Properties

Label 4020.2.g.c.1609.18
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 1609.18
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.37

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(2.20926 - 0.345224i) q^{5}\) \(+0.0620642i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(2.20926 - 0.345224i) q^{5}\) \(+0.0620642i q^{7}\) \(-1.00000 q^{9}\) \(+3.73721 q^{11}\) \(+3.61751i q^{13}\) \(+(-0.345224 - 2.20926i) q^{15}\) \(+5.75776i q^{17}\) \(-4.84485 q^{19}\) \(+0.0620642 q^{21}\) \(-3.34603i q^{23}\) \(+(4.76164 - 1.52538i) q^{25}\) \(+1.00000i q^{27}\) \(-4.90056 q^{29}\) \(+9.28015 q^{31}\) \(-3.73721i q^{33}\) \(+(0.0214260 + 0.137116i) q^{35}\) \(-3.35286i q^{37}\) \(+3.61751 q^{39}\) \(+9.38987 q^{41}\) \(+2.89223i q^{43}\) \(+(-2.20926 + 0.345224i) q^{45}\) \(+10.5191i q^{47}\) \(+6.99615 q^{49}\) \(+5.75776 q^{51}\) \(+9.91099i q^{53}\) \(+(8.25646 - 1.29017i) q^{55}\) \(+4.84485i q^{57}\) \(-9.42481 q^{59}\) \(-11.5713 q^{61}\) \(-0.0620642i q^{63}\) \(+(1.24885 + 7.99201i) q^{65}\) \(-1.00000i q^{67}\) \(-3.34603 q^{69}\) \(+14.9803 q^{71}\) \(+10.5508i q^{73}\) \(+(-1.52538 - 4.76164i) q^{75}\) \(+0.231947i q^{77}\) \(+13.4258 q^{79}\) \(+1.00000 q^{81}\) \(-3.66914i q^{83}\) \(+(1.98772 + 12.7204i) q^{85}\) \(+4.90056i q^{87}\) \(-5.66849 q^{89}\) \(-0.224518 q^{91}\) \(-9.28015i q^{93}\) \(+(-10.7035 + 1.67256i) q^{95}\) \(-2.89298i q^{97}\) \(-3.73721 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.20926 0.345224i 0.988010 0.154389i
\(6\) 0 0
\(7\) 0.0620642i 0.0234581i 0.999931 + 0.0117290i \(0.00373355\pi\)
−0.999931 + 0.0117290i \(0.996266\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.73721 1.12681 0.563405 0.826181i \(-0.309491\pi\)
0.563405 + 0.826181i \(0.309491\pi\)
\(12\) 0 0
\(13\) 3.61751i 1.00332i 0.865066 + 0.501659i \(0.167277\pi\)
−0.865066 + 0.501659i \(0.832723\pi\)
\(14\) 0 0
\(15\) −0.345224 2.20926i −0.0891364 0.570428i
\(16\) 0 0
\(17\) 5.75776i 1.39646i 0.715873 + 0.698231i \(0.246029\pi\)
−0.715873 + 0.698231i \(0.753971\pi\)
\(18\) 0 0
\(19\) −4.84485 −1.11148 −0.555742 0.831355i \(-0.687566\pi\)
−0.555742 + 0.831355i \(0.687566\pi\)
\(20\) 0 0
\(21\) 0.0620642 0.0135435
\(22\) 0 0
\(23\) 3.34603i 0.697696i −0.937179 0.348848i \(-0.886573\pi\)
0.937179 0.348848i \(-0.113427\pi\)
\(24\) 0 0
\(25\) 4.76164 1.52538i 0.952328 0.305075i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −4.90056 −0.910012 −0.455006 0.890488i \(-0.650363\pi\)
−0.455006 + 0.890488i \(0.650363\pi\)
\(30\) 0 0
\(31\) 9.28015 1.66676 0.833382 0.552697i \(-0.186401\pi\)
0.833382 + 0.552697i \(0.186401\pi\)
\(32\) 0 0
\(33\) 3.73721i 0.650564i
\(34\) 0 0
\(35\) 0.0214260 + 0.137116i 0.00362166 + 0.0231768i
\(36\) 0 0
\(37\) 3.35286i 0.551207i −0.961271 0.275604i \(-0.911122\pi\)
0.961271 0.275604i \(-0.0888778\pi\)
\(38\) 0 0
\(39\) 3.61751 0.579265
\(40\) 0 0
\(41\) 9.38987 1.46645 0.733226 0.679985i \(-0.238014\pi\)
0.733226 + 0.679985i \(0.238014\pi\)
\(42\) 0 0
\(43\) 2.89223i 0.441061i 0.975380 + 0.220530i \(0.0707788\pi\)
−0.975380 + 0.220530i \(0.929221\pi\)
\(44\) 0 0
\(45\) −2.20926 + 0.345224i −0.329337 + 0.0514629i
\(46\) 0 0
\(47\) 10.5191i 1.53436i 0.641429 + 0.767182i \(0.278342\pi\)
−0.641429 + 0.767182i \(0.721658\pi\)
\(48\) 0 0
\(49\) 6.99615 0.999450
\(50\) 0 0
\(51\) 5.75776 0.806248
\(52\) 0 0
\(53\) 9.91099i 1.36138i 0.732572 + 0.680689i \(0.238320\pi\)
−0.732572 + 0.680689i \(0.761680\pi\)
\(54\) 0 0
\(55\) 8.25646 1.29017i 1.11330 0.173967i
\(56\) 0 0
\(57\) 4.84485i 0.641716i
\(58\) 0 0
\(59\) −9.42481 −1.22701 −0.613503 0.789692i \(-0.710240\pi\)
−0.613503 + 0.789692i \(0.710240\pi\)
\(60\) 0 0
\(61\) −11.5713 −1.48156 −0.740779 0.671749i \(-0.765544\pi\)
−0.740779 + 0.671749i \(0.765544\pi\)
\(62\) 0 0
\(63\) 0.0620642i 0.00781935i
\(64\) 0 0
\(65\) 1.24885 + 7.99201i 0.154901 + 0.991287i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −3.34603 −0.402815
\(70\) 0 0
\(71\) 14.9803 1.77784 0.888920 0.458062i \(-0.151456\pi\)
0.888920 + 0.458062i \(0.151456\pi\)
\(72\) 0 0
\(73\) 10.5508i 1.23488i 0.786618 + 0.617441i \(0.211830\pi\)
−0.786618 + 0.617441i \(0.788170\pi\)
\(74\) 0 0
\(75\) −1.52538 4.76164i −0.176135 0.549827i
\(76\) 0 0
\(77\) 0.231947i 0.0264328i
\(78\) 0 0
\(79\) 13.4258 1.51052 0.755262 0.655423i \(-0.227510\pi\)
0.755262 + 0.655423i \(0.227510\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.66914i 0.402740i −0.979515 0.201370i \(-0.935461\pi\)
0.979515 0.201370i \(-0.0645394\pi\)
\(84\) 0 0
\(85\) 1.98772 + 12.7204i 0.215598 + 1.37972i
\(86\) 0 0
\(87\) 4.90056i 0.525395i
\(88\) 0 0
\(89\) −5.66849 −0.600859 −0.300429 0.953804i \(-0.597130\pi\)
−0.300429 + 0.953804i \(0.597130\pi\)
\(90\) 0 0
\(91\) −0.224518 −0.0235359
\(92\) 0 0
\(93\) 9.28015i 0.962307i
\(94\) 0 0
\(95\) −10.7035 + 1.67256i −1.09816 + 0.171601i
\(96\) 0 0
\(97\) 2.89298i 0.293737i −0.989156 0.146869i \(-0.953081\pi\)
0.989156 0.146869i \(-0.0469194\pi\)
\(98\) 0 0
\(99\) −3.73721 −0.375604
\(100\) 0 0
\(101\) −2.57914 −0.256634 −0.128317 0.991733i \(-0.540958\pi\)
−0.128317 + 0.991733i \(0.540958\pi\)
\(102\) 0 0
\(103\) 16.1600i 1.59229i −0.605105 0.796146i \(-0.706869\pi\)
0.605105 0.796146i \(-0.293131\pi\)
\(104\) 0 0
\(105\) 0.137116 0.0214260i 0.0133811 0.00209097i
\(106\) 0 0
\(107\) 6.20665i 0.600019i 0.953936 + 0.300010i \(0.0969899\pi\)
−0.953936 + 0.300010i \(0.903010\pi\)
\(108\) 0 0
\(109\) −4.56692 −0.437431 −0.218716 0.975789i \(-0.570187\pi\)
−0.218716 + 0.975789i \(0.570187\pi\)
\(110\) 0 0
\(111\) −3.35286 −0.318240
\(112\) 0 0
\(113\) 7.46157i 0.701925i 0.936390 + 0.350963i \(0.114146\pi\)
−0.936390 + 0.350963i \(0.885854\pi\)
\(114\) 0 0
\(115\) −1.15513 7.39225i −0.107716 0.689331i
\(116\) 0 0
\(117\) 3.61751i 0.334439i
\(118\) 0 0
\(119\) −0.357351 −0.0327583
\(120\) 0 0
\(121\) 2.96672 0.269702
\(122\) 0 0
\(123\) 9.38987i 0.846656i
\(124\) 0 0
\(125\) 9.99310 5.01378i 0.893810 0.448446i
\(126\) 0 0
\(127\) 4.69867i 0.416940i −0.978029 0.208470i \(-0.933152\pi\)
0.978029 0.208470i \(-0.0668483\pi\)
\(128\) 0 0
\(129\) 2.89223 0.254647
\(130\) 0 0
\(131\) 3.24849 0.283822 0.141911 0.989879i \(-0.454675\pi\)
0.141911 + 0.989879i \(0.454675\pi\)
\(132\) 0 0
\(133\) 0.300692i 0.0260733i
\(134\) 0 0
\(135\) 0.345224 + 2.20926i 0.0297121 + 0.190143i
\(136\) 0 0
\(137\) 14.5204i 1.24056i −0.784381 0.620280i \(-0.787019\pi\)
0.784381 0.620280i \(-0.212981\pi\)
\(138\) 0 0
\(139\) 5.51459 0.467741 0.233871 0.972268i \(-0.424861\pi\)
0.233871 + 0.972268i \(0.424861\pi\)
\(140\) 0 0
\(141\) 10.5191 0.885866
\(142\) 0 0
\(143\) 13.5194i 1.13055i
\(144\) 0 0
\(145\) −10.8266 + 1.69179i −0.899101 + 0.140496i
\(146\) 0 0
\(147\) 6.99615i 0.577033i
\(148\) 0 0
\(149\) 13.7886 1.12961 0.564803 0.825226i \(-0.308952\pi\)
0.564803 + 0.825226i \(0.308952\pi\)
\(150\) 0 0
\(151\) 0.495460 0.0403199 0.0201600 0.999797i \(-0.493582\pi\)
0.0201600 + 0.999797i \(0.493582\pi\)
\(152\) 0 0
\(153\) 5.75776i 0.465487i
\(154\) 0 0
\(155\) 20.5023 3.20373i 1.64678 0.257330i
\(156\) 0 0
\(157\) 17.7674i 1.41799i 0.705211 + 0.708997i \(0.250852\pi\)
−0.705211 + 0.708997i \(0.749148\pi\)
\(158\) 0 0
\(159\) 9.91099 0.785993
\(160\) 0 0
\(161\) 0.207669 0.0163666
\(162\) 0 0
\(163\) 16.8769i 1.32190i 0.750430 + 0.660950i \(0.229847\pi\)
−0.750430 + 0.660950i \(0.770153\pi\)
\(164\) 0 0
\(165\) −1.29017 8.25646i −0.100440 0.642764i
\(166\) 0 0
\(167\) 17.9078i 1.38575i −0.721060 0.692873i \(-0.756345\pi\)
0.721060 0.692873i \(-0.243655\pi\)
\(168\) 0 0
\(169\) −0.0863858 −0.00664506
\(170\) 0 0
\(171\) 4.84485 0.370495
\(172\) 0 0
\(173\) 7.43227i 0.565065i −0.959258 0.282533i \(-0.908825\pi\)
0.959258 0.282533i \(-0.0911746\pi\)
\(174\) 0 0
\(175\) 0.0946713 + 0.295527i 0.00715648 + 0.0223398i
\(176\) 0 0
\(177\) 9.42481i 0.708412i
\(178\) 0 0
\(179\) −8.78910 −0.656928 −0.328464 0.944516i \(-0.606531\pi\)
−0.328464 + 0.944516i \(0.606531\pi\)
\(180\) 0 0
\(181\) −14.2064 −1.05595 −0.527977 0.849259i \(-0.677049\pi\)
−0.527977 + 0.849259i \(0.677049\pi\)
\(182\) 0 0
\(183\) 11.5713i 0.855378i
\(184\) 0 0
\(185\) −1.15749 7.40734i −0.0851003 0.544599i
\(186\) 0 0
\(187\) 21.5179i 1.57355i
\(188\) 0 0
\(189\) −0.0620642 −0.00451450
\(190\) 0 0
\(191\) 3.33664 0.241431 0.120716 0.992687i \(-0.461481\pi\)
0.120716 + 0.992687i \(0.461481\pi\)
\(192\) 0 0
\(193\) 0.227371i 0.0163665i −0.999967 0.00818327i \(-0.997395\pi\)
0.999967 0.00818327i \(-0.00260484\pi\)
\(194\) 0 0
\(195\) 7.99201 1.24885i 0.572320 0.0894321i
\(196\) 0 0
\(197\) 17.8648i 1.27282i −0.771353 0.636408i \(-0.780420\pi\)
0.771353 0.636408i \(-0.219580\pi\)
\(198\) 0 0
\(199\) −7.02003 −0.497637 −0.248818 0.968550i \(-0.580042\pi\)
−0.248818 + 0.968550i \(0.580042\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 0.304149i 0.0213471i
\(204\) 0 0
\(205\) 20.7447 3.24161i 1.44887 0.226404i
\(206\) 0 0
\(207\) 3.34603i 0.232565i
\(208\) 0 0
\(209\) −18.1062 −1.25243
\(210\) 0 0
\(211\) 15.4786 1.06559 0.532795 0.846244i \(-0.321142\pi\)
0.532795 + 0.846244i \(0.321142\pi\)
\(212\) 0 0
\(213\) 14.9803i 1.02644i
\(214\) 0 0
\(215\) 0.998466 + 6.38968i 0.0680948 + 0.435773i
\(216\) 0 0
\(217\) 0.575965i 0.0390991i
\(218\) 0 0
\(219\) 10.5508 0.712959
\(220\) 0 0
\(221\) −20.8288 −1.40109
\(222\) 0 0
\(223\) 14.6955i 0.984081i 0.870572 + 0.492040i \(0.163749\pi\)
−0.870572 + 0.492040i \(0.836251\pi\)
\(224\) 0 0
\(225\) −4.76164 + 1.52538i −0.317443 + 0.101692i
\(226\) 0 0
\(227\) 1.83025i 0.121478i 0.998154 + 0.0607390i \(0.0193457\pi\)
−0.998154 + 0.0607390i \(0.980654\pi\)
\(228\) 0 0
\(229\) 19.5339 1.29084 0.645418 0.763830i \(-0.276683\pi\)
0.645418 + 0.763830i \(0.276683\pi\)
\(230\) 0 0
\(231\) 0.231947 0.0152610
\(232\) 0 0
\(233\) 3.91720i 0.256624i −0.991734 0.128312i \(-0.959044\pi\)
0.991734 0.128312i \(-0.0409559\pi\)
\(234\) 0 0
\(235\) 3.63144 + 23.2394i 0.236889 + 1.51597i
\(236\) 0 0
\(237\) 13.4258i 0.872101i
\(238\) 0 0
\(239\) −0.408885 −0.0264486 −0.0132243 0.999913i \(-0.504210\pi\)
−0.0132243 + 0.999913i \(0.504210\pi\)
\(240\) 0 0
\(241\) −0.711176 −0.0458109 −0.0229054 0.999738i \(-0.507292\pi\)
−0.0229054 + 0.999738i \(0.507292\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 15.4563 2.41524i 0.987466 0.154304i
\(246\) 0 0
\(247\) 17.5263i 1.11517i
\(248\) 0 0
\(249\) −3.66914 −0.232522
\(250\) 0 0
\(251\) 18.8243 1.18818 0.594091 0.804398i \(-0.297512\pi\)
0.594091 + 0.804398i \(0.297512\pi\)
\(252\) 0 0
\(253\) 12.5048i 0.786172i
\(254\) 0 0
\(255\) 12.7204 1.98772i 0.796581 0.124476i
\(256\) 0 0
\(257\) 29.3805i 1.83271i −0.400370 0.916354i \(-0.631118\pi\)
0.400370 0.916354i \(-0.368882\pi\)
\(258\) 0 0
\(259\) 0.208093 0.0129303
\(260\) 0 0
\(261\) 4.90056 0.303337
\(262\) 0 0
\(263\) 17.9546i 1.10713i 0.832806 + 0.553565i \(0.186733\pi\)
−0.832806 + 0.553565i \(0.813267\pi\)
\(264\) 0 0
\(265\) 3.42151 + 21.8959i 0.210182 + 1.34506i
\(266\) 0 0
\(267\) 5.66849i 0.346906i
\(268\) 0 0
\(269\) 3.37091 0.205528 0.102764 0.994706i \(-0.467231\pi\)
0.102764 + 0.994706i \(0.467231\pi\)
\(270\) 0 0
\(271\) 0.707519 0.0429787 0.0214893 0.999769i \(-0.493159\pi\)
0.0214893 + 0.999769i \(0.493159\pi\)
\(272\) 0 0
\(273\) 0.224518i 0.0135884i
\(274\) 0 0
\(275\) 17.7952 5.70065i 1.07309 0.343762i
\(276\) 0 0
\(277\) 31.4894i 1.89202i 0.324145 + 0.946008i \(0.394924\pi\)
−0.324145 + 0.946008i \(0.605076\pi\)
\(278\) 0 0
\(279\) −9.28015 −0.555588
\(280\) 0 0
\(281\) 3.98185 0.237537 0.118769 0.992922i \(-0.462105\pi\)
0.118769 + 0.992922i \(0.462105\pi\)
\(282\) 0 0
\(283\) 28.7478i 1.70888i −0.519553 0.854438i \(-0.673901\pi\)
0.519553 0.854438i \(-0.326099\pi\)
\(284\) 0 0
\(285\) 1.67256 + 10.7035i 0.0990738 + 0.634022i
\(286\) 0 0
\(287\) 0.582775i 0.0344001i
\(288\) 0 0
\(289\) −16.1518 −0.950106
\(290\) 0 0
\(291\) −2.89298 −0.169589
\(292\) 0 0
\(293\) 22.4818i 1.31340i −0.754151 0.656701i \(-0.771951\pi\)
0.754151 0.656701i \(-0.228049\pi\)
\(294\) 0 0
\(295\) −20.8218 + 3.25367i −1.21229 + 0.189436i
\(296\) 0 0
\(297\) 3.73721i 0.216855i
\(298\) 0 0
\(299\) 12.1043 0.700011
\(300\) 0 0
\(301\) −0.179504 −0.0103464
\(302\) 0 0
\(303\) 2.57914i 0.148168i
\(304\) 0 0
\(305\) −25.5641 + 3.99470i −1.46379 + 0.228736i
\(306\) 0 0
\(307\) 15.9009i 0.907511i 0.891126 + 0.453755i \(0.149916\pi\)
−0.891126 + 0.453755i \(0.850084\pi\)
\(308\) 0 0
\(309\) −16.1600 −0.919310
\(310\) 0 0
\(311\) −8.41108 −0.476948 −0.238474 0.971149i \(-0.576647\pi\)
−0.238474 + 0.971149i \(0.576647\pi\)
\(312\) 0 0
\(313\) 20.0588i 1.13379i −0.823790 0.566895i \(-0.808145\pi\)
0.823790 0.566895i \(-0.191855\pi\)
\(314\) 0 0
\(315\) −0.0214260 0.137116i −0.00120722 0.00772560i
\(316\) 0 0
\(317\) 14.2660i 0.801259i 0.916240 + 0.400629i \(0.131209\pi\)
−0.916240 + 0.400629i \(0.868791\pi\)
\(318\) 0 0
\(319\) −18.3144 −1.02541
\(320\) 0 0
\(321\) 6.20665 0.346421
\(322\) 0 0
\(323\) 27.8955i 1.55215i
\(324\) 0 0
\(325\) 5.51807 + 17.2253i 0.306087 + 0.955487i
\(326\) 0 0
\(327\) 4.56692i 0.252551i
\(328\) 0 0
\(329\) −0.652858 −0.0359932
\(330\) 0 0
\(331\) −22.8860 −1.25793 −0.628963 0.777435i \(-0.716520\pi\)
−0.628963 + 0.777435i \(0.716520\pi\)
\(332\) 0 0
\(333\) 3.35286i 0.183736i
\(334\) 0 0
\(335\) −0.345224 2.20926i −0.0188616 0.120705i
\(336\) 0 0
\(337\) 16.4698i 0.897166i −0.893741 0.448583i \(-0.851929\pi\)
0.893741 0.448583i \(-0.148071\pi\)
\(338\) 0 0
\(339\) 7.46157 0.405257
\(340\) 0 0
\(341\) 34.6819 1.87813
\(342\) 0 0
\(343\) 0.868659i 0.0469032i
\(344\) 0 0
\(345\) −7.39225 + 1.15513i −0.397985 + 0.0621901i
\(346\) 0 0
\(347\) 7.63004i 0.409602i 0.978804 + 0.204801i \(0.0656547\pi\)
−0.978804 + 0.204801i \(0.934345\pi\)
\(348\) 0 0
\(349\) −35.9413 −1.92389 −0.961946 0.273240i \(-0.911905\pi\)
−0.961946 + 0.273240i \(0.911905\pi\)
\(350\) 0 0
\(351\) −3.61751 −0.193088
\(352\) 0 0
\(353\) 3.59182i 0.191173i 0.995421 + 0.0955865i \(0.0304727\pi\)
−0.995421 + 0.0955865i \(0.969527\pi\)
\(354\) 0 0
\(355\) 33.0955 5.17157i 1.75652 0.274479i
\(356\) 0 0
\(357\) 0.357351i 0.0189130i
\(358\) 0 0
\(359\) 21.5358 1.13662 0.568309 0.822815i \(-0.307598\pi\)
0.568309 + 0.822815i \(0.307598\pi\)
\(360\) 0 0
\(361\) 4.47256 0.235398
\(362\) 0 0
\(363\) 2.96672i 0.155713i
\(364\) 0 0
\(365\) 3.64240 + 23.3095i 0.190652 + 1.22008i
\(366\) 0 0
\(367\) 8.57129i 0.447418i −0.974656 0.223709i \(-0.928183\pi\)
0.974656 0.223709i \(-0.0718165\pi\)
\(368\) 0 0
\(369\) −9.38987 −0.488817
\(370\) 0 0
\(371\) −0.615117 −0.0319353
\(372\) 0 0
\(373\) 4.42610i 0.229175i 0.993413 + 0.114587i \(0.0365546\pi\)
−0.993413 + 0.114587i \(0.963445\pi\)
\(374\) 0 0
\(375\) −5.01378 9.99310i −0.258911 0.516041i
\(376\) 0 0
\(377\) 17.7278i 0.913030i
\(378\) 0 0
\(379\) 31.6306 1.62475 0.812377 0.583133i \(-0.198173\pi\)
0.812377 + 0.583133i \(0.198173\pi\)
\(380\) 0 0
\(381\) −4.69867 −0.240720
\(382\) 0 0
\(383\) 38.3554i 1.95987i −0.199313 0.979936i \(-0.563871\pi\)
0.199313 0.979936i \(-0.436129\pi\)
\(384\) 0 0
\(385\) 0.0800735 + 0.512430i 0.00408093 + 0.0261159i
\(386\) 0 0
\(387\) 2.89223i 0.147020i
\(388\) 0 0
\(389\) −6.83638 −0.346618 −0.173309 0.984867i \(-0.555446\pi\)
−0.173309 + 0.984867i \(0.555446\pi\)
\(390\) 0 0
\(391\) 19.2657 0.974306
\(392\) 0 0
\(393\) 3.24849i 0.163865i
\(394\) 0 0
\(395\) 29.6611 4.63492i 1.49241 0.233208i
\(396\) 0 0
\(397\) 15.2569i 0.765722i −0.923806 0.382861i \(-0.874939\pi\)
0.923806 0.382861i \(-0.125061\pi\)
\(398\) 0 0
\(399\) −0.300692 −0.0150534
\(400\) 0 0
\(401\) 1.50327 0.0750696 0.0375348 0.999295i \(-0.488049\pi\)
0.0375348 + 0.999295i \(0.488049\pi\)
\(402\) 0 0
\(403\) 33.5711i 1.67229i
\(404\) 0 0
\(405\) 2.20926 0.345224i 0.109779 0.0171543i
\(406\) 0 0
\(407\) 12.5304i 0.621106i
\(408\) 0 0
\(409\) −4.59665 −0.227290 −0.113645 0.993521i \(-0.536253\pi\)
−0.113645 + 0.993521i \(0.536253\pi\)
\(410\) 0 0
\(411\) −14.5204 −0.716237
\(412\) 0 0
\(413\) 0.584943i 0.0287832i
\(414\) 0 0
\(415\) −1.26667 8.10607i −0.0621786 0.397912i
\(416\) 0 0
\(417\) 5.51459i 0.270051i
\(418\) 0 0
\(419\) −10.1376 −0.495255 −0.247628 0.968855i \(-0.579651\pi\)
−0.247628 + 0.968855i \(0.579651\pi\)
\(420\) 0 0
\(421\) 2.20988 0.107703 0.0538514 0.998549i \(-0.482850\pi\)
0.0538514 + 0.998549i \(0.482850\pi\)
\(422\) 0 0
\(423\) 10.5191i 0.511455i
\(424\) 0 0
\(425\) 8.78276 + 27.4164i 0.426026 + 1.32989i
\(426\) 0 0
\(427\) 0.718166i 0.0347545i
\(428\) 0 0
\(429\) 13.5194 0.652722
\(430\) 0 0
\(431\) 24.6797 1.18878 0.594389 0.804177i \(-0.297394\pi\)
0.594389 + 0.804177i \(0.297394\pi\)
\(432\) 0 0
\(433\) 34.3378i 1.65017i 0.565009 + 0.825085i \(0.308873\pi\)
−0.565009 + 0.825085i \(0.691127\pi\)
\(434\) 0 0
\(435\) 1.69179 + 10.8266i 0.0811152 + 0.519096i
\(436\) 0 0
\(437\) 16.2110i 0.775479i
\(438\) 0 0
\(439\) 31.7048 1.51319 0.756593 0.653886i \(-0.226862\pi\)
0.756593 + 0.653886i \(0.226862\pi\)
\(440\) 0 0
\(441\) −6.99615 −0.333150
\(442\) 0 0
\(443\) 25.5075i 1.21190i −0.795503 0.605949i \(-0.792793\pi\)
0.795503 0.605949i \(-0.207207\pi\)
\(444\) 0 0
\(445\) −12.5232 + 1.95690i −0.593655 + 0.0927659i
\(446\) 0 0
\(447\) 13.7886i 0.652178i
\(448\) 0 0
\(449\) −22.1343 −1.04458 −0.522291 0.852767i \(-0.674923\pi\)
−0.522291 + 0.852767i \(0.674923\pi\)
\(450\) 0 0
\(451\) 35.0919 1.65241
\(452\) 0 0
\(453\) 0.495460i 0.0232787i
\(454\) 0 0
\(455\) −0.496018 + 0.0775089i −0.0232537 + 0.00363367i
\(456\) 0 0
\(457\) 8.10869i 0.379308i 0.981851 + 0.189654i \(0.0607367\pi\)
−0.981851 + 0.189654i \(0.939263\pi\)
\(458\) 0 0
\(459\) −5.75776 −0.268749
\(460\) 0 0
\(461\) −29.3960 −1.36911 −0.684553 0.728963i \(-0.740003\pi\)
−0.684553 + 0.728963i \(0.740003\pi\)
\(462\) 0 0
\(463\) 7.79537i 0.362281i −0.983457 0.181141i \(-0.942021\pi\)
0.983457 0.181141i \(-0.0579790\pi\)
\(464\) 0 0
\(465\) −3.20373 20.5023i −0.148569 0.950769i
\(466\) 0 0
\(467\) 32.2930i 1.49434i 0.664631 + 0.747172i \(0.268589\pi\)
−0.664631 + 0.747172i \(0.731411\pi\)
\(468\) 0 0
\(469\) 0.0620642 0.00286586
\(470\) 0 0
\(471\) 17.7674 0.818679
\(472\) 0 0
\(473\) 10.8089i 0.496992i
\(474\) 0 0
\(475\) −23.0694 + 7.39022i −1.05850 + 0.339087i
\(476\) 0 0
\(477\) 9.91099i 0.453793i
\(478\) 0 0
\(479\) −9.14877 −0.418018 −0.209009 0.977914i \(-0.567024\pi\)
−0.209009 + 0.977914i \(0.567024\pi\)
\(480\) 0 0
\(481\) 12.1290 0.553036
\(482\) 0 0
\(483\) 0.207669i 0.00944926i
\(484\) 0 0
\(485\) −0.998724 6.39133i −0.0453497 0.290215i
\(486\) 0 0
\(487\) 11.6778i 0.529171i −0.964362 0.264586i \(-0.914765\pi\)
0.964362 0.264586i \(-0.0852351\pi\)
\(488\) 0 0
\(489\) 16.8769 0.763200
\(490\) 0 0
\(491\) 37.3324 1.68479 0.842394 0.538862i \(-0.181145\pi\)
0.842394 + 0.538862i \(0.181145\pi\)
\(492\) 0 0
\(493\) 28.2163i 1.27080i
\(494\) 0 0
\(495\) −8.25646 + 1.29017i −0.371100 + 0.0579890i
\(496\) 0 0
\(497\) 0.929743i 0.0417047i
\(498\) 0 0
\(499\) −3.59494 −0.160931 −0.0804657 0.996757i \(-0.525641\pi\)
−0.0804657 + 0.996757i \(0.525641\pi\)
\(500\) 0 0
\(501\) −17.9078 −0.800061
\(502\) 0 0
\(503\) 2.80672i 0.125146i −0.998040 0.0625728i \(-0.980069\pi\)
0.998040 0.0625728i \(-0.0199305\pi\)
\(504\) 0 0
\(505\) −5.69799 + 0.890381i −0.253557 + 0.0396214i
\(506\) 0 0
\(507\) 0.0863858i 0.00383653i
\(508\) 0 0
\(509\) −18.1919 −0.806342 −0.403171 0.915125i \(-0.632092\pi\)
−0.403171 + 0.915125i \(0.632092\pi\)
\(510\) 0 0
\(511\) −0.654828 −0.0289679
\(512\) 0 0
\(513\) 4.84485i 0.213905i
\(514\) 0 0
\(515\) −5.57881 35.7016i −0.245832 1.57320i
\(516\) 0 0
\(517\) 39.3120i 1.72894i
\(518\) 0 0
\(519\) −7.43227 −0.326241
\(520\) 0 0
\(521\) −29.4963 −1.29226 −0.646129 0.763229i \(-0.723613\pi\)
−0.646129 + 0.763229i \(0.723613\pi\)
\(522\) 0 0
\(523\) 13.5787i 0.593754i 0.954916 + 0.296877i \(0.0959452\pi\)
−0.954916 + 0.296877i \(0.904055\pi\)
\(524\) 0 0
\(525\) 0.295527 0.0946713i 0.0128979 0.00413179i
\(526\) 0 0
\(527\) 53.4329i 2.32757i
\(528\) 0 0
\(529\) 11.8041 0.513220
\(530\) 0 0
\(531\) 9.42481 0.409002
\(532\) 0 0
\(533\) 33.9680i 1.47132i
\(534\) 0 0
\(535\) 2.14268 + 13.7121i 0.0926362 + 0.592825i
\(536\) 0 0
\(537\) 8.78910i 0.379278i
\(538\) 0 0
\(539\) 26.1461 1.12619
\(540\) 0 0
\(541\) 13.9413 0.599384 0.299692 0.954036i \(-0.403116\pi\)
0.299692 + 0.954036i \(0.403116\pi\)
\(542\) 0 0
\(543\) 14.2064i 0.609655i
\(544\) 0 0
\(545\) −10.0895 + 1.57661i −0.432187 + 0.0675345i
\(546\) 0 0
\(547\) 34.5930i 1.47909i 0.673107 + 0.739545i \(0.264959\pi\)
−0.673107 + 0.739545i \(0.735041\pi\)
\(548\) 0 0
\(549\) 11.5713 0.493853
\(550\) 0 0
\(551\) 23.7425 1.01146
\(552\) 0 0
\(553\) 0.833263i 0.0354339i
\(554\) 0 0
\(555\) −7.40734 + 1.15749i −0.314424 + 0.0491327i
\(556\) 0 0
\(557\) 1.13485i 0.0480852i −0.999711 0.0240426i \(-0.992346\pi\)
0.999711 0.0240426i \(-0.00765373\pi\)
\(558\) 0 0
\(559\) −10.4627 −0.442524
\(560\) 0 0
\(561\) 21.5179 0.908489
\(562\) 0 0
\(563\) 32.2026i 1.35718i −0.734518 0.678589i \(-0.762592\pi\)
0.734518 0.678589i \(-0.237408\pi\)
\(564\) 0 0
\(565\) 2.57591 + 16.4845i 0.108369 + 0.693509i
\(566\) 0 0
\(567\) 0.0620642i 0.00260645i
\(568\) 0 0
\(569\) 0.597888 0.0250648 0.0125324 0.999921i \(-0.496011\pi\)
0.0125324 + 0.999921i \(0.496011\pi\)
\(570\) 0 0
\(571\) 3.09387 0.129474 0.0647372 0.997902i \(-0.479379\pi\)
0.0647372 + 0.997902i \(0.479379\pi\)
\(572\) 0 0
\(573\) 3.33664i 0.139390i
\(574\) 0 0
\(575\) −5.10396 15.9326i −0.212850 0.664436i
\(576\) 0 0
\(577\) 24.4178i 1.01653i −0.861202 0.508263i \(-0.830288\pi\)
0.861202 0.508263i \(-0.169712\pi\)
\(578\) 0 0
\(579\) −0.227371 −0.00944922
\(580\) 0 0
\(581\) 0.227722 0.00944750
\(582\) 0 0
\(583\) 37.0394i 1.53402i
\(584\) 0 0
\(585\) −1.24885 7.99201i −0.0516336 0.330429i
\(586\) 0 0
\(587\) 25.4585i 1.05079i −0.850860 0.525393i \(-0.823918\pi\)
0.850860 0.525393i \(-0.176082\pi\)
\(588\) 0 0
\(589\) −44.9609 −1.85258
\(590\) 0 0
\(591\) −17.8648 −0.734860
\(592\) 0 0
\(593\) 39.5909i 1.62580i −0.582401 0.812901i \(-0.697887\pi\)
0.582401 0.812901i \(-0.302113\pi\)
\(594\) 0 0
\(595\) −0.789480 + 0.123366i −0.0323655 + 0.00505751i
\(596\) 0 0
\(597\) 7.02003i 0.287311i
\(598\) 0 0
\(599\) 24.0181 0.981353 0.490677 0.871342i \(-0.336750\pi\)
0.490677 + 0.871342i \(0.336750\pi\)
\(600\) 0 0
\(601\) −11.0711 −0.451598 −0.225799 0.974174i \(-0.572499\pi\)
−0.225799 + 0.974174i \(0.572499\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 6.55426 1.02418i 0.266469 0.0416390i
\(606\) 0 0
\(607\) 17.3591i 0.704585i 0.935890 + 0.352292i \(0.114598\pi\)
−0.935890 + 0.352292i \(0.885402\pi\)
\(608\) 0 0
\(609\) −0.304149 −0.0123248
\(610\) 0 0
\(611\) −38.0529 −1.53945
\(612\) 0 0
\(613\) 48.6986i 1.96692i 0.181133 + 0.983459i \(0.442024\pi\)
−0.181133 + 0.983459i \(0.557976\pi\)
\(614\) 0 0
\(615\) −3.24161 20.7447i −0.130714 0.836505i
\(616\) 0 0
\(617\) 2.53591i 0.102092i −0.998696 0.0510458i \(-0.983745\pi\)
0.998696 0.0510458i \(-0.0162555\pi\)
\(618\) 0 0
\(619\) −49.0882 −1.97302 −0.986510 0.163702i \(-0.947656\pi\)
−0.986510 + 0.163702i \(0.947656\pi\)
\(620\) 0 0
\(621\) 3.34603 0.134272
\(622\) 0 0
\(623\) 0.351810i 0.0140950i
\(624\) 0 0
\(625\) 20.3464 14.5266i 0.813858 0.581064i
\(626\) 0 0
\(627\) 18.1062i 0.723092i
\(628\) 0 0
\(629\) 19.3050 0.769740
\(630\) 0 0
\(631\) −12.9294 −0.514712 −0.257356 0.966317i \(-0.582851\pi\)
−0.257356 + 0.966317i \(0.582851\pi\)
\(632\) 0 0
\(633\) 15.4786i 0.615219i
\(634\) 0 0
\(635\) −1.62209 10.3806i −0.0643708 0.411941i
\(636\) 0 0
\(637\) 25.3086i 1.00276i
\(638\) 0 0
\(639\) −14.9803 −0.592613
\(640\) 0 0
\(641\) −44.5813 −1.76086 −0.880428 0.474179i \(-0.842745\pi\)
−0.880428 + 0.474179i \(0.842745\pi\)
\(642\) 0 0
\(643\) 42.4654i 1.67467i −0.546689 0.837336i \(-0.684112\pi\)
0.546689 0.837336i \(-0.315888\pi\)
\(644\) 0 0
\(645\) 6.38968 0.998466i 0.251593 0.0393146i
\(646\) 0 0
\(647\) 37.5954i 1.47803i −0.673691 0.739013i \(-0.735292\pi\)
0.673691 0.739013i \(-0.264708\pi\)
\(648\) 0 0
\(649\) −35.2225 −1.38260
\(650\) 0 0
\(651\) 0.575965 0.0225739
\(652\) 0 0
\(653\) 3.15354i 0.123408i 0.998095 + 0.0617039i \(0.0196534\pi\)
−0.998095 + 0.0617039i \(0.980347\pi\)
\(654\) 0 0
\(655\) 7.17676 1.12146i 0.280419 0.0438190i
\(656\) 0 0
\(657\) 10.5508i 0.411627i
\(658\) 0 0
\(659\) −38.3854 −1.49528 −0.747641 0.664103i \(-0.768814\pi\)
−0.747641 + 0.664103i \(0.768814\pi\)
\(660\) 0 0
\(661\) −25.1892 −0.979746 −0.489873 0.871794i \(-0.662957\pi\)
−0.489873 + 0.871794i \(0.662957\pi\)
\(662\) 0 0
\(663\) 20.8288i 0.808922i
\(664\) 0 0
\(665\) −0.103806 0.664305i −0.00402542 0.0257607i
\(666\) 0 0
\(667\) 16.3975i 0.634912i
\(668\) 0 0
\(669\) 14.6955 0.568159
\(670\) 0 0
\(671\) −43.2445 −1.66944
\(672\) 0 0
\(673\) 16.8789i 0.650634i 0.945605 + 0.325317i \(0.105471\pi\)
−0.945605 + 0.325317i \(0.894529\pi\)
\(674\) 0 0
\(675\) 1.52538 + 4.76164i 0.0587118 + 0.183276i
\(676\) 0 0
\(677\) 37.6539i 1.44716i −0.690242 0.723579i \(-0.742496\pi\)
0.690242 0.723579i \(-0.257504\pi\)
\(678\) 0 0
\(679\) 0.179550 0.00689050
\(680\) 0 0
\(681\) 1.83025 0.0701354
\(682\) 0 0
\(683\) 46.7551i 1.78903i −0.447034 0.894517i \(-0.647520\pi\)
0.447034 0.894517i \(-0.352480\pi\)
\(684\) 0 0
\(685\) −5.01278 32.0792i −0.191528 1.22568i
\(686\) 0 0
\(687\) 19.5339i 0.745265i
\(688\) 0 0
\(689\) −35.8531 −1.36589
\(690\) 0 0
\(691\) −4.97821 −0.189380 −0.0946899 0.995507i \(-0.530186\pi\)
−0.0946899 + 0.995507i \(0.530186\pi\)
\(692\) 0 0
\(693\) 0.231947i 0.00881093i
\(694\) 0 0
\(695\) 12.1831 1.90377i 0.462133 0.0722140i
\(696\) 0 0
\(697\) 54.0646i 2.04784i
\(698\) 0 0
\(699\) −3.91720 −0.148162
\(700\) 0 0
\(701\) 17.2085 0.649958 0.324979 0.945721i \(-0.394643\pi\)
0.324979 + 0.945721i \(0.394643\pi\)
\(702\) 0 0
\(703\) 16.2441i 0.612659i
\(704\) 0 0
\(705\) 23.2394 3.63144i 0.875245 0.136768i
\(706\) 0 0
\(707\) 0.160072i 0.00602014i
\(708\) 0 0
\(709\) −28.1539 −1.05734 −0.528671 0.848827i \(-0.677309\pi\)
−0.528671 + 0.848827i \(0.677309\pi\)
\(710\) 0 0
\(711\) −13.4258 −0.503508
\(712\) 0 0
\(713\) 31.0517i 1.16290i
\(714\) 0 0
\(715\) 4.66722 + 29.8678i 0.174544 + 1.11699i
\(716\) 0 0
\(717\) 0.408885i 0.0152701i
\(718\) 0 0
\(719\) −34.0589 −1.27018 −0.635091 0.772437i \(-0.719038\pi\)
−0.635091 + 0.772437i \(0.719038\pi\)
\(720\) 0 0
\(721\) 1.00296 0.0373521
\(722\) 0 0
\(723\) 0.711176i 0.0264489i
\(724\) 0 0
\(725\) −23.3347 + 7.47521i −0.866630 + 0.277622i
\(726\) 0 0
\(727\) 5.65868i 0.209869i −0.994479 0.104934i \(-0.966537\pi\)
0.994479 0.104934i \(-0.0334633\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −16.6528 −0.615925
\(732\) 0 0
\(733\) 51.5641i 1.90456i 0.305222 + 0.952281i \(0.401269\pi\)
−0.305222 + 0.952281i \(0.598731\pi\)
\(734\) 0 0
\(735\) −2.41524 15.4563i −0.0890874 0.570114i
\(736\) 0 0
\(737\) 3.73721i 0.137662i
\(738\) 0 0
\(739\) −23.6118 −0.868574 −0.434287 0.900775i \(-0.643000\pi\)
−0.434287 + 0.900775i \(0.643000\pi\)
\(740\) 0 0
\(741\) −17.5263 −0.643845
\(742\) 0 0
\(743\) 42.7648i 1.56889i 0.620199 + 0.784444i \(0.287052\pi\)
−0.620199 + 0.784444i \(0.712948\pi\)
\(744\) 0 0
\(745\) 30.4625 4.76015i 1.11606 0.174398i
\(746\) 0 0
\(747\) 3.66914i 0.134247i
\(748\) 0 0
\(749\) −0.385210 −0.0140753
\(750\) 0 0
\(751\) −52.9184 −1.93102 −0.965510 0.260365i \(-0.916157\pi\)
−0.965510 + 0.260365i \(0.916157\pi\)
\(752\) 0 0
\(753\) 18.8243i 0.685997i
\(754\) 0 0
\(755\) 1.09460 0.171044i 0.0398365 0.00622495i
\(756\) 0 0
\(757\) 20.1352i 0.731827i 0.930649 + 0.365913i \(0.119243\pi\)
−0.930649 + 0.365913i \(0.880757\pi\)
\(758\) 0 0
\(759\) −12.5048 −0.453896
\(760\) 0 0
\(761\) 42.0948 1.52594 0.762968 0.646436i \(-0.223741\pi\)
0.762968 + 0.646436i \(0.223741\pi\)
\(762\) 0 0
\(763\) 0.283442i 0.0102613i
\(764\) 0 0
\(765\) −1.98772 12.7204i −0.0718660 0.459906i
\(766\) 0 0
\(767\) 34.0944i 1.23108i
\(768\) 0 0
\(769\) −15.9154 −0.573925 −0.286963 0.957942i \(-0.592646\pi\)
−0.286963 + 0.957942i \(0.592646\pi\)
\(770\) 0 0
\(771\) −29.3805 −1.05811
\(772\) 0 0
\(773\) 35.2489i 1.26782i 0.773409 + 0.633908i \(0.218550\pi\)
−0.773409 + 0.633908i \(0.781450\pi\)
\(774\) 0 0
\(775\) 44.1888 14.1557i 1.58731 0.508489i
\(776\) 0 0
\(777\) 0.208093i 0.00746529i
\(778\) 0 0
\(779\) −45.4925 −1.62994
\(780\) 0 0
\(781\) 55.9847 2.00329
\(782\) 0 0
\(783\) 4.90056i 0.175132i
\(784\) 0 0
\(785\) 6.13374 + 39.2528i 0.218922 + 1.40099i
\(786\) 0 0
\(787\) 5.42686i 0.193447i −0.995311 0.0967233i \(-0.969164\pi\)
0.995311 0.0967233i \(-0.0308362\pi\)
\(788\) 0 0
\(789\) 17.9546 0.639202
\(790\) 0 0
\(791\) −0.463096 −0.0164658
\(792\)