Properties

Label 1050.2.bc.e.607.3
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 28 x^{14} + 519 x^{12} - 5404 x^{10} + 40705 x^{8} - 194544 x^{6} + 672624 x^{4} - 1306368 x^{2} + 1679616\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.3
Root \(-1.90899 + 1.10215i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.e.493.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.965926 - 2.46313i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.965926 - 2.46313i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.55868 - 2.69971i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-2.30403 - 2.30403i) q^{13} +(-1.57052 - 2.12920i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.10215 - 0.295321i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-2.99522 + 5.18788i) q^{19} +(-2.62920 + 0.295509i) q^{21} +(-2.20431 - 2.20431i) q^{22} +(-0.295321 - 1.10215i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.82185 - 1.62920i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.06808 - 1.65017i) q^{28} +5.39943i q^{29} +(3.68788 - 2.12920i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-3.01114 + 0.806832i) q^{33} -1.14103 q^{34} -1.00000 q^{36} +(5.55960 - 1.48969i) q^{37} +(-1.55044 + 5.78632i) q^{38} +(-2.82185 + 1.62920i) q^{39} -10.2584i q^{41} +(-2.46313 + 0.965926i) q^{42} +(6.44695 - 6.44695i) q^{43} +(-2.69971 - 1.55868i) q^{44} +(-0.570516 - 0.988164i) q^{46} +(-1.10215 - 4.11329i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-5.13397 + 4.75839i) q^{49} +(-0.570516 + 0.988164i) q^{51} +(-3.14737 - 0.843334i) q^{52} +(-2.78442 - 0.746082i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.42471 - 1.05868i) q^{56} +(4.23588 + 4.23588i) q^{57} +(1.39747 + 5.21545i) q^{58} +(0.117360 + 0.203274i) q^{59} +(7.38403 + 4.26317i) q^{61} +(3.01114 - 3.01114i) q^{62} +(-0.395046 + 2.61609i) q^{63} -1.00000i q^{64} +(-2.69971 + 1.55868i) q^{66} +(3.60425 - 13.4513i) q^{67} +(-1.10215 + 0.295321i) q^{68} -1.14103 q^{69} +1.74161 q^{71} +(-0.965926 + 0.258819i) q^{72} +(-0.293478 + 1.09527i) q^{73} +(4.98460 - 2.87786i) q^{74} +5.99044i q^{76} +(-5.14416 + 6.44695i) q^{77} +(-2.30403 + 2.30403i) q^{78} +(-8.76189 - 5.05868i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.65507 - 9.90885i) q^{82} +(8.06061 + 8.06061i) q^{83} +(-2.12920 + 1.57052i) q^{84} +(4.55868 - 7.89587i) q^{86} +(5.21545 + 1.39747i) q^{87} +(-3.01114 - 0.806832i) q^{88} +(-9.18432 + 15.9077i) q^{89} +(-3.44960 + 7.90064i) q^{91} +(-0.806832 - 0.806832i) q^{92} +(-1.10215 - 4.11329i) q^{93} +(-2.12920 - 3.68788i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(-0.740585 + 0.740585i) q^{97} +(-3.72748 + 5.92503i) q^{98} +3.11736i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 4q^{11} - 8q^{14} + 8q^{16} + 4q^{19} - 4q^{21} - 8q^{24} + 16q^{34} - 16q^{36} + 12q^{44} + 8q^{46} - 96q^{49} + 8q^{51} - 8q^{54} - 4q^{56} - 40q^{59} - 24q^{61} + 12q^{66} + 16q^{69} + 104q^{71} + 48q^{74} + 12q^{79} + 8q^{81} + 4q^{84} + 52q^{86} - 60q^{89} - 52q^{91} + 4q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −0.965926 2.46313i −0.365086 0.930974i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −1.55868 2.69971i −0.469960 0.813994i 0.529450 0.848341i \(-0.322398\pi\)
−0.999410 + 0.0343469i \(0.989065\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) −2.30403 2.30403i −0.639023 0.639023i 0.311291 0.950315i \(-0.399239\pi\)
−0.950315 + 0.311291i \(0.899239\pi\)
\(14\) −1.57052 2.12920i −0.419738 0.569052i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.10215 0.295321i −0.267311 0.0716259i 0.122674 0.992447i \(-0.460853\pi\)
−0.389985 + 0.920821i \(0.627520\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) −2.99522 + 5.18788i −0.687151 + 1.19018i 0.285605 + 0.958348i \(0.407806\pi\)
−0.972756 + 0.231833i \(0.925528\pi\)
\(20\) 0 0
\(21\) −2.62920 + 0.295509i −0.573738 + 0.0644853i
\(22\) −2.20431 2.20431i −0.469960 0.469960i
\(23\) −0.295321 1.10215i −0.0615787 0.229815i 0.928277 0.371889i \(-0.121290\pi\)
−0.989856 + 0.142074i \(0.954623\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −2.82185 1.62920i −0.553411 0.319512i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −2.06808 1.65017i −0.390830 0.311852i
\(29\) 5.39943i 1.00265i 0.865260 + 0.501324i \(0.167154\pi\)
−0.865260 + 0.501324i \(0.832846\pi\)
\(30\) 0 0
\(31\) 3.68788 2.12920i 0.662362 0.382415i −0.130814 0.991407i \(-0.541759\pi\)
0.793176 + 0.608992i \(0.208426\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −3.01114 + 0.806832i −0.524172 + 0.140451i
\(34\) −1.14103 −0.195686
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 5.55960 1.48969i 0.913993 0.244904i 0.228977 0.973432i \(-0.426462\pi\)
0.685016 + 0.728528i \(0.259795\pi\)
\(38\) −1.55044 + 5.78632i −0.251515 + 0.938666i
\(39\) −2.82185 + 1.62920i −0.451858 + 0.260880i
\(40\) 0 0
\(41\) 10.2584i 1.60209i −0.598603 0.801046i \(-0.704277\pi\)
0.598603 0.801046i \(-0.295723\pi\)
\(42\) −2.46313 + 0.965926i −0.380069 + 0.149046i
\(43\) 6.44695 6.44695i 0.983150 0.983150i −0.0167102 0.999860i \(-0.505319\pi\)
0.999860 + 0.0167102i \(0.00531925\pi\)
\(44\) −2.69971 1.55868i −0.406997 0.234980i
\(45\) 0 0
\(46\) −0.570516 0.988164i −0.0841181 0.145697i
\(47\) −1.10215 4.11329i −0.160766 0.599985i −0.998542 0.0539725i \(-0.982812\pi\)
0.837777 0.546013i \(-0.183855\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −5.13397 + 4.75839i −0.733425 + 0.679770i
\(50\) 0 0
\(51\) −0.570516 + 0.988164i −0.0798883 + 0.138371i
\(52\) −3.14737 0.843334i −0.436461 0.116949i
\(53\) −2.78442 0.746082i −0.382469 0.102482i 0.0624615 0.998047i \(-0.480105\pi\)
−0.444930 + 0.895565i \(0.646772\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.42471 1.05868i −0.324015 0.141472i
\(57\) 4.23588 + 4.23588i 0.561056 + 0.561056i
\(58\) 1.39747 + 5.21545i 0.183497 + 0.684821i
\(59\) 0.117360 + 0.203274i 0.0152790 + 0.0264640i 0.873564 0.486710i \(-0.161803\pi\)
−0.858285 + 0.513174i \(0.828470\pi\)
\(60\) 0 0
\(61\) 7.38403 + 4.26317i 0.945428 + 0.545843i 0.891658 0.452710i \(-0.149543\pi\)
0.0537703 + 0.998553i \(0.482876\pi\)
\(62\) 3.01114 3.01114i 0.382415 0.382415i
\(63\) −0.395046 + 2.61609i −0.0497712 + 0.329597i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −2.69971 + 1.55868i −0.332312 + 0.191860i
\(67\) 3.60425 13.4513i 0.440330 1.64333i −0.287651 0.957735i \(-0.592874\pi\)
0.727981 0.685598i \(-0.240459\pi\)
\(68\) −1.10215 + 0.295321i −0.133656 + 0.0358129i
\(69\) −1.14103 −0.137364
\(70\) 0 0
\(71\) 1.74161 0.206691 0.103345 0.994646i \(-0.467045\pi\)
0.103345 + 0.994646i \(0.467045\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) −0.293478 + 1.09527i −0.0343490 + 0.128192i −0.980971 0.194152i \(-0.937804\pi\)
0.946622 + 0.322345i \(0.104471\pi\)
\(74\) 4.98460 2.87786i 0.579448 0.334545i
\(75\) 0 0
\(76\) 5.99044i 0.687151i
\(77\) −5.14416 + 6.44695i −0.586232 + 0.734698i
\(78\) −2.30403 + 2.30403i −0.260880 + 0.260880i
\(79\) −8.76189 5.05868i −0.985790 0.569146i −0.0817766 0.996651i \(-0.526059\pi\)
−0.904013 + 0.427505i \(0.859393\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −2.65507 9.90885i −0.293203 1.09425i
\(83\) 8.06061 + 8.06061i 0.884767 + 0.884767i 0.994015 0.109248i \(-0.0348441\pi\)
−0.109248 + 0.994015i \(0.534844\pi\)
\(84\) −2.12920 + 1.57052i −0.232314 + 0.171357i
\(85\) 0 0
\(86\) 4.55868 7.89587i 0.491575 0.851433i
\(87\) 5.21545 + 1.39747i 0.559154 + 0.149825i
\(88\) −3.01114 0.806832i −0.320988 0.0860086i
\(89\) −9.18432 + 15.9077i −0.973536 + 1.68621i −0.288850 + 0.957374i \(0.593273\pi\)
−0.684685 + 0.728839i \(0.740060\pi\)
\(90\) 0 0
\(91\) −3.44960 + 7.90064i −0.361616 + 0.828212i
\(92\) −0.806832 0.806832i −0.0841181 0.0841181i
\(93\) −1.10215 4.11329i −0.114288 0.426528i
\(94\) −2.12920 3.68788i −0.219610 0.380375i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −0.740585 + 0.740585i −0.0751950 + 0.0751950i −0.743704 0.668509i \(-0.766933\pi\)
0.668509 + 0.743704i \(0.266933\pi\)
\(98\) −3.72748 + 5.92503i −0.376532 + 0.598518i
\(99\) 3.11736i 0.313306i
\(100\) 0 0
\(101\) −10.0755 + 5.81707i −1.00255 + 0.578820i −0.909001 0.416795i \(-0.863153\pi\)
−0.0935457 + 0.995615i \(0.529820\pi\)
\(102\) −0.295321 + 1.10215i −0.0292411 + 0.109129i
\(103\) 10.2718 2.75232i 1.01211 0.271194i 0.285599 0.958349i \(-0.407807\pi\)
0.726511 + 0.687155i \(0.241141\pi\)
\(104\) −3.25839 −0.319512
\(105\) 0 0
\(106\) −2.88264 −0.279987
\(107\) 16.0605 4.30339i 1.55262 0.416024i 0.622305 0.782775i \(-0.286196\pi\)
0.930319 + 0.366750i \(0.119530\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 12.3420 7.12564i 1.18215 0.682512i 0.225636 0.974212i \(-0.427554\pi\)
0.956510 + 0.291700i \(0.0942208\pi\)
\(110\) 0 0
\(111\) 5.75572i 0.546309i
\(112\) −2.61609 0.395046i −0.247197 0.0373284i
\(113\) 7.08781 7.08781i 0.666765 0.666765i −0.290201 0.956966i \(-0.593722\pi\)
0.956966 + 0.290201i \(0.0937221\pi\)
\(114\) 5.18788 + 2.99522i 0.485889 + 0.280528i
\(115\) 0 0
\(116\) 2.69971 + 4.67604i 0.250662 + 0.434159i
\(117\) 0.843334 + 3.14737i 0.0779663 + 0.290974i
\(118\) 0.165972 + 0.165972i 0.0152790 + 0.0152790i
\(119\) 0.337185 + 3.00000i 0.0309097 + 0.275010i
\(120\) 0 0
\(121\) 0.641033 1.11030i 0.0582757 0.100937i
\(122\) 8.23581 + 2.20678i 0.745636 + 0.199792i
\(123\) −9.90885 2.65507i −0.893451 0.239399i
\(124\) 2.12920 3.68788i 0.191207 0.331181i
\(125\) 0 0
\(126\) 0.295509 + 2.62920i 0.0263260 + 0.234227i
\(127\) −0.705385 0.705385i −0.0625928 0.0625928i 0.675117 0.737710i \(-0.264093\pi\)
−0.737710 + 0.675117i \(0.764093\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −4.55868 7.89587i −0.401369 0.695192i
\(130\) 0 0
\(131\) −11.6997 6.75483i −1.02221 0.590172i −0.107466 0.994209i \(-0.534274\pi\)
−0.914743 + 0.404036i \(0.867607\pi\)
\(132\) −2.20431 + 2.20431i −0.191860 + 0.191860i
\(133\) 15.6716 + 2.36650i 1.35890 + 0.205202i
\(134\) 13.9258i 1.20300i
\(135\) 0 0
\(136\) −0.988164 + 0.570516i −0.0847343 + 0.0489214i
\(137\) −4.44327 + 16.5825i −0.379614 + 1.41674i 0.466870 + 0.884326i \(0.345382\pi\)
−0.846484 + 0.532414i \(0.821285\pi\)
\(138\) −1.10215 + 0.295321i −0.0938215 + 0.0251394i
\(139\) 11.1551 0.946167 0.473084 0.881017i \(-0.343141\pi\)
0.473084 + 0.881017i \(0.343141\pi\)
\(140\) 0 0
\(141\) −4.25839 −0.358621
\(142\) 1.68226 0.450761i 0.141172 0.0378270i
\(143\) −2.62898 + 9.81147i −0.219846 + 0.820477i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 1.13391i 0.0938432i
\(147\) 3.26748 + 6.19060i 0.269498 + 0.510592i
\(148\) 4.06991 4.06991i 0.334545 0.334545i
\(149\) 16.5790 + 9.57191i 1.35821 + 0.784161i 0.989382 0.145338i \(-0.0464269\pi\)
0.368825 + 0.929499i \(0.379760\pi\)
\(150\) 0 0
\(151\) 8.74656 + 15.1495i 0.711785 + 1.23285i 0.964187 + 0.265225i \(0.0854462\pi\)
−0.252402 + 0.967622i \(0.581221\pi\)
\(152\) 1.55044 + 5.78632i 0.125757 + 0.469333i
\(153\) 0.806832 + 0.806832i 0.0652285 + 0.0652285i
\(154\) −3.30029 + 7.55868i −0.265945 + 0.609096i
\(155\) 0 0
\(156\) −1.62920 + 2.82185i −0.130440 + 0.225929i
\(157\) −12.1063 3.24387i −0.966186 0.258889i −0.258969 0.965886i \(-0.583383\pi\)
−0.707217 + 0.706997i \(0.750049\pi\)
\(158\) −9.77262 2.61857i −0.777468 0.208322i
\(159\) −1.44132 + 2.49644i −0.114304 + 0.197981i
\(160\) 0 0
\(161\) −2.42948 + 1.79201i −0.191470 + 0.141230i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) −3.91019 14.5930i −0.306270 1.14301i −0.931847 0.362851i \(-0.881803\pi\)
0.625578 0.780162i \(-0.284863\pi\)
\(164\) −5.12920 8.88403i −0.400523 0.693726i
\(165\) 0 0
\(166\) 9.87219 + 5.69971i 0.766231 + 0.442384i
\(167\) 1.44769 1.44769i 0.112026 0.112026i −0.648872 0.760898i \(-0.724759\pi\)
0.760898 + 0.648872i \(0.224759\pi\)
\(168\) −1.65017 + 2.06808i −0.127313 + 0.159556i
\(169\) 2.38287i 0.183298i
\(170\) 0 0
\(171\) 5.18788 2.99522i 0.396727 0.229050i
\(172\) 2.35975 8.80669i 0.179929 0.671504i
\(173\) −11.8178 + 3.16658i −0.898493 + 0.240751i −0.678369 0.734721i \(-0.737313\pi\)
−0.220124 + 0.975472i \(0.570646\pi\)
\(174\) 5.39943 0.409329
\(175\) 0 0
\(176\) −3.11736 −0.234980
\(177\) 0.226722 0.0607501i 0.0170415 0.00456625i
\(178\) −4.75415 + 17.7427i −0.356339 + 1.32987i
\(179\) 16.5790 9.57191i 1.23917 0.715438i 0.270249 0.962790i \(-0.412894\pi\)
0.968926 + 0.247353i \(0.0795606\pi\)
\(180\) 0 0
\(181\) 5.22760i 0.388564i −0.980946 0.194282i \(-0.937762\pi\)
0.980946 0.194282i \(-0.0622377\pi\)
\(182\) −1.28722 + 8.52426i −0.0954148 + 0.631860i
\(183\) 6.02903 6.02903i 0.445679 0.445679i
\(184\) −0.988164 0.570516i −0.0728484 0.0420590i
\(185\) 0 0
\(186\) −2.12920 3.68788i −0.156120 0.270408i
\(187\) 0.920622 + 3.43581i 0.0673226 + 0.251251i
\(188\) −3.01114 3.01114i −0.219610 0.219610i
\(189\) 2.42471 + 1.05868i 0.176371 + 0.0770076i
\(190\) 0 0
\(191\) −5.12920 + 8.88403i −0.371136 + 0.642826i −0.989741 0.142876i \(-0.954365\pi\)
0.618605 + 0.785702i \(0.287698\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) −4.69340 1.25759i −0.337838 0.0905235i 0.0859114 0.996303i \(-0.472620\pi\)
−0.423750 + 0.905779i \(0.639286\pi\)
\(194\) −0.523673 + 0.907028i −0.0375975 + 0.0651208i
\(195\) 0 0
\(196\) −2.06696 + 6.68788i −0.147640 + 0.477705i
\(197\) 4.53011 + 4.53011i 0.322757 + 0.322757i 0.849824 0.527067i \(-0.176708\pi\)
−0.527067 + 0.849824i \(0.676708\pi\)
\(198\) 0.806832 + 3.01114i 0.0573391 + 0.213992i
\(199\) −1.28367 2.22339i −0.0909971 0.157612i 0.816934 0.576731i \(-0.195672\pi\)
−0.907931 + 0.419120i \(0.862339\pi\)
\(200\) 0 0
\(201\) −12.0601 6.96288i −0.850652 0.491124i
\(202\) −8.22658 + 8.22658i −0.578820 + 0.578820i
\(203\) 13.2995 5.21545i 0.933439 0.366052i
\(204\) 1.14103i 0.0798883i
\(205\) 0 0
\(206\) 9.20944 5.31707i 0.641652 0.370458i
\(207\) −0.295321 + 1.10215i −0.0205262 + 0.0766049i
\(208\) −3.14737 + 0.843334i −0.218231 + 0.0584747i
\(209\) 18.6744 1.29173
\(210\) 0 0
\(211\) 25.1746 1.73309 0.866546 0.499098i \(-0.166335\pi\)
0.866546 + 0.499098i \(0.166335\pi\)
\(212\) −2.78442 + 0.746082i −0.191234 + 0.0512411i
\(213\) 0.450761 1.68226i 0.0308856 0.115267i
\(214\) 14.3994 8.31351i 0.984325 0.568300i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −8.80669 7.02706i −0.597837 0.477028i
\(218\) 10.0772 10.0772i 0.682512 0.682512i
\(219\) 0.981996 + 0.566956i 0.0663572 + 0.0383113i
\(220\) 0 0
\(221\) 1.85897 + 3.21983i 0.125048 + 0.216589i
\(222\) −1.48969 5.55960i −0.0999815 0.373136i
\(223\) 7.35350 + 7.35350i 0.492427 + 0.492427i 0.909070 0.416643i \(-0.136794\pi\)
−0.416643 + 0.909070i \(0.636794\pi\)
\(224\) −2.62920 + 0.295509i −0.175671 + 0.0197445i
\(225\) 0 0
\(226\) 5.01184 8.68076i 0.333382 0.577435i
\(227\) −19.6517 5.26566i −1.30433 0.349494i −0.461245 0.887273i \(-0.652597\pi\)
−0.843086 + 0.537779i \(0.819264\pi\)
\(228\) 5.78632 + 1.55044i 0.383209 + 0.102680i
\(229\) 3.91643 6.78346i 0.258805 0.448263i −0.707117 0.707096i \(-0.750005\pi\)
0.965922 + 0.258833i \(0.0833380\pi\)
\(230\) 0 0
\(231\) 4.89587 + 6.63747i 0.322124 + 0.436714i
\(232\) 3.81797 + 3.81797i 0.250662 + 0.250662i
\(233\) −1.44769 5.40286i −0.0948415 0.353953i 0.902154 0.431414i \(-0.141985\pi\)
−0.996995 + 0.0774612i \(0.975319\pi\)
\(234\) 1.62920 + 2.82185i 0.106504 + 0.184470i
\(235\) 0 0
\(236\) 0.203274 + 0.117360i 0.0132320 + 0.00763949i
\(237\) −7.15405 + 7.15405i −0.464706 + 0.464706i
\(238\) 1.10215 + 2.81051i 0.0714420 + 0.182178i
\(239\) 12.3686i 0.800060i 0.916502 + 0.400030i \(0.131000\pi\)
−0.916502 + 0.400030i \(0.869000\pi\)
\(240\) 0 0
\(241\) 12.1145 6.99433i 0.780366 0.450544i −0.0561941 0.998420i \(-0.517897\pi\)
0.836560 + 0.547875i \(0.184563\pi\)
\(242\) 0.331823 1.23838i 0.0213304 0.0796061i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 8.52634 0.545843
\(245\) 0 0
\(246\) −10.2584 −0.654051
\(247\) 18.8541 5.05195i 1.19966 0.321448i
\(248\) 1.10215 4.11329i 0.0699868 0.261194i
\(249\) 9.87219 5.69971i 0.625625 0.361205i
\(250\) 0 0
\(251\) 17.0336i 1.07515i 0.843216 + 0.537575i \(0.180659\pi\)
−0.843216 + 0.537575i \(0.819341\pi\)
\(252\) 0.965926 + 2.46313i 0.0608476 + 0.155162i
\(253\) −2.51519 + 2.51519i −0.158128 + 0.158128i
\(254\) −0.863917 0.498783i −0.0542070 0.0312964i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.43164 + 20.2711i 0.338816 + 1.26448i 0.899672 + 0.436566i \(0.143805\pi\)
−0.560856 + 0.827913i \(0.689528\pi\)
\(258\) −6.44695 6.44695i −0.401369 0.401369i
\(259\) −9.03946 12.2551i −0.561685 0.761493i
\(260\) 0 0
\(261\) 2.69971 4.67604i 0.167108 0.289440i
\(262\) −13.0493 3.49656i −0.806191 0.216018i
\(263\) −18.4888 4.95406i −1.14007 0.305481i −0.361090 0.932531i \(-0.617595\pi\)
−0.778979 + 0.627050i \(0.784262\pi\)
\(264\) −1.55868 + 2.69971i −0.0959301 + 0.166156i
\(265\) 0 0
\(266\) 15.7501 1.77023i 0.965698 0.108540i
\(267\) 12.9886 + 12.9886i 0.794888 + 0.794888i
\(268\) −3.60425 13.4513i −0.220165 0.821666i
\(269\) −14.6138 25.3118i −0.891019 1.54329i −0.838656 0.544662i \(-0.816658\pi\)
−0.0523636 0.998628i \(-0.516675\pi\)
\(270\) 0 0
\(271\) 19.4796 + 11.2466i 1.18330 + 0.683180i 0.956776 0.290826i \(-0.0939299\pi\)
0.226526 + 0.974005i \(0.427263\pi\)
\(272\) −0.806832 + 0.806832i −0.0489214 + 0.0489214i
\(273\) 6.73861 + 5.37689i 0.407840 + 0.325424i
\(274\) 17.1675i 1.03713i
\(275\) 0 0
\(276\) −0.988164 + 0.570516i −0.0594805 + 0.0343411i
\(277\) −5.60865 + 20.9318i −0.336991 + 1.25767i 0.564703 + 0.825294i \(0.308991\pi\)
−0.901694 + 0.432374i \(0.857676\pi\)
\(278\) 10.7750 2.88717i 0.646244 0.173161i
\(279\) −4.25839 −0.254943
\(280\) 0 0
\(281\) 19.3758 1.15586 0.577930 0.816086i \(-0.303861\pi\)
0.577930 + 0.816086i \(0.303861\pi\)
\(282\) −4.11329 + 1.10215i −0.244943 + 0.0656323i
\(283\) −4.82531 + 18.0083i −0.286835 + 1.07048i 0.660653 + 0.750692i \(0.270280\pi\)
−0.947488 + 0.319792i \(0.896387\pi\)
\(284\) 1.50828 0.870803i 0.0894997 0.0516727i
\(285\) 0 0
\(286\) 10.1576i 0.600631i
\(287\) −25.2677 + 9.90885i −1.49151 + 0.584901i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) −13.5949 7.84902i −0.799700 0.461707i
\(290\) 0 0
\(291\) 0.523673 + 0.907028i 0.0306982 + 0.0531709i
\(292\) 0.293478 + 1.09527i 0.0171745 + 0.0640961i
\(293\) −11.4539 11.4539i −0.669145 0.669145i 0.288373 0.957518i \(-0.406886\pi\)
−0.957518 + 0.288373i \(0.906886\pi\)
\(294\) 4.75839 + 5.13397i 0.277515 + 0.299419i
\(295\) 0 0
\(296\) 2.87786 4.98460i 0.167272 0.289724i
\(297\) 3.01114 + 0.806832i 0.174724 + 0.0468172i
\(298\) 18.4915 + 4.95478i 1.07118 + 0.287023i
\(299\) −1.85897 + 3.21983i −0.107507 + 0.186207i
\(300\) 0 0
\(301\) −22.1069 9.65237i −1.27422 0.556353i
\(302\) 12.3695 + 12.3695i 0.711785 + 0.711785i
\(303\) 3.01114 + 11.2377i 0.172985 + 0.645590i
\(304\) 2.99522 + 5.18788i 0.171788 + 0.297545i
\(305\) 0 0
\(306\) 0.988164 + 0.570516i 0.0564896 + 0.0326143i
\(307\) 0.398902 0.398902i 0.0227665 0.0227665i −0.695632 0.718398i \(-0.744876\pi\)
0.718398 + 0.695632i \(0.244876\pi\)
\(308\) −1.23150 + 8.15530i −0.0701713 + 0.464691i
\(309\) 10.6341i 0.604955i
\(310\) 0 0
\(311\) −11.2317 + 6.48460i −0.636889 + 0.367708i −0.783415 0.621499i \(-0.786524\pi\)
0.146526 + 0.989207i \(0.453191\pi\)
\(312\) −0.843334 + 3.14737i −0.0477444 + 0.178185i
\(313\) 1.78875 0.479293i 0.101106 0.0270912i −0.207911 0.978148i \(-0.566667\pi\)
0.309017 + 0.951056i \(0.400000\pi\)
\(314\) −12.5333 −0.707297
\(315\) 0 0
\(316\) −10.1174 −0.569146
\(317\) −31.2821 + 8.38202i −1.75698 + 0.470781i −0.986094 0.166191i \(-0.946853\pi\)
−0.770886 + 0.636973i \(0.780186\pi\)
\(318\) −0.746082 + 2.78442i −0.0418382 + 0.156142i
\(319\) 14.5769 8.41598i 0.816150 0.471204i
\(320\) 0 0
\(321\) 16.6270i 0.928030i
\(322\) −1.88289 + 2.35975i −0.104930 + 0.131504i
\(323\) 4.83328 4.83328i 0.268931 0.268931i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) −7.55390 13.0837i −0.418372 0.724641i
\(327\) −3.68850 13.7657i −0.203975 0.761243i
\(328\) −7.25378 7.25378i −0.400523 0.400523i
\(329\) −9.06696 + 6.68788i −0.499877 + 0.368715i
\(330\) 0 0
\(331\) 5.80168 10.0488i 0.318889 0.552332i −0.661368 0.750062i \(-0.730024\pi\)
0.980257 + 0.197730i \(0.0633570\pi\)
\(332\) 11.0110 + 2.95039i 0.604307 + 0.161924i
\(333\) −5.55960 1.48969i −0.304664 0.0816346i
\(334\) 1.02367 1.77305i 0.0560129 0.0970172i
\(335\) 0 0
\(336\) −1.05868 + 2.42471i −0.0577557 + 0.132279i
\(337\) 9.45809 + 9.45809i 0.515215 + 0.515215i 0.916120 0.400905i \(-0.131304\pi\)
−0.400905 + 0.916120i \(0.631304\pi\)
\(338\) −0.616733 2.30168i −0.0335459 0.125195i
\(339\) −5.01184 8.68076i −0.272206 0.471474i
\(340\) 0 0
\(341\) −11.4964 6.63747i −0.622567 0.359439i
\(342\) 4.23588 4.23588i 0.229050 0.229050i
\(343\) 16.6796 + 8.04937i 0.900611 + 0.434625i
\(344\) 9.11736i 0.491575i
\(345\) 0 0
\(346\) −10.5956 + 6.11736i −0.569622 + 0.328871i
\(347\) 5.58708 20.8512i 0.299930 1.11935i −0.637293 0.770622i \(-0.719946\pi\)
0.937223 0.348732i \(-0.113388\pi\)
\(348\) 5.21545 1.39747i 0.279577 0.0749125i
\(349\) 14.9455 0.800016 0.400008 0.916512i \(-0.369007\pi\)
0.400008 + 0.916512i \(0.369007\pi\)
\(350\) 0 0
\(351\) 3.25839 0.173920
\(352\) −3.01114 + 0.806832i −0.160494 + 0.0430043i
\(353\) −9.43970 + 35.2295i −0.502425 + 1.87507i −0.0187553 + 0.999824i \(0.505970\pi\)
−0.483669 + 0.875251i \(0.660696\pi\)
\(354\) 0.203274 0.117360i 0.0108039 0.00623762i
\(355\) 0 0
\(356\) 18.3686i 0.973536i
\(357\) 2.98505 + 0.450761i 0.157985 + 0.0238568i
\(358\) 13.5367 13.5367i 0.715438 0.715438i
\(359\) −3.77518 2.17960i −0.199246 0.115035i 0.397058 0.917794i \(-0.370031\pi\)
−0.596304 + 0.802759i \(0.703365\pi\)
\(360\) 0 0
\(361\) −8.44271 14.6232i −0.444353 0.769642i
\(362\) −1.35300 5.04947i −0.0711122 0.265394i
\(363\) −0.906558 0.906558i −0.0475819 0.0475819i
\(364\) 0.962884 + 8.56696i 0.0504688 + 0.449030i
\(365\) 0 0
\(366\) 4.26317 7.38403i 0.222840 0.385969i
\(367\) −17.9178 4.80106i −0.935302 0.250614i −0.241188 0.970478i \(-0.577537\pi\)
−0.694114 + 0.719865i \(0.744204\pi\)
\(368\) −1.10215 0.295321i −0.0574537 0.0153947i
\(369\) −5.12920 + 8.88403i −0.267015 + 0.462484i
\(370\) 0 0
\(371\) 0.851846 + 7.57903i 0.0442256 + 0.393483i
\(372\) −3.01114 3.01114i −0.156120 0.156120i
\(373\) −5.05195 18.8541i −0.261580 0.976229i −0.964311 0.264773i \(-0.914703\pi\)
0.702731 0.711456i \(-0.251964\pi\)
\(374\) 1.77851 + 3.08046i 0.0919643 + 0.159287i
\(375\) 0 0
\(376\) −3.68788 2.12920i −0.190188 0.109805i
\(377\) 12.4404 12.4404i 0.640716 0.640716i
\(378\) 2.61609 + 0.395046i 0.134557 + 0.0203190i
\(379\) 37.4424i 1.92329i 0.274300 + 0.961644i \(0.411554\pi\)
−0.274300 + 0.961644i \(0.588446\pi\)
\(380\) 0 0
\(381\) −0.863917 + 0.498783i −0.0442598 + 0.0255534i
\(382\) −2.65507 + 9.90885i −0.135845 + 0.506981i
\(383\) 0.582793 0.156159i 0.0297794 0.00797935i −0.243899 0.969801i \(-0.578426\pi\)
0.273678 + 0.961821i \(0.411760\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −4.85897 −0.247315
\(387\) −8.80669 + 2.35975i −0.447669 + 0.119953i
\(388\) −0.271073 + 1.01166i −0.0137616 + 0.0513592i
\(389\) −17.6000 + 10.1614i −0.892357 + 0.515202i −0.874713 0.484642i \(-0.838950\pi\)
−0.0176441 + 0.999844i \(0.505617\pi\)
\(390\) 0 0
\(391\) 1.30196i 0.0658428i
\(392\) −0.265576 + 6.99496i −0.0134136 + 0.353299i
\(393\) −9.55278 + 9.55278i −0.481874 + 0.481874i
\(394\) 5.54823 + 3.20327i 0.279516 + 0.161379i
\(395\) 0 0
\(396\) 1.55868 + 2.69971i 0.0783266 + 0.135666i
\(397\) 3.10214 + 11.5774i 0.155692 + 0.581051i 0.999045 + 0.0436908i \(0.0139116\pi\)
−0.843353 + 0.537360i \(0.819422\pi\)
\(398\) −1.81539 1.81539i −0.0909971 0.0909971i
\(399\) 6.34196 14.5251i 0.317495 0.727163i
\(400\) 0 0
\(401\) −10.2584 + 17.7681i −0.512280 + 0.887294i 0.487619 + 0.873057i \(0.337866\pi\)
−0.999899 + 0.0142379i \(0.995468\pi\)
\(402\) −13.4513 3.60425i −0.670888 0.179764i
\(403\) −13.4027 3.59125i −0.667637 0.178893i
\(404\) −5.81707 + 10.0755i −0.289410 + 0.501273i
\(405\) 0 0
\(406\) 11.4964 8.47989i 0.570559 0.420850i
\(407\) −12.6874 12.6874i −0.628890 0.628890i
\(408\) 0.295321 + 1.10215i 0.0146206 + 0.0545647i
\(409\) −6.61219 11.4527i −0.326952 0.566297i 0.654954 0.755669i \(-0.272688\pi\)
−0.981905 + 0.189372i \(0.939355\pi\)
\(410\) 0 0
\(411\) 14.8675 + 8.58374i 0.733359 + 0.423405i
\(412\) 7.51948 7.51948i 0.370458 0.370458i
\(413\) 0.387327 0.485420i 0.0190591 0.0238860i
\(414\) 1.14103i 0.0560787i
\(415\) 0 0
\(416\) −2.82185 + 1.62920i −0.138353 + 0.0798779i
\(417\) 2.88717 10.7750i 0.141385 0.527656i
\(418\) 18.0381 4.83328i 0.882270 0.236404i
\(419\) 19.9791 0.976043 0.488022 0.872832i \(-0.337719\pi\)
0.488022 + 0.872832i \(0.337719\pi\)
\(420\) 0 0
\(421\) −20.2920 −0.988970 −0.494485 0.869186i \(-0.664643\pi\)
−0.494485 + 0.869186i \(0.664643\pi\)
\(422\) 24.3168 6.51567i 1.18372 0.317178i
\(423\) −1.10215 + 4.11329i −0.0535885 + 0.199995i
\(424\) −2.49644 + 1.44132i −0.121238 + 0.0699967i
\(425\) 0 0
\(426\) 1.74161i 0.0843811i
\(427\) 3.36830 22.3057i 0.163004 1.07945i
\(428\) 11.7571 11.7571i 0.568300 0.568300i
\(429\) 8.79673 + 5.07879i 0.424710 + 0.245206i
\(430\) 0 0
\(431\) 0.167764 + 0.290576i 0.00808092 + 0.0139966i 0.870038 0.492985i \(-0.164094\pi\)
−0.861957 + 0.506982i \(0.830761\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −4.53678 4.53678i −0.218024 0.218024i 0.589641 0.807665i \(-0.299269\pi\)
−0.807665 + 0.589641i \(0.799269\pi\)
\(434\) −10.3253 4.50828i −0.495633 0.216404i
\(435\) 0 0
\(436\) 7.12564 12.3420i 0.341256 0.591073i
\(437\) 6.60239 + 1.76910i 0.315835 + 0.0846277i
\(438\) 1.09527 + 0.293478i 0.0523342 + 0.0140229i
\(439\) 13.6209 23.5920i 0.650088 1.12599i −0.333013 0.942922i \(-0.608065\pi\)
0.983101 0.183063i \(-0.0586013\pi\)
\(440\) 0 0
\(441\) 6.82535 1.55390i 0.325017 0.0739953i
\(442\) 2.62898 + 2.62898i 0.125048 + 0.125048i
\(443\) −1.33672 4.98872i −0.0635097 0.237021i 0.926873 0.375374i \(-0.122486\pi\)
−0.990383 + 0.138353i \(0.955819\pi\)
\(444\) −2.87786 4.98460i −0.136577 0.236559i
\(445\) 0 0
\(446\) 9.00617 + 5.19971i 0.426454 + 0.246214i
\(447\) 13.5367 13.5367i 0.640265 0.640265i
\(448\) −2.46313 + 0.965926i −0.116372 + 0.0456357i
\(449\) 26.0501i 1.22938i 0.788768 + 0.614691i \(0.210719\pi\)
−0.788768 + 0.614691i \(0.789281\pi\)
\(450\) 0 0
\(451\) −27.6947 + 15.9896i −1.30409 + 0.752919i
\(452\) 2.59432 9.68212i 0.122026 0.455409i
\(453\) 16.8970 4.52755i 0.793893 0.212723i
\(454\) −20.3450 −0.954836
\(455\) 0 0
\(456\) 5.99044 0.280528
\(457\) 29.2530 7.83833i 1.36840 0.366661i 0.501506 0.865154i \(-0.332780\pi\)
0.866894 + 0.498493i \(0.166113\pi\)
\(458\) 2.02729 7.56596i 0.0947292 0.353534i
\(459\) 0.988164 0.570516i 0.0461235 0.0266294i
\(460\) 0 0
\(461\) 3.71793i 0.173161i 0.996245 + 0.0865807i \(0.0275940\pi\)
−0.996245 + 0.0865807i \(0.972406\pi\)
\(462\) 6.44695 + 5.14416i 0.299939 + 0.239328i
\(463\) −16.3674 + 16.3674i −0.760658 + 0.760658i −0.976441 0.215783i \(-0.930770\pi\)
0.215783 + 0.976441i \(0.430770\pi\)
\(464\) 4.67604 + 2.69971i 0.217080 + 0.125331i
\(465\) 0 0
\(466\) −2.79673 4.84407i −0.129556 0.224397i
\(467\) −7.00365 26.1380i −0.324090 1.20952i −0.915223 0.402947i \(-0.867986\pi\)
0.591133 0.806574i \(-0.298681\pi\)
\(468\) 2.30403 + 2.30403i 0.106504 + 0.106504i
\(469\) −36.6136 + 4.11519i −1.69066 + 0.190022i
\(470\) 0 0
\(471\) −6.26667 + 10.8542i −0.288753 + 0.500135i
\(472\) 0.226722 + 0.0607501i 0.0104357 + 0.00279625i
\(473\) −27.4536 7.35618i −1.26232 0.338237i
\(474\) −5.05868 + 8.76189i −0.232353 + 0.402447i
\(475\) 0 0
\(476\) 1.79201 + 2.42948i 0.0821367 + 0.111355i
\(477\) 2.03833 + 2.03833i 0.0933289 + 0.0933289i
\(478\) 3.20124 + 11.9472i 0.146421 + 0.546451i
\(479\) −21.0873 36.5243i −0.963503 1.66884i −0.713583 0.700571i \(-0.752929\pi\)
−0.249920 0.968266i \(-0.580404\pi\)
\(480\) 0 0
\(481\) −16.2418 9.37721i −0.740562 0.427564i
\(482\) 9.89148 9.89148i 0.450544 0.450544i
\(483\) 1.10215 + 2.81051i 0.0501497 + 0.127883i
\(484\) 1.28207i 0.0582757i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 8.09527 30.2120i 0.366832 1.36903i −0.498089 0.867126i \(-0.665965\pi\)
0.864921 0.501909i \(-0.167369\pi\)
\(488\) 8.23581 2.20678i 0.372818 0.0998962i
\(489\) −15.1078 −0.683199
\(490\) 0 0
\(491\) 26.7108 1.20544 0.602721 0.797952i \(-0.294083\pi\)
0.602721 + 0.797952i \(0.294083\pi\)
\(492\) −9.90885 + 2.65507i −0.446725 + 0.119700i
\(493\) 1.59456 5.95099i 0.0718156 0.268019i
\(494\) 16.9041 9.75961i 0.760553 0.439106i
\(495\) 0 0
\(496\) 4.25839i 0.191207i
\(497\) −1.68226 4.28980i −0.0754598 0.192424i
\(498\) 8.06061 8.06061i 0.361205 0.361205i
\(499\) −6.79373 3.92236i −0.304129 0.175589i 0.340167 0.940365i \(-0.389516\pi\)
−0.644296 + 0.764776i \(0.722850\pi\)
\(500\) 0 0
\(501\) −1.02367 1.77305i −0.0457343 0.0792142i
\(502\) 4.40861 + 16.4532i 0.196766 + 0.734341i
\(503\) 23.4463 + 23.4463i 1.04542 + 1.04542i 0.998918 + 0.0464999i \(0.0148067\pi\)
0.0464999 + 0.998918i \(0.485193\pi\)
\(504\) 1.57052 + 2.12920i 0.0699564 + 0.0948420i
\(505\) 0 0
\(506\) −1.77851 + 3.08046i −0.0790642 + 0.136943i
\(507\) −2.30168 0.616733i −0.102221 0.0273901i
\(508\) −0.963574 0.258189i −0.0427517 0.0114553i
\(509\) −6.72339 + 11.6452i −0.298009 + 0.516166i −0.975680 0.219198i \(-0.929656\pi\)
0.677671 + 0.735365i \(0.262989\pi\)
\(510\) 0 0
\(511\) 2.98128 0.335081i 0.131884 0.0148231i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.55044 5.78632i −0.0684536 0.255472i
\(514\) 10.4931 + 18.1746i 0.462831 + 0.801647i
\(515\) 0 0
\(516\) −7.89587 4.55868i −0.347596 0.200685i
\(517\) −9.38680 + 9.38680i −0.412831 + 0.412831i
\(518\) −11.9033 9.49790i −0.523001 0.417314i
\(519\) 12.2347i 0.537045i
\(520\) 0 0
\(521\) 5.28346 3.05040i 0.231472 0.133641i −0.379779 0.925077i \(-0.624000\pi\)
0.611251 + 0.791437i \(0.290667\pi\)
\(522\) 1.39747 5.21545i 0.0611658 0.228274i
\(523\) −11.3122 + 3.03110i −0.494649 + 0.132541i −0.497516 0.867455i \(-0.665754\pi\)
0.00286635 + 0.999996i \(0.499088\pi\)
\(524\) −13.5097 −0.590172
\(525\) 0 0
\(526\) −19.1410 −0.834589
\(527\) −4.69340 + 1.25759i −0.204448 + 0.0547816i
\(528\) −0.806832 + 3.01114i −0.0351129 + 0.131043i
\(529\) 18.7911 10.8490i 0.817002 0.471697i
\(530\) 0 0
\(531\) 0.234720i 0.0101860i
\(532\) 14.7552 5.78632i 0.639720 0.250869i
\(533\) −23.6357 + 23.6357i −1.02377 + 1.02377i
\(534\) 15.9077 + 9.18432i 0.688394 + 0.397444i
\(535\) 0 0
\(536\) −6.96288 12.0601i −0.300751 0.520916i
\(537\) −4.95478 18.4915i −0.213815 0.797967i
\(538\) −20.6670 20.6670i −0.891019 0.891019i
\(539\) 20.8485 + 6.44345i 0.898009 + 0.277539i
\(540\) 0 0
\(541\) −0.354252 + 0.613582i −0.0152305 + 0.0263800i −0.873540 0.486752i \(-0.838182\pi\)
0.858310 + 0.513132i \(0.171515\pi\)
\(542\) 21.7267 + 5.82165i 0.933241 + 0.250061i
\(543\) −5.04947 1.35300i −0.216694 0.0580629i
\(544\) −0.570516 + 0.988164i −0.0244607 + 0.0423672i
\(545\) 0 0
\(546\) 7.90064 + 3.44960i 0.338116 + 0.147629i
\(547\) 24.3712 + 24.3712i 1.04204 + 1.04204i 0.999077 + 0.0429611i \(0.0136792\pi\)
0.0429611 + 0.999077i \(0.486321\pi\)
\(548\) 4.44327 + 16.5825i 0.189807 + 0.708370i
\(549\) −4.26317 7.38403i −0.181948 0.315143i
\(550\) 0 0
\(551\) −28.0116 16.1725i −1.19333 0.688971i
\(552\) −0.806832 + 0.806832i −0.0343411 + 0.0343411i
\(553\) −3.99683 + 26.4679i −0.169962 + 1.12553i
\(554\) 21.6702i 0.920677i
\(555\) 0 0
\(556\) 9.66064 5.57757i 0.409703 0.236542i
\(557\) 5.47611 20.4371i 0.232030 0.865948i −0.747435 0.664335i \(-0.768715\pi\)
0.979465 0.201613i \(-0.0646184\pi\)
\(558\) −4.11329 + 1.10215i −0.174130 + 0.0466579i
\(559\) −29.7079 −1.25651
\(560\) 0 0
\(561\) 3.55701 0.150177
\(562\) 18.7155 5.01481i 0.789467 0.211537i
\(563\) 8.98894 33.5472i 0.378839 1.41385i −0.468815 0.883296i \(-0.655319\pi\)
0.847654 0.530549i \(-0.178014\pi\)
\(564\) −3.68788 + 2.12920i −0.155288 + 0.0896553i
\(565\) 0 0
\(566\) 18.6436i 0.783648i
\(567\) 1.65017 2.06808i 0.0693005 0.0868512i
\(568\) 1.23150 1.23150i 0.0516727 0.0516727i
\(569\) 4.58874 + 2.64931i 0.192370 + 0.111065i 0.593092 0.805135i \(-0.297907\pi\)
−0.400722 + 0.916200i \(0.631241\pi\)
\(570\) 0 0
\(571\) −12.9427 22.4174i −0.541636 0.938140i −0.998810 0.0487634i \(-0.984472\pi\)
0.457175 0.889377i \(-0.348861\pi\)
\(572\) 2.62898 + 9.81147i 0.109923 + 0.410238i
\(573\) 7.25378 + 7.25378i 0.303031 + 0.303031i
\(574\) −21.8421 + 16.1110i −0.911673 + 0.672459i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −20.2574 5.42795i −0.843326 0.225968i −0.188807 0.982014i \(-0.560462\pi\)
−0.654519 + 0.756046i \(0.727129\pi\)
\(578\) −15.1631 4.06295i −0.630704 0.168997i
\(579\) −2.42948 + 4.20799i −0.100966 + 0.174878i
\(580\) 0 0
\(581\) 12.0683 27.6403i 0.500679 1.14671i
\(582\) 0.740585 + 0.740585i 0.0306982 + 0.0306982i
\(583\) 2.32581 + 8.68003i 0.0963251 + 0.359490i
\(584\) 0.566956 + 0.981996i 0.0234608 + 0.0406353i
\(585\) 0 0
\(586\) −14.0281 8.09914i −0.579496 0.334572i
\(587\) 21.0917 21.0917i 0.870548 0.870548i −0.121984 0.992532i \(-0.538926\pi\)
0.992532 + 0.121984i \(0.0389257\pi\)
\(588\) 5.92503 + 3.72748i 0.244344 + 0.153719i
\(589\) 25.5097i 1.05111i
\(590\) 0 0
\(591\) 5.54823 3.20327i 0.228224 0.131765i
\(592\) 1.48969 5.55960i 0.0612259 0.228498i
\(593\) −23.1242 + 6.19610i −0.949595 + 0.254443i −0.700190 0.713956i \(-0.746902\pi\)
−0.249405 + 0.968399i \(0.580235\pi\)
\(594\) 3.11736 0.127907
\(595\) 0 0
\(596\) 19.1438 0.784161
\(597\) −2.47986 + 0.664478i −0.101494 + 0.0271953i
\(598\) −0.962272 + 3.59125i −0.0393502 + 0.146857i
\(599\) −22.3474 + 12.9022i −0.913088 + 0.527172i −0.881423 0.472327i \(-0.843414\pi\)
−0.0316646 + 0.999499i \(0.510081\pi\)
\(600\) 0 0
\(601\) 26.1745i 1.06768i −0.845586 0.533840i \(-0.820749\pi\)
0.845586 0.533840i \(-0.179251\pi\)
\(602\) −23.8519 3.60178i −0.972129 0.146798i
\(603\) −9.84701 + 9.84701i −0.401001 + 0.401001i
\(604\) 15.1495 + 8.74656i 0.616424 + 0.355892i
\(605\) 0 0
\(606\) 5.81707 + 10.0755i 0.236302 + 0.409288i
\(607\) 8.50340 + 31.7351i 0.345142 + 1.28809i 0.892446 + 0.451155i \(0.148988\pi\)
−0.547303 + 0.836934i \(0.684346\pi\)
\(608\) 4.23588 + 4.23588i 0.171788 + 0.171788i
\(609\) −1.59558 14.1962i −0.0646561 0.575257i
\(610\) 0 0
\(611\) −6.93776 + 12.0166i −0.280672 + 0.486138i
\(612\) 1.10215 + 0.295321i 0.0445519 + 0.0119376i
\(613\) −37.5024 10.0487i −1.51471 0.405864i −0.596711 0.802456i \(-0.703526\pi\)
−0.917995 + 0.396592i \(0.870193\pi\)
\(614\) 0.282066 0.488553i 0.0113833 0.0197164i
\(615\) 0 0
\(616\) 0.921208 + 8.19615i 0.0371165 + 0.330232i
\(617\) −16.2604 16.2604i −0.654618 0.654618i 0.299483 0.954102i \(-0.403186\pi\)
−0.954102 + 0.299483i \(0.903186\pi\)
\(618\) −2.75232 10.2718i −0.110715 0.413192i
\(619\) 13.8100 + 23.9195i 0.555069 + 0.961407i 0.997898 + 0.0648015i \(0.0206414\pi\)
−0.442829 + 0.896606i \(0.646025\pi\)
\(620\) 0 0
\(621\) 0.988164 + 0.570516i 0.0396536 + 0.0228940i
\(622\) −9.17061 + 9.17061i −0.367708 + 0.367708i
\(623\) 48.0540 + 7.25646i 1.92524 + 0.290724i
\(624\) 3.25839i 0.130440i
\(625\) 0 0
\(626\) 1.60375 0.925923i 0.0640986 0.0370073i
\(627\) 4.83328 18.0381i 0.193023 0.720371i
\(628\) −12.1063 + 3.24387i −0.483093 + 0.129444i
\(629\) −6.56747 −0.261862
\(630\) 0 0
\(631\) −19.7151 −0.784844 −0.392422 0.919785i \(-0.628363\pi\)
−0.392422 + 0.919785i \(0.628363\pi\)
\(632\) −9.77262 + 2.61857i −0.388734 + 0.104161i
\(633\) 6.51567 24.3168i 0.258975 0.966506i
\(634\) −28.0468 + 16.1928i −1.11388 + 0.643099i
\(635\) 0 0
\(636\) 2.88264i 0.114304i
\(637\) 22.7923 + 0.865352i 0.903065 + 0.0342865i
\(638\) 11.9020 11.9020i 0.471204 0.471204i
\(639\) −1.50828 0.870803i −0.0596665 0.0344485i
\(640\) 0 0
\(641\) 0.453156 + 0.784890i 0.0178986 + 0.0310013i 0.874836 0.484419i \(-0.160969\pi\)
−0.856937 + 0.515421i \(0.827636\pi\)
\(642\) −4.30339 16.0605i −0.169841 0.633856i
\(643\) −4.52704 4.52704i −0.178529 0.178529i 0.612185 0.790714i \(-0.290291\pi\)
−0.790714 + 0.612185i \(0.790291\pi\)
\(644\) −1.20799 + 2.76667i −0.0476014 + 0.109022i
\(645\) 0 0
\(646\) 3.41765 5.91954i 0.134466 0.232901i
\(647\) −10.1722 2.72563i −0.399910 0.107156i 0.0532577 0.998581i \(-0.483040\pi\)
−0.453168 + 0.891425i \(0.649706\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) 0.365854 0.633677i 0.0143610 0.0248740i
\(650\) 0 0
\(651\) −9.06696 + 6.68788i −0.355362 + 0.262119i
\(652\) −10.6828 10.6828i −0.418372 0.418372i
\(653\) −5.97781 22.3095i −0.233930 0.873037i −0.978628 0.205636i \(-0.934074\pi\)
0.744699 0.667401i \(-0.232593\pi\)
\(654\) −7.12564 12.3420i −0.278634 0.482609i
\(655\) 0 0
\(656\) −8.88403 5.12920i −0.346863 0.200261i
\(657\) 0.801797 0.801797i 0.0312811 0.0312811i
\(658\) −7.02706 + 8.80669i −0.273943 + 0.343321i
\(659\) 43.2474i 1.68468i −0.538947 0.842340i \(-0.681178\pi\)
0.538947 0.842340i \(-0.318822\pi\)
\(660\) 0 0
\(661\) −17.0787 + 9.86042i −0.664286 + 0.383526i −0.793908 0.608038i \(-0.791957\pi\)
0.129622 + 0.991563i \(0.458624\pi\)
\(662\) 3.00317 11.2080i 0.116721 0.435610i
\(663\) 3.59125 0.962272i 0.139473 0.0373716i
\(664\) 11.3994 0.442384
\(665\) 0 0
\(666\) −5.75572 −0.223030
\(667\) 5.95099 1.59456i 0.230423 0.0617418i
\(668\) 0.529892 1.97758i 0.0205021 0.0765150i
\(669\) 9.00617 5.19971i 0.348199 0.201033i
\(670\) 0 0
\(671\) 26.5797i 1.02610i
\(672\) −0.395046 + 2.61609i −0.0152392 + 0.100918i
\(673\) −15.0859 + 15.0859i −0.581517 + 0.581517i −0.935320 0.353803i \(-0.884888\pi\)
0.353803 + 0.935320i \(0.384888\pi\)
\(674\) 11.5837 + 6.68788i 0.446189 + 0.257607i
\(675\) 0 0
\(676\) −1.19144 2.06363i −0.0458245 0.0793704i
\(677\) −3.45209 12.8834i −0.132674 0.495148i 0.867322 0.497747i \(-0.165839\pi\)
−0.999997 + 0.00259937i \(0.999173\pi\)
\(678\) −7.08781 7.08781i −0.272206 0.272206i
\(679\) 2.53951 + 1.10880i 0.0974573 + 0.0425520i
\(680\) 0 0
\(681\) −10.1725 + 17.6193i −0.389810 + 0.675171i
\(682\) −12.8226 3.43581i −0.491003 0.131564i
\(683\) 31.8622 + 8.53746i 1.21918 + 0.326677i 0.810356 0.585938i \(-0.199274\pi\)
0.408819 + 0.912615i \(0.365941\pi\)
\(684\) 2.99522 5.18788i 0.114525 0.198363i
\(685\) 0 0
\(686\) 18.1945 + 3.45811i 0.694671 + 0.132031i
\(687\) −5.53867 5.53867i −0.211313 0.211313i
\(688\) −2.35975 8.80669i −0.0899645 0.335752i
\(689\) 4.69639 + 8.13438i 0.178918 + 0.309895i
\(690\) 0 0
\(691\) 32.0104 + 18.4812i 1.21773 + 0.703059i 0.964433 0.264329i \(-0.0851505\pi\)
0.253301 + 0.967388i \(0.418484\pi\)
\(692\) −8.65125 + 8.65125i −0.328871 + 0.328871i
\(693\) 7.67845 3.01114i 0.291680 0.114384i
\(694\) 21.5868i 0.819424i
\(695\) 0 0
\(696\) 4.67604 2.69971i 0.177245 0.102332i
\(697\) −3.02952 + 11.3063i −0.114751 + 0.428257i
\(698\) 14.4363 3.86819i 0.546421 0.146413i
\(699\) −5.59345 −0.211564
\(700\) 0 0
\(701\) 18.4397 0.696456 0.348228 0.937410i \(-0.386784\pi\)
0.348228 + 0.937410i \(0.386784\pi\)
\(702\) 3.14737 0.843334i 0.118790 0.0318296i
\(703\) −8.92391 + 33.3045i −0.336572 + 1.25610i
\(704\) −2.69971 + 1.55868i −0.101749 + 0.0587450i
\(705\) 0 0
\(706\) 36.4722i 1.37265i
\(707\) 24.0603 + 19.1983i 0.904882 + 0.722026i
\(708\) 0.165972 0.165972i 0.00623762 0.00623762i
\(709\) −33.7593 19.4909i −1.26786 0.731998i −0.293275 0.956028i \(-0.594745\pi\)
−0.974582 + 0.224030i \(0.928078\pi\)
\(710\) 0 0
\(711\) 5.05868 + 8.76189i 0.189715 + 0.328597i
\(712\) 4.75415 + 17.7427i 0.178169 + 0.664937i
\(713\) −3.43581 3.43581i −0.128672 0.128672i
\(714\) 3.00000 0.337185i 0.112272 0.0126188i
\(715\) 0 0
\(716\) 9.57191 16.5790i 0.357719 0.619587i
\(717\) 11.9472 + 3.20124i 0.446176 + 0.119552i
\(718\) −4.21067 1.12824i −0.157141 0.0421057i
\(719\) 9.01794 15.6195i 0.336312 0.582510i −0.647424 0.762130i \(-0.724154\pi\)
0.983736 + 0.179620i \(0.0574869\pi\)
\(720\) 0 0
\(721\) −16.7011 22.6422i −0.621982 0.843239i
\(722\) −11.9398 11.9398i −0.444353 0.444353i
\(723\) −3.62053 13.5120i −0.134649 0.502517i
\(724\) −2.61380 4.52723i −0.0971411 0.168253i
\(725\) 0 0
\(726\) −1.11030 0.641033i −0.0412072 0.0237910i
\(727\) −34.0615 + 34.0615i −1.26327 + 1.26327i −0.313774 + 0.949498i \(0.601593\pi\)
−0.949498 + 0.313774i \(0.898407\pi\)
\(728\) 3.14737 + 8.02583i 0.116649 + 0.297457i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −9.00944 + 5.20160i −0.333226 + 0.192388i
\(732\) 2.20678 8.23581i 0.0815649 0.304404i
\(733\) 32.6701 8.75391i 1.20670 0.323333i 0.401231 0.915977i \(-0.368582\pi\)
0.805465 + 0.592644i \(0.201916\pi\)
\(734\) −18.5499 −0.684689
\(735\) 0 0
\(736\) −1.14103 −0.0420590
\(737\) −41.9324 + 11.2358i −1.54460 + 0.413874i
\(738\) −2.65507 + 9.90885i −0.0977344 + 0.364750i
\(739\) −15.9959 + 9.23522i −0.588418 + 0.339723i −0.764472 0.644657i \(-0.777000\pi\)
0.176054 + 0.984381i \(0.443667\pi\)
\(740\) 0 0
\(741\) 19.5192i 0.717057i
\(742\) 2.78442 + 7.10030i 0.102219 + 0.260660i
\(743\) 32.1999 32.1999i 1.18130 1.18130i 0.201894 0.979407i \(-0.435290\pi\)
0.979407 0.201894i \(-0.0647096\pi\)
\(744\) −3.68788 2.12920i −0.135204 0.0780601i
\(745\) 0 0
\(746\) −9.75961 16.9041i −0.357325 0.618905i
\(747\) −2.95039 11.0110i −0.107949 0.402871i
\(748\) 2.51519 + 2.51519i 0.0919643 + 0.0919643i
\(749\) −26.1130 35.4022i −0.954149 1.29357i
\(750\) 0 0
\(751\) 4.62208 8.00567i 0.168662 0.292131i −0.769288 0.638902i \(-0.779389\pi\)
0.937950 + 0.346771i \(0.112722\pi\)
\(752\) −4.11329 1.10215i −0.149996 0.0401914i
\(753\) 16.4532 + 4.40861i 0.599587 + 0.160659i
\(754\) 8.79673 15.2364i 0.320358 0.554876i
\(755\) 0 0
\(756\) 2.62920 0.295509i 0.0956230 0.0107476i
\(757\) −15.1284 15.1284i −0.549850 0.549850i 0.376548 0.926397i \(-0.377111\pi\)
−0.926397 + 0.376548i \(0.877111\pi\)
\(758\) 9.69081 + 36.1666i 0.351986 + 1.31363i
\(759\) 1.77851 + 3.08046i 0.0645557 + 0.111814i
\(760\) 0 0
\(761\) 32.4867 + 18.7562i 1.17764 + 0.679913i 0.955468 0.295094i \(-0.0953511\pi\)
0.222175 + 0.975007i \(0.428684\pi\)
\(762\) −0.705385 + 0.705385i −0.0255534 + 0.0255534i
\(763\) −29.4728 23.5170i −1.06699 0.851371i
\(764\) 10.2584i 0.371136i
\(765\) 0 0
\(766\) 0.522518 0.301676i 0.0188794 0.0109000i
\(767\) 0.197948 0.738750i 0.00714747 0.0266747i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) −0.469440 −0.0169285 −0.00846423 0.999964i \(-0.502694\pi\)
−0.00846423 + 0.999964i \(0.502694\pi\)
\(770\) 0 0
\(771\) 20.9862 0.755800
\(772\) −4.69340 + 1.25759i −0.168919 + 0.0452618i
\(773\) −6.66314 + 24.8672i −0.239656 + 0.894410i 0.736338 + 0.676614i \(0.236553\pi\)
−0.975994 + 0.217796i \(0.930113\pi\)
\(774\) −7.89587 + 4.55868i −0.283811 + 0.163858i
\(775\) 0 0
\(776\) 1.04735i 0.0375975i
\(777\) −14.1771 + 5.55960i −0.508600 + 0.199450i
\(778\) −14.3704 + 14.3704i −0.515202 + 0.515202i
\(779\) 53.2193 + 30.7262i 1.90678 + 1.10088i
\(780\) 0 0
\(781\) −2.71461 4.70184i −0.0971363 0.168245i
\(782\) 0.336971 + 1.25759i 0.0120501 + 0.0449714i