Properties

Label 380.2.u.b.81.1
Level $380$
Weight $2$
Character 380.81
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([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("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 81.1
Root \(0.793225 + 1.37391i\) of defining polynomial
Character \(\chi\) \(=\) 380.81
Dual form 380.2.u.b.61.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.275484 + 1.56235i) q^{3} +(0.766044 + 0.642788i) q^{5} +(0.778817 + 1.34895i) q^{7} +(0.454036 + 0.165255i) q^{9} +O(q^{10})\) \(q+(-0.275484 + 1.56235i) q^{3} +(0.766044 + 0.642788i) q^{5} +(0.778817 + 1.34895i) q^{7} +(0.454036 + 0.165255i) q^{9} +(-1.44481 + 2.50249i) q^{11} +(-0.501215 - 2.84253i) q^{13} +(-1.21529 + 1.01975i) q^{15} +(-3.43909 + 1.25173i) q^{17} +(3.58062 + 2.48579i) q^{19} +(-2.32208 + 0.845169i) q^{21} +(-1.02545 + 0.860452i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-2.76294 + 4.78556i) q^{27} +(4.25138 + 1.54738i) q^{29} +(-0.0994869 - 0.172316i) q^{31} +(-3.51173 - 2.94670i) q^{33} +(-0.270480 + 1.53397i) q^{35} -6.14008 q^{37} +4.57910 q^{39} +(0.240699 - 1.36507i) q^{41} +(1.02726 + 0.861973i) q^{43} +(0.241587 + 0.418441i) q^{45} +(-1.00724 - 0.366604i) q^{47} +(2.28689 - 3.96101i) q^{49} +(-1.00822 - 5.71788i) q^{51} +(5.96388 - 5.00429i) q^{53} +(-2.71536 + 0.988309i) q^{55} +(-4.87007 + 4.90939i) q^{57} +(4.57626 - 1.66562i) q^{59} +(7.26890 - 6.09933i) q^{61} +(0.130689 + 0.741175i) q^{63} +(1.44319 - 2.49968i) q^{65} +(7.36834 + 2.68185i) q^{67} +(-1.06183 - 1.83915i) q^{69} +(1.21663 + 1.02087i) q^{71} +(2.01200 - 11.4106i) q^{73} -1.58645 q^{75} -4.50097 q^{77} +(2.38517 - 13.5270i) q^{79} +(-5.60516 - 4.70329i) q^{81} +(5.84996 + 10.1324i) q^{83} +(-3.43909 - 1.25173i) q^{85} +(-3.58873 + 6.21587i) q^{87} +(-2.54772 - 14.4488i) q^{89} +(3.44408 - 2.88993i) q^{91} +(0.296625 - 0.107963i) q^{93} +(1.14509 + 4.20580i) q^{95} +(-0.990001 + 0.360331i) q^{97} +(-1.06955 + 0.897455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.275484 + 1.56235i −0.159051 + 0.902023i 0.795937 + 0.605379i \(0.206978\pi\)
−0.954988 + 0.296644i \(0.904133\pi\)
\(4\) 0 0
\(5\) 0.766044 + 0.642788i 0.342585 + 0.287463i
\(6\) 0 0
\(7\) 0.778817 + 1.34895i 0.294365 + 0.509855i 0.974837 0.222919i \(-0.0715585\pi\)
−0.680472 + 0.732774i \(0.738225\pi\)
\(8\) 0 0
\(9\) 0.454036 + 0.165255i 0.151345 + 0.0550851i
\(10\) 0 0
\(11\) −1.44481 + 2.50249i −0.435627 + 0.754528i −0.997347 0.0727995i \(-0.976807\pi\)
0.561720 + 0.827328i \(0.310140\pi\)
\(12\) 0 0
\(13\) −0.501215 2.84253i −0.139012 0.788376i −0.971981 0.235057i \(-0.924472\pi\)
0.832969 0.553319i \(-0.186639\pi\)
\(14\) 0 0
\(15\) −1.21529 + 1.01975i −0.313787 + 0.263299i
\(16\) 0 0
\(17\) −3.43909 + 1.25173i −0.834101 + 0.303588i −0.723541 0.690281i \(-0.757487\pi\)
−0.110560 + 0.993869i \(0.535264\pi\)
\(18\) 0 0
\(19\) 3.58062 + 2.48579i 0.821452 + 0.570278i
\(20\) 0 0
\(21\) −2.32208 + 0.845169i −0.506720 + 0.184431i
\(22\) 0 0
\(23\) −1.02545 + 0.860452i −0.213820 + 0.179417i −0.743407 0.668839i \(-0.766791\pi\)
0.529587 + 0.848256i \(0.322347\pi\)
\(24\) 0 0
\(25\) 0.173648 + 0.984808i 0.0347296 + 0.196962i
\(26\) 0 0
\(27\) −2.76294 + 4.78556i −0.531728 + 0.920981i
\(28\) 0 0
\(29\) 4.25138 + 1.54738i 0.789462 + 0.287341i 0.705113 0.709095i \(-0.250896\pi\)
0.0843498 + 0.996436i \(0.473119\pi\)
\(30\) 0 0
\(31\) −0.0994869 0.172316i −0.0178684 0.0309489i 0.856953 0.515395i \(-0.172355\pi\)
−0.874821 + 0.484446i \(0.839021\pi\)
\(32\) 0 0
\(33\) −3.51173 2.94670i −0.611315 0.512954i
\(34\) 0 0
\(35\) −0.270480 + 1.53397i −0.0457195 + 0.259288i
\(36\) 0 0
\(37\) −6.14008 −1.00942 −0.504711 0.863288i \(-0.668401\pi\)
−0.504711 + 0.863288i \(0.668401\pi\)
\(38\) 0 0
\(39\) 4.57910 0.733243
\(40\) 0 0
\(41\) 0.240699 1.36507i 0.0375909 0.213188i −0.960227 0.279222i \(-0.909923\pi\)
0.997817 + 0.0660337i \(0.0210345\pi\)
\(42\) 0 0
\(43\) 1.02726 + 0.861973i 0.156656 + 0.131450i 0.717746 0.696305i \(-0.245174\pi\)
−0.561091 + 0.827754i \(0.689618\pi\)
\(44\) 0 0
\(45\) 0.241587 + 0.418441i 0.0360137 + 0.0623776i
\(46\) 0 0
\(47\) −1.00724 0.366604i −0.146920 0.0534747i 0.267513 0.963554i \(-0.413798\pi\)
−0.414434 + 0.910080i \(0.636020\pi\)
\(48\) 0 0
\(49\) 2.28689 3.96101i 0.326698 0.565858i
\(50\) 0 0
\(51\) −1.00822 5.71788i −0.141179 0.800664i
\(52\) 0 0
\(53\) 5.96388 5.00429i 0.819202 0.687392i −0.133583 0.991038i \(-0.542648\pi\)
0.952785 + 0.303645i \(0.0982038\pi\)
\(54\) 0 0
\(55\) −2.71536 + 0.988309i −0.366139 + 0.133264i
\(56\) 0 0
\(57\) −4.87007 + 4.90939i −0.645056 + 0.650265i
\(58\) 0 0
\(59\) 4.57626 1.66562i 0.595779 0.216846i −0.0264905 0.999649i \(-0.508433\pi\)
0.622269 + 0.782803i \(0.286211\pi\)
\(60\) 0 0
\(61\) 7.26890 6.09933i 0.930687 0.780939i −0.0452536 0.998976i \(-0.514410\pi\)
0.975941 + 0.218036i \(0.0699651\pi\)
\(62\) 0 0
\(63\) 0.130689 + 0.741175i 0.0164653 + 0.0933793i
\(64\) 0 0
\(65\) 1.44319 2.49968i 0.179006 0.310047i
\(66\) 0 0
\(67\) 7.36834 + 2.68185i 0.900185 + 0.327641i 0.750327 0.661067i \(-0.229896\pi\)
0.149858 + 0.988707i \(0.452118\pi\)
\(68\) 0 0
\(69\) −1.06183 1.83915i −0.127830 0.221407i
\(70\) 0 0
\(71\) 1.21663 + 1.02087i 0.144387 + 0.121155i 0.712120 0.702058i \(-0.247735\pi\)
−0.567733 + 0.823213i \(0.692180\pi\)
\(72\) 0 0
\(73\) 2.01200 11.4106i 0.235486 1.33551i −0.606101 0.795388i \(-0.707267\pi\)
0.841587 0.540121i \(-0.181622\pi\)
\(74\) 0 0
\(75\) −1.58645 −0.183188
\(76\) 0 0
\(77\) −4.50097 −0.512933
\(78\) 0 0
\(79\) 2.38517 13.5270i 0.268353 1.52191i −0.490962 0.871181i \(-0.663354\pi\)
0.759314 0.650724i \(-0.225534\pi\)
\(80\) 0 0
\(81\) −5.60516 4.70329i −0.622796 0.522588i
\(82\) 0 0
\(83\) 5.84996 + 10.1324i 0.642116 + 1.11218i 0.984960 + 0.172785i \(0.0552767\pi\)
−0.342843 + 0.939393i \(0.611390\pi\)
\(84\) 0 0
\(85\) −3.43909 1.25173i −0.373021 0.135769i
\(86\) 0 0
\(87\) −3.58873 + 6.21587i −0.384753 + 0.666411i
\(88\) 0 0
\(89\) −2.54772 14.4488i −0.270058 1.53157i −0.754236 0.656604i \(-0.771992\pi\)
0.484178 0.874970i \(-0.339119\pi\)
\(90\) 0 0
\(91\) 3.44408 2.88993i 0.361038 0.302946i
\(92\) 0 0
\(93\) 0.296625 0.107963i 0.0307586 0.0111952i
\(94\) 0 0
\(95\) 1.14509 + 4.20580i 0.117483 + 0.431506i
\(96\) 0 0
\(97\) −0.990001 + 0.360331i −0.100519 + 0.0365861i −0.391790 0.920055i \(-0.628144\pi\)
0.291271 + 0.956641i \(0.405922\pi\)
\(98\) 0 0
\(99\) −1.06955 + 0.897455i −0.107493 + 0.0901976i
\(100\) 0 0
\(101\) 2.84835 + 16.1538i 0.283421 + 1.60736i 0.710871 + 0.703322i \(0.248301\pi\)
−0.427450 + 0.904039i \(0.640588\pi\)
\(102\) 0 0
\(103\) 6.95403 12.0447i 0.685201 1.18680i −0.288172 0.957579i \(-0.593048\pi\)
0.973374 0.229225i \(-0.0736191\pi\)
\(104\) 0 0
\(105\) −2.32208 0.845169i −0.226612 0.0824800i
\(106\) 0 0
\(107\) −2.75086 4.76464i −0.265936 0.460615i 0.701872 0.712303i \(-0.252348\pi\)
−0.967808 + 0.251688i \(0.919014\pi\)
\(108\) 0 0
\(109\) 1.60334 + 1.34536i 0.153572 + 0.128862i 0.716336 0.697755i \(-0.245818\pi\)
−0.562764 + 0.826617i \(0.690262\pi\)
\(110\) 0 0
\(111\) 1.69149 9.59294i 0.160550 0.910522i
\(112\) 0 0
\(113\) −7.81671 −0.735334 −0.367667 0.929958i \(-0.619843\pi\)
−0.367667 + 0.929958i \(0.619843\pi\)
\(114\) 0 0
\(115\) −1.33863 −0.124828
\(116\) 0 0
\(117\) 0.242174 1.37344i 0.0223890 0.126974i
\(118\) 0 0
\(119\) −4.36693 3.66429i −0.400316 0.335905i
\(120\) 0 0
\(121\) 1.32504 + 2.29504i 0.120458 + 0.208640i
\(122\) 0 0
\(123\) 2.06641 + 0.752112i 0.186322 + 0.0678156i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −0.329089 1.86636i −0.0292019 0.165612i 0.966719 0.255839i \(-0.0823519\pi\)
−0.995921 + 0.0902270i \(0.971241\pi\)
\(128\) 0 0
\(129\) −1.62970 + 1.36748i −0.143487 + 0.120400i
\(130\) 0 0
\(131\) −16.1017 + 5.86053i −1.40681 + 0.512037i −0.930192 0.367073i \(-0.880360\pi\)
−0.476618 + 0.879110i \(0.658138\pi\)
\(132\) 0 0
\(133\) −0.564550 + 6.76605i −0.0489527 + 0.586691i
\(134\) 0 0
\(135\) −5.19263 + 1.88996i −0.446911 + 0.162662i
\(136\) 0 0
\(137\) −12.2275 + 10.2601i −1.04466 + 0.876575i −0.992522 0.122065i \(-0.961049\pi\)
−0.0521395 + 0.998640i \(0.516604\pi\)
\(138\) 0 0
\(139\) −1.04738 5.94001i −0.0888379 0.503825i −0.996462 0.0840415i \(-0.973217\pi\)
0.907624 0.419783i \(-0.137894\pi\)
\(140\) 0 0
\(141\) 0.850241 1.47266i 0.0716032 0.124020i
\(142\) 0 0
\(143\) 7.83756 + 2.85264i 0.655410 + 0.238550i
\(144\) 0 0
\(145\) 2.26211 + 3.91810i 0.187858 + 0.325380i
\(146\) 0 0
\(147\) 5.55847 + 4.66411i 0.458455 + 0.384690i
\(148\) 0 0
\(149\) 0.283411 1.60730i 0.0232179 0.131675i −0.970996 0.239097i \(-0.923148\pi\)
0.994214 + 0.107422i \(0.0342596\pi\)
\(150\) 0 0
\(151\) 16.4058 1.33508 0.667542 0.744572i \(-0.267347\pi\)
0.667542 + 0.744572i \(0.267347\pi\)
\(152\) 0 0
\(153\) −1.76832 −0.142960
\(154\) 0 0
\(155\) 0.0345515 0.195951i 0.00277524 0.0157392i
\(156\) 0 0
\(157\) −9.71716 8.15366i −0.775514 0.650733i 0.166601 0.986024i \(-0.446721\pi\)
−0.942115 + 0.335291i \(0.891165\pi\)
\(158\) 0 0
\(159\) 6.17549 + 10.6963i 0.489748 + 0.848269i
\(160\) 0 0
\(161\) −1.95934 0.713142i −0.154418 0.0562035i
\(162\) 0 0
\(163\) −6.21515 + 10.7650i −0.486808 + 0.843177i −0.999885 0.0151660i \(-0.995172\pi\)
0.513077 + 0.858343i \(0.328506\pi\)
\(164\) 0 0
\(165\) −0.796046 4.51460i −0.0619721 0.351461i
\(166\) 0 0
\(167\) −5.44945 + 4.57263i −0.421691 + 0.353841i −0.828806 0.559536i \(-0.810979\pi\)
0.407115 + 0.913377i \(0.366535\pi\)
\(168\) 0 0
\(169\) 4.38723 1.59682i 0.337480 0.122833i
\(170\) 0 0
\(171\) 1.21494 + 1.72035i 0.0929089 + 0.131559i
\(172\) 0 0
\(173\) 16.2471 5.91344i 1.23524 0.449591i 0.359851 0.933010i \(-0.382827\pi\)
0.875389 + 0.483419i \(0.160605\pi\)
\(174\) 0 0
\(175\) −1.19322 + 1.00123i −0.0901987 + 0.0756857i
\(176\) 0 0
\(177\) 1.34160 + 7.60857i 0.100841 + 0.571895i
\(178\) 0 0
\(179\) 1.59949 2.77040i 0.119551 0.207069i −0.800039 0.599949i \(-0.795188\pi\)
0.919590 + 0.392879i \(0.128521\pi\)
\(180\) 0 0
\(181\) 19.4111 + 7.06505i 1.44281 + 0.525141i 0.940574 0.339589i \(-0.110288\pi\)
0.502238 + 0.864729i \(0.332510\pi\)
\(182\) 0 0
\(183\) 7.52681 + 13.0368i 0.556398 + 0.963710i
\(184\) 0 0
\(185\) −4.70357 3.94677i −0.345814 0.290172i
\(186\) 0 0
\(187\) 1.83641 10.4148i 0.134291 0.761604i
\(188\) 0 0
\(189\) −8.60730 −0.626089
\(190\) 0 0
\(191\) 0.892691 0.0645929 0.0322964 0.999478i \(-0.489718\pi\)
0.0322964 + 0.999478i \(0.489718\pi\)
\(192\) 0 0
\(193\) 0.351812 1.99522i 0.0253240 0.143619i −0.969524 0.244996i \(-0.921213\pi\)
0.994848 + 0.101376i \(0.0323246\pi\)
\(194\) 0 0
\(195\) 3.50780 + 2.94339i 0.251199 + 0.210781i
\(196\) 0 0
\(197\) 10.4101 + 18.0308i 0.741687 + 1.28464i 0.951727 + 0.306946i \(0.0993071\pi\)
−0.210040 + 0.977693i \(0.567360\pi\)
\(198\) 0 0
\(199\) −6.28673 2.28818i −0.445655 0.162205i 0.109438 0.993994i \(-0.465095\pi\)
−0.555093 + 0.831789i \(0.687317\pi\)
\(200\) 0 0
\(201\) −6.21985 + 10.7731i −0.438715 + 0.759876i
\(202\) 0 0
\(203\) 1.22371 + 6.94003i 0.0858879 + 0.487095i
\(204\) 0 0
\(205\) 1.06184 0.890988i 0.0741620 0.0622293i
\(206\) 0 0
\(207\) −0.607784 + 0.221215i −0.0422439 + 0.0153755i
\(208\) 0 0
\(209\) −11.3940 + 5.36898i −0.788138 + 0.371380i
\(210\) 0 0
\(211\) −22.1048 + 8.04549i −1.52176 + 0.553874i −0.961586 0.274503i \(-0.911487\pi\)
−0.560170 + 0.828377i \(0.689264\pi\)
\(212\) 0 0
\(213\) −1.93012 + 1.61956i −0.132249 + 0.110970i
\(214\) 0 0
\(215\) 0.232861 + 1.32062i 0.0158810 + 0.0900655i
\(216\) 0 0
\(217\) 0.154964 0.268406i 0.0105197 0.0182206i
\(218\) 0 0
\(219\) 17.2731 + 6.28688i 1.16720 + 0.424828i
\(220\) 0 0
\(221\) 5.28179 + 9.14833i 0.355292 + 0.615383i
\(222\) 0 0
\(223\) −9.58190 8.04017i −0.641651 0.538409i 0.262874 0.964830i \(-0.415330\pi\)
−0.904525 + 0.426421i \(0.859774\pi\)
\(224\) 0 0
\(225\) −0.0839024 + 0.475834i −0.00559349 + 0.0317223i
\(226\) 0 0
\(227\) −18.0828 −1.20020 −0.600100 0.799925i \(-0.704873\pi\)
−0.600100 + 0.799925i \(0.704873\pi\)
\(228\) 0 0
\(229\) 12.0907 0.798974 0.399487 0.916739i \(-0.369188\pi\)
0.399487 + 0.916739i \(0.369188\pi\)
\(230\) 0 0
\(231\) 1.23995 7.03209i 0.0815825 0.462678i
\(232\) 0 0
\(233\) −4.83465 4.05675i −0.316729 0.265767i 0.470538 0.882380i \(-0.344060\pi\)
−0.787266 + 0.616613i \(0.788504\pi\)
\(234\) 0 0
\(235\) −0.535939 0.928273i −0.0349608 0.0605539i
\(236\) 0 0
\(237\) 20.4768 + 7.45294i 1.33011 + 0.484121i
\(238\) 0 0
\(239\) −8.77206 + 15.1937i −0.567418 + 0.982796i 0.429403 + 0.903113i \(0.358724\pi\)
−0.996820 + 0.0796830i \(0.974609\pi\)
\(240\) 0 0
\(241\) −1.58485 8.98812i −0.102089 0.578976i −0.992343 0.123512i \(-0.960584\pi\)
0.890254 0.455464i \(-0.150527\pi\)
\(242\) 0 0
\(243\) −3.80691 + 3.19437i −0.244213 + 0.204919i
\(244\) 0 0
\(245\) 4.29795 1.56432i 0.274586 0.0999410i
\(246\) 0 0
\(247\) 5.27126 11.4240i 0.335402 0.726889i
\(248\) 0 0
\(249\) −17.4419 + 6.34835i −1.10534 + 0.402310i
\(250\) 0 0
\(251\) 4.49910 3.77519i 0.283981 0.238288i −0.489659 0.871914i \(-0.662879\pi\)
0.773639 + 0.633626i \(0.218434\pi\)
\(252\) 0 0
\(253\) −0.671693 3.80936i −0.0422290 0.239492i
\(254\) 0 0
\(255\) 2.90305 5.02822i 0.181796 0.314880i
\(256\) 0 0
\(257\) 9.31369 + 3.38991i 0.580972 + 0.211457i 0.615754 0.787938i \(-0.288851\pi\)
−0.0347819 + 0.999395i \(0.511074\pi\)
\(258\) 0 0
\(259\) −4.78200 8.28266i −0.297139 0.514659i
\(260\) 0 0
\(261\) 1.67457 + 1.40513i 0.103653 + 0.0869753i
\(262\) 0 0
\(263\) −1.42509 + 8.08208i −0.0878748 + 0.498363i 0.908824 + 0.417179i \(0.136981\pi\)
−0.996699 + 0.0811836i \(0.974130\pi\)
\(264\) 0 0
\(265\) 7.78530 0.478247
\(266\) 0 0
\(267\) 23.2760 1.42447
\(268\) 0 0
\(269\) −1.17537 + 6.66588i −0.0716639 + 0.406426i 0.927781 + 0.373124i \(0.121713\pi\)
−0.999445 + 0.0333020i \(0.989398\pi\)
\(270\) 0 0
\(271\) −20.4073 17.1238i −1.23965 1.04019i −0.997551 0.0699434i \(-0.977718\pi\)
−0.242104 0.970250i \(-0.577837\pi\)
\(272\) 0 0
\(273\) 3.56628 + 6.17698i 0.215841 + 0.373848i
\(274\) 0 0
\(275\) −2.71536 0.988309i −0.163742 0.0595973i
\(276\) 0 0
\(277\) −2.27741 + 3.94459i −0.136836 + 0.237007i −0.926297 0.376793i \(-0.877027\pi\)
0.789461 + 0.613800i \(0.210360\pi\)
\(278\) 0 0
\(279\) −0.0166944 0.0946785i −0.000999466 0.00566826i
\(280\) 0 0
\(281\) −12.6515 + 10.6159i −0.754726 + 0.633291i −0.936748 0.350004i \(-0.886180\pi\)
0.182022 + 0.983294i \(0.441736\pi\)
\(282\) 0 0
\(283\) −26.2568 + 9.55670i −1.56081 + 0.568087i −0.970921 0.239401i \(-0.923049\pi\)
−0.589885 + 0.807487i \(0.700827\pi\)
\(284\) 0 0
\(285\) −6.88638 + 0.630391i −0.407914 + 0.0373411i
\(286\) 0 0
\(287\) 2.02888 0.738450i 0.119761 0.0435893i
\(288\) 0 0
\(289\) −2.76225 + 2.31780i −0.162485 + 0.136341i
\(290\) 0 0
\(291\) −0.290233 1.64599i −0.0170138 0.0964898i
\(292\) 0 0
\(293\) 14.5506 25.2024i 0.850055 1.47234i −0.0311034 0.999516i \(-0.509902\pi\)
0.881158 0.472822i \(-0.156765\pi\)
\(294\) 0 0
\(295\) 4.57626 + 1.66562i 0.266440 + 0.0969763i
\(296\) 0 0
\(297\) −7.98386 13.8285i −0.463271 0.802408i
\(298\) 0 0
\(299\) 2.95983 + 2.48359i 0.171172 + 0.143630i
\(300\) 0 0
\(301\) −0.362712 + 2.05704i −0.0209064 + 0.118566i
\(302\) 0 0
\(303\) −26.0225 −1.49495
\(304\) 0 0
\(305\) 9.48887 0.543331
\(306\) 0 0
\(307\) 4.58392 25.9967i 0.261618 1.48371i −0.516878 0.856059i \(-0.672906\pi\)
0.778496 0.627650i \(-0.215983\pi\)
\(308\) 0 0
\(309\) 16.9024 + 14.1828i 0.961541 + 0.806829i
\(310\) 0 0
\(311\) −13.2032 22.8685i −0.748682 1.29676i −0.948455 0.316913i \(-0.897354\pi\)
0.199772 0.979842i \(-0.435980\pi\)
\(312\) 0 0
\(313\) −8.12768 2.95823i −0.459404 0.167209i 0.101943 0.994790i \(-0.467494\pi\)
−0.561346 + 0.827581i \(0.689716\pi\)
\(314\) 0 0
\(315\) −0.376304 + 0.651778i −0.0212024 + 0.0367235i
\(316\) 0 0
\(317\) −3.90441 22.1430i −0.219293 1.24367i −0.873299 0.487184i \(-0.838024\pi\)
0.654006 0.756489i \(-0.273087\pi\)
\(318\) 0 0
\(319\) −10.0147 + 8.40337i −0.560718 + 0.470498i
\(320\) 0 0
\(321\) 8.20185 2.98523i 0.457782 0.166619i
\(322\) 0 0
\(323\) −15.4256 4.06687i −0.858303 0.226287i
\(324\) 0 0
\(325\) 2.71231 0.987201i 0.150452 0.0547601i
\(326\) 0 0
\(327\) −2.54361 + 2.13434i −0.140662 + 0.118029i
\(328\) 0 0
\(329\) −0.289922 1.64423i −0.0159839 0.0906492i
\(330\) 0 0
\(331\) 16.4183 28.4374i 0.902433 1.56306i 0.0781074 0.996945i \(-0.475112\pi\)
0.824326 0.566115i \(-0.191554\pi\)
\(332\) 0 0
\(333\) −2.78781 1.01468i −0.152771 0.0556042i
\(334\) 0 0
\(335\) 3.92061 + 6.79069i 0.214206 + 0.371015i
\(336\) 0 0
\(337\) 7.53496 + 6.32258i 0.410455 + 0.344413i 0.824518 0.565835i \(-0.191446\pi\)
−0.414063 + 0.910248i \(0.635891\pi\)
\(338\) 0 0
\(339\) 2.15338 12.2124i 0.116956 0.663288i
\(340\) 0 0
\(341\) 0.574959 0.0311358
\(342\) 0 0
\(343\) 18.0277 0.973404
\(344\) 0 0
\(345\) 0.368770 2.09140i 0.0198539 0.112597i
\(346\) 0 0
\(347\) −4.18184 3.50898i −0.224493 0.188372i 0.523603 0.851962i \(-0.324587\pi\)
−0.748096 + 0.663590i \(0.769032\pi\)
\(348\) 0 0
\(349\) 10.6624 + 18.4679i 0.570746 + 0.988562i 0.996490 + 0.0837176i \(0.0266794\pi\)
−0.425743 + 0.904844i \(0.639987\pi\)
\(350\) 0 0
\(351\) 14.9879 + 5.45516i 0.799996 + 0.291175i
\(352\) 0 0
\(353\) 9.11319 15.7845i 0.485046 0.840125i −0.514806 0.857307i \(-0.672136\pi\)
0.999852 + 0.0171818i \(0.00546940\pi\)
\(354\) 0 0
\(355\) 0.275787 + 1.56406i 0.0146372 + 0.0830119i
\(356\) 0 0
\(357\) 6.92792 5.81322i 0.366665 0.307668i
\(358\) 0 0
\(359\) −7.89375 + 2.87309i −0.416616 + 0.151636i −0.541819 0.840495i \(-0.682264\pi\)
0.125203 + 0.992131i \(0.460042\pi\)
\(360\) 0 0
\(361\) 6.64175 + 17.8013i 0.349566 + 0.936912i
\(362\) 0 0
\(363\) −3.95067 + 1.43793i −0.207357 + 0.0754716i
\(364\) 0 0
\(365\) 8.87587 7.44774i 0.464584 0.389832i
\(366\) 0 0
\(367\) −3.69051 20.9299i −0.192643 1.09253i −0.915736 0.401781i \(-0.868391\pi\)
0.723093 0.690751i \(-0.242720\pi\)
\(368\) 0 0
\(369\) 0.334872 0.580015i 0.0174327 0.0301944i
\(370\) 0 0
\(371\) 11.3953 + 4.14755i 0.591615 + 0.215330i
\(372\) 0 0
\(373\) 6.63332 + 11.4892i 0.343460 + 0.594890i 0.985073 0.172138i \(-0.0550676\pi\)
−0.641613 + 0.767029i \(0.721734\pi\)
\(374\) 0 0
\(375\) −1.21529 1.01975i −0.0627574 0.0526597i
\(376\) 0 0
\(377\) 2.26761 12.8603i 0.116788 0.662337i
\(378\) 0 0
\(379\) 3.03578 0.155937 0.0779687 0.996956i \(-0.475157\pi\)
0.0779687 + 0.996956i \(0.475157\pi\)
\(380\) 0 0
\(381\) 3.00656 0.154031
\(382\) 0 0
\(383\) 0.875551 4.96550i 0.0447386 0.253725i −0.954233 0.299064i \(-0.903326\pi\)
0.998972 + 0.0453388i \(0.0144367\pi\)
\(384\) 0 0
\(385\) −3.44795 2.89317i −0.175724 0.147450i
\(386\) 0 0
\(387\) 0.323967 + 0.561127i 0.0164682 + 0.0285237i
\(388\) 0 0
\(389\) 21.1539 + 7.69939i 1.07254 + 0.390374i 0.817128 0.576457i \(-0.195565\pi\)
0.255417 + 0.966831i \(0.417787\pi\)
\(390\) 0 0
\(391\) 2.44955 4.24275i 0.123879 0.214565i
\(392\) 0 0
\(393\) −4.72044 26.7709i −0.238114 1.35041i
\(394\) 0 0
\(395\) 10.5221 8.82911i 0.529426 0.444241i
\(396\) 0 0
\(397\) 17.4747 6.36025i 0.877028 0.319212i 0.136018 0.990706i \(-0.456569\pi\)
0.741010 + 0.671494i \(0.234347\pi\)
\(398\) 0 0
\(399\) −10.4154 2.74597i −0.521423 0.137470i
\(400\) 0 0
\(401\) −32.0658 + 11.6710i −1.60129 + 0.582822i −0.979691 0.200514i \(-0.935739\pi\)
−0.621599 + 0.783336i \(0.713517\pi\)
\(402\) 0 0
\(403\) −0.439951 + 0.369162i −0.0219155 + 0.0183893i
\(404\) 0 0
\(405\) −1.27059 7.20586i −0.0631360 0.358062i
\(406\) 0 0
\(407\) 8.87126 15.3655i 0.439732 0.761638i
\(408\) 0 0
\(409\) −11.5491 4.20354i −0.571068 0.207852i 0.0403143 0.999187i \(-0.487164\pi\)
−0.611383 + 0.791335i \(0.709386\pi\)
\(410\) 0 0
\(411\) −12.6613 21.9300i −0.624536 1.08173i
\(412\) 0 0
\(413\) 5.81091 + 4.87593i 0.285936 + 0.239929i
\(414\) 0 0
\(415\) −2.03167 + 11.5222i −0.0997307 + 0.565601i
\(416\) 0 0
\(417\) 9.56890 0.468591
\(418\) 0 0
\(419\) 4.91902 0.240310 0.120155 0.992755i \(-0.461661\pi\)
0.120155 + 0.992755i \(0.461661\pi\)
\(420\) 0 0
\(421\) −6.25015 + 35.4464i −0.304614 + 1.72755i 0.320704 + 0.947179i \(0.396081\pi\)
−0.625318 + 0.780370i \(0.715031\pi\)
\(422\) 0 0
\(423\) −0.396738 0.332902i −0.0192900 0.0161863i
\(424\) 0 0
\(425\) −1.82990 3.16948i −0.0887632 0.153742i
\(426\) 0 0
\(427\) 13.8888 + 5.05512i 0.672128 + 0.244634i
\(428\) 0 0
\(429\) −6.61594 + 11.4591i −0.319421 + 0.553253i
\(430\) 0 0
\(431\) 3.27126 + 18.5522i 0.157571 + 0.893630i 0.956397 + 0.292068i \(0.0943434\pi\)
−0.798826 + 0.601562i \(0.794545\pi\)
\(432\) 0 0
\(433\) −15.8007 + 13.2584i −0.759333 + 0.637156i −0.937953 0.346762i \(-0.887281\pi\)
0.178620 + 0.983918i \(0.442837\pi\)
\(434\) 0 0
\(435\) −6.74461 + 2.45484i −0.323379 + 0.117700i
\(436\) 0 0
\(437\) −5.81064 + 0.531916i −0.277961 + 0.0254450i
\(438\) 0 0
\(439\) −8.25467 + 3.00445i −0.393974 + 0.143395i −0.531408 0.847116i \(-0.678337\pi\)
0.137434 + 0.990511i \(0.456115\pi\)
\(440\) 0 0
\(441\) 1.69291 1.42052i 0.0806146 0.0676437i
\(442\) 0 0
\(443\) −1.60153 9.08274i −0.0760911 0.431534i −0.998926 0.0463378i \(-0.985245\pi\)
0.922835 0.385196i \(-0.125866\pi\)
\(444\) 0 0
\(445\) 7.33587 12.7061i 0.347753 0.602327i
\(446\) 0 0
\(447\) 2.43309 + 0.885573i 0.115081 + 0.0418862i
\(448\) 0 0
\(449\) −9.52581 16.4992i −0.449551 0.778644i 0.548806 0.835950i \(-0.315083\pi\)
−0.998357 + 0.0573052i \(0.981749\pi\)
\(450\) 0 0
\(451\) 3.06831 + 2.57462i 0.144481 + 0.121234i
\(452\) 0 0
\(453\) −4.51953 + 25.6316i −0.212346 + 1.20428i
\(454\) 0 0
\(455\) 4.49593 0.210772
\(456\) 0 0
\(457\) 6.37197 0.298068 0.149034 0.988832i \(-0.452384\pi\)
0.149034 + 0.988832i \(0.452384\pi\)
\(458\) 0 0
\(459\) 3.51180 19.9164i 0.163917 0.929617i
\(460\) 0 0
\(461\) −27.1446 22.7770i −1.26425 1.06083i −0.995216 0.0977013i \(-0.968851\pi\)
−0.269034 0.963131i \(-0.586705\pi\)
\(462\) 0 0
\(463\) 10.2314 + 17.7213i 0.475493 + 0.823578i 0.999606 0.0280707i \(-0.00893637\pi\)
−0.524113 + 0.851649i \(0.675603\pi\)
\(464\) 0 0
\(465\) 0.296625 + 0.107963i 0.0137557 + 0.00500666i
\(466\) 0 0
\(467\) 17.1827 29.7614i 0.795122 1.37719i −0.127640 0.991821i \(-0.540740\pi\)
0.922762 0.385371i \(-0.125927\pi\)
\(468\) 0 0
\(469\) 2.12089 + 12.0282i 0.0979338 + 0.555410i
\(470\) 0 0
\(471\) 15.4158 12.9354i 0.710322 0.596031i
\(472\) 0 0
\(473\) −3.64127 + 1.32532i −0.167426 + 0.0609381i
\(474\) 0 0
\(475\) −1.82625 + 3.95788i −0.0837942 + 0.181600i
\(476\) 0 0
\(477\) 3.53480 1.28656i 0.161847 0.0589076i
\(478\) 0 0
\(479\) −33.2281 + 27.8817i −1.51823 + 1.27395i −0.672852 + 0.739777i \(0.734931\pi\)
−0.845378 + 0.534169i \(0.820624\pi\)
\(480\) 0 0
\(481\) 3.07750 + 17.4534i 0.140322 + 0.795805i
\(482\) 0 0
\(483\) 1.65395 2.86472i 0.0752571 0.130349i
\(484\) 0 0
\(485\) −0.990001 0.360331i −0.0449537 0.0163618i
\(486\) 0 0
\(487\) −1.72596 2.98944i −0.0782105 0.135465i 0.824267 0.566201i \(-0.191587\pi\)
−0.902478 + 0.430736i \(0.858254\pi\)
\(488\) 0 0
\(489\) −15.1064 12.6758i −0.683137 0.573220i
\(490\) 0 0
\(491\) −1.83740 + 10.4204i −0.0829206 + 0.470266i 0.914865 + 0.403759i \(0.132297\pi\)
−0.997786 + 0.0665069i \(0.978815\pi\)
\(492\) 0 0
\(493\) −16.5578 −0.745725
\(494\) 0 0
\(495\) −1.39619 −0.0627542
\(496\) 0 0
\(497\) −0.429575 + 2.43624i −0.0192691 + 0.109280i
\(498\) 0 0
\(499\) −31.6480 26.5558i −1.41676 1.18880i −0.953050 0.302814i \(-0.902074\pi\)
−0.463709 0.885988i \(-0.653482\pi\)
\(500\) 0 0
\(501\) −5.64281 9.77364i −0.252102 0.436654i
\(502\) 0 0
\(503\) 24.9128 + 9.06752i 1.11081 + 0.404301i 0.831289 0.555840i \(-0.187603\pi\)
0.279518 + 0.960141i \(0.409825\pi\)
\(504\) 0 0
\(505\) −8.20149 + 14.2054i −0.364962 + 0.632132i
\(506\) 0 0
\(507\) 1.28618 + 7.29429i 0.0571213 + 0.323951i
\(508\) 0 0
\(509\) −18.4409 + 15.4738i −0.817380 + 0.685863i −0.952357 0.304985i \(-0.901348\pi\)
0.134977 + 0.990849i \(0.456904\pi\)
\(510\) 0 0
\(511\) 16.9593 6.17268i 0.750235 0.273063i
\(512\) 0 0
\(513\) −21.7889 + 10.2672i −0.962004 + 0.453308i
\(514\) 0 0
\(515\) 13.0693 4.75684i 0.575902 0.209611i
\(516\) 0 0
\(517\) 2.37269 1.99092i 0.104351 0.0875606i
\(518\) 0 0
\(519\) 4.76305 + 27.0126i 0.209075 + 1.18572i
\(520\) 0 0
\(521\) 0.0979457 0.169647i 0.00429108 0.00743237i −0.863872 0.503712i \(-0.831967\pi\)
0.868163 + 0.496279i \(0.165301\pi\)
\(522\) 0 0
\(523\) −11.2618 4.09894i −0.492442 0.179234i 0.0838494 0.996478i \(-0.473279\pi\)
−0.576292 + 0.817244i \(0.695501\pi\)
\(524\) 0 0
\(525\) −1.23555 2.14004i −0.0539240 0.0933991i
\(526\) 0 0
\(527\) 0.557837 + 0.468081i 0.0242998 + 0.0203899i
\(528\) 0 0
\(529\) −3.68274 + 20.8859i −0.160119 + 0.908082i
\(530\) 0 0
\(531\) 2.35304 0.102113
\(532\) 0 0
\(533\) −4.00090 −0.173298
\(534\) 0 0
\(535\) 0.955365 5.41815i 0.0413040 0.234247i
\(536\) 0 0
\(537\) 3.88769 + 3.26216i 0.167766 + 0.140773i
\(538\) 0 0
\(539\) 6.60825 + 11.4458i 0.284637 + 0.493006i
\(540\) 0 0
\(541\) −15.7983 5.75013i −0.679224 0.247217i −0.0207096 0.999786i \(-0.506593\pi\)
−0.658514 + 0.752568i \(0.728815\pi\)
\(542\) 0 0
\(543\) −16.3855 + 28.3805i −0.703169 + 1.21793i
\(544\) 0 0
\(545\) 0.363447 + 2.06121i 0.0155683 + 0.0882924i
\(546\) 0 0
\(547\) −34.1677 + 28.6701i −1.46090 + 1.22584i −0.536796 + 0.843712i \(0.680365\pi\)
−0.924108 + 0.382132i \(0.875190\pi\)
\(548\) 0 0
\(549\) 4.30829 1.56809i 0.183873 0.0669244i
\(550\) 0 0
\(551\) 11.3762 + 16.1086i 0.484641 + 0.686250i
\(552\) 0 0
\(553\) 20.1048 7.31756i 0.854945 0.311175i
\(554\) 0 0
\(555\) 7.46199 6.26135i 0.316744 0.265780i
\(556\) 0 0
\(557\) 3.97699 + 22.5547i 0.168511 + 0.955671i 0.945371 + 0.325998i \(0.105700\pi\)
−0.776860 + 0.629674i \(0.783189\pi\)
\(558\) 0 0
\(559\) 1.93531 3.35205i 0.0818548 0.141777i
\(560\) 0 0
\(561\) 15.7656 + 5.73821i 0.665625 + 0.242268i
\(562\) 0 0
\(563\) 7.97728 + 13.8170i 0.336202 + 0.582319i 0.983715 0.179735i \(-0.0575241\pi\)
−0.647513 + 0.762054i \(0.724191\pi\)
\(564\) 0 0
\(565\) −5.98794 5.02448i −0.251915 0.211382i
\(566\) 0 0
\(567\) 1.97911 11.2241i 0.0831148 0.471367i
\(568\) 0 0
\(569\) 1.86392 0.0781396 0.0390698 0.999236i \(-0.487561\pi\)
0.0390698 + 0.999236i \(0.487561\pi\)
\(570\) 0 0
\(571\) 38.4806 1.61036 0.805181 0.593029i \(-0.202068\pi\)
0.805181 + 0.593029i \(0.202068\pi\)
\(572\) 0 0
\(573\) −0.245922 + 1.39470i −0.0102736 + 0.0582642i
\(574\) 0 0
\(575\) −1.02545 0.860452i −0.0427641 0.0358833i
\(576\) 0 0
\(577\) 21.0547 + 36.4679i 0.876520 + 1.51818i 0.855135 + 0.518406i \(0.173474\pi\)
0.0213856 + 0.999771i \(0.493192\pi\)
\(578\) 0 0
\(579\) 3.02032 + 1.09931i 0.125520 + 0.0456856i
\(580\) 0 0
\(581\) −9.11209 + 15.7826i −0.378033 + 0.654773i
\(582\) 0 0
\(583\) 3.90649 + 22.1548i 0.161790 + 0.917558i
\(584\) 0 0
\(585\) 1.06835 0.896449i 0.0441707 0.0370636i
\(586\) 0 0
\(587\) −13.5996 + 4.94984i −0.561315 + 0.204302i −0.607067 0.794651i \(-0.707654\pi\)
0.0457518 + 0.998953i \(0.485432\pi\)
\(588\) 0 0
\(589\) 0.0721162 0.864304i 0.00297150 0.0356130i
\(590\) 0 0
\(591\) −31.0382 + 11.2970i −1.27674 + 0.464695i
\(592\) 0 0
\(593\) 33.6950 28.2735i 1.38369 1.16105i 0.415865 0.909427i \(-0.363479\pi\)
0.967824 0.251626i \(-0.0809654\pi\)
\(594\) 0 0
\(595\) −0.989903 5.61402i −0.0405821 0.230152i
\(596\) 0 0
\(597\) 5.30684 9.19171i 0.217194 0.376192i
\(598\) 0 0
\(599\) −9.54029 3.47238i −0.389806 0.141878i 0.139680 0.990197i \(-0.455393\pi\)
−0.529485 + 0.848319i \(0.677615\pi\)
\(600\) 0 0
\(601\) −0.342773 0.593701i −0.0139820 0.0242176i 0.858950 0.512060i \(-0.171117\pi\)
−0.872932 + 0.487842i \(0.837784\pi\)
\(602\) 0 0
\(603\) 2.90230 + 2.43531i 0.118191 + 0.0991737i
\(604\) 0 0
\(605\) −0.460181 + 2.60982i −0.0187090 + 0.106104i
\(606\) 0 0
\(607\) 3.25110 0.131958 0.0659791 0.997821i \(-0.478983\pi\)
0.0659791 + 0.997821i \(0.478983\pi\)
\(608\) 0 0
\(609\) −11.1799 −0.453031
\(610\) 0 0
\(611\) −0.537241 + 3.04685i −0.0217345 + 0.123262i
\(612\) 0 0
\(613\) 6.89548 + 5.78600i 0.278506 + 0.233694i 0.771331 0.636434i \(-0.219591\pi\)
−0.492825 + 0.870128i \(0.664036\pi\)
\(614\) 0 0
\(615\) 1.09951 + 1.90441i 0.0443367 + 0.0767934i
\(616\) 0 0
\(617\) 39.7314 + 14.4610i 1.59952 + 0.582179i 0.979330 0.202269i \(-0.0648314\pi\)
0.620195 + 0.784448i \(0.287054\pi\)
\(618\) 0 0
\(619\) 3.31494 5.74165i 0.133239 0.230776i −0.791685 0.610930i \(-0.790796\pi\)
0.924923 + 0.380154i \(0.124129\pi\)
\(620\) 0 0
\(621\) −1.28449 7.28471i −0.0515449 0.292326i
\(622\) 0 0
\(623\) 17.5065 14.6897i 0.701385 0.588532i
\(624\) 0 0
\(625\) −0.939693 + 0.342020i −0.0375877 + 0.0136808i
\(626\) 0 0
\(627\) −5.24935 19.2804i −0.209639 0.769986i
\(628\) 0 0
\(629\) 21.1163 7.68569i 0.841961 0.306449i
\(630\) 0 0
\(631\) −0.854975 + 0.717409i −0.0340360 + 0.0285596i −0.659647 0.751576i \(-0.729294\pi\)
0.625611 + 0.780135i \(0.284850\pi\)
\(632\) 0 0
\(633\) −6.48033 36.7518i −0.257570 1.46075i
\(634\) 0 0
\(635\) 0.947575 1.64125i 0.0376034 0.0651309i
\(636\) 0 0
\(637\) −12.4055 4.51524i −0.491524 0.178900i
\(638\) 0 0
\(639\) 0.383687 + 0.664566i 0.0151784 + 0.0262898i
\(640\) 0 0
\(641\) −8.06995 6.77149i −0.318744 0.267458i 0.469351 0.883012i \(-0.344488\pi\)
−0.788095 + 0.615554i \(0.788932\pi\)
\(642\) 0 0
\(643\) −7.95271 + 45.1021i −0.313624 + 1.77865i 0.266207 + 0.963916i \(0.414230\pi\)
−0.579831 + 0.814736i \(0.696882\pi\)
\(644\) 0 0
\(645\) −2.12742 −0.0837670
\(646\) 0 0
\(647\) 8.61113 0.338538 0.169269 0.985570i \(-0.445859\pi\)
0.169269 + 0.985570i \(0.445859\pi\)
\(648\) 0 0
\(649\) −2.44364 + 13.8585i −0.0959211 + 0.543996i
\(650\) 0 0
\(651\) 0.376653 + 0.316050i 0.0147622 + 0.0123870i
\(652\) 0 0
\(653\) 9.24321 + 16.0097i 0.361715 + 0.626508i 0.988243 0.152890i \(-0.0488582\pi\)
−0.626529 + 0.779398i \(0.715525\pi\)
\(654\) 0 0
\(655\) −16.1017 5.86053i −0.629145 0.228990i
\(656\) 0 0
\(657\) 2.79918 4.84832i 0.109206 0.189151i
\(658\) 0 0
\(659\) 2.46590 + 13.9848i 0.0960578 + 0.544771i 0.994418 + 0.105512i \(0.0336480\pi\)
−0.898360 + 0.439259i \(0.855241\pi\)
\(660\) 0 0
\(661\) −16.1090 + 13.5171i −0.626567 + 0.525752i −0.899860 0.436178i \(-0.856332\pi\)
0.273293 + 0.961931i \(0.411887\pi\)
\(662\) 0 0
\(663\) −15.7479 + 5.73178i −0.611599 + 0.222604i
\(664\) 0 0
\(665\) −4.78161 + 4.82021i −0.185423 + 0.186920i
\(666\) 0 0
\(667\) −5.69101 + 2.07136i −0.220357 + 0.0802034i
\(668\) 0 0
\(669\) 15.2012 12.7553i 0.587713 0.493149i
\(670\) 0 0
\(671\) 4.76131 + 27.0027i 0.183808 + 1.04243i
\(672\) 0 0
\(673\) −5.87529 + 10.1763i −0.226476 + 0.392267i −0.956761 0.290875i \(-0.906054\pi\)
0.730285 + 0.683142i \(0.239387\pi\)
\(674\) 0 0
\(675\) −5.19263 1.88996i −0.199865 0.0727447i
\(676\) 0 0
\(677\) −21.3188 36.9253i −0.819349 1.41915i −0.906162 0.422930i \(-0.861002\pi\)
0.0868130 0.996225i \(-0.472332\pi\)
\(678\) 0 0
\(679\) −1.25710 1.05483i −0.0482430 0.0404807i
\(680\) 0 0
\(681\) 4.98154 28.2517i 0.190893 1.08261i
\(682\) 0 0
\(683\) 27.4465 1.05021 0.525106 0.851037i \(-0.324026\pi\)
0.525106 + 0.851037i \(0.324026\pi\)
\(684\) 0 0
\(685\) −15.9618 −0.609869
\(686\) 0 0
\(687\) −3.33079 + 18.8898i −0.127078 + 0.720692i
\(688\) 0 0
\(689\) −17.2140 14.4443i −0.655803 0.550284i
\(690\) 0 0
\(691\) −11.7571 20.3638i −0.447260 0.774676i 0.550947 0.834540i \(-0.314267\pi\)
−0.998207 + 0.0598640i \(0.980933\pi\)
\(692\) 0 0
\(693\) −2.04360 0.743810i −0.0776300 0.0282550i
\(694\) 0 0
\(695\) 3.01582 5.22356i 0.114397 0.198141i
\(696\) 0 0
\(697\) 0.880911 + 4.99589i 0.0333669 + 0.189233i
\(698\) 0 0
\(699\) 7.66994 6.43584i 0.290104 0.243426i
\(700\) 0 0
\(701\) 40.2277 14.6417i 1.51938 0.553009i 0.558386 0.829581i \(-0.311421\pi\)
0.960993 + 0.276573i \(0.0891986\pi\)
\(702\) 0 0
\(703\) −21.9853 15.2629i −0.829192 0.575652i
\(704\) 0 0
\(705\) 1.59793 0.581599i 0.0601815 0.0219043i
\(706\) 0 0
\(707\) −19.5723 + 16.4231i −0.736092 + 0.617655i
\(708\) 0 0
\(709\) −1.27855 7.25100i −0.0480168 0.272317i 0.951341 0.308139i \(-0.0997062\pi\)
−0.999358 + 0.0358221i \(0.988595\pi\)
\(710\) 0 0
\(711\) 3.31836 5.74757i 0.124448 0.215551i
\(712\) 0 0
\(713\) 0.250289 + 0.0910976i 0.00937338 + 0.00341163i
\(714\) 0 0
\(715\) 4.17028 + 7.22313i 0.155960 + 0.270130i
\(716\) 0 0
\(717\) −21.3212 17.8906i −0.796256 0.668138i
\(718\) 0 0
\(719\) 5.42617 30.7734i 0.202362 1.14765i −0.699175 0.714951i \(-0.746449\pi\)
0.901537 0.432702i \(-0.142440\pi\)
\(720\) 0 0
\(721\) 21.6637 0.806797
\(722\) 0 0
\(723\) 14.4792 0.538487
\(724\) 0 0
\(725\) −0.785624 + 4.45550i −0.0291773 + 0.165473i
\(726\) 0 0
\(727\) 15.8464 + 13.2967i 0.587712 + 0.493149i 0.887469 0.460867i \(-0.152461\pi\)
−0.299758 + 0.954015i \(0.596906\pi\)
\(728\) 0 0
\(729\) −14.9175 25.8379i −0.552500 0.956959i
\(730\) 0 0
\(731\) −4.61179 1.67855i −0.170573 0.0620836i
\(732\) 0 0
\(733\) −6.58205 + 11.4005i −0.243114 + 0.421085i −0.961600 0.274456i \(-0.911502\pi\)
0.718486 + 0.695542i \(0.244835\pi\)
\(734\) 0 0
\(735\) 1.26000 + 7.14584i 0.0464759 + 0.263578i
\(736\) 0 0
\(737\) −17.3572 + 14.5644i −0.639359 + 0.536486i
\(738\) 0 0
\(739\) −15.0323 + 5.47130i −0.552971 + 0.201265i −0.603366 0.797464i \(-0.706174\pi\)
0.0503952 + 0.998729i \(0.483952\pi\)
\(740\) 0 0
\(741\) 16.3960 + 11.3827i 0.602324 + 0.418153i
\(742\) 0 0
\(743\) 28.1719 10.2537i 1.03353 0.376172i 0.231103 0.972929i \(-0.425767\pi\)
0.802422 + 0.596757i \(0.203544\pi\)
\(744\) 0 0
\(745\) 1.25026 1.04909i 0.0458059 0.0384358i
\(746\) 0 0
\(747\) 0.981651 + 5.56722i 0.0359167 + 0.203694i
\(748\) 0 0
\(749\) 4.28484 7.42156i 0.156565 0.271178i
\(750\) 0 0
\(751\) 12.2128 + 4.44508i 0.445650 + 0.162203i 0.555091 0.831790i \(-0.312684\pi\)
−0.109440 + 0.993993i \(0.534906\pi\)
\(752\) 0 0
\(753\) 4.65874 + 8.06917i 0.169774 + 0.294057i
\(754\) 0 0
\(755\) 12.5676 + 10.5454i 0.457380 + 0.383788i
\(756\) 0 0
\(757\) 6.44237 36.5365i 0.234152 1.32794i −0.610240 0.792217i \(-0.708927\pi\)
0.844392 0.535726i \(-0.179962\pi\)
\(758\) 0 0
\(759\) 6.13659 0.222744
\(760\) 0 0
\(761\) −46.3946 −1.68180 −0.840902 0.541188i \(-0.817975\pi\)
−0.840902 + 0.541188i \(0.817975\pi\)
\(762\) 0 0
\(763\) −0.566117 + 3.21061i −0.0204948 + 0.116232i
\(764\) 0 0
\(765\) −1.35461 1.13666i −0.0489761 0.0410959i
\(766\) 0 0
\(767\) −7.02828 12.1733i −0.253776 0.439554i
\(768\) 0 0
\(769\) 33.8986 + 12.3381i 1.22241 + 0.444923i 0.870993 0.491295i \(-0.163476\pi\)
0.351421 + 0.936217i \(0.385698\pi\)
\(770\) 0 0
\(771\) −7.86199 + 13.6174i −0.283143 + 0.490418i
\(772\) 0 0
\(773\) −8.52101 48.3250i −0.306479 1.73813i −0.616458 0.787388i \(-0.711433\pi\)
0.309979 0.950743i \(-0.399678\pi\)
\(774\) 0 0
\(775\) 0.152423 0.127898i 0.00547519 0.00459423i
\(776\) 0 0
\(777\) 14.2578 5.18940i 0.511495 0.186169i
\(778\) 0 0
\(779\) 4.25513 4.28949i 0.152456 0.153687i
\(780\) 0 0
\(781\) −4.31251 + 1.56963i −0.154314 + 0.0561656i
\(782\) 0 0
\(783\) −19.1514 + 16.0699i −0.684415 + 0.574292i
\(784\) 0 0
\(785\) −2.20270 12.4921i −0.0786178 0.445864i
\(786\) 0 0
\(787\) −18.5322 + 32.0988i −0.660603 + 1.14420i </