Properties

Label 810.4.e.q.541.1
Level $810$
Weight $4$
Character 810.541
Analytic conductor $47.792$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.541
Dual form 810.4.e.q.271.1

$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 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 −0.806966 0.590598i \(-0.798892\pi\)
0.914956 + 0.403554i \(0.132225\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) 21.0000 36.3731i 0.575613 0.996990i −0.420362 0.907356i \(-0.638097\pi\)
0.995975 0.0896338i \(-0.0285697\pi\)
\(12\) 0 0
\(13\) −10.0000 17.3205i −0.213346 0.369527i 0.739413 0.673252i \(-0.235103\pi\)
−0.952760 + 0.303725i \(0.901770\pi\)
\(14\) −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 0.885703 0.464253i \(-0.153677\pi\)
−0.844906 + 0.534914i \(0.820344\pi\)
\(24\) 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 −0.607460 0.794350i \(-0.707812\pi\)
0.991657 + 0.128901i \(0.0411449\pi\)
\(30\) 0 0
\(31\) −23.5000 40.7032i −0.136152 0.235823i 0.789885 0.613255i \(-0.210140\pi\)
−0.926037 + 0.377433i \(0.876807\pi\)
\(32\) 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 0.960707 0.277566i \(-0.0895276\pi\)
−0.720732 + 0.693213i \(0.756194\pi\)
\(42\) 0 0
\(43\) 89.0000 154.153i 0.315637 0.546699i −0.663936 0.747789i \(-0.731115\pi\)
0.979573 + 0.201091i \(0.0644486\pi\)
\(44\) −168.000 −0.575613
\(45\) 0 0
\(46\) 18.0000 0.0576947
\(47\) 72.0000 124.708i 0.223453 0.387032i −0.732401 0.680873i \(-0.761600\pi\)
0.955854 + 0.293842i \(0.0949338\pi\)
\(48\) 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 0.510069 0.860134i \(-0.329620\pi\)
−0.999932 + 0.0116655i \(0.996287\pi\)
\(60\) 0 0
\(61\) −110.500 + 191.392i −0.231936 + 0.401724i −0.958378 0.285503i \(-0.907839\pi\)
0.726442 + 0.687228i \(0.241173\pi\)
\(62\) −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 0.999940 0.0109338i \(-0.00348039\pi\)
−0.509439 + 0.860507i \(0.670147\pi\)
\(68\) 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 −0.999541 0.0302955i \(-0.990355\pi\)
0.526007 + 0.850480i \(0.323689\pi\)
\(80\) 80.0000 0.111803
\(81\) 0 0
\(82\) 252.000 0.339375
\(83\) 37.5000 64.9519i 0.0495923 0.0858964i −0.840164 0.542333i \(-0.817541\pi\)
0.889756 + 0.456437i \(0.150874\pi\)
\(84\) 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 0.106095 + 0.994356i \(0.466165\pi\)
−0.914185 + 0.405297i \(0.867168\pi\)
\(98\) 654.000 0.674122
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) −66.0000 + 114.315i −0.0650222 + 0.112622i −0.896704 0.442631i \(-0.854045\pi\)
0.831682 + 0.555253i \(0.187378\pi\)
\(102\) 0 0
\(103\) 446.000 + 772.495i 0.426657 + 0.738992i 0.996574 0.0827108i \(-0.0263578\pi\)
−0.569916 + 0.821703i \(0.693024\pi\)
\(104\) 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 −0.993276 0.115773i \(-0.963066\pi\)
0.396376 0.918088i \(-0.370268\pi\)
\(114\) 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 0.846391 0.532561i \(-0.178770\pi\)
−0.884407 + 0.466716i \(0.845437\pi\)
\(132\) 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 −0.840172 0.542321i \(-0.817546\pi\)
0.889749 + 0.456450i \(0.150879\pi\)
\(138\) 0 0
\(139\) −1138.00 1971.07i −0.694417 1.20276i −0.970377 0.241596i \(-0.922329\pi\)
0.275960 0.961169i \(-0.411004\pi\)
\(140\) 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 0.607351 0.794434i \(-0.292232\pi\)
−0.991675 + 0.128765i \(0.958899\pi\)
\(150\) 0 0
\(151\) −1312.00 + 2272.45i −0.707080 + 1.22470i 0.258856 + 0.965916i \(0.416655\pi\)
−0.965936 + 0.258782i \(0.916679\pi\)
\(152\) −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 0.911743 0.410761i \(-0.134737\pi\)
−0.811601 + 0.584212i \(0.801404\pi\)
\(158\) 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 0.639993 0.768380i \(-0.278937\pi\)
−0.985434 + 0.170060i \(0.945604\pi\)
\(168\) 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 −0.471441 0.881898i \(-0.656266\pi\)
0.999466 0.0326688i \(-0.0104007\pi\)
\(174\) 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 −0.692555 0.721366i \(-0.743515\pi\)
0.970998 + 0.239087i \(0.0768481\pi\)
\(192\) 0 0
\(193\) 2360.00 + 4087.64i 0.880189 + 1.52453i 0.851130 + 0.524955i \(0.175918\pi\)
0.0290591 + 0.999578i \(0.490749\pi\)
\(194\) 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 −0.947541 0.319635i \(-0.896440\pi\)
0.196958 0.980412i \(-0.436894\pi\)
\(212\) 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 −0.657298 0.753631i \(-0.728301\pi\)
0.981312 + 0.192421i \(0.0616341\pi\)
\(224\) 128.000 0.0381802
\(225\) 0 0
\(226\) −2868.00 −0.844144
\(227\) 1561.50 2704.60i 0.456566 0.790795i −0.542211 0.840242i \(-0.682413\pi\)
0.998777 + 0.0494474i \(0.0157460\pi\)
\(228\) 0 0
\(229\) −1013.50 1755.43i −0.292463 0.506560i 0.681929 0.731419i \(-0.261141\pi\)
−0.974391 + 0.224858i \(0.927808\pi\)
\(230\) −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 0.864073 + 0.503367i \(0.167905\pi\)
0.00389189 + 0.999992i \(0.498761\pi\)
\(240\) 0 0
\(241\) −1715.50 + 2971.33i −0.458527 + 0.794193i −0.998883 0.0472439i \(-0.984956\pi\)
0.540356 + 0.841436i \(0.318290\pi\)
\(242\) −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 0.545997 0.837787i \(-0.316151\pi\)
−0.998543 + 0.0539542i \(0.982817\pi\)
\(258\) 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 −0.957601 0.288098i \(-0.906977\pi\)
0.728300 + 0.685258i \(0.240311\pi\)
\(264\) 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 −0.782394 0.622784i \(-0.786002\pi\)
0.930544 + 0.366181i \(0.119335\pi\)
\(278\) −4552.00 −0.982053
\(279\) 0 0
\(280\) 160.000 0.0341494
\(281\) 2760.00 4780.46i 0.585935 1.01487i −0.408823 0.912614i \(-0.634061\pi\)
0.994758 0.102256i \(-0.0326060\pi\)
\(282\) 0 0
\(283\) −2719.00 4709.45i −0.571123 0.989214i −0.996451 0.0841746i \(-0.973175\pi\)
0.425328 0.905039i \(-0.360159\pi\)
\(284\) 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 −0.903609 0.428358i \(-0.859092\pi\)
0.0808352 0.996727i \(-0.474241\pi\)
\(294\) 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 −0.952706 0.303894i \(-0.901713\pi\)
0.213173 0.977014i \(-0.431620\pi\)
\(312\) 0 0
\(313\) 3950.00 6841.60i 0.713314 1.23550i −0.250293 0.968170i \(-0.580527\pi\)
0.963606 0.267325i \(-0.0861399\pi\)
\(314\) 788.000 0.141622
\(315\) 0 0
\(316\) 2660.00 0.473534
\(317\) −2209.50 + 3826.97i −0.391476 + 0.678056i −0.992644 0.121066i \(-0.961369\pi\)
0.601168 + 0.799122i \(0.294702\pi\)
\(318\) 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 −0.293891 0.955839i \(-0.594950\pi\)
0.974726 0.223402i \(-0.0717163\pi\)
\(332\) −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 0.936285 + 0.351242i \(0.114241\pi\)
−0.163957 + 0.986467i \(0.552426\pi\)
\(338\) −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 −0.930481 0.366340i \(-0.880611\pi\)
0.147980 0.988990i \(-0.452723\pi\)
\(348\) 0 0
\(349\) 3375.50 5846.54i 0.517726 0.896728i −0.482062 0.876137i \(-0.660112\pi\)
0.999788 0.0205906i \(-0.00655466\pi\)
\(350\) 200.000 0.0305441
\(351\) 0 0
\(352\) 1344.00 0.203510
\(353\) −2031.00 + 3517.80i −0.306230 + 0.530406i −0.977534 0.210776i \(-0.932401\pi\)
0.671304 + 0.741182i \(0.265734\pi\)
\(354\) 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 −0.898015 0.439964i \(-0.854991\pi\)
0.830028 + 0.557722i \(0.188324\pi\)
\(368\) −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 0.775101 0.631838i \(-0.217699\pi\)
−0.934738 + 0.355338i \(0.884366\pi\)
\(374\) 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 −0.998782 0.0493491i \(-0.984285\pi\)
0.456653 0.889645i \(-0.349048\pi\)
\(384\) 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 −0.482481 0.875907i \(-0.660264\pi\)
0.999798 0.0201127i \(-0.00640249\pi\)
\(390\) 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 0.688698 0.725048i \(-0.258183\pi\)
−0.972259 + 0.233906i \(0.924849\pi\)
\(402\) 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 0.834184 0.551486i \(-0.185939\pi\)
−0.894693 + 0.446682i \(0.852606\pi\)
\(410\) −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 0.913569 0.406684i \(-0.133315\pi\)
−0.808983 + 0.587832i \(0.799982\pi\)
\(420\) 0 0
\(421\) 8064.50 13968.1i 0.933586 1.61702i 0.156450 0.987686i \(-0.449995\pi\)
0.777136 0.629332i \(-0.216672\pi\)
\(422\) −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 −0.385833 0.922568i \(-0.626086\pi\)
0.991884 0.127143i \(-0.0405806\pi\)
\(440\) 1680.00 0.182025
\(441\) 0 0
\(442\) 3720.00 0.400322
\(443\) −1924.50 + 3333.33i −0.206401 + 0.357497i −0.950578 0.310485i \(-0.899509\pi\)
0.744177 + 0.667982i \(0.232842\pi\)
\(444\) 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 −0.736037 0.676941i \(-0.763305\pi\)
0.954267 + 0.298957i \(0.0966386\pi\)
\(458\) −4054.00 −0.413605
\(459\) 0 0
\(460\) −180.000 −0.0182447
\(461\) 5121.00 8869.83i 0.517373 0.896116i −0.482424 0.875938i \(-0.660243\pi\)
0.999796 0.0201776i \(-0.00642318\pi\)
\(462\) 0 0
\(463\) −1651.00 2859.62i −0.165720 0.287036i 0.771191 0.636604i \(-0.219662\pi\)
−0.936911 + 0.349568i \(0.886328\pi\)
\(464\) 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 0.230936 + 0.972969i \(0.425821\pi\)
−0.958084 + 0.286488i \(0.907512\pi\)
\(480\) 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 0.936274 + 0.351271i \(0.114250\pi\)
−0.163928 + 0.986472i \(0.552416\pi\)
\(492\) 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 0.961664 0.274229i \(-0.0884226\pi\)
−0.718321 + 0.695711i \(0.755089\pi\)
\(500\) −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 0.985190 + 0.171468i \(0.0548509\pi\)
−0.344100 + 0.938933i \(0.611816\pi\)
\(510\) 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 −0.772556 0.634947i \(-0.781022\pi\)
0.936158 + 0.351580i \(0.114355\pi\)
\(548\) −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 0.993639 0.112615i \(-0.0359227\pi\)
−0.594347 + 0.804209i \(0.702589\pi\)
\(564\) 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 −0.430648 0.902520i \(-0.641715\pi\)
0.996929 0.0783076i \(-0.0249516\pi\)
\(570\) 0 0
\(571\) 7494.50 + 12980.9i 0.549273 + 0.951369i 0.998325 + 0.0578633i \(0.0184287\pi\)
−0.449051 + 0.893506i \(0.648238\pi\)
\(572\) 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 −0.854903 0.518788i \(-0.826383\pi\)
0.876735 + 0.480973i \(0.159717\pi\)
\(588\) 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 0.989172 + 0.146758i \(0.0468840\pi\)
−0.367490 + 0.930028i \(0.619783\pi\)
\(600\) 0 0
\(601\) 5871.50 10169.7i 0.398508 0.690237i −0.595034 0.803701i \(-0.702861\pi\)
0.993542 + 0.113464i \(0.0361947\pi\)
\(602\) −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 0.908326 + 0.418262i \(0.137361\pi\)
−0.0919375 + 0.995765i \(0.529306\pi\)
\(608\) 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 0.971533 0.236903i \(-0.0761325\pi\)
−0.690931 + 0.722921i \(0.742799\pi\)
\(618\) 0 0
\(619\) −10654.0 + 18453.3i −0.691794 + 1.19822i 0.279456 + 0.960159i \(0.409846\pi\)
−0.971250 + 0.238064i \(0.923487\pi\)
\(620\) 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 −0.789945 0.613177i \(-0.789891\pi\)
0.926000 + 0.377524i \(0.123225\pi\)
\(642\) 0 0
\(643\) −3790.00 6564.47i −0.232446 0.402609i 0.726081 0.687609i \(-0.241340\pi\)
−0.958527 + 0.285000i \(0.908006\pi\)
\(644\) −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 0.605057 0.796182i \(-0.293150\pi\)
−0.992042 + 0.125904i \(0.959817\pi\)
\(654\) 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 0.0656288 + 0.997844i \(0.479095\pi\)
−0.896973 + 0.442086i \(0.854239\pi\)
\(660\) 0 0
\(661\) 4181.00 + 7241.70i 0.246024 + 0.426127i 0.962419 0.271569i \(-0.0875424\pi\)
−0.716395 + 0.697695i \(0.754209\pi\)
\(662\) −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 0.0297122 + 0.999558i \(0.490541\pi\)
−0.880499 + 0.474048i \(0.842792\pi\)
\(674\) 19112.0 1.09224
\(675\) 0 0
\(676\) −7188.00 −0.408967
\(677\) −3381.00 + 5856.06i −0.191939 + 0.332447i −0.945893 0.324480i \(-0.894811\pi\)
0.753954 + 0.656927i \(0.228144\pi\)
\(678\) 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 −0.354630 0.935007i \(-0.615393\pi\)
0.987055 0.160384i \(-0.0512733\pi\)
\(692\) −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 −0.107459 + 0.994209i \(0.534272\pi\)
−0.807281 + 0.590167i \(0.799062\pi\)
\(710\) 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 −0.869020 0.494778i \(-0.835249\pi\)
0.863000 + 0.505204i \(0.168583\pi\)
\(728\) 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 −0.973909 0.226939i \(-0.927128\pi\)
0.290420 0.956899i \(-0.406205\pi\)
\(734\) 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 0.641935 0.766759i \(-0.278132\pi\)
−0.985000 + 0.172553i \(0.944798\pi\)
\(744\) 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 −0.977304 0.211840i \(-0.932055\pi\)
0.305194 0.952290i \(-0.401279\pi\)
\(752\) 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 0.712016 0.702163i \(-0.247782\pi\)
−0.964099 + 0.265543i \(0.914449\pi\)
\(762\) 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 0.997421 0.0717734i \(-0.0228659\pi\)
−0.560868 + 0.827905i \(0.689533\pi\)
\(770\) 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