Properties

Label 378.4.g.c.163.2
Level $378$
Weight $4$
Character 378.163
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 163.2
Root \(2.24123 + 3.88192i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.c.109.2

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

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

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 0.499307 + 0.866425i \(0.333588\pi\)
−1.00000 0.000799938i \(0.999745\pi\)
\(6\) 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 \(-0.0810148\pi\)
−0.701938 + 0.712238i \(0.747681\pi\)
\(12\) 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 \(-0.248982\pi\)
−0.965093 + 0.261908i \(0.915648\pi\)
\(18\) 0 0
\(19\) −28.0911 + 48.6552i −0.339186 + 0.587487i −0.984280 0.176616i \(-0.943485\pi\)
0.645094 + 0.764103i \(0.276818\pi\)
\(20\) 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 \(-0.773851\pi\)
0.943840 + 0.330403i \(0.107185\pi\)
\(24\) 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 \(-0.305359\pi\)
0.574082 + 0.818798i \(0.305359\pi\)
\(30\) 0 0
\(31\) −111.582 193.266i −0.646474 1.11973i −0.983959 0.178395i \(-0.942909\pi\)
0.337484 0.941331i \(-0.390424\pi\)
\(32\) −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 −0.894683 0.446702i \(-0.852598\pi\)
0.834197 + 0.551467i \(0.185932\pi\)
\(38\) −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 \(-0.561056\pi\)
−0.190639 + 0.981660i \(0.561056\pi\)
\(42\) 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 −0.244185 0.969729i \(-0.578521\pi\)
0.961902 0.273394i \(-0.0881461\pi\)
\(48\) 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 \(-0.316334\pi\)
−0.998574 + 0.0533783i \(0.983001\pi\)
\(54\) 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 \(-0.253401\pi\)
−0.968636 + 0.248483i \(0.920068\pi\)
\(60\) 0 0
\(61\) −32.5638 + 56.4022i −0.0683503 + 0.118386i −0.898175 0.439638i \(-0.855107\pi\)
0.829825 + 0.558024i \(0.188440\pi\)
\(62\) 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 0.777513 0.628867i \(-0.216481\pi\)
−0.933371 + 0.358912i \(0.883148\pi\)
\(68\) −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 \(-0.180168\pi\)
0.844045 + 0.536272i \(0.180168\pi\)
\(72\) 0 0
\(73\) −573.557 993.429i −0.919585 1.59277i −0.800046 0.599939i \(-0.795192\pi\)
−0.119539 0.992829i \(-0.538142\pi\)
\(74\) −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 −0.999858 0.0168627i \(-0.994632\pi\)
0.514532 + 0.857471i \(0.327966\pi\)
\(80\) −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 \(-0.294849\pi\)
0.600800 + 0.799400i \(0.294849\pi\)
\(84\) 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 \(-0.710778\pi\)
0.990413 + 0.138136i \(0.0441110\pi\)
\(90\) 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 \(-0.0867525\pi\)
−0.714661 + 0.699471i \(0.753419\pi\)
\(102\) 0 0
\(103\) −80.1333 + 138.795i −0.0766580 + 0.132775i −0.901806 0.432141i \(-0.857758\pi\)
0.825148 + 0.564916i \(0.191092\pi\)
\(104\) −316.278 −0.298208
\(105\) 0 0
\(106\) 699.246 0.640724
\(107\) −984.295 + 1704.85i −0.889303 + 1.54032i −0.0486022 + 0.998818i \(0.515477\pi\)
−0.840701 + 0.541500i \(0.817857\pi\)
\(108\) 0 0
\(109\) −577.764 1000.72i −0.507704 0.879369i −0.999960 0.00891861i \(-0.997161\pi\)
0.492256 0.870450i \(-0.336172\pi\)
\(110\) 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 \(-0.704794\pi\)
−0.599901 + 0.800074i \(0.704794\pi\)
\(114\) 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 \(-0.849874\pi\)
0.838886 + 0.544307i \(0.183207\pi\)
\(132\) 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 \(-0.0675403\pi\)
−0.671168 + 0.741306i \(0.734207\pi\)
\(138\) 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 0.0424511 + 0.999099i \(0.486483\pi\)
−0.886470 + 0.462786i \(0.846850\pi\)
\(150\) 0 0
\(151\) −1362.59 2360.07i −0.734343 1.27192i −0.955011 0.296571i \(-0.904157\pi\)
0.220668 0.975349i \(-0.429176\pi\)
\(152\) −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 0.657667 0.753309i \(-0.271543\pi\)
−0.981218 + 0.192902i \(0.938210\pi\)
\(158\) −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 −0.830155 0.557532i \(-0.811748\pi\)
0.897915 + 0.440169i \(0.145082\pi\)
\(164\) 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 \(-0.913824\pi\)
−0.963576 + 0.267435i \(0.913824\pi\)
\(168\) 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 \(-0.816782\pi\)
0.890841 + 0.454315i \(0.150116\pi\)
\(174\) 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 0.980592 + 0.196059i \(0.0628146\pi\)
−0.320504 + 0.947247i \(0.603852\pi\)
\(180\) 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 \(-0.962026\pi\)
0.599518 + 0.800361i \(0.295359\pi\)
\(192\) 0 0
\(193\) −1306.12 2262.27i −0.487133 0.843739i 0.512758 0.858533i \(-0.328624\pi\)
−0.999891 + 0.0147947i \(0.995291\pi\)
\(194\) −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 \(-0.287866\pi\)
0.618189 + 0.786029i \(0.287866\pi\)
\(198\) 0 0
\(199\) 1812.08 + 3138.61i 0.645501 + 1.11804i 0.984185 + 0.177141i \(0.0566849\pi\)
−0.338684 + 0.940900i \(0.609982\pi\)
\(200\) −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 \(-0.288467\pi\)
−0.990083 + 0.140486i \(0.955133\pi\)
\(228\) 0 0
\(229\) 351.347 608.550i 0.101387 0.175608i −0.810869 0.585227i \(-0.801005\pi\)
0.912256 + 0.409620i \(0.134339\pi\)
\(230\) −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 \(-0.814925\pi\)
0.893478 + 0.449107i \(0.148258\pi\)
\(234\) 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 \(-0.492308\pi\)
0.0241643 + 0.999708i \(0.492308\pi\)
\(240\) 0 0
\(241\) 2030.95 + 3517.71i 0.542843 + 0.940232i 0.998739 + 0.0501987i \(0.0159854\pi\)
−0.455896 + 0.890033i \(0.650681\pi\)
\(242\) 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 \(-0.417401\pi\)
0.256589 + 0.966521i \(0.417401\pi\)
\(252\) 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 −0.443732 0.896159i \(-0.646346\pi\)
0.997963 0.0637964i \(-0.0203208\pi\)
\(258\) 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 −0.988418 0.151756i \(-0.951507\pi\)
0.362784 0.931873i \(-0.381826\pi\)
\(264\) 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 −0.957942 0.286960i \(-0.907355\pi\)
0.230456 0.973083i \(-0.425978\pi\)
\(270\) 0 0
\(271\) −3540.34 + 6132.05i −0.793580 + 1.37452i 0.130157 + 0.991493i \(0.458452\pi\)
−0.923737 + 0.383028i \(0.874881\pi\)
\(272\) 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 −0.999974 0.00716871i \(-0.997718\pi\)
0.493779 0.869588i \(-0.335615\pi\)
\(278\) 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 \(-0.161495\pi\)
0.874034 + 0.485865i \(0.161495\pi\)
\(282\) 0 0
\(283\) −101.417 175.660i −0.0213026 0.0368971i 0.855178 0.518335i \(-0.173448\pi\)
−0.876480 + 0.481438i \(0.840115\pi\)
\(284\) −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 \(-0.617257\pi\)
−0.360100 + 0.932914i \(0.617257\pi\)
\(294\) 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 −0.970276 0.242000i \(-0.922197\pi\)
0.275560 0.961284i \(-0.411137\pi\)
\(312\) 0 0
\(313\) 2901.80 5026.07i 0.524024 0.907636i −0.475585 0.879670i \(-0.657764\pi\)
0.999609 0.0279665i \(-0.00890316\pi\)
\(314\) 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 \(-0.710034\pi\)
0.990733 + 0.135823i \(0.0433678\pi\)
\(318\) 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 0.277549 + 0.960712i \(0.410478\pi\)
−0.970775 + 0.239992i \(0.922855\pi\)
\(332\) −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 \(-0.145681\pi\)
−0.831204 + 0.555967i \(0.812348\pi\)
\(348\) 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 \(-0.185547\pi\)
−0.894142 + 0.447783i \(0.852214\pi\)
\(354\) 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 0.456153 + 0.889901i \(0.349227\pi\)
−0.998754 + 0.0499105i \(0.984106\pi\)
\(360\) 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 0.939672 0.342075i \(-0.111130\pi\)
−0.766082 + 0.642742i \(0.777797\pi\)
\(368\) 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 −0.0781707 0.996940i \(-0.524908\pi\)
0.902461 0.430772i \(-0.141759\pi\)
\(374\) 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 0.175565 0.984468i \(-0.443825\pi\)
0.764791 0.644278i \(-0.222842\pi\)
\(384\) 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 −0.953014 0.302927i \(-0.902036\pi\)
0.214165 0.976798i \(-0.431297\pi\)
\(390\) 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 −0.895543 0.444975i \(-0.853212\pi\)
0.833131 + 0.553075i \(0.186546\pi\)
\(398\) −7248.31 −0.912877
\(399\) 0 0
\(400\) 5.54469 0.000693086
\(401\) 4246.79 7355.66i 0.528864 0.916020i −0.470569 0.882363i \(-0.655951\pi\)
0.999433 0.0336569i \(-0.0107153\pi\)
\(402\) 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 −0.997488 0.0708381i \(-0.977433\pi\)
0.437396 0.899269i \(-0.355901\pi\)
\(410\) 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 \(-0.417464\pi\)
0.256398 + 0.966571i \(0.417464\pi\)
\(420\) 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 \(-0.171607\pi\)
−0.873681 + 0.486498i \(0.838274\pi\)
\(432\) 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 −0.902057 0.431616i \(-0.857943\pi\)
0.824819 + 0.565396i \(0.191277\pi\)
\(440\) −1737.39 −0.188243
\(441\) 0 0
\(442\) −2834.59 −0.305040
\(443\) −6029.64 + 10443.6i −0.646674 + 1.12007i 0.337238 + 0.941420i \(0.390507\pi\)
−0.983912 + 0.178653i \(0.942826\pi\)
\(444\) 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 \(-0.525444\pi\)
−0.0798491 + 0.996807i \(0.525444\pi\)
\(450\) 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 −0.692206 0.721700i \(-0.743361\pi\)
0.971114 + 0.238618i \(0.0766944\pi\)
\(458\) 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 \(-0.658137\pi\)
−0.476616 + 0.879112i \(0.658137\pi\)
\(462\) 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 \(-0.940587\pi\)
0.652024 + 0.758198i \(0.273920\pi\)
\(468\) 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 −0.952884 0.303335i \(-0.901900\pi\)
0.213747 0.976889i \(-0.431433\pi\)
\(480\) 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 0.939585 0.342317i \(-0.111212\pi\)
−0.766247 + 0.642546i \(0.777878\pi\)
\(488\) −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 \(-0.176575\pi\)
0.850045 + 0.526711i \(0.176575\pi\)
\(492\) 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 −0.770940 0.636908i \(-0.780213\pi\)
0.937049 + 0.349199i \(0.113546\pi\)
\(500\) 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 \(-0.401471\pi\)
0.304620 + 0.952474i \(0.401471\pi\)
\(504\) 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 \(-0.975910\pi\)
0.564047 + 0.825743i \(0.309244\pi\)
\(510\) 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 \(-0.282362\pi\)
−0.987207 + 0.159446i \(0.949029\pi\)
\(522\) 0 0
\(523\) 3554.65 6156.84i 0.297197 0.514761i −0.678296 0.734788i \(-0.737281\pi\)
0.975494 + 0.220028i \(0.0706148\pi\)
\(524\) 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 −0.502173 0.864767i \(-0.667466\pi\)
0.999997 + 0.00251141i \(0.000799407\pi\)
\(542\) −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 \(-0.168443\pi\)
−0.868803 + 0.495158i \(0.835110\pi\)
\(558\) 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 0.998308 + 0.0581491i \(0.0185199\pi\)
−0.448795 + 0.893635i \(0.648147\pi\)
\(564\) 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 0.193382 + 0.981123i \(0.438054\pi\)
−0.946369 + 0.323088i \(0.895279\pi\)
\(570\) 0 0
\(571\) 9365.03 + 16220.7i 0.686364 + 1.18882i 0.973006 + 0.230780i \(0.0741278\pi\)
−0.286641 + 0.958038i \(0.592539\pi\)
\(572\) −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 0.732875 0.680363i \(-0.238178\pi\)
−0.955649 + 0.294507i \(0.904845\pi\)
\(578\) 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 \(-0.578741\pi\)
−0.244856 + 0.969559i \(0.578741\pi\)
\(588\) 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 \(-0.888096\pi\)
0.767642 + 0.640878i \(0.221430\pi\)
\(594\) 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 \(-0.0975397\pi\)
−0.737951 + 0.674855i \(0.764206\pi\)
\(600\) 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 −0.921251 0.388969i \(-0.872831\pi\)
0.797482 + 0.603342i \(0.206165\pi\)
\(608\) 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 0.712457 0.701716i \(-0.247582\pi\)
−0.963932 + 0.266148i \(0.914249\pi\)
\(614\) 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 \(-0.548553\pi\)
−0.151942 + 0.988389i \(0.548553\pi\)
\(618\) 0 0
\(619\) 3276.14 + 5674.44i 0.212729 + 0.368457i 0.952568 0.304327i \(-0.0984316\pi\)
−0.739839 + 0.672784i \(0.765098\pi\)
\(620\) −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 \(-0.286981\pi\)
−0.989416 + 0.145105i \(0.953648\pi\)
\(642\) 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 −0.899371 0.437187i \(-0.855975\pi\)
0.0710702 0.997471i \(-0.477359\pi\)
\(648\) 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 −0.0732872 0.997311i \(-0.523349\pi\)
0.900340 0.435187i \(-0.143318\pi\)
\(654\) 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 \(-0.603222\pi\)
−0.318627 + 0.947880i \(0.603222\pi\)
\(660\) 0 0
\(661\) 5517.83 + 9557.17i 0.324688 + 0.562376i 0.981449 0.191722i \(-0.0614073\pi\)
−0.656761 + 0.754099i \(0.728074\pi\)
\(662\) −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 \(-0.833379\pi\)
0.865953 + 0.500125i \(0.166713\pi\)
\(678\) 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 \(-0.256601\pi\)
−0.971085 + 0.238732i \(0.923268\pi\)
\(684\) 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 −0.645183 0.764028i \(-0.723219\pi\)
0.984259 + 0.176731i \(0.0565521\pi\)
\(692\) −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 \(-0.358216\pi\)
0.430843 + 0.902427i \(0.358216\pi\)
\(702\) 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 −0.491707 0.870761i \(-0.663627\pi\)
0.999954 0.00954922i \(-0.00303966\pi\)
\(710\) −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 \(-0.741773\pi\)
0.972292 + 0.233770i \(0.0751063\pi\)
\(720\) 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 −0.839904 0.542735i \(-0.817389\pi\)
0.889974 + 0.456011i \(0.150722\pi\)
\(734\) −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 0.670169 0.742208i \(-0.266221\pi\)
−0.977856 + 0.209280i \(0.932888\pi\)
\(740\) −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 \(-0.438515\pi\)
0.191961 + 0.981403i \(0.438515\pi\)
\(744\) 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 −0.921322 0.388800i \(-0.872890\pi\)
0.797372 + 0.603488i \(0.206223\pi\)
\(752\) 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 0.0703850 0.997520i \(-0.477577\pi\)
0.828685 0.559715i \(-0.189089\pi\)
\(762\) 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 \(-0.229513\pi\)
−0.947280 + 0.320408i \(0.896180\pi\)
\(774\) 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