Properties

Label 98.4.c.b.67.1
Level $98$
Weight $4$
Character 98.67
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 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.67
Dual form 98.4.c.b.79.1

$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.894977\pi\)
0.753612 + 0.657320i \(0.228310\pi\)
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −6.00000 10.3923i −0.536656 0.929516i −0.999081 0.0428575i \(-0.986354\pi\)
0.462425 0.886658i \(-0.346979\pi\)
\(6\) 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 0.323330 + 0.946286i \(0.395198\pi\)
−0.981173 + 0.193131i \(0.938136\pi\)
\(12\) −4.00000 6.92820i −0.0962250 0.166667i
\(13\) −56.0000 −1.19474 −0.597369 0.801966i \(-0.703787\pi\)
−0.597369 + 0.801966i \(0.703787\pi\)
\(14\) 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 0.0974001 + 0.995245i \(0.468947\pi\)
−0.910608 + 0.413272i \(0.864386\pi\)
\(18\) 23.0000 39.8372i 0.301175 0.521651i
\(19\) 1.00000 + 1.73205i 0.0120745 + 0.0209137i 0.872000 0.489507i \(-0.162823\pi\)
−0.859925 + 0.510420i \(0.829490\pi\)
\(20\) 48.0000 0.536656
\(21\) 0 0
\(22\) 96.0000 0.930330
\(23\) 60.0000 + 103.923i 0.543951 + 0.942150i 0.998672 + 0.0515165i \(0.0164055\pi\)
−0.454721 + 0.890634i \(0.650261\pi\)
\(24\) −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 −0.290197 0.956967i \(-0.593721\pi\)
0.973856 0.227165i \(-0.0729457\pi\)
\(32\) −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 0.657027 0.753867i \(-0.271814\pi\)
−0.981382 + 0.192068i \(0.938480\pi\)
\(38\) 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 \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(42\) 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 \(-0.172594\pi\)
−0.875186 + 0.483787i \(0.839261\pi\)
\(48\) 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 −0.956463 0.291854i \(-0.905728\pi\)
0.730984 + 0.682394i \(0.239061\pi\)
\(54\) 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 \(-0.784680\pi\)
0.932056 + 0.362314i \(0.118013\pi\)
\(60\) −48.0000 + 83.1384i −0.103280 + 0.178885i
\(61\) 190.000 + 329.090i 0.398803 + 0.690748i 0.993579 0.113144i \(-0.0360923\pi\)
−0.594775 + 0.803892i \(0.702759\pi\)
\(62\) −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 −0.556515 0.830837i \(-0.687862\pi\)
0.997784 + 0.0665376i \(0.0211952\pi\)
\(68\) −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 −0.125426 + 0.992103i \(0.540030\pi\)
−0.796473 + 0.604674i \(0.793304\pi\)
\(74\) −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 −0.998088 0.0618122i \(-0.980312\pi\)
0.445513 0.895275i \(-0.353021\pi\)
\(80\) −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 \(-0.580413\pi\)
−0.249945 + 0.968260i \(0.580413\pi\)
\(84\) 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 \(-0.241274\pi\)
−0.958469 + 0.285197i \(0.907941\pi\)
\(90\) −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 \(-0.254922\pi\)
0.696088 + 0.717957i \(0.254922\pi\)
\(98\) 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 0.214107 + 0.976810i \(0.431316\pi\)
−0.952996 + 0.302983i \(0.902017\pi\)
\(102\) −228.000 + 394.908i −0.221327 + 0.383350i
\(103\) 190.000 + 329.090i 0.181760 + 0.314817i 0.942480 0.334263i \(-0.108487\pi\)
−0.760720 + 0.649080i \(0.775154\pi\)
\(104\) −448.000 −0.422404
\(105\) 0 0
\(106\) 348.000 0.318875
\(107\) −318.000 550.792i −0.287310 0.497636i 0.685856 0.727737i \(-0.259428\pi\)
−0.973167 + 0.230101i \(0.926094\pi\)
\(108\) 200.000 346.410i 0.178195 0.308642i
\(109\) −73.0000 + 126.440i −0.0641480 + 0.111108i −0.896316 0.443416i \(-0.853766\pi\)
0.832168 + 0.554524i \(0.187100\pi\)
\(110\) −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 0.964744 + 0.263190i \(0.0847747\pi\)
−0.254443 + 0.967088i \(0.581892\pi\)
\(132\) 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 −0.853609 0.520915i \(-0.825591\pi\)
0.877930 + 0.478789i \(0.158924\pi\)
\(138\) 240.000 + 415.692i 0.148045 + 0.256421i
\(139\) 2338.00 1.42667 0.713333 0.700825i \(-0.247185\pi\)
0.713333 + 0.700825i \(0.247185\pi\)
\(140\) 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 0.970251 0.242101i \(-0.0778366\pi\)
−0.694791 + 0.719212i \(0.744503\pi\)
\(150\) −38.0000 + 65.8179i −0.0206846 + 0.0358267i
\(151\) 1376.00 2383.30i 0.741571 1.28444i −0.210208 0.977657i \(-0.567414\pi\)
0.951780 0.306783i \(-0.0992525\pi\)
\(152\) 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 \(-0.875527\pi\)
0.792345 + 0.610074i \(0.208860\pi\)
\(158\) −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 0.670285 0.742104i \(-0.266172\pi\)
−0.977823 + 0.209432i \(0.932838\pi\)
\(164\) 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 \(-0.634014\pi\)
−0.408690 + 0.912673i \(0.634014\pi\)
\(168\) 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 \(-0.220642\pi\)
−0.937983 + 0.346681i \(0.887309\pi\)
\(174\) −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 −0.990817 0.135213i \(-0.956828\pi\)
0.612506 + 0.790466i \(0.290162\pi\)
\(180\) 552.000 + 956.092i 0.228576 + 0.395905i
\(181\) 448.000 0.183976 0.0919878 0.995760i \(-0.470678\pi\)
0.0919878 + 0.995760i \(0.470678\pi\)
\(182\) 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 0.994274 0.106858i \(-0.0340789\pi\)
−0.589679 + 0.807638i \(0.700746\pi\)
\(192\) −64.0000 + 110.851i −0.0240563 + 0.0416667i
\(193\) −2215.00 + 3836.49i −0.826110 + 1.43086i 0.0749584 + 0.997187i \(0.476118\pi\)
−0.901068 + 0.433677i \(0.857216\pi\)
\(194\) −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 \(-0.966691\pi\)
0.587725 + 0.809061i \(0.300024\pi\)
\(200\) −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 \(-0.600698\pi\)
−0.311102 + 0.950377i \(0.600698\pi\)
\(224\) 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 \(-0.850373\pi\)
0.838031 + 0.545622i \(0.183707\pi\)
\(228\) 8.00000 13.8564i 0.00232374 0.00402484i
\(229\) −188.000 325.626i −0.0542506 0.0939648i 0.837625 0.546246i \(-0.183944\pi\)
−0.891875 + 0.452281i \(0.850610\pi\)
\(230\) −2880.00 −0.825659
\(231\) 0 0
\(232\) −432.000 −0.122251
\(233\) 1131.00 + 1958.95i 0.318001 + 0.550794i 0.980071 0.198648i \(-0.0636551\pi\)
−0.662070 + 0.749442i \(0.730322\pi\)
\(234\) −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 \(-0.828654\pi\)
0.873282 + 0.487215i \(0.161987\pi\)
\(242\) −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 \(-0.423626\pi\)
0.237641 + 0.971353i \(0.423626\pi\)
\(252\) 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 \(-0.0834406\pi\)
−0.707345 + 0.706869i \(0.750107\pi\)
\(258\) −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 −0.409640 0.912247i \(-0.634346\pi\)
0.994849 0.101365i \(-0.0323208\pi\)
\(264\) −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 −0.163764 0.986499i \(-0.552364\pi\)
0.936216 0.351426i \(-0.114303\pi\)
\(270\) 1200.00 2078.46i 0.270480 0.468486i
\(271\) 4096.00 + 7094.48i 0.918134 + 1.59025i 0.802247 + 0.596992i \(0.203638\pi\)
0.115887 + 0.993262i \(0.463029\pi\)
\(272\) 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 −0.966723 0.255825i \(-0.917653\pi\)
0.704912 + 0.709294i \(0.250986\pi\)
\(278\) −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 −0.429486 0.903074i \(-0.641305\pi\)
0.996828 0.0795914i \(-0.0253616\pi\)
\(284\) −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 \(-0.341603\pi\)
0.477334 + 0.878722i \(0.341603\pi\)
\(294\) 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 \(-0.483009\pi\)
0.0533549 + 0.998576i \(0.483009\pi\)
\(308\) 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 0.114660 + 0.993405i \(0.463422\pi\)
−0.917644 + 0.397404i \(0.869911\pi\)
\(312\) 448.000 775.959i 0.0812917 0.140801i
\(313\) −1385.00 2398.89i −0.250111 0.433205i 0.713445 0.700711i \(-0.247134\pi\)
−0.963556 + 0.267506i \(0.913801\pi\)
\(314\) 1040.00 0.186913
\(315\) 0 0
\(316\) 3104.00 0.552575
\(317\) −3783.00 6552.35i −0.670266 1.16094i −0.977828 0.209407i \(-0.932847\pi\)
0.307562 0.951528i \(-0.400487\pi\)
\(318\) −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 0.765684 + 0.643217i \(0.222401\pi\)
0.174201 + 0.984710i \(0.444266\pi\)
\(332\) 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 −0.309980 + 0.950743i \(0.600322\pi\)
−0.668378 + 0.743822i \(0.733011\pi\)
\(348\) 216.000 + 374.123i 0.0332725 + 0.0576296i
\(349\) −9632.00 −1.47733 −0.738666 0.674071i \(-0.764544\pi\)
−0.738666 + 0.674071i \(0.764544\pi\)
\(350\) 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 \(-0.915596\pi\)
0.709481 + 0.704724i \(0.248929\pi\)
\(354\) 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 0.927907 + 0.372812i \(0.121606\pi\)
−0.141089 + 0.989997i \(0.545060\pi\)
\(360\) 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 0.380697 + 0.924700i \(0.375684\pi\)
−0.991162 + 0.132656i \(0.957649\pi\)
\(368\) 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 0.930222 0.366997i \(-0.119614\pi\)
−0.782939 + 0.622098i \(0.786281\pi\)
\(374\) −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 0.992151 + 0.125043i \(0.0399069\pi\)
−0.387785 + 0.921750i \(0.626760\pi\)
\(384\) 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 0.408597 + 0.912715i \(0.366018\pi\)
−0.994733 + 0.102502i \(0.967315\pi\)
\(390\) 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 −0.905526 0.424291i \(-0.860523\pi\)
0.0853156 0.996354i \(-0.472810\pi\)
\(398\) 4568.00 0.575309
\(399\) 0 0
\(400\) 304.000 0.0380000
\(401\) 1761.00 + 3050.14i 0.219302 + 0.379842i 0.954595 0.297907i \(-0.0962886\pi\)
−0.735293 + 0.677750i \(0.762955\pi\)
\(402\) 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 −0.170185 0.985412i \(-0.554436\pi\)
0.938484 0.345322i \(-0.112230\pi\)
\(410\) 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 \(-0.530442\pi\)
−0.0954911 + 0.995430i \(0.530442\pi\)
\(420\) 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 −0.550320 0.834954i \(-0.685494\pi\)
0.998251 + 0.0591136i \(0.0188274\pi\)
\(432\) 800.000 + 1385.64i 0.0890973 + 0.154321i
\(433\) −2198.00 −0.243947 −0.121974 0.992533i \(-0.538922\pi\)
−0.121974 + 0.992533i \(0.538922\pi\)
\(434\) 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 \(-0.173173\pi\)
−0.876064 + 0.482195i \(0.839840\pi\)
\(440\) 4608.00 0.499268
\(441\) 0 0
\(442\) −12768.0 −1.37401
\(443\) −3594.00 6224.99i −0.385454 0.667626i 0.606378 0.795176i \(-0.292622\pi\)
−0.991832 + 0.127551i \(0.959288\pi\)
\(444\) −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 0.967135 0.254263i \(-0.0818328\pi\)
−0.703766 + 0.710432i \(0.748499\pi\)
\(458\) −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 \(-0.475664\pi\)
0.0763784 + 0.997079i \(0.475664\pi\)
\(462\) 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 −0.906879 0.421391i \(-0.861542\pi\)
0.0885046 0.996076i \(-0.471791\pi\)
\(468\) 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 \(-0.673487\pi\)
0.999770 + 0.0214244i \(0.00682012\pi\)
\(480\) −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 −0.988676 0.150068i \(-0.952051\pi\)
0.624300 + 0.781185i \(0.285384\pi\)
\(488\) 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 −0.892087 0.451864i \(-0.850759\pi\)
0.0547176 0.998502i \(-0.482574\pi\)
\(500\) 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 \(-0.413618\pi\)
0.268059 + 0.963403i \(0.413618\pi\)
\(504\) 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 \(-0.00248398\pi\)
−0.506743 + 0.862097i \(0.669151\pi\)
\(510\) 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 \(-0.889105\pi\)
0.765607 + 0.643309i \(0.222439\pi\)
\(522\) −1242.00 + 2151.21i −0.104140 + 0.180375i
\(523\) −503.000 871.222i −0.0420548 0.0728410i 0.844232 0.535978i \(-0.180057\pi\)
−0.886287 + 0.463137i \(0.846724\pi\)
\(524\) −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 0.994878 + 0.101084i \(0.0322309\pi\)
−0.409898 + 0.912131i \(0.634436\pi\)
\(542\) 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 −0.959753 0.280847i \(-0.909385\pi\)
0.723097 + 0.690747i \(0.242718\pi\)
\(558\) −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 \(-0.774307\pi\)
0.943366 + 0.331755i \(0.107641\pi\)
\(564\) −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 −0.907773 0.419462i \(-0.862219\pi\)
0.0906221 0.995885i \(-0.471114\pi\)
\(570\) 48.0000 83.1384i 0.00352719 0.00610927i
\(571\) −1648.00 + 2854.42i −0.120782 + 0.209201i −0.920076 0.391739i \(-0.871874\pi\)
0.799294 + 0.600940i \(0.205207\pi\)
\(572\) 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 −0.0241523 + 0.999708i \(0.507689\pi\)
−0.853697 + 0.520771i \(0.825645\pi\)
\(578\) −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 \(-0.518341\pi\)
−0.0575873 + 0.998340i \(0.518341\pi\)
\(588\) 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 \(-0.249670\pi\)
−0.965657 + 0.259821i \(0.916336\pi\)
\(594\) −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 −0.733537 0.679649i \(-0.762132\pi\)
0.955362 + 0.295437i \(0.0954653\pi\)
\(600\) −152.000 263.272i −0.0103423 0.0179134i
\(601\) −16058.0 −1.08988 −0.544941 0.838474i \(-0.683448\pi\)
−0.544941 + 0.838474i \(0.683448\pi\)
\(602\) 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 \(-0.0558018\pi\)
−0.643380 + 0.765547i \(0.722468\pi\)
\(608\) −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 −0.506663 0.862144i \(-0.669121\pi\)
0.999970 + 0.00771145i \(0.00245465\pi\)
\(614\) −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 \(-0.700791\pi\)
0.994259 + 0.106998i \(0.0341240\pi\)
\(620\) 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 0.0427309 + 0.999087i \(0.486394\pi\)
−0.886600 + 0.462537i \(0.846939\pi\)
\(642\) −1272.00 2203.17i −0.0781960 0.135439i
\(643\) 21490.0 1.31801 0.659007 0.752137i \(-0.270977\pi\)
0.659007 + 0.752137i \(0.270977\pi\)
\(644\) 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 −0.462800 0.886463i \(-0.653155\pi\)
0.999099 0.0424353i \(-0.0135116\pi\)
\(648\) −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 0.928733 0.370749i \(-0.120899\pi\)
−0.785445 + 0.618932i \(0.787566\pi\)
\(654\) −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 \(-0.946792\pi\)
0.637120 + 0.770764i \(0.280125\pi\)
\(662\) 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 \(-0.305467\pi\)
−0.996170 + 0.0874320i \(0.972134\pi\)
\(678\) 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 0.407356 + 0.913269i \(0.366451\pi\)
−0.994593 + 0.103854i \(0.966882\pi\)
\(684\) −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 \(-0.0491827\pi\)
−0.627323 + 0.778759i \(0.715849\pi\)
\(692\) 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 0.877215 0.480098i \(-0.159399\pi\)
−0.854385 + 0.519641i \(0.826066\pi\)
\(710\) −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 \(-0.195931\pi\)
−0.908272 + 0.418380i \(0.862598\pi\)
\(720\) −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 \(-0.465605\pi\)
0.107846 + 0.994168i \(0.465605\pi\)
\(728\) 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 \(-0.123063\pi\)
−0.789634 + 0.613578i \(0.789730\pi\)
\(734\) 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 −0.881515 0.472157i \(-0.843476\pi\)
0.849657 + 0.527336i \(0.176809\pi\)
\(740\) −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 −0.993639 0.112611i \(-0.964079\pi\)
0.399296 0.916822i \(-0.369255\pi\)
\(752\) −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 \(-0.183004\pi\)
−0.890536 + 0.454912i \(0.849671\pi\)
\(762\) −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 \(-0.577347\pi\)
−0.240609 + 0.970622i \(0.577347\pi\)
\(770\) 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 \(-0.765551\pi\)
0.952134 + 0.305682i \(0.0988845\pi\)
\(774\) −8648.00 + 14978.8i −0.401610 + 0.695608i
\(775\) 2242.00 + 3883.26i 0.103916 + 0.179988i
\(776\) 10640.0 0.492208
\(777\)