Properties

Label 880.2.bo.d.81.1
Level $880$
Weight $2$
Character 880.81
Analytic conductor $7.027$
Analytic rank $0$
Dimension $8$
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] = [880,2,Mod(81,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bo (of order \(5\), degree \(4\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(-0.386111 - 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 880.81
Dual form 880.2.bo.d.641.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0911485 + 0.280526i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(1.35666 + 4.17538i) q^{7} +(2.35666 + 1.71222i) q^{9} +O(q^{10})\) \(q+(-0.0911485 + 0.280526i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(1.35666 + 4.17538i) q^{7} +(2.35666 + 1.71222i) q^{9} +(-3.31118 - 0.189896i) q^{11} +(-4.82402 - 3.50485i) q^{13} +(-0.0911485 - 0.280526i) q^{15} +(1.34932 - 0.980336i) q^{17} +(-2.37743 + 7.31696i) q^{19} -1.29496 q^{21} +0.904706 q^{23} +(0.309017 - 0.951057i) q^{25} +(-1.41102 + 1.02516i) q^{27} +(-1.46443 - 4.50705i) q^{29} +(-4.14709 - 3.01303i) q^{31} +(0.355081 - 0.911566i) q^{33} +(-3.55179 - 2.58053i) q^{35} +(-0.0571606 - 0.175922i) q^{37} +(1.42291 - 1.03380i) q^{39} +(-0.810356 + 2.49402i) q^{41} -3.59822 q^{43} -2.91300 q^{45} +(0.239853 - 0.738191i) q^{47} +(-9.93016 + 7.21469i) q^{49} +(0.152022 + 0.467875i) q^{51} +(7.76295 + 5.64012i) q^{53} +(2.79042 - 1.79264i) q^{55} +(-1.83590 - 1.33386i) q^{57} +(3.47762 + 10.7030i) q^{59} +(-10.6708 + 7.75277i) q^{61} +(-3.95196 + 12.1629i) q^{63} +5.96281 q^{65} +7.79954 q^{67} +(-0.0824626 + 0.253794i) q^{69} +(-5.63943 + 4.09729i) q^{71} +(3.94122 + 12.1298i) q^{73} +(0.238630 + 0.173375i) q^{75} +(-3.69927 - 14.0831i) q^{77} +(-8.11547 - 5.89624i) q^{79} +(2.54152 + 7.82200i) q^{81} +(3.31316 - 2.40715i) q^{83} +(-0.515393 + 1.58622i) q^{85} +1.39783 q^{87} -0.466291 q^{89} +(8.08953 - 24.8970i) q^{91} +(1.22324 - 0.888733i) q^{93} +(-2.37743 - 7.31696i) q^{95} +(-5.74372 - 4.17306i) q^{97} +(-7.47820 - 6.11699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 2 q^{5} - q^{7} + 7 q^{9} - 3 q^{11} - 4 q^{13} - q^{15} - 3 q^{17} - 9 q^{19} - 4 q^{21} + 22 q^{23} - 2 q^{25} + 8 q^{27} - 17 q^{29} + 4 q^{31} + 21 q^{33} - 6 q^{35} + 24 q^{37} + 13 q^{39} - 4 q^{41} + 14 q^{43} - 8 q^{45} + 12 q^{47} - 15 q^{49} + 17 q^{51} + 35 q^{53} - 3 q^{55} - q^{57} - 21 q^{59} - 22 q^{61} - 5 q^{63} + 6 q^{65} - 14 q^{67} + 3 q^{69} - 40 q^{71} + 9 q^{73} - q^{75} - 4 q^{77} - 41 q^{79} + 24 q^{81} + 7 q^{83} - 8 q^{85} + 46 q^{87} - 24 q^{89} + 18 q^{91} + 3 q^{93} - 9 q^{95} + 4 q^{97} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\)

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
\(3\) −0.0911485 + 0.280526i −0.0526246 + 0.161962i −0.973915 0.226914i \(-0.927136\pi\)
0.921290 + 0.388876i \(0.127136\pi\)
\(4\) 0 0
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) 1.35666 + 4.17538i 0.512771 + 1.57815i 0.787302 + 0.616568i \(0.211477\pi\)
−0.274531 + 0.961578i \(0.588523\pi\)
\(8\) 0 0
\(9\) 2.35666 + 1.71222i 0.785555 + 0.570739i
\(10\) 0 0
\(11\) −3.31118 0.189896i −0.998360 0.0572559i
\(12\) 0 0
\(13\) −4.82402 3.50485i −1.33794 0.972071i −0.999517 0.0310775i \(-0.990106\pi\)
−0.338424 0.940994i \(-0.609894\pi\)
\(14\) 0 0
\(15\) −0.0911485 0.280526i −0.0235345 0.0724316i
\(16\) 0 0
\(17\) 1.34932 0.980336i 0.327258 0.237767i −0.412009 0.911180i \(-0.635173\pi\)
0.739266 + 0.673413i \(0.235173\pi\)
\(18\) 0 0
\(19\) −2.37743 + 7.31696i −0.545419 + 1.67863i 0.174573 + 0.984644i \(0.444145\pi\)
−0.719992 + 0.693982i \(0.755855\pi\)
\(20\) 0 0
\(21\) −1.29496 −0.282584
\(22\) 0 0
\(23\) 0.904706 0.188644 0.0943221 0.995542i \(-0.469932\pi\)
0.0943221 + 0.995542i \(0.469932\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0 0
\(27\) −1.41102 + 1.02516i −0.271551 + 0.197293i
\(28\) 0 0
\(29\) −1.46443 4.50705i −0.271938 0.836938i −0.990013 0.140973i \(-0.954977\pi\)
0.718076 0.695965i \(-0.245023\pi\)
\(30\) 0 0
\(31\) −4.14709 3.01303i −0.744839 0.541157i 0.149384 0.988779i \(-0.452271\pi\)
−0.894223 + 0.447622i \(0.852271\pi\)
\(32\) 0 0
\(33\) 0.355081 0.911566i 0.0618116 0.158683i
\(34\) 0 0
\(35\) −3.55179 2.58053i −0.600362 0.436189i
\(36\) 0 0
\(37\) −0.0571606 0.175922i −0.00939715 0.0289214i 0.946248 0.323442i \(-0.104840\pi\)
−0.955645 + 0.294521i \(0.904840\pi\)
\(38\) 0 0
\(39\) 1.42291 1.03380i 0.227847 0.165541i
\(40\) 0 0
\(41\) −0.810356 + 2.49402i −0.126556 + 0.389501i −0.994181 0.107719i \(-0.965645\pi\)
0.867625 + 0.497219i \(0.165645\pi\)
\(42\) 0 0
\(43\) −3.59822 −0.548723 −0.274361 0.961627i \(-0.588466\pi\)
−0.274361 + 0.961627i \(0.588466\pi\)
\(44\) 0 0
\(45\) −2.91300 −0.434244
\(46\) 0 0
\(47\) 0.239853 0.738191i 0.0349861 0.107676i −0.932038 0.362360i \(-0.881971\pi\)
0.967024 + 0.254683i \(0.0819712\pi\)
\(48\) 0 0
\(49\) −9.93016 + 7.21469i −1.41859 + 1.03067i
\(50\) 0 0
\(51\) 0.152022 + 0.467875i 0.0212873 + 0.0655157i
\(52\) 0 0
\(53\) 7.76295 + 5.64012i 1.06632 + 0.774729i 0.975248 0.221114i \(-0.0709694\pi\)
0.0910758 + 0.995844i \(0.470969\pi\)
\(54\) 0 0
\(55\) 2.79042 1.79264i 0.376260 0.241719i
\(56\) 0 0
\(57\) −1.83590 1.33386i −0.243171 0.176674i
\(58\) 0 0
\(59\) 3.47762 + 10.7030i 0.452748 + 1.39341i 0.873759 + 0.486359i \(0.161675\pi\)
−0.421012 + 0.907055i \(0.638325\pi\)
\(60\) 0 0
\(61\) −10.6708 + 7.75277i −1.36625 + 0.992640i −0.368233 + 0.929734i \(0.620037\pi\)
−0.998019 + 0.0629067i \(0.979963\pi\)
\(62\) 0 0
\(63\) −3.95196 + 12.1629i −0.497900 + 1.53238i
\(64\) 0 0
\(65\) 5.96281 0.739596
\(66\) 0 0
\(67\) 7.79954 0.952866 0.476433 0.879211i \(-0.341930\pi\)
0.476433 + 0.879211i \(0.341930\pi\)
\(68\) 0 0
\(69\) −0.0824626 + 0.253794i −0.00992734 + 0.0305532i
\(70\) 0 0
\(71\) −5.63943 + 4.09729i −0.669278 + 0.486259i −0.869783 0.493434i \(-0.835742\pi\)
0.200506 + 0.979693i \(0.435742\pi\)
\(72\) 0 0
\(73\) 3.94122 + 12.1298i 0.461285 + 1.41969i 0.863595 + 0.504186i \(0.168207\pi\)
−0.402310 + 0.915504i \(0.631793\pi\)
\(74\) 0 0
\(75\) 0.238630 + 0.173375i 0.0275546 + 0.0200196i
\(76\) 0 0
\(77\) −3.69927 14.0831i −0.421571 1.60492i
\(78\) 0 0
\(79\) −8.11547 5.89624i −0.913062 0.663378i 0.0287255 0.999587i \(-0.490855\pi\)
−0.941787 + 0.336209i \(0.890855\pi\)
\(80\) 0 0
\(81\) 2.54152 + 7.82200i 0.282391 + 0.869112i
\(82\) 0 0
\(83\) 3.31316 2.40715i 0.363667 0.264219i −0.390913 0.920428i \(-0.627841\pi\)
0.754580 + 0.656208i \(0.227841\pi\)
\(84\) 0 0
\(85\) −0.515393 + 1.58622i −0.0559023 + 0.172049i
\(86\) 0 0
\(87\) 1.39783 0.149863
\(88\) 0 0
\(89\) −0.466291 −0.0494267 −0.0247134 0.999695i \(-0.507867\pi\)
−0.0247134 + 0.999695i \(0.507867\pi\)
\(90\) 0 0
\(91\) 8.08953 24.8970i 0.848013 2.60992i
\(92\) 0 0
\(93\) 1.22324 0.888733i 0.126844 0.0921574i
\(94\) 0 0
\(95\) −2.37743 7.31696i −0.243919 0.750705i
\(96\) 0 0
\(97\) −5.74372 4.17306i −0.583186 0.423710i 0.256685 0.966495i \(-0.417370\pi\)
−0.839871 + 0.542785i \(0.817370\pi\)
\(98\) 0 0
\(99\) −7.47820 6.11699i −0.751588 0.614780i
\(100\) 0 0
\(101\) 13.1749 + 9.57214i 1.31095 + 0.952463i 0.999998 + 0.00203865i \(0.000648924\pi\)
0.310955 + 0.950425i \(0.399351\pi\)
\(102\) 0 0
\(103\) −0.985946 3.03443i −0.0971481 0.298991i 0.890659 0.454671i \(-0.150243\pi\)
−0.987808 + 0.155680i \(0.950243\pi\)
\(104\) 0 0
\(105\) 1.04765 0.761160i 0.102240 0.0742816i
\(106\) 0 0
\(107\) 4.06801 12.5201i 0.393270 1.21036i −0.537031 0.843562i \(-0.680454\pi\)
0.930301 0.366797i \(-0.119546\pi\)
\(108\) 0 0
\(109\) 1.33532 0.127900 0.0639502 0.997953i \(-0.479630\pi\)
0.0639502 + 0.997953i \(0.479630\pi\)
\(110\) 0 0
\(111\) 0.0545610 0.00517870
\(112\) 0 0
\(113\) −0.517444 + 1.59253i −0.0486770 + 0.149812i −0.972441 0.233151i \(-0.925096\pi\)
0.923764 + 0.382963i \(0.125096\pi\)
\(114\) 0 0
\(115\) −0.731923 + 0.531773i −0.0682521 + 0.0495881i
\(116\) 0 0
\(117\) −5.36752 16.5195i −0.496227 1.52723i
\(118\) 0 0
\(119\) 5.92385 + 4.30393i 0.543038 + 0.394541i
\(120\) 0 0
\(121\) 10.9279 + 1.25756i 0.993444 + 0.114324i
\(122\) 0 0
\(123\) −0.625776 0.454653i −0.0564243 0.0409946i
\(124\) 0 0
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) 0.729305 0.529871i 0.0647153 0.0470185i −0.554957 0.831879i \(-0.687265\pi\)
0.619673 + 0.784860i \(0.287265\pi\)
\(128\) 0 0
\(129\) 0.327972 1.00939i 0.0288763 0.0888722i
\(130\) 0 0
\(131\) 14.5527 1.27148 0.635739 0.771904i \(-0.280695\pi\)
0.635739 + 0.771904i \(0.280695\pi\)
\(132\) 0 0
\(133\) −33.7765 −2.92879
\(134\) 0 0
\(135\) 0.538961 1.65875i 0.0463864 0.142763i
\(136\) 0 0
\(137\) 16.6573 12.1022i 1.42313 1.03396i 0.431881 0.901931i \(-0.357850\pi\)
0.991246 0.132031i \(-0.0421498\pi\)
\(138\) 0 0
\(139\) 4.63035 + 14.2508i 0.392741 + 1.20873i 0.930707 + 0.365767i \(0.119193\pi\)
−0.537965 + 0.842967i \(0.680807\pi\)
\(140\) 0 0
\(141\) 0.185220 + 0.134570i 0.0155983 + 0.0113328i
\(142\) 0 0
\(143\) 15.3076 + 12.5213i 1.28009 + 1.04708i
\(144\) 0 0
\(145\) 3.83392 + 2.78551i 0.318390 + 0.231324i
\(146\) 0 0
\(147\) −1.11879 3.44328i −0.0922762 0.283997i
\(148\) 0 0
\(149\) −8.86891 + 6.44364i −0.726570 + 0.527884i −0.888476 0.458922i \(-0.848236\pi\)
0.161907 + 0.986806i \(0.448236\pi\)
\(150\) 0 0
\(151\) 1.82682 5.62238i 0.148665 0.457543i −0.848799 0.528715i \(-0.822674\pi\)
0.997464 + 0.0711723i \(0.0226740\pi\)
\(152\) 0 0
\(153\) 4.85844 0.392781
\(154\) 0 0
\(155\) 5.12608 0.411737
\(156\) 0 0
\(157\) −1.36780 + 4.20964i −0.109162 + 0.335966i −0.990685 0.136176i \(-0.956519\pi\)
0.881523 + 0.472142i \(0.156519\pi\)
\(158\) 0 0
\(159\) −2.28978 + 1.66362i −0.181592 + 0.131934i
\(160\) 0 0
\(161\) 1.22738 + 3.77749i 0.0967313 + 0.297708i
\(162\) 0 0
\(163\) −5.97430 4.34059i −0.467944 0.339981i 0.328696 0.944436i \(-0.393391\pi\)
−0.796639 + 0.604455i \(0.793391\pi\)
\(164\) 0 0
\(165\) 0.248539 + 0.946183i 0.0193487 + 0.0736603i
\(166\) 0 0
\(167\) −15.7658 11.4545i −1.21999 0.886375i −0.223892 0.974614i \(-0.571876\pi\)
−0.996099 + 0.0882386i \(0.971876\pi\)
\(168\) 0 0
\(169\) 6.96991 + 21.4512i 0.536147 + 1.65009i
\(170\) 0 0
\(171\) −18.1310 + 13.1730i −1.38651 + 1.00736i
\(172\) 0 0
\(173\) 2.93815 9.04269i 0.223383 0.687503i −0.775068 0.631877i \(-0.782285\pi\)
0.998452 0.0556257i \(-0.0177153\pi\)
\(174\) 0 0
\(175\) 4.39026 0.331872
\(176\) 0 0
\(177\) −3.31946 −0.249506
\(178\) 0 0
\(179\) −2.22879 + 6.85952i −0.166588 + 0.512705i −0.999150 0.0412273i \(-0.986873\pi\)
0.832562 + 0.553932i \(0.186873\pi\)
\(180\) 0 0
\(181\) 18.9225 13.7480i 1.40650 1.02188i 0.412676 0.910878i \(-0.364594\pi\)
0.993820 0.111002i \(-0.0354060\pi\)
\(182\) 0 0
\(183\) −1.20223 3.70009i −0.0888715 0.273518i
\(184\) 0 0
\(185\) 0.149648 + 0.108726i 0.0110024 + 0.00799369i
\(186\) 0 0
\(187\) −4.65400 + 2.98984i −0.340334 + 0.218639i
\(188\) 0 0
\(189\) −6.19473 4.50074i −0.450601 0.327380i
\(190\) 0 0
\(191\) 1.28728 + 3.96183i 0.0931441 + 0.286668i 0.986766 0.162153i \(-0.0518439\pi\)
−0.893621 + 0.448821i \(0.851844\pi\)
\(192\) 0 0
\(193\) 18.7417 13.6166i 1.34906 0.980148i 0.350000 0.936750i \(-0.386182\pi\)
0.999058 0.0433979i \(-0.0138183\pi\)
\(194\) 0 0
\(195\) −0.543502 + 1.67273i −0.0389210 + 0.119786i
\(196\) 0 0
\(197\) 10.1507 0.723209 0.361604 0.932332i \(-0.382229\pi\)
0.361604 + 0.932332i \(0.382229\pi\)
\(198\) 0 0
\(199\) 17.0131 1.20603 0.603014 0.797731i \(-0.293966\pi\)
0.603014 + 0.797731i \(0.293966\pi\)
\(200\) 0 0
\(201\) −0.710917 + 2.18798i −0.0501442 + 0.154328i
\(202\) 0 0
\(203\) 16.8319 12.2291i 1.18137 0.858315i
\(204\) 0 0
\(205\) −0.810356 2.49402i −0.0565977 0.174190i
\(206\) 0 0
\(207\) 2.13209 + 1.54905i 0.148190 + 0.107667i
\(208\) 0 0
\(209\) 9.26156 23.7763i 0.640635 1.64464i
\(210\) 0 0
\(211\) −4.86721 3.53624i −0.335073 0.243445i 0.407507 0.913202i \(-0.366398\pi\)
−0.742580 + 0.669757i \(0.766398\pi\)
\(212\) 0 0
\(213\) −0.635371 1.95547i −0.0435349 0.133987i
\(214\) 0 0
\(215\) 2.91102 2.11498i 0.198530 0.144240i
\(216\) 0 0
\(217\) 6.95437 21.4033i 0.472093 1.45295i
\(218\) 0 0
\(219\) −3.76197 −0.254211
\(220\) 0 0
\(221\) −9.94506 −0.668977
\(222\) 0 0
\(223\) −0.770711 + 2.37201i −0.0516107 + 0.158841i −0.973540 0.228517i \(-0.926612\pi\)
0.921929 + 0.387358i \(0.126612\pi\)
\(224\) 0 0
\(225\) 2.35666 1.71222i 0.157111 0.114148i
\(226\) 0 0
\(227\) 7.72396 + 23.7719i 0.512657 + 1.57780i 0.787505 + 0.616309i \(0.211373\pi\)
−0.274848 + 0.961488i \(0.588627\pi\)
\(228\) 0 0
\(229\) 2.24164 + 1.62865i 0.148132 + 0.107624i 0.659383 0.751807i \(-0.270818\pi\)
−0.511251 + 0.859432i \(0.670818\pi\)
\(230\) 0 0
\(231\) 4.28786 + 0.245909i 0.282121 + 0.0161796i
\(232\) 0 0
\(233\) 7.76676 + 5.64288i 0.508818 + 0.369678i 0.812375 0.583136i \(-0.198174\pi\)
−0.303557 + 0.952813i \(0.598174\pi\)
\(234\) 0 0
\(235\) 0.239853 + 0.738191i 0.0156463 + 0.0481543i
\(236\) 0 0
\(237\) 2.39376 1.73917i 0.155492 0.112971i
\(238\) 0 0
\(239\) −4.56394 + 14.0464i −0.295217 + 0.908584i 0.687932 + 0.725775i \(0.258519\pi\)
−0.983149 + 0.182808i \(0.941481\pi\)
\(240\) 0 0
\(241\) −10.4338 −0.672099 −0.336049 0.941844i \(-0.609091\pi\)
−0.336049 + 0.941844i \(0.609091\pi\)
\(242\) 0 0
\(243\) −7.65828 −0.491279
\(244\) 0 0
\(245\) 3.79298 11.6736i 0.242325 0.745799i
\(246\) 0 0
\(247\) 37.1136 26.9646i 2.36148 1.71572i
\(248\) 0 0
\(249\) 0.373280 + 1.14884i 0.0236557 + 0.0728047i
\(250\) 0 0
\(251\) −5.44787 3.95811i −0.343866 0.249834i 0.402425 0.915453i \(-0.368167\pi\)
−0.746291 + 0.665619i \(0.768167\pi\)
\(252\) 0 0
\(253\) −2.99565 0.171800i −0.188335 0.0108010i
\(254\) 0 0
\(255\) −0.397999 0.289163i −0.0249236 0.0181081i
\(256\) 0 0
\(257\) 2.39239 + 7.36301i 0.149233 + 0.459292i 0.997531 0.0702272i \(-0.0223724\pi\)
−0.848298 + 0.529519i \(0.822372\pi\)
\(258\) 0 0
\(259\) 0.656995 0.477335i 0.0408237 0.0296601i
\(260\) 0 0
\(261\) 4.26588 13.1290i 0.264051 0.812666i
\(262\) 0 0
\(263\) −18.1618 −1.11990 −0.559952 0.828525i \(-0.689181\pi\)
−0.559952 + 0.828525i \(0.689181\pi\)
\(264\) 0 0
\(265\) −9.59554 −0.589449
\(266\) 0 0
\(267\) 0.0425017 0.130807i 0.00260106 0.00800525i
\(268\) 0 0
\(269\) 8.67812 6.30502i 0.529114 0.384424i −0.290912 0.956750i \(-0.593959\pi\)
0.820026 + 0.572326i \(0.193959\pi\)
\(270\) 0 0
\(271\) 5.80566 + 17.8680i 0.352669 + 1.08540i 0.957349 + 0.288935i \(0.0933011\pi\)
−0.604680 + 0.796469i \(0.706699\pi\)
\(272\) 0 0
\(273\) 6.24692 + 4.53865i 0.378081 + 0.274692i
\(274\) 0 0
\(275\) −1.20381 + 3.09044i −0.0725927 + 0.186361i
\(276\) 0 0
\(277\) −23.3375 16.9557i −1.40221 1.01877i −0.994398 0.105701i \(-0.966291\pi\)
−0.407814 0.913065i \(-0.633709\pi\)
\(278\) 0 0
\(279\) −4.61432 14.2014i −0.276252 0.850217i
\(280\) 0 0
\(281\) −21.8873 + 15.9021i −1.30569 + 0.948637i −0.999994 0.00349313i \(-0.998888\pi\)
−0.305693 + 0.952130i \(0.598888\pi\)
\(282\) 0 0
\(283\) −3.97802 + 12.2431i −0.236468 + 0.727775i 0.760455 + 0.649391i \(0.224976\pi\)
−0.996923 + 0.0783842i \(0.975024\pi\)
\(284\) 0 0
\(285\) 2.26930 0.134422
\(286\) 0 0
\(287\) −11.5129 −0.679583
\(288\) 0 0
\(289\) −4.39369 + 13.5224i −0.258452 + 0.795435i
\(290\) 0 0
\(291\) 1.69418 1.23090i 0.0993148 0.0721565i
\(292\) 0 0
\(293\) 1.81972 + 5.60052i 0.106309 + 0.327186i 0.990035 0.140818i \(-0.0449733\pi\)
−0.883726 + 0.468004i \(0.844973\pi\)
\(294\) 0 0
\(295\) −9.10453 6.61483i −0.530086 0.385130i
\(296\) 0 0
\(297\) 4.86682 3.12656i 0.282401 0.181422i
\(298\) 0 0
\(299\) −4.36432 3.17086i −0.252395 0.183376i
\(300\) 0 0
\(301\) −4.88157 15.0239i −0.281369 0.865965i
\(302\) 0 0
\(303\) −3.88611 + 2.82343i −0.223251 + 0.162202i
\(304\) 0 0
\(305\) 4.07587 12.5442i 0.233384 0.718281i
\(306\) 0 0
\(307\) −6.85844 −0.391432 −0.195716 0.980661i \(-0.562703\pi\)
−0.195716 + 0.980661i \(0.562703\pi\)
\(308\) 0 0
\(309\) 0.941105 0.0535376
\(310\) 0 0
\(311\) 4.40946 13.5709i 0.250037 0.769536i −0.744730 0.667366i \(-0.767422\pi\)
0.994767 0.102170i \(-0.0325784\pi\)
\(312\) 0 0
\(313\) −1.29421 + 0.940297i −0.0731529 + 0.0531487i −0.623761 0.781615i \(-0.714396\pi\)
0.550608 + 0.834764i \(0.314396\pi\)
\(314\) 0 0
\(315\) −3.95196 12.1629i −0.222668 0.685300i
\(316\) 0 0
\(317\) 24.9627 + 18.1365i 1.40204 + 1.01864i 0.994420 + 0.105495i \(0.0336427\pi\)
0.407624 + 0.913150i \(0.366357\pi\)
\(318\) 0 0
\(319\) 3.99312 + 15.2018i 0.223572 + 0.851135i
\(320\) 0 0
\(321\) 3.14141 + 2.28237i 0.175337 + 0.127389i
\(322\) 0 0
\(323\) 3.96518 + 12.2036i 0.220629 + 0.679025i
\(324\) 0 0
\(325\) −4.82402 + 3.50485i −0.267588 + 0.194414i
\(326\) 0 0
\(327\) −0.121712 + 0.374592i −0.00673071 + 0.0207150i
\(328\) 0 0
\(329\) 3.40763 0.187869
\(330\) 0 0
\(331\) 1.16816 0.0642079 0.0321040 0.999485i \(-0.489779\pi\)
0.0321040 + 0.999485i \(0.489779\pi\)
\(332\) 0 0
\(333\) 0.166509 0.512461i 0.00912462 0.0280827i
\(334\) 0 0
\(335\) −6.30996 + 4.58446i −0.344750 + 0.250476i
\(336\) 0 0
\(337\) 4.33522 + 13.3424i 0.236154 + 0.726809i 0.996966 + 0.0778359i \(0.0248010\pi\)
−0.760812 + 0.648973i \(0.775199\pi\)
\(338\) 0 0
\(339\) −0.399582 0.290313i −0.0217023 0.0157677i
\(340\) 0 0
\(341\) 13.1596 + 10.7642i 0.712632 + 0.582916i
\(342\) 0 0
\(343\) −18.7334 13.6106i −1.01151 0.734905i
\(344\) 0 0
\(345\) −0.0824626 0.253794i −0.00443964 0.0136638i
\(346\) 0 0
\(347\) 26.9818 19.6034i 1.44846 1.05237i 0.462273 0.886738i \(-0.347034\pi\)
0.986188 0.165630i \(-0.0529659\pi\)
\(348\) 0 0
\(349\) −10.9166 + 33.5978i −0.584351 + 1.79845i 0.0175108 + 0.999847i \(0.494426\pi\)
−0.601862 + 0.798600i \(0.705574\pi\)
\(350\) 0 0
\(351\) 10.3998 0.555102
\(352\) 0 0
\(353\) 11.7558 0.625698 0.312849 0.949803i \(-0.398717\pi\)
0.312849 + 0.949803i \(0.398717\pi\)
\(354\) 0 0
\(355\) 2.15407 6.62955i 0.114326 0.351860i
\(356\) 0 0
\(357\) −1.74732 + 1.26950i −0.0924778 + 0.0671890i
\(358\) 0 0
\(359\) 0.840838 + 2.58783i 0.0443777 + 0.136581i 0.970790 0.239929i \(-0.0771242\pi\)
−0.926413 + 0.376510i \(0.877124\pi\)
\(360\) 0 0
\(361\) −32.5145 23.6232i −1.71129 1.24332i
\(362\) 0 0
\(363\) −1.34884 + 2.95093i −0.0707957 + 0.154884i
\(364\) 0 0
\(365\) −10.3183 7.49665i −0.540082 0.392393i
\(366\) 0 0
\(367\) −0.959060 2.95168i −0.0500625 0.154077i 0.922900 0.385040i \(-0.125812\pi\)
−0.972962 + 0.230963i \(0.925812\pi\)
\(368\) 0 0
\(369\) −6.18004 + 4.49006i −0.321720 + 0.233743i
\(370\) 0 0
\(371\) −13.0179 + 40.0650i −0.675857 + 2.08007i
\(372\) 0 0
\(373\) −27.4604 −1.42185 −0.710924 0.703269i \(-0.751723\pi\)
−0.710924 + 0.703269i \(0.751723\pi\)
\(374\) 0 0
\(375\) −0.294963 −0.0152318
\(376\) 0 0
\(377\) −8.73211 + 26.8747i −0.449727 + 1.38412i
\(378\) 0 0
\(379\) 11.2805 8.19577i 0.579441 0.420989i −0.259081 0.965855i \(-0.583420\pi\)
0.838523 + 0.544867i \(0.183420\pi\)
\(380\) 0 0
\(381\) 0.0821677 + 0.252886i 0.00420958 + 0.0129558i
\(382\) 0 0
\(383\) 6.59841 + 4.79402i 0.337163 + 0.244963i 0.743464 0.668776i \(-0.233182\pi\)
−0.406301 + 0.913739i \(0.633182\pi\)
\(384\) 0 0
\(385\) 11.2706 + 9.21908i 0.574403 + 0.469848i
\(386\) 0 0
\(387\) −8.47979 6.16093i −0.431052 0.313177i
\(388\) 0 0
\(389\) −0.958326 2.94942i −0.0485891 0.149542i 0.923818 0.382831i \(-0.125051\pi\)
−0.972407 + 0.233290i \(0.925051\pi\)
\(390\) 0 0
\(391\) 1.22074 0.886916i 0.0617352 0.0448533i
\(392\) 0 0
\(393\) −1.32646 + 4.08243i −0.0669111 + 0.205931i
\(394\) 0 0
\(395\) 10.0313 0.504728
\(396\) 0 0
\(397\) 23.1546 1.16209 0.581047 0.813870i \(-0.302643\pi\)
0.581047 + 0.813870i \(0.302643\pi\)
\(398\) 0 0
\(399\) 3.07868 9.47520i 0.154127 0.474353i
\(400\) 0 0
\(401\) 6.66933 4.84555i 0.333051 0.241975i −0.408673 0.912681i \(-0.634008\pi\)
0.741724 + 0.670705i \(0.234008\pi\)
\(402\) 0 0
\(403\) 9.44537 + 29.0699i 0.470507 + 1.44807i
\(404\) 0 0
\(405\) −6.65379 4.83426i −0.330630 0.240217i
\(406\) 0 0
\(407\) 0.155862 + 0.593366i 0.00772581 + 0.0294120i
\(408\) 0 0
\(409\) −1.76891 1.28518i −0.0874667 0.0635483i 0.543192 0.839608i \(-0.317215\pi\)
−0.630659 + 0.776060i \(0.717215\pi\)
\(410\) 0 0
\(411\) 1.87670 + 5.77590i 0.0925710 + 0.284904i
\(412\) 0 0
\(413\) −39.9712 + 29.0408i −1.96686 + 1.42900i
\(414\) 0 0
\(415\) −1.26552 + 3.89486i −0.0621217 + 0.191191i
\(416\) 0 0
\(417\) −4.41977 −0.216437
\(418\) 0 0
\(419\) −10.7348 −0.524429 −0.262215 0.965010i \(-0.584453\pi\)
−0.262215 + 0.965010i \(0.584453\pi\)
\(420\) 0 0
\(421\) 5.80597 17.8689i 0.282966 0.870878i −0.704036 0.710165i \(-0.748620\pi\)
0.987001 0.160714i \(-0.0513795\pi\)
\(422\) 0 0
\(423\) 1.82919 1.32899i 0.0889385 0.0646176i
\(424\) 0 0
\(425\) −0.515393 1.58622i −0.0250003 0.0769429i
\(426\) 0 0
\(427\) −46.8474 34.0366i −2.26711 1.64715i
\(428\) 0 0
\(429\) −4.90782 + 3.15290i −0.236952 + 0.152224i
\(430\) 0 0
\(431\) −7.26399 5.27760i −0.349894 0.254213i 0.398931 0.916981i \(-0.369381\pi\)
−0.748825 + 0.662768i \(0.769381\pi\)
\(432\) 0 0
\(433\) 9.73586 + 29.9639i 0.467876 + 1.43997i 0.855330 + 0.518084i \(0.173355\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(434\) 0 0
\(435\) −1.13087 + 0.821622i −0.0542208 + 0.0393937i
\(436\) 0 0
\(437\) −2.15087 + 6.61970i −0.102890 + 0.316663i
\(438\) 0 0
\(439\) −27.4750 −1.31131 −0.655655 0.755060i \(-0.727607\pi\)
−0.655655 + 0.755060i \(0.727607\pi\)
\(440\) 0 0
\(441\) −35.7552 −1.70263
\(442\) 0 0
\(443\) 9.33108 28.7181i 0.443333 1.36444i −0.440968 0.897523i \(-0.645365\pi\)
0.884301 0.466916i \(-0.154635\pi\)
\(444\) 0 0
\(445\) 0.377237 0.274079i 0.0178827 0.0129926i
\(446\) 0 0
\(447\) −0.999223 3.07529i −0.0472616 0.145456i
\(448\) 0 0
\(449\) 22.1525 + 16.0947i 1.04544 + 0.759558i 0.971340 0.237693i \(-0.0763912\pi\)
0.0741012 + 0.997251i \(0.476391\pi\)
\(450\) 0 0
\(451\) 3.15684 8.10428i 0.148650 0.381615i
\(452\) 0 0
\(453\) 1.41071 + 1.02494i 0.0662811 + 0.0481560i
\(454\) 0 0
\(455\) 8.08953 + 24.8970i 0.379243 + 1.16719i
\(456\) 0 0
\(457\) −11.5596 + 8.39854i −0.540735 + 0.392867i −0.824358 0.566069i \(-0.808464\pi\)
0.283623 + 0.958936i \(0.408464\pi\)
\(458\) 0 0
\(459\) −0.898905 + 2.76655i −0.0419573 + 0.129131i
\(460\) 0 0
\(461\) 8.78738 0.409269 0.204635 0.978838i \(-0.434399\pi\)
0.204635 + 0.978838i \(0.434399\pi\)
\(462\) 0 0
\(463\) 13.8394 0.643172 0.321586 0.946880i \(-0.395784\pi\)
0.321586 + 0.946880i \(0.395784\pi\)
\(464\) 0 0
\(465\) −0.467235 + 1.43800i −0.0216675 + 0.0666857i
\(466\) 0 0
\(467\) 20.1359 14.6296i 0.931778 0.676976i −0.0146495 0.999893i \(-0.504663\pi\)
0.946428 + 0.322916i \(0.104663\pi\)
\(468\) 0 0
\(469\) 10.5814 + 32.5661i 0.488602 + 1.50376i
\(470\) 0 0
\(471\) −1.05624 0.767405i −0.0486691 0.0353602i
\(472\) 0 0
\(473\) 11.9144 + 0.683288i 0.547823 + 0.0314176i
\(474\) 0 0
\(475\) 6.22418 + 4.52213i 0.285585 + 0.207490i
\(476\) 0 0
\(477\) 8.63757 + 26.5837i 0.395487 + 1.21718i
\(478\) 0 0
\(479\) −23.1303 + 16.8051i −1.05685 + 0.767846i −0.973503 0.228674i \(-0.926561\pi\)
−0.0833469 + 0.996521i \(0.526561\pi\)
\(480\) 0 0
\(481\) −0.340838 + 1.04899i −0.0155409 + 0.0478299i
\(482\) 0 0
\(483\) −1.17156 −0.0533079
\(484\) 0 0
\(485\) 7.09963 0.322377
\(486\) 0 0
\(487\) −1.43808 + 4.42594i −0.0651654 + 0.200559i −0.978338 0.207015i \(-0.933625\pi\)
0.913172 + 0.407574i \(0.133625\pi\)
\(488\) 0 0
\(489\) 1.76220 1.28031i 0.0796893 0.0578977i
\(490\) 0 0
\(491\) −7.70564 23.7155i −0.347751 1.07027i −0.960095 0.279675i \(-0.909773\pi\)
0.612344 0.790592i \(-0.290227\pi\)
\(492\) 0 0
\(493\) −6.39440 4.64581i −0.287989 0.209237i
\(494\) 0 0
\(495\) 9.64547 + 0.553168i 0.433532 + 0.0248630i
\(496\) 0 0
\(497\) −24.7586 17.9882i −1.11057 0.806879i
\(498\) 0 0
\(499\) −4.75417 14.6318i −0.212826 0.655010i −0.999301 0.0373883i \(-0.988096\pi\)
0.786475 0.617622i \(-0.211904\pi\)
\(500\) 0 0
\(501\) 4.65031 3.37865i 0.207761 0.150947i
\(502\) 0 0
\(503\) 10.1206 31.1481i 0.451257 1.38883i −0.424217 0.905560i \(-0.639451\pi\)
0.875474 0.483265i \(-0.160549\pi\)
\(504\) 0 0
\(505\) −16.2851 −0.724677
\(506\) 0 0
\(507\) −6.65292 −0.295467
\(508\) 0 0
\(509\) 4.85208 14.9332i 0.215065 0.661901i −0.784084 0.620654i \(-0.786867\pi\)
0.999149 0.0412466i \(-0.0131329\pi\)
\(510\) 0 0
\(511\) −45.2998 + 32.9122i −2.00394 + 1.45595i
\(512\) 0 0
\(513\) −4.14650 12.7616i −0.183073 0.563439i
\(514\) 0 0
\(515\) 2.58124 + 1.87538i 0.113743 + 0.0826391i
\(516\) 0 0
\(517\) −0.934376 + 2.39874i −0.0410938 + 0.105496i
\(518\) 0 0
\(519\) 2.26891 + 1.64846i 0.0995939 + 0.0723592i
\(520\) 0 0
\(521\) −10.3905 31.9786i −0.455215 1.40101i −0.870883 0.491490i \(-0.836452\pi\)
0.415668 0.909516i \(-0.363548\pi\)
\(522\) 0 0
\(523\) −18.5729 + 13.4940i −0.812136 + 0.590051i −0.914449 0.404701i \(-0.867376\pi\)
0.102313 + 0.994752i \(0.467376\pi\)
\(524\) 0 0
\(525\) −0.400166 + 1.23158i −0.0174647 + 0.0537507i
\(526\) 0 0
\(527\) −8.54952 −0.372423
\(528\) 0 0
\(529\) −22.1815 −0.964413
\(530\) 0 0
\(531\) −10.1303 + 31.1779i −0.439617 + 1.35300i
\(532\) 0 0
\(533\) 12.6503 9.19101i 0.547947 0.398107i
\(534\) 0 0
\(535\) 4.06801 + 12.5201i 0.175876 + 0.541289i
\(536\) 0 0
\(537\) −1.72113 1.25047i −0.0742720 0.0539618i
\(538\) 0 0
\(539\) 34.2506 22.0034i 1.47528 0.947756i
\(540\) 0 0
\(541\) 15.1914 + 11.0372i 0.653131 + 0.474528i 0.864336 0.502914i \(-0.167739\pi\)
−0.211205 + 0.977442i \(0.567739\pi\)
\(542\) 0 0
\(543\) 2.13192 + 6.56136i 0.0914893 + 0.281575i
\(544\) 0 0
\(545\) −1.08030 + 0.784881i −0.0462748 + 0.0336206i
\(546\) 0 0
\(547\) −5.95740 + 18.3350i −0.254720 + 0.783947i 0.739165 + 0.673525i \(0.235220\pi\)
−0.993885 + 0.110423i \(0.964780\pi\)
\(548\) 0 0
\(549\) −38.4218 −1.63980
\(550\) 0 0
\(551\) 36.4595 1.55323
\(552\) 0 0
\(553\) 13.6091 41.8844i 0.578717 1.78111i
\(554\) 0 0
\(555\) −0.0441407 + 0.0320701i −0.00187367 + 0.00136130i
\(556\) 0 0
\(557\) −5.54314 17.0600i −0.234870 0.722857i −0.997139 0.0755955i \(-0.975914\pi\)
0.762268 0.647261i \(-0.224086\pi\)
\(558\) 0 0
\(559\) 17.3579 + 12.6112i 0.734159 + 0.533398i
\(560\) 0 0
\(561\) −0.414525 1.57809i −0.0175012 0.0666270i
\(562\) 0 0
\(563\) −1.46665 1.06558i −0.0618120 0.0449090i 0.556450 0.830881i \(-0.312163\pi\)
−0.618262 + 0.785972i \(0.712163\pi\)
\(564\) 0 0
\(565\) −0.517444 1.59253i −0.0217690 0.0669982i
\(566\) 0 0
\(567\) −29.2119 + 21.2237i −1.22678 + 0.891310i
\(568\) 0 0
\(569\) 2.63761 8.11773i 0.110574 0.340313i −0.880424 0.474187i \(-0.842742\pi\)
0.990998 + 0.133874i \(0.0427419\pi\)
\(570\) 0 0
\(571\) 32.2491 1.34958 0.674792 0.738008i \(-0.264233\pi\)
0.674792 + 0.738008i \(0.264233\pi\)
\(572\) 0 0
\(573\) −1.22873 −0.0513310
\(574\) 0 0
\(575\) 0.279570 0.860427i 0.0116589 0.0358823i
\(576\) 0 0
\(577\) −24.2423 + 17.6131i −1.00922 + 0.733243i −0.964046 0.265736i \(-0.914385\pi\)
−0.0451763 + 0.998979i \(0.514385\pi\)
\(578\) 0 0
\(579\) 2.11155 + 6.49868i 0.0877530 + 0.270076i
\(580\) 0 0
\(581\) 14.5456 + 10.5680i 0.603455 + 0.438435i
\(582\) 0 0
\(583\) −24.6335 20.1496i −1.02022 0.834512i
\(584\) 0 0
\(585\) 14.0523 + 10.2096i 0.580993 + 0.422116i
\(586\) 0 0
\(587\) −3.02941 9.32357i −0.125037 0.384825i 0.868871 0.495039i \(-0.164846\pi\)
−0.993908 + 0.110214i \(0.964846\pi\)
\(588\) 0 0
\(589\) 31.9057 23.1808i 1.31465 0.955149i
\(590\) 0 0
\(591\) −0.925223 + 2.84754i −0.0380586 + 0.117132i
\(592\) 0 0
\(593\) 15.4666 0.635136 0.317568 0.948235i \(-0.397134\pi\)
0.317568 + 0.948235i \(0.397134\pi\)
\(594\) 0 0
\(595\) −7.32228 −0.300184
\(596\) 0 0
\(597\) −1.55072 + 4.77263i −0.0634668 + 0.195331i
\(598\) 0 0
\(599\) −0.225061 + 0.163516i −0.00919574 + 0.00668110i −0.592374 0.805663i \(-0.701809\pi\)
0.583178 + 0.812344i \(0.301809\pi\)
\(600\) 0 0
\(601\) 9.27220 + 28.5369i 0.378221 + 1.16404i 0.941280 + 0.337628i \(0.109624\pi\)
−0.563059 + 0.826417i \(0.690376\pi\)
\(602\) 0 0
\(603\) 18.3809 + 13.3545i 0.748528 + 0.543837i
\(604\) 0 0
\(605\) −9.58002 + 5.40586i −0.389483 + 0.219779i
\(606\) 0 0
\(607\) −18.0387 13.1059i −0.732169 0.531952i 0.158080 0.987426i \(-0.449470\pi\)
−0.890249 + 0.455474i \(0.849470\pi\)
\(608\) 0 0
\(609\) 1.89638 + 5.83646i 0.0768452 + 0.236505i
\(610\) 0 0
\(611\) −3.74430 + 2.72040i −0.151478 + 0.110055i
\(612\) 0 0
\(613\) −8.76829 + 26.9860i −0.354148 + 1.08996i 0.602354 + 0.798229i \(0.294230\pi\)
−0.956502 + 0.291726i \(0.905770\pi\)
\(614\) 0 0
\(615\) 0.773501 0.0311906
\(616\) 0 0
\(617\) −15.1603 −0.610332 −0.305166 0.952299i \(-0.598712\pi\)
−0.305166 + 0.952299i \(0.598712\pi\)
\(618\) 0 0
\(619\) 9.12336 28.0788i 0.366699 1.12858i −0.582212 0.813037i \(-0.697813\pi\)
0.948910 0.315545i \(-0.102187\pi\)
\(620\) 0 0
\(621\) −1.27656 + 0.927473i −0.0512265 + 0.0372182i
\(622\) 0 0
\(623\) −0.632600 1.94694i −0.0253446 0.0780026i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 0 0
\(627\) 5.82572 + 4.76529i 0.232657 + 0.190307i
\(628\) 0 0
\(629\) −0.249591 0.181338i −0.00995184 0.00723043i
\(630\) 0 0
\(631\) 14.1188 + 43.4532i 0.562061 + 1.72985i 0.676527 + 0.736418i \(0.263484\pi\)
−0.114466 + 0.993427i \(0.536516\pi\)
\(632\) 0 0
\(633\) 1.43565 1.04306i 0.0570618 0.0414579i
\(634\) 0 0
\(635\) −0.278570 + 0.857349i −0.0110547 + 0.0340229i
\(636\) 0 0
\(637\) 73.1897 2.89988
\(638\) 0 0
\(639\) −20.3057 −0.803281
\(640\) 0 0
\(641\) 11.1602 34.3475i 0.440801 1.35665i −0.446223 0.894922i \(-0.647231\pi\)
0.887024 0.461724i \(-0.152769\pi\)
\(642\) 0 0
\(643\) −27.0998 + 19.6892i −1.06871 + 0.776465i −0.975680 0.219198i \(-0.929656\pi\)
−0.0930318 + 0.995663i \(0.529656\pi\)
\(644\) 0 0
\(645\) 0.327972 + 1.00939i 0.0129139 + 0.0397449i
\(646\) 0 0
\(647\) 31.7188 + 23.0451i 1.24700 + 0.905996i 0.998044 0.0625198i \(-0.0199136\pi\)
0.248953 + 0.968516i \(0.419914\pi\)
\(648\) 0 0
\(649\) −9.48258 36.1000i −0.372224 1.41705i
\(650\) 0 0
\(651\) 5.37032 + 3.90177i 0.210480 + 0.152922i
\(652\) 0 0
\(653\) 7.65109 + 23.5476i 0.299410 + 0.921491i 0.981704 + 0.190412i \(0.0609825\pi\)
−0.682294 + 0.731078i \(0.739017\pi\)
\(654\) 0 0
\(655\) −11.7734 + 8.55388i −0.460025 + 0.334228i
\(656\) 0 0
\(657\) −11.4808 + 35.3342i −0.447907 + 1.37852i
\(658\) 0 0
\(659\) −24.8813 −0.969238 −0.484619 0.874725i \(-0.661042\pi\)
−0.484619 + 0.874725i \(0.661042\pi\)
\(660\) 0 0
\(661\) −5.94396 −0.231193 −0.115597 0.993296i \(-0.536878\pi\)
−0.115597 + 0.993296i \(0.536878\pi\)
\(662\) 0 0
\(663\) 0.906478 2.78985i 0.0352047 0.108349i
\(664\) 0 0
\(665\) 27.3258 19.8533i 1.05965 0.769879i
\(666\) 0 0
\(667\) −1.32488 4.07755i −0.0512995 0.157883i
\(668\) 0 0
\(669\) −0.595161 0.432410i −0.0230103 0.0167179i
\(670\) 0 0
\(671\) 36.8051 23.6445i 1.42085 0.912786i
\(672\) 0 0
\(673\) −30.6213 22.2477i −1.18036 0.857585i −0.188152 0.982140i \(-0.560250\pi\)
−0.992213 + 0.124555i \(0.960250\pi\)
\(674\) 0 0
\(675\) 0.538961 + 1.65875i 0.0207446 + 0.0638454i
\(676\) 0 0
\(677\) −0.153794 + 0.111738i −0.00591078 + 0.00429443i −0.590737 0.806864i \(-0.701163\pi\)
0.584826 + 0.811159i \(0.301163\pi\)
\(678\) 0 0
\(679\) 9.63181 29.6437i 0.369635 1.13762i
\(680\) 0 0
\(681\) −7.37267 −0.282521
\(682\) 0 0
\(683\) −23.0773 −0.883030 −0.441515 0.897254i \(-0.645559\pi\)
−0.441515 + 0.897254i \(0.645559\pi\)
\(684\) 0 0
\(685\) −6.36251 + 19.5818i −0.243099 + 0.748182i
\(686\) 0 0
\(687\) −0.661201 + 0.480391i −0.0252264 + 0.0183281i
\(688\) 0 0
\(689\) −17.6808 54.4160i −0.673586 2.07308i
\(690\) 0 0
\(691\) 37.7877 + 27.4544i 1.43751 + 1.04441i 0.988555 + 0.150862i \(0.0482049\pi\)
0.448958 + 0.893553i \(0.351795\pi\)
\(692\) 0 0
\(693\) 15.3953 39.5231i 0.584821 1.50136i
\(694\) 0 0
\(695\) −12.1224 8.80746i −0.459830 0.334086i
\(696\) 0 0
\(697\) 1.35155 + 4.15965i 0.0511936 + 0.157558i
\(698\) 0 0
\(699\) −2.29091 + 1.66444i −0.0866501 + 0.0629550i
\(700\) 0 0
\(701\) 1.28934 3.96818i 0.0486977 0.149876i −0.923751 0.382994i \(-0.874893\pi\)
0.972448 + 0.233118i \(0.0748929\pi\)
\(702\) 0 0
\(703\) 1.42311 0.0536737
\(704\) 0 0
\(705\) −0.228944 −0.00862254
\(706\) 0 0
\(707\) −22.0934 + 67.9965i −0.830908 + 2.55727i
\(708\) 0 0
\(709\) 7.07305 5.13887i 0.265634 0.192994i −0.446993 0.894537i \(-0.647505\pi\)
0.712627 + 0.701543i \(0.247505\pi\)
\(710\) 0 0
\(711\) −9.02981 27.7909i −0.338644 1.04224i
\(712\) 0 0
\(713\) −3.75189 2.72591i −0.140510 0.102086i
\(714\) 0 0
\(715\) −19.7440 1.13232i −0.738382 0.0423462i
\(716\) 0 0
\(717\) −3.52438 2.56061i −0.131620 0.0956278i
\(718\) 0 0
\(719\) 2.28722 + 7.03934i 0.0852990 + 0.262523i 0.984604 0.174798i \(-0.0559273\pi\)
−0.899305 + 0.437321i \(0.855927\pi\)
\(720\) 0 0
\(721\) 11.3323 8.23340i 0.422037 0.306628i
\(722\) 0 0
\(723\) 0.951024 2.92695i 0.0353690 0.108854i
\(724\) 0 0
\(725\) −4.73899 −0.176002
\(726\) 0 0
\(727\) −18.0187 −0.668275 −0.334137 0.942524i \(-0.608445\pi\)
−0.334137 + 0.942524i \(0.608445\pi\)
\(728\) 0 0
\(729\) −6.92653 + 21.3177i −0.256538 + 0.789543i
\(730\) 0 0
\(731\) −4.85514 + 3.52746i −0.179574 + 0.130468i
\(732\) 0 0
\(733\) −11.2463 34.6127i −0.415393 1.27845i −0.911899 0.410415i \(-0.865384\pi\)
0.496506 0.868033i \(-0.334616\pi\)
\(734\) 0 0
\(735\) 2.92903 + 2.12806i 0.108039 + 0.0784948i
\(736\) 0 0
\(737\) −25.8257 1.48110i −0.951302 0.0545572i
\(738\) 0 0
\(739\) −10.0576 7.30726i −0.369974 0.268802i 0.387226 0.921985i \(-0.373433\pi\)
−0.757200 + 0.653183i \(0.773433\pi\)
\(740\) 0 0
\(741\) 4.18144 + 12.8691i 0.153609 + 0.472759i
\(742\) 0 0
\(743\) 30.2327 21.9653i 1.10913 0.805829i 0.126602 0.991954i \(-0.459593\pi\)
0.982526 + 0.186125i \(0.0595928\pi\)
\(744\) 0 0
\(745\) 3.38762 10.4260i 0.124113 0.381980i
\(746\) 0 0
\(747\) 11.9296 0.436480
\(748\) 0 0
\(749\) 57.7950 2.11178
\(750\) 0 0
\(751\) 2.44111 7.51295i 0.0890772 0.274151i −0.896588 0.442866i \(-0.853962\pi\)
0.985665 + 0.168715i \(0.0539617\pi\)
\(752\) 0 0
\(753\) 1.60692 1.16749i 0.0585594 0.0425459i
\(754\) 0 0
\(755\) 1.82682 + 5.62238i 0.0664848 + 0.204619i
\(756\) 0 0
\(757\) 2.56487 + 1.86349i 0.0932219 + 0.0677297i 0.633420 0.773808i \(-0.281651\pi\)
−0.540198 + 0.841538i \(0.681651\pi\)
\(758\) 0 0
\(759\) 0.321244 0.824699i 0.0116604 0.0299347i
\(760\) 0 0
\(761\) −37.8368 27.4901i −1.37158 0.996514i −0.997612 0.0690739i \(-0.977996\pi\)
−0.373972 0.927440i \(-0.622004\pi\)
\(762\) 0 0
\(763\) 1.81158 + 5.57547i 0.0655836 + 0.201845i
\(764\) 0 0
\(765\) −3.93056 + 2.85572i −0.142110 + 0.103249i
\(766\) 0 0
\(767\) 20.7364 63.8201i 0.748748 2.30441i
\(768\) 0 0
\(769\) −1.95610 −0.0705388 −0.0352694 0.999378i \(-0.511229\pi\)
−0.0352694 + 0.999378i \(0.511229\pi\)
\(770\) 0 0
\(771\) −2.28358 −0.0822411
\(772\) 0 0
\(773\) −6.31718 + 19.4423i −0.227213 + 0.699290i 0.770846 + 0.637021i \(0.219834\pi\)
−0.998059 + 0.0622690i \(0.980166\pi\)
\(774\) 0 0
\(775\) −4.14709 + 3.01303i −0.148968 + 0.108231i
\(776\) 0 0
\(777\) 0.0740209 + 0.227813i 0.00265548 + 0.00817274i
\(778\) 0 0
\(779\) −16.3221 11.8587i −0.584800 0.424882i
\(780\) 0 0
\(781\) 19.4513 12.4960i 0.696021 0.447141i
\(782\) 0 0
\(783\) 6.68680 + 4.85825i 0.238967 + 0.173620i
\(784\) 0 0
\(785\) −1.36780 4.20964i −0.0488187 0.150249i
\(786\) 0 0
\(787\) −2.09694 + 1.52351i −0.0747478 + 0.0543074i −0.624532 0.781000i \(-0.714710\pi\)
0.549784 + 0.835307i \(0.314710\pi\)
\(788\) 0