Properties

Label 370.2.c.a.369.9
Level $370$
Weight $2$
Character 370.369
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.c (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: \(x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.9
Root \(1.78647i\) of defining polynomial
Character \(\chi\) \(=\) 370.369
Dual form 370.2.c.a.369.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.78647i q^{3} +1.00000 q^{4} +(2.21736 - 0.288618i) q^{5} -1.78647i q^{6} +3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.78647i q^{3} +1.00000 q^{4} +(2.21736 - 0.288618i) q^{5} -1.78647i q^{6} +3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +(-2.21736 + 0.288618i) q^{10} -0.908956 q^{11} +1.78647i q^{12} +2.22269 q^{13} -3.14934i q^{14} +(0.515607 + 3.96125i) q^{15} +1.00000 q^{16} +2.10043 q^{17} +0.191472 q^{18} -4.16694i q^{19} +(2.21736 - 0.288618i) q^{20} -5.62620 q^{21} +0.908956 q^{22} -7.66680 q^{23} -1.78647i q^{24} +(4.83340 - 1.27994i) q^{25} -2.22269 q^{26} +5.01735i q^{27} +3.14934i q^{28} +2.69676i q^{29} +(-0.515607 - 3.96125i) q^{30} +5.96563i q^{31} -1.00000 q^{32} -1.62382i q^{33} -2.10043 q^{34} +(0.908956 + 6.98323i) q^{35} -0.191472 q^{36} +(-1.10043 + 5.98240i) q^{37} +4.16694i q^{38} +3.97076i q^{39} +(-2.21736 + 0.288618i) q^{40} +2.32312 q^{41} +5.62620 q^{42} -5.72663 q^{43} -0.908956 q^{44} +(-0.424564 + 0.0552624i) q^{45} +7.66680 q^{46} -8.89435i q^{47} +1.78647i q^{48} -2.91834 q^{49} +(-4.83340 + 1.27994i) q^{50} +3.75235i q^{51} +2.22269 q^{52} -9.37592i q^{53} -5.01735i q^{54} +(-2.01549 + 0.262341i) q^{55} -3.14934i q^{56} +7.44411 q^{57} -2.69676i q^{58} -5.55880i q^{59} +(0.515607 + 3.96125i) q^{60} +3.16611i q^{61} -5.96563i q^{62} -0.603011i q^{63} +1.00000 q^{64} +(4.92850 - 0.641508i) q^{65} +1.62382i q^{66} +7.64933i q^{67} +2.10043 q^{68} -13.6965i q^{69} +(-0.908956 - 6.98323i) q^{70} +13.5157 q^{71} +0.191472 q^{72} -2.14851i q^{73} +(1.10043 - 5.98240i) q^{74} +(2.28658 + 8.63472i) q^{75} -4.16694i q^{76} -2.86261i q^{77} -3.97076i q^{78} -3.35774i q^{79} +(2.21736 - 0.288618i) q^{80} -9.53776 q^{81} -2.32312 q^{82} -16.2776i q^{83} -5.62620 q^{84} +(4.65741 - 0.606222i) q^{85} +5.72663 q^{86} -4.81767 q^{87} +0.908956 q^{88} -8.35832i q^{89} +(0.424564 - 0.0552624i) q^{90} +7.00000i q^{91} -7.66680 q^{92} -10.6574 q^{93} +8.89435i q^{94} +(-1.20265 - 9.23962i) q^{95} -1.78647i q^{96} -5.14283 q^{97} +2.91834 q^{98} +0.174040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.78647i 1.03142i 0.856764 + 0.515709i \(0.172472\pi\)
−0.856764 + 0.515709i \(0.827528\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.21736 0.288618i 0.991635 0.129074i
\(6\) 1.78647i 0.729323i
\(7\) 3.14934i 1.19034i 0.803600 + 0.595169i \(0.202915\pi\)
−0.803600 + 0.595169i \(0.797085\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.191472 −0.0638241
\(10\) −2.21736 + 0.288618i −0.701192 + 0.0912690i
\(11\) −0.908956 −0.274061 −0.137030 0.990567i \(-0.543756\pi\)
−0.137030 + 0.990567i \(0.543756\pi\)
\(12\) 1.78647i 0.515709i
\(13\) 2.22269 0.616462 0.308231 0.951311i \(-0.400263\pi\)
0.308231 + 0.951311i \(0.400263\pi\)
\(14\) 3.14934i 0.841696i
\(15\) 0.515607 + 3.96125i 0.133129 + 1.02279i
\(16\) 1.00000 0.250000
\(17\) 2.10043 0.509429 0.254714 0.967016i \(-0.418019\pi\)
0.254714 + 0.967016i \(0.418019\pi\)
\(18\) 0.191472 0.0451305
\(19\) 4.16694i 0.955962i −0.878370 0.477981i \(-0.841369\pi\)
0.878370 0.477981i \(-0.158631\pi\)
\(20\) 2.21736 0.288618i 0.495817 0.0645370i
\(21\) −5.62620 −1.22774
\(22\) 0.908956 0.193790
\(23\) −7.66680 −1.59864 −0.799319 0.600907i \(-0.794806\pi\)
−0.799319 + 0.600907i \(0.794806\pi\)
\(24\) 1.78647i 0.364662i
\(25\) 4.83340 1.27994i 0.966680 0.255988i
\(26\) −2.22269 −0.435905
\(27\) 5.01735i 0.965589i
\(28\) 3.14934i 0.595169i
\(29\) 2.69676i 0.500775i 0.968146 + 0.250387i \(0.0805580\pi\)
−0.968146 + 0.250387i \(0.919442\pi\)
\(30\) −0.515607 3.96125i −0.0941366 0.723222i
\(31\) 5.96563i 1.07146i 0.844390 + 0.535729i \(0.179963\pi\)
−0.844390 + 0.535729i \(0.820037\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.62382i 0.282671i
\(34\) −2.10043 −0.360221
\(35\) 0.908956 + 6.98323i 0.153642 + 1.18038i
\(36\) −0.191472 −0.0319121
\(37\) −1.10043 + 5.98240i −0.180909 + 0.983500i
\(38\) 4.16694i 0.675967i
\(39\) 3.97076i 0.635831i
\(40\) −2.21736 + 0.288618i −0.350596 + 0.0456345i
\(41\) 2.32312 0.362810 0.181405 0.983409i \(-0.441936\pi\)
0.181405 + 0.983409i \(0.441936\pi\)
\(42\) 5.62620 0.868141
\(43\) −5.72663 −0.873302 −0.436651 0.899631i \(-0.643836\pi\)
−0.436651 + 0.899631i \(0.643836\pi\)
\(44\) −0.908956 −0.137030
\(45\) −0.424564 + 0.0552624i −0.0632902 + 0.00823803i
\(46\) 7.66680 1.13041
\(47\) 8.89435i 1.29737i −0.761055 0.648687i \(-0.775318\pi\)
0.761055 0.648687i \(-0.224682\pi\)
\(48\) 1.78647i 0.257855i
\(49\) −2.91834 −0.416906
\(50\) −4.83340 + 1.27994i −0.683546 + 0.181011i
\(51\) 3.75235i 0.525434i
\(52\) 2.22269 0.308231
\(53\) 9.37592i 1.28788i −0.765075 0.643941i \(-0.777298\pi\)
0.765075 0.643941i \(-0.222702\pi\)
\(54\) 5.01735i 0.682775i
\(55\) −2.01549 + 0.262341i −0.271768 + 0.0353741i
\(56\) 3.14934i 0.420848i
\(57\) 7.44411 0.985997
\(58\) 2.69676i 0.354101i
\(59\) 5.55880i 0.723694i −0.932238 0.361847i \(-0.882146\pi\)
0.932238 0.361847i \(-0.117854\pi\)
\(60\) 0.515607 + 3.96125i 0.0665646 + 0.511395i
\(61\) 3.16611i 0.405378i 0.979243 + 0.202689i \(0.0649681\pi\)
−0.979243 + 0.202689i \(0.935032\pi\)
\(62\) 5.96563i 0.757636i
\(63\) 0.603011i 0.0759723i
\(64\) 1.00000 0.125000
\(65\) 4.92850 0.641508i 0.611306 0.0795692i
\(66\) 1.62382i 0.199879i
\(67\) 7.64933i 0.934515i 0.884121 + 0.467257i \(0.154758\pi\)
−0.884121 + 0.467257i \(0.845242\pi\)
\(68\) 2.10043 0.254714
\(69\) 13.6965i 1.64886i
\(70\) −0.908956 6.98323i −0.108641 0.834656i
\(71\) 13.5157 1.60402 0.802008 0.597313i \(-0.203765\pi\)
0.802008 + 0.597313i \(0.203765\pi\)
\(72\) 0.191472 0.0225652
\(73\) 2.14851i 0.251464i −0.992064 0.125732i \(-0.959872\pi\)
0.992064 0.125732i \(-0.0401279\pi\)
\(74\) 1.10043 5.98240i 0.127922 0.695439i
\(75\) 2.28658 + 8.63472i 0.264031 + 0.997051i
\(76\) 4.16694i 0.477981i
\(77\) 2.86261i 0.326225i
\(78\) 3.97076i 0.449600i
\(79\) 3.35774i 0.377775i −0.981999 0.188888i \(-0.939512\pi\)
0.981999 0.188888i \(-0.0604882\pi\)
\(80\) 2.21736 0.288618i 0.247909 0.0322685i
\(81\) −9.53776 −1.05975
\(82\) −2.32312 −0.256545
\(83\) 16.2776i 1.78670i −0.449361 0.893350i \(-0.648348\pi\)
0.449361 0.893350i \(-0.351652\pi\)
\(84\) −5.62620 −0.613869
\(85\) 4.65741 0.606222i 0.505167 0.0657540i
\(86\) 5.72663 0.617518
\(87\) −4.81767 −0.516509
\(88\) 0.908956 0.0968951
\(89\) 8.35832i 0.885980i −0.896527 0.442990i \(-0.853918\pi\)
0.896527 0.442990i \(-0.146082\pi\)
\(90\) 0.424564 0.0552624i 0.0447529 0.00582517i
\(91\) 7.00000i 0.733799i
\(92\) −7.66680 −0.799319
\(93\) −10.6574 −1.10512
\(94\) 8.89435i 0.917382i
\(95\) −1.20265 9.23962i −0.123390 0.947965i
\(96\) 1.78647i 0.182331i
\(97\) −5.14283 −0.522175 −0.261087 0.965315i \(-0.584081\pi\)
−0.261087 + 0.965315i \(0.584081\pi\)
\(98\) 2.91834 0.294797
\(99\) 0.174040 0.0174917
\(100\) 4.83340 1.27994i 0.483340 0.127994i
\(101\) −3.20212 −0.318623 −0.159311 0.987228i \(-0.550927\pi\)
−0.159311 + 0.987228i \(0.550927\pi\)
\(102\) 3.75235i 0.371538i
\(103\) 17.6871 1.74276 0.871382 0.490605i \(-0.163224\pi\)
0.871382 + 0.490605i \(0.163224\pi\)
\(104\) −2.22269 −0.217952
\(105\) −12.4753 + 1.62382i −1.21747 + 0.158469i
\(106\) 9.37592i 0.910670i
\(107\) 6.75126i 0.652669i −0.945254 0.326335i \(-0.894186\pi\)
0.945254 0.326335i \(-0.105814\pi\)
\(108\) 5.01735i 0.482795i
\(109\) 10.5304i 1.00863i −0.863520 0.504314i \(-0.831745\pi\)
0.863520 0.504314i \(-0.168255\pi\)
\(110\) 2.01549 0.262341i 0.192169 0.0250133i
\(111\) −10.6874 1.96588i −1.01440 0.186593i
\(112\) 3.14934i 0.297585i
\(113\) 6.32365 0.594879 0.297439 0.954741i \(-0.403867\pi\)
0.297439 + 0.954741i \(0.403867\pi\)
\(114\) −7.44411 −0.697205
\(115\) −17.0001 + 2.21278i −1.58527 + 0.206342i
\(116\) 2.69676i 0.250387i
\(117\) −0.425583 −0.0393452
\(118\) 5.55880i 0.511729i
\(119\) 6.61496i 0.606393i
\(120\) −0.515607 3.96125i −0.0470683 0.361611i
\(121\) −10.1738 −0.924891
\(122\) 3.16611i 0.286646i
\(123\) 4.15017i 0.374209i
\(124\) 5.96563i 0.535729i
\(125\) 10.3480 4.23310i 0.925552 0.378620i
\(126\) 0.603011i 0.0537205i
\(127\) 15.0472i 1.33522i −0.744512 0.667609i \(-0.767318\pi\)
0.744512 0.667609i \(-0.232682\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.2304i 0.900740i
\(130\) −4.92850 + 0.641508i −0.432258 + 0.0562639i
\(131\) 3.31974i 0.290047i 0.989428 + 0.145024i \(0.0463258\pi\)
−0.989428 + 0.145024i \(0.953674\pi\)
\(132\) 1.62382i 0.141336i
\(133\) 13.1231 1.13792
\(134\) 7.64933i 0.660802i
\(135\) 1.44810 + 11.1253i 0.124632 + 0.957512i
\(136\) −2.10043 −0.180110
\(137\) 17.9355i 1.53234i 0.642640 + 0.766168i \(0.277839\pi\)
−0.642640 + 0.766168i \(0.722161\pi\)
\(138\) 13.6965i 1.16592i
\(139\) 12.7472 1.08120 0.540601 0.841279i \(-0.318197\pi\)
0.540601 + 0.841279i \(0.318197\pi\)
\(140\) 0.908956 + 6.98323i 0.0768208 + 0.590191i
\(141\) 15.8895 1.33814
\(142\) −13.5157 −1.13421
\(143\) −2.02033 −0.168948
\(144\) −0.191472 −0.0159560
\(145\) 0.778332 + 5.97969i 0.0646370 + 0.496586i
\(146\) 2.14851i 0.177812i
\(147\) 5.21353i 0.430004i
\(148\) −1.10043 + 5.98240i −0.0904547 + 0.491750i
\(149\) −6.83795 −0.560186 −0.280093 0.959973i \(-0.590365\pi\)
−0.280093 + 0.959973i \(0.590365\pi\)
\(150\) −2.28658 8.63472i −0.186698 0.705022i
\(151\) −2.80702 −0.228432 −0.114216 0.993456i \(-0.536436\pi\)
−0.114216 + 0.993456i \(0.536436\pi\)
\(152\) 4.16694i 0.337984i
\(153\) −0.402174 −0.0325138
\(154\) 2.86261i 0.230676i
\(155\) 1.72179 + 13.2280i 0.138297 + 1.06250i
\(156\) 3.97076i 0.317915i
\(157\) 7.28275i 0.581227i 0.956841 + 0.290613i \(0.0938593\pi\)
−0.956841 + 0.290613i \(0.906141\pi\)
\(158\) 3.35774i 0.267127i
\(159\) 16.7498 1.32835
\(160\) −2.21736 + 0.288618i −0.175298 + 0.0228173i
\(161\) 24.1454i 1.90292i
\(162\) 9.53776 0.749357
\(163\) 22.2319 1.74134 0.870669 0.491870i \(-0.163686\pi\)
0.870669 + 0.491870i \(0.163686\pi\)
\(164\) 2.32312 0.181405
\(165\) −0.468665 3.60060i −0.0364855 0.280307i
\(166\) 16.2776i 1.26339i
\(167\) −11.5050 −0.890286 −0.445143 0.895459i \(-0.646847\pi\)
−0.445143 + 0.895459i \(0.646847\pi\)
\(168\) 5.62620 0.434071
\(169\) −8.05966 −0.619974
\(170\) −4.65741 + 0.606222i −0.357207 + 0.0464951i
\(171\) 0.797854i 0.0610134i
\(172\) −5.72663 −0.436651
\(173\) 15.7081i 1.19427i −0.802142 0.597134i \(-0.796306\pi\)
0.802142 0.597134i \(-0.203694\pi\)
\(174\) 4.81767 0.365227
\(175\) 4.03097 + 15.2220i 0.304713 + 1.15068i
\(176\) −0.908956 −0.0685152
\(177\) 9.93062 0.746431
\(178\) 8.35832i 0.626483i
\(179\) 11.3128i 0.845560i −0.906232 0.422780i \(-0.861054\pi\)
0.906232 0.422780i \(-0.138946\pi\)
\(180\) −0.424564 + 0.0552624i −0.0316451 + 0.00411901i
\(181\) 18.3136 1.36124 0.680618 0.732638i \(-0.261711\pi\)
0.680618 + 0.732638i \(0.261711\pi\)
\(182\) 7.00000i 0.518874i
\(183\) −5.65615 −0.418115
\(184\) 7.66680 0.565204
\(185\) −0.713423 + 13.5827i −0.0524519 + 0.998623i
\(186\) 10.6574 0.781439
\(187\) −1.90920 −0.139614
\(188\) 8.89435i 0.648687i
\(189\) −15.8013 −1.14938
\(190\) 1.20265 + 9.23962i 0.0872497 + 0.670313i
\(191\) 7.66002i 0.554260i 0.960832 + 0.277130i \(0.0893832\pi\)
−0.960832 + 0.277130i \(0.910617\pi\)
\(192\) 1.78647i 0.128927i
\(193\) −19.3148 −1.39031 −0.695156 0.718859i \(-0.744665\pi\)
−0.695156 + 0.718859i \(0.744665\pi\)
\(194\) 5.14283 0.369233
\(195\) 1.14603 + 8.80462i 0.0820692 + 0.630512i
\(196\) −2.91834 −0.208453
\(197\) 13.1193i 0.934709i 0.884070 + 0.467354i \(0.154793\pi\)
−0.884070 + 0.467354i \(0.845207\pi\)
\(198\) −0.174040 −0.0123685
\(199\) 6.04548i 0.428553i 0.976773 + 0.214277i \(0.0687394\pi\)
−0.976773 + 0.214277i \(0.931261\pi\)
\(200\) −4.83340 + 1.27994i −0.341773 + 0.0905056i
\(201\) −13.6653 −0.963876
\(202\) 3.20212 0.225300
\(203\) −8.49300 −0.596092
\(204\) 3.75235i 0.262717i
\(205\) 5.15119 0.670493i 0.359775 0.0468293i
\(206\) −17.6871 −1.23232
\(207\) 1.46798 0.102032
\(208\) 2.22269 0.154116
\(209\) 3.78757i 0.261992i
\(210\) 12.4753 1.62382i 0.860879 0.112054i
\(211\) 3.06975 0.211330 0.105665 0.994402i \(-0.466303\pi\)
0.105665 + 0.994402i \(0.466303\pi\)
\(212\) 9.37592i 0.643941i
\(213\) 24.1454i 1.65441i
\(214\) 6.75126i 0.461507i
\(215\) −12.6980 + 1.65281i −0.865997 + 0.112721i
\(216\) 5.01735i 0.341387i
\(217\) −18.7878 −1.27540
\(218\) 10.5304i 0.713208i
\(219\) 3.83824 0.259364
\(220\) −2.01549 + 0.262341i −0.135884 + 0.0176870i
\(221\) 4.66860 0.314044
\(222\) 10.6874 + 1.96588i 0.717289 + 0.131941i
\(223\) 13.9960i 0.937243i 0.883399 + 0.468621i \(0.155249\pi\)
−0.883399 + 0.468621i \(0.844751\pi\)
\(224\) 3.14934i 0.210424i
\(225\) −0.925462 + 0.245074i −0.0616975 + 0.0163382i
\(226\) −6.32365 −0.420643
\(227\) 11.9087 0.790409 0.395205 0.918593i \(-0.370674\pi\)
0.395205 + 0.918593i \(0.370674\pi\)
\(228\) 7.44411 0.492998
\(229\) −7.43448 −0.491285 −0.245642 0.969361i \(-0.578999\pi\)
−0.245642 + 0.969361i \(0.578999\pi\)
\(230\) 17.0001 2.21278i 1.12095 0.145906i
\(231\) 5.11397 0.336474
\(232\) 2.69676i 0.177051i
\(233\) 15.2152i 0.996782i −0.866952 0.498391i \(-0.833924\pi\)
0.866952 0.498391i \(-0.166076\pi\)
\(234\) 0.425583 0.0278212
\(235\) −2.56707 19.7220i −0.167457 1.28652i
\(236\) 5.55880i 0.361847i
\(237\) 5.99850 0.389644
\(238\) 6.61496i 0.428784i
\(239\) 29.1359i 1.88465i 0.334705 + 0.942323i \(0.391363\pi\)
−0.334705 + 0.942323i \(0.608637\pi\)
\(240\) 0.515607 + 3.96125i 0.0332823 + 0.255698i
\(241\) 7.08791i 0.456572i −0.973594 0.228286i \(-0.926688\pi\)
0.973594 0.228286i \(-0.0733121\pi\)
\(242\) 10.1738 0.653997
\(243\) 1.98686i 0.127457i
\(244\) 3.16611i 0.202689i
\(245\) −6.47102 + 0.842286i −0.413418 + 0.0538117i
\(246\) 4.15017i 0.264605i
\(247\) 9.26180i 0.589315i
\(248\) 5.96563i 0.378818i
\(249\) 29.0795 1.84284
\(250\) −10.3480 + 4.23310i −0.654464 + 0.267725i
\(251\) 17.3622i 1.09589i −0.836514 0.547946i \(-0.815410\pi\)
0.836514 0.547946i \(-0.184590\pi\)
\(252\) 0.603011i 0.0379861i
\(253\) 6.96879 0.438124
\(254\) 15.0472i 0.944142i
\(255\) 1.08300 + 8.32033i 0.0678199 + 0.521039i
\(256\) 1.00000 0.0625000
\(257\) −13.9118 −0.867797 −0.433899 0.900962i \(-0.642862\pi\)
−0.433899 + 0.900962i \(0.642862\pi\)
\(258\) 10.2304i 0.636920i
\(259\) −18.8406 3.46562i −1.17070 0.215343i
\(260\) 4.92850 0.641508i 0.305653 0.0397846i
\(261\) 0.516354i 0.0319615i
\(262\) 3.31974i 0.205094i
\(263\) 0.302157i 0.0186318i 0.999957 + 0.00931590i \(0.00296538\pi\)
−0.999957 + 0.00931590i \(0.997035\pi\)
\(264\) 1.62382i 0.0999394i
\(265\) −2.70606 20.7898i −0.166232 1.27711i
\(266\) −13.1231 −0.804630
\(267\) 14.9319 0.913816
\(268\) 7.64933i 0.467257i
\(269\) −28.8001 −1.75597 −0.877986 0.478687i \(-0.841113\pi\)
−0.877986 + 0.478687i \(0.841113\pi\)
\(270\) −1.44810 11.1253i −0.0881284 0.677063i
\(271\) 1.57340 0.0955770 0.0477885 0.998857i \(-0.484783\pi\)
0.0477885 + 0.998857i \(0.484783\pi\)
\(272\) 2.10043 0.127357
\(273\) −12.5053 −0.756854
\(274\) 17.9355i 1.08353i
\(275\) −4.39335 + 1.16341i −0.264929 + 0.0701564i
\(276\) 13.6965i 0.824432i
\(277\) 26.3430 1.58280 0.791398 0.611301i \(-0.209354\pi\)
0.791398 + 0.611301i \(0.209354\pi\)
\(278\) −12.7472 −0.764526
\(279\) 1.14225i 0.0683849i
\(280\) −0.908956 6.98323i −0.0543205 0.417328i
\(281\) 9.45482i 0.564027i 0.959410 + 0.282014i \(0.0910024\pi\)
−0.959410 + 0.282014i \(0.908998\pi\)
\(282\) −15.8895 −0.946205
\(283\) −21.7389 −1.29224 −0.646122 0.763234i \(-0.723610\pi\)
−0.646122 + 0.763234i \(0.723610\pi\)
\(284\) 13.5157 0.802008
\(285\) 16.5063 2.14851i 0.977749 0.127266i
\(286\) 2.02033 0.119464
\(287\) 7.31628i 0.431866i
\(288\) 0.191472 0.0112826
\(289\) −12.5882 −0.740482
\(290\) −0.778332 5.97969i −0.0457053 0.351139i
\(291\) 9.18750i 0.538581i
\(292\) 2.14851i 0.125732i
\(293\) 11.1283i 0.650121i −0.945693 0.325061i \(-0.894615\pi\)
0.945693 0.325061i \(-0.105385\pi\)
\(294\) 5.21353i 0.304059i
\(295\) −1.60437 12.3259i −0.0934100 0.717640i
\(296\) 1.10043 5.98240i 0.0639611 0.347720i
\(297\) 4.56055i 0.264630i
\(298\) 6.83795 0.396112
\(299\) −17.0409 −0.985500
\(300\) 2.28658 + 8.63472i 0.132016 + 0.498526i
\(301\) 18.0351i 1.03953i
\(302\) 2.80702 0.161526
\(303\) 5.72049i 0.328633i
\(304\) 4.16694i 0.238990i
\(305\) 0.913795 + 7.02041i 0.0523238 + 0.401987i
\(306\) 0.402174 0.0229908
\(307\) 15.9903i 0.912615i −0.889822 0.456308i \(-0.849172\pi\)
0.889822 0.456308i \(-0.150828\pi\)
\(308\) 2.86261i 0.163112i
\(309\) 31.5975i 1.79752i
\(310\) −1.72179 13.2280i −0.0977910 0.751298i
\(311\) 29.6416i 1.68082i 0.541949 + 0.840411i \(0.317687\pi\)
−0.541949 + 0.840411i \(0.682313\pi\)
\(312\) 3.97076i 0.224800i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 7.28275i 0.410989i
\(315\) −0.174040 1.33710i −0.00980604 0.0753368i
\(316\) 3.35774i 0.188888i
\(317\) 21.1397i 1.18732i −0.804715 0.593662i \(-0.797682\pi\)
0.804715 0.593662i \(-0.202318\pi\)
\(318\) −16.7498 −0.939282
\(319\) 2.45123i 0.137243i
\(320\) 2.21736 0.288618i 0.123954 0.0161342i
\(321\) 12.0609 0.673175
\(322\) 24.1454i 1.34557i
\(323\) 8.75236i 0.486994i
\(324\) −9.53776 −0.529875
\(325\) 10.7431 2.84491i 0.595922 0.157807i
\(326\) −22.2319 −1.23131
\(327\) 18.8122 1.04032
\(328\) −2.32312 −0.128273
\(329\) 28.0113 1.54431
\(330\) 0.468665 + 3.60060i 0.0257991 + 0.198207i
\(331\) 18.7324i 1.02963i −0.857302 0.514814i \(-0.827861\pi\)
0.857302 0.514814i \(-0.172139\pi\)
\(332\) 16.2776i 0.893350i
\(333\) 0.210702 1.14546i 0.0115464 0.0627710i
\(334\) 11.5050 0.629528
\(335\) 2.20774 + 16.9613i 0.120621 + 0.926697i
\(336\) −5.62620 −0.306934
\(337\) 13.9123i 0.757850i −0.925427 0.378925i \(-0.876294\pi\)
0.925427 0.378925i \(-0.123706\pi\)
\(338\) 8.05966 0.438388
\(339\) 11.2970i 0.613569i
\(340\) 4.65741 0.606222i 0.252584 0.0328770i
\(341\) 5.42250i 0.293645i
\(342\) 0.797854i 0.0431430i
\(343\) 12.8545i 0.694079i
\(344\) 5.72663 0.308759
\(345\) −3.95306 30.3701i −0.212825 1.63507i
\(346\) 15.7081i 0.844474i
\(347\) −24.5885 −1.31998 −0.659990 0.751274i \(-0.729440\pi\)
−0.659990 + 0.751274i \(0.729440\pi\)
\(348\) −4.81767 −0.258254
\(349\) −10.2324 −0.547726 −0.273863 0.961769i \(-0.588301\pi\)
−0.273863 + 0.961769i \(0.588301\pi\)
\(350\) −4.03097 15.2220i −0.215465 0.813651i
\(351\) 11.1520i 0.595249i
\(352\) 0.908956 0.0484475
\(353\) −1.74540 −0.0928981 −0.0464491 0.998921i \(-0.514791\pi\)
−0.0464491 + 0.998921i \(0.514791\pi\)
\(354\) −9.93062 −0.527806
\(355\) 29.9692 3.90087i 1.59060 0.207037i
\(356\) 8.35832i 0.442990i
\(357\) −11.8174 −0.625445
\(358\) 11.3128i 0.597901i
\(359\) 21.1922 1.11848 0.559240 0.829006i \(-0.311093\pi\)
0.559240 + 0.829006i \(0.311093\pi\)
\(360\) 0.424564 0.0552624i 0.0223765 0.00291258i
\(361\) 1.63660 0.0861371
\(362\) −18.3136 −0.962540
\(363\) 18.1752i 0.953949i
\(364\) 7.00000i 0.366900i
\(365\) −0.620097 4.76402i −0.0324574 0.249360i
\(366\) 5.65615 0.295652
\(367\) 9.69901i 0.506284i 0.967429 + 0.253142i \(0.0814640\pi\)
−0.967429 + 0.253142i \(0.918536\pi\)
\(368\) −7.66680 −0.399659
\(369\) −0.444812 −0.0231560
\(370\) 0.713423 13.5827i 0.0370891 0.706133i
\(371\) 29.5280 1.53302
\(372\) −10.6574 −0.552561
\(373\) 36.8658i 1.90884i −0.298466 0.954420i \(-0.596475\pi\)
0.298466 0.954420i \(-0.403525\pi\)
\(374\) 1.90920 0.0987223
\(375\) 7.56231 + 18.4864i 0.390516 + 0.954632i
\(376\) 8.89435i 0.458691i
\(377\) 5.99404i 0.308709i
\(378\) 15.8013 0.812733
\(379\) 31.7074 1.62870 0.814351 0.580372i \(-0.197093\pi\)
0.814351 + 0.580372i \(0.197093\pi\)
\(380\) −1.20265 9.23962i −0.0616949 0.473983i
\(381\) 26.8813 1.37717
\(382\) 7.66002i 0.391921i
\(383\) −3.45325 −0.176453 −0.0882265 0.996100i \(-0.528120\pi\)
−0.0882265 + 0.996100i \(0.528120\pi\)
\(384\) 1.78647i 0.0911654i
\(385\) −0.826202 6.34745i −0.0421071 0.323496i
\(386\) 19.3148 0.983099
\(387\) 1.09649 0.0557378
\(388\) −5.14283 −0.261087
\(389\) 39.2237i 1.98872i 0.106056 + 0.994360i \(0.466178\pi\)
−0.106056 + 0.994360i \(0.533822\pi\)
\(390\) −1.14603 8.80462i −0.0580317 0.445839i
\(391\) −16.1036 −0.814392
\(392\) 2.91834 0.147399
\(393\) −5.93062 −0.299160
\(394\) 13.1193i 0.660939i
\(395\) −0.969104 7.44533i −0.0487609 0.374615i
\(396\) 0.174040 0.00874584
\(397\) 5.75234i 0.288702i 0.989527 + 0.144351i \(0.0461094\pi\)
−0.989527 + 0.144351i \(0.953891\pi\)
\(398\) 6.04548i 0.303033i
\(399\) 23.4440i 1.17367i
\(400\) 4.83340 1.27994i 0.241670 0.0639971i
\(401\) 24.6273i 1.22983i 0.788594 + 0.614914i \(0.210809\pi\)
−0.788594 + 0.614914i \(0.789191\pi\)
\(402\) 13.6653 0.681563
\(403\) 13.2597i 0.660514i
\(404\) −3.20212 −0.159311
\(405\) −21.1487 + 2.75277i −1.05089 + 0.136786i
\(406\) 8.49300 0.421501
\(407\) 1.00024 5.43774i 0.0495801 0.269539i
\(408\) 3.75235i 0.185769i
\(409\) 25.1947i 1.24580i 0.782302 + 0.622899i \(0.214045\pi\)
−0.782302 + 0.622899i \(0.785955\pi\)
\(410\) −5.15119 + 0.670493i −0.254399 + 0.0331133i
\(411\) −32.0413 −1.58048
\(412\) 17.6871 0.871382
\(413\) 17.5065 0.861441
\(414\) −1.46798 −0.0721473
\(415\) −4.69801 36.0934i −0.230616 1.77175i
\(416\) −2.22269 −0.108976
\(417\) 22.7725i 1.11517i
\(418\) 3.78757i 0.185256i
\(419\) 7.19906 0.351697 0.175849 0.984417i \(-0.443733\pi\)
0.175849 + 0.984417i \(0.443733\pi\)
\(420\) −12.4753 + 1.62382i −0.608734 + 0.0792344i
\(421\) 34.0902i 1.66145i 0.556680 + 0.830727i \(0.312075\pi\)
−0.556680 + 0.830727i \(0.687925\pi\)
\(422\) −3.06975 −0.149433
\(423\) 1.70302i 0.0828038i
\(424\) 9.37592i 0.455335i
\(425\) 10.1522 2.68843i 0.492455 0.130408i
\(426\) 24.1454i 1.16985i
\(427\) −9.97114 −0.482537
\(428\) 6.75126i 0.326335i
\(429\) 3.60925i 0.174256i
\(430\) 12.6980 1.65281i 0.612353 0.0797055i
\(431\) 25.2123i 1.21443i −0.794536 0.607217i \(-0.792286\pi\)
0.794536 0.607217i \(-0.207714\pi\)
\(432\) 5.01735i 0.241397i
\(433\) 21.8683i 1.05092i 0.850817 + 0.525462i \(0.176107\pi\)
−0.850817 + 0.525462i \(0.823893\pi\)
\(434\) 18.7878 0.901843
\(435\) −10.6825 + 1.39047i −0.512188 + 0.0666678i
\(436\) 10.5304i 0.504314i
\(437\) 31.9471i 1.52824i
\(438\) −3.83824 −0.183398
\(439\) 9.00956i 0.430003i −0.976614 0.215001i \(-0.931024\pi\)
0.976614 0.215001i \(-0.0689756\pi\)
\(440\) 2.01549 0.262341i 0.0960845 0.0125066i
\(441\) 0.558782 0.0266086
\(442\) −4.66860 −0.222062
\(443\) 2.89007i 0.137311i 0.997640 + 0.0686557i \(0.0218710\pi\)
−0.997640 + 0.0686557i \(0.978129\pi\)
\(444\) −10.6874 1.96588i −0.507200 0.0932966i
\(445\) −2.41236 18.5334i −0.114357 0.878569i
\(446\) 13.9960i 0.662731i
\(447\) 12.2158i 0.577787i
\(448\) 3.14934i 0.148792i
\(449\) 18.1539i 0.856738i −0.903604 0.428369i \(-0.859088\pi\)
0.903604 0.428369i \(-0.140912\pi\)
\(450\) 0.925462 0.245074i 0.0436267 0.0115529i
\(451\) −2.11161 −0.0994319
\(452\) 6.32365 0.297439
\(453\) 5.01466i 0.235609i
\(454\) −11.9087 −0.558904
\(455\) 2.02033 + 15.5215i 0.0947143 + 0.727661i
\(456\) −7.44411 −0.348602
\(457\) −10.4140 −0.487146 −0.243573 0.969883i \(-0.578320\pi\)
−0.243573 + 0.969883i \(0.578320\pi\)
\(458\) 7.43448 0.347391
\(459\) 10.5386i 0.491899i
\(460\) −17.0001 + 2.21278i −0.792633 + 0.103171i
\(461\) 17.7433i 0.826390i −0.910643 0.413195i \(-0.864413\pi\)
0.910643 0.413195i \(-0.135587\pi\)
\(462\) −5.11397 −0.237923
\(463\) −11.6293 −0.540457 −0.270229 0.962796i \(-0.587099\pi\)
−0.270229 + 0.962796i \(0.587099\pi\)
\(464\) 2.69676i 0.125194i
\(465\) −23.6314 + 3.07592i −1.09588 + 0.142642i
\(466\) 15.2152i 0.704831i
\(467\) −6.25208 −0.289312 −0.144656 0.989482i \(-0.546207\pi\)
−0.144656 + 0.989482i \(0.546207\pi\)
\(468\) −0.425583 −0.0196726
\(469\) −24.0903 −1.11239
\(470\) 2.56707 + 19.7220i 0.118410 + 0.909708i
\(471\) −13.0104 −0.599488
\(472\) 5.55880i 0.255864i
\(473\) 5.20525 0.239338
\(474\) −5.99850 −0.275520
\(475\) −5.33344 20.1405i −0.244715 0.924109i
\(476\) 6.61496i 0.303196i
\(477\) 1.79523i 0.0821979i
\(478\) 29.1359i 1.33265i
\(479\) 16.4452i 0.751398i 0.926742 + 0.375699i \(0.122597\pi\)
−0.926742 + 0.375699i \(0.877403\pi\)
\(480\) −0.515607 3.96125i −0.0235341 0.180806i
\(481\) −2.44591 + 13.2970i −0.111524 + 0.606291i
\(482\) 7.08791i 0.322845i
\(483\) 43.1349 1.96271
\(484\) −10.1738 −0.462445
\(485\) −11.4035 + 1.48431i −0.517807 + 0.0673992i
\(486\) 1.98686i 0.0901259i
\(487\) −13.7966 −0.625184 −0.312592 0.949887i \(-0.601197\pi\)
−0.312592 + 0.949887i \(0.601197\pi\)
\(488\) 3.16611i 0.143323i
\(489\) 39.7166i 1.79605i
\(490\) 6.47102 0.842286i 0.292331 0.0380506i
\(491\) −39.0410 −1.76190 −0.880949 0.473211i \(-0.843095\pi\)
−0.880949 + 0.473211i \(0.843095\pi\)
\(492\) 4.15017i 0.187104i
\(493\) 5.66434i 0.255109i
\(494\) 9.26180i 0.416708i
\(495\) 0.385910 0.0502311i 0.0173454 0.00225772i
\(496\) 5.96563i 0.267865i
\(497\) 42.5655i 1.90932i
\(498\) −29.0795 −1.30308
\(499\) 40.0886i 1.79461i −0.441410 0.897306i \(-0.645521\pi\)
0.441410 0.897306i \(-0.354479\pi\)
\(500\) 10.3480 4.23310i 0.462776 0.189310i
\(501\) 20.5534i 0.918258i
\(502\) 17.3622i 0.774913i
\(503\) −12.0731 −0.538312 −0.269156 0.963097i \(-0.586745\pi\)
−0.269156 + 0.963097i \(0.586745\pi\)
\(504\) 0.603011i 0.0268603i
\(505\) −7.10026 + 0.924190i −0.315958 + 0.0411259i
\(506\) −6.96879 −0.309800
\(507\) 14.3983i 0.639453i
\(508\) 15.0472i 0.667609i
\(509\) 4.36466 0.193460 0.0967300 0.995311i \(-0.469162\pi\)
0.0967300 + 0.995311i \(0.469162\pi\)
\(510\) −1.08300 8.32033i −0.0479559 0.368430i
\(511\) 6.76637 0.299327
\(512\) −1.00000 −0.0441942
\(513\) 20.9070 0.923066
\(514\) 13.9118 0.613625
\(515\) 39.2188 5.10482i 1.72819 0.224945i
\(516\) 10.2304i 0.450370i
\(517\) 8.08458i 0.355559i
\(518\) 18.8406 + 3.46562i 0.827808 + 0.152271i
\(519\) 28.0621 1.23179
\(520\) −4.92850 + 0.641508i −0.216129 + 0.0281320i
\(521\) −16.7088 −0.732025 −0.366013 0.930610i \(-0.619277\pi\)
−0.366013 + 0.930610i \(0.619277\pi\)
\(522\) 0.516354i 0.0226002i
\(523\) −32.5266 −1.42229 −0.711144 0.703047i \(-0.751823\pi\)
−0.711144 + 0.703047i \(0.751823\pi\)
\(524\) 3.31974i 0.145024i
\(525\) −27.1937 + 7.20121i −1.18683 + 0.314287i
\(526\) 0.302157i 0.0131747i
\(527\) 12.5304i 0.545832i
\(528\) 1.62382i 0.0706678i
\(529\) 35.7798 1.55564
\(530\) 2.70606 + 20.7898i 0.117544 + 0.903052i
\(531\) 1.06436i 0.0461891i
\(532\) 13.1231 0.568959
\(533\) 5.16356 0.223659
\(534\) −14.9319 −0.646166
\(535\) −1.94854 14.9700i −0.0842426 0.647210i
\(536\) 7.64933i 0.330401i
\(537\) 20.2100 0.872126
\(538\) 28.8001 1.24166
\(539\) 2.65265 0.114258
\(540\) 1.44810 + 11.1253i 0.0623162 + 0.478756i
\(541\) 19.2331i 0.826894i 0.910528 + 0.413447i \(0.135675\pi\)
−0.910528 + 0.413447i \(0.864325\pi\)
\(542\) −1.57340 −0.0675832
\(543\) 32.7166i 1.40400i
\(544\) −2.10043 −0.0900551
\(545\) −3.03926 23.3497i −0.130188 1.00019i
\(546\) 12.5053 0.535177
\(547\) 8.88173 0.379755 0.189878 0.981808i \(-0.439191\pi\)
0.189878 + 0.981808i \(0.439191\pi\)
\(548\) 17.9355i 0.766168i
\(549\) 0.606222i 0.0258729i
\(550\) 4.39335 1.16341i 0.187333 0.0496080i
\(551\) 11.2372 0.478722
\(552\) 13.6965i 0.582962i
\(553\) 10.5747 0.449680
\(554\) −26.3430 −1.11921
\(555\) −24.2652 1.27451i −1.03000 0.0540998i
\(556\) 12.7472 0.540601
\(557\) 44.3010 1.87709 0.938547 0.345150i \(-0.112172\pi\)
0.938547 + 0.345150i \(0.112172\pi\)
\(558\) 1.14225i 0.0483554i
\(559\) −12.7285 −0.538358
\(560\) 0.908956 + 6.98323i 0.0384104 + 0.295095i
\(561\) 3.41072i 0.144001i
\(562\) 9.45482i 0.398828i
\(563\) 19.8885 0.838202 0.419101 0.907940i \(-0.362345\pi\)
0.419101 + 0.907940i \(0.362345\pi\)
\(564\) 15.8895 0.669068
\(565\) 14.0218 1.82512i 0.589903 0.0767834i
\(566\) 21.7389 0.913754
\(567\) 30.0376i 1.26146i
\(568\) −13.5157 −0.567106
\(569\) 3.13170i 0.131288i −0.997843 0.0656439i \(-0.979090\pi\)
0.997843 0.0656439i \(-0.0209101\pi\)
\(570\) −16.5063 + 2.14851i −0.691373 + 0.0899910i
\(571\) −19.2774 −0.806732 −0.403366 0.915039i \(-0.632160\pi\)
−0.403366 + 0.915039i \(0.632160\pi\)
\(572\) −2.02033 −0.0844741
\(573\) −13.6844 −0.571674
\(574\) 7.31628i 0.305376i
\(575\) −37.0567 + 9.81306i −1.54537 + 0.409233i
\(576\) −0.191472 −0.00797801
\(577\) 24.8001 1.03244 0.516220 0.856456i \(-0.327339\pi\)
0.516220 + 0.856456i \(0.327339\pi\)
\(578\) 12.5882 0.523600
\(579\) 34.5053i 1.43399i
\(580\) 0.778332 + 5.97969i 0.0323185 + 0.248293i
\(581\) 51.2637 2.12678
\(582\) 9.18750i 0.380834i
\(583\) 8.52230i 0.352958i
\(584\) 2.14851i 0.0889058i
\(585\) −0.943672 + 0.122831i −0.0390160 + 0.00507843i
\(586\) 11.1283i 0.459705i
\(587\) −16.1319 −0.665836 −0.332918 0.942956i \(-0.608033\pi\)
−0.332918 + 0.942956i \(0.608033\pi\)
\(588\) 5.21353i 0.215002i
\(589\) 24.8584 1.02427
\(590\) 1.60437 + 12.3259i 0.0660508 + 0.507448i
\(591\) −23.4372 −0.964076
\(592\) −1.10043 + 5.98240i −0.0452273 + 0.245875i
\(593\) 28.2040i 1.15820i 0.815256 + 0.579100i \(0.196596\pi\)
−0.815256 + 0.579100i \(0.803404\pi\)
\(594\) 4.56055i 0.187122i
\(595\) 1.90920 + 14.6678i 0.0782695 + 0.601320i
\(596\) −6.83795 −0.280093
\(597\) −10.8001 −0.442018
\(598\) 17.0409 0.696854
\(599\) −24.8280 −1.01444 −0.507222 0.861815i \(-0.669328\pi\)
−0.507222 + 0.861815i \(0.669328\pi\)
\(600\) −2.28658 8.63472i −0.0933491 0.352511i
\(601\) −2.87745 −0.117374 −0.0586868 0.998276i \(-0.518691\pi\)
−0.0586868 + 0.998276i \(0.518691\pi\)
\(602\) 18.0351i 0.735056i
\(603\) 1.46464i 0.0596446i
\(604\) −2.80702 −0.114216
\(605\) −22.5590 + 2.93634i −0.917154 + 0.119379i
\(606\) 5.72049i 0.232379i
\(607\) −25.7881 −1.04671 −0.523353 0.852116i \(-0.675319\pi\)
−0.523353 + 0.852116i \(0.675319\pi\)
\(608\) 4.16694i 0.168992i
\(609\) 15.1725i 0.614820i
\(610\) −0.913795 7.02041i −0.0369985 0.284248i
\(611\) 19.7694i 0.799783i
\(612\) −0.402174 −0.0162569
\(613\) 32.4248i 1.30962i 0.755792 + 0.654812i \(0.227252\pi\)
−0.755792 + 0.654812i \(0.772748\pi\)
\(614\) 15.9903i 0.645317i
\(615\) 1.19782 + 9.20244i 0.0483006 + 0.371078i
\(616\) 2.86261i 0.115338i
\(617\) 5.69333i 0.229205i 0.993411 + 0.114602i \(0.0365594\pi\)
−0.993411 + 0.114602i \(0.963441\pi\)
\(618\) 31.5975i 1.27104i
\(619\) −4.76393 −0.191478 −0.0957392 0.995406i \(-0.530521\pi\)
−0.0957392 + 0.995406i \(0.530521\pi\)
\(620\) 1.72179 + 13.2280i 0.0691487 + 0.531248i
\(621\) 38.4670i 1.54363i
\(622\) 29.6416i 1.18852i
\(623\) 26.3232 1.05462
\(624\) 3.97076i 0.158958i
\(625\) 21.7235 12.3729i 0.868940 0.494918i
\(626\) 10.0000 0.399680
\(627\) −6.76637 −0.270223
\(628\) 7.28275i 0.290613i
\(629\) −2.31137 + 12.5656i −0.0921604 + 0.501023i
\(630\) 0.174040 + 1.33710i 0.00693392 + 0.0532712i
\(631\) 8.72673i 0.347405i −0.984798 0.173703i \(-0.944427\pi\)
0.984798 0.173703i \(-0.0555732\pi\)
\(632\) 3.35774i 0.133564i
\(633\) 5.48401i 0.217970i
\(634\) 21.1397i 0.839564i
\(635\) −4.34288 33.3650i −0.172342 1.32405i
\(636\) 16.7498 0.664173
\(637\) −6.48656 −0.257007
\(638\) 2.45123i 0.0970453i
\(639\) −2.58788 −0.102375
\(640\) −2.21736 + 0.288618i −0.0876490 + 0.0114086i
\(641\) −41.1790 −1.62647 −0.813237 0.581933i \(-0.802297\pi\)
−0.813237 + 0.581933i \(0.802297\pi\)
\(642\) −12.0609 −0.476007
\(643\) 6.12834 0.241678 0.120839 0.992672i \(-0.461441\pi\)
0.120839 + 0.992672i \(0.461441\pi\)
\(644\) 24.1454i 0.951460i
\(645\) −2.95269 22.6846i −0.116262 0.893206i
\(646\) 8.75236i 0.344357i
\(647\) 31.3270 1.23159 0.615796 0.787905i \(-0.288834\pi\)
0.615796 + 0.787905i \(0.288834\pi\)
\(648\) 9.53776 0.374678
\(649\) 5.05270i 0.198336i
\(650\) −10.7431 + 2.84491i −0.421380 + 0.111587i
\(651\) 33.5638i 1.31547i
\(652\) 22.2319 0.870669
\(653\) −0.716146 −0.0280250 −0.0140125 0.999902i \(-0.504460\pi\)
−0.0140125 + 0.999902i \(0.504460\pi\)
\(654\) −18.8122 −0.735616
\(655\) 0.958138 + 7.36108i 0.0374375 + 0.287621i
\(656\) 2.32312 0.0907024
\(657\) 0.411379i 0.0160494i
\(658\) −28.0113 −1.09200
\(659\) −10.8796 −0.423810 −0.211905 0.977290i \(-0.567967\pi\)
−0.211905 + 0.977290i \(0.567967\pi\)
\(660\) −0.468665 3.60060i −0.0182427 0.140153i
\(661\) 37.4927i 1.45830i 0.684355 + 0.729149i \(0.260084\pi\)
−0.684355 + 0.729149i \(0.739916\pi\)
\(662\) 18.7324i 0.728057i
\(663\) 8.34030i 0.323910i
\(664\) 16.2776i 0.631694i
\(665\) 29.0987 3.78757i 1.12840 0.146876i
\(666\) −0.210702 + 1.14546i −0.00816452 + 0.0443858i
\(667\) 20.6755i 0.800558i
\(668\) −11.5050 −0.445143
\(669\) −25.0035 −0.966689
\(670\) −2.20774 16.9613i −0.0852922 0.655274i
\(671\) 2.87785i 0.111098i
\(672\) 5.62620 0.217035
\(673\) 38.2532i 1.47455i −0.675591 0.737277i \(-0.736111\pi\)
0.675591 0.737277i \(-0.263889\pi\)
\(674\) 13.9123i 0.535881i
\(675\) 6.42192 + 24.2508i 0.247180 + 0.933416i
\(676\) −8.05966 −0.309987
\(677\) 45.0250i 1.73045i 0.501381 + 0.865227i \(0.332825\pi\)
−0.501381 + 0.865227i \(0.667175\pi\)
\(678\) 11.2970i 0.433859i
\(679\) 16.1965i 0.621565i
\(680\) −4.65741 + 0.606222i −0.178604 + 0.0232475i
\(681\) 21.2746i 0.815243i
\(682\) 5.42250i 0.207638i
\(683\) −34.7787 −1.33077 −0.665384 0.746501i \(-0.731732\pi\)
−0.665384 + 0.746501i \(0.731732\pi\)
\(684\) 0.797854i 0.0305067i
\(685\) 5.17652 + 39.7696i 0.197785 + 1.51952i
\(686\) 12.8545i 0.490788i
\(687\) 13.2815i 0.506720i
\(688\) −5.72663 −0.218326
\(689\) 20.8397i 0.793931i
\(690\) 3.95306 + 30.3701i 0.150490 + 1.15617i
\(691\) 38.8781 1.47899 0.739497 0.673160i \(-0.235063\pi\)
0.739497 + 0.673160i \(0.235063\pi\)
\(692\) 15.7081i 0.597134i
\(693\) 0.548111i 0.0208210i
\(694\) 24.5885 0.933367
\(695\) 28.2652 3.67907i 1.07216 0.139555i
\(696\) 4.81767 0.182613
\(697\) 4.87954 0.184826
\(698\) 10.2324 0.387301
\(699\) 27.1815 1.02810
\(700\) 4.03097 + 15.2220i 0.152356 + 0.575338i
\(701\) 41.6474i 1.57300i −0.617589 0.786501i \(-0.711890\pi\)
0.617589 0.786501i \(-0.288110\pi\)
\(702\) 11.1520i 0.420905i
\(703\) 24.9283 + 4.58542i 0.940188 + 0.172942i
\(704\) −0.908956 −0.0342576
\(705\) 35.2328 4.58599i 1.32694 0.172718i
\(706\) 1.74540 0.0656889
\(707\) 10.0846i 0.379269i
\(708\) 9.93062 0.373216
\(709\) 3.86911i 0.145307i −0.997357 0.0726537i \(-0.976853\pi\)
0.997357 0.0726537i \(-0.0231468\pi\)
\(710\) −29.9692 + 3.90087i −1.12472 + 0.146397i
\(711\) 0.642914i 0.0241112i
\(712\) 8.35832i 0.313241i
\(713\) 45.7373i 1.71287i
\(714\) 11.8174 0.442256
\(715\) −4.47980 + 0.583102i −0.167535 + 0.0218068i
\(716\) 11.3128i 0.422780i
\(717\) −52.0504 −1.94386
\(718\) −21.1922 −0.790884
\(719\) −26.4440 −0.986194 −0.493097 0.869974i \(-0.664135\pi\)
−0.493097 + 0.869974i \(0.664135\pi\)
\(720\) −0.424564 + 0.0552624i −0.0158226 + 0.00205951i
\(721\) 55.7028i 2.07448i
\(722\) −1.63660 −0.0609081
\(723\) 12.6623 0.470917
\(724\) 18.3136 0.680618
\(725\) 3.45169 + 13.0345i 0.128193 + 0.484089i
\(726\) 18.1752i 0.674544i
\(727\) −28.3958 −1.05314 −0.526571 0.850131i \(-0.676522\pi\)
−0.526571 + 0.850131i \(0.676522\pi\)
\(728\) 7.00000i 0.259437i
\(729\) −25.0638 −0.928289
\(730\) 0.620097 + 4.76402i 0.0229508 + 0.176324i
\(731\) −12.0284 −0.444885
\(732\) −5.65615 −0.209057
\(733\) 19.8801i 0.734289i −0.930164 0.367144i \(-0.880336\pi\)
0.930164 0.367144i \(-0.119664\pi\)
\(734\) 9.69901i 0.357997i
\(735\) −1.50472 11.5603i −0.0555024 0.426407i
\(736\) 7.66680 0.282602
\(737\) 6.95291i 0.256114i
\(738\) 0.444812 0.0163738
\(739\) −42.1224 −1.54950 −0.774749 0.632269i \(-0.782124\pi\)
−0.774749 + 0.632269i \(0.782124\pi\)
\(740\) −0.713423 + 13.5827i −0.0262259 + 0.499312i
\(741\) 16.5459 0.607830
\(742\) −29.5280 −1.08401
\(743\) 23.5575i 0.864242i 0.901816 + 0.432121i \(0.142235\pi\)
−0.901816 + 0.432121i \(0.857765\pi\)
\(744\) 10.6574 0.390720
\(745\) −15.1622 + 1.97355i −0.555500 + 0.0723054i
\(746\) 36.8658i 1.34975i
\(747\) 3.11671i 0.114035i
\(748\) −1.90920 −0.0698072
\(749\) 21.2620 0.776897
\(750\) −7.56231 18.4864i −0.276136 0.675026i
\(751\) 32.6454 1.19125 0.595624 0.803263i \(-0.296905\pi\)
0.595624 + 0.803263i \(0.296905\pi\)
\(752\) 8.89435i 0.324344i
\(753\) 31.0170 1.13032
\(754\) 5.99404i 0.218290i
\(755\) −6.22419 + 0.810158i −0.226522 + 0.0294847i
\(756\) −15.8013 −0.574689
\(757\) 30.3562 1.10331 0.551657 0.834071i \(-0.313996\pi\)
0.551657 + 0.834071i \(0.313996\pi\)
\(758\) −31.7074 −1.15167
\(759\) 12.4495i 0.451889i
\(760\) 1.20265 + 9.23962i 0.0436249 + 0.335156i
\(761\) −38.6682 −1.40172 −0.700860 0.713299i \(-0.747200\pi\)
−0.700860 + 0.713299i \(0.747200\pi\)
\(762\) −26.8813 −0.973806
\(763\) 33.1638 1.20061
\(764\) 7.66002i 0.277130i
\(765\) −0.891766 + 0.116075i −0.0322419 + 0.00419669i
\(766\) 3.45325 0.124771
\(767\) 12.3555i 0.446130i
\(768\) 1.78647i 0.0644637i
\(769\) 23.8517i 0.860114i 0.902802 + 0.430057i \(0.141506\pi\)
−0.902802 + 0.430057i \(0.858494\pi\)
\(770\) 0.826202 + 6.34745i 0.0297742 + 0.228746i
\(771\) 24.8531i 0.895062i
\(772\) −19.3148 −0.695156
\(773\) 38.4580i 1.38324i 0.722262 + 0.691620i \(0.243103\pi\)
−0.722262 + 0.691620i \(0.756897\pi\)
\(774\) −1.09649 −0.0394125
\(775\) 7.63566 + 28.8343i 0.274281 + 1.03576i
\(776\) 5.14283 0.184617
\(777\) 6.19123 33.6581i 0.222109 1.20748i
\(778\) 39.2237i 1.40624i
\(779\) 9.68029i 0.346832i
\(780\) 1.14603 + 8.80462i 0.0410346 + 0.315256i
\(781\) −12.2852 −0.439598
\(782\) 16.1036 0.575862
\(783\) −13.5306 −0.483543
\(784\) −2.91834 −0.104226
\(785\) 2.10193 + 16.1485i 0.0750212 + 0.576365i
\(786\) 5.93062 0.211538
\(787\) 39.3808i 1.40378i −0.712288 0.701888i \(-0.752341\pi\)
0.712288