Properties

Label 126.4.g.e.37.2
Level $126$
Weight $4$
Character 126.37
Analytic conductor $7.434$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
Defining polynomial: \(x^{4} - x^{3} + 49 x^{2} + 48 x + 2304\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(3.72311 - 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.4.g.e.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} +(-12.3924 + 13.7633i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} +(-12.3924 + 13.7633i) q^{7} +8.00000 q^{8} +(10.4462 + 18.0934i) q^{10} +(-30.5618 - 52.9346i) q^{11} -59.2311 q^{13} +(-11.4462 - 35.2276i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-10.2311 - 17.7208i) q^{17} +(40.1693 - 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(79.1236 - 137.046i) q^{23} +(7.93822 + 13.7494i) q^{25} +(59.2311 - 102.591i) q^{26} +(72.4622 + 15.4022i) q^{28} -85.1236 q^{29} +(-121.747 - 210.872i) q^{31} +(-16.0000 - 27.7128i) q^{32} +40.9244 q^{34} +(59.7849 + 183.998i) q^{35} +(-145.185 + 251.468i) q^{37} +(80.3387 + 139.151i) q^{38} +(41.7849 - 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(-122.247 + 211.738i) q^{44} +(158.247 + 274.092i) q^{46} +(84.6453 - 146.610i) q^{47} +(-35.8547 - 341.121i) q^{49} -31.7529 q^{50} +(118.462 + 205.183i) q^{52} +(125.056 + 216.603i) q^{53} -638.510 q^{55} +(-99.1396 + 110.106i) q^{56} +(85.1236 - 147.438i) q^{58} +(402.610 + 697.341i) q^{59} +(-16.5858 + 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(-309.371 + 535.846i) q^{65} +(138.691 + 240.220i) q^{67} +(-40.9244 + 70.8832i) q^{68} +(-378.478 - 80.4472i) q^{70} -631.506 q^{71} +(384.142 + 665.353i) q^{73} +(-290.371 - 502.937i) q^{74} -321.355 q^{76} +(1107.29 + 235.359i) q^{77} +(209.365 - 362.631i) q^{79} +(83.5698 + 144.747i) q^{80} +(168.000 - 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(-7.62934 + 13.2144i) q^{86} +(-244.494 - 423.476i) q^{88} +(786.048 - 1361.48i) q^{89} +(734.018 - 815.213i) q^{91} -632.988 q^{92} +(169.291 + 293.220i) q^{94} +(-419.618 - 726.799i) q^{95} +1045.16 q^{97} +(626.693 + 279.019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} + 7q^{5} + 6q^{7} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} + 7q^{5} + 6q^{7} + 32q^{8} + 14q^{10} - 25q^{11} - 98q^{13} - 18q^{14} - 32q^{16} + 98q^{17} + 119q^{19} - 56q^{20} + 100q^{22} + 122q^{23} + 129q^{25} + 98q^{26} + 12q^{28} - 146q^{29} - 98q^{31} - 64q^{32} - 392q^{34} + 128q^{35} - 289q^{37} + 238q^{38} + 56q^{40} - 672q^{41} + 614q^{43} - 100q^{44} + 244q^{46} + 672q^{47} + 190q^{49} - 516q^{50} + 196q^{52} - 375q^{53} - 1526q^{55} + 48q^{56} + 146q^{58} + 763q^{59} + 406q^{61} + 392q^{62} + 256q^{64} - 654q^{65} + 1041q^{67} + 392q^{68} - 986q^{70} - 3304q^{71} + 189q^{73} - 578q^{74} - 952q^{76} + 3415q^{77} - 524q^{79} + 112q^{80} + 672q^{82} - 574q^{83} - 1244q^{85} - 614q^{86} - 200q^{88} + 2394q^{89} + 1783q^{91} - 976q^{92} + 1344q^{94} - 706q^{95} - 126q^{97} + 2090q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 5.22311 9.04669i 0.467169 0.809161i −0.532127 0.846664i \(-0.678607\pi\)
0.999296 + 0.0375035i \(0.0119405\pi\)
\(6\) 0 0
\(7\) −12.3924 + 13.7633i −0.669129 + 0.743146i
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 10.4462 + 18.0934i 0.330339 + 0.572163i
\(11\) −30.5618 52.9346i −0.837702 1.45094i −0.891811 0.452407i \(-0.850565\pi\)
0.0541093 0.998535i \(-0.482768\pi\)
\(12\) 0 0
\(13\) −59.2311 −1.26367 −0.631837 0.775102i \(-0.717699\pi\)
−0.631837 + 0.775102i \(0.717699\pi\)
\(14\) −11.4462 35.2276i −0.218509 0.672498i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −10.2311 17.7208i −0.145965 0.252819i 0.783767 0.621054i \(-0.213295\pi\)
−0.929733 + 0.368235i \(0.879962\pi\)
\(18\) 0 0
\(19\) 40.1693 69.5753i 0.485025 0.840088i −0.514827 0.857294i \(-0.672144\pi\)
0.999852 + 0.0172061i \(0.00547713\pi\)
\(20\) −41.7849 −0.467169
\(21\) 0 0
\(22\) 122.247 1.18469
\(23\) 79.1236 137.046i 0.717322 1.24244i −0.244735 0.969590i \(-0.578701\pi\)
0.962057 0.272848i \(-0.0879656\pi\)
\(24\) 0 0
\(25\) 7.93822 + 13.7494i 0.0635058 + 0.109995i
\(26\) 59.2311 102.591i 0.446776 0.773839i
\(27\) 0 0
\(28\) 72.4622 + 15.4022i 0.489074 + 0.103955i
\(29\) −85.1236 −0.545071 −0.272535 0.962146i \(-0.587862\pi\)
−0.272535 + 0.962146i \(0.587862\pi\)
\(30\) 0 0
\(31\) −121.747 210.872i −0.705369 1.22173i −0.966558 0.256447i \(-0.917448\pi\)
0.261190 0.965287i \(-0.415885\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 40.9244 0.206426
\(35\) 59.7849 + 183.998i 0.288728 + 0.888608i
\(36\) 0 0
\(37\) −145.185 + 251.468i −0.645090 + 1.11733i 0.339191 + 0.940718i \(0.389847\pi\)
−0.984281 + 0.176611i \(0.943487\pi\)
\(38\) 80.3387 + 139.151i 0.342965 + 0.594032i
\(39\) 0 0
\(40\) 41.7849 72.3735i 0.165169 0.286082i
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 0 0
\(43\) 7.62934 0.0270573 0.0135286 0.999908i \(-0.495694\pi\)
0.0135286 + 0.999908i \(0.495694\pi\)
\(44\) −122.247 + 211.738i −0.418851 + 0.725471i
\(45\) 0 0
\(46\) 158.247 + 274.092i 0.507223 + 0.878536i
\(47\) 84.6453 146.610i 0.262698 0.455006i −0.704260 0.709942i \(-0.748721\pi\)
0.966958 + 0.254936i \(0.0820545\pi\)
\(48\) 0 0
\(49\) −35.8547 341.121i −0.104533 0.994521i
\(50\) −31.7529 −0.0898107
\(51\) 0 0
\(52\) 118.462 + 205.183i 0.315918 + 0.547187i
\(53\) 125.056 + 216.603i 0.324109 + 0.561373i 0.981332 0.192324i \(-0.0616023\pi\)
−0.657223 + 0.753696i \(0.728269\pi\)
\(54\) 0 0
\(55\) −638.510 −1.56539
\(56\) −99.1396 + 110.106i −0.236573 + 0.262742i
\(57\) 0 0
\(58\) 85.1236 147.438i 0.192712 0.333786i
\(59\) 402.610 + 697.341i 0.888395 + 1.53875i 0.841772 + 0.539833i \(0.181513\pi\)
0.0466235 + 0.998913i \(0.485154\pi\)
\(60\) 0 0
\(61\) −16.5858 + 28.7274i −0.0348130 + 0.0602978i −0.882907 0.469548i \(-0.844417\pi\)
0.848094 + 0.529846i \(0.177750\pi\)
\(62\) 486.988 0.997542
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −309.371 + 535.846i −0.590349 + 1.02252i
\(66\) 0 0
\(67\) 138.691 + 240.220i 0.252893 + 0.438023i 0.964321 0.264736i \(-0.0852847\pi\)
−0.711428 + 0.702759i \(0.751951\pi\)
\(68\) −40.9244 + 70.8832i −0.0729826 + 0.126410i
\(69\) 0 0
\(70\) −378.478 80.4472i −0.646240 0.137361i
\(71\) −631.506 −1.05558 −0.527788 0.849376i \(-0.676979\pi\)
−0.527788 + 0.849376i \(0.676979\pi\)
\(72\) 0 0
\(73\) 384.142 + 665.353i 0.615896 + 1.06676i 0.990227 + 0.139468i \(0.0445391\pi\)
−0.374331 + 0.927295i \(0.622128\pi\)
\(74\) −290.371 502.937i −0.456147 0.790070i
\(75\) 0 0
\(76\) −321.355 −0.485025
\(77\) 1107.29 + 235.359i 1.63879 + 0.348333i
\(78\) 0 0
\(79\) 209.365 362.631i 0.298169 0.516445i −0.677548 0.735479i \(-0.736957\pi\)
0.975717 + 0.219034i \(0.0702906\pi\)
\(80\) 83.5698 + 144.747i 0.116792 + 0.202290i
\(81\) 0 0
\(82\) 168.000 290.985i 0.226250 0.391876i
\(83\) −761.714 −1.00734 −0.503668 0.863897i \(-0.668017\pi\)
−0.503668 + 0.863897i \(0.668017\pi\)
\(84\) 0 0
\(85\) −213.753 −0.272762
\(86\) −7.62934 + 13.2144i −0.00956619 + 0.0165691i
\(87\) 0 0
\(88\) −244.494 423.476i −0.296172 0.512986i
\(89\) 786.048 1361.48i 0.936190 1.62153i 0.163692 0.986511i \(-0.447660\pi\)
0.772498 0.635017i \(-0.219007\pi\)
\(90\) 0 0
\(91\) 734.018 815.213i 0.845561 0.939094i
\(92\) −632.988 −0.717322
\(93\) 0 0
\(94\) 169.291 + 293.220i 0.185755 + 0.321738i
\(95\) −419.618 726.799i −0.453178 0.784927i
\(96\) 0 0
\(97\) 1045.16 1.09402 0.547012 0.837125i \(-0.315765\pi\)
0.547012 + 0.837125i \(0.315765\pi\)
\(98\) 626.693 + 279.019i 0.645975 + 0.287604i
\(99\) 0 0
\(100\) 31.7529 54.9976i 0.0317529 0.0549976i
\(101\) −487.961 845.173i −0.480732 0.832652i 0.519024 0.854760i \(-0.326296\pi\)
−0.999756 + 0.0221078i \(0.992962\pi\)
\(102\) 0 0
\(103\) 321.572 556.979i 0.307626 0.532823i −0.670217 0.742165i \(-0.733799\pi\)
0.977842 + 0.209342i \(0.0671323\pi\)
\(104\) −473.849 −0.446776
\(105\) 0 0
\(106\) −500.224 −0.458359
\(107\) 155.797 269.849i 0.140762 0.243806i −0.787022 0.616925i \(-0.788378\pi\)
0.927784 + 0.373119i \(0.121712\pi\)
\(108\) 0 0
\(109\) 932.915 + 1615.86i 0.819790 + 1.41992i 0.905837 + 0.423626i \(0.139243\pi\)
−0.0860476 + 0.996291i \(0.527424\pi\)
\(110\) 638.510 1105.93i 0.553451 0.958604i
\(111\) 0 0
\(112\) −91.5698 281.821i −0.0772547 0.237764i
\(113\) −1720.49 −1.43231 −0.716153 0.697944i \(-0.754099\pi\)
−0.716153 + 0.697944i \(0.754099\pi\)
\(114\) 0 0
\(115\) −826.542 1431.61i −0.670221 1.16086i
\(116\) 170.247 + 294.877i 0.136268 + 0.236022i
\(117\) 0 0
\(118\) −1610.44 −1.25638
\(119\) 370.684 + 78.7906i 0.285551 + 0.0606952i
\(120\) 0 0
\(121\) −1202.54 + 2082.87i −0.903489 + 1.56489i
\(122\) −33.1715 57.4548i −0.0246165 0.0426370i
\(123\) 0 0
\(124\) −486.988 + 843.489i −0.352684 + 0.610867i
\(125\) 1471.63 1.05301
\(126\) 0 0
\(127\) 142.236 0.0993808 0.0496904 0.998765i \(-0.484177\pi\)
0.0496904 + 0.998765i \(0.484177\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −618.741 1071.69i −0.417440 0.723027i
\(131\) 1243.26 2153.38i 0.829189 1.43620i −0.0694870 0.997583i \(-0.522136\pi\)
0.898676 0.438614i \(-0.144530\pi\)
\(132\) 0 0
\(133\) 459.787 + 1415.07i 0.299764 + 0.922572i
\(134\) −554.764 −0.357644
\(135\) 0 0
\(136\) −81.8489 141.766i −0.0516065 0.0893851i
\(137\) −1298.61 2249.25i −0.809835 1.40268i −0.912978 0.408009i \(-0.866223\pi\)
0.103143 0.994667i \(-0.467110\pi\)
\(138\) 0 0
\(139\) 1600.52 0.976651 0.488325 0.872662i \(-0.337608\pi\)
0.488325 + 0.872662i \(0.337608\pi\)
\(140\) 517.817 575.096i 0.312597 0.347175i
\(141\) 0 0
\(142\) 631.506 1093.80i 0.373203 0.646406i
\(143\) 1810.21 + 3135.37i 1.05858 + 1.83352i
\(144\) 0 0
\(145\) −444.610 + 770.087i −0.254640 + 0.441050i
\(146\) −1536.57 −0.871008
\(147\) 0 0
\(148\) 1161.48 0.645090
\(149\) −1468.85 + 2544.13i −0.807605 + 1.39881i 0.106913 + 0.994268i \(0.465903\pi\)
−0.914518 + 0.404545i \(0.867430\pi\)
\(150\) 0 0
\(151\) −911.662 1579.05i −0.491325 0.850999i 0.508625 0.860988i \(-0.330154\pi\)
−0.999950 + 0.00998867i \(0.996820\pi\)
\(152\) 321.355 556.603i 0.171482 0.297016i
\(153\) 0 0
\(154\) −1514.94 + 1682.52i −0.792710 + 0.880398i
\(155\) −2543.59 −1.31811
\(156\) 0 0
\(157\) −316.824 548.755i −0.161053 0.278952i 0.774194 0.632949i \(-0.218156\pi\)
−0.935247 + 0.353997i \(0.884822\pi\)
\(158\) 418.730 + 725.261i 0.210838 + 0.365182i
\(159\) 0 0
\(160\) −334.279 −0.165169
\(161\) 905.666 + 2787.33i 0.443332 + 1.36443i
\(162\) 0 0
\(163\) 672.853 1165.42i 0.323325 0.560015i −0.657847 0.753151i \(-0.728533\pi\)
0.981172 + 0.193137i \(0.0618660\pi\)
\(164\) 336.000 + 581.969i 0.159983 + 0.277098i
\(165\) 0 0
\(166\) 761.714 1319.33i 0.356147 0.616865i
\(167\) 387.922 0.179750 0.0898751 0.995953i \(-0.471353\pi\)
0.0898751 + 0.995953i \(0.471353\pi\)
\(168\) 0 0
\(169\) 1311.32 0.596870
\(170\) 213.753 370.231i 0.0964359 0.167032i
\(171\) 0 0
\(172\) −15.2587 26.4288i −0.00676432 0.0117161i
\(173\) 311.330 539.239i 0.136821 0.236980i −0.789471 0.613788i \(-0.789645\pi\)
0.926291 + 0.376808i \(0.122978\pi\)
\(174\) 0 0
\(175\) −287.611 61.1329i −0.124236 0.0264069i
\(176\) 977.977 0.418851
\(177\) 0 0
\(178\) 1572.10 + 2722.95i 0.661986 + 1.14659i
\(179\) 224.965 + 389.651i 0.0939368 + 0.162703i 0.909164 0.416437i \(-0.136721\pi\)
−0.815228 + 0.579141i \(0.803388\pi\)
\(180\) 0 0
\(181\) 184.353 0.0757063 0.0378532 0.999283i \(-0.487948\pi\)
0.0378532 + 0.999283i \(0.487948\pi\)
\(182\) 677.972 + 2086.57i 0.276125 + 0.849818i
\(183\) 0 0
\(184\) 632.988 1096.37i 0.253612 0.439268i
\(185\) 1516.64 + 2626.89i 0.602732 + 1.04396i
\(186\) 0 0
\(187\) −625.362 + 1083.16i −0.244551 + 0.423574i
\(188\) −677.163 −0.262698
\(189\) 0 0
\(190\) 1678.47 0.640890
\(191\) −175.483 + 303.945i −0.0664789 + 0.115145i −0.897349 0.441321i \(-0.854510\pi\)
0.830870 + 0.556466i \(0.187843\pi\)
\(192\) 0 0
\(193\) −764.129 1323.51i −0.284991 0.493619i 0.687616 0.726074i \(-0.258657\pi\)
−0.972607 + 0.232456i \(0.925324\pi\)
\(194\) −1045.16 + 1810.28i −0.386796 + 0.669950i
\(195\) 0 0
\(196\) −1109.97 + 806.446i −0.404507 + 0.293894i
\(197\) 2874.65 1.03965 0.519823 0.854274i \(-0.325998\pi\)
0.519823 + 0.854274i \(0.325998\pi\)
\(198\) 0 0
\(199\) −2474.35 4285.70i −0.881418 1.52666i −0.849765 0.527162i \(-0.823256\pi\)
−0.0316529 0.999499i \(-0.510077\pi\)
\(200\) 63.5058 + 109.995i 0.0224527 + 0.0388892i
\(201\) 0 0
\(202\) 1951.84 0.679858
\(203\) 1054.89 1171.58i 0.364723 0.405067i
\(204\) 0 0
\(205\) −877.483 + 1519.84i −0.298956 + 0.517808i
\(206\) 643.144 + 1113.96i 0.217524 + 0.376763i
\(207\) 0 0
\(208\) 473.849 820.730i 0.157959 0.273593i
\(209\) −4910.58 −1.62523
\(210\) 0 0
\(211\) −5280.90 −1.72299 −0.861497 0.507762i \(-0.830473\pi\)
−0.861497 + 0.507762i \(0.830473\pi\)
\(212\) 500.224 866.413i 0.162054 0.280686i
\(213\) 0 0
\(214\) 311.595 + 539.698i 0.0995335 + 0.172397i
\(215\) 39.8489 69.0203i 0.0126403 0.0218937i
\(216\) 0 0
\(217\) 4411.03 + 937.585i 1.37991 + 0.293306i
\(218\) −3731.66 −1.15936
\(219\) 0 0
\(220\) 1277.02 + 2211.86i 0.391349 + 0.677836i
\(221\) 606.000 + 1049.62i 0.184452 + 0.319481i
\(222\) 0 0
\(223\) 3996.57 1.20013 0.600067 0.799950i \(-0.295141\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(224\) 579.698 + 123.217i 0.172914 + 0.0367536i
\(225\) 0 0
\(226\) 1720.49 2979.98i 0.506396 0.877104i
\(227\) −269.296 466.434i −0.0787392 0.136380i 0.823967 0.566638i \(-0.191756\pi\)
−0.902706 + 0.430257i \(0.858423\pi\)
\(228\) 0 0
\(229\) −2085.80 + 3612.72i −0.601895 + 1.04251i 0.390639 + 0.920544i \(0.372254\pi\)
−0.992534 + 0.121968i \(0.961079\pi\)
\(230\) 3306.17 0.947836
\(231\) 0 0
\(232\) −680.988 −0.192712
\(233\) 769.865 1333.45i 0.216461 0.374922i −0.737262 0.675607i \(-0.763882\pi\)
0.953724 + 0.300684i \(0.0972151\pi\)
\(234\) 0 0
\(235\) −884.224 1531.52i −0.245449 0.425129i
\(236\) 1610.44 2789.36i 0.444198 0.769373i
\(237\) 0 0
\(238\) −507.154 + 563.254i −0.138126 + 0.153405i
\(239\) −3132.67 −0.847848 −0.423924 0.905698i \(-0.639348\pi\)
−0.423924 + 0.905698i \(0.639348\pi\)
\(240\) 0 0
\(241\) −1303.35 2257.46i −0.348365 0.603386i 0.637594 0.770372i \(-0.279930\pi\)
−0.985959 + 0.166987i \(0.946596\pi\)
\(242\) −2405.09 4165.74i −0.638863 1.10654i
\(243\) 0 0
\(244\) 132.686 0.0348130
\(245\) −3273.29 1457.35i −0.853562 0.380026i
\(246\) 0 0
\(247\) −2379.27 + 4121.02i −0.612913 + 1.06160i
\(248\) −973.977 1686.98i −0.249385 0.431948i
\(249\) 0 0
\(250\) −1471.63 + 2548.93i −0.372295 + 0.644834i
\(251\) 3426.24 0.861603 0.430801 0.902447i \(-0.358231\pi\)
0.430801 + 0.902447i \(0.358231\pi\)
\(252\) 0 0
\(253\) −9672.63 −2.40361
\(254\) −142.236 + 246.359i −0.0351364 + 0.0608581i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2928.72 5072.69i 0.710850 1.23123i −0.253688 0.967286i \(-0.581644\pi\)
0.964538 0.263943i \(-0.0850230\pi\)
\(258\) 0 0
\(259\) −1661.82 5114.53i −0.398690 1.22703i
\(260\) 2474.97 0.590349
\(261\) 0 0
\(262\) 2486.51 + 4306.76i 0.586325 + 1.01554i
\(263\) −542.965 940.443i −0.127303 0.220495i 0.795328 0.606180i \(-0.207299\pi\)
−0.922631 + 0.385684i \(0.873965\pi\)
\(264\) 0 0
\(265\) 2612.73 0.605654
\(266\) −2910.76 618.695i −0.670940 0.142611i
\(267\) 0 0
\(268\) 554.764 960.880i 0.126446 0.219012i
\(269\) −2789.73 4831.95i −0.632315 1.09520i −0.987077 0.160245i \(-0.948772\pi\)
0.354763 0.934956i \(-0.384562\pi\)
\(270\) 0 0
\(271\) 280.164 485.258i 0.0627997 0.108772i −0.832916 0.553399i \(-0.813330\pi\)
0.895716 + 0.444627i \(0.146664\pi\)
\(272\) 327.396 0.0729826
\(273\) 0 0
\(274\) 5194.42 1.14528
\(275\) 485.212 840.413i 0.106398 0.184286i
\(276\) 0 0
\(277\) 2254.04 + 3904.11i 0.488924 + 0.846842i 0.999919 0.0127421i \(-0.00405606\pi\)
−0.510994 + 0.859584i \(0.670723\pi\)
\(278\) −1600.52 + 2772.19i −0.345298 + 0.598074i
\(279\) 0 0
\(280\) 478.279 + 1471.98i 0.102081 + 0.314170i
\(281\) 4329.75 0.919186 0.459593 0.888130i \(-0.347995\pi\)
0.459593 + 0.888130i \(0.347995\pi\)
\(282\) 0 0
\(283\) 435.526 + 754.353i 0.0914817 + 0.158451i 0.908135 0.418678i \(-0.137506\pi\)
−0.816653 + 0.577129i \(0.804173\pi\)
\(284\) 1263.01 + 2187.60i 0.263894 + 0.457078i
\(285\) 0 0
\(286\) −7240.83 −1.49706
\(287\) 2081.93 2312.23i 0.428197 0.475563i
\(288\) 0 0
\(289\) 2247.15 3892.18i 0.457388 0.792220i
\(290\) −889.220 1540.17i −0.180058 0.311869i
\(291\) 0 0
\(292\) 1536.57 2661.41i 0.307948 0.533381i
\(293\) −1651.91 −0.329372 −0.164686 0.986346i \(-0.552661\pi\)
−0.164686 + 0.986346i \(0.552661\pi\)
\(294\) 0 0
\(295\) 8411.50 1.66012
\(296\) −1161.48 + 2011.75i −0.228074 + 0.395035i
\(297\) 0 0
\(298\) −2937.71 5088.26i −0.571063 0.989110i
\(299\) −4686.58 + 8117.39i −0.906460 + 1.57004i
\(300\) 0 0
\(301\) −94.5461 + 105.005i −0.0181048 + 0.0201075i
\(302\) 3646.65 0.694838
\(303\) 0 0
\(304\) 642.709 + 1113.21i 0.121256 + 0.210022i
\(305\) 173.259 + 300.093i 0.0325271 + 0.0563386i
\(306\) 0 0
\(307\) 1016.42 0.188958 0.0944791 0.995527i \(-0.469881\pi\)
0.0944791 + 0.995527i \(0.469881\pi\)
\(308\) −1399.27 4306.47i −0.258866 0.796701i
\(309\) 0 0
\(310\) 2543.59 4405.64i 0.466021 0.807172i
\(311\) −4596.53 7961.42i −0.838087 1.45161i −0.891492 0.453037i \(-0.850341\pi\)
0.0534049 0.998573i \(-0.482993\pi\)
\(312\) 0 0
\(313\) 3346.30 5795.97i 0.604295 1.04667i −0.387868 0.921715i \(-0.626788\pi\)
0.992162 0.124954i \(-0.0398784\pi\)
\(314\) 1267.30 0.227763
\(315\) 0 0
\(316\) −1674.92 −0.298169
\(317\) 3526.25 6107.64i 0.624775 1.08214i −0.363809 0.931473i \(-0.618524\pi\)
0.988584 0.150669i \(-0.0481426\pi\)
\(318\) 0 0
\(319\) 2601.53 + 4505.98i 0.456607 + 0.790866i
\(320\) 334.279 578.988i 0.0583962 0.101145i
\(321\) 0 0
\(322\) −5733.47 1218.67i −0.992279 0.210913i
\(323\) −1643.91 −0.283187
\(324\) 0 0
\(325\) −470.190 814.393i −0.0802506 0.138998i
\(326\) 1345.71 + 2330.83i 0.228625 + 0.395990i
\(327\) 0 0
\(328\) −1344.00 −0.226250
\(329\) 968.869 + 2981.85i 0.162357 + 0.499680i
\(330\) 0 0
\(331\) −1570.19 + 2719.64i −0.260741 + 0.451616i −0.966439 0.256896i \(-0.917300\pi\)
0.705698 + 0.708513i \(0.250633\pi\)
\(332\) 1523.43 + 2638.65i 0.251834 + 0.436190i
\(333\) 0 0
\(334\) −387.922 + 671.900i −0.0635513 + 0.110074i
\(335\) 2897.60 0.472575
\(336\) 0 0
\(337\) 2743.87 0.443526 0.221763 0.975101i \(-0.428819\pi\)
0.221763 + 0.975101i \(0.428819\pi\)
\(338\) −1311.32 + 2271.28i −0.211026 + 0.365507i
\(339\) 0 0
\(340\) 427.506 + 740.462i 0.0681905 + 0.118109i
\(341\) −7441.62 + 12889.3i −1.18178 + 2.04690i
\(342\) 0 0
\(343\) 5139.26 + 3733.84i 0.809021 + 0.587780i
\(344\) 61.0347 0.00956619
\(345\) 0 0
\(346\) 622.660 + 1078.48i 0.0967468 + 0.167570i
\(347\) 5218.45 + 9038.62i 0.807323 + 1.39832i 0.914712 + 0.404107i \(0.132418\pi\)
−0.107389 + 0.994217i \(0.534249\pi\)
\(348\) 0 0
\(349\) −2257.01 −0.346175 −0.173087 0.984906i \(-0.555374\pi\)
−0.173087 + 0.984906i \(0.555374\pi\)
\(350\) 393.496 437.023i 0.0600950 0.0667425i
\(351\) 0 0
\(352\) −977.977 + 1693.91i −0.148086 + 0.256493i
\(353\) 2808.22 + 4863.98i 0.423418 + 0.733381i 0.996271 0.0862770i \(-0.0274970\pi\)
−0.572854 + 0.819658i \(0.694164\pi\)
\(354\) 0 0
\(355\) −3298.42 + 5713.04i −0.493133 + 0.854131i
\(356\) −6288.38 −0.936190
\(357\) 0 0
\(358\) −899.861 −0.132847
\(359\) −397.795 + 689.002i −0.0584815 + 0.101293i −0.893784 0.448498i \(-0.851959\pi\)
0.835302 + 0.549791i \(0.185293\pi\)
\(360\) 0 0
\(361\) 202.349 + 350.479i 0.0295013 + 0.0510977i
\(362\) −184.353 + 319.309i −0.0267662 + 0.0463605i
\(363\) 0 0
\(364\) −4292.02 912.287i −0.618030 0.131365i
\(365\) 8025.66 1.15091
\(366\) 0 0
\(367\) −4096.99 7096.19i −0.582727 1.00931i −0.995155 0.0983227i \(-0.968652\pi\)
0.412427 0.910990i \(-0.364681\pi\)
\(368\) 1265.98 + 2192.74i 0.179330 + 0.310609i
\(369\) 0 0
\(370\) −6066.55 −0.852392
\(371\) −4530.92 963.067i −0.634053 0.134771i
\(372\) 0 0
\(373\) −7038.69 + 12191.4i −0.977076 + 1.69235i −0.304170 + 0.952618i \(0.598379\pi\)
−0.672906 + 0.739728i \(0.734954\pi\)
\(374\) −1250.72 2166.32i −0.172923 0.299512i
\(375\) 0 0
\(376\) 677.163 1172.88i 0.0928777 0.160869i
\(377\) 5041.96 0.688791
\(378\) 0 0
\(379\) 6221.22 0.843173 0.421587 0.906788i \(-0.361473\pi\)
0.421587 + 0.906788i \(0.361473\pi\)
\(380\) −1678.47 + 2907.20i −0.226589 + 0.392463i
\(381\) 0 0
\(382\) −350.965 607.890i −0.0470077 0.0814197i
\(383\) −5350.71 + 9267.70i −0.713860 + 1.23644i 0.249537 + 0.968365i \(0.419722\pi\)
−0.963397 + 0.268077i \(0.913612\pi\)
\(384\) 0 0
\(385\) 7912.70 8787.98i 1.04745 1.16332i
\(386\) 3056.52 0.403038
\(387\) 0 0
\(388\) −2090.33 3620.56i −0.273506 0.473726i
\(389\) 2110.81 + 3656.03i 0.275121 + 0.476524i 0.970166 0.242443i \(-0.0779487\pi\)
−0.695044 + 0.718967i \(0.744615\pi\)
\(390\) 0 0
\(391\) −3238.09 −0.418816
\(392\) −286.837 2728.97i −0.0369578 0.351616i
\(393\) 0 0
\(394\) −2874.65 + 4979.04i −0.367570 + 0.636651i
\(395\) −2187.07 3788.12i −0.278591 0.482534i
\(396\) 0 0
\(397\) 6037.87 10457.9i 0.763305 1.32208i −0.177833 0.984061i \(-0.556909\pi\)
0.941138 0.338023i \(-0.109758\pi\)
\(398\) 9897.41 1.24651
\(399\) 0 0
\(400\) −254.023 −0.0317529
\(401\) −2753.19 + 4768.66i −0.342862 + 0.593855i −0.984963 0.172766i \(-0.944730\pi\)
0.642101 + 0.766620i \(0.278063\pi\)
\(402\) 0 0
\(403\) 7211.22 + 12490.2i 0.891356 + 1.54387i
\(404\) −1951.84 + 3380.69i −0.240366 + 0.416326i
\(405\) 0 0
\(406\) 974.343 + 2998.70i 0.119103 + 0.366559i
\(407\) 17748.5 2.16157
\(408\) 0 0
\(409\) −714.089 1236.84i −0.0863311 0.149530i 0.819627 0.572898i \(-0.194181\pi\)
−0.905958 + 0.423368i \(0.860848\pi\)
\(410\) −1754.97 3039.69i −0.211394 0.366145i
\(411\) 0 0
\(412\) −2572.58 −0.307626
\(413\) −14587.0 3100.53i −1.73796 0.369412i
\(414\) 0 0
\(415\) −3978.52 + 6890.99i −0.470597 + 0.815097i
\(416\) 947.698 + 1641.46i 0.111694 + 0.193460i
\(417\) 0 0
\(418\) 4910.58 8505.38i 0.574604 0.995244i
\(419\) −264.960 −0.0308929 −0.0154465 0.999881i \(-0.504917\pi\)
−0.0154465 + 0.999881i \(0.504917\pi\)
\(420\) 0 0
\(421\) −281.066 −0.0325375 −0.0162688 0.999868i \(-0.505179\pi\)
−0.0162688 + 0.999868i \(0.505179\pi\)
\(422\) 5280.90 9146.78i 0.609171 1.05511i
\(423\) 0 0
\(424\) 1000.45 + 1732.83i 0.114590 + 0.198475i
\(425\) 162.434 281.343i 0.0185393 0.0321110i
\(426\) 0 0
\(427\) −189.844 584.277i −0.0215157 0.0662181i
\(428\) −1246.38 −0.140762
\(429\) 0 0
\(430\) 79.6978 + 138.041i 0.00893806 + 0.0154812i
\(431\) −893.189 1547.05i −0.0998223 0.172897i 0.811789 0.583951i \(-0.198494\pi\)
−0.911611 + 0.411054i \(0.865161\pi\)
\(432\) 0 0
\(433\) 184.621 0.0204904 0.0102452 0.999948i \(-0.496739\pi\)
0.0102452 + 0.999948i \(0.496739\pi\)
\(434\) −6034.98 + 6702.55i −0.667484 + 0.741319i
\(435\) 0 0
\(436\) 3731.66 6463.43i 0.409895 0.709959i
\(437\) −6356.68 11010.1i −0.695838 1.20523i
\(438\) 0 0
\(439\) −5637.32 + 9764.12i −0.612881 + 1.06154i 0.377872 + 0.925858i \(0.376656\pi\)
−0.990752 + 0.135682i \(0.956677\pi\)
\(440\) −5108.08 −0.553451
\(441\) 0 0
\(442\) −2424.00 −0.260855
\(443\) 3984.92 6902.09i 0.427380 0.740244i −0.569259 0.822158i \(-0.692770\pi\)
0.996639 + 0.0819142i \(0.0261033\pi\)
\(444\) 0 0
\(445\) −8211.23 14222.3i −0.874718 1.51506i
\(446\) −3996.57 + 6922.25i −0.424311 + 0.734929i
\(447\) 0 0
\(448\) −793.116 + 880.849i −0.0836411 + 0.0928933i
\(449\) −8850.37 −0.930233 −0.465117 0.885249i \(-0.653988\pi\)
−0.465117 + 0.885249i \(0.653988\pi\)
\(450\) 0 0
\(451\) 5134.38 + 8893.00i 0.536072 + 0.928504i
\(452\) 3440.99 + 5959.97i 0.358076 + 0.620206i
\(453\) 0 0
\(454\) 1077.18 0.111354
\(455\) −3541.13 10898.4i −0.364858 1.12291i
\(456\) 0 0
\(457\) 6513.65 11282.0i 0.666730 1.15481i −0.312083 0.950055i \(-0.601027\pi\)
0.978813 0.204756i \(-0.0656400\pi\)
\(458\) −4171.61 7225.44i −0.425604 0.737167i
\(459\) 0 0
\(460\) −3306.17 + 5726.45i −0.335111 + 0.580429i
\(461\) −1261.05 −0.127403 −0.0637016 0.997969i \(-0.520291\pi\)
−0.0637016 + 0.997969i \(0.520291\pi\)
\(462\) 0 0
\(463\) −4005.47 −0.402052 −0.201026 0.979586i \(-0.564427\pi\)
−0.201026 + 0.979586i \(0.564427\pi\)
\(464\) 680.988 1179.51i 0.0681338 0.118011i
\(465\) 0 0
\(466\) 1539.73 + 2666.89i 0.153061 + 0.265110i
\(467\) 8548.91 14807.1i 0.847101 1.46722i −0.0366825 0.999327i \(-0.511679\pi\)
0.883784 0.467895i \(-0.154988\pi\)
\(468\) 0 0
\(469\) −5024.93 1068.07i −0.494733 0.105158i
\(470\) 3536.90 0.347117
\(471\) 0 0
\(472\) 3220.88 + 5578.72i 0.314095 + 0.544029i
\(473\) −233.166 403.856i −0.0226659 0.0392586i
\(474\) 0 0
\(475\) 1275.49 0.123208
\(476\) −468.430 1441.67i −0.0451060 0.138821i
\(477\) 0 0
\(478\) 3132.67 5425.95i 0.299760 0.519199i
\(479\) 5844.26 + 10122.6i 0.557477 + 0.965578i 0.997706 + 0.0676925i \(0.0215637\pi\)
−0.440230 + 0.897885i \(0.645103\pi\)
\(480\) 0 0
\(481\) 8599.49 14894.8i 0.815183 1.41194i
\(482\) 5213.39 0.492662
\(483\) 0 0
\(484\) 9620.36 0.903489
\(485\) 5459.01 9455.28i 0.511095 0.885242i
\(486\) 0 0
\(487\) 4812.40 + 8335.31i 0.447783 + 0.775583i 0.998241 0.0592793i \(-0.0188803\pi\)
−0.550458 + 0.834863i \(0.685547\pi\)
\(488\) −132.686 + 229.819i −0.0123082 + 0.0213185i
\(489\) 0 0
\(490\) 5797.49 4212.16i 0.534497 0.388338i
\(491\) 6320.63 0.580949 0.290475 0.956883i \(-0.406187\pi\)
0.290475 + 0.956883i \(0.406187\pi\)
\(492\) 0 0
\(493\) 870.908 + 1508.46i 0.0795613 + 0.137804i
\(494\) −4758.55 8242.05i −0.433395 0.750662i
\(495\) 0 0
\(496\) 3895.91 0.352684
\(497\) 7825.90 8691.58i 0.706317 0.784448i
\(498\) 0 0
\(499\) 7527.29 13037.6i 0.675286 1.16963i −0.301100 0.953593i \(-0.597354\pi\)
0.976385 0.216037i \(-0.0693130\pi\)
\(500\) −2943.25 5097.86i −0.263253 0.455967i
\(501\) 0 0
\(502\) −3426.24 + 5934.42i −0.304623 + 0.527622i
\(503\) −16559.1 −1.46786 −0.733930 0.679225i \(-0.762316\pi\)
−0.733930 + 0.679225i \(0.762316\pi\)
\(504\) 0 0
\(505\) −10194.7 −0.898333
\(506\) 9672.63 16753.5i 0.849804 1.47190i
\(507\) 0 0
\(508\) −284.471 492.718i −0.0248452 0.0430332i
\(509\) −6669.48 + 11551.9i −0.580785 + 1.00595i 0.414601 + 0.910003i \(0.363921\pi\)
−0.995387 + 0.0959462i \(0.969412\pi\)
\(510\) 0 0
\(511\) −13917.9 2958.31i −1.20487 0.256101i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 5857.44 + 10145.4i 0.502647 + 0.870610i
\(515\) −3359.21 5818.33i −0.287426 0.497837i
\(516\) 0 0
\(517\) −10347.6 −0.880250
\(518\) 10520.5 + 2236.17i 0.892359 + 0.189675i
\(519\) 0 0
\(520\) −2474.97 + 4286.77i −0.208720 + 0.361514i
\(521\) −3591.35 6220.40i −0.301996 0.523072i 0.674592 0.738191i \(-0.264320\pi\)
−0.976588 + 0.215118i \(0.930986\pi\)
\(522\) 0 0
\(523\) −4815.07 + 8339.94i −0.402578 + 0.697285i −0.994036 0.109050i \(-0.965219\pi\)
0.591459 + 0.806335i \(0.298552\pi\)
\(524\) −9946.04 −0.829189
\(525\) 0 0
\(526\) 2171.86 0.180034
\(527\) −2491.22 + 4314.91i −0.205919 + 0.356661i
\(528\) 0 0
\(529\) −6437.57 11150.2i −0.529101 0.916430i
\(530\) −2612.73 + 4525.37i −0.214131 + 0.370886i
\(531\) 0 0
\(532\) 3982.37 4422.89i 0.324544 0.360445i
\(533\) 9950.83 0.808664
\(534\) 0 0
\(535\) −1627.49 2818.90i −0.131519 0.227798i
\(536\) 1109.53 + 1921.76i 0.0894111 + 0.154865i
\(537\) 0 0
\(538\) 11158.9 0.894228
\(539\) −16961.3 + 12323.2i −1.35543 + 0.984783i
\(540\) 0 0
\(541\) −7774.74 + 13466.2i −0.617860 + 1.07016i 0.372016 + 0.928227i \(0.378667\pi\)
−0.989875 + 0.141938i \(0.954667\pi\)
\(542\) 560.327 + 970.515i 0.0444061 + 0.0769136i
\(543\) 0 0
\(544\) −327.396 + 567.066i −0.0258032 + 0.0446925i
\(545\) 19490.9 1.53192
\(546\) 0 0
\(547\) −5917.38 −0.462539 −0.231270 0.972890i \(-0.574288\pi\)
−0.231270 + 0.972890i \(0.574288\pi\)
\(548\) −5194.42 + 8997.01i −0.404918 + 0.701338i
\(549\) 0 0
\(550\) 970.425 + 1680.83i 0.0752346 + 0.130310i
\(551\) −3419.36 + 5922.50i −0.264373 + 0.457907i
\(552\) 0 0
\(553\) 2396.44 + 7375.42i 0.184280 + 0.567152i
\(554\) −9016.15 −0.691444
\(555\) 0 0
\(556\) −3201.04 5544.37i −0.244163 0.422902i
\(557\) 1065.93 + 1846.25i 0.0810862 + 0.140445i 0.903717 0.428131i \(-0.140828\pi\)
−0.822631 + 0.568576i \(0.807494\pi\)
\(558\) 0 0
\(559\) −451.894 −0.0341916
\(560\) −3027.83 643.578i −0.228480 0.0485645i
\(561\) 0 0
\(562\) −4329.75 + 7499.35i −0.324981 + 0.562884i
\(563\) −3687.95 6387.72i −0.276072 0.478171i 0.694333 0.719654i \(-0.255700\pi\)
−0.970405 + 0.241483i \(0.922366\pi\)
\(564\) 0 0
\(565\) −8986.33 + 15564.8i −0.669129 + 1.15897i
\(566\) −1742.10 −0.129375
\(567\) 0 0
\(568\) −5052.05 −0.373203
\(569\) −6350.42 + 10999.3i −0.467880 + 0.810391i −0.999326 0.0367005i \(-0.988315\pi\)
0.531447 + 0.847092i \(0.321649\pi\)
\(570\) 0 0
\(571\) 3845.06 + 6659.84i 0.281805 + 0.488101i 0.971829 0.235686i \(-0.0757335\pi\)
−0.690024 + 0.723786i \(0.742400\pi\)
\(572\) 7240.83 12541.5i 0.529291 0.916759i
\(573\) 0 0
\(574\) 1922.97 + 5918.24i 0.139831 + 0.430353i
\(575\) 2512.40 0.182216
\(576\) 0 0
\(577\) −1547.43 2680.23i −0.111647 0.193379i 0.804787 0.593563i \(-0.202279\pi\)
−0.916435 + 0.400185i \(0.868946\pi\)
\(578\) 4494.30 + 7784.35i 0.323422 + 0.560184i
\(579\) 0 0
\(580\) 3556.88 0.254640
\(581\) 9439.50 10483.7i 0.674038 0.748598i
\(582\) 0 0
\(583\) 7643.87 13239.6i 0.543013 0.940526i
\(584\) 3073.13 + 5322.82i 0.217752 + 0.377158i
\(585\) 0 0
\(586\) 1651.91 2861.20i 0.116450 0.201698i
\(587\) 9967.83 0.700880 0.350440 0.936585i \(-0.386032\pi\)
0.350440 + 0.936585i \(0.386032\pi\)
\(588\) 0 0
\(589\) −19562.0 −1.36849
\(590\) −8411.50 + 14569.1i −0.586942 + 1.01661i
\(591\) 0 0
\(592\) −2322.97 4023.49i −0.161272 0.279332i
\(593\) 884.864 1532.63i 0.0612766 0.106134i −0.833760 0.552127i \(-0.813816\pi\)
0.895036 + 0.445993i \(0.147149\pi\)
\(594\) 0 0
\(595\) 2648.92 2941.94i 0.182513 0.202702i
\(596\) 11750.8 0.807605
\(597\) 0 0
\(598\) −9373.15 16234.8i −0.640964 1.11018i
\(599\) −3173.66 5496.95i −0.216481 0.374957i 0.737248 0.675622i \(-0.236125\pi\)
−0.953730 + 0.300665i \(0.902791\pi\)
\(600\) 0 0
\(601\) 22005.7 1.49356 0.746781 0.665070i \(-0.231599\pi\)
0.746781 + 0.665070i \(0.231599\pi\)
\(602\) −87.3271 268.763i −0.00591227 0.0181960i
\(603\) 0 0
\(604\) −3646.65 + 6316.18i −0.245662 + 0.425500i
\(605\) 12562.0 + 21758.1i 0.844165 + 1.46214i
\(606\) 0 0
\(607\) −8853.55 + 15334.8i −0.592017 + 1.02540i 0.401943 + 0.915665i \(0.368335\pi\)
−0.993960 + 0.109740i \(0.964998\pi\)
\(608\) −2570.84 −0.171482
\(609\) 0 0
\(610\) −693.035 −0.0460003
\(611\) −5013.64 + 8683.87i −0.331964 + 0.574979i
\(612\) 0 0
\(613\) −7923.32 13723.6i −0.522055 0.904226i −0.999671 0.0256570i \(-0.991832\pi\)
0.477616 0.878569i \(-0.341501\pi\)
\(614\) −1016.42 + 1760.49i −0.0668068 + 0.115713i
\(615\) 0 0
\(616\) 8858.30 + 1882.87i 0.579401 + 0.123154i
\(617\) −29473.4 −1.92311 −0.961553 0.274621i \(-0.911448\pi\)
−0.961553 + 0.274621i \(0.911448\pi\)
\(618\) 0 0
\(619\) −5763.74 9983.08i −0.374255 0.648229i 0.615960 0.787778i \(-0.288768\pi\)
−0.990215 + 0.139548i \(0.955435\pi\)
\(620\) 5087.19 + 8811.27i 0.329527 + 0.570757i
\(621\) 0 0
\(622\) 18386.1 1.18523
\(623\) 8997.28 + 27690.6i 0.578601 + 1.78074i
\(624\) 0 0
\(625\) 6694.19 11594.7i 0.428428 0.742059i
\(626\) 6692.61 + 11591.9i 0.427301 + 0.740107i
\(627\) 0 0
\(628\) −1267.30 + 2195.02i −0.0805265 + 0.139476i
\(629\) 5941.63 0.376643
\(630\) 0 0
\(631\) 25846.1 1.63062 0.815308 0.579027i \(-0.196568\pi\)
0.815308 + 0.579027i \(0.196568\pi\)
\(632\) 1674.92 2901.04i 0.105419 0.182591i
\(633\) 0 0
\(634\) 7052.49 + 12215.3i 0.441783 + 0.765190i
\(635\) 742.912 1286.76i 0.0464277 0.0804151i
\(636\) 0 0
\(637\) 2123.71 + 20205.0i 0.132095 + 1.25675i
\(638\) −10406.1 −0.645739
\(639\) 0 0
\(640\) 668.558 + 1157.98i 0.0412923 + 0.0715204i
\(641\) 2767.39 + 4793.26i 0.170523 + 0.295355i 0.938603 0.344999i \(-0.112121\pi\)
−0.768080 + 0.640354i \(0.778788\pi\)
\(642\) 0 0
\(643\) 1634.56 0.100250 0.0501251 0.998743i \(-0.484038\pi\)
0.0501251 + 0.998743i \(0.484038\pi\)
\(644\) 7844.27 8711.98i 0.479981 0.533075i
\(645\) 0 0
\(646\) 1643.91 2847.33i 0.100122 0.173416i
\(647\) 3769.00 + 6528.10i 0.229018 + 0.396671i 0.957517 0.288375i \(-0.0931151\pi\)
−0.728499 + 0.685047i \(0.759782\pi\)
\(648\) 0 0
\(649\) 24608.9 42623.9i 1.48842 2.57802i
\(650\) 1880.76 0.113491
\(651\) 0 0
\(652\) −5382.83 −0.323325
\(653\) −6656.09 + 11528.7i −0.398887 + 0.690892i −0.993589 0.113054i \(-0.963937\pi\)
0.594702 + 0.803946i \(0.297270\pi\)
\(654\) 0 0
\(655\) −12987.3 22494.7i −0.774743 1.34189i
\(656\) 1344.00 2327.88i 0.0799914 0.138549i
\(657\) 0 0
\(658\) −6133.59 1303.72i −0.363392 0.0772407i
\(659\) −10962.0 −0.647981 −0.323991 0.946060i \(-0.605025\pi\)
−0.323991 + 0.946060i \(0.605025\pi\)
\(660\) 0 0
\(661\) 11816.3 + 20466.4i 0.695309 + 1.20431i 0.970076 + 0.242800i \(0.0780659\pi\)
−0.274767 + 0.961511i \(0.588601\pi\)
\(662\) −3140.37 5439.28i −0.184372 0.319341i
\(663\) 0 0
\(664\) −6093.71 −0.356147
\(665\) 15203.2 + 3231.51i 0.886550 + 0.188440i
\(666\) 0 0
\(667\) −6735.28 + 11665.8i −0.390991 + 0.677216i
\(668\) −775.843 1343.80i −0.0449376 0.0778341i
\(669\) 0 0
\(670\) −2897.60 + 5018.78i −0.167080 + 0.289392i
\(671\) 2027.56 0.116652
\(672\) 0 0
\(673\) 23483.0 1.34503 0.672513 0.740085i \(-0.265215\pi\)
0.672513 + 0.740085i \(0.265215\pi\)
\(674\) −2743.87 + 4752.53i −0.156810 + 0.271603i
\(675\) 0 0
\(676\) −2622.65 4542.56i −0.149218 0.258452i
\(677\) 12336.2 21367.0i 0.700325 1.21300i −0.268028 0.963411i \(-0.586372\pi\)
0.968352 0.249587i \(-0.0802948\pi\)
\(678\) 0 0
\(679\) −12952.1 + 14384.9i −0.732044 + 0.813020i
\(680\) −1710.02 −0.0964359
\(681\) 0 0
\(682\) −14883.2 25778.5i −0.835643 1.44738i
\(683\) 4469.73 + 7741.80i 0.250409 + 0.433721i 0.963638 0.267209i \(-0.0861016\pi\)
−0.713229 + 0.700931i \(0.752768\pi\)
\(684\) 0 0
\(685\) −27131.1 −1.51332
\(686\) −11606.5 + 5167.62i −0.645972 + 0.287610i
\(687\) 0 0
\(688\) −61.0347 + 105.715i −0.00338216 + 0.00585807i
\(689\) −7407.21 12829.7i −0.409568 0.709392i
\(690\) 0 0
\(691\) −7555.03 + 13085.7i −0.415929 + 0.720410i −0.995525 0.0944937i \(-0.969877\pi\)
0.579597 + 0.814904i \(0.303210\pi\)
\(692\) −2490.64 −0.136821
\(693\) 0 0
\(694\) −20873.8 −1.14173
\(695\) 8359.70 14479.4i 0.456261 0.790268i
\(696\) 0 0
\(697\) 1718.83 + 2977.09i 0.0934077 + 0.161787i
\(698\) 2257.01 3909.26i 0.122391 0.211988i
\(699\) 0 0
\(700\) 363.451 + 1118.58i 0.0196245 + 0.0603975i
\(701\) −18353.3 −0.988865 −0.494432 0.869216i \(-0.664624\pi\)
−0.494432 + 0.869216i \(0.664624\pi\)
\(702\) 0 0
\(703\) 11664.0 + 20202.6i 0.625769 + 1.08386i
\(704\) −1955.95 3387.81i −0.104713 0.181368i
\(705\) 0 0
\(706\) −11232.9 −0.598803
\(707\) 17679.4 + 3757.83i 0.940454 + 0.199898i
\(708\) 0 0
\(709\) 5036.85 8724.07i 0.266802 0.462115i −0.701232 0.712933i \(-0.747366\pi\)
0.968034 + 0.250818i \(0.0806997\pi\)
\(710\) −6596.85 11426.1i −0.348698 0.603962i
\(711\) 0 0
\(712\) 6288.38 10891.8i 0.330993 0.573297i
\(713\) −38532.3 −2.02391
\(714\) 0 0
\(715\) 37819.7 1.97815
\(716\) 899.861 1558.61i 0.0469684 0.0813517i
\(717\) 0 0
\(718\) −795.591 1378.00i −0.0413526 0.0716249i
\(719\) 9944.63 17224.6i 0.515817 0.893420i −0.484015 0.875060i \(-0.660822\pi\)
0.999831 0.0183607i \(-0.00584472\pi\)
\(720\) 0 0
\(721\) 3680.78 + 11328.2i 0.190124 + 0.585138i
\(722\) −809.397 −0.0417211
\(723\) 0 0
\(724\) −368.706 638.617i −0.0189266 0.0327818i
\(725\) −675.730 1170.40i −0.0346151 0.0599552i
\(726\) 0 0
\(727\) 13403.5 0.683780 0.341890 0.939740i \(-0.388933\pi\)
0.341890 + 0.939740i \(0.388933\pi\)
\(728\) 5872.15 6521.71i 0.298951 0.332020i
\(729\) 0 0
\(730\) −8025.66 + 13900.9i −0.406908 + 0.704786i
\(731\) −78.0566 135.198i −0.00394942 0.00684060i
\(732\) 0 0
\(733\) −6627.50 + 11479.2i −0.333960 + 0.578435i −0.983284 0.182076i \(-0.941718\pi\)
0.649325 + 0.760511i \(0.275052\pi\)
\(734\) 16387.9 0.824101
\(735\) 0 0
\(736\) −5063.91 −0.253612
\(737\) 8477.29 14683.1i 0.423698 0.733866i
\(738\) 0 0
\(739\) −7710.19 13354.4i −0.383794 0.664751i 0.607807 0.794085i \(-0.292049\pi\)
−0.991601 + 0.129334i \(0.958716\pi\)
\(740\) 6066.55 10507.6i 0.301366 0.521981i
\(741\) 0 0
\(742\) 6199.00 6884.71i 0.306701 0.340628i
\(743\) −943.019 −0.0465626 −0.0232813 0.999729i \(-0.507411\pi\)
−0.0232813 + 0.999729i \(0.507411\pi\)
\(744\) 0 0
\(745\) 15344.0 + 26576.5i 0.754576 + 1.30696i
\(746\) −14077.4 24382.7i −0.690897 1.19667i
\(747\) 0 0
\(748\) 5002.89 0.244551
\(749\) 1783.29 + 5488.37i 0.0869960 + 0.267744i
\(750\) 0 0
\(751\) 14297.9 24764.7i 0.694726 1.20330i −0.275547 0.961287i \(-0.588859\pi\)
0.970273 0.242013i \(-0.0778076\pi\)
\(752\) 1354.33 + 2345.76i 0.0656744 + 0.113751i
\(753\) 0 0
\(754\) −5041.96 + 8732.94i −0.243524 + 0.421797i
\(755\) −19046.9 −0.918127
\(756\) 0 0
\(757\) −28984.4 −1.39162 −0.695810 0.718226i \(-0.744955\pi\)
−0.695810 + 0.718226i \(0.744955\pi\)
\(758\) −6221.22 + 10775.5i −0.298107 + 0.516336i
\(759\) 0 0
\(760\) −3356.94 5814.39i −0.160222 0.277513i
\(761\) 4465.05 7733.70i 0.212691 0.368392i −0.739865 0.672756i \(-0.765110\pi\)
0.952556 + 0.304364i \(0.0984438\pi\)
\(762\) 0 0
\(763\) −33800.5 7184.46i −1.60375 0.340884i
\(764\) 1403.86 0.0664789
\(765\) 0 0
\(766\) −10701.4 18535.4i −0.504776 0.874297i
\(767\) −23847.0 41304.3i −1.12264 1.94447i
\(768\) 0 0
\(769\) 2373.15 0.111285 0.0556424 0.998451i \(-0.482279\pi\)
0.0556424 + 0.998451i \(0.482279\pi\)
\(770\) 7308.53 + 22493.2i 0.342053 + 1.05272i
\(771\) 0 0
\(772\) −3056.52 + 5294.04i −0.142495 + 0.246809i
\(773\) 13988.5 + 24228.8i 0.650881 + 1.12736i 0.982909 + 0.184089i \(0.0589336\pi\)
−0.332029 + 0.943269i \(0.607733\pi\)
\(774\) 0 0
\(775\) 1932.91 3347.90i 0.0895900 0.155174i
\(776\) 8361.32 0.386796
\(777\) 0 0
\(778\) −8443.23 −0.389080
\(779\) −6748.45 + 11688.7i −0.310383 + 0.537599i
\(780\) 0 0
\(781\) 19299.9 + 33428.5i 0.884259 + 1.53158i
\(782\) 3238.09 5608.53i 0.148074 0.256471i
\(783\) 0 0
\(784\) 5013.55 + 2232.15i 0.228387 + 0.101683i
\(785\) −6619.23 −0.300956
\(786\) 0 0
\(787\) −17180.5 29757.4i −0.778167 1.34782i −0.932997 </