Properties

Label 1512.2.c.g.757.19
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.19
Character \(\chi\) \(=\) 1512.757
Dual form 1512.2.c.g.757.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.13123 - 0.848721i) q^{2} +(0.559347 - 1.92019i) q^{4} +0.940450i q^{5} +1.00000 q^{7} +(-0.996957 - 2.64690i) q^{8} +O(q^{10})\) \(q+(1.13123 - 0.848721i) q^{2} +(0.559347 - 1.92019i) q^{4} +0.940450i q^{5} +1.00000 q^{7} +(-0.996957 - 2.64690i) q^{8} +(0.798179 + 1.06386i) q^{10} +5.98632i q^{11} +6.59017i q^{13} +(1.13123 - 0.848721i) q^{14} +(-3.37426 - 2.14810i) q^{16} -2.64225 q^{17} +5.83430i q^{19} +(1.80584 + 0.526037i) q^{20} +(5.08071 + 6.77188i) q^{22} +2.88452 q^{23} +4.11555 q^{25} +(5.59321 + 7.45497i) q^{26} +(0.559347 - 1.92019i) q^{28} -3.09794i q^{29} +3.52412 q^{31} +(-5.64020 + 0.433813i) q^{32} +(-2.98898 + 2.24253i) q^{34} +0.940450i q^{35} +0.213560i q^{37} +(4.95169 + 6.59991i) q^{38} +(2.48928 - 0.937588i) q^{40} -1.63291 q^{41} -7.16716i q^{43} +(11.4949 + 3.34843i) q^{44} +(3.26304 - 2.44815i) q^{46} -9.32639 q^{47} +1.00000 q^{49} +(4.65562 - 3.49296i) q^{50} +(12.6544 + 3.68619i) q^{52} +7.51044i q^{53} -5.62983 q^{55} +(-0.996957 - 2.64690i) q^{56} +(-2.62929 - 3.50448i) q^{58} -11.9280i q^{59} -1.48304i q^{61} +(3.98658 - 2.99099i) q^{62} +(-6.01215 + 5.27769i) q^{64} -6.19772 q^{65} -13.0555i q^{67} +(-1.47793 + 5.07362i) q^{68} +(0.798179 + 1.06386i) q^{70} -1.54642 q^{71} -2.96871 q^{73} +(0.181253 + 0.241584i) q^{74} +(11.2030 + 3.26339i) q^{76} +5.98632i q^{77} +15.9515 q^{79} +(2.02018 - 3.17332i) q^{80} +(-1.84719 + 1.38588i) q^{82} +8.74782i q^{83} -2.48490i q^{85} +(-6.08291 - 8.10768i) q^{86} +(15.8452 - 5.96810i) q^{88} +7.50339 q^{89} +6.59017i q^{91} +(1.61345 - 5.53883i) q^{92} +(-10.5503 + 7.91550i) q^{94} -5.48686 q^{95} +10.7529 q^{97} +(1.13123 - 0.848721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.13123 0.848721i 0.799898 0.600136i
\(3\) 0 0
\(4\) 0.559347 1.92019i 0.279673 0.960095i
\(5\) 0.940450i 0.420582i 0.977639 + 0.210291i \(0.0674411\pi\)
−0.977639 + 0.210291i \(0.932559\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.996957 2.64690i −0.352478 0.935820i
\(9\) 0 0
\(10\) 0.798179 + 1.06386i 0.252406 + 0.336423i
\(11\) 5.98632i 1.80494i 0.430749 + 0.902472i \(0.358249\pi\)
−0.430749 + 0.902472i \(0.641751\pi\)
\(12\) 0 0
\(13\) 6.59017i 1.82778i 0.405957 + 0.913892i \(0.366938\pi\)
−0.405957 + 0.913892i \(0.633062\pi\)
\(14\) 1.13123 0.848721i 0.302333 0.226830i
\(15\) 0 0
\(16\) −3.37426 2.14810i −0.843566 0.537026i
\(17\) −2.64225 −0.640840 −0.320420 0.947276i \(-0.603824\pi\)
−0.320420 + 0.947276i \(0.603824\pi\)
\(18\) 0 0
\(19\) 5.83430i 1.33848i 0.743047 + 0.669240i \(0.233380\pi\)
−0.743047 + 0.669240i \(0.766620\pi\)
\(20\) 1.80584 + 0.526037i 0.403799 + 0.117626i
\(21\) 0 0
\(22\) 5.08071 + 6.77188i 1.08321 + 1.44377i
\(23\) 2.88452 0.601464 0.300732 0.953709i \(-0.402769\pi\)
0.300732 + 0.953709i \(0.402769\pi\)
\(24\) 0 0
\(25\) 4.11555 0.823111
\(26\) 5.59321 + 7.45497i 1.09692 + 1.46204i
\(27\) 0 0
\(28\) 0.559347 1.92019i 0.105707 0.362882i
\(29\) 3.09794i 0.575274i −0.957740 0.287637i \(-0.907130\pi\)
0.957740 0.287637i \(-0.0928696\pi\)
\(30\) 0 0
\(31\) 3.52412 0.632950 0.316475 0.948601i \(-0.397501\pi\)
0.316475 + 0.948601i \(0.397501\pi\)
\(32\) −5.64020 + 0.433813i −0.997055 + 0.0766880i
\(33\) 0 0
\(34\) −2.98898 + 2.24253i −0.512606 + 0.384591i
\(35\) 0.940450i 0.158965i
\(36\) 0 0
\(37\) 0.213560i 0.0351090i 0.999846 + 0.0175545i \(0.00558806\pi\)
−0.999846 + 0.0175545i \(0.994412\pi\)
\(38\) 4.95169 + 6.59991i 0.803270 + 1.07065i
\(39\) 0 0
\(40\) 2.48928 0.937588i 0.393589 0.148246i
\(41\) −1.63291 −0.255017 −0.127509 0.991837i \(-0.540698\pi\)
−0.127509 + 0.991837i \(0.540698\pi\)
\(42\) 0 0
\(43\) 7.16716i 1.09298i −0.837465 0.546491i \(-0.815963\pi\)
0.837465 0.546491i \(-0.184037\pi\)
\(44\) 11.4949 + 3.34843i 1.73292 + 0.504795i
\(45\) 0 0
\(46\) 3.26304 2.44815i 0.481110 0.360960i
\(47\) −9.32639 −1.36039 −0.680197 0.733030i \(-0.738106\pi\)
−0.680197 + 0.733030i \(0.738106\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.65562 3.49296i 0.658405 0.493979i
\(51\) 0 0
\(52\) 12.6544 + 3.68619i 1.75485 + 0.511183i
\(53\) 7.51044i 1.03164i 0.856698 + 0.515819i \(0.172512\pi\)
−0.856698 + 0.515819i \(0.827488\pi\)
\(54\) 0 0
\(55\) −5.62983 −0.759126
\(56\) −0.996957 2.64690i −0.133224 0.353707i
\(57\) 0 0
\(58\) −2.62929 3.50448i −0.345243 0.460160i
\(59\) 11.9280i 1.55289i −0.630186 0.776444i \(-0.717021\pi\)
0.630186 0.776444i \(-0.282979\pi\)
\(60\) 0 0
\(61\) 1.48304i 0.189884i −0.995483 0.0949419i \(-0.969733\pi\)
0.995483 0.0949419i \(-0.0302665\pi\)
\(62\) 3.98658 2.99099i 0.506296 0.379856i
\(63\) 0 0
\(64\) −6.01215 + 5.27769i −0.751519 + 0.659711i
\(65\) −6.19772 −0.768733
\(66\) 0 0
\(67\) 13.0555i 1.59498i −0.603329 0.797492i \(-0.706160\pi\)
0.603329 0.797492i \(-0.293840\pi\)
\(68\) −1.47793 + 5.07362i −0.179226 + 0.615267i
\(69\) 0 0
\(70\) 0.798179 + 1.06386i 0.0954006 + 0.127156i
\(71\) −1.54642 −0.183526 −0.0917632 0.995781i \(-0.529250\pi\)
−0.0917632 + 0.995781i \(0.529250\pi\)
\(72\) 0 0
\(73\) −2.96871 −0.347461 −0.173731 0.984793i \(-0.555582\pi\)
−0.173731 + 0.984793i \(0.555582\pi\)
\(74\) 0.181253 + 0.241584i 0.0210702 + 0.0280836i
\(75\) 0 0
\(76\) 11.2030 + 3.26339i 1.28507 + 0.374337i
\(77\) 5.98632i 0.682204i
\(78\) 0 0
\(79\) 15.9515 1.79468 0.897341 0.441338i \(-0.145496\pi\)
0.897341 + 0.441338i \(0.145496\pi\)
\(80\) 2.02018 3.17332i 0.225863 0.354788i
\(81\) 0 0
\(82\) −1.84719 + 1.38588i −0.203988 + 0.153045i
\(83\) 8.74782i 0.960198i 0.877214 + 0.480099i \(0.159399\pi\)
−0.877214 + 0.480099i \(0.840601\pi\)
\(84\) 0 0
\(85\) 2.48490i 0.269526i
\(86\) −6.08291 8.10768i −0.655937 0.874273i
\(87\) 0 0
\(88\) 15.8452 5.96810i 1.68910 0.636202i
\(89\) 7.50339 0.795358 0.397679 0.917525i \(-0.369816\pi\)
0.397679 + 0.917525i \(0.369816\pi\)
\(90\) 0 0
\(91\) 6.59017i 0.690837i
\(92\) 1.61345 5.53883i 0.168213 0.577462i
\(93\) 0 0
\(94\) −10.5503 + 7.91550i −1.08818 + 0.816421i
\(95\) −5.48686 −0.562940
\(96\) 0 0
\(97\) 10.7529 1.09179 0.545894 0.837854i \(-0.316190\pi\)
0.545894 + 0.837854i \(0.316190\pi\)
\(98\) 1.13123 0.848721i 0.114271 0.0857337i
\(99\) 0 0
\(100\) 2.30202 7.90265i 0.230202 0.790265i
\(101\) 3.54920i 0.353159i 0.984286 + 0.176579i \(0.0565033\pi\)
−0.984286 + 0.176579i \(0.943497\pi\)
\(102\) 0 0
\(103\) 15.3303 1.51054 0.755271 0.655413i \(-0.227505\pi\)
0.755271 + 0.655413i \(0.227505\pi\)
\(104\) 17.4435 6.57012i 1.71048 0.644253i
\(105\) 0 0
\(106\) 6.37426 + 8.49601i 0.619123 + 0.825205i
\(107\) 2.41633i 0.233596i 0.993156 + 0.116798i \(0.0372629\pi\)
−0.993156 + 0.116798i \(0.962737\pi\)
\(108\) 0 0
\(109\) 6.86711i 0.657750i 0.944373 + 0.328875i \(0.106669\pi\)
−0.944373 + 0.328875i \(0.893331\pi\)
\(110\) −6.36861 + 4.77815i −0.607224 + 0.455579i
\(111\) 0 0
\(112\) −3.37426 2.14810i −0.318838 0.202977i
\(113\) −15.4539 −1.45378 −0.726891 0.686752i \(-0.759036\pi\)
−0.726891 + 0.686752i \(0.759036\pi\)
\(114\) 0 0
\(115\) 2.71274i 0.252965i
\(116\) −5.94864 1.73283i −0.552318 0.160889i
\(117\) 0 0
\(118\) −10.1235 13.4932i −0.931945 1.24215i
\(119\) −2.64225 −0.242215
\(120\) 0 0
\(121\) −24.8360 −2.25782
\(122\) −1.25869 1.67765i −0.113956 0.151888i
\(123\) 0 0
\(124\) 1.97120 6.76698i 0.177019 0.607692i
\(125\) 8.57272i 0.766767i
\(126\) 0 0
\(127\) 7.96760 0.707010 0.353505 0.935433i \(-0.384990\pi\)
0.353505 + 0.935433i \(0.384990\pi\)
\(128\) −2.32182 + 11.0729i −0.205222 + 0.978715i
\(129\) 0 0
\(130\) −7.01103 + 5.26013i −0.614908 + 0.461344i
\(131\) 1.53780i 0.134358i −0.997741 0.0671790i \(-0.978600\pi\)
0.997741 0.0671790i \(-0.0213999\pi\)
\(132\) 0 0
\(133\) 5.83430i 0.505898i
\(134\) −11.0805 14.7687i −0.957208 1.27582i
\(135\) 0 0
\(136\) 2.63421 + 6.99377i 0.225882 + 0.599711i
\(137\) 6.34042 0.541699 0.270849 0.962622i \(-0.412695\pi\)
0.270849 + 0.962622i \(0.412695\pi\)
\(138\) 0 0
\(139\) 8.13659i 0.690137i −0.938578 0.345068i \(-0.887856\pi\)
0.938578 0.345068i \(-0.112144\pi\)
\(140\) 1.80584 + 0.526037i 0.152622 + 0.0444583i
\(141\) 0 0
\(142\) −1.74935 + 1.31248i −0.146802 + 0.110141i
\(143\) −39.4509 −3.29905
\(144\) 0 0
\(145\) 2.91346 0.241950
\(146\) −3.35828 + 2.51960i −0.277933 + 0.208524i
\(147\) 0 0
\(148\) 0.410075 + 0.119454i 0.0337080 + 0.00981906i
\(149\) 15.2594i 1.25010i −0.780586 0.625048i \(-0.785079\pi\)
0.780586 0.625048i \(-0.214921\pi\)
\(150\) 0 0
\(151\) −0.728441 −0.0592797 −0.0296398 0.999561i \(-0.509436\pi\)
−0.0296398 + 0.999561i \(0.509436\pi\)
\(152\) 15.4428 5.81654i 1.25258 0.471784i
\(153\) 0 0
\(154\) 5.08071 + 6.77188i 0.409415 + 0.545694i
\(155\) 3.31425i 0.266207i
\(156\) 0 0
\(157\) 12.1207i 0.967337i 0.875251 + 0.483669i \(0.160696\pi\)
−0.875251 + 0.483669i \(0.839304\pi\)
\(158\) 18.0447 13.5384i 1.43556 1.07705i
\(159\) 0 0
\(160\) −0.407979 5.30432i −0.0322536 0.419343i
\(161\) 2.88452 0.227332
\(162\) 0 0
\(163\) 5.45067i 0.426929i 0.976951 + 0.213465i \(0.0684748\pi\)
−0.976951 + 0.213465i \(0.931525\pi\)
\(164\) −0.913361 + 3.13549i −0.0713215 + 0.244841i
\(165\) 0 0
\(166\) 7.42446 + 9.89577i 0.576250 + 0.768061i
\(167\) −1.96762 −0.152259 −0.0761297 0.997098i \(-0.524256\pi\)
−0.0761297 + 0.997098i \(0.524256\pi\)
\(168\) 0 0
\(169\) −30.4303 −2.34079
\(170\) −2.10899 2.81099i −0.161752 0.215593i
\(171\) 0 0
\(172\) −13.7623 4.00893i −1.04937 0.305678i
\(173\) 4.48602i 0.341066i 0.985352 + 0.170533i \(0.0545489\pi\)
−0.985352 + 0.170533i \(0.945451\pi\)
\(174\) 0 0
\(175\) 4.11555 0.311107
\(176\) 12.8592 20.1994i 0.969302 1.52259i
\(177\) 0 0
\(178\) 8.48804 6.36828i 0.636205 0.477323i
\(179\) 24.8086i 1.85428i −0.374716 0.927140i \(-0.622260\pi\)
0.374716 0.927140i \(-0.377740\pi\)
\(180\) 0 0
\(181\) 22.6114i 1.68070i 0.542048 + 0.840348i \(0.317649\pi\)
−0.542048 + 0.840348i \(0.682351\pi\)
\(182\) 5.59321 + 7.45497i 0.414596 + 0.552599i
\(183\) 0 0
\(184\) −2.87574 7.63503i −0.212002 0.562862i
\(185\) −0.200842 −0.0147662
\(186\) 0 0
\(187\) 15.8174i 1.15668i
\(188\) −5.21668 + 17.9084i −0.380466 + 1.30611i
\(189\) 0 0
\(190\) −6.20688 + 4.65681i −0.450295 + 0.337841i
\(191\) 16.3035 1.17968 0.589838 0.807521i \(-0.299191\pi\)
0.589838 + 0.807521i \(0.299191\pi\)
\(192\) 0 0
\(193\) 6.98388 0.502711 0.251355 0.967895i \(-0.419124\pi\)
0.251355 + 0.967895i \(0.419124\pi\)
\(194\) 12.1639 9.12617i 0.873319 0.655221i
\(195\) 0 0
\(196\) 0.559347 1.92019i 0.0399533 0.137156i
\(197\) 13.5891i 0.968182i −0.875018 0.484091i \(-0.839150\pi\)
0.875018 0.484091i \(-0.160850\pi\)
\(198\) 0 0
\(199\) 20.2305 1.43410 0.717052 0.697020i \(-0.245491\pi\)
0.717052 + 0.697020i \(0.245491\pi\)
\(200\) −4.10303 10.8935i −0.290128 0.770284i
\(201\) 0 0
\(202\) 3.01228 + 4.01495i 0.211943 + 0.282491i
\(203\) 3.09794i 0.217433i
\(204\) 0 0
\(205\) 1.53567i 0.107256i
\(206\) 17.3421 13.0112i 1.20828 0.906531i
\(207\) 0 0
\(208\) 14.1564 22.2370i 0.981568 1.54186i
\(209\) −34.9260 −2.41588
\(210\) 0 0
\(211\) 19.1090i 1.31552i −0.753230 0.657758i \(-0.771505\pi\)
0.753230 0.657758i \(-0.228495\pi\)
\(212\) 14.4215 + 4.20094i 0.990471 + 0.288522i
\(213\) 0 0
\(214\) 2.05079 + 2.73342i 0.140189 + 0.186853i
\(215\) 6.74035 0.459688
\(216\) 0 0
\(217\) 3.52412 0.239233
\(218\) 5.82826 + 7.76826i 0.394739 + 0.526133i
\(219\) 0 0
\(220\) −3.14903 + 10.8103i −0.212307 + 0.728833i
\(221\) 17.4129i 1.17132i
\(222\) 0 0
\(223\) −20.9241 −1.40118 −0.700592 0.713562i \(-0.747080\pi\)
−0.700592 + 0.713562i \(0.747080\pi\)
\(224\) −5.64020 + 0.433813i −0.376851 + 0.0289853i
\(225\) 0 0
\(226\) −17.4819 + 13.1161i −1.16288 + 0.872468i
\(227\) 2.48329i 0.164821i −0.996598 0.0824107i \(-0.973738\pi\)
0.996598 0.0824107i \(-0.0262619\pi\)
\(228\) 0 0
\(229\) 10.3155i 0.681669i −0.940123 0.340835i \(-0.889290\pi\)
0.940123 0.340835i \(-0.110710\pi\)
\(230\) 2.30236 + 3.06873i 0.151813 + 0.202346i
\(231\) 0 0
\(232\) −8.19995 + 3.08852i −0.538353 + 0.202771i
\(233\) −19.5208 −1.27885 −0.639424 0.768855i \(-0.720827\pi\)
−0.639424 + 0.768855i \(0.720827\pi\)
\(234\) 0 0
\(235\) 8.77100i 0.572157i
\(236\) −22.9040 6.67187i −1.49092 0.434302i
\(237\) 0 0
\(238\) −2.98898 + 2.24253i −0.193747 + 0.145362i
\(239\) −17.8520 −1.15475 −0.577376 0.816478i \(-0.695923\pi\)
−0.577376 + 0.816478i \(0.695923\pi\)
\(240\) 0 0
\(241\) 6.72097 0.432935 0.216468 0.976290i \(-0.430546\pi\)
0.216468 + 0.976290i \(0.430546\pi\)
\(242\) −28.0952 + 21.0788i −1.80603 + 1.35500i
\(243\) 0 0
\(244\) −2.84772 0.829534i −0.182307 0.0531054i
\(245\) 0.940450i 0.0600831i
\(246\) 0 0
\(247\) −38.4490 −2.44645
\(248\) −3.51339 9.32799i −0.223101 0.592328i
\(249\) 0 0
\(250\) 7.27584 + 9.69769i 0.460165 + 0.613336i
\(251\) 28.1618i 1.77756i 0.458336 + 0.888779i \(0.348445\pi\)
−0.458336 + 0.888779i \(0.651555\pi\)
\(252\) 0 0
\(253\) 17.2677i 1.08561i
\(254\) 9.01316 6.76227i 0.565536 0.424302i
\(255\) 0 0
\(256\) 6.77129 + 14.4965i 0.423206 + 0.906034i
\(257\) 24.9286 1.55500 0.777502 0.628880i \(-0.216486\pi\)
0.777502 + 0.628880i \(0.216486\pi\)
\(258\) 0 0
\(259\) 0.213560i 0.0132700i
\(260\) −3.46668 + 11.9008i −0.214994 + 0.738057i
\(261\) 0 0
\(262\) −1.30516 1.73960i −0.0806331 0.107473i
\(263\) 19.0635 1.17550 0.587751 0.809042i \(-0.300013\pi\)
0.587751 + 0.809042i \(0.300013\pi\)
\(264\) 0 0
\(265\) −7.06319 −0.433888
\(266\) 4.95169 + 6.59991i 0.303607 + 0.404666i
\(267\) 0 0
\(268\) −25.0691 7.30256i −1.53134 0.446075i
\(269\) 10.2410i 0.624406i 0.950015 + 0.312203i \(0.101067\pi\)
−0.950015 + 0.312203i \(0.898933\pi\)
\(270\) 0 0
\(271\) −4.45674 −0.270728 −0.135364 0.990796i \(-0.543220\pi\)
−0.135364 + 0.990796i \(0.543220\pi\)
\(272\) 8.91564 + 5.67583i 0.540590 + 0.344148i
\(273\) 0 0
\(274\) 7.17245 5.38125i 0.433304 0.325093i
\(275\) 24.6370i 1.48567i
\(276\) 0 0
\(277\) 16.0596i 0.964929i 0.875915 + 0.482465i \(0.160258\pi\)
−0.875915 + 0.482465i \(0.839742\pi\)
\(278\) −6.90569 9.20433i −0.414176 0.552039i
\(279\) 0 0
\(280\) 2.48928 0.937588i 0.148763 0.0560316i
\(281\) −31.3739 −1.87161 −0.935806 0.352516i \(-0.885326\pi\)
−0.935806 + 0.352516i \(0.885326\pi\)
\(282\) 0 0
\(283\) 16.4627i 0.978605i −0.872114 0.489302i \(-0.837251\pi\)
0.872114 0.489302i \(-0.162749\pi\)
\(284\) −0.864985 + 2.96942i −0.0513274 + 0.176203i
\(285\) 0 0
\(286\) −44.6279 + 33.4828i −2.63890 + 1.97988i
\(287\) −1.63291 −0.0963874
\(288\) 0 0
\(289\) −10.0185 −0.589324
\(290\) 3.29578 2.47271i 0.193535 0.145203i
\(291\) 0 0
\(292\) −1.66054 + 5.70049i −0.0971756 + 0.333596i
\(293\) 5.78733i 0.338100i −0.985608 0.169050i \(-0.945930\pi\)
0.985608 0.169050i \(-0.0540699\pi\)
\(294\) 0 0
\(295\) 11.2177 0.653117
\(296\) 0.565271 0.212910i 0.0328557 0.0123751i
\(297\) 0 0
\(298\) −12.9509 17.2618i −0.750228 0.999949i
\(299\) 19.0095i 1.09935i
\(300\) 0 0
\(301\) 7.16716i 0.413108i
\(302\) −0.824032 + 0.618243i −0.0474177 + 0.0355759i
\(303\) 0 0
\(304\) 12.5327 19.6864i 0.718798 1.12909i
\(305\) 1.39472 0.0798617
\(306\) 0 0
\(307\) 23.0312i 1.31446i −0.753691 0.657229i \(-0.771728\pi\)
0.753691 0.657229i \(-0.228272\pi\)
\(308\) 11.4949 + 3.34843i 0.654981 + 0.190794i
\(309\) 0 0
\(310\) 2.81288 + 3.74917i 0.159761 + 0.212939i
\(311\) 15.7123 0.890964 0.445482 0.895291i \(-0.353032\pi\)
0.445482 + 0.895291i \(0.353032\pi\)
\(312\) 0 0
\(313\) −6.53462 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(314\) 10.2871 + 13.7113i 0.580534 + 0.773771i
\(315\) 0 0
\(316\) 8.92241 30.6299i 0.501925 1.72307i
\(317\) 19.9169i 1.11865i 0.828949 + 0.559324i \(0.188939\pi\)
−0.828949 + 0.559324i \(0.811061\pi\)
\(318\) 0 0
\(319\) 18.5453 1.03834
\(320\) −4.96340 5.65413i −0.277463 0.316075i
\(321\) 0 0
\(322\) 3.26304 2.44815i 0.181842 0.136430i
\(323\) 15.4157i 0.857751i
\(324\) 0 0
\(325\) 27.1222i 1.50447i
\(326\) 4.62610 + 6.16594i 0.256216 + 0.341500i
\(327\) 0 0
\(328\) 1.62794 + 4.32214i 0.0898878 + 0.238650i
\(329\) −9.32639 −0.514180
\(330\) 0 0
\(331\) 21.3692i 1.17456i −0.809384 0.587280i \(-0.800199\pi\)
0.809384 0.587280i \(-0.199801\pi\)
\(332\) 16.7975 + 4.89307i 0.921882 + 0.268542i
\(333\) 0 0
\(334\) −2.22583 + 1.66996i −0.121792 + 0.0913763i
\(335\) 12.2780 0.670821
\(336\) 0 0
\(337\) −9.56768 −0.521185 −0.260592 0.965449i \(-0.583918\pi\)
−0.260592 + 0.965449i \(0.583918\pi\)
\(338\) −34.4236 + 25.8269i −1.87240 + 1.40480i
\(339\) 0 0
\(340\) −4.77149 1.38992i −0.258770 0.0753791i
\(341\) 21.0965i 1.14244i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −18.9707 + 7.14535i −1.02283 + 0.385251i
\(345\) 0 0
\(346\) 3.80737 + 5.07470i 0.204686 + 0.272818i
\(347\) 5.63471i 0.302487i −0.988497 0.151243i \(-0.951672\pi\)
0.988497 0.151243i \(-0.0483278\pi\)
\(348\) 0 0
\(349\) 33.2219i 1.77833i −0.457591 0.889163i \(-0.651287\pi\)
0.457591 0.889163i \(-0.348713\pi\)
\(350\) 4.65562 3.49296i 0.248854 0.186706i
\(351\) 0 0
\(352\) −2.59694 33.7640i −0.138417 1.79963i
\(353\) 6.20112 0.330052 0.165026 0.986289i \(-0.447229\pi\)
0.165026 + 0.986289i \(0.447229\pi\)
\(354\) 0 0
\(355\) 1.45433i 0.0771879i
\(356\) 4.19700 14.4079i 0.222440 0.763619i
\(357\) 0 0
\(358\) −21.0555 28.0641i −1.11282 1.48323i
\(359\) 1.76894 0.0933609 0.0466805 0.998910i \(-0.485136\pi\)
0.0466805 + 0.998910i \(0.485136\pi\)
\(360\) 0 0
\(361\) −15.0390 −0.791526
\(362\) 19.1908 + 25.5787i 1.00865 + 1.34438i
\(363\) 0 0
\(364\) 12.6544 + 3.68619i 0.663270 + 0.193209i
\(365\) 2.79192i 0.146136i
\(366\) 0 0
\(367\) 9.62872 0.502615 0.251308 0.967907i \(-0.419139\pi\)
0.251308 + 0.967907i \(0.419139\pi\)
\(368\) −9.73312 6.19625i −0.507374 0.323002i
\(369\) 0 0
\(370\) −0.227198 + 0.170459i −0.0118115 + 0.00886173i
\(371\) 7.51044i 0.389922i
\(372\) 0 0
\(373\) 19.6983i 1.01994i −0.860192 0.509970i \(-0.829657\pi\)
0.860192 0.509970i \(-0.170343\pi\)
\(374\) −13.4245 17.8930i −0.694165 0.925225i
\(375\) 0 0
\(376\) 9.29801 + 24.6860i 0.479508 + 1.27308i
\(377\) 20.4160 1.05148
\(378\) 0 0
\(379\) 16.3324i 0.838941i 0.907769 + 0.419470i \(0.137784\pi\)
−0.907769 + 0.419470i \(0.862216\pi\)
\(380\) −3.06906 + 10.5358i −0.157439 + 0.540476i
\(381\) 0 0
\(382\) 18.4429 13.8371i 0.943621 0.707966i
\(383\) 17.7037 0.904618 0.452309 0.891861i \(-0.350600\pi\)
0.452309 + 0.891861i \(0.350600\pi\)
\(384\) 0 0
\(385\) −5.62983 −0.286923
\(386\) 7.90035 5.92736i 0.402117 0.301695i
\(387\) 0 0
\(388\) 6.01458 20.6475i 0.305344 1.04822i
\(389\) 24.4174i 1.23801i −0.785387 0.619005i \(-0.787536\pi\)
0.785387 0.619005i \(-0.212464\pi\)
\(390\) 0 0
\(391\) −7.62162 −0.385442
\(392\) −0.996957 2.64690i −0.0503539 0.133689i
\(393\) 0 0
\(394\) −11.5333 15.3723i −0.581041 0.774447i
\(395\) 15.0016i 0.754811i
\(396\) 0 0
\(397\) 21.4996i 1.07903i 0.841975 + 0.539517i \(0.181393\pi\)
−0.841975 + 0.539517i \(0.818607\pi\)
\(398\) 22.8853 17.1701i 1.14714 0.860657i
\(399\) 0 0
\(400\) −13.8870 8.84064i −0.694348 0.442032i
\(401\) 29.0629 1.45133 0.725667 0.688046i \(-0.241531\pi\)
0.725667 + 0.688046i \(0.241531\pi\)
\(402\) 0 0
\(403\) 23.2245i 1.15690i
\(404\) 6.81515 + 1.98524i 0.339066 + 0.0987692i
\(405\) 0 0
\(406\) −2.62929 3.50448i −0.130489 0.173924i
\(407\) −1.27844 −0.0633698
\(408\) 0 0
\(409\) −5.96315 −0.294859 −0.147429 0.989073i \(-0.547100\pi\)
−0.147429 + 0.989073i \(0.547100\pi\)
\(410\) −1.30335 1.73719i −0.0643679 0.0857935i
\(411\) 0 0
\(412\) 8.57497 29.4371i 0.422458 1.45026i
\(413\) 11.9280i 0.586937i
\(414\) 0 0
\(415\) −8.22689 −0.403842
\(416\) −2.85890 37.1698i −0.140169 1.82240i
\(417\) 0 0
\(418\) −39.5092 + 29.6424i −1.93246 + 1.44986i
\(419\) 28.8317i 1.40852i −0.709941 0.704261i \(-0.751279\pi\)
0.709941 0.704261i \(-0.248721\pi\)
\(420\) 0 0
\(421\) 30.3324i 1.47831i 0.673534 + 0.739156i \(0.264776\pi\)
−0.673534 + 0.739156i \(0.735224\pi\)
\(422\) −16.2182 21.6166i −0.789488 1.05228i
\(423\) 0 0
\(424\) 19.8794 7.48758i 0.965428 0.363629i
\(425\) −10.8743 −0.527482
\(426\) 0 0
\(427\) 1.48304i 0.0717693i
\(428\) 4.63982 + 1.35157i 0.224274 + 0.0653305i
\(429\) 0 0
\(430\) 7.62486 5.72067i 0.367703 0.275875i
\(431\) 32.3775 1.55957 0.779785 0.626048i \(-0.215329\pi\)
0.779785 + 0.626048i \(0.215329\pi\)
\(432\) 0 0
\(433\) −30.9777 −1.48869 −0.744346 0.667794i \(-0.767239\pi\)
−0.744346 + 0.667794i \(0.767239\pi\)
\(434\) 3.98658 2.99099i 0.191362 0.143572i
\(435\) 0 0
\(436\) 13.1862 + 3.84110i 0.631502 + 0.183955i
\(437\) 16.8291i 0.805047i
\(438\) 0 0
\(439\) 8.76381 0.418274 0.209137 0.977886i \(-0.432935\pi\)
0.209137 + 0.977886i \(0.432935\pi\)
\(440\) 5.61270 + 14.9016i 0.267575 + 0.710406i
\(441\) 0 0
\(442\) −14.7787 19.6979i −0.702949 0.936934i
\(443\) 7.53477i 0.357988i 0.983850 + 0.178994i \(0.0572842\pi\)
−0.983850 + 0.178994i \(0.942716\pi\)
\(444\) 0 0
\(445\) 7.05656i 0.334513i
\(446\) −23.6699 + 17.7587i −1.12080 + 0.840901i
\(447\) 0 0
\(448\) −6.01215 + 5.27769i −0.284048 + 0.249347i
\(449\) 32.5584 1.53653 0.768263 0.640134i \(-0.221121\pi\)
0.768263 + 0.640134i \(0.221121\pi\)
\(450\) 0 0
\(451\) 9.77510i 0.460292i
\(452\) −8.64410 + 29.6745i −0.406584 + 1.39577i
\(453\) 0 0
\(454\) −2.10762 2.80916i −0.0989153 0.131840i
\(455\) −6.19772 −0.290554
\(456\) 0 0
\(457\) −3.81122 −0.178281 −0.0891407 0.996019i \(-0.528412\pi\)
−0.0891407 + 0.996019i \(0.528412\pi\)
\(458\) −8.75500 11.6692i −0.409094 0.545266i
\(459\) 0 0
\(460\) 5.20899 + 1.51736i 0.242870 + 0.0707475i
\(461\) 6.29754i 0.293306i −0.989188 0.146653i \(-0.953150\pi\)
0.989188 0.146653i \(-0.0468500\pi\)
\(462\) 0 0
\(463\) 12.8418 0.596811 0.298405 0.954439i \(-0.403545\pi\)
0.298405 + 0.954439i \(0.403545\pi\)
\(464\) −6.65471 + 10.4533i −0.308937 + 0.485281i
\(465\) 0 0
\(466\) −22.0824 + 16.5677i −1.02295 + 0.767482i
\(467\) 34.5588i 1.59919i −0.600538 0.799596i \(-0.705047\pi\)
0.600538 0.799596i \(-0.294953\pi\)
\(468\) 0 0
\(469\) 13.0555i 0.602847i
\(470\) −7.44412 9.92198i −0.343372 0.457667i
\(471\) 0 0
\(472\) −31.5721 + 11.8917i −1.45322 + 0.547359i
\(473\) 42.9049 1.97277
\(474\) 0 0
\(475\) 24.0114i 1.10172i
\(476\) −1.47793 + 5.07362i −0.0677410 + 0.232549i
\(477\) 0 0
\(478\) −20.1947 + 15.1514i −0.923684 + 0.693008i
\(479\) −16.5950 −0.758244 −0.379122 0.925347i \(-0.623774\pi\)
−0.379122 + 0.925347i \(0.623774\pi\)
\(480\) 0 0
\(481\) −1.40739 −0.0641717
\(482\) 7.60293 5.70422i 0.346304 0.259820i
\(483\) 0 0
\(484\) −13.8919 + 47.6899i −0.631452 + 2.16772i
\(485\) 10.1125i 0.459186i
\(486\) 0 0
\(487\) 26.4209 1.19724 0.598622 0.801032i \(-0.295715\pi\)
0.598622 + 0.801032i \(0.295715\pi\)
\(488\) −3.92546 + 1.47853i −0.177697 + 0.0669298i
\(489\) 0 0
\(490\) 0.798179 + 1.06386i 0.0360580 + 0.0480604i
\(491\) 3.70049i 0.167001i −0.996508 0.0835003i \(-0.973390\pi\)
0.996508 0.0835003i \(-0.0266100\pi\)
\(492\) 0 0
\(493\) 8.18554i 0.368658i
\(494\) −43.4945 + 32.6325i −1.95691 + 1.46820i
\(495\) 0 0
\(496\) −11.8913 7.57017i −0.533935 0.339911i
\(497\) −1.54642 −0.0693664
\(498\) 0 0
\(499\) 2.12488i 0.0951229i −0.998868 0.0475614i \(-0.984855\pi\)
0.998868 0.0475614i \(-0.0151450\pi\)
\(500\) 16.4613 + 4.79512i 0.736170 + 0.214444i
\(501\) 0 0
\(502\) 23.9015 + 31.8574i 1.06678 + 1.42186i
\(503\) −43.3846 −1.93443 −0.967213 0.253968i \(-0.918264\pi\)
−0.967213 + 0.253968i \(0.918264\pi\)
\(504\) 0 0
\(505\) −3.33785 −0.148532
\(506\) 14.6554 + 19.5336i 0.651512 + 0.868376i
\(507\) 0 0
\(508\) 4.45665 15.2993i 0.197732 0.678797i
\(509\) 2.34482i 0.103932i 0.998649 + 0.0519662i \(0.0165488\pi\)
−0.998649 + 0.0519662i \(0.983451\pi\)
\(510\) 0 0
\(511\) −2.96871 −0.131328
\(512\) 19.9634 + 10.6519i 0.882265 + 0.470753i
\(513\) 0 0
\(514\) 28.1999 21.1574i 1.24384 0.933214i
\(515\) 14.4174i 0.635306i
\(516\) 0 0
\(517\) 55.8307i 2.45543i
\(518\) 0.181253 + 0.241584i 0.00796378 + 0.0106146i
\(519\) 0 0
\(520\) 6.17886 + 16.4047i 0.270961 + 0.719396i
\(521\) 8.53436 0.373897 0.186949 0.982370i \(-0.440140\pi\)
0.186949 + 0.982370i \(0.440140\pi\)
\(522\) 0 0
\(523\) 30.8607i 1.34944i 0.738072 + 0.674722i \(0.235736\pi\)
−0.738072 + 0.674722i \(0.764264\pi\)
\(524\) −2.95287 0.860163i −0.128997 0.0375764i
\(525\) 0 0
\(526\) 21.5651 16.1795i 0.940282 0.705462i
\(527\) −9.31160 −0.405620
\(528\) 0 0
\(529\) −14.6796 −0.638241
\(530\) −7.99006 + 5.99467i −0.347066 + 0.260392i
\(531\) 0 0
\(532\) 11.2030 + 3.26339i 0.485710 + 0.141486i
\(533\) 10.7611i 0.466116i
\(534\) 0 0
\(535\) −2.27244 −0.0982461
\(536\) −34.5566 + 13.0158i −1.49262 + 0.562196i
\(537\) 0 0
\(538\) 8.69177 + 11.5849i 0.374729 + 0.499461i
\(539\) 5.98632i 0.257849i
\(540\) 0 0
\(541\) 15.2568i 0.655940i −0.944688 0.327970i \(-0.893636\pi\)
0.944688 0.327970i \(-0.106364\pi\)
\(542\) −5.04158 + 3.78253i −0.216554 + 0.162473i
\(543\) 0 0
\(544\) 14.9028 1.14624i 0.638953 0.0491447i
\(545\) −6.45817 −0.276638
\(546\) 0 0
\(547\) 35.6416i 1.52393i −0.647621 0.761963i \(-0.724236\pi\)
0.647621 0.761963i \(-0.275764\pi\)
\(548\) 3.54649 12.1748i 0.151499 0.520082i
\(549\) 0 0
\(550\) 20.9099 + 27.8701i 0.891603 + 1.18838i
\(551\) 18.0743 0.769992
\(552\) 0 0
\(553\) 15.9515 0.678326
\(554\) 13.6301 + 18.1671i 0.579089 + 0.771845i
\(555\) 0 0
\(556\) −15.6238 4.55118i −0.662597 0.193013i
\(557\) 28.3871i 1.20280i 0.798949 + 0.601399i \(0.205390\pi\)
−0.798949 + 0.601399i \(0.794610\pi\)
\(558\) 0 0
\(559\) 47.2328 1.99773
\(560\) 2.02018 3.17332i 0.0853684 0.134097i
\(561\) 0 0
\(562\) −35.4910 + 26.6277i −1.49710 + 1.12322i
\(563\) 13.0963i 0.551942i −0.961166 0.275971i \(-0.911001\pi\)
0.961166 0.275971i \(-0.0889993\pi\)
\(564\) 0 0
\(565\) 14.5336i 0.611435i
\(566\) −13.9722 18.6230i −0.587296 0.782784i
\(567\) 0 0
\(568\) 1.54172 + 4.09322i 0.0646889 + 0.171748i
\(569\) 20.0434 0.840263 0.420132 0.907463i \(-0.361984\pi\)
0.420132 + 0.907463i \(0.361984\pi\)
\(570\) 0 0
\(571\) 6.91621i 0.289434i −0.989473 0.144717i \(-0.953773\pi\)
0.989473 0.144717i \(-0.0462272\pi\)
\(572\) −22.0667 + 75.7532i −0.922656 + 3.16740i
\(573\) 0 0
\(574\) −1.84719 + 1.38588i −0.0771001 + 0.0578456i
\(575\) 11.8714 0.495071
\(576\) 0 0
\(577\) 23.2279 0.966992 0.483496 0.875347i \(-0.339367\pi\)
0.483496 + 0.875347i \(0.339367\pi\)
\(578\) −11.3332 + 8.50292i −0.471399 + 0.353675i
\(579\) 0 0
\(580\) 1.62963 5.59440i 0.0676669 0.232295i
\(581\) 8.74782i 0.362921i
\(582\) 0 0
\(583\) −44.9599 −1.86205
\(584\) 2.95968 + 7.85787i 0.122472 + 0.325161i
\(585\) 0 0
\(586\) −4.91183 6.54678i −0.202906 0.270445i
\(587\) 1.76774i 0.0729624i −0.999334 0.0364812i \(-0.988385\pi\)
0.999334 0.0364812i \(-0.0116149\pi\)
\(588\) 0 0
\(589\) 20.5607i 0.847191i
\(590\) 12.6897 9.52065i 0.522427 0.391959i
\(591\) 0 0
\(592\) 0.458749 0.720607i 0.0188545 0.0296167i
\(593\) 14.8807 0.611079 0.305540 0.952179i \(-0.401163\pi\)
0.305540 + 0.952179i \(0.401163\pi\)
\(594\) 0 0
\(595\) 2.48490i 0.101871i
\(596\) −29.3009 8.53528i −1.20021 0.349619i
\(597\) 0 0
\(598\) 16.1337 + 21.5040i 0.659757 + 0.879365i
\(599\) 1.47561 0.0602916 0.0301458 0.999546i \(-0.490403\pi\)
0.0301458 + 0.999546i \(0.490403\pi\)
\(600\) 0 0
\(601\) −11.1957 −0.456684 −0.228342 0.973581i \(-0.573330\pi\)
−0.228342 + 0.973581i \(0.573330\pi\)
\(602\) −6.08291 8.10768i −0.247921 0.330444i
\(603\) 0 0
\(604\) −0.407451 + 1.39875i −0.0165790 + 0.0569142i
\(605\) 23.3570i 0.949598i
\(606\) 0 0
\(607\) −31.4554 −1.27674 −0.638368 0.769731i \(-0.720390\pi\)
−0.638368 + 0.769731i \(0.720390\pi\)
\(608\) −2.53099 32.9066i −0.102645 1.33454i
\(609\) 0 0
\(610\) 1.57775 1.18373i 0.0638812 0.0479279i
\(611\) 61.4625i 2.48651i
\(612\) 0 0
\(613\) 18.9222i 0.764262i 0.924108 + 0.382131i \(0.124810\pi\)
−0.924108 + 0.382131i \(0.875190\pi\)
\(614\) −19.5470 26.0535i −0.788854 1.05143i
\(615\) 0 0
\(616\) 15.8452 5.96810i 0.638421 0.240462i
\(617\) −12.1549 −0.489339 −0.244669 0.969607i \(-0.578679\pi\)
−0.244669 + 0.969607i \(0.578679\pi\)
\(618\) 0 0
\(619\) 14.9619i 0.601371i −0.953723 0.300686i \(-0.902784\pi\)
0.953723 0.300686i \(-0.0972155\pi\)
\(620\) 6.36400 + 1.85382i 0.255584 + 0.0744511i
\(621\) 0 0
\(622\) 17.7742 13.3354i 0.712680 0.534700i
\(623\) 7.50339 0.300617
\(624\) 0 0
\(625\) 12.5156 0.500623
\(626\) −7.39213 + 5.54606i −0.295449 + 0.221665i
\(627\) 0 0
\(628\) 23.2741 + 6.77967i 0.928736 + 0.270538i
\(629\) 0.564278i 0.0224992i
\(630\) 0 0
\(631\) −8.71232 −0.346832 −0.173416 0.984849i \(-0.555481\pi\)
−0.173416 + 0.984849i \(0.555481\pi\)
\(632\) −15.9029 42.2220i −0.632585 1.67950i
\(633\) 0 0
\(634\) 16.9039 + 22.5306i 0.671340 + 0.894803i
\(635\) 7.49313i 0.297356i
\(636\) 0 0
\(637\) 6.59017i 0.261112i
\(638\) 20.9789 15.7398i 0.830563 0.623143i
\(639\) 0 0
\(640\) −10.4135 2.18356i −0.411630 0.0863127i
\(641\) 7.31021 0.288736 0.144368 0.989524i \(-0.453885\pi\)
0.144368 + 0.989524i \(0.453885\pi\)
\(642\) 0 0
\(643\) 11.1766i 0.440763i 0.975414 + 0.220381i \(0.0707302\pi\)
−0.975414 + 0.220381i \(0.929270\pi\)
\(644\) 1.61345 5.53883i 0.0635787 0.218260i
\(645\) 0 0
\(646\) −13.0836 17.4386i −0.514767 0.686113i
\(647\) −7.13625 −0.280555 −0.140277 0.990112i \(-0.544799\pi\)
−0.140277 + 0.990112i \(0.544799\pi\)
\(648\) 0 0
\(649\) 71.4046 2.80288
\(650\) 23.0192 + 30.6814i 0.902886 + 1.20342i
\(651\) 0 0
\(652\) 10.4663 + 3.04882i 0.409893 + 0.119401i
\(653\) 15.6385i 0.611982i 0.952034 + 0.305991i \(0.0989878\pi\)
−0.952034 + 0.305991i \(0.901012\pi\)
\(654\) 0 0
\(655\) 1.44622 0.0565086
\(656\) 5.50986 + 3.50765i 0.215124 + 0.136951i
\(657\) 0 0
\(658\) −10.5503 + 7.91550i −0.411292 + 0.308578i
\(659\) 1.73739i 0.0676791i 0.999427 + 0.0338395i \(0.0107735\pi\)
−0.999427 + 0.0338395i \(0.989226\pi\)
\(660\) 0 0
\(661\) 22.7968i 0.886691i 0.896351 + 0.443345i \(0.146208\pi\)
−0.896351 + 0.443345i \(0.853792\pi\)
\(662\) −18.1365 24.1735i −0.704896 0.939528i
\(663\) 0 0
\(664\) 23.1546 8.72121i 0.898573 0.338448i
\(665\) −5.48686 −0.212771
\(666\) 0 0
\(667\) 8.93608i 0.346006i
\(668\) −1.10058 + 3.77821i −0.0425829 + 0.146183i
\(669\) 0 0
\(670\) 13.8893 10.4206i 0.536589 0.402584i
\(671\) 8.87795 0.342729
\(672\) 0 0
\(673\) −13.1667 −0.507538 −0.253769 0.967265i \(-0.581670\pi\)
−0.253769 + 0.967265i \(0.581670\pi\)
\(674\) −10.8232 + 8.12029i −0.416895 + 0.312782i
\(675\) 0 0
\(676\) −17.0211 + 58.4320i −0.654658 + 2.24739i
\(677\) 37.3183i 1.43426i −0.696941 0.717129i \(-0.745456\pi\)
0.696941 0.717129i \(-0.254544\pi\)
\(678\) 0 0
\(679\) 10.7529 0.412657
\(680\) −6.57729 + 2.47734i −0.252227 + 0.0950017i
\(681\) 0 0
\(682\) 17.9050 + 23.8649i 0.685619 + 0.913835i
\(683\) 6.72259i 0.257233i 0.991694 + 0.128616i \(0.0410536\pi\)
−0.991694 + 0.128616i \(0.958946\pi\)
\(684\) 0 0
\(685\) 5.96285i 0.227829i
\(686\) 1.13123 0.848721i 0.0431904 0.0324043i
\(687\) 0 0
\(688\) −15.3958 + 24.1839i −0.586959 + 0.922001i
\(689\) −49.4951 −1.88561
\(690\) 0 0
\(691\) 8.18845i 0.311503i −0.987796 0.155752i \(-0.950220\pi\)
0.987796 0.155752i \(-0.0497800\pi\)
\(692\) 8.61401 + 2.50924i 0.327455 + 0.0953870i
\(693\) 0 0
\(694\) −4.78229 6.37413i −0.181533 0.241959i
\(695\) 7.65205 0.290259
\(696\) 0 0
\(697\) 4.31455 0.163425
\(698\) −28.1961 37.5815i −1.06724 1.42248i
\(699\) 0 0
\(700\) 2.30202 7.90265i 0.0870083 0.298692i
\(701\) 5.85226i 0.221037i −0.993874 0.110518i \(-0.964749\pi\)
0.993874 0.110518i \(-0.0352511\pi\)
\(702\) 0 0
\(703\) −1.24597 −0.0469927
\(704\) −31.5939 35.9907i −1.19074 1.35645i
\(705\) 0 0
\(706\) 7.01487 5.26301i 0.264008 0.198076i
\(707\) 3.54920i 0.133482i
\(708\) 0 0
\(709\) 45.3444i 1.70294i 0.524399 + 0.851472i \(0.324290\pi\)
−0.524399 + 0.851472i \(0.675710\pi\)
\(710\) −1.23432 1.64518i −0.0463232 0.0617424i
\(711\) 0 0
\(712\) −7.48056 19.8607i −0.280346 0.744312i
\(713\) 10.1654 0.380697
\(714\) 0 0
\(715\) 37.1015i 1.38752i
\(716\) −47.6372 13.8766i −1.78028 0.518593i
\(717\) 0 0
\(718\) 2.00107 1.50133i 0.0746792 0.0560293i
\(719\) 29.1182 1.08592 0.542962 0.839757i \(-0.317303\pi\)
0.542962 + 0.839757i \(0.317303\pi\)
\(720\) 0 0
\(721\) 15.3303 0.570931
\(722\) −17.0125 + 12.7639i −0.633140 + 0.475023i
\(723\) 0 0
\(724\) 43.4183 + 12.6476i 1.61363 + 0.470046i
\(725\) 12.7498i 0.473514i
\(726\) 0 0
\(727\) −42.5099 −1.57661 −0.788303 0.615287i \(-0.789040\pi\)
−0.788303 + 0.615287i \(0.789040\pi\)
\(728\) 17.4435 6.57012i 0.646500 0.243505i
\(729\) 0 0
\(730\) −2.36956 3.15829i −0.0877014 0.116894i
\(731\) 18.9374i 0.700426i
\(732\) 0 0
\(733\) 2.79234i 0.103137i 0.998669 + 0.0515687i \(0.0164221\pi\)
−0.998669 + 0.0515687i \(0.983578\pi\)
\(734\) 10.8923 8.17210i 0.402041 0.301638i
\(735\) 0 0
\(736\) −16.2693 + 1.25134i −0.599693 + 0.0461250i
\(737\) 78.1544 2.87886
\(738\) 0 0
\(739\) 15.4715i 0.569129i 0.958657 + 0.284565i \(0.0918490\pi\)
−0.958657 + 0.284565i \(0.908151\pi\)
\(740\) −0.112340 + 0.385655i −0.00412972 + 0.0141770i
\(741\) 0 0
\(742\) 6.37426 + 8.49601i 0.234007 + 0.311898i
\(743\) −18.2897 −0.670984 −0.335492 0.942043i \(-0.608903\pi\)
−0.335492 + 0.942043i \(0.608903\pi\)
\(744\) 0 0
\(745\) 14.3507 0.525768
\(746\) −16.7184 22.2832i −0.612103 0.815848i
\(747\) 0 0
\(748\) −30.3723 8.84739i −1.11052 0.323492i
\(749\) 2.41633i 0.0882908i
\(750\) 0 0
\(751\) 11.1167 0.405655 0.202828 0.979214i \(-0.434987\pi\)
0.202828 + 0.979214i \(0.434987\pi\)
\(752\) 31.4697 + 20.0341i 1.14758 + 0.730567i
\(753\) 0 0
\(754\) 23.0951 17.3275i 0.841074 0.631029i
\(755\) 0.685062i 0.0249320i
\(756\) 0 0
\(757\) 11.8173i 0.429507i 0.976668 + 0.214753i \(0.0688948\pi\)
−0.976668 + 0.214753i \(0.931105\pi\)
\(758\) 13.8617 + 18.4757i 0.503479 + 0.671067i
\(759\) 0 0
\(760\) 5.47016 + 14.5232i 0.198424 + 0.526811i
\(761\) −12.2039 −0.442390 −0.221195 0.975230i \(-0.570996\pi\)
−0.221195 + 0.975230i \(0.570996\pi\)
\(762\) 0 0
\(763\) 6.86711i 0.248606i
\(764\) 9.11929 31.3057i 0.329924 1.13260i
\(765\) 0 0
\(766\) 20.0269 15.0255i 0.723602 0.542894i
\(767\) 78.6073 2.83835
\(768\) 0 0
\(769\) −7.32578 −0.264175 −0.132087 0.991238i \(-0.542168\pi\)
−0.132087 + 0.991238i \(0.542168\pi\)
\(770\) −6.36861 + 4.77815i −0.229509 + 0.172193i
\(771\) 0 0
\(772\) 3.90641 13.4104i 0.140595 0.482650i
\(773\) 7.26470i 0.261293i −0.991429 0.130647i \(-0.958295\pi\)
0.991429 0.130647i \(-0.0417053\pi\)
\(774\) 0 0
\(775\) 14.5037 0.520988
\(776\) −10.7201 28.4617i −0.384831 1.02172i
\(777\) 0 0
\(778\) −20.7235 27.6216i −0.742975 0.990282i
\(779\) 9.52686i 0.341335i
\(780\) 0 0
\(781\) 9.25737i 0.331255i
\(782\) −8.62178 + 6.46863i −0.308314 + 0.231318i
\(783\) 0 0
\(784\) −3.37426 2.14810i −0.120509 0.0767180i
\(785\) −11.3989 −0.406844
\(786\) 0 0