Properties

Label 378.4.g.c.109.4
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 \(-0.338925 + 0.587036i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.c.163.4

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

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

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
\(5\) 8.05411 + 13.9501i 0.720381 + 1.24774i 0.960847 + 0.277080i \(0.0893665\pi\)
−0.240466 + 0.970658i \(0.577300\pi\)
\(6\) 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 \(-0.780381\pi\)
0.936864 + 0.349694i \(0.113715\pi\)
\(12\) 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 0.0630630 0.998010i \(-0.479913\pi\)
0.832770 0.553619i \(-0.186754\pi\)
\(18\) 0 0
\(19\) 62.5108 + 108.272i 0.754787 + 1.30733i 0.945480 + 0.325680i \(0.105593\pi\)
−0.190693 + 0.981650i \(0.561073\pi\)
\(20\) −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 \(-0.236841\pi\)
−0.954404 + 0.298517i \(0.903508\pi\)
\(24\) 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 \(-0.403714\pi\)
0.297900 + 0.954597i \(0.403714\pi\)
\(30\) 0 0
\(31\) −11.3809 + 19.7123i −0.0659379 + 0.114208i −0.897110 0.441808i \(-0.854337\pi\)
0.831172 + 0.556016i \(0.187671\pi\)
\(32\) −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 0.839581 + 0.543234i \(0.182800\pi\)
0.0506642 + 0.998716i \(0.483866\pi\)
\(38\) 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 \(-0.264425\pi\)
0.674348 + 0.738414i \(0.264425\pi\)
\(42\) 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 \(-0.0408099\pi\)
−0.606624 + 0.794989i \(0.707477\pi\)
\(48\) 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 \(-0.690432\pi\)
0.997214 + 0.0745926i \(0.0237656\pi\)
\(54\) 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 \(-0.898000\pi\)
0.747334 + 0.664449i \(0.231334\pi\)
\(60\) 0 0
\(61\) −304.912 528.123i −0.639999 1.10851i −0.985432 0.170068i \(-0.945601\pi\)
0.345433 0.938443i \(-0.387732\pi\)
\(62\) 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 −0.914931 0.403611i \(-0.867755\pi\)
0.807003 + 0.590548i \(0.201088\pi\)
\(68\) 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 \(-0.478304\pi\)
0.0681066 + 0.997678i \(0.478304\pi\)
\(72\) 0 0
\(73\) 489.415 847.692i 0.784681 1.35911i −0.144508 0.989504i \(-0.546160\pi\)
0.929189 0.369604i \(-0.120507\pi\)
\(74\) 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 0.999974 0.00717076i \(-0.00228254\pi\)
−0.506197 + 0.862418i \(0.668949\pi\)
\(80\) 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 \(-0.118320\pi\)
0.931707 + 0.363212i \(0.118320\pi\)
\(84\) 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 −0.960438 0.278493i \(-0.910165\pi\)
0.239037 0.971010i \(-0.423168\pi\)
\(90\) 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 \(-0.800912\pi\)
0.912377 + 0.409352i \(0.134245\pi\)
\(102\) 0 0
\(103\) 344.223 + 596.212i 0.329294 + 0.570354i 0.982372 0.186936i \(-0.0598559\pi\)
−0.653078 + 0.757291i \(0.726523\pi\)
\(104\) −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 \(-0.101002\pi\)
−0.745247 + 0.666789i \(0.767668\pi\)
\(108\) 0 0
\(109\) −685.492 + 1187.31i −0.602369 + 1.04333i 0.390093 + 0.920776i \(0.372443\pi\)
−0.992461 + 0.122558i \(0.960890\pi\)
\(110\) −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 \(-0.228874\pi\)
0.752446 + 0.658654i \(0.228874\pi\)
\(114\) 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 0.999996 + 0.00274396i \(0.000873432\pi\)
−0.497622 + 0.867394i \(0.665793\pi\)
\(132\) 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 \(-0.864683\pi\)
0.812665 + 0.582731i \(0.198016\pi\)
\(138\) 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 \(-0.0524422\pi\)
−0.635264 + 0.772295i \(0.719109\pi\)
\(150\) 0 0
\(151\) −258.424 + 447.604i −0.139273 + 0.241228i −0.927222 0.374513i \(-0.877810\pi\)
0.787948 + 0.615741i \(0.211143\pi\)
\(152\) 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 −0.652453 0.757829i \(-0.726260\pi\)
0.982526 + 0.186127i \(0.0595935\pi\)
\(158\) 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 −0.963130 0.269035i \(-0.913295\pi\)
0.248574 0.968613i \(-0.420038\pi\)
\(164\) −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 \(-0.814957\pi\)
−0.835733 + 0.549135i \(0.814957\pi\)
\(168\) 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 −0.997892 0.0648904i \(-0.979330\pi\)
0.442749 0.896645i \(-0.354003\pi\)
\(174\) 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 \(-0.929312\pi\)
0.678465 + 0.734633i \(0.262646\pi\)
\(180\) 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 −0.968580 0.248704i \(-0.919995\pi\)
0.268906 0.963167i \(-0.413338\pi\)
\(192\) 0 0
\(193\) 38.5601 66.7881i 0.0143815 0.0249094i −0.858745 0.512403i \(-0.828755\pi\)
0.873127 + 0.487494i \(0.162089\pi\)
\(194\) 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 \(-0.573166\pi\)
−0.227839 + 0.973699i \(0.573166\pi\)
\(198\) 0 0
\(199\) −2725.37 + 4720.48i −0.970837 + 1.68154i −0.277796 + 0.960640i \(0.589604\pi\)
−0.693041 + 0.720898i \(0.743729\pi\)
\(200\) −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 \(-0.804128\pi\)
0.908194 + 0.418550i \(0.137461\pi\)
\(228\) 0 0
\(229\) −3333.25 5773.36i −0.961867 1.66600i −0.717808 0.696241i \(-0.754854\pi\)
−0.244059 0.969760i \(-0.578479\pi\)
\(230\) −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 \(-0.330443\pi\)
−0.999959 + 0.00907927i \(0.997110\pi\)
\(234\) 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 \(-0.505130\pi\)
−0.0161168 + 0.999870i \(0.505130\pi\)
\(240\) 0 0
\(241\) −635.903 + 1101.42i −0.169967 + 0.294392i −0.938408 0.345529i \(-0.887699\pi\)
0.768441 + 0.639921i \(0.221033\pi\)
\(242\) 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 \(-0.486774\pi\)
0.0415374 + 0.999137i \(0.486774\pi\)
\(252\) 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 \(-0.0677024\pi\)
−0.671545 + 0.740964i \(0.734369\pi\)
\(258\) 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 \(-0.779816\pi\)
0.937484 + 0.348029i \(0.113149\pi\)
\(264\) 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 −0.141737 + 0.989904i \(0.545269\pi\)
−0.786414 + 0.617700i \(0.788065\pi\)
\(270\) 0 0
\(271\) −3197.35 5537.98i −0.716699 1.24136i −0.962301 0.271988i \(-0.912319\pi\)
0.245602 0.969371i \(-0.421014\pi\)
\(272\) −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 −0.240890 0.970553i \(-0.577439\pi\)
0.960968 0.276660i \(-0.0892275\pi\)
\(278\) 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 \(-0.324700\pi\)
0.523303 + 0.852147i \(0.324700\pi\)
\(282\) 0 0
\(283\) −1391.39 + 2409.96i −0.292261 + 0.506210i −0.974344 0.225064i \(-0.927741\pi\)
0.682083 + 0.731274i \(0.261074\pi\)
\(284\) −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 \(-0.447736\pi\)
0.163455 + 0.986551i \(0.447736\pi\)
\(294\) 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 −0.0433584 0.999060i \(-0.513806\pi\)
0.886890 0.461980i \(-0.152861\pi\)
\(312\) 0 0
\(313\) 1238.89 + 2145.82i 0.223726 + 0.387504i 0.955936 0.293574i \(-0.0948447\pi\)
−0.732211 + 0.681078i \(0.761511\pi\)
\(314\) −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 \(-0.0844523\pi\)
−0.709588 + 0.704617i \(0.751119\pi\)
\(318\) 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 0.885925 0.463828i \(-0.153524\pi\)
−0.844649 + 0.535320i \(0.820191\pi\)
\(332\) −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 \(-0.837313\pi\)
0.859707 + 0.510788i \(0.170646\pi\)
\(348\) 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 −0.0103815 + 0.999946i \(0.503305\pi\)
−0.860788 + 0.508964i \(0.830029\pi\)
\(354\) 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 −0.987986 0.154543i \(-0.950610\pi\)
0.360155 0.932892i \(-0.382724\pi\)
\(360\) 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 −0.968972 0.247170i \(-0.920499\pi\)
0.698541 + 0.715570i \(0.253833\pi\)
\(368\) −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 0.993346 + 0.115168i \(0.0367407\pi\)
−0.396934 + 0.917847i \(0.629926\pi\)
\(374\) −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 −0.990181 0.139795i \(-0.955356\pi\)
0.374025 0.927419i \(-0.377978\pi\)
\(384\) 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 \(-0.791561\pi\)
0.924006 + 0.382377i \(0.124894\pi\)
\(390\) 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 0.823054 0.567963i \(-0.192268\pi\)
−0.903398 + 0.428804i \(0.858935\pi\)
\(398\) 10901.5 1.37297
\(399\) 0 0
\(400\) 2151.59 0.268949
\(401\) −7512.71 13012.4i −0.935578 1.62047i −0.773600 0.633674i \(-0.781546\pi\)
−0.161978 0.986794i \(-0.551787\pi\)
\(402\) 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 −0.880124 0.474744i \(-0.842541\pi\)
0.851202 + 0.524838i \(0.175874\pi\)
\(410\) 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 \(-0.736597\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(420\) 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 \(-0.851095\pi\)
0.836792 + 0.547521i \(0.184428\pi\)
\(432\) 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 0.913778 0.406213i \(-0.133151\pi\)
−0.808680 + 0.588249i \(0.799818\pi\)
\(440\) 1556.99 0.168696
\(441\) 0 0
\(442\) 9984.29 1.07444
\(443\) 7267.01 + 12586.8i 0.779382 + 1.34993i 0.932299 + 0.361690i \(0.117800\pi\)
−0.152917 + 0.988239i \(0.548867\pi\)
\(444\) 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 \(-0.581167\pi\)
−0.252238 + 0.967665i \(0.581167\pi\)
\(450\) 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 0.719071 0.694937i \(-0.244568\pi\)
−0.961368 + 0.275265i \(0.911234\pi\)
\(458\) −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 \(-0.634841\pi\)
−0.411060 + 0.911608i \(0.634841\pi\)
\(462\) 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 0.936298 + 0.351206i \(0.114228\pi\)
−0.163995 + 0.986461i \(0.552438\pi\)
\(468\) 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 \(-0.983595\pi\)
0.543951 + 0.839117i \(0.316928\pi\)
\(480\) 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 −0.585533 0.810649i \(-0.699115\pi\)
0.994809 + 0.101762i \(0.0324480\pi\)
\(488\) −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 \(-0.242394\pi\)
0.723799 + 0.690010i \(0.242394\pi\)
\(492\) 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 0.995208 + 0.0977783i \(0.0311736\pi\)
−0.412926 + 0.910765i \(0.635493\pi\)
\(500\) 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 \(-0.696277\pi\)
−0.578284 + 0.815836i \(0.696277\pi\)
\(504\) 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 \(-0.177249\pi\)
−0.882167 + 0.470937i \(0.843916\pi\)
\(510\) 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 \(-0.860545\pi\)
0.820171 + 0.572118i \(0.193878\pi\)
\(522\) 0 0
\(523\) 6482.87 + 11228.7i 0.542019 + 0.938805i 0.998788 + 0.0492192i \(0.0156733\pi\)
−0.456769 + 0.889585i \(0.650993\pi\)
\(524\) −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 0.989327 + 0.145714i \(0.0465479\pi\)
−0.368471 + 0.929639i \(0.620119\pi\)
\(542\) −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 0.361133 + 0.932514i \(0.382390\pi\)
−0.988148 + 0.153507i \(0.950943\pi\)
\(558\) 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 −0.361954 0.932196i \(-0.617890\pi\)
0.988282 0.152637i \(-0.0487766\pi\)
\(564\) 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 −0.998042 0.0625539i \(-0.980075\pi\)
0.444848 0.895606i \(-0.353258\pi\)
\(570\) 0 0
\(571\) −3236.25 + 5605.35i −0.237186 + 0.410817i −0.959906 0.280323i \(-0.909558\pi\)
0.722720 + 0.691141i \(0.242892\pi\)
\(572\) −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 −0.987544 0.157342i \(-0.949708\pi\)
0.630034 + 0.776567i \(0.283041\pi\)
\(578\) −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 \(-0.487550\pi\)
0.0391039 + 0.999235i \(0.487550\pi\)
\(588\) 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 \(-0.175026\pi\)
−0.878856 + 0.477087i \(0.841693\pi\)
\(594\) 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 0.380076 + 0.924955i \(0.375898\pi\)
−0.991073 + 0.133323i \(0.957435\pi\)
\(600\) 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 0.838505 0.544894i \(-0.183430\pi\)
−0.891144 + 0.453720i \(0.850097\pi\)
\(608\) −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 −0.767688 0.640824i \(-0.778593\pi\)
0.938814 + 0.344425i \(0.111926\pi\)
\(614\) 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 \(-0.482339\pi\)
0.0554550 + 0.998461i \(0.482339\pi\)
\(618\) 0 0
\(619\) 6362.04 11019.4i 0.413105 0.715518i −0.582123 0.813101i \(-0.697778\pi\)
0.995227 + 0.0975825i \(0.0311110\pi\)
\(620\) 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 −0.0665155 0.997785i \(-0.521188\pi\)
0.897365 0.441289i \(-0.145478\pi\)
\(642\) 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 0.0770625 + 0.997026i \(0.475446\pi\)
−0.901981 + 0.431775i \(0.857887\pi\)
\(648\) 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 \(-0.290322\pi\)
−0.990884 + 0.134714i \(0.956988\pi\)
\(654\) 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 \(-0.391009\pi\)
0.335753 + 0.941950i \(0.391009\pi\)
\(660\) 0 0
\(661\) −2078.99 + 3600.91i −0.122335 + 0.211890i −0.920688 0.390300i \(-0.872371\pi\)
0.798353 + 0.602189i \(0.205705\pi\)
\(662\) 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 \(-0.0598158\pi\)
−0.652983 + 0.757373i \(0.726483\pi\)
\(678\) 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 −0.484474 0.874806i \(-0.660989\pi\)
0.999841 0.0178364i \(-0.00567781\pi\)
\(684\) 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 0.866597 0.499008i \(-0.166302\pi\)
−0.865453 + 0.500991i \(0.832969\pi\)
\(692\) 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 \(-0.794582\pi\)
−0.798896 + 0.601469i \(0.794582\pi\)
\(702\) 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 0.958325 0.285680i \(-0.0922194\pi\)
−0.726569 + 0.687094i \(0.758886\pi\)
\(710\) 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 \(-0.331469\pi\)
−0.999983 + 0.00585789i \(0.998135\pi\)
\(720\) 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 0.701818 0.712356i \(-0.252372\pi\)
−0.967828 + 0.251614i \(0.919039\pi\)
\(734\) 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 −0.0725462 0.997365i \(-0.523112\pi\)
0.900017 0.435856i \(-0.143554\pi\)
\(740\) −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 \(-0.199597\pi\)
0.809761 + 0.586760i \(0.199597\pi\)
\(744\) 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 0.994419 + 0.105499i \(0.0336439\pi\)
−0.405845 + 0.913942i \(0.633023\pi\)
\(752\) 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 \(-0.233188\pi\)
−0.950915 + 0.309452i \(0.899854\pi\)
\(762\) 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 \(-0.945522\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(774\) 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
\(785\)