Properties

Label 405.4.e.g.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.g.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(12.0000 + 20.7846i) q^{7} -15.0000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(3.50000 - 6.06218i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(12.0000 + 20.7846i) q^{7} -15.0000 q^{8} +5.00000 q^{10} +(-26.0000 - 45.0333i) q^{11} +(-11.0000 + 19.0526i) q^{13} +(12.0000 - 20.7846i) q^{14} +(-20.5000 - 35.5070i) q^{16} -14.0000 q^{17} -20.0000 q^{19} +(17.5000 + 30.3109i) q^{20} +(-26.0000 + 45.0333i) q^{22} +(84.0000 - 145.492i) q^{23} +(-12.5000 - 21.6506i) q^{25} +22.0000 q^{26} +168.000 q^{28} +(-115.000 - 199.186i) q^{29} +(144.000 - 249.415i) q^{31} +(-80.5000 + 139.430i) q^{32} +(7.00000 + 12.1244i) q^{34} -120.000 q^{35} -34.0000 q^{37} +(10.0000 + 17.3205i) q^{38} +(37.5000 - 64.9519i) q^{40} +(-61.0000 + 105.655i) q^{41} +(94.0000 + 162.813i) q^{43} -364.000 q^{44} -168.000 q^{46} +(-128.000 - 221.703i) q^{47} +(-116.500 + 201.784i) q^{49} +(-12.5000 + 21.6506i) q^{50} +(77.0000 + 133.368i) q^{52} -338.000 q^{53} +260.000 q^{55} +(-180.000 - 311.769i) q^{56} +(-115.000 + 199.186i) q^{58} +(-50.0000 + 86.6025i) q^{59} +(-371.000 - 642.591i) q^{61} -288.000 q^{62} -167.000 q^{64} +(-55.0000 - 95.2628i) q^{65} +(42.0000 - 72.7461i) q^{67} +(-49.0000 + 84.8705i) q^{68} +(60.0000 + 103.923i) q^{70} -328.000 q^{71} -38.0000 q^{73} +(17.0000 + 29.4449i) q^{74} +(-70.0000 + 121.244i) q^{76} +(624.000 - 1080.80i) q^{77} +(120.000 + 207.846i) q^{79} +205.000 q^{80} +122.000 q^{82} +(-606.000 - 1049.62i) q^{83} +(35.0000 - 60.6218i) q^{85} +(94.0000 - 162.813i) q^{86} +(390.000 + 675.500i) q^{88} +330.000 q^{89} -528.000 q^{91} +(-588.000 - 1018.45i) q^{92} +(-128.000 + 221.703i) q^{94} +(50.0000 - 86.6025i) q^{95} +(-433.000 - 749.978i) q^{97} +233.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 7 q^{4} - 5 q^{5} + 24 q^{7} - 30 q^{8} + O(q^{10}) \) \( 2 q - q^{2} + 7 q^{4} - 5 q^{5} + 24 q^{7} - 30 q^{8} + 10 q^{10} - 52 q^{11} - 22 q^{13} + 24 q^{14} - 41 q^{16} - 28 q^{17} - 40 q^{19} + 35 q^{20} - 52 q^{22} + 168 q^{23} - 25 q^{25} + 44 q^{26} + 336 q^{28} - 230 q^{29} + 288 q^{31} - 161 q^{32} + 14 q^{34} - 240 q^{35} - 68 q^{37} + 20 q^{38} + 75 q^{40} - 122 q^{41} + 188 q^{43} - 728 q^{44} - 336 q^{46} - 256 q^{47} - 233 q^{49} - 25 q^{50} + 154 q^{52} - 676 q^{53} + 520 q^{55} - 360 q^{56} - 230 q^{58} - 100 q^{59} - 742 q^{61} - 576 q^{62} - 334 q^{64} - 110 q^{65} + 84 q^{67} - 98 q^{68} + 120 q^{70} - 656 q^{71} - 76 q^{73} + 34 q^{74} - 140 q^{76} + 1248 q^{77} + 240 q^{79} + 410 q^{80} + 244 q^{82} - 1212 q^{83} + 70 q^{85} + 188 q^{86} + 780 q^{88} + 660 q^{89} - 1056 q^{91} - 1176 q^{92} - 256 q^{94} + 100 q^{95} - 866 q^{97} + 466 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.176777 0.306186i 0.763998 0.645219i \(-0.223234\pi\)
−0.940775 + 0.339032i \(0.889900\pi\)
\(3\) 0 0
\(4\) 3.50000 6.06218i 0.437500 0.757772i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 12.0000 + 20.7846i 0.647939 + 1.12226i 0.983614 + 0.180286i \(0.0577022\pi\)
−0.335675 + 0.941978i \(0.608964\pi\)
\(8\) −15.0000 −0.662913
\(9\) 0 0
\(10\) 5.00000 0.158114
\(11\) −26.0000 45.0333i −0.712663 1.23437i −0.963854 0.266431i \(-0.914155\pi\)
0.251191 0.967938i \(-0.419178\pi\)
\(12\) 0 0
\(13\) −11.0000 + 19.0526i −0.234681 + 0.406479i −0.959180 0.282797i \(-0.908738\pi\)
0.724499 + 0.689276i \(0.242071\pi\)
\(14\) 12.0000 20.7846i 0.229081 0.396780i
\(15\) 0 0
\(16\) −20.5000 35.5070i −0.320312 0.554798i
\(17\) −14.0000 −0.199735 −0.0998676 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 0 0
\(19\) −20.0000 −0.241490 −0.120745 0.992684i \(-0.538528\pi\)
−0.120745 + 0.992684i \(0.538528\pi\)
\(20\) 17.5000 + 30.3109i 0.195656 + 0.338886i
\(21\) 0 0
\(22\) −26.0000 + 45.0333i −0.251964 + 0.436415i
\(23\) 84.0000 145.492i 0.761531 1.31901i −0.180530 0.983569i \(-0.557781\pi\)
0.942061 0.335441i \(-0.108885\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 22.0000 0.165944
\(27\) 0 0
\(28\) 168.000 1.13389
\(29\) −115.000 199.186i −0.736378 1.27544i −0.954116 0.299437i \(-0.903201\pi\)
0.217738 0.976007i \(-0.430132\pi\)
\(30\) 0 0
\(31\) 144.000 249.415i 0.834296 1.44504i −0.0603071 0.998180i \(-0.519208\pi\)
0.894603 0.446862i \(-0.147459\pi\)
\(32\) −80.5000 + 139.430i −0.444704 + 0.770250i
\(33\) 0 0
\(34\) 7.00000 + 12.1244i 0.0353085 + 0.0611562i
\(35\) −120.000 −0.579534
\(36\) 0 0
\(37\) −34.0000 −0.151069 −0.0755347 0.997143i \(-0.524066\pi\)
−0.0755347 + 0.997143i \(0.524066\pi\)
\(38\) 10.0000 + 17.3205i 0.0426898 + 0.0739410i
\(39\) 0 0
\(40\) 37.5000 64.9519i 0.148232 0.256745i
\(41\) −61.0000 + 105.655i −0.232356 + 0.402453i −0.958501 0.285089i \(-0.907977\pi\)
0.726145 + 0.687542i \(0.241310\pi\)
\(42\) 0 0
\(43\) 94.0000 + 162.813i 0.333369 + 0.577412i 0.983170 0.182692i \(-0.0584812\pi\)
−0.649801 + 0.760104i \(0.725148\pi\)
\(44\) −364.000 −1.24716
\(45\) 0 0
\(46\) −168.000 −0.538484
\(47\) −128.000 221.703i −0.397249 0.688056i 0.596136 0.802883i \(-0.296702\pi\)
−0.993385 + 0.114827i \(0.963369\pi\)
\(48\) 0 0
\(49\) −116.500 + 201.784i −0.339650 + 0.588291i
\(50\) −12.5000 + 21.6506i −0.0353553 + 0.0612372i
\(51\) 0 0
\(52\) 77.0000 + 133.368i 0.205346 + 0.355669i
\(53\) −338.000 −0.875998 −0.437999 0.898976i \(-0.644313\pi\)
−0.437999 + 0.898976i \(0.644313\pi\)
\(54\) 0 0
\(55\) 260.000 0.637425
\(56\) −180.000 311.769i −0.429527 0.743963i
\(57\) 0 0
\(58\) −115.000 + 199.186i −0.260349 + 0.450938i
\(59\) −50.0000 + 86.6025i −0.110330 + 0.191096i −0.915903 0.401399i \(-0.868524\pi\)
0.805574 + 0.592496i \(0.201857\pi\)
\(60\) 0 0
\(61\) −371.000 642.591i −0.778716 1.34878i −0.932682 0.360700i \(-0.882538\pi\)
0.153966 0.988076i \(-0.450795\pi\)
\(62\) −288.000 −0.589936
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) −55.0000 95.2628i −0.104952 0.181783i
\(66\) 0 0
\(67\) 42.0000 72.7461i 0.0765838 0.132647i −0.825190 0.564855i \(-0.808932\pi\)
0.901774 + 0.432208i \(0.142265\pi\)
\(68\) −49.0000 + 84.8705i −0.0873842 + 0.151354i
\(69\) 0 0
\(70\) 60.0000 + 103.923i 0.102448 + 0.177445i
\(71\) −328.000 −0.548260 −0.274130 0.961693i \(-0.588390\pi\)
−0.274130 + 0.961693i \(0.588390\pi\)
\(72\) 0 0
\(73\) −38.0000 −0.0609255 −0.0304628 0.999536i \(-0.509698\pi\)
−0.0304628 + 0.999536i \(0.509698\pi\)
\(74\) 17.0000 + 29.4449i 0.0267055 + 0.0462553i
\(75\) 0 0
\(76\) −70.0000 + 121.244i −0.105652 + 0.182995i
\(77\) 624.000 1080.80i 0.923525 1.59959i
\(78\) 0 0
\(79\) 120.000 + 207.846i 0.170899 + 0.296006i 0.938735 0.344641i \(-0.111999\pi\)
−0.767835 + 0.640647i \(0.778666\pi\)
\(80\) 205.000 0.286496
\(81\) 0 0
\(82\) 122.000 0.164301
\(83\) −606.000 1049.62i −0.801411 1.38809i −0.918687 0.394986i \(-0.870750\pi\)
0.117276 0.993099i \(-0.462584\pi\)
\(84\) 0 0
\(85\) 35.0000 60.6218i 0.0446622 0.0773571i
\(86\) 94.0000 162.813i 0.117864 0.204146i
\(87\) 0 0
\(88\) 390.000 + 675.500i 0.472433 + 0.818279i
\(89\) 330.000 0.393033 0.196516 0.980501i \(-0.437037\pi\)
0.196516 + 0.980501i \(0.437037\pi\)
\(90\) 0 0
\(91\) −528.000 −0.608236
\(92\) −588.000 1018.45i −0.666340 1.15413i
\(93\) 0 0
\(94\) −128.000 + 221.703i −0.140449 + 0.243265i
\(95\) 50.0000 86.6025i 0.0539989 0.0935288i
\(96\) 0 0
\(97\) −433.000 749.978i −0.453242 0.785038i 0.545343 0.838213i \(-0.316399\pi\)
−0.998585 + 0.0531745i \(0.983066\pi\)
\(98\) 233.000 0.240169
\(99\) 0 0
\(100\) −175.000 −0.175000
\(101\) 609.000 + 1054.82i 0.599978 + 1.03919i 0.992824 + 0.119588i \(0.0381573\pi\)
−0.392846 + 0.919604i \(0.628509\pi\)
\(102\) 0 0
\(103\) 44.0000 76.2102i 0.0420917 0.0729050i −0.844212 0.536009i \(-0.819931\pi\)
0.886304 + 0.463104i \(0.153264\pi\)
\(104\) 165.000 285.788i 0.155573 0.269460i
\(105\) 0 0
\(106\) 169.000 + 292.717i 0.154856 + 0.268218i
\(107\) 36.0000 0.0325257 0.0162629 0.999868i \(-0.494823\pi\)
0.0162629 + 0.999868i \(0.494823\pi\)
\(108\) 0 0
\(109\) −970.000 −0.852378 −0.426189 0.904634i \(-0.640144\pi\)
−0.426189 + 0.904634i \(0.640144\pi\)
\(110\) −130.000 225.167i −0.112682 0.195171i
\(111\) 0 0
\(112\) 492.000 852.169i 0.415086 0.718950i
\(113\) −521.000 + 902.398i −0.433731 + 0.751243i −0.997191 0.0748996i \(-0.976136\pi\)
0.563460 + 0.826143i \(0.309470\pi\)
\(114\) 0 0
\(115\) 420.000 + 727.461i 0.340567 + 0.589879i
\(116\) −1610.00 −1.28866
\(117\) 0 0
\(118\) 100.000 0.0780148
\(119\) −168.000 290.985i −0.129416 0.224156i
\(120\) 0 0
\(121\) −686.500 + 1189.05i −0.515778 + 0.893353i
\(122\) −371.000 + 642.591i −0.275318 + 0.476864i
\(123\) 0 0
\(124\) −1008.00 1745.91i −0.730009 1.26441i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1936.00 1.35269 0.676347 0.736583i \(-0.263562\pi\)
0.676347 + 0.736583i \(0.263562\pi\)
\(128\) 727.500 + 1260.07i 0.502363 + 0.870119i
\(129\) 0 0
\(130\) −55.0000 + 95.2628i −0.0371063 + 0.0642700i
\(131\) −366.000 + 633.931i −0.244104 + 0.422800i −0.961879 0.273475i \(-0.911827\pi\)
0.717776 + 0.696274i \(0.245160\pi\)
\(132\) 0 0
\(133\) −240.000 415.692i −0.156471 0.271016i
\(134\) −84.0000 −0.0541529
\(135\) 0 0
\(136\) 210.000 0.132407
\(137\) 1107.00 + 1917.38i 0.690346 + 1.19571i 0.971725 + 0.236117i \(0.0758750\pi\)
−0.281379 + 0.959597i \(0.590792\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.00610208 + 0.0105691i −0.869060 0.494706i \(-0.835276\pi\)
0.862958 + 0.505275i \(0.168609\pi\)
\(140\) −420.000 + 727.461i −0.253546 + 0.439155i
\(141\) 0 0
\(142\) 164.000 + 284.056i 0.0969195 + 0.167870i
\(143\) 1144.00 0.668994
\(144\) 0 0
\(145\) 1150.00 0.658637
\(146\) 19.0000 + 32.9090i 0.0107702 + 0.0186546i
\(147\) 0 0
\(148\) −119.000 + 206.114i −0.0660928 + 0.114476i
\(149\) 665.000 1151.81i 0.365630 0.633290i −0.623247 0.782025i \(-0.714187\pi\)
0.988877 + 0.148735i \(0.0475201\pi\)
\(150\) 0 0
\(151\) 604.000 + 1046.16i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 300.000 0.160087
\(153\) 0 0
\(154\) −1248.00 −0.653031
\(155\) 720.000 + 1247.08i 0.373108 + 0.646243i
\(156\) 0 0
\(157\) 1757.00 3043.21i 0.893146 1.54697i 0.0570627 0.998371i \(-0.481827\pi\)
0.836083 0.548603i \(-0.184840\pi\)
\(158\) 120.000 207.846i 0.0604221 0.104654i
\(159\) 0 0
\(160\) −402.500 697.150i −0.198878 0.344466i
\(161\) 4032.00 1.97370
\(162\) 0 0
\(163\) −2068.00 −0.993732 −0.496866 0.867827i \(-0.665516\pi\)
−0.496866 + 0.867827i \(0.665516\pi\)
\(164\) 427.000 + 739.586i 0.203312 + 0.352146i
\(165\) 0 0
\(166\) −606.000 + 1049.62i −0.283342 + 0.490762i
\(167\) 12.0000 20.7846i 0.00556041 0.00963091i −0.863232 0.504808i \(-0.831563\pi\)
0.868792 + 0.495177i \(0.164897\pi\)
\(168\) 0 0
\(169\) 856.500 + 1483.50i 0.389850 + 0.675240i
\(170\) −70.0000 −0.0315809
\(171\) 0 0
\(172\) 1316.00 0.583396
\(173\) 309.000 + 535.204i 0.135797 + 0.235207i 0.925902 0.377765i \(-0.123307\pi\)
−0.790105 + 0.612972i \(0.789974\pi\)
\(174\) 0 0
\(175\) 300.000 519.615i 0.129588 0.224453i
\(176\) −1066.00 + 1846.37i −0.456550 + 0.790768i
\(177\) 0 0
\(178\) −165.000 285.788i −0.0694791 0.120341i
\(179\) 3340.00 1.39466 0.697328 0.716752i \(-0.254372\pi\)
0.697328 + 0.716752i \(0.254372\pi\)
\(180\) 0 0
\(181\) −178.000 −0.0730974 −0.0365487 0.999332i \(-0.511636\pi\)
−0.0365487 + 0.999332i \(0.511636\pi\)
\(182\) 264.000 + 457.261i 0.107522 + 0.186233i
\(183\) 0 0
\(184\) −1260.00 + 2182.38i −0.504828 + 0.874389i
\(185\) 85.0000 147.224i 0.0337801 0.0585089i
\(186\) 0 0
\(187\) 364.000 + 630.466i 0.142344 + 0.246547i
\(188\) −1792.00 −0.695186
\(189\) 0 0
\(190\) −100.000 −0.0381830
\(191\) 944.000 + 1635.06i 0.357620 + 0.619416i 0.987563 0.157225i \(-0.0502549\pi\)
−0.629943 + 0.776642i \(0.716922\pi\)
\(192\) 0 0
\(193\) −961.000 + 1664.50i −0.358416 + 0.620795i −0.987696 0.156384i \(-0.950016\pi\)
0.629280 + 0.777178i \(0.283350\pi\)
\(194\) −433.000 + 749.978i −0.160245 + 0.277553i
\(195\) 0 0
\(196\) 815.500 + 1412.49i 0.297194 + 0.514755i
\(197\) 2526.00 0.913554 0.456777 0.889581i \(-0.349004\pi\)
0.456777 + 0.889581i \(0.349004\pi\)
\(198\) 0 0
\(199\) −1160.00 −0.413217 −0.206609 0.978424i \(-0.566243\pi\)
−0.206609 + 0.978424i \(0.566243\pi\)
\(200\) 187.500 + 324.760i 0.0662913 + 0.114820i
\(201\) 0 0
\(202\) 609.000 1054.82i 0.212124 0.367410i
\(203\) 2760.00 4780.46i 0.954256 1.65282i
\(204\) 0 0
\(205\) −305.000 528.275i −0.103913 0.179982i
\(206\) −88.0000 −0.0297634
\(207\) 0 0
\(208\) 902.000 0.300685
\(209\) 520.000 + 900.666i 0.172101 + 0.298088i
\(210\) 0 0
\(211\) 2234.00 3869.40i 0.728886 1.26247i −0.228469 0.973551i \(-0.573372\pi\)
0.957354 0.288916i \(-0.0932948\pi\)
\(212\) −1183.00 + 2049.02i −0.383249 + 0.663807i
\(213\) 0 0
\(214\) −18.0000 31.1769i −0.00574979 0.00995893i
\(215\) −940.000 −0.298174
\(216\) 0 0
\(217\) 6912.00 2.16229
\(218\) 485.000 + 840.045i 0.150680 + 0.260986i
\(219\) 0 0
\(220\) 910.000 1576.17i 0.278874 0.483023i
\(221\) 154.000 266.736i 0.0468740 0.0811882i
\(222\) 0 0
\(223\) −3016.00 5223.87i −0.905678 1.56868i −0.820004 0.572358i \(-0.806029\pi\)
−0.0856746 0.996323i \(-0.527305\pi\)
\(224\) −3864.00 −1.15256
\(225\) 0 0
\(226\) 1042.00 0.306694
\(227\) −1318.00 2282.84i −0.385369 0.667478i 0.606451 0.795121i \(-0.292592\pi\)
−0.991820 + 0.127642i \(0.959259\pi\)
\(228\) 0 0
\(229\) −2415.00 + 4182.90i −0.696889 + 1.20705i 0.272650 + 0.962113i \(0.412100\pi\)
−0.969540 + 0.244935i \(0.921233\pi\)
\(230\) 420.000 727.461i 0.120409 0.208554i
\(231\) 0 0
\(232\) 1725.00 + 2987.79i 0.488154 + 0.845508i
\(233\) 2682.00 0.754093 0.377046 0.926194i \(-0.376940\pi\)
0.377046 + 0.926194i \(0.376940\pi\)
\(234\) 0 0
\(235\) 1280.00 0.355311
\(236\) 350.000 + 606.218i 0.0965384 + 0.167209i
\(237\) 0 0
\(238\) −168.000 + 290.985i −0.0457556 + 0.0792509i
\(239\) −1160.00 + 2009.18i −0.313950 + 0.543778i −0.979214 0.202831i \(-0.934986\pi\)
0.665263 + 0.746609i \(0.268319\pi\)
\(240\) 0 0
\(241\) −1001.00 1733.78i −0.267552 0.463414i 0.700677 0.713479i \(-0.252881\pi\)
−0.968229 + 0.250065i \(0.919548\pi\)
\(242\) 1373.00 0.364710
\(243\) 0 0
\(244\) −5194.00 −1.36275
\(245\) −582.500 1008.92i −0.151896 0.263092i
\(246\) 0 0
\(247\) 220.000 381.051i 0.0566731 0.0981608i
\(248\) −2160.00 + 3741.23i −0.553065 + 0.957937i
\(249\) 0 0
\(250\) −62.5000 108.253i −0.0158114 0.0273861i
\(251\) 132.000 0.0331943 0.0165971 0.999862i \(-0.494717\pi\)
0.0165971 + 0.999862i \(0.494717\pi\)
\(252\) 0 0
\(253\) −8736.00 −2.17086
\(254\) −968.000 1676.63i −0.239125 0.414176i
\(255\) 0 0
\(256\) 59.5000 103.057i 0.0145264 0.0251604i
\(257\) 3807.00 6593.92i 0.924024 1.60046i 0.130900 0.991396i \(-0.458213\pi\)
0.793124 0.609061i \(-0.208453\pi\)
\(258\) 0 0
\(259\) −408.000 706.677i −0.0978837 0.169540i
\(260\) −770.000 −0.183667
\(261\) 0 0
\(262\) 732.000 0.172607
\(263\) 2444.00 + 4233.13i 0.573017 + 0.992495i 0.996254 + 0.0864757i \(0.0275605\pi\)
−0.423237 + 0.906019i \(0.639106\pi\)
\(264\) 0 0
\(265\) 845.000 1463.58i 0.195879 0.339272i
\(266\) −240.000 + 415.692i −0.0553208 + 0.0958185i
\(267\) 0 0
\(268\) −294.000 509.223i −0.0670109 0.116066i
\(269\) 1270.00 0.287856 0.143928 0.989588i \(-0.454027\pi\)
0.143928 + 0.989588i \(0.454027\pi\)
\(270\) 0 0
\(271\) 1072.00 0.240293 0.120146 0.992756i \(-0.461664\pi\)
0.120146 + 0.992756i \(0.461664\pi\)
\(272\) 287.000 + 497.099i 0.0639777 + 0.110813i
\(273\) 0 0
\(274\) 1107.00 1917.38i 0.244074 0.422749i
\(275\) −650.000 + 1125.83i −0.142533 + 0.246874i
\(276\) 0 0
\(277\) 2697.00 + 4671.34i 0.585007 + 1.01326i 0.994875 + 0.101117i \(0.0322417\pi\)
−0.409867 + 0.912145i \(0.634425\pi\)
\(278\) 20.0000 0.00431482
\(279\) 0 0
\(280\) 1800.00 0.384181
\(281\) −1221.00 2114.83i −0.259213 0.448969i 0.706819 0.707395i \(-0.250130\pi\)
−0.966031 + 0.258425i \(0.916796\pi\)
\(282\) 0 0
\(283\) −1386.00 + 2400.62i −0.291128 + 0.504248i −0.974077 0.226218i \(-0.927364\pi\)
0.682949 + 0.730466i \(0.260697\pi\)
\(284\) −1148.00 + 1988.39i −0.239864 + 0.415456i
\(285\) 0 0
\(286\) −572.000 990.733i −0.118262 0.204837i
\(287\) −2928.00 −0.602210
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) −575.000 995.929i −0.116432 0.201665i
\(291\) 0 0
\(292\) −133.000 + 230.363i −0.0266549 + 0.0461677i
\(293\) −2271.00 + 3933.49i −0.452810 + 0.784289i −0.998559 0.0536589i \(-0.982912\pi\)
0.545750 + 0.837948i \(0.316245\pi\)
\(294\) 0 0
\(295\) −250.000 433.013i −0.0493409 0.0854609i
\(296\) 510.000 0.100146
\(297\) 0 0
\(298\) −1330.00 −0.258540
\(299\) 1848.00 + 3200.83i 0.357433 + 0.619093i
\(300\) 0 0
\(301\) −2256.00 + 3907.51i −0.432006 + 0.748256i
\(302\) 604.000 1046.16i 0.115087 0.199337i
\(303\) 0 0
\(304\) 410.000 + 710.141i 0.0773523 + 0.133978i
\(305\) 3710.00 0.696505
\(306\) 0 0
\(307\) 5116.00 0.951093 0.475546 0.879691i \(-0.342250\pi\)
0.475546 + 0.879691i \(0.342250\pi\)
\(308\) −4368.00 7565.60i −0.808084 1.39964i
\(309\) 0 0
\(310\) 720.000 1247.08i 0.131914 0.228481i
\(311\) 1404.00 2431.80i 0.255992 0.443391i −0.709172 0.705035i \(-0.750931\pi\)
0.965165 + 0.261644i \(0.0842646\pi\)
\(312\) 0 0
\(313\) 3659.00 + 6337.57i 0.660763 + 1.14448i 0.980415 + 0.196941i \(0.0631006\pi\)
−0.319652 + 0.947535i \(0.603566\pi\)
\(314\) −3514.00 −0.631549
\(315\) 0 0
\(316\) 1680.00 0.299074
\(317\) −1123.00 1945.09i −0.198971 0.344629i 0.749224 0.662317i \(-0.230427\pi\)
−0.948195 + 0.317688i \(0.897093\pi\)
\(318\) 0 0
\(319\) −5980.00 + 10357.7i −1.04958 + 1.81792i
\(320\) 417.500 723.131i 0.0729342 0.126326i
\(321\) 0 0
\(322\) −2016.00 3491.81i −0.348905 0.604321i
\(323\) 280.000 0.0482341
\(324\) 0 0
\(325\) 550.000 0.0938723
\(326\) 1034.00 + 1790.94i 0.175669 + 0.304267i
\(327\) 0 0
\(328\) 915.000 1584.83i 0.154032 0.266791i
\(329\) 3072.00 5320.86i 0.514787 0.891637i
\(330\) 0 0
\(331\) −666.000 1153.55i −0.110594 0.191555i 0.805416 0.592710i \(-0.201942\pi\)
−0.916010 + 0.401155i \(0.868609\pi\)
\(332\) −8484.00 −1.40247
\(333\) 0 0
\(334\) −24.0000 −0.00393180
\(335\) 210.000 + 363.731i 0.0342493 + 0.0593216i
\(336\) 0 0
\(337\) 5767.00 9988.74i 0.932191 1.61460i 0.152624 0.988284i \(-0.451228\pi\)
0.779567 0.626319i \(-0.215439\pi\)
\(338\) 856.500 1483.50i 0.137833 0.238733i
\(339\) 0 0
\(340\) −245.000 424.352i −0.0390794 0.0676875i
\(341\) −14976.0 −2.37829
\(342\) 0 0
\(343\) 2640.00 0.415588
\(344\) −1410.00 2442.19i −0.220994 0.382774i
\(345\) 0 0
\(346\) 309.000 535.204i 0.0480114 0.0831582i
\(347\) −5978.00 + 10354.2i −0.924830 + 1.60185i −0.132994 + 0.991117i \(0.542459\pi\)
−0.791835 + 0.610735i \(0.790874\pi\)
\(348\) 0 0
\(349\) −2435.00 4217.54i −0.373474 0.646877i 0.616623 0.787259i \(-0.288500\pi\)
−0.990097 + 0.140382i \(0.955167\pi\)
\(350\) −600.000 −0.0916324
\(351\) 0 0
\(352\) 8372.00 1.26770
\(353\) −5361.00 9285.52i −0.808321 1.40005i −0.914026 0.405655i \(-0.867043\pi\)
0.105705 0.994397i \(-0.466290\pi\)
\(354\) 0 0
\(355\) 820.000 1420.28i 0.122595 0.212340i
\(356\) 1155.00 2000.52i 0.171952 0.297829i
\(357\) 0 0
\(358\) −1670.00 2892.52i −0.246543 0.427024i
\(359\) 120.000 0.0176417 0.00882083 0.999961i \(-0.497192\pi\)
0.00882083 + 0.999961i \(0.497192\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 89.0000 + 154.153i 0.0129219 + 0.0223814i
\(363\) 0 0
\(364\) −1848.00 + 3200.83i −0.266103 + 0.460904i
\(365\) 95.0000 164.545i 0.0136234 0.0235964i
\(366\) 0 0
\(367\) −1968.00 3408.68i −0.279915 0.484827i 0.691448 0.722426i \(-0.256973\pi\)
−0.971363 + 0.237599i \(0.923640\pi\)
\(368\) −6888.00 −0.975711
\(369\) 0 0
\(370\) −170.000 −0.0238862
\(371\) −4056.00 7025.20i −0.567593 0.983100i
\(372\) 0 0
\(373\) −1511.00 + 2617.13i −0.209750 + 0.363297i −0.951636 0.307229i \(-0.900598\pi\)
0.741886 + 0.670526i \(0.233932\pi\)
\(374\) 364.000 630.466i 0.0503262 0.0871675i
\(375\) 0 0
\(376\) 1920.00 + 3325.54i 0.263342 + 0.456121i
\(377\) 5060.00 0.691255
\(378\) 0 0
\(379\) −13340.0 −1.80799 −0.903997 0.427539i \(-0.859381\pi\)
−0.903997 + 0.427539i \(0.859381\pi\)
\(380\) −350.000 606.218i −0.0472490 0.0818377i
\(381\) 0 0
\(382\) 944.000 1635.06i 0.126438 0.218997i
\(383\) 504.000 872.954i 0.0672407 0.116464i −0.830445 0.557101i \(-0.811914\pi\)
0.897686 + 0.440636i \(0.145247\pi\)
\(384\) 0 0
\(385\) 3120.00 + 5404.00i 0.413013 + 0.715359i
\(386\) 1922.00 0.253438
\(387\) 0 0
\(388\) −6062.00 −0.793174
\(389\) −4815.00 8339.82i −0.627584 1.08701i −0.988035 0.154229i \(-0.950711\pi\)
0.360451 0.932778i \(-0.382623\pi\)
\(390\) 0 0
\(391\) −1176.00 + 2036.89i −0.152105 + 0.263453i
\(392\) 1747.50 3026.76i 0.225158 0.389986i
\(393\) 0 0
\(394\) −1263.00 2187.58i −0.161495 0.279718i
\(395\) −1200.00 −0.152857
\(396\) 0 0
\(397\) 7126.00 0.900866 0.450433 0.892810i \(-0.351270\pi\)
0.450433 + 0.892810i \(0.351270\pi\)
\(398\) 580.000 + 1004.59i 0.0730472 + 0.126521i
\(399\) 0 0
\(400\) −512.500 + 887.676i −0.0640625 + 0.110960i
\(401\) 4359.00 7550.01i 0.542838 0.940223i −0.455901 0.890030i \(-0.650683\pi\)
0.998740 0.0501929i \(-0.0159836\pi\)
\(402\) 0 0
\(403\) 3168.00 + 5487.14i 0.391586 + 0.678248i
\(404\) 8526.00 1.04996
\(405\) 0 0
\(406\) −5520.00 −0.674761
\(407\) 884.000 + 1531.13i 0.107662 + 0.186475i
\(408\) 0 0
\(409\) 5435.00 9413.70i 0.657074 1.13809i −0.324295 0.945956i \(-0.605127\pi\)
0.981369 0.192130i \(-0.0615396\pi\)
\(410\) −305.000 + 528.275i −0.0367387 + 0.0636333i
\(411\) 0 0
\(412\) −308.000 533.472i −0.0368303 0.0637919i
\(413\) −2400.00 −0.285947
\(414\) 0 0
\(415\) 6060.00 0.716804
\(416\) −1771.00 3067.46i −0.208727 0.361526i
\(417\) 0 0
\(418\) 520.000 900.666i 0.0608470 0.105390i
\(419\) 4850.00 8400.45i 0.565484 0.979448i −0.431520 0.902103i \(-0.642023\pi\)
0.997004 0.0773445i \(-0.0246441\pi\)
\(420\) 0 0
\(421\) −431.000 746.514i −0.0498947 0.0864201i 0.839999 0.542587i \(-0.182555\pi\)
−0.889894 + 0.456167i \(0.849222\pi\)
\(422\) −4468.00 −0.515400
\(423\) 0 0
\(424\) 5070.00 0.580710
\(425\) 175.000 + 303.109i 0.0199735 + 0.0345952i
\(426\) 0 0
\(427\) 8904.00 15422.2i 1.00912 1.74785i
\(428\) 126.000 218.238i 0.0142300 0.0246471i
\(429\) 0 0
\(430\) 470.000 + 814.064i 0.0527103 + 0.0912969i
\(431\) 15792.0 1.76490 0.882452 0.470402i \(-0.155891\pi\)
0.882452 + 0.470402i \(0.155891\pi\)
\(432\) 0 0
\(433\) 11602.0 1.28766 0.643830 0.765169i \(-0.277345\pi\)
0.643830 + 0.765169i \(0.277345\pi\)
\(434\) −3456.00 5985.97i −0.382243 0.662064i
\(435\) 0 0
\(436\) −3395.00 + 5880.31i −0.372915 + 0.645908i
\(437\) −1680.00 + 2909.85i −0.183902 + 0.318528i
\(438\) 0 0
\(439\) 220.000 + 381.051i 0.0239181 + 0.0414273i 0.877737 0.479143i \(-0.159053\pi\)
−0.853819 + 0.520571i \(0.825719\pi\)
\(440\) −3900.00 −0.422557
\(441\) 0 0
\(442\) −308.000 −0.0331449
\(443\) 5094.00 + 8823.07i 0.546328 + 0.946268i 0.998522 + 0.0543481i \(0.0173081\pi\)
−0.452194 + 0.891920i \(0.649359\pi\)
\(444\) 0 0
\(445\) −825.000 + 1428.94i −0.0878848 + 0.152221i
\(446\) −3016.00 + 5223.87i −0.320206 + 0.554613i
\(447\) 0 0
\(448\) −2004.00 3471.03i −0.211340 0.366051i
\(449\) −13310.0 −1.39897 −0.699485 0.714647i \(-0.746587\pi\)
−0.699485 + 0.714647i \(0.746587\pi\)
\(450\) 0 0
\(451\) 6344.00 0.662367
\(452\) 3647.00 + 6316.79i 0.379514 + 0.657338i
\(453\) 0 0
\(454\) −1318.00 + 2282.84i −0.136248 + 0.235989i
\(455\) 1320.00 2286.31i 0.136006 0.235569i
\(456\) 0 0
\(457\) −1613.00 2793.80i −0.165105 0.285970i 0.771588 0.636123i \(-0.219463\pi\)
−0.936693 + 0.350153i \(0.886130\pi\)
\(458\) 4830.00 0.492775
\(459\) 0 0
\(460\) 5880.00 0.595992
\(461\) −3291.00 5700.18i −0.332488 0.575887i 0.650511 0.759497i \(-0.274555\pi\)
−0.982999 + 0.183610i \(0.941222\pi\)
\(462\) 0 0
\(463\) −7536.00 + 13052.7i −0.756431 + 1.31018i 0.188229 + 0.982125i \(0.439725\pi\)
−0.944660 + 0.328052i \(0.893608\pi\)
\(464\) −4715.00 + 8166.62i −0.471742 + 0.817081i
\(465\) 0 0
\(466\) −1341.00 2322.68i −0.133306 0.230893i
\(467\) 476.000 0.0471663 0.0235831 0.999722i \(-0.492493\pi\)
0.0235831 + 0.999722i \(0.492493\pi\)
\(468\) 0 0
\(469\) 2016.00 0.198487
\(470\) −640.000 1108.51i −0.0628106 0.108791i
\(471\) 0 0
\(472\) 750.000 1299.04i 0.0731389 0.126680i
\(473\) 4888.00 8466.26i 0.475160 0.823001i
\(474\) 0 0
\(475\) 250.000 + 433.013i 0.0241490 + 0.0418273i
\(476\) −2352.00 −0.226478
\(477\) 0 0
\(478\) 2320.00 0.221997
\(479\) 9840.00 + 17043.4i 0.938624 + 1.62575i 0.768040 + 0.640402i \(0.221232\pi\)
0.170585 + 0.985343i \(0.445434\pi\)
\(480\) 0 0
\(481\) 374.000 647.787i 0.0354531 0.0614065i
\(482\) −1001.00 + 1733.78i −0.0945940 + 0.163842i
\(483\) 0 0
\(484\) 4805.50 + 8323.37i 0.451305 + 0.781684i
\(485\) 4330.00 0.405392
\(486\) 0 0
\(487\) −5944.00 −0.553077 −0.276538 0.961003i \(-0.589187\pi\)
−0.276538 + 0.961003i \(0.589187\pi\)
\(488\) 5565.00 + 9638.86i 0.516221 + 0.894121i
\(489\) 0 0
\(490\) −582.500 + 1008.92i −0.0537034 + 0.0930170i
\(491\) −5386.00 + 9328.83i −0.495044 + 0.857442i −0.999984 0.00571287i \(-0.998182\pi\)
0.504939 + 0.863155i \(0.331515\pi\)
\(492\) 0 0
\(493\) 1610.00 + 2788.60i 0.147081 + 0.254751i
\(494\) −440.000 −0.0400740
\(495\) 0 0
\(496\) −11808.0 −1.06894
\(497\) −3936.00 6817.35i −0.355239 0.615292i
\(498\) 0 0
\(499\) −4070.00 + 7049.45i −0.365127 + 0.632418i −0.988796 0.149270i \(-0.952308\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(500\) 437.500 757.772i 0.0391312 0.0677772i
\(501\) 0 0
\(502\) −66.0000 114.315i −0.00586798 0.0101636i
\(503\) −13768.0 −1.22045 −0.610223 0.792229i \(-0.708920\pi\)
−0.610223 + 0.792229i \(0.708920\pi\)
\(504\) 0 0
\(505\) −6090.00 −0.536637
\(506\) 4368.00 + 7565.60i 0.383757 + 0.664687i
\(507\) 0 0
\(508\) 6776.00 11736.4i 0.591804 1.02503i
\(509\) −11075.0 + 19182.5i −0.964422 + 1.67043i −0.253262 + 0.967398i \(0.581503\pi\)
−0.711160 + 0.703030i \(0.751830\pi\)
\(510\) 0 0
\(511\) −456.000 789.815i −0.0394760 0.0683745i
\(512\) 11521.0 0.994455
\(513\) 0 0
\(514\) −7614.00 −0.653384
\(515\) 220.000 + 381.051i 0.0188240 + 0.0326041i
\(516\) 0 0
\(517\) −6656.00 + 11528.5i −0.566210 + 0.980704i
\(518\) −408.000 + 706.677i −0.0346071 + 0.0599413i
\(519\) 0 0
\(520\) 825.000 + 1428.94i 0.0695743 + 0.120506i
\(521\) 1562.00 0.131348 0.0656741 0.997841i \(-0.479080\pi\)
0.0656741 + 0.997841i \(0.479080\pi\)
\(522\) 0 0
\(523\) −668.000 −0.0558501 −0.0279250 0.999610i \(-0.508890\pi\)
−0.0279250 + 0.999610i \(0.508890\pi\)
\(524\) 2562.00 + 4437.51i 0.213591 + 0.369950i
\(525\) 0 0
\(526\) 2444.00 4233.13i 0.202592 0.350900i
\(527\) −2016.00 + 3491.81i −0.166638 + 0.288626i
\(528\) 0 0
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) −1690.00 −0.138507
\(531\) 0 0
\(532\) −3360.00 −0.273824
\(533\) −1342.00 2324.41i −0.109059 0.188896i
\(534\) 0 0
\(535\) −90.0000 + 155.885i −0.00727297 + 0.0125972i
\(536\) −630.000 + 1091.19i −0.0507684 + 0.0879334i
\(537\) 0 0
\(538\) −635.000 1099.85i −0.0508862 0.0881375i
\(539\) 12116.0 0.968225
\(540\) 0 0
\(541\) −6138.00 −0.487788 −0.243894 0.969802i \(-0.578425\pi\)
−0.243894 + 0.969802i \(0.578425\pi\)
\(542\) −536.000 928.379i −0.0424782 0.0735744i
\(543\) 0 0
\(544\) 1127.00 1952.02i 0.0888230 0.153846i
\(545\) 2425.00 4200.22i 0.190597 0.330124i
\(546\) 0 0
\(547\) 5242.00 + 9079.41i 0.409747 + 0.709703i 0.994861 0.101248i \(-0.0322836\pi\)
−0.585114 + 0.810951i \(0.698950\pi\)
\(548\) 15498.0 1.20811
\(549\) 0 0
\(550\) 1300.00 0.100786
\(551\) 2300.00 + 3983.72i 0.177828 + 0.308007i
\(552\) 0 0
\(553\) −2880.00 + 4988.31i −0.221465 + 0.383588i
\(554\) 2697.00 4671.34i 0.206831 0.358242i
\(555\) 0 0
\(556\) 70.0000 + 121.244i 0.00533932 + 0.00924797i
\(557\) 3606.00 0.274311 0.137155 0.990550i \(-0.456204\pi\)
0.137155 + 0.990550i \(0.456204\pi\)
\(558\) 0 0
\(559\) −4136.00 −0.312941
\(560\) 2460.00 + 4260.84i 0.185632 + 0.321524i
\(561\) 0 0
\(562\) −1221.00 + 2114.83i −0.0916455 + 0.158735i
\(563\) −6126.00 + 10610.5i −0.458579 + 0.794283i −0.998886 0.0471855i \(-0.984975\pi\)
0.540307 + 0.841468i \(0.318308\pi\)
\(564\) 0 0
\(565\) −2605.00 4511.99i −0.193970 0.335966i
\(566\) 2772.00 0.205858
\(567\) 0 0
\(568\) 4920.00 0.363448
\(569\) 7275.00 + 12600.7i 0.536000 + 0.928379i 0.999114 + 0.0420803i \(0.0133985\pi\)
−0.463114 + 0.886298i \(0.653268\pi\)
\(570\) 0 0
\(571\) 12734.0 22055.9i 0.933277 1.61648i 0.155600 0.987820i \(-0.450269\pi\)
0.777677 0.628663i \(-0.216398\pi\)
\(572\) 4004.00 6935.13i 0.292685 0.506945i
\(573\) 0 0
\(574\) 1464.00 + 2535.72i 0.106457 + 0.184389i
\(575\) −4200.00 −0.304612
\(576\) 0 0
\(577\) 12866.0 0.928282 0.464141 0.885761i \(-0.346363\pi\)
0.464141 + 0.885761i \(0.346363\pi\)
\(578\) 2358.50 + 4085.04i 0.169724 + 0.293971i
\(579\) 0 0
\(580\) 4025.00 6971.50i 0.288153 0.499096i
\(581\) 14544.0 25190.9i 1.03853 1.79879i
\(582\) 0 0
\(583\) 8788.00 + 15221.3i 0.624291 + 1.08130i
\(584\) 570.000 0.0403883
\(585\) 0 0
\(586\) 4542.00 0.320185
\(587\) 7422.00 + 12855.3i 0.521872 + 0.903908i 0.999676 + 0.0254422i \(0.00809939\pi\)
−0.477805 + 0.878466i \(0.658567\pi\)
\(588\) 0 0
\(589\) −2880.00 + 4988.31i −0.201474 + 0.348964i
\(590\) −250.000 + 433.013i −0.0174446 + 0.0302150i
\(591\) 0 0
\(592\) 697.000 + 1207.24i 0.0483894 + 0.0838129i
\(593\) 20402.0 1.41283 0.706416 0.707797i \(-0.250311\pi\)
0.706416 + 0.707797i \(0.250311\pi\)
\(594\) 0 0
\(595\) 1680.00 0.115753
\(596\) −4655.00 8062.70i −0.319927 0.554129i
\(597\) 0 0
\(598\) 1848.00 3200.83i 0.126372 0.218882i
\(599\) −5380.00 + 9318.43i −0.366980 + 0.635627i −0.989092 0.147301i \(-0.952941\pi\)
0.622112 + 0.782928i \(0.286275\pi\)
\(600\) 0 0
\(601\) −7141.00 12368.6i −0.484671 0.839475i 0.515174 0.857086i \(-0.327727\pi\)
−0.999845 + 0.0176105i \(0.994394\pi\)
\(602\) 4512.00 0.305474
\(603\) 0 0
\(604\) 8456.00 0.569652
\(605\) −3432.50 5945.26i −0.230663 0.399520i
\(606\) 0 0
\(607\) −5528.00 + 9574.78i −0.369645 + 0.640244i −0.989510 0.144464i \(-0.953854\pi\)
0.619865 + 0.784709i \(0.287187\pi\)
\(608\) 1610.00 2788.60i 0.107392 0.186008i
\(609\) 0 0
\(610\) −1855.00 3212.95i −0.123126 0.213260i
\(611\) 5632.00 0.372907
\(612\) 0 0
\(613\) −16418.0 −1.08176 −0.540878 0.841101i \(-0.681908\pi\)
−0.540878 + 0.841101i \(0.681908\pi\)
\(614\) −2558.00 4430.59i −0.168131 0.291212i
\(615\) 0 0
\(616\) −9360.00 + 16212.0i −0.612216 + 1.06039i
\(617\) 5187.00 8984.15i 0.338445 0.586204i −0.645695 0.763595i \(-0.723432\pi\)
0.984140 + 0.177391i \(0.0567657\pi\)
\(618\) 0 0
\(619\) 2630.00 + 4555.29i 0.170773 + 0.295788i 0.938690 0.344761i \(-0.112040\pi\)
−0.767917 + 0.640549i \(0.778707\pi\)
\(620\) 10080.0 0.652940
\(621\) 0 0
\(622\) −2808.00 −0.181014
\(623\) 3960.00 + 6858.92i 0.254661 + 0.441086i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 3659.00 6337.57i 0.233615 0.404633i
\(627\) 0 0
\(628\) −12299.0 21302.5i −0.781502 1.35360i
\(629\) 476.000 0.0301739
\(630\) 0 0
\(631\) 21352.0 1.34708 0.673542 0.739149i \(-0.264772\pi\)
0.673542 + 0.739149i \(0.264772\pi\)
\(632\) −1800.00 3117.69i −0.113291 0.196226i
\(633\) 0 0
\(634\) −1123.00 + 1945.09i −0.0703470 + 0.121845i
\(635\) −4840.00 + 8383.13i −0.302472 + 0.523896i
\(636\) 0 0
\(637\) −2563.00 4439.25i −0.159419 0.276121i
\(638\) 11960.0 0.742164
\(639\) 0 0
\(640\) −7275.00 −0.449328
\(641\) 14559.0 + 25216.9i 0.897108 + 1.55384i 0.831174 + 0.556012i \(0.187669\pi\)
0.0659331 + 0.997824i \(0.478998\pi\)
\(642\) 0 0
\(643\) −2886.00 + 4998.70i −0.177003 + 0.306578i −0.940853 0.338816i \(-0.889973\pi\)
0.763850 + 0.645394i \(0.223307\pi\)
\(644\) 14112.0 24442.7i 0.863495 1.49562i
\(645\) 0 0
\(646\) −140.000 242.487i −0.00852667 0.0147686i
\(647\) −14264.0 −0.866732 −0.433366 0.901218i \(-0.642674\pi\)
−0.433366 + 0.901218i \(0.642674\pi\)
\(648\) 0 0
\(649\) 5200.00 0.314511
\(650\) −275.000 476.314i −0.0165944 0.0287424i
\(651\) 0 0
\(652\) −7238.00 + 12536.6i −0.434758 + 0.753022i
\(653\) −3451.00 + 5977.31i −0.206812 + 0.358208i −0.950708 0.310086i \(-0.899642\pi\)
0.743897 + 0.668295i \(0.232975\pi\)
\(654\) 0 0
\(655\) −1830.00 3169.65i −0.109166 0.189082i
\(656\) 5002.00 0.297706
\(657\) 0 0
\(658\) −6144.00 −0.364009
\(659\) −10070.0 17441.8i −0.595253 1.03101i −0.993511 0.113735i \(-0.963719\pi\)
0.398258 0.917273i \(-0.369615\pi\)
\(660\) 0 0
\(661\) 1609.00 2786.87i 0.0946790 0.163989i −0.814796 0.579748i \(-0.803151\pi\)
0.909475 + 0.415759i \(0.136484\pi\)
\(662\) −666.000 + 1153.55i −0.0391009 + 0.0677248i
\(663\) 0 0
\(664\) 9090.00 + 15744.3i 0.531266 + 0.920179i
\(665\) 2400.00 0.139952
\(666\) 0 0
\(667\) −38640.0 −2.24310
\(668\) −84.0000 145.492i −0.00486536 0.00842704i
\(669\) 0 0
\(670\) 210.000 363.731i 0.0121090 0.0209733i
\(671\) −19292.0 + 33414.7i −1.10992 + 1.92245i
\(672\) 0 0
\(673\) 3759.00 + 6510.78i 0.215303 + 0.372915i 0.953366 0.301816i \(-0.0975928\pi\)
−0.738063 + 0.674731i \(0.764259\pi\)
\(674\) −11534.0 −0.659159
\(675\) 0 0
\(676\) 11991.0 0.682237
\(677\) 9057.00 + 15687.2i 0.514164 + 0.890558i 0.999865 + 0.0164327i \(0.00523093\pi\)
−0.485701 + 0.874125i \(0.661436\pi\)
\(678\) 0 0
\(679\) 10392.0 17999.5i 0.587347 1.01731i
\(680\) −525.000 + 909.327i −0.0296071 + 0.0512810i
\(681\) 0 0
\(682\) 7488.00 + 12969.6i 0.420426 + 0.728199i
\(683\) −23868.0 −1.33716 −0.668582 0.743638i \(-0.733099\pi\)
−0.668582 + 0.743638i \(0.733099\pi\)
\(684\) 0 0
\(685\) −11070.0 −0.617464
\(686\) −1320.00 2286.31i −0.0734662 0.127247i
\(687\) 0 0
\(688\) 3854.00 6675.32i 0.213564 0.369905i
\(689\) 3718.00 6439.76i 0.205580 0.356075i
\(690\) 0 0
\(691\) −86.0000 148.956i −0.00473458 0.00820053i 0.863648 0.504095i \(-0.168174\pi\)
−0.868383 + 0.495894i \(0.834840\pi\)
\(692\) 4326.00 0.237644
\(693\) 0 0
\(694\) 11956.0 0.653953
\(695\) −50.0000 86.6025i −0.00272893 0.00472665i
\(696\) 0 0
\(697\) 854.000 1479.17i 0.0464097 0.0803839i
\(698\) −2435.00 + 4217.54i −0.132043 + 0.228705i
\(699\) 0 0
\(700\) −2100.00 3637.31i −0.113389 0.196396i
\(701\) −22138.0 −1.19278 −0.596391 0.802694i \(-0.703399\pi\)
−0.596391 + 0.802694i \(0.703399\pi\)
\(702\) 0 0
\(703\) 680.000 0.0364818
\(704\) 4342.00 + 7520.56i 0.232451 + 0.402616i
\(705\) 0 0
\(706\) −5361.00 + 9285.52i −0.285785 + 0.494993i
\(707\) −14616.0 + 25315.7i −0.777498 + 1.34667i
\(708\) 0 0
\(709\) −1535.00 2658.70i −0.0813091 0.140831i 0.822503 0.568760i \(-0.192577\pi\)
−0.903812 + 0.427929i \(0.859243\pi\)
\(710\) −1640.00 −0.0866875
\(711\) 0 0
\(712\) −4950.00 −0.260546
\(713\) −24192.0 41901.8i −1.27068 2.20089i
\(714\) 0 0
\(715\) −2860.00 + 4953.67i −0.149592 + 0.259100i
\(716\) 11690.0 20247.7i 0.610162 1.05683i
\(717\) 0 0
\(718\) −60.0000 103.923i −0.00311864 0.00540163i
\(719\) 15600.0 0.809154 0.404577 0.914504i \(-0.367419\pi\)
0.404577 + 0.914504i \(0.367419\pi\)
\(720\) 0 0
\(721\) 2112.00 0.109092
\(722\) 3229.50 + 5593.66i 0.166468 + 0.288330i
\(723\) 0 0
\(724\) −623.000 + 1079.07i −0.0319801 + 0.0553912i
\(725\) −2875.00 + 4979.65i −0.147276 + 0.255089i
\(726\) 0 0
\(727\) −10348.0 17923.3i −0.527904 0.914356i −0.999471 0.0325260i \(-0.989645\pi\)
0.471567 0.881830i \(-0.343689\pi\)
\(728\) 7920.00 0.403207
\(729\) 0 0
\(730\) −190.000 −0.00963317
\(731\) −1316.00 2279.38i −0.0665855 0.115330i
\(732\) 0 0
\(733\) 15389.0 26654.5i 0.775451 1.34312i −0.159089 0.987264i \(-0.550856\pi\)
0.934541 0.355857i \(-0.115811\pi\)
\(734\) −1968.00 + 3408.68i −0.0989649 + 0.171412i
\(735\) 0 0
\(736\) 13524.0 + 23424.3i 0.677311 + 1.17314i
\(737\) −4368.00 −0.218314
\(738\) 0 0
\(739\) 11740.0 0.584388 0.292194 0.956359i \(-0.405615\pi\)
0.292194 + 0.956359i \(0.405615\pi\)
\(740\) −595.000 1030.57i −0.0295576 0.0511953i
\(741\) 0 0
\(742\) −4056.00 + 7025.20i −0.200674 + 0.347578i
\(743\) −1316.00 + 2279.38i −0.0649789 + 0.112547i −0.896685 0.442670i \(-0.854031\pi\)
0.831706 + 0.555217i \(0.187365\pi\)
\(744\) 0 0
\(745\) 3325.00 + 5759.07i 0.163515 + 0.283216i
\(746\) 3022.00 0.148315
\(747\) 0 0
\(748\) 5096.00 0.249102
\(749\) 432.000 + 748.246i 0.0210747 + 0.0365024i
\(750\) 0 0
\(751\) 10264.0 17777.8i 0.498720 0.863808i −0.501279 0.865286i \(-0.667137\pi\)
0.999999 + 0.00147745i \(0.000470287\pi\)
\(752\) −5248.00 + 9089.80i −0.254488 + 0.440786i
\(753\) 0 0
\(754\) −2530.00 4382.09i −0.122198 0.211653i
\(755\) −6040.00 −0.291150
\(756\) 0 0
\(757\) 21646.0 1.03928 0.519642 0.854384i \(-0.326066\pi\)
0.519642 + 0.854384i \(0.326066\pi\)
\(758\) 6670.00 + 11552.8i 0.319611 + 0.553583i
\(759\) 0 0
\(760\) −750.000 + 1299.04i −0.0357965 + 0.0620014i
\(761\) −9141.00 + 15832.7i −0.435428 + 0.754184i −0.997331 0.0730197i \(-0.976736\pi\)
0.561902 + 0.827204i \(0.310070\pi\)
\(762\) 0 0
\(763\) −11640.0 20161.1i −0.552289 0.956592i
\(764\) 13216.0 0.625835
\(765\) 0 0
\(766\) −1008.00 −0.0475464
\(767\) −1100.00 1905.26i −0.0517845 0.0896934i
\(768\) 0 0
\(769\) 12095.0 20949.2i 0.567174 0.982374i −0.429670 0.902986i \(-0.641370\pi\)
0.996844 0.0793882i \(-0.0252967\pi\)
\(770\) 3120.00 5404.00i 0.146022 0.252918i
\(771\) 0 0
\(772\) 6727.00 + 11651.5i 0.313614 + 0.543195i
\(773\) −25698.0 −1.19572 −0.597861 0.801600i \(-0.703982\pi\)
−0.597861 + 0.801600i \(0.703982\pi\)
\(774\) 0 0
\(775\) −7200.00 −0.333718
\(776\) 6495.00 + 11249.7i 0.300460 + 0.520412i
\(777\) 0 0
\(778\) −4815.00 + 8339.82i −0.221884 + 0.384315i
\(779\) 1220.00 2113.10i 0.0561117 0.0971884i
\(780\) 0 0
\(781\) 8528.00 + 14770.9i 0.390724 + 0.676755i
\(782\) 2352.00 0.107554
\(783\) 0 0
\(784\) 9553.00 0.435177
\(785\) 8785.00 + 15216.1i 0.399427 + 0.691828i
\(786\) 0 0
\(787\) −16718.0