Properties

Label 882.4.g.bj.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \(x^{4} - x^{3} + 49 x^{2} + 48 x + 2304\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(3.72311 - 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bj.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} -8.00000 q^{8} +(3.44622 + 5.96903i) q^{10} +(-18.0618 - 31.2839i) q^{11} -10.2311 q^{13} +(-8.00000 + 13.8564i) q^{16} +(59.2311 + 102.591i) q^{17} +(-19.3307 + 33.4817i) q^{19} +13.7849 q^{20} -72.2471 q^{22} +(18.1236 - 31.3909i) q^{23} +(56.5618 + 97.9679i) q^{25} +(-10.2311 + 17.7208i) q^{26} -12.1236 q^{29} +(-72.7471 - 126.002i) q^{31} +(16.0000 + 27.7128i) q^{32} +236.924 q^{34} +(0.685331 - 1.18703i) q^{37} +(38.6613 + 66.9634i) q^{38} +(13.7849 - 23.8761i) q^{40} -168.000 q^{41} +299.371 q^{43} +(-72.2471 + 125.136i) q^{44} +(-36.2471 - 62.7818i) q^{46} +(251.355 - 435.359i) q^{47} +226.247 q^{50} +(20.4622 + 35.4416i) q^{52} +(312.556 + 541.363i) q^{53} +124.490 q^{55} +(-12.1236 + 20.9986i) q^{58} +(-21.1098 - 36.5632i) q^{59} +(-219.586 + 380.334i) q^{61} -290.988 q^{62} +64.0000 q^{64} +(17.6293 - 30.5349i) q^{65} +(381.809 + 661.312i) q^{67} +(236.924 - 410.365i) q^{68} +1020.49 q^{71} +(289.642 + 501.674i) q^{73} +(-1.37066 - 2.37406i) q^{74} +154.645 q^{76} +(-471.365 + 816.428i) q^{79} +(-27.5698 - 47.7523i) q^{80} +(-168.000 + 290.985i) q^{82} +474.714 q^{83} -408.247 q^{85} +(299.371 - 518.525i) q^{86} +(144.494 + 250.271i) q^{88} +(410.952 - 711.790i) q^{89} -144.988 q^{92} +(-502.709 - 870.718i) q^{94} +(-66.6178 - 115.385i) q^{95} +1108.16 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} + 7q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} + 7q^{5} - 32q^{8} - 14q^{10} + 25q^{11} + 98q^{13} - 32q^{16} + 98q^{17} - 119q^{19} - 56q^{20} + 100q^{22} - 122q^{23} + 129q^{25} + 98q^{26} + 146q^{29} + 98q^{31} + 64q^{32} + 392q^{34} - 289q^{37} + 238q^{38} - 56q^{40} - 672q^{41} + 614q^{43} + 100q^{44} + 244q^{46} + 672q^{47} + 516q^{50} - 196q^{52} + 375q^{53} + 1526q^{55} + 146q^{58} + 763q^{59} - 406q^{61} + 392q^{62} + 256q^{64} + 654q^{65} + 1041q^{67} + 392q^{68} + 3304q^{71} - 189q^{73} + 578q^{74} + 952q^{76} - 524q^{79} + 112q^{80} - 672q^{82} - 574q^{83} - 1244q^{85} + 614q^{86} - 200q^{88} + 2394q^{89} + 976q^{92} - 1344q^{94} + 706q^{95} + 126q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −1.72311 + 2.98452i −0.154120 + 0.266943i −0.932738 0.360554i \(-0.882587\pi\)
0.778618 + 0.627498i \(0.215921\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 3.44622 + 5.96903i 0.108979 + 0.188757i
\(11\) −18.0618 31.2839i −0.495076 0.857496i 0.504908 0.863173i \(-0.331526\pi\)
−0.999984 + 0.00567700i \(0.998193\pi\)
\(12\) 0 0
\(13\) −10.2311 −0.218277 −0.109138 0.994027i \(-0.534809\pi\)
−0.109138 + 0.994027i \(0.534809\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 59.2311 + 102.591i 0.845038 + 1.46365i 0.885588 + 0.464472i \(0.153756\pi\)
−0.0405493 + 0.999178i \(0.512911\pi\)
\(18\) 0 0
\(19\) −19.3307 + 33.4817i −0.233408 + 0.404275i −0.958809 0.284052i \(-0.908321\pi\)
0.725401 + 0.688327i \(0.241655\pi\)
\(20\) 13.7849 0.154120
\(21\) 0 0
\(22\) −72.2471 −0.700143
\(23\) 18.1236 31.3909i 0.164305 0.284585i −0.772103 0.635497i \(-0.780795\pi\)
0.936408 + 0.350912i \(0.114128\pi\)
\(24\) 0 0
\(25\) 56.5618 + 97.9679i 0.452494 + 0.783743i
\(26\) −10.2311 + 17.7208i −0.0771725 + 0.133667i
\(27\) 0 0
\(28\) 0 0
\(29\) −12.1236 −0.0776306 −0.0388153 0.999246i \(-0.512358\pi\)
−0.0388153 + 0.999246i \(0.512358\pi\)
\(30\) 0 0
\(31\) −72.7471 126.002i −0.421476 0.730018i 0.574608 0.818429i \(-0.305155\pi\)
−0.996084 + 0.0884105i \(0.971821\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 236.924 1.19506
\(35\) 0 0
\(36\) 0 0
\(37\) 0.685331 1.18703i 0.00304507 0.00527422i −0.864499 0.502635i \(-0.832364\pi\)
0.867544 + 0.497361i \(0.165697\pi\)
\(38\) 38.6613 + 66.9634i 0.165045 + 0.285866i
\(39\) 0 0
\(40\) 13.7849 23.8761i 0.0544896 0.0943787i
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 0 0
\(43\) 299.371 1.06171 0.530856 0.847462i \(-0.321871\pi\)
0.530856 + 0.847462i \(0.321871\pi\)
\(44\) −72.2471 + 125.136i −0.247538 + 0.428748i
\(45\) 0 0
\(46\) −36.2471 62.7818i −0.116181 0.201232i
\(47\) 251.355 435.359i 0.780082 1.35114i −0.151812 0.988409i \(-0.548511\pi\)
0.931894 0.362732i \(-0.118156\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 226.247 0.639923
\(51\) 0 0
\(52\) 20.4622 + 35.4416i 0.0545692 + 0.0945167i
\(53\) 312.556 + 541.363i 0.810054 + 1.40305i 0.912825 + 0.408350i \(0.133896\pi\)
−0.102771 + 0.994705i \(0.532771\pi\)
\(54\) 0 0
\(55\) 124.490 0.305204
\(56\) 0 0
\(57\) 0 0
\(58\) −12.1236 + 20.9986i −0.0274466 + 0.0475388i
\(59\) −21.1098 36.5632i −0.0465806 0.0806800i 0.841795 0.539797i \(-0.181499\pi\)
−0.888376 + 0.459117i \(0.848166\pi\)
\(60\) 0 0
\(61\) −219.586 + 380.334i −0.460903 + 0.798307i −0.999006 0.0445717i \(-0.985808\pi\)
0.538103 + 0.842879i \(0.319141\pi\)
\(62\) −290.988 −0.596058
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 17.6293 30.5349i 0.0336408 0.0582675i
\(66\) 0 0
\(67\) 381.809 + 661.312i 0.696200 + 1.20585i 0.969775 + 0.244003i \(0.0784605\pi\)
−0.273575 + 0.961851i \(0.588206\pi\)
\(68\) 236.924 410.365i 0.422519 0.731825i
\(69\) 0 0
\(70\) 0 0
\(71\) 1020.49 1.70578 0.852890 0.522091i \(-0.174848\pi\)
0.852890 + 0.522091i \(0.174848\pi\)
\(72\) 0 0
\(73\) 289.642 + 501.674i 0.464384 + 0.804336i 0.999173 0.0406491i \(-0.0129426\pi\)
−0.534790 + 0.844985i \(0.679609\pi\)
\(74\) −1.37066 2.37406i −0.00215319 0.00372944i
\(75\) 0 0
\(76\) 154.645 0.233408
\(77\) 0 0
\(78\) 0 0
\(79\) −471.365 + 816.428i −0.671300 + 1.16273i 0.306236 + 0.951956i \(0.400930\pi\)
−0.977536 + 0.210770i \(0.932403\pi\)
\(80\) −27.5698 47.7523i −0.0385299 0.0667358i
\(81\) 0 0
\(82\) −168.000 + 290.985i −0.226250 + 0.391876i
\(83\) 474.714 0.627790 0.313895 0.949458i \(-0.398366\pi\)
0.313895 + 0.949458i \(0.398366\pi\)
\(84\) 0 0
\(85\) −408.247 −0.520948
\(86\) 299.371 518.525i 0.375372 0.650163i
\(87\) 0 0
\(88\) 144.494 + 250.271i 0.175036 + 0.303171i
\(89\) 410.952 711.790i 0.489447 0.847748i −0.510479 0.859890i \(-0.670532\pi\)
0.999926 + 0.0121424i \(0.00386515\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −144.988 −0.164305
\(93\) 0 0
\(94\) −502.709 870.718i −0.551601 0.955401i
\(95\) −66.6178 115.385i −0.0719457 0.124614i
\(96\) 0 0
\(97\) 1108.16 1.15997 0.579985 0.814627i \(-0.303058\pi\)
0.579985 + 0.814627i \(0.303058\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 226.247 391.871i 0.226247 0.391871i
\(101\) 942.961 + 1633.26i 0.928991 + 1.60906i 0.785013 + 0.619479i \(0.212656\pi\)
0.143978 + 0.989581i \(0.454011\pi\)
\(102\) 0 0
\(103\) 241.072 417.549i 0.230617 0.399440i −0.727373 0.686242i \(-0.759259\pi\)
0.957990 + 0.286802i \(0.0925923\pi\)
\(104\) 81.8489 0.0771725
\(105\) 0 0
\(106\) 1250.22 1.14559
\(107\) 865.297 1498.74i 0.781789 1.35410i −0.149109 0.988821i \(-0.547641\pi\)
0.930898 0.365278i \(-0.119026\pi\)
\(108\) 0 0
\(109\) −574.415 994.916i −0.504761 0.874272i −0.999985 0.00550668i \(-0.998247\pi\)
0.495223 0.868766i \(-0.335086\pi\)
\(110\) 124.490 215.623i 0.107906 0.186898i
\(111\) 0 0
\(112\) 0 0
\(113\) 1331.51 1.10847 0.554237 0.832359i \(-0.313010\pi\)
0.554237 + 0.832359i \(0.313010\pi\)
\(114\) 0 0
\(115\) 62.4578 + 108.180i 0.0506454 + 0.0877204i
\(116\) 24.2471 + 41.9972i 0.0194077 + 0.0336150i
\(117\) 0 0
\(118\) −84.4391 −0.0658750
\(119\) 0 0
\(120\) 0 0
\(121\) 13.0444 22.5936i 0.00980047 0.0169749i
\(122\) 439.172 + 760.667i 0.325908 + 0.564488i
\(123\) 0 0
\(124\) −290.988 + 504.007i −0.210738 + 0.365009i
\(125\) −820.627 −0.587193
\(126\) 0 0
\(127\) −830.236 −0.580090 −0.290045 0.957013i \(-0.593670\pi\)
−0.290045 + 0.957013i \(0.593670\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −35.2587 61.0698i −0.0237876 0.0412014i
\(131\) 986.245 1708.23i 0.657776 1.13930i −0.323414 0.946257i \(-0.604831\pi\)
0.981190 0.193044i \(-0.0618359\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1527.24 0.984575
\(135\) 0 0
\(136\) −473.849 820.730i −0.298766 0.517478i
\(137\) 34.3938 + 59.5718i 0.0214486 + 0.0371501i 0.876550 0.481310i \(-0.159839\pi\)
−0.855102 + 0.518460i \(0.826506\pi\)
\(138\) 0 0
\(139\) −1864.48 −1.13772 −0.568860 0.822435i \(-0.692615\pi\)
−0.568860 + 0.822435i \(0.692615\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1020.49 1767.55i 0.603084 1.04457i
\(143\) 184.792 + 320.069i 0.108064 + 0.187172i
\(144\) 0 0
\(145\) 20.8902 36.1829i 0.0119644 0.0207230i
\(146\) 1158.57 0.656738
\(147\) 0 0
\(148\) −5.48265 −0.00304507
\(149\) 10.1467 17.5746i 0.00557885 0.00966286i −0.863222 0.504824i \(-0.831558\pi\)
0.868801 + 0.495161i \(0.164891\pi\)
\(150\) 0 0
\(151\) 790.162 + 1368.60i 0.425844 + 0.737584i 0.996499 0.0836063i \(-0.0266438\pi\)
−0.570655 + 0.821190i \(0.693310\pi\)
\(152\) 154.645 267.854i 0.0825223 0.142933i
\(153\) 0 0
\(154\) 0 0
\(155\) 501.405 0.259831
\(156\) 0 0
\(157\) 1692.18 + 2930.93i 0.860193 + 1.48990i 0.871742 + 0.489965i \(0.162991\pi\)
−0.0115487 + 0.999933i \(0.503676\pi\)
\(158\) 942.730 + 1632.86i 0.474681 + 0.822171i
\(159\) 0 0
\(160\) −110.279 −0.0544896
\(161\) 0 0
\(162\) 0 0
\(163\) −785.853 + 1361.14i −0.377624 + 0.654065i −0.990716 0.135947i \(-0.956592\pi\)
0.613092 + 0.790012i \(0.289926\pi\)
\(164\) 336.000 + 581.969i 0.159983 + 0.277098i
\(165\) 0 0
\(166\) 474.714 822.228i 0.221957 0.384442i
\(167\) −2473.92 −1.14633 −0.573167 0.819439i \(-0.694285\pi\)
−0.573167 + 0.819439i \(0.694285\pi\)
\(168\) 0 0
\(169\) −2092.32 −0.952355
\(170\) −408.247 + 707.105i −0.184183 + 0.319014i
\(171\) 0 0
\(172\) −598.741 1037.05i −0.265428 0.459735i
\(173\) 2075.67 3595.17i 0.912198 1.57997i 0.101246 0.994861i \(-0.467717\pi\)
0.810952 0.585112i \(-0.198950\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 577.977 0.247538
\(177\) 0 0
\(178\) −821.904 1423.58i −0.346092 0.599448i
\(179\) 2108.97 + 3652.84i 0.880623 + 1.52528i 0.850650 + 0.525733i \(0.176209\pi\)
0.0299728 + 0.999551i \(0.490458\pi\)
\(180\) 0 0
\(181\) −3504.65 −1.43922 −0.719609 0.694380i \(-0.755679\pi\)
−0.719609 + 0.694380i \(0.755679\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −144.988 + 251.127i −0.0580907 + 0.100616i
\(185\) 2.36180 + 4.09076i 0.000938612 + 0.00162572i
\(186\) 0 0
\(187\) 2139.64 3705.96i 0.836716 1.44923i
\(188\) −2010.84 −0.780082
\(189\) 0 0
\(190\) −266.471 −0.101747
\(191\) −991.483 + 1717.30i −0.375608 + 0.650572i −0.990418 0.138103i \(-0.955899\pi\)
0.614810 + 0.788676i \(0.289233\pi\)
\(192\) 0 0
\(193\) −1055.87 1828.82i −0.393799 0.682080i 0.599148 0.800638i \(-0.295506\pi\)
−0.992947 + 0.118558i \(0.962173\pi\)
\(194\) 1108.16 1919.40i 0.410111 0.710333i
\(195\) 0 0
\(196\) 0 0
\(197\) 3932.65 1.42228 0.711141 0.703049i \(-0.248179\pi\)
0.711141 + 0.703049i \(0.248179\pi\)
\(198\) 0 0
\(199\) −276.352 478.656i −0.0984426 0.170508i 0.812598 0.582825i \(-0.198053\pi\)
−0.911040 + 0.412318i \(0.864719\pi\)
\(200\) −452.494 783.743i −0.159981 0.277095i
\(201\) 0 0
\(202\) 3771.84 1.31379
\(203\) 0 0
\(204\) 0 0
\(205\) 289.483 501.399i 0.0986261 0.170825i
\(206\) −482.144 835.098i −0.163071 0.282447i
\(207\) 0 0
\(208\) 81.8489 141.766i 0.0272846 0.0472583i
\(209\) 1396.58 0.462219
\(210\) 0 0
\(211\) 1720.90 0.561476 0.280738 0.959784i \(-0.409421\pi\)
0.280738 + 0.959784i \(0.409421\pi\)
\(212\) 1250.22 2165.45i 0.405027 0.701527i
\(213\) 0 0
\(214\) −1730.59 2997.48i −0.552808 0.957492i
\(215\) −515.849 + 893.476i −0.163631 + 0.283417i
\(216\) 0 0
\(217\) 0 0
\(218\) −2297.66 −0.713840
\(219\) 0 0
\(220\) −248.980 431.245i −0.0763009 0.132157i
\(221\) −606.000 1049.62i −0.184452 0.319481i
\(222\) 0 0
\(223\) −4788.43 −1.43793 −0.718963 0.695049i \(-0.755383\pi\)
−0.718963 + 0.695049i \(0.755383\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1331.51 2306.24i 0.391905 0.678799i
\(227\) 2043.80 + 3539.96i 0.597584 + 1.03505i 0.993177 + 0.116619i \(0.0372058\pi\)
−0.395593 + 0.918426i \(0.629461\pi\)
\(228\) 0 0
\(229\) −2033.30 + 3521.79i −0.586745 + 1.01627i 0.407911 + 0.913022i \(0.366257\pi\)
−0.994655 + 0.103250i \(0.967076\pi\)
\(230\) 249.831 0.0716234
\(231\) 0 0
\(232\) 96.9884 0.0274466
\(233\) −89.1351 + 154.387i −0.0250620 + 0.0434086i −0.878284 0.478139i \(-0.841312\pi\)
0.853222 + 0.521547i \(0.174645\pi\)
\(234\) 0 0
\(235\) 866.224 + 1500.34i 0.240452 + 0.416475i
\(236\) −84.4391 + 146.253i −0.0232903 + 0.0403400i
\(237\) 0 0
\(238\) 0 0
\(239\) −2118.67 −0.573412 −0.286706 0.958019i \(-0.592560\pi\)
−0.286706 + 0.958019i \(0.592560\pi\)
\(240\) 0 0
\(241\) 1199.15 + 2076.99i 0.320516 + 0.555149i 0.980595 0.196047i \(-0.0628105\pi\)
−0.660079 + 0.751196i \(0.729477\pi\)
\(242\) −26.0888 45.1872i −0.00692998 0.0120031i
\(243\) 0 0
\(244\) 1756.69 0.460903
\(245\) 0 0
\(246\) 0 0
\(247\) 197.774 342.555i 0.0509477 0.0882439i
\(248\) 581.977 + 1008.01i 0.149014 + 0.258100i
\(249\) 0 0
\(250\) −820.627 + 1421.37i −0.207604 + 0.359581i
\(251\) 1550.76 0.389973 0.194986 0.980806i \(-0.437534\pi\)
0.194986 + 0.980806i \(0.437534\pi\)
\(252\) 0 0
\(253\) −1309.37 −0.325374
\(254\) −830.236 + 1438.01i −0.205093 + 0.355231i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −2697.72 + 4672.59i −0.654783 + 1.13412i 0.327166 + 0.944967i \(0.393907\pi\)
−0.981948 + 0.189150i \(0.939427\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −141.035 −0.0336408
\(261\) 0 0
\(262\) −1972.49 3416.45i −0.465118 0.805607i
\(263\) −1790.97 3102.04i −0.419907 0.727301i 0.576022 0.817434i \(-0.304604\pi\)
−0.995930 + 0.0901330i \(0.971271\pi\)
\(264\) 0 0
\(265\) −2154.27 −0.499381
\(266\) 0 0
\(267\) 0 0
\(268\) 1527.24 2645.25i 0.348100 0.602927i
\(269\) −587.774 1018.05i −0.133224 0.230750i 0.791694 0.610918i \(-0.209200\pi\)
−0.924918 + 0.380168i \(0.875866\pi\)
\(270\) 0 0
\(271\) 129.664 224.584i 0.0290646 0.0503413i −0.851127 0.524959i \(-0.824080\pi\)
0.880192 + 0.474618i \(0.157414\pi\)
\(272\) −1895.40 −0.422519
\(273\) 0 0
\(274\) 137.575 0.0303329
\(275\) 2043.21 3538.95i 0.448038 0.776024i
\(276\) 0 0
\(277\) 649.461 + 1124.90i 0.140875 + 0.244003i 0.927826 0.373012i \(-0.121675\pi\)
−0.786951 + 0.617015i \(0.788342\pi\)
\(278\) −1864.48 + 3229.37i −0.402245 + 0.696708i
\(279\) 0 0
\(280\) 0 0
\(281\) −4524.25 −0.960477 −0.480238 0.877138i \(-0.659450\pi\)
−0.480238 + 0.877138i \(0.659450\pi\)
\(282\) 0 0
\(283\) 3239.03 + 5610.16i 0.680354 + 1.17841i 0.974873 + 0.222762i \(0.0715072\pi\)
−0.294519 + 0.955646i \(0.595160\pi\)
\(284\) −2040.99 3535.10i −0.426445 0.738624i
\(285\) 0 0
\(286\) 739.168 0.152825
\(287\) 0 0
\(288\) 0 0
\(289\) −4560.15 + 7898.41i −0.928180 + 1.60766i
\(290\) −41.7805 72.3659i −0.00846011 0.0146533i
\(291\) 0 0
\(292\) 1158.57 2006.70i 0.232192 0.402168i
\(293\) 2890.91 0.576413 0.288207 0.957568i \(-0.406941\pi\)
0.288207 + 0.957568i \(0.406941\pi\)
\(294\) 0 0
\(295\) 145.498 0.0287160
\(296\) −5.48265 + 9.49622i −0.00107660 + 0.00186472i
\(297\) 0 0
\(298\) −20.2934 35.1492i −0.00394485 0.00683267i
\(299\) −185.424 + 321.164i −0.0358641 + 0.0621184i
\(300\) 0 0
\(301\) 0 0
\(302\) 3160.65 0.602235
\(303\) 0 0
\(304\) −309.291 535.707i −0.0583521 0.101069i
\(305\) −756.741 1310.71i −0.142068 0.246070i
\(306\) 0 0
\(307\) 3137.42 0.583264 0.291632 0.956531i \(-0.405802\pi\)
0.291632 + 0.956531i \(0.405802\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 501.405 868.460i 0.0918642 0.159114i
\(311\) −3957.47 6854.55i −0.721568 1.24979i −0.960371 0.278725i \(-0.910088\pi\)
0.238803 0.971068i \(-0.423245\pi\)
\(312\) 0 0
\(313\) 3808.30 6596.18i 0.687726 1.19118i −0.284846 0.958573i \(-0.591943\pi\)
0.972572 0.232602i \(-0.0747241\pi\)
\(314\) 6768.70 1.21650
\(315\) 0 0
\(316\) 3770.92 0.671300
\(317\) 995.745 1724.68i 0.176425 0.305577i −0.764229 0.644945i \(-0.776880\pi\)
0.940653 + 0.339369i \(0.110213\pi\)
\(318\) 0 0
\(319\) 218.973 + 379.272i 0.0384330 + 0.0665679i
\(320\) −110.279 + 191.009i −0.0192650 + 0.0333679i
\(321\) 0 0
\(322\) 0 0
\(323\) −4579.91 −0.788956
\(324\) 0 0
\(325\) −578.690 1002.32i −0.0987690 0.171073i
\(326\) 1571.71 + 2722.28i 0.267021 + 0.462494i
\(327\) 0 0
\(328\) 1344.00 0.226250
\(329\) 0 0
\(330\) 0 0
\(331\) −1424.31 + 2466.99i −0.236518 + 0.409661i −0.959713 0.280983i \(-0.909340\pi\)
0.723195 + 0.690644i \(0.242673\pi\)
\(332\) −949.428 1644.46i −0.156948 0.271841i
\(333\) 0 0
\(334\) −2473.92 + 4284.96i −0.405290 + 0.701983i
\(335\) −2631.60 −0.429192
\(336\) 0 0
\(337\) −5813.87 −0.939768 −0.469884 0.882728i \(-0.655704\pi\)
−0.469884 + 0.882728i \(0.655704\pi\)
\(338\) −2092.32 + 3624.01i −0.336708 + 0.583196i
\(339\) 0 0
\(340\) 816.494 + 1414.21i 0.130237 + 0.225577i
\(341\) −2627.88 + 4551.63i −0.417325 + 0.722828i
\(342\) 0 0
\(343\) 0 0
\(344\) −2394.97 −0.375372
\(345\) 0 0
\(346\) −4151.34 7190.33i −0.645022 1.11721i
\(347\) −1717.55 2974.89i −0.265715 0.460231i 0.702036 0.712142i \(-0.252275\pi\)
−0.967751 + 0.251910i \(0.918941\pi\)
\(348\) 0 0
\(349\) 3034.99 0.465499 0.232750 0.972537i \(-0.425228\pi\)
0.232750 + 0.972537i \(0.425228\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 577.977 1001.09i 0.0875178 0.151585i
\(353\) −4110.22 7119.11i −0.619730 1.07340i −0.989535 0.144295i \(-0.953909\pi\)
0.369804 0.929110i \(-0.379425\pi\)
\(354\) 0 0
\(355\) −1758.42 + 3045.68i −0.262894 + 0.455346i
\(356\) −3287.62 −0.489447
\(357\) 0 0
\(358\) 8435.86 1.24539
\(359\) −4950.80 + 8575.03i −0.727836 + 1.26065i 0.229961 + 0.973200i \(0.426140\pi\)
−0.957796 + 0.287448i \(0.907193\pi\)
\(360\) 0 0
\(361\) 2682.15 + 4645.62i 0.391041 + 0.677303i
\(362\) −3504.65 + 6070.23i −0.508840 + 0.881337i
\(363\) 0 0
\(364\) 0 0
\(365\) −1996.34 −0.286283
\(366\) 0 0
\(367\) 5514.01 + 9550.55i 0.784276 + 1.35841i 0.929431 + 0.368997i \(0.120299\pi\)
−0.145155 + 0.989409i \(0.546368\pi\)
\(368\) 289.977 + 502.255i 0.0410763 + 0.0711463i
\(369\) 0 0
\(370\) 9.44721 0.00132740
\(371\) 0 0
\(372\) 0 0
\(373\) 1373.19 2378.43i 0.190619 0.330162i −0.754836 0.655913i \(-0.772284\pi\)
0.945456 + 0.325751i \(0.105617\pi\)
\(374\) −4279.28 7411.92i −0.591647 1.02476i
\(375\) 0 0
\(376\) −2010.84 + 3482.87i −0.275801 + 0.477701i
\(377\) 124.037 0.0169450
\(378\) 0 0
\(379\) −4184.22 −0.567095 −0.283547 0.958958i \(-0.591511\pi\)
−0.283547 + 0.958958i \(0.591511\pi\)
\(380\) −266.471 + 461.541i −0.0359728 + 0.0623068i
\(381\) 0 0
\(382\) 1982.97 + 3434.60i 0.265595 + 0.460024i
\(383\) −1530.29 + 2650.54i −0.204162 + 0.353619i −0.949865 0.312659i \(-0.898780\pi\)
0.745703 + 0.666278i \(0.232114\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4223.48 −0.556916
\(387\) 0 0
\(388\) −2216.33 3838.79i −0.289992 0.502282i
\(389\) 2459.81 + 4260.51i 0.320610 + 0.555312i 0.980614 0.195950i \(-0.0627789\pi\)
−0.660004 + 0.751262i \(0.729446\pi\)
\(390\) 0 0
\(391\) 4293.91 0.555377
\(392\) 0 0
\(393\) 0 0
\(394\) 3932.65 6811.55i 0.502853 0.870967i
\(395\) −1624.43 2813.59i −0.206921 0.358398i
\(396\) 0 0
\(397\) −6586.63 + 11408.4i −0.832678 + 1.44224i 0.0632286 + 0.997999i \(0.479860\pi\)
−0.895907 + 0.444242i \(0.853473\pi\)
\(398\) −1105.41 −0.139219
\(399\) 0 0
\(400\) −1809.98 −0.226247
\(401\) −1331.19 + 2305.69i −0.165777 + 0.287134i −0.936931 0.349515i \(-0.886346\pi\)
0.771154 + 0.636648i \(0.219680\pi\)
\(402\) 0 0
\(403\) 744.284 + 1289.14i 0.0919985 + 0.159346i
\(404\) 3771.84 6533.02i 0.464496 0.804530i
\(405\) 0 0
\(406\) 0 0
\(407\) −49.5132 −0.00603016
\(408\) 0 0
\(409\) −6496.09 11251.6i −0.785357 1.36028i −0.928786 0.370617i \(-0.879146\pi\)
0.143429 0.989661i \(-0.454187\pi\)
\(410\) −578.965 1002.80i −0.0697392 0.120792i
\(411\) 0 0
\(412\) −1928.58 −0.230617
\(413\) 0 0
\(414\) 0 0
\(415\) −817.984 + 1416.79i −0.0967549 + 0.167584i
\(416\) −163.698 283.533i −0.0192931 0.0334167i
\(417\) 0 0
\(418\) 1396.58 2418.96i 0.163419 0.283050i
\(419\) 7236.96 0.843791 0.421896 0.906644i \(-0.361365\pi\)
0.421896 + 0.906644i \(0.361365\pi\)
\(420\) 0 0
\(421\) 3706.07 0.429032 0.214516 0.976720i \(-0.431183\pi\)
0.214516 + 0.976720i \(0.431183\pi\)
\(422\) 1720.90 2980.68i 0.198512 0.343832i
\(423\) 0 0
\(424\) −2500.45 4330.90i −0.286397 0.496055i
\(425\) −6700.43 + 11605.5i −0.764750 + 1.32459i
\(426\) 0 0
\(427\) 0 0
\(428\) −6922.38 −0.781789
\(429\) 0 0
\(430\) 1031.70 + 1786.95i 0.115704 + 0.200406i
\(431\) −3191.19 5527.30i −0.356645 0.617728i 0.630753 0.775984i \(-0.282746\pi\)
−0.987398 + 0.158256i \(0.949413\pi\)
\(432\) 0 0
\(433\) 7275.62 0.807492 0.403746 0.914871i \(-0.367708\pi\)
0.403746 + 0.914871i \(0.367708\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2297.66 + 3979.66i −0.252381 + 0.437136i
\(437\) 700.681 + 1213.61i 0.0767005 + 0.132849i
\(438\) 0 0
\(439\) 4880.18 8452.72i 0.530566 0.918967i −0.468798 0.883305i \(-0.655313\pi\)
0.999364 0.0356614i \(-0.0113538\pi\)
\(440\) −995.918 −0.107906
\(441\) 0 0
\(442\) −2424.00 −0.260855
\(443\) −2866.58 + 4965.06i −0.307439 + 0.532499i −0.977801 0.209534i \(-0.932805\pi\)
0.670363 + 0.742034i \(0.266139\pi\)
\(444\) 0 0
\(445\) 1416.23 + 2452.99i 0.150867 + 0.261309i
\(446\) −4788.43 + 8293.81i −0.508383 + 0.880546i
\(447\) 0 0
\(448\) 0 0
\(449\) −16628.4 −1.74775 −0.873877 0.486147i \(-0.838402\pi\)
−0.873877 + 0.486147i \(0.838402\pi\)
\(450\) 0 0
\(451\) 3034.38 + 5255.70i 0.316814 + 0.548739i
\(452\) −2663.01 4612.47i −0.277118 0.479983i
\(453\) 0 0
\(454\) 8175.18 0.845111
\(455\) 0 0
\(456\) 0 0
\(457\) −8559.65 + 14825.8i −0.876157 + 1.51755i −0.0206311 + 0.999787i \(0.506568\pi\)
−0.855526 + 0.517761i \(0.826766\pi\)
\(458\) 4066.61 + 7043.57i 0.414891 + 0.718613i
\(459\) 0 0
\(460\) 249.831 432.720i 0.0253227 0.0438602i
\(461\) −6956.95 −0.702858 −0.351429 0.936215i \(-0.614304\pi\)
−0.351429 + 0.936215i \(0.614304\pi\)
\(462\) 0 0
\(463\) 6594.47 0.661924 0.330962 0.943644i \(-0.392627\pi\)
0.330962 + 0.943644i \(0.392627\pi\)
\(464\) 96.9884 167.989i 0.00970383 0.0168075i
\(465\) 0 0
\(466\) 178.270 + 308.773i 0.0177215 + 0.0306945i
\(467\) −7232.91 + 12527.8i −0.716700 + 1.24136i 0.245600 + 0.969371i \(0.421015\pi\)
−0.962300 + 0.271990i \(0.912318\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 3464.90 0.340050
\(471\) 0 0
\(472\) 168.878 + 292.506i 0.0164687 + 0.0285247i
\(473\) −5407.17 9365.49i −0.525627 0.910413i
\(474\) 0 0
\(475\) −4373.51 −0.422464
\(476\) 0 0
\(477\) 0 0
\(478\) −2118.67 + 3669.65i −0.202732 + 0.351142i
\(479\) 2037.74 + 3529.46i 0.194377 + 0.336671i 0.946696 0.322128i \(-0.104398\pi\)
−0.752319 + 0.658799i \(0.771065\pi\)
\(480\) 0 0
\(481\) −7.01170 + 12.1446i −0.000664669 + 0.00115124i
\(482\) 4796.61 0.453277
\(483\) 0 0
\(484\) −104.355 −0.00980047
\(485\) −1909.49 + 3307.33i −0.178774 + 0.309646i
\(486\) 0 0
\(487\) −2189.40 3792.14i −0.203719 0.352851i 0.746005 0.665940i \(-0.231969\pi\)
−0.949724 + 0.313089i \(0.898636\pi\)
\(488\) 1756.69 3042.67i 0.162954 0.282244i
\(489\) 0 0
\(490\) 0 0
\(491\) −6612.37 −0.607764 −0.303882 0.952710i \(-0.598283\pi\)
−0.303882 + 0.952710i \(0.598283\pi\)
\(492\) 0 0
\(493\) −718.092 1243.77i −0.0656008 0.113624i
\(494\) −395.548 685.110i −0.0360254 0.0623979i
\(495\) 0 0
\(496\) 2327.91 0.210738
\(497\) 0 0
\(498\) 0 0
\(499\) 5728.21 9921.56i 0.513888 0.890080i −0.485982 0.873969i \(-0.661538\pi\)
0.999870 0.0161114i \(-0.00512863\pi\)
\(500\) 1641.25 + 2842.73i 0.146798 + 0.254262i
\(501\) 0 0
\(502\) 1550.76 2686.00i 0.137876 0.238808i
\(503\) 7697.10 0.682300 0.341150 0.940009i \(-0.389184\pi\)
0.341150 + 0.940009i \(0.389184\pi\)
\(504\) 0 0
\(505\) −6499.30 −0.572704
\(506\) −1309.37 + 2267.90i −0.115037 + 0.199250i
\(507\) 0 0
\(508\) 1660.47 + 2876.02i 0.145023 + 0.251187i
\(509\) 2311.98 4004.47i 0.201330 0.348713i −0.747627 0.664118i \(-0.768807\pi\)
0.948957 + 0.315405i \(0.102140\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 5395.44 + 9345.18i 0.463001 + 0.801942i
\(515\) 830.788 + 1438.97i 0.0710852 + 0.123123i
\(516\) 0 0
\(517\) −18159.6 −1.54480
\(518\) 0 0
\(519\) 0 0
\(520\) −141.035 + 244.279i −0.0118938 + 0.0206007i
\(521\) 1743.35 + 3019.57i 0.146598 + 0.253915i 0.929968 0.367641i \(-0.119834\pi\)
−0.783370 + 0.621556i \(0.786501\pi\)
\(522\) 0 0
\(523\) −2207.57 + 3823.62i −0.184570 + 0.319685i −0.943432 0.331567i \(-0.892423\pi\)
0.758862 + 0.651252i \(0.225756\pi\)
\(524\) −7889.96 −0.657776
\(525\) 0 0
\(526\) −7163.86 −0.593839
\(527\) 8617.78 14926.4i 0.712327 1.23379i
\(528\) 0 0
\(529\) 5426.57 + 9399.10i 0.446008 + 0.772508i
\(530\) −2154.27 + 3731.31i −0.176558 + 0.305807i
\(531\) 0 0
\(532\) 0 0
\(533\) 1718.83 0.139682
\(534\) 0 0
\(535\) 2982.01 + 5164.99i 0.240978 + 0.417387i
\(536\) −3054.47 5290.50i −0.246144 0.426334i
\(537\) 0 0
\(538\) −2351.10 −0.188407
\(539\) 0 0
\(540\) 0 0
\(541\) 5402.24 9356.96i 0.429317 0.743599i −0.567496 0.823376i \(-0.692088\pi\)
0.996813 + 0.0797775i \(0.0254210\pi\)
\(542\) −259.327 449.168i −0.0205518 0.0355967i
\(543\) 0 0
\(544\) −1895.40 + 3282.92i −0.149383 + 0.258739i
\(545\) 3959.12 0.311175
\(546\) 0 0
\(547\) 18783.4 1.46823 0.734113 0.679027i \(-0.237598\pi\)
0.734113 + 0.679027i \(0.237598\pi\)
\(548\) 137.575 238.287i 0.0107243 0.0185750i
\(549\) 0 0
\(550\) −4086.42 7077.90i −0.316810 0.548732i
\(551\) 234.356 405.917i 0.0181196 0.0313841i
\(552\) 0 0
\(553\) 0 0
\(554\) 2597.85 0.199227
\(555\) 0 0
\(556\) 3728.96 + 6458.74i 0.284430 + 0.492647i
\(557\) −725.568 1256.72i −0.0551944 0.0955995i 0.837108 0.547038i \(-0.184245\pi\)
−0.892302 + 0.451438i \(0.850911\pi\)
\(558\) 0 0
\(559\) −3062.89 −0.231747
\(560\) 0 0
\(561\) 0 0
\(562\) −4524.25 + 7836.23i −0.339580 + 0.588169i
\(563\) −8390.55 14532.9i −0.628098 1.08790i −0.987933 0.154882i \(-0.950500\pi\)
0.359835 0.933016i \(-0.382833\pi\)
\(564\) 0 0
\(565\) −2294.33 + 3973.90i −0.170838 + 0.295900i
\(566\) 12956.1 0.962165
\(567\) 0 0
\(568\) −8163.95 −0.603084
\(569\) −7361.42 + 12750.4i −0.542367 + 0.939407i 0.456401 + 0.889774i \(0.349138\pi\)
−0.998768 + 0.0496328i \(0.984195\pi\)
\(570\) 0 0
\(571\) −4858.56 8415.27i −0.356085 0.616757i 0.631218 0.775605i \(-0.282555\pi\)
−0.987303 + 0.158849i \(0.949222\pi\)
\(572\) 739.168 1280.28i 0.0540318 0.0935858i
\(573\) 0 0
\(574\) 0 0
\(575\) 4100.40 0.297389
\(576\) 0 0
\(577\) −10094.4 17484.1i −0.728313 1.26148i −0.957596 0.288116i \(-0.906971\pi\)
0.229282 0.973360i \(-0.426362\pi\)
\(578\) 9120.30 + 15796.8i 0.656322 + 1.13678i
\(579\) 0 0
\(580\) −167.122 −0.0119644
\(581\) 0 0
\(582\) 0 0
\(583\) 11290.6 19556.0i 0.802076 1.38924i
\(584\) −2317.13 4013.39i −0.164184 0.284376i
\(585\) 0 0
\(586\) 2890.91 5007.21i 0.203793 0.352979i
\(587\) −21720.8 −1.52728 −0.763641 0.645641i \(-0.776590\pi\)
−0.763641 + 0.645641i \(0.776590\pi\)
\(588\) 0 0
\(589\) 5625.00 0.393504
\(590\) 145.498 252.010i 0.0101526 0.0175849i
\(591\) 0 0
\(592\) 10.9653 + 18.9924i 0.000761268 + 0.00131856i
\(593\) 9762.14 16908.5i 0.676025 1.17091i −0.300143 0.953894i \(-0.597034\pi\)
0.976168 0.217016i \(-0.0696322\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −81.1735 −0.00557885
\(597\) 0 0
\(598\) 370.848 + 642.328i 0.0253597 + 0.0439243i
\(599\) 5799.34 + 10044.7i 0.395583 + 0.685171i 0.993175 0.116630i \(-0.0372091\pi\)
−0.597592 + 0.801800i \(0.703876\pi\)
\(600\) 0 0
\(601\) 9335.68 0.633628 0.316814 0.948488i \(-0.397387\pi\)
0.316814 + 0.948488i \(0.397387\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3160.65 5474.40i 0.212922 0.368792i
\(605\) 44.9540 + 77.8626i 0.00302089 + 0.00523234i
\(606\) 0 0
\(607\) 7575.45 13121.1i 0.506553 0.877376i −0.493418 0.869792i \(-0.664253\pi\)
0.999971 0.00758385i \(-0.00241404\pi\)
\(608\) −1237.16 −0.0825223
\(609\) 0 0
\(610\) −3026.97 −0.200915
\(611\) −2571.64 + 4454.21i −0.170274 + 0.294923i
\(612\) 0 0
\(613\) −12396.7 21471.7i −0.816798 1.41474i −0.908029 0.418906i \(-0.862414\pi\)
0.0912312 0.995830i \(-0.470920\pi\)
\(614\) 3137.42 5434.17i 0.206215 0.357175i
\(615\) 0 0
\(616\) 0 0
\(617\) 25194.6 1.64391 0.821957 0.569550i \(-0.192882\pi\)
0.821957 + 0.569550i \(0.192882\pi\)
\(618\) 0 0
\(619\) −3023.24 5236.40i −0.196307 0.340014i 0.751021 0.660278i \(-0.229562\pi\)
−0.947328 + 0.320264i \(0.896228\pi\)
\(620\) −1002.81 1736.92i −0.0649578 0.112510i
\(621\) 0 0
\(622\) −15829.9 −1.02045
\(623\) 0 0
\(624\) 0 0
\(625\) −5656.19 + 9796.81i −0.361996 + 0.626996i
\(626\) −7616.61 13192.4i −0.486295 0.842288i
\(627\) 0 0
\(628\) 6768.70 11723.7i 0.430097 0.744949i
\(629\) 162.372 0.0102928
\(630\) 0 0
\(631\) −6537.14 −0.412424 −0.206212 0.978507i \(-0.566114\pi\)
−0.206212 + 0.978507i \(0.566114\pi\)
\(632\) 3770.92 6531.42i 0.237340 0.411086i
\(633\) 0 0
\(634\) −1991.49 3449.36i −0.124751 0.216075i
\(635\) 1430.59 2477.85i 0.0894034 0.154851i
\(636\) 0 0
\(637\) 0 0
\(638\) 875.892 0.0543525
\(639\) 0 0
\(640\) 220.558 + 382.018i 0.0136224 + 0.0235947i
\(641\) 4623.39 + 8007.95i 0.284888 + 0.493440i 0.972582 0.232561i \(-0.0747104\pi\)
−0.687694 + 0.726000i \(0.741377\pi\)
\(642\) 0 0
\(643\) 157.563 0.00966355 0.00483178 0.999988i \(-0.498462\pi\)
0.00483178 + 0.999988i \(0.498462\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −4579.91 + 7932.63i −0.278938 + 0.483135i
\(647\) 6353.00 + 11003.7i 0.386031 + 0.668625i 0.991912 0.126930i \(-0.0405124\pi\)
−0.605881 + 0.795556i \(0.707179\pi\)
\(648\) 0 0
\(649\) −762.560 + 1320.79i −0.0461219 + 0.0798854i
\(650\) −2314.76 −0.139680
\(651\) 0 0
\(652\) 6286.83 0.377624
\(653\) 8552.41 14813.2i 0.512529 0.887727i −0.487365 0.873198i \(-0.662042\pi\)
0.999894 0.0145285i \(-0.00462474\pi\)
\(654\) 0 0
\(655\) 3398.82 + 5886.93i 0.202752 + 0.351178i
\(656\) 1344.00 2327.88i 0.0799914 0.138549i
\(657\) 0 0
\(658\) 0 0
\(659\) 12518.0 0.739956 0.369978 0.929040i \(-0.379365\pi\)
0.369978 + 0.929040i \(0.379365\pi\)
\(660\) 0 0
\(661\) −2390.24 4140.01i −0.140650 0.243613i 0.787092 0.616836i \(-0.211586\pi\)
−0.927741 + 0.373223i \(0.878252\pi\)
\(662\) 2848.63 + 4933.97i 0.167243 + 0.289674i
\(663\) 0 0
\(664\) −3797.71 −0.221957
\(665\) 0 0
\(666\) 0 0
\(667\) −219.722 + 380.569i −0.0127551 + 0.0220925i
\(668\) 4947.84 + 8569.92i 0.286584 + 0.496377i
\(669\) 0 0
\(670\) −2631.60 + 4558.06i −0.151742 + 0.262826i
\(671\) 15864.4 0.912727
\(672\) 0 0
\(673\) −28447.0 −1.62935 −0.814673 0.579920i \(-0.803084\pi\)
−0.814673 + 0.579920i \(0.803084\pi\)
\(674\) −5813.87 + 10069.9i −0.332258 + 0.575488i
\(675\) 0 0
\(676\) 4184.65 + 7248.02i 0.238089 + 0.412382i
\(677\) 7939.27 13751.2i 0.450710 0.780653i −0.547720 0.836662i \(-0.684504\pi\)
0.998430 + 0.0560084i \(0.0178374\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3265.98 0.184183
\(681\) 0 0
\(682\) 5255.77 + 9103.26i 0.295093 + 0.511117i
\(683\) 1219.23 + 2111.76i 0.0683052 + 0.118308i 0.898155 0.439678i \(-0.144908\pi\)
−0.829850 + 0.557986i \(0.811574\pi\)
\(684\) 0 0
\(685\) −237.057 −0.0132226
\(686\) 0 0
\(687\) 0 0
\(688\) −2394.97 + 4148.20i −0.132714 + 0.229867i
\(689\) −3197.79 5538.74i −0.176816 0.306254i
\(690\) 0 0
\(691\) 11243.5 19474.3i 0.618990 1.07212i −0.370681 0.928760i \(-0.620876\pi\)
0.989670 0.143361i \(-0.0457910\pi\)
\(692\) −16605.4 −0.912198
\(693\) 0 0
\(694\) −6870.21 −0.375777
\(695\) 3212.70 5564.56i 0.175345 0.303706i
\(696\) 0 0
\(697\) −9950.83 17235.3i −0.540767 0.936635i
\(698\) 3034.99 5256.75i 0.164579 0.285059i
\(699\) 0 0
\(700\) 0 0
\(701\) −3916.29 −0.211008 −0.105504 0.994419i \(-0.533646\pi\)
−0.105504 + 0.994419i \(0.533646\pi\)
\(702\) 0 0
\(703\) 26.4958 + 45.8921i 0.00142149 + 0.00246210i
\(704\) −1155.95 2002.17i −0.0618844 0.107187i
\(705\) 0 0
\(706\) −16440.9 −0.876431
\(707\) 0 0
\(708\) 0 0
\(709\) 11455.2 19840.9i 0.606780 1.05097i −0.384987 0.922922i \(-0.625794\pi\)
0.991767 0.128053i \(-0.0408726\pi\)
\(710\) 3516.85 + 6091.36i 0.185894 + 0.321979i
\(711\) 0 0
\(712\) −3287.62 + 5694.32i −0.173046 + 0.299724i
\(713\) −5273.74 −0.277003
\(714\) 0 0
\(715\) −1273.67 −0.0666189
\(716\) 8435.86 14611.3i 0.440311 0.762642i
\(717\) 0 0
\(718\) 9901.59 + 17150.1i 0.514658 + 0.891413i
\(719\) 10236.4 17729.9i 0.530949 0.919630i −0.468399 0.883517i \(-0.655169\pi\)
0.999348 0.0361132i \(-0.0114977\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10728.6 0.553016
\(723\) 0 0
\(724\) 7009.29 + 12140.5i 0.359804 + 0.623199i
\(725\) −685.730 1187.72i −0.0351274 0.0608424i
\(726\) 0 0
\(727\) −11208.5 −0.571802 −0.285901 0.958259i \(-0.592293\pi\)
−0.285901 + 0.958259i \(0.592293\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −1996.34 + 3457.76i −0.101216 + 0.175312i
\(731\) 17732.1 + 30712.8i 0.897187 + 1.55397i
\(732\) 0 0
\(733\) −17719.0 + 30690.2i −0.892860 + 1.54648i −0.0564289 + 0.998407i \(0.517971\pi\)
−0.836431 + 0.548072i \(0.815362\pi\)
\(734\) 22056.1 1.10913
\(735\) 0 0
\(736\) 1159.91 0.0580907
\(737\) 13792.3 23889.0i 0.689343 1.19398i
\(738\) 0 0
\(739\) 8967.69 + 15532.5i 0.446389 + 0.773169i 0.998148 0.0608348i \(-0.0193763\pi\)
−0.551758 + 0.834004i \(0.686043\pi\)
\(740\) 9.44721 16.3630i 0.000469306 0.000812862i
\(741\) 0 0
\(742\) 0 0
\(743\) 19031.0 0.939676 0.469838 0.882753i \(-0.344312\pi\)
0.469838 + 0.882753i \(0.344312\pi\)
\(744\) 0 0
\(745\) 34.9677 + 60.5659i 0.00171962 + 0.00297847i
\(746\) −2746.37 4756.86i −0.134788 0.233460i
\(747\) 0 0
\(748\) −17117.1 −0.836716
\(749\) 0 0
\(750\) 0 0
\(751\) 1364.07 2362.63i 0.0662790 0.114799i −0.830982 0.556300i \(-0.812221\pi\)
0.897261 + 0.441501i \(0.145554\pi\)
\(752\) 4021.67 + 6965.74i 0.195020 + 0.337785i
\(753\) 0 0
\(754\) 124.037 214.839i 0.00599095 0.0103766i
\(755\) −5446.15 −0.262524
\(756\) 0 0
\(757\) −6617.58 −0.317728 −0.158864 0.987300i \(-0.550783\pi\)
−0.158864 + 0.987300i \(0.550783\pi\)
\(758\) −4184.22 + 7247.28i −0.200498 + 0.347273i
\(759\) 0 0
\(760\) 532.942 + 923.083i 0.0254366 + 0.0440575i
\(761\) −300.054 + 519.709i −0.0142930 + 0.0247562i −0.873083 0.487571i \(-0.837883\pi\)
0.858790 + 0.512327i \(0.171216\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 7931.86 0.375608
\(765\) 0 0
\(766\) 3060.58 + 5301.08i 0.144364 + 0.250047i
\(767\) 215.976 + 374.082i 0.0101675 + 0.0176106i
\(768\) 0 0
\(769\) 28329.2 1.32845 0.664223 0.747534i \(-0.268762\pi\)
0.664223 + 0.747534i \(0.268762\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4223.48 + 7315.29i −0.196900 + 0.341040i
\(773\) 11918.5 + 20643.5i 0.554565 + 0.960536i 0.997937 + 0.0641977i \(0.0204488\pi\)
−0.443372 + 0.896338i \(0.646218\pi\)
\(774\) 0 0
\(775\) 8229.41 14253.8i 0.381431 0.660658i
\(776\) −8865.32 −0.410111
\(777\) 0 0
\(778\) 9839.23 0.453411
\(779\) 3247.55 5624.93i 0.149365 0.258708i
\(780\) 0 0
\(781\) −18431.9 31925.1i −0.844490 1.46270i
\(782\) 4293.91 7437.28i 0.196356 0.340098i
\(783\) 0 0
\(784\) 0 0
\(785\) −11663.2 −0.530291
\(786\) 0 0
\(787\) −268.455 464.977i −0.0121593 0.0210606i 0.859882 0.510493i \(-0.170537\pi\)
−0.872041 + 0.489433i \(0.837204\pi\)
\(788\) −7865.30 13623.1i −0.355571 0.615866i
\(789\) 0 0
\(790\) −6497.71 −0.292631
\(791\)