Properties

Label 380.2.u.b.101.2
Level $380$
Weight $2$
Character 380.101
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 101.2
Root \(0.546970 - 0.947380i\) of defining polynomial
Character \(\chi\) \(=\) 380.101
Dual form 380.2.u.b.301.2

$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\)

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 0.621267 0.783599i \(-0.286618\pi\)
−0.0277695 + 0.999614i \(0.508840\pi\)
\(4\) 0 0
\(5\) 0.173648 + 0.984808i 0.0776578 + 0.440419i
\(6\) 0 0
\(7\) −1.81409 + 3.14209i −0.685661 + 1.18760i 0.287568 + 0.957760i \(0.407153\pi\)
−0.973229 + 0.229839i \(0.926180\pi\)
\(8\) 0 0
\(9\) −1.38140 1.15914i −0.460468 0.386378i
\(10\) 0 0
\(11\) 2.71941 + 4.71016i 0.819933 + 1.42017i 0.905731 + 0.423853i \(0.139323\pi\)
−0.0857978 + 0.996313i \(0.527344\pi\)
\(12\) 0 0
\(13\) 1.31766 0.479589i 0.365453 0.133014i −0.152765 0.988263i \(-0.548818\pi\)
0.518218 + 0.855248i \(0.326596\pi\)
\(14\) 0 0
\(15\) −0.189961 + 1.07732i −0.0490477 + 0.278163i
\(16\) 0 0
\(17\) −2.12355 + 1.78187i −0.515037 + 0.432168i −0.862898 0.505379i \(-0.831353\pi\)
0.347860 + 0.937546i \(0.386908\pi\)
\(18\) 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 −0.591546 0.806271i \(-0.701482\pi\)
0.831632 0.555327i \(-0.187407\pi\)
\(24\) 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 0.947710 0.319132i \(-0.103391\pi\)
−0.149715 + 0.988729i \(0.547836\pi\)
\(30\) 0 0
\(31\) 5.34951 9.26562i 0.960800 1.66416i 0.240302 0.970698i \(-0.422753\pi\)
0.720498 0.693457i \(-0.243913\pi\)
\(32\) 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 0.151147 0.988511i \(-0.451703\pi\)
−0.519618 + 0.854399i \(0.673926\pi\)
\(42\) 0 0
\(43\) 1.84304 + 10.4524i 0.281061 + 1.59397i 0.719026 + 0.694983i \(0.244588\pi\)
−0.437965 + 0.898992i \(0.644301\pi\)
\(44\) 0 0
\(45\) 0.901647 1.56170i 0.134410 0.232804i
\(46\) 0 0
\(47\) 3.67626 + 3.08475i 0.536238 + 0.449957i 0.870249 0.492612i \(-0.163958\pi\)
−0.334011 + 0.942569i \(0.608402\pi\)
\(48\) 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 −0.650194 0.759768i \(-0.725312\pi\)
0.870839 0.491569i \(-0.163577\pi\)
\(54\) 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 −0.518605 0.855014i \(-0.673548\pi\)
0.751970 + 0.659198i \(0.229104\pi\)
\(60\) 0 0
\(61\) −0.509501 + 2.88952i −0.0652349 + 0.369965i 0.934661 + 0.355540i \(0.115703\pi\)
−0.999896 + 0.0144254i \(0.995408\pi\)
\(62\) 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 0.536457 0.843927i \(-0.319762\pi\)
−0.737951 + 0.674854i \(0.764207\pi\)
\(68\) 0 0
\(69\) 3.62681 6.28182i 0.436617 0.756243i
\(70\) 0 0
\(71\) −2.83920 16.1019i −0.336951 1.91094i −0.407053 0.913405i \(-0.633443\pi\)
0.0701015 0.997540i \(-0.477668\pi\)
\(72\) 0 0
\(73\) −12.1383 4.41799i −1.42068 0.517087i −0.486438 0.873715i \(-0.661704\pi\)
−0.934246 + 0.356628i \(0.883926\pi\)
\(74\) 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 0.864763 0.502181i \(-0.167469\pi\)
0.339651 + 0.940552i \(0.389691\pi\)
\(80\) 0 0
\(81\) −0.0587363 0.333110i −0.00652625 0.0370122i
\(82\) 0 0
\(83\) 5.51438 9.55118i 0.605281 1.04838i −0.386726 0.922195i \(-0.626394\pi\)
0.992007 0.126183i \(-0.0402727\pi\)
\(84\) 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 0.283108 0.959088i \(-0.408635\pi\)
0.833363 + 0.552726i \(0.186412\pi\)
\(90\) 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 −0.931169 0.364589i \(-0.881210\pi\)
0.197354 + 0.980332i \(0.436765\pi\)
\(98\) 0 0
\(99\) 1.70311 9.65879i 0.171169 0.970745i
\(100\) 0 0
\(101\) 7.41652 2.69939i 0.737972 0.268600i 0.0544364 0.998517i \(-0.482664\pi\)
0.683535 + 0.729918i \(0.260442\pi\)
\(102\) 0 0
\(103\) 4.82309 + 8.35384i 0.475233 + 0.823129i 0.999598 0.0283656i \(-0.00903026\pi\)
−0.524364 + 0.851494i \(0.675697\pi\)
\(104\) 0 0
\(105\) −3.04044 2.55123i −0.296716 0.248975i
\(106\) 0 0
\(107\) −0.380492 + 0.659031i −0.0367835 + 0.0637109i −0.883831 0.467806i \(-0.845045\pi\)
0.847048 + 0.531517i \(0.178378\pi\)
\(108\) 0 0
\(109\) −2.75235 15.6093i −0.263627 1.49510i −0.772917 0.634507i \(-0.781203\pi\)
0.509290 0.860595i \(-0.329908\pi\)
\(110\) 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 −0.817040 0.576581i \(-0.804386\pi\)
−0.255270 + 0.966870i \(0.582164\pi\)
\(128\) 0 0
\(129\) −2.01618 + 11.4343i −0.177514 + 1.00673i
\(130\) 0 0
\(131\) 6.68167 5.60659i 0.583780 0.489850i −0.302406 0.953179i \(-0.597790\pi\)
0.886186 + 0.463329i \(0.153345\pi\)
\(132\) 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 −0.841763 0.539847i \(-0.818482\pi\)
0.975637 0.219390i \(-0.0704068\pi\)
\(138\) 0 0
\(139\) −1.34030 + 0.487829i −0.113683 + 0.0413771i −0.398235 0.917283i \(-0.630377\pi\)
0.284552 + 0.958660i \(0.408155\pi\)
\(140\) 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 0.617904 0.786253i \(-0.287982\pi\)
−0.0320520 + 0.999486i \(0.510204\pi\)
\(150\) 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 −0.995851 0.0909989i \(-0.970994\pi\)
0.904670 0.426112i \(-0.140117\pi\)
\(158\) 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 0.992647 + 0.121046i \(0.0386250\pi\)
−0.391494 + 0.920181i \(0.628042\pi\)
\(164\) 0 0
\(165\) −5.59093 + 2.03493i −0.435254 + 0.158419i
\(166\) 0 0
\(167\) −0.778544 + 4.41534i −0.0602456 + 0.341670i −1.00000 0.000180770i \(-0.999942\pi\)
0.939754 + 0.341850i \(0.111054\pi\)
\(168\) 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 −0.964334 0.264690i \(-0.914730\pi\)
0.0932138 + 0.995646i \(0.470286\pi\)
\(174\) 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 0.691642 + 0.722241i \(0.256888\pi\)
0.279658 + 0.960100i \(0.409779\pi\)
\(180\) 0 0
\(181\) 7.32648 + 6.14765i 0.544573 + 0.456951i 0.873098 0.487544i \(-0.162107\pi\)
−0.328525 + 0.944495i \(0.606552\pi\)
\(182\) 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 0.888514 0.458850i \(-0.151738\pi\)
0.385698 + 0.922625i \(0.373961\pi\)
\(194\) 0 0
\(195\) 0.266368 + 1.51065i 0.0190750 + 0.108180i
\(196\) 0 0
\(197\) 3.05611 5.29334i 0.217739 0.377135i −0.736377 0.676571i \(-0.763465\pi\)
0.954116 + 0.299436i \(0.0967985\pi\)
\(198\) 0 0
\(199\) 5.17943 + 4.34605i 0.367160 + 0.308084i 0.807637 0.589680i \(-0.200746\pi\)
−0.440477 + 0.897764i \(0.645191\pi\)
\(200\) 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 −0.807109 0.590403i \(-0.798969\pi\)
0.441280 + 0.897369i \(0.354525\pi\)
\(212\) 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 0.803355 + 0.595501i \(0.203046\pi\)
−0.551233 + 0.834351i \(0.685843\pi\)
\(224\) 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 −0.824204 0.566293i \(-0.808377\pi\)
0.580814 0.814036i \(-0.302734\pi\)
\(234\) 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 −0.999516 0.0311059i \(-0.990097\pi\)
0.472820 0.881159i \(-0.343236\pi\)
\(240\) 0 0
\(241\) 14.2617 5.19083i 0.918676 0.334371i 0.160964 0.986960i \(-0.448540\pi\)
0.757711 + 0.652590i \(0.226317\pi\)
\(242\) 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 −0.954350 0.298689i \(-0.903451\pi\)
0.998954 + 0.0457307i \(0.0145616\pi\)
\(252\) 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 0.691927 0.721968i \(-0.256762\pi\)
−0.590848 + 0.806783i \(0.701207\pi\)
\(258\) 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 −0.114922 0.993374i \(-0.536662\pi\)
−0.726564 + 0.687098i \(0.758884\pi\)
\(264\) 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 0.183715 0.982979i \(-0.441188\pi\)
−0.491113 + 0.871096i \(0.663410\pi\)
\(270\) 0 0
\(271\) 1.13162 + 6.41774i 0.0687410 + 0.389850i 0.999695 + 0.0247122i \(0.00786694\pi\)
−0.930954 + 0.365138i \(0.881022\pi\)
\(272\) 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 0.906484 0.422239i \(-0.138756\pi\)
−0.818912 + 0.573919i \(0.805422\pi\)
\(278\) 0 0
\(279\) −18.1299 + 6.59876i −1.08541 + 0.395057i
\(280\) 0 0
\(281\) −0.417979 + 2.37048i −0.0249345 + 0.141411i −0.994734 0.102495i \(-0.967318\pi\)
0.969799 + 0.243905i \(0.0784286\pi\)
\(282\) 0 0
\(283\) 0.821925 0.689677i 0.0488584 0.0409970i −0.618031 0.786153i \(-0.712070\pi\)
0.666890 + 0.745156i \(0.267625\pi\)
\(284\) 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 −0.975176 0.221432i \(-0.928927\pi\)
0.295822 0.955243i \(-0.404407\pi\)
\(294\) 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 −0.515530 0.856871i \(-0.672405\pi\)
−0.945705 + 0.325025i \(0.894627\pi\)
\(308\) 0 0
\(309\) 1.83240 + 10.3920i 0.104241 + 0.591183i
\(310\) 0 0
\(311\) 6.75505 11.7001i 0.383044 0.663451i −0.608452 0.793591i \(-0.708209\pi\)
0.991496 + 0.130140i \(0.0415426\pi\)
\(312\) 0 0
\(313\) −17.7886 14.9264i −1.00547 0.843692i −0.0177397 0.999843i \(-0.505647\pi\)
−0.987733 + 0.156151i \(0.950091\pi\)
\(314\) 0 0
\(315\) 3.27134 + 5.66612i 0.184319 + 0.319250i
\(316\) 0 0
\(317\) −4.96139 + 1.80580i −0.278659 + 0.101424i −0.477569 0.878594i \(-0.658482\pi\)
0.198910 + 0.980018i \(0.436260\pi\)
\(318\) 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 −0.999154 0.0411202i \(-0.986907\pi\)
0.463966 0.885853i \(-0.346426\pi\)
\(332\) 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 −0.999344 0.0362127i \(-0.988471\pi\)
0.926691 0.375825i \(-0.122640\pi\)
\(338\) 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 0.994391 0.105769i \(-0.0337304\pi\)
−0.970597 + 0.240711i \(0.922619\pi\)
\(348\) 0 0
\(349\) −0.851409 + 1.47468i −0.0455749 + 0.0789380i −0.887913 0.460011i \(-0.847845\pi\)
0.842338 + 0.538949i \(0.181179\pi\)
\(350\) 0 0
\(351\) −5.64423 4.73607i −0.301267 0.252793i
\(352\) 0 0
\(353\) 11.8829 + 20.5818i 0.632465 + 1.09546i 0.987046 + 0.160436i \(0.0512900\pi\)
−0.354582 + 0.935025i \(0.615377\pi\)
\(354\) 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 −0.766063 0.642765i \(-0.777787\pi\)
0.499975 + 0.866040i \(0.333343\pi\)
\(360\) 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 0.502757 0.864428i \(-0.332319\pi\)
0.940778 + 0.339024i \(0.110097\pi\)
\(368\) 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 −0.299401 0.954127i \(-0.596787\pi\)
0.975999 0.217775i \(-0.0698799\pi\)
\(374\) 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 0.220647 0.975354i \(-0.429183\pi\)
−0.457920 + 0.888993i \(0.651405\pi\)
\(384\) 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 0.243657 0.969861i \(-0.421653\pi\)
−0.912816 + 0.408370i \(0.866097\pi\)
\(390\) 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 −0.317449 0.948275i \(-0.602826\pi\)
0.878744 + 0.477293i \(0.158382\pi\)
\(398\) 0 0
\(399\) −15.8679 6.89328i −0.794389 0.345096i
\(400\) 0 0
\(401\) −0.893471 + 0.749711i −0.0446178 + 0.0374388i −0.664824 0.747000i \(-0.731493\pi\)
0.620206 + 0.784439i \(0.287049\pi\)
\(402\) 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 0.338343 0.941023i \(-0.390134\pi\)
−0.867974 + 0.496609i \(0.834578\pi\)
\(410\) 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 0.242151 0.970239i \(-0.422147\pi\)
−0.438159 + 0.898898i \(0.644369\pi\)
\(422\) 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 −0.292269 0.956336i \(-0.594410\pi\)
0.390830 + 0.920463i \(0.372188\pi\)
\(432\) 0 0
\(433\) 0.796344 4.51629i 0.0382699 0.217039i −0.959675 0.281110i \(-0.909297\pi\)
0.997945 + 0.0640711i \(0.0204084\pi\)
\(434\) 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 −0.212160 + 0.977235i \(0.568050\pi\)
−0.999230 + 0.0392414i \(0.987506\pi\)
\(440\) 0 0
\(441\) −1.93008 + 10.9460i −0.0919087 + 0.521240i
\(442\) 0 0
\(443\) −20.8133 + 7.57541i −0.988868 + 0.359919i −0.785282 0.619138i \(-0.787482\pi\)
−0.203586 + 0.979057i \(0.565260\pi\)
\(444\) 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 −0.799945 0.600073i \(-0.795138\pi\)
0.919651 + 0.392736i \(0.128472\pi\)
\(450\) 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 0.999353 0.0359561i \(-0.0114476\pi\)
−0.951383 + 0.308011i \(0.900337\pi\)
\(462\) 0 0
\(463\) 0.383739 0.664655i 0.0178339 0.0308891i −0.856971 0.515365i \(-0.827656\pi\)
0.874805 + 0.484476i \(0.160990\pi\)
\(464\) 0 0
\(465\) 8.96585 + 7.52325i 0.415782 + 0.348882i
\(466\) 0 0
\(467\) −7.70383 13.3434i −0.356491 0.617460i 0.630881 0.775880i \(-0.282694\pi\)
−0.987372 + 0.158419i \(0.949360\pi\)
\(468\) 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 −0.901253 0.433293i \(-0.857352\pi\)
0.995096 0.0989155i \(-0.0315373\pi\)
\(480\) 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 −0.451199 0.892424i \(-0.649003\pi\)
0.998461 0.0554623i \(-0.0176632\pi\)
\(488\) 0 0
\(489\) 2.91590 + 16.5369i 0.131862 + 0.747824i
\(490\) 0 0
\(491\) −31.1082 11.3225i −1.40390 0.510976i −0.474563 0.880221i \(-0.657394\pi\)
−0.929332 + 0.369245i \(0.879616\pi\)
\(492\) 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 0.974608 0.223919i \(-0.0718850\pi\)
−0.992416 + 0.122921i \(0.960774\pi\)
\(500\) 0 0
\(501\) −2.45232 + 4.24754i −0.109561 + 0.189766i
\(502\) 0 0
\(503\) 17.8176 + 14.9507i 0.794448 + 0.666621i 0.946842 0.321699i \(-0.104254\pi\)
−0.152394 + 0.988320i \(0.548698\pi\)
\(504\) 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 −0.924102 0.382145i \(-0.875186\pi\)
0.999073 0.0430371i \(-0.0137034\pi\)
\(510\) 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 0.996067 + 0.0886021i \(0.0282399\pi\)
−0.421302 + 0.906920i \(0.638427\pi\)
\(522\) 0 0
\(523\) −8.90505 7.47222i −0.389391 0.326737i 0.426985 0.904259i \(-0.359576\pi\)
−0.816376 + 0.577521i \(0.804020\pi\)
\(524\) 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 0.00234659 0.999997i \(-0.499253\pi\)
−0.984398 + 0.175959i \(0.943698\pi\)
\(542\) 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 0.865002 + 0.501769i \(0.167317\pi\)
−0.984451 + 0.175660i \(0.943794\pi\)
\(548\) 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 −0.609366 0.792889i \(-0.708576\pi\)
0.0428582 + 0.999081i \(0.486354\pi\)
\(558\) 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 −0.818280 0.574820i \(-0.805072\pi\)
0.906949 + 0.421241i \(0.138405\pi\)
\(564\) 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 −0.272156 0.962253i \(-0.587737\pi\)
0.969414 0.245432i \(-0.0789299\pi\)
\(578\) 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 −0.410022 0.912076i \(-0.634479\pi\)
0.827019 + 0.562173i \(0.190035\pi\)
\(588\) 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 −0.458075 0.888913i \(-0.651461\pi\)
0.734476 0.678634i \(-0.237428\pi\)
\(594\) 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 0.945831 0.324658i \(-0.105249\pi\)
−0.155484 + 0.987838i \(0.549694\pi\)
\(600\) 0 0
\(601\) −13.1344 + 22.7495i −0.535765 + 0.927972i 0.463361 + 0.886170i \(0.346643\pi\)
−0.999126 + 0.0418023i \(0.986690\pi\)
\(602\) 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 0.999154 0.0411237i \(-0.0130938\pi\)
−0.952963 + 0.303087i \(0.901983\pi\)
\(614\) 0 0
\(615\) 1.37332 2.37867i 0.0553777 0.0959171i
\(616\) 0 0
\(617\) −3.23564 2.71502i −0.130262 0.109303i 0.575329 0.817922i \(-0.304874\pi\)
−0.705591 + 0.708619i \(0.749318\pi\)
\(618\) 0 0
\(619\) 8.09543 + 14.0217i 0.325383 + 0.563579i 0.981590 0.191001i \(-0.0611735\pi\)
−0.656207 + 0.754581i \(0.727840\pi\)
\(620\) 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 0.655359 + 0.755317i \(0.272517\pi\)
−0.874170 + 0.485620i \(0.838594\pi\)
\(632\) 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 −0.666102 0.745861i \(-0.732038\pi\)
0.370832 0.928700i \(-0.379073\pi\)
\(642\) 0 0
\(643\) 22.8293 + 8.30920i 0.900301 + 0.327683i 0.750373 0.661014i \(-0.229874\pi\)
0.149928 + 0.988697i \(0.452096\pi\)
\(644\) 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 0.196135 + 0.980577i \(0.437161\pi\)
−0.947272 + 0.320430i \(0.896173\pi\)
\(654\) 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 −0.855346 0.518058i \(-0.826655\pi\)
−0.322232 + 0.946661i \(0.604433\pi\)
\(660\) 0 0
\(661\) 3.47112 19.6857i 0.135011 0.765685i −0.839841 0.542832i \(-0.817352\pi\)
0.974852 0.222853i \(-0.0715369\pi\)
\(662\) 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 0.911714 0.410824i \(-0.134759\pi\)
−0.811642 + 0.584156i \(0.801426\pi\)
\(674\) 0 0
\(675\) 4.02519 + 3.37754i 0.154930 + 0.130002i
\(676\) 0 0
\(677\) −2.39094 + 4.14124i −0.0918915 + 0.159161i −0.908307 0.418304i \(-0.862625\pi\)
0.816416 + 0.577465i \(0.195958\pi\)
\(678\) 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 −0.310111 0.950700i \(-0.600366\pi\)
0.978386 0.206786i \(-0.0663003\pi\)
\(692\) 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 −0.565608 0.824674i \(-0.691359\pi\)
0.713928 + 0.700219i \(0.246914\pi\)
\(702\) 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 −0.0569555 0.998377i \(-0.518139\pi\)
0.598114 + 0.801411i \(0.295917\pi\)
\(710\) 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 0.314301 0.949323i \(-0.398230\pi\)
−0.369445 + 0.929253i \(0.620452\pi\)
\(720\) 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 −0.681111 0.732180i \(-0.738503\pi\)
0.389615 0.920978i \(-0.372608\pi\)
\(728\) 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 −0.973041 0.230631i \(-0.925921\pi\)
0.286788 0.957994i \(-0.407412\pi\)
\(734\) 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 −0.185529 0.982639i \(-0.559400\pi\)
0.935493 + 0.353344i \(0.114956\pi\)
\(740\) 0 0
\(741\) 2.98542 + 5.98284i 0.109672 + 0.219785i
\(742\) 0 0
\(743\) −24.0072 + 20.1445i −0.880740 + 0.739028i −0.966331 0.257302i \(-0.917166\pi\)
0.0855914 + 0.996330i \(0.472722\pi\)
\(744\) 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 0.876799 0.480858i \(-0.159675\pi\)
−0.321298 + 0.946978i \(0.604119\pi\)
\(752\) 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 −0.605735 0.795667i \(-0.707121\pi\)
−0.975464 + 0.220157i \(0.929343\pi\)
\(758\) 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 0.347759 0.937584i \(-0.386943\pi\)
−0.862952 + 0.505286i \(0.831387\pi\)
\(770\) 0 0
\(771\) 1.15701 + 2.00399i 0.0416686 + 0.0721721i
\(772\) 0 0
\(773\) 36.8574 13.4150i 1.32567 0.482504i 0.420398 0.907340i \(-0.361891\pi\)
0.905270 + 0.424836i \(0.139668\pi\)
\(774\) 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 +