0.532159i
\(118\) 0 0
\(119\) 17.3586 + 10.0220i 1.59126 + 0.918715i
\(120\) 0 0
\(121\) 13.6892 + 23.7104i 1.24447 + 2.15549i
\(122\) 0 0
\(123\) −19.4668 + 11.2392i −1.75526 + 1.01340i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −3.70643 + 6.41972i −0.328892 + 0.569658i −0.982292 0.187354i \(-0.940009\pi\)
0.653400 + 0.757013i \(0.273342\pi\)
\(128\) 0 0
\(129\) 16.1194 1.41923
\(130\) 0 0
\(131\) 12.2800 1.07291 0.536456 0.843929i \(-0.319763\pi\)
0.536456 + 0.843929i \(0.319763\pi\)
\(132\) 0 0
\(133\) −4.74082 + 8.21134i −0.411081 + 0.712014i
\(134\) 0 0
\(135\) 9.88720i 0.850954i
\(136\) 0 0
\(137\) −12.6117 + 7.28134i −1.07749 + 0.622087i −0.930217 0.367009i \(-0.880382\pi\)
−0.147269 + 0.989096i \(0.547048\pi\)
\(138\) 0 0
\(139\) 1.22468 + 2.12121i 0.103876 + 0.179919i 0.913278 0.407336i \(-0.133542\pi\)
−0.809402 + 0.587255i \(0.800209\pi\)
\(140\) 0 0
\(141\) 9.11681 + 5.26359i 0.767774 + 0.443274i
\(142\) 0 0
\(143\) 21.5548 5.85728i 1.80251 0.489810i
\(144\) 0 0
\(145\) −2.58297 1.49128i −0.214504 0.123844i
\(146\) 0 0
\(147\) −3.88173 6.72335i −0.320159 0.554532i
\(148\) 0 0
\(149\) 6.99549 4.03885i 0.573092 0.330875i −0.185291 0.982684i \(-0.559323\pi\)
0.758384 + 0.651809i \(0.225989\pi\)
\(150\) 0 0
\(151\) 5.14185i 0.418438i 0.977869 + 0.209219i \(0.0670922\pi\)
−0.977869 + 0.209219i \(0.932908\pi\)
\(152\) 0 0
\(153\) 20.2688 35.1066i 1.63864 2.83820i
\(154\) 0 0
\(155\) 4.34508 0.349005
\(156\) 0 0
\(157\) 10.4778 0.836217 0.418109 0.908397i \(-0.362693\pi\)
0.418109 + 0.908397i \(0.362693\pi\)
\(158\) 0 0
\(159\) −11.8949 + 20.6026i −0.943328 + 1.63389i
\(160\) 0 0
\(161\) 5.54025i 0.436633i
\(162\) 0 0
\(163\) −0.773712 + 0.446703i −0.0606018 + 0.0349885i −0.529995 0.848001i \(-0.677806\pi\)
0.469393 + 0.882989i \(0.344473\pi\)
\(164\) 0 0
\(165\) 9.42110 + 16.3178i 0.733432 + 1.27034i
\(166\) 0 0
\(167\) −6.78586 3.91782i −0.525105 0.303170i 0.213916 0.976852i \(-0.431378\pi\)
−0.739021 + 0.673682i \(0.764712\pi\)
\(168\) 0 0
\(169\) −0.0918374 12.9997i −0.00706442 0.999975i
\(170\) 0 0
\(171\) 16.6069 + 9.58799i 1.26996 + 0.733212i
\(172\) 0 0
\(173\) 9.61828 + 16.6593i 0.731264 + 1.26659i 0.956343 + 0.292246i \(0.0944026\pi\)
−0.225079 + 0.974341i \(0.572264\pi\)
\(174\) 0 0
\(175\) −2.67664 + 1.54536i −0.202335 + 0.116818i
\(176\) 0 0
\(177\) 4.25310i 0.319682i
\(178\) 0 0
\(179\) −0.115064 + 0.199297i −0.00860032 + 0.0148962i −0.870294 0.492533i \(-0.836071\pi\)
0.861693 + 0.507430i \(0.169404\pi\)
\(180\) 0 0
\(181\) 9.26780 0.688870 0.344435 0.938810i \(-0.388071\pi\)
0.344435 + 0.938810i \(0.388071\pi\)
\(182\) 0 0
\(183\) −29.9437 −2.21350
\(184\) 0 0
\(185\) 4.80279 8.31867i 0.353108 0.611601i
\(186\) 0 0
\(187\) 40.1762i 2.93798i
\(188\) 0 0
\(189\) −26.4644 + 15.2792i −1.92500 + 1.11140i
\(190\) 0 0
\(191\) 1.07946 + 1.86968i 0.0781070 + 0.135285i 0.902433 0.430830i \(-0.141779\pi\)
−0.824326 + 0.566115i \(0.808446\pi\)
\(192\) 0 0
\(193\) 17.8233 + 10.2903i 1.28295 + 0.740710i 0.977386 0.211463i \(-0.0678227\pi\)
0.305561 + 0.952173i \(0.401156\pi\)
\(194\) 0 0
\(195\) 10.5825 2.87569i 0.757832 0.205932i
\(196\) 0 0
\(197\) −5.37114 3.10103i −0.382678 0.220939i 0.296305 0.955093i \(-0.404246\pi\)
−0.678983 + 0.734154i \(0.737579\pi\)
\(198\) 0 0
\(199\) 2.42864 + 4.20652i 0.172161 + 0.298192i 0.939175 0.343438i \(-0.111592\pi\)
−0.767014 + 0.641631i \(0.778258\pi\)
\(200\) 0 0
\(201\) 4.64252 2.68036i 0.327458 0.189058i
\(202\) 0 0
\(203\) 9.21822i 0.646992i
\(204\) 0 0
\(205\) 3.69526 6.40038i 0.258088 0.447022i
\(206\) 0 0
\(207\) 11.2048 0.778787
\(208\) 0 0
\(209\) −19.0050 −1.31460
\(210\) 0 0
\(211\) 0.494607 0.856684i 0.0340501 0.0589766i −0.848498 0.529198i \(-0.822493\pi\)
0.882548 + 0.470222i \(0.155826\pi\)
\(212\) 0 0
\(213\) 12.6606i 0.867490i
\(214\) 0 0
\(215\) −4.58977 + 2.64990i −0.313019 + 0.180722i
\(216\) 0 0
\(217\) −6.71469 11.6302i −0.455823 0.789508i
\(218\) 0 0
\(219\) 30.8454 + 17.8086i 2.08434 + 1.20339i
\(220\) 0 0
\(221\) 22.6073 + 5.97211i 1.52073 + 0.401728i
\(222\) 0 0
\(223\) −2.08118 1.20157i −0.139366 0.0804632i 0.428696 0.903449i \(-0.358973\pi\)
−0.568062 + 0.822986i \(0.692307\pi\)
\(224\) 0 0
\(225\) 3.12538 + 5.41331i 0.208359 + 0.360888i
\(226\) 0 0
\(227\) 22.9049 13.2242i 1.52025 0.877720i 0.520540 0.853837i \(-0.325731\pi\)
0.999715 0.0238823i \(-0.00760270\pi\)
\(228\) 0 0
\(229\) 0.715271i 0.0472664i −0.999721 0.0236332i \(-0.992477\pi\)
0.999721 0.0236332i \(-0.00752339\pi\)
\(230\) 0 0
\(231\) 29.1179 50.4337i 1.91582 3.31830i
\(232\) 0 0
\(233\) −9.27534 −0.607648 −0.303824 0.952728i \(-0.598263\pi\)
−0.303824 + 0.952728i \(0.598263\pi\)
\(234\) 0 0
\(235\) −3.46118 −0.225782
\(236\) 0 0
\(237\) −10.0085 + 17.3352i −0.650121 + 1.12604i
\(238\) 0 0
\(239\) 12.8779i 0.833001i −0.909136 0.416500i \(-0.863256\pi\)
0.909136 0.416500i \(-0.136744\pi\)
\(240\) 0 0
\(241\) −3.02528 + 1.74664i −0.194875 + 0.112511i −0.594263 0.804271i \(-0.702556\pi\)
0.399388 + 0.916782i \(0.369223\pi\)
\(242\) 0 0
\(243\) 2.38366 + 4.12863i 0.152912 + 0.264852i
\(244\) 0 0
\(245\) 2.21053 + 1.27625i 0.141226 + 0.0815367i
\(246\) 0 0
\(247\) −2.82505 + 10.6942i −0.179754 + 0.680456i
\(248\) 0 0
\(249\) −11.7556 6.78708i −0.744979 0.430114i
\(250\) 0 0
\(251\) −5.53107 9.58010i −0.349118 0.604690i 0.636975 0.770884i \(-0.280185\pi\)
−0.986093 + 0.166194i \(0.946852\pi\)
\(252\) 0 0
\(253\) −9.61712 + 5.55244i −0.604623 + 0.349079i
\(254\) 0 0
\(255\) 19.7249i 1.23522i
\(256\) 0 0
\(257\) −0.281244 + 0.487129i −0.0175435 + 0.0303863i −0.874664 0.484730i \(-0.838918\pi\)
0.857120 + 0.515116i \(0.172251\pi\)
\(258\) 0 0
\(259\) −29.6881 −1.84473
\(260\) 0 0
\(261\) 18.6432 1.15399
\(262\) 0 0
\(263\) 5.50854 9.54107i 0.339671 0.588328i −0.644700 0.764436i \(-0.723018\pi\)
0.984371 + 0.176108i \(0.0563509\pi\)
\(264\) 0 0
\(265\) 7.82172i 0.480485i
\(266\) 0 0
\(267\) −30.6023 + 17.6682i −1.87283 + 1.08128i
\(268\) 0 0
\(269\) 7.82588 + 13.5548i 0.477152 + 0.826452i 0.999657 0.0261842i \(-0.00833564\pi\)
−0.522505 + 0.852636i \(0.675002\pi\)
\(270\) 0 0
\(271\) 17.8011 + 10.2775i 1.08134 + 0.624312i 0.931257 0.364362i \(-0.118713\pi\)
0.150082 + 0.988674i \(0.452046\pi\)
\(272\) 0 0
\(273\) −24.0510 23.8817i −1.45563 1.44538i
\(274\) 0 0
\(275\) −5.36505 3.09751i −0.323525 0.186787i
\(276\) 0 0
\(277\) −13.8840 24.0478i −0.834210 1.44489i −0.894672 0.446723i \(-0.852591\pi\)
0.0604628 0.998170i \(-0.480742\pi\)
\(278\) 0 0
\(279\) −23.5213 + 13.5800i −1.40818 + 0.813014i
\(280\) 0 0
\(281\) 22.7781i 1.35883i 0.733755 + 0.679414i \(0.237766\pi\)
−0.733755 + 0.679414i \(0.762234\pi\)
\(282\) 0 0
\(283\) −2.25409 + 3.90420i −0.133992 + 0.232081i −0.925212 0.379451i \(-0.876113\pi\)
0.791220 + 0.611532i \(0.209446\pi\)
\(284\) 0 0
\(285\) −9.33068 −0.552702
\(286\) 0 0
\(287\) −22.8420 −1.34832
\(288\) 0 0
\(289\) −12.5291 + 21.7011i −0.737009 + 1.27654i
\(290\) 0 0
\(291\) 37.3652i 2.19038i
\(292\) 0 0
\(293\) −8.50606 + 4.91097i −0.496929 + 0.286902i −0.727445 0.686166i \(-0.759292\pi\)
0.230515 + 0.973069i \(0.425959\pi\)
\(294\) 0 0
\(295\) −0.699176 1.21101i −0.0407076 0.0705076i
\(296\) 0 0
\(297\) −53.0453 30.6257i −3.07800 1.77708i
\(298\) 0 0
\(299\) 1.69482 + 6.23695i 0.0980140 + 0.360692i
\(300\) 0 0
\(301\) 14.1856 + 8.19009i 0.817647 + 0.472069i
\(302\) 0 0
\(303\) 15.4669 + 26.7895i 0.888552 + 1.53902i
\(304\) 0 0
\(305\) 8.52605 4.92252i 0.488200 0.281862i
\(306\) 0 0
\(307\) 19.5716i 1.11701i −0.829501 0.558505i \(-0.811375\pi\)
0.829501 0.558505i \(-0.188625\pi\)
\(308\) 0 0
\(309\) −9.93289 + 17.2043i −0.565062 + 0.978716i
\(310\) 0 0
\(311\) 8.70881 0.493831 0.246916 0.969037i \(-0.420583\pi\)
0.246916 + 0.969037i \(0.420583\pi\)
\(312\) 0 0
\(313\) −3.24505 −0.183421 −0.0917105 0.995786i \(-0.529233\pi\)
−0.0917105 + 0.995786i \(0.529233\pi\)
\(314\) 0 0
\(315\) 9.65965 16.7310i 0.544259 0.942685i
\(316\) 0 0
\(317\) 20.7194i 1.16372i −0.813290 0.581858i \(-0.802326\pi\)
0.813290 0.581858i \(-0.197674\pi\)
\(318\) 0 0
\(319\) −16.0016 + 9.23851i −0.895915 + 0.517257i
\(320\) 0 0
\(321\) −27.6846 47.9511i −1.54520 2.67637i
\(322\) 0 0
\(323\) −17.2298 9.94765i −0.958694 0.553502i
\(324\) 0 0
\(325\) −2.54049 + 2.55850i −0.140921 + 0.141920i
\(326\) 0 0
\(327\) −38.5624 22.2640i −2.13251 1.23120i
\(328\) 0 0
\(329\) 5.34875 + 9.26431i 0.294886 + 0.510758i
\(330\) 0 0
\(331\) 4.07951 2.35531i 0.224230 0.129459i −0.383677 0.923467i \(-0.625342\pi\)
0.607907 + 0.794008i \(0.292009\pi\)
\(332\) 0 0
\(333\) 60.0421i 3.29029i
\(334\) 0 0
\(335\) −0.881260 + 1.52639i −0.0481484 + 0.0833955i
\(336\) 0 0
\(337\) 2.62561 0.143026 0.0715131 0.997440i \(-0.477217\pi\)
0.0715131 + 0.997440i \(0.477217\pi\)
\(338\) 0 0
\(339\) 8.27324 0.449341
\(340\) 0 0
\(341\) 13.4589 23.3116i 0.728842 1.26239i
\(342\) 0 0
\(343\) 13.7459i 0.742211i
\(344\) 0 0
\(345\) −4.72161 + 2.72602i −0.254203 + 0.146764i
\(346\) 0 0
\(347\) 3.71375 + 6.43240i 0.199364 + 0.345309i 0.948323 0.317308i \(-0.102779\pi\)
−0.748958 + 0.662617i \(0.769446\pi\)
\(348\) 0 0
\(349\) 9.73318 + 5.61946i 0.521005 + 0.300803i 0.737346 0.675515i \(-0.236079\pi\)
−0.216341 + 0.976318i \(0.569412\pi\)
\(350\) 0 0
\(351\) −25.1183 + 25.2964i −1.34072 + 1.35022i
\(352\) 0 0
\(353\) 3.02944 + 1.74905i 0.161241 + 0.0930924i 0.578449 0.815718i \(-0.303658\pi\)
−0.417208 + 0.908811i \(0.636991\pi\)
\(354\) 0 0
\(355\) 2.08131 + 3.60493i 0.110464 + 0.191330i
\(356\) 0 0
\(357\) 52.7963 30.4820i 2.79428 1.61328i
\(358\) 0 0
\(359\) 32.3856i 1.70925i 0.519246 + 0.854625i \(0.326213\pi\)
−0.519246 + 0.854625i \(0.673787\pi\)
\(360\) 0 0
\(361\) −4.79435 + 8.30406i −0.252334 + 0.437056i
\(362\) 0 0
\(363\) 83.2714 4.37062
\(364\) 0 0
\(365\) −11.7104 −0.612949
\(366\) 0 0
\(367\) 6.25931 10.8414i 0.326734 0.565919i −0.655128 0.755518i \(-0.727385\pi\)
0.981862 + 0.189599i \(0.0607187\pi\)
\(368\) 0 0
\(369\) 46.1963i 2.40488i
\(370\) 0 0
\(371\) −20.9359 + 12.0873i −1.08694 + 0.627544i
\(372\) 0 0
\(373\) 8.65692 + 14.9942i 0.448238 + 0.776372i 0.998271 0.0587712i \(-0.0187183\pi\)
−0.550033 + 0.835143i \(0.685385\pi\)
\(374\) 0 0
\(375\) −2.63402 1.52075i −0.136020 0.0785313i
\(376\) 0 0
\(377\) 2.81995 + 10.3774i 0.145235 + 0.534465i
\(378\) 0 0
\(379\) −12.3989 7.15848i −0.636886 0.367706i 0.146528 0.989207i \(-0.453190\pi\)
−0.783414 + 0.621500i \(0.786524\pi\)
\(380\) 0 0
\(381\) 11.2731 + 19.5256i 0.577540 + 1.00033i
\(382\) 0 0
\(383\) −24.4985 + 14.1442i −1.25182 + 0.722736i −0.971470 0.237163i \(-0.923782\pi\)
−0.280346 + 0.959899i \(0.590449\pi\)
\(384\) 0 0
\(385\) 19.1470i 0.975824i
\(386\) 0 0
\(387\) 16.5639 28.6895i 0.841990 1.45837i
\(388\) 0 0
\(389\) 12.7931 0.648638 0.324319 0.945948i \(-0.394865\pi\)
0.324319 + 0.945948i \(0.394865\pi\)
\(390\) 0 0
\(391\) −11.6251 −0.587907
\(392\) 0 0
\(393\) 18.6749 32.3459i 0.942024 1.63163i
\(394\) 0 0
\(395\) 6.58127i 0.331140i
\(396\) 0 0
\(397\) −13.9023 + 8.02648i −0.697735 + 0.402838i −0.806503 0.591229i \(-0.798643\pi\)
0.108768 + 0.994067i \(0.465309\pi\)
\(398\) 0 0
\(399\) 14.4192 + 24.9748i 0.721864 + 1.25031i
\(400\) 0 0
\(401\) −16.9103 9.76314i −0.844458 0.487548i 0.0143191 0.999897i \(-0.495442\pi\)
−0.858777 + 0.512349i \(0.828775\pi\)
\(402\) 0 0
\(403\) −11.1169 11.0386i −0.553771 0.549873i
\(404\) 0 0
\(405\) −9.80314 5.65985i −0.487122 0.281240i
\(406\) 0 0
\(407\) −29.7534 51.5344i −1.47482 2.55447i
\(408\) 0 0
\(409\) 13.1641 7.60030i 0.650923 0.375810i −0.137887 0.990448i \(-0.544031\pi\)
0.788810 + 0.614637i \(0.210698\pi\)
\(410\) 0 0
\(411\) 44.2925i 2.18479i
\(412\) 0 0
\(413\) −2.16095 + 3.74288i −0.106334 + 0.184175i
\(414\) 0 0
\(415\) 4.46298 0.219079
\(416\) 0 0
\(417\) 7.44975 0.364816
\(418\) 0 0
\(419\) −9.67886 + 16.7643i −0.472843 + 0.818989i −0.999517 0.0310787i \(-0.990106\pi\)
0.526673 + 0.850068i \(0.323439\pi\)
\(420\) 0 0
\(421\) 30.6285i 1.49274i −0.665530 0.746371i \(-0.731795\pi\)
0.665530 0.746371i \(-0.268205\pi\)
\(422\) 0 0
\(423\) 18.7364 10.8175i 0.910996 0.525964i
\(424\) 0 0
\(425\) −3.24262 5.61638i −0.157290 0.272434i
\(426\) 0 0
\(427\) −26.3516 15.2141i −1.27524 0.736261i
\(428\) 0 0
\(429\) 17.3514 65.6834i 0.837732 3.17122i
\(430\) 0 0
\(431\) 13.3769 + 7.72314i 0.644341 + 0.372011i 0.786285 0.617864i \(-0.212002\pi\)
−0.141943 + 0.989875i \(0.545335\pi\)
\(432\) 0 0
\(433\) −13.3779 23.1713i −0.642903 1.11354i −0.984782 0.173796i \(-0.944397\pi\)
0.341879 0.939744i \(-0.388937\pi\)
\(434\) 0 0
\(435\) −7.85612 + 4.53573i −0.376672 + 0.217472i
\(436\) 0 0
\(437\) 5.49915i 0.263060i
\(438\) 0 0
\(439\) 14.5047 25.1229i 0.692272 1.19905i −0.278819 0.960344i \(-0.589943\pi\)
0.971092 0.238707i \(-0.0767236\pi\)
\(440\) 0 0
\(441\) −15.9551 −0.759766
\(442\) 0 0
\(443\) 19.9797 0.949264 0.474632 0.880184i \(-0.342581\pi\)
0.474632 + 0.880184i \(0.342581\pi\)
\(444\) 0 0
\(445\) 5.80904 10.0616i 0.275375 0.476964i
\(446\) 0 0
\(447\) 24.5683i 1.16204i
\(448\) 0 0
\(449\) 24.2193 13.9830i 1.14298 0.659900i 0.195814 0.980641i \(-0.437265\pi\)
0.947167 + 0.320741i \(0.103932\pi\)
\(450\) 0 0
\(451\) −22.8922 39.6505i −1.07795 1.86707i
\(452\) 0 0
\(453\) 13.5438 + 7.81949i 0.636341 + 0.367392i
\(454\) 0 0
\(455\) 10.7741 + 2.84617i 0.505099 + 0.133430i
\(456\) 0 0
\(457\) 28.0087 + 16.1708i 1.31019 + 0.756439i 0.982128 0.188216i \(-0.0602706\pi\)
0.328064 + 0.944656i \(0.393604\pi\)
\(458\) 0 0
\(459\) −32.0604 55.5303i −1.49645 2.59193i
\(460\) 0 0
\(461\) −1.68552 + 0.973133i −0.0785023 + 0.0453233i −0.538737 0.842474i \(-0.681098\pi\)
0.460235 + 0.887797i \(0.347765\pi\)
\(462\) 0 0
\(463\) 36.4860i 1.69565i −0.530279 0.847823i \(-0.677913\pi\)
0.530279 0.847823i \(-0.322087\pi\)
\(464\) 0 0
\(465\) 6.60779 11.4450i 0.306429 0.530750i
\(466\) 0 0
\(467\) 35.9368 1.66296 0.831479 0.555556i \(-0.187495\pi\)
0.831479 + 0.555556i \(0.187495\pi\)
\(468\) 0 0
\(469\) 5.44745 0.251540
\(470\) 0 0
\(471\) 15.9341 27.5987i 0.734205 1.27168i
\(472\) 0 0
\(473\) 32.8324i 1.50964i
\(474\) 0 0
\(475\) 2.65678 1.53389i 0.121901 0.0703798i
\(476\) 0 0
\(477\) 24.4458 + 42.3414i 1.11930 + 1.93868i
\(478\) 0 0
\(479\) −15.6767 9.05094i −0.716286 0.413548i 0.0970982 0.995275i \(-0.469044\pi\)
−0.813384 + 0.581727i \(0.802377\pi\)
\(480\) 0 0
\(481\) −33.4214 + 9.08189i −1.52389 + 0.414099i
\(482\) 0 0
\(483\) 14.5931 + 8.42536i 0.664011 + 0.383367i
\(484\) 0 0
\(485\) −6.14254 10.6392i −0.278918 0.483101i
\(486\) 0 0
\(487\) −11.7913 + 6.80773i −0.534317 + 0.308488i −0.742772 0.669544i \(-0.766490\pi\)
0.208456 + 0.978032i \(0.433156\pi\)
\(488\) 0 0
\(489\) 2.71730i 0.122881i
\(490\) 0 0
\(491\) 18.5371 32.1071i 0.836565 1.44897i −0.0561840 0.998420i \(-0.517893\pi\)
0.892749 0.450553i \(-0.148773\pi\)
\(492\) 0 0
\(493\) −19.3426 −0.871146
\(494\) 0 0
\(495\) 38.7236 1.74050
\(496\) 0 0
\(497\) 6.43272 11.1418i 0.288547 0.499778i
\(498\) 0 0
\(499\) 10.5828i 0.473749i −0.971540 0.236875i \(-0.923877\pi\)
0.971540 0.236875i \(-0.0761231\pi\)
\(500\) 0 0
\(501\) −20.6392 + 11.9161i −0.922093 + 0.532370i
\(502\) 0 0
\(503\) −5.43223 9.40891i −0.242211 0.419522i 0.719133 0.694873i \(-0.244539\pi\)
−0.961344 + 0.275351i \(0.911206\pi\)
\(504\) 0 0
\(505\) −8.80797 5.08529i −0.391950 0.226292i
\(506\) 0 0
\(507\) −34.3811 19.5274i −1.52692 0.867242i
\(508\) 0 0
\(509\) −11.6029 6.69892i −0.514288 0.296924i 0.220306 0.975431i \(-0.429294\pi\)
−0.734595 + 0.678506i \(0.762628\pi\)
\(510\) 0 0
\(511\) 18.0967 + 31.3444i 0.800551 + 1.38659i
\(512\) 0 0
\(513\) 26.2681 15.1659i 1.15976 0.669591i
\(514\) 0 0
\(515\) 6.53156i 0.287815i
\(516\) 0 0
\(517\) −10.7210 + 18.5694i −0.471511 + 0.816680i
\(518\) 0 0
\(519\) 58.5081 2.56822
\(520\) 0 0
\(521\) 18.5320 0.811900 0.405950 0.913895i \(-0.366941\pi\)
0.405950 + 0.913895i \(0.366941\pi\)
\(522\) 0 0
\(523\) −17.5432 + 30.3858i −0.767113 + 1.32868i 0.172010 + 0.985095i \(0.444974\pi\)
−0.939122 + 0.343583i \(0.888359\pi\)
\(524\) 0 0
\(525\) 9.40042i 0.410268i
\(526\) 0 0
\(527\) 24.4036 14.0894i 1.06304 0.613745i
\(528\) 0 0
\(529\) 9.89338 + 17.1358i 0.430147 + 0.745037i
\(530\) 0 0
\(531\) 7.56972 + 4.37038i 0.328498 + 0.189658i
\(532\) 0 0
\(533\) −25.7144 + 6.98760i −1.11381 + 0.302666i
\(534\) 0 0
\(535\) 15.7656 + 9.10227i 0.681606 + 0.393525i
\(536\) 0 0
\(537\) 0.349969 + 0.606164i 0.0151023 + 0.0261579i
\(538\) 0 0
\(539\) 13.6943 7.90641i 0.589856 0.340553i
\(540\) 0 0
\(541\) 41.0429i 1.76457i −0.470714 0.882286i \(-0.656004\pi\)
0.470714 0.882286i \(-0.343996\pi\)
\(542\) 0 0
\(543\) 14.0940 24.4116i 0.604833 1.04760i
\(544\) 0 0
\(545\) 14.6401 0.627115
\(546\) 0 0
\(547\) 27.7275 1.18554 0.592771 0.805371i \(-0.298034\pi\)
0.592771 + 0.805371i \(0.298034\pi\)
\(548\) 0 0
\(549\) −30.7695 + 53.2943i −1.31321 + 2.27454i
\(550\) 0 0
\(551\) 9.14984i 0.389796i
\(552\) 0 0
\(553\) −17.6157 + 10.1704i −0.749094 + 0.432490i
\(554\) 0 0
\(555\) −14.6077 25.3013i −0.620063 1.07398i
\(556\) 0 0
\(557\) −12.0043 6.93067i −0.508637 0.293662i 0.223636 0.974673i \(-0.428207\pi\)
−0.732273 + 0.681011i \(0.761541\pi\)
\(558\) 0 0
\(559\) 18.4750 + 4.88047i 0.781408 + 0.206422i
\(560\) 0 0
\(561\) 105.825 + 61.0981i 4.46794 + 2.57956i
\(562\) 0 0
\(563\) 16.6980 + 28.9218i 0.703738 + 1.21891i 0.967145 + 0.254225i \(0.0818203\pi\)
−0.263407 + 0.964685i \(0.584846\pi\)
\(564\) 0 0
\(565\) −2.35569 + 1.36006i −0.0991045 + 0.0572180i
\(566\) 0 0
\(567\) 34.9859i 1.46927i
\(568\) 0 0
\(569\) 14.7539 25.5546i 0.618517 1.07130i −0.371240 0.928537i \(-0.621067\pi\)
0.989757 0.142766i \(-0.0455995\pi\)
\(570\) 0 0
\(571\) −40.4206 −1.69155 −0.845775 0.533540i \(-0.820861\pi\)
−0.845775 + 0.533540i \(0.820861\pi\)
\(572\) 0 0
\(573\) 6.56637 0.274314
\(574\) 0 0
\(575\) 0.896274 1.55239i 0.0373772 0.0647393i
\(576\) 0 0
\(577\) 16.2824i 0.677847i −0.940814 0.338924i \(-0.889937\pi\)
0.940814 0.338924i \(-0.110063\pi\)
\(578\) 0 0
\(579\) 54.2096 31.2979i 2.25287 1.30070i
\(580\) 0 0
\(581\) −6.89689 11.9458i −0.286131 0.495594i
\(582\) 0 0
\(583\) −41.9639 24.2279i −1.73797 1.00342i
\(584\) 0 0
\(585\) 5.75618 21.7900i 0.237989 0.900904i
\(586\) 0 0
\(587\) 6.62733 + 3.82629i 0.273539 + 0.157928i 0.630495 0.776193i \(-0.282852\pi\)
−0.356956 + 0.934121i \(0.616185\pi\)
\(588\) 0 0
\(589\) 6.66488 + 11.5439i 0.274622 + 0.475658i
\(590\) 0 0
\(591\) −16.3363 + 9.43179i −0.671987 + 0.387972i
\(592\) 0 0
\(593\) 14.4087i 0.591695i 0.955235 + 0.295848i \(0.0956021\pi\)
−0.955235 + 0.295848i \(0.904398\pi\)
\(594\) 0 0
\(595\) −10.0220 + 17.3586i −0.410862 + 0.711634i
\(596\) 0 0
\(597\) 14.7734 0.604636
\(598\) 0 0
\(599\) −3.99980 −0.163427 −0.0817136 0.996656i \(-0.526039\pi\)
−0.0817136 + 0.996656i \(0.526039\pi\)
\(600\) 0 0
\(601\) 0.0101359 0.0175559i 0.000413451 0.000716119i −0.865819 0.500358i \(-0.833202\pi\)
0.866232 + 0.499642i \(0.166535\pi\)
\(602\) 0 0
\(603\) 11.0171i 0.448651i
\(604\) 0 0
\(605\) −23.7104 + 13.6892i −0.963963 + 0.556544i
\(606\) 0 0
\(607\) 5.89836 + 10.2163i 0.239407 + 0.414665i 0.960544 0.278127i \(-0.0897136\pi\)
−0.721137 + 0.692792i \(0.756380\pi\)
\(608\) 0 0
\(609\) 24.2810 + 14.0186i 0.983916 + 0.568064i
\(610\) 0 0
\(611\) 8.85541 + 8.79308i 0.358252 + 0.355730i
\(612\) 0 0
\(613\) −17.1624 9.90874i −0.693184 0.400210i 0.111620 0.993751i \(-0.464396\pi\)
−0.804804 + 0.593541i \(0.797730\pi\)
\(614\) 0 0
\(615\) −11.2392 19.4668i −0.453206 0.784976i
\(616\) 0 0
\(617\) −7.71489 + 4.45419i −0.310590 + 0.179319i −0.647190 0.762328i \(-0.724056\pi\)
0.336601 + 0.941647i \(0.390723\pi\)
\(618\) 0 0
\(619\) 17.6823i 0.710710i 0.934731 + 0.355355i \(0.115640\pi\)
−0.934731 + 0.355355i \(0.884360\pi\)
\(620\) 0 0
\(621\) 8.86164 15.3488i 0.355605 0.615927i
\(622\) 0 0
\(623\) −35.9082 −1.43863
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −28.9019 + 50.0596i −1.15423 + 1.99919i
\(628\) 0 0
\(629\) 62.2944i 2.48384i
\(630\) 0 0
\(631\) −12.1488 + 7.01411i −0.483636 + 0.279227i −0.721930 0.691966i \(-0.756745\pi\)
0.238295 + 0.971193i \(0.423412\pi\)
\(632\) 0 0
\(633\) −1.50435 2.60561i −0.0597925 0.103564i
\(634\) 0 0
\(635\) −6.41972 3.70643i −0.254759 0.147085i
\(636\) 0 0
\(637\) −2.41334 8.88112i −0.0956202 0.351883i
\(638\) 0 0
\(639\) −22.5335 13.0097i −0.891412 0.514657i
\(640\) 0 0
\(641\) 0.933393 + 1.61668i 0.0368668 + 0.0638552i 0.883870 0.467733i \(-0.154929\pi\)
−0.847003 + 0.531588i \(0.821596\pi\)
\(642\) 0 0
\(643\) −20.9377 + 12.0884i −0.825702 + 0.476719i −0.852379 0.522925i \(-0.824841\pi\)
0.0266766 + 0.999644i \(0.491508\pi\)
\(644\) 0 0
\(645\) 16.1194i 0.634700i
\(646\) 0 0
\(647\) −15.0185 + 26.0128i −0.590438 + 1.02267i 0.403735 + 0.914876i \(0.367712\pi\)
−0.994173 + 0.107793i \(0.965622\pi\)
\(648\) 0 0
\(649\) −8.66283 −0.340046
\(650\) 0 0
\(651\) −40.8455 −1.60086
\(652\) 0 0
\(653\) −11.5424 + 19.9920i −0.451689 + 0.782347i −0.998491 0.0549141i \(-0.982512\pi\)
0.546803 + 0.837262i \(0.315845\pi\)
\(654\) 0 0
\(655\) 12.2800i 0.479820i
\(656\) 0 0
\(657\) 63.3919 36.5993i 2.47315 1.42788i
\(658\) 0 0
\(659\) −9.25948 16.0379i −0.360698 0.624747i 0.627378 0.778715i \(-0.284128\pi\)
−0.988076 + 0.153968i \(0.950795\pi\)
\(660\) 0 0
\(661\) −10.3917 5.99967i −0.404192 0.233360i 0.284099 0.958795i \(-0.408305\pi\)
−0.688291 + 0.725435i \(0.741639\pi\)
\(662\) 0 0
\(663\) 50.1108 50.4661i 1.94614 1.95994i
\(664\) 0 0
\(665\) −8.21134 4.74082i −0.318422 0.183841i
\(666\) 0 0
\(667\) −2.67319 4.63010i −0.103506 0.179278i
\(668\) 0 0
\(669\) −6.32994 + 3.65459i −0.244729 + 0.141295i
\(670\) 0 0
\(671\) 60.9902i 2.35450i
\(672\) 0 0
\(673\) −22.2641 + 38.5625i −0.858218 + 1.48648i 0.0154099 + 0.999881i \(0.495095\pi\)
−0.873628 + 0.486595i \(0.838239\pi\)
\(674\) 0 0
\(675\) 9.88720 0.380558
\(676\) 0 0
\(677\) 4.47823 0.172112 0.0860561 0.996290i \(-0.472574\pi\)
0.0860561 + 0.996290i \(0.472574\pi\)
\(678\) 0 0
\(679\) −18.9848 + 32.8827i −0.728571 + 1.26192i
\(680\) 0 0
\(681\) 80.4428i 3.08258i
\(682\) 0 0
\(683\) 3.98035 2.29806i 0.152304 0.0879326i −0.421911 0.906637i \(-0.638641\pi\)
0.574215 + 0.818704i \(0.305307\pi\)
\(684\) 0 0
\(685\) −7.28134 12.6117i −0.278206 0.481867i
\(686\) 0 0
\(687\) −1.88404 1.08775i −0.0718805 0.0415003i
\(688\) 0 0
\(689\) −19.8710 + 20.0119i −0.757025 + 0.762392i
\(690\) 0 0
\(691\) 2.86876 + 1.65628i 0.109133 + 0.0630078i 0.553573 0.832801i \(-0.313264\pi\)
−0.444440 + 0.895809i \(0.646597\pi\)
\(692\) 0 0
\(693\) −59.8418 103.649i −2.27320 3.93730i
\(694\) 0 0
\(695\) −2.12121 + 1.22468i −0.0804621 + 0.0464548i
\(696\) 0 0
\(697\) 47.9293i 1.81545i
\(698\) 0 0
\(699\) −14.1055 + 24.4314i −0.533519 + 0.924082i
\(700\) 0 0
\(701\) 44.4676 1.67952 0.839759 0.542959i \(-0.182696\pi\)
0.839759 + 0.542959i \(0.182696\pi\)
\(702\) 0 0
\(703\) 29.4678 1.11140
\(704\) 0 0
\(705\) −5.26359 + 9.11681i −0.198238 + 0.343359i
\(706\) 0 0
\(707\) 31.4343i 1.18221i
\(708\) 0 0
\(709\) 13.8293 7.98436i 0.519371 0.299859i −0.217306 0.976103i \(-0.569727\pi\)
0.736677 + 0.676244i \(0.236394\pi\)
\(710\) 0 0
\(711\) 20.5690 + 35.6265i 0.771396 + 1.33610i
\(712\) 0 0
\(713\) 6.74526 + 3.89438i 0.252612 + 0.145846i
\(714\) 0 0
\(715\) 5.85728 + 21.5548i 0.219050 + 0.806105i
\(716\) 0 0
\(717\) −33.9206 19.5841i −1.26679 0.731381i
\(718\) 0 0
\(719\) −17.2084 29.8058i −0.641764 1.11157i −0.985039 0.172333i \(-0.944869\pi\)
0.343274 0.939235i \(-0.388464\pi\)
\(720\) 0 0
\(721\) −17.4826 + 10.0936i −0.651086 + 0.375905i
\(722\) 0 0
\(723\) 10.6249i 0.395143i
\(724\) 0 0
\(725\) 1.49128 2.58297i 0.0553847 0.0959291i
\(726\) 0 0
\(727\) 7.77676 0.288424 0.144212 0.989547i \(-0.453935\pi\)
0.144212 + 0.989547i \(0.453935\pi\)
\(728\) 0 0
\(729\) −19.4592 −0.720712
\(730\) 0 0
\(731\) −17.1852 + 29.7657i −0.635619 + 1.10092i
\(732\) 0 0
\(733\) 0.931223i 0.0343955i −0.999852 0.0171978i \(-0.994526\pi\)
0.999852 0.0171978i \(-0.00547448\pi\)
\(734\) 0 0
\(735\) 6.72335 3.88173i 0.247994 0.143180i
\(736\) 0 0
\(737\) 5.45943 + 9.45601i 0.201101 + 0.348317i
\(738\) 0 0
\(739\) −33.3027 19.2273i −1.22506 0.707288i −0.259066 0.965860i \(-0.583415\pi\)
−0.965992 + 0.258572i \(0.916748\pi\)
\(740\) 0 0
\(741\) 23.8725 + 23.7045i 0.876980 + 0.870806i
\(742\) 0 0
\(743\) 36.8202 + 21.2582i 1.35080 + 0.779886i 0.988362 0.152121i \(-0.0486103\pi\)
0.362440 + 0.932007i \(0.381944\pi\)
\(744\) 0 0
\(745\) 4.03885 + 6.99549i 0.147972 + 0.256295i
\(746\) 0 0
\(747\) −24.1595 + 13.9485i −0.883950 + 0.510349i
\(748\) 0 0
\(749\) 56.2650i 2.05588i
\(750\) 0 0
\(751\) 7.05453 12.2188i 0.257423 0.445870i −0.708128 0.706085i \(-0.750460\pi\)
0.965551 + 0.260214i \(0.0837932\pi\)
\(752\) 0 0
\(753\) −33.6456 −1.22611
\(754\) 0 0
\(755\) −5.14185 −0.187131
\(756\) 0 0
\(757\) −12.5112 + 21.6700i −0.454727 + 0.787610i −0.998672 0.0515105i \(-0.983596\pi\)
0.543946 + 0.839120i \(0.316930\pi\)
\(758\) 0 0
\(759\) 33.7756i 1.22598i
\(760\) 0 0
\(761\) −14.2177 + 8.20862i −0.515393 + 0.297562i −0.735048 0.678015i \(-0.762840\pi\)
0.219655 + 0.975578i \(0.429507\pi\)
\(762\) 0 0
\(763\) −22.6242 39.1863i −0.819052 1.41864i
\(764\) 0 0
\(765\) 35.1066 + 20.2688i 1.26928 + 0.732821i
\(766\) 0 0
\(767\) −1.28771 + 4.87461i −0.0464966 + 0.176012i
\(768\) 0 0
\(769\) −16.6459 9.61052i −0.600267 0.346564i 0.168880 0.985637i \(-0.445985\pi\)
−0.769146 + 0.639073i \(0.779318\pi\)
\(770\) 0 0
\(771\) 0.855406 + 1.48161i 0.0308067 + 0.0533588i
\(772\) 0 0
\(773\) −11.1605 + 6.44353i −0.401416 + 0.231758i −0.687095 0.726568i \(-0.741114\pi\)
0.285679 + 0.958325i \(0.407781\pi\)
\(774\) 0 0
\(775\) 4.34508i 0.156080i
\(776\) 0 0
\(777\) −45.1482 + 78.1990i −1.61968 + 2.80537i
\(778\) 0 0
\(779\) 22.6725 0.812327
\(780\) 0 0
\(781\) 25.7875 0.922749
\(782\) 0 0
\(783\) 14.7446 25.5383i 0.526928 0.912665i
\(784\) 0 0
\(785\) 10.4778i 0.373968i
\(786\) 0 0
\(787\) 16.5436 9.55146i 0.589716 0.340473i −0.175269 0.984521i \(-0.556080\pi\)
0.764985 + 0.644048i \(0.222746\pi\)
\(788\) 0 0
\(789\)