Properties

Label 441.2.f.g.148.2
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.2
Root \(-1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.g.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23025 - 2.13086i) q^{2} +(1.66238 - 0.486291i) q^{3} +(-2.02704 + 3.51094i) q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 - 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 - 1.61680i) q^{9} +O(q^{10})\) \(q+(-1.23025 - 2.13086i) q^{2} +(1.66238 - 0.486291i) q^{3} +(-2.02704 + 3.51094i) q^{4} +(1.82904 - 3.16799i) q^{5} +(-3.08137 - 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 - 1.61680i) q^{9} -9.00071 q^{10} +(-0.203210 - 0.351971i) q^{11} +(-1.66238 + 6.82226i) q^{12} +(0.243398 - 0.421578i) q^{13} +(1.50000 - 6.15585i) q^{15} +(-2.16372 - 3.74766i) q^{16} +4.85584 q^{17} +(-6.55408 - 3.39569i) q^{18} -1.97351 q^{19} +(7.41507 + 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-2.32383 + 4.02499i) q^{23} +(8.40183 - 2.45776i) q^{24} +(-4.19076 - 7.25860i) q^{25} -1.19777 q^{26} +(3.41468 - 3.91663i) q^{27} +(-3.82383 - 6.62307i) q^{29} +(-14.9626 + 4.37697i) q^{30} +(-3.51360 + 6.08573i) q^{31} +(-0.269748 + 0.467216i) q^{32} +(-0.508974 - 0.486291i) q^{33} +(-5.97391 - 10.3471i) q^{34} +(0.554084 + 12.1496i) q^{36} +2.32743 q^{37} +(2.42792 + 4.20528i) q^{38} +(0.199612 - 0.819187i) q^{39} +(9.24411 - 16.0113i) q^{40} +(-3.75700 + 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +1.64766 q^{44} +(-0.499960 - 10.9628i) q^{45} +11.4356 q^{46} +(3.15811 + 5.47002i) q^{47} +(-5.41938 - 5.17786i) q^{48} +(-10.3114 + 17.8598i) q^{50} +(8.07227 - 2.36135i) q^{51} +(0.986757 + 1.70911i) q^{52} -3.56867 q^{53} +(-12.5467 - 2.45776i) q^{54} -1.48672 q^{55} +(-3.28074 + 0.959702i) q^{57} +(-9.40856 + 16.2961i) q^{58} +(-3.05919 + 5.29868i) q^{59} +(18.5723 + 17.7446i) q^{60} +(4.01356 + 6.95169i) q^{61} +17.2905 q^{62} -7.32743 q^{64} +(-0.890369 - 1.54216i) q^{65} +(-0.410052 + 1.68281i) q^{66} +(-1.80039 + 3.11836i) q^{67} +(-9.84299 + 17.0486i) q^{68} +(-1.90578 + 7.82115i) q^{69} +8.46050 q^{71} +(12.7719 - 8.17147i) q^{72} +1.97351 q^{73} +(-2.86333 - 4.95943i) q^{74} +(-10.4964 - 10.0287i) q^{75} +(4.00040 - 6.92889i) q^{76} +(-1.99115 + 0.582462i) q^{78} +(-4.08113 - 7.06872i) q^{79} -15.8301 q^{80} +(3.77188 - 8.17147i) q^{81} +18.4882 q^{82} +(-6.08600 - 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +(2.86333 - 4.95943i) q^{86} +(-9.57742 - 9.15059i) q^{87} +(-1.02704 - 1.77889i) q^{88} +14.8301 q^{89} +(-22.7452 + 14.5524i) q^{90} +(-9.42101 - 16.3177i) q^{92} +(-2.88151 + 11.8255i) q^{93} +(7.77056 - 13.4590i) q^{94} +(-3.60963 + 6.25206i) q^{95} +(-0.221221 + 0.907869i) q^{96} +(4.74375 + 8.21642i) q^{97} +(-1.08259 - 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} - 8q^{11} + 18q^{15} - 6q^{16} - 42q^{18} - 6q^{22} - 4q^{23} - 12q^{25} - 22q^{29} - 48q^{30} - 16q^{32} - 30q^{36} - 12q^{37} + 24q^{39} - 6q^{43} - 28q^{44} + 24q^{46} - 56q^{50} - 18q^{51} + 56q^{53} - 6q^{57} - 18q^{58} + 108q^{60} - 48q^{64} + 6q^{65} + 76q^{71} + 60q^{72} - 36q^{74} + 36q^{78} + 6q^{79} - 48q^{81} + 30q^{85} + 36q^{86} + 6q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23025 2.13086i −0.869920 1.50675i −0.862078 0.506776i \(-0.830837\pi\)
−0.00784213 0.999969i \(-0.502496\pi\)
\(3\) 1.66238 0.486291i 0.959778 0.280760i
\(4\) −2.02704 + 3.51094i −1.01352 + 1.75547i
\(5\) 1.82904 3.16799i 0.817970 1.41677i −0.0892047 0.996013i \(-0.528433\pi\)
0.907175 0.420753i \(-0.138234\pi\)
\(6\) −3.08137 2.94405i −1.25796 1.20190i
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) 2.52704 1.61680i 0.842347 0.538935i
\(10\) −9.00071 −2.84628
\(11\) −0.203210 0.351971i −0.0612702 0.106123i 0.833763 0.552122i \(-0.186182\pi\)
−0.895033 + 0.445999i \(0.852848\pi\)
\(12\) −1.66238 + 6.82226i −0.479889 + 1.96942i
\(13\) 0.243398 0.421578i 0.0675065 0.116925i −0.830297 0.557322i \(-0.811829\pi\)
0.897803 + 0.440397i \(0.145162\pi\)
\(14\) 0 0
\(15\) 1.50000 6.15585i 0.387298 1.58943i
\(16\) −2.16372 3.74766i −0.540929 0.936916i
\(17\) 4.85584 1.17771 0.588857 0.808237i \(-0.299578\pi\)
0.588857 + 0.808237i \(0.299578\pi\)
\(18\) −6.55408 3.39569i −1.54481 0.800373i
\(19\) −1.97351 −0.452755 −0.226378 0.974040i \(-0.572688\pi\)
−0.226378 + 0.974040i \(0.572688\pi\)
\(20\) 7.41507 + 12.8433i 1.65806 + 2.87185i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −2.32383 + 4.02499i −0.484552 + 0.839269i −0.999843 0.0177464i \(-0.994351\pi\)
0.515290 + 0.857016i \(0.327684\pi\)
\(24\) 8.40183 2.45776i 1.71502 0.501687i
\(25\) −4.19076 7.25860i −0.838151 1.45172i
\(26\) −1.19777 −0.234901
\(27\) 3.41468 3.91663i 0.657155 0.753756i
\(28\) 0 0
\(29\) −3.82383 6.62307i −0.710068 1.22987i −0.964831 0.262870i \(-0.915331\pi\)
0.254764 0.967003i \(-0.418002\pi\)
\(30\) −14.9626 + 4.37697i −2.73179 + 0.799121i
\(31\) −3.51360 + 6.08573i −0.631061 + 1.09303i 0.356274 + 0.934381i \(0.384047\pi\)
−0.987335 + 0.158648i \(0.949286\pi\)
\(32\) −0.269748 + 0.467216i −0.0476851 + 0.0825930i
\(33\) −0.508974 0.486291i −0.0886010 0.0846524i
\(34\) −5.97391 10.3471i −1.02452 1.77452i
\(35\) 0 0
\(36\) 0.554084 + 12.1496i 0.0923474 + 2.02494i
\(37\) 2.32743 0.382627 0.191314 0.981529i \(-0.438725\pi\)
0.191314 + 0.981529i \(0.438725\pi\)
\(38\) 2.42792 + 4.20528i 0.393861 + 0.682187i
\(39\) 0.199612 0.819187i 0.0319635 0.131175i
\(40\) 9.24411 16.0113i 1.46162 2.53160i
\(41\) −3.75700 + 6.50731i −0.586744 + 1.01627i 0.407911 + 0.913022i \(0.366257\pi\)
−0.994655 + 0.103249i \(0.967076\pi\)
\(42\) 0 0
\(43\) 1.16372 + 2.01561i 0.177465 + 0.307378i 0.941012 0.338374i \(-0.109877\pi\)
−0.763547 + 0.645753i \(0.776544\pi\)
\(44\) 1.64766 0.248395
\(45\) −0.499960 10.9628i −0.0745297 1.63424i
\(46\) 11.4356 1.68609
\(47\) 3.15811 + 5.47002i 0.460658 + 0.797884i 0.998994 0.0448469i \(-0.0142800\pi\)
−0.538335 + 0.842731i \(0.680947\pi\)
\(48\) −5.41938 5.17786i −0.782220 0.747360i
\(49\) 0 0
\(50\) −10.3114 + 17.8598i −1.45825 + 2.52576i
\(51\) 8.07227 2.36135i 1.13034 0.330655i
\(52\) 0.986757 + 1.70911i 0.136839 + 0.237011i
\(53\) −3.56867 −0.490195 −0.245097 0.969498i \(-0.578820\pi\)
−0.245097 + 0.969498i \(0.578820\pi\)
\(54\) −12.5467 2.45776i −1.70739 0.334458i
\(55\) −1.48672 −0.200469
\(56\) 0 0
\(57\) −3.28074 + 0.959702i −0.434544 + 0.127116i
\(58\) −9.40856 + 16.2961i −1.23540 + 2.13978i
\(59\) −3.05919 + 5.29868i −0.398273 + 0.689829i −0.993513 0.113719i \(-0.963724\pi\)
0.595240 + 0.803548i \(0.297057\pi\)
\(60\) 18.5723 + 17.7446i 2.39767 + 2.29082i
\(61\) 4.01356 + 6.95169i 0.513884 + 0.890073i 0.999870 + 0.0161063i \(0.00512703\pi\)
−0.485987 + 0.873966i \(0.661540\pi\)
\(62\) 17.2905 2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −0.890369 1.54216i −0.110437 0.191282i
\(66\) −0.410052 + 1.68281i −0.0504739 + 0.207140i
\(67\) −1.80039 + 3.11836i −0.219952 + 0.380969i −0.954793 0.297271i \(-0.903924\pi\)
0.734841 + 0.678240i \(0.237257\pi\)
\(68\) −9.84299 + 17.0486i −1.19364 + 2.06744i
\(69\) −1.90578 + 7.82115i −0.229429 + 0.941555i
\(70\) 0 0
\(71\) 8.46050 1.00408 0.502039 0.864845i \(-0.332584\pi\)
0.502039 + 0.864845i \(0.332584\pi\)
\(72\) 12.7719 8.17147i 1.50518 0.963017i
\(73\) 1.97351 0.230982 0.115491 0.993309i \(-0.463156\pi\)
0.115491 + 0.993309i \(0.463156\pi\)
\(74\) −2.86333 4.95943i −0.332855 0.576522i
\(75\) −10.4964 10.0287i −1.21202 1.15801i
\(76\) 4.00040 6.92889i 0.458877 0.794798i
\(77\) 0 0
\(78\) −1.99115 + 0.582462i −0.225453 + 0.0659509i
\(79\) −4.08113 7.06872i −0.459163 0.795293i 0.539754 0.841823i \(-0.318517\pi\)
−0.998917 + 0.0465297i \(0.985184\pi\)
\(80\) −15.8301 −1.76986
\(81\) 3.77188 8.17147i 0.419098 0.907941i
\(82\) 18.4882 2.04168
\(83\) −6.08600 10.5413i −0.668025 1.15705i −0.978456 0.206457i \(-0.933807\pi\)
0.310431 0.950596i \(-0.399527\pi\)
\(84\) 0 0
\(85\) 8.88151 15.3832i 0.963336 1.66855i
\(86\) 2.86333 4.95943i 0.308760 0.534789i
\(87\) −9.57742 9.15059i −1.02681 0.981047i
\(88\) −1.02704 1.77889i −0.109483 0.189630i
\(89\) 14.8301 1.57199 0.785996 0.618231i \(-0.212151\pi\)
0.785996 + 0.618231i \(0.212151\pi\)
\(90\) −22.7452 + 14.5524i −2.39755 + 1.53396i
\(91\) 0 0
\(92\) −9.42101 16.3177i −0.982208 1.70123i
\(93\) −2.88151 + 11.8255i −0.298799 + 1.22624i
\(94\) 7.77056 13.4590i 0.801472 1.38819i
\(95\) −3.60963 + 6.25206i −0.370340 + 0.641448i
\(96\) −0.221221 + 0.907869i −0.0225783 + 0.0926590i
\(97\) 4.74375 + 8.21642i 0.481655 + 0.834251i 0.999778 0.0210547i \(-0.00670241\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(98\) 0 0
\(99\) −1.08259 0.560893i −0.108804 0.0563719i
\(100\) 33.9794 3.39794
\(101\) −4.35588 7.54461i −0.433426 0.750716i 0.563739 0.825953i \(-0.309362\pi\)
−0.997166 + 0.0752364i \(0.976029\pi\)
\(102\) −14.9626 14.2958i −1.48152 1.41550i
\(103\) −4.01356 + 6.95169i −0.395468 + 0.684970i −0.993161 0.116755i \(-0.962751\pi\)
0.597693 + 0.801725i \(0.296084\pi\)
\(104\) 1.23016 2.13069i 0.120627 0.208931i
\(105\) 0 0
\(106\) 4.39037 + 7.60434i 0.426430 + 0.738599i
\(107\) 12.8420 1.24148 0.620742 0.784015i \(-0.286831\pi\)
0.620742 + 0.784015i \(0.286831\pi\)
\(108\) 6.82935 + 19.9279i 0.657155 + 1.91756i
\(109\) 2.60078 0.249109 0.124555 0.992213i \(-0.460250\pi\)
0.124555 + 0.992213i \(0.460250\pi\)
\(110\) 1.82904 + 3.16799i 0.174392 + 0.302056i
\(111\) 3.86908 1.13181i 0.367237 0.107427i
\(112\) 0 0
\(113\) 6.97509 12.0812i 0.656162 1.13651i −0.325440 0.945563i \(-0.605512\pi\)
0.981601 0.190942i \(-0.0611544\pi\)
\(114\) 6.08113 + 5.81012i 0.569550 + 0.544167i
\(115\) 8.50075 + 14.7237i 0.792699 + 1.37300i
\(116\) 31.0043 2.87867
\(117\) −0.0665320 1.45887i −0.00615088 0.134873i
\(118\) 15.0543 1.38586
\(119\) 0 0
\(120\) 7.58113 31.1122i 0.692059 2.84014i
\(121\) 5.41741 9.38323i 0.492492 0.853021i
\(122\) 9.87538 17.1047i 0.894075 1.54858i
\(123\) −3.08113 + 12.6446i −0.277816 + 1.14013i
\(124\) −14.2444 24.6721i −1.27919 2.21562i
\(125\) −12.3698 −1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) 9.55408 + 16.5482i 0.844470 + 1.46266i
\(129\) 2.91472 + 2.78482i 0.256626 + 0.245190i
\(130\) −2.19076 + 3.79450i −0.192142 + 0.332800i
\(131\) 4.25696 7.37327i 0.371932 0.644205i −0.617931 0.786233i \(-0.712029\pi\)
0.989863 + 0.142027i \(0.0453621\pi\)
\(132\) 2.73905 0.801244i 0.238404 0.0697393i
\(133\) 0 0
\(134\) 8.85973 0.765364
\(135\) −6.16225 17.9813i −0.530362 1.54758i
\(136\) 24.5418 2.10444
\(137\) −0.188621 0.326702i −0.0161150 0.0279120i 0.857855 0.513891i \(-0.171796\pi\)
−0.873970 + 0.485979i \(0.838463\pi\)
\(138\) 19.0104 5.56103i 1.61827 0.473386i
\(139\) 9.50067 16.4556i 0.805837 1.39575i −0.109888 0.993944i \(-0.535049\pi\)
0.915725 0.401806i \(-0.131617\pi\)
\(140\) 0 0
\(141\) 7.91002 + 7.55750i 0.666144 + 0.636457i
\(142\) −10.4086 18.0281i −0.873467 1.51289i
\(143\) −0.197844 −0.0165446
\(144\) −11.5270 5.97220i −0.960587 0.497683i
\(145\) −27.9757 −2.32326
\(146\) −2.42792 4.20528i −0.200936 0.348032i
\(147\) 0 0
\(148\) −4.71780 + 8.17147i −0.387801 + 0.671691i
\(149\) 4.85087 8.40196i 0.397399 0.688315i −0.596005 0.802981i \(-0.703246\pi\)
0.993404 + 0.114665i \(0.0365795\pi\)
\(150\) −8.45640 + 34.7042i −0.690462 + 2.83359i
\(151\) 6.41741 + 11.1153i 0.522242 + 0.904549i 0.999665 + 0.0258756i \(0.00823738\pi\)
−0.477424 + 0.878673i \(0.658429\pi\)
\(152\) −9.97430 −0.809023
\(153\) 12.2709 7.85095i 0.992045 0.634711i
\(154\) 0 0
\(155\) 12.8530 + 22.2621i 1.03238 + 1.78813i
\(156\) 2.47150 + 2.36135i 0.197878 + 0.189059i
\(157\) −10.4743 + 18.1420i −0.835937 + 1.44789i 0.0573276 + 0.998355i \(0.481742\pi\)
−0.893265 + 0.449531i \(0.851591\pi\)
\(158\) −10.0416 + 17.3926i −0.798869 + 1.38368i
\(159\) −5.93251 + 1.73541i −0.470478 + 0.137627i
\(160\) 0.986757 + 1.70911i 0.0780100 + 0.135117i
\(161\) 0 0
\(162\) −22.0526 + 2.01561i −1.73262 + 0.158362i
\(163\) −11.1623 −0.874295 −0.437148 0.899390i \(-0.644011\pi\)
−0.437148 + 0.899390i \(0.644011\pi\)
\(164\) −15.2312 26.3812i −1.18936 2.06002i
\(165\) −2.47150 + 0.722977i −0.192406 + 0.0562837i
\(166\) −14.9746 + 25.9368i −1.16226 + 2.01309i
\(167\) −1.73012 + 2.99665i −0.133880 + 0.231888i −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(168\) 0 0
\(169\) 6.38151 + 11.0531i 0.490886 + 0.850239i
\(170\) −43.7060 −3.35210
\(171\) −4.98715 + 3.19079i −0.381377 + 0.244006i
\(172\) −9.43560 −0.719458
\(173\) 3.02680 + 5.24258i 0.230124 + 0.398586i 0.957844 0.287288i \(-0.0927536\pi\)
−0.727721 + 0.685874i \(0.759420\pi\)
\(174\) −7.71599 + 31.6657i −0.584948 + 2.40057i
\(175\) 0 0
\(176\) −0.879379 + 1.52313i −0.0662857 + 0.114810i
\(177\) −2.50885 + 10.2961i −0.188577 + 0.773902i
\(178\) −18.2448 31.6010i −1.36751 2.36859i
\(179\) 9.13307 0.682638 0.341319 0.939948i \(-0.389126\pi\)
0.341319 + 0.939948i \(0.389126\pi\)
\(180\) 39.5033 + 20.4668i 2.94440 + 1.52550i
\(181\) 11.9478 0.888074 0.444037 0.896008i \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 0 0
\(183\) 10.0526 + 9.60462i 0.743111 + 0.709994i
\(184\) −11.7448 + 20.3427i −0.865841 + 1.49968i
\(185\) 4.25696 7.37327i 0.312978 0.542093i
\(186\) 28.7434 8.40819i 2.10757 0.616519i
\(187\) −0.986757 1.70911i −0.0721588 0.124983i
\(188\) −25.6065 −1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) −4.57014 7.91571i −0.330683 0.572760i 0.651963 0.758251i \(-0.273946\pi\)
−0.982646 + 0.185491i \(0.940613\pi\)
\(192\) −12.1810 + 3.56326i −0.879088 + 0.257156i
\(193\) −8.47150 + 14.6731i −0.609792 + 1.05619i 0.381483 + 0.924376i \(0.375414\pi\)
−0.991274 + 0.131814i \(0.957920\pi\)
\(194\) 11.6720 20.2165i 0.838003 1.45146i
\(195\) −2.23008 2.13069i −0.159699 0.152582i
\(196\) 0 0
\(197\) −21.3173 −1.51880 −0.759398 0.650627i \(-0.774506\pi\)
−0.759398 + 0.650627i \(0.774506\pi\)
\(198\) 0.136673 + 2.99689i 0.00971293 + 0.212979i
\(199\) 9.97430 0.707060 0.353530 0.935423i \(-0.384981\pi\)
0.353530 + 0.935423i \(0.384981\pi\)
\(200\) −21.1804 36.6856i −1.49768 2.59406i
\(201\) −1.47650 + 6.05943i −0.104145 + 0.427399i
\(202\) −10.7177 + 18.5635i −0.754092 + 1.30613i
\(203\) 0 0
\(204\) −8.07227 + 33.1278i −0.565172 + 2.31941i
\(205\) 13.7434 + 23.8042i 0.959879 + 1.66256i
\(206\) 19.7508 1.37610
\(207\) 0.635211 + 13.9285i 0.0441502 + 0.968099i
\(208\) −2.10658 −0.146065
\(209\) 0.401038 + 0.694619i 0.0277404 + 0.0480478i
\(210\) 0 0
\(211\) −2.44592 + 4.23645i −0.168384 + 0.291649i −0.937852 0.347036i \(-0.887188\pi\)
0.769468 + 0.638685i \(0.220521\pi\)
\(212\) 7.23385 12.5294i 0.496823 0.860523i
\(213\) 14.0646 4.11427i 0.963691 0.281905i
\(214\) −15.7989 27.3645i −1.07999 1.87060i
\(215\) 8.51392 0.580644
\(216\) 17.2581 19.7950i 1.17426 1.34688i
\(217\) 0 0
\(218\) −3.19961 5.54189i −0.216705 0.375344i
\(219\) 3.28074 0.959702i 0.221692 0.0648507i
\(220\) 3.01364 5.21978i 0.203179 0.351917i
\(221\) 1.18190 2.04712i 0.0795034 0.137704i
\(222\) −7.17167 6.85206i −0.481331 0.459880i
\(223\) 11.7044 + 20.2727i 0.783786 + 1.35756i 0.929722 + 0.368263i \(0.120047\pi\)
−0.145936 + 0.989294i \(0.546619\pi\)
\(224\) 0 0
\(225\) −22.3260 11.5672i −1.48840 0.771144i
\(226\) −34.3245 −2.28323
\(227\) 3.05919 + 5.29868i 0.203046 + 0.351686i 0.949508 0.313742i \(-0.101583\pi\)
−0.746463 + 0.665427i \(0.768249\pi\)
\(228\) 3.28074 13.4638i 0.217272 0.891664i
\(229\) −0.730195 + 1.26473i −0.0482526 + 0.0835760i −0.889143 0.457630i \(-0.848699\pi\)
0.840890 + 0.541206i \(0.182032\pi\)
\(230\) 20.9161 36.2278i 1.37917 2.38879i
\(231\) 0 0
\(232\) −19.3260 33.4736i −1.26881 2.19765i
\(233\) −13.2484 −0.867934 −0.433967 0.900929i \(-0.642887\pi\)
−0.433967 + 0.900929i \(0.642887\pi\)
\(234\) −3.02680 + 1.93655i −0.197868 + 0.126596i
\(235\) 23.1052 1.50722
\(236\) −12.4022 21.4813i −0.807316 1.39831i
\(237\) −10.2219 9.76631i −0.663981 0.634390i
\(238\) 0 0
\(239\) −9.69436 + 16.7911i −0.627076 + 1.08613i 0.361060 + 0.932543i \(0.382415\pi\)
−0.988136 + 0.153584i \(0.950918\pi\)
\(240\) −26.3157 + 7.69802i −1.69867 + 0.496905i
\(241\) 2.52684 + 4.37662i 0.162768 + 0.281923i 0.935860 0.352371i \(-0.114624\pi\)
−0.773092 + 0.634294i \(0.781291\pi\)
\(242\) −26.6591 −1.71371
\(243\) 2.29661 15.4184i 0.147327 0.989088i
\(244\) −32.5426 −2.08333
\(245\) 0 0
\(246\) 30.7345 8.99066i 1.95956 0.573223i
\(247\) −0.480350 + 0.831990i −0.0305639 + 0.0529383i
\(248\) −17.7580 + 30.7578i −1.12764 + 1.95312i
\(249\) −15.2434 14.5640i −0.966010 0.922959i
\(250\) 15.2180 + 26.3584i 0.962472 + 1.66705i
\(251\) −15.0928 −0.952647 −0.476324 0.879270i \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) 19.1228 + 33.1216i 1.19987 + 2.07823i
\(255\) 7.28376 29.8918i 0.456127 1.87190i
\(256\) 16.1804 28.0253i 1.01128 1.75158i
\(257\) 3.85592 6.67865i 0.240526 0.416603i −0.720338 0.693623i \(-0.756014\pi\)
0.960864 + 0.277020i \(0.0893469\pi\)
\(258\) 2.34822 9.63688i 0.146194 0.599966i
\(259\) 0 0
\(260\) 7.21926 0.447720
\(261\) −20.3712 10.5544i −1.26095 0.653300i
\(262\) −20.9485 −1.29420
\(263\) −2.10603 3.64776i −0.129864 0.224930i 0.793760 0.608231i \(-0.208121\pi\)
−0.923624 + 0.383301i \(0.874787\pi\)
\(264\) −2.57240 2.45776i −0.158320 0.151264i
\(265\) −6.52724 + 11.3055i −0.400965 + 0.694492i
\(266\) 0 0
\(267\) 24.6534 7.21177i 1.50876 0.441353i
\(268\) −7.29893 12.6421i −0.445853 0.772240i
\(269\) −20.7507 −1.26519 −0.632596 0.774482i \(-0.718011\pi\)
−0.632596 + 0.774482i \(0.718011\pi\)
\(270\) −30.7345 + 35.2524i −1.87044 + 2.14540i
\(271\) 28.4889 1.73057 0.865287 0.501276i \(-0.167136\pi\)
0.865287 + 0.501276i \(0.167136\pi\)
\(272\) −10.5067 18.1981i −0.637060 1.10342i
\(273\) 0 0
\(274\) −0.464103 + 0.803851i −0.0280375 + 0.0485624i
\(275\) −1.70321 + 2.95005i −0.102707 + 0.177895i
\(276\) −23.5965 22.5449i −1.42034 1.35704i
\(277\) −8.58113 14.8629i −0.515590 0.893028i −0.999836 0.0180962i \(-0.994239\pi\)
0.484246 0.874932i \(-0.339094\pi\)
\(278\) −46.7529 −2.80405
\(279\) 0.960429 + 21.0597i 0.0574994 + 1.26081i
\(280\) 0 0
\(281\) −4.72140 8.17770i −0.281655 0.487841i 0.690138 0.723678i \(-0.257550\pi\)
−0.971793 + 0.235837i \(0.924217\pi\)
\(282\) 6.37266 26.1528i 0.379486 1.55738i
\(283\) 8.43422 14.6085i 0.501362 0.868385i −0.498636 0.866811i \(-0.666166\pi\)
0.999999 0.00157378i \(-0.000500949\pi\)
\(284\) −17.1498 + 29.7043i −1.01765 + 1.76263i
\(285\) −2.96027 + 12.1487i −0.175351 + 0.719625i
\(286\) 0.243398 + 0.421578i 0.0143924 + 0.0249284i
\(287\) 0 0
\(288\) 0.0737345 + 1.61680i 0.00434485 + 0.0952711i
\(289\) 6.57918 0.387011
\(290\) 34.4172 + 59.6124i 2.02105 + 3.50056i
\(291\) 11.8815 + 11.3520i 0.696507 + 0.665466i
\(292\) −4.00040 + 6.92889i −0.234105 + 0.405483i
\(293\) −1.86143 + 3.22409i −0.108746 + 0.188353i −0.915262 0.402858i \(-0.868017\pi\)
0.806517 + 0.591211i \(0.201350\pi\)
\(294\) 0 0
\(295\) 11.1908 + 19.3830i 0.651551 + 1.12852i
\(296\) 11.7630 0.683712
\(297\) −2.07244 0.405967i −0.120255 0.0235566i
\(298\) −23.8712 −1.38282
\(299\) 1.13123 + 1.95935i 0.0654209 + 0.113312i
\(300\) 56.4868 16.5239i 3.26126 0.954006i
\(301\) 0 0
\(302\) 15.7901 27.3492i 0.908617 1.57377i
\(303\) −10.9100 10.4238i −0.626764 0.598832i
\(304\) 4.27012 + 7.39607i 0.244908 + 0.424194i
\(305\) 29.3638 1.68137
\(306\) −31.8256 16.4889i −1.81935 0.942610i
\(307\) −30.5691 −1.74467 −0.872335 0.488908i \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 0 0
\(309\) −3.29153 + 13.5081i −0.187249 + 0.768451i
\(310\) 31.6249 54.7759i 1.79617 3.11106i
\(311\) −5.21739 + 9.03678i −0.295851 + 0.512429i −0.975182 0.221403i \(-0.928936\pi\)
0.679332 + 0.733831i \(0.262270\pi\)
\(312\) 1.00885 4.14024i 0.0571151 0.234395i
\(313\) −0.309930 0.536815i −0.0175183 0.0303426i 0.857133 0.515095i \(-0.172243\pi\)
−0.874652 + 0.484752i \(0.838910\pi\)
\(314\) 51.5440 2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) −5.12422 8.87541i −0.287805 0.498493i 0.685481 0.728091i \(-0.259592\pi\)
−0.973285 + 0.229598i \(0.926259\pi\)
\(318\) 10.9964 + 10.5063i 0.616648 + 0.589166i
\(319\) −1.55408 + 2.69175i −0.0870120 + 0.150709i
\(320\) −13.4021 + 23.2132i −0.749203 + 1.29766i
\(321\) 21.3484 6.24496i 1.19155 0.348560i
\(322\) 0 0
\(323\) −9.58307 −0.533216
\(324\) 21.0438 + 29.8068i 1.16910 + 1.65593i
\(325\) −4.08009 −0.226323
\(326\) 13.7324 + 23.7852i 0.760567 + 1.31734i
\(327\) 4.32349 1.26473i 0.239090 0.0699400i
\(328\) −18.9882 + 32.8885i −1.04845 + 1.81596i
\(329\) 0 0
\(330\) 4.58113 + 4.37697i 0.252183 + 0.240944i
\(331\) 10.1819 + 17.6356i 0.559648 + 0.969339i 0.997526 + 0.0703042i \(0.0223970\pi\)
−0.437878 + 0.899035i \(0.644270\pi\)
\(332\) 49.3463 2.70823
\(333\) 5.88151 3.76300i 0.322305 0.206211i
\(334\) 8.51392 0.465861
\(335\) 6.58596 + 11.4072i 0.359829 + 0.623242i
\(336\) 0 0
\(337\) 2.85594 4.94662i 0.155573 0.269460i −0.777695 0.628642i \(-0.783611\pi\)
0.933267 + 0.359182i \(0.116944\pi\)
\(338\) 15.7017 27.1962i 0.854062 1.47928i
\(339\) 5.72030 23.4755i 0.310684 1.27502i
\(340\) 36.0064 + 62.3649i 1.95272 + 3.38221i
\(341\) 2.85600 0.154661
\(342\) 12.9346 + 6.70145i 0.699422 + 0.362373i
\(343\) 0 0
\(344\) 5.88151 + 10.1871i 0.317110 + 0.549251i
\(345\) 21.2915 + 20.3427i 1.14630 + 1.09521i
\(346\) 7.44746 12.8994i 0.400378 0.693475i
\(347\) −4.44066 + 7.69145i −0.238387 + 0.412899i −0.960252 0.279136i \(-0.909952\pi\)
0.721865 + 0.692034i \(0.243285\pi\)
\(348\) 51.5410 15.0771i 2.76289 0.808217i
\(349\) −10.4874 18.1648i −0.561379 0.972337i −0.997376 0.0723893i \(-0.976938\pi\)
0.435997 0.899948i \(-0.356396\pi\)
\(350\) 0 0
\(351\) −0.820039 2.39285i −0.0437704 0.127721i
\(352\) 0.219262 0.0116867
\(353\) 7.38268 + 12.7872i 0.392941 + 0.680593i 0.992836 0.119485i \(-0.0381245\pi\)
−0.599895 + 0.800078i \(0.704791\pi\)
\(354\) 25.0261 7.32078i 1.33012 0.389095i
\(355\) 15.4746 26.8028i 0.821306 1.42254i
\(356\) −30.0613 + 52.0677i −1.59325 + 2.75959i
\(357\) 0 0
\(358\) −11.2360 19.4613i −0.593840 1.02856i
\(359\) 7.21206 0.380638 0.190319 0.981722i \(-0.439048\pi\)
0.190319 + 0.981722i \(0.439048\pi\)
\(360\) −2.52684 55.4071i −0.133176 2.92021i
\(361\) −15.1052 −0.795013
\(362\) −14.6988 25.4591i −0.772554 1.33810i
\(363\) 4.44284 18.2330i 0.233188 0.956983i
\(364\) 0 0
\(365\) 3.60963 6.25206i 0.188937 0.327248i
\(366\) 8.09884 33.2368i 0.423333 1.73732i
\(367\) 5.48711 + 9.50396i 0.286425 + 0.496103i 0.972954 0.231000i \(-0.0741998\pi\)
−0.686529 + 0.727103i \(0.740866\pi\)
\(368\) 20.1124 1.04843
\(369\) 1.02696 + 22.5186i 0.0534614 + 1.17227i
\(370\) −20.9485 −1.08906
\(371\) 0 0
\(372\) −35.6775 34.0875i −1.84979 1.76736i
\(373\) 0.271884 0.470916i 0.0140776 0.0243831i −0.858901 0.512142i \(-0.828852\pi\)
0.872978 + 0.487759i \(0.162185\pi\)
\(374\) −2.42792 + 4.20528i −0.125545 + 0.217450i
\(375\) −20.5634 + 6.01534i −1.06189 + 0.310631i
\(376\) 15.9614 + 27.6459i 0.823145 + 1.42573i
\(377\) −3.72286 −0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) −14.6337 25.3464i −0.750695 1.30024i
\(381\) −25.8397 + 7.55879i −1.32381 + 0.387249i
\(382\) −11.2448 + 19.4766i −0.575336 + 0.996511i
\(383\) −17.8569 + 30.9291i −0.912447 + 1.58041i −0.101851 + 0.994800i \(0.532477\pi\)
−0.810596 + 0.585606i \(0.800857\pi\)
\(384\) 23.9298 + 22.8633i 1.22116 + 1.16674i
\(385\) 0 0
\(386\) 41.6883 2.12188
\(387\) 6.19961 + 3.21204i 0.315144 + 0.163277i
\(388\) −38.4632 −1.95267
\(389\) −19.3296 33.4798i −0.980048 1.69749i −0.662156 0.749366i \(-0.730359\pi\)
−0.317892 0.948127i \(-0.602975\pi\)
\(390\) −1.79665 + 7.37327i −0.0909768 + 0.373360i
\(391\) −11.2842 + 19.5447i −0.570664 + 0.988420i
\(392\) 0 0
\(393\) 3.49115 14.3273i 0.176105 0.722718i
\(394\) 26.2257 + 45.4242i 1.32123 + 2.28844i
\(395\) −29.8581 −1.50233
\(396\) 4.16372 2.66395i 0.209235 0.133869i
\(397\) −11.9478 −0.599644 −0.299822 0.953995i \(-0.596927\pi\)
−0.299822 + 0.953995i \(0.596927\pi\)
\(398\) −12.2709 21.2538i −0.615085 1.06536i
\(399\) 0 0
\(400\) −18.1352 + 31.4111i −0.906761 + 1.57056i
\(401\) −16.1783 + 28.0216i −0.807906 + 1.39933i 0.106406 + 0.994323i \(0.466066\pi\)
−0.914312 + 0.405011i \(0.867268\pi\)
\(402\) 14.7283 4.30841i 0.734579 0.214884i
\(403\) 1.71041 + 2.96251i 0.0852015 + 0.147573i
\(404\) 35.3182 1.75715
\(405\) −18.9882 26.8952i −0.943530 1.33643i
\(406\) 0 0
\(407\) −0.472958 0.819187i −0.0234437 0.0406056i
\(408\) 40.7979 11.9345i 2.01980 0.590844i
\(409\) −9.48751 + 16.4328i −0.469127 + 0.812552i −0.999377 0.0352893i \(-0.988765\pi\)
0.530250 + 0.847841i \(0.322098\pi\)
\(410\) 33.8157 58.5704i 1.67004 2.89259i
\(411\) −0.472433 0.451379i −0.0233034 0.0222649i
\(412\) −16.2713 28.1827i −0.801630 1.38846i
\(413\) 0 0
\(414\) 28.8982 18.4891i 1.42027 0.908691i
\(415\) −44.5261 −2.18570
\(416\) 0.131312 + 0.227439i 0.00643811 + 0.0111511i
\(417\) 7.79153 31.9757i 0.381553 1.56586i
\(418\) 0.986757 1.70911i 0.0482639 0.0835955i
\(419\) 8.64523 14.9740i 0.422347 0.731526i −0.573822 0.818980i \(-0.694540\pi\)
0.996169 + 0.0874539i \(0.0278730\pi\)
\(420\) 0 0
\(421\) −9.30039 16.1087i −0.453273 0.785092i 0.545314 0.838232i \(-0.316410\pi\)
−0.998587 + 0.0531397i \(0.983077\pi\)
\(422\) 12.0364 0.585922
\(423\) 16.8246 + 8.71690i 0.818042 + 0.423830i
\(424\) −18.0364 −0.875924
\(425\) −20.3496 35.2466i −0.987103 1.70971i
\(426\) −26.0699 24.9081i −1.26309 1.20680i
\(427\) 0 0
\(428\) −26.0313 + 45.0876i −1.25827 + 2.17939i
\(429\) −0.328893 + 0.0962098i −0.0158791 + 0.00464505i
\(430\) −10.4743 18.1420i −0.505114 0.874883i
\(431\) −15.8784 −0.764835 −0.382418 0.923990i \(-0.624908\pi\)
−0.382418 + 0.923990i \(0.624908\pi\)
\(432\) −22.0666 4.32260i −1.06168 0.207971i
\(433\) 40.4367 1.94326 0.971631 0.236501i \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 0 0
\(435\) −46.5064 + 13.6043i −2.22981 + 0.652278i
\(436\) −5.27188 + 9.13117i −0.252477 + 0.437304i
\(437\) 4.58611 7.94338i 0.219384 0.379984i
\(438\) −6.08113 5.81012i −0.290567 0.277618i
\(439\) −6.23047 10.7915i −0.297364 0.515050i 0.678168 0.734907i \(-0.262774\pi\)
−0.975532 + 0.219857i \(0.929441\pi\)
\(440\) −7.51399 −0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) 4.11537 + 7.12802i 0.195527 + 0.338663i 0.947073 0.321018i \(-0.104025\pi\)
−0.751546 + 0.659680i \(0.770692\pi\)
\(444\) −3.86908 + 15.8783i −0.183619 + 0.753553i
\(445\) 27.1249 46.9817i 1.28584 2.22715i
\(446\) 28.7988 49.8810i 1.36366 2.36193i
\(447\) 3.97822 16.3262i 0.188163 0.772204i
\(448\) 0 0
\(449\) 5.64474 0.266392 0.133196 0.991090i \(-0.457476\pi\)
0.133196 + 0.991090i \(0.457476\pi\)
\(450\) 2.81858 + 61.8040i 0.132869 + 2.91347i
\(451\) 3.05384 0.143800
\(452\) 28.2776 + 48.9783i 1.33007 + 2.30374i
\(453\) 16.0735 + 15.3571i 0.755197 + 0.721541i
\(454\) 7.52716 13.0374i 0.353267 0.611876i
\(455\) 0 0
\(456\) −16.5811 + 4.85041i −0.776482 + 0.227141i
\(457\) −2.53443 4.38977i −0.118556 0.205345i 0.800640 0.599146i \(-0.204493\pi\)
−0.919196 + 0.393801i \(0.871160\pi\)
\(458\) 3.59330 0.167904
\(459\) 16.5811 19.0185i 0.773941 0.887709i
\(460\) −68.9255 −3.21367
\(461\) 3.88831 + 6.73475i 0.181097 + 0.313669i 0.942254 0.334898i \(-0.108702\pi\)
−0.761158 + 0.648567i \(0.775369\pi\)
\(462\) 0 0
\(463\) 4.58998 7.95008i 0.213314 0.369472i −0.739435 0.673228i \(-0.764907\pi\)
0.952750 + 0.303756i \(0.0982408\pi\)
\(464\) −16.5474 + 28.6609i −0.768192 + 1.33055i
\(465\) 32.1925 + 30.7578i 1.49289 + 1.42636i
\(466\) 16.2989 + 28.2306i 0.755033 + 1.30776i
\(467\) −13.7654 −0.636989 −0.318494 0.947925i \(-0.603177\pi\)
−0.318494 + 0.947925i \(0.603177\pi\)
\(468\) 5.25688 + 2.72361i 0.242999 + 0.125899i
\(469\) 0 0
\(470\) −28.4253 49.2340i −1.31116 2.27100i
\(471\) −8.58998 + 35.2524i −0.395805 + 1.62435i
\(472\) −15.4614 + 26.7800i −0.711669 + 1.23265i
\(473\) 0.472958 0.819187i 0.0217466 0.0376663i
\(474\) −8.23518 + 33.7964i −0.378254 + 1.55232i
\(475\) 8.27052 + 14.3250i 0.379477 + 0.657274i
\(476\) 0 0
\(477\) −9.01819 + 5.76985i −0.412914 + 0.264183i
\(478\) 47.7060 2.18202
\(479\) −4.35588 7.54461i −0.199025 0.344722i 0.749187 0.662358i \(-0.230444\pi\)
−0.948213 + 0.317636i \(0.897111\pi\)
\(480\) 2.47150 + 2.36135i 0.112808 + 0.107780i
\(481\) 0.566492 0.981194i 0.0258298 0.0447386i
\(482\) 6.21731 10.7687i 0.283191 0.490501i
\(483\) 0 0
\(484\) 21.9626 + 38.0404i 0.998302 + 1.72911i
\(485\) 34.7060 1.57592
\(486\) −35.6798 + 14.0747i −1.61847 + 0.638442i
\(487\) −18.0364 −0.817306 −0.408653 0.912690i \(-0.634001\pi\)
−0.408653 + 0.912690i \(0.634001\pi\)
\(488\) 20.2849 + 35.1344i 0.918253 + 1.59046i
\(489\) −18.5560 + 5.42810i −0.839129 + 0.245467i
\(490\) 0 0
\(491\) −1.02344 + 1.77266i −0.0461874 + 0.0799989i −0.888195 0.459467i \(-0.848040\pi\)
0.842007 + 0.539466i \(0.181374\pi\)
\(492\) −38.1490 36.4489i −1.71989 1.64324i
\(493\) −18.5679 32.1606i −0.836257 1.44844i
\(494\) 2.36381 0.106353
\(495\) −3.75700 + 2.40373i −0.168864 + 0.108040i
\(496\) 30.4097 1.36544
\(497\) 0 0
\(498\) −12.2807 + 50.3990i −0.550313 + 2.25843i
\(499\) 19.5438 33.8508i 0.874899 1.51537i 0.0180291 0.999837i \(-0.494261\pi\)
0.856870 0.515532i \(-0.172406\pi\)
\(500\) 25.0742 43.4297i 1.12135 1.94224i
\(501\) −1.41887 + 5.82292i −0.0633906 + 0.260149i
\(502\) 18.5679 + 32.1606i 0.828727 + 1.43540i
\(503\) 5.11846 0.228221 0.114111 0.993468i \(-0.463598\pi\)
0.114111 + 0.993468i \(0.463598\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) −2.32383 4.02499i −0.103307 0.178933i
\(507\) 15.9836 + 15.2712i 0.709855 + 0.678219i
\(508\) 31.5079 54.5732i 1.39794 2.42130i
\(509\) 14.7636 25.5713i 0.654386 1.13343i −0.327662 0.944795i \(-0.606261\pi\)
0.982047 0.188634i \(-0.0604060\pi\)
\(510\) −72.6562 + 21.2538i −3.21727 + 0.941136i
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) −6.73891 + 7.72952i −0.297530 + 0.341267i
\(514\) −18.9750 −0.836952
\(515\) 14.6819 + 25.4298i 0.646962 + 1.12057i
\(516\) −15.6856 + 4.58845i −0.690520 + 0.201995i
\(517\) 1.28352 2.22313i 0.0564493 0.0977730i
\(518\) 0 0
\(519\) 7.58113 + 7.24327i 0.332775 + 0.317944i
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) 1.06470 0.0466454 0.0233227 0.999728i \(-0.492575\pi\)
0.0233227 + 0.999728i \(0.492575\pi\)
\(522\) 2.57179 + 56.3927i 0.112564 + 2.46824i
\(523\) 13.3819 0.585149 0.292574 0.956243i \(-0.405488\pi\)
0.292574 + 0.956243i \(0.405488\pi\)
\(524\) 17.2581 + 29.8918i 0.753922 + 1.30583i
\(525\) 0 0
\(526\) −5.18190 + 8.97532i −0.225942 + 0.391343i
\(527\) −17.0615 + 29.5513i −0.743210 + 1.28728i
\(528\) −0.721181 + 2.95966i −0.0313854 + 0.128803i
\(529\) 0.699612 + 1.21176i 0.0304179 + 0.0526853i
\(530\) 32.1206 1.39523
\(531\) 0.836219 + 18.3361i 0.0362888 + 0.795719i
\(532\) 0 0
\(533\) 1.82889 + 3.16774i 0.0792181 + 0.137210i
\(534\) −45.6972 43.6606i −1.97751 1.88938i
\(535\) 23.4885 40.6833i 1.01550 1.75889i
\(536\) −9.09931 + 15.7605i −0.393031 + 0.680749i
\(537\) 15.1827 4.44133i 0.655181 0.191658i
\(538\) 25.5286 + 44.2168i 1.10062 + 1.90632i
\(539\) 0 0
\(540\) 75.6224 + 14.8136i 3.25427 + 0.637475i
\(541\) −34.0875 −1.46554 −0.732769 0.680478i \(-0.761772\pi\)
−0.732769 + 0.680478i \(0.761772\pi\)
\(542\) −35.0485 60.7058i −1.50546 2.60754i
\(543\) 19.8619 5.81012i 0.852354 0.249336i
\(544\) −1.30985 + 2.26873i −0.0561594 + 0.0972709i
\(545\) 4.75692 8.23922i 0.203764 0.352930i
\(546\) 0 0
\(547\) 2.97150 + 5.14678i 0.127052 + 0.220060i 0.922533 0.385918i \(-0.126115\pi\)
−0.795481 + 0.605978i \(0.792782\pi\)
\(548\) 1.52937 0.0653316
\(549\) 21.3820 + 11.0781i 0.912560 + 0.472800i
\(550\) 8.38151 0.357389
\(551\) 7.54638 + 13.0707i 0.321487 + 0.556831i
\(552\) −9.63198 + 39.5287i −0.409964 + 1.68245i
\(553\) 0 0
\(554\) −21.1139 + 36.5704i −0.897044 + 1.55373i
\(555\) 3.49115 14.3273i 0.148191 0.608161i
\(556\) 38.5165 + 66.7126i 1.63346 + 2.82924i
\(557\) −30.0803 −1.27454 −0.637272 0.770639i \(-0.719937\pi\)
−0.637272 + 0.770639i \(0.719937\pi\)
\(558\) 43.6937 27.9553i 1.84970 1.18344i
\(559\) 1.13298 0.0479202
\(560\) 0 0
\(561\) −2.47150 2.36135i −0.104347 0.0996963i
\(562\) −11.6170 + 20.1213i −0.490035 + 0.848765i
\(563\) −9.81060 + 16.9925i −0.413468 + 0.716147i −0.995266 0.0971860i \(-0.969016\pi\)
0.581799 + 0.813333i \(0.302349\pi\)
\(564\) −42.5679 + 12.4522i −1.79243 + 0.524333i
\(565\) −25.5154 44.1940i −1.07344 1.85926i
\(566\) −41.5049 −1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) 0.687159 + 1.19019i 0.0288072 + 0.0498955i 0.880070 0.474845i \(-0.157496\pi\)
−0.851262 + 0.524740i \(0.824162\pi\)
\(570\) 29.5290 8.63800i 1.23683 0.361806i
\(571\) −8.69076 + 15.0528i −0.363697 + 0.629941i −0.988566 0.150788i \(-0.951819\pi\)
0.624869 + 0.780729i \(0.285152\pi\)
\(572\) 0.401038 0.694619i 0.0167683 0.0290435i
\(573\) −11.4467 10.9365i −0.478191 0.456880i
\(574\) 0 0
\(575\) 38.9545 1.62451
\(576\) −18.5167 + 11.8470i −0.771530 + 0.493626i
\(577\) 27.0548 1.12631 0.563153 0.826353i \(-0.309588\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(578\) −8.09406 14.0193i −0.336668 0.583127i
\(579\) −6.94750 + 28.5119i −0.288728 + 1.18491i
\(580\) 56.7080 98.2211i 2.35467 4.07841i
\(581\) 0 0
\(582\) 9.57227 39.2837i 0.396783 1.62836i
\(583\) 0.725191 + 1.25607i 0.0300344 + 0.0520210i
\(584\) 9.97430 0.412740
\(585\) −4.74338 2.45756i −0.196115 0.101608i
\(586\) 9.16010 0.378400
\(587\) 3.75700 + 6.50731i 0.155068 + 0.268585i 0.933084 0.359659i \(-0.117107\pi\)
−0.778016 + 0.628245i \(0.783774\pi\)
\(588\) 0 0
\(589\) 6.93414 12.0103i 0.285716 0.494875i
\(590\) 27.5349 47.6919i 1.13359 1.96344i
\(591\) −35.4376 + 10.3664i −1.45771 + 0.426417i
\(592\) −5.03590 8.72243i −0.206974 0.358490i
\(593\) −35.5808 −1.46113 −0.730565 0.682843i \(-0.760743\pi\)
−0.730565 + 0.682843i \(0.760743\pi\)
\(594\) 1.68456 + 4.91551i 0.0691184 + 0.201686i
\(595\) 0 0
\(596\) 19.6659 + 34.0623i 0.805545 + 1.39524i
\(597\) 16.5811 4.85041i 0.678620 0.198514i
\(598\) 2.78340 4.82100i 0.113822 0.197145i
\(599\) 5.74105 9.94379i 0.234573 0.406292i −0.724576 0.689195i \(-0.757964\pi\)
0.959148 + 0.282903i \(0.0912975\pi\)
\(600\) −53.0499 50.6857i −2.16575 2.06924i
\(601\) −0.190030 0.329142i −0.00775150 0.0134260i 0.862124 0.506698i \(-0.169134\pi\)
−0.869875 + 0.493272i \(0.835801\pi\)
\(602\) 0 0
\(603\) 0.492129 + 10.7911i 0.0200411 + 0.439448i
\(604\) −52.0335 −2.11721
\(605\) −19.8173 34.3246i −0.805688 1.39549i
\(606\) −8.78959 + 36.0716i −0.357053 + 1.46531i
\(607\) −9.27044 + 16.0569i −0.376275 + 0.651728i −0.990517 0.137390i \(-0.956129\pi\)
0.614242 + 0.789118i \(0.289462\pi\)
\(608\) 0.532351 0.922058i 0.0215897 0.0373944i
\(609\) 0 0
\(610\) −36.1249 62.5702i −1.46265 2.53339i
\(611\) 3.07472 0.124390
\(612\) 2.69054 + 58.9966i 0.108759 + 2.38480i
\(613\) 7.32451 0.295834 0.147917 0.989000i \(-0.452743\pi\)
0.147917 + 0.989000i \(0.452743\pi\)
\(614\) 37.6077 + 65.1385i 1.51772 + 2.62877i
\(615\) 34.4226 + 32.8885i 1.38805 + 1.32619i
\(616\) 0 0
\(617\) 12.7427 22.0710i 0.513002 0.888546i −0.486884 0.873466i \(-0.661867\pi\)
0.999886 0.0150791i \(-0.00480000\pi\)
\(618\) 32.8334 9.60462i 1.32075 0.386354i
\(619\) 16.4482 + 28.4891i 0.661108 + 1.14507i 0.980325 + 0.197391i \(0.0632468\pi\)
−0.319217 + 0.947682i \(0.603420\pi\)
\(620\) −104.214 −4.18535
\(621\) 7.82927 + 22.8456i 0.314178 + 0.916764i
\(622\) 25.6748 1.02947
\(623\) 0 0
\(624\) −3.50194 + 1.02441i −0.140190 + 0.0410092i
\(625\) −1.67111 + 2.89444i −0.0668443 + 0.115778i
\(626\) −0.762585 + 1.32084i −0.0304790 + 0.0527912i
\(627\) 1.00447 + 0.959702i 0.0401145 + 0.0383268i
\(628\) −42.4636 73.5490i −1.69448 2.93493i
\(629\) 11.3016 0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) −20.6264 35.7259i −0.820472 1.42110i
\(633\) −2.00590 + 8.23203i −0.0797275 + 0.327194i
\(634\) −12.6082 + 21.8380i −0.500734 + 0.867297i
\(635\) −28.4301 + 49.2424i −1.12822 + 1.95413i
\(636\) 5.93251 24.3464i 0.235239 0.965399i
\(637\) 0 0
\(638\) 7.64766 0.302774
\(639\) 21.3801 13.6790i 0.845782 0.541132i
\(640\) 69.8991 2.76301
\(641\) −5.73025 9.92509i −0.226331 0.392017i 0.730387 0.683034i \(-0.239340\pi\)
−0.956718 + 0.291016i \(0.906007\pi\)
\(642\) −39.5710 37.8075i −1.56174 1.49214i
\(643\) −8.69078 + 15.0529i −0.342731 + 0.593627i −0.984939 0.172903i \(-0.944685\pi\)
0.642208 + 0.766531i \(0.278019\pi\)
\(644\) 0 0
\(645\) 14.1534 4.14024i 0.557290 0.163022i
\(646\) 11.7896 + 20.4202i 0.463855 + 0.803421i
\(647\) −25.3439 −0.996372 −0.498186 0.867070i \(-0.666000\pi\)
−0.498186 + 0.867070i \(0.666000\pi\)
\(648\) 19.0634 41.2993i 0.748882 1.62239i
\(649\) 2.48664 0.0976091
\(650\) 5.01954 + 8.69410i 0.196883 + 0.341011i
\(651\) 0 0
\(652\) 22.6264 39.1900i 0.886116 1.53480i
\(653\) −7.04163 + 12.1965i −0.275560 + 0.477284i −0.970276 0.242000i \(-0.922197\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(654\) −8.01396 7.65681i −0.313370 0.299405i
\(655\) −15.5723 26.9720i −0.608459 1.05388i
\(656\) 32.5163 1.26955
\(657\) 4.98715 3.19079i 0.194567 0.124484i
\(658\) 0 0
\(659\) −19.0854 33.0569i −0.743462 1.28771i −0.950910 0.309467i \(-0.899849\pi\)
0.207449 0.978246i \(-0.433484\pi\)
\(660\) 2.47150 10.1428i 0.0962028 0.394807i
\(661\) −0.176866 + 0.306341i −0.00687930 + 0.0119153i −0.869445 0.494031i \(-0.835523\pi\)
0.862565 + 0.505946i \(0.168856\pi\)
\(662\) 25.0526 43.3924i 0.973698 1.68649i
\(663\) 0.969283 3.97784i 0.0376438 0.154487i
\(664\) −30.7591 53.2764i −1.19369 2.06752i
\(665\) 0 0
\(666\) −15.2542 7.90324i −0.591087 0.306244i
\(667\) 35.5438 1.37626
\(668\) −7.01403 12.1487i −0.271381 0.470046i
\(669\) 29.3157 + 28.0092i 1.13341 + 1.08290i
\(670\) 16.2048 28.0675i 0.626045 1.08434i
\(671\) 1.63119 2.82531i 0.0629715 0.109070i
\(672\) 0 0
\(673\) 10.5555 + 18.2827i 0.406886 + 0.704748i 0.994539 0.104365i \(-0.0332811\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(674\) −14.0541 −0.541343
\(675\) −42.7393 8.37215i −1.64504 0.322244i
\(676\) −51.7424 −1.99009
\(677\) 10.5732 + 18.3133i 0.406361 + 0.703837i 0.994479 0.104938i \(-0.0334643\pi\)
−0.588118 + 0.808775i \(0.700131\pi\)
\(678\) −57.0605 + 16.6917i −2.19140 + 0.641041i
\(679\) 0 0
\(680\) 44.8879 77.7482i 1.72137 2.98151i
\(681\) 7.66225 + 7.32078i 0.293618 + 0.280533i
\(682\) −3.51360 6.08573i −0.134543 0.233035i
\(683\) 34.7716 1.33050 0.665249 0.746622i \(-0.268326\pi\)
0.665249 + 0.746622i \(0.268326\pi\)
\(684\) −1.09349 23.9775i −0.0418107 0.916801i
\(685\) −1.37998 −0.0527264
\(686\) 0 0
\(687\) −0.598835 + 2.45756i −0.0228470 + 0.0937618i
\(688\) 5.03590 8.72243i 0.191992 0.332539i
\(689\) −0.868609 + 1.50447i −0.0330914 + 0.0573159i
\(690\) 17.1534 70.3959i 0.653019 2.67993i
\(691\) 17.3246 + 30.0071i 0.659059 + 1.14152i 0.980860 + 0.194716i \(0.0623785\pi\)
−0.321801 + 0.946807i \(0.604288\pi\)
\(692\) −24.5418 −0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) −34.7542 60.1960i −1.31830 2.28336i
\(696\) −48.4051 46.2479i −1.83479 1.75302i
\(697\) −18.2434 + 31.5985i −0.691017 + 1.19688i
\(698\) −25.8044 + 44.6945i −0.976710 + 1.69171i
\(699\) −22.0240 + 6.44260i −0.833024 + 0.243681i
\(700\) 0 0
\(701\) −48.6050 −1.83579 −0.917894 0.396826i \(-0.870111\pi\)
−0.917894 + 0.396826i \(0.870111\pi\)
\(702\) −4.08998 + 4.69120i −0.154366 + 0.177058i
\(703\) −4.59322 −0.173236
\(704\) 1.48901 + 2.57904i 0.0561192 + 0.0972012i
\(705\) 38.4098 11.2359i 1.44660 0.423167i
\(706\) 18.1651 31.4629i 0.683654 1.18412i
\(707\) 0 0
\(708\) −31.0634 29.6791i −1.16743 1.11541i
\(709\) −2.05408 3.55778i −0.0771428 0.133615i 0.824873 0.565318i \(-0.191246\pi\)
−0.902016 + 0.431702i \(0.857913\pi\)
\(710\) −76.1506 −2.85788
\(711\) −21.7419 11.2646i −0.815386 0.422454i
\(712\) 74.9528 2.80898
\(713\) −16.3300 28.2844i −0.611564 1.05926i
\(714\) 0 0
\(715\) −0.361864 + 0.626767i −0.0135330 + 0.0234398i
\(716\) −18.5131 + 32.0657i −0.691868 + 1.19835i
\(717\) −7.95037 + 32.6276i −0.296912 + 1.21850i
\(718\) −8.87266 15.3679i −0.331125 0.573525i
\(719\) −48.2816 −1.80060 −0.900299 0.435271i \(-0.856653\pi\)
−0.900299 + 0.435271i \(0.856653\pi\)
\(720\) −40.0032 + 25.5941i −1.49083 + 0.953837i
\(721\) 0 0
\(722\) 18.5833 + 32.1872i 0.691597 + 1.19788i
\(723\) 6.32889 + 6.04684i 0.235374 + 0.224884i
\(724\) −24.2187 + 41.9481i −0.900082 + 1.55899i
\(725\) −32.0495 + 55.5114i −1.19029 + 2.06164i
\(726\) −44.3177 + 12.9641i −1.64478 + 0.481143i
\(727\) −20.5151 35.5332i −0.760863 1.31785i −0.942406 0.334470i \(-0.891443\pi\)
0.181543 0.983383i \(-0.441891\pi\)
\(728\) 0 0
\(729\) −3.67996 26.7480i −0.136295 0.990668i
\(730\) −17.7630 −0.657439
\(731\) 5.65082 + 9.78750i 0.209003 + 0.362004i
\(732\) −54.0983 + 15.8252i −1.99953 + 0.584916i
\(733\) 15.2714 26.4508i 0.564062 0.976983i −0.433075 0.901358i \(-0.642571\pi\)
0.997136 0.0756253i \(-0.0240953\pi\)
\(734\) 13.5011 23.3845i 0.498334 0.863139i
\(735\) 0 0
\(736\) −1.25370 2.17147i −0.0462118 0.0800413i
\(737\) 1.46343 0.0539061
\(738\) 46.7205 29.8918i 1.71981 1.10033i
\(739\) 23.8200 0.876234 0.438117 0.898918i \(-0.355646\pi\)
0.438117 + 0.898918i \(0.355646\pi\)
\(740\) 17.2581 + 29.8918i 0.634419 + 1.09885i
\(741\) −0.393936 + 1.61668i −0.0144716 + 0.0593901i
\(742\) 0 0
\(743\) −5.26089 + 9.11213i −0.193003 + 0.334292i −0.946244 0.323453i \(-0.895156\pi\)
0.753241 + 0.657745i \(0.228490\pi\)
\(744\) −14.5634 + 59.7669i −0.533921 + 2.19116i
\(745\) −17.7449 30.7350i −0.650121 1.12604i
\(746\) −1.33794 −0.0489855
\(747\) −32.4227 16.7983i −1.18629 0.614619i
\(748\) 8.00079 0.292538
\(749\) 0 0
\(750\) 38.1160 + 36.4174i 1.39180 + 1.32977i
\(751\) 5.13521 8.89445i 0.187386 0.324563i −0.756992 0.653425i \(-0.773332\pi\)
0.944378 + 0.328862i \(0.106665\pi\)
\(752\) 13.6665 23.6711i 0.498367 0.863197i
\(753\) −25.0900 + 7.33948i −0.914330 + 0.267465i
\(754\) 4.58005 + 7.93288i 0.166796 + 0.288899i
\(755\) 46.9507 1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) 27.9159 + 48.3518i 1.01395 + 1.75622i
\(759\) 3.14009 0.918558i 0.113978 0.0333416i
\(760\) −18.2434 + 31.5985i −0.661757 + 1.14620i
\(761\) 13.8302 23.9547i 0.501345 0.868355i −0.498654 0.866801i \(-0.666172\pi\)
0.999999 0.00155404i \(-0.000494668\pi\)
\(762\) 47.8961 + 45.7616i 1.73509 + 1.65777i
\(763\) 0 0
\(764\) 37.0554 1.34062
\(765\) −2.42773 53.2338i −0.0877747 1.92467i
\(766\) 87.8742 3.17502
\(767\) 1.48920 + 2.57938i 0.0537720 + 0.0931359i
\(768\) 13.2696 54.4573i 0.478827 1.96506i
\(769\) −16.9613 + 29.3778i −0.611640 + 1.05939i 0.379324 + 0.925264i \(0.376157\pi\)
−0.990964 + 0.134128i \(0.957177\pi\)
\(770\) 0 0
\(771\) 3.16225 12.9776i 0.113886 0.467376i
\(772\) −34.3442 59.4858i −1.23607 2.14094i
\(773\) 28.5956 1.02851 0.514256 0.857637i \(-0.328068\pi\)
0.514256 + 0.857637i \(0.328068\pi\)
\(774\) −0.782679 17.1621i −0.0281328 0.616880i
\(775\) 58.8986 2.11570
\(776\) 23.9753 + 41.5265i 0.860664 + 1.49071i
\(777\) 0 0
\(778\) −47.5605 + 82.3772i −1.70513 + 2.95337i
\(779\) 7.41449 12.8423i 0.265652 0.460122i
\(780\) 12.0012 3.51066i 0.429711 0.125702i
\(781\) −1.71926 2.97785i −0.0615200 0.106556i