Properties

Label 441.2.f.g.148.1
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 148.1
Root \(1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.g.295.1

$q$-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 \(0.471567\pi\)
−0.907175 + 0.420753i \(0.861766\pi\)
\(6\) 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 −0.897803 0.440397i \(-0.854838\pi\)
0.830297 + 0.557322i \(0.188171\pi\)
\(14\) 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 \(-0.700422\pi\)
−0.588857 + 0.808237i \(0.700422\pi\)
\(18\) −6.55408 3.39569i −1.54481 0.800373i
\(19\) 1.97351 0.452755 0.226378 0.974040i \(-0.427312\pi\)
0.226378 + 0.974040i \(0.427312\pi\)
\(20\) −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 \(-0.615953\pi\)
0.987335 0.158648i \(-0.0507136\pi\)
\(32\) −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 \(-0.633743\pi\)
0.994655 0.103249i \(-0.0329240\pi\)
\(42\) 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 0.538335 0.842731i \(-0.319053\pi\)
−0.998994 + 0.0448469i \(0.985720\pi\)
\(48\) 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 −0.595240 0.803548i \(-0.702943\pi\)
0.993513 + 0.113719i \(0.0362763\pi\)
\(60\) 18.5723 + 17.7446i 2.39767 + 2.29082i
\(61\) −4.01356 6.95169i −0.513884 0.890073i −0.999870 0.0161063i \(-0.994873\pi\)
0.485987 0.873966i \(-0.338460\pi\)
\(62\) −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 \(-0.536844\pi\)
−0.115491 + 0.993309i \(0.536844\pi\)
\(74\) −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 \(0.0661933\pi\)
−0.310431 + 0.950596i \(0.600473\pi\)
\(84\) 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 \(-0.787849\pi\)
−0.785996 + 0.618231i \(0.787849\pi\)
\(90\) 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 0.518123 0.855306i \(-0.326631\pi\)
−0.999778 + 0.0210547i \(0.993298\pi\)
\(98\) 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 0.997166 0.0752364i \(-0.0239711\pi\)
−0.563739 + 0.825953i \(0.690638\pi\)
\(102\) −14.9626 14.2958i −1.48152 1.41550i
\(103\) 4.01356 6.95169i 0.395468 0.684970i −0.597693 0.801725i \(-0.703916\pi\)
0.993161 + 0.116755i \(0.0372492\pi\)
\(104\) −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 −0.989863 0.142027i \(-0.954638\pi\)
0.617931 + 0.786233i \(0.287971\pi\)
\(132\) −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 \(0.464951\pi\)
−0.915725 + 0.401806i \(0.868383\pi\)
\(140\) 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 \(-0.518258\pi\)
0.893265 0.449531i \(-0.148409\pi\)
\(158\) −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 −0.791289 0.611443i \(-0.790590\pi\)
0.925169 + 0.379555i \(0.123923\pi\)
\(168\) 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 0.727721 0.685874i \(-0.240580\pi\)
−0.957844 + 0.287288i \(0.907246\pi\)
\(174\) 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 \(-0.646454\pi\)
−0.444037 + 0.896008i \(0.646454\pi\)
\(182\) 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 \(-0.615019\pi\)
−0.353530 + 0.935423i \(0.615019\pi\)
\(200\) −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 \(-0.879953\pi\)
0.145936 0.989294i \(-0.453381\pi\)
\(224\) 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 0.746463 0.665427i \(-0.231751\pi\)
−0.949508 + 0.313742i \(0.898417\pi\)
\(228\) 3.28074 13.4638i 0.217272 0.891664i
\(229\) 0.730195 1.26473i 0.0482526 0.0835760i −0.840890 0.541206i \(-0.817968\pi\)
0.889143 + 0.457630i \(0.151301\pi\)
\(230\) −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 0.773092 0.634294i \(-0.218709\pi\)
−0.935860 + 0.352371i \(0.885376\pi\)
\(242\) −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 \(-0.341969\pi\)
0.476324 + 0.879270i \(0.341969\pi\)
\(252\) 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 −0.960864 0.277020i \(-0.910653\pi\)
0.720338 + 0.693623i \(0.243986\pi\)
\(258\) −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 \(-0.281989\pi\)
0.632596 + 0.774482i \(0.281989\pi\)
\(270\) −30.7345 + 35.2524i −1.87044 + 2.14540i
\(271\) −28.4889 −1.73057 −0.865287 0.501276i \(-0.832864\pi\)
−0.865287 + 0.501276i \(0.832864\pi\)
\(272\) 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 \(0.333834\pi\)
−0.999999 + 0.00157378i \(0.999499\pi\)
\(284\) −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 −0.806517 0.591211i \(-0.798650\pi\)
0.915262 + 0.402858i \(0.131983\pi\)
\(294\) 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 \(-0.162605\pi\)
0.872335 + 0.488908i \(0.162605\pi\)
\(308\) 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 −0.679332 0.733831i \(-0.737730\pi\)
0.975182 + 0.221403i \(0.0710635\pi\)
\(312\) 1.00885 4.14024i 0.0571151 0.234395i
\(313\) 0.309930 + 0.536815i 0.0175183 + 0.0303426i 0.874652 0.484752i \(-0.161090\pi\)
−0.857133 + 0.515095i \(0.827757\pi\)
\(314\) −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 \(0.0230624\pi\)
−0.435997 + 0.899948i \(0.643604\pi\)
\(350\) 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 0.599895 0.800078i \(-0.295209\pi\)
−0.992836 + 0.119485i \(0.961876\pi\)
\(354\) 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 0.686529 0.727103i \(-0.259134\pi\)
−0.972954 + 0.231000i \(0.925800\pi\)
\(368\) 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 \(-0.467523\pi\)
0.810596 0.585606i \(-0.199143\pi\)
\(384\) −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 \(-0.403073\pi\)
0.299822 + 0.953995i \(0.403073\pi\)
\(398\) 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 −0.530250 0.847841i \(-0.677902\pi\)
0.999377 + 0.0352893i \(0.0112353\pi\)
\(410\) 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 −0.996169 0.0874539i \(-0.972127\pi\)
0.573822 + 0.818980i \(0.305460\pi\)
\(420\) 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 \(-0.923999\pi\)
−0.971631 + 0.236501i \(0.923999\pi\)
\(434\) 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 0.975532 0.219857i \(-0.0705591\pi\)
−0.678168 + 0.734907i \(0.737226\pi\)
\(440\) 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 0.761158 0.648567i \(-0.224631\pi\)
−0.942254 + 0.334898i \(0.891298\pi\)
\(462\) 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 \(-0.396823\pi\)
0.318494 + 0.947925i \(0.396823\pi\)
\(468\) −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 0.948213 0.317636i \(-0.102889\pi\)
−0.749187 + 0.662358i \(0.769556\pi\)
\(480\) 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 \(-0.536402\pi\)
−0.114111 + 0.993468i \(0.536402\pi\)
\(504\) 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 \(0.393739\pi\)
−0.982047 + 0.188634i \(0.939594\pi\)
\(510\) 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 \(-0.507425\pi\)
−0.0233227 + 0.999728i \(0.507425\pi\)
\(522\) 2.57179 + 56.3927i 0.112564 + 2.46824i
\(523\) −13.3819 −0.585149 −0.292574 0.956243i \(-0.594512\pi\)
−0.292574 + 0.956243i \(0.594512\pi\)
\(524\) −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 −0.581799 0.813333i \(-0.697651\pi\)
0.995266 + 0.0971860i \(0.0309842\pi\)
\(564\) −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 \(-0.690412\pi\)
−0.563153 + 0.826353i \(0.690412\pi\)
\(578\) −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 0.778016 0.628245i \(-0.216226\pi\)
−0.933084 + 0.359659i \(0.882893\pi\)
\(588\) 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 \(-0.239257\pi\)
0.730565 + 0.682843i \(0.239257\pi\)
\(594\) −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 0.869875 0.493272i \(-0.164199\pi\)
−0.862124 + 0.506698i \(0.830866\pi\)
\(602\) 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 −0.614242 0.789118i \(-0.710538\pi\)
0.990517 + 0.137390i \(0.0438713\pi\)
\(608\) −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 \(-0.936753\pi\)
0.319217 0.947682i \(-0.396580\pi\)
\(620\) −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 −0.642208 0.766531i \(-0.721981\pi\)
0.984939 + 0.172903i \(0.0553147\pi\)
\(644\) 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 \(-0.334000\pi\)
0.498186 + 0.867070i \(0.334000\pi\)
\(648\) 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 −0.862565 0.505946i \(-0.831144\pi\)
0.869445 + 0.494031i \(0.164477\pi\)
\(662\) 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 0.588118 0.808775i \(-0.299869\pi\)
−0.994479 + 0.104938i \(0.966536\pi\)
\(678\) 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 \(-0.937622\pi\)
0.321801 0.946807i \(-0.395712\pi\)
\(692\) 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 \(-0.143347\pi\)
0.900299 + 0.435271i \(0.143347\pi\)
\(720\) 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 \(0.108557\pi\)
−0.181543 + 0.983383i \(0.558109\pi\)
\(728\) 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 \(0.357429\pi\)
−0.997136 + 0.0756253i \(0.975905\pi\)
\(734\) −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 \(0.333828\pi\)
−0.999999 + 0.00155404i \(0.999505\pi\)
\(762\) −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 \(-0.623843\pi\)
0.990964 0.134128i \(-0.0428233\pi\)
\(770\) 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 \(-0.671932\pi\)
−0.514256 + 0.857637i \(0.671932\pi\)
\(774\) −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