Properties

Label 1386.2.k.t.793.2
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.t.991.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(0.292893 + 0.507306i) q^{10} +(0.500000 + 0.866025i) q^{11} -3.82843 q^{13} +(2.62132 - 0.358719i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.82843 + 3.16693i) q^{17} +(0.292893 - 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(-3.12132 + 5.40629i) q^{23} +(2.32843 + 4.03295i) q^{25} +(-1.91421 + 3.31552i) q^{26} +(1.00000 - 2.44949i) q^{28} -2.65685 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +3.65685 q^{34} +(-1.53553 + 0.210133i) q^{35} +(4.70711 - 8.15295i) q^{37} +(-0.292893 - 0.507306i) q^{38} +(0.292893 - 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(0.500000 - 0.866025i) q^{44} +(3.12132 + 5.40629i) q^{46} +(-5.24264 + 9.08052i) q^{47} +(-1.74264 + 6.77962i) q^{49} +4.65685 q^{50} +(1.91421 + 3.31552i) q^{52} +(3.94975 + 6.84116i) q^{53} -0.585786 q^{55} +(-1.62132 - 2.09077i) q^{56} +(-1.32843 + 2.30090i) q^{58} +(-2.79289 - 4.83743i) q^{59} +(-5.91421 + 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.12132 - 1.94218i) q^{65} +(-1.37868 - 2.38794i) q^{67} +(1.82843 - 3.16693i) q^{68} +(-0.585786 + 1.43488i) q^{70} +11.0711 q^{71} +(4.70711 + 8.15295i) q^{73} +(-4.70711 - 8.15295i) q^{74} -0.585786 q^{76} +(-1.00000 + 2.44949i) q^{77} +(6.62132 - 11.4685i) q^{79} +(-0.292893 - 0.507306i) q^{80} +(2.70711 - 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(-2.82843 + 4.89898i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(6.24264 - 10.8126i) q^{89} +(-6.20711 - 8.00436i) q^{91} +6.24264 q^{92} +(5.24264 + 9.08052i) q^{94} +(0.171573 + 0.297173i) q^{95} -3.82843 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 2q^{7} - 4q^{8} + 4q^{10} + 2q^{11} - 4q^{13} + 2q^{14} - 2q^{16} - 4q^{17} + 4q^{19} + 8q^{20} + 4q^{22} - 4q^{23} - 2q^{25} - 2q^{26} + 4q^{28} + 12q^{29} + 8q^{31} + 2q^{32} - 8q^{34} + 8q^{35} + 16q^{37} - 4q^{38} + 4q^{40} + 16q^{41} + 2q^{44} + 4q^{46} - 4q^{47} + 10q^{49} - 4q^{50} + 2q^{52} - 4q^{53} - 8q^{55} + 2q^{56} + 6q^{58} - 14q^{59} - 18q^{61} + 16q^{62} + 4q^{64} - 4q^{65} - 14q^{67} - 4q^{68} - 8q^{70} + 16q^{71} + 16q^{73} - 16q^{74} - 8q^{76} - 4q^{77} + 18q^{79} - 4q^{80} + 8q^{82} - 8q^{83} + 48q^{85} - 2q^{88} + 8q^{89} - 22q^{91} + 8q^{92} + 4q^{94} + 12q^{95} - 4q^{97} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.292893 + 0.507306i −0.130986 + 0.226874i −0.924057 0.382255i \(-0.875148\pi\)
0.793071 + 0.609129i \(0.208481\pi\)
\(6\) 0 0
\(7\) 1.62132 + 2.09077i 0.612801 + 0.790237i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.292893 + 0.507306i 0.0926210 + 0.160424i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) −3.82843 −1.06181 −0.530907 0.847430i \(-0.678149\pi\)
−0.530907 + 0.847430i \(0.678149\pi\)
\(14\) 2.62132 0.358719i 0.700577 0.0958718i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.82843 + 3.16693i 0.443459 + 0.768093i 0.997943 0.0641009i \(-0.0204179\pi\)
−0.554485 + 0.832194i \(0.687085\pi\)
\(18\) 0 0
\(19\) 0.292893 0.507306i 0.0671943 0.116384i −0.830471 0.557062i \(-0.811929\pi\)
0.897665 + 0.440678i \(0.145262\pi\)
\(20\) 0.585786 0.130986
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −3.12132 + 5.40629i −0.650840 + 1.12729i 0.332079 + 0.943252i \(0.392250\pi\)
−0.982919 + 0.184037i \(0.941083\pi\)
\(24\) 0 0
\(25\) 2.32843 + 4.03295i 0.465685 + 0.806591i
\(26\) −1.91421 + 3.31552i −0.375408 + 0.650226i
\(27\) 0 0
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) −2.65685 −0.493365 −0.246683 0.969096i \(-0.579341\pi\)
−0.246683 + 0.969096i \(0.579341\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.65685 0.627145
\(35\) −1.53553 + 0.210133i −0.259553 + 0.0355190i
\(36\) 0 0
\(37\) 4.70711 8.15295i 0.773844 1.34034i −0.161599 0.986857i \(-0.551665\pi\)
0.935442 0.353480i \(-0.115002\pi\)
\(38\) −0.292893 0.507306i −0.0475136 0.0822959i
\(39\) 0 0
\(40\) 0.292893 0.507306i 0.0463105 0.0802121i
\(41\) 5.41421 0.845558 0.422779 0.906233i \(-0.361055\pi\)
0.422779 + 0.906233i \(0.361055\pi\)
\(42\) 0 0
\(43\) −5.65685 −0.862662 −0.431331 0.902194i \(-0.641956\pi\)
−0.431331 + 0.902194i \(0.641956\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) 3.12132 + 5.40629i 0.460214 + 0.797113i
\(47\) −5.24264 + 9.08052i −0.764718 + 1.32453i 0.175678 + 0.984448i \(0.443788\pi\)
−0.940396 + 0.340082i \(0.889545\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 4.65685 0.658579
\(51\) 0 0
\(52\) 1.91421 + 3.31552i 0.265454 + 0.459779i
\(53\) 3.94975 + 6.84116i 0.542540 + 0.939706i 0.998757 + 0.0498379i \(0.0158705\pi\)
−0.456218 + 0.889868i \(0.650796\pi\)
\(54\) 0 0
\(55\) −0.585786 −0.0789874
\(56\) −1.62132 2.09077i −0.216658 0.279391i
\(57\) 0 0
\(58\) −1.32843 + 2.30090i −0.174431 + 0.302123i
\(59\) −2.79289 4.83743i −0.363604 0.629780i 0.624947 0.780667i \(-0.285120\pi\)
−0.988551 + 0.150887i \(0.951787\pi\)
\(60\) 0 0
\(61\) −5.91421 + 10.2437i −0.757237 + 1.31157i 0.187017 + 0.982357i \(0.440118\pi\)
−0.944254 + 0.329217i \(0.893215\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.12132 1.94218i 0.139083 0.240898i
\(66\) 0 0
\(67\) −1.37868 2.38794i −0.168433 0.291734i 0.769436 0.638723i \(-0.220537\pi\)
−0.937869 + 0.346990i \(0.887204\pi\)
\(68\) 1.82843 3.16693i 0.221729 0.384047i
\(69\) 0 0
\(70\) −0.585786 + 1.43488i −0.0700149 + 0.171501i
\(71\) 11.0711 1.31389 0.656947 0.753937i \(-0.271848\pi\)
0.656947 + 0.753937i \(0.271848\pi\)
\(72\) 0 0
\(73\) 4.70711 + 8.15295i 0.550925 + 0.954230i 0.998208 + 0.0598379i \(0.0190584\pi\)
−0.447283 + 0.894393i \(0.647608\pi\)
\(74\) −4.70711 8.15295i −0.547190 0.947761i
\(75\) 0 0
\(76\) −0.585786 −0.0671943
\(77\) −1.00000 + 2.44949i −0.113961 + 0.279145i
\(78\) 0 0
\(79\) 6.62132 11.4685i 0.744957 1.29030i −0.205258 0.978708i \(-0.565803\pi\)
0.950215 0.311595i \(-0.100863\pi\)
\(80\) −0.292893 0.507306i −0.0327465 0.0567185i
\(81\) 0 0
\(82\) 2.70711 4.68885i 0.298950 0.517796i
\(83\) 12.1421 1.33277 0.666386 0.745607i \(-0.267840\pi\)
0.666386 + 0.745607i \(0.267840\pi\)
\(84\) 0 0
\(85\) −2.14214 −0.232347
\(86\) −2.82843 + 4.89898i −0.304997 + 0.528271i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 6.24264 10.8126i 0.661719 1.14613i −0.318445 0.947941i \(-0.603161\pi\)
0.980164 0.198189i \(-0.0635060\pi\)
\(90\) 0 0
\(91\) −6.20711 8.00436i −0.650682 0.839085i
\(92\) 6.24264 0.650840
\(93\) 0 0
\(94\) 5.24264 + 9.08052i 0.540737 + 0.936584i
\(95\) 0.171573 + 0.297173i 0.0176030 + 0.0304893i
\(96\) 0 0
\(97\) −3.82843 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(98\) 5.00000 + 4.89898i 0.505076 + 0.494872i
\(99\) 0 0
\(100\) 2.32843 4.03295i 0.232843 0.403295i
\(101\) 3.08579 + 5.34474i 0.307047 + 0.531821i 0.977715 0.209936i \(-0.0673257\pi\)
−0.670668 + 0.741758i \(0.733992\pi\)
\(102\) 0 0
\(103\) −6.70711 + 11.6170i −0.660871 + 1.14466i 0.319516 + 0.947581i \(0.396480\pi\)
−0.980387 + 0.197081i \(0.936854\pi\)
\(104\) 3.82843 0.375408
\(105\) 0 0
\(106\) 7.89949 0.767267
\(107\) −1.53553 + 2.65962i −0.148446 + 0.257115i −0.930653 0.365903i \(-0.880760\pi\)
0.782207 + 0.623018i \(0.214094\pi\)
\(108\) 0 0
\(109\) −8.24264 14.2767i −0.789502 1.36746i −0.926272 0.376854i \(-0.877006\pi\)
0.136771 0.990603i \(-0.456328\pi\)
\(110\) −0.292893 + 0.507306i −0.0279263 + 0.0483697i
\(111\) 0 0
\(112\) −2.62132 + 0.358719i −0.247691 + 0.0338958i
\(113\) 8.17157 0.768717 0.384358 0.923184i \(-0.374423\pi\)
0.384358 + 0.923184i \(0.374423\pi\)
\(114\) 0 0
\(115\) −1.82843 3.16693i −0.170502 0.295318i
\(116\) 1.32843 + 2.30090i 0.123341 + 0.213634i
\(117\) 0 0
\(118\) −5.58579 −0.514213
\(119\) −3.65685 + 8.95743i −0.335223 + 0.821126i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 5.91421 + 10.2437i 0.535448 + 0.927423i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 15.7279 1.39563 0.697814 0.716279i \(-0.254156\pi\)
0.697814 + 0.716279i \(0.254156\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.12132 1.94218i −0.0983463 0.170341i
\(131\) −0.292893 + 0.507306i −0.0255902 + 0.0443235i −0.878537 0.477674i \(-0.841480\pi\)
0.852947 + 0.521998i \(0.174813\pi\)
\(132\) 0 0
\(133\) 1.53553 0.210133i 0.133148 0.0182208i
\(134\) −2.75736 −0.238200
\(135\) 0 0
\(136\) −1.82843 3.16693i −0.156786 0.271562i
\(137\) −8.32843 14.4253i −0.711546 1.23243i −0.964277 0.264897i \(-0.914662\pi\)
0.252731 0.967537i \(-0.418671\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0.949747 + 1.22474i 0.0802683 + 0.103510i
\(141\) 0 0
\(142\) 5.53553 9.58783i 0.464532 0.804592i
\(143\) −1.91421 3.31552i −0.160075 0.277257i
\(144\) 0 0
\(145\) 0.778175 1.34784i 0.0646239 0.111932i
\(146\) 9.41421 0.779126
\(147\) 0 0
\(148\) −9.41421 −0.773844
\(149\) 8.82843 15.2913i 0.723253 1.25271i −0.236436 0.971647i \(-0.575979\pi\)
0.959689 0.281064i \(-0.0906873\pi\)
\(150\) 0 0
\(151\) 7.86396 + 13.6208i 0.639960 + 1.10844i 0.985441 + 0.170018i \(0.0543825\pi\)
−0.345481 + 0.938426i \(0.612284\pi\)
\(152\) −0.292893 + 0.507306i −0.0237568 + 0.0411479i
\(153\) 0 0
\(154\) 1.62132 + 2.09077i 0.130650 + 0.168479i
\(155\) −2.34315 −0.188206
\(156\) 0 0
\(157\) −8.82843 15.2913i −0.704585 1.22038i −0.966841 0.255379i \(-0.917800\pi\)
0.262256 0.964998i \(-0.415534\pi\)
\(158\) −6.62132 11.4685i −0.526764 0.912382i
\(159\) 0 0
\(160\) −0.585786 −0.0463105
\(161\) −16.3640 + 2.23936i −1.28966 + 0.176486i
\(162\) 0 0
\(163\) −4.86396 + 8.42463i −0.380975 + 0.659868i −0.991202 0.132359i \(-0.957745\pi\)
0.610227 + 0.792227i \(0.291078\pi\)
\(164\) −2.70711 4.68885i −0.211390 0.366137i
\(165\) 0 0
\(166\) 6.07107 10.5154i 0.471206 0.816153i
\(167\) −13.7279 −1.06230 −0.531149 0.847278i \(-0.678240\pi\)
−0.531149 + 0.847278i \(0.678240\pi\)
\(168\) 0 0
\(169\) 1.65685 0.127450
\(170\) −1.07107 + 1.85514i −0.0821472 + 0.142283i
\(171\) 0 0
\(172\) 2.82843 + 4.89898i 0.215666 + 0.373544i
\(173\) −4.91421 + 8.51167i −0.373621 + 0.647130i −0.990120 0.140226i \(-0.955217\pi\)
0.616499 + 0.787356i \(0.288551\pi\)
\(174\) 0 0
\(175\) −4.65685 + 11.4069i −0.352025 + 0.862282i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −6.24264 10.8126i −0.467906 0.810436i
\(179\) 0.449747 + 0.778985i 0.0336157 + 0.0582241i 0.882344 0.470605i \(-0.155964\pi\)
−0.848728 + 0.528829i \(0.822631\pi\)
\(180\) 0 0
\(181\) −7.65685 −0.569129 −0.284565 0.958657i \(-0.591849\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(182\) −10.0355 + 1.37333i −0.743883 + 0.101798i
\(183\) 0 0
\(184\) 3.12132 5.40629i 0.230107 0.398557i
\(185\) 2.75736 + 4.77589i 0.202725 + 0.351130i
\(186\) 0 0
\(187\) −1.82843 + 3.16693i −0.133708 + 0.231589i
\(188\) 10.4853 0.764718
\(189\) 0 0
\(190\) 0.343146 0.0248944
\(191\) −3.58579 + 6.21076i −0.259458 + 0.449395i −0.966097 0.258180i \(-0.916877\pi\)
0.706639 + 0.707575i \(0.250211\pi\)
\(192\) 0 0
\(193\) −10.9497 18.9655i −0.788180 1.36517i −0.927081 0.374862i \(-0.877690\pi\)
0.138901 0.990306i \(-0.455643\pi\)
\(194\) −1.91421 + 3.31552i −0.137433 + 0.238040i
\(195\) 0 0
\(196\) 6.74264 1.88064i 0.481617 0.134331i
\(197\) 0.514719 0.0366722 0.0183361 0.999832i \(-0.494163\pi\)
0.0183361 + 0.999832i \(0.494163\pi\)
\(198\) 0 0
\(199\) −0.0502525 0.0870399i −0.00356231 0.00617010i 0.864239 0.503082i \(-0.167801\pi\)
−0.867801 + 0.496912i \(0.834467\pi\)
\(200\) −2.32843 4.03295i −0.164645 0.285173i
\(201\) 0 0
\(202\) 6.17157 0.434230
\(203\) −4.30761 5.55487i −0.302335 0.389876i
\(204\) 0 0
\(205\) −1.58579 + 2.74666i −0.110756 + 0.191835i
\(206\) 6.70711 + 11.6170i 0.467306 + 0.809398i
\(207\) 0 0
\(208\) 1.91421 3.31552i 0.132727 0.229890i
\(209\) 0.585786 0.0405197
\(210\) 0 0
\(211\) 7.41421 0.510416 0.255208 0.966886i \(-0.417856\pi\)
0.255208 + 0.966886i \(0.417856\pi\)
\(212\) 3.94975 6.84116i 0.271270 0.469853i
\(213\) 0 0
\(214\) 1.53553 + 2.65962i 0.104967 + 0.181808i
\(215\) 1.65685 2.86976i 0.112997 0.195716i
\(216\) 0 0
\(217\) −4.00000 + 9.79796i −0.271538 + 0.665129i
\(218\) −16.4853 −1.11652
\(219\) 0 0
\(220\) 0.292893 + 0.507306i 0.0197469 + 0.0342026i
\(221\) −7.00000 12.1244i −0.470871 0.815572i
\(222\) 0 0
\(223\) 8.58579 0.574947 0.287473 0.957789i \(-0.407185\pi\)
0.287473 + 0.957789i \(0.407185\pi\)
\(224\) −1.00000 + 2.44949i −0.0668153 + 0.163663i
\(225\) 0 0
\(226\) 4.08579 7.07679i 0.271782 0.470741i
\(227\) −14.4142 24.9662i −0.956705 1.65706i −0.730417 0.683001i \(-0.760674\pi\)
−0.226288 0.974061i \(-0.572659\pi\)
\(228\) 0 0
\(229\) −11.6569 + 20.1903i −0.770307 + 1.33421i 0.167088 + 0.985942i \(0.446564\pi\)
−0.937395 + 0.348268i \(0.886770\pi\)
\(230\) −3.65685 −0.241126
\(231\) 0 0
\(232\) 2.65685 0.174431
\(233\) 0.707107 1.22474i 0.0463241 0.0802357i −0.841934 0.539581i \(-0.818583\pi\)
0.888258 + 0.459345i \(0.151916\pi\)
\(234\) 0 0
\(235\) −3.07107 5.31925i −0.200334 0.346989i
\(236\) −2.79289 + 4.83743i −0.181802 + 0.314890i
\(237\) 0 0
\(238\) 5.92893 + 7.64564i 0.384316 + 0.495593i
\(239\) −20.2132 −1.30748 −0.653742 0.756718i \(-0.726802\pi\)
−0.653742 + 0.756718i \(0.726802\pi\)
\(240\) 0 0
\(241\) −6.12132 10.6024i −0.394309 0.682963i 0.598704 0.800971i \(-0.295683\pi\)
−0.993013 + 0.118007i \(0.962349\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 11.8284 0.757237
\(245\) −2.92893 2.86976i −0.187123 0.183342i
\(246\) 0 0
\(247\) −1.12132 + 1.94218i −0.0713479 + 0.123578i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) 0 0
\(250\) −2.82843 + 4.89898i −0.178885 + 0.309839i
\(251\) 26.1421 1.65008 0.825038 0.565077i \(-0.191153\pi\)
0.825038 + 0.565077i \(0.191153\pi\)
\(252\) 0 0
\(253\) −6.24264 −0.392471
\(254\) 7.86396 13.6208i 0.493429 0.854644i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.5711 + 21.7737i −0.784162 + 1.35821i 0.145337 + 0.989382i \(0.453573\pi\)
−0.929499 + 0.368826i \(0.879760\pi\)
\(258\) 0 0
\(259\) 24.6777 3.37706i 1.53340 0.209840i
\(260\) −2.24264 −0.139083
\(261\) 0 0
\(262\) 0.292893 + 0.507306i 0.0180950 + 0.0313415i
\(263\) −8.52082 14.7585i −0.525416 0.910047i −0.999562 0.0296008i \(-0.990576\pi\)
0.474146 0.880446i \(-0.342757\pi\)
\(264\) 0 0
\(265\) −4.62742 −0.284260
\(266\) 0.585786 1.43488i 0.0359169 0.0879780i
\(267\) 0 0
\(268\) −1.37868 + 2.38794i −0.0842163 + 0.145867i
\(269\) 1.17157 + 2.02922i 0.0714321 + 0.123724i 0.899529 0.436861i \(-0.143910\pi\)
−0.828097 + 0.560585i \(0.810576\pi\)
\(270\) 0 0
\(271\) −2.27817 + 3.94591i −0.138389 + 0.239697i −0.926887 0.375340i \(-0.877526\pi\)
0.788498 + 0.615038i \(0.210859\pi\)
\(272\) −3.65685 −0.221729
\(273\) 0 0
\(274\) −16.6569 −1.00628
\(275\) −2.32843 + 4.03295i −0.140409 + 0.243196i
\(276\) 0 0
\(277\) −0.914214 1.58346i −0.0549298 0.0951412i 0.837253 0.546816i \(-0.184160\pi\)
−0.892183 + 0.451675i \(0.850827\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.53553 0.210133i 0.0917657 0.0125578i
\(281\) −8.72792 −0.520664 −0.260332 0.965519i \(-0.583832\pi\)
−0.260332 + 0.965519i \(0.583832\pi\)
\(282\) 0 0
\(283\) 11.7071 + 20.2773i 0.695915 + 1.20536i 0.969871 + 0.243618i \(0.0783344\pi\)
−0.273956 + 0.961742i \(0.588332\pi\)
\(284\) −5.53553 9.58783i −0.328474 0.568933i
\(285\) 0 0
\(286\) −3.82843 −0.226380
\(287\) 8.77817 + 11.3199i 0.518159 + 0.668191i
\(288\) 0 0
\(289\) 1.81371 3.14144i 0.106689 0.184790i
\(290\) −0.778175 1.34784i −0.0456960 0.0791478i
\(291\) 0 0
\(292\) 4.70711 8.15295i 0.275463 0.477115i
\(293\) 10.8284 0.632603 0.316302 0.948659i \(-0.397559\pi\)
0.316302 + 0.948659i \(0.397559\pi\)
\(294\) 0 0
\(295\) 3.27208 0.190508
\(296\) −4.70711 + 8.15295i −0.273595 + 0.473880i
\(297\) 0 0
\(298\) −8.82843 15.2913i −0.511417 0.885800i
\(299\) 11.9497 20.6976i 0.691072 1.19697i
\(300\) 0 0
\(301\) −9.17157 11.8272i −0.528641 0.681707i
\(302\) 15.7279 0.905040
\(303\) 0 0
\(304\) 0.292893 + 0.507306i 0.0167986 + 0.0290960i
\(305\) −3.46447 6.00063i −0.198375 0.343595i
\(306\) 0 0
\(307\) 9.89949 0.564994 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) 2.62132 0.358719i 0.149364 0.0204399i
\(309\) 0 0
\(310\) −1.17157 + 2.02922i −0.0665409 + 0.115252i
\(311\) 8.36396 + 14.4868i 0.474277 + 0.821471i 0.999566 0.0294522i \(-0.00937629\pi\)
−0.525289 + 0.850924i \(0.676043\pi\)
\(312\) 0 0
\(313\) 10.3284 17.8894i 0.583797 1.01117i −0.411227 0.911533i \(-0.634900\pi\)
0.995024 0.0996335i \(-0.0317670\pi\)
\(314\) −17.6569 −0.996434
\(315\) 0 0
\(316\) −13.2426 −0.744957
\(317\) 4.34315 7.52255i 0.243935 0.422508i −0.717896 0.696150i \(-0.754895\pi\)
0.961832 + 0.273642i \(0.0882282\pi\)
\(318\) 0 0
\(319\) −1.32843 2.30090i −0.0743776 0.128826i
\(320\) −0.292893 + 0.507306i −0.0163732 + 0.0283593i
\(321\) 0 0
\(322\) −6.24264 + 15.2913i −0.347889 + 0.852150i
\(323\) 2.14214 0.119192
\(324\) 0 0
\(325\) −8.91421 15.4399i −0.494472 0.856450i
\(326\) 4.86396 + 8.42463i 0.269390 + 0.466597i
\(327\) 0 0
\(328\) −5.41421 −0.298950
\(329\) −27.4853 + 3.76127i −1.51531 + 0.207366i
\(330\) 0 0
\(331\) 12.0355 20.8462i 0.661533 1.14581i −0.318680 0.947862i \(-0.603240\pi\)
0.980213 0.197946i \(-0.0634271\pi\)
\(332\) −6.07107 10.5154i −0.333193 0.577107i
\(333\) 0 0
\(334\) −6.86396 + 11.8887i −0.375579 + 0.650522i
\(335\) 1.61522 0.0882491
\(336\) 0 0
\(337\) −28.2426 −1.53847 −0.769237 0.638963i \(-0.779364\pi\)
−0.769237 + 0.638963i \(0.779364\pi\)
\(338\) 0.828427 1.43488i 0.0450605 0.0780471i
\(339\) 0 0
\(340\) 1.07107 + 1.85514i 0.0580868 + 0.100609i
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 5.65685 0.304997
\(345\) 0 0
\(346\) 4.91421 + 8.51167i 0.264190 + 0.457590i
\(347\) 8.70711 + 15.0812i 0.467422 + 0.809599i 0.999307 0.0372179i \(-0.0118495\pi\)
−0.531885 + 0.846816i \(0.678516\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 7.55025 + 9.73641i 0.403578 + 0.520433i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −1.34315 2.32640i −0.0714884 0.123822i 0.828065 0.560632i \(-0.189442\pi\)
−0.899554 + 0.436810i \(0.856108\pi\)
\(354\) 0 0
\(355\) −3.24264 + 5.61642i −0.172101 + 0.298089i
\(356\) −12.4853 −0.661719
\(357\) 0 0
\(358\) 0.899495 0.0475398
\(359\) 9.62132 16.6646i 0.507794 0.879525i −0.492165 0.870502i \(-0.663794\pi\)
0.999959 0.00902308i \(-0.00287218\pi\)
\(360\) 0 0
\(361\) 9.32843 + 16.1573i 0.490970 + 0.850385i
\(362\) −3.82843 + 6.63103i −0.201218 + 0.348519i
\(363\) 0 0
\(364\) −3.82843 + 9.37769i −0.200664 + 0.491525i
\(365\) −5.51472 −0.288654
\(366\) 0 0
\(367\) 5.36396 + 9.29065i 0.279996 + 0.484968i 0.971384 0.237516i \(-0.0763334\pi\)
−0.691387 + 0.722485i \(0.743000\pi\)
\(368\) −3.12132 5.40629i −0.162710 0.281822i
\(369\) 0 0
\(370\) 5.51472 0.286697
\(371\) −7.89949 + 19.3497i −0.410121 + 1.00459i
\(372\) 0 0
\(373\) 9.98528 17.2950i 0.517018 0.895502i −0.482786 0.875738i \(-0.660375\pi\)
0.999805 0.0197638i \(-0.00629142\pi\)
\(374\) 1.82843 + 3.16693i 0.0945457 + 0.163758i
\(375\) 0 0
\(376\) 5.24264 9.08052i 0.270369 0.468292i
\(377\) 10.1716 0.523863
\(378\) 0 0
\(379\) 27.8701 1.43159 0.715794 0.698311i \(-0.246065\pi\)
0.715794 + 0.698311i \(0.246065\pi\)
\(380\) 0.171573 0.297173i 0.00880150 0.0152447i
\(381\) 0 0
\(382\) 3.58579 + 6.21076i 0.183465 + 0.317770i
\(383\) −3.19239 + 5.52938i −0.163123 + 0.282538i −0.935987 0.352034i \(-0.885490\pi\)
0.772864 + 0.634572i \(0.218824\pi\)
\(384\) 0 0
\(385\) −0.949747 1.22474i −0.0484036 0.0624188i
\(386\) −21.8995 −1.11465
\(387\) 0 0
\(388\) 1.91421 + 3.31552i 0.0971795 + 0.168320i
\(389\) −11.3640 19.6830i −0.576176 0.997966i −0.995913 0.0903199i \(-0.971211\pi\)
0.419737 0.907646i \(-0.362122\pi\)
\(390\) 0 0
\(391\) −22.8284 −1.15448
\(392\) 1.74264 6.77962i 0.0880166 0.342422i
\(393\) 0 0
\(394\) 0.257359 0.445759i 0.0129656 0.0224570i
\(395\) 3.87868 + 6.71807i 0.195158 + 0.338023i
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) −0.100505 −0.00503786
\(399\) 0 0
\(400\) −4.65685 −0.232843
\(401\) 9.15685 15.8601i 0.457271 0.792017i −0.541544 0.840672i \(-0.682160\pi\)
0.998816 + 0.0486549i \(0.0154934\pi\)
\(402\) 0 0
\(403\) −7.65685 13.2621i −0.381415 0.660630i
\(404\) 3.08579 5.34474i 0.153524 0.265911i
\(405\) 0 0
\(406\) −6.96447 + 0.953065i −0.345641 + 0.0472998i
\(407\) 9.41421 0.466645
\(408\) 0 0
\(409\) −1.36396 2.36245i −0.0674435 0.116816i 0.830332 0.557269i \(-0.188151\pi\)
−0.897775 + 0.440454i \(0.854818\pi\)
\(410\) 1.58579 + 2.74666i 0.0783164 + 0.135648i
\(411\) 0 0
\(412\) 13.4142 0.660871
\(413\) 5.58579 13.6823i 0.274859 0.673263i
\(414\) 0 0
\(415\) −3.55635 + 6.15978i −0.174574 + 0.302372i
\(416\) −1.91421 3.31552i −0.0938520 0.162557i
\(417\) 0 0
\(418\) 0.292893 0.507306i 0.0143259 0.0248131i
\(419\) 26.1421 1.27713 0.638563 0.769569i \(-0.279529\pi\)
0.638563 + 0.769569i \(0.279529\pi\)
\(420\) 0 0
\(421\) 0.686292 0.0334478 0.0167239 0.999860i \(-0.494676\pi\)
0.0167239 + 0.999860i \(0.494676\pi\)
\(422\) 3.70711 6.42090i 0.180459 0.312564i
\(423\) 0 0
\(424\) −3.94975 6.84116i −0.191817 0.332236i
\(425\) −8.51472 + 14.7479i −0.413025 + 0.715379i
\(426\) 0 0
\(427\) −31.0061 + 4.24309i −1.50049 + 0.205337i
\(428\) 3.07107 0.148446
\(429\) 0 0
\(430\) −1.65685 2.86976i −0.0799006 0.138392i
\(431\) −8.79289 15.2297i −0.423539 0.733591i 0.572744 0.819734i \(-0.305879\pi\)
−0.996283 + 0.0861437i \(0.972546\pi\)
\(432\) 0 0
\(433\) 26.1421 1.25631 0.628155 0.778088i \(-0.283810\pi\)
0.628155 + 0.778088i \(0.283810\pi\)
\(434\) 6.48528 + 8.36308i 0.311303 + 0.401441i
\(435\) 0 0
\(436\) −8.24264 + 14.2767i −0.394751 + 0.683729i
\(437\) 1.82843 + 3.16693i 0.0874655 + 0.151495i
\(438\) 0 0
\(439\) 13.6924 23.7159i 0.653502 1.13190i −0.328765 0.944412i \(-0.606632\pi\)
0.982267 0.187487i \(-0.0600342\pi\)
\(440\) 0.585786 0.0279263
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) 6.31371 10.9357i 0.299973 0.519569i −0.676156 0.736758i \(-0.736356\pi\)
0.976130 + 0.217189i \(0.0696889\pi\)
\(444\) 0 0
\(445\) 3.65685 + 6.33386i 0.173352 + 0.300254i
\(446\) 4.29289 7.43551i 0.203274 0.352082i
\(447\) 0 0
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) −22.3431 −1.05444 −0.527219 0.849729i \(-0.676765\pi\)
−0.527219 + 0.849729i \(0.676765\pi\)
\(450\) 0 0
\(451\) 2.70711 + 4.68885i 0.127473 + 0.220789i
\(452\) −4.08579 7.07679i −0.192179 0.332864i
\(453\) 0 0
\(454\) −28.8284 −1.35299
\(455\) 5.87868 0.804479i 0.275597 0.0377146i
\(456\) 0 0
\(457\) 5.82843 10.0951i 0.272642 0.472230i −0.696895 0.717173i \(-0.745436\pi\)
0.969538 + 0.244943i \(0.0787691\pi\)
\(458\) 11.6569 + 20.1903i 0.544689 + 0.943429i
\(459\) 0 0
\(460\) −1.82843 + 3.16693i −0.0852509 + 0.147659i
\(461\) 8.31371 0.387208 0.193604 0.981080i \(-0.437982\pi\)
0.193604 + 0.981080i \(0.437982\pi\)
\(462\) 0 0
\(463\) 12.8284 0.596188 0.298094 0.954537i \(-0.403649\pi\)
0.298094 + 0.954537i \(0.403649\pi\)
\(464\) 1.32843 2.30090i 0.0616707 0.106817i
\(465\) 0 0
\(466\) −0.707107 1.22474i −0.0327561 0.0567352i
\(467\) −17.0000 + 29.4449i −0.786666 + 1.36255i 0.141332 + 0.989962i \(0.454861\pi\)
−0.927999 + 0.372584i \(0.878472\pi\)
\(468\) 0 0
\(469\) 2.75736 6.75412i 0.127323 0.311876i
\(470\) −6.14214 −0.283316
\(471\) 0 0
\(472\) 2.79289 + 4.83743i 0.128553 + 0.222661i
\(473\) −2.82843 4.89898i −0.130051 0.225255i
\(474\) 0 0
\(475\) 2.72792 0.125166
\(476\) 9.58579 1.31178i 0.439364 0.0601256i
\(477\) 0 0
\(478\) −10.1066 + 17.5051i −0.462265 + 0.800667i
\(479\) −5.96447 10.3308i −0.272523 0.472024i 0.696984 0.717087i \(-0.254525\pi\)
−0.969507 + 0.245062i \(0.921192\pi\)
\(480\) 0 0
\(481\) −18.0208 + 31.2130i −0.821678 + 1.42319i
\(482\) −12.2426 −0.557637
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 1.12132 1.94218i 0.0509165 0.0881900i
\(486\) 0 0
\(487\) 4.82843 + 8.36308i 0.218797 + 0.378967i 0.954440 0.298402i \(-0.0964534\pi\)
−0.735644 + 0.677369i \(0.763120\pi\)
\(488\) 5.91421 10.2437i 0.267724 0.463711i
\(489\) 0 0
\(490\) −3.94975 + 1.10165i −0.178431 + 0.0497676i
\(491\) −19.1716 −0.865201 −0.432600 0.901586i \(-0.642404\pi\)
−0.432600 + 0.901586i \(0.642404\pi\)
\(492\) 0 0
\(493\) −4.85786 8.41407i −0.218787 0.378951i
\(494\) 1.12132 + 1.94218i 0.0504506 + 0.0873830i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 17.9497 + 23.1471i 0.805156 + 1.03829i
\(498\) 0 0
\(499\) −11.0711 + 19.1757i −0.495609 + 0.858420i −0.999987 0.00506282i \(-0.998388\pi\)
0.504378 + 0.863483i \(0.331722\pi\)
\(500\) 2.82843 + 4.89898i 0.126491 + 0.219089i
\(501\) 0 0
\(502\) 13.0711 22.6398i 0.583390 1.01046i
\(503\) −4.21320 −0.187857 −0.0939287 0.995579i \(-0.529943\pi\)
−0.0939287 + 0.995579i \(0.529943\pi\)
\(504\) 0 0
\(505\) −3.61522 −0.160875
\(506\) −3.12132 + 5.40629i −0.138760 + 0.240339i
\(507\) 0 0
\(508\) −7.86396 13.6208i −0.348907 0.604324i
\(509\) 4.65685 8.06591i 0.206411 0.357515i −0.744170 0.667990i \(-0.767155\pi\)
0.950582 + 0.310475i \(0.100488\pi\)
\(510\) 0 0
\(511\) −9.41421 + 23.0600i −0.416460 + 1.02012i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.5711 + 21.7737i 0.554486 + 0.960398i
\(515\) −3.92893 6.80511i −0.173129 0.299869i
\(516\) 0 0
\(517\) −10.4853 −0.461142
\(518\) 9.41421 23.0600i 0.413637 1.01320i
\(519\) 0 0
\(520\) −1.12132 + 1.94218i −0.0491731 + 0.0851704i
\(521\) −14.1421 24.4949i −0.619578 1.07314i −0.989563 0.144103i \(-0.953970\pi\)
0.369984 0.929038i \(-0.379363\pi\)
\(522\) 0 0
\(523\) 6.36396 11.0227i 0.278277 0.481989i −0.692680 0.721245i \(-0.743570\pi\)
0.970957 + 0.239256i \(0.0769035\pi\)
\(524\) 0.585786 0.0255902
\(525\) 0 0
\(526\) −17.0416 −0.743050
\(527\) −7.31371 + 12.6677i −0.318590 + 0.551814i
\(528\) 0 0
\(529\) −7.98528 13.8309i −0.347186 0.601344i
\(530\) −2.31371 + 4.00746i −0.100501 + 0.174073i
\(531\) 0 0
\(532\) −0.949747 1.22474i −0.0411768 0.0530994i
\(533\) −20.7279 −0.897826
\(534\) 0 0
\(535\) −0.899495 1.55797i −0.0388886 0.0673570i
\(536\) 1.37868 + 2.38794i 0.0595499 + 0.103143i
\(537\) 0 0
\(538\) 2.34315 0.101020
\(539\) −6.74264 + 1.88064i −0.290426 + 0.0810048i
\(540\) 0 0
\(541\) 6.42893 11.1352i 0.276401 0.478741i −0.694086 0.719892i \(-0.744191\pi\)
0.970488 + 0.241151i \(0.0775248\pi\)
\(542\) 2.27817 + 3.94591i 0.0978560 + 0.169492i
\(543\) 0 0
\(544\) −1.82843 + 3.16693i −0.0783932 + 0.135781i
\(545\) 9.65685 0.413654
\(546\) 0 0
\(547\) 34.8701 1.49094 0.745468 0.666541i \(-0.232226\pi\)
0.745468 + 0.666541i \(0.232226\pi\)
\(548\) −8.32843 + 14.4253i −0.355773 + 0.616217i
\(549\) 0 0
\(550\) 2.32843 + 4.03295i 0.0992845 + 0.171966i
\(551\) −0.778175 + 1.34784i −0.0331514 + 0.0574198i
\(552\) 0 0
\(553\) 34.7132 4.75039i 1.47616 0.202007i
\(554\) −1.82843 −0.0776824
\(555\) 0 0
\(556\) 0 0
\(557\) 3.75736 + 6.50794i 0.159204 + 0.275750i 0.934582 0.355748i \(-0.115774\pi\)
−0.775378 + 0.631498i \(0.782440\pi\)
\(558\) 0 0
\(559\) 21.6569 0.915987
\(560\) 0.585786 1.43488i 0.0247540 0.0606347i
\(561\) 0 0
\(562\) −4.36396 + 7.55860i −0.184083 + 0.318840i
\(563\) 4.53553 + 7.85578i 0.191150 + 0.331081i 0.945632 0.325240i \(-0.105445\pi\)
−0.754482 + 0.656321i \(0.772112\pi\)
\(564\) 0 0
\(565\) −2.39340 + 4.14549i −0.100691 + 0.174402i
\(566\) 23.4142 0.984173
\(567\) 0 0
\(568\) −11.0711 −0.464532
\(569\) −2.00000 + 3.46410i −0.0838444 + 0.145223i −0.904898 0.425628i \(-0.860053\pi\)
0.821054 + 0.570851i \(0.193387\pi\)
\(570\) 0 0
\(571\) −13.1924 22.8499i −0.552084 0.956238i −0.998124 0.0612248i \(-0.980499\pi\)
0.446040 0.895013i \(-0.352834\pi\)
\(572\) −1.91421 + 3.31552i −0.0800373 + 0.138629i
\(573\) 0 0
\(574\) 14.1924 1.94218i 0.592379 0.0810652i
\(575\) −29.0711 −1.21235
\(576\) 0 0
\(577\) 4.84315 + 8.38857i 0.201623 + 0.349221i 0.949051 0.315121i \(-0.102045\pi\)
−0.747429 + 0.664342i \(0.768712\pi\)
\(578\) −1.81371 3.14144i −0.0754403 0.130666i
\(579\) 0 0
\(580\) −1.55635 −0.0646239
\(581\) 19.6863 + 25.3864i 0.816725 + 1.05321i
\(582\) 0 0
\(583\) −3.94975 + 6.84116i −0.163582 + 0.283332i
\(584\) −4.70711 8.15295i −0.194781 0.337371i
\(585\) 0 0
\(586\) 5.41421 9.37769i 0.223659 0.387389i
\(587\) 25.1005 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(588\) 0 0
\(589\) 2.34315 0.0965476
\(590\) 1.63604 2.83370i 0.0673547 0.116662i
\(591\) 0 0
\(592\) 4.70711 + 8.15295i 0.193461 + 0.335084i
\(593\) 11.8492 20.5235i 0.486590 0.842799i −0.513291 0.858215i \(-0.671574\pi\)
0.999881 + 0.0154159i \(0.00490721\pi\)
\(594\) 0 0
\(595\) −3.47309 4.47871i −0.142383 0.183609i
\(596\) −17.6569 −0.723253
\(597\) 0 0
\(598\) −11.9497 20.6976i −0.488662 0.846387i
\(599\) 21.3137 + 36.9164i 0.870855 + 1.50836i 0.861114 + 0.508412i \(0.169767\pi\)
0.00974040 + 0.999953i \(0.496899\pi\)
\(600\) 0 0
\(601\) 31.9411 1.30291 0.651453 0.758689i \(-0.274160\pi\)
0.651453 + 0.758689i \(0.274160\pi\)
\(602\) −14.8284 + 2.02922i −0.604362 + 0.0827050i
\(603\) 0 0
\(604\) 7.86396 13.6208i 0.319980 0.554222i
\(605\) −0.292893 0.507306i −0.0119078 0.0206249i
\(606\) 0 0
\(607\) 21.4853 37.2136i 0.872061 1.51045i 0.0121994 0.999926i \(-0.496117\pi\)
0.859861 0.510528i \(-0.170550\pi\)
\(608\) 0.585786 0.0237568
\(609\) 0 0
\(610\) −6.92893 −0.280544
\(611\) 20.0711 34.7641i 0.811988 1.40641i
\(612\) 0 0
\(613\) −14.3137 24.7921i −0.578125 1.00134i −0.995694 0.0926971i \(-0.970451\pi\)
0.417569 0.908645i \(-0.362882\pi\)
\(614\) 4.94975 8.57321i 0.199756 0.345987i
\(615\) 0 0
\(616\) 1.00000 2.44949i 0.0402911 0.0986928i
\(617\) 41.9706 1.68967 0.844836 0.535026i \(-0.179698\pi\)
0.844836 + 0.535026i \(0.179698\pi\)
\(618\) 0 0
\(619\) 10.9706 + 19.0016i 0.440944 + 0.763738i 0.997760 0.0668984i \(-0.0213104\pi\)
−0.556816 + 0.830636i \(0.687977\pi\)
\(620\) 1.17157 + 2.02922i 0.0470515 + 0.0814956i
\(621\) 0 0
\(622\) 16.7279 0.670729
\(623\) 32.7279 4.47871i 1.31122 0.179436i
\(624\) 0 0
\(625\) −9.98528 + 17.2950i −0.399411 + 0.691801i
\(626\) −10.3284 17.8894i −0.412807 0.715003i
\(627\) 0 0
\(628\) −8.82843 + 15.2913i −0.352293 + 0.610189i
\(629\) 34.4264 1.37267
\(630\) 0 0
\(631\) 23.2721 0.926447 0.463223 0.886242i \(-0.346693\pi\)
0.463223 + 0.886242i \(0.346693\pi\)
\(632\) −6.62132 + 11.4685i −0.263382 + 0.456191i
\(633\) 0 0
\(634\) −4.34315 7.52255i −0.172488 0.298759i
\(635\) −4.60660 + 7.97887i −0.182807 + 0.316632i
\(636\) 0 0
\(637\) 6.67157 25.9553i 0.264337 1.02839i
\(638\) −2.65685 −0.105186
\(639\) 0 0
\(640\) 0.292893 + 0.507306i 0.0115776 + 0.0200530i
\(641\) 7.64214 + 13.2366i 0.301846 + 0.522813i 0.976554 0.215272i \(-0.0690638\pi\)
−0.674708 + 0.738085i \(0.735730\pi\)
\(642\) 0 0
\(643\) 1.58579 0.0625373 0.0312687 0.999511i \(-0.490045\pi\)
0.0312687 + 0.999511i \(0.490045\pi\)
\(644\) 10.1213 + 13.0519i 0.398836 + 0.514318i
\(645\) 0 0
\(646\) 1.07107 1.85514i 0.0421406 0.0729897i
\(647\) 15.0919 + 26.1399i 0.593323 + 1.02767i 0.993781 + 0.111351i \(0.0355177\pi\)
−0.400458 + 0.916315i \(0.631149\pi\)
\(648\) 0 0
\(649\) 2.79289 4.83743i 0.109631 0.189886i
\(650\) −17.8284 −0.699288
\(651\) 0 0
\(652\) 9.72792 0.380975
\(653\) −9.19239 + 15.9217i −0.359726 + 0.623064i −0.987915 0.154997i \(-0.950463\pi\)
0.628189 + 0.778061i \(0.283796\pi\)
\(654\) 0 0
\(655\) −0.171573 0.297173i −0.00670391 0.0116115i
\(656\) −2.70711 + 4.68885i −0.105695 + 0.183069i
\(657\) 0 0
\(658\) −10.4853 + 25.6836i −0.408759 + 1.00125i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −9.48528 16.4290i −0.368935 0.639014i 0.620465 0.784234i \(-0.286944\pi\)
−0.989399 + 0.145221i \(0.953611\pi\)
\(662\) −12.0355 20.8462i −0.467774 0.810209i
\(663\) 0 0
\(664\) −12.1421 −0.471206
\(665\) −0.343146 + 0.840532i −0.0133066 + 0.0325944i
\(666\) 0 0
\(667\) 8.29289 14.3637i 0.321102 0.556165i
\(668\) 6.86396 + 11.8887i 0.265575 + 0.459989i
\(669\) 0 0
\(670\) 0.807612 1.39882i 0.0312008 0.0540413i
\(671\) −11.8284 −0.456631
\(672\) 0 0
\(673\) 5.55635 0.214182 0.107091 0.994249i \(-0.465846\pi\)
0.107091 + 0.994249i \(0.465846\pi\)
\(674\) −14.1213 + 24.4588i −0.543933 + 0.942119i
\(675\) 0 0
\(676\) −0.828427 1.43488i −0.0318626 0.0551876i
\(677\) −17.6569 + 30.5826i −0.678608 + 1.17538i 0.296792 + 0.954942i \(0.404083\pi\)
−0.975400 + 0.220441i \(0.929250\pi\)
\(678\) 0 0
\(679\) −6.20711 8.00436i −0.238207 0.307179i
\(680\) 2.14214 0.0821472
\(681\) 0 0
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) 6.79289 + 11.7656i 0.259923 + 0.450200i 0.966221 0.257715i \(-0.0829695\pi\)
−0.706298 + 0.707914i \(0.749636\pi\)
\(684\) 0 0
\(685\) 9.75736 0.372810
\(686\) −2.13604 + 18.3967i −0.0815543 + 0.702388i
\(687\) 0 0
\(688\) 2.82843 4.89898i 0.107833 0.186772i
\(689\) −15.1213 26.1909i −0.576076 0.997794i
\(690\) 0 0
\(691\) −14.0355 + 24.3103i −0.533937 + 0.924806i 0.465277 + 0.885165i \(0.345955\pi\)
−0.999214 + 0.0396407i \(0.987379\pi\)
\(692\) 9.82843 0.373621
\(693\) 0 0
\(694\) 17.4142 0.661035
\(695\) 0 0
\(696\) 0 0
\(697\) 9.89949 + 17.1464i 0.374970 + 0.649467i
\(698\) 0 0
\(699\) 0 0
\(700\) 12.2071 1.67050i 0.461385 0.0631391i
\(701\) 26.1127 0.986263 0.493132 0.869955i \(-0.335852\pi\)
0.493132 + 0.869955i \(0.335852\pi\)
\(702\) 0 0
\(703\) −2.75736 4.77589i −0.103996 0.180126i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −2.68629 −0.101100
\(707\) −6.17157 + 15.1172i −0.232106 + 0.568541i
\(708\) 0 0
\(709\) 6.02082 10.4284i 0.226116 0.391645i −0.730537 0.682873i \(-0.760730\pi\)
0.956654 + 0.291228i \(0.0940637\pi\)
\(710\) 3.24264 + 5.61642i 0.121694 + 0.210780i
\(711\) 0 0
\(712\) −6.24264 + 10.8126i −0.233953 + 0.405218i
\(713\) −24.9706 −0.935155
\(714\) 0 0
\(715\) 2.24264 0.0838700
\(716\) 0.449747 0.778985i 0.0168079 0.0291121i
\(717\) 0 0
\(718\) −9.62132 16.6646i −0.359064 0.621918i
\(719\) −0.757359 + 1.31178i −0.0282447 + 0.0489213i −0.879802 0.475340i \(-0.842325\pi\)
0.851558 + 0.524261i \(0.175658\pi\)
\(720\) 0 0
\(721\) −35.1630 + 4.81194i −1.30954 + 0.179206i
\(722\) 18.6569 0.694336
\(723\) 0 0
\(724\) 3.82843 + 6.63103i 0.142282 + 0.246440i
\(725\) −6.18629 10.7150i −0.229753 0.397944i
\(726\) 0 0
\(727\) 36.4264 1.35098 0.675490 0.737369i \(-0.263932\pi\)
0.675490 + 0.737369i \(0.263932\pi\)
\(728\) 6.20711 + 8.00436i 0.230051 + 0.296661i
\(729\) 0 0
\(730\) −2.75736 + 4.77589i −0.102054 + 0.176763i
\(731\) −10.3431 17.9149i −0.382555 0.662605i
\(732\) 0 0
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 10.7279 0.395975
\(735\) 0 0
\(736\) −6.24264 −0.230107
\(737\) 1.37868 2.38794i 0.0507843 0.0879610i
\(738\) 0 0
\(739\) 26.2132 + 45.4026i 0.964268 + 1.67016i 0.711568 + 0.702617i \(0.247985\pi\)
0.252700 + 0.967545i \(0.418681\pi\)
\(740\) 2.75736 4.77589i 0.101363 0.175565i
\(741\) 0 0
\(742\) 12.8076 + 16.5160i 0.470182 + 0.606323i
\(743\) 13.3137 0.488433 0.244216 0.969721i \(-0.421469\pi\)
0.244216 + 0.969721i \(0.421469\pi\)
\(744\) 0 0
\(745\) 5.17157 + 8.95743i 0.189472 + 0.328175i
\(746\) −9.98528 17.2950i −0.365587 0.633215i
\(747\) 0 0
\(748\) 3.65685 0.133708
\(749\) −8.05025 + 1.10165i −0.294150 + 0.0402535i
\(750\) 0 0
\(751\) −22.8284 + 39.5400i −0.833021 + 1.44283i 0.0626103 + 0.998038i \(0.480057\pi\)
−0.895631 + 0.444797i \(0.853276\pi\)
\(752\) −5.24264 9.08052i −0.191179 0.331132i
\(753\) 0 0
\(754\) 5.08579 8.80884i 0.185213 0.320799i
\(755\) −9.21320 −0.335303
\(756\) 0 0
\(757\) 8.34315 0.303237 0.151618 0.988439i \(-0.451552\pi\)
0.151618 + 0.988439i \(0.451552\pi\)
\(758\) 13.9350 24.1362i 0.506143 0.876665i
\(759\) 0 0
\(760\) −0.171573 0.297173i −0.00622360 0.0107796i
\(761\) 15.4853 26.8213i 0.561341 0.972271i −0.436039 0.899928i \(-0.643619\pi\)
0.997380 0.0723433i \(-0.0230477\pi\)
\(762\) 0 0
\(763\) 16.4853 40.3805i 0.596807 1.46187i
\(764\) 7.17157 0.259458
\(765\) 0 0
\(766\) 3.19239 + 5.52938i 0.115346 + 0.199785i
\(767\) 10.6924 + 18.5198i 0.386080 + 0.668710i
\(768\) 0 0
\(769\) 22.9706 0.828340 0.414170 0.910200i \(-0.364072\pi\)
0.414170 + 0.910200i \(0.364072\pi\)
\(770\) −1.53553 + 0.210133i −0.0553368 + 0.00757267i
\(771\) 0 0
\(772\) −10.9497 + 18.9655i −0.394090 + 0.682584i
\(773\) −10.9706 19.0016i −0.394584 0.683439i 0.598464 0.801150i \(-0.295778\pi\)
−0.993048 + 0.117710i \(0.962445\pi\)
\(774\) 0 0
\(775\) −9.31371 + 16.1318i −0.334558 + 0.579472i
\(776\) 3.82843 0.137433
\(777\) 0 0
\(778\) −22.7279 −0.814835
\(779\) 1.58579 2.74666i 0.0568167 0.0984094i
\(780\) 0 0
\(781\) 5.53553 + 9.58783i 0.198077 + 0.343079i
\(782\) −11.4142 + 19.7700i −0.408171 + 0.706974i
\(783\) 0 0
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 10.3431 0.369163
\(786\) 0 0
\(787\) −6.77817 11.7401i −0.241616 0.418491i 0.719559 0.694431i \(-0.244344\pi\)
−0.961175 + 0.275941i \(0.911011\pi\)
\(788\) −0.257359 0.445759i −0.00916805 0.0158795i
\(789\) 0 0
\(790\) 7.75736 0.275994 <