Properties

Label 63.6.e.c.37.2
Level $63$
Weight $6$
Character 63.37
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 37.2
Root \(-3.69493 + 2.71062i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.6.e.c.46.2

$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

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

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 −0.432279 0.901740i \(-0.642291\pi\)
0.997069 0.0765049i \(-0.0243761\pi\)
\(3\) 0 0
\(4\) −4.41520 7.64735i −0.137975 0.238980i
\(5\) 19.3645 33.5404i 0.346403 0.599988i −0.639204 0.769037i \(-0.720736\pi\)
0.985608 + 0.169049i \(0.0540695\pi\)
\(6\) 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 −0.961739 0.273968i \(-0.911664\pi\)
0.243606 0.969874i \(-0.421670\pi\)
\(12\) 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 −0.997667 0.0682711i \(-0.978252\pi\)
0.439709 0.898140i \(-0.355082\pi\)
\(18\) 0 0
\(19\) −471.237 + 816.206i −0.299471 + 0.518699i −0.976015 0.217703i \(-0.930144\pi\)
0.676544 + 0.736402i \(0.263477\pi\)
\(20\) −341.993 −0.191180
\(21\) 0 0
\(22\) −3683.05 −1.62238
\(23\) −816.040 + 1413.42i −0.321656 + 0.557124i −0.980830 0.194866i \(-0.937573\pi\)
0.659174 + 0.751991i \(0.270906\pi\)
\(24\) 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 0.988873 0.148763i \(-0.0475291\pi\)
−0.623269 + 0.782008i \(0.714196\pi\)
\(32\) −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 0.311691 0.950184i \(-0.399105\pi\)
0.667038 0.745024i \(-0.267562\pi\)
\(38\) 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 −0.956316 0.292335i \(-0.905568\pi\)
0.731327 + 0.682027i \(0.238901\pi\)
\(48\) 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 0.840389 0.541984i \(-0.182327\pi\)
−0.889566 + 0.456806i \(0.848993\pi\)
\(54\) 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 0.717035 + 0.697037i \(0.245499\pi\)
0.245135 + 0.969489i \(0.421168\pi\)
\(60\) 0 0
\(61\) −20548.9 + 35591.8i −0.707073 + 1.22469i 0.258865 + 0.965913i \(0.416651\pi\)
−0.965938 + 0.258773i \(0.916682\pi\)
\(62\) 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 −0.972404 0.233305i \(-0.925046\pi\)
0.284153 0.958779i \(-0.408288\pi\)
\(68\) −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 0.990984 + 0.133983i \(0.0427767\pi\)
−0.379459 + 0.925208i \(0.623890\pi\)
\(74\) −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 −0.427416 0.904055i \(-0.640576\pi\)
0.996643 0.0818739i \(-0.0260905\pi\)
\(80\) −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 −0.808762 0.588137i \(-0.799862\pi\)
0.913722 + 0.406340i \(0.133195\pi\)
\(90\) 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 −0.902459 0.430776i \(-0.858240\pi\)
0.0781663 0.996940i \(-0.475093\pi\)
\(102\) 0 0
\(103\) −56410.1 + 97705.1i −0.523918 + 0.907453i 0.475694 + 0.879611i \(0.342197\pi\)
−0.999612 + 0.0278422i \(0.991136\pi\)
\(104\) 57960.5 0.525471
\(105\) 0 0
\(106\) −12852.2 −0.111100
\(107\) −11154.7 + 19320.6i −0.0941890 + 0.163140i −0.909270 0.416207i \(-0.863359\pi\)
0.815081 + 0.579347i \(0.196692\pi\)
\(108\) 0 0
\(109\) 41909.8 + 72589.8i 0.337869 + 0.585207i 0.984032 0.177993i \(-0.0569604\pi\)
−0.646162 + 0.763200i \(0.723627\pi\)
\(110\) −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 −0.996402 0.0847580i \(-0.972988\pi\)
0.571603 + 0.820530i \(0.306322\pi\)
\(132\) 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 0.906240 0.422763i \(-0.138940\pi\)
−0.819244 + 0.573446i \(0.805606\pi\)
\(138\) 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 −0.631893 0.775056i \(-0.717722\pi\)
0.987164 + 0.159708i \(0.0510551\pi\)
\(150\) 0 0
\(151\) −70849.3 122715.i −0.252868 0.437980i 0.711447 0.702740i \(-0.248040\pi\)
−0.964314 + 0.264761i \(0.914707\pi\)
\(152\) −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 −0.805536 0.592546i \(-0.798123\pi\)
−0.110392 0.993888i \(-0.535211\pi\)
\(158\) −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 −0.352579 0.935782i \(-0.614695\pi\)
0.986701 0.162549i \(-0.0519714\pi\)
\(164\) −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 −0.957137 0.289634i \(-0.906466\pi\)
0.729399 + 0.684088i \(0.239800\pi\)
\(174\) 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 −0.977531 0.210792i \(-0.932396\pi\)
0.306214 0.951963i \(-0.400938\pi\)
\(180\) 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 0.326785 + 0.945099i \(0.394035\pi\)
−0.981872 + 0.189545i \(0.939299\pi\)
\(192\) 0 0
\(193\) 278655. + 482645.i 0.538485 + 0.932684i 0.998986 + 0.0450243i \(0.0143365\pi\)
−0.460501 + 0.887659i \(0.652330\pi\)
\(194\) 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 0.920398 0.390982i \(-0.127865\pi\)
−0.798800 + 0.601597i \(0.794531\pi\)
\(200\) 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 0.866031 0.499991i \(-0.166663\pi\)
−0.866020 + 0.500009i \(0.833330\pi\)
\(228\) 0 0
\(229\) 38689.5 67012.2i 0.0487534 0.0844433i −0.840619 0.541627i \(-0.817808\pi\)
0.889372 + 0.457184i \(0.151142\pi\)
\(230\) 403896. 0.503443
\(231\) 0 0
\(232\) 216679. 0.264299
\(233\) −51828.6 + 89769.9i −0.0625432 + 0.108328i −0.895602 0.444857i \(-0.853254\pi\)
0.833058 + 0.553185i \(0.186588\pi\)
\(234\) 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 0.798458 0.602050i \(-0.205649\pi\)
−0.920620 + 0.390460i \(0.872316\pi\)
\(242\) 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 −0.996814 0.0797589i \(-0.974585\pi\)
0.567480 + 0.823387i \(0.307918\pi\)
\(258\) 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 0.983270 0.182155i \(-0.0583073\pi\)
−0.649386 + 0.760459i \(0.724974\pi\)
\(264\) 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 0.971938 0.235238i \(-0.0755871\pi\)
−0.689691 + 0.724104i \(0.742254\pi\)
\(270\) 0 0
\(271\) −270330. + 468225.i −0.223599 + 0.387285i −0.955898 0.293698i \(-0.905114\pi\)
0.732299 + 0.680983i \(0.238447\pi\)
\(272\) −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 0.933916 0.357491i \(-0.116368\pi\)
−0.776555 + 0.630050i \(0.783035\pi\)
\(278\) 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 0.922327 0.386411i \(-0.126285\pi\)
−0.795805 + 0.605553i \(0.792952\pi\)
\(284\) 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 0.574923 0.818208i \(-0.305032\pi\)
−0.996050 + 0.0887939i \(0.971699\pi\)
\(312\) 0 0
\(313\) 411400. 712566.i 0.237358 0.411116i −0.722598 0.691269i \(-0.757052\pi\)
0.959955 + 0.280153i \(0.0903853\pi\)
\(314\) −3.61520e6 −2.06923
\(315\) 0 0
\(316\) −557652. −0.314156
\(317\) −883467. + 1.53021e6i −0.493790 + 0.855269i −0.999974 0.00715584i \(-0.997722\pi\)
0.506184 + 0.862425i \(0.331056\pi\)
\(318\) 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 −0.865642 0.500663i \(-0.833090\pi\)
0.866408 + 0.499337i \(0.166423\pi\)
\(332\) 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 0.887245 + 0.461299i \(0.152617\pi\)
−0.0441252 + 0.999026i \(0.514050\pi\)
\(348\) 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 0.904212 0.427085i \(-0.140459\pi\)
−0.821972 + 0.569528i \(0.807126\pi\)
\(354\) 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 0.318866 + 0.947800i \(0.396698\pi\)
−0.980252 + 0.197753i \(0.936635\pi\)
\(360\) 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 0.908742 0.417358i \(-0.137044\pi\)
−0.815814 + 0.578314i \(0.803711\pi\)
\(368\) 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 −0.935724 0.352734i \(-0.885252\pi\)
0.773339 + 0.633993i \(0.218585\pi\)
\(374\) 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 0.358696 + 0.933454i \(0.383222\pi\)
−0.987743 + 0.156087i \(0.950112\pi\)
\(384\) 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 0.850974 0.525208i \(-0.176013\pi\)
−0.880331 + 0.474361i \(0.842679\pi\)
\(390\) 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 −0.976170 0.217007i \(-0.930371\pi\)
0.676019 + 0.736885i \(0.263704\pi\)
\(398\) 868126. 0.274710
\(399\) 0 0
\(400\) 1.99654e6 0.623920
\(401\) 669915. 1.16033e6i 0.208046 0.360346i −0.743053 0.669232i \(-0.766623\pi\)
0.951099 + 0.308887i \(0.0999564\pi\)
\(402\) 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 −0.685043 0.728503i \(-0.740217\pi\)
−0.288381 0.957516i \(-0.593117\pi\)
\(410\) −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 0.992930 0.118699i \(-0.0378725\pi\)
−0.599262 + 0.800553i \(0.704539\pi\)
\(432\) 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 −0.937031 0.349245i \(-0.886438\pi\)
0.770971 + 0.636871i \(0.219771\pi\)
\(440\) −3.30494e6 −0.813827
\(441\) 0 0
\(442\) −3.32635e6 −0.809864
\(443\) −386171. + 668867.i −0.0934910 + 0.161931i −0.908978 0.416844i \(-0.863136\pi\)
0.815487 + 0.578776i \(0.196469\pi\)
\(444\) 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 −0.999733 0.0231196i \(-0.992640\pi\)
0.519889 + 0.854234i \(0.325973\pi\)
\(458\) −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 −0.684530 0.728985i \(-0.739993\pi\)
0.973584 + 0.228328i \(0.0733258\pi\)
\(468\) 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 0.910628 0.413228i \(-0.135599\pi\)
−0.813180 + 0.582013i \(0.802265\pi\)
\(480\) 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 0.615161 0.788401i \(-0.289091\pi\)
−0.990356 + 0.138544i \(0.955758\pi\)
\(488\) −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 −0.945601 0.325327i \(-0.894526\pi\)
0.754542 + 0.656251i \(0.227859\pi\)
\(500\) −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 0.0178348 + 0.999841i \(0.494323\pi\)
−0.874805 + 0.484475i \(0.839011\pi\)
\(510\) 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 0.646640 0.762795i \(-0.276174\pi\)
−0.983920 + 0.178609i \(0.942840\pi\)
\(522\) 0 0
\(523\) −1.80263e6 + 3.12224e6i −0.288172 + 0.499128i −0.973373 0.229225i \(-0.926381\pi\)
0.685202 + 0.728353i \(0.259714\pi\)
\(524\) 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 −0.509193 0.860653i \(-0.670056\pi\)
0.999943 + 0.0106475i \(0.00338926\pi\)
\(542\) 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 0.996569 0.0827611i \(-0.0263738\pi\)
−0.569958 + 0.821674i \(0.693040\pi\)
\(558\) 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 −0.925086 0.379758i \(-0.876007\pi\)
0.133663 0.991027i \(-0.457326\pi\)
\(564\) 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 −0.865331 0.501200i \(-0.832892\pi\)
0.866718 + 0.498799i \(0.166225\pi\)
\(570\) 0 0
\(571\) −3.55823e6 6.16304e6i −0.456714 0.791051i 0.542071 0.840333i \(-0.317640\pi\)
−0.998785 + 0.0492811i \(0.984307\pi\)
\(572\) −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 0.978793 + 0.204854i \(0.0656719\pi\)
−0.311988 + 0.950086i \(0.600995\pi\)
\(578\) 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 −0.714401 0.699736i \(-0.753301\pi\)
0.963190 + 0.268821i \(0.0866342\pi\)
\(594\) 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 −0.928696 0.370842i \(-0.879069\pi\)
0.143189 0.989695i \(-0.454264\pi\)
\(600\) 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 −0.769739 0.638359i \(-0.779613\pi\)
0.937705 + 0.347434i \(0.112947\pi\)
\(608\) 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 0.990793 0.135388i \(-0.0432282\pi\)
−0.612646 + 0.790357i \(0.709895\pi\)
\(614\) −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 0.985095 0.172012i \(-0.0550268\pi\)
−0.641514 + 0.767111i \(0.721693\pi\)
\(620\) −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 −0.939791 0.341749i \(-0.888981\pi\)
0.173932 0.984758i \(-0.444353\pi\)
\(642\) 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 0.991316 + 0.131500i \(0.0419792\pi\)
−0.381776 + 0.924255i \(0.624687\pi\)
\(648\) 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 0.183774 + 0.982969i \(0.441169\pi\)
−0.943163 + 0.332332i \(0.892165\pi\)
\(654\) 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 0.657389 0.753551i \(-0.271661\pi\)
−0.981289 + 0.192540i \(0.938327\pi\)
\(662\) −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 −0.981619 0.190852i \(-0.938875\pi\)
0.656092 + 0.754681i \(0.272208\pi\)
\(678\) 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 0.986460 0.164001i \(-0.0524399\pi\)
−0.635259 + 0.772299i \(0.719107\pi\)
\(684\) 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 0.326471 + 0.945207i \(0.394140\pi\)
−0.981809 + 0.189872i \(0.939193\pi\)
\(692\) 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 −0.951669 0.307126i \(-0.900633\pi\)
0.741813 + 0.670606i \(0.233966\pi\)
\(710\) 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 −0.616081 0.787683i \(-0.711280\pi\)
0.990194 + 0.139700i \(0.0446138\pi\)
\(720\) 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 0.486109 + 0.873898i \(0.338416\pi\)
−0.999873 + 0.0159667i \(0.994917\pi\)
\(734\) 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 0.673372 0.739304i \(-0.264845\pi\)
−0.976942 + 0.213505i \(0.931512\pi\)
\(740\) −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 −0.923971 0.382462i \(-0.875076\pi\)
0.793207 + 0.608952i \(0.208410\pi\)
\(752\) 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 0.401797 + 0.915729i \(0.368386\pi\)
−0.993943 + 0.109898i \(0.964947\pi\)
\(762\) 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 0.805218 0.592979i \(-0.202048\pi\)
−0.916144 + 0.400849i \(0.868715\pi\)
\(774\) 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