Properties

Label 78.2.g.a.47.3
Level $78$
Weight $2$
Character 78.47
Analytic conductor $0.623$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.58498535041007616.52
Defining polynomial: \( x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.3
Root \(-0.0980500 + 1.72927i\) of defining polynomial
Character \(\chi\) \(=\) 78.47
Dual form 78.2.g.a.5.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.339111 + 2.98077i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.29211 + 1.15345i) q^{3} -1.00000i q^{4} +(1.82732 - 1.82732i) q^{5} +(-1.72927 + 0.0980500i) q^{6} +(-2.63122 + 2.63122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.339111 + 2.98077i) q^{9} +2.58423i q^{10} +(-2.30690 - 2.30690i) q^{11} +(1.15345 - 1.29211i) q^{12} +(1.63122 - 3.21545i) q^{13} -3.72111i q^{14} +(4.46883 - 0.253383i) q^{15} -1.00000 q^{16} -1.34775 q^{17} +(-2.34751 - 1.86794i) q^{18} +(-3.58423 - 3.58423i) q^{19} +(-1.82732 - 1.82732i) q^{20} +(-6.43482 + 0.364855i) q^{21} +3.26245 q^{22} +3.65465 q^{23} +(0.0980500 + 1.72927i) q^{24} -1.67822i q^{25} +(1.12022 + 3.42711i) q^{26} +(-3.00000 + 4.24264i) q^{27} +(2.63122 + 2.63122i) q^{28} -3.65465i q^{29} +(-2.98077 + 3.33911i) q^{30} +(0.321779 + 0.321779i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.319883 - 5.64166i) q^{33} +(0.953002 - 0.953002i) q^{34} +9.61619i q^{35} +(2.98077 - 0.339111i) q^{36} +(1.95300 - 1.95300i) q^{37} +5.06886 q^{38} +(5.81658 - 2.27319i) q^{39} +2.58423 q^{40} +(-7.89729 + 7.89729i) q^{41} +(4.29211 - 4.80810i) q^{42} +9.10912i q^{43} +(-2.30690 + 2.30690i) q^{44} +(6.06650 + 4.82717i) q^{45} +(-2.58423 + 2.58423i) q^{46} +(4.72222 + 4.72222i) q^{47} +(-1.29211 - 1.15345i) q^{48} -6.84667i q^{49} +(1.18668 + 1.18668i) q^{50} +(-1.74144 - 1.55456i) q^{51} +(-3.21545 - 1.63122i) q^{52} -0.216838i q^{53} +(-0.878680 - 5.12132i) q^{54} -8.43090 q^{55} -3.72111 q^{56} +(-0.497002 - 8.76544i) q^{57} +(2.58423 + 2.58423i) q^{58} +(-3.65465 - 3.65465i) q^{59} +(-0.253383 - 4.46883i) q^{60} +6.52489 q^{61} -0.455064 q^{62} +(-8.73535 - 6.95080i) q^{63} +1.00000i q^{64} +(-2.89489 - 8.85644i) q^{65} +(4.21545 + 3.76307i) q^{66} +(2.26245 + 2.26245i) q^{67} +1.34775i q^{68} +(4.72222 + 4.21545i) q^{69} +(-6.79967 - 6.79967i) q^{70} +(0.108419 - 0.108419i) q^{71} +(-1.86794 + 2.34751i) q^{72} +(-3.58423 + 3.58423i) q^{73} +2.76196i q^{74} +(1.93574 - 2.16845i) q^{75} +(-3.58423 + 3.58423i) q^{76} +12.1399 q^{77} +(-2.50556 + 5.72033i) q^{78} +4.09400 q^{79} +(-1.82732 + 1.82732i) q^{80} +(-8.77001 + 2.02162i) q^{81} -11.1685i q^{82} +(10.5753 - 10.5753i) q^{83} +(0.364855 + 6.43482i) q^{84} +(-2.46277 + 2.46277i) q^{85} +(-6.44112 - 6.44112i) q^{86} +(4.21545 - 4.72222i) q^{87} -3.26245i q^{88} +(8.85644 + 8.85644i) q^{89} +(-7.70299 + 0.876338i) q^{90} +(4.16845 + 12.7527i) q^{91} -3.65465i q^{92} +(0.0446190 + 0.786930i) q^{93} -6.67822 q^{94} -13.0991 q^{95} +(1.72927 - 0.0980500i) q^{96} +(0.168451 + 0.168451i) q^{97} +(4.84133 + 4.84133i) q^{98} +(6.09404 - 7.65863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.29211 + 1.15345i 0.746002 + 0.665944i
\(4\) 1.00000i 0.500000i
\(5\) 1.82732 1.82732i 0.817204 0.817204i −0.168498 0.985702i \(-0.553892\pi\)
0.985702 + 0.168498i \(0.0538917\pi\)
\(6\) −1.72927 + 0.0980500i −0.705973 + 0.0400288i
\(7\) −2.63122 + 2.63122i −0.994509 + 0.994509i −0.999985 0.00547608i \(-0.998257\pi\)
0.00547608 + 0.999985i \(0.498257\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.339111 + 2.98077i 0.113037 + 0.993591i
\(10\) 2.58423i 0.817204i
\(11\) −2.30690 2.30690i −0.695556 0.695556i 0.267893 0.963449i \(-0.413673\pi\)
−0.963449 + 0.267893i \(0.913673\pi\)
\(12\) 1.15345 1.29211i 0.332972 0.373001i
\(13\) 1.63122 3.21545i 0.452420 0.891805i
\(14\) 3.72111i 0.994509i
\(15\) 4.46883 0.253383i 1.15385 0.0654233i
\(16\) −1.00000 −0.250000
\(17\) −1.34775 −0.326877 −0.163439 0.986554i \(-0.552259\pi\)
−0.163439 + 0.986554i \(0.552259\pi\)
\(18\) −2.34751 1.86794i −0.553314 0.440277i
\(19\) −3.58423 3.58423i −0.822278 0.822278i 0.164157 0.986434i \(-0.447510\pi\)
−0.986434 + 0.164157i \(0.947510\pi\)
\(20\) −1.82732 1.82732i −0.408602 0.408602i
\(21\) −6.43482 + 0.364855i −1.40419 + 0.0796179i
\(22\) 3.26245 0.695556
\(23\) 3.65465 0.762047 0.381023 0.924565i \(-0.375572\pi\)
0.381023 + 0.924565i \(0.375572\pi\)
\(24\) 0.0980500 + 1.72927i 0.0200144 + 0.352986i
\(25\) 1.67822i 0.335644i
\(26\) 1.12022 + 3.42711i 0.219693 + 0.672112i
\(27\) −3.00000 + 4.24264i −0.577350 + 0.816497i
\(28\) 2.63122 + 2.63122i 0.497254 + 0.497254i
\(29\) 3.65465i 0.678651i −0.940669 0.339325i \(-0.889801\pi\)
0.940669 0.339325i \(-0.110199\pi\)
\(30\) −2.98077 + 3.33911i −0.544212 + 0.609635i
\(31\) 0.321779 + 0.321779i 0.0577932 + 0.0577932i 0.735413 0.677619i \(-0.236988\pi\)
−0.677619 + 0.735413i \(0.736988\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.319883 5.64166i −0.0556845 0.982087i
\(34\) 0.953002 0.953002i 0.163439 0.163439i
\(35\) 9.61619i 1.62543i
\(36\) 2.98077 0.339111i 0.496795 0.0565184i
\(37\) 1.95300 1.95300i 0.321072 0.321072i −0.528107 0.849178i \(-0.677098\pi\)
0.849178 + 0.528107i \(0.177098\pi\)
\(38\) 5.06886 0.822278
\(39\) 5.81658 2.27319i 0.931398 0.364002i
\(40\) 2.58423 0.408602
\(41\) −7.89729 + 7.89729i −1.23335 + 1.23335i −0.270680 + 0.962670i \(0.587248\pi\)
−0.962670 + 0.270680i \(0.912752\pi\)
\(42\) 4.29211 4.80810i 0.662287 0.741905i
\(43\) 9.10912i 1.38913i 0.719431 + 0.694564i \(0.244403\pi\)
−0.719431 + 0.694564i \(0.755597\pi\)
\(44\) −2.30690 + 2.30690i −0.347778 + 0.347778i
\(45\) 6.06650 + 4.82717i 0.904340 + 0.719592i
\(46\) −2.58423 + 2.58423i −0.381023 + 0.381023i
\(47\) 4.72222 + 4.72222i 0.688806 + 0.688806i 0.961968 0.273162i \(-0.0880695\pi\)
−0.273162 + 0.961968i \(0.588070\pi\)
\(48\) −1.29211 1.15345i −0.186500 0.166486i
\(49\) 6.84667i 0.978096i
\(50\) 1.18668 + 1.18668i 0.167822 + 0.167822i
\(51\) −1.74144 1.55456i −0.243851 0.217682i
\(52\) −3.21545 1.63122i −0.445903 0.226210i
\(53\) 0.216838i 0.0297851i −0.999889 0.0148925i \(-0.995259\pi\)
0.999889 0.0148925i \(-0.00474061\pi\)
\(54\) −0.878680 5.12132i −0.119573 0.696923i
\(55\) −8.43090 −1.13682
\(56\) −3.72111 −0.497254
\(57\) −0.497002 8.76544i −0.0658295 1.16101i
\(58\) 2.58423 + 2.58423i 0.339325 + 0.339325i
\(59\) −3.65465 3.65465i −0.475794 0.475794i 0.427989 0.903784i \(-0.359222\pi\)
−0.903784 + 0.427989i \(0.859222\pi\)
\(60\) −0.253383 4.46883i −0.0327117 0.576924i
\(61\) 6.52489 0.835427 0.417713 0.908579i \(-0.362832\pi\)
0.417713 + 0.908579i \(0.362832\pi\)
\(62\) −0.455064 −0.0577932
\(63\) −8.73535 6.95080i −1.10055 0.875719i
\(64\) 1.00000i 0.125000i
\(65\) −2.89489 8.85644i −0.359067 1.09851i
\(66\) 4.21545 + 3.76307i 0.518886 + 0.463201i
\(67\) 2.26245 + 2.26245i 0.276402 + 0.276402i 0.831671 0.555269i \(-0.187385\pi\)
−0.555269 + 0.831671i \(0.687385\pi\)
\(68\) 1.34775i 0.163439i
\(69\) 4.72222 + 4.21545i 0.568488 + 0.507480i
\(70\) −6.79967 6.79967i −0.812717 0.812717i
\(71\) 0.108419 0.108419i 0.0128670 0.0128670i −0.700644 0.713511i \(-0.747104\pi\)
0.713511 + 0.700644i \(0.247104\pi\)
\(72\) −1.86794 + 2.34751i −0.220138 + 0.276657i
\(73\) −3.58423 + 3.58423i −0.419502 + 0.419502i −0.885032 0.465530i \(-0.845864\pi\)
0.465530 + 0.885032i \(0.345864\pi\)
\(74\) 2.76196i 0.321072i
\(75\) 1.93574 2.16845i 0.223520 0.250391i
\(76\) −3.58423 + 3.58423i −0.411139 + 0.411139i
\(77\) 12.1399 1.38347
\(78\) −2.50556 + 5.72033i −0.283698 + 0.647700i
\(79\) 4.09400 0.460611 0.230305 0.973118i \(-0.426028\pi\)
0.230305 + 0.973118i \(0.426028\pi\)
\(80\) −1.82732 + 1.82732i −0.204301 + 0.204301i
\(81\) −8.77001 + 2.02162i −0.974445 + 0.224625i
\(82\) 11.1685i 1.23335i
\(83\) 10.5753 10.5753i 1.16079 1.16079i 0.176492 0.984302i \(-0.443525\pi\)
0.984302 0.176492i \(-0.0564751\pi\)
\(84\) 0.364855 + 6.43482i 0.0398090 + 0.702096i
\(85\) −2.46277 + 2.46277i −0.267125 + 0.267125i
\(86\) −6.44112 6.44112i −0.694564 0.694564i
\(87\) 4.21545 4.72222i 0.451944 0.506275i
\(88\) 3.26245i 0.347778i
\(89\) 8.85644 + 8.85644i 0.938780 + 0.938780i 0.998231 0.0594508i \(-0.0189349\pi\)
−0.0594508 + 0.998231i \(0.518935\pi\)
\(90\) −7.70299 + 0.876338i −0.811966 + 0.0923742i
\(91\) 4.16845 + 12.7527i 0.436972 + 1.33684i
\(92\) 3.65465i 0.381023i
\(93\) 0.0446190 + 0.786930i 0.00462678 + 0.0816008i
\(94\) −6.67822 −0.688806
\(95\) −13.0991 −1.34394
\(96\) 1.72927 0.0980500i 0.176493 0.0100072i
\(97\) 0.168451 + 0.168451i 0.0171036 + 0.0171036i 0.715607 0.698503i \(-0.246150\pi\)
−0.698503 + 0.715607i \(0.746150\pi\)
\(98\) 4.84133 + 4.84133i 0.489048 + 0.489048i
\(99\) 6.09404 7.65863i 0.612475 0.769721i
\(100\) −1.67822 −0.167822
\(101\) −17.7129 −1.76250 −0.881248 0.472653i \(-0.843296\pi\)
−0.881248 + 0.472653i \(0.843296\pi\)
\(102\) 2.33063 0.132147i 0.230766 0.0130845i
\(103\) 7.90600i 0.779002i −0.921026 0.389501i \(-0.872648\pi\)
0.921026 0.389501i \(-0.127352\pi\)
\(104\) 3.42711 1.12022i 0.336056 0.109846i
\(105\) −11.0918 + 12.4252i −1.08245 + 1.21258i
\(106\) 0.153328 + 0.153328i 0.0148925 + 0.0148925i
\(107\) 4.61380i 0.446033i 0.974815 + 0.223016i \(0.0715903\pi\)
−0.974815 + 0.223016i \(0.928410\pi\)
\(108\) 4.24264 + 3.00000i 0.408248 + 0.288675i
\(109\) 9.21545 + 9.21545i 0.882680 + 0.882680i 0.993806 0.111126i \(-0.0354458\pi\)
−0.111126 + 0.993806i \(0.535446\pi\)
\(110\) 5.96154 5.96154i 0.568411 0.568411i
\(111\) 4.77619 0.270810i 0.453336 0.0257042i
\(112\) 2.63122 2.63122i 0.248627 0.248627i
\(113\) 3.43781i 0.323402i −0.986840 0.161701i \(-0.948302\pi\)
0.986840 0.161701i \(-0.0516980\pi\)
\(114\) 6.54954 + 5.84667i 0.613421 + 0.547591i
\(115\) 6.67822 6.67822i 0.622747 0.622747i
\(116\) −3.65465 −0.339325
\(117\) 10.1377 + 3.77191i 0.937229 + 0.348713i
\(118\) 5.16845 0.475794
\(119\) 3.54623 3.54623i 0.325082 0.325082i
\(120\) 3.33911 + 2.98077i 0.304818 + 0.272106i
\(121\) 0.356442i 0.0324038i
\(122\) −4.61380 + 4.61380i −0.417713 + 0.417713i
\(123\) −19.3133 + 1.09507i −1.74142 + 0.0987389i
\(124\) 0.321779 0.321779i 0.0288966 0.0288966i
\(125\) 6.06996 + 6.06996i 0.542914 + 0.542914i
\(126\) 11.0918 1.26187i 0.988135 0.112416i
\(127\) 11.0745i 0.982699i −0.870962 0.491349i \(-0.836504\pi\)
0.870962 0.491349i \(-0.163496\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −10.5069 + 11.7700i −0.925081 + 1.03629i
\(130\) 8.30944 + 4.21545i 0.728786 + 0.369719i
\(131\) 18.1015i 1.58153i −0.612118 0.790767i \(-0.709682\pi\)
0.612118 0.790767i \(-0.290318\pi\)
\(132\) −5.64166 + 0.319883i −0.491044 + 0.0278422i
\(133\) 18.8618 1.63553
\(134\) −3.19958 −0.276402
\(135\) 2.27071 + 13.2346i 0.195431 + 1.13906i
\(136\) −0.953002 0.953002i −0.0817193 0.0817193i
\(137\) 0.976593 + 0.976593i 0.0834360 + 0.0834360i 0.747593 0.664157i \(-0.231209\pi\)
−0.664157 + 0.747593i \(0.731209\pi\)
\(138\) −6.31988 + 0.358338i −0.537984 + 0.0305038i
\(139\) −7.10912 −0.602988 −0.301494 0.953468i \(-0.597485\pi\)
−0.301494 + 0.953468i \(0.597485\pi\)
\(140\) 9.61619 0.812717
\(141\) 0.654800 + 11.5485i 0.0551441 + 0.972557i
\(142\) 0.153328i 0.0128670i
\(143\) −11.1808 + 3.65465i −0.934984 + 0.305617i
\(144\) −0.339111 2.98077i −0.0282592 0.248398i
\(145\) −6.67822 6.67822i −0.554596 0.554596i
\(146\) 5.06886i 0.419502i
\(147\) 7.89729 8.84667i 0.651357 0.729661i
\(148\) −1.95300 1.95300i −0.160536 0.160536i
\(149\) 8.85644 8.85644i 0.725548 0.725548i −0.244182 0.969729i \(-0.578519\pi\)
0.969729 + 0.244182i \(0.0785194\pi\)
\(150\) 0.164550 + 2.90210i 0.0134354 + 0.236956i
\(151\) −11.7997 + 11.7997i −0.960244 + 0.960244i −0.999239 0.0389955i \(-0.987584\pi\)
0.0389955 + 0.999239i \(0.487584\pi\)
\(152\) 5.06886i 0.411139i
\(153\) −0.457036 4.01733i −0.0369492 0.324782i
\(154\) −8.58423 + 8.58423i −0.691737 + 0.691737i
\(155\) 1.17599 0.0944576
\(156\) −2.27319 5.81658i −0.182001 0.465699i
\(157\) −18.8618 −1.50534 −0.752668 0.658401i \(-0.771233\pi\)
−0.752668 + 0.658401i \(0.771233\pi\)
\(158\) −2.89489 + 2.89489i −0.230305 + 0.230305i
\(159\) 0.250112 0.280180i 0.0198352 0.0222197i
\(160\) 2.58423i 0.204301i
\(161\) −9.61619 + 9.61619i −0.757862 + 0.757862i
\(162\) 4.77183 7.63084i 0.374910 0.599535i
\(163\) −2.81201 + 2.81201i −0.220254 + 0.220254i −0.808605 0.588352i \(-0.799777\pi\)
0.588352 + 0.808605i \(0.299777\pi\)
\(164\) 7.89729 + 7.89729i 0.616675 + 0.616675i
\(165\) −10.8937 9.72461i −0.848071 0.757060i
\(166\) 14.9558i 1.16079i
\(167\) −0.959150 0.959150i −0.0742212 0.0742212i 0.669022 0.743243i \(-0.266713\pi\)
−0.743243 + 0.669022i \(0.766713\pi\)
\(168\) −4.80810 4.29211i −0.370953 0.331144i
\(169\) −7.67822 10.4902i −0.590632 0.806941i
\(170\) 3.48289i 0.267125i
\(171\) 9.46831 11.8992i 0.724060 0.909955i
\(172\) 9.10912 0.694564
\(173\) 17.4960 1.33020 0.665099 0.746755i \(-0.268389\pi\)
0.665099 + 0.746755i \(0.268389\pi\)
\(174\) 0.358338 + 6.31988i 0.0271655 + 0.479109i
\(175\) 4.41577 + 4.41577i 0.333801 + 0.333801i
\(176\) 2.30690 + 2.30690i 0.173889 + 0.173889i
\(177\) −0.506767 8.93766i −0.0380909 0.671796i
\(178\) −12.5249 −0.938780
\(179\) −18.1015 −1.35297 −0.676484 0.736458i \(-0.736497\pi\)
−0.676484 + 0.736458i \(0.736497\pi\)
\(180\) 4.82717 6.06650i 0.359796 0.452170i
\(181\) 1.90600i 0.141672i −0.997488 0.0708361i \(-0.977433\pi\)
0.997488 0.0708361i \(-0.0225667\pi\)
\(182\) −11.9650 6.06996i −0.886908 0.449936i
\(183\) 8.43090 + 7.52613i 0.623230 + 0.556348i
\(184\) 2.58423 + 2.58423i 0.190512 + 0.190512i
\(185\) 7.13753i 0.524762i
\(186\) −0.587994 0.524893i −0.0431138 0.0384870i
\(187\) 3.10912 + 3.10912i 0.227361 + 0.227361i
\(188\) 4.72222 4.72222i 0.344403 0.344403i
\(189\) −3.26967 19.0570i −0.237833 1.38619i
\(190\) 9.26245 9.26245i 0.671969 0.671969i
\(191\) 6.35014i 0.459480i −0.973252 0.229740i \(-0.926212\pi\)
0.973252 0.229740i \(-0.0737876\pi\)
\(192\) −1.15345 + 1.29211i −0.0832430 + 0.0932502i
\(193\) −4.26245 + 4.26245i −0.306818 + 0.306818i −0.843674 0.536856i \(-0.819612\pi\)
0.536856 + 0.843674i \(0.319612\pi\)
\(194\) −0.238226 −0.0171036
\(195\) 6.47492 14.7826i 0.463679 1.05861i
\(196\) −6.84667 −0.489048
\(197\) −2.78647 + 2.78647i −0.198528 + 0.198528i −0.799369 0.600841i \(-0.794833\pi\)
0.600841 + 0.799369i \(0.294833\pi\)
\(198\) 1.10633 + 9.72461i 0.0786235 + 0.691098i
\(199\) 17.2927i 1.22585i −0.790142 0.612923i \(-0.789993\pi\)
0.790142 0.612923i \(-0.210007\pi\)
\(200\) 1.18668 1.18668i 0.0839111 0.0839111i
\(201\) 0.313719 + 5.53295i 0.0221280 + 0.390264i
\(202\) 12.5249 12.5249i 0.881248 0.881248i
\(203\) 9.61619 + 9.61619i 0.674924 + 0.674924i
\(204\) −1.55456 + 1.74144i −0.108841 + 0.121925i
\(205\) 28.8618i 2.01580i
\(206\) 5.59039 + 5.59039i 0.389501 + 0.389501i
\(207\) 1.23933 + 10.8937i 0.0861393 + 0.757162i
\(208\) −1.63122 + 3.21545i −0.113105 + 0.222951i
\(209\) 16.5369i 1.14388i
\(210\) −0.942868 16.6290i −0.0650641 1.14751i
\(211\) 9.41577 0.648209 0.324104 0.946021i \(-0.394937\pi\)
0.324104 + 0.946021i \(0.394937\pi\)
\(212\) −0.216838 −0.0148925
\(213\) 0.265146 0.0150338i 0.0181675 0.00103010i
\(214\) −3.26245 3.26245i −0.223016 0.223016i
\(215\) 16.6453 + 16.6453i 1.13520 + 1.13520i
\(216\) −5.12132 + 0.878680i −0.348462 + 0.0597866i
\(217\) −1.69334 −0.114952
\(218\) −13.0326 −0.882680
\(219\) −8.76544 + 0.497002i −0.592314 + 0.0335843i
\(220\) 8.43090i 0.568411i
\(221\) −2.19848 + 4.33362i −0.147886 + 0.291511i
\(222\) −3.18578 + 3.56877i −0.213816 + 0.239520i
\(223\) −5.89367 5.89367i −0.394669 0.394669i 0.481679 0.876348i \(-0.340027\pi\)
−0.876348 + 0.481679i \(0.840027\pi\)
\(224\) 3.72111i 0.248627i
\(225\) 5.00240 0.569103i 0.333493 0.0379402i
\(226\) 2.43090 + 2.43090i 0.161701 + 0.161701i
\(227\) −9.22759 + 9.22759i −0.612457 + 0.612457i −0.943586 0.331129i \(-0.892571\pi\)
0.331129 + 0.943586i \(0.392571\pi\)
\(228\) −8.76544 + 0.497002i −0.580506 + 0.0329148i
\(229\) 9.21545 9.21545i 0.608974 0.608974i −0.333704 0.942678i \(-0.608299\pi\)
0.942678 + 0.333704i \(0.108299\pi\)
\(230\) 9.44443i 0.622747i
\(231\) 15.6862 + 14.0028i 1.03207 + 0.921316i
\(232\) 2.58423 2.58423i 0.169663 0.169663i
\(233\) −2.52374 −0.165335 −0.0826677 0.996577i \(-0.526344\pi\)
−0.0826677 + 0.996577i \(0.526344\pi\)
\(234\) −9.83557 + 4.50128i −0.642971 + 0.294258i
\(235\) 17.2580 1.12579
\(236\) −3.65465 + 3.65465i −0.237897 + 0.237897i
\(237\) 5.28990 + 4.72222i 0.343616 + 0.306741i
\(238\) 5.01512i 0.325082i
\(239\) −7.20087 + 7.20087i −0.465786 + 0.465786i −0.900546 0.434760i \(-0.856833\pi\)
0.434760 + 0.900546i \(0.356833\pi\)
\(240\) −4.46883 + 0.253383i −0.288462 + 0.0163558i
\(241\) 20.4460 20.4460i 1.31704 1.31704i 0.400939 0.916105i \(-0.368684\pi\)
0.916105 0.400939i \(-0.131316\pi\)
\(242\) 0.252043 + 0.252043i 0.0162019 + 0.0162019i
\(243\) −13.6637 7.50359i −0.876525 0.481356i
\(244\) 6.52489i 0.417713i
\(245\) −12.5111 12.5111i −0.799304 0.799304i
\(246\) 12.8822 14.4309i 0.821342 0.920080i
\(247\) −17.3716 + 5.67822i −1.10533 + 0.361297i
\(248\) 0.455064i 0.0288966i
\(249\) 25.8626 1.46642i 1.63898 0.0929303i
\(250\) −8.58423 −0.542914
\(251\) 18.4901 1.16708 0.583541 0.812083i \(-0.301667\pi\)
0.583541 + 0.812083i \(0.301667\pi\)
\(252\) −6.95080 + 8.73535i −0.437859 + 0.550276i
\(253\) −8.43090 8.43090i −0.530046 0.530046i
\(254\) 7.83082 + 7.83082i 0.491349 + 0.491349i
\(255\) −6.02286 + 0.341497i −0.377166 + 0.0213854i
\(256\) 1.00000 0.0625000
\(257\) 13.6696 0.852688 0.426344 0.904561i \(-0.359801\pi\)
0.426344 + 0.904561i \(0.359801\pi\)
\(258\) −0.893149 15.7522i −0.0556050 0.980686i
\(259\) 10.2776i 0.638617i
\(260\) −8.85644 + 2.89489i −0.549253 + 0.179534i
\(261\) 10.8937 1.23933i 0.674301 0.0767126i
\(262\) 12.7997 + 12.7997i 0.790767 + 0.790767i
\(263\) 14.6186i 0.901421i 0.892670 + 0.450710i \(0.148829\pi\)
−0.892670 + 0.450710i \(0.851171\pi\)
\(264\) 3.76307 4.21545i 0.231601 0.259443i
\(265\) −0.396234 0.396234i −0.0243405 0.0243405i
\(266\) −13.3373 + 13.3373i −0.817763 + 0.817763i
\(267\) 1.22807 + 21.6590i 0.0751564 + 1.32551i
\(268\) 2.26245 2.26245i 0.138201 0.138201i
\(269\) 15.7946i 0.963012i −0.876443 0.481506i \(-0.840090\pi\)
0.876443 0.481506i \(-0.159910\pi\)
\(270\) −10.9639 7.75268i −0.667244 0.471813i
\(271\) 16.2306 16.2306i 0.985937 0.985937i −0.0139655 0.999902i \(-0.504445\pi\)
0.999902 + 0.0139655i \(0.00444549\pi\)
\(272\) 1.34775 0.0817193
\(273\) −9.32345 + 21.2860i −0.564281 + 1.28829i
\(274\) −1.38111 −0.0834360
\(275\) −3.87149 + 3.87149i −0.233459 + 0.233459i
\(276\) 4.21545 4.72222i 0.253740 0.284244i
\(277\) 26.1489i 1.57114i 0.618775 + 0.785568i \(0.287629\pi\)
−0.618775 + 0.785568i \(0.712371\pi\)
\(278\) 5.02691 5.02691i 0.301494 0.301494i
\(279\) −0.850031 + 1.06827i −0.0508900 + 0.0639555i
\(280\) −6.79967 + 6.79967i −0.406358 + 0.406358i
\(281\) −3.06665 3.06665i −0.182941 0.182941i 0.609695 0.792636i \(-0.291292\pi\)
−0.792636 + 0.609695i \(0.791292\pi\)
\(282\) −8.62901 7.70299i −0.513850 0.458706i
\(283\) 9.35644i 0.556183i −0.960555 0.278091i \(-0.910298\pi\)
0.960555 0.278091i \(-0.0897018\pi\)
\(284\) −0.108419 0.108419i −0.00643350 0.00643350i
\(285\) −16.9255 15.1091i −1.00258 0.894987i
\(286\) 5.32178 10.4902i 0.314683 0.620300i
\(287\) 41.5591i 2.45315i
\(288\) 2.34751 + 1.86794i 0.138328 + 0.110069i
\(289\) −15.1836 −0.893151
\(290\) 9.44443 0.554596
\(291\) 0.0233580 + 0.411957i 0.00136927 + 0.0241493i
\(292\) 3.58423 + 3.58423i 0.209751 + 0.209751i
\(293\) −3.00331 3.00331i −0.175455 0.175455i 0.613916 0.789371i \(-0.289593\pi\)
−0.789371 + 0.613916i \(0.789593\pi\)
\(294\) 0.671316 + 11.8398i 0.0391520 + 0.690509i
\(295\) −13.3564 −0.777642
\(296\) 2.76196 0.160536
\(297\) 16.7080 2.86665i 0.969498 0.166340i
\(298\) 12.5249i 0.725548i
\(299\) 5.96154 11.7513i 0.344765 0.679597i
\(300\) −2.16845 1.93574i −0.125196 0.111760i
\(301\) −23.9681 23.9681i −1.38150 1.38150i
\(302\) 16.6873i 0.960244i
\(303\) −22.8870 20.4309i −1.31483 1.17372i
\(304\) 3.58423 + 3.58423i 0.205569 + 0.205569i
\(305\) 11.9231 11.9231i 0.682714 0.682714i
\(306\) 3.16386 + 2.51751i 0.180866 + 0.143916i
\(307\) −3.24732 + 3.24732i −0.185335 + 0.185335i −0.793676 0.608341i \(-0.791835\pi\)
0.608341 + 0.793676i \(0.291835\pi\)
\(308\) 12.1399i 0.691737i
\(309\) 9.11917 10.2154i 0.518772 0.581137i
\(310\) −0.831549 + 0.831549i −0.0472288 + 0.0472288i
\(311\) −3.43781 −0.194940 −0.0974701 0.995238i \(-0.531075\pi\)
−0.0974701 + 0.995238i \(0.531075\pi\)
\(312\) 5.72033 + 2.50556i 0.323850 + 0.141849i
\(313\) 1.50977 0.0853373 0.0426686 0.999089i \(-0.486414\pi\)
0.0426686 + 0.999089i \(0.486414\pi\)
\(314\) 13.3373 13.3373i 0.752668 0.752668i
\(315\) −28.6637 + 3.26095i −1.61502 + 0.183734i
\(316\) 4.09400i 0.230305i
\(317\) −16.1657 + 16.1657i −0.907958 + 0.907958i −0.996107 0.0881494i \(-0.971905\pi\)
0.0881494 + 0.996107i \(0.471905\pi\)
\(318\) 0.0212610 + 0.374973i 0.00119226 + 0.0210274i
\(319\) −8.43090 + 8.43090i −0.472040 + 0.472040i
\(320\) 1.82732 + 1.82732i 0.102150 + 0.102150i
\(321\) −5.32178 + 5.96154i −0.297033 + 0.332741i
\(322\) 13.5993i 0.757862i
\(323\) 4.83063 + 4.83063i 0.268784 + 0.268784i
\(324\) 2.02162 + 8.77001i 0.112312 + 0.487223i
\(325\) −5.39623 2.73755i −0.299329 0.151852i
\(326\) 3.97678i 0.220254i
\(327\) 1.27785 + 22.5369i 0.0706652 + 1.24630i
\(328\) −11.1685 −0.616675
\(329\) −24.8504 −1.37005
\(330\) 14.5793 0.826650i 0.802565 0.0455056i
\(331\) 5.52489 + 5.52489i 0.303676 + 0.303676i 0.842450 0.538774i \(-0.181112\pi\)
−0.538774 + 0.842450i \(0.681112\pi\)
\(332\) −10.5753 10.5753i −0.580397 0.580397i
\(333\) 6.48374 + 5.15917i 0.355307 + 0.282721i
\(334\) 1.35644 0.0742212
\(335\) 8.26844 0.451753
\(336\) 6.43482 0.364855i 0.351048 0.0199045i
\(337\) 18.8271i 1.02558i 0.858514 + 0.512790i \(0.171388\pi\)
−0.858514 + 0.512790i \(0.828612\pi\)
\(338\) 12.8470 + 1.98839i 0.698787 + 0.108154i
\(339\) 3.96534 4.44204i 0.215368 0.241258i
\(340\) 2.46277 + 2.46277i 0.133563 + 0.133563i
\(341\) 1.48462i 0.0803968i
\(342\) 1.71890 + 15.1091i 0.0929477 + 0.817008i
\(343\) −0.403440 0.403440i −0.0217837 0.0217837i
\(344\) −6.44112 + 6.44112i −0.347282 + 0.347282i
\(345\) 16.3320 0.926027i 0.879285 0.0498556i
\(346\) −12.3716 + 12.3716i −0.665099 + 0.665099i
\(347\) 29.2823i 1.57195i 0.618256 + 0.785977i \(0.287840\pi\)
−0.618256 + 0.785977i \(0.712160\pi\)
\(348\) −4.72222 4.21545i −0.253137 0.225972i
\(349\) 4.87855 4.87855i 0.261143 0.261143i −0.564376 0.825518i \(-0.690883\pi\)
0.825518 + 0.564376i \(0.190883\pi\)
\(350\) −6.24485 −0.333801
\(351\) 8.74832 + 16.5670i 0.466951 + 0.884283i
\(352\) −3.26245 −0.173889
\(353\) 5.59039 5.59039i 0.297546 0.297546i −0.542506 0.840052i \(-0.682524\pi\)
0.840052 + 0.542506i \(0.182524\pi\)
\(354\) 6.67822 + 5.96154i 0.354943 + 0.316853i
\(355\) 0.396234i 0.0210299i
\(356\) 8.85644 8.85644i 0.469390 0.469390i
\(357\) 8.67252 0.491733i 0.458998 0.0260253i
\(358\) 12.7997 12.7997i 0.676484 0.676484i
\(359\) −12.8822 12.8822i −0.679899 0.679899i 0.280079 0.959977i \(-0.409639\pi\)
−0.959977 + 0.280079i \(0.909639\pi\)
\(360\) 0.876338 + 7.70299i 0.0461871 + 0.405983i
\(361\) 6.69334i 0.352281i
\(362\) 1.34775 + 1.34775i 0.0708361 + 0.0708361i
\(363\) 0.411138 0.460564i 0.0215791 0.0241733i
\(364\) 12.7527 4.16845i 0.668422 0.218486i
\(365\) 13.0991i 0.685637i
\(366\) −11.2833 + 0.639766i −0.589789 + 0.0334411i
\(367\) 7.56910 0.395104 0.197552 0.980292i \(-0.436701\pi\)
0.197552 + 0.980292i \(0.436701\pi\)
\(368\) −3.65465 −0.190512
\(369\) −26.2181 20.8620i −1.36486 1.08603i
\(370\) 5.04700 + 5.04700i 0.262381 + 0.262381i
\(371\) 0.570551 + 0.570551i 0.0296215 + 0.0296215i
\(372\) 0.786930 0.0446190i 0.0408004 0.00231339i
\(373\) 15.8120 0.818715 0.409357 0.912374i \(-0.365753\pi\)
0.409357 + 0.912374i \(0.365753\pi\)
\(374\) −4.39696 −0.227361
\(375\) 0.841683 + 14.8445i 0.0434643 + 0.766565i
\(376\) 6.67822i 0.344403i
\(377\) −11.7513 5.96154i −0.605224 0.307035i
\(378\) 15.7873 + 11.1633i 0.812013 + 0.574180i
\(379\) 5.33690 + 5.33690i 0.274138 + 0.274138i 0.830764 0.556625i \(-0.187904\pi\)
−0.556625 + 0.830764i \(0.687904\pi\)
\(380\) 13.0991i 0.671969i
\(381\) 12.7738 14.3094i 0.654423 0.733095i
\(382\) 4.49023 + 4.49023i 0.229740 + 0.229740i
\(383\) 10.8555 10.8555i 0.554691 0.554691i −0.373100 0.927791i \(-0.621705\pi\)
0.927791 + 0.373100i \(0.121705\pi\)
\(384\) −0.0980500 1.72927i −0.00500359 0.0882466i
\(385\) 22.1836 22.1836i 1.13058 1.13058i
\(386\) 6.02801i 0.306818i
\(387\) −27.1522 + 3.08900i −1.38022 + 0.157023i
\(388\) 0.168451 0.168451i 0.00855180 0.00855180i
\(389\) 4.61380 0.233929 0.116964 0.993136i \(-0.462684\pi\)
0.116964 + 0.993136i \(0.462684\pi\)
\(390\) 5.87443 + 15.0314i 0.297464 + 0.761142i
\(391\) −4.92554 −0.249096
\(392\) 4.84133 4.84133i 0.244524 0.244524i
\(393\) 20.8791 23.3891i 1.05321 1.17983i
\(394\) 3.94067i 0.198528i
\(395\) 7.48105 7.48105i 0.376413 0.376413i
\(396\) −7.65863 6.09404i −0.384861 0.306237i
\(397\) −12.5400 + 12.5400i −0.629365 + 0.629365i −0.947908 0.318543i \(-0.896806\pi\)
0.318543 + 0.947908i \(0.396806\pi\)
\(398\) 12.2278 + 12.2278i 0.612923 + 0.612923i
\(399\) 24.3716 + 21.7561i 1.22010 + 1.08917i
\(400\) 1.67822i 0.0839111i
\(401\) 3.63720 + 3.63720i 0.181633 + 0.181633i 0.792067 0.610434i \(-0.209005\pi\)
−0.610434 + 0.792067i \(0.709005\pi\)
\(402\) −4.13422 3.69056i −0.206196 0.184068i
\(403\) 1.55956 0.509770i 0.0776870 0.0253935i
\(404\) 17.7129i 0.881248i
\(405\) −12.3315 + 19.7198i −0.612756 + 0.979885i
\(406\) −13.5993 −0.674924
\(407\) −9.01075 −0.446646
\(408\) −0.132147 2.33063i −0.00654224 0.115383i
\(409\) 18.5993 + 18.5993i 0.919679 + 0.919679i 0.997006 0.0773272i \(-0.0246386\pi\)
−0.0773272 + 0.997006i \(0.524639\pi\)
\(410\) −20.4084 20.4084i −1.00790 1.00790i
\(411\) 0.135418 + 2.38832i 0.00667968 + 0.117807i
\(412\) −7.90600 −0.389501
\(413\) 19.2324 0.946364
\(414\) −8.57933 6.82665i −0.421651 0.335512i
\(415\) 38.6491i 1.89721i
\(416\) −1.12022 3.42711i −0.0549231 0.168028i
\(417\) −9.18578 8.20001i −0.449830 0.401556i
\(418\) −11.6933 11.6933i −0.571940 0.571940i
\(419\) 0.353712i 0.0172800i 0.999963 + 0.00863998i \(0.00275023\pi\)
−0.999963 + 0.00863998i \(0.997250\pi\)
\(420\) 12.4252 + 11.0918i 0.606288 + 0.541224i
\(421\) −22.9088 22.9088i −1.11651 1.11651i −0.992250 0.124256i \(-0.960346\pi\)
−0.124256 0.992250i \(-0.539654\pi\)
\(422\) −6.65796 + 6.65796i −0.324104 + 0.324104i
\(423\) −12.4745 + 15.6772i −0.606531 + 0.762252i
\(424\) 0.153328 0.153328i 0.00744626 0.00744626i
\(425\) 2.26182i 0.109714i
\(426\) −0.176856 + 0.198117i −0.00856870 + 0.00959880i
\(427\) −17.1685 + 17.1685i −0.830840 + 0.830840i
\(428\) 4.61380 0.223016
\(429\) −18.6623 8.17424i −0.901023 0.394656i
\(430\) −23.5400 −1.13520
\(431\) 5.89820 5.89820i 0.284106 0.284106i −0.550638 0.834744i \(-0.685615\pi\)
0.834744 + 0.550638i \(0.185615\pi\)
\(432\) 3.00000 4.24264i 0.144338 0.204124i
\(433\) 37.6093i 1.80739i 0.428177 + 0.903695i \(0.359156\pi\)
−0.428177 + 0.903695i \(0.640844\pi\)
\(434\) 1.19738 1.19738i 0.0574758 0.0574758i
\(435\) −0.926027 16.3320i −0.0443996 0.783060i
\(436\) 9.21545 9.21545i 0.441340 0.441340i
\(437\) −13.0991 13.0991i −0.626614 0.626614i
\(438\) 5.84667 6.54954i 0.279365 0.312949i
\(439\) 18.0000i 0.859093i 0.903045 + 0.429547i \(0.141327\pi\)
−0.903045 + 0.429547i \(0.858673\pi\)
\(440\) −5.96154 5.96154i −0.284205 0.284205i
\(441\) 20.4084 2.32178i 0.971827 0.110561i
\(442\) −1.50977 4.61889i −0.0718124 0.219698i
\(443\) 30.8018i 1.46344i 0.681608 + 0.731718i \(0.261281\pi\)
−0.681608 + 0.731718i \(0.738719\pi\)
\(444\) −0.270810 4.77619i −0.0128521 0.226668i
\(445\) 32.3671 1.53435
\(446\) 8.33491 0.394669
\(447\) 21.6590 1.22807i 1.02443 0.0580855i
\(448\) −2.63122 2.63122i −0.124314 0.124314i
\(449\) −19.2149 19.2149i −0.906809 0.906809i 0.0892043 0.996013i \(-0.471568\pi\)
−0.996013 + 0.0892043i \(0.971568\pi\)
\(450\) −3.13481 + 3.93964i −0.147776 + 0.185717i
\(451\) 36.4365 1.71573
\(452\) −3.43781 −0.161701
\(453\) −28.8568 + 1.63619i −1.35581 + 0.0768747i
\(454\) 13.0498i 0.612457i
\(455\) 30.9204 + 15.6862i 1.44957 + 0.735378i
\(456\) 5.84667 6.54954i 0.273796 0.306710i
\(457\) 11.4656 + 11.4656i 0.536336 + 0.536336i 0.922451 0.386115i \(-0.126183\pi\)
−0.386115 + 0.922451i \(0.626183\pi\)
\(458\) 13.0326i 0.608974i
\(459\) 4.04325 5.71801i 0.188723 0.266894i
\(460\) −6.67822 6.67822i −0.311374 0.311374i
\(461\) −2.60452 + 2.60452i −0.121305 + 0.121305i −0.765153 0.643848i \(-0.777337\pi\)
0.643848 + 0.765153i \(0.277337\pi\)
\(462\) −20.9933 + 1.19032i −0.976695 + 0.0553787i
\(463\) 8.20311 8.20311i 0.381231 0.381231i −0.490315 0.871546i \(-0.663118\pi\)
0.871546 + 0.490315i \(0.163118\pi\)
\(464\) 3.65465i 0.169663i
\(465\) 1.51951 + 1.35644i 0.0704655 + 0.0629035i
\(466\) 1.78455 1.78455i 0.0826677 0.0826677i
\(467\) −22.7603 −1.05322 −0.526612 0.850106i \(-0.676538\pi\)
−0.526612 + 0.850106i \(0.676538\pi\)
\(468\) 3.77191 10.1377i 0.174357 0.468615i
\(469\) −11.9060 −0.549768
\(470\) −12.2033 + 12.2033i −0.562895 + 0.562895i
\(471\) −24.3716 21.7561i −1.12298 1.00247i
\(472\) 5.16845i 0.237897i
\(473\) 21.0138 21.0138i 0.966216 0.966216i
\(474\) −7.07964 + 0.401416i −0.325179 + 0.0184377i
\(475\) −6.01512 + 6.01512i −0.275993 + 0.275993i
\(476\) −3.54623 3.54623i −0.162541 0.162541i
\(477\) 0.646346 0.0735322i 0.0295942 0.00336681i
\(478\) 10.1836i 0.465786i
\(479\) 17.3876 + 17.3876i 0.794460 + 0.794460i 0.982216 0.187755i \(-0.0601212\pi\)
−0.187755 + 0.982216i \(0.560121\pi\)
\(480\) 2.98077 3.33911i 0.136053 0.152409i
\(481\) −3.09400 9.46556i −0.141074 0.431592i
\(482\) 28.9150i 1.31704i
\(483\) −23.5170 + 1.33342i −1.07006 + 0.0606725i
\(484\) −0.356442 −0.0162019
\(485\) 0.615628 0.0279542
\(486\) 14.9675 4.35584i 0.678941 0.197585i
\(487\) −10.0151 10.0151i −0.453829 0.453829i 0.442795 0.896623i \(-0.353987\pi\)
−0.896623 + 0.442795i \(0.853987\pi\)
\(488\) 4.61380 + 4.61380i 0.208857 + 0.208857i
\(489\) −6.87694 + 0.389923i −0.310986 + 0.0176329i
\(490\) 17.6933 0.799304
\(491\) 0.822276 0.0371088 0.0185544 0.999828i \(-0.494094\pi\)
0.0185544 + 0.999828i \(0.494094\pi\)
\(492\) 1.09507 + 19.3133i 0.0493694 + 0.870711i
\(493\) 4.92554i 0.221835i
\(494\) 8.26844 16.2987i 0.372015 0.733311i
\(495\) −2.85901 25.1306i −0.128503 1.12954i
\(496\) −0.321779 0.321779i −0.0144483 0.0144483i
\(497\) 0.570551i 0.0255927i
\(498\) −17.2507 + 19.3246i −0.773024 + 0.865955i
\(499\) −4.32178 4.32178i −0.193469 0.193469i 0.603724 0.797193i \(-0.293683\pi\)
−0.797193 + 0.603724i \(0.793683\pi\)
\(500\) 6.06996 6.06996i 0.271457 0.271457i
\(501\) −0.132999 2.34566i −0.00594197 0.104796i
\(502\) −13.0745 + 13.0745i −0.583541 + 0.583541i
\(503\) 38.1212i 1.69974i −0.526991 0.849871i \(-0.676680\pi\)
0.526991 0.849871i \(-0.323320\pi\)
\(504\) −1.26187 11.0918i −0.0562081 0.494067i
\(505\) −32.3671 + 32.3671i −1.44032 + 1.44032i
\(506\) 11.9231 0.530046
\(507\) 2.17882 22.4110i 0.0967647 0.995307i
\(508\) −11.0745 −0.491349
\(509\) −20.7795 + 20.7795i −0.921036 + 0.921036i −0.997103 0.0760664i \(-0.975764\pi\)
0.0760664 + 0.997103i \(0.475764\pi\)
\(510\) 4.01733 4.50028i 0.177890 0.199276i
\(511\) 18.8618i 0.834397i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 25.9593 4.45390i 1.14613 0.196645i
\(514\) −9.66589 + 9.66589i −0.426344 + 0.426344i
\(515\) −14.4468 14.4468i −0.636603 0.636603i
\(516\) 11.7700 + 10.5069i 0.518146 + 0.462541i
\(517\) 21.7873i 0.958206i
\(518\) −7.26734 7.26734i −0.319309 0.319309i
\(519\) 22.6068 + 20.1808i 0.992331 + 0.885838i
\(520\) 4.21545 8.30944i 0.184860 0.364393i
\(521\) 0.171761i 0.00752497i −0.999993 0.00376248i \(-0.998802\pi\)
0.999993 0.00376248i \(-0.00119764\pi\)
\(522\) −6.82665 + 8.57933i −0.298794 + 0.375507i
\(523\) 20.8618 0.912223 0.456111 0.889923i \(-0.349242\pi\)
0.456111 + 0.889923i \(0.349242\pi\)
\(524\) −18.1015 −0.790767
\(525\) 0.612308 + 10.7990i 0.0267233 + 0.471309i
\(526\) −10.3369 10.3369i −0.450710 0.450710i
\(527\) −0.433677 0.433677i −0.0188913 0.0188913i
\(528\) 0.319883 + 5.64166i 0.0139211 + 0.245522i
\(529\) −9.64356 −0.419285
\(530\) 0.560360 0.0243405
\(531\) 9.65434 12.1330i 0.418963 0.526527i
\(532\) 18.8618i 0.817763i
\(533\) 12.5111 + 38.2756i 0.541915 + 1.65790i
\(534\) −16.1836 14.4468i −0.700332 0.625175i
\(535\) 8.43090 + 8.43090i 0.364499 + 0.364499i
\(536\) 3.19958i 0.138201i
\(537\) −23.3891 20.8791i −1.00932 0.901001i
\(538\) 11.1685 + 11.1685i 0.481506 + 0.481506i
\(539\) −15.7946 + 15.7946i −0.680320 + 0.680320i
\(540\) 13.2346 2.27071i 0.569528 0.0977156i
\(541\) −22.6021 + 22.6021i −0.971742 + 0.971742i −0.999612 0.0278698i \(-0.991128\pi\)
0.0278698 + 0.999612i \(0.491128\pi\)
\(542\) 22.9535i 0.985937i
\(543\) 2.19848 2.46277i 0.0943458 0.105688i
\(544\) −0.953002 + 0.953002i −0.0408596 + 0.0408596i
\(545\) 33.6792 1.44266
\(546\) −8.45879 21.6441i −0.362003 0.926284i
\(547\) 33.7527 1.44316 0.721580 0.692331i \(-0.243416\pi\)
0.721580 + 0.692331i \(0.243416\pi\)
\(548\) 0.976593 0.976593i 0.0417180 0.0417180i
\(549\) 2.21266 + 19.4492i 0.0944340 + 0.830073i
\(550\) 5.47511i 0.233459i
\(551\) −13.0991 + 13.0991i −0.558039 + 0.558039i
\(552\) 0.358338 + 6.31988i 0.0152519 + 0.268992i
\(553\) −10.7722 + 10.7722i −0.458081 + 0.458081i
\(554\) −18.4901 18.4901i −0.785568 0.785568i
\(555\) 8.23278 9.22250i 0.349462 0.391473i
\(556\) 7.10912i 0.301494i
\(557\) −7.40027 7.40027i −0.313559 0.313559i 0.532727 0.846287i \(-0.321167\pi\)
−0.846287 + 0.532727i \(0.821167\pi\)
\(558\) −0.154317 1.35644i −0.00653276 0.0574228i
\(559\) 29.2899 + 14.8590i 1.23883 + 0.628469i
\(560\) 9.61619i 0.406358i
\(561\) 0.431122 + 7.60354i 0.0182020 + 0.321022i
\(562\) 4.33690 0.182941
\(563\) −38.1111 −1.60619 −0.803095 0.595851i \(-0.796815\pi\)
−0.803095 + 0.595851i \(0.796815\pi\)
\(564\) 11.5485 0.654800i 0.486278 0.0275720i
\(565\) −6.28199 6.28199i −0.264285 0.264285i
\(566\) 6.61600 + 6.61600i 0.278091 + 0.278091i
\(567\) 17.7565 28.3952i 0.745703 1.19249i
\(568\) 0.153328 0.00643350
\(569\) 38.2930 1.60533 0.802663 0.596433i \(-0.203416\pi\)
0.802663 + 0.596433i \(0.203416\pi\)
\(570\) 22.6519 1.28436i 0.948783 0.0537961i
\(571\) 34.6145i 1.44857i −0.689500 0.724285i \(-0.742170\pi\)
0.689500 0.724285i \(-0.257830\pi\)
\(572\) 3.65465 + 11.1808i 0.152808 + 0.467492i
\(573\) 7.32457 8.20510i 0.305988 0.342773i
\(574\) 29.3867 + 29.3867i 1.22658 + 1.22658i
\(575\) 6.13331i 0.255777i
\(576\) −2.98077 + 0.339111i −0.124199 + 0.0141296i
\(577\) 4.72243 + 4.72243i 0.196597 + 0.196597i 0.798540 0.601942i \(-0.205606\pi\)
−0.601942 + 0.798540i \(0.705606\pi\)
\(578\) 10.7364 10.7364i 0.446576 0.446576i
\(579\) −10.4241 + 0.591046i −0.433210 + 0.0245631i
\(580\) −6.67822 + 6.67822i −0.277298 + 0.277298i
\(581\) 55.6522i 2.30884i
\(582\) −0.307814 0.274781i −0.0127593 0.0113900i
\(583\) −0.500224 + 0.500224i −0.0207172 + 0.0207172i
\(584\) −5.06886 −0.209751
\(585\) 25.4173 11.6323i 1.05088 0.480937i
\(586\) 4.24732 0.175455
\(587\) 11.0090 11.0090i 0.454391 0.454391i −0.442418 0.896809i \(-0.645879\pi\)
0.896809 + 0.442418i \(0.145879\pi\)
\(588\) −8.84667 7.89729i −0.364831 0.325679i
\(589\) 2.30666i 0.0950441i
\(590\) 9.44443 9.44443i 0.388821 0.388821i
\(591\) −6.81449 + 0.386383i −0.280311 + 0.0158937i
\(592\) −1.95300 + 1.95300i −0.0802679 + 0.0802679i
\(593\) 8.06905 + 8.06905i 0.331356 + 0.331356i 0.853101 0.521745i \(-0.174719\pi\)
−0.521745 + 0.853101i \(0.674719\pi\)
\(594\) −9.78734 + 13.8414i −0.401579 + 0.567919i
\(595\) 12.9602i 0.531317i
\(596\) −8.85644 8.85644i −0.362774 0.362774i
\(597\) 19.9462 22.3441i 0.816345 0.914483i
\(598\) 4.09400 + 12.5249i 0.167416 + 0.512181i
\(599\) 22.0180i 0.899633i 0.893121 + 0.449816i \(0.148511\pi\)
−0.893121 + 0.449816i \(0.851489\pi\)
\(600\) 2.90210 0.164550i 0.118478 0.00671771i
\(601\) −38.2529 −1.56037 −0.780184 0.625550i \(-0.784875\pi\)
−0.780184 + 0.625550i \(0.784875\pi\)
\(602\) 33.8960 1.38150
\(603\) −5.97662 + 7.51106i −0.243387 + 0.305874i
\(604\) 11.7997 + 11.7997i 0.480122 + 0.480122i
\(605\) −0.651335 0.651335i −0.0264805 0.0264805i
\(606\) 30.6304 1.73675i 1.24427 0.0705506i
\(607\) 8.06933 0.327524 0.163762 0.986500i \(-0.447637\pi\)
0.163762 + 0.986500i \(0.447637\pi\)
\(608\) −5.06886 −0.205569
\(609\) 1.33342 + 23.5170i 0.0540328 + 0.952957i
\(610\) 16.8618i 0.682714i
\(611\) 22.8870 7.48105i 0.925910 0.302651i
\(612\) −4.01733 + 0.457036i −0.162391 + 0.0184746i
\(613\) −23.0896 23.0896i −0.932579 0.932579i 0.0652872 0.997867i \(-0.479204\pi\)
−0.997867 + 0.0652872i \(0.979204\pi\)
\(614\) 4.59241i 0.185335i
\(615\) −33.2906 + 37.2927i −1.34241 + 1.50379i
\(616\) 8.58423 + 8.58423i 0.345868 + 0.345868i
\(617\) −32.9195 + 32.9195i −1.32529 + 1.32529i −0.415858 + 0.909430i \(0.636519\pi\)
−0.909430 + 0.415858i \(0.863481\pi\)
\(618\) 0.775184 + 13.6716i 0.0311825 + 0.549954i
\(619\) −25.3716 + 25.3716i −1.01977 + 1.01977i −0.0199687 + 0.999801i \(0.506357\pi\)
−0.999801 + 0.0199687i \(0.993643\pi\)
\(620\) 1.17599i 0.0472288i
\(621\) −10.9639 + 15.5054i −0.439968 + 0.622208i
\(622\) 2.43090 2.43090i 0.0974701 0.0974701i
\(623\) −46.6065 −1.86725
\(624\) −5.81658 + 2.27319i −0.232850 + 0.0910004i
\(625\) 30.5747 1.22299
\(626\) −1.06757 + 1.06757i −0.0426686 + 0.0426686i
\(627\) −19.0745 + 21.3675i −0.761760 + 0.853337i
\(628\) 18.8618i 0.752668i
\(629\) −2.63216 + 2.63216i −0.104951 + 0.104951i
\(630\) 17.9624 22.5741i 0.715641 0.899375i
\(631\) −0.200326 + 0.200326i −0.00797485 + 0.00797485i −0.711083 0.703108i \(-0.751795\pi\)
0.703108 + 0.711083i \(0.251795\pi\)
\(632\) 2.89489 + 2.89489i 0.115153 + 0.115153i
\(633\) 12.1662 + 10.8606i 0.483565 + 0.431671i
\(634\) 22.8618i 0.907958i
\(635\) −20.2366 20.2366i −0.803065 0.803065i
\(636\) −0.280180 0.250112i −0.0111099 0.00991759i
\(637\) −22.0151 11.1685i −0.872271 0.442510i
\(638\) 11.9231i 0.472040i
\(639\) 0.359939 + 0.286407i 0.0142390 + 0.0113301i
\(640\) −2.58423 −0.102150
\(641\) 34.2846 1.35416 0.677081 0.735908i \(-0.263245\pi\)
0.677081 + 0.735908i \(0.263245\pi\)
\(642\) −0.452383 7.97851i −0.0178541 0.314887i
\(643\) −10.7873 10.7873i −0.425411 0.425411i 0.461651 0.887062i \(-0.347257\pi\)
−0.887062 + 0.461651i \(0.847257\pi\)
\(644\) 9.61619 + 9.61619i 0.378931 + 0.378931i
\(645\) 2.30810 + 40.7071i 0.0908813 + 1.60284i
\(646\) −6.83155 −0.268784
\(647\) −2.69550 −0.105971 −0.0529855 0.998595i \(-0.516874\pi\)
−0.0529855 + 0.998595i \(0.516874\pi\)
\(648\) −7.63084 4.77183i −0.299768 0.187455i
\(649\) 16.8618i 0.661883i
\(650\) 5.75146 1.87997i 0.225591 0.0737385i
\(651\) −2.18799 1.95319i −0.0857541 0.0765514i
\(652\) 2.81201 + 2.81201i 0.110127 + 0.110127i
\(653\) 43.4774i 1.70140i −0.525651 0.850700i \(-0.676178\pi\)
0.525651 0.850700i \(-0.323822\pi\)
\(654\) −16.8396 15.0325i −0.658481 0.587815i
\(655\) −33.0772 33.0772i −1.29243 1.29243i
\(656\) 7.89729 7.89729i 0.308337 0.308337i
\(657\) −11.8992 9.46831i −0.464232 0.369394i
\(658\) 17.5719 17.5719i 0.685024 0.685024i
\(659\) 39.2972i 1.53080i −0.643553 0.765401i \(-0.722540\pi\)
0.643553 0.765401i \(-0.277460\pi\)
\(660\) −9.72461 + 10.8937i −0.378530 + 0.424036i
\(661\) 27.4958 27.4958i 1.06946 1.06946i 0.0720628 0.997400i \(-0.477042\pi\)
0.997400 0.0720628i \(-0.0229582\pi\)
\(662\) −7.81338 −0.303676
\(663\) −7.83929 + 3.06369i −0.304453 + 0.118984i
\(664\) 14.9558 0.580397
\(665\) 34.4666 34.4666i 1.33656 1.33656i
\(666\) −8.23278 + 0.936611i −0.319014 + 0.0362929i
\(667\) 13.3564i 0.517164i
\(668\) −0.959150 + 0.959150i −0.0371106 + 0.0371106i
\(669\) −0.817238 14.4133i −0.0315962 0.557252i
\(670\) −5.84667 + 5.84667i −0.225877 + 0.225877i
\(671\) −15.0523 15.0523i −0.581086 0.581086i
\(672\) −4.29211 + 4.80810i −0.165572 + 0.185476i
\(673\) 7.29153i 0.281068i 0.990076 + 0.140534i \(0.0448819\pi\)
−0.990076 + 0.140534i \(0.955118\pi\)
\(674\) −13.3128 13.3128i −0.512790 0.512790i
\(675\) 7.12009 + 5.03466i 0.274052 + 0.193784i
\(676\) −10.4902 + 7.67822i −0.403470 + 0.295316i
\(677\) 16.3200i 0.627230i −0.949550 0.313615i \(-0.898460\pi\)
0.949550 0.313615i \(-0.101540\pi\)
\(678\) 0.337077 + 5.94491i 0.0129454 + 0.228313i
\(679\) −0.886464 −0.0340194
\(680\) −3.48289 −0.133563
\(681\) −22.5666 + 1.27953i −0.864756 + 0.0490318i
\(682\) 1.04979 + 1.04979i 0.0401984 + 0.0401984i
\(683\) −0.171761 0.171761i −0.00657223 0.00657223i 0.703813 0.710385i \(-0.251479\pi\)
−0.710385 + 0.703813i \(0.751479\pi\)
\(684\) −11.8992 9.46831i −0.454978 0.362030i
\(685\) 3.56910 0.136368
\(686\) 0.570551 0.0217837
\(687\) 22.5369 1.27785i 0.859838 0.0487529i
\(688\) 9.10912i 0.347282i
\(689\) −0.697233 0.353712i −0.0265625 0.0134754i
\(690\) −10.8937 + 12.2033i −0.414715 + 0.464571i
\(691\) 18.3218 + 18.3218i 0.696993 + 0.696993i 0.963761 0.266768i \(-0.0859556\pi\)
−0.266768 + 0.963761i \(0.585956\pi\)
\(692\) 17.4960i 0.665099i
\(693\) 4.11678 + 36.1864i 0.156383 + 1.37461i
\(694\) −20.7057 20.7057i −0.785977 0.785977i
\(695\) −12.9907 + 12.9907i −0.492764 + 0.492764i
\(696\) 6.31988 0.358338i 0.239555 0.0135828i
\(697\) 10.6436 10.6436i 0.403153 0.403153i
\(698\) 6.89931i 0.261143i
\(699\) −3.26095 2.91100i −0.123341 0.110104i
\(700\) 4.41577 4.41577i 0.166901 0.166901i
\(701\) −33.7243 −1.27375 −0.636874 0.770968i \(-0.719773\pi\)
−0.636874 + 0.770968i \(0.719773\pi\)
\(702\) −17.9007 5.52867i −0.675617 0.208666i
\(703\) −14.0000 −0.528020
\(704\) 2.30690 2.30690i 0.0869445 0.0869445i
\(705\) 22.2993 + 19.9063i 0.839841 + 0.749713i
\(706\) 7.90600i 0.297546i
\(707\) 46.6065 46.6065i 1.75282 1.75282i
\(708\) −8.93766 + 0.506767i −0.335898 + 0.0190455i
\(709\) −3.79689 + 3.79689i −0.142595 + 0.142595i −0.774801 0.632206i \(-0.782150\pi\)
0.632206 + 0.774801i \(0.282150\pi\)
\(710\) 0.280180 + 0.280180i 0.0105150 + 0.0105150i
\(711\) 1.38832 + 12.2033i 0.0520660 + 0.457658i
\(712\) 12.5249i 0.469390i
\(713\) 1.17599 + 1.17599i 0.0440411 + 0.0440411i
\(714\) −5.78469 + 6.48010i −0.216487 + 0.242512i
\(715\) −13.7527 + 27.1091i −0.514321 + 1.01382i
\(716\) 18.1015i 0.676484i
\(717\) −17.6102 + 0.998500i −0.657664 + 0.0372897i
\(718\) 18.2182 0.679899
\(719\) 30.6300 1.14231 0.571153 0.820844i \(-0.306496\pi\)
0.571153 + 0.820844i \(0.306496\pi\)
\(720\) −6.06650 4.82717i −0.226085 0.179898i
\(721\) 20.8025 + 20.8025i 0.774724 + 0.774724i
\(722\) −4.73291 4.73291i −0.176141 0.176141i
\(723\) 50.0020 2.83512i 1.85959 0.105439i
\(724\) −1.90600 −0.0708361
\(725\) −6.13331 −0.227785
\(726\) 0.0349492 + 0.616386i 0.00129709 + 0.0228762i
\(727\) 0.430897i 0.0159811i 0.999968 + 0.00799055i \(0.00254350\pi\)
−0.999968 + 0.00799055i \(0.997457\pi\)
\(728\) −6.06996 + 11.9650i −0.224968 + 0.443454i
\(729\) −9.00000 25.4558i −0.333333 0.942809i
\(730\) −9.26245 9.26245i −0.342819 0.342819i
\(731\) 12.2768i 0.454074i
\(732\) 7.52613 8.43090i 0.278174 0.311615i
\(733\) 8.50256 + 8.50256i 0.314049 + 0.314049i 0.846476 0.532427i \(-0.178720\pi\)
−0.532427 + 0.846476i \(0.678720\pi\)
\(734\) −5.35216 + 5.35216i −0.197552 + 0.197552i
\(735\) −1.73483 30.5966i −0.0639903 1.12857i
\(736\) 2.58423 2.58423i 0.0952558 0.0952558i
\(737\) 10.4385i 0.384506i
\(738\) 33.2906 3.78734i 1.22544 0.139414i
\(739\) 15.1836 15.1836i 0.558537 0.558537i −0.370354 0.928891i \(-0.620764\pi\)
0.928891 + 0.370354i \(0.120764\pi\)
\(740\) −7.13753 −0.262381
\(741\) −28.9956 12.7003i −1.06518 0.466558i
\(742\) −0.806880 −0.0296215
\(743\) −1.06757 + 1.06757i −0.0391653 + 0.0391653i −0.726418 0.687253i \(-0.758816\pi\)
0.687253 + 0.726418i \(0.258816\pi\)
\(744\) −0.524893 + 0.587994i −0.0192435 + 0.0215569i
\(745\) 32.3671i 1.18584i
\(746\) −11.1808 + 11.1808i −0.409357 + 0.409357i
\(747\) 35.1089 + 27.9365i 1.28457 + 1.02214i
\(748\) 3.10912 3.10912i 0.113681 0.113681i
\(749\) −12.1399 12.1399i −0.443583 0.443583i
\(750\) −11.0918 9.90147i −0.405015 0.361550i
\(751\) 1.88134i 0.0686509i 0.999411 + 0.0343255i \(0.0109283\pi\)
−0.999411 + 0.0343255i \(0.989072\pi\)
\(752\) −4.72222 4.72222i −0.172201 0.172201i
\(753\) 23.8913 + 21.3274i 0.870646 + 0.777212i
\(754\) 12.5249 4.09400i 0.456130 0.149095i
\(755\) 43.1236i 1.56943i
\(756\) −19.0570 + 3.26967i −0.693097 + 0.118917i
\(757\) −28.6189 −1.04017 −0.520086 0.854114i \(-0.674100\pi\)
−0.520086 + 0.854114i \(0.674100\pi\)
\(758\) −7.54752 −0.274138
\(759\) −1.16906 20.6183i −0.0424342 0.748396i
\(760\) −9.26245 9.26245i −0.335984 0.335984i
\(761\) −30.4408 30.4408i −1.10348 1.10348i −0.993988 0.109490i \(-0.965078\pi\)
−0.109490 0.993988i \(-0.534922\pi\)
\(762\) 1.08585 + 19.1508i 0.0393362 + 0.693759i
\(763\) −48.4958 −1.75567
\(764\) −6.35014 −0.229740
\(765\) −8.17612 6.50581i −0.295608 0.235218i
\(766\) 15.3520i 0.554691i
\(767\) −17.7129 + 5.78978i −0.639575 + 0.209057i
\(768\) 1.29211 + 1.15345i 0.0466251 + 0.0416215i
\(769\) 14.9956 + 14.9956i 0.540755 + 0.540755i 0.923750 0.382996i \(-0.125108\pi\)
−0.382996 + 0.923750i \(0.625108\pi\)
\(770\) 31.3723i 1.13058i
\(771\) 17.6627 + 15.7672i 0.636107 + 0.567843i
\(772\) 4.26245 + 4.26245i 0.153409 + 0.153409i
\(773\) 6.25917 6.25917i 0.225127 0.225127i −0.585527 0.810653i \(-0.699112\pi\)
0.810653 + 0.585527i \(0.199112\pi\)
\(774\) 17.0153 21.3838i 0.611601 0.768623i
\(775\) 0.540016 0.540016i 0.0193980