Properties

Label 261.3.s.a.37.2
Level $261$
Weight $3$
Character 261.37
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 37.2
Character \(\chi\) \(=\) 261.37
Dual form 261.3.s.a.127.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +O(q^{10})\) \(q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +(-0.0321993 - 0.285777i) q^{10} +(-3.95365 + 6.29219i) q^{11} +(-10.7515 + 2.45395i) q^{13} +(0.0632391 + 0.180727i) q^{14} +(3.55744 + 15.5862i) q^{16} +(4.26171 + 4.26171i) q^{17} +(-13.0613 + 1.47165i) q^{19} +(-7.77298 + 34.0556i) q^{20} +(-0.191278 + 0.152539i) q^{22} +(6.32686 + 3.04685i) q^{23} +(-31.9876 + 40.1112i) q^{25} +(-0.360785 - 0.0406507i) q^{26} -23.2571i q^{28} +(-29.0000 - 0.0339620i) q^{29} +(2.37249 + 0.830170i) q^{31} +(-0.176871 + 1.56977i) q^{32} +(0.0860924 + 0.178773i) q^{34} +(22.0425 - 45.7716i) q^{35} +(-17.7197 - 28.2007i) q^{37} +(-0.421880 - 0.0962915i) q^{38} +(-1.22387 + 1.94778i) q^{40} +(2.70371 - 2.70371i) q^{41} +(-11.9973 - 34.2863i) q^{43} +(28.0492 - 9.81484i) q^{44} +(0.163476 + 0.163476i) q^{46} +(-7.75262 - 4.87130i) q^{47} +(3.37698 - 14.7955i) q^{49} +(-1.43017 + 0.898634i) q^{50} +(39.7327 + 19.1342i) q^{52} +(-39.1941 + 18.8749i) q^{53} +(64.5052 + 7.26799i) q^{55} +(0.505844 - 1.44562i) q^{56} +(-0.900803 - 0.316389i) q^{58} -70.7916 q^{59} +(-11.5282 + 102.316i) q^{61} +(0.0646980 + 0.0515949i) q^{62} +(27.7234 - 57.5683i) q^{64} +(60.0619 + 75.3153i) q^{65} +(26.2176 + 5.98401i) q^{67} +(-2.69850 - 23.9498i) q^{68} +(1.18267 - 1.18267i) q^{70} +(93.3221 - 21.3002i) q^{71} +(-83.5084 + 29.2208i) q^{73} +(-0.243995 - 1.06901i) q^{74} +(44.5050 + 27.9644i) q^{76} +(-42.9470 + 4.83897i) q^{77} +(51.8104 - 32.5546i) q^{79} +(109.183 - 87.0704i) q^{80} +(0.113416 - 0.0546185i) q^{82} +(-18.9679 + 23.7849i) q^{83} +(17.3882 - 49.6926i) q^{85} -1.19590i q^{86} +1.95696 q^{88} +(-97.6073 - 34.1543i) q^{89} +(-50.1443 - 39.9887i) q^{91} +(-12.1841 - 25.3006i) q^{92} +(-0.187944 - 0.235674i) q^{94} +(61.0853 + 97.2168i) q^{95} +(-12.7840 - 113.461i) q^{97} +(0.265820 - 0.423050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0310749 + 0.0108736i 0.0155375 + 0.00543680i 0.338037 0.941133i \(-0.390237\pi\)
−0.322499 + 0.946570i \(0.604523\pi\)
\(3\) 0 0
\(4\) −3.12648 2.49328i −0.781620 0.623321i
\(5\) −3.79007 7.87017i −0.758015 1.57403i −0.817584 0.575809i \(-0.804687\pi\)
0.0595693 0.998224i \(-0.481027\pi\)
\(6\) 0 0
\(7\) 3.62612 + 4.54701i 0.518017 + 0.649572i 0.970187 0.242360i \(-0.0779214\pi\)
−0.452170 + 0.891932i \(0.649350\pi\)
\(8\) −0.140107 0.222980i −0.0175134 0.0278724i
\(9\) 0 0
\(10\) −0.0321993 0.285777i −0.00321993 0.0285777i
\(11\) −3.95365 + 6.29219i −0.359422 + 0.572017i −0.976668 0.214753i \(-0.931105\pi\)
0.617246 + 0.786770i \(0.288248\pi\)
\(12\) 0 0
\(13\) −10.7515 + 2.45395i −0.827037 + 0.188766i −0.615031 0.788503i \(-0.710857\pi\)
−0.212006 + 0.977268i \(0.567999\pi\)
\(14\) 0.0632391 + 0.180727i 0.00451708 + 0.0129091i
\(15\) 0 0
\(16\) 3.55744 + 15.5862i 0.222340 + 0.974135i
\(17\) 4.26171 + 4.26171i 0.250689 + 0.250689i 0.821253 0.570564i \(-0.193275\pi\)
−0.570564 + 0.821253i \(0.693275\pi\)
\(18\) 0 0
\(19\) −13.0613 + 1.47165i −0.687436 + 0.0774554i −0.448771 0.893647i \(-0.648138\pi\)
−0.238664 + 0.971102i \(0.576710\pi\)
\(20\) −7.77298 + 34.0556i −0.388649 + 1.70278i
\(21\) 0 0
\(22\) −0.191278 + 0.152539i −0.00869445 + 0.00693360i
\(23\) 6.32686 + 3.04685i 0.275081 + 0.132472i 0.566339 0.824173i \(-0.308359\pi\)
−0.291258 + 0.956645i \(0.594074\pi\)
\(24\) 0 0
\(25\) −31.9876 + 40.1112i −1.27951 + 1.60445i
\(26\) −0.360785 0.0406507i −0.0138763 0.00156349i
\(27\) 0 0
\(28\) 23.2571i 0.830609i
\(29\) −29.0000 0.0339620i −0.999999 0.00117110i
\(30\) 0 0
\(31\) 2.37249 + 0.830170i 0.0765319 + 0.0267797i 0.368273 0.929718i \(-0.379949\pi\)
−0.291742 + 0.956497i \(0.594235\pi\)
\(32\) −0.176871 + 1.56977i −0.00552722 + 0.0490554i
\(33\) 0 0
\(34\) 0.0860924 + 0.178773i 0.00253213 + 0.00525802i
\(35\) 22.0425 45.7716i 0.629784 1.30776i
\(36\) 0 0
\(37\) −17.7197 28.2007i −0.478910 0.762182i 0.516661 0.856190i \(-0.327175\pi\)
−0.995571 + 0.0940085i \(0.970032\pi\)
\(38\) −0.421880 0.0962915i −0.0111021 0.00253399i
\(39\) 0 0
\(40\) −1.22387 + 1.94778i −0.0305967 + 0.0486944i
\(41\) 2.70371 2.70371i 0.0659440 0.0659440i −0.673366 0.739310i \(-0.735152\pi\)
0.739310 + 0.673366i \(0.235152\pi\)
\(42\) 0 0
\(43\) −11.9973 34.2863i −0.279007 0.797356i −0.995057 0.0993068i \(-0.968337\pi\)
0.716050 0.698049i \(-0.245948\pi\)
\(44\) 28.0492 9.81484i 0.637482 0.223065i
\(45\) 0 0
\(46\) 0.163476 + 0.163476i 0.00355384 + 0.00355384i
\(47\) −7.75262 4.87130i −0.164949 0.103645i 0.447027 0.894520i \(-0.352483\pi\)
−0.611977 + 0.790876i \(0.709625\pi\)
\(48\) 0 0
\(49\) 3.37698 14.7955i 0.0689180 0.301949i
\(50\) −1.43017 + 0.898634i −0.0286033 + 0.0179727i
\(51\) 0 0
\(52\) 39.7327 + 19.1342i 0.764090 + 0.367966i
\(53\) −39.1941 + 18.8749i −0.739511 + 0.356130i −0.765417 0.643535i \(-0.777467\pi\)
0.0259061 + 0.999664i \(0.491753\pi\)
\(54\) 0 0
\(55\) 64.5052 + 7.26799i 1.17282 + 0.132145i
\(56\) 0.505844 1.44562i 0.00903293 0.0258146i
\(57\) 0 0
\(58\) −0.900803 0.316389i −0.0155311 0.00545499i
\(59\) −70.7916 −1.19986 −0.599929 0.800054i \(-0.704804\pi\)
−0.599929 + 0.800054i \(0.704804\pi\)
\(60\) 0 0
\(61\) −11.5282 + 102.316i −0.188988 + 1.67731i 0.438537 + 0.898713i \(0.355497\pi\)
−0.627524 + 0.778597i \(0.715932\pi\)
\(62\) 0.0646980 + 0.0515949i 0.00104352 + 0.000832176i
\(63\) 0 0
\(64\) 27.7234 57.5683i 0.433178 0.899504i
\(65\) 60.0619 + 75.3153i 0.924030 + 1.15870i
\(66\) 0 0
\(67\) 26.2176 + 5.98401i 0.391308 + 0.0893135i 0.413648 0.910437i \(-0.364254\pi\)
−0.0223398 + 0.999750i \(0.507112\pi\)
\(68\) −2.69850 23.9498i −0.0396838 0.352203i
\(69\) 0 0
\(70\) 1.18267 1.18267i 0.0168953 0.0168953i
\(71\) 93.3221 21.3002i 1.31440 0.300002i 0.492835 0.870123i \(-0.335961\pi\)
0.821561 + 0.570121i \(0.193104\pi\)
\(72\) 0 0
\(73\) −83.5084 + 29.2208i −1.14395 + 0.400286i −0.834705 0.550697i \(-0.814362\pi\)
−0.309245 + 0.950982i \(0.600076\pi\)
\(74\) −0.243995 1.06901i −0.00329723 0.0144461i
\(75\) 0 0
\(76\) 44.5050 + 27.9644i 0.585593 + 0.367952i
\(77\) −42.9470 + 4.83897i −0.557753 + 0.0628437i
\(78\) 0 0
\(79\) 51.8104 32.5546i 0.655828 0.412084i −0.162601 0.986692i \(-0.551988\pi\)
0.818429 + 0.574608i \(0.194846\pi\)
\(80\) 109.183 87.0704i 1.36478 1.08838i
\(81\) 0 0
\(82\) 0.113416 0.0546185i 0.00138313 0.000666079i
\(83\) −18.9679 + 23.7849i −0.228528 + 0.286566i −0.882854 0.469647i \(-0.844381\pi\)
0.654326 + 0.756213i \(0.272953\pi\)
\(84\) 0 0
\(85\) 17.3882 49.6926i 0.204567 0.584619i
\(86\) 1.19590i 0.0139058i
\(87\) 0 0
\(88\) 1.95696 0.0222382
\(89\) −97.6073 34.1543i −1.09671 0.383756i −0.279530 0.960137i \(-0.590179\pi\)
−0.817181 + 0.576381i \(0.804464\pi\)
\(90\) 0 0
\(91\) −50.1443 39.9887i −0.551036 0.439436i
\(92\) −12.1841 25.3006i −0.132436 0.275006i
\(93\) 0 0
\(94\) −0.187944 0.235674i −0.00199940 0.00250717i
\(95\) 61.0853 + 97.2168i 0.643004 + 1.02333i
\(96\) 0 0
\(97\) −12.7840 113.461i −0.131794 1.16970i −0.869273 0.494333i \(-0.835413\pi\)
0.737479 0.675370i \(-0.236016\pi\)
\(98\) 0.265820 0.423050i 0.00271245 0.00431684i
\(99\) 0 0
\(100\) 200.017 45.6527i 2.00017 0.456527i
\(101\) −42.0839 120.269i −0.416672 1.19078i −0.940747 0.339109i \(-0.889875\pi\)
0.524075 0.851672i \(-0.324411\pi\)
\(102\) 0 0
\(103\) −36.2231 158.704i −0.351681 1.54081i −0.773299 0.634041i \(-0.781395\pi\)
0.421618 0.906773i \(-0.361462\pi\)
\(104\) 2.05354 + 2.05354i 0.0197456 + 0.0197456i
\(105\) 0 0
\(106\) −1.42319 + 0.160355i −0.0134263 + 0.00151278i
\(107\) 15.1003 66.1586i 0.141124 0.618304i −0.854051 0.520189i \(-0.825861\pi\)
0.995175 0.0981152i \(-0.0312814\pi\)
\(108\) 0 0
\(109\) −8.50965 + 6.78622i −0.0780702 + 0.0622589i −0.661747 0.749727i \(-0.730185\pi\)
0.583677 + 0.811986i \(0.301613\pi\)
\(110\) 1.92547 + 0.927256i 0.0175042 + 0.00842960i
\(111\) 0 0
\(112\) −57.9707 + 72.6930i −0.517596 + 0.649044i
\(113\) 56.1593 + 6.32764i 0.496985 + 0.0559968i 0.356900 0.934143i \(-0.383834\pi\)
0.140085 + 0.990139i \(0.455262\pi\)
\(114\) 0 0
\(115\) 61.3412i 0.533402i
\(116\) 90.5831 + 72.4114i 0.780889 + 0.624236i
\(117\) 0 0
\(118\) −2.19984 0.769759i −0.0186427 0.00652338i
\(119\) −3.92457 + 34.8315i −0.0329796 + 0.292702i
\(120\) 0 0
\(121\) 28.5396 + 59.2630i 0.235864 + 0.489777i
\(122\) −1.47078 + 3.05411i −0.0120556 + 0.0250337i
\(123\) 0 0
\(124\) −5.34769 8.51079i −0.0431265 0.0686354i
\(125\) 224.012 + 51.1293i 1.79210 + 0.409035i
\(126\) 0 0
\(127\) −121.534 + 193.421i −0.956962 + 1.52300i −0.108262 + 0.994122i \(0.534529\pi\)
−0.848700 + 0.528875i \(0.822614\pi\)
\(128\) 5.95556 5.95556i 0.0465278 0.0465278i
\(129\) 0 0
\(130\) 1.04747 + 2.99351i 0.00805749 + 0.0230270i
\(131\) −196.490 + 68.7549i −1.49993 + 0.524847i −0.950508 0.310701i \(-0.899436\pi\)
−0.549418 + 0.835547i \(0.685151\pi\)
\(132\) 0 0
\(133\) −54.0533 54.0533i −0.406416 0.406416i
\(134\) 0.749644 + 0.471033i 0.00559436 + 0.00351517i
\(135\) 0 0
\(136\) 0.353178 1.54737i 0.00259689 0.0113777i
\(137\) −58.6681 + 36.8636i −0.428235 + 0.269078i −0.728857 0.684665i \(-0.759948\pi\)
0.300623 + 0.953743i \(0.402805\pi\)
\(138\) 0 0
\(139\) 97.5136 + 46.9601i 0.701537 + 0.337842i 0.750419 0.660962i \(-0.229852\pi\)
−0.0488824 + 0.998805i \(0.515566\pi\)
\(140\) −183.037 + 88.1459i −1.30741 + 0.629614i
\(141\) 0 0
\(142\) 3.13159 + 0.352845i 0.0220534 + 0.00248482i
\(143\) 27.0668 77.3524i 0.189278 0.540926i
\(144\) 0 0
\(145\) 109.645 + 228.363i 0.756171 + 1.57492i
\(146\) −2.91275 −0.0199504
\(147\) 0 0
\(148\) −14.9122 + 132.349i −0.100758 + 0.894251i
\(149\) −42.7218 34.0695i −0.286724 0.228654i 0.469556 0.882902i \(-0.344414\pi\)
−0.756280 + 0.654248i \(0.772985\pi\)
\(150\) 0 0
\(151\) 83.0312 172.416i 0.549875 1.14183i −0.422058 0.906569i \(-0.638692\pi\)
0.971933 0.235259i \(-0.0755937\pi\)
\(152\) 2.15813 + 2.70621i 0.0141982 + 0.0178040i
\(153\) 0 0
\(154\) −1.38719 0.316618i −0.00900774 0.00205596i
\(155\) −2.45833 21.8183i −0.0158602 0.140763i
\(156\) 0 0
\(157\) −45.4322 + 45.4322i −0.289377 + 0.289377i −0.836834 0.547457i \(-0.815596\pi\)
0.547457 + 0.836834i \(0.315596\pi\)
\(158\) 1.96399 0.448268i 0.0124303 0.00283714i
\(159\) 0 0
\(160\) 13.0247 4.55755i 0.0814046 0.0284847i
\(161\) 9.08786 + 39.8165i 0.0564463 + 0.247307i
\(162\) 0 0
\(163\) −249.812 156.967i −1.53259 0.962990i −0.992615 0.121309i \(-0.961291\pi\)
−0.539975 0.841681i \(-0.681566\pi\)
\(164\) −15.1942 + 1.71197i −0.0926474 + 0.0104389i
\(165\) 0 0
\(166\) −0.848053 + 0.532867i −0.00510875 + 0.00321004i
\(167\) −44.5238 + 35.5065i −0.266610 + 0.212614i −0.747665 0.664076i \(-0.768825\pi\)
0.481055 + 0.876690i \(0.340254\pi\)
\(168\) 0 0
\(169\) −42.6913 + 20.5591i −0.252611 + 0.121651i
\(170\) 1.08067 1.35512i 0.00635691 0.00797131i
\(171\) 0 0
\(172\) −47.9762 + 137.108i −0.278931 + 0.797140i
\(173\) 335.481i 1.93920i −0.244702 0.969598i \(-0.578690\pi\)
0.244702 0.969598i \(-0.421310\pi\)
\(174\) 0 0
\(175\) −298.377 −1.70501
\(176\) −112.136 39.2381i −0.637136 0.222944i
\(177\) 0 0
\(178\) −2.66176 2.12268i −0.0149537 0.0119252i
\(179\) −69.3056 143.915i −0.387182 0.803992i −0.999906 0.0136949i \(-0.995641\pi\)
0.612724 0.790297i \(-0.290074\pi\)
\(180\) 0 0
\(181\) 152.161 + 190.804i 0.840671 + 1.05417i 0.997781 + 0.0665866i \(0.0212109\pi\)
−0.157110 + 0.987581i \(0.550218\pi\)
\(182\) −1.12341 1.78790i −0.00617258 0.00982360i
\(183\) 0 0
\(184\) −0.207053 1.83765i −0.00112529 0.00998721i
\(185\) −154.785 + 246.340i −0.836678 + 1.33157i
\(186\) 0 0
\(187\) −43.6648 + 9.96621i −0.233502 + 0.0532952i
\(188\) 12.0929 + 34.5595i 0.0643239 + 0.183827i
\(189\) 0 0
\(190\) 0.841128 + 3.68522i 0.00442699 + 0.0193959i
\(191\) 166.578 + 166.578i 0.872137 + 0.872137i 0.992705 0.120568i \(-0.0384716\pi\)
−0.120568 + 0.992705i \(0.538472\pi\)
\(192\) 0 0
\(193\) 188.693 21.2606i 0.977683 0.110158i 0.391362 0.920237i \(-0.372004\pi\)
0.586321 + 0.810078i \(0.300576\pi\)
\(194\) 0.836468 3.66481i 0.00431169 0.0188908i
\(195\) 0 0
\(196\) −47.4475 + 37.8381i −0.242079 + 0.193052i
\(197\) 208.010 + 100.172i 1.05589 + 0.508488i 0.879532 0.475839i \(-0.157856\pi\)
0.176353 + 0.984327i \(0.443570\pi\)
\(198\) 0 0
\(199\) −93.3547 + 117.063i −0.469119 + 0.588257i −0.958955 0.283558i \(-0.908485\pi\)
0.489836 + 0.871815i \(0.337057\pi\)
\(200\) 13.4257 + 1.51271i 0.0671285 + 0.00756356i
\(201\) 0 0
\(202\) 4.19495i 0.0207671i
\(203\) −105.003 131.986i −0.517256 0.650179i
\(204\) 0 0
\(205\) −31.5259 11.0314i −0.153785 0.0538116i
\(206\) 0.600050 5.32559i 0.00291286 0.0258524i
\(207\) 0 0
\(208\) −76.4955 158.845i −0.367767 0.763676i
\(209\) 42.3797 88.0024i 0.202774 0.421064i
\(210\) 0 0
\(211\) −66.0800 105.166i −0.313175 0.498416i 0.652632 0.757675i \(-0.273665\pi\)
−0.965808 + 0.259259i \(0.916522\pi\)
\(212\) 169.600 + 38.7101i 0.799999 + 0.182595i
\(213\) 0 0
\(214\) 1.18862 1.89168i 0.00555430 0.00883962i
\(215\) −224.368 + 224.368i −1.04357 + 1.04357i
\(216\) 0 0
\(217\) 4.82813 + 13.7980i 0.0222495 + 0.0635853i
\(218\) −0.338227 + 0.118351i −0.00155150 + 0.000542894i
\(219\) 0 0
\(220\) −183.553 183.553i −0.834332 0.834332i
\(221\) −56.2778 35.3617i −0.254651 0.160008i
\(222\) 0 0
\(223\) −26.1358 + 114.508i −0.117201 + 0.513491i 0.881913 + 0.471412i \(0.156255\pi\)
−0.999114 + 0.0420792i \(0.986602\pi\)
\(224\) −7.77912 + 4.88795i −0.0347282 + 0.0218212i
\(225\) 0 0
\(226\) 1.67634 + 0.807285i 0.00741745 + 0.00357206i
\(227\) −223.061 + 107.420i −0.982646 + 0.473217i −0.855014 0.518604i \(-0.826452\pi\)
−0.127632 + 0.991822i \(0.540738\pi\)
\(228\) 0 0
\(229\) 131.941 + 14.8662i 0.576162 + 0.0649179i 0.395237 0.918579i \(-0.370662\pi\)
0.180925 + 0.983497i \(0.442091\pi\)
\(230\) 0.666999 1.90617i 0.00290000 0.00828772i
\(231\) 0 0
\(232\) 4.05554 + 6.47116i 0.0174808 + 0.0278929i
\(233\) 300.048 1.28776 0.643879 0.765128i \(-0.277324\pi\)
0.643879 + 0.765128i \(0.277324\pi\)
\(234\) 0 0
\(235\) −8.95491 + 79.4770i −0.0381060 + 0.338200i
\(236\) 221.328 + 176.503i 0.937832 + 0.747896i
\(237\) 0 0
\(238\) −0.500699 + 1.03971i −0.00210378 + 0.00436854i
\(239\) 137.342 + 172.222i 0.574654 + 0.720594i 0.981191 0.193041i \(-0.0618350\pi\)
−0.406536 + 0.913635i \(0.633264\pi\)
\(240\) 0 0
\(241\) −32.7575 7.47668i −0.135923 0.0310236i 0.154018 0.988068i \(-0.450779\pi\)
−0.289941 + 0.957044i \(0.593636\pi\)
\(242\) 0.242464 + 2.15192i 0.00100192 + 0.00889224i
\(243\) 0 0
\(244\) 291.145 291.145i 1.19322 1.19322i
\(245\) −129.242 + 29.4987i −0.527519 + 0.120403i
\(246\) 0 0
\(247\) 136.817 47.8742i 0.553914 0.193823i
\(248\) −0.147292 0.645329i −0.000593920 0.00260213i
\(249\) 0 0
\(250\) 6.40521 + 4.02466i 0.0256208 + 0.0160986i
\(251\) 51.8762 5.84504i 0.206678 0.0232870i −0.00801842 0.999968i \(-0.502552\pi\)
0.214696 + 0.976681i \(0.431124\pi\)
\(252\) 0 0
\(253\) −44.1855 + 27.7636i −0.174646 + 0.109738i
\(254\) −5.87984 + 4.68902i −0.0231490 + 0.0184607i
\(255\) 0 0
\(256\) −230.023 + 110.773i −0.898528 + 0.432709i
\(257\) 21.9630 27.5408i 0.0854593 0.107163i −0.737264 0.675605i \(-0.763882\pi\)
0.822723 + 0.568443i \(0.192454\pi\)
\(258\) 0 0
\(259\) 63.9752 182.831i 0.247008 0.705910i
\(260\) 385.223i 1.48163i
\(261\) 0 0
\(262\) −6.85354 −0.0261585
\(263\) −72.7181 25.4452i −0.276495 0.0967497i 0.188470 0.982079i \(-0.439647\pi\)
−0.464965 + 0.885329i \(0.653933\pi\)
\(264\) 0 0
\(265\) 297.097 + 236.927i 1.12112 + 0.894063i
\(266\) −1.09195 2.26746i −0.00410507 0.00852428i
\(267\) 0 0
\(268\) −67.0491 84.0769i −0.250183 0.313720i
\(269\) 40.6748 + 64.7335i 0.151207 + 0.240645i 0.913735 0.406310i \(-0.133185\pi\)
−0.762528 + 0.646955i \(0.776042\pi\)
\(270\) 0 0
\(271\) −38.5675 342.296i −0.142316 1.26309i −0.838372 0.545098i \(-0.816492\pi\)
0.696057 0.717987i \(-0.254936\pi\)
\(272\) −51.2630 + 81.5846i −0.188467 + 0.299943i
\(273\) 0 0
\(274\) −2.22395 + 0.507602i −0.00811660 + 0.00185256i
\(275\) −125.920 359.858i −0.457890 1.30857i
\(276\) 0 0
\(277\) 57.6112 + 252.411i 0.207983 + 0.911232i 0.965907 + 0.258889i \(0.0833565\pi\)
−0.757924 + 0.652343i \(0.773786\pi\)
\(278\) 2.51960 + 2.51960i 0.00906333 + 0.00906333i
\(279\) 0 0
\(280\) −13.2944 + 1.49792i −0.0474802 + 0.00534973i
\(281\) 90.9123 398.313i 0.323531 1.41748i −0.507689 0.861540i \(-0.669500\pi\)
0.831220 0.555943i \(-0.187643\pi\)
\(282\) 0 0
\(283\) −122.197 + 97.4487i −0.431791 + 0.344342i −0.815142 0.579261i \(-0.803341\pi\)
0.383351 + 0.923603i \(0.374770\pi\)
\(284\) −344.877 166.084i −1.21435 0.584802i
\(285\) 0 0
\(286\) 1.68220 2.10941i 0.00588181 0.00737555i
\(287\) 22.0977 + 2.48981i 0.0769955 + 0.00867531i
\(288\) 0 0
\(289\) 252.676i 0.874310i
\(290\) 0.924073 + 8.28861i 0.00318646 + 0.0285814i
\(291\) 0 0
\(292\) 333.943 + 116.852i 1.14364 + 0.400177i
\(293\) −15.8049 + 140.273i −0.0539417 + 0.478746i 0.937480 + 0.348040i \(0.113153\pi\)
−0.991421 + 0.130706i \(0.958276\pi\)
\(294\) 0 0
\(295\) 268.305 + 557.142i 0.909509 + 1.88862i
\(296\) −3.80553 + 7.90226i −0.0128565 + 0.0266968i
\(297\) 0 0
\(298\) −0.957120 1.52325i −0.00321181 0.00511157i
\(299\) −75.4999 17.2324i −0.252508 0.0576333i
\(300\) 0 0
\(301\) 112.396 178.878i 0.373410 0.594279i
\(302\) 4.45497 4.45497i 0.0147516 0.0147516i
\(303\) 0 0
\(304\) −69.4021 198.340i −0.228297 0.652434i
\(305\) 848.937 297.056i 2.78340 0.973953i
\(306\) 0 0
\(307\) 211.914 + 211.914i 0.690275 + 0.690275i 0.962292 0.272017i \(-0.0876908\pi\)
−0.272017 + 0.962292i \(0.587691\pi\)
\(308\) 146.338 + 91.9501i 0.475123 + 0.298539i
\(309\) 0 0
\(310\) 0.160851 0.704733i 0.000518873 0.00227333i
\(311\) −0.482806 + 0.303367i −0.00155243 + 0.000975456i −0.532808 0.846236i \(-0.678863\pi\)
0.531256 + 0.847212i \(0.321720\pi\)
\(312\) 0 0
\(313\) −11.9391 5.74959i −0.0381442 0.0183693i 0.414714 0.909952i \(-0.363881\pi\)
−0.452859 + 0.891582i \(0.649596\pi\)
\(314\) −1.90581 + 0.917792i −0.00606947 + 0.00292290i
\(315\) 0 0
\(316\) −243.152 27.3966i −0.769468 0.0866982i
\(317\) −168.368 + 481.169i −0.531131 + 1.51788i 0.295614 + 0.955307i \(0.404476\pi\)
−0.826745 + 0.562577i \(0.809810\pi\)
\(318\) 0 0
\(319\) 114.869 182.339i 0.360092 0.571596i
\(320\) −558.146 −1.74421
\(321\) 0 0
\(322\) −0.150544 + 1.33611i −0.000467527 + 0.00414942i
\(323\) −61.9352 49.3917i −0.191750 0.152915i
\(324\) 0 0
\(325\) 245.483 509.751i 0.755333 1.56847i
\(326\) −6.05610 7.59411i −0.0185770 0.0232948i
\(327\) 0 0
\(328\) −0.981680 0.224062i −0.00299293 0.000683116i
\(329\) −5.96210 52.9151i −0.0181219 0.160836i
\(330\) 0 0
\(331\) −88.5260 + 88.5260i −0.267450 + 0.267450i −0.828072 0.560622i \(-0.810562\pi\)
0.560622 + 0.828072i \(0.310562\pi\)
\(332\) 118.605 27.0709i 0.357245 0.0815388i
\(333\) 0 0
\(334\) −1.76966 + 0.619230i −0.00529838 + 0.00185398i
\(335\) −52.2717 229.017i −0.156035 0.683633i
\(336\) 0 0
\(337\) 175.703 + 110.401i 0.521373 + 0.327601i 0.766876 0.641795i \(-0.221810\pi\)
−0.245503 + 0.969396i \(0.578953\pi\)
\(338\) −1.55018 + 0.174664i −0.00458634 + 0.000516756i
\(339\) 0 0
\(340\) −178.262 + 112.009i −0.524299 + 0.329439i
\(341\) −14.6036 + 11.6460i −0.0428257 + 0.0341524i
\(342\) 0 0
\(343\) 336.275 161.942i 0.980394 0.472133i
\(344\) −5.96424 + 7.47891i −0.0173379 + 0.0217410i
\(345\) 0 0
\(346\) 3.64788 10.4251i 0.0105430 0.0301302i
\(347\) 98.9513i 0.285162i 0.989783 + 0.142581i \(0.0455402\pi\)
−0.989783 + 0.142581i \(0.954460\pi\)
\(348\) 0 0
\(349\) 293.432 0.840780 0.420390 0.907343i \(-0.361893\pi\)
0.420390 + 0.907343i \(0.361893\pi\)
\(350\) −9.27205 3.24443i −0.0264916 0.00926980i
\(351\) 0 0
\(352\) −9.17803 7.31923i −0.0260739 0.0207933i
\(353\) 139.632 + 289.949i 0.395558 + 0.821385i 0.999700 + 0.0245079i \(0.00780188\pi\)
−0.604142 + 0.796877i \(0.706484\pi\)
\(354\) 0 0
\(355\) −521.333 653.731i −1.46854 1.84150i
\(356\) 220.011 + 350.145i 0.618008 + 0.983554i
\(357\) 0 0
\(358\) −0.588799 5.22573i −0.00164469 0.0145970i
\(359\) 246.904 392.946i 0.687756 1.09456i −0.302209 0.953242i \(-0.597724\pi\)
0.989965 0.141315i \(-0.0451332\pi\)
\(360\) 0 0
\(361\) −183.518 + 41.8867i −0.508360 + 0.116030i
\(362\) 2.65368 + 7.58377i 0.00733060 + 0.0209497i
\(363\) 0 0
\(364\) 57.0718 + 250.048i 0.156791 + 0.686944i
\(365\) 546.476 + 546.476i 1.49719 + 1.49719i
\(366\) 0 0
\(367\) 97.2298 10.9552i 0.264931 0.0298506i 0.0215005 0.999769i \(-0.493156\pi\)
0.243431 + 0.969918i \(0.421727\pi\)
\(368\) −24.9814 + 109.450i −0.0678841 + 0.297420i
\(369\) 0 0
\(370\) −7.48855 + 5.97192i −0.0202393 + 0.0161403i
\(371\) −227.946 109.773i −0.614411 0.295885i
\(372\) 0 0
\(373\) 205.926 258.222i 0.552079 0.692285i −0.424992 0.905197i \(-0.639723\pi\)
0.977071 + 0.212912i \(0.0682946\pi\)
\(374\) −1.46525 0.165094i −0.00391778 0.000441428i
\(375\) 0 0
\(376\) 2.41118i 0.00641272i
\(377\) 311.876 70.7995i 0.827257 0.187797i
\(378\) 0 0
\(379\) −219.932 76.9574i −0.580295 0.203054i 0.0241400 0.999709i \(-0.492315\pi\)
−0.604435 + 0.796655i \(0.706601\pi\)
\(380\) 51.4069 456.249i 0.135281 1.20066i
\(381\) 0 0
\(382\) 3.36510 + 6.98771i 0.00880917 + 0.0182924i
\(383\) 101.754 211.295i 0.265677 0.551685i −0.724865 0.688891i \(-0.758098\pi\)
0.990543 + 0.137206i \(0.0438123\pi\)
\(384\) 0 0
\(385\) 200.856 + 319.660i 0.521703 + 0.830286i
\(386\) 6.09480 + 1.39110i 0.0157896 + 0.00360388i
\(387\) 0 0
\(388\) −242.922 + 386.608i −0.626087 + 0.996412i
\(389\) −297.193 + 297.193i −0.763992 + 0.763992i −0.977041 0.213049i \(-0.931661\pi\)
0.213049 + 0.977041i \(0.431661\pi\)
\(390\) 0 0
\(391\) 13.9784 + 39.9481i 0.0357505 + 0.102169i
\(392\) −3.77224 + 1.31996i −0.00962306 + 0.00336725i
\(393\) 0 0
\(394\) 5.37465 + 5.37465i 0.0136412 + 0.0136412i
\(395\) −452.575 284.372i −1.14576 0.719929i
\(396\) 0 0
\(397\) 61.8313 270.901i 0.155746 0.682370i −0.835405 0.549635i \(-0.814767\pi\)
0.991152 0.132735i \(-0.0423759\pi\)
\(398\) −4.17389 + 2.62263i −0.0104872 + 0.00658952i
\(399\) 0 0
\(400\) −738.975 355.871i −1.84744 0.889679i
\(401\) −198.105 + 95.4022i −0.494027 + 0.237911i −0.664272 0.747491i \(-0.731258\pi\)
0.170245 + 0.985402i \(0.445544\pi\)
\(402\) 0 0
\(403\) −27.5450 3.10357i −0.0683498 0.00770117i
\(404\) −168.290 + 480.945i −0.416559 + 1.19046i
\(405\) 0 0
\(406\) −1.82779 5.24322i −0.00450195 0.0129143i
\(407\) 247.502 0.608112
\(408\) 0 0
\(409\) 43.0110 381.733i 0.105161 0.933333i −0.824737 0.565516i \(-0.808677\pi\)
0.929898 0.367816i \(-0.119895\pi\)
\(410\) −0.859713 0.685599i −0.00209686 0.00167219i
\(411\) 0 0
\(412\) −282.443 + 586.499i −0.685541 + 1.42354i
\(413\) −256.698 321.890i −0.621546 0.779394i
\(414\) 0 0
\(415\) 259.081 + 59.1336i 0.624292 + 0.142491i
\(416\) −1.95053 17.3114i −0.00468877 0.0416140i
\(417\) 0 0
\(418\) 2.27385 2.27385i 0.00543983 0.00543983i
\(419\) 258.143 58.9194i 0.616092 0.140619i 0.0969251 0.995292i \(-0.469099\pi\)
0.519167 + 0.854673i \(0.326242\pi\)
\(420\) 0 0
\(421\) 210.923 73.8051i 0.501005 0.175309i −0.0679329 0.997690i \(-0.521640\pi\)
0.568937 + 0.822381i \(0.307355\pi\)
\(422\) −0.909903 3.98655i −0.00215617 0.00944679i
\(423\) 0 0
\(424\) 9.70009 + 6.09497i 0.0228776 + 0.0143749i
\(425\) −307.265 + 34.6204i −0.722976 + 0.0814598i
\(426\) 0 0
\(427\) −507.034 + 318.591i −1.18743 + 0.746114i
\(428\) −212.163 + 169.194i −0.495707 + 0.395313i
\(429\) 0 0
\(430\) −9.41192 + 4.53254i −0.0218882 + 0.0105408i
\(431\) 131.485 164.877i 0.305069 0.382545i −0.605539 0.795816i \(-0.707042\pi\)
0.910608 + 0.413271i \(0.135614\pi\)
\(432\) 0 0
\(433\) −53.6896 + 153.436i −0.123995 + 0.354356i −0.989102 0.147230i \(-0.952964\pi\)
0.865108 + 0.501586i \(0.167250\pi\)
\(434\) 0.481271i 0.00110892i
\(435\) 0 0
\(436\) 43.5252 0.0998284
\(437\) −87.1207 30.4849i −0.199361 0.0697594i
\(438\) 0 0
\(439\) −404.677 322.719i −0.921816 0.735124i 0.0427165 0.999087i \(-0.486399\pi\)
−0.964533 + 0.263963i \(0.914970\pi\)
\(440\) −7.41704 15.4016i −0.0168569 0.0350037i
\(441\) 0 0
\(442\) −1.36432 1.71080i −0.00308670 0.00387060i
\(443\) 205.271 + 326.686i 0.463365 + 0.737440i 0.993907 0.110218i \(-0.0351548\pi\)
−0.530543 + 0.847658i \(0.678012\pi\)
\(444\) 0 0
\(445\) 101.139 + 897.633i 0.227278 + 2.01715i
\(446\) −2.05729 + 3.27415i −0.00461275 + 0.00734115i
\(447\) 0 0
\(448\) 362.292 82.6907i 0.808687 0.184577i
\(449\) −51.5162 147.225i −0.114735 0.327895i 0.872168 0.489206i \(-0.162713\pi\)
−0.986904 + 0.161311i \(0.948428\pi\)
\(450\) 0 0
\(451\) 6.32274 + 27.7017i 0.0140194 + 0.0614229i
\(452\) −159.804 159.804i −0.353549 0.353549i
\(453\) 0 0
\(454\) −8.09964 + 0.912610i −0.0178406 + 0.00201016i
\(455\) −124.667 + 546.204i −0.273994 + 1.20045i
\(456\) 0 0
\(457\) −551.243 + 439.602i −1.20622 + 0.961930i −0.999863 0.0165465i \(-0.994733\pi\)
−0.206359 + 0.978476i \(0.566161\pi\)
\(458\) 3.93841 + 1.89664i 0.00859916 + 0.00414114i
\(459\) 0 0
\(460\) −152.941 + 191.782i −0.332481 + 0.416917i
\(461\) −472.975 53.2915i −1.02598 0.115600i −0.417097 0.908862i \(-0.636952\pi\)
−0.608880 + 0.793262i \(0.708381\pi\)
\(462\) 0 0
\(463\) 436.814i 0.943442i 0.881748 + 0.471721i \(0.156367\pi\)
−0.881748 + 0.471721i \(0.843633\pi\)
\(464\) −102.636 452.119i −0.221199 0.974395i
\(465\) 0 0
\(466\) 9.32396 + 3.26259i 0.0200085 + 0.00700127i
\(467\) −22.5274 + 199.936i −0.0482385 + 0.428128i 0.946262 + 0.323400i \(0.104826\pi\)
−0.994501 + 0.104728i \(0.966603\pi\)
\(468\) 0 0
\(469\) 67.8589 + 140.911i 0.144689 + 0.300449i
\(470\) −1.14247 + 2.37237i −0.00243080 + 0.00504760i
\(471\) 0 0
\(472\) 9.91842 + 15.7851i 0.0210136 + 0.0334430i
\(473\) 263.169 + 60.0666i 0.556383 + 0.126991i
\(474\) 0 0
\(475\) 358.770 570.979i 0.755305 1.20206i
\(476\) 99.1149 99.1149i 0.208225 0.208225i
\(477\) 0 0
\(478\) 2.39524 + 6.84519i 0.00501095 + 0.0143205i
\(479\) 625.859 218.997i 1.30659 0.457197i 0.414913 0.909861i \(-0.363812\pi\)
0.891681 + 0.452664i \(0.149526\pi\)
\(480\) 0 0
\(481\) 259.716 + 259.716i 0.539950 + 0.539950i
\(482\) −0.936638 0.588529i −0.00194323 0.00122101i
\(483\) 0 0
\(484\) 58.5312 256.442i 0.120932 0.529839i
\(485\) −844.506 + 530.638i −1.74125 + 1.09410i
\(486\) 0 0
\(487\) −98.2132 47.2970i −0.201670 0.0971191i 0.330323 0.943868i \(-0.392842\pi\)
−0.531993 + 0.846749i \(0.678557\pi\)
\(488\) 24.4296 11.7647i 0.0500606 0.0241079i
\(489\) 0 0
\(490\) −4.33695 0.488657i −0.00885092 0.000997259i
\(491\) 152.864 436.860i 0.311332 0.889735i −0.676805 0.736162i \(-0.736636\pi\)
0.988137 0.153573i \(-0.0490781\pi\)
\(492\) 0 0
\(493\) −123.445 123.734i −0.250395 0.250982i
\(494\) 4.77213 0.00966019
\(495\) 0 0
\(496\) −4.49917 + 39.9313i −0.00907092 + 0.0805066i
\(497\) 435.249 + 347.099i 0.875752 + 0.698389i
\(498\) 0 0
\(499\) −119.381 + 247.898i −0.239241 + 0.496789i −0.985672 0.168674i \(-0.946052\pi\)
0.746431 + 0.665463i \(0.231766\pi\)
\(500\) −572.890 718.381i −1.14578 1.43676i
\(501\) 0 0
\(502\) 1.67561 + 0.382446i 0.00333786 + 0.000761845i
\(503\) 59.4343 + 527.494i 0.118160 + 1.04870i 0.903191 + 0.429239i \(0.141218\pi\)
−0.785031 + 0.619456i \(0.787353\pi\)
\(504\) 0 0
\(505\) −787.035 + 787.035i −1.55849 + 1.55849i
\(506\) −1.67495 + 0.382297i −0.00331018 + 0.000755528i
\(507\) 0 0
\(508\) 862.227 301.706i 1.69730 0.593910i
\(509\) −19.4786 85.3413i −0.0382683 0.167665i 0.952183 0.305529i \(-0.0988333\pi\)
−0.990451 + 0.137864i \(0.955976\pi\)
\(510\) 0 0
\(511\) −435.679 273.755i −0.852600 0.535724i
\(512\) −41.8304 + 4.71315i −0.0816999 + 0.00920537i
\(513\) 0 0
\(514\) 0.981968 0.617011i 0.00191044 0.00120041i
\(515\) −1111.74 + 886.582i −2.15871 + 1.72152i
\(516\) 0 0
\(517\) 61.3023 29.5216i 0.118573 0.0571018i
\(518\) 3.97605 4.98581i 0.00767577 0.00962512i
\(519\) 0 0
\(520\) 8.37865 23.9448i 0.0161128 0.0460477i
\(521\) 416.078i 0.798613i −0.916817 0.399307i \(-0.869251\pi\)
0.916817 0.399307i \(-0.130749\pi\)
\(522\) 0 0
\(523\) −244.076 −0.466684 −0.233342 0.972395i \(-0.574966\pi\)
−0.233342 + 0.972395i \(0.574966\pi\)
\(524\) 785.748 + 274.945i 1.49952 + 0.524705i
\(525\) 0 0
\(526\) −1.98303 1.58141i −0.00377002 0.00300649i
\(527\) 6.57292 + 13.6488i 0.0124723 + 0.0258991i
\(528\) 0 0
\(529\) −299.080 375.035i −0.565369 0.708951i
\(530\) 6.65602 + 10.5930i 0.0125585 + 0.0199868i
\(531\) 0 0
\(532\) 34.2263 + 303.767i 0.0643351 + 0.570990i
\(533\) −22.4341 + 35.7036i −0.0420902 + 0.0669861i
\(534\) 0 0
\(535\) −577.910 + 131.904i −1.08021 + 0.246550i
\(536\) −2.33897 6.68440i −0.00436376 0.0124709i
\(537\) 0 0
\(538\) 0.560080 + 2.45387i 0.00104104 + 0.00456110i
\(539\) 79.7449 + 79.7449i 0.147950 + 0.147950i
\(540\) 0 0
\(541\) 741.239 83.5176i 1.37013 0.154376i 0.603959 0.797015i \(-0.293589\pi\)
0.766169 + 0.642639i \(0.222160\pi\)
\(542\) 2.52350 11.0562i 0.00465591 0.0203989i
\(543\) 0 0
\(544\) −7.44370 + 5.93615i −0.0136833 + 0.0109120i
\(545\) 85.6609 + 41.2521i 0.157176 + 0.0756919i
\(546\) 0 0
\(547\) 206.292 258.682i 0.377133 0.472910i −0.556651 0.830746i \(-0.687914\pi\)
0.933784 + 0.357836i \(0.116485\pi\)
\(548\) 275.336 + 31.0229i 0.502438 + 0.0566112i
\(549\) 0 0
\(550\) 12.5518i 0.0228214i
\(551\) 378.827 42.2343i 0.687526 0.0766503i
\(552\) 0 0
\(553\) 335.897 + 117.535i 0.607408 + 0.212541i
\(554\) −0.954352 + 8.47011i −0.00172266 + 0.0152890i
\(555\) 0 0
\(556\) −187.789 389.949i −0.337751 0.701347i
\(557\) −8.12730 + 16.8765i −0.0145912 + 0.0302989i −0.908137 0.418673i \(-0.862495\pi\)
0.893546 + 0.448972i \(0.148210\pi\)
\(558\) 0 0
\(559\) 213.126 + 339.188i 0.381262 + 0.606776i
\(560\) 791.819 + 180.728i 1.41396 + 0.322728i
\(561\) 0 0
\(562\) 7.15619 11.3890i 0.0127334 0.0202651i
\(563\) 682.747 682.747i 1.21269 1.21269i 0.242557 0.970137i \(-0.422014\pi\)
0.970137 0.242557i \(-0.0779860\pi\)
\(564\) 0 0
\(565\) −163.048 465.966i −0.288581 0.824718i
\(566\) −4.85688 + 1.69949i −0.00858105 + 0.00300264i
\(567\) 0 0
\(568\) −17.8246 17.8246i −0.0313814 0.0313814i
\(569\) −814.946 512.065i −1.43224 0.899938i −0.432245 0.901756i \(-0.642278\pi\)
−0.999998 + 0.00181851i \(0.999421\pi\)
\(570\) 0 0
\(571\) −32.2889 + 141.467i −0.0565480 + 0.247753i −0.995300 0.0968408i \(-0.969126\pi\)
0.938752 + 0.344594i \(0.111983\pi\)
\(572\) −277.485 + 174.356i −0.485114 + 0.304817i
\(573\) 0 0
\(574\) 0.659612 + 0.317652i 0.00114915 + 0.000553401i
\(575\) −324.594 + 156.316i −0.564512 + 0.271855i
\(576\) 0 0
\(577\) 263.320 + 29.6690i 0.456360 + 0.0514194i 0.337153 0.941450i \(-0.390536\pi\)
0.119207 + 0.992869i \(0.461965\pi\)
\(578\) 2.74749 7.85188i 0.00475344 0.0135846i
\(579\) 0 0
\(580\) 226.573 987.349i 0.390643 1.70233i
\(581\) −176.930 −0.304527
\(582\) 0 0
\(583\) 36.1952 321.241i 0.0620844 0.551014i
\(584\) 18.2158 + 14.5266i 0.0311914 + 0.0248743i
\(585\) 0 0
\(586\) −2.01640 + 4.18711i −0.00344096 + 0.00714523i
\(587\) −606.443 760.455i −1.03312 1.29549i −0.954379 0.298599i \(-0.903481\pi\)
−0.0787436 0.996895i \(-0.525091\pi\)
\(588\) 0 0
\(589\) −32.2094 7.35160i −0.0546850 0.0124815i
\(590\) 2.27944 + 20.2306i 0.00386346 + 0.0342891i
\(591\) 0 0
\(592\) 376.504 376.504i 0.635987 0.635987i
\(593\) −829.756 + 189.386i −1.39925 + 0.319370i −0.854597 0.519291i \(-0.826196\pi\)
−0.544654 + 0.838661i \(0.683339\pi\)
\(594\) 0 0
\(595\) 289.004 101.127i 0.485721 0.169961i
\(596\) 48.6239 + 213.035i 0.0815837 + 0.357442i
\(597\) 0 0
\(598\) −2.15878 1.35645i −0.00361000 0.00226831i
\(599\) 970.894 109.393i 1.62086 0.182627i 0.745638 0.666351i \(-0.232145\pi\)
0.875220 + 0.483724i \(0.160716\pi\)
\(600\) 0 0
\(601\) −265.894 + 167.072i −0.442419 + 0.277990i −0.734764 0.678323i \(-0.762707\pi\)
0.292345 + 0.956313i \(0.405564\pi\)
\(602\) 5.43776 4.33647i 0.00903282 0.00720343i
\(603\) 0 0
\(604\) −689.477 + 332.035i −1.14152 + 0.549726i
\(605\) 358.243 449.223i 0.592137 0.742517i
\(606\) 0 0
\(607\) −250.177 + 714.965i −0.412154 + 1.17787i 0.531536 + 0.847036i \(0.321615\pi\)
−0.943690 + 0.330832i \(0.892671\pi\)
\(608\) 20.7635i 0.0341505i
\(609\) 0 0
\(610\) 29.6107 0.0485422
\(611\) 95.3061 + 33.3491i 0.155984 + 0.0545811i
\(612\) 0 0
\(613\) −84.7718 67.6033i −0.138290 0.110283i 0.551902 0.833909i \(-0.313902\pi\)
−0.690192 + 0.723627i \(0.742474\pi\)
\(614\) 4.28096 + 8.88950i 0.00697224 + 0.0144780i
\(615\) 0 0
\(616\) 7.09618 + 8.89833i 0.0115198 + 0.0144453i
\(617\) 477.375 + 759.739i 0.773704 + 1.23134i 0.968136 + 0.250427i \(0.0805709\pi\)
−0.194432 + 0.980916i \(0.562286\pi\)
\(618\) 0 0
\(619\) −34.8184 309.021i −0.0562494 0.499227i −0.989976 0.141239i \(-0.954891\pi\)
0.933726 0.357988i \(-0.116537\pi\)
\(620\) −46.7133 + 74.3437i −0.0753440 + 0.119909i
\(621\) 0 0
\(622\) −0.0183018 + 0.00417728i −2.94242e−5 + 6.71588e-6i
\(623\) −198.636 567.668i −0.318837 0.911185i
\(624\) 0 0
\(625\) −161.220 706.351i −0.257952 1.13016i
\(626\) −0.308489 0.308489i −0.000492794 0.000492794i
\(627\) 0 0
\(628\) 255.318 28.7674i 0.406558 0.0458080i
\(629\) 44.6672 195.700i 0.0710130 0.311128i
\(630\) 0 0
\(631\) −60.2526 + 48.0499i −0.0954875 + 0.0761487i −0.670070 0.742298i \(-0.733736\pi\)
0.574582 + 0.818447i \(0.305164\pi\)
\(632\) −14.5180 6.99151i −0.0229716 0.0110625i
\(633\) 0 0
\(634\) −10.4641 + 13.1215i −0.0165049 + 0.0206964i
\(635\) 1982.88 + 223.416i 3.12264 + 0.351837i
\(636\) 0 0
\(637\) 167.361i 0.262733i
\(638\) 5.55224 4.41714i 0.00870257 0.00692341i
\(639\) 0 0
\(640\) −69.4433 24.2993i −0.108505 0.0379676i
\(641\) −36.9672 + 328.093i −0.0576712 + 0.511846i 0.931356 + 0.364110i \(0.118627\pi\)
−0.989027 + 0.147735i \(0.952802\pi\)
\(642\) 0 0
\(643\) −351.977 730.888i −0.547399 1.13668i −0.972793 0.231677i \(-0.925579\pi\)
0.425394 0.905008i \(-0.360135\pi\)
\(644\) 70.8608 147.144i 0.110032 0.228485i
\(645\) 0 0
\(646\) −1.38757 2.20830i −0.00214794 0.00341842i
\(647\) −643.781 146.939i −0.995024 0.227108i −0.306146 0.951985i \(-0.599039\pi\)
−0.688878 + 0.724877i \(0.741897\pi\)
\(648\) 0 0
\(649\) 279.885 445.434i 0.431255 0.686339i
\(650\) 13.1712 13.1712i 0.0202634 0.0202634i
\(651\) 0 0
\(652\) 389.668 + 1113.61i 0.597650 + 1.70799i
\(653\) −510.481 + 178.625i −0.781747 + 0.273545i −0.691502 0.722375i \(-0.743051\pi\)
−0.0902449 + 0.995920i \(0.528765\pi\)
\(654\) 0 0
\(655\) 1285.83 + 1285.83i 1.96309 + 1.96309i
\(656\) 51.7587 + 32.5221i 0.0789004 + 0.0495764i
\(657\) 0 0
\(658\) 0.390105 1.70916i 0.000592865 0.00259751i
\(659\) −67.5559 + 42.4482i −0.102513 + 0.0644131i −0.582313 0.812965i \(-0.697852\pi\)
0.479800 + 0.877378i \(0.340709\pi\)
\(660\) 0 0
\(661\) −174.005 83.7962i −0.263245 0.126772i 0.297606 0.954689i \(-0.403812\pi\)
−0.560851 + 0.827917i \(0.689526\pi\)
\(662\) −3.71354 + 1.78834i −0.00560957 + 0.00270143i
\(663\) 0 0
\(664\) 7.96109 + 0.897000i 0.0119896 + 0.00135090i
\(665\) −220.543 + 630.275i −0.331643 + 0.947782i
\(666\) 0 0
\(667\) −183.375 88.5736i −0.274925 0.132794i
\(668\) 227.731 0.340914
\(669\) 0 0
\(670\) 0.865900 7.68507i 0.00129239 0.0114703i
\(671\) −598.213 477.059i −0.891524 0.710967i
\(672\) 0 0
\(673\) 217.268 451.162i 0.322835 0.670374i −0.674880 0.737927i \(-0.735805\pi\)
0.997716 + 0.0675528i \(0.0215191\pi\)
\(674\) 4.25949 + 5.34124i 0.00631973 + 0.00792469i
\(675\) 0 0
\(676\) 184.733 + 42.1641i 0.273274 + 0.0623730i
\(677\) −32.4892 288.350i −0.0479900 0.425923i −0.994619 0.103598i \(-0.966964\pi\)
0.946629 0.322325i \(-0.104464\pi\)
\(678\) 0 0
\(679\) 469.552 469.552i 0.691535 0.691535i
\(680\) −13.5166 + 3.08509i −0.0198774 + 0.00453689i
\(681\) 0 0
\(682\) −0.580438 + 0.203104i −0.000851082 + 0.000297807i
\(683\) 135.936 + 595.576i 0.199028 + 0.871999i 0.971517 + 0.236971i \(0.0761546\pi\)
−0.772489 + 0.635029i \(0.780988\pi\)
\(684\) 0 0
\(685\) 512.480 + 322.012i 0.748145 + 0.470091i
\(686\) 12.2106 1.37581i 0.0177997 0.00200555i
\(687\) 0 0
\(688\) 491.712 308.963i 0.714698 0.449075i
\(689\) 375.076 299.113i 0.544378 0.434127i
\(690\) 0 0
\(691\) 525.520 253.077i 0.760521 0.366248i −0.0130852 0.999914i \(-0.504165\pi\)
0.773606 + 0.633667i \(0.218451\pi\)
\(692\) −836.449 + 1048.87i −1.20874 + 1.51571i
\(693\) 0 0
\(694\) −1.07596 + 3.07490i −0.00155037 + 0.00443070i
\(695\) 945.431i 1.36033i
\(696\) 0 0
\(697\) 23.0448 0.0330629
\(698\) 9.11839 + 3.19066i 0.0130636 + 0.00457115i
\(699\) 0 0
\(700\) 932.869 + 743.938i 1.33267 + 1.06277i
\(701\) 400.779 + 832.225i 0.571724 + 1.18720i 0.963642 + 0.267197i \(0.0860975\pi\)
−0.391918 + 0.920000i \(0.628188\pi\)
\(702\) 0 0
\(703\) 272.943 + 342.260i 0.388255 + 0.486857i
\(704\) 252.622 + 402.046i 0.358838 + 0.571088i
\(705\) 0 0
\(706\) 1.18627 + 10.5284i 0.00168027 + 0.0149128i
\(707\) 394.262 627.465i 0.557655 0.887503i
\(708\) 0 0
\(709\) −776.868 + 177.315i −1.09572 + 0.250092i −0.731924 0.681386i \(-0.761378\pi\)
−0.363799 + 0.931478i \(0.618520\pi\)
\(710\) −9.09199 25.9834i −0.0128056 0.0365964i
\(711\) 0 0
\(712\) 6.05979 + 26.5497i 0.00851094 + 0.0372889i
\(713\) 12.4810 + 12.4810i 0.0175049 + 0.0175049i
\(714\) 0 0
\(715\) −711.362 + 80.1512i −0.994911 + 0.112100i
\(716\) −142.137 + 622.744i −0.198516 + 0.869754i
\(717\) 0 0
\(718\) 11.9453 9.52604i 0.0166369 0.0132675i
\(719\) −1063.27 512.044i −1.47882 0.712162i −0.491495 0.870880i \(-0.663550\pi\)
−0.987324 + 0.158718i \(0.949264\pi\)
\(720\) 0 0
\(721\) 590.278 740.186i 0.818694 1.02661i
\(722\) −6.15826 0.693870i −0.00852945 0.000961038i
\(723\) 0 0
\(724\) 975.927i 1.34797i
\(725\) 929.003 1162.14i 1.28138 1.60295i
\(726\) 0 0
\(727\) −870.912 304.745i −1.19795 0.419182i −0.343721 0.939072i \(-0.611687\pi\)
−0.854233 + 0.519890i \(0.825973\pi\)
\(728\) −1.89109 + 16.7839i −0.00259765 + 0.0230548i
\(729\) 0 0
\(730\) 11.0395 + 22.9239i 0.0151227 + 0.0314025i
\(731\) 94.9894 197.247i 0.129944 0.269832i
\(732\) 0 0
\(733\) 503.422 + 801.192i 0.686797 + 1.09303i 0.990131 + 0.140147i \(0.0447574\pi\)
−0.303334 + 0.952884i \(0.598100\pi\)
\(734\) 3.14053 + 0.716806i 0.00427866 + 0.000976575i
\(735\) 0 0
\(736\) −5.90191 + 9.39283i −0.00801890 + 0.0127620i
\(737\) −141.308 + 141.308i −0.191734 + 0.191734i
\(738\) 0 0
\(739\) −400.530 1144.65i −0.541990 1.54892i −0.810559 0.585657i \(-0.800836\pi\)
0.268569 0.963260i \(-0.413449\pi\)
\(740\) 1098.13 384.252i 1.48396 0.519259i
\(741\) 0 0
\(742\) −5.88979 5.88979i −0.00793772 0.00793772i
\(743\) −670.026 421.005i −0.901785 0.566629i −0.000569123 1.00000i \(-0.500181\pi\)
−0.901216 + 0.433371i \(0.857324\pi\)
\(744\) 0 0
\(745\) −106.214 + 465.354i −0.142569 + 0.624636i
\(746\) 9.20693 5.78510i 0.0123417 0.00775482i
\(747\) 0 0
\(748\) 161.366 + 77.7096i 0.215730 + 0.103890i
\(749\) 355.579 171.238i 0.474738 0.228622i
\(750\) 0 0
\(751\) −73.9585 8.33312i −0.0984800 0.0110960i 0.0625869 0.998040i \(-0.480065\pi\)
−0.161067 + 0.986943i \(0.551494\pi\)
\(752\) 48.3453 138.163i 0.0642890 0.183727i
\(753\) 0 0
\(754\) 10.4614 + 1.19112i 0.0138745 + 0.00157974i
\(755\) −1671.64 −2.21409
\(756\) 0 0
\(757\) −21.2663 + 188.743i −0.0280928 + 0.249331i 0.971815 + 0.235745i \(0.0757531\pi\)
−0.999908 + 0.0135854i \(0.995675\pi\)
\(758\) −5.99756 4.78289i −0.00791235 0.00630989i
\(759\) 0 0
\(760\) 13.1188 27.2416i 0.0172616 0.0358442i
\(761\) −363.348 455.624i −0.477461 0.598717i 0.483520 0.875334i \(-0.339358\pi\)
−0.960980 + 0.276617i \(0.910787\pi\)
\(762\) 0 0
\(763\) −61.7139 14.0858i −0.0808833 0.0184611i
\(764\) −105.476 936.130i −0.138058 1.22530i
\(765\) 0 0
\(766\) 5.45955 5.45955i 0.00712735 0.00712735i
\(767\) 761.114 173.719i 0.992326 0.226492i
\(768\) 0 0
\(769\) −652.165 + 228.202i −0.848069 + 0.296752i −0.719109 0.694898i \(-0.755450\pi\)
−0.128960 + 0.991650i \(0.541164\pi\)
\(770\) 2.76573 + 12.1174i 0.00359185 + 0.0157369i
\(771\) 0 0
\(772\) −642.953 403.994i −0.832840 0.523308i
\(773\) 42.4335 4.78110i 0.0548945 0.00618513i −0.0844745 0.996426i \(-0.526921\pi\)
0.139369 + 0.990241i \(0.455493\pi\)
\(774\) 0 0
\(775\) −109.189 + 68.6083i −0.140890 + 0.0885268i
\(776\) −23.5084 + 18.7473i −0.0302943 + 0.0241589i
\(777\) 0 0
\(778\) −12.4668 + 6.00370i −0.0160242 + 0.00771684i
\(779\) −31.3349 + 39.2928i −0.0402246 + 0.0504400i
\(780\) 0 0
\(781\) −234.938 + 671.414i −0.300817 + 0.859684i
\(782\) 1.39338i 0.00178182i
\(783\) 0 0
\(784\) 242.619 0.309463
\(785\) 529.750 + 185.368i 0.674841 + 0.236137i
\(786\) 0 0
\(787\) −294.003