Properties

Label 380.2.d.b.379.8
Level $380$
Weight $2$
Character 380.379
Analytic conductor $3.034$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.8
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.27059 + 0.620975i) q^{2} -0.701989i q^{3} +(1.22878 - 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 + 0.891938i) q^{6} +1.18642 q^{7} +(-0.581371 + 2.76803i) q^{8} +2.50721 q^{9} +O(q^{10})\) \(q+(-1.27059 + 0.620975i) q^{2} -0.701989i q^{3} +(1.22878 - 1.57800i) q^{4} +(-1.10449 + 1.94425i) q^{5} +(0.435918 + 0.891938i) q^{6} +1.18642 q^{7} +(-0.581371 + 2.76803i) q^{8} +2.50721 q^{9} +(0.196019 - 3.15620i) q^{10} -1.72011i q^{11} +(-1.10774 - 0.862590i) q^{12} -2.64385 q^{13} +(-1.50745 + 0.736738i) q^{14} +(1.36484 + 0.775339i) q^{15} +(-0.980197 - 3.87804i) q^{16} +4.62546i q^{17} +(-3.18563 + 1.55692i) q^{18} +(2.08114 + 3.82999i) q^{19} +(1.71086 + 4.13194i) q^{20} -0.832855i q^{21} +(1.06815 + 2.18555i) q^{22} +6.62976 q^{23} +(1.94313 + 0.408116i) q^{24} +(-2.56021 - 4.29480i) q^{25} +(3.35924 - 1.64177i) q^{26} -3.86600i q^{27} +(1.45785 - 1.87218i) q^{28} +7.53366i q^{29} +(-2.21562 - 0.137603i) q^{30} +10.9809 q^{31} +(3.65359 + 4.31871i) q^{32} -1.20750 q^{33} +(-2.87229 - 5.87705i) q^{34} +(-1.31039 + 2.30670i) q^{35} +(3.08081 - 3.95639i) q^{36} +8.43930 q^{37} +(-5.02260 - 3.57400i) q^{38} +1.85596i q^{39} +(-4.73963 - 4.18759i) q^{40} +7.40097i q^{41} +(0.517182 + 1.05821i) q^{42} -9.29752 q^{43} +(-2.71435 - 2.11364i) q^{44} +(-2.76919 + 4.87464i) q^{45} +(-8.42368 + 4.11691i) q^{46} +4.10213 q^{47} +(-2.72234 + 0.688088i) q^{48} -5.59240 q^{49} +(5.91993 + 3.86709i) q^{50} +3.24702 q^{51} +(-3.24871 + 4.17201i) q^{52} -1.98886 q^{53} +(2.40069 + 4.91209i) q^{54} +(3.34433 + 1.89985i) q^{55} +(-0.689751 + 3.28406i) q^{56} +(2.68861 - 1.46094i) q^{57} +(-4.67822 - 9.57217i) q^{58} +3.13673 q^{59} +(2.90058 - 1.20100i) q^{60} +3.75579 q^{61} +(-13.9522 + 6.81889i) q^{62} +2.97461 q^{63} +(-7.32402 - 3.21851i) q^{64} +(2.92011 - 5.14031i) q^{65} +(1.53424 - 0.749828i) q^{66} -9.50799i q^{67} +(7.29900 + 5.68367i) q^{68} -4.65402i q^{69} +(0.232561 - 3.74458i) q^{70} -9.11343 q^{71} +(-1.45762 + 6.94004i) q^{72} -6.47318i q^{73} +(-10.7229 + 5.24059i) q^{74} +(-3.01490 + 1.79724i) q^{75} +(8.60101 + 1.42216i) q^{76} -2.04078i q^{77} +(-1.15250 - 2.35815i) q^{78} -6.38375 q^{79} +(8.62250 + 2.37751i) q^{80} +4.80774 q^{81} +(-4.59581 - 9.40357i) q^{82} -10.7908 q^{83} +(-1.31425 - 1.02340i) q^{84} +(-8.99304 - 5.10877i) q^{85} +(11.8133 - 5.77353i) q^{86} +5.28855 q^{87} +(4.76133 + 1.00002i) q^{88} -14.1018i q^{89} +(0.491461 - 7.91325i) q^{90} -3.13673 q^{91} +(8.14651 - 10.4618i) q^{92} -7.70851i q^{93} +(-5.21211 + 2.54732i) q^{94} +(-9.74506 - 0.183919i) q^{95} +(3.03169 - 2.56478i) q^{96} +3.39949 q^{97} +(7.10563 - 3.47274i) q^{98} -4.31269i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} - 8q^{16} - 20q^{20} - 40q^{24} - 84q^{25} - 24q^{26} + 24q^{30} + 24q^{36} - 40q^{44} - 12q^{45} + 128q^{49} - 120q^{54} + 24q^{61} + 72q^{64} + 112q^{66} + 32q^{74} + 56q^{76} + 96q^{80} - 72q^{81} + 44q^{85} - 40q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27059 + 0.620975i −0.898440 + 0.439096i
\(3\) 0.701989i 0.405294i −0.979252 0.202647i \(-0.935046\pi\)
0.979252 0.202647i \(-0.0649543\pi\)
\(4\) 1.22878 1.57800i 0.614390 0.789002i
\(5\) −1.10449 + 1.94425i −0.493942 + 0.869495i
\(6\) 0.435918 + 0.891938i 0.177963 + 0.364132i
\(7\) 1.18642 0.448425 0.224213 0.974540i \(-0.428019\pi\)
0.224213 + 0.974540i \(0.428019\pi\)
\(8\) −0.581371 + 2.76803i −0.205546 + 0.978648i
\(9\) 2.50721 0.835737
\(10\) 0.196019 3.15620i 0.0619866 0.998077i
\(11\) 1.72011i 0.518634i −0.965792 0.259317i \(-0.916503\pi\)
0.965792 0.259317i \(-0.0834974\pi\)
\(12\) −1.10774 0.862590i −0.319778 0.249008i
\(13\) −2.64385 −0.733273 −0.366636 0.930364i \(-0.619491\pi\)
−0.366636 + 0.930364i \(0.619491\pi\)
\(14\) −1.50745 + 0.736738i −0.402884 + 0.196902i
\(15\) 1.36484 + 0.775339i 0.352401 + 0.200192i
\(16\) −0.980197 3.87804i −0.245049 0.969511i
\(17\) 4.62546i 1.12184i 0.827870 + 0.560919i \(0.189552\pi\)
−0.827870 + 0.560919i \(0.810448\pi\)
\(18\) −3.18563 + 1.55692i −0.750860 + 0.366968i
\(19\) 2.08114 + 3.82999i 0.477447 + 0.878660i
\(20\) 1.71086 + 4.13194i 0.382560 + 0.923931i
\(21\) 0.832855i 0.181744i
\(22\) 1.06815 + 2.18555i 0.227730 + 0.465962i
\(23\) 6.62976 1.38240 0.691200 0.722664i \(-0.257082\pi\)
0.691200 + 0.722664i \(0.257082\pi\)
\(24\) 1.94313 + 0.408116i 0.396640 + 0.0833063i
\(25\) −2.56021 4.29480i −0.512042 0.858960i
\(26\) 3.35924 1.64177i 0.658802 0.321977i
\(27\) 3.86600i 0.744012i
\(28\) 1.45785 1.87218i 0.275508 0.353809i
\(29\) 7.53366i 1.39897i 0.714649 + 0.699483i \(0.246586\pi\)
−0.714649 + 0.699483i \(0.753414\pi\)
\(30\) −2.21562 0.137603i −0.404514 0.0251228i
\(31\) 10.9809 1.97224 0.986118 0.166044i \(-0.0530995\pi\)
0.986118 + 0.166044i \(0.0530995\pi\)
\(32\) 3.65359 + 4.31871i 0.645870 + 0.763447i
\(33\) −1.20750 −0.210199
\(34\) −2.87229 5.87705i −0.492594 1.00791i
\(35\) −1.31039 + 2.30670i −0.221496 + 0.389904i
\(36\) 3.08081 3.95639i 0.513469 0.659399i
\(37\) 8.43930 1.38741 0.693706 0.720258i \(-0.255977\pi\)
0.693706 + 0.720258i \(0.255977\pi\)
\(38\) −5.02260 3.57400i −0.814774 0.579779i
\(39\) 1.85596i 0.297191i
\(40\) −4.73963 4.18759i −0.749401 0.662116i
\(41\) 7.40097i 1.15584i 0.816095 + 0.577918i \(0.196135\pi\)
−0.816095 + 0.577918i \(0.803865\pi\)
\(42\) 0.517182 + 1.05821i 0.0798029 + 0.163286i
\(43\) −9.29752 −1.41786 −0.708930 0.705279i \(-0.750822\pi\)
−0.708930 + 0.705279i \(0.750822\pi\)
\(44\) −2.71435 2.11364i −0.409203 0.318644i
\(45\) −2.76919 + 4.87464i −0.412806 + 0.726669i
\(46\) −8.42368 + 4.11691i −1.24200 + 0.607005i
\(47\) 4.10213 0.598357 0.299178 0.954197i \(-0.403287\pi\)
0.299178 + 0.954197i \(0.403287\pi\)
\(48\) −2.72234 + 0.688088i −0.392936 + 0.0993169i
\(49\) −5.59240 −0.798915
\(50\) 5.91993 + 3.86709i 0.837205 + 0.546890i
\(51\) 3.24702 0.454674
\(52\) −3.24871 + 4.17201i −0.450516 + 0.578554i
\(53\) −1.98886 −0.273190 −0.136595 0.990627i \(-0.543616\pi\)
−0.136595 + 0.990627i \(0.543616\pi\)
\(54\) 2.40069 + 4.91209i 0.326693 + 0.668451i
\(55\) 3.34433 + 1.89985i 0.450949 + 0.256175i
\(56\) −0.689751 + 3.28406i −0.0921719 + 0.438850i
\(57\) 2.68861 1.46094i 0.356115 0.193506i
\(58\) −4.67822 9.57217i −0.614280 1.25689i
\(59\) 3.13673 0.408367 0.204183 0.978933i \(-0.434546\pi\)
0.204183 + 0.978933i \(0.434546\pi\)
\(60\) 2.90058 1.20100i 0.374463 0.155049i
\(61\) 3.75579 0.480880 0.240440 0.970664i \(-0.422708\pi\)
0.240440 + 0.970664i \(0.422708\pi\)
\(62\) −13.9522 + 6.81889i −1.77194 + 0.866000i
\(63\) 2.97461 0.374766
\(64\) −7.32402 3.21851i −0.915502 0.402313i
\(65\) 2.92011 5.14031i 0.362194 0.637577i
\(66\) 1.53424 0.749828i 0.188851 0.0922974i
\(67\) 9.50799i 1.16159i −0.814051 0.580793i \(-0.802743\pi\)
0.814051 0.580793i \(-0.197257\pi\)
\(68\) 7.29900 + 5.68367i 0.885133 + 0.689247i
\(69\) 4.65402i 0.560278i
\(70\) 0.232561 3.74458i 0.0277964 0.447563i
\(71\) −9.11343 −1.08157 −0.540783 0.841162i \(-0.681872\pi\)
−0.540783 + 0.841162i \(0.681872\pi\)
\(72\) −1.45762 + 6.94004i −0.171782 + 0.817892i
\(73\) 6.47318i 0.757628i −0.925473 0.378814i \(-0.876332\pi\)
0.925473 0.378814i \(-0.123668\pi\)
\(74\) −10.7229 + 5.24059i −1.24651 + 0.609207i
\(75\) −3.01490 + 1.79724i −0.348131 + 0.207527i
\(76\) 8.60101 + 1.42216i 0.986604 + 0.163133i
\(77\) 2.04078i 0.232569i
\(78\) −1.15250 2.35815i −0.130495 0.267008i
\(79\) −6.38375 −0.718228 −0.359114 0.933294i \(-0.616921\pi\)
−0.359114 + 0.933294i \(0.616921\pi\)
\(80\) 8.62250 + 2.37751i 0.964025 + 0.265813i
\(81\) 4.80774 0.534194
\(82\) −4.59581 9.40357i −0.507523 1.03845i
\(83\) −10.7908 −1.18444 −0.592221 0.805775i \(-0.701749\pi\)
−0.592221 + 0.805775i \(0.701749\pi\)
\(84\) −1.31425 1.02340i −0.143396 0.111662i
\(85\) −8.99304 5.10877i −0.975433 0.554124i
\(86\) 11.8133 5.77353i 1.27386 0.622576i
\(87\) 5.28855 0.566992
\(88\) 4.76133 + 1.00002i 0.507560 + 0.106603i
\(89\) 14.1018i 1.49479i −0.664383 0.747393i \(-0.731305\pi\)
0.664383 0.747393i \(-0.268695\pi\)
\(90\) 0.491461 7.91325i 0.0518045 0.834130i
\(91\) −3.13673 −0.328818
\(92\) 8.14651 10.4618i 0.849333 1.09072i
\(93\) 7.70851i 0.799335i
\(94\) −5.21211 + 2.54732i −0.537588 + 0.262736i
\(95\) −9.74506 0.183919i −0.999822 0.0188697i
\(96\) 3.03169 2.56478i 0.309420 0.261767i
\(97\) 3.39949 0.345166 0.172583 0.984995i \(-0.444789\pi\)
0.172583 + 0.984995i \(0.444789\pi\)
\(98\) 7.10563 3.47274i 0.717777 0.350800i
\(99\) 4.31269i 0.433442i
\(100\) −9.92315 1.23735i −0.992315 0.123735i
\(101\) −2.13821 −0.212760 −0.106380 0.994326i \(-0.533926\pi\)
−0.106380 + 0.994326i \(0.533926\pi\)
\(102\) −4.12562 + 2.01632i −0.408497 + 0.199645i
\(103\) 15.7171i 1.54865i 0.632786 + 0.774327i \(0.281911\pi\)
−0.632786 + 0.774327i \(0.718089\pi\)
\(104\) 1.53706 7.31827i 0.150721 0.717616i
\(105\) 1.61928 + 0.919879i 0.158025 + 0.0897710i
\(106\) 2.52701 1.23503i 0.245445 0.119957i
\(107\) 13.2975i 1.28552i −0.766069 0.642758i \(-0.777790\pi\)
0.766069 0.642758i \(-0.222210\pi\)
\(108\) −6.10057 4.75047i −0.587028 0.457114i
\(109\) 1.70706i 0.163507i 0.996653 + 0.0817535i \(0.0260520\pi\)
−0.996653 + 0.0817535i \(0.973948\pi\)
\(110\) −5.42902 0.337175i −0.517637 0.0321483i
\(111\) 5.92430i 0.562309i
\(112\) −1.16293 4.60100i −0.109886 0.434753i
\(113\) −9.19317 −0.864821 −0.432410 0.901677i \(-0.642337\pi\)
−0.432410 + 0.901677i \(0.642337\pi\)
\(114\) −2.50891 + 3.52581i −0.234981 + 0.330223i
\(115\) −7.32249 + 12.8899i −0.682826 + 1.20199i
\(116\) 11.8882 + 9.25722i 1.10379 + 0.859511i
\(117\) −6.62870 −0.612823
\(118\) −3.98548 + 1.94783i −0.366893 + 0.179312i
\(119\) 5.48775i 0.503061i
\(120\) −2.93964 + 3.32717i −0.268351 + 0.303727i
\(121\) 8.04121 0.731019
\(122\) −4.77206 + 2.33225i −0.432042 + 0.211152i
\(123\) 5.19540 0.468453
\(124\) 13.4932 17.3280i 1.21172 1.55610i
\(125\) 11.1779 0.234124i 0.999781 0.0209407i
\(126\) −3.77950 + 1.84716i −0.336705 + 0.164558i
\(127\) 12.3190i 1.09314i −0.837415 0.546568i \(-0.815934\pi\)
0.837415 0.546568i \(-0.184066\pi\)
\(128\) 11.3044 0.458637i 0.999178 0.0405381i
\(129\) 6.52676i 0.574649i
\(130\) −0.518245 + 8.34452i −0.0454531 + 0.731863i
\(131\) 14.7118i 1.28537i −0.766128 0.642687i \(-0.777819\pi\)
0.766128 0.642687i \(-0.222181\pi\)
\(132\) −1.48375 + 1.90544i −0.129144 + 0.165848i
\(133\) 2.46912 + 4.54399i 0.214100 + 0.394014i
\(134\) 5.90422 + 12.0807i 0.510047 + 1.04362i
\(135\) 7.51647 + 4.26996i 0.646915 + 0.367499i
\(136\) −12.8034 2.68911i −1.09788 0.230589i
\(137\) 3.46578i 0.296101i 0.988980 + 0.148051i \(0.0472999\pi\)
−0.988980 + 0.148051i \(0.952700\pi\)
\(138\) 2.89003 + 5.91333i 0.246015 + 0.503376i
\(139\) 1.06058i 0.0899572i 0.998988 + 0.0449786i \(0.0143220\pi\)
−0.998988 + 0.0449786i \(0.985678\pi\)
\(140\) 2.02980 + 4.90223i 0.171550 + 0.414314i
\(141\) 2.87965i 0.242510i
\(142\) 11.5794 5.65921i 0.971722 0.474910i
\(143\) 4.54773i 0.380300i
\(144\) −2.45756 9.72307i −0.204797 0.810256i
\(145\) −14.6473 8.32085i −1.21639 0.691009i
\(146\) 4.01968 + 8.22473i 0.332671 + 0.680683i
\(147\) 3.92581i 0.323795i
\(148\) 10.3701 13.3173i 0.852413 1.09467i
\(149\) −4.26937 −0.349760 −0.174880 0.984590i \(-0.555954\pi\)
−0.174880 + 0.984590i \(0.555954\pi\)
\(150\) 2.71466 4.15573i 0.221651 0.339314i
\(151\) −4.16229 −0.338722 −0.169361 0.985554i \(-0.554170\pi\)
−0.169361 + 0.985554i \(0.554170\pi\)
\(152\) −11.8115 + 3.53403i −0.958036 + 0.286648i
\(153\) 11.5970i 0.937562i
\(154\) 1.26727 + 2.59299i 0.102120 + 0.208949i
\(155\) −12.1283 + 21.3497i −0.974171 + 1.71485i
\(156\) 2.92871 + 2.28056i 0.234484 + 0.182591i
\(157\) 8.17675i 0.652576i 0.945270 + 0.326288i \(0.105798\pi\)
−0.945270 + 0.326288i \(0.894202\pi\)
\(158\) 8.11110 3.96415i 0.645285 0.315371i
\(159\) 1.39616i 0.110722i
\(160\) −12.4320 + 2.33353i −0.982836 + 0.184481i
\(161\) 7.86569 0.619903
\(162\) −6.10865 + 2.98549i −0.479941 + 0.234562i
\(163\) −5.59539 −0.438265 −0.219132 0.975695i \(-0.570323\pi\)
−0.219132 + 0.975695i \(0.570323\pi\)
\(164\) 11.6788 + 9.09416i 0.911958 + 0.710135i
\(165\) 1.33367 2.34768i 0.103826 0.182767i
\(166\) 13.7106 6.70081i 1.06415 0.520084i
\(167\) 6.53146i 0.505419i 0.967542 + 0.252710i \(0.0813217\pi\)
−0.967542 + 0.252710i \(0.918678\pi\)
\(168\) 2.30537 + 0.484198i 0.177863 + 0.0373567i
\(169\) −6.01004 −0.462311
\(170\) 14.5989 + 0.906677i 1.11968 + 0.0695389i
\(171\) 5.21787 + 9.60260i 0.399020 + 0.734329i
\(172\) −11.4246 + 14.6715i −0.871119 + 1.11869i
\(173\) 14.8750 1.13093 0.565463 0.824774i \(-0.308698\pi\)
0.565463 + 0.824774i \(0.308698\pi\)
\(174\) −6.71956 + 3.28406i −0.509409 + 0.248964i
\(175\) −3.03749 5.09545i −0.229613 0.385180i
\(176\) −6.67068 + 1.68605i −0.502821 + 0.127091i
\(177\) 2.20195i 0.165508i
\(178\) 8.75685 + 17.9175i 0.656354 + 1.34298i
\(179\) −19.7404 −1.47547 −0.737735 0.675091i \(-0.764105\pi\)
−0.737735 + 0.675091i \(0.764105\pi\)
\(180\) 4.28949 + 10.3597i 0.319720 + 0.772163i
\(181\) 15.9415i 1.18492i 0.805598 + 0.592462i \(0.201844\pi\)
−0.805598 + 0.592462i \(0.798156\pi\)
\(182\) 3.98548 1.94783i 0.295423 0.144383i
\(183\) 2.63653i 0.194898i
\(184\) −3.85435 + 18.3514i −0.284146 + 1.35288i
\(185\) −9.32112 + 16.4081i −0.685302 + 1.20635i
\(186\) 4.78679 + 9.79432i 0.350984 + 0.718155i
\(187\) 7.95632 0.581824
\(188\) 5.04061 6.47318i 0.367625 0.472105i
\(189\) 4.58671i 0.333634i
\(190\) 12.4962 5.81775i 0.906566 0.422064i
\(191\) 15.6844i 1.13489i −0.823413 0.567443i \(-0.807933\pi\)
0.823413 0.567443i \(-0.192067\pi\)
\(192\) −2.25936 + 5.14138i −0.163055 + 0.371047i
\(193\) 3.56232 0.256421 0.128211 0.991747i \(-0.459077\pi\)
0.128211 + 0.991747i \(0.459077\pi\)
\(194\) −4.31935 + 2.11100i −0.310111 + 0.151561i
\(195\) −3.60844 2.04988i −0.258406 0.146795i
\(196\) −6.87184 + 8.82484i −0.490845 + 0.630345i
\(197\) 2.70209i 0.192516i −0.995356 0.0962581i \(-0.969313\pi\)
0.995356 0.0962581i \(-0.0306874\pi\)
\(198\) 2.67807 + 5.47965i 0.190322 + 0.389422i
\(199\) 13.1477i 0.932018i −0.884780 0.466009i \(-0.845691\pi\)
0.884780 0.466009i \(-0.154309\pi\)
\(200\) 13.3766 4.58987i 0.945868 0.324553i
\(201\) −6.67450 −0.470783
\(202\) 2.71678 1.32777i 0.191152 0.0934219i
\(203\) 8.93811i 0.627332i
\(204\) 3.98988 5.12381i 0.279347 0.358739i
\(205\) −14.3893 8.17429i −1.00499 0.570917i
\(206\) −9.75993 19.9700i −0.680007 1.39137i
\(207\) 16.6222 1.15532
\(208\) 2.59150 + 10.2530i 0.179688 + 0.710916i
\(209\) 6.58802 3.57981i 0.455703 0.247620i
\(210\) −2.62866 0.163255i −0.181394 0.0112657i
\(211\) −6.41162 −0.441394 −0.220697 0.975342i \(-0.570833\pi\)
−0.220697 + 0.975342i \(0.570833\pi\)
\(212\) −2.44387 + 3.13842i −0.167846 + 0.215548i
\(213\) 6.39753i 0.438351i
\(214\) 8.25740 + 16.8956i 0.564465 + 1.15496i
\(215\) 10.2690 18.0767i 0.700341 1.23282i
\(216\) 10.7012 + 2.24758i 0.728126 + 0.152929i
\(217\) 13.0280 0.884401
\(218\) −1.06004 2.16897i −0.0717952 0.146901i
\(219\) −4.54410 −0.307062
\(220\) 7.10742 2.94287i 0.479182 0.198409i
\(221\) 12.2290i 0.822614i
\(222\) 3.67884 + 7.52733i 0.246908 + 0.505202i
\(223\) 0.157095i 0.0105198i 0.999986 + 0.00525991i \(0.00167429\pi\)
−0.999986 + 0.00525991i \(0.998326\pi\)
\(224\) 4.33470 + 5.12381i 0.289624 + 0.342349i
\(225\) −6.41899 10.7680i −0.427932 0.717865i
\(226\) 11.6807 5.70873i 0.776990 0.379739i
\(227\) 0.135219i 0.00897481i −0.999990 0.00448740i \(-0.998572\pi\)
0.999990 0.00448740i \(-0.00142839\pi\)
\(228\) 0.998343 6.03782i 0.0661169 0.399864i
\(229\) 14.9570 0.988387 0.494193 0.869352i \(-0.335463\pi\)
0.494193 + 0.869352i \(0.335463\pi\)
\(230\) 1.29956 20.9248i 0.0856902 1.37974i
\(231\) −1.43261 −0.0942586
\(232\) −20.8534 4.37985i −1.36909 0.287551i
\(233\) 10.4373i 0.683772i 0.939741 + 0.341886i \(0.111066\pi\)
−0.939741 + 0.341886i \(0.888934\pi\)
\(234\) 8.42233 4.11625i 0.550585 0.269088i
\(235\) −4.53075 + 7.97556i −0.295554 + 0.520268i
\(236\) 3.85435 4.94977i 0.250897 0.322202i
\(237\) 4.48132i 0.291093i
\(238\) −3.40775 6.97266i −0.220892 0.451970i
\(239\) 6.72707i 0.435138i −0.976045 0.217569i \(-0.930187\pi\)
0.976045 0.217569i \(-0.0698127\pi\)
\(240\) 1.66898 6.05290i 0.107732 0.390713i
\(241\) 13.0619i 0.841390i −0.907202 0.420695i \(-0.861786\pi\)
0.907202 0.420695i \(-0.138214\pi\)
\(242\) −10.2170 + 4.99339i −0.656777 + 0.320987i
\(243\) 14.9730i 0.960518i
\(244\) 4.61505 5.92666i 0.295448 0.379416i
\(245\) 6.17675 10.8730i 0.394618 0.694652i
\(246\) −6.60120 + 3.22621i −0.420877 + 0.205696i
\(247\) −5.50224 10.1259i −0.350099 0.644298i
\(248\) −6.38400 + 30.3956i −0.405385 + 1.93012i
\(249\) 7.57502i 0.480047i
\(250\) −14.0571 + 7.23866i −0.889048 + 0.457813i
\(251\) 16.5588i 1.04518i 0.852584 + 0.522591i \(0.175034\pi\)
−0.852584 + 0.522591i \(0.824966\pi\)
\(252\) 3.65514 4.69395i 0.230252 0.295691i
\(253\) 11.4039i 0.716959i
\(254\) 7.64980 + 15.6524i 0.479991 + 0.982117i
\(255\) −3.58630 + 6.31302i −0.224583 + 0.395337i
\(256\) −14.0784 + 7.60249i −0.879902 + 0.475156i
\(257\) −3.05273 −0.190424 −0.0952119 0.995457i \(-0.530353\pi\)
−0.0952119 + 0.995457i \(0.530353\pi\)
\(258\) −4.05295 8.29281i −0.252326 0.516288i
\(259\) 10.0126 0.622151
\(260\) −4.52326 10.9242i −0.280521 0.677493i
\(261\) 18.8885i 1.16917i
\(262\) 9.13565 + 18.6926i 0.564402 + 1.15483i
\(263\) 8.31015 0.512426 0.256213 0.966620i \(-0.417525\pi\)
0.256213 + 0.966620i \(0.417525\pi\)
\(264\) 0.702006 3.34240i 0.0432055 0.205711i
\(265\) 2.19667 3.86683i 0.134940 0.237538i
\(266\) −5.95893 4.24027i −0.365365 0.259988i
\(267\) −9.89929 −0.605827
\(268\) −15.0036 11.6832i −0.916494 0.713667i
\(269\) 2.87965i 0.175575i −0.996139 0.0877876i \(-0.972020\pi\)
0.996139 0.0877876i \(-0.0279797\pi\)
\(270\) −12.2019 0.757809i −0.742582 0.0461188i
\(271\) 9.36177i 0.568687i 0.958722 + 0.284343i \(0.0917756\pi\)
−0.958722 + 0.284343i \(0.908224\pi\)
\(272\) 17.9377 4.53386i 1.08763 0.274906i
\(273\) 2.20195i 0.133268i
\(274\) −2.15216 4.40357i −0.130017 0.266029i
\(275\) −7.38755 + 4.40385i −0.445486 + 0.265562i
\(276\) −7.34406 5.71876i −0.442060 0.344229i
\(277\) 3.82001i 0.229522i 0.993393 + 0.114761i \(0.0366102\pi\)
−0.993393 + 0.114761i \(0.963390\pi\)
\(278\) −0.658593 1.34756i −0.0394998 0.0808212i
\(279\) 27.5316 1.64827
\(280\) −5.62320 4.96825i −0.336051 0.296910i
\(281\) 26.2895i 1.56830i −0.620573 0.784149i \(-0.713100\pi\)
0.620573 0.784149i \(-0.286900\pi\)
\(282\) 1.78819 + 3.65884i 0.106485 + 0.217881i
\(283\) 15.1066 0.897995 0.448997 0.893533i \(-0.351781\pi\)
0.448997 + 0.893533i \(0.351781\pi\)
\(284\) −11.1984 + 14.3810i −0.664503 + 0.853357i
\(285\) −0.129109 + 6.84092i −0.00764775 + 0.405221i
\(286\) −2.82403 5.77828i −0.166988 0.341677i
\(287\) 8.78067i 0.518307i
\(288\) 9.16033 + 10.8279i 0.539777 + 0.638041i
\(289\) −4.39487 −0.258522
\(290\) 23.7777 + 1.47674i 1.39628 + 0.0867171i
\(291\) 2.38641i 0.139894i
\(292\) −10.2147 7.95411i −0.597770 0.465479i
\(293\) −16.8794 −0.986105 −0.493052 0.870000i \(-0.664119\pi\)
−0.493052 + 0.870000i \(0.664119\pi\)
\(294\) −2.43783 4.98808i −0.142177 0.290910i
\(295\) −3.46448 + 6.09858i −0.201710 + 0.355073i
\(296\) −4.90637 + 23.3603i −0.285177 + 1.35779i
\(297\) −6.64997 −0.385870
\(298\) 5.42460 2.65117i 0.314239 0.153578i
\(299\) −17.5281 −1.01368
\(300\) −0.868604 + 6.96594i −0.0501489 + 0.402179i
\(301\) −11.0308 −0.635804
\(302\) 5.28855 2.58468i 0.304322 0.148731i
\(303\) 1.50100i 0.0862302i
\(304\) 12.8129 11.8249i 0.734872 0.678205i
\(305\) −4.14823 + 7.30220i −0.237527 + 0.418123i
\(306\) −7.20145 14.7350i −0.411679 0.842344i
\(307\) 27.0057i 1.54129i −0.637262 0.770647i \(-0.719933\pi\)
0.637262 0.770647i \(-0.280067\pi\)
\(308\) −3.22036 2.50767i −0.183497 0.142888i
\(309\) 11.0332 0.627659
\(310\) 2.15247 34.6580i 0.122252 1.96844i
\(311\) 9.15647i 0.519216i 0.965714 + 0.259608i \(0.0835934\pi\)
−0.965714 + 0.259608i \(0.916407\pi\)
\(312\) −5.13735 1.07900i −0.290845 0.0610863i
\(313\) 10.2932i 0.581805i −0.956753 0.290903i \(-0.906044\pi\)
0.956753 0.290903i \(-0.0939555\pi\)
\(314\) −5.07756 10.3893i −0.286543 0.586301i
\(315\) −3.28542 + 5.78339i −0.185113 + 0.325857i
\(316\) −7.84422 + 10.0736i −0.441272 + 0.566683i
\(317\) −19.0000 −1.06714 −0.533572 0.845754i \(-0.679151\pi\)
−0.533572 + 0.845754i \(0.679151\pi\)
\(318\) −0.866977 1.77394i −0.0486177 0.0994774i
\(319\) 12.9588 0.725551
\(320\) 14.3469 10.6849i 0.802015 0.597304i
\(321\) −9.33469 −0.521012
\(322\) −9.99404 + 4.88439i −0.556946 + 0.272197i
\(323\) −17.7155 + 9.62625i −0.985715 + 0.535619i
\(324\) 5.90766 7.58664i 0.328203 0.421480i
\(325\) 6.76882 + 11.3548i 0.375466 + 0.629852i
\(326\) 7.10943 3.47460i 0.393755 0.192440i
\(327\) 1.19834 0.0662683
\(328\) −20.4861 4.30271i −1.13116 0.237577i
\(329\) 4.86685 0.268318
\(330\) −0.236693 + 3.81111i −0.0130295 + 0.209795i
\(331\) 0.915268 0.0503077 0.0251538 0.999684i \(-0.491992\pi\)
0.0251538 + 0.999684i \(0.491992\pi\)
\(332\) −13.2595 + 17.0279i −0.727710 + 0.934528i
\(333\) 21.1591 1.15951
\(334\) −4.05587 8.29878i −0.221927 0.454089i
\(335\) 18.4859 + 10.5015i 1.00999 + 0.573756i
\(336\) −3.22985 + 0.816362i −0.176203 + 0.0445362i
\(337\) 35.9416 1.95786 0.978932 0.204188i \(-0.0654554\pi\)
0.978932 + 0.204188i \(0.0654554\pi\)
\(338\) 7.63628 3.73209i 0.415359 0.202999i
\(339\) 6.45351i 0.350506i
\(340\) −19.1121 + 7.91351i −1.03650 + 0.429170i
\(341\) 18.8885i 1.02287i
\(342\) −12.5927 8.96077i −0.680937 0.484543i
\(343\) −14.9399 −0.806679
\(344\) 5.40531 25.7359i 0.291435 1.38758i
\(345\) 9.04857 + 5.14031i 0.487158 + 0.276745i
\(346\) −18.9000 + 9.23700i −1.01607 + 0.496584i
\(347\) −0.105896 −0.00568479 −0.00284239 0.999996i \(-0.500905\pi\)
−0.00284239 + 0.999996i \(0.500905\pi\)
\(348\) 6.49847 8.34535i 0.348354 0.447358i
\(349\) −16.2260 −0.868558 −0.434279 0.900778i \(-0.642997\pi\)
−0.434279 + 0.900778i \(0.642997\pi\)
\(350\) 7.02354 + 4.58800i 0.375424 + 0.245239i
\(351\) 10.2211i 0.545564i
\(352\) 7.42868 6.28460i 0.395950 0.334970i
\(353\) 13.2151i 0.703367i −0.936119 0.351683i \(-0.885609\pi\)
0.936119 0.351683i \(-0.114391\pi\)
\(354\) 1.36735 + 2.79776i 0.0726740 + 0.148699i
\(355\) 10.0657 17.7188i 0.534231 0.940415i
\(356\) −22.2527 17.3280i −1.17939 0.918381i
\(357\) 3.85234 0.203887
\(358\) 25.0819 12.2583i 1.32562 0.647872i
\(359\) 5.71624i 0.301692i −0.988557 0.150846i \(-0.951800\pi\)
0.988557 0.150846i \(-0.0481997\pi\)
\(360\) −11.8833 10.4992i −0.626302 0.553355i
\(361\) −10.3377 + 15.9415i −0.544088 + 0.839028i
\(362\) −9.89929 20.2551i −0.520295 1.06458i
\(363\) 5.64484i 0.296277i
\(364\) −3.85435 + 4.94977i −0.202023 + 0.259438i
\(365\) 12.5855 + 7.14955i 0.658753 + 0.374225i
\(366\) 1.63722 + 3.34994i 0.0855787 + 0.175104i
\(367\) 30.6312 1.59893 0.799467 0.600710i \(-0.205115\pi\)
0.799467 + 0.600710i \(0.205115\pi\)
\(368\) −6.49847 25.7105i −0.338756 1.34025i
\(369\) 18.5558i 0.965976i
\(370\) 1.65426 26.6361i 0.0860010 1.38474i
\(371\) −2.35962 −0.122506
\(372\) −12.1641 9.47206i −0.630677 0.491103i
\(373\) 3.34176 0.173030 0.0865150 0.996251i \(-0.472427\pi\)
0.0865150 + 0.996251i \(0.472427\pi\)
\(374\) −10.1092 + 4.94067i −0.522734 + 0.255476i
\(375\) −0.164352 7.84675i −0.00848712 0.405205i
\(376\) −2.38486 + 11.3548i −0.122990 + 0.585580i
\(377\) 19.9179i 1.02582i
\(378\) 2.84823 + 5.82781i 0.146497 + 0.299750i
\(379\) 18.4712 0.948804 0.474402 0.880308i \(-0.342664\pi\)
0.474402 + 0.880308i \(0.342664\pi\)
\(380\) −12.2648 + 15.1518i −0.629169 + 0.777268i
\(381\) −8.64781 −0.443041
\(382\) 9.73964 + 19.9284i 0.498323 + 1.01963i
\(383\) 5.94860i 0.303959i −0.988384 0.151980i \(-0.951435\pi\)
0.988384 0.151980i \(-0.0485648\pi\)
\(384\) −0.321958 7.93557i −0.0164298 0.404960i
\(385\) 3.96779 + 2.25402i 0.202217 + 0.114876i
\(386\) −4.52623 + 2.21211i −0.230379 + 0.112593i
\(387\) −23.3109 −1.18496
\(388\) 4.17723 5.36442i 0.212067 0.272337i
\(389\) −31.9734 −1.62111 −0.810557 0.585660i \(-0.800835\pi\)
−0.810557 + 0.585660i \(0.800835\pi\)
\(390\) 5.85776 + 0.363802i 0.296619 + 0.0184218i
\(391\) 30.6657i 1.55083i
\(392\) 3.25126 15.4800i 0.164213 0.781856i
\(393\) −10.3275 −0.520954
\(394\) 1.67793 + 3.43325i 0.0845330 + 0.172964i
\(395\) 7.05078 12.4116i 0.354763 0.624495i
\(396\) −6.80545 5.29935i −0.341986 0.266302i
\(397\) 17.6776i 0.887212i −0.896222 0.443606i \(-0.853699\pi\)
0.896222 0.443606i \(-0.146301\pi\)
\(398\) 8.16441 + 16.7053i 0.409245 + 0.837363i
\(399\) 3.18983 1.73329i 0.159691 0.0867732i
\(400\) −14.1459 + 14.1384i −0.707296 + 0.706918i
\(401\) 26.2151i 1.30912i 0.756010 + 0.654560i \(0.227146\pi\)
−0.756010 + 0.654560i \(0.772854\pi\)
\(402\) 8.48053 4.14470i 0.422971 0.206719i
\(403\) −29.0320 −1.44619
\(404\) −2.62739 + 3.37410i −0.130718 + 0.167868i
\(405\) −5.31010 + 9.34745i −0.263861 + 0.464479i
\(406\) −5.55034 11.3566i −0.275459 0.563620i
\(407\) 14.5166i 0.719560i
\(408\) −1.88772 + 8.98786i −0.0934562 + 0.444966i
\(409\) 28.4449i 1.40651i 0.710938 + 0.703255i \(0.248271\pi\)
−0.710938 + 0.703255i \(0.751729\pi\)
\(410\) 23.3589 + 1.45073i 1.15361 + 0.0716464i
\(411\) 2.43294 0.120008
\(412\) 24.8017 + 19.3129i 1.22189 + 0.951478i
\(413\) 3.72148 0.183122
\(414\) −21.1199 + 10.3220i −1.03799 + 0.507297i
\(415\) 11.9183 20.9800i 0.585047 1.02987i
\(416\) −9.65956 11.4180i −0.473599 0.559815i
\(417\) 0.744515 0.0364591
\(418\) −6.14768 + 8.63945i −0.300693 + 0.422569i
\(419\) 27.0191i 1.31997i 0.751279 + 0.659985i \(0.229437\pi\)
−0.751279 + 0.659985i \(0.770563\pi\)
\(420\) 3.44131 1.42490i 0.167919 0.0695279i
\(421\) 13.9691i 0.680811i −0.940279 0.340406i \(-0.889436\pi\)
0.940279 0.340406i \(-0.110564\pi\)
\(422\) 8.14651 3.98145i 0.396566 0.193814i
\(423\) 10.2849 0.500069
\(424\) 1.15626 5.50522i 0.0561531 0.267357i
\(425\) 19.8654 11.8421i 0.963615 0.574428i
\(426\) −3.97270 8.12861i −0.192478 0.393833i
\(427\) 4.45596 0.215639
\(428\) −20.9835 16.3397i −1.01428 0.789809i
\(429\) 3.19246 0.154133
\(430\) −1.82249 + 29.3448i −0.0878882 + 1.41513i
\(431\) 1.73199 0.0834270 0.0417135 0.999130i \(-0.486718\pi\)
0.0417135 + 0.999130i \(0.486718\pi\)
\(432\) −14.9925 + 3.78944i −0.721328 + 0.182320i
\(433\) −11.6977 −0.562155 −0.281078 0.959685i \(-0.590692\pi\)
−0.281078 + 0.959685i \(0.590692\pi\)
\(434\) −16.5533 + 8.09009i −0.794582 + 0.388337i
\(435\) −5.84114 + 10.2823i −0.280061 + 0.492996i
\(436\) 2.69375 + 2.09760i 0.129007 + 0.100457i
\(437\) 13.7975 + 25.3919i 0.660023 + 1.21466i
\(438\) 5.77367 2.82177i 0.275877 0.134829i
\(439\) −28.7806 −1.37362 −0.686810 0.726837i \(-0.740990\pi\)
−0.686810 + 0.726837i \(0.740990\pi\)
\(440\) −7.20314 + 8.15270i −0.343396 + 0.388665i
\(441\) −14.0213 −0.667683
\(442\) 7.59392 + 15.5380i 0.361206 + 0.739069i
\(443\) 30.7613 1.46151 0.730756 0.682638i \(-0.239167\pi\)
0.730756 + 0.682638i \(0.239167\pi\)
\(444\) −9.34857 7.27966i −0.443663 0.345477i
\(445\) 27.4174 + 15.5753i 1.29971 + 0.738338i
\(446\) −0.0975518 0.199602i −0.00461921 0.00945144i
\(447\) 2.99705i 0.141756i
\(448\) −8.68937 3.81851i −0.410534 0.180408i
\(449\) 27.7447i 1.30936i −0.755908 0.654678i \(-0.772804\pi\)
0.755908 0.654678i \(-0.227196\pi\)
\(450\) 14.8425 + 9.69562i 0.699683 + 0.457056i
\(451\) 12.7305 0.599456
\(452\) −11.2964 + 14.5069i −0.531338 + 0.682346i
\(453\) 2.92188i 0.137282i
\(454\) 0.0839677 + 0.171808i 0.00394080 + 0.00806333i
\(455\) 3.46448 6.09858i 0.162417 0.285906i
\(456\) 2.48085 + 8.29152i 0.116177 + 0.388286i
\(457\) 32.5891i 1.52445i 0.647311 + 0.762226i \(0.275894\pi\)
−0.647311 + 0.762226i \(0.724106\pi\)
\(458\) −19.0042 + 9.28793i −0.888007 + 0.433996i
\(459\) 17.8820 0.834662
\(460\) 11.3426 + 27.3938i 0.528851 + 1.27724i
\(461\) 8.64842 0.402797 0.201398 0.979509i \(-0.435451\pi\)
0.201398 + 0.979509i \(0.435451\pi\)
\(462\) 1.82025 0.889613i 0.0846857 0.0413885i
\(463\) 18.6070 0.864739 0.432370 0.901697i \(-0.357678\pi\)
0.432370 + 0.901697i \(0.357678\pi\)
\(464\) 29.2159 7.38447i 1.35631 0.342816i
\(465\) 14.9873 + 8.51396i 0.695017 + 0.394825i
\(466\) −6.48131 13.2615i −0.300241 0.614328i
\(467\) −16.9119 −0.782591 −0.391295 0.920265i \(-0.627973\pi\)
−0.391295 + 0.920265i \(0.627973\pi\)
\(468\) −8.14521 + 10.4601i −0.376513 + 0.483519i
\(469\) 11.2805i 0.520884i
\(470\) 0.804094 12.9471i 0.0370901 0.597206i
\(471\) 5.73999 0.264485
\(472\) −1.82360 + 8.68256i −0.0839380 + 0.399647i
\(473\) 15.9928i 0.735350i
\(474\) −2.78279 5.69391i −0.127818 0.261530i
\(475\) 11.1209 18.7437i 0.510262 0.860019i
\(476\) 8.65969 + 6.74324i 0.396916 + 0.309076i
\(477\) −4.98648 −0.228315
\(478\) 4.17734 + 8.54733i 0.191067 + 0.390946i
\(479\) 31.4108i 1.43520i −0.696458 0.717598i \(-0.745242\pi\)
0.696458 0.717598i \(-0.254758\pi\)
\(480\) 1.63811 + 8.72713i 0.0747691 + 0.398337i
\(481\) −22.3123 −1.01735
\(482\) 8.11110 + 16.5963i 0.369451 + 0.755939i
\(483\) 5.52163i 0.251243i
\(484\) 9.88088 12.6891i 0.449131 0.576775i
\(485\) −3.75470 + 6.60946i −0.170492 + 0.300120i
\(486\) 9.29785 + 19.0245i 0.421759 + 0.862968i
\(487\) 19.4993i 0.883599i −0.897114 0.441800i \(-0.854340\pi\)
0.897114 0.441800i \(-0.145660\pi\)
\(488\) −2.18351 + 10.3962i −0.0988428 + 0.470612i
\(489\) 3.92790i 0.177626i
\(490\) −1.09622 + 17.6507i −0.0495220 + 0.797378i
\(491\) 10.3678i 0.467893i −0.972249 0.233947i \(-0.924836\pi\)
0.972249 0.233947i \(-0.0751641\pi\)
\(492\) 6.38400 8.19836i 0.287813 0.369611i
\(493\) −34.8467 −1.56941
\(494\) 13.2790 + 9.44912i 0.597451 + 0.425136i
\(495\) 8.38494 + 4.76332i 0.376875 + 0.214095i
\(496\) −10.7635 42.5846i −0.483295 1.91210i
\(497\) −10.8124 −0.485001
\(498\) −4.70389 9.62471i −0.210787 0.431294i
\(499\) 25.0012i 1.11921i 0.828760 + 0.559604i \(0.189047\pi\)
−0.828760 + 0.559604i \(0.810953\pi\)
\(500\) 13.3657 17.9264i 0.597733 0.801695i
\(501\) 4.58501 0.204843
\(502\) −10.2826 21.0394i −0.458934 0.939033i
\(503\) −17.0206 −0.758909 −0.379454 0.925210i \(-0.623888\pi\)
−0.379454 + 0.925210i \(0.623888\pi\)
\(504\) −1.72935 + 8.23382i −0.0770315 + 0.366764i
\(505\) 2.36163 4.15721i 0.105091 0.184993i
\(506\) 7.08156 + 14.4897i 0.314814 + 0.644145i
\(507\) 4.21899i 0.187372i
\(508\) −19.4395 15.1374i −0.862487 0.671612i
\(509\) 33.2834i 1.47526i −0.675205 0.737630i \(-0.735945\pi\)
0.675205 0.737630i \(-0.264055\pi\)
\(510\) 0.636477 10.2482i 0.0281837 0.453800i
\(511\) 7.67992i 0.339740i
\(512\) 13.1669 18.4020i 0.581901 0.813260i
\(513\) 14.8068 8.04571i 0.653734 0.355227i
\(514\) 3.87875 1.89567i 0.171084 0.0836142i
\(515\) −30.5580 17.3594i −1.34655 0.764946i
\(516\) 10.2993 + 8.01996i 0.453400 + 0.353059i
\(517\) 7.05613i 0.310328i
\(518\) −12.7218 + 6.21756i −0.558966 + 0.273184i
\(519\) 10.4421i 0.458357i
\(520\) 12.5309 + 11.0714i 0.549515 + 0.485512i
\(521\) 24.6478i 1.07984i 0.841717 + 0.539920i \(0.181545\pi\)
−0.841717 + 0.539920i \(0.818455\pi\)
\(522\) −11.7293 23.9995i −0.513376 1.05043i
\(523\) 19.1156i 0.835866i 0.908478 + 0.417933i \(0.137245\pi\)
−0.908478 + 0.417933i \(0.862755\pi\)
\(524\) −23.2153 18.0776i −1.01416 0.789722i
\(525\) −3.57695 + 2.13228i −0.156111 + 0.0930605i
\(526\) −10.5588 + 5.16039i −0.460384 + 0.225004i
\(527\) 50.7919i 2.21253i
\(528\) 1.18359 + 4.68274i 0.0515091 + 0.203790i
\(529\) 20.9537 0.911029
\(530\) −0.389853 + 6.27722i −0.0169341 + 0.272665i
\(531\) 7.86443 0.341287
\(532\) 10.2044 + 1.68729i 0.442418 + 0.0731531i
\(533\) 19.5671i 0.847544i
\(534\) 12.5779 6.14721i 0.544299 0.266016i
\(535\) 25.8536 + 14.6869i 1.11775 + 0.634971i
\(536\) 26.3184 + 5.52767i 1.13678 + 0.238759i
\(537\) 13.8576i 0.597998i
\(538\) 1.78819 + 3.65884i 0.0770943 + 0.157744i
\(539\) 9.61957i 0.414344i
\(540\) 15.9741 6.61419i 0.687416 0.284629i
\(541\) 13.6698 0.587713 0.293856 0.955850i \(-0.405061\pi\)
0.293856 + 0.955850i \(0.405061\pi\)
\(542\) −5.81342 11.8949i −0.249708 0.510931i
\(543\) 11.1908 0.480242
\(544\) −19.9760 + 16.8995i −0.856465 + 0.724562i
\(545\) −3.31895 1.88543i −0.142168 0.0807630i
\(546\) −1.36735 2.79776i −0.0585173 0.119733i
\(547\) 25.5816i 1.09379i 0.837200 + 0.546896i \(0.184191\pi\)
−0.837200 + 0.546896i \(0.815809\pi\)
\(548\) 5.46901 + 4.25868i 0.233625 + 0.181922i
\(549\) 9.41657 0.401889
\(550\) 6.65184 10.1830i 0.283636 0.434203i
\(551\) −28.8539 + 15.6786i −1.22922 + 0.667933i
\(552\) 12.8825 + 2.70571i 0.548314 + 0.115163i
\(553\) −7.57382 −0.322072
\(554\) −2.37213 4.85365i −0.100782 0.206212i
\(555\) 11.5183 + 6.54332i 0.488925 + 0.277748i
\(556\) 1.67360 + 1.30322i 0.0709764 + 0.0552688i
\(557\) 36.7162i 1.55571i −0.628442 0.777857i \(-0.716307\pi\)
0.628442 0.777857i \(-0.283693\pi\)
\(558\) −34.9812 + 17.0964i −1.48087 + 0.723749i
\(559\) 24.5813 1.03968
\(560\) 10.2299 + 2.82073i 0.432293 + 0.119197i
\(561\) 5.58525i 0.235809i
\(562\) 16.3251 + 33.4030i 0.688632 + 1.40902i
\(563\) 0.293515i 0.0123702i 0.999981 + 0.00618509i \(0.00196879\pi\)
−0.999981 + 0.00618509i \(0.998031\pi\)
\(564\) −4.54410 3.53846i −0.191341 0.148996i
\(565\) 10.1538 17.8738i 0.427172 0.751957i
\(566\) −19.1943 + 9.38082i −0.806795 + 0.394305i
\(567\) 5.70401 0.239546
\(568\) 5.29828 25.2263i 0.222311 1.05847i
\(569\) 8.44922i 0.354210i −0.984192 0.177105i \(-0.943327\pi\)
0.984192 0.177105i \(-0.0566732\pi\)
\(570\) −4.08400 8.77216i −0.171060 0.367425i
\(571\) 24.5184i 1.02606i −0.858370 0.513032i \(-0.828522\pi\)
0.858370 0.513032i \(-0.171478\pi\)
\(572\) 7.17634 + 5.58816i 0.300058 + 0.233653i
\(573\) −11.0103 −0.459962
\(574\) −5.45258 11.1566i −0.227586 0.465668i
\(575\) −16.9736 28.4735i −0.707846 1.18743i
\(576\) −18.3629 8.06948i −0.765119 0.336228i
\(577\) 17.9579i 0.747599i 0.927510 + 0.373799i \(0.121945\pi\)
−0.927510 + 0.373799i \(0.878055\pi\)
\(578\) 5.58406 2.72910i 0.232266 0.113516i
\(579\) 2.50071i 0.103926i
\(580\) −31.1287 + 12.8890i −1.29255 + 0.535188i
\(581\) −12.8024 −0.531134
\(582\) 1.48190 + 3.03214i 0.0614267 + 0.125686i
\(583\) 3.42106i 0.141686i
\(584\) 17.9180 + 3.76332i 0.741451 + 0.155727i
\(585\) 7.32132 12.8878i 0.302699 0.532847i
\(586\) 21.4467 10.4817i 0.885956 0.432994i
\(587\) 4.71144 0.194462 0.0972310 0.995262i \(-0.469001\pi\)
0.0972310 + 0.995262i \(0.469001\pi\)
\(588\) 6.19494 + 4.82395i 0.255475 + 0.198936i
\(589\) 22.8529 + 42.0569i 0.941639 + 1.73293i
\(590\) 0.614857 9.90012i 0.0253133 0.407582i
\(591\) −1.89684 −0.0780256
\(592\) −8.27218 32.7280i −0.339984 1.34511i
\(593\) 7.62570i 0.313150i −0.987666 0.156575i \(-0.949955\pi\)
0.987666 0.156575i \(-0.0500453\pi\)
\(594\) 8.44936 4.12946i 0.346681 0.169434i
\(595\) −10.6695 6.06115i −0.437409 0.248483i
\(596\) −5.24612 + 6.73709i −0.214889 + 0.275962i
\(597\) −9.22956 −0.377741
\(598\) 22.2710 10.8845i 0.910727 0.445101i
\(599\) 1.28533 0.0525171 0.0262585 0.999655i \(-0.491641\pi\)
0.0262585 + 0.999655i \(0.491641\pi\)
\(600\) −3.22204 9.39022i −0.131539 0.383354i
\(601\) 35.4629i 1.44656i −0.690554 0.723280i \(-0.742633\pi\)
0.690554 0.723280i \(-0.257367\pi\)
\(602\) 14.0156 6.84984i 0.571232 0.279179i
\(603\) 23.8385i 0.970780i
\(604\) −5.11454 + 6.56811i −0.208108 + 0.267253i
\(605\) −8.88142 + 15.6341i −0.361081 + 0.635617i
\(606\) −0.932083 1.90715i −0.0378633 0.0774727i
\(607\) 15.3707i 0.623877i 0.950102 + 0.311939i \(0.100978\pi\)
−0.950102 + 0.311939i \(0.899022\pi\)
\(608\) −8.93697 + 22.9811i −0.362442 + 0.932006i
\(609\) 6.27445 0.254254
\(610\) 0.736206 11.8540i 0.0298081 0.479956i
\(611\) −10.8454 −0.438759
\(612\) 18.3001 + 14.2502i 0.739739 + 0.576029i
\(613\) 2.12630i 0.0858804i 0.999078 + 0.0429402i \(0.0136725\pi\)
−0.999078 + 0.0429402i \(0.986328\pi\)
\(614\) 16.7698 + 34.3130i 0.676775 + 1.38476i
\(615\) −5.73826 + 10.1011i −0.231389 + 0.407318i
\(616\) 5.64895 + 1.18645i 0.227603 + 0.0478035i
\(617\) 16.3926i 0.659940i −0.943991 0.329970i \(-0.892961\pi\)
0.943991 0.329970i \(-0.107039\pi\)
\(618\) −14.0187 + 6.85137i −0.563914 + 0.275602i
\(619\) 43.4349i 1.74580i −0.487902 0.872898i \(-0.662238\pi\)
0.487902 0.872898i \(-0.337762\pi\)
\(620\) 18.7869 + 45.3727i 0.754499 + 1.82221i
\(621\) 25.6306i 1.02852i
\(622\) −5.68594 11.6341i −0.227985 0.466485i
\(623\) 16.7307i 0.670300i
\(624\) 7.19747 1.81920i 0.288130 0.0728264i
\(625\) −11.8907 + 21.9912i −0.475626 + 0.879647i
\(626\) 6.39181 + 13.0784i 0.255468 + 0.522717i
\(627\) −2.51299 4.62472i −0.100359 0.184694i
\(628\) 12.9030 + 10.0474i 0.514884 + 0.400936i
\(629\) 39.0357i 1.55645i
\(630\) 0.583080 9.38846i 0.0232304 0.374045i
\(631\) 46.6693i 1.85788i 0.370235 + 0.928938i \(0.379277\pi\)
−0.370235 + 0.928938i \(0.620723\pi\)
\(632\) 3.71132 17.6704i 0.147629 0.702892i
\(633\) 4.50088i 0.178894i
\(634\) 24.1411 11.7985i 0.958766 0.468578i
\(635\) 23.9512 + 13.6062i 0.950476 + 0.539946i
\(636\) 2.20314 + 1.71557i 0.0873602 + 0.0680267i
\(637\) 14.7855 0.585822
\(638\) −16.4652 + 8.04707i −0.651865 + 0.318586i
\(639\) −22.8493 −0.903904
\(640\) −11.5939 + 22.4851i −0.458289 + 0.888803i
\(641\) 3.84520i 0.151876i −0.997113 0.0759381i \(-0.975805\pi\)
0.997113 0.0759381i \(-0.0241952\pi\)
\(642\) 11.8605 5.79661i 0.468098 0.228774i
\(643\) 4.94936 0.195184 0.0975919 0.995227i \(-0.468886\pi\)
0.0975919 + 0.995227i \(0.468886\pi\)
\(644\) 9.66521 12.4121i 0.380862 0.489105i
\(645\) −12.6896 7.20873i −0.499654 0.283844i
\(646\) 16.5314 23.2318i 0.650418 0.914045i
\(647\) −5.93211 −0.233215 −0.116608 0.993178i \(-0.537202\pi\)
−0.116608 + 0.993178i \(0.537202\pi\)
\(648\) −2.79508 + 13.3080i −0.109801 + 0.522787i
\(649\) 5.39553i 0.211793i
\(650\) −15.6514 10.2240i −0.613899 0.401019i
\(651\) 9.14554i 0.358442i
\(652\) −6.87551 + 8.82955i −0.269266 + 0.345792i
\(653\) 24.4578i 0.957109i 0.878058 + 0.478555i \(0.158839\pi\)
−0.878058 + 0.478555i \(0.841161\pi\)
\(654\) −1.52259 + 0.744138i −0.0595381 + 0.0290981i
\(655\) 28.6034 + 16.2490i 1.11763 + 0.634901i
\(656\) 28.7013 7.25441i 1.12060 0.283237i
\(657\) 16.2296i 0.633178i
\(658\) −6.18376 + 3.02219i −0.241068 + 0.117817i
\(659\) −43.0449 −1.67679 −0.838395 0.545063i \(-0.816506\pi\)
−0.838395 + 0.545063i \(0.816506\pi\)
\(660\) −2.06587 4.98933i −0.0804137 0.194209i
\(661\) 10.9394i 0.425494i 0.977107 + 0.212747i \(0.0682411\pi\)
−0.977107 + 0.212747i \(0.931759\pi\)
\(662\) −1.16293 + 0.568358i −0.0451985 + 0.0220899i
\(663\) −8.58465 −0.333400
\(664\) 6.27345 29.8693i 0.243457 1.15915i
\(665\) −11.5618 0.218205i −0.448346 0.00846164i
\(666\) −26.8845 + 13.1393i −1.04175 + 0.509137i
\(667\) 49.9463i 1.93393i
\(668\) 10.3067 + 8.02572i 0.398777 + 0.310525i
\(669\) 0.110279 0.00426362
\(670\) −30.0091 1.86374i −1.15935 0.0720027i
\(671\) 6.46040i 0.249401i
\(672\) 3.59686 3.04291i 0.138752 0.117383i
\(673\) −27.0370 −1.04220 −0.521099 0.853496i \(-0.674478\pi\)
−0.521099 + 0.853496i \(0.674478\pi\)
\(674\) −45.6669 + 22.3188i −1.75902 + 0.859689i
\(675\) −16.6037 + 9.89777i −0.639077 + 0.380966i
\(676\) −7.38503 + 9.48388i −0.284039 + 0.364765i
\(677\) −46.8713 −1.80141 −0.900705 0.434432i \(-0.856949\pi\)
−0.900705 + 0.434432i \(0.856949\pi\)
\(678\) −4.00746 8.19974i −0.153906 0.314909i
\(679\) 4.03324 0.154781
\(680\) 19.3695 21.9230i 0.742788 0.840707i
\(681\) −0.0949223 −0.00363743
\(682\) 11.7293 + 23.9995i 0.449137 + 0.918987i
\(683\) 24.4592i 0.935906i −0.883753 0.467953i \(-0.844992\pi\)
0.883753 0.467953i \(-0.155008\pi\)
\(684\) 21.5646 + 3.56566i 0.824542 + 0.136337i
\(685\) −6.73833 3.82791i −0.257458 0.146257i
\(686\) 18.9824 9.27731i 0.724753 0.354209i
\(687\) 10.4997i 0.400587i
\(688\) 9.11341 + 36.0562i 0.347445 + 1.37463i
\(689\) 5.25824 0.200323
\(690\) −14.6890 0.912274i −0.559200 0.0347297i
\(691\) 30.6383i 1.16554i −0.812638 0.582768i \(-0.801969\pi\)
0.812638 0.582768i \(-0.198031\pi\)
\(692\) 18.2781 23.4728i 0.694830 0.892303i
\(693\) 5.11667i 0.194366i
\(694\) 0.134550 0.0657587i 0.00510744 0.00249617i
\(695\) −2.06203 1.17140i −0.0782173 0.0444337i
\(696\) −3.07461 + 14.6389i −0.116543 + 0.554885i
\(697\) −34.2329 −1.29666
\(698\) 20.6166 10.0759i 0.780348 0.381380i
\(699\) 7.32688 0.277128
\(700\) −11.7730 1.46802i −0.444979 0.0554858i
\(701\) 0.610212 0.0230474 0.0115237 0.999934i \(-0.496332\pi\)
0.0115237 + 0.999934i \(0.496332\pi\)
\(702\) −6.34707 12.9868i −0.239555 0.490157i
\(703\) 17.5634 + 32.3225i 0.662417 + 1.21906i
\(704\) −5.53620 + 12.5981i −0.208653 + 0.474810i
\(705\) 5.59875 + 3.18054i 0.210861 + 0.119786i
\(706\) 8.20622 + 16.7909i 0.308845 + 0.631933i
\(707\) −2.53682 −0.0954069
\(708\) −3.47468 2.70571i −0.130587 0.101687i
\(709\) 21.9791 0.825444 0.412722 0.910857i \(-0.364578\pi\)
0.412722 + 0.910857i \(0.364578\pi\)
\(710\) −1.78640 + 28.7638i −0.0670425 + 1.07949i
\(711\) −16.0054 −0.600249
\(712\) 39.0342 + 8.19836i 1.46287 + 0.307247i
\(713\) 72.8010 2.72642
\(714\) −4.89473 + 2.39221i −0.183181 + 0.0895260i
\(715\) −8.84192 5.02292i −0.330669 0.187846i
\(716\) −24.2567 + 31.1505i −0.906514 + 1.16415i
\(717\) −4.72233 −0.176359
\(718\) 3.54964 + 7.26298i 0.132472 + 0.271052i
\(719\) 4.73226i 0.176483i 0.996099 + 0.0882417i \(0.0281248\pi\)
−0.996099 + 0.0882417i \(0.971875\pi\)
\(720\) 21.6184 + 5.96091i 0.805671 + 0.222150i
\(721\) 18.6471i 0.694456i
\(722\) 3.23562 26.6745i 0.120417 0.992723i
\(723\) −9.16930 −0.341010
\(724\) 25.1558 + 19.5886i 0.934908 + 0.728006i
\(725\) 32.3556 19.2878i 1.20166 0.716329i
\(726\) 3.50530 + 7.17226i 0.130094 + 0.266187i
\(727\) −42.9864 −1.59428 −0.797139 0.603795i \(-0.793654\pi\)
−0.797139 + 0.603795i \(0.793654\pi\)
\(728\) 1.82360 8.68256i 0.0675871 0.321797i
\(729\) 3.91236 0.144902
\(730\) −20.4306 1.26886i −0.756171 0.0469628i
\(731\) 43.0053i 1.59061i
\(732\) −4.16045 3.23971i −0.153775 0.119743i
\(733\) 33.6704i 1.24364i 0.783159 + 0.621822i \(0.213607\pi\)
−0.783159 + 0.621822i \(0.786393\pi\)
\(734\) −38.9195 + 19.0212i −1.43655 + 0.702085i
\(735\) −7.63274 4.33601i −0.281538 0.159936i
\(736\) 24.2224 + 28.6320i 0.892850 + 1.05539i
\(737\) −16.3548 −0.602438
\(738\) −11.5227 23.5767i −0.424156 0.867872i
\(739\) 12.2734i 0.451484i 0.974187 + 0.225742i \(0.0724806\pi\)
−0.974187 + 0.225742i \(0.927519\pi\)
\(740\) 14.4385 + 34.8707i 0.530769 + 1.28187i
\(741\) −7.10829 + 3.86251i −0.261130 + 0.141893i
\(742\) 2.99811 1.46527i 0.110064 0.0537916i
\(743\) 4.12811i 0.151446i 0.997129 + 0.0757229i \(0.0241264\pi\)
−0.997129 + 0.0757229i \(0.975874\pi\)
\(744\) 21.3374 + 4.48150i 0.782267 + 0.164300i
\(745\) 4.71547 8.30072i 0.172761 0.304115i
\(746\) −4.24600 + 2.07515i −0.155457 + 0.0759767i
\(747\) −27.0548 −0.989883
\(748\) 9.77657 12.5551i 0.357467 0.459060i
\(749\) 15.7764i 0.576458i
\(750\) 5.08146 + 9.86792i 0.185549 + 0.360326i
\(751\) −41.3777 −1.50989 −0.754947 0.655786i \(-0.772338\pi\)
−0.754947 + 0.655786i \(0.772338\pi\)
\(752\) −4.02089 15.9082i −0.146627 0.580113i
\(753\) 11.6241 0.423605
\(754\) 12.3685 + 25.3074i 0.450435 + 0.921642i
\(755\) 4.59720 8.09253i 0.167309 0.294517i
\(756\) −7.23785 5.63606i −0.263238 0.204982i
\(757\) 18.2143i 0.662011i 0.943629 + 0.331005i \(0.107388\pi\)
−0.943629 + 0.331005i \(0.892612\pi\)
\(758\) −23.4693 + 11.4702i −0.852443 + 0.416615i
\(759\) −8.00544 −0.290579
\(760\) 6.17459 26.8677i 0.223976 0.974595i
\(761\) 47.2371 1.71234 0.856172 0.516691i \(-0.172836\pi\)
0.856172 + 0.516691i \(0.172836\pi\)
\(762\) 10.9878 5.37008i 0.398046 0.194537i
\(763\) 2.02530i 0.0733207i
\(764\) −24.7501 19.2727i −0.895428 0.697263i
\(765\) −22.5475 12.8088i −0.815205 0.463102i
\(766\) 3.69393 + 7.55821i 0.133467 + 0.273089i
\(767\) −8.29304 −0.299444
\(768\) 5.33687 + 9.88290i 0.192578 + 0.356619i
\(769\) 3.39246 0.122335 0.0611676 0.998128i \(-0.480518\pi\)
0.0611676 + 0.998128i \(0.480518\pi\)
\(770\) −6.44111 0.400032i −0.232121 0.0144161i
\(771\) 2.14298i 0.0771775i
\(772\) 4.37730 5.62135i 0.157543 0.202317i
\(773\) 28.9244 1.04034 0.520169 0.854063i \(-0.325869\pi\)
0.520169 + 0.854063i \(0.325869\pi\)
\(774\) 29.6185 14.4755i 1.06461 0.520310i
\(775\) −28.1135 47.1610i −1.00987 1.69407i
\(776\) −1.97637 + 9.40991i −0.0709474 + 0.337796i
\(777\) 7.02872i 0.252154i
\(778\) 40.6249 19.8547i 1.45647 0.711824i
\(779\) −28.3456 + 15.4025i −1.01559 + 0.551851i
\(780\) −7.66870 + 3.17528i −0.274584 + 0.113693i
\(781\) 15.6761i