Properties

Label 403.2.c.b.311.14
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.14
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.19

$q$-expansion

\(f(q)\) \(=\) \(q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} +O(q^{10})\) \(q-0.624841i q^{2} -2.78388 q^{3} +1.60957 q^{4} -0.619834i q^{5} +1.73948i q^{6} +2.35216i q^{7} -2.25541i q^{8} +4.74999 q^{9} -0.387298 q^{10} +1.21518i q^{11} -4.48086 q^{12} +(-0.818917 + 3.51132i) q^{13} +1.46972 q^{14} +1.72554i q^{15} +1.80988 q^{16} +4.00546 q^{17} -2.96799i q^{18} -4.95017i q^{19} -0.997669i q^{20} -6.54812i q^{21} +0.759295 q^{22} +2.11759 q^{23} +6.27879i q^{24} +4.61581 q^{25} +(2.19402 + 0.511692i) q^{26} -4.87176 q^{27} +3.78597i q^{28} +10.4829 q^{29} +1.07819 q^{30} +1.00000i q^{31} -5.64170i q^{32} -3.38292i q^{33} -2.50277i q^{34} +1.45795 q^{35} +7.64546 q^{36} +10.5475i q^{37} -3.09307 q^{38} +(2.27977 - 9.77510i) q^{39} -1.39798 q^{40} -1.88041i q^{41} -4.09153 q^{42} -5.95396 q^{43} +1.95592i q^{44} -2.94420i q^{45} -1.32315i q^{46} -12.5015i q^{47} -5.03848 q^{48} +1.46736 q^{49} -2.88414i q^{50} -11.1507 q^{51} +(-1.31811 + 5.65173i) q^{52} -2.74137 q^{53} +3.04407i q^{54} +0.753211 q^{55} +5.30507 q^{56} +13.7807i q^{57} -6.55011i q^{58} +7.46822i q^{59} +2.77739i q^{60} -6.44716 q^{61} +0.624841 q^{62} +11.1727i q^{63} +0.0945869 q^{64} +(2.17644 + 0.507592i) q^{65} -2.11379 q^{66} +13.2892i q^{67} +6.44708 q^{68} -5.89511 q^{69} -0.910984i q^{70} +2.71975i q^{71} -10.7132i q^{72} -7.81310i q^{73} +6.59050 q^{74} -12.8498 q^{75} -7.96766i q^{76} -2.85830 q^{77} +(-6.10788 - 1.42449i) q^{78} +2.11825 q^{79} -1.12182i q^{80} -0.687580 q^{81} -1.17495 q^{82} +11.0061i q^{83} -10.5397i q^{84} -2.48272i q^{85} +3.72027i q^{86} -29.1830 q^{87} +2.74073 q^{88} -2.01694i q^{89} -1.83966 q^{90} +(-8.25917 - 1.92622i) q^{91} +3.40841 q^{92} -2.78388i q^{93} -7.81144 q^{94} -3.06828 q^{95} +15.7058i q^{96} +5.43723i q^{97} -0.916869i q^{98} +5.77210i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.624841i 0.441829i −0.975293 0.220915i \(-0.929096\pi\)
0.975293 0.220915i \(-0.0709042\pi\)
\(3\) −2.78388 −1.60727 −0.803637 0.595120i \(-0.797105\pi\)
−0.803637 + 0.595120i \(0.797105\pi\)
\(4\) 1.60957 0.804787
\(5\) 0.619834i 0.277198i −0.990349 0.138599i \(-0.955740\pi\)
0.990349 0.138599i \(-0.0442599\pi\)
\(6\) 1.73948i 0.710140i
\(7\) 2.35216i 0.889031i 0.895771 + 0.444516i \(0.146624\pi\)
−0.895771 + 0.444516i \(0.853376\pi\)
\(8\) 2.25541i 0.797408i
\(9\) 4.74999 1.58333
\(10\) −0.387298 −0.122474
\(11\) 1.21518i 0.366391i 0.983077 + 0.183196i \(0.0586441\pi\)
−0.983077 + 0.183196i \(0.941356\pi\)
\(12\) −4.48086 −1.29351
\(13\) −0.818917 + 3.51132i −0.227127 + 0.973865i
\(14\) 1.46972 0.392800
\(15\) 1.72554i 0.445533i
\(16\) 1.80988 0.452469
\(17\) 4.00546 0.971466 0.485733 0.874107i \(-0.338553\pi\)
0.485733 + 0.874107i \(0.338553\pi\)
\(18\) 2.96799i 0.699561i
\(19\) 4.95017i 1.13565i −0.823151 0.567823i \(-0.807786\pi\)
0.823151 0.567823i \(-0.192214\pi\)
\(20\) 0.997669i 0.223086i
\(21\) 6.54812i 1.42892i
\(22\) 0.759295 0.161882
\(23\) 2.11759 0.441547 0.220774 0.975325i \(-0.429142\pi\)
0.220774 + 0.975325i \(0.429142\pi\)
\(24\) 6.27879i 1.28165i
\(25\) 4.61581 0.923161
\(26\) 2.19402 + 0.511692i 0.430282 + 0.100351i
\(27\) −4.87176 −0.937570
\(28\) 3.78597i 0.715481i
\(29\) 10.4829 1.94662 0.973309 0.229500i \(-0.0737092\pi\)
0.973309 + 0.229500i \(0.0737092\pi\)
\(30\) 1.07819 0.196850
\(31\) 1.00000i 0.179605i
\(32\) 5.64170i 0.997322i
\(33\) 3.38292i 0.588891i
\(34\) 2.50277i 0.429222i
\(35\) 1.45795 0.246438
\(36\) 7.64546 1.27424
\(37\) 10.5475i 1.73400i 0.498310 + 0.866999i \(0.333954\pi\)
−0.498310 + 0.866999i \(0.666046\pi\)
\(38\) −3.09307 −0.501761
\(39\) 2.27977 9.77510i 0.365055 1.56527i
\(40\) −1.39798 −0.221040
\(41\) 1.88041i 0.293670i −0.989161 0.146835i \(-0.953091\pi\)
0.989161 0.146835i \(-0.0469086\pi\)
\(42\) −4.09153 −0.631337
\(43\) −5.95396 −0.907970 −0.453985 0.891009i \(-0.649998\pi\)
−0.453985 + 0.891009i \(0.649998\pi\)
\(44\) 1.95592i 0.294867i
\(45\) 2.94420i 0.438896i
\(46\) 1.32315i 0.195089i
\(47\) 12.5015i 1.82353i −0.410712 0.911765i \(-0.634720\pi\)
0.410712 0.911765i \(-0.365280\pi\)
\(48\) −5.03848 −0.727242
\(49\) 1.46736 0.209623
\(50\) 2.88414i 0.407880i
\(51\) −11.1507 −1.56141
\(52\) −1.31811 + 5.65173i −0.182789 + 0.783754i
\(53\) −2.74137 −0.376557 −0.188278 0.982116i \(-0.560291\pi\)
−0.188278 + 0.982116i \(0.560291\pi\)
\(54\) 3.04407i 0.414246i
\(55\) 0.753211 0.101563
\(56\) 5.30507 0.708920
\(57\) 13.7807i 1.82529i
\(58\) 6.55011i 0.860072i
\(59\) 7.46822i 0.972280i 0.873881 + 0.486140i \(0.161595\pi\)
−0.873881 + 0.486140i \(0.838405\pi\)
\(60\) 2.77739i 0.358560i
\(61\) −6.44716 −0.825474 −0.412737 0.910850i \(-0.635427\pi\)
−0.412737 + 0.910850i \(0.635427\pi\)
\(62\) 0.624841 0.0793549
\(63\) 11.1727i 1.40763i
\(64\) 0.0945869 0.0118234
\(65\) 2.17644 + 0.507592i 0.269954 + 0.0629591i
\(66\) −2.11379 −0.260189
\(67\) 13.2892i 1.62353i 0.583985 + 0.811764i \(0.301493\pi\)
−0.583985 + 0.811764i \(0.698507\pi\)
\(68\) 6.44708 0.781823
\(69\) −5.89511 −0.709688
\(70\) 0.910984i 0.108883i
\(71\) 2.71975i 0.322775i 0.986891 + 0.161388i \(0.0515969\pi\)
−0.986891 + 0.161388i \(0.948403\pi\)
\(72\) 10.7132i 1.26256i
\(73\) 7.81310i 0.914455i −0.889350 0.457227i \(-0.848843\pi\)
0.889350 0.457227i \(-0.151157\pi\)
\(74\) 6.59050 0.766131
\(75\) −12.8498 −1.48377
\(76\) 7.96766i 0.913953i
\(77\) −2.85830 −0.325733
\(78\) −6.10788 1.42449i −0.691581 0.161292i
\(79\) 2.11825 0.238322 0.119161 0.992875i \(-0.461980\pi\)
0.119161 + 0.992875i \(0.461980\pi\)
\(80\) 1.12182i 0.125424i
\(81\) −0.687580 −0.0763978
\(82\) −1.17495 −0.129752
\(83\) 11.0061i 1.20808i 0.796955 + 0.604039i \(0.206443\pi\)
−0.796955 + 0.604039i \(0.793557\pi\)
\(84\) 10.5397i 1.14997i
\(85\) 2.48272i 0.269289i
\(86\) 3.72027i 0.401168i
\(87\) −29.1830 −3.12875
\(88\) 2.74073 0.292163
\(89\) 2.01694i 0.213795i −0.994270 0.106898i \(-0.965908\pi\)
0.994270 0.106898i \(-0.0340917\pi\)
\(90\) −1.83966 −0.193917
\(91\) −8.25917 1.92622i −0.865797 0.201923i
\(92\) 3.40841 0.355352
\(93\) 2.78388i 0.288675i
\(94\) −7.81144 −0.805689
\(95\) −3.06828 −0.314799
\(96\) 15.7058i 1.60297i
\(97\) 5.43723i 0.552067i 0.961148 + 0.276034i \(0.0890201\pi\)
−0.961148 + 0.276034i \(0.910980\pi\)
\(98\) 0.916869i 0.0926178i
\(99\) 5.77210i 0.580118i
\(100\) 7.42948 0.742948
\(101\) −12.4640 −1.24022 −0.620108 0.784516i \(-0.712911\pi\)
−0.620108 + 0.784516i \(0.712911\pi\)
\(102\) 6.96742i 0.689877i
\(103\) −12.3489 −1.21678 −0.608388 0.793640i \(-0.708184\pi\)
−0.608388 + 0.793640i \(0.708184\pi\)
\(104\) 7.91947 + 1.84699i 0.776567 + 0.181112i
\(105\) −4.05875 −0.396093
\(106\) 1.71292i 0.166374i
\(107\) −2.92701 −0.282965 −0.141482 0.989941i \(-0.545187\pi\)
−0.141482 + 0.989941i \(0.545187\pi\)
\(108\) −7.84145 −0.754544
\(109\) 9.65896i 0.925160i −0.886577 0.462580i \(-0.846924\pi\)
0.886577 0.462580i \(-0.153076\pi\)
\(110\) 0.470637i 0.0448735i
\(111\) 29.3630i 2.78701i
\(112\) 4.25711i 0.402259i
\(113\) 11.8792 1.11750 0.558748 0.829337i \(-0.311282\pi\)
0.558748 + 0.829337i \(0.311282\pi\)
\(114\) 8.61072 0.806468
\(115\) 1.31255i 0.122396i
\(116\) 16.8729 1.56661
\(117\) −3.88984 + 16.6787i −0.359616 + 1.54195i
\(118\) 4.66645 0.429582
\(119\) 9.42146i 0.863664i
\(120\) 3.89181 0.355272
\(121\) 9.52333 0.865758
\(122\) 4.02845i 0.364718i
\(123\) 5.23482i 0.472008i
\(124\) 1.60957i 0.144544i
\(125\) 5.96020i 0.533097i
\(126\) 6.98116 0.621932
\(127\) −8.62348 −0.765210 −0.382605 0.923912i \(-0.624973\pi\)
−0.382605 + 0.923912i \(0.624973\pi\)
\(128\) 11.3425i 1.00255i
\(129\) 16.5751 1.45936
\(130\) 0.317164 1.35993i 0.0278172 0.119273i
\(131\) 11.3070 0.987898 0.493949 0.869491i \(-0.335553\pi\)
0.493949 + 0.869491i \(0.335553\pi\)
\(132\) 5.44506i 0.473932i
\(133\) 11.6436 1.00962
\(134\) 8.30360 0.717322
\(135\) 3.01968i 0.259893i
\(136\) 9.03394i 0.774654i
\(137\) 6.79159i 0.580244i −0.956990 0.290122i \(-0.906304\pi\)
0.956990 0.290122i \(-0.0936960\pi\)
\(138\) 3.68350i 0.313561i
\(139\) 4.80698 0.407723 0.203862 0.979000i \(-0.434651\pi\)
0.203862 + 0.979000i \(0.434651\pi\)
\(140\) 2.34667 0.198330
\(141\) 34.8027i 2.93091i
\(142\) 1.69941 0.142611
\(143\) −4.26689 0.995132i −0.356815 0.0832171i
\(144\) 8.59689 0.716408
\(145\) 6.49763i 0.539599i
\(146\) −4.88195 −0.404033
\(147\) −4.08497 −0.336922
\(148\) 16.9770i 1.39550i
\(149\) 10.3179i 0.845277i −0.906298 0.422639i \(-0.861104\pi\)
0.906298 0.422639i \(-0.138896\pi\)
\(150\) 8.02911i 0.655574i
\(151\) 7.91075i 0.643768i −0.946779 0.321884i \(-0.895684\pi\)
0.946779 0.321884i \(-0.104316\pi\)
\(152\) −11.1646 −0.905573
\(153\) 19.0259 1.53815
\(154\) 1.78598i 0.143918i
\(155\) 0.619834 0.0497863
\(156\) 3.66945 15.7337i 0.293791 1.25971i
\(157\) −4.63624 −0.370012 −0.185006 0.982737i \(-0.559230\pi\)
−0.185006 + 0.982737i \(0.559230\pi\)
\(158\) 1.32357i 0.105298i
\(159\) 7.63166 0.605230
\(160\) −3.49692 −0.276456
\(161\) 4.98089i 0.392549i
\(162\) 0.429628i 0.0337548i
\(163\) 7.44256i 0.582946i −0.956579 0.291473i \(-0.905855\pi\)
0.956579 0.291473i \(-0.0941454\pi\)
\(164\) 3.02665i 0.236342i
\(165\) −2.09685 −0.163239
\(166\) 6.87707 0.533764
\(167\) 6.43784i 0.498175i 0.968481 + 0.249087i \(0.0801306\pi\)
−0.968481 + 0.249087i \(0.919869\pi\)
\(168\) −14.7687 −1.13943
\(169\) −11.6588 5.75096i −0.896827 0.442381i
\(170\) −1.55130 −0.118980
\(171\) 23.5132i 1.79810i
\(172\) −9.58333 −0.730722
\(173\) −10.0469 −0.763854 −0.381927 0.924192i \(-0.624739\pi\)
−0.381927 + 0.924192i \(0.624739\pi\)
\(174\) 18.2347i 1.38237i
\(175\) 10.8571i 0.820719i
\(176\) 2.19933i 0.165781i
\(177\) 20.7906i 1.56272i
\(178\) −1.26027 −0.0944610
\(179\) −19.8830 −1.48612 −0.743061 0.669223i \(-0.766627\pi\)
−0.743061 + 0.669223i \(0.766627\pi\)
\(180\) 4.73891i 0.353218i
\(181\) 6.79278 0.504903 0.252452 0.967609i \(-0.418763\pi\)
0.252452 + 0.967609i \(0.418763\pi\)
\(182\) −1.20358 + 5.16067i −0.0892153 + 0.382534i
\(183\) 17.9481 1.32676
\(184\) 4.77603i 0.352093i
\(185\) 6.53770 0.480661
\(186\) −1.73948 −0.127545
\(187\) 4.86736i 0.355936i
\(188\) 20.1221i 1.46755i
\(189\) 11.4591i 0.833529i
\(190\) 1.91719i 0.139087i
\(191\) 10.4860 0.758738 0.379369 0.925245i \(-0.376141\pi\)
0.379369 + 0.925245i \(0.376141\pi\)
\(192\) −0.263319 −0.0190034
\(193\) 12.9006i 0.928604i 0.885677 + 0.464302i \(0.153695\pi\)
−0.885677 + 0.464302i \(0.846305\pi\)
\(194\) 3.39740 0.243919
\(195\) −6.05894 1.41308i −0.433890 0.101192i
\(196\) 2.36183 0.168702
\(197\) 20.5640i 1.46513i −0.680699 0.732563i \(-0.738324\pi\)
0.680699 0.732563i \(-0.261676\pi\)
\(198\) 3.60664 0.256313
\(199\) −1.44890 −0.102710 −0.0513549 0.998680i \(-0.516354\pi\)
−0.0513549 + 0.998680i \(0.516354\pi\)
\(200\) 10.4105i 0.736136i
\(201\) 36.9954i 2.60945i
\(202\) 7.78803i 0.547964i
\(203\) 24.6573i 1.73060i
\(204\) −17.9479 −1.25660
\(205\) −1.16554 −0.0814048
\(206\) 7.71612i 0.537607i
\(207\) 10.0585 0.699115
\(208\) −1.48214 + 6.35506i −0.102768 + 0.440644i
\(209\) 6.01535 0.416090
\(210\) 2.53607i 0.175006i
\(211\) −7.11123 −0.489557 −0.244779 0.969579i \(-0.578715\pi\)
−0.244779 + 0.969579i \(0.578715\pi\)
\(212\) −4.41244 −0.303048
\(213\) 7.57146i 0.518788i
\(214\) 1.82892i 0.125022i
\(215\) 3.69046i 0.251688i
\(216\) 10.9878i 0.747625i
\(217\) −2.35216 −0.159675
\(218\) −6.03531 −0.408763
\(219\) 21.7507i 1.46978i
\(220\) 1.21235 0.0817365
\(221\) −3.28014 + 14.0644i −0.220646 + 0.946077i
\(222\) −18.3472 −1.23138
\(223\) 8.70644i 0.583026i −0.956567 0.291513i \(-0.905841\pi\)
0.956567 0.291513i \(-0.0941587\pi\)
\(224\) 13.2702 0.886650
\(225\) 21.9250 1.46167
\(226\) 7.42258i 0.493743i
\(227\) 0.260146i 0.0172665i −0.999963 0.00863326i \(-0.997252\pi\)
0.999963 0.00863326i \(-0.00274809\pi\)
\(228\) 22.1810i 1.46897i
\(229\) 1.38191i 0.0913190i −0.998957 0.0456595i \(-0.985461\pi\)
0.998957 0.0456595i \(-0.0145389\pi\)
\(230\) −0.820136 −0.0540782
\(231\) 7.95715 0.523542
\(232\) 23.6431i 1.55225i
\(233\) 14.6663 0.960823 0.480412 0.877043i \(-0.340487\pi\)
0.480412 + 0.877043i \(0.340487\pi\)
\(234\) 10.4216 + 2.43053i 0.681278 + 0.158889i
\(235\) −7.74885 −0.505479
\(236\) 12.0207i 0.782478i
\(237\) −5.89696 −0.383048
\(238\) 5.88691 0.381592
\(239\) 27.1469i 1.75599i −0.478670 0.877995i \(-0.658881\pi\)
0.478670 0.877995i \(-0.341119\pi\)
\(240\) 3.12302i 0.201590i
\(241\) 22.9384i 1.47759i 0.673929 + 0.738796i \(0.264605\pi\)
−0.673929 + 0.738796i \(0.735395\pi\)
\(242\) 5.95057i 0.382517i
\(243\) 16.5294 1.06036
\(244\) −10.3772 −0.664331
\(245\) 0.909522i 0.0581072i
\(246\) 3.27093 0.208547
\(247\) 17.3816 + 4.05377i 1.10597 + 0.257935i
\(248\) 2.25541 0.143219
\(249\) 30.6397i 1.94171i
\(250\) −3.72418 −0.235538
\(251\) −5.40311 −0.341041 −0.170521 0.985354i \(-0.554545\pi\)
−0.170521 + 0.985354i \(0.554545\pi\)
\(252\) 17.9833i 1.13284i
\(253\) 2.57325i 0.161779i
\(254\) 5.38830i 0.338092i
\(255\) 6.91159i 0.432821i
\(256\) −6.89809 −0.431130
\(257\) −21.4190 −1.33608 −0.668042 0.744124i \(-0.732867\pi\)
−0.668042 + 0.744124i \(0.732867\pi\)
\(258\) 10.3568i 0.644786i
\(259\) −24.8093 −1.54158
\(260\) 3.50314 + 0.817008i 0.217255 + 0.0506687i
\(261\) 49.7934 3.08214
\(262\) 7.06508i 0.436482i
\(263\) 6.53589 0.403020 0.201510 0.979486i \(-0.435415\pi\)
0.201510 + 0.979486i \(0.435415\pi\)
\(264\) −7.62987 −0.469586
\(265\) 1.69920i 0.104381i
\(266\) 7.27537i 0.446082i
\(267\) 5.61492i 0.343628i
\(268\) 21.3899i 1.30659i
\(269\) −18.8323 −1.14822 −0.574112 0.818777i \(-0.694653\pi\)
−0.574112 + 0.818777i \(0.694653\pi\)
\(270\) 1.88682 0.114828
\(271\) 18.1725i 1.10390i 0.833877 + 0.551950i \(0.186116\pi\)
−0.833877 + 0.551950i \(0.813884\pi\)
\(272\) 7.24938 0.439558
\(273\) 22.9925 + 5.36236i 1.39157 + 0.324545i
\(274\) −4.24366 −0.256369
\(275\) 5.60904i 0.338238i
\(276\) −9.48861 −0.571147
\(277\) −31.5861 −1.89782 −0.948912 0.315541i \(-0.897814\pi\)
−0.948912 + 0.315541i \(0.897814\pi\)
\(278\) 3.00360i 0.180144i
\(279\) 4.74999i 0.284374i
\(280\) 3.28826i 0.196511i
\(281\) 27.0399i 1.61306i 0.591191 + 0.806531i \(0.298658\pi\)
−0.591191 + 0.806531i \(0.701342\pi\)
\(282\) 21.7461 1.29496
\(283\) 32.3052 1.92035 0.960173 0.279405i \(-0.0901371\pi\)
0.960173 + 0.279405i \(0.0901371\pi\)
\(284\) 4.37764i 0.259765i
\(285\) 8.54173 0.505968
\(286\) −0.621799 + 2.66613i −0.0367678 + 0.157651i
\(287\) 4.42301 0.261082
\(288\) 26.7980i 1.57909i
\(289\) −0.956311 −0.0562536
\(290\) −4.05998 −0.238410
\(291\) 15.1366i 0.887323i
\(292\) 12.5758i 0.735941i
\(293\) 18.6860i 1.09165i −0.837899 0.545825i \(-0.816216\pi\)
0.837899 0.545825i \(-0.183784\pi\)
\(294\) 2.55245i 0.148862i
\(295\) 4.62906 0.269514
\(296\) 23.7889 1.38270
\(297\) 5.92007i 0.343517i
\(298\) −6.44706 −0.373468
\(299\) −1.73413 + 7.43553i −0.100287 + 0.430008i
\(300\) −20.6828 −1.19412
\(301\) 14.0046i 0.807213i
\(302\) −4.94296 −0.284435
\(303\) 34.6983 1.99337
\(304\) 8.95919i 0.513845i
\(305\) 3.99617i 0.228820i
\(306\) 11.8881i 0.679600i
\(307\) 21.9423i 1.25231i −0.779698 0.626156i \(-0.784627\pi\)
0.779698 0.626156i \(-0.215373\pi\)
\(308\) −4.60064 −0.262146
\(309\) 34.3779 1.95569
\(310\) 0.387298i 0.0219970i
\(311\) −17.9051 −1.01531 −0.507653 0.861562i \(-0.669487\pi\)
−0.507653 + 0.861562i \(0.669487\pi\)
\(312\) −22.0468 5.14180i −1.24816 0.291097i
\(313\) −4.73057 −0.267388 −0.133694 0.991023i \(-0.542684\pi\)
−0.133694 + 0.991023i \(0.542684\pi\)
\(314\) 2.89691i 0.163482i
\(315\) 6.92523 0.390192
\(316\) 3.40948 0.191798
\(317\) 19.0145i 1.06796i −0.845496 0.533981i \(-0.820695\pi\)
0.845496 0.533981i \(-0.179305\pi\)
\(318\) 4.76857i 0.267408i
\(319\) 12.7386i 0.713223i
\(320\) 0.0586282i 0.00327742i
\(321\) 8.14845 0.454802
\(322\) 3.11227 0.173440
\(323\) 19.8277i 1.10324i
\(324\) −1.10671 −0.0614840
\(325\) −3.77996 + 16.2076i −0.209674 + 0.899035i
\(326\) −4.65042 −0.257563
\(327\) 26.8894i 1.48699i
\(328\) −4.24108 −0.234175
\(329\) 29.4055 1.62118
\(330\) 1.31020i 0.0721239i
\(331\) 24.5020i 1.34675i −0.739301 0.673375i \(-0.764844\pi\)
0.739301 0.673375i \(-0.235156\pi\)
\(332\) 17.7152i 0.972245i
\(333\) 50.1005i 2.74549i
\(334\) 4.02262 0.220108
\(335\) 8.23707 0.450039
\(336\) 11.8513i 0.646541i
\(337\) 6.91654 0.376768 0.188384 0.982095i \(-0.439675\pi\)
0.188384 + 0.982095i \(0.439675\pi\)
\(338\) −3.59343 + 7.28486i −0.195457 + 0.396244i
\(339\) −33.0701 −1.79612
\(340\) 3.99612i 0.216720i
\(341\) −1.21518 −0.0658058
\(342\) −14.6920 −0.794454
\(343\) 19.9166i 1.07539i
\(344\) 13.4286i 0.724022i
\(345\) 3.65399i 0.196724i
\(346\) 6.27773i 0.337493i
\(347\) −17.8295 −0.957137 −0.478569 0.878050i \(-0.658844\pi\)
−0.478569 + 0.878050i \(0.658844\pi\)
\(348\) −46.9722 −2.51797
\(349\) 7.98868i 0.427624i 0.976875 + 0.213812i \(0.0685880\pi\)
−0.976875 + 0.213812i \(0.931412\pi\)
\(350\) 6.78395 0.362618
\(351\) 3.98956 17.1063i 0.212947 0.913067i
\(352\) 6.85569 0.365410
\(353\) 4.94127i 0.262997i −0.991316 0.131499i \(-0.958021\pi\)
0.991316 0.131499i \(-0.0419789\pi\)
\(354\) −12.9908 −0.690455
\(355\) 1.68579 0.0894727
\(356\) 3.24642i 0.172060i
\(357\) 26.2282i 1.38814i
\(358\) 12.4237i 0.656612i
\(359\) 9.47701i 0.500178i 0.968223 + 0.250089i \(0.0804598\pi\)
−0.968223 + 0.250089i \(0.919540\pi\)
\(360\) −6.64038 −0.349979
\(361\) −5.50414 −0.289691
\(362\) 4.24441i 0.223081i
\(363\) −26.5118 −1.39151
\(364\) −13.2938 3.10039i −0.696782 0.162505i
\(365\) −4.84283 −0.253485
\(366\) 11.2147i 0.586202i
\(367\) −11.4595 −0.598183 −0.299091 0.954225i \(-0.596684\pi\)
−0.299091 + 0.954225i \(0.596684\pi\)
\(368\) 3.83257 0.199787
\(369\) 8.93190i 0.464976i
\(370\) 4.08502i 0.212370i
\(371\) 6.44814i 0.334771i
\(372\) 4.48086i 0.232322i
\(373\) 34.3146 1.77674 0.888372 0.459124i \(-0.151836\pi\)
0.888372 + 0.459124i \(0.151836\pi\)
\(374\) 3.04132 0.157263
\(375\) 16.5925i 0.856833i
\(376\) −28.1960 −1.45410
\(377\) −8.58458 + 36.8087i −0.442129 + 1.89574i
\(378\) −7.16013 −0.368277
\(379\) 29.0334i 1.49135i 0.666311 + 0.745674i \(0.267872\pi\)
−0.666311 + 0.745674i \(0.732128\pi\)
\(380\) −4.93863 −0.253346
\(381\) 24.0067 1.22990
\(382\) 6.55206i 0.335233i
\(383\) 19.8755i 1.01559i −0.861478 0.507794i \(-0.830461\pi\)
0.861478 0.507794i \(-0.169539\pi\)
\(384\) 31.5762i 1.61137i
\(385\) 1.77167i 0.0902926i
\(386\) 8.06081 0.410284
\(387\) −28.2812 −1.43762
\(388\) 8.75163i 0.444297i
\(389\) −25.2071 −1.27805 −0.639024 0.769187i \(-0.720662\pi\)
−0.639024 + 0.769187i \(0.720662\pi\)
\(390\) −0.882948 + 3.78587i −0.0447098 + 0.191705i
\(391\) 8.48190 0.428948
\(392\) 3.30951i 0.167155i
\(393\) −31.4774 −1.58782
\(394\) −12.8492 −0.647335
\(395\) 1.31296i 0.0660624i
\(396\) 9.29062i 0.466871i
\(397\) 7.74047i 0.388483i −0.980954 0.194241i \(-0.937775\pi\)
0.980954 0.194241i \(-0.0622245\pi\)
\(398\) 0.905332i 0.0453802i
\(399\) −32.4143 −1.62274
\(400\) 8.35404 0.417702
\(401\) 7.36568i 0.367825i −0.982943 0.183912i \(-0.941124\pi\)
0.982943 0.183912i \(-0.0588762\pi\)
\(402\) −23.1162 −1.15293
\(403\) −3.51132 0.818917i −0.174911 0.0407931i
\(404\) −20.0618 −0.998110
\(405\) 0.426186i 0.0211773i
\(406\) 15.4069 0.764631
\(407\) −12.8171 −0.635321
\(408\) 25.1494i 1.24508i
\(409\) 8.29760i 0.410290i 0.978732 + 0.205145i \(0.0657666\pi\)
−0.978732 + 0.205145i \(0.934233\pi\)
\(410\) 0.728277i 0.0359670i
\(411\) 18.9070i 0.932612i
\(412\) −19.8765 −0.979246
\(413\) −17.5664 −0.864387
\(414\) 6.28497i 0.308889i
\(415\) 6.82196 0.334877
\(416\) 19.8098 + 4.62008i 0.971257 + 0.226518i
\(417\) −13.3821 −0.655323
\(418\) 3.75864i 0.183841i
\(419\) 6.23536 0.304617 0.152309 0.988333i \(-0.451329\pi\)
0.152309 + 0.988333i \(0.451329\pi\)
\(420\) −6.53285 −0.318771
\(421\) 10.9675i 0.534525i −0.963624 0.267262i \(-0.913881\pi\)
0.963624 0.267262i \(-0.0861190\pi\)
\(422\) 4.44339i 0.216301i
\(423\) 59.3819i 2.88725i
\(424\) 6.18292i 0.300269i
\(425\) 18.4884 0.896820
\(426\) −4.73096 −0.229216
\(427\) 15.1647i 0.733872i
\(428\) −4.71124 −0.227726
\(429\) 11.8785 + 2.77033i 0.573500 + 0.133753i
\(430\) 2.30595 0.111203
\(431\) 7.82125i 0.376736i −0.982098 0.188368i \(-0.939680\pi\)
0.982098 0.188368i \(-0.0603198\pi\)
\(432\) −8.81728 −0.424221
\(433\) −33.6131 −1.61534 −0.807671 0.589633i \(-0.799272\pi\)
−0.807671 + 0.589633i \(0.799272\pi\)
\(434\) 1.46972i 0.0705489i
\(435\) 18.0886i 0.867283i
\(436\) 15.5468i 0.744557i
\(437\) 10.4824i 0.501441i
\(438\) 13.5908 0.649391
\(439\) 17.3442 0.827793 0.413896 0.910324i \(-0.364168\pi\)
0.413896 + 0.910324i \(0.364168\pi\)
\(440\) 1.69880i 0.0809870i
\(441\) 6.96996 0.331903
\(442\) 8.78804 + 2.04956i 0.418004 + 0.0974877i
\(443\) −10.2049 −0.484849 −0.242425 0.970170i \(-0.577943\pi\)
−0.242425 + 0.970170i \(0.577943\pi\)
\(444\) 47.2619i 2.24295i
\(445\) −1.25017 −0.0592637
\(446\) −5.44014 −0.257598
\(447\) 28.7239i 1.35859i
\(448\) 0.222483i 0.0105113i
\(449\) 3.32509i 0.156921i 0.996917 + 0.0784604i \(0.0250004\pi\)
−0.996917 + 0.0784604i \(0.975000\pi\)
\(450\) 13.6996i 0.645808i
\(451\) 2.28503 0.107598
\(452\) 19.1204 0.899347
\(453\) 22.0226i 1.03471i
\(454\) −0.162550 −0.00762885
\(455\) −1.19394 + 5.11932i −0.0559726 + 0.239997i
\(456\) 31.0810 1.45550
\(457\) 29.0747i 1.36006i −0.733185 0.680029i \(-0.761967\pi\)
0.733185 0.680029i \(-0.238033\pi\)
\(458\) −0.863472 −0.0403474
\(459\) −19.5136 −0.910817
\(460\) 2.11265i 0.0985028i
\(461\) 28.7557i 1.33929i 0.742684 + 0.669643i \(0.233553\pi\)
−0.742684 + 0.669643i \(0.766447\pi\)
\(462\) 4.97195i 0.231316i
\(463\) 34.6020i 1.60809i −0.594568 0.804045i \(-0.702677\pi\)
0.594568 0.804045i \(-0.297323\pi\)
\(464\) 18.9727 0.880784
\(465\) −1.72554 −0.0800202
\(466\) 9.16412i 0.424520i
\(467\) 33.1318 1.53316 0.766578 0.642152i \(-0.221958\pi\)
0.766578 + 0.642152i \(0.221958\pi\)
\(468\) −6.26099 + 26.8457i −0.289414 + 1.24094i
\(469\) −31.2582 −1.44337
\(470\) 4.84180i 0.223335i
\(471\) 12.9067 0.594711
\(472\) 16.8439 0.775303
\(473\) 7.23514i 0.332672i
\(474\) 3.68466i 0.169242i
\(475\) 22.8490i 1.04838i
\(476\) 15.1645i 0.695065i
\(477\) −13.0215 −0.596213
\(478\) −16.9625 −0.775847
\(479\) 28.5444i 1.30423i −0.758122 0.652113i \(-0.773883\pi\)
0.758122 0.652113i \(-0.226117\pi\)
\(480\) 9.73500 0.444340
\(481\) −37.0356 8.63752i −1.68868 0.393837i
\(482\) 14.3328 0.652843
\(483\) 13.8662i 0.630934i
\(484\) 15.3285 0.696750
\(485\) 3.37018 0.153032
\(486\) 10.3282i 0.468499i
\(487\) 22.2944i 1.01026i 0.863044 + 0.505129i \(0.168555\pi\)
−0.863044 + 0.505129i \(0.831445\pi\)
\(488\) 14.5410i 0.658239i
\(489\) 20.7192i 0.936955i
\(490\) −0.568307 −0.0256735
\(491\) −2.28882 −0.103293 −0.0516465 0.998665i \(-0.516447\pi\)
−0.0516465 + 0.998665i \(0.516447\pi\)
\(492\) 8.42584i 0.379866i
\(493\) 41.9886 1.89107
\(494\) 2.53296 10.8607i 0.113963 0.488648i
\(495\) 3.57774 0.160808
\(496\) 1.80988i 0.0812659i
\(497\) −6.39728 −0.286957
\(498\) −19.1449 −0.857905
\(499\) 10.7617i 0.481758i −0.970555 0.240879i \(-0.922564\pi\)
0.970555 0.240879i \(-0.0774358\pi\)
\(500\) 9.59339i 0.429029i
\(501\) 17.9222i 0.800703i
\(502\) 3.37608i 0.150682i
\(503\) 15.7196 0.700901 0.350451 0.936581i \(-0.386028\pi\)
0.350451 + 0.936581i \(0.386028\pi\)
\(504\) 25.1990 1.12245
\(505\) 7.72562i 0.343786i
\(506\) 1.60787 0.0714787
\(507\) 32.4566 + 16.0100i 1.44145 + 0.711028i
\(508\) −13.8801 −0.615831
\(509\) 9.05022i 0.401144i 0.979679 + 0.200572i \(0.0642800\pi\)
−0.979679 + 0.200572i \(0.935720\pi\)
\(510\) 4.31864 0.191233
\(511\) 18.3776 0.812979
\(512\) 18.3748i 0.812059i
\(513\) 24.1160i 1.06475i
\(514\) 13.3835i 0.590321i
\(515\) 7.65429i 0.337288i
\(516\) 26.6788 1.17447
\(517\) 15.1916 0.668125
\(518\) 15.5019i 0.681114i
\(519\) 27.9694 1.22772
\(520\) 1.14483 4.90875i 0.0502041 0.215263i
\(521\) −14.5767 −0.638615 −0.319308 0.947651i \(-0.603450\pi\)
−0.319308 + 0.947651i \(0.603450\pi\)
\(522\) 31.1130i 1.36178i
\(523\) 21.1296 0.923935 0.461967 0.886897i \(-0.347144\pi\)
0.461967 + 0.886897i \(0.347144\pi\)
\(524\) 18.1995 0.795048
\(525\) 30.2248i 1.31912i
\(526\) 4.08389i 0.178066i
\(527\) 4.00546i 0.174480i
\(528\) 6.12267i 0.266455i
\(529\) −18.5158 −0.805036
\(530\) 1.06173 0.0461185
\(531\) 35.4740i 1.53944i
\(532\) 18.7412 0.812533
\(533\) 6.60271 + 1.53990i 0.285995 + 0.0667003i
\(534\) 3.50843 0.151825
\(535\) 1.81426i 0.0784373i
\(536\) 29.9725 1.29461
\(537\) 55.3518 2.38861
\(538\) 11.7672i 0.507319i
\(539\) 1.78311i 0.0768042i
\(540\) 4.86040i 0.209158i
\(541\) 16.1842i 0.695811i 0.937530 + 0.347906i \(0.113107\pi\)
−0.937530 + 0.347906i \(0.886893\pi\)
\(542\) 11.3549 0.487736
\(543\) −18.9103 −0.811518
\(544\) 22.5976i 0.968864i
\(545\) −5.98695 −0.256453
\(546\) 3.35062 14.3667i 0.143393 0.614837i
\(547\) −21.4532 −0.917274 −0.458637 0.888624i \(-0.651662\pi\)
−0.458637 + 0.888624i \(0.651662\pi\)
\(548\) 10.9316i 0.466973i
\(549\) −30.6239 −1.30700
\(550\) 3.50476 0.149443
\(551\) 51.8919i 2.21067i
\(552\) 13.2959i 0.565910i
\(553\) 4.98246i 0.211876i
\(554\) 19.7363i 0.838514i
\(555\) −18.2002 −0.772554
\(556\) 7.73720 0.328130
\(557\) 24.1842i 1.02472i 0.858772 + 0.512359i \(0.171228\pi\)
−0.858772 + 0.512359i \(0.828772\pi\)
\(558\) 2.96799 0.125645
\(559\) 4.87579 20.9063i 0.206224 0.884240i
\(560\) 2.63870 0.111506
\(561\) 13.5501i 0.572087i
\(562\) 16.8956 0.712698
\(563\) −29.9506 −1.26227 −0.631133 0.775675i \(-0.717410\pi\)
−0.631133 + 0.775675i \(0.717410\pi\)
\(564\) 56.0174i 2.35876i
\(565\) 7.36311i 0.309768i
\(566\) 20.1856i 0.848465i
\(567\) 1.61730i 0.0679200i
\(568\) 6.13415 0.257383
\(569\) 7.78865 0.326517 0.163259 0.986583i \(-0.447800\pi\)
0.163259 + 0.986583i \(0.447800\pi\)
\(570\) 5.33722i 0.223551i
\(571\) 20.2796 0.848676 0.424338 0.905504i \(-0.360507\pi\)
0.424338 + 0.905504i \(0.360507\pi\)
\(572\) −6.86788 1.60174i −0.287160 0.0669721i
\(573\) −29.1917 −1.21950
\(574\) 2.76367i 0.115354i
\(575\) 9.77437 0.407619
\(576\) 0.449287 0.0187203
\(577\) 16.5988i 0.691016i −0.938416 0.345508i \(-0.887707\pi\)
0.938416 0.345508i \(-0.112293\pi\)
\(578\) 0.597542i 0.0248545i
\(579\) 35.9137i 1.49252i
\(580\) 10.4584i 0.434262i
\(581\) −25.8881 −1.07402
\(582\) −9.45797 −0.392045
\(583\) 3.33127i 0.137967i
\(584\) −17.6217 −0.729193
\(585\) 10.3380 + 2.41106i 0.427426 + 0.0996850i
\(586\) −11.6758 −0.482323
\(587\) 12.9010i 0.532482i 0.963907 + 0.266241i \(0.0857816\pi\)
−0.963907 + 0.266241i \(0.914218\pi\)
\(588\) −6.57505 −0.271151
\(589\) 4.95017 0.203968
\(590\) 2.89243i 0.119079i
\(591\) 57.2478i 2.35486i
\(592\) 19.0897i 0.784580i
\(593\) 44.5857i 1.83091i 0.402415 + 0.915457i \(0.368171\pi\)
−0.402415 + 0.915457i \(0.631829\pi\)
\(594\) −3.69910 −0.151776
\(595\) 5.83974 0.239406
\(596\) 16.6075i 0.680268i
\(597\) 4.03356 0.165083
\(598\) 4.64602 + 1.08355i 0.189990 + 0.0443098i
\(599\) −7.39164 −0.302014 −0.151007 0.988533i \(-0.548252\pi\)
−0.151007 + 0.988533i \(0.548252\pi\)
\(600\) 28.9817i 1.18317i
\(601\) 20.6091 0.840662 0.420331 0.907371i \(-0.361914\pi\)
0.420331 + 0.907371i \(0.361914\pi\)
\(602\) −8.75066 −0.356650
\(603\) 63.1233i 2.57058i
\(604\) 12.7329i 0.518096i
\(605\) 5.90289i 0.239986i
\(606\) 21.6809i 0.880728i
\(607\) 32.5879 1.32270 0.661350 0.750077i \(-0.269984\pi\)
0.661350 + 0.750077i \(0.269984\pi\)
\(608\) −27.9274 −1.13260
\(609\) 68.6430i 2.78155i
\(610\) 2.49697 0.101099
\(611\) 43.8968 + 10.2377i 1.77587 + 0.414172i
\(612\) 30.6236 1.23788
\(613\) 2.62416i 0.105989i 0.998595 + 0.0529943i \(0.0168765\pi\)
−0.998595 + 0.0529943i \(0.983123\pi\)
\(614\) −13.7104 −0.553308
\(615\) 3.24472 0.130840
\(616\) 6.44663i 0.259742i
\(617\) 2.69130i 0.108348i 0.998532 + 0.0541738i \(0.0172525\pi\)
−0.998532 + 0.0541738i \(0.982748\pi\)
\(618\) 21.4807i 0.864082i
\(619\) 27.2021i 1.09334i −0.837347 0.546672i \(-0.815895\pi\)
0.837347 0.546672i \(-0.184105\pi\)
\(620\) 0.997669 0.0400673
\(621\) −10.3164 −0.413982
\(622\) 11.1878i 0.448592i
\(623\) 4.74416 0.190071
\(624\) 4.12609 17.6917i 0.165176 0.708235i
\(625\) 19.3847 0.775388
\(626\) 2.95585i 0.118140i
\(627\) −16.7460 −0.668771
\(628\) −7.46237 −0.297781
\(629\) 42.2475i 1.68452i
\(630\) 4.32716i 0.172398i
\(631\) 26.9529i 1.07298i 0.843907 + 0.536490i \(0.180250\pi\)
−0.843907 + 0.536490i \(0.819750\pi\)
\(632\) 4.77752i 0.190040i
\(633\) 19.7968 0.786853
\(634\) −11.8811 −0.471857
\(635\) 5.34512i 0.212115i
\(636\) 12.2837 0.487081
\(637\) −1.20165 + 5.15239i −0.0476111 + 0.204145i
\(638\) 7.95958 0.315123
\(639\) 12.9188i 0.511059i
\(640\) −7.03047 −0.277904
\(641\) −11.3030 −0.446441 −0.223220 0.974768i \(-0.571657\pi\)
−0.223220 + 0.974768i \(0.571657\pi\)
\(642\) 5.09148i 0.200945i
\(643\) 13.9895i 0.551693i −0.961202 0.275847i \(-0.911042\pi\)
0.961202 0.275847i \(-0.0889582\pi\)
\(644\) 8.01712i 0.315919i
\(645\) 10.2738i 0.404531i
\(646\) −12.3891 −0.487444
\(647\) −22.5333 −0.885877 −0.442938 0.896552i \(-0.646064\pi\)
−0.442938 + 0.896552i \(0.646064\pi\)
\(648\) 1.55077i 0.0609202i
\(649\) −9.07525 −0.356235
\(650\) 10.1272 + 2.36187i 0.397220 + 0.0926403i
\(651\) 6.54812 0.256641
\(652\) 11.9794i 0.469148i
\(653\) −10.7751 −0.421663 −0.210831 0.977522i \(-0.567617\pi\)
−0.210831 + 0.977522i \(0.567617\pi\)
\(654\) 16.8016 0.656994
\(655\) 7.00847i 0.273844i
\(656\) 3.40330i 0.132877i
\(657\) 37.1121i 1.44788i
\(658\) 18.3737i 0.716282i
\(659\) −39.5160 −1.53932 −0.769662 0.638452i \(-0.779575\pi\)
−0.769662 + 0.638452i \(0.779575\pi\)
\(660\) −3.37503 −0.131373
\(661\) 40.9839i 1.59409i 0.603921 + 0.797044i \(0.293604\pi\)
−0.603921 + 0.797044i \(0.706396\pi\)
\(662\) −15.3098 −0.595033
\(663\) 9.13150 39.1537i 0.354638 1.52060i
\(664\) 24.8233 0.963330
\(665\) 7.21707i 0.279866i
\(666\) 31.3048 1.21304
\(667\) 22.1984 0.859524
\(668\) 10.3622i 0.400925i
\(669\) 24.2377i 0.937083i
\(670\) 5.14686i 0.198840i
\(671\) 7.83446i 0.302446i
\(672\) −36.9425 −1.42509
\(673\) −16.4585 −0.634430 −0.317215 0.948354i \(-0.602748\pi\)
−0.317215 + 0.948354i \(0.602748\pi\)
\(674\) 4.32174i 0.166467i
\(675\) −22.4871 −0.865528
\(676\) −18.7656 9.25659i −0.721755 0.356023i
\(677\) 31.8404 1.22372 0.611862 0.790964i \(-0.290421\pi\)
0.611862 + 0.790964i \(0.290421\pi\)
\(678\) 20.6636i 0.793580i
\(679\) −12.7892 −0.490805
\(680\) −5.59955 −0.214733
\(681\) 0.724216i 0.0277520i
\(682\) 0.759295i 0.0290749i
\(683\) 3.58966i 0.137354i −0.997639 0.0686772i \(-0.978122\pi\)
0.997639 0.0686772i \(-0.0218779\pi\)
\(684\) 37.8463i 1.44709i
\(685\) −4.20966 −0.160843
\(686\) 12.4447 0.475140
\(687\) 3.84706i 0.146775i
\(688\) −10.7759 −0.410828
\(689\) 2.24496 9.62584i 0.0855260 0.366715i
\(690\) 2.28316 0.0869185
\(691\) 30.1287i 1.14615i 0.819503 + 0.573075i \(0.194250\pi\)
−0.819503 + 0.573075i \(0.805750\pi\)
\(692\) −16.1713 −0.614740
\(693\) −13.5769 −0.515743
\(694\) 11.1406i 0.422891i
\(695\) 2.97953i 0.113020i
\(696\) 65.8196i 2.49489i
\(697\) 7.53188i 0.285290i
\(698\) 4.99165 0.188937
\(699\) −40.8293 −1.54431
\(700\) 17.4753i 0.660504i
\(701\) −11.0470 −0.417238 −0.208619 0.977997i \(-0.566897\pi\)
−0.208619 + 0.977997i \(0.566897\pi\)
\(702\) −10.6887 2.49284i −0.403419 0.0940862i
\(703\) 52.2118 1.96921
\(704\) 0.114940i 0.00433197i
\(705\) 21.5719 0.812444
\(706\) −3.08751 −0.116200
\(707\) 29.3173i 1.10259i
\(708\) 33.4641i 1.25766i
\(709\) 41.5907i 1.56197i 0.624549 + 0.780986i \(0.285283\pi\)
−0.624549 + 0.780986i \(0.714717\pi\)
\(710\) 1.05335i 0.0395316i
\(711\) 10.0617 0.377342
\(712\) −4.54903 −0.170482
\(713\) 2.11759i 0.0793043i
\(714\) −16.3885 −0.613323
\(715\) −0.616817 + 2.64477i −0.0230676 + 0.0989086i
\(716\) −32.0031 −1.19601
\(717\) 75.5738i 2.82236i
\(718\) 5.92163 0.220993
\(719\) −38.3515 −1.43027 −0.715134 0.698987i \(-0.753635\pi\)
−0.715134 + 0.698987i \(0.753635\pi\)
\(720\) 5.32865i 0.198587i
\(721\) 29.0466i 1.08175i
\(722\) 3.43921i 0.127994i
\(723\) 63.8578i 2.37490i
\(724\) 10.9335 0.406340
\(725\) 48.3868 1.79704
\(726\) 16.5657i 0.614810i
\(727\) 49.9648 1.85309 0.926546 0.376182i \(-0.122763\pi\)
0.926546 + 0.376182i \(0.122763\pi\)
\(728\) −4.34441 + 18.6278i −0.161015 + 0.690393i
\(729\) −43.9531 −1.62789
\(730\) 3.02600i 0.111997i
\(731\) −23.8483 −0.882062
\(732\) 28.8888 1.06776
\(733\) 32.9576i 1.21732i −0.793433 0.608658i \(-0.791708\pi\)
0.793433 0.608658i \(-0.208292\pi\)
\(734\) 7.16038i 0.264294i
\(735\) 2.53200i 0.0933943i
\(736\) 11.9468i 0.440365i
\(737\) −16.1487 −0.594846
\(738\) −5.58102 −0.205440
\(739\) 19.5295i 0.718406i 0.933259 + 0.359203i \(0.116951\pi\)
−0.933259 + 0.359203i \(0.883049\pi\)
\(740\) 10.5229 0.386830
\(741\) −48.3883 11.2852i −1.77759 0.414573i
\(742\) −4.02906 −0.147911
\(743\) 19.0224i 0.697864i −0.937148 0.348932i \(-0.886544\pi\)
0.937148 0.348932i \(-0.113456\pi\)
\(744\) −6.27879 −0.230192
\(745\) −6.39540 −0.234309
\(746\) 21.4412i 0.785018i
\(747\) 52.2789i 1.91278i
\(748\) 7.83437i 0.286453i
\(749\) 6.88478i 0.251565i
\(750\) 10.3677 0.378574
\(751\) −26.8083 −0.978248 −0.489124 0.872214i \(-0.662683\pi\)
−0.489124 + 0.872214i \(0.662683\pi\)
\(752\) 22.6262i 0.825091i
\(753\) 15.0416 0.548146
\(754\) 22.9996 + 5.36400i 0.837594 + 0.195345i
\(755\) −4.90335 −0.178451
\(756\) 18.4443i 0.670813i
\(757\) −17.2202 −0.625880 −0.312940 0.949773i \(-0.601314\pi\)
−0.312940 + 0.949773i \(0.601314\pi\)
\(758\) 18.1413 0.658921
\(759\) 7.16363i 0.260023i
\(760\) 6.92023i 0.251023i
\(761\) 43.3306i 1.57073i −0.619032 0.785366i \(-0.712475\pi\)
0.619032 0.785366i \(-0.287525\pi\)
\(762\) 15.0004i 0.543406i
\(763\) 22.7194 0.822496
\(764\) 16.8779 0.610622
\(765\) 11.7929i 0.426373i
\(766\) −12.4190 −0.448716
\(767\) −26.2233 6.11585i −0.946870 0.220831i
\(768\) 19.2034 0.692945
\(769\) 29.5903i 1.06705i 0.845783 + 0.533527i \(0.179134\pi\)
−0.845783 + 0.533527i \(0.820866\pi\)
\(770\) 1.10701 0.0398939
\(771\) 59.6280 2.14745
\(772\) 20.7644i 0.747328i
\(773\) 47.4918i 1.70816i −0.520142 0.854080i \(-0.674121\pi\)
0.520142 0.854080i \(-0.325879\pi\)
\(774\) 17.6713i 0.635180i
\(775\) 4.61581i 0.165805i
\(776\) 12.2632 0.440223
\(777\) 69.0662 2.47774
\(778\) 15.7504i 0.564679i
\(779\) −9.30832 −0.333505
\(780\) −9.75231 2.27445i −0.349189 0.0814384i
\(781\) −3.30499 −0.118262
\(782\) 5.29984i 0.189522i
\(783\) −51.0699