Properties

Label 441.2.g.g.67.2
Level $441$
Weight $2$
Character 441.67
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.g (of order \(3\), degree \(2\), not 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 67.2
Root \(-1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.g.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +O(q^{10})\) \(q+(-1.23025 + 2.13086i) q^{2} +(0.410052 - 1.68281i) q^{3} +(-2.02704 - 3.51094i) q^{4} +3.65808 q^{5} +(3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(-2.66372 - 1.38008i) q^{9} +(-4.50036 + 7.79485i) q^{10} +0.406421 q^{11} +(-6.73945 + 1.97146i) q^{12} +(-0.243398 + 0.421578i) q^{13} +(1.50000 - 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +(2.42792 - 4.20528i) q^{17} +(6.21780 - 3.97816i) q^{18} +(-0.986757 - 1.70911i) q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +4.64766 q^{23} +(2.07244 - 8.50508i) q^{24} +8.38151 q^{25} +(-0.598883 - 1.03729i) q^{26} +(-3.41468 + 3.91663i) q^{27} +(-3.82383 - 6.62307i) q^{29} +(11.2719 + 10.7695i) q^{30} +(3.51360 + 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(0.166653 - 0.683930i) q^{33} +(5.97391 + 10.3471i) q^{34} +(0.554084 + 12.1496i) q^{36} +(-1.16372 - 2.01561i) q^{37} +4.85584 q^{38} +(0.609631 + 0.582462i) q^{39} +18.4882 q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} +(-0.823832 - 1.42692i) q^{44} +(-9.74407 - 5.04844i) q^{45} +(-5.71780 + 9.90352i) q^{46} +(-3.15811 + 5.47002i) q^{47} +(5.41938 + 5.17786i) q^{48} +(-10.3114 + 17.8598i) q^{50} +(-6.08113 - 5.81012i) q^{51} +1.97351 q^{52} +(1.78434 - 3.09056i) q^{53} +(-4.14487 - 12.0946i) q^{54} +1.48672 q^{55} +(-3.28074 + 0.959702i) q^{57} +18.8171 q^{58} +(3.05919 + 5.29868i) q^{59} +(-24.6534 + 7.21177i) q^{60} +(-4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(1.25233 + 1.19652i) q^{66} +(-1.80039 - 3.11836i) q^{67} -19.6860 q^{68} +(1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(-13.4626 - 6.97504i) q^{72} +(0.986757 - 1.70911i) q^{73} +5.72665 q^{74} +(3.43685 - 14.1045i) q^{75} +(-4.00040 + 6.92889i) q^{76} +(-1.99115 + 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} +(-7.91503 + 13.7092i) q^{80} +(5.19076 + 7.35228i) q^{81} +(9.24411 + 16.0113i) q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} -5.72665 q^{86} +(-12.7134 + 3.71899i) q^{87} +2.05408 q^{88} +(7.41507 + 12.8433i) q^{89} +(22.7452 - 14.5524i) q^{90} +(-9.42101 - 16.3177i) q^{92} +(11.6819 - 3.41726i) q^{93} +(-7.77056 - 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.896848 + 0.262352i) q^{96} +(-4.74375 - 8.21642i) q^{97} +(-1.08259 - 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + 16q^{11} + 18q^{15} - 6q^{16} + 18q^{18} - 6q^{22} + 8q^{23} + 24q^{25} - 22q^{29} + 42q^{30} - 16q^{32} - 30q^{36} + 6q^{37} + 24q^{39} - 6q^{43} + 14q^{44} - 12q^{46} - 56q^{50} - 18q^{51} - 28q^{53} - 6q^{57} + 36q^{58} - 126q^{60} - 48q^{64} + 6q^{65} + 76q^{71} - 30q^{72} + 72q^{74} + 36q^{78} + 6q^{79} + 24q^{81} + 30q^{85} - 72q^{86} - 12q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 −0.00784213 + 0.999969i \(0.502496\pi\)
−0.862078 + 0.506776i \(0.830837\pi\)
\(3\) 0.410052 1.68281i 0.236743 0.971572i
\(4\) −2.02704 3.51094i −1.01352 1.75547i
\(5\) 3.65808 1.63594 0.817970 0.575260i \(-0.195099\pi\)
0.817970 + 0.575260i \(0.195099\pi\)
\(6\) 3.08137 + 2.94405i 1.25796 + 1.20190i
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) −2.66372 1.38008i −0.887905 0.460027i
\(10\) −4.50036 + 7.79485i −1.42314 + 2.46495i
\(11\) 0.406421 0.122540 0.0612702 0.998121i \(-0.480485\pi\)
0.0612702 + 0.998121i \(0.480485\pi\)
\(12\) −6.73945 + 1.97146i −1.94551 + 0.569113i
\(13\) −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
\(17\) 2.42792 4.20528i 0.588857 1.01993i −0.405525 0.914084i \(-0.632911\pi\)
0.994382 0.105847i \(-0.0337553\pi\)
\(18\) 6.21780 3.97816i 1.46555 0.937660i
\(19\) −0.986757 1.70911i −0.226378 0.392097i 0.730354 0.683069i \(-0.239355\pi\)
−0.956732 + 0.290971i \(0.906022\pi\)
\(20\) −7.41507 12.8433i −1.65806 2.87185i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) 4.64766 0.969105 0.484552 0.874762i \(-0.338982\pi\)
0.484552 + 0.874762i \(0.338982\pi\)
\(24\) 2.07244 8.50508i 0.423034 1.73609i
\(25\) 8.38151 1.67630
\(26\) −0.598883 1.03729i −0.117451 0.203430i
\(27\) −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 \(-0.418002\pi\)
\(30\) 11.2719 + 10.7695i 2.05795 + 1.96624i
\(31\) 3.51360 + 6.08573i 0.631061 + 1.09303i 0.987335 + 0.158648i \(0.0507136\pi\)
−0.356274 + 0.934381i \(0.615953\pi\)
\(32\) −0.269748 0.467216i −0.0476851 0.0825930i
\(33\) 0.166653 0.683930i 0.0290106 0.119057i
\(34\) 5.97391 + 10.3471i 1.02452 + 1.77452i
\(35\) 0 0
\(36\) 0.554084 + 12.1496i 0.0923474 + 2.02494i
\(37\) −1.16372 2.01561i −0.191314 0.331365i 0.754372 0.656447i \(-0.227941\pi\)
−0.945686 + 0.325082i \(0.894608\pi\)
\(38\) 4.85584 0.787721
\(39\) 0.609631 + 0.582462i 0.0976191 + 0.0932686i
\(40\) 18.4882 2.92324
\(41\) 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 \(0.776544\pi\)
\(44\) −0.823832 1.42692i −0.124197 0.215116i
\(45\) −9.74407 5.04844i −1.45256 0.752577i
\(46\) −5.71780 + 9.90352i −0.843044 + 1.46019i
\(47\) −3.15811 + 5.47002i −0.460658 + 0.797884i −0.998994 0.0448469i \(-0.985720\pi\)
0.538335 + 0.842731i \(0.319053\pi\)
\(48\) 5.41938 + 5.17786i 0.782220 + 0.747360i
\(49\) 0 0
\(50\) −10.3114 + 17.8598i −1.45825 + 2.52576i
\(51\) −6.08113 5.81012i −0.851528 0.813579i
\(52\) 1.97351 0.273677
\(53\) 1.78434 3.09056i 0.245097 0.424521i −0.717062 0.697010i \(-0.754513\pi\)
0.962159 + 0.272489i \(0.0878467\pi\)
\(54\) −4.14487 12.0946i −0.564046 1.64587i
\(55\) 1.48672 0.200469
\(56\) 0 0
\(57\) −3.28074 + 0.959702i −0.434544 + 0.127116i
\(58\) 18.8171 2.47081
\(59\) 3.05919 + 5.29868i 0.398273 + 0.689829i 0.993513 0.113719i \(-0.0362763\pi\)
−0.595240 + 0.803548i \(0.702943\pi\)
\(60\) −24.6534 + 7.21177i −3.18274 + 0.931035i
\(61\) −4.01356 + 6.95169i −0.513884 + 0.890073i 0.485987 + 0.873966i \(0.338460\pi\)
−0.999870 + 0.0161063i \(0.994873\pi\)
\(62\) −17.2905 −2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −0.890369 + 1.54216i −0.110437 + 0.191282i
\(66\) 1.25233 + 1.19652i 0.154151 + 0.147282i
\(67\) −1.80039 3.11836i −0.219952 0.380969i 0.734841 0.678240i \(-0.237257\pi\)
−0.954793 + 0.297271i \(0.903924\pi\)
\(68\) −19.6860 −2.38728
\(69\) 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 \(0.332584\pi\)
\(72\) −13.4626 6.97504i −1.58659 0.822017i
\(73\) 0.986757 1.70911i 0.115491 0.200037i −0.802485 0.596673i \(-0.796489\pi\)
0.917976 + 0.396636i \(0.129822\pi\)
\(74\) 5.72665 0.665710
\(75\) 3.43685 14.1045i 0.396854 1.62865i
\(76\) −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 −0.998917 0.0465297i \(-0.985184\pi\)
0.539754 + 0.841823i \(0.318517\pi\)
\(80\) −7.91503 + 13.7092i −0.884928 + 1.53274i
\(81\) 5.19076 + 7.35228i 0.576751 + 0.816920i
\(82\) 9.24411 + 16.0113i 1.02084 + 1.76815i
\(83\) 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
\(86\) −5.72665 −0.617521
\(87\) −12.7134 + 3.71899i −1.36301 + 0.398718i
\(88\) 2.05408 0.218966
\(89\) 7.41507 + 12.8433i 0.785996 + 1.36139i 0.928402 + 0.371577i \(0.121183\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(90\) 22.7452 14.5524i 2.39755 1.53396i
\(91\) 0 0
\(92\) −9.42101 16.3177i −0.982208 1.70123i
\(93\) 11.6819 3.41726i 1.21136 0.354354i
\(94\) −7.77056 13.4590i −0.801472 1.38819i
\(95\) −3.60963 6.25206i −0.370340 0.641448i
\(96\) −0.896848 + 0.262352i −0.0915342 + 0.0267762i
\(97\) −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
\(100\) −16.9897 29.4270i −1.69897 2.94270i
\(101\) −8.71176 −0.866852 −0.433426 0.901189i \(-0.642696\pi\)
−0.433426 + 0.901189i \(0.642696\pi\)
\(102\) 19.8619 5.81012i 1.96662 0.575287i
\(103\) −8.02712 −0.790936 −0.395468 0.918480i \(-0.629418\pi\)
−0.395468 + 0.918480i \(0.629418\pi\)
\(104\) −1.23016 + 2.13069i −0.120627 + 0.208931i
\(105\) 0 0
\(106\) 4.39037 + 7.60434i 0.426430 + 0.738599i
\(107\) −6.42101 11.1215i −0.620742 1.07516i −0.989348 0.145571i \(-0.953498\pi\)
0.368605 0.929586i \(-0.379835\pi\)
\(108\) 20.6727 + 4.04955i 1.98924 + 0.389669i
\(109\) −1.30039 + 2.25234i −0.124555 + 0.215735i −0.921559 0.388239i \(-0.873084\pi\)
0.797004 + 0.603974i \(0.206417\pi\)
\(110\) −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 \(-0.0611544\pi\)
\(114\) 1.99115 8.17147i 0.186488 0.765328i
\(115\) 17.0015 1.58540
\(116\) −15.5021 + 26.8505i −1.43934 + 2.49301i
\(117\) 1.23016 0.787055i 0.113728 0.0727633i
\(118\) −15.0543 −1.38586
\(119\) 0 0
\(120\) 7.58113 31.1122i 0.692059 2.84014i
\(121\) −10.8348 −0.984984
\(122\) −9.87538 17.1047i −0.894075 1.54858i
\(123\) −9.41002 8.99066i −0.848473 0.810660i
\(124\) 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
\(129\) 3.86908 1.13181i 0.340654 0.0996502i
\(130\) −2.19076 3.79450i −0.192142 0.332800i
\(131\) 8.51392 0.743864 0.371932 0.928260i \(-0.378695\pi\)
0.371932 + 0.928260i \(0.378695\pi\)
\(132\) −2.73905 + 0.801244i −0.238404 + 0.0697393i
\(133\) 0 0
\(134\) 8.85973 0.765364
\(135\) −12.4911 + 14.3273i −1.07507 + 1.23310i
\(136\) 12.2709 21.2538i 1.05222 1.82250i
\(137\) 0.377242 0.0322300 0.0161150 0.999870i \(-0.494870\pi\)
0.0161150 + 0.999870i \(0.494870\pi\)
\(138\) 14.3212 + 13.6829i 1.21910 + 1.16477i
\(139\) −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
\(143\) −0.0989221 + 0.171338i −0.00827228 + 0.0143280i
\(144\) 10.9356 6.99661i 0.911300 0.583051i
\(145\) −13.9879 24.2277i −1.16163 2.01200i
\(146\) 2.42792 + 4.20528i 0.200936 + 0.348032i
\(147\) 0 0
\(148\) −4.71780 + 8.17147i −0.387801 + 0.671691i
\(149\) −9.70175 −0.794798 −0.397399 0.917646i \(-0.630087\pi\)
−0.397399 + 0.917646i \(0.630087\pi\)
\(150\) 25.8265 + 24.6756i 2.10873 + 2.01475i
\(151\) −12.8348 −1.04448 −0.522242 0.852798i \(-0.674904\pi\)
−0.522242 + 0.852798i \(0.674904\pi\)
\(152\) −4.98715 8.63800i −0.404511 0.700634i
\(153\) −12.2709 + 7.85095i −0.992045 + 0.634711i
\(154\) 0 0
\(155\) 12.8530 + 22.2621i 1.03238 + 1.78813i
\(156\) 0.809243 3.32105i 0.0647913 0.265897i
\(157\) 10.4743 + 18.1420i 0.835937 + 1.44789i 0.893265 + 0.449531i \(0.148409\pi\)
−0.0573276 + 0.998355i \(0.518258\pi\)
\(158\) −10.0416 17.3926i −0.798869 1.38368i
\(159\) −4.46917 4.26999i −0.354428 0.338633i
\(160\) −0.986757 1.70911i −0.0780100 0.135117i
\(161\) 0 0
\(162\) −22.0526 + 2.01561i −1.73262 + 0.158362i
\(163\) 5.58113 + 9.66679i 0.437148 + 0.757162i 0.997468 0.0711140i \(-0.0226554\pi\)
−0.560321 + 0.828276i \(0.689322\pi\)
\(164\) −30.4624 −2.37871
\(165\) 0.609631 2.50187i 0.0474597 0.194770i
\(166\) −29.9492 −2.32451
\(167\) 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
\(170\) 21.8530 + 37.8505i 1.67605 + 2.90300i
\(171\) 0.269726 + 5.91439i 0.0206265 + 0.452285i
\(172\) 4.71780 8.17147i 0.359729 0.623069i
\(173\) −3.02680 + 5.24258i −0.230124 + 0.398586i −0.957844 0.287288i \(-0.907246\pi\)
0.727721 + 0.685874i \(0.240580\pi\)
\(174\) 7.71599 31.6657i 0.584948 2.40057i
\(175\) 0 0
\(176\) −0.879379 + 1.52313i −0.0662857 + 0.114810i
\(177\) 10.1711 2.97532i 0.764507 0.223638i
\(178\) −36.4896 −2.73501
\(179\) −4.56654 + 7.90947i −0.341319 + 0.591182i −0.984678 0.174383i \(-0.944207\pi\)
0.643359 + 0.765565i \(0.277540\pi\)
\(180\) 2.02688 + 44.4442i 0.151075 + 3.31268i
\(181\) −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
\(184\) 23.4897 1.73168
\(185\) −4.25696 7.37327i −0.312978 0.542093i
\(186\) −7.08998 + 29.0966i −0.519863 + 2.13347i
\(187\) 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 −0.982646 0.185491i \(-0.940613\pi\)
0.651963 + 0.758251i \(0.273946\pi\)
\(192\) −3.00463 + 12.3307i −0.216840 + 0.889891i
\(193\) −8.47150 14.6731i −0.609792 1.05619i −0.991274 0.131814i \(-0.957920\pi\)
0.381483 0.924376i \(-0.375414\pi\)
\(194\) 23.3441 1.67601
\(195\) 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 \(0.774506\pi\)
\(198\) 2.52704 1.61680i 0.179589 0.114901i
\(199\) 4.98715 8.63800i 0.353530 0.612332i −0.633335 0.773877i \(-0.718315\pi\)
0.986865 + 0.161546i \(0.0516479\pi\)
\(200\) 42.3609 2.99537
\(201\) −5.98587 + 1.75103i −0.422211 + 0.123508i
\(202\) 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
\(206\) 9.87538 17.1047i 0.688051 1.19174i
\(207\) −12.3801 6.41415i −0.860473 0.445814i
\(208\) −1.05329 1.82435i −0.0730324 0.126496i
\(209\) −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 \(0.220521\pi\)
\(212\) −14.4677 −0.993646
\(213\) 3.46924 14.2374i 0.237709 0.975533i
\(214\) 31.5979 2.15998
\(215\) 4.25696 + 7.37327i 0.290322 + 0.502853i
\(216\) −17.2581 + 19.7950i −1.17426 + 1.34688i
\(217\) 0 0
\(218\) −3.19961 5.54189i −0.216705 0.375344i
\(219\) −2.47150 2.36135i −0.167008 0.159565i
\(220\) −3.01364 5.21978i −0.203179 0.351917i
\(221\) 1.18190 + 2.04712i 0.0795034 + 0.137704i
\(222\) 2.34822 9.63688i 0.157602 0.646785i
\(223\) −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
\(226\) 17.1623 + 29.7259i 1.14162 + 1.97734i
\(227\) 6.11839 0.406092 0.203046 0.979169i \(-0.434916\pi\)
0.203046 + 0.979169i \(0.434916\pi\)
\(228\) 10.0197 + 9.57312i 0.663568 + 0.633995i
\(229\) −1.46039 −0.0965052 −0.0482526 0.998835i \(-0.515365\pi\)
−0.0482526 + 0.998835i \(0.515365\pi\)
\(230\) −20.9161 + 36.2278i −1.37917 + 2.38879i
\(231\) 0 0
\(232\) −19.3260 33.4736i −1.26881 2.19765i
\(233\) 6.62422 + 11.4735i 0.433967 + 0.751653i 0.997211 0.0746378i \(-0.0237801\pi\)
−0.563244 + 0.826291i \(0.690447\pi\)
\(234\) 0.163702 + 3.58956i 0.0107016 + 0.234657i
\(235\) −11.5526 + 20.0097i −0.753610 + 1.30529i
\(236\) 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 \(0.950918\pi\)
\(240\) 19.8245 + 18.9410i 1.27967 + 1.22264i
\(241\) 5.05368 0.325536 0.162768 0.986664i \(-0.447958\pi\)
0.162768 + 0.986664i \(0.447958\pi\)
\(242\) 13.3296 23.0875i 0.856857 1.48412i
\(243\) 14.5010 5.72026i 0.930239 0.366955i
\(244\) 32.5426 2.08333
\(245\) 0 0
\(246\) 30.7345 8.99066i 1.95956 0.573223i
\(247\) 0.960699 0.0611278
\(248\) 17.7580 + 30.7578i 1.12764 + 1.95312i
\(249\) 20.2345 5.91913i 1.28231 0.375110i
\(250\) −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
\(255\) −22.2452 21.2538i −1.39305 1.33097i
\(256\) 16.1804 + 28.0253i 1.01128 + 1.75158i
\(257\) 7.71184 0.481051 0.240526 0.970643i \(-0.422680\pi\)
0.240526 + 0.970643i \(0.422680\pi\)
\(258\) −2.34822 + 9.63688i −0.146194 + 0.599966i
\(259\) 0 0
\(260\) 7.21926 0.447720
\(261\) 1.04523 + 22.9192i 0.0646981 + 1.41866i
\(262\) −10.4743 + 18.1420i −0.647102 + 1.12081i
\(263\) 4.21206 0.259727 0.129864 0.991532i \(-0.458546\pi\)
0.129864 + 0.991532i \(0.458546\pi\)
\(264\) 0.842281 3.45664i 0.0518388 0.212741i
\(265\) 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
\(269\) −10.3753 + 17.9706i −0.632596 + 1.09569i 0.354423 + 0.935085i \(0.384677\pi\)
−0.987019 + 0.160603i \(0.948656\pi\)
\(270\) −15.1623 44.2431i −0.922745 2.69255i
\(271\) 14.2444 + 24.6721i 0.865287 + 1.49872i 0.866762 + 0.498723i \(0.166197\pi\)
−0.00147433 + 0.999999i \(0.500469\pi\)
\(272\) 10.5067 + 18.1981i 0.637060 + 1.10342i
\(273\) 0 0
\(274\) −0.464103 + 0.803851i −0.0280375 + 0.0485624i
\(275\) 3.40642 0.205415
\(276\) −31.3227 + 9.16270i −1.88540 + 0.551530i
\(277\) 17.1623 1.03118 0.515590 0.856835i \(-0.327573\pi\)
0.515590 + 0.856835i \(0.327573\pi\)
\(278\) −23.3765 40.4892i −1.40203 2.42838i
\(279\) −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 \(0.924217\pi\)
\(282\) −25.8353 + 7.55750i −1.53847 + 0.450043i
\(283\) −8.43422 14.6085i −0.501362 0.868385i −0.999999 0.00157378i \(-0.999499\pi\)
0.498636 0.866811i \(-0.333834\pi\)
\(284\) −17.1498 29.7043i −1.01765 1.76263i
\(285\) −12.0012 + 3.51066i −0.710889 + 0.207954i
\(286\) −0.243398 0.421578i −0.0143924 0.0249284i
\(287\) 0 0
\(288\) 0.0737345 + 1.61680i 0.00434485 + 0.0952711i
\(289\) −3.28959 5.69774i −0.193505 0.335161i
\(290\) 68.8344 4.04210
\(291\) −15.7719 + 4.61369i −0.924564 + 0.270459i
\(292\) −8.00079 −0.468211
\(293\) 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
\(296\) −5.88151 10.1871i −0.341856 0.592112i
\(297\) −1.38780 + 1.59180i −0.0805280 + 0.0923655i
\(298\) 11.9356 20.6731i 0.691411 1.19756i
\(299\) −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
\(303\) −3.57227 + 14.6603i −0.205222 + 0.842210i
\(304\) 8.54024 0.489817
\(305\) −14.6819 + 25.4298i −0.840683 + 1.45611i
\(306\) −1.63295 35.8062i −0.0933493 2.04691i
\(307\) 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
\(310\) −63.2498 −3.59235
\(311\) 5.21739 + 9.03678i 0.295851 + 0.512429i 0.975182 0.221403i \(-0.0710635\pi\)
−0.679332 + 0.733831i \(0.737730\pi\)
\(312\) 3.08113 + 2.94381i 0.174434 + 0.166661i
\(313\) 0.309930 0.536815i 0.0175183 0.0303426i −0.857133 0.515095i \(-0.827757\pi\)
0.874652 + 0.484752i \(0.161090\pi\)
\(314\) −51.5440 −2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) −5.12422 + 8.87541i −0.287805 + 0.498493i −0.973285 0.229598i \(-0.926259\pi\)
0.685481 + 0.728091i \(0.259592\pi\)
\(318\) 14.5970 4.26999i 0.818557 0.239449i
\(319\) −1.55408 2.69175i −0.0870120 0.150709i
\(320\) −26.8043 −1.49841
\(321\) −21.3484 + 6.24496i −1.19155 + 0.348560i
\(322\) 0 0
\(323\) −9.58307 −0.533216
\(324\) 15.2915 33.1278i 0.849530 1.84043i
\(325\) −2.04005 + 3.53346i −0.113161 + 0.196001i
\(326\) −27.4648 −1.52113
\(327\) 3.25704 + 3.11188i 0.180115 + 0.172088i
\(328\) 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 −0.437878 0.899035i \(-0.644270\pi\)
0.997526 0.0703042i \(-0.0223970\pi\)
\(332\) 24.6731 42.7351i 1.35411 2.34539i
\(333\) 0.318097 + 6.97504i 0.0174316 + 0.382230i
\(334\) 4.25696 + 7.37327i 0.232930 + 0.403447i
\(335\) −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 \(0.116944\pi\)
\(338\) −31.4035 −1.70812
\(339\) −17.4703 16.6917i −0.948855 0.906569i
\(340\) −72.0128 −3.90544
\(341\) 1.42800 + 2.47337i 0.0773305 + 0.133940i
\(342\) −12.9346 6.70145i −0.699422 0.362373i
\(343\) 0 0
\(344\) 5.88151 + 10.1871i 0.317110 + 0.549251i
\(345\) 6.97150 28.6103i 0.375333 1.54033i
\(346\) −7.44746 12.8994i −0.400378 0.693475i
\(347\) −4.44066 7.69145i −0.238387 0.412899i 0.721865 0.692034i \(-0.243285\pi\)
−0.960252 + 0.279136i \(0.909952\pi\)
\(348\) 38.8277 + 37.0973i 2.08138 + 1.98862i
\(349\) 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
\(352\) −0.109631 0.189886i −0.00584335 0.0101210i
\(353\) 14.7654 0.785881 0.392941 0.919564i \(-0.371458\pi\)
0.392941 + 0.919564i \(0.371458\pi\)
\(354\) −6.17305 + 25.3336i −0.328094 + 1.34647i
\(355\) 30.9492 1.64261
\(356\) 30.0613 52.0677i 1.59325 2.75959i
\(357\) 0 0
\(358\) −11.2360 19.4613i −0.593840 1.02856i
\(359\) −3.60603 6.24583i −0.190319 0.329642i 0.755037 0.655682i \(-0.227619\pi\)
−0.945356 + 0.326040i \(0.894286\pi\)
\(360\) −49.2474 25.5152i −2.59556 1.34477i
\(361\) 7.55262 13.0815i 0.397506 0.688501i
\(362\) 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
\(366\) −32.8334 + 9.60462i −1.71623 + 0.502042i
\(367\) 10.9742 0.572850 0.286425 0.958103i \(-0.407533\pi\)
0.286425 + 0.958103i \(0.407533\pi\)
\(368\) −10.0562 + 17.4179i −0.524217 + 0.907970i
\(369\) −18.9882 + 12.1487i −0.988485 + 0.632434i
\(370\) 20.9485 1.08906
\(371\) 0 0
\(372\) −35.6775 34.0875i −1.84979 1.76736i
\(373\) −0.543767 −0.0281552 −0.0140776 0.999901i \(-0.504481\pi\)
−0.0140776 + 0.999901i \(0.504481\pi\)
\(374\) 2.42792 + 4.20528i 0.125545 + 0.217450i
\(375\) 5.07227 20.8161i 0.261931 1.07494i
\(376\) −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
\(381\) −6.37375 + 26.1572i −0.326537 + 1.34008i
\(382\) −11.2448 19.4766i −0.575336 0.996511i
\(383\) −35.7139 −1.82489 −0.912447 0.409194i \(-0.865810\pi\)
−0.912447 + 0.409194i \(0.865810\pi\)
\(384\) −23.9298 22.8633i −1.22116 1.16674i
\(385\) 0 0
\(386\) 41.6883 2.12188
\(387\) −0.318097 6.97504i −0.0161698 0.354561i
\(388\) −19.2316 + 33.3101i −0.976336 + 1.69106i
\(389\) 38.6591 1.96010 0.980048 0.198761i \(-0.0636919\pi\)
0.980048 + 0.198761i \(0.0636919\pi\)
\(390\) −7.28376 + 2.13069i −0.368828 + 0.107892i
\(391\) 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
\(395\) −14.9291 + 25.8579i −0.751163 + 1.30105i
\(396\) 0.225191 + 4.93786i 0.0113163 + 0.248137i
\(397\) −5.97391 10.3471i −0.299822 0.519307i 0.676273 0.736651i \(-0.263594\pi\)
−0.976095 + 0.217344i \(0.930261\pi\)
\(398\) 12.2709 + 21.2538i 0.615085 + 1.06536i
\(399\) 0 0
\(400\) −18.1352 + 31.4111i −0.906761 + 1.57056i
\(401\) 32.3566 1.61581 0.807906 0.589311i \(-0.200601\pi\)
0.807906 + 0.589311i \(0.200601\pi\)
\(402\) 3.63295 14.9093i 0.181195 0.743606i
\(403\) −3.42082 −0.170403
\(404\) 17.6591 + 30.5865i 0.878573 + 1.52173i
\(405\) 18.9882 + 26.8952i 0.943530 + 1.33643i
\(406\) 0 0
\(407\) −0.472958 0.819187i −0.0234437 0.0406056i
\(408\) −30.7345 29.3648i −1.52159 1.45378i
\(409\) 9.48751 + 16.4328i 0.469127 + 0.812552i 0.999377 0.0352893i \(-0.0112353\pi\)
−0.530250 + 0.847841i \(0.677902\pi\)
\(410\) 33.8157 + 58.5704i 1.67004 + 2.89259i
\(411\) 0.154689 0.634828i 0.00763024 0.0313138i
\(412\) 16.2713 + 28.1827i 0.801630 + 1.38846i
\(413\) 0 0
\(414\) 28.8982 18.4891i 1.42027 0.908691i
\(415\) 22.2630 + 38.5607i 1.09285 + 1.89287i
\(416\) 0.262624 0.0128762
\(417\) 23.7960 + 22.7355i 1.16530 + 1.11336i
\(418\) 1.97351 0.0965277
\(419\) −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 \(0.983077\pi\)
\(422\) −6.01819 10.4238i −0.292961 0.507423i
\(423\) 15.9614 10.2121i 0.776069 0.496530i
\(424\) 9.01819 15.6200i 0.437962 0.758572i
\(425\) 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
\(429\) 0.247767 + 0.236725i 0.0119623 + 0.0114292i
\(430\) −20.9485 −1.01023
\(431\) 7.93920 13.7511i 0.382418 0.662367i −0.608990 0.793178i \(-0.708425\pi\)
0.991407 + 0.130811i \(0.0417582\pi\)
\(432\) −7.28982 21.2715i −0.350732 1.02343i
\(433\) −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
\(436\) 10.5438 0.504955
\(437\) −4.58611 7.94338i −0.219384 0.379984i
\(438\) 8.07227 2.36135i 0.385708 0.112830i
\(439\) 6.23047 10.7915i 0.297364 0.515050i −0.678168 0.734907i \(-0.737226\pi\)
0.975532 + 0.219857i \(0.0705591\pi\)
\(440\) 7.51399 0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) 4.11537 7.12802i 0.195527 0.338663i −0.751546 0.659680i \(-0.770692\pi\)
0.947073 + 0.321018i \(0.104025\pi\)
\(444\) 11.8165 + 11.2899i 0.560787 + 0.535795i
\(445\) 27.1249 + 46.9817i 1.28584 + 2.22715i
\(446\) 57.5976 2.72732
\(447\) −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 \(0.457476\pi\)
\(450\) 52.1146 33.3430i 2.45670 1.57180i
\(451\) 1.52692 2.64471i 0.0718999 0.124534i
\(452\) −56.5552 −2.66013
\(453\) −5.26294 + 21.5986i −0.247275 + 1.01479i
\(454\) −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 −0.919196 0.393801i \(-0.871160\pi\)
0.800640 + 0.599146i \(0.204493\pi\)
\(458\) 1.79665 3.11188i 0.0839518 0.145409i
\(459\) 8.17996 + 23.8689i 0.381808 + 1.11411i
\(460\) −34.4628 59.6913i −1.60683 2.78312i
\(461\) −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 \(0.0982408\pi\)
\(464\) 33.0947 1.53638
\(465\) 42.7333 12.5006i 1.98171 0.579702i
\(466\) −32.5979 −1.51007
\(467\) −6.88272 11.9212i −0.318494 0.551648i 0.661680 0.749787i \(-0.269844\pi\)
−0.980174 + 0.198138i \(0.936511\pi\)
\(468\) −5.25688 2.72361i −0.242999 0.125899i
\(469\) 0 0
\(470\) −28.4253 49.2340i −1.31116 2.27100i
\(471\) 34.8245 10.1871i 1.60463 0.469396i
\(472\) 15.4614 + 26.7800i 0.711669 + 1.23265i
\(473\) 0.472958 + 0.819187i 0.0217466 + 0.0376663i
\(474\) −33.3861 + 9.76631i −1.53347 + 0.448581i
\(475\) −8.27052 14.3250i −0.379477 0.657274i
\(476\) 0 0
\(477\) −9.01819 + 5.76985i −0.412914 + 0.264183i
\(478\) −23.8530 41.3146i −1.09101 1.88969i
\(479\) −8.71176 −0.398050 −0.199025 0.979994i \(-0.563778\pi\)
−0.199025 + 0.979994i \(0.563778\pi\)
\(480\) −3.28074 + 0.959702i −0.149745 + 0.0438042i
\(481\) 1.13298 0.0516597
\(482\) −6.21731 + 10.7687i −0.283191 + 0.490501i
\(483\) 0 0
\(484\) 21.9626 + 38.0404i 0.998302 + 1.72911i
\(485\) −17.3530 30.0563i −0.787960 1.36479i
\(486\) −5.65082 + 37.9369i −0.256326 + 1.72085i
\(487\) 9.01819 15.6200i 0.408653 0.707808i −0.586086 0.810249i \(-0.699332\pi\)
0.994739 + 0.102441i \(0.0326653\pi\)
\(488\) −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 \(0.181374\pi\)
\(492\) −12.4911 + 51.2624i −0.563144 + 2.31109i
\(493\) −37.1358 −1.67251
\(494\) −1.18190 + 2.04712i −0.0531763 + 0.0921041i
\(495\) −3.96019 2.05179i −0.177997 0.0922211i
\(496\) −30.4097 −1.36544
\(497\) 0 0
\(498\) −12.2807 + 50.3990i −0.550313 + 2.25843i
\(499\) −39.0875 −1.74980 −0.874899 0.484305i \(-0.839072\pi\)
−0.874899 + 0.484305i \(0.839072\pi\)
\(500\) −25.0742 43.4297i −1.12135 1.94224i
\(501\) −4.33336 4.14024i −0.193600 0.184972i
\(502\) −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
\(507\) 21.2171 6.20655i 0.942283 0.275642i
\(508\) 31.5079 + 54.5732i 1.39794 + 2.42130i
\(509\) 29.5272 1.30877 0.654386 0.756161i \(-0.272927\pi\)
0.654386 + 0.756161i \(0.272927\pi\)
\(510\) 72.6562 21.2538i 3.21727 0.941136i
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) 10.0634 + 1.97131i 0.444311 + 0.0870354i
\(514\) −9.48751 + 16.4328i −0.418476 + 0.724822i
\(515\) −29.3638 −1.29392
\(516\) −11.8165 11.2899i −0.520193 0.497010i
\(517\) −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
\(521\) 0.532351 0.922058i 0.0233227 0.0403961i −0.854128 0.520062i \(-0.825909\pi\)
0.877451 + 0.479666i \(0.159242\pi\)
\(522\) −50.1234 25.9691i −2.19384 1.13664i
\(523\) 6.69094 + 11.5890i 0.292574 + 0.506754i 0.974418 0.224745i \(-0.0721548\pi\)
−0.681843 + 0.731498i \(0.738821\pi\)
\(524\) −17.2581 29.8918i −0.753922 1.30583i
\(525\) 0 0
\(526\) −5.18190 + 8.97532i −0.225942 + 0.391343i
\(527\) 34.1230 1.48642
\(528\) 2.20255 + 2.10439i 0.0958536 + 0.0915818i
\(529\) −1.39922 −0.0608358
\(530\) 16.0603 + 27.8173i 0.697615 + 1.20830i
\(531\) −0.836219 18.3361i −0.0362888 0.795719i
\(532\) 0 0
\(533\) 1.82889 + 3.16774i 0.0792181 + 0.137210i
\(534\) −14.9626 + 61.4052i −0.647497 + 2.65726i
\(535\) −23.4885 40.6833i −1.01550 1.75889i
\(536\) −9.09931 15.7605i −0.393031 0.680749i
\(537\) 11.4376 + 10.9279i 0.493571 + 0.471575i
\(538\) −25.5286 44.2168i −1.10062 1.90632i
\(539\) 0 0
\(540\) 75.6224 + 14.8136i 3.25427 + 0.637475i
\(541\) 17.0438 + 29.5207i 0.732769 + 1.26919i 0.955695 + 0.294358i \(0.0951056\pi\)
−0.222927 + 0.974835i \(0.571561\pi\)
\(542\) −70.0970 −3.01092
\(543\) −4.89922 + 20.1059i −0.210246 + 0.862828i
\(544\) −2.61970 −0.112319
\(545\) −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 \(0.792782\pi\)
\(548\) −0.764686 1.32448i −0.0326658 0.0565788i
\(549\) 20.2849 12.9783i 0.865737 0.553900i
\(550\) −4.19076 + 7.25860i −0.178694 + 0.309508i
\(551\) −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
\(555\) −14.1534 + 4.14024i −0.600778 + 0.175743i
\(556\) 77.0331 3.26693
\(557\) 15.0402 26.0503i 0.637272 1.10379i −0.348756 0.937213i \(-0.613396\pi\)
0.986029 0.166575i \(-0.0532707\pi\)
\(558\) 46.0568 + 23.8622i 1.94974 + 1.01017i
\(559\) −1.13298 −0.0479202
\(560\) 0 0
\(561\) −2.47150 2.36135i −0.104347 0.0996963i
\(562\) 23.2340 0.980069
\(563\) 9.81060 + 16.9925i 0.413468 + 0.716147i 0.995266 0.0971860i \(-0.0309842\pi\)
−0.581799 + 0.813333i \(0.697651\pi\)
\(564\) 10.5000 43.0910i 0.442130 1.81446i
\(565\) 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 −0.851262 0.524740i \(-0.824162\pi\)
0.880070 + 0.474845i \(0.157496\pi\)
\(570\) 7.28376 29.8918i 0.305083 1.25203i
\(571\) −8.69076 15.0528i −0.363697 0.629941i 0.624869 0.780729i \(-0.285152\pi\)
−0.988566 + 0.150788i \(0.951819\pi\)
\(572\) 0.802077 0.0335365
\(573\) 11.4467 + 10.9365i 0.478191 + 0.456880i
\(574\) 0 0
\(575\) 38.9545 1.62451
\(576\) 19.5182 + 10.1124i 0.813258 + 0.421352i
\(577\) 13.5274 23.4301i 0.563153 0.975409i −0.434066 0.900881i \(-0.642922\pi\)
0.997219 0.0745283i \(-0.0237451\pi\)
\(578\) 16.1881 0.673337
\(579\) −28.1658 + 8.23922i −1.17053 + 0.342410i
\(580\) −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
\(584\) 4.98715 8.63800i 0.206370 0.357443i
\(585\) 4.50000 2.87911i 0.186052 0.119036i
\(586\) 4.58005 + 7.93288i 0.189200 + 0.327704i
\(587\) −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
\(590\) −55.0698 −2.26719
\(591\) −8.74120 + 35.8730i −0.359565 + 1.47562i
\(592\) 10.0718 0.413948
\(593\) −17.7904 30.8139i −0.730565 1.26538i −0.956642 0.291266i \(-0.905924\pi\)
0.226077 0.974109i \(-0.427410\pi\)
\(594\) −1.68456 4.91551i −0.0691184 0.201686i
\(595\) 0 0
\(596\) 19.6659 + 34.0623i 0.805545 + 1.39524i
\(597\) −12.4911 11.9345i −0.511229 0.488445i
\(598\) −2.78340 4.82100i −0.113822 0.197145i
\(599\) 5.74105 + 9.94379i 0.234573 + 0.406292i 0.959148 0.282903i \(-0.0912975\pi\)
−0.724576 + 0.689195i \(0.757964\pi\)
\(600\) 17.3702 71.2854i 0.709133 2.91021i
\(601\) 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
\(604\) 26.0167 + 45.0623i 1.05861 + 1.83356i
\(605\) −39.6346 −1.61138
\(606\) −26.8442 25.6478i −1.09047 1.04187i
\(607\) −18.5409 −0.752551 −0.376275 0.926508i \(-0.622795\pi\)
−0.376275 + 0.926508i \(0.622795\pi\)
\(608\) −0.532351 + 0.922058i −0.0215897 + 0.0373944i
\(609\) 0 0
\(610\) −36.1249 62.5702i −1.46265 2.53339i
\(611\) −1.53736 2.66278i −0.0621949 0.107725i
\(612\) 52.4379 + 27.1682i 2.11967 + 1.09821i
\(613\) −3.66225 + 6.34321i −0.147917 + 0.256200i −0.930457 0.366400i \(-0.880590\pi\)
0.782540 + 0.622600i \(0.213924\pi\)
\(614\) −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 \(-0.00480000\pi\)
\(618\) −24.7345 23.6322i −0.994968 0.950627i
\(619\) 32.8963 1.32222 0.661108 0.750291i \(-0.270087\pi\)
0.661108 + 0.750291i \(0.270087\pi\)
\(620\) 52.1072 90.2523i 2.09267 3.62462i
\(621\) −15.8703 + 18.2032i −0.636852 + 0.730468i
\(622\) −25.6748 −1.02947
\(623\) 0 0
\(624\) −3.50194 + 1.02441i −0.140190 + 0.0410092i
\(625\) 3.34221 0.133689
\(626\) 0.762585 + 1.32084i 0.0304790 + 0.0527912i
\(627\) −1.33336 + 0.390043i −0.0532493 + 0.0155768i
\(628\) 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
\(633\) 6.12620 + 5.85318i 0.243495 + 0.232643i
\(634\) −12.6082 21.8380i −0.500734 0.867297i
\(635\) −56.8603 −2.25643
\(636\) −5.93251 + 24.3464i −0.235239 + 0.965399i
\(637\) 0 0
\(638\) 7.64766 0.302774
\(639\) −22.5364 11.6762i −0.891525 0.461902i
\(640\) 34.9496 60.5344i 1.38150 2.39283i
\(641\) 11.4605 0.452663 0.226331 0.974050i \(-0.427327\pi\)
0.226331 + 0.974050i \(0.427327\pi\)
\(642\) 12.9568 53.1733i 0.511362 2.09858i
\(643\) 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
\(647\) −12.6720 + 21.9485i −0.498186 + 0.862883i −0.999998 0.00209358i \(-0.999334\pi\)
0.501812 + 0.864977i \(0.332667\pi\)
\(648\) 26.2345 + 37.1590i 1.03059 + 1.45975i
\(649\) 1.24332 + 2.15349i 0.0488045 + 0.0845320i
\(650\) −5.01954 8.69410i −0.196883 0.341011i
\(651\) 0 0
\(652\) 22.6264 39.1900i 0.886116 1.53480i
\(653\) 14.0833 0.551121 0.275560 0.961284i \(-0.411137\pi\)
0.275560 + 0.961284i \(0.411137\pi\)
\(654\) −10.6380 + 3.11188i −0.415977 + 0.121684i
\(655\) 31.1445 1.21692
\(656\) 16.2581 + 28.1599i 0.634774 + 1.09946i
\(657\) −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 \(-0.433484\pi\)
\(660\) −10.0197 + 2.93101i −0.390014 + 0.114089i
\(661\) 0.176866 + 0.306341i 0.00687930 + 0.0119153i 0.869445 0.494031i \(-0.164477\pi\)
−0.862565 + 0.505946i \(0.831144\pi\)
\(662\) 25.0526 + 43.3924i 0.973698 + 1.68649i
\(663\) 3.92955 1.14950i 0.152611 0.0446428i
\(664\) 30.7591 + 53.2764i 1.19369 + 2.06752i
\(665\) 0 0
\(666\) −15.2542 7.90324i −0.591087 0.306244i
\(667\) −17.7719 30.7818i −0.688130 1.19188i
\(668\) −14.0281 −0.542762
\(669\) −38.9145 + 11.3835i −1.50452 + 0.440112i
\(670\) 32.4096 1.25209
\(671\) −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 \(0.699948\pi\)
\(674\) 7.02704 + 12.1712i 0.270672 + 0.468817i
\(675\) −28.6202 + 32.8273i −1.10159 + 1.26352i
\(676\) 25.8712 44.8102i 0.995046 1.72347i
\(677\) −10.5732 + 18.3133i −0.406361 + 0.703837i −0.994479 0.104938i \(-0.966536\pi\)
0.588118 + 0.808775i \(0.299869\pi\)
\(678\) 57.0605 16.6917i 2.19140 0.641041i
\(679\) 0 0
\(680\) 44.8879 77.7482i 1.72137 2.98151i
\(681\) 2.50885 10.2961i 0.0961395 0.394547i
\(682\) −7.02720 −0.269085
\(683\) −17.3858 + 30.1131i −0.665249 + 1.15224i 0.313969 + 0.949433i \(0.398341\pi\)
−0.979218 + 0.202811i \(0.934992\pi\)
\(684\) 20.2183 12.9357i 0.773067 0.494610i
\(685\) 1.37998 0.0527264
\(686\) 0 0
\(687\) −0.598835 + 2.45756i −0.0228470 + 0.0937618i
\(688\) −10.0718 −0.383984
\(689\) 0.868609 + 1.50447i 0.0330914 + 0.0573159i
\(690\) 52.3879 + 50.0532i 1.99437 + 1.90549i
\(691\) −17.3246 + 30.0071i −0.659059 + 1.14152i 0.321801 + 0.946807i \(0.395712\pi\)
−0.980860 + 0.194716i \(0.937622\pi\)
\(692\) 24.5418 0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) −34.7542 + 60.1960i −1.31830 + 2.28336i
\(696\) −64.2544 + 18.7961i −2.43556 + 0.712464i
\(697\) −18.2434 31.5985i −0.691017 1.19688i
\(698\) −51.6087 −1.95342
\(699\) 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 \(0.870111\pi\)
\(702\) 6.10769 + 1.19643i 0.230520 + 0.0451562i
\(703\) −2.29661 + 3.97784i −0.0866182 + 0.150027i
\(704\) −2.97802 −0.112238
\(705\) 28.9354 + 27.6459i 1.08977 + 1.04121i
\(706\) −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 −0.902016 0.431702i \(-0.857913\pi\)
0.824873 + 0.565318i \(0.191246\pi\)
\(710\) −38.0753 + 65.9483i −1.42894 + 2.47500i
\(711\) 20.6264 13.1968i 0.773549 0.494918i
\(712\) 37.4764 + 64.9110i 1.40449 + 2.43264i
\(713\) 16.3300 + 28.2844i 0.611564 + 1.05926i
\(714\) 0 0
\(715\) −0.361864 + 0.626767i −0.0135330 + 0.0234398i
\(716\) 37.0263 1.38374
\(717\) 24.2811 + 23.1990i 0.906795 + 0.866383i
\(718\) 17.7453 0.662249
\(719\) −24.1408 41.8131i −0.900299 1.55936i −0.827106 0.562047i \(-0.810014\pi\)
−0.0731939 0.997318i \(-0.523319\pi\)
\(720\) 40.0032 25.5941i 1.49083 0.953837i
\(721\) 0 0
\(722\) 18.5833 + 32.1872i 0.691597 + 1.19788i
\(723\) 2.07227 8.50440i 0.0770686 0.316282i
\(724\) 24.2187 + 41.9481i 0.900082 + 1.55899i
\(725\) −32.0495 55.5114i −1.19029 2.06164i
\(726\) −33.3861 31.8982i −1.23907 1.18385i
\(727\) 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
\(730\) 8.88151 + 15.3832i 0.328720 + 0.569359i
\(731\) 11.3016 0.418006
\(732\) 13.3442 54.7631i 0.493214 2.02410i
\(733\) 30.5428 1.12812 0.564062 0.825733i \(-0.309238\pi\)
0.564062 + 0.825733i \(0.309238\pi\)
\(734\) −13.5011 + 23.3845i −0.498334 + 0.863139i
\(735\) 0 0
\(736\) −1.25370 2.17147i −0.0462118 0.0800413i
\(737\) −0.731715 1.26737i −0.0269531 0.0466841i
\(738\) −2.52684 55.4071i −0.0930143 2.03956i
\(739\) −11.9100 + 20.6288i −0.438117 + 0.758841i −0.997544 0.0700384i \(-0.977688\pi\)
0.559427 + 0.828880i \(0.311021\pi\)
\(740\) −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 \(0.228490\pi\)
\(744\) 59.0413 17.2711i 2.16456 0.633191i
\(745\) −35.4897 −1.30024
\(746\) 0.668971 1.15869i 0.0244928 0.0424227i
\(747\) −1.66358 36.4781i −0.0608673 1.33466i
\(748\) −8.00079 −0.292538
\(749\) 0 0
\(750\) 38.1160 + 36.4174i 1.39180 + 1.32977i
\(751\) −10.2704 −0.374773 −0.187386 0.982286i \(-0.560002\pi\)
−0.187386 + 0.982286i \(0.560002\pi\)
\(752\) −13.6665 23.6711i −0.498367 0.863197i
\(753\) 6.18882 25.3983i 0.225533 0.925565i
\(754\) −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
\(759\) 0.774549 3.17868i 0.0281144 0.115379i
\(760\) −18.2434 31.5985i −0.661757 1.14620i
\(761\) 27.6604 1.00269 0.501345 0.865247i \(-0.332839\pi\)
0.501345 + 0.865247i \(0.332839\pi\)
\(762\) −47.8961 45.7616i −1.73509 1.65777i
\(763\) 0 0
\(764\) 37.0554 1.34062
\(765\) −44.8879 + 28.7194i −1.62293 + 1.03835i
\(766\) 43.9371 76.1013i 1.58751 2.74965i
\(767\) −2.97841 −0.107544
\(768\) 53.7962 15.7368i 1.94120 0.567853i
\(769\) 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
\(773\) 14.2978 24.7645i 0.514256 0.890717i −0.485607 0.874177i \(-0.661401\pi\)
0.999863 0.0165403i \(-0.00526518\pi\)
\(774\) 15.2542 + 7.90324i 0.548300 + 0.284076i
\(775\) 29.4493 + 51.0077i 1.05785 + 1.83225i
\(776\) −23.9753 41.5265i −0.860664 1.49071i
\(777\) 0 0
\(778\) −47.5605 + 82.3772i −1.70513 + 2.95337i
\(779\) −14.8290 −0.531303
\(780\) 2.96027 12.1487i 0.105995 0.434992i
\(781\) 3.43852 0.123040