Properties

Label 378.4.g.f.163.1
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 163.1
Root \(-0.338925 + 0.587036i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.f.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-8.05411 + 13.9501i) q^{5} +(6.77345 + 17.2372i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-8.05411 + 13.9501i) q^{5} +(6.77345 + 17.2372i) q^{7} -8.00000 q^{8} +(16.1082 + 27.9003i) q^{10} +(-6.04111 - 10.4635i) q^{11} -39.7518 q^{13} +(36.6291 + 5.50523i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-62.7914 - 108.758i) q^{17} +(62.5108 - 108.272i) q^{19} +64.4329 q^{20} -24.1645 q^{22} +(24.1212 - 41.7792i) q^{23} +(-67.2373 - 116.458i) q^{25} +(-39.7518 + 68.8521i) q^{26} +(46.1645 - 57.9383i) q^{28} -93.0461 q^{29} +(-11.3809 - 19.7123i) q^{31} +(16.0000 + 27.7128i) q^{32} -251.166 q^{34} +(-295.015 - 44.3397i) q^{35} +(200.361 - 347.035i) q^{37} +(-125.022 - 216.544i) q^{38} +(64.4329 - 111.601i) q^{40} -354.070 q^{41} +225.918 q^{43} +(-24.1645 + 41.8541i) q^{44} +(-48.2424 - 83.5583i) q^{46} +(-124.107 + 214.960i) q^{47} +(-251.241 + 233.510i) q^{49} -268.949 q^{50} +(79.5036 + 137.704i) q^{52} +(-167.460 - 290.050i) q^{53} +194.623 q^{55} +(-54.1876 - 137.897i) q^{56} +(-93.0461 + 161.161i) q^{58} +(91.4364 + 158.373i) q^{59} +(-304.912 + 528.123i) q^{61} -45.5237 q^{62} +64.0000 q^{64} +(320.165 - 554.542i) q^{65} +(-59.1898 - 102.520i) q^{67} +(-251.166 + 435.032i) q^{68} +(-371.814 + 466.641i) q^{70} -81.4905 q^{71} +(489.415 + 847.692i) q^{73} +(-400.721 - 694.069i) q^{74} -500.086 q^{76} +(139.442 - 175.006i) q^{77} +(346.714 - 600.527i) q^{79} +(-128.866 - 223.202i) q^{80} +(-354.070 + 613.268i) q^{82} -1409.05 q^{83} +2022.92 q^{85} +(225.918 - 391.301i) q^{86} +(48.3289 + 83.7081i) q^{88} +(605.706 - 1049.11i) q^{89} +(-269.256 - 685.209i) q^{91} -192.970 q^{92} +(248.215 + 429.921i) q^{94} +(1006.94 + 1744.07i) q^{95} -1336.50 q^{97} +(153.211 + 668.672i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10}) \) 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
\(5\) −8.05411 + 13.9501i −0.720381 + 1.24774i 0.240466 + 0.970658i \(0.422700\pi\)
−0.960847 + 0.277080i \(0.910633\pi\)
\(6\) 0 0
\(7\) 6.77345 + 17.2372i 0.365732 + 0.930720i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 16.1082 + 27.9003i 0.509387 + 0.882283i
\(11\) −6.04111 10.4635i −0.165588 0.286806i 0.771276 0.636501i \(-0.219619\pi\)
−0.936864 + 0.349694i \(0.886285\pi\)
\(12\) 0 0
\(13\) −39.7518 −0.848089 −0.424045 0.905641i \(-0.639390\pi\)
−0.424045 + 0.905641i \(0.639390\pi\)
\(14\) 36.6291 + 5.50523i 0.699253 + 0.105095i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −62.7914 108.758i −0.895833 1.55163i −0.832770 0.553619i \(-0.813246\pi\)
−0.0630630 0.998010i \(-0.520087\pi\)
\(18\) 0 0
\(19\) 62.5108 108.272i 0.754787 1.30733i −0.190693 0.981650i \(-0.561073\pi\)
0.945480 0.325680i \(-0.105593\pi\)
\(20\) 64.4329 0.720381
\(21\) 0 0
\(22\) −24.1645 −0.234176
\(23\) 24.1212 41.7792i 0.218679 0.378763i −0.735725 0.677280i \(-0.763159\pi\)
0.954404 + 0.298517i \(0.0964919\pi\)
\(24\) 0 0
\(25\) −67.2373 116.458i −0.537899 0.931668i
\(26\) −39.7518 + 68.8521i −0.299845 + 0.519346i
\(27\) 0 0
\(28\) 46.1645 57.9383i 0.311581 0.391047i
\(29\) −93.0461 −0.595801 −0.297900 0.954597i \(-0.596286\pi\)
−0.297900 + 0.954597i \(0.596286\pi\)
\(30\) 0 0
\(31\) −11.3809 19.7123i −0.0659379 0.114208i 0.831172 0.556016i \(-0.187671\pi\)
−0.897110 + 0.441808i \(0.854337\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −251.166 −1.26690
\(35\) −295.015 44.3397i −1.42476 0.214137i
\(36\) 0 0
\(37\) 200.361 347.035i 0.890245 1.54195i 0.0506642 0.998716i \(-0.483866\pi\)
0.839581 0.543234i \(-0.182800\pi\)
\(38\) −125.022 216.544i −0.533715 0.924422i
\(39\) 0 0
\(40\) 64.4329 111.601i 0.254693 0.441142i
\(41\) −354.070 −1.34870 −0.674348 0.738414i \(-0.735575\pi\)
−0.674348 + 0.738414i \(0.735575\pi\)
\(42\) 0 0
\(43\) 225.918 0.801212 0.400606 0.916250i \(-0.368800\pi\)
0.400606 + 0.916250i \(0.368800\pi\)
\(44\) −24.1645 + 41.8541i −0.0827938 + 0.143403i
\(45\) 0 0
\(46\) −48.2424 83.5583i −0.154630 0.267826i
\(47\) −124.107 + 214.960i −0.385169 + 0.667132i −0.991793 0.127857i \(-0.959190\pi\)
0.606624 + 0.794989i \(0.292523\pi\)
\(48\) 0 0
\(49\) −251.241 + 233.510i −0.732481 + 0.680788i
\(50\) −268.949 −0.760704
\(51\) 0 0
\(52\) 79.5036 + 137.704i 0.212022 + 0.367233i
\(53\) −167.460 290.050i −0.434008 0.751724i 0.563206 0.826316i \(-0.309568\pi\)
−0.997214 + 0.0745926i \(0.976234\pi\)
\(54\) 0 0
\(55\) 194.623 0.477145
\(56\) −54.1876 137.897i −0.129306 0.329059i
\(57\) 0 0
\(58\) −93.0461 + 161.161i −0.210647 + 0.364852i
\(59\) 91.4364 + 158.373i 0.201763 + 0.349464i 0.949097 0.314985i \(-0.102000\pi\)
−0.747334 + 0.664449i \(0.768666\pi\)
\(60\) 0 0
\(61\) −304.912 + 528.123i −0.639999 + 1.10851i 0.345433 + 0.938443i \(0.387732\pi\)
−0.985432 + 0.170068i \(0.945601\pi\)
\(62\) −45.5237 −0.0932502
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 320.165 554.542i 0.610948 1.05819i
\(66\) 0 0
\(67\) −59.1898 102.520i −0.107928 0.186937i 0.807003 0.590548i \(-0.201088\pi\)
−0.914931 + 0.403611i \(0.867755\pi\)
\(68\) −251.166 + 435.032i −0.447917 + 0.775814i
\(69\) 0 0
\(70\) −371.814 + 466.641i −0.634860 + 0.796775i
\(71\) −81.4905 −0.136213 −0.0681066 0.997678i \(-0.521696\pi\)
−0.0681066 + 0.997678i \(0.521696\pi\)
\(72\) 0 0
\(73\) 489.415 + 847.692i 0.784681 + 1.35911i 0.929189 + 0.369604i \(0.120507\pi\)
−0.144508 + 0.989504i \(0.546160\pi\)
\(74\) −400.721 694.069i −0.629498 1.09032i
\(75\) 0 0
\(76\) −500.086 −0.754787
\(77\) 139.442 175.006i 0.206376 0.259010i
\(78\) 0 0
\(79\) 346.714 600.527i 0.493777 0.855247i −0.506197 0.862418i \(-0.668949\pi\)
0.999974 + 0.00717076i \(0.00228254\pi\)
\(80\) −128.866 223.202i −0.180095 0.311934i
\(81\) 0 0
\(82\) −354.070 + 613.268i −0.476836 + 0.825904i
\(83\) −1409.05 −1.86341 −0.931707 0.363212i \(-0.881680\pi\)
−0.931707 + 0.363212i \(0.881680\pi\)
\(84\) 0 0
\(85\) 2022.92 2.58137
\(86\) 225.918 391.301i 0.283271 0.490640i
\(87\) 0 0
\(88\) 48.3289 + 83.7081i 0.0585441 + 0.101401i
\(89\) 605.706 1049.11i 0.721401 1.24950i −0.239037 0.971010i \(-0.576832\pi\)
0.960438 0.278493i \(-0.0898348\pi\)
\(90\) 0 0
\(91\) −269.256 685.209i −0.310173 0.789334i
\(92\) −192.970 −0.218679
\(93\) 0 0
\(94\) 248.215 + 429.921i 0.272355 + 0.471733i
\(95\) 1006.94 + 1744.07i 1.08747 + 1.88355i
\(96\) 0 0
\(97\) −1336.50 −1.39898 −0.699492 0.714641i \(-0.746590\pi\)
−0.699492 + 0.714641i \(0.746590\pi\)
\(98\) 153.211 + 668.672i 0.157925 + 0.689246i
\(99\) 0 0
\(100\) −268.949 + 465.834i −0.268949 + 0.465834i
\(101\) −103.208 178.762i −0.101679 0.176114i 0.810697 0.585465i \(-0.199088\pi\)
−0.912377 + 0.409352i \(0.865755\pi\)
\(102\) 0 0
\(103\) 344.223 596.212i 0.329294 0.570354i −0.653078 0.757291i \(-0.726523\pi\)
0.982372 + 0.186936i \(0.0598559\pi\)
\(104\) 318.014 0.299845
\(105\) 0 0
\(106\) −669.841 −0.613780
\(107\) −226.713 + 392.678i −0.204833 + 0.354781i −0.950079 0.312008i \(-0.898998\pi\)
0.745247 + 0.666789i \(0.232332\pi\)
\(108\) 0 0
\(109\) −685.492 1187.31i −0.602369 1.04333i −0.992461 0.122558i \(-0.960890\pi\)
0.390093 0.920776i \(-0.372443\pi\)
\(110\) 194.623 337.097i 0.168696 0.292191i
\(111\) 0 0
\(112\) −293.033 44.0418i −0.247223 0.0371568i
\(113\) −1807.69 −1.50489 −0.752446 0.658654i \(-0.771126\pi\)
−0.752446 + 0.658654i \(0.771126\pi\)
\(114\) 0 0
\(115\) 388.550 + 672.988i 0.315065 + 0.545708i
\(116\) 186.092 + 322.321i 0.148950 + 0.257989i
\(117\) 0 0
\(118\) 365.746 0.285336
\(119\) 1449.37 1819.01i 1.11650 1.40125i
\(120\) 0 0
\(121\) 592.510 1026.26i 0.445161 0.771042i
\(122\) 609.824 + 1056.25i 0.452548 + 0.783836i
\(123\) 0 0
\(124\) −45.5237 + 78.8493i −0.0329689 + 0.0571039i
\(125\) 152.620 0.109206
\(126\) 0 0
\(127\) −196.476 −0.137279 −0.0686394 0.997642i \(-0.521866\pi\)
−0.0686394 + 0.997642i \(0.521866\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −640.330 1109.08i −0.432005 0.748255i
\(131\) −753.242 + 1304.65i −0.502374 + 0.870138i 0.497622 + 0.867394i \(0.334207\pi\)
−0.999996 + 0.00274396i \(0.999127\pi\)
\(132\) 0 0
\(133\) 2289.71 + 344.136i 1.49281 + 0.224364i
\(134\) −236.759 −0.152634
\(135\) 0 0
\(136\) 502.332 + 870.064i 0.316725 + 0.548583i
\(137\) 157.673 + 273.097i 0.0983277 + 0.170309i 0.910993 0.412423i \(-0.135317\pi\)
−0.812665 + 0.582731i \(0.801984\pi\)
\(138\) 0 0
\(139\) −324.501 −0.198013 −0.0990064 0.995087i \(-0.531566\pi\)
−0.0990064 + 0.995087i \(0.531566\pi\)
\(140\) 436.433 + 1110.64i 0.263466 + 0.670474i
\(141\) 0 0
\(142\) −81.4905 + 141.146i −0.0481587 + 0.0834132i
\(143\) 240.145 + 415.943i 0.140433 + 0.243237i
\(144\) 0 0
\(145\) 749.403 1298.00i 0.429204 0.743403i
\(146\) 1957.66 1.10971
\(147\) 0 0
\(148\) −1602.88 −0.890245
\(149\) −638.745 + 1106.34i −0.351195 + 0.608287i −0.986459 0.164008i \(-0.947558\pi\)
0.635264 + 0.772295i \(0.280891\pi\)
\(150\) 0 0
\(151\) −258.424 447.604i −0.139273 0.241228i 0.787948 0.615741i \(-0.211143\pi\)
−0.927222 + 0.374513i \(0.877810\pi\)
\(152\) −500.086 + 866.175i −0.266858 + 0.462211i
\(153\) 0 0
\(154\) −163.677 416.527i −0.0856457 0.217953i
\(155\) 366.653 0.190002
\(156\) 0 0
\(157\) 649.320 + 1124.66i 0.330073 + 0.571702i 0.982526 0.186127i \(-0.0595935\pi\)
−0.652453 + 0.757829i \(0.726260\pi\)
\(158\) −693.428 1201.05i −0.349153 0.604751i
\(159\) 0 0
\(160\) −515.463 −0.254693
\(161\) 883.539 + 132.793i 0.432501 + 0.0650034i
\(162\) 0 0
\(163\) −1487.02 + 2575.60i −0.714556 + 1.23765i 0.248574 + 0.968613i \(0.420038\pi\)
−0.963130 + 0.269035i \(0.913295\pi\)
\(164\) 708.141 + 1226.54i 0.337174 + 0.584002i
\(165\) 0 0
\(166\) −1409.05 + 2440.55i −0.658816 + 1.14110i
\(167\) 3607.22 1.67147 0.835733 0.549135i \(-0.185043\pi\)
0.835733 + 0.549135i \(0.185043\pi\)
\(168\) 0 0
\(169\) −616.796 −0.280745
\(170\) 2022.92 3503.79i 0.912651 1.58076i
\(171\) 0 0
\(172\) −451.835 782.602i −0.200303 0.346935i
\(173\) 1263.21 2187.94i 0.555143 0.961536i −0.442749 0.896645i \(-0.645997\pi\)
0.997892 0.0648904i \(-0.0206698\pi\)
\(174\) 0 0
\(175\) 1551.99 1947.81i 0.670396 0.841374i
\(176\) 193.316 0.0827938
\(177\) 0 0
\(178\) −1211.41 2098.23i −0.510108 0.883532i
\(179\) 711.221 + 1231.87i 0.296979 + 0.514382i 0.975443 0.220251i \(-0.0706877\pi\)
−0.678465 + 0.734633i \(0.737354\pi\)
\(180\) 0 0
\(181\) 2494.29 1.02431 0.512153 0.858894i \(-0.328848\pi\)
0.512153 + 0.858894i \(0.328848\pi\)
\(182\) −1456.07 218.843i −0.593029 0.0891302i
\(183\) 0 0
\(184\) −192.970 + 334.233i −0.0773148 + 0.133913i
\(185\) 3227.45 + 5590.11i 1.28263 + 2.22158i
\(186\) 0 0
\(187\) −758.661 + 1314.04i −0.296678 + 0.513861i
\(188\) 992.859 0.385169
\(189\) 0 0
\(190\) 4027.75 1.53791
\(191\) 1846.91 3198.94i 0.699674 1.21187i −0.268906 0.963167i \(-0.586662\pi\)
0.968580 0.248704i \(-0.0800047\pi\)
\(192\) 0 0
\(193\) 38.5601 + 66.7881i 0.0143815 + 0.0249094i 0.873127 0.487494i \(-0.162089\pi\)
−0.858745 + 0.512403i \(0.828755\pi\)
\(194\) −1336.50 + 2314.89i −0.494615 + 0.856699i
\(195\) 0 0
\(196\) 1311.38 + 403.304i 0.477910 + 0.146977i
\(197\) 1259.96 0.455679 0.227839 0.973699i \(-0.426834\pi\)
0.227839 + 0.973699i \(0.426834\pi\)
\(198\) 0 0
\(199\) −2725.37 4720.48i −0.970837 1.68154i −0.693041 0.720898i \(-0.743729\pi\)
−0.277796 0.960640i \(-0.589604\pi\)
\(200\) 537.899 + 931.668i 0.190176 + 0.329394i
\(201\) 0 0
\(202\) −412.833 −0.143796
\(203\) −630.242 1603.85i −0.217903 0.554524i
\(204\) 0 0
\(205\) 2851.72 4939.33i 0.971575 1.68282i
\(206\) −688.446 1192.42i −0.232846 0.403301i
\(207\) 0 0
\(208\) 318.014 550.817i 0.106011 0.183617i
\(209\) −1510.54 −0.499934
\(210\) 0 0
\(211\) 326.412 0.106498 0.0532492 0.998581i \(-0.483042\pi\)
0.0532492 + 0.998581i \(0.483042\pi\)
\(212\) −669.841 + 1160.20i −0.217004 + 0.375862i
\(213\) 0 0
\(214\) 453.425 + 785.355i 0.144839 + 0.250868i
\(215\) −1819.57 + 3151.58i −0.577178 + 0.999702i
\(216\) 0 0
\(217\) 262.697 329.695i 0.0821799 0.103139i
\(218\) −2741.97 −0.851878
\(219\) 0 0
\(220\) −389.246 674.195i −0.119286 0.206610i
\(221\) 2496.07 + 4323.32i 0.759746 + 1.31592i
\(222\) 0 0
\(223\) −3095.25 −0.929477 −0.464738 0.885448i \(-0.653852\pi\)
−0.464738 + 0.885448i \(0.653852\pi\)
\(224\) −369.316 + 463.506i −0.110160 + 0.138256i
\(225\) 0 0
\(226\) −1807.69 + 3131.01i −0.532060 + 0.921555i
\(227\) −313.357 542.750i −0.0916221 0.158694i 0.816572 0.577244i \(-0.195872\pi\)
−0.908194 + 0.418550i \(0.862539\pi\)
\(228\) 0 0
\(229\) −3333.25 + 5773.36i −0.961867 + 1.66600i −0.244059 + 0.969760i \(0.578479\pi\)
−0.717808 + 0.696241i \(0.754854\pi\)
\(230\) 1554.20 0.445569
\(231\) 0 0
\(232\) 744.369 0.210647
\(233\) 1750.26 3031.53i 0.492117 0.852371i −0.507842 0.861450i \(-0.669557\pi\)
0.999959 + 0.00907927i \(0.00289006\pi\)
\(234\) 0 0
\(235\) −1999.15 3462.63i −0.554937 0.961179i
\(236\) 365.746 633.490i 0.100881 0.174732i
\(237\) 0 0
\(238\) −1701.26 4329.39i −0.463345 1.17913i
\(239\) 119.098 0.0322335 0.0161168 0.999870i \(-0.494870\pi\)
0.0161168 + 0.999870i \(0.494870\pi\)
\(240\) 0 0
\(241\) −635.903 1101.42i −0.169967 0.294392i 0.768441 0.639921i \(-0.221033\pi\)
−0.938408 + 0.345529i \(0.887699\pi\)
\(242\) −1185.02 2052.51i −0.314777 0.545209i
\(243\) 0 0
\(244\) 2439.29 0.639999
\(245\) −1233.98 5385.56i −0.321779 1.40437i
\(246\) 0 0
\(247\) −2484.91 + 4304.00i −0.640127 + 1.10873i
\(248\) 91.0474 + 157.699i 0.0233126 + 0.0403785i
\(249\) 0 0
\(250\) 152.620 264.346i 0.0386102 0.0668748i
\(251\) −330.354 −0.0830749 −0.0415374 0.999137i \(-0.513226\pi\)
−0.0415374 + 0.999137i \(0.513226\pi\)
\(252\) 0 0
\(253\) −582.876 −0.144842
\(254\) −196.476 + 340.306i −0.0485354 + 0.0840658i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1260.40 + 2183.08i −0.305921 + 0.529870i −0.977466 0.211093i \(-0.932298\pi\)
0.671545 + 0.740964i \(0.265631\pi\)
\(258\) 0 0
\(259\) 7339.03 + 1103.03i 1.76072 + 0.264629i
\(260\) −2561.32 −0.610948
\(261\) 0 0
\(262\) 1506.48 + 2609.31i 0.355232 + 0.615281i
\(263\) −713.729 1236.21i −0.167340 0.289841i 0.770144 0.637870i \(-0.220184\pi\)
−0.937484 + 0.348029i \(0.886851\pi\)
\(264\) 0 0
\(265\) 5394.97 1.25061
\(266\) 2885.78 3621.77i 0.665182 0.834830i
\(267\) 0 0
\(268\) −236.759 + 410.079i −0.0539641 + 0.0934686i
\(269\) 4094.93 + 7092.63i 0.928151 + 1.60760i 0.786414 + 0.617700i \(0.211935\pi\)
0.141737 + 0.989904i \(0.454731\pi\)
\(270\) 0 0
\(271\) −3197.35 + 5537.98i −0.716699 + 1.24136i 0.245602 + 0.969371i \(0.421014\pi\)
−0.962301 + 0.271988i \(0.912319\pi\)
\(272\) 2009.33 0.447917
\(273\) 0 0
\(274\) 630.691 0.139056
\(275\) −812.377 + 1407.08i −0.178139 + 0.308545i
\(276\) 0 0
\(277\) 3319.70 + 5749.90i 0.720078 + 1.24721i 0.960968 + 0.276660i \(0.0892275\pi\)
−0.240890 + 0.970553i \(0.577439\pi\)
\(278\) −324.501 + 562.052i −0.0700081 + 0.121258i
\(279\) 0 0
\(280\) 2360.12 + 354.718i 0.503729 + 0.0757087i
\(281\) −4929.95 −1.04661 −0.523303 0.852147i \(-0.675300\pi\)
−0.523303 + 0.852147i \(0.675300\pi\)
\(282\) 0 0
\(283\) −1391.39 2409.96i −0.292261 0.506210i 0.682083 0.731274i \(-0.261074\pi\)
−0.974344 + 0.225064i \(0.927741\pi\)
\(284\) 162.981 + 282.291i 0.0340533 + 0.0589821i
\(285\) 0 0
\(286\) 960.580 0.198602
\(287\) −2398.28 6103.18i −0.493261 1.25526i
\(288\) 0 0
\(289\) −5429.03 + 9403.36i −1.10503 + 1.91397i
\(290\) −1498.81 2596.01i −0.303493 0.525665i
\(291\) 0 0
\(292\) 1957.66 3390.77i 0.392341 0.679554i
\(293\) −1639.57 −0.326910 −0.163455 0.986551i \(-0.552264\pi\)
−0.163455 + 0.986551i \(0.552264\pi\)
\(294\) 0 0
\(295\) −2945.76 −0.581385
\(296\) −1602.88 + 2776.28i −0.314749 + 0.545162i
\(297\) 0 0
\(298\) 1277.49 + 2212.68i 0.248332 + 0.430124i
\(299\) −958.861 + 1660.80i −0.185459 + 0.321225i
\(300\) 0 0
\(301\) 1530.24 + 3894.18i 0.293029 + 0.745705i
\(302\) −1033.70 −0.196962
\(303\) 0 0
\(304\) 1000.17 + 1732.35i 0.188697 + 0.326832i
\(305\) −4911.59 8507.12i −0.922087 1.59710i
\(306\) 0 0
\(307\) −10332.5 −1.92087 −0.960436 0.278502i \(-0.910162\pi\)
−0.960436 + 0.278502i \(0.910162\pi\)
\(308\) −885.123 133.031i −0.163749 0.0246108i
\(309\) 0 0
\(310\) 366.653 635.061i 0.0671757 0.116352i
\(311\) −4626.39 8013.14i −0.843532 1.46104i −0.886890 0.461980i \(-0.847139\pi\)
0.0433584 0.999060i \(-0.486194\pi\)
\(312\) 0 0
\(313\) 1238.89 2145.82i 0.223726 0.387504i −0.732211 0.681078i \(-0.761511\pi\)
0.955936 + 0.293574i \(0.0948447\pi\)
\(314\) 2597.28 0.466793
\(315\) 0 0
\(316\) −2773.71 −0.493777
\(317\) −1441.61 + 2496.94i −0.255422 + 0.442404i −0.965010 0.262213i \(-0.915548\pi\)
0.709588 + 0.704617i \(0.248881\pi\)
\(318\) 0 0
\(319\) 562.102 + 973.589i 0.0986573 + 0.170879i
\(320\) −515.463 + 892.808i −0.0900477 + 0.155967i
\(321\) 0 0
\(322\) 1113.54 1397.54i 0.192718 0.241869i
\(323\) −15700.6 −2.70465
\(324\) 0 0
\(325\) 2672.80 + 4629.43i 0.456186 + 0.790137i
\(326\) 2974.05 + 5151.20i 0.505267 + 0.875149i
\(327\) 0 0
\(328\) 2832.56 0.476836
\(329\) −4545.95 683.240i −0.761782 0.114493i
\(330\) 0 0
\(331\) 248.565 430.528i 0.0412761 0.0714923i −0.844649 0.535320i \(-0.820191\pi\)
0.885925 + 0.463828i \(0.153524\pi\)
\(332\) 2818.10 + 4881.09i 0.465853 + 0.806882i
\(333\) 0 0
\(334\) 3607.22 6247.89i 0.590953 1.02356i
\(335\) 1906.89 0.310998
\(336\) 0 0
\(337\) 6711.07 1.08479 0.542397 0.840123i \(-0.317517\pi\)
0.542397 + 0.840123i \(0.317517\pi\)
\(338\) −616.796 + 1068.32i −0.0992583 + 0.171920i
\(339\) 0 0
\(340\) −4045.83 7007.59i −0.645341 1.11776i
\(341\) −137.507 + 238.169i −0.0218370 + 0.0378228i
\(342\) 0 0
\(343\) −5726.82 2749.02i −0.901514 0.432749i
\(344\) −1807.34 −0.283271
\(345\) 0 0
\(346\) −2526.41 4375.87i −0.392545 0.679908i
\(347\) 80.8131 + 139.972i 0.0125022 + 0.0216545i 0.872209 0.489134i \(-0.162687\pi\)
−0.859707 + 0.510788i \(0.829354\pi\)
\(348\) 0 0
\(349\) −3970.85 −0.609040 −0.304520 0.952506i \(-0.598496\pi\)
−0.304520 + 0.952506i \(0.598496\pi\)
\(350\) −1821.71 4635.93i −0.278213 0.708002i
\(351\) 0 0
\(352\) 193.316 334.833i 0.0292720 0.0507007i
\(353\) 5777.83 + 10007.5i 0.871169 + 1.50891i 0.860788 + 0.508964i \(0.169971\pi\)
0.0103815 + 0.999946i \(0.496695\pi\)
\(354\) 0 0
\(355\) 656.333 1136.80i 0.0981255 0.169958i
\(356\) −4845.65 −0.721401
\(357\) 0 0
\(358\) 2844.88 0.419991
\(359\) 4270.56 7396.82i 0.627831 1.08744i −0.360155 0.932892i \(-0.617276\pi\)
0.987986 0.154543i \(-0.0493904\pi\)
\(360\) 0 0
\(361\) −4385.70 7596.25i −0.639407 1.10749i
\(362\) 2494.29 4320.24i 0.362147 0.627257i
\(363\) 0 0
\(364\) −1835.12 + 2303.15i −0.264248 + 0.331642i
\(365\) −15767.2 −2.26108
\(366\) 0 0
\(367\) −1901.32 3293.18i −0.270431 0.468400i 0.698541 0.715570i \(-0.253833\pi\)
−0.968972 + 0.247170i \(0.920499\pi\)
\(368\) 385.939 + 668.467i 0.0546698 + 0.0946908i
\(369\) 0 0
\(370\) 12909.8 1.81392
\(371\) 3865.35 4851.18i 0.540914 0.678869i
\(372\) 0 0
\(373\) 4296.45 7441.66i 0.596412 1.03302i −0.396934 0.917847i \(-0.629926\pi\)
0.993346 0.115168i \(-0.0367407\pi\)
\(374\) 1517.32 + 2628.08i 0.209783 + 0.363355i
\(375\) 0 0
\(376\) 992.859 1719.68i 0.136178 0.235867i
\(377\) 3698.75 0.505292
\(378\) 0 0
\(379\) −9415.95 −1.27616 −0.638080 0.769970i \(-0.720271\pi\)
−0.638080 + 0.769970i \(0.720271\pi\)
\(380\) 4027.75 6976.27i 0.543735 0.941776i
\(381\) 0 0
\(382\) −3693.82 6397.88i −0.494744 0.856922i
\(383\) 4618.37 7999.25i 0.616156 1.06721i −0.374025 0.927419i \(-0.622022\pi\)
0.990181 0.139795i \(-0.0446442\pi\)
\(384\) 0 0
\(385\) 1318.27 + 3354.76i 0.174507 + 0.444089i
\(386\) 154.241 0.0203384
\(387\) 0 0
\(388\) 2673.01 + 4629.78i 0.349746 + 0.605777i
\(389\) −1003.96 1738.90i −0.130855 0.226648i 0.793151 0.609025i \(-0.208439\pi\)
−0.924006 + 0.382377i \(0.875106\pi\)
\(390\) 0 0
\(391\) −6058.42 −0.783600
\(392\) 2009.93 1868.08i 0.258971 0.240695i
\(393\) 0 0
\(394\) 1259.96 2182.32i 0.161107 0.279045i
\(395\) 5584.95 + 9673.41i 0.711416 + 1.23221i
\(396\) 0 0
\(397\) −635.532 + 1100.77i −0.0803437 + 0.139159i −0.903398 0.428804i \(-0.858935\pi\)
0.823054 + 0.567963i \(0.192268\pi\)
\(398\) −10901.5 −1.37297
\(399\) 0 0
\(400\) 2151.59 0.268949
\(401\) 7512.71 13012.4i 0.935578 1.62047i 0.161978 0.986794i \(-0.448213\pi\)
0.773600 0.633674i \(-0.218454\pi\)
\(402\) 0 0
\(403\) 452.412 + 783.600i 0.0559212 + 0.0968583i
\(404\) −412.833 + 715.048i −0.0508396 + 0.0880568i
\(405\) 0 0
\(406\) −3408.20 512.240i −0.416616 0.0626159i
\(407\) −4841.61 −0.589655
\(408\) 0 0
\(409\) −239.226 414.352i −0.0289217 0.0500939i 0.851202 0.524838i \(-0.175874\pi\)
−0.880124 + 0.474744i \(0.842541\pi\)
\(410\) −5703.44 9878.66i −0.687007 1.18993i
\(411\) 0 0
\(412\) −2753.78 −0.329294
\(413\) −2110.56 + 2648.83i −0.251462 + 0.315595i
\(414\) 0 0
\(415\) 11348.6 19656.4i 1.34237 2.32505i
\(416\) −636.028 1101.63i −0.0749612 0.129837i
\(417\) 0 0
\(418\) −1510.54 + 2616.33i −0.176753 + 0.306146i
\(419\) 11608.0 1.35343 0.676715 0.736245i \(-0.263403\pi\)
0.676715 + 0.736245i \(0.263403\pi\)
\(420\) 0 0
\(421\) −3833.92 −0.443833 −0.221917 0.975066i \(-0.571231\pi\)
−0.221917 + 0.975066i \(0.571231\pi\)
\(422\) 326.412 565.363i 0.0376529 0.0652167i
\(423\) 0 0
\(424\) 1339.68 + 2320.40i 0.153445 + 0.265775i
\(425\) −8443.86 + 14625.2i −0.963735 + 1.66924i
\(426\) 0 0
\(427\) −11168.7 1678.61i −1.26578 0.190243i
\(428\) 1813.70 0.204833
\(429\) 0 0
\(430\) 3639.13 + 6303.16i 0.408127 + 0.706896i
\(431\) 499.024 + 864.334i 0.0557706 + 0.0965975i 0.892563 0.450923i \(-0.148905\pi\)
−0.836792 + 0.547521i \(0.815572\pi\)
\(432\) 0 0
\(433\) 1298.17 0.144079 0.0720396 0.997402i \(-0.477049\pi\)
0.0720396 + 0.997402i \(0.477049\pi\)
\(434\) −308.352 784.700i −0.0341046 0.0867899i
\(435\) 0 0
\(436\) −2741.97 + 4749.23i −0.301184 + 0.521667i
\(437\) −3015.67 5223.30i −0.330112 0.571772i
\(438\) 0 0
\(439\) 966.704 1674.38i 0.105099 0.182036i −0.808680 0.588249i \(-0.799818\pi\)
0.913778 + 0.406213i \(0.133151\pi\)
\(440\) −1556.99 −0.168696
\(441\) 0 0
\(442\) 9984.29 1.07444
\(443\) −7267.01 + 12586.8i −0.779382 + 1.34993i 0.152917 + 0.988239i \(0.451133\pi\)
−0.932299 + 0.361690i \(0.882200\pi\)
\(444\) 0 0
\(445\) 9756.84 + 16899.3i 1.03937 + 1.80024i
\(446\) −3095.25 + 5361.13i −0.328620 + 0.569186i
\(447\) 0 0
\(448\) 433.500 + 1103.18i 0.0457165 + 0.116340i
\(449\) 4799.65 0.504476 0.252238 0.967665i \(-0.418833\pi\)
0.252238 + 0.967665i \(0.418833\pi\)
\(450\) 0 0
\(451\) 2138.98 + 3704.82i 0.223327 + 0.386814i
\(452\) 3615.37 + 6262.01i 0.376223 + 0.651638i
\(453\) 0 0
\(454\) −1253.43 −0.129573
\(455\) 11727.4 + 1762.58i 1.20832 + 0.181607i
\(456\) 0 0
\(457\) −2367.14 + 4100.00i −0.242297 + 0.419671i −0.961368 0.275265i \(-0.911234\pi\)
0.719071 + 0.694937i \(0.244568\pi\)
\(458\) 6666.50 + 11546.7i 0.680142 + 1.17804i
\(459\) 0 0
\(460\) 1554.20 2691.95i 0.157532 0.272854i
\(461\) 8137.41 0.822119 0.411060 0.911608i \(-0.365159\pi\)
0.411060 + 0.911608i \(0.365159\pi\)
\(462\) 0 0
\(463\) 8671.77 0.870435 0.435218 0.900325i \(-0.356671\pi\)
0.435218 + 0.900325i \(0.356671\pi\)
\(464\) 744.369 1289.28i 0.0744751 0.128995i
\(465\) 0 0
\(466\) −3500.51 6063.07i −0.347979 0.602717i
\(467\) −7794.04 + 13499.7i −0.772303 + 1.33767i 0.163995 + 0.986461i \(0.447562\pi\)
−0.936298 + 0.351206i \(0.885772\pi\)
\(468\) 0 0
\(469\) 1366.23 1714.68i 0.134513 0.168820i
\(470\) −7996.60 −0.784799
\(471\) 0 0
\(472\) −731.492 1266.98i −0.0713340 0.123554i
\(473\) −1364.79 2363.89i −0.132671 0.229793i
\(474\) 0 0
\(475\) −16812.2 −1.62400
\(476\) −9199.98 1382.73i −0.885883 0.133145i
\(477\) 0 0
\(478\) 119.098 206.284i 0.0113963 0.0197389i
\(479\) 4767.04 + 8256.76i 0.454722 + 0.787601i 0.998672 0.0515163i \(-0.0164054\pi\)
−0.543951 + 0.839117i \(0.683072\pi\)
\(480\) 0 0
\(481\) −7964.69 + 13795.2i −0.755007 + 1.30771i
\(482\) −2543.61 −0.240370
\(483\) 0 0
\(484\) −4740.08 −0.445161
\(485\) 10764.3 18644.4i 1.00780 1.74556i
\(486\) 0 0
\(487\) 4398.55 + 7618.51i 0.409276 + 0.708887i 0.994809 0.101762i \(-0.0324480\pi\)
−0.585533 + 0.810649i \(0.699115\pi\)
\(488\) 2439.29 4224.98i 0.226274 0.391918i
\(489\) 0 0
\(490\) −10562.0 3248.25i −0.973764 0.299471i
\(491\) −15749.6 −1.44760 −0.723799 0.690010i \(-0.757606\pi\)
−0.723799 + 0.690010i \(0.757606\pi\)
\(492\) 0 0
\(493\) 5842.50 + 10119.5i 0.533738 + 0.924461i
\(494\) 4969.83 + 8608.00i 0.452638 + 0.783992i
\(495\) 0 0
\(496\) 364.190 0.0329689
\(497\) −551.971 1404.67i −0.0498175 0.126776i
\(498\) 0 0
\(499\) 6490.60 11242.0i 0.582283 1.00854i −0.412926 0.910765i \(-0.635493\pi\)
0.995208 0.0977783i \(-0.0311736\pi\)
\(500\) −305.240 528.692i −0.0273015 0.0472876i
\(501\) 0 0
\(502\) −330.354 + 572.191i −0.0293714 + 0.0508727i
\(503\) 13047.4 1.15657 0.578284 0.815836i \(-0.303723\pi\)
0.578284 + 0.815836i \(0.303723\pi\)
\(504\) 0 0
\(505\) 3325.00 0.292991
\(506\) −582.876 + 1009.57i −0.0512095 + 0.0886974i
\(507\) 0 0
\(508\) 392.952 + 680.612i 0.0343197 + 0.0594435i
\(509\) 381.720 661.159i 0.0332406 0.0575744i −0.848927 0.528511i \(-0.822751\pi\)
0.882167 + 0.470937i \(0.156084\pi\)
\(510\) 0 0
\(511\) −11296.8 + 14177.9i −0.977967 + 1.22739i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2520.80 + 4366.15i 0.216319 + 0.374675i
\(515\) 5544.82 + 9603.91i 0.474435 + 0.821745i
\(516\) 0 0
\(517\) 2998.99 0.255117
\(518\) 9249.54 11608.5i 0.784559 0.984653i
\(519\) 0 0
\(520\) −2561.32 + 4436.34i −0.216003 + 0.374127i
\(521\) 1015.38 + 1758.68i 0.0853829 + 0.147887i 0.905554 0.424230i \(-0.139455\pi\)
−0.820171 + 0.572118i \(0.806122\pi\)
\(522\) 0 0
\(523\) 6482.87 11228.7i 0.542019 0.938805i −0.456769 0.889585i \(-0.650993\pi\)
0.998788 0.0492192i \(-0.0156733\pi\)
\(524\) 6025.94 0.502374
\(525\) 0 0
\(526\) −2854.91 −0.236654
\(527\) −1429.25 + 2475.53i −0.118139 + 0.204622i
\(528\) 0 0
\(529\) 4919.83 + 8521.40i 0.404359 + 0.700370i
\(530\) 5394.97 9344.36i 0.442156 0.765836i
\(531\) 0 0
\(532\) −3387.31 8620.08i −0.276050 0.702496i
\(533\) 14074.9 1.14381
\(534\) 0 0
\(535\) −3651.93 6325.34i −0.295116 0.511155i
\(536\) 473.519 + 820.158i 0.0381584 + 0.0660923i
\(537\) 0 0
\(538\) 16379.7 1.31260
\(539\) 3961.11 + 1218.20i 0.316544 + 0.0973500i
\(540\) 0 0
\(541\) 7812.43 13531.5i 0.620855 1.07535i −0.368471 0.929639i \(-0.620119\pi\)
0.989327 0.145714i \(-0.0465479\pi\)
\(542\) 6394.70 + 11076.0i 0.506782 + 0.877773i
\(543\) 0 0
\(544\) 2009.33 3480.26i 0.158362 0.274292i
\(545\) 22084.1 1.73574
\(546\) 0 0
\(547\) −14437.8 −1.12855 −0.564273 0.825588i \(-0.690843\pi\)
−0.564273 + 0.825588i \(0.690843\pi\)
\(548\) 630.691 1092.39i 0.0491639 0.0851543i
\(549\) 0 0
\(550\) 1624.75 + 2814.16i 0.125963 + 0.218175i
\(551\) −5816.38 + 10074.3i −0.449703 + 0.778908i
\(552\) 0 0
\(553\) 12699.8 + 1908.74i 0.976586 + 0.146777i
\(554\) 13278.8 1.01834
\(555\) 0 0
\(556\) 649.001 + 1124.10i 0.0495032 + 0.0857421i
\(557\) 8242.53 + 14276.5i 0.627015 + 1.08602i 0.988148 + 0.153507i \(0.0490567\pi\)
−0.361133 + 0.932514i \(0.617610\pi\)
\(558\) 0 0
\(559\) −8980.63 −0.679499
\(560\) 2974.51 3733.13i 0.224457 0.281703i
\(561\) 0 0
\(562\) −4929.95 + 8538.92i −0.370031 + 0.640912i
\(563\) −8366.91 14491.9i −0.626329 1.08483i −0.988282 0.152637i \(-0.951223\pi\)
0.361954 0.932196i \(-0.382110\pi\)
\(564\) 0 0
\(565\) 14559.3 25217.5i 1.08410 1.87771i
\(566\) −5565.57 −0.413319
\(567\) 0 0
\(568\) 651.924 0.0481587
\(569\) 7508.37 13004.9i 0.553194 0.958160i −0.444848 0.895606i \(-0.646742\pi\)
0.998042 0.0625539i \(-0.0199245\pi\)
\(570\) 0 0
\(571\) −3236.25 5605.35i −0.237186 0.410817i 0.722720 0.691141i \(-0.242892\pi\)
−0.959906 + 0.280323i \(0.909558\pi\)
\(572\) 960.580 1663.77i 0.0702166 0.121619i
\(573\) 0 0
\(574\) −12969.3 1949.24i −0.943080 0.141742i
\(575\) −6487.38 −0.470509
\(576\) 0 0
\(577\) −4955.10 8582.48i −0.357510 0.619226i 0.630034 0.776567i \(-0.283041\pi\)
−0.987544 + 0.157342i \(0.949708\pi\)
\(578\) 10858.1 + 18806.7i 0.781377 + 1.35338i
\(579\) 0 0
\(580\) −5995.23 −0.429204
\(581\) −9544.12 24288.0i −0.681509 1.73432i
\(582\) 0 0
\(583\) −2023.29 + 3504.45i −0.143733 + 0.248952i
\(584\) −3915.32 6781.54i −0.277427 0.480517i
\(585\) 0 0
\(586\) −1639.57 + 2839.81i −0.115580 + 0.200191i
\(587\) −1112.26 −0.0782079 −0.0391039 0.999235i \(-0.512450\pi\)
−0.0391039 + 0.999235i \(0.512450\pi\)
\(588\) 0 0
\(589\) −2845.72 −0.199076
\(590\) −2945.76 + 5102.20i −0.205551 + 0.356024i
\(591\) 0 0
\(592\) 3205.77 + 5552.56i 0.222561 + 0.385488i
\(593\) 379.191 656.778i 0.0262589 0.0454817i −0.852597 0.522568i \(-0.824974\pi\)
0.878856 + 0.477087i \(0.158307\pi\)
\(594\) 0 0
\(595\) 13702.1 + 34869.4i 0.944087 + 2.40253i
\(596\) 5109.96 0.351195
\(597\) 0 0
\(598\) 1917.72 + 3321.59i 0.131140 + 0.227140i
\(599\) 8957.35 + 15514.6i 0.610997 + 1.05828i 0.991073 + 0.133323i \(0.0425646\pi\)
−0.380076 + 0.924955i \(0.624102\pi\)
\(600\) 0 0
\(601\) 19337.1 1.31244 0.656221 0.754569i \(-0.272154\pi\)
0.656221 + 0.754569i \(0.272154\pi\)
\(602\) 8275.17 + 1243.73i 0.560250 + 0.0842037i
\(603\) 0 0
\(604\) −1033.70 + 1790.42i −0.0696366 + 0.120614i
\(605\) 9544.28 + 16531.2i 0.641372 + 1.11089i
\(606\) 0 0
\(607\) −787.211 + 1363.49i −0.0526391 + 0.0911736i −0.891144 0.453720i \(-0.850097\pi\)
0.838505 + 0.544894i \(0.183430\pi\)
\(608\) 4000.69 0.266858
\(609\) 0 0
\(610\) −19646.3 −1.30403
\(611\) 4933.49 8545.06i 0.326657 0.565787i
\(612\) 0 0
\(613\) 2597.21 + 4498.49i 0.171126 + 0.296399i 0.938814 0.344425i \(-0.111926\pi\)
−0.767688 + 0.640824i \(0.778593\pi\)
\(614\) −10332.5 + 17896.4i −0.679131 + 1.17629i
\(615\) 0 0
\(616\) −1115.54 + 1400.05i −0.0729649 + 0.0915739i
\(617\) −1699.80 −0.110910 −0.0554550 0.998461i \(-0.517661\pi\)
−0.0554550 + 0.998461i \(0.517661\pi\)
\(618\) 0 0
\(619\) 6362.04 + 11019.4i 0.413105 + 0.715518i 0.995227 0.0975825i \(-0.0311110\pi\)
−0.582123 + 0.813101i \(0.697778\pi\)
\(620\) −733.305 1270.12i −0.0475004 0.0822731i
\(621\) 0 0
\(622\) −18505.6 −1.19293
\(623\) 22186.5 + 3334.55i 1.42678 + 0.214440i
\(624\) 0 0
\(625\) 7175.45 12428.2i 0.459229 0.795407i
\(626\) −2477.78 4291.63i −0.158198 0.274007i
\(627\) 0 0
\(628\) 2597.28 4498.62i 0.165036 0.285851i
\(629\) −50323.7 −3.19004
\(630\) 0 0
\(631\) −14921.6 −0.941392 −0.470696 0.882295i \(-0.655997\pi\)
−0.470696 + 0.882295i \(0.655997\pi\)
\(632\) −2773.71 + 4804.21i −0.174577 + 0.302375i
\(633\) 0 0
\(634\) 2883.22 + 4993.88i 0.180611 + 0.312827i
\(635\) 1582.44 2740.86i 0.0988931 0.171288i
\(636\) 0 0
\(637\) 9987.27 9282.45i 0.621209 0.577369i
\(638\) 2248.41 0.139522
\(639\) 0 0
\(640\) 1030.93 + 1785.62i 0.0636733 + 0.110285i
\(641\) −13483.7 23354.5i −0.830850 1.43907i −0.897365 0.441289i \(-0.854522\pi\)
0.0665155 0.997785i \(-0.478812\pi\)
\(642\) 0 0
\(643\) 12146.2 0.744947 0.372473 0.928043i \(-0.378510\pi\)
0.372473 + 0.928043i \(0.378510\pi\)
\(644\) −1307.07 3326.25i −0.0799779 0.203529i
\(645\) 0 0
\(646\) −15700.6 + 27194.2i −0.956239 + 1.65626i
\(647\) 13575.9 + 23514.1i 0.824919 + 1.42880i 0.901981 + 0.431775i \(0.142113\pi\)
−0.0770625 + 0.997026i \(0.524554\pi\)
\(648\) 0 0
\(649\) 1104.76 1913.49i 0.0668189 0.115734i
\(650\) 10691.2 0.645144
\(651\) 0 0
\(652\) 11896.2 0.714556
\(653\) 6320.52 10947.5i 0.378776 0.656060i −0.612108 0.790774i \(-0.709678\pi\)
0.990884 + 0.134714i \(0.0430117\pi\)
\(654\) 0 0
\(655\) −12133.4 21015.6i −0.723802 1.25366i
\(656\) 2832.56 4906.14i 0.168587 0.292001i
\(657\) 0 0
\(658\) −5729.35 + 7190.57i −0.339443 + 0.426015i
\(659\) −11360.0 −0.671506 −0.335753 0.941950i \(-0.608991\pi\)
−0.335753 + 0.941950i \(0.608991\pi\)
\(660\) 0 0
\(661\) −2078.99 3600.91i −0.122335 0.211890i 0.798353 0.602189i \(-0.205705\pi\)
−0.920688 + 0.390300i \(0.872371\pi\)
\(662\) −497.131 861.056i −0.0291866 0.0505527i
\(663\) 0 0
\(664\) 11272.4 0.658816
\(665\) −23242.4 + 29170.1i −1.35534 + 1.70100i
\(666\) 0 0
\(667\) −2244.38 + 3887.39i −0.130289 + 0.225668i
\(668\) −7214.44 12495.8i −0.417867 0.723766i
\(669\) 0 0
\(670\) 1906.89 3302.82i 0.109954 0.190447i
\(671\) 7368.03 0.423904
\(672\) 0 0
\(673\) 8753.81 0.501389 0.250694 0.968066i \(-0.419341\pi\)
0.250694 + 0.968066i \(0.419341\pi\)
\(674\) 6711.07 11623.9i 0.383532 0.664297i
\(675\) 0 0
\(676\) 1233.59 + 2136.65i 0.0701862 + 0.121566i
\(677\) −5802.61 + 10050.4i −0.329413 + 0.570560i −0.982395 0.186813i \(-0.940184\pi\)
0.652983 + 0.757373i \(0.273517\pi\)
\(678\) 0 0
\(679\) −9052.73 23037.6i −0.511652 1.30206i
\(680\) −16183.3 −0.912651
\(681\) 0 0
\(682\) 275.014 + 476.338i 0.0154411 + 0.0267448i
\(683\) −9199.15 15933.4i −0.515367 0.892642i −0.999841 0.0178364i \(-0.994322\pi\)
0.484474 0.874806i \(-0.339011\pi\)
\(684\) 0 0
\(685\) −5079.66 −0.283334
\(686\) −10488.3 + 7170.13i −0.583737 + 0.399063i
\(687\) 0 0
\(688\) −1807.34 + 3130.41i −0.100152 + 0.173468i
\(689\) 6656.84 + 11530.0i 0.368077 + 0.637529i
\(690\) 0 0
\(691\) 20.7919 36.0127i 0.00114466 0.00198261i −0.865453 0.500991i \(-0.832969\pi\)
0.866597 + 0.499008i \(0.166302\pi\)
\(692\) −10105.6 −0.555143
\(693\) 0 0
\(694\) 323.252 0.0176808
\(695\) 2613.56 4526.83i 0.142645 0.247068i
\(696\) 0 0
\(697\) 22232.6 + 38508.0i 1.20821 + 2.09267i
\(698\) −3970.85 + 6877.72i −0.215328 + 0.372959i
\(699\) 0 0
\(700\) −9851.38 1480.63i −0.531924 0.0799464i
\(701\) 29655.0 1.59779 0.798896 0.601469i \(-0.205418\pi\)
0.798896 + 0.601469i \(0.205418\pi\)
\(702\) 0 0
\(703\) −25049.4 43386.8i −1.34389 2.32769i
\(704\) −386.631 669.665i −0.0206985 0.0358508i
\(705\) 0 0
\(706\) 23111.3 1.23202
\(707\) 2382.28 2989.85i 0.126725 0.159045i
\(708\) 0 0
\(709\) 4375.23 7578.13i 0.231757 0.401414i −0.726569 0.687094i \(-0.758886\pi\)
0.958325 + 0.285680i \(0.0922194\pi\)
\(710\) −1312.67 2273.60i −0.0693852 0.120179i
\(711\) 0 0
\(712\) −4845.65 + 8392.91i −0.255054 + 0.441766i
\(713\) −1098.09 −0.0576769
\(714\) 0 0
\(715\) −7736.62 −0.404662
\(716\) 2844.88 4927.48i 0.148489 0.257191i
\(717\) 0 0
\(718\) −8541.11 14793.6i −0.443944 0.768933i
\(719\) 9541.72 16526.8i 0.494918 0.857224i −0.505065 0.863082i \(-0.668531\pi\)
0.999983 + 0.00585789i \(0.00186464\pi\)
\(720\) 0 0
\(721\) 12608.6 + 1895.03i 0.651274 + 0.0978842i
\(722\) −17542.8 −0.904259
\(723\) 0 0
\(724\) −4988.59 8640.49i −0.256076 0.443537i
\(725\) 6256.17 + 10836.0i 0.320480 + 0.555088i
\(726\) 0 0
\(727\) 15050.9 0.767821 0.383910 0.923370i \(-0.374577\pi\)
0.383910 + 0.923370i \(0.374577\pi\)
\(728\) 2154.05 + 5481.67i 0.109663 + 0.279072i
\(729\) 0 0
\(730\) −15767.2 + 27309.6i −0.799412 + 1.38462i
\(731\) −14185.7 24570.4i −0.717752 1.24318i
\(732\) 0 0
\(733\) −5279.02 + 9143.53i −0.266010 + 0.460742i −0.967828 0.251614i \(-0.919039\pi\)
0.701818 + 0.712356i \(0.252372\pi\)
\(734\) −7605.28 −0.382447
\(735\) 0 0
\(736\) 1543.76 0.0773148
\(737\) −715.145 + 1238.67i −0.0357432 + 0.0619090i
\(738\) 0 0
\(739\) 16623.4 + 28792.5i 0.827470 + 1.43322i 0.900017 + 0.435856i \(0.143554\pi\)
−0.0725462 + 0.997365i \(0.523112\pi\)
\(740\) 12909.8 22360.4i 0.641316 1.11079i
\(741\) 0 0
\(742\) −4537.13 11546.2i −0.224479 0.571258i
\(743\) −32799.7 −1.61952 −0.809761 0.586760i \(-0.800403\pi\)
−0.809761 + 0.586760i \(0.800403\pi\)
\(744\) 0 0
\(745\) −10289.0 17821.1i −0.505988 0.876397i
\(746\) −8592.89 14883.3i −0.421727 0.730452i
\(747\) 0 0
\(748\) 6069.29 0.296678
\(749\) −8304.28 1248.10i −0.405116 0.0608875i
\(750\) 0 0
\(751\) 12113.3 20980.8i 0.588574 1.01944i −0.405845 0.913942i \(-0.633023\pi\)
0.994419 0.105499i \(-0.0336439\pi\)
\(752\) −1985.72 3439.37i −0.0962922 0.166783i
\(753\) 0 0
\(754\) 3698.75 6406.42i 0.178648 0.309427i
\(755\) 8325.51 0.401319
\(756\) 0 0
\(757\) −3116.97 −0.149654 −0.0748271 0.997197i \(-0.523840\pi\)
−0.0748271 + 0.997197i \(0.523840\pi\)
\(758\) −9415.95 + 16308.9i −0.451191 + 0.781485i
\(759\) 0 0
\(760\) −8055.50 13952.5i −0.384478 0.665936i
\(761\) 4355.33 7543.65i 0.207464 0.359339i −0.743451 0.668791i \(-0.766812\pi\)
0.950915 + 0.309452i \(0.100146\pi\)
\(762\) 0 0
\(763\) 15822.7 19858.1i 0.750746 0.942217i
\(764\) −14775.3 −0.699674
\(765\) 0 0
\(766\) −9236.74 15998.5i −0.435688 0.754634i
\(767\) −3634.76 6295.59i −0.171113 0.296376i
\(768\) 0 0
\(769\) −14498.2 −0.679868 −0.339934 0.940449i \(-0.610405\pi\)
−0.339934 + 0.940449i \(0.610405\pi\)
\(770\) 7128.88 + 1071.45i 0.333645 + 0.0501457i
\(771\) 0 0
\(772\) 154.241 267.153i 0.00719073 0.0124547i
\(773\) 7418.91 + 12849.9i 0.345200 + 0.597904i 0.985390 0.170312i \(-0.0544777\pi\)
−0.640190 + 0.768217i \(0.721144\pi\)
\(774\) 0 0
\(775\) −1530.45 + 2650.81i −0.0709358 + 0.122864i
\(776\) 10692.0 0.494615
\(777\) 0 0
\(778\) −4015.82 −0.185057
\(779\) −22133.2 + 38335.9i −1.01798 + 1.76319i
\(780\) 0 0
\(781\) 492.293 + 852.677i 0.0225552 + 0.0390668i
\(782\) −6058.42 + 10493.5i −0.277044 + 0.479855i
\(783\) 0 0
\(784\) −1225.69 5349.38i −0.0558348 0.243685i