Properties

Label 810.4.e.q.271.1
Level $810$
Weight $4$
Character 810.271
Analytic conductor $47.792$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.7915471046\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.271
Dual form 810.4.e.q.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(21.0000 + 36.3731i) q^{11} +(-10.0000 + 17.3205i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(-8.00000 - 13.8564i) q^{16} -93.0000 q^{17} +59.0000 q^{19} +(-10.0000 - 17.3205i) q^{20} +(-42.0000 + 72.7461i) q^{22} +(4.50000 - 7.79423i) q^{23} +(-12.5000 - 21.6506i) q^{25} -40.0000 q^{26} -16.0000 q^{28} +(60.0000 + 103.923i) q^{29} +(-23.5000 + 40.7032i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-93.0000 - 161.081i) q^{34} -20.0000 q^{35} -262.000 q^{37} +(59.0000 + 102.191i) q^{38} +(20.0000 - 34.6410i) q^{40} +(63.0000 - 109.119i) q^{41} +(89.0000 + 154.153i) q^{43} -168.000 q^{44} +18.0000 q^{46} +(72.0000 + 124.708i) q^{47} +(163.500 - 283.190i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-40.0000 - 69.2820i) q^{52} -741.000 q^{53} -210.000 q^{55} +(-16.0000 - 27.7128i) q^{56} +(-120.000 + 207.846i) q^{58} +(-222.000 + 384.515i) q^{59} +(-110.500 - 191.392i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(-50.0000 - 86.6025i) q^{65} +(269.000 - 465.922i) q^{67} +(186.000 - 322.161i) q^{68} +(-20.0000 - 34.6410i) q^{70} -690.000 q^{71} -1126.00 q^{73} +(-262.000 - 453.797i) q^{74} +(-118.000 + 204.382i) q^{76} +(-84.0000 + 145.492i) q^{77} +(-332.500 - 575.907i) q^{79} +80.0000 q^{80} +252.000 q^{82} +(37.5000 + 64.9519i) q^{83} +(232.500 - 402.702i) q^{85} +(-178.000 + 308.305i) q^{86} +(-168.000 - 290.985i) q^{88} +1086.00 q^{89} -80.0000 q^{91} +(18.0000 + 31.1769i) q^{92} +(-144.000 + 249.415i) q^{94} +(-147.500 + 255.477i) q^{95} +(-772.000 - 1337.14i) q^{97} +654.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8} - 20 q^{10} + 42 q^{11} - 20 q^{13} - 8 q^{14} - 16 q^{16} - 186 q^{17} + 118 q^{19} - 20 q^{20} - 84 q^{22} + 9 q^{23} - 25 q^{25} - 80 q^{26} - 32 q^{28} + 120 q^{29} - 47 q^{31} + 32 q^{32} - 186 q^{34} - 40 q^{35} - 524 q^{37} + 118 q^{38} + 40 q^{40} + 126 q^{41} + 178 q^{43} - 336 q^{44} + 36 q^{46} + 144 q^{47} + 327 q^{49} + 50 q^{50} - 80 q^{52} - 1482 q^{53} - 420 q^{55} - 32 q^{56} - 240 q^{58} - 444 q^{59} - 221 q^{61} - 188 q^{62} + 128 q^{64} - 100 q^{65} + 538 q^{67} + 372 q^{68} - 40 q^{70} - 1380 q^{71} - 2252 q^{73} - 524 q^{74} - 236 q^{76} - 168 q^{77} - 665 q^{79} + 160 q^{80} + 504 q^{82} + 75 q^{83} + 465 q^{85} - 356 q^{86} - 336 q^{88} + 2172 q^{89} - 160 q^{91} + 36 q^{92} - 288 q^{94} - 295 q^{95} - 1544 q^{97} + 1308 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.107990 + 0.187044i 0.914956 0.403554i \(-0.132225\pi\)
−0.806966 + 0.590598i \(0.798892\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) 21.0000 + 36.3731i 0.575613 + 0.996990i 0.995975 + 0.0896338i \(0.0285697\pi\)
−0.420362 + 0.907356i \(0.638097\pi\)
\(12\) 0 0
\(13\) −10.0000 + 17.3205i −0.213346 + 0.369527i −0.952760 0.303725i \(-0.901770\pi\)
0.739413 + 0.673252i \(0.235103\pi\)
\(14\) −4.00000 + 6.92820i −0.0763604 + 0.132260i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −93.0000 −1.32681 −0.663406 0.748259i \(-0.730890\pi\)
−0.663406 + 0.748259i \(0.730890\pi\)
\(18\) 0 0
\(19\) 59.0000 0.712396 0.356198 0.934410i \(-0.384073\pi\)
0.356198 + 0.934410i \(0.384073\pi\)
\(20\) −10.0000 17.3205i −0.111803 0.193649i
\(21\) 0 0
\(22\) −42.0000 + 72.7461i −0.407020 + 0.704979i
\(23\) 4.50000 7.79423i 0.0407963 0.0706613i −0.844906 0.534914i \(-0.820344\pi\)
0.885703 + 0.464253i \(0.153677\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −40.0000 −0.301717
\(27\) 0 0
\(28\) −16.0000 −0.107990
\(29\) 60.0000 + 103.923i 0.384197 + 0.665449i 0.991657 0.128901i \(-0.0411449\pi\)
−0.607460 + 0.794350i \(0.707812\pi\)
\(30\) 0 0
\(31\) −23.5000 + 40.7032i −0.136152 + 0.235823i −0.926037 0.377433i \(-0.876807\pi\)
0.789885 + 0.613255i \(0.210140\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −93.0000 161.081i −0.469099 0.812503i
\(35\) −20.0000 −0.0965891
\(36\) 0 0
\(37\) −262.000 −1.16412 −0.582061 0.813145i \(-0.697754\pi\)
−0.582061 + 0.813145i \(0.697754\pi\)
\(38\) 59.0000 + 102.191i 0.251870 + 0.436252i
\(39\) 0 0
\(40\) 20.0000 34.6410i 0.0790569 0.136931i
\(41\) 63.0000 109.119i 0.239974 0.415648i −0.720732 0.693213i \(-0.756194\pi\)
0.960707 + 0.277566i \(0.0895276\pi\)
\(42\) 0 0
\(43\) 89.0000 + 154.153i 0.315637 + 0.546699i 0.979573 0.201091i \(-0.0644486\pi\)
−0.663936 + 0.747789i \(0.731115\pi\)
\(44\) −168.000 −0.575613
\(45\) 0 0
\(46\) 18.0000 0.0576947
\(47\) 72.0000 + 124.708i 0.223453 + 0.387032i 0.955854 0.293842i \(-0.0949338\pi\)
−0.732401 + 0.680873i \(0.761600\pi\)
\(48\) 0 0
\(49\) 163.500 283.190i 0.476676 0.825628i
\(50\) 25.0000 43.3013i 0.0707107 0.122474i
\(51\) 0 0
\(52\) −40.0000 69.2820i −0.106673 0.184763i
\(53\) −741.000 −1.92046 −0.960228 0.279217i \(-0.909925\pi\)
−0.960228 + 0.279217i \(0.909925\pi\)
\(54\) 0 0
\(55\) −210.000 −0.514844
\(56\) −16.0000 27.7128i −0.0381802 0.0661300i
\(57\) 0 0
\(58\) −120.000 + 207.846i −0.271668 + 0.470544i
\(59\) −222.000 + 384.515i −0.489863 + 0.848468i −0.999932 0.0116655i \(-0.996287\pi\)
0.510069 + 0.860134i \(0.329620\pi\)
\(60\) 0 0
\(61\) −110.500 191.392i −0.231936 0.401724i 0.726442 0.687228i \(-0.241173\pi\)
−0.958378 + 0.285503i \(0.907839\pi\)
\(62\) −94.0000 −0.192549
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −50.0000 86.6025i −0.0954113 0.165257i
\(66\) 0 0
\(67\) 269.000 465.922i 0.490501 0.849573i −0.509439 0.860507i \(-0.670147\pi\)
0.999940 + 0.0109338i \(0.00348039\pi\)
\(68\) 186.000 322.161i 0.331703 0.574527i
\(69\) 0 0
\(70\) −20.0000 34.6410i −0.0341494 0.0591485i
\(71\) −690.000 −1.15335 −0.576676 0.816973i \(-0.695650\pi\)
−0.576676 + 0.816973i \(0.695650\pi\)
\(72\) 0 0
\(73\) −1126.00 −1.80532 −0.902660 0.430355i \(-0.858388\pi\)
−0.902660 + 0.430355i \(0.858388\pi\)
\(74\) −262.000 453.797i −0.411579 0.712877i
\(75\) 0 0
\(76\) −118.000 + 204.382i −0.178099 + 0.308477i
\(77\) −84.0000 + 145.492i −0.124321 + 0.215330i
\(78\) 0 0
\(79\) −332.500 575.907i −0.473534 0.820185i 0.526007 0.850480i \(-0.323689\pi\)
−0.999541 + 0.0302955i \(0.990355\pi\)
\(80\) 80.0000 0.111803
\(81\) 0 0
\(82\) 252.000 0.339375
\(83\) 37.5000 + 64.9519i 0.0495923 + 0.0858964i 0.889756 0.456437i \(-0.150874\pi\)
−0.840164 + 0.542333i \(0.817541\pi\)
\(84\) 0 0
\(85\) 232.500 402.702i 0.296684 0.513872i
\(86\) −178.000 + 308.305i −0.223189 + 0.386574i
\(87\) 0 0
\(88\) −168.000 290.985i −0.203510 0.352489i
\(89\) 1086.00 1.29344 0.646718 0.762729i \(-0.276141\pi\)
0.646718 + 0.762729i \(0.276141\pi\)
\(90\) 0 0
\(91\) −80.0000 −0.0921569
\(92\) 18.0000 + 31.1769i 0.0203981 + 0.0353306i
\(93\) 0 0
\(94\) −144.000 + 249.415i −0.158005 + 0.273673i
\(95\) −147.500 + 255.477i −0.159297 + 0.275910i
\(96\) 0 0
\(97\) −772.000 1337.14i −0.808090 1.39965i −0.914185 0.405297i \(-0.867168\pi\)
0.106095 0.994356i \(-0.466165\pi\)
\(98\) 654.000 0.674122
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) −66.0000 114.315i −0.0650222 0.112622i 0.831682 0.555253i \(-0.187378\pi\)
−0.896704 + 0.442631i \(0.854045\pi\)
\(102\) 0 0
\(103\) 446.000 772.495i 0.426657 0.738992i −0.569916 0.821703i \(-0.693024\pi\)
0.996574 + 0.0827108i \(0.0263578\pi\)
\(104\) 80.0000 138.564i 0.0754293 0.130647i
\(105\) 0 0
\(106\) −741.000 1283.45i −0.678984 1.17603i
\(107\) 1140.00 1.02998 0.514990 0.857196i \(-0.327795\pi\)
0.514990 + 0.857196i \(0.327795\pi\)
\(108\) 0 0
\(109\) −1735.00 −1.52461 −0.762307 0.647216i \(-0.775933\pi\)
−0.762307 + 0.647216i \(0.775933\pi\)
\(110\) −210.000 363.731i −0.182025 0.315276i
\(111\) 0 0
\(112\) 32.0000 55.4256i 0.0269975 0.0467610i
\(113\) −717.000 + 1241.88i −0.596900 + 1.03386i 0.396376 + 0.918088i \(0.370268\pi\)
−0.993276 + 0.115773i \(0.963066\pi\)
\(114\) 0 0
\(115\) 22.5000 + 38.9711i 0.0182447 + 0.0316007i
\(116\) −480.000 −0.384197
\(117\) 0 0
\(118\) −888.000 −0.692771
\(119\) −186.000 322.161i −0.143282 0.248172i
\(120\) 0 0
\(121\) −216.500 + 374.989i −0.162660 + 0.281735i
\(122\) 221.000 382.783i 0.164003 0.284062i
\(123\) 0 0
\(124\) −94.0000 162.813i −0.0680762 0.117911i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 686.000 0.479312 0.239656 0.970858i \(-0.422965\pi\)
0.239656 + 0.970858i \(0.422965\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 100.000 173.205i 0.0674660 0.116855i
\(131\) −57.0000 + 98.7269i −0.0380161 + 0.0658459i −0.884407 0.466716i \(-0.845437\pi\)
0.846391 + 0.532561i \(0.178770\pi\)
\(132\) 0 0
\(133\) 118.000 + 204.382i 0.0769316 + 0.133249i
\(134\) 1076.00 0.693673
\(135\) 0 0
\(136\) 744.000 0.469099
\(137\) 79.5000 + 137.698i 0.0495777 + 0.0858711i 0.889749 0.456450i \(-0.150879\pi\)
−0.840172 + 0.542321i \(0.817546\pi\)
\(138\) 0 0
\(139\) −1138.00 + 1971.07i −0.694417 + 1.20276i 0.275960 + 0.961169i \(0.411004\pi\)
−0.970377 + 0.241596i \(0.922329\pi\)
\(140\) 40.0000 69.2820i 0.0241473 0.0418243i
\(141\) 0 0
\(142\) −690.000 1195.12i −0.407771 0.706280i
\(143\) −840.000 −0.491219
\(144\) 0 0
\(145\) −600.000 −0.343636
\(146\) −1126.00 1950.29i −0.638277 1.10553i
\(147\) 0 0
\(148\) 524.000 907.595i 0.291031 0.504080i
\(149\) −699.000 + 1210.70i −0.384324 + 0.665669i −0.991675 0.128765i \(-0.958899\pi\)
0.607351 + 0.794434i \(0.292232\pi\)
\(150\) 0 0
\(151\) −1312.00 2272.45i −0.707080 1.22470i −0.965936 0.258782i \(-0.916679\pi\)
0.258856 0.965916i \(-0.416655\pi\)
\(152\) −472.000 −0.251870
\(153\) 0 0
\(154\) −336.000 −0.175816
\(155\) −117.500 203.516i −0.0608892 0.105463i
\(156\) 0 0
\(157\) 197.000 341.214i 0.100142 0.173451i −0.811601 0.584212i \(-0.801404\pi\)
0.911743 + 0.410761i \(0.134737\pi\)
\(158\) 665.000 1151.81i 0.334839 0.579958i
\(159\) 0 0
\(160\) 80.0000 + 138.564i 0.0395285 + 0.0684653i
\(161\) 36.0000 0.0176223
\(162\) 0 0
\(163\) −3346.00 −1.60785 −0.803923 0.594733i \(-0.797258\pi\)
−0.803923 + 0.594733i \(0.797258\pi\)
\(164\) 252.000 + 436.477i 0.119987 + 0.207824i
\(165\) 0 0
\(166\) −75.0000 + 129.904i −0.0350670 + 0.0607379i
\(167\) −745.500 + 1291.24i −0.345440 + 0.598320i −0.985434 0.170060i \(-0.945604\pi\)
0.639993 + 0.768380i \(0.278937\pi\)
\(168\) 0 0
\(169\) 898.500 + 1556.25i 0.408967 + 0.708351i
\(170\) 930.000 0.419575
\(171\) 0 0
\(172\) −712.000 −0.315637
\(173\) 1201.50 + 2081.06i 0.528025 + 0.914566i 0.999466 + 0.0326688i \(0.0104007\pi\)
−0.471441 + 0.881898i \(0.656266\pi\)
\(174\) 0 0
\(175\) 50.0000 86.6025i 0.0215980 0.0374088i
\(176\) 336.000 581.969i 0.143903 0.249248i
\(177\) 0 0
\(178\) 1086.00 + 1881.01i 0.457299 + 0.792064i
\(179\) 2640.00 1.10236 0.551181 0.834386i \(-0.314177\pi\)
0.551181 + 0.834386i \(0.314177\pi\)
\(180\) 0 0
\(181\) 1073.00 0.440638 0.220319 0.975428i \(-0.429290\pi\)
0.220319 + 0.975428i \(0.429290\pi\)
\(182\) −80.0000 138.564i −0.0325824 0.0564344i
\(183\) 0 0
\(184\) −36.0000 + 62.3538i −0.0144237 + 0.0249825i
\(185\) 655.000 1134.49i 0.260306 0.450863i
\(186\) 0 0
\(187\) −1953.00 3382.70i −0.763730 1.32282i
\(188\) −576.000 −0.223453
\(189\) 0 0
\(190\) −590.000 −0.225279
\(191\) 735.000 + 1273.06i 0.278444 + 0.482279i 0.970998 0.239087i \(-0.0768481\pi\)
−0.692555 + 0.721366i \(0.743515\pi\)
\(192\) 0 0
\(193\) 2360.00 4087.64i 0.880189 1.52453i 0.0290591 0.999578i \(-0.490749\pi\)
0.851130 0.524955i \(-0.175918\pi\)
\(194\) 1544.00 2674.29i 0.571406 0.989704i
\(195\) 0 0
\(196\) 654.000 + 1132.76i 0.238338 + 0.412814i
\(197\) 765.000 0.276670 0.138335 0.990385i \(-0.455825\pi\)
0.138335 + 0.990385i \(0.455825\pi\)
\(198\) 0 0
\(199\) 668.000 0.237956 0.118978 0.992897i \(-0.462038\pi\)
0.118978 + 0.992897i \(0.462038\pi\)
\(200\) 100.000 + 173.205i 0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 132.000 228.631i 0.0459777 0.0796356i
\(203\) −240.000 + 415.692i −0.0829788 + 0.143724i
\(204\) 0 0
\(205\) 315.000 + 545.596i 0.107320 + 0.185883i
\(206\) 1784.00 0.603384
\(207\) 0 0
\(208\) 320.000 0.106673
\(209\) 1239.00 + 2146.01i 0.410064 + 0.710252i
\(210\) 0 0
\(211\) −2300.50 + 3984.58i −0.750583 + 1.30005i 0.196958 + 0.980412i \(0.436894\pi\)
−0.947541 + 0.319635i \(0.896440\pi\)
\(212\) 1482.00 2566.90i 0.480114 0.831582i
\(213\) 0 0
\(214\) 1140.00 + 1974.54i 0.364153 + 0.630732i
\(215\) −890.000 −0.282314
\(216\) 0 0
\(217\) −188.000 −0.0588123
\(218\) −1735.00 3005.11i −0.539032 0.933631i
\(219\) 0 0
\(220\) 420.000 727.461i 0.128711 0.222934i
\(221\) 930.000 1610.81i 0.283070 0.490292i
\(222\) 0 0
\(223\) 1079.00 + 1868.88i 0.324014 + 0.561209i 0.981312 0.192421i \(-0.0616341\pi\)
−0.657298 + 0.753631i \(0.728301\pi\)
\(224\) 128.000 0.0381802
\(225\) 0 0
\(226\) −2868.00 −0.844144
\(227\) 1561.50 + 2704.60i 0.456566 + 0.790795i 0.998777 0.0494474i \(-0.0157460\pi\)
−0.542211 + 0.840242i \(0.682413\pi\)
\(228\) 0 0
\(229\) −1013.50 + 1755.43i −0.292463 + 0.506560i −0.974391 0.224858i \(-0.927808\pi\)
0.681929 + 0.731419i \(0.261141\pi\)
\(230\) −45.0000 + 77.9423i −0.0129009 + 0.0223451i
\(231\) 0 0
\(232\) −480.000 831.384i −0.135834 0.235272i
\(233\) 438.000 0.123152 0.0615758 0.998102i \(-0.480387\pi\)
0.0615758 + 0.998102i \(0.480387\pi\)
\(234\) 0 0
\(235\) −720.000 −0.199862
\(236\) −888.000 1538.06i −0.244932 0.424234i
\(237\) 0 0
\(238\) 372.000 644.323i 0.101316 0.175484i
\(239\) 3207.00 5554.69i 0.867965 1.50336i 0.00389189 0.999992i \(-0.498761\pi\)
0.864073 0.503367i \(-0.167905\pi\)
\(240\) 0 0
\(241\) −1715.50 2971.33i −0.458527 0.794193i 0.540356 0.841436i \(-0.318290\pi\)
−0.998883 + 0.0472439i \(0.984956\pi\)
\(242\) −866.000 −0.230035
\(243\) 0 0
\(244\) 884.000 0.231936
\(245\) 817.500 + 1415.95i 0.213176 + 0.369232i
\(246\) 0 0
\(247\) −590.000 + 1021.91i −0.151987 + 0.263249i
\(248\) 188.000 325.626i 0.0481371 0.0833760i
\(249\) 0 0
\(250\) 125.000 + 216.506i 0.0316228 + 0.0547723i
\(251\) −7308.00 −1.83776 −0.918878 0.394541i \(-0.870904\pi\)
−0.918878 + 0.394541i \(0.870904\pi\)
\(252\) 0 0
\(253\) 378.000 0.0939314
\(254\) 686.000 + 1188.19i 0.169462 + 0.293518i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1864.50 + 3229.41i −0.452546 + 0.783833i −0.998543 0.0539542i \(-0.982817\pi\)
0.545997 + 0.837787i \(0.316151\pi\)
\(258\) 0 0
\(259\) −524.000 907.595i −0.125713 0.217742i
\(260\) 400.000 0.0954113
\(261\) 0 0
\(262\) −228.000 −0.0537629
\(263\) −978.000 1693.95i −0.229301 0.397160i 0.728300 0.685258i \(-0.240311\pi\)
−0.957601 + 0.288098i \(0.906977\pi\)
\(264\) 0 0
\(265\) 1852.50 3208.62i 0.429427 0.743789i
\(266\) −236.000 + 408.764i −0.0543988 + 0.0942215i
\(267\) 0 0
\(268\) 1076.00 + 1863.69i 0.245251 + 0.424787i
\(269\) −990.000 −0.224392 −0.112196 0.993686i \(-0.535788\pi\)
−0.112196 + 0.993686i \(0.535788\pi\)
\(270\) 0 0
\(271\) 8495.00 1.90419 0.952093 0.305808i \(-0.0989266\pi\)
0.952093 + 0.305808i \(0.0989266\pi\)
\(272\) 744.000 + 1288.65i 0.165852 + 0.287263i
\(273\) 0 0
\(274\) −159.000 + 275.396i −0.0350567 + 0.0607200i
\(275\) 525.000 909.327i 0.115123 0.199398i
\(276\) 0 0
\(277\) 683.000 + 1182.99i 0.148150 + 0.256603i 0.930544 0.366181i \(-0.119335\pi\)
−0.782394 + 0.622784i \(0.786002\pi\)
\(278\) −4552.00 −0.982053
\(279\) 0 0
\(280\) 160.000 0.0341494
\(281\) 2760.00 + 4780.46i 0.585935 + 1.01487i 0.994758 + 0.102256i \(0.0326060\pi\)
−0.408823 + 0.912614i \(0.634061\pi\)
\(282\) 0 0
\(283\) −2719.00 + 4709.45i −0.571123 + 0.989214i 0.425328 + 0.905039i \(0.360159\pi\)
−0.996451 + 0.0841746i \(0.973175\pi\)
\(284\) 1380.00 2390.23i 0.288338 0.499416i
\(285\) 0 0
\(286\) −840.000 1454.92i −0.173672 0.300809i
\(287\) 504.000 0.103659
\(288\) 0 0
\(289\) 3736.00 0.760432
\(290\) −600.000 1039.23i −0.121494 0.210434i
\(291\) 0 0
\(292\) 2252.00 3900.58i 0.451330 0.781726i
\(293\) −4126.50 + 7147.31i −0.822774 + 1.42509i 0.0808352 + 0.996727i \(0.474241\pi\)
−0.903609 + 0.428358i \(0.859092\pi\)
\(294\) 0 0
\(295\) −1110.00 1922.58i −0.219074 0.379447i
\(296\) 2096.00 0.411579
\(297\) 0 0
\(298\) −2796.00 −0.543517
\(299\) 90.0000 + 155.885i 0.0174075 + 0.0301506i
\(300\) 0 0
\(301\) −356.000 + 616.610i −0.0681711 + 0.118076i
\(302\) 2624.00 4544.90i 0.499981 0.865992i
\(303\) 0 0
\(304\) −472.000 817.528i −0.0890495 0.154238i
\(305\) 1105.00 0.207450
\(306\) 0 0
\(307\) 9290.00 1.72706 0.863531 0.504295i \(-0.168248\pi\)
0.863531 + 0.504295i \(0.168248\pi\)
\(308\) −336.000 581.969i −0.0621603 0.107665i
\(309\) 0 0
\(310\) 235.000 407.032i 0.0430552 0.0745737i
\(311\) −4056.00 + 7025.20i −0.739533 + 1.28091i 0.213173 + 0.977014i \(0.431620\pi\)
−0.952706 + 0.303894i \(0.901713\pi\)
\(312\) 0 0
\(313\) 3950.00 + 6841.60i 0.713314 + 1.23550i 0.963606 + 0.267325i \(0.0861399\pi\)
−0.250293 + 0.968170i \(0.580527\pi\)
\(314\) 788.000 0.141622
\(315\) 0 0
\(316\) 2660.00 0.473534
\(317\) −2209.50 3826.97i −0.391476 0.678056i 0.601168 0.799122i \(-0.294702\pi\)
−0.992644 + 0.121066i \(0.961369\pi\)
\(318\) 0 0
\(319\) −2520.00 + 4364.77i −0.442298 + 0.766082i
\(320\) −160.000 + 277.128i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 36.0000 + 62.3538i 0.00623044 + 0.0107914i
\(323\) −5487.00 −0.945216
\(324\) 0 0
\(325\) 500.000 0.0853385
\(326\) −3346.00 5795.44i −0.568460 0.984601i
\(327\) 0 0
\(328\) −504.000 + 872.954i −0.0848437 + 0.146954i
\(329\) −288.000 + 498.831i −0.0482613 + 0.0835910i
\(330\) 0 0
\(331\) 4100.00 + 7101.41i 0.680835 + 1.17924i 0.974726 + 0.223402i \(0.0717163\pi\)
−0.293891 + 0.955839i \(0.594950\pi\)
\(332\) −300.000 −0.0495923
\(333\) 0 0
\(334\) −2982.00 −0.488526
\(335\) 1345.00 + 2329.61i 0.219359 + 0.379941i
\(336\) 0 0
\(337\) 4778.00 8275.74i 0.772327 1.33771i −0.163957 0.986467i \(-0.552426\pi\)
0.936285 0.351242i \(-0.114241\pi\)
\(338\) −1797.00 + 3112.50i −0.289183 + 0.500880i
\(339\) 0 0
\(340\) 930.000 + 1610.81i 0.148342 + 0.256936i
\(341\) −1974.00 −0.313484
\(342\) 0 0
\(343\) 2680.00 0.421885
\(344\) −712.000 1233.22i −0.111594 0.193287i
\(345\) 0 0
\(346\) −2403.00 + 4162.12i −0.373370 + 0.646696i
\(347\) −5058.00 + 8760.71i −0.782500 + 1.35533i 0.147980 + 0.988990i \(0.452723\pi\)
−0.930481 + 0.366340i \(0.880611\pi\)
\(348\) 0 0
\(349\) 3375.50 + 5846.54i 0.517726 + 0.896728i 0.999788 + 0.0205906i \(0.00655466\pi\)
−0.482062 + 0.876137i \(0.660112\pi\)
\(350\) 200.000 0.0305441
\(351\) 0 0
\(352\) 1344.00 0.203510
\(353\) −2031.00 3517.80i −0.306230 0.530406i 0.671304 0.741182i \(-0.265734\pi\)
−0.977534 + 0.210776i \(0.932401\pi\)
\(354\) 0 0
\(355\) 1725.00 2987.79i 0.257897 0.446691i
\(356\) −2172.00 + 3762.01i −0.323359 + 0.560074i
\(357\) 0 0
\(358\) 2640.00 + 4572.61i 0.389744 + 0.675056i
\(359\) 8778.00 1.29049 0.645244 0.763977i \(-0.276756\pi\)
0.645244 + 0.763977i \(0.276756\pi\)
\(360\) 0 0
\(361\) −3378.00 −0.492492
\(362\) 1073.00 + 1858.49i 0.155789 + 0.269835i
\(363\) 0 0
\(364\) 160.000 277.128i 0.0230392 0.0399051i
\(365\) 2815.00 4875.72i 0.403682 0.699197i
\(366\) 0 0
\(367\) −478.000 827.920i −0.0679875 0.117758i 0.830028 0.557722i \(-0.188324\pi\)
−0.898015 + 0.439964i \(0.854991\pi\)
\(368\) −144.000 −0.0203981
\(369\) 0 0
\(370\) 2620.00 0.368128
\(371\) −1482.00 2566.90i −0.207390 0.359210i
\(372\) 0 0
\(373\) −1150.00 + 1991.86i −0.159637 + 0.276500i −0.934738 0.355338i \(-0.884366\pi\)
0.775101 + 0.631838i \(0.217699\pi\)
\(374\) 3906.00 6765.39i 0.540039 0.935374i
\(375\) 0 0
\(376\) −576.000 997.661i −0.0790025 0.136836i
\(377\) −2400.00 −0.327868
\(378\) 0 0
\(379\) 29.0000 0.00393042 0.00196521 0.999998i \(-0.499374\pi\)
0.00196521 + 0.999998i \(0.499374\pi\)
\(380\) −590.000 1021.91i −0.0796483 0.137955i
\(381\) 0 0
\(382\) −1470.00 + 2546.11i −0.196889 + 0.341022i
\(383\) −4063.50 + 7038.19i −0.542128 + 0.938994i 0.456653 + 0.889645i \(0.349048\pi\)
−0.998782 + 0.0493491i \(0.984285\pi\)
\(384\) 0 0
\(385\) −420.000 727.461i −0.0555979 0.0962983i
\(386\) 9440.00 1.24478
\(387\) 0 0
\(388\) 6176.00 0.808090
\(389\) 3969.00 + 6874.51i 0.517317 + 0.896019i 0.999798 + 0.0201127i \(0.00640249\pi\)
−0.482481 + 0.875907i \(0.660264\pi\)
\(390\) 0 0
\(391\) −418.500 + 724.863i −0.0541290 + 0.0937542i
\(392\) −1308.00 + 2265.52i −0.168531 + 0.291903i
\(393\) 0 0
\(394\) 765.000 + 1325.02i 0.0978176 + 0.169425i
\(395\) 3325.00 0.423542
\(396\) 0 0
\(397\) 272.000 0.0343861 0.0171931 0.999852i \(-0.494527\pi\)
0.0171931 + 0.999852i \(0.494527\pi\)
\(398\) 668.000 + 1157.01i 0.0841302 + 0.145718i
\(399\) 0 0
\(400\) −200.000 + 346.410i −0.0250000 + 0.0433013i
\(401\) −2277.00 + 3943.88i −0.283561 + 0.491142i −0.972259 0.233906i \(-0.924849\pi\)
0.688698 + 0.725048i \(0.258183\pi\)
\(402\) 0 0
\(403\) −470.000 814.064i −0.0580952 0.100624i
\(404\) 528.000 0.0650222
\(405\) 0 0
\(406\) −960.000 −0.117350
\(407\) −5502.00 9529.74i −0.670084 1.16062i
\(408\) 0 0
\(409\) −500.500 + 866.891i −0.0605089 + 0.104804i −0.894693 0.446682i \(-0.852606\pi\)
0.834184 + 0.551486i \(0.185939\pi\)
\(410\) −630.000 + 1091.19i −0.0758865 + 0.131439i
\(411\) 0 0
\(412\) 1784.00 + 3089.98i 0.213329 + 0.369496i
\(413\) −1776.00 −0.211601
\(414\) 0 0
\(415\) −375.000 −0.0443567
\(416\) 320.000 + 554.256i 0.0377146 + 0.0653237i
\(417\) 0 0
\(418\) −2478.00 + 4292.02i −0.289959 + 0.502224i
\(419\) 897.000 1553.65i 0.104585 0.181147i −0.808983 0.587832i \(-0.799982\pi\)
0.913569 + 0.406684i \(0.133315\pi\)
\(420\) 0 0
\(421\) 8064.50 + 13968.1i 0.933586 + 1.61702i 0.777136 + 0.629332i \(0.216672\pi\)
0.156450 + 0.987686i \(0.449995\pi\)
\(422\) −9202.00 −1.06148
\(423\) 0 0
\(424\) 5928.00 0.678984
\(425\) 1162.50 + 2013.51i 0.132681 + 0.229811i
\(426\) 0 0
\(427\) 442.000 765.566i 0.0500934 0.0867643i
\(428\) −2280.00 + 3949.08i −0.257495 + 0.445995i
\(429\) 0 0
\(430\) −890.000 1541.53i −0.0998130 0.172881i
\(431\) −13356.0 −1.49266 −0.746329 0.665577i \(-0.768186\pi\)
−0.746329 + 0.665577i \(0.768186\pi\)
\(432\) 0 0
\(433\) −11500.0 −1.27634 −0.638169 0.769896i \(-0.720308\pi\)
−0.638169 + 0.769896i \(0.720308\pi\)
\(434\) −188.000 325.626i −0.0207933 0.0360150i
\(435\) 0 0
\(436\) 3470.00 6010.22i 0.381153 0.660177i
\(437\) 265.500 459.859i 0.0290631 0.0503388i
\(438\) 0 0
\(439\) 5574.50 + 9655.32i 0.606051 + 1.04971i 0.991884 + 0.127143i \(0.0405806\pi\)
−0.385833 + 0.922568i \(0.626086\pi\)
\(440\) 1680.00 0.182025
\(441\) 0 0
\(442\) 3720.00 0.400322
\(443\) −1924.50 3333.33i −0.206401 0.357497i 0.744177 0.667982i \(-0.232842\pi\)
−0.950578 + 0.310485i \(0.899509\pi\)
\(444\) 0 0
\(445\) −2715.00 + 4702.52i −0.289221 + 0.500945i
\(446\) −2158.00 + 3737.77i −0.229113 + 0.396835i
\(447\) 0 0
\(448\) 128.000 + 221.703i 0.0134987 + 0.0233805i
\(449\) 18048.0 1.89697 0.948483 0.316828i \(-0.102618\pi\)
0.948483 + 0.316828i \(0.102618\pi\)
\(450\) 0 0
\(451\) 5292.00 0.552529
\(452\) −2868.00 4967.52i −0.298450 0.516930i
\(453\) 0 0
\(454\) −3123.00 + 5409.19i −0.322841 + 0.559176i
\(455\) 200.000 346.410i 0.0206069 0.0356922i
\(456\) 0 0
\(457\) 2132.00 + 3692.73i 0.218229 + 0.377984i 0.954267 0.298957i \(-0.0966386\pi\)
−0.736037 + 0.676941i \(0.763305\pi\)
\(458\) −4054.00 −0.413605
\(459\) 0 0
\(460\) −180.000 −0.0182447
\(461\) 5121.00 + 8869.83i 0.517373 + 0.896116i 0.999796 + 0.0201776i \(0.00642318\pi\)
−0.482424 + 0.875938i \(0.660243\pi\)
\(462\) 0 0
\(463\) −1651.00 + 2859.62i −0.165720 + 0.287036i −0.936911 0.349568i \(-0.886328\pi\)
0.771191 + 0.636604i \(0.219662\pi\)
\(464\) 960.000 1662.77i 0.0960493 0.166362i
\(465\) 0 0
\(466\) 438.000 + 758.638i 0.0435407 + 0.0754147i
\(467\) −1923.00 −0.190548 −0.0952739 0.995451i \(-0.530373\pi\)
−0.0952739 + 0.995451i \(0.530373\pi\)
\(468\) 0 0
\(469\) 2152.00 0.211877
\(470\) −720.000 1247.08i −0.0706620 0.122390i
\(471\) 0 0
\(472\) 1776.00 3076.12i 0.173193 0.299979i
\(473\) −3738.00 + 6474.41i −0.363369 + 0.629373i
\(474\) 0 0
\(475\) −737.500 1277.39i −0.0712396 0.123391i
\(476\) 1488.00 0.143282
\(477\) 0 0
\(478\) 12828.0 1.22749
\(479\) −7623.00 13203.4i −0.727148 1.25946i −0.958084 0.286488i \(-0.907512\pi\)
0.230936 0.972969i \(-0.425821\pi\)
\(480\) 0 0
\(481\) 2620.00 4537.97i 0.248361 0.430174i
\(482\) 3431.00 5942.67i 0.324228 0.561579i
\(483\) 0 0
\(484\) −866.000 1499.96i −0.0813298 0.140867i
\(485\) 7720.00 0.722778
\(486\) 0 0
\(487\) −8206.00 −0.763551 −0.381776 0.924255i \(-0.624687\pi\)
−0.381776 + 0.924255i \(0.624687\pi\)
\(488\) 884.000 + 1531.13i 0.0820016 + 0.142031i
\(489\) 0 0
\(490\) −1635.00 + 2831.90i −0.150738 + 0.261086i
\(491\) 8403.00 14554.4i 0.772346 1.33774i −0.163928 0.986472i \(-0.552416\pi\)
0.936274 0.351271i \(-0.114250\pi\)
\(492\) 0 0
\(493\) −5580.00 9664.84i −0.509758 0.882926i
\(494\) −2360.00 −0.214942
\(495\) 0 0
\(496\) 752.000 0.0680762
\(497\) −1380.00 2390.23i −0.124550 0.215727i
\(498\) 0 0
\(499\) 2712.50 4698.19i 0.243343 0.421483i −0.718321 0.695711i \(-0.755089\pi\)
0.961664 + 0.274229i \(0.0884226\pi\)
\(500\) −250.000 + 433.013i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) −7308.00 12657.8i −0.649745 1.12539i
\(503\) −19665.0 −1.74318 −0.871589 0.490236i \(-0.836910\pi\)
−0.871589 + 0.490236i \(0.836910\pi\)
\(504\) 0 0
\(505\) 660.000 0.0581577
\(506\) 378.000 + 654.715i 0.0332098 + 0.0575210i
\(507\) 0 0
\(508\) −1372.00 + 2376.37i −0.119828 + 0.207548i
\(509\) 7362.00 12751.4i 0.641090 1.11040i −0.344100 0.938933i \(-0.611816\pi\)
0.985190 0.171468i \(-0.0548509\pi\)
\(510\) 0 0
\(511\) −2252.00 3900.58i −0.194956 0.337674i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −7458.00 −0.639997
\(515\) 2230.00 + 3862.47i 0.190807 + 0.330487i
\(516\) 0 0
\(517\) −3024.00 + 5237.72i −0.257244 + 0.445560i
\(518\) 1048.00 1815.19i 0.0888928 0.153967i
\(519\) 0 0
\(520\) 400.000 + 692.820i 0.0337330 + 0.0584273i
\(521\) 2058.00 0.173057 0.0865284 0.996249i \(-0.472423\pi\)
0.0865284 + 0.996249i \(0.472423\pi\)
\(522\) 0 0
\(523\) 11912.0 0.995938 0.497969 0.867195i \(-0.334079\pi\)
0.497969 + 0.867195i \(0.334079\pi\)
\(524\) −228.000 394.908i −0.0190081 0.0329229i
\(525\) 0 0
\(526\) 1956.00 3387.89i 0.162140 0.280835i
\(527\) 2185.50 3785.40i 0.180649 0.312893i
\(528\) 0 0
\(529\) 6043.00 + 10466.8i 0.496671 + 0.860260i
\(530\) 7410.00 0.607302
\(531\) 0 0
\(532\) −944.000 −0.0769316
\(533\) 1260.00 + 2182.38i 0.102395 + 0.177354i
\(534\) 0 0
\(535\) −2850.00 + 4936.34i −0.230311 + 0.398910i
\(536\) −2152.00 + 3727.37i −0.173418 + 0.300369i
\(537\) 0 0
\(538\) −990.000 1714.73i −0.0793344 0.137411i
\(539\) 13734.0 1.09752
\(540\) 0 0
\(541\) −5170.00 −0.410861 −0.205430 0.978672i \(-0.565859\pi\)
−0.205430 + 0.978672i \(0.565859\pi\)
\(542\) 8495.00 + 14713.8i 0.673232 + 1.16607i
\(543\) 0 0
\(544\) −1488.00 + 2577.29i −0.117275 + 0.203126i
\(545\) 4337.50 7512.77i 0.340914 0.590480i
\(546\) 0 0
\(547\) 2093.00 + 3625.18i 0.163602 + 0.283367i 0.936158 0.351580i \(-0.114355\pi\)
−0.772556 + 0.634947i \(0.781022\pi\)
\(548\) −636.000 −0.0495777
\(549\) 0 0
\(550\) 2100.00 0.162808
\(551\) 3540.00 + 6131.46i 0.273701 + 0.474063i
\(552\) 0 0
\(553\) 1330.00 2303.63i 0.102274 0.177143i
\(554\) −1366.00 + 2365.98i −0.104758 + 0.181446i
\(555\) 0 0
\(556\) −4552.00 7884.30i −0.347208 0.601382i
\(557\) 13026.0 0.990896 0.495448 0.868637i \(-0.335004\pi\)
0.495448 + 0.868637i \(0.335004\pi\)
\(558\) 0 0
\(559\) −3560.00 −0.269359
\(560\) 160.000 + 277.128i 0.0120736 + 0.0209121i
\(561\) 0 0
\(562\) −5520.00 + 9560.92i −0.414319 + 0.717621i
\(563\) 5334.00 9238.76i 0.399292 0.691594i −0.594347 0.804209i \(-0.702589\pi\)
0.993639 + 0.112615i \(0.0359227\pi\)
\(564\) 0 0
\(565\) −3585.00 6209.40i −0.266942 0.462357i
\(566\) −10876.0 −0.807690
\(567\) 0 0
\(568\) 5520.00 0.407771
\(569\) 7686.00 + 13312.5i 0.566281 + 0.980827i 0.996929 + 0.0783076i \(0.0249516\pi\)
−0.430648 + 0.902520i \(0.641715\pi\)
\(570\) 0 0
\(571\) 7494.50 12980.9i 0.549273 0.951369i −0.449051 0.893506i \(-0.648238\pi\)
0.998325 0.0578633i \(-0.0184287\pi\)
\(572\) 1680.00 2909.85i 0.122805 0.212704i
\(573\) 0 0
\(574\) 504.000 + 872.954i 0.0366490 + 0.0634780i
\(575\) −225.000 −0.0163185
\(576\) 0 0
\(577\) −1066.00 −0.0769119 −0.0384559 0.999260i \(-0.512244\pi\)
−0.0384559 + 0.999260i \(0.512244\pi\)
\(578\) 3736.00 + 6470.94i 0.268853 + 0.465667i
\(579\) 0 0
\(580\) 1200.00 2078.46i 0.0859091 0.148799i
\(581\) −150.000 + 259.808i −0.0107109 + 0.0185519i
\(582\) 0 0
\(583\) −15561.0 26952.4i −1.10544 1.91468i
\(584\) 9008.00 0.638277
\(585\) 0 0
\(586\) −16506.0 −1.16358
\(587\) 310.500 + 537.802i 0.0218325 + 0.0378151i 0.876735 0.480973i \(-0.159717\pi\)
−0.854903 + 0.518788i \(0.826383\pi\)
\(588\) 0 0
\(589\) −1386.50 + 2401.49i −0.0969945 + 0.167999i
\(590\) 2220.00 3845.15i 0.154908 0.268309i
\(591\) 0 0
\(592\) 2096.00 + 3630.38i 0.145515 + 0.252040i
\(593\) −20187.0 −1.39794 −0.698972 0.715149i \(-0.746359\pi\)
−0.698972 + 0.715149i \(0.746359\pi\)
\(594\) 0 0
\(595\) 1860.00 0.128156
\(596\) −2796.00 4842.81i −0.192162 0.332835i
\(597\) 0 0
\(598\) −180.000 + 311.769i −0.0123089 + 0.0213197i
\(599\) 9114.00 15785.9i 0.621683 1.07679i −0.367490 0.930028i \(-0.619783\pi\)
0.989172 0.146758i \(-0.0468840\pi\)
\(600\) 0 0
\(601\) 5871.50 + 10169.7i 0.398508 + 0.690237i 0.993542 0.113464i \(-0.0361947\pi\)
−0.595034 + 0.803701i \(0.702861\pi\)
\(602\) −1424.00 −0.0964085
\(603\) 0 0
\(604\) 10496.0 0.707080
\(605\) −1082.50 1874.94i −0.0727436 0.125996i
\(606\) 0 0
\(607\) 12209.0 21146.6i 0.816389 1.41403i −0.0919375 0.995765i \(-0.529306\pi\)
0.908326 0.418262i \(-0.137361\pi\)
\(608\) 944.000 1635.06i 0.0629675 0.109063i
\(609\) 0 0
\(610\) 1105.00 + 1913.92i 0.0733445 + 0.127036i
\(611\) −2880.00 −0.190691
\(612\) 0 0
\(613\) 2672.00 0.176054 0.0880270 0.996118i \(-0.471944\pi\)
0.0880270 + 0.996118i \(0.471944\pi\)
\(614\) 9290.00 + 16090.8i 0.610609 + 1.05761i
\(615\) 0 0
\(616\) 672.000 1163.94i 0.0439540 0.0761305i
\(617\) 4300.50 7448.68i 0.280602 0.486017i −0.690931 0.722921i \(-0.742799\pi\)
0.971533 + 0.236903i \(0.0761325\pi\)
\(618\) 0 0
\(619\) −10654.0 18453.3i −0.691794 1.19822i −0.971250 0.238064i \(-0.923487\pi\)
0.279456 0.960159i \(-0.409846\pi\)
\(620\) 940.000 0.0608892
\(621\) 0 0
\(622\) −16224.0 −1.04586
\(623\) 2172.00 + 3762.01i 0.139678 + 0.241929i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −7900.00 + 13683.2i −0.504389 + 0.873627i
\(627\) 0 0
\(628\) 788.000 + 1364.86i 0.0500711 + 0.0867256i
\(629\) 24366.0 1.54457
\(630\) 0 0
\(631\) −19015.0 −1.19964 −0.599822 0.800134i \(-0.704762\pi\)
−0.599822 + 0.800134i \(0.704762\pi\)
\(632\) 2660.00 + 4607.26i 0.167419 + 0.289979i
\(633\) 0 0
\(634\) 4419.00 7653.93i 0.276815 0.479458i
\(635\) −1715.00 + 2970.47i −0.107177 + 0.185637i
\(636\) 0 0
\(637\) 3270.00 + 5663.81i 0.203394 + 0.352289i
\(638\) −10080.0 −0.625503
\(639\) 0 0
\(640\) −640.000 −0.0395285
\(641\) 2208.00 + 3824.37i 0.136054 + 0.235653i 0.926000 0.377524i \(-0.123225\pi\)
−0.789945 + 0.613177i \(0.789891\pi\)
\(642\) 0 0
\(643\) −3790.00 + 6564.47i −0.232446 + 0.402609i −0.958527 0.285000i \(-0.908006\pi\)
0.726081 + 0.687609i \(0.241340\pi\)
\(644\) −72.0000 + 124.708i −0.00440559 + 0.00763070i
\(645\) 0 0
\(646\) −5487.00 9503.76i −0.334184 0.578824i
\(647\) −14901.0 −0.905439 −0.452719 0.891653i \(-0.649546\pi\)
−0.452719 + 0.891653i \(0.649546\pi\)
\(648\) 0 0
\(649\) −18648.0 −1.12789
\(650\) 500.000 + 866.025i 0.0301717 + 0.0522589i
\(651\) 0 0
\(652\) 6692.00 11590.9i 0.401962 0.696218i
\(653\) −6457.50 + 11184.7i −0.386985 + 0.670278i −0.992042 0.125904i \(-0.959817\pi\)
0.605057 + 0.796182i \(0.293150\pi\)
\(654\) 0 0
\(655\) −285.000 493.634i −0.0170013 0.0294472i
\(656\) −2016.00 −0.119987
\(657\) 0 0
\(658\) −1152.00 −0.0682517
\(659\) −14064.0 24359.6i −0.831344 1.43993i −0.896973 0.442086i \(-0.854239\pi\)
0.0656288 0.997844i \(-0.479095\pi\)
\(660\) 0 0
\(661\) 4181.00 7241.70i 0.246024 0.426127i −0.716395 0.697695i \(-0.754209\pi\)
0.962419 + 0.271569i \(0.0875424\pi\)
\(662\) −8200.00 + 14202.8i −0.481423 + 0.833849i
\(663\) 0 0
\(664\) −300.000 519.615i −0.0175335 0.0303689i
\(665\) −1180.00 −0.0688097
\(666\) 0 0
\(667\) 1080.00 0.0626953
\(668\) −2982.00 5164.98i −0.172720 0.299160i
\(669\) 0 0
\(670\) −2690.00 + 4659.22i −0.155110 + 0.268659i
\(671\) 4641.00 8038.45i 0.267010 0.462475i
\(672\) 0 0
\(673\) −14854.0 25727.9i −0.850787 1.47361i −0.880499 0.474048i \(-0.842792\pi\)
0.0297122 0.999558i \(-0.490541\pi\)
\(674\) 19112.0 1.09224
\(675\) 0 0
\(676\) −7188.00 −0.408967
\(677\) −3381.00 5856.06i −0.191939 0.332447i 0.753954 0.656927i \(-0.228144\pi\)
−0.945893 + 0.324480i \(0.894811\pi\)
\(678\) 0 0
\(679\) 3088.00 5348.57i 0.174531 0.302297i
\(680\) −1860.00 + 3221.61i −0.104894 + 0.181681i
\(681\) 0 0
\(682\) −1974.00 3419.07i −0.110833 0.191969i
\(683\) −19155.0 −1.07313 −0.536563 0.843860i \(-0.680278\pi\)
−0.536563 + 0.843860i \(0.680278\pi\)
\(684\) 0 0
\(685\) −795.000 −0.0443436
\(686\) 2680.00 + 4641.90i 0.149159 + 0.258350i
\(687\) 0 0
\(688\) 1424.00 2466.44i 0.0789091 0.136675i
\(689\) 7410.00 12834.5i 0.409722 0.709659i
\(690\) 0 0
\(691\) 11487.5 + 19896.9i 0.632424 + 1.09539i 0.987055 + 0.160384i \(0.0512733\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(692\) −9612.00 −0.528025
\(693\) 0 0
\(694\) −20232.0 −1.10662
\(695\) −5690.00 9855.37i −0.310553 0.537893i
\(696\) 0 0
\(697\) −5859.00 + 10148.1i −0.318401 + 0.551487i
\(698\) −6751.00 + 11693.1i −0.366088 + 0.634082i
\(699\) 0 0
\(700\) 200.000 + 346.410i 0.0107990 + 0.0187044i
\(701\) −6450.00 −0.347522 −0.173761 0.984788i \(-0.555592\pi\)
−0.173761 + 0.984788i \(0.555592\pi\)
\(702\) 0 0
\(703\) −15458.0 −0.829317
\(704\) 1344.00 + 2327.88i 0.0719516 + 0.124624i
\(705\) 0 0
\(706\) 4062.00 7035.59i 0.216537 0.375054i
\(707\) 264.000 457.261i 0.0140435 0.0243240i
\(708\) 0 0
\(709\) −17269.0 29910.8i −0.914740 1.58438i −0.807281 0.590167i \(-0.799062\pi\)
−0.107459 0.994209i \(-0.534272\pi\)
\(710\) 6900.00 0.364722
\(711\) 0 0
\(712\) −8688.00 −0.457299
\(713\) 211.500 + 366.329i 0.0111090 + 0.0192414i
\(714\) 0 0
\(715\) 2100.00 3637.31i 0.109840 0.190248i
\(716\) −5280.00 + 9145.23i −0.275591 + 0.477337i
\(717\) 0 0
\(718\) 8778.00 + 15203.9i 0.456256 + 0.790259i
\(719\) 27114.0 1.40637 0.703186 0.711006i \(-0.251760\pi\)
0.703186 + 0.711006i \(0.251760\pi\)
\(720\) 0 0
\(721\) 3568.00 0.184299
\(722\) −3378.00 5850.87i −0.174122 0.301588i
\(723\) 0 0
\(724\) −2146.00 + 3716.98i −0.110159 + 0.190802i
\(725\) 1500.00 2598.08i 0.0768395 0.133090i
\(726\) 0 0
\(727\) −118.000 204.382i −0.00601978 0.0104266i 0.863000 0.505204i \(-0.168583\pi\)
−0.869020 + 0.494778i \(0.835249\pi\)
\(728\) 640.000 0.0325824
\(729\) 0 0
\(730\) 11260.0 0.570892
\(731\) −8277.00 14336.2i −0.418791 0.725367i
\(732\) 0 0
\(733\) −13564.0 + 23493.5i −0.683489 + 1.18384i 0.290420 + 0.956899i \(0.406205\pi\)
−0.973909 + 0.226939i \(0.927128\pi\)
\(734\) 956.000 1655.84i 0.0480744 0.0832673i
\(735\) 0 0
\(736\) −144.000 249.415i −0.00721183 0.0124913i
\(737\) 22596.0 1.12935
\(738\) 0 0
\(739\) 5249.00 0.261282 0.130641 0.991430i \(-0.458296\pi\)
0.130641 + 0.991430i \(0.458296\pi\)
\(740\) 2620.00 + 4537.97i 0.130153 + 0.225431i
\(741\) 0 0
\(742\) 2964.00 5133.80i 0.146647 0.254000i
\(743\) −6948.00 + 12034.3i −0.343065 + 0.594206i −0.985000 0.172553i \(-0.944798\pi\)
0.641935 + 0.766759i \(0.278132\pi\)
\(744\) 0 0
\(745\) −3495.00 6053.52i −0.171875 0.297696i
\(746\) −4600.00 −0.225761
\(747\) 0 0
\(748\) 15624.0 0.763730
\(749\) 2280.00 + 3949.08i 0.111227 + 0.192652i
\(750\) 0 0
\(751\) −13832.5 + 23958.6i −0.672111 + 1.16413i 0.305194 + 0.952290i \(0.401279\pi\)
−0.977304 + 0.211840i \(0.932055\pi\)
\(752\) 1152.00 1995.32i 0.0558632 0.0967579i
\(753\) 0 0
\(754\) −2400.00 4156.92i −0.115919 0.200777i
\(755\) 13120.0 0.632431
\(756\) 0 0
\(757\) −8122.00 −0.389959 −0.194980 0.980807i \(-0.562464\pi\)
−0.194980 + 0.980807i \(0.562464\pi\)
\(758\) 29.0000 + 50.2295i 0.00138961 + 0.00240688i
\(759\) 0 0
\(760\) 1180.00 2043.82i 0.0563199 0.0975489i
\(761\) −5292.00 + 9166.01i −0.252083 + 0.436620i −0.964099 0.265543i \(-0.914449\pi\)
0.712016 + 0.702163i \(0.247782\pi\)
\(762\) 0 0
\(763\) −3470.00 6010.22i −0.164643 0.285170i
\(764\) −5880.00 −0.278444
\(765\) 0 0
\(766\) −16254.0 −0.766685
\(767\) −4440.00 7690.31i −0.209021 0.362035i
\(768\) 0 0
\(769\) 9309.50 16124.5i 0.436553 0.756132i −0.560868 0.827905i \(-0.689533\pi\)
0.997421 + 0.0717734i \(0.0228659\pi\)
\(770\) 840.000 1454.92i 0.0393136 0.0680932i
\(771\) 0 0
\(772\) 9440.00 + 16350.6i 0.440095 + 0.762266i
\(773\) 22251.0 1.03533 0.517667 0.855582i \(-0.326801\pi\)
0.517667 + 0.855582i \(0.326801\pi\)
\(774\) 0 0
\(775\) 1175.00 0.0544610
\(776\) 6176.00 + 10697.1i 0.285703 + 0.494852i
\(777\) 0 0
\(778\) −7938.00 + 13749.0i −0.365798 + 0.633581i
\(779\) 3717.00 6438.03i 0.170957 0.296106i
\(780\) 0 0
\(781\) −14490.0 25097.4i −0.663883 1.14988i
\(782\) −1674.00 −0.0765500
\(783\) 0 0
\(784\) −5232.00 −0.238338
\(785\) 985.000 + 1706.07i 0.0447849 + 0.0775697i