Properties

Label 378.4.g.f.109.4
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 109.4
Root \(0.445324 + 0.771324i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.f.163.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.50453 + 11.2662i) q^{5} +(18.4787 - 1.24034i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.50453 + 11.2662i) q^{5} +(18.4787 - 1.24034i) q^{7} -8.00000 q^{8} +(-13.0091 + 22.5324i) q^{10} +(13.6652 - 23.6688i) q^{11} +81.3058 q^{13} +(20.6270 + 30.7657i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-3.11340 + 5.39257i) q^{17} +(29.0966 + 50.3968i) q^{19} -52.0363 q^{20} +54.6607 q^{22} +(0.151573 + 0.262533i) q^{23} +(-22.1179 + 38.3094i) q^{25} +(81.3058 + 140.826i) q^{26} +(-32.6607 + 66.4927i) q^{28} -48.9779 q^{29} +(-0.201323 + 0.348702i) q^{31} +(16.0000 - 27.7128i) q^{32} -12.4536 q^{34} +(134.169 + 200.116i) q^{35} +(-103.469 - 179.213i) q^{37} +(-58.1932 + 100.794i) q^{38} +(-52.0363 - 90.1295i) q^{40} -322.582 q^{41} +13.5700 q^{43} +(54.6607 + 94.6751i) q^{44} +(-0.303147 + 0.525066i) q^{46} +(271.328 + 469.953i) q^{47} +(339.923 - 45.8396i) q^{49} -88.4717 q^{50} +(-162.612 + 281.652i) q^{52} +(-326.119 + 564.854i) q^{53} +355.542 q^{55} +(-147.829 + 9.92269i) q^{56} +(-48.9779 - 84.8323i) q^{58} +(-141.268 + 244.683i) q^{59} +(97.9748 + 169.697i) q^{61} -0.805294 q^{62} +64.0000 q^{64} +(528.857 + 916.007i) q^{65} +(-18.4344 + 31.9293i) q^{67} +(-12.4536 - 21.5703i) q^{68} +(-212.443 + 432.504i) q^{70} -121.705 q^{71} +(-92.0556 + 159.445i) q^{73} +(206.938 - 358.427i) q^{74} -232.773 q^{76} +(223.157 - 454.317i) q^{77} +(-552.442 - 956.858i) q^{79} +(104.073 - 180.259i) q^{80} +(-322.582 - 558.729i) q^{82} +993.883 q^{83} -81.0049 q^{85} +(13.5700 + 23.5040i) q^{86} +(-109.321 + 189.350i) q^{88} +(-795.853 - 1378.46i) q^{89} +(1502.42 - 100.847i) q^{91} -1.21259 q^{92} +(-542.655 + 939.907i) q^{94} +(-378.520 + 655.616i) q^{95} -361.831 q^{97} +(419.320 + 542.925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10}) \) 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
\(5\) 6.50453 + 11.2662i 0.581783 + 1.00768i 0.995268 + 0.0971671i \(0.0309781\pi\)
−0.413485 + 0.910511i \(0.635689\pi\)
\(6\) 0 0
\(7\) 18.4787 1.24034i 0.997755 0.0669719i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −13.0091 + 22.5324i −0.411383 + 0.712536i
\(11\) 13.6652 23.6688i 0.374564 0.648764i −0.615698 0.787983i \(-0.711126\pi\)
0.990262 + 0.139218i \(0.0444590\pi\)
\(12\) 0 0
\(13\) 81.3058 1.73463 0.867315 0.497760i \(-0.165844\pi\)
0.867315 + 0.497760i \(0.165844\pi\)
\(14\) 20.6270 + 30.7657i 0.393771 + 0.587319i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −3.11340 + 5.39257i −0.0444183 + 0.0769347i −0.887380 0.461039i \(-0.847477\pi\)
0.842962 + 0.537974i \(0.180810\pi\)
\(18\) 0 0
\(19\) 29.0966 + 50.3968i 0.351327 + 0.608517i 0.986482 0.163868i \(-0.0523971\pi\)
−0.635155 + 0.772385i \(0.719064\pi\)
\(20\) −52.0363 −0.581783
\(21\) 0 0
\(22\) 54.6607 0.529714
\(23\) 0.151573 + 0.262533i 0.00137414 + 0.00238008i 0.866712 0.498809i \(-0.166229\pi\)
−0.865338 + 0.501190i \(0.832896\pi\)
\(24\) 0 0
\(25\) −22.1179 + 38.3094i −0.176943 + 0.306475i
\(26\) 81.3058 + 140.826i 0.613284 + 1.06224i
\(27\) 0 0
\(28\) −32.6607 + 66.4927i −0.220439 + 0.448783i
\(29\) −48.9779 −0.313620 −0.156810 0.987629i \(-0.550121\pi\)
−0.156810 + 0.987629i \(0.550121\pi\)
\(30\) 0 0
\(31\) −0.201323 + 0.348702i −0.00116641 + 0.00202028i −0.866608 0.498990i \(-0.833705\pi\)
0.865442 + 0.501010i \(0.167038\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −12.4536 −0.0628169
\(35\) 134.169 + 200.116i 0.647963 + 0.966453i
\(36\) 0 0
\(37\) −103.469 179.213i −0.459735 0.796284i 0.539212 0.842170i \(-0.318722\pi\)
−0.998947 + 0.0458863i \(0.985389\pi\)
\(38\) −58.1932 + 100.794i −0.248426 + 0.430286i
\(39\) 0 0
\(40\) −52.0363 90.1295i −0.205691 0.356268i
\(41\) −322.582 −1.22875 −0.614377 0.789013i \(-0.710593\pi\)
−0.614377 + 0.789013i \(0.710593\pi\)
\(42\) 0 0
\(43\) 13.5700 0.0481258 0.0240629 0.999710i \(-0.492340\pi\)
0.0240629 + 0.999710i \(0.492340\pi\)
\(44\) 54.6607 + 94.6751i 0.187282 + 0.324382i
\(45\) 0 0
\(46\) −0.303147 + 0.525066i −0.000971664 + 0.00168297i
\(47\) 271.328 + 469.953i 0.842068 + 1.45851i 0.888143 + 0.459567i \(0.151995\pi\)
−0.0460745 + 0.998938i \(0.514671\pi\)
\(48\) 0 0
\(49\) 339.923 45.8396i 0.991030 0.133643i
\(50\) −88.4717 −0.250236
\(51\) 0 0
\(52\) −162.612 + 281.652i −0.433657 + 0.751117i
\(53\) −326.119 + 564.854i −0.845205 + 1.46394i 0.0402385 + 0.999190i \(0.487188\pi\)
−0.885443 + 0.464747i \(0.846145\pi\)
\(54\) 0 0
\(55\) 355.542 0.871661
\(56\) −147.829 + 9.92269i −0.352760 + 0.0236781i
\(57\) 0 0
\(58\) −48.9779 84.8323i −0.110881 0.192052i
\(59\) −141.268 + 244.683i −0.311720 + 0.539916i −0.978735 0.205129i \(-0.934239\pi\)
0.667015 + 0.745045i \(0.267572\pi\)
\(60\) 0 0
\(61\) 97.9748 + 169.697i 0.205646 + 0.356189i 0.950338 0.311219i \(-0.100737\pi\)
−0.744693 + 0.667408i \(0.767404\pi\)
\(62\) −0.805294 −0.00164956
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 528.857 + 916.007i 1.00918 + 1.74795i
\(66\) 0 0
\(67\) −18.4344 + 31.9293i −0.0336137 + 0.0582207i −0.882343 0.470607i \(-0.844035\pi\)
0.848729 + 0.528828i \(0.177368\pi\)
\(68\) −12.4536 21.5703i −0.0222091 0.0384674i
\(69\) 0 0
\(70\) −212.443 + 432.504i −0.362739 + 0.738487i
\(71\) −121.705 −0.203433 −0.101716 0.994813i \(-0.532433\pi\)
−0.101716 + 0.994813i \(0.532433\pi\)
\(72\) 0 0
\(73\) −92.0556 + 159.445i −0.147593 + 0.255639i −0.930337 0.366705i \(-0.880486\pi\)
0.782744 + 0.622343i \(0.213819\pi\)
\(74\) 206.938 358.427i 0.325081 0.563058i
\(75\) 0 0
\(76\) −232.773 −0.351327
\(77\) 223.157 454.317i 0.330274 0.672393i
\(78\) 0 0
\(79\) −552.442 956.858i −0.786767 1.36272i −0.927938 0.372735i \(-0.878420\pi\)
0.141171 0.989985i \(-0.454913\pi\)
\(80\) 104.073 180.259i 0.145446 0.251920i
\(81\) 0 0
\(82\) −322.582 558.729i −0.434430 0.752455i
\(83\) 993.883 1.31437 0.657186 0.753729i \(-0.271747\pi\)
0.657186 + 0.753729i \(0.271747\pi\)
\(84\) 0 0
\(85\) −81.0049 −0.103367
\(86\) 13.5700 + 23.5040i 0.0170150 + 0.0294709i
\(87\) 0 0
\(88\) −109.321 + 189.350i −0.132428 + 0.229373i
\(89\) −795.853 1378.46i −0.947868 1.64176i −0.749904 0.661547i \(-0.769900\pi\)
−0.197965 0.980209i \(-0.563433\pi\)
\(90\) 0 0
\(91\) 1502.42 100.847i 1.73074 0.116171i
\(92\) −1.21259 −0.00137414
\(93\) 0 0
\(94\) −542.655 + 939.907i −0.595432 + 1.03132i
\(95\) −378.520 + 655.616i −0.408793 + 0.708050i
\(96\) 0 0
\(97\) −361.831 −0.378746 −0.189373 0.981905i \(-0.560646\pi\)
−0.189373 + 0.981905i \(0.560646\pi\)
\(98\) 419.320 + 542.925i 0.432221 + 0.559629i
\(99\) 0 0
\(100\) −88.4717 153.238i −0.0884717 0.153238i
\(101\) −292.761 + 507.078i −0.288424 + 0.499566i −0.973434 0.228969i \(-0.926465\pi\)
0.685010 + 0.728534i \(0.259798\pi\)
\(102\) 0 0
\(103\) −818.558 1417.78i −0.783057 1.35629i −0.930153 0.367172i \(-0.880326\pi\)
0.147096 0.989122i \(-0.453007\pi\)
\(104\) −650.447 −0.613284
\(105\) 0 0
\(106\) −1304.47 −1.19530
\(107\) 743.870 + 1288.42i 0.672081 + 1.16408i 0.977313 + 0.211800i \(0.0679325\pi\)
−0.305232 + 0.952278i \(0.598734\pi\)
\(108\) 0 0
\(109\) 661.260 1145.34i 0.581075 1.00645i −0.414277 0.910151i \(-0.635965\pi\)
0.995352 0.0963011i \(-0.0307012\pi\)
\(110\) 355.542 + 615.818i 0.308179 + 0.533781i
\(111\) 0 0
\(112\) −165.016 246.125i −0.139219 0.207649i
\(113\) −1342.87 −1.11794 −0.558968 0.829189i \(-0.688803\pi\)
−0.558968 + 0.829189i \(0.688803\pi\)
\(114\) 0 0
\(115\) −1.97183 + 3.41531i −0.00159890 + 0.00276938i
\(116\) 97.9559 169.665i 0.0784050 0.135801i
\(117\) 0 0
\(118\) −565.071 −0.440839
\(119\) −50.8429 + 103.509i −0.0391661 + 0.0797368i
\(120\) 0 0
\(121\) 292.026 + 505.804i 0.219403 + 0.380018i
\(122\) −195.950 + 339.395i −0.145413 + 0.251863i
\(123\) 0 0
\(124\) −0.805294 1.39481i −0.000583206 0.00101014i
\(125\) 1050.67 0.751795
\(126\) 0 0
\(127\) 579.894 0.405175 0.202588 0.979264i \(-0.435065\pi\)
0.202588 + 0.979264i \(0.435065\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1057.71 + 1832.01i −0.713597 + 1.23599i
\(131\) −1422.68 2464.15i −0.948853 1.64346i −0.747846 0.663873i \(-0.768912\pi\)
−0.201008 0.979590i \(-0.564422\pi\)
\(132\) 0 0
\(133\) 600.176 + 895.177i 0.391292 + 0.583622i
\(134\) −73.7375 −0.0475370
\(135\) 0 0
\(136\) 24.9072 43.1405i 0.0157042 0.0272005i
\(137\) 1264.00 2189.32i 0.788255 1.36530i −0.138780 0.990323i \(-0.544318\pi\)
0.927035 0.374975i \(-0.122349\pi\)
\(138\) 0 0
\(139\) 1466.86 0.895092 0.447546 0.894261i \(-0.352298\pi\)
0.447546 + 0.894261i \(0.352298\pi\)
\(140\) −961.562 + 64.5425i −0.580477 + 0.0389631i
\(141\) 0 0
\(142\) −121.705 210.799i −0.0719244 0.124577i
\(143\) 1111.06 1924.41i 0.649730 1.12537i
\(144\) 0 0
\(145\) −318.579 551.794i −0.182459 0.316028i
\(146\) −368.222 −0.208728
\(147\) 0 0
\(148\) 827.751 0.459735
\(149\) −1104.10 1912.37i −0.607059 1.05146i −0.991722 0.128400i \(-0.959016\pi\)
0.384663 0.923057i \(-0.374317\pi\)
\(150\) 0 0
\(151\) −1224.97 + 2121.71i −0.660175 + 1.14346i 0.320394 + 0.947284i \(0.396185\pi\)
−0.980569 + 0.196172i \(0.937149\pi\)
\(152\) −232.773 403.175i −0.124213 0.215143i
\(153\) 0 0
\(154\) 1010.06 67.7977i 0.528524 0.0354759i
\(155\) −5.23806 −0.00271439
\(156\) 0 0
\(157\) 1565.68 2711.84i 0.795893 1.37853i −0.126378 0.991982i \(-0.540335\pi\)
0.922271 0.386544i \(-0.126331\pi\)
\(158\) 1104.88 1913.72i 0.556328 0.963589i
\(159\) 0 0
\(160\) 416.290 0.205691
\(161\) 3.12651 + 4.66326i 0.00153045 + 0.00228271i
\(162\) 0 0
\(163\) 1810.22 + 3135.39i 0.869860 + 1.50664i 0.862139 + 0.506672i \(0.169125\pi\)
0.00772179 + 0.999970i \(0.497542\pi\)
\(164\) 645.165 1117.46i 0.307188 0.532066i
\(165\) 0 0
\(166\) 993.883 + 1721.46i 0.464700 + 0.804885i
\(167\) −1156.26 −0.535775 −0.267887 0.963450i \(-0.586326\pi\)
−0.267887 + 0.963450i \(0.586326\pi\)
\(168\) 0 0
\(169\) 4413.64 2.00894
\(170\) −81.0049 140.305i −0.0365458 0.0632992i
\(171\) 0 0
\(172\) −27.1400 + 47.0079i −0.0120314 + 0.0208391i
\(173\) 531.941 + 921.349i 0.233773 + 0.404907i 0.958915 0.283692i \(-0.0915594\pi\)
−0.725142 + 0.688599i \(0.758226\pi\)
\(174\) 0 0
\(175\) −361.194 + 735.341i −0.156021 + 0.317637i
\(176\) −437.286 −0.187282
\(177\) 0 0
\(178\) 1591.71 2756.92i 0.670244 1.16090i
\(179\) 875.381 1516.20i 0.365526 0.633109i −0.623335 0.781955i \(-0.714223\pi\)
0.988860 + 0.148846i \(0.0475559\pi\)
\(180\) 0 0
\(181\) −3313.36 −1.36066 −0.680332 0.732904i \(-0.738164\pi\)
−0.680332 + 0.732904i \(0.738164\pi\)
\(182\) 1677.10 + 2501.43i 0.683047 + 1.01878i
\(183\) 0 0
\(184\) −1.21259 2.10026i −0.000485832 0.000841486i
\(185\) 1346.03 2331.40i 0.534932 0.926529i
\(186\) 0 0
\(187\) 85.0903 + 147.381i 0.0332750 + 0.0576340i
\(188\) −2170.62 −0.842068
\(189\) 0 0
\(190\) −1514.08 −0.578120
\(191\) 265.789 + 460.360i 0.100690 + 0.174400i 0.911969 0.410259i \(-0.134562\pi\)
−0.811279 + 0.584659i \(0.801228\pi\)
\(192\) 0 0
\(193\) 1145.72 1984.44i 0.427309 0.740121i −0.569324 0.822113i \(-0.692795\pi\)
0.996633 + 0.0819920i \(0.0261282\pi\)
\(194\) −361.831 626.710i −0.133907 0.231934i
\(195\) 0 0
\(196\) −521.053 + 1269.21i −0.189888 + 0.462539i
\(197\) −2967.84 −1.07335 −0.536674 0.843789i \(-0.680320\pi\)
−0.536674 + 0.843789i \(0.680320\pi\)
\(198\) 0 0
\(199\) −1568.96 + 2717.52i −0.558899 + 0.968041i 0.438690 + 0.898638i \(0.355443\pi\)
−0.997589 + 0.0694024i \(0.977891\pi\)
\(200\) 176.943 306.475i 0.0625590 0.108355i
\(201\) 0 0
\(202\) −1171.05 −0.407894
\(203\) −905.048 + 60.7491i −0.312916 + 0.0210037i
\(204\) 0 0
\(205\) −2098.25 3634.27i −0.714868 1.23819i
\(206\) 1637.12 2835.57i 0.553705 0.959045i
\(207\) 0 0
\(208\) −650.447 1126.61i −0.216829 0.375558i
\(209\) 1590.44 0.526379
\(210\) 0 0
\(211\) 1306.36 0.426226 0.213113 0.977028i \(-0.431640\pi\)
0.213113 + 0.977028i \(0.431640\pi\)
\(212\) −1304.47 2259.42i −0.422602 0.731969i
\(213\) 0 0
\(214\) −1487.74 + 2576.84i −0.475233 + 0.823127i
\(215\) 88.2667 + 152.882i 0.0279988 + 0.0484953i
\(216\) 0 0
\(217\) −3.28768 + 6.69327i −0.00102849 + 0.00209386i
\(218\) 2645.04 0.821765
\(219\) 0 0
\(220\) −711.085 + 1231.64i −0.217915 + 0.377440i
\(221\) −253.138 + 438.447i −0.0770493 + 0.133453i
\(222\) 0 0
\(223\) 2155.86 0.647387 0.323693 0.946162i \(-0.395075\pi\)
0.323693 + 0.946162i \(0.395075\pi\)
\(224\) 261.286 531.942i 0.0779370 0.158669i
\(225\) 0 0
\(226\) −1342.87 2325.92i −0.395250 0.684594i
\(227\) 2564.22 4441.37i 0.749751 1.29861i −0.198191 0.980163i \(-0.563507\pi\)
0.947942 0.318444i \(-0.103160\pi\)
\(228\) 0 0
\(229\) −2973.64 5150.49i −0.858094 1.48626i −0.873744 0.486386i \(-0.838315\pi\)
0.0156498 0.999878i \(-0.495018\pi\)
\(230\) −7.88732 −0.00226119
\(231\) 0 0
\(232\) 391.824 0.110881
\(233\) 2567.16 + 4446.46i 0.721804 + 1.25020i 0.960276 + 0.279052i \(0.0900203\pi\)
−0.238471 + 0.971150i \(0.576646\pi\)
\(234\) 0 0
\(235\) −3529.72 + 6113.66i −0.979803 + 1.69707i
\(236\) −565.071 978.732i −0.155860 0.269958i
\(237\) 0 0
\(238\) −230.126 + 15.4467i −0.0626759 + 0.00420697i
\(239\) −7241.83 −1.95998 −0.979989 0.199050i \(-0.936214\pi\)
−0.979989 + 0.199050i \(0.936214\pi\)
\(240\) 0 0
\(241\) 3332.02 5771.23i 0.890599 1.54256i 0.0514393 0.998676i \(-0.483619\pi\)
0.839159 0.543886i \(-0.183048\pi\)
\(242\) −584.052 + 1011.61i −0.155142 + 0.268713i
\(243\) 0 0
\(244\) −783.798 −0.205646
\(245\) 2727.48 + 3531.47i 0.711234 + 0.920888i
\(246\) 0 0
\(247\) 2365.72 + 4097.56i 0.609423 + 1.05555i
\(248\) 1.61059 2.78962i 0.000412389 0.000714278i
\(249\) 0 0
\(250\) 1050.67 + 1819.81i 0.265800 + 0.460379i
\(251\) 6024.90 1.51509 0.757546 0.652781i \(-0.226398\pi\)
0.757546 + 0.652781i \(0.226398\pi\)
\(252\) 0 0
\(253\) 8.28511 0.00205882
\(254\) 579.894 + 1004.41i 0.143251 + 0.248118i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1936.59 3354.27i −0.470043 0.814138i 0.529371 0.848391i \(-0.322428\pi\)
−0.999413 + 0.0342531i \(0.989095\pi\)
\(258\) 0 0
\(259\) −2134.25 3183.29i −0.512031 0.763707i
\(260\) −4230.85 −1.00918
\(261\) 0 0
\(262\) 2845.35 4928.30i 0.670941 1.16210i
\(263\) −2416.95 + 4186.28i −0.566675 + 0.981511i 0.430216 + 0.902726i \(0.358437\pi\)
−0.996892 + 0.0787847i \(0.974896\pi\)
\(264\) 0 0
\(265\) −8485.00 −1.96690
\(266\) −950.316 + 1934.71i −0.219051 + 0.445958i
\(267\) 0 0
\(268\) −73.7375 127.717i −0.0168069 0.0291103i
\(269\) −1026.81 + 1778.49i −0.232736 + 0.403110i −0.958612 0.284715i \(-0.908101\pi\)
0.725876 + 0.687825i \(0.241434\pi\)
\(270\) 0 0
\(271\) −82.2034 142.380i −0.0184262 0.0319151i 0.856665 0.515873i \(-0.172532\pi\)
−0.875091 + 0.483958i \(0.839199\pi\)
\(272\) 99.6288 0.0222091
\(273\) 0 0
\(274\) 5056.01 1.11476
\(275\) 604.491 + 1047.01i 0.132553 + 0.229589i
\(276\) 0 0
\(277\) −1454.42 + 2519.13i −0.315479 + 0.546425i −0.979539 0.201254i \(-0.935498\pi\)
0.664061 + 0.747679i \(0.268832\pi\)
\(278\) 1466.86 + 2540.68i 0.316463 + 0.548130i
\(279\) 0 0
\(280\) −1073.35 1600.93i −0.229090 0.341693i
\(281\) −4676.92 −0.992888 −0.496444 0.868069i \(-0.665361\pi\)
−0.496444 + 0.868069i \(0.665361\pi\)
\(282\) 0 0
\(283\) −843.271 + 1460.59i −0.177128 + 0.306795i −0.940896 0.338696i \(-0.890014\pi\)
0.763768 + 0.645491i \(0.223347\pi\)
\(284\) 243.410 421.599i 0.0508582 0.0880890i
\(285\) 0 0
\(286\) 4444.24 0.918857
\(287\) −5960.90 + 400.111i −1.22600 + 0.0822919i
\(288\) 0 0
\(289\) 2437.11 + 4221.20i 0.496054 + 0.859191i
\(290\) 637.157 1103.59i 0.129018 0.223465i
\(291\) 0 0
\(292\) −368.222 637.780i −0.0737965 0.127819i
\(293\) 6140.31 1.22430 0.612151 0.790741i \(-0.290304\pi\)
0.612151 + 0.790741i \(0.290304\pi\)
\(294\) 0 0
\(295\) −3675.53 −0.725415
\(296\) 827.751 + 1433.71i 0.162541 + 0.281529i
\(297\) 0 0
\(298\) 2208.21 3824.73i 0.429256 0.743492i
\(299\) 12.3238 + 21.3455i 0.00238363 + 0.00412856i
\(300\) 0 0
\(301\) 250.756 16.8314i 0.0480177 0.00322307i
\(302\) −4899.87 −0.933628
\(303\) 0 0
\(304\) 465.546 806.349i 0.0878319 0.152129i
\(305\) −1274.56 + 2207.60i −0.239282 + 0.414449i
\(306\) 0 0
\(307\) −7548.41 −1.40329 −0.701645 0.712526i \(-0.747551\pi\)
−0.701645 + 0.712526i \(0.747551\pi\)
\(308\) 1127.49 + 1681.67i 0.208586 + 0.311111i
\(309\) 0 0
\(310\) −5.23806 9.07259i −0.000959683 0.00166222i
\(311\) 850.079 1472.38i 0.154995 0.268460i −0.778062 0.628188i \(-0.783797\pi\)
0.933057 + 0.359728i \(0.117130\pi\)
\(312\) 0 0
\(313\) 1467.61 + 2541.98i 0.265030 + 0.459045i 0.967571 0.252597i \(-0.0812848\pi\)
−0.702542 + 0.711643i \(0.747951\pi\)
\(314\) 6262.73 1.12556
\(315\) 0 0
\(316\) 4419.54 0.786767
\(317\) 1817.34 + 3147.72i 0.321993 + 0.557709i 0.980899 0.194517i \(-0.0623138\pi\)
−0.658906 + 0.752225i \(0.728980\pi\)
\(318\) 0 0
\(319\) −669.292 + 1159.25i −0.117471 + 0.203465i
\(320\) 416.290 + 721.036i 0.0727229 + 0.125960i
\(321\) 0 0
\(322\) −4.95049 + 10.0785i −0.000856771 + 0.00174427i
\(323\) −362.358 −0.0624214
\(324\) 0 0
\(325\) −1798.32 + 3114.78i −0.306931 + 0.531621i
\(326\) −3620.44 + 6270.78i −0.615084 + 1.06536i
\(327\) 0 0
\(328\) 2580.66 0.434430
\(329\) 5596.68 + 8347.58i 0.937857 + 1.39884i
\(330\) 0 0
\(331\) 199.480 + 345.509i 0.0331251 + 0.0573743i 0.882113 0.471038i \(-0.156121\pi\)
−0.848988 + 0.528413i \(0.822787\pi\)
\(332\) −1987.77 + 3442.91i −0.328593 + 0.569140i
\(333\) 0 0
\(334\) −1156.26 2002.71i −0.189425 0.328094i
\(335\) −479.628 −0.0782236
\(336\) 0 0
\(337\) −1094.51 −0.176918 −0.0884592 0.996080i \(-0.528194\pi\)
−0.0884592 + 0.996080i \(0.528194\pi\)
\(338\) 4413.64 + 7644.65i 0.710268 + 1.23022i
\(339\) 0 0
\(340\) 162.010 280.609i 0.0258418 0.0447593i
\(341\) 5.50224 + 9.53016i 0.000873792 + 0.00151345i
\(342\) 0 0
\(343\) 6224.47 1268.67i 0.979854 0.199714i
\(344\) −108.560 −0.0170150
\(345\) 0 0
\(346\) −1063.88 + 1842.70i −0.165302 + 0.286312i
\(347\) −1373.78 + 2379.45i −0.212531 + 0.368115i −0.952506 0.304520i \(-0.901504\pi\)
0.739975 + 0.672634i \(0.234837\pi\)
\(348\) 0 0
\(349\) −2780.82 −0.426516 −0.213258 0.976996i \(-0.568407\pi\)
−0.213258 + 0.976996i \(0.568407\pi\)
\(350\) −1634.84 + 109.735i −0.249674 + 0.0167588i
\(351\) 0 0
\(352\) −437.286 757.401i −0.0662142 0.114686i
\(353\) 510.735 884.620i 0.0770076 0.133381i −0.824950 0.565206i \(-0.808797\pi\)
0.901958 + 0.431825i \(0.142130\pi\)
\(354\) 0 0
\(355\) −791.635 1371.15i −0.118354 0.204995i
\(356\) 6366.83 0.947868
\(357\) 0 0
\(358\) 3501.53 0.516931
\(359\) 1956.68 + 3389.06i 0.287659 + 0.498239i 0.973250 0.229747i \(-0.0737898\pi\)
−0.685592 + 0.727986i \(0.740456\pi\)
\(360\) 0 0
\(361\) 1736.27 3007.31i 0.253138 0.438448i
\(362\) −3313.36 5738.91i −0.481067 0.833233i
\(363\) 0 0
\(364\) −2655.51 + 5406.24i −0.382380 + 0.778473i
\(365\) −2395.12 −0.343469
\(366\) 0 0
\(367\) −2359.67 + 4087.06i −0.335623 + 0.581316i −0.983604 0.180340i \(-0.942280\pi\)
0.647981 + 0.761656i \(0.275613\pi\)
\(368\) 2.42517 4.20053i 0.000343535 0.000595020i
\(369\) 0 0
\(370\) 5384.14 0.756508
\(371\) −5325.63 + 10842.3i −0.745265 + 1.51726i
\(372\) 0 0
\(373\) −3950.30 6842.11i −0.548361 0.949789i −0.998387 0.0567733i \(-0.981919\pi\)
0.450026 0.893015i \(-0.351415\pi\)
\(374\) −170.181 + 294.762i −0.0235290 + 0.0407534i
\(375\) 0 0
\(376\) −2170.62 3759.63i −0.297716 0.515659i
\(377\) −3982.19 −0.544014
\(378\) 0 0
\(379\) −6062.83 −0.821706 −0.410853 0.911702i \(-0.634769\pi\)
−0.410853 + 0.911702i \(0.634769\pi\)
\(380\) −1514.08 2622.46i −0.204396 0.354025i
\(381\) 0 0
\(382\) −531.577 + 920.719i −0.0711986 + 0.123320i
\(383\) 1373.25 + 2378.53i 0.183210 + 0.317330i 0.942972 0.332872i \(-0.108018\pi\)
−0.759762 + 0.650202i \(0.774684\pi\)
\(384\) 0 0
\(385\) 6569.95 440.992i 0.869704 0.0583767i
\(386\) 4582.88 0.604307
\(387\) 0 0
\(388\) 723.662 1253.42i 0.0946865 0.164002i
\(389\) 6931.88 12006.4i 0.903497 1.56490i 0.0805753 0.996749i \(-0.474324\pi\)
0.822922 0.568155i \(-0.192342\pi\)
\(390\) 0 0
\(391\) −1.88764 −0.000244148
\(392\) −2719.39 + 366.716i −0.350382 + 0.0472499i
\(393\) 0 0
\(394\) −2967.84 5140.45i −0.379486 0.657289i
\(395\) 7186.76 12447.8i 0.915456 1.58562i
\(396\) 0 0
\(397\) 2267.06 + 3926.67i 0.286601 + 0.496408i 0.972996 0.230821i \(-0.0741412\pi\)
−0.686395 + 0.727229i \(0.740808\pi\)
\(398\) −6275.85 −0.790402
\(399\) 0 0
\(400\) 707.774 0.0884717
\(401\) 3616.09 + 6263.25i 0.450322 + 0.779980i 0.998406 0.0564433i \(-0.0179760\pi\)
−0.548084 + 0.836423i \(0.684643\pi\)
\(402\) 0 0
\(403\) −16.3688 + 28.3515i −0.00202329 + 0.00350444i
\(404\) −1171.05 2028.31i −0.144212 0.249783i
\(405\) 0 0
\(406\) −1010.27 1506.84i −0.123495 0.184195i
\(407\) −5655.68 −0.688800
\(408\) 0 0
\(409\) −2831.73 + 4904.70i −0.342348 + 0.592963i −0.984868 0.173305i \(-0.944555\pi\)
0.642521 + 0.766268i \(0.277889\pi\)
\(410\) 4196.50 7268.55i 0.505488 0.875531i
\(411\) 0 0
\(412\) 6548.46 0.783057
\(413\) −2306.95 + 4696.64i −0.274861 + 0.559580i
\(414\) 0 0
\(415\) 6464.75 + 11197.3i 0.764679 + 1.32446i
\(416\) 1300.89 2253.21i 0.153321 0.265560i
\(417\) 0 0
\(418\) 1590.44 + 2754.73i 0.186103 + 0.322340i
\(419\) −1506.26 −0.175622 −0.0878109 0.996137i \(-0.527987\pi\)
−0.0878109 + 0.996137i \(0.527987\pi\)
\(420\) 0 0
\(421\) −12171.3 −1.40901 −0.704506 0.709698i \(-0.748831\pi\)
−0.704506 + 0.709698i \(0.748831\pi\)
\(422\) 1306.36 + 2262.69i 0.150694 + 0.261009i
\(423\) 0 0
\(424\) 2608.95 4518.83i 0.298825 0.517580i
\(425\) −137.724 238.545i −0.0157190 0.0272262i
\(426\) 0 0
\(427\) 2020.93 + 3014.26i 0.229039 + 0.341617i
\(428\) −5950.96 −0.672081
\(429\) 0 0
\(430\) −176.533 + 305.765i −0.0197981 + 0.0342914i
\(431\) −1010.84 + 1750.82i −0.112971 + 0.195671i −0.916967 0.398964i \(-0.869370\pi\)
0.803996 + 0.594635i \(0.202703\pi\)
\(432\) 0 0
\(433\) 5605.18 0.622096 0.311048 0.950394i \(-0.399320\pi\)
0.311048 + 0.950394i \(0.399320\pi\)
\(434\) −14.8808 + 0.998835i −0.00164585 + 0.000110474i
\(435\) 0 0
\(436\) 2645.04 + 4581.34i 0.290538 + 0.503226i
\(437\) −8.82055 + 15.2776i −0.000965547 + 0.00167238i
\(438\) 0 0
\(439\) 6372.97 + 11038.3i 0.692859 + 1.20007i 0.970897 + 0.239497i \(0.0769825\pi\)
−0.278038 + 0.960570i \(0.589684\pi\)
\(440\) −2844.34 −0.308179
\(441\) 0 0
\(442\) −1012.55 −0.108964
\(443\) 1303.21 + 2257.23i 0.139768 + 0.242086i 0.927409 0.374049i \(-0.122031\pi\)
−0.787640 + 0.616135i \(0.788698\pi\)
\(444\) 0 0
\(445\) 10353.3 17932.5i 1.10291 1.91029i
\(446\) 2155.86 + 3734.06i 0.228886 + 0.396442i
\(447\) 0 0
\(448\) 1182.64 79.3815i 0.124719 0.00837148i
\(449\) −7512.78 −0.789644 −0.394822 0.918758i \(-0.629194\pi\)
−0.394822 + 0.918758i \(0.629194\pi\)
\(450\) 0 0
\(451\) −4408.15 + 7635.13i −0.460247 + 0.797171i
\(452\) 2685.75 4651.85i 0.279484 0.484081i
\(453\) 0 0
\(454\) 10256.9 1.06031
\(455\) 10908.7 + 16270.6i 1.12398 + 1.67644i
\(456\) 0 0
\(457\) −978.068 1694.06i −0.100114 0.173403i 0.811617 0.584189i \(-0.198587\pi\)
−0.911731 + 0.410787i \(0.865254\pi\)
\(458\) 5947.28 10301.0i 0.606764 1.05095i
\(459\) 0 0
\(460\) −7.88732 13.6612i −0.000799452 0.00138469i
\(461\) −4344.87 −0.438961 −0.219480 0.975617i \(-0.570436\pi\)
−0.219480 + 0.975617i \(0.570436\pi\)
\(462\) 0 0
\(463\) 12010.6 1.20557 0.602786 0.797903i \(-0.294057\pi\)
0.602786 + 0.797903i \(0.294057\pi\)
\(464\) 391.824 + 678.658i 0.0392025 + 0.0679007i
\(465\) 0 0
\(466\) −5134.33 + 8892.91i −0.510393 + 0.884026i
\(467\) −2711.13 4695.82i −0.268643 0.465303i 0.699869 0.714271i \(-0.253242\pi\)
−0.968512 + 0.248968i \(0.919908\pi\)
\(468\) 0 0
\(469\) −301.040 + 612.876i −0.0296391 + 0.0603411i
\(470\) −14118.9 −1.38565
\(471\) 0 0
\(472\) 1130.14 1957.46i 0.110210 0.190889i
\(473\) 185.437 321.186i 0.0180262 0.0312223i
\(474\) 0 0
\(475\) −2574.23 −0.248660
\(476\) −256.881 383.144i −0.0247355 0.0368936i
\(477\) 0 0
\(478\) −7241.83 12543.2i −0.692957 1.20024i
\(479\) 1821.01 3154.09i 0.173704 0.300864i −0.766008 0.642831i \(-0.777760\pi\)
0.939712 + 0.341967i \(0.111093\pi\)
\(480\) 0 0
\(481\) −8412.63 14571.1i −0.797469 1.38126i
\(482\) 13328.1 1.25950
\(483\) 0 0
\(484\) −2336.21 −0.219403
\(485\) −2353.54 4076.45i −0.220348 0.381654i
\(486\) 0 0
\(487\) −2332.62 + 4040.21i −0.217045 + 0.375933i −0.953903 0.300114i \(-0.902975\pi\)
0.736858 + 0.676047i \(0.236308\pi\)
\(488\) −783.798 1357.58i −0.0727067 0.125932i
\(489\) 0 0
\(490\) −3389.21 + 8255.60i −0.312467 + 0.761123i
\(491\) 8983.95 0.825744 0.412872 0.910789i \(-0.364526\pi\)
0.412872 + 0.910789i \(0.364526\pi\)
\(492\) 0 0
\(493\) 152.488 264.117i 0.0139305 0.0241282i
\(494\) −4731.45 + 8195.11i −0.430927 + 0.746388i
\(495\) 0 0
\(496\) 6.44235 0.000583206
\(497\) −2248.95 + 150.955i −0.202976 + 0.0136243i
\(498\) 0 0
\(499\) −91.1916 157.948i −0.00818095 0.0141698i 0.861906 0.507068i \(-0.169271\pi\)
−0.870087 + 0.492898i \(0.835937\pi\)
\(500\) −2101.33 + 3639.61i −0.187949 + 0.325537i
\(501\) 0 0
\(502\) 6024.90 + 10435.4i 0.535666 + 0.927801i
\(503\) −16507.0 −1.46325 −0.731623 0.681709i \(-0.761237\pi\)
−0.731623 + 0.681709i \(0.761237\pi\)
\(504\) 0 0
\(505\) −7617.11 −0.671202
\(506\) 8.28511 + 14.3502i 0.000727901 + 0.00126076i
\(507\) 0 0
\(508\) −1159.79 + 2008.81i −0.101294 + 0.175446i
\(509\) −8221.25 14239.6i −0.715914 1.24000i −0.962606 0.270906i \(-0.912677\pi\)
0.246692 0.969094i \(-0.420656\pi\)
\(510\) 0 0
\(511\) −1503.30 + 3060.51i −0.130141 + 0.264949i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 3873.17 6708.53i 0.332370 0.575682i
\(515\) 10648.7 18444.0i 0.911139 1.57814i
\(516\) 0 0
\(517\) 14831.0 1.26163
\(518\) 3379.37 6879.93i 0.286643 0.583565i
\(519\) 0 0
\(520\) −4230.85 7328.05i −0.356798 0.617993i
\(521\) 8460.51 14654.0i 0.711443 1.23226i −0.252873 0.967500i \(-0.581375\pi\)
0.964316 0.264756i \(-0.0852913\pi\)
\(522\) 0 0
\(523\) 401.147 + 694.806i 0.0335390 + 0.0580913i 0.882308 0.470673i \(-0.155989\pi\)
−0.848769 + 0.528764i \(0.822656\pi\)
\(524\) 11381.4 0.948853
\(525\) 0 0
\(526\) −9667.81 −0.801400
\(527\) −1.25360 2.17130i −0.000103620 0.000179475i
\(528\) 0 0
\(529\) 6083.45 10536.9i 0.499996 0.866019i
\(530\) −8485.00 14696.5i −0.695406 1.20448i
\(531\) 0 0
\(532\) −4301.34 + 288.717i −0.350539 + 0.0235291i
\(533\) −26227.8 −2.13143
\(534\) 0 0
\(535\) −9677.06 + 16761.2i −0.782011 + 1.35448i
\(536\) 147.475 255.434i 0.0118842 0.0205841i
\(537\) 0 0
\(538\) −4107.26 −0.329138
\(539\) 3560.14 8671.97i 0.284501 0.693002i
\(540\) 0 0
\(541\) −3844.50 6658.87i −0.305523 0.529181i 0.671855 0.740683i \(-0.265498\pi\)
−0.977378 + 0.211502i \(0.932165\pi\)
\(542\) 164.407 284.761i 0.0130293 0.0225674i
\(543\) 0 0
\(544\) 99.6288 + 172.562i 0.00785212 + 0.0136003i
\(545\) 17204.8 1.35224
\(546\) 0 0
\(547\) −22735.9 −1.77718 −0.888590 0.458702i \(-0.848314\pi\)
−0.888590 + 0.458702i \(0.848314\pi\)
\(548\) 5056.01 + 8757.26i 0.394128 + 0.682649i
\(549\) 0 0
\(550\) −1208.98 + 2094.02i −0.0937294 + 0.162344i
\(551\) −1425.09 2468.33i −0.110183 0.190843i
\(552\) 0 0
\(553\) −11395.2 16996.3i −0.876264 1.30697i
\(554\) −5817.67 −0.446154
\(555\) 0 0
\(556\) −2933.73 + 5081.37i −0.223773 + 0.387586i
\(557\) 2610.78 4522.01i 0.198604 0.343992i −0.749472 0.662036i \(-0.769693\pi\)
0.948076 + 0.318044i \(0.103026\pi\)
\(558\) 0 0
\(559\) 1103.32 0.0834804
\(560\) 1699.54 3460.03i 0.128248 0.261095i
\(561\) 0 0
\(562\) −4676.92 8100.66i −0.351039 0.608017i
\(563\) 10098.1 17490.5i 0.755926 1.30930i −0.188987 0.981980i \(-0.560520\pi\)
0.944913 0.327322i \(-0.106146\pi\)
\(564\) 0 0
\(565\) −8734.76 15129.1i −0.650397 1.12652i
\(566\) −3373.08 −0.250497
\(567\) 0 0
\(568\) 973.641 0.0719244
\(569\) −12415.9 21504.9i −0.914763 1.58442i −0.807248 0.590212i \(-0.799044\pi\)
−0.107515 0.994203i \(-0.534289\pi\)
\(570\) 0 0
\(571\) 3951.24 6843.75i 0.289587 0.501580i −0.684124 0.729366i \(-0.739815\pi\)
0.973711 + 0.227786i \(0.0731486\pi\)
\(572\) 4444.24 + 7697.64i 0.324865 + 0.562683i
\(573\) 0 0
\(574\) −6653.91 9924.46i −0.483848 0.721671i
\(575\) −13.4100 −0.000972581
\(576\) 0 0
\(577\) 6371.20 11035.2i 0.459682 0.796193i −0.539262 0.842138i \(-0.681297\pi\)
0.998944 + 0.0459452i \(0.0146300\pi\)
\(578\) −4874.23 + 8442.41i −0.350763 + 0.607540i
\(579\) 0 0
\(580\) 2548.63 0.182459
\(581\) 18365.6 1232.75i 1.31142 0.0880259i
\(582\) 0 0
\(583\) 8912.94 + 15437.7i 0.633167 + 1.09668i
\(584\) 736.445 1275.56i 0.0521820 0.0903819i
\(585\) 0 0
\(586\) 6140.31 + 10635.3i 0.432856 + 0.749729i
\(587\) 3400.10 0.239075 0.119537 0.992830i \(-0.461859\pi\)
0.119537 + 0.992830i \(0.461859\pi\)
\(588\) 0 0
\(589\) −23.4313 −0.00163917
\(590\) −3675.53 6366.20i −0.256473 0.444224i
\(591\) 0 0
\(592\) −1655.50 + 2867.41i −0.114934 + 0.199071i
\(593\) −1714.44 2969.49i −0.118724 0.205636i 0.800538 0.599282i \(-0.204547\pi\)
−0.919262 + 0.393645i \(0.871214\pi\)
\(594\) 0 0
\(595\) −1496.86 + 100.473i −0.103135 + 0.00692270i
\(596\) 8832.84 0.607059
\(597\) 0 0
\(598\) −24.6476 + 42.6909i −0.00168548 + 0.00291933i
\(599\) 4138.34 7167.82i 0.282284 0.488930i −0.689663 0.724130i \(-0.742241\pi\)
0.971947 + 0.235200i \(0.0755746\pi\)
\(600\) 0 0
\(601\) −17691.1 −1.20072 −0.600362 0.799728i \(-0.704977\pi\)
−0.600362 + 0.799728i \(0.704977\pi\)
\(602\) 279.909 + 417.491i 0.0189506 + 0.0282652i
\(603\) 0 0
\(604\) −4899.87 8486.82i −0.330087 0.571728i
\(605\) −3798.98 + 6580.04i −0.255290 + 0.442176i
\(606\) 0 0
\(607\) 1300.25 + 2252.09i 0.0869445 + 0.150592i 0.906218 0.422810i \(-0.138956\pi\)
−0.819274 + 0.573403i \(0.805623\pi\)
\(608\) 1862.18 0.124213
\(609\) 0 0
\(610\) −5098.24 −0.338396
\(611\) 22060.5 + 38210.0i 1.46068 + 2.52997i
\(612\) 0 0
\(613\) 8333.19 14433.5i 0.549061 0.951001i −0.449278 0.893392i \(-0.648319\pi\)
0.998339 0.0576096i \(-0.0183479\pi\)
\(614\) −7548.41 13074.2i −0.496138 0.859337i
\(615\) 0 0
\(616\) −1785.26 + 3634.54i −0.116770 + 0.237727i
\(617\) −7263.76 −0.473951 −0.236976 0.971516i \(-0.576156\pi\)
−0.236976 + 0.971516i \(0.576156\pi\)
\(618\) 0 0
\(619\) −1890.69 + 3274.77i −0.122768 + 0.212640i −0.920858 0.389898i \(-0.872510\pi\)
0.798091 + 0.602538i \(0.205844\pi\)
\(620\) 10.4761 18.1452i 0.000678599 0.00117537i
\(621\) 0 0
\(622\) 3400.32 0.219197
\(623\) −16416.1 24485.0i −1.05569 1.57459i
\(624\) 0 0
\(625\) 9598.84 + 16625.7i 0.614325 + 1.06404i
\(626\) −2935.23 + 5083.96i −0.187404 + 0.324594i
\(627\) 0 0
\(628\) 6262.73 + 10847.4i 0.397946 + 0.689263i
\(629\) 1288.56 0.0816825
\(630\) 0 0
\(631\) 22105.4 1.39462 0.697309 0.716771i \(-0.254381\pi\)
0.697309 + 0.716771i \(0.254381\pi\)
\(632\) 4419.54 + 7654.86i 0.278164 + 0.481794i
\(633\) 0 0
\(634\) −3634.68 + 6295.45i −0.227684 + 0.394360i
\(635\) 3771.94 + 6533.19i 0.235724 + 0.408286i
\(636\) 0 0
\(637\) 27637.7 3727.02i 1.71907 0.231821i
\(638\) −2677.17 −0.166129
\(639\) 0 0
\(640\) −832.580 + 1442.07i −0.0514229 + 0.0890670i
\(641\) 1414.80 2450.50i 0.0871779 0.150997i −0.819139 0.573595i \(-0.805548\pi\)
0.906317 + 0.422598i \(0.138882\pi\)
\(642\) 0 0
\(643\) −3281.09 −0.201234 −0.100617 0.994925i \(-0.532082\pi\)
−0.100617 + 0.994925i \(0.532082\pi\)
\(644\) −22.4070 + 1.50402i −0.00137106 + 9.20288e-5i
\(645\) 0 0
\(646\) −362.358 627.622i −0.0220693 0.0382252i
\(647\) 10054.5 17414.8i 0.610945 1.05819i −0.380137 0.924930i \(-0.624123\pi\)
0.991082 0.133257i \(-0.0425436\pi\)
\(648\) 0 0
\(649\) 3860.90 + 6687.27i 0.233519 + 0.404466i
\(650\) −7193.27 −0.434067
\(651\) 0 0
\(652\) −14481.7 −0.869860
\(653\) −4343.67 7523.46i −0.260308 0.450866i 0.706016 0.708196i \(-0.250491\pi\)
−0.966324 + 0.257330i \(0.917157\pi\)
\(654\) 0 0
\(655\) 18507.7 32056.3i 1.10405 1.91228i
\(656\) 2580.66 + 4469.83i 0.153594 + 0.266033i
\(657\) 0 0
\(658\) −8861.76 + 18041.3i −0.525026 + 1.06888i
\(659\) −24386.8 −1.44154 −0.720771 0.693174i \(-0.756212\pi\)
−0.720771 + 0.693174i \(0.756212\pi\)
\(660\) 0 0
\(661\) −7767.45 + 13453.6i −0.457063 + 0.791657i −0.998804 0.0488887i \(-0.984432\pi\)
0.541741 + 0.840545i \(0.317765\pi\)
\(662\) −398.960 + 691.018i −0.0234230 + 0.0405698i
\(663\) 0 0
\(664\) −7951.06 −0.464700
\(665\) −6181.36 + 12584.4i −0.360456 + 0.733838i
\(666\) 0 0
\(667\) −7.42375 12.8583i −0.000430958 0.000746441i
\(668\) 2312.53 4005.42i 0.133944 0.231997i
\(669\) 0 0
\(670\) −479.628 830.741i −0.0276562 0.0479020i
\(671\) 5355.37 0.308110
\(672\) 0 0
\(673\) 14978.7 0.857930 0.428965 0.903321i \(-0.358878\pi\)
0.428965 + 0.903321i \(0.358878\pi\)
\(674\) −1094.51 1895.74i −0.0625501 0.108340i
\(675\) 0 0
\(676\) −8827.28 + 15289.3i −0.502235 + 0.869896i
\(677\) −1096.32 1898.87i −0.0622376 0.107799i 0.833228 0.552930i \(-0.186490\pi\)
−0.895465 + 0.445131i \(0.853157\pi\)
\(678\) 0 0
\(679\) −6686.16 + 448.792i −0.377896 + 0.0253653i
\(680\) 648.039 0.0365458
\(681\) 0 0
\(682\) −11.0045 + 19.0603i −0.000617864 + 0.00107017i
\(683\) −9228.24 + 15983.8i −0.516997 + 0.895465i 0.482808 + 0.875726i \(0.339617\pi\)
−0.999805 + 0.0197389i \(0.993716\pi\)
\(684\) 0 0
\(685\) 32887.0 1.83437
\(686\) 8421.88 + 9512.43i 0.468730 + 0.529426i
\(687\) 0 0
\(688\) −108.560 188.032i −0.00601572 0.0104195i
\(689\) −26515.4 + 45925.9i −1.46612 + 2.53939i
\(690\) 0 0
\(691\) 15365.7 + 26614.2i 0.845933 + 1.46520i 0.884809 + 0.465955i \(0.154289\pi\)
−0.0388756 + 0.999244i \(0.512378\pi\)
\(692\) −4255.53 −0.233773
\(693\) 0 0
\(694\) −5495.11 −0.300564
\(695\) 9541.27 + 16526.0i 0.520749 + 0.901964i
\(696\) 0 0
\(697\) 1004.33 1739.55i 0.0545791 0.0945338i
\(698\) −2780.82 4816.53i −0.150796 0.261187i
\(699\) 0 0
\(700\) −1824.91 2721.89i −0.0985357 0.146968i
\(701\) 10749.1 0.579153 0.289577 0.957155i \(-0.406486\pi\)
0.289577 + 0.957155i \(0.406486\pi\)
\(702\) 0 0
\(703\) 6021.19 10429.0i 0.323035 0.559513i
\(704\) 874.571 1514.80i 0.0468205 0.0810955i
\(705\) 0 0
\(706\) 2042.94 0.108905
\(707\) −4780.90 + 9733.25i −0.254320 + 0.517760i
\(708\) 0 0
\(709\) 16684.6 + 28898.6i 0.883785 + 1.53076i 0.847100 + 0.531433i \(0.178346\pi\)
0.0366848 + 0.999327i \(0.488320\pi\)
\(710\) 1583.27 2742.30i 0.0836888 0.144953i
\(711\) 0 0
\(712\) 6366.83 + 11027.7i 0.335122 + 0.580448i
\(713\) −0.122061 −6.41125e−6
\(714\) 0 0
\(715\) 28907.7 1.51201
\(716\) 3501.53 + 6064.82i 0.182763 + 0.316554i
\(717\) 0 0
\(718\) −3913.35 + 6778.13i −0.203405 + 0.352308i
\(719\) 3355.34 + 5811.63i 0.174038 + 0.301442i 0.939828 0.341648i \(-0.110985\pi\)
−0.765790 + 0.643091i \(0.777652\pi\)
\(720\) 0 0
\(721\) −16884.4 25183.5i −0.872132 1.30081i
\(722\) 6945.10 0.357991
\(723\) 0 0
\(724\) 6626.72 11477.8i 0.340166 0.589185i
\(725\) 1083.29 1876.31i 0.0554930 0.0961167i
\(726\) 0 0
\(727\) −35427.5 −1.80733 −0.903667 0.428236i \(-0.859135\pi\)
−0.903667 + 0.428236i \(0.859135\pi\)
\(728\) −12019.4 + 806.773i −0.611907 + 0.0410728i
\(729\) 0 0
\(730\) −2395.12 4148.46i −0.121435 0.210331i
\(731\) −42.2489 + 73.1773i −0.00213766 + 0.00370254i
\(732\) 0 0
\(733\) −7700.32 13337.4i −0.388019 0.672069i 0.604164 0.796860i \(-0.293507\pi\)
−0.992183 + 0.124791i \(0.960174\pi\)
\(734\) −9438.67 −0.474642
\(735\) 0 0
\(736\) 9.70070 0.000485832
\(737\) 503.818 + 872.639i 0.0251810 + 0.0436147i
\(738\) 0 0
\(739\) 42.2335 73.1506i 0.00210228 0.00364126i −0.864972 0.501820i \(-0.832664\pi\)
0.867075 + 0.498178i \(0.165997\pi\)
\(740\) 5384.14 + 9325.60i 0.267466 + 0.463265i
\(741\) 0 0
\(742\) −24105.0 + 1617.99i −1.19262 + 0.0800515i
\(743\) 23071.8 1.13919 0.569597 0.821924i \(-0.307099\pi\)
0.569597 + 0.821924i \(0.307099\pi\)
\(744\) 0 0
\(745\) 14363.4 24878.1i 0.706353 1.22344i
\(746\) 7900.59 13684.2i 0.387750 0.671602i
\(747\) 0 0
\(748\) −680.723 −0.0332750
\(749\) 15343.8 + 22885.7i 0.748532 + 1.11645i
\(750\) 0 0
\(751\) 16010.6 + 27731.1i 0.777940 + 1.34743i 0.933127 + 0.359547i \(0.117069\pi\)
−0.155186 + 0.987885i \(0.549598\pi\)
\(752\) 4341.24 7519.25i 0.210517 0.364626i
\(753\) 0 0
\(754\) −3982.19 6897.36i −0.192338 0.333139i
\(755\) −31871.4 −1.53631
\(756\) 0 0
\(757\) −26055.9 −1.25101 −0.625507 0.780218i \(-0.715108\pi\)
−0.625507 + 0.780218i \(0.715108\pi\)
\(758\) −6062.83 10501.1i −0.290517 0.503190i
\(759\) 0 0
\(760\) 3028.16 5244.92i 0.144530 0.250333i
\(761\) 2459.81 + 4260.51i 0.117172 + 0.202948i 0.918646 0.395082i \(-0.129284\pi\)
−0.801474 + 0.598030i \(0.795950\pi\)
\(762\) 0 0
\(763\) 10798.6 21984.5i 0.512367 1.04311i
\(764\) −2126.31 −0.100690
\(765\) 0 0
\(766\) −2746.49 + 4757.06i −0.129549 + 0.224386i
\(767\) −11485.9 + 19894.2i −0.540719 + 0.936553i
\(768\) 0 0
\(769\) −19360.7 −0.907887 −0.453943 0.891031i \(-0.649983\pi\)
−0.453943 + 0.891031i \(0.649983\pi\)
\(770\) 7333.78 + 10938.5i 0.343235 + 0.511943i
\(771\) 0 0
\(772\) 4582.88 + 7937.78i 0.213655 + 0.370061i
\(773\) 12460.2 21581.7i 0.579769 1.00419i −0.415737 0.909485i \(-0.636476\pi\)
0.995505 0.0947040i \(-0.0301905\pi\)
\(774\) 0 0
\(775\) −8.90572 15.4252i −0.000412778 0.000714952i
\(776\) 2894.65 0.133907
\(777\) 0 0
\(778\) 27727.5 1.27774
\(779\) −9386.06 16257.1i −0.431695 0.747717i
\(780\) 0 0
\(781\) −1663.12 + 2880.61i −0.0761987 + 0.131980i
\(782\) −1.88764 3.26948i −8.63193e−5 0.000149509i
\(783\) 0 0
\(784\) −3354.56 4343.40i