Properties

Label 108.4.b.b.107.8
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.8
Root \(-2.18604 - 2.07664i\) of defining polynomial
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.b.107.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +O(q^{10})\) \(q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +(4.18188 - 0.627790i) q^{10} -56.3941 q^{11} -41.3170 q^{13} +(-73.2423 + 10.9953i) q^{14} +(52.9643 - 35.9274i) q^{16} -51.0410i q^{17} +79.0640i q^{19} +(3.51196 + 11.4335i) q^{20} +(-23.6801 - 157.739i) q^{22} -27.3688 q^{23} +122.765 q^{25} +(-17.3491 - 115.567i) q^{26} +(-61.5093 - 200.248i) q^{28} +134.567i q^{29} +187.192i q^{31} +(122.732 + 133.060i) q^{32} +(142.766 - 21.4323i) q^{34} +39.1491 q^{35} -196.585 q^{37} +(-221.149 + 33.1992i) q^{38} +(-30.5057 + 14.6242i) q^{40} -298.015i q^{41} +465.576i q^{43} +(431.267 - 132.470i) q^{44} +(-11.4922 - 76.5529i) q^{46} +373.845 q^{47} -342.667 q^{49} +(51.5492 + 343.383i) q^{50} +(315.966 - 97.0539i) q^{52} +620.093i q^{53} +84.3140i q^{55} +(534.283 - 256.131i) q^{56} +(-376.396 + 56.5052i) q^{58} +321.152 q^{59} +674.699 q^{61} +(-523.593 + 78.6026i) q^{62} +(-320.644 + 399.164i) q^{64} +61.7724i q^{65} -576.075i q^{67} +(119.896 + 390.329i) q^{68} +(16.4388 + 109.503i) q^{70} -223.813 q^{71} +70.1371 q^{73} +(-82.5465 - 549.864i) q^{74} +(-185.722 - 604.631i) q^{76} -1476.69i q^{77} -1052.32i q^{79} +(-53.7145 - 79.1862i) q^{80} +(833.574 - 125.137i) q^{82} -1219.05 q^{83} -76.3107 q^{85} +(-1302.26 + 195.497i) q^{86} +(551.621 + 1150.66i) q^{88} +1340.64i q^{89} -1081.89i q^{91} +(209.299 - 64.2895i) q^{92} +(156.979 + 1045.68i) q^{94} +118.207 q^{95} -576.059 q^{97} +(-143.887 - 958.467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{4} + O(q^{10}) \) \( 12q + 6q^{4} + 42q^{10} - 72q^{13} + 114q^{16} + 66q^{22} - 384q^{25} - 282q^{28} - 324q^{34} - 240q^{37} + 774q^{40} + 1752q^{46} + 288q^{49} + 924q^{52} - 948q^{58} + 144q^{61} - 3066q^{64} - 3558q^{70} + 156q^{73} + 576q^{76} + 5832q^{82} - 168q^{85} + 5022q^{88} - 3444q^{94} + 516q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.419903 + 2.79708i 0.148458 + 0.988919i
\(3\) 0 0
\(4\) −7.64736 + 2.34901i −0.955920 + 0.293626i
\(5\) 1.49508i 0.133724i −0.997762 0.0668622i \(-0.978701\pi\)
0.997762 0.0668622i \(-0.0212988\pi\)
\(6\) 0 0
\(7\) 26.1852i 1.41387i 0.707279 + 0.706935i \(0.249923\pi\)
−0.707279 + 0.706935i \(0.750077\pi\)
\(8\) −9.78152 20.4040i −0.432286 0.901736i
\(9\) 0 0
\(10\) 4.18188 0.627790i 0.132243 0.0198525i
\(11\) −56.3941 −1.54577 −0.772885 0.634546i \(-0.781187\pi\)
−0.772885 + 0.634546i \(0.781187\pi\)
\(12\) 0 0
\(13\) −41.3170 −0.881482 −0.440741 0.897634i \(-0.645284\pi\)
−0.440741 + 0.897634i \(0.645284\pi\)
\(14\) −73.2423 + 10.9953i −1.39820 + 0.209900i
\(15\) 0 0
\(16\) 52.9643 35.9274i 0.827568 0.561366i
\(17\) 51.0410i 0.728192i −0.931361 0.364096i \(-0.881378\pi\)
0.931361 0.364096i \(-0.118622\pi\)
\(18\) 0 0
\(19\) 79.0640i 0.954659i 0.878724 + 0.477330i \(0.158395\pi\)
−0.878724 + 0.477330i \(0.841605\pi\)
\(20\) 3.51196 + 11.4335i 0.0392650 + 0.127830i
\(21\) 0 0
\(22\) −23.6801 157.739i −0.229482 1.52864i
\(23\) −27.3688 −0.248121 −0.124061 0.992275i \(-0.539592\pi\)
−0.124061 + 0.992275i \(0.539592\pi\)
\(24\) 0 0
\(25\) 122.765 0.982118
\(26\) −17.3491 115.567i −0.130863 0.871714i
\(27\) 0 0
\(28\) −61.5093 200.248i −0.415149 1.35155i
\(29\) 134.567i 0.861674i 0.902430 + 0.430837i \(0.141782\pi\)
−0.902430 + 0.430837i \(0.858218\pi\)
\(30\) 0 0
\(31\) 187.192i 1.08454i 0.840204 + 0.542270i \(0.182435\pi\)
−0.840204 + 0.542270i \(0.817565\pi\)
\(32\) 122.732 + 133.060i 0.678004 + 0.735058i
\(33\) 0 0
\(34\) 142.766 21.4323i 0.720123 0.108106i
\(35\) 39.1491 0.189069
\(36\) 0 0
\(37\) −196.585 −0.873469 −0.436734 0.899590i \(-0.643865\pi\)
−0.436734 + 0.899590i \(0.643865\pi\)
\(38\) −221.149 + 33.1992i −0.944081 + 0.141727i
\(39\) 0 0
\(40\) −30.5057 + 14.6242i −0.120584 + 0.0578072i
\(41\) 298.015i 1.13517i −0.823313 0.567587i \(-0.807877\pi\)
0.823313 0.567587i \(-0.192123\pi\)
\(42\) 0 0
\(43\) 465.576i 1.65115i 0.564289 + 0.825577i \(0.309150\pi\)
−0.564289 + 0.825577i \(0.690850\pi\)
\(44\) 431.267 132.470i 1.47763 0.453878i
\(45\) 0 0
\(46\) −11.4922 76.5529i −0.0368356 0.245372i
\(47\) 373.845 1.16023 0.580116 0.814534i \(-0.303007\pi\)
0.580116 + 0.814534i \(0.303007\pi\)
\(48\) 0 0
\(49\) −342.667 −0.999028
\(50\) 51.5492 + 343.383i 0.145803 + 0.971235i
\(51\) 0 0
\(52\) 315.966 97.0539i 0.842627 0.258826i
\(53\) 620.093i 1.60710i 0.595237 + 0.803550i \(0.297058\pi\)
−0.595237 + 0.803550i \(0.702942\pi\)
\(54\) 0 0
\(55\) 84.3140i 0.206707i
\(56\) 534.283 256.131i 1.27494 0.611196i
\(57\) 0 0
\(58\) −376.396 + 56.5052i −0.852125 + 0.127922i
\(59\) 321.152 0.708652 0.354326 0.935122i \(-0.384710\pi\)
0.354326 + 0.935122i \(0.384710\pi\)
\(60\) 0 0
\(61\) 674.699 1.41617 0.708085 0.706127i \(-0.249559\pi\)
0.708085 + 0.706127i \(0.249559\pi\)
\(62\) −523.593 + 78.6026i −1.07252 + 0.161009i
\(63\) 0 0
\(64\) −320.644 + 399.164i −0.626257 + 0.779616i
\(65\) 61.7724i 0.117876i
\(66\) 0 0
\(67\) 576.075i 1.05043i −0.850970 0.525215i \(-0.823985\pi\)
0.850970 0.525215i \(-0.176015\pi\)
\(68\) 119.896 + 390.329i 0.213816 + 0.696094i
\(69\) 0 0
\(70\) 16.4388 + 109.503i 0.0280688 + 0.186974i
\(71\) −223.813 −0.374110 −0.187055 0.982349i \(-0.559894\pi\)
−0.187055 + 0.982349i \(0.559894\pi\)
\(72\) 0 0
\(73\) 70.1371 0.112451 0.0562255 0.998418i \(-0.482093\pi\)
0.0562255 + 0.998418i \(0.482093\pi\)
\(74\) −82.5465 549.864i −0.129673 0.863790i
\(75\) 0 0
\(76\) −185.722 604.631i −0.280313 0.912578i
\(77\) 1476.69i 2.18552i
\(78\) 0 0
\(79\) 1052.32i 1.49868i −0.662187 0.749338i \(-0.730372\pi\)
0.662187 0.749338i \(-0.269628\pi\)
\(80\) −53.7145 79.1862i −0.0750684 0.110666i
\(81\) 0 0
\(82\) 833.574 125.137i 1.12260 0.168526i
\(83\) −1219.05 −1.61214 −0.806070 0.591820i \(-0.798409\pi\)
−0.806070 + 0.591820i \(0.798409\pi\)
\(84\) 0 0
\(85\) −76.3107 −0.0973771
\(86\) −1302.26 + 195.497i −1.63286 + 0.245127i
\(87\) 0 0
\(88\) 551.621 + 1150.66i 0.668215 + 1.39388i
\(89\) 1340.64i 1.59672i 0.602183 + 0.798358i \(0.294298\pi\)
−0.602183 + 0.798358i \(0.705702\pi\)
\(90\) 0 0
\(91\) 1081.89i 1.24630i
\(92\) 209.299 64.2895i 0.237184 0.0728548i
\(93\) 0 0
\(94\) 156.979 + 1045.68i 0.172246 + 1.14737i
\(95\) 118.207 0.127661
\(96\) 0 0
\(97\) −576.059 −0.602989 −0.301494 0.953468i \(-0.597485\pi\)
−0.301494 + 0.953468i \(0.597485\pi\)
\(98\) −143.887 958.467i −0.148314 0.987957i
\(99\) 0 0
\(100\) −938.826 + 288.375i −0.938826 + 0.288375i
\(101\) 116.079i 0.114359i 0.998364 + 0.0571797i \(0.0182108\pi\)
−0.998364 + 0.0571797i \(0.981789\pi\)
\(102\) 0 0
\(103\) 165.074i 0.157915i −0.996878 0.0789573i \(-0.974841\pi\)
0.996878 0.0789573i \(-0.0251591\pi\)
\(104\) 404.143 + 843.030i 0.381052 + 0.794864i
\(105\) 0 0
\(106\) −1734.45 + 260.379i −1.58929 + 0.238587i
\(107\) −936.718 −0.846318 −0.423159 0.906056i \(-0.639079\pi\)
−0.423159 + 0.906056i \(0.639079\pi\)
\(108\) 0 0
\(109\) 346.957 0.304885 0.152443 0.988312i \(-0.451286\pi\)
0.152443 + 0.988312i \(0.451286\pi\)
\(110\) −235.833 + 35.4037i −0.204417 + 0.0306874i
\(111\) 0 0
\(112\) 940.768 + 1386.88i 0.793698 + 1.17007i
\(113\) 1462.22i 1.21729i −0.793443 0.608645i \(-0.791713\pi\)
0.793443 0.608645i \(-0.208287\pi\)
\(114\) 0 0
\(115\) 40.9187i 0.0331799i
\(116\) −316.100 1029.09i −0.253010 0.823691i
\(117\) 0 0
\(118\) 134.853 + 898.290i 0.105205 + 0.700799i
\(119\) 1336.52 1.02957
\(120\) 0 0
\(121\) 1849.30 1.38941
\(122\) 283.308 + 1887.19i 0.210242 + 1.40048i
\(123\) 0 0
\(124\) −439.716 1431.53i −0.318449 1.03673i
\(125\) 370.429i 0.265058i
\(126\) 0 0
\(127\) 265.004i 0.185160i 0.995705 + 0.0925800i \(0.0295114\pi\)
−0.995705 + 0.0925800i \(0.970489\pi\)
\(128\) −1251.13 729.258i −0.863950 0.503577i
\(129\) 0 0
\(130\) −172.783 + 25.9384i −0.116569 + 0.0174996i
\(131\) −1151.86 −0.768231 −0.384115 0.923285i \(-0.625493\pi\)
−0.384115 + 0.923285i \(0.625493\pi\)
\(132\) 0 0
\(133\) −2070.31 −1.34976
\(134\) 1611.33 241.896i 1.03879 0.155945i
\(135\) 0 0
\(136\) −1041.44 + 499.259i −0.656637 + 0.314787i
\(137\) 2348.67i 1.46467i 0.680943 + 0.732337i \(0.261570\pi\)
−0.680943 + 0.732337i \(0.738430\pi\)
\(138\) 0 0
\(139\) 215.240i 0.131341i −0.997841 0.0656706i \(-0.979081\pi\)
0.997841 0.0656706i \(-0.0209187\pi\)
\(140\) −299.388 + 91.9616i −0.180735 + 0.0555155i
\(141\) 0 0
\(142\) −93.9799 626.025i −0.0555396 0.369964i
\(143\) 2330.04 1.36257
\(144\) 0 0
\(145\) 201.190 0.115227
\(146\) 29.4508 + 196.179i 0.0166943 + 0.111205i
\(147\) 0 0
\(148\) 1503.36 461.779i 0.834967 0.256473i
\(149\) 219.954i 0.120935i 0.998170 + 0.0604674i \(0.0192591\pi\)
−0.998170 + 0.0604674i \(0.980741\pi\)
\(150\) 0 0
\(151\) 1148.02i 0.618703i −0.950948 0.309351i \(-0.899888\pi\)
0.950948 0.309351i \(-0.100112\pi\)
\(152\) 1613.22 773.366i 0.860851 0.412686i
\(153\) 0 0
\(154\) 4130.44 620.068i 2.16130 0.324458i
\(155\) 279.869 0.145030
\(156\) 0 0
\(157\) −276.320 −0.140463 −0.0702316 0.997531i \(-0.522374\pi\)
−0.0702316 + 0.997531i \(0.522374\pi\)
\(158\) 2943.43 441.873i 1.48207 0.222491i
\(159\) 0 0
\(160\) 198.936 183.495i 0.0982952 0.0906658i
\(161\) 716.659i 0.350811i
\(162\) 0 0
\(163\) 1419.15i 0.681941i 0.940074 + 0.340971i \(0.110756\pi\)
−0.940074 + 0.340971i \(0.889244\pi\)
\(164\) 700.040 + 2279.03i 0.333317 + 1.08514i
\(165\) 0 0
\(166\) −511.880 3409.77i −0.239335 1.59428i
\(167\) 3508.69 1.62581 0.812906 0.582394i \(-0.197884\pi\)
0.812906 + 0.582394i \(0.197884\pi\)
\(168\) 0 0
\(169\) −489.908 −0.222990
\(170\) −32.0431 213.447i −0.0144564 0.0962980i
\(171\) 0 0
\(172\) −1093.64 3560.43i −0.484822 1.57837i
\(173\) 330.965i 0.145450i −0.997352 0.0727248i \(-0.976831\pi\)
0.997352 0.0727248i \(-0.0231695\pi\)
\(174\) 0 0
\(175\) 3214.62i 1.38859i
\(176\) −2986.88 + 2026.10i −1.27923 + 0.867743i
\(177\) 0 0
\(178\) −3749.89 + 562.939i −1.57902 + 0.237045i
\(179\) −1136.75 −0.474662 −0.237331 0.971429i \(-0.576273\pi\)
−0.237331 + 0.971429i \(0.576273\pi\)
\(180\) 0 0
\(181\) 2056.92 0.844692 0.422346 0.906435i \(-0.361207\pi\)
0.422346 + 0.906435i \(0.361207\pi\)
\(182\) 3026.15 454.291i 1.23249 0.185023i
\(183\) 0 0
\(184\) 267.709 + 558.432i 0.107259 + 0.223740i
\(185\) 293.911i 0.116804i
\(186\) 0 0
\(187\) 2878.42i 1.12562i
\(188\) −2858.93 + 878.164i −1.10909 + 0.340674i
\(189\) 0 0
\(190\) 49.6356 + 330.636i 0.0189523 + 0.126247i
\(191\) −1983.23 −0.751316 −0.375658 0.926758i \(-0.622583\pi\)
−0.375658 + 0.926758i \(0.622583\pi\)
\(192\) 0 0
\(193\) −189.908 −0.0708283 −0.0354141 0.999373i \(-0.511275\pi\)
−0.0354141 + 0.999373i \(0.511275\pi\)
\(194\) −241.889 1611.29i −0.0895185 0.596307i
\(195\) 0 0
\(196\) 2620.50 804.926i 0.954991 0.293340i
\(197\) 2160.42i 0.781337i 0.920531 + 0.390669i \(0.127756\pi\)
−0.920531 + 0.390669i \(0.872244\pi\)
\(198\) 0 0
\(199\) 2656.23i 0.946205i 0.881007 + 0.473103i \(0.156866\pi\)
−0.881007 + 0.473103i \(0.843134\pi\)
\(200\) −1200.83 2504.89i −0.424556 0.885611i
\(201\) 0 0
\(202\) −324.683 + 48.7419i −0.113092 + 0.0169776i
\(203\) −3523.68 −1.21829
\(204\) 0 0
\(205\) −445.558 −0.151801
\(206\) 461.725 69.3149i 0.156165 0.0234437i
\(207\) 0 0
\(208\) −2188.33 + 1484.41i −0.729486 + 0.494834i
\(209\) 4458.75i 1.47568i
\(210\) 0 0
\(211\) 1001.20i 0.326662i 0.986571 + 0.163331i \(0.0522239\pi\)
−0.986571 + 0.163331i \(0.947776\pi\)
\(212\) −1456.60 4742.07i −0.471886 1.53626i
\(213\) 0 0
\(214\) −393.331 2620.08i −0.125643 0.836939i
\(215\) 696.075 0.220800
\(216\) 0 0
\(217\) −4901.68 −1.53340
\(218\) 145.688 + 970.469i 0.0452626 + 0.301507i
\(219\) 0 0
\(220\) −198.054 644.780i −0.0606946 0.197596i
\(221\) 2108.86i 0.641888i
\(222\) 0 0
\(223\) 3193.62i 0.959015i 0.877538 + 0.479507i \(0.159185\pi\)
−0.877538 + 0.479507i \(0.840815\pi\)
\(224\) −3484.20 + 3213.76i −1.03928 + 0.958610i
\(225\) 0 0
\(226\) 4089.94 613.989i 1.20380 0.180717i
\(227\) −1714.72 −0.501366 −0.250683 0.968069i \(-0.580655\pi\)
−0.250683 + 0.968069i \(0.580655\pi\)
\(228\) 0 0
\(229\) −407.497 −0.117590 −0.0587951 0.998270i \(-0.518726\pi\)
−0.0587951 + 0.998270i \(0.518726\pi\)
\(230\) −114.453 + 17.1819i −0.0328122 + 0.00492582i
\(231\) 0 0
\(232\) 2745.71 1316.27i 0.777003 0.372490i
\(233\) 3210.54i 0.902702i −0.892346 0.451351i \(-0.850942\pi\)
0.892346 0.451351i \(-0.149058\pi\)
\(234\) 0 0
\(235\) 558.930i 0.155151i
\(236\) −2455.97 + 754.389i −0.677415 + 0.208079i
\(237\) 0 0
\(238\) 561.209 + 3738.36i 0.152848 + 1.01816i
\(239\) 1561.19 0.422532 0.211266 0.977429i \(-0.432241\pi\)
0.211266 + 0.977429i \(0.432241\pi\)
\(240\) 0 0
\(241\) 1460.89 0.390475 0.195238 0.980756i \(-0.437452\pi\)
0.195238 + 0.980756i \(0.437452\pi\)
\(242\) 776.526 + 5172.65i 0.206269 + 1.37401i
\(243\) 0 0
\(244\) −5159.67 + 1584.87i −1.35375 + 0.415824i
\(245\) 512.316i 0.133594i
\(246\) 0 0
\(247\) 3266.69i 0.841515i
\(248\) 3819.47 1831.03i 0.977970 0.468832i
\(249\) 0 0
\(250\) 1036.12 155.544i 0.262120 0.0393499i
\(251\) −6868.44 −1.72722 −0.863609 0.504162i \(-0.831802\pi\)
−0.863609 + 0.504162i \(0.831802\pi\)
\(252\) 0 0
\(253\) 1543.44 0.383539
\(254\) −741.239 + 111.276i −0.183108 + 0.0274885i
\(255\) 0 0
\(256\) 1514.44 3805.74i 0.369737 0.929137i
\(257\) 4450.84i 1.08029i 0.841570 + 0.540147i \(0.181632\pi\)
−0.841570 + 0.540147i \(0.818368\pi\)
\(258\) 0 0
\(259\) 5147.62i 1.23497i
\(260\) −145.104 472.396i −0.0346114 0.112680i
\(261\) 0 0
\(262\) −483.668 3221.84i −0.114050 0.759718i
\(263\) 6525.31 1.52991 0.764957 0.644081i \(-0.222760\pi\)
0.764957 + 0.644081i \(0.222760\pi\)
\(264\) 0 0
\(265\) 927.091 0.214909
\(266\) −869.329 5790.83i −0.200383 1.33481i
\(267\) 0 0
\(268\) 1353.20 + 4405.46i 0.308433 + 1.00413i
\(269\) 3222.22i 0.730343i −0.930940 0.365171i \(-0.881010\pi\)
0.930940 0.365171i \(-0.118990\pi\)
\(270\) 0 0
\(271\) 7368.93i 1.65177i −0.563837 0.825886i \(-0.690675\pi\)
0.563837 0.825886i \(-0.309325\pi\)
\(272\) −1833.77 2703.35i −0.408782 0.602628i
\(273\) 0 0
\(274\) −6569.42 + 986.212i −1.44844 + 0.217443i
\(275\) −6923.21 −1.51813
\(276\) 0 0
\(277\) 9078.61 1.96924 0.984622 0.174699i \(-0.0558952\pi\)
0.984622 + 0.174699i \(0.0558952\pi\)
\(278\) 602.045 90.3800i 0.129886 0.0194987i
\(279\) 0 0
\(280\) −382.938 798.798i −0.0817319 0.170490i
\(281\) 2613.34i 0.554801i −0.960754 0.277400i \(-0.910527\pi\)
0.960754 0.277400i \(-0.0894729\pi\)
\(282\) 0 0
\(283\) 927.970i 0.194919i −0.995239 0.0974596i \(-0.968928\pi\)
0.995239 0.0974596i \(-0.0310717\pi\)
\(284\) 1711.58 525.739i 0.357619 0.109848i
\(285\) 0 0
\(286\) 978.388 + 6517.31i 0.202284 + 1.34747i
\(287\) 7803.60 1.60499
\(288\) 0 0
\(289\) 2307.81 0.469736
\(290\) 84.4801 + 562.745i 0.0171064 + 0.113950i
\(291\) 0 0
\(292\) −536.364 + 164.753i −0.107494 + 0.0330185i
\(293\) 5351.73i 1.06707i 0.845778 + 0.533535i \(0.179137\pi\)
−0.845778 + 0.533535i \(0.820863\pi\)
\(294\) 0 0
\(295\) 480.150i 0.0947641i
\(296\) 1922.90 + 4011.11i 0.377589 + 0.787639i
\(297\) 0 0
\(298\) −615.229 + 92.3591i −0.119595 + 0.0179538i
\(299\) 1130.80 0.218714
\(300\) 0 0
\(301\) −12191.2 −2.33452
\(302\) 3211.10 482.055i 0.611847 0.0918514i
\(303\) 0 0
\(304\) 2840.57 + 4187.57i 0.535913 + 0.790045i
\(305\) 1008.73i 0.189377i
\(306\) 0 0
\(307\) 1892.38i 0.351804i 0.984408 + 0.175902i \(0.0562842\pi\)
−0.984408 + 0.175902i \(0.943716\pi\)
\(308\) 3468.76 + 11292.8i 0.641725 + 2.08918i
\(309\) 0 0
\(310\) 117.518 + 782.816i 0.0215308 + 0.143422i
\(311\) 5645.22 1.02930 0.514648 0.857402i \(-0.327923\pi\)
0.514648 + 0.857402i \(0.327923\pi\)
\(312\) 0 0
\(313\) −818.001 −0.147719 −0.0738597 0.997269i \(-0.523532\pi\)
−0.0738597 + 0.997269i \(0.523532\pi\)
\(314\) −116.027 772.890i −0.0208529 0.138907i
\(315\) 0 0
\(316\) 2471.91 + 8047.49i 0.440050 + 1.43262i
\(317\) 1946.72i 0.344917i −0.985017 0.172458i \(-0.944829\pi\)
0.985017 0.172458i \(-0.0551710\pi\)
\(318\) 0 0
\(319\) 7588.81i 1.33195i
\(320\) 596.784 + 479.390i 0.104254 + 0.0837459i
\(321\) 0 0
\(322\) 2004.55 300.927i 0.346924 0.0520807i
\(323\) 4035.51 0.695176
\(324\) 0 0
\(325\) −5072.27 −0.865719
\(326\) −3969.48 + 595.905i −0.674385 + 0.101240i
\(327\) 0 0
\(328\) −6080.69 + 2915.04i −1.02363 + 0.490720i
\(329\) 9789.22i 1.64042i
\(330\) 0 0
\(331\) 3404.83i 0.565396i −0.959209 0.282698i \(-0.908771\pi\)
0.959209 0.282698i \(-0.0912295\pi\)
\(332\) 9322.48 2863.55i 1.54108 0.473366i
\(333\) 0 0
\(334\) 1473.31 + 9814.11i 0.241365 + 1.60780i
\(335\) −861.281 −0.140468
\(336\) 0 0
\(337\) 7072.15 1.14316 0.571579 0.820547i \(-0.306331\pi\)
0.571579 + 0.820547i \(0.306331\pi\)
\(338\) −205.714 1370.31i −0.0331046 0.220519i
\(339\) 0 0
\(340\) 583.575 179.254i 0.0930848 0.0285924i
\(341\) 10556.6i 1.67645i
\(342\) 0 0
\(343\) 8.73194i 0.00137458i
\(344\) 9499.60 4554.04i 1.48891 0.713771i
\(345\) 0 0
\(346\) 925.736 138.973i 0.143838 0.0215932i
\(347\) 5783.02 0.894665 0.447332 0.894368i \(-0.352374\pi\)
0.447332 + 0.894368i \(0.352374\pi\)
\(348\) 0 0
\(349\) 1748.60 0.268196 0.134098 0.990968i \(-0.457186\pi\)
0.134098 + 0.990968i \(0.457186\pi\)
\(350\) −8991.57 + 1349.83i −1.37320 + 0.206147i
\(351\) 0 0
\(352\) −6921.36 7503.79i −1.04804 1.13623i
\(353\) 9552.31i 1.44028i 0.693830 + 0.720139i \(0.255922\pi\)
−0.693830 + 0.720139i \(0.744078\pi\)
\(354\) 0 0
\(355\) 334.620i 0.0500276i
\(356\) −3149.18 10252.4i −0.468837 1.52633i
\(357\) 0 0
\(358\) −477.323 3179.58i −0.0704673 0.469402i
\(359\) 921.392 0.135457 0.0677287 0.997704i \(-0.478425\pi\)
0.0677287 + 0.997704i \(0.478425\pi\)
\(360\) 0 0
\(361\) 607.881 0.0886254
\(362\) 863.704 + 5753.37i 0.125401 + 0.835332i
\(363\) 0 0
\(364\) 2541.38 + 8273.64i 0.365946 + 1.19136i
\(365\) 104.861i 0.0150375i
\(366\) 0 0
\(367\) 8490.66i 1.20765i 0.797115 + 0.603827i \(0.206358\pi\)
−0.797115 + 0.603827i \(0.793642\pi\)
\(368\) −1449.57 + 983.291i −0.205337 + 0.139287i
\(369\) 0 0
\(370\) −822.094 + 123.414i −0.115510 + 0.0173405i
\(371\) −16237.3 −2.27223
\(372\) 0 0
\(373\) 2824.92 0.392142 0.196071 0.980590i \(-0.437182\pi\)
0.196071 + 0.980590i \(0.437182\pi\)
\(374\) −8051.17 + 1208.65i −1.11314 + 0.167107i
\(375\) 0 0
\(376\) −3656.77 7627.92i −0.501552 1.04622i
\(377\) 5559.92i 0.759550i
\(378\) 0 0
\(379\) 5322.35i 0.721348i −0.932692 0.360674i \(-0.882547\pi\)
0.932692 0.360674i \(-0.117453\pi\)
\(380\) −903.975 + 277.670i −0.122034 + 0.0374847i
\(381\) 0 0
\(382\) −832.763 5547.26i −0.111539 0.742990i
\(383\) −8320.49 −1.11007 −0.555035 0.831827i \(-0.687295\pi\)
−0.555035 + 0.831827i \(0.687295\pi\)
\(384\) 0 0
\(385\) −2207.78 −0.292257
\(386\) −79.7428 531.188i −0.0105150 0.0700434i
\(387\) 0 0
\(388\) 4405.33 1353.17i 0.576409 0.177053i
\(389\) 8358.52i 1.08944i −0.838617 0.544722i \(-0.816635\pi\)
0.838617 0.544722i \(-0.183365\pi\)
\(390\) 0 0
\(391\) 1396.93i 0.180680i
\(392\) 3351.80 + 6991.76i 0.431866 + 0.900860i
\(393\) 0 0
\(394\) −6042.87 + 907.166i −0.772679 + 0.115996i
\(395\) −1573.31 −0.200410
\(396\) 0 0
\(397\) 7283.17 0.920735 0.460367 0.887728i \(-0.347718\pi\)
0.460367 + 0.887728i \(0.347718\pi\)
\(398\) −7429.69 + 1115.36i −0.935720 + 0.140472i
\(399\) 0 0
\(400\) 6502.15 4410.62i 0.812769 0.551327i
\(401\) 1549.41i 0.192952i −0.995335 0.0964759i \(-0.969243\pi\)
0.995335 0.0964759i \(-0.0307571\pi\)
\(402\) 0 0
\(403\) 7734.22i 0.956003i
\(404\) −272.671 887.699i −0.0335789 0.109318i
\(405\) 0 0
\(406\) −1479.60 9856.03i −0.180866 1.20479i
\(407\) 11086.2 1.35018
\(408\) 0 0
\(409\) 3291.67 0.397952 0.198976 0.980004i \(-0.436238\pi\)
0.198976 + 0.980004i \(0.436238\pi\)
\(410\) −187.091 1246.26i −0.0225360 0.150118i
\(411\) 0 0
\(412\) 387.759 + 1262.38i 0.0463678 + 0.150954i
\(413\) 8409.45i 1.00194i
\(414\) 0 0
\(415\) 1822.58i 0.215583i
\(416\) −5070.91 5497.62i −0.597649 0.647940i
\(417\) 0 0
\(418\) 12471.5 1872.24i 1.45933 0.219077i
\(419\) −5299.78 −0.617927 −0.308964 0.951074i \(-0.599982\pi\)
−0.308964 + 0.951074i \(0.599982\pi\)
\(420\) 0 0
\(421\) −10681.4 −1.23653 −0.618265 0.785970i \(-0.712164\pi\)
−0.618265 + 0.785970i \(0.712164\pi\)
\(422\) −2800.45 + 420.408i −0.323042 + 0.0484956i
\(423\) 0 0
\(424\) 12652.4 6065.45i 1.44918 0.694727i
\(425\) 6266.04i 0.715170i
\(426\) 0 0
\(427\) 17667.2i 2.00228i
\(428\) 7163.43 2200.36i 0.809012 0.248501i
\(429\) 0 0
\(430\) 292.284 + 1946.98i 0.0327795 + 0.218353i
\(431\) −9866.13 −1.10263 −0.551316 0.834296i \(-0.685874\pi\)
−0.551316 + 0.834296i \(0.685874\pi\)
\(432\) 0 0
\(433\) −12560.2 −1.39400 −0.697002 0.717069i \(-0.745483\pi\)
−0.697002 + 0.717069i \(0.745483\pi\)
\(434\) −2058.23 13710.4i −0.227645 1.51641i
\(435\) 0 0
\(436\) −2653.31 + 815.005i −0.291446 + 0.0895221i
\(437\) 2163.89i 0.236871i
\(438\) 0 0
\(439\) 929.228i 0.101024i 0.998723 + 0.0505121i \(0.0160854\pi\)
−0.998723 + 0.0505121i \(0.983915\pi\)
\(440\) 1720.34 824.719i 0.186396 0.0893567i
\(441\) 0 0
\(442\) −5898.66 + 885.516i −0.634775 + 0.0952935i
\(443\) 4373.85 0.469092 0.234546 0.972105i \(-0.424640\pi\)
0.234546 + 0.972105i \(0.424640\pi\)
\(444\) 0 0
\(445\) 2004.37 0.213520
\(446\) −8932.81 + 1341.01i −0.948388 + 0.142373i
\(447\) 0 0
\(448\) −10452.2 8396.13i −1.10228 0.885446i
\(449\) 14149.5i 1.48721i 0.668618 + 0.743606i \(0.266886\pi\)
−0.668618 + 0.743606i \(0.733114\pi\)
\(450\) 0 0
\(451\) 16806.3i 1.75472i
\(452\) 3434.76 + 11182.1i 0.357428 + 1.16363i
\(453\) 0 0
\(454\) −720.017 4796.22i −0.0744319 0.495810i
\(455\) −1617.52 −0.166661
\(456\) 0 0
\(457\) −12582.4 −1.28792 −0.643960 0.765059i \(-0.722710\pi\)
−0.643960 + 0.765059i \(0.722710\pi\)
\(458\) −171.109 1139.80i −0.0174572 0.116287i
\(459\) 0 0
\(460\) −96.1183 312.920i −0.00974247 0.0317173i
\(461\) 10602.2i 1.07114i 0.844492 + 0.535568i \(0.179902\pi\)
−0.844492 + 0.535568i \(0.820098\pi\)
\(462\) 0 0
\(463\) 5080.88i 0.509997i 0.966941 + 0.254999i \(0.0820750\pi\)
−0.966941 + 0.254999i \(0.917925\pi\)
\(464\) 4834.66 + 7127.27i 0.483714 + 0.713093i
\(465\) 0 0
\(466\) 8980.16 1348.12i 0.892699 0.134013i
\(467\) −6903.92 −0.684102 −0.342051 0.939681i \(-0.611121\pi\)
−0.342051 + 0.939681i \(0.611121\pi\)
\(468\) 0 0
\(469\) 15084.7 1.48517
\(470\) 1563.37 234.696i 0.153432 0.0230335i
\(471\) 0 0
\(472\) −3141.36 6552.78i −0.306341 0.639017i
\(473\) 26255.8i 2.55231i
\(474\) 0 0
\(475\) 9706.27i 0.937588i
\(476\) −10220.9 + 3139.50i −0.984186 + 0.302308i
\(477\) 0 0
\(478\) 655.548 + 4366.78i 0.0627282 + 0.417849i
\(479\) 5114.56 0.487871 0.243936 0.969791i \(-0.421561\pi\)
0.243936 + 0.969791i \(0.421561\pi\)
\(480\) 0 0
\(481\) 8122.29 0.769947
\(482\) 613.434 + 4086.25i 0.0579692 + 0.386148i
\(483\) 0 0
\(484\) −14142.3 + 4344.02i −1.32816 + 0.407966i
\(485\) 861.257i 0.0806344i
\(486\) 0 0
\(487\) 15594.2i 1.45101i 0.688218 + 0.725504i \(0.258393\pi\)
−0.688218 + 0.725504i \(0.741607\pi\)
\(488\) −6599.58 13766.5i −0.612191 1.27701i
\(489\) 0 0
\(490\) −1432.99 + 215.123i −0.132114 + 0.0198332i
\(491\) 10521.0 0.967023 0.483511 0.875338i \(-0.339361\pi\)
0.483511 + 0.875338i \(0.339361\pi\)
\(492\) 0 0
\(493\) 6868.46 0.627464
\(494\) 9137.20 1371.69i 0.832190 0.124930i
\(495\) 0 0
\(496\) 6725.34 + 9914.52i 0.608824 + 0.897531i
\(497\) 5860.61i 0.528942i
\(498\) 0 0
\(499\) 8984.43i 0.806009i −0.915198 0.403004i \(-0.867966\pi\)
0.915198 0.403004i \(-0.132034\pi\)
\(500\) 870.141 + 2832.81i 0.0778278 + 0.253374i
\(501\) 0 0
\(502\) −2884.08 19211.6i −0.256420 1.70808i
\(503\) 4299.12 0.381090 0.190545 0.981678i \(-0.438974\pi\)
0.190545 + 0.981678i \(0.438974\pi\)
\(504\) 0 0
\(505\) 173.548 0.0152926
\(506\) 648.095 + 4317.13i 0.0569394 + 0.379288i
\(507\) 0 0
\(508\) −622.497 2026.58i −0.0543678 0.176998i
\(509\) 2984.83i 0.259922i 0.991519 + 0.129961i \(0.0414853\pi\)
−0.991519 + 0.129961i \(0.958515\pi\)
\(510\) 0 0
\(511\) 1836.56i 0.158991i
\(512\) 11280.9 + 2637.98i 0.973731 + 0.227702i
\(513\) 0 0
\(514\) −12449.4 + 1868.92i −1.06832 + 0.160378i
\(515\) −246.799 −0.0211170
\(516\) 0 0
\(517\) −21082.7 −1.79345
\(518\) 14398.3 2161.50i 1.22129 0.183341i
\(519\) 0 0
\(520\) 1260.40 604.228i 0.106293 0.0509560i
\(521\) 12255.7i 1.03058i 0.857016 + 0.515290i \(0.172316\pi\)
−0.857016 + 0.515290i \(0.827684\pi\)
\(522\) 0 0
\(523\) 15148.5i 1.26654i −0.773932 0.633269i \(-0.781713\pi\)
0.773932 0.633269i \(-0.218287\pi\)
\(524\) 8808.67 2705.72i 0.734367 0.225572i
\(525\) 0 0
\(526\) 2739.99 + 18251.8i 0.227128 + 1.51296i
\(527\) 9554.49 0.789754
\(528\) 0 0
\(529\) −11417.9 −0.938436
\(530\) 389.288 + 2593.15i 0.0319049 + 0.212527i
\(531\) 0 0
\(532\) 15832.4 4863.17i 1.29027 0.396326i
\(533\) 12313.1i 1.00064i
\(534\) 0 0
\(535\) 1400.47i 0.113173i
\(536\) −11754.2 + 5634.89i −0.947211 + 0.454086i
\(537\) 0 0
\(538\) 9012.82 1353.02i 0.722250 0.108425i
\(539\) 19324.4 1.54427
\(540\) 0 0
\(541\) 5723.84 0.454875 0.227437 0.973793i \(-0.426965\pi\)
0.227437 + 0.973793i \(0.426965\pi\)
\(542\) 20611.5 3094.23i 1.63347 0.245219i
\(543\) 0 0
\(544\) 6791.50 6264.36i 0.535263 0.493717i
\(545\) 518.730i 0.0407706i
\(546\) 0 0
\(547\) 8367.43i 0.654051i 0.945016 + 0.327025i \(0.106046\pi\)
−0.945016 + 0.327025i \(0.893954\pi\)
\(548\) −5517.04 17961.1i −0.430066 1.40011i
\(549\) 0 0
\(550\) −2907.08 19364.8i −0.225378 1.50131i
\(551\) −10639.4 −0.822605
\(552\) 0 0
\(553\) 27555.3 2.11893
\(554\) 3812.13 + 25393.6i 0.292350 + 1.94742i
\(555\) 0 0
\(556\) 505.601 + 1646.02i 0.0385652 + 0.125552i
\(557\) 15824.2i 1.20375i 0.798589 + 0.601877i \(0.205580\pi\)
−0.798589 + 0.601877i \(0.794420\pi\)
\(558\) 0 0
\(559\) 19236.2i 1.45546i
\(560\) 2073.51 1406.53i 0.156467 0.106137i
\(561\) 0 0
\(562\) 7309.74 1097.35i 0.548653 0.0823647i
\(563\) 2781.72 0.208233 0.104117 0.994565i \(-0.466798\pi\)
0.104117 + 0.994565i \(0.466798\pi\)
\(564\) 0 0
\(565\) −2186.14 −0.162781
\(566\) 2595.61 389.657i 0.192759 0.0289373i
\(567\) 0 0
\(568\) 2189.24 + 4566.68i 0.161722 + 0.337348i
\(569\) 4687.63i 0.345370i 0.984977 + 0.172685i \(0.0552443\pi\)
−0.984977 + 0.172685i \(0.944756\pi\)
\(570\) 0 0
\(571\) 15169.4i 1.11177i −0.831259 0.555885i \(-0.812379\pi\)
0.831259 0.555885i \(-0.187621\pi\)
\(572\) −17818.6 + 5473.27i −1.30251 + 0.400085i
\(573\) 0 0
\(574\) 3276.75 + 21827.3i 0.238274 + 1.58720i
\(575\) −3359.92 −0.243684
\(576\) 0 0
\(577\) −14452.3 −1.04273 −0.521367 0.853332i \(-0.674578\pi\)
−0.521367 + 0.853332i \(0.674578\pi\)
\(578\) 969.057 + 6455.15i 0.0697361 + 0.464531i
\(579\) 0 0
\(580\) −1538.57 + 472.596i −0.110148 + 0.0338336i
\(581\) 31921.0i 2.27936i
\(582\) 0 0
\(583\) 34969.6i 2.48421i
\(584\) −686.047 1431.07i −0.0486110 0.101401i
\(585\) 0 0
\(586\) −14969.3 + 2247.21i −1.05525 + 0.158415i
\(587\) 7405.55 0.520715 0.260358 0.965512i \(-0.416160\pi\)
0.260358 + 0.965512i \(0.416160\pi\)
\(588\) 0 0
\(589\) −14800.2 −1.03537
\(590\) 1343.02 201.616i 0.0937140 0.0140685i
\(591\) 0 0
\(592\) −10412.0 + 7062.79i −0.722855 + 0.490336i
\(593\) 19888.1i 1.37725i −0.725120 0.688623i \(-0.758216\pi\)
0.725120 0.688623i \(-0.241784\pi\)
\(594\) 0 0
\(595\) 1998.21i 0.137679i
\(596\) −516.672 1682.06i −0.0355096 0.115604i
\(597\) 0 0
\(598\) 474.824 + 3162.93i 0.0324699 + 0.216291i
\(599\) 2335.49 0.159308 0.0796539 0.996823i \(-0.474618\pi\)
0.0796539 + 0.996823i \(0.474618\pi\)
\(600\) 0 0
\(601\) 24547.9 1.66611 0.833054 0.553192i \(-0.186590\pi\)
0.833054 + 0.553192i \(0.186590\pi\)
\(602\) −5119.12 34099.9i −0.346578 2.30865i
\(603\) 0 0
\(604\) 2696.70 + 8779.29i 0.181667 + 0.591431i
\(605\) 2764.86i 0.185798i
\(606\) 0 0
\(607\) 18328.9i 1.22561i 0.790233 + 0.612806i \(0.209959\pi\)
−0.790233 + 0.612806i \(0.790041\pi\)
\(608\) −10520.2 + 9703.68i −0.701730 + 0.647263i
\(609\) 0 0
\(610\) 2821.51 423.570i 0.187278 0.0281145i
\(611\) −15446.1 −1.02272
\(612\) 0 0
\(613\) 6450.01 0.424981 0.212491 0.977163i \(-0.431843\pi\)
0.212491 + 0.977163i \(0.431843\pi\)
\(614\) −5293.15 + 794.616i −0.347906 + 0.0522282i
\(615\) 0 0
\(616\) −30130.4 + 14444.3i −1.97076 + 0.944769i
\(617\) 6724.96i 0.438795i 0.975636 + 0.219398i \(0.0704092\pi\)
−0.975636 + 0.219398i \(0.929591\pi\)
\(618\) 0 0
\(619\) 3136.55i 0.203665i −0.994802 0.101832i \(-0.967529\pi\)
0.994802 0.101832i \(-0.0324705\pi\)
\(620\) −2140.26 + 657.413i −0.138637 + 0.0425844i
\(621\) 0 0
\(622\) 2370.44 + 15790.2i 0.152807 + 1.01789i
\(623\) −35105.0 −2.25755
\(624\) 0 0
\(625\) 14791.8 0.946673
\(626\) −343.481 2288.02i −0.0219301 0.146082i
\(627\) 0 0
\(628\) 2113.12 649.077i 0.134272 0.0412436i
\(629\) 10033.9i 0.636053i
\(630\) 0 0
\(631\) 6061.57i 0.382420i 0.981549 + 0.191210i \(0.0612412\pi\)
−0.981549 + 0.191210i \(0.938759\pi\)
\(632\) −21471.5 + 10293.3i −1.35141 + 0.647857i
\(633\) 0 0
\(634\) 5445.14 817.433i 0.341095 0.0512057i
\(635\) 396.204 0.0247604
\(636\) 0 0
\(637\) 14157.9 0.880625
\(638\) 21226.6 3186.56i 1.31719 0.197739i
\(639\) 0 0
\(640\) −1090.30 + 1870.55i −0.0673406 + 0.115531i
\(641\) 18603.3i 1.14631i 0.819446 + 0.573157i \(0.194281\pi\)
−0.819446 + 0.573157i \(0.805719\pi\)
\(642\) 0 0
\(643\) 21602.4i 1.32491i −0.749103 0.662453i \(-0.769515\pi\)
0.749103 0.662453i \(-0.230485\pi\)
\(644\) 1683.44 + 5480.55i 0.103007 + 0.335348i
\(645\) 0 0
\(646\) 1694.52 + 11287.7i 0.103204 + 0.687472i
\(647\) −672.754 −0.0408790 −0.0204395 0.999791i \(-0.506507\pi\)
−0.0204395 + 0.999791i \(0.506507\pi\)
\(648\) 0 0
\(649\) −18111.1 −1.09541
\(650\) −2129.86 14187.6i −0.128523 0.856126i
\(651\) 0 0
\(652\) −3333.59 10852.8i −0.200236 0.651882i
\(653\) 3322.88i 0.199134i −0.995031 0.0995668i \(-0.968254\pi\)
0.995031 0.0995668i \(-0.0317457\pi\)
\(654\) 0 0
\(655\) 1722.12i 0.102731i
\(656\) −10706.9 15784.2i −0.637248 0.939434i
\(657\) 0 0
\(658\) −27381.3 + 4110.52i −1.62224 + 0.243533i
\(659\) 25093.7 1.48332 0.741662 0.670773i \(-0.234038\pi\)
0.741662 + 0.670773i \(0.234038\pi\)
\(660\) 0 0
\(661\) −28966.3 −1.70447 −0.852237 0.523157i \(-0.824754\pi\)
−0.852237 + 0.523157i \(0.824754\pi\)
\(662\) 9523.59 1429.70i 0.559131 0.0839376i
\(663\) 0 0
\(664\) 11924.1 + 24873.4i 0.696906 + 1.45373i
\(665\) 3095.29i 0.180496i
\(666\) 0 0
\(667\) 3682.95i 0.213800i
\(668\) −26832.2 + 8241.94i −1.55415 + 0.477381i
\(669\) 0 0
\(670\) −361.654 2409.08i −0.0208536 0.138912i
\(671\) −38049.1 −2.18907
\(672\) 0 0
\(673\) −4710.36 −0.269793 −0.134897 0.990860i \(-0.543070\pi\)
−0.134897 + 0.990860i \(0.543070\pi\)
\(674\) 2969.62 + 19781.4i 0.169711 + 1.13049i
\(675\) 0 0
\(676\) 3746.51 1150.80i 0.213160 0.0654755i
\(677\) 4784.53i 0.271617i 0.990735 + 0.135808i \(0.0433631\pi\)
−0.990735 + 0.135808i \(0.956637\pi\)
\(678\) 0 0
\(679\) 15084.2i 0.852548i
\(680\) 746.434 + 1557.04i 0.0420948 + 0.0878085i
\(681\) 0 0
\(682\) 29527.6 4432.73i 1.65787 0.248883i
\(683\) 18019.8 1.00953 0.504764 0.863258i \(-0.331580\pi\)
0.504764 + 0.863258i \(0.331580\pi\)
\(684\) 0 0
\(685\) 3511.46 0.195863
\(686\) −24.4240 + 3.66657i −0.00135935 + 0.000204067i
\(687\) 0 0
\(688\) 16726.9 + 24658.9i 0.926902 + 1.36644i
\(689\) 25620.4i 1.41663i
\(690\) 0 0
\(691\) 16956.5i 0.933511i 0.884386 + 0.466756i \(0.154577\pi\)
−0.884386 + 0.466756i \(0.845423\pi\)
\(692\) 777.439 + 2531.01i 0.0427078 + 0.139038i
\(693\) 0 0
\(694\) 2428.31 + 16175.6i 0.132820 + 0.884751i
\(695\) −321.802 −0.0175635
\(696\) 0 0
\(697\) −15211.0 −0.826625
\(698\) 734.243 + 4890.99i 0.0398159 + 0.265225i
\(699\) 0 0
\(700\) −7551.17 24583.4i −0.407725 1.32738i
\(701\) 30620.5i 1.64982i −0.565266 0.824909i \(-0.691226\pi\)
0.565266 0.824909i \(-0.308774\pi\)
\(702\) 0 0
\(703\) 15542.8i 0.833865i
\(704\) 18082.4 22510.5i 0.968050 1.20511i
\(705\) 0 0
\(706\) −26718.6 + 4011.04i −1.42432 + 0.213821i
\(707\) −3039.56 −0.161689
\(708\) 0 0
\(709\) 24192.8 1.28149 0.640747 0.767752i \(-0.278625\pi\)
0.640747 + 0.767752i \(0.278625\pi\)
\(710\) −935.961 + 140.508i −0.0494732 + 0.00742700i
\(711\) 0 0
\(712\) 27354.4 13113.5i 1.43982 0.690238i
\(713\) 5123.23i 0.269098i
\(714\) 0 0
\(715\) 3483.60i 0.182209i
\(716\) 8693.11 2670.23i 0.453739 0.139373i
\(717\) 0 0
\(718\) 386.895 + 2577.21i 0.0201098 + 0.133956i
\(719\) −37146.6 −1.92675 −0.963377 0.268151i \(-0.913588\pi\)
−0.963377 + 0.268151i \(0.913588\pi\)
\(720\) 0 0
\(721\) 4322.49 0.223271
\(722\) 255.251 + 1700.30i 0.0131571 + 0.0876433i
\(723\) 0 0
\(724\) −15730.0 + 4831.71i −0.807459 + 0.248024i
\(725\) 16520.1i 0.846265i
\(726\) 0 0
\(727\) 14614.3i 0.745551i 0.927922 + 0.372775i \(0.121594\pi\)
−0.927922 + 0.372775i \(0.878406\pi\)
\(728\) −22074.9 + 10582.6i −1.12383 + 0.538759i
\(729\) 0 0
\(730\) 293.305 44.0314i 0.0148708 0.00223243i
\(731\) 23763.5 1.20236
\(732\) 0 0
\(733\) −8044.73 −0.405374 −0.202687 0.979244i \(-0.564967\pi\)
−0.202687 + 0.979244i \(0.564967\pi\)
\(734\) −23749.1 + 3565.25i −1.19427 + 0.179286i
\(735\) 0 0
\(736\) −3359.03 3641.68i −0.168227 0.182384i
\(737\) 32487.3i 1.62372i
\(738\) 0 0
\(739\) 7025.01i 0.349688i −0.984596 0.174844i \(-0.944058\pi\)
0.984596 0.174844i \(-0.0559420\pi\)
\(740\) −690.399 2247.64i −0.0342967 0.111655i
\(741\) 0 0
\(742\) −6818.08 45417.0i −0.337331 2.24705i
\(743\) 27063.4 1.33629 0.668143 0.744033i \(-0.267089\pi\)
0.668143 + 0.744033i \(0.267089\pi\)
\(744\) 0 0
\(745\) 328.849 0.0161719
\(746\) 1186.19 + 7901.54i 0.0582166 + 0.387796i
\(747\) 0 0
\(748\) −6761.42 22012.3i −0.330511 1.07600i
\(749\) 24528.2i 1.19658i
\(750\) 0 0
\(751\) 11434.2i 0.555579i −0.960642 0.277789i \(-0.910398\pi\)
0.960642 0.277789i \(-0.0896017\pi\)
\(752\) 19800.4 13431.3i 0.960170 0.651315i
\(753\) 0 0
\(754\) 15551.6 2334.62i 0.751133 0.112761i
\(755\) −1716.38 −0.0827357
\(756\) 0 0
\(757\) 22087.2 1.06046 0.530232 0.847853i \(-0.322105\pi\)
0.530232 + 0.847853i \(0.322105\pi\)
\(758\) 14887.1 2234.87i 0.713354 0.107090i
\(759\) 0 0
\(760\) −1156.25 2411.90i −0.0551862 0.115117i
\(761\) 35524.0i 1.69218i 0.533043 + 0.846088i \(0.321048\pi\)
−0.533043 + 0.846088i \(0.678952\pi\)
\(762\) 0 0
\(763\) 9085.16i 0.431068i
\(764\) 15166.5 4658.62i 0.718198 0.220606i
\(765\) 0 0
\(766\) −3493.79 23273.1i −0.164799 1.09777i
\(767\) −13269.0 −0.624664
\(768\) 0 0
\(769\) 21213.0 0.994745 0.497372 0.867537i \(-0.334298\pi\)
0.497372 + 0.867537i \(0.334298\pi\)
\(770\) −927.054 6175.36i −0.0433879 0.289019i
\(771\) 0 0
\(772\) 1452.29 446.095i 0.0677062 0.0207970i
\(773\) 14370.7i 0.668663i 0.942456 + 0.334332i \(0.108511\pi\)
−0.942456 + 0.334332i \(0.891489\pi\)
\(774\) 0 0
\(775\) 22980.6i 1.06515i
\(776\) 5634.73 + 11753.9i 0.260664 + 0.543737i
\(777\) 0 0
\(778\) 23379.5 3509.77i 1.07737 0.161737i
\(779\) 23562.3 1.08371
\(780\) 0 0
\(781\) 12621.8 0.578287
\(782\) −3907.34 + 586.575i −0.178678 + 0.0268234i
\(783\) 0 0
\(784\) −18149.1 + 12311.1i −0.826763 + 0.560820i
\(785\) 413.122i 0.0187834i
\(786\) 0 0
\(787\) 41642.9i 1.88616i 0.332564 + 0.943081i \(0.392086\pi\)
−0.332564 + 0.943081i \(0.607914\pi\)
\(788\) −5074.84 16521.5i −0.229421 0.746896i
\(789\) 0 0
\(790\) −660.637 4400.68i −0.0297524 0.198189i
\(791\) 38288.5 1.72109