Properties

Label 117.4.q.d.10.1
Level $117$
Weight $4$
Character 117.10
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-17})\)
Defining polynomial: \( x^{4} - 17x^{2} + 289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.1
Root \(-3.57071 + 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.d.82.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.57071 + 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} +3.05006i q^{5} +(-5.78786 - 3.34162i) q^{7} +4.12311i q^{8} +O(q^{10})\) \(q+(-3.57071 + 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} +3.05006i q^{5} +(-5.78786 - 3.34162i) q^{7} +4.12311i q^{8} +(-6.28786 - 10.8909i) q^{10} +(27.9293 - 16.1250i) q^{11} +(-22.1364 - 41.3156i) q^{13} +27.5557 q^{14} +(27.5000 + 47.6314i) q^{16} +(14.4293 - 24.9923i) q^{17} +(87.6364 + 50.5969i) q^{19} +(23.7729 + 13.7253i) q^{20} +(-66.4850 + 115.155i) q^{22} +(59.4950 + 103.048i) q^{23} +115.697 q^{25} +(164.217 + 101.891i) q^{26} +(-52.0907 + 30.0746i) q^{28} +(80.0557 + 138.661i) q^{29} -38.0705i q^{31} +(-224.955 - 129.878i) q^{32} +118.987i q^{34} +(10.1921 - 17.6533i) q^{35} +(283.682 - 163.784i) q^{37} -417.233 q^{38} -12.5757 q^{40} +(-48.5707 + 28.0423i) q^{41} +(63.9393 - 110.746i) q^{43} -290.250i q^{44} +(-424.879 - 245.304i) q^{46} -517.983i q^{47} +(-149.167 - 258.365i) q^{49} +(-413.121 + 238.516i) q^{50} +(-421.637 - 13.3838i) q^{52} +695.546 q^{53} +(49.1821 + 85.1860i) q^{55} +(13.7779 - 23.8639i) q^{56} +(-571.712 - 330.078i) q^{58} +(-568.566 - 328.262i) q^{59} +(-350.652 + 607.347i) q^{61} +(78.4843 + 135.939i) q^{62} +631.000 q^{64} +(126.015 - 67.5174i) q^{65} +(-49.5150 + 28.5875i) q^{67} +(-129.864 - 224.930i) q^{68} +84.0465i q^{70} +(267.798 + 154.613i) q^{71} +389.711i q^{73} +(-675.299 + 1169.65i) q^{74} +(788.728 - 455.372i) q^{76} -215.534 q^{77} +901.820 q^{79} +(-145.279 + 83.8766i) q^{80} +(115.621 - 200.262i) q^{82} -687.095i q^{83} +(76.2279 + 44.0102i) q^{85} +527.257i q^{86} +(66.4850 + 115.155i) q^{88} +(927.113 - 535.269i) q^{89} +(-9.93858 + 313.100i) q^{91} +1070.91 q^{92} +(1067.85 + 1849.57i) q^{94} +(-154.324 + 267.296i) q^{95} +(-1519.43 - 877.242i) q^{97} +(1065.27 + 615.032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.57071 + 2.06155i −1.26244 + 0.728869i −0.973546 0.228493i \(-0.926620\pi\)
−0.288892 + 0.957362i \(0.593287\pi\)
\(3\) 0 0
\(4\) 4.50000 7.79423i 0.562500 0.974279i
\(5\) 3.05006i 0.272806i 0.990653 + 0.136403i \(0.0435541\pi\)
−0.990653 + 0.136403i \(0.956446\pi\)
\(6\) 0 0
\(7\) −5.78786 3.34162i −0.312515 0.180431i 0.335536 0.942027i \(-0.391082\pi\)
−0.648051 + 0.761597i \(0.724416\pi\)
\(8\) 4.12311i 0.182217i
\(9\) 0 0
\(10\) −6.28786 10.8909i −0.198840 0.344400i
\(11\) 27.9293 16.1250i 0.765545 0.441988i −0.0657380 0.997837i \(-0.520940\pi\)
0.831283 + 0.555849i \(0.187607\pi\)
\(12\) 0 0
\(13\) −22.1364 41.3156i −0.472272 0.881453i
\(14\) 27.5557 0.526041
\(15\) 0 0
\(16\) 27.5000 + 47.6314i 0.429688 + 0.744241i
\(17\) 14.4293 24.9923i 0.205860 0.356560i −0.744547 0.667571i \(-0.767334\pi\)
0.950406 + 0.311011i \(0.100668\pi\)
\(18\) 0 0
\(19\) 87.6364 + 50.5969i 1.05817 + 0.610933i 0.924925 0.380150i \(-0.124128\pi\)
0.133242 + 0.991083i \(0.457461\pi\)
\(20\) 23.7729 + 13.7253i 0.265789 + 0.153453i
\(21\) 0 0
\(22\) −66.4850 + 115.155i −0.644302 + 1.11596i
\(23\) 59.4950 + 103.048i 0.539372 + 0.934220i 0.998938 + 0.0460765i \(0.0146718\pi\)
−0.459566 + 0.888144i \(0.651995\pi\)
\(24\) 0 0
\(25\) 115.697 0.925577
\(26\) 164.217 + 101.891i 1.23868 + 0.768555i
\(27\) 0 0
\(28\) −52.0907 + 30.0746i −0.351579 + 0.202984i
\(29\) 80.0557 + 138.661i 0.512620 + 0.887883i 0.999893 + 0.0146339i \(0.00465827\pi\)
−0.487273 + 0.873250i \(0.662008\pi\)
\(30\) 0 0
\(31\) 38.0705i 0.220570i −0.993900 0.110285i \(-0.964824\pi\)
0.993900 0.110285i \(-0.0351763\pi\)
\(32\) −224.955 129.878i −1.24271 0.717480i
\(33\) 0 0
\(34\) 118.987i 0.600179i
\(35\) 10.1921 17.6533i 0.0492225 0.0852558i
\(36\) 0 0
\(37\) 283.682 163.784i 1.26046 0.727727i 0.287297 0.957841i \(-0.407243\pi\)
0.973164 + 0.230114i \(0.0739099\pi\)
\(38\) −417.233 −1.78116
\(39\) 0 0
\(40\) −12.5757 −0.0497099
\(41\) −48.5707 + 28.0423i −0.185011 + 0.106816i −0.589645 0.807662i \(-0.700732\pi\)
0.404634 + 0.914479i \(0.367399\pi\)
\(42\) 0 0
\(43\) 63.9393 110.746i 0.226759 0.392759i −0.730087 0.683355i \(-0.760520\pi\)
0.956846 + 0.290596i \(0.0938536\pi\)
\(44\) 290.250i 0.994472i
\(45\) 0 0
\(46\) −424.879 245.304i −1.36185 0.786264i
\(47\) 517.983i 1.60757i −0.594923 0.803783i \(-0.702817\pi\)
0.594923 0.803783i \(-0.297183\pi\)
\(48\) 0 0
\(49\) −149.167 258.365i −0.434890 0.753251i
\(50\) −413.121 + 238.516i −1.16848 + 0.674624i
\(51\) 0 0
\(52\) −421.637 13.3838i −1.12443 0.0356923i
\(53\) 695.546 1.80265 0.901326 0.433141i \(-0.142595\pi\)
0.901326 + 0.433141i \(0.142595\pi\)
\(54\) 0 0
\(55\) 49.1821 + 85.1860i 0.120577 + 0.208845i
\(56\) 13.7779 23.8639i 0.0328776 0.0569456i
\(57\) 0 0
\(58\) −571.712 330.078i −1.29430 0.747265i
\(59\) −568.566 328.262i −1.25459 0.724339i −0.282574 0.959245i \(-0.591188\pi\)
−0.972018 + 0.234906i \(0.924522\pi\)
\(60\) 0 0
\(61\) −350.652 + 607.347i −0.736007 + 1.27480i 0.218274 + 0.975888i \(0.429957\pi\)
−0.954280 + 0.298913i \(0.903376\pi\)
\(62\) 78.4843 + 135.939i 0.160766 + 0.278456i
\(63\) 0 0
\(64\) 631.000 1.23242
\(65\) 126.015 67.5174i 0.240465 0.128839i
\(66\) 0 0
\(67\) −49.5150 + 28.5875i −0.0902869 + 0.0521271i −0.544464 0.838784i \(-0.683267\pi\)
0.454177 + 0.890912i \(0.349933\pi\)
\(68\) −129.864 224.930i −0.231592 0.401130i
\(69\) 0 0
\(70\) 84.0465i 0.143507i
\(71\) 267.798 + 154.613i 0.447630 + 0.258440i 0.706829 0.707385i \(-0.250125\pi\)
−0.259199 + 0.965824i \(0.583458\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i 0.949946 + 0.312413i \(0.101137\pi\)
−0.949946 + 0.312413i \(0.898863\pi\)
\(74\) −675.299 + 1169.65i −1.06084 + 1.83742i
\(75\) 0 0
\(76\) 788.728 455.372i 1.19044 0.687300i
\(77\) −215.534 −0.318992
\(78\) 0 0
\(79\) 901.820 1.28434 0.642169 0.766563i \(-0.278035\pi\)
0.642169 + 0.766563i \(0.278035\pi\)
\(80\) −145.279 + 83.8766i −0.203033 + 0.117221i
\(81\) 0 0
\(82\) 115.621 200.262i 0.155710 0.269698i
\(83\) 687.095i 0.908657i −0.890834 0.454328i \(-0.849879\pi\)
0.890834 0.454328i \(-0.150121\pi\)
\(84\) 0 0
\(85\) 76.2279 + 44.0102i 0.0972714 + 0.0561597i
\(86\) 527.257i 0.661111i
\(87\) 0 0
\(88\) 66.4850 + 115.155i 0.0805378 + 0.139496i
\(89\) 927.113 535.269i 1.10420 0.637510i 0.166879 0.985977i \(-0.446631\pi\)
0.937321 + 0.348467i \(0.113298\pi\)
\(90\) 0 0
\(91\) −9.93858 + 313.100i −0.0114489 + 0.360679i
\(92\) 1070.91 1.21359
\(93\) 0 0
\(94\) 1067.85 + 1849.57i 1.17170 + 2.02945i
\(95\) −154.324 + 267.296i −0.166666 + 0.288674i
\(96\) 0 0
\(97\) −1519.43 877.242i −1.59046 0.918251i −0.993228 0.116182i \(-0.962935\pi\)
−0.597230 0.802070i \(-0.703732\pi\)
\(98\) 1065.27 + 615.032i 1.09804 + 0.633955i
\(99\) 0 0
\(100\) 520.637 901.770i 0.520637 0.901770i
\(101\) 320.420 + 554.984i 0.315673 + 0.546762i 0.979580 0.201053i \(-0.0644364\pi\)
−0.663907 + 0.747815i \(0.731103\pi\)
\(102\) 0 0
\(103\) 693.153 0.663091 0.331546 0.943439i \(-0.392430\pi\)
0.331546 + 0.943439i \(0.392430\pi\)
\(104\) 170.349 91.2708i 0.160616 0.0860562i
\(105\) 0 0
\(106\) −2483.59 + 1433.90i −2.27574 + 1.31390i
\(107\) −202.838 351.325i −0.183262 0.317420i 0.759727 0.650242i \(-0.225332\pi\)
−0.942990 + 0.332822i \(0.891999\pi\)
\(108\) 0 0
\(109\) 479.516i 0.421370i −0.977554 0.210685i \(-0.932431\pi\)
0.977554 0.210685i \(-0.0675694\pi\)
\(110\) −351.231 202.783i −0.304441 0.175769i
\(111\) 0 0
\(112\) 367.578i 0.310115i
\(113\) −773.602 + 1339.92i −0.644021 + 1.11548i 0.340506 + 0.940242i \(0.389402\pi\)
−0.984527 + 0.175235i \(0.943932\pi\)
\(114\) 0 0
\(115\) −314.304 + 181.463i −0.254861 + 0.147144i
\(116\) 1441.00 1.15339
\(117\) 0 0
\(118\) 2706.91 2.11179
\(119\) −167.029 + 96.4344i −0.128668 + 0.0742868i
\(120\) 0 0
\(121\) −145.470 + 251.961i −0.109294 + 0.189302i
\(122\) 2891.55i 2.14581i
\(123\) 0 0
\(124\) −296.730 171.317i −0.214896 0.124070i
\(125\) 734.140i 0.525308i
\(126\) 0 0
\(127\) −1247.58 2160.87i −0.871690 1.50981i −0.860248 0.509876i \(-0.829691\pi\)
−0.0114416 0.999935i \(-0.503642\pi\)
\(128\) −453.481 + 261.817i −0.313144 + 0.180794i
\(129\) 0 0
\(130\) −310.773 + 500.872i −0.209666 + 0.337918i
\(131\) −43.7571 −0.0291838 −0.0145919 0.999894i \(-0.504645\pi\)
−0.0145919 + 0.999894i \(0.504645\pi\)
\(132\) 0 0
\(133\) −338.151 585.695i −0.220462 0.381851i
\(134\) 117.869 204.156i 0.0759877 0.131615i
\(135\) 0 0
\(136\) 103.046 + 59.4935i 0.0649713 + 0.0375112i
\(137\) 178.569 + 103.097i 0.111359 + 0.0642932i 0.554645 0.832087i \(-0.312854\pi\)
−0.443286 + 0.896380i \(0.646187\pi\)
\(138\) 0 0
\(139\) 50.0000 86.6025i 0.0305104 0.0528456i −0.850367 0.526190i \(-0.823620\pi\)
0.880877 + 0.473344i \(0.156953\pi\)
\(140\) −91.7293 158.880i −0.0553753 0.0959128i
\(141\) 0 0
\(142\) −1274.97 −0.753474
\(143\) −1284.47 796.966i −0.751137 0.466053i
\(144\) 0 0
\(145\) −422.923 + 244.175i −0.242220 + 0.139846i
\(146\) −803.411 1391.55i −0.455416 0.788804i
\(147\) 0 0
\(148\) 2948.11i 1.63739i
\(149\) 329.480 + 190.225i 0.181155 + 0.104590i 0.587835 0.808981i \(-0.299980\pi\)
−0.406680 + 0.913571i \(0.633314\pi\)
\(150\) 0 0
\(151\) 1517.45i 0.817805i 0.912578 + 0.408902i \(0.134088\pi\)
−0.912578 + 0.408902i \(0.865912\pi\)
\(152\) −208.616 + 361.334i −0.111323 + 0.192816i
\(153\) 0 0
\(154\) 769.611 444.335i 0.402708 0.232504i
\(155\) 116.117 0.0601726
\(156\) 0 0
\(157\) 1450.16 0.737166 0.368583 0.929595i \(-0.379843\pi\)
0.368583 + 0.929595i \(0.379843\pi\)
\(158\) −3220.14 + 1859.15i −1.62140 + 0.936114i
\(159\) 0 0
\(160\) 396.135 686.126i 0.195733 0.339019i
\(161\) 795.239i 0.389277i
\(162\) 0 0
\(163\) 2028.54 + 1171.18i 0.974772 + 0.562785i 0.900688 0.434467i \(-0.143063\pi\)
0.0740844 + 0.997252i \(0.476397\pi\)
\(164\) 504.762i 0.240337i
\(165\) 0 0
\(166\) 1416.48 + 2453.42i 0.662292 + 1.14712i
\(167\) −34.7043 + 20.0365i −0.0160808 + 0.00928428i −0.508019 0.861346i \(-0.669622\pi\)
0.491938 + 0.870630i \(0.336289\pi\)
\(168\) 0 0
\(169\) −1216.96 + 1829.16i −0.553918 + 0.832571i
\(170\) −362.917 −0.163732
\(171\) 0 0
\(172\) −575.454 996.715i −0.255104 0.441853i
\(173\) −954.770 + 1653.71i −0.419594 + 0.726759i −0.995899 0.0904765i \(-0.971161\pi\)
0.576304 + 0.817235i \(0.304494\pi\)
\(174\) 0 0
\(175\) −669.639 386.616i −0.289257 0.167002i
\(176\) 1536.11 + 886.874i 0.657890 + 0.379833i
\(177\) 0 0
\(178\) −2206.97 + 3822.58i −0.929322 + 1.60963i
\(179\) 254.979 + 441.637i 0.106470 + 0.184411i 0.914338 0.404953i \(-0.132712\pi\)
−0.807868 + 0.589363i \(0.799379\pi\)
\(180\) 0 0
\(181\) 2136.88 0.877531 0.438766 0.898602i \(-0.355416\pi\)
0.438766 + 0.898602i \(0.355416\pi\)
\(182\) −609.985 1138.48i −0.248435 0.463680i
\(183\) 0 0
\(184\) −424.879 + 245.304i −0.170231 + 0.0982830i
\(185\) 499.551 + 865.247i 0.198528 + 0.343861i
\(186\) 0 0
\(187\) 930.688i 0.363950i
\(188\) −4037.28 2330.92i −1.56622 0.904256i
\(189\) 0 0
\(190\) 1272.58i 0.485911i
\(191\) 2028.87 3514.11i 0.768607 1.33127i −0.169711 0.985494i \(-0.554283\pi\)
0.938318 0.345773i \(-0.112383\pi\)
\(192\) 0 0
\(193\) −756.381 + 436.697i −0.282101 + 0.162871i −0.634374 0.773026i \(-0.718742\pi\)
0.352273 + 0.935897i \(0.385409\pi\)
\(194\) 7233.92 2.67714
\(195\) 0 0
\(196\) −2685.01 −0.978502
\(197\) −3591.62 + 2073.62i −1.29895 + 0.749947i −0.980222 0.197901i \(-0.936588\pi\)
−0.318724 + 0.947848i \(0.603254\pi\)
\(198\) 0 0
\(199\) −1202.03 + 2081.98i −0.428189 + 0.741646i −0.996712 0.0810216i \(-0.974182\pi\)
0.568523 + 0.822667i \(0.307515\pi\)
\(200\) 477.032i 0.168656i
\(201\) 0 0
\(202\) −2288.26 1321.13i −0.797035 0.460169i
\(203\) 1070.06i 0.369969i
\(204\) 0 0
\(205\) −85.5307 148.144i −0.0291401 0.0504722i
\(206\) −2475.05 + 1428.97i −0.837111 + 0.483307i
\(207\) 0 0
\(208\) 1359.17 2190.57i 0.453083 0.730233i
\(209\) 3263.50 1.08010
\(210\) 0 0
\(211\) −1934.43 3350.53i −0.631144 1.09317i −0.987318 0.158754i \(-0.949252\pi\)
0.356174 0.934420i \(-0.384081\pi\)
\(212\) 3129.96 5421.24i 1.01399 1.75629i
\(213\) 0 0
\(214\) 1448.55 + 836.322i 0.462715 + 0.267149i
\(215\) 337.782 + 195.019i 0.107147 + 0.0618612i
\(216\) 0 0
\(217\) −127.217 + 220.346i −0.0397975 + 0.0689313i
\(218\) 988.547 + 1712.21i 0.307123 + 0.531953i
\(219\) 0 0
\(220\) 885.279 0.271298
\(221\) −1351.98 42.9153i −0.411512 0.0130624i
\(222\) 0 0
\(223\) 2436.61 1406.78i 0.731692 0.422443i −0.0873487 0.996178i \(-0.527839\pi\)
0.819041 + 0.573735i \(0.194506\pi\)
\(224\) 868.005 + 1503.43i 0.258911 + 0.448447i
\(225\) 0 0
\(226\) 6379.29i 1.87763i
\(227\) −3913.02 2259.19i −1.14413 0.660561i −0.196677 0.980468i \(-0.563015\pi\)
−0.947449 + 0.319907i \(0.896348\pi\)
\(228\) 0 0
\(229\) 1305.27i 0.376658i 0.982106 + 0.188329i \(0.0603070\pi\)
−0.982106 + 0.188329i \(0.939693\pi\)
\(230\) 748.192 1295.91i 0.214497 0.371520i
\(231\) 0 0
\(232\) −571.712 + 330.078i −0.161788 + 0.0934082i
\(233\) −3360.55 −0.944879 −0.472440 0.881363i \(-0.656627\pi\)
−0.472440 + 0.881363i \(0.656627\pi\)
\(234\) 0 0
\(235\) 1579.88 0.438553
\(236\) −5117.09 + 2954.35i −1.41142 + 0.814882i
\(237\) 0 0
\(238\) 397.609 688.679i 0.108291 0.187565i
\(239\) 4737.17i 1.28210i 0.767499 + 0.641050i \(0.221501\pi\)
−0.767499 + 0.641050i \(0.778499\pi\)
\(240\) 0 0
\(241\) 4144.17 + 2392.64i 1.10767 + 0.639516i 0.938226 0.346023i \(-0.112468\pi\)
0.169448 + 0.985539i \(0.445801\pi\)
\(242\) 1199.58i 0.318643i
\(243\) 0 0
\(244\) 3155.87 + 5466.13i 0.828007 + 1.43415i
\(245\) 788.029 454.969i 0.205491 0.118640i
\(246\) 0 0
\(247\) 150.484 4740.79i 0.0387655 1.22125i
\(248\) 156.969 0.0401916
\(249\) 0 0
\(250\) −1513.47 2621.41i −0.382881 0.663169i
\(251\) 1636.93 2835.25i 0.411642 0.712985i −0.583428 0.812165i \(-0.698289\pi\)
0.995069 + 0.0991805i \(0.0316221\pi\)
\(252\) 0 0
\(253\) 3323.31 + 1918.71i 0.825828 + 0.476792i
\(254\) 8909.48 + 5143.89i 2.20091 + 1.27069i
\(255\) 0 0
\(256\) −1444.50 + 2501.95i −0.352661 + 0.610827i
\(257\) 3272.91 + 5668.84i 0.794390 + 1.37592i 0.923226 + 0.384258i \(0.125543\pi\)
−0.128835 + 0.991666i \(0.541124\pi\)
\(258\) 0 0
\(259\) −2189.22 −0.525217
\(260\) 40.8214 1286.02i 0.00973706 0.306752i
\(261\) 0 0
\(262\) 156.244 90.2077i 0.0368428 0.0212712i
\(263\) 44.1007 + 76.3847i 0.0103398 + 0.0179091i 0.871149 0.491019i \(-0.163375\pi\)
−0.860809 + 0.508928i \(0.830042\pi\)
\(264\) 0 0
\(265\) 2121.46i 0.491773i
\(266\) 2414.88 + 1394.23i 0.556639 + 0.321376i
\(267\) 0 0
\(268\) 514.575i 0.117286i
\(269\) −2263.80 + 3921.01i −0.513109 + 0.888730i 0.486776 + 0.873527i \(0.338173\pi\)
−0.999884 + 0.0152033i \(0.995160\pi\)
\(270\) 0 0
\(271\) −7206.91 + 4160.91i −1.61546 + 0.932684i −0.627380 + 0.778713i \(0.715873\pi\)
−0.988075 + 0.153971i \(0.950794\pi\)
\(272\) 1587.22 0.353821
\(273\) 0 0
\(274\) −850.160 −0.187445
\(275\) 3231.34 1865.61i 0.708571 0.409094i
\(276\) 0 0
\(277\) −1440.65 + 2495.29i −0.312493 + 0.541254i −0.978901 0.204333i \(-0.934497\pi\)
0.666408 + 0.745587i \(0.267831\pi\)
\(278\) 412.311i 0.0889523i
\(279\) 0 0
\(280\) 72.7864 + 42.0233i 0.0155351 + 0.00896918i
\(281\) 2817.99i 0.598247i −0.954214 0.299123i \(-0.903306\pi\)
0.954214 0.299123i \(-0.0966942\pi\)
\(282\) 0 0
\(283\) 132.301 + 229.152i 0.0277896 + 0.0481330i 0.879586 0.475740i \(-0.157820\pi\)
−0.851796 + 0.523873i \(0.824486\pi\)
\(284\) 2410.18 1391.52i 0.503584 0.290744i
\(285\) 0 0
\(286\) 6229.45 + 197.738i 1.28796 + 0.0408829i
\(287\) 374.827 0.0770918
\(288\) 0 0
\(289\) 2040.09 + 3533.54i 0.415244 + 0.719223i
\(290\) 1006.76 1743.76i 0.203858 0.353093i
\(291\) 0 0
\(292\) 3037.50 + 1753.70i 0.608754 + 0.351464i
\(293\) −3717.43 2146.26i −0.741211 0.427938i 0.0812984 0.996690i \(-0.474093\pi\)
−0.822509 + 0.568751i \(0.807427\pi\)
\(294\) 0 0
\(295\) 1001.22 1734.16i 0.197604 0.342260i
\(296\) 675.299 + 1169.65i 0.132604 + 0.229678i
\(297\) 0 0
\(298\) −1568.64 −0.304929
\(299\) 2940.50 4739.19i 0.568740 0.916638i
\(300\) 0 0
\(301\) −740.143 + 427.322i −0.141731 + 0.0818286i
\(302\) −3128.31 5418.39i −0.596072 1.03243i
\(303\) 0 0
\(304\) 5565.66i 1.05004i
\(305\) −1852.45 1069.51i −0.347773 0.200787i
\(306\) 0 0
\(307\) 7026.26i 1.30622i −0.757263 0.653110i \(-0.773464\pi\)
0.757263 0.653110i \(-0.226536\pi\)
\(308\) −969.904 + 1679.92i −0.179433 + 0.310787i
\(309\) 0 0
\(310\) −414.621 + 239.382i −0.0759642 + 0.0438580i
\(311\) −1133.21 −0.206618 −0.103309 0.994649i \(-0.532943\pi\)
−0.103309 + 0.994649i \(0.532943\pi\)
\(312\) 0 0
\(313\) −5285.95 −0.954566 −0.477283 0.878750i \(-0.658378\pi\)
−0.477283 + 0.878750i \(0.658378\pi\)
\(314\) −5178.09 + 2989.57i −0.930626 + 0.537297i
\(315\) 0 0
\(316\) 4058.19 7028.99i 0.722440 1.25130i
\(317\) 4782.16i 0.847296i 0.905827 + 0.423648i \(0.139251\pi\)
−0.905827 + 0.423648i \(0.860749\pi\)
\(318\) 0 0
\(319\) 4471.80 + 2581.79i 0.784867 + 0.453143i
\(320\) 1924.59i 0.336212i
\(321\) 0 0
\(322\) 1639.43 + 2839.57i 0.283732 + 0.491438i
\(323\) 2529.06 1460.15i 0.435668 0.251533i
\(324\) 0 0
\(325\) −2561.12 4780.10i −0.437124 0.815852i
\(326\) −9657.80 −1.64079
\(327\) 0 0
\(328\) −115.621 200.262i −0.0194638 0.0337123i
\(329\) −1730.90 + 2998.01i −0.290054 + 0.502388i
\(330\) 0 0
\(331\) −7508.43 4334.99i −1.24683 0.719857i −0.276353 0.961056i \(-0.589126\pi\)
−0.970476 + 0.241199i \(0.922459\pi\)
\(332\) −5355.38 3091.93i −0.885285 0.511120i
\(333\) 0 0
\(334\) 82.6128 143.090i 0.0135340 0.0234417i
\(335\) −87.1936 151.024i −0.0142206 0.0246308i
\(336\) 0 0
\(337\) −8526.59 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(338\) 574.497 9040.23i 0.0924513 1.45480i
\(339\) 0 0
\(340\) 686.051 396.092i 0.109430 0.0631796i
\(341\) −613.886 1063.28i −0.0974891 0.168856i
\(342\) 0 0
\(343\) 4286.19i 0.674731i
\(344\) 456.618 + 263.628i 0.0715674 + 0.0413195i
\(345\) 0 0
\(346\) 7873.23i 1.22332i
\(347\) −6290.74 + 10895.9i −0.973213 + 1.68565i −0.287501 + 0.957780i \(0.592825\pi\)
−0.685711 + 0.727874i \(0.740509\pi\)
\(348\) 0 0
\(349\) 7760.61 4480.59i 1.19030 0.687222i 0.231928 0.972733i \(-0.425497\pi\)
0.958375 + 0.285511i \(0.0921633\pi\)
\(350\) 3188.12 0.486892
\(351\) 0 0
\(352\) −8377.11 −1.26847
\(353\) 4640.16 2679.00i 0.699634 0.403934i −0.107577 0.994197i \(-0.534309\pi\)
0.807211 + 0.590263i \(0.200976\pi\)
\(354\) 0 0
\(355\) −471.579 + 816.799i −0.0705037 + 0.122116i
\(356\) 9634.84i 1.43440i
\(357\) 0 0
\(358\) −1820.92 1051.31i −0.268822 0.155205i
\(359\) 2705.40i 0.397731i −0.980027 0.198866i \(-0.936274\pi\)
0.980027 0.198866i \(-0.0637257\pi\)
\(360\) 0 0
\(361\) 1690.60 + 2928.20i 0.246478 + 0.426913i
\(362\) −7630.19 + 4405.29i −1.10783 + 0.639605i
\(363\) 0 0
\(364\) 2395.65 + 1486.42i 0.344962 + 0.214037i
\(365\) −1188.64 −0.170456
\(366\) 0 0
\(367\) −5236.88 9070.54i −0.744858 1.29013i −0.950261 0.311455i \(-0.899184\pi\)
0.205403 0.978678i \(-0.434150\pi\)
\(368\) −3272.22 + 5667.66i −0.463523 + 0.802846i
\(369\) 0 0
\(370\) −3567.51 2059.70i −0.501259 0.289402i
\(371\) −4025.72 2324.25i −0.563356 0.325254i
\(372\) 0 0
\(373\) 6381.51 11053.1i 0.885850 1.53434i 0.0411127 0.999155i \(-0.486910\pi\)
0.844737 0.535182i \(-0.179757\pi\)
\(374\) 1918.66 + 3323.22i 0.265272 + 0.459464i
\(375\) 0 0
\(376\) 2135.70 0.292926
\(377\) 3956.70 6377.00i 0.540531 0.871173i
\(378\) 0 0
\(379\) −2007.47 + 1159.01i −0.272076 + 0.157083i −0.629831 0.776733i \(-0.716876\pi\)
0.357755 + 0.933816i \(0.383542\pi\)
\(380\) 1388.91 + 2405.67i 0.187499 + 0.324758i
\(381\) 0 0
\(382\) 16730.5i 2.24086i
\(383\) 1717.63 + 991.672i 0.229156 + 0.132303i 0.610183 0.792261i \(-0.291096\pi\)
−0.381027 + 0.924564i \(0.624429\pi\)
\(384\) 0 0
\(385\) 657.392i 0.0870229i
\(386\) 1800.55 3118.64i 0.237424 0.411230i
\(387\) 0 0
\(388\) −13674.8 + 7895.17i −1.78927 + 1.03303i
\(389\) −3244.51 −0.422887 −0.211444 0.977390i \(-0.567816\pi\)
−0.211444 + 0.977390i \(0.567816\pi\)
\(390\) 0 0
\(391\) 3433.88 0.444140
\(392\) 1065.27 615.032i 0.137255 0.0792444i
\(393\) 0 0
\(394\) 8549.77 14808.6i 1.09323 1.89352i
\(395\) 2750.60i 0.350374i
\(396\) 0 0
\(397\) 3256.02 + 1879.86i 0.411624 + 0.237651i 0.691487 0.722389i \(-0.256956\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(398\) 9912.20i 1.24838i
\(399\) 0 0
\(400\) 3181.67 + 5510.82i 0.397709 + 0.688852i
\(401\) −1729.93 + 998.773i −0.215432 + 0.124380i −0.603833 0.797110i \(-0.706361\pi\)
0.388401 + 0.921490i \(0.373027\pi\)
\(402\) 0 0
\(403\) −1572.90 + 842.744i −0.194422 + 0.104169i
\(404\) 5767.56 0.710264
\(405\) 0 0
\(406\) 2205.99 + 3820.89i 0.269659 + 0.467063i
\(407\) 5282.03 9148.74i 0.643293 1.11422i
\(408\) 0 0
\(409\) 4499.20 + 2597.62i 0.543940 + 0.314044i 0.746674 0.665190i \(-0.231650\pi\)
−0.202735 + 0.979234i \(0.564983\pi\)
\(410\) 610.811 + 352.652i 0.0735752 + 0.0424787i
\(411\) 0 0
\(412\) 3119.19 5402.59i 0.372989 0.646035i
\(413\) 2193.85 + 3799.86i 0.261386 + 0.452734i
\(414\) 0 0
\(415\) 2095.68 0.247887
\(416\) −386.280 + 12169.2i −0.0455263 + 1.43424i
\(417\) 0 0
\(418\) −11653.0 + 6727.87i −1.36356 + 0.787251i
\(419\) −3411.05 5908.12i −0.397711 0.688855i 0.595732 0.803183i \(-0.296862\pi\)
−0.993443 + 0.114328i \(0.963529\pi\)
\(420\) 0 0
\(421\) 7537.70i 0.872601i 0.899801 + 0.436300i \(0.143712\pi\)
−0.899801 + 0.436300i \(0.856288\pi\)
\(422\) 13814.6 + 7975.85i 1.59356 + 0.920043i
\(423\) 0 0
\(424\) 2867.81i 0.328474i
\(425\) 1669.43 2891.53i 0.190539 0.330023i
\(426\) 0 0
\(427\) 4059.05 2343.49i 0.460026 0.265596i
\(428\) −3651.08 −0.412340
\(429\) 0 0
\(430\) −1608.16 −0.180355
\(431\) 11608.4 6702.10i 1.29735 0.749023i 0.317401 0.948291i \(-0.397190\pi\)
0.979945 + 0.199268i \(0.0638565\pi\)
\(432\) 0 0
\(433\) −8857.97 + 15342.5i −0.983110 + 1.70280i −0.333061 + 0.942905i \(0.608081\pi\)
−0.650050 + 0.759892i \(0.725252\pi\)
\(434\) 1049.06i 0.116029i
\(435\) 0 0
\(436\) −3737.46 2157.82i −0.410531 0.237020i
\(437\) 12041.1i 1.31808i
\(438\) 0 0
\(439\) 3581.73 + 6203.75i 0.389401 + 0.674462i 0.992369 0.123303i \(-0.0393488\pi\)
−0.602968 + 0.797765i \(0.706015\pi\)
\(440\) −351.231 + 202.783i −0.0380552 + 0.0219712i
\(441\) 0 0
\(442\) 4916.02 2633.95i 0.529030 0.283448i
\(443\) 10169.2 1.09064 0.545321 0.838227i \(-0.316408\pi\)
0.545321 + 0.838227i \(0.316408\pi\)
\(444\) 0 0
\(445\) 1632.60 + 2827.75i 0.173916 + 0.301232i
\(446\) −5800.29 + 10046.4i −0.615811 + 1.06662i
\(447\) 0 0
\(448\) −3652.14 2108.56i −0.385150 0.222367i
\(449\) 14845.8 + 8571.24i 1.56040 + 0.900895i 0.997217 + 0.0745603i \(0.0237553\pi\)
0.563179 + 0.826335i \(0.309578\pi\)
\(450\) 0 0
\(451\) −904.364 + 1566.40i −0.0944231 + 0.163546i
\(452\) 6962.42 + 12059.3i 0.724524 + 1.25491i
\(453\) 0 0
\(454\) 18629.7 1.92585
\(455\) −954.974 30.3133i −0.0983954 0.00312331i
\(456\) 0 0
\(457\) 12203.3 7045.57i 1.24912 0.721177i 0.278183 0.960528i \(-0.410268\pi\)
0.970933 + 0.239351i \(0.0769346\pi\)
\(458\) −2690.88 4660.74i −0.274534 0.475507i
\(459\) 0 0
\(460\) 3266.34i 0.331074i
\(461\) −2530.72 1461.11i −0.255678 0.147616i 0.366684 0.930346i \(-0.380493\pi\)
−0.622361 + 0.782730i \(0.713826\pi\)
\(462\) 0 0
\(463\) 2072.61i 0.208040i 0.994575 + 0.104020i \(0.0331706\pi\)
−0.994575 + 0.104020i \(0.966829\pi\)
\(464\) −4403.06 + 7626.33i −0.440533 + 0.763025i
\(465\) 0 0
\(466\) 11999.6 6927.95i 1.19285 0.688693i
\(467\) −2664.19 −0.263992 −0.131996 0.991250i \(-0.542139\pi\)
−0.131996 + 0.991250i \(0.542139\pi\)
\(468\) 0 0
\(469\) 382.114 0.0376213
\(470\) −5641.29 + 3257.00i −0.553646 + 0.319648i
\(471\) 0 0
\(472\) 1353.46 2344.26i 0.131987 0.228608i
\(473\) 4124.08i 0.400899i
\(474\) 0 0
\(475\) 10139.3 + 5853.92i 0.979415 + 0.565466i
\(476\) 1735.82i 0.167145i
\(477\) 0 0
\(478\) −9765.92 16915.1i −0.934483 1.61857i
\(479\) −4521.26 + 2610.35i −0.431277 + 0.248998i −0.699890 0.714250i \(-0.746768\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(480\) 0 0
\(481\) −13046.5 8094.91i −1.23674 0.767351i
\(482\) −19730.2 −1.86449
\(483\) 0 0
\(484\) 1309.23 + 2267.65i 0.122955 + 0.212965i
\(485\) 2675.64 4634.34i 0.250504 0.433886i
\(486\) 0 0
\(487\) 10586.8 + 6112.30i 0.985081 + 0.568737i 0.903800 0.427954i \(-0.140766\pi\)
0.0812808 + 0.996691i \(0.474099\pi\)
\(488\) −2504.16 1445.78i −0.232291 0.134113i
\(489\) 0 0
\(490\) −1875.88 + 3249.13i −0.172946 + 0.299552i
\(491\) −9826.61 17020.2i −0.903195 1.56438i −0.823323 0.567574i \(-0.807882\pi\)
−0.0798720 0.996805i \(-0.525451\pi\)
\(492\) 0 0
\(493\) 4620.59 0.422111
\(494\) 9236.04 + 17238.2i 0.841193 + 1.57001i
\(495\) 0 0
\(496\) 1813.35 1046.94i 0.164157 0.0947760i
\(497\) −1033.32 1789.76i −0.0932608 0.161532i
\(498\) 0 0
\(499\) 11713.6i 1.05084i −0.850842 0.525422i \(-0.823907\pi\)
0.850842 0.525422i \(-0.176093\pi\)
\(500\) 5722.06 + 3303.63i 0.511796 + 0.295486i
\(501\) 0 0
\(502\) 13498.5i 1.20013i
\(503\) 6501.67 11261.2i 0.576332 0.998236i −0.419563 0.907726i \(-0.637817\pi\)
0.995896 0.0905104i \(-0.0288498\pi\)
\(504\) 0 0
\(505\) −1692.73 + 977.300i −0.149160 + 0.0861174i
\(506\) −15822.1 −1.39008
\(507\) 0 0
\(508\) −22456.4 −1.96130
\(509\) 4614.99 2664.47i 0.401878 0.232024i −0.285416 0.958404i \(-0.592132\pi\)
0.687294 + 0.726379i \(0.258798\pi\)
\(510\) 0 0
\(511\) 1302.27 2255.59i 0.112738 0.195267i
\(512\) 16100.7i 1.38976i
\(513\) 0 0
\(514\) −23373.2 13494.5i −2.00574 1.15801i
\(515\) 2114.16i 0.180895i
\(516\) 0 0
\(517\) −8352.47 14466.9i −0.710524 1.23066i
\(518\) 7817.06 4513.18i 0.663054 0.382814i
\(519\) 0 0
\(520\) 278.381 + 519.573i 0.0234766 + 0.0438169i
\(521\) 11700.3 0.983876 0.491938 0.870630i \(-0.336289\pi\)
0.491938 + 0.870630i \(0.336289\pi\)
\(522\) 0 0
\(523\) 2267.52 + 3927.46i 0.189583 + 0.328367i 0.945111 0.326749i \(-0.105953\pi\)
−0.755528 + 0.655116i \(0.772620\pi\)
\(524\) −196.907 + 341.053i −0.0164159 + 0.0284332i
\(525\) 0 0
\(526\) −314.942 181.832i −0.0261067 0.0150727i
\(527\) −951.467 549.330i −0.0786462 0.0454064i
\(528\) 0 0
\(529\) −995.810 + 1724.79i −0.0818451 + 0.141760i
\(530\) −4373.49 7575.11i −0.358438 0.620834i
\(531\) 0 0
\(532\) −6086.73 −0.496040
\(533\) 2233.77 + 1385.97i 0.181529 + 0.112632i
\(534\) 0 0
\(535\) 1071.56 618.667i 0.0865939 0.0499950i
\(536\) −117.869 204.156i −0.00949847 0.0164518i
\(537\) 0 0
\(538\) 18667.8i 1.49596i
\(539\) −8332.26 4810.63i −0.665855 0.384432i
\(540\) 0 0
\(541\) 5184.89i 0.412044i 0.978547 + 0.206022i \(0.0660519\pi\)
−0.978547 + 0.206022i \(0.933948\pi\)
\(542\) 17155.9 29714.8i 1.35961 2.35491i
\(543\) 0 0
\(544\) −6491.88 + 3748.09i −0.511649 + 0.295401i
\(545\) 1462.55 0.114952
\(546\) 0 0
\(547\) 5609.12 0.438443 0.219222 0.975675i \(-0.429648\pi\)
0.219222 + 0.975675i \(0.429648\pi\)
\(548\) 1607.12 927.873i 0.125279 0.0723299i
\(549\) 0 0
\(550\) −7692.12 + 13323.2i −0.596351 + 1.03291i
\(551\) 16202.3i 1.25271i
\(552\) 0 0
\(553\) −5219.61 3013.54i −0.401375 0.231734i
\(554\) 11879.9i 0.911066i
\(555\) 0 0
\(556\) −450.000 779.423i −0.0343242 0.0594512i
\(557\) −17450.9 + 10075.3i −1.32750 + 0.766432i −0.984912 0.173055i \(-0.944636\pi\)
−0.342586 + 0.939486i \(0.611303\pi\)
\(558\) 0 0
\(559\) −5990.93 190.167i −0.453290 0.0143886i
\(560\) 1121.14 0.0846011
\(561\) 0 0
\(562\) 5809.44 + 10062.2i 0.436044 + 0.755250i
\(563\) −8146.10 + 14109.5i −0.609800 + 1.05620i 0.381474 + 0.924380i \(0.375417\pi\)
−0.991273 + 0.131824i \(0.957917\pi\)
\(564\) 0 0
\(565\) −4086.83 2359.53i −0.304308 0.175692i
\(566\) −944.816 545.490i −0.0701654 0.0405100i
\(567\) 0 0
\(568\) −637.486 + 1104.16i −0.0470921 + 0.0815660i
\(569\) −5230.27 9059.09i −0.385350 0.667446i 0.606468 0.795108i \(-0.292586\pi\)
−0.991818 + 0.127662i \(0.959253\pi\)
\(570\) 0 0
\(571\) −2225.96 −0.163141 −0.0815705 0.996668i \(-0.525994\pi\)
−0.0815705 + 0.996668i \(0.525994\pi\)
\(572\) −11991.8 + 6425.09i −0.876580 + 0.469662i
\(573\) 0 0
\(574\) −1338.40 + 772.726i −0.0973236 + 0.0561898i
\(575\) 6883.40 + 11922.4i 0.499231 + 0.864693i
\(576\) 0 0
\(577\) 4686.23i 0.338112i 0.985606 + 0.169056i \(0.0540718\pi\)
−0.985606 + 0.169056i \(0.945928\pi\)
\(578\) −14569.2 8411.51i −1.04844 0.605316i
\(579\) 0 0
\(580\) 4395.14i 0.314652i
\(581\) −2296.01 + 3976.81i −0.163949 + 0.283969i
\(582\) 0 0
\(583\) 19426.1 11215.7i 1.38001 0.796750i
\(584\) −1606.82 −0.113854
\(585\) 0 0
\(586\) 17698.5 1.24764
\(587\) −10470.7 + 6045.28i −0.736241 + 0.425069i −0.820701 0.571358i \(-0.806417\pi\)
0.0844601 + 0.996427i \(0.473083\pi\)
\(588\) 0 0
\(589\) 1926.25 3336.36i 0.134753 0.233400i
\(590\) 8256.25i 0.576109i
\(591\) 0 0
\(592\) 15602.5 + 9008.12i 1.08321 + 0.625391i
\(593\) 6135.97i 0.424914i 0.977170 + 0.212457i \(0.0681466\pi\)
−0.977170 + 0.212457i \(0.931853\pi\)
\(594\) 0 0
\(595\) −294.131 509.449i −0.0202658 0.0351015i
\(596\) 2965.32 1712.03i 0.203799 0.117663i
\(597\) 0 0
\(598\) −729.579 + 22984.3i −0.0498908 + 1.57174i
\(599\) 6198.80 0.422831 0.211416 0.977396i \(-0.432193\pi\)
0.211416 + 0.977396i \(0.432193\pi\)
\(600\) 0 0
\(601\) −9172.69 15887.6i −0.622565 1.07831i −0.989006 0.147873i \(-0.952757\pi\)
0.366441 0.930441i \(-0.380576\pi\)
\(602\) 1761.89 3051.69i 0.119285 0.206607i
\(603\) 0 0
\(604\) 11827.4 + 6828.53i 0.796770 + 0.460015i
\(605\) −768.497 443.692i −0.0516427 0.0298159i
\(606\) 0 0
\(607\) −5194.06 + 8996.38i −0.347315 + 0.601568i −0.985772 0.168090i \(-0.946240\pi\)
0.638456 + 0.769658i \(0.279573\pi\)
\(608\) −13142.8 22764.1i −0.876665 1.51843i
\(609\) 0 0
\(610\) 8819.40 0.585389
\(611\) −21400.8 + 11466.3i −1.41699 + 0.759209i
\(612\) 0 0
\(613\) −696.701 + 402.240i −0.0459045 + 0.0265030i −0.522777 0.852470i \(-0.675104\pi\)
0.476872 + 0.878973i \(0.341770\pi\)
\(614\) 14485.0 + 25088.8i 0.952064 + 1.64902i
\(615\) 0 0
\(616\) 888.671i 0.0581259i
\(617\) 13179.4 + 7609.13i 0.859940 + 0.496486i 0.863992 0.503505i \(-0.167957\pi\)
−0.00405239 + 0.999992i \(0.501290\pi\)
\(618\) 0 0
\(619\) 11462.5i 0.744291i 0.928174 + 0.372145i \(0.121378\pi\)
−0.928174 + 0.372145i \(0.878622\pi\)
\(620\) 522.527 905.044i 0.0338471 0.0586249i
\(621\) 0 0
\(622\) 4046.36 2336.17i 0.260843 0.150598i
\(623\) −7154.66 −0.460105
\(624\) 0 0
\(625\) 12223.0 0.782270
\(626\) 18874.6 10897.3i 1.20508 0.695754i
\(627\) 0 0
\(628\) 6525.70 11302.8i 0.414656 0.718205i
\(629\) 9453.14i 0.599239i
\(630\) 0 0
\(631\) −3869.99 2234.34i −0.244155 0.140963i 0.372930 0.927860i \(-0.378353\pi\)
−0.617085 + 0.786896i \(0.711687\pi\)
\(632\) 3718.30i 0.234028i
\(633\) 0 0
\(634\) −9858.67 17075.7i −0.617568 1.06966i
\(635\) 6590.77 3805.18i 0.411885 0.237802i
\(636\) 0 0
\(637\) −7372.48 + 11882.2i −0.458569 + 0.739074i
\(638\) −21290.0 −1.32113
\(639\) 0 0
\(640\) −798.558 1383.14i −0.0493215 0.0854274i
\(641\) −3071.18 + 5319.44i −0.189242 + 0.327777i −0.944998 0.327077i \(-0.893936\pi\)
0.755756 + 0.654854i \(0.227270\pi\)
\(642\) 0 0
\(643\) −17959.8 10369.1i −1.10150 0.635951i −0.164886 0.986313i \(-0.552726\pi\)
−0.936615 + 0.350361i \(0.886059\pi\)
\(644\) −6198.27 3578.58i −0.379264 0.218968i
\(645\) 0 0
\(646\) −6020.37 + 10427.6i −0.366669 + 0.635090i
\(647\) −426.379 738.509i −0.0259083 0.0448745i 0.852781 0.522269i \(-0.174914\pi\)
−0.878689 + 0.477395i \(0.841581\pi\)
\(648\) 0 0
\(649\) −21172.8 −1.28060
\(650\) 18999.5 + 11788.5i 1.14649 + 0.711357i
\(651\) 0 0
\(652\) 18256.9 10540.6i 1.09662 0.633133i
\(653\) −3672.88 6361.61i −0.220108 0.381239i 0.734732 0.678357i \(-0.237308\pi\)
−0.954841 + 0.297118i \(0.903974\pi\)
\(654\) 0 0
\(655\) 133.462i 0.00796151i
\(656\) −2671.39 1542.33i −0.158994 0.0917954i
\(657\) 0 0
\(658\) 14273.4i 0.845645i
\(659\) 6270.33 10860.5i 0.370648 0.641982i −0.619017 0.785378i \(-0.712469\pi\)
0.989665 + 0.143396i \(0.0458022\pi\)
\(660\) 0 0
\(661\) 1942.45 1121.48i 0.114301 0.0659915i −0.441760 0.897133i \(-0.645646\pi\)
0.556060 + 0.831142i \(0.312312\pi\)
\(662\) 35747.3 2.09873
\(663\) 0 0
\(664\) 2832.97 0.165573
\(665\) 1786.41 1031.38i 0.104171 0.0601433i
\(666\) 0 0
\(667\) −9525.83 + 16499.2i −0.552986 + 0.957800i
\(668\) 360.658i 0.0208896i
\(669\) 0 0
\(670\) 622.687 + 359.508i 0.0359052 + 0.0207299i
\(671\) 22617.0i 1.30122i
\(672\) 0 0
\(673\) −2388.23 4136.53i −0.136790 0.236927i 0.789490 0.613763i \(-0.210345\pi\)
−0.926280 + 0.376837i \(0.877012\pi\)
\(674\) 30446.0 17578.0i 1.73997 1.00457i
\(675\) 0 0
\(676\) 8780.58 + 17716.5i 0.499578 + 1.00799i
\(677\) 7933.57 0.450387 0.225193 0.974314i \(-0.427699\pi\)
0.225193 + 0.974314i \(0.427699\pi\)
\(678\) 0 0
\(679\) 5862.82 + 10154.7i 0.331361 + 0.573935i
\(680\) −181.459 + 314.295i −0.0102333 + 0.0177245i
\(681\) 0 0
\(682\) 4384.02 + 2531.12i 0.246148 + 0.142114i
\(683\) −20415.5 11786.9i −1.14374 0.660340i −0.196388 0.980526i \(-0.562921\pi\)
−0.947355 + 0.320186i \(0.896255\pi\)
\(684\) 0 0
\(685\) −314.452 + 544.647i −0.0175396 + 0.0303794i
\(686\) −8836.21 15304.8i −0.491790 0.851806i
\(687\) 0 0
\(688\) 7033.32 0.389743
\(689\) −15396.9 28736.9i −0.851343 1.58895i
\(690\) 0 0
\(691\) −10863.2 + 6271.89i −0.598056 + 0.345288i −0.768276 0.640118i \(-0.778885\pi\)
0.170221 + 0.985406i \(0.445552\pi\)
\(692\) 8592.93 + 14883.4i 0.472044 + 0.817604i
\(693\) 0 0
\(694\) 51874.8i 2.83738i
\(695\) 264.143 + 152.503i 0.0144166 + 0.00832340i
\(696\) 0 0
\(697\) 1618.52i 0.0879568i
\(698\) −18473.9 + 31997.8i −1.00179 + 1.73515i
\(699\) 0 0
\(700\) −6026.75 + 3479.54i −0.325414 + 0.187878i
\(701\) −581.786 −0.0313463 −0.0156731 0.999877i \(-0.504989\pi\)
−0.0156731 + 0.999877i \(0.504989\pi\)
\(702\) 0 0
\(703\) 33147.9 1.77837
\(704\) 17623.4 10174.9i 0.943475 0.544715i
\(705\) 0 0
\(706\) −11045.8 + 19131.9i −0.588830 + 1.01988i
\(707\) 4282.89i 0.227828i
\(708\) 0 0
\(709\) −17963.1 10371.0i −0.951507 0.549353i −0.0579583 0.998319i \(-0.518459\pi\)
−0.893549 + 0.448966i \(0.851792\pi\)
\(710\) 3888.74i 0.205552i
\(711\) 0 0
\(712\) 2206.97 + 3822.58i 0.116165 + 0.201204i
\(713\) 3923.10 2265.00i 0.206061 0.118969i
\(714\) 0 0
\(715\) 2430.79 3917.70i 0.127142 0.204914i
\(716\) 4589.63 0.239556
\(717\) 0 0
\(718\) 5577.32 + 9660.21i 0.289894 + 0.502111i
\(719\) −12675.1 + 21953.9i −0.657443 + 1.13872i 0.323832 + 0.946114i \(0.395029\pi\)
−0.981275 + 0.192610i \(0.938305\pi\)
\(720\) 0 0
\(721\) −4011.87 2316.25i −0.207226 0.119642i
\(722\) −12073.3 6970.50i −0.622328 0.359301i
\(723\) 0 0
\(724\) 9615.97 16655.3i 0.493611 0.854960i
\(725\) 9262.22 + 16042.6i 0.474469 + 0.821805i
\(726\) 0 0
\(727\) −33428.2 −1.70534 −0.852672 0.522447i \(-0.825019\pi\)
−0.852672 + 0.522447i \(0.825019\pi\)
\(728\) −1290.95 40.9778i −0.0657220 0.00208618i
\(729\) 0 0
\(730\) 4244.30 2450.45i 0.215190 0.124240i
\(731\) −1845.20 3195.97i −0.0933612 0.161706i
\(732\) 0 0
\(733\) 3842.67i 0.193632i −0.995302 0.0968160i \(-0.969134\pi\)
0.995302 0.0968160i \(-0.0308658\pi\)
\(734\) 37398.8 + 21592.2i 1.88067 + 1.08581i
\(735\) 0 0
\(736\) 30908.3i 1.54796i
\(737\) −921.946 + 1596.86i −0.0460791 + 0.0798114i
\(738\) 0 0
\(739\) −25140.4 + 14514.8i −1.25143 + 0.722511i −0.971393 0.237479i \(-0.923679\pi\)
−0.280034 + 0.959990i \(0.590346\pi\)
\(740\) 8991.91 0.446688
\(741\) 0 0
\(742\) 19166.3 0.948269
\(743\) 30308.0 17498.3i 1.49649 0.864000i 0.496500 0.868037i \(-0.334618\pi\)
0.999992 + 0.00403656i \(0.00128488\pi\)
\(744\) 0 0
\(745\) −580.199 + 1004.93i −0.0285327 + 0.0494200i
\(746\) 52623.2i 2.58267i
\(747\) 0 0
\(748\) −7253.99 4188.10i −0.354589 0.204722i
\(749\) 2711.23i 0.132265i
\(750\) 0 0
\(751\) 5227.06 + 9053.52i 0.253979 + 0.439904i 0.964618 0.263653i \(-0.0849274\pi\)
−0.710639 + 0.703557i \(0.751594\pi\)
\(752\) 24672.3 14244.5i 1.19642 0.690751i
\(753\) 0 0
\(754\) −981.712 + 30927.4i −0.0474162 + 1.49378i
\(755\) −4628.32 −0.223102
\(756\) 0 0
\(757\) 14065.2 + 24361.6i 0.675308 + 1.16967i 0.976379 + 0.216065i \(0.0693225\pi\)
−0.301071 + 0.953602i \(0.597344\pi\)
\(758\) 4778.73 8277.00i 0.228986 0.396615i
\(759\) 0 0
\(760\) −1102.09 636.292i −0.0526014 0.0303694i
\(761\) −18261.9 10543.5i −0.869899 0.502236i −0.00258400 0.999997i \(-0.500823\pi\)
−0.867315 + 0.497761i \(0.834156\pi\)
\(762\) 0 0
\(763\) −1602.36 + 2775.37i −0.0760280 + 0.131684i
\(764\) −18259.8 31627.0i −0.864683 1.49768i
\(765\) 0 0
\(766\) −8177.54 −0.385727
\(767\) −976.309 + 30757.2i −0.0459615 + 1.44795i
\(768\) 0 0
\(769\) 16911.7 9763.96i 0.793044 0.457864i −0.0479893 0.998848i \(-0.515281\pi\)
0.841033 + 0.540984i \(0.181948\pi\)
\(770\) 1355.25 + 2347.36i 0.0634283 + 0.109861i
\(771\) 0 0
\(772\) 7860.55i 0.366460i
\(773\) −25419.6 14676.0i −1.18277 0.682870i −0.226113 0.974101i \(-0.572602\pi\)
−0.956653 + 0.291231i \(0.905935\pi\)
\(774\) 0 0
\(775\) 4404.64i 0.204154i
\(776\) 3616.96 6264.76i 0.167321 0.289809i
\(777\) 0 0
\(778\) 11585.2 6688.73i 0.533869 0.308229i
\(779\) −5675.42 −0.261031
\(780\) 0 0
\(781\) 9972.54 0.456908
\(782\) −12261.4 + 7079.13i −0.560700 + 0.323720i
\(783\)