Properties

Label 380.2.u.b.301.2
Level $380$
Weight $2$
Character 380.301
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 301.2
Root \(0.546970 + 0.947380i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.b.101.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.02797 - 0.374150i) q^{3} +(0.173648 - 0.984808i) q^{5} +(-1.81409 - 3.14209i) q^{7} +(-1.38140 + 1.15914i) q^{9} +O(q^{10})\) \(q+(1.02797 - 0.374150i) q^{3} +(0.173648 - 0.984808i) q^{5} +(-1.81409 - 3.14209i) q^{7} +(-1.38140 + 1.15914i) q^{9} +(2.71941 - 4.71016i) q^{11} +(1.31766 + 0.479589i) q^{13} +(-0.189961 - 1.07732i) q^{15} +(-2.12355 - 1.78187i) q^{17} +(1.94623 - 3.90028i) q^{19} +(-3.04044 - 2.55123i) q^{21} +(1.15141 + 6.52999i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(-2.62726 + 4.55055i) q^{27} +(4.29734 - 3.60589i) q^{29} +(5.34951 + 9.26562i) q^{31} +(1.03316 - 5.85936i) q^{33} +(-3.40937 + 1.24091i) q^{35} -3.37063 q^{37} +1.53395 q^{39} +(-2.35936 + 0.858738i) q^{41} +(1.84304 - 10.4524i) q^{43} +(0.901647 + 1.56170i) q^{45} +(3.67626 - 3.08475i) q^{47} +(-3.08183 + 5.33789i) q^{49} +(-2.84963 - 1.03718i) q^{51} +(1.60632 + 9.10987i) q^{53} +(-4.16638 - 3.49601i) q^{55} +(0.541374 - 4.73754i) q^{57} +(1.79251 + 1.50409i) q^{59} +(-0.509501 - 2.88952i) q^{61} +(6.14810 + 2.23772i) q^{63} +(0.701112 - 1.21436i) q^{65} +(-1.64930 + 1.38393i) q^{67} +(3.62681 + 6.28182i) q^{69} +(-2.83920 + 16.1019i) q^{71} +(-12.1383 + 4.41799i) q^{73} -1.09394 q^{75} -19.7330 q^{77} +(10.7051 - 3.89632i) q^{79} +(-0.0587363 + 0.333110i) q^{81} +(5.51438 + 9.55118i) q^{83} +(-2.12355 + 1.78187i) q^{85} +(3.06838 - 5.31459i) q^{87} +(10.5328 + 3.83361i) q^{89} +(-0.883438 - 5.01023i) q^{91} +(8.96585 + 7.52325i) q^{93} +(-3.50307 - 2.59394i) q^{95} +(-7.22724 - 6.06437i) q^{97} +(1.70311 + 9.65879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

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
\(3\) 1.02797 0.374150i 0.593498 0.216015i −0.0277695 0.999614i \(-0.508840\pi\)
0.621267 + 0.783599i \(0.286618\pi\)
\(4\) 0 0
\(5\) 0.173648 0.984808i 0.0776578 0.440419i
\(6\) 0 0
\(7\) −1.81409 3.14209i −0.685661 1.18760i −0.973229 0.229839i \(-0.926180\pi\)
0.287568 0.957760i \(-0.407153\pi\)
\(8\) 0 0
\(9\) −1.38140 + 1.15914i −0.460468 + 0.386378i
\(10\) 0 0
\(11\) 2.71941 4.71016i 0.819933 1.42017i −0.0857978 0.996313i \(-0.527344\pi\)
0.905731 0.423853i \(-0.139323\pi\)
\(12\) 0 0
\(13\) 1.31766 + 0.479589i 0.365453 + 0.133014i 0.518218 0.855248i \(-0.326596\pi\)
−0.152765 + 0.988263i \(0.548818\pi\)
\(14\) 0 0
\(15\) −0.189961 1.07732i −0.0490477 0.278163i
\(16\) 0 0
\(17\) −2.12355 1.78187i −0.515037 0.432168i 0.347860 0.937546i \(-0.386908\pi\)
−0.862898 + 0.505379i \(0.831353\pi\)
\(18\) 0 0
\(19\) 1.94623 3.90028i 0.446496 0.894786i
\(20\) 0 0
\(21\) −3.04044 2.55123i −0.663478 0.556724i
\(22\) 0 0
\(23\) 1.15141 + 6.52999i 0.240086 + 1.36160i 0.831632 + 0.555327i \(0.187407\pi\)
−0.591546 + 0.806271i \(0.701482\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) −2.62726 + 4.55055i −0.505616 + 0.875753i
\(28\) 0 0
\(29\) 4.29734 3.60589i 0.797995 0.669597i −0.149715 0.988729i \(-0.547836\pi\)
0.947710 + 0.319132i \(0.103391\pi\)
\(30\) 0 0
\(31\) 5.34951 + 9.26562i 0.960800 + 1.66416i 0.720498 + 0.693457i \(0.243913\pi\)
0.240302 + 0.970698i \(0.422753\pi\)
\(32\) 0 0
\(33\) 1.03316 5.85936i 0.179851 1.01998i
\(34\) 0 0
\(35\) −3.40937 + 1.24091i −0.576289 + 0.209752i
\(36\) 0 0
\(37\) −3.37063 −0.554128 −0.277064 0.960851i \(-0.589361\pi\)
−0.277064 + 0.960851i \(0.589361\pi\)
\(38\) 0 0
\(39\) 1.53395 0.245629
\(40\) 0 0
\(41\) −2.35936 + 0.858738i −0.368471 + 0.134112i −0.519618 0.854399i \(-0.673926\pi\)
0.151147 + 0.988511i \(0.451703\pi\)
\(42\) 0 0
\(43\) 1.84304 10.4524i 0.281061 1.59397i −0.437965 0.898992i \(-0.644301\pi\)
0.719026 0.694983i \(-0.244588\pi\)
\(44\) 0 0
\(45\) 0.901647 + 1.56170i 0.134410 + 0.232804i
\(46\) 0 0
\(47\) 3.67626 3.08475i 0.536238 0.449957i −0.334011 0.942569i \(-0.608402\pi\)
0.870249 + 0.492612i \(0.163958\pi\)
\(48\) 0 0
\(49\) −3.08183 + 5.33789i −0.440262 + 0.762556i
\(50\) 0 0
\(51\) −2.84963 1.03718i −0.399028 0.145234i
\(52\) 0 0
\(53\) 1.60632 + 9.10987i 0.220645 + 1.25134i 0.870839 + 0.491569i \(0.163577\pi\)
−0.650194 + 0.759768i \(0.725312\pi\)
\(54\) 0 0
\(55\) −4.16638 3.49601i −0.561794 0.471401i
\(56\) 0 0
\(57\) 0.541374 4.73754i 0.0717067 0.627503i
\(58\) 0 0
\(59\) 1.79251 + 1.50409i 0.233365 + 0.195816i 0.751970 0.659198i \(-0.229104\pi\)
−0.518605 + 0.855014i \(0.673548\pi\)
\(60\) 0 0
\(61\) −0.509501 2.88952i −0.0652349 0.369965i −0.999896 0.0144254i \(-0.995408\pi\)
0.934661 0.355540i \(-0.115703\pi\)
\(62\) 0 0
\(63\) 6.14810 + 2.23772i 0.774588 + 0.281927i
\(64\) 0 0
\(65\) 0.701112 1.21436i 0.0869623 0.150623i
\(66\) 0 0
\(67\) −1.64930 + 1.38393i −0.201494 + 0.169074i −0.737951 0.674854i \(-0.764207\pi\)
0.536457 + 0.843927i \(0.319762\pi\)
\(68\) 0 0
\(69\) 3.62681 + 6.28182i 0.436617 + 0.756243i
\(70\) 0 0
\(71\) −2.83920 + 16.1019i −0.336951 + 1.91094i 0.0701015 + 0.997540i \(0.477668\pi\)
−0.407053 + 0.913405i \(0.633443\pi\)
\(72\) 0 0
\(73\) −12.1383 + 4.41799i −1.42068 + 0.517087i −0.934246 0.356628i \(-0.883926\pi\)
−0.486438 + 0.873715i \(0.661704\pi\)
\(74\) 0 0
\(75\) −1.09394 −0.126317
\(76\) 0 0
\(77\) −19.7330 −2.24878
\(78\) 0 0
\(79\) 10.7051 3.89632i 1.20441 0.438371i 0.339651 0.940552i \(-0.389691\pi\)
0.864763 + 0.502181i \(0.167469\pi\)
\(80\) 0 0
\(81\) −0.0587363 + 0.333110i −0.00652625 + 0.0370122i
\(82\) 0 0
\(83\) 5.51438 + 9.55118i 0.605281 + 1.04838i 0.992007 + 0.126183i \(0.0402727\pi\)
−0.386726 + 0.922195i \(0.626394\pi\)
\(84\) 0 0
\(85\) −2.12355 + 1.78187i −0.230332 + 0.193271i
\(86\) 0 0
\(87\) 3.06838 5.31459i 0.328965 0.569784i
\(88\) 0 0
\(89\) 10.5328 + 3.83361i 1.11647 + 0.406362i 0.833363 0.552726i \(-0.186412\pi\)
0.283108 + 0.959088i \(0.408635\pi\)
\(90\) 0 0
\(91\) −0.883438 5.01023i −0.0926095 0.525215i
\(92\) 0 0
\(93\) 8.96585 + 7.52325i 0.929716 + 0.780124i
\(94\) 0 0
\(95\) −3.50307 2.59394i −0.359407 0.266133i
\(96\) 0 0
\(97\) −7.22724 6.06437i −0.733815 0.615744i 0.197354 0.980332i \(-0.436765\pi\)
−0.931169 + 0.364589i \(0.881210\pi\)
\(98\) 0 0
\(99\) 1.70311 + 9.65879i 0.171169 + 0.970745i
\(100\) 0 0
\(101\) 7.41652 + 2.69939i 0.737972 + 0.268600i 0.683535 0.729918i \(-0.260442\pi\)
0.0544364 + 0.998517i \(0.482664\pi\)
\(102\) 0 0
\(103\) 4.82309 8.35384i 0.475233 0.823129i −0.524364 0.851494i \(-0.675697\pi\)
0.999598 + 0.0283656i \(0.00903026\pi\)
\(104\) 0 0
\(105\) −3.04044 + 2.55123i −0.296716 + 0.248975i
\(106\) 0 0
\(107\) −0.380492 0.659031i −0.0367835 0.0637109i 0.847048 0.531517i \(-0.178378\pi\)
−0.883831 + 0.467806i \(0.845045\pi\)
\(108\) 0 0
\(109\) −2.75235 + 15.6093i −0.263627 + 1.49510i 0.509290 + 0.860595i \(0.329908\pi\)
−0.772917 + 0.634507i \(0.781203\pi\)
\(110\) 0 0
\(111\) −3.46490 + 1.26112i −0.328874 + 0.119700i
\(112\) 0 0
\(113\) −7.02323 −0.660690 −0.330345 0.943860i \(-0.607165\pi\)
−0.330345 + 0.943860i \(0.607165\pi\)
\(114\) 0 0
\(115\) 6.63073 0.618319
\(116\) 0 0
\(117\) −2.37613 + 0.864840i −0.219673 + 0.0799545i
\(118\) 0 0
\(119\) −1.74650 + 9.90488i −0.160101 + 0.907979i
\(120\) 0 0
\(121\) −9.29039 16.0914i −0.844581 1.46286i
\(122\) 0 0
\(123\) −2.10405 + 1.76551i −0.189716 + 0.159191i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −12.0843 4.39833i −1.07231 0.390289i −0.255270 0.966870i \(-0.582164\pi\)
−0.817040 + 0.576581i \(0.804386\pi\)
\(128\) 0 0
\(129\) −2.01618 11.4343i −0.177514 1.00673i
\(130\) 0 0
\(131\) 6.68167 + 5.60659i 0.583780 + 0.489850i 0.886186 0.463329i \(-0.153345\pi\)
−0.302406 + 0.953179i \(0.597790\pi\)
\(132\) 0 0
\(133\) −15.7857 + 0.960215i −1.36879 + 0.0832612i
\(134\) 0 0
\(135\) 4.02519 + 3.37754i 0.346434 + 0.290692i
\(136\) 0 0
\(137\) 1.56695 + 8.88664i 0.133874 + 0.759237i 0.975637 + 0.219390i \(0.0704068\pi\)
−0.841763 + 0.539847i \(0.818482\pi\)
\(138\) 0 0
\(139\) −1.34030 0.487829i −0.113683 0.0413771i 0.284552 0.958660i \(-0.408155\pi\)
−0.398235 + 0.917283i \(0.630377\pi\)
\(140\) 0 0
\(141\) 2.62492 4.54650i 0.221058 0.382884i
\(142\) 0 0
\(143\) 5.84220 4.90219i 0.488549 0.409941i
\(144\) 0 0
\(145\) −2.80489 4.85821i −0.232933 0.403452i
\(146\) 0 0
\(147\) −1.17086 + 6.64025i −0.0965705 + 0.547679i
\(148\) 0 0
\(149\) 7.15124 2.60284i 0.585852 0.213233i −0.0320520 0.999486i \(-0.510204\pi\)
0.617904 + 0.786253i \(0.287982\pi\)
\(150\) 0 0
\(151\) −0.549782 −0.0447406 −0.0223703 0.999750i \(-0.507121\pi\)
−0.0223703 + 0.999750i \(0.507121\pi\)
\(152\) 0 0
\(153\) 4.99892 0.404138
\(154\) 0 0
\(155\) 10.0538 3.65928i 0.807540 0.293920i
\(156\) 0 0
\(157\) −1.14249 + 6.47938i −0.0911806 + 0.517111i 0.904670 + 0.426112i \(0.140117\pi\)
−0.995851 + 0.0909989i \(0.970994\pi\)
\(158\) 0 0
\(159\) 5.05970 + 8.76366i 0.401260 + 0.695003i
\(160\) 0 0
\(161\) 18.4291 15.4638i 1.45242 1.21872i
\(162\) 0 0
\(163\) 7.67500 13.2935i 0.601153 1.04123i −0.391494 0.920181i \(-0.628042\pi\)
0.992647 0.121046i \(-0.0386250\pi\)
\(164\) 0 0
\(165\) −5.59093 2.03493i −0.435254 0.158419i
\(166\) 0 0
\(167\) −0.778544 4.41534i −0.0602456 0.341670i 0.939754 0.341850i \(-0.111054\pi\)
−1.00000 0.000180770i \(0.999942\pi\)
\(168\) 0 0
\(169\) −8.45236 7.09237i −0.650181 0.545567i
\(170\) 0 0
\(171\) 1.83242 + 7.64380i 0.140129 + 0.584536i
\(172\) 0 0
\(173\) −11.4578 9.61423i −0.871120 0.730956i 0.0932138 0.995646i \(-0.470286\pi\)
−0.964334 + 0.264690i \(0.914730\pi\)
\(174\) 0 0
\(175\) 0.630026 + 3.57306i 0.0476255 + 0.270098i
\(176\) 0 0
\(177\) 2.40540 + 0.875492i 0.180801 + 0.0658060i
\(178\) 0 0
\(179\) 12.9951 22.5082i 0.971300 1.68234i 0.279658 0.960100i \(-0.409779\pi\)
0.691642 0.722241i \(-0.256888\pi\)
\(180\) 0 0
\(181\) 7.32648 6.14765i 0.544573 0.456951i −0.328525 0.944495i \(-0.606552\pi\)
0.873098 + 0.487544i \(0.162107\pi\)
\(182\) 0 0
\(183\) −1.60486 2.77971i −0.118635 0.205482i
\(184\) 0 0
\(185\) −0.585304 + 3.31942i −0.0430324 + 0.244049i
\(186\) 0 0
\(187\) −14.1677 + 5.15663i −1.03605 + 0.377090i
\(188\) 0 0
\(189\) 19.0643 1.38673
\(190\) 0 0
\(191\) −10.6025 −0.767172 −0.383586 0.923505i \(-0.625311\pi\)
−0.383586 + 0.923505i \(0.625311\pi\)
\(192\) 0 0
\(193\) 17.7019 6.44297i 1.27421 0.463775i 0.385698 0.922625i \(-0.373961\pi\)
0.888514 + 0.458850i \(0.151738\pi\)
\(194\) 0 0
\(195\) 0.266368 1.51065i 0.0190750 0.108180i
\(196\) 0 0
\(197\) 3.05611 + 5.29334i 0.217739 + 0.377135i 0.954116 0.299436i \(-0.0967985\pi\)
−0.736377 + 0.676571i \(0.763465\pi\)
\(198\) 0 0
\(199\) 5.17943 4.34605i 0.367160 0.308084i −0.440477 0.897764i \(-0.645191\pi\)
0.807637 + 0.589680i \(0.200746\pi\)
\(200\) 0 0
\(201\) −1.17763 + 2.03972i −0.0830638 + 0.143871i
\(202\) 0 0
\(203\) −19.1258 6.96122i −1.34237 0.488582i
\(204\) 0 0
\(205\) 0.435993 + 2.47264i 0.0304511 + 0.172697i
\(206\) 0 0
\(207\) −9.15971 7.68591i −0.636644 0.534208i
\(208\) 0 0
\(209\) −13.0783 19.7735i −0.904647 1.36776i
\(210\) 0 0
\(211\) −5.31397 4.45895i −0.365829 0.306967i 0.441280 0.897369i \(-0.354525\pi\)
−0.807109 + 0.590403i \(0.798969\pi\)
\(212\) 0 0
\(213\) 3.10592 + 17.6145i 0.212814 + 1.20693i
\(214\) 0 0
\(215\) −9.97356 3.63008i −0.680191 0.247569i
\(216\) 0 0
\(217\) 19.4090 33.6173i 1.31757 2.28209i
\(218\) 0 0
\(219\) −10.8248 + 9.08311i −0.731474 + 0.613780i
\(220\) 0 0
\(221\) −1.94356 3.36634i −0.130738 0.226444i
\(222\) 0 0
\(223\) 3.76498 21.3522i 0.252122 1.42985i −0.551233 0.834351i \(-0.685843\pi\)
0.803355 0.595501i \(-0.203046\pi\)
\(224\) 0 0
\(225\) 1.69454 0.616763i 0.112969 0.0411175i
\(226\) 0 0
\(227\) 23.7457 1.57605 0.788027 0.615640i \(-0.211103\pi\)
0.788027 + 0.615640i \(0.211103\pi\)
\(228\) 0 0
\(229\) −14.4053 −0.951928 −0.475964 0.879465i \(-0.657901\pi\)
−0.475964 + 0.879465i \(0.657901\pi\)
\(230\) 0 0
\(231\) −20.2849 + 7.38310i −1.33465 + 0.485772i
\(232\) 0 0
\(233\) −3.71518 + 21.0698i −0.243389 + 1.38033i 0.580814 + 0.814036i \(0.302734\pi\)
−0.824204 + 0.566293i \(0.808377\pi\)
\(234\) 0 0
\(235\) −2.39951 4.15607i −0.156527 0.271112i
\(236\) 0 0
\(237\) 9.54665 8.01059i 0.620122 0.520344i
\(238\) 0 0
\(239\) −8.14253 + 14.1033i −0.526697 + 0.912265i 0.472820 + 0.881159i \(0.343236\pi\)
−0.999516 + 0.0311059i \(0.990097\pi\)
\(240\) 0 0
\(241\) 14.2617 + 5.19083i 0.918676 + 0.334371i 0.757711 0.652590i \(-0.226317\pi\)
0.160964 + 0.986960i \(0.448540\pi\)
\(242\) 0 0
\(243\) −2.67306 15.1597i −0.171477 0.972493i
\(244\) 0 0
\(245\) 4.72164 + 3.96193i 0.301655 + 0.253118i
\(246\) 0 0
\(247\) 4.43500 4.20585i 0.282192 0.267612i
\(248\) 0 0
\(249\) 9.24217 + 7.75510i 0.585699 + 0.491460i
\(250\) 0 0
\(251\) 0.706652 + 4.00762i 0.0446035 + 0.252959i 0.998954 0.0457307i \(-0.0145616\pi\)
−0.954350 + 0.298689i \(0.903451\pi\)
\(252\) 0 0
\(253\) 33.8885 + 12.3344i 2.13055 + 0.775457i
\(254\) 0 0
\(255\) −1.51626 + 2.62624i −0.0949517 + 0.164461i
\(256\) 0 0
\(257\) 1.62041 1.35969i 0.101079 0.0848151i −0.590848 0.806783i \(-0.701207\pi\)
0.691927 + 0.721968i \(0.256762\pi\)
\(258\) 0 0
\(259\) 6.11462 + 10.5908i 0.379944 + 0.658083i
\(260\) 0 0
\(261\) −1.75664 + 9.96238i −0.108733 + 0.616656i
\(262\) 0 0
\(263\) −13.6466 + 4.96697i −0.841487 + 0.306276i −0.726564 0.687098i \(-0.758884\pi\)
−0.114922 + 0.993374i \(0.536662\pi\)
\(264\) 0 0
\(265\) 9.25041 0.568248
\(266\) 0 0
\(267\) 12.2617 0.750403
\(268\) 0 0
\(269\) −5.04169 + 1.83503i −0.307397 + 0.111884i −0.491113 0.871096i \(-0.663410\pi\)
0.183715 + 0.982979i \(0.441188\pi\)
\(270\) 0 0
\(271\) 1.13162 6.41774i 0.0687410 0.389850i −0.930954 0.365138i \(-0.881022\pi\)
0.999695 0.0247122i \(-0.00786694\pi\)
\(272\) 0 0
\(273\) −2.78272 4.81982i −0.168418 0.291709i
\(274\) 0 0
\(275\) −4.16638 + 3.49601i −0.251242 + 0.210817i
\(276\) 0 0
\(277\) 1.45749 2.52445i 0.0875724 0.151680i −0.818912 0.573919i \(-0.805422\pi\)
0.906484 + 0.422239i \(0.138756\pi\)
\(278\) 0 0
\(279\) −18.1299 6.59876i −1.08541 0.395057i
\(280\) 0 0
\(281\) −0.417979 2.37048i −0.0249345 0.141411i 0.969799 0.243905i \(-0.0784286\pi\)
−0.994734 + 0.102495i \(0.967318\pi\)
\(282\) 0 0
\(283\) 0.821925 + 0.689677i 0.0488584 + 0.0409970i 0.666890 0.745156i \(-0.267625\pi\)
−0.618031 + 0.786153i \(0.712070\pi\)
\(284\) 0 0
\(285\) −4.57156 1.35582i −0.270796 0.0803116i
\(286\) 0 0
\(287\) 6.97833 + 5.85551i 0.411918 + 0.345640i
\(288\) 0 0
\(289\) −1.61761 9.17393i −0.0951536 0.539643i
\(290\) 0 0
\(291\) −9.69835 3.52991i −0.568527 0.206927i
\(292\) 0 0
\(293\) −11.6287 + 20.1414i −0.679354 + 1.17668i 0.295822 + 0.955243i \(0.404407\pi\)
−0.975176 + 0.221432i \(0.928927\pi\)
\(294\) 0 0
\(295\) 1.79251 1.50409i 0.104364 0.0875716i
\(296\) 0 0
\(297\) 14.2892 + 24.7496i 0.829143 + 1.43612i
\(298\) 0 0
\(299\) −1.61454 + 9.15652i −0.0933713 + 0.529535i
\(300\) 0 0
\(301\) −36.1858 + 13.1706i −2.08572 + 0.759139i
\(302\) 0 0
\(303\) 8.63393 0.496006
\(304\) 0 0
\(305\) −2.93410 −0.168006
\(306\) 0 0
\(307\) −25.6029 + 9.31870i −1.46124 + 0.531846i −0.945705 0.325025i \(-0.894627\pi\)
−0.515530 + 0.856871i \(0.672405\pi\)
\(308\) 0 0
\(309\) 1.83240 10.3920i 0.104241 0.591183i
\(310\) 0 0
\(311\) 6.75505 + 11.7001i 0.383044 + 0.663451i 0.991496 0.130140i \(-0.0415426\pi\)
−0.608452 + 0.793591i \(0.708209\pi\)
\(312\) 0 0
\(313\) −17.7886 + 14.9264i −1.00547 + 0.843692i −0.987733 0.156151i \(-0.950091\pi\)
−0.0177397 + 0.999843i \(0.505647\pi\)
\(314\) 0 0
\(315\) 3.27134 5.66612i 0.184319 0.319250i
\(316\) 0 0
\(317\) −4.96139 1.80580i −0.278659 0.101424i 0.198910 0.980018i \(-0.436260\pi\)
−0.477569 + 0.878594i \(0.658482\pi\)
\(318\) 0 0
\(319\) −5.29810 30.0470i −0.296637 1.68231i
\(320\) 0 0
\(321\) −0.637709 0.535102i −0.0355935 0.0298665i
\(322\) 0 0
\(323\) −11.0827 + 4.81452i −0.616660 + 0.267887i
\(324\) 0 0
\(325\) −1.07417 0.901333i −0.0595840 0.0499969i
\(326\) 0 0
\(327\) 3.01090 + 17.0757i 0.166503 + 0.944287i
\(328\) 0 0
\(329\) −16.3616 5.95515i −0.902046 0.328318i
\(330\) 0 0
\(331\) −9.73690 + 16.8648i −0.535188 + 0.926973i 0.463966 + 0.885853i \(0.346426\pi\)
−0.999154 + 0.0411202i \(0.986907\pi\)
\(332\) 0 0
\(333\) 4.65620 3.90702i 0.255158 0.214103i
\(334\) 0 0
\(335\) 1.07650 + 1.86456i 0.0588157 + 0.101872i
\(336\) 0 0
\(337\) −1.33374 + 7.56400i −0.0726533 + 0.412037i 0.926691 + 0.375825i \(0.122640\pi\)
−0.999344 + 0.0362127i \(0.988471\pi\)
\(338\) 0 0
\(339\) −7.21965 + 2.62774i −0.392118 + 0.142719i
\(340\) 0 0
\(341\) 58.1901 3.15117
\(342\) 0 0
\(343\) −3.03436 −0.163840
\(344\) 0 0
\(345\) 6.81618 2.48089i 0.366971 0.133566i
\(346\) 0 0
\(347\) 0.443233 2.51370i 0.0237940 0.134942i −0.970597 0.240711i \(-0.922619\pi\)
0.994391 + 0.105769i \(0.0337304\pi\)
\(348\) 0 0
\(349\) −0.851409 1.47468i −0.0455749 0.0789380i 0.842338 0.538949i \(-0.181179\pi\)
−0.887913 + 0.460011i \(0.847845\pi\)
\(350\) 0 0
\(351\) −5.64423 + 4.73607i −0.301267 + 0.252793i
\(352\) 0 0
\(353\) 11.8829 20.5818i 0.632465 1.09546i −0.354582 0.935025i \(-0.615377\pi\)
0.987046 0.160436i \(-0.0512900\pi\)
\(354\) 0 0
\(355\) 15.3643 + 5.59213i 0.815450 + 0.296800i
\(356\) 0 0
\(357\) 1.91056 + 10.8353i 0.101118 + 0.573468i
\(358\) 0 0
\(359\) −5.04166 4.23046i −0.266089 0.223275i 0.499975 0.866040i \(-0.333343\pi\)
−0.766063 + 0.642765i \(0.777787\pi\)
\(360\) 0 0
\(361\) −11.4244 15.1817i −0.601283 0.799036i
\(362\) 0 0
\(363\) −15.5708 13.0655i −0.817256 0.685759i
\(364\) 0 0
\(365\) 2.24307 + 12.7211i 0.117408 + 0.665853i
\(366\) 0 0
\(367\) 27.6541 + 10.0653i 1.44353 + 0.525404i 0.940778 0.339024i \(-0.110097\pi\)
0.502757 + 0.864428i \(0.332319\pi\)
\(368\) 0 0
\(369\) 2.26384 3.92109i 0.117851 0.204124i
\(370\) 0 0
\(371\) 25.7101 21.5733i 1.33480 1.12003i
\(372\) 0 0
\(373\) 13.0673 + 22.6332i 0.676598 + 1.17190i 0.975999 + 0.217775i \(0.0698799\pi\)
−0.299401 + 0.954127i \(0.596787\pi\)
\(374\) 0 0
\(375\) −0.189961 + 1.07732i −0.00980953 + 0.0556326i
\(376\) 0 0
\(377\) 7.39177 2.69039i 0.380696 0.138562i
\(378\) 0 0
\(379\) −16.3067 −0.837620 −0.418810 0.908074i \(-0.637553\pi\)
−0.418810 + 0.908074i \(0.637553\pi\)
\(380\) 0 0
\(381\) −14.0679 −0.720722
\(382\) 0 0
\(383\) −4.64354 + 1.69011i −0.237274 + 0.0863606i −0.457920 0.888993i \(-0.651405\pi\)
0.220647 + 0.975354i \(0.429183\pi\)
\(384\) 0 0
\(385\) −3.42660 + 19.4332i −0.174636 + 0.990408i
\(386\) 0 0
\(387\) 9.56975 + 16.5753i 0.486458 + 0.842570i
\(388\) 0 0
\(389\) −13.1979 + 11.0743i −0.669159 + 0.561491i −0.912816 0.408370i \(-0.866097\pi\)
0.243657 + 0.969861i \(0.421653\pi\)
\(390\) 0 0
\(391\) 9.19053 15.9185i 0.464785 0.805031i
\(392\) 0 0
\(393\) 8.96625 + 3.26345i 0.452287 + 0.164619i
\(394\) 0 0
\(395\) −1.97822 11.2190i −0.0995348 0.564490i
\(396\) 0 0
\(397\) 11.1837 + 9.38426i 0.561295 + 0.470983i 0.878744 0.477293i \(-0.158382\pi\)
−0.317449 + 0.948275i \(0.602826\pi\)
\(398\) 0 0
\(399\) −15.8679 + 6.89328i −0.794389 + 0.345096i
\(400\) 0 0
\(401\) −0.893471 0.749711i −0.0446178 0.0374388i 0.620206 0.784439i \(-0.287049\pi\)
−0.664824 + 0.747000i \(0.731493\pi\)
\(402\) 0 0
\(403\) 2.60514 + 14.7745i 0.129771 + 0.735971i
\(404\) 0 0
\(405\) 0.317850 + 0.115688i 0.0157941 + 0.00574858i
\(406\) 0 0
\(407\) −9.16613 + 15.8762i −0.454348 + 0.786954i
\(408\) 0 0
\(409\) −10.7111 + 8.98771i −0.529631 + 0.444413i −0.867974 0.496609i \(-0.834578\pi\)
0.338343 + 0.941023i \(0.390134\pi\)
\(410\) 0 0
\(411\) 4.93571 + 8.54891i 0.243461 + 0.421686i
\(412\) 0 0
\(413\) 1.47423 8.36078i 0.0725422 0.411407i
\(414\) 0 0
\(415\) 10.3636 3.77206i 0.508731 0.185163i
\(416\) 0 0
\(417\) −1.56031 −0.0764085
\(418\) 0 0
\(419\) −8.57709 −0.419018 −0.209509 0.977807i \(-0.567187\pi\)
−0.209509 + 0.977807i \(0.567187\pi\)
\(420\) 0 0
\(421\) −4.02175 + 1.46380i −0.196008 + 0.0713411i −0.438159 0.898898i \(-0.644369\pi\)
0.242151 + 0.970239i \(0.422147\pi\)
\(422\) 0 0
\(423\) −1.50276 + 8.52257i −0.0730666 + 0.414381i
\(424\) 0 0
\(425\) 1.38605 + 2.40071i 0.0672334 + 0.116452i
\(426\) 0 0
\(427\) −8.15487 + 6.84275i −0.394642 + 0.331144i
\(428\) 0 0
\(429\) 4.17144 7.22515i 0.201399 0.348833i
\(430\) 0 0
\(431\) 2.04618 + 0.744750i 0.0985612 + 0.0358733i 0.390830 0.920463i \(-0.372188\pi\)
−0.292269 + 0.956336i \(0.594410\pi\)
\(432\) 0 0
\(433\) 0.796344 + 4.51629i 0.0382699 + 0.217039i 0.997945 0.0640711i \(-0.0204084\pi\)
−0.959675 + 0.281110i \(0.909297\pi\)
\(434\) 0 0
\(435\) −4.70103 3.94463i −0.225397 0.189131i
\(436\) 0 0
\(437\) 27.7097 + 8.21804i 1.32554 + 0.393122i
\(438\) 0 0
\(439\) −25.3814 21.2975i −1.21139 1.01648i −0.999230 0.0392414i \(-0.987506\pi\)
−0.212160 0.977235i \(-0.568050\pi\)
\(440\) 0 0
\(441\) −1.93008 10.9460i −0.0919087 0.521240i
\(442\) 0 0
\(443\) −20.8133 7.57541i −0.988868 0.359919i −0.203586 0.979057i \(-0.565260\pi\)
−0.785282 + 0.619138i \(0.787482\pi\)
\(444\) 0 0
\(445\) 5.60437 9.70705i 0.265673 0.460158i
\(446\) 0 0
\(447\) 6.37739 5.35127i 0.301640 0.253106i
\(448\) 0 0
\(449\) 2.53652 + 4.39338i 0.119706 + 0.207336i 0.919651 0.392736i \(-0.128472\pi\)
−0.799945 + 0.600073i \(0.795138\pi\)
\(450\) 0 0
\(451\) −2.37129 + 13.4482i −0.111660 + 0.633253i
\(452\) 0 0
\(453\) −0.565158 + 0.205701i −0.0265535 + 0.00966467i
\(454\) 0 0
\(455\) −5.08752 −0.238507
\(456\) 0 0
\(457\) −15.0185 −0.702536 −0.351268 0.936275i \(-0.614249\pi\)
−0.351268 + 0.936275i \(0.614249\pi\)
\(458\) 0 0
\(459\) 13.6876 4.98189i 0.638883 0.232535i
\(460\) 0 0
\(461\) 1.02997 5.84127i 0.0479707 0.272055i −0.951383 0.308011i \(-0.900337\pi\)
0.999353 + 0.0359561i \(0.0114476\pi\)
\(462\) 0 0
\(463\) 0.383739 + 0.664655i 0.0178339 + 0.0308891i 0.874805 0.484476i \(-0.160990\pi\)
−0.856971 + 0.515365i \(0.827656\pi\)
\(464\) 0 0
\(465\) 8.96585 7.52325i 0.415782 0.348882i
\(466\) 0 0
\(467\) −7.70383 + 13.3434i −0.356491 + 0.617460i −0.987372 0.158419i \(-0.949360\pi\)
0.630881 + 0.775880i \(0.282694\pi\)
\(468\) 0 0
\(469\) 7.34041 + 2.67169i 0.338949 + 0.123367i
\(470\) 0 0
\(471\) 1.24982 + 7.08806i 0.0575885 + 0.326600i
\(472\) 0 0
\(473\) −44.2204 37.1053i −2.03326 1.70611i
\(474\) 0 0
\(475\) −3.16283 + 2.99941i −0.145121 + 0.137623i
\(476\) 0 0
\(477\) −12.7785 10.7225i −0.585089 0.490948i
\(478\) 0 0
\(479\) 2.05385 + 11.6479i 0.0938427 + 0.532208i 0.995096 + 0.0989155i \(0.0315373\pi\)
−0.901253 + 0.433293i \(0.857352\pi\)
\(480\) 0 0
\(481\) −4.44135 1.61652i −0.202508 0.0737069i
\(482\) 0 0
\(483\) 13.1587 22.7916i 0.598742 1.03705i
\(484\) 0 0
\(485\) −7.22724 + 6.06437i −0.328172 + 0.275369i
\(486\) 0 0
\(487\) 12.0770 + 20.9180i 0.547262 + 0.947886i 0.998461 + 0.0554623i \(0.0176632\pi\)
−0.451199 + 0.892424i \(0.649003\pi\)
\(488\) 0 0
\(489\) 2.91590 16.5369i 0.131862 0.747824i
\(490\) 0 0
\(491\) −31.1082 + 11.3225i −1.40390 + 0.510976i −0.929332 0.369245i \(-0.879616\pi\)
−0.474563 + 0.880221i \(0.657394\pi\)
\(492\) 0 0
\(493\) −15.5509 −0.700376
\(494\) 0 0
\(495\) 9.80779 0.440828
\(496\) 0 0
\(497\) 55.7443 20.2892i 2.50047 0.910097i
\(498\) 0 0
\(499\) −0.397816 + 2.25613i −0.0178087 + 0.100998i −0.992416 0.122921i \(-0.960774\pi\)
0.974608 + 0.223919i \(0.0718850\pi\)
\(500\) 0 0
\(501\) −2.45232 4.24754i −0.109561 0.189766i
\(502\) 0 0
\(503\) 17.8176 14.9507i 0.794448 0.666621i −0.152394 0.988320i \(-0.548698\pi\)
0.946842 + 0.321699i \(0.104254\pi\)
\(504\) 0 0
\(505\) 3.94625 6.83510i 0.175606 0.304158i
\(506\) 0 0
\(507\) −11.3424 4.12828i −0.503732 0.183343i
\(508\) 0 0
\(509\) 1.69142 + 9.59254i 0.0749710 + 0.425182i 0.999073 + 0.0430371i \(0.0137034\pi\)
−0.924102 + 0.382145i \(0.875186\pi\)
\(510\) 0 0
\(511\) 35.9018 + 30.1252i 1.58820 + 1.33266i
\(512\) 0 0
\(513\) 12.6352 + 19.1035i 0.557856 + 0.843438i
\(514\) 0 0
\(515\) −7.38941 6.20045i −0.325616 0.273224i
\(516\) 0 0
\(517\) −4.53239 25.7045i −0.199334 1.13048i
\(518\) 0 0
\(519\) −15.3754 5.59619i −0.674905 0.245645i
\(520\) 0 0
\(521\) 13.1193 22.7232i 0.574765 0.995523i −0.421302 0.906920i \(-0.638427\pi\)
0.996067 0.0886021i \(-0.0282399\pi\)
\(522\) 0 0
\(523\) −8.90505 + 7.47222i −0.389391 + 0.326737i −0.816376 0.577521i \(-0.804020\pi\)
0.426985 + 0.904259i \(0.359576\pi\)
\(524\) 0 0
\(525\) 1.98451 + 3.43726i 0.0866109 + 0.150014i
\(526\) 0 0
\(527\) 5.15019 29.2082i 0.224346 1.27233i
\(528\) 0 0
\(529\) −19.7021 + 7.17099i −0.856615 + 0.311782i
\(530\) 0 0
\(531\) −4.21962 −0.183116
\(532\) 0 0
\(533\) −3.52068 −0.152498
\(534\) 0 0
\(535\) −0.715090 + 0.260272i −0.0309161 + 0.0112525i
\(536\) 0 0
\(537\) 4.93712 27.9998i 0.213052 1.20828i
\(538\) 0 0
\(539\) 16.7615 + 29.0318i 0.721971 + 1.25049i
\(540\) 0 0
\(541\) −22.8419 + 19.1666i −0.982051 + 0.824039i −0.984398 0.175959i \(-0.943698\pi\)
0.00234659 + 0.999997i \(0.499253\pi\)
\(542\) 0 0
\(543\) 5.23125 9.06079i 0.224494 0.388836i
\(544\) 0 0
\(545\) 14.8942 + 5.42106i 0.637999 + 0.232213i
\(546\) 0 0
\(547\) −2.79368 15.8437i −0.119449 0.677429i −0.984451 0.175660i \(-0.943794\pi\)
0.865002 0.501769i \(-0.167317\pi\)
\(548\) 0 0
\(549\) 4.05317 + 3.40101i 0.172985 + 0.145152i
\(550\) 0 0
\(551\) −5.70039 23.7787i −0.242845 1.01301i
\(552\) 0 0
\(553\) −31.6625 26.5680i −1.34643 1.12979i
\(554\) 0 0
\(555\) 0.640288 + 3.63125i 0.0271787 + 0.154138i
\(556\) 0 0
\(557\) −13.3701 4.86630i −0.566508 0.206192i 0.0428582 0.999081i \(-0.486354\pi\)
−0.609366 + 0.792889i \(0.708576\pi\)
\(558\) 0 0
\(559\) 7.44135 12.8888i 0.314736 0.545138i
\(560\) 0 0
\(561\) −12.6346 + 10.6017i −0.533434 + 0.447604i
\(562\) 0 0
\(563\) 2.10390 + 3.64407i 0.0886690 + 0.153579i 0.906949 0.421241i \(-0.138405\pi\)
−0.818280 + 0.574820i \(0.805072\pi\)
\(564\) 0 0
\(565\) −1.21957 + 6.91653i −0.0513077 + 0.290981i
\(566\) 0 0
\(567\) 1.15322 0.419736i 0.0484305 0.0176273i
\(568\) 0 0
\(569\) 0.192878 0.00808588 0.00404294 0.999992i \(-0.498713\pi\)
0.00404294 + 0.999992i \(0.498713\pi\)
\(570\) 0 0
\(571\) −11.7824 −0.493079 −0.246540 0.969133i \(-0.579294\pi\)
−0.246540 + 0.969133i \(0.579294\pi\)
\(572\) 0 0
\(573\) −10.8991 + 3.96693i −0.455315 + 0.165721i
\(574\) 0 0
\(575\) 1.15141 6.52999i 0.0480173 0.272320i
\(576\) 0 0
\(577\) 16.7487 + 29.0096i 0.697258 + 1.20769i 0.969414 + 0.245432i \(0.0789299\pi\)
−0.272156 + 0.962253i \(0.587737\pi\)
\(578\) 0 0
\(579\) 15.7864 13.2463i 0.656059 0.550499i
\(580\) 0 0
\(581\) 20.0071 34.6534i 0.830036 1.43766i
\(582\) 0 0
\(583\) 47.2772 + 17.2075i 1.95802 + 0.712661i
\(584\) 0 0
\(585\) 0.439091 + 2.49021i 0.0181542 + 0.102957i
\(586\) 0 0
\(587\) 10.1030 + 8.47746i 0.416997 + 0.349902i 0.827019 0.562173i \(-0.190035\pi\)
−0.410022 + 0.912076i \(0.634479\pi\)
\(588\) 0 0
\(589\) 46.5499 2.83155i 1.91806 0.116672i
\(590\) 0 0
\(591\) 5.12209 + 4.29794i 0.210694 + 0.176794i
\(592\) 0 0
\(593\) 6.73080 + 38.1723i 0.276401 + 1.56755i 0.734476 + 0.678634i \(0.237428\pi\)
−0.458075 + 0.888913i \(0.651461\pi\)
\(594\) 0 0
\(595\) 9.45113 + 3.43993i 0.387458 + 0.141023i
\(596\) 0 0
\(597\) 3.69821 6.40549i 0.151358 0.262159i
\(598\) 0 0
\(599\) 19.3433 16.2310i 0.790347 0.663180i −0.155484 0.987838i \(-0.549694\pi\)
0.945831 + 0.324658i \(0.105249\pi\)
\(600\) 0 0
\(601\) −13.1344 22.7495i −0.535765 0.927972i −0.999126 0.0418023i \(-0.986690\pi\)
0.463361 0.886170i \(-0.346643\pi\)
\(602\) 0 0
\(603\) 0.674191 3.82353i 0.0274552 0.155706i
\(604\) 0 0
\(605\) −17.4602 + 6.35500i −0.709859 + 0.258367i
\(606\) 0 0
\(607\) 36.0403 1.46283 0.731415 0.681933i \(-0.238860\pi\)
0.731415 + 0.681933i \(0.238860\pi\)
\(608\) 0 0
\(609\) −22.2652 −0.902233
\(610\) 0 0
\(611\) 6.32348 2.30156i 0.255820 0.0931110i
\(612\) 0 0
\(613\) 1.14364 6.48591i 0.0461912 0.261964i −0.952963 0.303087i \(-0.901983\pi\)
0.999154 + 0.0411237i \(0.0130938\pi\)
\(614\) 0 0
\(615\) 1.37332 + 2.37867i 0.0553777 + 0.0959171i
\(616\) 0 0
\(617\) −3.23564 + 2.71502i −0.130262 + 0.109303i −0.705591 0.708619i \(-0.749318\pi\)
0.575329 + 0.817922i \(0.304874\pi\)
\(618\) 0 0
\(619\) 8.09543 14.0217i 0.325383 0.563579i −0.656207 0.754581i \(-0.727840\pi\)
0.981590 + 0.191001i \(0.0611735\pi\)
\(620\) 0 0
\(621\) −32.7401 11.9164i −1.31382 0.478190i
\(622\) 0 0
\(623\) −7.06180 40.0495i −0.282925 1.60455i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) −20.8424 15.4333i −0.832364 0.616346i
\(628\) 0 0
\(629\) 7.15772 + 6.00604i 0.285397 + 0.239476i
\(630\) 0 0
\(631\) −5.49646 31.1720i −0.218811 1.24094i −0.874170 0.485620i \(-0.838594\pi\)
0.655359 0.755317i \(-0.272517\pi\)
\(632\) 0 0
\(633\) −7.13090 2.59544i −0.283428 0.103159i
\(634\) 0 0
\(635\) −6.42993 + 11.1370i −0.255164 + 0.441957i
\(636\) 0 0
\(637\) −6.62081 + 5.55552i −0.262326 + 0.220118i
\(638\) 0 0
\(639\) −14.7422 25.5342i −0.583192 1.01012i
\(640\) 0 0
\(641\) −7.47565 + 42.3965i −0.295270 + 1.67456i 0.370832 + 0.928700i \(0.379073\pi\)
−0.666102 + 0.745861i \(0.732038\pi\)
\(642\) 0 0
\(643\) 22.8293 8.30920i 0.900301 0.327683i 0.149928 0.988697i \(-0.452096\pi\)
0.750373 + 0.661014i \(0.229874\pi\)
\(644\) 0 0
\(645\) −11.6107 −0.457170
\(646\) 0 0
\(647\) −28.7229 −1.12921 −0.564606 0.825360i \(-0.690972\pi\)
−0.564606 + 0.825360i \(0.690972\pi\)
\(648\) 0 0
\(649\) 11.9591 4.35275i 0.469435 0.170860i
\(650\) 0 0
\(651\) 7.37389 41.8194i 0.289005 1.63903i
\(652\) 0 0
\(653\) −19.1944 33.2458i −0.751137 1.30101i −0.947272 0.320430i \(-0.896173\pi\)
0.196135 0.980577i \(-0.437161\pi\)
\(654\) 0 0
\(655\) 6.68167 5.60659i 0.261074 0.219067i
\(656\) 0 0
\(657\) 11.6469 20.1730i 0.454388 0.787024i
\(658\) 0 0
\(659\) −30.2296 11.0027i −1.17758 0.428603i −0.322232 0.946661i \(-0.604433\pi\)
−0.855346 + 0.518058i \(0.826655\pi\)
\(660\) 0 0
\(661\) 3.47112 + 19.6857i 0.135011 + 0.765685i 0.974852 + 0.222853i \(0.0715369\pi\)
−0.839841 + 0.542832i \(0.817352\pi\)
\(662\) 0 0
\(663\) −3.25743 2.73331i −0.126508 0.106153i
\(664\) 0 0
\(665\) −1.79553 + 15.7126i −0.0696276 + 0.609308i
\(666\) 0 0
\(667\) 28.4945 + 23.9097i 1.10331 + 0.925787i
\(668\) 0 0
\(669\) −4.11866 23.3581i −0.159237 0.903076i
\(670\) 0 0
\(671\) −14.9956 5.45797i −0.578900 0.210702i
\(672\) 0 0
\(673\) 2.59611 4.49660i 0.100073 0.173331i −0.811642 0.584156i \(-0.801426\pi\)
0.911714 + 0.410824i \(0.134759\pi\)
\(674\) 0 0
\(675\) 4.02519 3.37754i 0.154930 0.130002i
\(676\) 0 0
\(677\) −2.39094 4.14124i −0.0918915 0.159161i 0.816416 0.577465i \(-0.195958\pi\)
−0.908307 + 0.418304i \(0.862625\pi\)
\(678\) 0 0
\(679\) −5.94398 + 33.7100i −0.228109 + 1.29367i
\(680\) 0 0
\(681\) 24.4098 8.88443i 0.935384 0.340452i
\(682\) 0 0
\(683\) −2.33827 −0.0894714 −0.0447357 0.998999i \(-0.514245\pi\)
−0.0447357 + 0.998999i \(0.514245\pi\)
\(684\) 0 0
\(685\) 9.02373 0.344779
\(686\) 0 0
\(687\) −14.8082 + 5.38974i −0.564967 + 0.205631i
\(688\) 0 0
\(689\) −2.25242 + 12.7741i −0.0858102 + 0.486654i
\(690\) 0 0
\(691\) 17.5669 + 30.4267i 0.668275 + 1.15749i 0.978386 + 0.206786i \(0.0663003\pi\)
−0.310111 + 0.950700i \(0.600366\pi\)
\(692\) 0 0
\(693\) 27.2592 22.8732i 1.03549 0.868882i
\(694\) 0 0
\(695\) −0.713158 + 1.23523i −0.0270516 + 0.0468548i
\(696\) 0 0
\(697\) 6.54040 + 2.38051i 0.247735 + 0.0901683i
\(698\) 0 0
\(699\) 4.06418 + 23.0491i 0.153722 + 0.871798i
\(700\) 0 0
\(701\) 3.92698 + 3.29513i 0.148320 + 0.124455i 0.713928 0.700219i \(-0.246914\pi\)
−0.565608 + 0.824674i \(0.691359\pi\)
\(702\) 0 0
\(703\) −6.56002 + 13.1464i −0.247416 + 0.495826i
\(704\) 0 0
\(705\) −4.02161 3.37453i −0.151463 0.127092i
\(706\) 0 0
\(707\) −4.97248 28.2003i −0.187009 1.06058i
\(708\) 0 0
\(709\) 14.4095 + 5.24461i 0.541158 + 0.196966i 0.598114 0.801411i \(-0.295917\pi\)
−0.0569555 + 0.998377i \(0.518139\pi\)
\(710\) 0 0
\(711\) −10.2716 + 17.7910i −0.385217 + 0.667215i
\(712\) 0 0
\(713\) −54.3450 + 45.6008i −2.03523 + 1.70776i
\(714\) 0 0
\(715\) −3.81322 6.60470i −0.142607 0.247002i
\(716\) 0 0
\(717\) −3.09352 + 17.5442i −0.115530 + 0.655202i
\(718\) 0 0
\(719\) −1.47862 + 0.538174i −0.0551432 + 0.0200705i −0.369445 0.929253i \(-0.620452\pi\)
0.314301 + 0.949323i \(0.398230\pi\)
\(720\) 0 0
\(721\) −34.9981 −1.30340
\(722\) 0 0
\(723\) 16.6027 0.617461
\(724\) 0 0
\(725\) −5.27146 + 1.91866i −0.195777 + 0.0712571i
\(726\) 0 0
\(727\) −7.85960 + 44.5740i −0.291496 + 1.65316i 0.389615 + 0.920978i \(0.372608\pi\)
−0.681111 + 0.732180i \(0.738503\pi\)
\(728\) 0 0
\(729\) −8.92718 15.4623i −0.330636 0.572679i
\(730\) 0 0
\(731\) −22.5386 + 18.9122i −0.833621 + 0.699491i
\(732\) 0 0
\(733\) −18.5796 + 32.1808i −0.686253 + 1.18863i 0.286788 + 0.957994i \(0.407412\pi\)
−0.973041 + 0.230631i \(0.925921\pi\)
\(734\) 0 0
\(735\) 6.33605 + 2.30614i 0.233709 + 0.0850631i
\(736\) 0 0
\(737\) 2.03339 + 11.5319i 0.0749009 + 0.424784i
\(738\) 0 0
\(739\) 20.3874 + 17.1071i 0.749964 + 0.629295i 0.935493 0.353344i \(-0.114956\pi\)
−0.185529 + 0.982639i \(0.559400\pi\)
\(740\) 0 0
\(741\) 2.98542 5.98284i 0.109672 0.219785i
\(742\) 0 0
\(743\) −24.0072 20.1445i −0.880740 0.739028i 0.0855914 0.996330i \(-0.472722\pi\)
−0.966331 + 0.257302i \(0.917166\pi\)
\(744\) 0 0
\(745\) −1.32150 7.49457i −0.0484158 0.274580i
\(746\) 0 0
\(747\) −18.6887 6.80212i −0.683783 0.248877i
\(748\) 0 0
\(749\) −1.38049 + 2.39108i −0.0504420 + 0.0873682i
\(750\) 0 0
\(751\) 15.2232 12.7737i 0.555501 0.466121i −0.321298 0.946978i \(-0.604119\pi\)
0.876799 + 0.480858i \(0.159675\pi\)
\(752\) 0 0
\(753\) 2.22587 + 3.85531i 0.0811150 + 0.140495i
\(754\) 0 0
\(755\) −0.0954687 + 0.541430i −0.00347446 + 0.0197046i
\(756\) 0 0
\(757\) −43.5045 + 15.8344i −1.58120 + 0.575509i −0.975464 0.220157i \(-0.929343\pi\)
−0.605735 + 0.795667i \(0.707121\pi\)
\(758\) 0 0
\(759\) 39.4512 1.43199
\(760\) 0 0
\(761\) 38.1331 1.38232 0.691161 0.722701i \(-0.257099\pi\)
0.691161 + 0.722701i \(0.257099\pi\)
\(762\) 0 0
\(763\) 54.0390 19.6686i 1.95634 0.712050i
\(764\) 0 0
\(765\) 0.868053 4.92297i 0.0313845 0.177990i
\(766\) 0 0
\(767\) 1.64057 + 2.84155i 0.0592375 + 0.102602i
\(768\) 0 0
\(769\) −14.2867 + 11.9880i −0.515193 + 0.432298i −0.862952 0.505286i \(-0.831387\pi\)
0.347759 + 0.937584i \(0.386943\pi\)
\(770\) 0 0
\(771\) 1.15701 2.00399i 0.0416686 0.0721721i
\(772\) 0 0
\(773\) 36.8574 + 13.4150i 1.32567 + 0.482504i 0.905270 0.424836i \(-0.139668\pi\)
0.420398 + 0.907340i \(0.361891\pi\)
\(774\) 0 0
\(775\) −1.85787 10.5365i −0.0667365 0.378481i
\(776\) 0 0
\(777\) 10.2482 + 8.59926i 0.367652 + 0.308497i
\(778\) 0 0
\(779\) −1.24255 + 10.8735i −0.0445188 + 0.389583i
\(780\) 0 0
\(781\) 68.1216 + 57.1608i 2.43758 + 2.04537i
\(782\) 0 0
\(783\) 5.11857 + 29.0288i 0.182923 + 1.03741i
\(784\) 0 0
\(785\) 6.18255 + 2.25027i 0.220665 + 0.0803154i
\(786\) 0 0
\(787\) 12.0053 20.7938i 0.427942 0.741218i