Properties

Label 240.3.l.d.161.7
Level $240$
Weight $3$
Character 240.161
Analytic conductor $6.540$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.681615360000.5
Defining polynomial: \(x^{8} - 4 x^{7} - 2 x^{6} + 20 x^{5} + 49 x^{4} - 136 x^{3} + 168 x^{2} - 96 x + 864\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 161.7
Root \(3.22255 - 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 240.161
Dual form 240.3.l.d.161.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.87275 - 0.864473i) q^{3} -2.23607i q^{5} -9.02416 q^{7} +(7.50537 - 4.96683i) q^{9} +O(q^{10})\) \(q+(2.87275 - 0.864473i) q^{3} -2.23607i q^{5} -9.02416 q^{7} +(7.50537 - 4.96683i) q^{9} -21.8827i q^{11} +21.6599 q^{13} +(-1.93302 - 6.42366i) q^{15} -12.1078i q^{17} -3.03757 q^{19} +(-25.9241 + 7.80114i) q^{21} +28.5735i q^{23} -5.00000 q^{25} +(17.2674 - 20.7566i) q^{27} +12.0364i q^{29} -2.19085 q^{31} +(-18.9170 - 62.8636i) q^{33} +20.1786i q^{35} +0.839959 q^{37} +(62.2233 - 18.7244i) q^{39} +35.5690i q^{41} +12.7152 q^{43} +(-11.1062 - 16.7825i) q^{45} -22.5481i q^{47} +32.4354 q^{49} +(-10.4668 - 34.7826i) q^{51} +9.13775i q^{53} -48.9312 q^{55} +(-8.72618 + 2.62590i) q^{57} +80.4459i q^{59} -57.8816 q^{61} +(-67.7297 + 44.8214i) q^{63} -48.4329i q^{65} +63.0560 q^{67} +(24.7011 + 82.0846i) q^{69} -17.0218i q^{71} +52.1181 q^{73} +(-14.3637 + 4.32237i) q^{75} +197.473i q^{77} +7.46224 q^{79} +(31.6612 - 74.5558i) q^{81} +82.3758i q^{83} -27.0738 q^{85} +(10.4051 + 34.5774i) q^{87} -27.5850i q^{89} -195.462 q^{91} +(-6.29376 + 1.89393i) q^{93} +6.79221i q^{95} +114.989 q^{97} +(-108.688 - 164.238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} - 8 q^{13} + 8 q^{19} + 28 q^{21} - 40 q^{25} - 20 q^{27} - 120 q^{31} - 112 q^{33} + 8 q^{37} + 72 q^{39} + 328 q^{43} - 60 q^{45} + 64 q^{49} - 64 q^{51} + 40 q^{55} + 72 q^{57} + 8 q^{61} - 88 q^{63} - 152 q^{67} + 100 q^{69} + 32 q^{73} - 20 q^{75} - 88 q^{79} + 224 q^{81} + 152 q^{87} - 560 q^{91} - 368 q^{93} + 144 q^{97} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 2.87275 0.864473i 0.957583 0.288158i
\(4\) 0 0
\(5\) 2.23607i 0.447214i
\(6\) 0 0
\(7\) −9.02416 −1.28917 −0.644583 0.764535i \(-0.722969\pi\)
−0.644583 + 0.764535i \(0.722969\pi\)
\(8\) 0 0
\(9\) 7.50537 4.96683i 0.833930 0.551870i
\(10\) 0 0
\(11\) 21.8827i 1.98934i −0.103119 0.994669i \(-0.532882\pi\)
0.103119 0.994669i \(-0.467118\pi\)
\(12\) 0 0
\(13\) 21.6599 1.66614 0.833071 0.553166i \(-0.186580\pi\)
0.833071 + 0.553166i \(0.186580\pi\)
\(14\) 0 0
\(15\) −1.93302 6.42366i −0.128868 0.428244i
\(16\) 0 0
\(17\) 12.1078i 0.712221i −0.934444 0.356111i \(-0.884103\pi\)
0.934444 0.356111i \(-0.115897\pi\)
\(18\) 0 0
\(19\) −3.03757 −0.159872 −0.0799361 0.996800i \(-0.525472\pi\)
−0.0799361 + 0.996800i \(0.525472\pi\)
\(20\) 0 0
\(21\) −25.9241 + 7.80114i −1.23448 + 0.371483i
\(22\) 0 0
\(23\) 28.5735i 1.24233i 0.783681 + 0.621164i \(0.213340\pi\)
−0.783681 + 0.621164i \(0.786660\pi\)
\(24\) 0 0
\(25\) −5.00000 −0.200000
\(26\) 0 0
\(27\) 17.2674 20.7566i 0.639532 0.768765i
\(28\) 0 0
\(29\) 12.0364i 0.415047i 0.978230 + 0.207523i \(0.0665403\pi\)
−0.978230 + 0.207523i \(0.933460\pi\)
\(30\) 0 0
\(31\) −2.19085 −0.0706725 −0.0353363 0.999375i \(-0.511250\pi\)
−0.0353363 + 0.999375i \(0.511250\pi\)
\(32\) 0 0
\(33\) −18.9170 62.8636i −0.573243 1.90496i
\(34\) 0 0
\(35\) 20.1786i 0.576532i
\(36\) 0 0
\(37\) 0.839959 0.0227016 0.0113508 0.999936i \(-0.496387\pi\)
0.0113508 + 0.999936i \(0.496387\pi\)
\(38\) 0 0
\(39\) 62.2233 18.7244i 1.59547 0.480112i
\(40\) 0 0
\(41\) 35.5690i 0.867537i 0.901024 + 0.433769i \(0.142816\pi\)
−0.901024 + 0.433769i \(0.857184\pi\)
\(42\) 0 0
\(43\) 12.7152 0.295702 0.147851 0.989010i \(-0.452764\pi\)
0.147851 + 0.989010i \(0.452764\pi\)
\(44\) 0 0
\(45\) −11.1062 16.7825i −0.246804 0.372945i
\(46\) 0 0
\(47\) 22.5481i 0.479746i −0.970804 0.239873i \(-0.922894\pi\)
0.970804 0.239873i \(-0.0771058\pi\)
\(48\) 0 0
\(49\) 32.4354 0.661947
\(50\) 0 0
\(51\) −10.4668 34.7826i −0.205232 0.682011i
\(52\) 0 0
\(53\) 9.13775i 0.172410i 0.996277 + 0.0862052i \(0.0274741\pi\)
−0.996277 + 0.0862052i \(0.972526\pi\)
\(54\) 0 0
\(55\) −48.9312 −0.889659
\(56\) 0 0
\(57\) −8.72618 + 2.62590i −0.153091 + 0.0460684i
\(58\) 0 0
\(59\) 80.4459i 1.36349i 0.731590 + 0.681745i \(0.238779\pi\)
−0.731590 + 0.681745i \(0.761221\pi\)
\(60\) 0 0
\(61\) −57.8816 −0.948878 −0.474439 0.880288i \(-0.657349\pi\)
−0.474439 + 0.880288i \(0.657349\pi\)
\(62\) 0 0
\(63\) −67.7297 + 44.8214i −1.07507 + 0.711452i
\(64\) 0 0
\(65\) 48.4329i 0.745122i
\(66\) 0 0
\(67\) 63.0560 0.941135 0.470567 0.882364i \(-0.344049\pi\)
0.470567 + 0.882364i \(0.344049\pi\)
\(68\) 0 0
\(69\) 24.7011 + 82.0846i 0.357986 + 1.18963i
\(70\) 0 0
\(71\) 17.0218i 0.239743i −0.992789 0.119872i \(-0.961752\pi\)
0.992789 0.119872i \(-0.0382483\pi\)
\(72\) 0 0
\(73\) 52.1181 0.713947 0.356973 0.934115i \(-0.383809\pi\)
0.356973 + 0.934115i \(0.383809\pi\)
\(74\) 0 0
\(75\) −14.3637 + 4.32237i −0.191517 + 0.0576316i
\(76\) 0 0
\(77\) 197.473i 2.56459i
\(78\) 0 0
\(79\) 7.46224 0.0944588 0.0472294 0.998884i \(-0.484961\pi\)
0.0472294 + 0.998884i \(0.484961\pi\)
\(80\) 0 0
\(81\) 31.6612 74.5558i 0.390879 0.920442i
\(82\) 0 0
\(83\) 82.3758i 0.992480i 0.868185 + 0.496240i \(0.165286\pi\)
−0.868185 + 0.496240i \(0.834714\pi\)
\(84\) 0 0
\(85\) −27.0738 −0.318515
\(86\) 0 0
\(87\) 10.4051 + 34.5774i 0.119599 + 0.397442i
\(88\) 0 0
\(89\) 27.5850i 0.309944i −0.987919 0.154972i \(-0.950471\pi\)
0.987919 0.154972i \(-0.0495287\pi\)
\(90\) 0 0
\(91\) −195.462 −2.14793
\(92\) 0 0
\(93\) −6.29376 + 1.89393i −0.0676748 + 0.0203648i
\(94\) 0 0
\(95\) 6.79221i 0.0714970i
\(96\) 0 0
\(97\) 114.989 1.18545 0.592727 0.805404i \(-0.298051\pi\)
0.592727 + 0.805404i \(0.298051\pi\)
\(98\) 0 0
\(99\) −108.688 164.238i −1.09786 1.65897i
\(100\) 0 0
\(101\) 122.804i 1.21588i 0.793982 + 0.607941i \(0.208004\pi\)
−0.793982 + 0.607941i \(0.791996\pi\)
\(102\) 0 0
\(103\) 46.8275 0.454636 0.227318 0.973821i \(-0.427004\pi\)
0.227318 + 0.973821i \(0.427004\pi\)
\(104\) 0 0
\(105\) 17.4439 + 57.9681i 0.166132 + 0.552077i
\(106\) 0 0
\(107\) 105.086i 0.982113i 0.871128 + 0.491056i \(0.163389\pi\)
−0.871128 + 0.491056i \(0.836611\pi\)
\(108\) 0 0
\(109\) −116.777 −1.07135 −0.535673 0.844426i \(-0.679942\pi\)
−0.535673 + 0.844426i \(0.679942\pi\)
\(110\) 0 0
\(111\) 2.41299 0.726122i 0.0217387 0.00654164i
\(112\) 0 0
\(113\) 10.8116i 0.0956779i 0.998855 + 0.0478389i \(0.0152334\pi\)
−0.998855 + 0.0478389i \(0.984767\pi\)
\(114\) 0 0
\(115\) 63.8924 0.555586
\(116\) 0 0
\(117\) 162.565 107.581i 1.38945 0.919494i
\(118\) 0 0
\(119\) 109.262i 0.918171i
\(120\) 0 0
\(121\) −357.853 −2.95747
\(122\) 0 0
\(123\) 30.7485 + 102.181i 0.249988 + 0.830739i
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) 192.459 1.51543 0.757714 0.652587i \(-0.226316\pi\)
0.757714 + 0.652587i \(0.226316\pi\)
\(128\) 0 0
\(129\) 36.5276 10.9919i 0.283159 0.0852089i
\(130\) 0 0
\(131\) 48.6360i 0.371267i −0.982619 0.185633i \(-0.940566\pi\)
0.982619 0.185633i \(-0.0594337\pi\)
\(132\) 0 0
\(133\) 27.4115 0.206102
\(134\) 0 0
\(135\) −46.4133 38.6110i −0.343802 0.286007i
\(136\) 0 0
\(137\) 157.869i 1.15233i −0.817335 0.576163i \(-0.804549\pi\)
0.817335 0.576163i \(-0.195451\pi\)
\(138\) 0 0
\(139\) 164.752 1.18526 0.592632 0.805473i \(-0.298089\pi\)
0.592632 + 0.805473i \(0.298089\pi\)
\(140\) 0 0
\(141\) −19.4922 64.7749i −0.138243 0.459397i
\(142\) 0 0
\(143\) 473.977i 3.31452i
\(144\) 0 0
\(145\) 26.9141 0.185615
\(146\) 0 0
\(147\) 93.1788 28.0396i 0.633869 0.190745i
\(148\) 0 0
\(149\) 262.935i 1.76467i −0.470626 0.882333i \(-0.655972\pi\)
0.470626 0.882333i \(-0.344028\pi\)
\(150\) 0 0
\(151\) −15.8171 −0.104749 −0.0523745 0.998628i \(-0.516679\pi\)
−0.0523745 + 0.998628i \(0.516679\pi\)
\(152\) 0 0
\(153\) −60.1372 90.8733i −0.393054 0.593943i
\(154\) 0 0
\(155\) 4.89889i 0.0316057i
\(156\) 0 0
\(157\) −6.11941 −0.0389771 −0.0194886 0.999810i \(-0.506204\pi\)
−0.0194886 + 0.999810i \(0.506204\pi\)
\(158\) 0 0
\(159\) 7.89934 + 26.2505i 0.0496814 + 0.165097i
\(160\) 0 0
\(161\) 257.852i 1.60157i
\(162\) 0 0
\(163\) 170.444 1.04567 0.522833 0.852435i \(-0.324875\pi\)
0.522833 + 0.852435i \(0.324875\pi\)
\(164\) 0 0
\(165\) −140.567 + 42.2998i −0.851922 + 0.256362i
\(166\) 0 0
\(167\) 61.2668i 0.366867i 0.983032 + 0.183434i \(0.0587212\pi\)
−0.983032 + 0.183434i \(0.941279\pi\)
\(168\) 0 0
\(169\) 300.149 1.77603
\(170\) 0 0
\(171\) −22.7981 + 15.0871i −0.133322 + 0.0882286i
\(172\) 0 0
\(173\) 262.548i 1.51762i 0.651312 + 0.758810i \(0.274219\pi\)
−0.651312 + 0.758810i \(0.725781\pi\)
\(174\) 0 0
\(175\) 45.1208 0.257833
\(176\) 0 0
\(177\) 69.5434 + 231.101i 0.392900 + 1.30566i
\(178\) 0 0
\(179\) 6.88752i 0.0384778i 0.999815 + 0.0192389i \(0.00612431\pi\)
−0.999815 + 0.0192389i \(0.993876\pi\)
\(180\) 0 0
\(181\) 218.536 1.20738 0.603691 0.797218i \(-0.293696\pi\)
0.603691 + 0.797218i \(0.293696\pi\)
\(182\) 0 0
\(183\) −166.279 + 50.0371i −0.908630 + 0.273427i
\(184\) 0 0
\(185\) 1.87821i 0.0101525i
\(186\) 0 0
\(187\) −264.951 −1.41685
\(188\) 0 0
\(189\) −155.823 + 187.311i −0.824462 + 0.991065i
\(190\) 0 0
\(191\) 75.2506i 0.393982i −0.980405 0.196991i \(-0.936883\pi\)
0.980405 0.196991i \(-0.0631170\pi\)
\(192\) 0 0
\(193\) −212.587 −1.10149 −0.550744 0.834674i \(-0.685656\pi\)
−0.550744 + 0.834674i \(0.685656\pi\)
\(194\) 0 0
\(195\) −41.8690 139.136i −0.214713 0.713516i
\(196\) 0 0
\(197\) 190.640i 0.967718i −0.875146 0.483859i \(-0.839235\pi\)
0.875146 0.483859i \(-0.160765\pi\)
\(198\) 0 0
\(199\) −209.996 −1.05526 −0.527629 0.849475i \(-0.676919\pi\)
−0.527629 + 0.849475i \(0.676919\pi\)
\(200\) 0 0
\(201\) 181.144 54.5102i 0.901214 0.271195i
\(202\) 0 0
\(203\) 108.618i 0.535064i
\(204\) 0 0
\(205\) 79.5348 0.387974
\(206\) 0 0
\(207\) 141.920 + 214.455i 0.685603 + 1.03601i
\(208\) 0 0
\(209\) 66.4703i 0.318040i
\(210\) 0 0
\(211\) −176.419 −0.836110 −0.418055 0.908422i \(-0.637288\pi\)
−0.418055 + 0.908422i \(0.637288\pi\)
\(212\) 0 0
\(213\) −14.7149 48.8993i −0.0690839 0.229574i
\(214\) 0 0
\(215\) 28.4320i 0.132242i
\(216\) 0 0
\(217\) 19.7706 0.0911086
\(218\) 0 0
\(219\) 149.722 45.0547i 0.683663 0.205729i
\(220\) 0 0
\(221\) 262.252i 1.18666i
\(222\) 0 0
\(223\) −132.362 −0.593552 −0.296776 0.954947i \(-0.595911\pi\)
−0.296776 + 0.954947i \(0.595911\pi\)
\(224\) 0 0
\(225\) −37.5269 + 24.8341i −0.166786 + 0.110374i
\(226\) 0 0
\(227\) 187.624i 0.826537i −0.910609 0.413268i \(-0.864387\pi\)
0.910609 0.413268i \(-0.135613\pi\)
\(228\) 0 0
\(229\) −178.571 −0.779788 −0.389894 0.920860i \(-0.627488\pi\)
−0.389894 + 0.920860i \(0.627488\pi\)
\(230\) 0 0
\(231\) 170.710 + 567.291i 0.739005 + 2.45580i
\(232\) 0 0
\(233\) 296.711i 1.27344i 0.771097 + 0.636718i \(0.219708\pi\)
−0.771097 + 0.636718i \(0.780292\pi\)
\(234\) 0 0
\(235\) −50.4190 −0.214549
\(236\) 0 0
\(237\) 21.4371 6.45091i 0.0904521 0.0272190i
\(238\) 0 0
\(239\) 137.976i 0.577306i −0.957434 0.288653i \(-0.906793\pi\)
0.957434 0.288653i \(-0.0932074\pi\)
\(240\) 0 0
\(241\) 42.5687 0.176633 0.0883167 0.996092i \(-0.471851\pi\)
0.0883167 + 0.996092i \(0.471851\pi\)
\(242\) 0 0
\(243\) 26.5032 241.550i 0.109067 0.994034i
\(244\) 0 0
\(245\) 72.5278i 0.296032i
\(246\) 0 0
\(247\) −65.7933 −0.266370
\(248\) 0 0
\(249\) 71.2117 + 236.645i 0.285991 + 0.950382i
\(250\) 0 0
\(251\) 205.885i 0.820259i 0.912027 + 0.410130i \(0.134517\pi\)
−0.912027 + 0.410130i \(0.865483\pi\)
\(252\) 0 0
\(253\) 625.267 2.47141
\(254\) 0 0
\(255\) −77.7762 + 23.4046i −0.305005 + 0.0917826i
\(256\) 0 0
\(257\) 188.382i 0.733004i 0.930417 + 0.366502i \(0.119445\pi\)
−0.930417 + 0.366502i \(0.880555\pi\)
\(258\) 0 0
\(259\) −7.57992 −0.0292661
\(260\) 0 0
\(261\) 59.7825 + 90.3373i 0.229052 + 0.346120i
\(262\) 0 0
\(263\) 188.745i 0.717660i 0.933403 + 0.358830i \(0.116824\pi\)
−0.933403 + 0.358830i \(0.883176\pi\)
\(264\) 0 0
\(265\) 20.4326 0.0771043
\(266\) 0 0
\(267\) −23.8465 79.2447i −0.0893127 0.296797i
\(268\) 0 0
\(269\) 333.372i 1.23930i −0.784878 0.619651i \(-0.787274\pi\)
0.784878 0.619651i \(-0.212726\pi\)
\(270\) 0 0
\(271\) −262.047 −0.966964 −0.483482 0.875354i \(-0.660628\pi\)
−0.483482 + 0.875354i \(0.660628\pi\)
\(272\) 0 0
\(273\) −561.513 + 168.972i −2.05682 + 0.618944i
\(274\) 0 0
\(275\) 109.414i 0.397868i
\(276\) 0 0
\(277\) −400.100 −1.44440 −0.722202 0.691682i \(-0.756870\pi\)
−0.722202 + 0.691682i \(0.756870\pi\)
\(278\) 0 0
\(279\) −16.4431 + 10.8816i −0.0589360 + 0.0390020i
\(280\) 0 0
\(281\) 350.698i 1.24804i 0.781410 + 0.624018i \(0.214501\pi\)
−0.781410 + 0.624018i \(0.785499\pi\)
\(282\) 0 0
\(283\) 464.015 1.63963 0.819814 0.572630i \(-0.194077\pi\)
0.819814 + 0.572630i \(0.194077\pi\)
\(284\) 0 0
\(285\) 5.87169 + 19.5123i 0.0206024 + 0.0684643i
\(286\) 0 0
\(287\) 320.981i 1.11840i
\(288\) 0 0
\(289\) 142.402 0.492741
\(290\) 0 0
\(291\) 330.334 99.4049i 1.13517 0.341598i
\(292\) 0 0
\(293\) 47.4080i 0.161802i −0.996722 0.0809009i \(-0.974220\pi\)
0.996722 0.0809009i \(-0.0257797\pi\)
\(294\) 0 0
\(295\) 179.883 0.609771
\(296\) 0 0
\(297\) −454.212 377.857i −1.52933 1.27224i
\(298\) 0 0
\(299\) 618.899i 2.06990i
\(300\) 0 0
\(301\) −114.744 −0.381209
\(302\) 0 0
\(303\) 106.161 + 352.785i 0.350366 + 1.16431i
\(304\) 0 0
\(305\) 129.427i 0.424351i
\(306\) 0 0
\(307\) −461.894 −1.50454 −0.752270 0.658855i \(-0.771041\pi\)
−0.752270 + 0.658855i \(0.771041\pi\)
\(308\) 0 0
\(309\) 134.524 40.4812i 0.435352 0.131007i
\(310\) 0 0
\(311\) 123.057i 0.395681i −0.980234 0.197841i \(-0.936607\pi\)
0.980234 0.197841i \(-0.0633929\pi\)
\(312\) 0 0
\(313\) 97.4353 0.311295 0.155647 0.987813i \(-0.450254\pi\)
0.155647 + 0.987813i \(0.450254\pi\)
\(314\) 0 0
\(315\) 100.224 + 151.448i 0.318171 + 0.480788i
\(316\) 0 0
\(317\) 252.388i 0.796175i −0.917347 0.398088i \(-0.869674\pi\)
0.917347 0.398088i \(-0.130326\pi\)
\(318\) 0 0
\(319\) 263.388 0.825668
\(320\) 0 0
\(321\) 90.8441 + 301.886i 0.283003 + 0.940454i
\(322\) 0 0
\(323\) 36.7782i 0.113864i
\(324\) 0 0
\(325\) −108.299 −0.333229
\(326\) 0 0
\(327\) −335.470 + 100.950i −1.02590 + 0.308716i
\(328\) 0 0
\(329\) 203.477i 0.618472i
\(330\) 0 0
\(331\) 303.273 0.916231 0.458116 0.888893i \(-0.348525\pi\)
0.458116 + 0.888893i \(0.348525\pi\)
\(332\) 0 0
\(333\) 6.30420 4.17193i 0.0189315 0.0125283i
\(334\) 0 0
\(335\) 140.998i 0.420888i
\(336\) 0 0
\(337\) −352.738 −1.04670 −0.523350 0.852118i \(-0.675318\pi\)
−0.523350 + 0.852118i \(0.675318\pi\)
\(338\) 0 0
\(339\) 9.34634 + 31.0590i 0.0275703 + 0.0916195i
\(340\) 0 0
\(341\) 47.9417i 0.140592i
\(342\) 0 0
\(343\) 149.481 0.435806
\(344\) 0 0
\(345\) 183.547 55.2332i 0.532019 0.160096i
\(346\) 0 0
\(347\) 280.382i 0.808018i 0.914755 + 0.404009i \(0.132384\pi\)
−0.914755 + 0.404009i \(0.867616\pi\)
\(348\) 0 0
\(349\) −586.721 −1.68115 −0.840575 0.541696i \(-0.817783\pi\)
−0.840575 + 0.541696i \(0.817783\pi\)
\(350\) 0 0
\(351\) 374.008 449.586i 1.06555 1.28087i
\(352\) 0 0
\(353\) 558.927i 1.58336i −0.610935 0.791681i \(-0.709206\pi\)
0.610935 0.791681i \(-0.290794\pi\)
\(354\) 0 0
\(355\) −38.0618 −0.107216
\(356\) 0 0
\(357\) 94.4544 + 313.883i 0.264578 + 0.879225i
\(358\) 0 0
\(359\) 323.554i 0.901264i −0.892710 0.450632i \(-0.851199\pi\)
0.892710 0.450632i \(-0.148801\pi\)
\(360\) 0 0
\(361\) −351.773 −0.974441
\(362\) 0 0
\(363\) −1028.02 + 309.355i −2.83202 + 0.852217i
\(364\) 0 0
\(365\) 116.540i 0.319287i
\(366\) 0 0
\(367\) −176.636 −0.481296 −0.240648 0.970612i \(-0.577360\pi\)
−0.240648 + 0.970612i \(0.577360\pi\)
\(368\) 0 0
\(369\) 176.665 + 266.959i 0.478768 + 0.723466i
\(370\) 0 0
\(371\) 82.4605i 0.222265i
\(372\) 0 0
\(373\) 367.327 0.984790 0.492395 0.870372i \(-0.336122\pi\)
0.492395 + 0.870372i \(0.336122\pi\)
\(374\) 0 0
\(375\) 9.66511 + 32.1183i 0.0257736 + 0.0856488i
\(376\) 0 0
\(377\) 260.706i 0.691527i
\(378\) 0 0
\(379\) −611.014 −1.61217 −0.806087 0.591798i \(-0.798418\pi\)
−0.806087 + 0.591798i \(0.798418\pi\)
\(380\) 0 0
\(381\) 552.887 166.376i 1.45115 0.436682i
\(382\) 0 0
\(383\) 13.6994i 0.0357687i −0.999840 0.0178844i \(-0.994307\pi\)
0.999840 0.0178844i \(-0.00569307\pi\)
\(384\) 0 0
\(385\) 441.563 1.14692
\(386\) 0 0
\(387\) 95.4322 63.1542i 0.246595 0.163189i
\(388\) 0 0
\(389\) 379.601i 0.975838i 0.872889 + 0.487919i \(0.162244\pi\)
−0.872889 + 0.487919i \(0.837756\pi\)
\(390\) 0 0
\(391\) 345.962 0.884812
\(392\) 0 0
\(393\) −42.0445 139.719i −0.106983 0.355519i
\(394\) 0 0
\(395\) 16.6861i 0.0422432i
\(396\) 0 0
\(397\) 450.560 1.13491 0.567456 0.823404i \(-0.307928\pi\)
0.567456 + 0.823404i \(0.307928\pi\)
\(398\) 0 0
\(399\) 78.7464 23.6965i 0.197359 0.0593898i
\(400\) 0 0
\(401\) 503.683i 1.25607i 0.778186 + 0.628034i \(0.216140\pi\)
−0.778186 + 0.628034i \(0.783860\pi\)
\(402\) 0 0
\(403\) −47.4535 −0.117751
\(404\) 0 0
\(405\) −166.712 70.7966i −0.411634 0.174806i
\(406\) 0 0
\(407\) 18.3806i 0.0451611i
\(408\) 0 0
\(409\) 240.726 0.588573 0.294286 0.955717i \(-0.404918\pi\)
0.294286 + 0.955717i \(0.404918\pi\)
\(410\) 0 0
\(411\) −136.473 453.517i −0.332051 1.10345i
\(412\) 0 0
\(413\) 725.957i 1.75776i
\(414\) 0 0
\(415\) 184.198 0.443850
\(416\) 0 0
\(417\) 473.290 142.423i 1.13499 0.341543i
\(418\) 0 0
\(419\) 676.873i 1.61545i −0.589561 0.807724i \(-0.700699\pi\)
0.589561 0.807724i \(-0.299301\pi\)
\(420\) 0 0
\(421\) 683.755 1.62412 0.812061 0.583572i \(-0.198346\pi\)
0.812061 + 0.583572i \(0.198346\pi\)
\(422\) 0 0
\(423\) −111.992 169.232i −0.264757 0.400075i
\(424\) 0 0
\(425\) 60.5388i 0.142444i
\(426\) 0 0
\(427\) 522.332 1.22326
\(428\) 0 0
\(429\) −409.740 1361.62i −0.955105 3.17393i
\(430\) 0 0
\(431\) 213.608i 0.495610i −0.968810 0.247805i \(-0.920291\pi\)
0.968810 0.247805i \(-0.0797092\pi\)
\(432\) 0 0
\(433\) −383.579 −0.885864 −0.442932 0.896555i \(-0.646062\pi\)
−0.442932 + 0.896555i \(0.646062\pi\)
\(434\) 0 0
\(435\) 77.3175 23.2665i 0.177741 0.0534863i
\(436\) 0 0
\(437\) 86.7941i 0.198614i
\(438\) 0 0
\(439\) −523.900 −1.19340 −0.596698 0.802466i \(-0.703521\pi\)
−0.596698 + 0.802466i \(0.703521\pi\)
\(440\) 0 0
\(441\) 243.440 161.101i 0.552018 0.365309i
\(442\) 0 0
\(443\) 391.277i 0.883243i 0.897201 + 0.441622i \(0.145597\pi\)
−0.897201 + 0.441622i \(0.854403\pi\)
\(444\) 0 0
\(445\) −61.6819 −0.138611
\(446\) 0 0
\(447\) −227.301 755.347i −0.508502 1.68981i
\(448\) 0 0
\(449\) 375.014i 0.835220i −0.908626 0.417610i \(-0.862868\pi\)
0.908626 0.417610i \(-0.137132\pi\)
\(450\) 0 0
\(451\) 778.347 1.72582
\(452\) 0 0
\(453\) −45.4386 + 13.6735i −0.100306 + 0.0301843i
\(454\) 0 0
\(455\) 437.066i 0.960585i
\(456\) 0 0
\(457\) −734.032 −1.60620 −0.803098 0.595847i \(-0.796817\pi\)
−0.803098 + 0.595847i \(0.796817\pi\)
\(458\) 0 0
\(459\) −251.317 209.069i −0.547531 0.455488i
\(460\) 0 0
\(461\) 775.239i 1.68165i 0.541310 + 0.840823i \(0.317928\pi\)
−0.541310 + 0.840823i \(0.682072\pi\)
\(462\) 0 0
\(463\) 323.967 0.699714 0.349857 0.936803i \(-0.386230\pi\)
0.349857 + 0.936803i \(0.386230\pi\)
\(464\) 0 0
\(465\) 4.23496 + 14.0733i 0.00910743 + 0.0302651i
\(466\) 0 0
\(467\) 160.785i 0.344294i −0.985071 0.172147i \(-0.944930\pi\)
0.985071 0.172147i \(-0.0550704\pi\)
\(468\) 0 0
\(469\) −569.027 −1.21328
\(470\) 0 0
\(471\) −17.5795 + 5.29007i −0.0373239 + 0.0112316i
\(472\) 0 0
\(473\) 278.243i 0.588252i
\(474\) 0 0
\(475\) 15.1879 0.0319744
\(476\) 0 0
\(477\) 45.3856 + 68.5822i 0.0951481 + 0.143778i
\(478\) 0 0
\(479\) 61.7565i 0.128928i −0.997920 0.0644640i \(-0.979466\pi\)
0.997920 0.0644640i \(-0.0205338\pi\)
\(480\) 0 0
\(481\) 18.1934 0.0378241
\(482\) 0 0
\(483\) −222.906 740.744i −0.461504 1.53363i
\(484\) 0 0
\(485\) 257.123i 0.530151i
\(486\) 0 0
\(487\) −129.969 −0.266876 −0.133438 0.991057i \(-0.542602\pi\)
−0.133438 + 0.991057i \(0.542602\pi\)
\(488\) 0 0
\(489\) 489.642 147.344i 1.00131 0.301317i
\(490\) 0 0
\(491\) 810.511i 1.65074i 0.564595 + 0.825368i \(0.309032\pi\)
−0.564595 + 0.825368i \(0.690968\pi\)
\(492\) 0 0
\(493\) 145.733 0.295605
\(494\) 0 0
\(495\) −367.247 + 243.033i −0.741914 + 0.490976i
\(496\) 0 0
\(497\) 153.607i 0.309069i
\(498\) 0 0
\(499\) 600.897 1.20420 0.602101 0.798420i \(-0.294330\pi\)
0.602101 + 0.798420i \(0.294330\pi\)
\(500\) 0 0
\(501\) 52.9635 + 176.004i 0.105716 + 0.351306i
\(502\) 0 0
\(503\) 688.332i 1.36845i 0.729270 + 0.684226i \(0.239860\pi\)
−0.729270 + 0.684226i \(0.760140\pi\)
\(504\) 0 0
\(505\) 274.598 0.543759
\(506\) 0 0
\(507\) 862.254 259.471i 1.70070 0.511777i
\(508\) 0 0
\(509\) 823.791i 1.61845i 0.587498 + 0.809225i \(0.300113\pi\)
−0.587498 + 0.809225i \(0.699887\pi\)
\(510\) 0 0
\(511\) −470.322 −0.920395
\(512\) 0 0
\(513\) −52.4508 + 63.0498i −0.102243 + 0.122904i
\(514\) 0 0
\(515\) 104.710i 0.203320i
\(516\) 0 0
\(517\) −493.413 −0.954377
\(518\) 0 0
\(519\) 226.966 + 754.235i 0.437314 + 1.45325i
\(520\) 0 0
\(521\) 964.525i 1.85130i −0.378386 0.925648i \(-0.623521\pi\)
0.378386 0.925648i \(-0.376479\pi\)
\(522\) 0 0
\(523\) −462.679 −0.884664 −0.442332 0.896851i \(-0.645849\pi\)
−0.442332 + 0.896851i \(0.645849\pi\)
\(524\) 0 0
\(525\) 129.621 39.0057i 0.246897 0.0742966i
\(526\) 0 0
\(527\) 26.5263i 0.0503345i
\(528\) 0 0
\(529\) −287.447 −0.543378
\(530\) 0 0
\(531\) 399.561 + 603.777i 0.752469 + 1.13706i
\(532\) 0 0
\(533\) 770.420i 1.44544i
\(534\) 0 0
\(535\) 234.980 0.439214
\(536\) 0 0
\(537\) 5.95408 + 19.7861i 0.0110877 + 0.0368457i
\(538\) 0 0
\(539\) 709.775i 1.31684i
\(540\) 0 0
\(541\) −516.752 −0.955180 −0.477590 0.878583i \(-0.658490\pi\)
−0.477590 + 0.878583i \(0.658490\pi\)
\(542\) 0 0
\(543\) 627.800 188.919i 1.15617 0.347917i
\(544\) 0 0
\(545\) 261.120i 0.479120i
\(546\) 0 0
\(547\) −478.953 −0.875599 −0.437799 0.899073i \(-0.644242\pi\)
−0.437799 + 0.899073i \(0.644242\pi\)
\(548\) 0 0
\(549\) −434.423 + 287.488i −0.791298 + 0.523657i
\(550\) 0 0
\(551\) 36.5613i 0.0663544i
\(552\) 0 0
\(553\) −67.3404 −0.121773
\(554\) 0 0
\(555\) −1.62366 5.39561i −0.00292551 0.00972182i
\(556\) 0 0
\(557\) 343.982i 0.617561i 0.951133 + 0.308781i \(0.0999209\pi\)
−0.951133 + 0.308781i \(0.900079\pi\)
\(558\) 0 0
\(559\) 275.409 0.492682
\(560\) 0 0
\(561\) −761.137 + 229.043i −1.35675 + 0.408276i
\(562\) 0 0
\(563\) 394.056i 0.699922i 0.936764 + 0.349961i \(0.113805\pi\)
−0.936764 + 0.349961i \(0.886195\pi\)
\(564\) 0 0
\(565\) 24.1755 0.0427885
\(566\) 0 0
\(567\) −285.716 + 672.803i −0.503908 + 1.18660i
\(568\) 0 0
\(569\) 537.452i 0.944556i 0.881450 + 0.472278i \(0.156568\pi\)
−0.881450 + 0.472278i \(0.843432\pi\)
\(570\) 0 0
\(571\) −710.555 −1.24440 −0.622202 0.782856i \(-0.713762\pi\)
−0.622202 + 0.782856i \(0.713762\pi\)
\(572\) 0 0
\(573\) −65.0521 216.176i −0.113529 0.377271i
\(574\) 0 0
\(575\) 142.868i 0.248466i
\(576\) 0 0
\(577\) 452.846 0.784828 0.392414 0.919789i \(-0.371640\pi\)
0.392414 + 0.919789i \(0.371640\pi\)
\(578\) 0 0
\(579\) −610.709 + 183.776i −1.05477 + 0.317402i
\(580\) 0 0
\(581\) 743.372i 1.27947i
\(582\) 0 0
\(583\) 199.959 0.342983
\(584\) 0 0
\(585\) −240.558 363.507i −0.411210 0.621379i
\(586\) 0 0
\(587\) 1103.34i 1.87963i 0.341690 + 0.939813i \(0.389001\pi\)
−0.341690 + 0.939813i \(0.610999\pi\)
\(588\) 0 0
\(589\) 6.65486 0.0112986
\(590\) 0 0
\(591\) −164.804 547.662i −0.278855 0.926670i
\(592\) 0 0
\(593\) 249.474i 0.420698i −0.977626 0.210349i \(-0.932540\pi\)
0.977626 0.210349i \(-0.0674601\pi\)
\(594\) 0 0
\(595\) 244.318 0.410619
\(596\) 0 0
\(597\) −603.267 + 181.536i −1.01050 + 0.304081i
\(598\) 0 0
\(599\) 596.120i 0.995191i 0.867409 + 0.497596i \(0.165784\pi\)
−0.867409 + 0.497596i \(0.834216\pi\)
\(600\) 0 0
\(601\) 476.515 0.792871 0.396435 0.918063i \(-0.370247\pi\)
0.396435 + 0.918063i \(0.370247\pi\)
\(602\) 0 0
\(603\) 473.259 313.188i 0.784841 0.519384i
\(604\) 0 0
\(605\) 800.185i 1.32262i
\(606\) 0 0
\(607\) −27.8813 −0.0459329 −0.0229664 0.999736i \(-0.507311\pi\)
−0.0229664 + 0.999736i \(0.507311\pi\)
\(608\) 0 0
\(609\) −93.8973 312.032i −0.154183 0.512368i
\(610\) 0 0
\(611\) 488.388i 0.799325i
\(612\) 0 0
\(613\) 465.472 0.759334 0.379667 0.925123i \(-0.376039\pi\)
0.379667 + 0.925123i \(0.376039\pi\)
\(614\) 0 0
\(615\) 228.483 68.7557i 0.371518 0.111798i
\(616\) 0 0
\(617\) 48.6709i 0.0788832i 0.999222 + 0.0394416i \(0.0125579\pi\)
−0.999222 + 0.0394416i \(0.987442\pi\)
\(618\) 0 0
\(619\) 213.318 0.344617 0.172309 0.985043i \(-0.444877\pi\)
0.172309 + 0.985043i \(0.444877\pi\)
\(620\) 0 0
\(621\) 593.091 + 493.389i 0.955058 + 0.794508i
\(622\) 0 0
\(623\) 248.931i 0.399569i
\(624\) 0 0
\(625\) 25.0000 0.0400000
\(626\) 0 0
\(627\) 57.4618 + 190.953i 0.0916456 + 0.304549i
\(628\) 0 0
\(629\) 10.1700i 0.0161686i
\(630\) 0 0
\(631\) −582.489 −0.923121 −0.461560 0.887109i \(-0.652710\pi\)
−0.461560 + 0.887109i \(0.652710\pi\)
\(632\) 0 0
\(633\) −506.808 + 152.510i −0.800644 + 0.240931i
\(634\) 0 0
\(635\) 430.352i 0.677720i
\(636\) 0 0
\(637\) 702.546 1.10290
\(638\) 0 0
\(639\) −84.5442 127.755i −0.132307 0.199929i
\(640\) 0 0
\(641\) 319.635i 0.498650i −0.968420 0.249325i \(-0.919791\pi\)
0.968420 0.249325i \(-0.0802088\pi\)
\(642\) 0 0
\(643\) −458.627 −0.713261 −0.356630 0.934246i \(-0.616074\pi\)
−0.356630 + 0.934246i \(0.616074\pi\)
\(644\) 0 0
\(645\) −24.5787 81.6781i −0.0381066 0.126633i
\(646\) 0 0
\(647\) 507.599i 0.784543i −0.919850 0.392271i \(-0.871689\pi\)
0.919850 0.392271i \(-0.128311\pi\)
\(648\) 0 0
\(649\) 1760.38 2.71244
\(650\) 0 0
\(651\) 56.7959 17.0911i 0.0872440 0.0262536i
\(652\) 0 0
\(653\) 1197.20i 1.83339i 0.399591 + 0.916694i \(0.369152\pi\)
−0.399591 + 0.916694i \(0.630848\pi\)
\(654\) 0 0
\(655\) −108.753 −0.166036
\(656\) 0 0
\(657\) 391.166 258.862i 0.595382 0.394006i
\(658\) 0 0
\(659\) 632.173i 0.959291i 0.877462 + 0.479645i \(0.159235\pi\)
−0.877462 + 0.479645i \(0.840765\pi\)
\(660\) 0 0
\(661\) −565.316 −0.855243 −0.427622 0.903958i \(-0.640648\pi\)
−0.427622 + 0.903958i \(0.640648\pi\)
\(662\) 0 0
\(663\) −226.710 753.385i −0.341946 1.13633i
\(664\) 0 0
\(665\) 61.2940i 0.0921715i
\(666\) 0 0
\(667\) −343.921 −0.515624
\(668\) 0 0
\(669\) −380.243 + 114.423i −0.568375 + 0.171036i
\(670\) 0 0
\(671\) 1266.61i 1.88764i
\(672\) 0 0
\(673\) −306.607 −0.455582 −0.227791 0.973710i \(-0.573150\pi\)
−0.227791 + 0.973710i \(0.573150\pi\)
\(674\) 0 0
\(675\) −86.3368 + 103.783i −0.127906 + 0.153753i
\(676\) 0 0
\(677\) 546.672i 0.807491i −0.914871 0.403746i \(-0.867708\pi\)
0.914871 0.403746i \(-0.132292\pi\)
\(678\) 0 0
\(679\) −1037.68 −1.52824
\(680\) 0 0
\(681\) −162.196 538.996i −0.238173 0.791478i
\(682\) 0 0
\(683\) 812.204i 1.18917i −0.804032 0.594586i \(-0.797316\pi\)
0.804032 0.594586i \(-0.202684\pi\)
\(684\) 0 0
\(685\) −353.005 −0.515335
\(686\) 0 0
\(687\) −512.991 + 154.370i −0.746712 + 0.224702i
\(688\) 0 0
\(689\) 197.922i 0.287260i
\(690\) 0 0
\(691\) 45.9358 0.0664773 0.0332387 0.999447i \(-0.489418\pi\)
0.0332387 + 0.999447i \(0.489418\pi\)
\(692\) 0 0
\(693\) 980.815 + 1482.11i 1.41532 + 2.13869i
\(694\) 0 0
\(695\) 368.396i 0.530066i
\(696\) 0 0
\(697\) 430.661 0.617879
\(698\) 0 0
\(699\) 256.498 + 852.375i 0.366950 + 1.21942i
\(700\) 0 0
\(701\) 674.615i 0.962360i 0.876622 + 0.481180i \(0.159792\pi\)
−0.876622 + 0.481180i \(0.840208\pi\)
\(702\) 0 0
\(703\) −2.55143 −0.00362935
\(704\) 0 0
\(705\) −144.841 + 43.5859i −0.205448 + 0.0618240i
\(706\) 0 0
\(707\) 1108.20i 1.56747i
\(708\) 0 0
\(709\) 656.626 0.926129 0.463065 0.886324i \(-0.346750\pi\)
0.463065 + 0.886324i \(0.346750\pi\)
\(710\) 0 0
\(711\) 56.0069 37.0637i 0.0787720 0.0521290i
\(712\) 0 0
\(713\) 62.6003i 0.0877984i
\(714\) 0 0
\(715\) −1059.84 −1.48230
\(716\) 0 0
\(717\) −119.277 396.371i −0.166355 0.552819i
\(718\) 0 0
\(719\) 644.279i 0.896076i −0.894014 0.448038i \(-0.852123\pi\)
0.894014 0.448038i \(-0.147877\pi\)
\(720\) 0 0
\(721\) −422.579 −0.586101
\(722\) 0 0
\(723\) 122.289 36.7995i 0.169141 0.0508983i
\(724\) 0 0
\(725\) 60.1818i 0.0830094i
\(726\) 0 0
\(727\) 981.269 1.34975 0.674875 0.737932i \(-0.264197\pi\)
0.674875 + 0.737932i \(0.264197\pi\)
\(728\) 0 0
\(729\) −132.677 716.825i −0.181998 0.983299i
\(730\) 0 0
\(731\) 153.953i 0.210605i
\(732\) 0 0
\(733\) −127.756 −0.174292 −0.0871460 0.996196i \(-0.527775\pi\)
−0.0871460 + 0.996196i \(0.527775\pi\)
\(734\) 0 0
\(735\) −62.6983 208.354i −0.0853039 0.283475i
\(736\) 0 0
\(737\) 1379.84i 1.87223i
\(738\) 0 0
\(739\) 1401.59 1.89660 0.948302 0.317368i \(-0.102799\pi\)
0.948302 + 0.317368i \(0.102799\pi\)
\(740\) 0 0
\(741\) −189.008 + 56.8766i −0.255071 + 0.0767565i
\(742\) 0 0
\(743\) 11.6734i 0.0157112i −0.999969 0.00785561i \(-0.997499\pi\)
0.999969 0.00785561i \(-0.00250055\pi\)
\(744\) 0 0
\(745\) −587.941 −0.789183
\(746\) 0 0
\(747\) 409.147 + 618.261i 0.547720 + 0.827659i
\(748\) 0 0
\(749\) 948.313i 1.26611i
\(750\) 0 0
\(751\) −380.403 −0.506529 −0.253264 0.967397i \(-0.581504\pi\)
−0.253264 + 0.967397i \(0.581504\pi\)
\(752\) 0 0
\(753\) 177.982 + 591.456i 0.236364 + 0.785466i
\(754\) 0 0
\(755\) 35.3681i 0.0468452i
\(756\) 0 0
\(757\) 63.6621 0.0840979 0.0420490 0.999116i \(-0.486611\pi\)
0.0420490 + 0.999116i \(0.486611\pi\)
\(758\) 0 0
\(759\) 1796.23 540.526i 2.36658 0.712156i
\(760\) 0 0
\(761\) 377.891i 0.496571i −0.968687 0.248286i \(-0.920133\pi\)
0.968687 0.248286i \(-0.0798671\pi\)
\(762\) 0 0
\(763\) 1053.81 1.38114
\(764\) 0 0
\(765\) −203.199 + 134.471i −0.265619 + 0.175779i
\(766\) 0 0
\(767\) 1742.45i 2.27177i
\(768\) 0 0
\(769\) 231.920 0.301586 0.150793 0.988565i \(-0.451817\pi\)
0.150793 + 0.988565i \(0.451817\pi\)
\(770\) 0 0
\(771\) 162.851 + 541.174i 0.211221 + 0.701912i
\(772\) 0 0
\(773\) 1509.05i 1.95220i −0.217320 0.976101i \(-0.569731\pi\)
0.217320 0.976101i \(-0.430269\pi\)
\(774\) 0 0
\(775\) 10.9542 0.0141345
\(776\) 0 0
\(777\) −21.7752 + 6.55264i −0.0280247 + 0.00843326i
\(778\) 0 0
\(779\) 108.043i 0.138695i
\(780\) 0 0
\(781\) −372.483 −0.476930
\(782\) 0 0
\(783\) 249.834 + 207.836i 0.319073 + 0.265436i
\(784\) 0 0
\(785\) 13.6834i 0.0174311i
\(786\) 0 0
\(787\) −1171.43 −1.48848 −0.744240 0.667912i \(-0.767188\pi\)
−0.744240 + 0.667912i \(0.767188\pi\)
\(788\) 0 0
\(789\) 163.165 + 542.216i 0.206799 + 0.687219i
\(790\) 0 0
\(791\) 97.5656i 0.123345i
\(792\) 0 0
\(793\) −1253.71 −1.58097
\(794\) 0 0
\(795\) 58.6978 17.6635i 0.0738337 0.0222182i
\(796\) 0 0
\(797\) 988.589i 1.24039i 0.784448 + 0.620194i \(0.212946\pi\)
−0.784448 + 0.620194i \(0.787054\pi\)
\(798\) 0 0
\(799\) −273.007 −0.341685