Properties

Label 378.4.g.f.109.3
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(2.24123 + 3.88192i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.f.163.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.59791 + 9.69587i) q^{5} +(-16.7643 - 7.87127i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.59791 + 9.69587i) q^{5} +(-16.7643 - 7.87127i) q^{7} -8.00000 q^{8} +(-11.1958 + 19.3917i) q^{10} +(-9.69889 + 16.7990i) q^{11} -39.5348 q^{13} +(-3.13090 - 36.9080i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(17.9246 - 31.0464i) q^{17} +(-28.0911 - 48.6552i) q^{19} -44.7833 q^{20} -38.7956 q^{22} +(-20.4926 - 35.4943i) q^{23} +(-0.173272 + 0.300115i) q^{25} +(-39.5348 - 68.4763i) q^{26} +(60.7956 - 42.3308i) q^{28} -179.308 q^{29} +(-111.582 + 193.266i) q^{31} +(16.0000 - 27.7128i) q^{32} +71.6986 q^{34} +(-17.5265 - 206.608i) q^{35} +(-13.6130 - 23.5785i) q^{37} +(56.1821 - 97.3103i) q^{38} +(-44.7833 - 77.5670i) q^{40} +100.096 q^{41} -61.7538 q^{43} +(-38.7956 - 67.1959i) q^{44} +(40.9853 - 70.9886i) q^{46} +(-231.260 - 400.554i) q^{47} +(219.086 + 263.913i) q^{49} -0.693086 q^{50} +(79.0696 - 136.953i) q^{52} +(174.811 - 302.782i) q^{53} -217.174 q^{55} +(134.115 + 62.9702i) q^{56} +(-179.308 - 310.571i) q^{58} +(121.964 - 211.248i) q^{59} +(-32.5638 - 56.4022i) q^{61} -446.328 q^{62} +64.0000 q^{64} +(-221.312 - 383.324i) q^{65} +(-85.4760 + 148.049i) q^{67} +(71.6986 + 124.186i) q^{68} +(340.328 - 236.964i) q^{70} -1009.91 q^{71} +(-573.557 + 993.429i) q^{73} +(27.2261 - 47.1570i) q^{74} +224.729 q^{76} +(294.825 - 205.281i) q^{77} +(-340.780 - 590.248i) q^{79} +(89.5666 - 155.134i) q^{80} +(100.096 + 173.371i) q^{82} -908.609 q^{83} +401.362 q^{85} +(-61.7538 - 106.961i) q^{86} +(77.5911 - 134.392i) q^{88} +(-315.344 - 546.192i) q^{89} +(662.775 + 311.189i) q^{91} +163.941 q^{92} +(462.519 - 801.107i) q^{94} +(314.503 - 544.735i) q^{95} +1330.32 q^{97} +(-238.025 + 643.382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8} + 4 q^{10} + 32 q^{11} - 4 q^{13} + 36 q^{14} - 64 q^{16} - 58 q^{17} + 70 q^{19} + 16 q^{20} + 128 q^{22} + 86 q^{23} - 156 q^{25} - 4 q^{26} + 48 q^{28} - 212 q^{29} - 64 q^{31} + 128 q^{32} - 232 q^{34} + 8 q^{35} - 146 q^{37} - 140 q^{38} + 16 q^{40} - 780 q^{41} + 880 q^{43} + 128 q^{44} - 172 q^{46} - 306 q^{47} + 50 q^{49} - 624 q^{50} + 8 q^{52} - 90 q^{53} - 64 q^{55} - 48 q^{56} - 212 q^{58} + 148 q^{59} - 364 q^{61} - 256 q^{62} + 512 q^{64} + 1296 q^{65} - 954 q^{67} - 232 q^{68} + 20 q^{70} - 1360 q^{71} - 54 q^{73} + 292 q^{74} - 560 q^{76} + 2224 q^{77} - 226 q^{79} - 32 q^{80} - 780 q^{82} - 3136 q^{83} + 3920 q^{85} + 880 q^{86} - 256 q^{88} - 1458 q^{89} + 3836 q^{91} - 688 q^{92} + 612 q^{94} + 1310 q^{95} - 4344 q^{97} + 776 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 5.59791 + 9.69587i 0.500693 + 0.867225i 1.00000 0.000799938i \(0.000254628\pi\)
−0.499307 + 0.866425i \(0.666412\pi\)
\(6\) 0 0
\(7\) −16.7643 7.87127i −0.905189 0.425009i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −11.1958 + 19.3917i −0.354043 + 0.613221i
\(11\) −9.69889 + 16.7990i −0.265848 + 0.460462i −0.967785 0.251777i \(-0.918985\pi\)
0.701938 + 0.712238i \(0.252319\pi\)
\(12\) 0 0
\(13\) −39.5348 −0.843460 −0.421730 0.906721i \(-0.638577\pi\)
−0.421730 + 0.906721i \(0.638577\pi\)
\(14\) −3.13090 36.9080i −0.0597692 0.704576i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 17.9246 31.0464i 0.255727 0.442933i −0.709366 0.704841i \(-0.751018\pi\)
0.965093 + 0.261908i \(0.0843517\pi\)
\(18\) 0 0
\(19\) −28.0911 48.6552i −0.339186 0.587487i 0.645094 0.764103i \(-0.276818\pi\)
−0.984280 + 0.176616i \(0.943485\pi\)
\(20\) −44.7833 −0.500693
\(21\) 0 0
\(22\) −38.7956 −0.375966
\(23\) −20.4926 35.4943i −0.185783 0.321786i 0.758057 0.652188i \(-0.226149\pi\)
−0.943840 + 0.330403i \(0.892815\pi\)
\(24\) 0 0
\(25\) −0.173272 + 0.300115i −0.00138617 + 0.00240092i
\(26\) −39.5348 68.4763i −0.298208 0.516512i
\(27\) 0 0
\(28\) 60.7956 42.3308i 0.410331 0.285706i
\(29\) −179.308 −1.14816 −0.574082 0.818798i \(-0.694641\pi\)
−0.574082 + 0.818798i \(0.694641\pi\)
\(30\) 0 0
\(31\) −111.582 + 193.266i −0.646474 + 1.11973i 0.337484 + 0.941331i \(0.390424\pi\)
−0.983959 + 0.178395i \(0.942909\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 71.6986 0.361653
\(35\) −17.5265 206.608i −0.0846435 0.997801i
\(36\) 0 0
\(37\) −13.6130 23.5785i −0.0604857 0.104764i 0.834197 0.551467i \(-0.185932\pi\)
−0.894683 + 0.446702i \(0.852598\pi\)
\(38\) 56.1821 97.3103i 0.239841 0.415416i
\(39\) 0 0
\(40\) −44.7833 77.5670i −0.177022 0.306610i
\(41\) 100.096 0.381277 0.190639 0.981660i \(-0.438944\pi\)
0.190639 + 0.981660i \(0.438944\pi\)
\(42\) 0 0
\(43\) −61.7538 −0.219009 −0.109504 0.993986i \(-0.534926\pi\)
−0.109504 + 0.993986i \(0.534926\pi\)
\(44\) −38.7956 67.1959i −0.132924 0.230231i
\(45\) 0 0
\(46\) 40.9853 70.9886i 0.131368 0.227537i
\(47\) −231.260 400.554i −0.717717 1.24312i −0.961902 0.273394i \(-0.911854\pi\)
0.244185 0.969729i \(-0.421479\pi\)
\(48\) 0 0
\(49\) 219.086 + 263.913i 0.638735 + 0.769427i
\(50\) −0.693086 −0.00196034
\(51\) 0 0
\(52\) 79.0696 136.953i 0.210865 0.365229i
\(53\) 174.811 302.782i 0.453060 0.784723i −0.545514 0.838102i \(-0.683666\pi\)
0.998574 + 0.0533783i \(0.0169989\pi\)
\(54\) 0 0
\(55\) −217.174 −0.532432
\(56\) 134.115 + 62.9702i 0.320033 + 0.150263i
\(57\) 0 0
\(58\) −179.308 310.571i −0.405937 0.703104i
\(59\) 121.964 211.248i 0.269125 0.466139i −0.699511 0.714622i \(-0.746599\pi\)
0.968636 + 0.248483i \(0.0799320\pi\)
\(60\) 0 0
\(61\) −32.5638 56.4022i −0.0683503 0.118386i 0.829825 0.558024i \(-0.188440\pi\)
−0.898175 + 0.439638i \(0.855107\pi\)
\(62\) −446.328 −0.914253
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −221.312 383.324i −0.422314 0.731470i
\(66\) 0 0
\(67\) −85.4760 + 148.049i −0.155859 + 0.269956i −0.933371 0.358912i \(-0.883148\pi\)
0.777513 + 0.628867i \(0.216481\pi\)
\(68\) 71.6986 + 124.186i 0.127864 + 0.221466i
\(69\) 0 0
\(70\) 340.328 236.964i 0.581100 0.404609i
\(71\) −1009.91 −1.68809 −0.844045 0.536272i \(-0.819832\pi\)
−0.844045 + 0.536272i \(0.819832\pi\)
\(72\) 0 0
\(73\) −573.557 + 993.429i −0.919585 + 1.59277i −0.119539 + 0.992829i \(0.538142\pi\)
−0.800046 + 0.599939i \(0.795192\pi\)
\(74\) 27.2261 47.1570i 0.0427699 0.0740796i
\(75\) 0 0
\(76\) 224.729 0.339186
\(77\) 294.825 205.281i 0.436343 0.303818i
\(78\) 0 0
\(79\) −340.780 590.248i −0.485325 0.840608i 0.514532 0.857471i \(-0.327966\pi\)
−0.999858 + 0.0168627i \(0.994632\pi\)
\(80\) 89.5666 155.134i 0.125173 0.216806i
\(81\) 0 0
\(82\) 100.096 + 173.371i 0.134802 + 0.233484i
\(83\) −908.609 −1.20160 −0.600800 0.799400i \(-0.705151\pi\)
−0.600800 + 0.799400i \(0.705151\pi\)
\(84\) 0 0
\(85\) 401.362 0.512163
\(86\) −61.7538 106.961i −0.0774312 0.134115i
\(87\) 0 0
\(88\) 77.5911 134.392i 0.0939914 0.162798i
\(89\) −315.344 546.192i −0.375578 0.650520i 0.614836 0.788655i \(-0.289222\pi\)
−0.990413 + 0.138136i \(0.955889\pi\)
\(90\) 0 0
\(91\) 662.775 + 311.189i 0.763491 + 0.358478i
\(92\) 163.941 0.185783
\(93\) 0 0
\(94\) 462.519 801.107i 0.507502 0.879020i
\(95\) 314.503 544.735i 0.339656 0.588301i
\(96\) 0 0
\(97\) 1330.32 1.39252 0.696258 0.717792i \(-0.254847\pi\)
0.696258 + 0.717792i \(0.254847\pi\)
\(98\) −238.025 + 643.382i −0.245349 + 0.663177i
\(99\) 0 0
\(100\) −0.693086 1.20046i −0.000693086 0.00120046i
\(101\) −252.164 + 436.762i −0.248429 + 0.430291i −0.963090 0.269180i \(-0.913247\pi\)
0.714661 + 0.699471i \(0.246581\pi\)
\(102\) 0 0
\(103\) −80.1333 138.795i −0.0766580 0.132775i 0.825148 0.564916i \(-0.191092\pi\)
−0.901806 + 0.432141i \(0.857758\pi\)
\(104\) 316.278 0.298208
\(105\) 0 0
\(106\) 699.246 0.640724
\(107\) 984.295 + 1704.85i 0.889303 + 1.54032i 0.840701 + 0.541500i \(0.182143\pi\)
0.0486022 + 0.998818i \(0.484523\pi\)
\(108\) 0 0
\(109\) −577.764 + 1000.72i −0.507704 + 0.879369i 0.492256 + 0.870450i \(0.336172\pi\)
−0.999960 + 0.00891861i \(0.997161\pi\)
\(110\) −217.174 376.157i −0.188243 0.326047i
\(111\) 0 0
\(112\) 25.0472 + 295.264i 0.0211316 + 0.249105i
\(113\) 1441.21 1.19980 0.599901 0.800074i \(-0.295206\pi\)
0.599901 + 0.800074i \(0.295206\pi\)
\(114\) 0 0
\(115\) 229.432 397.388i 0.186040 0.322231i
\(116\) 358.617 621.143i 0.287041 0.497169i
\(117\) 0 0
\(118\) 487.857 0.380601
\(119\) −544.869 + 379.383i −0.419732 + 0.292252i
\(120\) 0 0
\(121\) 477.363 + 826.817i 0.358650 + 0.621200i
\(122\) 65.1276 112.804i 0.0483310 0.0837117i
\(123\) 0 0
\(124\) −446.328 773.062i −0.323237 0.559863i
\(125\) 1395.60 0.998609
\(126\) 0 0
\(127\) −989.467 −0.691346 −0.345673 0.938355i \(-0.612349\pi\)
−0.345673 + 0.938355i \(0.612349\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 442.625 766.649i 0.298621 0.517227i
\(131\) 77.8773 + 134.887i 0.0519402 + 0.0899631i 0.890827 0.454344i \(-0.150126\pi\)
−0.838886 + 0.544307i \(0.816793\pi\)
\(132\) 0 0
\(133\) 87.9504 + 1036.78i 0.0573403 + 0.675944i
\(134\) −341.904 −0.220418
\(135\) 0 0
\(136\) −143.397 + 248.371i −0.0904133 + 0.156600i
\(137\) −491.335 + 851.017i −0.306406 + 0.530710i −0.977573 0.210596i \(-0.932460\pi\)
0.671168 + 0.741306i \(0.265793\pi\)
\(138\) 0 0
\(139\) −2232.74 −1.36243 −0.681216 0.732082i \(-0.738549\pi\)
−0.681216 + 0.732082i \(0.738549\pi\)
\(140\) 750.763 + 352.501i 0.453222 + 0.212799i
\(141\) 0 0
\(142\) −1009.91 1749.22i −0.596830 1.03374i
\(143\) 383.444 664.144i 0.224232 0.388381i
\(144\) 0 0
\(145\) −1003.75 1738.55i −0.574877 0.995716i
\(146\) −2294.23 −1.30049
\(147\) 0 0
\(148\) 108.904 0.0604857
\(149\) 1535.08 + 2658.84i 0.844019 + 1.46188i 0.886470 + 0.462786i \(0.153150\pi\)
−0.0424511 + 0.999099i \(0.513517\pi\)
\(150\) 0 0
\(151\) −1362.59 + 2360.07i −0.734343 + 1.27192i 0.220668 + 0.975349i \(0.429176\pi\)
−0.955011 + 0.296571i \(0.904157\pi\)
\(152\) 224.729 + 389.241i 0.119920 + 0.207708i
\(153\) 0 0
\(154\) 650.382 + 305.370i 0.340320 + 0.159789i
\(155\) −2498.50 −1.29474
\(156\) 0 0
\(157\) −636.491 + 1102.43i −0.323551 + 0.560407i −0.981218 0.192902i \(-0.938210\pi\)
0.657667 + 0.753309i \(0.271543\pi\)
\(158\) 681.559 1180.50i 0.343177 0.594400i
\(159\) 0 0
\(160\) 358.266 0.177022
\(161\) 64.1604 + 756.341i 0.0314071 + 0.370236i
\(162\) 0 0
\(163\) 141.011 + 244.238i 0.0677597 + 0.117363i 0.897915 0.440169i \(-0.145082\pi\)
−0.830155 + 0.557532i \(0.811748\pi\)
\(164\) −200.192 + 346.743i −0.0953193 + 0.165098i
\(165\) 0 0
\(166\) −908.609 1573.76i −0.424830 0.735827i
\(167\) 4159.02 1.92715 0.963576 0.267435i \(-0.0861761\pi\)
0.963576 + 0.267435i \(0.0861761\pi\)
\(168\) 0 0
\(169\) −633.999 −0.288575
\(170\) 401.362 + 695.180i 0.181077 + 0.313635i
\(171\) 0 0
\(172\) 123.508 213.922i 0.0547522 0.0948335i
\(173\) −118.262 204.835i −0.0519727 0.0900194i 0.838869 0.544334i \(-0.183218\pi\)
−0.890841 + 0.454315i \(0.849884\pi\)
\(174\) 0 0
\(175\) 5.26707 3.66737i 0.00227516 0.00158415i
\(176\) 310.364 0.132924
\(177\) 0 0
\(178\) 630.688 1092.38i 0.265574 0.459987i
\(179\) −1580.82 + 2738.06i −0.660088 + 1.14331i 0.320504 + 0.947247i \(0.396148\pi\)
−0.980592 + 0.196059i \(0.937185\pi\)
\(180\) 0 0
\(181\) −3304.47 −1.35701 −0.678506 0.734595i \(-0.737372\pi\)
−0.678506 + 0.734595i \(0.737372\pi\)
\(182\) 123.780 + 1459.15i 0.0504129 + 0.594282i
\(183\) 0 0
\(184\) 163.941 + 283.954i 0.0656842 + 0.113768i
\(185\) 152.409 263.981i 0.0605695 0.104909i
\(186\) 0 0
\(187\) 347.698 + 602.231i 0.135969 + 0.235505i
\(188\) 1850.08 0.717717
\(189\) 0 0
\(190\) 1258.01 0.480346
\(191\) 1038.38 + 1798.53i 0.393374 + 0.681344i 0.992892 0.119017i \(-0.0379744\pi\)
−0.599518 + 0.800361i \(0.704641\pi\)
\(192\) 0 0
\(193\) −1306.12 + 2262.27i −0.487133 + 0.843739i −0.999891 0.0147947i \(-0.995291\pi\)
0.512758 + 0.858533i \(0.328624\pi\)
\(194\) 1330.32 + 2304.19i 0.492329 + 0.852738i
\(195\) 0 0
\(196\) −1352.39 + 231.110i −0.492855 + 0.0842239i
\(197\) −3418.62 −1.23638 −0.618189 0.786029i \(-0.712134\pi\)
−0.618189 + 0.786029i \(0.712134\pi\)
\(198\) 0 0
\(199\) 1812.08 3138.61i 0.645501 1.11804i −0.338684 0.940900i \(-0.609982\pi\)
0.984185 0.177141i \(-0.0566849\pi\)
\(200\) 1.38617 2.40092i 0.000490086 0.000848854i
\(201\) 0 0
\(202\) −1008.66 −0.351331
\(203\) 3005.99 + 1411.39i 1.03931 + 0.487979i
\(204\) 0 0
\(205\) 560.329 + 970.517i 0.190903 + 0.330653i
\(206\) 160.267 277.590i 0.0542054 0.0938864i
\(207\) 0 0
\(208\) 316.278 + 547.810i 0.105433 + 0.182614i
\(209\) 1089.81 0.360687
\(210\) 0 0
\(211\) 4087.38 1.33359 0.666794 0.745242i \(-0.267666\pi\)
0.666794 + 0.745242i \(0.267666\pi\)
\(212\) 699.246 + 1211.13i 0.226530 + 0.392362i
\(213\) 0 0
\(214\) −1968.59 + 3409.70i −0.628832 + 1.08917i
\(215\) −345.693 598.757i −0.109656 0.189930i
\(216\) 0 0
\(217\) 3391.84 2361.68i 1.06108 0.738807i
\(218\) −2311.05 −0.718002
\(219\) 0 0
\(220\) 434.348 752.313i 0.133108 0.230550i
\(221\) −708.647 + 1227.41i −0.215696 + 0.373596i
\(222\) 0 0
\(223\) −3393.50 −1.01904 −0.509520 0.860459i \(-0.670177\pi\)
−0.509520 + 0.860459i \(0.670177\pi\)
\(224\) −486.364 + 338.647i −0.145074 + 0.101012i
\(225\) 0 0
\(226\) 1441.21 + 2496.25i 0.424194 + 0.734726i
\(227\) 1276.99 2211.80i 0.373377 0.646707i −0.616706 0.787194i \(-0.711533\pi\)
0.990083 + 0.140486i \(0.0448666\pi\)
\(228\) 0 0
\(229\) 351.347 + 608.550i 0.101387 + 0.175608i 0.912256 0.409620i \(-0.134339\pi\)
−0.810869 + 0.585227i \(0.801005\pi\)
\(230\) 917.728 0.263101
\(231\) 0 0
\(232\) 1434.47 0.405937
\(233\) −205.573 356.063i −0.0578006 0.100114i 0.835677 0.549221i \(-0.185075\pi\)
−0.893478 + 0.449107i \(0.851742\pi\)
\(234\) 0 0
\(235\) 2589.14 4484.53i 0.718711 1.24484i
\(236\) 487.857 + 844.994i 0.134563 + 0.233070i
\(237\) 0 0
\(238\) −1201.98 564.359i −0.327364 0.153706i
\(239\) −178.567 −0.0483286 −0.0241643 0.999708i \(-0.507692\pi\)
−0.0241643 + 0.999708i \(0.507692\pi\)
\(240\) 0 0
\(241\) 2030.95 3517.71i 0.542843 0.940232i −0.455896 0.890033i \(-0.650681\pi\)
0.998739 0.0501987i \(-0.0159854\pi\)
\(242\) −954.726 + 1653.63i −0.253604 + 0.439255i
\(243\) 0 0
\(244\) 260.510 0.0683503
\(245\) −1332.44 + 3601.60i −0.347456 + 0.939173i
\(246\) 0 0
\(247\) 1110.57 + 1923.57i 0.286090 + 0.495522i
\(248\) 892.655 1546.12i 0.228563 0.395883i
\(249\) 0 0
\(250\) 1395.60 + 2417.25i 0.353062 + 0.611521i
\(251\) −2040.70 −0.513178 −0.256589 0.966521i \(-0.582599\pi\)
−0.256589 + 0.966521i \(0.582599\pi\)
\(252\) 0 0
\(253\) 795.023 0.197560
\(254\) −989.467 1713.81i −0.244428 0.423361i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2283.44 3955.04i −0.554231 0.959956i −0.997963 0.0637964i \(-0.979679\pi\)
0.443732 0.896159i \(-0.353654\pi\)
\(258\) 0 0
\(259\) 42.6211 + 502.430i 0.0102253 + 0.120539i
\(260\) 1770.50 0.422314
\(261\) 0 0
\(262\) −155.755 + 269.775i −0.0367273 + 0.0636135i
\(263\) 2668.42 4621.83i 0.625634 1.08363i −0.362784 0.931873i \(-0.618174\pi\)
0.988418 0.151756i \(-0.0484928\pi\)
\(264\) 0 0
\(265\) 3914.32 0.907376
\(266\) −1707.81 + 1189.12i −0.393657 + 0.274096i
\(267\) 0 0
\(268\) −341.904 592.195i −0.0779295 0.134978i
\(269\) 3209.62 5559.22i 0.727486 1.26004i −0.230456 0.973083i \(-0.574022\pi\)
0.957942 0.286960i \(-0.0926448\pi\)
\(270\) 0 0
\(271\) −3540.34 6132.05i −0.793580 1.37452i −0.923737 0.383028i \(-0.874881\pi\)
0.130157 0.991493i \(-0.458452\pi\)
\(272\) −573.589 −0.127864
\(273\) 0 0
\(274\) −1965.34 −0.433323
\(275\) −3.36108 5.82157i −0.000737022 0.00127656i
\(276\) 0 0
\(277\) −2333.66 + 4042.02i −0.506195 + 0.876756i 0.493779 + 0.869588i \(0.335615\pi\)
−0.999974 + 0.00716871i \(0.997718\pi\)
\(278\) −2232.74 3867.21i −0.481693 0.834316i
\(279\) 0 0
\(280\) 140.212 + 1652.86i 0.0299260 + 0.352776i
\(281\) −8234.13 −1.74807 −0.874034 0.485865i \(-0.838505\pi\)
−0.874034 + 0.485865i \(0.838505\pi\)
\(282\) 0 0
\(283\) −101.417 + 175.660i −0.0213026 + 0.0368971i −0.876480 0.481438i \(-0.840115\pi\)
0.855178 + 0.518335i \(0.173448\pi\)
\(284\) 2019.82 3498.43i 0.422023 0.730964i
\(285\) 0 0
\(286\) 1533.77 0.317112
\(287\) −1678.04 787.882i −0.345128 0.162046i
\(288\) 0 0
\(289\) 1813.91 + 3141.79i 0.369207 + 0.639485i
\(290\) 2007.51 3477.10i 0.406499 0.704078i
\(291\) 0 0
\(292\) −2294.23 3973.72i −0.459793 0.796384i
\(293\) 3612.05 0.720199 0.360100 0.932914i \(-0.382743\pi\)
0.360100 + 0.932914i \(0.382743\pi\)
\(294\) 0 0
\(295\) 2730.98 0.538997
\(296\) 108.904 + 188.628i 0.0213849 + 0.0370398i
\(297\) 0 0
\(298\) −3070.16 + 5317.68i −0.596812 + 1.03371i
\(299\) 810.172 + 1403.26i 0.156701 + 0.271413i
\(300\) 0 0
\(301\) 1035.26 + 486.081i 0.198244 + 0.0930806i
\(302\) −5450.35 −1.03852
\(303\) 0 0
\(304\) −449.457 + 778.483i −0.0847965 + 0.146872i
\(305\) 364.579 631.469i 0.0684450 0.118550i
\(306\) 0 0
\(307\) −4684.69 −0.870910 −0.435455 0.900210i \(-0.643413\pi\)
−0.435455 + 0.900210i \(0.643413\pi\)
\(308\) 121.465 + 1431.86i 0.0224712 + 0.264896i
\(309\) 0 0
\(310\) −2498.50 4327.54i −0.457760 0.792863i
\(311\) 3810.20 6599.46i 0.694716 1.20328i −0.275560 0.961284i \(-0.588863\pi\)
0.970276 0.242000i \(-0.0778033\pi\)
\(312\) 0 0
\(313\) 2901.80 + 5026.07i 0.524024 + 0.907636i 0.999609 + 0.0279665i \(0.00890316\pi\)
−0.475585 + 0.879670i \(0.657764\pi\)
\(314\) −2545.96 −0.457570
\(315\) 0 0
\(316\) 2726.24 0.485325
\(317\) −2131.98 3692.69i −0.377740 0.654266i 0.612993 0.790089i \(-0.289966\pi\)
−0.990733 + 0.135823i \(0.956632\pi\)
\(318\) 0 0
\(319\) 1739.09 3012.20i 0.305237 0.528685i
\(320\) 358.266 + 620.536i 0.0625866 + 0.108403i
\(321\) 0 0
\(322\) −1245.86 + 867.470i −0.215618 + 0.150131i
\(323\) −2014.09 −0.346956
\(324\) 0 0
\(325\) 6.85026 11.8650i 0.00116918 0.00202508i
\(326\) −282.022 + 488.476i −0.0479133 + 0.0829883i
\(327\) 0 0
\(328\) −800.768 −0.134802
\(329\) 724.051 + 8535.32i 0.121332 + 1.43030i
\(330\) 0 0
\(331\) −4174.62 7230.66i −0.693226 1.20070i −0.970775 0.239992i \(-0.922855\pi\)
0.277549 0.960712i \(-0.410478\pi\)
\(332\) 1817.22 3147.51i 0.300400 0.520308i
\(333\) 0 0
\(334\) 4159.02 + 7203.63i 0.681351 + 1.18013i
\(335\) −1913.95 −0.312150
\(336\) 0 0
\(337\) 9133.23 1.47632 0.738158 0.674628i \(-0.235696\pi\)
0.738158 + 0.674628i \(0.235696\pi\)
\(338\) −633.999 1098.12i −0.102027 0.176715i
\(339\) 0 0
\(340\) −802.725 + 1390.36i −0.128041 + 0.221773i
\(341\) −2164.44 3748.92i −0.343728 0.595354i
\(342\) 0 0
\(343\) −1595.50 6148.82i −0.251164 0.967945i
\(344\) 494.031 0.0774312
\(345\) 0 0
\(346\) 236.524 409.671i 0.0367502 0.0636533i
\(347\) −425.840 + 737.577i −0.0658798 + 0.114107i −0.897084 0.441860i \(-0.854319\pi\)
0.831204 + 0.555967i \(0.187652\pi\)
\(348\) 0 0
\(349\) 2348.88 0.360266 0.180133 0.983642i \(-0.442347\pi\)
0.180133 + 0.983642i \(0.442347\pi\)
\(350\) 11.6191 + 5.45547i 0.00177448 + 0.000833163i
\(351\) 0 0
\(352\) 310.364 + 537.567i 0.0469957 + 0.0813989i
\(353\) 393.157 680.969i 0.0592795 0.102675i −0.834863 0.550458i \(-0.814453\pi\)
0.894142 + 0.447783i \(0.147786\pi\)
\(354\) 0 0
\(355\) −5653.40 9791.97i −0.845214 1.46395i
\(356\) 2522.75 0.375578
\(357\) 0 0
\(358\) −6323.27 −0.933506
\(359\) 3690.81 + 6392.67i 0.542601 + 0.939812i 0.998754 + 0.0499105i \(0.0158936\pi\)
−0.456153 + 0.889901i \(0.650773\pi\)
\(360\) 0 0
\(361\) 1851.28 3206.52i 0.269906 0.467491i
\(362\) −3304.47 5723.50i −0.479776 0.830996i
\(363\) 0 0
\(364\) −2403.54 + 1673.54i −0.346098 + 0.240982i
\(365\) −12842.9 −1.84172
\(366\) 0 0
\(367\) 1220.46 2113.90i 0.173590 0.300667i −0.766082 0.642742i \(-0.777797\pi\)
0.939672 + 0.342075i \(0.111130\pi\)
\(368\) −327.882 + 567.908i −0.0464457 + 0.0804464i
\(369\) 0 0
\(370\) 609.637 0.0856582
\(371\) −5313.88 + 3699.96i −0.743619 + 0.517769i
\(372\) 0 0
\(373\) 5938.04 + 10285.0i 0.824290 + 1.42771i 0.902461 + 0.430772i \(0.141759\pi\)
−0.0781707 + 0.996940i \(0.524908\pi\)
\(374\) −695.397 + 1204.46i −0.0961446 + 0.166527i
\(375\) 0 0
\(376\) 1850.08 + 3204.43i 0.253751 + 0.439510i
\(377\) 7088.92 0.968430
\(378\) 0 0
\(379\) −4202.37 −0.569554 −0.284777 0.958594i \(-0.591920\pi\)
−0.284777 + 0.958594i \(0.591920\pi\)
\(380\) 1258.01 + 2178.94i 0.169828 + 0.294151i
\(381\) 0 0
\(382\) −2076.76 + 3597.05i −0.278158 + 0.481783i
\(383\) −7048.40 12208.2i −0.940357 1.62875i −0.764791 0.644278i \(-0.777158\pi\)
−0.175565 0.984468i \(-0.556175\pi\)
\(384\) 0 0
\(385\) 3640.78 + 1709.44i 0.481952 + 0.226288i
\(386\) −5224.48 −0.688910
\(387\) 0 0
\(388\) −2660.65 + 4608.38i −0.348129 + 0.602977i
\(389\) 5668.66 9818.40i 0.738849 1.27972i −0.214165 0.976798i \(-0.568703\pi\)
0.953014 0.302927i \(-0.0979637\pi\)
\(390\) 0 0
\(391\) −1469.29 −0.190039
\(392\) −1752.69 2111.31i −0.225827 0.272033i
\(393\) 0 0
\(394\) −3418.62 5921.22i −0.437126 0.757124i
\(395\) 3815.31 6608.31i 0.485998 0.841773i
\(396\) 0 0
\(397\) −493.685 855.088i −0.0624115 0.108100i 0.833131 0.553075i \(-0.186546\pi\)
−0.895543 + 0.444975i \(0.853212\pi\)
\(398\) 7248.31 0.912877
\(399\) 0 0
\(400\) 5.54469 0.000693086
\(401\) −4246.79 7355.66i −0.528864 0.916020i −0.999433 0.0336569i \(-0.989285\pi\)
0.470569 0.882363i \(-0.344049\pi\)
\(402\) 0 0
\(403\) 4411.37 7640.72i 0.545275 0.944445i
\(404\) −1008.66 1747.05i −0.124214 0.215146i
\(405\) 0 0
\(406\) 561.397 + 6617.91i 0.0686248 + 0.808969i
\(407\) 528.126 0.0643200
\(408\) 0 0
\(409\) −4632.80 + 8024.25i −0.560091 + 0.970107i 0.437396 + 0.899269i \(0.355901\pi\)
−0.997488 + 0.0708381i \(0.977433\pi\)
\(410\) −1120.66 + 1941.03i −0.134989 + 0.233807i
\(411\) 0 0
\(412\) 641.066 0.0766580
\(413\) −3707.44 + 2581.43i −0.441723 + 0.307563i
\(414\) 0 0
\(415\) −5086.31 8809.75i −0.601632 1.04206i
\(416\) −632.557 + 1095.62i −0.0745521 + 0.129128i
\(417\) 0 0
\(418\) 1089.81 + 1887.60i 0.127522 + 0.220875i
\(419\) −4398.11 −0.512797 −0.256398 0.966571i \(-0.582536\pi\)
−0.256398 + 0.966571i \(0.582536\pi\)
\(420\) 0 0
\(421\) −9335.15 −1.08068 −0.540341 0.841446i \(-0.681705\pi\)
−0.540341 + 0.841446i \(0.681705\pi\)
\(422\) 4087.38 + 7079.56i 0.471495 + 0.816653i
\(423\) 0 0
\(424\) −1398.49 + 2422.26i −0.160181 + 0.277442i
\(425\) 6.21166 + 10.7589i 0.000708964 + 0.00122796i
\(426\) 0 0
\(427\) 101.954 + 1201.86i 0.0115548 + 0.136211i
\(428\) −7874.36 −0.889303
\(429\) 0 0
\(430\) 691.385 1197.51i 0.0775385 0.134301i
\(431\) 138.876 240.540i 0.0155207 0.0268827i −0.858161 0.513381i \(-0.828393\pi\)
0.873681 + 0.486498i \(0.161726\pi\)
\(432\) 0 0
\(433\) 706.915 0.0784577 0.0392289 0.999230i \(-0.487510\pi\)
0.0392289 + 0.999230i \(0.487510\pi\)
\(434\) 7482.39 + 3513.17i 0.827572 + 0.388565i
\(435\) 0 0
\(436\) −2311.05 4002.86i −0.253852 0.439684i
\(437\) −1151.32 + 1994.14i −0.126030 + 0.218290i
\(438\) 0 0
\(439\) −710.440 1230.52i −0.0772379 0.133780i 0.824819 0.565396i \(-0.191277\pi\)
−0.902057 + 0.431616i \(0.857943\pi\)
\(440\) 1737.39 0.188243
\(441\) 0 0
\(442\) −2834.59 −0.305040
\(443\) 6029.64 + 10443.6i 0.646674 + 1.12007i 0.983912 + 0.178653i \(0.0571741\pi\)
−0.337238 + 0.941420i \(0.609493\pi\)
\(444\) 0 0
\(445\) 3530.54 6115.07i 0.376098 0.651421i
\(446\) −3393.50 5877.72i −0.360285 0.624032i
\(447\) 0 0
\(448\) −1072.92 503.761i −0.113149 0.0531261i
\(449\) 1519.39 0.159698 0.0798491 0.996807i \(-0.474556\pi\)
0.0798491 + 0.996807i \(0.474556\pi\)
\(450\) 0 0
\(451\) −970.820 + 1681.51i −0.101362 + 0.175564i
\(452\) −2882.42 + 4992.50i −0.299951 + 0.519530i
\(453\) 0 0
\(454\) 5107.94 0.528034
\(455\) 692.907 + 8168.19i 0.0713934 + 0.841606i
\(456\) 0 0
\(457\) 2724.80 + 4719.49i 0.278908 + 0.483082i 0.971114 0.238618i \(-0.0766944\pi\)
−0.692206 + 0.721700i \(0.743361\pi\)
\(458\) −702.694 + 1217.10i −0.0716915 + 0.124173i
\(459\) 0 0
\(460\) 917.728 + 1589.55i 0.0930202 + 0.161116i
\(461\) 9435.17 0.953232 0.476616 0.879112i \(-0.341863\pi\)
0.476616 + 0.879112i \(0.341863\pi\)
\(462\) 0 0
\(463\) −17319.2 −1.73843 −0.869214 0.494436i \(-0.835375\pi\)
−0.869214 + 0.494436i \(0.835375\pi\)
\(464\) 1434.47 + 2484.57i 0.143520 + 0.248585i
\(465\) 0 0
\(466\) 411.146 712.126i 0.0408712 0.0707910i
\(467\) 3336.47 + 5778.93i 0.330606 + 0.572627i 0.982631 0.185571i \(-0.0594134\pi\)
−0.652024 + 0.758198i \(0.726080\pi\)
\(468\) 0 0
\(469\) 2598.28 1809.13i 0.255815 0.178120i
\(470\) 10356.6 1.01641
\(471\) 0 0
\(472\) −975.715 + 1689.99i −0.0951502 + 0.164805i
\(473\) 598.944 1037.40i 0.0582230 0.100845i
\(474\) 0 0
\(475\) 19.4695 0.00188068
\(476\) −224.481 2646.25i −0.0216157 0.254812i
\(477\) 0 0
\(478\) −178.567 309.287i −0.0170868 0.0295951i
\(479\) 7748.69 13421.1i 0.739138 1.28022i −0.213747 0.976889i \(-0.568567\pi\)
0.952884 0.303335i \(-0.0981000\pi\)
\(480\) 0 0
\(481\) 538.189 + 932.171i 0.0510173 + 0.0883645i
\(482\) 8123.81 0.767696
\(483\) 0 0
\(484\) −3818.90 −0.358650
\(485\) 7447.04 + 12898.7i 0.697222 + 1.20762i
\(486\) 0 0
\(487\) 1862.88 3226.60i 0.173337 0.300229i −0.766247 0.642546i \(-0.777878\pi\)
0.939585 + 0.342317i \(0.111212\pi\)
\(488\) 260.510 + 451.217i 0.0241655 + 0.0418558i
\(489\) 0 0
\(490\) −7570.59 + 1293.74i −0.697968 + 0.119276i
\(491\) −18496.7 −1.70009 −0.850045 0.526711i \(-0.823425\pi\)
−0.850045 + 0.526711i \(0.823425\pi\)
\(492\) 0 0
\(493\) −3214.04 + 5566.88i −0.293617 + 0.508559i
\(494\) −2221.15 + 3847.14i −0.202296 + 0.350387i
\(495\) 0 0
\(496\) 3570.62 0.323237
\(497\) 16930.5 + 7949.28i 1.52804 + 0.717453i
\(498\) 0 0
\(499\) 1851.59 + 3207.04i 0.166109 + 0.287709i 0.937049 0.349199i \(-0.113546\pi\)
−0.770940 + 0.636908i \(0.780213\pi\)
\(500\) −2791.20 + 4834.50i −0.249652 + 0.432410i
\(501\) 0 0
\(502\) −2040.70 3534.59i −0.181436 0.314256i
\(503\) −6872.91 −0.609240 −0.304620 0.952474i \(-0.598529\pi\)
−0.304620 + 0.952474i \(0.598529\pi\)
\(504\) 0 0
\(505\) −5646.38 −0.497546
\(506\) 795.023 + 1377.02i 0.0698480 + 0.120980i
\(507\) 0 0
\(508\) 1978.93 3427.61i 0.172837 0.299362i
\(509\) 4973.42 + 8614.22i 0.433091 + 0.750135i 0.997138 0.0756076i \(-0.0240896\pi\)
−0.564047 + 0.825743i \(0.690756\pi\)
\(510\) 0 0
\(511\) 17434.8 12139.6i 1.50934 1.05093i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 4566.89 7910.08i 0.391900 0.678791i
\(515\) 897.159 1553.92i 0.0767641 0.132959i
\(516\) 0 0
\(517\) 8971.85 0.763214
\(518\) −827.613 + 576.252i −0.0701993 + 0.0488785i
\(519\) 0 0
\(520\) 1770.50 + 3066.59i 0.149311 + 0.258614i
\(521\) 4227.85 7322.84i 0.355519 0.615777i −0.631688 0.775223i \(-0.717638\pi\)
0.987207 + 0.159446i \(0.0509709\pi\)
\(522\) 0 0
\(523\) 3554.65 + 6156.84i 0.297197 + 0.514761i 0.975494 0.220028i \(-0.0706148\pi\)
−0.678296 + 0.734788i \(0.737281\pi\)
\(524\) −623.018 −0.0519402
\(525\) 0 0
\(526\) 10673.7 0.884780
\(527\) 4000.13 + 6928.43i 0.330642 + 0.572689i
\(528\) 0 0
\(529\) 5243.60 9082.19i 0.430969 0.746461i
\(530\) 3914.32 + 6779.80i 0.320806 + 0.555652i
\(531\) 0 0
\(532\) −3767.43 1768.90i −0.307028 0.144157i
\(533\) −3957.27 −0.321592
\(534\) 0 0
\(535\) −11020.0 + 19087.2i −0.890535 + 1.54245i
\(536\) 683.808 1184.39i 0.0551045 0.0954437i
\(537\) 0 0
\(538\) 12838.5 1.02882
\(539\) −6558.36 + 1120.76i −0.524098 + 0.0895629i
\(540\) 0 0
\(541\) 6264.28 + 10850.1i 0.497823 + 0.862256i 0.999997 0.00251141i \(-0.000799407\pi\)
−0.502173 + 0.864767i \(0.667466\pi\)
\(542\) 7080.68 12264.1i 0.561146 0.971933i
\(543\) 0 0
\(544\) −573.589 993.484i −0.0452066 0.0783002i
\(545\) −12937.1 −1.01681
\(546\) 0 0
\(547\) 4698.99 0.367302 0.183651 0.982991i \(-0.441208\pi\)
0.183651 + 0.982991i \(0.441208\pi\)
\(548\) −1965.34 3404.07i −0.153203 0.265355i
\(549\) 0 0
\(550\) 6.72217 11.6431i 0.000521153 0.000902664i
\(551\) 5036.97 + 8724.28i 0.389441 + 0.674532i
\(552\) 0 0
\(553\) 1066.95 + 12577.5i 0.0820456 + 0.967177i
\(554\) −9334.65 −0.715868
\(555\) 0 0
\(556\) 4465.47 7734.42i 0.340608 0.589951i
\(557\) 73.3775 127.094i 0.00558188 0.00966809i −0.863221 0.504826i \(-0.831557\pi\)
0.868803 + 0.495158i \(0.164890\pi\)
\(558\) 0 0
\(559\) 2441.43 0.184725
\(560\) −2722.63 + 1895.72i −0.205450 + 0.143051i
\(561\) 0 0
\(562\) −8234.13 14261.9i −0.618035 1.07047i
\(563\) −7340.75 + 12714.5i −0.549513 + 0.951784i 0.448795 + 0.893635i \(0.351853\pi\)
−0.998308 + 0.0581491i \(0.981480\pi\)
\(564\) 0 0
\(565\) 8067.77 + 13973.8i 0.600732 + 1.04050i
\(566\) −405.669 −0.0301264
\(567\) 0 0
\(568\) 8079.29 0.596830
\(569\) 10220.1 + 17701.8i 0.752987 + 1.30421i 0.946369 + 0.323088i \(0.104721\pi\)
−0.193382 + 0.981123i \(0.561946\pi\)
\(570\) 0 0
\(571\) 9365.03 16220.7i 0.686364 1.18882i −0.286641 0.958038i \(-0.592539\pi\)
0.973006 0.230780i \(-0.0741278\pi\)
\(572\) 1533.77 + 2656.58i 0.112116 + 0.194191i
\(573\) 0 0
\(574\) −313.391 3694.34i −0.0227886 0.268639i
\(575\) 14.2032 0.00103011
\(576\) 0 0
\(577\) −3087.66 + 5347.98i −0.222774 + 0.385856i −0.955649 0.294507i \(-0.904845\pi\)
0.732875 + 0.680363i \(0.238178\pi\)
\(578\) −3627.83 + 6283.58i −0.261069 + 0.452184i
\(579\) 0 0
\(580\) 8030.03 0.574877
\(581\) 15232.2 + 7151.90i 1.08768 + 0.510690i
\(582\) 0 0
\(583\) 3390.95 + 5873.30i 0.240890 + 0.417234i
\(584\) 4588.45 7947.43i 0.325122 0.563129i
\(585\) 0 0
\(586\) 3612.05 + 6256.26i 0.254629 + 0.441030i
\(587\) 6964.63 0.489712 0.244856 0.969559i \(-0.421259\pi\)
0.244856 + 0.969559i \(0.421259\pi\)
\(588\) 0 0
\(589\) 12537.8 0.877100
\(590\) 2730.98 + 4730.20i 0.190564 + 0.330067i
\(591\) 0 0
\(592\) −217.809 + 377.256i −0.0151214 + 0.0261911i
\(593\) 2472.15 + 4281.89i 0.171196 + 0.296520i 0.938838 0.344359i \(-0.111904\pi\)
−0.767642 + 0.640878i \(0.778570\pi\)
\(594\) 0 0
\(595\) −6728.58 3159.23i −0.463605 0.217674i
\(596\) −12280.7 −0.844019
\(597\) 0 0
\(598\) −1620.34 + 2806.52i −0.110804 + 0.191918i
\(599\) −3158.77 + 5471.16i −0.215466 + 0.373198i −0.953417 0.301657i \(-0.902460\pi\)
0.737951 + 0.674855i \(0.235794\pi\)
\(600\) 0 0
\(601\) −22912.5 −1.55511 −0.777555 0.628816i \(-0.783540\pi\)
−0.777555 + 0.628816i \(0.783540\pi\)
\(602\) 193.345 + 2279.21i 0.0130900 + 0.154308i
\(603\) 0 0
\(604\) −5450.35 9440.29i −0.367172 0.635960i
\(605\) −5344.47 + 9256.90i −0.359147 + 0.622060i
\(606\) 0 0
\(607\) −1850.95 3205.93i −0.123769 0.214374i 0.797482 0.603342i \(-0.206165\pi\)
−0.921251 + 0.388969i \(0.872831\pi\)
\(608\) −1797.83 −0.119920
\(609\) 0 0
\(610\) 1458.32 0.0967958
\(611\) 9142.81 + 15835.8i 0.605366 + 1.04852i
\(612\) 0 0
\(613\) −3816.69 + 6610.70i −0.251476 + 0.435569i −0.963932 0.266148i \(-0.914249\pi\)
0.712457 + 0.701716i \(0.247582\pi\)
\(614\) −4684.69 8114.12i −0.307913 0.533322i
\(615\) 0 0
\(616\) −2358.60 + 1642.25i −0.154270 + 0.107416i
\(617\) 4657.33 0.303885 0.151942 0.988389i \(-0.451447\pi\)
0.151942 + 0.988389i \(0.451447\pi\)
\(618\) 0 0
\(619\) 3276.14 5674.44i 0.212729 0.368457i −0.739839 0.672784i \(-0.765098\pi\)
0.952568 + 0.304327i \(0.0984316\pi\)
\(620\) 4997.01 8655.07i 0.323685 0.560639i
\(621\) 0 0
\(622\) 15240.8 0.982477
\(623\) 987.312 + 11638.7i 0.0634925 + 0.748467i
\(624\) 0 0
\(625\) 7834.10 + 13569.1i 0.501382 + 0.868420i
\(626\) −5803.60 + 10052.1i −0.370541 + 0.641796i
\(627\) 0 0
\(628\) −2545.96 4409.74i −0.161775 0.280203i
\(629\) −976.036 −0.0618714
\(630\) 0 0
\(631\) −17505.8 −1.10443 −0.552215 0.833702i \(-0.686217\pi\)
−0.552215 + 0.833702i \(0.686217\pi\)
\(632\) 2726.24 + 4721.98i 0.171588 + 0.297200i
\(633\) 0 0
\(634\) 4263.95 7385.38i 0.267103 0.462636i
\(635\) −5538.95 9593.74i −0.346152 0.599553i
\(636\) 0 0
\(637\) −8661.53 10433.8i −0.538748 0.648981i
\(638\) 6956.37 0.431670
\(639\) 0 0
\(640\) −716.533 + 1241.07i −0.0442554 + 0.0766526i
\(641\) 5989.15 10373.5i 0.369044 0.639203i −0.620373 0.784307i \(-0.713019\pi\)
0.989416 + 0.145105i \(0.0463519\pi\)
\(642\) 0 0
\(643\) −14582.6 −0.894370 −0.447185 0.894441i \(-0.647573\pi\)
−0.447185 + 0.894441i \(0.647573\pi\)
\(644\) −2748.36 1290.42i −0.168169 0.0789594i
\(645\) 0 0
\(646\) −2014.09 3488.51i −0.122668 0.212467i
\(647\) 13631.5 23610.5i 0.828300 1.43466i −0.0710702 0.997471i \(-0.522641\pi\)
0.899371 0.437187i \(-0.144025\pi\)
\(648\) 0 0
\(649\) 2365.84 + 4097.75i 0.143093 + 0.247844i
\(650\) 27.4010 0.00165347
\(651\) 0 0
\(652\) −1128.09 −0.0677597
\(653\) −13800.8 23903.6i −0.827053 1.43250i −0.900340 0.435187i \(-0.856682\pi\)
0.0732872 0.997311i \(-0.476651\pi\)
\(654\) 0 0
\(655\) −871.900 + 1510.18i −0.0520122 + 0.0900877i
\(656\) −800.768 1386.97i −0.0476596 0.0825489i
\(657\) 0 0
\(658\) −14059.6 + 9789.42i −0.832977 + 0.579987i
\(659\) 10780.5 0.637254 0.318627 0.947880i \(-0.396778\pi\)
0.318627 + 0.947880i \(0.396778\pi\)
\(660\) 0 0
\(661\) 5517.83 9557.17i 0.324688 0.562376i −0.656761 0.754099i \(-0.728074\pi\)
0.981449 + 0.191722i \(0.0614073\pi\)
\(662\) 8349.24 14461.3i 0.490185 0.849025i
\(663\) 0 0
\(664\) 7268.87 0.424830
\(665\) −9560.19 + 6656.58i −0.557486 + 0.388167i
\(666\) 0 0
\(667\) 3674.50 + 6364.42i 0.213309 + 0.369462i
\(668\) −8318.03 + 14407.3i −0.481788 + 0.834481i
\(669\) 0 0
\(670\) −1913.95 3315.06i −0.110362 0.191152i
\(671\) 1263.33 0.0726831
\(672\) 0 0
\(673\) −28007.8 −1.60419 −0.802097 0.597193i \(-0.796283\pi\)
−0.802097 + 0.597193i \(0.796283\pi\)
\(674\) 9133.23 + 15819.2i 0.521957 + 0.904055i
\(675\) 0 0
\(676\) 1268.00 2196.24i 0.0721437 0.124957i
\(677\) 2.53680 + 4.39387i 0.000144014 + 0.000249439i 0.866097 0.499875i \(-0.166621\pi\)
−0.865953 + 0.500125i \(0.833287\pi\)
\(678\) 0 0
\(679\) −22302.0 10471.3i −1.26049 0.591831i
\(680\) −3210.90 −0.181077
\(681\) 0 0
\(682\) 4328.88 7497.85i 0.243052 0.420979i
\(683\) 4976.40 8619.37i 0.278794 0.482886i −0.692291 0.721618i \(-0.743399\pi\)
0.971085 + 0.238732i \(0.0767319\pi\)
\(684\) 0 0
\(685\) −11001.8 −0.613660
\(686\) 9054.56 8912.31i 0.503943 0.496026i
\(687\) 0 0
\(688\) 494.031 + 855.686i 0.0273761 + 0.0474168i
\(689\) −6911.14 + 11970.4i −0.382138 + 0.661883i
\(690\) 0 0
\(691\) 6159.06 + 10667.8i 0.339076 + 0.587298i 0.984259 0.176731i \(-0.0565521\pi\)
−0.645183 + 0.764028i \(0.723219\pi\)
\(692\) 946.094 0.0519727
\(693\) 0 0
\(694\) −1703.36 −0.0931681
\(695\) −12498.7 21648.3i −0.682160 1.18154i
\(696\) 0 0
\(697\) 1794.18 3107.62i 0.0975030 0.168880i
\(698\) 2348.88 + 4068.38i 0.127373 + 0.220617i
\(699\) 0 0
\(700\) 2.16999 + 25.5804i 0.000117168 + 0.00138121i
\(701\) −15992.8 −0.861685 −0.430843 0.902427i \(-0.641784\pi\)
−0.430843 + 0.902427i \(0.641784\pi\)
\(702\) 0 0
\(703\) −764.810 + 1324.69i −0.0410318 + 0.0710692i
\(704\) −620.729 + 1075.13i −0.0332310 + 0.0575577i
\(705\) 0 0
\(706\) 1572.63 0.0838338
\(707\) 7665.24 5337.17i 0.407752 0.283911i
\(708\) 0 0
\(709\) 9594.98 + 16619.0i 0.508247 + 0.880310i 0.999954 + 0.00954922i \(0.00303966\pi\)
−0.491707 + 0.870761i \(0.663627\pi\)
\(710\) 11306.8 19583.9i 0.597657 1.03517i
\(711\) 0 0
\(712\) 2522.75 + 4369.54i 0.132787 + 0.229993i
\(713\) 9146.43 0.480416
\(714\) 0 0
\(715\) 8585.94 0.449085
\(716\) −6323.27 10952.2i −0.330044 0.571653i
\(717\) 0 0
\(718\) −7381.62 + 12785.3i −0.383677 + 0.664547i
\(719\) −5469.47 9473.40i −0.283695 0.491375i 0.688597 0.725145i \(-0.258227\pi\)
−0.972292 + 0.233770i \(0.924894\pi\)
\(720\) 0 0
\(721\) 250.889 + 2957.56i 0.0129592 + 0.152767i
\(722\) 7405.13 0.381704
\(723\) 0 0
\(724\) 6608.93 11447.0i 0.339253 0.587603i
\(725\) 31.0691 53.8132i 0.00159155 0.00275665i
\(726\) 0 0
\(727\) −24352.3 −1.24233 −0.621166 0.783679i \(-0.713341\pi\)
−0.621166 + 0.783679i \(0.713341\pi\)
\(728\) −5302.20 2489.51i −0.269935 0.126741i
\(729\) 0 0
\(730\) −12842.9 22244.5i −0.651146 1.12782i
\(731\) −1106.92 + 1917.23i −0.0560065 + 0.0970061i
\(732\) 0 0
\(733\) 993.651 + 1721.05i 0.0500700 + 0.0867239i 0.889974 0.456011i \(-0.150722\pi\)
−0.839904 + 0.542735i \(0.817389\pi\)
\(734\) 4881.85 0.245494
\(735\) 0 0
\(736\) −1311.53 −0.0656842
\(737\) −1658.04 2871.82i −0.0828695 0.143534i
\(738\) 0 0
\(739\) −6181.23 + 10706.2i −0.307687 + 0.532929i −0.977856 0.209280i \(-0.932888\pi\)
0.670169 + 0.742208i \(0.266221\pi\)
\(740\) 609.637 + 1055.92i 0.0302848 + 0.0524547i
\(741\) 0 0
\(742\) −11722.4 5503.95i −0.579976 0.272313i
\(743\) −7775.46 −0.383922 −0.191961 0.981403i \(-0.561485\pi\)
−0.191961 + 0.981403i \(0.561485\pi\)
\(744\) 0 0
\(745\) −17186.5 + 29767.9i −0.845188 + 1.46391i
\(746\) −11876.1 + 20570.0i −0.582861 + 1.00954i
\(747\) 0 0
\(748\) −2781.59 −0.135969
\(749\) −3081.73 36328.3i −0.150339 1.77224i
\(750\) 0 0
\(751\) −2550.98 4418.42i −0.123950 0.214688i 0.797372 0.603488i \(-0.206223\pi\)
−0.921322 + 0.388800i \(0.872890\pi\)
\(752\) −3700.16 + 6408.86i −0.179429 + 0.310781i
\(753\) 0 0
\(754\) 7088.92 + 12278.4i 0.342392 + 0.593040i
\(755\) −30510.6 −1.47072
\(756\) 0 0
\(757\) 10003.6 0.480302 0.240151 0.970736i \(-0.422803\pi\)
0.240151 + 0.970736i \(0.422803\pi\)
\(758\) −4202.37 7278.71i −0.201368 0.348779i
\(759\) 0 0
\(760\) −2516.02 + 4357.88i −0.120086 + 0.207996i
\(761\) −18874.3 32691.2i −0.899070 1.55724i −0.828685 0.559715i \(-0.810911\pi\)
−0.0703850 0.997520i \(-0.522423\pi\)
\(762\) 0 0
\(763\) 17562.7 12228.6i 0.833307 0.580217i
\(764\) −8307.03 −0.393374
\(765\) 0 0
\(766\) 14096.8 24416.4i 0.664933 1.15170i
\(767\) −4821.84 + 8351.67i −0.226997 + 0.393170i
\(768\) 0 0
\(769\) 4279.68 0.200688 0.100344 0.994953i \(-0.468006\pi\)
0.100344 + 0.994953i \(0.468006\pi\)
\(770\) 679.951 + 8015.46i 0.0318230 + 0.375139i
\(771\) 0 0
\(772\) −5224.48 9049.07i −0.243566 0.421869i
\(773\) 4215.77 7301.93i 0.196159 0.339757i −0.751121 0.660165i \(-0.770487\pi\)
0.947280 + 0.320408i \(0.103820\pi\)
\(774\) 0 0
\(775\) −38.6680 66.9749i −0.00179225 0.00310427i
\(776\) −10642.6 −0.492329
\(777\) 0 0
\(778\) 22674.6 1.04489
\(779\) −2811.80 4870.18i −0.129324 0.223995i
\(780\) 0 0
\(781\) 9795.02 16965.5i 0.448775 0.777301i
\(782\) −1469.29 2544.89i −0.0671890 0.116375i
\(783\) 0 0
\(784\) 1904.20 5147.05i 0.0867438 0.234469i