Properties

Label 882.4.g.z.667.2
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 667.2
Root \(-3.22311 + 5.58259i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.z.361.2

$q$-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 −0.778618 0.627498i \(-0.784079\pi\)
0.932738 + 0.360554i \(0.117413\pi\)
\(6\) 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 0.999984 0.00567700i \(-0.00180706\pi\)
−0.504908 + 0.863173i \(0.668474\pi\)
\(12\) 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 \(-0.846244\pi\)
0.0405493 0.999178i \(-0.487089\pi\)
\(18\) 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 −0.936408 0.350912i \(-0.885872\pi\)
0.772103 + 0.635497i \(0.219205\pi\)
\(24\) 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 \(-0.487642\pi\)
0.0388153 + 0.999246i \(0.487642\pi\)
\(30\) 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 \(-0.396329\pi\)
0.319966 + 0.947429i \(0.396329\pi\)
\(42\) 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 \(0.451489\pi\)
−0.931894 + 0.362732i \(0.881844\pi\)
\(48\) 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 \(-0.866104\pi\)
0.102771 0.994705i \(-0.467229\pi\)
\(54\) 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 0.888376 0.459117i \(-0.151834\pi\)
−0.841795 + 0.539797i \(0.818501\pi\)
\(60\) 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 \(-0.825152\pi\)
−0.852890 + 0.522091i \(0.825152\pi\)
\(72\) 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 \(-0.601634\pi\)
−0.313895 + 0.949458i \(0.601634\pi\)
\(84\) 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 −0.999926 0.0121424i \(-0.996135\pi\)
0.510479 + 0.859890i \(0.329468\pi\)
\(90\) 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 \(-0.787344\pi\)
−0.143978 0.989581i \(-0.545989\pi\)
\(102\) 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 \(0.452359\pi\)
−0.930898 + 0.365278i \(0.880974\pi\)
\(108\) 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 \(-0.686990\pi\)
−0.554237 + 0.832359i \(0.686990\pi\)
\(114\) 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 \(0.395169\pi\)
−0.981190 + 0.193044i \(0.938164\pi\)
\(132\) 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 0.855102 0.518460i \(-0.173494\pi\)
−0.876550 + 0.481310i \(0.840161\pi\)
\(138\) 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 −0.868801 0.495161i \(-0.835109\pi\)
0.863222 + 0.504824i \(0.168442\pi\)
\(150\) 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 \(-0.305715\pi\)
0.573167 + 0.819439i \(0.305715\pi\)
\(168\) 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 \(0.532283\pi\)
−0.810952 + 0.585112i \(0.801050\pi\)
\(174\) 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 \(-0.823791\pi\)
−0.0299728 0.999551i \(-0.509542\pi\)
\(180\) 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 −0.614810 0.788676i \(-0.710767\pi\)
0.990418 + 0.138103i \(0.0441005\pi\)
\(192\) 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 \(-0.751821\pi\)
−0.711141 + 0.703049i \(0.751821\pi\)
\(198\) 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 \(-0.962794\pi\)
0.395593 0.918426i \(-0.370539\pi\)
\(228\) 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 −0.853222 0.521547i \(-0.825355\pi\)
0.878284 + 0.478139i \(0.158688\pi\)
\(234\) 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 \(-0.407440\pi\)
0.286706 + 0.958019i \(0.407440\pi\)
\(240\) 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 \(-0.562466\pi\)
−0.194986 + 0.980806i \(0.562466\pi\)
\(252\) 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 \(-0.606093\pi\)
0.981948 0.189150i \(-0.0605732\pi\)
\(258\) 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 0.995930 0.0901330i \(-0.0287292\pi\)
−0.576022 + 0.817434i \(0.695396\pi\)
\(264\) 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 0.924918 0.380168i \(-0.124134\pi\)
−0.791694 + 0.610918i \(0.790800\pi\)
\(270\) 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 \(-0.340550\pi\)
0.480238 + 0.877138i \(0.340550\pi\)
\(282\) 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 \(-0.593059\pi\)
−0.288207 + 0.957568i \(0.593059\pi\)
\(294\) 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 \(0.0899118\pi\)
−0.238803 + 0.971068i \(0.576755\pi\)
\(312\) 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 −0.940653 0.339369i \(-0.889787\pi\)
0.764229 + 0.644945i \(0.223120\pi\)
\(318\) 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 0.967751 0.251910i \(-0.0810587\pi\)
−0.702036 + 0.712142i \(0.747725\pi\)
\(348\) 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 \(0.0460914\pi\)
−0.369804 + 0.929110i \(0.620575\pi\)
\(354\) 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 \(-0.573860\pi\)
0.957796 0.287448i \(-0.0928070\pi\)
\(360\) 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 −0.745703 0.666278i \(-0.767886\pi\)
0.949865 + 0.312659i \(0.101220\pi\)
\(384\) 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 0.660004 0.751262i \(-0.270554\pi\)
−0.980614 + 0.195950i \(0.937221\pi\)
\(390\) 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 −0.771154 0.636648i \(-0.780320\pi\)
0.936931 + 0.349515i \(0.113654\pi\)
\(402\) 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 \(-0.638635\pi\)
−0.421896 + 0.906644i \(0.638635\pi\)
\(420\) 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 0.987398 0.158256i \(-0.0505871\pi\)
−0.630753 + 0.775984i \(0.717254\pi\)
\(432\) 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 −0.670363 0.742034i \(-0.733861\pi\)
0.977801 + 0.209534i \(0.0671948\pi\)
\(444\) 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 \(-0.161598\pi\)
0.873877 + 0.486147i \(0.161598\pi\)
\(450\) 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 \(-0.385696\pi\)
0.351429 + 0.936215i \(0.385696\pi\)
\(462\) 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 \(-0.578985\pi\)
0.962300 0.271990i \(-0.0876818\pi\)
\(468\) 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 0.752319 0.658799i \(-0.228935\pi\)
−0.946696 + 0.322128i \(0.895602\pi\)
\(480\) 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 \(-0.401717\pi\)
0.303882 + 0.952710i \(0.401717\pi\)
\(492\) 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 \(-0.610816\pi\)
−0.341150 + 0.940009i \(0.610816\pi\)
\(504\) 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 −0.948957 0.315405i \(-0.897860\pi\)
0.747627 + 0.664118i \(0.231193\pi\)
\(510\) 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 0.783370 0.621556i \(-0.213499\pi\)
−0.929968 + 0.367641i \(0.880166\pi\)
\(522\) 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 0.892302 0.451438i \(-0.149089\pi\)
−0.837108 + 0.547038i \(0.815755\pi\)
\(558\) 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 \(0.0494998\pi\)
−0.359835 + 0.933016i \(0.617167\pi\)
\(564\) 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 \(-0.650862\pi\)
0.998768 0.0496328i \(-0.0158051\pi\)
\(570\) 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 \(-0.223410\pi\)
0.763641 + 0.645641i \(0.223410\pi\)
\(588\) 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 \(0.402966\pi\)
−0.976168 + 0.217016i \(0.930368\pi\)
\(594\) 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 0.597592 0.801800i \(-0.296124\pi\)
−0.993175 + 0.116630i \(0.962791\pi\)
\(600\) 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 \(-0.807118\pi\)
−0.821957 + 0.569550i \(0.807118\pi\)
\(618\) 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 0.687694 0.726000i \(-0.258623\pi\)
−0.972582 + 0.232561i \(0.925290\pi\)
\(642\) 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 0.605881 0.795556i \(-0.292821\pi\)
−0.991912 + 0.126930i \(0.959488\pi\)
\(648\) 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 \(0.337958\pi\)
−0.999894 + 0.0145285i \(0.995375\pi\)
\(654\) 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 \(-0.620635\pi\)
−0.369978 + 0.929040i \(0.620635\pi\)
\(660\) 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 −0.998430 0.0560084i \(-0.982163\pi\)
0.547720 + 0.836662i \(0.315496\pi\)
\(678\) 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 0.829850 0.557986i \(-0.188426\pi\)
−0.898155 + 0.439678i \(0.855092\pi\)
\(684\) 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 \(-0.466354\pi\)
0.105504 + 0.994419i \(0.466354\pi\)
\(702\) 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 \(0.344831\pi\)
−0.999348 + 0.0361132i \(0.988502\pi\)
\(720\) 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 \(-0.655688\pi\)
−0.469838 + 0.882753i \(0.655688\pi\)
\(744\) 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 −0.858790 0.512327i \(-0.828784\pi\)
0.873083 + 0.487571i \(0.162117\pi\)
\(762\) 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 \(-0.979551\pi\)
0.443372 0.896338i \(-0.353782\pi\)
\(774\) 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
\(791\) 0