Properties

Label 880.2.bo.i.641.2
Level $880$
Weight $2$
Character 880.641
Analytic conductor $7.027$
Analytic rank $0$
Dimension $12$
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: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 \) 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 641.2
Root \(0.0307040 + 0.0223078i\) of defining polynomial
Character \(\chi\) \(=\) 880.641
Dual form 880.2.bo.i.81.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.320745 + 0.987151i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.804092 - 2.47474i) q^{7} +(1.55546 - 1.13011i) q^{9} +O(q^{10})\) \(q+(0.320745 + 0.987151i) q^{3} +(0.809017 + 0.587785i) q^{5} +(0.804092 - 2.47474i) q^{7} +(1.55546 - 1.13011i) q^{9} +(-1.34374 - 3.03222i) q^{11} +(2.32799 - 1.69139i) q^{13} +(-0.320745 + 0.987151i) q^{15} +(-0.655541 - 0.476279i) q^{17} +(-1.59165 - 4.89860i) q^{19} +2.70085 q^{21} -4.98262 q^{23} +(0.309017 + 0.951057i) q^{25} +(4.13366 + 3.00328i) q^{27} +(2.07948 - 6.39997i) q^{29} +(-3.35001 + 2.43392i) q^{31} +(2.56226 - 2.29904i) q^{33} +(2.10514 - 1.52947i) q^{35} +(1.25193 - 3.85304i) q^{37} +(2.41635 + 1.75558i) q^{39} +(3.01626 + 9.28309i) q^{41} +5.92912 q^{43} +1.92266 q^{45} +(0.299099 + 0.920531i) q^{47} +(0.185338 + 0.134656i) q^{49} +(0.259897 - 0.799882i) q^{51} +(-3.61991 + 2.63002i) q^{53} +(0.695188 - 3.24295i) q^{55} +(4.32514 - 3.14240i) q^{57} +(-2.10365 + 6.47438i) q^{59} +(2.11402 + 1.53592i) q^{61} +(-1.54599 - 4.75807i) q^{63} +2.87756 q^{65} +15.8408 q^{67} +(-1.59815 - 4.91860i) q^{69} +(-1.14351 - 0.830809i) q^{71} +(-4.06139 + 12.4997i) q^{73} +(-0.839721 + 0.610093i) q^{75} +(-8.58445 + 0.887220i) q^{77} +(4.60431 - 3.34522i) q^{79} +(0.143559 - 0.441831i) q^{81} +(6.44760 + 4.68445i) q^{83} +(-0.250394 - 0.770635i) q^{85} +6.98472 q^{87} -14.5196 q^{89} +(-2.31382 - 7.12121i) q^{91} +(-3.47715 - 2.52630i) q^{93} +(1.59165 - 4.89860i) q^{95} +(2.42159 - 1.75939i) q^{97} +(-5.51687 - 3.19793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37} + 33 q^{39} + 2 q^{41} + 36 q^{43} - 10 q^{45} + 16 q^{47} - 16 q^{49} + 10 q^{51} + 19 q^{53} - 6 q^{55} + 62 q^{57} - 46 q^{59} + 18 q^{61} + 7 q^{63} + 2 q^{65} + 44 q^{67} - q^{69} + 6 q^{71} + 25 q^{73} - 4 q^{75} + 10 q^{77} - 19 q^{79} + 30 q^{81} - 3 q^{85} - 6 q^{87} - 50 q^{89} + 46 q^{91} - 37 q^{93} + 4 q^{95} - 31 q^{97} - 79 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

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
\(3\) 0.320745 + 0.987151i 0.185182 + 0.569932i 0.999951 0.00985324i \(-0.00313643\pi\)
−0.814769 + 0.579785i \(0.803136\pi\)
\(4\) 0 0
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) 0 0
\(7\) 0.804092 2.47474i 0.303918 0.935364i −0.676160 0.736755i \(-0.736357\pi\)
0.980079 0.198610i \(-0.0636427\pi\)
\(8\) 0 0
\(9\) 1.55546 1.13011i 0.518487 0.376703i
\(10\) 0 0
\(11\) −1.34374 3.03222i −0.405152 0.914249i
\(12\) 0 0
\(13\) 2.32799 1.69139i 0.645669 0.469106i −0.216124 0.976366i \(-0.569342\pi\)
0.861793 + 0.507260i \(0.169342\pi\)
\(14\) 0 0
\(15\) −0.320745 + 0.987151i −0.0828160 + 0.254881i
\(16\) 0 0
\(17\) −0.655541 0.476279i −0.158992 0.115515i 0.505445 0.862859i \(-0.331328\pi\)
−0.664437 + 0.747345i \(0.731328\pi\)
\(18\) 0 0
\(19\) −1.59165 4.89860i −0.365150 1.12381i −0.949887 0.312592i \(-0.898803\pi\)
0.584738 0.811222i \(-0.301197\pi\)
\(20\) 0 0
\(21\) 2.70085 0.589374
\(22\) 0 0
\(23\) −4.98262 −1.03895 −0.519474 0.854486i \(-0.673872\pi\)
−0.519474 + 0.854486i \(0.673872\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 0 0
\(27\) 4.13366 + 3.00328i 0.795523 + 0.577981i
\(28\) 0 0
\(29\) 2.07948 6.39997i 0.386149 1.18845i −0.549494 0.835498i \(-0.685179\pi\)
0.935643 0.352947i \(-0.114821\pi\)
\(30\) 0 0
\(31\) −3.35001 + 2.43392i −0.601679 + 0.437146i −0.846475 0.532429i \(-0.821279\pi\)
0.244795 + 0.969575i \(0.421279\pi\)
\(32\) 0 0
\(33\) 2.56226 2.29904i 0.446033 0.400212i
\(34\) 0 0
\(35\) 2.10514 1.52947i 0.355834 0.258528i
\(36\) 0 0
\(37\) 1.25193 3.85304i 0.205816 0.633436i −0.793863 0.608097i \(-0.791933\pi\)
0.999679 0.0253395i \(-0.00806668\pi\)
\(38\) 0 0
\(39\) 2.41635 + 1.75558i 0.386925 + 0.281117i
\(40\) 0 0
\(41\) 3.01626 + 9.28309i 0.471061 + 1.44978i 0.851198 + 0.524845i \(0.175877\pi\)
−0.380137 + 0.924930i \(0.624123\pi\)
\(42\) 0 0
\(43\) 5.92912 0.904182 0.452091 0.891972i \(-0.350678\pi\)
0.452091 + 0.891972i \(0.350678\pi\)
\(44\) 0 0
\(45\) 1.92266 0.286613
\(46\) 0 0
\(47\) 0.299099 + 0.920531i 0.0436280 + 0.134273i 0.970498 0.241109i \(-0.0775113\pi\)
−0.926870 + 0.375383i \(0.877511\pi\)
\(48\) 0 0
\(49\) 0.185338 + 0.134656i 0.0264769 + 0.0192366i
\(50\) 0 0
\(51\) 0.259897 0.799882i 0.0363929 0.112006i
\(52\) 0 0
\(53\) −3.61991 + 2.63002i −0.497233 + 0.361261i −0.807959 0.589239i \(-0.799428\pi\)
0.310726 + 0.950499i \(0.399428\pi\)
\(54\) 0 0
\(55\) 0.695188 3.24295i 0.0937391 0.437279i
\(56\) 0 0
\(57\) 4.32514 3.14240i 0.572879 0.416221i
\(58\) 0 0
\(59\) −2.10365 + 6.47438i −0.273872 + 0.842892i 0.715643 + 0.698466i \(0.246134\pi\)
−0.989516 + 0.144426i \(0.953866\pi\)
\(60\) 0 0
\(61\) 2.11402 + 1.53592i 0.270672 + 0.196655i 0.714839 0.699289i \(-0.246500\pi\)
−0.444167 + 0.895944i \(0.646500\pi\)
\(62\) 0 0
\(63\) −1.54599 4.75807i −0.194777 0.599461i
\(64\) 0 0
\(65\) 2.87756 0.356917
\(66\) 0 0
\(67\) 15.8408 1.93526 0.967629 0.252378i \(-0.0812125\pi\)
0.967629 + 0.252378i \(0.0812125\pi\)
\(68\) 0 0
\(69\) −1.59815 4.91860i −0.192395 0.592130i
\(70\) 0 0
\(71\) −1.14351 0.830809i −0.135710 0.0985989i 0.517859 0.855466i \(-0.326729\pi\)
−0.653569 + 0.756867i \(0.726729\pi\)
\(72\) 0 0
\(73\) −4.06139 + 12.4997i −0.475349 + 1.46297i 0.370137 + 0.928977i \(0.379311\pi\)
−0.845486 + 0.533998i \(0.820689\pi\)
\(74\) 0 0
\(75\) −0.839721 + 0.610093i −0.0969626 + 0.0704475i
\(76\) 0 0
\(77\) −8.58445 + 0.887220i −0.978289 + 0.101108i
\(78\) 0 0
\(79\) 4.60431 3.34522i 0.518025 0.376367i −0.297834 0.954618i \(-0.596264\pi\)
0.815859 + 0.578250i \(0.196264\pi\)
\(80\) 0 0
\(81\) 0.143559 0.441831i 0.0159510 0.0490923i
\(82\) 0 0
\(83\) 6.44760 + 4.68445i 0.707716 + 0.514186i 0.882436 0.470432i \(-0.155902\pi\)
−0.174720 + 0.984618i \(0.555902\pi\)
\(84\) 0 0
\(85\) −0.250394 0.770635i −0.0271591 0.0835871i
\(86\) 0 0
\(87\) 6.98472 0.748841
\(88\) 0 0
\(89\) −14.5196 −1.53907 −0.769535 0.638605i \(-0.779512\pi\)
−0.769535 + 0.638605i \(0.779512\pi\)
\(90\) 0 0
\(91\) −2.31382 7.12121i −0.242554 0.746506i
\(92\) 0 0
\(93\) −3.47715 2.52630i −0.360564 0.261965i
\(94\) 0 0
\(95\) 1.59165 4.89860i 0.163300 0.502585i
\(96\) 0 0
\(97\) 2.42159 1.75939i 0.245876 0.178639i −0.458021 0.888941i \(-0.651442\pi\)
0.703897 + 0.710302i \(0.251442\pi\)
\(98\) 0 0
\(99\) −5.51687 3.19793i −0.554466 0.321404i
\(100\) 0 0
\(101\) 12.4346 9.03428i 1.23729 0.898944i 0.239876 0.970804i \(-0.422893\pi\)
0.997415 + 0.0718593i \(0.0228932\pi\)
\(102\) 0 0
\(103\) −1.69746 + 5.22424i −0.167256 + 0.514760i −0.999195 0.0401060i \(-0.987230\pi\)
0.831940 + 0.554866i \(0.187230\pi\)
\(104\) 0 0
\(105\) 2.18504 + 1.58752i 0.213238 + 0.154926i
\(106\) 0 0
\(107\) 1.92725 + 5.93147i 0.186315 + 0.573417i 0.999969 0.00793218i \(-0.00252492\pi\)
−0.813654 + 0.581349i \(0.802525\pi\)
\(108\) 0 0
\(109\) −19.1460 −1.83385 −0.916927 0.399056i \(-0.869338\pi\)
−0.916927 + 0.399056i \(0.869338\pi\)
\(110\) 0 0
\(111\) 4.20508 0.399129
\(112\) 0 0
\(113\) −3.35842 10.3362i −0.315934 0.972344i −0.975368 0.220582i \(-0.929204\pi\)
0.659435 0.751762i \(-0.270796\pi\)
\(114\) 0 0
\(115\) −4.03103 2.92871i −0.375895 0.273104i
\(116\) 0 0
\(117\) 1.70965 5.26177i 0.158057 0.486451i
\(118\) 0 0
\(119\) −1.70578 + 1.23932i −0.156369 + 0.113609i
\(120\) 0 0
\(121\) −7.38873 + 8.14903i −0.671703 + 0.740821i
\(122\) 0 0
\(123\) −8.19637 + 5.95501i −0.739041 + 0.536945i
\(124\) 0 0
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) 15.3227 + 11.1326i 1.35967 + 0.987861i 0.998466 + 0.0553760i \(0.0176358\pi\)
0.361209 + 0.932485i \(0.382364\pi\)
\(128\) 0 0
\(129\) 1.90173 + 5.85293i 0.167438 + 0.515322i
\(130\) 0 0
\(131\) −14.5409 −1.27045 −0.635224 0.772328i \(-0.719092\pi\)
−0.635224 + 0.772328i \(0.719092\pi\)
\(132\) 0 0
\(133\) −13.4026 −1.16215
\(134\) 0 0
\(135\) 1.57892 + 4.85941i 0.135891 + 0.418231i
\(136\) 0 0
\(137\) 16.1674 + 11.7463i 1.38128 + 1.00356i 0.996760 + 0.0804370i \(0.0256316\pi\)
0.384516 + 0.923118i \(0.374368\pi\)
\(138\) 0 0
\(139\) 0.639884 1.96936i 0.0542742 0.167039i −0.920245 0.391343i \(-0.872011\pi\)
0.974519 + 0.224304i \(0.0720108\pi\)
\(140\) 0 0
\(141\) −0.812769 + 0.590512i −0.0684475 + 0.0497300i
\(142\) 0 0
\(143\) −8.25687 4.78621i −0.690474 0.400243i
\(144\) 0 0
\(145\) 5.44414 3.95540i 0.452111 0.328478i
\(146\) 0 0
\(147\) −0.0734796 + 0.226147i −0.00606049 + 0.0186523i
\(148\) 0 0
\(149\) −0.408306 0.296651i −0.0334497 0.0243026i 0.570935 0.820995i \(-0.306581\pi\)
−0.604384 + 0.796693i \(0.706581\pi\)
\(150\) 0 0
\(151\) −3.74492 11.5257i −0.304757 0.937947i −0.979768 0.200139i \(-0.935861\pi\)
0.675010 0.737808i \(-0.264139\pi\)
\(152\) 0 0
\(153\) −1.55791 −0.125950
\(154\) 0 0
\(155\) −4.14084 −0.332600
\(156\) 0 0
\(157\) −3.67275 11.3036i −0.293117 0.902123i −0.983847 0.179010i \(-0.942711\pi\)
0.690730 0.723113i \(-0.257289\pi\)
\(158\) 0 0
\(159\) −3.75729 2.72983i −0.297973 0.216490i
\(160\) 0 0
\(161\) −4.00649 + 12.3307i −0.315756 + 0.971796i
\(162\) 0 0
\(163\) 0.0510648 0.0371008i 0.00399970 0.00290596i −0.585784 0.810468i \(-0.699213\pi\)
0.589783 + 0.807562i \(0.299213\pi\)
\(164\) 0 0
\(165\) 3.42426 0.353904i 0.266578 0.0275514i
\(166\) 0 0
\(167\) −6.10284 + 4.43397i −0.472252 + 0.343111i −0.798318 0.602236i \(-0.794277\pi\)
0.326066 + 0.945347i \(0.394277\pi\)
\(168\) 0 0
\(169\) −1.45846 + 4.48866i −0.112189 + 0.345282i
\(170\) 0 0
\(171\) −8.01169 5.82084i −0.612669 0.445130i
\(172\) 0 0
\(173\) −0.436524 1.34348i −0.0331883 0.102143i 0.933090 0.359643i \(-0.117101\pi\)
−0.966278 + 0.257500i \(0.917101\pi\)
\(174\) 0 0
\(175\) 2.60210 0.196700
\(176\) 0 0
\(177\) −7.06593 −0.531108
\(178\) 0 0
\(179\) 4.88918 + 15.0473i 0.365434 + 1.12469i 0.949709 + 0.313135i \(0.101379\pi\)
−0.584274 + 0.811556i \(0.698621\pi\)
\(180\) 0 0
\(181\) −15.3530 11.1546i −1.14118 0.829115i −0.153895 0.988087i \(-0.549182\pi\)
−0.987283 + 0.158973i \(0.949182\pi\)
\(182\) 0 0
\(183\) −0.838128 + 2.57949i −0.0619562 + 0.190682i
\(184\) 0 0
\(185\) 3.27759 2.38131i 0.240973 0.175077i
\(186\) 0 0
\(187\) −0.563306 + 2.62774i −0.0411930 + 0.192159i
\(188\) 0 0
\(189\) 10.7562 7.81482i 0.782397 0.568445i
\(190\) 0 0
\(191\) −3.20344 + 9.85919i −0.231793 + 0.713386i 0.765738 + 0.643153i \(0.222374\pi\)
−0.997531 + 0.0702325i \(0.977626\pi\)
\(192\) 0 0
\(193\) 0.492410 + 0.357757i 0.0354444 + 0.0257519i 0.605366 0.795947i \(-0.293027\pi\)
−0.569922 + 0.821699i \(0.693027\pi\)
\(194\) 0 0
\(195\) 0.922962 + 2.84058i 0.0660947 + 0.203418i
\(196\) 0 0
\(197\) 11.1521 0.794553 0.397277 0.917699i \(-0.369955\pi\)
0.397277 + 0.917699i \(0.369955\pi\)
\(198\) 0 0
\(199\) −8.91481 −0.631954 −0.315977 0.948767i \(-0.602332\pi\)
−0.315977 + 0.948767i \(0.602332\pi\)
\(200\) 0 0
\(201\) 5.08084 + 15.6372i 0.358375 + 1.10297i
\(202\) 0 0
\(203\) −14.1662 10.2923i −0.994271 0.722380i
\(204\) 0 0
\(205\) −3.01626 + 9.28309i −0.210665 + 0.648359i
\(206\) 0 0
\(207\) −7.75027 + 5.63090i −0.538681 + 0.391375i
\(208\) 0 0
\(209\) −12.7149 + 11.4087i −0.879505 + 0.789154i
\(210\) 0 0
\(211\) 14.0806 10.2302i 0.969351 0.704275i 0.0140475 0.999901i \(-0.495528\pi\)
0.955304 + 0.295627i \(0.0955284\pi\)
\(212\) 0 0
\(213\) 0.453359 1.39530i 0.0310637 0.0956041i
\(214\) 0 0
\(215\) 4.79676 + 3.48505i 0.327136 + 0.237678i
\(216\) 0 0
\(217\) 3.32962 + 10.2475i 0.226029 + 0.695646i
\(218\) 0 0
\(219\) −13.6417 −0.921822
\(220\) 0 0
\(221\) −2.33167 −0.156845
\(222\) 0 0
\(223\) 0.474865 + 1.46148i 0.0317993 + 0.0978683i 0.965696 0.259674i \(-0.0836150\pi\)
−0.933897 + 0.357542i \(0.883615\pi\)
\(224\) 0 0
\(225\) 1.55546 + 1.13011i 0.103697 + 0.0753406i
\(226\) 0 0
\(227\) −3.12047 + 9.60382i −0.207113 + 0.637428i 0.792507 + 0.609863i \(0.208775\pi\)
−0.999620 + 0.0275653i \(0.991225\pi\)
\(228\) 0 0
\(229\) −1.93578 + 1.40643i −0.127920 + 0.0929395i −0.649906 0.760015i \(-0.725192\pi\)
0.521985 + 0.852954i \(0.325192\pi\)
\(230\) 0 0
\(231\) −3.62924 8.18958i −0.238786 0.538835i
\(232\) 0 0
\(233\) 6.70453 4.87113i 0.439229 0.319118i −0.346100 0.938198i \(-0.612494\pi\)
0.785328 + 0.619079i \(0.212494\pi\)
\(234\) 0 0
\(235\) −0.299099 + 0.920531i −0.0195111 + 0.0600489i
\(236\) 0 0
\(237\) 4.77905 + 3.47218i 0.310433 + 0.225542i
\(238\) 0 0
\(239\) −1.40975 4.33878i −0.0911894 0.280652i 0.895052 0.445961i \(-0.147138\pi\)
−0.986242 + 0.165309i \(0.947138\pi\)
\(240\) 0 0
\(241\) 23.4148 1.50828 0.754139 0.656715i \(-0.228054\pi\)
0.754139 + 0.656715i \(0.228054\pi\)
\(242\) 0 0
\(243\) 15.8106 1.01425
\(244\) 0 0
\(245\) 0.0707928 + 0.217878i 0.00452279 + 0.0139197i
\(246\) 0 0
\(247\) −11.9908 8.71180i −0.762954 0.554319i
\(248\) 0 0
\(249\) −2.55623 + 7.86727i −0.161995 + 0.498568i
\(250\) 0 0
\(251\) −22.4458 + 16.3079i −1.41677 + 1.02934i −0.424474 + 0.905440i \(0.639541\pi\)
−0.992294 + 0.123903i \(0.960459\pi\)
\(252\) 0 0
\(253\) 6.69534 + 15.1084i 0.420933 + 0.949858i
\(254\) 0 0
\(255\) 0.680420 0.494354i 0.0426096 0.0309577i
\(256\) 0 0
\(257\) −7.87507 + 24.2370i −0.491233 + 1.51186i 0.331512 + 0.943451i \(0.392441\pi\)
−0.822746 + 0.568410i \(0.807559\pi\)
\(258\) 0 0
\(259\) −8.52861 6.19640i −0.529942 0.385026i
\(260\) 0 0
\(261\) −3.99812 12.3049i −0.247477 0.761657i
\(262\) 0 0
\(263\) −16.1271 −0.994442 −0.497221 0.867624i \(-0.665646\pi\)
−0.497221 + 0.867624i \(0.665646\pi\)
\(264\) 0 0
\(265\) −4.47445 −0.274863
\(266\) 0 0
\(267\) −4.65707 14.3330i −0.285008 0.877165i
\(268\) 0 0
\(269\) −14.1769 10.3001i −0.864380 0.628009i 0.0646931 0.997905i \(-0.479393\pi\)
−0.929073 + 0.369896i \(0.879393\pi\)
\(270\) 0 0
\(271\) −2.26740 + 6.97834i −0.137735 + 0.423904i −0.996005 0.0892933i \(-0.971539\pi\)
0.858271 + 0.513197i \(0.171539\pi\)
\(272\) 0 0
\(273\) 6.28757 4.56818i 0.380541 0.276479i
\(274\) 0 0
\(275\) 2.46858 2.21498i 0.148861 0.133568i
\(276\) 0 0
\(277\) 14.0824 10.2315i 0.846131 0.614750i −0.0779455 0.996958i \(-0.524836\pi\)
0.924077 + 0.382207i \(0.124836\pi\)
\(278\) 0 0
\(279\) −2.46021 + 7.57175i −0.147289 + 0.453309i
\(280\) 0 0
\(281\) −11.1504 8.10126i −0.665179 0.483281i 0.203229 0.979131i \(-0.434856\pi\)
−0.868408 + 0.495851i \(0.834856\pi\)
\(282\) 0 0
\(283\) −3.58164 11.0232i −0.212906 0.655259i −0.999296 0.0375273i \(-0.988052\pi\)
0.786389 0.617731i \(-0.211948\pi\)
\(284\) 0 0
\(285\) 5.34617 0.316680
\(286\) 0 0
\(287\) 25.3986 1.49923
\(288\) 0 0
\(289\) −5.05040 15.5435i −0.297082 0.914325i
\(290\) 0 0
\(291\) 2.51350 + 1.82616i 0.147344 + 0.107052i
\(292\) 0 0
\(293\) −4.98906 + 15.3547i −0.291464 + 0.897034i 0.692922 + 0.721012i \(0.256323\pi\)
−0.984386 + 0.176021i \(0.943677\pi\)
\(294\) 0 0
\(295\) −5.50744 + 4.00139i −0.320655 + 0.232970i
\(296\) 0 0
\(297\) 3.55205 16.5698i 0.206111 0.961476i
\(298\) 0 0
\(299\) −11.5995 + 8.42754i −0.670817 + 0.487377i
\(300\) 0 0
\(301\) 4.76756 14.6730i 0.274797 0.845739i
\(302\) 0 0
\(303\) 12.9065 + 9.37715i 0.741461 + 0.538703i
\(304\) 0 0
\(305\) 0.807482 + 2.48518i 0.0462363 + 0.142301i
\(306\) 0 0
\(307\) 14.3107 0.816753 0.408377 0.912814i \(-0.366095\pi\)
0.408377 + 0.912814i \(0.366095\pi\)
\(308\) 0 0
\(309\) −5.70157 −0.324351
\(310\) 0 0
\(311\) 6.91405 + 21.2793i 0.392060 + 1.20664i 0.931228 + 0.364438i \(0.118739\pi\)
−0.539167 + 0.842199i \(0.681261\pi\)
\(312\) 0 0
\(313\) −9.33349 6.78118i −0.527560 0.383295i 0.291884 0.956454i \(-0.405718\pi\)
−0.819444 + 0.573159i \(0.805718\pi\)
\(314\) 0 0
\(315\) 1.54599 4.75807i 0.0871068 0.268087i
\(316\) 0 0
\(317\) 20.4935 14.8894i 1.15103 0.836272i 0.162413 0.986723i \(-0.448072\pi\)
0.988618 + 0.150451i \(0.0480724\pi\)
\(318\) 0 0
\(319\) −22.2004 + 2.29446i −1.24298 + 0.128465i
\(320\) 0 0
\(321\) −5.23711 + 3.80498i −0.292307 + 0.212373i
\(322\) 0 0
\(323\) −1.28970 + 3.96930i −0.0717610 + 0.220858i
\(324\) 0 0
\(325\) 2.32799 + 1.69139i 0.129134 + 0.0938212i
\(326\) 0 0
\(327\) −6.14098 18.9000i −0.339597 1.04517i
\(328\) 0 0
\(329\) 2.51858 0.138854
\(330\) 0 0
\(331\) 20.9669 1.15244 0.576221 0.817294i \(-0.304527\pi\)
0.576221 + 0.817294i \(0.304527\pi\)
\(332\) 0 0
\(333\) −2.40703 7.40807i −0.131904 0.405960i
\(334\) 0 0
\(335\) 12.8154 + 9.31097i 0.700183 + 0.508713i
\(336\) 0 0
\(337\) −5.60649 + 17.2550i −0.305405 + 0.939940i 0.674121 + 0.738621i \(0.264523\pi\)
−0.979526 + 0.201319i \(0.935477\pi\)
\(338\) 0 0
\(339\) 9.12616 6.63054i 0.495665 0.360122i
\(340\) 0 0
\(341\) 11.8817 + 6.88741i 0.643432 + 0.372974i
\(342\) 0 0
\(343\) 15.2183 11.0567i 0.821708 0.597006i
\(344\) 0 0
\(345\) 1.59815 4.91860i 0.0860415 0.264809i
\(346\) 0 0
\(347\) 15.3632 + 11.1620i 0.824740 + 0.599209i 0.918066 0.396427i \(-0.129750\pi\)
−0.0933260 + 0.995636i \(0.529750\pi\)
\(348\) 0 0
\(349\) 4.98048 + 15.3283i 0.266599 + 0.820507i 0.991321 + 0.131465i \(0.0419682\pi\)
−0.724722 + 0.689041i \(0.758032\pi\)
\(350\) 0 0
\(351\) 14.7028 0.784779
\(352\) 0 0
\(353\) 28.0252 1.49163 0.745816 0.666152i \(-0.232060\pi\)
0.745816 + 0.666152i \(0.232060\pi\)
\(354\) 0 0
\(355\) −0.436782 1.34428i −0.0231820 0.0713468i
\(356\) 0 0
\(357\) −1.77052 1.28636i −0.0937059 0.0680813i
\(358\) 0 0
\(359\) −1.61893 + 4.98255i −0.0854438 + 0.262969i −0.984646 0.174565i \(-0.944148\pi\)
0.899202 + 0.437534i \(0.144148\pi\)
\(360\) 0 0
\(361\) −6.09156 + 4.42578i −0.320609 + 0.232936i
\(362\) 0 0
\(363\) −10.4142 4.68004i −0.546605 0.245638i
\(364\) 0 0
\(365\) −10.6328 + 7.72522i −0.556549 + 0.404356i
\(366\) 0 0
\(367\) 8.12960 25.0203i 0.424362 1.30605i −0.479242 0.877683i \(-0.659089\pi\)
0.903604 0.428368i \(-0.140911\pi\)
\(368\) 0 0
\(369\) 15.1826 + 11.0308i 0.790373 + 0.574240i
\(370\) 0 0
\(371\) 3.59787 + 11.0731i 0.186792 + 0.574887i
\(372\) 0 0
\(373\) −36.0081 −1.86443 −0.932215 0.361905i \(-0.882127\pi\)
−0.932215 + 0.361905i \(0.882127\pi\)
\(374\) 0 0
\(375\) −1.03795 −0.0535996
\(376\) 0 0
\(377\) −5.98382 18.4163i −0.308182 0.948487i
\(378\) 0 0
\(379\) −11.4027 8.28455i −0.585717 0.425549i 0.255063 0.966924i \(-0.417904\pi\)
−0.840781 + 0.541376i \(0.817904\pi\)
\(380\) 0 0
\(381\) −6.07490 + 18.6966i −0.311226 + 0.957856i
\(382\) 0 0
\(383\) 1.73227 1.25857i 0.0885148 0.0643098i −0.542648 0.839960i \(-0.682578\pi\)
0.631162 + 0.775651i \(0.282578\pi\)
\(384\) 0 0
\(385\) −7.46646 4.32804i −0.380526 0.220577i
\(386\) 0 0
\(387\) 9.22251 6.70054i 0.468806 0.340608i
\(388\) 0 0
\(389\) −9.04878 + 27.8493i −0.458791 + 1.41201i 0.407834 + 0.913056i \(0.366284\pi\)
−0.866626 + 0.498959i \(0.833716\pi\)
\(390\) 0 0
\(391\) 3.26631 + 2.37312i 0.165185 + 0.120014i
\(392\) 0 0
\(393\) −4.66393 14.3541i −0.235264 0.724069i
\(394\) 0 0
\(395\) 5.69123 0.286357
\(396\) 0 0
\(397\) 9.09620 0.456525 0.228263 0.973600i \(-0.426696\pi\)
0.228263 + 0.973600i \(0.426696\pi\)
\(398\) 0 0
\(399\) −4.29881 13.2304i −0.215210 0.662348i
\(400\) 0 0
\(401\) −26.1810 19.0216i −1.30741 0.949892i −0.307416 0.951575i \(-0.599464\pi\)
−0.999999 + 0.00168265i \(0.999464\pi\)
\(402\) 0 0
\(403\) −3.68209 + 11.3323i −0.183418 + 0.564503i
\(404\) 0 0
\(405\) 0.375843 0.273066i 0.0186758 0.0135688i
\(406\) 0 0
\(407\) −13.3655 + 1.38135i −0.662505 + 0.0684712i
\(408\) 0 0
\(409\) 16.8777 12.2624i 0.834548 0.606335i −0.0862941 0.996270i \(-0.527502\pi\)
0.920842 + 0.389935i \(0.127502\pi\)
\(410\) 0 0
\(411\) −6.40977 + 19.7273i −0.316171 + 0.973074i
\(412\) 0 0
\(413\) 14.3309 + 10.4120i 0.705177 + 0.512341i
\(414\) 0 0
\(415\) 2.46276 + 7.57961i 0.120892 + 0.372068i
\(416\) 0 0
\(417\) 2.14930 0.105251
\(418\) 0 0
\(419\) 36.4444 1.78043 0.890213 0.455545i \(-0.150556\pi\)
0.890213 + 0.455545i \(0.150556\pi\)
\(420\) 0 0
\(421\) −10.0210 30.8414i −0.488392 1.50312i −0.827007 0.562191i \(-0.809959\pi\)
0.338616 0.940925i \(-0.390041\pi\)
\(422\) 0 0
\(423\) 1.50554 + 1.09384i 0.0732017 + 0.0531841i
\(424\) 0 0
\(425\) 0.250394 0.770635i 0.0121459 0.0373813i
\(426\) 0 0
\(427\) 5.50088 3.99662i 0.266206 0.193410i
\(428\) 0 0
\(429\) 2.07636 9.68593i 0.100248 0.467641i
\(430\) 0 0
\(431\) 23.3589 16.9712i 1.12516 0.817476i 0.140176 0.990127i \(-0.455233\pi\)
0.984983 + 0.172650i \(0.0552330\pi\)
\(432\) 0 0
\(433\) 2.33475 7.18563i 0.112201 0.345320i −0.879152 0.476542i \(-0.841890\pi\)
0.991353 + 0.131222i \(0.0418901\pi\)
\(434\) 0 0
\(435\) 5.65076 + 4.10552i 0.270933 + 0.196844i
\(436\) 0 0
\(437\) 7.93059 + 24.4079i 0.379372 + 1.16759i
\(438\) 0 0
\(439\) 1.96072 0.0935801 0.0467900 0.998905i \(-0.485101\pi\)
0.0467900 + 0.998905i \(0.485101\pi\)
\(440\) 0 0
\(441\) 0.440462 0.0209744
\(442\) 0 0
\(443\) −1.86431 5.73776i −0.0885761 0.272609i 0.896950 0.442131i \(-0.145778\pi\)
−0.985526 + 0.169522i \(0.945778\pi\)
\(444\) 0 0
\(445\) −11.7466 8.53438i −0.556841 0.404568i
\(446\) 0 0
\(447\) 0.161878 0.498209i 0.00765656 0.0235645i
\(448\) 0 0
\(449\) −7.94777 + 5.77440i −0.375079 + 0.272511i −0.759314 0.650725i \(-0.774465\pi\)
0.384235 + 0.923235i \(0.374465\pi\)
\(450\) 0 0
\(451\) 24.0953 21.6200i 1.13460 1.01805i
\(452\) 0 0
\(453\) 10.1764 7.39361i 0.478130 0.347382i
\(454\) 0 0
\(455\) 2.31382 7.12121i 0.108474 0.333848i
\(456\) 0 0
\(457\) 6.33363 + 4.60165i 0.296275 + 0.215256i 0.725985 0.687711i \(-0.241384\pi\)
−0.429710 + 0.902967i \(0.641384\pi\)
\(458\) 0 0
\(459\) −1.27939 3.93754i −0.0597166 0.183789i
\(460\) 0 0
\(461\) −3.19972 −0.149026 −0.0745130 0.997220i \(-0.523740\pi\)
−0.0745130 + 0.997220i \(0.523740\pi\)
\(462\) 0 0
\(463\) 21.2096 0.985696 0.492848 0.870115i \(-0.335956\pi\)
0.492848 + 0.870115i \(0.335956\pi\)
\(464\) 0 0
\(465\) −1.32815 4.08763i −0.0615916 0.189559i
\(466\) 0 0
\(467\) −25.3195 18.3957i −1.17165 0.851252i −0.180443 0.983586i \(-0.557753\pi\)
−0.991205 + 0.132334i \(0.957753\pi\)
\(468\) 0 0
\(469\) 12.7374 39.2018i 0.588160 1.81017i
\(470\) 0 0
\(471\) 9.98031 7.25112i 0.459869 0.334114i
\(472\) 0 0
\(473\) −7.96718 17.9784i −0.366331 0.826647i
\(474\) 0 0
\(475\) 4.16699 3.02750i 0.191195 0.138911i
\(476\) 0 0
\(477\) −2.65842 + 8.18178i −0.121721 + 0.374618i
\(478\) 0 0
\(479\) 14.5641 + 10.5814i 0.665451 + 0.483478i 0.868499 0.495690i \(-0.165085\pi\)
−0.203049 + 0.979169i \(0.565085\pi\)
\(480\) 0 0
\(481\) −3.60250 11.0873i −0.164260 0.505540i
\(482\) 0 0
\(483\) −13.4573 −0.612330
\(484\) 0 0
\(485\) 2.99325 0.135917
\(486\) 0 0
\(487\) −6.51634 20.0552i −0.295284 0.908789i −0.983126 0.182929i \(-0.941442\pi\)
0.687843 0.725860i \(-0.258558\pi\)
\(488\) 0 0
\(489\) 0.0530028 + 0.0385088i 0.00239687 + 0.00174143i
\(490\) 0 0
\(491\) 6.80014 20.9287i 0.306886 0.944498i −0.672081 0.740478i \(-0.734599\pi\)
0.978967 0.204020i \(-0.0654008\pi\)
\(492\) 0 0
\(493\) −4.41135 + 3.20503i −0.198677 + 0.144348i
\(494\) 0 0
\(495\) −2.58355 5.82992i −0.116122 0.262035i
\(496\) 0 0
\(497\) −2.97553 + 2.16185i −0.133471 + 0.0969721i
\(498\) 0 0
\(499\) −4.98306 + 15.3363i −0.223072 + 0.686546i 0.775409 + 0.631459i \(0.217544\pi\)
−0.998482 + 0.0550871i \(0.982456\pi\)
\(500\) 0 0
\(501\) −6.33445 4.60225i −0.283003 0.205613i
\(502\) 0 0
\(503\) −0.978639 3.01194i −0.0436354 0.134296i 0.926865 0.375394i \(-0.122493\pi\)
−0.970501 + 0.241098i \(0.922493\pi\)
\(504\) 0 0
\(505\) 15.3700 0.683957
\(506\) 0 0
\(507\) −4.89878 −0.217563
\(508\) 0 0
\(509\) 8.95663 + 27.5657i 0.396996 + 1.22183i 0.927396 + 0.374080i \(0.122041\pi\)
−0.530401 + 0.847747i \(0.677959\pi\)
\(510\) 0 0
\(511\) 27.6677 + 20.1018i 1.22395 + 0.889250i
\(512\) 0 0
\(513\) 8.13251 25.0293i 0.359059 1.10507i
\(514\) 0 0
\(515\) −4.44401 + 3.22876i −0.195826 + 0.142276i
\(516\) 0 0
\(517\) 2.38934 2.14389i 0.105083 0.0942881i
\(518\) 0 0
\(519\) 1.18621 0.861831i 0.0520688 0.0378302i
\(520\) 0 0
\(521\) −4.89783 + 15.0740i −0.214578 + 0.660402i 0.784606 + 0.619995i \(0.212865\pi\)
−0.999183 + 0.0404070i \(0.987135\pi\)
\(522\) 0 0
\(523\) −19.4915 14.1614i −0.852305 0.619236i 0.0734754 0.997297i \(-0.476591\pi\)
−0.925781 + 0.378061i \(0.876591\pi\)
\(524\) 0 0
\(525\) 0.834609 + 2.56866i 0.0364253 + 0.112106i
\(526\) 0 0
\(527\) 3.35529 0.146159
\(528\) 0 0
\(529\) 1.82653 0.0794143
\(530\) 0 0
\(531\) 4.04460 + 12.4480i 0.175521 + 0.540197i
\(532\) 0 0
\(533\) 22.7231 + 16.5093i 0.984248 + 0.715098i
\(534\) 0 0
\(535\) −1.92725 + 5.93147i −0.0833224 + 0.256440i
\(536\) 0 0
\(537\) −13.2858 + 9.65272i −0.573326 + 0.416545i
\(538\) 0 0
\(539\) 0.159261 0.742928i 0.00685985 0.0320002i
\(540\) 0 0
\(541\) 17.2488 12.5320i 0.741584 0.538792i −0.151623 0.988438i \(-0.548450\pi\)
0.893207 + 0.449646i \(0.148450\pi\)
\(542\) 0 0
\(543\) 6.08688 18.7335i 0.261213 0.803931i
\(544\) 0 0
\(545\) −15.4894 11.2537i −0.663494 0.482057i
\(546\) 0 0
\(547\) 9.05977 + 27.8831i 0.387368 + 1.19220i 0.934748 + 0.355312i \(0.115625\pi\)
−0.547380 + 0.836884i \(0.684375\pi\)
\(548\) 0 0
\(549\) 5.02403 0.214420
\(550\) 0 0
\(551\) −34.6607 −1.47659
\(552\) 0 0
\(553\) −4.57628 14.0843i −0.194603 0.598927i
\(554\) 0 0
\(555\) 3.40198 + 2.47169i 0.144406 + 0.104917i
\(556\) 0 0
\(557\) −0.520009 + 1.60042i −0.0220335 + 0.0678122i −0.961469 0.274914i \(-0.911350\pi\)
0.939435 + 0.342727i \(0.111350\pi\)
\(558\) 0 0
\(559\) 13.8029 10.0284i 0.583802 0.424157i
\(560\) 0 0
\(561\) −2.77465 + 0.286766i −0.117146 + 0.0121073i
\(562\) 0 0
\(563\) 0.929018 0.674971i 0.0391534 0.0284466i −0.568036 0.823003i \(-0.692297\pi\)
0.607190 + 0.794557i \(0.292297\pi\)
\(564\) 0 0
\(565\) 3.35842 10.3362i 0.141290 0.434846i
\(566\) 0 0
\(567\) −0.977981 0.710545i −0.0410714 0.0298401i
\(568\) 0 0
\(569\) −2.06568 6.35751i −0.0865979 0.266521i 0.898375 0.439229i \(-0.144748\pi\)
−0.984973 + 0.172708i \(0.944748\pi\)
\(570\) 0 0
\(571\) −17.7964 −0.744756 −0.372378 0.928081i \(-0.621458\pi\)
−0.372378 + 0.928081i \(0.621458\pi\)
\(572\) 0 0
\(573\) −10.7600 −0.449505
\(574\) 0 0
\(575\) −1.53972 4.73876i −0.0642106 0.197620i
\(576\) 0 0
\(577\) 37.1992 + 27.0268i 1.54862 + 1.12514i 0.944624 + 0.328156i \(0.106427\pi\)
0.603999 + 0.796985i \(0.293573\pi\)
\(578\) 0 0
\(579\) −0.195222 + 0.600832i −0.00811315 + 0.0249697i
\(580\) 0 0
\(581\) 16.7773 12.1894i 0.696039 0.505702i
\(582\) 0 0
\(583\) 12.8390 + 7.44231i 0.531737 + 0.308229i
\(584\) 0 0
\(585\) 4.47593 3.25195i 0.185057 0.134452i
\(586\) 0 0
\(587\) −1.45930 + 4.49126i −0.0602318 + 0.185374i −0.976645 0.214859i \(-0.931071\pi\)
0.916413 + 0.400233i \(0.131071\pi\)
\(588\) 0 0
\(589\) 17.2548 + 12.5364i 0.710974 + 0.516553i
\(590\) 0 0
\(591\) 3.57697 + 11.0088i 0.147137 + 0.452841i
\(592\) 0 0
\(593\) 3.67545 0.150932 0.0754662 0.997148i \(-0.475955\pi\)
0.0754662 + 0.997148i \(0.475955\pi\)
\(594\) 0 0
\(595\) −2.10846 −0.0864385
\(596\) 0 0
\(597\) −2.85938 8.80026i −0.117027 0.360171i
\(598\) 0 0
\(599\) −32.2566 23.4358i −1.31797 0.957562i −0.999955 0.00947590i \(-0.996984\pi\)
−0.318015 0.948086i \(-0.603016\pi\)
\(600\) 0 0
\(601\) −3.81563 + 11.7433i −0.155643 + 0.479019i −0.998225 0.0595481i \(-0.981034\pi\)
0.842583 + 0.538567i \(0.181034\pi\)
\(602\) 0 0
\(603\) 24.6397 17.9018i 1.00341 0.729017i
\(604\) 0 0
\(605\) −10.7675 + 2.24971i −0.437761 + 0.0914638i
\(606\) 0 0
\(607\) −15.9430 + 11.5833i −0.647108 + 0.470151i −0.862285 0.506424i \(-0.830967\pi\)
0.215177 + 0.976575i \(0.430967\pi\)
\(608\) 0 0
\(609\) 5.61636 17.2854i 0.227586 0.700439i
\(610\) 0 0
\(611\) 2.25327 + 1.63710i 0.0911577 + 0.0662300i
\(612\) 0 0
\(613\) 11.6699 + 35.9163i 0.471343 + 1.45065i 0.850826 + 0.525447i \(0.176102\pi\)
−0.379483 + 0.925199i \(0.623898\pi\)
\(614\) 0 0
\(615\) −10.1313 −0.408532
\(616\) 0 0
\(617\) −3.49353 −0.140644 −0.0703222 0.997524i \(-0.522403\pi\)
−0.0703222 + 0.997524i \(0.522403\pi\)
\(618\) 0 0
\(619\) −2.00503 6.17083i −0.0805888 0.248027i 0.902642 0.430392i \(-0.141625\pi\)
−0.983231 + 0.182365i \(0.941625\pi\)
\(620\) 0 0
\(621\) −20.5965 14.9642i −0.826507 0.600493i
\(622\) 0 0
\(623\) −11.6751 + 35.9321i −0.467751 + 1.43959i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) 0 0
\(627\) −15.3403 8.89222i −0.612633 0.355121i
\(628\) 0 0
\(629\) −2.65581 + 1.92956i −0.105894 + 0.0769366i
\(630\) 0 0
\(631\) −10.1152 + 31.1312i −0.402678 + 1.23932i 0.520141 + 0.854081i \(0.325880\pi\)
−0.922819 + 0.385235i \(0.874120\pi\)
\(632\) 0 0
\(633\) 14.6150 + 10.6184i 0.580895 + 0.422045i
\(634\) 0 0
\(635\) 5.85277 + 18.0130i 0.232260 + 0.714823i
\(636\) 0 0
\(637\) 0.659221 0.0261193
\(638\) 0 0
\(639\) −2.71759 −0.107506
\(640\) 0 0
\(641\) −2.22299 6.84167i −0.0878029 0.270230i 0.897508 0.440997i \(-0.145375\pi\)
−0.985311 + 0.170768i \(0.945375\pi\)
\(642\) 0 0
\(643\) 6.64278 + 4.82626i 0.261966 + 0.190329i 0.711013 0.703179i \(-0.248237\pi\)
−0.449047 + 0.893508i \(0.648237\pi\)
\(644\) 0 0
\(645\) −1.90173 + 5.85293i −0.0748807 + 0.230459i
\(646\) 0 0
\(647\) −39.6425 + 28.8019i −1.55851 + 1.13232i −0.621286 + 0.783584i \(0.713389\pi\)
−0.937221 + 0.348737i \(0.886611\pi\)
\(648\) 0 0
\(649\) 22.4585 2.32113i 0.881574 0.0911124i
\(650\) 0 0
\(651\) −9.04788 + 6.57367i −0.354614 + 0.257642i
\(652\) 0 0
\(653\) −13.5490 + 41.6995i −0.530213 + 1.63183i 0.223557 + 0.974691i \(0.428233\pi\)
−0.753770 + 0.657138i \(0.771767\pi\)
\(654\) 0 0
\(655\) −11.7639 8.54695i −0.459652 0.333957i
\(656\) 0 0
\(657\) 7.80865 + 24.0325i 0.304644 + 0.937599i
\(658\) 0 0
\(659\) 37.2905 1.45263 0.726315 0.687362i \(-0.241231\pi\)
0.726315 + 0.687362i \(0.241231\pi\)
\(660\) 0 0
\(661\) 35.5579 1.38304 0.691520 0.722357i \(-0.256941\pi\)
0.691520 + 0.722357i \(0.256941\pi\)
\(662\) 0 0
\(663\) −0.747870 2.30171i −0.0290449 0.0893909i
\(664\) 0 0
\(665\) −10.8429 7.87784i −0.420471 0.305490i
\(666\) 0 0
\(667\) −10.3612 + 31.8886i −0.401189 + 1.23473i
\(668\) 0 0
\(669\) −1.29040 + 0.937527i −0.0498896 + 0.0362469i
\(670\) 0 0
\(671\) 1.81657 8.47404i 0.0701280 0.327137i
\(672\) 0 0
\(673\) 11.0203 8.00673i 0.424802 0.308637i −0.354765 0.934955i \(-0.615439\pi\)
0.779567 + 0.626319i \(0.215439\pi\)
\(674\) 0 0
\(675\) −1.57892 + 4.85941i −0.0607725 + 0.187039i
\(676\) 0 0
\(677\) −5.57612 4.05129i −0.214308 0.155704i 0.475453 0.879741i \(-0.342284\pi\)
−0.689761 + 0.724038i \(0.742284\pi\)
\(678\) 0 0
\(679\) −2.40685 7.40753i −0.0923665 0.284275i
\(680\) 0 0
\(681\) −10.4813 −0.401644
\(682\) 0 0
\(683\) −8.29642 −0.317454 −0.158727 0.987323i \(-0.550739\pi\)
−0.158727 + 0.987323i \(0.550739\pi\)
\(684\) 0 0
\(685\) 6.17540 + 19.0059i 0.235950 + 0.726180i
\(686\) 0 0
\(687\) −2.00925 1.45981i −0.0766577 0.0556951i
\(688\) 0 0
\(689\) −3.97875 + 12.2453i −0.151578 + 0.466510i
\(690\) 0 0
\(691\) 14.8505 10.7895i 0.564939 0.410452i −0.268324 0.963329i \(-0.586470\pi\)
0.833263 + 0.552877i \(0.186470\pi\)
\(692\) 0 0
\(693\) −12.3501 + 11.0814i −0.469142 + 0.420948i
\(694\) 0 0
\(695\) 1.67524 1.21713i 0.0635454 0.0461684i
\(696\) 0 0
\(697\) 2.44406 7.52203i 0.0925752 0.284917i
\(698\) 0 0
\(699\) 6.95898 + 5.05600i 0.263213 + 0.191235i
\(700\) 0 0
\(701\) −8.67175 26.6889i −0.327528 1.00803i −0.970287 0.241958i \(-0.922210\pi\)
0.642759 0.766068i \(-0.277790\pi\)
\(702\) 0 0
\(703\) −20.8671 −0.787018
\(704\) 0 0
\(705\) −1.00464 −0.0378369
\(706\) 0 0
\(707\) −12.3589 38.0369i −0.464805 1.43052i
\(708\) 0 0
\(709\) 13.1536 + 9.55667i 0.493995 + 0.358908i 0.806719 0.590936i \(-0.201241\pi\)
−0.312724 + 0.949844i \(0.601241\pi\)
\(710\) 0 0
\(711\) 3.38135 10.4067i 0.126811 0.390283i
\(712\) 0 0
\(713\) 16.6918 12.1273i 0.625114 0.454172i
\(714\) 0 0
\(715\) −3.86669 8.72539i −0.144606 0.326311i
\(716\) 0 0
\(717\) 3.83086 2.78328i 0.143066 0.103944i
\(718\) 0 0
\(719\) 1.16026 3.57092i 0.0432705 0.133173i −0.927087 0.374845i \(-0.877696\pi\)
0.970358 + 0.241672i \(0.0776959\pi\)
\(720\) 0 0
\(721\) 11.5637 + 8.40155i 0.430656 + 0.312890i
\(722\) 0 0
\(723\) 7.51017 + 23.1139i 0.279306 + 0.859616i
\(724\) 0 0
\(725\) 6.72933 0.249921
\(726\) 0 0
\(727\) −35.1985 −1.30544 −0.652720 0.757599i \(-0.726372\pi\)
−0.652720 + 0.757599i \(0.726372\pi\)
\(728\) 0 0
\(729\) 4.64050 + 14.2820i 0.171871 + 0.528963i
\(730\) 0 0
\(731\) −3.88678 2.82391i −0.143758 0.104446i
\(732\) 0 0
\(733\) −6.26899 + 19.2940i −0.231550 + 0.712639i 0.766010 + 0.642829i \(0.222239\pi\)
−0.997560 + 0.0698100i \(0.977761\pi\)
\(734\) 0 0
\(735\) −0.192372 + 0.139766i −0.00709575 + 0.00515536i
\(736\) 0 0
\(737\) −21.2859 48.0327i −0.784074 1.76931i
\(738\) 0 0
\(739\) 12.6479 9.18923i 0.465260 0.338031i −0.330331 0.943865i \(-0.607160\pi\)
0.795591 + 0.605834i \(0.207160\pi\)
\(740\) 0 0
\(741\) 4.75389 14.6310i 0.174638 0.537482i
\(742\) 0 0
\(743\) −16.1671 11.7461i −0.593114 0.430922i 0.250314 0.968165i \(-0.419466\pi\)
−0.843428 + 0.537242i \(0.819466\pi\)
\(744\) 0 0
\(745\) −0.155959 0.479992i −0.00571389 0.0175856i
\(746\) 0 0
\(747\) 15.3229 0.560637
\(748\) 0 0
\(749\) 16.2286 0.592979
\(750\) 0 0
\(751\) −9.71724 29.9066i −0.354587 1.09131i −0.956248 0.292556i \(-0.905494\pi\)
0.601661 0.798751i \(-0.294506\pi\)
\(752\) 0 0
\(753\) −23.2977 16.9268i −0.849016 0.616846i
\(754\) 0 0
\(755\) 3.74492 11.5257i 0.136292 0.419463i
\(756\) 0 0
\(757\) −36.7173 + 26.6766i −1.33451 + 0.969579i −0.334885 + 0.942259i \(0.608697\pi\)
−0.999627 + 0.0273202i \(0.991303\pi\)
\(758\) 0 0
\(759\) −12.7668 + 11.4553i −0.463405 + 0.415800i
\(760\) 0 0
\(761\) −28.8093 + 20.9312i −1.04434 + 0.758754i −0.971127 0.238563i \(-0.923324\pi\)
−0.0732080 + 0.997317i \(0.523324\pi\)
\(762\) 0 0
\(763\) −15.3951 + 47.3814i −0.557342 + 1.71532i
\(764\) 0 0
\(765\) −1.26038 0.915719i −0.0455691 0.0331079i
\(766\) 0 0
\(767\) 6.05338 + 18.6304i 0.218575 + 0.672705i
\(768\) 0 0
\(769\) −18.9907 −0.684821 −0.342411 0.939550i \(-0.611243\pi\)
−0.342411 + 0.939550i \(0.611243\pi\)
\(770\) 0 0
\(771\) −26.4514 −0.952625
\(772\) 0 0
\(773\) 13.4981 + 41.5429i 0.485493 + 1.49419i 0.831265 + 0.555876i \(0.187617\pi\)
−0.345772 + 0.938318i \(0.612383\pi\)
\(774\) 0 0
\(775\) −3.35001 2.43392i −0.120336 0.0874291i
\(776\) 0 0
\(777\) 3.38128 10.4065i 0.121303 0.373331i
\(778\) 0 0
\(779\) 40.6733 29.5509i 1.45727 1.05877i
\(780\) 0 0
\(781\) −0.982618 + 4.58377i −0.0351608 + 0.164020i
\(782\) 0 0
\(783\) 27.8167 20.2100i 0.994089 0.722248i
\(784\) 0 0
\(785\) 3.67275 11.3036i 0.131086 0.403442i
\(786\) 0 0
\(787\) −41.1672 29.9097i −1.46745 1.06617i −0.981343 0.192266i \(-0.938416\pi\)
−0.486108