Properties

Label 1110.2.d.h.889.3
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(889,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (of order \(2\), degree \(1\), 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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.3
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.h.889.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} +1.00000 q^{6} +3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} +1.00000 q^{6} +3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.22474 - 0.224745i) q^{10} +1.44949 q^{11} +1.00000i q^{12} -0.550510i q^{13} -3.44949 q^{14} +(2.22474 + 0.224745i) q^{15} +1.00000 q^{16} +3.44949i q^{17} -1.00000i q^{18} -3.00000 q^{19} +(0.224745 - 2.22474i) q^{20} +3.44949 q^{21} +1.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.89898 - 1.00000i) q^{25} +0.550510 q^{26} +1.00000i q^{27} -3.44949i q^{28} -3.55051 q^{29} +(-0.224745 + 2.22474i) q^{30} -2.00000 q^{31} +1.00000i q^{32} -1.44949i q^{33} -3.44949 q^{34} +(-7.67423 - 0.775255i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -3.00000i q^{38} -0.550510 q^{39} +(2.22474 + 0.224745i) q^{40} -0.449490 q^{41} +3.44949i q^{42} +6.89898i q^{43} -1.44949 q^{44} +(0.224745 - 2.22474i) q^{45} +1.00000 q^{46} -6.44949i q^{47} -1.00000i q^{48} -4.89898 q^{49} +(1.00000 - 4.89898i) q^{50} +3.44949 q^{51} +0.550510i q^{52} +3.00000i q^{53} -1.00000 q^{54} +(-0.325765 + 3.22474i) q^{55} +3.44949 q^{56} +3.00000i q^{57} -3.55051i q^{58} +3.34847 q^{59} +(-2.22474 - 0.224745i) q^{60} -14.8990 q^{61} -2.00000i q^{62} -3.44949i q^{63} -1.00000 q^{64} +(1.22474 + 0.123724i) q^{65} +1.44949 q^{66} +6.89898i q^{67} -3.44949i q^{68} -1.00000 q^{69} +(0.775255 - 7.67423i) q^{70} -1.34847 q^{71} +1.00000i q^{72} +8.79796i q^{73} +1.00000 q^{74} +(-1.00000 + 4.89898i) q^{75} +3.00000 q^{76} +5.00000i q^{77} -0.550510i q^{78} -13.3485 q^{79} +(-0.224745 + 2.22474i) q^{80} +1.00000 q^{81} -0.449490i q^{82} +1.44949i q^{83} -3.44949 q^{84} +(-7.67423 - 0.775255i) q^{85} -6.89898 q^{86} +3.55051i q^{87} -1.44949i q^{88} -0.348469 q^{89} +(2.22474 + 0.224745i) q^{90} +1.89898 q^{91} +1.00000i q^{92} +2.00000i q^{93} +6.44949 q^{94} +(0.674235 - 6.67423i) q^{95} +1.00000 q^{96} +3.34847i q^{97} -4.89898i q^{98} -1.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 12 q^{26} - 24 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 16 q^{35} + 4 q^{36} - 12 q^{39} + 4 q^{40} + 8 q^{41} + 4 q^{44} - 4 q^{45} + 4 q^{46} + 4 q^{50} + 4 q^{51} - 4 q^{54} - 16 q^{55} + 4 q^{56} - 16 q^{59} - 4 q^{60} - 40 q^{61} - 4 q^{64} - 4 q^{66} - 4 q^{69} + 8 q^{70} + 24 q^{71} + 4 q^{74} - 4 q^{75} + 12 q^{76} - 24 q^{79} + 4 q^{80} + 4 q^{81} - 4 q^{84} - 16 q^{85} - 8 q^{86} + 28 q^{89} + 4 q^{90} - 12 q^{91} + 16 q^{94} - 12 q^{95} + 4 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −0.224745 + 2.22474i −0.100509 + 0.994936i
\(6\) 1.00000 0.408248
\(7\) 3.44949i 1.30378i 0.758312 + 0.651892i \(0.226025\pi\)
−0.758312 + 0.651892i \(0.773975\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −2.22474 0.224745i −0.703526 0.0710706i
\(11\) 1.44949 0.437038 0.218519 0.975833i \(-0.429878\pi\)
0.218519 + 0.975833i \(0.429878\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.550510i 0.152684i −0.997082 0.0763420i \(-0.975676\pi\)
0.997082 0.0763420i \(-0.0243241\pi\)
\(14\) −3.44949 −0.921915
\(15\) 2.22474 + 0.224745i 0.574427 + 0.0580289i
\(16\) 1.00000 0.250000
\(17\) 3.44949i 0.836624i 0.908303 + 0.418312i \(0.137378\pi\)
−0.908303 + 0.418312i \(0.862622\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0.224745 2.22474i 0.0502545 0.497468i
\(21\) 3.44949 0.752740
\(22\) 1.44949i 0.309032i
\(23\) 1.00000i 0.208514i −0.994550 0.104257i \(-0.966753\pi\)
0.994550 0.104257i \(-0.0332465\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.89898 1.00000i −0.979796 0.200000i
\(26\) 0.550510 0.107964
\(27\) 1.00000i 0.192450i
\(28\) 3.44949i 0.651892i
\(29\) −3.55051 −0.659313 −0.329657 0.944101i \(-0.606933\pi\)
−0.329657 + 0.944101i \(0.606933\pi\)
\(30\) −0.224745 + 2.22474i −0.0410326 + 0.406181i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.44949i 0.252324i
\(34\) −3.44949 −0.591583
\(35\) −7.67423 0.775255i −1.29718 0.131042i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 3.00000i 0.486664i
\(39\) −0.550510 −0.0881522
\(40\) 2.22474 + 0.224745i 0.351763 + 0.0355353i
\(41\) −0.449490 −0.0701985 −0.0350993 0.999384i \(-0.511175\pi\)
−0.0350993 + 0.999384i \(0.511175\pi\)
\(42\) 3.44949i 0.532268i
\(43\) 6.89898i 1.05208i 0.850458 + 0.526042i \(0.176325\pi\)
−0.850458 + 0.526042i \(0.823675\pi\)
\(44\) −1.44949 −0.218519
\(45\) 0.224745 2.22474i 0.0335030 0.331645i
\(46\) 1.00000 0.147442
\(47\) 6.44949i 0.940755i −0.882465 0.470377i \(-0.844118\pi\)
0.882465 0.470377i \(-0.155882\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −4.89898 −0.699854
\(50\) 1.00000 4.89898i 0.141421 0.692820i
\(51\) 3.44949 0.483025
\(52\) 0.550510i 0.0763420i
\(53\) 3.00000i 0.412082i 0.978543 + 0.206041i \(0.0660580\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.325765 + 3.22474i −0.0439262 + 0.434825i
\(56\) 3.44949 0.460957
\(57\) 3.00000i 0.397360i
\(58\) 3.55051i 0.466205i
\(59\) 3.34847 0.435934 0.217967 0.975956i \(-0.430058\pi\)
0.217967 + 0.975956i \(0.430058\pi\)
\(60\) −2.22474 0.224745i −0.287213 0.0290144i
\(61\) −14.8990 −1.90762 −0.953809 0.300412i \(-0.902876\pi\)
−0.953809 + 0.300412i \(0.902876\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 3.44949i 0.434595i
\(64\) −1.00000 −0.125000
\(65\) 1.22474 + 0.123724i 0.151911 + 0.0153461i
\(66\) 1.44949 0.178420
\(67\) 6.89898i 0.842844i 0.906865 + 0.421422i \(0.138469\pi\)
−0.906865 + 0.421422i \(0.861531\pi\)
\(68\) 3.44949i 0.418312i
\(69\) −1.00000 −0.120386
\(70\) 0.775255 7.67423i 0.0926607 0.917246i
\(71\) −1.34847 −0.160034 −0.0800169 0.996794i \(-0.525497\pi\)
−0.0800169 + 0.996794i \(0.525497\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 8.79796i 1.02972i 0.857273 + 0.514862i \(0.172157\pi\)
−0.857273 + 0.514862i \(0.827843\pi\)
\(74\) 1.00000 0.116248
\(75\) −1.00000 + 4.89898i −0.115470 + 0.565685i
\(76\) 3.00000 0.344124
\(77\) 5.00000i 0.569803i
\(78\) 0.550510i 0.0623330i
\(79\) −13.3485 −1.50182 −0.750910 0.660404i \(-0.770385\pi\)
−0.750910 + 0.660404i \(0.770385\pi\)
\(80\) −0.224745 + 2.22474i −0.0251272 + 0.248734i
\(81\) 1.00000 0.111111
\(82\) 0.449490i 0.0496378i
\(83\) 1.44949i 0.159102i 0.996831 + 0.0795511i \(0.0253487\pi\)
−0.996831 + 0.0795511i \(0.974651\pi\)
\(84\) −3.44949 −0.376370
\(85\) −7.67423 0.775255i −0.832388 0.0840882i
\(86\) −6.89898 −0.743936
\(87\) 3.55051i 0.380655i
\(88\) 1.44949i 0.154516i
\(89\) −0.348469 −0.0369377 −0.0184688 0.999829i \(-0.505879\pi\)
−0.0184688 + 0.999829i \(0.505879\pi\)
\(90\) 2.22474 + 0.224745i 0.234509 + 0.0236902i
\(91\) 1.89898 0.199067
\(92\) 1.00000i 0.104257i
\(93\) 2.00000i 0.207390i
\(94\) 6.44949 0.665214
\(95\) 0.674235 6.67423i 0.0691750 0.684762i
\(96\) 1.00000 0.102062
\(97\) 3.34847i 0.339986i 0.985445 + 0.169993i \(0.0543744\pi\)
−0.985445 + 0.169993i \(0.945626\pi\)
\(98\) 4.89898i 0.494872i
\(99\) −1.44949 −0.145679
\(100\) 4.89898 + 1.00000i 0.489898 + 0.100000i
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 3.44949i 0.341550i
\(103\) 10.2474i 1.00971i 0.863204 + 0.504856i \(0.168454\pi\)
−0.863204 + 0.504856i \(0.831546\pi\)
\(104\) −0.550510 −0.0539820
\(105\) −0.775255 + 7.67423i −0.0756572 + 0.748929i
\(106\) −3.00000 −0.291386
\(107\) 1.65153i 0.159660i 0.996809 + 0.0798298i \(0.0254377\pi\)
−0.996809 + 0.0798298i \(0.974562\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −2.34847 −0.224943 −0.112471 0.993655i \(-0.535877\pi\)
−0.112471 + 0.993655i \(0.535877\pi\)
\(110\) −3.22474 0.325765i −0.307467 0.0310605i
\(111\) −1.00000 −0.0949158
\(112\) 3.44949i 0.325946i
\(113\) 7.10102i 0.668008i −0.942572 0.334004i \(-0.891600\pi\)
0.942572 0.334004i \(-0.108400\pi\)
\(114\) −3.00000 −0.280976
\(115\) 2.22474 + 0.224745i 0.207459 + 0.0209576i
\(116\) 3.55051 0.329657
\(117\) 0.550510i 0.0508947i
\(118\) 3.34847i 0.308252i
\(119\) −11.8990 −1.09078
\(120\) 0.224745 2.22474i 0.0205163 0.203090i
\(121\) −8.89898 −0.808998
\(122\) 14.8990i 1.34889i
\(123\) 0.449490i 0.0405291i
\(124\) 2.00000 0.179605
\(125\) 3.32577 10.6742i 0.297465 0.954733i
\(126\) 3.44949 0.307305
\(127\) 15.4495i 1.37092i 0.728110 + 0.685460i \(0.240399\pi\)
−0.728110 + 0.685460i \(0.759601\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.89898 0.607421
\(130\) −0.123724 + 1.22474i −0.0108513 + 0.107417i
\(131\) 20.4495 1.78668 0.893340 0.449381i \(-0.148355\pi\)
0.893340 + 0.449381i \(0.148355\pi\)
\(132\) 1.44949i 0.126162i
\(133\) 10.3485i 0.897326i
\(134\) −6.89898 −0.595981
\(135\) −2.22474 0.224745i −0.191476 0.0193430i
\(136\) 3.44949 0.295791
\(137\) 7.34847i 0.627822i −0.949452 0.313911i \(-0.898361\pi\)
0.949452 0.313911i \(-0.101639\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) 16.6969 1.41622 0.708108 0.706104i \(-0.249549\pi\)
0.708108 + 0.706104i \(0.249549\pi\)
\(140\) 7.67423 + 0.775255i 0.648591 + 0.0655210i
\(141\) −6.44949 −0.543145
\(142\) 1.34847i 0.113161i
\(143\) 0.797959i 0.0667287i
\(144\) −1.00000 −0.0833333
\(145\) 0.797959 7.89898i 0.0662669 0.655975i
\(146\) −8.79796 −0.728124
\(147\) 4.89898i 0.404061i
\(148\) 1.00000i 0.0821995i
\(149\) 3.10102 0.254045 0.127023 0.991900i \(-0.459458\pi\)
0.127023 + 0.991900i \(0.459458\pi\)
\(150\) −4.89898 1.00000i −0.400000 0.0816497i
\(151\) 7.24745 0.589789 0.294895 0.955530i \(-0.404715\pi\)
0.294895 + 0.955530i \(0.404715\pi\)
\(152\) 3.00000i 0.243332i
\(153\) 3.44949i 0.278875i
\(154\) −5.00000 −0.402911
\(155\) 0.449490 4.44949i 0.0361039 0.357392i
\(156\) 0.550510 0.0440761
\(157\) 4.00000i 0.319235i −0.987179 0.159617i \(-0.948974\pi\)
0.987179 0.159617i \(-0.0510260\pi\)
\(158\) 13.3485i 1.06195i
\(159\) 3.00000 0.237915
\(160\) −2.22474 0.224745i −0.175882 0.0177676i
\(161\) 3.44949 0.271858
\(162\) 1.00000i 0.0785674i
\(163\) 2.10102i 0.164565i 0.996609 + 0.0822823i \(0.0262209\pi\)
−0.996609 + 0.0822823i \(0.973779\pi\)
\(164\) 0.449490 0.0350993
\(165\) 3.22474 + 0.325765i 0.251046 + 0.0253608i
\(166\) −1.44949 −0.112502
\(167\) 0.797959i 0.0617479i −0.999523 0.0308740i \(-0.990171\pi\)
0.999523 0.0308740i \(-0.00982905\pi\)
\(168\) 3.44949i 0.266134i
\(169\) 12.6969 0.976688
\(170\) 0.775255 7.67423i 0.0594594 0.588587i
\(171\) 3.00000 0.229416
\(172\) 6.89898i 0.526042i
\(173\) 19.6969i 1.49753i −0.662835 0.748765i \(-0.730647\pi\)
0.662835 0.748765i \(-0.269353\pi\)
\(174\) −3.55051 −0.269163
\(175\) 3.44949 16.8990i 0.260757 1.27744i
\(176\) 1.44949 0.109259
\(177\) 3.34847i 0.251686i
\(178\) 0.348469i 0.0261189i
\(179\) 22.6969 1.69645 0.848224 0.529637i \(-0.177672\pi\)
0.848224 + 0.529637i \(0.177672\pi\)
\(180\) −0.224745 + 2.22474i −0.0167515 + 0.165823i
\(181\) 3.34847 0.248890 0.124445 0.992227i \(-0.460285\pi\)
0.124445 + 0.992227i \(0.460285\pi\)
\(182\) 1.89898i 0.140762i
\(183\) 14.8990i 1.10136i
\(184\) −1.00000 −0.0737210
\(185\) 2.22474 + 0.224745i 0.163566 + 0.0165236i
\(186\) −2.00000 −0.146647
\(187\) 5.00000i 0.365636i
\(188\) 6.44949i 0.470377i
\(189\) −3.44949 −0.250913
\(190\) 6.67423 + 0.674235i 0.484200 + 0.0489141i
\(191\) −5.69694 −0.412216 −0.206108 0.978529i \(-0.566080\pi\)
−0.206108 + 0.978529i \(0.566080\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 17.5959i 1.26658i −0.773914 0.633291i \(-0.781704\pi\)
0.773914 0.633291i \(-0.218296\pi\)
\(194\) −3.34847 −0.240406
\(195\) 0.123724 1.22474i 0.00886009 0.0877058i
\(196\) 4.89898 0.349927
\(197\) 20.7980i 1.48179i 0.671619 + 0.740897i \(0.265599\pi\)
−0.671619 + 0.740897i \(0.734401\pi\)
\(198\) 1.44949i 0.103011i
\(199\) 21.7980 1.54522 0.772608 0.634883i \(-0.218952\pi\)
0.772608 + 0.634883i \(0.218952\pi\)
\(200\) −1.00000 + 4.89898i −0.0707107 + 0.346410i
\(201\) 6.89898 0.486616
\(202\) 10.0000i 0.703598i
\(203\) 12.2474i 0.859602i
\(204\) −3.44949 −0.241513
\(205\) 0.101021 1.00000i 0.00705558 0.0698430i
\(206\) −10.2474 −0.713974
\(207\) 1.00000i 0.0695048i
\(208\) 0.550510i 0.0381710i
\(209\) −4.34847 −0.300790
\(210\) −7.67423 0.775255i −0.529573 0.0534977i
\(211\) 8.44949 0.581687 0.290843 0.956771i \(-0.406064\pi\)
0.290843 + 0.956771i \(0.406064\pi\)
\(212\) 3.00000i 0.206041i
\(213\) 1.34847i 0.0923956i
\(214\) −1.65153 −0.112896
\(215\) −15.3485 1.55051i −1.04676 0.105744i
\(216\) 1.00000 0.0680414
\(217\) 6.89898i 0.468333i
\(218\) 2.34847i 0.159058i
\(219\) 8.79796 0.594511
\(220\) 0.325765 3.22474i 0.0219631 0.217412i
\(221\) 1.89898 0.127739
\(222\) 1.00000i 0.0671156i
\(223\) 15.5959i 1.04438i 0.852829 + 0.522190i \(0.174885\pi\)
−0.852829 + 0.522190i \(0.825115\pi\)
\(224\) −3.44949 −0.230479
\(225\) 4.89898 + 1.00000i 0.326599 + 0.0666667i
\(226\) 7.10102 0.472353
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 3.00000i 0.198680i
\(229\) 1.55051 0.102461 0.0512303 0.998687i \(-0.483686\pi\)
0.0512303 + 0.998687i \(0.483686\pi\)
\(230\) −0.224745 + 2.22474i −0.0148192 + 0.146695i
\(231\) 5.00000 0.328976
\(232\) 3.55051i 0.233102i
\(233\) 2.89898i 0.189918i 0.995481 + 0.0949592i \(0.0302721\pi\)
−0.995481 + 0.0949592i \(0.969728\pi\)
\(234\) −0.550510 −0.0359880
\(235\) 14.3485 + 1.44949i 0.935991 + 0.0945543i
\(236\) −3.34847 −0.217967
\(237\) 13.3485i 0.867076i
\(238\) 11.8990i 0.771296i
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) 2.22474 + 0.224745i 0.143607 + 0.0145072i
\(241\) −14.2474 −0.917759 −0.458879 0.888499i \(-0.651749\pi\)
−0.458879 + 0.888499i \(0.651749\pi\)
\(242\) 8.89898i 0.572048i
\(243\) 1.00000i 0.0641500i
\(244\) 14.8990 0.953809
\(245\) 1.10102 10.8990i 0.0703416 0.696310i
\(246\) −0.449490 −0.0286584
\(247\) 1.65153i 0.105084i
\(248\) 2.00000i 0.127000i
\(249\) 1.44949 0.0918577
\(250\) 10.6742 + 3.32577i 0.675098 + 0.210340i
\(251\) 8.69694 0.548946 0.274473 0.961595i \(-0.411497\pi\)
0.274473 + 0.961595i \(0.411497\pi\)
\(252\) 3.44949i 0.217297i
\(253\) 1.44949i 0.0911286i
\(254\) −15.4495 −0.969387
\(255\) −0.775255 + 7.67423i −0.0485484 + 0.480579i
\(256\) 1.00000 0.0625000
\(257\) 5.44949i 0.339930i −0.985450 0.169965i \(-0.945635\pi\)
0.985450 0.169965i \(-0.0543654\pi\)
\(258\) 6.89898i 0.429512i
\(259\) 3.44949 0.214341
\(260\) −1.22474 0.123724i −0.0759555 0.00767306i
\(261\) 3.55051 0.219771
\(262\) 20.4495i 1.26337i
\(263\) 22.4495i 1.38429i 0.721756 + 0.692147i \(0.243335\pi\)
−0.721756 + 0.692147i \(0.756665\pi\)
\(264\) −1.44949 −0.0892099
\(265\) −6.67423 0.674235i −0.409995 0.0414179i
\(266\) 10.3485 0.634505
\(267\) 0.348469i 0.0213260i
\(268\) 6.89898i 0.421422i
\(269\) −22.5959 −1.37770 −0.688849 0.724905i \(-0.741884\pi\)
−0.688849 + 0.724905i \(0.741884\pi\)
\(270\) 0.224745 2.22474i 0.0136775 0.135394i
\(271\) −12.8990 −0.783557 −0.391779 0.920060i \(-0.628140\pi\)
−0.391779 + 0.920060i \(0.628140\pi\)
\(272\) 3.44949i 0.209156i
\(273\) 1.89898i 0.114931i
\(274\) 7.34847 0.443937
\(275\) −7.10102 1.44949i −0.428208 0.0874075i
\(276\) 1.00000 0.0601929
\(277\) 15.4495i 0.928270i 0.885765 + 0.464135i \(0.153635\pi\)
−0.885765 + 0.464135i \(0.846365\pi\)
\(278\) 16.6969i 1.00142i
\(279\) 2.00000 0.119737
\(280\) −0.775255 + 7.67423i −0.0463304 + 0.458623i
\(281\) 4.34847 0.259408 0.129704 0.991553i \(-0.458597\pi\)
0.129704 + 0.991553i \(0.458597\pi\)
\(282\) 6.44949i 0.384062i
\(283\) 21.6969i 1.28975i 0.764288 + 0.644875i \(0.223090\pi\)
−0.764288 + 0.644875i \(0.776910\pi\)
\(284\) 1.34847 0.0800169
\(285\) −6.67423 0.674235i −0.395348 0.0399382i
\(286\) 0.797959 0.0471843
\(287\) 1.55051i 0.0915237i
\(288\) 1.00000i 0.0589256i
\(289\) 5.10102 0.300060
\(290\) 7.89898 + 0.797959i 0.463844 + 0.0468578i
\(291\) 3.34847 0.196291
\(292\) 8.79796i 0.514862i
\(293\) 16.1010i 0.940632i 0.882498 + 0.470316i \(0.155860\pi\)
−0.882498 + 0.470316i \(0.844140\pi\)
\(294\) −4.89898 −0.285714
\(295\) −0.752551 + 7.44949i −0.0438152 + 0.433726i
\(296\) −1.00000 −0.0581238
\(297\) 1.44949i 0.0841079i
\(298\) 3.10102i 0.179637i
\(299\) −0.550510 −0.0318368
\(300\) 1.00000 4.89898i 0.0577350 0.282843i
\(301\) −23.7980 −1.37169
\(302\) 7.24745i 0.417044i
\(303\) 10.0000i 0.574485i
\(304\) −3.00000 −0.172062
\(305\) 3.34847 33.1464i 0.191733 1.89796i
\(306\) 3.44949 0.197194
\(307\) 20.4495i 1.16711i 0.812072 + 0.583557i \(0.198340\pi\)
−0.812072 + 0.583557i \(0.801660\pi\)
\(308\) 5.00000i 0.284901i
\(309\) 10.2474 0.582957
\(310\) 4.44949 + 0.449490i 0.252714 + 0.0255293i
\(311\) 30.4949 1.72921 0.864603 0.502455i \(-0.167570\pi\)
0.864603 + 0.502455i \(0.167570\pi\)
\(312\) 0.550510i 0.0311665i
\(313\) 13.5505i 0.765920i −0.923765 0.382960i \(-0.874905\pi\)
0.923765 0.382960i \(-0.125095\pi\)
\(314\) 4.00000 0.225733
\(315\) 7.67423 + 0.775255i 0.432394 + 0.0436807i
\(316\) 13.3485 0.750910
\(317\) 8.89898i 0.499816i 0.968270 + 0.249908i \(0.0804005\pi\)
−0.968270 + 0.249908i \(0.919600\pi\)
\(318\) 3.00000i 0.168232i
\(319\) −5.14643 −0.288145
\(320\) 0.224745 2.22474i 0.0125636 0.124367i
\(321\) 1.65153 0.0921795
\(322\) 3.44949i 0.192233i
\(323\) 10.3485i 0.575804i
\(324\) −1.00000 −0.0555556
\(325\) −0.550510 + 2.69694i −0.0305368 + 0.149599i
\(326\) −2.10102 −0.116365
\(327\) 2.34847i 0.129871i
\(328\) 0.449490i 0.0248189i
\(329\) 22.2474 1.22654
\(330\) −0.325765 + 3.22474i −0.0179328 + 0.177516i
\(331\) −28.6969 −1.57733 −0.788663 0.614825i \(-0.789226\pi\)
−0.788663 + 0.614825i \(0.789226\pi\)
\(332\) 1.44949i 0.0795511i
\(333\) 1.00000i 0.0547997i
\(334\) 0.797959 0.0436624
\(335\) −15.3485 1.55051i −0.838576 0.0847134i
\(336\) 3.44949 0.188185
\(337\) 0.101021i 0.00550294i −0.999996 0.00275147i \(-0.999124\pi\)
0.999996 0.00275147i \(-0.000875821\pi\)
\(338\) 12.6969i 0.690622i
\(339\) −7.10102 −0.385674
\(340\) 7.67423 + 0.775255i 0.416194 + 0.0420441i
\(341\) −2.89898 −0.156989
\(342\) 3.00000i 0.162221i
\(343\) 7.24745i 0.391325i
\(344\) 6.89898 0.371968
\(345\) 0.224745 2.22474i 0.0120999 0.119776i
\(346\) 19.6969 1.05891
\(347\) 15.5505i 0.834795i 0.908724 + 0.417398i \(0.137058\pi\)
−0.908724 + 0.417398i \(0.862942\pi\)
\(348\) 3.55051i 0.190327i
\(349\) 31.1464 1.66723 0.833615 0.552346i \(-0.186267\pi\)
0.833615 + 0.552346i \(0.186267\pi\)
\(350\) 16.8990 + 3.44949i 0.903288 + 0.184383i
\(351\) 0.550510 0.0293841
\(352\) 1.44949i 0.0772581i
\(353\) 16.6969i 0.888688i −0.895856 0.444344i \(-0.853437\pi\)
0.895856 0.444344i \(-0.146563\pi\)
\(354\) 3.34847 0.177969
\(355\) 0.303062 3.00000i 0.0160848 0.159223i
\(356\) 0.348469 0.0184688
\(357\) 11.8990i 0.629761i
\(358\) 22.6969i 1.19957i
\(359\) 2.44949 0.129279 0.0646396 0.997909i \(-0.479410\pi\)
0.0646396 + 0.997909i \(0.479410\pi\)
\(360\) −2.22474 0.224745i −0.117254 0.0118451i
\(361\) −10.0000 −0.526316
\(362\) 3.34847i 0.175992i
\(363\) 8.89898i 0.467075i
\(364\) −1.89898 −0.0995336
\(365\) −19.5732 1.97730i −1.02451 0.103496i
\(366\) −14.8990 −0.778782
\(367\) 25.2474i 1.31791i 0.752184 + 0.658953i \(0.229000\pi\)
−0.752184 + 0.658953i \(0.771000\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 0.449490 0.0233995
\(370\) −0.224745 + 2.22474i −0.0116839 + 0.115659i
\(371\) −10.3485 −0.537266
\(372\) 2.00000i 0.103695i
\(373\) 31.8434i 1.64879i −0.566017 0.824394i \(-0.691516\pi\)
0.566017 0.824394i \(-0.308484\pi\)
\(374\) −5.00000 −0.258544
\(375\) −10.6742 3.32577i −0.551215 0.171742i
\(376\) −6.44949 −0.332607
\(377\) 1.95459i 0.100667i
\(378\) 3.44949i 0.177423i
\(379\) 14.6515 0.752599 0.376299 0.926498i \(-0.377196\pi\)
0.376299 + 0.926498i \(0.377196\pi\)
\(380\) −0.674235 + 6.67423i −0.0345875 + 0.342381i
\(381\) 15.4495 0.791501
\(382\) 5.69694i 0.291481i
\(383\) 4.79796i 0.245164i 0.992458 + 0.122582i \(0.0391175\pi\)
−0.992458 + 0.122582i \(0.960883\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −11.1237 1.12372i −0.566917 0.0572703i
\(386\) 17.5959 0.895609
\(387\) 6.89898i 0.350695i
\(388\) 3.34847i 0.169993i
\(389\) 0.202041 0.0102439 0.00512194 0.999987i \(-0.498370\pi\)
0.00512194 + 0.999987i \(0.498370\pi\)
\(390\) 1.22474 + 0.123724i 0.0620174 + 0.00626503i
\(391\) 3.44949 0.174448
\(392\) 4.89898i 0.247436i
\(393\) 20.4495i 1.03154i
\(394\) −20.7980 −1.04779
\(395\) 3.00000 29.6969i 0.150946 1.49422i
\(396\) 1.44949 0.0728396
\(397\) 3.10102i 0.155636i −0.996968 0.0778179i \(-0.975205\pi\)
0.996968 0.0778179i \(-0.0247953\pi\)
\(398\) 21.7980i 1.09263i
\(399\) −10.3485 −0.518071
\(400\) −4.89898 1.00000i −0.244949 0.0500000i
\(401\) 27.9444 1.39548 0.697738 0.716353i \(-0.254190\pi\)
0.697738 + 0.716353i \(0.254190\pi\)
\(402\) 6.89898i 0.344090i
\(403\) 1.10102i 0.0548457i
\(404\) −10.0000 −0.497519
\(405\) −0.224745 + 2.22474i −0.0111677 + 0.110548i
\(406\) 12.2474 0.607831
\(407\) 1.44949i 0.0718485i
\(408\) 3.44949i 0.170775i
\(409\) 3.75255 0.185552 0.0927759 0.995687i \(-0.470426\pi\)
0.0927759 + 0.995687i \(0.470426\pi\)
\(410\) 1.00000 + 0.101021i 0.0493865 + 0.00498905i
\(411\) −7.34847 −0.362473
\(412\) 10.2474i 0.504856i
\(413\) 11.5505i 0.568363i
\(414\) −1.00000 −0.0491473
\(415\) −3.22474 0.325765i −0.158296 0.0159912i
\(416\) 0.550510 0.0269910
\(417\) 16.6969i 0.817653i
\(418\) 4.34847i 0.212691i
\(419\) 28.5505 1.39478 0.697392 0.716690i \(-0.254344\pi\)
0.697392 + 0.716690i \(0.254344\pi\)
\(420\) 0.775255 7.67423i 0.0378286 0.374464i
\(421\) −12.8990 −0.628658 −0.314329 0.949314i \(-0.601779\pi\)
−0.314329 + 0.949314i \(0.601779\pi\)
\(422\) 8.44949i 0.411315i
\(423\) 6.44949i 0.313585i
\(424\) 3.00000 0.145693
\(425\) 3.44949 16.8990i 0.167325 0.819721i
\(426\) −1.34847 −0.0653335
\(427\) 51.3939i 2.48712i
\(428\) 1.65153i 0.0798298i
\(429\) −0.797959 −0.0385258
\(430\) 1.55051 15.3485i 0.0747722 0.740169i
\(431\) −19.0000 −0.915198 −0.457599 0.889159i \(-0.651290\pi\)
−0.457599 + 0.889159i \(0.651290\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 0.595918i 0.0286380i 0.999897 + 0.0143190i \(0.00455803\pi\)
−0.999897 + 0.0143190i \(0.995442\pi\)
\(434\) 6.89898 0.331162
\(435\) −7.89898 0.797959i −0.378727 0.0382592i
\(436\) 2.34847 0.112471
\(437\) 3.00000i 0.143509i
\(438\) 8.79796i 0.420383i
\(439\) −8.44949 −0.403272 −0.201636 0.979461i \(-0.564626\pi\)
−0.201636 + 0.979461i \(0.564626\pi\)
\(440\) 3.22474 + 0.325765i 0.153734 + 0.0155303i
\(441\) 4.89898 0.233285
\(442\) 1.89898i 0.0903252i
\(443\) 13.5959i 0.645962i 0.946406 + 0.322981i \(0.104685\pi\)
−0.946406 + 0.322981i \(0.895315\pi\)
\(444\) 1.00000 0.0474579
\(445\) 0.0783167 0.775255i 0.00371257 0.0367506i
\(446\) −15.5959 −0.738488
\(447\) 3.10102i 0.146673i
\(448\) 3.44949i 0.162973i
\(449\) 3.30306 0.155881 0.0779406 0.996958i \(-0.475166\pi\)
0.0779406 + 0.996958i \(0.475166\pi\)
\(450\) −1.00000 + 4.89898i −0.0471405 + 0.230940i
\(451\) −0.651531 −0.0306794
\(452\) 7.10102i 0.334004i
\(453\) 7.24745i 0.340515i
\(454\) 8.00000 0.375459
\(455\) −0.426786 + 4.22474i −0.0200080 + 0.198059i
\(456\) 3.00000 0.140488
\(457\) 35.5959i 1.66511i 0.553945 + 0.832553i \(0.313122\pi\)
−0.553945 + 0.832553i \(0.686878\pi\)
\(458\) 1.55051i 0.0724506i
\(459\) −3.44949 −0.161008
\(460\) −2.22474 0.224745i −0.103729 0.0104788i
\(461\) 8.69694 0.405057 0.202528 0.979276i \(-0.435084\pi\)
0.202528 + 0.979276i \(0.435084\pi\)
\(462\) 5.00000i 0.232621i
\(463\) 25.3485i 1.17804i −0.808117 0.589022i \(-0.799513\pi\)
0.808117 0.589022i \(-0.200487\pi\)
\(464\) −3.55051 −0.164828
\(465\) −4.44949 0.449490i −0.206340 0.0208446i
\(466\) −2.89898 −0.134293
\(467\) 25.8434i 1.19589i 0.801538 + 0.597944i \(0.204016\pi\)
−0.801538 + 0.597944i \(0.795984\pi\)
\(468\) 0.550510i 0.0254473i
\(469\) −23.7980 −1.09889
\(470\) −1.44949 + 14.3485i −0.0668600 + 0.661846i
\(471\) −4.00000 −0.184310
\(472\) 3.34847i 0.154126i
\(473\) 10.0000i 0.459800i
\(474\) −13.3485 −0.613115
\(475\) 14.6969 + 3.00000i 0.674342 + 0.137649i
\(476\) 11.8990 0.545389
\(477\) 3.00000i 0.137361i
\(478\) 2.00000i 0.0914779i
\(479\) −42.5959 −1.94626 −0.973129 0.230262i \(-0.926042\pi\)
−0.973129 + 0.230262i \(0.926042\pi\)
\(480\) −0.224745 + 2.22474i −0.0102582 + 0.101545i
\(481\) −0.550510 −0.0251011
\(482\) 14.2474i 0.648954i
\(483\) 3.44949i 0.156957i
\(484\) 8.89898 0.404499
\(485\) −7.44949 0.752551i −0.338264 0.0341716i
\(486\) 1.00000 0.0453609
\(487\) 15.7980i 0.715874i −0.933746 0.357937i \(-0.883480\pi\)
0.933746 0.357937i \(-0.116520\pi\)
\(488\) 14.8990i 0.674445i
\(489\) 2.10102 0.0950114
\(490\) 10.8990 + 1.10102i 0.492366 + 0.0497390i
\(491\) −17.9444 −0.809819 −0.404909 0.914357i \(-0.632697\pi\)
−0.404909 + 0.914357i \(0.632697\pi\)
\(492\) 0.449490i 0.0202646i
\(493\) 12.2474i 0.551597i
\(494\) −1.65153 −0.0743059
\(495\) 0.325765 3.22474i 0.0146421 0.144942i
\(496\) −2.00000 −0.0898027
\(497\) 4.65153i 0.208650i
\(498\) 1.44949i 0.0649532i
\(499\) −10.5959 −0.474338 −0.237169 0.971468i \(-0.576220\pi\)
−0.237169 + 0.971468i \(0.576220\pi\)
\(500\) −3.32577 + 10.6742i −0.148733 + 0.477366i
\(501\) −0.797959 −0.0356502
\(502\) 8.69694i 0.388163i
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) −3.44949 −0.153652
\(505\) −2.24745 + 22.2474i −0.100010 + 0.989998i
\(506\) 1.44949 0.0644377
\(507\) 12.6969i 0.563891i
\(508\) 15.4495i 0.685460i
\(509\) 16.5959 0.735601 0.367801 0.929905i \(-0.380111\pi\)
0.367801 + 0.929905i \(0.380111\pi\)
\(510\) −7.67423 0.775255i −0.339821 0.0343289i
\(511\) −30.3485 −1.34254
\(512\) 1.00000i 0.0441942i
\(513\) 3.00000i 0.132453i
\(514\) 5.44949 0.240367
\(515\) −22.7980 2.30306i −1.00460 0.101485i
\(516\) −6.89898 −0.303711
\(517\) 9.34847i 0.411145i
\(518\) 3.44949i 0.151562i
\(519\) −19.6969 −0.864600
\(520\) 0.123724 1.22474i 0.00542567 0.0537086i
\(521\) −7.14643 −0.313091 −0.156545 0.987671i \(-0.550036\pi\)
−0.156545 + 0.987671i \(0.550036\pi\)
\(522\) 3.55051i 0.155402i
\(523\) 31.3939i 1.37276i −0.727244 0.686379i \(-0.759199\pi\)
0.727244 0.686379i \(-0.240801\pi\)
\(524\) −20.4495 −0.893340
\(525\) −16.8990 3.44949i −0.737532 0.150548i
\(526\) −22.4495 −0.978844
\(527\) 6.89898i 0.300524i
\(528\) 1.44949i 0.0630809i
\(529\) 22.0000 0.956522
\(530\) 0.674235 6.67423i 0.0292869 0.289910i
\(531\) −3.34847 −0.145311
\(532\) 10.3485i 0.448663i
\(533\) 0.247449i 0.0107182i
\(534\) −0.348469 −0.0150797
\(535\) −3.67423 0.371173i −0.158851 0.0160472i
\(536\) 6.89898 0.297991
\(537\) 22.6969i 0.979445i
\(538\) 22.5959i 0.974179i
\(539\) −7.10102 −0.305863
\(540\) 2.22474 + 0.224745i 0.0957378 + 0.00967148i
\(541\) −42.3485 −1.82070 −0.910351 0.413836i \(-0.864189\pi\)
−0.910351 + 0.413836i \(0.864189\pi\)
\(542\) 12.8990i 0.554059i
\(543\) 3.34847i 0.143697i
\(544\) −3.44949 −0.147896
\(545\) 0.527806 5.22474i 0.0226087 0.223803i
\(546\) 1.89898 0.0812688
\(547\) 22.7980i 0.974770i 0.873187 + 0.487385i \(0.162049\pi\)
−0.873187 + 0.487385i \(0.837951\pi\)
\(548\) 7.34847i 0.313911i
\(549\) 14.8990 0.635873
\(550\) 1.44949 7.10102i 0.0618065 0.302789i
\(551\) 10.6515 0.453770
\(552\) 1.00000i 0.0425628i
\(553\) 46.0454i 1.95805i
\(554\) −15.4495 −0.656386
\(555\) 0.224745 2.22474i 0.00953989 0.0944352i
\(556\) −16.6969 −0.708108
\(557\) 21.5505i 0.913124i 0.889691 + 0.456562i \(0.150919\pi\)
−0.889691 + 0.456562i \(0.849081\pi\)
\(558\) 2.00000i 0.0846668i
\(559\) 3.79796 0.160637
\(560\) −7.67423 0.775255i −0.324296 0.0327605i
\(561\) 5.00000 0.211100
\(562\) 4.34847i 0.183429i
\(563\) 28.7423i 1.21135i 0.795714 + 0.605673i \(0.207096\pi\)
−0.795714 + 0.605673i \(0.792904\pi\)
\(564\) 6.44949 0.271573
\(565\) 15.7980 + 1.59592i 0.664625 + 0.0671408i
\(566\) −21.6969 −0.911990
\(567\) 3.44949i 0.144865i
\(568\) 1.34847i 0.0565805i
\(569\) 14.3485 0.601519 0.300760 0.953700i \(-0.402760\pi\)
0.300760 + 0.953700i \(0.402760\pi\)
\(570\) 0.674235 6.67423i 0.0282406 0.279553i
\(571\) −4.44949 −0.186205 −0.0931027 0.995657i \(-0.529678\pi\)
−0.0931027 + 0.995657i \(0.529678\pi\)
\(572\) 0.797959i 0.0333643i
\(573\) 5.69694i 0.237993i
\(574\) 1.55051 0.0647170
\(575\) −1.00000 + 4.89898i −0.0417029 + 0.204302i
\(576\) 1.00000 0.0416667
\(577\) 28.6969i 1.19467i −0.801992 0.597335i \(-0.796226\pi\)
0.801992 0.597335i \(-0.203774\pi\)
\(578\) 5.10102i 0.212174i
\(579\) −17.5959 −0.731261
\(580\) −0.797959 + 7.89898i −0.0331334 + 0.327987i
\(581\) −5.00000 −0.207435
\(582\) 3.34847i 0.138799i
\(583\) 4.34847i 0.180095i
\(584\) 8.79796 0.364062
\(585\) −1.22474 0.123724i −0.0506370 0.00511537i
\(586\) −16.1010 −0.665127
\(587\) 46.2929i 1.91071i 0.295459 + 0.955355i \(0.404527\pi\)
−0.295459 + 0.955355i \(0.595473\pi\)
\(588\) 4.89898i 0.202031i
\(589\) 6.00000 0.247226
\(590\) −7.44949 0.752551i −0.306691 0.0309820i
\(591\) 20.7980 0.855514
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) −1.44949 −0.0594733
\(595\) 2.67423 26.4722i 0.109633 1.08525i
\(596\) −3.10102 −0.127023
\(597\) 21.7980i 0.892131i
\(598\) 0.550510i 0.0225120i
\(599\) 29.1464 1.19089 0.595445 0.803396i \(-0.296976\pi\)
0.595445 + 0.803396i \(0.296976\pi\)
\(600\) 4.89898 + 1.00000i 0.200000 + 0.0408248i
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) 23.7980i 0.969932i
\(603\) 6.89898i 0.280948i
\(604\) −7.24745 −0.294895
\(605\) 2.00000 19.7980i 0.0813116 0.804901i
\(606\) 10.0000 0.406222
\(607\) 38.8990i 1.57886i −0.613840 0.789430i \(-0.710376\pi\)
0.613840 0.789430i \(-0.289624\pi\)
\(608\) 3.00000i 0.121666i
\(609\) −12.2474 −0.496292
\(610\) 33.1464 + 3.34847i 1.34206 + 0.135576i
\(611\) −3.55051 −0.143638
\(612\) 3.44949i 0.139437i
\(613\) 22.0000i 0.888572i −0.895885 0.444286i \(-0.853457\pi\)
0.895885 0.444286i \(-0.146543\pi\)
\(614\) −20.4495 −0.825274
\(615\) −1.00000 0.101021i −0.0403239 0.00407354i
\(616\) 5.00000 0.201456
\(617\) 32.7423i 1.31816i −0.752074 0.659079i \(-0.770946\pi\)
0.752074 0.659079i \(-0.229054\pi\)
\(618\) 10.2474i 0.412213i
\(619\) 13.5505 0.544641 0.272320 0.962207i \(-0.412209\pi\)
0.272320 + 0.962207i \(0.412209\pi\)
\(620\) −0.449490 + 4.44949i −0.0180519 + 0.178696i
\(621\) 1.00000 0.0401286
\(622\) 30.4949i 1.22273i
\(623\) 1.20204i 0.0481588i
\(624\) −0.550510 −0.0220380
\(625\) 23.0000 + 9.79796i 0.920000 + 0.391918i
\(626\) 13.5505 0.541587
\(627\) 4.34847i 0.173661i
\(628\) 4.00000i 0.159617i
\(629\) 3.44949 0.137540
\(630\) −0.775255 + 7.67423i −0.0308869 + 0.305749i
\(631\) −30.6969 −1.22203 −0.611013 0.791621i \(-0.709238\pi\)
−0.611013 + 0.791621i \(0.709238\pi\)
\(632\) 13.3485i 0.530974i
\(633\) 8.44949i 0.335837i
\(634\) −8.89898 −0.353424
\(635\) −34.3712 3.47219i −1.36398 0.137790i
\(636\) −3.00000 −0.118958
\(637\) 2.69694i 0.106857i
\(638\) 5.14643i 0.203749i
\(639\) 1.34847 0.0533446
\(640\) 2.22474 + 0.224745i 0.0879408 + 0.00888382i
\(641\) −11.1010 −0.438464 −0.219232 0.975673i \(-0.570355\pi\)
−0.219232 + 0.975673i \(0.570355\pi\)
\(642\) 1.65153i 0.0651807i
\(643\) 18.3031i 0.721802i 0.932604 + 0.360901i \(0.117531\pi\)
−0.932604 + 0.360901i \(0.882469\pi\)
\(644\) −3.44949 −0.135929
\(645\) −1.55051 + 15.3485i −0.0610513 + 0.604345i
\(646\) 10.3485 0.407155
\(647\) 29.2020i 1.14805i −0.818838 0.574025i \(-0.805381\pi\)
0.818838 0.574025i \(-0.194619\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 4.85357 0.190519
\(650\) −2.69694 0.550510i −0.105783 0.0215928i
\(651\) −6.89898 −0.270392
\(652\) 2.10102i 0.0822823i
\(653\) 34.6969i 1.35780i 0.734233 + 0.678898i \(0.237542\pi\)
−0.734233 + 0.678898i \(0.762458\pi\)
\(654\) −2.34847 −0.0918324
\(655\) −4.59592 + 45.4949i −0.179577 + 1.77763i
\(656\) −0.449490 −0.0175496
\(657\) 8.79796i 0.343241i
\(658\) 22.2474i 0.867296i
\(659\) −1.30306 −0.0507601 −0.0253800 0.999678i \(-0.508080\pi\)
−0.0253800 + 0.999678i \(0.508080\pi\)
\(660\) −3.22474 0.325765i −0.125523 0.0126804i
\(661\) −39.9444 −1.55366 −0.776828 0.629712i \(-0.783173\pi\)
−0.776828 + 0.629712i \(0.783173\pi\)
\(662\) 28.6969i 1.11534i
\(663\) 1.89898i 0.0737503i
\(664\) 1.44949 0.0562511
\(665\) 23.0227 + 2.32577i 0.892782 + 0.0901893i
\(666\) −1.00000 −0.0387492
\(667\) 3.55051i 0.137476i
\(668\) 0.797959i 0.0308740i
\(669\) 15.5959 0.602973
\(670\) 1.55051 15.3485i 0.0599014 0.592963i
\(671\) −21.5959 −0.833701
\(672\) 3.44949i 0.133067i
\(673\) 5.69694i 0.219601i 0.993954 + 0.109800i \(0.0350212\pi\)
−0.993954 + 0.109800i \(0.964979\pi\)
\(674\) 0.101021 0.00389116
\(675\) 1.00000 4.89898i 0.0384900 0.188562i
\(676\) −12.6969 −0.488344
\(677\) 7.00000i 0.269032i 0.990911 + 0.134516i \(0.0429479\pi\)
−0.990911 + 0.134516i \(0.957052\pi\)
\(678\) 7.10102i 0.272713i
\(679\) −11.5505 −0.443268
\(680\) −0.775255 + 7.67423i −0.0297297 + 0.294293i
\(681\) −8.00000 −0.306561
\(682\) 2.89898i 0.111008i
\(683\) 12.9444i 0.495303i −0.968849 0.247652i \(-0.920341\pi\)
0.968849 0.247652i \(-0.0796588\pi\)
\(684\) −3.00000 −0.114708
\(685\) 16.3485 + 1.65153i 0.624643 + 0.0631017i
\(686\) −7.24745 −0.276709
\(687\) 1.55051i 0.0591557i
\(688\) 6.89898i 0.263021i
\(689\) 1.65153 0.0629183
\(690\) 2.22474 + 0.224745i 0.0846946 + 0.00855589i
\(691\) 39.1464 1.48920 0.744600 0.667511i \(-0.232640\pi\)
0.744600 + 0.667511i \(0.232640\pi\)
\(692\) 19.6969i 0.748765i
\(693\) 5.00000i 0.189934i
\(694\) −15.5505 −0.590289
\(695\) −3.75255 + 37.1464i −0.142342 + 1.40904i
\(696\) 3.55051 0.134582
\(697\) 1.55051i 0.0587298i
\(698\) 31.1464i 1.17891i
\(699\) 2.89898 0.109649
\(700\) −3.44949 + 16.8990i −0.130378 + 0.638721i
\(701\) −35.5959 −1.34444 −0.672220 0.740352i \(-0.734659\pi\)
−0.672220 + 0.740352i \(0.734659\pi\)
\(702\) 0.550510i 0.0207777i
\(703\) 3.00000i 0.113147i
\(704\) −1.44949 −0.0546297
\(705\) 1.44949 14.3485i 0.0545909 0.540395i
\(706\) 16.6969 0.628398
\(707\) 34.4949i 1.29731i
\(708\) 3.34847i 0.125843i
\(709\) 40.8434 1.53390 0.766952 0.641704i \(-0.221772\pi\)
0.766952 + 0.641704i \(0.221772\pi\)
\(710\) 3.00000 + 0.303062i 0.112588 + 0.0113737i
\(711\) 13.3485 0.500607
\(712\) 0.348469i 0.0130594i
\(713\) 2.00000i 0.0749006i
\(714\) −11.8990 −0.445308
\(715\) 1.77526 + 0.179337i 0.0663908 + 0.00670683i
\(716\) −22.6969 −0.848224
\(717\) 2.00000i 0.0746914i
\(718\) 2.44949i 0.0914141i
\(719\) −1.75255 −0.0653591 −0.0326796 0.999466i \(-0.510404\pi\)
−0.0326796 + 0.999466i \(0.510404\pi\)
\(720\) 0.224745 2.22474i 0.00837575 0.0829113i
\(721\) −35.3485 −1.31645
\(722\) 10.0000i 0.372161i
\(723\) 14.2474i 0.529868i
\(724\) −3.34847 −0.124445
\(725\) 17.3939 + 3.55051i 0.645992 + 0.131863i
\(726\) −8.89898 −0.330272
\(727\) 31.8434i 1.18101i 0.807036 + 0.590503i \(0.201070\pi\)
−0.807036 + 0.590503i \(0.798930\pi\)
\(728\) 1.89898i 0.0703809i
\(729\) −1.00000 −0.0370370
\(730\) 1.97730 19.5732i 0.0731830 0.724437i
\(731\) −23.7980 −0.880199
\(732\) 14.8990i 0.550682i
\(733\) 6.40408i 0.236540i −0.992981 0.118270i \(-0.962265\pi\)
0.992981 0.118270i \(-0.0377349\pi\)
\(734\) −25.2474 −0.931900
\(735\) −10.8990 1.10102i −0.402015 0.0406118i
\(736\) 1.00000 0.0368605
\(737\) 10.0000i 0.368355i
\(738\) 0.449490i 0.0165459i
\(739\) −12.2020 −0.448859 −0.224430 0.974490i \(-0.572052\pi\)
−0.224430 + 0.974490i \(0.572052\pi\)
\(740\) −2.22474 0.224745i −0.0817832 0.00826179i
\(741\) 1.65153 0.0606705
\(742\) 10.3485i 0.379904i
\(743\) 40.0454i 1.46912i 0.678542 + 0.734562i \(0.262612\pi\)
−0.678542 + 0.734562i \(0.737388\pi\)
\(744\) 2.00000 0.0733236
\(745\) −0.696938 + 6.89898i −0.0255338 + 0.252759i
\(746\) 31.8434 1.16587
\(747\) 1.44949i 0.0530341i
\(748\) 5.00000i 0.182818i
\(749\) −5.69694 −0.208162
\(750\) 3.32577 10.6742i 0.121440 0.389768i
\(751\) 12.8990 0.470690 0.235345 0.971912i \(-0.424378\pi\)
0.235345 + 0.971912i \(0.424378\pi\)
\(752\) 6.44949i 0.235189i
\(753\) 8.69694i 0.316934i
\(754\) −1.95459 −0.0711821
\(755\) −1.62883 + 16.1237i −0.0592791 + 0.586802i
\(756\) 3.44949 0.125457
\(757\) 41.0454i 1.49182i 0.666046 + 0.745910i \(0.267985\pi\)
−0.666046 + 0.745910i \(0.732015\pi\)
\(758\) 14.6515i 0.532168i
\(759\) −1.44949 −0.0526131
\(760\) −6.67423 0.674235i −0.242100 0.0244571i
\(761\) −45.1918 −1.63820 −0.819101 0.573649i \(-0.805527\pi\)
−0.819101 + 0.573649i \(0.805527\pi\)
\(762\) 15.4495i 0.559676i
\(763\) 8.10102i 0.293277i
\(764\) 5.69694 0.206108
\(765\) 7.67423 + 0.775255i 0.277463 + 0.0280294i
\(766\) −4.79796 −0.173357
\(767\) 1.84337i 0.0665601i
\(768\) 1.00000i 0.0360844i
\(769\) −8.44949 −0.304696 −0.152348 0.988327i \(-0.548684\pi\)
−0.152348 + 0.988327i \(0.548684\pi\)
\(770\) 1.12372 11.1237i 0.0404962 0.400871i
\(771\) −5.44949 −0.196259
\(772\) 17.5959i 0.633291i
\(773\) 5.69694i 0.204905i −0.994738 0.102452i \(-0.967331\pi\)
0.994738 0.102452i \(-0.0326689\pi\)
\(774\) 6.89898 0.247979
\(775\) 9.79796 + 2.00000i 0.351953 + 0.0718421i
\(776\) 3.34847 0.120203
\(777\) 3.44949i 0.123750i
\(778\) 0.202041i 0.00724352i
\(779\) 1.34847 0.0483139
\(780\) −0.123724 + 1.22474i −0.00443004 + 0.0438529i
\(781\) −1.95459