Properties

Label 117.4.q.d.82.1
Level $117$
Weight $4$
Character 117.82
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 82.1
Root \(-3.57071 - 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.d.10.1

$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

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

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 −0.288892 0.957362i \(-0.593287\pi\)
−0.973546 + 0.228493i \(0.926620\pi\)
\(3\) 0 0
\(4\) 4.50000 + 7.79423i 0.562500 + 0.974279i
\(5\) 3.05006i 0.272806i −0.990653 0.136403i \(-0.956446\pi\)
0.990653 0.136403i \(-0.0435541\pi\)
\(6\) 0 0
\(7\) −5.78786 + 3.34162i −0.312515 + 0.180431i −0.648051 0.761597i \(-0.724416\pi\)
0.335536 + 0.942027i \(0.391082\pi\)
\(8\) 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 0.831283 0.555849i \(-0.187607\pi\)
−0.0657380 + 0.997837i \(0.520940\pi\)
\(12\) 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 0.950406 0.311011i \(-0.100668\pi\)
−0.744547 + 0.667571i \(0.767334\pi\)
\(18\) 0 0
\(19\) 87.6364 50.5969i 1.05817 0.610933i 0.133242 0.991083i \(-0.457461\pi\)
0.924925 + 0.380150i \(0.124128\pi\)
\(20\) 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 −0.459566 0.888144i \(-0.651995\pi\)
0.998938 0.0460765i \(-0.0146718\pi\)
\(24\) 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 −0.487273 0.873250i \(-0.662008\pi\)
0.999893 0.0146339i \(-0.00465827\pi\)
\(30\) 0 0
\(31\) 38.0705i 0.220570i 0.993900 + 0.110285i \(0.0351763\pi\)
−0.993900 + 0.110285i \(0.964824\pi\)
\(32\) −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 0.973164 0.230114i \(-0.0739099\pi\)
0.287297 + 0.957841i \(0.407243\pi\)
\(38\) −417.233 −1.78116
\(39\) 0 0
\(40\) −12.5757 −0.0497099
\(41\) −48.5707 28.0423i −0.185011 0.106816i 0.404634 0.914479i \(-0.367399\pi\)
−0.589645 + 0.807662i \(0.700732\pi\)
\(42\) 0 0
\(43\) 63.9393 + 110.746i 0.226759 + 0.392759i 0.956846 0.290596i \(-0.0938536\pi\)
−0.730087 + 0.683355i \(0.760520\pi\)
\(44\) 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 \(0.297183\pi\)
−0.594923 + 0.803783i \(0.702817\pi\)
\(48\) 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 −0.972018 0.234906i \(-0.924522\pi\)
−0.282574 + 0.959245i \(0.591188\pi\)
\(60\) 0 0
\(61\) −350.652 607.347i −0.736007 1.27480i −0.954280 0.298913i \(-0.903376\pi\)
0.218274 0.975888i \(-0.429957\pi\)
\(62\) 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 0.454177 0.890912i \(-0.349933\pi\)
−0.544464 + 0.838784i \(0.683267\pi\)
\(68\) −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 −0.259199 0.965824i \(-0.583458\pi\)
0.706829 + 0.707385i \(0.250125\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i −0.949946 0.312413i \(-0.898863\pi\)
0.949946 0.312413i \(-0.101137\pi\)
\(74\) −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 \(0.150121\pi\)
−0.890834 + 0.454328i \(0.849879\pi\)
\(84\) 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 0.937321 0.348467i \(-0.113298\pi\)
0.166879 + 0.985977i \(0.446631\pi\)
\(90\) 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 −0.597230 + 0.802070i \(0.703732\pi\)
−0.993228 + 0.116182i \(0.962935\pi\)
\(98\) 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 −0.663907 0.747815i \(-0.731103\pi\)
0.979580 + 0.201053i \(0.0644364\pi\)
\(102\) 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 −0.942990 0.332822i \(-0.891999\pi\)
0.759727 + 0.650242i \(0.225332\pi\)
\(108\) 0 0
\(109\) 479.516i 0.421370i 0.977554 + 0.210685i \(0.0675694\pi\)
−0.977554 + 0.210685i \(0.932431\pi\)
\(110\) −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 −0.984527 0.175235i \(-0.943932\pi\)
0.340506 0.940242i \(-0.389402\pi\)
\(114\) 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 −0.0114416 + 0.999935i \(0.503642\pi\)
−0.860248 + 0.509876i \(0.829691\pi\)
\(128\) −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 −0.443286 0.896380i \(-0.646187\pi\)
0.554645 + 0.832087i \(0.312854\pi\)
\(138\) 0 0
\(139\) 50.0000 + 86.6025i 0.0305104 + 0.0528456i 0.880877 0.473344i \(-0.156953\pi\)
−0.850367 + 0.526190i \(0.823620\pi\)
\(140\) −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 −0.406680 0.913571i \(-0.633314\pi\)
0.587835 + 0.808981i \(0.299980\pi\)
\(150\) 0 0
\(151\) 1517.45i 0.817805i −0.912578 0.408902i \(-0.865912\pi\)
0.912578 0.408902i \(-0.134088\pi\)
\(152\) −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 0.0740844 0.997252i \(-0.476397\pi\)
0.900688 + 0.434467i \(0.143063\pi\)
\(164\) 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 0.491938 0.870630i \(-0.336289\pi\)
−0.508019 + 0.861346i \(0.669622\pi\)
\(168\) 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 0.576304 0.817235i \(-0.304494\pi\)
−0.995899 + 0.0904765i \(0.971161\pi\)
\(174\) 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 −0.807868 0.589363i \(-0.799379\pi\)
0.914338 + 0.404953i \(0.132712\pi\)
\(180\) 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 0.938318 + 0.345773i \(0.112383\pi\)
−0.169711 + 0.985494i \(0.554283\pi\)
\(192\) 0 0
\(193\) −756.381 436.697i −0.282101 0.162871i 0.352273 0.935897i \(-0.385409\pi\)
−0.634374 + 0.773026i \(0.718742\pi\)
\(194\) 7233.92 2.67714
\(195\) 0 0
\(196\) −2685.01 −0.978502
\(197\) −3591.62 2073.62i −1.29895 0.749947i −0.318724 0.947848i \(-0.603254\pi\)
−0.980222 + 0.197901i \(0.936588\pi\)
\(198\) 0 0
\(199\) −1202.03 2081.98i −0.428189 0.741646i 0.568523 0.822667i \(-0.307515\pi\)
−0.996712 + 0.0810216i \(0.974182\pi\)
\(200\) 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 0.356174 + 0.934420i \(0.384081\pi\)
−0.987318 + 0.158754i \(0.949252\pi\)
\(212\) 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 0.819041 0.573735i \(-0.194506\pi\)
−0.0873487 + 0.996178i \(0.527839\pi\)
\(224\) 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 −0.947449 0.319907i \(-0.896348\pi\)
−0.196677 + 0.980468i \(0.563015\pi\)
\(228\) 0 0
\(229\) 1305.27i 0.376658i −0.982106 0.188329i \(-0.939693\pi\)
0.982106 0.188329i \(-0.0603070\pi\)
\(230\) 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 \(-0.778499\pi\)
0.767499 0.641050i \(-0.221501\pi\)
\(240\) 0 0
\(241\) 4144.17 2392.64i 1.10767 0.639516i 0.169448 0.985539i \(-0.445801\pi\)
0.938226 + 0.346023i \(0.112468\pi\)
\(242\) 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 0.995069 0.0991805i \(-0.0316221\pi\)
−0.583428 + 0.812165i \(0.698289\pi\)
\(252\) 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 −0.128835 0.991666i \(-0.541124\pi\)
0.923226 0.384258i \(-0.125543\pi\)
\(258\) 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 −0.860809 0.508928i \(-0.830042\pi\)
0.871149 + 0.491019i \(0.163375\pi\)
\(264\) 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 −0.999884 0.0152033i \(-0.995160\pi\)
0.486776 0.873527i \(-0.338173\pi\)
\(270\) 0 0
\(271\) −7206.91 4160.91i −1.61546 0.932684i −0.988075 0.153971i \(-0.950794\pi\)
−0.627380 0.778713i \(-0.715873\pi\)
\(272\) 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 0.666408 0.745587i \(-0.267831\pi\)
−0.978901 + 0.204333i \(0.934497\pi\)
\(278\) 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 \(0.0966942\pi\)
−0.954214 + 0.299123i \(0.903306\pi\)
\(282\) 0 0
\(283\) 132.301 229.152i 0.0277896 0.0481330i −0.851796 0.523873i \(-0.824486\pi\)
0.879586 + 0.475740i \(0.157820\pi\)
\(284\) 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 −0.822509 0.568751i \(-0.807427\pi\)
0.0812984 + 0.996690i \(0.474093\pi\)
\(294\) 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 \(0.226536\pi\)
−0.757263 + 0.653110i \(0.773464\pi\)
\(308\) −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 \(-0.860749\pi\)
0.905827 0.423648i \(-0.139251\pi\)
\(318\) 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 −0.970476 0.241199i \(-0.922459\pi\)
−0.276353 + 0.961056i \(0.589126\pi\)
\(332\) −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 −0.685711 0.727874i \(-0.740509\pi\)
−0.287501 0.957780i \(-0.592825\pi\)
\(348\) 0 0
\(349\) 7760.61 + 4480.59i 1.19030 + 0.687222i 0.958375 0.285511i \(-0.0921633\pi\)
0.231928 + 0.972733i \(0.425497\pi\)
\(350\) 3188.12 0.486892
\(351\) 0 0
\(352\) −8377.11 −1.26847
\(353\) 4640.16 + 2679.00i 0.699634 + 0.403934i 0.807211 0.590263i \(-0.200976\pi\)
−0.107577 + 0.994197i \(0.534309\pi\)
\(354\) 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 \(0.0637257\pi\)
−0.980027 + 0.198866i \(0.936274\pi\)
\(360\) 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 0.205403 + 0.978678i \(0.434150\pi\)
−0.950261 + 0.311455i \(0.899184\pi\)
\(368\) −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 0.844737 + 0.535182i \(0.179757\pi\)
0.0411127 + 0.999155i \(0.486910\pi\)
\(374\) 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 0.357755 0.933816i \(-0.383542\pi\)
−0.629831 + 0.776733i \(0.716876\pi\)
\(380\) 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 −0.381027 0.924564i \(-0.624429\pi\)
0.610183 + 0.792261i \(0.291096\pi\)
\(384\) 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 −0.279863 0.960040i \(-0.590289\pi\)
0.691487 + 0.722389i \(0.256956\pi\)
\(398\) 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 0.388401 0.921490i \(-0.373027\pi\)
−0.603833 + 0.797110i \(0.706361\pi\)
\(402\) 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 −0.202735 0.979234i \(-0.564983\pi\)
0.746674 + 0.665190i \(0.231650\pi\)
\(410\) 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 −0.993443 0.114328i \(-0.963529\pi\)
0.595732 + 0.803183i \(0.296862\pi\)
\(420\) 0 0
\(421\) 7537.70i 0.872601i −0.899801 0.436300i \(-0.856288\pi\)
0.899801 0.436300i \(-0.143712\pi\)
\(422\) 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 0.979945 0.199268i \(-0.0638565\pi\)
0.317401 + 0.948291i \(0.397190\pi\)
\(432\) 0 0
\(433\) −8857.97 15342.5i −0.983110 1.70280i −0.650050 0.759892i \(-0.725252\pi\)
−0.333061 0.942905i \(-0.608081\pi\)
\(434\) 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 −0.602968 0.797765i \(-0.706015\pi\)
0.992369 + 0.123303i \(0.0393488\pi\)
\(440\) −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 0.563179 0.826335i \(-0.309578\pi\)
0.997217 0.0745603i \(-0.0237553\pi\)
\(450\) 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 0.970933 0.239351i \(-0.0769346\pi\)
0.278183 + 0.960528i \(0.410268\pi\)
\(458\) −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 −0.622361 0.782730i \(-0.713826\pi\)
0.366684 + 0.930346i \(0.380493\pi\)
\(462\) 0 0
\(463\) 2072.61i 0.208040i −0.994575 0.104020i \(-0.966829\pi\)
0.994575 0.104020i \(-0.0331706\pi\)
\(464\) −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 0.268614 0.963248i \(-0.413434\pi\)
−0.699890 + 0.714250i \(0.746768\pi\)
\(480\) 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 0.0812808 0.996691i \(-0.474099\pi\)
0.903800 + 0.427954i \(0.140766\pi\)
\(488\) −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 −0.0798720 + 0.996805i \(0.525451\pi\)
−0.823323 + 0.567574i \(0.807882\pi\)
\(492\) 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 \(0.176093\pi\)
−0.850842 + 0.525422i \(0.823907\pi\)
\(500\) 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 0.995896 + 0.0905104i \(0.0288498\pi\)
−0.419563 + 0.907726i \(0.637817\pi\)
\(504\) 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 0.687294 0.726379i \(-0.258798\pi\)
−0.285416 + 0.958404i \(0.592132\pi\)
\(510\) 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 −0.755528 0.655116i \(-0.772620\pi\)
0.945111 + 0.326749i \(0.105953\pi\)
\(524\) −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 \(-0.933948\pi\)
0.978547 0.206022i \(-0.0660519\pi\)
\(542\) 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 −0.342586 0.939486i \(-0.611303\pi\)
−0.984912 + 0.173055i \(0.944636\pi\)
\(558\) 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 −0.991273 0.131824i \(-0.957917\pi\)
0.381474 0.924380i \(-0.375417\pi\)
\(564\) 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 −0.991818 0.127662i \(-0.959253\pi\)
0.606468 + 0.795108i \(0.292586\pi\)
\(570\) 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 \(-0.945928\pi\)
0.985606 0.169056i \(-0.0540718\pi\)
\(578\) −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 0.0844601 0.996427i \(-0.473083\pi\)
−0.820701 + 0.571358i \(0.806417\pi\)
\(588\) 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 \(-0.931853\pi\)
0.977170 0.212457i \(-0.0681466\pi\)
\(594\) 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 0.366441 + 0.930441i \(0.380576\pi\)
−0.989006 + 0.147873i \(0.952757\pi\)
\(602\) 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 0.638456 0.769658i \(-0.279573\pi\)
−0.985772 + 0.168090i \(0.946240\pi\)
\(608\) −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 0.476872 0.878973i \(-0.341770\pi\)
−0.522777 + 0.852470i \(0.675104\pi\)
\(614\) 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 −0.00405239 0.999992i \(-0.501290\pi\)
0.863992 + 0.503505i \(0.167957\pi\)
\(618\) 0 0
\(619\) 11462.5i 0.744291i −0.928174 0.372145i \(-0.878622\pi\)
0.928174 0.372145i \(-0.121378\pi\)
\(620\) 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 −0.617085 0.786896i \(-0.711687\pi\)
0.372930 + 0.927860i \(0.378353\pi\)
\(632\) 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 0.755756 0.654854i \(-0.227270\pi\)
−0.944998 + 0.327077i \(0.893936\pi\)
\(642\) 0 0
\(643\) −17959.8 + 10369.1i −1.10150 + 0.635951i −0.936615 0.350361i \(-0.886059\pi\)
−0.164886 + 0.986313i \(0.552726\pi\)
\(644\) −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 −0.878689 0.477395i \(-0.841581\pi\)
0.852781 + 0.522269i \(0.174914\pi\)
\(648\) 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 −0.954841 0.297118i \(-0.903974\pi\)
0.734732 + 0.678357i \(0.237308\pi\)
\(654\) 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 0.989665 0.143396i \(-0.0458022\pi\)
−0.619017 + 0.785378i \(0.712469\pi\)
\(660\) 0 0
\(661\) 1942.45 + 1121.48i 0.114301 + 0.0659915i 0.556060 0.831142i \(-0.312312\pi\)
−0.441760 + 0.897133i \(0.645646\pi\)
\(662\) 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 −0.926280 0.376837i \(-0.877012\pi\)
0.789490 + 0.613763i \(0.210345\pi\)
\(674\) 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 −0.947355 0.320186i \(-0.896255\pi\)
−0.196388 + 0.980526i \(0.562921\pi\)
\(684\) 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 0.170221 0.985406i \(-0.445552\pi\)
−0.768276 + 0.640118i \(0.778885\pi\)
\(692\) 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 −0.893549 0.448966i \(-0.851792\pi\)
−0.0579583 + 0.998319i \(0.518459\pi\)
\(710\) 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 −0.981275 0.192610i \(-0.938305\pi\)
0.323832 0.946114i \(-0.395029\pi\)
\(720\) 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 \(0.0308658\pi\)
−0.995302 + 0.0968160i \(0.969134\pi\)
\(734\) 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 −0.280034 0.959990i \(-0.590346\pi\)
−0.971393 + 0.237479i \(0.923679\pi\)
\(740\) 8991.91 0.446688
\(741\) 0 0
\(742\) 19166.3 0.948269
\(743\) 30308.0 + 17498.3i 1.49649 + 0.864000i 0.999992 0.00403656i \(-0.00128488\pi\)
0.496500 + 0.868037i \(0.334618\pi\)
\(744\) 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 −0.710639 0.703557i \(-0.751594\pi\)
0.964618 + 0.263653i \(0.0849274\pi\)
\(752\) 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 −0.301071 0.953602i \(-0.597344\pi\)
0.976379 0.216065i \(-0.0693225\pi\)
\(758\) 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 −0.867315 0.497761i \(-0.834156\pi\)
−0.00258400 + 0.999997i \(0.500823\pi\)
\(762\) 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 0.841033 0.540984i \(-0.181948\pi\)
−0.0479893 + 0.998848i \(0.515281\pi\)
\(770\) 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 −0.956653 0.291231i \(-0.905935\pi\)
−0.226113 + 0.974101i \(0.572602\pi\)
\(774\) 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