Properties

Label 378.4.g.c.109.1
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 109.1
Root \(0.445324 - 0.771324i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.c.163.1

$q$-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 \(-0.969022\pi\)
0.413485 0.910511i \(-0.364311\pi\)
\(6\) 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 −0.990262 0.139218i \(-0.955541\pi\)
0.615698 + 0.787983i \(0.288874\pi\)
\(12\) 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 −0.842962 0.537974i \(-0.819190\pi\)
0.887380 + 0.461039i \(0.152523\pi\)
\(18\) 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 0.865338 0.501190i \(-0.167104\pi\)
−0.866712 + 0.498809i \(0.833771\pi\)
\(24\) 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 \(-0.449879\pi\)
0.156810 + 0.987629i \(0.449879\pi\)
\(30\) 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 \(-0.289407\pi\)
0.614377 + 0.789013i \(0.289407\pi\)
\(42\) 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 \(-0.848005\pi\)
0.0460745 0.998938i \(-0.485329\pi\)
\(48\) 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 \(-0.512812\pi\)
0.885443 0.464747i \(-0.153855\pi\)
\(54\) 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 −0.667015 0.745045i \(-0.732428\pi\)
0.978735 + 0.205129i \(0.0657615\pi\)
\(60\) 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 \(-0.467567\pi\)
0.101716 + 0.994813i \(0.467567\pi\)
\(72\) 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 \(-0.728253\pi\)
−0.657186 + 0.753729i \(0.728253\pi\)
\(84\) 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 \(0.230100\pi\)
0.197965 + 0.980209i \(0.436567\pi\)
\(90\) 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 −0.685010 0.728534i \(-0.740202\pi\)
0.973434 + 0.228969i \(0.0735353\pi\)
\(102\) 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 \(-0.932067\pi\)
0.305232 0.952278i \(-0.401266\pi\)
\(108\) 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 \(-0.311197\pi\)
0.558968 + 0.829189i \(0.311197\pi\)
\(114\) 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 \(0.231088\pi\)
0.201008 + 0.979590i \(0.435578\pi\)
\(132\) 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 \(0.455682\pi\)
−0.927035 + 0.374975i \(0.877651\pi\)
\(138\) 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 \(0.0409842\pi\)
−0.384663 + 0.923057i \(0.625683\pi\)
\(150\) 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 \(-0.413674\pi\)
0.267887 + 0.963450i \(0.413674\pi\)
\(168\) 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 0.725142 0.688599i \(-0.241774\pi\)
−0.958915 + 0.283692i \(0.908441\pi\)
\(174\) 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 −0.988860 0.148846i \(-0.952444\pi\)
0.623335 + 0.781955i \(0.285777\pi\)
\(180\) 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 0.811279 0.584659i \(-0.198772\pi\)
−0.911969 + 0.410259i \(0.865438\pi\)
\(192\) 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 \(-0.319680\pi\)
0.536674 + 0.843789i \(0.319680\pi\)
\(198\) 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 \(0.436493\pi\)
−0.947942 + 0.318444i \(0.896840\pi\)
\(228\) 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 \(-0.909980\pi\)
0.238471 0.971150i \(-0.423354\pi\)
\(234\) 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 \(-0.0637858\pi\)
0.979989 + 0.199050i \(0.0637858\pi\)
\(240\) 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 \(-0.773602\pi\)
−0.757546 + 0.652781i \(0.773602\pi\)
\(252\) 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 0.999413 0.0342531i \(-0.0109052\pi\)
−0.529371 + 0.848391i \(0.677572\pi\)
\(258\) 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 \(-0.641563\pi\)
0.996892 0.0787847i \(-0.0251040\pi\)
\(264\) 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 −0.725876 0.687825i \(-0.758566\pi\)
0.958612 + 0.284715i \(0.0918989\pi\)
\(270\) 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 \(-0.334639\pi\)
0.496444 + 0.868069i \(0.334639\pi\)
\(282\) 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 \(-0.709696\pi\)
−0.612151 + 0.790741i \(0.709696\pi\)
\(294\) 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 −0.933057 0.359728i \(-0.882870\pi\)
0.778062 + 0.628188i \(0.216203\pi\)
\(312\) 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 0.658906 0.752225i \(-0.271020\pi\)
−0.980899 + 0.194517i \(0.937686\pi\)
\(318\) 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 −0.739975 0.672634i \(-0.765163\pi\)
0.952506 + 0.304520i \(0.0984960\pi\)
\(348\) 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 −0.901958 0.431825i \(-0.857870\pi\)
0.824950 + 0.565206i \(0.191203\pi\)
\(354\) 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 0.685592 0.727986i \(-0.259544\pi\)
−0.973250 + 0.229747i \(0.926210\pi\)
\(360\) 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 0.759762 0.650202i \(-0.225316\pi\)
−0.942972 + 0.332872i \(0.891982\pi\)
\(384\) 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 \(0.525676\pi\)
−0.822922 + 0.568155i \(0.807658\pi\)
\(390\) 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 0.548084 0.836423i \(-0.315357\pi\)
−0.998406 + 0.0564433i \(0.982024\pi\)
\(402\) 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 \(-0.472013\pi\)
0.0878109 + 0.996137i \(0.472013\pi\)
\(420\) 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 −0.803996 0.594635i \(-0.797297\pi\)
0.916967 + 0.398964i \(0.130630\pi\)
\(432\) 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 0.787640 0.616135i \(-0.211302\pi\)
−0.927409 + 0.374049i \(0.877969\pi\)
\(444\) 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 \(-0.370806\pi\)
0.394822 + 0.918758i \(0.370806\pi\)
\(450\) 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 \(-0.429564\pi\)
0.219480 + 0.975617i \(0.429564\pi\)
\(462\) 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 0.968512 0.248968i \(-0.0800915\pi\)
−0.699869 + 0.714271i \(0.746758\pi\)
\(468\) 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 −0.939712 0.341967i \(-0.888907\pi\)
0.766008 + 0.642831i \(0.222240\pi\)
\(480\) 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 \(-0.635474\pi\)
−0.412872 + 0.910789i \(0.635474\pi\)
\(492\) 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 \(-0.238763\pi\)
0.731623 + 0.681709i \(0.238763\pi\)
\(504\) 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 \(0.0873231\pi\)
−0.246692 + 0.969094i \(0.579344\pi\)
\(510\) 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 \(0.418625\pi\)
−0.964316 + 0.264756i \(0.914709\pi\)
\(522\) 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 −0.948076 0.318044i \(-0.896974\pi\)
0.749472 + 0.662036i \(0.230307\pi\)
\(558\) 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 \(0.439480\pi\)
−0.944913 + 0.327322i \(0.893854\pi\)
\(564\) 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 \(0.200956\pi\)
0.107515 + 0.994203i \(0.465711\pi\)
\(570\) 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 \(-0.538141\pi\)
−0.119537 + 0.992830i \(0.538141\pi\)
\(588\) 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 0.919262 0.393645i \(-0.128786\pi\)
−0.800538 + 0.599282i \(0.795453\pi\)
\(594\) 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 −0.971947 0.235200i \(-0.924425\pi\)
0.689663 + 0.724130i \(0.257759\pi\)
\(600\) 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 \(-0.423844\pi\)
0.236976 + 0.971516i \(0.423844\pi\)
\(618\) 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 −0.906317 0.422598i \(-0.861118\pi\)
0.819139 + 0.573595i \(0.194452\pi\)
\(642\) 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 \(0.375877\pi\)
−0.991082 + 0.133257i \(0.957456\pi\)
\(648\) 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 0.966324 0.257330i \(-0.0828427\pi\)
−0.706016 + 0.708196i \(0.749509\pi\)
\(654\) 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 \(-0.243788\pi\)
0.720771 + 0.693174i \(0.243788\pi\)
\(660\) 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 0.895465 0.445131i \(-0.146843\pi\)
−0.833228 + 0.552930i \(0.813510\pi\)
\(678\) 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 \(-0.660383\pi\)
0.999805 0.0197389i \(-0.00628351\pi\)
\(684\) 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 \(-0.593514\pi\)
−0.289577 + 0.957155i \(0.593514\pi\)
\(702\) 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 0.765790 0.643091i \(-0.222348\pi\)
−0.939828 + 0.341648i \(0.889015\pi\)
\(720\) 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 \(-0.692901\pi\)
−0.569597 + 0.821924i \(0.692901\pi\)
\(744\) 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 0.801474 0.598030i \(-0.204050\pi\)
−0.918646 + 0.395082i \(0.870716\pi\)
\(762\) 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 \(0.363524\pi\)
−0.995505 + 0.0947040i \(0.969810\pi\)
\(774\) 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 −0.152813