Properties

Label 126.3.n.a.73.2
Level $126$
Weight $3$
Character 126.73
Analytic conductor $3.433$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.43325133094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 126.73
Dual form 126.3.n.a.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-7.24264 + 4.18154i) q^{5} +(-6.74264 - 1.88064i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-7.24264 + 4.18154i) q^{5} +(-6.74264 - 1.88064i) q^{7} -2.82843 q^{8} +(-10.2426 - 5.91359i) q^{10} +(3.00000 - 5.19615i) q^{11} +17.8639i q^{13} +(-2.46447 - 9.58783i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(16.2426 + 9.37769i) q^{17} +(-14.7426 + 8.51167i) q^{19} -16.7262i q^{20} +8.48528 q^{22} +(6.72792 + 11.6531i) q^{23} +(22.4706 - 38.9202i) q^{25} +(-21.8787 + 12.6317i) q^{26} +(10.0000 - 9.79796i) q^{28} -33.9411 q^{29} +(12.7721 + 7.37396i) q^{31} +(2.82843 - 4.89898i) q^{32} +26.5241i q^{34} +(56.6985 - 14.5738i) q^{35} +(-2.98528 - 5.17066i) q^{37} +(-20.8492 - 12.0373i) q^{38} +(20.4853 - 11.8272i) q^{40} +35.2354i q^{41} +15.4853 q^{43} +(6.00000 + 10.3923i) q^{44} +(-9.51472 + 16.4800i) q^{46} +(28.7574 - 16.6031i) q^{47} +(41.9264 + 25.3609i) q^{49} +63.5563 q^{50} +(-30.9411 - 17.8639i) q^{52} +(-17.2721 + 29.9161i) q^{53} +50.1785i q^{55} +(19.0711 + 5.31925i) q^{56} +(-24.0000 - 41.5692i) q^{58} +(-23.6985 - 13.6823i) q^{59} +(-34.9706 + 20.1903i) q^{61} +20.8567i q^{62} +8.00000 q^{64} +(-74.6985 - 129.382i) q^{65} +(57.1985 - 99.0707i) q^{67} +(-32.4853 + 18.7554i) q^{68} +(57.9411 + 59.1359i) q^{70} -18.6030 q^{71} +(-101.353 - 58.5161i) q^{73} +(4.22183 - 7.31242i) q^{74} -34.0467i q^{76} +(-30.0000 + 29.3939i) q^{77} +(44.1690 + 76.5030i) q^{79} +(28.9706 + 16.7262i) q^{80} +(-43.1543 + 24.9152i) q^{82} +75.7601i q^{83} -156.853 q^{85} +(10.9497 + 18.9655i) q^{86} +(-8.48528 + 14.6969i) q^{88} +(18.0000 - 10.3923i) q^{89} +(33.5955 - 120.450i) q^{91} -26.9117 q^{92} +(40.6690 + 23.4803i) q^{94} +(71.1838 - 123.294i) q^{95} -30.5826i q^{97} +(-1.41421 + 69.2820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{4} - 12 q^{5} - 10 q^{7} - 24 q^{10} + 12 q^{11} - 24 q^{14} - 8 q^{16} + 48 q^{17} - 42 q^{19} - 24 q^{23} + 22 q^{25} - 96 q^{26} + 40 q^{28} + 102 q^{31} + 108 q^{35} + 22 q^{37} - 24 q^{38} + 48 q^{40} + 28 q^{43} + 24 q^{44} - 72 q^{46} + 132 q^{47} - 2 q^{49} + 192 q^{50} + 12 q^{52} - 120 q^{53} + 48 q^{56} - 96 q^{58} + 24 q^{59} - 72 q^{61} + 32 q^{64} - 180 q^{65} + 110 q^{67} - 96 q^{68} + 96 q^{70} - 312 q^{71} - 66 q^{73} + 48 q^{74} - 120 q^{77} - 10 q^{79} + 48 q^{80} + 48 q^{82} - 288 q^{85} + 24 q^{86} + 72 q^{89} - 222 q^{91} + 96 q^{92} - 24 q^{94} + 132 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −7.24264 + 4.18154i −1.44853 + 0.836308i −0.998394 0.0566528i \(-0.981957\pi\)
−0.450134 + 0.892961i \(0.648624\pi\)
\(6\) 0 0
\(7\) −6.74264 1.88064i −0.963234 0.268662i
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) −10.2426 5.91359i −1.02426 0.591359i
\(11\) 3.00000 5.19615i 0.272727 0.472377i −0.696832 0.717234i \(-0.745408\pi\)
0.969559 + 0.244857i \(0.0787410\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i 0.726590 + 0.687072i \(0.241104\pi\)
−0.726590 + 0.687072i \(0.758896\pi\)
\(14\) −2.46447 9.58783i −0.176033 0.684845i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 16.2426 + 9.37769i 0.955449 + 0.551629i 0.894770 0.446528i \(-0.147340\pi\)
0.0606799 + 0.998157i \(0.480673\pi\)
\(18\) 0 0
\(19\) −14.7426 + 8.51167i −0.775928 + 0.447983i −0.834985 0.550272i \(-0.814524\pi\)
0.0590569 + 0.998255i \(0.481191\pi\)
\(20\) 16.7262i 0.836308i
\(21\) 0 0
\(22\) 8.48528 0.385695
\(23\) 6.72792 + 11.6531i 0.292518 + 0.506657i 0.974405 0.224802i \(-0.0721734\pi\)
−0.681886 + 0.731458i \(0.738840\pi\)
\(24\) 0 0
\(25\) 22.4706 38.9202i 0.898823 1.55681i
\(26\) −21.8787 + 12.6317i −0.841488 + 0.485833i
\(27\) 0 0
\(28\) 10.0000 9.79796i 0.357143 0.349927i
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) 0 0
\(31\) 12.7721 + 7.37396i 0.412003 + 0.237870i 0.691650 0.722233i \(-0.256884\pi\)
−0.279647 + 0.960103i \(0.590218\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 26.5241i 0.780121i
\(35\) 56.6985 14.5738i 1.61996 0.416396i
\(36\) 0 0
\(37\) −2.98528 5.17066i −0.0806833 0.139748i 0.822860 0.568244i \(-0.192377\pi\)
−0.903544 + 0.428496i \(0.859044\pi\)
\(38\) −20.8492 12.0373i −0.548664 0.316771i
\(39\) 0 0
\(40\) 20.4853 11.8272i 0.512132 0.295680i
\(41\) 35.2354i 0.859399i 0.902972 + 0.429700i \(0.141381\pi\)
−0.902972 + 0.429700i \(0.858619\pi\)
\(42\) 0 0
\(43\) 15.4853 0.360123 0.180061 0.983655i \(-0.442370\pi\)
0.180061 + 0.983655i \(0.442370\pi\)
\(44\) 6.00000 + 10.3923i 0.136364 + 0.236189i
\(45\) 0 0
\(46\) −9.51472 + 16.4800i −0.206842 + 0.358260i
\(47\) 28.7574 16.6031i 0.611859 0.353257i −0.161834 0.986818i \(-0.551741\pi\)
0.773693 + 0.633561i \(0.218408\pi\)
\(48\) 0 0
\(49\) 41.9264 + 25.3609i 0.855641 + 0.517570i
\(50\) 63.5563 1.27113
\(51\) 0 0
\(52\) −30.9411 17.8639i −0.595022 0.343536i
\(53\) −17.2721 + 29.9161i −0.325888 + 0.564455i −0.981692 0.190477i \(-0.938997\pi\)
0.655803 + 0.754932i \(0.272330\pi\)
\(54\) 0 0
\(55\) 50.1785i 0.912336i
\(56\) 19.0711 + 5.31925i 0.340555 + 0.0949865i
\(57\) 0 0
\(58\) −24.0000 41.5692i −0.413793 0.716711i
\(59\) −23.6985 13.6823i −0.401669 0.231904i 0.285535 0.958368i \(-0.407829\pi\)
−0.687204 + 0.726465i \(0.741162\pi\)
\(60\) 0 0
\(61\) −34.9706 + 20.1903i −0.573288 + 0.330988i −0.758461 0.651718i \(-0.774049\pi\)
0.185174 + 0.982706i \(0.440715\pi\)
\(62\) 20.8567i 0.336399i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −74.6985 129.382i −1.14921 1.99049i
\(66\) 0 0
\(67\) 57.1985 99.0707i 0.853709 1.47867i −0.0241291 0.999709i \(-0.507681\pi\)
0.877838 0.478958i \(-0.158985\pi\)
\(68\) −32.4853 + 18.7554i −0.477725 + 0.275814i
\(69\) 0 0
\(70\) 57.9411 + 59.1359i 0.827730 + 0.844799i
\(71\) −18.6030 −0.262015 −0.131007 0.991381i \(-0.541821\pi\)
−0.131007 + 0.991381i \(0.541821\pi\)
\(72\) 0 0
\(73\) −101.353 58.5161i −1.38839 0.801590i −0.395260 0.918569i \(-0.629346\pi\)
−0.993134 + 0.116979i \(0.962679\pi\)
\(74\) 4.22183 7.31242i 0.0570517 0.0988164i
\(75\) 0 0
\(76\) 34.0467i 0.447983i
\(77\) −30.0000 + 29.3939i −0.389610 + 0.381739i
\(78\) 0 0
\(79\) 44.1690 + 76.5030i 0.559102 + 0.968393i 0.997572 + 0.0696469i \(0.0221873\pi\)
−0.438470 + 0.898746i \(0.644479\pi\)
\(80\) 28.9706 + 16.7262i 0.362132 + 0.209077i
\(81\) 0 0
\(82\) −43.1543 + 24.9152i −0.526272 + 0.303843i
\(83\) 75.7601i 0.912772i 0.889782 + 0.456386i \(0.150856\pi\)
−0.889782 + 0.456386i \(0.849144\pi\)
\(84\) 0 0
\(85\) −156.853 −1.84533
\(86\) 10.9497 + 18.9655i 0.127323 + 0.220529i
\(87\) 0 0
\(88\) −8.48528 + 14.6969i −0.0964237 + 0.167011i
\(89\) 18.0000 10.3923i 0.202247 0.116767i −0.395456 0.918485i \(-0.629413\pi\)
0.597703 + 0.801717i \(0.296080\pi\)
\(90\) 0 0
\(91\) 33.5955 120.450i 0.369181 1.32362i
\(92\) −26.9117 −0.292518
\(93\) 0 0
\(94\) 40.6690 + 23.4803i 0.432649 + 0.249790i
\(95\) 71.1838 123.294i 0.749303 1.29783i
\(96\) 0 0
\(97\) 30.5826i 0.315284i −0.987496 0.157642i \(-0.949611\pi\)
0.987496 0.157642i \(-0.0503892\pi\)
\(98\) −1.41421 + 69.2820i −0.0144308 + 0.706960i
\(99\) 0 0
\(100\) 44.9411 + 77.8403i 0.449411 + 0.778403i
\(101\) −110.823 63.9839i −1.09726 0.633504i −0.161761 0.986830i \(-0.551717\pi\)
−0.935500 + 0.353326i \(0.885051\pi\)
\(102\) 0 0
\(103\) −70.1102 + 40.4781i −0.680681 + 0.392992i −0.800112 0.599851i \(-0.795226\pi\)
0.119430 + 0.992843i \(0.461893\pi\)
\(104\) 50.5266i 0.485833i
\(105\) 0 0
\(106\) −48.8528 −0.460876
\(107\) 84.7279 + 146.753i 0.791850 + 1.37152i 0.924820 + 0.380404i \(0.124215\pi\)
−0.132971 + 0.991120i \(0.542452\pi\)
\(108\) 0 0
\(109\) −89.4706 + 154.968i −0.820831 + 1.42172i 0.0842335 + 0.996446i \(0.473156\pi\)
−0.905064 + 0.425275i \(0.860177\pi\)
\(110\) −61.4558 + 35.4815i −0.558689 + 0.322560i
\(111\) 0 0
\(112\) 6.97056 + 27.1185i 0.0622372 + 0.242129i
\(113\) 17.3970 0.153955 0.0769777 0.997033i \(-0.475473\pi\)
0.0769777 + 0.997033i \(0.475473\pi\)
\(114\) 0 0
\(115\) −97.4558 56.2662i −0.847442 0.489271i
\(116\) 33.9411 58.7878i 0.292596 0.506791i
\(117\) 0 0
\(118\) 38.6995i 0.327962i
\(119\) −91.8823 93.7769i −0.772120 0.788041i
\(120\) 0 0
\(121\) 42.5000 + 73.6122i 0.351240 + 0.608365i
\(122\) −49.4558 28.5533i −0.405376 0.234044i
\(123\) 0 0
\(124\) −25.5442 + 14.7479i −0.206001 + 0.118935i
\(125\) 166.769i 1.33415i
\(126\) 0 0
\(127\) 167.426 1.31832 0.659159 0.752004i \(-0.270912\pi\)
0.659159 + 0.752004i \(0.270912\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 105.640 182.973i 0.812612 1.40749i
\(131\) 1.54416 0.891519i 0.0117874 0.00680549i −0.494095 0.869408i \(-0.664500\pi\)
0.505882 + 0.862603i \(0.331167\pi\)
\(132\) 0 0
\(133\) 115.412 29.6656i 0.867757 0.223049i
\(134\) 161.782 1.20733
\(135\) 0 0
\(136\) −45.9411 26.5241i −0.337802 0.195030i
\(137\) 50.4853 87.4431i 0.368506 0.638271i −0.620826 0.783948i \(-0.713203\pi\)
0.989332 + 0.145677i \(0.0465362\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i 0.862799 + 0.505548i \(0.168710\pi\)
−0.862799 + 0.505548i \(0.831290\pi\)
\(140\) −31.4558 + 112.779i −0.224685 + 0.805561i
\(141\) 0 0
\(142\) −13.1543 22.7840i −0.0926361 0.160450i
\(143\) 92.8234 + 53.5916i 0.649115 + 0.374766i
\(144\) 0 0
\(145\) 245.823 141.926i 1.69533 0.978801i
\(146\) 165.508i 1.13362i
\(147\) 0 0
\(148\) 11.9411 0.0806833
\(149\) 91.4558 + 158.406i 0.613798 + 1.06313i 0.990594 + 0.136833i \(0.0436922\pi\)
−0.376797 + 0.926296i \(0.622974\pi\)
\(150\) 0 0
\(151\) 144.397 250.103i 0.956271 1.65631i 0.224840 0.974396i \(-0.427814\pi\)
0.731432 0.681915i \(-0.238852\pi\)
\(152\) 41.6985 24.0746i 0.274332 0.158386i
\(153\) 0 0
\(154\) −57.2132 15.9577i −0.371514 0.103622i
\(155\) −123.338 −0.795730
\(156\) 0 0
\(157\) 162.000 + 93.5307i 1.03185 + 0.595737i 0.917513 0.397705i \(-0.130193\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(158\) −62.4645 + 108.192i −0.395345 + 0.684757i
\(159\) 0 0
\(160\) 47.3087i 0.295680i
\(161\) −23.4487 91.2255i −0.145644 0.566618i
\(162\) 0 0
\(163\) −8.02944 13.9074i −0.0492604 0.0853214i 0.840344 0.542054i \(-0.182353\pi\)
−0.889604 + 0.456732i \(0.849020\pi\)
\(164\) −61.0294 35.2354i −0.372131 0.214850i
\(165\) 0 0
\(166\) −92.7868 + 53.5705i −0.558957 + 0.322714i
\(167\) 176.117i 1.05459i −0.849681 0.527297i \(-0.823206\pi\)
0.849681 0.527297i \(-0.176794\pi\)
\(168\) 0 0
\(169\) −150.118 −0.888271
\(170\) −110.912 192.105i −0.652422 1.13003i
\(171\) 0 0
\(172\) −15.4853 + 26.8213i −0.0900307 + 0.155938i
\(173\) 200.184 115.576i 1.15713 0.668070i 0.206517 0.978443i \(-0.433787\pi\)
0.950615 + 0.310373i \(0.100454\pi\)
\(174\) 0 0
\(175\) −224.706 + 220.166i −1.28403 + 1.25809i
\(176\) −24.0000 −0.136364
\(177\) 0 0
\(178\) 25.4558 + 14.6969i 0.143010 + 0.0825671i
\(179\) −42.6396 + 73.8540i −0.238210 + 0.412592i −0.960201 0.279311i \(-0.909894\pi\)
0.721991 + 0.691903i \(0.243227\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i 0.999881 + 0.0154325i \(0.00491250\pi\)
−0.999881 + 0.0154325i \(0.995087\pi\)
\(182\) 171.276 44.0249i 0.941075 0.241895i
\(183\) 0 0
\(184\) −19.0294 32.9600i −0.103421 0.179130i
\(185\) 43.2426 + 24.9662i 0.233744 + 0.134952i
\(186\) 0 0
\(187\) 97.4558 56.2662i 0.521154 0.300889i
\(188\) 66.4123i 0.353257i
\(189\) 0 0
\(190\) 201.338 1.05967
\(191\) 92.6985 + 160.558i 0.485332 + 0.840620i 0.999858 0.0168547i \(-0.00536527\pi\)
−0.514526 + 0.857475i \(0.672032\pi\)
\(192\) 0 0
\(193\) −113.897 + 197.275i −0.590140 + 1.02215i 0.404073 + 0.914727i \(0.367594\pi\)
−0.994213 + 0.107425i \(0.965739\pi\)
\(194\) 37.4558 21.6251i 0.193071 0.111470i
\(195\) 0 0
\(196\) −85.8528 + 47.2577i −0.438025 + 0.241111i
\(197\) −123.161 −0.625185 −0.312593 0.949887i \(-0.601197\pi\)
−0.312593 + 0.949887i \(0.601197\pi\)
\(198\) 0 0
\(199\) 5.39697 + 3.11594i 0.0271205 + 0.0156580i 0.513499 0.858090i \(-0.328349\pi\)
−0.486378 + 0.873748i \(0.661682\pi\)
\(200\) −63.5563 + 110.083i −0.317782 + 0.550414i
\(201\) 0 0
\(202\) 180.974i 0.895910i
\(203\) 228.853 + 63.8309i 1.12735 + 0.314438i
\(204\) 0 0
\(205\) −147.338 255.197i −0.718722 1.24486i
\(206\) −99.1508 57.2447i −0.481314 0.277887i
\(207\) 0 0
\(208\) 61.8823 35.7277i 0.297511 0.171768i
\(209\) 102.140i 0.488708i
\(210\) 0 0
\(211\) −124.912 −0.591999 −0.295999 0.955188i \(-0.595653\pi\)
−0.295999 + 0.955188i \(0.595653\pi\)
\(212\) −34.5442 59.8322i −0.162944 0.282228i
\(213\) 0 0
\(214\) −119.823 + 207.540i −0.559922 + 0.969814i
\(215\) −112.154 + 64.7523i −0.521648 + 0.301174i
\(216\) 0 0
\(217\) −72.2498 73.7396i −0.332948 0.339814i
\(218\) −253.061 −1.16083
\(219\) 0 0
\(220\) −86.9117 50.1785i −0.395053 0.228084i
\(221\) −167.522 + 290.156i −0.758017 + 1.31292i
\(222\) 0 0
\(223\) 228.631i 1.02525i 0.858613 + 0.512625i \(0.171327\pi\)
−0.858613 + 0.512625i \(0.828673\pi\)
\(224\) −28.2843 + 27.7128i −0.126269 + 0.123718i
\(225\) 0 0
\(226\) 12.3015 + 21.3068i 0.0544315 + 0.0942781i
\(227\) 146.823 + 84.7685i 0.646799 + 0.373430i 0.787229 0.616661i \(-0.211515\pi\)
−0.140430 + 0.990091i \(0.544848\pi\)
\(228\) 0 0
\(229\) 30.0442 17.3460i 0.131197 0.0757467i −0.432965 0.901411i \(-0.642533\pi\)
0.564162 + 0.825664i \(0.309199\pi\)
\(230\) 159.145i 0.691934i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) −127.243 220.391i −0.546106 0.945883i −0.998536 0.0540833i \(-0.982776\pi\)
0.452431 0.891800i \(-0.350557\pi\)
\(234\) 0 0
\(235\) −138.853 + 240.500i −0.590863 + 1.02340i
\(236\) 47.3970 27.3647i 0.200835 0.115952i
\(237\) 0 0
\(238\) 49.8823 178.843i 0.209589 0.751440i
\(239\) −197.147 −0.824884 −0.412442 0.910984i \(-0.635324\pi\)
−0.412442 + 0.910984i \(0.635324\pi\)
\(240\) 0 0
\(241\) 76.6173 + 44.2350i 0.317914 + 0.183548i 0.650462 0.759538i \(-0.274575\pi\)
−0.332548 + 0.943086i \(0.607908\pi\)
\(242\) −60.1041 + 104.103i −0.248364 + 0.430179i
\(243\) 0 0
\(244\) 80.7611i 0.330988i
\(245\) −409.706 8.36308i −1.67227 0.0341350i
\(246\) 0 0
\(247\) −152.051 263.361i −0.615592 1.06624i
\(248\) −36.1249 20.8567i −0.145665 0.0840997i
\(249\) 0 0
\(250\) −204.250 + 117.924i −0.816999 + 0.471695i
\(251\) 215.903i 0.860172i −0.902788 0.430086i \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(252\) 0 0
\(253\) 80.7351 0.319111
\(254\) 118.388 + 205.055i 0.466096 + 0.807302i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 3.72792 2.15232i 0.0145055 0.00837477i −0.492730 0.870182i \(-0.664001\pi\)
0.507235 + 0.861808i \(0.330668\pi\)
\(258\) 0 0
\(259\) 10.4045 + 40.4781i 0.0401720 + 0.156286i
\(260\) 298.794 1.14921
\(261\) 0 0
\(262\) 2.18377 + 1.26080i 0.00833499 + 0.00481221i
\(263\) 141.338 244.805i 0.537407 0.930817i −0.461635 0.887070i \(-0.652737\pi\)
0.999043 0.0437468i \(-0.0139295\pi\)
\(264\) 0 0
\(265\) 288.896i 1.09017i
\(266\) 117.941 + 120.373i 0.443388 + 0.452531i
\(267\) 0 0
\(268\) 114.397 + 198.141i 0.426854 + 0.739333i
\(269\) 330.765 + 190.967i 1.22961 + 0.709914i 0.966948 0.254974i \(-0.0820669\pi\)
0.262660 + 0.964888i \(0.415400\pi\)
\(270\) 0 0
\(271\) −73.0294 + 42.1636i −0.269481 + 0.155585i −0.628652 0.777687i \(-0.716393\pi\)
0.359171 + 0.933272i \(0.383060\pi\)
\(272\) 75.0215i 0.275814i
\(273\) 0 0
\(274\) 142.794 0.521146
\(275\) −134.823 233.521i −0.490267 0.849167i
\(276\) 0 0
\(277\) 68.5589 118.747i 0.247505 0.428691i −0.715328 0.698789i \(-0.753723\pi\)
0.962833 + 0.270098i \(0.0870560\pi\)
\(278\) −172.128 + 99.3784i −0.619167 + 0.357476i
\(279\) 0 0
\(280\) −160.368 + 41.2211i −0.572741 + 0.147218i
\(281\) 325.103 1.15695 0.578474 0.815701i \(-0.303648\pi\)
0.578474 + 0.815701i \(0.303648\pi\)
\(282\) 0 0
\(283\) 168.507 + 97.2876i 0.595432 + 0.343773i 0.767242 0.641357i \(-0.221628\pi\)
−0.171811 + 0.985130i \(0.554962\pi\)
\(284\) 18.6030 32.2214i 0.0655036 0.113456i
\(285\) 0 0
\(286\) 151.580i 0.530000i
\(287\) 66.2649 237.579i 0.230888 0.827803i
\(288\) 0 0
\(289\) 31.3823 + 54.3557i 0.108589 + 0.188082i
\(290\) 347.647 + 200.714i 1.19878 + 0.692117i
\(291\) 0 0
\(292\) 202.706 117.032i 0.694197 0.400795i
\(293\) 239.702i 0.818095i −0.912513 0.409048i \(-0.865861\pi\)
0.912513 0.409048i \(-0.134139\pi\)
\(294\) 0 0
\(295\) 228.853 0.775772
\(296\) 8.44365 + 14.6248i 0.0285258 + 0.0494082i
\(297\) 0 0
\(298\) −129.338 + 224.020i −0.434020 + 0.751745i
\(299\) −208.169 + 120.187i −0.696219 + 0.401962i
\(300\) 0 0
\(301\) −104.412 29.1222i −0.346883 0.0967515i
\(302\) 408.416 1.35237
\(303\) 0 0
\(304\) 58.9706 + 34.0467i 0.193982 + 0.111996i
\(305\) 168.853 292.462i 0.553616 0.958891i
\(306\) 0 0
\(307\) 540.272i 1.75984i −0.475120 0.879921i \(-0.657595\pi\)
0.475120 0.879921i \(-0.342405\pi\)
\(308\) −20.9117 81.3554i −0.0678951 0.264141i
\(309\) 0 0
\(310\) −87.2132 151.058i −0.281333 0.487283i
\(311\) −350.044 202.098i −1.12554 0.649832i −0.182732 0.983163i \(-0.558494\pi\)
−0.942810 + 0.333330i \(0.891828\pi\)
\(312\) 0 0
\(313\) −113.706 + 65.6482i −0.363278 + 0.209739i −0.670518 0.741893i \(-0.733928\pi\)
0.307240 + 0.951632i \(0.400595\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) −176.676 −0.559102
\(317\) −46.9706 81.3554i −0.148172 0.256642i 0.782380 0.622802i \(-0.214006\pi\)
−0.930552 + 0.366160i \(0.880672\pi\)
\(318\) 0 0
\(319\) −101.823 + 176.363i −0.319196 + 0.552863i
\(320\) −57.9411 + 33.4523i −0.181066 + 0.104539i
\(321\) 0 0
\(322\) 95.1472 93.2248i 0.295488 0.289518i
\(323\) −319.279 −0.988481
\(324\) 0 0
\(325\) 695.265 + 401.411i 2.13928 + 1.23511i
\(326\) 11.3553 19.6680i 0.0348323 0.0603314i
\(327\) 0 0
\(328\) 99.6607i 0.303843i
\(329\) −225.125 + 57.8664i −0.684270 + 0.175886i
\(330\) 0 0
\(331\) 130.684 + 226.351i 0.394815 + 0.683840i 0.993078 0.117460i \(-0.0374754\pi\)
−0.598263 + 0.801300i \(0.704142\pi\)
\(332\) −131.220 75.7601i −0.395242 0.228193i
\(333\) 0 0
\(334\) 215.698 124.534i 0.645804 0.372855i
\(335\) 956.711i 2.85585i
\(336\) 0 0
\(337\) 136.265 0.404347 0.202173 0.979350i \(-0.435200\pi\)
0.202173 + 0.979350i \(0.435200\pi\)
\(338\) −106.149 183.856i −0.314051 0.543952i
\(339\) 0 0
\(340\) 156.853 271.677i 0.461332 0.799050i
\(341\) 76.6325 44.2438i 0.224729 0.129747i
\(342\) 0 0
\(343\) −235.000 249.848i −0.685131 0.728420i
\(344\) −43.7990 −0.127323
\(345\) 0 0
\(346\) 283.103 + 163.449i 0.818216 + 0.472397i
\(347\) −161.095 + 279.026i −0.464252 + 0.804108i −0.999167 0.0407975i \(-0.987010\pi\)
0.534915 + 0.844906i \(0.320343\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i −0.868088 0.496411i \(-0.834651\pi\)
0.868088 0.496411i \(-0.165349\pi\)
\(350\) −428.538 119.526i −1.22439 0.341504i
\(351\) 0 0
\(352\) −16.9706 29.3939i −0.0482118 0.0835053i
\(353\) 537.448 + 310.296i 1.52252 + 0.879025i 0.999646 + 0.0266116i \(0.00847174\pi\)
0.522869 + 0.852413i \(0.324862\pi\)
\(354\) 0 0
\(355\) 134.735 77.7893i 0.379535 0.219125i
\(356\) 41.5692i 0.116767i
\(357\) 0 0
\(358\) −120.603 −0.336880
\(359\) 10.1177 + 17.5245i 0.0281831 + 0.0488146i 0.879773 0.475394i \(-0.157695\pi\)
−0.851590 + 0.524209i \(0.824361\pi\)
\(360\) 0 0
\(361\) −35.6030 + 61.6663i −0.0986234 + 0.170821i
\(362\) −6.84210 + 3.95029i −0.0189008 + 0.0109124i
\(363\) 0 0
\(364\) 175.029 + 178.639i 0.480850 + 0.490766i
\(365\) 978.749 2.68151
\(366\) 0 0
\(367\) −269.831 155.787i −0.735234 0.424488i 0.0850998 0.996372i \(-0.472879\pi\)
−0.820334 + 0.571885i \(0.806212\pi\)
\(368\) 26.9117 46.6124i 0.0731296 0.126664i
\(369\) 0 0
\(370\) 70.6149i 0.190851i
\(371\) 172.721 169.231i 0.465555 0.456149i
\(372\) 0 0
\(373\) 340.691 + 590.094i 0.913380 + 1.58202i 0.809255 + 0.587457i \(0.199871\pi\)
0.104125 + 0.994564i \(0.466796\pi\)
\(374\) 137.823 + 79.5724i 0.368512 + 0.212760i
\(375\) 0 0
\(376\) −81.3381 + 46.9606i −0.216325 + 0.124895i
\(377\) 606.320i 1.60828i
\(378\) 0 0
\(379\) −624.779 −1.64849 −0.824246 0.566231i \(-0.808401\pi\)
−0.824246 + 0.566231i \(0.808401\pi\)
\(380\) 142.368 + 246.588i 0.374651 + 0.648915i
\(381\) 0 0
\(382\) −131.095 + 227.064i −0.343182 + 0.594408i
\(383\) −119.772 + 69.1502i −0.312720 + 0.180549i −0.648143 0.761519i \(-0.724454\pi\)
0.335423 + 0.942068i \(0.391121\pi\)
\(384\) 0 0
\(385\) 94.3675 338.336i 0.245110 0.878794i
\(386\) −322.149 −0.834584
\(387\) 0 0
\(388\) 52.9706 + 30.5826i 0.136522 + 0.0788211i
\(389\) −281.787 + 488.069i −0.724388 + 1.25468i 0.234838 + 0.972035i \(0.424544\pi\)
−0.959226 + 0.282642i \(0.908789\pi\)
\(390\) 0 0
\(391\) 252.370i 0.645446i
\(392\) −118.586 71.7315i −0.302515 0.182989i
\(393\) 0 0
\(394\) −87.0883 150.841i −0.221036 0.382846i
\(395\) −639.801 369.389i −1.61975 0.935163i
\(396\) 0 0
\(397\) −392.603 + 226.669i −0.988923 + 0.570955i −0.904952 0.425513i \(-0.860094\pi\)
−0.0839711 + 0.996468i \(0.526760\pi\)
\(398\) 8.81321i 0.0221438i
\(399\) 0 0
\(400\) −179.765 −0.449411
\(401\) −137.875 238.807i −0.343828 0.595528i 0.641312 0.767280i \(-0.278390\pi\)
−0.985140 + 0.171752i \(0.945057\pi\)
\(402\) 0 0
\(403\) −131.727 + 228.159i −0.326867 + 0.566151i
\(404\) 221.647 127.968i 0.548631 0.316752i
\(405\) 0 0
\(406\) 83.6468 + 325.422i 0.206026 + 0.801531i
\(407\) −35.8234 −0.0880181
\(408\) 0 0
\(409\) −377.441 217.916i −0.922839 0.532801i −0.0382993 0.999266i \(-0.512194\pi\)
−0.884540 + 0.466465i \(0.845527\pi\)
\(410\) 208.368 360.903i 0.508213 0.880252i
\(411\) 0 0
\(412\) 161.913i 0.392992i
\(413\) 134.059 + 136.823i 0.324598 + 0.331291i
\(414\) 0 0
\(415\) −316.794 548.703i −0.763359 1.32218i
\(416\) 87.5147 + 50.5266i 0.210372 + 0.121458i
\(417\) 0 0
\(418\) −125.095 + 72.2239i −0.299271 + 0.172784i
\(419\) 301.257i 0.718991i −0.933147 0.359496i \(-0.882949\pi\)
0.933147 0.359496i \(-0.117051\pi\)
\(420\) 0 0
\(421\) −203.794 −0.484071 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(422\) −88.3259 152.985i −0.209303 0.362524i
\(423\) 0 0
\(424\) 48.8528 84.6156i 0.115219 0.199565i
\(425\) 729.963 421.444i 1.71756 0.991633i
\(426\) 0 0
\(427\) 273.765 70.3688i 0.641135 0.164798i
\(428\) −338.912 −0.791850
\(429\) 0 0
\(430\) −158.610 91.5736i −0.368861 0.212962i
\(431\) −197.860 + 342.703i −0.459072 + 0.795136i −0.998912 0.0466317i \(-0.985151\pi\)
0.539840 + 0.841767i \(0.318485\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i 0.998693 + 0.0511184i \(0.0162786\pi\)
−0.998693 + 0.0511184i \(0.983721\pi\)
\(434\) 39.2239 140.629i 0.0903777 0.324031i
\(435\) 0 0
\(436\) −178.941 309.935i −0.410415 0.710860i
\(437\) −198.375 114.532i −0.453947 0.262086i
\(438\) 0 0
\(439\) 344.558 198.931i 0.784871 0.453146i −0.0532827 0.998579i \(-0.516968\pi\)
0.838154 + 0.545434i \(0.183635\pi\)
\(440\) 141.926i 0.322560i
\(441\) 0 0
\(442\) −473.823 −1.07200
\(443\) −59.2721 102.662i −0.133797 0.231743i 0.791340 0.611376i \(-0.209384\pi\)
−0.925137 + 0.379633i \(0.876050\pi\)
\(444\) 0 0
\(445\) −86.9117 + 150.535i −0.195307 + 0.338282i
\(446\) −280.014 + 161.666i −0.627835 + 0.362481i
\(447\) 0 0
\(448\) −53.9411 15.0451i −0.120404 0.0335828i
\(449\) −713.897 −1.58997 −0.794985 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(450\) 0 0
\(451\) 183.088 + 105.706i 0.405961 + 0.234382i
\(452\) −17.3970 + 30.1324i −0.0384889 + 0.0666647i
\(453\) 0 0
\(454\) 239.762i 0.528109i
\(455\) 260.345 + 1012.85i 0.572187 + 2.22605i
\(456\) 0 0
\(457\) 62.5883 + 108.406i 0.136955 + 0.237213i 0.926342 0.376682i \(-0.122935\pi\)
−0.789388 + 0.613895i \(0.789602\pi\)
\(458\) 42.4889 + 24.5310i 0.0927704 + 0.0535610i
\(459\) 0 0
\(460\) 194.912 112.532i 0.423721 0.244635i
\(461\) 655.767i 1.42249i 0.702945 + 0.711244i \(0.251868\pi\)
−0.702945 + 0.711244i \(0.748132\pi\)
\(462\) 0 0
\(463\) 869.396 1.87775 0.938873 0.344265i \(-0.111872\pi\)
0.938873 + 0.344265i \(0.111872\pi\)
\(464\) 67.8823 + 117.576i 0.146298 + 0.253395i
\(465\) 0 0
\(466\) 179.948 311.680i 0.386155 0.668840i
\(467\) 231.551 133.686i 0.495827 0.286266i −0.231162 0.972915i \(-0.574253\pi\)
0.726989 + 0.686649i \(0.240919\pi\)
\(468\) 0 0
\(469\) −571.985 + 560.428i −1.21958 + 1.19494i
\(470\) −392.735 −0.835607
\(471\) 0 0
\(472\) 67.0294 + 38.6995i 0.142012 + 0.0819904i
\(473\) 46.4558 80.4639i 0.0982153 0.170114i
\(474\) 0 0
\(475\) 765.048i 1.61063i
\(476\) 254.309 65.3678i 0.534262 0.137327i
\(477\) 0 0
\(478\) −139.404 241.455i −0.291640 0.505136i
\(479\) −235.331 135.868i −0.491296 0.283650i 0.233816 0.972281i \(-0.424879\pi\)
−0.725112 + 0.688631i \(0.758212\pi\)
\(480\) 0 0
\(481\) 92.3680 53.3287i 0.192033 0.110870i
\(482\) 125.116i 0.259576i
\(483\) 0 0
\(484\) −170.000 −0.351240
\(485\) 127.882 + 221.499i 0.263675 + 0.456698i
\(486\) 0 0
\(487\) 280.757 486.285i 0.576503 0.998532i −0.419374 0.907814i \(-0.637750\pi\)
0.995877 0.0907186i \(-0.0289164\pi\)
\(488\) 98.9117 57.1067i 0.202688 0.117022i
\(489\) 0 0
\(490\) −279.463 507.698i −0.570333 1.03612i
\(491\) 406.441 0.827781 0.413891 0.910327i \(-0.364170\pi\)
0.413891 + 0.910327i \(0.364170\pi\)
\(492\) 0 0
\(493\) −551.294 318.289i −1.11824 0.645618i
\(494\) 215.033 372.448i 0.435289 0.753944i
\(495\) 0 0
\(496\) 58.9917i 0.118935i
\(497\) 125.434 + 34.9856i 0.252381 + 0.0703935i
\(498\) 0 0
\(499\) 185.713 + 321.665i 0.372171 + 0.644619i 0.989899 0.141773i \(-0.0452802\pi\)
−0.617728 + 0.786391i \(0.711947\pi\)
\(500\) −288.853 166.769i −0.577706 0.333538i
\(501\) 0 0
\(502\) 264.426 152.667i 0.526746 0.304117i
\(503\) 64.6292i 0.128488i 0.997934 + 0.0642438i \(0.0204635\pi\)
−0.997934 + 0.0642438i \(0.979536\pi\)
\(504\) 0 0
\(505\) 1070.21 2.11922
\(506\) 57.0883 + 98.8799i 0.112823 + 0.195415i
\(507\) 0 0
\(508\) −167.426 + 289.991i −0.329580 + 0.570849i
\(509\) −871.889 + 503.385i −1.71294 + 0.988969i −0.782410 + 0.622764i \(0.786010\pi\)
−0.930534 + 0.366205i \(0.880657\pi\)
\(510\) 0 0
\(511\) 573.338 + 585.161i 1.12199 + 1.14513i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) 5.27208 + 3.04384i 0.0102570 + 0.00592186i
\(515\) 338.522 586.337i 0.657324 1.13852i
\(516\) 0 0
\(517\) 199.237i 0.385371i
\(518\) −42.2183 + 41.3653i −0.0815024 + 0.0798557i
\(519\) 0 0
\(520\) 211.279 + 365.946i 0.406306 + 0.703743i
\(521\) 322.294 + 186.077i 0.618607 + 0.357153i 0.776327 0.630331i \(-0.217081\pi\)
−0.157719 + 0.987484i \(0.550414\pi\)
\(522\) 0 0
\(523\) −551.904 + 318.642i −1.05527 + 0.609258i −0.924119 0.382105i \(-0.875199\pi\)
−0.131147 + 0.991363i \(0.541866\pi\)
\(524\) 3.56608i 0.00680549i
\(525\) 0 0
\(526\) 399.765 0.760009
\(527\) 138.302 + 239.545i 0.262432 + 0.454545i
\(528\) 0 0
\(529\) 173.970 301.325i 0.328866 0.569613i
\(530\) 353.823 204.280i 0.667591 0.385434i
\(531\) 0 0
\(532\) −64.0294 + 229.564i −0.120356 + 0.431512i
\(533\) −629.440 −1.18094
\(534\) 0 0
\(535\) −1227.31 708.586i −2.29403 1.32446i
\(536\) −161.782 + 280.214i −0.301832 + 0.522788i
\(537\) 0 0
\(538\) 540.136i 1.00397i
\(539\) 257.558 141.773i 0.477845 0.263030i
\(540\) 0 0
\(541\) −110.412 191.239i −0.204088 0.353491i 0.745754 0.666222i \(-0.232090\pi\)
−0.949842 + 0.312731i \(0.898756\pi\)
\(542\) −103.279 59.6283i −0.190552 0.110015i
\(543\) 0 0
\(544\) 91.8823 53.0482i 0.168901 0.0975152i
\(545\) 1496.50i 2.74587i
\(546\) 0 0
\(547\) −160.676 −0.293741 −0.146870 0.989156i \(-0.546920\pi\)
−0.146870 + 0.989156i \(0.546920\pi\)
\(548\) 100.971 + 174.886i 0.184253 + 0.319135i
\(549\) 0 0
\(550\) 190.669 330.248i 0.346671 0.600452i
\(551\) 500.382 288.896i 0.908134 0.524311i
\(552\) 0 0
\(553\) −153.942 598.898i −0.278375 1.08300i
\(554\) 193.914 0.350025
\(555\) 0 0
\(556\) −243.426 140.542i −0.437817 0.252774i
\(557\) −237.177 + 410.802i −0.425811 + 0.737526i −0.996496 0.0836431i \(-0.973344\pi\)
0.570685 + 0.821169i \(0.306678\pi\)
\(558\) 0 0
\(559\) 276.627i 0.494860i
\(560\) −163.882 167.262i −0.292647 0.298681i
\(561\) 0 0
\(562\) 229.882 + 398.168i 0.409043 + 0.708484i
\(563\) 430.301 + 248.434i 0.764300 + 0.441269i 0.830837 0.556515i \(-0.187862\pi\)
−0.0665378 + 0.997784i \(0.521195\pi\)
\(564\) 0 0
\(565\) −126.000 + 72.7461i −0.223009 + 0.128754i
\(566\) 275.171i 0.486168i
\(567\) 0 0
\(568\) 52.6173 0.0926361
\(569\) 392.647 + 680.084i 0.690065 + 1.19523i 0.971816 + 0.235740i \(0.0757512\pi\)
−0.281752 + 0.959487i \(0.590915\pi\)
\(570\) 0 0
\(571\) 357.521 619.245i 0.626132 1.08449i −0.362189 0.932105i \(-0.617970\pi\)
0.988321 0.152388i \(-0.0486963\pi\)
\(572\) −185.647 + 107.183i −0.324557 + 0.187383i
\(573\) 0 0
\(574\) 337.831 86.8364i 0.588555 0.151283i
\(575\) 604.721 1.05169
\(576\) 0 0
\(577\) 669.117 + 386.315i 1.15965 + 0.669524i 0.951220 0.308514i \(-0.0998317\pi\)
0.208429 + 0.978038i \(0.433165\pi\)
\(578\) −44.3812 + 76.8705i −0.0767841 + 0.132994i
\(579\) 0 0
\(580\) 567.705i 0.978801i
\(581\) 142.477 510.823i 0.245228 0.879214i
\(582\) 0 0
\(583\) 103.632 + 179.497i 0.177757 + 0.307885i
\(584\) 286.669 + 165.508i 0.490872 + 0.283405i
\(585\) 0 0
\(586\) 293.574 169.495i 0.500979 0.289240i
\(587\) 436.477i 0.743572i −0.928318 0.371786i \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 0 0
\(589\) −251.059 −0.426246
\(590\) 161.823 + 280.286i 0.274277 + 0.475062i
\(591\) 0 0
\(592\) −11.9411 + 20.6826i −0.0201708 + 0.0349369i
\(593\) −722.397 + 417.076i −1.21821 + 0.703332i −0.964534 0.263958i \(-0.914972\pi\)
−0.253673 + 0.967290i \(0.581639\pi\)
\(594\) 0 0
\(595\) 1057.60 + 294.983i 1.77748 + 0.495770i
\(596\) −365.823 −0.613798
\(597\) 0 0
\(598\) −294.396 169.970i −0.492301 0.284230i
\(599\) 436.794 756.549i 0.729205 1.26302i −0.228014 0.973658i \(-0.573223\pi\)
0.957220 0.289363i \(-0.0934434\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i −0.986203 0.165542i \(-0.947063\pi\)
0.986203 0.165542i \(-0.0529375\pi\)
\(602\) −38.1630 148.470i −0.0633936 0.246628i
\(603\) 0 0
\(604\) 288.794 + 500.206i 0.478136 + 0.828155i
\(605\) −615.624 355.431i −1.01756 0.587489i
\(606\) 0 0
\(607\) 137.654 79.4748i 0.226778 0.130930i −0.382307 0.924035i \(-0.624870\pi\)
0.609085 + 0.793105i \(0.291537\pi\)
\(608\) 96.2985i 0.158386i
\(609\) 0 0
\(610\) 477.588 0.782931
\(611\) 296.595 + 513.718i 0.485426 + 0.840782i
\(612\) 0 0
\(613\) 357.368 618.979i 0.582981 1.00975i −0.412143 0.911119i \(-0.635219\pi\)
0.995124 0.0986338i \(-0.0314473\pi\)
\(614\) 661.695 382.030i 1.07768 0.622198i
\(615\) 0 0
\(616\) 84.8528 83.1384i 0.137748 0.134965i
\(617\) 639.381 1.03627 0.518137 0.855298i \(-0.326626\pi\)
0.518137 + 0.855298i \(0.326626\pi\)
\(618\) 0 0
\(619\) 148.978 + 86.0126i 0.240676 + 0.138954i 0.615487 0.788147i \(-0.288959\pi\)
−0.374812 + 0.927101i \(0.622293\pi\)
\(620\) 123.338 213.628i 0.198932 0.344561i
\(621\) 0 0
\(622\) 571.619i 0.919002i
\(623\) −140.912 + 36.2201i −0.226182 + 0.0581382i
\(624\) 0 0
\(625\) −135.588 234.846i −0.216941 0.375753i
\(626\) −160.805 92.8406i −0.256876 0.148308i
\(627\) 0 0
\(628\) −324.000 + 187.061i −0.515924 + 0.297869i
\(629\) 111.980i 0.178029i
\(630\) 0 0
\(631\) −1141.06 −1.80833 −0.904166 0.427180i \(-0.859507\pi\)
−0.904166 + 0.427180i \(0.859507\pi\)
\(632\) −124.929 216.383i −0.197672 0.342379i
\(633\) 0 0
\(634\) 66.4264 115.054i 0.104774 0.181473i
\(635\) −1212.61 + 700.100i −1.90962 + 1.10252i
\(636\) 0 0
\(637\) −453.044 + 748.968i −0.711215 + 1.17577i
\(638\) −288.000 −0.451411
\(639\) 0 0
\(640\) −81.9411 47.3087i −0.128033 0.0739199i
\(641\) 114.551 198.409i 0.178707 0.309530i −0.762731 0.646716i \(-0.776142\pi\)
0.941438 + 0.337186i \(0.109475\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i −0.834975 0.550288i \(-0.814518\pi\)
0.834975 0.550288i \(-0.185482\pi\)
\(644\) 181.456 + 50.6111i 0.281764 + 0.0785887i
\(645\) 0 0
\(646\) −225.765 391.036i −0.349481 0.605318i
\(647\) −1021.37 589.687i −1.57862 0.911417i −0.995052 0.0993530i \(-0.968323\pi\)
−0.583568 0.812064i \(-0.698344\pi\)
\(648\) 0 0
\(649\) −142.191 + 82.0940i −0.219092 + 0.126493i
\(650\) 1135.36i 1.74671i
\(651\) 0 0
\(652\) 32.1177 0.0492604
\(653\) −77.3818 134.029i −0.118502 0.205252i 0.800672 0.599103i \(-0.204476\pi\)
−0.919174 + 0.393851i \(0.871143\pi\)
\(654\) 0 0
\(655\) −7.45584 + 12.9139i −0.0113830 + 0.0197159i
\(656\) 122.059 70.4707i 0.186065 0.107425i
\(657\) 0 0
\(658\) −230.059 234.803i −0.349634 0.356843i
\(659\) −591.308 −0.897280 −0.448640 0.893712i \(-0.648092\pi\)
−0.448640 + 0.893712i \(0.648092\pi\)
\(660\) 0 0
\(661\) 140.441 + 81.0837i 0.212468 + 0.122668i 0.602458 0.798151i \(-0.294188\pi\)
−0.389990 + 0.920819i \(0.627522\pi\)
\(662\) −184.815 + 320.109i −0.279176 + 0.483548i
\(663\) 0 0
\(664\) 214.282i 0.322714i
\(665\) −711.838 + 697.456i −1.07043 + 1.04881i
\(666\) 0 0
\(667\) −228.353 395.519i −0.342359 0.592983i
\(668\) 305.044 + 176.117i 0.456652 + 0.263648i
\(669\) 0 0
\(670\) −1171.73 + 676.497i −1.74885 + 1.00970i
\(671\) 242.283i 0.361078i
\(672\) 0 0
\(673\) 42.3238 0.0628883 0.0314441 0.999506i \(-0.489989\pi\)
0.0314441 + 0.999506i \(0.489989\pi\)
\(674\) 96.3539 + 166.890i 0.142958 + 0.247611i
\(675\) 0 0
\(676\) 150.118 260.012i 0.222068 0.384632i
\(677\) −430.721 + 248.677i −0.636220 + 0.367322i −0.783157 0.621824i \(-0.786392\pi\)
0.146937 + 0.989146i \(0.453059\pi\)
\(678\) 0 0
\(679\) −57.5147 + 206.207i −0.0847050 + 0.303693i
\(680\) 443.647 0.652422
\(681\) 0 0
\(682\) 108.375 + 62.5701i 0.158907 + 0.0917451i
\(683\) 608.080 1053.23i 0.890308 1.54206i 0.0508015 0.998709i \(-0.483822\pi\)
0.839506 0.543350i \(-0.182844\pi\)
\(684\) 0 0
\(685\) 844.425i 1.23274i
\(686\) 139.830 464.484i 0.203834 0.677091i
\(687\) 0 0
\(688\) −30.9706 53.6426i −0.0450154 0.0779689i
\(689\) −534.418 308.546i −0.775642 0.447817i
\(690\) 0 0
\(691\) −932.182 + 538.196i −1.34903 + 0.778865i −0.988113 0.153731i \(-0.950871\pi\)
−0.360921 + 0.932596i \(0.617538\pi\)
\(692\) 462.305i 0.668070i
\(693\) 0 0
\(694\) −455.647 −0.656552
\(695\) −587.683 1017.90i −0.845588 1.46460i
\(696\) 0 0
\(697\) −330.426 + 572.315i −0.474069 + 0.821112i
\(698\) 424.368 245.009i 0.607976 0.351015i
\(699\) 0 0
\(700\) −156.632 609.367i −0.223761 0.870525i
\(701\) 695.897 0.992720 0.496360 0.868117i \(-0.334670\pi\)
0.496360 + 0.868117i \(0.334670\pi\)
\(702\) 0 0
\(703\) 88.0219 + 50.8194i 0.125209 + 0.0722894i
\(704\) 24.0000 41.5692i 0.0340909 0.0590472i
\(705\) 0 0
\(706\) 877.649i 1.24313i
\(707\) 626.912 + 639.839i 0.886721 + 0.905006i
\(708\) 0 0
\(709\) −127.412 220.684i −0.179707 0.311261i 0.762073 0.647491i \(-0.224182\pi\)
−0.941780 + 0.336229i \(0.890848\pi\)
\(710\) 190.544 + 110.011i 0.268372 + 0.154945i
\(711\) 0 0
\(712\) −50.9117 + 29.3939i −0.0715052 + 0.0412835i
\(713\) 198.446i 0.278325i
\(714\) 0 0
\(715\) −896.382 −1.25368
\(716\) −85.2792 147.708i −0.119105 0.206296i
\(717\) 0 0
\(718\) −14.3087 + 24.7833i −0.0199285 + 0.0345172i
\(719\) 964.925 557.100i 1.34204 0.774826i 0.354931 0.934892i \(-0.384504\pi\)
0.987106 + 0.160066i \(0.0511709\pi\)
\(720\) 0 0
\(721\) 548.852 141.078i 0.761238 0.195669i
\(722\) −100.701 −0.139474
\(723\) 0 0
\(724\) −9.67619 5.58655i −0.0133649 0.00771623i
\(725\) −762.676 + 1320.99i −1.05197 + 1.82206i
\(726\) 0 0
\(727\) 398.345i 0.547930i 0.961740 + 0.273965i \(0.0883353\pi\)
−0.961740 + 0.273965i \(0.911665\pi\)
\(728\) −95.0223 + 340.683i −0.130525 + 0.467971i
\(729\) 0 0
\(730\) 692.080 + 1198.72i 0.948055 + 1.64208i
\(731\) 251.522 + 145.216i 0.344079 + 0.198654i
\(732\) 0 0
\(733\) 818.514 472.569i 1.11666 0.644706i 0.176116 0.984369i \(-0.443646\pi\)
0.940547 + 0.339663i \(0.110313\pi\)
\(734\) 440.632i 0.600316i
\(735\) 0 0
\(736\) 76.1177 0.103421
\(737\) −343.191 594.424i −0.465659 0.806546i
\(738\) 0 0
\(739\) −96.3162 + 166.825i −0.130333 + 0.225744i −0.923805 0.382863i \(-0.874938\pi\)
0.793472 + 0.608607i \(0.208271\pi\)
\(740\) −86.4853 + 49.9323i −0.116872 + 0.0674761i
\(741\) 0 0
\(742\) 329.397 + 91.8744i 0.443931 + 0.123820i
\(743\) 911.616 1.22694 0.613470 0.789718i \(-0.289773\pi\)
0.613470 + 0.789718i \(0.289773\pi\)
\(744\) 0 0
\(745\) −1324.76 764.853i −1.77821 1.02665i
\(746\) −481.810 + 834.519i −0.645858 + 1.11866i
\(747\) 0 0
\(748\) 225.065i 0.300889i
\(749\) −295.301 1148.85i −0.394260 1.53384i
\(750\) 0 0
\(751\) 195.831 + 339.189i 0.260760 + 0.451650i 0.966444 0.256877i \(-0.0826935\pi\)
−0.705684 + 0.708527i \(0.749360\pi\)
\(752\) −115.029 66.4123i −0.152965 0.0883142i
\(753\) 0 0
\(754\) 742.587 428.733i 0.984863 0.568611i
\(755\) 2415.21i 3.19895i
\(756\) 0 0
\(757\) −152.823 −0.201879 −0.100940 0.994893i \(-0.532185\pi\)
−0.100940 + 0.994893i \(0.532185\pi\)
\(758\) −441.785 765.195i −0.582830 1.00949i
\(759\) 0 0
\(760\) −201.338 + 348.728i −0.264919 + 0.458852i
\(761\) 109.331 63.1223i 0.143667 0.0829465i −0.426443 0.904514i \(-0.640234\pi\)
0.570111 + 0.821568i \(0.306900\pi\)
\(762\) 0 0
\(763\) 894.706 876.629i 1.17262 1.14892i
\(764\) −370.794 −0.485332
\(765\) 0 0
\(766\) −169.383 97.7931i −0.221126 0.127667i
\(767\) 244.419 423.347i 0.318669 0.551951i
\(768\) 0 0
\(769\) 369.148i 0.480037i 0.970768 + 0.240018i \(0.0771535\pi\)
−0.970768 + 0.240018i \(0.922847\pi\)
\(770\) 481.103 123.663i 0.624809 0.160602i
\(771\) 0 0
\(772\) −227.794 394.551i −0.295070 0.511076i
\(773\) 1215.65 + 701.853i 1.57263 + 0.907961i 0.995845 + 0.0910674i \(0.0290279\pi\)
0.576789 + 0.816893i \(0.304305\pi\)
\(774\) 0 0
\(775\) 573.992 331.394i 0.740634 0.427605i
\(776\) 86.5006i 0.111470i
\(777\) 0 0
\(778\) −797.013 −1.02444
\(779\) −299.912 519.462i −0.384996 0.666832i
\(780\) 0 0
\(781\) −55.8091 + 96.6642i −0.0714585 + 0.123770i
\(782\) −309.088 + 178.452i −0.395254 + 0.228200i
\(783\) 0 0
\(784\) 4.00000 195.959i 0.00510204 0.249948i
\(785\) −1564.41 −1.99288
\(786\) 0 0