Properties

Label 1386.2.k.u.991.2
Level $1386$
Weight $2$
Character 1386.991
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.u.793.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.20711 + 2.09077i) q^{5} +(1.62132 - 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.20711 + 2.09077i) q^{5} +(1.62132 - 2.09077i) q^{7} -1.00000 q^{8} +(-1.20711 + 2.09077i) q^{10} +(0.500000 - 0.866025i) q^{11} -6.82843 q^{13} +(2.62132 + 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.91421 + 6.77962i) q^{17} +(2.41421 + 4.18154i) q^{19} -2.41421 q^{20} +1.00000 q^{22} +(2.62132 + 4.54026i) q^{23} +(-0.414214 + 0.717439i) q^{25} +(-3.41421 - 5.91359i) q^{26} +(1.00000 + 2.44949i) q^{28} +2.82843 q^{29} +(-5.24264 + 9.08052i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.82843 q^{34} +(6.32843 + 0.866025i) q^{35} +(0.828427 + 1.43488i) q^{37} +(-2.41421 + 4.18154i) q^{38} +(-1.20711 - 2.09077i) q^{40} +6.65685 q^{41} +2.82843 q^{43} +(0.500000 + 0.866025i) q^{44} +(-2.62132 + 4.54026i) q^{46} +(-0.378680 - 0.655892i) q^{47} +(-1.74264 - 6.77962i) q^{49} -0.828427 q^{50} +(3.41421 - 5.91359i) q^{52} +(-5.41421 + 9.37769i) q^{53} +2.41421 q^{55} +(-1.62132 + 2.09077i) q^{56} +(1.41421 + 2.44949i) q^{58} +(3.82843 - 6.63103i) q^{59} +(2.20711 + 3.82282i) q^{61} -10.4853 q^{62} +1.00000 q^{64} +(-8.24264 - 14.2767i) q^{65} +(-1.74264 + 3.01834i) q^{67} +(-3.91421 - 6.77962i) q^{68} +(2.41421 + 5.91359i) q^{70} +9.31371 q^{71} +(-0.414214 + 0.717439i) q^{73} +(-0.828427 + 1.43488i) q^{74} -4.82843 q^{76} +(-1.00000 - 2.44949i) q^{77} +(-6.62132 - 11.4685i) q^{79} +(1.20711 - 2.09077i) q^{80} +(3.32843 + 5.76500i) q^{82} +4.17157 q^{83} -18.8995 q^{85} +(1.41421 + 2.44949i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} +(-11.0711 + 14.2767i) q^{91} -5.24264 q^{92} +(0.378680 - 0.655892i) q^{94} +(-5.82843 + 10.0951i) q^{95} -15.8284 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} - 2q^{7} - 4q^{8} - 2q^{10} + 2q^{11} - 16q^{13} + 2q^{14} - 2q^{16} - 10q^{17} + 4q^{19} - 4q^{20} + 4q^{22} + 2q^{23} + 4q^{25} - 8q^{26} + 4q^{28} - 4q^{31} + 2q^{32} - 20q^{34} + 14q^{35} - 8q^{37} - 4q^{38} - 2q^{40} + 4q^{41} + 2q^{44} - 2q^{46} - 10q^{47} + 10q^{49} + 8q^{50} + 8q^{52} - 16q^{53} + 4q^{55} + 2q^{56} + 4q^{59} + 6q^{61} - 8q^{62} + 4q^{64} - 16q^{65} + 10q^{67} - 10q^{68} + 4q^{70} - 8q^{71} + 4q^{73} + 8q^{74} - 8q^{76} - 4q^{77} - 18q^{79} + 2q^{80} + 2q^{82} + 28q^{83} - 36q^{85} - 2q^{88} + 8q^{89} - 16q^{91} - 4q^{92} + 10q^{94} - 12q^{95} - 52q^{97} + 20q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 1.20711 + 2.09077i 0.539835 + 0.935021i 0.998912 + 0.0466249i \(0.0148465\pi\)
−0.459078 + 0.888396i \(0.651820\pi\)
\(6\) 0 0
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.20711 + 2.09077i −0.381721 + 0.661160i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) −6.82843 −1.89386 −0.946932 0.321433i \(-0.895836\pi\)
−0.946932 + 0.321433i \(0.895836\pi\)
\(14\) 2.62132 + 0.358719i 0.700577 + 0.0958718i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.91421 + 6.77962i −0.949336 + 1.64430i −0.202509 + 0.979280i \(0.564910\pi\)
−0.746827 + 0.665018i \(0.768424\pi\)
\(18\) 0 0
\(19\) 2.41421 + 4.18154i 0.553859 + 0.959311i 0.997991 + 0.0633502i \(0.0201785\pi\)
−0.444133 + 0.895961i \(0.646488\pi\)
\(20\) −2.41421 −0.539835
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 2.62132 + 4.54026i 0.546583 + 0.946710i 0.998505 + 0.0546524i \(0.0174051\pi\)
−0.451922 + 0.892057i \(0.649262\pi\)
\(24\) 0 0
\(25\) −0.414214 + 0.717439i −0.0828427 + 0.143488i
\(26\) −3.41421 5.91359i −0.669582 1.15975i
\(27\) 0 0
\(28\) 1.00000 + 2.44949i 0.188982 + 0.462910i
\(29\) 2.82843 0.525226 0.262613 0.964901i \(-0.415416\pi\)
0.262613 + 0.964901i \(0.415416\pi\)
\(30\) 0 0
\(31\) −5.24264 + 9.08052i −0.941606 + 1.63091i −0.179198 + 0.983813i \(0.557350\pi\)
−0.762408 + 0.647097i \(0.775983\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −7.82843 −1.34256
\(35\) 6.32843 + 0.866025i 1.06970 + 0.146385i
\(36\) 0 0
\(37\) 0.828427 + 1.43488i 0.136193 + 0.235892i 0.926052 0.377395i \(-0.123180\pi\)
−0.789860 + 0.613287i \(0.789847\pi\)
\(38\) −2.41421 + 4.18154i −0.391637 + 0.678335i
\(39\) 0 0
\(40\) −1.20711 2.09077i −0.190860 0.330580i
\(41\) 6.65685 1.03963 0.519813 0.854280i \(-0.326002\pi\)
0.519813 + 0.854280i \(0.326002\pi\)
\(42\) 0 0
\(43\) 2.82843 0.431331 0.215666 0.976467i \(-0.430808\pi\)
0.215666 + 0.976467i \(0.430808\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −2.62132 + 4.54026i −0.386493 + 0.669425i
\(47\) −0.378680 0.655892i −0.0552361 0.0956717i 0.837085 0.547073i \(-0.184258\pi\)
−0.892321 + 0.451401i \(0.850924\pi\)
\(48\) 0 0
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) −0.828427 −0.117157
\(51\) 0 0
\(52\) 3.41421 5.91359i 0.473466 0.820068i
\(53\) −5.41421 + 9.37769i −0.743699 + 1.28813i 0.207101 + 0.978320i \(0.433597\pi\)
−0.950800 + 0.309806i \(0.899736\pi\)
\(54\) 0 0
\(55\) 2.41421 0.325532
\(56\) −1.62132 + 2.09077i −0.216658 + 0.279391i
\(57\) 0 0
\(58\) 1.41421 + 2.44949i 0.185695 + 0.321634i
\(59\) 3.82843 6.63103i 0.498419 0.863287i −0.501580 0.865112i \(-0.667248\pi\)
0.999998 + 0.00182490i \(0.000580884\pi\)
\(60\) 0 0
\(61\) 2.20711 + 3.82282i 0.282591 + 0.489462i 0.972022 0.234889i \(-0.0754727\pi\)
−0.689431 + 0.724351i \(0.742139\pi\)
\(62\) −10.4853 −1.33163
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.24264 14.2767i −1.02237 1.77080i
\(66\) 0 0
\(67\) −1.74264 + 3.01834i −0.212897 + 0.368749i −0.952620 0.304163i \(-0.901623\pi\)
0.739723 + 0.672912i \(0.234957\pi\)
\(68\) −3.91421 6.77962i −0.474668 0.822149i
\(69\) 0 0
\(70\) 2.41421 + 5.91359i 0.288554 + 0.706809i
\(71\) 9.31371 1.10533 0.552667 0.833402i \(-0.313610\pi\)
0.552667 + 0.833402i \(0.313610\pi\)
\(72\) 0 0
\(73\) −0.414214 + 0.717439i −0.0484800 + 0.0839699i −0.889247 0.457427i \(-0.848771\pi\)
0.840767 + 0.541397i \(0.182104\pi\)
\(74\) −0.828427 + 1.43488i −0.0963027 + 0.166801i
\(75\) 0 0
\(76\) −4.82843 −0.553859
\(77\) −1.00000 2.44949i −0.113961 0.279145i
\(78\) 0 0
\(79\) −6.62132 11.4685i −0.744957 1.29030i −0.950215 0.311595i \(-0.899137\pi\)
0.205258 0.978708i \(-0.434197\pi\)
\(80\) 1.20711 2.09077i 0.134959 0.233755i
\(81\) 0 0
\(82\) 3.32843 + 5.76500i 0.367563 + 0.636638i
\(83\) 4.17157 0.457890 0.228945 0.973439i \(-0.426472\pi\)
0.228945 + 0.973439i \(0.426472\pi\)
\(84\) 0 0
\(85\) −18.8995 −2.04994
\(86\) 1.41421 + 2.44949i 0.152499 + 0.264135i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −2.24264 3.88437i −0.237719 0.411742i 0.722340 0.691538i \(-0.243067\pi\)
−0.960060 + 0.279796i \(0.909733\pi\)
\(90\) 0 0
\(91\) −11.0711 + 14.2767i −1.16056 + 1.49660i
\(92\) −5.24264 −0.546583
\(93\) 0 0
\(94\) 0.378680 0.655892i 0.0390578 0.0676501i
\(95\) −5.82843 + 10.0951i −0.597984 + 1.03574i
\(96\) 0 0
\(97\) −15.8284 −1.60713 −0.803567 0.595215i \(-0.797067\pi\)
−0.803567 + 0.595215i \(0.797067\pi\)
\(98\) 5.00000 4.89898i 0.505076 0.494872i
\(99\) 0 0
\(100\) −0.414214 0.717439i −0.0414214 0.0717439i
\(101\) 7.07107 12.2474i 0.703598 1.21867i −0.263598 0.964633i \(-0.584909\pi\)
0.967195 0.254034i \(-0.0817575\pi\)
\(102\) 0 0
\(103\) 7.41421 + 12.8418i 0.730544 + 1.26534i 0.956651 + 0.291237i \(0.0940669\pi\)
−0.226107 + 0.974103i \(0.572600\pi\)
\(104\) 6.82843 0.669582
\(105\) 0 0
\(106\) −10.8284 −1.05175
\(107\) −2.67157 4.62730i −0.258271 0.447338i 0.707508 0.706705i \(-0.249819\pi\)
−0.965779 + 0.259367i \(0.916486\pi\)
\(108\) 0 0
\(109\) 2.62132 4.54026i 0.251077 0.434878i −0.712746 0.701423i \(-0.752549\pi\)
0.963823 + 0.266545i \(0.0858819\pi\)
\(110\) 1.20711 + 2.09077i 0.115093 + 0.199347i
\(111\) 0 0
\(112\) −2.62132 0.358719i −0.247691 0.0338958i
\(113\) 7.65685 0.720296 0.360148 0.932895i \(-0.382726\pi\)
0.360148 + 0.932895i \(0.382726\pi\)
\(114\) 0 0
\(115\) −6.32843 + 10.9612i −0.590129 + 1.02213i
\(116\) −1.41421 + 2.44949i −0.131306 + 0.227429i
\(117\) 0 0
\(118\) 7.65685 0.704871
\(119\) 7.82843 + 19.1757i 0.717631 + 1.75783i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.20711 + 3.82282i −0.199822 + 0.346102i
\(123\) 0 0
\(124\) −5.24264 9.08052i −0.470803 0.815455i
\(125\) 10.0711 0.900784
\(126\) 0 0
\(127\) −7.24264 −0.642680 −0.321340 0.946964i \(-0.604133\pi\)
−0.321340 + 0.946964i \(0.604133\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 8.24264 14.2767i 0.722927 1.25215i
\(131\) −3.65685 6.33386i −0.319501 0.553392i 0.660883 0.750489i \(-0.270182\pi\)
−0.980384 + 0.197097i \(0.936849\pi\)
\(132\) 0 0
\(133\) 12.6569 + 1.73205i 1.09749 + 0.150188i
\(134\) −3.48528 −0.301082
\(135\) 0 0
\(136\) 3.91421 6.77962i 0.335641 0.581347i
\(137\) 0.414214 0.717439i 0.0353887 0.0612949i −0.847789 0.530334i \(-0.822066\pi\)
0.883177 + 0.469039i \(0.155400\pi\)
\(138\) 0 0
\(139\) −6.00000 −0.508913 −0.254457 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) −3.91421 + 5.04757i −0.330811 + 0.426597i
\(141\) 0 0
\(142\) 4.65685 + 8.06591i 0.390795 + 0.676876i
\(143\) −3.41421 + 5.91359i −0.285511 + 0.494519i
\(144\) 0 0
\(145\) 3.41421 + 5.91359i 0.283535 + 0.491097i
\(146\) −0.828427 −0.0685611
\(147\) 0 0
\(148\) −1.65685 −0.136193
\(149\) −5.65685 9.79796i −0.463428 0.802680i 0.535701 0.844407i \(-0.320047\pi\)
−0.999129 + 0.0417274i \(0.986714\pi\)
\(150\) 0 0
\(151\) 3.62132 6.27231i 0.294699 0.510433i −0.680216 0.733012i \(-0.738114\pi\)
0.974915 + 0.222578i \(0.0714473\pi\)
\(152\) −2.41421 4.18154i −0.195819 0.339168i
\(153\) 0 0
\(154\) 1.62132 2.09077i 0.130650 0.168479i
\(155\) −25.3137 −2.03325
\(156\) 0 0
\(157\) 7.41421 12.8418i 0.591719 1.02489i −0.402282 0.915516i \(-0.631783\pi\)
0.994001 0.109371i \(-0.0348837\pi\)
\(158\) 6.62132 11.4685i 0.526764 0.912382i
\(159\) 0 0
\(160\) 2.41421 0.190860
\(161\) 13.7426 + 1.88064i 1.08307 + 0.148215i
\(162\) 0 0
\(163\) −1.50000 2.59808i −0.117489 0.203497i 0.801283 0.598286i \(-0.204151\pi\)
−0.918772 + 0.394789i \(0.870818\pi\)
\(164\) −3.32843 + 5.76500i −0.259906 + 0.450171i
\(165\) 0 0
\(166\) 2.08579 + 3.61269i 0.161888 + 0.280399i
\(167\) −0.485281 −0.0375522 −0.0187761 0.999824i \(-0.505977\pi\)
−0.0187761 + 0.999824i \(0.505977\pi\)
\(168\) 0 0
\(169\) 33.6274 2.58672
\(170\) −9.44975 16.3674i −0.724763 1.25533i
\(171\) 0 0
\(172\) −1.41421 + 2.44949i −0.107833 + 0.186772i
\(173\) 8.07107 + 13.9795i 0.613632 + 1.06284i 0.990623 + 0.136625i \(0.0436254\pi\)
−0.376991 + 0.926217i \(0.623041\pi\)
\(174\) 0 0
\(175\) 0.828427 + 2.02922i 0.0626232 + 0.153395i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 2.24264 3.88437i 0.168093 0.291146i
\(179\) −4.41421 + 7.64564i −0.329934 + 0.571462i −0.982498 0.186271i \(-0.940360\pi\)
0.652565 + 0.757733i \(0.273693\pi\)
\(180\) 0 0
\(181\) −13.6569 −1.01511 −0.507553 0.861621i \(-0.669450\pi\)
−0.507553 + 0.861621i \(0.669450\pi\)
\(182\) −17.8995 2.44949i −1.32680 0.181568i
\(183\) 0 0
\(184\) −2.62132 4.54026i −0.193246 0.334712i
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) 3.91421 + 6.77962i 0.286236 + 0.495775i
\(188\) 0.757359 0.0552361
\(189\) 0 0
\(190\) −11.6569 −0.845677
\(191\) 6.65685 + 11.5300i 0.481673 + 0.834282i 0.999779 0.0210344i \(-0.00669595\pi\)
−0.518106 + 0.855317i \(0.673363\pi\)
\(192\) 0 0
\(193\) 7.41421 12.8418i 0.533687 0.924373i −0.465539 0.885027i \(-0.654139\pi\)
0.999226 0.0393452i \(-0.0125272\pi\)
\(194\) −7.91421 13.7078i −0.568207 0.984164i
\(195\) 0 0
\(196\) 6.74264 + 1.88064i 0.481617 + 0.134331i
\(197\) 20.4853 1.45952 0.729758 0.683706i \(-0.239633\pi\)
0.729758 + 0.683706i \(0.239633\pi\)
\(198\) 0 0
\(199\) 9.82843 17.0233i 0.696719 1.20675i −0.272879 0.962048i \(-0.587976\pi\)
0.969598 0.244704i \(-0.0786908\pi\)
\(200\) 0.414214 0.717439i 0.0292893 0.0507306i
\(201\) 0 0
\(202\) 14.1421 0.995037
\(203\) 4.58579 5.91359i 0.321859 0.415053i
\(204\) 0 0
\(205\) 8.03553 + 13.9180i 0.561226 + 0.972072i
\(206\) −7.41421 + 12.8418i −0.516573 + 0.894730i
\(207\) 0 0
\(208\) 3.41421 + 5.91359i 0.236733 + 0.410034i
\(209\) 4.82843 0.333989
\(210\) 0 0
\(211\) 9.17157 0.631397 0.315699 0.948860i \(-0.397761\pi\)
0.315699 + 0.948860i \(0.397761\pi\)
\(212\) −5.41421 9.37769i −0.371850 0.644063i
\(213\) 0 0
\(214\) 2.67157 4.62730i 0.182625 0.316316i
\(215\) 3.41421 + 5.91359i 0.232847 + 0.403304i
\(216\) 0 0
\(217\) 10.4853 + 25.6836i 0.711787 + 1.74352i
\(218\) 5.24264 0.355076
\(219\) 0 0
\(220\) −1.20711 + 2.09077i −0.0813831 + 0.140960i
\(221\) 26.7279 46.2941i 1.79791 3.11408i
\(222\) 0 0
\(223\) 9.31371 0.623692 0.311846 0.950133i \(-0.399053\pi\)
0.311846 + 0.950133i \(0.399053\pi\)
\(224\) −1.00000 2.44949i −0.0668153 0.163663i
\(225\) 0 0
\(226\) 3.82843 + 6.63103i 0.254663 + 0.441090i
\(227\) −5.15685 + 8.93193i −0.342272 + 0.592833i −0.984854 0.173384i \(-0.944530\pi\)
0.642582 + 0.766217i \(0.277863\pi\)
\(228\) 0 0
\(229\) −5.65685 9.79796i −0.373815 0.647467i 0.616334 0.787485i \(-0.288617\pi\)
−0.990149 + 0.140018i \(0.955284\pi\)
\(230\) −12.6569 −0.834568
\(231\) 0 0
\(232\) −2.82843 −0.185695
\(233\) −7.15685 12.3960i −0.468861 0.812091i 0.530505 0.847682i \(-0.322002\pi\)
−0.999366 + 0.0355903i \(0.988669\pi\)
\(234\) 0 0
\(235\) 0.914214 1.58346i 0.0596367 0.103294i
\(236\) 3.82843 + 6.63103i 0.249209 + 0.431643i
\(237\) 0 0
\(238\) −12.6924 + 16.3674i −0.822725 + 1.06094i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 4.48528 7.76874i 0.288922 0.500428i −0.684630 0.728890i \(-0.740036\pi\)
0.973553 + 0.228462i \(0.0733697\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) −4.41421 −0.282591
\(245\) 12.0711 11.8272i 0.771192 0.755611i
\(246\) 0 0
\(247\) −16.4853 28.5533i −1.04893 1.81681i
\(248\) 5.24264 9.08052i 0.332908 0.576614i
\(249\) 0 0
\(250\) 5.03553 + 8.72180i 0.318475 + 0.551615i
\(251\) 2.14214 0.135210 0.0676052 0.997712i \(-0.478464\pi\)
0.0676052 + 0.997712i \(0.478464\pi\)
\(252\) 0 0
\(253\) 5.24264 0.329602
\(254\) −3.62132 6.27231i −0.227222 0.393560i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.4142 + 26.6982i 0.961512 + 1.66539i 0.718707 + 0.695313i \(0.244734\pi\)
0.242805 + 0.970075i \(0.421932\pi\)
\(258\) 0 0
\(259\) 4.34315 + 0.594346i 0.269870 + 0.0369309i
\(260\) 16.4853 1.02237
\(261\) 0 0
\(262\) 3.65685 6.33386i 0.225921 0.391307i
\(263\) −6.65685 + 11.5300i −0.410479 + 0.710971i −0.994942 0.100450i \(-0.967972\pi\)
0.584463 + 0.811420i \(0.301305\pi\)
\(264\) 0 0
\(265\) −26.1421 −1.60590
\(266\) 4.82843 + 11.8272i 0.296050 + 0.725171i
\(267\) 0 0
\(268\) −1.74264 3.01834i −0.106449 0.184375i
\(269\) 3.03553 5.25770i 0.185080 0.320568i −0.758524 0.651646i \(-0.774079\pi\)
0.943603 + 0.331078i \(0.107412\pi\)
\(270\) 0 0
\(271\) −4.65685 8.06591i −0.282884 0.489969i 0.689210 0.724562i \(-0.257958\pi\)
−0.972094 + 0.234593i \(0.924624\pi\)
\(272\) 7.82843 0.474668
\(273\) 0 0
\(274\) 0.828427 0.0500471
\(275\) 0.414214 + 0.717439i 0.0249780 + 0.0432632i
\(276\) 0 0
\(277\) 0.585786 1.01461i 0.0351965 0.0609621i −0.847891 0.530171i \(-0.822128\pi\)
0.883087 + 0.469209i \(0.155461\pi\)
\(278\) −3.00000 5.19615i −0.179928 0.311645i
\(279\) 0 0
\(280\) −6.32843 0.866025i −0.378196 0.0517549i
\(281\) −19.4853 −1.16239 −0.581197 0.813763i \(-0.697416\pi\)
−0.581197 + 0.813763i \(0.697416\pi\)
\(282\) 0 0
\(283\) 15.0711 26.1039i 0.895882 1.55171i 0.0631728 0.998003i \(-0.479878\pi\)
0.832709 0.553711i \(-0.186789\pi\)
\(284\) −4.65685 + 8.06591i −0.276333 + 0.478624i
\(285\) 0 0
\(286\) −6.82843 −0.403773
\(287\) 10.7929 13.9180i 0.637084 0.821551i
\(288\) 0 0
\(289\) −22.1421 38.3513i −1.30248 2.25596i
\(290\) −3.41421 + 5.91359i −0.200490 + 0.347258i
\(291\) 0 0
\(292\) −0.414214 0.717439i −0.0242400 0.0419849i
\(293\) −7.17157 −0.418968 −0.209484 0.977812i \(-0.567178\pi\)
−0.209484 + 0.977812i \(0.567178\pi\)
\(294\) 0 0
\(295\) 18.4853 1.07625
\(296\) −0.828427 1.43488i −0.0481513 0.0834006i
\(297\) 0 0
\(298\) 5.65685 9.79796i 0.327693 0.567581i
\(299\) −17.8995 31.0028i −1.03515 1.79294i
\(300\) 0 0
\(301\) 4.58579 5.91359i 0.264320 0.340854i
\(302\) 7.24264 0.416767
\(303\) 0 0
\(304\) 2.41421 4.18154i 0.138465 0.239828i
\(305\) −5.32843 + 9.22911i −0.305105 + 0.528457i
\(306\) 0 0
\(307\) 10.6274 0.606539 0.303269 0.952905i \(-0.401922\pi\)
0.303269 + 0.952905i \(0.401922\pi\)
\(308\) 2.62132 + 0.358719i 0.149364 + 0.0204399i
\(309\) 0 0
\(310\) −12.6569 21.9223i −0.718861 1.24510i
\(311\) −16.1066 + 27.8975i −0.913322 + 1.58192i −0.103981 + 0.994579i \(0.533158\pi\)
−0.809340 + 0.587340i \(0.800175\pi\)
\(312\) 0 0
\(313\) 3.34315 + 5.79050i 0.188966 + 0.327298i 0.944906 0.327343i \(-0.106153\pi\)
−0.755940 + 0.654641i \(0.772820\pi\)
\(314\) 14.8284 0.836817
\(315\) 0 0
\(316\) 13.2426 0.744957
\(317\) 9.93503 + 17.2080i 0.558007 + 0.966496i 0.997663 + 0.0683299i \(0.0217670\pi\)
−0.439656 + 0.898166i \(0.644900\pi\)
\(318\) 0 0
\(319\) 1.41421 2.44949i 0.0791808 0.137145i
\(320\) 1.20711 + 2.09077i 0.0674793 + 0.116878i
\(321\) 0 0
\(322\) 5.24264 + 12.8418i 0.292161 + 0.715645i
\(323\) −37.7990 −2.10319
\(324\) 0 0
\(325\) 2.82843 4.89898i 0.156893 0.271746i
\(326\) 1.50000 2.59808i 0.0830773 0.143894i
\(327\) 0 0
\(328\) −6.65685 −0.367563
\(329\) −1.98528 0.271680i −0.109452 0.0149782i
\(330\) 0 0
\(331\) 8.15685 + 14.1281i 0.448341 + 0.776550i 0.998278 0.0586563i \(-0.0186816\pi\)
−0.549937 + 0.835206i \(0.685348\pi\)
\(332\) −2.08579 + 3.61269i −0.114472 + 0.198272i
\(333\) 0 0
\(334\) −0.242641 0.420266i −0.0132767 0.0229959i
\(335\) −8.41421 −0.459718
\(336\) 0 0
\(337\) 26.4853 1.44275 0.721373 0.692547i \(-0.243512\pi\)
0.721373 + 0.692547i \(0.243512\pi\)
\(338\) 16.8137 + 29.1222i 0.914545 + 1.58404i
\(339\) 0 0
\(340\) 9.44975 16.3674i 0.512485 0.887649i
\(341\) 5.24264 + 9.08052i 0.283905 + 0.491738i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) −2.82843 −0.152499
\(345\) 0 0
\(346\) −8.07107 + 13.9795i −0.433903 + 0.751543i
\(347\) 16.5711 28.7019i 0.889582 1.54080i 0.0492108 0.998788i \(-0.484329\pi\)
0.840371 0.542012i \(-0.182337\pi\)
\(348\) 0 0
\(349\) 9.72792 0.520724 0.260362 0.965511i \(-0.416158\pi\)
0.260362 + 0.965511i \(0.416158\pi\)
\(350\) −1.34315 + 1.73205i −0.0717942 + 0.0925820i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −5.58579 + 9.67487i −0.297301 + 0.514941i −0.975518 0.219921i \(-0.929420\pi\)
0.678216 + 0.734862i \(0.262753\pi\)
\(354\) 0 0
\(355\) 11.2426 + 19.4728i 0.596697 + 1.03351i
\(356\) 4.48528 0.237719
\(357\) 0 0
\(358\) −8.82843 −0.466597
\(359\) 4.24264 + 7.34847i 0.223918 + 0.387837i 0.955994 0.293385i \(-0.0947819\pi\)
−0.732076 + 0.681223i \(0.761449\pi\)
\(360\) 0 0
\(361\) −2.15685 + 3.73578i −0.113519 + 0.196620i
\(362\) −6.82843 11.8272i −0.358894 0.621623i
\(363\) 0 0
\(364\) −6.82843 16.7262i −0.357907 0.876689i
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −11.2426 + 19.4728i −0.586861 + 1.01647i 0.407780 + 0.913080i \(0.366303\pi\)
−0.994641 + 0.103393i \(0.967030\pi\)
\(368\) 2.62132 4.54026i 0.136646 0.236677i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 10.8284 + 26.5241i 0.562184 + 1.37706i
\(372\) 0 0
\(373\) −4.86396 8.42463i −0.251846 0.436211i 0.712188 0.701989i \(-0.247704\pi\)
−0.964034 + 0.265778i \(0.914371\pi\)
\(374\) −3.91421 + 6.77962i −0.202399 + 0.350566i
\(375\) 0 0
\(376\) 0.378680 + 0.655892i 0.0195289 + 0.0338251i
\(377\) −19.3137 −0.994707
\(378\) 0 0
\(379\) 30.6569 1.57474 0.787368 0.616483i \(-0.211443\pi\)
0.787368 + 0.616483i \(0.211443\pi\)
\(380\) −5.82843 10.0951i −0.298992 0.517869i
\(381\) 0 0
\(382\) −6.65685 + 11.5300i −0.340594 + 0.589927i
\(383\) 11.1421 + 19.2987i 0.569337 + 0.986120i 0.996632 + 0.0820076i \(0.0261332\pi\)
−0.427295 + 0.904112i \(0.640533\pi\)
\(384\) 0 0
\(385\) 3.91421 5.04757i 0.199487 0.257248i
\(386\) 14.8284 0.754747
\(387\) 0 0
\(388\) 7.91421 13.7078i 0.401783 0.695909i
\(389\) 11.8640 20.5490i 0.601527 1.04187i −0.391063 0.920364i \(-0.627893\pi\)
0.992590 0.121511i \(-0.0387740\pi\)
\(390\) 0 0
\(391\) −41.0416 −2.07556
\(392\) 1.74264 + 6.77962i 0.0880166 + 0.342422i
\(393\) 0 0
\(394\) 10.2426 + 17.7408i 0.516017 + 0.893767i
\(395\) 15.9853 27.6873i 0.804307 1.39310i
\(396\) 0 0
\(397\) 2.24264 + 3.88437i 0.112555 + 0.194951i 0.916800 0.399347i \(-0.130763\pi\)
−0.804245 + 0.594298i \(0.797430\pi\)
\(398\) 19.6569 0.985309
\(399\) 0 0
\(400\) 0.828427 0.0414214
\(401\) 11.8995 + 20.6105i 0.594232 + 1.02924i 0.993655 + 0.112474i \(0.0358774\pi\)
−0.399422 + 0.916767i \(0.630789\pi\)
\(402\) 0 0
\(403\) 35.7990 62.0057i 1.78327 3.08872i
\(404\) 7.07107 + 12.2474i 0.351799 + 0.609333i
\(405\) 0 0
\(406\) 7.41421 + 1.01461i 0.367961 + 0.0503543i
\(407\) 1.65685 0.0821272
\(408\) 0 0
\(409\) −19.7279 + 34.1698i −0.975483 + 1.68959i −0.297151 + 0.954831i \(0.596036\pi\)
−0.678332 + 0.734756i \(0.737297\pi\)
\(410\) −8.03553 + 13.9180i −0.396847 + 0.687359i
\(411\) 0 0
\(412\) −14.8284 −0.730544
\(413\) −7.65685 18.7554i −0.376769 0.922892i
\(414\) 0 0
\(415\) 5.03553 + 8.72180i 0.247185 + 0.428136i
\(416\) −3.41421 + 5.91359i −0.167396 + 0.289938i
\(417\) 0 0
\(418\) 2.41421 + 4.18154i 0.118083 + 0.204526i
\(419\) −13.7990 −0.674125 −0.337062 0.941482i \(-0.609433\pi\)
−0.337062 + 0.941482i \(0.609433\pi\)
\(420\) 0 0
\(421\) 9.17157 0.446995 0.223498 0.974704i \(-0.428253\pi\)
0.223498 + 0.974704i \(0.428253\pi\)
\(422\) 4.58579 + 7.94282i 0.223233 + 0.386650i
\(423\) 0 0
\(424\) 5.41421 9.37769i 0.262937 0.455421i
\(425\) −3.24264 5.61642i −0.157291 0.272436i
\(426\) 0 0
\(427\) 11.5711 + 1.58346i 0.559963 + 0.0766292i
\(428\) 5.34315 0.258271
\(429\) 0 0
\(430\) −3.41421 + 5.91359i −0.164648 + 0.285179i
\(431\) −12.4142 + 21.5020i −0.597972 + 1.03572i 0.395149 + 0.918617i \(0.370693\pi\)
−0.993120 + 0.117100i \(0.962640\pi\)
\(432\) 0 0
\(433\) −15.3431 −0.737345 −0.368672 0.929559i \(-0.620188\pi\)
−0.368672 + 0.929559i \(0.620188\pi\)
\(434\) −17.0000 + 21.9223i −0.816026 + 1.05230i
\(435\) 0 0
\(436\) 2.62132 + 4.54026i 0.125538 + 0.217439i
\(437\) −12.6569 + 21.9223i −0.605459 + 1.04869i
\(438\) 0 0
\(439\) 16.6924 + 28.9121i 0.796684 + 1.37990i 0.921764 + 0.387751i \(0.126748\pi\)
−0.125080 + 0.992147i \(0.539919\pi\)
\(440\) −2.41421 −0.115093
\(441\) 0 0
\(442\) 53.4558 2.54264
\(443\) 12.8284 + 22.2195i 0.609497 + 1.05568i 0.991323 + 0.131446i \(0.0419619\pi\)
−0.381826 + 0.924234i \(0.624705\pi\)
\(444\) 0 0
\(445\) 5.41421 9.37769i 0.256658 0.444545i
\(446\) 4.65685 + 8.06591i 0.220508 + 0.381932i
\(447\) 0 0
\(448\) 1.62132 2.09077i 0.0766002 0.0987796i
\(449\) 39.1127 1.84584 0.922921 0.384989i \(-0.125795\pi\)
0.922921 + 0.384989i \(0.125795\pi\)
\(450\) 0 0
\(451\) 3.32843 5.76500i 0.156730 0.271463i
\(452\) −3.82843 + 6.63103i −0.180074 + 0.311897i
\(453\) 0 0
\(454\) −10.3137 −0.484046
\(455\) −43.2132 5.91359i −2.02587 0.277233i
\(456\) 0 0
\(457\) 5.31371 + 9.20361i 0.248565 + 0.430527i 0.963128 0.269044i \(-0.0867078\pi\)
−0.714563 + 0.699571i \(0.753374\pi\)
\(458\) 5.65685 9.79796i 0.264327 0.457829i
\(459\) 0 0
\(460\) −6.32843 10.9612i −0.295064 0.511067i
\(461\) 12.3431 0.574878 0.287439 0.957799i \(-0.407196\pi\)
0.287439 + 0.957799i \(0.407196\pi\)
\(462\) 0 0
\(463\) −39.1127 −1.81772 −0.908861 0.417100i \(-0.863046\pi\)
−0.908861 + 0.417100i \(0.863046\pi\)
\(464\) −1.41421 2.44949i −0.0656532 0.113715i
\(465\) 0 0
\(466\) 7.15685 12.3960i 0.331535 0.574235i
\(467\) 15.4853 + 26.8213i 0.716573 + 1.24114i 0.962350 + 0.271815i \(0.0876238\pi\)
−0.245776 + 0.969327i \(0.579043\pi\)
\(468\) 0 0
\(469\) 3.48528 + 8.53716i 0.160935 + 0.394209i
\(470\) 1.82843 0.0843391
\(471\) 0 0
\(472\) −3.82843 + 6.63103i −0.176218 + 0.305218i
\(473\) 1.41421 2.44949i 0.0650256 0.112628i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) −20.5208 2.80821i −0.940570 0.128714i
\(477\) 0 0
\(478\) −10.0000 17.3205i −0.457389 0.792222i
\(479\) 5.41421 9.37769i 0.247382 0.428478i −0.715417 0.698698i \(-0.753763\pi\)
0.962799 + 0.270220i \(0.0870965\pi\)
\(480\) 0 0
\(481\) −5.65685 9.79796i −0.257930 0.446748i
\(482\) 8.97056 0.408598
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −19.1066 33.0936i −0.867586 1.50270i
\(486\) 0 0
\(487\) −0.656854 + 1.13770i −0.0297649 + 0.0515543i −0.880524 0.474001i \(-0.842809\pi\)
0.850759 + 0.525556i \(0.176143\pi\)
\(488\) −2.20711 3.82282i −0.0999110 0.173051i
\(489\) 0 0
\(490\) 16.2782 + 4.54026i 0.735373 + 0.205108i
\(491\) −29.6274 −1.33707 −0.668533 0.743682i \(-0.733078\pi\)
−0.668533 + 0.743682i \(0.733078\pi\)
\(492\) 0 0
\(493\) −11.0711 + 19.1757i −0.498616 + 0.863628i
\(494\) 16.4853 28.5533i 0.741708 1.28468i
\(495\) 0 0
\(496\) 10.4853 0.470803
\(497\) 15.1005 19.4728i 0.677350 0.873476i
\(498\) 0 0
\(499\) −12.8284 22.2195i −0.574279 0.994681i −0.996120 0.0880107i \(-0.971949\pi\)
0.421840 0.906670i \(-0.361384\pi\)
\(500\) −5.03553 + 8.72180i −0.225196 + 0.390051i
\(501\) 0 0
\(502\) 1.07107 + 1.85514i 0.0478041 + 0.0827991i
\(503\) 24.9706 1.11338 0.556691 0.830720i \(-0.312071\pi\)
0.556691 + 0.830720i \(0.312071\pi\)
\(504\) 0 0
\(505\) 34.1421 1.51931
\(506\) 2.62132 + 4.54026i 0.116532 + 0.201839i
\(507\) 0 0
\(508\) 3.62132 6.27231i 0.160670 0.278289i
\(509\) 15.4142 + 26.6982i 0.683223 + 1.18338i 0.973992 + 0.226584i \(0.0727556\pi\)
−0.290769 + 0.956793i \(0.593911\pi\)
\(510\) 0 0
\(511\) 0.828427 + 2.02922i 0.0366475 + 0.0897676i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.4142 + 26.6982i −0.679892 + 1.17761i
\(515\) −17.8995 + 31.0028i −0.788746 + 1.36615i
\(516\) 0 0
\(517\) −0.757359 −0.0333086
\(518\) 1.65685 + 4.05845i 0.0727980 + 0.178318i
\(519\) 0 0
\(520\) 8.24264 + 14.2767i 0.361464 + 0.626074i
\(521\) 3.34315 5.79050i 0.146466 0.253686i −0.783453 0.621451i \(-0.786543\pi\)
0.929919 + 0.367765i \(0.119877\pi\)
\(522\) 0 0
\(523\) −9.72792 16.8493i −0.425372 0.736766i 0.571083 0.820892i \(-0.306524\pi\)
−0.996455 + 0.0841260i \(0.973190\pi\)
\(524\) 7.31371 0.319501
\(525\) 0 0
\(526\) −13.3137 −0.580505
\(527\) −41.0416 71.0862i −1.78780 3.09656i
\(528\) 0 0
\(529\) −2.24264 + 3.88437i −0.0975061 + 0.168886i
\(530\) −13.0711 22.6398i −0.567771 0.983408i
\(531\) 0 0
\(532\) −7.82843 + 10.0951i −0.339405 + 0.437679i
\(533\) −45.4558 −1.96891
\(534\) 0 0
\(535\) 6.44975 11.1713i 0.278847 0.482977i
\(536\) 1.74264 3.01834i 0.0752706 0.130373i
\(537\) 0 0
\(538\) 6.07107 0.261742
\(539\) −6.74264 1.88064i −0.290426 0.0810048i
\(540\) 0 0
\(541\) 18.2782 + 31.6587i 0.785840 + 1.36111i 0.928496 + 0.371343i \(0.121102\pi\)
−0.142656 + 0.989772i \(0.545564\pi\)
\(542\) 4.65685 8.06591i 0.200029 0.346460i
\(543\) 0 0
\(544\) 3.91421 + 6.77962i 0.167821 + 0.290674i
\(545\) 12.6569 0.542160
\(546\) 0 0
\(547\) −7.85786 −0.335978 −0.167989 0.985789i \(-0.553727\pi\)
−0.167989 + 0.985789i \(0.553727\pi\)
\(548\) 0.414214 + 0.717439i 0.0176943 + 0.0306475i
\(549\) 0 0
\(550\) −0.414214 + 0.717439i −0.0176621 + 0.0305917i
\(551\) 6.82843 + 11.8272i 0.290901 + 0.503855i
\(552\) 0 0
\(553\) −34.7132 4.75039i −1.47616 0.202007i
\(554\) 1.17157 0.0497754
\(555\) 0 0
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) 6.24264 10.8126i 0.264509 0.458143i −0.702926 0.711263i \(-0.748123\pi\)
0.967435 + 0.253120i \(0.0814567\pi\)
\(558\) 0 0
\(559\) −19.3137 −0.816883
\(560\) −2.41421 5.91359i −0.102019 0.249895i
\(561\) 0 0
\(562\) −9.74264 16.8747i −0.410968 0.711818i
\(563\) 7.17157 12.4215i 0.302246 0.523505i −0.674399 0.738368i \(-0.735597\pi\)
0.976644 + 0.214863i \(0.0689303\pi\)
\(564\) 0 0
\(565\) 9.24264 + 16.0087i 0.388841 + 0.673492i
\(566\) 30.1421 1.26697
\(567\) 0 0
\(568\) −9.31371 −0.390795
\(569\) −11.0000 19.0526i −0.461144 0.798725i 0.537874 0.843025i \(-0.319228\pi\)
−0.999018 + 0.0443003i \(0.985894\pi\)
\(570\) 0 0
\(571\) 5.17157 8.95743i 0.216424 0.374857i −0.737288 0.675578i \(-0.763894\pi\)
0.953712 + 0.300721i \(0.0972274\pi\)
\(572\) −3.41421 5.91359i −0.142755 0.247260i
\(573\) 0 0
\(574\) 17.4497 + 2.38794i 0.728338 + 0.0996708i
\(575\) −4.34315 −0.181122
\(576\) 0 0
\(577\) 11.5711 20.0417i 0.481710 0.834346i −0.518070 0.855338i \(-0.673349\pi\)
0.999780 + 0.0209924i \(0.00668258\pi\)
\(578\) 22.1421 38.3513i 0.920991 1.59520i
\(579\) 0 0
\(580\) −6.82843 −0.283535
\(581\) 6.76346 8.72180i 0.280595 0.361841i
\(582\) 0 0
\(583\) 5.41421 + 9.37769i 0.224234 + 0.388384i
\(584\) 0.414214 0.717439i 0.0171403 0.0296878i
\(585\) 0 0
\(586\) −3.58579 6.21076i −0.148127 0.256564i
\(587\) −0.142136 −0.00586657 −0.00293328 0.999996i \(-0.500934\pi\)
−0.00293328 + 0.999996i \(0.500934\pi\)
\(588\) 0 0
\(589\) −50.6274 −2.08607
\(590\) 9.24264 + 16.0087i 0.380513 + 0.659069i
\(591\) 0 0
\(592\) 0.828427 1.43488i 0.0340481 0.0589731i
\(593\) −13.9706 24.1977i −0.573702 0.993681i −0.996181 0.0873088i \(-0.972173\pi\)
0.422479 0.906373i \(-0.361160\pi\)
\(594\) 0 0
\(595\) −30.6421 + 39.5145i −1.25621 + 1.61994i
\(596\) 11.3137 0.463428
\(597\) 0 0
\(598\) 17.8995 31.0028i 0.731965 1.26780i
\(599\) −9.52082 + 16.4905i −0.389010 + 0.673785i −0.992317 0.123724i \(-0.960516\pi\)
0.603307 + 0.797509i \(0.293850\pi\)
\(600\) 0 0
\(601\) −20.0000 −0.815817 −0.407909 0.913023i \(-0.633742\pi\)
−0.407909 + 0.913023i \(0.633742\pi\)
\(602\) 7.41421 + 1.01461i 0.302181 + 0.0413525i
\(603\) 0 0
\(604\) 3.62132 + 6.27231i 0.147349 + 0.255217i
\(605\) 1.20711 2.09077i 0.0490759 0.0850019i
\(606\) 0 0
\(607\) −1.89340 3.27946i −0.0768507 0.133109i 0.825039 0.565076i \(-0.191153\pi\)
−0.901890 + 0.431967i \(0.857820\pi\)
\(608\) 4.82843 0.195819
\(609\) 0 0
\(610\) −10.6569 −0.431483
\(611\) 2.58579 + 4.47871i 0.104610 + 0.181189i
\(612\) 0 0
\(613\) 5.55025 9.61332i 0.224173 0.388278i −0.731898 0.681414i \(-0.761365\pi\)
0.956071 + 0.293136i \(0.0946987\pi\)
\(614\) 5.31371 + 9.20361i 0.214444 + 0.371428i
\(615\) 0 0
\(616\) 1.00000 + 2.44949i 0.0402911 + 0.0986928i
\(617\) 7.51472 0.302531 0.151266 0.988493i \(-0.451665\pi\)
0.151266 + 0.988493i \(0.451665\pi\)
\(618\) 0 0
\(619\) −8.74264 + 15.1427i −0.351396 + 0.608636i −0.986494 0.163795i \(-0.947626\pi\)
0.635098 + 0.772432i \(0.280960\pi\)
\(620\) 12.6569 21.9223i 0.508311 0.880421i
\(621\) 0 0
\(622\) −32.2132 −1.29163
\(623\) −11.7574 1.60896i −0.471049 0.0644615i
\(624\) 0 0
\(625\) 14.2279 + 24.6435i 0.569117 + 0.985739i
\(626\) −3.34315 + 5.79050i −0.133619 + 0.231435i
\(627\) 0 0
\(628\) 7.41421 + 12.8418i 0.295859 + 0.512443i
\(629\) −12.9706 −0.517170
\(630\) 0 0
\(631\) −34.9706 −1.39216 −0.696078 0.717966i \(-0.745073\pi\)
−0.696078 + 0.717966i \(0.745073\pi\)
\(632\) 6.62132 + 11.4685i 0.263382 + 0.456191i
\(633\) 0 0
\(634\) −9.93503 + 17.2080i −0.394570 + 0.683416i
\(635\) −8.74264 15.1427i −0.346941 0.600920i
\(636\) 0 0
\(637\) 11.8995 + 46.2941i 0.471475 + 1.83424i
\(638\) 2.82843 0.111979
\(639\) 0 0
\(640\) −1.20711 + 2.09077i −0.0477151 + 0.0826450i
\(641\) −2.34315 + 4.05845i −0.0925487 + 0.160299i −0.908583 0.417705i \(-0.862835\pi\)
0.816034 + 0.578004i \(0.196168\pi\)
\(642\) 0 0
\(643\) 6.34315 0.250149 0.125075 0.992147i \(-0.460083\pi\)
0.125075 + 0.992147i \(0.460083\pi\)
\(644\) −8.50000 + 10.9612i −0.334947 + 0.431930i
\(645\) 0 0
\(646\) −18.8995 32.7349i −0.743591 1.28794i
\(647\) −8.34924 + 14.4613i −0.328243 + 0.568533i −0.982163 0.188030i \(-0.939790\pi\)
0.653921 + 0.756563i \(0.273123\pi\)
\(648\) 0 0
\(649\) −3.82843 6.63103i −0.150279 0.260291i
\(650\) 5.65685 0.221880
\(651\) 0 0
\(652\) 3.00000 0.117489
\(653\) −13.1777 22.8244i −0.515682 0.893188i −0.999834 0.0182037i \(-0.994205\pi\)
0.484152 0.874984i \(-0.339128\pi\)
\(654\) 0 0
\(655\) 8.82843 15.2913i 0.344955 0.597480i
\(656\) −3.32843 5.76500i −0.129953 0.225086i
\(657\) 0 0
\(658\) −0.757359 1.85514i −0.0295249 0.0723210i
\(659\) −30.9411 −1.20530 −0.602648 0.798007i \(-0.705888\pi\)
−0.602648 + 0.798007i \(0.705888\pi\)
\(660\) 0 0
\(661\) 2.51472 4.35562i 0.0978112 0.169414i −0.812967 0.582309i \(-0.802149\pi\)
0.910778 + 0.412895i \(0.135483\pi\)
\(662\) −8.15685 + 14.1281i −0.317025 + 0.549104i
\(663\) 0 0
\(664\) −4.17157 −0.161888
\(665\) 11.6569 + 28.5533i 0.452033 + 1.10725i
\(666\) 0 0
\(667\) 7.41421 + 12.8418i 0.287079 + 0.497236i
\(668\) 0.242641 0.420266i 0.00938805 0.0162606i
\(669\) 0 0
\(670\) −4.20711 7.28692i −0.162535 0.281518i
\(671\) 4.41421 0.170409
\(672\) 0 0
\(673\) −20.6274 −0.795128 −0.397564 0.917574i \(-0.630144\pi\)
−0.397564 + 0.917574i \(0.630144\pi\)
\(674\) 13.2426 + 22.9369i 0.510087 + 0.883497i
\(675\) 0 0
\(676\) −16.8137 + 29.1222i −0.646681 + 1.12008i
\(677\) −15.3848 26.6472i −0.591285 1.02414i −0.994060 0.108836i \(-0.965288\pi\)
0.402775 0.915299i \(-0.368046\pi\)
\(678\) 0 0
\(679\) −25.6630 + 33.0936i −0.984854 + 1.27002i
\(680\) 18.8995 0.724763
\(681\) 0 0
\(682\) −5.24264 + 9.08052i −0.200751 + 0.347711i
\(683\) 3.17157 5.49333i 0.121357 0.210196i −0.798946 0.601403i \(-0.794609\pi\)
0.920303 + 0.391206i \(0.127942\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) −2.13604 18.3967i −0.0815543 0.702388i
\(687\) 0 0
\(688\) −1.41421 2.44949i −0.0539164 0.0933859i
\(689\) 36.9706 64.0349i 1.40847 2.43954i
\(690\) 0 0
\(691\) −0.428932 0.742932i −0.0163173 0.0282625i 0.857751 0.514065i \(-0.171861\pi\)
−0.874069 + 0.485802i \(0.838528\pi\)
\(692\) −16.1421 −0.613632
\(693\) 0 0
\(694\) 33.1421 1.25806
\(695\) −7.24264 12.5446i −0.274729 0.475845i
\(696\) 0 0
\(697\) −26.0563 + 45.1309i −0.986955 + 1.70946i
\(698\) 4.86396 + 8.42463i 0.184104 + 0.318877i
\(699\) 0 0
\(700\) −2.17157 0.297173i −0.0820777 0.0112321i
\(701\) 0.142136 0.00536839 0.00268419 0.999996i \(-0.499146\pi\)
0.00268419 + 0.999996i \(0.499146\pi\)
\(702\) 0 0
\(703\) −4.00000 + 6.92820i −0.150863 + 0.261302i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −11.1716 −0.420448
\(707\) −14.1421 34.6410i −0.531870 1.30281i
\(708\) 0 0
\(709\) −16.0711 27.8359i −0.603562 1.04540i −0.992277 0.124042i \(-0.960414\pi\)
0.388715 0.921358i \(-0.372919\pi\)
\(710\) −11.2426 + 19.4728i −0.421929 + 0.730802i
\(711\) 0 0
\(712\) 2.24264 + 3.88437i 0.0840465 + 0.145573i
\(713\) −54.9706 −2.05866
\(714\) 0 0
\(715\) −16.4853 −0.616515
\(716\) −4.41421 7.64564i −0.164967 0.285731i
\(717\) 0 0
\(718\) −4.24264 + 7.34847i −0.158334 + 0.274242i
\(719\) 13.1066 + 22.7013i 0.488794 + 0.846616i 0.999917 0.0128919i \(-0.00410372\pi\)
−0.511123 + 0.859508i \(0.670770\pi\)
\(720\) 0 0
\(721\) 38.8701 + 5.31925i 1.44760 + 0.198099i
\(722\) −4.31371 −0.160540
\(723\) 0 0
\(724\) 6.82843 11.8272i 0.253776 0.439554i
\(725\) −1.17157 + 2.02922i −0.0435111 + 0.0753635i
\(726\) 0 0
\(727\) −15.5147 −0.575409 −0.287705 0.957719i \(-0.592892\pi\)
−0.287705 + 0.957719i \(0.592892\pi\)
\(728\) 11.0711 14.2767i 0.410321 0.529129i
\(729\) 0 0
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) −11.0711 + 19.1757i −0.409478 + 0.709237i
\(732\) 0 0
\(733\) 11.6213 + 20.1287i 0.429243 + 0.743471i 0.996806 0.0798589i \(-0.0254470\pi\)
−0.567563 + 0.823330i \(0.692114\pi\)
\(734\) −22.4853 −0.829947
\(735\) 0 0
\(736\) 5.24264 0.193246
\(737\) 1.74264 + 3.01834i 0.0641910 + 0.111182i
\(738\) 0 0
\(739\) 17.0000 29.4449i 0.625355 1.08315i −0.363117 0.931744i \(-0.618287\pi\)
0.988472 0.151403i \(-0.0483792\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) −17.5563 + 22.6398i −0.644514 + 0.831132i
\(743\) 2.34315 0.0859617 0.0429808 0.999076i \(-0.486315\pi\)
0.0429808 + 0.999076i \(0.486315\pi\)
\(744\) 0 0
\(745\) 13.6569 23.6544i 0.500348 0.866629i
\(746\) 4.86396 8.42463i 0.178082 0.308448i
\(747\) 0 0
\(748\) −7.82843 −0.286236
\(749\) −14.0061 1.91669i −0.511772 0.0700343i
\(750\) 0 0
\(751\) 4.89949 + 8.48617i 0.178785 + 0.309665i 0.941465 0.337112i \(-0.109450\pi\)
−0.762680 + 0.646777i \(0.776117\pi\)
\(752\) −0.378680 + 0.655892i −0.0138090 + 0.0239179i
\(753\) 0 0
\(754\) −9.65685 16.7262i −0.351682 0.609131i
\(755\) 17.4853 0.636355
\(756\) 0 0
\(757\) 8.34315 0.303237 0.151618 0.988439i \(-0.451552\pi\)
0.151618 + 0.988439i \(0.451552\pi\)
\(758\) 15.3284 + 26.5496i 0.556754 + 0.964325i
\(759\) 0 0
\(760\) 5.82843 10.0951i 0.211419 0.366189i
\(761\) −13.2279 22.9114i −0.479512 0.830539i 0.520212 0.854037i \(-0.325853\pi\)
−0.999724 + 0.0234983i \(0.992520\pi\)
\(762\) 0 0
\(763\) −5.24264 12.8418i −0.189796 0.464904i
\(764\) −13.3137 −0.481673
\(765\) 0 0
\(766\) −11.1421 + 19.2987i −0.402582 + 0.697292i
\(767\) −26.1421 + 45.2795i −0.943938 + 1.63495i
\(768\) 0 0
\(769\) 9.51472 0.343110 0.171555 0.985175i \(-0.445121\pi\)
0.171555 + 0.985175i \(0.445121\pi\)
\(770\) 6.32843 + 0.866025i 0.228061 + 0.0312094i
\(771\) 0 0
\(772\) 7.41421 + 12.8418i 0.266843 + 0.462186i
\(773\) 11.3787 19.7085i 0.409263 0.708864i −0.585545 0.810640i \(-0.699119\pi\)
0.994807 + 0.101776i \(0.0324526\pi\)
\(774\) 0 0
\(775\) −4.34315 7.52255i −0.156010 0.270218i
\(776\) 15.8284 0.568207
\(777\) 0 0
\(778\) 23.7279 0.850687
\(779\) 16.0711 + 27.8359i 0.575806 + 0.997325i
\(780\) 0 0
\(781\) 4.65685 8.06591i 0.166635 0.288621i
\(782\) −20.5208 35.5431i −0.733823 1.27102i
\(783\) 0 0
\(784\) −5.00000 + 4.89898i −0.178571 + 0.174964i
\(785\) 35.7990 1.27772
\(786\) 0 0
\(787\) −17.3848 + 30.1113i −0.619700 + 1.07335i 0.369840 + 0.929095i \(0.379413\pi\)
−0.989540 + 0.144257i \(0.953921\pi\)
\(788\) −10.2426 + 17.7408i −0.364879 + 0.631989i
\(789\) 0 0
\(790\) 31.9706