Properties

Label 4020.2.g.c.1609.21
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.21
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000i q^{3}\) \(+(-2.22744 - 0.196195i) q^{5}\) \(-0.128273i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000i q^{3}\) \(+(-2.22744 - 0.196195i) q^{5}\) \(-0.128273i q^{7}\) \(-1.00000 q^{9}\) \(+0.0389925 q^{11}\) \(+3.81852i q^{13}\) \(+(0.196195 - 2.22744i) q^{15}\) \(-6.63903i q^{17}\) \(+7.30512 q^{19}\) \(+0.128273 q^{21}\) \(+3.64921i q^{23}\) \(+(4.92301 + 0.874027i) q^{25}\) \(-1.00000i q^{27}\) \(-8.25219 q^{29}\) \(-7.07939 q^{31}\) \(+0.0389925i q^{33}\) \(+(-0.0251666 + 0.285721i) q^{35}\) \(+7.37252i q^{37}\) \(-3.81852 q^{39}\) \(+1.87351 q^{41}\) \(+7.72398i q^{43}\) \(+(2.22744 + 0.196195i) q^{45}\) \(-9.62406i q^{47}\) \(+6.98355 q^{49}\) \(+6.63903 q^{51}\) \(+3.82384i q^{53}\) \(+(-0.0868535 - 0.00765013i) q^{55}\) \(+7.30512i q^{57}\) \(+9.48802 q^{59}\) \(-6.69509 q^{61}\) \(+0.128273i q^{63}\) \(+(0.749174 - 8.50553i) q^{65}\) \(+1.00000i q^{67}\) \(-3.64921 q^{69}\) \(+4.88025 q^{71}\) \(+0.309819i q^{73}\) \(+(-0.874027 + 4.92301i) q^{75}\) \(-0.00500168i q^{77}\) \(-5.72909 q^{79}\) \(+1.00000 q^{81}\) \(+14.6840i q^{83}\) \(+(-1.30255 + 14.7881i) q^{85}\) \(-8.25219i q^{87}\) \(-11.6793 q^{89}\) \(+0.489813 q^{91}\) \(-7.07939i q^{93}\) \(+(-16.2718 - 1.43323i) q^{95}\) \(-7.10494i q^{97}\) \(-0.0389925 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −2.22744 0.196195i −0.996143 0.0877411i
\(6\) 0 0
\(7\) 0.128273i 0.0484827i −0.999706 0.0242413i \(-0.992283\pi\)
0.999706 0.0242413i \(-0.00771701\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 0.0389925 0.0117567 0.00587834 0.999983i \(-0.498129\pi\)
0.00587834 + 0.999983i \(0.498129\pi\)
\(12\) 0 0
\(13\) 3.81852i 1.05907i 0.848289 + 0.529533i \(0.177633\pi\)
−0.848289 + 0.529533i \(0.822367\pi\)
\(14\) 0 0
\(15\) 0.196195 2.22744i 0.0506573 0.575124i
\(16\) 0 0
\(17\) 6.63903i 1.61020i −0.593137 0.805101i \(-0.702111\pi\)
0.593137 0.805101i \(-0.297889\pi\)
\(18\) 0 0
\(19\) 7.30512 1.67591 0.837955 0.545739i \(-0.183751\pi\)
0.837955 + 0.545739i \(0.183751\pi\)
\(20\) 0 0
\(21\) 0.128273 0.0279915
\(22\) 0 0
\(23\) 3.64921i 0.760914i 0.924799 + 0.380457i \(0.124233\pi\)
−0.924799 + 0.380457i \(0.875767\pi\)
\(24\) 0 0
\(25\) 4.92301 + 0.874027i 0.984603 + 0.174805i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −8.25219 −1.53239 −0.766197 0.642606i \(-0.777853\pi\)
−0.766197 + 0.642606i \(0.777853\pi\)
\(30\) 0 0
\(31\) −7.07939 −1.27150 −0.635748 0.771896i \(-0.719308\pi\)
−0.635748 + 0.771896i \(0.719308\pi\)
\(32\) 0 0
\(33\) 0.0389925i 0.00678772i
\(34\) 0 0
\(35\) −0.0251666 + 0.285721i −0.00425392 + 0.0482957i
\(36\) 0 0
\(37\) 7.37252i 1.21204i 0.795451 + 0.606018i \(0.207234\pi\)
−0.795451 + 0.606018i \(0.792766\pi\)
\(38\) 0 0
\(39\) −3.81852 −0.611452
\(40\) 0 0
\(41\) 1.87351 0.292593 0.146296 0.989241i \(-0.453265\pi\)
0.146296 + 0.989241i \(0.453265\pi\)
\(42\) 0 0
\(43\) 7.72398i 1.17790i 0.808171 + 0.588948i \(0.200458\pi\)
−0.808171 + 0.588948i \(0.799542\pi\)
\(44\) 0 0
\(45\) 2.22744 + 0.196195i 0.332048 + 0.0292470i
\(46\) 0 0
\(47\) 9.62406i 1.40381i −0.712269 0.701907i \(-0.752332\pi\)
0.712269 0.701907i \(-0.247668\pi\)
\(48\) 0 0
\(49\) 6.98355 0.997649
\(50\) 0 0
\(51\) 6.63903 0.929651
\(52\) 0 0
\(53\) 3.82384i 0.525244i 0.964899 + 0.262622i \(0.0845872\pi\)
−0.964899 + 0.262622i \(0.915413\pi\)
\(54\) 0 0
\(55\) −0.0868535 0.00765013i −0.0117113 0.00103154i
\(56\) 0 0
\(57\) 7.30512i 0.967587i
\(58\) 0 0
\(59\) 9.48802 1.23524 0.617618 0.786478i \(-0.288098\pi\)
0.617618 + 0.786478i \(0.288098\pi\)
\(60\) 0 0
\(61\) −6.69509 −0.857218 −0.428609 0.903490i \(-0.640996\pi\)
−0.428609 + 0.903490i \(0.640996\pi\)
\(62\) 0 0
\(63\) 0.128273i 0.0161609i
\(64\) 0 0
\(65\) 0.749174 8.50553i 0.0929236 1.05498i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −3.64921 −0.439314
\(70\) 0 0
\(71\) 4.88025 0.579179 0.289590 0.957151i \(-0.406481\pi\)
0.289590 + 0.957151i \(0.406481\pi\)
\(72\) 0 0
\(73\) 0.309819i 0.0362615i 0.999836 + 0.0181308i \(0.00577152\pi\)
−0.999836 + 0.0181308i \(0.994228\pi\)
\(74\) 0 0
\(75\) −0.874027 + 4.92301i −0.100924 + 0.568461i
\(76\) 0 0
\(77\) 0.00500168i 0.000569995i
\(78\) 0 0
\(79\) −5.72909 −0.644573 −0.322286 0.946642i \(-0.604451\pi\)
−0.322286 + 0.946642i \(0.604451\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 14.6840i 1.61178i 0.592066 + 0.805889i \(0.298312\pi\)
−0.592066 + 0.805889i \(0.701688\pi\)
\(84\) 0 0
\(85\) −1.30255 + 14.7881i −0.141281 + 1.60399i
\(86\) 0 0
\(87\) 8.25219i 0.884728i
\(88\) 0 0
\(89\) −11.6793 −1.23800 −0.619000 0.785391i \(-0.712462\pi\)
−0.619000 + 0.785391i \(0.712462\pi\)
\(90\) 0 0
\(91\) 0.489813 0.0513464
\(92\) 0 0
\(93\) 7.07939i 0.734099i
\(94\) 0 0
\(95\) −16.2718 1.43323i −1.66945 0.147046i
\(96\) 0 0
\(97\) 7.10494i 0.721397i −0.932682 0.360699i \(-0.882538\pi\)
0.932682 0.360699i \(-0.117462\pi\)
\(98\) 0 0
\(99\) −0.0389925 −0.00391889
\(100\) 0 0
\(101\) −10.7135 −1.06604 −0.533018 0.846104i \(-0.678942\pi\)
−0.533018 + 0.846104i \(0.678942\pi\)
\(102\) 0 0
\(103\) 14.2892i 1.40796i −0.710220 0.703980i \(-0.751405\pi\)
0.710220 0.703980i \(-0.248595\pi\)
\(104\) 0 0
\(105\) −0.285721 0.0251666i −0.0278835 0.00245600i
\(106\) 0 0
\(107\) 8.57849i 0.829314i −0.909978 0.414657i \(-0.863902\pi\)
0.909978 0.414657i \(-0.136098\pi\)
\(108\) 0 0
\(109\) −19.4768 −1.86554 −0.932771 0.360470i \(-0.882616\pi\)
−0.932771 + 0.360470i \(0.882616\pi\)
\(110\) 0 0
\(111\) −7.37252 −0.699769
\(112\) 0 0
\(113\) 13.6083i 1.28016i 0.768307 + 0.640082i \(0.221100\pi\)
−0.768307 + 0.640082i \(0.778900\pi\)
\(114\) 0 0
\(115\) 0.715958 8.12842i 0.0667634 0.757979i
\(116\) 0 0
\(117\) 3.81852i 0.353022i
\(118\) 0 0
\(119\) −0.851610 −0.0780669
\(120\) 0 0
\(121\) −10.9985 −0.999862
\(122\) 0 0
\(123\) 1.87351i 0.168929i
\(124\) 0 0
\(125\) −10.7943 2.91272i −0.965468 0.260521i
\(126\) 0 0
\(127\) 13.3524i 1.18483i 0.805631 + 0.592417i \(0.201826\pi\)
−0.805631 + 0.592417i \(0.798174\pi\)
\(128\) 0 0
\(129\) −7.72398 −0.680058
\(130\) 0 0
\(131\) −10.7666 −0.940684 −0.470342 0.882484i \(-0.655869\pi\)
−0.470342 + 0.882484i \(0.655869\pi\)
\(132\) 0 0
\(133\) 0.937051i 0.0812526i
\(134\) 0 0
\(135\) −0.196195 + 2.22744i −0.0168858 + 0.191708i
\(136\) 0 0
\(137\) 8.39755i 0.717451i −0.933443 0.358726i \(-0.883211\pi\)
0.933443 0.358726i \(-0.116789\pi\)
\(138\) 0 0
\(139\) −20.3819 −1.72877 −0.864387 0.502827i \(-0.832293\pi\)
−0.864387 + 0.502827i \(0.832293\pi\)
\(140\) 0 0
\(141\) 9.62406 0.810492
\(142\) 0 0
\(143\) 0.148893i 0.0124511i
\(144\) 0 0
\(145\) 18.3813 + 1.61904i 1.52648 + 0.134454i
\(146\) 0 0
\(147\) 6.98355i 0.575993i
\(148\) 0 0
\(149\) −8.64717 −0.708404 −0.354202 0.935169i \(-0.615247\pi\)
−0.354202 + 0.935169i \(0.615247\pi\)
\(150\) 0 0
\(151\) −11.9792 −0.974854 −0.487427 0.873164i \(-0.662065\pi\)
−0.487427 + 0.873164i \(0.662065\pi\)
\(152\) 0 0
\(153\) 6.63903i 0.536734i
\(154\) 0 0
\(155\) 15.7690 + 1.38894i 1.26659 + 0.111563i
\(156\) 0 0
\(157\) 8.35135i 0.666510i 0.942837 + 0.333255i \(0.108147\pi\)
−0.942837 + 0.333255i \(0.891853\pi\)
\(158\) 0 0
\(159\) −3.82384 −0.303250
\(160\) 0 0
\(161\) 0.468096 0.0368911
\(162\) 0 0
\(163\) 5.06915i 0.397046i 0.980096 + 0.198523i \(0.0636145\pi\)
−0.980096 + 0.198523i \(0.936385\pi\)
\(164\) 0 0
\(165\) 0.00765013 0.0868535i 0.000595562 0.00676154i
\(166\) 0 0
\(167\) 0.558745i 0.0432370i −0.999766 0.0216185i \(-0.993118\pi\)
0.999766 0.0216185i \(-0.00688191\pi\)
\(168\) 0 0
\(169\) −1.58107 −0.121621
\(170\) 0 0
\(171\) −7.30512 −0.558637
\(172\) 0 0
\(173\) 13.7845i 1.04802i −0.851714 0.524008i \(-0.824436\pi\)
0.851714 0.524008i \(-0.175564\pi\)
\(174\) 0 0
\(175\) 0.112114 0.631490i 0.00847504 0.0477362i
\(176\) 0 0
\(177\) 9.48802i 0.713163i
\(178\) 0 0
\(179\) 8.05610 0.602141 0.301071 0.953602i \(-0.402656\pi\)
0.301071 + 0.953602i \(0.402656\pi\)
\(180\) 0 0
\(181\) 14.8933 1.10701 0.553506 0.832845i \(-0.313289\pi\)
0.553506 + 0.832845i \(0.313289\pi\)
\(182\) 0 0
\(183\) 6.69509i 0.494915i
\(184\) 0 0
\(185\) 1.44645 16.4219i 0.106345 1.20736i
\(186\) 0 0
\(187\) 0.258872i 0.0189306i
\(188\) 0 0
\(189\) −0.128273 −0.00933050
\(190\) 0 0
\(191\) 3.66876 0.265462 0.132731 0.991152i \(-0.457625\pi\)
0.132731 + 0.991152i \(0.457625\pi\)
\(192\) 0 0
\(193\) 12.1084i 0.871585i 0.900047 + 0.435793i \(0.143532\pi\)
−0.900047 + 0.435793i \(0.856468\pi\)
\(194\) 0 0
\(195\) 8.50553 + 0.749174i 0.609094 + 0.0536495i
\(196\) 0 0
\(197\) 3.59577i 0.256188i 0.991762 + 0.128094i \(0.0408859\pi\)
−0.991762 + 0.128094i \(0.959114\pi\)
\(198\) 0 0
\(199\) −7.80795 −0.553491 −0.276745 0.960943i \(-0.589256\pi\)
−0.276745 + 0.960943i \(0.589256\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 1.05853i 0.0742946i
\(204\) 0 0
\(205\) −4.17314 0.367573i −0.291464 0.0256724i
\(206\) 0 0
\(207\) 3.64921i 0.253638i
\(208\) 0 0
\(209\) 0.284845 0.0197031
\(210\) 0 0
\(211\) −23.8266 −1.64029 −0.820146 0.572154i \(-0.806108\pi\)
−0.820146 + 0.572154i \(0.806108\pi\)
\(212\) 0 0
\(213\) 4.88025i 0.334389i
\(214\) 0 0
\(215\) 1.51541 17.2047i 0.103350 1.17335i
\(216\) 0 0
\(217\) 0.908096i 0.0616456i
\(218\) 0 0
\(219\) −0.309819 −0.0209356
\(220\) 0 0
\(221\) 25.3513 1.70531
\(222\) 0 0
\(223\) 8.63279i 0.578094i 0.957315 + 0.289047i \(0.0933384\pi\)
−0.957315 + 0.289047i \(0.906662\pi\)
\(224\) 0 0
\(225\) −4.92301 0.874027i −0.328201 0.0582685i
\(226\) 0 0
\(227\) 8.58160i 0.569581i 0.958590 + 0.284790i \(0.0919240\pi\)
−0.958590 + 0.284790i \(0.908076\pi\)
\(228\) 0 0
\(229\) −3.20564 −0.211835 −0.105917 0.994375i \(-0.533778\pi\)
−0.105917 + 0.994375i \(0.533778\pi\)
\(230\) 0 0
\(231\) 0.00500168 0.000329087
\(232\) 0 0
\(233\) 11.2934i 0.739854i −0.929061 0.369927i \(-0.879383\pi\)
0.929061 0.369927i \(-0.120617\pi\)
\(234\) 0 0
\(235\) −1.88819 + 21.4371i −0.123172 + 1.39840i
\(236\) 0 0
\(237\) 5.72909i 0.372144i
\(238\) 0 0
\(239\) −21.5672 −1.39507 −0.697534 0.716552i \(-0.745719\pi\)
−0.697534 + 0.716552i \(0.745719\pi\)
\(240\) 0 0
\(241\) 9.36087 0.602987 0.301493 0.953468i \(-0.402515\pi\)
0.301493 + 0.953468i \(0.402515\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −15.5555 1.37014i −0.993802 0.0875349i
\(246\) 0 0
\(247\) 27.8947i 1.77490i
\(248\) 0 0
\(249\) −14.6840 −0.930561
\(250\) 0 0
\(251\) −10.7667 −0.679589 −0.339794 0.940500i \(-0.610358\pi\)
−0.339794 + 0.940500i \(0.610358\pi\)
\(252\) 0 0
\(253\) 0.142292i 0.00894581i
\(254\) 0 0
\(255\) −14.7881 1.30255i −0.926065 0.0815686i
\(256\) 0 0
\(257\) 22.0839i 1.37756i 0.724972 + 0.688779i \(0.241853\pi\)
−0.724972 + 0.688779i \(0.758147\pi\)
\(258\) 0 0
\(259\) 0.945697 0.0587627
\(260\) 0 0
\(261\) 8.25219 0.510798
\(262\) 0 0
\(263\) 21.5995i 1.33188i −0.746006 0.665940i \(-0.768031\pi\)
0.746006 0.665940i \(-0.231969\pi\)
\(264\) 0 0
\(265\) 0.750218 8.51738i 0.0460855 0.523218i
\(266\) 0 0
\(267\) 11.6793i 0.714759i
\(268\) 0 0
\(269\) −6.86649 −0.418657 −0.209329 0.977845i \(-0.567128\pi\)
−0.209329 + 0.977845i \(0.567128\pi\)
\(270\) 0 0
\(271\) −13.7804 −0.837101 −0.418550 0.908194i \(-0.637462\pi\)
−0.418550 + 0.908194i \(0.637462\pi\)
\(272\) 0 0
\(273\) 0.489813i 0.0296448i
\(274\) 0 0
\(275\) 0.191960 + 0.0340805i 0.0115757 + 0.00205513i
\(276\) 0 0
\(277\) 13.0593i 0.784660i −0.919825 0.392330i \(-0.871669\pi\)
0.919825 0.392330i \(-0.128331\pi\)
\(278\) 0 0
\(279\) 7.07939 0.423832
\(280\) 0 0
\(281\) −1.32410 −0.0789894 −0.0394947 0.999220i \(-0.512575\pi\)
−0.0394947 + 0.999220i \(0.512575\pi\)
\(282\) 0 0
\(283\) 5.70161i 0.338926i −0.985537 0.169463i \(-0.945797\pi\)
0.985537 0.169463i \(-0.0542033\pi\)
\(284\) 0 0
\(285\) 1.43323 16.2718i 0.0848972 0.963855i
\(286\) 0 0
\(287\) 0.240321i 0.0141857i
\(288\) 0 0
\(289\) −27.0768 −1.59275
\(290\) 0 0
\(291\) 7.10494 0.416499
\(292\) 0 0
\(293\) 20.4885i 1.19695i 0.801142 + 0.598475i \(0.204226\pi\)
−0.801142 + 0.598475i \(0.795774\pi\)
\(294\) 0 0
\(295\) −21.1340 1.86150i −1.23047 0.108381i
\(296\) 0 0
\(297\) 0.0389925i 0.00226257i
\(298\) 0 0
\(299\) −13.9346 −0.805858
\(300\) 0 0
\(301\) 0.990778 0.0571075
\(302\) 0 0
\(303\) 10.7135i 0.615476i
\(304\) 0 0
\(305\) 14.9129 + 1.31354i 0.853912 + 0.0752132i
\(306\) 0 0
\(307\) 30.2141i 1.72441i −0.506559 0.862205i \(-0.669083\pi\)
0.506559 0.862205i \(-0.330917\pi\)
\(308\) 0 0
\(309\) 14.2892 0.812886
\(310\) 0 0
\(311\) −4.73813 −0.268675 −0.134337 0.990936i \(-0.542891\pi\)
−0.134337 + 0.990936i \(0.542891\pi\)
\(312\) 0 0
\(313\) 28.2789i 1.59842i 0.601053 + 0.799209i \(0.294748\pi\)
−0.601053 + 0.799209i \(0.705252\pi\)
\(314\) 0 0
\(315\) 0.0251666 0.285721i 0.00141797 0.0160986i
\(316\) 0 0
\(317\) 17.4748i 0.981484i −0.871305 0.490742i \(-0.836726\pi\)
0.871305 0.490742i \(-0.163274\pi\)
\(318\) 0 0
\(319\) −0.321773 −0.0180159
\(320\) 0 0
\(321\) 8.57849 0.478805
\(322\) 0 0
\(323\) 48.4990i 2.69855i
\(324\) 0 0
\(325\) −3.33749 + 18.7986i −0.185131 + 1.04276i
\(326\) 0 0
\(327\) 19.4768i 1.07707i
\(328\) 0 0
\(329\) −1.23451 −0.0680607
\(330\) 0 0
\(331\) 14.5657 0.800602 0.400301 0.916384i \(-0.368906\pi\)
0.400301 + 0.916384i \(0.368906\pi\)
\(332\) 0 0
\(333\) 7.37252i 0.404012i
\(334\) 0 0
\(335\) 0.196195 2.22744i 0.0107193 0.121698i
\(336\) 0 0
\(337\) 11.5522i 0.629286i 0.949210 + 0.314643i \(0.101885\pi\)
−0.949210 + 0.314643i \(0.898115\pi\)
\(338\) 0 0
\(339\) −13.6083 −0.739103
\(340\) 0 0
\(341\) −0.276043 −0.0149486
\(342\) 0 0
\(343\) 1.79371i 0.0968514i
\(344\) 0 0
\(345\) 8.12842 + 0.715958i 0.437619 + 0.0385459i
\(346\) 0 0
\(347\) 35.1190i 1.88529i 0.333802 + 0.942643i \(0.391668\pi\)
−0.333802 + 0.942643i \(0.608332\pi\)
\(348\) 0 0
\(349\) 13.5558 0.725625 0.362813 0.931862i \(-0.381817\pi\)
0.362813 + 0.931862i \(0.381817\pi\)
\(350\) 0 0
\(351\) 3.81852 0.203817
\(352\) 0 0
\(353\) 2.02952i 0.108021i 0.998540 + 0.0540103i \(0.0172004\pi\)
−0.998540 + 0.0540103i \(0.982800\pi\)
\(354\) 0 0
\(355\) −10.8705 0.957482i −0.576946 0.0508178i
\(356\) 0 0
\(357\) 0.851610i 0.0450720i
\(358\) 0 0
\(359\) −7.15157 −0.377445 −0.188723 0.982030i \(-0.560435\pi\)
−0.188723 + 0.982030i \(0.560435\pi\)
\(360\) 0 0
\(361\) 34.3648 1.80867
\(362\) 0 0
\(363\) 10.9985i 0.577270i
\(364\) 0 0
\(365\) 0.0607849 0.690104i 0.00318163 0.0361217i
\(366\) 0 0
\(367\) 28.1192i 1.46781i 0.679251 + 0.733906i \(0.262305\pi\)
−0.679251 + 0.733906i \(0.737695\pi\)
\(368\) 0 0
\(369\) −1.87351 −0.0975309
\(370\) 0 0
\(371\) 0.490495 0.0254652
\(372\) 0 0
\(373\) 33.3825i 1.72848i 0.503079 + 0.864240i \(0.332200\pi\)
−0.503079 + 0.864240i \(0.667800\pi\)
\(374\) 0 0
\(375\) 2.91272 10.7943i 0.150412 0.557413i
\(376\) 0 0
\(377\) 31.5111i 1.62291i
\(378\) 0 0
\(379\) 6.25718 0.321410 0.160705 0.987002i \(-0.448623\pi\)
0.160705 + 0.987002i \(0.448623\pi\)
\(380\) 0 0
\(381\) −13.3524 −0.684064
\(382\) 0 0
\(383\) 21.9335i 1.12075i −0.828239 0.560375i \(-0.810657\pi\)
0.828239 0.560375i \(-0.189343\pi\)
\(384\) 0 0
\(385\) −0.000981306 0.0111410i −5.00120e−5 0.000567797i
\(386\) 0 0
\(387\) 7.72398i 0.392632i
\(388\) 0 0
\(389\) −15.3986 −0.780739 −0.390369 0.920658i \(-0.627653\pi\)
−0.390369 + 0.920658i \(0.627653\pi\)
\(390\) 0 0
\(391\) 24.2273 1.22523
\(392\) 0 0
\(393\) 10.7666i 0.543104i
\(394\) 0 0
\(395\) 12.7612 + 1.12402i 0.642087 + 0.0565555i
\(396\) 0 0
\(397\) 3.69910i 0.185652i −0.995682 0.0928262i \(-0.970410\pi\)
0.995682 0.0928262i \(-0.0295901\pi\)
\(398\) 0 0
\(399\) 0.937051 0.0469112
\(400\) 0 0
\(401\) −25.1620 −1.25653 −0.628265 0.777999i \(-0.716235\pi\)
−0.628265 + 0.777999i \(0.716235\pi\)
\(402\) 0 0
\(403\) 27.0328i 1.34660i
\(404\) 0 0
\(405\) −2.22744 0.196195i −0.110683 0.00974901i
\(406\) 0 0
\(407\) 0.287473i 0.0142495i
\(408\) 0 0
\(409\) −13.9226 −0.688430 −0.344215 0.938891i \(-0.611855\pi\)
−0.344215 + 0.938891i \(0.611855\pi\)
\(410\) 0 0
\(411\) 8.39755 0.414221
\(412\) 0 0
\(413\) 1.21706i 0.0598875i
\(414\) 0 0
\(415\) 2.88093 32.7078i 0.141419 1.60556i
\(416\) 0 0
\(417\) 20.3819i 0.998108i
\(418\) 0 0
\(419\) 6.28480 0.307033 0.153516 0.988146i \(-0.450940\pi\)
0.153516 + 0.988146i \(0.450940\pi\)
\(420\) 0 0
\(421\) 30.2864 1.47607 0.738035 0.674763i \(-0.235754\pi\)
0.738035 + 0.674763i \(0.235754\pi\)
\(422\) 0 0
\(423\) 9.62406i 0.467938i
\(424\) 0 0
\(425\) 5.80270 32.6841i 0.281472 1.58541i
\(426\) 0 0
\(427\) 0.858799i 0.0415602i
\(428\) 0 0
\(429\) −0.148893 −0.00718864
\(430\) 0 0
\(431\) 7.21790 0.347674 0.173837 0.984774i \(-0.444383\pi\)
0.173837 + 0.984774i \(0.444383\pi\)
\(432\) 0 0
\(433\) 21.0149i 1.00991i −0.863145 0.504957i \(-0.831508\pi\)
0.863145 0.504957i \(-0.168492\pi\)
\(434\) 0 0
\(435\) −1.61904 + 18.3813i −0.0776270 + 0.881316i
\(436\) 0 0
\(437\) 26.6580i 1.27522i
\(438\) 0 0
\(439\) 37.4029 1.78514 0.892572 0.450905i \(-0.148899\pi\)
0.892572 + 0.450905i \(0.148899\pi\)
\(440\) 0 0
\(441\) −6.98355 −0.332550
\(442\) 0 0
\(443\) 27.5717i 1.30997i 0.755641 + 0.654986i \(0.227325\pi\)
−0.755641 + 0.654986i \(0.772675\pi\)
\(444\) 0 0
\(445\) 26.0149 + 2.29141i 1.23322 + 0.108623i
\(446\) 0 0
\(447\) 8.64717i 0.408997i
\(448\) 0 0
\(449\) 7.43854 0.351046 0.175523 0.984475i \(-0.443838\pi\)
0.175523 + 0.984475i \(0.443838\pi\)
\(450\) 0 0
\(451\) 0.0730527 0.00343992
\(452\) 0 0
\(453\) 11.9792i 0.562832i
\(454\) 0 0
\(455\) −1.09103 0.0960989i −0.0511483 0.00450519i
\(456\) 0 0
\(457\) 16.6425i 0.778505i 0.921131 + 0.389253i \(0.127267\pi\)
−0.921131 + 0.389253i \(0.872733\pi\)
\(458\) 0 0
\(459\) −6.63903 −0.309884
\(460\) 0 0
\(461\) 23.7119 1.10438 0.552188 0.833720i \(-0.313793\pi\)
0.552188 + 0.833720i \(0.313793\pi\)
\(462\) 0 0
\(463\) 27.3481i 1.27097i 0.772112 + 0.635486i \(0.219200\pi\)
−0.772112 + 0.635486i \(0.780800\pi\)
\(464\) 0 0
\(465\) −1.38894 + 15.7690i −0.0644106 + 0.731268i
\(466\) 0 0
\(467\) 17.6793i 0.818102i 0.912512 + 0.409051i \(0.134140\pi\)
−0.912512 + 0.409051i \(0.865860\pi\)
\(468\) 0 0
\(469\) 0.128273 0.00592310
\(470\) 0 0
\(471\) −8.35135 −0.384810
\(472\) 0 0
\(473\) 0.301177i 0.0138481i
\(474\) 0 0
\(475\) 35.9632 + 6.38488i 1.65011 + 0.292958i
\(476\) 0 0
\(477\) 3.82384i 0.175081i
\(478\) 0 0
\(479\) −21.5193 −0.983242 −0.491621 0.870809i \(-0.663595\pi\)
−0.491621 + 0.870809i \(0.663595\pi\)
\(480\) 0 0
\(481\) −28.1521 −1.28363
\(482\) 0 0
\(483\) 0.468096i 0.0212991i
\(484\) 0 0
\(485\) −1.39395 + 15.8259i −0.0632962 + 0.718615i
\(486\) 0 0
\(487\) 35.6523i 1.61556i −0.589485 0.807780i \(-0.700669\pi\)
0.589485 0.807780i \(-0.299331\pi\)
\(488\) 0 0
\(489\) −5.06915 −0.229235
\(490\) 0 0
\(491\) −37.7609 −1.70413 −0.852064 0.523438i \(-0.824649\pi\)
−0.852064 + 0.523438i \(0.824649\pi\)
\(492\) 0 0
\(493\) 54.7866i 2.46746i
\(494\) 0 0
\(495\) 0.0868535 + 0.00765013i 0.00390378 + 0.000343848i
\(496\) 0 0
\(497\) 0.626005i 0.0280802i
\(498\) 0 0
\(499\) −16.8673 −0.755084 −0.377542 0.925992i \(-0.623231\pi\)
−0.377542 + 0.925992i \(0.623231\pi\)
\(500\) 0 0
\(501\) 0.558745 0.0249629
\(502\) 0 0
\(503\) 20.4352i 0.911162i 0.890194 + 0.455581i \(0.150568\pi\)
−0.890194 + 0.455581i \(0.849432\pi\)
\(504\) 0 0
\(505\) 23.8638 + 2.10194i 1.06192 + 0.0935351i
\(506\) 0 0
\(507\) 1.58107i 0.0702180i
\(508\) 0 0
\(509\) 37.1112 1.64492 0.822462 0.568820i \(-0.192600\pi\)
0.822462 + 0.568820i \(0.192600\pi\)
\(510\) 0 0
\(511\) 0.0397414 0.00175806
\(512\) 0 0
\(513\) 7.30512i 0.322529i
\(514\) 0 0
\(515\) −2.80348 + 31.8285i −0.123536 + 1.40253i
\(516\) 0 0
\(517\) 0.375266i 0.0165042i
\(518\) 0 0
\(519\) 13.7845 0.605072
\(520\) 0 0
\(521\) 6.14633 0.269276 0.134638 0.990895i \(-0.457013\pi\)
0.134638 + 0.990895i \(0.457013\pi\)
\(522\) 0 0
\(523\) 22.5742i 0.987103i 0.869717 + 0.493551i \(0.164301\pi\)
−0.869717 + 0.493551i \(0.835699\pi\)
\(524\) 0 0
\(525\) 0.631490 + 0.112114i 0.0275605 + 0.00489306i
\(526\) 0 0
\(527\) 47.0003i 2.04737i
\(528\) 0 0
\(529\) 9.68324 0.421010
\(530\) 0 0
\(531\) −9.48802 −0.411745
\(532\) 0 0
\(533\) 7.15402i 0.309875i
\(534\) 0 0
\(535\) −1.68306 + 19.1081i −0.0727649 + 0.826116i
\(536\) 0 0
\(537\) 8.05610i 0.347646i
\(538\) 0 0
\(539\) 0.272306 0.0117290
\(540\) 0 0
\(541\) 10.5657 0.454254 0.227127 0.973865i \(-0.427067\pi\)
0.227127 + 0.973865i \(0.427067\pi\)
\(542\) 0 0
\(543\) 14.8933i 0.639134i
\(544\) 0 0
\(545\) 43.3835 + 3.82126i 1.85835 + 0.163685i
\(546\) 0 0
\(547\) 38.7727i 1.65780i −0.559397 0.828900i \(-0.688967\pi\)
0.559397 0.828900i \(-0.311033\pi\)
\(548\) 0 0
\(549\) 6.69509 0.285739
\(550\) 0 0
\(551\) −60.2833 −2.56815
\(552\) 0 0
\(553\) 0.734888i 0.0312506i
\(554\) 0 0
\(555\) 16.4219 + 1.44645i 0.697070 + 0.0613985i
\(556\) 0 0
\(557\) 16.3818i 0.694119i 0.937843 + 0.347059i \(0.112820\pi\)
−0.937843 + 0.347059i \(0.887180\pi\)
\(558\) 0 0
\(559\) −29.4941 −1.24747
\(560\) 0 0
\(561\) 0.258872 0.0109296
\(562\) 0 0
\(563\) 14.7878i 0.623231i −0.950208 0.311616i \(-0.899130\pi\)
0.950208 0.311616i \(-0.100870\pi\)
\(564\) 0 0
\(565\) 2.66989 30.3118i 0.112323 1.27523i
\(566\) 0 0
\(567\) 0.128273i 0.00538696i
\(568\) 0 0
\(569\) 35.0863 1.47089 0.735447 0.677582i \(-0.236972\pi\)
0.735447 + 0.677582i \(0.236972\pi\)
\(570\) 0 0
\(571\) 10.3369 0.432585 0.216292 0.976329i \(-0.430604\pi\)
0.216292 + 0.976329i \(0.430604\pi\)
\(572\) 0 0
\(573\) 3.66876i 0.153265i
\(574\) 0 0
\(575\) −3.18951 + 17.9651i −0.133012 + 0.749198i
\(576\) 0 0
\(577\) 1.76255i 0.0733760i 0.999327 + 0.0366880i \(0.0116808\pi\)
−0.999327 + 0.0366880i \(0.988319\pi\)
\(578\) 0 0
\(579\) −12.1084 −0.503210
\(580\) 0 0
\(581\) 1.88356 0.0781434
\(582\) 0 0
\(583\) 0.149101i 0.00617512i
\(584\) 0 0
\(585\) −0.749174 + 8.50553i −0.0309745 + 0.351661i
\(586\) 0 0
\(587\) 4.55117i 0.187847i −0.995579 0.0939235i \(-0.970059\pi\)
0.995579 0.0939235i \(-0.0299409\pi\)
\(588\) 0 0
\(589\) −51.7158 −2.13091
\(590\) 0 0
\(591\) −3.59577 −0.147910
\(592\) 0 0
\(593\) 2.67480i 0.109841i −0.998491 0.0549203i \(-0.982510\pi\)
0.998491 0.0549203i \(-0.0174905\pi\)
\(594\) 0 0
\(595\) 1.89691 + 0.167082i 0.0777658 + 0.00684968i
\(596\) 0 0
\(597\) 7.80795i 0.319558i
\(598\) 0 0
\(599\) −26.0897 −1.06600 −0.532998 0.846116i \(-0.678935\pi\)
−0.532998 + 0.846116i \(0.678935\pi\)
\(600\) 0 0
\(601\) −37.9540 −1.54818 −0.774088 0.633078i \(-0.781791\pi\)
−0.774088 + 0.633078i \(0.781791\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 24.4985 + 2.15785i 0.996006 + 0.0877290i
\(606\) 0 0
\(607\) 14.7399i 0.598273i −0.954210 0.299137i \(-0.903301\pi\)
0.954210 0.299137i \(-0.0966986\pi\)
\(608\) 0 0
\(609\) −1.05853 −0.0428940
\(610\) 0 0
\(611\) 36.7497 1.48673
\(612\) 0 0
\(613\) 13.6655i 0.551944i −0.961166 0.275972i \(-0.911000\pi\)
0.961166 0.275972i \(-0.0889996\pi\)
\(614\) 0 0
\(615\) 0.367573 4.17314i 0.0148220 0.168277i
\(616\) 0 0
\(617\) 40.4183i 1.62718i −0.581438 0.813590i \(-0.697510\pi\)
0.581438 0.813590i \(-0.302490\pi\)
\(618\) 0 0
\(619\) −4.32869 −0.173985 −0.0869923 0.996209i \(-0.527726\pi\)
−0.0869923 + 0.996209i \(0.527726\pi\)
\(620\) 0 0
\(621\) 3.64921 0.146438
\(622\) 0 0
\(623\) 1.49814i 0.0600215i
\(624\) 0 0
\(625\) 23.4722 + 8.60570i 0.938886 + 0.344228i
\(626\) 0 0
\(627\) 0.284845i 0.0113756i
\(628\) 0 0
\(629\) 48.9464 1.95162
\(630\) 0 0
\(631\) −13.0385 −0.519054 −0.259527 0.965736i \(-0.583567\pi\)
−0.259527 + 0.965736i \(0.583567\pi\)
\(632\) 0 0
\(633\) 23.8266i 0.947023i
\(634\) 0 0
\(635\) 2.61968 29.7417i 0.103959 1.18026i
\(636\) 0 0
\(637\) 26.6668i 1.05658i
\(638\) 0 0
\(639\) −4.88025 −0.193060
\(640\) 0 0
\(641\) 17.0995 0.675391 0.337695 0.941255i \(-0.390353\pi\)
0.337695 + 0.941255i \(0.390353\pi\)
\(642\) 0 0
\(643\) 0.255024i 0.0100571i −0.999987 0.00502857i \(-0.998399\pi\)
0.999987 0.00502857i \(-0.00160065\pi\)
\(644\) 0 0
\(645\) 17.2047 + 1.51541i 0.677435 + 0.0596691i
\(646\) 0 0
\(647\) 31.4978i 1.23831i −0.785270 0.619153i \(-0.787476\pi\)
0.785270 0.619153i \(-0.212524\pi\)
\(648\) 0 0
\(649\) 0.369961 0.0145223
\(650\) 0 0
\(651\) −0.908096 −0.0355911
\(652\) 0 0
\(653\) 24.0739i 0.942083i −0.882111 0.471042i \(-0.843878\pi\)
0.882111 0.471042i \(-0.156122\pi\)
\(654\) 0 0
\(655\) 23.9820 + 2.11236i 0.937056 + 0.0825367i
\(656\) 0 0
\(657\) 0.309819i 0.0120872i
\(658\) 0 0
\(659\) −48.0291 −1.87095 −0.935474 0.353397i \(-0.885027\pi\)
−0.935474 + 0.353397i \(0.885027\pi\)
\(660\) 0 0
\(661\) 24.6120 0.957295 0.478647 0.878007i \(-0.341127\pi\)
0.478647 + 0.878007i \(0.341127\pi\)
\(662\) 0 0
\(663\) 25.3513i 0.984562i
\(664\) 0 0
\(665\) −0.183845 + 2.08723i −0.00712919 + 0.0809392i
\(666\) 0 0
\(667\) 30.1140i 1.16602i
\(668\) 0 0
\(669\) −8.63279 −0.333763
\(670\) 0 0
\(671\) −0.261058 −0.0100780
\(672\) 0 0
\(673\) 27.8417i 1.07322i 0.843831 + 0.536609i \(0.180295\pi\)
−0.843831 + 0.536609i \(0.819705\pi\)
\(674\) 0 0
\(675\) 0.874027 4.92301i 0.0336413 0.189487i
\(676\) 0 0
\(677\) 43.7995i 1.68335i −0.539983 0.841676i \(-0.681569\pi\)
0.539983 0.841676i \(-0.318431\pi\)
\(678\) 0 0
\(679\) −0.911372 −0.0349753
\(680\) 0 0
\(681\) −8.58160 −0.328848
\(682\) 0 0
\(683\) 2.92819i 0.112044i −0.998430 0.0560221i \(-0.982158\pi\)
0.998430 0.0560221i \(-0.0178417\pi\)
\(684\) 0 0
\(685\) −1.64756 + 18.7051i −0.0629500 + 0.714684i
\(686\) 0 0
\(687\) 3.20564i 0.122303i
\(688\) 0 0
\(689\) −14.6014 −0.556268
\(690\) 0 0
\(691\) 5.44751 0.207233 0.103617 0.994617i \(-0.466959\pi\)
0.103617 + 0.994617i \(0.466959\pi\)
\(692\) 0 0
\(693\) 0.00500168i 0.000189998i
\(694\) 0 0
\(695\) 45.3997 + 3.99884i 1.72211 + 0.151685i
\(696\) 0 0
\(697\) 12.4383i 0.471134i
\(698\) 0 0
\(699\) 11.2934 0.427155
\(700\) 0 0
\(701\) 40.7153 1.53780 0.768898 0.639372i \(-0.220806\pi\)
0.768898 + 0.639372i \(0.220806\pi\)
\(702\) 0 0
\(703\) 53.8572i 2.03126i
\(704\) 0 0
\(705\) −21.4371 1.88819i −0.807367 0.0711135i
\(706\) 0 0
\(707\) 1.37426i 0.0516843i
\(708\) 0 0
\(709\) 32.6966 1.22795 0.613974 0.789326i \(-0.289570\pi\)
0.613974 + 0.789326i \(0.289570\pi\)
\(710\) 0 0
\(711\) 5.72909 0.214858
\(712\) 0 0
\(713\) 25.8342i 0.967499i
\(714\) 0 0
\(715\) 0.0292122 0.331652i 0.00109247 0.0124031i
\(716\) 0 0
\(717\) 21.5672i 0.805442i
\(718\) 0 0
\(719\) −25.1366 −0.937436 −0.468718 0.883348i \(-0.655284\pi\)
−0.468718 + 0.883348i \(0.655284\pi\)
\(720\) 0 0
\(721\) −1.83292 −0.0682616
\(722\) 0 0
\(723\) 9.36087i 0.348135i
\(724\) 0 0
\(725\) −40.6257 7.21264i −1.50880 0.267871i
\(726\) 0 0
\(727\) 15.0875i 0.559564i 0.960064 + 0.279782i \(0.0902622\pi\)
−0.960064 + 0.279782i \(0.909738\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 51.2797 1.89665
\(732\) 0 0
\(733\) 21.1707i 0.781959i 0.920399 + 0.390980i \(0.127864\pi\)
−0.920399 + 0.390980i \(0.872136\pi\)
\(734\) 0 0
\(735\) 1.37014 15.5555i 0.0505383 0.573772i
\(736\) 0 0
\(737\) 0.0389925i 0.00143631i
\(738\) 0 0
\(739\) −33.3401 −1.22643 −0.613217 0.789914i \(-0.710125\pi\)
−0.613217 + 0.789914i \(0.710125\pi\)
\(740\) 0 0
\(741\) −27.8947 −1.02474
\(742\) 0 0
\(743\) 16.8561i 0.618391i 0.950998 + 0.309196i \(0.100060\pi\)
−0.950998 + 0.309196i \(0.899940\pi\)
\(744\) 0 0
\(745\) 19.2611 + 1.69653i 0.705672 + 0.0621561i
\(746\) 0 0
\(747\) 14.6840i 0.537260i
\(748\) 0 0
\(749\) −1.10039 −0.0402074
\(750\) 0 0
\(751\) 9.45818 0.345134 0.172567 0.984998i \(-0.444794\pi\)
0.172567 + 0.984998i \(0.444794\pi\)
\(752\) 0 0
\(753\) 10.7667i 0.392361i
\(754\) 0 0
\(755\) 26.6830 + 2.35026i 0.971095 + 0.0855348i
\(756\) 0 0
\(757\) 37.9574i 1.37959i −0.724007 0.689793i \(-0.757702\pi\)
0.724007 0.689793i \(-0.242298\pi\)
\(758\) 0 0
\(759\) −0.142292 −0.00516487
\(760\) 0 0
\(761\) 29.9280 1.08489 0.542444 0.840092i \(-0.317499\pi\)
0.542444 + 0.840092i \(0.317499\pi\)
\(762\) 0 0
\(763\) 2.49835i 0.0904465i
\(764\) 0 0
\(765\) 1.30255 14.7881i 0.0470936 0.534664i
\(766\) 0 0
\(767\) 36.2302i 1.30820i
\(768\) 0 0
\(769\) 5.03061 0.181408 0.0907042 0.995878i \(-0.471088\pi\)
0.0907042 + 0.995878i \(0.471088\pi\)
\(770\) 0 0
\(771\) −22.0839 −0.795333
\(772\) 0 0
\(773\) 18.4372i 0.663141i 0.943430 + 0.331571i \(0.107579\pi\)
−0.943430 + 0.331571i \(0.892421\pi\)
\(774\) 0 0
\(775\) −34.8520 6.18758i −1.25192 0.222264i
\(776\) 0 0
\(777\) 0.945697i 0.0339267i
\(778\) 0 0
\(779\) 13.6862 0.490359
\(780\) 0 0
\(781\) 0.190293 0.00680922
\(782\) 0 0
\(783\) 8.25219i 0.294909i
\(784\) 0 0
\(785\) 1.63849 18.6022i 0.0584804 0.663940i
\(786\) 0 0
\(787\) 35.9859i 1.28276i 0.767224 + 0.641379i \(0.221637\pi\)
−0.767224 + 0.641379i \(0.778363\pi\)
\(788\) 0 0
\(789\) 21.5995 0.768961
\(790\) 0 0
\(791\) 1.74558 0.0620658
\(792\) 0