Properties

Label 225.4.f.d.107.7
Level $225$
Weight $4$
Character 225.107
Analytic conductor $13.275$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: 16.0.11007531417600000000.1
Defining polynomial: \(x^{16} - 7 x^{12} + 48 x^{8} - 7 x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.7
Root \(0.159959 - 0.596975i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.d.143.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.80252 - 2.80252i) q^{2} -7.70820i q^{4} +(-25.0049 - 25.0049i) q^{7} +(0.817763 + 0.817763i) q^{8} +O(q^{10})\) \(q+(2.80252 - 2.80252i) q^{2} -7.70820i q^{4} +(-25.0049 - 25.0049i) q^{7} +(0.817763 + 0.817763i) q^{8} -42.1900i q^{11} +(-25.7196 + 25.7196i) q^{13} -140.153 q^{14} +66.2492 q^{16} +(-42.0974 + 42.0974i) q^{17} -58.9149i q^{19} +(-118.238 - 118.238i) q^{22} +(-141.932 - 141.932i) q^{23} +144.159i q^{26} +(-192.743 + 192.743i) q^{28} -79.0799 q^{29} +184.915 q^{31} +(179.122 - 179.122i) q^{32} +235.957i q^{34} +(81.4436 + 81.4436i) q^{37} +(-165.110 - 165.110i) q^{38} -14.0217i q^{41} +(152.170 - 152.170i) q^{43} -325.209 q^{44} -795.532 q^{46} +(199.038 - 199.038i) q^{47} +907.489i q^{49} +(198.252 + 198.252i) q^{52} +(-84.5353 - 84.5353i) q^{53} -40.8962i q^{56} +(-221.623 + 221.623i) q^{58} +665.733 q^{59} +600.830 q^{61} +(518.227 - 518.227i) q^{62} -473.994i q^{64} +(6.22801 + 6.22801i) q^{67} +(324.495 + 324.495i) q^{68} +750.823i q^{71} +(418.654 - 418.654i) q^{73} +456.494 q^{74} -454.128 q^{76} +(-1054.96 + 1054.96i) q^{77} -825.830i q^{79} +(-39.2961 - 39.2961i) q^{82} +(-463.072 - 463.072i) q^{83} -852.917i q^{86} +(34.5014 - 34.5014i) q^{88} -646.747 q^{89} +1286.23 q^{91} +(-1094.04 + 1094.04i) q^{92} -1115.62i q^{94} +(371.515 + 371.515i) q^{97} +(2543.25 + 2543.25i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 416 q^{16} + 1456 q^{31} - 4464 q^{46} + 6608 q^{61} - 9520 q^{76} + 7056 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.80252 2.80252i 0.990839 0.990839i −0.00911901 0.999958i \(-0.502903\pi\)
0.999958 + 0.00911901i \(0.00290271\pi\)
\(3\) 0 0
\(4\) 7.70820i 0.963525i
\(5\) 0 0
\(6\) 0 0
\(7\) −25.0049 25.0049i −1.35014 1.35014i −0.885502 0.464635i \(-0.846186\pi\)
−0.464635 0.885502i \(-0.653814\pi\)
\(8\) 0.817763 + 0.817763i 0.0361404 + 0.0361404i
\(9\) 0 0
\(10\) 0 0
\(11\) 42.1900i 1.15643i −0.815884 0.578216i \(-0.803749\pi\)
0.815884 0.578216i \(-0.196251\pi\)
\(12\) 0 0
\(13\) −25.7196 + 25.7196i −0.548719 + 0.548719i −0.926070 0.377351i \(-0.876835\pi\)
0.377351 + 0.926070i \(0.376835\pi\)
\(14\) −140.153 −2.67554
\(15\) 0 0
\(16\) 66.2492 1.03514
\(17\) −42.0974 + 42.0974i −0.600595 + 0.600595i −0.940471 0.339875i \(-0.889615\pi\)
0.339875 + 0.940471i \(0.389615\pi\)
\(18\) 0 0
\(19\) 58.9149i 0.711368i −0.934606 0.355684i \(-0.884248\pi\)
0.934606 0.355684i \(-0.115752\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −118.238 118.238i −1.14584 1.14584i
\(23\) −141.932 141.932i −1.28673 1.28673i −0.936761 0.349969i \(-0.886192\pi\)
−0.349969 0.936761i \(-0.613808\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 144.159i 1.08738i
\(27\) 0 0
\(28\) −192.743 + 192.743i −1.30089 + 1.30089i
\(29\) −79.0799 −0.506372 −0.253186 0.967418i \(-0.581478\pi\)
−0.253186 + 0.967418i \(0.581478\pi\)
\(30\) 0 0
\(31\) 184.915 1.07134 0.535672 0.844426i \(-0.320058\pi\)
0.535672 + 0.844426i \(0.320058\pi\)
\(32\) 179.122 179.122i 0.989521 0.989521i
\(33\) 0 0
\(34\) 235.957i 1.19019i
\(35\) 0 0
\(36\) 0 0
\(37\) 81.4436 + 81.4436i 0.361872 + 0.361872i 0.864502 0.502630i \(-0.167634\pi\)
−0.502630 + 0.864502i \(0.667634\pi\)
\(38\) −165.110 165.110i −0.704852 0.704852i
\(39\) 0 0
\(40\) 0 0
\(41\) 14.0217i 0.0534104i −0.999643 0.0267052i \(-0.991498\pi\)
0.999643 0.0267052i \(-0.00850154\pi\)
\(42\) 0 0
\(43\) 152.170 152.170i 0.539667 0.539667i −0.383764 0.923431i \(-0.625372\pi\)
0.923431 + 0.383764i \(0.125372\pi\)
\(44\) −325.209 −1.11425
\(45\) 0 0
\(46\) −795.532 −2.54989
\(47\) 199.038 199.038i 0.617718 0.617718i −0.327228 0.944945i \(-0.606114\pi\)
0.944945 + 0.327228i \(0.106114\pi\)
\(48\) 0 0
\(49\) 907.489i 2.64574i
\(50\) 0 0
\(51\) 0 0
\(52\) 198.252 + 198.252i 0.528705 + 0.528705i
\(53\) −84.5353 84.5353i −0.219091 0.219091i 0.589024 0.808115i \(-0.299512\pi\)
−0.808115 + 0.589024i \(0.799512\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 40.8962i 0.0975889i
\(57\) 0 0
\(58\) −221.623 + 221.623i −0.501733 + 0.501733i
\(59\) 665.733 1.46900 0.734501 0.678608i \(-0.237416\pi\)
0.734501 + 0.678608i \(0.237416\pi\)
\(60\) 0 0
\(61\) 600.830 1.26112 0.630560 0.776140i \(-0.282825\pi\)
0.630560 + 0.776140i \(0.282825\pi\)
\(62\) 518.227 518.227i 1.06153 1.06153i
\(63\) 0 0
\(64\) 473.994i 0.925769i
\(65\) 0 0
\(66\) 0 0
\(67\) 6.22801 + 6.22801i 0.0113563 + 0.0113563i 0.712762 0.701406i \(-0.247444\pi\)
−0.701406 + 0.712762i \(0.747444\pi\)
\(68\) 324.495 + 324.495i 0.578689 + 0.578689i
\(69\) 0 0
\(70\) 0 0
\(71\) 750.823i 1.25502i 0.778609 + 0.627509i \(0.215925\pi\)
−0.778609 + 0.627509i \(0.784075\pi\)
\(72\) 0 0
\(73\) 418.654 418.654i 0.671230 0.671230i −0.286770 0.958000i \(-0.592581\pi\)
0.958000 + 0.286770i \(0.0925815\pi\)
\(74\) 456.494 0.717113
\(75\) 0 0
\(76\) −454.128 −0.685421
\(77\) −1054.96 + 1054.96i −1.56134 + 1.56134i
\(78\) 0 0
\(79\) 825.830i 1.17612i −0.808819 0.588058i \(-0.799893\pi\)
0.808819 0.588058i \(-0.200107\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −39.2961 39.2961i −0.0529211 0.0529211i
\(83\) −463.072 463.072i −0.612394 0.612394i 0.331175 0.943569i \(-0.392555\pi\)
−0.943569 + 0.331175i \(0.892555\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 852.917i 1.06945i
\(87\) 0 0
\(88\) 34.5014 34.5014i 0.0417939 0.0417939i
\(89\) −646.747 −0.770281 −0.385140 0.922858i \(-0.625847\pi\)
−0.385140 + 0.922858i \(0.625847\pi\)
\(90\) 0 0
\(91\) 1286.23 1.48169
\(92\) −1094.04 + 1094.04i −1.23980 + 1.23980i
\(93\) 0 0
\(94\) 1115.62i 1.22412i
\(95\) 0 0
\(96\) 0 0
\(97\) 371.515 + 371.515i 0.388883 + 0.388883i 0.874289 0.485406i \(-0.161328\pi\)
−0.485406 + 0.874289i \(0.661328\pi\)
\(98\) 2543.25 + 2543.25i 2.62150 + 2.62150i
\(99\) 0 0
\(100\) 0 0
\(101\) 1579.77i 1.55636i −0.628040 0.778181i \(-0.716142\pi\)
0.628040 0.778181i \(-0.283858\pi\)
\(102\) 0 0
\(103\) −31.4262 + 31.4262i −0.0300633 + 0.0300633i −0.721979 0.691915i \(-0.756767\pi\)
0.691915 + 0.721979i \(0.256767\pi\)
\(104\) −42.0652 −0.0396618
\(105\) 0 0
\(106\) −473.823 −0.434168
\(107\) −669.877 + 669.877i −0.605229 + 0.605229i −0.941695 0.336467i \(-0.890768\pi\)
0.336467 + 0.941695i \(0.390768\pi\)
\(108\) 0 0
\(109\) 1174.82i 1.03236i −0.856479 0.516182i \(-0.827353\pi\)
0.856479 0.516182i \(-0.172647\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1656.55 1656.55i −1.39759 1.39759i
\(113\) −594.951 594.951i −0.495295 0.495295i 0.414675 0.909970i \(-0.363895\pi\)
−0.909970 + 0.414675i \(0.863895\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 609.564i 0.487902i
\(117\) 0 0
\(118\) 1865.73 1865.73i 1.45554 1.45554i
\(119\) 2105.28 1.62177
\(120\) 0 0
\(121\) −448.994 −0.337336
\(122\) 1683.84 1683.84i 1.24957 1.24957i
\(123\) 0 0
\(124\) 1425.36i 1.03227i
\(125\) 0 0
\(126\) 0 0
\(127\) 137.380 + 137.380i 0.0959882 + 0.0959882i 0.753470 0.657482i \(-0.228378\pi\)
−0.657482 + 0.753470i \(0.728378\pi\)
\(128\) 104.604 + 104.604i 0.0722327 + 0.0722327i
\(129\) 0 0
\(130\) 0 0
\(131\) 492.508i 0.328478i 0.986421 + 0.164239i \(0.0525168\pi\)
−0.986421 + 0.164239i \(0.947483\pi\)
\(132\) 0 0
\(133\) −1473.16 + 1473.16i −0.960445 + 0.960445i
\(134\) 34.9082 0.0225045
\(135\) 0 0
\(136\) −68.8514 −0.0434115
\(137\) −176.482 + 176.482i −0.110057 + 0.110057i −0.759991 0.649934i \(-0.774797\pi\)
0.649934 + 0.759991i \(0.274797\pi\)
\(138\) 0 0
\(139\) 1224.98i 0.747491i 0.927531 + 0.373746i \(0.121927\pi\)
−0.927531 + 0.373746i \(0.878073\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2104.19 + 2104.19i 1.24352 + 1.24352i
\(143\) 1085.11 + 1085.11i 0.634556 + 0.634556i
\(144\) 0 0
\(145\) 0 0
\(146\) 2346.57i 1.33016i
\(147\) 0 0
\(148\) 627.784 627.784i 0.348673 0.348673i
\(149\) 41.9404 0.0230597 0.0115298 0.999934i \(-0.496330\pi\)
0.0115298 + 0.999934i \(0.496330\pi\)
\(150\) 0 0
\(151\) −47.2182 −0.0254474 −0.0127237 0.999919i \(-0.504050\pi\)
−0.0127237 + 0.999919i \(0.504050\pi\)
\(152\) 48.1784 48.1784i 0.0257091 0.0257091i
\(153\) 0 0
\(154\) 5913.06i 3.09408i
\(155\) 0 0
\(156\) 0 0
\(157\) 1856.06 + 1856.06i 0.943502 + 0.943502i 0.998487 0.0549853i \(-0.0175112\pi\)
−0.0549853 + 0.998487i \(0.517511\pi\)
\(158\) −2314.40 2314.40i −1.16534 1.16534i
\(159\) 0 0
\(160\) 0 0
\(161\) 7097.97i 3.47452i
\(162\) 0 0
\(163\) −295.059 + 295.059i −0.141784 + 0.141784i −0.774436 0.632652i \(-0.781966\pi\)
0.632652 + 0.774436i \(0.281966\pi\)
\(164\) −108.082 −0.0514623
\(165\) 0 0
\(166\) −2595.53 −1.21357
\(167\) −1081.41 + 1081.41i −0.501092 + 0.501092i −0.911777 0.410685i \(-0.865289\pi\)
0.410685 + 0.911777i \(0.365289\pi\)
\(168\) 0 0
\(169\) 874.000i 0.397815i
\(170\) 0 0
\(171\) 0 0
\(172\) −1172.96 1172.96i −0.519983 0.519983i
\(173\) −2369.97 2369.97i −1.04154 1.04154i −0.999099 0.0424371i \(-0.986488\pi\)
−0.0424371 0.999099i \(-0.513512\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2795.05i 1.19707i
\(177\) 0 0
\(178\) −1812.52 + 1812.52i −0.763225 + 0.763225i
\(179\) −2631.01 −1.09861 −0.549304 0.835623i \(-0.685107\pi\)
−0.549304 + 0.835623i \(0.685107\pi\)
\(180\) 0 0
\(181\) −492.319 −0.202176 −0.101088 0.994878i \(-0.532232\pi\)
−0.101088 + 0.994878i \(0.532232\pi\)
\(182\) 3604.69 3604.69i 1.46812 1.46812i
\(183\) 0 0
\(184\) 232.133i 0.0930058i
\(185\) 0 0
\(186\) 0 0
\(187\) 1776.09 + 1776.09i 0.694548 + 0.694548i
\(188\) −1534.23 1534.23i −0.595187 0.595187i
\(189\) 0 0
\(190\) 0 0
\(191\) 1285.52i 0.487000i 0.969901 + 0.243500i \(0.0782956\pi\)
−0.969901 + 0.243500i \(0.921704\pi\)
\(192\) 0 0
\(193\) 49.9908 49.9908i 0.0186446 0.0186446i −0.697723 0.716368i \(-0.745803\pi\)
0.716368 + 0.697723i \(0.245803\pi\)
\(194\) 2082.35 0.770640
\(195\) 0 0
\(196\) 6995.11 2.54924
\(197\) 3313.77 3313.77i 1.19846 1.19846i 0.223829 0.974628i \(-0.428144\pi\)
0.974628 0.223829i \(-0.0718557\pi\)
\(198\) 0 0
\(199\) 1653.72i 0.589092i −0.955637 0.294546i \(-0.904832\pi\)
0.955637 0.294546i \(-0.0951684\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −4427.32 4427.32i −1.54211 1.54211i
\(203\) 1977.39 + 1977.39i 0.683671 + 0.683671i
\(204\) 0 0
\(205\) 0 0
\(206\) 176.145i 0.0595758i
\(207\) 0 0
\(208\) −1703.91 + 1703.91i −0.568003 + 0.568003i
\(209\) −2485.62 −0.822649
\(210\) 0 0
\(211\) −3436.40 −1.12119 −0.560597 0.828089i \(-0.689428\pi\)
−0.560597 + 0.828089i \(0.689428\pi\)
\(212\) −651.616 + 651.616i −0.211100 + 0.211100i
\(213\) 0 0
\(214\) 3754.69i 1.19937i
\(215\) 0 0
\(216\) 0 0
\(217\) −4623.78 4623.78i −1.44646 1.44646i
\(218\) −3292.46 3292.46i −1.02291 1.02291i
\(219\) 0 0
\(220\) 0 0
\(221\) 2165.46i 0.659116i
\(222\) 0 0
\(223\) −2589.81 + 2589.81i −0.777699 + 0.777699i −0.979439 0.201740i \(-0.935340\pi\)
0.201740 + 0.979439i \(0.435340\pi\)
\(224\) −8957.88 −2.67198
\(225\) 0 0
\(226\) −3334.72 −0.981515
\(227\) −3944.75 + 3944.75i −1.15340 + 1.15340i −0.167536 + 0.985866i \(0.553581\pi\)
−0.985866 + 0.167536i \(0.946419\pi\)
\(228\) 0 0
\(229\) 2269.08i 0.654783i −0.944889 0.327391i \(-0.893830\pi\)
0.944889 0.327391i \(-0.106170\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −64.6687 64.6687i −0.0183005 0.0183005i
\(233\) 1757.84 + 1757.84i 0.494247 + 0.494247i 0.909642 0.415394i \(-0.136356\pi\)
−0.415394 + 0.909642i \(0.636356\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5131.61i 1.41542i
\(237\) 0 0
\(238\) 5900.09 5900.09i 1.60692 1.60692i
\(239\) −3570.92 −0.966458 −0.483229 0.875494i \(-0.660536\pi\)
−0.483229 + 0.875494i \(0.660536\pi\)
\(240\) 0 0
\(241\) 6036.32 1.61342 0.806708 0.590950i \(-0.201247\pi\)
0.806708 + 0.590950i \(0.201247\pi\)
\(242\) −1258.31 + 1258.31i −0.334245 + 0.334245i
\(243\) 0 0
\(244\) 4631.32i 1.21512i
\(245\) 0 0
\(246\) 0 0
\(247\) 1515.27 + 1515.27i 0.390341 + 0.390341i
\(248\) 151.217 + 151.217i 0.0387188 + 0.0387188i
\(249\) 0 0
\(250\) 0 0
\(251\) 3085.33i 0.775874i −0.921686 0.387937i \(-0.873188\pi\)
0.921686 0.387937i \(-0.126812\pi\)
\(252\) 0 0
\(253\) −5988.09 + 5988.09i −1.48802 + 1.48802i
\(254\) 770.020 0.190218
\(255\) 0 0
\(256\) 4378.26 1.06891
\(257\) 490.380 490.380i 0.119023 0.119023i −0.645086 0.764110i \(-0.723179\pi\)
0.764110 + 0.645086i \(0.223179\pi\)
\(258\) 0 0
\(259\) 4072.98i 0.977153i
\(260\) 0 0
\(261\) 0 0
\(262\) 1380.26 + 1380.26i 0.325469 + 0.325469i
\(263\) −157.421 157.421i −0.0369087 0.0369087i 0.688412 0.725320i \(-0.258308\pi\)
−0.725320 + 0.688412i \(0.758308\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 8257.11i 1.90329i
\(267\) 0 0
\(268\) 48.0067 48.0067i 0.0109421 0.0109421i
\(269\) 6197.83 1.40479 0.702395 0.711787i \(-0.252114\pi\)
0.702395 + 0.711787i \(0.252114\pi\)
\(270\) 0 0
\(271\) −4561.66 −1.02251 −0.511257 0.859428i \(-0.670820\pi\)
−0.511257 + 0.859428i \(0.670820\pi\)
\(272\) −2788.92 + 2788.92i −0.621703 + 0.621703i
\(273\) 0 0
\(274\) 989.185i 0.218098i
\(275\) 0 0
\(276\) 0 0
\(277\) −900.134 900.134i −0.195248 0.195248i 0.602711 0.797960i \(-0.294087\pi\)
−0.797960 + 0.602711i \(0.794087\pi\)
\(278\) 3433.02 + 3433.02i 0.740644 + 0.740644i
\(279\) 0 0
\(280\) 0 0
\(281\) 4485.95i 0.952346i 0.879352 + 0.476173i \(0.157976\pi\)
−0.879352 + 0.476173i \(0.842024\pi\)
\(282\) 0 0
\(283\) 4735.98 4735.98i 0.994788 0.994788i −0.00519838 0.999986i \(-0.501655\pi\)
0.999986 + 0.00519838i \(0.00165470\pi\)
\(284\) 5787.49 1.20924
\(285\) 0 0
\(286\) 6082.08 1.25749
\(287\) −350.612 + 350.612i −0.0721113 + 0.0721113i
\(288\) 0 0
\(289\) 1368.62i 0.278570i
\(290\) 0 0
\(291\) 0 0
\(292\) −3227.07 3227.07i −0.646747 0.646747i
\(293\) −4617.95 4617.95i −0.920763 0.920763i 0.0763199 0.997083i \(-0.475683\pi\)
−0.997083 + 0.0763199i \(0.975683\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 133.203i 0.0261564i
\(297\) 0 0
\(298\) 117.539 117.539i 0.0228484 0.0228484i
\(299\) 7300.86 1.41211
\(300\) 0 0
\(301\) −7609.98 −1.45725
\(302\) −132.330 + 132.330i −0.0252143 + 0.0252143i
\(303\) 0 0
\(304\) 3903.06i 0.736369i
\(305\) 0 0
\(306\) 0 0
\(307\) 5000.27 + 5000.27i 0.929578 + 0.929578i 0.997678 0.0681008i \(-0.0216940\pi\)
−0.0681008 + 0.997678i \(0.521694\pi\)
\(308\) 8131.81 + 8131.81i 1.50439 + 1.50439i
\(309\) 0 0
\(310\) 0 0
\(311\) 6874.37i 1.25341i −0.779257 0.626704i \(-0.784404\pi\)
0.779257 0.626704i \(-0.215596\pi\)
\(312\) 0 0
\(313\) 3422.07 3422.07i 0.617976 0.617976i −0.327036 0.945012i \(-0.606050\pi\)
0.945012 + 0.327036i \(0.106050\pi\)
\(314\) 10403.3 1.86972
\(315\) 0 0
\(316\) −6365.66 −1.13322
\(317\) 4689.86 4689.86i 0.830943 0.830943i −0.156703 0.987646i \(-0.550086\pi\)
0.987646 + 0.156703i \(0.0500865\pi\)
\(318\) 0 0
\(319\) 3336.38i 0.585584i
\(320\) 0 0
\(321\) 0 0
\(322\) 19892.2 + 19892.2i 3.44270 + 3.44270i
\(323\) 2480.16 + 2480.16i 0.427244 + 0.427244i
\(324\) 0 0
\(325\) 0 0
\(326\) 1653.82i 0.280971i
\(327\) 0 0
\(328\) 11.4665 11.4665i 0.00193027 0.00193027i
\(329\) −9953.87 −1.66801
\(330\) 0 0
\(331\) 952.081 0.158100 0.0790500 0.996871i \(-0.474811\pi\)
0.0790500 + 0.996871i \(0.474811\pi\)
\(332\) −3569.45 + 3569.45i −0.590057 + 0.590057i
\(333\) 0 0
\(334\) 6061.36i 0.993003i
\(335\) 0 0
\(336\) 0 0
\(337\) −4007.99 4007.99i −0.647860 0.647860i 0.304615 0.952476i \(-0.401472\pi\)
−0.952476 + 0.304615i \(0.901472\pi\)
\(338\) 2449.40 + 2449.40i 0.394171 + 0.394171i
\(339\) 0 0
\(340\) 0 0
\(341\) 7801.55i 1.23894i
\(342\) 0 0
\(343\) 14115.0 14115.0i 2.22198 2.22198i
\(344\) 248.878 0.0390075
\(345\) 0 0
\(346\) −13283.8 −2.06399
\(347\) 1873.29 1873.29i 0.289809 0.289809i −0.547196 0.837005i \(-0.684305\pi\)
0.837005 + 0.547196i \(0.184305\pi\)
\(348\) 0 0
\(349\) 10642.2i 1.63228i 0.577857 + 0.816138i \(0.303889\pi\)
−0.577857 + 0.816138i \(0.696111\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −7557.17 7557.17i −1.14431 1.14431i
\(353\) 5699.37 + 5699.37i 0.859339 + 0.859339i 0.991260 0.131921i \(-0.0421146\pi\)
−0.131921 + 0.991260i \(0.542115\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 4985.25i 0.742185i
\(357\) 0 0
\(358\) −7373.45 + 7373.45i −1.08854 + 1.08854i
\(359\) 12273.5 1.80437 0.902186 0.431347i \(-0.141962\pi\)
0.902186 + 0.431347i \(0.141962\pi\)
\(360\) 0 0
\(361\) 3388.04 0.493955
\(362\) −1379.73 + 1379.73i −0.200323 + 0.200323i
\(363\) 0 0
\(364\) 9914.55i 1.42765i
\(365\) 0 0
\(366\) 0 0
\(367\) −2865.51 2865.51i −0.407571 0.407571i 0.473320 0.880891i \(-0.343055\pi\)
−0.880891 + 0.473320i \(0.843055\pi\)
\(368\) −9402.86 9402.86i −1.33195 1.33195i
\(369\) 0 0
\(370\) 0 0
\(371\) 4227.59i 0.591606i
\(372\) 0 0
\(373\) −3859.53 + 3859.53i −0.535762 + 0.535762i −0.922281 0.386519i \(-0.873677\pi\)
0.386519 + 0.922281i \(0.373677\pi\)
\(374\) 9955.04 1.37637
\(375\) 0 0
\(376\) 325.533 0.0446491
\(377\) 2033.91 2033.91i 0.277856 0.277856i
\(378\) 0 0
\(379\) 2981.39i 0.404073i −0.979378 0.202036i \(-0.935244\pi\)
0.979378 0.202036i \(-0.0647560\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3602.69 + 3602.69i 0.482539 + 0.482539i
\(383\) 10252.4 + 10252.4i 1.36782 + 1.36782i 0.863540 + 0.504280i \(0.168242\pi\)
0.504280 + 0.863540i \(0.331758\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 280.200i 0.0369477i
\(387\) 0 0
\(388\) 2863.71 2863.71i 0.374698 0.374698i
\(389\) −6840.61 −0.891601 −0.445801 0.895132i \(-0.647081\pi\)
−0.445801 + 0.895132i \(0.647081\pi\)
\(390\) 0 0
\(391\) 11949.9 1.54561
\(392\) −742.111 + 742.111i −0.0956181 + 0.0956181i
\(393\) 0 0
\(394\) 18573.8i 2.37496i
\(395\) 0 0
\(396\) 0 0
\(397\) 288.543 + 288.543i 0.0364774 + 0.0364774i 0.725110 0.688633i \(-0.241789\pi\)
−0.688633 + 0.725110i \(0.741789\pi\)
\(398\) −4634.59 4634.59i −0.583696 0.583696i
\(399\) 0 0
\(400\) 0 0
\(401\) 4765.08i 0.593409i −0.954969 0.296704i \(-0.904112\pi\)
0.954969 0.296704i \(-0.0958876\pi\)
\(402\) 0 0
\(403\) −4755.94 + 4755.94i −0.587867 + 0.587867i
\(404\) −12177.2 −1.49959
\(405\) 0 0
\(406\) 11083.3 1.35482
\(407\) 3436.10 3436.10i 0.418480 0.418480i
\(408\) 0 0
\(409\) 8132.87i 0.983239i 0.870810 + 0.491619i \(0.163595\pi\)
−0.870810 + 0.491619i \(0.836405\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 242.240 + 242.240i 0.0289668 + 0.0289668i
\(413\) −16646.6 16646.6i −1.98335 1.98335i
\(414\) 0 0
\(415\) 0 0
\(416\) 9213.93i 1.08594i
\(417\) 0 0
\(418\) −6965.98 + 6965.98i −0.815113 + 0.815113i
\(419\) 222.003 0.0258844 0.0129422 0.999916i \(-0.495880\pi\)
0.0129422 + 0.999916i \(0.495880\pi\)
\(420\) 0 0
\(421\) 4412.17 0.510774 0.255387 0.966839i \(-0.417797\pi\)
0.255387 + 0.966839i \(0.417797\pi\)
\(422\) −9630.58 + 9630.58i −1.11092 + 1.11092i
\(423\) 0 0
\(424\) 138.260i 0.0158361i
\(425\) 0 0
\(426\) 0 0
\(427\) −15023.7 15023.7i −1.70269 1.70269i
\(428\) 5163.55 + 5163.55i 0.583153 + 0.583153i
\(429\) 0 0
\(430\) 0 0
\(431\) 10285.6i 1.14952i −0.818323 0.574758i \(-0.805096\pi\)
0.818323 0.574758i \(-0.194904\pi\)
\(432\) 0 0
\(433\) 6616.98 6616.98i 0.734392 0.734392i −0.237094 0.971487i \(-0.576195\pi\)
0.971487 + 0.237094i \(0.0761951\pi\)
\(434\) −25916.4 −2.86642
\(435\) 0 0
\(436\) −9055.78 −0.994709
\(437\) −8361.88 + 8361.88i −0.915339 + 0.915339i
\(438\) 0 0
\(439\) 11483.9i 1.24852i −0.781219 0.624258i \(-0.785402\pi\)
0.781219 0.624258i \(-0.214598\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6068.74 6068.74i −0.653078 0.653078i
\(443\) 3420.37 + 3420.37i 0.366832 + 0.366832i 0.866320 0.499489i \(-0.166479\pi\)
−0.499489 + 0.866320i \(0.666479\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 14516.0i 1.54115i
\(447\) 0 0
\(448\) −11852.2 + 11852.2i −1.24992 + 1.24992i
\(449\) −11995.6 −1.26082 −0.630410 0.776262i \(-0.717113\pi\)
−0.630410 + 0.776262i \(0.717113\pi\)
\(450\) 0 0
\(451\) −591.576 −0.0617655
\(452\) −4586.01 + 4586.01i −0.477229 + 0.477229i
\(453\) 0 0
\(454\) 22110.5i 2.28567i
\(455\) 0 0
\(456\) 0 0
\(457\) 3243.45 + 3243.45i 0.331996 + 0.331996i 0.853344 0.521348i \(-0.174571\pi\)
−0.521348 + 0.853344i \(0.674571\pi\)
\(458\) −6359.14 6359.14i −0.648785 0.648785i
\(459\) 0 0
\(460\) 0 0
\(461\) 15008.4i 1.51629i −0.652087 0.758144i \(-0.726106\pi\)
0.652087 0.758144i \(-0.273894\pi\)
\(462\) 0 0
\(463\) 1250.28 1250.28i 0.125498 0.125498i −0.641568 0.767066i \(-0.721716\pi\)
0.767066 + 0.641568i \(0.221716\pi\)
\(464\) −5238.98 −0.524168
\(465\) 0 0
\(466\) 9852.73 0.979440
\(467\) 4274.49 4274.49i 0.423554 0.423554i −0.462871 0.886426i \(-0.653181\pi\)
0.886426 + 0.462871i \(0.153181\pi\)
\(468\) 0 0
\(469\) 311.461i 0.0306651i
\(470\) 0 0
\(471\) 0 0
\(472\) 544.412 + 544.412i 0.0530903 + 0.0530903i
\(473\) −6420.04 6420.04i −0.624088 0.624088i
\(474\) 0 0
\(475\) 0 0
\(476\) 16227.9i 1.56262i
\(477\) 0 0
\(478\) −10007.6 + 10007.6i −0.957605 + 0.957605i
\(479\) 7189.29 0.685776 0.342888 0.939376i \(-0.388595\pi\)
0.342888 + 0.939376i \(0.388595\pi\)
\(480\) 0 0
\(481\) −4189.40 −0.397132
\(482\) 16916.9 16916.9i 1.59864 1.59864i
\(483\) 0 0
\(484\) 3460.94i 0.325032i
\(485\) 0 0
\(486\) 0 0
\(487\) −923.729 923.729i −0.0859510 0.0859510i 0.662824 0.748775i \(-0.269358\pi\)
−0.748775 + 0.662824i \(0.769358\pi\)
\(488\) 491.337 + 491.337i 0.0455774 + 0.0455774i
\(489\) 0 0
\(490\) 0 0
\(491\) 434.588i 0.0399444i −0.999801 0.0199722i \(-0.993642\pi\)
0.999801 0.0199722i \(-0.00635777\pi\)
\(492\) 0 0
\(493\) 3329.06 3329.06i 0.304124 0.304124i
\(494\) 8493.13 0.773531
\(495\) 0 0
\(496\) 12250.5 1.10900
\(497\) 18774.2 18774.2i 1.69445 1.69445i
\(498\) 0 0
\(499\) 7228.02i 0.648438i −0.945982 0.324219i \(-0.894899\pi\)
0.945982 0.324219i \(-0.105101\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −8646.70 8646.70i −0.768767 0.768767i
\(503\) −1240.98 1240.98i −0.110005 0.110005i 0.649962 0.759967i \(-0.274785\pi\)
−0.759967 + 0.649962i \(0.774785\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 33563.5i 2.94877i
\(507\) 0 0
\(508\) 1058.95 1058.95i 0.0924871 0.0924871i
\(509\) −20683.3 −1.80112 −0.900561 0.434730i \(-0.856844\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(510\) 0 0
\(511\) −20936.8 −1.81250
\(512\) 11433.3 11433.3i 0.986887 0.986887i
\(513\) 0 0
\(514\) 2748.59i 0.235866i
\(515\) 0 0
\(516\) 0 0
\(517\) −8397.42 8397.42i −0.714349 0.714349i
\(518\) −11414.6 11414.6i −0.968201 0.968201i
\(519\) 0 0
\(520\) 0 0
\(521\) 1904.89i 0.160182i 0.996788 + 0.0800908i \(0.0255210\pi\)
−0.996788 + 0.0800908i \(0.974479\pi\)
\(522\) 0 0
\(523\) 1799.72 1799.72i 0.150471 0.150471i −0.627857 0.778329i \(-0.716068\pi\)
0.778329 + 0.627857i \(0.216068\pi\)
\(524\) 3796.35 0.316497
\(525\) 0 0
\(526\) −882.349 −0.0731411
\(527\) −7784.44 + 7784.44i −0.643445 + 0.643445i
\(528\) 0 0
\(529\) 28122.2i 2.31135i
\(530\) 0 0
\(531\) 0 0
\(532\) 11355.4 + 11355.4i 0.925413 + 0.925413i
\(533\) 360.634 + 360.634i 0.0293073 + 0.0293073i
\(534\) 0 0
\(535\) 0 0
\(536\) 10.1861i 0.000820842i
\(537\) 0 0
\(538\) 17369.5 17369.5i 1.39192 1.39192i
\(539\) 38286.9 3.05962
\(540\) 0 0
\(541\) −19472.7 −1.54749 −0.773747 0.633494i \(-0.781620\pi\)
−0.773747 + 0.633494i \(0.781620\pi\)
\(542\) −12784.1 + 12784.1i −1.01315 + 1.01315i
\(543\) 0 0
\(544\) 15081.2i 1.18860i
\(545\) 0 0
\(546\) 0 0
\(547\) 15899.0 + 15899.0i 1.24277 + 1.24277i 0.958849 + 0.283916i \(0.0916336\pi\)
0.283916 + 0.958849i \(0.408366\pi\)
\(548\) 1360.36 + 1360.36i 0.106043 + 0.106043i
\(549\) 0 0
\(550\) 0 0
\(551\) 4658.98i 0.360217i
\(552\) 0 0
\(553\) −20649.8 + 20649.8i −1.58792 + 1.58792i
\(554\) −5045.28 −0.386920
\(555\) 0 0
\(556\) 9442.38 0.720227
\(557\) 2403.47 2403.47i 0.182834 0.182834i −0.609756 0.792589i \(-0.708732\pi\)
0.792589 + 0.609756i \(0.208732\pi\)
\(558\) 0 0
\(559\) 7827.51i 0.592251i
\(560\) 0 0
\(561\) 0 0
\(562\) 12571.9 + 12571.9i 0.943622 + 0.943622i
\(563\) 7264.48 + 7264.48i 0.543803 + 0.543803i 0.924642 0.380838i \(-0.124365\pi\)
−0.380838 + 0.924642i \(0.624365\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 26545.4i 1.97135i
\(567\) 0 0
\(568\) −613.995 + 613.995i −0.0453568 + 0.0453568i
\(569\) −5273.08 −0.388505 −0.194252 0.980952i \(-0.562228\pi\)
−0.194252 + 0.980952i \(0.562228\pi\)
\(570\) 0 0
\(571\) 14061.0 1.03053 0.515267 0.857030i \(-0.327693\pi\)
0.515267 + 0.857030i \(0.327693\pi\)
\(572\) 8364.26 8364.26i 0.611411 0.611411i
\(573\) 0 0
\(574\) 1965.19i 0.142901i
\(575\) 0 0
\(576\) 0 0
\(577\) 10570.7 + 10570.7i 0.762673 + 0.762673i 0.976805 0.214131i \(-0.0686921\pi\)
−0.214131 + 0.976805i \(0.568692\pi\)
\(578\) 3835.57 + 3835.57i 0.276018 + 0.276018i
\(579\) 0 0
\(580\) 0 0
\(581\) 23158.1i 1.65363i
\(582\) 0 0
\(583\) −3566.54 + 3566.54i −0.253364 + 0.253364i
\(584\) 684.720 0.0485170
\(585\) 0 0
\(586\) −25883.8 −1.82466
\(587\) −7292.50 + 7292.50i −0.512766 + 0.512766i −0.915373 0.402607i \(-0.868104\pi\)
0.402607 + 0.915373i \(0.368104\pi\)
\(588\) 0 0
\(589\) 10894.2i 0.762121i
\(590\) 0 0
\(591\) 0 0
\(592\) 5395.58 + 5395.58i 0.374589 + 0.374589i
\(593\) 454.363 + 454.363i 0.0314645 + 0.0314645i 0.722664 0.691199i \(-0.242917\pi\)
−0.691199 + 0.722664i \(0.742917\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 323.285i 0.0222186i
\(597\) 0 0
\(598\) 20460.8 20460.8i 1.39917 1.39917i
\(599\) −7281.47 −0.496683 −0.248341 0.968673i \(-0.579885\pi\)
−0.248341 + 0.968673i \(0.579885\pi\)
\(600\) 0 0
\(601\) 14273.8 0.968786 0.484393 0.874850i \(-0.339040\pi\)
0.484393 + 0.874850i \(0.339040\pi\)
\(602\) −21327.1 + 21327.1i −1.44390 + 1.44390i
\(603\) 0 0
\(604\) 363.967i 0.0245192i
\(605\) 0 0
\(606\) 0 0
\(607\) 7824.40 + 7824.40i 0.523200 + 0.523200i 0.918536 0.395336i \(-0.129372\pi\)
−0.395336 + 0.918536i \(0.629372\pi\)
\(608\) −10553.0 10553.0i −0.703914 0.703914i
\(609\) 0 0
\(610\) 0 0
\(611\) 10238.4i 0.677907i
\(612\) 0 0
\(613\) −2893.58 + 2893.58i −0.190653 + 0.190653i −0.795978 0.605325i \(-0.793043\pi\)
0.605325 + 0.795978i \(0.293043\pi\)
\(614\) 28026.7 1.84212
\(615\) 0 0
\(616\) −1725.41 −0.112855
\(617\) −2847.70 + 2847.70i −0.185809 + 0.185809i −0.793881 0.608073i \(-0.791943\pi\)
0.608073 + 0.793881i \(0.291943\pi\)
\(618\) 0 0
\(619\) 16644.3i 1.08076i −0.841421 0.540380i \(-0.818281\pi\)
0.841421 0.540380i \(-0.181719\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −19265.5 19265.5i −1.24193 1.24193i
\(623\) 16171.8 + 16171.8i 1.03998 + 1.03998i
\(624\) 0 0
\(625\) 0 0
\(626\) 19180.8i 1.22463i
\(627\) 0 0
\(628\) 14306.9 14306.9i 0.909088 0.909088i
\(629\) −6857.13 −0.434677
\(630\) 0 0
\(631\) −5327.30 −0.336096 −0.168048 0.985779i \(-0.553746\pi\)
−0.168048 + 0.985779i \(0.553746\pi\)
\(632\) 675.333 675.333i 0.0425053 0.0425053i
\(633\) 0 0
\(634\) 26286.8i 1.64666i
\(635\) 0 0
\(636\) 0 0
\(637\) −23340.3 23340.3i −1.45177 1.45177i
\(638\) 9350.26 + 9350.26i 0.580220 + 0.580220i
\(639\) 0 0
\(640\) 0 0
\(641\) 16450.6i 1.01367i 0.862044 + 0.506834i \(0.169184\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(642\) 0 0
\(643\) 21894.3 21894.3i 1.34281 1.34281i 0.449555 0.893252i \(-0.351582\pi\)
0.893252 0.449555i \(-0.148418\pi\)
\(644\) 54712.6 3.34779
\(645\) 0 0
\(646\) 13901.4 0.846661
\(647\) 7768.11 7768.11i 0.472018 0.472018i −0.430549 0.902567i \(-0.641680\pi\)
0.902567 + 0.430549i \(0.141680\pi\)
\(648\) 0 0
\(649\) 28087.3i 1.69880i
\(650\) 0 0
\(651\) 0 0
\(652\) 2274.38 + 2274.38i 0.136613 + 0.136613i
\(653\) 14364.4 + 14364.4i 0.860831 + 0.860831i 0.991435 0.130603i \(-0.0416914\pi\)
−0.130603 + 0.991435i \(0.541691\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 928.928i 0.0552874i
\(657\) 0 0
\(658\) −27895.9 + 27895.9i −1.65273 + 1.65273i
\(659\) −18185.5 −1.07497 −0.537486 0.843272i \(-0.680626\pi\)
−0.537486 + 0.843272i \(0.680626\pi\)
\(660\) 0 0
\(661\) 8833.96 0.519820 0.259910 0.965633i \(-0.416307\pi\)
0.259910 + 0.965633i \(0.416307\pi\)
\(662\) 2668.22 2668.22i 0.156652 0.156652i
\(663\) 0 0
\(664\) 757.366i 0.0442643i
\(665\) 0 0
\(666\) 0 0
\(667\) 11223.9 + 11223.9i 0.651564 + 0.651564i
\(668\) 8335.76 + 8335.76i 0.482815 + 0.482815i
\(669\) 0 0
\(670\) 0 0
\(671\) 25349.0i 1.45840i
\(672\) 0 0
\(673\) −12769.6 + 12769.6i −0.731398 + 0.731398i −0.970897 0.239499i \(-0.923017\pi\)
0.239499 + 0.970897i \(0.423017\pi\)
\(674\) −22464.9 −1.28385
\(675\) 0 0
\(676\) 6736.97 0.383305
\(677\) 1478.18 1478.18i 0.0839157 0.0839157i −0.663903 0.747819i \(-0.731101\pi\)
0.747819 + 0.663903i \(0.231101\pi\)
\(678\) 0 0
\(679\) 18579.4i 1.05009i
\(680\) 0 0
\(681\) 0 0
\(682\) −21864.0 21864.0i −1.22759 1.22759i
\(683\) 2681.69 + 2681.69i 0.150237 + 0.150237i 0.778224 0.627987i \(-0.216121\pi\)
−0.627987 + 0.778224i \(0.716121\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 79115.0i 4.40324i
\(687\) 0 0
\(688\) 10081.1 10081.1i 0.558633 0.558633i
\(689\) 4348.44 0.240439
\(690\) 0 0
\(691\) −23210.5 −1.27782 −0.638908 0.769283i \(-0.720614\pi\)
−0.638908 + 0.769283i \(0.720614\pi\)
\(692\) −18268.2 + 18268.2i −1.00355 + 1.00355i
\(693\) 0 0
\(694\) 10499.9i 0.574308i
\(695\) 0 0
\(696\) 0 0
\(697\) 590.278 + 590.278i 0.0320780 + 0.0320780i
\(698\) 29825.0 + 29825.0i 1.61732 + 1.61732i
\(699\) 0 0
\(700\) 0 0
\(701\) 26169.3i 1.40999i 0.709213 + 0.704995i \(0.249051\pi\)
−0.709213 + 0.704995i \(0.750949\pi\)
\(702\) 0 0
\(703\) 4798.24 4798.24i 0.257424 0.257424i
\(704\) −19997.8 −1.07059
\(705\) 0 0
\(706\) 31945.1 1.70293
\(707\) −39501.9 + 39501.9i −2.10130 + 2.10130i
\(708\) 0 0
\(709\) 13604.6i 0.720636i 0.932830 + 0.360318i \(0.117332\pi\)
−0.932830 + 0.360318i \(0.882668\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −528.886 528.886i −0.0278382 0.0278382i
\(713\) −26245.3 26245.3i −1.37853 1.37853i
\(714\) 0 0
\(715\) 0 0
\(716\) 20280.4i 1.05854i
\(717\) 0 0
\(718\) 34396.6 34396.6i 1.78784 1.78784i
\(719\) −15020.4 −0.779088 −0.389544 0.921008i \(-0.627367\pi\)
−0.389544 + 0.921008i \(0.627367\pi\)
\(720\) 0 0
\(721\) 1571.62 0.0811792
\(722\) 9495.04 9495.04i 0.489430 0.489430i
\(723\) 0 0
\(724\) 3794.89i 0.194801i
\(725\) 0 0
\(726\) 0 0
\(727\) −1195.38 1195.38i −0.0609824 0.0609824i 0.675958 0.736940i \(-0.263730\pi\)
−0.736940 + 0.675958i \(0.763730\pi\)
\(728\) 1051.83 + 1051.83i 0.0535489 + 0.0535489i
\(729\) 0 0
\(730\) 0 0
\(731\) 12811.9i 0.648243i
\(732\) 0 0
\(733\) −14097.2 + 14097.2i −0.710359 + 0.710359i −0.966610 0.256251i \(-0.917513\pi\)
0.256251 + 0.966610i \(0.417513\pi\)
\(734\) −16061.3 −0.807674
\(735\) 0 0
\(736\) −50846.3 −2.54649
\(737\) 262.759 262.759i 0.0131328 0.0131328i
\(738\) 0 0
\(739\) 8052.39i 0.400828i −0.979711 0.200414i \(-0.935771\pi\)
0.979711 0.200414i \(-0.0642287\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 11847.9 + 11847.9i 0.586186 + 0.586186i
\(743\) 6706.82 + 6706.82i 0.331156 + 0.331156i 0.853026 0.521869i \(-0.174765\pi\)
−0.521869 + 0.853026i \(0.674765\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 21632.8i 1.06171i
\(747\) 0 0
\(748\) 13690.5 13690.5i 0.669215 0.669215i
\(749\) 33500.4 1.63428
\(750\) 0 0
\(751\) −17782.1 −0.864018 −0.432009 0.901869i \(-0.642195\pi\)
−0.432009 + 0.901869i \(0.642195\pi\)
\(752\) 13186.1 13186.1i 0.639427 0.639427i
\(753\) 0 0
\(754\) 11400.1i 0.550621i
\(755\) 0 0
\(756\) 0 0
\(757\) 3547.92 + 3547.92i 0.170345 + 0.170345i 0.787131 0.616786i \(-0.211566\pi\)
−0.616786 + 0.787131i \(0.711566\pi\)
\(758\) −8355.39 8355.39i −0.400371 0.400371i
\(759\) 0 0
\(760\) 0 0
\(761\) 29802.3i 1.41962i −0.704392 0.709811i \(-0.748780\pi\)
0.704392 0.709811i \(-0.251220\pi\)
\(762\) 0 0
\(763\) −29376.3 + 29376.3i −1.39383 + 1.39383i
\(764\) 9909.05 0.469237
\(765\) 0 0
\(766\) 57465.3 2.71058
\(767\) −17122.4 + 17122.4i −0.806069 + 0.806069i
\(768\) 0 0
\(769\) 1720.92i 0.0806994i −0.999186 0.0403497i \(-0.987153\pi\)
0.999186 0.0403497i \(-0.0128472\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −385.339 385.339i −0.0179646 0.0179646i
\(773\) −8247.02 8247.02i −0.383732 0.383732i 0.488713 0.872445i \(-0.337467\pi\)
−0.872445 + 0.488713i \(0.837467\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 607.622i 0.0281087i
\(777\) 0 0
\(778\) −19170.9 + 19170.9i −0.883434 + 0.883434i
\(779\) −826.088 −0.0379944
\(780\) 0 0
\(781\) 31677.2 1.45134
\(782\) 33489.8 33489.8i 1.53145 1.53145i
\(783\) 0 0
\(784\) 60120.5i 2.73872i
\(785\) 0 0
\(786\) 0 0
\(787\) 24948.6 + 24948.6i 1.13001 + 1.13001i 0.990174 + 0.139840i \(0.0446590\pi\)
0.139840 + 0.990174i \(0.455341\pi\)
\(788\) −25543.2 25543.2i −1.15474 1.15474i
\(789\) 0 0
\(790\) 0 0
\(791\) 29753.4i 1.33743i
\(792\) 0 0
\(793\) −15453.1 + 15453.1i −0.692001 + 0.692001i
\(794\) 1617.29 0.0722866
\(795\) 0 0