Properties

Label 98.4.c.c.79.1
Level $98$
Weight $4$
Character 98.79
Analytic conductor $5.782$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.4.c.c.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +(12.0000 + 20.7846i) q^{10} +(-24.0000 - 41.5692i) q^{11} +(4.00000 - 6.92820i) q^{12} +56.0000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.0000 + 98.7269i) q^{17} +(23.0000 + 39.8372i) q^{18} +(-1.00000 + 1.73205i) q^{19} -48.0000 q^{20} +96.0000 q^{22} +(60.0000 - 103.923i) q^{23} +(8.00000 + 13.8564i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-56.0000 + 96.9948i) q^{26} +100.000 q^{27} -54.0000 q^{29} +(-24.0000 + 41.5692i) q^{30} +(-118.000 - 204.382i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(48.0000 - 83.1384i) q^{33} -228.000 q^{34} -92.0000 q^{36} +(-73.0000 + 126.440i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(56.0000 + 96.9948i) q^{39} +(48.0000 - 83.1384i) q^{40} +126.000 q^{41} -376.000 q^{43} +(-96.0000 + 166.277i) q^{44} +(-138.000 - 239.023i) q^{45} +(120.000 + 207.846i) q^{46} +(6.00000 - 10.3923i) q^{47} -32.0000 q^{48} +38.0000 q^{50} +(-114.000 + 197.454i) q^{51} +(-112.000 - 193.990i) q^{52} +(-87.0000 - 150.688i) q^{53} +(-100.000 + 173.205i) q^{54} -576.000 q^{55} -4.00000 q^{57} +(54.0000 - 93.5307i) q^{58} +(-69.0000 - 119.512i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-190.000 + 329.090i) q^{61} +472.000 q^{62} +64.0000 q^{64} +(336.000 - 581.969i) q^{65} +(96.0000 + 166.277i) q^{66} +(242.000 + 419.156i) q^{67} +(228.000 - 394.908i) q^{68} +240.000 q^{69} +576.000 q^{71} +(92.0000 - 159.349i) q^{72} +(575.000 + 995.929i) q^{73} +(-146.000 - 252.879i) q^{74} +(19.0000 - 32.9090i) q^{75} +8.00000 q^{76} -224.000 q^{78} +(-388.000 + 672.036i) q^{79} +(96.0000 + 166.277i) q^{80} +(-210.500 - 364.597i) q^{81} +(-126.000 + 218.238i) q^{82} +378.000 q^{83} +1368.00 q^{85} +(376.000 - 651.251i) q^{86} +(-54.0000 - 93.5307i) q^{87} +(-192.000 - 332.554i) q^{88} +(195.000 - 337.750i) q^{89} +552.000 q^{90} -480.000 q^{92} +(236.000 - 408.764i) q^{93} +(12.0000 + 20.7846i) q^{94} +(12.0000 + 20.7846i) q^{95} +(32.0000 - 55.4256i) q^{96} -1330.00 q^{97} -1104.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9} + 24 q^{10} - 48 q^{11} + 8 q^{12} + 112 q^{13} + 48 q^{15} - 16 q^{16} + 114 q^{17} + 46 q^{18} - 2 q^{19} - 96 q^{20} + 192 q^{22} + 120 q^{23} + 16 q^{24} - 19 q^{25} - 112 q^{26} + 200 q^{27} - 108 q^{29} - 48 q^{30} - 236 q^{31} - 32 q^{32} + 96 q^{33} - 456 q^{34} - 184 q^{36} - 146 q^{37} - 4 q^{38} + 112 q^{39} + 96 q^{40} + 252 q^{41} - 752 q^{43} - 192 q^{44} - 276 q^{45} + 240 q^{46} + 12 q^{47} - 64 q^{48} + 76 q^{50} - 228 q^{51} - 224 q^{52} - 174 q^{53} - 200 q^{54} - 1152 q^{55} - 8 q^{57} + 108 q^{58} - 138 q^{59} - 96 q^{60} - 380 q^{61} + 944 q^{62} + 128 q^{64} + 672 q^{65} + 192 q^{66} + 484 q^{67} + 456 q^{68} + 480 q^{69} + 1152 q^{71} + 184 q^{72} + 1150 q^{73} - 292 q^{74} + 38 q^{75} + 16 q^{76} - 448 q^{78} - 776 q^{79} + 192 q^{80} - 421 q^{81} - 252 q^{82} + 756 q^{83} + 2736 q^{85} + 752 q^{86} - 108 q^{87} - 384 q^{88} + 390 q^{89} + 1104 q^{90} - 960 q^{92} + 472 q^{93} + 24 q^{94} + 24 q^{95} + 64 q^{96} - 2660 q^{97} - 2208 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 1.00000 + 1.73205i 0.192450 + 0.333333i 0.946062 0.323987i \(-0.105023\pi\)
−0.753612 + 0.657320i \(0.771690\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 6.00000 10.3923i 0.536656 0.929516i −0.462425 0.886658i \(-0.653021\pi\)
0.999081 0.0428575i \(-0.0136462\pi\)
\(6\) −4.00000 −0.272166
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) 12.0000 + 20.7846i 0.379473 + 0.657267i
\(11\) −24.0000 41.5692i −0.657843 1.13942i −0.981173 0.193131i \(-0.938136\pi\)
0.323330 0.946286i \(-0.395198\pi\)
\(12\) 4.00000 6.92820i 0.0962250 0.166667i
\(13\) 56.0000 1.19474 0.597369 0.801966i \(-0.296213\pi\)
0.597369 + 0.801966i \(0.296213\pi\)
\(14\) 0 0
\(15\) 24.0000 0.413118
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 57.0000 + 98.7269i 0.813208 + 1.40852i 0.910608 + 0.413272i \(0.135614\pi\)
−0.0974001 + 0.995245i \(0.531053\pi\)
\(18\) 23.0000 + 39.8372i 0.301175 + 0.521651i
\(19\) −1.00000 + 1.73205i −0.0120745 + 0.0209137i −0.872000 0.489507i \(-0.837177\pi\)
0.859925 + 0.510420i \(0.170510\pi\)
\(20\) −48.0000 −0.536656
\(21\) 0 0
\(22\) 96.0000 0.930330
\(23\) 60.0000 103.923i 0.543951 0.942150i −0.454721 0.890634i \(-0.650261\pi\)
0.998672 0.0515165i \(-0.0164055\pi\)
\(24\) 8.00000 + 13.8564i 0.0680414 + 0.117851i
\(25\) −9.50000 16.4545i −0.0760000 0.131636i
\(26\) −56.0000 + 96.9948i −0.422404 + 0.731625i
\(27\) 100.000 0.712778
\(28\) 0 0
\(29\) −54.0000 −0.345778 −0.172889 0.984941i \(-0.555310\pi\)
−0.172889 + 0.984941i \(0.555310\pi\)
\(30\) −24.0000 + 41.5692i −0.146059 + 0.252982i
\(31\) −118.000 204.382i −0.683659 1.18413i −0.973856 0.227165i \(-0.927054\pi\)
0.290197 0.956967i \(-0.406279\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 48.0000 83.1384i 0.253204 0.438562i
\(34\) −228.000 −1.15005
\(35\) 0 0
\(36\) −92.0000 −0.425926
\(37\) −73.0000 + 126.440i −0.324355 + 0.561799i −0.981382 0.192068i \(-0.938480\pi\)
0.657027 + 0.753867i \(0.271814\pi\)
\(38\) −2.00000 3.46410i −0.00853797 0.0147882i
\(39\) 56.0000 + 96.9948i 0.229928 + 0.398246i
\(40\) 48.0000 83.1384i 0.189737 0.328634i
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 0 0
\(43\) −376.000 −1.33348 −0.666738 0.745292i \(-0.732310\pi\)
−0.666738 + 0.745292i \(0.732310\pi\)
\(44\) −96.0000 + 166.277i −0.328921 + 0.569709i
\(45\) −138.000 239.023i −0.457152 0.791810i
\(46\) 120.000 + 207.846i 0.384631 + 0.666201i
\(47\) 6.00000 10.3923i 0.0186211 0.0322526i −0.856565 0.516040i \(-0.827406\pi\)
0.875186 + 0.483787i \(0.160739\pi\)
\(48\) −32.0000 −0.0962250
\(49\) 0 0
\(50\) 38.0000 0.107480
\(51\) −114.000 + 197.454i −0.313004 + 0.542138i
\(52\) −112.000 193.990i −0.298685 0.517337i
\(53\) −87.0000 150.688i −0.225479 0.390540i 0.730984 0.682394i \(-0.239061\pi\)
−0.956463 + 0.291854i \(0.905728\pi\)
\(54\) −100.000 + 173.205i −0.252005 + 0.436486i
\(55\) −576.000 −1.41214
\(56\) 0 0
\(57\) −4.00000 −0.00929496
\(58\) 54.0000 93.5307i 0.122251 0.211745i
\(59\) −69.0000 119.512i −0.152255 0.263713i 0.779801 0.626027i \(-0.215320\pi\)
−0.932056 + 0.362314i \(0.881987\pi\)
\(60\) −48.0000 83.1384i −0.103280 0.178885i
\(61\) −190.000 + 329.090i −0.398803 + 0.690748i −0.993579 0.113144i \(-0.963908\pi\)
0.594775 + 0.803892i \(0.297241\pi\)
\(62\) 472.000 0.966840
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 336.000 581.969i 0.641164 1.11053i
\(66\) 96.0000 + 166.277i 0.179042 + 0.310110i
\(67\) 242.000 + 419.156i 0.441269 + 0.764300i 0.997784 0.0665376i \(-0.0211952\pi\)
−0.556515 + 0.830837i \(0.687862\pi\)
\(68\) 228.000 394.908i 0.406604 0.704259i
\(69\) 240.000 0.418733
\(70\) 0 0
\(71\) 576.000 0.962798 0.481399 0.876502i \(-0.340129\pi\)
0.481399 + 0.876502i \(0.340129\pi\)
\(72\) 92.0000 159.349i 0.150588 0.260825i
\(73\) 575.000 + 995.929i 0.921899 + 1.59678i 0.796473 + 0.604674i \(0.206696\pi\)
0.125426 + 0.992103i \(0.459970\pi\)
\(74\) −146.000 252.879i −0.229353 0.397252i
\(75\) 19.0000 32.9090i 0.0292524 0.0506667i
\(76\) 8.00000 0.0120745
\(77\) 0 0
\(78\) −224.000 −0.325167
\(79\) −388.000 + 672.036i −0.552575 + 0.957088i 0.445513 + 0.895275i \(0.353021\pi\)
−0.998088 + 0.0618122i \(0.980312\pi\)
\(80\) 96.0000 + 166.277i 0.134164 + 0.232379i
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) −126.000 + 218.238i −0.169687 + 0.293907i
\(83\) 378.000 0.499890 0.249945 0.968260i \(-0.419587\pi\)
0.249945 + 0.968260i \(0.419587\pi\)
\(84\) 0 0
\(85\) 1368.00 1.74565
\(86\) 376.000 651.251i 0.471455 0.816584i
\(87\) −54.0000 93.5307i −0.0665449 0.115259i
\(88\) −192.000 332.554i −0.232583 0.402845i
\(89\) 195.000 337.750i 0.232247 0.402263i −0.726222 0.687460i \(-0.758726\pi\)
0.958469 + 0.285197i \(0.0920590\pi\)
\(90\) 552.000 0.646510
\(91\) 0 0
\(92\) −480.000 −0.543951
\(93\) 236.000 408.764i 0.263140 0.455773i
\(94\) 12.0000 + 20.7846i 0.0131671 + 0.0228061i
\(95\) 12.0000 + 20.7846i 0.0129597 + 0.0224469i
\(96\) 32.0000 55.4256i 0.0340207 0.0589256i
\(97\) −1330.00 −1.39218 −0.696088 0.717957i \(-0.745078\pi\)
−0.696088 + 0.717957i \(0.745078\pi\)
\(98\) 0 0
\(99\) −1104.00 −1.12077
\(100\) −38.0000 + 65.8179i −0.0380000 + 0.0658179i
\(101\) 750.000 + 1299.04i 0.738889 + 1.27979i 0.952996 + 0.302983i \(0.0979826\pi\)
−0.214107 + 0.976810i \(0.568684\pi\)
\(102\) −228.000 394.908i −0.221327 0.383350i
\(103\) −190.000 + 329.090i −0.181760 + 0.314817i −0.942480 0.334263i \(-0.891513\pi\)
0.760720 + 0.649080i \(0.224846\pi\)
\(104\) 448.000 0.422404
\(105\) 0 0
\(106\) 348.000 0.318875
\(107\) −318.000 + 550.792i −0.287310 + 0.497636i −0.973167 0.230101i \(-0.926094\pi\)
0.685856 + 0.727737i \(0.259428\pi\)
\(108\) −200.000 346.410i −0.178195 0.308642i
\(109\) −73.0000 126.440i −0.0641480 0.111108i 0.832168 0.554524i \(-0.187100\pi\)
−0.896316 + 0.443416i \(0.853766\pi\)
\(110\) 576.000 997.661i 0.499268 0.864757i
\(111\) −292.000 −0.249688
\(112\) 0 0
\(113\) 198.000 0.164834 0.0824171 0.996598i \(-0.473736\pi\)
0.0824171 + 0.996598i \(0.473736\pi\)
\(114\) 4.00000 6.92820i 0.00328627 0.00569198i
\(115\) −720.000 1247.08i −0.583829 1.01122i
\(116\) 108.000 + 187.061i 0.0864444 + 0.149726i
\(117\) 644.000 1115.44i 0.508870 0.881389i
\(118\) 276.000 0.215321
\(119\) 0 0
\(120\) 192.000 0.146059
\(121\) −486.500 + 842.643i −0.365515 + 0.633090i
\(122\) −380.000 658.179i −0.281997 0.488432i
\(123\) 126.000 + 218.238i 0.0923662 + 0.159983i
\(124\) −472.000 + 817.528i −0.341829 + 0.592066i
\(125\) 1272.00 0.910169
\(126\) 0 0
\(127\) −376.000 −0.262713 −0.131357 0.991335i \(-0.541933\pi\)
−0.131357 + 0.991335i \(0.541933\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) −376.000 651.251i −0.256628 0.444492i
\(130\) 672.000 + 1163.94i 0.453372 + 0.785263i
\(131\) −1065.00 + 1844.63i −0.710301 + 1.23028i 0.254443 + 0.967088i \(0.418108\pi\)
−0.964744 + 0.263190i \(0.915225\pi\)
\(132\) −384.000 −0.253204
\(133\) 0 0
\(134\) −968.000 −0.624048
\(135\) 600.000 1039.23i 0.382517 0.662539i
\(136\) 456.000 + 789.815i 0.287512 + 0.497986i
\(137\) 39.0000 + 67.5500i 0.0243211 + 0.0421254i 0.877930 0.478789i \(-0.158924\pi\)
−0.853609 + 0.520915i \(0.825591\pi\)
\(138\) −240.000 + 415.692i −0.148045 + 0.256421i
\(139\) −2338.00 −1.42667 −0.713333 0.700825i \(-0.752815\pi\)
−0.713333 + 0.700825i \(0.752815\pi\)
\(140\) 0 0
\(141\) 24.0000 0.0143345
\(142\) −576.000 + 997.661i −0.340400 + 0.589591i
\(143\) −1344.00 2327.88i −0.785951 1.36131i
\(144\) 184.000 + 318.697i 0.106481 + 0.184431i
\(145\) −324.000 + 561.184i −0.185564 + 0.321406i
\(146\) −2300.00 −1.30376
\(147\) 0 0
\(148\) 584.000 0.324355
\(149\) 501.000 867.757i 0.275460 0.477110i −0.694791 0.719212i \(-0.744503\pi\)
0.970251 + 0.242101i \(0.0778366\pi\)
\(150\) 38.0000 + 65.8179i 0.0206846 + 0.0358267i
\(151\) 1376.00 + 2383.30i 0.741571 + 1.28444i 0.951780 + 0.306783i \(0.0992525\pi\)
−0.210208 + 0.977657i \(0.567414\pi\)
\(152\) −8.00000 + 13.8564i −0.00426898 + 0.00739410i
\(153\) 2622.00 1.38546
\(154\) 0 0
\(155\) −2832.00 −1.46756
\(156\) 224.000 387.979i 0.114964 0.199123i
\(157\) 260.000 + 450.333i 0.132167 + 0.228920i 0.924512 0.381154i \(-0.124473\pi\)
−0.792345 + 0.610074i \(0.791140\pi\)
\(158\) −776.000 1344.07i −0.390729 0.676763i
\(159\) 174.000 301.377i 0.0867868 0.150319i
\(160\) −384.000 −0.189737
\(161\) 0 0
\(162\) 842.000 0.408357
\(163\) −640.000 + 1108.51i −0.307538 + 0.532671i −0.977823 0.209432i \(-0.932838\pi\)
0.670285 + 0.742104i \(0.266172\pi\)
\(164\) −252.000 436.477i −0.119987 0.207824i
\(165\) −576.000 997.661i −0.271767 0.470714i
\(166\) −378.000 + 654.715i −0.176738 + 0.306119i
\(167\) 1764.00 0.817380 0.408690 0.912673i \(-0.365986\pi\)
0.408690 + 0.912673i \(0.365986\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) −1368.00 + 2369.45i −0.617181 + 1.06899i
\(171\) 23.0000 + 39.8372i 0.0102857 + 0.0178153i
\(172\) 752.000 + 1302.50i 0.333369 + 0.577412i
\(173\) 384.000 665.108i 0.168757 0.292296i −0.769226 0.638977i \(-0.779358\pi\)
0.937983 + 0.346681i \(0.112691\pi\)
\(174\) 216.000 0.0941087
\(175\) 0 0
\(176\) 768.000 0.328921
\(177\) 138.000 239.023i 0.0586029 0.101503i
\(178\) 390.000 + 675.500i 0.164223 + 0.284443i
\(179\) −906.000 1569.24i −0.378311 0.655253i 0.612506 0.790466i \(-0.290162\pi\)
−0.990817 + 0.135213i \(0.956828\pi\)
\(180\) −552.000 + 956.092i −0.228576 + 0.395905i
\(181\) −448.000 −0.183976 −0.0919878 0.995760i \(-0.529322\pi\)
−0.0919878 + 0.995760i \(0.529322\pi\)
\(182\) 0 0
\(183\) −760.000 −0.306999
\(184\) 480.000 831.384i 0.192316 0.333100i
\(185\) 876.000 + 1517.28i 0.348134 + 0.602986i
\(186\) 472.000 + 817.528i 0.186068 + 0.322280i
\(187\) 2736.00 4738.89i 1.06993 1.85317i
\(188\) −48.0000 −0.0186211
\(189\) 0 0
\(190\) −48.0000 −0.0183278
\(191\) 1068.00 1849.83i 0.404596 0.700780i −0.589679 0.807638i \(-0.700746\pi\)
0.994274 + 0.106858i \(0.0340789\pi\)
\(192\) 64.0000 + 110.851i 0.0240563 + 0.0416667i
\(193\) −2215.00 3836.49i −0.826110 1.43086i −0.901068 0.433677i \(-0.857216\pi\)
0.0749584 0.997187i \(-0.476118\pi\)
\(194\) 1330.00 2303.63i 0.492208 0.852530i
\(195\) 1344.00 0.493568
\(196\) 0 0
\(197\) 198.000 0.0716087 0.0358044 0.999359i \(-0.488601\pi\)
0.0358044 + 0.999359i \(0.488601\pi\)
\(198\) 1104.00 1912.18i 0.396252 0.686328i
\(199\) 1142.00 + 1978.00i 0.406805 + 0.704607i 0.994530 0.104454i \(-0.0333094\pi\)
−0.587725 + 0.809061i \(0.699976\pi\)
\(200\) −76.0000 131.636i −0.0268701 0.0465403i
\(201\) −484.000 + 838.313i −0.169844 + 0.294179i
\(202\) −3000.00 −1.04495
\(203\) 0 0
\(204\) 912.000 0.313004
\(205\) 756.000 1309.43i 0.257567 0.446120i
\(206\) −380.000 658.179i −0.128524 0.222609i
\(207\) −1380.00 2390.23i −0.463365 0.802572i
\(208\) −448.000 + 775.959i −0.149342 + 0.258669i
\(209\) 96.0000 0.0317725
\(210\) 0 0
\(211\) 4412.00 1.43950 0.719750 0.694233i \(-0.244256\pi\)
0.719750 + 0.694233i \(0.244256\pi\)
\(212\) −348.000 + 602.754i −0.112739 + 0.195270i
\(213\) 576.000 + 997.661i 0.185290 + 0.320933i
\(214\) −636.000 1101.58i −0.203159 0.351882i
\(215\) −2256.00 + 3907.51i −0.715618 + 1.23949i
\(216\) 800.000 0.252005
\(217\) 0 0
\(218\) 292.000 0.0907190
\(219\) −1150.00 + 1991.86i −0.354839 + 0.614600i
\(220\) 1152.00 + 1995.32i 0.353036 + 0.611476i
\(221\) 3192.00 + 5528.71i 0.971571 + 1.68281i
\(222\) 292.000 505.759i 0.0882782 0.152902i
\(223\) 2072.00 0.622204 0.311102 0.950377i \(-0.399302\pi\)
0.311102 + 0.950377i \(0.399302\pi\)
\(224\) 0 0
\(225\) −437.000 −0.129481
\(226\) −198.000 + 342.946i −0.0582777 + 0.100940i
\(227\) 183.000 + 316.965i 0.0535072 + 0.0926772i 0.891538 0.452945i \(-0.149627\pi\)
−0.838031 + 0.545622i \(0.816293\pi\)
\(228\) 8.00000 + 13.8564i 0.00232374 + 0.00402484i
\(229\) 188.000 325.626i 0.0542506 0.0939648i −0.837625 0.546246i \(-0.816056\pi\)
0.891875 + 0.452281i \(0.149390\pi\)
\(230\) 2880.00 0.825659
\(231\) 0 0
\(232\) −432.000 −0.122251
\(233\) 1131.00 1958.95i 0.318001 0.550794i −0.662070 0.749442i \(-0.730322\pi\)
0.980071 + 0.198648i \(0.0636551\pi\)
\(234\) 1288.00 + 2230.88i 0.359826 + 0.623236i
\(235\) −72.0000 124.708i −0.0199862 0.0346172i
\(236\) −276.000 + 478.046i −0.0761274 + 0.131857i
\(237\) −1552.00 −0.425372
\(238\) 0 0
\(239\) 2592.00 0.701517 0.350758 0.936466i \(-0.385924\pi\)
0.350758 + 0.936466i \(0.385924\pi\)
\(240\) −192.000 + 332.554i −0.0516398 + 0.0894427i
\(241\) −55.0000 95.2628i −0.0147007 0.0254623i 0.858581 0.512677i \(-0.171346\pi\)
−0.873282 + 0.487215i \(0.838013\pi\)
\(242\) −973.000 1685.29i −0.258458 0.447662i
\(243\) 1771.00 3067.46i 0.467530 0.809785i
\(244\) 1520.00 0.398803
\(245\) 0 0
\(246\) −504.000 −0.130625
\(247\) −56.0000 + 96.9948i −0.0144259 + 0.0249864i
\(248\) −944.000 1635.06i −0.241710 0.418654i
\(249\) 378.000 + 654.715i 0.0962039 + 0.166630i
\(250\) −1272.00 + 2203.17i −0.321793 + 0.557362i
\(251\) −1890.00 −0.475282 −0.237641 0.971353i \(-0.576374\pi\)
−0.237641 + 0.971353i \(0.576374\pi\)
\(252\) 0 0
\(253\) −5760.00 −1.43134
\(254\) 376.000 651.251i 0.0928832 0.160878i
\(255\) 1368.00 + 2369.45i 0.335951 + 0.581884i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1065.00 + 1844.63i −0.258494 + 0.447724i −0.965839 0.259144i \(-0.916559\pi\)
0.707345 + 0.706869i \(0.249893\pi\)
\(258\) 1504.00 0.362926
\(259\) 0 0
\(260\) −2688.00 −0.641164
\(261\) −621.000 + 1075.60i −0.147276 + 0.255089i
\(262\) −2130.00 3689.27i −0.502259 0.869938i
\(263\) 2496.00 + 4323.20i 0.585209 + 1.01361i 0.994849 + 0.101365i \(0.0323208\pi\)
−0.409640 + 0.912247i \(0.634346\pi\)
\(264\) 384.000 665.108i 0.0895211 0.155055i
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) 780.000 0.178784
\(268\) 968.000 1676.63i 0.220634 0.382150i
\(269\) −3408.00 5902.83i −0.772451 1.33793i −0.936216 0.351426i \(-0.885697\pi\)
0.163764 0.986499i \(-0.447636\pi\)
\(270\) 1200.00 + 2078.46i 0.270480 + 0.468486i
\(271\) −4096.00 + 7094.48i −0.918134 + 1.59025i −0.115887 + 0.993262i \(0.536971\pi\)
−0.802247 + 0.596992i \(0.796362\pi\)
\(272\) −1824.00 −0.406604
\(273\) 0 0
\(274\) −156.000 −0.0343953
\(275\) −456.000 + 789.815i −0.0999921 + 0.173191i
\(276\) −480.000 831.384i −0.104683 0.181317i
\(277\) −1207.00 2090.59i −0.261811 0.453470i 0.704912 0.709294i \(-0.250986\pi\)
−0.966723 + 0.255825i \(0.917653\pi\)
\(278\) 2338.00 4049.53i 0.504403 0.873651i
\(279\) −5428.00 −1.16475
\(280\) 0 0
\(281\) 1962.00 0.416524 0.208262 0.978073i \(-0.433219\pi\)
0.208262 + 0.978073i \(0.433219\pi\)
\(282\) −24.0000 + 41.5692i −0.00506801 + 0.00877805i
\(283\) −2701.00 4678.27i −0.567342 0.982665i −0.996828 0.0795914i \(-0.974638\pi\)
0.429486 0.903074i \(-0.358695\pi\)
\(284\) −1152.00 1995.32i −0.240699 0.416904i
\(285\) −24.0000 + 41.5692i −0.00498820 + 0.00863982i
\(286\) 5376.00 1.11150
\(287\) 0 0
\(288\) −736.000 −0.150588
\(289\) −4041.50 + 7000.08i −0.822613 + 1.42481i
\(290\) −648.000 1122.37i −0.131213 0.227268i
\(291\) −1330.00 2303.63i −0.267924 0.464059i
\(292\) 2300.00 3983.72i 0.460950 0.798388i
\(293\) −4788.00 −0.954669 −0.477334 0.878722i \(-0.658397\pi\)
−0.477334 + 0.878722i \(0.658397\pi\)
\(294\) 0 0
\(295\) −1656.00 −0.326834
\(296\) −584.000 + 1011.52i −0.114677 + 0.198626i
\(297\) −2400.00 4156.92i −0.468896 0.812152i
\(298\) 1002.00 + 1735.51i 0.194780 + 0.337368i
\(299\) 3360.00 5819.69i 0.649879 1.12562i
\(300\) −152.000 −0.0292524
\(301\) 0 0
\(302\) −5504.00 −1.04874
\(303\) −1500.00 + 2598.08i −0.284399 + 0.492593i
\(304\) −16.0000 27.7128i −0.00301863 0.00522842i
\(305\) 2280.00 + 3949.08i 0.428041 + 0.741388i
\(306\) −2622.00 + 4541.44i −0.489836 + 0.848421i
\(307\) −574.000 −0.106710 −0.0533549 0.998576i \(-0.516991\pi\)
−0.0533549 + 0.998576i \(0.516991\pi\)
\(308\) 0 0
\(309\) −760.000 −0.139919
\(310\) 2832.00 4905.17i 0.518861 0.898693i
\(311\) 4404.00 + 7627.95i 0.802984 + 1.39081i 0.917644 + 0.397404i \(0.130089\pi\)
−0.114660 + 0.993405i \(0.536578\pi\)
\(312\) 448.000 + 775.959i 0.0812917 + 0.140801i
\(313\) 1385.00 2398.89i 0.250111 0.433205i −0.713445 0.700711i \(-0.752866\pi\)
0.963556 + 0.267506i \(0.0861995\pi\)
\(314\) −1040.00 −0.186913
\(315\) 0 0
\(316\) 3104.00 0.552575
\(317\) −3783.00 + 6552.35i −0.670266 + 1.16094i 0.307562 + 0.951528i \(0.400487\pi\)
−0.977828 + 0.209407i \(0.932847\pi\)
\(318\) 348.000 + 602.754i 0.0613675 + 0.106292i
\(319\) 1296.00 + 2244.74i 0.227467 + 0.393985i
\(320\) 384.000 665.108i 0.0670820 0.116190i
\(321\) −1272.00 −0.221172
\(322\) 0 0
\(323\) −228.000 −0.0392763
\(324\) −842.000 + 1458.39i −0.144376 + 0.250066i
\(325\) −532.000 921.451i −0.0908002 0.157270i
\(326\) −1280.00 2217.03i −0.217462 0.376655i
\(327\) 146.000 252.879i 0.0246906 0.0427653i
\(328\) 1008.00 0.169687
\(329\) 0 0
\(330\) 2304.00 0.384336
\(331\) 5660.00 9803.41i 0.939884 1.62793i 0.174201 0.984710i \(-0.444266\pi\)
0.765684 0.643217i \(-0.222401\pi\)
\(332\) −756.000 1309.43i −0.124973 0.216459i
\(333\) 1679.00 + 2908.11i 0.276302 + 0.478569i
\(334\) −1764.00 + 3055.34i −0.288987 + 0.500541i
\(335\) 5808.00 0.947239
\(336\) 0 0
\(337\) −4786.00 −0.773620 −0.386810 0.922159i \(-0.626423\pi\)
−0.386810 + 0.922159i \(0.626423\pi\)
\(338\) −939.000 + 1626.40i −0.151109 + 0.261729i
\(339\) 198.000 + 342.946i 0.0317224 + 0.0549448i
\(340\) −2736.00 4738.89i −0.436413 0.755890i
\(341\) −5664.00 + 9810.34i −0.899480 + 1.55795i
\(342\) −92.0000 −0.0145462
\(343\) 0 0
\(344\) −3008.00 −0.471455
\(345\) 1440.00 2494.15i 0.224716 0.389219i
\(346\) 768.000 + 1330.22i 0.119329 + 0.206684i
\(347\) −6324.00 10953.5i −0.978358 1.69457i −0.668378 0.743822i \(-0.733011\pi\)
−0.309980 0.950743i \(-0.600322\pi\)
\(348\) −216.000 + 374.123i −0.0332725 + 0.0576296i
\(349\) 9632.00 1.47733 0.738666 0.674071i \(-0.235456\pi\)
0.738666 + 0.674071i \(0.235456\pi\)
\(350\) 0 0
\(351\) 5600.00 0.851584
\(352\) −768.000 + 1330.22i −0.116291 + 0.201422i
\(353\) 1695.00 + 2935.83i 0.255569 + 0.442658i 0.965050 0.262066i \(-0.0844040\pi\)
−0.709481 + 0.704724i \(0.751071\pi\)
\(354\) 276.000 + 478.046i 0.0414385 + 0.0717736i
\(355\) 3456.00 5985.97i 0.516691 0.894936i
\(356\) −1560.00 −0.232247
\(357\) 0 0
\(358\) 3624.00 0.535012
\(359\) 5352.00 9269.94i 0.786818 1.36281i −0.141089 0.989997i \(-0.545060\pi\)
0.927907 0.372812i \(-0.121606\pi\)
\(360\) −1104.00 1912.18i −0.161628 0.279947i
\(361\) 3427.50 + 5936.60i 0.499708 + 0.865520i
\(362\) 448.000 775.959i 0.0650452 0.112662i
\(363\) −1946.00 −0.281373
\(364\) 0 0
\(365\) 13800.0 1.97897
\(366\) 760.000 1316.36i 0.108541 0.187998i
\(367\) 4292.00 + 7433.96i 0.610465 + 1.05736i 0.991162 + 0.132656i \(0.0423507\pi\)
−0.380697 + 0.924700i \(0.624316\pi\)
\(368\) 960.000 + 1662.77i 0.135988 + 0.235538i
\(369\) 1449.00 2509.74i 0.204423 0.354070i
\(370\) −3504.00 −0.492336
\(371\) 0 0
\(372\) −1888.00 −0.263140
\(373\) 1061.00 1837.71i 0.147283 0.255101i −0.782939 0.622098i \(-0.786281\pi\)
0.930222 + 0.366997i \(0.119614\pi\)
\(374\) 5472.00 + 9477.78i 0.756552 + 1.31039i
\(375\) 1272.00 + 2203.17i 0.175162 + 0.303390i
\(376\) 48.0000 83.1384i 0.00658354 0.0114030i
\(377\) −3024.00 −0.413114
\(378\) 0 0
\(379\) −4912.00 −0.665732 −0.332866 0.942974i \(-0.608016\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(380\) 48.0000 83.1384i 0.00647986 0.0112235i
\(381\) −376.000 651.251i −0.0505592 0.0875711i
\(382\) 2136.00 + 3699.66i 0.286092 + 0.495526i
\(383\) −4530.00 + 7846.19i −0.604366 + 1.04679i 0.387785 + 0.921750i \(0.373240\pi\)
−0.992151 + 0.125043i \(0.960093\pi\)
\(384\) −256.000 −0.0340207
\(385\) 0 0
\(386\) 8860.00 1.16830
\(387\) −4324.00 + 7489.39i −0.567962 + 0.983739i
\(388\) 2660.00 + 4607.26i 0.348044 + 0.602830i
\(389\) −4497.00 7789.03i −0.586136 1.01522i −0.994733 0.102502i \(-0.967315\pi\)
0.408597 0.912715i \(-0.366018\pi\)
\(390\) −1344.00 + 2327.88i −0.174503 + 0.302248i
\(391\) 13680.0 1.76938
\(392\) 0 0
\(393\) −4260.00 −0.546790
\(394\) −198.000 + 342.946i −0.0253175 + 0.0438512i
\(395\) 4656.00 + 8064.43i 0.593086 + 1.02725i
\(396\) 2208.00 + 3824.37i 0.280192 + 0.485307i
\(397\) 6488.00 11237.5i 0.820210 1.42065i −0.0853156 0.996354i \(-0.527190\pi\)
0.905526 0.424291i \(-0.139477\pi\)
\(398\) −4568.00 −0.575309
\(399\) 0 0
\(400\) 304.000 0.0380000
\(401\) 1761.00 3050.14i 0.219302 0.379842i −0.735293 0.677750i \(-0.762955\pi\)
0.954595 + 0.297907i \(0.0962886\pi\)
\(402\) −968.000 1676.63i −0.120098 0.208016i
\(403\) −6608.00 11445.4i −0.816794 1.41473i
\(404\) 3000.00 5196.15i 0.369445 0.639897i
\(405\) −5052.00 −0.619842
\(406\) 0 0
\(407\) 7008.00 0.853498
\(408\) −912.000 + 1579.63i −0.110664 + 0.191675i
\(409\) −6355.00 11007.2i −0.768300 1.33073i −0.938484 0.345322i \(-0.887770\pi\)
0.170185 0.985412i \(-0.445564\pi\)
\(410\) 1512.00 + 2618.86i 0.182128 + 0.315454i
\(411\) −78.0000 + 135.100i −0.00936121 + 0.0162141i
\(412\) 1520.00 0.181760
\(413\) 0 0
\(414\) 5520.00 0.655298
\(415\) 2268.00 3928.29i 0.268269 0.464656i
\(416\) −896.000 1551.92i −0.105601 0.182906i
\(417\) −2338.00 4049.53i −0.274562 0.475555i
\(418\) −96.0000 + 166.277i −0.0112333 + 0.0194566i
\(419\) 1638.00 0.190982 0.0954911 0.995430i \(-0.469558\pi\)
0.0954911 + 0.995430i \(0.469558\pi\)
\(420\) 0 0
\(421\) −12850.0 −1.48758 −0.743789 0.668414i \(-0.766973\pi\)
−0.743789 + 0.668414i \(0.766973\pi\)
\(422\) −4412.00 + 7641.81i −0.508940 + 0.881510i
\(423\) −138.000 239.023i −0.0158624 0.0274745i
\(424\) −696.000 1205.51i −0.0797187 0.138077i
\(425\) 1083.00 1875.81i 0.123608 0.214095i
\(426\) −2304.00 −0.262040
\(427\) 0 0
\(428\) 2544.00 0.287310
\(429\) 2688.00 4655.75i 0.302513 0.523967i
\(430\) −4512.00 7815.01i −0.506019 0.876450i
\(431\) 4008.00 + 6942.06i 0.447932 + 0.775840i 0.998251 0.0591136i \(-0.0188274\pi\)
−0.550320 + 0.834954i \(0.685494\pi\)
\(432\) −800.000 + 1385.64i −0.0890973 + 0.154321i
\(433\) 2198.00 0.243947 0.121974 0.992533i \(-0.461078\pi\)
0.121974 + 0.992533i \(0.461078\pi\)
\(434\) 0 0
\(435\) −1296.00 −0.142847
\(436\) −292.000 + 505.759i −0.0320740 + 0.0555538i
\(437\) 120.000 + 207.846i 0.0131359 + 0.0227520i
\(438\) −2300.00 3983.72i −0.250909 0.434588i
\(439\) 188.000 325.626i 0.0204391 0.0354015i −0.855625 0.517596i \(-0.826827\pi\)
0.876064 + 0.482195i \(0.160160\pi\)
\(440\) −4608.00 −0.499268
\(441\) 0 0
\(442\) −12768.0 −1.37401
\(443\) −3594.00 + 6224.99i −0.385454 + 0.667626i −0.991832 0.127551i \(-0.959288\pi\)
0.606378 + 0.795176i \(0.292622\pi\)
\(444\) 584.000 + 1011.52i 0.0624221 + 0.108118i
\(445\) −2340.00 4053.00i −0.249273 0.431754i
\(446\) −2072.00 + 3588.81i −0.219982 + 0.381020i
\(447\) 2004.00 0.212049
\(448\) 0 0
\(449\) −14670.0 −1.54192 −0.770958 0.636886i \(-0.780222\pi\)
−0.770958 + 0.636886i \(0.780222\pi\)
\(450\) 437.000 756.906i 0.0457786 0.0792909i
\(451\) −3024.00 5237.72i −0.315731 0.546862i
\(452\) −396.000 685.892i −0.0412086 0.0713753i
\(453\) −2752.00 + 4766.60i −0.285431 + 0.494381i
\(454\) −732.000 −0.0756706
\(455\) 0 0
\(456\) −32.0000 −0.00328627
\(457\) 2573.00 4456.57i 0.263370 0.456169i −0.703766 0.710432i \(-0.748499\pi\)
0.967135 + 0.254263i \(0.0818328\pi\)
\(458\) 376.000 + 651.251i 0.0383610 + 0.0664432i
\(459\) 5700.00 + 9872.69i 0.579637 + 1.00396i
\(460\) −2880.00 + 4988.31i −0.291915 + 0.505611i
\(461\) −1512.00 −0.152757 −0.0763784 0.997079i \(-0.524336\pi\)
−0.0763784 + 0.997079i \(0.524336\pi\)
\(462\) 0 0
\(463\) 7184.00 0.721099 0.360549 0.932740i \(-0.382589\pi\)
0.360549 + 0.932740i \(0.382589\pi\)
\(464\) 432.000 748.246i 0.0432222 0.0748630i
\(465\) −2832.00 4905.17i −0.282432 0.489186i
\(466\) 2262.00 + 3917.90i 0.224861 + 0.389470i
\(467\) 8259.00 14305.0i 0.818375 1.41747i −0.0885046 0.996076i \(-0.528209\pi\)
0.906879 0.421391i \(-0.138458\pi\)
\(468\) −5152.00 −0.508870
\(469\) 0 0
\(470\) 288.000 0.0282648
\(471\) −520.000 + 900.666i −0.0508712 + 0.0881115i
\(472\) −552.000 956.092i −0.0538302 0.0932367i
\(473\) 9024.00 + 15630.0i 0.877218 + 1.51939i
\(474\) 1552.00 2688.14i 0.150392 0.260486i
\(475\) 38.0000 0.00367065
\(476\) 0 0
\(477\) −4002.00 −0.384149
\(478\) −2592.00 + 4489.48i −0.248024 + 0.429590i
\(479\) −5046.00 8739.93i −0.481331 0.833690i 0.518439 0.855114i \(-0.326513\pi\)
−0.999770 + 0.0214244i \(0.993180\pi\)
\(480\) −384.000 665.108i −0.0365148 0.0632456i
\(481\) −4088.00 + 7080.62i −0.387519 + 0.671203i
\(482\) 220.000 0.0207899
\(483\) 0 0
\(484\) 3892.00 0.365515
\(485\) −7980.00 + 13821.8i −0.747120 + 1.29405i
\(486\) 3542.00 + 6134.92i 0.330593 + 0.572605i
\(487\) −3916.00 6782.71i −0.364376 0.631117i 0.624300 0.781185i \(-0.285384\pi\)
−0.988676 + 0.150068i \(0.952051\pi\)
\(488\) −1520.00 + 2632.72i −0.140998 + 0.244216i
\(489\) −2560.00 −0.236743
\(490\) 0 0
\(491\) −6732.00 −0.618759 −0.309380 0.950939i \(-0.600121\pi\)
−0.309380 + 0.950939i \(0.600121\pi\)
\(492\) 504.000 872.954i 0.0461831 0.0799914i
\(493\) −3078.00 5331.25i −0.281189 0.487034i
\(494\) −112.000 193.990i −0.0102006 0.0176680i
\(495\) −6624.00 + 11473.1i −0.601468 + 1.04177i
\(496\) 3776.00 0.341829
\(497\) 0 0
\(498\) −1512.00 −0.136053
\(499\) −9334.00 + 16167.0i −0.837369 + 1.45037i 0.0547176 + 0.998502i \(0.482574\pi\)
−0.892087 + 0.451864i \(0.850759\pi\)
\(500\) −2544.00 4406.34i −0.227542 0.394115i
\(501\) 1764.00 + 3055.34i 0.157305 + 0.272460i
\(502\) 1890.00 3273.58i 0.168038 0.291049i
\(503\) −6048.00 −0.536117 −0.268059 0.963403i \(-0.586382\pi\)
−0.268059 + 0.963403i \(0.586382\pi\)
\(504\) 0 0
\(505\) 18000.0 1.58612
\(506\) 5760.00 9976.61i 0.506054 0.876511i
\(507\) 939.000 + 1626.40i 0.0822534 + 0.142467i
\(508\) 752.000 + 1302.50i 0.0656784 + 0.113758i
\(509\) −5664.00 + 9810.34i −0.493227 + 0.854294i −0.999970 0.00780356i \(-0.997516\pi\)
0.506743 + 0.862097i \(0.330849\pi\)
\(510\) −5472.00 −0.475106
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −100.000 + 173.205i −0.00860645 + 0.0149068i
\(514\) −2130.00 3689.27i −0.182783 0.316589i
\(515\) 2280.00 + 3949.08i 0.195085 + 0.337897i
\(516\) −1504.00 + 2605.00i −0.128314 + 0.222246i
\(517\) −576.000 −0.0489989
\(518\) 0 0
\(519\) 1536.00 0.129909
\(520\) 2688.00 4655.75i 0.226686 0.392631i
\(521\) 2073.00 + 3590.54i 0.174318 + 0.301928i 0.939925 0.341381i \(-0.110895\pi\)
−0.765607 + 0.643309i \(0.777561\pi\)
\(522\) −1242.00 2151.21i −0.104140 0.180375i
\(523\) 503.000 871.222i 0.0420548 0.0728410i −0.844232 0.535978i \(-0.819943\pi\)
0.886287 + 0.463137i \(0.153276\pi\)
\(524\) 8520.00 0.710301
\(525\) 0 0
\(526\) −9984.00 −0.827610
\(527\) 13452.0 23299.5i 1.11191 1.92589i
\(528\) 768.000 + 1330.22i 0.0633010 + 0.109640i
\(529\) −1116.50 1933.83i −0.0917646 0.158941i
\(530\) 2088.00 3616.52i 0.171126 0.296399i
\(531\) −3174.00 −0.259397
\(532\) 0 0
\(533\) 7056.00 0.573413
\(534\) −780.000 + 1351.00i −0.0632096 + 0.109482i
\(535\) 3816.00 + 6609.51i 0.308374 + 0.534119i
\(536\) 1936.00 + 3353.25i 0.156012 + 0.270221i
\(537\) 1812.00 3138.48i 0.145612 0.252207i
\(538\) 13632.0 1.09241
\(539\) 0 0
\(540\) −4800.00 −0.382517
\(541\) 7361.00 12749.6i 0.584980 1.01321i −0.409898 0.912131i \(-0.634436\pi\)
0.994878 0.101084i \(-0.0322309\pi\)
\(542\) −8192.00 14189.0i −0.649219 1.12448i
\(543\) −448.000 775.959i −0.0354061 0.0613252i
\(544\) 1824.00 3159.26i 0.143756 0.248993i
\(545\) −1752.00 −0.137702
\(546\) 0 0
\(547\) −13480.0 −1.05368 −0.526840 0.849964i \(-0.676623\pi\)
−0.526840 + 0.849964i \(0.676623\pi\)
\(548\) 156.000 270.200i 0.0121606 0.0210627i
\(549\) 4370.00 + 7569.06i 0.339721 + 0.588415i
\(550\) −912.000 1579.63i −0.0707051 0.122465i
\(551\) 54.0000 93.5307i 0.00417509 0.00723148i
\(552\) 1920.00 0.148045
\(553\) 0 0
\(554\) 4828.00 0.370256
\(555\) −1752.00 + 3034.55i −0.133997 + 0.232089i
\(556\) 4676.00 + 8099.07i 0.356666 + 0.617764i
\(557\) −3111.00 5388.41i −0.236656 0.409900i 0.723097 0.690747i \(-0.242718\pi\)
−0.959753 + 0.280847i \(0.909385\pi\)
\(558\) 5428.00 9401.57i 0.411802 0.713262i
\(559\) −21056.0 −1.59316
\(560\) 0 0
\(561\) 10944.0 0.823629
\(562\) −1962.00 + 3398.28i −0.147263 + 0.255068i
\(563\) −2463.00 4266.04i −0.184375 0.319347i 0.758991 0.651101i \(-0.225693\pi\)
−0.943366 + 0.331755i \(0.892359\pi\)
\(564\) −48.0000 83.1384i −0.00358363 0.00620702i
\(565\) 1188.00 2057.68i 0.0884594 0.153216i
\(566\) 10804.0 0.802343
\(567\) 0 0
\(568\) 4608.00 0.340400
\(569\) −11091.0 + 19210.2i −0.817151 + 1.41535i 0.0906221 + 0.995885i \(0.471114\pi\)
−0.907773 + 0.419462i \(0.862219\pi\)
\(570\) −48.0000 83.1384i −0.00352719 0.00610927i
\(571\) −1648.00 2854.42i −0.120782 0.209201i 0.799294 0.600940i \(-0.205207\pi\)
−0.920076 + 0.391739i \(0.871874\pi\)
\(572\) −5376.00 + 9311.51i −0.392975 + 0.680653i
\(573\) 4272.00 0.311458
\(574\) 0 0
\(575\) −2280.00 −0.165361
\(576\) 736.000 1274.79i 0.0532407 0.0922157i
\(577\) 12167.0 + 21073.9i 0.877849 + 1.52048i 0.853697 + 0.520771i \(0.174355\pi\)
0.0241523 + 0.999708i \(0.492311\pi\)
\(578\) −8083.00 14000.2i −0.581676 1.00749i
\(579\) 4430.00 7672.99i 0.317970 0.550740i
\(580\) 2592.00 0.185564
\(581\) 0 0
\(582\) 5320.00 0.378902
\(583\) −4176.00 + 7233.04i −0.296659 + 0.513829i
\(584\) 4600.00 + 7967.43i 0.325941 + 0.564546i
\(585\) −7728.00 13385.3i −0.546177 0.946006i
\(586\) 4788.00 8293.06i 0.337526 0.584613i
\(587\) 1638.00 0.115175 0.0575873 0.998340i \(-0.481659\pi\)
0.0575873 + 0.998340i \(0.481659\pi\)
\(588\) 0 0
\(589\) 472.000 0.0330194
\(590\) 1656.00 2868.28i 0.115553 0.200144i
\(591\) 198.000 + 342.946i 0.0137811 + 0.0238696i
\(592\) −1168.00 2023.04i −0.0810887 0.140450i
\(593\) 3723.00 6448.43i 0.257817 0.446552i −0.707840 0.706373i \(-0.750330\pi\)
0.965657 + 0.259821i \(0.0836636\pi\)
\(594\) 9600.00 0.663119
\(595\) 0 0
\(596\) −4008.00 −0.275460
\(597\) −2284.00 + 3956.00i −0.156579 + 0.271203i
\(598\) 6720.00 + 11639.4i 0.459534 + 0.795936i
\(599\) 3252.00 + 5632.63i 0.221825 + 0.384212i 0.955362 0.295437i \(-0.0954653\pi\)
−0.733537 + 0.679649i \(0.762132\pi\)
\(600\) 152.000 263.272i 0.0103423 0.0179134i
\(601\) 16058.0 1.08988 0.544941 0.838474i \(-0.316552\pi\)
0.544941 + 0.838474i \(0.316552\pi\)
\(602\) 0 0
\(603\) 11132.0 0.751791
\(604\) 5504.00 9533.21i 0.370786 0.642220i
\(605\) 5838.00 + 10111.7i 0.392311 + 0.679503i
\(606\) −3000.00 5196.15i −0.201100 0.348316i
\(607\) −5104.00 + 8840.39i −0.341293 + 0.591137i −0.984673 0.174410i \(-0.944198\pi\)
0.643380 + 0.765547i \(0.277532\pi\)
\(608\) 64.0000 0.00426898
\(609\) 0 0
\(610\) −9120.00 −0.605341
\(611\) 336.000 581.969i 0.0222473 0.0385335i
\(612\) −5244.00 9082.87i −0.346366 0.599924i
\(613\) 7487.00 + 12967.9i 0.493307 + 0.854432i 0.999970 0.00771145i \(-0.00245465\pi\)
−0.506663 + 0.862144i \(0.669121\pi\)
\(614\) 574.000 994.197i 0.0377276 0.0653461i
\(615\) 3024.00 0.198276
\(616\) 0 0
\(617\) 7254.00 0.473314 0.236657 0.971593i \(-0.423948\pi\)
0.236657 + 0.971593i \(0.423948\pi\)
\(618\) 760.000 1316.36i 0.0494687 0.0856824i
\(619\) −6229.00 10788.9i −0.404466 0.700556i 0.589793 0.807555i \(-0.299209\pi\)
−0.994259 + 0.106998i \(0.965876\pi\)
\(620\) 5664.00 + 9810.34i 0.366890 + 0.635472i
\(621\) 6000.00 10392.3i 0.387716 0.671544i
\(622\) −17616.0 −1.13559
\(623\) 0 0
\(624\) −1792.00 −0.114964
\(625\) 8819.50 15275.8i 0.564448 0.977653i
\(626\) 2770.00 + 4797.78i 0.176855 + 0.306322i
\(627\) 96.0000 + 166.277i 0.00611463 + 0.0105908i
\(628\) 1040.00 1801.33i 0.0660836 0.114460i
\(629\) −16644.0 −1.05507
\(630\) 0 0
\(631\) 28352.0 1.78871 0.894354 0.447359i \(-0.147635\pi\)
0.894354 + 0.447359i \(0.147635\pi\)
\(632\) −3104.00 + 5376.29i −0.195365 + 0.338382i
\(633\) 4412.00 + 7641.81i 0.277032 + 0.479834i
\(634\) −7566.00 13104.7i −0.473950 0.820905i
\(635\) −2256.00 + 3907.51i −0.140987 + 0.244196i
\(636\) −1392.00 −0.0867868
\(637\) 0 0
\(638\) −5184.00 −0.321687
\(639\) 6624.00 11473.1i 0.410080 0.710280i
\(640\) 768.000 + 1330.22i 0.0474342 + 0.0821584i
\(641\) −13695.0 23720.4i −0.843869 1.46162i −0.886600 0.462537i \(-0.846939\pi\)
0.0427309 0.999087i \(-0.486394\pi\)
\(642\) 1272.00 2203.17i 0.0781960 0.135439i
\(643\) −21490.0 −1.31801 −0.659007 0.752137i \(-0.729023\pi\)
−0.659007 + 0.752137i \(0.729023\pi\)
\(644\) 0 0
\(645\) −9024.00 −0.550883
\(646\) 228.000 394.908i 0.0138863 0.0240518i
\(647\) −8826.00 15287.1i −0.536300 0.928898i −0.999099 0.0424353i \(-0.986488\pi\)
0.462800 0.886463i \(-0.346845\pi\)
\(648\) −1684.00 2916.77i −0.102089 0.176824i
\(649\) −3312.00 + 5736.55i −0.200320 + 0.346964i
\(650\) 2128.00 0.128411
\(651\) 0 0
\(652\) 5120.00 0.307538
\(653\) 2391.00 4141.33i 0.143288 0.248182i −0.785445 0.618932i \(-0.787566\pi\)
0.928733 + 0.370749i \(0.120899\pi\)
\(654\) 292.000 + 505.759i 0.0174589 + 0.0302397i
\(655\) 12780.0 + 22135.6i 0.762375 + 1.32047i
\(656\) −1008.00 + 1745.91i −0.0599936 + 0.103912i
\(657\) 26450.0 1.57064
\(658\) 0 0
\(659\) −27144.0 −1.60452 −0.802261 0.596973i \(-0.796370\pi\)
−0.802261 + 0.596973i \(0.796370\pi\)
\(660\) −2304.00 + 3990.65i −0.135883 + 0.235357i
\(661\) 5930.00 + 10271.1i 0.348941 + 0.604384i 0.986062 0.166380i \(-0.0532079\pi\)
−0.637120 + 0.770764i \(0.719875\pi\)
\(662\) 11320.0 + 19606.8i 0.664599 + 1.15112i
\(663\) −6384.00 + 11057.4i −0.373958 + 0.647714i
\(664\) 3024.00 0.176738
\(665\) 0 0
\(666\) −6716.00 −0.390750
\(667\) −3240.00 + 5611.84i −0.188086 + 0.325774i
\(668\) −3528.00 6110.68i −0.204345 0.353936i
\(669\) 2072.00 + 3588.81i 0.119743 + 0.207401i
\(670\) −5808.00 + 10059.8i −0.334899 + 0.580063i
\(671\) 18240.0 1.04940
\(672\) 0 0
\(673\) 5546.00 0.317656 0.158828 0.987306i \(-0.449228\pi\)
0.158828 + 0.987306i \(0.449228\pi\)
\(674\) 4786.00 8289.60i 0.273516 0.473744i
\(675\) −950.000 1645.45i −0.0541711 0.0938272i
\(676\) −1878.00 3252.79i −0.106850 0.185070i
\(677\) 7440.00 12886.5i 0.422367 0.731561i −0.573804 0.818993i \(-0.694533\pi\)
0.996170 + 0.0874320i \(0.0278660\pi\)
\(678\) −792.000 −0.0448622
\(679\) 0 0
\(680\) 10944.0 0.617181
\(681\) −366.000 + 633.931i −0.0205949 + 0.0356715i
\(682\) −11328.0 19620.7i −0.636029 1.10163i
\(683\) −10482.0 18155.4i −0.587237 1.01712i −0.994593 0.103854i \(-0.966882\pi\)
0.407356 0.913269i \(-0.366451\pi\)
\(684\) 92.0000 159.349i 0.00514285 0.00890767i
\(685\) 936.000 0.0522084
\(686\) 0 0
\(687\) 752.000 0.0417621
\(688\) 3008.00 5210.01i 0.166684 0.288706i
\(689\) −4872.00 8438.55i −0.269388 0.466594i
\(690\) 2880.00 + 4988.31i 0.158898 + 0.275220i
\(691\) −6553.00 + 11350.1i −0.360764 + 0.624861i −0.988087 0.153898i \(-0.950817\pi\)
0.627323 + 0.778759i \(0.284151\pi\)
\(692\) −3072.00 −0.168757
\(693\) 0 0
\(694\) 25296.0 1.38361
\(695\) −14028.0 + 24297.2i −0.765629 + 1.32611i
\(696\) −432.000 748.246i −0.0235272 0.0407503i
\(697\) 7182.00 + 12439.6i 0.390298 + 0.676016i
\(698\) −9632.00 + 16683.1i −0.522316 + 0.904678i
\(699\) 4524.00 0.244797
\(700\) 0 0
\(701\) −4590.00 −0.247307 −0.123653 0.992325i \(-0.539461\pi\)
−0.123653 + 0.992325i \(0.539461\pi\)
\(702\) −5600.00 + 9699.48i −0.301080 + 0.521486i
\(703\) −146.000 252.879i −0.00783285 0.0135669i
\(704\) −1536.00 2660.43i −0.0822304 0.142427i
\(705\) 144.000 249.415i 0.00769270 0.0133241i
\(706\) −6780.00 −0.361429
\(707\) 0 0
\(708\) −1104.00 −0.0586029
\(709\) 431.000 746.514i 0.0228301 0.0395429i −0.854385 0.519641i \(-0.826066\pi\)
0.877215 + 0.480098i \(0.159399\pi\)
\(710\) 6912.00 + 11971.9i 0.365356 + 0.632815i
\(711\) 8924.00 + 15456.8i 0.470712 + 0.815297i
\(712\) 1560.00 2702.00i 0.0821116 0.142221i
\(713\) −28320.0 −1.48751
\(714\) 0 0
\(715\) −32256.0 −1.68714
\(716\) −3624.00 + 6276.95i −0.189155 + 0.327627i
\(717\) 2592.00 + 4489.48i 0.135007 + 0.233839i
\(718\) 10704.0 + 18539.9i 0.556365 + 0.963652i
\(719\) 1770.00 3065.73i 0.0918079 0.159016i −0.816464 0.577396i \(-0.804069\pi\)
0.908272 + 0.418380i \(0.137402\pi\)
\(720\) 4416.00 0.228576
\(721\) 0 0
\(722\) −13710.0 −0.706694
\(723\) 110.000 190.526i 0.00565829 0.00980045i
\(724\) 896.000 + 1551.92i 0.0459939 + 0.0796638i
\(725\) 513.000 + 888.542i 0.0262791 + 0.0455167i
\(726\) 1946.00 3370.57i 0.0994805 0.172305i
\(727\) −4228.00 −0.215692 −0.107846 0.994168i \(-0.534395\pi\)
−0.107846 + 0.994168i \(0.534395\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) −13800.0 + 23902.3i −0.699672 + 1.21187i
\(731\) −21432.0 37121.3i −1.08439 1.87822i
\(732\) 1520.00 + 2632.72i 0.0767497 + 0.132934i
\(733\) −2710.00 + 4693.86i −0.136557 + 0.236523i −0.926191 0.377054i \(-0.876937\pi\)
0.789634 + 0.613578i \(0.210270\pi\)
\(734\) −17168.0 −0.863328
\(735\) 0 0
\(736\) −3840.00 −0.192316
\(737\) 11616.0 20119.5i 0.580571 1.00558i
\(738\) 2898.00 + 5019.48i 0.144549 + 0.250365i
\(739\) −640.000 1108.51i −0.0318576 0.0551790i 0.849657 0.527336i \(-0.176809\pi\)
−0.881515 + 0.472157i \(0.843476\pi\)
\(740\) 3504.00 6069.11i 0.174067 0.301493i
\(741\) −224.000 −0.0111051
\(742\) 0 0
\(743\) −35712.0 −1.76332 −0.881660 0.471886i \(-0.843573\pi\)
−0.881660 + 0.471886i \(0.843573\pi\)
\(744\) 1888.00 3270.11i 0.0930342 0.161140i
\(745\) −6012.00 10413.1i −0.295655 0.512089i
\(746\) 2122.00 + 3675.41i 0.104145 + 0.180384i
\(747\) 4347.00 7529.22i 0.212916 0.368782i
\(748\) −21888.0 −1.06993
\(749\) 0 0
\(750\) −5088.00 −0.247717
\(751\) −12232.0 + 21186.4i −0.594344 + 1.02943i 0.399296 + 0.916822i \(0.369255\pi\)
−0.993639 + 0.112611i \(0.964079\pi\)
\(752\) 96.0000 + 166.277i 0.00465527 + 0.00806316i
\(753\) −1890.00 3273.58i −0.0914680 0.158427i
\(754\) 3024.00 5237.72i 0.146058 0.252980i
\(755\) 33024.0 1.59188
\(756\) 0 0
\(757\) 30242.0 1.45200 0.726000 0.687695i \(-0.241377\pi\)
0.726000 + 0.687695i \(0.241377\pi\)
\(758\) 4912.00 8507.83i 0.235372 0.407676i
\(759\) −5760.00 9976.61i −0.275461 0.477112i
\(760\) 96.0000 + 166.277i 0.00458196 + 0.00793618i
\(761\) 1077.00 1865.42i 0.0513025 0.0888586i −0.839234 0.543771i \(-0.816996\pi\)
0.890536 + 0.454912i \(0.150329\pi\)
\(762\) 1504.00 0.0715015
\(763\) 0 0
\(764\) −8544.00 −0.404596
\(765\) 15732.0 27248.6i 0.743519 1.28781i
\(766\) −9060.00 15692.4i −0.427351 0.740194i
\(767\) −3864.00 6692.64i −0.181905 0.315068i
\(768\) 256.000 443.405i 0.0120281 0.0208333i
\(769\) 10262.0 0.481219 0.240609 0.970622i \(-0.422653\pi\)
0.240609 + 0.970622i \(0.422653\pi\)
\(770\) 0 0
\(771\) −4260.00 −0.198989
\(772\) −8860.00 + 15346.0i −0.413055 + 0.715432i
\(773\) −4542.00 7866.97i −0.211338 0.366048i 0.740795 0.671731i \(-0.234449\pi\)
−0.952134 + 0.305682i \(0.901115\pi\)
\(774\) −8648.00 14978.8i −0.401610 0.695608i
\(775\) −2242.00 + 3883.26i −0.103916 + 0.179988i
\(776\) −10640.0 −0.492208
\(777\) 0