Properties

Label 1512.2.j.d.323.8
Level 1512
Weight 2
Character 1512.323
Analytic conductor 12.073
Analytic rank 0
Dimension 48
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.8
Character \(\chi\) = 1512.323
Dual form 1512.2.j.d.323.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25654 + 0.648937i) q^{2} +(1.15776 - 1.63082i) q^{4} -1.27600 q^{5} +1.00000i q^{7} +(-0.396469 + 2.80050i) q^{8} +O(q^{10})\) \(q+(-1.25654 + 0.648937i) q^{2} +(1.15776 - 1.63082i) q^{4} -1.27600 q^{5} +1.00000i q^{7} +(-0.396469 + 2.80050i) q^{8} +(1.60334 - 0.828043i) q^{10} +6.57401i q^{11} -4.05196i q^{13} +(-0.648937 - 1.25654i) q^{14} +(-1.31917 - 3.77621i) q^{16} -6.09788i q^{17} -2.08352 q^{19} +(-1.47730 + 2.08093i) q^{20} +(-4.26611 - 8.26047i) q^{22} -6.85760 q^{23} -3.37182 q^{25} +(2.62946 + 5.09143i) q^{26} +(1.63082 + 1.15776i) q^{28} +6.53304 q^{29} +3.26844i q^{31} +(4.10811 + 3.88889i) q^{32} +(3.95714 + 7.66220i) q^{34} -1.27600i q^{35} -2.95562i q^{37} +(2.61802 - 1.35208i) q^{38} +(0.505894 - 3.57344i) q^{40} +3.35381i q^{41} +10.9901 q^{43} +(10.7210 + 7.61114i) q^{44} +(8.61682 - 4.45015i) q^{46} -7.12041 q^{47} -1.00000 q^{49} +(4.23682 - 2.18810i) q^{50} +(-6.60803 - 4.69121i) q^{52} -2.87278 q^{53} -8.38843i q^{55} +(-2.80050 - 0.396469i) q^{56} +(-8.20900 + 4.23953i) q^{58} -7.75213i q^{59} -12.0251i q^{61} +(-2.12101 - 4.10691i) q^{62} +(-7.68562 - 2.22063i) q^{64} +5.17030i q^{65} -3.01966 q^{67} +(-9.94457 - 7.05990i) q^{68} +(0.828043 + 1.60334i) q^{70} -3.48158 q^{71} +2.76889 q^{73} +(1.91801 + 3.71384i) q^{74} +(-2.41223 + 3.39786i) q^{76} -6.57401 q^{77} -0.849261i q^{79} +(1.68326 + 4.81845i) q^{80} +(-2.17641 - 4.21418i) q^{82} -15.8068i q^{83} +7.78089i q^{85} +(-13.8095 + 7.13191i) q^{86} +(-18.4105 - 2.60639i) q^{88} -4.06349i q^{89} +4.05196 q^{91} +(-7.93947 + 11.1835i) q^{92} +(8.94705 - 4.62070i) q^{94} +2.65858 q^{95} -4.90438 q^{97} +(1.25654 - 0.648937i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{4} + O(q^{10}) \) \( 48q - 4q^{4} - 12q^{10} - 12q^{16} + 16q^{19} - 24q^{22} + 48q^{25} + 8q^{28} + 12q^{34} + 32q^{40} + 64q^{43} + 60q^{46} - 48q^{49} + 16q^{52} + 36q^{58} - 4q^{64} + 32q^{67} + 12q^{70} - 32q^{76} + 36q^{82} + 24q^{88} - 60q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25654 + 0.648937i −0.888505 + 0.458867i
\(3\) 0 0
\(4\) 1.15776 1.63082i 0.578881 0.815412i
\(5\) −1.27600 −0.570644 −0.285322 0.958432i \(-0.592101\pi\)
−0.285322 + 0.958432i \(0.592101\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −0.396469 + 2.80050i −0.140173 + 0.990127i
\(9\) 0 0
\(10\) 1.60334 0.828043i 0.507020 0.261850i
\(11\) 6.57401i 1.98214i 0.133353 + 0.991069i \(0.457426\pi\)
−0.133353 + 0.991069i \(0.542574\pi\)
\(12\) 0 0
\(13\) 4.05196i 1.12381i −0.827201 0.561906i \(-0.810068\pi\)
0.827201 0.561906i \(-0.189932\pi\)
\(14\) −0.648937 1.25654i −0.173436 0.335823i
\(15\) 0 0
\(16\) −1.31917 3.77621i −0.329793 0.944053i
\(17\) 6.09788i 1.47895i −0.673182 0.739477i \(-0.735073\pi\)
0.673182 0.739477i \(-0.264927\pi\)
\(18\) 0 0
\(19\) −2.08352 −0.477993 −0.238997 0.971020i \(-0.576819\pi\)
−0.238997 + 0.971020i \(0.576819\pi\)
\(20\) −1.47730 + 2.08093i −0.330335 + 0.465310i
\(21\) 0 0
\(22\) −4.26611 8.26047i −0.909538 1.76114i
\(23\) −6.85760 −1.42991 −0.714954 0.699171i \(-0.753552\pi\)
−0.714954 + 0.699171i \(0.753552\pi\)
\(24\) 0 0
\(25\) −3.37182 −0.674365
\(26\) 2.62946 + 5.09143i 0.515680 + 0.998511i
\(27\) 0 0
\(28\) 1.63082 + 1.15776i 0.308197 + 0.218797i
\(29\) 6.53304 1.21316 0.606578 0.795024i \(-0.292542\pi\)
0.606578 + 0.795024i \(0.292542\pi\)
\(30\) 0 0
\(31\) 3.26844i 0.587028i 0.955955 + 0.293514i \(0.0948248\pi\)
−0.955955 + 0.293514i \(0.905175\pi\)
\(32\) 4.10811 + 3.88889i 0.726218 + 0.687465i
\(33\) 0 0
\(34\) 3.95714 + 7.66220i 0.678643 + 1.31406i
\(35\) 1.27600i 0.215683i
\(36\) 0 0
\(37\) 2.95562i 0.485901i −0.970039 0.242950i \(-0.921885\pi\)
0.970039 0.242950i \(-0.0781152\pi\)
\(38\) 2.61802 1.35208i 0.424699 0.219336i
\(39\) 0 0
\(40\) 0.505894 3.57344i 0.0799889 0.565010i
\(41\) 3.35381i 0.523777i 0.965098 + 0.261888i \(0.0843452\pi\)
−0.965098 + 0.261888i \(0.915655\pi\)
\(42\) 0 0
\(43\) 10.9901 1.67598 0.837991 0.545685i \(-0.183730\pi\)
0.837991 + 0.545685i \(0.183730\pi\)
\(44\) 10.7210 + 7.61114i 1.61626 + 1.14742i
\(45\) 0 0
\(46\) 8.61682 4.45015i 1.27048 0.656138i
\(47\) −7.12041 −1.03862 −0.519310 0.854586i \(-0.673811\pi\)
−0.519310 + 0.854586i \(0.673811\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 4.23682 2.18810i 0.599176 0.309444i
\(51\) 0 0
\(52\) −6.60803 4.69121i −0.916369 0.650553i
\(53\) −2.87278 −0.394607 −0.197304 0.980342i \(-0.563218\pi\)
−0.197304 + 0.980342i \(0.563218\pi\)
\(54\) 0 0
\(55\) 8.38843i 1.13110i
\(56\) −2.80050 0.396469i −0.374233 0.0529804i
\(57\) 0 0
\(58\) −8.20900 + 4.23953i −1.07789 + 0.556677i
\(59\) 7.75213i 1.00924i −0.863341 0.504621i \(-0.831632\pi\)
0.863341 0.504621i \(-0.168368\pi\)
\(60\) 0 0
\(61\) 12.0251i 1.53966i −0.638249 0.769830i \(-0.720341\pi\)
0.638249 0.769830i \(-0.279659\pi\)
\(62\) −2.12101 4.10691i −0.269368 0.521578i
\(63\) 0 0
\(64\) −7.68562 2.22063i −0.960703 0.277578i
\(65\) 5.17030i 0.641296i
\(66\) 0 0
\(67\) −3.01966 −0.368910 −0.184455 0.982841i \(-0.559052\pi\)
−0.184455 + 0.982841i \(0.559052\pi\)
\(68\) −9.94457 7.05990i −1.20596 0.856138i
\(69\) 0 0
\(70\) 0.828043 + 1.60334i 0.0989700 + 0.191636i
\(71\) −3.48158 −0.413188 −0.206594 0.978427i \(-0.566238\pi\)
−0.206594 + 0.978427i \(0.566238\pi\)
\(72\) 0 0
\(73\) 2.76889 0.324075 0.162037 0.986785i \(-0.448194\pi\)
0.162037 + 0.986785i \(0.448194\pi\)
\(74\) 1.91801 + 3.71384i 0.222964 + 0.431725i
\(75\) 0 0
\(76\) −2.41223 + 3.39786i −0.276701 + 0.389761i
\(77\) −6.57401 −0.749177
\(78\) 0 0
\(79\) 0.849261i 0.0955494i −0.998858 0.0477747i \(-0.984787\pi\)
0.998858 0.0477747i \(-0.0152129\pi\)
\(80\) 1.68326 + 4.81845i 0.188194 + 0.538719i
\(81\) 0 0
\(82\) −2.17641 4.21418i −0.240344 0.465378i
\(83\) 15.8068i 1.73503i −0.497414 0.867513i \(-0.665717\pi\)
0.497414 0.867513i \(-0.334283\pi\)
\(84\) 0 0
\(85\) 7.78089i 0.843956i
\(86\) −13.8095 + 7.13191i −1.48912 + 0.769053i
\(87\) 0 0
\(88\) −18.4105 2.60639i −1.96257 0.277842i
\(89\) 4.06349i 0.430729i −0.976534 0.215365i \(-0.930906\pi\)
0.976534 0.215365i \(-0.0690940\pi\)
\(90\) 0 0
\(91\) 4.05196 0.424761
\(92\) −7.93947 + 11.1835i −0.827747 + 1.16596i
\(93\) 0 0
\(94\) 8.94705 4.62070i 0.922818 0.476589i
\(95\) 2.65858 0.272764
\(96\) 0 0
\(97\) −4.90438 −0.497964 −0.248982 0.968508i \(-0.580096\pi\)
−0.248982 + 0.968508i \(0.580096\pi\)
\(98\) 1.25654 0.648937i 0.126929 0.0655525i
\(99\) 0 0
\(100\) −3.90377 + 5.49885i −0.390377 + 0.549885i
\(101\) −16.5134 −1.64314 −0.821572 0.570105i \(-0.806902\pi\)
−0.821572 + 0.570105i \(0.806902\pi\)
\(102\) 0 0
\(103\) 10.7097i 1.05526i −0.849475 0.527629i \(-0.823081\pi\)
0.849475 0.527629i \(-0.176919\pi\)
\(104\) 11.3475 + 1.60648i 1.11272 + 0.157528i
\(105\) 0 0
\(106\) 3.60975 1.86425i 0.350610 0.181072i
\(107\) 9.41994i 0.910660i −0.890323 0.455330i \(-0.849521\pi\)
0.890323 0.455330i \(-0.150479\pi\)
\(108\) 0 0
\(109\) 7.95370i 0.761826i −0.924611 0.380913i \(-0.875610\pi\)
0.924611 0.380913i \(-0.124390\pi\)
\(110\) 5.44356 + 10.5404i 0.519023 + 1.00498i
\(111\) 0 0
\(112\) 3.77621 1.31917i 0.356819 0.124650i
\(113\) 1.56398i 0.147127i 0.997291 + 0.0735636i \(0.0234372\pi\)
−0.997291 + 0.0735636i \(0.976563\pi\)
\(114\) 0 0
\(115\) 8.75029 0.815969
\(116\) 7.56371 10.6542i 0.702273 0.989221i
\(117\) 0 0
\(118\) 5.03064 + 9.74083i 0.463108 + 0.896716i
\(119\) 6.09788 0.558992
\(120\) 0 0
\(121\) −32.2175 −2.92887
\(122\) 7.80354 + 15.1100i 0.706499 + 1.36799i
\(123\) 0 0
\(124\) 5.33024 + 3.78407i 0.478670 + 0.339820i
\(125\) 10.6824 0.955467
\(126\) 0 0
\(127\) 19.7895i 1.75603i 0.478629 + 0.878017i \(0.341134\pi\)
−0.478629 + 0.878017i \(0.658866\pi\)
\(128\) 11.0983 2.19719i 0.980961 0.194206i
\(129\) 0 0
\(130\) −3.35519 6.49666i −0.294270 0.569795i
\(131\) 13.6907i 1.19616i −0.801436 0.598080i \(-0.795931\pi\)
0.801436 0.598080i \(-0.204069\pi\)
\(132\) 0 0
\(133\) 2.08352i 0.180664i
\(134\) 3.79431 1.95957i 0.327778 0.169281i
\(135\) 0 0
\(136\) 17.0771 + 2.41762i 1.46435 + 0.207309i
\(137\) 20.0099i 1.70956i −0.518990 0.854780i \(-0.673692\pi\)
0.518990 0.854780i \(-0.326308\pi\)
\(138\) 0 0
\(139\) −11.0306 −0.935607 −0.467804 0.883832i \(-0.654955\pi\)
−0.467804 + 0.883832i \(0.654955\pi\)
\(140\) −2.08093 1.47730i −0.175871 0.124855i
\(141\) 0 0
\(142\) 4.37473 2.25932i 0.367119 0.189598i
\(143\) 26.6376 2.22755
\(144\) 0 0
\(145\) −8.33616 −0.692280
\(146\) −3.47921 + 1.79684i −0.287942 + 0.148707i
\(147\) 0 0
\(148\) −4.82009 3.42190i −0.396209 0.281279i
\(149\) 0.391867 0.0321030 0.0160515 0.999871i \(-0.494890\pi\)
0.0160515 + 0.999871i \(0.494890\pi\)
\(150\) 0 0
\(151\) 10.3302i 0.840662i −0.907371 0.420331i \(-0.861914\pi\)
0.907371 0.420331i \(-0.138086\pi\)
\(152\) 0.826053 5.83492i 0.0670018 0.473274i
\(153\) 0 0
\(154\) 8.26047 4.26611i 0.665648 0.343773i
\(155\) 4.17052i 0.334984i
\(156\) 0 0
\(157\) 9.78139i 0.780640i −0.920679 0.390320i \(-0.872364\pi\)
0.920679 0.390320i \(-0.127636\pi\)
\(158\) 0.551117 + 1.06713i 0.0438445 + 0.0848961i
\(159\) 0 0
\(160\) −5.24194 4.96222i −0.414412 0.392298i
\(161\) 6.85760i 0.540455i
\(162\) 0 0
\(163\) 1.11525 0.0873533 0.0436766 0.999046i \(-0.486093\pi\)
0.0436766 + 0.999046i \(0.486093\pi\)
\(164\) 5.46947 + 3.88291i 0.427094 + 0.303205i
\(165\) 0 0
\(166\) 10.2576 + 19.8619i 0.796147 + 1.54158i
\(167\) −16.7973 −1.29982 −0.649908 0.760013i \(-0.725193\pi\)
−0.649908 + 0.760013i \(0.725193\pi\)
\(168\) 0 0
\(169\) −3.41837 −0.262951
\(170\) −5.04931 9.77697i −0.387264 0.749859i
\(171\) 0 0
\(172\) 12.7240 17.9230i 0.970194 1.36661i
\(173\) −18.2063 −1.38420 −0.692100 0.721802i \(-0.743314\pi\)
−0.692100 + 0.721802i \(0.743314\pi\)
\(174\) 0 0
\(175\) 3.37182i 0.254886i
\(176\) 24.8248 8.67223i 1.87124 0.653694i
\(177\) 0 0
\(178\) 2.63695 + 5.10592i 0.197648 + 0.382705i
\(179\) 8.03488i 0.600555i 0.953852 + 0.300278i \(0.0970793\pi\)
−0.953852 + 0.300278i \(0.902921\pi\)
\(180\) 0 0
\(181\) 18.5478i 1.37865i 0.724454 + 0.689323i \(0.242092\pi\)
−0.724454 + 0.689323i \(0.757908\pi\)
\(182\) −5.09143 + 2.62946i −0.377402 + 0.194909i
\(183\) 0 0
\(184\) 2.71883 19.2047i 0.200435 1.41579i
\(185\) 3.77137i 0.277276i
\(186\) 0 0
\(187\) 40.0875 2.93149
\(188\) −8.24375 + 11.6121i −0.601237 + 0.846902i
\(189\) 0 0
\(190\) −3.34060 + 1.72525i −0.242352 + 0.125163i
\(191\) −22.8458 −1.65306 −0.826532 0.562890i \(-0.809689\pi\)
−0.826532 + 0.562890i \(0.809689\pi\)
\(192\) 0 0
\(193\) 3.49311 0.251439 0.125720 0.992066i \(-0.459876\pi\)
0.125720 + 0.992066i \(0.459876\pi\)
\(194\) 6.16252 3.18263i 0.442443 0.228499i
\(195\) 0 0
\(196\) −1.15776 + 1.63082i −0.0826973 + 0.116487i
\(197\) 21.9432 1.56339 0.781693 0.623663i \(-0.214356\pi\)
0.781693 + 0.623663i \(0.214356\pi\)
\(198\) 0 0
\(199\) 23.0870i 1.63660i 0.574793 + 0.818299i \(0.305082\pi\)
−0.574793 + 0.818299i \(0.694918\pi\)
\(200\) 1.33682 9.44280i 0.0945278 0.667707i
\(201\) 0 0
\(202\) 20.7497 10.7161i 1.45994 0.753985i
\(203\) 6.53304i 0.458529i
\(204\) 0 0
\(205\) 4.27946i 0.298890i
\(206\) 6.94992 + 13.4571i 0.484224 + 0.937602i
\(207\) 0 0
\(208\) −15.3011 + 5.34522i −1.06094 + 0.370625i
\(209\) 13.6971i 0.947448i
\(210\) 0 0
\(211\) −1.71426 −0.118014 −0.0590072 0.998258i \(-0.518793\pi\)
−0.0590072 + 0.998258i \(0.518793\pi\)
\(212\) −3.32600 + 4.68500i −0.228431 + 0.321767i
\(213\) 0 0
\(214\) 6.11294 + 11.8365i 0.417872 + 0.809126i
\(215\) −14.0234 −0.956389
\(216\) 0 0
\(217\) −3.26844 −0.221876
\(218\) 5.16145 + 9.99411i 0.349577 + 0.676886i
\(219\) 0 0
\(220\) −13.6800 9.71181i −0.922309 0.654770i
\(221\) −24.7084 −1.66206
\(222\) 0 0
\(223\) 0.545891i 0.0365556i 0.999833 + 0.0182778i \(0.00581832\pi\)
−0.999833 + 0.0182778i \(0.994182\pi\)
\(224\) −3.88889 + 4.10811i −0.259837 + 0.274484i
\(225\) 0 0
\(226\) −1.01493 1.96520i −0.0675119 0.130723i
\(227\) 1.60514i 0.106537i 0.998580 + 0.0532685i \(0.0169639\pi\)
−0.998580 + 0.0532685i \(0.983036\pi\)
\(228\) 0 0
\(229\) 1.39412i 0.0921257i 0.998939 + 0.0460629i \(0.0146675\pi\)
−0.998939 + 0.0460629i \(0.985333\pi\)
\(230\) −10.9951 + 5.67839i −0.724993 + 0.374422i
\(231\) 0 0
\(232\) −2.59015 + 18.2958i −0.170052 + 1.20118i
\(233\) 10.0130i 0.655971i −0.944683 0.327985i \(-0.893630\pi\)
0.944683 0.327985i \(-0.106370\pi\)
\(234\) 0 0
\(235\) 9.08565 0.592682
\(236\) −12.6424 8.97513i −0.822948 0.584231i
\(237\) 0 0
\(238\) −7.66220 + 3.95714i −0.496667 + 0.256503i
\(239\) 9.62073 0.622313 0.311157 0.950359i \(-0.399284\pi\)
0.311157 + 0.950359i \(0.399284\pi\)
\(240\) 0 0
\(241\) 13.9788 0.900456 0.450228 0.892914i \(-0.351343\pi\)
0.450228 + 0.892914i \(0.351343\pi\)
\(242\) 40.4825 20.9071i 2.60231 1.34396i
\(243\) 0 0
\(244\) −19.6109 13.9222i −1.25546 0.891280i
\(245\) 1.27600 0.0815206
\(246\) 0 0
\(247\) 8.44235i 0.537174i
\(248\) −9.15326 1.29583i −0.581233 0.0822855i
\(249\) 0 0
\(250\) −13.4229 + 6.93223i −0.848937 + 0.438433i
\(251\) 6.99814i 0.441719i 0.975306 + 0.220859i \(0.0708862\pi\)
−0.975306 + 0.220859i \(0.929114\pi\)
\(252\) 0 0
\(253\) 45.0819i 2.83427i
\(254\) −12.8421 24.8662i −0.805787 1.56024i
\(255\) 0 0
\(256\) −12.5196 + 9.96294i −0.782474 + 0.622684i
\(257\) 4.39346i 0.274057i −0.990567 0.137028i \(-0.956245\pi\)
0.990567 0.137028i \(-0.0437551\pi\)
\(258\) 0 0
\(259\) 2.95562 0.183653
\(260\) 8.43184 + 5.98598i 0.522921 + 0.371235i
\(261\) 0 0
\(262\) 8.88438 + 17.2028i 0.548879 + 1.06279i
\(263\) −8.54094 −0.526657 −0.263328 0.964706i \(-0.584820\pi\)
−0.263328 + 0.964706i \(0.584820\pi\)
\(264\) 0 0
\(265\) 3.66567 0.225180
\(266\) 1.35208 + 2.61802i 0.0829010 + 0.160521i
\(267\) 0 0
\(268\) −3.49605 + 4.92453i −0.213555 + 0.300814i
\(269\) 14.7389 0.898647 0.449324 0.893369i \(-0.351665\pi\)
0.449324 + 0.893369i \(0.351665\pi\)
\(270\) 0 0
\(271\) 4.21696i 0.256162i 0.991764 + 0.128081i \(0.0408817\pi\)
−0.991764 + 0.128081i \(0.959118\pi\)
\(272\) −23.0269 + 8.04414i −1.39621 + 0.487748i
\(273\) 0 0
\(274\) 12.9852 + 25.1431i 0.784462 + 1.51895i
\(275\) 22.1664i 1.33668i
\(276\) 0 0
\(277\) 2.73096i 0.164088i 0.996629 + 0.0820438i \(0.0261447\pi\)
−0.996629 + 0.0820438i \(0.973855\pi\)
\(278\) 13.8604 7.15819i 0.831291 0.429320i
\(279\) 0 0
\(280\) 3.57344 + 0.505894i 0.213554 + 0.0302330i
\(281\) 9.32789i 0.556455i −0.960515 0.278228i \(-0.910253\pi\)
0.960515 0.278228i \(-0.0897469\pi\)
\(282\) 0 0
\(283\) 20.2355 1.20288 0.601438 0.798919i \(-0.294595\pi\)
0.601438 + 0.798919i \(0.294595\pi\)
\(284\) −4.03084 + 5.67784i −0.239187 + 0.336918i
\(285\) 0 0
\(286\) −33.4711 + 17.2861i −1.97919 + 1.02215i
\(287\) −3.35381 −0.197969
\(288\) 0 0
\(289\) −20.1841 −1.18730
\(290\) 10.4747 5.40964i 0.615094 0.317665i
\(291\) 0 0
\(292\) 3.20572 4.51558i 0.187601 0.264254i
\(293\) 0.259973 0.0151878 0.00759391 0.999971i \(-0.497583\pi\)
0.00759391 + 0.999971i \(0.497583\pi\)
\(294\) 0 0
\(295\) 9.89172i 0.575918i
\(296\) 8.27722 + 1.17181i 0.481103 + 0.0681101i
\(297\) 0 0
\(298\) −0.492395 + 0.254297i −0.0285237 + 0.0147310i
\(299\) 27.7867i 1.60695i
\(300\) 0 0
\(301\) 10.9901i 0.633461i
\(302\) 6.70367 + 12.9803i 0.385753 + 0.746933i
\(303\) 0 0
\(304\) 2.74852 + 7.86783i 0.157639 + 0.451251i
\(305\) 15.3441i 0.878598i
\(306\) 0 0
\(307\) 25.8255 1.47394 0.736969 0.675927i \(-0.236257\pi\)
0.736969 + 0.675927i \(0.236257\pi\)
\(308\) −7.61114 + 10.7210i −0.433685 + 0.610888i
\(309\) 0 0
\(310\) 2.70640 + 5.24041i 0.153713 + 0.297635i
\(311\) 19.8253 1.12419 0.562094 0.827074i \(-0.309996\pi\)
0.562094 + 0.827074i \(0.309996\pi\)
\(312\) 0 0
\(313\) 10.2201 0.577673 0.288837 0.957378i \(-0.406732\pi\)
0.288837 + 0.957378i \(0.406732\pi\)
\(314\) 6.34750 + 12.2907i 0.358210 + 0.693602i
\(315\) 0 0
\(316\) −1.38500 0.983243i −0.0779121 0.0553117i
\(317\) 3.21191 0.180399 0.0901995 0.995924i \(-0.471250\pi\)
0.0901995 + 0.995924i \(0.471250\pi\)
\(318\) 0 0
\(319\) 42.9482i 2.40464i
\(320\) 9.80685 + 2.83352i 0.548220 + 0.158398i
\(321\) 0 0
\(322\) 4.45015 + 8.61682i 0.247997 + 0.480196i
\(323\) 12.7051i 0.706930i
\(324\) 0 0
\(325\) 13.6625i 0.757859i
\(326\) −1.40135 + 0.723728i −0.0776138 + 0.0400836i
\(327\) 0 0
\(328\) −9.39234 1.32968i −0.518605 0.0734193i
\(329\) 7.12041i 0.392561i
\(330\) 0 0
\(331\) −29.8260 −1.63939 −0.819694 0.572802i \(-0.805856\pi\)
−0.819694 + 0.572802i \(0.805856\pi\)
\(332\) −25.7782 18.3006i −1.41476 1.00437i
\(333\) 0 0
\(334\) 21.1064 10.9004i 1.15489 0.596443i
\(335\) 3.85308 0.210516
\(336\) 0 0
\(337\) −26.9588 −1.46854 −0.734271 0.678857i \(-0.762476\pi\)
−0.734271 + 0.678857i \(0.762476\pi\)
\(338\) 4.29530 2.21830i 0.233633 0.120660i
\(339\) 0 0
\(340\) 12.6893 + 9.00843i 0.688172 + 0.488551i
\(341\) −21.4867 −1.16357
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −4.35725 + 30.7779i −0.234927 + 1.65943i
\(345\) 0 0
\(346\) 22.8769 11.8147i 1.22987 0.635164i
\(347\) 1.73769i 0.0932843i 0.998912 + 0.0466421i \(0.0148520\pi\)
−0.998912 + 0.0466421i \(0.985148\pi\)
\(348\) 0 0
\(349\) 16.8981i 0.904536i 0.891882 + 0.452268i \(0.149385\pi\)
−0.891882 + 0.452268i \(0.850615\pi\)
\(350\) 2.18810 + 4.23682i 0.116959 + 0.226467i
\(351\) 0 0
\(352\) −25.5656 + 27.0067i −1.36265 + 1.43946i
\(353\) 12.2774i 0.653459i 0.945118 + 0.326730i \(0.105947\pi\)
−0.945118 + 0.326730i \(0.894053\pi\)
\(354\) 0 0
\(355\) 4.44249 0.235783
\(356\) −6.62684 4.70456i −0.351222 0.249341i
\(357\) 0 0
\(358\) −5.21413 10.0961i −0.275575 0.533596i
\(359\) −3.77380 −0.199173 −0.0995867 0.995029i \(-0.531752\pi\)
−0.0995867 + 0.995029i \(0.531752\pi\)
\(360\) 0 0
\(361\) −14.6589 −0.771522
\(362\) −12.0363 23.3060i −0.632616 1.22493i
\(363\) 0 0
\(364\) 4.69121 6.60803i 0.245886 0.346355i
\(365\) −3.53311 −0.184931
\(366\) 0 0
\(367\) 28.6703i 1.49658i −0.663372 0.748289i \(-0.730875\pi\)
0.663372 0.748289i \(-0.269125\pi\)
\(368\) 9.04634 + 25.8958i 0.471573 + 1.34991i
\(369\) 0 0
\(370\) −2.44738 4.73886i −0.127233 0.246361i
\(371\) 2.87278i 0.149147i
\(372\) 0 0
\(373\) 27.3540i 1.41634i 0.706043 + 0.708169i \(0.250478\pi\)
−0.706043 + 0.708169i \(0.749522\pi\)
\(374\) −50.3714 + 26.0142i −2.60464 + 1.34516i
\(375\) 0 0
\(376\) 2.82302 19.9407i 0.145586 1.02836i
\(377\) 26.4716i 1.36336i
\(378\) 0 0
\(379\) −18.6336 −0.957146 −0.478573 0.878048i \(-0.658846\pi\)
−0.478573 + 0.878048i \(0.658846\pi\)
\(380\) 3.07800 4.33567i 0.157898 0.222415i
\(381\) 0 0
\(382\) 28.7065 14.8255i 1.46875 0.758537i
\(383\) 27.8368 1.42240 0.711198 0.702992i \(-0.248153\pi\)
0.711198 + 0.702992i \(0.248153\pi\)
\(384\) 0 0
\(385\) 8.38843 0.427514
\(386\) −4.38921 + 2.26680i −0.223405 + 0.115377i
\(387\) 0 0
\(388\) −5.67810 + 7.99817i −0.288262 + 0.406046i
\(389\) −7.10860 −0.360420 −0.180210 0.983628i \(-0.557678\pi\)
−0.180210 + 0.983628i \(0.557678\pi\)
\(390\) 0 0
\(391\) 41.8168i 2.11477i
\(392\) 0.396469 2.80050i 0.0200247 0.141447i
\(393\) 0 0
\(394\) −27.5724 + 14.2397i −1.38908 + 0.717387i
\(395\) 1.08366i 0.0545247i
\(396\) 0 0
\(397\) 32.8312i 1.64775i 0.566771 + 0.823875i \(0.308192\pi\)
−0.566771 + 0.823875i \(0.691808\pi\)
\(398\) −14.9820 29.0097i −0.750981 1.45412i
\(399\) 0 0
\(400\) 4.44801 + 12.7327i 0.222401 + 0.636637i
\(401\) 29.0585i 1.45111i 0.688164 + 0.725555i \(0.258417\pi\)
−0.688164 + 0.725555i \(0.741583\pi\)
\(402\) 0 0
\(403\) 13.2436 0.659709
\(404\) −19.1186 + 26.9304i −0.951185 + 1.33984i
\(405\) 0 0
\(406\) −4.23953 8.20900i −0.210404 0.407406i
\(407\) 19.4303 0.963122
\(408\) 0 0
\(409\) −5.68368 −0.281040 −0.140520 0.990078i \(-0.544877\pi\)
−0.140520 + 0.990078i \(0.544877\pi\)
\(410\) 2.77710 + 5.37729i 0.137151 + 0.265565i
\(411\) 0 0
\(412\) −17.4656 12.3993i −0.860470 0.610869i
\(413\) 7.75213 0.381458
\(414\) 0 0
\(415\) 20.1695i 0.990083i
\(416\) 15.7576 16.6459i 0.772581 0.816131i
\(417\) 0 0
\(418\) 8.88855 + 17.2109i 0.434753 + 0.841812i
\(419\) 2.00749i 0.0980722i 0.998797 + 0.0490361i \(0.0156149\pi\)
−0.998797 + 0.0490361i \(0.984385\pi\)
\(420\) 0 0
\(421\) 16.4735i 0.802871i −0.915887 0.401435i \(-0.868511\pi\)
0.915887 0.401435i \(-0.131489\pi\)
\(422\) 2.15403 1.11244i 0.104856 0.0541530i
\(423\) 0 0
\(424\) 1.13897 8.04524i 0.0553133 0.390711i
\(425\) 20.5610i 0.997354i
\(426\) 0 0
\(427\) 12.0251 0.581936
\(428\) −15.3623 10.9061i −0.742563 0.527164i
\(429\) 0 0
\(430\) 17.6209 9.10031i 0.849757 0.438856i
\(431\) −17.2399 −0.830417 −0.415209 0.909726i \(-0.636291\pi\)
−0.415209 + 0.909726i \(0.636291\pi\)
\(432\) 0 0
\(433\) −38.1465 −1.83321 −0.916603 0.399799i \(-0.869080\pi\)
−0.916603 + 0.399799i \(0.869080\pi\)
\(434\) 4.10691 2.12101i 0.197138 0.101812i
\(435\) 0 0
\(436\) −12.9711 9.20850i −0.621202 0.441007i
\(437\) 14.2880 0.683487
\(438\) 0 0
\(439\) 7.30831i 0.348806i 0.984674 + 0.174403i \(0.0557996\pi\)
−0.984674 + 0.174403i \(0.944200\pi\)
\(440\) 23.4918 + 3.32575i 1.11993 + 0.158549i
\(441\) 0 0
\(442\) 31.0469 16.0342i 1.47675 0.762667i
\(443\) 21.7787i 1.03474i 0.855763 + 0.517368i \(0.173088\pi\)
−0.855763 + 0.517368i \(0.826912\pi\)
\(444\) 0 0
\(445\) 5.18501i 0.245793i
\(446\) −0.354249 0.685931i −0.0167742 0.0324798i
\(447\) 0 0
\(448\) 2.22063 7.68562i 0.104915 0.363112i
\(449\) 1.30200i 0.0614451i −0.999528 0.0307225i \(-0.990219\pi\)
0.999528 0.0307225i \(-0.00978083\pi\)
\(450\) 0 0
\(451\) −22.0479 −1.03820
\(452\) 2.55058 + 1.81072i 0.119969 + 0.0851692i
\(453\) 0 0
\(454\) −1.04163 2.01692i −0.0488863 0.0946585i
\(455\) −5.17030 −0.242387
\(456\) 0 0
\(457\) 3.17657 0.148594 0.0742968 0.997236i \(-0.476329\pi\)
0.0742968 + 0.997236i \(0.476329\pi\)
\(458\) −0.904692 1.75176i −0.0422735 0.0818542i
\(459\) 0 0
\(460\) 10.1308 14.2702i 0.472349 0.665351i
\(461\) 8.56764 0.399035 0.199517 0.979894i \(-0.436063\pi\)
0.199517 + 0.979894i \(0.436063\pi\)
\(462\) 0 0
\(463\) 19.9440i 0.926877i −0.886129 0.463438i \(-0.846615\pi\)
0.886129 0.463438i \(-0.153385\pi\)
\(464\) −8.61819 24.6702i −0.400090 1.14528i
\(465\) 0 0
\(466\) 6.49777 + 12.5816i 0.301004 + 0.582833i
\(467\) 11.5091i 0.532579i 0.963893 + 0.266290i \(0.0857978\pi\)
−0.963893 + 0.266290i \(0.914202\pi\)
\(468\) 0 0
\(469\) 3.01966i 0.139435i
\(470\) −11.4164 + 5.89601i −0.526601 + 0.271963i
\(471\) 0 0
\(472\) 21.7099 + 3.07348i 0.999278 + 0.141468i
\(473\) 72.2493i 3.32203i
\(474\) 0 0
\(475\) 7.02528 0.322342
\(476\) 7.05990 9.94457i 0.323590 0.455808i
\(477\) 0 0
\(478\) −12.0888 + 6.24324i −0.552928 + 0.285559i
\(479\) −5.91391 −0.270213 −0.135107 0.990831i \(-0.543138\pi\)
−0.135107 + 0.990831i \(0.543138\pi\)
\(480\) 0 0
\(481\) −11.9760 −0.546061
\(482\) −17.5649 + 9.07138i −0.800059 + 0.413190i
\(483\) 0 0
\(484\) −37.3003 + 52.5411i −1.69547 + 2.38823i
\(485\) 6.25798 0.284160
\(486\) 0 0
\(487\) 20.4470i 0.926541i −0.886217 0.463271i \(-0.846676\pi\)
0.886217 0.463271i \(-0.153324\pi\)
\(488\) 33.6764 + 4.76759i 1.52446 + 0.215819i
\(489\) 0 0
\(490\) −1.60334 + 0.828043i −0.0724315 + 0.0374072i
\(491\) 24.0391i 1.08487i −0.840098 0.542434i \(-0.817503\pi\)
0.840098 0.542434i \(-0.182497\pi\)
\(492\) 0 0
\(493\) 39.8377i 1.79420i
\(494\) −5.47855 10.6081i −0.246492 0.477282i
\(495\) 0 0
\(496\) 12.3423 4.31162i 0.554186 0.193598i
\(497\) 3.48158i 0.156170i
\(498\) 0 0
\(499\) 29.1375 1.30438 0.652188 0.758057i \(-0.273851\pi\)
0.652188 + 0.758057i \(0.273851\pi\)
\(500\) 12.3677 17.4212i 0.553102 0.779099i
\(501\) 0 0
\(502\) −4.54135 8.79342i −0.202690 0.392469i
\(503\) −9.70604 −0.432771 −0.216386 0.976308i \(-0.569427\pi\)
−0.216386 + 0.976308i \(0.569427\pi\)
\(504\) 0 0
\(505\) 21.0711 0.937651
\(506\) 29.2553 + 56.6470i 1.30056 + 2.51827i
\(507\) 0 0
\(508\) 32.2732 + 22.9115i 1.43189 + 1.01654i
\(509\) −15.5042 −0.687213 −0.343606 0.939114i \(-0.611649\pi\)
−0.343606 + 0.939114i \(0.611649\pi\)
\(510\) 0 0
\(511\) 2.76889i 0.122489i
\(512\) 9.26598 20.6432i 0.409502 0.912309i
\(513\) 0 0
\(514\) 2.85108 + 5.52054i 0.125756 + 0.243501i
\(515\) 13.6656i 0.602177i
\(516\) 0 0
\(517\) 46.8096i 2.05869i
\(518\) −3.71384 + 1.91801i −0.163177 + 0.0842725i
\(519\) 0 0
\(520\) −14.4794 2.04986i −0.634965 0.0898924i
\(521\) 6.22420i 0.272687i −0.990662 0.136344i \(-0.956465\pi\)
0.990662 0.136344i \(-0.0435351\pi\)
\(522\) 0 0
\(523\) 33.3752 1.45939 0.729697 0.683770i \(-0.239661\pi\)
0.729697 + 0.683770i \(0.239661\pi\)
\(524\) −22.3271 15.8506i −0.975363 0.692435i
\(525\) 0 0
\(526\) 10.7320 5.54253i 0.467937 0.241666i
\(527\) 19.9305 0.868188
\(528\) 0 0
\(529\) 24.0267 1.04464
\(530\) −4.60605 + 2.37879i −0.200074 + 0.103328i
\(531\) 0 0
\(532\) −3.39786 2.41223i −0.147316 0.104583i
\(533\) 13.5895 0.588626
\(534\) 0 0
\(535\) 12.0198i 0.519663i
\(536\) 1.19720 8.45656i 0.0517112 0.365268i
\(537\) 0 0
\(538\) −18.5200 + 9.56462i −0.798452 + 0.412360i
\(539\) 6.57401i 0.283162i
\(540\) 0 0
\(541\) 4.04207i 0.173782i 0.996218 + 0.0868911i \(0.0276932\pi\)
−0.996218 + 0.0868911i \(0.972307\pi\)
\(542\) −2.73654 5.29876i −0.117544 0.227601i
\(543\) 0 0
\(544\) 23.7140 25.0507i 1.01673 1.07404i
\(545\) 10.1489i 0.434732i
\(546\) 0 0
\(547\) −19.7497 −0.844436 −0.422218 0.906494i \(-0.638748\pi\)
−0.422218 + 0.906494i \(0.638748\pi\)
\(548\) −32.6326 23.1667i −1.39400 0.989633i
\(549\) 0 0
\(550\) 14.3846 + 27.8529i 0.613361 + 1.18765i
\(551\) −13.6117 −0.579880
\(552\) 0 0
\(553\) 0.849261 0.0361143
\(554\) −1.77222 3.43155i −0.0752944 0.145793i
\(555\) 0 0
\(556\) −12.7709 + 17.9890i −0.541605 + 0.762905i
\(557\) 11.2192 0.475373 0.237687 0.971342i \(-0.423611\pi\)
0.237687 + 0.971342i \(0.423611\pi\)
\(558\) 0 0
\(559\) 44.5316i 1.88349i
\(560\) −4.81845 + 1.68326i −0.203617 + 0.0711308i
\(561\) 0 0
\(562\) 6.05321 + 11.7208i 0.255339 + 0.494413i
\(563\) 8.66666i 0.365256i −0.983182 0.182628i \(-0.941540\pi\)
0.983182 0.182628i \(-0.0584604\pi\)
\(564\) 0 0
\(565\) 1.99564i 0.0839573i
\(566\) −25.4266 + 13.1316i −1.06876 + 0.551961i
\(567\) 0 0
\(568\) 1.38034 9.75017i 0.0579177 0.409108i
\(569\) 27.0778i 1.13516i 0.823317 + 0.567581i \(0.192121\pi\)
−0.823317 + 0.567581i \(0.807879\pi\)
\(570\) 0 0
\(571\) 19.5104 0.816485 0.408243 0.912873i \(-0.366142\pi\)
0.408243 + 0.912873i \(0.366142\pi\)
\(572\) 30.8400 43.4412i 1.28949 1.81637i
\(573\) 0 0
\(574\) 4.21418 2.17641i 0.175896 0.0908415i
\(575\) 23.1226 0.964280
\(576\) 0 0
\(577\) −23.4544 −0.976421 −0.488211 0.872726i \(-0.662350\pi\)
−0.488211 + 0.872726i \(0.662350\pi\)
\(578\) 25.3621 13.0982i 1.05492 0.544814i
\(579\) 0 0
\(580\) −9.65129 + 13.5948i −0.400748 + 0.564493i
\(581\) 15.8068 0.655778
\(582\) 0 0
\(583\) 18.8857i 0.782165i
\(584\) −1.09778 + 7.75430i −0.0454265 + 0.320875i
\(585\) 0 0
\(586\) −0.326666 + 0.168706i −0.0134944 + 0.00696919i
\(587\) 8.29331i 0.342302i −0.985245 0.171151i \(-0.945251\pi\)
0.985245 0.171151i \(-0.0547485\pi\)
\(588\) 0 0
\(589\) 6.80987i 0.280596i
\(590\) −6.41910 12.4293i −0.264270 0.511706i
\(591\) 0 0
\(592\) −11.1610 + 3.89897i −0.458716 + 0.160246i
\(593\) 5.99359i 0.246127i 0.992399 + 0.123064i \(0.0392719\pi\)
−0.992399 + 0.123064i \(0.960728\pi\)
\(594\) 0 0
\(595\) −7.78089 −0.318986
\(596\) 0.453689 0.639066i 0.0185838 0.0261772i
\(597\) 0 0
\(598\) −18.0318 34.9150i −0.737376 1.42778i
\(599\) −41.0912 −1.67894 −0.839470 0.543405i \(-0.817135\pi\)
−0.839470 + 0.543405i \(0.817135\pi\)
\(600\) 0 0
\(601\) −14.9084 −0.608128 −0.304064 0.952652i \(-0.598344\pi\)
−0.304064 + 0.952652i \(0.598344\pi\)
\(602\) −7.13191 13.8095i −0.290675 0.562833i
\(603\) 0 0
\(604\) −16.8468 11.9600i −0.685486 0.486644i
\(605\) 41.1096 1.67134
\(606\) 0 0
\(607\) 21.1672i 0.859152i −0.903031 0.429576i \(-0.858663\pi\)
0.903031 0.429576i \(-0.141337\pi\)
\(608\) −8.55934 8.10259i −0.347127 0.328604i
\(609\) 0 0
\(610\) −9.95732 19.2803i −0.403160 0.780638i
\(611\) 28.8516i 1.16721i
\(612\) 0 0
\(613\) 21.0293i 0.849367i −0.905342 0.424683i \(-0.860385\pi\)
0.905342 0.424683i \(-0.139615\pi\)
\(614\) −32.4506 + 16.7591i −1.30960 + 0.676342i
\(615\) 0 0
\(616\) 2.60639 18.4105i 0.105014 0.741781i
\(617\) 29.2848i 1.17896i −0.807783 0.589480i \(-0.799333\pi\)
0.807783 0.589480i \(-0.200667\pi\)
\(618\) 0 0
\(619\) 43.6407 1.75407 0.877034 0.480428i \(-0.159519\pi\)
0.877034 + 0.480428i \(0.159519\pi\)
\(620\) −6.80139 4.82848i −0.273150 0.193916i
\(621\) 0 0
\(622\) −24.9111 + 12.8653i −0.998846 + 0.515853i
\(623\) 4.06349 0.162800
\(624\) 0 0
\(625\) 3.22833 0.129133
\(626\) −12.8419 + 6.63219i −0.513266 + 0.265075i
\(627\) 0 0
\(628\) −15.9517 11.3245i −0.636543 0.451898i
\(629\) −18.0230 −0.718624
\(630\) 0 0
\(631\) 33.7501i 1.34357i 0.740747 + 0.671784i \(0.234472\pi\)
−0.740747 + 0.671784i \(0.765528\pi\)
\(632\) 2.37836 + 0.336706i 0.0946060 + 0.0133934i
\(633\) 0 0
\(634\) −4.03588 + 2.08433i −0.160285 + 0.0827792i
\(635\) 25.2514i 1.00207i
\(636\) 0 0
\(637\) 4.05196i 0.160544i
\(638\) −27.8707 53.9660i −1.10341 2.13653i
\(639\) 0 0
\(640\) −14.1614 + 2.80361i −0.559780 + 0.110822i
\(641\) 13.1478i 0.519306i −0.965702 0.259653i \(-0.916392\pi\)
0.965702 0.259653i \(-0.0836083\pi\)
\(642\) 0 0
\(643\) −26.7796 −1.05608 −0.528042 0.849218i \(-0.677074\pi\)
−0.528042 + 0.849218i \(0.677074\pi\)
\(644\) −11.1835 7.93947i −0.440693 0.312859i
\(645\) 0 0
\(646\) −8.24479 15.9644i −0.324387 0.628110i
\(647\) −13.7850 −0.541944 −0.270972 0.962587i \(-0.587345\pi\)
−0.270972 + 0.962587i \(0.587345\pi\)
\(648\) 0 0
\(649\) 50.9626 2.00046
\(650\) −8.86609 17.1674i −0.347757 0.673361i
\(651\) 0 0
\(652\) 1.29120 1.81878i 0.0505672 0.0712289i
\(653\) −34.5245 −1.35105 −0.675524 0.737338i \(-0.736083\pi\)
−0.675524 + 0.737338i \(0.736083\pi\)
\(654\) 0 0
\(655\) 17.4693i 0.682582i
\(656\) 12.6647 4.42424i 0.494473 0.172738i
\(657\) 0 0
\(658\) 4.62070 + 8.94705i 0.180134 + 0.348792i
\(659\) 31.8035i 1.23889i 0.785040 + 0.619445i \(0.212642\pi\)
−0.785040 + 0.619445i \(0.787358\pi\)
\(660\) 0 0
\(661\) 14.7156i 0.572370i −0.958174 0.286185i \(-0.907613\pi\)
0.958174 0.286185i \(-0.0923873\pi\)
\(662\) 37.4775 19.3552i 1.45660 0.752261i
\(663\) 0 0
\(664\) 44.2671 + 6.26692i 1.71790 + 0.243204i
\(665\) 2.65858i 0.103095i
\(666\) 0 0
\(667\) −44.8010 −1.73470
\(668\) −19.4473 + 27.3935i −0.752439 + 1.05989i
\(669\) 0 0
\(670\) −4.84154 + 2.50041i −0.187045 + 0.0965991i
\(671\) 79.0532 3.05182
\(672\) 0 0
\(673\) 14.1705 0.546233 0.273116 0.961981i \(-0.411946\pi\)
0.273116 + 0.961981i \(0.411946\pi\)
\(674\) 33.8747 17.4946i 1.30481 0.673866i
\(675\) 0 0
\(676\) −3.95766 + 5.57475i −0.152218 + 0.214414i
\(677\) 33.9994 1.30670 0.653351 0.757055i \(-0.273362\pi\)
0.653351 + 0.757055i \(0.273362\pi\)
\(678\) 0 0
\(679\) 4.90438i 0.188213i
\(680\) −21.7904 3.08488i −0.835624 0.118300i
\(681\) 0 0
\(682\) 26.9988 13.9435i 1.03384 0.533925i
\(683\) 24.7265i 0.946132i 0.881027 + 0.473066i \(0.156853\pi\)
−0.881027 + 0.473066i \(0.843147\pi\)
\(684\) 0 0
\(685\) 25.5326i 0.975551i
\(686\) 0.648937 + 1.25654i 0.0247765 + 0.0479747i
\(687\) 0 0
\(688\) −14.4979 41.5011i −0.552726 1.58222i
\(689\) 11.6404i 0.443464i
\(690\) 0 0
\(691\) −19.2490 −0.732267 −0.366134 0.930562i \(-0.619319\pi\)
−0.366134 + 0.930562i \(0.619319\pi\)
\(692\) −21.0786 + 29.6913i −0.801288 + 1.12869i
\(693\) 0 0
\(694\) −1.12765 2.18347i −0.0428051 0.0828835i
\(695\) 14.0751 0.533899
\(696\) 0 0
\(697\) 20.4511 0.774641
\(698\) −10.9658 21.2331i −0.415062 0.803685i
\(699\) 0 0
\(700\) −5.49885 3.90377i −0.207837 0.147549i
\(701\) 13.4914 0.509563 0.254781 0.966999i \(-0.417996\pi\)
0.254781 + 0.966999i \(0.417996\pi\)
\(702\) 0 0
\(703\) 6.15810i 0.232257i
\(704\) 14.5984 50.5253i 0.550198 1.90425i
\(705\) 0 0
\(706\) −7.96724 15.4270i −0.299851 0.580601i
\(707\) 16.5134i 0.621050i
\(708\) 0 0
\(709\) 12.1839i 0.457575i −0.973476 0.228788i \(-0.926524\pi\)
0.973476 0.228788i \(-0.0734761\pi\)
\(710\) −5.58215 + 2.88290i −0.209494 + 0.108193i
\(711\) 0 0
\(712\) 11.3798 + 1.61105i 0.426477 + 0.0603766i
\(713\) 22.4136i 0.839397i
\(714\) 0 0
\(715\) −33.9896 −1.27114
\(716\) 13.1035 + 9.30248i 0.489700 + 0.347650i
\(717\) 0 0
\(718\) 4.74191 2.44896i 0.176967 0.0913942i
\(719\) −2.14139 −0.0798603 −0.0399301 0.999202i \(-0.512714\pi\)
−0.0399301 + 0.999202i \(0.512714\pi\)
\(720\) 0 0
\(721\) 10.7097 0.398850
\(722\) 18.4195 9.51271i 0.685501 0.354026i
\(723\) 0 0
\(724\) 30.2482 + 21.4739i 1.12416 + 0.798073i
\(725\) −22.0283 −0.818109
\(726\) 0 0
\(727\) 36.8865i 1.36804i −0.729462 0.684022i \(-0.760229\pi\)
0.729462 0.684022i \(-0.239771\pi\)
\(728\) −1.60648 + 11.3475i −0.0595400 + 0.420567i
\(729\) 0 0
\(730\) 4.43948 2.29276i 0.164312 0.0848590i
\(731\) 67.0166i 2.47870i
\(732\) 0 0
\(733\) 28.2007i 1.04162i 0.853674 + 0.520808i \(0.174369\pi\)
−0.853674 + 0.520808i \(0.825631\pi\)
\(734\) 18.6052 + 36.0253i 0.686731 + 1.32972i
\(735\) 0 0
\(736\) −28.1718 26.6684i −1.03842 0.983012i
\(737\) 19.8513i 0.731230i
\(738\) 0 0
\(739\) −13.9006 −0.511341 −0.255670 0.966764i \(-0.582296\pi\)
−0.255670 + 0.966764i \(0.582296\pi\)
\(740\) 6.15044 + 4.36635i 0.226095 + 0.160510i
\(741\) 0 0
\(742\) 1.86425 + 3.60975i 0.0684389 + 0.132518i
\(743\) −5.81892 −0.213476 −0.106738 0.994287i \(-0.534041\pi\)
−0.106738 + 0.994287i \(0.534041\pi\)
\(744\) 0 0
\(745\) −0.500022 −0.0183194
\(746\) −17.7510 34.3713i −0.649911 1.25842i
\(747\) 0 0
\(748\) 46.4118 65.3756i 1.69698 2.39037i
\(749\) 9.41994 0.344197
\(750\) 0 0
\(751\) 36.7860i 1.34234i −0.741304 0.671170i \(-0.765792\pi\)
0.741304 0.671170i \(-0.234208\pi\)
\(752\) 9.39304 + 26.8882i 0.342529 + 0.980512i
\(753\) 0 0
\(754\) 17.1784 + 33.2625i 0.625600 + 1.21135i
\(755\) 13.1814i 0.479719i
\(756\) 0 0
\(757\) 16.6555i 0.605356i −0.953093 0.302678i \(-0.902119\pi\)
0.953093 0.302678i \(-0.0978806\pi\)
\(758\) 23.4138 12.0921i 0.850429 0.439203i
\(759\) 0 0
\(760\) −1.05404 + 7.44535i −0.0382342 + 0.270071i
\(761\) 38.2510i 1.38660i 0.720651 + 0.693298i \(0.243843\pi\)
−0.720651 + 0.693298i \(0.756157\pi\)
\(762\) 0 0
\(763\) 7.95370 0.287943
\(764\) −26.4500 + 37.2575i −0.956928 + 1.34793i
\(765\) 0 0
\(766\) −34.9780 + 18.0643i −1.26380 + 0.652691i
\(767\) −31.4113 −1.13420
\(768\) 0 0
\(769\) −40.1021 −1.44612 −0.723059 0.690787i \(-0.757264\pi\)
−0.723059 + 0.690787i \(0.757264\pi\)
\(770\) −10.5404 + 5.44356i −0.379848 + 0.196172i
\(771\) 0 0
\(772\) 4.04419 5.69664i 0.145554 0.205027i
\(773\) 1.84516 0.0663659 0.0331830 0.999449i \(-0.489436\pi\)
0.0331830 + 0.999449i \(0.489436\pi\)
\(774\) 0 0
\(775\) 11.0206i 0.395871i
\(776\) 1.94443 13.7347i 0.0698011 0.493047i
\(777\) 0 0
\(778\) 8.93221 4.61303i 0.320235 0.165385i
\(779\) 6.98774i 0.250362i
\(780\) 0 0
\(781\) 22.8879i 0.818994i
\(782\) &