Properties

Label 675.2.e.e.451.4
Level $675$
Weight $2$
Character 675.451
Analytic conductor $5.390$
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] = [675,2,Mod(226,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1223810289.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.4
Root \(1.31686 - 2.28087i\) of defining polynomial
Character \(\chi\) \(=\) 675.451
Dual form 675.2.e.e.226.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31686 - 2.28087i) q^{2} +(-2.46825 - 4.27513i) q^{4} +(0.898714 - 1.55662i) q^{7} -7.73393 q^{8} +O(q^{10})\) \(q+(1.31686 - 2.28087i) q^{2} +(-2.46825 - 4.27513i) q^{4} +(0.898714 - 1.55662i) q^{7} -7.73393 q^{8} +(0.904062 - 1.56588i) q^{11} +(-0.985914 - 1.70765i) q^{13} +(-2.36696 - 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} -4.80812 q^{17} +2.96467 q^{19} +(-2.38105 - 4.12410i) q^{22} +(-0.866963 - 1.50162i) q^{23} -5.19325 q^{26} -8.87300 q^{28} +(-3.68382 + 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(6.08789 + 10.5445i) q^{32} +(-6.33163 + 10.9667i) q^{34} +11.6351 q^{37} +(3.90406 - 6.76203i) q^{38} +(-1.23324 - 2.13603i) q^{41} +(3.63907 - 6.30306i) q^{43} -8.92580 q^{44} -4.56668 q^{46} +(3.14604 - 5.44910i) q^{47} +(1.88463 + 3.26427i) q^{49} +(-4.86696 + 8.42983i) q^{52} -1.72540 q^{53} +(-6.95059 + 12.0388i) q^{56} +(9.70218 + 16.8047i) q^{58} +(5.51300 + 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} +6.90833 q^{62} +11.0756 q^{64} +(-4.55187 - 7.88407i) q^{67} +(11.8676 + 20.5554i) q^{68} -1.27460 q^{71} -3.58770 q^{73} +(15.3218 - 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(-1.62499 - 2.81456i) q^{77} +(-1.05545 + 1.82809i) q^{79} -6.49602 q^{82} +(0.549415 - 0.951614i) q^{83} +(-9.58431 - 16.6005i) q^{86} +(-6.99195 + 12.1104i) q^{88} +13.2935 q^{89} -3.54422 q^{91} +(-4.27976 + 7.41277i) q^{92} +(-8.28580 - 14.3514i) q^{94} +(1.91638 - 3.31926i) q^{97} +9.92718 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 4 q^{4} + q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 4 q^{4} + q^{7} - 18 q^{8} - q^{11} - 2 q^{13} + 3 q^{14} - 4 q^{16} - 22 q^{17} + 4 q^{19} - 3 q^{22} + 15 q^{23} + 20 q^{26} - 8 q^{28} + q^{29} + 4 q^{31} + 10 q^{32} - 9 q^{34} - 2 q^{37} + 23 q^{38} - 5 q^{41} + 10 q^{43} - 44 q^{44} + 20 q^{47} + 3 q^{49} - 17 q^{52} - 40 q^{53} - 30 q^{56} + 18 q^{58} + 17 q^{59} + 13 q^{61} + 12 q^{62} + 38 q^{64} - 17 q^{67} + 34 q^{68} + 16 q^{71} + 4 q^{73} + 40 q^{74} - 11 q^{76} + 12 q^{77} + 7 q^{79} + 24 q^{82} + 30 q^{83} - 34 q^{86} - 9 q^{88} + 18 q^{89} - 34 q^{91} - 12 q^{92} - 3 q^{94} + 19 q^{97} - 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31686 2.28087i 0.931162 1.61282i 0.149823 0.988713i \(-0.452130\pi\)
0.781339 0.624107i \(-0.214537\pi\)
\(3\) 0 0
\(4\) −2.46825 4.27513i −1.23412 2.13757i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.898714 1.55662i 0.339682 0.588346i −0.644691 0.764443i \(-0.723014\pi\)
0.984373 + 0.176097i \(0.0563473\pi\)
\(8\) −7.73393 −2.73436
\(9\) 0 0
\(10\) 0 0
\(11\) 0.904062 1.56588i 0.272585 0.472131i −0.696938 0.717131i \(-0.745455\pi\)
0.969523 + 0.245000i \(0.0787881\pi\)
\(12\) 0 0
\(13\) −0.985914 1.70765i −0.273443 0.473618i 0.696298 0.717753i \(-0.254829\pi\)
−0.969741 + 0.244135i \(0.921496\pi\)
\(14\) −2.36696 4.09970i −0.632598 1.09569i
\(15\) 0 0
\(16\) −5.24801 + 9.08982i −1.31200 + 2.27246i
\(17\) −4.80812 −1.16614 −0.583071 0.812421i \(-0.698149\pi\)
−0.583071 + 0.812421i \(0.698149\pi\)
\(18\) 0 0
\(19\) 2.96467 0.680142 0.340071 0.940400i \(-0.389549\pi\)
0.340071 + 0.940400i \(0.389549\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.38105 4.12410i −0.507641 0.879261i
\(23\) −0.866963 1.50162i −0.180774 0.313110i 0.761370 0.648317i \(-0.224527\pi\)
−0.942144 + 0.335207i \(0.891194\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −5.19325 −1.01848
\(27\) 0 0
\(28\) −8.87300 −1.67684
\(29\) −3.68382 + 6.38057i −0.684069 + 1.18484i 0.289659 + 0.957130i \(0.406458\pi\)
−0.973728 + 0.227713i \(0.926875\pi\)
\(30\) 0 0
\(31\) 1.31151 + 2.27161i 0.235555 + 0.407993i 0.959434 0.281934i \(-0.0909760\pi\)
−0.723879 + 0.689927i \(0.757643\pi\)
\(32\) 6.08789 + 10.5445i 1.07620 + 1.86403i
\(33\) 0 0
\(34\) −6.33163 + 10.9667i −1.08587 + 1.88078i
\(35\) 0 0
\(36\) 0 0
\(37\) 11.6351 1.91280 0.956399 0.292063i \(-0.0943417\pi\)
0.956399 + 0.292063i \(0.0943417\pi\)
\(38\) 3.90406 6.76203i 0.633322 1.09695i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.23324 2.13603i −0.192600 0.333592i 0.753511 0.657435i \(-0.228359\pi\)
−0.946111 + 0.323842i \(0.895025\pi\)
\(42\) 0 0
\(43\) 3.63907 6.30306i 0.554953 0.961207i −0.442954 0.896544i \(-0.646069\pi\)
0.997907 0.0646628i \(-0.0205972\pi\)
\(44\) −8.92580 −1.34562
\(45\) 0 0
\(46\) −4.56668 −0.673321
\(47\) 3.14604 5.44910i 0.458897 0.794833i −0.540006 0.841661i \(-0.681578\pi\)
0.998903 + 0.0468283i \(0.0149113\pi\)
\(48\) 0 0
\(49\) 1.88463 + 3.26427i 0.269233 + 0.466324i
\(50\) 0 0
\(51\) 0 0
\(52\) −4.86696 + 8.42983i −0.674926 + 1.16901i
\(53\) −1.72540 −0.237001 −0.118501 0.992954i \(-0.537809\pi\)
−0.118501 + 0.992954i \(0.537809\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −6.95059 + 12.0388i −0.928811 + 1.60875i
\(57\) 0 0
\(58\) 9.70218 + 16.8047i 1.27396 + 2.20656i
\(59\) 5.51300 + 9.54880i 0.717732 + 1.24315i 0.961896 + 0.273414i \(0.0881529\pi\)
−0.244165 + 0.969734i \(0.578514\pi\)
\(60\) 0 0
\(61\) 6.33521 10.9729i 0.811141 1.40494i −0.100925 0.994894i \(-0.532180\pi\)
0.912066 0.410043i \(-0.134486\pi\)
\(62\) 6.90833 0.877358
\(63\) 0 0
\(64\) 11.0756 1.38445
\(65\) 0 0
\(66\) 0 0
\(67\) −4.55187 7.88407i −0.556100 0.963193i −0.997817 0.0660386i \(-0.978964\pi\)
0.441717 0.897154i \(-0.354369\pi\)
\(68\) 11.8676 + 20.5554i 1.43916 + 2.49271i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.27460 −0.151268 −0.0756338 0.997136i \(-0.524098\pi\)
−0.0756338 + 0.997136i \(0.524098\pi\)
\(72\) 0 0
\(73\) −3.58770 −0.419908 −0.209954 0.977711i \(-0.567331\pi\)
−0.209954 + 0.977711i \(0.567331\pi\)
\(74\) 15.3218 26.5382i 1.78112 3.08500i
\(75\) 0 0
\(76\) −7.31755 12.6744i −0.839380 1.45385i
\(77\) −1.62499 2.81456i −0.185184 0.320749i
\(78\) 0 0
\(79\) −1.05545 + 1.82809i −0.118747 + 0.205676i −0.919272 0.393624i \(-0.871221\pi\)
0.800524 + 0.599300i \(0.204555\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.49602 −0.717366
\(83\) 0.549415 0.951614i 0.0603061 0.104453i −0.834296 0.551317i \(-0.814126\pi\)
0.894602 + 0.446863i \(0.147459\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −9.58431 16.6005i −1.03350 1.79008i
\(87\) 0 0
\(88\) −6.99195 + 12.1104i −0.745344 + 1.29097i
\(89\) 13.2935 1.40910 0.704552 0.709653i \(-0.251148\pi\)
0.704552 + 0.709653i \(0.251148\pi\)
\(90\) 0 0
\(91\) −3.54422 −0.371535
\(92\) −4.27976 + 7.41277i −0.446196 + 0.772834i
\(93\) 0 0
\(94\) −8.28580 14.3514i −0.854615 1.48024i
\(95\) 0 0
\(96\) 0 0
\(97\) 1.91638 3.31926i 0.194579 0.337020i −0.752184 0.658954i \(-0.770999\pi\)
0.946762 + 0.321933i \(0.104333\pi\)
\(98\) 9.92718 1.00280
\(99\) 0 0
\(100\) 0 0
\(101\) 3.27618 5.67452i 0.325993 0.564636i −0.655720 0.755004i \(-0.727635\pi\)
0.981713 + 0.190368i \(0.0609682\pi\)
\(102\) 0 0
\(103\) 4.03779 + 6.99365i 0.397855 + 0.689105i 0.993461 0.114172i \(-0.0364214\pi\)
−0.595606 + 0.803277i \(0.703088\pi\)
\(104\) 7.62499 + 13.2069i 0.747691 + 1.29504i
\(105\) 0 0
\(106\) −2.27211 + 3.93541i −0.220687 + 0.382241i
\(107\) 8.97674 0.867814 0.433907 0.900958i \(-0.357135\pi\)
0.433907 + 0.900958i \(0.357135\pi\)
\(108\) 0 0
\(109\) −6.34164 −0.607419 −0.303710 0.952765i \(-0.598225\pi\)
−0.303710 + 0.952765i \(0.598225\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 9.43292 + 16.3383i 0.891327 + 1.54382i
\(113\) −7.45127 12.9060i −0.700957 1.21409i −0.968131 0.250444i \(-0.919423\pi\)
0.267174 0.963648i \(-0.413910\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 36.3704 3.37691
\(117\) 0 0
\(118\) 29.0394 2.67330
\(119\) −4.32113 + 7.48441i −0.396117 + 0.686095i
\(120\) 0 0
\(121\) 3.86534 + 6.69497i 0.351395 + 0.608634i
\(122\) −16.6852 28.8996i −1.51061 2.61645i
\(123\) 0 0
\(124\) 6.47428 11.2138i 0.581408 1.00703i
\(125\) 0 0
\(126\) 0 0
\(127\) 3.62303 0.321492 0.160746 0.986996i \(-0.448610\pi\)
0.160746 + 0.986996i \(0.448610\pi\)
\(128\) 2.40922 4.17289i 0.212947 0.368835i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.64673 + 6.31631i 0.318616 + 0.551859i 0.980200 0.198012i \(-0.0634486\pi\)
−0.661584 + 0.749871i \(0.730115\pi\)
\(132\) 0 0
\(133\) 2.66439 4.61486i 0.231032 0.400159i
\(134\) −23.9767 −2.07127
\(135\) 0 0
\(136\) 37.1857 3.18865
\(137\) −3.56310 + 6.17148i −0.304417 + 0.527265i −0.977131 0.212637i \(-0.931795\pi\)
0.672715 + 0.739902i \(0.265128\pi\)
\(138\) 0 0
\(139\) 7.35533 + 12.7398i 0.623871 + 1.08058i 0.988758 + 0.149525i \(0.0477744\pi\)
−0.364887 + 0.931052i \(0.618892\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.67848 + 2.90721i −0.140855 + 0.243967i
\(143\) −3.56531 −0.298146
\(144\) 0 0
\(145\) 0 0
\(146\) −4.72450 + 8.18308i −0.391003 + 0.677236i
\(147\) 0 0
\(148\) −28.7183 49.7416i −2.36063 4.08873i
\(149\) −0.282655 0.489572i −0.0231560 0.0401073i 0.854215 0.519920i \(-0.174038\pi\)
−0.877371 + 0.479812i \(0.840705\pi\)
\(150\) 0 0
\(151\) −0.0766925 + 0.132835i −0.00624115 + 0.0108100i −0.869129 0.494585i \(-0.835320\pi\)
0.862888 + 0.505395i \(0.168653\pi\)
\(152\) −22.9285 −1.85975
\(153\) 0 0
\(154\) −8.55953 −0.689746
\(155\) 0 0
\(156\) 0 0
\(157\) 5.73035 + 9.92525i 0.457332 + 0.792121i 0.998819 0.0485874i \(-0.0154719\pi\)
−0.541487 + 0.840709i \(0.682139\pi\)
\(158\) 2.77976 + 4.81469i 0.221146 + 0.383036i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.11661 −0.245623
\(162\) 0 0
\(163\) −22.0595 −1.72783 −0.863915 0.503637i \(-0.831995\pi\)
−0.863915 + 0.503637i \(0.831995\pi\)
\(164\) −6.08789 + 10.5445i −0.475384 + 0.823389i
\(165\) 0 0
\(166\) −1.44701 2.50629i −0.112310 0.194526i
\(167\) 8.53421 + 14.7817i 0.660397 + 1.14384i 0.980511 + 0.196462i \(0.0629452\pi\)
−0.320115 + 0.947379i \(0.603721\pi\)
\(168\) 0 0
\(169\) 4.55595 7.89113i 0.350457 0.607010i
\(170\) 0 0
\(171\) 0 0
\(172\) −35.9285 −2.73953
\(173\) 5.97233 10.3444i 0.454067 0.786468i −0.544567 0.838718i \(-0.683306\pi\)
0.998634 + 0.0522497i \(0.0166392\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.48906 + 16.4355i 0.715265 + 1.23887i
\(177\) 0 0
\(178\) 17.5056 30.3207i 1.31210 2.27263i
\(179\) −8.54921 −0.638998 −0.319499 0.947587i \(-0.603515\pi\)
−0.319499 + 0.947587i \(0.603515\pi\)
\(180\) 0 0
\(181\) −10.5524 −0.784351 −0.392176 0.919890i \(-0.628277\pi\)
−0.392176 + 0.919890i \(0.628277\pi\)
\(182\) −4.66724 + 8.08390i −0.345959 + 0.599219i
\(183\) 0 0
\(184\) 6.70503 + 11.6135i 0.494301 + 0.856155i
\(185\) 0 0
\(186\) 0 0
\(187\) −4.34684 + 7.52895i −0.317873 + 0.550571i
\(188\) −31.0608 −2.26534
\(189\) 0 0
\(190\) 0 0
\(191\) −8.66862 + 15.0145i −0.627239 + 1.08641i 0.360864 + 0.932618i \(0.382482\pi\)
−0.988103 + 0.153792i \(0.950852\pi\)
\(192\) 0 0
\(193\) −0.779763 1.35059i −0.0561286 0.0972175i 0.836596 0.547821i \(-0.184542\pi\)
−0.892724 + 0.450603i \(0.851209\pi\)
\(194\) −5.04721 8.74202i −0.362369 0.627641i
\(195\) 0 0
\(196\) 9.30346 16.1141i 0.664533 1.15100i
\(197\) −17.9767 −1.28079 −0.640395 0.768046i \(-0.721229\pi\)
−0.640395 + 0.768046i \(0.721229\pi\)
\(198\) 0 0
\(199\) 11.0225 0.781362 0.390681 0.920526i \(-0.372240\pi\)
0.390681 + 0.920526i \(0.372240\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −8.62856 14.9451i −0.607104 1.05153i
\(203\) 6.62141 + 11.4686i 0.464732 + 0.804939i
\(204\) 0 0
\(205\) 0 0
\(206\) 21.2688 1.48187
\(207\) 0 0
\(208\) 20.6964 1.43503
\(209\) 2.68025 4.64232i 0.185397 0.321116i
\(210\) 0 0
\(211\) 11.9643 + 20.7227i 0.823655 + 1.42661i 0.902943 + 0.429760i \(0.141402\pi\)
−0.0792886 + 0.996852i \(0.525265\pi\)
\(212\) 4.25871 + 7.37630i 0.292489 + 0.506606i
\(213\) 0 0
\(214\) 11.8211 20.4748i 0.808076 1.39963i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.71470 0.320055
\(218\) −8.35107 + 14.4645i −0.565606 + 0.979658i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.74040 + 8.21061i 0.318874 + 0.552305i
\(222\) 0 0
\(223\) −10.8553 + 18.8020i −0.726927 + 1.25907i 0.231249 + 0.972895i \(0.425719\pi\)
−0.958176 + 0.286180i \(0.907615\pi\)
\(224\) 21.8851 1.46226
\(225\) 0 0
\(226\) −39.2492 −2.61082
\(227\) 7.05010 12.2111i 0.467932 0.810481i −0.531397 0.847123i \(-0.678333\pi\)
0.999328 + 0.0366416i \(0.0116660\pi\)
\(228\) 0 0
\(229\) −1.83879 3.18488i −0.121511 0.210463i 0.798853 0.601526i \(-0.205441\pi\)
−0.920364 + 0.391064i \(0.872107\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 28.4904 49.3469i 1.87049 3.23978i
\(233\) 5.34164 0.349943 0.174971 0.984574i \(-0.444017\pi\)
0.174971 + 0.984574i \(0.444017\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 27.2149 47.1376i 1.77154 3.06840i
\(237\) 0 0
\(238\) 11.3807 + 19.7119i 0.737698 + 1.27773i
\(239\) −11.0167 19.0815i −0.712613 1.23428i −0.963873 0.266362i \(-0.914178\pi\)
0.251260 0.967920i \(-0.419155\pi\)
\(240\) 0 0
\(241\) 9.32358 16.1489i 0.600585 1.04024i −0.392148 0.919902i \(-0.628268\pi\)
0.992733 0.120341i \(-0.0383988\pi\)
\(242\) 20.3605 1.30882
\(243\) 0 0
\(244\) −62.5475 −4.00420
\(245\) 0 0
\(246\) 0 0
\(247\) −2.92291 5.06263i −0.185980 0.322127i
\(248\) −10.1431 17.5684i −0.644091 1.11560i
\(249\) 0 0
\(250\) 0 0
\(251\) −14.6929 −0.927407 −0.463704 0.885990i \(-0.653480\pi\)
−0.463704 + 0.885990i \(0.653480\pi\)
\(252\) 0 0
\(253\) −3.13515 −0.197105
\(254\) 4.77103 8.26366i 0.299361 0.518508i
\(255\) 0 0
\(256\) 4.73035 + 8.19320i 0.295647 + 0.512075i
\(257\) 11.1045 + 19.2335i 0.692678 + 1.19975i 0.970957 + 0.239253i \(0.0769025\pi\)
−0.278280 + 0.960500i \(0.589764\pi\)
\(258\) 0 0
\(259\) 10.4566 18.1114i 0.649743 1.12539i
\(260\) 0 0
\(261\) 0 0
\(262\) 19.2089 1.18673
\(263\) 2.87001 4.97100i 0.176972 0.306525i −0.763870 0.645370i \(-0.776703\pi\)
0.940842 + 0.338846i \(0.110036\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −7.01727 12.1543i −0.430256 0.745226i
\(267\) 0 0
\(268\) −22.4703 + 38.9197i −1.37259 + 2.37740i
\(269\) 15.6162 0.952139 0.476070 0.879408i \(-0.342061\pi\)
0.476070 + 0.879408i \(0.342061\pi\)
\(270\) 0 0
\(271\) −6.75315 −0.410225 −0.205112 0.978738i \(-0.565756\pi\)
−0.205112 + 0.978738i \(0.565756\pi\)
\(272\) 25.2331 43.7050i 1.52998 2.65000i
\(273\) 0 0
\(274\) 9.38423 + 16.2540i 0.566922 + 0.981938i
\(275\) 0 0
\(276\) 0 0
\(277\) −15.1483 + 26.2376i −0.910172 + 1.57646i −0.0963529 + 0.995347i \(0.530718\pi\)
−0.813820 + 0.581118i \(0.802616\pi\)
\(278\) 38.7438 2.32370
\(279\) 0 0
\(280\) 0 0
\(281\) 9.31755 16.1385i 0.555838 0.962740i −0.441999 0.897015i \(-0.645731\pi\)
0.997838 0.0657249i \(-0.0209360\pi\)
\(282\) 0 0
\(283\) 2.83683 + 4.91354i 0.168632 + 0.292079i 0.937939 0.346800i \(-0.112732\pi\)
−0.769307 + 0.638879i \(0.779398\pi\)
\(284\) 3.14604 + 5.44910i 0.186683 + 0.323345i
\(285\) 0 0
\(286\) −4.69502 + 8.13201i −0.277622 + 0.480856i
\(287\) −4.43332 −0.261690
\(288\) 0 0
\(289\) 6.11806 0.359886
\(290\) 0 0
\(291\) 0 0
\(292\) 8.85533 + 15.3379i 0.518219 + 0.897582i
\(293\) 9.13867 + 15.8286i 0.533887 + 0.924720i 0.999216 + 0.0395819i \(0.0126026\pi\)
−0.465329 + 0.885138i \(0.654064\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −89.9850 −5.23027
\(297\) 0 0
\(298\) −1.48887 −0.0862478
\(299\) −1.70950 + 2.96094i −0.0988631 + 0.171236i
\(300\) 0 0
\(301\) −6.54097 11.3293i −0.377015 0.653009i
\(302\) 0.201987 + 0.349852i 0.0116230 + 0.0201317i
\(303\) 0 0
\(304\) −15.5586 + 26.9483i −0.892349 + 1.54559i
\(305\) 0 0
\(306\) 0 0
\(307\) −15.5050 −0.884915 −0.442458 0.896789i \(-0.645893\pi\)
−0.442458 + 0.896789i \(0.645893\pi\)
\(308\) −8.02174 + 13.8941i −0.457081 + 0.791688i
\(309\) 0 0
\(310\) 0 0
\(311\) 15.2232 + 26.3673i 0.863228 + 1.49515i 0.868796 + 0.495170i \(0.164894\pi\)
−0.00556798 + 0.999984i \(0.501772\pi\)
\(312\) 0 0
\(313\) 3.47468 6.01832i 0.196401 0.340176i −0.750958 0.660350i \(-0.770408\pi\)
0.947359 + 0.320174i \(0.103741\pi\)
\(314\) 30.1843 1.70340
\(315\) 0 0
\(316\) 10.4205 0.586196
\(317\) −8.07253 + 13.9820i −0.453398 + 0.785309i −0.998595 0.0529995i \(-0.983122\pi\)
0.545196 + 0.838308i \(0.316455\pi\)
\(318\) 0 0
\(319\) 6.66081 + 11.5369i 0.372934 + 0.645940i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.10414 + 7.10858i −0.228715 + 0.396146i
\(323\) −14.2545 −0.793142
\(324\) 0 0
\(325\) 0 0
\(326\) −29.0493 + 50.3148i −1.60889 + 2.78668i
\(327\) 0 0
\(328\) 9.53779 + 16.5199i 0.526636 + 0.912160i
\(329\) −5.65478 9.79436i −0.311758 0.539981i
\(330\) 0 0
\(331\) −6.31112 + 10.9312i −0.346890 + 0.600832i −0.985695 0.168537i \(-0.946096\pi\)
0.638805 + 0.769369i \(0.279429\pi\)
\(332\) −5.42437 −0.297701
\(333\) 0 0
\(334\) 44.9535 2.45975
\(335\) 0 0
\(336\) 0 0
\(337\) 3.46020 + 5.99324i 0.188489 + 0.326473i 0.944747 0.327801i \(-0.106308\pi\)
−0.756258 + 0.654274i \(0.772974\pi\)
\(338\) −11.9991 20.7831i −0.652665 1.13045i
\(339\) 0 0
\(340\) 0 0
\(341\) 4.74276 0.256835
\(342\) 0 0
\(343\) 19.3570 1.04518
\(344\) −28.1443 + 48.7474i −1.51744 + 2.62828i
\(345\) 0 0
\(346\) −15.7295 27.2442i −0.845621 1.46466i
\(347\) 6.90317 + 11.9566i 0.370581 + 0.641866i 0.989655 0.143467i \(-0.0458251\pi\)
−0.619074 + 0.785333i \(0.712492\pi\)
\(348\) 0 0
\(349\) −3.28384 + 5.68778i −0.175780 + 0.304460i −0.940431 0.339985i \(-0.889578\pi\)
0.764651 + 0.644445i \(0.222911\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 22.0153 1.17342
\(353\) −1.76250 + 3.05273i −0.0938082 + 0.162481i −0.909111 0.416555i \(-0.863237\pi\)
0.815302 + 0.579035i \(0.196571\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −32.8116 56.8313i −1.73901 3.01205i
\(357\) 0 0
\(358\) −11.2581 + 19.4996i −0.595010 + 1.03059i
\(359\) −22.9285 −1.21012 −0.605061 0.796179i \(-0.706851\pi\)
−0.605061 + 0.796179i \(0.706851\pi\)
\(360\) 0 0
\(361\) −10.2107 −0.537407
\(362\) −13.8960 + 24.0686i −0.730358 + 1.26502i
\(363\) 0 0
\(364\) 8.74801 + 15.1520i 0.458520 + 0.794181i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.08966 + 3.61939i −0.109079 + 0.188931i −0.915397 0.402551i \(-0.868124\pi\)
0.806318 + 0.591482i \(0.201457\pi\)
\(368\) 18.1993 0.948706
\(369\) 0 0
\(370\) 0 0
\(371\) −1.55064 + 2.68578i −0.0805051 + 0.139439i
\(372\) 0 0
\(373\) −3.42045 5.92440i −0.177104 0.306754i 0.763783 0.645473i \(-0.223340\pi\)
−0.940888 + 0.338719i \(0.890006\pi\)
\(374\) 11.4484 + 19.8292i 0.591982 + 1.02534i
\(375\) 0 0
\(376\) −24.3312 + 42.1429i −1.25479 + 2.17336i
\(377\) 14.5277 0.748217
\(378\) 0 0
\(379\) −12.7764 −0.656280 −0.328140 0.944629i \(-0.606422\pi\)
−0.328140 + 0.944629i \(0.606422\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 22.8307 + 39.5440i 1.16812 + 2.02325i
\(383\) 3.76730 + 6.52515i 0.192500 + 0.333420i 0.946078 0.323939i \(-0.105007\pi\)
−0.753578 + 0.657358i \(0.771674\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.10736 −0.209059
\(387\) 0 0
\(388\) −18.9204 −0.960538
\(389\) 2.72588 4.72135i 0.138207 0.239382i −0.788611 0.614893i \(-0.789199\pi\)
0.926818 + 0.375511i \(0.122533\pi\)
\(390\) 0 0
\(391\) 4.16847 + 7.22000i 0.210808 + 0.365131i
\(392\) −14.5756 25.2456i −0.736177 1.27510i
\(393\) 0 0
\(394\) −23.6729 + 41.0026i −1.19262 + 2.06568i
\(395\) 0 0
\(396\) 0 0
\(397\) −5.64549 −0.283339 −0.141670 0.989914i \(-0.545247\pi\)
−0.141670 + 0.989914i \(0.545247\pi\)
\(398\) 14.5151 25.1408i 0.727574 1.26020i
\(399\) 0 0
\(400\) 0 0
\(401\) −2.75209 4.76676i −0.137433 0.238040i 0.789091 0.614276i \(-0.210552\pi\)
−0.926524 + 0.376235i \(0.877218\pi\)
\(402\) 0 0
\(403\) 2.58608 4.47922i 0.128822 0.223126i
\(404\) −32.3458 −1.60926
\(405\) 0 0
\(406\) 34.8779 1.73096
\(407\) 10.5188 18.2192i 0.521400 0.903091i
\(408\) 0 0
\(409\) −16.4265 28.4515i −0.812238 1.40684i −0.911295 0.411755i \(-0.864916\pi\)
0.0990570 0.995082i \(-0.468417\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 19.9325 34.5241i 0.982005 1.70088i
\(413\) 19.8184 0.975202
\(414\) 0 0
\(415\) 0 0
\(416\) 12.0043 20.7920i 0.588558 1.01941i
\(417\) 0 0
\(418\) −7.05903 12.2266i −0.345268 0.598022i
\(419\) 11.4295 + 19.7965i 0.558369 + 0.967124i 0.997633 + 0.0687656i \(0.0219060\pi\)
−0.439264 + 0.898358i \(0.644761\pi\)
\(420\) 0 0
\(421\) −8.97071 + 15.5377i −0.437205 + 0.757262i −0.997473 0.0710498i \(-0.977365\pi\)
0.560267 + 0.828312i \(0.310698\pi\)
\(422\) 63.0212 3.06782
\(423\) 0 0
\(424\) 13.3441 0.648046
\(425\) 0 0
\(426\) 0 0
\(427\) −11.3871 19.7230i −0.551060 0.954463i
\(428\) −22.1568 38.3768i −1.07099 1.85501i
\(429\) 0 0
\(430\) 0 0
\(431\) 6.18871 0.298100 0.149050 0.988830i \(-0.452378\pi\)
0.149050 + 0.988830i \(0.452378\pi\)
\(432\) 0 0
\(433\) −3.11806 −0.149844 −0.0749221 0.997189i \(-0.523871\pi\)
−0.0749221 + 0.997189i \(0.523871\pi\)
\(434\) 6.20861 10.7536i 0.298023 0.516190i
\(435\) 0 0
\(436\) 15.6528 + 27.1114i 0.749631 + 1.29840i
\(437\) −2.57026 4.45182i −0.122952 0.212960i
\(438\) 0 0
\(439\) −6.75494 + 11.6999i −0.322396 + 0.558406i −0.980982 0.194100i \(-0.937822\pi\)
0.658586 + 0.752505i \(0.271155\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 24.9698 1.18769
\(443\) −12.1387 + 21.0248i −0.576726 + 0.998918i 0.419126 + 0.907928i \(0.362337\pi\)
−0.995852 + 0.0909904i \(0.970997\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 28.5899 + 49.5192i 1.35377 + 2.34480i
\(447\) 0 0
\(448\) 9.95377 17.2404i 0.470271 0.814534i
\(449\) 24.1437 1.13941 0.569705 0.821849i \(-0.307057\pi\)
0.569705 + 0.821849i \(0.307057\pi\)
\(450\) 0 0
\(451\) −4.45970 −0.209999
\(452\) −36.7832 + 63.7104i −1.73014 + 2.99668i
\(453\) 0 0
\(454\) −18.5680 32.1607i −0.871440 1.50938i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.41078 2.44355i 0.0659937 0.114304i −0.831141 0.556062i \(-0.812312\pi\)
0.897134 + 0.441758i \(0.145645\pi\)
\(458\) −9.68573 −0.452585
\(459\) 0 0
\(460\) 0 0
\(461\) 10.7286 18.5825i 0.499681 0.865474i −0.500318 0.865841i \(-0.666784\pi\)
1.00000 0.000367761i \(0.000117062\pi\)
\(462\) 0 0
\(463\) 9.90167 + 17.1502i 0.460170 + 0.797037i 0.998969 0.0453970i \(-0.0144553\pi\)
−0.538799 + 0.842434i \(0.681122\pi\)
\(464\) −38.6655 66.9706i −1.79500 3.10903i
\(465\) 0 0
\(466\) 7.03421 12.1836i 0.325853 0.564395i
\(467\) −22.7210 −1.05140 −0.525701 0.850669i \(-0.676197\pi\)
−0.525701 + 0.850669i \(0.676197\pi\)
\(468\) 0 0
\(469\) −16.3633 −0.755588
\(470\) 0 0
\(471\) 0 0
\(472\) −42.6372 73.8497i −1.96253 3.39921i
\(473\) −6.57989 11.3967i −0.302544 0.524021i
\(474\) 0 0
\(475\) 0 0
\(476\) 42.6625 1.95543
\(477\) 0 0
\(478\) −58.0300 −2.65423
\(479\) 10.6440 18.4359i 0.486336 0.842359i −0.513541 0.858065i \(-0.671666\pi\)
0.999877 + 0.0157065i \(0.00499974\pi\)
\(480\) 0 0
\(481\) −11.4712 19.8687i −0.523042 0.905935i
\(482\) −24.5557 42.5318i −1.11848 1.93727i
\(483\) 0 0
\(484\) 19.0813 33.0497i 0.867330 1.50226i
\(485\) 0 0
\(486\) 0 0
\(487\) −9.58690 −0.434424 −0.217212 0.976124i \(-0.569696\pi\)
−0.217212 + 0.976124i \(0.569696\pi\)
\(488\) −48.9961 + 84.8637i −2.21795 + 3.84160i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.9222 32.7742i −0.853945 1.47908i −0.877620 0.479357i \(-0.840870\pi\)
0.0236745 0.999720i \(-0.492463\pi\)
\(492\) 0 0
\(493\) 17.7123 30.6786i 0.797721 1.38169i
\(494\) −15.3963 −0.692711
\(495\) 0 0
\(496\) −27.5314 −1.23619
\(497\) −1.14550 + 1.98407i −0.0513829 + 0.0889977i
\(498\) 0 0
\(499\) −8.46266 14.6577i −0.378840 0.656171i 0.612053 0.790816i \(-0.290344\pi\)
−0.990894 + 0.134646i \(0.957010\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −19.3485 + 33.5126i −0.863566 + 1.49574i
\(503\) −40.4168 −1.80210 −0.901048 0.433719i \(-0.857201\pi\)
−0.901048 + 0.433719i \(0.857201\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.12856 + 7.15088i −0.183537 + 0.317896i
\(507\) 0 0
\(508\) −8.94253 15.4889i −0.396761 0.687210i
\(509\) −20.7034 35.8593i −0.917660 1.58943i −0.802959 0.596034i \(-0.796742\pi\)
−0.114701 0.993400i \(-0.536591\pi\)
\(510\) 0 0
\(511\) −3.22431 + 5.58467i −0.142635 + 0.247051i
\(512\) 34.5537 1.52707
\(513\) 0 0
\(514\) 58.4922 2.57998
\(515\) 0 0
\(516\) 0 0
\(517\) −5.68843 9.85265i −0.250177 0.433319i
\(518\) −27.5398 47.7004i −1.21003 2.09584i
\(519\) 0 0
\(520\) 0 0
\(521\) 17.0301 0.746103 0.373052 0.927811i \(-0.378311\pi\)
0.373052 + 0.927811i \(0.378311\pi\)
\(522\) 0 0
\(523\) 9.57651 0.418751 0.209376 0.977835i \(-0.432857\pi\)
0.209376 + 0.977835i \(0.432857\pi\)
\(524\) 18.0021 31.1805i 0.786424 1.36213i
\(525\) 0 0
\(526\) −7.55880 13.0922i −0.329579 0.570848i
\(527\) −6.30592 10.9222i −0.274690 0.475777i
\(528\) 0 0
\(529\) 9.99675 17.3149i 0.434641 0.752821i
\(530\) 0 0
\(531\) 0 0
\(532\) −26.3055 −1.14049
\(533\) −2.43174 + 4.21189i −0.105330 + 0.182437i
\(534\) 0 0
\(535\) 0 0
\(536\) 35.2038 + 60.9748i 1.52057 + 2.63371i
\(537\) 0 0
\(538\) 20.5644 35.6187i 0.886596 1.53563i
\(539\) 6.81528 0.293555
\(540\) 0 0
\(541\) −0.833751 −0.0358458 −0.0179229 0.999839i \(-0.505705\pi\)
−0.0179229 + 0.999839i \(0.505705\pi\)
\(542\) −8.89297 + 15.4031i −0.381986 + 0.661619i
\(543\) 0 0
\(544\) −29.2713 50.6994i −1.25500 2.17372i
\(545\) 0 0
\(546\) 0 0
\(547\) 14.1635 24.5319i 0.605587 1.04891i −0.386371 0.922343i \(-0.626272\pi\)
0.991958 0.126565i \(-0.0403951\pi\)
\(548\) 35.1785 1.50275
\(549\) 0 0
\(550\) 0 0
\(551\) −10.9213 + 18.9163i −0.465264 + 0.805861i
\(552\) 0 0
\(553\) 1.89709 + 3.28586i 0.0806727 + 0.139729i
\(554\) 39.8964 + 69.1026i 1.69504 + 2.93589i
\(555\) 0 0
\(556\) 36.3096 62.8901i 1.53987 2.66713i
\(557\) −11.5042 −0.487448 −0.243724 0.969845i \(-0.578369\pi\)
−0.243724 + 0.969845i \(0.578369\pi\)
\(558\) 0 0
\(559\) −14.3512 −0.606993
\(560\) 0 0
\(561\) 0 0
\(562\) −24.5398 42.5043i −1.03515 1.79293i
\(563\) 16.5030 + 28.5840i 0.695517 + 1.20467i 0.970006 + 0.243080i \(0.0781578\pi\)
−0.274490 + 0.961590i \(0.588509\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.9429 0.628095
\(567\) 0 0
\(568\) 9.85769 0.413619
\(569\) −13.5044 + 23.3903i −0.566135 + 0.980574i 0.430809 + 0.902443i \(0.358228\pi\)
−0.996943 + 0.0781305i \(0.975105\pi\)
\(570\) 0 0
\(571\) 12.2122 + 21.1521i 0.511064 + 0.885189i 0.999918 + 0.0128232i \(0.00408185\pi\)
−0.488854 + 0.872366i \(0.662585\pi\)
\(572\) 8.80007 + 15.2422i 0.367950 + 0.637307i
\(573\) 0 0
\(574\) −5.83807 + 10.1118i −0.243676 + 0.422060i
\(575\) 0 0
\(576\) 0 0
\(577\) 14.7976 0.616033 0.308017 0.951381i \(-0.400335\pi\)
0.308017 + 0.951381i \(0.400335\pi\)
\(578\) 8.05663 13.9545i 0.335112 0.580431i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.987533 1.71046i −0.0409698 0.0709617i
\(582\) 0 0
\(583\) −1.55987 + 2.70177i −0.0646030 + 0.111896i
\(584\) 27.7470 1.14818
\(585\) 0 0
\(586\) 48.1375 1.98854
\(587\) 15.2890 26.4813i 0.631044 1.09300i −0.356295 0.934374i \(-0.615960\pi\)
0.987339 0.158626i \(-0.0507065\pi\)
\(588\) 0 0
\(589\) 3.88821 + 6.73457i 0.160211 + 0.277493i
\(590\) 0 0
\(591\) 0 0
\(592\) −61.0611 + 105.761i −2.50960 + 4.34675i
\(593\) 5.09990 0.209428 0.104714 0.994502i \(-0.466607\pi\)
0.104714 + 0.994502i \(0.466607\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.39532 + 2.41677i −0.0571547 + 0.0989949i
\(597\) 0 0
\(598\) 4.50236 + 7.79831i 0.184115 + 0.318897i
\(599\) −0.282655 0.489572i −0.0115490 0.0200034i 0.860193 0.509968i \(-0.170343\pi\)
−0.871742 + 0.489965i \(0.837010\pi\)
\(600\) 0 0
\(601\) 5.50480 9.53459i 0.224546 0.388924i −0.731637 0.681694i \(-0.761244\pi\)
0.956183 + 0.292770i \(0.0945769\pi\)
\(602\) −34.4542 −1.40425
\(603\) 0 0
\(604\) 0.757185 0.0308094
\(605\) 0 0
\(606\) 0 0
\(607\) 9.54913 + 16.5396i 0.387587 + 0.671321i 0.992124 0.125256i \(-0.0399753\pi\)
−0.604537 + 0.796577i \(0.706642\pi\)
\(608\) 18.0486 + 31.2611i 0.731967 + 1.26780i
\(609\) 0 0
\(610\) 0 0
\(611\) −12.4069 −0.501929
\(612\) 0 0
\(613\) 9.33918 0.377206 0.188603 0.982053i \(-0.439604\pi\)
0.188603 + 0.982053i \(0.439604\pi\)
\(614\) −20.4179 + 35.3648i −0.823999 + 1.42721i
\(615\) 0 0
\(616\) 12.5675 + 21.7676i 0.506360 + 0.877041i
\(617\) −12.2077 21.1444i −0.491464 0.851241i 0.508488 0.861069i \(-0.330205\pi\)
−0.999952 + 0.00982861i \(0.996871\pi\)
\(618\) 0 0
\(619\) −19.7431 + 34.1961i −0.793544 + 1.37446i 0.130216 + 0.991486i \(0.458433\pi\)
−0.923760 + 0.382973i \(0.874900\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 80.1874 3.21522
\(623\) 11.9470 20.6928i 0.478647 0.829040i
\(624\) 0 0
\(625\) 0 0
\(626\) −9.15135 15.8506i −0.365761 0.633517i
\(627\) 0 0
\(628\) 28.2879 48.9960i 1.12881 1.95515i
\(629\) −55.9430 −2.23059
\(630\) 0 0
\(631\) 42.1634 1.67850 0.839249 0.543747i \(-0.182995\pi\)
0.839249 + 0.543747i \(0.182995\pi\)
\(632\) 8.16277 14.1383i 0.324698 0.562393i
\(633\) 0 0
\(634\) 21.2608 + 36.8248i 0.844375 + 1.46250i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.71616 6.43658i 0.147240 0.255027i
\(638\) 35.0855 1.38905
\(639\) 0 0
\(640\) 0 0
\(641\) 17.6577 30.5841i 0.697438 1.20800i −0.271913 0.962322i \(-0.587656\pi\)
0.969352 0.245677i \(-0.0790103\pi\)
\(642\) 0 0
\(643\) −7.09771 12.2936i −0.279906 0.484812i 0.691455 0.722420i \(-0.256970\pi\)
−0.971361 + 0.237608i \(0.923637\pi\)
\(644\) 7.69256 + 13.3239i 0.303129 + 0.525036i
\(645\) 0 0
\(646\) −18.7712 + 32.5127i −0.738544 + 1.27919i
\(647\) −17.4897 −0.687593 −0.343796 0.939044i \(-0.611713\pi\)
−0.343796 + 0.939044i \(0.611713\pi\)
\(648\) 0 0
\(649\) 19.9364 0.782572
\(650\) 0 0
\(651\) 0 0
\(652\) 54.4483 + 94.3072i 2.13236 + 3.69335i
\(653\) −5.48858 9.50650i −0.214785 0.372018i 0.738421 0.674340i \(-0.235572\pi\)
−0.953206 + 0.302322i \(0.902238\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 25.8882 1.01077
\(657\) 0 0
\(658\) −29.7862 −1.16119
\(659\) −7.89381 + 13.6725i −0.307499 + 0.532604i −0.977815 0.209472i \(-0.932825\pi\)
0.670316 + 0.742076i \(0.266159\pi\)
\(660\) 0 0
\(661\) −24.9466 43.2088i −0.970311 1.68063i −0.694614 0.719383i \(-0.744425\pi\)
−0.275697 0.961245i \(-0.588909\pi\)
\(662\) 16.6217 + 28.7897i 0.646022 + 1.11894i
\(663\) 0 0
\(664\) −4.24913 + 7.35972i −0.164898 + 0.285612i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.7750 0.494649
\(668\) 42.1291 72.9698i 1.63002 2.82328i
\(669\) 0 0
\(670\) 0 0
\(671\) −11.4549 19.8404i −0.442210 0.765929i
\(672\) 0 0
\(673\) −14.4197 + 24.9757i −0.555840 + 0.962743i 0.441998 + 0.897016i \(0.354270\pi\)
−0.997838 + 0.0657266i \(0.979063\pi\)
\(674\) 18.2264 0.702055
\(675\) 0 0
\(676\) −44.9809 −1.73003
\(677\) 5.23181 9.06176i 0.201075 0.348272i −0.747800 0.663924i \(-0.768890\pi\)
0.948875 + 0.315652i \(0.102223\pi\)
\(678\) 0 0
\(679\) −3.44455 5.96614i −0.132190 0.228959i
\(680\) 0 0
\(681\) 0 0
\(682\) 6.24556 10.8176i 0.239155 0.414228i
\(683\) 16.1875 0.619396 0.309698 0.950835i \(-0.399772\pi\)
0.309698 + 0.950835i \(0.399772\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 25.4904 44.1507i 0.973229 1.68568i
\(687\) 0 0
\(688\) 38.1958 + 66.1570i 1.45620 + 2.52221i
\(689\) 1.70109 + 2.94638i 0.0648065 + 0.112248i
\(690\) 0 0
\(691\) −4.94181 + 8.55946i −0.187995 + 0.325617i −0.944582 0.328276i \(-0.893532\pi\)
0.756586 + 0.653894i \(0.226866\pi\)
\(692\) −58.9648 −2.24150
\(693\) 0 0
\(694\) 36.3621 1.38029
\(695\) 0 0
\(696\) 0 0
\(697\) 5.92957 + 10.2703i 0.224598 + 0.389016i
\(698\) 8.64872 + 14.9800i 0.327359 + 0.567002i
\(699\) 0 0
\(700\) 0 0
\(701\) −43.9692 −1.66069 −0.830346 0.557248i \(-0.811857\pi\)
−0.830346 + 0.557248i \(0.811857\pi\)
\(702\) 0 0
\(703\) 34.4942 1.30097
\(704\) 10.0130 17.3430i 0.377379 0.653640i
\(705\) 0 0
\(706\) 4.64193 + 8.04005i 0.174701 + 0.302591i
\(707\) −5.88870 10.1995i −0.221467 0.383593i
\(708\) 0 0
\(709\) −12.6130 + 21.8464i −0.473692 + 0.820458i −0.999546 0.0301162i \(-0.990412\pi\)
0.525855 + 0.850574i \(0.323746\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −102.811 −3.85299
\(713\) 2.27407 3.93880i 0.0851645 0.147509i
\(714\) 0 0
\(715\) 0 0
\(716\) 21.1016 + 36.5490i 0.788603 + 1.36590i
\(717\) 0 0
\(718\) −30.1937 + 52.2971i −1.12682 + 1.95171i
\(719\) 36.8600 1.37465 0.687323 0.726352i \(-0.258786\pi\)
0.687323 + 0.726352i \(0.258786\pi\)
\(720\) 0 0
\(721\) 14.5153 0.540576
\(722\) −13.4461 + 23.2893i −0.500412 + 0.866740i
\(723\) 0 0
\(724\) 26.0459 + 45.1128i 0.967988 + 1.67660i
\(725\) 0 0
\(726\) 0 0
\(727\) 19.1226 33.1213i 0.709217 1.22840i −0.255931 0.966695i \(-0.582382\pi\)
0.965148 0.261705i \(-0.0842847\pi\)
\(728\) 27.4107 1.01591
\(729\) 0 0
\(730\) 0 0
\(731\) −17.4971 + 30.3059i −0.647154 + 1.12090i
\(732\) 0 0
\(733\) −19.7916 34.2801i −0.731020 1.26616i −0.956448 0.291903i \(-0.905711\pi\)
0.225428 0.974260i \(-0.427622\pi\)
\(734\) 5.50358 + 9.53248i 0.203141 + 0.351850i
\(735\) 0 0
\(736\) 10.5559 18.2834i 0.389097 0.673936i
\(737\) −16.4607 −0.606338
\(738\) 0 0
\(739\) −8.24773 −0.303398 −0.151699 0.988427i \(-0.548474\pi\)
−0.151699 + 0.988427i \(0.548474\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 4.08395 + 7.07361i 0.149927 + 0.259680i
\(743\) 0.654091 + 1.13292i 0.0239963 + 0.0415627i 0.877774 0.479075i \(-0.159028\pi\)
−0.853778 + 0.520637i \(0.825694\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −18.0171 −0.659651
\(747\) 0 0
\(748\) 42.9164 1.56918
\(749\) 8.06752 13.9734i 0.294781 0.510575i
\(750\) 0 0
\(751\) −14.2234 24.6357i −0.519020 0.898969i −0.999756 0.0221034i \(-0.992964\pi\)
0.480736 0.876866i \(-0.340370\pi\)
\(752\) 33.0209 + 57.1939i 1.20415 + 2.08565i
\(753\) 0 0
\(754\) 19.1310 33.1359i 0.696711 1.20674i
\(755\) 0 0
\(756\) 0 0
\(757\) −38.2012 −1.38845 −0.694223 0.719760i \(-0.744252\pi\)
−0.694223 + 0.719760i \(0.744252\pi\)
\(758\) −16.8248 + 29.1414i −0.611103 + 1.05846i
\(759\) 0 0
\(760\) 0 0
\(761\) 11.0952 + 19.2174i 0.402200 + 0.696632i 0.993991 0.109460i \(-0.0349121\pi\)
−0.591791 + 0.806092i \(0.701579\pi\)
\(762\) 0 0
\(763\) −5.69932 + 9.87152i −0.206329 + 0.357373i
\(764\) 85.5852 3.09637
\(765\) 0 0
\(766\) 19.8440 0.716994
\(767\) 10.8707 18.8286i 0.392518 0.679861i
\(768\) 0 0
\(769\) 8.45652 + 14.6471i 0.304950 + 0.528189i 0.977250 0.212090i \(-0.0680270\pi\)
−0.672300 + 0.740279i \(0.734694\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.84930 + 6.66718i −0.138539 + 0.239957i
\(773\) 38.6464 1.39001 0.695007 0.719003i \(-0.255401\pi\)
0.695007 + 0.719003i \(0.255401\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.8211 + 25.6709i −0.532047 + 0.921533i
\(777\) 0 0
\(778\) −7.17920 12.4347i −0.257387 0.445807i
\(779\) −3.65615 6.33264i −0.130995 0.226890i
\(780\) 0 0
\(781\) −1.15232 + 1.99588i −0.0412333 + 0.0714181i
\(782\) 21.9572 0.785187
\(783\) 0 0
\(784\) −39.5622 −1.41294
\(785\) 0 0
\(786\) 0 0
\(787\) −5.45734 9.45240i −0.194533 0.336942i 0.752214 0.658919i \(-0.228986\pi\)
−0.946747 + 0.321977i \(0.895653\pi\)
\(788\) 44.3711 + 76.8530i 1.58065 + 2.73777i