Properties

Label 585.2.bu.c.316.4
Level $585$
Weight $2$
Character 585.316
Analytic conductor $4.671$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bu (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.4
Root \(1.20036 + 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 585.316
Dual form 585.2.bu.c.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.16117 + 1.24775i) q^{2} +(2.11378 + 3.66117i) q^{4} +1.00000i q^{5} +(-1.64996 + 0.952606i) q^{7} +5.55889i q^{8} +O(q^{10})\) \(q+(2.16117 + 1.24775i) q^{2} +(2.11378 + 3.66117i) q^{4} +1.00000i q^{5} +(-1.64996 + 0.952606i) q^{7} +5.55889i q^{8} +(-1.24775 + 2.16117i) q^{10} +(-0.926118 - 0.534695i) q^{11} +(1.40072 + 3.32235i) q^{13} -4.75447 q^{14} +(-2.70857 + 4.69138i) q^{16} +(-0.318632 - 0.551886i) q^{17} +(4.96410 - 2.86603i) q^{19} +(-3.66117 + 2.11378i) q^{20} +(-1.33433 - 2.31114i) q^{22} +(-1.90893 + 3.30636i) q^{23} -1.00000 q^{25} +(-1.11827 + 8.92792i) q^{26} +(-6.97531 - 4.02720i) q^{28} +(4.72756 - 8.18837i) q^{29} -1.46410i q^{31} +(-2.07908 + 1.20036i) q^{32} -1.59030i q^{34} +(-0.952606 - 1.64996i) q^{35} +(0.655970 + 0.378725i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(0.232051 + 0.133975i) q^{41} +(0.318632 + 0.551886i) q^{43} -4.52091i q^{44} +(-8.25104 + 4.76374i) q^{46} -9.44613i q^{47} +(-1.68508 + 2.91865i) q^{49} +(-2.16117 - 1.24775i) q^{50} +(-9.20287 + 12.1510i) q^{52} +6.99102 q^{53} +(0.534695 - 0.926118i) q^{55} +(-5.29543 - 9.17196i) q^{56} +(20.4341 - 11.7977i) q^{58} +(0.641756 - 0.370518i) q^{59} +(-2.09928 - 3.63606i) q^{61} +(1.82684 - 3.16418i) q^{62} +4.84325 q^{64} +(-3.32235 + 1.40072i) q^{65} +(-7.01029 - 4.04739i) q^{67} +(1.34703 - 2.33313i) q^{68} -4.75447i q^{70} +(-8.45663 + 4.88244i) q^{71} +3.71649i q^{73} +(0.945110 + 1.63698i) q^{74} +(20.9860 + 12.1163i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(-4.69138 - 2.70857i) q^{80} +(0.334335 + 0.579085i) q^{82} -5.11778i q^{83} +(0.551886 - 0.318632i) q^{85} +1.59030i q^{86} +(2.97231 - 5.14819i) q^{88} +(10.8932 + 6.28917i) q^{89} +(-5.47602 - 4.14741i) q^{91} -16.1402 q^{92} +(11.7864 - 20.4147i) q^{94} +(2.86603 + 4.96410i) q^{95} +(-3.65597 + 2.11078i) q^{97} +(-7.28351 + 4.20514i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} - 6q^{7} + O(q^{10}) \) \( 8q + 2q^{4} - 6q^{7} - 2q^{10} - 4q^{14} - 2q^{16} + 2q^{17} + 12q^{19} - 12q^{20} - 12q^{22} + 10q^{23} - 8q^{25} - 10q^{26} - 18q^{28} + 8q^{29} - 6q^{32} - 10q^{35} + 6q^{37} + 16q^{38} - 12q^{40} - 12q^{41} - 2q^{43} - 42q^{46} + 12q^{49} - 6q^{52} + 24q^{53} - 12q^{56} + 36q^{58} + 12q^{59} - 28q^{61} - 4q^{62} - 8q^{64} + 8q^{65} + 6q^{67} + 14q^{68} - 10q^{74} + 54q^{76} + 36q^{77} - 16q^{79} + 4q^{82} + 18q^{85} - 18q^{88} - 24q^{89} + 28q^{91} - 44q^{92} + 32q^{94} + 16q^{95} - 30q^{97} - 72q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16117 + 1.24775i 1.52818 + 0.882295i 0.999438 + 0.0335125i \(0.0106693\pi\)
0.528742 + 0.848783i \(0.322664\pi\)
\(3\) 0 0
\(4\) 2.11378 + 3.66117i 1.05689 + 1.83059i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −1.64996 + 0.952606i −0.623627 + 0.360051i −0.778280 0.627918i \(-0.783907\pi\)
0.154653 + 0.987969i \(0.450574\pi\)
\(8\) 5.55889i 1.96536i
\(9\) 0 0
\(10\) −1.24775 + 2.16117i −0.394574 + 0.683423i
\(11\) −0.926118 0.534695i −0.279235 0.161217i 0.353842 0.935305i \(-0.384875\pi\)
−0.633077 + 0.774089i \(0.718208\pi\)
\(12\) 0 0
\(13\) 1.40072 + 3.32235i 0.388490 + 0.921453i
\(14\) −4.75447 −1.27069
\(15\) 0 0
\(16\) −2.70857 + 4.69138i −0.677142 + 1.17284i
\(17\) −0.318632 0.551886i −0.0772795 0.133852i 0.824796 0.565431i \(-0.191290\pi\)
−0.902075 + 0.431579i \(0.857957\pi\)
\(18\) 0 0
\(19\) 4.96410 2.86603i 1.13884 0.657511i 0.192699 0.981258i \(-0.438276\pi\)
0.946144 + 0.323747i \(0.104943\pi\)
\(20\) −3.66117 + 2.11378i −0.818663 + 0.472655i
\(21\) 0 0
\(22\) −1.33433 2.31114i −0.284481 0.492736i
\(23\) −1.90893 + 3.30636i −0.398039 + 0.689423i −0.993484 0.113973i \(-0.963642\pi\)
0.595445 + 0.803396i \(0.296976\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −1.11827 + 8.92792i −0.219311 + 1.75091i
\(27\) 0 0
\(28\) −6.97531 4.02720i −1.31821 0.761069i
\(29\) 4.72756 8.18837i 0.877886 1.52054i 0.0242288 0.999706i \(-0.492287\pi\)
0.853657 0.520836i \(-0.174380\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) −2.07908 + 1.20036i −0.367534 + 0.212196i
\(33\) 0 0
\(34\) 1.59030i 0.272733i
\(35\) −0.952606 1.64996i −0.161020 0.278895i
\(36\) 0 0
\(37\) 0.655970 + 0.378725i 0.107841 + 0.0622619i 0.552950 0.833214i \(-0.313502\pi\)
−0.445110 + 0.895476i \(0.646835\pi\)
\(38\) 14.3044 2.32048
\(39\) 0 0
\(40\) −5.55889 −0.878938
\(41\) 0.232051 + 0.133975i 0.0362402 + 0.0209233i 0.518011 0.855374i \(-0.326673\pi\)
−0.481770 + 0.876297i \(0.660006\pi\)
\(42\) 0 0
\(43\) 0.318632 + 0.551886i 0.0485909 + 0.0841618i 0.889298 0.457328i \(-0.151194\pi\)
−0.840707 + 0.541490i \(0.817860\pi\)
\(44\) 4.52091i 0.681552i
\(45\) 0 0
\(46\) −8.25104 + 4.76374i −1.21655 + 0.702375i
\(47\) 9.44613i 1.37786i −0.724828 0.688930i \(-0.758081\pi\)
0.724828 0.688930i \(-0.241919\pi\)
\(48\) 0 0
\(49\) −1.68508 + 2.91865i −0.240726 + 0.416950i
\(50\) −2.16117 1.24775i −0.305636 0.176459i
\(51\) 0 0
\(52\) −9.20287 + 12.1510i −1.27621 + 1.68504i
\(53\) 6.99102 0.960290 0.480145 0.877189i \(-0.340584\pi\)
0.480145 + 0.877189i \(0.340584\pi\)
\(54\) 0 0
\(55\) 0.534695 0.926118i 0.0720982 0.124878i
\(56\) −5.29543 9.17196i −0.707632 1.22565i
\(57\) 0 0
\(58\) 20.4341 11.7977i 2.68313 1.54911i
\(59\) 0.641756 0.370518i 0.0835495 0.0482373i −0.457643 0.889136i \(-0.651306\pi\)
0.541193 + 0.840899i \(0.317973\pi\)
\(60\) 0 0
\(61\) −2.09928 3.63606i −0.268785 0.465550i 0.699763 0.714375i \(-0.253289\pi\)
−0.968548 + 0.248825i \(0.919956\pi\)
\(62\) 1.82684 3.16418i 0.232009 0.401851i
\(63\) 0 0
\(64\) 4.84325 0.605406
\(65\) −3.32235 + 1.40072i −0.412086 + 0.173738i
\(66\) 0 0
\(67\) −7.01029 4.04739i −0.856443 0.494468i 0.00637624 0.999980i \(-0.497970\pi\)
−0.862820 + 0.505512i \(0.831304\pi\)
\(68\) 1.34703 2.33313i 0.163352 0.282934i
\(69\) 0 0
\(70\) 4.75447i 0.568268i
\(71\) −8.45663 + 4.88244i −1.00362 + 0.579439i −0.909317 0.416105i \(-0.863395\pi\)
−0.0943010 + 0.995544i \(0.530062\pi\)
\(72\) 0 0
\(73\) 3.71649i 0.434982i 0.976062 + 0.217491i \(0.0697873\pi\)
−0.976062 + 0.217491i \(0.930213\pi\)
\(74\) 0.945110 + 1.63698i 0.109867 + 0.190295i
\(75\) 0 0
\(76\) 20.9860 + 12.1163i 2.40726 + 1.38983i
\(77\) 2.03741 0.232185
\(78\) 0 0
\(79\) −9.31937 −1.04851 −0.524255 0.851561i \(-0.675656\pi\)
−0.524255 + 0.851561i \(0.675656\pi\)
\(80\) −4.69138 2.70857i −0.524512 0.302827i
\(81\) 0 0
\(82\) 0.334335 + 0.579085i 0.0369211 + 0.0639492i
\(83\) 5.11778i 0.561749i −0.959744 0.280875i \(-0.909376\pi\)
0.959744 0.280875i \(-0.0906245\pi\)
\(84\) 0 0
\(85\) 0.551886 0.318632i 0.0598605 0.0345605i
\(86\) 1.59030i 0.171486i
\(87\) 0 0
\(88\) 2.97231 5.14819i 0.316849 0.548799i
\(89\) 10.8932 + 6.28917i 1.15467 + 0.666650i 0.950021 0.312185i \(-0.101061\pi\)
0.204651 + 0.978835i \(0.434394\pi\)
\(90\) 0 0
\(91\) −5.47602 4.14741i −0.574043 0.434767i
\(92\) −16.1402 −1.68273
\(93\) 0 0
\(94\) 11.7864 20.4147i 1.21568 2.10562i
\(95\) 2.86603 + 4.96410i 0.294048 + 0.509306i
\(96\) 0 0
\(97\) −3.65597 + 2.11078i −0.371208 + 0.214317i −0.673986 0.738744i \(-0.735419\pi\)
0.302778 + 0.953061i \(0.402086\pi\)
\(98\) −7.28351 + 4.20514i −0.735746 + 0.424783i
\(99\) 0 0
\(100\) −2.11378 3.66117i −0.211378 0.366117i
\(101\) 7.62379 13.2048i 0.758595 1.31393i −0.184972 0.982744i \(-0.559219\pi\)
0.943567 0.331181i \(-0.107447\pi\)
\(102\) 0 0
\(103\) 13.5269 1.33285 0.666423 0.745574i \(-0.267824\pi\)
0.666423 + 0.745574i \(0.267824\pi\)
\(104\) −18.4686 + 7.78645i −1.81099 + 0.763524i
\(105\) 0 0
\(106\) 15.1088 + 8.72307i 1.46750 + 0.847259i
\(107\) −3.68137 + 6.37632i −0.355891 + 0.616422i −0.987270 0.159053i \(-0.949156\pi\)
0.631379 + 0.775475i \(0.282489\pi\)
\(108\) 0 0
\(109\) 10.0760i 0.965103i 0.875868 + 0.482551i \(0.160290\pi\)
−0.875868 + 0.482551i \(0.839710\pi\)
\(110\) 2.31114 1.33433i 0.220358 0.127224i
\(111\) 0 0
\(112\) 10.3208i 0.975223i
\(113\) −3.34403 5.79203i −0.314580 0.544868i 0.664768 0.747050i \(-0.268530\pi\)
−0.979348 + 0.202181i \(0.935197\pi\)
\(114\) 0 0
\(115\) −3.30636 1.90893i −0.308320 0.178008i
\(116\) 39.9721 3.71131
\(117\) 0 0
\(118\) 1.84926 0.170238
\(119\) 1.05146 + 0.607061i 0.0963872 + 0.0556492i
\(120\) 0 0
\(121\) −4.92820 8.53590i −0.448018 0.775991i
\(122\) 10.4775i 0.948592i
\(123\) 0 0
\(124\) 5.36033 3.09479i 0.481372 0.277920i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 0.744750 1.28994i 0.0660859 0.114464i −0.831089 0.556139i \(-0.812282\pi\)
0.897175 + 0.441675i \(0.145616\pi\)
\(128\) 14.6253 + 8.44391i 1.29270 + 0.746343i
\(129\) 0 0
\(130\) −8.92792 1.11827i −0.783030 0.0980789i
\(131\) −4.12676 −0.360557 −0.180278 0.983616i \(-0.557700\pi\)
−0.180278 + 0.983616i \(0.557700\pi\)
\(132\) 0 0
\(133\) −5.46039 + 9.45767i −0.473476 + 0.820084i
\(134\) −10.1003 17.4942i −0.872533 1.51127i
\(135\) 0 0
\(136\) 3.06787 1.77124i 0.263068 0.151882i
\(137\) −17.4155 + 10.0548i −1.48790 + 0.859041i −0.999905 0.0138029i \(-0.995606\pi\)
−0.487999 + 0.872844i \(0.662273\pi\)
\(138\) 0 0
\(139\) −10.4126 18.0352i −0.883189 1.52973i −0.847776 0.530355i \(-0.822059\pi\)
−0.0354130 0.999373i \(-0.511275\pi\)
\(140\) 4.02720 6.97531i 0.340360 0.589521i
\(141\) 0 0
\(142\) −24.3683 −2.04494
\(143\) 0.479208 3.82584i 0.0400734 0.319933i
\(144\) 0 0
\(145\) 8.18837 + 4.72756i 0.680007 + 0.392602i
\(146\) −4.63726 + 8.03198i −0.383783 + 0.664731i
\(147\) 0 0
\(148\) 3.20216i 0.263216i
\(149\) −11.5768 + 6.68388i −0.948410 + 0.547565i −0.892587 0.450876i \(-0.851112\pi\)
−0.0558233 + 0.998441i \(0.517778\pi\)
\(150\) 0 0
\(151\) 18.2984i 1.48910i −0.667567 0.744550i \(-0.732664\pi\)
0.667567 0.744550i \(-0.267336\pi\)
\(152\) 15.9319 + 27.5949i 1.29225 + 2.23824i
\(153\) 0 0
\(154\) 4.40320 + 2.54219i 0.354820 + 0.204856i
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) 2.42229 0.193320 0.0966599 0.995317i \(-0.469184\pi\)
0.0966599 + 0.995317i \(0.469184\pi\)
\(158\) −20.1408 11.6283i −1.60231 0.925096i
\(159\) 0 0
\(160\) −1.20036 2.07908i −0.0948968 0.164366i
\(161\) 7.27382i 0.573258i
\(162\) 0 0
\(163\) −13.8416 + 7.99144i −1.08416 + 0.625938i −0.932015 0.362421i \(-0.881950\pi\)
−0.152142 + 0.988359i \(0.548617\pi\)
\(164\) 1.13277i 0.0884545i
\(165\) 0 0
\(166\) 6.38573 11.0604i 0.495629 0.858454i
\(167\) 12.4648 + 7.19658i 0.964558 + 0.556888i 0.897573 0.440866i \(-0.145329\pi\)
0.0669853 + 0.997754i \(0.478662\pi\)
\(168\) 0 0
\(169\) −9.07597 + 9.30735i −0.698151 + 0.715950i
\(170\) 1.59030 0.121970
\(171\) 0 0
\(172\) −1.34703 + 2.33313i −0.102710 + 0.177900i
\(173\) 12.1745 + 21.0868i 0.925608 + 1.60320i 0.790581 + 0.612358i \(0.209779\pi\)
0.135027 + 0.990842i \(0.456888\pi\)
\(174\) 0 0
\(175\) 1.64996 0.952606i 0.124725 0.0720103i
\(176\) 5.01691 2.89651i 0.378164 0.218333i
\(177\) 0 0
\(178\) 15.6947 + 27.1840i 1.17636 + 2.03752i
\(179\) −1.89414 + 3.28075i −0.141575 + 0.245215i −0.928090 0.372356i \(-0.878550\pi\)
0.786515 + 0.617571i \(0.211883\pi\)
\(180\) 0 0
\(181\) 8.48794 0.630904 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(182\) −6.65968 15.7960i −0.493649 1.17088i
\(183\) 0 0
\(184\) −18.3797 10.6115i −1.35497 0.782291i
\(185\) −0.378725 + 0.655970i −0.0278444 + 0.0482279i
\(186\) 0 0
\(187\) 0.681482i 0.0498349i
\(188\) 34.5839 19.9670i 2.52229 1.45625i
\(189\) 0 0
\(190\) 14.3044i 1.03775i
\(191\) −2.72155 4.71386i −0.196924 0.341083i 0.750605 0.660751i \(-0.229762\pi\)
−0.947530 + 0.319668i \(0.896429\pi\)
\(192\) 0 0
\(193\) 10.5288 + 6.07880i 0.757879 + 0.437562i 0.828534 0.559939i \(-0.189176\pi\)
−0.0706548 + 0.997501i \(0.522509\pi\)
\(194\) −10.5349 −0.756363
\(195\) 0 0
\(196\) −14.2476 −1.01768
\(197\) −3.79172 2.18915i −0.270149 0.155970i 0.358807 0.933412i \(-0.383184\pi\)
−0.628955 + 0.777442i \(0.716517\pi\)
\(198\) 0 0
\(199\) 10.4186 + 18.0456i 0.738558 + 1.27922i 0.953144 + 0.302516i \(0.0978265\pi\)
−0.214586 + 0.976705i \(0.568840\pi\)
\(200\) 5.55889i 0.393073i
\(201\) 0 0
\(202\) 32.9526 19.0252i 2.31854 1.33861i
\(203\) 18.0140i 1.26434i
\(204\) 0 0
\(205\) −0.133975 + 0.232051i −0.00935719 + 0.0162071i
\(206\) 29.2340 + 16.8783i 2.03683 + 1.17596i
\(207\) 0 0
\(208\) −19.3803 2.42749i −1.34378 0.168316i
\(209\) −6.12979 −0.424007
\(210\) 0 0
\(211\) 5.32684 9.22635i 0.366715 0.635168i −0.622335 0.782751i \(-0.713816\pi\)
0.989050 + 0.147583i \(0.0471492\pi\)
\(212\) 14.7775 + 25.5953i 1.01492 + 1.75789i
\(213\) 0 0
\(214\) −15.9121 + 9.18688i −1.08773 + 0.628002i
\(215\) −0.551886 + 0.318632i −0.0376383 + 0.0217305i
\(216\) 0 0
\(217\) 1.39471 + 2.41571i 0.0946792 + 0.163989i
\(218\) −12.5723 + 21.7759i −0.851505 + 1.47485i
\(219\) 0 0
\(220\) 4.52091 0.304799
\(221\) 1.38724 1.83164i 0.0933161 0.123210i
\(222\) 0 0
\(223\) −18.4804 10.6697i −1.23754 0.714494i −0.268949 0.963155i \(-0.586676\pi\)
−0.968591 + 0.248661i \(0.920010\pi\)
\(224\) 2.28694 3.96110i 0.152803 0.264662i
\(225\) 0 0
\(226\) 16.6901i 1.11021i
\(227\) −13.5842 + 7.84283i −0.901613 + 0.520547i −0.877723 0.479168i \(-0.840938\pi\)
−0.0238900 + 0.999715i \(0.507605\pi\)
\(228\) 0 0
\(229\) 7.62085i 0.503600i 0.967779 + 0.251800i \(0.0810225\pi\)
−0.967779 + 0.251800i \(0.918977\pi\)
\(230\) −4.76374 8.25104i −0.314112 0.544058i
\(231\) 0 0
\(232\) 45.5182 + 26.2800i 2.98842 + 1.72536i
\(233\) −19.0550 −1.24833 −0.624166 0.781292i \(-0.714561\pi\)
−0.624166 + 0.781292i \(0.714561\pi\)
\(234\) 0 0
\(235\) 9.44613 0.616198
\(236\) 2.71306 + 1.56639i 0.176605 + 0.101963i
\(237\) 0 0
\(238\) 1.51493 + 2.62393i 0.0981980 + 0.170084i
\(239\) 12.7535i 0.824954i −0.910968 0.412477i \(-0.864664\pi\)
0.910968 0.412477i \(-0.135336\pi\)
\(240\) 0 0
\(241\) −22.4550 + 12.9644i −1.44646 + 0.835111i −0.998268 0.0588285i \(-0.981263\pi\)
−0.448187 + 0.893940i \(0.647930\pi\)
\(242\) 24.5967i 1.58114i
\(243\) 0 0
\(244\) 8.87483 15.3717i 0.568153 0.984069i
\(245\) −2.91865 1.68508i −0.186466 0.107656i
\(246\) 0 0
\(247\) 16.4752 + 12.4780i 1.04829 + 0.793954i
\(248\) 8.13878 0.516813
\(249\) 0 0
\(250\) 1.24775 2.16117i 0.0789149 0.136685i
\(251\) −3.80593 6.59207i −0.240228 0.416088i 0.720551 0.693402i \(-0.243889\pi\)
−0.960779 + 0.277314i \(0.910556\pi\)
\(252\) 0 0
\(253\) 3.53578 2.04139i 0.222293 0.128341i
\(254\) 3.21907 1.85853i 0.201982 0.116614i
\(255\) 0 0
\(256\) 16.2286 + 28.1087i 1.01429 + 1.75680i
\(257\) −0.167891 + 0.290796i −0.0104728 + 0.0181394i −0.871214 0.490903i \(-0.836667\pi\)
0.860742 + 0.509042i \(0.170000\pi\)
\(258\) 0 0
\(259\) −1.44310 −0.0896700
\(260\) −12.1510 9.20287i −0.753572 0.570738i
\(261\) 0 0
\(262\) −8.91865 5.14918i −0.550996 0.318118i
\(263\) −2.68795 + 4.65566i −0.165746 + 0.287080i −0.936920 0.349544i \(-0.886336\pi\)
0.771174 + 0.636624i \(0.219670\pi\)
\(264\) 0 0
\(265\) 6.99102i 0.429455i
\(266\) −23.6017 + 13.6264i −1.44711 + 0.835491i
\(267\) 0 0
\(268\) 34.2212i 2.09039i
\(269\) −0.655192 1.13483i −0.0399478 0.0691916i 0.845360 0.534197i \(-0.179386\pi\)
−0.885308 + 0.465005i \(0.846052\pi\)
\(270\) 0 0
\(271\) −10.0851 5.82266i −0.612629 0.353701i 0.161365 0.986895i \(-0.448410\pi\)
−0.773994 + 0.633194i \(0.781744\pi\)
\(272\) 3.45214 0.209317
\(273\) 0 0
\(274\) −50.1838 −3.03171
\(275\) 0.926118 + 0.534695i 0.0558470 + 0.0322433i
\(276\) 0 0
\(277\) −10.1581 17.5943i −0.610338 1.05714i −0.991183 0.132498i \(-0.957700\pi\)
0.380845 0.924639i \(-0.375633\pi\)
\(278\) 51.9697i 3.11693i
\(279\) 0 0
\(280\) 9.17196 5.29543i 0.548129 0.316463i
\(281\) 11.8744i 0.708366i −0.935176 0.354183i \(-0.884759\pi\)
0.935176 0.354183i \(-0.115241\pi\)
\(282\) 0 0
\(283\) −11.3261 + 19.6173i −0.673264 + 1.16613i 0.303709 + 0.952765i \(0.401775\pi\)
−0.976973 + 0.213363i \(0.931558\pi\)
\(284\) −35.7509 20.6408i −2.12143 1.22481i
\(285\) 0 0
\(286\) 5.80936 7.67038i 0.343515 0.453559i
\(287\) −0.510500 −0.0301339
\(288\) 0 0
\(289\) 8.29695 14.3707i 0.488056 0.845337i
\(290\) 11.7977 + 20.4341i 0.692782 + 1.19993i
\(291\) 0 0
\(292\) −13.6067 + 7.85584i −0.796272 + 0.459728i
\(293\) 16.1191 9.30636i 0.941687 0.543683i 0.0511983 0.998689i \(-0.483696\pi\)
0.890489 + 0.455005i \(0.150363\pi\)
\(294\) 0 0
\(295\) 0.370518 + 0.641756i 0.0215724 + 0.0373645i
\(296\) −2.10529 + 3.64647i −0.122367 + 0.211946i
\(297\) 0 0
\(298\) −33.3593 −1.93245
\(299\) −13.6587 1.71083i −0.789905 0.0989400i
\(300\) 0 0
\(301\) −1.05146 0.607061i −0.0606052 0.0349904i
\(302\) 22.8319 39.5459i 1.31383 2.27561i
\(303\) 0 0
\(304\) 31.0513i 1.78091i
\(305\) 3.63606 2.09928i 0.208200 0.120204i
\(306\) 0 0
\(307\) 3.14776i 0.179652i −0.995957 0.0898262i \(-0.971369\pi\)
0.995957 0.0898262i \(-0.0286311\pi\)
\(308\) 4.30664 + 7.45932i 0.245394 + 0.425034i
\(309\) 0 0
\(310\) 3.16418 + 1.82684i 0.179713 + 0.103757i
\(311\) −3.18059 −0.180355 −0.0901774 0.995926i \(-0.528743\pi\)
−0.0901774 + 0.995926i \(0.528743\pi\)
\(312\) 0 0
\(313\) 35.3533 1.99829 0.999144 0.0413596i \(-0.0131689\pi\)
0.999144 + 0.0413596i \(0.0131689\pi\)
\(314\) 5.23499 + 3.02242i 0.295427 + 0.170565i
\(315\) 0 0
\(316\) −19.6991 34.1198i −1.10816 1.91939i
\(317\) 13.6357i 0.765858i 0.923778 + 0.382929i \(0.125085\pi\)
−0.923778 + 0.382929i \(0.874915\pi\)
\(318\) 0 0
\(319\) −8.75656 + 5.05560i −0.490273 + 0.283059i
\(320\) 4.84325i 0.270746i
\(321\) 0 0
\(322\) 9.07594 15.7200i 0.505782 0.876041i
\(323\) −3.16344 1.82641i −0.176018 0.101624i
\(324\) 0 0
\(325\) −1.40072 3.32235i −0.0776980 0.184291i
\(326\) −39.8854 −2.20905
\(327\) 0 0
\(328\) −0.744750 + 1.28994i −0.0411219 + 0.0712253i
\(329\) 8.99844 + 15.5858i 0.496100 + 0.859271i
\(330\) 0 0
\(331\) −24.9380 + 14.3980i −1.37072 + 0.791383i −0.991018 0.133727i \(-0.957305\pi\)
−0.379698 + 0.925110i \(0.623972\pi\)
\(332\) 18.7371 10.8179i 1.02833 0.593707i
\(333\) 0 0
\(334\) 17.9591 + 31.1061i 0.982679 + 1.70205i
\(335\) 4.04739 7.01029i 0.221133 0.383013i
\(336\) 0 0
\(337\) −11.7493 −0.640026 −0.320013 0.947413i \(-0.603687\pi\)
−0.320013 + 0.947413i \(0.603687\pi\)
\(338\) −31.2280 + 8.79023i −1.69858 + 0.478125i
\(339\) 0 0
\(340\) 2.33313 + 1.34703i 0.126532 + 0.0730532i
\(341\) −0.782847 + 1.35593i −0.0423936 + 0.0734278i
\(342\) 0 0
\(343\) 19.7574i 1.06680i
\(344\) −3.06787 + 1.77124i −0.165409 + 0.0954987i
\(345\) 0 0
\(346\) 60.7630i 3.26664i
\(347\) 0.949887 + 1.64525i 0.0509926 + 0.0883218i 0.890395 0.455189i \(-0.150428\pi\)
−0.839402 + 0.543510i \(0.817095\pi\)
\(348\) 0 0
\(349\) −8.89329 5.13454i −0.476047 0.274846i 0.242721 0.970096i \(-0.421960\pi\)
−0.718768 + 0.695250i \(0.755293\pi\)
\(350\) 4.75447 0.254137
\(351\) 0 0
\(352\) 2.56730 0.136838
\(353\) 0.693330 + 0.400294i 0.0369022 + 0.0213055i 0.518338 0.855176i \(-0.326551\pi\)
−0.481435 + 0.876482i \(0.659884\pi\)
\(354\) 0 0
\(355\) −4.88244 8.45663i −0.259133 0.448831i
\(356\) 53.1756i 2.81830i
\(357\) 0 0
\(358\) −8.18714 + 4.72685i −0.432704 + 0.249822i
\(359\) 8.13272i 0.429228i 0.976699 + 0.214614i \(0.0688494\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(360\) 0 0
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) 18.3439 + 10.5909i 0.964135 + 0.556643i
\(363\) 0 0
\(364\) 3.60929 28.8154i 0.189178 1.51034i
\(365\) −3.71649 −0.194530
\(366\) 0 0
\(367\) 10.2632 17.7765i 0.535737 0.927924i −0.463390 0.886154i \(-0.653367\pi\)
0.999127 0.0417696i \(-0.0132996\pi\)
\(368\) −10.3409 17.9110i −0.539057 0.933675i
\(369\) 0 0
\(370\) −1.63698 + 0.945110i −0.0851025 + 0.0491339i
\(371\) −11.5349 + 6.65968i −0.598863 + 0.345754i
\(372\) 0 0
\(373\) 8.90292 + 15.4203i 0.460976 + 0.798433i 0.999010 0.0444897i \(-0.0141662\pi\)
−0.538034 + 0.842923i \(0.680833\pi\)
\(374\) −0.850322 + 1.47280i −0.0439691 + 0.0761568i
\(375\) 0 0
\(376\) 52.5100 2.70800
\(377\) 33.8266 + 4.23697i 1.74216 + 0.218215i
\(378\) 0 0
\(379\) −1.77150 1.02277i −0.0909956 0.0525363i 0.453812 0.891098i \(-0.350064\pi\)
−0.544807 + 0.838561i \(0.683397\pi\)
\(380\) −12.1163 + 20.9860i −0.621553 + 1.07656i
\(381\) 0 0
\(382\) 13.5833i 0.694982i
\(383\) 6.84611 3.95261i 0.349820 0.201969i −0.314786 0.949163i \(-0.601933\pi\)
0.664606 + 0.747194i \(0.268599\pi\)
\(384\) 0 0
\(385\) 2.03741i 0.103836i
\(386\) 15.1697 + 26.2747i 0.772117 + 1.33735i
\(387\) 0 0
\(388\) −15.4558 8.92343i −0.784651 0.453018i
\(389\) −9.21171 −0.467052 −0.233526 0.972351i \(-0.575026\pi\)
−0.233526 + 0.972351i \(0.575026\pi\)
\(390\) 0 0
\(391\) 2.43298 0.123041
\(392\) −16.2244 9.36719i −0.819458 0.473114i
\(393\) 0 0
\(394\) −5.46304 9.46226i −0.275224 0.476702i
\(395\) 9.31937i 0.468908i
\(396\) 0 0
\(397\) 5.50305 3.17719i 0.276190 0.159458i −0.355507 0.934674i \(-0.615692\pi\)
0.631697 + 0.775215i \(0.282359\pi\)
\(398\) 51.9996i 2.60651i
\(399\) 0 0
\(400\) 2.70857 4.69138i 0.135428 0.234569i
\(401\) −3.61063 2.08460i −0.180306 0.104100i 0.407130 0.913370i \(-0.366530\pi\)
−0.587437 + 0.809270i \(0.699863\pi\)
\(402\) 0 0
\(403\) 4.86425 2.05080i 0.242306 0.102157i
\(404\) 64.4600 3.20701
\(405\) 0 0
\(406\) −22.4770 + 38.9314i −1.11552 + 1.93213i
\(407\) −0.405004 0.701487i −0.0200753 0.0347714i
\(408\) 0 0
\(409\) 8.80580 5.08403i 0.435419 0.251389i −0.266234 0.963909i \(-0.585779\pi\)
0.701652 + 0.712519i \(0.252446\pi\)
\(410\) −0.579085 + 0.334335i −0.0285989 + 0.0165116i
\(411\) 0 0
\(412\) 28.5929 + 49.5244i 1.40867 + 2.43989i
\(413\) −0.705915 + 1.22268i −0.0347358 + 0.0601642i
\(414\) 0 0
\(415\) 5.11778 0.251222
\(416\) −6.90023 5.22607i −0.338311 0.256229i
\(417\) 0 0
\(418\) −13.2475 7.64847i −0.647959 0.374099i
\(419\) 14.2954 24.7604i 0.698378 1.20963i −0.270651 0.962677i \(-0.587239\pi\)
0.969029 0.246948i \(-0.0794277\pi\)
\(420\) 0 0
\(421\) 2.01797i 0.0983498i 0.998790 + 0.0491749i \(0.0156592\pi\)
−0.998790 + 0.0491749i \(0.984341\pi\)
\(422\) 23.0244 13.2932i 1.12081 0.647101i
\(423\) 0 0
\(424\) 38.8623i 1.88732i
\(425\) 0.318632 + 0.551886i 0.0154559 + 0.0267704i
\(426\) 0 0
\(427\) 6.92747 + 3.99957i 0.335244 + 0.193553i
\(428\) −31.1264 −1.50455
\(429\) 0 0
\(430\) −1.59030 −0.0766908
\(431\) −17.8508 10.3061i −0.859842 0.496430i 0.00411765 0.999992i \(-0.498689\pi\)
−0.863959 + 0.503562i \(0.832023\pi\)
\(432\) 0 0
\(433\) 14.7178 + 25.4920i 0.707292 + 1.22507i 0.965858 + 0.259072i \(0.0834168\pi\)
−0.258566 + 0.965994i \(0.583250\pi\)
\(434\) 6.96103i 0.334140i
\(435\) 0 0
\(436\) −36.8899 + 21.2984i −1.76670 + 1.02001i
\(437\) 21.8841i 1.04686i
\(438\) 0 0
\(439\) 8.47602 14.6809i 0.404538 0.700681i −0.589729 0.807601i \(-0.700765\pi\)
0.994268 + 0.106920i \(0.0340988\pi\)
\(440\) 5.14819 + 2.97231i 0.245430 + 0.141699i
\(441\) 0 0
\(442\) 5.28351 2.22756i 0.251311 0.105954i
\(443\) 24.1399 1.14692 0.573461 0.819233i \(-0.305600\pi\)
0.573461 + 0.819233i \(0.305600\pi\)
\(444\) 0 0
\(445\) −6.28917 + 10.8932i −0.298135 + 0.516385i
\(446\) −26.6262 46.1180i −1.26079 2.18375i
\(447\) 0 0
\(448\) −7.99118 + 4.61371i −0.377548 + 0.217977i
\(449\) −18.0679 + 10.4315i −0.852676 + 0.492293i −0.861553 0.507668i \(-0.830508\pi\)
0.00887706 + 0.999961i \(0.497174\pi\)
\(450\) 0 0
\(451\) −0.143271 0.248153i −0.00674637 0.0116851i
\(452\) 14.1371 24.4861i 0.664952 1.15173i
\(453\) 0 0
\(454\) −39.1437 −1.83710
\(455\) 4.14741 5.47602i 0.194434 0.256720i
\(456\) 0 0
\(457\) 26.4708 + 15.2830i 1.23825 + 0.714906i 0.968737 0.248089i \(-0.0798027\pi\)
0.269517 + 0.962996i \(0.413136\pi\)
\(458\) −9.50894 + 16.4700i −0.444324 + 0.769591i
\(459\) 0 0
\(460\) 16.1402i 0.752541i
\(461\) −4.05146 + 2.33911i −0.188695 + 0.108943i −0.591372 0.806399i \(-0.701413\pi\)
0.402676 + 0.915342i \(0.368080\pi\)
\(462\) 0 0
\(463\) 14.0011i 0.650688i 0.945596 + 0.325344i \(0.105480\pi\)
−0.945596 + 0.325344i \(0.894520\pi\)
\(464\) 25.6098 + 44.3575i 1.18891 + 2.05925i
\(465\) 0 0
\(466\) −41.1811 23.7759i −1.90768 1.10140i
\(467\) −6.98506 −0.323230 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(468\) 0 0
\(469\) 15.4223 0.712135
\(470\) 20.4147 + 11.7864i 0.941661 + 0.543668i
\(471\) 0 0
\(472\) 2.05967 + 3.56745i 0.0948039 + 0.164205i
\(473\) 0.681482i 0.0313346i
\(474\) 0 0
\(475\) −4.96410 + 2.86603i −0.227769 + 0.131502i
\(476\) 5.13277i 0.235260i
\(477\) 0 0
\(478\) 15.9132 27.5625i 0.727853 1.26068i
\(479\) 14.1065 + 8.14438i 0.644542 + 0.372126i 0.786362 0.617766i \(-0.211962\pi\)
−0.141820 + 0.989892i \(0.545296\pi\)
\(480\) 0 0
\(481\) −0.339423 + 2.70985i −0.0154764 + 0.123558i
\(482\) −64.7056 −2.94726
\(483\) 0 0
\(484\) 20.8343 36.0860i 0.947012 1.64027i
\(485\) −2.11078 3.65597i −0.0958454 0.166009i
\(486\) 0 0
\(487\) 17.3559 10.0204i 0.786471 0.454069i −0.0522474 0.998634i \(-0.516638\pi\)
0.838719 + 0.544565i \(0.183305\pi\)
\(488\) 20.2125 11.6697i 0.914975 0.528261i
\(489\) 0 0
\(490\) −4.20514 7.28351i −0.189969 0.329035i
\(491\) 7.89916 13.6818i 0.356484 0.617449i −0.630887 0.775875i \(-0.717309\pi\)
0.987371 + 0.158426i \(0.0506420\pi\)
\(492\) 0 0
\(493\) −6.02540 −0.271370
\(494\) 20.0364 + 47.5241i 0.901481 + 2.13821i
\(495\) 0 0
\(496\) 6.86865 + 3.96562i 0.308411 + 0.178061i
\(497\) 9.30208 16.1117i 0.417255 0.722708i
\(498\) 0 0
\(499\) 1.24651i 0.0558016i 0.999611 + 0.0279008i \(0.00888226\pi\)
−0.999611 + 0.0279008i \(0.991118\pi\)
\(500\) 3.66117 2.11378i 0.163733 0.0945311i
\(501\) 0 0
\(502\) 18.9955i 0.847809i
\(503\) −3.82672 6.62808i −0.170625 0.295532i 0.768013 0.640434i \(-0.221245\pi\)
−0.938639 + 0.344902i \(0.887912\pi\)
\(504\) 0 0
\(505\) 13.2048 + 7.62379i 0.587605 + 0.339254i
\(506\) 10.1886 0.452938
\(507\) 0 0
\(508\) 6.29695 0.279382
\(509\) 22.2777 + 12.8621i 0.987444 + 0.570101i 0.904509 0.426454i \(-0.140237\pi\)
0.0829345 + 0.996555i \(0.473571\pi\)
\(510\) 0 0
\(511\) −3.54035 6.13207i −0.156616 0.271267i
\(512\) 47.2215i 2.08691i
\(513\) 0 0
\(514\) −0.725685 + 0.418974i −0.0320086 + 0.0184802i
\(515\) 13.5269i 0.596067i
\(516\) 0 0
\(517\) −5.05080 + 8.74824i −0.222134 + 0.384747i
\(518\) −3.11879 1.80064i −0.137032 0.0791154i
\(519\) 0 0
\(520\) −7.78645 18.4686i −0.341458 0.809900i
\(521\) 30.1519 1.32098 0.660490 0.750835i \(-0.270349\pi\)
0.660490 + 0.750835i \(0.270349\pi\)
\(522\) 0 0
\(523\) −1.96876 + 3.41000i −0.0860880 + 0.149109i −0.905854 0.423589i \(-0.860770\pi\)
0.819766 + 0.572698i \(0.194103\pi\)
\(524\) −8.72307 15.1088i −0.381069 0.660031i
\(525\) 0 0
\(526\) −11.6182 + 6.70779i −0.506579 + 0.292473i
\(527\) −0.808017 + 0.466509i −0.0351978 + 0.0203215i
\(528\) 0 0
\(529\) 4.21200 + 7.29539i 0.183130 + 0.317191i
\(530\) −8.72307 + 15.1088i −0.378906 + 0.656284i
\(531\) 0 0
\(532\) −46.1682 −2.00165
\(533\) −0.120072 + 0.958614i −0.00520088 + 0.0415222i
\(534\) 0 0
\(535\) −6.37632 3.68137i −0.275672 0.159159i
\(536\) 22.4990 38.9694i 0.971809 1.68322i
\(537\) 0 0
\(538\) 3.27007i 0.140983i
\(539\) 3.12117 1.80201i 0.134438 0.0776180i
\(540\) 0 0
\(541\) 15.8881i 0.683083i 0.939867 + 0.341541i \(0.110949\pi\)
−0.939867 + 0.341541i \(0.889051\pi\)
\(542\) −14.5305 25.1675i −0.624138 1.08104i
\(543\) 0 0
\(544\) 1.32492 + 0.764945i 0.0568057 + 0.0327968i
\(545\) −10.0760 −0.431607
\(546\) 0 0
\(547\) −6.56107 −0.280531 −0.140266 0.990114i \(-0.544796\pi\)
−0.140266 + 0.990114i \(0.544796\pi\)
\(548\) −73.6249 42.5074i −3.14510 1.81582i
\(549\) 0 0
\(550\) 1.33433 + 2.31114i 0.0568962 + 0.0985471i
\(551\) 54.1972i 2.30888i
\(552\) 0 0
\(553\) 15.3766 8.87769i 0.653880 0.377518i
\(554\) 50.6990i 2.15399i
\(555\) 0 0
\(556\) 44.0200 76.2450i 1.86687 3.23351i
\(557\) −6.79835 3.92503i −0.288055 0.166309i 0.349009 0.937119i \(-0.386518\pi\)
−0.637065 + 0.770810i \(0.719852\pi\)
\(558\) 0 0
\(559\) −1.38724 + 1.83164i −0.0586741 + 0.0774702i
\(560\) 10.3208 0.436133
\(561\) 0 0
\(562\) 14.8163 25.6626i 0.624988 1.08251i
\(563\) 7.77976 + 13.4749i 0.327878 + 0.567901i 0.982091 0.188410i \(-0.0603333\pi\)
−0.654213 + 0.756310i \(0.727000\pi\)
\(564\) 0 0
\(565\) 5.79203 3.34403i 0.243673 0.140684i
\(566\) −48.9552 + 28.2643i −2.05774 + 1.18804i
\(567\) 0 0
\(568\) −27.1409 47.0095i −1.13881 1.97247i
\(569\) −1.73957 + 3.01303i −0.0729267 + 0.126313i −0.900183 0.435512i \(-0.856567\pi\)
0.827256 + 0.561825i \(0.189901\pi\)
\(570\) 0 0
\(571\) 21.5118 0.900240 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(572\) 15.0200 6.33252i 0.628018 0.264776i
\(573\) 0 0
\(574\) −1.10328 0.636978i −0.0460500 0.0265870i
\(575\) 1.90893 3.30636i 0.0796078 0.137885i
\(576\) 0 0
\(577\) 9.97608i 0.415310i 0.978202 + 0.207655i \(0.0665831\pi\)
−0.978202 + 0.207655i \(0.933417\pi\)
\(578\) 35.8623 20.7051i 1.49167 0.861218i
\(579\) 0 0
\(580\) 39.9721i 1.65975i
\(581\) 4.87523 + 8.44414i 0.202259 + 0.350322i
\(582\) 0 0
\(583\) −6.47451 3.73806i −0.268147 0.154815i
\(584\) −20.6595 −0.854898
\(585\) 0 0
\(586\) 46.4482 1.91876
\(587\) −20.8341 12.0286i −0.859915 0.496472i 0.00406862 0.999992i \(-0.498705\pi\)
−0.863984 + 0.503519i \(0.832038\pi\)
\(588\) 0 0
\(589\) −4.19615 7.26795i −0.172899 0.299471i
\(590\) 1.84926i 0.0761328i
\(591\) 0 0
\(592\) −3.55348 + 2.05160i −0.146047 + 0.0843203i
\(593\) 0.940219i 0.0386102i 0.999814 + 0.0193051i \(0.00614538\pi\)
−0.999814 + 0.0193051i \(0.993855\pi\)
\(594\) 0 0
\(595\) −0.607061 + 1.05146i −0.0248871 + 0.0431057i
\(596\) −48.9417 28.2565i −2.00473 1.15743i
\(597\) 0 0
\(598\) −27.3842 20.7401i −1.11982 0.848128i
\(599\) 11.4270 0.466896 0.233448 0.972369i \(-0.424999\pi\)
0.233448 + 0.972369i \(0.424999\pi\)
\(600\) 0 0
\(601\) 18.0215 31.2142i 0.735114 1.27325i −0.219560 0.975599i \(-0.570462\pi\)
0.954674 0.297655i \(-0.0962045\pi\)
\(602\) −1.51493 2.62393i −0.0617437 0.106943i
\(603\) 0 0
\(604\) 66.9935 38.6787i 2.72593 1.57381i
\(605\) 8.53590 4.92820i 0.347034 0.200360i
\(606\) 0 0
\(607\) −19.9454 34.5464i −0.809557 1.40219i −0.913171 0.407576i \(-0.866374\pi\)
0.103614 0.994618i \(-0.466959\pi\)
\(608\) −6.88052 + 11.9174i −0.279042 + 0.483315i
\(609\) 0 0
\(610\) 10.4775 0.424223
\(611\) 31.3833 13.2314i 1.26963 0.535285i
\(612\) 0 0
\(613\) 0.299187 + 0.172736i 0.0120841 + 0.00697673i 0.506030 0.862516i \(-0.331113\pi\)
−0.493946 + 0.869493i \(0.664446\pi\)
\(614\) 3.92763 6.80286i 0.158506 0.274541i
\(615\) 0 0
\(616\) 11.3258i 0.456328i
\(617\) −33.5022 + 19.3425i −1.34875 + 0.778700i −0.988072 0.153991i \(-0.950787\pi\)
−0.360676 + 0.932691i \(0.617454\pi\)
\(618\) 0 0
\(619\) 14.8971i 0.598764i −0.954133 0.299382i \(-0.903219\pi\)
0.954133 0.299382i \(-0.0967805\pi\)
\(620\) 3.09479 + 5.36033i 0.124290 + 0.215276i
\(621\) 0 0
\(622\) −6.87381 3.96859i −0.275615 0.159126i
\(623\) −23.9644 −0.960113
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 76.4047 + 44.1123i 3.05374 + 1.76308i
\(627\) 0 0
\(628\) 5.12019 + 8.86842i 0.204318 + 0.353889i
\(629\) 0.482694i 0.0192463i
\(630\) 0 0
\(631\) 33.6408 19.4225i 1.33922 0.773198i 0.352526 0.935802i \(-0.385323\pi\)
0.986691 + 0.162604i \(0.0519893\pi\)
\(632\) 51.8053i 2.06071i
\(633\) 0 0
\(634\) −17.0140 + 29.4691i −0.675713 + 1.17037i
\(635\) 1.28994 + 0.744750i 0.0511899 + 0.0295545i
\(636\) 0 0
\(637\) −12.0571 1.51022i −0.477719 0.0598370i
\(638\) −25.2326 −0.998967
\(639\) 0 0
\(640\) −8.44391 + 14.6253i −0.333775 + 0.578115i
\(641\) −18.5908 32.2003i −0.734293 1.27183i −0.955033 0.296501i \(-0.904180\pi\)
0.220739 0.975333i \(-0.429153\pi\)
\(642\) 0 0
\(643\) 7.88410 4.55189i 0.310918 0.179509i −0.336419 0.941712i \(-0.609216\pi\)
0.647337 + 0.762204i \(0.275882\pi\)
\(644\) 26.6307 15.3753i 1.04940 0.605870i
\(645\) 0 0
\(646\) −4.55783 7.89439i −0.179325 0.310601i
\(647\) 9.56118 16.5605i 0.375889 0.651059i −0.614571 0.788862i \(-0.710671\pi\)
0.990460 + 0.137803i \(0.0440041\pi\)
\(648\) 0 0
\(649\) −0.792455 −0.0311066
\(650\) 1.11827 8.92792i 0.0438622 0.350182i
\(651\) 0 0
\(652\) −58.5161 33.7843i −2.29167 1.32309i
\(653\) 17.3162 29.9926i 0.677636 1.17370i −0.298055 0.954549i \(-0.596338\pi\)
0.975691 0.219152i \(-0.0703289\pi\)
\(654\) 0 0
\(655\) 4.12676i 0.161246i
\(656\) −1.25705 + 0.725758i −0.0490796 + 0.0283361i
\(657\) 0 0
\(658\) 44.9114i 1.75083i
\(659\) −3.34926 5.80109i −0.130469 0.225978i 0.793389 0.608715i \(-0.208315\pi\)
−0.923857 + 0.382737i \(0.874982\pi\)
\(660\) 0 0
\(661\) 5.22004 + 3.01379i 0.203036 + 0.117223i 0.598071 0.801443i \(-0.295934\pi\)
−0.395035 + 0.918666i \(0.629268\pi\)
\(662\) −71.8604 −2.79294
\(663\) 0 0
\(664\) 28.4492 1.10404
\(665\) −9.45767 5.46039i −0.366753 0.211745i
\(666\) 0 0
\(667\) 18.0491 + 31.2620i 0.698865 + 1.21047i
\(668\) 60.8479i 2.35428i
\(669\) 0 0
\(670\) 17.4942 10.1003i 0.675861 0.390209i
\(671\) 4.48990i 0.173330i
\(672\) 0 0
\(673\) 11.6784 20.2276i 0.450169 0.779715i −0.548227 0.836329i \(-0.684697\pi\)
0.998396 + 0.0566140i \(0.0180304\pi\)
\(674\) −25.3923 14.6603i −0.978075 0.564692i
\(675\) 0 0
\(676\) −53.2604 13.5550i −2.04848 0.521346i
\(677\) 45.4042 1.74503 0.872513 0.488590i \(-0.162489\pi\)
0.872513 + 0.488590i \(0.162489\pi\)
\(678\) 0 0
\(679\) 4.02148 6.96540i 0.154330 0.267308i
\(680\) 1.77124 + 3.06787i 0.0679239 + 0.117648i
\(681\) 0 0
\(682\) −3.38374 + 1.95360i −0.129570 + 0.0748073i
\(683\) −22.0817 + 12.7489i −0.844934 + 0.487823i −0.858938 0.512079i \(-0.828875\pi\)
0.0140045 + 0.999902i \(0.495542\pi\)
\(684\) 0 0
\(685\) −10.0548 17.4155i −0.384175 0.665411i
\(686\) 24.6523 42.6991i 0.941230 1.63026i
\(687\) 0 0
\(688\) −3.45214 −0.131612
\(689\) 9.79246 + 23.2266i 0.373063 + 0.884862i
\(690\) 0 0
\(691\) 5.71257 + 3.29815i 0.217316 + 0.125468i 0.604707 0.796448i \(-0.293290\pi\)
−0.387391 + 0.921916i \(0.626624\pi\)
\(692\) −51.4683 + 89.1457i −1.95653 + 3.38881i
\(693\) 0 0
\(694\) 4.74090i 0.179962i
\(695\) 18.0352 10.4126i 0.684115 0.394974i
\(696\) 0 0
\(697\) 0.170754i 0.00646778i
\(698\) −12.8133 22.1933i −0.484990 0.840028i
\(699\) 0 0
\(700\) 6.97531 + 4.02720i 0.263642 + 0.152214i
\(701\) 29.2474 1.10466 0.552329 0.833626i \(-0.313739\pi\)
0.552329 + 0.833626i \(0.313739\pi\)
\(702\) 0 0
\(703\) 4.34174 0.163752
\(704\) −4.48542 2.58966i −0.169051 0.0976015i
\(705\) 0 0
\(706\) 0.998937 + 1.73021i 0.0375955 + 0.0651173i
\(707\) 29.0499i 1.09253i
\(708\) 0 0
\(709\) −9.46865 + 5.46673i −0.355603 + 0.205307i −0.667150 0.744923i \(-0.732486\pi\)
0.311548 + 0.950231i \(0.399153\pi\)
\(710\) 24.3683i 0.914527i
\(711\) 0 0
\(712\) −34.9608 + 60.5538i −1.31021 + 2.26935i
\(713\) 4.84084 + 2.79486i 0.181291 + 0.104668i
\(714\) 0 0
\(715\) 3.82584 + 0.479208i 0.143078 + 0.0179214i
\(716\) −16.0152 −0.598516
\(717\) 0 0
\(718\) −10.1476 + 17.5762i −0.378706 + 0.655938i
\(719\) −8.02989 13.9082i −0.299464 0.518688i 0.676549 0.736398i \(-0.263475\pi\)
−0.976014 + 0.217710i \(0.930141\pi\)
\(720\) 0 0
\(721\) −22.3189 + 12.8858i −0.831199 + 0.479893i
\(722\) 29.9461 17.2894i 1.11448 0.643444i
\(723\) 0 0
\(724\) 17.9416 + 31.0758i 0.666796 + 1.15492i
\(725\) −4.72756 + 8.18837i −0.175577 + 0.304108i
\(726\) 0 0
\(727\) −51.3754 −1.90541 −0.952704 0.303900i \(-0.901711\pi\)
−0.952704 + 0.303900i \(0.901711\pi\)
\(728\) 23.0550 30.4406i 0.854475 1.12820i
\(729\) 0 0
\(730\) −8.03198 4.63726i −0.297277 0.171633i
\(731\) 0.203052 0.351697i 0.00751016 0.0130080i
\(732\) 0 0
\(733\) 9.82358i 0.362842i −0.983406 0.181421i \(-0.941930\pi\)
0.983406 0.181421i \(-0.0580697\pi\)
\(734\) 44.3613 25.6120i 1.63741 0.945357i
\(735\) 0 0
\(736\) 9.16560i 0.337848i
\(737\) 4.32824 + 7.49673i 0.159433 + 0.276146i
\(738\) 0 0
\(739\) 42.5082 + 24.5421i 1.56369 + 0.902797i 0.996879 + 0.0789487i \(0.0251563\pi\)
0.566811 + 0.823848i \(0.308177\pi\)
\(740\) −3.20216 −0.117714
\(741\) 0 0
\(742\) −33.2386 −1.22023
\(743\) 35.3663 + 20.4188i 1.29746 + 0.749091i 0.979966 0.199167i \(-0.0638237\pi\)
0.317499 + 0.948259i \(0.397157\pi\)
\(744\) 0 0
\(745\) −6.68388 11.5768i −0.244878 0.424142i
\(746\) 44.4346i 1.62687i
\(747\) 0 0
\(748\) −2.49503 + 1.44050i −0.0912272 + 0.0526700i
\(749\) 14.0276i 0.512557i
\(750\) 0 0
\(751\) −1.36340 + 2.36148i −0.0497512 + 0.0861716i −0.889829 0.456295i \(-0.849176\pi\)
0.840077 + 0.542467i \(0.182510\pi\)
\(752\) 44.3154 + 25.5855i 1.61601 + 0.933006i
\(753\) 0 0
\(754\) 67.8184 + 51.3641i 2.46980 + 1.87057i
\(755\) 18.2984 0.665946
\(756\) 0 0
\(757\) −7.40301 + 12.8224i −0.269067 + 0.466038i −0.968621 0.248542i \(-0.920049\pi\)
0.699554 + 0.714580i \(0.253382\pi\)
\(758\) −2.55234 4.42078i −0.0927051 0.160570i
\(759\) 0 0
\(760\) −27.5949 + 15.9319i −1.00097 + 0.577911i
\(761\) −9.84575 + 5.68445i −0.356908 + 0.206061i −0.667724 0.744409i \(-0.732731\pi\)
0.310815 + 0.950470i \(0.399398\pi\)
\(762\) 0 0
\(763\) −9.59843 16.6250i −0.347486 0.601864i
\(764\) 11.5055 19.9281i 0.416255 0.720975i
\(765\) 0 0
\(766\) 19.7275 0.712784
\(767\) 2.12991 + 1.61314i 0.0769065 + 0.0582472i
\(768\) 0 0
\(769\) 18.2352 + 10.5281i 0.657579 + 0.379654i 0.791354 0.611358i \(-0.209377\pi\)
−0.133775 + 0.991012i \(0.542710\pi\)
\(770\) −2.54219 + 4.40320i −0.0916142 + 0.158680i
\(771\) 0 0
\(772\) 51.3970i 1.84982i
\(773\) −12.1961 + 7.04144i −0.438664 + 0.253263i −0.703031 0.711159i \(-0.748170\pi\)
0.264367 + 0.964422i \(0.414837\pi\)
\(774\) 0 0
\(775\) 1.46410i 0.0525921i
\(776\) −11.7336 20.3231i −0.421210 0.729558i
\(777\) 0 0
\(778\) −19.9081 11.4940i −0.713740 0.412078i
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 10.4425 0.373660
\(782\) 5.25809 + 3.03576i 0.188029 + 0.108558i
\(783\) 0 0
\(784\) −9.12832 15.8107i −0.326011 0.564668i
\(785\) 2.42229i 0.0864552i
\(786\) 0 0
\(787\) −28.5998 + 16.5121i −1.01947 + 0.588593i −0.913951 0.405823i \(-0.866985\pi\)
−0.105522 + 0.994417i \(0.533651\pi\)
\(788\) 18.5095i 0.659374i
\(789\) 0 0
\(790\)