Properties

Label 378.4.g.f.163.2
Level $378$
Weight $4$
Character 378.163
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(-1.84763 + 3.20018i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.f.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.04834 + 8.74398i) q^{5} +(-5.48778 - 17.6885i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-5.04834 + 8.74398i) q^{5} +(-5.48778 - 17.6885i) q^{7} -8.00000 q^{8} +(10.0967 + 17.4880i) q^{10} +(18.0748 + 31.3065i) q^{11} -4.01927 q^{13} +(-36.1252 - 8.18341i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(18.9802 + 32.8747i) q^{17} +(-28.5163 + 49.3917i) q^{19} +40.3867 q^{20} +72.2993 q^{22} +(39.2198 - 67.9308i) q^{23} +(11.5285 + 19.9680i) q^{25} +(-4.01927 + 6.96157i) q^{26} +(-50.2993 + 54.3873i) q^{28} +215.332 q^{29} +(91.1642 + 157.901i) q^{31} +(16.0000 + 27.7128i) q^{32} +75.9208 q^{34} +(182.372 + 41.3127i) q^{35} +(-156.279 + 270.683i) q^{37} +(57.0327 + 98.7835i) q^{38} +(40.3867 - 69.9518i) q^{40} +186.557 q^{41} +262.266 q^{43} +(72.2993 - 125.226i) q^{44} +(-78.4397 - 135.862i) q^{46} +(-68.9606 + 119.443i) q^{47} +(-282.768 + 194.142i) q^{49} +46.1142 q^{50} +(8.03853 + 13.9231i) q^{52} +(273.767 + 474.179i) q^{53} -364.991 q^{55} +(43.9023 + 141.508i) q^{56} +(215.332 - 372.967i) q^{58} +(1.86703 + 3.23378i) q^{59} +(57.5008 - 99.5943i) q^{61} +364.657 q^{62} +64.0000 q^{64} +(20.2906 - 35.1444i) q^{65} +(-313.900 - 543.690i) q^{67} +(75.9208 - 131.499i) q^{68} +(253.928 - 274.566i) q^{70} +533.107 q^{71} +(149.197 + 258.417i) q^{73} +(312.557 + 541.365i) q^{74} +228.131 q^{76} +(454.576 - 491.521i) q^{77} +(433.508 - 750.857i) q^{79} +(-80.7734 - 139.904i) q^{80} +(186.557 - 323.126i) q^{82} -244.224 q^{83} -383.274 q^{85} +(262.266 - 454.258i) q^{86} +(-144.599 - 250.452i) q^{88} +(-223.508 + 387.128i) q^{89} +(22.0569 + 71.0949i) q^{91} -313.759 q^{92} +(137.921 + 238.887i) q^{94} +(-287.920 - 498.692i) q^{95} -1803.99 q^{97} +(53.4948 + 683.911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 2 q^{5} + 6 q^{7} - 64 q^{8} + 4 q^{10} + 32 q^{11} - 4 q^{13} + 36 q^{14} - 64 q^{16} - 58 q^{17} + 70 q^{19} + 16 q^{20} + 128 q^{22} + 86 q^{23} - 156 q^{25} - 4 q^{26} + 48 q^{28} - 212 q^{29} - 64 q^{31} + 128 q^{32} - 232 q^{34} + 8 q^{35} - 146 q^{37} - 140 q^{38} + 16 q^{40} - 780 q^{41} + 880 q^{43} + 128 q^{44} - 172 q^{46} - 306 q^{47} + 50 q^{49} - 624 q^{50} + 8 q^{52} - 90 q^{53} - 64 q^{55} - 48 q^{56} - 212 q^{58} + 148 q^{59} - 364 q^{61} - 256 q^{62} + 512 q^{64} + 1296 q^{65} - 954 q^{67} - 232 q^{68} + 20 q^{70} - 1360 q^{71} - 54 q^{73} + 292 q^{74} - 560 q^{76} + 2224 q^{77} - 226 q^{79} - 32 q^{80} - 780 q^{82} - 3136 q^{83} + 3920 q^{85} + 880 q^{86} - 256 q^{88} - 1458 q^{89} + 3836 q^{91} - 688 q^{92} + 612 q^{94} + 1310 q^{95} - 4344 q^{97} + 776 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −5.04834 + 8.74398i −0.451537 + 0.782085i −0.998482 0.0550835i \(-0.982458\pi\)
0.546945 + 0.837169i \(0.315791\pi\)
\(6\) 0 0
\(7\) −5.48778 17.6885i −0.296312 0.955091i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 10.0967 + 17.4880i 0.319285 + 0.553018i
\(11\) 18.0748 + 31.3065i 0.495433 + 0.858116i 0.999986 0.00526523i \(-0.00167598\pi\)
−0.504553 + 0.863381i \(0.668343\pi\)
\(12\) 0 0
\(13\) −4.01927 −0.0857495 −0.0428748 0.999080i \(-0.513652\pi\)
−0.0428748 + 0.999080i \(0.513652\pi\)
\(14\) −36.1252 8.18341i −0.689634 0.156222i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 18.9802 + 32.8747i 0.270787 + 0.469017i 0.969064 0.246811i \(-0.0793828\pi\)
−0.698277 + 0.715828i \(0.746049\pi\)
\(18\) 0 0
\(19\) −28.5163 + 49.3917i −0.344321 + 0.596381i −0.985230 0.171236i \(-0.945224\pi\)
0.640909 + 0.767617i \(0.278557\pi\)
\(20\) 40.3867 0.451537
\(21\) 0 0
\(22\) 72.2993 0.700648
\(23\) 39.2198 67.9308i 0.355561 0.615850i −0.631653 0.775251i \(-0.717623\pi\)
0.987214 + 0.159402i \(0.0509565\pi\)
\(24\) 0 0
\(25\) 11.5285 + 19.9680i 0.0922284 + 0.159744i
\(26\) −4.01927 + 6.96157i −0.0303170 + 0.0525107i
\(27\) 0 0
\(28\) −50.2993 + 54.3873i −0.339488 + 0.367080i
\(29\) 215.332 1.37884 0.689418 0.724364i \(-0.257866\pi\)
0.689418 + 0.724364i \(0.257866\pi\)
\(30\) 0 0
\(31\) 91.1642 + 157.901i 0.528180 + 0.914834i 0.999460 + 0.0328507i \(0.0104586\pi\)
−0.471281 + 0.881983i \(0.656208\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 75.9208 0.382950
\(35\) 182.372 + 41.3127i 0.880759 + 0.199518i
\(36\) 0 0
\(37\) −156.279 + 270.683i −0.694380 + 1.20270i 0.276010 + 0.961155i \(0.410988\pi\)
−0.970389 + 0.241546i \(0.922346\pi\)
\(38\) 57.0327 + 98.7835i 0.243472 + 0.421705i
\(39\) 0 0
\(40\) 40.3867 69.9518i 0.159642 0.276509i
\(41\) 186.557 0.710617 0.355308 0.934749i \(-0.384376\pi\)
0.355308 + 0.934749i \(0.384376\pi\)
\(42\) 0 0
\(43\) 262.266 0.930121 0.465061 0.885279i \(-0.346033\pi\)
0.465061 + 0.885279i \(0.346033\pi\)
\(44\) 72.2993 125.226i 0.247717 0.429058i
\(45\) 0 0
\(46\) −78.4397 135.862i −0.251420 0.435472i
\(47\) −68.9606 + 119.443i −0.214020 + 0.370693i −0.952969 0.303068i \(-0.901989\pi\)
0.738949 + 0.673761i \(0.235322\pi\)
\(48\) 0 0
\(49\) −282.768 + 194.142i −0.824398 + 0.566011i
\(50\) 46.1142 0.130431
\(51\) 0 0
\(52\) 8.03853 + 13.9231i 0.0214374 + 0.0371306i
\(53\) 273.767 + 474.179i 0.709526 + 1.22893i 0.965033 + 0.262127i \(0.0844241\pi\)
−0.255508 + 0.966807i \(0.582243\pi\)
\(54\) 0 0
\(55\) −364.991 −0.894826
\(56\) 43.9023 + 141.508i 0.104762 + 0.337676i
\(57\) 0 0
\(58\) 215.332 372.967i 0.487492 0.844361i
\(59\) 1.86703 + 3.23378i 0.00411976 + 0.00713564i 0.868078 0.496428i \(-0.165355\pi\)
−0.863958 + 0.503564i \(0.832022\pi\)
\(60\) 0 0
\(61\) 57.5008 99.5943i 0.120692 0.209045i −0.799349 0.600868i \(-0.794822\pi\)
0.920041 + 0.391822i \(0.128155\pi\)
\(62\) 364.657 0.746959
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 20.2906 35.1444i 0.0387191 0.0670635i
\(66\) 0 0
\(67\) −313.900 543.690i −0.572373 0.991378i −0.996322 0.0856924i \(-0.972690\pi\)
0.423949 0.905686i \(-0.360644\pi\)
\(68\) 75.9208 131.499i 0.135393 0.234508i
\(69\) 0 0
\(70\) 253.928 274.566i 0.433574 0.468812i
\(71\) 533.107 0.891100 0.445550 0.895257i \(-0.353008\pi\)
0.445550 + 0.895257i \(0.353008\pi\)
\(72\) 0 0
\(73\) 149.197 + 258.417i 0.239208 + 0.414320i 0.960487 0.278324i \(-0.0897789\pi\)
−0.721279 + 0.692644i \(0.756446\pi\)
\(74\) 312.557 + 541.365i 0.491001 + 0.850438i
\(75\) 0 0
\(76\) 228.131 0.344321
\(77\) 454.576 491.521i 0.672775 0.727454i
\(78\) 0 0
\(79\) 433.508 750.857i 0.617385 1.06934i −0.372576 0.928002i \(-0.621525\pi\)
0.989961 0.141340i \(-0.0451412\pi\)
\(80\) −80.7734 139.904i −0.112884 0.195521i
\(81\) 0 0
\(82\) 186.557 323.126i 0.251241 0.435162i
\(83\) −244.224 −0.322977 −0.161489 0.986875i \(-0.551630\pi\)
−0.161489 + 0.986875i \(0.551630\pi\)
\(84\) 0 0
\(85\) −383.274 −0.489081
\(86\) 262.266 454.258i 0.328847 0.569580i
\(87\) 0 0
\(88\) −144.599 250.452i −0.175162 0.303390i
\(89\) −223.508 + 387.128i −0.266200 + 0.461073i −0.967877 0.251423i \(-0.919102\pi\)
0.701677 + 0.712495i \(0.252435\pi\)
\(90\) 0 0
\(91\) 22.0569 + 71.0949i 0.0254087 + 0.0818986i
\(92\) −313.759 −0.355561
\(93\) 0 0
\(94\) 137.921 + 238.887i 0.151335 + 0.262120i
\(95\) −287.920 498.692i −0.310947 0.538576i
\(96\) 0 0
\(97\) −1803.99 −1.88832 −0.944162 0.329481i \(-0.893126\pi\)
−0.944162 + 0.329481i \(0.893126\pi\)
\(98\) 53.4948 + 683.911i 0.0551407 + 0.704954i
\(99\) 0 0
\(100\) 46.1142 79.8721i 0.0461142 0.0798721i
\(101\) 842.134 + 1458.62i 0.829658 + 1.43701i 0.898307 + 0.439369i \(0.144798\pi\)
−0.0686484 + 0.997641i \(0.521869\pi\)
\(102\) 0 0
\(103\) −820.532 + 1421.20i −0.784946 + 1.35957i 0.144085 + 0.989565i \(0.453976\pi\)
−0.929031 + 0.370001i \(0.879357\pi\)
\(104\) 32.1541 0.0303170
\(105\) 0 0
\(106\) 1095.07 1.00342
\(107\) 160.547 278.076i 0.145053 0.251239i −0.784340 0.620332i \(-0.786998\pi\)
0.929393 + 0.369092i \(0.120331\pi\)
\(108\) 0 0
\(109\) −280.005 484.982i −0.246051 0.426173i 0.716376 0.697715i \(-0.245800\pi\)
−0.962427 + 0.271542i \(0.912466\pi\)
\(110\) −364.991 + 632.184i −0.316369 + 0.547967i
\(111\) 0 0
\(112\) 289.002 + 65.4673i 0.243822 + 0.0552329i
\(113\) −1870.65 −1.55731 −0.778655 0.627452i \(-0.784098\pi\)
−0.778655 + 0.627452i \(0.784098\pi\)
\(114\) 0 0
\(115\) 395.990 + 685.875i 0.321098 + 0.556158i
\(116\) −430.665 745.934i −0.344709 0.597053i
\(117\) 0 0
\(118\) 7.46811 0.00582623
\(119\) 477.346 516.141i 0.367716 0.397602i
\(120\) 0 0
\(121\) 12.1012 20.9598i 0.00909179 0.0157474i
\(122\) −115.002 199.189i −0.0853423 0.147817i
\(123\) 0 0
\(124\) 364.657 631.604i 0.264090 0.457417i
\(125\) −1494.88 −1.06965
\(126\) 0 0
\(127\) 790.048 0.552011 0.276006 0.961156i \(-0.410989\pi\)
0.276006 + 0.961156i \(0.410989\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −40.5812 70.2888i −0.0273785 0.0474210i
\(131\) 819.041 1418.62i 0.546259 0.946148i −0.452267 0.891882i \(-0.649385\pi\)
0.998527 0.0542661i \(-0.0172819\pi\)
\(132\) 0 0
\(133\) 1030.16 + 233.361i 0.671625 + 0.152143i
\(134\) −1255.60 −0.809457
\(135\) 0 0
\(136\) −151.842 262.997i −0.0957376 0.165822i
\(137\) 994.660 + 1722.80i 0.620289 + 1.07437i 0.989432 + 0.144999i \(0.0463178\pi\)
−0.369143 + 0.929373i \(0.620349\pi\)
\(138\) 0 0
\(139\) −655.628 −0.400069 −0.200035 0.979789i \(-0.564105\pi\)
−0.200035 + 0.979789i \(0.564105\pi\)
\(140\) −221.634 714.382i −0.133796 0.431259i
\(141\) 0 0
\(142\) 533.107 923.368i 0.315052 0.545685i
\(143\) −72.6475 125.829i −0.0424832 0.0735830i
\(144\) 0 0
\(145\) −1087.07 + 1882.86i −0.622596 + 1.07837i
\(146\) 596.788 0.338291
\(147\) 0 0
\(148\) 1250.23 0.694380
\(149\) 1494.77 2589.01i 0.821853 1.42349i −0.0824482 0.996595i \(-0.526274\pi\)
0.904301 0.426895i \(-0.140393\pi\)
\(150\) 0 0
\(151\) 547.979 + 949.128i 0.295324 + 0.511516i 0.975060 0.221940i \(-0.0712391\pi\)
−0.679736 + 0.733457i \(0.737906\pi\)
\(152\) 228.131 395.134i 0.121736 0.210853i
\(153\) 0 0
\(154\) −396.763 1278.87i −0.207611 0.669183i
\(155\) −1840.91 −0.953971
\(156\) 0 0
\(157\) −250.513 433.901i −0.127345 0.220567i 0.795302 0.606213i \(-0.207312\pi\)
−0.922647 + 0.385646i \(0.873979\pi\)
\(158\) −867.015 1501.71i −0.436557 0.756139i
\(159\) 0 0
\(160\) −323.094 −0.159642
\(161\) −1416.83 320.952i −0.693550 0.157109i
\(162\) 0 0
\(163\) −1134.21 + 1964.50i −0.545018 + 0.943998i 0.453588 + 0.891211i \(0.350144\pi\)
−0.998606 + 0.0527870i \(0.983190\pi\)
\(164\) −373.114 646.252i −0.177654 0.307706i
\(165\) 0 0
\(166\) −244.224 + 423.009i −0.114190 + 0.197782i
\(167\) −1369.97 −0.634799 −0.317400 0.948292i \(-0.602810\pi\)
−0.317400 + 0.948292i \(0.602810\pi\)
\(168\) 0 0
\(169\) −2180.85 −0.992647
\(170\) −383.274 + 663.850i −0.172916 + 0.299500i
\(171\) 0 0
\(172\) −524.532 908.516i −0.232530 0.402754i
\(173\) −921.885 + 1596.75i −0.405142 + 0.701727i −0.994338 0.106264i \(-0.966111\pi\)
0.589196 + 0.807990i \(0.299445\pi\)
\(174\) 0 0
\(175\) 289.939 313.503i 0.125242 0.135421i
\(176\) −578.395 −0.247717
\(177\) 0 0
\(178\) 447.017 + 774.255i 0.188232 + 0.326028i
\(179\) −530.785 919.346i −0.221635 0.383884i 0.733669 0.679507i \(-0.237806\pi\)
−0.955305 + 0.295623i \(0.904473\pi\)
\(180\) 0 0
\(181\) 2441.54 1.00264 0.501320 0.865262i \(-0.332848\pi\)
0.501320 + 0.865262i \(0.332848\pi\)
\(182\) 145.197 + 32.8913i 0.0591358 + 0.0133960i
\(183\) 0 0
\(184\) −313.759 + 543.446i −0.125710 + 0.217736i
\(185\) −1577.90 2732.99i −0.627077 1.08613i
\(186\) 0 0
\(187\) −686.128 + 1188.41i −0.268314 + 0.464733i
\(188\) 551.685 0.214020
\(189\) 0 0
\(190\) −1151.68 −0.439746
\(191\) −1846.08 + 3197.50i −0.699359 + 1.21132i 0.269331 + 0.963048i \(0.413198\pi\)
−0.968689 + 0.248277i \(0.920136\pi\)
\(192\) 0 0
\(193\) −1571.16 2721.33i −0.585982 1.01495i −0.994752 0.102313i \(-0.967376\pi\)
0.408770 0.912637i \(-0.365958\pi\)
\(194\) −1803.99 + 3124.60i −0.667623 + 1.15636i
\(195\) 0 0
\(196\) 1238.06 + 591.255i 0.451189 + 0.215472i
\(197\) −2273.51 −0.822236 −0.411118 0.911582i \(-0.634862\pi\)
−0.411118 + 0.911582i \(0.634862\pi\)
\(198\) 0 0
\(199\) 1368.26 + 2369.89i 0.487403 + 0.844206i 0.999895 0.0144854i \(-0.00461100\pi\)
−0.512492 + 0.858692i \(0.671278\pi\)
\(200\) −92.2284 159.744i −0.0326076 0.0564781i
\(201\) 0 0
\(202\) 3368.54 1.17331
\(203\) −1181.70 3808.92i −0.408566 1.31691i
\(204\) 0 0
\(205\) −941.803 + 1631.25i −0.320870 + 0.555763i
\(206\) 1641.06 + 2842.41i 0.555041 + 0.961359i
\(207\) 0 0
\(208\) 32.1541 55.6926i 0.0107187 0.0185653i
\(209\) −2061.71 −0.682352
\(210\) 0 0
\(211\) 2915.84 0.951349 0.475675 0.879621i \(-0.342204\pi\)
0.475675 + 0.879621i \(0.342204\pi\)
\(212\) 1095.07 1896.72i 0.354763 0.614467i
\(213\) 0 0
\(214\) −321.094 556.151i −0.102568 0.177653i
\(215\) −1324.01 + 2293.25i −0.419984 + 0.727434i
\(216\) 0 0
\(217\) 2292.75 2479.09i 0.717244 0.775536i
\(218\) −1120.02 −0.347969
\(219\) 0 0
\(220\) 729.983 + 1264.37i 0.223707 + 0.387471i
\(221\) −76.2865 132.132i −0.0232198 0.0402179i
\(222\) 0 0
\(223\) −1875.11 −0.563078 −0.281539 0.959550i \(-0.590845\pi\)
−0.281539 + 0.959550i \(0.590845\pi\)
\(224\) 402.395 435.098i 0.120027 0.129782i
\(225\) 0 0
\(226\) −1870.65 + 3240.06i −0.550592 + 0.953654i
\(227\) 2019.15 + 3497.27i 0.590377 + 1.02256i 0.994182 + 0.107717i \(0.0343542\pi\)
−0.403805 + 0.914845i \(0.632312\pi\)
\(228\) 0 0
\(229\) −686.456 + 1188.98i −0.198089 + 0.343099i −0.947909 0.318542i \(-0.896807\pi\)
0.749820 + 0.661642i \(0.230140\pi\)
\(230\) 1583.96 0.454101
\(231\) 0 0
\(232\) −1722.66 −0.487492
\(233\) 2087.15 3615.06i 0.586841 1.01644i −0.407802 0.913070i \(-0.633705\pi\)
0.994643 0.103368i \(-0.0329620\pi\)
\(234\) 0 0
\(235\) −696.273 1205.98i −0.193276 0.334764i
\(236\) 7.46811 12.9351i 0.00205988 0.00356782i
\(237\) 0 0
\(238\) −416.637 1342.93i −0.113473 0.365753i
\(239\) −5544.70 −1.50066 −0.750329 0.661065i \(-0.770105\pi\)
−0.750329 + 0.661065i \(0.770105\pi\)
\(240\) 0 0
\(241\) −2445.07 4234.98i −0.653530 1.13195i −0.982260 0.187524i \(-0.939954\pi\)
0.328730 0.944424i \(-0.393379\pi\)
\(242\) −24.2023 41.9197i −0.00642887 0.0111351i
\(243\) 0 0
\(244\) −460.007 −0.120692
\(245\) −270.060 3452.61i −0.0704224 0.900324i
\(246\) 0 0
\(247\) 114.615 198.519i 0.0295253 0.0511394i
\(248\) −729.313 1263.21i −0.186740 0.323443i
\(249\) 0 0
\(250\) −1494.88 + 2589.22i −0.378179 + 0.655026i
\(251\) 7560.15 1.90117 0.950583 0.310470i \(-0.100487\pi\)
0.950583 + 0.310470i \(0.100487\pi\)
\(252\) 0 0
\(253\) 2835.57 0.704627
\(254\) 790.048 1368.40i 0.195165 0.338037i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1616.43 2799.74i 0.392335 0.679545i −0.600422 0.799683i \(-0.705001\pi\)
0.992757 + 0.120139i \(0.0383340\pi\)
\(258\) 0 0
\(259\) 5645.60 + 1278.89i 1.35444 + 0.306821i
\(260\) −162.325 −0.0387191
\(261\) 0 0
\(262\) −1638.08 2837.24i −0.386263 0.669028i
\(263\) 2142.26 + 3710.51i 0.502272 + 0.869961i 0.999997 + 0.00262575i \(0.000835803\pi\)
−0.497724 + 0.867335i \(0.665831\pi\)
\(264\) 0 0
\(265\) −5528.28 −1.28151
\(266\) 1434.35 1550.93i 0.330623 0.357494i
\(267\) 0 0
\(268\) −1255.60 + 2174.76i −0.286186 + 0.495689i
\(269\) 3348.26 + 5799.36i 0.758912 + 1.31447i 0.943406 + 0.331640i \(0.107602\pi\)
−0.184495 + 0.982834i \(0.559065\pi\)
\(270\) 0 0
\(271\) 3157.89 5469.63i 0.707854 1.22604i −0.257798 0.966199i \(-0.582997\pi\)
0.965652 0.259840i \(-0.0836698\pi\)
\(272\) −607.367 −0.135393
\(273\) 0 0
\(274\) 3978.64 0.877221
\(275\) −416.753 + 721.837i −0.0913860 + 0.158285i
\(276\) 0 0
\(277\) −1377.62 2386.12i −0.298821 0.517573i 0.677045 0.735941i \(-0.263260\pi\)
−0.975866 + 0.218368i \(0.929927\pi\)
\(278\) −655.628 + 1135.58i −0.141446 + 0.244991i
\(279\) 0 0
\(280\) −1458.98 330.501i −0.311395 0.0705401i
\(281\) 1453.00 0.308464 0.154232 0.988035i \(-0.450710\pi\)
0.154232 + 0.988035i \(0.450710\pi\)
\(282\) 0 0
\(283\) −2715.92 4704.11i −0.570476 0.988093i −0.996517 0.0833890i \(-0.973426\pi\)
0.426042 0.904704i \(-0.359908\pi\)
\(284\) −1066.21 1846.74i −0.222775 0.385858i
\(285\) 0 0
\(286\) −290.590 −0.0600803
\(287\) −1023.78 3299.92i −0.210565 0.678704i
\(288\) 0 0
\(289\) 1736.00 3006.85i 0.353349 0.612018i
\(290\) 2174.14 + 3765.73i 0.440242 + 0.762521i
\(291\) 0 0
\(292\) 596.788 1033.67i 0.119604 0.207160i
\(293\) 6227.21 1.24163 0.620815 0.783957i \(-0.286802\pi\)
0.620815 + 0.783957i \(0.286802\pi\)
\(294\) 0 0
\(295\) −37.7015 −0.00744091
\(296\) 1250.23 2165.46i 0.245500 0.425219i
\(297\) 0 0
\(298\) −2989.53 5178.02i −0.581138 1.00656i
\(299\) −157.635 + 273.032i −0.0304892 + 0.0528088i
\(300\) 0 0
\(301\) −1439.26 4639.10i −0.275606 0.888350i
\(302\) 2191.92 0.417651
\(303\) 0 0
\(304\) −456.261 790.268i −0.0860802 0.149095i
\(305\) 580.567 + 1005.57i 0.108994 + 0.188783i
\(306\) 0 0
\(307\) 8621.61 1.60281 0.801403 0.598125i \(-0.204088\pi\)
0.801403 + 0.598125i \(0.204088\pi\)
\(308\) −2611.83 591.655i −0.483191 0.109457i
\(309\) 0 0
\(310\) −1840.91 + 3188.55i −0.337280 + 0.584186i
\(311\) 3712.11 + 6429.56i 0.676831 + 1.17230i 0.975930 + 0.218083i \(0.0699804\pi\)
−0.299100 + 0.954222i \(0.596686\pi\)
\(312\) 0 0
\(313\) −1633.30 + 2828.96i −0.294951 + 0.510870i −0.974974 0.222321i \(-0.928637\pi\)
0.680022 + 0.733191i \(0.261970\pi\)
\(314\) −1002.05 −0.180092
\(315\) 0 0
\(316\) −3468.06 −0.617385
\(317\) 2440.25 4226.63i 0.432359 0.748868i −0.564717 0.825285i \(-0.691015\pi\)
0.997076 + 0.0764167i \(0.0243479\pi\)
\(318\) 0 0
\(319\) 3892.10 + 6741.31i 0.683121 + 1.18320i
\(320\) −323.094 + 559.615i −0.0564421 + 0.0977607i
\(321\) 0 0
\(322\) −1972.73 + 2133.06i −0.341416 + 0.369164i
\(323\) −2164.98 −0.372950
\(324\) 0 0
\(325\) −46.3363 80.2568i −0.00790854 0.0136980i
\(326\) 2268.41 + 3929.01i 0.385386 + 0.667508i
\(327\) 0 0
\(328\) −1492.46 −0.251241
\(329\) 2491.22 + 564.333i 0.417463 + 0.0945675i
\(330\) 0 0
\(331\) 4799.58 8313.11i 0.797005 1.38045i −0.124554 0.992213i \(-0.539750\pi\)
0.921558 0.388240i \(-0.126917\pi\)
\(332\) 488.449 + 846.018i 0.0807443 + 0.139853i
\(333\) 0 0
\(334\) −1369.97 + 2372.86i −0.224436 + 0.388734i
\(335\) 6338.69 1.03379
\(336\) 0 0
\(337\) −2895.79 −0.468082 −0.234041 0.972227i \(-0.575195\pi\)
−0.234041 + 0.972227i \(0.575195\pi\)
\(338\) −2180.85 + 3777.34i −0.350954 + 0.607870i
\(339\) 0 0
\(340\) 766.548 + 1327.70i 0.122270 + 0.211778i
\(341\) −3295.55 + 5708.07i −0.523356 + 0.906478i
\(342\) 0 0
\(343\) 4985.85 + 3936.35i 0.784871 + 0.619659i
\(344\) −2098.13 −0.328847
\(345\) 0 0
\(346\) 1843.77 + 3193.50i 0.286479 + 0.496196i
\(347\) 2678.81 + 4639.83i 0.414426 + 0.717807i 0.995368 0.0961381i \(-0.0306490\pi\)
−0.580942 + 0.813945i \(0.697316\pi\)
\(348\) 0 0
\(349\) −6049.21 −0.927813 −0.463906 0.885884i \(-0.653553\pi\)
−0.463906 + 0.885884i \(0.653553\pi\)
\(350\) −253.065 815.692i −0.0386482 0.124573i
\(351\) 0 0
\(352\) −578.395 + 1001.81i −0.0875811 + 0.151695i
\(353\) 3440.28 + 5958.74i 0.518718 + 0.898446i 0.999763 + 0.0217505i \(0.00692394\pi\)
−0.481045 + 0.876696i \(0.659743\pi\)
\(354\) 0 0
\(355\) −2691.30 + 4661.47i −0.402365 + 0.696916i
\(356\) 1788.07 0.266200
\(357\) 0 0
\(358\) −2123.14 −0.313440
\(359\) 2995.95 5189.15i 0.440447 0.762876i −0.557276 0.830328i \(-0.688153\pi\)
0.997723 + 0.0674511i \(0.0214867\pi\)
\(360\) 0 0
\(361\) 1803.14 + 3123.13i 0.262886 + 0.455333i
\(362\) 2441.54 4228.86i 0.354487 0.613989i
\(363\) 0 0
\(364\) 202.166 218.597i 0.0291110 0.0314769i
\(365\) −3012.79 −0.432045
\(366\) 0 0
\(367\) 3285.52 + 5690.70i 0.467311 + 0.809406i 0.999302 0.0373437i \(-0.0118896\pi\)
−0.531992 + 0.846749i \(0.678556\pi\)
\(368\) 627.518 + 1086.89i 0.0888903 + 0.153962i
\(369\) 0 0
\(370\) −6311.58 −0.886820
\(371\) 6885.16 7444.74i 0.963503 1.04181i
\(372\) 0 0
\(373\) 1866.81 3233.41i 0.259141 0.448846i −0.706871 0.707343i \(-0.749894\pi\)
0.966012 + 0.258497i \(0.0832272\pi\)
\(374\) 1372.26 + 2376.82i 0.189726 + 0.328616i
\(375\) 0 0
\(376\) 551.685 955.546i 0.0756675 0.131060i
\(377\) −865.479 −0.118235
\(378\) 0 0
\(379\) 8419.14 1.14106 0.570531 0.821276i \(-0.306738\pi\)
0.570531 + 0.821276i \(0.306738\pi\)
\(380\) −1151.68 + 1994.77i −0.155474 + 0.269288i
\(381\) 0 0
\(382\) 3692.15 + 6395.00i 0.494521 + 0.856536i
\(383\) −2665.21 + 4616.28i −0.355577 + 0.615877i −0.987217 0.159385i \(-0.949049\pi\)
0.631640 + 0.775262i \(0.282382\pi\)
\(384\) 0 0
\(385\) 2002.99 + 6456.16i 0.265148 + 0.854640i
\(386\) −6284.64 −0.828704
\(387\) 0 0
\(388\) 3607.98 + 6249.21i 0.472081 + 0.817668i
\(389\) −3905.58 6764.67i −0.509051 0.881703i −0.999945 0.0104832i \(-0.996663\pi\)
0.490894 0.871219i \(-0.336670\pi\)
\(390\) 0 0
\(391\) 2977.60 0.385125
\(392\) 2262.15 1553.13i 0.291469 0.200115i
\(393\) 0 0
\(394\) −2273.51 + 3937.83i −0.290704 + 0.503515i
\(395\) 4376.99 + 7581.16i 0.557544 + 0.965695i
\(396\) 0 0
\(397\) −455.847 + 789.550i −0.0576279 + 0.0998145i −0.893400 0.449262i \(-0.851687\pi\)
0.835772 + 0.549076i \(0.185020\pi\)
\(398\) 5473.03 0.689292
\(399\) 0 0
\(400\) −368.913 −0.0461142
\(401\) −834.008 + 1444.54i −0.103861 + 0.179893i −0.913272 0.407349i \(-0.866453\pi\)
0.809411 + 0.587242i \(0.199786\pi\)
\(402\) 0 0
\(403\) −366.413 634.646i −0.0452912 0.0784466i
\(404\) 3368.54 5834.48i 0.414829 0.718505i
\(405\) 0 0
\(406\) −7778.93 1762.15i −0.950892 0.215405i
\(407\) −11298.8 −1.37608
\(408\) 0 0
\(409\) −4555.24 7889.90i −0.550714 0.953864i −0.998223 0.0595852i \(-0.981022\pi\)
0.447509 0.894279i \(-0.352311\pi\)
\(410\) 1883.61 + 3262.50i 0.226889 + 0.392984i
\(411\) 0 0
\(412\) 6564.26 0.784946
\(413\) 46.9551 50.7713i 0.00559445 0.00604913i
\(414\) 0 0
\(415\) 1232.93 2135.49i 0.145836 0.252596i
\(416\) −64.3083 111.385i −0.00757926 0.0131277i
\(417\) 0 0
\(418\) −2061.71 + 3570.99i −0.241248 + 0.417853i
\(419\) 12626.4 1.47217 0.736085 0.676889i \(-0.236672\pi\)
0.736085 + 0.676889i \(0.236672\pi\)
\(420\) 0 0
\(421\) −4805.61 −0.556320 −0.278160 0.960535i \(-0.589725\pi\)
−0.278160 + 0.960535i \(0.589725\pi\)
\(422\) 2915.84 5050.38i 0.336353 0.582580i
\(423\) 0 0
\(424\) −2190.14 3793.43i −0.250855 0.434494i
\(425\) −437.628 + 757.994i −0.0499484 + 0.0865132i
\(426\) 0 0
\(427\) −2077.23 470.553i −0.235420 0.0533294i
\(428\) −1284.38 −0.145053
\(429\) 0 0
\(430\) 2648.02 + 4586.50i 0.296974 + 0.514374i
\(431\) −3341.06 5786.89i −0.373395 0.646739i 0.616690 0.787206i \(-0.288473\pi\)
−0.990085 + 0.140467i \(0.955140\pi\)
\(432\) 0 0
\(433\) −8502.27 −0.943632 −0.471816 0.881697i \(-0.656401\pi\)
−0.471816 + 0.881697i \(0.656401\pi\)
\(434\) −2001.16 6450.24i −0.221333 0.713414i
\(435\) 0 0
\(436\) −1120.02 + 1939.93i −0.123026 + 0.213087i
\(437\) 2236.81 + 3874.27i 0.244854 + 0.424100i
\(438\) 0 0
\(439\) 6814.77 11803.5i 0.740891 1.28326i −0.211199 0.977443i \(-0.567737\pi\)
0.952090 0.305818i \(-0.0989299\pi\)
\(440\) 2919.93 0.316369
\(441\) 0 0
\(442\) −305.146 −0.0328378
\(443\) 3427.16 5936.02i 0.367561 0.636634i −0.621623 0.783317i \(-0.713526\pi\)
0.989184 + 0.146683i \(0.0468597\pi\)
\(444\) 0 0
\(445\) −2256.69 3908.70i −0.240399 0.416383i
\(446\) −1875.11 + 3247.78i −0.199078 + 0.344813i
\(447\) 0 0
\(448\) −351.218 1132.07i −0.0370391 0.119386i
\(449\) −10372.3 −1.09019 −0.545097 0.838373i \(-0.683507\pi\)
−0.545097 + 0.838373i \(0.683507\pi\)
\(450\) 0 0
\(451\) 3371.98 + 5840.45i 0.352063 + 0.609791i
\(452\) 3741.30 + 6480.13i 0.389328 + 0.674335i
\(453\) 0 0
\(454\) 8076.59 0.834919
\(455\) −733.003 166.047i −0.0755247 0.0171085i
\(456\) 0 0
\(457\) 3950.40 6842.30i 0.404359 0.700370i −0.589888 0.807485i \(-0.700828\pi\)
0.994247 + 0.107115i \(0.0341613\pi\)
\(458\) 1372.91 + 2377.95i 0.140070 + 0.242608i
\(459\) 0 0
\(460\) 1583.96 2743.50i 0.160549 0.278079i
\(461\) −11359.7 −1.14767 −0.573834 0.818972i \(-0.694544\pi\)
−0.573834 + 0.818972i \(0.694544\pi\)
\(462\) 0 0
\(463\) 7346.85 0.737445 0.368723 0.929539i \(-0.379795\pi\)
0.368723 + 0.929539i \(0.379795\pi\)
\(464\) −1722.66 + 2983.73i −0.172354 + 0.298527i
\(465\) 0 0
\(466\) −4174.31 7230.11i −0.414959 0.718731i
\(467\) −473.289 + 819.760i −0.0468976 + 0.0812291i −0.888521 0.458835i \(-0.848267\pi\)
0.841624 + 0.540064i \(0.181600\pi\)
\(468\) 0 0
\(469\) −7894.47 + 8536.08i −0.777256 + 0.840426i
\(470\) −2785.09 −0.273333
\(471\) 0 0
\(472\) −14.9362 25.8703i −0.00145656 0.00252283i
\(473\) 4740.41 + 8210.64i 0.460813 + 0.798151i
\(474\) 0 0
\(475\) −1315.01 −0.127025
\(476\) −2742.66 621.292i −0.264096 0.0598253i
\(477\) 0 0
\(478\) −5544.70 + 9603.71i −0.530562 + 0.918961i
\(479\) −7657.75 13263.6i −0.730462 1.26520i −0.956686 0.291122i \(-0.905971\pi\)
0.226224 0.974075i \(-0.427362\pi\)
\(480\) 0 0
\(481\) 628.125 1087.95i 0.0595427 0.103131i
\(482\) −9780.28 −0.924231
\(483\) 0 0
\(484\) −96.8094 −0.00909179
\(485\) 9107.15 15774.1i 0.852649 1.47683i
\(486\) 0 0
\(487\) 4320.19 + 7482.78i 0.401984 + 0.696257i 0.993965 0.109695i \(-0.0349873\pi\)
−0.591981 + 0.805952i \(0.701654\pi\)
\(488\) −460.007 + 796.755i −0.0426711 + 0.0739086i
\(489\) 0 0
\(490\) −6250.16 2984.86i −0.576232 0.275188i
\(491\) −13425.6 −1.23399 −0.616996 0.786966i \(-0.711651\pi\)
−0.616996 + 0.786966i \(0.711651\pi\)
\(492\) 0 0
\(493\) 4087.05 + 7078.99i 0.373371 + 0.646697i
\(494\) −229.229 397.037i −0.0208776 0.0361610i
\(495\) 0 0
\(496\) −2917.25 −0.264090
\(497\) −2925.57 9429.88i −0.264044 0.851082i
\(498\) 0 0
\(499\) 5489.01 9507.24i 0.492429 0.852911i −0.507533 0.861632i \(-0.669443\pi\)
0.999962 + 0.00872085i \(0.00277597\pi\)
\(500\) 2989.77 + 5178.43i 0.267413 + 0.463173i
\(501\) 0 0
\(502\) 7560.15 13094.6i 0.672164 1.16422i
\(503\) −7829.41 −0.694028 −0.347014 0.937860i \(-0.612804\pi\)
−0.347014 + 0.937860i \(0.612804\pi\)
\(504\) 0 0
\(505\) −17005.5 −1.49849
\(506\) 2835.57 4911.35i 0.249123 0.431494i
\(507\) 0 0
\(508\) −1580.10 2736.81i −0.138003 0.239028i
\(509\) −9091.90 + 15747.6i −0.791732 + 1.37132i 0.133162 + 0.991094i \(0.457487\pi\)
−0.924894 + 0.380225i \(0.875847\pi\)
\(510\) 0 0
\(511\) 3752.25 4057.21i 0.324833 0.351234i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −3232.86 5599.48i −0.277423 0.480511i
\(515\) −8284.65 14349.4i −0.708865 1.22779i
\(516\) 0 0
\(517\) −4985.80 −0.424130
\(518\) 7860.71 8499.57i 0.666756 0.720946i
\(519\) 0 0
\(520\) −162.325 + 281.155i −0.0136893 + 0.0237105i
\(521\) 11202.3 + 19402.9i 0.941997 + 1.63159i 0.761656 + 0.647982i \(0.224387\pi\)
0.180341 + 0.983604i \(0.442280\pi\)
\(522\) 0 0
\(523\) −2843.67 + 4925.38i −0.237753 + 0.411801i −0.960069 0.279763i \(-0.909744\pi\)
0.722316 + 0.691563i \(0.243078\pi\)
\(524\) −6552.33 −0.546259
\(525\) 0 0
\(526\) 8569.05 0.710320
\(527\) −3460.63 + 5993.99i −0.286048 + 0.495450i
\(528\) 0 0
\(529\) 3007.11 + 5208.46i 0.247153 + 0.428081i
\(530\) −5528.28 + 9575.27i −0.453082 + 0.784761i
\(531\) 0 0
\(532\) −1251.93 4035.30i −0.102027 0.328858i
\(533\) −749.822 −0.0609351
\(534\) 0 0
\(535\) 1620.99 + 2807.64i 0.130994 + 0.226888i
\(536\) 2511.20 + 4349.52i 0.202364 + 0.350505i
\(537\) 0 0
\(538\) 13393.1 1.07326
\(539\) −11188.9 5343.42i −0.894137 0.427008i
\(540\) 0 0
\(541\) 6508.78 11273.5i 0.517254 0.895910i −0.482545 0.875871i \(-0.660288\pi\)
0.999799 0.0200392i \(-0.00637910\pi\)
\(542\) −6315.79 10939.3i −0.500528 0.866940i
\(543\) 0 0
\(544\) −607.367 + 1051.99i −0.0478688 + 0.0829112i
\(545\) 5654.23 0.444405
\(546\) 0 0
\(547\) −6353.31 −0.496614 −0.248307 0.968681i \(-0.579874\pi\)
−0.248307 + 0.968681i \(0.579874\pi\)
\(548\) 3978.64 6891.21i 0.310144 0.537186i
\(549\) 0 0
\(550\) 833.506 + 1443.67i 0.0646197 + 0.111925i
\(551\) −6140.49 + 10635.6i −0.474762 + 0.822311i
\(552\) 0 0
\(553\) −15660.6 3547.57i −1.20426 0.272799i
\(554\) −5510.50 −0.422597
\(555\) 0 0
\(556\) 1311.26 + 2271.16i 0.100017 + 0.173235i
\(557\) −7759.69 13440.2i −0.590285 1.02240i −0.994194 0.107604i \(-0.965682\pi\)
0.403909 0.914799i \(-0.367651\pi\)
\(558\) 0 0
\(559\) −1054.12 −0.0797574
\(560\) −2031.42 + 2196.52i −0.153292 + 0.165750i
\(561\) 0 0
\(562\) 1453.00 2516.66i 0.109059 0.188895i
\(563\) −9095.49 15753.9i −0.680869 1.17930i −0.974716 0.223448i \(-0.928269\pi\)
0.293847 0.955853i \(-0.405064\pi\)
\(564\) 0 0
\(565\) 9443.68 16356.9i 0.703184 1.21795i
\(566\) −10863.7 −0.806774
\(567\) 0 0
\(568\) −4264.85 −0.315052
\(569\) 6159.38 10668.4i 0.453804 0.786012i −0.544814 0.838557i \(-0.683400\pi\)
0.998619 + 0.0525449i \(0.0167333\pi\)
\(570\) 0 0
\(571\) 8694.98 + 15060.2i 0.637257 + 1.10376i 0.986032 + 0.166555i \(0.0532644\pi\)
−0.348775 + 0.937206i \(0.613402\pi\)
\(572\) −290.590 + 503.317i −0.0212416 + 0.0367915i
\(573\) 0 0
\(574\) −6739.41 1526.67i −0.490065 0.111014i
\(575\) 1808.59 0.131171
\(576\) 0 0
\(577\) −1625.45 2815.37i −0.117276 0.203129i 0.801411 0.598114i \(-0.204083\pi\)
−0.918687 + 0.394985i \(0.870750\pi\)
\(578\) −3472.01 6013.69i −0.249855 0.432762i
\(579\) 0 0
\(580\) 8696.57 0.622596
\(581\) 1340.25 + 4319.97i 0.0957022 + 0.308473i
\(582\) 0 0
\(583\) −9896.60 + 17141.4i −0.703045 + 1.21771i
\(584\) −1193.58 2067.33i −0.0845728 0.146484i
\(585\) 0 0
\(586\) 6227.21 10785.8i 0.438982 0.760339i
\(587\) 6993.54 0.491745 0.245872 0.969302i \(-0.420926\pi\)
0.245872 + 0.969302i \(0.420926\pi\)
\(588\) 0 0
\(589\) −10398.7 −0.727453
\(590\) −37.7015 + 65.3010i −0.00263076 + 0.00455661i
\(591\) 0 0
\(592\) −2500.46 4330.92i −0.173595 0.300675i
\(593\) 5001.10 8662.15i 0.346324 0.599851i −0.639269 0.768983i \(-0.720763\pi\)
0.985593 + 0.169132i \(0.0540963\pi\)
\(594\) 0 0
\(595\) 2103.32 + 6779.56i 0.144921 + 0.467117i
\(596\) −11958.1 −0.821853
\(597\) 0 0
\(598\) 315.270 + 546.064i 0.0215591 + 0.0373415i
\(599\) 12362.1 + 21411.8i 0.843241 + 1.46054i 0.887140 + 0.461500i \(0.152688\pi\)
−0.0438997 + 0.999036i \(0.513978\pi\)
\(600\) 0 0
\(601\) −4825.50 −0.327515 −0.163757 0.986501i \(-0.552361\pi\)
−0.163757 + 0.986501i \(0.552361\pi\)
\(602\) −9474.42 2146.23i −0.641443 0.145305i
\(603\) 0 0
\(604\) 2191.92 3796.51i 0.147662 0.255758i
\(605\) 122.182 + 211.625i 0.00821056 + 0.0142211i
\(606\) 0 0
\(607\) −12365.1 + 21417.0i −0.826826 + 1.43210i 0.0736896 + 0.997281i \(0.476523\pi\)
−0.900516 + 0.434824i \(0.856811\pi\)
\(608\) −1825.04 −0.121736
\(609\) 0 0
\(610\) 2322.27 0.154141
\(611\) 277.171 480.074i 0.0183521 0.0317868i
\(612\) 0 0
\(613\) 3804.29 + 6589.22i 0.250659 + 0.434154i 0.963707 0.266961i \(-0.0860195\pi\)
−0.713049 + 0.701115i \(0.752686\pi\)
\(614\) 8621.61 14933.1i 0.566677 0.981514i
\(615\) 0 0
\(616\) −3636.61 + 3932.16i −0.237862 + 0.257194i
\(617\) −25089.8 −1.63708 −0.818538 0.574452i \(-0.805215\pi\)
−0.818538 + 0.574452i \(0.805215\pi\)
\(618\) 0 0
\(619\) −11452.5 19836.3i −0.743642 1.28803i −0.950827 0.309724i \(-0.899763\pi\)
0.207185 0.978302i \(-0.433570\pi\)
\(620\) 3681.82 + 6377.10i 0.238493 + 0.413082i
\(621\) 0 0
\(622\) 14848.4 0.957183
\(623\) 8074.29 + 1829.06i 0.519245 + 0.117624i
\(624\) 0 0
\(625\) 6105.62 10575.2i 0.390760 0.676815i
\(626\) 3266.61 + 5657.93i 0.208562 + 0.361240i
\(627\) 0 0
\(628\) −1002.05 + 1735.60i −0.0636723 + 0.110284i
\(629\) −11864.8 −0.752116
\(630\) 0 0
\(631\) 2253.93 0.142199 0.0710996 0.997469i \(-0.477349\pi\)
0.0710996 + 0.997469i \(0.477349\pi\)
\(632\) −3468.06 + 6006.86i −0.218279 + 0.378070i
\(633\) 0 0
\(634\) −4880.49 8453.26i −0.305724 0.529530i
\(635\) −3988.43 + 6908.17i −0.249254 + 0.431720i
\(636\) 0 0
\(637\) 1136.52 780.307i 0.0706917 0.0485352i
\(638\) 15568.4 0.966079
\(639\) 0 0
\(640\) 646.187 + 1119.23i 0.0399106 + 0.0691272i
\(641\) 6014.77 + 10417.9i 0.370623 + 0.641938i 0.989661 0.143423i \(-0.0458109\pi\)
−0.619039 + 0.785361i \(0.712478\pi\)
\(642\) 0 0
\(643\) −4738.59 −0.290625 −0.145312 0.989386i \(-0.546419\pi\)
−0.145312 + 0.989386i \(0.546419\pi\)
\(644\) 1721.84 + 5549.93i 0.105357 + 0.339593i
\(645\) 0 0
\(646\) −2164.98 + 3749.86i −0.131858 + 0.228384i
\(647\) −2869.84 4970.71i −0.174382 0.302038i 0.765565 0.643358i \(-0.222459\pi\)
−0.939947 + 0.341320i \(0.889126\pi\)
\(648\) 0 0
\(649\) −67.4924 + 116.900i −0.00408214 + 0.00707047i
\(650\) −185.345 −0.0111844
\(651\) 0 0
\(652\) 9073.65 0.545018
\(653\) −863.084 + 1494.91i −0.0517230 + 0.0895868i −0.890728 0.454537i \(-0.849805\pi\)
0.839005 + 0.544124i \(0.183138\pi\)
\(654\) 0 0
\(655\) 8269.59 + 14323.4i 0.493313 + 0.854442i
\(656\) −1492.46 + 2585.01i −0.0888271 + 0.153853i
\(657\) 0 0
\(658\) 3468.67 3750.58i 0.205506 0.222208i
\(659\) −10987.7 −0.649501 −0.324751 0.945800i \(-0.605280\pi\)
−0.324751 + 0.945800i \(0.605280\pi\)
\(660\) 0 0
\(661\) −16020.4 27748.1i −0.942695 1.63280i −0.760302 0.649570i \(-0.774949\pi\)
−0.182393 0.983226i \(-0.558384\pi\)
\(662\) −9599.15 16626.2i −0.563567 0.976127i
\(663\) 0 0
\(664\) 1953.80 0.114190
\(665\) −7241.09 + 7829.60i −0.422252 + 0.456570i
\(666\) 0 0
\(667\) 8445.31 14627.7i 0.490260 0.849156i
\(668\) 2739.94 + 4745.72i 0.158700 + 0.274876i
\(669\) 0 0
\(670\) 6338.69 10978.9i 0.365500 0.633065i
\(671\) 4157.27 0.239180
\(672\) 0 0
\(673\) −13026.7 −0.746124 −0.373062 0.927806i \(-0.621692\pi\)
−0.373062 + 0.927806i \(0.621692\pi\)
\(674\) −2895.79 + 5015.65i −0.165492 + 0.286641i
\(675\) 0 0
\(676\) 4361.69 + 7554.67i 0.248162 + 0.429829i
\(677\) 2360.39 4088.32i 0.133999 0.232093i −0.791216 0.611537i \(-0.790551\pi\)
0.925215 + 0.379444i \(0.123885\pi\)
\(678\) 0 0
\(679\) 9899.91 + 31909.9i 0.559534 + 1.80352i
\(680\) 3066.19 0.172916
\(681\) 0 0
\(682\) 6591.11 + 11416.1i 0.370068 + 0.640977i
\(683\) 5585.00 + 9673.51i 0.312890 + 0.541942i 0.978987 0.203924i \(-0.0653694\pi\)
−0.666096 + 0.745866i \(0.732036\pi\)
\(684\) 0 0
\(685\) −20085.5 −1.12033
\(686\) 11803.8 4699.40i 0.656956 0.261551i
\(687\) 0 0
\(688\) −2098.13 + 3634.07i −0.116265 + 0.201377i
\(689\) −1100.34 1905.85i −0.0608415 0.105381i
\(690\) 0 0
\(691\) 6986.42 12100.8i 0.384625 0.666190i −0.607092 0.794632i \(-0.707664\pi\)
0.991717 + 0.128441i \(0.0409974\pi\)
\(692\) 7375.08 0.405142
\(693\) 0 0
\(694\) 10715.2 0.586087
\(695\) 3309.83 5732.79i 0.180646 0.312888i
\(696\) 0 0
\(697\) 3540.89 + 6133.00i 0.192426 + 0.333291i
\(698\) −6049.21 + 10477.5i −0.328031 + 0.568167i
\(699\) 0 0
\(700\) −1665.88 377.371i −0.0899493 0.0203761i
\(701\) 9694.83 0.522352 0.261176 0.965291i \(-0.415890\pi\)
0.261176 + 0.965291i \(0.415890\pi\)
\(702\) 0 0
\(703\) −8912.99 15437.7i −0.478179 0.828230i
\(704\) 1156.79 + 2003.62i 0.0619292 + 0.107264i
\(705\) 0 0
\(706\) 13761.1 0.733578
\(707\) 21179.4 22900.7i 1.12664 1.21820i
\(708\) 0 0
\(709\) −12712.8 + 22019.3i −0.673399 + 1.16636i 0.303535 + 0.952820i \(0.401833\pi\)
−0.976934 + 0.213541i \(0.931500\pi\)
\(710\) 5382.61 + 9322.95i 0.284515 + 0.492794i
\(711\) 0 0
\(712\) 1788.07 3097.02i 0.0941160 0.163014i
\(713\) 14301.8 0.751200
\(714\) 0 0
\(715\) 1467.00 0.0767309
\(716\) −2123.14 + 3677.39i −0.110818 + 0.191942i
\(717\) 0 0
\(718\) −5991.91 10378.3i −0.311443 0.539435i
\(719\) 8796.40 15235.8i 0.456259 0.790264i −0.542500 0.840056i \(-0.682522\pi\)
0.998760 + 0.0497912i \(0.0158556\pi\)
\(720\) 0 0
\(721\) 29641.9 + 6714.76i 1.53110 + 0.346839i
\(722\) 7212.55 0.371778
\(723\) 0 0
\(724\) −4883.07 8457.73i −0.250660 0.434156i
\(725\) 2482.47 + 4299.76i 0.127168 + 0.220261i
\(726\) 0 0
\(727\) −10087.1 −0.514596 −0.257298 0.966332i \(-0.582832\pi\)
−0.257298 + 0.966332i \(0.582832\pi\)
\(728\) −176.455 568.759i −0.00898332 0.0289555i
\(729\) 0 0
\(730\) −3012.79 + 5218.30i −0.152751 + 0.264572i
\(731\) 4977.86 + 8621.91i 0.251865 + 0.436242i
\(732\) 0 0
\(733\) −15904.3 + 27547.1i −0.801417 + 1.38810i 0.117266 + 0.993101i \(0.462587\pi\)
−0.918683 + 0.394995i \(0.870746\pi\)
\(734\) 13142.1 0.660877
\(735\) 0 0
\(736\) 2510.07 0.125710
\(737\) 11347.4 19654.2i 0.567145 0.982324i
\(738\) 0 0
\(739\) 8287.63 + 14354.6i 0.412538 + 0.714536i 0.995166 0.0982021i \(-0.0313092\pi\)
−0.582629 + 0.812738i \(0.697976\pi\)
\(740\) −6311.58 + 10932.0i −0.313538 + 0.543064i
\(741\) 0 0
\(742\) −6009.51 19370.2i −0.297326 0.958358i
\(743\) 11053.4 0.545773 0.272886 0.962046i \(-0.412022\pi\)
0.272886 + 0.962046i \(0.412022\pi\)
\(744\) 0 0
\(745\) 15092.2 + 26140.4i 0.742194 + 1.28552i
\(746\) −3733.61 6466.81i −0.183240 0.317382i
\(747\) 0 0
\(748\) 5489.02 0.268314
\(749\) −5799.80 1313.82i −0.282937 0.0640935i
\(750\) 0 0
\(751\) −1589.84 + 2753.68i −0.0772490 + 0.133799i −0.902062 0.431606i \(-0.857947\pi\)
0.824813 + 0.565405i \(0.191280\pi\)
\(752\) −1103.37 1911.09i −0.0535050 0.0926733i
\(753\) 0 0
\(754\) −865.479 + 1499.05i −0.0418022 + 0.0724036i
\(755\) −11065.5 −0.533399
\(756\) 0 0
\(757\) −31130.8 −1.49467 −0.747336 0.664446i \(-0.768667\pi\)
−0.747336 + 0.664446i \(0.768667\pi\)
\(758\) 8419.14 14582.4i 0.403426 0.698755i
\(759\) 0 0
\(760\) 2303.36 + 3989.54i 0.109936 + 0.190416i
\(761\) 3915.15 6781.24i 0.186497 0.323022i −0.757583 0.652739i \(-0.773620\pi\)
0.944080 + 0.329717i \(0.106953\pi\)
\(762\) 0 0
\(763\) −7042.02 + 7614.35i −0.334126 + 0.361282i
\(764\) 14768.6 0.699359
\(765\) 0 0
\(766\) 5330.42 + 9232.56i 0.251431 + 0.435491i
\(767\) −7.50408 12.9974i −0.000353268 0.000611878i
\(768\) 0 0
\(769\) 9389.21 0.440291 0.220145 0.975467i \(-0.429347\pi\)
0.220145 + 0.975467i \(0.429347\pi\)
\(770\) 13185.4 + 2986.88i 0.617102 + 0.139792i
\(771\) 0 0
\(772\) −6284.64 + 10885.3i −0.292991 + 0.507475i
\(773\) 13896.1 + 24068.8i 0.646584 + 1.11992i 0.983933 + 0.178537i \(0.0571363\pi\)
−0.337349 + 0.941380i \(0.609530\pi\)
\(774\) 0 0
\(775\) −2101.98 + 3640.74i −0.0974263 + 0.168747i
\(776\) 14431.9 0.667623
\(777\) 0 0
\(778\) −15622.3 −0.719907
\(779\) −5319.92 + 9214.37i −0.244680 + 0.423798i
\(780\) 0 0
\(781\) 9635.81 + 16689.7i 0.441481 + 0.764667i
\(782\) 2977.60 5157.36i 0.136162 0.235840i
\(783\) 0 0
\(784\) −427.958 5471.29i −0.0194952 0.249239i