Properties

Label 380.2.u.b.321.1
Level $380$
Weight $2$
Character 380.321
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 321.1
Root \(1.37427 + 2.38031i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.b.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.10551 - 1.76673i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(-1.23778 - 2.14391i) q^{7} +(0.790885 + 4.48533i) q^{9} +O(q^{10})\) \(q+(-2.10551 - 1.76673i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(-1.23778 - 2.14391i) q^{7} +(0.790885 + 4.48533i) q^{9} +(0.186396 - 0.322847i) q^{11} +(-2.64101 + 2.21607i) q^{13} +(2.58279 + 0.940059i) q^{15} +(-0.361680 + 2.05119i) q^{17} +(0.0754994 + 4.35825i) q^{19} +(-1.18154 + 6.70085i) q^{21} +(-0.815458 - 0.296802i) q^{23} +(0.766044 - 0.642788i) q^{25} +(2.13635 - 3.70026i) q^{27} +(1.80276 + 10.2240i) q^{29} +(-0.935507 - 1.62035i) q^{31} +(-0.962842 + 0.350446i) q^{33} +(1.89640 + 1.59127i) q^{35} -6.21229 q^{37} +9.47590 q^{39} +(-6.08529 - 5.10617i) q^{41} +(-3.27429 + 1.19174i) q^{43} +(-2.27726 - 3.94434i) q^{45} +(-0.871070 - 4.94008i) q^{47} +(0.435777 - 0.754789i) q^{49} +(4.38543 - 3.67981i) q^{51} +(7.54214 + 2.74511i) q^{53} +(-0.0647345 + 0.367128i) q^{55} +(7.54089 - 9.30972i) q^{57} +(-1.44337 + 8.18576i) q^{59} +(-12.1477 - 4.42141i) q^{61} +(8.63719 - 7.24746i) q^{63} +(1.72380 - 2.98571i) q^{65} +(-1.28954 - 7.31335i) q^{67} +(1.19258 + 2.06562i) q^{69} +(-2.31925 + 0.844139i) q^{71} +(-3.87343 - 3.25019i) q^{73} -2.74855 q^{75} -0.922870 q^{77} +(-11.9174 - 9.99989i) q^{79} +(1.80409 - 0.656635i) q^{81} +(-3.14735 - 5.45137i) q^{83} +(-0.361680 - 2.05119i) q^{85} +(14.2673 - 24.7117i) q^{87} +(-0.811454 + 0.680891i) q^{89} +(8.02006 + 2.91906i) q^{91} +(-0.892999 + 5.06445i) q^{93} +(-1.56155 - 4.06959i) q^{95} +(-2.49008 + 14.1219i) q^{97} +(1.59549 + 0.580711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\)

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
\(3\) −2.10551 1.76673i −1.21562 1.02002i −0.999042 0.0437583i \(-0.986067\pi\)
−0.216575 0.976266i \(-0.569489\pi\)
\(4\) 0 0
\(5\) −0.939693 + 0.342020i −0.420243 + 0.152956i
\(6\) 0 0
\(7\) −1.23778 2.14391i −0.467839 0.810320i 0.531486 0.847067i \(-0.321634\pi\)
−0.999325 + 0.0367467i \(0.988301\pi\)
\(8\) 0 0
\(9\) 0.790885 + 4.48533i 0.263628 + 1.49511i
\(10\) 0 0
\(11\) 0.186396 0.322847i 0.0562004 0.0973419i −0.836556 0.547881i \(-0.815435\pi\)
0.892757 + 0.450539i \(0.148768\pi\)
\(12\) 0 0
\(13\) −2.64101 + 2.21607i −0.732486 + 0.614628i −0.930808 0.365508i \(-0.880895\pi\)
0.198322 + 0.980137i \(0.436451\pi\)
\(14\) 0 0
\(15\) 2.58279 + 0.940059i 0.666874 + 0.242722i
\(16\) 0 0
\(17\) −0.361680 + 2.05119i −0.0877204 + 0.497487i 0.909016 + 0.416761i \(0.136835\pi\)
−0.996736 + 0.0807258i \(0.974276\pi\)
\(18\) 0 0
\(19\) 0.0754994 + 4.35825i 0.0173208 + 0.999850i
\(20\) 0 0
\(21\) −1.18154 + 6.70085i −0.257833 + 1.46225i
\(22\) 0 0
\(23\) −0.815458 0.296802i −0.170035 0.0618876i 0.255600 0.966783i \(-0.417727\pi\)
−0.425635 + 0.904895i \(0.639949\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) 2.13635 3.70026i 0.411140 0.712115i
\(28\) 0 0
\(29\) 1.80276 + 10.2240i 0.334764 + 1.89854i 0.429547 + 0.903044i \(0.358673\pi\)
−0.0947830 + 0.995498i \(0.530216\pi\)
\(30\) 0 0
\(31\) −0.935507 1.62035i −0.168022 0.291023i 0.769702 0.638403i \(-0.220405\pi\)
−0.937724 + 0.347380i \(0.887071\pi\)
\(32\) 0 0
\(33\) −0.962842 + 0.350446i −0.167609 + 0.0610048i
\(34\) 0 0
\(35\) 1.89640 + 1.59127i 0.320549 + 0.268973i
\(36\) 0 0
\(37\) −6.21229 −1.02129 −0.510647 0.859790i \(-0.670594\pi\)
−0.510647 + 0.859790i \(0.670594\pi\)
\(38\) 0 0
\(39\) 9.47590 1.51736
\(40\) 0 0
\(41\) −6.08529 5.10617i −0.950363 0.797449i 0.0289956 0.999580i \(-0.490769\pi\)
−0.979359 + 0.202130i \(0.935214\pi\)
\(42\) 0 0
\(43\) −3.27429 + 1.19174i −0.499324 + 0.181739i −0.579390 0.815050i \(-0.696709\pi\)
0.0800658 + 0.996790i \(0.474487\pi\)
\(44\) 0 0
\(45\) −2.27726 3.94434i −0.339474 0.587987i
\(46\) 0 0
\(47\) −0.871070 4.94008i −0.127059 0.720585i −0.980064 0.198683i \(-0.936334\pi\)
0.853005 0.521902i \(-0.174777\pi\)
\(48\) 0 0
\(49\) 0.435777 0.754789i 0.0622539 0.107827i
\(50\) 0 0
\(51\) 4.38543 3.67981i 0.614083 0.515277i
\(52\) 0 0
\(53\) 7.54214 + 2.74511i 1.03599 + 0.377070i 0.803360 0.595494i \(-0.203044\pi\)
0.232633 + 0.972565i \(0.425266\pi\)
\(54\) 0 0
\(55\) −0.0647345 + 0.367128i −0.00872880 + 0.0495035i
\(56\) 0 0
\(57\) 7.54089 9.30972i 0.998816 1.23310i
\(58\) 0 0
\(59\) −1.44337 + 8.18576i −0.187911 + 1.06569i 0.734248 + 0.678882i \(0.237535\pi\)
−0.922158 + 0.386813i \(0.873576\pi\)
\(60\) 0 0
\(61\) −12.1477 4.42141i −1.55536 0.566104i −0.585691 0.810535i \(-0.699177\pi\)
−0.969667 + 0.244431i \(0.921399\pi\)
\(62\) 0 0
\(63\) 8.63719 7.24746i 1.08818 0.913094i
\(64\) 0 0
\(65\) 1.72380 2.98571i 0.213811 0.370332i
\(66\) 0 0
\(67\) −1.28954 7.31335i −0.157543 0.893468i −0.956424 0.291980i \(-0.905686\pi\)
0.798882 0.601488i \(-0.205425\pi\)
\(68\) 0 0
\(69\) 1.19258 + 2.06562i 0.143570 + 0.248671i
\(70\) 0 0
\(71\) −2.31925 + 0.844139i −0.275245 + 0.100181i −0.475955 0.879470i \(-0.657897\pi\)
0.200710 + 0.979651i \(0.435675\pi\)
\(72\) 0 0
\(73\) −3.87343 3.25019i −0.453350 0.380406i 0.387327 0.921942i \(-0.373398\pi\)
−0.840677 + 0.541536i \(0.817843\pi\)
\(74\) 0 0
\(75\) −2.74855 −0.317375
\(76\) 0 0
\(77\) −0.922870 −0.105171
\(78\) 0 0
\(79\) −11.9174 9.99989i −1.34081 1.12508i −0.981416 0.191891i \(-0.938538\pi\)
−0.359397 0.933185i \(-0.617018\pi\)
\(80\) 0 0
\(81\) 1.80409 0.656635i 0.200454 0.0729594i
\(82\) 0 0
\(83\) −3.14735 5.45137i −0.345467 0.598366i 0.639972 0.768398i \(-0.278946\pi\)
−0.985438 + 0.170033i \(0.945613\pi\)
\(84\) 0 0
\(85\) −0.361680 2.05119i −0.0392298 0.222483i
\(86\) 0 0
\(87\) 14.2673 24.7117i 1.52961 2.64937i
\(88\) 0 0
\(89\) −0.811454 + 0.680891i −0.0860140 + 0.0721743i −0.684781 0.728749i \(-0.740102\pi\)
0.598767 + 0.800923i \(0.295658\pi\)
\(90\) 0 0
\(91\) 8.02006 + 2.91906i 0.840731 + 0.306001i
\(92\) 0 0
\(93\) −0.892999 + 5.06445i −0.0925996 + 0.525159i
\(94\) 0 0
\(95\) −1.56155 4.06959i −0.160212 0.417531i
\(96\) 0 0
\(97\) −2.49008 + 14.1219i −0.252829 + 1.43387i 0.548755 + 0.835983i \(0.315102\pi\)
−0.801584 + 0.597882i \(0.796009\pi\)
\(98\) 0 0
\(99\) 1.59549 + 0.580711i 0.160353 + 0.0583637i
\(100\) 0 0
\(101\) 13.1480 11.0324i 1.30827 1.09777i 0.319618 0.947546i \(-0.396445\pi\)
0.988652 0.150223i \(-0.0479991\pi\)
\(102\) 0 0
\(103\) −9.36128 + 16.2142i −0.922394 + 1.59763i −0.126695 + 0.991942i \(0.540437\pi\)
−0.795699 + 0.605692i \(0.792896\pi\)
\(104\) 0 0
\(105\) −1.18154 6.70085i −0.115307 0.653936i
\(106\) 0 0
\(107\) 0.706719 + 1.22407i 0.0683211 + 0.118336i 0.898162 0.439664i \(-0.144902\pi\)
−0.829841 + 0.557999i \(0.811569\pi\)
\(108\) 0 0
\(109\) −11.6749 + 4.24930i −1.11825 + 0.407009i −0.834013 0.551745i \(-0.813962\pi\)
−0.284236 + 0.958754i \(0.591740\pi\)
\(110\) 0 0
\(111\) 13.0800 + 10.9755i 1.24150 + 1.04174i
\(112\) 0 0
\(113\) 10.6415 1.00107 0.500536 0.865716i \(-0.333136\pi\)
0.500536 + 0.865716i \(0.333136\pi\)
\(114\) 0 0
\(115\) 0.867792 0.0809220
\(116\) 0 0
\(117\) −12.0286 10.0932i −1.11204 0.933114i
\(118\) 0 0
\(119\) 4.84525 1.76352i 0.444163 0.161662i
\(120\) 0 0
\(121\) 5.43051 + 9.40593i 0.493683 + 0.855084i
\(122\) 0 0
\(123\) 3.79142 + 21.5022i 0.341860 + 1.93879i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −0.188463 + 0.158139i −0.0167234 + 0.0140326i −0.651111 0.758983i \(-0.725697\pi\)
0.634388 + 0.773015i \(0.281252\pi\)
\(128\) 0 0
\(129\) 8.99954 + 3.27557i 0.792365 + 0.288397i
\(130\) 0 0
\(131\) −1.50790 + 8.55170i −0.131745 + 0.747165i 0.845326 + 0.534252i \(0.179406\pi\)
−0.977071 + 0.212914i \(0.931705\pi\)
\(132\) 0 0
\(133\) 9.25022 5.55643i 0.802095 0.481804i
\(134\) 0 0
\(135\) −0.741945 + 4.20778i −0.0638565 + 0.362148i
\(136\) 0 0
\(137\) 12.9469 + 4.71230i 1.10613 + 0.402599i 0.829573 0.558398i \(-0.188584\pi\)
0.276559 + 0.960997i \(0.410806\pi\)
\(138\) 0 0
\(139\) 3.85051 3.23096i 0.326596 0.274047i −0.464715 0.885460i \(-0.653843\pi\)
0.791311 + 0.611414i \(0.209399\pi\)
\(140\) 0 0
\(141\) −6.89376 + 11.9403i −0.580559 + 1.00556i
\(142\) 0 0
\(143\) 0.223179 + 1.26571i 0.0186631 + 0.105844i
\(144\) 0 0
\(145\) −5.19084 8.99080i −0.431076 0.746646i
\(146\) 0 0
\(147\) −2.25105 + 0.819313i −0.185663 + 0.0675758i
\(148\) 0 0
\(149\) −12.1638 10.2066i −0.996496 0.836159i −0.0100007 0.999950i \(-0.503183\pi\)
−0.986495 + 0.163791i \(0.947628\pi\)
\(150\) 0 0
\(151\) 7.84823 0.638680 0.319340 0.947640i \(-0.396539\pi\)
0.319340 + 0.947640i \(0.396539\pi\)
\(152\) 0 0
\(153\) −9.48632 −0.766924
\(154\) 0 0
\(155\) 1.43328 + 1.20266i 0.115124 + 0.0966003i
\(156\) 0 0
\(157\) −12.4130 + 4.51795i −0.990662 + 0.360572i −0.785977 0.618256i \(-0.787839\pi\)
−0.204686 + 0.978828i \(0.565617\pi\)
\(158\) 0 0
\(159\) −11.0302 19.1048i −0.874750 1.51511i
\(160\) 0 0
\(161\) 0.373045 + 2.11564i 0.0294001 + 0.166736i
\(162\) 0 0
\(163\) −2.03055 + 3.51702i −0.159045 + 0.275474i −0.934525 0.355898i \(-0.884175\pi\)
0.775479 + 0.631373i \(0.217508\pi\)
\(164\) 0 0
\(165\) 0.784916 0.658623i 0.0611056 0.0512737i
\(166\) 0 0
\(167\) −23.3720 8.50671i −1.80858 0.658269i −0.997286 0.0736309i \(-0.976541\pi\)
−0.811294 0.584638i \(-0.801236\pi\)
\(168\) 0 0
\(169\) −0.193455 + 1.09714i −0.0148811 + 0.0843950i
\(170\) 0 0
\(171\) −19.4885 + 3.78551i −1.49032 + 0.289485i
\(172\) 0 0
\(173\) −0.714147 + 4.05013i −0.0542956 + 0.307926i −0.999846 0.0175502i \(-0.994413\pi\)
0.945550 + 0.325476i \(0.105524\pi\)
\(174\) 0 0
\(175\) −2.32627 0.846695i −0.175850 0.0640041i
\(176\) 0 0
\(177\) 17.5011 14.6852i 1.31546 1.10380i
\(178\) 0 0
\(179\) −10.4256 + 18.0577i −0.779249 + 1.34970i 0.153126 + 0.988207i \(0.451066\pi\)
−0.932375 + 0.361492i \(0.882267\pi\)
\(180\) 0 0
\(181\) −3.38402 19.1918i −0.251533 1.42651i −0.804819 0.593521i \(-0.797737\pi\)
0.553286 0.832991i \(-0.313374\pi\)
\(182\) 0 0
\(183\) 17.7657 + 30.7711i 1.31328 + 2.27467i
\(184\) 0 0
\(185\) 5.83764 2.12473i 0.429192 0.156213i
\(186\) 0 0
\(187\) 0.594805 + 0.499100i 0.0434964 + 0.0364978i
\(188\) 0 0
\(189\) −10.5773 −0.769389
\(190\) 0 0
\(191\) 6.58959 0.476806 0.238403 0.971166i \(-0.423376\pi\)
0.238403 + 0.971166i \(0.423376\pi\)
\(192\) 0 0
\(193\) −15.7958 13.2543i −1.13701 0.954064i −0.137673 0.990478i \(-0.543962\pi\)
−0.999337 + 0.0364135i \(0.988407\pi\)
\(194\) 0 0
\(195\) −8.90443 + 3.24095i −0.637660 + 0.232089i
\(196\) 0 0
\(197\) 10.9479 + 18.9623i 0.780004 + 1.35101i 0.931938 + 0.362616i \(0.118116\pi\)
−0.151934 + 0.988391i \(0.548550\pi\)
\(198\) 0 0
\(199\) 0.141474 + 0.802338i 0.0100288 + 0.0568762i 0.989411 0.145138i \(-0.0463625\pi\)
−0.979383 + 0.202014i \(0.935251\pi\)
\(200\) 0 0
\(201\) −10.2056 + 17.6766i −0.719848 + 1.24681i
\(202\) 0 0
\(203\) 19.6878 16.5200i 1.38181 1.15948i
\(204\) 0 0
\(205\) 7.46472 + 2.71693i 0.521358 + 0.189759i
\(206\) 0 0
\(207\) 0.686324 3.89234i 0.0477028 0.270536i
\(208\) 0 0
\(209\) 1.42112 + 0.787983i 0.0983007 + 0.0545059i
\(210\) 0 0
\(211\) 1.55282 8.80649i 0.106901 0.606264i −0.883543 0.468349i \(-0.844849\pi\)
0.990444 0.137915i \(-0.0440400\pi\)
\(212\) 0 0
\(213\) 6.37458 + 2.32016i 0.436779 + 0.158975i
\(214\) 0 0
\(215\) 2.66922 2.23974i 0.182040 0.152749i
\(216\) 0 0
\(217\) −2.31591 + 4.01128i −0.157214 + 0.272303i
\(218\) 0 0
\(219\) 2.41332 + 13.6866i 0.163077 + 0.924856i
\(220\) 0 0
\(221\) −3.59039 6.21874i −0.241516 0.418318i
\(222\) 0 0
\(223\) −7.48167 + 2.72311i −0.501010 + 0.182353i −0.580148 0.814511i \(-0.697005\pi\)
0.0791384 + 0.996864i \(0.474783\pi\)
\(224\) 0 0
\(225\) 3.48897 + 2.92759i 0.232598 + 0.195173i
\(226\) 0 0
\(227\) −11.5327 −0.765453 −0.382727 0.923862i \(-0.625015\pi\)
−0.382727 + 0.923862i \(0.625015\pi\)
\(228\) 0 0
\(229\) −1.84953 −0.122220 −0.0611102 0.998131i \(-0.519464\pi\)
−0.0611102 + 0.998131i \(0.519464\pi\)
\(230\) 0 0
\(231\) 1.94311 + 1.63047i 0.127848 + 0.107277i
\(232\) 0 0
\(233\) 19.4029 7.06206i 1.27112 0.462651i 0.383637 0.923484i \(-0.374671\pi\)
0.887487 + 0.460833i \(0.152449\pi\)
\(234\) 0 0
\(235\) 2.50814 + 4.34423i 0.163613 + 0.283387i
\(236\) 0 0
\(237\) 7.42509 + 42.1098i 0.482311 + 2.73532i
\(238\) 0 0
\(239\) 12.3934 21.4659i 0.801660 1.38852i −0.116863 0.993148i \(-0.537284\pi\)
0.918523 0.395368i \(-0.129383\pi\)
\(240\) 0 0
\(241\) 12.3502 10.3631i 0.795548 0.667544i −0.151564 0.988447i \(-0.548431\pi\)
0.947112 + 0.320904i \(0.103987\pi\)
\(242\) 0 0
\(243\) −17.0037 6.18883i −1.09079 0.397014i
\(244\) 0 0
\(245\) −0.151344 + 0.858314i −0.00966901 + 0.0548357i
\(246\) 0 0
\(247\) −9.85759 11.3429i −0.627223 0.721730i
\(248\) 0 0
\(249\) −3.00434 + 17.0385i −0.190392 + 1.07977i
\(250\) 0 0
\(251\) −16.0425 5.83899i −1.01259 0.368554i −0.218165 0.975912i \(-0.570007\pi\)
−0.794428 + 0.607358i \(0.792229\pi\)
\(252\) 0 0
\(253\) −0.247819 + 0.207945i −0.0155803 + 0.0130734i
\(254\) 0 0
\(255\) −2.86239 + 4.95780i −0.179250 + 0.310469i
\(256\) 0 0
\(257\) 0.202646 + 1.14926i 0.0126407 + 0.0716890i 0.990476 0.137689i \(-0.0439673\pi\)
−0.977835 + 0.209378i \(0.932856\pi\)
\(258\) 0 0
\(259\) 7.68948 + 13.3186i 0.477801 + 0.827576i
\(260\) 0 0
\(261\) −44.4321 + 16.1720i −2.75028 + 1.00102i
\(262\) 0 0
\(263\) 7.18738 + 6.03093i 0.443193 + 0.371883i 0.836903 0.547352i \(-0.184364\pi\)
−0.393710 + 0.919235i \(0.628809\pi\)
\(264\) 0 0
\(265\) −8.02618 −0.493044
\(266\) 0 0
\(267\) 2.91148 0.178180
\(268\) 0 0
\(269\) 5.63696 + 4.72997i 0.343692 + 0.288392i 0.798251 0.602325i \(-0.205759\pi\)
−0.454559 + 0.890716i \(0.650203\pi\)
\(270\) 0 0
\(271\) −10.0761 + 3.66739i −0.612078 + 0.222778i −0.629412 0.777071i \(-0.716704\pi\)
0.0173340 + 0.999850i \(0.494482\pi\)
\(272\) 0 0
\(273\) −11.7291 20.3154i −0.709879 1.22955i
\(274\) 0 0
\(275\) −0.0647345 0.367128i −0.00390364 0.0221386i
\(276\) 0 0
\(277\) 8.06323 13.9659i 0.484472 0.839131i −0.515369 0.856969i \(-0.672345\pi\)
0.999841 + 0.0178380i \(0.00567832\pi\)
\(278\) 0 0
\(279\) 6.52791 5.47757i 0.390816 0.327933i
\(280\) 0 0
\(281\) 28.7858 + 10.4772i 1.71722 + 0.625016i 0.997593 0.0693473i \(-0.0220917\pi\)
0.719625 + 0.694363i \(0.244314\pi\)
\(282\) 0 0
\(283\) −0.924150 + 5.24111i −0.0549350 + 0.311552i −0.999877 0.0156861i \(-0.995007\pi\)
0.944942 + 0.327238i \(0.106118\pi\)
\(284\) 0 0
\(285\) −3.90201 + 11.3274i −0.231135 + 0.670978i
\(286\) 0 0
\(287\) −3.41486 + 19.3666i −0.201573 + 1.14318i
\(288\) 0 0
\(289\) 11.8982 + 4.33059i 0.699894 + 0.254741i
\(290\) 0 0
\(291\) 30.1926 25.3346i 1.76992 1.48514i
\(292\) 0 0
\(293\) −1.76580 + 3.05845i −0.103159 + 0.178677i −0.912985 0.407994i \(-0.866228\pi\)
0.809826 + 0.586671i \(0.199562\pi\)
\(294\) 0 0
\(295\) −1.44337 8.18576i −0.0840362 0.476593i
\(296\) 0 0
\(297\) −0.796411 1.37942i −0.0462124 0.0800423i
\(298\) 0 0
\(299\) 2.81137 1.02326i 0.162586 0.0591764i
\(300\) 0 0
\(301\) 6.60785 + 5.54464i 0.380870 + 0.319588i
\(302\) 0 0
\(303\) −47.1746 −2.71011
\(304\) 0 0
\(305\) 12.9273 0.740218
\(306\) 0 0
\(307\) 16.1951 + 13.5893i 0.924303 + 0.775582i 0.974786 0.223143i \(-0.0716316\pi\)
−0.0504828 + 0.998725i \(0.516076\pi\)
\(308\) 0 0
\(309\) 48.3565 17.6003i 2.75090 1.00125i
\(310\) 0 0
\(311\) −3.60633 6.24635i −0.204496 0.354198i 0.745476 0.666533i \(-0.232222\pi\)
−0.949972 + 0.312335i \(0.898889\pi\)
\(312\) 0 0
\(313\) −3.08980 17.5231i −0.174646 0.990465i −0.938552 0.345138i \(-0.887832\pi\)
0.763906 0.645327i \(-0.223279\pi\)
\(314\) 0 0
\(315\) −5.63752 + 9.76448i −0.317638 + 0.550166i
\(316\) 0 0
\(317\) −17.5594 + 14.7341i −0.986237 + 0.827551i −0.985019 0.172448i \(-0.944832\pi\)
−0.00121811 + 0.999999i \(0.500388\pi\)
\(318\) 0 0
\(319\) 3.63680 + 1.32369i 0.203622 + 0.0741122i
\(320\) 0 0
\(321\) 0.674606 3.82588i 0.0376529 0.213540i
\(322\) 0 0
\(323\) −8.96690 1.42143i −0.498932 0.0790904i
\(324\) 0 0
\(325\) −0.598669 + 3.39522i −0.0332082 + 0.188333i
\(326\) 0 0
\(327\) 32.0889 + 11.6794i 1.77452 + 0.645873i
\(328\) 0 0
\(329\) −9.51287 + 7.98225i −0.524462 + 0.440076i
\(330\) 0 0
\(331\) 16.0847 27.8595i 0.884095 1.53130i 0.0373483 0.999302i \(-0.488109\pi\)
0.846747 0.531996i \(-0.178558\pi\)
\(332\) 0 0
\(333\) −4.91321 27.8642i −0.269242 1.52695i
\(334\) 0 0
\(335\) 3.71309 + 6.43126i 0.202868 + 0.351377i
\(336\) 0 0
\(337\) 21.8033 7.93577i 1.18770 0.432289i 0.328787 0.944404i \(-0.393360\pi\)
0.858917 + 0.512115i \(0.171138\pi\)
\(338\) 0 0
\(339\) −22.4059 18.8008i −1.21692 1.02112i
\(340\) 0 0
\(341\) −0.697497 −0.0377716
\(342\) 0 0
\(343\) −19.4866 −1.05218
\(344\) 0 0
\(345\) −1.82715 1.53316i −0.0983702 0.0825424i
\(346\) 0 0
\(347\) 12.9601 4.71711i 0.695737 0.253228i 0.0301473 0.999545i \(-0.490402\pi\)
0.665590 + 0.746318i \(0.268180\pi\)
\(348\) 0 0
\(349\) −0.487253 0.843948i −0.0260821 0.0451755i 0.852690 0.522418i \(-0.174970\pi\)
−0.878772 + 0.477242i \(0.841636\pi\)
\(350\) 0 0
\(351\) 2.55793 + 14.5067i 0.136532 + 0.774312i
\(352\) 0 0
\(353\) 7.30765 12.6572i 0.388947 0.673676i −0.603361 0.797468i \(-0.706172\pi\)
0.992308 + 0.123792i \(0.0395057\pi\)
\(354\) 0 0
\(355\) 1.89067 1.58646i 0.100346 0.0842007i
\(356\) 0 0
\(357\) −13.3174 4.84714i −0.704831 0.256538i
\(358\) 0 0
\(359\) 0.311258 1.76523i 0.0164276 0.0931653i −0.975492 0.220036i \(-0.929382\pi\)
0.991919 + 0.126871i \(0.0404935\pi\)
\(360\) 0 0
\(361\) −18.9886 + 0.658090i −0.999400 + 0.0346363i
\(362\) 0 0
\(363\) 5.18376 29.3986i 0.272077 1.54302i
\(364\) 0 0
\(365\) 4.75146 + 1.72939i 0.248703 + 0.0905204i
\(366\) 0 0
\(367\) −25.2610 + 21.1965i −1.31861 + 1.10645i −0.332015 + 0.943274i \(0.607728\pi\)
−0.986597 + 0.163173i \(0.947827\pi\)
\(368\) 0 0
\(369\) 18.0901 31.3330i 0.941732 1.63113i
\(370\) 0 0
\(371\) −3.45028 19.5675i −0.179130 1.01589i
\(372\) 0 0
\(373\) −9.08808 15.7410i −0.470563 0.815039i 0.528870 0.848703i \(-0.322616\pi\)
−0.999433 + 0.0336640i \(0.989282\pi\)
\(374\) 0 0
\(375\) 2.58279 0.940059i 0.133375 0.0485445i
\(376\) 0 0
\(377\) −27.4182 23.0066i −1.41211 1.18490i
\(378\) 0 0
\(379\) −1.90439 −0.0978220 −0.0489110 0.998803i \(-0.515575\pi\)
−0.0489110 + 0.998803i \(0.515575\pi\)
\(380\) 0 0
\(381\) 0.676201 0.0346428
\(382\) 0 0
\(383\) 1.42516 + 1.19585i 0.0728221 + 0.0611050i 0.678472 0.734626i \(-0.262642\pi\)
−0.605650 + 0.795731i \(0.707087\pi\)
\(384\) 0 0
\(385\) 0.867214 0.315640i 0.0441973 0.0160865i
\(386\) 0 0
\(387\) −7.93495 13.7437i −0.403356 0.698633i
\(388\) 0 0
\(389\) −1.24054 7.03542i −0.0628976 0.356710i −0.999971 0.00757846i \(-0.997588\pi\)
0.937074 0.349132i \(-0.113523\pi\)
\(390\) 0 0
\(391\) 0.903734 1.56531i 0.0457038 0.0791613i
\(392\) 0 0
\(393\) 18.2835 15.3417i 0.922279 0.773884i
\(394\) 0 0
\(395\) 14.6189 + 5.32083i 0.735555 + 0.267720i
\(396\) 0 0
\(397\) 4.23145 23.9977i 0.212370 1.20441i −0.673041 0.739605i \(-0.735012\pi\)
0.885412 0.464807i \(-0.153876\pi\)
\(398\) 0 0
\(399\) −29.2932 4.64354i −1.46649 0.232468i
\(400\) 0 0
\(401\) 1.86333 10.5675i 0.0930504 0.527715i −0.902277 0.431157i \(-0.858106\pi\)
0.995327 0.0965581i \(-0.0307833\pi\)
\(402\) 0 0
\(403\) 6.06149 + 2.20620i 0.301944 + 0.109899i
\(404\) 0 0
\(405\) −1.47071 + 1.23407i −0.0730800 + 0.0613214i
\(406\) 0 0
\(407\) −1.15794 + 2.00562i −0.0573971 + 0.0994147i
\(408\) 0 0
\(409\) −2.17903 12.3579i −0.107746 0.611058i −0.990088 0.140449i \(-0.955145\pi\)
0.882342 0.470609i \(-0.155966\pi\)
\(410\) 0 0
\(411\) −18.9346 32.7956i −0.933973 1.61769i
\(412\) 0 0
\(413\) 19.3361 7.03776i 0.951466 0.346305i
\(414\) 0 0
\(415\) 4.82202 + 4.04616i 0.236704 + 0.198618i
\(416\) 0 0
\(417\) −13.8156 −0.676550
\(418\) 0 0
\(419\) 28.0502 1.37034 0.685171 0.728383i \(-0.259728\pi\)
0.685171 + 0.728383i \(0.259728\pi\)
\(420\) 0 0
\(421\) 16.0840 + 13.4961i 0.783885 + 0.657758i 0.944224 0.329304i \(-0.106814\pi\)
−0.160339 + 0.987062i \(0.551259\pi\)
\(422\) 0 0
\(423\) 21.4690 7.81407i 1.04386 0.379933i
\(424\) 0 0
\(425\) 1.04142 + 1.80379i 0.0505162 + 0.0874966i
\(426\) 0 0
\(427\) 5.55718 + 31.5164i 0.268931 + 1.52518i
\(428\) 0 0
\(429\) 1.76627 3.05926i 0.0852761 0.147703i
\(430\) 0 0
\(431\) −18.9587 + 15.9082i −0.913207 + 0.766271i −0.972726 0.231956i \(-0.925488\pi\)
0.0595196 + 0.998227i \(0.481043\pi\)
\(432\) 0 0
\(433\) 29.6829 + 10.8037i 1.42647 + 0.519192i 0.935917 0.352219i \(-0.114573\pi\)
0.490552 + 0.871412i \(0.336795\pi\)
\(434\) 0 0
\(435\) −4.95498 + 28.1011i −0.237573 + 1.34734i
\(436\) 0 0
\(437\) 1.23197 3.57637i 0.0589332 0.171081i
\(438\) 0 0
\(439\) −0.765999 + 4.34420i −0.0365591 + 0.207337i −0.997616 0.0690148i \(-0.978014\pi\)
0.961056 + 0.276352i \(0.0891255\pi\)
\(440\) 0 0
\(441\) 3.73013 + 1.35766i 0.177625 + 0.0646503i
\(442\) 0 0
\(443\) −20.2239 + 16.9699i −0.960868 + 0.806264i −0.981094 0.193531i \(-0.938006\pi\)
0.0202259 + 0.999795i \(0.493561\pi\)
\(444\) 0 0
\(445\) 0.529639 0.917362i 0.0251073 0.0434871i
\(446\) 0 0
\(447\) 7.57859 + 42.9803i 0.358455 + 2.03290i
\(448\) 0 0
\(449\) −2.30028 3.98419i −0.108557 0.188026i 0.806629 0.591058i \(-0.201290\pi\)
−0.915186 + 0.403032i \(0.867956\pi\)
\(450\) 0 0
\(451\) −2.78278 + 1.01285i −0.131036 + 0.0476932i
\(452\) 0 0
\(453\) −16.5245 13.8657i −0.776390 0.651469i
\(454\) 0 0
\(455\) −8.53477 −0.400116
\(456\) 0 0
\(457\) −30.9048 −1.44566 −0.722832 0.691024i \(-0.757160\pi\)
−0.722832 + 0.691024i \(0.757160\pi\)
\(458\) 0 0
\(459\) 6.81727 + 5.72037i 0.318203 + 0.267004i
\(460\) 0 0
\(461\) −1.86577 + 0.679084i −0.0868975 + 0.0316281i −0.385103 0.922874i \(-0.625834\pi\)
0.298206 + 0.954502i \(0.403612\pi\)
\(462\) 0 0
\(463\) 15.2283 + 26.3762i 0.707719 + 1.22581i 0.965701 + 0.259656i \(0.0836091\pi\)
−0.257982 + 0.966150i \(0.583058\pi\)
\(464\) 0 0
\(465\) −0.892999 5.06445i −0.0414118 0.234858i
\(466\) 0 0
\(467\) 2.51096 4.34911i 0.116193 0.201253i −0.802063 0.597240i \(-0.796264\pi\)
0.918256 + 0.395987i \(0.129597\pi\)
\(468\) 0 0
\(469\) −14.0830 + 11.8170i −0.650291 + 0.545659i
\(470\) 0 0
\(471\) 34.1177 + 12.4178i 1.57206 + 0.572182i
\(472\) 0 0
\(473\) −0.225562 + 1.27923i −0.0103714 + 0.0588190i
\(474\) 0 0
\(475\) 2.85926 + 3.29008i 0.131192 + 0.150959i
\(476\) 0 0
\(477\) −6.34778 + 36.0001i −0.290645 + 1.64833i
\(478\) 0 0
\(479\) −18.3361 6.67381i −0.837800 0.304934i −0.112744 0.993624i \(-0.535964\pi\)
−0.725056 + 0.688690i \(0.758186\pi\)
\(480\) 0 0
\(481\) 16.4067 13.7669i 0.748083 0.627716i
\(482\) 0 0
\(483\) 2.95233 5.11358i 0.134336 0.232676i
\(484\) 0 0
\(485\) −2.49008 14.1219i −0.113069 0.641244i
\(486\) 0 0
\(487\) 20.0327 + 34.6977i 0.907770 + 1.57230i 0.817155 + 0.576419i \(0.195550\pi\)
0.0906158 + 0.995886i \(0.471116\pi\)
\(488\) 0 0
\(489\) 10.4890 3.81768i 0.474329 0.172642i
\(490\) 0 0
\(491\) −19.6384 16.4785i −0.886267 0.743666i 0.0811912 0.996699i \(-0.474128\pi\)
−0.967458 + 0.253033i \(0.918572\pi\)
\(492\) 0 0
\(493\) −21.6233 −0.973866
\(494\) 0 0
\(495\) −1.69789 −0.0763143
\(496\) 0 0
\(497\) 4.68049 + 3.92740i 0.209949 + 0.176168i
\(498\) 0 0
\(499\) −15.9733 + 5.81381i −0.715064 + 0.260262i −0.673829 0.738887i \(-0.735351\pi\)
−0.0412351 + 0.999149i \(0.513129\pi\)
\(500\) 0 0
\(501\) 34.1809 + 59.2031i 1.52709 + 2.64500i
\(502\) 0 0
\(503\) 6.12040 + 34.7105i 0.272895 + 1.54767i 0.745569 + 0.666428i \(0.232178\pi\)
−0.472674 + 0.881237i \(0.656711\pi\)
\(504\) 0 0
\(505\) −8.58172 + 14.8640i −0.381881 + 0.661438i
\(506\) 0 0
\(507\) 2.34567 1.96825i 0.104175 0.0874130i
\(508\) 0 0
\(509\) −13.6138 4.95503i −0.603422 0.219628i 0.0222005 0.999754i \(-0.492933\pi\)
−0.625623 + 0.780126i \(0.715155\pi\)
\(510\) 0 0
\(511\) −2.17364 + 12.3273i −0.0961560 + 0.545328i
\(512\) 0 0
\(513\) 16.2879 + 9.03135i 0.719130 + 0.398744i
\(514\) 0 0
\(515\) 3.25114 18.4381i 0.143262 0.812481i
\(516\) 0 0
\(517\) −1.75725 0.639587i −0.0772838 0.0281290i
\(518\) 0 0
\(519\) 8.65914 7.26588i 0.380094 0.318937i
\(520\) 0 0
\(521\) −12.5675 + 21.7676i −0.550593 + 0.953655i 0.447639 + 0.894214i \(0.352265\pi\)
−0.998232 + 0.0594407i \(0.981068\pi\)
\(522\) 0 0
\(523\) −5.70365 32.3470i −0.249403 1.41444i −0.810040 0.586374i \(-0.800555\pi\)
0.560637 0.828062i \(-0.310556\pi\)
\(524\) 0 0
\(525\) 3.40211 + 5.89263i 0.148480 + 0.257176i
\(526\) 0 0
\(527\) 3.66199 1.33286i 0.159519 0.0580601i
\(528\) 0 0
\(529\) −17.0421 14.3001i −0.740963 0.621742i
\(530\) 0 0
\(531\) −37.8574 −1.64287
\(532\) 0 0
\(533\) 27.3870 1.18626
\(534\) 0 0
\(535\) −1.08276 0.908540i −0.0468116 0.0392796i
\(536\) 0 0
\(537\) 53.8545 19.6014i 2.32399 0.845865i
\(538\) 0 0
\(539\) −0.162454 0.281379i −0.00699739 0.0121198i
\(540\) 0 0
\(541\) −2.04353 11.5894i −0.0878583 0.498269i −0.996703 0.0811349i \(-0.974146\pi\)
0.908845 0.417134i \(-0.136966\pi\)
\(542\) 0 0
\(543\) −26.7816 + 46.3871i −1.14931 + 1.99066i
\(544\) 0 0
\(545\) 9.51744 7.98608i 0.407682 0.342086i
\(546\) 0 0
\(547\) −3.82799 1.39327i −0.163673 0.0595721i 0.258884 0.965908i \(-0.416645\pi\)
−0.422557 + 0.906336i \(0.638867\pi\)
\(548\) 0 0
\(549\) 10.2240 57.9834i 0.436352 2.47467i
\(550\) 0 0
\(551\) −44.4224 + 8.62878i −1.89246 + 0.367598i
\(552\) 0 0
\(553\) −6.68765 + 37.9275i −0.284388 + 1.61284i
\(554\) 0 0
\(555\) −16.0451 5.83992i −0.681075 0.247891i
\(556\) 0 0
\(557\) −34.2928 + 28.7751i −1.45303 + 1.21924i −0.522705 + 0.852514i \(0.675077\pi\)
−0.930329 + 0.366726i \(0.880479\pi\)
\(558\) 0 0
\(559\) 6.00645 10.4035i 0.254046 0.440020i
\(560\) 0 0
\(561\) −0.370590 2.10172i −0.0156463 0.0887348i
\(562\) 0 0
\(563\) 5.16725 + 8.94994i 0.217774 + 0.377195i 0.954127 0.299402i \(-0.0967872\pi\)
−0.736353 + 0.676597i \(0.763454\pi\)
\(564\) 0 0
\(565\) −9.99977 + 3.63962i −0.420694 + 0.153120i
\(566\) 0 0
\(567\) −3.64084 3.05503i −0.152901 0.128299i
\(568\) 0 0
\(569\) −24.2727 −1.01756 −0.508782 0.860895i \(-0.669904\pi\)
−0.508782 + 0.860895i \(0.669904\pi\)
\(570\) 0 0
\(571\) 43.4628 1.81886 0.909431 0.415854i \(-0.136517\pi\)
0.909431 + 0.415854i \(0.136517\pi\)
\(572\) 0 0
\(573\) −13.8745 11.6421i −0.579614 0.486354i
\(574\) 0 0
\(575\) −0.815458 + 0.296802i −0.0340069 + 0.0123775i
\(576\) 0 0
\(577\) 12.1169 + 20.9871i 0.504434 + 0.873705i 0.999987 + 0.00512748i \(0.00163213\pi\)
−0.495553 + 0.868578i \(0.665035\pi\)
\(578\) 0 0
\(579\) 9.84153 + 55.8141i 0.409000 + 2.31955i
\(580\) 0 0
\(581\) −7.79149 + 13.4952i −0.323245 + 0.559877i
\(582\) 0 0
\(583\) 2.29207 1.92328i 0.0949279 0.0796540i
\(584\) 0 0
\(585\) 14.7552 + 5.37046i 0.610053 + 0.222041i
\(586\) 0 0
\(587\) −0.667422 + 3.78514i −0.0275475 + 0.156229i −0.995479 0.0949863i \(-0.969719\pi\)
0.967931 + 0.251216i \(0.0808304\pi\)
\(588\) 0 0
\(589\) 6.99123 4.19950i 0.288069 0.173038i
\(590\) 0 0
\(591\) 10.4504 59.2673i 0.429873 2.43793i
\(592\) 0 0
\(593\) 19.1592 + 6.97336i 0.786772 + 0.286362i 0.703994 0.710206i \(-0.251398\pi\)
0.0827786 + 0.996568i \(0.473621\pi\)
\(594\) 0 0
\(595\) −3.94988 + 3.31434i −0.161929 + 0.135875i
\(596\) 0 0
\(597\) 1.11964 1.93928i 0.0458239 0.0793694i
\(598\) 0 0
\(599\) −1.00673 5.70947i −0.0411340 0.233283i 0.957309 0.289067i \(-0.0933451\pi\)
−0.998443 + 0.0557846i \(0.982234\pi\)
\(600\) 0 0
\(601\) 5.24705 + 9.08816i 0.214032 + 0.370714i 0.952973 0.303056i \(-0.0980071\pi\)
−0.738941 + 0.673770i \(0.764674\pi\)
\(602\) 0 0
\(603\) 31.7829 11.5680i 1.29430 0.471087i
\(604\) 0 0
\(605\) −8.32003 6.98133i −0.338257 0.283832i
\(606\) 0 0
\(607\) 14.7382 0.598204 0.299102 0.954221i \(-0.403313\pi\)
0.299102 + 0.954221i \(0.403313\pi\)
\(608\) 0 0
\(609\) −70.6393 −2.86245
\(610\) 0 0
\(611\) 13.2481 + 11.1165i 0.535960 + 0.449724i
\(612\) 0 0
\(613\) −10.8362 + 3.94406i −0.437671 + 0.159299i −0.551452 0.834207i \(-0.685926\pi\)
0.113781 + 0.993506i \(0.463704\pi\)
\(614\) 0 0
\(615\) −10.9169 18.9087i −0.440214 0.762473i
\(616\) 0 0
\(617\) 0.153442 + 0.870215i 0.00617736 + 0.0350335i 0.987741 0.156104i \(-0.0498935\pi\)
−0.981563 + 0.191137i \(0.938782\pi\)
\(618\) 0 0
\(619\) 21.0474 36.4551i 0.845965 1.46525i −0.0388160 0.999246i \(-0.512359\pi\)
0.884781 0.466008i \(-0.154308\pi\)
\(620\) 0 0
\(621\) −2.84035 + 2.38333i −0.113979 + 0.0956399i
\(622\) 0 0
\(623\) 2.46417 + 0.896885i 0.0987249 + 0.0359329i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) −1.60002 4.16984i −0.0638987 0.166527i
\(628\) 0 0
\(629\) 2.24686 12.7426i 0.0895883 0.508081i
\(630\) 0 0
\(631\) −19.6598 7.15557i −0.782643 0.284859i −0.0803687 0.996765i \(-0.525610\pi\)
−0.702274 + 0.711906i \(0.747832\pi\)
\(632\) 0 0
\(633\) −18.8282 + 15.7987i −0.748354 + 0.627944i
\(634\) 0 0
\(635\) 0.123011 0.213060i 0.00488152 0.00845505i
\(636\) 0 0
\(637\) 0.521773 + 2.95912i 0.0206734 + 0.117245i
\(638\) 0 0
\(639\) −5.62051 9.73500i −0.222344 0.385111i
\(640\) 0 0
\(641\) −43.1639 + 15.7104i −1.70487 + 0.620523i −0.996366 0.0851809i \(-0.972853\pi\)
−0.708507 + 0.705704i \(0.750631\pi\)
\(642\) 0 0
\(643\) −6.82283 5.72504i −0.269066 0.225773i 0.498264 0.867025i \(-0.333971\pi\)
−0.767331 + 0.641252i \(0.778415\pi\)
\(644\) 0 0
\(645\) −9.57711 −0.377098
\(646\) 0 0
\(647\) −13.2110 −0.519379 −0.259689 0.965692i \(-0.583620\pi\)
−0.259689 + 0.965692i \(0.583620\pi\)
\(648\) 0 0
\(649\) 2.37371 + 1.99178i 0.0931761 + 0.0781840i
\(650\) 0 0
\(651\) 11.9630 4.35419i 0.468868 0.170654i
\(652\) 0 0
\(653\) −15.6670 27.1360i −0.613095 1.06191i −0.990715 0.135952i \(-0.956591\pi\)
0.377620 0.925961i \(-0.376743\pi\)
\(654\) 0 0
\(655\) −1.50790 8.55170i −0.0589183 0.334143i
\(656\) 0 0
\(657\) 11.5147 19.9441i 0.449233 0.778095i
\(658\) 0 0
\(659\) 5.90427 4.95427i 0.229998 0.192991i −0.520504 0.853859i \(-0.674256\pi\)
0.750502 + 0.660868i \(0.229812\pi\)
\(660\) 0 0
\(661\) 11.0245 + 4.01257i 0.428801 + 0.156071i 0.547400 0.836871i \(-0.315618\pi\)
−0.118598 + 0.992942i \(0.537840\pi\)
\(662\) 0 0
\(663\) −3.42725 + 19.4369i −0.133103 + 0.754866i
\(664\) 0 0
\(665\) −6.79195 + 8.38510i −0.263380 + 0.325160i
\(666\) 0 0
\(667\) 1.56442 8.87227i 0.0605746 0.343536i
\(668\) 0 0
\(669\) 20.5637 + 7.48459i 0.795040 + 0.289371i
\(670\) 0 0
\(671\) −3.69172 + 3.09772i −0.142517 + 0.119586i
\(672\) 0 0
\(673\) −10.9349 + 18.9398i −0.421509 + 0.730075i −0.996087 0.0883747i \(-0.971833\pi\)
0.574578 + 0.818450i \(0.305166\pi\)
\(674\) 0 0
\(675\) −0.741945 4.20778i −0.0285575 0.161958i
\(676\) 0 0
\(677\) 9.90091 + 17.1489i 0.380523 + 0.659085i 0.991137 0.132843i \(-0.0424107\pi\)
−0.610614 + 0.791928i \(0.709077\pi\)
\(678\) 0 0
\(679\) 33.3583 12.1414i 1.28017 0.465945i
\(680\) 0 0
\(681\) 24.2823 + 20.3752i 0.930499 + 0.780781i
\(682\) 0 0
\(683\) 30.3561 1.16154 0.580771 0.814067i \(-0.302751\pi\)
0.580771 + 0.814067i \(0.302751\pi\)
\(684\) 0 0
\(685\) −13.7779 −0.526425
\(686\) 0 0
\(687\) 3.89421 + 3.26763i 0.148573 + 0.124668i
\(688\) 0 0
\(689\) −26.0023 + 9.46405i −0.990608 + 0.360552i
\(690\) 0 0
\(691\) 23.5595 + 40.8063i 0.896246 + 1.55234i 0.832254 + 0.554394i \(0.187050\pi\)
0.0639920 + 0.997950i \(0.479617\pi\)
\(692\) 0 0
\(693\) −0.729884 4.13938i −0.0277260 0.157242i
\(694\) 0 0
\(695\) −2.51324 + 4.35307i −0.0953328 + 0.165121i
\(696\) 0 0
\(697\) 12.6747 10.6353i 0.480087 0.402841i
\(698\) 0 0
\(699\) −53.3297 19.4104i −2.01712 0.734170i
\(700\) 0 0
\(701\) 0.348816 1.97823i 0.0131746 0.0747168i −0.977512 0.210882i \(-0.932367\pi\)
0.990686 + 0.136165i \(0.0434777\pi\)
\(702\) 0 0
\(703\) −0.469024 27.0747i −0.0176896 1.02114i
\(704\) 0 0
\(705\) 2.39418 13.5781i 0.0901700 0.511379i
\(706\) 0 0
\(707\) −39.9269 14.5322i −1.50160 0.546539i
\(708\) 0 0
\(709\) −12.6356 + 10.6025i −0.474541 + 0.398187i −0.848448 0.529279i \(-0.822462\pi\)
0.373907 + 0.927466i \(0.378018\pi\)
\(710\) 0 0
\(711\) 35.4275 61.3623i 1.32864 2.30127i
\(712\) 0 0
\(713\) 0.281944 + 1.59898i 0.0105589 + 0.0598824i
\(714\) 0 0
\(715\) −0.642617 1.11305i −0.0240325 0.0416255i
\(716\) 0 0
\(717\) −64.0189 + 23.3010i −2.39083 + 0.870191i
\(718\) 0 0
\(719\) 15.2913 + 12.8309i 0.570268 + 0.478511i 0.881735 0.471746i \(-0.156376\pi\)
−0.311467 + 0.950257i \(0.600820\pi\)
\(720\) 0 0
\(721\) 46.3490 1.72613
\(722\) 0 0
\(723\) −44.3123 −1.64799
\(724\) 0 0
\(725\) 7.95283 + 6.67322i 0.295361 + 0.247837i
\(726\) 0 0
\(727\) 36.7157 13.3634i 1.36171 0.495622i 0.445127 0.895467i \(-0.353158\pi\)
0.916583 + 0.399845i \(0.130936\pi\)
\(728\) 0 0
\(729\) 21.9876 + 38.0837i 0.814356 + 1.41051i
\(730\) 0 0
\(731\) −1.26025 7.14722i −0.0466120 0.264350i
\(732\) 0 0
\(733\) 1.22945 2.12946i 0.0454106 0.0786535i −0.842427 0.538811i \(-0.818874\pi\)
0.887837 + 0.460157i \(0.152207\pi\)
\(734\) 0 0
\(735\) 1.83507 1.53981i 0.0676875 0.0567966i
\(736\) 0 0
\(737\) −2.60146 0.946853i −0.0958259 0.0348778i
\(738\) 0 0
\(739\) −6.33250 + 35.9134i −0.232945 + 1.32110i 0.613954 + 0.789342i \(0.289578\pi\)
−0.846899 + 0.531754i \(0.821533\pi\)
\(740\) 0 0
\(741\) 0.715425 + 41.2983i 0.0262818 + 1.51713i
\(742\) 0 0
\(743\) 6.71560 38.0861i 0.246372 1.39724i −0.570914 0.821010i \(-0.693411\pi\)
0.817285 0.576233i \(-0.195478\pi\)
\(744\) 0 0
\(745\) 14.9211 + 5.43083i 0.546666 + 0.198970i
\(746\) 0 0
\(747\) 21.9620 18.4283i 0.803548 0.674257i
\(748\) 0 0
\(749\) 1.74953 3.03028i 0.0639265 0.110724i
\(750\) 0 0
\(751\) −3.43069 19.4564i −0.125188 0.709975i −0.981196 0.193013i \(-0.938174\pi\)
0.856008 0.516962i \(-0.172937\pi\)
\(752\) 0 0
\(753\) 23.4617 + 40.6369i 0.854992 + 1.48089i
\(754\) 0 0
\(755\) −7.37492 + 2.68425i −0.268401 + 0.0976900i
\(756\) 0 0
\(757\) −14.5962 12.2477i −0.530507 0.445149i 0.337769 0.941229i \(-0.390328\pi\)
−0.868277 + 0.496080i \(0.834772\pi\)
\(758\) 0 0
\(759\) 0.889170 0.0322748
\(760\) 0 0
\(761\) −32.2550 −1.16924 −0.584621 0.811307i \(-0.698757\pi\)
−0.584621 + 0.811307i \(0.698757\pi\)
\(762\) 0 0
\(763\) 23.5611 + 19.7701i 0.852968 + 0.715725i
\(764\) 0 0
\(765\) 8.91423 3.24451i 0.322295 0.117306i
\(766\) 0 0
\(767\) −14.3283 24.8173i −0.517364 0.896101i
\(768\) 0 0
\(769\) 4.13012 + 23.4231i 0.148936 + 0.844658i 0.964122 + 0.265459i \(0.0855234\pi\)
−0.815186 + 0.579199i \(0.803365\pi\)
\(770\) 0 0
\(771\) 1.60377 2.77781i 0.0577583 0.100040i
\(772\) 0 0
\(773\) −11.4378 + 9.59750i −0.411391 + 0.345198i −0.824877 0.565313i \(-0.808756\pi\)
0.413486 + 0.910511i \(0.364311\pi\)
\(774\) 0 0
\(775\) −1.75818 0.639924i −0.0631556 0.0229868i
\(776\) 0 0
\(777\) 7.34008 41.6277i 0.263324 1.49338i
\(778\) 0 0
\(779\) 21.7945 26.9067i 0.780869 0.964033i
\(780\) 0 0
\(781\) −0.159771 + 0.906107i −0.00571706 + 0.0324231i
\(782\) 0 0
\(783\) 41.6826 + 15.1712i 1.48962 + 0.542176i
\(784\) 0 0
\(785\) 10.1191 8.49097i 0.361168 0.303056i
\(786\) 0 0
\(787\) 6.08890 10.5463i 0.217046