Properties

Label 1008.2.t.g.961.1
Level $1008$
Weight $2$
Character 1008.961
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\), degree \(2\), not 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.961
Dual form 1008.2.t.g.193.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73025 - 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 + 1.38008i) q^{7} +(2.98755 + 0.273062i) q^{9} +O(q^{10})\) \(q+(-1.73025 - 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 + 1.38008i) q^{7} +(2.98755 + 0.273062i) q^{9} +3.64766 q^{11} +(0.730252 + 1.26483i) q^{13} +(0.796790 + 0.0363376i) q^{15} +(-1.86693 - 3.23361i) q^{17} +(2.02704 - 3.51094i) q^{19} +(4.01459 - 2.20977i) q^{21} -1.13307 q^{23} -4.78794 q^{25} +(-5.14766 - 0.708209i) q^{27} +(-4.48755 + 7.77266i) q^{29} +(-0.257295 + 0.445647i) q^{31} +(-6.31138 - 0.287831i) q^{33} +(1.03950 - 0.635534i) q^{35} +(-4.55408 + 7.88791i) q^{37} +(-1.16372 - 2.24611i) q^{39} +(-0.472958 - 0.819187i) q^{41} +(-4.66372 + 8.07779i) q^{43} +(-1.37578 - 0.125747i) q^{45} +(1.16372 + 2.01561i) q^{47} +(3.19076 - 6.23049i) q^{49} +(2.97509 + 5.74228i) q^{51} +(6.21780 + 10.7695i) q^{53} -1.67977 q^{55} +(-3.78434 + 5.91486i) q^{57} +(-6.44805 + 11.1684i) q^{59} +(-6.04163 - 10.4644i) q^{61} +(-7.12062 + 3.50667i) q^{63} +(-0.336285 - 0.582462i) q^{65} +(-1.16012 + 2.00938i) q^{67} +(1.96050 + 0.0894089i) q^{69} -1.67977 q^{71} +(-6.62062 - 11.4673i) q^{73} +(8.28434 + 0.377808i) q^{75} +(-8.23385 + 5.03407i) q^{77} +(-2.50360 - 4.33636i) q^{79} +(8.85087 + 1.63157i) q^{81} +(-3.32383 + 5.75705i) q^{83} +(0.859728 + 1.48909i) q^{85} +(8.37792 - 13.0946i) q^{87} +(-1.36333 + 2.36135i) q^{89} +(-3.39397 - 1.84730i) q^{91} +(0.480350 - 0.750780i) q^{93} +(-0.933463 + 1.61680i) q^{95} +(-5.59358 + 9.68836i) q^{97} +(10.8976 + 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.73025 0.0789082i −0.998962 0.0455577i
\(4\) 0 0
\(5\) −0.460505 −0.205944 −0.102972 0.994684i \(-0.532835\pi\)
−0.102972 + 0.994684i \(0.532835\pi\)
\(6\) 0 0
\(7\) −2.25729 + 1.38008i −0.853177 + 0.521621i
\(8\) 0 0
\(9\) 2.98755 + 0.273062i 0.995849 + 0.0910208i
\(10\) 0 0
\(11\) 3.64766 1.09981 0.549906 0.835227i \(-0.314664\pi\)
0.549906 + 0.835227i \(0.314664\pi\)
\(12\) 0 0
\(13\) 0.730252 + 1.26483i 0.202536 + 0.350802i 0.949345 0.314236i \(-0.101748\pi\)
−0.746809 + 0.665038i \(0.768415\pi\)
\(14\) 0 0
\(15\) 0.796790 + 0.0363376i 0.205730 + 0.00938234i
\(16\) 0 0
\(17\) −1.86693 3.23361i −0.452796 0.784266i 0.545763 0.837940i \(-0.316240\pi\)
−0.998558 + 0.0536743i \(0.982907\pi\)
\(18\) 0 0
\(19\) 2.02704 3.51094i 0.465035 0.805465i −0.534168 0.845378i \(-0.679375\pi\)
0.999203 + 0.0399136i \(0.0127083\pi\)
\(20\) 0 0
\(21\) 4.01459 2.20977i 0.876055 0.482211i
\(22\) 0 0
\(23\) −1.13307 −0.236262 −0.118131 0.992998i \(-0.537690\pi\)
−0.118131 + 0.992998i \(0.537690\pi\)
\(24\) 0 0
\(25\) −4.78794 −0.957587
\(26\) 0 0
\(27\) −5.14766 0.708209i −0.990668 0.136295i
\(28\) 0 0
\(29\) −4.48755 + 7.77266i −0.833317 + 1.44335i 0.0620772 + 0.998071i \(0.480228\pi\)
−0.895394 + 0.445275i \(0.853106\pi\)
\(30\) 0 0
\(31\) −0.257295 + 0.445647i −0.0462115 + 0.0800406i −0.888206 0.459446i \(-0.848048\pi\)
0.841994 + 0.539486i \(0.181381\pi\)
\(32\) 0 0
\(33\) −6.31138 0.287831i −1.09867 0.0501049i
\(34\) 0 0
\(35\) 1.03950 0.635534i 0.175707 0.107425i
\(36\) 0 0
\(37\) −4.55408 + 7.88791i −0.748687 + 1.29676i 0.199765 + 0.979844i \(0.435982\pi\)
−0.948452 + 0.316920i \(0.897351\pi\)
\(38\) 0 0
\(39\) −1.16372 2.24611i −0.186344 0.359665i
\(40\) 0 0
\(41\) −0.472958 0.819187i −0.0738636 0.127936i 0.826728 0.562602i \(-0.190200\pi\)
−0.900592 + 0.434666i \(0.856866\pi\)
\(42\) 0 0
\(43\) −4.66372 + 8.07779i −0.711210 + 1.23185i 0.253193 + 0.967416i \(0.418519\pi\)
−0.964403 + 0.264436i \(0.914814\pi\)
\(44\) 0 0
\(45\) −1.37578 0.125747i −0.205089 0.0187452i
\(46\) 0 0
\(47\) 1.16372 + 2.01561i 0.169745 + 0.294007i 0.938330 0.345740i \(-0.112372\pi\)
−0.768585 + 0.639748i \(0.779039\pi\)
\(48\) 0 0
\(49\) 3.19076 6.23049i 0.455822 0.890071i
\(50\) 0 0
\(51\) 2.97509 + 5.74228i 0.416596 + 0.804080i
\(52\) 0 0
\(53\) 6.21780 + 10.7695i 0.854080 + 1.47931i 0.877495 + 0.479585i \(0.159213\pi\)
−0.0234151 + 0.999726i \(0.507454\pi\)
\(54\) 0 0
\(55\) −1.67977 −0.226500
\(56\) 0 0
\(57\) −3.78434 + 5.91486i −0.501248 + 0.783443i
\(58\) 0 0
\(59\) −6.44805 + 11.1684i −0.839465 + 1.45400i 0.0508779 + 0.998705i \(0.483798\pi\)
−0.890343 + 0.455291i \(0.849535\pi\)
\(60\) 0 0
\(61\) −6.04163 10.4644i −0.773552 1.33983i −0.935605 0.353049i \(-0.885145\pi\)
0.162053 0.986782i \(-0.448188\pi\)
\(62\) 0 0
\(63\) −7.12062 + 3.50667i −0.897114 + 0.441799i
\(64\) 0 0
\(65\) −0.336285 0.582462i −0.0417110 0.0722456i
\(66\) 0 0
\(67\) −1.16012 + 2.00938i −0.141731 + 0.245485i −0.928148 0.372210i \(-0.878600\pi\)
0.786418 + 0.617695i \(0.211933\pi\)
\(68\) 0 0
\(69\) 1.96050 + 0.0894089i 0.236017 + 0.0107636i
\(70\) 0 0
\(71\) −1.67977 −0.199352 −0.0996758 0.995020i \(-0.531781\pi\)
−0.0996758 + 0.995020i \(0.531781\pi\)
\(72\) 0 0
\(73\) −6.62062 11.4673i −0.774885 1.34214i −0.934859 0.355019i \(-0.884474\pi\)
0.159974 0.987121i \(-0.448859\pi\)
\(74\) 0 0
\(75\) 8.28434 + 0.377808i 0.956593 + 0.0436255i
\(76\) 0 0
\(77\) −8.23385 + 5.03407i −0.938334 + 0.573685i
\(78\) 0 0
\(79\) −2.50360 4.33636i −0.281677 0.487879i 0.690121 0.723694i \(-0.257557\pi\)
−0.971798 + 0.235815i \(0.924224\pi\)
\(80\) 0 0
\(81\) 8.85087 + 1.63157i 0.983430 + 0.181286i
\(82\) 0 0
\(83\) −3.32383 + 5.75705i −0.364838 + 0.631918i −0.988750 0.149577i \(-0.952209\pi\)
0.623912 + 0.781494i \(0.285542\pi\)
\(84\) 0 0
\(85\) 0.859728 + 1.48909i 0.0932506 + 0.161515i
\(86\) 0 0
\(87\) 8.37792 13.0946i 0.898207 1.40388i
\(88\) 0 0
\(89\) −1.36333 + 2.36135i −0.144512 + 0.250303i −0.929191 0.369600i \(-0.879495\pi\)
0.784679 + 0.619903i \(0.212828\pi\)
\(90\) 0 0
\(91\) −3.39397 1.84730i −0.355784 0.193649i
\(92\) 0 0
\(93\) 0.480350 0.750780i 0.0498099 0.0778522i
\(94\) 0 0
\(95\) −0.933463 + 1.61680i −0.0957713 + 0.165881i
\(96\) 0 0
\(97\) −5.59358 + 9.68836i −0.567942 + 0.983704i 0.428827 + 0.903386i \(0.358927\pi\)
−0.996769 + 0.0803178i \(0.974406\pi\)
\(98\) 0 0
\(99\) 10.8976 + 0.996040i 1.09525 + 0.100106i
\(100\) 0 0
\(101\) 13.7558 1.36876 0.684378 0.729127i \(-0.260074\pi\)
0.684378 + 0.729127i \(0.260074\pi\)
\(102\) 0 0
\(103\) −11.1623 −1.09985 −0.549925 0.835214i \(-0.685344\pi\)
−0.549925 + 0.835214i \(0.685344\pi\)
\(104\) 0 0
\(105\) −1.84874 + 1.01761i −0.180418 + 0.0993085i
\(106\) 0 0
\(107\) 3.89037 6.73832i 0.376096 0.651418i −0.614394 0.788999i \(-0.710600\pi\)
0.990490 + 0.137581i \(0.0439329\pi\)
\(108\) 0 0
\(109\) −3.75729 6.50783i −0.359884 0.623337i 0.628058 0.778167i \(-0.283850\pi\)
−0.987941 + 0.154830i \(0.950517\pi\)
\(110\) 0 0
\(111\) 8.50214 13.2887i 0.806987 1.26131i
\(112\) 0 0
\(113\) 3.03064 + 5.24922i 0.285099 + 0.493805i 0.972633 0.232346i \(-0.0746403\pi\)
−0.687534 + 0.726152i \(0.741307\pi\)
\(114\) 0 0
\(115\) 0.521786 0.0486568
\(116\) 0 0
\(117\) 1.83628 + 3.97816i 0.169765 + 0.367781i
\(118\) 0 0
\(119\) 8.67684 + 4.72270i 0.795405 + 0.432929i
\(120\) 0 0
\(121\) 2.30545 0.209586
\(122\) 0 0
\(123\) 0.753696 + 1.45472i 0.0679585 + 0.131168i
\(124\) 0 0
\(125\) 4.50739 0.403153
\(126\) 0 0
\(127\) −8.80992 −0.781754 −0.390877 0.920443i \(-0.627828\pi\)
−0.390877 + 0.920443i \(0.627828\pi\)
\(128\) 0 0
\(129\) 8.70681 13.6086i 0.766592 1.19817i
\(130\) 0 0
\(131\) −21.1373 −1.84678 −0.923389 0.383865i \(-0.874593\pi\)
−0.923389 + 0.383865i \(0.874593\pi\)
\(132\) 0 0
\(133\) 0.269748 + 10.7227i 0.0233901 + 0.929777i
\(134\) 0 0
\(135\) 2.37052 + 0.326134i 0.204022 + 0.0280691i
\(136\) 0 0
\(137\) −4.40642 −0.376466 −0.188233 0.982124i \(-0.560276\pi\)
−0.188233 + 0.982124i \(0.560276\pi\)
\(138\) 0 0
\(139\) 1.01245 + 1.75362i 0.0858751 + 0.148740i 0.905764 0.423783i \(-0.139298\pi\)
−0.819889 + 0.572523i \(0.805965\pi\)
\(140\) 0 0
\(141\) −1.85447 3.57935i −0.156175 0.301435i
\(142\) 0 0
\(143\) 2.66372 + 4.61369i 0.222751 + 0.385816i
\(144\) 0 0
\(145\) 2.06654 3.57935i 0.171617 0.297249i
\(146\) 0 0
\(147\) −6.01245 + 10.5286i −0.495899 + 0.868380i
\(148\) 0 0
\(149\) −9.16225 −0.750601 −0.375300 0.926903i \(-0.622460\pi\)
−0.375300 + 0.926903i \(0.622460\pi\)
\(150\) 0 0
\(151\) 0.103896 0.00845496 0.00422748 0.999991i \(-0.498654\pi\)
0.00422748 + 0.999991i \(0.498654\pi\)
\(152\) 0 0
\(153\) −4.69455 10.1703i −0.379532 0.822224i
\(154\) 0 0
\(155\) 0.118485 0.205223i 0.00951698 0.0164839i
\(156\) 0 0
\(157\) −10.4911 + 18.1712i −0.837285 + 1.45022i 0.0548721 + 0.998493i \(0.482525\pi\)
−0.892157 + 0.451726i \(0.850808\pi\)
\(158\) 0 0
\(159\) −9.90856 19.1247i −0.785800 1.51668i
\(160\) 0 0
\(161\) 2.55768 1.56373i 0.201574 0.123239i
\(162\) 0 0
\(163\) 11.5182 19.9501i 0.902174 1.56261i 0.0775078 0.996992i \(-0.475304\pi\)
0.824666 0.565620i \(-0.191363\pi\)
\(164\) 0 0
\(165\) 2.90642 + 0.132547i 0.226265 + 0.0103188i
\(166\) 0 0
\(167\) 5.31498 + 9.20581i 0.411285 + 0.712367i 0.995031 0.0995698i \(-0.0317467\pi\)
−0.583745 + 0.811937i \(0.698413\pi\)
\(168\) 0 0
\(169\) 5.43346 9.41103i 0.417959 0.723926i
\(170\) 0 0
\(171\) 7.01459 9.93559i 0.536419 0.759793i
\(172\) 0 0
\(173\) −1.46936 2.54500i −0.111713 0.193493i 0.804748 0.593617i \(-0.202301\pi\)
−0.916461 + 0.400124i \(0.868967\pi\)
\(174\) 0 0
\(175\) 10.8078 6.60773i 0.816991 0.499498i
\(176\) 0 0
\(177\) 12.0380 18.8153i 0.904834 1.41424i
\(178\) 0 0
\(179\) 4.58113 + 7.93474i 0.342409 + 0.593071i 0.984880 0.173240i \(-0.0554237\pi\)
−0.642470 + 0.766311i \(0.722090\pi\)
\(180\) 0 0
\(181\) 22.4284 1.66709 0.833545 0.552452i \(-0.186308\pi\)
0.833545 + 0.552452i \(0.186308\pi\)
\(182\) 0 0
\(183\) 9.62782 + 18.5828i 0.711709 + 1.37368i
\(184\) 0 0
\(185\) 2.09718 3.63242i 0.154188 0.267061i
\(186\) 0 0
\(187\) −6.80992 11.7951i −0.497990 0.862545i
\(188\) 0 0
\(189\) 12.5972 5.50555i 0.916310 0.400470i
\(190\) 0 0
\(191\) 1.24484 + 2.15613i 0.0900736 + 0.156012i 0.907542 0.419962i \(-0.137956\pi\)
−0.817468 + 0.575974i \(0.804623\pi\)
\(192\) 0 0
\(193\) −2.24484 + 3.88818i −0.161587 + 0.279877i −0.935438 0.353491i \(-0.884995\pi\)
0.773851 + 0.633368i \(0.218328\pi\)
\(194\) 0 0
\(195\) 0.535897 + 1.03434i 0.0383763 + 0.0740708i
\(196\) 0 0
\(197\) 12.7339 0.907249 0.453625 0.891193i \(-0.350131\pi\)
0.453625 + 0.891193i \(0.350131\pi\)
\(198\) 0 0
\(199\) 1.47296 + 2.55124i 0.104415 + 0.180852i 0.913499 0.406841i \(-0.133370\pi\)
−0.809084 + 0.587693i \(0.800036\pi\)
\(200\) 0 0
\(201\) 2.16585 3.38519i 0.152767 0.238773i
\(202\) 0 0
\(203\) −0.597178 23.7384i −0.0419137 1.66611i
\(204\) 0 0
\(205\) 0.217799 + 0.377240i 0.0152118 + 0.0263476i
\(206\) 0 0
\(207\) −3.38511 0.309400i −0.235282 0.0215048i
\(208\) 0 0
\(209\) 7.39397 12.8067i 0.511451 0.885860i
\(210\) 0 0
\(211\) 0.608168 + 1.05338i 0.0418680 + 0.0725176i 0.886200 0.463303i \(-0.153336\pi\)
−0.844332 + 0.535820i \(0.820002\pi\)
\(212\) 0 0
\(213\) 2.90642 + 0.132547i 0.199145 + 0.00908200i
\(214\) 0 0
\(215\) 2.14766 3.71986i 0.146469 0.253693i
\(216\) 0 0
\(217\) −0.0342393 1.36104i −0.00232432 0.0923937i
\(218\) 0 0
\(219\) 10.5505 + 20.3637i 0.712936 + 1.37605i
\(220\) 0 0
\(221\) 2.72665 4.72270i 0.183415 0.317683i
\(222\) 0 0
\(223\) 0.445916 0.772349i 0.0298607 0.0517203i −0.850709 0.525637i \(-0.823827\pi\)
0.880570 + 0.473917i \(0.157160\pi\)
\(224\) 0 0
\(225\) −14.3042 1.30740i −0.953612 0.0871603i
\(226\) 0 0
\(227\) 14.6519 0.972483 0.486242 0.873824i \(-0.338368\pi\)
0.486242 + 0.873824i \(0.338368\pi\)
\(228\) 0 0
\(229\) −9.57587 −0.632791 −0.316396 0.948627i \(-0.602473\pi\)
−0.316396 + 0.948627i \(0.602473\pi\)
\(230\) 0 0
\(231\) 14.6439 8.06049i 0.963496 0.530341i
\(232\) 0 0
\(233\) 7.21420 12.4954i 0.472618 0.818598i −0.526891 0.849933i \(-0.676642\pi\)
0.999509 + 0.0313345i \(0.00997571\pi\)
\(234\) 0 0
\(235\) −0.535897 0.928200i −0.0349580 0.0605491i
\(236\) 0 0
\(237\) 3.98968 + 7.70055i 0.259158 + 0.500205i
\(238\) 0 0
\(239\) 9.15486 + 15.8567i 0.592179 + 1.02568i 0.993938 + 0.109938i \(0.0350654\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(240\) 0 0
\(241\) 0.0933847 0.00601544 0.00300772 0.999995i \(-0.499043\pi\)
0.00300772 + 0.999995i \(0.499043\pi\)
\(242\) 0 0
\(243\) −15.1855 3.52144i −0.974150 0.225901i
\(244\) 0 0
\(245\) −1.46936 + 2.86917i −0.0938739 + 0.183305i
\(246\) 0 0
\(247\) 5.92101 0.376745
\(248\) 0 0
\(249\) 6.20535 9.69886i 0.393248 0.614641i
\(250\) 0 0
\(251\) 18.2733 1.15340 0.576702 0.816955i \(-0.304339\pi\)
0.576702 + 0.816955i \(0.304339\pi\)
\(252\) 0 0
\(253\) −4.13307 −0.259844
\(254\) 0 0
\(255\) −1.37005 2.64435i −0.0857956 0.165595i
\(256\) 0 0
\(257\) −21.0512 −1.31314 −0.656568 0.754267i \(-0.727992\pi\)
−0.656568 + 0.754267i \(0.727992\pi\)
\(258\) 0 0
\(259\) −0.606032 24.0903i −0.0376570 1.49690i
\(260\) 0 0
\(261\) −15.5292 + 21.9958i −0.961232 + 1.36151i
\(262\) 0 0
\(263\) 5.16518 0.318499 0.159249 0.987238i \(-0.449093\pi\)
0.159249 + 0.987238i \(0.449093\pi\)
\(264\) 0 0
\(265\) −2.86333 4.95943i −0.175893 0.304655i
\(266\) 0 0
\(267\) 2.54523 3.97816i 0.155766 0.243459i
\(268\) 0 0
\(269\) 8.42840 + 14.5984i 0.513889 + 0.890081i 0.999870 + 0.0161123i \(0.00512891\pi\)
−0.485981 + 0.873969i \(0.661538\pi\)
\(270\) 0 0
\(271\) −12.5562 + 21.7480i −0.762736 + 1.32110i 0.178699 + 0.983904i \(0.442811\pi\)
−0.941435 + 0.337194i \(0.890522\pi\)
\(272\) 0 0
\(273\) 5.72665 + 3.46410i 0.346593 + 0.209657i
\(274\) 0 0
\(275\) −17.4648 −1.05317
\(276\) 0 0
\(277\) 3.38151 0.203176 0.101588 0.994827i \(-0.467608\pi\)
0.101588 + 0.994827i \(0.467608\pi\)
\(278\) 0 0
\(279\) −0.890369 + 1.26113i −0.0533050 + 0.0755022i
\(280\) 0 0
\(281\) −10.1388 + 17.5609i −0.604831 + 1.04760i 0.387248 + 0.921976i \(0.373426\pi\)
−0.992078 + 0.125622i \(0.959907\pi\)
\(282\) 0 0
\(283\) 8.67471 15.0250i 0.515658 0.893145i −0.484177 0.874970i \(-0.660881\pi\)
0.999835 0.0181754i \(-0.00578571\pi\)
\(284\) 0 0
\(285\) 1.74271 2.72382i 0.103229 0.161345i
\(286\) 0 0
\(287\) 2.19815 + 1.19643i 0.129753 + 0.0706228i
\(288\) 0 0
\(289\) 1.52918 2.64861i 0.0899517 0.155801i
\(290\) 0 0
\(291\) 10.4428 16.3219i 0.612168 0.956809i
\(292\) 0 0
\(293\) −4.93560 8.54871i −0.288341 0.499421i 0.685073 0.728474i \(-0.259770\pi\)
−0.973414 + 0.229054i \(0.926437\pi\)
\(294\) 0 0
\(295\) 2.96936 5.14308i 0.172883 0.299442i
\(296\) 0 0
\(297\) −18.7769 2.58331i −1.08955 0.149899i
\(298\) 0 0
\(299\) −0.827430 1.43315i −0.0478515 0.0828813i
\(300\) 0 0
\(301\) −0.620621 24.6703i −0.0357720 1.42197i
\(302\) 0 0
\(303\) −23.8011 1.08545i −1.36734 0.0623574i
\(304\) 0 0
\(305\) 2.78220 + 4.81891i 0.159308 + 0.275930i
\(306\) 0 0
\(307\) −7.78794 −0.444481 −0.222240 0.974992i \(-0.571337\pi\)
−0.222240 + 0.974992i \(0.571337\pi\)
\(308\) 0 0
\(309\) 19.3135 + 0.880794i 1.09871 + 0.0501066i
\(310\) 0 0
\(311\) 7.70535 13.3461i 0.436930 0.756785i −0.560521 0.828140i \(-0.689399\pi\)
0.997451 + 0.0713552i \(0.0227324\pi\)
\(312\) 0 0
\(313\) −4.24844 7.35851i −0.240136 0.415928i 0.720617 0.693334i \(-0.243859\pi\)
−0.960753 + 0.277406i \(0.910525\pi\)
\(314\) 0 0
\(315\) 3.27908 1.61484i 0.184755 0.0909859i
\(316\) 0 0
\(317\) 7.05262 + 12.2155i 0.396115 + 0.686091i 0.993243 0.116055i \(-0.0370249\pi\)
−0.597128 + 0.802146i \(0.703692\pi\)
\(318\) 0 0
\(319\) −16.3691 + 28.3520i −0.916491 + 1.58741i
\(320\) 0 0
\(321\) −7.26303 + 11.3520i −0.405383 + 0.633607i
\(322\) 0 0
\(323\) −15.1373 −0.842264
\(324\) 0 0
\(325\) −3.49640 6.05594i −0.193945 0.335923i
\(326\) 0 0
\(327\) 5.98755 + 11.5567i 0.331112 + 0.639085i
\(328\) 0 0
\(329\) −5.40856 2.94381i −0.298183 0.162298i
\(330\) 0 0
\(331\) 13.7719 + 23.8536i 0.756971 + 1.31111i 0.944388 + 0.328832i \(0.106655\pi\)
−0.187417 + 0.982280i \(0.560012\pi\)
\(332\) 0 0
\(333\) −15.7594 + 22.3219i −0.863611 + 1.22323i
\(334\) 0 0
\(335\) 0.534239 0.925330i 0.0291886 0.0505562i
\(336\) 0 0
\(337\) 0.748440 + 1.29634i 0.0407701 + 0.0706159i 0.885690 0.464276i \(-0.153686\pi\)
−0.844920 + 0.534892i \(0.820352\pi\)
\(338\) 0 0
\(339\) −4.82957 9.32162i −0.262306 0.506281i
\(340\) 0 0
\(341\) −0.938524 + 1.62557i −0.0508239 + 0.0880296i
\(342\) 0 0
\(343\) 1.39610 + 18.4676i 0.0753825 + 0.997155i
\(344\) 0 0
\(345\) −0.902822 0.0411732i −0.0486063 0.00221669i
\(346\) 0 0
\(347\) −9.14406 + 15.8380i −0.490879 + 0.850228i −0.999945 0.0105001i \(-0.996658\pi\)
0.509066 + 0.860728i \(0.329991\pi\)
\(348\) 0 0
\(349\) −3.90136 + 6.75735i −0.208835 + 0.361713i −0.951348 0.308119i \(-0.900300\pi\)
0.742513 + 0.669832i \(0.233634\pi\)
\(350\) 0 0
\(351\) −2.86333 7.02811i −0.152833 0.375133i
\(352\) 0 0
\(353\) 26.9253 1.43309 0.716544 0.697542i \(-0.245723\pi\)
0.716544 + 0.697542i \(0.245723\pi\)
\(354\) 0 0
\(355\) 0.773541 0.0410553
\(356\) 0 0
\(357\) −14.6405 8.85614i −0.774856 0.468717i
\(358\) 0 0
\(359\) 3.13161 5.42411i 0.165280 0.286274i −0.771475 0.636260i \(-0.780481\pi\)
0.936755 + 0.349987i \(0.113814\pi\)
\(360\) 0 0
\(361\) 1.28220 + 2.22084i 0.0674842 + 0.116886i
\(362\) 0 0
\(363\) −3.98901 0.181919i −0.209369 0.00954827i
\(364\) 0 0
\(365\) 3.04883 + 5.28073i 0.159583 + 0.276406i
\(366\) 0 0
\(367\) −29.2733 −1.52806 −0.764028 0.645183i \(-0.776781\pi\)
−0.764028 + 0.645183i \(0.776781\pi\)
\(368\) 0 0
\(369\) −1.18929 2.57651i −0.0619122 0.134128i
\(370\) 0 0
\(371\) −28.8982 15.7290i −1.50032 0.816608i
\(372\) 0 0
\(373\) 17.8597 0.924742 0.462371 0.886687i \(-0.346999\pi\)
0.462371 + 0.886687i \(0.346999\pi\)
\(374\) 0 0
\(375\) −7.79893 0.355670i −0.402735 0.0183667i
\(376\) 0 0
\(377\) −13.1082 −0.675105
\(378\) 0 0
\(379\) 22.4255 1.15192 0.575960 0.817478i \(-0.304629\pi\)
0.575960 + 0.817478i \(0.304629\pi\)
\(380\) 0 0
\(381\) 15.2434 + 0.695175i 0.780942 + 0.0356149i
\(382\) 0 0
\(383\) 14.1403 0.722534 0.361267 0.932462i \(-0.382344\pi\)
0.361267 + 0.932462i \(0.382344\pi\)
\(384\) 0 0
\(385\) 3.79173 2.31821i 0.193244 0.118147i
\(386\) 0 0
\(387\) −16.1388 + 22.8593i −0.820382 + 1.16200i
\(388\) 0 0
\(389\) −23.1301 −1.17275 −0.586373 0.810041i \(-0.699445\pi\)
−0.586373 + 0.810041i \(0.699445\pi\)
\(390\) 0 0
\(391\) 2.11537 + 3.66392i 0.106979 + 0.185292i
\(392\) 0 0
\(393\) 36.5729 + 1.66791i 1.84486 + 0.0841350i
\(394\) 0 0
\(395\) 1.15292 + 1.99691i 0.0580097 + 0.100476i
\(396\) 0 0
\(397\) −5.13307 + 8.89075i −0.257622 + 0.446214i −0.965604 0.260016i \(-0.916272\pi\)
0.707983 + 0.706230i \(0.249605\pi\)
\(398\) 0 0
\(399\) 0.379379 18.5743i 0.0189927 0.929877i
\(400\) 0 0
\(401\) 34.0335 1.69955 0.849775 0.527146i \(-0.176738\pi\)
0.849775 + 0.527146i \(0.176738\pi\)
\(402\) 0 0
\(403\) −0.751560 −0.0374379
\(404\) 0 0
\(405\) −4.07587 0.751347i −0.202532 0.0373348i
\(406\) 0 0
\(407\) −16.6118 + 28.7724i −0.823415 + 1.42620i
\(408\) 0 0
\(409\) 1.74484 3.02215i 0.0862769 0.149436i −0.819658 0.572854i \(-0.805836\pi\)
0.905935 + 0.423418i \(0.139170\pi\)
\(410\) 0 0
\(411\) 7.62422 + 0.347703i 0.376075 + 0.0171509i
\(412\) 0 0
\(413\) −0.858071 34.1091i −0.0422229 1.67840i
\(414\) 0 0
\(415\) 1.53064 2.65115i 0.0751362 0.130140i
\(416\) 0 0
\(417\) −1.61342 3.11410i −0.0790097 0.152498i
\(418\) 0 0
\(419\) −14.4897 25.0969i −0.707867 1.22606i −0.965647 0.259858i \(-0.916324\pi\)
0.257779 0.966204i \(-0.417009\pi\)
\(420\) 0 0
\(421\) −1.06128 + 1.83819i −0.0517237 + 0.0895881i −0.890728 0.454537i \(-0.849805\pi\)
0.839004 + 0.544125i \(0.183138\pi\)
\(422\) 0 0
\(423\) 2.92627 + 6.33951i 0.142280 + 0.308237i
\(424\) 0 0
\(425\) 8.93872 + 15.4823i 0.433592 + 0.751003i
\(426\) 0 0
\(427\) 28.0795 + 15.2833i 1.35886 + 0.739612i
\(428\) 0 0
\(429\) −4.24484 8.19304i −0.204943 0.395564i
\(430\) 0 0
\(431\) −10.9356 18.9410i −0.526749 0.912356i −0.999514 0.0311679i \(-0.990077\pi\)
0.472765 0.881189i \(-0.343256\pi\)
\(432\) 0 0
\(433\) −13.0512 −0.627199 −0.313599 0.949555i \(-0.601535\pi\)
−0.313599 + 0.949555i \(0.601535\pi\)
\(434\) 0 0
\(435\) −3.85807 + 6.03011i −0.184980 + 0.289122i
\(436\) 0 0
\(437\) −2.29679 + 3.97816i −0.109870 + 0.190301i
\(438\) 0 0
\(439\) 2.43200 + 4.21235i 0.116073 + 0.201044i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796303\pi\)
\(440\) 0 0
\(441\) 11.2339 17.7426i 0.534945 0.844887i
\(442\) 0 0
\(443\) −5.76975 9.99350i −0.274129 0.474805i 0.695786 0.718249i \(-0.255056\pi\)
−0.969915 + 0.243444i \(0.921723\pi\)
\(444\) 0 0
\(445\) 0.627819 1.08741i 0.0297615 0.0515484i
\(446\) 0 0
\(447\) 15.8530 + 0.722977i 0.749822 + 0.0341957i
\(448\) 0 0
\(449\) −26.4251 −1.24708 −0.623538 0.781793i \(-0.714306\pi\)
−0.623538 + 0.781793i \(0.714306\pi\)
\(450\) 0 0
\(451\) −1.72519 2.98812i −0.0812361 0.140705i
\(452\) 0 0
\(453\) −0.179767 0.00819828i −0.00844618 0.000385189i
\(454\) 0 0
\(455\) 1.56294 + 0.850689i 0.0732717 + 0.0398809i
\(456\) 0 0
\(457\) 1.86906 + 3.23731i 0.0874310 + 0.151435i 0.906425 0.422368i \(-0.138801\pi\)
−0.818994 + 0.573803i \(0.805468\pi\)
\(458\) 0 0
\(459\) 7.32023 + 17.9677i 0.341679 + 0.838661i
\(460\) 0 0
\(461\) −7.90496 + 13.6918i −0.368171 + 0.637690i −0.989280 0.146034i \(-0.953349\pi\)
0.621109 + 0.783724i \(0.286682\pi\)
\(462\) 0 0
\(463\) −19.1965 33.2493i −0.892137 1.54523i −0.837309 0.546730i \(-0.815872\pi\)
−0.0548278 0.998496i \(-0.517461\pi\)
\(464\) 0 0
\(465\) −0.221203 + 0.345738i −0.0102581 + 0.0160332i
\(466\) 0 0
\(467\) −3.15652 + 5.46725i −0.146066 + 0.252994i −0.929770 0.368140i \(-0.879995\pi\)
0.783704 + 0.621134i \(0.213328\pi\)
\(468\) 0 0
\(469\) −0.154382 6.13682i −0.00712869 0.283372i
\(470\) 0 0
\(471\) 19.5862 30.6129i 0.902484 1.41057i
\(472\) 0 0
\(473\) −17.0117 + 29.4651i −0.782197 + 1.35481i
\(474\) 0 0
\(475\) −9.70535 + 16.8102i −0.445312 + 0.771303i
\(476\) 0 0
\(477\) 15.6352 + 33.8724i 0.715887 + 1.55091i
\(478\) 0 0
\(479\) 20.4136 0.932722 0.466361 0.884594i \(-0.345565\pi\)
0.466361 + 0.884594i \(0.345565\pi\)
\(480\) 0 0
\(481\) −13.3025 −0.606543
\(482\) 0 0
\(483\) −4.54883 + 2.50383i −0.206979 + 0.113928i
\(484\) 0 0
\(485\) 2.57587 4.46154i 0.116964 0.202588i
\(486\) 0 0
\(487\) −6.18190 10.7074i −0.280129 0.485197i 0.691287 0.722580i \(-0.257044\pi\)
−0.971416 + 0.237383i \(0.923710\pi\)
\(488\) 0 0
\(489\) −21.5036 + 33.6098i −0.972426 + 1.51989i
\(490\) 0 0
\(491\) −0.207004 0.358541i −0.00934194 0.0161807i 0.861317 0.508069i \(-0.169640\pi\)
−0.870659 + 0.491888i \(0.836307\pi\)
\(492\) 0 0
\(493\) 33.5117 1.50929
\(494\) 0 0
\(495\) −5.01838 0.458681i −0.225560 0.0206162i
\(496\) 0 0
\(497\) 3.79173 2.31821i 0.170082 0.103986i
\(498\) 0 0
\(499\) 0.923935 0.0413610 0.0206805 0.999786i \(-0.493417\pi\)
0.0206805 + 0.999786i \(0.493417\pi\)
\(500\) 0 0
\(501\) −8.46984 16.3478i −0.378404 0.730365i
\(502\) 0 0
\(503\) 23.8142 1.06182 0.530911 0.847428i \(-0.321850\pi\)
0.530911 + 0.847428i \(0.321850\pi\)
\(504\) 0 0
\(505\) −6.33463 −0.281887
\(506\) 0 0
\(507\) −10.1439 + 15.8547i −0.450505 + 0.704133i
\(508\) 0 0
\(509\) −30.6342 −1.35784 −0.678919 0.734213i \(-0.737551\pi\)
−0.678919 + 0.734213i \(0.737551\pi\)
\(510\) 0 0
\(511\) 30.7704 + 16.7480i 1.36120 + 0.740887i
\(512\) 0 0
\(513\) −12.9210 + 16.6376i −0.570477 + 0.734567i
\(514\) 0 0
\(515\) 5.14027 0.226507
\(516\) 0 0
\(517\) 4.24484 + 7.35228i 0.186688 + 0.323353i
\(518\) 0 0
\(519\) 2.34154 + 4.51945i 0.102782 + 0.198382i
\(520\) 0 0
\(521\) −13.4518 23.2993i −0.589336 1.02076i −0.994320 0.106436i \(-0.966056\pi\)
0.404984 0.914324i \(-0.367277\pi\)
\(522\) 0 0
\(523\) 7.85301 13.6018i 0.343388 0.594766i −0.641671 0.766980i \(-0.721759\pi\)
0.985060 + 0.172214i \(0.0550920\pi\)
\(524\) 0 0
\(525\) −19.2216 + 10.5802i −0.838899 + 0.461759i
\(526\) 0 0
\(527\) 1.92140 0.0836975
\(528\) 0 0
\(529\) −21.7161 −0.944180
\(530\) 0 0
\(531\) −22.3135 + 31.6053i −0.968324 + 1.37155i
\(532\) 0 0
\(533\) 0.690757 1.19643i 0.0299200 0.0518230i
\(534\) 0 0
\(535\) −1.79153 + 3.10303i −0.0774548 + 0.134156i
\(536\) 0 0
\(537\) −7.30039 14.0906i −0.315035 0.608054i
\(538\) 0 0
\(539\) 11.6388 22.7267i 0.501319 0.978910i
\(540\) 0 0
\(541\) −2.05934 + 3.56688i −0.0885379 + 0.153352i −0.906893 0.421360i \(-0.861553\pi\)
0.818355 + 0.574713i \(0.194886\pi\)
\(542\) 0 0
\(543\) −38.8068 1.76979i −1.66536 0.0759488i
\(544\) 0 0
\(545\) 1.73025 + 2.99689i 0.0741159 + 0.128372i
\(546\) 0 0
\(547\) 11.8602 20.5425i 0.507106 0.878333i −0.492860 0.870108i \(-0.664049\pi\)
0.999966 0.00822465i \(-0.00261802\pi\)
\(548\) 0 0
\(549\) −15.1922 32.9127i −0.648388 1.40468i
\(550\) 0 0
\(551\) 18.1929 + 31.5110i 0.775043 + 1.34241i
\(552\) 0 0
\(553\) 11.6359 + 6.33327i 0.494808 + 0.269318i
\(554\) 0 0
\(555\) −3.91528 + 6.11952i −0.166194 + 0.259759i
\(556\) 0 0
\(557\) −21.0313 36.4273i −0.891125 1.54347i −0.838528 0.544859i \(-0.816583\pi\)
−0.0525975 0.998616i \(-0.516750\pi\)
\(558\) 0 0
\(559\) −13.6228 −0.576181
\(560\) 0 0
\(561\) 10.8521 + 20.9459i 0.458178 + 0.884336i
\(562\) 0 0
\(563\) 5.91216 10.2402i 0.249168 0.431571i −0.714127 0.700016i \(-0.753176\pi\)
0.963295 + 0.268445i \(0.0865097\pi\)
\(564\) 0 0
\(565\) −1.39562 2.41729i −0.0587144 0.101696i
\(566\) 0 0
\(567\) −22.2307 + 8.53197i −0.933603 + 0.358309i
\(568\) 0 0
\(569\) −7.10078 12.2989i −0.297680 0.515597i 0.677925 0.735131i \(-0.262880\pi\)
−0.975605 + 0.219534i \(0.929546\pi\)
\(570\) 0 0
\(571\) 5.97869 10.3554i 0.250200 0.433360i −0.713380 0.700777i \(-0.752837\pi\)
0.963581 + 0.267417i \(0.0861701\pi\)
\(572\) 0 0
\(573\) −1.98375 3.82888i −0.0828725 0.159954i
\(574\) 0 0
\(575\) 5.42509 0.226242
\(576\) 0 0
\(577\) 21.3135 + 36.9161i 0.887293 + 1.53684i 0.843062 + 0.537816i \(0.180750\pi\)
0.0442307 + 0.999021i \(0.485916\pi\)
\(578\) 0 0
\(579\) 4.19095 6.55040i 0.174170 0.272225i
\(580\) 0 0
\(581\) −0.442317 17.5825i −0.0183504 0.729445i
\(582\) 0 0
\(583\) 22.6804 + 39.2837i 0.939328 + 1.62696i
\(584\) 0 0
\(585\) −0.845618 1.83196i −0.0349620 0.0757422i
\(586\) 0 0
\(587\) −20.5328 + 35.5638i −0.847478 + 1.46788i 0.0359730 + 0.999353i \(0.488547\pi\)
−0.883451 + 0.468523i \(0.844786\pi\)
\(588\) 0 0
\(589\) 1.04309 + 1.80669i 0.0429799 + 0.0744434i
\(590\) 0 0
\(591\) −22.0328 1.00481i −0.906307 0.0413322i
\(592\) 0 0
\(593\) 16.1008 27.8874i 0.661180 1.14520i −0.319126 0.947712i \(-0.603389\pi\)
0.980306 0.197485i \(-0.0632772\pi\)
\(594\) 0 0
\(595\) −3.99573 2.17483i −0.163809 0.0891592i
\(596\) 0 0
\(597\) −2.34728 4.53051i −0.0960676 0.185422i
\(598\) 0 0
\(599\) 9.53590 16.5167i 0.389626 0.674852i −0.602773 0.797913i \(-0.705938\pi\)
0.992399 + 0.123060i \(0.0392709\pi\)
\(600\) 0 0
\(601\) 4.27188 7.39912i 0.174254 0.301816i −0.765649 0.643259i \(-0.777582\pi\)
0.939903 + 0.341442i \(0.110915\pi\)
\(602\) 0 0
\(603\) −4.01459 + 5.68634i −0.163487 + 0.231565i
\(604\) 0 0
\(605\) −1.06167 −0.0431631
\(606\) 0 0
\(607\) −38.0115 −1.54284 −0.771419 0.636328i \(-0.780453\pi\)
−0.771419 + 0.636328i \(0.780453\pi\)
\(608\) 0 0
\(609\) −0.839883 + 41.1205i −0.0340338 + 1.66629i
\(610\) 0 0
\(611\) −1.69961 + 2.94381i −0.0687589 + 0.119094i
\(612\) 0 0
\(613\) 11.3296 + 19.6234i 0.457597 + 0.792581i 0.998833 0.0482894i \(-0.0153770\pi\)
−0.541237 + 0.840870i \(0.682044\pi\)
\(614\) 0 0
\(615\) −0.347081 0.669906i −0.0139956 0.0270132i
\(616\) 0 0
\(617\) −10.1388 17.5609i −0.408173 0.706977i 0.586512 0.809941i \(-0.300501\pi\)
−0.994685 + 0.102964i \(0.967167\pi\)
\(618\) 0 0
\(619\) −2.06128 −0.0828499 −0.0414249 0.999142i \(-0.513190\pi\)
−0.0414249 + 0.999142i \(0.513190\pi\)
\(620\) 0 0
\(621\) 5.83269 + 0.802453i 0.234058 + 0.0322013i
\(622\) 0 0
\(623\) −0.181424 7.21177i −0.00726860 0.288933i
\(624\) 0 0
\(625\) 21.8640 0.874560
\(626\) 0 0
\(627\) −13.8040 + 21.5754i −0.551278 + 0.861640i
\(628\) 0 0
\(629\) 34.0085 1.35601
\(630\) 0 0
\(631\) −1.63715 −0.0651740 −0.0325870 0.999469i \(-0.510375\pi\)
−0.0325870 + 0.999469i \(0.510375\pi\)
\(632\) 0 0
\(633\) −0.969165 1.87060i −0.0385208 0.0743497i
\(634\) 0 0
\(635\) 4.05701 0.160998
\(636\) 0 0
\(637\) 10.2106 0.514055i 0.404559 0.0203676i
\(638\) 0 0
\(639\) −5.01838 0.458681i −0.198524 0.0181451i
\(640\) 0 0
\(641\) 21.9325 0.866281 0.433140 0.901326i \(-0.357405\pi\)
0.433140 + 0.901326i \(0.357405\pi\)
\(642\) 0 0
\(643\) 14.1819 + 24.5638i 0.559280 + 0.968701i 0.997557 + 0.0698609i \(0.0222555\pi\)
−0.438277 + 0.898840i \(0.644411\pi\)
\(644\) 0 0
\(645\) −4.00953 + 6.26683i −0.157875 + 0.246756i
\(646\) 0 0
\(647\) −17.3904 30.1210i −0.683686 1.18418i −0.973848 0.227201i \(-0.927042\pi\)
0.290162 0.956978i \(-0.406291\pi\)
\(648\) 0 0
\(649\) −23.5203 + 40.7384i −0.923253 + 1.59912i
\(650\) 0 0
\(651\) −0.0481549 + 2.35765i −0.00188734 + 0.0924037i
\(652\) 0 0
\(653\) −3.19863 −0.125172 −0.0625860 0.998040i \(-0.519935\pi\)
−0.0625860 + 0.998040i \(0.519935\pi\)
\(654\) 0 0
\(655\) 9.73385 0.380333
\(656\) 0 0
\(657\) −16.6481 36.0668i −0.649506 1.40710i
\(658\) 0 0
\(659\) −5.30418 + 9.18711i −0.206622 + 0.357879i −0.950648 0.310271i \(-0.899580\pi\)
0.744027 + 0.668150i \(0.232914\pi\)
\(660\) 0 0
\(661\) −5.06507 + 8.77297i −0.197009 + 0.341229i −0.947557 0.319586i \(-0.896456\pi\)
0.750549 + 0.660815i \(0.229789\pi\)
\(662\) 0 0
\(663\) −5.09046 + 7.95631i −0.197697 + 0.308998i
\(664\) 0 0
\(665\) −0.124220 4.93786i −0.00481705 0.191482i
\(666\) 0 0
\(667\) 5.08472 8.80700i 0.196881 0.341008i
\(668\) 0 0
\(669\) −0.832492 + 1.30117i −0.0321860 + 0.0503062i
\(670\) 0 0
\(671\) −22.0378 38.1707i −0.850761 1.47356i
\(672\) 0 0
\(673\) 1.60817 2.78543i 0.0619903 0.107370i −0.833365 0.552724i \(-0.813589\pi\)
0.895355 + 0.445353i \(0.146922\pi\)
\(674\) 0 0
\(675\) 24.6467 + 3.39086i 0.948651 + 0.130514i
\(676\) 0 0
\(677\) 14.6819 + 25.4298i 0.564271 + 0.977347i 0.997117 + 0.0758786i \(0.0241762\pi\)
−0.432846 + 0.901468i \(0.642491\pi\)
\(678\) 0 0
\(679\) −0.744363 29.5891i −0.0285660 1.13552i
\(680\) 0 0
\(681\) −25.3515 1.15616i −0.971473 0.0443041i
\(682\) 0 0
\(683\) −12.6278 21.8720i −0.483190 0.836910i 0.516624 0.856213i \(-0.327189\pi\)
−0.999814 + 0.0193029i \(0.993855\pi\)
\(684\) 0 0
\(685\) 2.02918 0.0775309
\(686\) 0 0
\(687\) 16.5687 + 0.755615i 0.632134 + 0.0288285i
\(688\) 0 0
\(689\) −9.08113 + 15.7290i −0.345963 + 0.599226i
\(690\) 0 0
\(691\) −7.68190 13.3054i −0.292233 0.506163i 0.682104 0.731255i \(-0.261065\pi\)
−0.974338 + 0.225092i \(0.927732\pi\)
\(692\) 0 0
\(693\) −25.9736 + 12.7912i −0.986657 + 0.485896i
\(694\) 0 0
\(695\) −0.466240 0.807551i −0.0176855 0.0306321i
\(696\) 0 0
\(697\) −1.76595 + 3.05872i −0.0668903 + 0.115857i
\(698\) 0 0
\(699\) −13.4684 + 21.0509i −0.509421 + 0.796217i
\(700\) 0 0
\(701\) −13.3700 −0.504980 −0.252490 0.967600i \(-0.581249\pi\)
−0.252490 + 0.967600i \(0.581249\pi\)
\(702\) 0 0
\(703\) 18.4626 + 31.9782i 0.696332 + 1.20608i
\(704\) 0 0
\(705\) 0.853994 + 1.64831i 0.0321633 + 0.0620788i
\(706\) 0 0
\(707\) −31.0510 + 18.9842i −1.16779 + 0.713972i
\(708\) 0 0
\(709\) 0.562939 + 0.975038i 0.0211416 + 0.0366183i 0.876403 0.481579i \(-0.159937\pi\)
−0.855261 + 0.518197i \(0.826603\pi\)
\(710\) 0 0
\(711\) −6.29552 13.6387i −0.236101 0.511492i
\(712\) 0 0
\(713\) 0.291534 0.504951i 0.0109180 0.0189106i
\(714\) 0 0
\(715\) −1.22665 2.12463i −0.0458743 0.0794565i
\(716\) 0 0
\(717\) −14.5890 28.1585i −0.544836 1.05160i
\(718\) 0 0
\(719\) −9.13667 + 15.8252i −0.340740 + 0.590180i −0.984570 0.174989i \(-0.944011\pi\)
0.643830 + 0.765169i \(0.277344\pi\)
\(720\) 0 0
\(721\) 25.1965 15.4048i 0.938366 0.573705i
\(722\) 0 0
\(723\) −0.161579 0.00736882i −0.00600919 0.000274050i
\(724\) 0 0
\(725\) 21.4861 37.2150i 0.797973 1.38213i
\(726\) 0 0
\(727\) 14.8478 25.7171i 0.550673 0.953793i −0.447553 0.894257i \(-0.647705\pi\)
0.998226 0.0595359i \(-0.0189621\pi\)
\(728\) 0 0
\(729\) 25.9969 + 7.29124i 0.962847 + 0.270046i
\(730\) 0 0
\(731\) 34.8272 1.28813
\(732\) 0 0
\(733\) 19.2278 0.710195 0.355098 0.934829i \(-0.384448\pi\)
0.355098 + 0.934829i \(0.384448\pi\)
\(734\) 0 0
\(735\) 2.76876 4.84845i 0.102127 0.178838i
\(736\) 0 0
\(737\) −4.23171 + 7.32955i −0.155877 + 0.269987i
\(738\) 0 0
\(739\) 15.1336 + 26.2121i 0.556697 + 0.964227i 0.997769 + 0.0667556i \(0.0212648\pi\)
−0.441073 + 0.897471i \(0.645402\pi\)
\(740\) 0 0
\(741\) −10.2448 0.467216i −0.376354 0.0171636i
\(742\) 0 0
\(743\) 11.8815 + 20.5794i 0.435890 + 0.754984i 0.997368 0.0725076i \(-0.0231002\pi\)
−0.561477 + 0.827492i \(0.689767\pi\)
\(744\) 0 0
\(745\) 4.21926 0.154582
\(746\) 0 0
\(747\) −11.5021 + 16.2918i −0.420841 + 0.596087i
\(748\) 0 0
\(749\) 0.517709 + 20.5794i 0.0189167 + 0.751954i
\(750\) 0 0
\(751\) −12.6683 −0.462273 −0.231136 0.972921i \(-0.574244\pi\)
−0.231136 + 0.972921i \(0.574244\pi\)
\(752\) 0 0
\(753\) −31.6175 1.44192i −1.15221 0.0525464i
\(754\) 0 0
\(755\) −0.0478448 −0.00174125
\(756\) 0 0
\(757\) −29.0799 −1.05693 −0.528464 0.848955i \(-0.677232\pi\)
−0.528464 + 0.848955i \(0.677232\pi\)
\(758\) 0 0
\(759\) 7.15126 + 0.326134i 0.259574 + 0.0118379i
\(760\) 0 0
\(761\) 29.2029 1.05860 0.529302 0.848433i \(-0.322454\pi\)
0.529302 + 0.848433i \(0.322454\pi\)
\(762\) 0 0
\(763\) 17.4626 + 9.50471i 0.632190 + 0.344094i
\(764\) 0 0
\(765\) 2.16186 + 4.68350i 0.0781623 + 0.169332i
\(766\) 0 0
\(767\) −18.8348 −0.680086
\(768\) 0 0
\(769\) 12.5869 + 21.8011i 0.453894 + 0.786167i 0.998624 0.0524443i \(-0.0167012\pi\)
−0.544730 + 0.838611i \(0.683368\pi\)
\(770\) 0 0
\(771\) 36.4238 + 1.66111i 1.31177 + 0.0598234i
\(772\) 0 0
\(773\) −0.752039 1.30257i −0.0270490 0.0468502i 0.852184 0.523242i \(-0.175278\pi\)
−0.879233 + 0.476392i \(0.841944\pi\)
\(774\) 0 0
\(775\) 1.23191 2.13373i 0.0442515 0.0766458i
\(776\) 0 0
\(777\) −0.852336 + 41.7302i −0.0305774 + 1.49706i
\(778\) 0 0
\(779\) −3.83482 −0.137397
\(780\) 0 0
\(781\) −6.12722 −0.219249
\(782\) 0 0
\(783\) 28.6050 36.8329i 1.02226 1.31630i
\(784\) 0 0
\(785\) 4.83122 8.36792i 0.172434 0.298664i
\(786\) 0 0
\(787\) −7.47656 + 12.9498i −0.266510 + 0.461610i −0.967958 0.251111i \(-0.919204\pi\)
0.701448 +