Properties

Label 63.6.e.c.46.2
Level $63$
Weight $6$
Character 63.46
Analytic conductor $10.104$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-83})\)
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.2
Root \(-3.69493 - 2.71062i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.6.e.c.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(3.19493 + 5.53379i) q^{2} +(-4.41520 + 7.64735i) q^{4} +(19.3645 + 33.5404i) q^{5} +(-87.5000 + 95.6596i) q^{7} +148.051 q^{8} +O(q^{10})\) \(q+(3.19493 + 5.53379i) q^{2} +(-4.41520 + 7.64735i) q^{4} +(19.3645 + 33.5404i) q^{5} +(-87.5000 + 95.6596i) q^{7} +148.051 q^{8} +(-123.737 + 214.318i) q^{10} +(-288.195 + 499.168i) q^{11} +391.491 q^{13} +(-808.916 - 178.580i) q^{14} +(614.298 + 1064.00i) q^{16} +(-664.850 + 1151.55i) q^{17} +(-471.237 - 816.206i) q^{19} -341.993 q^{20} -3683.05 q^{22} +(-816.040 - 1413.42i) q^{23} +(812.530 - 1407.34i) q^{25} +(1250.79 + 2166.43i) q^{26} +(-345.212 - 1091.50i) q^{28} +1463.54 q^{29} +(1956.21 - 3388.25i) q^{31} +(-1556.47 + 2695.89i) q^{32} -8496.61 q^{34} +(-4902.85 - 1082.38i) q^{35} +(8150.17 + 14116.5i) q^{37} +(3011.14 - 5215.45i) q^{38} +(2866.93 + 4965.67i) q^{40} +13103.8 q^{41} +14733.5 q^{43} +(-2544.88 - 4407.86i) q^{44} +(5214.38 - 9031.58i) q^{46} +(-3407.26 - 5901.55i) q^{47} +(-1494.50 - 16740.4i) q^{49} +10383.9 q^{50} +(-1728.51 + 2993.87i) q^{52} +(-1005.67 + 1741.87i) q^{53} -22323.0 q^{55} +(-12954.4 + 14162.5i) q^{56} +(4675.93 + 8098.94i) q^{58} +(25726.6 - 44559.7i) q^{59} +(-20548.9 - 35591.8i) q^{61} +24999.8 q^{62} +19423.8 q^{64} +(7581.04 + 13130.8i) q^{65} +(-25289.1 + 43802.0i) q^{67} +(-5870.89 - 10168.7i) q^{68} +(-9674.63 - 30589.5i) q^{70} -39970.6 q^{71} +(27843.3 - 48226.0i) q^{73} +(-52078.5 + 90202.6i) q^{74} +8322.42 q^{76} +(-22533.2 - 71245.8i) q^{77} +(31575.7 + 54690.7i) q^{79} +(-23791.2 + 41207.6i) q^{80} +(41865.9 + 72513.8i) q^{82} -45572.4 q^{83} -51498.1 q^{85} +(47072.5 + 81532.0i) q^{86} +(-42667.5 + 73902.2i) q^{88} +(7843.34 + 13585.1i) q^{89} +(-34255.5 + 37449.9i) q^{91} +14411.9 q^{92} +(21771.9 - 37710.1i) q^{94} +(18250.6 - 31610.9i) q^{95} +3128.49 q^{97} +(87863.1 - 61754.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25} - 2508 q^{26} + 13531 q^{28} + 4434 q^{29} - 4294 q^{31} + 1017 q^{32} - 35880 q^{34} - 15414 q^{35} + 19109 q^{37} - 6828 q^{38} - 10545 q^{40} + 25716 q^{41} - 5542 q^{43} - 36579 q^{44} + 40740 q^{46} - 23160 q^{47} - 5978 q^{49} + 58704 q^{50} - 33424 q^{52} - 31653 q^{53} + 35778 q^{55} - 65625 q^{56} + 2277 q^{58} + 41097 q^{59} - 42052 q^{61} + 204114 q^{62} - 60062 q^{64} - 23106 q^{65} - 30763 q^{67} + 44748 q^{68} + 151179 q^{70} - 204192 q^{71} + 28577 q^{73} - 77784 q^{74} + 170384 q^{76} + 96873 q^{77} + 18464 q^{79} - 71511 q^{80} + 86040 q^{82} - 122358 q^{83} - 247272 q^{85} + 258510 q^{86} - 212565 q^{88} + 29322 q^{89} - 161875 q^{91} - 333816 q^{92} - 109938 q^{94} - 61662 q^{95} - 19582 q^{97} + 462021 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.19493 + 5.53379i 0.564790 + 0.978245i 0.997069 + 0.0765049i \(0.0243761\pi\)
−0.432279 + 0.901740i \(0.642291\pi\)
\(3\) 0 0
\(4\) −4.41520 + 7.64735i −0.137975 + 0.238980i
\(5\) 19.3645 + 33.5404i 0.346403 + 0.599988i 0.985608 0.169049i \(-0.0540695\pi\)
−0.639204 + 0.769037i \(0.720736\pi\)
\(6\) 0 0
\(7\) −87.5000 + 95.6596i −0.674937 + 0.737876i
\(8\) 148.051 0.817872
\(9\) 0 0
\(10\) −123.737 + 214.318i −0.391290 + 0.677734i
\(11\) −288.195 + 499.168i −0.718133 + 1.24384i 0.243606 + 0.969874i \(0.421670\pi\)
−0.961739 + 0.273968i \(0.911664\pi\)
\(12\) 0 0
\(13\) 391.491 0.642486 0.321243 0.946997i \(-0.395899\pi\)
0.321243 + 0.946997i \(0.395899\pi\)
\(14\) −808.916 178.580i −1.10302 0.243508i
\(15\) 0 0
\(16\) 614.298 + 1064.00i 0.599901 + 1.03906i
\(17\) −664.850 + 1151.55i −0.557958 + 0.966412i 0.439709 + 0.898140i \(0.355082\pi\)
−0.997667 + 0.0682711i \(0.978252\pi\)
\(18\) 0 0
\(19\) −471.237 816.206i −0.299471 0.518699i 0.676544 0.736402i \(-0.263477\pi\)
−0.976015 + 0.217703i \(0.930144\pi\)
\(20\) −341.993 −0.191180
\(21\) 0 0
\(22\) −3683.05 −1.62238
\(23\) −816.040 1413.42i −0.321656 0.557124i 0.659174 0.751991i \(-0.270906\pi\)
−0.980830 + 0.194866i \(0.937573\pi\)
\(24\) 0 0
\(25\) 812.530 1407.34i 0.260009 0.450350i
\(26\) 1250.79 + 2166.43i 0.362869 + 0.628508i
\(27\) 0 0
\(28\) −345.212 1091.50i −0.0832130 0.263105i
\(29\) 1463.54 0.323155 0.161577 0.986860i \(-0.448342\pi\)
0.161577 + 0.986860i \(0.448342\pi\)
\(30\) 0 0
\(31\) 1956.21 3388.25i 0.365604 0.633245i −0.623269 0.782008i \(-0.714196\pi\)
0.988873 + 0.148763i \(0.0475291\pi\)
\(32\) −1556.47 + 2695.89i −0.268700 + 0.465401i
\(33\) 0 0
\(34\) −8496.61 −1.26052
\(35\) −4902.85 1082.38i −0.676517 0.149351i
\(36\) 0 0
\(37\) 8150.17 + 14116.5i 0.978729 + 1.69521i 0.667038 + 0.745024i \(0.267562\pi\)
0.311691 + 0.950184i \(0.399105\pi\)
\(38\) 3011.14 5215.45i 0.338277 0.585912i
\(39\) 0 0
\(40\) 2866.93 + 4965.67i 0.283314 + 0.490714i
\(41\) 13103.8 1.21741 0.608707 0.793395i \(-0.291688\pi\)
0.608707 + 0.793395i \(0.291688\pi\)
\(42\) 0 0
\(43\) 14733.5 1.21516 0.607582 0.794257i \(-0.292140\pi\)
0.607582 + 0.794257i \(0.292140\pi\)
\(44\) −2544.88 4407.86i −0.198169 0.343238i
\(45\) 0 0
\(46\) 5214.38 9031.58i 0.363336 0.629316i
\(47\) −3407.26 5901.55i −0.224989 0.389692i 0.731327 0.682027i \(-0.238901\pi\)
−0.956316 + 0.292335i \(0.905568\pi\)
\(48\) 0 0
\(49\) −1494.50 16740.4i −0.0889213 0.996039i
\(50\) 10383.9 0.587403
\(51\) 0 0
\(52\) −1728.51 + 2993.87i −0.0886470 + 0.153541i
\(53\) −1005.67 + 1741.87i −0.0491775 + 0.0851779i −0.889566 0.456806i \(-0.848993\pi\)
0.840389 + 0.541984i \(0.182327\pi\)
\(54\) 0 0
\(55\) −22323.0 −0.995054
\(56\) −12954.4 + 14162.5i −0.552012 + 0.603488i
\(57\) 0 0
\(58\) 4675.93 + 8098.94i 0.182515 + 0.316125i
\(59\) 25726.6 44559.7i 0.962170 1.66653i 0.245135 0.969489i \(-0.421168\pi\)
0.717035 0.697037i \(-0.245499\pi\)
\(60\) 0 0
\(61\) −20548.9 35591.8i −0.707073 1.22469i −0.965938 0.258773i \(-0.916682\pi\)
0.258865 0.965913i \(-0.416651\pi\)
\(62\) 24999.8 0.825958
\(63\) 0 0
\(64\) 19423.8 0.592766
\(65\) 7581.04 + 13130.8i 0.222559 + 0.385484i
\(66\) 0 0
\(67\) −25289.1 + 43802.0i −0.688250 + 1.19208i 0.284153 + 0.958779i \(0.408288\pi\)
−0.972404 + 0.233305i \(0.925046\pi\)
\(68\) −5870.89 10168.7i −0.153968 0.266681i
\(69\) 0 0
\(70\) −9674.63 30589.5i −0.235988 0.746151i
\(71\) −39970.6 −0.941012 −0.470506 0.882397i \(-0.655929\pi\)
−0.470506 + 0.882397i \(0.655929\pi\)
\(72\) 0 0
\(73\) 27843.3 48226.0i 0.611524 1.05919i −0.379459 0.925208i \(-0.623890\pi\)
0.990984 0.133983i \(-0.0427767\pi\)
\(74\) −52078.5 + 90202.6i −1.10555 + 1.91487i
\(75\) 0 0
\(76\) 8322.42 0.165278
\(77\) −22533.2 71245.8i −0.433107 1.36941i
\(78\) 0 0
\(79\) 31575.7 + 54690.7i 0.569226 + 0.985929i 0.996643 + 0.0818739i \(0.0260905\pi\)
−0.427416 + 0.904055i \(0.640576\pi\)
\(80\) −23791.2 + 41207.6i −0.415615 + 0.719867i
\(81\) 0 0
\(82\) 41865.9 + 72513.8i 0.687583 + 1.19093i
\(83\) −45572.4 −0.726116 −0.363058 0.931766i \(-0.618267\pi\)
−0.363058 + 0.931766i \(0.618267\pi\)
\(84\) 0 0
\(85\) −51498.1 −0.773114
\(86\) 47072.5 + 81532.0i 0.686312 + 1.18873i
\(87\) 0 0
\(88\) −42667.5 + 73902.2i −0.587341 + 1.01730i
\(89\) 7843.34 + 13585.1i 0.104961 + 0.181797i 0.913722 0.406340i \(-0.133195\pi\)
−0.808762 + 0.588137i \(0.799862\pi\)
\(90\) 0 0
\(91\) −34255.5 + 37449.9i −0.433637 + 0.474075i
\(92\) 14411.9 0.177522
\(93\) 0 0
\(94\) 21771.9 37710.1i 0.254143 0.440188i
\(95\) 18250.6 31610.9i 0.207476 0.359358i
\(96\) 0 0
\(97\) 3128.49 0.0337603 0.0168801 0.999858i \(-0.494627\pi\)
0.0168801 + 0.999858i \(0.494627\pi\)
\(98\) 87863.1 61754.8i 0.924148 0.649539i
\(99\) 0 0
\(100\) 7174.96 + 12427.4i 0.0717496 + 0.124274i
\(101\) −84505.5 + 146368.i −0.824292 + 1.42772i 0.0781663 + 0.996940i \(0.475093\pi\)
−0.902459 + 0.430776i \(0.858240\pi\)
\(102\) 0 0
\(103\) −56410.1 97705.1i −0.523918 0.907453i −0.999612 0.0278422i \(-0.991136\pi\)
0.475694 0.879611i \(-0.342197\pi\)
\(104\) 57960.5 0.525471
\(105\) 0 0
\(106\) −12852.2 −0.111100
\(107\) −11154.7 19320.6i −0.0941890 0.163140i 0.815081 0.579347i \(-0.196692\pi\)
−0.909270 + 0.416207i \(0.863359\pi\)
\(108\) 0 0
\(109\) 41909.8 72589.8i 0.337869 0.585207i −0.646162 0.763200i \(-0.723627\pi\)
0.984032 + 0.177993i \(0.0569604\pi\)
\(110\) −71320.6 123531.i −0.561996 0.973406i
\(111\) 0 0
\(112\) −155532. 34336.1i −1.17159 0.258646i
\(113\) 40928.4 0.301529 0.150764 0.988570i \(-0.451826\pi\)
0.150764 + 0.988570i \(0.451826\pi\)
\(114\) 0 0
\(115\) 31604.4 54740.5i 0.222845 0.385980i
\(116\) −6461.84 + 11192.2i −0.0445873 + 0.0772275i
\(117\) 0 0
\(118\) 328779. 2.17369
\(119\) −51982.8 164360.i −0.336505 1.06397i
\(120\) 0 0
\(121\) −85587.1 148241.i −0.531429 0.920462i
\(122\) 131305. 227427.i 0.798695 1.38338i
\(123\) 0 0
\(124\) 17274.1 + 29919.6i 0.100888 + 0.174744i
\(125\) 183965. 1.05308
\(126\) 0 0
\(127\) 83270.1 0.458120 0.229060 0.973412i \(-0.426435\pi\)
0.229060 + 0.973412i \(0.426435\pi\)
\(128\) 111865. + 193756.i 0.603488 + 1.04527i
\(129\) 0 0
\(130\) −48441.9 + 83903.8i −0.251398 + 0.435435i
\(131\) −83437.4 144518.i −0.424798 0.735772i 0.571603 0.820530i \(-0.306322\pi\)
−0.996402 + 0.0847580i \(0.972988\pi\)
\(132\) 0 0
\(133\) 119311. + 26339.7i 0.584860 + 0.129117i
\(134\) −323188. −1.55487
\(135\) 0 0
\(136\) −98431.5 + 170488.i −0.456338 + 0.790401i
\(137\) 19111.9 33102.9i 0.0869969 0.150683i −0.819244 0.573446i \(-0.805606\pi\)
0.906240 + 0.422763i \(0.138940\pi\)
\(138\) 0 0
\(139\) 106263. 0.466492 0.233246 0.972418i \(-0.425065\pi\)
0.233246 + 0.972418i \(0.425065\pi\)
\(140\) 29924.4 32714.9i 0.129034 0.141067i
\(141\) 0 0
\(142\) −127703. 221189.i −0.531474 0.920540i
\(143\) −112826. + 195420.i −0.461390 + 0.799151i
\(144\) 0 0
\(145\) 28340.8 + 49087.8i 0.111942 + 0.193889i
\(146\) 355830. 1.38153
\(147\) 0 0
\(148\) −143938. −0.540160
\(149\) 96277.8 + 166758.i 0.355271 + 0.615348i 0.987164 0.159708i \(-0.0510551\pi\)
−0.631893 + 0.775056i \(0.717722\pi\)
\(150\) 0 0
\(151\) −70849.3 + 122715.i −0.252868 + 0.437980i −0.964314 0.264761i \(-0.914707\pi\)
0.711447 + 0.702740i \(0.248040\pi\)
\(152\) −69766.9 120840.i −0.244929 0.424230i
\(153\) 0 0
\(154\) 322267. 352319.i 1.09500 1.19711i
\(155\) 151524. 0.506586
\(156\) 0 0
\(157\) −282885. + 489972.i −0.915928 + 1.58643i −0.110392 + 0.993888i \(0.535211\pi\)
−0.805536 + 0.592546i \(0.798123\pi\)
\(158\) −201764. + 349466.i −0.642986 + 1.11368i
\(159\) 0 0
\(160\) −120562. −0.372314
\(161\) 206611. + 45612.4i 0.628186 + 0.138682i
\(162\) 0 0
\(163\) 215101. + 372565.i 0.634121 + 1.09833i 0.986701 + 0.162549i \(0.0519714\pi\)
−0.352579 + 0.935782i \(0.614695\pi\)
\(164\) −57856.0 + 100210.i −0.167973 + 0.290937i
\(165\) 0 0
\(166\) −145601. 252188.i −0.410103 0.710319i
\(167\) 240265. 0.666653 0.333327 0.942811i \(-0.391829\pi\)
0.333327 + 0.942811i \(0.391829\pi\)
\(168\) 0 0
\(169\) −218028. −0.587212
\(170\) −164533. 284979.i −0.436647 0.756295i
\(171\) 0 0
\(172\) −65051.3 + 112672.i −0.167662 + 0.290399i
\(173\) −89650.1 155279.i −0.227738 0.394454i 0.729399 0.684088i \(-0.239800\pi\)
−0.957137 + 0.289634i \(0.906466\pi\)
\(174\) 0 0
\(175\) 63529.4 + 200869.i 0.156812 + 0.495812i
\(176\) −708151. −1.72323
\(177\) 0 0
\(178\) −50117.9 + 86806.8i −0.118561 + 0.205354i
\(179\) −287780. + 498449.i −0.671317 + 1.16275i 0.306214 + 0.951963i \(0.400938\pi\)
−0.977531 + 0.210792i \(0.932396\pi\)
\(180\) 0 0
\(181\) 581006. 1.31821 0.659105 0.752051i \(-0.270935\pi\)
0.659105 + 0.752051i \(0.270935\pi\)
\(182\) −316684. 69912.7i −0.708675 0.156451i
\(183\) 0 0
\(184\) −120815. 209258.i −0.263073 0.455657i
\(185\) −315648. + 546719.i −0.678070 + 1.17445i
\(186\) 0 0
\(187\) −383213. 663744.i −0.801376 1.38802i
\(188\) 60174.9 0.124171
\(189\) 0 0
\(190\) 233237. 0.468721
\(191\) −330280. 572062.i −0.655087 1.13464i −0.981872 0.189545i \(-0.939299\pi\)
0.326785 0.945099i \(-0.394035\pi\)
\(192\) 0 0
\(193\) 278655. 482645.i 0.538485 0.932684i −0.460501 0.887659i \(-0.652330\pi\)
0.998986 0.0450243i \(-0.0143365\pi\)
\(194\) 9995.33 + 17312.4i 0.0190675 + 0.0330258i
\(195\) 0 0
\(196\) 134618. + 62483.3i 0.250302 + 0.116178i
\(197\) 761400. 1.39781 0.698904 0.715216i \(-0.253672\pi\)
0.698904 + 0.715216i \(0.253672\pi\)
\(198\) 0 0
\(199\) 67929.9 117658.i 0.121598 0.210615i −0.798800 0.601597i \(-0.794531\pi\)
0.920398 + 0.390982i \(0.127865\pi\)
\(200\) 120296. 208358.i 0.212655 0.368328i
\(201\) 0 0
\(202\) −1.07996e6 −1.86221
\(203\) −128060. + 140002.i −0.218109 + 0.238448i
\(204\) 0 0
\(205\) 253750. + 439507.i 0.421716 + 0.730434i
\(206\) 360453. 624323.i 0.591807 1.02504i
\(207\) 0 0
\(208\) 240492. + 416545.i 0.385428 + 0.667581i
\(209\) 543232. 0.860240
\(210\) 0 0
\(211\) −991157. −1.53263 −0.766313 0.642467i \(-0.777911\pi\)
−0.766313 + 0.642467i \(0.777911\pi\)
\(212\) −8880.48 15381.4i −0.0135705 0.0235048i
\(213\) 0 0
\(214\) 71277.3 123456.i 0.106394 0.184280i
\(215\) 285307. + 494167.i 0.420937 + 0.729084i
\(216\) 0 0
\(217\) 152951. + 483602.i 0.220496 + 0.697170i
\(218\) 535596. 0.763301
\(219\) 0 0
\(220\) 98560.7 170712.i 0.137293 0.237798i
\(221\) −260283. + 450823.i −0.358480 + 0.620906i
\(222\) 0 0
\(223\) 543344. 0.731666 0.365833 0.930681i \(-0.380784\pi\)
0.365833 + 0.930681i \(0.380784\pi\)
\(224\) −121696. 384782.i −0.162053 0.512383i
\(225\) 0 0
\(226\) 130764. + 226489.i 0.170300 + 0.294969i
\(227\) 8.16704 14.1457i 1.05196e−5 1.82205e-5i −0.866020 0.500009i \(-0.833330\pi\)
0.866031 + 0.499991i \(0.166663\pi\)
\(228\) 0 0
\(229\) 38689.5 + 67012.2i 0.0487534 + 0.0844433i 0.889372 0.457184i \(-0.151142\pi\)
−0.840619 + 0.541627i \(0.817808\pi\)
\(230\) 403896. 0.503443
\(231\) 0 0
\(232\) 216679. 0.264299
\(233\) −51828.6 89769.9i −0.0625432 0.108328i 0.833058 0.553185i \(-0.186588\pi\)
−0.895602 + 0.444857i \(0.853254\pi\)
\(234\) 0 0
\(235\) 131960. 228561.i 0.155874 0.269981i
\(236\) 227176. + 393480.i 0.265511 + 0.459878i
\(237\) 0 0
\(238\) 743453. 812782.i 0.850768 0.930104i
\(239\) −689109. −0.780356 −0.390178 0.920739i \(-0.627587\pi\)
−0.390178 + 0.920739i \(0.627587\pi\)
\(240\) 0 0
\(241\) −110148. + 190782.i −0.122161 + 0.211590i −0.920620 0.390460i \(-0.872316\pi\)
0.798458 + 0.602050i \(0.205649\pi\)
\(242\) 546890. 947242.i 0.600291 1.03973i
\(243\) 0 0
\(244\) 362910. 0.390234
\(245\) 532539. 374297.i 0.566809 0.398383i
\(246\) 0 0
\(247\) −184485. 319537.i −0.192406 0.333257i
\(248\) 289618. 501633.i 0.299017 0.517913i
\(249\) 0 0
\(250\) 587757. + 1.01803e6i 0.594768 + 1.03017i
\(251\) −1.43641e6 −1.43912 −0.719558 0.694433i \(-0.755655\pi\)
−0.719558 + 0.694433i \(0.755655\pi\)
\(252\) 0 0
\(253\) 940714. 0.923966
\(254\) 266042. + 460799.i 0.258742 + 0.448154i
\(255\) 0 0
\(256\) −404021. + 699785.i −0.385305 + 0.667367i
\(257\) −454598. 787388.i −0.429334 0.743628i 0.567480 0.823387i \(-0.307918\pi\)
−0.996814 + 0.0797589i \(0.974585\pi\)
\(258\) 0 0
\(259\) −2.06352e6 455553.i −1.91143 0.421977i
\(260\) −133887. −0.122830
\(261\) 0 0
\(262\) 533154. 923450.i 0.479843 0.831113i
\(263\) 374528. 648702.i 0.333884 0.578304i −0.649386 0.760459i \(-0.724974\pi\)
0.983270 + 0.182155i \(0.0583073\pi\)
\(264\) 0 0
\(265\) −77897.4 −0.0681410
\(266\) 235433. + 744396.i 0.204015 + 0.645060i
\(267\) 0 0
\(268\) −223313. 386789.i −0.189923 0.328956i
\(269\) 334972. 580189.i 0.282246 0.488865i −0.689691 0.724104i \(-0.742254\pi\)
0.971938 + 0.235238i \(0.0755871\pi\)
\(270\) 0 0
\(271\) −270330. 468225.i −0.223599 0.387285i 0.732299 0.680983i \(-0.238447\pi\)
−0.955898 + 0.293698i \(0.905114\pi\)
\(272\) −1.63367e6 −1.33888
\(273\) 0 0
\(274\) 244246. 0.196540
\(275\) 468334. + 811178.i 0.373443 + 0.646821i
\(276\) 0 0
\(277\) 200955. 348064.i 0.157362 0.272558i −0.776555 0.630050i \(-0.783035\pi\)
0.933916 + 0.357491i \(0.116368\pi\)
\(278\) 339502. + 588035.i 0.263470 + 0.456343i
\(279\) 0 0
\(280\) −725871. 160247.i −0.553304 0.122150i
\(281\) 429139. 0.324214 0.162107 0.986773i \(-0.448171\pi\)
0.162107 + 0.986773i \(0.448171\pi\)
\(282\) 0 0
\(283\) 170463. 295251.i 0.126522 0.219142i −0.795805 0.605553i \(-0.792952\pi\)
0.922327 + 0.386411i \(0.126285\pi\)
\(284\) 176478. 305669.i 0.129836 0.224883i
\(285\) 0 0
\(286\) −1.44188e6 −1.04235
\(287\) −1.14658e6 + 1.25351e6i −0.821678 + 0.898301i
\(288\) 0 0
\(289\) −174123. 301590.i −0.122634 0.212409i
\(290\) −181094. + 313664.i −0.126447 + 0.219013i
\(291\) 0 0
\(292\) 245868. + 425855.i 0.168750 + 0.292284i
\(293\) 388847. 0.264612 0.132306 0.991209i \(-0.457762\pi\)
0.132306 + 0.991209i \(0.457762\pi\)
\(294\) 0 0
\(295\) 1.99273e6 1.33319
\(296\) 1.20664e6 + 2.08996e6i 0.800475 + 1.38646i
\(297\) 0 0
\(298\) −615202. + 1.06556e6i −0.401307 + 0.695085i
\(299\) −319472. 553342.i −0.206659 0.357945i
\(300\) 0 0
\(301\) −1.28918e6 + 1.40940e6i −0.820158 + 0.896640i
\(302\) −905435. −0.571268
\(303\) 0 0
\(304\) 578960. 1.00279e6i 0.359306 0.622336i
\(305\) 795840. 1.37844e6i 0.489865 0.848471i
\(306\) 0 0
\(307\) −2.35747e6 −1.42758 −0.713789 0.700361i \(-0.753022\pi\)
−0.713789 + 0.700361i \(0.753022\pi\)
\(308\) 644330. + 142246.i 0.387018 + 0.0854402i
\(309\) 0 0
\(310\) 484110. + 838503.i 0.286114 + 0.495565i
\(311\) −718314. + 1.24416e6i −0.421127 + 0.729414i −0.996050 0.0887939i \(-0.971699\pi\)
0.574923 + 0.818208i \(0.305032\pi\)
\(312\) 0 0
\(313\) 411400. + 712566.i 0.237358 + 0.411116i 0.959955 0.280153i \(-0.0903853\pi\)
−0.722598 + 0.691269i \(0.757052\pi\)
\(314\) −3.61520e6 −2.06923
\(315\) 0 0
\(316\) −557652. −0.314156
\(317\) −883467. 1.53021e6i −0.493790 0.855269i 0.506184 0.862425i \(-0.331056\pi\)
−0.999974 + 0.00715584i \(0.997722\pi\)
\(318\) 0 0
\(319\) −421786. + 730555.i −0.232068 + 0.401954i
\(320\) 376132. + 651480.i 0.205336 + 0.355653i
\(321\) 0 0
\(322\) 407698. + 1.28907e6i 0.219129 + 0.692845i
\(323\) 1.25321e6 0.668370
\(324\) 0 0
\(325\) 318098. 550962.i 0.167052 0.289343i
\(326\) −1.37446e6 + 2.38064e6i −0.716291 + 1.24065i
\(327\) 0 0
\(328\) 1.94003e6 0.995689
\(329\) 862675. + 190448.i 0.439397 + 0.0970036i
\(330\) 0 0
\(331\) 1526.14 + 2643.35i 0.000765638 + 0.00132612i 0.866408 0.499337i \(-0.166423\pi\)
−0.865642 + 0.500663i \(0.833090\pi\)
\(332\) 201211. 348508.i 0.100186 0.173527i
\(333\) 0 0
\(334\) 767632. + 1.32958e6i 0.376519 + 0.652150i
\(335\) −1.95885e6 −0.953649
\(336\) 0 0
\(337\) 2.02939e6 0.973398 0.486699 0.873570i \(-0.338201\pi\)
0.486699 + 0.873570i \(0.338201\pi\)
\(338\) −696584. 1.20652e6i −0.331651 0.574437i
\(339\) 0 0
\(340\) 227374. 393824.i 0.106670 0.184759i
\(341\) 1.12754e6 + 1.95295e6i 0.525104 + 0.909507i
\(342\) 0 0
\(343\) 1.73215e6 + 1.32182e6i 0.794969 + 0.606650i
\(344\) 2.18130e6 0.993848
\(345\) 0 0
\(346\) 572852. 992209.i 0.257248 0.445567i
\(347\) 1.89109e6 3.27547e6i 0.843119 1.46033i −0.0441252 0.999026i \(-0.514050\pi\)
0.887245 0.461299i \(-0.152617\pi\)
\(348\) 0 0
\(349\) 291147. 0.127953 0.0639763 0.997951i \(-0.479622\pi\)
0.0639763 + 0.997951i \(0.479622\pi\)
\(350\) −908592. + 993320.i −0.396460 + 0.433430i
\(351\) 0 0
\(352\) −897136. 1.55389e6i −0.385924 0.668440i
\(353\) 192538. 333486.i 0.0822394 0.142443i −0.821972 0.569528i \(-0.807126\pi\)
0.904212 + 0.427085i \(0.140459\pi\)
\(354\) 0 0
\(355\) −774013. 1.34063e6i −0.325970 0.564596i
\(356\) −138520. −0.0579277
\(357\) 0 0
\(358\) −3.67775e6 −1.51661
\(359\) −1.61507e6 2.79738e6i −0.661385 1.14555i −0.980252 0.197753i \(-0.936635\pi\)
0.318866 0.947800i \(-0.396698\pi\)
\(360\) 0 0
\(361\) 793921. 1.37511e6i 0.320634 0.555354i
\(362\) 1.85628e6 + 3.21517e6i 0.744511 + 1.28953i
\(363\) 0 0
\(364\) −135148. 427312.i −0.0534632 0.169041i
\(365\) 2.15669e6 0.847336
\(366\) 0 0
\(367\) 239779. 415310.i 0.0929280 0.160956i −0.815814 0.578314i \(-0.803711\pi\)
0.908742 + 0.417358i \(0.137044\pi\)
\(368\) 1.00258e6 1.73653e6i 0.385923 0.668439i
\(369\) 0 0
\(370\) −4.03390e6 −1.53187
\(371\) −78630.6 248616.i −0.0296590 0.0937766i
\(372\) 0 0
\(373\) −436333. 755751.i −0.162385 0.281259i 0.773339 0.633993i \(-0.218585\pi\)
−0.935724 + 0.352734i \(0.885252\pi\)
\(374\) 2.44868e6 4.24124e6i 0.905217 1.56788i
\(375\) 0 0
\(376\) −504447. 873728.i −0.184012 0.318718i
\(377\) 572965. 0.207622
\(378\) 0 0
\(379\) −2.43493e6 −0.870742 −0.435371 0.900251i \(-0.643383\pi\)
−0.435371 + 0.900251i \(0.643383\pi\)
\(380\) 161160. + 279137.i 0.0572529 + 0.0991650i
\(381\) 0 0
\(382\) 2.11044e6 3.65540e6i 0.739973 1.28167i
\(383\) −1.80584e6 3.12781e6i −0.629047 1.08954i −0.987743 0.156087i \(-0.950112\pi\)
0.358696 0.933454i \(-0.383222\pi\)
\(384\) 0 0
\(385\) 1.95327e6 2.13541e6i 0.671598 0.734226i
\(386\) 3.56114e6 1.21652
\(387\) 0 0
\(388\) −13812.9 + 23924.7i −0.00465807 + 0.00806802i
\(389\) −87616.2 + 151756.i −0.0293569 + 0.0508477i −0.880331 0.474361i \(-0.842679\pi\)
0.850974 + 0.525208i \(0.176013\pi\)
\(390\) 0 0
\(391\) 2.17018e6 0.717882
\(392\) −221262. 2.47843e6i −0.0727262 0.814632i
\(393\) 0 0
\(394\) 2.43262e6 + 4.21343e6i 0.789467 + 1.36740i
\(395\) −1.22290e6 + 2.11812e6i −0.394364 + 0.683058i
\(396\) 0 0
\(397\) −942577. 1.63259e6i −0.300152 0.519878i 0.676019 0.736885i \(-0.263704\pi\)
−0.976170 + 0.217007i \(0.930371\pi\)
\(398\) 868126. 0.274710
\(399\) 0 0
\(400\) 1.99654e6 0.623920
\(401\) 669915. + 1.16033e6i 0.208046 + 0.360346i 0.951099 0.308887i \(-0.0999564\pi\)
−0.743053 + 0.669232i \(0.766623\pi\)
\(402\) 0 0
\(403\) 765839. 1.32647e6i 0.234895 0.406851i
\(404\) −746217. 1.29249e6i −0.227463 0.393978i
\(405\) 0 0
\(406\) −1.18388e6 261360.i −0.356446 0.0786909i
\(407\) −9.39535e6 −2.81143
\(408\) 0 0
\(409\) −3.29314e6 + 5.70388e6i −0.973423 + 1.68602i −0.288381 + 0.957516i \(0.593117\pi\)
−0.685043 + 0.728503i \(0.740217\pi\)
\(410\) −1.62143e6 + 2.80839e6i −0.476362 + 0.825084i
\(411\) 0 0
\(412\) 996247. 0.289150
\(413\) 2.01149e6 + 6.35996e6i 0.580286 + 1.83476i
\(414\) 0 0
\(415\) −882487. 1.52851e6i −0.251529 0.435661i
\(416\) −609346. + 1.05542e6i −0.172636 + 0.299014i
\(417\) 0 0
\(418\) 1.73559e6 + 3.00613e6i 0.485855 + 0.841525i
\(419\) 6.96869e6 1.93917 0.969585 0.244754i \(-0.0787071\pi\)
0.969585 + 0.244754i \(0.0787071\pi\)
\(420\) 0 0
\(421\) 3.84041e6 1.05602 0.528010 0.849238i \(-0.322938\pi\)
0.528010 + 0.849238i \(0.322938\pi\)
\(422\) −3.16668e6 5.48485e6i −0.865612 1.49928i
\(423\) 0 0
\(424\) −148890. + 257886.i −0.0402209 + 0.0696647i
\(425\) 1.08042e6 + 1.87134e6i 0.290149 + 0.502552i
\(426\) 0 0
\(427\) 5.20272e6 + 1.14858e6i 1.38090 + 0.304854i
\(428\) 197002. 0.0519829
\(429\) 0 0
\(430\) −1.82308e6 + 3.15766e6i −0.475481 + 0.823558i
\(431\) 1.51818e6 2.62957e6i 0.393668 0.681854i −0.599262 0.800553i \(-0.704539\pi\)
0.992930 + 0.118699i \(0.0378725\pi\)
\(432\) 0 0
\(433\) −941529. −0.241332 −0.120666 0.992693i \(-0.538503\pi\)
−0.120666 + 0.992693i \(0.538503\pi\)
\(434\) −2.18749e6 + 2.39147e6i −0.557469 + 0.609454i
\(435\) 0 0
\(436\) 370080. + 640997.i 0.0932351 + 0.161488i
\(437\) −769096. + 1.33211e6i −0.192653 + 0.333686i
\(438\) 0 0
\(439\) −670546. 1.16142e6i −0.166061 0.287626i 0.770971 0.636871i \(-0.219771\pi\)
−0.937031 + 0.349245i \(0.886438\pi\)
\(440\) −3.30494e6 −0.813827
\(441\) 0 0
\(442\) −3.32635e6 −0.809864
\(443\) −386171. 668867.i −0.0934910 0.161931i 0.815487 0.578776i \(-0.196469\pi\)
−0.908978 + 0.416844i \(0.863136\pi\)
\(444\) 0 0
\(445\) −303765. + 526137.i −0.0727174 + 0.125950i
\(446\) 1.73595e6 + 3.00675e6i 0.413238 + 0.715748i
\(447\) 0 0
\(448\) −1.69958e6 + 1.85807e6i −0.400080 + 0.437388i
\(449\) −2.25684e6 −0.528304 −0.264152 0.964481i \(-0.585092\pi\)
−0.264152 + 0.964481i \(0.585092\pi\)
\(450\) 0 0
\(451\) −3.77646e6 + 6.54101e6i −0.874265 + 1.51427i
\(452\) −180707. + 312994.i −0.0416034 + 0.0720593i
\(453\) 0 0
\(454\) 104.373 2.37655e−5
\(455\) −1.91942e6 423742.i −0.434653 0.0959561i
\(456\) 0 0
\(457\) −2.14235e6 3.71066e6i −0.479844 0.831114i 0.519889 0.854234i \(-0.325973\pi\)
−0.999733 + 0.0231196i \(0.992640\pi\)
\(458\) −247221. + 428199.i −0.0550708 + 0.0953854i
\(459\) 0 0
\(460\) 279080. + 483381.i 0.0614942 + 0.106511i
\(461\) 3.10462e6 0.680387 0.340193 0.940355i \(-0.389507\pi\)
0.340193 + 0.940355i \(0.389507\pi\)
\(462\) 0 0
\(463\) −3.53386e6 −0.766121 −0.383060 0.923723i \(-0.625130\pi\)
−0.383060 + 0.923723i \(0.625130\pi\)
\(464\) 899053. + 1.55721e6i 0.193861 + 0.335777i
\(465\) 0 0
\(466\) 331178. 573617.i 0.0706475 0.122365i
\(467\) 1.36230e6 + 2.35957e6i 0.289054 + 0.500657i 0.973584 0.228328i \(-0.0733258\pi\)
−0.684530 + 0.728985i \(0.739993\pi\)
\(468\) 0 0
\(469\) −1.97728e6 6.25182e6i −0.415085 1.31242i
\(470\) 1.68641e6 0.352143
\(471\) 0 0
\(472\) 3.80883e6 6.59709e6i 0.786932 1.36301i
\(473\) −4.24612e6 + 7.35449e6i −0.872649 + 1.51147i
\(474\) 0 0
\(475\) −1.53158e6 −0.311461
\(476\) 1.48643e6 + 328153.i 0.300697 + 0.0663833i
\(477\) 0 0
\(478\) −2.20166e6 3.81338e6i −0.440737 0.763379i
\(479\) 489342. 847566.i 0.0974482 0.168785i −0.813180 0.582013i \(-0.802265\pi\)
0.910628 + 0.413228i \(0.135599\pi\)
\(480\) 0 0
\(481\) 3.19072e6 + 5.52649e6i 0.628819 + 1.08915i
\(482\) −1.40766e6 −0.275982
\(483\) 0 0
\(484\) 1.51154e6 0.293296
\(485\) 60581.8 + 104931.i 0.0116947 + 0.0202558i
\(486\) 0 0
\(487\) −1.96372e6 + 3.40126e6i −0.375195 + 0.649857i −0.990356 0.138544i \(-0.955758\pi\)
0.615161 + 0.788401i \(0.289091\pi\)
\(488\) −3.04228e6 5.26938e6i −0.578295 1.00164i
\(489\) 0 0
\(490\) 3.77271e6 + 1.75111e6i 0.709844 + 0.329475i
\(491\) −2.63241e6 −0.492777 −0.246388 0.969171i \(-0.579244\pi\)
−0.246388 + 0.969171i \(0.579244\pi\)
\(492\) 0 0
\(493\) −973037. + 1.68535e6i −0.180307 + 0.312301i
\(494\) 1.17883e6 2.04180e6i 0.217338 0.376440i
\(495\) 0 0
\(496\) 4.80678e6 0.877305
\(497\) 3.49743e6 3.82357e6i 0.635123 0.694350i
\(498\) 0 0
\(499\) −1.06272e6 1.84069e6i −0.191059 0.330924i 0.754542 0.656251i \(-0.227859\pi\)
−0.945601 + 0.325327i \(0.894526\pi\)
\(500\) −812244. + 1.40685e6i −0.145299 + 0.251665i
\(501\) 0 0
\(502\) −4.58925e6 7.94881e6i −0.812798 1.40781i
\(503\) −2.60929e6 −0.459835 −0.229917 0.973210i \(-0.573846\pi\)
−0.229917 + 0.973210i \(0.573846\pi\)
\(504\) 0 0
\(505\) −6.54564e6 −1.14215
\(506\) 3.00552e6 + 5.20571e6i 0.521847 + 0.903865i
\(507\) 0 0
\(508\) −367654. + 636795.i −0.0632092 + 0.109481i
\(509\) −5.00911e6 8.67603e6i −0.856970 1.48432i −0.874805 0.484475i \(-0.839011\pi\)
0.0178348 0.999841i \(-0.494323\pi\)
\(510\) 0 0
\(511\) 2.17699e6 + 6.88326e6i 0.368811 + 1.16612i
\(512\) 1.99607e6 0.336512
\(513\) 0 0
\(514\) 2.90482e6 5.03130e6i 0.484967 0.839987i
\(515\) 2.18471e6 3.78403e6i 0.362974 0.628689i
\(516\) 0 0
\(517\) 3.92782e6 0.646287
\(518\) −4.07187e6 1.28745e7i −0.666760 2.10818i
\(519\) 0 0
\(520\) 1.12238e6 + 1.94402e6i 0.182025 + 0.315277i
\(521\) −2.08970e6 + 3.61947e6i −0.337280 + 0.584186i −0.983920 0.178609i \(-0.942840\pi\)
0.646640 + 0.762795i \(0.276174\pi\)
\(522\) 0 0
\(523\) −1.80263e6 3.12224e6i −0.288172 0.499128i 0.685202 0.728353i \(-0.259714\pi\)
−0.973373 + 0.229225i \(0.926381\pi\)
\(524\) 1.47357e6 0.234446
\(525\) 0 0
\(526\) 4.78637e6 0.754297
\(527\) 2.60117e6 + 4.50536e6i 0.407983 + 0.706648i
\(528\) 0 0
\(529\) 1.88633e6 3.26722e6i 0.293075 0.507621i
\(530\) −248877. 431068.i −0.0384853 0.0666586i
\(531\) 0 0
\(532\) −728212. + 796119.i −0.111552 + 0.121955i
\(533\) 5.13003e6 0.782172
\(534\) 0 0
\(535\) 432013. 748268.i 0.0652547 0.113025i
\(536\) −3.74407e6 + 6.48492e6i −0.562901 + 0.974972i
\(537\) 0 0
\(538\) 4.28086e6 0.637640
\(539\) 8.78699e6 + 4.07850e6i 1.30277 + 0.604684i
\(540\) 0 0
\(541\) 3.34083e6 + 5.78648e6i 0.490751 + 0.850005i 0.999943 0.0106475i \(-0.00338926\pi\)
−0.509193 + 0.860653i \(0.670056\pi\)
\(542\) 1.72737e6 2.99189e6i 0.252573 0.437470i
\(543\) 0 0
\(544\) −2.06964e6 3.58473e6i −0.299846 0.519349i
\(545\) 3.24625e6 0.468156
\(546\) 0 0
\(547\) 8.69076e6 1.24191 0.620954 0.783847i \(-0.286745\pi\)
0.620954 + 0.783847i \(0.286745\pi\)
\(548\) 168766. + 292312.i 0.0240068 + 0.0415810i
\(549\) 0 0
\(550\) −2.99259e6 + 5.18332e6i −0.421833 + 0.730636i
\(551\) −689676. 1.19455e6i −0.0967756 0.167620i
\(552\) 0 0
\(553\) −7.99456e6 1.76492e6i −1.11168 0.245421i
\(554\) 2.56815e6 0.355505
\(555\) 0 0
\(556\) −469171. + 812628.i −0.0643642 + 0.111482i
\(557\) 3.12371e6 5.41042e6i 0.426612 0.738913i −0.569958 0.821674i \(-0.693040\pi\)
0.996569 + 0.0827611i \(0.0263738\pi\)
\(558\) 0 0
\(559\) 5.76803e6 0.780725
\(560\) −1.86017e6 5.88152e6i −0.250658 0.792537i
\(561\) 0 0
\(562\) 1.37107e6 + 2.37476e6i 0.183113 + 0.317161i
\(563\) −5.95223e6 + 1.03096e7i −0.791423 + 1.37078i 0.133663 + 0.991027i \(0.457326\pi\)
−0.925086 + 0.379758i \(0.876007\pi\)
\(564\) 0 0
\(565\) 792560. + 1.37275e6i 0.104451 + 0.180914i
\(566\) 2.17848e6 0.285833
\(567\) 0 0
\(568\) −5.91768e6 −0.769627
\(569\) 10707.2 + 18545.4i 0.00138642 + 0.00240135i 0.866718 0.498799i \(-0.166225\pi\)
−0.865331 + 0.501200i \(0.832892\pi\)
\(570\) 0 0
\(571\) −3.55823e6 + 6.16304e6i −0.456714 + 0.791051i −0.998785 0.0492811i \(-0.984307\pi\)
0.542071 + 0.840333i \(0.317640\pi\)
\(572\) −996297. 1.72564e6i −0.127321 0.220526i
\(573\) 0 0
\(574\) −1.05999e7 2.34009e6i −1.34283 0.296451i
\(575\) −2.65223e6 −0.334534
\(576\) 0 0
\(577\) 5.33259e6 9.23632e6i 0.666805 1.15494i −0.311988 0.950086i \(-0.600995\pi\)
0.978793 0.204854i \(-0.0656719\pi\)
\(578\) 1.11262e6 1.92712e6i 0.138525 0.239932i
\(579\) 0 0
\(580\) −500522. −0.0617808
\(581\) 3.98758e6 4.35943e6i 0.490083 0.535784i
\(582\) 0 0
\(583\) −579659. 1.00400e6i −0.0706319 0.122338i
\(584\) 4.12222e6 7.13990e6i 0.500149 0.866283i
\(585\) 0 0
\(586\) 1.24234e6 + 2.15180e6i 0.149450 + 0.258856i
\(587\) 1.30101e7 1.55843 0.779213 0.626759i \(-0.215619\pi\)
0.779213 + 0.626759i \(0.215619\pi\)
\(588\) 0 0
\(589\) −3.68735e6 −0.437952
\(590\) 6.36664e6 + 1.10273e7i 0.752975 + 1.30419i
\(591\) 0 0
\(592\) −1.00133e7 + 1.73435e7i −1.17428 + 2.03391i
\(593\) 2.13043e6 + 3.69002e6i 0.248789 + 0.430915i 0.963190 0.268821i \(-0.0866342\pi\)
−0.714401 + 0.699736i \(0.753301\pi\)
\(594\) 0 0
\(595\) 4.50608e6 4.92628e6i 0.521803 0.570462i
\(596\) −1.70034e6 −0.196074
\(597\) 0 0
\(598\) 2.04139e6 3.53578e6i 0.233438 0.404327i
\(599\) −6.89790e6 + 1.19475e7i −0.785507 + 1.36054i 0.143189 + 0.989695i \(0.454264\pi\)
−0.928696 + 0.370842i \(0.879069\pi\)
\(600\) 0 0
\(601\) 4.99695e6 0.564311 0.282155 0.959369i \(-0.408951\pi\)
0.282155 + 0.959369i \(0.408951\pi\)
\(602\) −1.19182e7 2.63111e6i −1.34035 0.295902i
\(603\) 0 0
\(604\) −625628. 1.08362e6i −0.0697788 0.120860i
\(605\) 3.31471e6 5.74125e6i 0.368177 0.637702i
\(606\) 0 0
\(607\) 1.52473e6 + 2.64091e6i 0.167966 + 0.290926i 0.937705 0.347434i \(-0.112947\pi\)
−0.769739 + 0.638359i \(0.779613\pi\)
\(608\) 2.93387e6 0.321871
\(609\) 0 0
\(610\) 1.01706e7 1.10668
\(611\) −1.33391e6 2.31040e6i −0.144552 0.250372i
\(612\) 0 0
\(613\) 3.51813e6 6.09357e6i 0.378147 0.654969i −0.612646 0.790357i \(-0.709895\pi\)
0.990793 + 0.135388i \(0.0432282\pi\)
\(614\) −7.53195e6 1.30457e7i −0.806281 1.39652i
\(615\) 0 0
\(616\) −3.33605e6 1.05480e7i −0.354226 1.12000i
\(617\) −1.00066e7 −1.05822 −0.529108 0.848554i \(-0.677473\pi\)
−0.529108 + 0.848554i \(0.677473\pi\)
\(618\) 0 0
\(619\) 3.27533e6 5.67304e6i 0.343581 0.595099i −0.641514 0.767111i \(-0.721693\pi\)
0.985095 + 0.172012i \(0.0550268\pi\)
\(620\) −669010. + 1.15876e6i −0.0698962 + 0.121064i
\(621\) 0 0
\(622\) −9.17986e6 −0.951393
\(623\) −1.98583e6 438403.i −0.204985 0.0452536i
\(624\) 0 0
\(625\) 1.02325e6 + 1.77232e6i 0.104781 + 0.181485i
\(626\) −2.62879e6 + 4.55320e6i −0.268114 + 0.464388i
\(627\) 0 0
\(628\) −2.49799e6 4.32665e6i −0.252750 0.437777i
\(629\) −2.16746e7 −2.18436
\(630\) 0 0
\(631\) 2.22672e6 0.222635 0.111317 0.993785i \(-0.464493\pi\)
0.111317 + 0.993785i \(0.464493\pi\)
\(632\) 4.67480e6 + 8.09699e6i 0.465554 + 0.806364i
\(633\) 0 0
\(634\) 5.64524e6 9.77784e6i 0.557775 0.966095i
\(635\) 1.61249e6 + 2.79291e6i 0.158694 + 0.274867i
\(636\) 0 0
\(637\) −585084. 6.55373e6i −0.0571307 0.639941i
\(638\) −5.39031e6 −0.524279
\(639\) 0 0
\(640\) −4.33242e6 + 7.50397e6i −0.418101 + 0.724171i
\(641\) −7.96698e6 + 1.37992e7i −0.765859 + 1.32651i 0.173932 + 0.984758i \(0.444353\pi\)
−0.939791 + 0.341749i \(0.888981\pi\)
\(642\) 0 0
\(643\) −1.49933e7 −1.43011 −0.715056 0.699067i \(-0.753599\pi\)
−0.715056 + 0.699067i \(0.753599\pi\)
\(644\) −1.26104e6 + 1.37864e6i −0.119816 + 0.130989i
\(645\) 0 0
\(646\) 4.00391e6 + 6.93498e6i 0.377488 + 0.653829i
\(647\) 6.49027e6 1.12415e7i 0.609540 1.05575i −0.381776 0.924255i \(-0.624687\pi\)
0.991316 0.131500i \(-0.0419792\pi\)
\(648\) 0 0
\(649\) 1.48285e7 + 2.56838e7i 1.38193 + 2.39357i
\(650\) 4.06521e6 0.377398
\(651\) 0 0
\(652\) −3.79885e6 −0.349972
\(653\) −8.27460e6 1.43320e7i −0.759389 1.31530i −0.943163 0.332332i \(-0.892165\pi\)
0.183774 0.982969i \(-0.441169\pi\)
\(654\) 0 0
\(655\) 3.23145e6 5.59704e6i 0.294303 0.509748i
\(656\) 8.04966e6 + 1.39424e7i 0.730328 + 1.26497i
\(657\) 0 0
\(658\) 1.70229e6 + 5.38233e6i 0.153274 + 0.484625i
\(659\) −5.86879e6 −0.526423 −0.263212 0.964738i \(-0.584782\pi\)
−0.263212 + 0.964738i \(0.584782\pi\)
\(660\) 0 0
\(661\) −3.63843e6 + 6.30195e6i −0.323900 + 0.561011i −0.981289 0.192540i \(-0.938327\pi\)
0.657389 + 0.753551i \(0.271661\pi\)
\(662\) −9751.81 + 16890.6i −0.000864849 + 0.00149796i
\(663\) 0 0
\(664\) −6.74702e6 −0.593870
\(665\) 1.42696e6 + 4.51179e6i 0.125129 + 0.395635i
\(666\) 0 0
\(667\) −1.19431e6 2.06861e6i −0.103945 0.180038i
\(668\) −1.06082e6 + 1.83739e6i −0.0919815 + 0.159317i
\(669\) 0 0
\(670\) −6.25838e6 1.08398e7i −0.538611 0.932902i
\(671\) 2.36884e7 2.03109
\(672\) 0 0
\(673\) −1.82417e7 −1.55248 −0.776241 0.630437i \(-0.782876\pi\)
−0.776241 + 0.630437i \(0.782876\pi\)
\(674\) 6.48376e6 + 1.12302e7i 0.549765 + 0.952222i
\(675\) 0 0
\(676\) 962636. 1.66733e6i 0.0810205 0.140332i
\(677\) −3.88203e6 6.72387e6i −0.325527 0.563829i 0.656092 0.754681i \(-0.272208\pi\)
−0.981619 + 0.190852i \(0.938875\pi\)
\(678\) 0 0
\(679\) −273743. + 299270.i −0.0227860 + 0.0249109i
\(680\) −7.62432e6 −0.632308
\(681\) 0 0
\(682\) −7.20482e6 + 1.24791e7i −0.593147 + 1.02736i
\(683\) 4.28162e6 7.41598e6i 0.351201 0.608299i −0.635259 0.772299i \(-0.719107\pi\)
0.986460 + 0.164001i \(0.0524399\pi\)
\(684\) 0 0
\(685\) 1.48038e6 0.120544
\(686\) −1.78059e6 + 1.38085e7i −0.144462 + 1.12030i
\(687\) 0 0
\(688\) 9.05076e6 + 1.56764e7i 0.728978 + 1.26263i
\(689\) −393712. + 681928.i −0.0315959 + 0.0547256i
\(690\) 0 0
\(691\) −8.22547e6 1.42469e7i −0.655338 1.13508i −0.981809 0.189872i \(-0.939193\pi\)
0.326471 0.945207i \(-0.394140\pi\)
\(692\) 1.58329e6 0.125689
\(693\) 0 0
\(694\) 2.41677e7 1.90474
\(695\) 2.05773e6 + 3.56409e6i 0.161594 + 0.279890i
\(696\) 0 0
\(697\) −8.71208e6 + 1.50898e7i −0.679266 + 1.17652i
\(698\) 930197. + 1.61115e6i 0.0722664 + 0.125169i
\(699\) 0 0
\(700\) −1.81661e6 401044.i −0.140125 0.0309347i
\(701\) 1.66928e7 1.28302 0.641512 0.767113i \(-0.278307\pi\)
0.641512 + 0.767113i \(0.278307\pi\)
\(702\) 0 0
\(703\) 7.68132e6 1.33044e7i 0.586202 1.01533i
\(704\) −5.59783e6 + 9.69573e6i −0.425685 + 0.737308i
\(705\) 0 0
\(706\) 2.46059e6 0.185792
\(707\) −6.60725e6 2.08909e7i −0.497132 1.57184i
\(708\) 0 0
\(709\) −2.80890e6 4.86515e6i −0.209855 0.363480i 0.741813 0.670606i \(-0.233966\pi\)
−0.951669 + 0.307126i \(0.900633\pi\)
\(710\) 4.94584e6 8.56644e6i 0.368209 0.637756i
\(711\) 0 0
\(712\) 1.16121e6 + 2.01128e6i 0.0858443 + 0.148687i
\(713\) −6.38537e6 −0.470395
\(714\) 0 0
\(715\) −8.73927e6 −0.639308
\(716\) −2.54121e6 4.40150e6i −0.185250 0.320862i
\(717\) 0 0
\(718\) 1.03201e7 1.78749e7i 0.747087 1.29399i
\(719\) 5.18592e6 + 8.98227e6i 0.374113 + 0.647983i 0.990194 0.139700i \(-0.0446138\pi\)
−0.616081 + 0.787683i \(0.711280\pi\)
\(720\) 0 0
\(721\) 1.42823e7 + 3.15303e6i 1.02320 + 0.225887i
\(722\) 1.01461e7 0.724363
\(723\) 0 0
\(724\) −2.56526e6 + 4.44316e6i −0.181880 + 0.315025i
\(725\) 1.18917e6 2.05971e6i 0.0840233 0.145533i
\(726\) 0 0
\(727\) 1.15369e7 0.809565 0.404783 0.914413i \(-0.367347\pi\)
0.404783 + 0.914413i \(0.367347\pi\)
\(728\) −5.07155e6 + 5.54448e6i −0.354660 + 0.387733i
\(729\) 0 0
\(730\) 6.89049e6 + 1.19347e7i 0.478567 + 0.828902i
\(731\) −9.79557e6 + 1.69664e7i −0.678010 + 1.17435i
\(732\) 0 0
\(733\) −7.47349e6 1.29445e7i −0.513764 0.889865i −0.999873 0.0159667i \(-0.994917\pi\)
0.486109 0.873898i \(-0.338416\pi\)
\(734\) 3.06432e6 0.209939
\(735\) 0 0
\(736\) 5.08058e6 0.345715
\(737\) −1.45764e7 2.52470e7i −0.988510 1.71215i
\(738\) 0 0
\(739\) −4.50682e6 + 7.80604e6i −0.303570 + 0.525799i −0.976942 0.213505i \(-0.931512\pi\)
0.673372 + 0.739304i \(0.264845\pi\)
\(740\) −2.78730e6 4.82775e6i −0.187113 0.324090i
\(741\) 0 0
\(742\) 1.12457e6 1.22944e6i 0.0749853 0.0819779i
\(743\) 2.10239e7 1.39714 0.698571 0.715541i \(-0.253820\pi\)
0.698571 + 0.715541i \(0.253820\pi\)
\(744\) 0 0
\(745\) −3.72875e6 + 6.45838e6i −0.246134 + 0.426317i
\(746\) 2.78811e6 4.82915e6i 0.183427 0.317705i
\(747\) 0 0
\(748\) 6.76785e6 0.442279
\(749\) 2.82424e6 + 623493.i 0.183949 + 0.0406094i
\(750\) 0 0
\(751\) −2.02110e6 3.50064e6i −0.130764 0.226489i 0.793207 0.608952i \(-0.208410\pi\)
−0.923971 + 0.382462i \(0.875076\pi\)
\(752\) 4.18615e6 7.25062e6i 0.269942 0.467553i
\(753\) 0 0
\(754\) 1.83058e6 + 3.17066e6i 0.117263 + 0.203106i
\(755\) −5.48786e6 −0.350377
\(756\) 0 0
\(757\) −1.82059e7 −1.15471 −0.577353 0.816495i \(-0.695914\pi\)
−0.577353 + 0.816495i \(0.695914\pi\)
\(758\) −7.77945e6 1.34744e7i −0.491786 0.851798i
\(759\) 0 0
\(760\) 2.70201e6 4.68001e6i 0.169689 0.293909i
\(761\) −9.45999e6 1.63852e7i −0.592146 1.02563i −0.993943 0.109898i \(-0.964947\pi\)
0.401797 0.915729i \(-0.368386\pi\)
\(762\) 0 0
\(763\) 3.27681e6 + 1.03607e7i 0.203770 + 0.644283i
\(764\) 5.83301e6 0.361542
\(765\) 0 0
\(766\) 1.15391e7 1.99863e7i 0.710559 1.23072i
\(767\) 1.00717e7 1.74447e7i 0.618180 1.07072i
\(768\) 0 0
\(769\) −1.12831e7 −0.688037 −0.344019 0.938963i \(-0.611788\pi\)
−0.344019 + 0.938963i \(0.611788\pi\)
\(770\) 1.80575e7 + 3.98646e6i 1.09756 + 0.242304i
\(771\) 0 0
\(772\) 2.46064e6 + 4.26195e6i 0.148595 + 0.257374i
\(773\) −1.84282e6 + 3.19186e6i −0.110926 + 0.192130i −0.916144 0.400849i \(-0.868715\pi\)
0.805218 + 0.592979i \(0.202048\pi\)
\(774\) 0 0
\(775\) −3.17896e6 5.50611e6i −0.190121 0.329299i
\(776\) 463176. 0.0276116
\(777\) 0 0
\(778\) −1.11971e6 −0.0663219
\(779\) −6.17501e6 1.06954e7i −0.364581 0.631472i