Properties

Label 261.3.s.a.37.1
Level $261$
Weight $3$
Character 261.37
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 37.1
Character \(\chi\) \(=\) 261.37
Dual form 261.3.s.a.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +O(q^{10})\) \(q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +(-0.373160 - 3.31188i) q^{10} +(6.63034 - 10.5521i) q^{11} +(-3.80625 + 0.868753i) q^{13} +(1.15817 + 3.30986i) q^{14} +(-2.54008 - 11.1288i) q^{16} +(-7.59392 - 7.59392i) q^{17} +(-0.137534 + 0.0154964i) q^{19} +(0.393648 - 1.72469i) q^{20} +(-17.0718 + 13.6143i) q^{22} +(-26.7367 - 12.8757i) q^{23} +(13.3313 - 16.7170i) q^{25} +(6.79757 + 0.765903i) q^{26} +1.86129i q^{28} +(-8.15475 + 27.8298i) q^{29} +(-54.1874 - 18.9610i) q^{31} +(1.62926 - 14.4601i) q^{32} +(8.16437 + 16.9535i) q^{34} +(1.65175 - 3.42989i) q^{35} +(-29.9166 - 47.6121i) q^{37} +(0.236424 + 0.0539622i) q^{38} +(-8.74180 + 13.9125i) q^{40} +(25.9162 - 25.9162i) q^{41} +(5.16003 + 14.7465i) q^{43} +(-10.9397 + 3.82798i) q^{44} +(36.7664 + 36.7664i) q^{46} +(-55.9924 - 35.1824i) q^{47} +(10.0122 - 43.8665i) q^{49} +(-31.7215 + 19.9320i) q^{50} +(3.27134 + 1.57540i) q^{52} +(-29.3541 + 14.1362i) q^{53} +(23.5562 + 2.65415i) q^{55} +(5.70980 - 16.3177i) q^{56} +(29.5914 - 41.3062i) q^{58} -0.396318 q^{59} +(-6.99907 + 62.1184i) q^{61} +(78.6432 + 62.7159i) q^{62} +(-30.8736 + 64.1097i) q^{64} +(-4.63022 - 5.80611i) q^{65} +(-21.7870 - 4.97273i) q^{67} +(1.11828 + 9.92505i) q^{68} +(-4.71654 + 4.71654i) q^{70} +(64.8290 - 14.7968i) q^{71} +(76.3640 - 26.7209i) q^{73} +(21.9237 + 96.0540i) q^{74} +(0.108989 + 0.0684824i) q^{76} +(-24.7846 + 2.79256i) q^{77} +(67.7630 - 42.5783i) q^{79} +(16.9760 - 13.5379i) q^{80} +(-57.8580 + 27.8629i) q^{82} +(68.4247 - 85.8019i) q^{83} +(6.74697 - 19.2817i) q^{85} -27.3741i q^{86} +107.650 q^{88} +(77.7390 + 27.2021i) q^{89} +(6.10889 + 4.87167i) q^{91} +(11.9746 + 24.8656i) q^{92} +(72.2411 + 90.5875i) q^{94} +(-0.140067 - 0.222915i) q^{95} +(19.5392 + 173.415i) q^{97} +(-41.9436 + 66.7529i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65381 0.578694i −0.826906 0.289347i −0.116546 0.993185i \(-0.537182\pi\)
−0.710360 + 0.703838i \(0.751468\pi\)
\(3\) 0 0
\(4\) −0.727117 0.579856i −0.181779 0.144964i
\(5\) 0.825315 + 1.71379i 0.165063 + 0.342757i 0.967051 0.254583i \(-0.0819384\pi\)
−0.801988 + 0.597341i \(0.796224\pi\)
\(6\) 0 0
\(7\) −1.24782 1.56472i −0.178260 0.223531i 0.684671 0.728852i \(-0.259946\pi\)
−0.862932 + 0.505320i \(0.831374\pi\)
\(8\) 4.59573 + 7.31406i 0.574466 + 0.914257i
\(9\) 0 0
\(10\) −0.373160 3.31188i −0.0373160 0.331188i
\(11\) 6.63034 10.5521i 0.602758 0.959284i −0.396392 0.918081i \(-0.629738\pi\)
0.999151 0.0412032i \(-0.0131191\pi\)
\(12\) 0 0
\(13\) −3.80625 + 0.868753i −0.292789 + 0.0668271i −0.366392 0.930460i \(-0.619407\pi\)
0.0736036 + 0.997288i \(0.476550\pi\)
\(14\) 1.15817 + 3.30986i 0.0827265 + 0.236419i
\(15\) 0 0
\(16\) −2.54008 11.1288i −0.158755 0.695550i
\(17\) −7.59392 7.59392i −0.446701 0.446701i 0.447555 0.894256i \(-0.352295\pi\)
−0.894256 + 0.447555i \(0.852295\pi\)
\(18\) 0 0
\(19\) −0.137534 + 0.0154964i −0.00723865 + 0.000815600i −0.115583 0.993298i \(-0.536874\pi\)
0.108344 + 0.994113i \(0.465445\pi\)
\(20\) 0.393648 1.72469i 0.0196824 0.0862343i
\(21\) 0 0
\(22\) −17.0718 + 13.6143i −0.775991 + 0.618832i
\(23\) −26.7367 12.8757i −1.16247 0.559814i −0.249710 0.968321i \(-0.580335\pi\)
−0.912755 + 0.408507i \(0.866050\pi\)
\(24\) 0 0
\(25\) 13.3313 16.7170i 0.533253 0.668678i
\(26\) 6.79757 + 0.765903i 0.261445 + 0.0294578i
\(27\) 0 0
\(28\) 1.86129i 0.0664747i
\(29\) −8.15475 + 27.8298i −0.281198 + 0.959650i
\(30\) 0 0
\(31\) −54.1874 18.9610i −1.74798 0.611645i −0.749264 0.662272i \(-0.769593\pi\)
−0.998718 + 0.0506263i \(0.983878\pi\)
\(32\) 1.62926 14.4601i 0.0509145 0.451879i
\(33\) 0 0
\(34\) 8.16437 + 16.9535i 0.240128 + 0.498632i
\(35\) 1.65175 3.42989i 0.0471928 0.0979968i
\(36\) 0 0
\(37\) −29.9166 47.6121i −0.808558 1.28681i −0.954706 0.297550i \(-0.903831\pi\)
0.146149 0.989263i \(-0.453312\pi\)
\(38\) 0.236424 + 0.0539622i 0.00622167 + 0.00142006i
\(39\) 0 0
\(40\) −8.74180 + 13.9125i −0.218545 + 0.347812i
\(41\) 25.9162 25.9162i 0.632101 0.632101i −0.316493 0.948595i \(-0.602506\pi\)
0.948595 + 0.316493i \(0.102506\pi\)
\(42\) 0 0
\(43\) 5.16003 + 14.7465i 0.120001 + 0.342943i 0.988178 0.153312i \(-0.0489940\pi\)
−0.868177 + 0.496255i \(0.834708\pi\)
\(44\) −10.9397 + 3.82798i −0.248631 + 0.0869996i
\(45\) 0 0
\(46\) 36.7664 + 36.7664i 0.799270 + 0.799270i
\(47\) −55.9924 35.1824i −1.19133 0.748561i −0.217547 0.976050i \(-0.569806\pi\)
−0.973781 + 0.227489i \(0.926948\pi\)
\(48\) 0 0
\(49\) 10.0122 43.8665i 0.204331 0.895234i
\(50\) −31.7215 + 19.9320i −0.634431 + 0.398639i
\(51\) 0 0
\(52\) 3.27134 + 1.57540i 0.0629104 + 0.0302961i
\(53\) −29.3541 + 14.1362i −0.553851 + 0.266720i −0.689806 0.723995i \(-0.742304\pi\)
0.135955 + 0.990715i \(0.456590\pi\)
\(54\) 0 0
\(55\) 23.5562 + 2.65415i 0.428295 + 0.0482572i
\(56\) 5.70980 16.3177i 0.101961 0.291387i
\(57\) 0 0
\(58\) 29.5914 41.3062i 0.510196 0.712176i
\(59\) −0.396318 −0.00671725 −0.00335862 0.999994i \(-0.501069\pi\)
−0.00335862 + 0.999994i \(0.501069\pi\)
\(60\) 0 0
\(61\) −6.99907 + 62.1184i −0.114739 + 1.01834i 0.795984 + 0.605317i \(0.206954\pi\)
−0.910723 + 0.413018i \(0.864475\pi\)
\(62\) 78.6432 + 62.7159i 1.26844 + 1.01155i
\(63\) 0 0
\(64\) −30.8736 + 64.1097i −0.482400 + 1.00171i
\(65\) −4.63022 5.80611i −0.0712341 0.0893247i
\(66\) 0 0
\(67\) −21.7870 4.97273i −0.325179 0.0742199i 0.0568153 0.998385i \(-0.481905\pi\)
−0.381994 + 0.924165i \(0.624763\pi\)
\(68\) 1.11828 + 9.92505i 0.0164454 + 0.145957i
\(69\) 0 0
\(70\) −4.71654 + 4.71654i −0.0673791 + 0.0673791i
\(71\) 64.8290 14.7968i 0.913085 0.208406i 0.259928 0.965628i \(-0.416301\pi\)
0.653157 + 0.757222i \(0.273444\pi\)
\(72\) 0 0
\(73\) 76.3640 26.7209i 1.04608 0.366040i 0.248108 0.968732i \(-0.420191\pi\)
0.797974 + 0.602692i \(0.205905\pi\)
\(74\) 21.9237 + 96.0540i 0.296266 + 1.29803i
\(75\) 0 0
\(76\) 0.108989 + 0.0684824i 0.00143407 + 0.000901084i
\(77\) −24.7846 + 2.79256i −0.321878 + 0.0362670i
\(78\) 0 0
\(79\) 67.7630 42.5783i 0.857759 0.538966i −0.0298547 0.999554i \(-0.509504\pi\)
0.887614 + 0.460588i \(0.152362\pi\)
\(80\) 16.9760 13.5379i 0.212200 0.169224i
\(81\) 0 0
\(82\) −57.8580 + 27.8629i −0.705585 + 0.339792i
\(83\) 68.4247 85.8019i 0.824394 1.03376i −0.174401 0.984675i \(-0.555799\pi\)
0.998795 0.0490825i \(-0.0156297\pi\)
\(84\) 0 0
\(85\) 6.74697 19.2817i 0.0793761 0.226844i
\(86\) 27.3741i 0.318303i
\(87\) 0 0
\(88\) 107.650 1.22330
\(89\) 77.7390 + 27.2021i 0.873472 + 0.305641i 0.729533 0.683945i \(-0.239737\pi\)
0.143939 + 0.989587i \(0.454023\pi\)
\(90\) 0 0
\(91\) 6.10889 + 4.87167i 0.0671306 + 0.0535349i
\(92\) 11.9746 + 24.8656i 0.130159 + 0.270278i
\(93\) 0 0
\(94\) 72.2411 + 90.5875i 0.768522 + 0.963697i
\(95\) −0.140067 0.222915i −0.00147439 0.00234647i
\(96\) 0 0
\(97\) 19.5392 + 173.415i 0.201435 + 1.78778i 0.534794 + 0.844983i \(0.320389\pi\)
−0.333359 + 0.942800i \(0.608182\pi\)
\(98\) −41.9436 + 66.7529i −0.427996 + 0.681152i
\(99\) 0 0
\(100\) −19.3869 + 4.42492i −0.193869 + 0.0442492i
\(101\) 1.74084 + 4.97504i 0.0172360 + 0.0492578i 0.952180 0.305538i \(-0.0988362\pi\)
−0.934944 + 0.354795i \(0.884550\pi\)
\(102\) 0 0
\(103\) −15.5109 67.9577i −0.150591 0.659783i −0.992714 0.120497i \(-0.961551\pi\)
0.842123 0.539286i \(-0.181306\pi\)
\(104\) −23.8466 23.8466i −0.229294 0.229294i
\(105\) 0 0
\(106\) 56.7267 6.39156i 0.535157 0.0602977i
\(107\) −18.2372 + 79.9024i −0.170441 + 0.746751i 0.815377 + 0.578931i \(0.196530\pi\)
−0.985818 + 0.167820i \(0.946327\pi\)
\(108\) 0 0
\(109\) −78.0488 + 62.2418i −0.716044 + 0.571026i −0.912298 0.409527i \(-0.865694\pi\)
0.196254 + 0.980553i \(0.437122\pi\)
\(110\) −37.4216 18.0213i −0.340196 0.163830i
\(111\) 0 0
\(112\) −14.2439 + 17.8613i −0.127178 + 0.159476i
\(113\) −53.9781 6.08187i −0.477683 0.0538219i −0.130159 0.991493i \(-0.541549\pi\)
−0.347524 + 0.937671i \(0.612977\pi\)
\(114\) 0 0
\(115\) 56.4475i 0.490848i
\(116\) 22.0668 15.5070i 0.190231 0.133681i
\(117\) 0 0
\(118\) 0.655435 + 0.229347i 0.00555453 + 0.00194362i
\(119\) −2.40649 + 21.3582i −0.0202226 + 0.179481i
\(120\) 0 0
\(121\) −14.8860 30.9112i −0.123025 0.255464i
\(122\) 47.5227 98.6819i 0.389530 0.808868i
\(123\) 0 0
\(124\) 28.4059 + 45.2078i 0.229080 + 0.364579i
\(125\) 86.0135 + 19.6320i 0.688108 + 0.157056i
\(126\) 0 0
\(127\) 47.8514 76.1551i 0.376783 0.599646i −0.603472 0.797384i \(-0.706217\pi\)
0.980255 + 0.197738i \(0.0633594\pi\)
\(128\) 47.0009 47.0009i 0.367195 0.367195i
\(129\) 0 0
\(130\) 4.29755 + 12.2817i 0.0330581 + 0.0944746i
\(131\) 129.814 45.4240i 0.990949 0.346748i 0.214359 0.976755i \(-0.431234\pi\)
0.776590 + 0.630007i \(0.216948\pi\)
\(132\) 0 0
\(133\) 0.195866 + 0.195866i 0.00147268 + 0.00147268i
\(134\) 33.1539 + 20.8320i 0.247417 + 0.155462i
\(135\) 0 0
\(136\) 20.6428 90.4420i 0.151785 0.665015i
\(137\) −100.340 + 63.0480i −0.732411 + 0.460204i −0.845904 0.533335i \(-0.820939\pi\)
0.113494 + 0.993539i \(0.463796\pi\)
\(138\) 0 0
\(139\) −198.977 95.8224i −1.43149 0.689370i −0.452217 0.891908i \(-0.649367\pi\)
−0.979274 + 0.202538i \(0.935081\pi\)
\(140\) −3.18985 + 1.53615i −0.0227847 + 0.0109725i
\(141\) 0 0
\(142\) −115.778 13.0450i −0.815337 0.0918665i
\(143\) −16.0696 + 45.9242i −0.112375 + 0.321148i
\(144\) 0 0
\(145\) −54.4246 + 8.99291i −0.375342 + 0.0620200i
\(146\) −141.755 −0.970924
\(147\) 0 0
\(148\) −5.85526 + 51.9669i −0.0395626 + 0.351127i
\(149\) −195.444 155.861i −1.31170 1.04605i −0.995241 0.0974435i \(-0.968933\pi\)
−0.316462 0.948605i \(-0.602495\pi\)
\(150\) 0 0
\(151\) 81.6119 169.469i 0.540476 1.12231i −0.434638 0.900605i \(-0.643124\pi\)
0.975114 0.221705i \(-0.0711622\pi\)
\(152\) −0.745412 0.934717i −0.00490402 0.00614945i
\(153\) 0 0
\(154\) 42.6052 + 9.72435i 0.276657 + 0.0631451i
\(155\) −12.2266 108.514i −0.0788815 0.700093i
\(156\) 0 0
\(157\) 25.4802 25.4802i 0.162294 0.162294i −0.621288 0.783582i \(-0.713390\pi\)
0.783582 + 0.621288i \(0.213390\pi\)
\(158\) −136.707 + 31.2025i −0.865235 + 0.197484i
\(159\) 0 0
\(160\) 26.1262 9.14195i 0.163289 0.0571372i
\(161\) 13.2158 + 57.9021i 0.0820856 + 0.359640i
\(162\) 0 0
\(163\) 132.376 + 83.1771i 0.812120 + 0.510289i 0.872921 0.487861i \(-0.162223\pi\)
−0.0608014 + 0.998150i \(0.519366\pi\)
\(164\) −33.8717 + 3.81642i −0.206535 + 0.0232709i
\(165\) 0 0
\(166\) −162.815 + 102.303i −0.980811 + 0.616284i
\(167\) −159.364 + 127.089i −0.954276 + 0.761010i −0.971057 0.238849i \(-0.923230\pi\)
0.0167802 + 0.999859i \(0.494658\pi\)
\(168\) 0 0
\(169\) −138.531 + 66.7130i −0.819709 + 0.394751i
\(170\) −22.3164 + 27.9839i −0.131273 + 0.164611i
\(171\) 0 0
\(172\) 4.79892 13.7145i 0.0279007 0.0797356i
\(173\) 108.217i 0.625531i −0.949830 0.312765i \(-0.898745\pi\)
0.949830 0.312765i \(-0.101255\pi\)
\(174\) 0 0
\(175\) −42.7925 −0.244529
\(176\) −134.274 46.9845i −0.762921 0.266958i
\(177\) 0 0
\(178\) −112.824 89.9742i −0.633843 0.505473i
\(179\) 50.0799 + 103.992i 0.279776 + 0.580961i 0.992746 0.120234i \(-0.0383645\pi\)
−0.712970 + 0.701195i \(0.752650\pi\)
\(180\) 0 0
\(181\) −59.6313 74.7753i −0.329455 0.413123i 0.589324 0.807897i \(-0.299394\pi\)
−0.918778 + 0.394774i \(0.870823\pi\)
\(182\) −7.28374 11.5920i −0.0400206 0.0636924i
\(183\) 0 0
\(184\) −28.7009 254.727i −0.155983 1.38439i
\(185\) 56.9062 90.5657i 0.307601 0.489544i
\(186\) 0 0
\(187\) −130.482 + 29.7817i −0.697766 + 0.159261i
\(188\) 20.3123 + 58.0492i 0.108044 + 0.308772i
\(189\) 0 0
\(190\) 0.102645 + 0.449715i 0.000540234 + 0.00236692i
\(191\) 42.1854 + 42.1854i 0.220866 + 0.220866i 0.808863 0.587997i \(-0.200083\pi\)
−0.587997 + 0.808863i \(0.700083\pi\)
\(192\) 0 0
\(193\) −304.307 + 34.2872i −1.57672 + 0.177654i −0.856521 0.516112i \(-0.827379\pi\)
−0.720201 + 0.693766i \(0.755950\pi\)
\(194\) 68.0401 298.103i 0.350722 1.53661i
\(195\) 0 0
\(196\) −32.7163 + 26.0904i −0.166920 + 0.133114i
\(197\) −66.4296 31.9908i −0.337206 0.162390i 0.257616 0.966247i \(-0.417063\pi\)
−0.594822 + 0.803858i \(0.702777\pi\)
\(198\) 0 0
\(199\) 156.727 196.529i 0.787571 0.987583i −0.212375 0.977188i \(-0.568120\pi\)
0.999946 0.0103945i \(-0.00330874\pi\)
\(200\) 183.536 + 20.6795i 0.917680 + 0.103398i
\(201\) 0 0
\(202\) 9.23519i 0.0457188i
\(203\) 53.7216 21.9668i 0.264638 0.108211i
\(204\) 0 0
\(205\) 65.8037 + 23.0257i 0.320994 + 0.112321i
\(206\) −13.6746 + 121.365i −0.0663815 + 0.589152i
\(207\) 0 0
\(208\) 19.3364 + 40.1524i 0.0929632 + 0.193040i
\(209\) −0.748379 + 1.55403i −0.00358076 + 0.00743553i
\(210\) 0 0
\(211\) 98.3713 + 156.557i 0.466215 + 0.741976i 0.994231 0.107258i \(-0.0342070\pi\)
−0.528017 + 0.849234i \(0.677064\pi\)
\(212\) 29.5408 + 6.74249i 0.139343 + 0.0318042i
\(213\) 0 0
\(214\) 76.3999 121.590i 0.357009 0.568177i
\(215\) −21.0137 + 21.0137i −0.0977383 + 0.0977383i
\(216\) 0 0
\(217\) 37.9476 + 108.448i 0.174874 + 0.499761i
\(218\) 165.097 57.7700i 0.757326 0.265000i
\(219\) 0 0
\(220\) −15.5891 15.5891i −0.0708595 0.0708595i
\(221\) 35.5016 + 22.3072i 0.160641 + 0.100937i
\(222\) 0 0
\(223\) −15.1512 + 66.3816i −0.0679425 + 0.297676i −0.997471 0.0710748i \(-0.977357\pi\)
0.929528 + 0.368750i \(0.120214\pi\)
\(224\) −24.6591 + 15.4943i −0.110085 + 0.0691711i
\(225\) 0 0
\(226\) 85.7502 + 41.2951i 0.379426 + 0.182722i
\(227\) −95.4082 + 45.9461i −0.420300 + 0.202406i −0.632066 0.774915i \(-0.717793\pi\)
0.211766 + 0.977320i \(0.432079\pi\)
\(228\) 0 0
\(229\) 316.964 + 35.7133i 1.38412 + 0.155953i 0.772408 0.635126i \(-0.219052\pi\)
0.611714 + 0.791079i \(0.290480\pi\)
\(230\) −32.6658 + 93.3536i −0.142025 + 0.405885i
\(231\) 0 0
\(232\) −241.026 + 68.2540i −1.03891 + 0.294198i
\(233\) 279.358 1.19896 0.599481 0.800389i \(-0.295374\pi\)
0.599481 + 0.800389i \(0.295374\pi\)
\(234\) 0 0
\(235\) 14.0836 124.995i 0.0599302 0.531896i
\(236\) 0.288169 + 0.229807i 0.00122106 + 0.000973759i
\(237\) 0 0
\(238\) 16.3398 33.9299i 0.0686545 0.142563i
\(239\) 0.0841531 + 0.105525i 0.000352105 + 0.000441525i 0.782008 0.623269i \(-0.214196\pi\)
−0.781655 + 0.623711i \(0.785624\pi\)
\(240\) 0 0
\(241\) 457.706 + 104.468i 1.89919 + 0.433479i 0.999992 0.00405456i \(-0.00129061\pi\)
0.899202 + 0.437533i \(0.144148\pi\)
\(242\) 6.73061 + 59.7358i 0.0278124 + 0.246842i
\(243\) 0 0
\(244\) 41.1089 41.1089i 0.168479 0.168479i
\(245\) 83.4410 19.0449i 0.340575 0.0777341i
\(246\) 0 0
\(247\) 0.510028 0.178467i 0.00206489 0.000722536i
\(248\) −110.349 483.470i −0.444955 1.94947i
\(249\) 0 0
\(250\) −130.889 82.2432i −0.523557 0.328973i
\(251\) 275.015 30.9867i 1.09568 0.123453i 0.454426 0.890785i \(-0.349844\pi\)
0.641251 + 0.767331i \(0.278416\pi\)
\(252\) 0 0
\(253\) −313.140 + 196.759i −1.23771 + 0.777703i
\(254\) −123.208 + 98.2549i −0.485070 + 0.386830i
\(255\) 0 0
\(256\) 151.509 72.9629i 0.591832 0.285011i
\(257\) −256.872 + 322.107i −0.999501 + 1.25333i −0.0322581 + 0.999480i \(0.510270\pi\)
−0.967242 + 0.253854i \(0.918302\pi\)
\(258\) 0 0
\(259\) −37.1689 + 106.223i −0.143509 + 0.410126i
\(260\) 6.90658i 0.0265638i
\(261\) 0 0
\(262\) −240.975 −0.919752
\(263\) −80.4619 28.1548i −0.305939 0.107053i 0.172943 0.984932i \(-0.444672\pi\)
−0.478882 + 0.877879i \(0.658958\pi\)
\(264\) 0 0
\(265\) −48.4528 38.6398i −0.182841 0.145811i
\(266\) −0.210579 0.437272i −0.000791651 0.00164388i
\(267\) 0 0
\(268\) 12.9582 + 16.2491i 0.0483515 + 0.0606309i
\(269\) 190.483 + 303.152i 0.708116 + 1.12696i 0.986064 + 0.166364i \(0.0532026\pi\)
−0.277949 + 0.960596i \(0.589655\pi\)
\(270\) 0 0
\(271\) 6.38164 + 56.6386i 0.0235485 + 0.208999i 0.999977 0.00684439i \(-0.00217865\pi\)
−0.976428 + 0.215843i \(0.930750\pi\)
\(272\) −65.2221 + 103.800i −0.239787 + 0.381619i
\(273\) 0 0
\(274\) 202.429 46.2032i 0.738794 0.168625i
\(275\) −88.0082 251.513i −0.320030 0.914593i
\(276\) 0 0
\(277\) 49.3432 + 216.187i 0.178134 + 0.780458i 0.982491 + 0.186311i \(0.0596531\pi\)
−0.804357 + 0.594147i \(0.797490\pi\)
\(278\) 273.619 + 273.619i 0.984242 + 0.984242i
\(279\) 0 0
\(280\) 32.6774 3.68186i 0.116705 0.0131495i
\(281\) 13.4153 58.7763i 0.0477413 0.209168i −0.945431 0.325821i \(-0.894359\pi\)
0.993173 + 0.116653i \(0.0372164\pi\)
\(282\) 0 0
\(283\) 86.1969 68.7397i 0.304583 0.242897i −0.459256 0.888304i \(-0.651884\pi\)
0.763838 + 0.645408i \(0.223312\pi\)
\(284\) −55.7183 26.8325i −0.196191 0.0944807i
\(285\) 0 0
\(286\) 53.1521 66.6507i 0.185847 0.233044i
\(287\) −72.8903 8.21276i −0.253973 0.0286159i
\(288\) 0 0
\(289\) 173.665i 0.600916i
\(290\) 95.2123 + 16.6226i 0.328318 + 0.0573194i
\(291\) 0 0
\(292\) −71.0198 24.8509i −0.243218 0.0851058i
\(293\) −27.3886 + 243.081i −0.0934766 + 0.829628i 0.856253 + 0.516557i \(0.172786\pi\)
−0.949730 + 0.313071i \(0.898642\pi\)
\(294\) 0 0
\(295\) −0.327087 0.679203i −0.00110877 0.00230238i
\(296\) 210.749 437.624i 0.711989 1.47846i
\(297\) 0 0
\(298\) 233.031 + 370.867i 0.781985 + 1.24452i
\(299\) 112.953 + 25.7807i 0.377768 + 0.0862230i
\(300\) 0 0
\(301\) 16.6354 26.4751i 0.0552671 0.0879570i
\(302\) −233.041 + 233.041i −0.771660 + 0.771660i
\(303\) 0 0
\(304\) 0.521804 + 1.49123i 0.00171646 + 0.00490536i
\(305\) −112.234 + 39.2724i −0.367981 + 0.128762i
\(306\) 0 0
\(307\) −94.4266 94.4266i −0.307579 0.307579i 0.536391 0.843970i \(-0.319787\pi\)
−0.843970 + 0.536391i \(0.819787\pi\)
\(308\) 19.6406 + 12.3410i 0.0637681 + 0.0400682i
\(309\) 0 0
\(310\) −42.5761 + 186.538i −0.137342 + 0.601736i
\(311\) 147.871 92.9137i 0.475471 0.298758i −0.272896 0.962044i \(-0.587981\pi\)
0.748366 + 0.663286i \(0.230839\pi\)
\(312\) 0 0
\(313\) −1.30805 0.629925i −0.00417908 0.00201254i 0.431793 0.901973i \(-0.357881\pi\)
−0.435972 + 0.899960i \(0.643595\pi\)
\(314\) −56.8847 + 27.3942i −0.181161 + 0.0872428i
\(315\) 0 0
\(316\) −73.9609 8.33339i −0.234053 0.0263715i
\(317\) 28.4216 81.2242i 0.0896579 0.256228i −0.890319 0.455336i \(-0.849519\pi\)
0.979977 + 0.199109i \(0.0638047\pi\)
\(318\) 0 0
\(319\) 239.595 + 270.571i 0.751082 + 0.848186i
\(320\) −135.351 −0.422971
\(321\) 0 0
\(322\) 11.6512 103.407i 0.0361838 0.321140i
\(323\) 1.16210 + 0.926746i 0.00359784 + 0.00286918i
\(324\) 0 0
\(325\) −36.2195 + 75.2106i −0.111445 + 0.231417i
\(326\) −170.790 214.164i −0.523897 0.656945i
\(327\) 0 0
\(328\) 308.656 + 70.4487i 0.941024 + 0.214783i
\(329\) 14.8180 + 131.514i 0.0450396 + 0.399738i
\(330\) 0 0
\(331\) 266.303 266.303i 0.804542 0.804542i −0.179260 0.983802i \(-0.557370\pi\)
0.983802 + 0.179260i \(0.0573702\pi\)
\(332\) −99.5055 + 22.7115i −0.299715 + 0.0684080i
\(333\) 0 0
\(334\) 337.104 117.958i 1.00929 0.353167i
\(335\) −9.45893 41.4423i −0.0282356 0.123708i
\(336\) 0 0
\(337\) 298.132 + 187.329i 0.884665 + 0.555872i 0.895995 0.444064i \(-0.146464\pi\)
−0.0113300 + 0.999936i \(0.503607\pi\)
\(338\) 267.711 30.1637i 0.792043 0.0892418i
\(339\) 0 0
\(340\) −16.0865 + 10.1078i −0.0473131 + 0.0297288i
\(341\) −559.360 + 446.075i −1.64035 + 1.30814i
\(342\) 0 0
\(343\) −169.487 + 81.6206i −0.494131 + 0.237961i
\(344\) −84.1429 + 105.512i −0.244601 + 0.306720i
\(345\) 0 0
\(346\) −62.6244 + 178.970i −0.180995 + 0.517255i
\(347\) 641.193i 1.84782i −0.382610 0.923910i \(-0.624975\pi\)
0.382610 0.923910i \(-0.375025\pi\)
\(348\) 0 0
\(349\) −467.597 −1.33982 −0.669910 0.742443i \(-0.733667\pi\)
−0.669910 + 0.742443i \(0.733667\pi\)
\(350\) 70.7708 + 24.7638i 0.202202 + 0.0707536i
\(351\) 0 0
\(352\) −141.782 113.068i −0.402791 0.321215i
\(353\) −89.7057 186.276i −0.254124 0.527694i 0.734408 0.678709i \(-0.237460\pi\)
−0.988531 + 0.151015i \(0.951746\pi\)
\(354\) 0 0
\(355\) 78.8630 + 98.8910i 0.222149 + 0.278566i
\(356\) −40.7521 64.8565i −0.114472 0.182181i
\(357\) 0 0
\(358\) −22.6432 200.964i −0.0632492 0.561353i
\(359\) 93.0423 148.076i 0.259171 0.412468i −0.691639 0.722243i \(-0.743111\pi\)
0.950810 + 0.309775i \(0.100254\pi\)
\(360\) 0 0
\(361\) −351.930 + 80.3258i −0.974876 + 0.222509i
\(362\) 55.3470 + 158.173i 0.152892 + 0.436941i
\(363\) 0 0
\(364\) −1.61700 7.08455i −0.00444231 0.0194630i
\(365\) 108.818 + 108.818i 0.298132 + 0.298132i
\(366\) 0 0
\(367\) −272.112 + 30.6597i −0.741450 + 0.0835413i −0.474606 0.880198i \(-0.657409\pi\)
−0.266844 + 0.963740i \(0.585981\pi\)
\(368\) −75.3781 + 330.253i −0.204832 + 0.897426i
\(369\) 0 0
\(370\) −146.522 + 116.847i −0.396005 + 0.315804i
\(371\) 58.7479 + 28.2915i 0.158350 + 0.0762574i
\(372\) 0 0
\(373\) 30.4398 38.1703i 0.0816080 0.102333i −0.739351 0.673320i \(-0.764868\pi\)
0.820959 + 0.570987i \(0.193439\pi\)
\(374\) 233.028 + 26.2559i 0.623069 + 0.0702030i
\(375\) 0 0
\(376\) 571.220i 1.51920i
\(377\) 6.86181 113.012i 0.0182011 0.299766i
\(378\) 0 0
\(379\) 156.410 + 54.7303i 0.412692 + 0.144407i 0.528636 0.848849i \(-0.322704\pi\)
−0.115944 + 0.993256i \(0.536989\pi\)
\(380\) −0.0274137 + 0.243304i −7.21414e−5 + 0.000640273i
\(381\) 0 0
\(382\) −45.3543 94.1793i −0.118729 0.246543i
\(383\) −70.7762 + 146.968i −0.184794 + 0.383729i −0.972700 0.232067i \(-0.925451\pi\)
0.787906 + 0.615796i \(0.211165\pi\)
\(384\) 0 0
\(385\) −25.2410 40.1708i −0.0655610 0.104340i
\(386\) 523.109 + 119.396i 1.35521 + 0.309317i
\(387\) 0 0
\(388\) 86.3484 137.423i 0.222548 0.354182i
\(389\) 309.216 309.216i 0.794899 0.794899i −0.187387 0.982286i \(-0.560002\pi\)
0.982286 + 0.187387i \(0.0600020\pi\)
\(390\) 0 0
\(391\) 105.259 + 300.814i 0.269205 + 0.769345i
\(392\) 366.855 128.368i 0.935856 0.327470i
\(393\) 0 0
\(394\) 91.3492 + 91.3492i 0.231851 + 0.231851i
\(395\) 128.896 + 80.9907i 0.326319 + 0.205040i
\(396\) 0 0
\(397\) −22.7855 + 99.8297i −0.0573942 + 0.251460i −0.995484 0.0949326i \(-0.969736\pi\)
0.938090 + 0.346393i \(0.112594\pi\)
\(398\) −372.927 + 234.325i −0.937002 + 0.588757i
\(399\) 0 0
\(400\) −219.902 105.899i −0.549756 0.264748i
\(401\) −122.533 + 59.0090i −0.305569 + 0.147155i −0.580384 0.814343i \(-0.697098\pi\)
0.274815 + 0.961497i \(0.411383\pi\)
\(402\) 0 0
\(403\) 222.724 + 25.0949i 0.552664 + 0.0622703i
\(404\) 1.61901 4.62687i 0.00400745 0.0114526i
\(405\) 0 0
\(406\) −101.558 + 5.24061i −0.250142 + 0.0129079i
\(407\) −700.766 −1.72178
\(408\) 0 0
\(409\) −38.6381 + 342.922i −0.0944696 + 0.838441i 0.853719 + 0.520734i \(0.174342\pi\)
−0.948189 + 0.317708i \(0.897087\pi\)
\(410\) −95.5022 76.1604i −0.232932 0.185757i
\(411\) 0 0
\(412\) −28.1274 + 58.4072i −0.0682705 + 0.141765i
\(413\) 0.494534 + 0.620126i 0.00119742 + 0.00150152i
\(414\) 0 0
\(415\) 203.518 + 46.4516i 0.490405 + 0.111932i
\(416\) 6.36087 + 56.4543i 0.0152906 + 0.135707i
\(417\) 0 0
\(418\) 2.13698 2.13698i 0.00511240 0.00511240i
\(419\) −200.129 + 45.6781i −0.477635 + 0.109017i −0.454559 0.890717i \(-0.650203\pi\)
−0.0230758 + 0.999734i \(0.507346\pi\)
\(420\) 0 0
\(421\) −30.0377 + 10.5107i −0.0713485 + 0.0249659i −0.365717 0.930726i \(-0.619176\pi\)
0.294369 + 0.955692i \(0.404891\pi\)
\(422\) −72.0891 315.843i −0.170827 0.748443i
\(423\) 0 0
\(424\) −238.296 149.731i −0.562019 0.353140i
\(425\) −228.184 + 25.7102i −0.536904 + 0.0604946i
\(426\) 0 0
\(427\) 105.932 66.5612i 0.248083 0.155881i
\(428\) 59.5924 47.5234i 0.139235 0.111036i
\(429\) 0 0
\(430\) 46.9133 22.5922i 0.109101 0.0525401i
\(431\) 404.927 507.763i 0.939507 1.17810i −0.0443267 0.999017i \(-0.514114\pi\)
0.983833 0.179087i \(-0.0573143\pi\)
\(432\) 0 0
\(433\) 98.3588 281.093i 0.227156 0.649176i −0.772739 0.634724i \(-0.781114\pi\)
0.999896 0.0144521i \(-0.00460042\pi\)
\(434\) 201.313i 0.463855i
\(435\) 0 0
\(436\) 92.8419 0.212940
\(437\) 3.87674 + 1.35653i 0.00887126 + 0.00310419i
\(438\) 0 0
\(439\) −104.158 83.0632i −0.237262 0.189210i 0.497640 0.867384i \(-0.334200\pi\)
−0.734902 + 0.678174i \(0.762772\pi\)
\(440\) 88.8453 + 184.489i 0.201921 + 0.419294i
\(441\) 0 0
\(442\) −45.8040 57.4364i −0.103629 0.129947i
\(443\) 174.139 + 277.141i 0.393091 + 0.625601i 0.983373 0.181596i \(-0.0581263\pi\)
−0.590282 + 0.807197i \(0.700983\pi\)
\(444\) 0 0
\(445\) 17.5407 + 155.678i 0.0394174 + 0.349839i
\(446\) 63.4719 101.015i 0.142314 0.226491i
\(447\) 0 0
\(448\) 138.839 31.6890i 0.309908 0.0707344i
\(449\) −73.6423 210.458i −0.164014 0.468725i 0.832318 0.554299i \(-0.187013\pi\)
−0.996332 + 0.0855735i \(0.972728\pi\)
\(450\) 0 0
\(451\) −101.638 445.303i −0.225361 0.987369i
\(452\) 35.7218 + 35.7218i 0.0790305 + 0.0790305i
\(453\) 0 0
\(454\) 184.376 20.7742i 0.406114 0.0457581i
\(455\) −3.30724 + 14.4900i −0.00726867 + 0.0318461i
\(456\) 0 0
\(457\) −606.218 + 483.443i −1.32652 + 1.05786i −0.333150 + 0.942874i \(0.608112\pi\)
−0.993367 + 0.114988i \(0.963317\pi\)
\(458\) −503.532 242.488i −1.09941 0.529450i
\(459\) 0 0
\(460\) −32.7314 + 41.0439i −0.0711553 + 0.0892259i
\(461\) 485.426 + 54.6943i 1.05298 + 0.118643i 0.621450 0.783454i \(-0.286544\pi\)
0.431534 + 0.902097i \(0.357973\pi\)
\(462\) 0 0
\(463\) 770.815i 1.66483i −0.554155 0.832414i \(-0.686958\pi\)
0.554155 0.832414i \(-0.313042\pi\)
\(464\) 330.426 + 20.0627i 0.712126 + 0.0432386i
\(465\) 0 0
\(466\) −462.006 161.663i −0.991429 0.346916i
\(467\) −93.5969 + 830.696i −0.200422 + 1.77879i 0.343003 + 0.939334i \(0.388556\pi\)
−0.543425 + 0.839458i \(0.682873\pi\)
\(468\) 0 0
\(469\) 19.4053 + 40.2956i 0.0413760 + 0.0859182i
\(470\) −95.6258 + 198.569i −0.203459 + 0.422487i
\(471\) 0 0
\(472\) −1.82137 2.89869i −0.00385883 0.00614129i
\(473\) 189.820 + 43.3252i 0.401311 + 0.0915966i
\(474\) 0 0
\(475\) −1.57446 + 2.50574i −0.00331466 + 0.00527525i
\(476\) 14.1345 14.1345i 0.0296943 0.0296943i
\(477\) 0 0
\(478\) −0.0781069 0.223217i −0.000163404 0.000466981i
\(479\) 701.949 245.623i 1.46545 0.512782i 0.524522 0.851397i \(-0.324244\pi\)
0.940925 + 0.338615i \(0.109958\pi\)
\(480\) 0 0
\(481\) 155.233 + 155.233i 0.322731 + 0.322731i
\(482\) −696.504 437.643i −1.44503 0.907972i
\(483\) 0 0
\(484\) −7.10015 + 31.1078i −0.0146697 + 0.0642723i
\(485\) −281.070 + 176.608i −0.579526 + 0.364140i
\(486\) 0 0
\(487\) −808.881 389.537i −1.66095 0.799870i −0.998721 0.0505653i \(-0.983898\pi\)
−0.662226 0.749304i \(-0.730388\pi\)
\(488\) −486.504 + 234.288i −0.996934 + 0.480098i
\(489\) 0 0
\(490\) −149.017 16.7902i −0.304116 0.0342657i
\(491\) −144.911 + 414.132i −0.295135 + 0.843446i 0.696865 + 0.717203i \(0.254578\pi\)
−0.991999 + 0.126244i \(0.959708\pi\)
\(492\) 0 0
\(493\) 273.264 149.411i 0.554288 0.303065i
\(494\) −0.946768 −0.00191653
\(495\) 0 0
\(496\) −73.3730 + 651.204i −0.147929 + 1.31291i
\(497\) −104.048 82.9755i −0.209352 0.166953i
\(498\) 0 0
\(499\) 275.489 572.059i 0.552082 1.14641i −0.419071 0.907954i \(-0.637644\pi\)
0.971153 0.238457i \(-0.0766416\pi\)
\(500\) −51.1581 64.1502i −0.102316 0.128300i
\(501\) 0 0
\(502\) −472.755 107.903i −0.941743 0.214947i
\(503\) −87.3784 775.505i −0.173714 1.54176i −0.713921 0.700226i \(-0.753083\pi\)
0.540207 0.841532i \(-0.318346\pi\)
\(504\) 0 0
\(505\) −7.08940 + 7.08940i −0.0140384 + 0.0140384i
\(506\) 631.738 144.190i 1.24849 0.284960i
\(507\) 0 0
\(508\) −78.9526 + 27.6267i −0.155418 + 0.0543833i
\(509\) 219.690 + 962.525i 0.431611 + 1.89101i 0.453511 + 0.891251i \(0.350171\pi\)
−0.0218997 + 0.999760i \(0.506971\pi\)
\(510\) 0 0
\(511\) −137.099 86.1453i −0.268296 0.168582i
\(512\) −556.996 + 62.7584i −1.08788 + 0.122575i
\(513\) 0 0
\(514\) 611.219 384.054i 1.18914 0.747187i
\(515\) 103.663 82.6688i 0.201288 0.160522i
\(516\) 0 0
\(517\) −742.497 + 357.568i −1.43617 + 0.691621i
\(518\) 122.941 154.163i 0.237337 0.297612i
\(519\) 0 0
\(520\) 21.1870 60.5490i 0.0407442 0.116440i
\(521\) 535.964i 1.02872i −0.857574 0.514361i \(-0.828029\pi\)
0.857574 0.514361i \(-0.171971\pi\)
\(522\) 0 0
\(523\) 915.345 1.75018 0.875091 0.483959i \(-0.160801\pi\)
0.875091 + 0.483959i \(0.160801\pi\)
\(524\) −120.729 42.2451i −0.230400 0.0806204i
\(525\) 0 0
\(526\) 116.776 + 93.1257i 0.222007 + 0.177045i
\(527\) 267.507 + 555.483i 0.507603 + 1.05405i
\(528\) 0 0
\(529\) 219.241 + 274.920i 0.414445 + 0.519697i
\(530\) 57.7712 + 91.9423i 0.109002 + 0.173476i
\(531\) 0 0
\(532\) −0.0288433 0.255991i −5.42167e−5 0.000481187i
\(533\) −76.1287 + 121.158i −0.142831 + 0.227314i
\(534\) 0 0
\(535\) −151.987 + 34.6900i −0.284088 + 0.0648412i
\(536\) −63.7561 182.205i −0.118948 0.339934i
\(537\) 0 0
\(538\) −139.591 611.588i −0.259463 1.13678i
\(539\) −396.500 396.500i −0.735622 0.735622i
\(540\) 0 0
\(541\) 28.3793 3.19758i 0.0524572 0.00591051i −0.0856969 0.996321i \(-0.527312\pi\)
0.138154 + 0.990411i \(0.455883\pi\)
\(542\) 22.2224 97.3627i 0.0410007 0.179636i
\(543\) 0 0
\(544\) −122.181 + 97.4365i −0.224598 + 0.179111i
\(545\) −171.084 82.3897i −0.313916 0.151174i
\(546\) 0 0
\(547\) −73.0250 + 91.5704i −0.133501 + 0.167405i −0.844088 0.536204i \(-0.819858\pi\)
0.710588 + 0.703609i \(0.248429\pi\)
\(548\) 109.518 + 12.3397i 0.199850 + 0.0225177i
\(549\) 0 0
\(550\) 466.885i 0.848882i
\(551\) 0.690296 3.95393i 0.00125281 0.00717591i
\(552\) 0 0
\(553\) −151.179 52.8999i −0.273380 0.0956599i
\(554\) 43.5016 386.087i 0.0785227 0.696908i
\(555\) 0 0
\(556\) 89.1165 + 185.052i 0.160281 + 0.332828i
\(557\) 376.472 781.753i 0.675893 1.40351i −0.227109 0.973869i \(-0.572927\pi\)
0.903002 0.429636i \(-0.141358\pi\)
\(558\) 0 0
\(559\) −32.4515 51.6462i −0.0580527 0.0923904i
\(560\) −42.3661 9.66979i −0.0756538 0.0172675i
\(561\) 0 0
\(562\) −56.1999 + 89.4416i −0.0999998 + 0.159149i
\(563\) −66.7692 + 66.7692i −0.118595 + 0.118595i −0.763914 0.645318i \(-0.776725\pi\)
0.645318 + 0.763914i \(0.276725\pi\)
\(564\) 0 0
\(565\) −34.1260 97.5264i −0.0603999 0.172613i
\(566\) −182.333 + 63.8010i −0.322143 + 0.112723i
\(567\) 0 0
\(568\) 406.161 + 406.161i 0.715073 + 0.715073i
\(569\) −586.687 368.640i −1.03108 0.647873i −0.0934960 0.995620i \(-0.529804\pi\)
−0.937589 + 0.347746i \(0.886947\pi\)
\(570\) 0 0
\(571\) 122.100 534.957i 0.213836 0.936877i −0.748096 0.663590i \(-0.769032\pi\)
0.961933 0.273287i \(-0.0881109\pi\)
\(572\) 38.3139 24.0742i 0.0669823 0.0420878i
\(573\) 0 0
\(574\) 115.794 + 55.7635i 0.201732 + 0.0971490i
\(575\) −571.679 + 275.306i −0.994224 + 0.478793i
\(576\) 0 0
\(577\) 377.501 + 42.5342i 0.654248 + 0.0737161i 0.432848 0.901467i \(-0.357509\pi\)
0.221400 + 0.975183i \(0.428937\pi\)
\(578\) −100.499 + 287.209i −0.173873 + 0.496901i
\(579\) 0 0
\(580\) 44.7876 + 25.0196i 0.0772201 + 0.0431372i
\(581\) −219.638 −0.378034
\(582\) 0 0
\(583\) −45.4608 + 403.476i −0.0779774 + 0.692068i
\(584\) 546.386 + 435.728i 0.935593 + 0.746110i
\(585\) 0 0
\(586\) 185.965 386.161i 0.317347 0.658977i
\(587\) −227.442 285.204i −0.387466 0.485867i 0.549398 0.835561i \(-0.314857\pi\)
−0.936864 + 0.349694i \(0.886286\pi\)
\(588\) 0 0
\(589\) 7.74646 + 1.76808i 0.0131519 + 0.00300183i
\(590\) 0.147890 + 1.31256i 0.000250661 + 0.00222468i
\(591\) 0 0
\(592\) −453.875 + 453.875i −0.766680 + 0.766680i
\(593\) 79.2074 18.0786i 0.133571 0.0304866i −0.155213 0.987881i \(-0.549606\pi\)
0.288784 + 0.957394i \(0.406749\pi\)
\(594\) 0 0
\(595\) −38.5895 + 13.5031i −0.0648564 + 0.0226942i
\(596\) 51.7333 + 226.659i 0.0868009 + 0.380300i
\(597\) 0 0
\(598\) −171.883 108.001i −0.287430 0.180604i
\(599\) −110.418 + 12.4411i −0.184337 + 0.0207698i −0.203650 0.979044i \(-0.565281\pi\)
0.0193132 + 0.999813i \(0.493852\pi\)
\(600\) 0 0
\(601\) −240.700 + 151.242i −0.400499 + 0.251650i −0.717189 0.696879i \(-0.754571\pi\)
0.316690 + 0.948529i \(0.397429\pi\)
\(602\) −42.8328 + 34.1580i −0.0711508 + 0.0567409i
\(603\) 0 0
\(604\) −157.609 + 75.9005i −0.260942 + 0.125663i
\(605\) 40.6895 51.0230i 0.0672553 0.0843355i
\(606\) 0 0
\(607\) −103.263 + 295.109i −0.170120 + 0.486176i −0.997104 0.0760501i \(-0.975769\pi\)
0.826984 + 0.562226i \(0.190055\pi\)
\(608\) 2.01401i 0.00331252i
\(609\) 0 0
\(610\) 208.341 0.341542
\(611\) 243.686 + 85.2694i 0.398832 + 0.139557i
\(612\) 0 0
\(613\) −109.428 87.2662i −0.178513 0.142359i 0.530157 0.847899i \(-0.322133\pi\)
−0.708670 + 0.705540i \(0.750704\pi\)
\(614\) 101.520 + 210.808i 0.165342 + 0.343336i
\(615\) 0 0
\(616\) −134.328 168.442i −0.218065 0.273445i
\(617\) 530.280 + 843.935i 0.859448 + 1.36780i 0.928943 + 0.370222i \(0.120718\pi\)
−0.0694948 + 0.997582i \(0.522139\pi\)
\(618\) 0 0
\(619\) 2.68832 + 23.8595i 0.00434301 + 0.0385452i 0.995697 0.0926708i \(-0.0295404\pi\)
−0.991354 + 0.131216i \(0.958112\pi\)
\(620\) −54.0326 + 85.9923i −0.0871493 + 0.138697i
\(621\) 0 0
\(622\) −298.320 + 68.0896i −0.479614 + 0.109469i
\(623\) −54.4409 155.583i −0.0873851 0.249732i
\(624\) 0 0
\(625\) −81.6042 357.531i −0.130567 0.572050i
\(626\) 1.79874 + 1.79874i 0.00287339 + 0.00287339i
\(627\) 0 0
\(628\) −33.3019 + 3.75222i −0.0530285 + 0.00597488i
\(629\) −134.378 + 588.747i −0.213637 + 0.936005i
\(630\) 0 0
\(631\) −198.431 + 158.243i −0.314470 + 0.250782i −0.767986 0.640467i \(-0.778741\pi\)
0.453516 + 0.891248i \(0.350170\pi\)
\(632\) 622.840 + 299.944i 0.985507 + 0.474595i
\(633\) 0 0
\(634\) −94.0079 + 117.882i −0.148277 + 0.185934i
\(635\) 170.006 + 19.1551i 0.267726 + 0.0301655i
\(636\) 0 0
\(637\) 175.665i 0.275769i
\(638\) −239.668 586.127i −0.375655 0.918694i
\(639\) 0 0
\(640\) 119.340 + 41.7589i 0.186469 + 0.0652483i
\(641\) 38.2084 339.109i 0.0596075 0.529031i −0.928056 0.372440i \(-0.878521\pi\)
0.987664 0.156591i \(-0.0500503\pi\)
\(642\) 0 0
\(643\) 251.743 + 522.750i 0.391513 + 0.812985i 0.999814 + 0.0192789i \(0.00613705\pi\)
−0.608301 + 0.793706i \(0.708149\pi\)
\(644\) 23.9655 49.7648i 0.0372135 0.0772746i
\(645\) 0 0
\(646\) −1.38560 2.20517i −0.00214489 0.00341357i
\(647\) 442.664 + 101.035i 0.684179 + 0.156160i 0.550462 0.834860i \(-0.314451\pi\)
0.133717 + 0.991020i \(0.457309\pi\)
\(648\) 0 0
\(649\) −2.62772 + 4.18199i −0.00404888 + 0.00644375i
\(650\) 103.424 103.424i 0.159114 0.159114i
\(651\) 0 0
\(652\) −48.0217 137.238i −0.0736529 0.210488i
\(653\) 551.878 193.110i 0.845142 0.295728i 0.127240 0.991872i \(-0.459388\pi\)
0.717902 + 0.696144i \(0.245102\pi\)
\(654\) 0 0
\(655\) 184.985 + 184.985i 0.282419 + 0.282419i
\(656\) −354.245 222.587i −0.540007 0.339309i
\(657\) 0 0
\(658\) 51.6000 226.074i 0.0784194 0.343578i
\(659\) −761.337 + 478.379i −1.15529 + 0.725917i −0.966643 0.256128i \(-0.917553\pi\)
−0.188648 + 0.982045i \(0.560410\pi\)
\(660\) 0 0
\(661\) 992.160 + 477.799i 1.50100 + 0.722843i 0.990561 0.137072i \(-0.0437693\pi\)
0.510437 + 0.859915i \(0.329484\pi\)
\(662\) −594.524 + 286.308i −0.898073 + 0.432489i
\(663\) 0 0
\(664\) 942.021 + 106.140i 1.41871 + 0.159850i
\(665\) −0.174021 + 0.497323i −0.000261686 + 0.000747855i
\(666\) 0 0
\(667\) 576.360 639.080i 0.864109 0.958141i
\(668\) 189.569 0.283787
\(669\) 0 0
\(670\) −8.33910 + 74.0116i −0.0124464 + 0.110465i
\(671\) 609.076 + 485.722i 0.907713 + 0.723877i
\(672\) 0 0
\(673\) −231.236 + 480.167i −0.343590 + 0.713473i −0.999131 0.0416874i \(-0.986727\pi\)
0.655540 + 0.755160i \(0.272441\pi\)
\(674\) −384.649 482.334i −0.570695 0.715629i
\(675\) 0 0
\(676\) 139.412 + 31.8199i 0.206231 + 0.0470708i
\(677\) 0.426844 + 3.78834i 0.000630493 + 0.00559578i 0.994024 0.109166i \(-0.0348181\pi\)
−0.993393 + 0.114762i \(0.963389\pi\)
\(678\) 0 0
\(679\) 246.964 246.964i 0.363718 0.363718i
\(680\) 172.035 39.2659i 0.252993 0.0577439i
\(681\) 0 0
\(682\) 1183.22 414.026i 1.73492 0.607076i
\(683\) −122.389 536.221i −0.179193 0.785096i −0.982004 0.188862i \(-0.939520\pi\)
0.802810 0.596234i \(-0.203337\pi\)
\(684\) 0 0
\(685\) −190.863 119.927i −0.278632 0.175076i
\(686\) 327.533 36.9041i 0.477453 0.0537961i
\(687\) 0 0
\(688\) 151.004 94.8823i 0.219483 0.137910i
\(689\) 99.4483 79.3073i 0.144337 0.115105i
\(690\) 0 0
\(691\) 689.611 332.099i 0.997990 0.480606i 0.137734 0.990469i \(-0.456018\pi\)
0.860256 + 0.509863i \(0.170304\pi\)
\(692\) −62.7502 + 78.6862i −0.0906795 + 0.113708i
\(693\) 0 0
\(694\) −371.055 + 1060.41i −0.534661 + 1.52797i
\(695\) 420.088i 0.604443i
\(696\) 0 0
\(697\) −393.610 −0.564721
\(698\) 773.318 + 270.596i 1.10790 + 0.387673i
\(699\) 0 0
\(700\) 31.1151 + 24.8135i 0.0444502 + 0.0354479i
\(701\) −391.731 813.437i −0.558817 1.16040i −0.968695 0.248255i \(-0.920143\pi\)
0.409878 0.912141i \(-0.365571\pi\)
\(702\) 0 0
\(703\) 4.85238 + 6.08469i 0.00690239 + 0.00865532i
\(704\) 471.791 + 750.852i 0.670158 + 1.06655i
\(705\) 0 0
\(706\) 40.5597 + 359.978i 0.0574500 + 0.509883i
\(707\) 5.61228 8.93189i 0.00793816 0.0126335i
\(708\) 0 0
\(709\) 1016.73 232.062i 1.43403 0.327309i 0.566243 0.824238i \(-0.308396\pi\)
0.867791 + 0.496929i \(0.165539\pi\)
\(710\) −73.1969 209.185i −0.103094 0.294626i
\(711\) 0 0
\(712\) 158.310 + 693.601i 0.222345 + 0.974159i
\(713\) 1204.66 + 1204.66i 1.68956 + 1.68956i
\(714\) 0 0
\(715\) −91.9667 + 10.3622i −0.128625 + 0.0144925i
\(716\) 23.8865 104.653i 0.0333610 0.146164i
\(717\) 0 0
\(718\) −239.565 + 191.047i −0.333656 + 0.266082i
\(719\) −623.735 300.375i −0.867504 0.417768i −0.0534590 0.998570i \(-0.517025\pi\)
−0.814045 + 0.580802i \(0.802739\pi\)
\(720\) 0 0
\(721\) −86.9799 + 109.069i −0.120638 + 0.151275i
\(722\) 628.511 + 70.8162i 0.870514 + 0.0980833i
\(723\) 0 0
\(724\) 88.9479i 0.122856i
\(725\) 356.517 + 507.331i 0.491747 + 0.699768i
\(726\) 0 0
\(727\) −280.613 98.1906i −0.385987 0.135063i 0.130308 0.991474i \(-0.458403\pi\)
−0.516295 + 0.856411i \(0.672689\pi\)
\(728\) −7.55693 + 67.0696i −0.0103804 + 0.0921286i
\(729\) 0 0
\(730\) −116.993 242.938i −0.160264 0.332791i
\(731\) 72.7991 151.169i 0.0995884 0.206797i
\(732\) 0 0
\(733\) −270.527 430.541i −0.369068 0.587369i 0.609627 0.792689i \(-0.291319\pi\)
−0.978695 + 0.205320i \(0.934177\pi\)
\(734\) 467.765 + 106.764i 0.637282 + 0.145455i
\(735\) 0 0
\(736\) −229.746 + 365.638i −0.312154 + 0.496791i
\(737\) −196.928 + 196.928i −0.267202 + 0.267202i
\(738\) 0 0
\(739\) −123.481 352.888i −0.167092 0.477521i 0.829640 0.558298i \(-0.188546\pi\)
−0.996732 + 0.0807770i \(0.974260\pi\)
\(740\) −93.8925 + 32.8544i −0.126882 + 0.0443978i
\(741\) 0 0
\(742\) −80.7858 80.7858i −0.108876 0.108876i
\(743\) 61.7282 + 38.7864i 0.0830797 + 0.0522024i 0.572931 0.819603i \(-0.305806\pi\)
−0.489852 + 0.871806i \(0.662949\pi\)
\(744\) 0 0
\(745\) 105.810 463.583i 0.142027 0.622260i
\(746\) −72.4306 + 45.5112i −0.0970920 + 0.0610069i
\(747\) 0 0
\(748\) 112.145 + 54.0062i 0.149926 + 0.0722008i
\(749\) 147.782 71.1679i 0.197305 0.0950172i
\(750\) 0 0
\(751\) −690.638 77.8162i −0.919624 0.103617i −0.360555 0.932738i \(-0.617413\pi\)
−0.559069 + 0.829121i \(0.688841\pi\)
\(752\) −249.312 + 712.494i −0.331533 + 0.947466i
\(753\) 0 0
\(754\) −76.7475 + 182.930i −0.101787 + 0.242612i
\(755\) 357.789 0.473892
\(756\) 0 0
\(757\) −10.1618 + 90.1883i −0.0134238 + 0.119139i −0.998637 0.0521936i \(-0.983379\pi\)
0.985213 + 0.171333i \(0.0548073\pi\)
\(758\) −227.001 181.027i −0.299474 0.238822i
\(759\) 0 0
\(760\) 0.986704 2.04891i 0.00129829 0.00269594i
\(761\) −135.413 169.803i −0.177941 0.223131i 0.684860 0.728675i \(-0.259863\pi\)
−0.862801 + 0.505543i \(0.831292\pi\)
\(762\) 0 0
\(763\) 194.782 + 44.4578i 0.255285 + 0.0582670i
\(764\) −6.21225 55.1352i −0.00813121 0.0721665i
\(765\) 0 0
\(766\) 202.100 202.100i 0.263838 0.263838i
\(767\) 1.50849 0.344302i 0.00196673 0.000448894i
\(768\) 0 0
\(769\) 768.761 269.001i 0.999689 0.349806i 0.219678 0.975572i \(-0.429499\pi\)
0.780011 + 0.625766i \(0.215214\pi\)
\(770\) 18.4972 + 81.0417i 0.0240224 + 0.105249i
\(771\) 0 0
\(772\) 241.149 + 151.524i 0.312369 + 0.196274i
\(773\) −247.757 + 27.9155i −0.320514 + 0.0361132i −0.270756 0.962648i \(-0.587274\pi\)
−0.0497581 + 0.998761i \(0.515845\pi\)
\(774\) 0 0
\(775\) −1039.36 + 653.074i −1.34111 + 0.842676i
\(776\) −1178.57 + 939.878i −1.51878 + 1.21118i
\(777\) 0 0
\(778\) −690.326 + 332.443i −0.887308 + 0.427305i
\(779\) −3.16275 + 3.96597i −0.00406002 + 0.00509110i
\(780\) 0 0
\(781\) 273.701 782.192i 0.350449 1.00153i
\(782\) 558.402i 0.714070i
\(783\) 0 0
\(784\) −513.613 −0.655119
\(785\) 64.6968 + 22.6384i 0.0824163 + 0.0288387i
\(786\) 0 0
\(787\) −430.893 343.626i −0.547513 0.436627i 0.310263 0.950651i