Properties

Label 380.2.u.a.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: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) 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 \(2.91971 + 1.06269i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.a.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.38017 - 1.99720i) q^{3} +(0.939693 - 0.342020i) q^{5} +(2.42255 + 4.19598i) q^{7} +(1.15545 + 6.55290i) q^{9} +O(q^{10})\) \(q+(-2.38017 - 1.99720i) q^{3} +(0.939693 - 0.342020i) q^{5} +(2.42255 + 4.19598i) q^{7} +(1.15545 + 6.55290i) q^{9} +(-0.912094 + 1.57979i) q^{11} +(4.37893 - 3.67435i) q^{13} +(-2.91971 - 1.06269i) q^{15} +(0.843866 - 4.78580i) q^{17} +(3.11816 + 3.04583i) q^{19} +(2.61412 - 14.8254i) q^{21} +(-3.49160 - 1.27084i) q^{23} +(0.766044 - 0.642788i) q^{25} +(5.67662 - 9.83220i) q^{27} +(0.509115 + 2.88733i) q^{29} +(-0.598860 - 1.03726i) q^{31} +(5.32609 - 1.93854i) q^{33} +(3.71156 + 3.11437i) q^{35} +3.79201 q^{37} -17.7610 q^{39} +(6.35728 + 5.33439i) q^{41} +(9.07952 - 3.30467i) q^{43} +(3.32699 + 5.76252i) q^{45} +(0.728153 + 4.12956i) q^{47} +(-8.23747 + 14.2677i) q^{49} +(-11.5667 + 9.70564i) q^{51} +(-1.62200 - 0.590361i) q^{53} +(-0.316767 + 1.79647i) q^{55} +(-1.33861 - 13.4772i) q^{57} +(1.96003 - 11.1159i) q^{59} +(1.03692 + 0.377409i) q^{61} +(-24.6966 + 20.7229i) q^{63} +(2.85814 - 4.95044i) q^{65} +(-0.781955 - 4.43469i) q^{67} +(5.77248 + 9.99823i) q^{69} +(-6.95459 + 2.53126i) q^{71} +(-5.48272 - 4.60055i) q^{73} -3.10709 q^{75} -8.83836 q^{77} +(2.27175 + 1.90623i) q^{79} +(-14.3900 + 5.23754i) q^{81} +(5.31509 + 9.20601i) q^{83} +(-0.843866 - 4.78580i) q^{85} +(4.55479 - 7.88913i) q^{87} +(1.63837 - 1.37475i) q^{89} +(26.0257 + 9.47256i) q^{91} +(-0.646218 + 3.66488i) q^{93} +(3.97185 + 1.79567i) q^{95} +(-1.46425 + 8.30419i) q^{97} +(-11.4061 - 4.15148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 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
\(3\) −2.38017 1.99720i −1.37419 1.15308i −0.971307 0.237830i \(-0.923564\pi\)
−0.402883 0.915252i \(-0.631992\pi\)
\(4\) 0 0
\(5\) 0.939693 0.342020i 0.420243 0.152956i
\(6\) 0 0
\(7\) 2.42255 + 4.19598i 0.915637 + 1.58593i 0.805966 + 0.591962i \(0.201646\pi\)
0.109671 + 0.993968i \(0.465020\pi\)
\(8\) 0 0
\(9\) 1.15545 + 6.55290i 0.385151 + 2.18430i
\(10\) 0 0
\(11\) −0.912094 + 1.57979i −0.275007 + 0.476326i −0.970137 0.242558i \(-0.922013\pi\)
0.695130 + 0.718884i \(0.255347\pi\)
\(12\) 0 0
\(13\) 4.37893 3.67435i 1.21450 1.01908i 0.215401 0.976526i \(-0.430894\pi\)
0.999094 0.0425570i \(-0.0135504\pi\)
\(14\) 0 0
\(15\) −2.91971 1.06269i −0.753865 0.274384i
\(16\) 0 0
\(17\) 0.843866 4.78580i 0.204668 1.16073i −0.693294 0.720655i \(-0.743841\pi\)
0.897962 0.440073i \(-0.145047\pi\)
\(18\) 0 0
\(19\) 3.11816 + 3.04583i 0.715354 + 0.698762i
\(20\) 0 0
\(21\) 2.61412 14.8254i 0.570448 3.23517i
\(22\) 0 0
\(23\) −3.49160 1.27084i −0.728050 0.264988i −0.0487107 0.998813i \(-0.515511\pi\)
−0.679339 + 0.733824i \(0.737733\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) 5.67662 9.83220i 1.09247 1.89221i
\(28\) 0 0
\(29\) 0.509115 + 2.88733i 0.0945402 + 0.536164i 0.994887 + 0.100992i \(0.0322015\pi\)
−0.900347 + 0.435173i \(0.856687\pi\)
\(30\) 0 0
\(31\) −0.598860 1.03726i −0.107559 0.186297i 0.807222 0.590248i \(-0.200970\pi\)
−0.914781 + 0.403951i \(0.867637\pi\)
\(32\) 0 0
\(33\) 5.32609 1.93854i 0.927154 0.337456i
\(34\) 0 0
\(35\) 3.71156 + 3.11437i 0.627368 + 0.526424i
\(36\) 0 0
\(37\) 3.79201 0.623403 0.311701 0.950180i \(-0.399101\pi\)
0.311701 + 0.950180i \(0.399101\pi\)
\(38\) 0 0
\(39\) −17.7610 −2.84403
\(40\) 0 0
\(41\) 6.35728 + 5.33439i 0.992841 + 0.833092i 0.985977 0.166884i \(-0.0533706\pi\)
0.00686419 + 0.999976i \(0.497815\pi\)
\(42\) 0 0
\(43\) 9.07952 3.30467i 1.38461 0.503958i 0.461040 0.887379i \(-0.347477\pi\)
0.923574 + 0.383421i \(0.125254\pi\)
\(44\) 0 0
\(45\) 3.32699 + 5.76252i 0.495959 + 0.859026i
\(46\) 0 0
\(47\) 0.728153 + 4.12956i 0.106212 + 0.602359i 0.990729 + 0.135851i \(0.0433768\pi\)
−0.884517 + 0.466508i \(0.845512\pi\)
\(48\) 0 0
\(49\) −8.23747 + 14.2677i −1.17678 + 2.03825i
\(50\) 0 0
\(51\) −11.5667 + 9.70564i −1.61967 + 1.35906i
\(52\) 0 0
\(53\) −1.62200 0.590361i −0.222799 0.0810923i 0.228209 0.973612i \(-0.426713\pi\)
−0.451008 + 0.892520i \(0.648935\pi\)
\(54\) 0 0
\(55\) −0.316767 + 1.79647i −0.0427128 + 0.242237i
\(56\) 0 0
\(57\) −1.33861 13.4772i −0.177303 1.78509i
\(58\) 0 0
\(59\) 1.96003 11.1159i 0.255174 1.44716i −0.540451 0.841376i \(-0.681746\pi\)
0.795625 0.605789i \(-0.207143\pi\)
\(60\) 0 0
\(61\) 1.03692 + 0.377409i 0.132764 + 0.0483223i 0.407548 0.913184i \(-0.366384\pi\)
−0.274784 + 0.961506i \(0.588606\pi\)
\(62\) 0 0
\(63\) −24.6966 + 20.7229i −3.11149 + 2.61085i
\(64\) 0 0
\(65\) 2.85814 4.95044i 0.354509 0.614027i
\(66\) 0 0
\(67\) −0.781955 4.43469i −0.0955311 0.541784i −0.994583 0.103942i \(-0.966854\pi\)
0.899052 0.437841i \(-0.144257\pi\)
\(68\) 0 0
\(69\) 5.77248 + 9.99823i 0.694925 + 1.20365i
\(70\) 0 0
\(71\) −6.95459 + 2.53126i −0.825358 + 0.300406i −0.719952 0.694023i \(-0.755836\pi\)
−0.105406 + 0.994429i \(0.533614\pi\)
\(72\) 0 0
\(73\) −5.48272 4.60055i −0.641704 0.538454i 0.262837 0.964840i \(-0.415342\pi\)
−0.904541 + 0.426386i \(0.859786\pi\)
\(74\) 0 0
\(75\) −3.10709 −0.358775
\(76\) 0 0
\(77\) −8.83836 −1.00723
\(78\) 0 0
\(79\) 2.27175 + 1.90623i 0.255592 + 0.214467i 0.761576 0.648076i \(-0.224426\pi\)
−0.505984 + 0.862543i \(0.668870\pi\)
\(80\) 0 0
\(81\) −14.3900 + 5.23754i −1.59889 + 0.581949i
\(82\) 0 0
\(83\) 5.31509 + 9.20601i 0.583407 + 1.01049i 0.995072 + 0.0991559i \(0.0316142\pi\)
−0.411664 + 0.911335i \(0.635052\pi\)
\(84\) 0 0
\(85\) −0.843866 4.78580i −0.0915301 0.519093i
\(86\) 0 0
\(87\) 4.55479 7.88913i 0.488325 0.845804i
\(88\) 0 0
\(89\) 1.63837 1.37475i 0.173667 0.145724i −0.551811 0.833969i \(-0.686063\pi\)
0.725478 + 0.688245i \(0.241619\pi\)
\(90\) 0 0
\(91\) 26.0257 + 9.47256i 2.72823 + 0.992994i
\(92\) 0 0
\(93\) −0.646218 + 3.66488i −0.0670097 + 0.380031i
\(94\) 0 0
\(95\) 3.97185 + 1.79567i 0.407503 + 0.184232i
\(96\) 0 0
\(97\) −1.46425 + 8.30419i −0.148672 + 0.843162i 0.815673 + 0.578514i \(0.196367\pi\)
−0.964345 + 0.264649i \(0.914744\pi\)
\(98\) 0 0
\(99\) −11.4061 4.15148i −1.14636 0.417240i
\(100\) 0 0
\(101\) −2.77564 + 2.32904i −0.276187 + 0.231748i −0.770351 0.637621i \(-0.779919\pi\)
0.494164 + 0.869369i \(0.335474\pi\)
\(102\) 0 0
\(103\) 1.18900 2.05941i 0.117155 0.202919i −0.801484 0.598016i \(-0.795956\pi\)
0.918639 + 0.395097i \(0.129289\pi\)
\(104\) 0 0
\(105\) −2.61412 14.8254i −0.255112 1.44681i
\(106\) 0 0
\(107\) −8.94605 15.4950i −0.864847 1.49796i −0.867199 0.497962i \(-0.834082\pi\)
0.00235182 0.999997i \(-0.499251\pi\)
\(108\) 0 0
\(109\) −3.36634 + 1.22525i −0.322437 + 0.117357i −0.498167 0.867081i \(-0.665993\pi\)
0.175731 + 0.984438i \(0.443771\pi\)
\(110\) 0 0
\(111\) −9.02562 7.57339i −0.856674 0.718834i
\(112\) 0 0
\(113\) −9.39037 −0.883371 −0.441686 0.897170i \(-0.645619\pi\)
−0.441686 + 0.897170i \(0.645619\pi\)
\(114\) 0 0
\(115\) −3.71569 −0.346490
\(116\) 0 0
\(117\) 29.1373 + 24.4491i 2.69374 + 2.26032i
\(118\) 0 0
\(119\) 22.1254 8.05299i 2.02823 0.738217i
\(120\) 0 0
\(121\) 3.83617 + 6.64444i 0.348743 + 0.604040i
\(122\) 0 0
\(123\) −4.47756 25.3935i −0.403728 2.28965i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) −6.76401 + 5.67568i −0.600209 + 0.503635i −0.891513 0.452996i \(-0.850355\pi\)
0.291304 + 0.956631i \(0.405911\pi\)
\(128\) 0 0
\(129\) −28.2108 10.2679i −2.48383 0.904039i
\(130\) 0 0
\(131\) 1.47788 8.38149i 0.129123 0.732294i −0.849650 0.527347i \(-0.823187\pi\)
0.978773 0.204947i \(-0.0657022\pi\)
\(132\) 0 0
\(133\) −5.22635 + 20.4624i −0.453182 + 1.77431i
\(134\) 0 0
\(135\) 1.97147 11.1808i 0.169677 0.962287i
\(136\) 0 0
\(137\) 14.9783 + 5.45166i 1.27968 + 0.465767i 0.890327 0.455321i \(-0.150475\pi\)
0.389356 + 0.921088i \(0.372698\pi\)
\(138\) 0 0
\(139\) −4.15128 + 3.48334i −0.352107 + 0.295453i −0.801636 0.597813i \(-0.796037\pi\)
0.449528 + 0.893266i \(0.351592\pi\)
\(140\) 0 0
\(141\) 6.51442 11.2833i 0.548613 0.950226i
\(142\) 0 0
\(143\) 1.81073 + 10.2692i 0.151421 + 0.858750i
\(144\) 0 0
\(145\) 1.46594 + 2.53908i 0.121739 + 0.210859i
\(146\) 0 0
\(147\) 48.1020 17.5077i 3.96738 1.44401i
\(148\) 0 0
\(149\) −13.6788 11.4779i −1.12061 0.940306i −0.121978 0.992533i \(-0.538924\pi\)
−0.998635 + 0.0522265i \(0.983368\pi\)
\(150\) 0 0
\(151\) −0.621968 −0.0506150 −0.0253075 0.999680i \(-0.508056\pi\)
−0.0253075 + 0.999680i \(0.508056\pi\)
\(152\) 0 0
\(153\) 32.3359 2.61420
\(154\) 0 0
\(155\) −0.917507 0.769880i −0.0736960 0.0618383i
\(156\) 0 0
\(157\) −13.9123 + 5.06368i −1.11033 + 0.404125i −0.831113 0.556104i \(-0.812296\pi\)
−0.279213 + 0.960229i \(0.590073\pi\)
\(158\) 0 0
\(159\) 2.68157 + 4.64462i 0.212662 + 0.368342i
\(160\) 0 0
\(161\) −3.12616 17.7294i −0.246376 1.39727i
\(162\) 0 0
\(163\) −10.1692 + 17.6136i −0.796516 + 1.37961i 0.125356 + 0.992112i \(0.459993\pi\)
−0.921872 + 0.387494i \(0.873341\pi\)
\(164\) 0 0
\(165\) 4.34187 3.64326i 0.338014 0.283628i
\(166\) 0 0
\(167\) −20.8798 7.59961i −1.61572 0.588076i −0.633164 0.774018i \(-0.718244\pi\)
−0.982561 + 0.185942i \(0.940466\pi\)
\(168\) 0 0
\(169\) 3.41668 19.3769i 0.262821 1.49053i
\(170\) 0 0
\(171\) −16.3561 + 23.9523i −1.25079 + 1.83168i
\(172\) 0 0
\(173\) −1.51218 + 8.57600i −0.114969 + 0.652021i 0.871797 + 0.489868i \(0.162955\pi\)
−0.986766 + 0.162153i \(0.948156\pi\)
\(174\) 0 0
\(175\) 4.55290 + 1.65712i 0.344167 + 0.125266i
\(176\) 0 0
\(177\) −26.8658 + 22.5431i −2.01936 + 1.69444i
\(178\) 0 0
\(179\) −5.74445 + 9.94968i −0.429360 + 0.743674i −0.996817 0.0797296i \(-0.974594\pi\)
0.567456 + 0.823404i \(0.307928\pi\)
\(180\) 0 0
\(181\) 0.727493 + 4.12582i 0.0540741 + 0.306670i 0.999834 0.0181957i \(-0.00579218\pi\)
−0.945760 + 0.324865i \(0.894681\pi\)
\(182\) 0 0
\(183\) −1.71429 2.96923i −0.126724 0.219492i
\(184\) 0 0
\(185\) 3.56332 1.29694i 0.261981 0.0953532i
\(186\) 0 0
\(187\) 6.79089 + 5.69824i 0.496599 + 0.416696i
\(188\) 0 0
\(189\) 55.0075 4.00121
\(190\) 0 0
\(191\) 17.7153 1.28183 0.640917 0.767610i \(-0.278554\pi\)
0.640917 + 0.767610i \(0.278554\pi\)
\(192\) 0 0
\(193\) 5.80295 + 4.86926i 0.417706 + 0.350497i 0.827290 0.561776i \(-0.189882\pi\)
−0.409584 + 0.912272i \(0.634326\pi\)
\(194\) 0 0
\(195\) −16.6899 + 6.07461i −1.19519 + 0.435012i
\(196\) 0 0
\(197\) −8.43937 14.6174i −0.601280 1.04145i −0.992628 0.121205i \(-0.961324\pi\)
0.391347 0.920243i \(-0.372009\pi\)
\(198\) 0 0
\(199\) −1.21363 6.88285i −0.0860321 0.487912i −0.997129 0.0757203i \(-0.975874\pi\)
0.911097 0.412192i \(-0.135237\pi\)
\(200\) 0 0
\(201\) −6.99576 + 12.1170i −0.493443 + 0.854668i
\(202\) 0 0
\(203\) −10.8818 + 9.13093i −0.763754 + 0.640866i
\(204\) 0 0
\(205\) 7.79836 + 2.83837i 0.544661 + 0.198240i
\(206\) 0 0
\(207\) 4.29330 24.3485i 0.298405 1.69234i
\(208\) 0 0
\(209\) −7.65584 + 2.14796i −0.529565 + 0.148577i
\(210\) 0 0
\(211\) 2.10682 11.9484i 0.145040 0.822561i −0.822296 0.569060i \(-0.807307\pi\)
0.967335 0.253500i \(-0.0815818\pi\)
\(212\) 0 0
\(213\) 21.6085 + 7.86486i 1.48059 + 0.538891i
\(214\) 0 0
\(215\) 7.40169 6.21076i 0.504791 0.423570i
\(216\) 0 0
\(217\) 2.90154 5.02561i 0.196969 0.341160i
\(218\) 0 0
\(219\) 3.86159 + 21.9002i 0.260942 + 1.47988i
\(220\) 0 0
\(221\) −13.8895 24.0573i −0.934309 1.61827i
\(222\) 0 0
\(223\) 0.405042 0.147423i 0.0271236 0.00987219i −0.328423 0.944531i \(-0.606517\pi\)
0.355546 + 0.934659i \(0.384295\pi\)
\(224\) 0 0
\(225\) 5.09725 + 4.27710i 0.339816 + 0.285140i
\(226\) 0 0
\(227\) −15.9051 −1.05566 −0.527828 0.849351i \(-0.676993\pi\)
−0.527828 + 0.849351i \(0.676993\pi\)
\(228\) 0 0
\(229\) −11.5868 −0.765676 −0.382838 0.923815i \(-0.625053\pi\)
−0.382838 + 0.923815i \(0.625053\pi\)
\(230\) 0 0
\(231\) 21.0368 + 17.6519i 1.38412 + 1.16141i
\(232\) 0 0
\(233\) 1.73793 0.632557i 0.113856 0.0414402i −0.284464 0.958687i \(-0.591816\pi\)
0.398320 + 0.917247i \(0.369593\pi\)
\(234\) 0 0
\(235\) 2.09663 + 3.63148i 0.136769 + 0.236891i
\(236\) 0 0
\(237\) −1.60004 9.07428i −0.103934 0.589438i
\(238\) 0 0
\(239\) 4.35757 7.54753i 0.281868 0.488209i −0.689977 0.723831i \(-0.742379\pi\)
0.971845 + 0.235622i \(0.0757128\pi\)
\(240\) 0 0
\(241\) 11.4106 9.57467i 0.735024 0.616758i −0.196472 0.980509i \(-0.562949\pi\)
0.931496 + 0.363751i \(0.118504\pi\)
\(242\) 0 0
\(243\) 12.7054 + 4.62438i 0.815051 + 0.296654i
\(244\) 0 0
\(245\) −2.86084 + 16.2247i −0.182773 + 1.03655i
\(246\) 0 0
\(247\) 24.8456 + 1.88026i 1.58089 + 0.119638i
\(248\) 0 0
\(249\) 5.73541 32.5271i 0.363467 2.06132i
\(250\) 0 0
\(251\) −1.14690 0.417438i −0.0723918 0.0263484i 0.305570 0.952169i \(-0.401153\pi\)
−0.377962 + 0.925821i \(0.623375\pi\)
\(252\) 0 0
\(253\) 5.19234 4.35689i 0.326439 0.273915i
\(254\) 0 0
\(255\) −7.54965 + 13.0764i −0.472777 + 0.818874i
\(256\) 0 0
\(257\) 0.792264 + 4.49315i 0.0494201 + 0.280275i 0.999496 0.0317435i \(-0.0101060\pi\)
−0.950076 + 0.312019i \(0.898995\pi\)
\(258\) 0 0
\(259\) 9.18633 + 15.9112i 0.570811 + 0.988673i
\(260\) 0 0
\(261\) −18.3321 + 6.67235i −1.13473 + 0.413008i
\(262\) 0 0
\(263\) −4.77092 4.00327i −0.294187 0.246852i 0.483733 0.875216i \(-0.339281\pi\)
−0.777920 + 0.628363i \(0.783725\pi\)
\(264\) 0 0
\(265\) −1.72610 −0.106034
\(266\) 0 0
\(267\) −6.64524 −0.406682
\(268\) 0 0
\(269\) 5.53601 + 4.64527i 0.337537 + 0.283227i 0.795762 0.605609i \(-0.207070\pi\)
−0.458226 + 0.888836i \(0.651515\pi\)
\(270\) 0 0
\(271\) 1.18940 0.432907i 0.0722511 0.0262973i −0.305642 0.952147i \(-0.598871\pi\)
0.377893 + 0.925849i \(0.376649\pi\)
\(272\) 0 0
\(273\) −43.0268 74.5246i −2.60410 4.51044i
\(274\) 0 0
\(275\) 0.316767 + 1.79647i 0.0191018 + 0.108331i
\(276\) 0 0
\(277\) 10.6737 18.4875i 0.641323 1.11080i −0.343815 0.939038i \(-0.611719\pi\)
0.985138 0.171767i \(-0.0549475\pi\)
\(278\) 0 0
\(279\) 6.10508 5.12277i 0.365502 0.306692i
\(280\) 0 0
\(281\) −23.0219 8.37929i −1.37337 0.499867i −0.453210 0.891404i \(-0.649721\pi\)
−0.920162 + 0.391537i \(0.871943\pi\)
\(282\) 0 0
\(283\) 4.49853 25.5125i 0.267410 1.51656i −0.494673 0.869079i \(-0.664712\pi\)
0.762083 0.647479i \(-0.224177\pi\)
\(284\) 0 0
\(285\) −5.86734 12.2066i −0.347551 0.723054i
\(286\) 0 0
\(287\) −6.98216 + 39.5978i −0.412144 + 2.33739i
\(288\) 0 0
\(289\) −6.21702 2.26281i −0.365707 0.133107i
\(290\) 0 0
\(291\) 20.0703 16.8409i 1.17654 0.987234i
\(292\) 0 0
\(293\) 15.5929 27.0077i 0.910947 1.57781i 0.0982181 0.995165i \(-0.468686\pi\)
0.812729 0.582642i \(-0.197981\pi\)
\(294\) 0 0
\(295\) −1.96003 11.1159i −0.114117 0.647192i
\(296\) 0 0
\(297\) 10.3552 + 17.9358i 0.600871 + 1.04074i
\(298\) 0 0
\(299\) −19.9590 + 7.26448i −1.15426 + 0.420116i
\(300\) 0 0
\(301\) 35.8619 + 30.0917i 2.06704 + 1.73446i
\(302\) 0 0
\(303\) 11.2581 0.646758
\(304\) 0 0
\(305\) 1.10347 0.0631845
\(306\) 0 0
\(307\) −21.3108 17.8819i −1.21627 1.02057i −0.999011 0.0444593i \(-0.985843\pi\)
−0.217260 0.976114i \(-0.569712\pi\)
\(308\) 0 0
\(309\) −6.94305 + 2.52706i −0.394976 + 0.143760i
\(310\) 0 0
\(311\) 3.08016 + 5.33500i 0.174660 + 0.302520i 0.940044 0.341054i \(-0.110784\pi\)
−0.765384 + 0.643574i \(0.777451\pi\)
\(312\) 0 0
\(313\) −0.945877 5.36433i −0.0534641 0.303210i 0.946336 0.323183i \(-0.104753\pi\)
−0.999801 + 0.0199732i \(0.993642\pi\)
\(314\) 0 0
\(315\) −16.1196 + 27.9200i −0.908236 + 1.57311i
\(316\) 0 0
\(317\) −9.31397 + 7.81535i −0.523125 + 0.438954i −0.865719 0.500530i \(-0.833139\pi\)
0.342595 + 0.939483i \(0.388694\pi\)
\(318\) 0 0
\(319\) −5.02575 1.82922i −0.281388 0.102417i
\(320\) 0 0
\(321\) −9.65350 + 54.7477i −0.538806 + 3.05572i
\(322\) 0 0
\(323\) 17.2081 12.3526i 0.957482 0.687318i
\(324\) 0 0
\(325\) 0.992622 5.62944i 0.0550607 0.312265i
\(326\) 0 0
\(327\) 10.4595 + 3.80695i 0.578412 + 0.210525i
\(328\) 0 0
\(329\) −15.5636 + 13.0594i −0.858046 + 0.719986i
\(330\) 0 0
\(331\) 3.30878 5.73097i 0.181867 0.315003i −0.760649 0.649163i \(-0.775119\pi\)
0.942516 + 0.334160i \(0.108453\pi\)
\(332\) 0 0
\(333\) 4.38149 + 24.8487i 0.240104 + 1.36170i
\(334\) 0 0
\(335\) −2.25155 3.89980i −0.123015 0.213069i
\(336\) 0 0
\(337\) −29.9295 + 10.8935i −1.63037 + 0.593404i −0.985317 0.170737i \(-0.945385\pi\)
−0.645049 + 0.764142i \(0.723163\pi\)
\(338\) 0 0
\(339\) 22.3506 + 18.7544i 1.21392 + 1.01860i
\(340\) 0 0
\(341\) 2.18487 0.118317
\(342\) 0 0
\(343\) −45.9070 −2.47874
\(344\) 0 0
\(345\) 8.84395 + 7.42096i 0.476142 + 0.399531i
\(346\) 0 0
\(347\) −10.4671 + 3.80972i −0.561904 + 0.204516i −0.607328 0.794452i \(-0.707758\pi\)
0.0454237 + 0.998968i \(0.485536\pi\)
\(348\) 0 0
\(349\) 9.79484 + 16.9652i 0.524306 + 0.908124i 0.999600 + 0.0282970i \(0.00900841\pi\)
−0.475294 + 0.879827i \(0.657658\pi\)
\(350\) 0 0
\(351\) −11.2695 63.9124i −0.601520 3.41139i
\(352\) 0 0
\(353\) −8.11101 + 14.0487i −0.431706 + 0.747736i −0.997020 0.0771393i \(-0.975421\pi\)
0.565315 + 0.824875i \(0.308755\pi\)
\(354\) 0 0
\(355\) −5.66943 + 4.75722i −0.300902 + 0.252487i
\(356\) 0 0
\(357\) −68.7456 25.0213i −3.63840 1.32427i
\(358\) 0 0
\(359\) −1.55322 + 8.80876i −0.0819760 + 0.464909i 0.915992 + 0.401196i \(0.131405\pi\)
−0.997968 + 0.0637129i \(0.979706\pi\)
\(360\) 0 0
\(361\) 0.445808 + 18.9948i 0.0234636 + 0.999725i
\(362\) 0 0
\(363\) 4.13953 23.4765i 0.217269 1.23219i
\(364\) 0 0
\(365\) −6.72556 2.44790i −0.352032 0.128129i
\(366\) 0 0
\(367\) −10.3150 + 8.65534i −0.538441 + 0.451805i −0.871004 0.491276i \(-0.836531\pi\)
0.332564 + 0.943081i \(0.392086\pi\)
\(368\) 0 0
\(369\) −27.6102 + 47.8222i −1.43733 + 2.48953i
\(370\) 0 0
\(371\) −1.45224 8.23607i −0.0753966 0.427595i
\(372\) 0 0
\(373\) 1.36277 + 2.36039i 0.0705616 + 0.122216i 0.899148 0.437646i \(-0.144188\pi\)
−0.828586 + 0.559862i \(0.810854\pi\)
\(374\) 0 0
\(375\) −2.91971 + 1.06269i −0.150773 + 0.0548769i
\(376\) 0 0
\(377\) 12.8385 + 10.7727i 0.661214 + 0.554825i
\(378\) 0 0
\(379\) 5.80317 0.298089 0.149044 0.988831i \(-0.452380\pi\)
0.149044 + 0.988831i \(0.452380\pi\)
\(380\) 0 0
\(381\) 27.4349 1.40553
\(382\) 0 0
\(383\) 17.2926 + 14.5102i 0.883612 + 0.741439i 0.966919 0.255085i \(-0.0821035\pi\)
−0.0833062 + 0.996524i \(0.526548\pi\)
\(384\) 0 0
\(385\) −8.30535 + 3.02290i −0.423280 + 0.154061i
\(386\) 0 0
\(387\) 32.1461 + 55.6787i 1.63408 + 2.83031i
\(388\) 0 0
\(389\) 1.68123 + 9.53473i 0.0852417 + 0.483430i 0.997304 + 0.0733786i \(0.0233781\pi\)
−0.912062 + 0.410051i \(0.865511\pi\)
\(390\) 0 0
\(391\) −9.02844 + 15.6377i −0.456588 + 0.790833i
\(392\) 0 0
\(393\) −20.2571 + 16.9977i −1.02184 + 0.857421i
\(394\) 0 0
\(395\) 2.78672 + 1.01428i 0.140215 + 0.0510341i
\(396\) 0 0
\(397\) −4.13744 + 23.4646i −0.207652 + 1.17765i 0.685559 + 0.728017i \(0.259558\pi\)
−0.893212 + 0.449637i \(0.851553\pi\)
\(398\) 0 0
\(399\) 53.3070 38.2658i 2.66869 1.91569i
\(400\) 0 0
\(401\) 2.33695 13.2535i 0.116702 0.661849i −0.869192 0.494475i \(-0.835360\pi\)
0.985894 0.167373i \(-0.0535286\pi\)
\(402\) 0 0
\(403\) −6.43361 2.34164i −0.320481 0.116646i
\(404\) 0 0
\(405\) −11.7309 + 9.84336i −0.582911 + 0.489121i
\(406\) 0 0
\(407\) −3.45867 + 5.99059i −0.171440 + 0.296943i
\(408\) 0 0
\(409\) 0.775482 + 4.39798i 0.0383451 + 0.217466i 0.997959 0.0638535i \(-0.0203390\pi\)
−0.959614 + 0.281319i \(0.909228\pi\)
\(410\) 0 0
\(411\) −24.7628 42.8905i −1.22146 2.11563i
\(412\) 0 0
\(413\) 51.3902 18.7045i 2.52875 0.920389i
\(414\) 0 0
\(415\) 8.14320 + 6.83295i 0.399734 + 0.335417i
\(416\) 0 0
\(417\) 16.8377 0.824544
\(418\) 0 0
\(419\) −17.4692 −0.853428 −0.426714 0.904387i \(-0.640329\pi\)
−0.426714 + 0.904387i \(0.640329\pi\)
\(420\) 0 0
\(421\) −29.8887 25.0796i −1.45669 1.22231i −0.927511 0.373795i \(-0.878056\pi\)
−0.529177 0.848512i \(-0.677499\pi\)
\(422\) 0 0
\(423\) −26.2192 + 9.54302i −1.27482 + 0.463998i
\(424\) 0 0
\(425\) −2.42982 4.20856i −0.117863 0.204145i
\(426\) 0 0
\(427\) 0.928395 + 5.26519i 0.0449282 + 0.254800i
\(428\) 0 0
\(429\) 16.1997 28.0587i 0.782128 1.35469i
\(430\) 0 0
\(431\) 20.5508 17.2442i 0.989899 0.830624i 0.00434553 0.999991i \(-0.498617\pi\)
0.985553 + 0.169367i \(0.0541723\pi\)
\(432\) 0 0
\(433\) 5.89712 + 2.14638i 0.283398 + 0.103148i 0.479808 0.877373i \(-0.340706\pi\)
−0.196411 + 0.980522i \(0.562929\pi\)
\(434\) 0 0
\(435\) 1.58186 8.97119i 0.0758445 0.430136i
\(436\) 0 0
\(437\) −7.01660 14.5975i −0.335650 0.698294i
\(438\) 0 0
\(439\) 0.00971623 0.0551035i 0.000463731 0.00262995i −0.984575 0.174963i \(-0.944019\pi\)
0.985039 + 0.172333i \(0.0551305\pi\)
\(440\) 0 0
\(441\) −103.013 37.4936i −4.90537 1.78541i
\(442\) 0 0
\(443\) 15.3122 12.8484i 0.727504 0.610448i −0.201946 0.979397i \(-0.564727\pi\)
0.929450 + 0.368948i \(0.120282\pi\)
\(444\) 0 0
\(445\) 1.06937 1.85220i 0.0506929 0.0878028i
\(446\) 0 0
\(447\) 9.63426 + 54.6386i 0.455685 + 2.58432i
\(448\) 0 0
\(449\) −4.25179 7.36432i −0.200654 0.347544i 0.748085 0.663603i \(-0.230974\pi\)
−0.948739 + 0.316059i \(0.897640\pi\)
\(450\) 0 0
\(451\) −14.2257 + 5.17772i −0.669861 + 0.243809i
\(452\) 0 0
\(453\) 1.48039 + 1.24219i 0.0695546 + 0.0583633i
\(454\) 0 0
\(455\) 27.6959 1.29840
\(456\) 0 0
\(457\) 1.93292 0.0904182 0.0452091 0.998978i \(-0.485605\pi\)
0.0452091 + 0.998978i \(0.485605\pi\)
\(458\) 0 0
\(459\) −42.2646 35.4642i −1.97274 1.65533i
\(460\) 0 0
\(461\) −27.5172 + 10.0154i −1.28160 + 0.466465i −0.890962 0.454078i \(-0.849969\pi\)
−0.390641 + 0.920543i \(0.627747\pi\)
\(462\) 0 0
\(463\) −10.6298 18.4113i −0.494007 0.855645i 0.505969 0.862552i \(-0.331135\pi\)
−0.999976 + 0.00690629i \(0.997802\pi\)
\(464\) 0 0
\(465\) 0.646218 + 3.66488i 0.0299676 + 0.169955i
\(466\) 0 0
\(467\) 17.7562 30.7546i 0.821658 1.42315i −0.0827897 0.996567i \(-0.526383\pi\)
0.904447 0.426586i \(-0.140284\pi\)
\(468\) 0 0
\(469\) 16.7135 14.0243i 0.771759 0.647583i
\(470\) 0 0
\(471\) 43.2268 + 15.7333i 1.99179 + 0.724951i
\(472\) 0 0
\(473\) −3.06067 + 17.3579i −0.140730 + 0.798119i
\(474\) 0 0
\(475\) 4.34647 + 0.328930i 0.199430 + 0.0150924i
\(476\) 0 0
\(477\) 1.99443 11.3110i 0.0913185 0.517893i
\(478\) 0 0
\(479\) 34.3531 + 12.5035i 1.56963 + 0.571299i 0.972917 0.231154i \(-0.0742501\pi\)
0.596715 + 0.802453i \(0.296472\pi\)
\(480\) 0 0
\(481\) 16.6049 13.9332i 0.757120 0.635299i
\(482\) 0 0
\(483\) −27.9682 + 48.4424i −1.27260 + 2.20420i
\(484\) 0 0
\(485\) 1.46425 + 8.30419i 0.0664883 + 0.377074i
\(486\) 0 0
\(487\) −5.64591 9.77901i −0.255841 0.443129i 0.709283 0.704924i \(-0.249019\pi\)
−0.965124 + 0.261795i \(0.915686\pi\)
\(488\) 0 0
\(489\) 59.3824 21.6134i 2.68536 0.977392i
\(490\) 0 0
\(491\) 26.9477 + 22.6118i 1.21613 + 1.02046i 0.999018 + 0.0443097i \(0.0141088\pi\)
0.217114 + 0.976146i \(0.430336\pi\)
\(492\) 0 0
\(493\) 14.2478 0.641690
\(494\) 0 0
\(495\) −12.1381 −0.545568
\(496\) 0 0
\(497\) −27.4689 23.0492i −1.23215 1.03390i
\(498\) 0 0
\(499\) −1.75976 + 0.640499i −0.0787775 + 0.0286727i −0.381108 0.924530i \(-0.624457\pi\)
0.302331 + 0.953203i \(0.402235\pi\)
\(500\) 0 0
\(501\) 34.5194 + 59.7893i 1.54221 + 2.67119i
\(502\) 0 0
\(503\) 4.67710 + 26.5252i 0.208542 + 1.18270i 0.891768 + 0.452493i \(0.149465\pi\)
−0.683226 + 0.730207i \(0.739424\pi\)
\(504\) 0 0
\(505\) −1.81167 + 3.13791i −0.0806184 + 0.139635i
\(506\) 0 0
\(507\) −46.8318 + 39.2966i −2.07987 + 1.74522i
\(508\) 0 0
\(509\) −21.3143 7.75777i −0.944739 0.343857i −0.176704 0.984264i \(-0.556543\pi\)
−0.768036 + 0.640407i \(0.778766\pi\)
\(510\) 0 0
\(511\) 6.02164 34.1504i 0.266382 1.51073i
\(512\) 0 0
\(513\) 47.6478 13.3683i 2.10370 0.590225i
\(514\) 0 0
\(515\) 0.412935 2.34187i 0.0181961 0.103195i
\(516\) 0 0
\(517\) −7.18800 2.61622i −0.316128 0.115061i
\(518\) 0 0
\(519\) 20.7272 17.3922i 0.909823 0.763432i
\(520\) 0 0
\(521\) 11.3485 19.6561i 0.497186 0.861151i −0.502809 0.864398i \(-0.667700\pi\)
0.999995 + 0.00324627i \(0.00103332\pi\)
\(522\) 0 0
\(523\) −4.91928 27.8986i −0.215105 1.21992i −0.880724 0.473630i \(-0.842943\pi\)
0.665619 0.746292i \(-0.268168\pi\)
\(524\) 0 0
\(525\) −7.52706 13.0373i −0.328508 0.568992i
\(526\) 0 0
\(527\) −5.46946 + 1.99072i −0.238254 + 0.0867172i
\(528\) 0 0
\(529\) −7.04276 5.90957i −0.306207 0.256938i
\(530\) 0 0
\(531\) 75.1059 3.25932
\(532\) 0 0
\(533\) 47.4385 2.05479
\(534\) 0 0
\(535\) −13.7061 11.5008i −0.592568 0.497224i
\(536\) 0 0
\(537\) 33.5442 12.2091i 1.44754 0.526861i
\(538\) 0 0
\(539\) −15.0267 26.0270i −0.647246 1.12106i
\(540\) 0 0
\(541\) 5.93465 + 33.6570i 0.255150 + 1.44703i 0.795686 + 0.605709i \(0.207110\pi\)
−0.540536 + 0.841321i \(0.681779\pi\)
\(542\) 0 0
\(543\) 6.50851 11.2731i 0.279307 0.483774i
\(544\) 0 0
\(545\) −2.74427 + 2.30271i −0.117551 + 0.0986373i
\(546\) 0 0
\(547\) −9.80260 3.56786i −0.419129 0.152550i 0.123842 0.992302i \(-0.460478\pi\)
−0.542971 + 0.839751i \(0.682701\pi\)
\(548\) 0 0
\(549\) −1.27501 + 7.23092i −0.0544160 + 0.308608i
\(550\) 0 0
\(551\) −7.20683 + 10.5538i −0.307021 + 0.449609i
\(552\) 0 0
\(553\) −2.49505 + 14.1502i −0.106100 + 0.601726i
\(554\) 0 0
\(555\) −11.0716 4.02972i −0.469961 0.171052i
\(556\) 0 0
\(557\) 34.2712 28.7569i 1.45212 1.21847i 0.521098 0.853497i \(-0.325523\pi\)
0.931018 0.364973i \(-0.118922\pi\)
\(558\) 0 0
\(559\) 27.6160 47.8323i 1.16803 2.02309i
\(560\) 0 0
\(561\) −4.78296 27.1255i −0.201937 1.14524i
\(562\) 0 0
\(563\) 22.6253 + 39.1882i 0.953544 + 1.65159i 0.737666 + 0.675166i \(0.235928\pi\)
0.215877 + 0.976420i \(0.430739\pi\)
\(564\) 0 0
\(565\) −8.82406 + 3.21169i −0.371231 + 0.135117i
\(566\) 0 0
\(567\) −56.8371 47.6920i −2.38694 2.00288i
\(568\) 0 0
\(569\) −29.3968 −1.23238 −0.616188 0.787599i \(-0.711324\pi\)
−0.616188 + 0.787599i \(0.711324\pi\)
\(570\) 0 0
\(571\) 13.9236 0.582685 0.291342 0.956619i \(-0.405898\pi\)
0.291342 + 0.956619i \(0.405898\pi\)
\(572\) 0 0
\(573\) −42.1653 35.3809i −1.76148 1.47806i
\(574\) 0 0
\(575\) −3.49160 + 1.27084i −0.145610 + 0.0529977i
\(576\) 0 0
\(577\) −18.9117 32.7560i −0.787305 1.36365i −0.927613 0.373544i \(-0.878143\pi\)
0.140308 0.990108i \(-0.455191\pi\)
\(578\) 0 0
\(579\) −4.08713 23.1793i −0.169855 0.963298i
\(580\) 0 0
\(581\) −25.7521 + 44.6040i −1.06838 + 1.85049i
\(582\) 0 0
\(583\) 2.41207 2.02397i 0.0998977 0.0838241i
\(584\) 0 0
\(585\) 35.7422 + 13.0091i 1.47776 + 0.537860i
\(586\) 0 0
\(587\) −1.92362 + 10.9094i −0.0793961 + 0.450278i 0.919030 + 0.394188i \(0.128974\pi\)
−0.998426 + 0.0560893i \(0.982137\pi\)
\(588\) 0 0
\(589\) 1.29197 5.05836i 0.0532347 0.208426i
\(590\) 0 0
\(591\) −9.10675 + 51.6470i −0.374602 + 2.12447i
\(592\) 0 0
\(593\) −6.04698 2.20092i −0.248320 0.0903810i 0.214862 0.976645i \(-0.431070\pi\)
−0.463181 + 0.886263i \(0.653292\pi\)
\(594\) 0 0
\(595\) 18.0368 15.1347i 0.739437 0.620461i
\(596\) 0 0
\(597\) −10.8578 + 18.8062i −0.444378 + 0.769686i
\(598\) 0 0
\(599\) 2.10667 + 11.9475i 0.0860760 + 0.488161i 0.997119 + 0.0758504i \(0.0241672\pi\)
−0.911043 + 0.412311i \(0.864722\pi\)
\(600\) 0 0
\(601\) 4.88333 + 8.45817i 0.199195 + 0.345016i 0.948268 0.317472i \(-0.102834\pi\)
−0.749073 + 0.662488i \(0.769501\pi\)
\(602\) 0 0
\(603\) 28.1565 10.2481i 1.14662 0.417337i
\(604\) 0 0
\(605\) 5.87735 + 4.93168i 0.238948 + 0.200501i
\(606\) 0 0
\(607\) 39.3662 1.59782 0.798912 0.601448i \(-0.205409\pi\)
0.798912 + 0.601448i \(0.205409\pi\)
\(608\) 0 0
\(609\) 44.1368 1.78851
\(610\) 0 0
\(611\) 18.3620 + 15.4076i 0.742847 + 0.623323i
\(612\) 0 0
\(613\) −26.8857 + 9.78559i −1.08590 + 0.395236i −0.822101 0.569341i \(-0.807198\pi\)
−0.263801 + 0.964577i \(0.584976\pi\)
\(614\) 0 0
\(615\) −12.8926 22.3307i −0.519880 0.900459i
\(616\) 0 0
\(617\) 1.47446 + 8.36209i 0.0593596 + 0.336645i 0.999996 0.00277049i \(-0.000881874\pi\)
−0.940637 + 0.339415i \(0.889771\pi\)
\(618\) 0 0
\(619\) −1.44286 + 2.49910i −0.0579932 + 0.100447i −0.893564 0.448935i \(-0.851804\pi\)
0.835571 + 0.549382i \(0.185137\pi\)
\(620\) 0 0
\(621\) −32.3157 + 27.1161i −1.29678 + 1.08813i
\(622\) 0 0
\(623\) 9.73746 + 3.54415i 0.390123 + 0.141993i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) 22.5121 + 10.1777i 0.899045 + 0.406459i
\(628\) 0 0
\(629\) 3.19995 18.1478i 0.127590 0.723601i
\(630\) 0 0
\(631\) −18.8983 6.87842i −0.752329 0.273826i −0.0627438 0.998030i \(-0.519985\pi\)
−0.689586 + 0.724204i \(0.742207\pi\)
\(632\) 0 0
\(633\) −28.8779 + 24.2314i −1.14779 + 0.963112i
\(634\) 0 0
\(635\) −4.41489 + 7.64682i −0.175200 + 0.303455i
\(636\) 0 0
\(637\) 16.3534 + 92.7447i 0.647945 + 3.67468i
\(638\) 0 0
\(639\) −24.6228 42.6480i −0.974063 1.68713i
\(640\) 0 0
\(641\) 10.1310 3.68738i 0.400151 0.145643i −0.134103 0.990967i \(-0.542815\pi\)
0.534253 + 0.845325i \(0.320593\pi\)
\(642\) 0 0
\(643\) −19.0031 15.9455i −0.749410 0.628830i 0.185937 0.982562i \(-0.440468\pi\)
−0.935347 + 0.353732i \(0.884912\pi\)
\(644\) 0 0
\(645\) −30.0214 −1.18209
\(646\) 0 0
\(647\) 9.02231 0.354704 0.177352 0.984148i \(-0.443247\pi\)
0.177352 + 0.984148i \(0.443247\pi\)
\(648\) 0 0
\(649\) 15.7731 + 13.2352i 0.619147 + 0.519526i
\(650\) 0 0
\(651\) −16.9433 + 6.16684i −0.664059 + 0.241698i
\(652\) 0 0
\(653\) −0.239792 0.415332i −0.00938379 0.0162532i 0.861295 0.508105i \(-0.169654\pi\)
−0.870679 + 0.491851i \(0.836320\pi\)
\(654\) 0 0
\(655\) −1.47788 8.38149i −0.0577457 0.327492i
\(656\) 0 0
\(657\) 23.8119 41.2434i 0.928991 1.60906i
\(658\) 0 0
\(659\) −30.2891 + 25.4156i −1.17989 + 0.990049i −0.179915 + 0.983682i \(0.557582\pi\)
−0.999980 + 0.00636726i \(0.997973\pi\)
\(660\) 0 0
\(661\) 34.9478 + 12.7199i 1.35931 + 0.494749i 0.915841 0.401541i \(-0.131525\pi\)
0.443470 + 0.896289i \(0.353747\pi\)
\(662\) 0 0
\(663\) −14.9879 + 85.0005i −0.582081 + 3.30115i
\(664\) 0 0
\(665\) 2.08738 + 21.0159i 0.0809452 + 0.814960i
\(666\) 0 0
\(667\) 1.89171 10.7284i 0.0732473 0.415406i
\(668\) 0 0
\(669\) −1.25850 0.458056i −0.0486564 0.0177095i
\(670\) 0 0
\(671\) −1.54200 + 1.29389i −0.0595282 + 0.0499501i
\(672\) 0 0
\(673\) 1.24483 2.15611i 0.0479848 0.0831121i −0.841035 0.540980i \(-0.818053\pi\)
0.889020 + 0.457868i \(0.151387\pi\)
\(674\) 0 0
\(675\) −1.97147 11.1808i −0.0758819 0.430348i
\(676\) 0 0
\(677\) 23.7550 + 41.1449i 0.912980 + 1.58133i 0.809832 + 0.586662i \(0.199558\pi\)
0.103149 + 0.994666i \(0.467108\pi\)
\(678\) 0 0
\(679\) −38.3914 + 13.9733i −1.47333 + 0.536247i
\(680\) 0 0
\(681\) 37.8567 + 31.7655i 1.45067 + 1.21726i
\(682\) 0 0
\(683\) −34.0911 −1.30446 −0.652229 0.758022i \(-0.726166\pi\)
−0.652229 + 0.758022i \(0.726166\pi\)
\(684\) 0 0
\(685\) 15.9396 0.609020
\(686\) 0 0
\(687\) 27.5785 + 23.1411i 1.05218 + 0.882888i
\(688\) 0 0
\(689\) −9.27183 + 3.37467i −0.353229 + 0.128565i
\(690\) 0 0
\(691\) −18.0270 31.2237i −0.685779 1.18780i −0.973191 0.229997i \(-0.926128\pi\)
0.287412 0.957807i \(-0.407205\pi\)
\(692\) 0 0
\(693\) −10.2123 57.9169i −0.387933 2.20008i
\(694\) 0 0
\(695\) −2.70956 + 4.69309i −0.102779 + 0.178019i
\(696\) 0 0
\(697\) 30.8940 25.9232i 1.17020 0.981911i
\(698\) 0 0
\(699\) −5.39991 1.96541i −0.204243 0.0743385i
\(700\) 0 0
\(701\) −0.00505498 + 0.0286682i −0.000190924 + 0.00108278i −0.984903 0.173107i \(-0.944619\pi\)
0.984712 + 0.174190i \(0.0557305\pi\)
\(702\) 0 0
\(703\) 11.8241 + 11.5498i 0.445954 + 0.435610i
\(704\) 0 0
\(705\) 2.26243 12.8309i 0.0852082 0.483240i
\(706\) 0 0
\(707\) −16.4967 6.00432i −0.620424 0.225816i
\(708\) 0 0
\(709\) −15.5141 + 13.0179i −0.582643 + 0.488896i −0.885814 0.464041i \(-0.846399\pi\)
0.303171 + 0.952936i \(0.401955\pi\)
\(710\) 0 0
\(711\) −9.86641 + 17.0891i −0.370019 + 0.640892i
\(712\) 0 0
\(713\) 0.772796 + 4.38275i 0.0289414 + 0.164135i
\(714\) 0 0
\(715\) 5.21379 + 9.03054i 0.194985 + 0.337723i
\(716\) 0 0
\(717\) −25.4456 + 9.26145i −0.950285 + 0.345875i
\(718\) 0 0
\(719\) 26.5829 + 22.3057i 0.991373 + 0.831861i 0.985766 0.168123i \(-0.0537707\pi\)
0.00560732 + 0.999984i \(0.498215\pi\)
\(720\) 0 0
\(721\) 11.5216 0.429088
\(722\) 0 0
\(723\) −46.2817 −1.72124
\(724\) 0 0
\(725\) 2.24595 + 1.88457i 0.0834124 + 0.0699913i
\(726\) 0 0
\(727\) 5.49635 2.00051i 0.203848 0.0741947i −0.238078 0.971246i \(-0.576517\pi\)
0.441926 + 0.897051i \(0.354295\pi\)
\(728\) 0 0
\(729\) 1.96519 + 3.40381i 0.0727849 + 0.126067i
\(730\) 0 0
\(731\) −8.15362 46.2415i −0.301573 1.71030i
\(732\) 0 0
\(733\) 12.8746 22.2995i 0.475534 0.823650i −0.524073 0.851673i \(-0.675588\pi\)
0.999607 + 0.0280237i \(0.00892138\pi\)
\(734\) 0 0
\(735\) 39.2131 32.9037i 1.44640 1.21367i
\(736\) 0 0
\(737\) 7.71911 + 2.80953i 0.284337 + 0.103490i
\(738\) 0 0
\(739\) 6.21157 35.2276i 0.228496 1.29587i −0.627391 0.778704i \(-0.715877\pi\)
0.855887 0.517162i \(-0.173012\pi\)
\(740\) 0 0
\(741\) −55.3815 54.0970i −2.03449 1.98730i
\(742\) 0 0
\(743\) −1.58183 + 8.97099i −0.0580316 + 0.329114i −0.999978 0.00664994i \(-0.997883\pi\)
0.941946 + 0.335764i \(0.108994\pi\)
\(744\) 0 0
\(745\) −16.7796 6.10726i −0.614756 0.223753i
\(746\) 0 0
\(747\) −54.1847 + 45.4664i −1.98251 + 1.66353i
\(748\) 0 0
\(749\) 43.3444 75.0748i 1.58377 2.74317i
\(750\) 0 0
\(751\) −0.364246 2.06574i −0.0132915 0.0753799i 0.977441 0.211211i \(-0.0677407\pi\)
−0.990732 + 0.135831i \(0.956630\pi\)
\(752\) 0 0
\(753\) 1.89611 + 3.28416i 0.0690981 + 0.119681i
\(754\) 0 0
\(755\) −0.584458 + 0.212725i −0.0212706 + 0.00774187i
\(756\) 0 0
\(757\) −24.9150 20.9061i −0.905550 0.759847i 0.0657172 0.997838i \(-0.479066\pi\)
−0.971267 + 0.237992i \(0.923511\pi\)
\(758\) 0 0
\(759\) −21.0602 −0.764436
\(760\) 0 0
\(761\) −12.1184 −0.439293 −0.219646 0.975580i \(-0.570490\pi\)
−0.219646 + 0.975580i \(0.570490\pi\)
\(762\) 0 0
\(763\) −13.2962 11.1569i −0.481356 0.403905i
\(764\) 0 0
\(765\) 30.3858 11.0595i 1.09860 0.399858i
\(766\) 0 0
\(767\) −32.2609 55.8775i −1.16487 2.01762i
\(768\) 0 0
\(769\) −1.16096 6.58415i −0.0418654 0.237431i 0.956693 0.291097i \(-0.0940203\pi\)
−0.998559 + 0.0536666i \(0.982909\pi\)
\(770\) 0 0
\(771\) 7.08799 12.2768i 0.255268 0.442136i
\(772\) 0 0
\(773\) 33.3313 27.9683i 1.19884 1.00595i 0.199182 0.979962i \(-0.436171\pi\)
0.999662 0.0259878i \(-0.00827309\pi\)
\(774\) 0 0
\(775\) −1.12549 0.409645i −0.0404288 0.0147149i
\(776\) 0 0
\(777\) 9.91278 56.2182i 0.355619 2.01682i
\(778\) 0 0
\(779\) 3.57534 + 35.9967i 0.128100 + 1.28972i
\(780\) 0 0
\(781\) 2.34437 13.2956i 0.0838881 0.475753i
\(782\) 0 0
\(783\) 31.2789 + 11.3846i 1.11782 + 0.406852i
\(784\) 0 0
\(785\) −11.3414 + 9.51660i −0.404793 + 0.339662i
\(786\) 0 0
\(787\) 21.3877 37.0446i 0.762389 1.32050i −0.179227 0.983808i \(-0.557360\pi\)