Properties

Label 370.2.b.d.149.2
Level $370$
Weight $2$
Character 370.149
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.2
Root \(-1.95884 + 1.95884i\) of defining polynomial
Character \(\chi\) \(=\) 370.149
Dual form 370.2.b.d.149.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.09441i q^{3} -1.00000 q^{4} +(1.74265 + 1.40113i) q^{5} -1.09441 q^{6} +3.20984i q^{7} +1.00000i q^{8} +1.80226 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.09441i q^{3} -1.00000 q^{4} +(1.74265 + 1.40113i) q^{5} -1.09441 q^{6} +3.20984i q^{7} +1.00000i q^{8} +1.80226 q^{9} +(1.40113 - 1.74265i) q^{10} +3.82327 q^{11} +1.09441i q^{12} +0.147332i q^{13} +3.20984 q^{14} +(1.53341 - 1.90718i) q^{15} +1.00000 q^{16} -0.978989i q^{17} -1.80226i q^{18} -2.67594 q^{19} +(-1.74265 - 1.40113i) q^{20} +3.51289 q^{21} -3.82327i q^{22} -2.33616i q^{23} +1.09441 q^{24} +(1.07367 + 4.88336i) q^{25} +0.147332 q^{26} -5.25565i q^{27} -3.20984i q^{28} -6.30425 q^{29} +(-1.90718 - 1.53341i) q^{30} -3.62372 q^{31} -1.00000i q^{32} -4.18424i q^{33} -0.978989 q^{34} +(-4.49740 + 5.59362i) q^{35} -1.80226 q^{36} -1.00000i q^{37} +2.67594i q^{38} +0.161242 q^{39} +(-1.40113 + 1.74265i) q^{40} +11.8265 q^{41} -3.51289i q^{42} -4.53390i q^{43} -3.82327 q^{44} +(3.14071 + 2.52520i) q^{45} -2.33616 q^{46} -6.23085i q^{47} -1.09441i q^{48} -3.30305 q^{49} +(4.88336 - 1.07367i) q^{50} -1.07142 q^{51} -0.147332i q^{52} +11.2978i q^{53} -5.25565 q^{54} +(6.66263 + 5.35690i) q^{55} -3.20984 q^{56} +2.92858i q^{57} +6.30425i q^{58} -6.92858 q^{59} +(-1.53341 + 1.90718i) q^{60} +10.4885 q^{61} +3.62372i q^{62} +5.78496i q^{63} -1.00000 q^{64} +(-0.206432 + 0.256749i) q^{65} -4.18424 q^{66} -2.80936i q^{67} +0.978989i q^{68} -2.55672 q^{69} +(5.59362 + 4.49740i) q^{70} -12.3189 q^{71} +1.80226i q^{72} -13.9966i q^{73} -1.00000 q^{74} +(5.34441 - 1.17503i) q^{75} +2.67594 q^{76} +12.2721i q^{77} -0.161242i q^{78} -15.6057 q^{79} +(1.74265 + 1.40113i) q^{80} -0.345071 q^{81} -11.8265i q^{82} +13.5371i q^{83} -3.51289 q^{84} +(1.37169 - 1.70604i) q^{85} -4.53390 q^{86} +6.89945i q^{87} +3.82327i q^{88} +6.46929 q^{89} +(2.52520 - 3.14071i) q^{90} -0.472913 q^{91} +2.33616i q^{92} +3.96585i q^{93} -6.23085 q^{94} +(-4.66323 - 3.74934i) q^{95} -1.09441 q^{96} +3.07063i q^{97} +3.30305i q^{98} +6.89054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + O(q^{10}) \) \( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36} - 40 q^{39} - 2 q^{40} - 14 q^{41} - 6 q^{44} + 2 q^{45} + 12 q^{46} - 60 q^{49} + 8 q^{50} - 40 q^{51} + 42 q^{55} - 2 q^{56} - 40 q^{59} - 18 q^{61} - 10 q^{64} + 4 q^{65} + 40 q^{66} - 32 q^{69} - 6 q^{70} + 12 q^{71} - 10 q^{74} + 50 q^{75} + 8 q^{76} - 40 q^{79} + 6 q^{80} - 14 q^{81} - 32 q^{84} + 36 q^{85} - 34 q^{86} - 24 q^{89} + 44 q^{90} + 32 q^{91} - 24 q^{94} + 12 q^{95} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.09441i 0.631859i −0.948783 0.315930i \(-0.897684\pi\)
0.948783 0.315930i \(-0.102316\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.74265 + 1.40113i 0.779337 + 0.626605i
\(6\) −1.09441 −0.446792
\(7\) 3.20984i 1.21320i 0.795006 + 0.606602i \(0.207468\pi\)
−0.795006 + 0.606602i \(0.792532\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.80226 0.600754
\(10\) 1.40113 1.74265i 0.443076 0.551075i
\(11\) 3.82327 1.15276 0.576380 0.817182i \(-0.304465\pi\)
0.576380 + 0.817182i \(0.304465\pi\)
\(12\) 1.09441i 0.315930i
\(13\) 0.147332i 0.0408626i 0.999791 + 0.0204313i \(0.00650394\pi\)
−0.999791 + 0.0204313i \(0.993496\pi\)
\(14\) 3.20984 0.857865
\(15\) 1.53341 1.90718i 0.395926 0.492432i
\(16\) 1.00000 0.250000
\(17\) 0.978989i 0.237440i −0.992928 0.118720i \(-0.962121\pi\)
0.992928 0.118720i \(-0.0378790\pi\)
\(18\) 1.80226i 0.424797i
\(19\) −2.67594 −0.613903 −0.306951 0.951725i \(-0.599309\pi\)
−0.306951 + 0.951725i \(0.599309\pi\)
\(20\) −1.74265 1.40113i −0.389669 0.313302i
\(21\) 3.51289 0.766574
\(22\) 3.82327i 0.815124i
\(23\) 2.33616i 0.487122i −0.969886 0.243561i \(-0.921684\pi\)
0.969886 0.243561i \(-0.0783157\pi\)
\(24\) 1.09441 0.223396
\(25\) 1.07367 + 4.88336i 0.214733 + 0.976673i
\(26\) 0.147332 0.0288942
\(27\) 5.25565i 1.01145i
\(28\) 3.20984i 0.606602i
\(29\) −6.30425 −1.17067 −0.585335 0.810792i \(-0.699037\pi\)
−0.585335 + 0.810792i \(0.699037\pi\)
\(30\) −1.90718 1.53341i −0.348202 0.279962i
\(31\) −3.62372 −0.650839 −0.325420 0.945570i \(-0.605506\pi\)
−0.325420 + 0.945570i \(0.605506\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.18424i 0.728382i
\(34\) −0.978989 −0.167895
\(35\) −4.49740 + 5.59362i −0.760199 + 0.945495i
\(36\) −1.80226 −0.300377
\(37\) 1.00000i 0.164399i
\(38\) 2.67594i 0.434095i
\(39\) 0.161242 0.0258194
\(40\) −1.40113 + 1.74265i −0.221538 + 0.275537i
\(41\) 11.8265 1.84698 0.923491 0.383620i \(-0.125323\pi\)
0.923491 + 0.383620i \(0.125323\pi\)
\(42\) 3.51289i 0.542050i
\(43\) 4.53390i 0.691413i −0.938343 0.345706i \(-0.887639\pi\)
0.938343 0.345706i \(-0.112361\pi\)
\(44\) −3.82327 −0.576380
\(45\) 3.14071 + 2.52520i 0.468190 + 0.376435i
\(46\) −2.33616 −0.344448
\(47\) 6.23085i 0.908863i −0.890782 0.454431i \(-0.849843\pi\)
0.890782 0.454431i \(-0.150157\pi\)
\(48\) 1.09441i 0.157965i
\(49\) −3.30305 −0.471864
\(50\) 4.88336 1.07367i 0.690612 0.151839i
\(51\) −1.07142 −0.150028
\(52\) 0.147332i 0.0204313i
\(53\) 11.2978i 1.55188i 0.630807 + 0.775939i \(0.282724\pi\)
−0.630807 + 0.775939i \(0.717276\pi\)
\(54\) −5.25565 −0.715204
\(55\) 6.66263 + 5.35690i 0.898389 + 0.722325i
\(56\) −3.20984 −0.428932
\(57\) 2.92858i 0.387900i
\(58\) 6.30425i 0.827788i
\(59\) −6.92858 −0.902025 −0.451012 0.892518i \(-0.648937\pi\)
−0.451012 + 0.892518i \(0.648937\pi\)
\(60\) −1.53341 + 1.90718i −0.197963 + 0.246216i
\(61\) 10.4885 1.34291 0.671457 0.741044i \(-0.265669\pi\)
0.671457 + 0.741044i \(0.265669\pi\)
\(62\) 3.62372i 0.460213i
\(63\) 5.78496i 0.728837i
\(64\) −1.00000 −0.125000
\(65\) −0.206432 + 0.256749i −0.0256047 + 0.0318458i
\(66\) −4.18424 −0.515044
\(67\) 2.80936i 0.343218i −0.985165 0.171609i \(-0.945103\pi\)
0.985165 0.171609i \(-0.0548966\pi\)
\(68\) 0.978989i 0.118720i
\(69\) −2.55672 −0.307793
\(70\) 5.59362 + 4.49740i 0.668566 + 0.537542i
\(71\) −12.3189 −1.46198 −0.730990 0.682388i \(-0.760941\pi\)
−0.730990 + 0.682388i \(0.760941\pi\)
\(72\) 1.80226i 0.212399i
\(73\) 13.9966i 1.63818i −0.573665 0.819090i \(-0.694479\pi\)
0.573665 0.819090i \(-0.305521\pi\)
\(74\) −1.00000 −0.116248
\(75\) 5.34441 1.17503i 0.617120 0.135681i
\(76\) 2.67594 0.306951
\(77\) 12.2721i 1.39853i
\(78\) 0.161242i 0.0182571i
\(79\) −15.6057 −1.75578 −0.877890 0.478861i \(-0.841050\pi\)
−0.877890 + 0.478861i \(0.841050\pi\)
\(80\) 1.74265 + 1.40113i 0.194834 + 0.156651i
\(81\) −0.345071 −0.0383412
\(82\) 11.8265i 1.30601i
\(83\) 13.5371i 1.48589i 0.669354 + 0.742944i \(0.266571\pi\)
−0.669354 + 0.742944i \(0.733429\pi\)
\(84\) −3.51289 −0.383287
\(85\) 1.37169 1.70604i 0.148781 0.185046i
\(86\) −4.53390 −0.488903
\(87\) 6.89945i 0.739699i
\(88\) 3.82327i 0.407562i
\(89\) 6.46929 0.685743 0.342872 0.939382i \(-0.388600\pi\)
0.342872 + 0.939382i \(0.388600\pi\)
\(90\) 2.52520 3.14071i 0.266180 0.331060i
\(91\) −0.472913 −0.0495747
\(92\) 2.33616i 0.243561i
\(93\) 3.96585i 0.411239i
\(94\) −6.23085 −0.642663
\(95\) −4.66323 3.74934i −0.478437 0.384674i
\(96\) −1.09441 −0.111698
\(97\) 3.07063i 0.311775i 0.987775 + 0.155887i \(0.0498237\pi\)
−0.987775 + 0.155887i \(0.950176\pi\)
\(98\) 3.30305i 0.333658i
\(99\) 6.89054 0.692525
\(100\) −1.07367 4.88336i −0.107367 0.488336i
\(101\) −6.57513 −0.654250 −0.327125 0.944981i \(-0.606080\pi\)
−0.327125 + 0.944981i \(0.606080\pi\)
\(102\) 1.07142i 0.106086i
\(103\) 2.52180i 0.248480i −0.992252 0.124240i \(-0.960351\pi\)
0.992252 0.124240i \(-0.0396493\pi\)
\(104\) −0.147332 −0.0144471
\(105\) 6.12173 + 4.92201i 0.597420 + 0.480339i
\(106\) 11.2978 1.09734
\(107\) 5.70291i 0.551321i −0.961255 0.275661i \(-0.911103\pi\)
0.961255 0.275661i \(-0.0888966\pi\)
\(108\) 5.25565i 0.505726i
\(109\) −11.9318 −1.14286 −0.571428 0.820652i \(-0.693610\pi\)
−0.571428 + 0.820652i \(0.693610\pi\)
\(110\) 5.35690 6.66263i 0.510761 0.635257i
\(111\) −1.09441 −0.103877
\(112\) 3.20984i 0.303301i
\(113\) 2.18044i 0.205119i −0.994727 0.102559i \(-0.967297\pi\)
0.994727 0.102559i \(-0.0327031\pi\)
\(114\) 2.92858 0.274287
\(115\) 3.27326 4.07111i 0.305233 0.379633i
\(116\) 6.30425 0.585335
\(117\) 0.265531i 0.0245484i
\(118\) 6.92858i 0.637828i
\(119\) 3.14239 0.288063
\(120\) 1.90718 + 1.53341i 0.174101 + 0.139981i
\(121\) 3.61741 0.328856
\(122\) 10.4885i 0.949583i
\(123\) 12.9430i 1.16703i
\(124\) 3.62372 0.325420
\(125\) −4.97120 + 10.0143i −0.444638 + 0.895710i
\(126\) 5.78496 0.515365
\(127\) 5.39390i 0.478631i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.96195 −0.436876
\(130\) 0.256749 + 0.206432i 0.0225184 + 0.0181053i
\(131\) −8.97060 −0.783765 −0.391883 0.920015i \(-0.628176\pi\)
−0.391883 + 0.920015i \(0.628176\pi\)
\(132\) 4.18424i 0.364191i
\(133\) 8.58933i 0.744789i
\(134\) −2.80936 −0.242692
\(135\) 7.36386 9.15877i 0.633780 0.788262i
\(136\) 0.978989 0.0839476
\(137\) 2.70352i 0.230978i 0.993309 + 0.115489i \(0.0368434\pi\)
−0.993309 + 0.115489i \(0.963157\pi\)
\(138\) 2.55672i 0.217642i
\(139\) −4.30358 −0.365025 −0.182512 0.983204i \(-0.558423\pi\)
−0.182512 + 0.983204i \(0.558423\pi\)
\(140\) 4.49740 5.59362i 0.380100 0.472748i
\(141\) −6.81912 −0.574273
\(142\) 12.3189i 1.03378i
\(143\) 0.563292i 0.0471048i
\(144\) 1.80226 0.150188
\(145\) −10.9861 8.83308i −0.912346 0.733547i
\(146\) −13.9966 −1.15837
\(147\) 3.61490i 0.298152i
\(148\) 1.00000i 0.0821995i
\(149\) −21.6949 −1.77732 −0.888659 0.458568i \(-0.848362\pi\)
−0.888659 + 0.458568i \(0.848362\pi\)
\(150\) −1.17503 5.34441i −0.0959411 0.436370i
\(151\) 2.06744 0.168246 0.0841230 0.996455i \(-0.473191\pi\)
0.0841230 + 0.996455i \(0.473191\pi\)
\(152\) 2.67594i 0.217047i
\(153\) 1.76439i 0.142643i
\(154\) 12.2721 0.988912
\(155\) −6.31488 5.07731i −0.507223 0.407819i
\(156\) −0.161242 −0.0129097
\(157\) 18.5439i 1.47996i −0.672627 0.739982i \(-0.734834\pi\)
0.672627 0.739982i \(-0.265166\pi\)
\(158\) 15.6057i 1.24152i
\(159\) 12.3645 0.980569
\(160\) 1.40113 1.74265i 0.110769 0.137769i
\(161\) 7.49868 0.590979
\(162\) 0.345071i 0.0271113i
\(163\) 21.6240i 1.69372i −0.531817 0.846860i \(-0.678490\pi\)
0.531817 0.846860i \(-0.321510\pi\)
\(164\) −11.8265 −0.923491
\(165\) 5.86266 7.29167i 0.456408 0.567655i
\(166\) 13.5371 1.05068
\(167\) 11.7729i 0.911012i 0.890233 + 0.455506i \(0.150542\pi\)
−0.890233 + 0.455506i \(0.849458\pi\)
\(168\) 3.51289i 0.271025i
\(169\) 12.9783 0.998330
\(170\) −1.70604 1.37169i −0.130847 0.105204i
\(171\) −4.82274 −0.368804
\(172\) 4.53390i 0.345706i
\(173\) 14.0158i 1.06560i 0.846240 + 0.532801i \(0.178861\pi\)
−0.846240 + 0.532801i \(0.821139\pi\)
\(174\) 6.89945 0.523046
\(175\) −15.6748 + 3.44629i −1.18490 + 0.260515i
\(176\) 3.82327 0.288190
\(177\) 7.58273i 0.569953i
\(178\) 6.46929i 0.484894i
\(179\) 12.4160 0.928019 0.464009 0.885830i \(-0.346410\pi\)
0.464009 + 0.885830i \(0.346410\pi\)
\(180\) −3.14071 2.52520i −0.234095 0.188218i
\(181\) 8.19748 0.609314 0.304657 0.952462i \(-0.401458\pi\)
0.304657 + 0.952462i \(0.401458\pi\)
\(182\) 0.472913i 0.0350546i
\(183\) 11.4787i 0.848532i
\(184\) 2.33616 0.172224
\(185\) 1.40113 1.74265i 0.103013 0.128122i
\(186\) 3.96585 0.290790
\(187\) 3.74294i 0.273711i
\(188\) 6.23085i 0.454431i
\(189\) 16.8698 1.22710
\(190\) −3.74934 + 4.66323i −0.272006 + 0.338306i
\(191\) 8.00137 0.578959 0.289479 0.957184i \(-0.406518\pi\)
0.289479 + 0.957184i \(0.406518\pi\)
\(192\) 1.09441i 0.0789824i
\(193\) 14.0420i 1.01077i −0.862895 0.505383i \(-0.831351\pi\)
0.862895 0.505383i \(-0.168649\pi\)
\(194\) 3.07063 0.220458
\(195\) 0.280989 + 0.225922i 0.0201221 + 0.0161786i
\(196\) 3.30305 0.235932
\(197\) 3.36608i 0.239823i −0.992785 0.119912i \(-0.961739\pi\)
0.992785 0.119912i \(-0.0382612\pi\)
\(198\) 6.89054i 0.489689i
\(199\) 14.8890 1.05545 0.527725 0.849415i \(-0.323045\pi\)
0.527725 + 0.849415i \(0.323045\pi\)
\(200\) −4.88336 + 1.07367i −0.345306 + 0.0759197i
\(201\) −3.07460 −0.216866
\(202\) 6.57513i 0.462624i
\(203\) 20.2356i 1.42026i
\(204\) 1.07142 0.0750142
\(205\) 20.6094 + 16.5704i 1.43942 + 1.15733i
\(206\) −2.52180 −0.175702
\(207\) 4.21037i 0.292641i
\(208\) 0.147332i 0.0102157i
\(209\) −10.2308 −0.707683
\(210\) 4.92201 6.12173i 0.339651 0.422440i
\(211\) −9.80544 −0.675035 −0.337517 0.941319i \(-0.609587\pi\)
−0.337517 + 0.941319i \(0.609587\pi\)
\(212\) 11.2978i 0.775939i
\(213\) 13.4819i 0.923766i
\(214\) −5.70291 −0.389843
\(215\) 6.35258 7.90100i 0.433242 0.538844i
\(216\) 5.25565 0.357602
\(217\) 11.6316i 0.789601i
\(218\) 11.9318i 0.808121i
\(219\) −15.3181 −1.03510
\(220\) −6.66263 5.35690i −0.449194 0.361162i
\(221\) 0.144237 0.00970241
\(222\) 1.09441i 0.0734522i
\(223\) 15.4447i 1.03425i −0.855910 0.517125i \(-0.827002\pi\)
0.855910 0.517125i \(-0.172998\pi\)
\(224\) 3.20984 0.214466
\(225\) 1.93503 + 8.80110i 0.129002 + 0.586740i
\(226\) −2.18044 −0.145041
\(227\) 6.46090i 0.428825i −0.976743 0.214413i \(-0.931216\pi\)
0.976743 0.214413i \(-0.0687837\pi\)
\(228\) 2.92858i 0.193950i
\(229\) −7.97458 −0.526975 −0.263488 0.964663i \(-0.584873\pi\)
−0.263488 + 0.964663i \(0.584873\pi\)
\(230\) −4.07111 3.27326i −0.268441 0.215832i
\(231\) 13.4307 0.883676
\(232\) 6.30425i 0.413894i
\(233\) 25.2907i 1.65685i 0.560103 + 0.828423i \(0.310762\pi\)
−0.560103 + 0.828423i \(0.689238\pi\)
\(234\) 0.265531 0.0173583
\(235\) 8.73023 10.8582i 0.569497 0.708310i
\(236\) 6.92858 0.451012
\(237\) 17.0791i 1.10941i
\(238\) 3.14239i 0.203691i
\(239\) −5.11481 −0.330850 −0.165425 0.986222i \(-0.552900\pi\)
−0.165425 + 0.986222i \(0.552900\pi\)
\(240\) 1.53341 1.90718i 0.0989815 0.123108i
\(241\) 16.4415 1.05909 0.529544 0.848282i \(-0.322363\pi\)
0.529544 + 0.848282i \(0.322363\pi\)
\(242\) 3.61741i 0.232536i
\(243\) 15.3893i 0.987225i
\(244\) −10.4885 −0.671457
\(245\) −5.75606 4.62800i −0.367741 0.295672i
\(246\) −12.9430 −0.825217
\(247\) 0.394252i 0.0250857i
\(248\) 3.62372i 0.230107i
\(249\) 14.8152 0.938872
\(250\) 10.0143 + 4.97120i 0.633363 + 0.314407i
\(251\) 6.35586 0.401178 0.200589 0.979675i \(-0.435714\pi\)
0.200589 + 0.979675i \(0.435714\pi\)
\(252\) 5.78496i 0.364418i
\(253\) 8.93177i 0.561535i
\(254\) 5.39390 0.338444
\(255\) −1.86711 1.50120i −0.116923 0.0940085i
\(256\) 1.00000 0.0625000
\(257\) 5.45772i 0.340443i 0.985406 + 0.170222i \(0.0544484\pi\)
−0.985406 + 0.170222i \(0.945552\pi\)
\(258\) 4.96195i 0.308918i
\(259\) 3.20984 0.199450
\(260\) 0.206432 0.256749i 0.0128024 0.0159229i
\(261\) −11.3619 −0.703284
\(262\) 8.97060i 0.554206i
\(263\) 14.8882i 0.918044i −0.888425 0.459022i \(-0.848200\pi\)
0.888425 0.459022i \(-0.151800\pi\)
\(264\) 4.18424 0.257522
\(265\) −15.8298 + 19.6882i −0.972414 + 1.20944i
\(266\) −8.58933 −0.526646
\(267\) 7.08007i 0.433293i
\(268\) 2.80936i 0.171609i
\(269\) −15.5573 −0.948546 −0.474273 0.880378i \(-0.657289\pi\)
−0.474273 + 0.880378i \(0.657289\pi\)
\(270\) −9.15877 7.36386i −0.557385 0.448150i
\(271\) 0.462920 0.0281204 0.0140602 0.999901i \(-0.495524\pi\)
0.0140602 + 0.999901i \(0.495524\pi\)
\(272\) 0.978989i 0.0593599i
\(273\) 0.517562i 0.0313242i
\(274\) 2.70352 0.163326
\(275\) 4.10492 + 18.6704i 0.247536 + 1.12587i
\(276\) 2.55672 0.153896
\(277\) 9.12112i 0.548035i −0.961725 0.274018i \(-0.911647\pi\)
0.961725 0.274018i \(-0.0883526\pi\)
\(278\) 4.30358i 0.258111i
\(279\) −6.53089 −0.390994
\(280\) −5.59362 4.49740i −0.334283 0.268771i
\(281\) −24.8734 −1.48382 −0.741912 0.670497i \(-0.766081\pi\)
−0.741912 + 0.670497i \(0.766081\pi\)
\(282\) 6.81912i 0.406073i
\(283\) 19.7259i 1.17258i 0.810100 + 0.586292i \(0.199413\pi\)
−0.810100 + 0.586292i \(0.800587\pi\)
\(284\) 12.3189 0.730990
\(285\) −4.10333 + 5.10350i −0.243060 + 0.302305i
\(286\) 0.563292 0.0333081
\(287\) 37.9610i 2.24077i
\(288\) 1.80226i 0.106199i
\(289\) 16.0416 0.943622
\(290\) −8.83308 + 10.9861i −0.518696 + 0.645126i
\(291\) 3.36053 0.196998
\(292\) 13.9966i 0.819090i
\(293\) 2.65528i 0.155123i −0.996988 0.0775615i \(-0.975287\pi\)
0.996988 0.0775615i \(-0.0247134\pi\)
\(294\) 3.61490 0.210825
\(295\) −12.0741 9.70785i −0.702981 0.565213i
\(296\) 1.00000 0.0581238
\(297\) 20.0938i 1.16596i
\(298\) 21.6949i 1.25675i
\(299\) 0.344191 0.0199051
\(300\) −5.34441 + 1.17503i −0.308560 + 0.0678406i
\(301\) 14.5531 0.838825
\(302\) 2.06744i 0.118968i
\(303\) 7.19590i 0.413394i
\(304\) −2.67594 −0.153476
\(305\) 18.2778 + 14.6957i 1.04658 + 0.841476i
\(306\) −1.76439 −0.100864
\(307\) 25.3545i 1.44706i 0.690295 + 0.723528i \(0.257481\pi\)
−0.690295 + 0.723528i \(0.742519\pi\)
\(308\) 12.2721i 0.699267i
\(309\) −2.75989 −0.157005
\(310\) −5.07731 + 6.31488i −0.288372 + 0.358661i
\(311\) 11.1234 0.630748 0.315374 0.948967i \(-0.397870\pi\)
0.315374 + 0.948967i \(0.397870\pi\)
\(312\) 0.161242i 0.00912855i
\(313\) 3.49109i 0.197328i 0.995121 + 0.0986640i \(0.0314569\pi\)
−0.995121 + 0.0986640i \(0.968543\pi\)
\(314\) −18.5439 −1.04649
\(315\) −8.10549 + 10.0812i −0.456693 + 0.568010i
\(316\) 15.6057 0.877890
\(317\) 18.3656i 1.03152i −0.856734 0.515759i \(-0.827510\pi\)
0.856734 0.515759i \(-0.172490\pi\)
\(318\) 12.3645i 0.693367i
\(319\) −24.1029 −1.34950
\(320\) −1.74265 1.40113i −0.0974172 0.0783256i
\(321\) −6.24134 −0.348357
\(322\) 7.49868i 0.417885i
\(323\) 2.61972i 0.145765i
\(324\) 0.345071 0.0191706
\(325\) −0.719477 + 0.158186i −0.0399094 + 0.00877457i
\(326\) −21.6240 −1.19764
\(327\) 13.0583i 0.722124i
\(328\) 11.8265i 0.653007i
\(329\) 20.0000 1.10264
\(330\) −7.29167 5.86266i −0.401393 0.322729i
\(331\) −21.9365 −1.20574 −0.602870 0.797839i \(-0.705976\pi\)
−0.602870 + 0.797839i \(0.705976\pi\)
\(332\) 13.5371i 0.742944i
\(333\) 1.80226i 0.0987633i
\(334\) 11.7729 0.644183
\(335\) 3.93628 4.89574i 0.215062 0.267483i
\(336\) 3.51289 0.191644
\(337\) 8.65472i 0.471453i 0.971819 + 0.235726i \(0.0757469\pi\)
−0.971819 + 0.235726i \(0.924253\pi\)
\(338\) 12.9783i 0.705926i
\(339\) −2.38630 −0.129606
\(340\) −1.37169 + 1.70604i −0.0743904 + 0.0925228i
\(341\) −13.8545 −0.750262
\(342\) 4.82274i 0.260784i
\(343\) 11.8666i 0.640737i
\(344\) 4.53390 0.244451
\(345\) −4.45547 3.58230i −0.239874 0.192864i
\(346\) 14.0158 0.753495
\(347\) 21.3265i 1.14486i 0.819952 + 0.572432i \(0.194000\pi\)
−0.819952 + 0.572432i \(0.806000\pi\)
\(348\) 6.89945i 0.369849i
\(349\) 1.16305 0.0622569 0.0311285 0.999515i \(-0.490090\pi\)
0.0311285 + 0.999515i \(0.490090\pi\)
\(350\) 3.44629 + 15.6748i 0.184212 + 0.837853i
\(351\) 0.774328 0.0413306
\(352\) 3.82327i 0.203781i
\(353\) 0.470079i 0.0250198i −0.999922 0.0125099i \(-0.996018\pi\)
0.999922 0.0125099i \(-0.00398213\pi\)
\(354\) 7.58273 0.403017
\(355\) −21.4675 17.2603i −1.13938 0.916083i
\(356\) −6.46929 −0.342872
\(357\) 3.43908i 0.182015i
\(358\) 12.4160i 0.656208i
\(359\) 33.3086 1.75796 0.878981 0.476856i \(-0.158224\pi\)
0.878981 + 0.476856i \(0.158224\pi\)
\(360\) −2.52520 + 3.14071i −0.133090 + 0.165530i
\(361\) −11.8393 −0.623123
\(362\) 8.19748i 0.430850i
\(363\) 3.95894i 0.207790i
\(364\) 0.472913 0.0247874
\(365\) 19.6111 24.3912i 1.02649 1.27669i
\(366\) −11.4787 −0.600003
\(367\) 11.1884i 0.584029i 0.956414 + 0.292014i \(0.0943255\pi\)
−0.956414 + 0.292014i \(0.905674\pi\)
\(368\) 2.33616i 0.121781i
\(369\) 21.3144 1.10958
\(370\) −1.74265 1.40113i −0.0905961 0.0728413i
\(371\) −36.2642 −1.88275
\(372\) 3.96585i 0.205620i
\(373\) 23.1634i 1.19936i 0.800242 + 0.599678i \(0.204705\pi\)
−0.800242 + 0.599678i \(0.795295\pi\)
\(374\) −3.74294 −0.193543
\(375\) 10.9598 + 5.44055i 0.565963 + 0.280949i
\(376\) 6.23085 0.321331
\(377\) 0.928820i 0.0478366i
\(378\) 16.8698i 0.867688i
\(379\) 26.7721 1.37519 0.687595 0.726095i \(-0.258667\pi\)
0.687595 + 0.726095i \(0.258667\pi\)
\(380\) 4.66323 + 3.74934i 0.239219 + 0.192337i
\(381\) 5.90315 0.302428
\(382\) 8.00137i 0.409386i
\(383\) 22.3189i 1.14044i 0.821492 + 0.570220i \(0.193142\pi\)
−0.821492 + 0.570220i \(0.806858\pi\)
\(384\) 1.09441 0.0558490
\(385\) −17.1948 + 21.3860i −0.876327 + 1.08993i
\(386\) −14.0420 −0.714720
\(387\) 8.17127i 0.415369i
\(388\) 3.07063i 0.155887i
\(389\) 24.3011 1.23211 0.616057 0.787701i \(-0.288729\pi\)
0.616057 + 0.787701i \(0.288729\pi\)
\(390\) 0.225922 0.280989i 0.0114400 0.0142284i
\(391\) −2.28707 −0.115662
\(392\) 3.30305i 0.166829i
\(393\) 9.81754i 0.495229i
\(394\) −3.36608 −0.169581
\(395\) −27.1953 21.8657i −1.36835 1.10018i
\(396\) −6.89054 −0.346262
\(397\) 28.1888i 1.41476i −0.706835 0.707378i \(-0.749878\pi\)
0.706835 0.707378i \(-0.250122\pi\)
\(398\) 14.8890i 0.746316i
\(399\) −9.40027 −0.470602
\(400\) 1.07367 + 4.88336i 0.0536833 + 0.244168i
\(401\) −15.9528 −0.796644 −0.398322 0.917246i \(-0.630407\pi\)
−0.398322 + 0.917246i \(0.630407\pi\)
\(402\) 3.07460i 0.153347i
\(403\) 0.533891i 0.0265950i
\(404\) 6.57513 0.327125
\(405\) −0.601339 0.483490i −0.0298808 0.0240248i
\(406\) −20.2356 −1.00428
\(407\) 3.82327i 0.189513i
\(408\) 1.07142i 0.0530431i
\(409\) −31.6014 −1.56259 −0.781294 0.624164i \(-0.785440\pi\)
−0.781294 + 0.624164i \(0.785440\pi\)
\(410\) 16.5704 20.6094i 0.818354 1.01783i
\(411\) 2.95877 0.145945
\(412\) 2.52180i 0.124240i
\(413\) 22.2396i 1.09434i
\(414\) −4.21037 −0.206928
\(415\) −18.9672 + 23.5904i −0.931064 + 1.15801i
\(416\) 0.147332 0.00722356
\(417\) 4.70989i 0.230644i
\(418\) 10.2308i 0.500407i
\(419\) 18.4266 0.900197 0.450098 0.892979i \(-0.351389\pi\)
0.450098 + 0.892979i \(0.351389\pi\)
\(420\) −6.12173 4.92201i −0.298710 0.240170i
\(421\) −19.1570 −0.933655 −0.466828 0.884348i \(-0.654603\pi\)
−0.466828 + 0.884348i \(0.654603\pi\)
\(422\) 9.80544i 0.477322i
\(423\) 11.2296i 0.546003i
\(424\) −11.2978 −0.548672
\(425\) 4.78076 1.05111i 0.231901 0.0509862i
\(426\) 13.4819 0.653201
\(427\) 33.6663i 1.62923i
\(428\) 5.70291i 0.275661i
\(429\) 0.616473 0.0297636
\(430\) −7.90100 6.35258i −0.381020 0.306349i
\(431\) −10.3947 −0.500694 −0.250347 0.968156i \(-0.580545\pi\)
−0.250347 + 0.968156i \(0.580545\pi\)
\(432\) 5.25565i 0.252863i
\(433\) 3.36622i 0.161770i 0.996723 + 0.0808852i \(0.0257747\pi\)
−0.996723 + 0.0808852i \(0.974225\pi\)
\(434\) −11.6316 −0.558332
\(435\) −9.66703 + 12.0233i −0.463499 + 0.576475i
\(436\) 11.9318 0.571428
\(437\) 6.25142i 0.299046i
\(438\) 15.3181i 0.731926i
\(439\) 32.5045 1.55135 0.775677 0.631130i \(-0.217409\pi\)
0.775677 + 0.631130i \(0.217409\pi\)
\(440\) −5.35690 + 6.66263i −0.255380 + 0.317628i
\(441\) −5.95296 −0.283474
\(442\) 0.144237i 0.00686064i
\(443\) 23.5479i 1.11879i −0.828900 0.559397i \(-0.811033\pi\)
0.828900 0.559397i \(-0.188967\pi\)
\(444\) 1.09441 0.0519385
\(445\) 11.2737 + 9.06432i 0.534425 + 0.429690i
\(446\) −15.4447 −0.731325
\(447\) 23.7432i 1.12302i
\(448\) 3.20984i 0.151651i
\(449\) −12.5629 −0.592878 −0.296439 0.955052i \(-0.595799\pi\)
−0.296439 + 0.955052i \(0.595799\pi\)
\(450\) 8.80110 1.93503i 0.414888 0.0912180i
\(451\) 45.2158 2.12913
\(452\) 2.18044i 0.102559i
\(453\) 2.26263i 0.106308i
\(454\) −6.46090 −0.303225
\(455\) −0.824122 0.662612i −0.0386354 0.0310637i
\(456\) −2.92858 −0.137143
\(457\) 6.53390i 0.305643i −0.988254 0.152821i \(-0.951164\pi\)
0.988254 0.152821i \(-0.0488359\pi\)
\(458\) 7.97458i 0.372628i
\(459\) −5.14523 −0.240159
\(460\) −3.27326 + 4.07111i −0.152617 + 0.189816i
\(461\) 24.7616 1.15326 0.576631 0.817005i \(-0.304367\pi\)
0.576631 + 0.817005i \(0.304367\pi\)
\(462\) 13.4307i 0.624853i
\(463\) 25.9239i 1.20479i 0.798200 + 0.602393i \(0.205786\pi\)
−0.798200 + 0.602393i \(0.794214\pi\)
\(464\) −6.30425 −0.292667
\(465\) −5.55667 + 6.91109i −0.257684 + 0.320494i
\(466\) 25.2907 1.17157
\(467\) 28.8182i 1.33355i −0.745261 0.666773i \(-0.767675\pi\)
0.745261 0.666773i \(-0.232325\pi\)
\(468\) 0.265531i 0.0122742i
\(469\) 9.01759 0.416394
\(470\) −10.8582 8.73023i −0.500851 0.402696i
\(471\) −20.2947 −0.935129
\(472\) 6.92858i 0.318914i
\(473\) 17.3343i 0.797033i
\(474\) 17.0791 0.784469
\(475\) −2.87307 13.0676i −0.131825 0.599582i
\(476\) −3.14239 −0.144031
\(477\) 20.3617i 0.932297i
\(478\) 5.11481i 0.233946i
\(479\) 41.7873 1.90931 0.954655 0.297714i \(-0.0962241\pi\)
0.954655 + 0.297714i \(0.0962241\pi\)
\(480\) −1.90718 1.53341i −0.0870504 0.0699905i
\(481\) 0.147332 0.00671778
\(482\) 16.4415i 0.748888i
\(483\) 8.20665i 0.373416i
\(484\) −3.61741 −0.164428
\(485\) −4.30235 + 5.35103i −0.195360 + 0.242978i
\(486\) −15.3893 −0.698073
\(487\) 9.34463i 0.423446i −0.977330 0.211723i \(-0.932093\pi\)
0.977330 0.211723i \(-0.0679074\pi\)
\(488\) 10.4885i 0.474791i
\(489\) −23.6655 −1.07019
\(490\) −4.62800 + 5.75606i −0.209072 + 0.260032i
\(491\) −10.7558 −0.485404 −0.242702 0.970101i \(-0.578034\pi\)
−0.242702 + 0.970101i \(0.578034\pi\)
\(492\) 12.9430i 0.583516i
\(493\) 6.17179i 0.277963i
\(494\) −0.394252 −0.0177383
\(495\) 12.0078 + 9.65454i 0.539710 + 0.433939i
\(496\) −3.62372 −0.162710
\(497\) 39.5415i 1.77368i
\(498\) 14.8152i 0.663883i
\(499\) −29.0702 −1.30136 −0.650680 0.759352i \(-0.725516\pi\)
−0.650680 + 0.759352i \(0.725516\pi\)
\(500\) 4.97120 10.0143i 0.222319 0.447855i
\(501\) 12.8844 0.575631
\(502\) 6.35586i 0.283676i
\(503\) 36.2683i 1.61712i 0.588412 + 0.808561i \(0.299753\pi\)
−0.588412 + 0.808561i \(0.700247\pi\)
\(504\) −5.78496 −0.257683
\(505\) −11.4582 9.21261i −0.509881 0.409956i
\(506\) −8.93177 −0.397065
\(507\) 14.2036i 0.630804i
\(508\) 5.39390i 0.239316i
\(509\) 22.2170 0.984751 0.492375 0.870383i \(-0.336129\pi\)
0.492375 + 0.870383i \(0.336129\pi\)
\(510\) −1.50120 + 1.86711i −0.0664741 + 0.0826769i
\(511\) 44.9268 1.98745
\(512\) 1.00000i 0.0441942i
\(513\) 14.0638i 0.620933i
\(514\) 5.45772 0.240730
\(515\) 3.53337 4.39462i 0.155699 0.193650i
\(516\) 4.96195 0.218438
\(517\) 23.8222i 1.04770i
\(518\) 3.20984i 0.141032i
\(519\) 15.3391 0.673311
\(520\) −0.256749 0.206432i −0.0112592 0.00905263i
\(521\) 41.2732 1.80821 0.904107 0.427306i \(-0.140537\pi\)
0.904107 + 0.427306i \(0.140537\pi\)
\(522\) 11.3619i 0.497297i
\(523\) 11.0354i 0.482545i 0.970457 + 0.241273i \(0.0775648\pi\)
−0.970457 + 0.241273i \(0.922435\pi\)
\(524\) 8.97060 0.391883
\(525\) 3.77167 + 17.1547i 0.164609 + 0.748692i
\(526\) −14.8882 −0.649155
\(527\) 3.54758i 0.154535i
\(528\) 4.18424i 0.182096i
\(529\) 17.5424 0.762712
\(530\) 19.6882 + 15.8298i 0.855201 + 0.687601i
\(531\) −12.4871 −0.541895
\(532\) 8.58933i 0.372395i
\(533\) 1.74242i 0.0754726i
\(534\) −7.08007 −0.306385
\(535\) 7.99052 9.93818i 0.345460 0.429665i
\(536\) 2.80936 0.121346
\(537\) 13.5883i 0.586377i
\(538\) 15.5573i 0.670723i
\(539\) −12.6285 −0.543946
\(540\) −7.36386 + 9.15877i −0.316890 + 0.394131i
\(541\) −32.2338 −1.38584 −0.692920 0.721014i \(-0.743676\pi\)
−0.692920 + 0.721014i \(0.743676\pi\)
\(542\) 0.462920i 0.0198841i
\(543\) 8.97142i 0.385001i
\(544\) −0.978989 −0.0419738
\(545\) −20.7929 16.7180i −0.890670 0.716119i
\(546\) 0.517562 0.0221496
\(547\) 15.0234i 0.642355i −0.947019 0.321177i \(-0.895921\pi\)
0.947019 0.321177i \(-0.104079\pi\)
\(548\) 2.70352i 0.115489i
\(549\) 18.9030 0.806760
\(550\) 18.6704 4.10492i 0.796110 0.175034i
\(551\) 16.8698 0.718677
\(552\) 2.55672i 0.108821i
\(553\) 50.0918i 2.13012i
\(554\) −9.12112 −0.387519
\(555\) −1.90718 1.53341i −0.0809553 0.0650898i
\(556\) 4.30358 0.182512
\(557\) 39.1275i 1.65788i −0.559334 0.828942i \(-0.688943\pi\)
0.559334 0.828942i \(-0.311057\pi\)
\(558\) 6.53089i 0.276475i
\(559\) 0.667989 0.0282529
\(560\) −4.49740 + 5.59362i −0.190050 + 0.236374i
\(561\) −4.09632 −0.172947
\(562\) 24.8734i 1.04922i
\(563\) 27.1970i 1.14622i −0.819479 0.573109i \(-0.805737\pi\)
0.819479 0.573109i \(-0.194263\pi\)
\(564\) 6.81912 0.287137
\(565\) 3.05508 3.79975i 0.128528 0.159857i
\(566\) 19.7259 0.829142
\(567\) 1.10762i 0.0465157i
\(568\) 12.3189i 0.516888i
\(569\) 33.4499 1.40229 0.701146 0.713018i \(-0.252672\pi\)
0.701146 + 0.713018i \(0.252672\pi\)
\(570\) 5.10350 + 4.10333i 0.213762 + 0.171869i
\(571\) 28.9145 1.21003 0.605017 0.796213i \(-0.293166\pi\)
0.605017 + 0.796213i \(0.293166\pi\)
\(572\) 0.563292i 0.0235524i
\(573\) 8.75680i 0.365821i
\(574\) 37.9610 1.58446
\(575\) 11.4083 2.50825i 0.475759 0.104601i
\(576\) −1.80226 −0.0750942
\(577\) 33.5613i 1.39717i −0.715525 0.698587i \(-0.753812\pi\)
0.715525 0.698587i \(-0.246188\pi\)
\(578\) 16.0416i 0.667242i
\(579\) −15.3678 −0.638663
\(580\) 10.9861 + 8.83308i 0.456173 + 0.366774i
\(581\) −43.4518 −1.80268
\(582\) 3.36053i 0.139299i
\(583\) 43.1948i 1.78894i
\(584\) 13.9966 0.579184
\(585\) −0.372044 + 0.462728i −0.0153821 + 0.0191315i
\(586\) −2.65528 −0.109689
\(587\) 4.83581i 0.199595i 0.995008 + 0.0997976i \(0.0318195\pi\)
−0.995008 + 0.0997976i \(0.968180\pi\)
\(588\) 3.61490i 0.149076i
\(589\) 9.69686 0.399552
\(590\) −9.70785 + 12.0741i −0.399666 + 0.497083i
\(591\) −3.68388 −0.151535
\(592\) 1.00000i 0.0410997i
\(593\) 43.1680i 1.77270i 0.463020 + 0.886348i \(0.346766\pi\)
−0.463020 + 0.886348i \(0.653234\pi\)
\(594\) −20.0938 −0.824459
\(595\) 5.47610 + 4.40290i 0.224498 + 0.180501i
\(596\) 21.6949 0.888659
\(597\) 16.2947i 0.666896i
\(598\) 0.344191i 0.0140750i
\(599\) 38.7714 1.58416 0.792078 0.610420i \(-0.208999\pi\)
0.792078 + 0.610420i \(0.208999\pi\)
\(600\) 1.17503 + 5.34441i 0.0479706 + 0.218185i
\(601\) 1.56064 0.0636597 0.0318299 0.999493i \(-0.489867\pi\)
0.0318299 + 0.999493i \(0.489867\pi\)
\(602\) 14.5531i 0.593139i
\(603\) 5.06320i 0.206190i
\(604\) −2.06744 −0.0841230
\(605\) 6.30389 + 5.06847i 0.256289 + 0.206062i
\(606\) 7.19590 0.292314
\(607\) 21.0494i 0.854370i −0.904164 0.427185i \(-0.859505\pi\)
0.904164 0.427185i \(-0.140495\pi\)
\(608\) 2.67594i 0.108524i
\(609\) −22.1461 −0.897405
\(610\) 14.6957 18.2778i 0.595013 0.740045i
\(611\) 0.918005 0.0371385
\(612\) 1.76439i 0.0713214i
\(613\) 5.28786i 0.213574i −0.994282 0.106787i \(-0.965944\pi\)
0.994282 0.106787i \(-0.0340564\pi\)
\(614\) 25.3545 1.02322
\(615\) 18.1349 22.5552i 0.731268 0.909512i
\(616\) −12.2721 −0.494456
\(617\) 34.8545i 1.40319i 0.712576 + 0.701595i \(0.247528\pi\)
−0.712576 + 0.701595i \(0.752472\pi\)
\(618\) 2.75989i 0.111019i
\(619\) 7.30122 0.293461 0.146730 0.989177i \(-0.453125\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(620\) 6.31488 + 5.07731i 0.253612 + 0.203910i
\(621\) −12.2780 −0.492701
\(622\) 11.1234i 0.446006i
\(623\) 20.7654i 0.831946i
\(624\) 0.161242 0.00645486
\(625\) −22.6945 + 10.4862i −0.907779 + 0.419448i
\(626\) 3.49109 0.139532
\(627\) 11.1968i 0.447156i
\(628\) 18.5439i 0.739982i
\(629\) −0.978989 −0.0390348
\(630\) 10.0812 + 8.10549i 0.401644 + 0.322930i
\(631\) 24.2752 0.966381 0.483190 0.875515i \(-0.339478\pi\)
0.483190 + 0.875515i \(0.339478\pi\)
\(632\) 15.6057i 0.620762i
\(633\) 10.7312i 0.426527i
\(634\) −18.3656 −0.729393
\(635\) −7.55756 + 9.39969i −0.299913 + 0.373015i
\(636\) −12.3645 −0.490285
\(637\) 0.486646i 0.0192816i
\(638\) 24.1029i 0.954241i
\(639\) −22.2018 −0.878290
\(640\) −1.40113 + 1.74265i −0.0553845 + 0.0688843i
\(641\) −8.22087 −0.324705 −0.162353 0.986733i \(-0.551908\pi\)
−0.162353 + 0.986733i \(0.551908\pi\)
\(642\) 6.24134i 0.246326i
\(643\) 29.7758i 1.17424i 0.809499 + 0.587121i \(0.199739\pi\)
−0.809499 + 0.587121i \(0.800261\pi\)
\(644\) −7.49868 −0.295489
\(645\) −8.64695 6.95234i −0.340473 0.273748i
\(646\) 2.61972 0.103071
\(647\) 35.6356i 1.40098i 0.713662 + 0.700490i \(0.247035\pi\)
−0.713662 + 0.700490i \(0.752965\pi\)
\(648\) 0.345071i 0.0135557i
\(649\) −26.4899 −1.03982
\(650\) 0.158186 + 0.719477i 0.00620455 + 0.0282202i
\(651\) −12.7297 −0.498917
\(652\) 21.6240i 0.846860i
\(653\) 37.6128i 1.47190i 0.677035 + 0.735951i \(0.263264\pi\)
−0.677035 + 0.735951i \(0.736736\pi\)
\(654\) 13.0583 0.510619
\(655\) −15.6326 12.5690i −0.610818 0.491111i
\(656\) 11.8265 0.461746
\(657\) 25.2256i 0.984142i
\(658\) 20.0000i 0.779681i
\(659\) −45.0553 −1.75510 −0.877552 0.479481i \(-0.840825\pi\)
−0.877552 + 0.479481i \(0.840825\pi\)
\(660\) −5.86266 + 7.29167i −0.228204 + 0.283828i
\(661\) 7.32365 0.284857 0.142429 0.989805i \(-0.454509\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(662\) 21.9365i 0.852587i
\(663\) 0.157854i 0.00613056i
\(664\) −13.5371 −0.525341
\(665\) 12.0348 14.9682i 0.466688 0.580442i
\(666\) −1.80226 −0.0698362
\(667\) 14.7277i 0.570260i
\(668\) 11.7729i 0.455506i
\(669\) −16.9028 −0.653501
\(670\) −4.89574 3.93628i −0.189139 0.152072i
\(671\) 40.1003 1.54806
\(672\) 3.51289i 0.135512i
\(673\) 8.58807i 0.331046i −0.986206 0.165523i \(-0.947069\pi\)
0.986206 0.165523i \(-0.0529312\pi\)
\(674\) 8.65472 0.333368
\(675\) 25.6653 5.64282i 0.987857 0.217192i
\(676\) −12.9783 −0.499165
\(677\) 9.13523i 0.351096i 0.984471 + 0.175548i \(0.0561697\pi\)
−0.984471 + 0.175548i \(0.943830\pi\)
\(678\) 2.38630i 0.0916454i
\(679\) −9.85621 −0.378247
\(680\) 1.70604 + 1.37169i 0.0654235 + 0.0526020i
\(681\) −7.07089 −0.270957
\(682\) 13.8545i 0.530515i
\(683\) 40.7414i 1.55893i −0.626449 0.779463i \(-0.715492\pi\)
0.626449 0.779463i \(-0.284508\pi\)
\(684\) 4.82274 0.184402
\(685\) −3.78799 + 4.71130i −0.144732 + 0.180009i
\(686\) 11.8666 0.453069
\(687\) 8.72748i 0.332974i
\(688\) 4.53390i 0.172853i
\(689\) −1.66454 −0.0634139
\(690\) −3.58230 + 4.45547i −0.136376 + 0.169617i
\(691\) −28.7543 −1.09387 −0.546933 0.837176i \(-0.684205\pi\)
−0.546933 + 0.837176i \(0.684205\pi\)
\(692\) 14.0158i 0.532801i
\(693\) 22.1175i 0.840174i
\(694\) 21.3265 0.809541
\(695\) −7.49964 6.02988i −0.284477 0.228726i
\(696\) −6.89945 −0.261523
\(697\) 11.5780i 0.438547i
\(698\) 1.16305i 0.0440223i
\(699\) 27.6784 1.04689
\(700\) 15.6748 3.44629i 0.592452 0.130258i
\(701\) −7.87020 −0.297253 −0.148627 0.988893i \(-0.547485\pi\)
−0.148627 + 0.988893i \(0.547485\pi\)
\(702\) 0.774328i 0.0292251i
\(703\) 2.67594i 0.100925i
\(704\) −3.82327 −0.144095
\(705\) −11.8833 9.55447i −0.447553 0.359842i
\(706\) −0.470079 −0.0176917
\(707\) 21.1051i 0.793738i
\(708\) 7.58273i 0.284976i
\(709\) −33.0458 −1.24106 −0.620530 0.784182i \(-0.713083\pi\)
−0.620530 + 0.784182i \(0.713083\pi\)
\(710\) −17.2603 + 21.4675i −0.647769 + 0.805660i
\(711\) −28.1256 −1.05479
\(712\) 6.46929i 0.242447i
\(713\) 8.46558i 0.317039i
\(714\) −3.43908 −0.128704
\(715\) −0.789245 + 0.981621i −0.0295161 + 0.0367105i
\(716\) −12.4160 −0.464009
\(717\) 5.59771i 0.209050i
\(718\) 33.3086i 1.24307i
\(719\) −4.94138 −0.184282 −0.0921412 0.995746i \(-0.529371\pi\)
−0.0921412 + 0.995746i \(0.529371\pi\)
\(720\) 3.14071 + 2.52520i 0.117047 + 0.0941088i
\(721\) 8.09456 0.301457
\(722\) 11.8393i 0.440615i
\(723\) 17.9937i 0.669195i
\(724\) −8.19748 −0.304657
\(725\) −6.76866 30.7859i −0.251382 1.14336i
\(726\) −3.95894 −0.146930
\(727\) 42.5178i 1.57690i −0.615101 0.788448i \(-0.710885\pi\)
0.615101 0.788448i \(-0.289115\pi\)
\(728\) 0.472913i 0.0175273i
\(729\) −17.8775 −0.662129
\(730\) −24.3912 19.6111i −0.902759 0.725839i
\(731\) −4.43863 −0.164169
\(732\) 11.4787i 0.424266i
\(733\) 10.2114i 0.377167i 0.982057 + 0.188584i \(0.0603896\pi\)
−0.982057 + 0.188584i \(0.939610\pi\)
\(734\) 11.1884 0.412971
\(735\) −5.06494 + 6.29951i −0.186823 + 0.232361i
\(736\) −2.33616 −0.0861119
\(737\) 10.7410i 0.395648i
\(738\) 21.3144i 0.784593i
\(739\) −25.5528 −0.939975 −0.469988 0.882673i \(-0.655742\pi\)
−0.469988 + 0.882673i \(0.655742\pi\)
\(740\) −1.40113 + 1.74265i −0.0515066 + 0.0640611i
\(741\) −0.431475 −0.0158506
\(742\) 36.2642i 1.33130i
\(743\) 44.2852i 1.62467i 0.583193 + 0.812334i \(0.301803\pi\)
−0.583193 + 0.812334i \(0.698197\pi\)
\(744\) −3.96585 −0.145395
\(745\) −37.8067 30.3974i −1.38513 1.11368i
\(746\) 23.1634 0.848072
\(747\) 24.3974i 0.892652i
\(748\) 3.74294i 0.136855i
\(749\) 18.3054 0.668865
\(750\) 5.44055 10.9598i 0.198661 0.400196i
\(751\) 41.2897 1.50668 0.753342 0.657629i \(-0.228440\pi\)
0.753342 + 0.657629i \(0.228440\pi\)
\(752\) 6.23085i 0.227216i
\(753\) 6.95593i 0.253488i
\(754\) −0.928820 −0.0338256
\(755\) 3.60283 + 2.89676i 0.131120 + 0.105424i
\(756\) −16.8698 −0.613548
\(757\) 6.57802i 0.239082i −0.992829 0.119541i \(-0.961858\pi\)
0.992829 0.119541i \(-0.0381423\pi\)
\(758\) 26.7721i 0.972406i
\(759\) −9.77504 −0.354811
\(760\) 3.74934 4.66323i 0.136003 0.169153i
\(761\) 20.3166 0.736475 0.368237 0.929732i \(-0.379961\pi\)
0.368237 + 0.929732i \(0.379961\pi\)
\(762\) 5.90315i 0.213849i
\(763\) 38.2990i 1.38652i
\(764\) −8.00137 −0.289479
\(765\) 2.47215 3.07472i 0.0893806 0.111167i
\(766\) 22.3189 0.806413
\(767\) 1.02080i 0.0368591i
\(768\) 1.09441i 0.0394912i
\(769\) −25.2435 −0.910303 −0.455151 0.890414i \(-0.650415\pi\)
−0.455151 + 0.890414i \(0.650415\pi\)
\(770\) 21.3860 + 17.1948i 0.770696 + 0.619657i
\(771\) 5.97300 0.215112
\(772\) 14.0420i 0.505383i
\(773\) 48.9781i 1.76162i −0.473470 0.880810i \(-0.656999\pi\)
0.473470 0.880810i \(-0.343001\pi\)
\(774\) −8.17127 −0.293710
\(775\) −3.89067 17.6959i −0.139757 0.635657i
\(776\) −3.07063 −0.110229
\(777\) 3.51289i 0.126024i
\(778\) 24.3011i 0.871237i
\(779\) −31.6469 −1.13387
\(780\) −0.280989 0.225922i −0.0100610 0.00808929i
\(781\) −47.0984 −1.68531
\(782\) 2.28707i 0.0817855i
\(783\) 33.1330i 1.18408i
\(784\) −3.30305 −0.117966
\(785\) 25.9824 32.3155i 0.927352 1.15339i
\(786\) 9.81754 0.350180
\(787\) 3.78073i 0.134768i 0.997727 + 0.0673842i \(0.0214653\pi\)
−0.997727 + 0.0673842i \(0.978535\pi\)