Properties

Label 270.3.b.d.269.1
Level $270$
Weight $3$
Character 270.269
Analytic conductor $7.357$
Analytic rank $0$
Dimension $4$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [270,3,Mod(269,270)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(270, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("270.269");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 270.b (of order \(2\), degree \(1\), 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: \(7.35696713773\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.31744.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 14x^{2} + 31 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 269.1
Root \(-3.35300i\) of defining polynomial
Character \(\chi\) \(=\) 270.269
Dual form 270.3.b.d.269.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421 q^{2} +2.00000 q^{4} +(1.58579 - 4.74186i) q^{5} +0.813575i q^{7} -2.82843 q^{8} +O(q^{10})\) \(q-1.41421 q^{2} +2.00000 q^{4} +(1.58579 - 4.74186i) q^{5} +0.813575i q^{7} -2.82843 q^{8} +(-2.24264 + 6.70601i) q^{10} -15.3762i q^{11} +5.89243i q^{13} -1.15057i q^{14} +4.00000 q^{16} -12.8995 q^{17} +1.24264 q^{19} +(3.17157 - 9.48373i) q^{20} +21.7452i q^{22} -4.79899 q^{23} +(-19.9706 - 15.0392i) q^{25} -8.33316i q^{26} +1.62715i q^{28} -42.6768i q^{29} +4.21320 q^{31} -5.65685 q^{32} +18.2426 q^{34} +(3.85786 + 1.29016i) q^{35} -70.3144i q^{37} -1.75736 q^{38} +(-4.48528 + 13.4120i) q^{40} -7.04300i q^{41} -41.0496i q^{43} -30.7523i q^{44} +6.78680 q^{46} -79.7990 q^{47} +48.3381 q^{49} +(28.2426 + 21.2686i) q^{50} +11.7849i q^{52} +63.7279 q^{53} +(-72.9117 - 24.3833i) q^{55} -2.30114i q^{56} +60.3541i q^{58} +36.6448i q^{59} -82.9411 q^{61} -5.95837 q^{62} +8.00000 q^{64} +(27.9411 + 9.34414i) q^{65} +89.0027i q^{67} -25.7990 q^{68} +(-5.45584 - 1.82456i) q^{70} +69.6982i q^{71} -89.6188i q^{73} +99.4396i q^{74} +2.48528 q^{76} +12.5097 q^{77} +134.095 q^{79} +(6.34315 - 18.9675i) q^{80} +9.96031i q^{82} +109.024 q^{83} +(-20.4558 + 61.1677i) q^{85} +58.0529i q^{86} +43.4904i q^{88} +137.514i q^{89} -4.79394 q^{91} -9.59798 q^{92} +112.853 q^{94} +(1.97056 - 5.89243i) q^{95} -90.6298i q^{97} -68.3604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{4} + 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{4} + 12 q^{5} + 8 q^{10} + 16 q^{16} - 12 q^{17} - 12 q^{19} + 24 q^{20} + 60 q^{23} - 12 q^{25} - 68 q^{31} + 56 q^{34} + 72 q^{35} - 24 q^{38} + 16 q^{40} + 112 q^{46} - 240 q^{47} - 180 q^{49} + 96 q^{50} + 204 q^{53} - 88 q^{55} - 196 q^{61} - 120 q^{62} + 32 q^{64} - 24 q^{65} - 24 q^{68} + 80 q^{70} - 24 q^{76} - 312 q^{77} + 180 q^{79} + 48 q^{80} + 108 q^{83} + 20 q^{85} + 456 q^{91} + 120 q^{92} + 112 q^{94} - 60 q^{95} - 528 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(217\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 0 0
\(4\) 2.00000 0.500000
\(5\) 1.58579 4.74186i 0.317157 0.948373i
\(6\) 0 0
\(7\) 0.813575i 0.116225i 0.998310 + 0.0581125i \(0.0185082\pi\)
−0.998310 + 0.0581125i \(0.981492\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) −2.24264 + 6.70601i −0.224264 + 0.670601i
\(11\) 15.3762i 1.39783i −0.715203 0.698917i \(-0.753666\pi\)
0.715203 0.698917i \(-0.246334\pi\)
\(12\) 0 0
\(13\) 5.89243i 0.453264i 0.973980 + 0.226632i \(0.0727715\pi\)
−0.973980 + 0.226632i \(0.927229\pi\)
\(14\) 1.15057i 0.0821835i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) −12.8995 −0.758794 −0.379397 0.925234i \(-0.623869\pi\)
−0.379397 + 0.925234i \(0.623869\pi\)
\(18\) 0 0
\(19\) 1.24264 0.0654021 0.0327011 0.999465i \(-0.489589\pi\)
0.0327011 + 0.999465i \(0.489589\pi\)
\(20\) 3.17157 9.48373i 0.158579 0.474186i
\(21\) 0 0
\(22\) 21.7452i 0.988417i
\(23\) −4.79899 −0.208652 −0.104326 0.994543i \(-0.533268\pi\)
−0.104326 + 0.994543i \(0.533268\pi\)
\(24\) 0 0
\(25\) −19.9706 15.0392i −0.798823 0.601567i
\(26\) 8.33316i 0.320506i
\(27\) 0 0
\(28\) 1.62715i 0.0581125i
\(29\) 42.6768i 1.47161i −0.677192 0.735807i \(-0.736803\pi\)
0.677192 0.735807i \(-0.263197\pi\)
\(30\) 0 0
\(31\) 4.21320 0.135910 0.0679549 0.997688i \(-0.478353\pi\)
0.0679549 + 0.997688i \(0.478353\pi\)
\(32\) −5.65685 −0.176777
\(33\) 0 0
\(34\) 18.2426 0.536548
\(35\) 3.85786 + 1.29016i 0.110225 + 0.0368616i
\(36\) 0 0
\(37\) 70.3144i 1.90039i −0.311657 0.950195i \(-0.600884\pi\)
0.311657 0.950195i \(-0.399116\pi\)
\(38\) −1.75736 −0.0462463
\(39\) 0 0
\(40\) −4.48528 + 13.4120i −0.112132 + 0.335300i
\(41\) 7.04300i 0.171781i −0.996305 0.0858903i \(-0.972627\pi\)
0.996305 0.0858903i \(-0.0273735\pi\)
\(42\) 0 0
\(43\) 41.0496i 0.954643i −0.878729 0.477321i \(-0.841608\pi\)
0.878729 0.477321i \(-0.158392\pi\)
\(44\) 30.7523i 0.698917i
\(45\) 0 0
\(46\) 6.78680 0.147539
\(47\) −79.7990 −1.69785 −0.848925 0.528513i \(-0.822750\pi\)
−0.848925 + 0.528513i \(0.822750\pi\)
\(48\) 0 0
\(49\) 48.3381 0.986492
\(50\) 28.2426 + 21.2686i 0.564853 + 0.425372i
\(51\) 0 0
\(52\) 11.7849i 0.226632i
\(53\) 63.7279 1.20241 0.601207 0.799093i \(-0.294687\pi\)
0.601207 + 0.799093i \(0.294687\pi\)
\(54\) 0 0
\(55\) −72.9117 24.3833i −1.32567 0.443333i
\(56\) 2.30114i 0.0410918i
\(57\) 0 0
\(58\) 60.3541i 1.04059i
\(59\) 36.6448i 0.621098i 0.950557 + 0.310549i \(0.100513\pi\)
−0.950557 + 0.310549i \(0.899487\pi\)
\(60\) 0 0
\(61\) −82.9411 −1.35969 −0.679845 0.733356i \(-0.737953\pi\)
−0.679845 + 0.733356i \(0.737953\pi\)
\(62\) −5.95837 −0.0961027
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 27.9411 + 9.34414i 0.429863 + 0.143756i
\(66\) 0 0
\(67\) 89.0027i 1.32840i 0.747556 + 0.664199i \(0.231227\pi\)
−0.747556 + 0.664199i \(0.768773\pi\)
\(68\) −25.7990 −0.379397
\(69\) 0 0
\(70\) −5.45584 1.82456i −0.0779406 0.0260651i
\(71\) 69.6982i 0.981665i 0.871254 + 0.490833i \(0.163307\pi\)
−0.871254 + 0.490833i \(0.836693\pi\)
\(72\) 0 0
\(73\) 89.6188i 1.22766i −0.789440 0.613828i \(-0.789629\pi\)
0.789440 0.613828i \(-0.210371\pi\)
\(74\) 99.4396i 1.34378i
\(75\) 0 0
\(76\) 2.48528 0.0327011
\(77\) 12.5097 0.162463
\(78\) 0 0
\(79\) 134.095 1.69741 0.848705 0.528866i \(-0.177383\pi\)
0.848705 + 0.528866i \(0.177383\pi\)
\(80\) 6.34315 18.9675i 0.0792893 0.237093i
\(81\) 0 0
\(82\) 9.96031i 0.121467i
\(83\) 109.024 1.31355 0.656773 0.754088i \(-0.271921\pi\)
0.656773 + 0.754088i \(0.271921\pi\)
\(84\) 0 0
\(85\) −20.4558 + 61.1677i −0.240657 + 0.719620i
\(86\) 58.0529i 0.675034i
\(87\) 0 0
\(88\) 43.4904i 0.494209i
\(89\) 137.514i 1.54510i 0.634953 + 0.772551i \(0.281020\pi\)
−0.634953 + 0.772551i \(0.718980\pi\)
\(90\) 0 0
\(91\) −4.79394 −0.0526807
\(92\) −9.59798 −0.104326
\(93\) 0 0
\(94\) 112.853 1.20056
\(95\) 1.97056 5.89243i 0.0207428 0.0620256i
\(96\) 0 0
\(97\) 90.6298i 0.934328i −0.884171 0.467164i \(-0.845276\pi\)
0.884171 0.467164i \(-0.154724\pi\)
\(98\) −68.3604 −0.697555
\(99\) 0 0
\(100\) −39.9411 30.0783i −0.399411 0.300783i
\(101\) 49.7198i 0.492275i 0.969235 + 0.246138i \(0.0791615\pi\)
−0.969235 + 0.246138i \(0.920839\pi\)
\(102\) 0 0
\(103\) 128.844i 1.25091i 0.780259 + 0.625456i \(0.215087\pi\)
−0.780259 + 0.625456i \(0.784913\pi\)
\(104\) 16.6663i 0.160253i
\(105\) 0 0
\(106\) −90.1249 −0.850235
\(107\) 6.42641 0.0600599 0.0300299 0.999549i \(-0.490440\pi\)
0.0300299 + 0.999549i \(0.490440\pi\)
\(108\) 0 0
\(109\) 108.279 0.993387 0.496694 0.867926i \(-0.334547\pi\)
0.496694 + 0.867926i \(0.334547\pi\)
\(110\) 103.113 + 34.4832i 0.937388 + 0.313484i
\(111\) 0 0
\(112\) 3.25430i 0.0290563i
\(113\) −30.4264 −0.269260 −0.134630 0.990896i \(-0.542985\pi\)
−0.134630 + 0.990896i \(0.542985\pi\)
\(114\) 0 0
\(115\) −7.61017 + 22.7562i −0.0661754 + 0.197880i
\(116\) 85.3536i 0.735807i
\(117\) 0 0
\(118\) 51.8235i 0.439182i
\(119\) 10.4947i 0.0881909i
\(120\) 0 0
\(121\) −115.426 −0.953937
\(122\) 117.296 0.961446
\(123\) 0 0
\(124\) 8.42641 0.0679549
\(125\) −102.983 + 70.8488i −0.823862 + 0.566790i
\(126\) 0 0
\(127\) 133.725i 1.05296i 0.850189 + 0.526478i \(0.176488\pi\)
−0.850189 + 0.526478i \(0.823512\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 0 0
\(130\) −39.5147 13.2146i −0.303959 0.101651i
\(131\) 61.7838i 0.471632i −0.971798 0.235816i \(-0.924224\pi\)
0.971798 0.235816i \(-0.0757763\pi\)
\(132\) 0 0
\(133\) 1.01098i 0.00760137i
\(134\) 125.869i 0.939319i
\(135\) 0 0
\(136\) 36.4853 0.268274
\(137\) −163.919 −1.19649 −0.598244 0.801314i \(-0.704135\pi\)
−0.598244 + 0.801314i \(0.704135\pi\)
\(138\) 0 0
\(139\) 182.250 1.31115 0.655575 0.755130i \(-0.272426\pi\)
0.655575 + 0.755130i \(0.272426\pi\)
\(140\) 7.71573 + 2.58031i 0.0551123 + 0.0184308i
\(141\) 0 0
\(142\) 98.5682i 0.694142i
\(143\) 90.6030 0.633588
\(144\) 0 0
\(145\) −202.368 67.6763i −1.39564 0.466733i
\(146\) 126.740i 0.868084i
\(147\) 0 0
\(148\) 140.629i 0.950195i
\(149\) 189.535i 1.27205i −0.771670 0.636023i \(-0.780578\pi\)
0.771670 0.636023i \(-0.219422\pi\)
\(150\) 0 0
\(151\) −113.338 −0.750583 −0.375292 0.926907i \(-0.622457\pi\)
−0.375292 + 0.926907i \(0.622457\pi\)
\(152\) −3.51472 −0.0231231
\(153\) 0 0
\(154\) −17.6913 −0.114879
\(155\) 6.68124 19.9784i 0.0431048 0.128893i
\(156\) 0 0
\(157\) 113.189i 0.720946i −0.932770 0.360473i \(-0.882615\pi\)
0.932770 0.360473i \(-0.117385\pi\)
\(158\) −189.640 −1.20025
\(159\) 0 0
\(160\) −8.97056 + 26.8240i −0.0560660 + 0.167650i
\(161\) 3.90434i 0.0242506i
\(162\) 0 0
\(163\) 152.414i 0.935053i 0.883979 + 0.467527i \(0.154855\pi\)
−0.883979 + 0.467527i \(0.845145\pi\)
\(164\) 14.0860i 0.0858903i
\(165\) 0 0
\(166\) −154.184 −0.928818
\(167\) 105.853 0.633849 0.316925 0.948451i \(-0.397350\pi\)
0.316925 + 0.948451i \(0.397350\pi\)
\(168\) 0 0
\(169\) 134.279 0.794552
\(170\) 28.9289 86.5041i 0.170170 0.508848i
\(171\) 0 0
\(172\) 82.0993i 0.477321i
\(173\) 110.012 0.635909 0.317954 0.948106i \(-0.397004\pi\)
0.317954 + 0.948106i \(0.397004\pi\)
\(174\) 0 0
\(175\) 12.2355 16.2476i 0.0699171 0.0928432i
\(176\) 61.5047i 0.349458i
\(177\) 0 0
\(178\) 194.474i 1.09255i
\(179\) 118.407i 0.661492i −0.943720 0.330746i \(-0.892700\pi\)
0.943720 0.330746i \(-0.107300\pi\)
\(180\) 0 0
\(181\) 172.397 0.952469 0.476235 0.879318i \(-0.342001\pi\)
0.476235 + 0.879318i \(0.342001\pi\)
\(182\) 6.77965 0.0372508
\(183\) 0 0
\(184\) 13.5736 0.0737695
\(185\) −333.421 111.504i −1.80228 0.602722i
\(186\) 0 0
\(187\) 198.345i 1.06067i
\(188\) −159.598 −0.848925
\(189\) 0 0
\(190\) −2.78680 + 8.33316i −0.0146674 + 0.0438587i
\(191\) 289.393i 1.51515i −0.652749 0.757574i \(-0.726384\pi\)
0.652749 0.757574i \(-0.273616\pi\)
\(192\) 0 0
\(193\) 127.833i 0.662347i −0.943570 0.331173i \(-0.892555\pi\)
0.943570 0.331173i \(-0.107445\pi\)
\(194\) 128.170i 0.660670i
\(195\) 0 0
\(196\) 96.6762 0.493246
\(197\) 280.414 1.42342 0.711711 0.702472i \(-0.247920\pi\)
0.711711 + 0.702472i \(0.247920\pi\)
\(198\) 0 0
\(199\) 156.426 0.786062 0.393031 0.919525i \(-0.371426\pi\)
0.393031 + 0.919525i \(0.371426\pi\)
\(200\) 56.4853 + 42.5372i 0.282426 + 0.212686i
\(201\) 0 0
\(202\) 70.3144i 0.348091i
\(203\) 34.7208 0.171038
\(204\) 0 0
\(205\) −33.3970 11.1687i −0.162912 0.0544815i
\(206\) 182.213i 0.884528i
\(207\) 0 0
\(208\) 23.5697i 0.113316i
\(209\) 19.1070i 0.0914213i
\(210\) 0 0
\(211\) 22.5076 0.106671 0.0533355 0.998577i \(-0.483015\pi\)
0.0533355 + 0.998577i \(0.483015\pi\)
\(212\) 127.456 0.601207
\(213\) 0 0
\(214\) −9.08831 −0.0424687
\(215\) −194.652 65.0959i −0.905357 0.302772i
\(216\) 0 0
\(217\) 3.42776i 0.0157961i
\(218\) −153.130 −0.702431
\(219\) 0 0
\(220\) −145.823 48.7666i −0.662834 0.221666i
\(221\) 76.0094i 0.343934i
\(222\) 0 0
\(223\) 354.826i 1.59115i 0.605856 + 0.795575i \(0.292831\pi\)
−0.605856 + 0.795575i \(0.707169\pi\)
\(224\) 4.60228i 0.0205459i
\(225\) 0 0
\(226\) 43.0294 0.190396
\(227\) −415.098 −1.82862 −0.914312 0.405011i \(-0.867268\pi\)
−0.914312 + 0.405011i \(0.867268\pi\)
\(228\) 0 0
\(229\) −220.220 −0.961661 −0.480830 0.876814i \(-0.659665\pi\)
−0.480830 + 0.876814i \(0.659665\pi\)
\(230\) 10.7624 32.1821i 0.0467931 0.139922i
\(231\) 0 0
\(232\) 120.708i 0.520294i
\(233\) 10.0345 0.0430665 0.0215332 0.999768i \(-0.493145\pi\)
0.0215332 + 0.999768i \(0.493145\pi\)
\(234\) 0 0
\(235\) −126.544 + 378.396i −0.538486 + 1.61020i
\(236\) 73.2895i 0.310549i
\(237\) 0 0
\(238\) 14.8418i 0.0623603i
\(239\) 114.363i 0.478507i 0.970957 + 0.239253i \(0.0769027\pi\)
−0.970957 + 0.239253i \(0.923097\pi\)
\(240\) 0 0
\(241\) −63.7208 −0.264402 −0.132201 0.991223i \(-0.542204\pi\)
−0.132201 + 0.991223i \(0.542204\pi\)
\(242\) 163.238 0.674535
\(243\) 0 0
\(244\) −165.882 −0.679845
\(245\) 76.6539 229.213i 0.312873 0.935562i
\(246\) 0 0
\(247\) 7.32218i 0.0296444i
\(248\) −11.9167 −0.0480514
\(249\) 0 0
\(250\) 145.640 100.195i 0.582558 0.400781i
\(251\) 229.631i 0.914866i 0.889244 + 0.457433i \(0.151231\pi\)
−0.889244 + 0.457433i \(0.848769\pi\)
\(252\) 0 0
\(253\) 73.7901i 0.291660i
\(254\) 189.116i 0.744552i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 388.227 1.51061 0.755306 0.655372i \(-0.227488\pi\)
0.755306 + 0.655372i \(0.227488\pi\)
\(258\) 0 0
\(259\) 57.2061 0.220873
\(260\) 55.8823 + 18.6883i 0.214932 + 0.0718780i
\(261\) 0 0
\(262\) 87.3755i 0.333494i
\(263\) 226.877 0.862651 0.431325 0.902196i \(-0.358046\pi\)
0.431325 + 0.902196i \(0.358046\pi\)
\(264\) 0 0
\(265\) 101.059 302.189i 0.381354 1.14034i
\(266\) 1.42974i 0.00537498i
\(267\) 0 0
\(268\) 178.005i 0.664199i
\(269\) 226.772i 0.843019i 0.906824 + 0.421509i \(0.138500\pi\)
−0.906824 + 0.421509i \(0.861500\pi\)
\(270\) 0 0
\(271\) 322.889 1.19147 0.595737 0.803180i \(-0.296860\pi\)
0.595737 + 0.803180i \(0.296860\pi\)
\(272\) −51.5980 −0.189698
\(273\) 0 0
\(274\) 231.816 0.846045
\(275\) −231.245 + 307.071i −0.840890 + 1.11662i
\(276\) 0 0
\(277\) 200.564i 0.724058i 0.932167 + 0.362029i \(0.117916\pi\)
−0.932167 + 0.362029i \(0.882084\pi\)
\(278\) −257.740 −0.927123
\(279\) 0 0
\(280\) −10.9117 3.64911i −0.0389703 0.0130326i
\(281\) 128.030i 0.455624i 0.973705 + 0.227812i \(0.0731572\pi\)
−0.973705 + 0.227812i \(0.926843\pi\)
\(282\) 0 0
\(283\) 420.235i 1.48493i −0.669885 0.742465i \(-0.733656\pi\)
0.669885 0.742465i \(-0.266344\pi\)
\(284\) 139.396i 0.490833i
\(285\) 0 0
\(286\) −128.132 −0.448014
\(287\) 5.73001 0.0199652
\(288\) 0 0
\(289\) −122.603 −0.424232
\(290\) 286.191 + 95.7087i 0.986865 + 0.330030i
\(291\) 0 0
\(292\) 179.238i 0.613828i
\(293\) 137.434 0.469056 0.234528 0.972109i \(-0.424645\pi\)
0.234528 + 0.972109i \(0.424645\pi\)
\(294\) 0 0
\(295\) 173.765 + 58.1108i 0.589032 + 0.196986i
\(296\) 198.879i 0.671889i
\(297\) 0 0
\(298\) 268.043i 0.899473i
\(299\) 28.2777i 0.0945744i
\(300\) 0 0
\(301\) 33.3970 0.110953
\(302\) 160.284 0.530743
\(303\) 0 0
\(304\) 4.97056 0.0163505
\(305\) −131.527 + 393.296i −0.431236 + 1.28949i
\(306\) 0 0
\(307\) 117.849i 0.383872i −0.981407 0.191936i \(-0.938523\pi\)
0.981407 0.191936i \(-0.0614766\pi\)
\(308\) 25.0193 0.0812316
\(309\) 0 0
\(310\) −9.44870 + 28.2538i −0.0304797 + 0.0911412i
\(311\) 499.326i 1.60555i 0.596283 + 0.802774i \(0.296644\pi\)
−0.596283 + 0.802774i \(0.703356\pi\)
\(312\) 0 0
\(313\) 491.806i 1.57127i −0.618693 0.785633i \(-0.712338\pi\)
0.618693 0.785633i \(-0.287662\pi\)
\(314\) 160.073i 0.509786i
\(315\) 0 0
\(316\) 268.191 0.848705
\(317\) −241.399 −0.761511 −0.380756 0.924676i \(-0.624336\pi\)
−0.380756 + 0.924676i \(0.624336\pi\)
\(318\) 0 0
\(319\) −656.205 −2.05707
\(320\) 12.6863 37.9349i 0.0396447 0.118547i
\(321\) 0 0
\(322\) 5.52157i 0.0171477i
\(323\) −16.0294 −0.0496267
\(324\) 0 0
\(325\) 88.6173 117.675i 0.272669 0.362078i
\(326\) 215.545i 0.661182i
\(327\) 0 0
\(328\) 19.9206i 0.0607336i
\(329\) 64.9225i 0.197333i
\(330\) 0 0
\(331\) −87.8091 −0.265284 −0.132642 0.991164i \(-0.542346\pi\)
−0.132642 + 0.991164i \(0.542346\pi\)
\(332\) 218.049 0.656773
\(333\) 0 0
\(334\) −149.698 −0.448199
\(335\) 422.039 + 141.139i 1.25982 + 0.421311i
\(336\) 0 0
\(337\) 452.138i 1.34166i −0.741613 0.670828i \(-0.765939\pi\)
0.741613 0.670828i \(-0.234061\pi\)
\(338\) −189.899 −0.561833
\(339\) 0 0
\(340\) −40.9117 + 122.335i −0.120328 + 0.359810i
\(341\) 64.7829i 0.189979i
\(342\) 0 0
\(343\) 79.1919i 0.230880i
\(344\) 116.106i 0.337517i
\(345\) 0 0
\(346\) −155.581 −0.449655
\(347\) 189.411 0.545854 0.272927 0.962035i \(-0.412008\pi\)
0.272927 + 0.962035i \(0.412008\pi\)
\(348\) 0 0
\(349\) −155.794 −0.446401 −0.223200 0.974773i \(-0.571650\pi\)
−0.223200 + 0.974773i \(0.571650\pi\)
\(350\) −17.3036 + 22.9775i −0.0494389 + 0.0656500i
\(351\) 0 0
\(352\) 86.9807i 0.247104i
\(353\) 263.387 0.746138 0.373069 0.927804i \(-0.378305\pi\)
0.373069 + 0.927804i \(0.378305\pi\)
\(354\) 0 0
\(355\) 330.500 + 110.527i 0.930985 + 0.311342i
\(356\) 275.028i 0.772551i
\(357\) 0 0
\(358\) 167.453i 0.467745i
\(359\) 79.6346i 0.221823i −0.993830 0.110912i \(-0.964623\pi\)
0.993830 0.110912i \(-0.0353771\pi\)
\(360\) 0 0
\(361\) −359.456 −0.995723
\(362\) −243.806 −0.673498
\(363\) 0 0
\(364\) −9.58788 −0.0263403
\(365\) −424.960 142.116i −1.16428 0.389360i
\(366\) 0 0
\(367\) 475.953i 1.29688i −0.761268 0.648438i \(-0.775423\pi\)
0.761268 0.648438i \(-0.224577\pi\)
\(368\) −19.1960 −0.0521629
\(369\) 0 0
\(370\) 471.529 + 157.690i 1.27440 + 0.426189i
\(371\) 51.8475i 0.139751i
\(372\) 0 0
\(373\) 61.7838i 0.165640i −0.996565 0.0828201i \(-0.973607\pi\)
0.996565 0.0828201i \(-0.0263927\pi\)
\(374\) 280.502i 0.750005i
\(375\) 0 0
\(376\) 225.706 0.600281
\(377\) 251.470 0.667030
\(378\) 0 0
\(379\) −142.345 −0.375581 −0.187791 0.982209i \(-0.560133\pi\)
−0.187791 + 0.982209i \(0.560133\pi\)
\(380\) 3.94113 11.7849i 0.0103714 0.0310128i
\(381\) 0 0
\(382\) 409.264i 1.07137i
\(383\) 357.520 0.933472 0.466736 0.884397i \(-0.345430\pi\)
0.466736 + 0.884397i \(0.345430\pi\)
\(384\) 0 0
\(385\) 19.8377 59.3192i 0.0515264 0.154076i
\(386\) 180.783i 0.468350i
\(387\) 0 0
\(388\) 181.260i 0.467164i
\(389\) 411.079i 1.05676i 0.849009 + 0.528379i \(0.177200\pi\)
−0.849009 + 0.528379i \(0.822800\pi\)
\(390\) 0 0
\(391\) 61.9045 0.158324
\(392\) −136.721 −0.348777
\(393\) 0 0
\(394\) −396.566 −1.00651
\(395\) 212.647 635.863i 0.538346 1.60978i
\(396\) 0 0
\(397\) 457.462i 1.15230i 0.817345 + 0.576149i \(0.195445\pi\)
−0.817345 + 0.576149i \(0.804555\pi\)
\(398\) −221.220 −0.555830
\(399\) 0 0
\(400\) −79.8823 60.1567i −0.199706 0.150392i
\(401\) 467.283i 1.16529i −0.812725 0.582647i \(-0.802017\pi\)
0.812725 0.582647i \(-0.197983\pi\)
\(402\) 0 0
\(403\) 24.8260i 0.0616030i
\(404\) 99.4396i 0.246138i
\(405\) 0 0
\(406\) −49.1026 −0.120942
\(407\) −1081.17 −2.65643
\(408\) 0 0
\(409\) −448.574 −1.09676 −0.548378 0.836230i \(-0.684755\pi\)
−0.548378 + 0.836230i \(0.684755\pi\)
\(410\) 47.2304 + 15.7949i 0.115196 + 0.0385242i
\(411\) 0 0
\(412\) 257.688i 0.625456i
\(413\) −29.8133 −0.0721871
\(414\) 0 0
\(415\) 172.889 516.979i 0.416601 1.24573i
\(416\) 33.3326i 0.0801265i
\(417\) 0 0
\(418\) 27.0214i 0.0646446i
\(419\) 360.834i 0.861180i 0.902548 + 0.430590i \(0.141694\pi\)
−0.902548 + 0.430590i \(0.858306\pi\)
\(420\) 0 0
\(421\) 357.059 0.848121 0.424060 0.905634i \(-0.360604\pi\)
0.424060 + 0.905634i \(0.360604\pi\)
\(422\) −31.8305 −0.0754278
\(423\) 0 0
\(424\) −180.250 −0.425117
\(425\) 257.610 + 193.998i 0.606142 + 0.456465i
\(426\) 0 0
\(427\) 67.4789i 0.158030i
\(428\) 12.8528 0.0300299
\(429\) 0 0
\(430\) 275.279 + 92.0596i 0.640184 + 0.214092i
\(431\) 655.947i 1.52192i −0.648800 0.760959i \(-0.724729\pi\)
0.648800 0.760959i \(-0.275271\pi\)
\(432\) 0 0
\(433\) 164.372i 0.379612i −0.981822 0.189806i \(-0.939214\pi\)
0.981822 0.189806i \(-0.0607859\pi\)
\(434\) 4.84758i 0.0111695i
\(435\) 0 0
\(436\) 216.558 0.496694
\(437\) −5.96342 −0.0136463
\(438\) 0 0
\(439\) −132.286 −0.301336 −0.150668 0.988584i \(-0.548142\pi\)
−0.150668 + 0.988584i \(0.548142\pi\)
\(440\) 206.225 + 68.9664i 0.468694 + 0.156742i
\(441\) 0 0
\(442\) 107.494i 0.243198i
\(443\) 455.485 1.02818 0.514092 0.857735i \(-0.328129\pi\)
0.514092 + 0.857735i \(0.328129\pi\)
\(444\) 0 0
\(445\) 652.073 + 218.068i 1.46533 + 0.490040i
\(446\) 501.800i 1.12511i
\(447\) 0 0
\(448\) 6.50860i 0.0145281i
\(449\) 415.749i 0.925944i −0.886373 0.462972i \(-0.846783\pi\)
0.886373 0.462972i \(-0.153217\pi\)
\(450\) 0 0
\(451\) −108.294 −0.240121
\(452\) −60.8528 −0.134630
\(453\) 0 0
\(454\) 587.037 1.29303
\(455\) −7.60216 + 22.7322i −0.0167081 + 0.0499609i
\(456\) 0 0
\(457\) 303.643i 0.664426i −0.943204 0.332213i \(-0.892205\pi\)
0.943204 0.332213i \(-0.107795\pi\)
\(458\) 311.439 0.679997
\(459\) 0 0
\(460\) −15.2203 + 45.5123i −0.0330877 + 0.0989398i
\(461\) 428.790i 0.930130i 0.885277 + 0.465065i \(0.153969\pi\)
−0.885277 + 0.465065i \(0.846031\pi\)
\(462\) 0 0
\(463\) 814.484i 1.75914i 0.475765 + 0.879572i \(0.342171\pi\)
−0.475765 + 0.879572i \(0.657829\pi\)
\(464\) 170.707i 0.367903i
\(465\) 0 0
\(466\) −14.1909 −0.0304526
\(467\) −607.118 −1.30004 −0.650019 0.759918i \(-0.725239\pi\)
−0.650019 + 0.759918i \(0.725239\pi\)
\(468\) 0 0
\(469\) −72.4104 −0.154393
\(470\) 178.960 535.133i 0.380767 1.13858i
\(471\) 0 0
\(472\) 103.647i 0.219591i
\(473\) −631.186 −1.33443
\(474\) 0 0
\(475\) −24.8162 18.6883i −0.0522447 0.0393438i
\(476\) 20.9894i 0.0440954i
\(477\) 0 0
\(478\) 161.734i 0.338355i
\(479\) 343.889i 0.717931i −0.933351 0.358965i \(-0.883130\pi\)
0.933351 0.358965i \(-0.116870\pi\)
\(480\) 0 0
\(481\) 414.323 0.861378
\(482\) 90.1148 0.186960
\(483\) 0 0
\(484\) −230.853 −0.476969
\(485\) −429.754 143.720i −0.886092 0.296329i
\(486\) 0 0
\(487\) 300.759i 0.617576i −0.951131 0.308788i \(-0.900077\pi\)
0.951131 0.308788i \(-0.0999233\pi\)
\(488\) 234.593 0.480723
\(489\) 0 0
\(490\) −108.405 + 324.156i −0.221235 + 0.661542i
\(491\) 173.914i 0.354203i −0.984193 0.177101i \(-0.943328\pi\)
0.984193 0.177101i \(-0.0566720\pi\)
\(492\) 0 0
\(493\) 550.509i 1.11665i
\(494\) 10.3551i 0.0209618i
\(495\) 0 0
\(496\) 16.8528 0.0339774
\(497\) −56.7048 −0.114094
\(498\) 0 0
\(499\) −761.610 −1.52627 −0.763136 0.646237i \(-0.776342\pi\)
−0.763136 + 0.646237i \(0.776342\pi\)
\(500\) −205.966 + 141.698i −0.411931 + 0.283395i
\(501\) 0 0
\(502\) 324.748i 0.646908i
\(503\) −280.632 −0.557917 −0.278959 0.960303i \(-0.589989\pi\)
−0.278959 + 0.960303i \(0.589989\pi\)
\(504\) 0 0
\(505\) 235.765 + 78.8450i 0.466860 + 0.156129i
\(506\) 104.355i 0.206235i
\(507\) 0 0
\(508\) 267.451i 0.526478i
\(509\) 633.176i 1.24396i −0.783032 0.621981i \(-0.786328\pi\)
0.783032 0.621981i \(-0.213672\pi\)
\(510\) 0 0
\(511\) 72.9117 0.142684
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −549.037 −1.06816
\(515\) 610.960 + 204.319i 1.18633 + 0.396736i
\(516\) 0 0
\(517\) 1227.00i 2.37331i
\(518\) −80.9016 −0.156181
\(519\) 0 0
\(520\) −79.0294 26.4292i −0.151980 0.0508254i
\(521\) 92.3966i 0.177345i 0.996061 + 0.0886723i \(0.0282624\pi\)
−0.996061 + 0.0886723i \(0.971738\pi\)
\(522\) 0 0
\(523\) 818.552i 1.56511i −0.622582 0.782554i \(-0.713916\pi\)
0.622582 0.782554i \(-0.286084\pi\)
\(524\) 123.568i 0.235816i
\(525\) 0 0
\(526\) −320.853 −0.609986
\(527\) −54.3482 −0.103128
\(528\) 0 0
\(529\) −505.970 −0.956464
\(530\) −142.919 + 427.360i −0.269658 + 0.806340i
\(531\) 0 0
\(532\) 2.02196i 0.00380068i
\(533\) 41.5004 0.0778620
\(534\) 0 0
\(535\) 10.1909 30.4732i 0.0190484 0.0569592i
\(536\) 251.738i 0.469660i
\(537\) 0 0
\(538\) 320.704i 0.596104i
\(539\) 743.254i 1.37895i
\(540\) 0 0
\(541\) −376.985 −0.696830 −0.348415 0.937340i \(-0.613280\pi\)
−0.348415 + 0.937340i \(0.613280\pi\)
\(542\) −456.635 −0.842499
\(543\) 0 0
\(544\) 72.9706 0.134137
\(545\) 171.708 513.445i 0.315060 0.942102i
\(546\) 0 0
\(547\) 337.346i 0.616721i 0.951270 + 0.308360i \(0.0997803\pi\)
−0.951270 + 0.308360i \(0.900220\pi\)
\(548\) −327.838 −0.598244
\(549\) 0 0
\(550\) 327.029 434.263i 0.594599 0.789570i
\(551\) 53.0319i 0.0962467i
\(552\) 0 0
\(553\) 109.097i 0.197282i
\(554\) 283.640i 0.511986i
\(555\) 0 0
\(556\) 364.500 0.655575
\(557\) 303.338 0.544593 0.272296 0.962213i \(-0.412217\pi\)
0.272296 + 0.962213i \(0.412217\pi\)
\(558\) 0 0
\(559\) 241.882 0.432705
\(560\) 15.4315 + 5.16063i 0.0275562 + 0.00921541i
\(561\) 0 0
\(562\) 181.062i 0.322175i
\(563\) 234.093 0.415796 0.207898 0.978150i \(-0.433338\pi\)
0.207898 + 0.978150i \(0.433338\pi\)
\(564\) 0 0
\(565\) −48.2498 + 144.278i −0.0853978 + 0.255359i
\(566\) 594.302i 1.05000i
\(567\) 0 0
\(568\) 197.136i 0.347071i
\(569\) 66.5257i 0.116917i −0.998290 0.0584584i \(-0.981381\pi\)
0.998290 0.0584584i \(-0.0186185\pi\)
\(570\) 0 0
\(571\) 1115.54 1.95365 0.976826 0.214035i \(-0.0686607\pi\)
0.976826 + 0.214035i \(0.0686607\pi\)
\(572\) 181.206 0.316794
\(573\) 0 0
\(574\) −8.10346 −0.0141175
\(575\) 95.8385 + 72.1728i 0.166676 + 0.125518i
\(576\) 0 0
\(577\) 957.356i 1.65920i −0.558361 0.829598i \(-0.688570\pi\)
0.558361 0.829598i \(-0.311430\pi\)
\(578\) 173.387 0.299977
\(579\) 0 0
\(580\) −404.735 135.353i −0.697819 0.233366i
\(581\) 88.6996i 0.152667i
\(582\) 0 0
\(583\) 979.891i 1.68077i
\(584\) 253.480i 0.434042i
\(585\) 0 0
\(586\) −194.360 −0.331673
\(587\) −79.8974 −0.136111 −0.0680557 0.997682i \(-0.521680\pi\)
−0.0680557 + 0.997682i \(0.521680\pi\)
\(588\) 0 0
\(589\) 5.23550 0.00888879
\(590\) −245.740 82.1810i −0.416509 0.139290i
\(591\) 0 0
\(592\) 281.258i 0.475097i
\(593\) −213.831 −0.360593 −0.180296 0.983612i \(-0.557706\pi\)
−0.180296 + 0.983612i \(0.557706\pi\)
\(594\) 0 0
\(595\) −49.7645 16.6424i −0.0836378 0.0279704i
\(596\) 379.070i 0.636023i
\(597\) 0 0
\(598\) 39.9908i 0.0668742i
\(599\) 915.493i 1.52837i 0.644998 + 0.764184i \(0.276858\pi\)
−0.644998 + 0.764184i \(0.723142\pi\)
\(600\) 0 0
\(601\) 479.426 0.797714 0.398857 0.917013i \(-0.369407\pi\)
0.398857 + 0.917013i \(0.369407\pi\)
\(602\) −47.2304 −0.0784559
\(603\) 0 0
\(604\) −226.676 −0.375292
\(605\) −183.042 + 547.336i −0.302548 + 0.904688i
\(606\) 0 0
\(607\) 219.893i 0.362261i 0.983459 + 0.181131i \(0.0579757\pi\)
−0.983459 + 0.181131i \(0.942024\pi\)
\(608\) −7.02944 −0.0115616
\(609\) 0 0
\(610\) 186.007 556.204i 0.304930 0.911810i
\(611\) 470.210i 0.769575i
\(612\) 0 0
\(613\) 862.066i 1.40631i 0.711038 + 0.703154i \(0.248225\pi\)
−0.711038 + 0.703154i \(0.751775\pi\)
\(614\) 166.663i 0.271438i
\(615\) 0 0
\(616\) −35.3827 −0.0574394
\(617\) 695.423 1.12710 0.563552 0.826080i \(-0.309434\pi\)
0.563552 + 0.826080i \(0.309434\pi\)
\(618\) 0 0
\(619\) −512.073 −0.827259 −0.413629 0.910445i \(-0.635739\pi\)
−0.413629 + 0.910445i \(0.635739\pi\)
\(620\) 13.3625 39.9569i 0.0215524 0.0644466i
\(621\) 0 0
\(622\) 706.153i 1.13529i
\(623\) −111.878 −0.179580
\(624\) 0 0
\(625\) 172.647 + 600.681i 0.276235 + 0.961090i
\(626\) 695.519i 1.11105i
\(627\) 0 0
\(628\) 226.377i 0.360473i
\(629\) 907.020i 1.44200i
\(630\) 0 0
\(631\) −643.375 −1.01961 −0.509806 0.860290i \(-0.670283\pi\)
−0.509806 + 0.860290i \(0.670283\pi\)
\(632\) −379.279 −0.600125
\(633\) 0 0
\(634\) 341.390 0.538470
\(635\) 634.108 + 212.060i 0.998595 + 0.333953i
\(636\) 0 0
\(637\) 284.829i 0.447141i
\(638\) 928.014 1.45457
\(639\) 0 0
\(640\) −17.9411 + 53.6481i −0.0280330 + 0.0838251i
\(641\) 196.925i 0.307215i 0.988132 + 0.153608i \(0.0490892\pi\)
−0.988132 + 0.153608i \(0.950911\pi\)
\(642\) 0 0
\(643\) 236.954i 0.368513i −0.982878 0.184256i \(-0.941012\pi\)
0.982878 0.184256i \(-0.0589877\pi\)
\(644\) 7.80868i 0.0121253i
\(645\) 0 0
\(646\) 22.6690 0.0350914
\(647\) 17.3818 0.0268653 0.0134326 0.999910i \(-0.495724\pi\)
0.0134326 + 0.999910i \(0.495724\pi\)
\(648\) 0 0
\(649\) 563.456 0.868191
\(650\) −125.324 + 166.418i −0.192806 + 0.256028i
\(651\) 0 0
\(652\) 304.827i 0.467527i
\(653\) −785.704 −1.20322 −0.601611 0.798789i \(-0.705474\pi\)
−0.601611 + 0.798789i \(0.705474\pi\)
\(654\) 0 0
\(655\) −292.971 97.9760i −0.447283 0.149582i
\(656\) 28.1720i 0.0429451i
\(657\) 0 0
\(658\) 91.8143i 0.139535i
\(659\) 498.767i 0.756855i 0.925631 + 0.378427i \(0.123535\pi\)
−0.925631 + 0.378427i \(0.876465\pi\)
\(660\) 0 0
\(661\) 303.133 0.458597 0.229299 0.973356i \(-0.426357\pi\)
0.229299 + 0.973356i \(0.426357\pi\)
\(662\) 124.181 0.187584
\(663\) 0 0
\(664\) −308.368 −0.464409
\(665\) 4.79394 + 1.60320i 0.00720893 + 0.00241083i
\(666\) 0 0
\(667\) 204.805i 0.307055i
\(668\) 211.706 0.316925
\(669\) 0 0
\(670\) −596.853 199.601i −0.890825 0.297912i
\(671\) 1275.32i 1.90062i
\(672\) 0 0
\(673\) 463.133i 0.688163i 0.938940 + 0.344081i \(0.111810\pi\)
−0.938940 + 0.344081i \(0.888190\pi\)
\(674\) 639.420i 0.948694i
\(675\) 0 0
\(676\) 268.558 0.397276
\(677\) 311.064 0.459474 0.229737 0.973253i \(-0.426213\pi\)
0.229737 + 0.973253i \(0.426213\pi\)
\(678\) 0 0
\(679\) 73.7342 0.108592
\(680\) 57.8579 173.008i 0.0850851 0.254424i
\(681\) 0 0
\(682\) 91.6169i 0.134336i
\(683\) 232.009 0.339691 0.169846 0.985471i \(-0.445673\pi\)
0.169846 + 0.985471i \(0.445673\pi\)
\(684\) 0 0
\(685\) −259.940 + 777.281i −0.379475 + 1.13472i
\(686\) 111.994i 0.163257i
\(687\) 0 0
\(688\) 164.199i 0.238661i
\(689\) 375.513i 0.545011i
\(690\) 0 0
\(691\) −552.904 −0.800150 −0.400075 0.916482i \(-0.631016\pi\)
−0.400075 + 0.916482i \(0.631016\pi\)
\(692\) 220.024 0.317954
\(693\) 0 0
\(694\) −267.868 −0.385977
\(695\) 289.009 864.204i 0.415841 1.24346i
\(696\) 0 0
\(697\) 90.8512i 0.130346i
\(698\) 220.326 0.315653
\(699\) 0 0
\(700\) 24.4710 32.4951i 0.0349586 0.0464216i
\(701\) 250.274i 0.357024i 0.983938 + 0.178512i \(0.0571284\pi\)
−0.983938 + 0.178512i \(0.942872\pi\)
\(702\) 0 0
\(703\) 87.3755i 0.124290i
\(704\) 123.009i 0.174729i
\(705\) 0 0
\(706\) −372.485 −0.527600
\(707\) −40.4508 −0.0572147
\(708\) 0 0
\(709\) 1170.57 1.65102 0.825510 0.564388i \(-0.190888\pi\)
0.825510 + 0.564388i \(0.190888\pi\)
\(710\) −467.397 156.308i −0.658306 0.220152i
\(711\) 0 0
\(712\) 388.949i 0.546276i
\(713\) −20.2191 −0.0283578
\(714\) 0 0
\(715\) 143.677 429.627i 0.200947 0.600877i
\(716\) 236.814i 0.330746i
\(717\) 0 0
\(718\) 112.620i 0.156853i
\(719\) 168.127i 0.233834i −0.993142 0.116917i \(-0.962699\pi\)
0.993142 0.116917i \(-0.0373012\pi\)
\(720\) 0 0
\(721\) −104.824 −0.145387
\(722\) 508.347 0.704082
\(723\) 0 0
\(724\) 344.794 0.476235
\(725\) −641.823 + 852.279i −0.885274 + 1.17556i
\(726\) 0 0
\(727\) 382.835i 0.526595i 0.964715 + 0.263298i \(0.0848101\pi\)
−0.964715 + 0.263298i \(0.915190\pi\)
\(728\) 13.5593 0.0186254
\(729\) 0 0
\(730\) 600.985 + 200.983i 0.823267 + 0.275319i
\(731\) 529.520i 0.724377i
\(732\) 0 0
\(733\) 1403.08i 1.91416i 0.289819 + 0.957082i \(0.406405\pi\)
−0.289819 + 0.957082i \(0.593595\pi\)
\(734\) 673.099i 0.917029i
\(735\) 0 0
\(736\) 27.1472 0.0368848
\(737\) 1368.52 1.85688
\(738\) 0 0
\(739\) 899.125 1.21668 0.608339 0.793677i \(-0.291836\pi\)
0.608339 + 0.793677i \(0.291836\pi\)
\(740\) −666.843 223.007i −0.901139 0.301361i
\(741\) 0 0
\(742\) 73.3234i 0.0988186i
\(743\) −316.587 −0.426093 −0.213046 0.977042i \(-0.568339\pi\)
−0.213046 + 0.977042i \(0.568339\pi\)
\(744\) 0 0
\(745\) −898.749 300.562i −1.20637 0.403439i
\(746\) 87.3755i 0.117125i
\(747\) 0 0
\(748\) 396.689i 0.530334i
\(749\) 5.22837i 0.00698046i
\(750\) 0 0
\(751\) −286.433 −0.381402 −0.190701 0.981648i \(-0.561076\pi\)
−0.190701 + 0.981648i \(0.561076\pi\)
\(752\) −319.196 −0.424463
\(753\) 0 0
\(754\) −355.632 −0.471661
\(755\) −179.730 + 537.434i −0.238053 + 0.711833i
\(756\) 0 0
\(757\) 783.221i 1.03464i 0.855793 + 0.517319i \(0.173070\pi\)
−0.855793 + 0.517319i \(0.826930\pi\)
\(758\) 201.307 0.265576
\(759\) 0 0
\(760\) −5.57359 + 16.6663i −0.00733368 + 0.0219294i
\(761\) 1031.91i 1.35599i −0.735064 0.677997i \(-0.762848\pi\)
0.735064 0.677997i \(-0.237152\pi\)
\(762\) 0 0
\(763\) 88.0933i 0.115456i
\(764\) 578.787i 0.757574i
\(765\) 0 0
\(766\) −505.609 −0.660064
\(767\) −215.927 −0.281521
\(768\) 0 0
\(769\) −831.250 −1.08095 −0.540475 0.841360i \(-0.681755\pi\)
−0.540475 + 0.841360i \(0.681755\pi\)
\(770\) −28.0547 + 83.8900i −0.0364347 + 0.108948i
\(771\) 0 0
\(772\) 255.666i 0.331173i
\(773\) −395.360 −0.511462 −0.255731 0.966748i \(-0.582316\pi\)
−0.255731 + 0.966748i \(0.582316\pi\)
\(774\) 0 0
\(775\) −84.1400 63.3631i −0.108568 0.0817588i
\(776\) 256.340i 0.330335i
\(777\) 0 0
\(778\) 581.353i 0.747240i
\(779\) 8.75192i 0.0112348i
\(780\) 0 0
\(781\) 1071.69 1.37220
\(782\) −87.5462 −0.111952
\(783\) 0 0
\(784\) 193.352 0.246623
\(785\) −536.725 179.493i −0.683726 0.228653i
\(786\) 0 0
\(787\) 573.929i 0.729262i −0.931152 0.364631i \(-0.881195\pi\)
0.931152 0.364631i \(-0.118805\pi\)
\(788\) 560.828 0.711711