Properties

Label 380.2.d.b.379.6
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 379.6
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.7

$q$-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} +(2.61068 - 1.78448i) 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} +(-4.42521 + 0.646167i) 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} +(1.25268 + 1.83267i) 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} +(0.265946 + 6.15867i) q^{38} -1.85596i q^{39} +(6.02386 + 1.92693i) 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} +(0.586003 + 7.04674i) 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} +(-0.453602 - 3.10645i) 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} +(-3.09737 + 2.11714i) 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} +(3.48647 - 7.99028i) q^{76} -2.04078i q^{77} +(-1.15250 + 2.35815i) q^{78} +6.38375 q^{79} +(-6.45726 - 6.18900i) 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} +(6.54552 - 4.47406i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} + O(q^{10}) \) \( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96} + O(q^{100}) \)

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 \(0.0649543\pi\)
−0.979252 + 0.202647i \(0.935046\pi\)
\(4\) 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 \(-0.571981\pi\)
−0.224213 + 0.974540i \(0.571981\pi\)
\(8\) −0.581371 2.76803i −0.205546 0.978648i
\(9\) 2.50721 0.835737
\(10\) 2.61068 1.78448i 0.825569 0.564301i
\(11\) 1.72011i 0.518634i 0.965792 + 0.259317i \(0.0834974\pi\)
−0.965792 + 0.259317i \(0.916503\pi\)
\(12\) −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
\(20\) −4.42521 + 0.646167i −0.989507 + 0.144487i
\(21\) 0.832855i 0.181744i
\(22\) 1.06815 2.18555i 0.227730 0.465962i
\(23\) −6.62976 −1.38240 −0.691200 0.722664i \(-0.742918\pi\)
−0.691200 + 0.722664i \(0.742918\pi\)
\(24\) 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 \(0.753414\pi\)
\(30\) 1.25268 + 1.83267i 0.228708 + 0.334598i
\(31\) −10.9809 −1.97224 −0.986118 0.166044i \(-0.946901\pi\)
−0.986118 + 0.166044i \(0.946901\pi\)
\(32\) 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 \(0.255977\pi\)
\(38\) 0.265946 + 6.15867i 0.0431422 + 0.999069i
\(39\) 1.85596i 0.297191i
\(40\) 6.02386 + 1.92693i 0.952456 + 0.304675i
\(41\) 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 \(-0.249178\pi\)
0.708930 + 0.705279i \(0.249178\pi\)
\(44\) −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 \(-0.596713\pi\)
−0.299178 + 0.954197i \(0.596713\pi\)
\(48\) −2.72234 0.688088i −0.392936 0.0993169i
\(49\) −5.59240 −0.798915
\(50\) 0.586003 + 7.04674i 0.0828734 + 0.996560i
\(51\) −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 \(-0.565454\pi\)
−0.204183 + 0.978933i \(0.565454\pi\)
\(60\) −0.453602 3.10645i −0.0585598 0.401041i
\(61\) 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 \(0.197257\pi\)
−0.814051 + 0.580793i \(0.802743\pi\)
\(68\) −7.29900 + 5.68367i −0.885133 + 0.689247i
\(69\) 4.65402i 0.560278i
\(70\) −3.09737 + 2.11714i −0.370206 + 0.253047i
\(71\) 9.11343 1.08157 0.540783 0.841162i \(-0.318128\pi\)
0.540783 + 0.841162i \(0.318128\pi\)
\(72\) −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
\(76\) 3.48647 7.99028i 0.399926 0.916547i
\(77\) 2.04078i 0.232569i
\(78\) −1.15250 + 2.35815i −0.130495 + 0.267008i
\(79\) 6.38375 0.718228 0.359114 0.933294i \(-0.383079\pi\)
0.359114 + 0.933294i \(0.383079\pi\)
\(80\) −6.45726 6.18900i −0.721944 0.691951i
\(81\) 4.80774 0.534194
\(82\) 4.59581 9.40357i 0.507523 1.03845i
\(83\) 10.7908 1.18444 0.592221 0.805775i \(-0.298251\pi\)
0.592221 + 0.805775i \(0.298251\pi\)
\(84\) 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 \(-0.268695\pi\)
\(90\) 6.54552 4.47406i 0.689959 0.471607i
\(91\) 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
\(100\) 3.63128 9.31739i 0.363128 0.931739i
\(101\) −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 \(-0.718089\pi\)
0.632786 0.774327i \(-0.281911\pi\)
\(104\) 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 \(0.222210\pi\)
−0.766069 + 0.642758i \(0.777790\pi\)
\(108\) −6.10057 + 4.75047i −0.587028 + 0.457114i
\(109\) 1.70706i 0.163507i 0.996653 + 0.0817535i \(0.0260520\pi\)
−0.996653 + 0.0817535i \(0.973948\pi\)
\(110\) 3.06950 + 4.49067i 0.292666 + 0.428168i
\(111\) 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 \(0.642337\pi\)
\(114\) −4.32332 + 0.186691i −0.404916 + 0.0174852i
\(115\) 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
\(120\) −1.35268 + 4.22869i −0.123483 + 0.386024i
\(121\) 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 \(0.184066\pi\)
−0.837415 + 0.546568i \(0.815934\pi\)
\(128\) 11.3044 + 0.458637i 0.999178 + 0.0405381i
\(129\) 6.52676i 0.574649i
\(130\) −6.90225 + 4.71789i −0.605367 + 0.413787i
\(131\) 14.7118i 1.28537i 0.766128 + 0.642687i \(0.222181\pi\)
−0.766128 + 0.642687i \(0.777819\pi\)
\(132\) −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 \(-0.985678\pi\)
0.998988 0.0449786i \(-0.0143220\pi\)
\(140\) 5.25017 0.766627i 0.443720 0.0647918i
\(141\) 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 \(0.555954\pi\)
\(150\) −4.94674 + 0.411368i −0.403899 + 0.0335880i
\(151\) 4.16229 0.338722 0.169361 0.985554i \(-0.445830\pi\)
0.169361 + 0.985554i \(0.445830\pi\)
\(152\) −9.39163 + 7.98732i −0.761762 + 0.647857i
\(153\) 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
\(160\) 4.36130 + 11.8735i 0.344791 + 0.938679i
\(161\) 7.86569 0.619903
\(162\) −6.10865 2.98549i −0.479941 0.234562i
\(163\) 5.59539 0.438265 0.219132 0.975695i \(-0.429677\pi\)
0.219132 + 0.975695i \(0.429677\pi\)
\(164\) −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 \(-0.918678\pi\)
0.967542 0.252710i \(-0.0813217\pi\)
\(168\) −2.30537 + 0.484198i −0.177863 + 0.0373567i
\(169\) −6.01004 −0.462311
\(170\) 8.25403 + 12.0756i 0.633055 + 0.926155i
\(171\) −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 \(-0.235895\pi\)
0.737735 + 0.675091i \(0.235895\pi\)
\(180\) −11.0949 + 1.62008i −0.826967 + 0.120753i
\(181\) 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
\(190\) −12.2677 6.28512i −0.889995 0.455971i
\(191\) 15.6844i 1.13489i 0.823413 + 0.567443i \(0.192067\pi\)
−0.823413 + 0.567443i \(0.807933\pi\)
\(192\) −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 \(0.154309\pi\)
−0.884780 + 0.466009i \(0.845691\pi\)
\(200\) −10.3997 + 9.58362i −0.735372 + 0.677664i
\(201\) −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
\(210\) −1.48621 2.17432i −0.102558 0.150042i
\(211\) 6.41162 0.441394 0.220697 0.975342i \(-0.429167\pi\)
0.220697 + 0.975342i \(0.429167\pi\)
\(212\) −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
\(220\) −1.11148 7.61186i −0.0749361 0.513192i
\(221\) 12.2290i 0.822614i
\(222\) 3.67884 7.52733i 0.246908 0.505202i
\(223\) 0.157095i 0.0105198i −0.999986 0.00525991i \(-0.998326\pi\)
0.999986 0.00525991i \(-0.00167429\pi\)
\(224\) −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 \(0.00142839\pi\)
−0.999990 + 0.00448740i \(0.998572\pi\)
\(228\) 5.60909 + 2.44747i 0.371471 + 0.162087i
\(229\) 14.9570 0.988387 0.494193 0.869352i \(-0.335463\pi\)
0.494193 + 0.869352i \(0.335463\pi\)
\(230\) −17.3082 + 11.8306i −1.14127 + 0.780090i
\(231\) 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 \(0.0698127\pi\)
−0.976045 + 0.217569i \(0.930187\pi\)
\(240\) 4.34461 4.53293i 0.280443 0.292599i
\(241\) 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
\(250\) −14.3479 6.64371i −0.907438 0.420185i
\(251\) 16.5588i 1.04518i −0.852584 0.522591i \(-0.824966\pi\)
0.852584 0.522591i \(-0.175034\pi\)
\(252\) −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
\(260\) 11.6996 1.70837i 0.725578 0.105949i
\(261\) 18.8885i 1.16917i
\(262\) 9.13565 18.6926i 0.564402 1.15483i
\(263\) −8.31015 −0.512426 −0.256213 0.966620i \(-0.582475\pi\)
−0.256213 + 0.966620i \(0.582475\pi\)
\(264\) 0.702006 + 3.34240i 0.0432055 + 0.205711i
\(265\) 2.19667 3.86683i 0.134940 0.237538i
\(266\) −0.315524 7.30679i −0.0193460 0.448008i
\(267\) 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 \(-0.0279797\pi\)
\(270\) 6.89879 + 10.0929i 0.419847 + 0.614234i
\(271\) 9.36177i 0.568687i −0.958722 0.284343i \(-0.908224\pi\)
0.958722 0.284343i \(-0.0917756\pi\)
\(272\) −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
\(280\) −7.14685 2.28615i −0.427106 0.136624i
\(281\) 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 \(-0.648219\pi\)
−0.448997 + 0.893533i \(0.648219\pi\)
\(284\) 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
\(290\) 13.4437 + 19.6680i 0.789438 + 1.15494i
\(291\) 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
\(300\) 6.54071 + 2.54912i 0.377628 + 0.147174i
\(301\) −11.0308 −0.635804
\(302\) −5.28855 2.58468i −0.304322 0.148731i
\(303\) 1.50100i 0.0862302i
\(304\) 16.8928 4.31662i 0.968869 0.247575i
\(305\) −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 \(0.280067\pi\)
−0.637262 + 0.770647i \(0.719933\pi\)
\(308\) 3.22036 2.50767i 0.183497 0.142888i
\(309\) 11.0332 0.627659
\(310\) −28.6677 + 19.5953i −1.62822 + 1.11294i
\(311\) 9.15647i 0.519216i −0.965714 0.259608i \(-0.916407\pi\)
0.965714 0.259608i \(-0.0835934\pi\)
\(312\) −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
\(320\) 1.83171 17.7945i 0.102396 0.994744i
\(321\) −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
\(330\) −3.15240 + 2.15476i −0.173534 + 0.118616i
\(331\) −0.915268 −0.0503077 −0.0251538 0.999684i \(-0.508008\pi\)
−0.0251538 + 0.999684i \(0.508008\pi\)
\(332\) 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
\(340\) −2.98882 20.4686i −0.162091 1.11007i
\(341\) 18.8885i 1.02287i
\(342\) 0.666783 + 15.4411i 0.0360555 + 0.834959i
\(343\) 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 \(-0.499095\pi\)
0.00284239 + 0.999996i \(0.499095\pi\)
\(348\) −6.49847 8.34535i −0.348354 0.447358i
\(349\) −16.2260 −0.868558 −0.434279 0.900778i \(-0.642997\pi\)
−0.434279 + 0.900778i \(0.642997\pi\)
\(350\) −0.695247 8.36041i −0.0371625 0.446883i
\(351\) 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 \(0.0481997\pi\)
−0.988557 + 0.150846i \(0.951800\pi\)
\(360\) 15.1031 + 4.83123i 0.796003 + 0.254628i
\(361\) −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 \(-0.794885\pi\)
−0.799467 + 0.600710i \(0.794885\pi\)
\(368\) 6.49847 25.7105i 0.338756 1.34025i
\(369\) 18.5558i 0.965976i
\(370\) 22.0323 15.0597i 1.14541 0.782919i
\(371\) 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 \(-0.657336\pi\)
−0.474402 + 0.880308i \(0.657336\pi\)
\(380\) 11.6843 + 15.6037i 0.599393 + 0.800455i
\(381\) −8.64781 −0.443041
\(382\) 9.73964 19.9284i 0.498323 1.01963i
\(383\) 5.94860i 0.303959i 0.988384 + 0.151980i \(0.0485648\pi\)
−0.988384 + 0.151980i \(0.951435\pi\)
\(384\) −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 \(0.800835\pi\)
\(390\) −3.31191 4.84530i −0.167705 0.245351i
\(391\) 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
\(400\) 19.1649 5.71885i 0.958247 0.285942i
\(401\) 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 \(0.751729\pi\)
\(410\) 13.2069 + 19.3215i 0.652240 + 0.954223i
\(411\) −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
\(418\) −10.5936 + 0.457458i −0.518151 + 0.0223750i
\(419\) 27.0191i 1.31997i −0.751279 0.659985i \(-0.770563\pi\)
0.751279 0.659985i \(-0.229437\pi\)
\(420\) 0.538164 + 3.68556i 0.0262597 + 0.179837i
\(421\) 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
\(430\) 24.2728 16.5912i 1.17054 0.800100i
\(431\) −1.73199 −0.0834270 −0.0417135 0.999130i \(-0.513282\pi\)
−0.0417135 + 0.999130i \(0.513282\pi\)
\(432\) −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 \(-0.259010\pi\)
0.686810 + 0.726837i \(0.259010\pi\)
\(440\) −3.31454 + 10.3617i −0.158015 + 0.493976i
\(441\) −14.0213 −0.667683
\(442\) −7.59392 + 15.5380i −0.361206 + 0.739069i
\(443\) −30.7613 −1.46151 −0.730756 0.682638i \(-0.760833\pi\)
−0.730756 + 0.682638i \(0.760833\pi\)
\(444\) −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 \(-0.227196\pi\)
\(450\) 1.46923 + 17.6677i 0.0692604 + 0.832862i
\(451\) −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
\(456\) −5.60701 6.59282i −0.262572 0.308737i
\(457\) 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
\(460\) 29.3380 4.28393i 1.36789 0.199739i
\(461\) 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 \(-0.642322\pi\)
−0.432370 + 0.901697i \(0.642322\pi\)
\(464\) −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 \(-0.372027\pi\)
0.391295 + 0.920265i \(0.372027\pi\)
\(468\) −8.14521 10.4601i −0.376513 0.483519i
\(469\) 11.2805i 0.520884i
\(470\) −10.7093 + 7.32015i −0.493985 + 0.337653i
\(471\) −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 \(0.254758\pi\)
−0.696458 + 0.717598i \(0.745242\pi\)
\(480\) −8.33504 + 3.06158i −0.380441 + 0.139742i
\(481\) −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 \(0.145660\pi\)
−0.897114 + 0.441800i \(0.854340\pi\)
\(488\) −2.18351 10.3962i −0.0988428 0.470612i
\(489\) 3.92790i 0.177626i
\(490\) −14.6000 + 9.97951i −0.659559 + 0.450828i
\(491\) 10.3678i 0.467893i 0.972249 + 0.233947i \(0.0751641\pi\)
−0.972249 + 0.233947i \(0.924836\pi\)
\(492\) −6.38400 8.19836i −0.287813 0.369611i
\(493\) −34.8467 −1.56941
\(494\) −0.703122 16.2826i −0.0316350 0.732590i
\(495\) −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 \(-0.810953\pi\)
0.828760 0.559604i \(-0.189047\pi\)
\(500\) 14.1046 + 17.3511i 0.630778 + 0.775964i
\(501\) 4.58501 0.204843
\(502\) −10.2826 + 21.0394i −0.458934 + 0.939033i
\(503\) 17.0206 0.758909 0.379454 0.925210i \(-0.376112\pi\)
0.379454 + 0.925210i \(0.376112\pi\)
\(504\) 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 \(-0.264055\pi\)
\(510\) −8.47693 + 5.79424i −0.375365 + 0.256573i
\(511\) 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
\(520\) −15.9262 5.09452i −0.698410 0.223410i
\(521\) 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 \(-0.862755\pi\)
0.908478 0.417933i \(-0.137245\pi\)
\(524\) −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
\(530\) −5.19226 + 3.54907i −0.225538 + 0.154162i
\(531\) −7.86443 −0.341287
\(532\) −4.13643 + 9.47984i −0.179337 + 0.411003i
\(533\) 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
\(540\) −2.49808 17.1079i −0.107500 0.736205i
\(541\) 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 \(-0.815809\pi\)
0.837200 0.546896i \(-0.184191\pi\)
\(548\) −5.46901 + 4.25868i −0.233625 + 0.181922i
\(549\) 9.41657 0.401889
\(550\) −12.1212 + 1.00799i −0.516850 + 0.0429810i
\(551\) 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
\(560\) 7.66104 + 7.34277i 0.323738 + 0.310289i
\(561\) 5.58525i 0.235809i
\(562\) −16.3251 + 33.4030i −0.688632 + 1.40902i
\(563\) 0.293515i 0.0123702i −0.999981 0.00618509i \(-0.998031\pi\)
0.999981 0.00618509i \(-0.00196879\pi\)
\(564\) 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 \(-0.0566732\pi\)
\(570\) 4.41209 8.61181i 0.184802 0.360709i
\(571\) 24.5184i 1.02606i 0.858370 + 0.513032i \(0.171478\pi\)
−0.858370 + 0.513032i \(0.828522\pi\)
\(572\) 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
\(580\) −4.86801 33.3380i −0.202133 1.38429i
\(581\) −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 \(-0.530999\pi\)
−0.0972310 + 0.995262i \(0.530999\pi\)
\(588\) 6.19494 4.82395i 0.255475 0.198936i
\(589\) 22.8529 + 42.0569i 0.941639 + 1.73293i
\(590\) −8.18898 + 5.59741i −0.337135 + 0.230442i
\(591\) 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 \(-0.508359\pi\)
−0.0262585 + 0.999655i \(0.508359\pi\)
\(600\) −6.72759 7.30049i −0.274653 0.298041i
\(601\) 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 \(-0.899022\pi\)
0.950102 0.311939i \(-0.100978\pi\)
\(608\) −24.1443 5.00536i −0.979180 0.202994i
\(609\) 6.27445 0.254254
\(610\) 9.80517 6.70213i 0.397000 0.271361i
\(611\) 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 \(0.337762\pi\)
−0.487902 + 0.872898i \(0.662238\pi\)
\(620\) 48.5930 7.09553i 1.95154 0.284963i
\(621\) 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
\(630\) −7.76575 + 5.30813i −0.309395 + 0.211481i
\(631\) 46.6693i 1.85788i −0.370235 0.928938i \(-0.620723\pi\)
0.370235 0.928938i \(-0.379277\pi\)
\(632\) −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
\(640\) −13.3773 + 21.4720i −0.528784 + 0.848756i
\(641\) 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 \(-0.531114\pi\)
−0.0975919 + 0.995227i \(0.531114\pi\)
\(644\) 9.66521 + 12.4121i 0.380862 + 0.489105i
\(645\) −12.6896 7.20873i −0.499654 0.283844i
\(646\) −28.4867 + 1.23012i −1.12079 + 0.0483985i
\(647\) 5.93211 0.233215 0.116608 0.993178i \(-0.462798\pi\)
0.116608 + 0.993178i \(0.462798\pi\)
\(648\) −2.79508 13.3080i −0.109801 0.522787i
\(649\) 5.39553i 0.211793i
\(650\) −1.54931 18.6306i −0.0607688 0.730750i
\(651\) 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 \(-0.183494\pi\)
0.838395 + 0.545063i \(0.183494\pi\)
\(660\) 5.34345 0.780248i 0.207993 0.0303711i
\(661\) 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
\(670\) 16.9668 + 24.8223i 0.655484 + 0.958969i
\(671\) 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
\(680\) −8.91294 + 27.8631i −0.341796 + 1.06850i
\(681\) −0.0949223 −0.00363743
\(682\) −11.7293 + 23.9995i −0.449137 + 0.918987i
\(683\) 24.4592i 0.935906i 0.883753 + 0.467953i \(0.155008\pi\)
−0.883753 + 0.467953i \(0.844992\pi\)
\(684\) 8.74133 20.0333i 0.334233 0.765993i
\(685\) −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
\(690\) −8.30498 12.1501i −0.316165 0.462548i
\(691\) 30.6383i 1.16554i 0.812638 + 0.582768i \(0.198031\pi\)
−0.812638 + 0.582768i \(0.801969\pi\)
\(692\) 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
\(700\) −4.30823 + 11.0544i −0.162836 + 0.417816i
\(701\) 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 \(0.364578\pi\)
\(710\) 23.7922 16.2627i 0.892907 0.610329i
\(711\) 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 \(-0.971875\pi\)
0.996099 0.0882417i \(-0.0281248\pi\)
\(720\) −16.1897 15.5171i −0.603355 0.578289i
\(721\) 18.6471i 0.694456i
\(722\) 23.0342 13.8357i 0.857244 0.514910i
\(723\) 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 \(-0.206346\pi\)
0.797139 + 0.603795i \(0.206346\pi\)
\(728\) −1.82360 8.68256i −0.0675871 0.321797i
\(729\) 3.91236 0.144902
\(730\) −11.5512 16.8994i −0.427530 0.625474i
\(731\) 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 \(-0.927519\pi\)
0.974187 0.225742i \(-0.0724806\pi\)
\(740\) −37.3457 + 5.45320i −1.37285 + 0.200464i
\(741\) −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 \(-0.975874\pi\)
0.997129 0.0757229i \(-0.0241264\pi\)
\(744\) −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
\(750\) 4.66381 10.0720i 0.170298 0.367779i
\(751\) 41.3777 1.50989 0.754947 0.655786i \(-0.227662\pi\)
0.754947 + 0.655786i \(0.227662\pi\)
\(752\) 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
\(760\) −5.15640 27.0816i −0.187042 0.982352i
\(761\) 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 \(0.480518\pi\)
\(770\) −3.64173 5.32783i −0.131239 0.192001i
\(771\) 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
\(780\) 1.19926 + 8.21299i 0.0429403 + 0.294072i
\(781\)