Properties

Label 108.3.d.d.55.5
Level 108
Weight 3
Character 108.55
Analytic conductor 2.943
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.207360000.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.5
Root \(1.14412 - 1.98168i\) of \(x^{8} + 6 x^{6} + 32 x^{4} + 24 x^{2} + 16\)
Character \(\chi\) \(=\) 108.55
Dual form 108.3.d.d.55.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.270091 - 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} +7.40492 q^{5} -9.47802i q^{7} +(-3.16228 + 7.34847i) q^{8} +O(q^{10})\) \(q+(0.270091 - 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} +7.40492 q^{5} -9.47802i q^{7} +(-3.16228 + 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} -6.77022i q^{11} -14.4164 q^{13} +(-18.7824 - 2.55992i) q^{14} +(13.7082 + 8.25137i) q^{16} +17.8933 q^{17} +5.19615i q^{19} +(-28.5393 - 7.92672i) q^{20} +(-13.4164 - 1.82857i) q^{22} +24.9366i q^{23} +29.8328 q^{25} +(-3.89374 + 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} +29.6197 q^{29} +17.1275i q^{31} +(20.0540 - 24.9366i) q^{32} +(4.83282 - 35.4588i) q^{34} -70.1839i q^{35} +6.41641 q^{37} +(10.2971 + 1.40343i) q^{38} +(-23.4164 + 54.4148i) q^{40} +8.64290 q^{41} +50.1329i q^{43} +(-7.24730 + 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} +52.0175i q^{47} -40.8328 q^{49} +(8.05757 - 59.1191i) q^{50} +(55.5623 + 15.4323i) q^{52} -82.6921 q^{53} -50.1329i q^{55} +(69.6489 + 29.9721i) q^{56} +(8.00000 - 58.6967i) q^{58} +83.7244i q^{59} -8.41641 q^{61} +(33.9411 + 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} -106.752 q^{65} -29.0588i q^{67} +(-68.9626 - 19.1542i) q^{68} +(-139.082 - 18.9560i) q^{70} -113.287i q^{71} +2.16718 q^{73} +(1.73301 - 12.7153i) q^{74} +(5.56231 - 20.0265i) q^{76} -64.1683 q^{77} -149.485i q^{79} +(101.508 + 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} +13.5404i q^{83} +132.498 q^{85} +(99.3474 + 13.5404i) q^{86} +(49.7508 + 21.4093i) q^{88} +17.8933 q^{89} +136.639i q^{91} +(26.6938 - 96.1083i) q^{92} +(103.082 + 14.0495i) q^{94} +38.4771i q^{95} -138.331 q^{97} +(-11.0286 + 80.9175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + O(q^{10}) \) \( 8q - 4q^{4} + 16q^{10} - 8q^{13} + 56q^{16} + 24q^{25} - 108q^{28} - 176q^{34} - 56q^{37} - 80q^{40} + 288q^{46} - 112q^{49} + 364q^{52} + 64q^{58} + 40q^{61} - 352q^{64} - 576q^{70} + 232q^{73} - 36q^{76} + 448q^{82} + 416q^{85} + 720q^{88} + 288q^{94} - 248q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.270091 1.98168i 0.135045 0.990839i
\(3\) 0 0
\(4\) −3.85410 1.07047i −0.963525 0.267617i
\(5\) 7.40492 1.48098 0.740492 0.672065i \(-0.234593\pi\)
0.740492 + 0.672065i \(0.234593\pi\)
\(6\) 0 0
\(7\) 9.47802i 1.35400i −0.735982 0.677001i \(-0.763279\pi\)
0.735982 0.677001i \(-0.236721\pi\)
\(8\) −3.16228 + 7.34847i −0.395285 + 0.918559i
\(9\) 0 0
\(10\) 2.00000 14.6742i 0.200000 1.46742i
\(11\) 6.77022i 0.615475i −0.951471 0.307737i \(-0.900428\pi\)
0.951471 0.307737i \(-0.0995718\pi\)
\(12\) 0 0
\(13\) −14.4164 −1.10895 −0.554477 0.832199i \(-0.687082\pi\)
−0.554477 + 0.832199i \(0.687082\pi\)
\(14\) −18.7824 2.55992i −1.34160 0.182852i
\(15\) 0 0
\(16\) 13.7082 + 8.25137i 0.856763 + 0.515711i
\(17\) 17.8933 1.05255 0.526274 0.850315i \(-0.323589\pi\)
0.526274 + 0.850315i \(0.323589\pi\)
\(18\) 0 0
\(19\) 5.19615i 0.273482i 0.990607 + 0.136741i \(0.0436628\pi\)
−0.990607 + 0.136741i \(0.956337\pi\)
\(20\) −28.5393 7.92672i −1.42697 0.396336i
\(21\) 0 0
\(22\) −13.4164 1.82857i −0.609837 0.0831170i
\(23\) 24.9366i 1.08420i 0.840313 + 0.542101i \(0.182371\pi\)
−0.840313 + 0.542101i \(0.817629\pi\)
\(24\) 0 0
\(25\) 29.8328 1.19331
\(26\) −3.89374 + 28.5687i −0.149759 + 1.09880i
\(27\) 0 0
\(28\) −10.1459 + 36.5292i −0.362354 + 1.30462i
\(29\) 29.6197 1.02137 0.510684 0.859768i \(-0.329392\pi\)
0.510684 + 0.859768i \(0.329392\pi\)
\(30\) 0 0
\(31\) 17.1275i 0.552499i 0.961086 + 0.276249i \(0.0890916\pi\)
−0.961086 + 0.276249i \(0.910908\pi\)
\(32\) 20.0540 24.9366i 0.626688 0.779270i
\(33\) 0 0
\(34\) 4.83282 35.4588i 0.142142 1.04291i
\(35\) 70.1839i 2.00526i
\(36\) 0 0
\(37\) 6.41641 0.173416 0.0867082 0.996234i \(-0.472365\pi\)
0.0867082 + 0.996234i \(0.472365\pi\)
\(38\) 10.2971 + 1.40343i 0.270976 + 0.0369324i
\(39\) 0 0
\(40\) −23.4164 + 54.4148i −0.585410 + 1.36037i
\(41\) 8.64290 0.210803 0.105401 0.994430i \(-0.466387\pi\)
0.105401 + 0.994430i \(0.466387\pi\)
\(42\) 0 0
\(43\) 50.1329i 1.16588i 0.812514 + 0.582941i \(0.198098\pi\)
−0.812514 + 0.582941i \(0.801902\pi\)
\(44\) −7.24730 + 26.0931i −0.164711 + 0.593026i
\(45\) 0 0
\(46\) 49.4164 + 6.73516i 1.07427 + 0.146416i
\(47\) 52.0175i 1.10676i 0.832930 + 0.553378i \(0.186661\pi\)
−0.832930 + 0.553378i \(0.813339\pi\)
\(48\) 0 0
\(49\) −40.8328 −0.833323
\(50\) 8.05757 59.1191i 0.161151 1.18238i
\(51\) 0 0
\(52\) 55.5623 + 15.4323i 1.06851 + 0.296775i
\(53\) −82.6921 −1.56023 −0.780114 0.625637i \(-0.784839\pi\)
−0.780114 + 0.625637i \(0.784839\pi\)
\(54\) 0 0
\(55\) 50.1329i 0.911508i
\(56\) 69.6489 + 29.9721i 1.24373 + 0.535216i
\(57\) 0 0
\(58\) 8.00000 58.6967i 0.137931 1.01201i
\(59\) 83.7244i 1.41906i 0.704676 + 0.709529i \(0.251092\pi\)
−0.704676 + 0.709529i \(0.748908\pi\)
\(60\) 0 0
\(61\) −8.41641 −0.137974 −0.0689869 0.997618i \(-0.521977\pi\)
−0.0689869 + 0.997618i \(0.521977\pi\)
\(62\) 33.9411 + 4.62597i 0.547438 + 0.0746124i
\(63\) 0 0
\(64\) −44.0000 46.4758i −0.687500 0.726184i
\(65\) −106.752 −1.64234
\(66\) 0 0
\(67\) 29.0588i 0.433713i −0.976203 0.216856i \(-0.930420\pi\)
0.976203 0.216856i \(-0.0695804\pi\)
\(68\) −68.9626 19.1542i −1.01416 0.281679i
\(69\) 0 0
\(70\) −139.082 18.9560i −1.98689 0.270800i
\(71\) 113.287i 1.59559i −0.602928 0.797796i \(-0.705999\pi\)
0.602928 0.797796i \(-0.294001\pi\)
\(72\) 0 0
\(73\) 2.16718 0.0296875 0.0148437 0.999890i \(-0.495275\pi\)
0.0148437 + 0.999890i \(0.495275\pi\)
\(74\) 1.73301 12.7153i 0.0234191 0.171828i
\(75\) 0 0
\(76\) 5.56231 20.0265i 0.0731882 0.263507i
\(77\) −64.1683 −0.833354
\(78\) 0 0
\(79\) 149.485i 1.89221i −0.323861 0.946105i \(-0.604981\pi\)
0.323861 0.946105i \(-0.395019\pi\)
\(80\) 101.508 + 61.1007i 1.26885 + 0.763759i
\(81\) 0 0
\(82\) 2.33437 17.1275i 0.0284679 0.208871i
\(83\) 13.5404i 0.163138i 0.996668 + 0.0815690i \(0.0259931\pi\)
−0.996668 + 0.0815690i \(0.974007\pi\)
\(84\) 0 0
\(85\) 132.498 1.55881
\(86\) 99.3474 + 13.5404i 1.15520 + 0.157447i
\(87\) 0 0
\(88\) 49.7508 + 21.4093i 0.565350 + 0.243288i
\(89\) 17.8933 0.201048 0.100524 0.994935i \(-0.467948\pi\)
0.100524 + 0.994935i \(0.467948\pi\)
\(90\) 0 0
\(91\) 136.639i 1.50153i
\(92\) 26.6938 96.1083i 0.290150 1.04466i
\(93\) 0 0
\(94\) 103.082 + 14.0495i 1.09662 + 0.149462i
\(95\) 38.4771i 0.405022i
\(96\) 0 0
\(97\) −138.331 −1.42610 −0.713048 0.701115i \(-0.752686\pi\)
−0.713048 + 0.701115i \(0.752686\pi\)
\(98\) −11.0286 + 80.9175i −0.112536 + 0.825689i
\(99\) 0 0
\(100\) −114.979 31.9350i −1.14979 0.319350i
\(101\) 97.5019 0.965366 0.482683 0.875795i \(-0.339662\pi\)
0.482683 + 0.875795i \(0.339662\pi\)
\(102\) 0 0
\(103\) 42.4835i 0.412461i −0.978503 0.206231i \(-0.933880\pi\)
0.978503 0.206231i \(-0.0661197\pi\)
\(104\) 45.5887 105.939i 0.438353 1.01864i
\(105\) 0 0
\(106\) −22.3344 + 163.869i −0.210702 + 1.54594i
\(107\) 97.2648i 0.909017i 0.890742 + 0.454509i \(0.150185\pi\)
−0.890742 + 0.454509i \(0.849815\pi\)
\(108\) 0 0
\(109\) −96.8328 −0.888374 −0.444187 0.895934i \(-0.646507\pi\)
−0.444187 + 0.895934i \(0.646507\pi\)
\(110\) −99.3474 13.5404i −0.903158 0.123095i
\(111\) 0 0
\(112\) 78.2067 129.927i 0.698274 1.16006i
\(113\) 38.8701 0.343983 0.171991 0.985098i \(-0.444980\pi\)
0.171991 + 0.985098i \(0.444980\pi\)
\(114\) 0 0
\(115\) 184.654i 1.60568i
\(116\) −114.157 31.7069i −0.984114 0.273335i
\(117\) 0 0
\(118\) 165.915 + 22.6132i 1.40606 + 0.191637i
\(119\) 169.593i 1.42515i
\(120\) 0 0
\(121\) 75.1641 0.621191
\(122\) −2.27319 + 16.6786i −0.0186327 + 0.136710i
\(123\) 0 0
\(124\) 18.3344 66.0110i 0.147858 0.532347i
\(125\) 35.7866 0.286293
\(126\) 0 0
\(127\) 99.0165i 0.779657i −0.920887 0.389829i \(-0.872534\pi\)
0.920887 0.389829i \(-0.127466\pi\)
\(128\) −103.984 + 74.6412i −0.812376 + 0.583134i
\(129\) 0 0
\(130\) −28.8328 + 211.549i −0.221791 + 1.62730i
\(131\) 54.1618i 0.413449i −0.978399 0.206724i \(-0.933720\pi\)
0.978399 0.206724i \(-0.0662803\pi\)
\(132\) 0 0
\(133\) 49.2492 0.370295
\(134\) −57.5851 7.84850i −0.429740 0.0585709i
\(135\) 0 0
\(136\) −56.5836 + 131.488i −0.416056 + 0.966826i
\(137\) −5.55944 −0.0405798 −0.0202899 0.999794i \(-0.506459\pi\)
−0.0202899 + 0.999794i \(0.506459\pi\)
\(138\) 0 0
\(139\) 152.517i 1.09724i 0.836070 + 0.548622i \(0.184847\pi\)
−0.836070 + 0.548622i \(0.815153\pi\)
\(140\) −75.1295 + 270.496i −0.536640 + 1.93211i
\(141\) 0 0
\(142\) −224.498 30.5978i −1.58097 0.215477i
\(143\) 97.6023i 0.682534i
\(144\) 0 0
\(145\) 219.331 1.51263
\(146\) 0.585336 4.29466i 0.00400915 0.0294155i
\(147\) 0 0
\(148\) −24.7295 6.86855i −0.167091 0.0464091i
\(149\) 136.979 0.919325 0.459663 0.888094i \(-0.347970\pi\)
0.459663 + 0.888094i \(0.347970\pi\)
\(150\) 0 0
\(151\) 77.9879i 0.516476i 0.966081 + 0.258238i \(0.0831419\pi\)
−0.966081 + 0.258238i \(0.916858\pi\)
\(152\) −38.1838 16.4317i −0.251209 0.108103i
\(153\) 0 0
\(154\) −17.3313 + 127.161i −0.112541 + 0.825720i
\(155\) 126.827i 0.818242i
\(156\) 0 0
\(157\) −72.1641 −0.459644 −0.229822 0.973233i \(-0.573814\pi\)
−0.229822 + 0.973233i \(0.573814\pi\)
\(158\) −296.230 40.3744i −1.87488 0.255534i
\(159\) 0 0
\(160\) 148.498 184.654i 0.928115 1.15409i
\(161\) 236.350 1.46801
\(162\) 0 0
\(163\) 56.5785i 0.347108i −0.984824 0.173554i \(-0.944475\pi\)
0.984824 0.173554i \(-0.0555250\pi\)
\(164\) −33.3106 9.25194i −0.203114 0.0564143i
\(165\) 0 0
\(166\) 26.8328 + 3.65715i 0.161643 + 0.0220310i
\(167\) 201.637i 1.20741i −0.797208 0.603705i \(-0.793691\pi\)
0.797208 0.603705i \(-0.206309\pi\)
\(168\) 0 0
\(169\) 38.8328 0.229780
\(170\) 35.7866 262.569i 0.210509 1.54453i
\(171\) 0 0
\(172\) 53.6656 193.217i 0.312009 1.12336i
\(173\) 92.5500 0.534971 0.267485 0.963562i \(-0.413807\pi\)
0.267485 + 0.963562i \(0.413807\pi\)
\(174\) 0 0
\(175\) 282.756i 1.61575i
\(176\) 55.8636 92.8076i 0.317407 0.527316i
\(177\) 0 0
\(178\) 4.83282 35.4588i 0.0271507 0.199207i
\(179\) 4.28851i 0.0239581i −0.999928 0.0119791i \(-0.996187\pi\)
0.999928 0.0119791i \(-0.00381315\pi\)
\(180\) 0 0
\(181\) −289.748 −1.60082 −0.800408 0.599456i \(-0.795384\pi\)
−0.800408 + 0.599456i \(0.795384\pi\)
\(182\) 270.775 + 36.9049i 1.48777 + 0.202774i
\(183\) 0 0
\(184\) −183.246 78.8566i −0.995903 0.428568i
\(185\) 47.5130 0.256827
\(186\) 0 0
\(187\) 121.142i 0.647816i
\(188\) 55.6830 200.481i 0.296186 1.06639i
\(189\) 0 0
\(190\) 76.2492 + 10.3923i 0.401312 + 0.0546963i
\(191\) 92.6389i 0.485020i 0.970149 + 0.242510i \(0.0779708\pi\)
−0.970149 + 0.242510i \(0.922029\pi\)
\(192\) 0 0
\(193\) −243.164 −1.25992 −0.629959 0.776629i \(-0.716928\pi\)
−0.629959 + 0.776629i \(0.716928\pi\)
\(194\) −37.3620 + 274.128i −0.192588 + 1.41303i
\(195\) 0 0
\(196\) 157.374 + 43.7102i 0.802928 + 0.223011i
\(197\) −139.432 −0.707779 −0.353890 0.935287i \(-0.615141\pi\)
−0.353890 + 0.935287i \(0.615141\pi\)
\(198\) 0 0
\(199\) 110.993i 0.557756i −0.960327 0.278878i \(-0.910038\pi\)
0.960327 0.278878i \(-0.0899624\pi\)
\(200\) −94.3396 + 219.226i −0.471698 + 1.09613i
\(201\) 0 0
\(202\) 26.3344 193.217i 0.130368 0.956522i
\(203\) 280.736i 1.38293i
\(204\) 0 0
\(205\) 64.0000 0.312195
\(206\) −84.1887 11.4744i −0.408683 0.0557010i
\(207\) 0 0
\(208\) −197.623 118.955i −0.950111 0.571900i
\(209\) 35.1791 0.168321
\(210\) 0 0
\(211\) 265.095i 1.25637i 0.778062 + 0.628187i \(0.216203\pi\)
−0.778062 + 0.628187i \(0.783797\pi\)
\(212\) 318.704 + 88.5191i 1.50332 + 0.417543i
\(213\) 0 0
\(214\) 192.748 + 26.2703i 0.900690 + 0.122759i
\(215\) 371.230i 1.72665i
\(216\) 0 0
\(217\) 162.334 0.748085
\(218\) −26.1536 + 191.892i −0.119971 + 0.880236i
\(219\) 0 0
\(220\) −53.6656 + 193.217i −0.243935 + 0.878261i
\(221\) −257.957 −1.16723
\(222\) 0 0
\(223\) 317.925i 1.42567i −0.701330 0.712837i \(-0.747410\pi\)
0.701330 0.712837i \(-0.252590\pi\)
\(224\) −236.350 190.072i −1.05513 0.848538i
\(225\) 0 0
\(226\) 10.4984 77.0280i 0.0464533 0.340832i
\(227\) 249.366i 1.09853i −0.835648 0.549265i \(-0.814908\pi\)
0.835648 0.549265i \(-0.185092\pi\)
\(228\) 0 0
\(229\) 152.334 0.665216 0.332608 0.943065i \(-0.392071\pi\)
0.332608 + 0.943065i \(0.392071\pi\)
\(230\) 365.924 + 49.8733i 1.59098 + 0.216840i
\(231\) 0 0
\(232\) −93.6656 + 217.659i −0.403731 + 0.938186i
\(233\) −346.793 −1.48838 −0.744191 0.667966i \(-0.767165\pi\)
−0.744191 + 0.667966i \(0.767165\pi\)
\(234\) 0 0
\(235\) 385.186i 1.63909i
\(236\) 89.6241 322.682i 0.379763 1.36730i
\(237\) 0 0
\(238\) −336.079 45.8055i −1.41210 0.192460i
\(239\) 104.035i 0.435293i 0.976028 + 0.217647i \(0.0698380\pi\)
−0.976028 + 0.217647i \(0.930162\pi\)
\(240\) 0 0
\(241\) 281.827 1.16940 0.584702 0.811248i \(-0.301211\pi\)
0.584702 + 0.811248i \(0.301211\pi\)
\(242\) 20.3011 148.951i 0.0838889 0.615500i
\(243\) 0 0
\(244\) 32.4377 + 9.00948i 0.132941 + 0.0369241i
\(245\) −302.364 −1.23414
\(246\) 0 0
\(247\) 74.9099i 0.303279i
\(248\) −125.861 54.1618i −0.507502 0.218394i
\(249\) 0 0
\(250\) 9.66563 70.9176i 0.0386625 0.283670i
\(251\) 271.484i 1.08161i 0.841148 + 0.540804i \(0.181880\pi\)
−0.841148 + 0.540804i \(0.818120\pi\)
\(252\) 0 0
\(253\) 168.827 0.667299
\(254\) −196.219 26.7434i −0.772515 0.105289i
\(255\) 0 0
\(256\) 119.830 + 226.223i 0.468085 + 0.883684i
\(257\) −459.105 −1.78640 −0.893200 0.449659i \(-0.851545\pi\)
−0.893200 + 0.449659i \(0.851545\pi\)
\(258\) 0 0
\(259\) 60.8148i 0.234806i
\(260\) 411.434 + 114.275i 1.58244 + 0.439518i
\(261\) 0 0
\(262\) −107.331 14.6286i −0.409661 0.0558343i
\(263\) 203.782i 0.774835i 0.921904 + 0.387418i \(0.126633\pi\)
−0.921904 + 0.387418i \(0.873367\pi\)
\(264\) 0 0
\(265\) −612.328 −2.31067
\(266\) 13.3018 97.5961i 0.0500066 0.366903i
\(267\) 0 0
\(268\) −31.1064 + 111.995i −0.116069 + 0.417893i
\(269\) 323.363 1.20209 0.601047 0.799213i \(-0.294750\pi\)
0.601047 + 0.799213i \(0.294750\pi\)
\(270\) 0 0
\(271\) 104.928i 0.387190i 0.981082 + 0.193595i \(0.0620148\pi\)
−0.981082 + 0.193595i \(0.937985\pi\)
\(272\) 245.285 + 147.644i 0.901783 + 0.542810i
\(273\) 0 0
\(274\) −1.50155 + 11.0170i −0.00548012 + 0.0402081i
\(275\) 201.975i 0.734454i
\(276\) 0 0
\(277\) −48.8328 −0.176292 −0.0881459 0.996108i \(-0.528094\pi\)
−0.0881459 + 0.996108i \(0.528094\pi\)
\(278\) 302.240 + 41.1934i 1.08719 + 0.148178i
\(279\) 0 0
\(280\) 515.745 + 221.941i 1.84194 + 0.792647i
\(281\) 29.6197 0.105408 0.0527040 0.998610i \(-0.483216\pi\)
0.0527040 + 0.998610i \(0.483216\pi\)
\(282\) 0 0
\(283\) 385.186i 1.36108i 0.732711 + 0.680540i \(0.238255\pi\)
−0.732711 + 0.680540i \(0.761745\pi\)
\(284\) −121.270 + 436.620i −0.427007 + 1.53739i
\(285\) 0 0
\(286\) 193.416 + 26.3615i 0.676281 + 0.0921730i
\(287\) 81.9176i 0.285427i
\(288\) 0 0
\(289\) 31.1703 0.107856
\(290\) 59.2393 434.644i 0.204274 1.49877i
\(291\) 0 0
\(292\) −8.35255 2.31990i −0.0286046 0.00794486i
\(293\) 281.410 0.960443 0.480222 0.877147i \(-0.340556\pi\)
0.480222 + 0.877147i \(0.340556\pi\)
\(294\) 0 0
\(295\) 619.972i 2.10160i
\(296\) −20.2905 + 47.1508i −0.0685489 + 0.159293i
\(297\) 0 0
\(298\) 36.9969 271.449i 0.124151 0.910904i
\(299\) 359.497i 1.20233i
\(300\) 0 0
\(301\) 475.161 1.57861
\(302\) 154.547 + 21.0638i 0.511745 + 0.0697477i
\(303\) 0 0
\(304\) −42.8754 + 71.2299i −0.141037 + 0.234309i
\(305\) −62.3228 −0.204337
\(306\) 0 0
\(307\) 553.961i 1.80443i −0.431282 0.902217i \(-0.641939\pi\)
0.431282 0.902217i \(-0.358061\pi\)
\(308\) 247.311 + 68.6900i 0.802958 + 0.223019i
\(309\) 0 0
\(310\) 251.331 + 34.2549i 0.810746 + 0.110500i
\(311\) 15.6847i 0.0504331i −0.999682 0.0252166i \(-0.991972\pi\)
0.999682 0.0252166i \(-0.00802753\pi\)
\(312\) 0 0
\(313\) −308.161 −0.984540 −0.492270 0.870443i \(-0.663833\pi\)
−0.492270 + 0.870443i \(0.663833\pi\)
\(314\) −19.4909 + 143.006i −0.0620728 + 0.455433i
\(315\) 0 0
\(316\) −160.018 + 576.129i −0.506387 + 1.82319i
\(317\) −496.107 −1.56500 −0.782502 0.622648i \(-0.786057\pi\)
−0.782502 + 0.622648i \(0.786057\pi\)
\(318\) 0 0
\(319\) 200.532i 0.628626i
\(320\) −325.816 344.150i −1.01818 1.07547i
\(321\) 0 0
\(322\) 63.8359 468.370i 0.198248 1.45456i
\(323\) 92.9763i 0.287852i
\(324\) 0 0
\(325\) −430.082 −1.32333
\(326\) −112.120 15.2813i −0.343928 0.0468753i
\(327\) 0 0
\(328\) −27.3313 + 63.5121i −0.0833270 + 0.193634i
\(329\) 493.023 1.49855
\(330\) 0 0
\(331\) 86.5060i 0.261347i 0.991425 + 0.130674i \(0.0417140\pi\)
−0.991425 + 0.130674i \(0.958286\pi\)
\(332\) 14.4946 52.1863i 0.0436584 0.157188i
\(333\) 0 0
\(334\) −399.580 54.4604i −1.19635 0.163055i
\(335\) 215.178i 0.642322i
\(336\) 0 0
\(337\) 320.659 0.951512 0.475756 0.879577i \(-0.342175\pi\)
0.475756 + 0.879577i \(0.342175\pi\)
\(338\) 10.4884 76.9542i 0.0310307 0.227675i
\(339\) 0 0
\(340\) −510.663 141.835i −1.50195 0.417162i
\(341\) 115.957 0.340049
\(342\) 0 0
\(343\) 77.4087i 0.225681i
\(344\) −368.400 158.534i −1.07093 0.460856i
\(345\) 0 0
\(346\) 24.9969 183.404i 0.0722454 0.530070i
\(347\) 674.759i 1.94455i 0.233842 + 0.972275i \(0.424870\pi\)
−0.233842 + 0.972275i \(0.575130\pi\)
\(348\) 0 0
\(349\) 153.918 0.441026 0.220513 0.975384i \(-0.429227\pi\)
0.220513 + 0.975384i \(0.429227\pi\)
\(350\) −560.331 76.3698i −1.60095 0.218199i
\(351\) 0 0
\(352\) −168.827 135.770i −0.479621 0.385711i
\(353\) 623.228 1.76552 0.882759 0.469825i \(-0.155683\pi\)
0.882759 + 0.469825i \(0.155683\pi\)
\(354\) 0 0
\(355\) 838.881i 2.36305i
\(356\) −68.9626 19.1542i −0.193715 0.0538039i
\(357\) 0 0
\(358\) −8.49845 1.15829i −0.0237387 0.00323544i
\(359\) 160.341i 0.446633i −0.974746 0.223316i \(-0.928312\pi\)
0.974746 0.223316i \(-0.0716883\pi\)
\(360\) 0 0
\(361\) 334.000 0.925208
\(362\) −78.2582 + 574.187i −0.216183 + 1.58615i
\(363\) 0 0
\(364\) 146.267 526.621i 0.401834 1.44676i
\(365\) 16.0478 0.0439666
\(366\) 0 0
\(367\) 284.585i 0.775435i −0.921778 0.387717i \(-0.873264\pi\)
0.921778 0.387717i \(-0.126736\pi\)
\(368\) −205.761 + 341.837i −0.559134 + 0.928904i
\(369\) 0 0
\(370\) 12.8328 94.1555i 0.0346833 0.254474i
\(371\) 783.757i 2.11255i
\(372\) 0 0
\(373\) 301.420 0.808095 0.404048 0.914738i \(-0.367603\pi\)
0.404048 + 0.914738i \(0.367603\pi\)
\(374\) −240.064 32.7192i −0.641882 0.0874846i
\(375\) 0 0
\(376\) −382.249 164.494i −1.01662 0.437484i
\(377\) −427.009 −1.13265
\(378\) 0 0
\(379\) 248.547i 0.655796i 0.944713 + 0.327898i \(0.106340\pi\)
−0.944713 + 0.327898i \(0.893660\pi\)
\(380\) 41.1884 148.295i 0.108391 0.390249i
\(381\) 0 0
\(382\) 183.580 + 25.0209i 0.480577 + 0.0654997i
\(383\) 488.131i 1.27449i −0.770660 0.637247i \(-0.780073\pi\)
0.770660 0.637247i \(-0.219927\pi\)
\(384\) 0 0
\(385\) −475.161 −1.23418
\(386\) −65.6764 + 481.873i −0.170146 + 1.24838i
\(387\) 0 0
\(388\) 533.143 + 148.079i 1.37408 + 0.381647i
\(389\) 415.867 1.06907 0.534534 0.845147i \(-0.320487\pi\)
0.534534 + 0.845147i \(0.320487\pi\)
\(390\) 0 0
\(391\) 446.199i 1.14117i
\(392\) 129.125 300.059i 0.329400 0.765456i
\(393\) 0 0
\(394\) −37.6594 + 276.310i −0.0955823 + 0.701295i
\(395\) 1106.92i 2.80233i
\(396\) 0 0
\(397\) −670.827 −1.68974 −0.844870 0.534972i \(-0.820322\pi\)
−0.844870 + 0.534972i \(0.820322\pi\)
\(398\) −219.953 29.9783i −0.552646 0.0753223i
\(399\) 0 0
\(400\) 408.954 + 246.162i 1.02239 + 0.615404i
\(401\) −114.742 −0.286139 −0.143070 0.989713i \(-0.545697\pi\)
−0.143070 + 0.989713i \(0.545697\pi\)
\(402\) 0 0
\(403\) 246.916i 0.612696i
\(404\) −375.782 104.373i −0.930154 0.258348i
\(405\) 0 0
\(406\) −556.328 75.8241i −1.37027 0.186759i
\(407\) 43.4405i 0.106733i
\(408\) 0 0
\(409\) −146.672 −0.358611 −0.179305 0.983793i \(-0.557385\pi\)
−0.179305 + 0.983793i \(0.557385\pi\)
\(410\) 17.2858 126.827i 0.0421605 0.309335i
\(411\) 0 0
\(412\) −45.4772 + 163.736i −0.110381 + 0.397417i
\(413\) 793.541 1.92141
\(414\) 0 0
\(415\) 100.266i 0.241605i
\(416\) −289.107 + 359.497i −0.694969 + 0.864175i
\(417\) 0 0
\(418\) 9.50155 69.7137i 0.0227310 0.166779i
\(419\) 536.872i 1.28132i 0.767825 + 0.640659i \(0.221339\pi\)
−0.767825 + 0.640659i \(0.778661\pi\)
\(420\) 0 0
\(421\) −367.413 −0.872716 −0.436358 0.899773i \(-0.643732\pi\)
−0.436358 + 0.899773i \(0.643732\pi\)
\(422\) 525.333 + 71.5997i 1.24486 + 0.169668i
\(423\) 0 0
\(424\) 261.495 607.660i 0.616734 1.43316i
\(425\) 533.808 1.25602
\(426\) 0 0
\(427\) 79.7709i 0.186817i
\(428\) 104.119 374.869i 0.243268 0.875861i
\(429\) 0 0
\(430\) 735.659 + 100.266i 1.71084 + 0.233177i
\(431\) 735.353i 1.70616i −0.521784 0.853078i \(-0.674733\pi\)
0.521784 0.853078i \(-0.325267\pi\)
\(432\) 0 0
\(433\) 765.161 1.76712 0.883558 0.468322i \(-0.155141\pi\)
0.883558 + 0.468322i \(0.155141\pi\)
\(434\) 43.8450 321.695i 0.101025 0.741232i
\(435\) 0 0
\(436\) 373.204 + 103.656i 0.855971 + 0.237744i
\(437\) −129.575 −0.296509
\(438\) 0 0
\(439\) 46.3847i 0.105660i 0.998604 + 0.0528299i \(0.0168241\pi\)
−0.998604 + 0.0528299i \(0.983176\pi\)
\(440\) 368.400 + 158.534i 0.837274 + 0.360305i
\(441\) 0 0
\(442\) −69.6718 + 511.188i −0.157629 + 1.15653i
\(443\) 139.693i 0.315334i 0.987492 + 0.157667i \(0.0503973\pi\)
−0.987492 + 0.157667i \(0.949603\pi\)
\(444\) 0 0
\(445\) 132.498 0.297749
\(446\) −630.026 85.8686i −1.41261 0.192531i
\(447\) 0 0
\(448\) −440.498 + 417.033i −0.983255 + 0.930877i
\(449\) 267.139 0.594963 0.297482 0.954728i \(-0.403853\pi\)
0.297482 + 0.954728i \(0.403853\pi\)
\(450\) 0 0
\(451\) 58.5144i 0.129744i
\(452\) −149.809 41.6091i −0.331436 0.0920555i
\(453\) 0 0
\(454\) −494.164 67.3516i −1.08847 0.148351i
\(455\) 1011.80i 2.22374i
\(456\) 0 0
\(457\) 237.830 0.520415 0.260208 0.965553i \(-0.416209\pi\)
0.260208 + 0.965553i \(0.416209\pi\)
\(458\) 41.1441 301.878i 0.0898343 0.659122i
\(459\) 0 0
\(460\) 197.666 711.674i 0.429708 1.54712i
\(461\) −298.650 −0.647830 −0.323915 0.946086i \(-0.604999\pi\)
−0.323915 + 0.946086i \(0.604999\pi\)
\(462\) 0 0
\(463\) 489.535i 1.05731i 0.848837 + 0.528655i \(0.177304\pi\)
−0.848837 + 0.528655i \(0.822696\pi\)
\(464\) 406.033 + 244.403i 0.875070 + 0.526731i
\(465\) 0 0
\(466\) −93.6656 + 687.233i −0.200999 + 1.47475i
\(467\) 454.280i 0.972762i 0.873747 + 0.486381i \(0.161683\pi\)
−0.873747 + 0.486381i \(0.838317\pi\)
\(468\) 0 0
\(469\) −275.420 −0.587248
\(470\) 763.314 + 104.035i 1.62407 + 0.221351i
\(471\) 0 0
\(472\) −615.246 264.760i −1.30349 0.560932i
\(473\) 339.411 0.717571
\(474\) 0 0
\(475\) 155.016i 0.326349i
\(476\) −181.544 + 653.629i −0.381394 + 1.37317i
\(477\) 0 0
\(478\) 206.164 + 28.0989i 0.431306 + 0.0587843i
\(479\) 3.61359i 0.00754403i −0.999993 0.00377201i \(-0.998799\pi\)
0.999993 0.00377201i \(-0.00120067\pi\)
\(480\) 0 0
\(481\) −92.5016 −0.192311
\(482\) 76.1188 558.490i 0.157923 1.15869i
\(483\) 0 0
\(484\) −289.690 80.4606i −0.598533 0.166241i
\(485\) −1024.33 −2.11202
\(486\) 0 0
\(487\) 874.538i 1.79577i 0.440234 + 0.897883i \(0.354896\pi\)
−0.440234 + 0.897883i \(0.645104\pi\)
\(488\) 26.6150 61.8477i 0.0545390 0.126737i
\(489\) 0 0
\(490\) −81.6656 + 599.188i −0.166665 + 1.22283i
\(491\) 645.196i 1.31404i −0.753871 0.657022i \(-0.771816\pi\)
0.753871 0.657022i \(-0.228184\pi\)
\(492\) 0 0
\(493\) 529.994 1.07504
\(494\) −148.447 20.2325i −0.300501 0.0409564i
\(495\) 0 0
\(496\) −141.325 + 234.787i −0.284930 + 0.473360i
\(497\) −1073.74 −2.16043
\(498\) 0 0
\(499\) 564.842i 1.13195i −0.824423 0.565974i \(-0.808500\pi\)
0.824423 0.565974i \(-0.191500\pi\)
\(500\) −137.925 38.3084i −0.275850 0.0766167i
\(501\) 0 0
\(502\) 537.994 + 73.3253i 1.07170 + 0.146066i
\(503\) 483.048i 0.960334i −0.877177 0.480167i \(-0.840576\pi\)
0.877177 0.480167i \(-0.159424\pi\)
\(504\) 0 0
\(505\) 721.994 1.42969
\(506\) 45.5985 334.560i 0.0901156 0.661186i
\(507\) 0 0
\(508\) −105.994 + 381.620i −0.208649 + 0.751220i
\(509\) 216.004 0.424369 0.212184 0.977230i \(-0.431942\pi\)
0.212184 + 0.977230i \(0.431942\pi\)
\(510\) 0 0
\(511\) 20.5406i 0.0401969i
\(512\) 480.666 176.363i 0.938801 0.344459i
\(513\) 0 0
\(514\) −124.000 + 909.799i −0.241245 + 1.77004i
\(515\) 314.587i 0.610848i
\(516\) 0 0
\(517\) 352.170 0.681180
\(518\) −120.515 16.4255i −0.232655 0.0317095i
\(519\) 0 0
\(520\) 337.580 784.466i 0.649193 1.50859i
\(521\) −454.806 −0.872949 −0.436475 0.899717i \(-0.643773\pi\)
−0.436475 + 0.899717i \(0.643773\pi\)
\(522\) 0 0
\(523\) 325.041i 0.621493i −0.950493 0.310747i \(-0.899421\pi\)
0.950493 0.310747i \(-0.100579\pi\)
\(524\) −57.9784 + 208.745i −0.110646 + 0.398368i
\(525\) 0 0
\(526\) 403.830 + 55.0395i 0.767737 + 0.104638i
\(527\) 306.467i 0.581531i
\(528\) 0 0
\(529\) −92.8359 −0.175493
\(530\) −165.384 + 1213.44i −0.312046 + 2.28951i
\(531\) 0 0
\(532\) −189.812 52.7196i −0.356789 0.0990971i
\(533\) −124.600 −0.233770
\(534\) 0 0
\(535\) 720.238i 1.34624i
\(536\) 213.537 + 91.8919i 0.398391 + 0.171440i
\(537\) 0 0
\(538\) 87.3375 640.802i 0.162337 1.19108i
\(539\) 276.447i 0.512889i
\(540\) 0 0
\(541\) −962.574 −1.77925 −0.889625 0.456692i \(-0.849034\pi\)
−0.889625 + 0.456692i \(0.849034\pi\)
\(542\) 207.935 + 28.3402i 0.383643 + 0.0522882i
\(543\) 0 0
\(544\) 358.833 446.199i 0.659619 0.820218i
\(545\) −717.039 −1.31567
\(546\) 0 0
\(547\) 133.470i 0.244003i −0.992530 0.122002i \(-0.961069\pi\)
0.992530 0.122002i \(-0.0389313\pi\)
\(548\) 21.4266 + 5.95119i 0.0390997 + 0.0108598i
\(549\) 0 0
\(550\) −400.249 54.5515i −0.727726 0.0991846i
\(551\) 153.908i 0.279325i
\(552\) 0 0
\(553\) −1416.82 −2.56206
\(554\) −13.1893 + 96.7710i −0.0238074 + 0.174677i
\(555\) 0 0
\(556\) 163.264 587.816i 0.293641 1.05722i
\(557\) −413.437 −0.742258 −0.371129 0.928581i \(-0.621029\pi\)
−0.371129 + 0.928581i \(0.621029\pi\)
\(558\) 0 0
\(559\) 722.737i 1.29291i
\(560\) 579.114 962.096i 1.03413 1.71803i
\(561\) 0 0
\(562\) 8.00000 58.6967i 0.0142349 0.104442i
\(563\) 516.562i 0.917516i 0.888561 + 0.458758i \(0.151706\pi\)
−0.888561 + 0.458758i \(0.848294\pi\)
\(564\) 0 0
\(565\) 287.830 0.509433
\(566\) 763.314 + 104.035i 1.34861 + 0.183808i
\(567\) 0 0
\(568\) 832.486 + 358.245i 1.46564 + 0.630713i
\(569\) −468.355 −0.823120 −0.411560 0.911383i \(-0.635016\pi\)
−0.411560 + 0.911383i \(0.635016\pi\)
\(570\) 0 0
\(571\) 675.972i 1.18384i −0.805997 0.591919i \(-0.798370\pi\)
0.805997 0.591919i \(-0.201630\pi\)
\(572\) 104.480 376.169i 0.182657 0.657638i
\(573\) 0 0
\(574\) −162.334 22.1252i −0.282812 0.0385456i
\(575\) 743.930i 1.29379i
\(576\) 0 0
\(577\) −354.823 −0.614945 −0.307473 0.951557i \(-0.599483\pi\)
−0.307473 + 0.951557i \(0.599483\pi\)
\(578\) 8.41881 61.7695i 0.0145654 0.106868i
\(579\) 0 0
\(580\) −845.325 234.787i −1.45746 0.404805i
\(581\) 128.337 0.220889
\(582\) 0 0
\(583\) 559.844i 0.960281i
\(584\) −6.85324 + 15.9255i −0.0117350 + 0.0272697i
\(585\) 0 0
\(586\) 76.0062 557.664i 0.129703 0.951645i
\(587\) 220.479i 0.375603i −0.982207 0.187801i \(-0.939864\pi\)
0.982207 0.187801i \(-0.0601361\pi\)
\(588\) 0 0
\(589\) −88.9969 −0.151098
\(590\) 1228.59 + 167.449i 2.08235 + 0.283811i
\(591\) 0 0
\(592\) 87.9574 + 52.9442i 0.148577 + 0.0894327i
\(593\) 993.520 1.67541 0.837707 0.546121i \(-0.183896\pi\)
0.837707 + 0.546121i \(0.183896\pi\)
\(594\) 0 0
\(595\) 1255.82i 2.11063i
\(596\) −527.933 146.632i −0.885793 0.246027i
\(597\) 0 0
\(598\) −712.407 97.0967i −1.19132 0.162369i
\(599\) 280.736i 0.468674i −0.972155 0.234337i \(-0.924708\pi\)
0.972155 0.234337i \(-0.0752919\pi\)
\(600\) 0 0
\(601\) 561.830 0.934825 0.467412 0.884039i \(-0.345186\pi\)
0.467412 + 0.884039i \(0.345186\pi\)
\(602\) 128.337 941.616i 0.213184 1.56415i
\(603\) 0 0
\(604\) 83.4834 300.573i 0.138218 0.497638i
\(605\) 556.584 0.919973
\(606\) 0 0
\(607\) 84.0527i 0.138472i −0.997600 0.0692362i \(-0.977944\pi\)
0.997600 0.0692362i \(-0.0220562\pi\)
\(608\) 129.575 + 104.204i 0.213116 + 0.171388i
\(609\) 0 0
\(610\) −16.8328 + 123.504i −0.0275948 + 0.202465i
\(611\) 749.906i 1.22734i
\(612\) 0 0
\(613\) 730.234 1.19125 0.595623 0.803264i \(-0.296905\pi\)
0.595623 + 0.803264i \(0.296905\pi\)
\(614\) −1097.77 149.620i −1.78790 0.243681i
\(615\) 0 0
\(616\) 202.918 471.539i 0.329412 0.765485i
\(617\) −549.786 −0.891064 −0.445532 0.895266i \(-0.646985\pi\)
−0.445532 + 0.895266i \(0.646985\pi\)
\(618\) 0 0
\(619\) 73.1269i 0.118137i −0.998254 0.0590685i \(-0.981187\pi\)
0.998254 0.0590685i \(-0.0188131\pi\)
\(620\) 135.765 488.806i 0.218975 0.788397i
\(621\) 0 0
\(622\) −31.0820 4.23629i −0.0499711 0.00681076i
\(623\) 169.593i 0.272220i
\(624\) 0 0
\(625\) −480.823 −0.769318
\(626\) −83.2314 + 610.676i −0.132958 + 0.975521i
\(627\) 0 0
\(628\) 278.128 + 77.2492i 0.442879 + 0.123008i
\(629\) 114.811 0.182529
\(630\) 0 0
\(631\) 779.849i 1.23589i 0.786220 + 0.617947i \(0.212035\pi\)
−0.786220 + 0.617947i \(0.787965\pi\)
\(632\) 1098.48 + 472.712i 1.73811 + 0.747962i
\(633\) 0 0
\(634\) −133.994 + 983.124i −0.211347 + 1.55067i
\(635\) 733.209i 1.15466i
\(636\) 0 0
\(637\) 588.663 0.924117
\(638\) −397.390 54.1618i −0.622868 0.0848931i
\(639\) 0 0
\(640\) −769.994 + 552.712i −1.20312 + 0.863612i
\(641\) 444.341 0.693200 0.346600 0.938013i \(-0.387336\pi\)
0.346600 + 0.938013i \(0.387336\pi\)
\(642\) 0 0
\(643\) 446.199i 0.693933i −0.937878 0.346966i \(-0.887212\pi\)
0.937878 0.346966i \(-0.112788\pi\)
\(644\) −910.917 253.005i −1.41447 0.392864i
\(645\) 0 0
\(646\) 184.249 + 25.1120i 0.285216 + 0.0388731i
\(647\) 861.386i 1.33135i 0.746240 + 0.665677i \(0.231857\pi\)
−0.746240 + 0.665677i \(0.768143\pi\)
\(648\) 0 0
\(649\) 566.833 0.873394
\(650\) −116.161 + 852.284i −0.178710 + 1.31121i
\(651\) 0 0
\(652\) −60.5654 + 218.059i −0.0928917 + 0.334447i
\(653\) −876.302 −1.34196 −0.670982 0.741474i \(-0.734127\pi\)
−0.670982 + 0.741474i \(0.734127\pi\)
\(654\) 0 0
\(655\) 401.064i 0.612311i
\(656\) 118.479 + 71.3158i 0.180608 + 0.108713i
\(657\) 0 0
\(658\) 133.161 977.013i 0.202372 1.48482i
\(659\) 565.760i 0.858513i −0.903183 0.429257i \(-0.858776\pi\)
0.903183 0.429257i \(-0.141224\pi\)
\(660\) 0 0
\(661\) 632.580 0.957005 0.478503 0.878086i \(-0.341180\pi\)
0.478503 + 0.878086i \(0.341180\pi\)
\(662\) 171.427 + 23.3645i 0.258953 + 0.0352938i
\(663\) 0 0
\(664\) −99.5016 42.8187i −0.149852 0.0644859i
\(665\) 364.686 0.548401
\(666\) 0 0
\(667\) 738.615i 1.10737i
\(668\) −215.846 + 777.131i −0.323123 + 1.16337i
\(669\) 0 0
\(670\) −426.413 58.1175i −0.636438 0.0867426i
\(671\) 56.9810i 0.0849195i
\(672\) 0 0
\(673\) −1072.66 −1.59385 −0.796924 0.604080i \(-0.793541\pi\)
−0.796924 + 0.604080i \(0.793541\pi\)
\(674\) 86.6071 635.444i 0.128497 0.942795i
\(675\) 0 0
\(676\) −149.666 41.5692i −0.221399 0.0614929i
\(677\) 478.798 0.707234 0.353617 0.935390i \(-0.384952\pi\)
0.353617 + 0.935390i \(0.384952\pi\)
\(678\) 0 0
\(679\) 1311.11i 1.93094i
\(680\) −418.997 + 973.661i −0.616172 + 1.43185i
\(681\) 0 0
\(682\) 31.3188 229.789i 0.0459221 0.336934i
\(683\) 318.418i 0.466206i 0.972452 + 0.233103i \(0.0748879\pi\)
−0.972452 + 0.233103i \(0.925112\pi\)
\(684\) 0 0
\(685\) −41.1672 −0.0600981
\(686\) −153.399 20.9074i −0.223614 0.0304772i
\(687\) 0 0
\(688\) −413.666 + 687.233i −0.601258 + 0.998885i
\(689\) 1192.12 1.73022
\(690\) 0 0
\(691\) 1121.30i 1.62272i −0.584545 0.811362i \(-0.698727\pi\)
0.584545 0.811362i \(-0.301273\pi\)
\(692\) −356.697 99.0716i −0.515458 0.143167i
\(693\) 0 0
\(694\) 1337.15 + 182.246i 1.92674 + 0.262602i
\(695\) 1129.38i 1.62500i
\(696\) 0 0
\(697\) 154.650 0.221880
\(698\) 41.5718 305.016i 0.0595585 0.436986i
\(699\) 0 0
\(700\) −302.681 + 1089.77i −0.432401 + 1.55681i
\(701\) −413.437 −0.589782 −0.294891 0.955531i \(-0.595283\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(702\) 0 0
\(703\) 33.3406i 0.0474262i
\(704\) −314.652 + 297.890i −0.446948 + 0.423139i
\(705\) 0 0
\(706\) 168.328 1235.04i 0.238425 1.74935i
\(707\) 924.125i 1.30711i
\(708\) 0 0
\(709\) −682.915 −0.963209 −0.481604 0.876389i \(-0.659946\pi\)
−0.481604 + 0.876389i \(0.659946\pi\)
\(710\) −1662.39 226.574i −2.34140 0.319118i
\(711\) 0 0
\(712\) −56.5836 + 131.488i −0.0794713 + 0.184675i
\(713\) −427.101 −0.599020
\(714\) 0 0
\(715\) 722.737i 1.01082i
\(716\) −4.59070 + 16.5284i −0.00641160 + 0.0230843i
\(717\) 0 0
\(718\) −317.745 43.3066i −0.442541 0.0603157i
\(719\) 286.374i 0.398295i 0.979970 + 0.199148i \(0.0638173\pi\)
−0.979970 + 0.199148i \(0.936183\pi\)
\(720\) 0 0
\(721\) −402.659 −0.558474
\(722\) 90.2103 661.881i 0.124945 0.916732i
\(723\) 0 0
\(724\) 1116.72 + 310.165i 1.54243 + 0.428405i
\(725\) 883.638 1.21881
\(726\) 0 0
\(727\) 322.923i 0.444186i 0.975026 + 0.222093i \(0.0712888\pi\)
−0.975026 + 0.222093i \(0.928711\pi\)
\(728\) −1004.09 432.090i −1.37924 0.593531i
\(729\) 0 0
\(730\) 4.33437 31.8016i 0.00593749 0.0435639i
\(731\) 897.044i 1.22715i
\(732\) 0 0
\(733\) −521.830 −0.711910 −0.355955 0.934503i \(-0.615844\pi\)
−0.355955 + 0.934503i \(0.615844\pi\)
\(734\) −563.955 76.8636i −0.768331 0.104719i
\(735\) 0 0
\(736\) 621.836 + 500.080i 0.844886 + 0.679457i
\(737\) −196.734 −0.266939
\(738\) 0 0
\(739\) 965.020i 1.30585i 0.757424 + 0.652923i \(0.226458\pi\)
−0.757424 + 0.652923i \(0.773542\pi\)
\(740\) −183.120 50.8610i −0.247459 0.0687311i
\(741\) 0 0
\(742\) 1553.15 + 211.686i 2.09320 + 0.285290i
\(743\) 1097.33i 1.47689i −0.674312 0.738447i \(-0.735560\pi\)
0.674312 0.738447i \(-0.264440\pi\)
\(744\) 0 0
\(745\) 1014.32 1.36151
\(746\) 81.4106 597.317i 0.109130 0.800693i
\(747\) 0 0
\(748\) −129.678 + 466.892i −0.173366 + 0.624188i
\(749\) 921.878 1.23081
\(750\) 0 0
\(751\) 1381.05i 1.83894i −0.393154 0.919472i \(-0.628616\pi\)
0.393154 0.919472i \(-0.371384\pi\)
\(752\) −429.216 + 713.067i −0.570766 + 0.948227i
\(753\) 0 0
\(754\) −115.331 + 846.195i −0.152959 + 1.12227i
\(755\) 577.494i 0.764892i
\(756\) 0 0
\(757\) −516.252 −0.681971 −0.340986 0.940068i \(-0.610761\pi\)
−0.340986 + 0.940068i \(0.610761\pi\)
\(758\) 492.540 + 67.1301i 0.649788 + 0.0885622i
\(759\) 0 0
\(760\) −282.748 121.675i −0.372036 0.160099i
\(761\) 1216.18 1.59814 0.799069 0.601239i \(-0.205326\pi\)
0.799069 + 0.601239i \(0.205326\pi\)
\(762\) 0 0
\(763\) 917.783i 1.20286i
\(764\) 99.1668 357.040i 0.129799 0.467329i
\(765\) 0 0
\(766\) −967.319 131.840i −1.26282 0.172114i
\(767\) 1207.00i 1.57367i
\(768\) 0 0
\(769\) 1004.33 1.30601 0.653007 0.757352i \(-0.273507\pi\)
0.653007 + 0.757352i \(0.273507\pi\)
\(770\) −128.337 + 941.616i −0.166671 + 1.22288i
\(771\) 0 0
\(772\) 937.179 + 260.299i 1.21396 + 0.337175i
\(773\) 382.580 0.494929 0.247464 0.968897i \(-0.420403\pi\)
0.247464 + 0.968897i \(0.420403\pi\)
\(774\) 0 0
\(775\) 510.960i 0.659304i
\(776\) 437.442 1016.52i 0.563714 1.30995i
\(777\) 0 0
\(778\) 112.322 824.116i 0.144373 1.05927i
\(779\) 44.9098i 0.0576506i
\(780\) 0 0
\(781\) −766.978 −0.982046
\(782\) 884.223 + 120.514i 1.13072 + 0.154110i
\(783\) 0 0
\(784\) −559.745 336.927i −0.713960 0.429754i
\(785\) −534.369 −0.680725
\(786\) 0 0
\(787\) 477.268i 0.606440i 0.952921 + 0.303220i \(0.0980617\pi\)
−0.952921 + 0.303220i \(0.901938\pi\)
\(788\) 537.387 + 149.258i 0.681963 + 0.189413i
\(789\) 0 0
\(790\) −2193.56 298.969i −2.77666 0.378442i
\(791\) 368.411i 0.465754i
\(792\) 0 0
\(793\) 121.334 0.153007
\(794\) −181.184 + 1329.36i −0.228192 +