Properties

Label 126.3.n.a.19.2
Level $126$
Weight $3$
Character 126.19
Analytic conductor $3.433$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
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 19.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 126.19
Dual form 126.3.n.a.73.2

$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 −0.450134 0.892961i \(-0.648624\pi\)
−0.998394 + 0.0566528i \(0.981957\pi\)
\(6\) 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 0.969559 0.244857i \(-0.0787410\pi\)
−0.696832 + 0.717234i \(0.745408\pi\)
\(12\) 0 0
\(13\) 17.8639i 1.37414i −0.726590 0.687072i \(-0.758896\pi\)
0.726590 0.687072i \(-0.241104\pi\)
\(14\) −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 0.0606799 0.998157i \(-0.480673\pi\)
0.894770 + 0.446528i \(0.147340\pi\)
\(18\) 0 0
\(19\) −14.7426 8.51167i −0.775928 0.447983i 0.0590569 0.998255i \(-0.481191\pi\)
−0.834985 + 0.550272i \(0.814524\pi\)
\(20\) 16.7262i 0.836308i
\(21\) 0 0
\(22\) 8.48528 0.385695
\(23\) 6.72792 11.6531i 0.292518 0.506657i −0.681886 0.731458i \(-0.738840\pi\)
0.974405 + 0.224802i \(0.0721734\pi\)
\(24\) 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 −0.279647 0.960103i \(-0.590218\pi\)
0.691650 + 0.722233i \(0.256884\pi\)
\(32\) 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 −0.903544 0.428496i \(-0.859044\pi\)
0.822860 + 0.568244i \(0.192377\pi\)
\(38\) −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 \(-0.858619\pi\)
0.902972 0.429700i \(-0.141381\pi\)
\(42\) 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 0.773693 0.633561i \(-0.218408\pi\)
−0.161834 + 0.986818i \(0.551741\pi\)
\(48\) 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 0.655803 0.754932i \(-0.272330\pi\)
−0.981692 + 0.190477i \(0.938997\pi\)
\(54\) 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 −0.687204 0.726465i \(-0.741162\pi\)
0.285535 + 0.958368i \(0.407829\pi\)
\(60\) 0 0
\(61\) −34.9706 20.1903i −0.573288 0.330988i 0.185174 0.982706i \(-0.440715\pi\)
−0.758461 + 0.651718i \(0.774049\pi\)
\(62\) 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 0.877838 + 0.478958i \(0.158985\pi\)
−0.0241291 + 0.999709i \(0.507681\pi\)
\(68\) −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 −0.993134 0.116979i \(-0.962679\pi\)
−0.395260 + 0.918569i \(0.629346\pi\)
\(74\) 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 −0.438470 0.898746i \(-0.644479\pi\)
0.997572 0.0696469i \(-0.0221873\pi\)
\(80\) 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 \(-0.849144\pi\)
0.889782 0.456386i \(-0.150856\pi\)
\(84\) 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 0.597703 0.801717i \(-0.296080\pi\)
−0.395456 + 0.918485i \(0.629413\pi\)
\(90\) 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 \(0.0503892\pi\)
−0.987496 + 0.157642i \(0.949611\pi\)
\(98\) −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 −0.935500 0.353326i \(-0.885051\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(102\) 0 0
\(103\) −70.1102 40.4781i −0.680681 0.392992i 0.119430 0.992843i \(-0.461893\pi\)
−0.800112 + 0.599851i \(0.795226\pi\)
\(104\) 50.5266i 0.485833i
\(105\) 0 0
\(106\) −48.8528 −0.460876
\(107\) 84.7279 146.753i 0.791850 1.37152i −0.132971 0.991120i \(-0.542452\pi\)
0.924820 0.380404i \(-0.124215\pi\)
\(108\) 0 0
\(109\) −89.4706 154.968i −0.820831 1.42172i −0.905064 0.425275i \(-0.860177\pi\)
0.0842335 0.996446i \(-0.473156\pi\)
\(110\) −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 0.505882 0.862603i \(-0.331167\pi\)
−0.494095 + 0.869408i \(0.664500\pi\)
\(132\) 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 0.989332 0.145677i \(-0.0465362\pi\)
−0.620826 + 0.783948i \(0.713203\pi\)
\(138\) 0 0
\(139\) 140.542i 1.01110i −0.862799 0.505548i \(-0.831290\pi\)
0.862799 0.505548i \(-0.168710\pi\)
\(140\) −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 −0.376797 0.926296i \(-0.622974\pi\)
0.990594 0.136833i \(-0.0436922\pi\)
\(150\) 0 0
\(151\) 144.397 + 250.103i 0.956271 + 1.65631i 0.731432 + 0.681915i \(0.238852\pi\)
0.224840 + 0.974396i \(0.427814\pi\)
\(152\) 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 0.114334 0.993442i \(-0.463527\pi\)
0.917513 + 0.397705i \(0.130193\pi\)
\(158\) −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 −0.889604 0.456732i \(-0.849020\pi\)
0.840344 + 0.542054i \(0.182353\pi\)
\(164\) −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 \(0.176794\pi\)
−0.849681 + 0.527297i \(0.823206\pi\)
\(168\) 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 0.950615 0.310373i \(-0.100454\pi\)
0.206517 + 0.978443i \(0.433787\pi\)
\(174\) 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 0.721991 0.691903i \(-0.243227\pi\)
−0.960201 + 0.279311i \(0.909894\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i −0.999881 0.0154325i \(-0.995087\pi\)
0.999881 0.0154325i \(-0.00491250\pi\)
\(182\) 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 −0.514526 0.857475i \(-0.672032\pi\)
0.999858 + 0.0168547i \(0.00536527\pi\)
\(192\) 0 0
\(193\) −113.897 197.275i −0.590140 1.02215i −0.994213 0.107425i \(-0.965739\pi\)
0.404073 0.914727i \(-0.367594\pi\)
\(194\) 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 −0.486378 0.873748i \(-0.661682\pi\)
0.513499 + 0.858090i \(0.328349\pi\)
\(200\) −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 \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) −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 −0.140430 0.990091i \(-0.544848\pi\)
0.787229 + 0.616661i \(0.211515\pi\)
\(228\) 0 0
\(229\) 30.0442 + 17.3460i 0.131197 + 0.0757467i 0.564162 0.825664i \(-0.309199\pi\)
−0.432965 + 0.901411i \(0.642533\pi\)
\(230\) 159.145i 0.691934i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) −127.243 + 220.391i −0.546106 + 0.945883i 0.452431 + 0.891800i \(0.350557\pi\)
−0.998536 + 0.0540833i \(0.982776\pi\)
\(234\) 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 −0.332548 0.943086i \(-0.607908\pi\)
0.650462 + 0.759538i \(0.274575\pi\)
\(242\) −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 \(0.141517\pi\)
−0.902788 + 0.430086i \(0.858483\pi\)
\(252\) 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 0.507235 0.861808i \(-0.330668\pi\)
−0.492730 + 0.870182i \(0.664001\pi\)
\(258\) 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 0.999043 + 0.0437468i \(0.0139295\pi\)
−0.461635 + 0.887070i \(0.652737\pi\)
\(264\) 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 0.262660 0.964888i \(-0.415400\pi\)
0.966948 + 0.254974i \(0.0820669\pi\)
\(270\) 0 0
\(271\) −73.0294 42.1636i −0.269481 0.155585i 0.359171 0.933272i \(-0.383060\pi\)
−0.628652 + 0.777687i \(0.716393\pi\)
\(272\) 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 0.962833 0.270098i \(-0.0870560\pi\)
−0.715328 + 0.698789i \(0.753723\pi\)
\(278\) −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 −0.171811 0.985130i \(-0.554962\pi\)
0.767242 + 0.641357i \(0.221628\pi\)
\(284\) 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 \(0.134139\pi\)
−0.912513 + 0.409048i \(0.865861\pi\)
\(294\) 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 \(0.342405\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(308\) −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 −0.942810 0.333330i \(-0.891828\pi\)
−0.182732 + 0.983163i \(0.558494\pi\)
\(312\) 0 0
\(313\) −113.706 65.6482i −0.363278 0.209739i 0.307240 0.951632i \(-0.400595\pi\)
−0.670518 + 0.741893i \(0.733928\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) −176.676 −0.559102
\(317\) −46.9706 + 81.3554i −0.148172 + 0.256642i −0.930552 0.366160i \(-0.880672\pi\)
0.782380 + 0.622802i \(0.214006\pi\)
\(318\) 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 −0.598263 0.801300i \(-0.704142\pi\)
0.993078 + 0.117460i \(0.0374754\pi\)
\(332\) −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 0.534915 0.844906i \(-0.320343\pi\)
−0.999167 + 0.0407975i \(0.987010\pi\)
\(348\) 0 0
\(349\) 346.495i 0.992821i 0.868088 + 0.496411i \(0.165349\pi\)
−0.868088 + 0.496411i \(0.834651\pi\)
\(350\) −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 0.522869 0.852413i \(-0.324862\pi\)
0.999646 0.0266116i \(-0.00847174\pi\)
\(354\) 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 −0.851590 0.524209i \(-0.824361\pi\)
0.879773 + 0.475394i \(0.157695\pi\)
\(360\) 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 −0.820334 0.571885i \(-0.806212\pi\)
0.0850998 + 0.996372i \(0.472879\pi\)
\(368\) 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 0.104125 0.994564i \(-0.466796\pi\)
0.809255 0.587457i \(-0.199871\pi\)
\(374\) 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 0.335423 0.942068i \(-0.391121\pi\)
−0.648143 + 0.761519i \(0.724454\pi\)
\(384\) 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 −0.959226 0.282642i \(-0.908789\pi\)
0.234838 0.972035i \(-0.424544\pi\)
\(390\) 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 −0.0839711 0.996468i \(-0.526760\pi\)
−0.904952 + 0.425513i \(0.860094\pi\)
\(398\) 8.81321i 0.0221438i
\(399\) 0 0
\(400\) −179.765 −0.449411
\(401\) −137.875 + 238.807i −0.343828 + 0.595528i −0.985140 0.171752i \(-0.945057\pi\)
0.641312 + 0.767280i \(0.278390\pi\)
\(402\) 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 −0.884540 0.466465i \(-0.845527\pi\)
−0.0382993 + 0.999266i \(0.512194\pi\)
\(410\) 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 \(0.117051\pi\)
−0.933147 + 0.359496i \(0.882949\pi\)
\(420\) 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 0.539840 0.841767i \(-0.318485\pi\)
−0.998912 + 0.0466317i \(0.985151\pi\)
\(432\) 0 0
\(433\) 44.2685i 0.102237i −0.998693 0.0511184i \(-0.983721\pi\)
0.998693 0.0511184i \(-0.0162786\pi\)
\(434\) 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 0.838154 0.545434i \(-0.183635\pi\)
−0.0532827 + 0.998579i \(0.516968\pi\)
\(440\) 141.926i 0.322560i
\(441\) 0 0
\(442\) −473.823 −1.07200
\(443\) −59.2721 + 102.662i −0.133797 + 0.231743i −0.925137 0.379633i \(-0.876050\pi\)
0.791340 + 0.611376i \(0.209384\pi\)
\(444\) 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 −0.789388 0.613895i \(-0.789602\pi\)
0.926342 + 0.376682i \(0.122935\pi\)
\(458\) 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 \(-0.748132\pi\)
0.702945 0.711244i \(-0.251868\pi\)
\(462\) 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 0.726989 0.686649i \(-0.240919\pi\)
−0.231162 + 0.972915i \(0.574253\pi\)
\(468\) 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 −0.725112 0.688631i \(-0.758212\pi\)
0.233816 + 0.972281i \(0.424879\pi\)
\(480\) 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 0.995877 + 0.0907186i \(0.0289164\pi\)
−0.419374 + 0.907814i \(0.637750\pi\)
\(488\) 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 −0.617728 0.786391i \(-0.711947\pi\)
0.989899 + 0.141773i \(0.0452802\pi\)
\(500\) −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 \(-0.979536\pi\)
0.997934 0.0642438i \(-0.0204635\pi\)
\(504\) 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 −0.930534 0.366205i \(-0.880657\pi\)
−0.782410 0.622764i \(-0.786010\pi\)
\(510\) 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 −0.157719 0.987484i \(-0.550414\pi\)
0.776327 + 0.630331i \(0.217081\pi\)
\(522\) 0 0
\(523\) −551.904 318.642i −1.05527 0.609258i −0.131147 0.991363i \(-0.541866\pi\)
−0.924119 + 0.382105i \(0.875199\pi\)
\(524\) 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 −0.949842 0.312731i \(-0.898756\pi\)
0.745754 + 0.666222i \(0.232090\pi\)
\(542\) −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 0.570685 0.821169i \(-0.306678\pi\)
−0.996496 + 0.0836431i \(0.973344\pi\)
\(558\) 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 −0.0665378 0.997784i \(-0.521195\pi\)
0.830837 + 0.556515i \(0.187862\pi\)
\(564\) 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 −0.281752 0.959487i \(-0.590915\pi\)
0.971816 0.235740i \(-0.0757512\pi\)
\(570\) 0 0
\(571\) 357.521 + 619.245i 0.626132 + 1.08449i 0.988321 + 0.152388i \(0.0486963\pi\)
−0.362189 + 0.932105i \(0.617970\pi\)
\(572\) −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 0.208429 0.978038i \(-0.433165\pi\)
0.951220 + 0.308514i \(0.0998317\pi\)
\(578\) −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 \(0.121254\pi\)
−0.928318 + 0.371786i \(0.878746\pi\)
\(588\) 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 −0.253673 0.967290i \(-0.581639\pi\)
−0.964534 + 0.263958i \(0.914972\pi\)
\(594\) 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 0.957220 + 0.289363i \(0.0934434\pi\)
−0.228014 + 0.973658i \(0.573223\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i 0.986203 + 0.165542i \(0.0529375\pi\)
−0.986203 + 0.165542i \(0.947063\pi\)
\(602\) −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 0.609085 0.793105i \(-0.291537\pi\)
−0.382307 + 0.924035i \(0.624870\pi\)
\(608\) 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 0.995124 + 0.0986338i \(0.0314473\pi\)
−0.412143 + 0.911119i \(0.635219\pi\)
\(614\) 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 −0.374812 0.927101i \(-0.622293\pi\)
0.615487 + 0.788147i \(0.288959\pi\)
\(620\) 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 0.941438 0.337186i \(-0.109475\pi\)
−0.762731 + 0.646716i \(0.776142\pi\)
\(642\) 0 0
\(643\) 707.670i 1.10058i 0.834975 + 0.550288i \(0.185482\pi\)
−0.834975 + 0.550288i \(0.814518\pi\)
\(644\) 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 −0.583568 + 0.812064i \(0.698344\pi\)
−0.995052 + 0.0993530i \(0.968323\pi\)
\(648\) 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 −0.919174 0.393851i \(-0.871143\pi\)
0.800672 + 0.599103i \(0.204476\pi\)
\(654\) 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 −0.389990 0.920819i \(-0.627522\pi\)
0.602458 + 0.798151i \(0.294188\pi\)
\(662\) −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 0.146937 0.989146i \(-0.453059\pi\)
−0.783157 + 0.621824i \(0.786392\pi\)
\(678\) 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 0.839506 + 0.543350i \(0.182844\pi\)
0.0508015 + 0.998709i \(0.483822\pi\)
\(684\) 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 −0.360921 0.932596i \(-0.617538\pi\)
−0.988113 + 0.153731i \(0.950871\pi\)
\(692\) 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 −0.941780 0.336229i \(-0.890848\pi\)
0.762073 + 0.647491i \(0.224182\pi\)
\(710\) 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 0.987106 0.160066i \(-0.0511709\pi\)
0.354931 + 0.934892i \(0.384504\pi\)
\(720\) 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 \(-0.911665\pi\)
0.961740 0.273965i \(-0.0883353\pi\)
\(728\) −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 0.940547 0.339663i \(-0.110313\pi\)
0.176116 + 0.984369i \(0.443646\pi\)
\(734\) 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 0.793472 0.608607i \(-0.208271\pi\)
−0.923805 + 0.382863i \(0.874938\pi\)
\(740\) −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 −0.705684 0.708527i \(-0.749360\pi\)
0.966444 + 0.256877i \(0.0826935\pi\)
\(752\) −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 0.570111 0.821568i \(-0.306900\pi\)
−0.426443 + 0.904514i \(0.640234\pi\)
\(762\) 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 \(-0.922847\pi\)
0.970768 0.240018i \(-0.0771535\pi\)
\(770\) 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 0.576789 0.816893i \(-0.304305\pi\)
0.995845 0.0910674i \(-0.0290279\pi\)
\(774\) 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