Properties

Label 39.4.j.b.4.2
Level $39$
Weight $4$
Character 39.4
Analytic conductor $2.301$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Root \(3.57071 + 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 39.4
Dual form 39.4.j.b.10.2

$q$-expansion

\(f(q)\) \(=\) \(q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(3.57071 + 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} +3.05006i q^{5} +(10.7121 - 6.18466i) q^{6} +(-5.78786 + 3.34162i) q^{7} +4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.28786 + 10.8909i) q^{10} +(-27.9293 - 16.1250i) q^{11} +27.0000 q^{12} +(-22.1364 + 41.3156i) q^{13} -27.5557 q^{14} +(7.92429 + 4.57509i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-14.4293 - 24.9923i) q^{17} -37.1080i q^{18} +(87.6364 - 50.5969i) q^{19} +(-23.7729 + 13.7253i) q^{20} +20.0497i q^{21} +(-66.4850 - 115.155i) q^{22} +(-59.4950 + 103.048i) q^{23} +(10.7121 + 6.18466i) q^{24} +115.697 q^{25} +(-164.217 + 101.891i) q^{26} -27.0000 q^{27} +(-52.0907 - 30.0746i) q^{28} +(-80.0557 + 138.661i) q^{29} +(18.8636 + 32.6727i) q^{30} +38.0705i q^{31} +(224.955 - 129.878i) q^{32} +(-83.7879 + 48.3749i) q^{33} -118.987i q^{34} +(-10.1921 - 17.6533i) q^{35} +(40.5000 - 70.1481i) q^{36} +(283.682 + 163.784i) q^{37} +417.233 q^{38} +(74.1364 + 119.486i) q^{39} -12.5757 q^{40} +(48.5707 + 28.0423i) q^{41} +(-41.3336 + 71.5918i) q^{42} +(63.9393 + 110.746i) q^{43} -290.250i q^{44} +(23.7729 - 13.7253i) q^{45} +(-424.879 + 245.304i) q^{46} -517.983i q^{47} +(-82.5000 - 142.894i) q^{48} +(-149.167 + 258.365i) q^{49} +(413.121 + 238.516i) q^{50} -86.5757 q^{51} +(-421.637 + 13.3838i) q^{52} -695.546 q^{53} +(-96.4093 - 55.6619i) q^{54} +(49.1821 - 85.1860i) q^{55} +(-13.7779 - 23.8639i) q^{56} -303.581i q^{57} +(-571.712 + 330.078i) q^{58} +(568.566 - 328.262i) q^{59} +82.3516i q^{60} +(-350.652 - 607.347i) q^{61} +(-78.4843 + 135.939i) q^{62} +(52.0907 + 30.0746i) q^{63} +631.000 q^{64} +(-126.015 - 67.5174i) q^{65} -398.910 q^{66} +(-49.5150 - 28.5875i) q^{67} +(129.864 - 224.930i) q^{68} +(178.485 + 309.145i) q^{69} -84.0465i q^{70} +(-267.798 + 154.613i) q^{71} +(32.1364 - 18.5540i) q^{72} -389.711i q^{73} +(675.299 + 1169.65i) q^{74} +(173.546 - 300.590i) q^{75} +(788.728 + 455.372i) q^{76} +215.534 q^{77} +(18.3943 + 579.485i) q^{78} +901.820 q^{79} +(145.279 + 83.8766i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(115.621 + 200.262i) q^{82} -687.095i q^{83} +(-156.272 + 90.2238i) q^{84} +(76.2279 - 44.0102i) q^{85} +527.257i q^{86} +(240.167 + 415.982i) q^{87} +(66.4850 - 115.155i) q^{88} +(-927.113 - 535.269i) q^{89} +113.181 q^{90} +(-9.93858 - 313.100i) q^{91} -1070.91 q^{92} +(98.9100 + 57.1057i) q^{93} +(1067.85 - 1849.57i) q^{94} +(154.324 + 267.296i) q^{95} -779.267i q^{96} +(-1519.43 + 877.242i) q^{97} +(-1065.27 + 615.032i) q^{98} +290.250i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 \(-0.0733797\pi\)
0.288892 + 0.957362i \(0.406713\pi\)
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 4.50000 + 7.79423i 0.562500 + 0.974279i
\(5\) 3.05006i 0.272806i 0.990653 + 0.136403i \(0.0435541\pi\)
−0.990653 + 0.136403i \(0.956446\pi\)
\(6\) 10.7121 6.18466i 0.728869 0.420813i
\(7\) −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
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −6.28786 + 10.8909i −0.198840 + 0.344400i
\(11\) −27.9293 16.1250i −0.765545 0.441988i 0.0657380 0.997837i \(-0.479060\pi\)
−0.831283 + 0.555849i \(0.812393\pi\)
\(12\) 27.0000 0.649519
\(13\) −22.1364 + 41.3156i −0.472272 + 0.881453i
\(14\) −27.5557 −0.526041
\(15\) 7.92429 + 4.57509i 0.136403 + 0.0787522i
\(16\) 27.5000 47.6314i 0.429688 0.744241i
\(17\) −14.4293 24.9923i −0.205860 0.356560i 0.744547 0.667571i \(-0.232666\pi\)
−0.950406 + 0.311011i \(0.899332\pi\)
\(18\) 37.1080i 0.485913i
\(19\) 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
\(21\) 20.0497i 0.208343i
\(22\) −66.4850 115.155i −0.644302 1.11596i
\(23\) −59.4950 + 103.048i −0.539372 + 0.934220i 0.459566 + 0.888144i \(0.348005\pi\)
−0.998938 + 0.0460765i \(0.985328\pi\)
\(24\) 10.7121 + 6.18466i 0.0911086 + 0.0526016i
\(25\) 115.697 0.925577
\(26\) −164.217 + 101.891i −1.23868 + 0.768555i
\(27\) −27.0000 −0.192450
\(28\) −52.0907 30.0746i −0.351579 0.202984i
\(29\) −80.0557 + 138.661i −0.512620 + 0.887883i 0.487273 + 0.873250i \(0.337992\pi\)
−0.999893 + 0.0146339i \(0.995342\pi\)
\(30\) 18.8636 + 32.6727i 0.114800 + 0.198840i
\(31\) 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
\(33\) −83.7879 + 48.3749i −0.441988 + 0.255182i
\(34\) 118.987i 0.600179i
\(35\) −10.1921 17.6533i −0.0492225 0.0852558i
\(36\) 40.5000 70.1481i 0.187500 0.324760i
\(37\) 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
\(39\) 74.1364 + 119.486i 0.304393 + 0.490590i
\(40\) −12.5757 −0.0497099
\(41\) 48.5707 + 28.0423i 0.185011 + 0.106816i 0.589645 0.807662i \(-0.299268\pi\)
−0.404634 + 0.914479i \(0.632601\pi\)
\(42\) −41.3336 + 71.5918i −0.151855 + 0.263021i
\(43\) 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
\(45\) 23.7729 13.7253i 0.0787522 0.0454676i
\(46\) −424.879 + 245.304i −1.36185 + 0.786264i
\(47\) 517.983i 1.60757i −0.594923 0.803783i \(-0.702817\pi\)
0.594923 0.803783i \(-0.297183\pi\)
\(48\) −82.5000 142.894i −0.248080 0.429688i
\(49\) −149.167 + 258.365i −0.434890 + 0.753251i
\(50\) 413.121 + 238.516i 1.16848 + 0.674624i
\(51\) −86.5757 −0.237706
\(52\) −421.637 + 13.3838i −1.12443 + 0.0356923i
\(53\) −695.546 −1.80265 −0.901326 0.433141i \(-0.857405\pi\)
−0.901326 + 0.433141i \(0.857405\pi\)
\(54\) −96.4093 55.6619i −0.242956 0.140271i
\(55\) 49.1821 85.1860i 0.120577 0.208845i
\(56\) −13.7779 23.8639i −0.0328776 0.0569456i
\(57\) 303.581i 0.705445i
\(58\) −571.712 + 330.078i −1.29430 + 0.747265i
\(59\) 568.566 328.262i 1.25459 0.724339i 0.282574 0.959245i \(-0.408812\pi\)
0.972018 + 0.234906i \(0.0754783\pi\)
\(60\) 82.3516i 0.177192i
\(61\) −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
\(63\) 52.0907 + 30.0746i 0.104172 + 0.0601435i
\(64\) 631.000 1.23242
\(65\) −126.015 67.5174i −0.240465 0.128839i
\(66\) −398.910 −0.743976
\(67\) −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
\(69\) 178.485 + 309.145i 0.311407 + 0.539372i
\(70\) 84.0465i 0.143507i
\(71\) −267.798 + 154.613i −0.447630 + 0.258440i −0.706829 0.707385i \(-0.749875\pi\)
0.259199 + 0.965824i \(0.416542\pi\)
\(72\) 32.1364 18.5540i 0.0526016 0.0303695i
\(73\) 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
\(75\) 173.546 300.590i 0.267191 0.462789i
\(76\) 788.728 + 455.372i 1.19044 + 0.687300i
\(77\) 215.534 0.318992
\(78\) 18.3943 + 579.485i 0.0267018 + 0.841202i
\(79\) 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
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 115.621 + 200.262i 0.155710 + 0.269698i
\(83\) 687.095i 0.908657i −0.890834 0.454328i \(-0.849879\pi\)
0.890834 0.454328i \(-0.150121\pi\)
\(84\) −156.272 + 90.2238i −0.202984 + 0.117193i
\(85\) 76.2279 44.0102i 0.0972714 0.0561597i
\(86\) 527.257i 0.661111i
\(87\) 240.167 + 415.982i 0.295961 + 0.512620i
\(88\) 66.4850 115.155i 0.0805378 0.139496i
\(89\) −927.113 535.269i −1.10420 0.637510i −0.166879 0.985977i \(-0.553369\pi\)
−0.937321 + 0.348467i \(0.886702\pi\)
\(90\) 113.181 0.132560
\(91\) −9.93858 313.100i −0.0114489 0.360679i
\(92\) −1070.91 −1.21359
\(93\) 98.9100 + 57.1057i 0.110285 + 0.0636730i
\(94\) 1067.85 1849.57i 1.17170 2.02945i
\(95\) 154.324 + 267.296i 0.166666 + 0.288674i
\(96\) 779.267i 0.828475i
\(97\) −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
\(99\) 290.250i 0.294658i
\(100\) 520.637 + 901.770i 0.520637 + 0.901770i
\(101\) −320.420 + 554.984i −0.315673 + 0.546762i −0.979580 0.201053i \(-0.935564\pi\)
0.663907 + 0.747815i \(0.268897\pi\)
\(102\) −309.137 178.480i −0.300090 0.173257i
\(103\) 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
\(105\) −61.1528 −0.0568372
\(106\) −2483.59 1433.90i −2.27574 1.31390i
\(107\) 202.838 351.325i 0.183262 0.317420i −0.759727 0.650242i \(-0.774668\pi\)
0.942990 + 0.332822i \(0.108001\pi\)
\(108\) −121.500 210.444i −0.108253 0.187500i
\(109\) 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
\(111\) 851.046 491.352i 0.727727 0.420154i
\(112\) 367.578i 0.310115i
\(113\) 773.602 + 1339.92i 0.644021 + 1.11548i 0.984527 + 0.175235i \(0.0560684\pi\)
−0.340506 + 0.940242i \(0.610598\pi\)
\(114\) 625.849 1084.00i 0.514177 0.890580i
\(115\) −314.304 181.463i −0.254861 0.147144i
\(116\) −1441.00 −1.15339
\(117\) 421.637 13.3838i 0.333166 0.0105755i
\(118\) 2706.91 2.11179
\(119\) 167.029 + 96.4344i 0.128668 + 0.0742868i
\(120\) −18.8636 + 32.6727i −0.0143500 + 0.0248549i
\(121\) −145.470 251.961i −0.109294 0.189302i
\(122\) 2891.55i 2.14581i
\(123\) 145.712 84.1269i 0.106816 0.0616705i
\(124\) −296.730 + 171.317i −0.214896 + 0.124070i
\(125\) 734.140i 0.525308i
\(126\) 124.001 + 214.776i 0.0876735 + 0.151855i
\(127\) −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
\(129\) 383.636 0.261839
\(130\) −310.773 500.872i −0.209666 0.337918i
\(131\) 43.7571 0.0291838 0.0145919 0.999894i \(-0.495355\pi\)
0.0145919 + 0.999894i \(0.495355\pi\)
\(132\) −754.091 435.374i −0.497236 0.287079i
\(133\) −338.151 + 585.695i −0.220462 + 0.381851i
\(134\) −117.869 204.156i −0.0759877 0.131615i
\(135\) 82.3516i 0.0525015i
\(136\) 103.046 59.4935i 0.0649713 0.0375112i
\(137\) −178.569 + 103.097i −0.111359 + 0.0642932i −0.554645 0.832087i \(-0.687146\pi\)
0.443286 + 0.896380i \(0.353813\pi\)
\(138\) 1471.83i 0.907899i
\(139\) 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
\(141\) −1345.76 776.974i −0.803783 0.464064i
\(142\) −1274.97 −0.753474
\(143\) 1284.47 796.966i 0.751137 0.466053i
\(144\) −495.000 −0.286458
\(145\) −422.923 244.175i −0.242220 0.139846i
\(146\) 803.411 1391.55i 0.455416 0.788804i
\(147\) 447.501 + 775.095i 0.251084 + 0.434890i
\(148\) 2948.11i 1.63739i
\(149\) −329.480 + 190.225i −0.181155 + 0.104590i −0.587835 0.808981i \(-0.700020\pi\)
0.406680 + 0.913571i \(0.366686\pi\)
\(150\) 1239.36 715.547i 0.674624 0.389495i
\(151\) 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
\(153\) −129.864 + 224.930i −0.0686199 + 0.118853i
\(154\) 769.611 + 444.335i 0.402708 + 0.232504i
\(155\) −116.117 −0.0601726
\(156\) −597.684 + 1115.52i −0.306750 + 0.572520i
\(157\) 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
\(159\) −1043.32 + 1807.08i −0.520381 + 0.901326i
\(160\) 396.135 + 686.126i 0.195733 + 0.339019i
\(161\) 795.239i 0.389277i
\(162\) −289.228 + 166.986i −0.140271 + 0.0809854i
\(163\) 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
\(165\) −147.546 255.558i −0.0696150 0.120577i
\(166\) 1416.48 2453.42i 0.662292 1.14712i
\(167\) 34.7043 + 20.0365i 0.0160808 + 0.00928428i 0.508019 0.861346i \(-0.330378\pi\)
−0.491938 + 0.870630i \(0.663711\pi\)
\(168\) −82.6671 −0.0379637
\(169\) −1216.96 1829.16i −0.553918 0.832571i
\(170\) 362.917 0.163732
\(171\) −788.728 455.372i −0.352722 0.203644i
\(172\) −575.454 + 996.715i −0.255104 + 0.441853i
\(173\) 954.770 + 1653.71i 0.419594 + 0.726759i 0.995899 0.0904765i \(-0.0288390\pi\)
−0.576304 + 0.817235i \(0.695506\pi\)
\(174\) 1980.47i 0.862868i
\(175\) −669.639 + 386.616i −0.289257 + 0.167002i
\(176\) −1536.11 + 886.874i −0.657890 + 0.379833i
\(177\) 1969.57i 0.836395i
\(178\) −2206.97 3822.58i −0.929322 1.60963i
\(179\) −254.979 + 441.637i −0.106470 + 0.184411i −0.914338 0.404953i \(-0.867288\pi\)
0.807868 + 0.589363i \(0.200621\pi\)
\(180\) 213.956 + 123.527i 0.0885962 + 0.0511510i
\(181\) 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
\(183\) −2103.91 −0.849867
\(184\) −424.879 245.304i −0.170231 0.0982830i
\(185\) −499.551 + 865.247i −0.198528 + 0.343861i
\(186\) 235.453 + 407.816i 0.0928185 + 0.160766i
\(187\) 930.688i 0.363950i
\(188\) 4037.28 2330.92i 1.56622 0.904256i
\(189\) 156.272 90.2238i 0.0601435 0.0347239i
\(190\) 1272.58i 0.485911i
\(191\) −2028.87 3514.11i −0.768607 1.33127i −0.938318 0.345773i \(-0.887617\pi\)
0.169711 0.985494i \(-0.445717\pi\)
\(192\) 946.500 1639.39i 0.355770 0.616211i
\(193\) −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
\(195\) −364.438 + 226.120i −0.133836 + 0.0830401i
\(196\) −2685.01 −0.978502
\(197\) 3591.62 + 2073.62i 1.29895 + 0.749947i 0.980222 0.197901i \(-0.0634124\pi\)
0.318724 + 0.947848i \(0.396746\pi\)
\(198\) −598.365 + 1036.40i −0.214767 + 0.371988i
\(199\) −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
\(201\) −148.545 + 85.7625i −0.0521271 + 0.0300956i
\(202\) −2288.26 + 1321.13i −0.797035 + 0.460169i
\(203\) 1070.06i 0.369969i
\(204\) −389.591 674.791i −0.133710 0.231592i
\(205\) −85.5307 + 148.144i −0.0291401 + 0.0504722i
\(206\) 2475.05 + 1428.97i 0.837111 + 0.483307i
\(207\) 1070.91 0.359582
\(208\) 1359.17 + 2190.57i 0.453083 + 0.730233i
\(209\) −3263.50 −1.08010
\(210\) −218.359 126.070i −0.0717535 0.0414269i
\(211\) −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
\(213\) 927.679i 0.298420i
\(214\) 1448.55 836.322i 0.462715 0.267149i
\(215\) −337.782 + 195.019i −0.107147 + 0.0618612i
\(216\) 111.324i 0.0350677i
\(217\) −127.217 220.346i −0.0397975 0.0689313i
\(218\) −988.547 + 1712.21i −0.307123 + 0.531953i
\(219\) −1012.50 584.567i −0.312413 0.180372i
\(220\) 885.279 0.271298
\(221\) 1351.98 42.9153i 0.411512 0.0130624i
\(222\) 4051.79 1.22495
\(223\) 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
\(225\) −520.637 901.770i −0.154263 0.267191i
\(226\) 6379.29i 1.87763i
\(227\) 3913.02 2259.19i 1.14413 0.660561i 0.196677 0.980468i \(-0.436985\pi\)
0.947449 + 0.319907i \(0.103652\pi\)
\(228\) 2366.18 1366.12i 0.687300 0.396813i
\(229\) 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
\(231\) 323.301 559.975i 0.0920852 0.159496i
\(232\) −571.712 330.078i −0.161788 0.0934082i
\(233\) 3360.55 0.944879 0.472440 0.881363i \(-0.343373\pi\)
0.472440 + 0.881363i \(0.343373\pi\)
\(234\) 1533.14 + 821.437i 0.428309 + 0.229483i
\(235\) 1579.88 0.438553
\(236\) 5117.09 + 2954.35i 1.41142 + 0.814882i
\(237\) 1352.73 2343.00i 0.370756 0.642169i
\(238\) 397.609 + 688.679i 0.108291 + 0.187565i
\(239\) 4737.17i 1.28210i 0.767499 + 0.641050i \(0.221501\pi\)
−0.767499 + 0.641050i \(0.778499\pi\)
\(240\) 435.836 251.630i 0.117221 0.0676777i
\(241\) 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
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 3155.87 5466.13i 0.828007 1.43415i
\(245\) −788.029 454.969i −0.205491 0.118640i
\(246\) 693.729 0.179799
\(247\) 150.484 + 4740.79i 0.0387655 + 1.22125i
\(248\) −156.969 −0.0401916
\(249\) −1785.13 1030.64i −0.454328 0.262307i
\(250\) −1513.47 + 2621.41i −0.382881 + 0.663169i
\(251\) −1636.93 2835.25i −0.411642 0.712985i 0.583428 0.812165i \(-0.301711\pi\)
−0.995069 + 0.0991805i \(0.968378\pi\)
\(252\) 541.343i 0.135323i
\(253\) 3323.31 1918.71i 0.825828 0.476792i
\(254\) −8909.48 + 5143.89i −2.20091 + 1.27069i
\(255\) 264.061i 0.0648476i
\(256\) −1444.50 2501.95i −0.352661 0.610827i
\(257\) −3272.91 + 5668.84i −0.794390 + 1.37592i 0.128835 + 0.991666i \(0.458876\pi\)
−0.923226 + 0.384258i \(0.874457\pi\)
\(258\) 1369.85 + 790.885i 0.330556 + 0.190846i
\(259\) −2189.22 −0.525217
\(260\) −40.8214 1286.02i −0.00973706 0.306752i
\(261\) 1441.00 0.341746
\(262\) 156.244 + 90.2077i 0.0368428 + 0.0212712i
\(263\) −44.1007 + 76.3847i −0.0103398 + 0.0179091i −0.871149 0.491019i \(-0.836625\pi\)
0.860809 + 0.508928i \(0.169958\pi\)
\(264\) −199.455 345.466i −0.0464985 0.0805378i
\(265\) 2121.46i 0.491773i
\(266\) −2414.88 + 1394.23i −0.556639 + 0.321376i
\(267\) −2781.34 + 1605.81i −0.637510 + 0.368067i
\(268\) 514.575i 0.117286i
\(269\) 2263.80 + 3921.01i 0.513109 + 0.888730i 0.999884 + 0.0152033i \(0.00483956\pi\)
−0.486776 + 0.873527i \(0.661827\pi\)
\(270\) 169.772 294.054i 0.0382667 0.0662798i
\(271\) −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
\(273\) −828.366 443.829i −0.183645 0.0983948i
\(274\) −850.160 −0.187445
\(275\) −3231.34 1865.61i −0.708571 0.409094i
\(276\) −1606.36 + 2782.31i −0.350333 + 0.606794i
\(277\) −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
\(279\) 296.730 171.317i 0.0636730 0.0367616i
\(280\) 72.7864 42.0233i 0.0155351 0.00896918i
\(281\) 2817.99i 0.598247i −0.954214 0.299123i \(-0.903306\pi\)
0.954214 0.299123i \(-0.0966942\pi\)
\(282\) −3203.55 5548.71i −0.676484 1.17170i
\(283\) 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
\(285\) 925.941 0.192449
\(286\) 6229.45 197.738i 1.28796 0.0408829i
\(287\) −374.827 −0.0770918
\(288\) −2024.59 1168.90i −0.414238 0.239160i
\(289\) 2040.09 3533.54i 0.415244 0.719223i
\(290\) −1006.76 1743.76i −0.203858 0.353093i
\(291\) 5263.45i 1.06031i
\(292\) 3037.50 1753.70i 0.608754 0.351464i
\(293\) 3717.43 2146.26i 0.741211 0.427938i −0.0812984 0.996690i \(-0.525907\pi\)
0.822509 + 0.568751i \(0.192573\pi\)
\(294\) 3690.19i 0.732028i
\(295\) 1001.22 + 1734.16i 0.197604 + 0.342260i
\(296\) −675.299 + 1169.65i −0.132604 + 0.229678i
\(297\) 754.091 + 435.374i 0.147329 + 0.0850606i
\(298\) −1568.64 −0.304929
\(299\) −2940.50 4739.19i −0.568740 0.916638i
\(300\) 3123.82 0.601180
\(301\) −740.143 427.322i −0.141731 0.0818286i
\(302\) 3128.31 5418.39i 0.596072 1.03243i
\(303\) 961.260 + 1664.95i 0.182254 + 0.315673i
\(304\) 5565.66i 1.05004i
\(305\) 1852.45 1069.51i 0.347773 0.200787i
\(306\) −927.411 + 535.441i −0.173257 + 0.100030i
\(307\) 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
\(309\) 1039.73 1800.86i 0.191418 0.331546i
\(310\) −414.621 239.382i −0.0759642 0.0438580i
\(311\) 1133.21 0.206618 0.103309 0.994649i \(-0.467057\pi\)
0.103309 + 0.994649i \(0.467057\pi\)
\(312\) −492.651 + 305.672i −0.0893939 + 0.0554657i
\(313\) −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
\(315\) −91.7293 + 158.880i −0.0164075 + 0.0284186i
\(316\) 4058.19 + 7028.99i 0.722440 + 1.25130i
\(317\) 4782.16i 0.847296i 0.905827 + 0.423648i \(0.139251\pi\)
−0.905827 + 0.423648i \(0.860749\pi\)
\(318\) −7450.78 + 4301.71i −1.31390 + 0.758579i
\(319\) 4471.80 2581.79i 0.784867 0.453143i
\(320\) 1924.59i 0.336212i
\(321\) −608.514 1053.98i −0.105807 0.183262i
\(322\) 1639.43 2839.57i 0.283732 0.491438i
\(323\) −2529.06 1460.15i −0.435668 0.251533i
\(324\) −729.000 −0.125000
\(325\) −2561.12 + 4780.10i −0.437124 + 0.815852i
\(326\) 9657.80 1.64079
\(327\) 1245.82 + 719.274i 0.210685 + 0.121639i
\(328\) −115.621 + 200.262i −0.0194638 + 0.0337123i
\(329\) 1730.90 + 2998.01i 0.290054 + 0.502388i
\(330\) 1216.70i 0.202961i
\(331\) −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
\(333\) 2948.11i 0.485152i
\(334\) 82.6128 + 143.090i 0.0135340 + 0.0234417i
\(335\) 87.1936 151.024i 0.0142206 0.0246308i
\(336\) 954.996 + 551.367i 0.155058 + 0.0895225i
\(337\) −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
\(339\) 4641.61 0.743651
\(340\) 686.051 + 396.092i 0.109430 + 0.0631796i
\(341\) 613.886 1063.28i 0.0974891 0.168856i
\(342\) −1877.55 3252.01i −0.296860 0.514177i
\(343\) 4286.19i 0.674731i
\(344\) −456.618 + 263.628i −0.0715674 + 0.0413195i
\(345\) −942.911 + 544.390i −0.147144 + 0.0849535i
\(346\) 7873.23i 1.22332i
\(347\) 6290.74 + 10895.9i 0.973213 + 1.68565i 0.685711 + 0.727874i \(0.259491\pi\)
0.287501 + 0.957780i \(0.407175\pi\)
\(348\) −2161.50 + 3743.84i −0.332956 + 0.576697i
\(349\) 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
\(351\) 597.684 1115.52i 0.0908889 0.169636i
\(352\) −8377.11 −1.26847
\(353\) −4640.16 2679.00i −0.699634 0.403934i 0.107577 0.994197i \(-0.465691\pi\)
−0.807211 + 0.590263i \(0.799024\pi\)
\(354\) 4060.37 7032.77i 0.609622 1.05590i
\(355\) −471.579 816.799i −0.0705037 0.122116i
\(356\) 9634.84i 1.43440i
\(357\) 501.088 289.303i 0.0742868 0.0428895i
\(358\) −1820.92 + 1051.31i −0.268822 + 0.155205i
\(359\) 2705.40i 0.397731i −0.980027 0.198866i \(-0.936274\pi\)
0.980027 0.198866i \(-0.0637257\pi\)
\(360\) 56.5907 + 98.0180i 0.00828498 + 0.0143500i
\(361\) 1690.60 2928.20i 0.246478 0.426913i
\(362\) 7630.19 + 4405.29i 1.10783 + 0.639605i
\(363\) −872.820 −0.126202
\(364\) 2395.65 1486.42i 0.344962 0.214037i
\(365\) 1188.64 0.170456
\(366\) −7512.47 4337.33i −1.07290 0.619442i
\(367\) −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
\(369\) 504.762i 0.0712110i
\(370\) −3567.51 + 2059.70i −0.501259 + 0.289402i
\(371\) 4025.72 2324.25i 0.563356 0.325254i
\(372\) 1027.90i 0.143264i
\(373\) 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
\(375\) 1907.35 + 1101.21i 0.262654 + 0.151643i
\(376\) 2135.70 0.292926
\(377\) −3956.70 6377.00i −0.540531 0.871173i
\(378\) 744.004 0.101237
\(379\) −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
\(381\) 3742.73 + 6482.60i 0.503270 + 0.871690i
\(382\) 16730.5i 2.24086i
\(383\) −1717.63 + 991.672i −0.229156 + 0.132303i −0.610183 0.792261i \(-0.708904\pi\)
0.381027 + 0.924564i \(0.375571\pi\)
\(384\) 1360.44 785.452i 0.180794 0.104381i
\(385\) 657.392i 0.0870229i
\(386\) −1800.55 3118.64i −0.237424 0.411230i
\(387\) 575.454 996.715i 0.0755864 0.130920i
\(388\) −13674.8 7895.17i −1.78927 1.03303i
\(389\) 3244.51 0.422887 0.211444 0.977390i \(-0.432184\pi\)
0.211444 + 0.977390i \(0.432184\pi\)
\(390\) −1767.46 + 56.1036i −0.229485 + 0.00728441i
\(391\) 3433.88 0.444140
\(392\) −1065.27 615.032i −0.137255 0.0792444i
\(393\) 65.6357 113.684i 0.00842464 0.0145919i
\(394\) 8549.77 + 14808.6i 1.09323 + 1.89352i
\(395\) 2750.60i 0.350374i
\(396\) −2262.27 + 1306.12i −0.287079 + 0.165745i
\(397\) 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
\(399\) 1014.45 + 1757.09i 0.127284 + 0.220462i
\(400\) 3181.67 5510.82i 0.397709 0.688852i
\(401\) 1729.93 + 998.773i 0.215432 + 0.124380i 0.603833 0.797110i \(-0.293639\pi\)
−0.388401 + 0.921490i \(0.626973\pi\)
\(402\) −707.216 −0.0877431
\(403\) −1572.90 842.744i −0.194422 0.104169i
\(404\) −5767.56 −0.710264
\(405\) −213.956 123.527i −0.0262507 0.0151559i
\(406\) 2205.99 3820.89i 0.269659 0.467063i
\(407\) −5282.03 9148.74i −0.643293 1.11422i
\(408\) 356.961i 0.0433142i
\(409\) 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
\(411\) 618.582i 0.0742394i
\(412\) 3119.19 + 5402.59i 0.372989 + 0.646035i
\(413\) −2193.85 + 3799.86i −0.261386 + 0.452734i
\(414\) 3823.91 + 2207.74i 0.453950 + 0.262088i
\(415\) 2095.68 0.247887
\(416\) 386.280 + 12169.2i 0.0455263 + 1.43424i
\(417\) 300.000 0.0352304
\(418\) −11653.0 6727.87i −1.36356 0.787251i
\(419\) 3411.05 5908.12i 0.397711 0.688855i −0.595732 0.803183i \(-0.703138\pi\)
0.993443 + 0.114328i \(0.0364714\pi\)
\(420\) −275.188 476.639i −0.0319709 0.0553753i
\(421\) 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
\(423\) −4037.28 + 2330.92i −0.464064 + 0.267928i
\(424\) 2867.81i 0.328474i
\(425\) −1669.43 2891.53i −0.190539 0.330023i
\(426\) −1912.46 + 3312.48i −0.217509 + 0.376737i
\(427\) 4059.05 + 2343.49i 0.460026 + 0.265596i
\(428\) 3651.08 0.412340
\(429\) −143.876 4532.59i −0.0161920 0.510107i
\(430\) −1608.16 −0.180355
\(431\) −11608.4 6702.10i −1.29735 0.749023i −0.317401 0.948291i \(-0.602810\pi\)
−0.979945 + 0.199268i \(0.936143\pi\)
\(432\) −742.500 + 1286.05i −0.0826934 + 0.143229i
\(433\) −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
\(435\) −1268.77 + 732.524i −0.139846 + 0.0807398i
\(436\) −3737.46 + 2157.82i −0.410531 + 0.237020i
\(437\) 12041.1i 1.31808i
\(438\) −2410.23 4174.64i −0.262935 0.455416i
\(439\) 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
\(441\) 2685.01 0.289926
\(442\) 4916.02 + 2633.95i 0.529030 + 0.283448i
\(443\) −10169.2 −1.09064 −0.545321 0.838227i \(-0.683592\pi\)
−0.545321 + 0.838227i \(0.683592\pi\)
\(444\) 7659.42 + 4422.17i 0.818693 + 0.472673i
\(445\) 1632.60 2827.75i 0.173916 0.301232i
\(446\) 5800.29 + 10046.4i 0.615811 + 1.06662i
\(447\) 1141.35i 0.120770i
\(448\) −3652.14 + 2108.56i −0.385150 + 0.222367i
\(449\) −14845.8 + 8571.24i −1.56040 + 0.900895i −0.563179 + 0.826335i \(0.690422\pi\)
−0.997217 + 0.0745603i \(0.976245\pi\)
\(450\) 4293.28i 0.449750i
\(451\) −904.364 1566.40i −0.0944231 0.163546i
\(452\) −6962.42 + 12059.3i −0.724524 + 1.25491i
\(453\) −3942.46 2276.18i −0.408902 0.236080i
\(454\) 18629.7 1.92585
\(455\) 954.974 30.3133i 0.0983954 0.00312331i
\(456\) 1251.70 0.128544
\(457\) 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
\(459\) 389.591 + 674.791i 0.0396177 + 0.0686199i
\(460\) 3266.34i 0.331074i
\(461\) 2530.72 1461.11i 0.255678 0.147616i −0.366684 0.930346i \(-0.619507\pi\)
0.622361 + 0.782730i \(0.286174\pi\)
\(462\) 2308.83 1333.01i 0.232504 0.134236i
\(463\) 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
\(465\) −174.176 + 301.681i −0.0173703 + 0.0300863i
\(466\) 11999.6 + 6927.95i 1.19285 + 0.688693i
\(467\) 2664.19 0.263992 0.131996 0.991250i \(-0.457861\pi\)
0.131996 + 0.991250i \(0.457861\pi\)
\(468\) 2001.68 + 3226.11i 0.197709 + 0.318647i
\(469\) 382.114 0.0376213
\(470\) 5641.29 + 3257.00i 0.553646 + 0.319648i
\(471\) 2175.23 3767.61i 0.212801 0.368583i
\(472\) 1353.46 + 2344.26i 0.131987 + 0.228608i
\(473\) 4124.08i 0.400899i
\(474\) 9660.42 5577.45i 0.936114 0.540466i
\(475\) 10139.3 5853.92i 0.979415 0.565466i
\(476\) 1735.82i 0.167145i
\(477\) 3129.96 + 5421.24i 0.300442 + 0.520381i
\(478\) −9765.92 + 16915.1i −0.934483 + 1.61857i
\(479\) 4521.26 + 2610.35i 0.431277 + 0.248998i 0.699890 0.714250i \(-0.253232\pi\)
−0.268614 + 0.963248i \(0.586566\pi\)
\(480\) 2376.81 0.226013
\(481\) −13046.5 + 8094.91i −1.23674 + 0.767351i
\(482\) 19730.2 1.86449
\(483\) −2066.09 1192.86i −0.194639 0.112375i
\(484\) 1309.23 2267.65i 0.122955 0.212965i
\(485\) −2675.64 4634.34i −0.250504 0.433886i
\(486\) 1001.91i 0.0935139i
\(487\) 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
\(489\) 7027.08i 0.649848i
\(490\) −1875.88 3249.13i −0.172946 0.299552i
\(491\) 9826.61 17020.2i 0.903195 1.56438i 0.0798720 0.996805i \(-0.474549\pi\)
0.823323 0.567574i \(-0.192118\pi\)
\(492\) 1311.41 + 757.143i 0.120168 + 0.0693793i
\(493\) 4620.59 0.422111
\(494\) −9236.04 + 17238.2i −0.841193 + 1.57001i
\(495\) −885.279 −0.0803845
\(496\) 1813.35 + 1046.94i 0.164157 + 0.0947760i
\(497\) 1033.32 1789.76i 0.0932608 0.161532i
\(498\) −4249.45 7360.26i −0.382374 0.662292i
\(499\) 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
\(501\) 104.113 60.1096i 0.00928428 0.00536028i
\(502\) 13498.5i 1.20013i
\(503\) −6501.67 11261.2i −0.576332 0.998236i −0.995896 0.0905104i \(-0.971150\pi\)
0.419563 0.907726i \(-0.362183\pi\)
\(504\) −124.001 + 214.776i −0.0109592 + 0.0189819i
\(505\) −1692.73 977.300i −0.149160 0.0861174i
\(506\) 15822.1 1.39008
\(507\) −6577.73 + 418.008i −0.576188 + 0.0366162i
\(508\) −22456.4 −1.96130
\(509\) −4614.99 2664.47i −0.401878 0.232024i 0.285416 0.958404i \(-0.407868\pi\)
−0.687294 + 0.726379i \(0.741202\pi\)
\(510\) 544.376 942.886i 0.0472654 0.0818661i
\(511\) 1302.27 + 2255.59i 0.112738 + 0.195267i
\(512\) 16100.7i 1.38976i
\(513\) −2366.18 + 1366.12i −0.203644 + 0.117574i
\(514\) −23373.2 + 13494.5i −2.00574 + 1.15801i
\(515\) 2114.16i 0.180895i
\(516\) 1726.36 + 2990.14i 0.147284 + 0.255104i
\(517\) −8352.47 + 14466.9i −0.710524 + 1.23066i
\(518\) −7817.06 4513.18i −0.663054 0.382814i
\(519\) 5728.62 0.484506
\(520\) 278.381 519.573i 0.0234766 0.0438169i
\(521\) −11700.3 −0.983876 −0.491938 0.870630i \(-0.663711\pi\)
−0.491938 + 0.870630i \(0.663711\pi\)
\(522\) 5145.41 + 2970.70i 0.431434 + 0.249088i
\(523\) 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
\(525\) 2319.70i 0.192838i
\(526\) −314.942 + 181.832i −0.0261067 + 0.0150727i
\(527\) 951.467 549.330i 0.0786462 0.0454064i
\(528\) 5321.24i 0.438594i
\(529\) −995.810 1724.79i −0.0818451 0.141760i
\(530\) 4373.49 7575.11i 0.358438 0.620834i
\(531\) −5117.09 2954.35i −0.418197 0.241446i
\(532\) −6086.73 −0.496040
\(533\) −2233.77 + 1385.97i −0.181529 + 0.112632i
\(534\) −13241.8 −1.07309
\(535\) 1071.56 + 618.667i 0.0865939 + 0.0499950i
\(536\) 117.869 204.156i 0.00949847 0.0164518i
\(537\) 764.938 + 1324.91i 0.0614702 + 0.106470i
\(538\) 18667.8i 1.49596i
\(539\) 8332.26 4810.63i 0.665855 0.384432i
\(540\) 641.867 370.582i 0.0511510 0.0295321i
\(541\) 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
\(543\) 3205.32 5551.78i 0.253321 0.438766i
\(544\) −6491.88 3748.09i −0.511649 0.295401i
\(545\) −1462.55 −0.114952
\(546\) −2042.88 3292.51i −0.160123 0.258070i
\(547\) 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
\(549\) −3155.87 + 5466.13i −0.245336 + 0.424934i
\(550\) −7692.12 13323.2i −0.596351 1.03291i
\(551\) 16202.3i 1.25271i
\(552\) −1274.64 + 735.913i −0.0982830 + 0.0567437i
\(553\) −5219.61 + 3013.54i −0.401375 + 0.231734i
\(554\) 11879.9i 0.911066i
\(555\) 1498.65 + 2595.74i 0.114620 + 0.198528i
\(556\) −450.000 + 779.423i −0.0343242 + 0.0594512i
\(557\) 17450.9 + 10075.3i 1.32750 + 0.766432i 0.984912 0.173055i \(-0.0553637\pi\)
0.342586 + 0.939486i \(0.388697\pi\)
\(558\) 1412.72 0.107178
\(559\) −5990.93 + 190.167i −0.453290 + 0.0143886i
\(560\) −1121.14 −0.0846011
\(561\) 2418.00 + 1396.03i 0.181975 + 0.105063i
\(562\) 5809.44 10062.2i 0.436044 0.755250i
\(563\) 8146.10 + 14109.5i 0.609800 + 1.05620i 0.991273 + 0.131824i \(0.0420834\pi\)
−0.381474 + 0.924380i \(0.624583\pi\)
\(564\) 13985.5i 1.04414i
\(565\) −4086.83 + 2359.53i −0.304308 + 0.175692i
\(566\) 944.816 545.490i 0.0701654 0.0405100i
\(567\) 541.343i 0.0400957i
\(568\) −637.486 1104.16i −0.0470921 0.0815660i
\(569\) 5230.27 9059.09i 0.385350 0.667446i −0.606468 0.795108i \(-0.707414\pi\)
0.991818 + 0.127662i \(0.0407474\pi\)
\(570\) 3306.27 + 1908.88i 0.242955 + 0.140270i
\(571\) −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
\(573\) −12173.2 −0.887511
\(574\) −1338.40 772.726i −0.0973236 0.0561898i
\(575\) −6883.40 + 11922.4i −0.499231 + 0.864693i
\(576\) −2839.50 4918.16i −0.205404 0.355770i
\(577\) 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
\(579\) −2269.14 + 1310.09i −0.162871 + 0.0940337i
\(580\) 4395.14i 0.314652i
\(581\) 2296.01 + 3976.81i 0.163949 + 0.283969i
\(582\) −10850.9 + 18794.3i −0.772824 + 1.33857i
\(583\) 19426.1 + 11215.7i 1.38001 + 0.796750i
\(584\) 1606.82 0.113854
\(585\) 40.8214 + 1286.02i 0.00288505 + 0.0908894i
\(586\) 17698.5 1.24764
\(587\) 10470.7 + 6045.28i 0.736241 + 0.425069i 0.820701 0.571358i \(-0.193583\pi\)
−0.0844601 + 0.996427i \(0.526917\pi\)
\(588\) −4027.51 + 6975.86i −0.282469 + 0.489251i
\(589\) 1926.25 + 3336.36i 0.134753 + 0.233400i
\(590\) 8256.25i 0.576109i
\(591\) 10774.9 6220.87i 0.749947 0.432982i
\(592\) 15602.5 9008.12i 1.08321 0.625391i
\(593\) 6135.97i 0.424914i 0.977170 + 0.212457i \(0.0681466\pi\)
−0.977170 + 0.212457i \(0.931853\pi\)
\(594\) 1795.09 + 3109.20i 0.123996 + 0.214767i
\(595\) −294.131 + 509.449i −0.0202658 + 0.0351015i
\(596\) −2965.32 1712.03i −0.203799 0.117663i
\(597\) −7212.18 −0.494431
\(598\) −729.579 22984.3i −0.0498908 1.57174i
\(599\) −6198.80 −0.422831 −0.211416 0.977396i \(-0.567807\pi\)
−0.211416 + 0.977396i \(0.567807\pi\)
\(600\) 1239.36 + 715.547i 0.0843281 + 0.0486868i
\(601\) −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
\(603\) 514.575i 0.0347514i
\(604\) 11827.4 6828.53i 0.796770 0.460015i
\(605\) 768.497 443.692i 0.0516427 0.0298159i
\(606\) 7926.75i 0.531357i
\(607\) −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
\(609\) −2780.11 1605.10i −0.184985 0.106801i
\(610\) 8819.40 0.585389
\(611\) 21400.8 + 11466.3i 1.41699 + 0.759209i
\(612\) −2337.54 −0.154395
\(613\) −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
\(615\) 256.592 + 444.431i 0.0168241 + 0.0291401i
\(616\) 888.671i 0.0581259i
\(617\) −13179.4 + 7609.13i −0.859940 + 0.496486i −0.863992 0.503505i \(-0.832043\pi\)
0.00405239 + 0.999992i \(0.498710\pi\)
\(618\) 7425.15 4286.91i 0.483307 0.279037i
\(619\) 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
\(621\) 1606.36 2782.31i 0.103802 0.179791i
\(622\) 4046.36 + 2336.17i 0.260843 + 0.150598i
\(623\) 7154.66 0.460105
\(624\) 7730.01 245.370i 0.495911 0.0157414i
\(625\) 12223.0 0.782270
\(626\) −18874.6 10897.3i −1.20508 0.695754i
\(627\) −4895.25 + 8478.81i −0.311798 + 0.540050i
\(628\) 6525.70 + 11302.8i 0.414656 + 0.718205i
\(629\) 9453.14i 0.599239i
\(630\) −655.078 + 378.209i −0.0414269 + 0.0239178i
\(631\) −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
\(633\) 5803.28 + 10051.6i 0.364391 + 0.631144i
\(634\) −9858.67 + 17075.7i −0.617568 + 1.06966i
\(635\) −6590.77 3805.18i −0.411885 0.237802i
\(636\) −18779.7 −1.17086
\(637\) −7372.48 11882.2i −0.458569 0.739074i
\(638\) 21290.0 1.32113
\(639\) 2410.18 + 1391.52i 0.149210 + 0.0861465i
\(640\) −798.558 + 1383.14i −0.0493215 + 0.0854274i
\(641\) 3071.18 + 5319.44i 0.189242 + 0.327777i 0.944998 0.327077i \(-0.106064\pi\)
−0.755756 + 0.654854i \(0.772730\pi\)
\(642\) 5017.93i 0.308477i
\(643\) −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
\(645\) 1170.11i 0.0714312i
\(646\) −6020.37 10427.6i −0.366669 0.635090i
\(647\) 426.379 738.509i 0.0259083 0.0448745i −0.852781 0.522269i \(-0.825086\pi\)
0.878689 + 0.477395i \(0.158419\pi\)
\(648\) −289.228 166.986i −0.0175339 0.0101232i
\(649\) −21172.8 −1.28060
\(650\) −18999.5 + 11788.5i −1.14649 + 0.711357i
\(651\) −763.303 −0.0459542
\(652\) 18256.9 + 10540.6i 1.09662 + 0.633133i
\(653\) 3672.88 6361.61i 0.220108 0.381239i −0.734732 0.678357i \(-0.762692\pi\)
0.954841 + 0.297118i \(0.0960256\pi\)
\(654\) 2965.64 + 5136.64i 0.177318 + 0.307123i
\(655\) 133.462i 0.00796151i
\(656\) 2671.39 1542.33i 0.158994 0.0917954i
\(657\) −3037.50 + 1753.70i −0.180372 + 0.104138i
\(658\) 14273.4i 0.845645i
\(659\) −6270.33 10860.5i −0.370648 0.641982i 0.619017 0.785378i \(-0.287531\pi\)
−0.989665 + 0.143396i \(0.954198\pi\)
\(660\) 1327.92 2300.02i 0.0783169 0.135649i
\(661\) 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
\(663\) 1916.48 3576.93i 0.112262 0.209527i
\(664\) 2832.97 0.165573
\(665\) −1786.41 1031.38i −0.104171 0.0601433i
\(666\) 6077.69 10526.9i 0.353612 0.612474i
\(667\) −9525.83 16499.2i −0.552986 0.957800i
\(668\) 360.658i 0.0208896i
\(669\) 7309.83 4220.33i 0.422443 0.243897i
\(670\) 622.687 359.508i 0.0359052 0.0207299i
\(671\) 22617.0i 1.30122i
\(672\) 2604.01 + 4510.29i 0.149482 + 0.258911i
\(673\) −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
\(675\) −3123.82 −0.178127
\(676\) 8780.58 17716.5i 0.499578 1.00799i
\(677\) −7933.57 −0.450387 −0.225193 0.974314i \(-0.572301\pi\)
−0.225193 + 0.974314i \(0.572301\pi\)
\(678\) 16573.9 + 9568.93i 0.938814 + 0.542024i
\(679\) 5862.82 10154.7i 0.331361 0.573935i
\(680\) 181.459 + 314.295i 0.0102333 + 0.0177245i
\(681\) 13555.1i 0.762750i
\(682\) 4384.02 2531.12i 0.246148 0.142114i
\(683\) 20415.5 11786.9i 1.14374 0.660340i 0.196388 0.980526i \(-0.437079\pi\)
0.947355 + 0.320186i \(0.103745\pi\)
\(684\) 8196.70i 0.458200i
\(685\) −314.452 544.647i −0.0175396 0.0303794i
\(686\) 8836.21 15304.8i 0.491790 0.851806i
\(687\) −3391.19 1957.90i −0.188329 0.108732i
\(688\) 7033.32 0.389743
\(689\) 15396.9 28736.9i 0.851343 1.58895i
\(690\) −4489.15 −0.247680
\(691\) −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
\(693\) −969.904 1679.92i −0.0531654 0.0920852i
\(694\) 51874.8i 2.83738i
\(695\) −264.143 + 152.503i −0.0144166 + 0.00832340i
\(696\) −1715.14 + 990.234i −0.0934082 + 0.0539292i
\(697\) 1618.52i 0.0879568i
\(698\) 18473.9 + 31997.8i 1.00179 + 1.73515i
\(699\) 5040.82 8730.96i 0.272763 0.472440i
\(700\) −6026.75 3479.54i −0.325414 0.187878i
\(701\) 581.786 0.0313463 0.0156731 0.999877i \(-0.495011\pi\)
0.0156731 + 0.999877i \(0.495011\pi\)
\(702\) 4433.86 2751.05i 0.238384 0.147908i
\(703\) 33147.9 1.77837
\(704\) −17623.4 10174.9i −0.943475 0.544715i
\(705\) 2369.82 4104.64i 0.126599 0.219276i
\(706\) −11045.8 19131.9i −0.588830 1.01988i
\(707\) 4282.89i 0.227828i
\(708\) 15351.3 8863.06i 0.814882 0.470472i
\(709\) −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
\(711\) −4058.19 7028.99i −0.214056 0.370756i
\(712\) 2206.97 3822.58i 0.116165 0.201204i
\(713\) −3923.10 2265.00i −0.206061 0.118969i
\(714\) 2385.66 0.125043
\(715\) 2430.79 + 3917.70i 0.127142 + 0.204914i
\(716\) −4589.63 −0.239556
\(717\) 12307.5 + 7105.75i 0.641050 + 0.370110i
\(718\) 5577.32 9660.21i 0.289894 0.502111i
\(719\) 12675.1 + 21953.9i 0.657443 + 1.13872i 0.981275 + 0.192610i \(0.0616953\pi\)
−0.323832 + 0.946114i \(0.604971\pi\)
\(720\) 1509.78i 0.0781474i
\(721\) −4011.87 + 2316.25i −0.207226 + 0.119642i
\(722\) 12073.3 6970.50i 0.622328 0.359301i
\(723\) 14355.8i 0.738449i
\(724\) 9615.97 + 16655.3i 0.493611 + 0.854960i
\(725\) −9262.22 + 16042.6i −0.474469 + 0.821805i
\(726\) −3116.59 1799.36i −0.159322 0.0919844i
\(727\) −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
\(729\) 729.000 0.0370370
\(730\) 4244.30 + 2450.45i 0.215190 + 0.124240i
\(731\) 1845.20 3195.97i 0.0933612 0.161706i
\(732\) −9467.61 16398.4i −0.478050 0.828007i
\(733\) 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
\(735\) −2364.09 + 1364.91i −0.118640 + 0.0684970i
\(736\) 30908.3i 1.54796i
\(737\) 921.946 + 1596.86i 0.0460791 + 0.0798114i
\(738\) 1040.59 1802.36i 0.0519035 0.0898994i
\(739\) −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
\(741\) 12542.7 + 6720.21i 0.621816 + 0.333162i
\(742\) 19166.3 0.948269
\(743\) −30308.0 17498.3i −1.49649 0.864000i −0.496500 0.868037i \(-0.665382\pi\)
−0.999992 + 0.00403656i \(0.998715\pi\)
\(744\) −235.453 + 407.816i −0.0116023 + 0.0200958i
\(745\) −580.199 1004.93i −0.0285327 0.0494200i
\(746\) 52623.2i 2.58267i
\(747\) −5355.38 + 3091.93i −0.262307 + 0.151443i
\(748\) −7253.99 + 4188.10i −0.354589 + 0.204722i
\(749\) 2711.23i 0.132265i
\(750\) 4540.41 + 7864.22i 0.221056 + 0.382881i
\(751\) 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
\(753\) −9821.58 −0.475323
\(754\) −981.712 30927.4i −0.0474162 1.49378i
\(755\) 4628.32 0.223102
\(756\) 1406.45 + 812.014i 0.0676615 + 0.0390644i
\(757\) 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
\(759\) 11512.3i 0.550552i
\(760\) −1102.09 + 636.292i −0.0526014 + 0.0303694i
\(761\) 18261.9 10543.5i 0.869899 0.502236i 0.00258400 0.999997i \(-0.499177\pi\)
0.867315 + 0.497761i \(0.165844\pi\)
\(762\) 30863.4i 1.46727i
\(763\) −1602.36 2775.37i −0.0760280 0.131684i
\(764\) 18259.8 31627.0i 0.864683 1.49768i
\(765\) −686.051 396.092i −0.0324238 0.0187199i
\(766\) −8177.54 −0.385727
\(767\) 976.309 + 30757.2i 0.0459615 + 1.44795i
\(768\) −8667.00 −0.407218
\(769\) 16911.7 + 9763.96i 0.793044 + 0.457864i 0.841033 0.540984i \(-0.181948\pi\)