Properties

Label 315.2.bz.a.82.1
Level 315
Weight 2
Character 315.82
Analytic conductor 2.515
Analytic rank 1
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.bz (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 82.1
Root \(-0.866025 + 0.500000i\)
Character \(\chi\) = 315.82
Dual form 315.2.bz.a.73.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.133975i) q^{2} +(-1.50000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.36603 - 1.36603i) q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.133975i) q^{2} +(-1.50000 + 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.36603 - 1.36603i) q^{8} +(-0.232051 - 1.13397i) q^{10} +(-1.36603 - 2.36603i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(1.36603 + 0.0980762i) q^{14} +(1.23205 - 2.13397i) q^{16} +(-3.73205 - 1.00000i) q^{17} +(0.366025 - 0.633975i) q^{19} +(-1.73205 - 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-0.0358984 - 0.133975i) q^{23} +(-4.96410 - 0.598076i) q^{25} +(1.26795 + 0.732051i) q^{26} +(4.50000 - 0.866025i) q^{28} +3.00000i q^{29} +(-6.46410 + 3.73205i) q^{31} +(-1.33013 + 4.96410i) q^{32} +2.00000 q^{34} +(2.26795 - 5.46410i) q^{35} +(-4.73205 + 1.26795i) q^{37} +(-0.0980762 + 0.366025i) q^{38} +(2.86603 + 3.23205i) q^{40} +6.46410i q^{41} +(2.83013 - 2.83013i) q^{43} +(4.09808 + 2.36603i) q^{44} +(0.0358984 + 0.0621778i) q^{46} +(-2.36603 - 8.83013i) q^{47} +(5.50000 + 4.33013i) q^{49} +(2.56218 - 0.366025i) q^{50} +(4.73205 + 1.26795i) q^{52} +(-6.83013 - 1.83013i) q^{53} +(5.46410 - 2.73205i) q^{55} +(-4.59808 + 2.23205i) q^{56} +(-0.401924 - 1.50000i) q^{58} +(4.09808 + 7.09808i) q^{59} +(1.33013 + 0.767949i) q^{61} +(2.73205 - 2.73205i) q^{62} +2.26795i q^{64} +(4.73205 - 4.19615i) q^{65} +(2.86603 - 10.6962i) q^{67} +(6.46410 - 1.73205i) q^{68} +(-0.401924 + 3.03590i) q^{70} -1.26795 q^{71} +(-3.46410 + 12.9282i) q^{73} +(2.19615 - 1.26795i) q^{74} +1.26795i q^{76} +(1.36603 + 7.09808i) q^{77} +(2.83013 + 1.63397i) q^{79} +(4.59808 + 3.03590i) q^{80} +(-0.866025 - 3.23205i) q^{82} +(2.09808 + 2.09808i) q^{83} +(2.73205 - 8.19615i) q^{85} +(-1.03590 + 1.79423i) q^{86} +(-5.09808 - 1.36603i) q^{88} +(0.330127 - 0.571797i) q^{89} +(3.26795 + 6.73205i) q^{91} +(0.169873 + 0.169873i) q^{92} +(2.36603 + 4.09808i) q^{94} +(1.36603 + 0.901924i) q^{95} +(-5.92820 + 5.92820i) q^{97} +(-3.33013 - 1.42820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{4} - 4q^{5} - 10q^{7} + 2q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{4} - 4q^{5} - 10q^{7} + 2q^{8} + 6q^{10} - 2q^{11} - 8q^{13} + 2q^{14} - 2q^{16} - 8q^{17} - 2q^{19} + 4q^{22} - 14q^{23} - 6q^{25} + 12q^{26} + 18q^{28} - 12q^{31} + 12q^{32} + 8q^{34} + 16q^{35} - 12q^{37} + 10q^{38} + 8q^{40} - 6q^{43} + 6q^{44} + 14q^{46} - 6q^{47} + 22q^{49} - 14q^{50} + 12q^{52} - 10q^{53} + 8q^{55} - 8q^{56} - 12q^{58} + 6q^{59} - 12q^{61} + 4q^{62} + 12q^{65} + 8q^{67} + 12q^{68} - 12q^{70} - 12q^{71} - 12q^{74} + 2q^{77} - 6q^{79} + 8q^{80} - 2q^{83} + 4q^{85} - 18q^{86} - 10q^{88} - 16q^{89} + 20q^{91} + 18q^{92} + 6q^{94} + 2q^{95} + 4q^{97} + 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 + 0.133975i −0.353553 + 0.0947343i −0.431224 0.902245i \(-0.641918\pi\)
0.0776710 + 0.996979i \(0.475252\pi\)
\(3\) 0 0
\(4\) −1.50000 + 0.866025i −0.750000 + 0.433013i
\(5\) −0.133975 + 2.23205i −0.0599153 + 0.998203i
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.36603 1.36603i 0.482963 0.482963i
\(9\) 0 0
\(10\) −0.232051 1.13397i −0.0733809 0.358594i
\(11\) −1.36603 2.36603i −0.411872 0.713384i 0.583222 0.812313i \(-0.301792\pi\)
−0.995094 + 0.0989291i \(0.968458\pi\)
\(12\) 0 0
\(13\) −2.00000 2.00000i −0.554700 0.554700i 0.373094 0.927794i \(-0.378297\pi\)
−0.927794 + 0.373094i \(0.878297\pi\)
\(14\) 1.36603 + 0.0980762i 0.365086 + 0.0262120i
\(15\) 0 0
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) −3.73205 1.00000i −0.905155 0.242536i −0.223926 0.974606i \(-0.571888\pi\)
−0.681229 + 0.732070i \(0.738554\pi\)
\(18\) 0 0
\(19\) 0.366025 0.633975i 0.0839720 0.145444i −0.820981 0.570956i \(-0.806573\pi\)
0.904953 + 0.425512i \(0.139906\pi\)
\(20\) −1.73205 3.46410i −0.387298 0.774597i
\(21\) 0 0
\(22\) 1.00000 + 1.00000i 0.213201 + 0.213201i
\(23\) −0.0358984 0.133975i −0.00748533 0.0279356i 0.962082 0.272760i \(-0.0879364\pi\)
−0.969567 + 0.244824i \(0.921270\pi\)
\(24\) 0 0
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) 1.26795 + 0.732051i 0.248665 + 0.143567i
\(27\) 0 0
\(28\) 4.50000 0.866025i 0.850420 0.163663i
\(29\) 3.00000i 0.557086i 0.960424 + 0.278543i \(0.0898515\pi\)
−0.960424 + 0.278543i \(0.910149\pi\)
\(30\) 0 0
\(31\) −6.46410 + 3.73205i −1.16099 + 0.670296i −0.951540 0.307524i \(-0.900500\pi\)
−0.209447 + 0.977820i \(0.567166\pi\)
\(32\) −1.33013 + 4.96410i −0.235135 + 0.877537i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 2.26795 5.46410i 0.383353 0.923602i
\(36\) 0 0
\(37\) −4.73205 + 1.26795i −0.777944 + 0.208450i −0.625878 0.779921i \(-0.715259\pi\)
−0.152066 + 0.988370i \(0.548593\pi\)
\(38\) −0.0980762 + 0.366025i −0.0159101 + 0.0593772i
\(39\) 0 0
\(40\) 2.86603 + 3.23205i 0.453158 + 0.511032i
\(41\) 6.46410i 1.00952i 0.863259 + 0.504762i \(0.168420\pi\)
−0.863259 + 0.504762i \(0.831580\pi\)
\(42\) 0 0
\(43\) 2.83013 2.83013i 0.431590 0.431590i −0.457579 0.889169i \(-0.651283\pi\)
0.889169 + 0.457579i \(0.151283\pi\)
\(44\) 4.09808 + 2.36603i 0.617808 + 0.356692i
\(45\) 0 0
\(46\) 0.0358984 + 0.0621778i 0.00529293 + 0.00916762i
\(47\) −2.36603 8.83013i −0.345120 1.28801i −0.892472 0.451103i \(-0.851031\pi\)
0.547351 0.836903i \(-0.315636\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 2.56218 0.366025i 0.362347 0.0517638i
\(51\) 0 0
\(52\) 4.73205 + 1.26795i 0.656217 + 0.175833i
\(53\) −6.83013 1.83013i −0.938190 0.251387i −0.242846 0.970065i \(-0.578081\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 0 0
\(55\) 5.46410 2.73205i 0.736779 0.368390i
\(56\) −4.59808 + 2.23205i −0.614444 + 0.298270i
\(57\) 0 0
\(58\) −0.401924 1.50000i −0.0527752 0.196960i
\(59\) 4.09808 + 7.09808i 0.533524 + 0.924091i 0.999233 + 0.0391530i \(0.0124660\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(60\) 0 0
\(61\) 1.33013 + 0.767949i 0.170305 + 0.0983258i 0.582730 0.812666i \(-0.301985\pi\)
−0.412424 + 0.910992i \(0.635318\pi\)
\(62\) 2.73205 2.73205i 0.346971 0.346971i
\(63\) 0 0
\(64\) 2.26795i 0.283494i
\(65\) 4.73205 4.19615i 0.586939 0.520469i
\(66\) 0 0
\(67\) 2.86603 10.6962i 0.350141 1.30674i −0.536350 0.843996i \(-0.680197\pi\)
0.886490 0.462747i \(-0.153136\pi\)
\(68\) 6.46410 1.73205i 0.783887 0.210042i
\(69\) 0 0
\(70\) −0.401924 + 3.03590i −0.0480391 + 0.362859i
\(71\) −1.26795 −0.150478 −0.0752389 0.997166i \(-0.523972\pi\)
−0.0752389 + 0.997166i \(0.523972\pi\)
\(72\) 0 0
\(73\) −3.46410 + 12.9282i −0.405442 + 1.51313i 0.397796 + 0.917474i \(0.369775\pi\)
−0.803238 + 0.595658i \(0.796891\pi\)
\(74\) 2.19615 1.26795i 0.255298 0.147396i
\(75\) 0 0
\(76\) 1.26795i 0.145444i
\(77\) 1.36603 + 7.09808i 0.155673 + 0.808901i
\(78\) 0 0
\(79\) 2.83013 + 1.63397i 0.318414 + 0.183837i 0.650686 0.759347i \(-0.274482\pi\)
−0.332271 + 0.943184i \(0.607815\pi\)
\(80\) 4.59808 + 3.03590i 0.514081 + 0.339424i
\(81\) 0 0
\(82\) −0.866025 3.23205i −0.0956365 0.356920i
\(83\) 2.09808 + 2.09808i 0.230294 + 0.230294i 0.812815 0.582522i \(-0.197934\pi\)
−0.582522 + 0.812815i \(0.697934\pi\)
\(84\) 0 0
\(85\) 2.73205 8.19615i 0.296333 0.888998i
\(86\) −1.03590 + 1.79423i −0.111704 + 0.193477i
\(87\) 0 0
\(88\) −5.09808 1.36603i −0.543457 0.145619i
\(89\) 0.330127 0.571797i 0.0349934 0.0606103i −0.847998 0.529999i \(-0.822192\pi\)
0.882992 + 0.469389i \(0.155526\pi\)
\(90\) 0 0
\(91\) 3.26795 + 6.73205i 0.342574 + 0.705711i
\(92\) 0.169873 + 0.169873i 0.0177105 + 0.0177105i
\(93\) 0 0
\(94\) 2.36603 + 4.09808i 0.244037 + 0.422684i
\(95\) 1.36603 + 0.901924i 0.140151 + 0.0925354i
\(96\) 0 0
\(97\) −5.92820 + 5.92820i −0.601918 + 0.601918i −0.940821 0.338903i \(-0.889944\pi\)
0.338903 + 0.940821i \(0.389944\pi\)
\(98\) −3.33013 1.42820i −0.336394 0.144270i
\(99\) 0 0
\(100\) 7.96410 3.40192i 0.796410 0.340192i
\(101\) −7.16025 + 4.13397i −0.712472 + 0.411346i −0.811976 0.583691i \(-0.801608\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 4.59808 1.23205i 0.453062 0.121398i −0.0250698 0.999686i \(-0.507981\pi\)
0.478132 + 0.878288i \(0.341314\pi\)
\(104\) −5.46410 −0.535799
\(105\) 0 0
\(106\) 3.66025 0.355515
\(107\) −12.6962 + 3.40192i −1.22738 + 0.328876i −0.813560 0.581481i \(-0.802474\pi\)
−0.413823 + 0.910357i \(0.635807\pi\)
\(108\) 0 0
\(109\) −8.76795 + 5.06218i −0.839817 + 0.484869i −0.857202 0.514980i \(-0.827799\pi\)
0.0173849 + 0.999849i \(0.494466\pi\)
\(110\) −2.36603 + 2.09808i −0.225592 + 0.200044i
\(111\) 0 0
\(112\) −4.92820 + 4.26795i −0.465671 + 0.403283i
\(113\) 7.73205 7.73205i 0.727370 0.727370i −0.242725 0.970095i \(-0.578041\pi\)
0.970095 + 0.242725i \(0.0780413\pi\)
\(114\) 0 0
\(115\) 0.303848 0.0621778i 0.0283339 0.00579811i
\(116\) −2.59808 4.50000i −0.241225 0.417815i
\(117\) 0 0
\(118\) −3.00000 3.00000i −0.276172 0.276172i
\(119\) 8.46410 + 5.73205i 0.775903 + 0.525456i
\(120\) 0 0
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) −0.767949 0.205771i −0.0695269 0.0186297i
\(123\) 0 0
\(124\) 6.46410 11.1962i 0.580493 1.00544i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 0.464102 + 0.464102i 0.0411824 + 0.0411824i 0.727398 0.686216i \(-0.240729\pi\)
−0.686216 + 0.727398i \(0.740729\pi\)
\(128\) −2.96410 11.0622i −0.261992 0.977768i
\(129\) 0 0
\(130\) −1.80385 + 2.73205i −0.158208 + 0.239617i
\(131\) 13.3923 + 7.73205i 1.17009 + 0.675552i 0.953702 0.300755i \(-0.0972385\pi\)
0.216390 + 0.976307i \(0.430572\pi\)
\(132\) 0 0
\(133\) −1.46410 + 1.26795i −0.126954 + 0.109945i
\(134\) 5.73205i 0.495174i
\(135\) 0 0
\(136\) −6.46410 + 3.73205i −0.554292 + 0.320021i
\(137\) 3.53590 13.1962i 0.302092 1.12742i −0.633327 0.773884i \(-0.718311\pi\)
0.935420 0.353539i \(-0.115022\pi\)
\(138\) 0 0
\(139\) −5.66025 −0.480096 −0.240048 0.970761i \(-0.577163\pi\)
−0.240048 + 0.970761i \(0.577163\pi\)
\(140\) 1.33013 + 10.1603i 0.112416 + 0.858698i
\(141\) 0 0
\(142\) 0.633975 0.169873i 0.0532020 0.0142554i
\(143\) −2.00000 + 7.46410i −0.167248 + 0.624180i
\(144\) 0 0
\(145\) −6.69615 0.401924i −0.556085 0.0333780i
\(146\) 6.92820i 0.573382i
\(147\) 0 0
\(148\) 6.00000 6.00000i 0.493197 0.493197i
\(149\) −0.696152 0.401924i −0.0570310 0.0329269i 0.471213 0.882019i \(-0.343816\pi\)
−0.528244 + 0.849092i \(0.677150\pi\)
\(150\) 0 0
\(151\) −6.92820 12.0000i −0.563809 0.976546i −0.997159 0.0753205i \(-0.976002\pi\)
0.433350 0.901226i \(-0.357331\pi\)
\(152\) −0.366025 1.36603i −0.0296886 0.110799i
\(153\) 0 0
\(154\) −1.63397 3.36603i −0.131669 0.271242i
\(155\) −7.46410 14.9282i −0.599531 1.19906i
\(156\) 0 0
\(157\) −4.63397 1.24167i −0.369831 0.0990960i 0.0691164 0.997609i \(-0.477982\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −1.63397 0.437822i −0.129992 0.0348313i
\(159\) 0 0
\(160\) −10.9019 3.63397i −0.861873 0.287291i
\(161\) −0.0262794 + 0.366025i −0.00207111 + 0.0288468i
\(162\) 0 0
\(163\) −3.63397 13.5622i −0.284635 1.06227i −0.949106 0.314958i \(-0.898010\pi\)
0.664471 0.747314i \(-0.268657\pi\)
\(164\) −5.59808 9.69615i −0.437136 0.757142i
\(165\) 0 0
\(166\) −1.33013 0.767949i −0.103238 0.0596044i
\(167\) −11.7583 + 11.7583i −0.909887 + 0.909887i −0.996263 0.0863757i \(-0.972471\pi\)
0.0863757 + 0.996263i \(0.472471\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) −0.267949 + 4.46410i −0.0205508 + 0.342381i
\(171\) 0 0
\(172\) −1.79423 + 6.69615i −0.136809 + 0.510577i
\(173\) −19.9282 + 5.33975i −1.51511 + 0.405973i −0.918130 0.396280i \(-0.870301\pi\)
−0.596984 + 0.802253i \(0.703634\pi\)
\(174\) 0 0
\(175\) 11.8923 + 5.79423i 0.898974 + 0.438003i
\(176\) −6.73205 −0.507447
\(177\) 0 0
\(178\) −0.0884573 + 0.330127i −0.00663015 + 0.0247441i
\(179\) −6.80385 + 3.92820i −0.508543 + 0.293608i −0.732235 0.681052i \(-0.761523\pi\)
0.223691 + 0.974660i \(0.428189\pi\)
\(180\) 0 0
\(181\) 1.19615i 0.0889093i −0.999011 0.0444547i \(-0.985845\pi\)
0.999011 0.0444547i \(-0.0141550\pi\)
\(182\) −2.53590 2.92820i −0.187973 0.217053i
\(183\) 0 0
\(184\) −0.232051 0.133975i −0.0171070 0.00987674i
\(185\) −2.19615 10.7321i −0.161464 0.789036i
\(186\) 0 0
\(187\) 2.73205 + 10.1962i 0.199787 + 0.745617i
\(188\) 11.1962 + 11.1962i 0.816563 + 0.816563i
\(189\) 0 0
\(190\) −0.803848 0.267949i −0.0583172 0.0194391i
\(191\) 6.63397 11.4904i 0.480018 0.831415i −0.519720 0.854337i \(-0.673964\pi\)
0.999737 + 0.0229220i \(0.00729695\pi\)
\(192\) 0 0
\(193\) −7.83013 2.09808i −0.563625 0.151023i −0.0342537 0.999413i \(-0.510905\pi\)
−0.529371 + 0.848390i \(0.677572\pi\)
\(194\) 2.16987 3.75833i 0.155788 0.269832i
\(195\) 0 0
\(196\) −12.0000 1.73205i −0.857143 0.123718i
\(197\) 10.1244 + 10.1244i 0.721330 + 0.721330i 0.968876 0.247546i \(-0.0796240\pi\)
−0.247546 + 0.968876i \(0.579624\pi\)
\(198\) 0 0
\(199\) −5.53590 9.58846i −0.392429 0.679708i 0.600340 0.799745i \(-0.295032\pi\)
−0.992769 + 0.120037i \(0.961699\pi\)
\(200\) −7.59808 + 5.96410i −0.537265 + 0.421726i
\(201\) 0 0
\(202\) 3.02628 3.02628i 0.212928 0.212928i
\(203\) 2.59808 7.50000i 0.182349 0.526397i
\(204\) 0 0
\(205\) −14.4282 0.866025i −1.00771 0.0604858i
\(206\) −2.13397 + 1.23205i −0.148681 + 0.0858410i
\(207\) 0 0
\(208\) −6.73205 + 1.80385i −0.466784 + 0.125074i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −0.196152 −0.0135037 −0.00675184 0.999977i \(-0.502149\pi\)
−0.00675184 + 0.999977i \(0.502149\pi\)
\(212\) 11.8301 3.16987i 0.812496 0.217708i
\(213\) 0 0
\(214\) 5.89230 3.40192i 0.402790 0.232551i
\(215\) 5.93782 + 6.69615i 0.404956 + 0.456674i
\(216\) 0 0
\(217\) 19.3923 3.73205i 1.31644 0.253348i
\(218\) 3.70577 3.70577i 0.250987 0.250987i
\(219\) 0 0
\(220\) −5.83013 + 8.83013i −0.393067 + 0.595327i
\(221\) 5.46410 + 9.46410i 0.367555 + 0.636624i
\(222\) 0 0
\(223\) 18.1244 + 18.1244i 1.21370 + 1.21370i 0.969802 + 0.243895i \(0.0784252\pi\)
0.243895 + 0.969802i \(0.421575\pi\)
\(224\) 7.62436 11.2583i 0.509424 0.752229i
\(225\) 0 0
\(226\) −2.83013 + 4.90192i −0.188257 + 0.326071i
\(227\) 19.0263 + 5.09808i 1.26282 + 0.338371i 0.827275 0.561797i \(-0.189890\pi\)
0.435543 + 0.900168i \(0.356556\pi\)
\(228\) 0 0
\(229\) −9.19615 + 15.9282i −0.607699 + 1.05257i 0.383920 + 0.923366i \(0.374574\pi\)
−0.991619 + 0.129199i \(0.958759\pi\)
\(230\) −0.143594 + 0.0717968i −0.00946828 + 0.00473414i
\(231\) 0 0
\(232\) 4.09808 + 4.09808i 0.269052 + 0.269052i
\(233\) 1.73205 + 6.46410i 0.113470 + 0.423477i 0.999168 0.0407854i \(-0.0129860\pi\)
−0.885698 + 0.464263i \(0.846319\pi\)
\(234\) 0 0
\(235\) 20.0263 4.09808i 1.30637 0.267329i
\(236\) −12.2942 7.09808i −0.800286 0.462045i
\(237\) 0 0
\(238\) −5.00000 1.73205i −0.324102 0.112272i
\(239\) 2.39230i 0.154745i −0.997002 0.0773727i \(-0.975347\pi\)
0.997002 0.0773727i \(-0.0246531\pi\)
\(240\) 0 0
\(241\) 21.4641 12.3923i 1.38262 0.798259i 0.390155 0.920749i \(-0.372422\pi\)
0.992470 + 0.122491i \(0.0390882\pi\)
\(242\) −0.473721 + 1.76795i −0.0304519 + 0.113648i
\(243\) 0 0
\(244\) −2.66025 −0.170305
\(245\) −10.4019 + 11.6962i −0.664555 + 0.747240i
\(246\) 0 0
\(247\) −2.00000 + 0.535898i −0.127257 + 0.0340984i
\(248\) −3.73205 + 13.9282i −0.236985 + 0.884442i
\(249\) 0 0
\(250\) 0.473721 + 5.76795i 0.0299607 + 0.364797i
\(251\) 21.8564i 1.37956i −0.724017 0.689782i \(-0.757706\pi\)
0.724017 0.689782i \(-0.242294\pi\)
\(252\) 0 0
\(253\) −0.267949 + 0.267949i −0.0168458 + 0.0168458i
\(254\) −0.294229 0.169873i −0.0184615 0.0106588i
\(255\) 0 0
\(256\) 0.696152 + 1.20577i 0.0435095 + 0.0753607i
\(257\) 0.732051 + 2.73205i 0.0456641 + 0.170421i 0.984992 0.172600i \(-0.0552167\pi\)
−0.939328 + 0.343020i \(0.888550\pi\)
\(258\) 0 0
\(259\) 12.9282 + 0.928203i 0.803319 + 0.0576757i
\(260\) −3.46410 + 10.3923i −0.214834 + 0.644503i
\(261\) 0 0
\(262\) −7.73205 2.07180i −0.477688 0.127996i
\(263\) 15.1603 + 4.06218i 0.934821 + 0.250485i 0.693909 0.720062i \(-0.255887\pi\)
0.240912 + 0.970547i \(0.422553\pi\)
\(264\) 0 0
\(265\) 5.00000 15.0000i 0.307148 0.921443i
\(266\) 0.562178 0.830127i 0.0344693 0.0508984i
\(267\) 0 0
\(268\) 4.96410 + 18.5263i 0.303231 + 1.13167i
\(269\) −11.4282 19.7942i −0.696790 1.20688i −0.969574 0.244800i \(-0.921278\pi\)
0.272784 0.962075i \(-0.412056\pi\)
\(270\) 0 0
\(271\) 18.4186 + 10.6340i 1.11885 + 0.645968i 0.941107 0.338109i \(-0.109787\pi\)
0.177742 + 0.984077i \(0.443121\pi\)
\(272\) −6.73205 + 6.73205i −0.408191 + 0.408191i
\(273\) 0 0
\(274\) 7.07180i 0.427223i
\(275\) 5.36603 + 12.5622i 0.323584 + 0.757528i
\(276\) 0 0
\(277\) −1.39230 + 5.19615i −0.0836555 + 0.312207i −0.995056 0.0993135i \(-0.968335\pi\)
0.911401 + 0.411520i \(0.135002\pi\)
\(278\) 2.83013 0.758330i 0.169740 0.0454816i
\(279\) 0 0
\(280\) −4.36603 10.5622i −0.260920 0.631211i
\(281\) 0.928203 0.0553720 0.0276860 0.999617i \(-0.491186\pi\)
0.0276860 + 0.999617i \(0.491186\pi\)
\(282\) 0 0
\(283\) −0.509619 + 1.90192i −0.0302937 + 0.113058i −0.979417 0.201847i \(-0.935306\pi\)
0.949123 + 0.314904i \(0.101972\pi\)
\(284\) 1.90192 1.09808i 0.112858 0.0651588i
\(285\) 0 0
\(286\) 4.00000i 0.236525i
\(287\) 5.59808 16.1603i 0.330444 0.953910i
\(288\) 0 0
\(289\) −1.79423 1.03590i −0.105543 0.0609352i
\(290\) 3.40192 0.696152i 0.199768 0.0408795i
\(291\) 0 0
\(292\) −6.00000 22.3923i −0.351123 1.31041i
\(293\) 2.39230 + 2.39230i 0.139760 + 0.139760i 0.773525 0.633765i \(-0.218492\pi\)
−0.633765 + 0.773525i \(0.718492\pi\)
\(294\) 0 0
\(295\) −16.3923 + 8.19615i −0.954397 + 0.477198i
\(296\) −4.73205 + 8.19615i −0.275045 + 0.476392i
\(297\) 0 0
\(298\) 0.401924 + 0.107695i 0.0232828 + 0.00623861i
\(299\) −0.196152 + 0.339746i −0.0113438 + 0.0196480i
\(300\) 0 0
\(301\) −9.52628 + 4.62436i −0.549086 + 0.266543i
\(302\) 5.07180 + 5.07180i 0.291849 + 0.291849i
\(303\) 0 0
\(304\) −0.901924 1.56218i −0.0517289 0.0895970i
\(305\) −1.89230 + 2.86603i −0.108353 + 0.164108i
\(306\) 0 0
\(307\) 6.29423 6.29423i 0.359231 0.359231i −0.504299 0.863529i \(-0.668249\pi\)
0.863529 + 0.504299i \(0.168249\pi\)
\(308\) −8.19615 9.46410i −0.467019 0.539267i
\(309\) 0 0
\(310\) 5.73205 + 6.46410i 0.325559 + 0.367136i
\(311\) 13.2224 7.63397i 0.749775 0.432883i −0.0758374 0.997120i \(-0.524163\pi\)
0.825613 + 0.564237i \(0.190830\pi\)
\(312\) 0 0
\(313\) −5.19615 + 1.39230i −0.293704 + 0.0786977i −0.402662 0.915349i \(-0.631915\pi\)
0.108958 + 0.994046i \(0.465248\pi\)
\(314\) 2.48334 0.140143
\(315\) 0 0
\(316\) −5.66025 −0.318414
\(317\) −9.19615 + 2.46410i −0.516507 + 0.138398i −0.507651 0.861563i \(-0.669486\pi\)
−0.00885679 + 0.999961i \(0.502819\pi\)
\(318\) 0 0
\(319\) 7.09808 4.09808i 0.397416 0.229448i
\(320\) −5.06218 0.303848i −0.282984 0.0169856i
\(321\) 0 0
\(322\) −0.0358984 0.186533i −0.00200054 0.0103951i
\(323\) −2.00000 + 2.00000i −0.111283 + 0.111283i
\(324\) 0 0
\(325\) 8.73205 + 11.1244i 0.484367 + 0.617068i
\(326\) 3.63397 + 6.29423i 0.201267 + 0.348605i
\(327\) 0 0
\(328\) 8.83013 + 8.83013i 0.487562 + 0.487562i
\(329\) −1.73205 + 24.1244i −0.0954911 + 1.33002i
\(330\) 0 0
\(331\) 0.928203 1.60770i 0.0510187 0.0883669i −0.839388 0.543532i \(-0.817087\pi\)
0.890407 + 0.455165i \(0.150420\pi\)
\(332\) −4.96410 1.33013i −0.272440 0.0730002i
\(333\) 0 0
\(334\) 4.30385 7.45448i 0.235496 0.407891i
\(335\) 23.4904 + 7.83013i 1.28342 + 0.427806i
\(336\) 0 0
\(337\) 9.53590 + 9.53590i 0.519453 + 0.519453i 0.917406 0.397953i \(-0.130279\pi\)
−0.397953 + 0.917406i \(0.630279\pi\)
\(338\) 0.669873 + 2.50000i 0.0364363 + 0.135982i
\(339\) 0 0
\(340\) 3.00000 + 14.6603i 0.162698 + 0.795064i
\(341\) 17.6603 + 10.1962i 0.956356 + 0.552153i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 7.73205i 0.416884i
\(345\) 0 0
\(346\) 9.24871 5.33975i 0.497214 0.287067i
\(347\) 7.79423 29.0885i 0.418416 1.56155i −0.359477 0.933154i \(-0.617045\pi\)
0.777893 0.628396i \(-0.216288\pi\)
\(348\) 0 0
\(349\) 6.26795 0.335516 0.167758 0.985828i \(-0.446347\pi\)
0.167758 + 0.985828i \(0.446347\pi\)
\(350\) −6.72243 1.30385i −0.359329 0.0696936i
\(351\) 0 0
\(352\) 13.5622 3.63397i 0.722867 0.193691i
\(353\) −3.63397 + 13.5622i −0.193417 + 0.721842i 0.799254 + 0.600993i \(0.205228\pi\)
−0.992671 + 0.120849i \(0.961438\pi\)
\(354\) 0 0
\(355\) 0.169873 2.83013i 0.00901592 0.150208i
\(356\) 1.14359i 0.0606103i
\(357\) 0 0
\(358\) 2.87564 2.87564i 0.151983 0.151983i
\(359\) −29.6603 17.1244i −1.56541 0.903789i −0.996693 0.0812542i \(-0.974107\pi\)
−0.568715 0.822535i \(-0.692559\pi\)
\(360\) 0 0
\(361\) 9.23205 + 15.9904i 0.485897 + 0.841599i
\(362\) 0.160254 + 0.598076i 0.00842277 + 0.0314342i
\(363\) 0 0
\(364\) −10.7321 7.26795i −0.562512 0.380944i
\(365\) −28.3923 9.46410i −1.48612 0.495374i
\(366\) 0 0
\(367\) 0.500000 + 0.133975i 0.0260998 + 0.00699342i 0.271845 0.962341i \(-0.412366\pi\)
−0.245746 + 0.969334i \(0.579033\pi\)
\(368\) −0.330127 0.0884573i −0.0172091 0.00461115i
\(369\) 0 0
\(370\) 2.53590 + 5.07180i 0.131835 + 0.263670i
\(371\) 15.4904 + 10.4904i 0.804221 + 0.544633i
\(372\) 0 0
\(373\) 2.07180 + 7.73205i 0.107274 + 0.400350i 0.998593 0.0530251i \(-0.0168863\pi\)
−0.891320 + 0.453376i \(0.850220\pi\)
\(374\) −2.73205 4.73205i −0.141271 0.244689i
\(375\) 0 0
\(376\) −15.2942 8.83013i −0.788740 0.455379i
\(377\) 6.00000 6.00000i 0.309016 0.309016i
\(378\) 0 0
\(379\) 2.33975i 0.120185i 0.998193 + 0.0600923i \(0.0191395\pi\)
−0.998193 + 0.0600923i \(0.980860\pi\)
\(380\) −2.83013 0.169873i −0.145182 0.00871430i
\(381\) 0 0
\(382\) −1.77757 + 6.63397i −0.0909483 + 0.339424i
\(383\) −30.5526 + 8.18653i −1.56116 + 0.418312i −0.933031 0.359795i \(-0.882847\pi\)
−0.628131 + 0.778107i \(0.716180\pi\)
\(384\) 0 0
\(385\) −16.0263 + 2.09808i −0.816775 + 0.106928i
\(386\) 4.19615 0.213579
\(387\) 0 0
\(388\) 3.75833 14.0263i 0.190800 0.712076i
\(389\) 4.26795 2.46410i 0.216394 0.124935i −0.387886 0.921707i \(-0.626794\pi\)
0.604279 + 0.796773i \(0.293461\pi\)
\(390\) 0 0
\(391\) 0.535898i 0.0271015i
\(392\) 13.4282 1.59808i 0.678227 0.0807150i
\(393\) 0 0
\(394\) −6.41858 3.70577i −0.323364 0.186694i
\(395\) −4.02628 + 6.09808i −0.202584 + 0.306828i
\(396\) 0 0
\(397\) −0.973721 3.63397i −0.0488696 0.182384i 0.937177 0.348855i \(-0.113429\pi\)
−0.986046 + 0.166471i \(0.946763\pi\)
\(398\) 4.05256 + 4.05256i 0.203136 + 0.203136i
\(399\) 0 0
\(400\) −7.39230 + 9.85641i −0.369615 + 0.492820i
\(401\) 5.50000 9.52628i 0.274657 0.475720i −0.695392 0.718631i \(-0.744769\pi\)
0.970049 + 0.242911i \(0.0781024\pi\)
\(402\) 0 0
\(403\) 20.3923 + 5.46410i 1.01581 + 0.272186i
\(404\) 7.16025 12.4019i 0.356236 0.617019i
\(405\) 0 0
\(406\) −0.294229 + 4.09808i −0.0146023 + 0.203384i
\(407\) 9.46410 + 9.46410i 0.469118 + 0.469118i
\(408\) 0 0
\(409\) −10.4282 18.0622i −0.515641 0.893117i −0.999835 0.0181564i \(-0.994220\pi\)
0.484194 0.874961i \(-0.339113\pi\)
\(410\) 7.33013 1.50000i 0.362009 0.0740797i
\(411\) 0 0
\(412\) −5.83013 + 5.83013i −0.287230 + 0.287230i
\(413\) −4.09808 21.2942i −0.201653 1.04782i
\(414\) 0 0
\(415\) −4.96410 + 4.40192i −0.243678 + 0.216082i
\(416\) 12.5885 7.26795i 0.617200 0.356341i
\(417\) 0 0
\(418\) 1.00000 0.267949i 0.0489116 0.0131058i
\(419\) −23.8564 −1.16546 −0.582731 0.812665i \(-0.698016\pi\)
−0.582731 + 0.812665i \(0.698016\pi\)
\(420\) 0 0
\(421\) −17.3397 −0.845088 −0.422544 0.906343i \(-0.638863\pi\)
−0.422544 + 0.906343i \(0.638863\pi\)
\(422\) 0.0980762 0.0262794i 0.00477428 0.00127926i
\(423\) 0 0
\(424\) −11.8301 + 6.83013i −0.574522 + 0.331700i
\(425\) 17.9282 + 7.19615i 0.869646 + 0.349065i
\(426\) 0 0
\(427\) −2.66025 3.07180i −0.128739 0.148655i
\(428\) 16.0981 16.0981i 0.778130 0.778130i
\(429\) 0 0
\(430\) −3.86603 2.55256i −0.186436 0.123095i
\(431\) 3.09808 + 5.36603i 0.149229 + 0.258472i 0.930943 0.365165i \(-0.118987\pi\)
−0.781714 + 0.623637i \(0.785654\pi\)
\(432\) 0 0
\(433\) −17.5359 17.5359i −0.842721 0.842721i 0.146491 0.989212i \(-0.453202\pi\)
−0.989212 + 0.146491i \(0.953202\pi\)
\(434\) −9.19615 + 4.46410i −0.441429 + 0.214284i
\(435\) 0 0
\(436\) 8.76795 15.1865i 0.419909 0.727303i
\(437\) −0.0980762 0.0262794i −0.00469162 0.00125712i
\(438\) 0 0
\(439\) 1.66025 2.87564i 0.0792396 0.137247i −0.823682 0.567051i \(-0.808084\pi\)
0.902922 + 0.429804i \(0.141417\pi\)
\(440\) 3.73205 11.1962i 0.177919 0.533756i
\(441\) 0 0
\(442\) −4.00000 4.00000i −0.190261 0.190261i
\(443\) 3.50000 + 13.0622i 0.166290 + 0.620603i 0.997872 + 0.0652010i \(0.0207689\pi\)
−0.831582 + 0.555402i \(0.812564\pi\)
\(444\) 0 0
\(445\) 1.23205 + 0.813467i 0.0584048 + 0.0385620i
\(446\) −11.4904 6.63397i −0.544085 0.314128i
\(447\) 0 0
\(448\) 1.96410 5.66987i 0.0927951 0.267876i
\(449\) 33.0526i 1.55985i 0.625875 + 0.779923i \(0.284742\pi\)
−0.625875 + 0.779923i \(0.715258\pi\)
\(450\) 0 0
\(451\) 15.2942 8.83013i 0.720177 0.415794i
\(452\) −4.90192 + 18.2942i −0.230567 + 0.860488i
\(453\) 0 0
\(454\) −10.1962 −0.478529
\(455\) −15.4641 + 6.39230i −0.724968 + 0.299676i
\(456\) 0 0
\(457\) −11.7321 + 3.14359i −0.548802 + 0.147051i −0.522557 0.852604i \(-0.675022\pi\)
−0.0262453 + 0.999656i \(0.508355\pi\)
\(458\) 2.46410 9.19615i 0.115140 0.429708i
\(459\) 0 0
\(460\) −0.401924 + 0.356406i −0.0187398 + 0.0166175i
\(461\) 5.60770i 0.261176i 0.991437 + 0.130588i \(0.0416866\pi\)
−0.991437 + 0.130588i \(0.958313\pi\)
\(462\) 0 0
\(463\) −4.75833 + 4.75833i −0.221138 + 0.221138i −0.808978 0.587839i \(-0.799979\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(464\) 6.40192 + 3.69615i 0.297202 + 0.171590i
\(465\) 0 0
\(466\) −1.73205 3.00000i −0.0802357 0.138972i
\(467\) −3.64359 13.5981i −0.168605 0.629244i −0.997553 0.0699173i \(-0.977726\pi\)
0.828947 0.559327i \(-0.188940\pi\)
\(468\) 0 0
\(469\) −16.4282 + 24.2583i −0.758584 + 1.12015i
\(470\) −9.46410 + 4.73205i −0.436546 + 0.218273i
\(471\) 0 0
\(472\) 15.2942 + 4.09808i 0.703974 + 0.188629i
\(473\) −10.5622 2.83013i −0.485649 0.130129i
\(474\) 0 0
\(475\) −2.19615 + 2.92820i −0.100766 + 0.134355i
\(476\) −17.6603 1.26795i −0.809456 0.0581164i
\(477\) 0 0
\(478\) 0.320508 + 1.19615i 0.0146597 + 0.0547107i
\(479\) −6.53590 11.3205i −0.298633 0.517247i 0.677191 0.735808i \(-0.263197\pi\)
−0.975823 + 0.218560i \(0.929864\pi\)
\(480\) 0 0
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) −9.07180 + 9.07180i −0.413209 + 0.413209i
\(483\) 0 0
\(484\) 6.12436i 0.278380i
\(485\) −12.4378 14.0263i −0.564772 0.636901i
\(486\) 0 0
\(487\) 7.29423 27.2224i 0.330533 1.23357i −0.578098 0.815967i \(-0.696205\pi\)
0.908631 0.417599i \(-0.137128\pi\)
\(488\) 2.86603 0.767949i 0.129739 0.0347634i
\(489\) 0 0
\(490\) 3.63397 7.24167i 0.164166 0.327145i
\(491\) −37.7128 −1.70196 −0.850978 0.525202i \(-0.823990\pi\)
−0.850978 + 0.525202i \(0.823990\pi\)
\(492\) 0 0
\(493\) 3.00000 11.1962i 0.135113 0.504249i
\(494\) 0.928203 0.535898i 0.0417618 0.0241112i
\(495\) 0 0
\(496\) 18.3923i 0.825839i
\(497\) 3.16987 + 1.09808i 0.142188 + 0.0492554i
\(498\) 0 0
\(499\) −9.97372 5.75833i −0.446485 0.257778i 0.259860 0.965646i \(-0.416324\pi\)
−0.706345 + 0.707868i \(0.749657\pi\)
\(500\) 6.52628 + 18.2321i 0.291864 + 0.815362i
\(501\) 0 0
\(502\) 2.92820 + 10.9282i 0.130692 + 0.487750i
\(503\) 17.6340 + 17.6340i 0.786260 + 0.786260i 0.980879 0.194619i \(-0.0623470\pi\)
−0.194619 + 0.980879i \(0.562347\pi\)
\(504\) 0 0
\(505\) −8.26795 16.5359i −0.367919 0.735838i
\(506\) 0.0980762 0.169873i 0.00436002 0.00755178i
\(507\) 0 0
\(508\) −1.09808 0.294229i −0.0487193 0.0130543i
\(509\) 19.4545 33.6962i 0.862305 1.49356i −0.00739389 0.999973i \(-0.502354\pi\)
0.869699 0.493583i \(-0.164313\pi\)
\(510\) 0 0
\(511\) 19.8564 29.3205i 0.878396 1.29706i
\(512\) 15.6865 + 15.6865i 0.693253 + 0.693253i
\(513\) 0 0
\(514\) −0.732051 1.26795i −0.0322894 0.0559268i
\(515\) 2.13397 + 10.4282i 0.0940342 + 0.459522i
\(516\) 0 0
\(517\) −17.6603 + 17.6603i −0.776697 + 0.776697i
\(518\) −6.58846 + 1.26795i −0.289480 + 0.0557105i
\(519\) 0 0
\(520\) 0.732051 12.1962i 0.0321026 0.534837i
\(521\) 20.6603 11.9282i 0.905142 0.522584i 0.0262772 0.999655i \(-0.491635\pi\)
0.878865 + 0.477071i \(0.158301\pi\)
\(522\) 0 0
\(523\) −42.8827 + 11.4904i −1.87513 + 0.502439i −0.875307 + 0.483568i \(0.839341\pi\)
−0.999822 + 0.0188717i \(0.993993\pi\)
\(524\) −26.7846 −1.17009
\(525\) 0 0
\(526\) −8.12436 −0.354239
\(527\) 27.8564 7.46410i 1.21344 0.325141i
\(528\) 0 0
\(529\) 19.9019 11.4904i 0.865301 0.499582i
\(530\) −0.490381 + 8.16987i −0.0213008 + 0.354877i
\(531\) 0 0
\(532\) 1.09808 3.16987i 0.0476076 0.137431i
\(533\) 12.9282 12.9282i 0.559983 0.559983i
\(534\) 0 0
\(535\) −5.89230 28.7942i −0.254747 1.24488i
\(536\) −10.6962 18.5263i −0.462003 0.800213i
\(537\) 0 0
\(538\) 8.36603 + 8.36603i 0.360685 + 0.360685i
\(539\) 2.73205 18.9282i 0.117678 0.815295i
\(540\) 0 0
\(541\) −18.3564 + 31.7942i −0.789204 + 1.36694i 0.137252 + 0.990536i \(0.456173\pi\)
−0.926455 + 0.376404i \(0.877160\pi\)
\(542\) −10.6340 2.84936i −0.456768 0.122391i
\(543\) 0 0
\(544\) 9.92820 17.1962i 0.425668 0.737279i
\(545\) −10.1244 20.2487i −0.433680 0.867359i
\(546\) 0 0
\(547\) −16.7583 16.7583i −0.716534 0.716534i 0.251359 0.967894i \(-0.419122\pi\)
−0.967894 + 0.251359i \(0.919122\pi\)
\(548\) 6.12436 + 22.8564i 0.261620 + 0.976377i
\(549\) 0 0
\(550\) −4.36603 5.56218i −0.186168 0.237172i
\(551\) 1.90192 + 1.09808i 0.0810247 + 0.0467796i
\(552\) 0 0
\(553\) −5.66025 6.53590i −0.240698 0.277935i
\(554\) 2.78461i 0.118307i
\(555\) 0 0
\(556\) 8.49038 4.90192i 0.360072 0.207888i
\(557\) −8.36603 + 31.2224i −0.354480 + 1.32294i 0.526658 + 0.850077i \(0.323445\pi\)
−0.881138 + 0.472860i \(0.843222\pi\)
\(558\) 0 0
\(559\) −11.3205 −0.478806
\(560\) −8.86603 11.5718i −0.374658 0.488998i
\(561\) 0 0
\(562\) −0.464102 + 0.124356i −0.0195769 + 0.00524563i
\(563\) 6.35641 23.7224i 0.267891 0.999781i −0.692567 0.721354i \(-0.743520\pi\)
0.960457 0.278427i \(-0.0898132\pi\)
\(564\) 0 0
\(565\) 16.2224 + 18.2942i 0.682483 + 0.769644i
\(566\) 1.01924i 0.0428418i
\(567\) 0 0
\(568\) −1.73205 + 1.73205i −0.0726752 + 0.0726752i
\(569\) 25.0526 + 14.4641i 1.05026 + 0.606367i 0.922722 0.385467i \(-0.125960\pi\)
0.127536 + 0.991834i \(0.459293\pi\)
\(570\) 0 0
\(571\) 9.02628 + 15.6340i 0.377738 + 0.654261i 0.990733 0.135826i \(-0.0433687\pi\)
−0.612995 + 0.790087i \(0.710035\pi\)
\(572\) −3.46410 12.9282i −0.144841 0.540555i
\(573\) 0 0
\(574\) −0.633975 + 8.83013i −0.0264616 + 0.368562i
\(575\) 0.0980762 + 0.686533i 0.00409006 + 0.0286304i
\(576\) 0 0
\(577\) 5.63397 + 1.50962i 0.234545 + 0.0628463i 0.374177 0.927357i \(-0.377925\pi\)
−0.139632 + 0.990204i \(0.544592\pi\)
\(578\) 1.03590 + 0.277568i 0.0430877 + 0.0115453i
\(579\) 0 0
\(580\) 10.3923 5.19615i 0.431517 0.215758i
\(581\) −3.42820 7.06218i −0.142226 0.292989i
\(582\) 0 0
\(583\) 5.00000 + 18.6603i 0.207079 + 0.772829i
\(584\) 12.9282 + 22.3923i 0.534973 + 0.926600i
\(585\) 0 0
\(586\) −1.51666 0.875644i −0.0626527 0.0361725i
\(587\) −15.7846 + 15.7846i −0.651501 + 0.651501i −0.953354 0.301854i \(-0.902395\pi\)
0.301854 + 0.953354i \(0.402395\pi\)
\(588\) 0 0
\(589\) 5.46410i 0.225144i
\(590\) 7.09808 6.29423i 0.292223 0.259129i
\(591\) 0 0
\(592\) −3.12436 + 11.6603i −0.128410 + 0.479233i
\(593\) −20.7583 + 5.56218i −0.852442 + 0.228411i −0.658481 0.752598i \(-0.728801\pi\)
−0.193962 + 0.981009i \(0.562134\pi\)
\(594\) 0 0
\(595\) −13.9282 + 18.1244i −0.571001 + 0.743026i
\(596\) 1.39230 0.0570310
\(597\) 0 0
\(598\) 0.0525589 0.196152i 0.00214929 0.00802127i
\(599\) 15.3397 8.85641i 0.626765 0.361863i −0.152733 0.988267i \(-0.548807\pi\)
0.779498 + 0.626405i \(0.215474\pi\)
\(600\) 0 0
\(601\) 41.1769i 1.67964i −0.542864 0.839821i \(-0.682660\pi\)
0.542864 0.839821i \(-0.317340\pi\)
\(602\) 4.14359 3.58846i 0.168880 0.146255i
\(603\) 0 0
\(604\) 20.7846 + 12.0000i 0.845714 + 0.488273i
\(605\) 6.59808 + 4.35641i 0.268250 + 0.177113i
\(606\) 0 0
\(607\) 3.40192 + 12.6962i 0.138080 + 0.515321i 0.999966 + 0.00821951i \(0.00261638\pi\)
−0.861886 + 0.507101i \(0.830717\pi\)
\(608\) 2.66025 + 2.66025i 0.107888 + 0.107888i
\(609\) 0 0
\(610\) 0.562178 1.68653i 0.0227619 0.0682857i
\(611\) −12.9282 + 22.3923i −0.523019 + 0.905896i
\(612\) 0 0
\(613\) 24.3923 + 6.53590i 0.985196 + 0.263982i 0.715231 0.698888i \(-0.246321\pi\)
0.269965 + 0.962870i \(0.412988\pi\)
\(614\) −2.30385 + 3.99038i −0.0929757 + 0.161039i
\(615\) 0 0
\(616\) 11.5622 + 7.83013i 0.465853 + 0.315485i
\(617\) −33.9090 33.9090i −1.36512 1.36512i −0.867249 0.497874i \(-0.834114\pi\)
−0.497874 0.867249i \(-0.665886\pi\)
\(618\) 0 0
\(619\) 5.09808 + 8.83013i 0.204909 + 0.354913i 0.950104 0.311934i \(-0.100977\pi\)
−0.745195 + 0.666847i \(0.767643\pi\)
\(620\) 24.1244 + 15.9282i 0.968857 + 0.639692i
\(621\) 0 0
\(622\) −5.58846 + 5.58846i −0.224077 + 0.224077i
\(623\) −1.32051 + 1.14359i −0.0529050 + 0.0458171i
\(624\) 0 0
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 2.41154 1.39230i 0.0963846 0.0556477i
\(627\) 0 0
\(628\) 8.02628 2.15064i 0.320283 0.0858197i
\(629\) 18.9282 0.754717
\(630\) 0 0
\(631\) −4.58846 −0.182664 −0.0913318 0.995821i \(-0.529112\pi\)
−0.0913318 + 0.995821i \(0.529112\pi\)
\(632\) 6.09808 1.63397i 0.242568 0.0649960i
\(633\) 0 0
\(634\) 4.26795 2.46410i 0.169502 0.0978620i
\(635\) −1.09808 + 0.973721i −0.0435758 + 0.0386409i
\(636\) 0 0
\(637\) −2.33975 19.6603i −0.0927041 0.778968i
\(638\) −3.00000 + 3.00000i −0.118771 + 0.118771i
\(639\) 0 0
\(640\) 25.0885 5.13397i 0.991708 0.202938i
\(641\) 5.33013 + 9.23205i 0.210527 + 0.364644i 0.951880 0.306472i \(-0.0991486\pi\)
−0.741352 + 0.671116i \(0.765815\pi\)
\(642\) 0 0
\(643\) 17.5359 + 17.5359i 0.691548 + 0.691548i 0.962573 0.271024i \(-0.0873623\pi\)
−0.271024 + 0.962573i \(0.587362\pi\)
\(644\) −0.277568 0.571797i −0.0109377 0.0225319i
\(645\) 0 0
\(646\) 0.732051 1.26795i 0.0288022 0.0498868i
\(647\) −39.5526 10.5981i −1.55497 0.416653i −0.623904 0.781501i \(-0.714454\pi\)
−0.931067 + 0.364847i \(0.881121\pi\)
\(648\) 0 0
\(649\) 11.1962 19.3923i 0.439487 0.761215i
\(650\) −5.85641 4.39230i −0.229707 0.172280i
\(651\) 0 0
\(652\) 17.1962 + 17.1962i 0.673453 + 0.673453i
\(653\) 5.26795 + 19.6603i 0.206151 + 0.769365i 0.989096 + 0.147274i \(0.0470500\pi\)
−0.782945 + 0.622091i \(0.786283\pi\)
\(654\) 0 0
\(655\) −19.0526 + 28.8564i −0.744445 + 1.12751i
\(656\) 13.7942 + 7.96410i 0.538574 + 0.310946i
\(657\) 0 0
\(658\) −2.36603 12.2942i −0.0922373 0.479279i
\(659\) 27.6603i 1.07749i 0.842469 + 0.538745i \(0.181101\pi\)
−0.842469 + 0.538745i \(0.818899\pi\)
\(660\) 0 0
\(661\) −41.7224 + 24.0885i −1.62281 + 0.936932i −0.636652 + 0.771151i \(0.719681\pi\)
−0.986163 + 0.165781i \(0.946985\pi\)
\(662\) −0.248711 + 0.928203i −0.00966644 + 0.0360756i
\(663\) 0 0
\(664\) 5.73205 0.222447
\(665\) −2.63397 3.43782i −0.102141 0.133313i
\(666\) 0 0
\(667\) 0.401924 0.107695i 0.0155626 0.00416997i
\(668\) 7.45448 27.8205i 0.288423 1.07641i
\(669\) 0 0
\(670\) −12.7942 0.767949i −0.494284 0.0296685i
\(671\) 4.19615i 0.161991i
\(672\) 0 0
\(673\) 4.39230 4.39230i 0.169311 0.169311i −0.617366 0.786676i \(-0.711800\pi\)
0.786676 + 0.617366i \(0.211800\pi\)
\(674\) −6.04552 3.49038i −0.232865 0.134444i
\(675\) 0 0
\(676\) 4.33013 + 7.50000i 0.166543 + 0.288462i
\(677\) 6.92820 + 25.8564i 0.266272 + 0.993742i 0.961467 + 0.274921i \(0.0886516\pi\)
−0.695194 + 0.718822i \(0.744682\pi\)
\(678\) 0 0
\(679\) 19.9545 9.68653i 0.765783 0.371735i
\(680\) −7.46410 14.9282i −0.286235 0.572470i
\(681\) 0 0
\(682\) −10.1962 2.73205i −0.390431 0.104616i
\(683\) −17.0622 4.57180i −0.652866 0.174935i −0.0828417 0.996563i \(-0.526400\pi\)
−0.570024 + 0.821628i \(0.693066\pi\)
\(684\) 0 0
\(685\) 28.9808 + 9.66025i 1.10730 + 0.369099i
\(686\) 7.08846 + 6.45448i 0.270639 + 0.246433i
\(687\) 0 0
\(688\) −2.55256 9.52628i −0.0973154 0.363186i
\(689\) 10.0000 + 17.3205i 0.380970 + 0.659859i
\(690\) 0 0
\(691\) −44.0263 25.4186i −1.67484 0.966969i −0.964867 0.262738i \(-0.915375\pi\)
−0.709971 0.704231i \(-0.751292\pi\)
\(692\) 25.2679 25.2679i 0.960543 0.960543i
\(693\) 0 0
\(694\) 15.5885i 0.591730i
\(695\) 0.758330 12.6340i 0.0287651 0.479234i
\(696\) 0 0
\(697\) 6.46410 24.1244i 0.244845 0.913775i
\(698\) −3.13397 + 0.839746i −0.118623 + 0.0317849i
\(699\) 0 0
\(700\) −22.8564 + 1.60770i −0.863891 + 0.0607652i
\(701\) 20.2679 0.765510 0.382755 0.923850i \(-0.374975\pi\)
0.382755 + 0.923850i \(0.374975\pi\)
\(702\) 0 0
\(703\) −0.928203 + 3.46410i −0.0350078 + 0.130651i
\(704\) 5.36603 3.09808i 0.202240 0.116763i
\(705\) 0 0
\(706\) 7.26795i 0.273533i
\(707\) 21.4808 4.13397i 0.807867 0.155474i
\(708\) 0 0
\(709\) 18.9904 + 10.9641i 0.713199 + 0.411765i 0.812244 0.583317i \(-0.198246\pi\)
−0.0990456 + 0.995083i \(0.531579\pi\)
\(710\) 0.294229 + 1.43782i 0.0110422 + 0.0539605i
\(711\) 0 0
\(712\) −0.330127 1.23205i −0.0123720 0.0461731i
\(713\) 0.732051 + 0.732051i 0.0274155 + 0.0274155i
\(714\) 0 0
\(715\) −16.3923 5.46410i −0.613037 0.204346i
\(716\) 6.80385 11.7846i 0.254272 0.440412i
\(717\) 0 0
\(718\) 17.1244 + 4.58846i 0.639075 + 0.171240i
\(719\) −19.2942 + 33.4186i −0.719553 + 1.24630i 0.241624 + 0.970370i \(0.422320\pi\)
−0.961177 + 0.275933i \(0.911013\pi\)
\(720\) 0 0
\(721\) −12.5622 0.901924i −0.467840 0.0335894i
\(722\) −6.75833 6.75833i −0.251519 0.251519i
\(723\) 0 0
\(724\) 1.03590 + 1.79423i 0.0384989 + 0.0666820i
\(725\) 1.79423 14.8923i 0.0666360 0.553086i
\(726\) 0 0
\(727\) −10.0981 + 10.0981i −0.374517 + 0.374517i −0.869119 0.494602i \(-0.835314\pi\)
0.494602 + 0.869119i \(0.335314\pi\)
\(728\) 13.6603 + 4.73205i 0.506283 + 0.175381i
\(729\) 0 0
\(730\) 15.4641 + 0.928203i 0.572352 + 0.0343543i
\(731\) −13.3923 + 7.73205i −0.495332 + 0.285980i
\(732\) 0 0
\(733\) −4.36603 + 1.16987i −0.161263 + 0.0432102i −0.338547 0.940949i \(-0.609935\pi\)
0.177284 + 0.984160i \(0.443269\pi\)
\(734\) −0.267949 −0.00989019
\(735\) 0 0
\(736\) 0.712813 0.0262746
\(737\) −29.2224 + 7.83013i −1.07642 + 0.288426i
\(738\) 0 0
\(739\) −19.5622 + 11.2942i −0.719606 + 0.415465i −0.814608 0.580012i \(-0.803048\pi\)
0.0950014 + 0.995477i \(0.469714\pi\)
\(740\) 12.5885 + 14.1962i 0.462761 + 0.521861i
\(741\) 0 0
\(742\) −9.15064 3.16987i −0.335930 0.116370i
\(743\) 6.16987 6.16987i 0.226351 0.226351i −0.584816 0.811166i \(-0.698833\pi\)
0.811166 + 0.584816i \(0.198833\pi\)
\(744\) 0 0
\(745\) 0.990381 1.50000i 0.0362848 0.0549557i
\(746\) −2.07180 3.58846i −0.0758539 0.131383i
\(747\) 0 0
\(748\) −12.9282 12.9282i −0.472702 0.472702i
\(749\) 34.6865 + 2.49038i 1.26742 + 0.0909965i
\(750\) 0 0
\(751\) 3.19615 5.53590i 0.116629 0.202008i −0.801801 0.597592i \(-0.796124\pi\)
0.918430 + 0.395584i \(0.129458\pi\)
\(752\) −21.7583 5.83013i −0.793445 0.212603i
\(753\) 0 0
\(754\) −2.19615 + 3.80385i −0.0799792 + 0.138528i
\(755\) 27.7128 13.8564i 1.00857 0.504286i
\(756\) 0 0
\(757\) 12.7321 + 12.7321i 0.462754 + 0.462754i 0.899557 0.436803i \(-0.143889\pi\)
−0.436803 + 0.899557i \(0.643889\pi\)
\(758\) −0.313467 1.16987i −0.0113856 0.0424917i
\(759\) 0 0
\(760\) 3.09808 0.633975i 0.112379 0.0229967i
\(761\) −24.9282 14.3923i −0.903647 0.521721i −0.0252651 0.999681i \(-0.508043\pi\)
−0.878382 + 0.477960i \(0.841376\pi\)
\(762\) 0 0
\(763\) 26.3038 5.06218i 0.952263 0.183263i
\(764\) 22.9808i 0.831415i
\(765\) 0 0
\(766\) 14.1795 8.18653i 0.512326 0.295791i
\(767\) 6.00000 22.3923i 0.216647 0.808539i
\(768\) 0 0
\(769\) 15.1769 0.547294 0.273647 0.961830i \(-0.411770\pi\)
0.273647 + 0.961830i \(0.411770\pi\)
\(770\) 7.73205 3.19615i 0.278644 0.115181i
\(771\) 0 0
\(772\) 13.5622 3.63397i 0.488113 0.130790i
\(773\) −4.07180 + 15.1962i −0.146452 + 0.546568i 0.853234 + 0.521528i \(0.174638\pi\)
−0.999686 + 0.0250395i \(0.992029\pi\)
\(774\) 0 0
\(775\) 34.3205 14.6603i 1.23283 0.526612i
\(776\) 16.1962i 0.581408i
\(777\) 0 0
\(778\) −1.80385 + 1.80385i −0.0646711 + 0.0646711i
\(779\) 4.09808 + 2.36603i 0.146829 + 0.0847717i
\(780\) 0 0
\(781\) 1.73205 + 3.00000i 0.0619777 + 0.107348i
\(782\) −0.0717968 0.267949i −0.00256745 0.00958184i
\(783\) 0 0
\(784\) 16.0167 6.40192i 0.572024 0.228640i
\(785\) 3.39230 10.1769i 0.121077 0.363230i
\(786\) 0 0
\(787\) 31.1865 + 8.35641i 1.11168 + 0.297874i 0.767512 0.641034i \(-0.221494\pi\)
0.344168 + 0.938908i \(0.388161\pi\)
\(788\) −23.9545 6.41858i −0.853343 0.228653i
\(789\) 0 0
\(790\) 1.19615 3.58846i 0.0425572 0.127672i
\(791\) −26.0263 + 12.6340i −0.925388