Properties

Label 804.2.q.b.25.3
Level 804
Weight 2
Character 804.25
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 25.3
Character \(\chi\) = 804.25
Dual form 804.2.q.b.193.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(-0.494572 + 0.317842i) q^{5} +(0.597152 + 4.15328i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(-0.494572 + 0.317842i) q^{5} +(0.597152 + 4.15328i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-3.69287 + 2.37326i) q^{11} +(0.305369 - 0.668664i) q^{13} +(-0.0836667 + 0.581915i) q^{15} +(1.69671 + 0.498199i) q^{17} +(-0.290555 + 2.02085i) q^{19} +(3.52989 + 2.26853i) q^{21} +(-4.46336 + 5.15100i) q^{23} +(-1.93350 + 4.23377i) q^{25} +(-0.841254 - 0.540641i) q^{27} -4.58239 q^{29} +(-1.01278 - 2.21768i) q^{31} +(-0.624723 + 4.34504i) q^{33} +(-1.61542 - 1.86430i) q^{35} +5.57561 q^{37} +(-0.305369 - 0.668664i) q^{39} +(-3.79415 - 1.11406i) q^{41} +(9.78801 + 2.87402i) q^{43} +(0.384992 + 0.444304i) q^{45} +(4.93013 - 5.68967i) q^{47} +(-10.1767 + 2.98816i) q^{49} +(1.48762 - 0.956037i) q^{51} +(7.24167 - 2.12635i) q^{53} +(1.07207 - 2.34750i) q^{55} +(1.33699 + 1.54296i) q^{57} +(5.10988 + 11.1891i) q^{59} +(8.08332 + 5.19484i) q^{61} +(4.02603 - 1.18215i) q^{63} +(0.0615028 + 0.427761i) q^{65} +(-1.33908 + 8.07508i) q^{67} +(0.969982 + 6.74637i) q^{69} +(0.981003 - 0.288048i) q^{71} +(-8.46705 - 5.44144i) q^{73} +(1.93350 + 4.23377i) q^{75} +(-12.0620 - 13.9203i) q^{77} +(2.34861 - 5.14274i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(3.95887 - 2.54421i) q^{83} +(-0.997494 + 0.292891i) q^{85} +(-3.00083 + 3.46314i) q^{87} +(-2.92583 - 3.37658i) q^{89} +(2.95950 + 0.868988i) q^{91} +(-2.33924 - 0.686863i) q^{93} +(-0.498612 - 1.09181i) q^{95} +8.38224 q^{97} +(2.87466 + 3.31753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(1\)

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 0
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) −0.494572 + 0.317842i −0.221179 + 0.142143i −0.646539 0.762881i \(-0.723784\pi\)
0.425359 + 0.905025i \(0.360148\pi\)
\(6\) 0 0
\(7\) 0.597152 + 4.15328i 0.225702 + 1.56979i 0.715913 + 0.698190i \(0.246011\pi\)
−0.490211 + 0.871604i \(0.663080\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) −3.69287 + 2.37326i −1.11344 + 0.715566i −0.962041 0.272906i \(-0.912015\pi\)
−0.151402 + 0.988472i \(0.548379\pi\)
\(12\) 0 0
\(13\) 0.305369 0.668664i 0.0846940 0.185454i −0.862546 0.505978i \(-0.831132\pi\)
0.947240 + 0.320524i \(0.103859\pi\)
\(14\) 0 0
\(15\) −0.0836667 + 0.581915i −0.0216027 + 0.150250i
\(16\) 0 0
\(17\) 1.69671 + 0.498199i 0.411513 + 0.120831i 0.480935 0.876756i \(-0.340297\pi\)
−0.0694221 + 0.997587i \(0.522116\pi\)
\(18\) 0 0
\(19\) −0.290555 + 2.02085i −0.0666578 + 0.463615i 0.928966 + 0.370165i \(0.120699\pi\)
−0.995624 + 0.0934506i \(0.970210\pi\)
\(20\) 0 0
\(21\) 3.52989 + 2.26853i 0.770286 + 0.495033i
\(22\) 0 0
\(23\) −4.46336 + 5.15100i −0.930676 + 1.07406i 0.0664118 + 0.997792i \(0.478845\pi\)
−0.997088 + 0.0762648i \(0.975701\pi\)
\(24\) 0 0
\(25\) −1.93350 + 4.23377i −0.386699 + 0.846754i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) −4.58239 −0.850928 −0.425464 0.904975i \(-0.639889\pi\)
−0.425464 + 0.904975i \(0.639889\pi\)
\(30\) 0 0
\(31\) −1.01278 2.21768i −0.181901 0.398307i 0.796613 0.604490i \(-0.206623\pi\)
−0.978513 + 0.206183i \(0.933896\pi\)
\(32\) 0 0
\(33\) −0.624723 + 4.34504i −0.108750 + 0.756375i
\(34\) 0 0
\(35\) −1.61542 1.86430i −0.273056 0.315124i
\(36\) 0 0
\(37\) 5.57561 0.916624 0.458312 0.888791i \(-0.348454\pi\)
0.458312 + 0.888791i \(0.348454\pi\)
\(38\) 0 0
\(39\) −0.305369 0.668664i −0.0488981 0.107072i
\(40\) 0 0
\(41\) −3.79415 1.11406i −0.592547 0.173987i −0.0283082 0.999599i \(-0.509012\pi\)
−0.564239 + 0.825612i \(0.690830\pi\)
\(42\) 0 0
\(43\) 9.78801 + 2.87402i 1.49266 + 0.438284i 0.923388 0.383867i \(-0.125408\pi\)
0.569269 + 0.822151i \(0.307226\pi\)
\(44\) 0 0
\(45\) 0.384992 + 0.444304i 0.0573912 + 0.0662330i
\(46\) 0 0
\(47\) 4.93013 5.68967i 0.719133 0.829923i −0.272070 0.962278i \(-0.587708\pi\)
0.991203 + 0.132354i \(0.0422536\pi\)
\(48\) 0 0
\(49\) −10.1767 + 2.98816i −1.45382 + 0.426879i
\(50\) 0 0
\(51\) 1.48762 0.956037i 0.208309 0.133872i
\(52\) 0 0
\(53\) 7.24167 2.12635i 0.994719 0.292076i 0.256432 0.966562i \(-0.417453\pi\)
0.738287 + 0.674486i \(0.235635\pi\)
\(54\) 0 0
\(55\) 1.07207 2.34750i 0.144558 0.316537i
\(56\) 0 0
\(57\) 1.33699 + 1.54296i 0.177088 + 0.204371i
\(58\) 0 0
\(59\) 5.10988 + 11.1891i 0.665250 + 1.45669i 0.877548 + 0.479488i \(0.159178\pi\)
−0.212299 + 0.977205i \(0.568095\pi\)
\(60\) 0 0
\(61\) 8.08332 + 5.19484i 1.03496 + 0.665131i 0.943736 0.330700i \(-0.107285\pi\)
0.0912273 + 0.995830i \(0.470921\pi\)
\(62\) 0 0
\(63\) 4.02603 1.18215i 0.507232 0.148937i
\(64\) 0 0
\(65\) 0.0615028 + 0.427761i 0.00762848 + 0.0530573i
\(66\) 0 0
\(67\) −1.33908 + 8.07508i −0.163595 + 0.986528i
\(68\) 0 0
\(69\) 0.969982 + 6.74637i 0.116772 + 0.812168i
\(70\) 0 0
\(71\) 0.981003 0.288048i 0.116424 0.0341851i −0.223002 0.974818i \(-0.571586\pi\)
0.339425 + 0.940633i \(0.389767\pi\)
\(72\) 0 0
\(73\) −8.46705 5.44144i −0.990994 0.636873i −0.0585864 0.998282i \(-0.518659\pi\)
−0.932407 + 0.361409i \(0.882296\pi\)
\(74\) 0 0
\(75\) 1.93350 + 4.23377i 0.223261 + 0.488873i
\(76\) 0 0
\(77\) −12.0620 13.9203i −1.37460 1.58637i
\(78\) 0 0
\(79\) 2.34861 5.14274i 0.264240 0.578604i −0.730281 0.683147i \(-0.760611\pi\)
0.994520 + 0.104543i \(0.0333380\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) 3.95887 2.54421i 0.434543 0.279264i −0.305027 0.952344i \(-0.598665\pi\)
0.739570 + 0.673080i \(0.235029\pi\)
\(84\) 0 0
\(85\) −0.997494 + 0.292891i −0.108193 + 0.0317685i
\(86\) 0 0
\(87\) −3.00083 + 3.46314i −0.321722 + 0.371287i
\(88\) 0 0
\(89\) −2.92583 3.37658i −0.310137 0.357917i 0.579187 0.815195i \(-0.303370\pi\)
−0.889324 + 0.457277i \(0.848825\pi\)
\(90\) 0 0
\(91\) 2.95950 + 0.868988i 0.310240 + 0.0910947i
\(92\) 0 0
\(93\) −2.33924 0.686863i −0.242568 0.0712244i
\(94\) 0 0
\(95\) −0.498612 1.09181i −0.0511565 0.112017i
\(96\) 0 0
\(97\) 8.38224 0.851087 0.425544 0.904938i \(-0.360083\pi\)
0.425544 + 0.904938i \(0.360083\pi\)
\(98\) 0 0
\(99\) 2.87466 + 3.31753i 0.288914 + 0.333425i
\(100\) 0 0
\(101\) 2.23446 15.5410i 0.222337 1.54639i −0.506828 0.862047i \(-0.669182\pi\)
0.729165 0.684338i \(-0.239909\pi\)
\(102\) 0 0
\(103\) 0.353899 + 0.774930i 0.0348707 + 0.0763561i 0.926266 0.376871i \(-0.123000\pi\)
−0.891395 + 0.453227i \(0.850273\pi\)
\(104\) 0 0
\(105\) −2.46682 −0.240737
\(106\) 0 0
\(107\) −10.2879 6.61164i −0.994570 0.639171i −0.0612142 0.998125i \(-0.519497\pi\)
−0.933355 + 0.358954i \(0.883134\pi\)
\(108\) 0 0
\(109\) −5.80264 + 12.7060i −0.555792 + 1.21701i 0.398232 + 0.917285i \(0.369624\pi\)
−0.954024 + 0.299730i \(0.903104\pi\)
\(110\) 0 0
\(111\) 3.65124 4.21376i 0.346561 0.399953i
\(112\) 0 0
\(113\) −12.6785 8.14800i −1.19270 0.766500i −0.215019 0.976610i \(-0.568981\pi\)
−0.977678 + 0.210110i \(0.932618\pi\)
\(114\) 0 0
\(115\) 0.570251 3.96618i 0.0531762 0.369849i
\(116\) 0 0
\(117\) −0.705316 0.207100i −0.0652065 0.0191464i
\(118\) 0 0
\(119\) −1.05597 + 7.34442i −0.0968005 + 0.673262i
\(120\) 0 0
\(121\) 3.43535 7.52238i 0.312305 0.683852i
\(122\) 0 0
\(123\) −3.32659 + 2.13787i −0.299949 + 0.192765i
\(124\) 0 0
\(125\) −0.807750 5.61802i −0.0722474 0.502491i
\(126\) 0 0
\(127\) 0.183221 + 1.27433i 0.0162583 + 0.113079i 0.996334 0.0855431i \(-0.0272625\pi\)
−0.980076 + 0.198622i \(0.936353\pi\)
\(128\) 0 0
\(129\) 8.58182 5.51520i 0.755587 0.485587i
\(130\) 0 0
\(131\) 2.96329 3.41982i 0.258904 0.298791i −0.611384 0.791334i \(-0.709387\pi\)
0.870288 + 0.492543i \(0.163932\pi\)
\(132\) 0 0
\(133\) −8.56668 −0.742825
\(134\) 0 0
\(135\) 0.587899 0.0505983
\(136\) 0 0
\(137\) −7.31498 + 8.44193i −0.624961 + 0.721243i −0.976641 0.214877i \(-0.931065\pi\)
0.351680 + 0.936120i \(0.385610\pi\)
\(138\) 0 0
\(139\) −12.4567 + 8.00543i −1.05656 + 0.679011i −0.949029 0.315190i \(-0.897932\pi\)
−0.107534 + 0.994201i \(0.534295\pi\)
\(140\) 0 0
\(141\) −1.07142 7.45188i −0.0902297 0.627562i
\(142\) 0 0
\(143\) 0.459229 + 3.19401i 0.0384027 + 0.267097i
\(144\) 0 0
\(145\) 2.26632 1.45648i 0.188208 0.120954i
\(146\) 0 0
\(147\) −4.40604 + 9.64788i −0.363404 + 0.795744i
\(148\) 0 0
\(149\) −0.395047 + 2.74762i −0.0323635 + 0.225093i −0.999584 0.0288452i \(-0.990817\pi\)
0.967220 + 0.253939i \(0.0817261\pi\)
\(150\) 0 0
\(151\) 3.04434 + 0.893899i 0.247745 + 0.0727445i 0.403247 0.915091i \(-0.367881\pi\)
−0.155502 + 0.987836i \(0.549700\pi\)
\(152\) 0 0
\(153\) 0.251661 1.75034i 0.0203456 0.141507i
\(154\) 0 0
\(155\) 1.20576 + 0.774898i 0.0968493 + 0.0622413i
\(156\) 0 0
\(157\) 15.8766 18.3225i 1.26709 1.46230i 0.442287 0.896874i \(-0.354167\pi\)
0.824801 0.565423i \(-0.191287\pi\)
\(158\) 0 0
\(159\) 3.13530 6.86535i 0.248645 0.544457i
\(160\) 0 0
\(161\) −24.0589 15.4617i −1.89610 1.21855i
\(162\) 0 0
\(163\) 20.2473 1.58589 0.792945 0.609293i \(-0.208547\pi\)
0.792945 + 0.609293i \(0.208547\pi\)
\(164\) 0 0
\(165\) −1.07207 2.34750i −0.0834603 0.182753i
\(166\) 0 0
\(167\) −1.82959 + 12.7251i −0.141578 + 0.984698i 0.787895 + 0.615809i \(0.211171\pi\)
−0.929473 + 0.368889i \(0.879738\pi\)
\(168\) 0 0
\(169\) 8.15933 + 9.41637i 0.627641 + 0.724336i
\(170\) 0 0
\(171\) 2.04163 0.156128
\(172\) 0 0
\(173\) −2.41690 5.29228i −0.183754 0.402364i 0.795229 0.606310i \(-0.207351\pi\)
−0.978982 + 0.203945i \(0.934624\pi\)
\(174\) 0 0
\(175\) −18.7386 5.50216i −1.41651 0.415924i
\(176\) 0 0
\(177\) 11.8024 + 3.46550i 0.887122 + 0.260483i
\(178\) 0 0
\(179\) 12.2800 + 14.1718i 0.917847 + 1.05925i 0.998047 + 0.0624734i \(0.0198989\pi\)
−0.0801993 + 0.996779i \(0.525556\pi\)
\(180\) 0 0
\(181\) 14.4598 16.6875i 1.07479 1.24038i 0.105511 0.994418i \(-0.466352\pi\)
0.969281 0.245957i \(-0.0791023\pi\)
\(182\) 0 0
\(183\) 9.21945 2.70707i 0.681521 0.200113i
\(184\) 0 0
\(185\) −2.75754 + 1.77216i −0.202738 + 0.130292i
\(186\) 0 0
\(187\) −7.44810 + 2.18696i −0.544659 + 0.159926i
\(188\) 0 0
\(189\) 1.74308 3.81681i 0.126790 0.277632i
\(190\) 0 0
\(191\) −9.81541 11.3276i −0.710218 0.819636i 0.279876 0.960036i \(-0.409707\pi\)
−0.990095 + 0.140400i \(0.955161\pi\)
\(192\) 0 0
\(193\) 1.17496 + 2.57281i 0.0845757 + 0.185195i 0.947195 0.320660i \(-0.103905\pi\)
−0.862619 + 0.505854i \(0.831177\pi\)
\(194\) 0 0
\(195\) 0.363556 + 0.233643i 0.0260348 + 0.0167316i
\(196\) 0 0
\(197\) 5.65570 1.66066i 0.402952 0.118317i −0.0739753 0.997260i \(-0.523569\pi\)
0.476928 + 0.878943i \(0.341750\pi\)
\(198\) 0 0
\(199\) −0.873858 6.07781i −0.0619461 0.430845i −0.997068 0.0765189i \(-0.975619\pi\)
0.935122 0.354326i \(-0.115290\pi\)
\(200\) 0 0
\(201\) 5.22582 + 6.30006i 0.368601 + 0.444372i
\(202\) 0 0
\(203\) −2.73638 19.0320i −0.192056 1.33578i
\(204\) 0 0
\(205\) 2.23058 0.654956i 0.155790 0.0457441i
\(206\) 0 0
\(207\) 5.73377 + 3.68487i 0.398525 + 0.256116i
\(208\) 0 0
\(209\) −3.72304 8.15231i −0.257528 0.563907i
\(210\) 0 0
\(211\) −2.46479 2.84452i −0.169683 0.195825i 0.664538 0.747254i \(-0.268628\pi\)
−0.834222 + 0.551429i \(0.814083\pi\)
\(212\) 0 0
\(213\) 0.424728 0.930024i 0.0291019 0.0637242i
\(214\) 0 0
\(215\) −5.75436 + 1.68963i −0.392444 + 0.115232i
\(216\) 0 0
\(217\) 8.60587 5.53065i 0.584204 0.375445i
\(218\) 0 0
\(219\) −9.65711 + 2.83558i −0.652567 + 0.191611i
\(220\) 0 0
\(221\) 0.851250 0.982395i 0.0572613 0.0660830i
\(222\) 0 0
\(223\) −13.1488 15.1745i −0.880507 1.01616i −0.999729 0.0232915i \(-0.992585\pi\)
0.119222 0.992868i \(-0.461960\pi\)
\(224\) 0 0
\(225\) 4.46584 + 1.31129i 0.297723 + 0.0874193i
\(226\) 0 0
\(227\) 17.4762 + 5.13147i 1.15993 + 0.340587i 0.804407 0.594079i \(-0.202483\pi\)
0.355527 + 0.934666i \(0.384301\pi\)
\(228\) 0 0
\(229\) −11.4945 25.1694i −0.759577 1.66324i −0.748349 0.663305i \(-0.769153\pi\)
−0.0112286 0.999937i \(-0.503574\pi\)
\(230\) 0 0
\(231\) −18.4193 −1.21190
\(232\) 0 0
\(233\) 3.94989 + 4.55842i 0.258766 + 0.298632i 0.870235 0.492636i \(-0.163967\pi\)
−0.611469 + 0.791268i \(0.709421\pi\)
\(234\) 0 0
\(235\) −0.629886 + 4.38095i −0.0410892 + 0.285782i
\(236\) 0 0
\(237\) −2.34861 5.14274i −0.152559 0.334057i
\(238\) 0 0
\(239\) 3.83055 0.247778 0.123889 0.992296i \(-0.460463\pi\)
0.123889 + 0.992296i \(0.460463\pi\)
\(240\) 0 0
\(241\) 1.76048 + 1.13139i 0.113403 + 0.0728794i 0.596113 0.802901i \(-0.296711\pi\)
−0.482710 + 0.875780i \(0.660348\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 4.08336 4.71245i 0.260876 0.301067i
\(246\) 0 0
\(247\) 1.26255 + 0.811388i 0.0803338 + 0.0516274i
\(248\) 0 0
\(249\) 0.669722 4.65802i 0.0424419 0.295190i
\(250\) 0 0
\(251\) 12.1750 + 3.57490i 0.768480 + 0.225646i 0.642395 0.766374i \(-0.277941\pi\)
0.126084 + 0.992020i \(0.459759\pi\)
\(252\) 0 0
\(253\) 4.25795 29.6147i 0.267695 1.86186i
\(254\) 0 0
\(255\) −0.431868 + 0.945659i −0.0270446 + 0.0592194i
\(256\) 0 0
\(257\) −0.204620 + 0.131501i −0.0127638 + 0.00820282i −0.547007 0.837128i \(-0.684233\pi\)
0.534243 + 0.845331i \(0.320597\pi\)
\(258\) 0 0
\(259\) 3.32948 + 23.1571i 0.206884 + 1.43891i
\(260\) 0 0
\(261\) 0.652142 + 4.53575i 0.0403666 + 0.280756i
\(262\) 0 0
\(263\) −13.6921 + 8.79936i −0.844290 + 0.542592i −0.889789 0.456372i \(-0.849148\pi\)
0.0454993 + 0.998964i \(0.485512\pi\)
\(264\) 0 0
\(265\) −2.90568 + 3.35334i −0.178495 + 0.205994i
\(266\) 0 0
\(267\) −4.46786 −0.273429
\(268\) 0 0
\(269\) −15.3389 −0.935226 −0.467613 0.883933i \(-0.654886\pi\)
−0.467613 + 0.883933i \(0.654886\pi\)
\(270\) 0 0
\(271\) −1.38277 + 1.59580i −0.0839971 + 0.0969378i −0.796192 0.605044i \(-0.793156\pi\)
0.712195 + 0.701982i \(0.247701\pi\)
\(272\) 0 0
\(273\) 2.59480 1.66758i 0.157044 0.100926i
\(274\) 0 0
\(275\) −2.90770 20.2235i −0.175341 1.21952i
\(276\) 0 0
\(277\) 2.28511 + 15.8933i 0.137299 + 0.954934i 0.935697 + 0.352804i \(0.114772\pi\)
−0.798398 + 0.602129i \(0.794319\pi\)
\(278\) 0 0
\(279\) −2.05097 + 1.31808i −0.122789 + 0.0789114i
\(280\) 0 0
\(281\) −0.171736 + 0.376050i −0.0102449 + 0.0224333i −0.914685 0.404167i \(-0.867562\pi\)
0.904440 + 0.426600i \(0.140289\pi\)
\(282\) 0 0
\(283\) −3.10270 + 21.5798i −0.184436 + 1.28278i 0.661681 + 0.749786i \(0.269843\pi\)
−0.846117 + 0.532997i \(0.821066\pi\)
\(284\) 0 0
\(285\) −1.15165 0.338156i −0.0682181 0.0200306i
\(286\) 0 0
\(287\) 2.36134 16.4234i 0.139385 0.969446i
\(288\) 0 0
\(289\) −11.6707 7.50029i −0.686511 0.441194i
\(290\) 0 0
\(291\) 5.48920 6.33487i 0.321782 0.371357i
\(292\) 0 0
\(293\) 0.284265 0.622453i 0.0166069 0.0363641i −0.901147 0.433514i \(-0.857273\pi\)
0.917754 + 0.397150i \(0.130001\pi\)
\(294\) 0 0
\(295\) −6.08356 3.90967i −0.354199 0.227630i
\(296\) 0 0
\(297\) 4.38973 0.254718
\(298\) 0 0
\(299\) 2.08131 + 4.55744i 0.120366 + 0.263564i
\(300\) 0 0
\(301\) −6.09169 + 42.3686i −0.351119 + 2.44209i
\(302\) 0 0
\(303\) −10.2818 11.8659i −0.590676 0.681676i
\(304\) 0 0
\(305\) −5.64892 −0.323456
\(306\) 0 0
\(307\) 6.54789 + 14.3379i 0.373708 + 0.818306i 0.999273 + 0.0381338i \(0.0121413\pi\)
−0.625565 + 0.780172i \(0.715131\pi\)
\(308\) 0 0
\(309\) 0.817408 + 0.240013i 0.0465007 + 0.0136538i
\(310\) 0 0
\(311\) 23.0760 + 6.77573i 1.30852 + 0.384216i 0.860337 0.509725i \(-0.170253\pi\)
0.448183 + 0.893942i \(0.352071\pi\)
\(312\) 0 0
\(313\) 10.0254 + 11.5700i 0.566671 + 0.653974i 0.964685 0.263406i \(-0.0848458\pi\)
−0.398014 + 0.917379i \(0.630300\pi\)
\(314\) 0 0
\(315\) −1.61542 + 1.86430i −0.0910188 + 0.105041i
\(316\) 0 0
\(317\) −0.910124 + 0.267237i −0.0511177 + 0.0150095i −0.307191 0.951648i \(-0.599389\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(318\) 0 0
\(319\) 16.9222 10.8752i 0.947460 0.608895i
\(320\) 0 0
\(321\) −11.7339 + 3.44538i −0.654922 + 0.192302i
\(322\) 0 0
\(323\) −1.49977 + 3.28405i −0.0834497 + 0.182729i
\(324\) 0 0
\(325\) 2.24054 + 2.58572i 0.124283 + 0.143430i
\(326\) 0 0
\(327\) 5.80264 + 12.7060i 0.320887 + 0.702644i
\(328\) 0 0
\(329\) 26.5748 + 17.0786i 1.46512 + 0.941575i
\(330\) 0 0
\(331\) −0.525438 + 0.154283i −0.0288807 + 0.00848013i −0.296141 0.955144i \(-0.595700\pi\)
0.267260 + 0.963624i \(0.413882\pi\)
\(332\) 0 0
\(333\) −0.793491 5.51885i −0.0434831 0.302431i
\(334\) 0 0
\(335\) −1.90433 4.41932i −0.104045 0.241453i
\(336\) 0 0
\(337\) 2.34907 + 16.3381i 0.127962 + 0.889994i 0.948133 + 0.317875i \(0.102969\pi\)
−0.820171 + 0.572119i \(0.806122\pi\)
\(338\) 0 0
\(339\) −14.4605 + 4.24599i −0.785388 + 0.230611i
\(340\) 0 0
\(341\) 9.00321 + 5.78601i 0.487551 + 0.313330i
\(342\) 0 0
\(343\) −6.28616 13.7648i −0.339421 0.743228i
\(344\) 0 0
\(345\) −2.62401 3.02827i −0.141272 0.163036i
\(346\) 0 0
\(347\) 13.0307 28.5333i 0.699525 1.53175i −0.141021 0.990007i \(-0.545038\pi\)
0.840546 0.541740i \(-0.182234\pi\)
\(348\) 0 0
\(349\) −7.02621 + 2.06308i −0.376104 + 0.110434i −0.464321 0.885667i \(-0.653701\pi\)
0.0882164 + 0.996101i \(0.471883\pi\)
\(350\) 0 0
\(351\) −0.618399 + 0.397421i −0.0330077 + 0.0212128i
\(352\) 0 0
\(353\) 6.78260 1.99155i 0.361001 0.106000i −0.0962018 0.995362i \(-0.530669\pi\)
0.457203 + 0.889362i \(0.348851\pi\)
\(354\) 0 0
\(355\) −0.393622 + 0.454265i −0.0208913 + 0.0241099i
\(356\) 0 0
\(357\) 4.85903 + 5.60762i 0.257167 + 0.296787i
\(358\) 0 0
\(359\) 28.2491 + 8.29470i 1.49093 + 0.437777i 0.922839 0.385186i \(-0.125863\pi\)
0.568094 + 0.822964i \(0.307681\pi\)
\(360\) 0 0
\(361\) 14.2309 + 4.17858i 0.748997 + 0.219925i
\(362\) 0 0
\(363\) −3.43535 7.52238i −0.180309 0.394822i
\(364\) 0 0
\(365\) 5.91709 0.309715
\(366\) 0 0
\(367\) −7.33324 8.46301i −0.382792 0.441765i 0.531355 0.847150i \(-0.321683\pi\)
−0.914146 + 0.405384i \(0.867138\pi\)
\(368\) 0 0
\(369\) −0.562760 + 3.91408i −0.0292961 + 0.203759i
\(370\) 0 0
\(371\) 13.1557 + 28.8069i 0.683009 + 1.49558i
\(372\) 0 0
\(373\) −29.7927 −1.54261 −0.771303 0.636468i \(-0.780395\pi\)
−0.771303 + 0.636468i \(0.780395\pi\)
\(374\) 0 0
\(375\) −4.77478 3.06857i −0.246569 0.158460i
\(376\) 0 0
\(377\) −1.39932 + 3.06408i −0.0720685 + 0.157808i
\(378\) 0 0
\(379\) 6.20647 7.16265i 0.318805 0.367921i −0.573616 0.819124i \(-0.694460\pi\)
0.892421 + 0.451204i \(0.149005\pi\)
\(380\) 0 0
\(381\) 1.08306 + 0.696040i 0.0554869 + 0.0356592i
\(382\) 0 0
\(383\) −4.70141 + 32.6990i −0.240231 + 1.67084i 0.410752 + 0.911747i \(0.365266\pi\)
−0.650982 + 0.759093i \(0.725643\pi\)
\(384\) 0 0
\(385\) 10.3900 + 3.05079i 0.529525 + 0.155482i
\(386\) 0 0
\(387\) 1.45179 10.0974i 0.0737985 0.513280i
\(388\) 0 0
\(389\) −1.65092 + 3.61500i −0.0837047 + 0.183288i −0.946856 0.321657i \(-0.895760\pi\)
0.863151 + 0.504945i \(0.168487\pi\)
\(390\) 0 0
\(391\) −10.1393 + 6.51611i −0.512765 + 0.329534i
\(392\) 0 0
\(393\) −0.643985 4.47902i −0.0324848 0.225937i
\(394\) 0 0
\(395\) 0.473023 + 3.28995i 0.0238004 + 0.165535i
\(396\) 0 0
\(397\) −1.18727 + 0.763009i −0.0595872 + 0.0382943i −0.570095 0.821579i \(-0.693094\pi\)
0.510508 + 0.859873i \(0.329457\pi\)
\(398\) 0 0
\(399\) −5.60998 + 6.47426i −0.280850 + 0.324119i
\(400\) 0 0
\(401\) −9.44230 −0.471526 −0.235763 0.971811i \(-0.575759\pi\)
−0.235763 + 0.971811i \(0.575759\pi\)
\(402\) 0 0
\(403\) −1.79215 −0.0892735
\(404\) 0 0
\(405\) 0.384992 0.444304i 0.0191304 0.0220777i
\(406\) 0 0
\(407\) −20.5900 + 13.2324i −1.02061 + 0.655905i
\(408\) 0 0
\(409\) 0.0501255 + 0.348631i 0.00247855 + 0.0172387i 0.991023 0.133690i \(-0.0426827\pi\)
−0.988545 + 0.150929i \(0.951774\pi\)
\(410\) 0 0
\(411\) 1.58970 + 11.0566i 0.0784139 + 0.545381i
\(412\) 0 0
\(413\) −43.4200 + 27.9044i −2.13656 + 1.37308i
\(414\) 0 0
\(415\) −1.14929 + 2.51659i −0.0564164 + 0.123535i
\(416\) 0 0
\(417\) −2.10730 + 14.6566i −0.103195 + 0.717736i
\(418\) 0 0
\(419\) 19.6011 + 5.75542i 0.957579 + 0.281170i 0.722939 0.690912i \(-0.242791\pi\)
0.234640 + 0.972082i \(0.424609\pi\)
\(420\) 0 0
\(421\) 0.554770 3.85851i 0.0270378 0.188052i −0.971826 0.235697i \(-0.924263\pi\)
0.998864 + 0.0476452i \(0.0151717\pi\)
\(422\) 0 0
\(423\) −6.33339 4.07022i −0.307940 0.197901i
\(424\) 0 0
\(425\) −5.38985 + 6.22021i −0.261446 + 0.301725i
\(426\) 0 0
\(427\) −16.7487 + 36.6744i −0.810524 + 1.77480i
\(428\) 0 0
\(429\) 2.71460 + 1.74457i 0.131062 + 0.0842286i
\(430\) 0 0
\(431\) 34.3078 1.65255 0.826275 0.563267i \(-0.190456\pi\)
0.826275 + 0.563267i \(0.190456\pi\)
\(432\) 0 0
\(433\) −7.92406 17.3513i −0.380806 0.833849i −0.998861 0.0477139i \(-0.984806\pi\)
0.618055 0.786135i \(-0.287921\pi\)
\(434\) 0 0
\(435\) 0.383393 2.66656i 0.0183823 0.127852i
\(436\) 0 0
\(437\) −9.11255 10.5164i −0.435913 0.503070i
\(438\) 0 0
\(439\) −25.2960 −1.20731 −0.603657 0.797244i \(-0.706290\pi\)
−0.603657 + 0.797244i \(0.706290\pi\)
\(440\) 0 0
\(441\) 4.40604 + 9.64788i 0.209811 + 0.459423i
\(442\) 0 0
\(443\) −14.1608 4.15800i −0.672802 0.197552i −0.0725515 0.997365i \(-0.523114\pi\)
−0.600250 + 0.799812i \(0.704932\pi\)
\(444\) 0 0
\(445\) 2.52025 + 0.740013i 0.119471 + 0.0350800i
\(446\) 0 0
\(447\) 1.81781 + 2.09786i 0.0859794 + 0.0992255i
\(448\) 0 0
\(449\) 5.83003 6.72822i 0.275136 0.317524i −0.601318 0.799010i \(-0.705357\pi\)
0.876454 + 0.481486i \(0.159903\pi\)
\(450\) 0 0
\(451\) 16.6553 4.89043i 0.784267 0.230281i
\(452\) 0 0
\(453\) 2.66918 1.71538i 0.125409 0.0805956i
\(454\) 0 0
\(455\) −1.73989 + 0.510877i −0.0815672 + 0.0239503i
\(456\) 0 0
\(457\) 9.79507 21.4482i 0.458194 1.00330i −0.529702 0.848184i \(-0.677696\pi\)
0.987896 0.155121i \(-0.0495767\pi\)
\(458\) 0 0
\(459\) −1.15802 1.33642i −0.0540516 0.0623789i
\(460\) 0 0
\(461\) 14.3405 + 31.4014i 0.667905 + 1.46251i 0.874968 + 0.484180i \(0.160882\pi\)
−0.207063 + 0.978328i \(0.566391\pi\)
\(462\) 0 0
\(463\) −8.47795 5.44845i −0.394004 0.253211i 0.328606 0.944467i \(-0.393421\pi\)
−0.722610 + 0.691256i \(0.757058\pi\)
\(464\) 0 0
\(465\) 1.37524 0.403806i 0.0637751 0.0187260i
\(466\) 0 0
\(467\) 2.92132 + 20.3182i 0.135183 + 0.940216i 0.938651 + 0.344869i \(0.112076\pi\)
−0.803468 + 0.595347i \(0.797014\pi\)
\(468\) 0 0
\(469\) −34.3377 0.739537i −1.58557 0.0341487i
\(470\) 0 0
\(471\) −3.45031 23.9974i −0.158982 1.10574i
\(472\) 0 0
\(473\) −42.9667 + 12.6162i −1.97561 + 0.580092i
\(474\) 0 0
\(475\) −7.99404 5.13745i −0.366792 0.235723i
\(476\) 0 0
\(477\) −3.13530 6.86535i −0.143555 0.314343i
\(478\) 0 0
\(479\) 6.54181 + 7.54966i 0.298903 + 0.344953i 0.885257 0.465103i \(-0.153983\pi\)
−0.586354 + 0.810055i \(0.699437\pi\)
\(480\) 0 0
\(481\) 1.70261 3.72821i 0.0776325 0.169992i
\(482\) 0 0
\(483\) −27.4404 + 8.05722i −1.24858 + 0.366616i
\(484\) 0 0
\(485\) −4.14562 + 2.66423i −0.188243 + 0.120976i
\(486\) 0 0
\(487\) −9.48412 + 2.78479i −0.429767 + 0.126191i −0.489460 0.872026i \(-0.662806\pi\)
0.0596931 + 0.998217i \(0.480988\pi\)
\(488\) 0 0
\(489\) 13.2592 15.3019i 0.599600 0.691975i
\(490\) 0 0
\(491\) 24.2434 + 27.9784i 1.09409 + 1.26265i 0.962482 + 0.271347i \(0.0874692\pi\)
0.131610 + 0.991302i \(0.457985\pi\)
\(492\) 0 0
\(493\) −7.77499 2.28294i −0.350168 0.102819i
\(494\) 0 0
\(495\) −2.47618 0.727071i −0.111296 0.0326794i
\(496\) 0 0
\(497\) 1.78215 + 3.90237i 0.0799405 + 0.175045i
\(498\) 0 0
\(499\) 20.3365 0.910386 0.455193 0.890393i \(-0.349570\pi\)
0.455193 + 0.890393i \(0.349570\pi\)
\(500\) 0 0
\(501\) 8.41886 + 9.71589i 0.376127 + 0.434074i
\(502\) 0 0
\(503\) 0.931065 6.47570i 0.0415142 0.288737i −0.958479 0.285162i \(-0.907953\pi\)
0.999994 0.00357569i \(-0.00113818\pi\)
\(504\) 0 0
\(505\) 3.83448 + 8.39634i 0.170632 + 0.373632i
\(506\) 0 0
\(507\) 12.4596 0.553352
\(508\) 0 0
\(509\) 31.8659 + 20.4789i 1.41243 + 0.907713i 0.999995 0.00327348i \(-0.00104198\pi\)
0.412435 + 0.910987i \(0.364678\pi\)
\(510\) 0 0
\(511\) 17.5437 38.4154i 0.776090 1.69940i
\(512\) 0 0
\(513\) 1.33699 1.54296i 0.0590294 0.0681235i
\(514\) 0 0
\(515\) −0.421334 0.270775i −0.0185662 0.0119318i
\(516\) 0 0
\(517\) −4.70323 + 32.7117i −0.206848 + 1.43866i
\(518\) 0 0
\(519\) −5.58237 1.63913i −0.245039 0.0719499i
\(520\) 0 0
\(521\) −4.66692 + 32.4592i −0.204462 + 1.42206i 0.586378 + 0.810038i \(0.300554\pi\)
−0.790839 + 0.612024i \(0.790356\pi\)
\(522\) 0 0
\(523\) 17.8650 39.1189i 0.781181 1.71055i 0.0808539 0.996726i \(-0.474235\pi\)
0.700327 0.713822i \(-0.253037\pi\)
\(524\) 0 0
\(525\) −16.4294 + 10.5586i −0.717040 + 0.460814i
\(526\) 0 0
\(527\) −0.613549 4.26733i −0.0267266 0.185888i
\(528\) 0 0
\(529\) −3.33791 23.2157i −0.145126 1.00938i
\(530\) 0 0
\(531\) 10.3480 6.65024i 0.449064 0.288596i
\(532\) 0 0
\(533\) −1.90355 + 2.19681i −0.0824518 + 0.0951545i
\(534\) 0 0
\(535\) 7.18957 0.310832
\(536\) 0 0
\(537\) 18.7520 0.809209
\(538\) 0 0
\(539\) 30.4897 35.1869i 1.31328 1.51561i
\(540\) 0 0
\(541\) 7.34270 4.71887i 0.315687 0.202880i −0.373195 0.927753i \(-0.621738\pi\)
0.688883 + 0.724873i \(0.258102\pi\)
\(542\) 0 0
\(543\) −3.14242 21.8560i −0.134854 0.937932i
\(544\) 0 0
\(545\) −1.16868 8.12835i −0.0500608 0.348180i
\(546\) 0 0
\(547\) −25.4396 + 16.3491i −1.08772 + 0.699036i −0.956328 0.292295i \(-0.905581\pi\)
−0.131393 + 0.991330i \(0.541945\pi\)
\(548\) 0 0
\(549\) 3.99158 8.74035i 0.170357 0.373029i
\(550\) 0 0
\(551\) 1.33143 9.26033i 0.0567210 0.394503i
\(552\) 0 0
\(553\) 22.7618 + 6.68345i 0.967928 + 0.284209i
\(554\) 0 0
\(555\) −0.466493 + 3.24453i −0.0198015 + 0.137723i
\(556\) 0 0
\(557\) 31.3565 + 20.1516i 1.32862 + 0.853852i 0.996013 0.0892137i \(-0.0284354\pi\)
0.332607 + 0.943066i \(0.392072\pi\)
\(558\) 0 0
\(559\) 4.91070 5.66725i 0.207701 0.239699i
\(560\) 0 0
\(561\) −3.22467 + 7.06105i −0.136146 + 0.298118i
\(562\) 0 0
\(563\) −9.09383 5.84425i −0.383259 0.246306i 0.334798 0.942290i \(-0.391332\pi\)
−0.718057 + 0.695984i \(0.754968\pi\)
\(564\) 0 0
\(565\) 8.86023 0.372753
\(566\) 0 0
\(567\) −1.74308 3.81681i −0.0732024 0.160291i
\(568\) 0 0
\(569\) 5.14906 35.8125i 0.215860 1.50134i −0.537239 0.843430i \(-0.680533\pi\)
0.753099 0.657907i \(-0.228558\pi\)
\(570\) 0 0
\(571\) 3.30313 + 3.81202i 0.138232 + 0.159528i 0.820644 0.571439i \(-0.193615\pi\)
−0.682413 + 0.730967i \(0.739069\pi\)
\(572\) 0 0
\(573\) −14.9886 −0.626156
\(574\) 0 0
\(575\) −13.1782 28.8563i −0.549570 1.20339i
\(576\) 0 0
\(577\) 40.3634 + 11.8518i 1.68035 + 0.493395i 0.976239 0.216697i \(-0.0695282\pi\)
0.704110 + 0.710091i \(0.251346\pi\)
\(578\) 0 0
\(579\) 2.71384 + 0.796855i 0.112783 + 0.0331161i
\(580\) 0 0
\(581\) 12.9309 + 14.9230i 0.536463 + 0.619112i
\(582\) 0 0
\(583\) −21.6962 + 25.0387i −0.898563 + 1.03700i
\(584\) 0 0
\(585\) 0.414655 0.121754i 0.0171439 0.00503389i
\(586\) 0 0
\(587\) −27.4354 + 17.6316i −1.13238 + 0.727735i −0.966055 0.258336i \(-0.916826\pi\)
−0.166323 + 0.986071i \(0.553190\pi\)
\(588\) 0 0
\(589\) 4.77587 1.40232i 0.196786 0.0577817i
\(590\) 0 0
\(591\) 2.44865 5.36180i 0.100724 0.220555i
\(592\) 0 0
\(593\) 8.35464 + 9.64177i 0.343084 + 0.395940i 0.900901 0.434024i \(-0.142907\pi\)
−0.557818 + 0.829964i \(0.688361\pi\)
\(594\) 0 0
\(595\) −1.81211 3.96798i −0.0742894 0.162671i
\(596\) 0 0
\(597\) −5.16556 3.31970i −0.211412 0.135866i
\(598\) 0 0
\(599\) 9.78054 2.87183i 0.399622 0.117340i −0.0757449 0.997127i \(-0.524133\pi\)
0.475367 + 0.879788i \(0.342315\pi\)
\(600\) 0 0
\(601\) 0.785168 + 5.46097i 0.0320277 + 0.222757i 0.999549 0.0300323i \(-0.00956101\pi\)
−0.967521 + 0.252790i \(0.918652\pi\)
\(602\) 0 0
\(603\) 8.18346 + 0.176248i 0.333256 + 0.00717739i
\(604\) 0 0
\(605\) 0.691898 + 4.81226i 0.0281297 + 0.195646i
\(606\) 0 0
\(607\) 5.36688 1.57586i 0.217835 0.0639621i −0.170994 0.985272i \(-0.554698\pi\)
0.388829 + 0.921310i \(0.372880\pi\)
\(608\) 0 0
\(609\) −16.1753 10.3953i −0.655458 0.421237i
\(610\) 0 0
\(611\) −2.29897 5.03404i −0.0930064 0.203656i
\(612\) 0 0
\(613\) 6.14011 + 7.08607i 0.247997 + 0.286204i 0.866076 0.499912i \(-0.166634\pi\)
−0.618079 + 0.786116i \(0.712089\pi\)
\(614\) 0 0
\(615\) 0.965734 2.11466i 0.0389422 0.0852714i
\(616\) 0 0
\(617\) 38.0311 11.1669i 1.53108 0.449564i 0.595696 0.803210i \(-0.296876\pi\)
0.935380 + 0.353645i \(0.115058\pi\)
\(618\) 0 0
\(619\) 9.63379 6.19126i 0.387215 0.248848i −0.332521 0.943096i \(-0.607899\pi\)
0.719736 + 0.694248i \(0.244263\pi\)
\(620\) 0 0
\(621\) 6.53966 1.92022i 0.262428 0.0770557i
\(622\) 0 0
\(623\) 12.2768 14.1681i 0.491858 0.567634i
\(624\) 0 0
\(625\) −13.0547 15.0659i −0.522188 0.602637i
\(626\) 0 0
\(627\) −8.59918 2.52495i −0.343418 0.100837i
\(628\) 0 0
\(629\) 9.46019 + 2.77776i 0.377202 + 0.110757i
\(630\) 0 0
\(631\) −19.9145 43.6068i −0.792786 1.73596i −0.668500 0.743712i \(-0.733063\pi\)
−0.124286 0.992246i \(-0.539664\pi\)
\(632\) 0 0
\(633\) −3.76384 −0.149599
\(634\) 0 0
\(635\) −0.495652 0.572013i −0.0196694 0.0226997i
\(636\) 0 0
\(637\) −1.10958 + 7.71730i −0.0439632 + 0.305770i
\(638\) 0 0
\(639\) −0.424728 0.930024i −0.0168020 0.0367912i
\(640\) 0 0
\(641\) −33.3452 −1.31706 −0.658529 0.752556i \(-0.728821\pi\)
−0.658529 + 0.752556i \(0.728821\pi\)
\(642\) 0 0
\(643\) −6.50043 4.17757i −0.256352 0.164747i 0.406153 0.913805i \(-0.366870\pi\)
−0.662505 + 0.749058i \(0.730506\pi\)
\(644\) 0 0
\(645\) −2.49137 + 5.45533i −0.0980974 + 0.214803i
\(646\) 0 0
\(647\) 2.28881 2.64143i 0.0899825 0.103845i −0.708973 0.705236i \(-0.750841\pi\)
0.798955 + 0.601391i \(0.205386\pi\)
\(648\) 0 0
\(649\) −45.4248 29.1927i −1.78308 1.14591i
\(650\) 0 0
\(651\) 1.45585 10.1257i 0.0570594 0.396857i
\(652\) 0 0
\(653\) 5.54261 + 1.62746i 0.216899 + 0.0636873i 0.388377 0.921501i \(-0.373036\pi\)
−0.171478 + 0.985188i \(0.554854\pi\)
\(654\) 0 0
\(655\) −0.378598 + 2.63321i −0.0147931 + 0.102888i
\(656\) 0 0
\(657\) −4.18107 + 9.15527i −0.163119 + 0.357181i
\(658\) 0 0
\(659\) −18.5119 + 11.8969i −0.721120 + 0.463436i −0.849026 0.528351i \(-0.822811\pi\)
0.127906 + 0.991786i \(0.459174\pi\)
\(660\) 0 0
\(661\) 5.35099 + 37.2169i 0.208129 + 1.44757i 0.779254 + 0.626708i \(0.215598\pi\)
−0.571125 + 0.820863i \(0.693493\pi\)
\(662\) 0 0
\(663\) −0.184994 1.28666i −0.00718458 0.0499699i
\(664\) 0 0
\(665\) 4.23684 2.72285i 0.164298 0.105588i
\(666\) 0 0
\(667\) 20.4529 23.6039i 0.791938 0.913945i
\(668\) 0 0
\(669\) −20.0787 −0.776289
\(670\) 0 0
\(671\) −42.1794 −1.62832
\(672\) 0 0
\(673\) −18.7228 + 21.6073i −0.721712 + 0.832900i −0.991512 0.130017i \(-0.958497\pi\)
0.269800 + 0.962916i \(0.413042\pi\)
\(674\) 0 0
\(675\) 3.91551 2.51635i 0.150708 0.0968542i
\(676\) 0 0
\(677\) −1.50688 10.4806i −0.0579141 0.402801i −0.998072 0.0620629i \(-0.980232\pi\)
0.940158 0.340738i \(-0.110677\pi\)
\(678\) 0 0
\(679\) 5.00547 + 34.8138i 0.192092 + 1.33603i
\(680\) 0 0
\(681\) 15.3226 9.84721i 0.587162 0.377346i
\(682\) 0 0
\(683\) −14.9693 + 32.7781i −0.572783 + 1.25422i 0.372519 + 0.928025i \(0.378494\pi\)
−0.945302 + 0.326196i \(0.894233\pi\)
\(684\) 0 0
\(685\) 0.934581 6.50015i 0.0357085 0.248358i
\(686\) 0 0
\(687\) −26.5491 7.79551i −1.01291 0.297417i
\(688\) 0 0
\(689\) 0.789567 5.49156i 0.0300801 0.209212i
\(690\) 0 0
\(691\) −20.7743 13.3508i −0.790291 0.507889i 0.0821437 0.996620i \(-0.473823\pi\)
−0.872434 + 0.488732i \(0.837460\pi\)
\(692\) 0 0
\(693\) −12.0620 + 13.9203i −0.458199 + 0.528790i
\(694\) 0 0
\(695\) 3.61627 7.91852i 0.137173 0.300367i
\(696\) 0 0
\(697\) −5.88255 3.78049i −0.222818 0.143196i
\(698\) 0 0
\(699\) 6.03165 0.228138
\(700\) 0 0
\(701\) −5.28605 11.5748i −0.199651 0.437175i 0.783152 0.621830i \(-0.213611\pi\)
−0.982803 + 0.184655i \(0.940883\pi\)
\(702\) 0 0
\(703\) −1.62002 + 11.2675i −0.0611002 + 0.424961i
\(704\) 0 0
\(705\) 2.89842 + 3.34495i 0.109161 + 0.125978i
\(706\) 0 0
\(707\) 65.8804 2.47769
\(708\) 0 0
\(709\) 4.00188 + 8.76290i 0.150294 + 0.329098i 0.969772 0.244013i \(-0.0784639\pi\)
−0.819478 + 0.573110i \(0.805737\pi\)
\(710\) 0 0
\(711\) −5.42464 1.59282i −0.203440 0.0597354i
\(712\) 0 0
\(713\) 15.9437 + 4.68148i 0.597095 + 0.175323i
\(714\) 0 0
\(715\) −1.24231 1.43371i −0.0464599 0.0536176i
\(716\) 0 0
\(717\) 2.50848 2.89494i 0.0936808 0.108113i
\(718\) 0 0
\(719\) −11.3586 + 3.33519i −0.423605 + 0.124382i −0.486585 0.873633i \(-0.661758\pi\)
0.0629802 + 0.998015i \(0.479939\pi\)
\(720\) 0 0
\(721\) −3.00717 + 1.93259i −0.111993 + 0.0719735i
\(722\) 0 0
\(723\) 2.00792 0.589578i 0.0746753 0.0219266i
\(724\) 0 0
\(725\) 8.86004 19.4008i 0.329053 0.720527i
\(726\) 0 0
\(727\) −29.2389 33.7434i −1.08441 1.25148i −0.966009 0.258509i \(-0.916769\pi\)
−0.118401 0.992966i \(-0.537777\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) 15.1756 + 9.75276i 0.561290 + 0.360719i
\(732\) 0 0
\(733\) 6.83950 2.00826i 0.252623 0.0741768i −0.152969 0.988231i \(-0.548884\pi\)
0.405592 + 0.914054i \(0.367065\pi\)
\(734\) 0 0
\(735\) −0.887399 6.17200i −0.0327322 0.227658i
\(736\) 0 0
\(737\) −14.2192 32.9982i −0.523772 1.21551i
\(738\) 0 0
\(739\) −6.82496 47.4687i −0.251060 1.74616i −0.591872 0.806032i \(-0.701611\pi\)
0.340812 0.940131i \(-0.389298\pi\)
\(740\) 0 0
\(741\) 1.44000 0.422821i 0.0528996 0.0155327i
\(742\) 0 0
\(743\) −36.8061 23.6539i −1.35029 0.867776i −0.352600 0.935774i \(-0.614703\pi\)
−0.997685 + 0.0679979i \(0.978339\pi\)
\(744\) 0 0
\(745\) −0.677928 1.48446i −0.0248374 0.0543863i
\(746\) 0 0
\(747\) −3.08172 3.55650i −0.112754 0.130125i
\(748\) 0 0
\(749\) 21.3166 46.6768i 0.778890 1.70553i
\(750\) 0 0
\(751\) 12.6209 3.70584i 0.460544 0.135228i −0.0432267 0.999065i \(-0.513764\pi\)
0.503771 + 0.863837i \(0.331946\pi\)
\(752\) 0 0
\(753\) 10.6747 6.86019i 0.389006 0.249999i
\(754\) 0 0
\(755\) −1.78976 + 0.525522i −0.0651362 + 0.0191257i
\(756\) 0 0
\(757\) 2.31387 2.67034i 0.0840989 0.0970553i −0.712141 0.702037i \(-0.752274\pi\)
0.796239 + 0.604982i \(0.206820\pi\)
\(758\) 0 0
\(759\) −19.5929 22.6115i −0.711179 0.820744i
\(760\) 0 0
\(761\) −2.33044 0.684279i −0.0844784 0.0248051i 0.239220 0.970965i \(-0.423108\pi\)
−0.323699 + 0.946160i \(0.604926\pi\)
\(762\) 0 0
\(763\) −56.2367 16.5126i −2.03590 0.597796i
\(764\) 0 0
\(765\) 0.431868 + 0.945659i 0.0156142 + 0.0341904i
\(766\) 0 0
\(767\) 9.04213 0.326492
\(768\) 0 0
\(769\) 28.0140 + 32.3299i 1.01021 + 1.16585i 0.986103 + 0.166138i \(0.0531296\pi\)
0.0241097 + 0.999709i \(0.492325\pi\)
\(770\) 0 0
\(771\) −0.0346155 + 0.240756i −0.00124665 + 0.00867063i
\(772\) 0 0
\(773\) −3.73649 8.18178i −0.134392 0.294278i 0.830457 0.557083i \(-0.188080\pi\)
−0.964849 + 0.262805i \(0.915352\pi\)
\(774\) 0 0
\(775\) 11.3473 0.407609
\(776\) 0 0
\(777\) 19.6813 + 12.6484i 0.706063 + 0.453759i
\(778\) 0 0
\(779\) 3.35377 7.34372i 0.120161 0.263116i
\(780\) 0 0
\(781\) −2.93910 + 3.39190i −0.105169 + 0.121372i