Properties

Label 441.2.g.g.67.1
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 67.1
Root \(1.82904 + 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.g.79.1

$q$-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 \(-0.804901\pi\)
−0.817970 + 0.575260i \(0.804901\pi\)
\(6\) −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 −0.830297 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
\(17\) −2.42792 + 4.20528i −0.588857 + 1.01993i 0.405525 + 0.914084i \(0.367089\pi\)
−0.994382 + 0.105847i \(0.966245\pi\)
\(18\) 6.21780 3.97816i 1.46555 0.937660i
\(19\) 0.986757 + 1.70911i 0.226378 + 0.392097i 0.956732 0.290971i \(-0.0939784\pi\)
−0.730354 + 0.683069i \(0.760645\pi\)
\(20\) 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 \(-0.949286\pi\)
0.356274 0.934381i \(-0.384047\pi\)
\(32\) −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 \(0.366257\pi\)
−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 \(0.776544\pi\)
\(44\) −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 −0.538335 0.842731i \(-0.680947\pi\)
0.998994 + 0.0448469i \(0.0142800\pi\)
\(48\) −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 0.595240 0.803548i \(-0.297057\pi\)
−0.993513 + 0.113719i \(0.963724\pi\)
\(60\) −24.6534 + 7.21177i −3.18274 + 0.931035i
\(61\) 4.01356 6.95169i 0.513884 0.890073i −0.485987 0.873966i \(-0.661540\pi\)
0.999870 0.0161063i \(-0.00512703\pi\)
\(62\) 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 −0.917976 0.396636i \(-0.870178\pi\)
0.802485 + 0.596673i \(0.203511\pi\)
\(74\) 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 \(-0.933807\pi\)
0.310431 0.950596i \(-0.399527\pi\)
\(84\) 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 \(-0.878817\pi\)
0.142406 0.989808i \(-0.454516\pi\)
\(90\) −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 0.999778 0.0210547i \(-0.00670241\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(98\) 0 0
\(99\) −1.08259 0.560893i −0.108804 0.0563719i
\(100\) −16.9897 29.4270i −1.69897 2.94270i
\(101\) 8.71176 0.866852 0.433426 0.901189i \(-0.357304\pi\)
0.433426 + 0.901189i \(0.357304\pi\)
\(102\) 19.8619 5.81012i 1.96662 0.575287i
\(103\) 8.02712 0.790936 0.395468 0.918480i \(-0.370582\pi\)
0.395468 + 0.918480i \(0.370582\pi\)
\(104\) 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 \(-0.621305\pi\)
−0.371932 + 0.928260i \(0.621305\pi\)
\(132\) 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 \(-0.535049\pi\)
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
\(143\) 0.0989221 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 \(-0.851591\pi\)
0.0573276 0.998355i \(-0.481742\pi\)
\(158\) −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 −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(168\) 0 0
\(169\) 6.38151 + 11.0531i 0.490886 + 0.850239i
\(170\) 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 −0.727721 0.685874i \(-0.759420\pi\)
0.957844 + 0.287288i \(0.0927536\pi\)
\(174\) −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 \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 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 −0.986865 0.161546i \(-0.948352\pi\)
0.633335 + 0.773877i \(0.281685\pi\)
\(200\) 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 \(0.120047\pi\)
−0.145936 + 0.989294i \(0.546619\pi\)
\(224\) 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 \(-0.565084\pi\)
−0.203046 + 0.979169i \(0.565084\pi\)
\(228\) 10.0197 + 9.57312i 0.663568 + 0.633995i
\(229\) 1.46039 0.0965052 0.0482526 0.998835i \(-0.484635\pi\)
0.0482526 + 0.998835i \(0.484635\pi\)
\(230\) 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 \(-0.552042\pi\)
−0.162768 + 0.986664i \(0.552042\pi\)
\(242\) 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 \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) 19.1228 33.1216i 1.19987 2.07823i
\(255\) 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 \(-0.577320\pi\)
−0.240526 + 0.970643i \(0.577320\pi\)
\(258\) 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 \(-0.615323\pi\)
0.987019 0.160603i \(-0.0513439\pi\)
\(270\) −15.1623 44.2431i −0.922745 2.69255i
\(271\) −14.2444 24.6721i −0.865287 1.49872i −0.866762 0.498723i \(-0.833803\pi\)
0.00147433 0.999999i \(-0.499531\pi\)
\(272\) −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 \(0.000500949\pi\)
−0.498636 + 0.866811i \(0.666166\pi\)
\(284\) −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 −0.915262 0.402858i \(-0.868017\pi\)
0.806517 + 0.591211i \(0.201350\pi\)
\(294\) 0 0
\(295\) 11.1908 + 19.3830i 0.651551 + 1.12852i
\(296\) −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 \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 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 0.679332 0.733831i \(-0.262270\pi\)
−0.975182 + 0.221403i \(0.928936\pi\)
\(312\) 3.08113 + 2.94381i 0.174434 + 0.166661i
\(313\) −0.309930 + 0.536815i −0.0175183 + 0.0303426i −0.874652 0.484752i \(-0.838910\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(314\) 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 \(-0.976938\pi\)
0.435997 0.899948i \(-0.356396\pi\)
\(350\) 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 \(-0.628542\pi\)
−0.392941 + 0.919564i \(0.628542\pi\)
\(354\) −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 \(-0.592467\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(368\) −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 \(-0.134190\pi\)
0.912447 + 0.409194i \(0.134190\pi\)
\(384\) 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 0.976095 0.217344i \(-0.0697394\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(398\) −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 0.530250 0.847841i \(-0.322098\pi\)
−0.999377 + 0.0352893i \(0.988765\pi\)
\(410\) 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 −0.573822 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 \(0.983077\pi\)
\(422\) −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 \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 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 −0.975532 0.219857i \(-0.929441\pi\)
0.678168 + 0.734907i \(0.262774\pi\)
\(440\) −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 0.942254 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 \(0.0982408\pi\)
\(464\) 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 0.980174 0.198138i \(-0.0634895\pi\)
−0.661680 + 0.749787i \(0.730156\pi\)
\(468\) 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 \(-0.436222\pi\)
0.199025 + 0.979994i \(0.436222\pi\)
\(480\) −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 \(-0.463598\pi\)
0.114111 + 0.993468i \(0.463598\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) −2.32383 + 4.02499i −0.103307 + 0.178933i
\(507\) −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 \(-0.727073\pi\)
−0.654386 + 0.756161i \(0.727073\pi\)
\(510\) −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 −0.877451 0.479666i \(-0.840758\pi\)
0.854128 + 0.520062i \(0.174091\pi\)
\(522\) −50.1234 25.9691i −2.19384 1.13664i
\(523\) −6.69094 11.5890i −0.292574 0.506754i 0.681843 0.731498i \(-0.261179\pi\)
−0.974418 + 0.224745i \(0.927845\pi\)
\(524\) 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 0.581799 0.813333i \(-0.302349\pi\)
−0.995266 + 0.0971860i \(0.969016\pi\)
\(564\) 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 \(0.357078\pi\)
−0.997219 + 0.0745283i \(0.976255\pi\)
\(578\) 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 0.933084 0.359659i \(-0.117107\pi\)
−0.778016 + 0.628245i \(0.783774\pi\)
\(588\) 0 0
\(589\) 6.93414 12.0103i 0.285716 0.494875i
\(590\) −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 \(0.0940765\pi\)
−0.226077 + 0.974109i \(0.572590\pi\)
\(594\) 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 0.862124 0.506698i \(-0.169134\pi\)
−0.869875 + 0.493272i \(0.835801\pi\)
\(602\) 0 0
\(603\) 0.492129 + 10.7911i 0.0200411 + 0.439448i
\(604\) 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 \(-0.377205\pi\)
0.376275 + 0.926508i \(0.377205\pi\)
\(608\) 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 \(-0.729913\pi\)
−0.661108 + 0.750291i \(0.729913\pi\)
\(620\) 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 −0.984939 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
\(647\) 12.6720 21.9485i 0.498186 0.862883i −0.501812 0.864977i \(-0.667333\pi\)
0.999998 + 0.00209358i \(0.000666408\pi\)
\(648\) 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 0.862565 0.505946i \(-0.168856\pi\)
−0.869445 + 0.494031i \(0.835523\pi\)
\(662\) 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 −0.588118 0.808775i \(-0.700131\pi\)
0.994479 + 0.104938i \(0.0334643\pi\)
\(678\) −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 \(-0.604288\pi\)
0.980860 0.194716i \(-0.0623785\pi\)
\(692\) −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 \(0.189986\pi\)
0.0731939 + 0.997318i \(0.476681\pi\)
\(720\) −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 \(-0.891443\pi\)
0.181543 0.983383i \(-0.441891\pi\)
\(728\) 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 \(-0.690762\pi\)
−0.564062 + 0.825733i \(0.690762\pi\)
\(734\) 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 \(-0.667161\pi\)
−0.501345 + 0.865247i \(0.667161\pi\)
\(762\) 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 \(0.376157\pi\)
−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
\(773\) −14.2978 + 24.7645i −0.514256 + 0.890717i 0.485607 + 0.874177i \(0.338599\pi\)
−0.999863 + 0.0165403i \(0.994735\pi\)
\(774\) 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