Properties

Label 144.3.m.c.91.1
Level $144$
Weight $3$
Character 144.91
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.1
Root \(-1.96679 - 0.362960i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.c.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +O(q^{10})\) \(q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +(3.95895 + 2.72539i) q^{10} +(5.59560 - 5.59560i) q^{11} +(-13.5782 + 13.5782i) q^{13} +(11.2949 - 2.08441i) q^{14} +(11.9232 - 10.6695i) q^{16} -19.7023 q^{17} +(-21.6943 - 21.6943i) q^{19} +(-8.77563 - 3.92333i) q^{20} +(-8.97439 + 13.0363i) q^{22} -24.9257 q^{23} -19.2247i q^{25} +(21.7771 - 31.6337i) q^{26} +(-21.4581 + 8.19918i) q^{28} +(-1.50581 + 1.50581i) q^{29} +2.20037i q^{31} +(-19.5777 + 25.3123i) q^{32} +(38.7504 - 7.15116i) q^{34} +(9.75877 + 9.75877i) q^{35} +(27.6956 + 27.6956i) q^{37} +(50.5423 + 34.7940i) q^{38} +(18.6838 + 4.53116i) q^{40} +51.3127i q^{41} +(21.4400 - 21.4400i) q^{43} +(12.9191 - 28.8971i) q^{44} +(49.0236 - 9.04703i) q^{46} -76.5216i q^{47} -16.0202 q^{49} +(6.97781 + 37.8110i) q^{50} +(-31.3491 + 70.1211i) q^{52} +(56.5145 + 56.5145i) q^{53} -19.0173 q^{55} +(39.2276 - 23.9145i) q^{56} +(2.41506 - 3.50816i) q^{58} +(48.0041 - 48.0041i) q^{59} +(-51.5587 + 51.5587i) q^{61} +(-0.798646 - 4.32766i) q^{62} +(29.3180 - 56.8899i) q^{64} +46.1469 q^{65} +(63.4445 + 63.4445i) q^{67} +(-73.6182 + 28.1297i) q^{68} +(-22.7355 - 15.6514i) q^{70} -43.4856 q^{71} -73.9992i q^{73} +(-64.5239 - 44.4190i) q^{74} +(-112.035 - 50.0876i) q^{76} +(-32.1344 + 32.1344i) q^{77} +4.12659i q^{79} +(-38.3918 - 2.13036i) q^{80} +(-18.6245 - 100.921i) q^{82} +(-38.4428 - 38.4428i) q^{83} +(33.4803 + 33.4803i) q^{85} +(-34.3862 + 49.9499i) q^{86} +(-14.9206 + 61.5236i) q^{88} -52.9839i q^{89} +(77.9767 - 77.9767i) q^{91} +(-93.1353 + 35.5872i) q^{92} +(27.7743 + 150.502i) q^{94} +73.7305i q^{95} +23.1008 q^{97} +(31.5084 - 5.81471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96679 + 0.362960i −0.983395 + 0.181480i
\(3\) 0 0
\(4\) 3.73652 1.42773i 0.934130 0.356933i
\(5\) −1.69930 1.69930i −0.339861 0.339861i 0.516454 0.856315i \(-0.327252\pi\)
−0.856315 + 0.516454i \(0.827252\pi\)
\(6\) 0 0
\(7\) −5.74280 −0.820400 −0.410200 0.911996i \(-0.634541\pi\)
−0.410200 + 0.911996i \(0.634541\pi\)
\(8\) −6.83074 + 4.16426i −0.853842 + 0.520532i
\(9\) 0 0
\(10\) 3.95895 + 2.72539i 0.395895 + 0.272539i
\(11\) 5.59560 5.59560i 0.508691 0.508691i −0.405434 0.914125i \(-0.632879\pi\)
0.914125 + 0.405434i \(0.132879\pi\)
\(12\) 0 0
\(13\) −13.5782 + 13.5782i −1.04447 + 1.04447i −0.0455110 + 0.998964i \(0.514492\pi\)
−0.998964 + 0.0455110i \(0.985508\pi\)
\(14\) 11.2949 2.08441i 0.806777 0.148886i
\(15\) 0 0
\(16\) 11.9232 10.6695i 0.745198 0.666844i
\(17\) −19.7023 −1.15896 −0.579481 0.814986i \(-0.696745\pi\)
−0.579481 + 0.814986i \(0.696745\pi\)
\(18\) 0 0
\(19\) −21.6943 21.6943i −1.14181 1.14181i −0.988120 0.153687i \(-0.950885\pi\)
−0.153687 0.988120i \(-0.549115\pi\)
\(20\) −8.77563 3.92333i −0.438782 0.196167i
\(21\) 0 0
\(22\) −8.97439 + 13.0363i −0.407927 + 0.592561i
\(23\) −24.9257 −1.08373 −0.541863 0.840467i \(-0.682281\pi\)
−0.541863 + 0.840467i \(0.682281\pi\)
\(24\) 0 0
\(25\) 19.2247i 0.768989i
\(26\) 21.7771 31.6337i 0.837580 1.21668i
\(27\) 0 0
\(28\) −21.4581 + 8.19918i −0.766360 + 0.292828i
\(29\) −1.50581 + 1.50581i −0.0519245 + 0.0519245i −0.732592 0.680668i \(-0.761690\pi\)
0.680668 + 0.732592i \(0.261690\pi\)
\(30\) 0 0
\(31\) 2.20037i 0.0709796i 0.999370 + 0.0354898i \(0.0112991\pi\)
−0.999370 + 0.0354898i \(0.988701\pi\)
\(32\) −19.5777 + 25.3123i −0.611805 + 0.791009i
\(33\) 0 0
\(34\) 38.7504 7.15116i 1.13972 0.210328i
\(35\) 9.75877 + 9.75877i 0.278822 + 0.278822i
\(36\) 0 0
\(37\) 27.6956 + 27.6956i 0.748530 + 0.748530i 0.974203 0.225673i \(-0.0724580\pi\)
−0.225673 + 0.974203i \(0.572458\pi\)
\(38\) 50.5423 + 34.7940i 1.33006 + 0.915631i
\(39\) 0 0
\(40\) 18.6838 + 4.53116i 0.467096 + 0.113279i
\(41\) 51.3127i 1.25153i 0.780012 + 0.625764i \(0.215213\pi\)
−0.780012 + 0.625764i \(0.784787\pi\)
\(42\) 0 0
\(43\) 21.4400 21.4400i 0.498606 0.498606i −0.412398 0.911004i \(-0.635309\pi\)
0.911004 + 0.412398i \(0.135309\pi\)
\(44\) 12.9191 28.8971i 0.293615 0.656752i
\(45\) 0 0
\(46\) 49.0236 9.04703i 1.06573 0.196675i
\(47\) 76.5216i 1.62812i −0.580781 0.814060i \(-0.697253\pi\)
0.580781 0.814060i \(-0.302747\pi\)
\(48\) 0 0
\(49\) −16.0202 −0.326944
\(50\) 6.97781 + 37.8110i 0.139556 + 0.756220i
\(51\) 0 0
\(52\) −31.3491 + 70.1211i −0.602868 + 1.34848i
\(53\) 56.5145 + 56.5145i 1.06631 + 1.06631i 0.997639 + 0.0686712i \(0.0218759\pi\)
0.0686712 + 0.997639i \(0.478124\pi\)
\(54\) 0 0
\(55\) −19.0173 −0.345768
\(56\) 39.2276 23.9145i 0.700492 0.427044i
\(57\) 0 0
\(58\) 2.41506 3.50816i 0.0416390 0.0604855i
\(59\) 48.0041 48.0041i 0.813628 0.813628i −0.171547 0.985176i \(-0.554877\pi\)
0.985176 + 0.171547i \(0.0548767\pi\)
\(60\) 0 0
\(61\) −51.5587 + 51.5587i −0.845224 + 0.845224i −0.989533 0.144308i \(-0.953904\pi\)
0.144308 + 0.989533i \(0.453904\pi\)
\(62\) −0.798646 4.32766i −0.0128814 0.0698010i
\(63\) 0 0
\(64\) 29.3180 56.8899i 0.458093 0.888904i
\(65\) 46.1469 0.709952
\(66\) 0 0
\(67\) 63.4445 + 63.4445i 0.946934 + 0.946934i 0.998661 0.0517277i \(-0.0164728\pi\)
−0.0517277 + 0.998661i \(0.516473\pi\)
\(68\) −73.6182 + 28.1297i −1.08262 + 0.413672i
\(69\) 0 0
\(70\) −22.7355 15.6514i −0.324793 0.223591i
\(71\) −43.4856 −0.612473 −0.306237 0.951955i \(-0.599070\pi\)
−0.306237 + 0.951955i \(0.599070\pi\)
\(72\) 0 0
\(73\) 73.9992i 1.01369i −0.862038 0.506844i \(-0.830812\pi\)
0.862038 0.506844i \(-0.169188\pi\)
\(74\) −64.5239 44.4190i −0.871944 0.600257i
\(75\) 0 0
\(76\) −112.035 50.0876i −1.47414 0.659047i
\(77\) −32.1344 + 32.1344i −0.417330 + 0.417330i
\(78\) 0 0
\(79\) 4.12659i 0.0522354i 0.999659 + 0.0261177i \(0.00831446\pi\)
−0.999659 + 0.0261177i \(0.991686\pi\)
\(80\) −38.3918 2.13036i −0.479898 0.0266295i
\(81\) 0 0
\(82\) −18.6245 100.921i −0.227127 1.23075i
\(83\) −38.4428 38.4428i −0.463166 0.463166i 0.436526 0.899692i \(-0.356209\pi\)
−0.899692 + 0.436526i \(0.856209\pi\)
\(84\) 0 0
\(85\) 33.4803 + 33.4803i 0.393886 + 0.393886i
\(86\) −34.3862 + 49.9499i −0.399839 + 0.580813i
\(87\) 0 0
\(88\) −14.9206 + 61.5236i −0.169552 + 0.699132i
\(89\) 52.9839i 0.595325i −0.954671 0.297662i \(-0.903793\pi\)
0.954671 0.297662i \(-0.0962070\pi\)
\(90\) 0 0
\(91\) 77.9767 77.9767i 0.856887 0.856887i
\(92\) −93.1353 + 35.5872i −1.01234 + 0.386817i
\(93\) 0 0
\(94\) 27.7743 + 150.502i 0.295471 + 1.60108i
\(95\) 73.7305i 0.776111i
\(96\) 0 0
\(97\) 23.1008 0.238153 0.119077 0.992885i \(-0.462007\pi\)
0.119077 + 0.992885i \(0.462007\pi\)
\(98\) 31.5084 5.81471i 0.321515 0.0593337i
\(99\) 0 0
\(100\) −27.4478 71.8336i −0.274478 0.718336i
\(101\) −16.1216 16.1216i −0.159619 0.159619i 0.622779 0.782398i \(-0.286004\pi\)
−0.782398 + 0.622779i \(0.786004\pi\)
\(102\) 0 0
\(103\) −98.8380 −0.959592 −0.479796 0.877380i \(-0.659289\pi\)
−0.479796 + 0.877380i \(0.659289\pi\)
\(104\) 36.2060 149.292i 0.348134 1.43550i
\(105\) 0 0
\(106\) −131.665 90.6395i −1.24212 0.855090i
\(107\) −15.6655 + 15.6655i −0.146406 + 0.146406i −0.776511 0.630104i \(-0.783012\pi\)
0.630104 + 0.776511i \(0.283012\pi\)
\(108\) 0 0
\(109\) 84.6938 84.6938i 0.777008 0.777008i −0.202313 0.979321i \(-0.564846\pi\)
0.979321 + 0.202313i \(0.0648459\pi\)
\(110\) 37.4029 6.90250i 0.340027 0.0627500i
\(111\) 0 0
\(112\) −68.4724 + 61.2728i −0.611360 + 0.547079i
\(113\) −63.8537 −0.565077 −0.282538 0.959256i \(-0.591176\pi\)
−0.282538 + 0.959256i \(0.591176\pi\)
\(114\) 0 0
\(115\) 42.3563 + 42.3563i 0.368316 + 0.368316i
\(116\) −3.47659 + 7.77638i −0.0299706 + 0.0670377i
\(117\) 0 0
\(118\) −76.9903 + 111.837i −0.652461 + 0.947775i
\(119\) 113.147 0.950812
\(120\) 0 0
\(121\) 58.3785i 0.482467i
\(122\) 82.6913 120.119i 0.677798 0.984580i
\(123\) 0 0
\(124\) 3.14154 + 8.22172i 0.0253350 + 0.0663042i
\(125\) −75.1513 + 75.1513i −0.601210 + 0.601210i
\(126\) 0 0
\(127\) 36.8901i 0.290473i −0.989397 0.145237i \(-0.953606\pi\)
0.989397 0.145237i \(-0.0463944\pi\)
\(128\) −37.0135 + 122.532i −0.289168 + 0.957278i
\(129\) 0 0
\(130\) −90.7612 + 16.7495i −0.698163 + 0.128842i
\(131\) 40.4136 + 40.4136i 0.308500 + 0.308500i 0.844328 0.535827i \(-0.180000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(132\) 0 0
\(133\) 124.586 + 124.586i 0.936738 + 0.936738i
\(134\) −147.810 101.754i −1.10306 0.759360i
\(135\) 0 0
\(136\) 134.582 82.0456i 0.989570 0.603276i
\(137\) 253.499i 1.85036i −0.379531 0.925179i \(-0.623915\pi\)
0.379531 0.925179i \(-0.376085\pi\)
\(138\) 0 0
\(139\) 67.8065 67.8065i 0.487816 0.487816i −0.419800 0.907617i \(-0.637900\pi\)
0.907617 + 0.419800i \(0.137900\pi\)
\(140\) 50.3967 + 22.5309i 0.359977 + 0.160935i
\(141\) 0 0
\(142\) 85.5270 15.7835i 0.602303 0.111152i
\(143\) 151.956i 1.06263i
\(144\) 0 0
\(145\) 5.11766 0.0352942
\(146\) 26.8588 + 145.541i 0.183964 + 0.996856i
\(147\) 0 0
\(148\) 143.027 + 63.9433i 0.966400 + 0.432049i
\(149\) 43.9337 + 43.9337i 0.294857 + 0.294857i 0.838996 0.544138i \(-0.183143\pi\)
−0.544138 + 0.838996i \(0.683143\pi\)
\(150\) 0 0
\(151\) −223.084 −1.47738 −0.738688 0.674047i \(-0.764554\pi\)
−0.738688 + 0.674047i \(0.764554\pi\)
\(152\) 238.529 + 57.8475i 1.56927 + 0.380576i
\(153\) 0 0
\(154\) 51.5381 74.8651i 0.334663 0.486137i
\(155\) 3.73909 3.73909i 0.0241232 0.0241232i
\(156\) 0 0
\(157\) −78.8526 + 78.8526i −0.502246 + 0.502246i −0.912135 0.409889i \(-0.865567\pi\)
0.409889 + 0.912135i \(0.365567\pi\)
\(158\) −1.49779 8.11614i −0.00947968 0.0513680i
\(159\) 0 0
\(160\) 76.2818 9.74473i 0.476761 0.0609045i
\(161\) 143.143 0.889089
\(162\) 0 0
\(163\) 52.2425 + 52.2425i 0.320506 + 0.320506i 0.848961 0.528455i \(-0.177228\pi\)
−0.528455 + 0.848961i \(0.677228\pi\)
\(164\) 73.2607 + 191.731i 0.446712 + 1.16909i
\(165\) 0 0
\(166\) 89.5620 + 61.6556i 0.539530 + 0.371419i
\(167\) −96.5201 −0.577965 −0.288982 0.957334i \(-0.593317\pi\)
−0.288982 + 0.957334i \(0.593317\pi\)
\(168\) 0 0
\(169\) 199.734i 1.18186i
\(170\) −78.0006 53.6966i −0.458827 0.315863i
\(171\) 0 0
\(172\) 49.5005 110.722i 0.287794 0.643731i
\(173\) 46.3076 46.3076i 0.267674 0.267674i −0.560488 0.828162i \(-0.689386\pi\)
0.828162 + 0.560488i \(0.189386\pi\)
\(174\) 0 0
\(175\) 110.404i 0.630879i
\(176\) 7.01501 126.419i 0.0398580 0.718293i
\(177\) 0 0
\(178\) 19.2310 + 104.208i 0.108040 + 0.585439i
\(179\) 93.5440 + 93.5440i 0.522592 + 0.522592i 0.918353 0.395761i \(-0.129519\pi\)
−0.395761 + 0.918353i \(0.629519\pi\)
\(180\) 0 0
\(181\) −115.810 115.810i −0.639836 0.639836i 0.310679 0.950515i \(-0.399444\pi\)
−0.950515 + 0.310679i \(0.899444\pi\)
\(182\) −125.061 + 181.666i −0.687150 + 0.998166i
\(183\) 0 0
\(184\) 170.261 103.797i 0.925331 0.564114i
\(185\) 94.1266i 0.508792i
\(186\) 0 0
\(187\) −110.246 + 110.246i −0.589553 + 0.589553i
\(188\) −109.252 285.925i −0.581130 1.52088i
\(189\) 0 0
\(190\) −26.7612 145.012i −0.140849 0.763223i
\(191\) 35.2964i 0.184798i 0.995722 + 0.0923991i \(0.0294535\pi\)
−0.995722 + 0.0923991i \(0.970546\pi\)
\(192\) 0 0
\(193\) −364.339 −1.88777 −0.943884 0.330277i \(-0.892858\pi\)
−0.943884 + 0.330277i \(0.892858\pi\)
\(194\) −45.4345 + 8.38468i −0.234198 + 0.0432200i
\(195\) 0 0
\(196\) −59.8599 + 22.8726i −0.305408 + 0.116697i
\(197\) −130.582 130.582i −0.662851 0.662851i 0.293200 0.956051i \(-0.405280\pi\)
−0.956051 + 0.293200i \(0.905280\pi\)
\(198\) 0 0
\(199\) −12.7493 −0.0640670 −0.0320335 0.999487i \(-0.510198\pi\)
−0.0320335 + 0.999487i \(0.510198\pi\)
\(200\) 80.0567 + 131.319i 0.400283 + 0.656595i
\(201\) 0 0
\(202\) 37.5592 + 25.8562i 0.185937 + 0.128001i
\(203\) 8.64756 8.64756i 0.0425988 0.0425988i
\(204\) 0 0
\(205\) 87.1958 87.1958i 0.425346 0.425346i
\(206\) 194.394 35.8743i 0.943658 0.174147i
\(207\) 0 0
\(208\) −17.0225 + 306.767i −0.0818388 + 1.47484i
\(209\) −242.786 −1.16165
\(210\) 0 0
\(211\) 8.59499 + 8.59499i 0.0407345 + 0.0407345i 0.727181 0.686446i \(-0.240830\pi\)
−0.686446 + 0.727181i \(0.740830\pi\)
\(212\) 291.855 + 130.480i 1.37667 + 0.615471i
\(213\) 0 0
\(214\) 25.1247 36.4966i 0.117405 0.170545i
\(215\) −72.8663 −0.338913
\(216\) 0 0
\(217\) 12.6363i 0.0582317i
\(218\) −135.834 + 197.315i −0.623094 + 0.905117i
\(219\) 0 0
\(220\) −71.0583 + 27.1515i −0.322992 + 0.123416i
\(221\) 267.522 267.522i 1.21051 1.21051i
\(222\) 0 0
\(223\) 50.5909i 0.226865i 0.993546 + 0.113433i \(0.0361846\pi\)
−0.993546 + 0.113433i \(0.963815\pi\)
\(224\) 112.431 145.363i 0.501925 0.648944i
\(225\) 0 0
\(226\) 125.587 23.1763i 0.555693 0.102550i
\(227\) −31.7175 31.7175i −0.139725 0.139725i 0.633785 0.773509i \(-0.281501\pi\)
−0.773509 + 0.633785i \(0.781501\pi\)
\(228\) 0 0
\(229\) −169.826 169.826i −0.741599 0.741599i 0.231287 0.972886i \(-0.425706\pi\)
−0.972886 + 0.231287i \(0.925706\pi\)
\(230\) −98.6796 67.9323i −0.429042 0.295358i
\(231\) 0 0
\(232\) 4.01521 16.5564i 0.0173070 0.0713636i
\(233\) 363.082i 1.55829i 0.626844 + 0.779145i \(0.284346\pi\)
−0.626844 + 0.779145i \(0.715654\pi\)
\(234\) 0 0
\(235\) −130.033 + 130.033i −0.553334 + 0.553334i
\(236\) 110.831 247.905i 0.469624 1.05045i
\(237\) 0 0
\(238\) −222.536 + 41.0677i −0.935024 + 0.172553i
\(239\) 27.6282i 0.115599i −0.998328 0.0577996i \(-0.981592\pi\)
0.998328 0.0577996i \(-0.0184084\pi\)
\(240\) 0 0
\(241\) 368.121 1.52747 0.763737 0.645527i \(-0.223362\pi\)
0.763737 + 0.645527i \(0.223362\pi\)
\(242\) −21.1891 114.818i −0.0875581 0.474456i
\(243\) 0 0
\(244\) −119.038 + 266.262i −0.487861 + 1.09124i
\(245\) 27.2233 + 27.2233i 0.111115 + 0.111115i
\(246\) 0 0
\(247\) 589.139 2.38518
\(248\) −9.16290 15.0301i −0.0369472 0.0606054i
\(249\) 0 0
\(250\) 120.530 175.084i 0.482119 0.700334i
\(251\) −329.839 + 329.839i −1.31410 + 1.31410i −0.395734 + 0.918365i \(0.629510\pi\)
−0.918365 + 0.395734i \(0.870490\pi\)
\(252\) 0 0
\(253\) −139.474 + 139.474i −0.551281 + 0.551281i
\(254\) 13.3896 + 72.5551i 0.0527151 + 0.285650i
\(255\) 0 0
\(256\) 28.3236 254.428i 0.110639 0.993861i
\(257\) −23.6762 −0.0921252 −0.0460626 0.998939i \(-0.514667\pi\)
−0.0460626 + 0.998939i \(0.514667\pi\)
\(258\) 0 0
\(259\) −159.050 159.050i −0.614094 0.614094i
\(260\) 172.429 65.8854i 0.663188 0.253405i
\(261\) 0 0
\(262\) −94.1535 64.8164i −0.359364 0.247391i
\(263\) −243.854 −0.927202 −0.463601 0.886044i \(-0.653443\pi\)
−0.463601 + 0.886044i \(0.653443\pi\)
\(264\) 0 0
\(265\) 192.071i 0.724794i
\(266\) −290.255 199.815i −1.09118 0.751184i
\(267\) 0 0
\(268\) 327.644 + 146.480i 1.22255 + 0.546567i
\(269\) −234.293 + 234.293i −0.870976 + 0.870976i −0.992579 0.121603i \(-0.961197\pi\)
0.121603 + 0.992579i \(0.461197\pi\)
\(270\) 0 0
\(271\) 30.9533i 0.114219i 0.998368 + 0.0571094i \(0.0181884\pi\)
−0.998368 + 0.0571094i \(0.981812\pi\)
\(272\) −234.914 + 210.214i −0.863655 + 0.772846i
\(273\) 0 0
\(274\) 92.0100 + 498.579i 0.335803 + 1.81963i
\(275\) −107.574 107.574i −0.391178 0.391178i
\(276\) 0 0
\(277\) −41.4479 41.4479i −0.149631 0.149631i 0.628322 0.777953i \(-0.283742\pi\)
−0.777953 + 0.628322i \(0.783742\pi\)
\(278\) −108.750 + 157.972i −0.391187 + 0.568245i
\(279\) 0 0
\(280\) −107.298 26.0216i −0.383206 0.0929342i
\(281\) 93.3971i 0.332374i −0.986094 0.166187i \(-0.946854\pi\)
0.986094 0.166187i \(-0.0531455\pi\)
\(282\) 0 0
\(283\) 40.0982 40.0982i 0.141690 0.141690i −0.632704 0.774394i \(-0.718055\pi\)
0.774394 + 0.632704i \(0.218055\pi\)
\(284\) −162.485 + 62.0858i −0.572130 + 0.218612i
\(285\) 0 0
\(286\) −55.1540 298.866i −0.192846 1.04498i
\(287\) 294.678i 1.02675i
\(288\) 0 0
\(289\) 99.1824 0.343192
\(290\) −10.0654 + 1.85750i −0.0347081 + 0.00640519i
\(291\) 0 0
\(292\) −105.651 276.500i −0.361819 0.946917i
\(293\) −141.326 141.326i −0.482340 0.482340i 0.423538 0.905878i \(-0.360788\pi\)
−0.905878 + 0.423538i \(0.860788\pi\)
\(294\) 0 0
\(295\) −163.147 −0.553041
\(296\) −304.513 73.8499i −1.02876 0.249493i
\(297\) 0 0
\(298\) −102.355 70.4622i −0.343472 0.236450i
\(299\) 338.445 338.445i 1.13192 1.13192i
\(300\) 0 0
\(301\) −123.126 + 123.126i −0.409056 + 0.409056i
\(302\) 438.759 80.9705i 1.45284 0.268114i
\(303\) 0 0
\(304\) −490.133 27.1974i −1.61228 0.0894652i
\(305\) 175.228 0.574517
\(306\) 0 0
\(307\) −285.548 285.548i −0.930125 0.930125i 0.0675885 0.997713i \(-0.478470\pi\)
−0.997713 + 0.0675885i \(0.978470\pi\)
\(308\) −74.1916 + 165.950i −0.240882 + 0.538799i
\(309\) 0 0
\(310\) −5.99687 + 8.71115i −0.0193447 + 0.0281005i
\(311\) 365.454 1.17509 0.587547 0.809190i \(-0.300094\pi\)
0.587547 + 0.809190i \(0.300094\pi\)
\(312\) 0 0
\(313\) 461.508i 1.47447i 0.675638 + 0.737234i \(0.263868\pi\)
−0.675638 + 0.737234i \(0.736132\pi\)
\(314\) 126.466 183.707i 0.402758 0.585054i
\(315\) 0 0
\(316\) 5.89167 + 15.4191i 0.0186445 + 0.0487946i
\(317\) 319.216 319.216i 1.00699 1.00699i 0.00701388 0.999975i \(-0.497767\pi\)
0.999975 0.00701388i \(-0.00223261\pi\)
\(318\) 0 0
\(319\) 16.8518i 0.0528270i
\(320\) −146.493 + 46.8531i −0.457792 + 0.146416i
\(321\) 0 0
\(322\) −281.533 + 51.9553i −0.874325 + 0.161352i
\(323\) 427.429 + 427.429i 1.32331 + 1.32331i
\(324\) 0 0
\(325\) 261.037 + 261.037i 0.803190 + 0.803190i
\(326\) −121.712 83.7881i −0.373350 0.257019i
\(327\) 0 0
\(328\) −213.679 350.503i −0.651461 1.06861i
\(329\) 439.448i 1.33571i
\(330\) 0 0
\(331\) −85.7864 + 85.7864i −0.259173 + 0.259173i −0.824718 0.565544i \(-0.808666\pi\)
0.565544 + 0.824718i \(0.308666\pi\)
\(332\) −198.528 88.7562i −0.597976 0.267338i
\(333\) 0 0
\(334\) 189.835 35.0329i 0.568367 0.104889i
\(335\) 215.623i 0.643651i
\(336\) 0 0
\(337\) 258.256 0.766339 0.383170 0.923678i \(-0.374832\pi\)
0.383170 + 0.923678i \(0.374832\pi\)
\(338\) 72.4953 + 392.834i 0.214483 + 1.16223i
\(339\) 0 0
\(340\) 172.901 + 77.2989i 0.508531 + 0.227350i
\(341\) 12.3124 + 12.3124i 0.0361067 + 0.0361067i
\(342\) 0 0
\(343\) 373.398 1.08862
\(344\) −57.1695 + 235.733i −0.166190 + 0.685271i
\(345\) 0 0
\(346\) −74.2695 + 107.885i −0.214652 + 0.311807i
\(347\) −27.7237 + 27.7237i −0.0798953 + 0.0798953i −0.745925 0.666030i \(-0.767992\pi\)
0.666030 + 0.745925i \(0.267992\pi\)
\(348\) 0 0
\(349\) 321.089 321.089i 0.920027 0.920027i −0.0770037 0.997031i \(-0.524535\pi\)
0.997031 + 0.0770037i \(0.0245353\pi\)
\(350\) −40.0722 217.141i −0.114492 0.620403i
\(351\) 0 0
\(352\) 32.0882 + 251.187i 0.0911596 + 0.713599i
\(353\) 241.363 0.683748 0.341874 0.939746i \(-0.388938\pi\)
0.341874 + 0.939746i \(0.388938\pi\)
\(354\) 0 0
\(355\) 73.8953 + 73.8953i 0.208156 + 0.208156i
\(356\) −75.6468 197.975i −0.212491 0.556111i
\(357\) 0 0
\(358\) −217.934 150.029i −0.608754 0.419074i
\(359\) 363.821 1.01343 0.506714 0.862114i \(-0.330860\pi\)
0.506714 + 0.862114i \(0.330860\pi\)
\(360\) 0 0
\(361\) 580.287i 1.60744i
\(362\) 269.809 + 185.740i 0.745329 + 0.513094i
\(363\) 0 0
\(364\) 180.032 402.692i 0.494593 1.10630i
\(365\) −125.747 + 125.747i −0.344513 + 0.344513i
\(366\) 0 0
\(367\) 411.402i 1.12099i −0.828159 0.560493i \(-0.810612\pi\)
0.828159 0.560493i \(-0.189388\pi\)
\(368\) −297.193 + 265.945i −0.807590 + 0.722676i
\(369\) 0 0
\(370\) 34.1642 + 185.127i 0.0923356 + 0.500344i
\(371\) −324.551 324.551i −0.874801 0.874801i
\(372\) 0 0
\(373\) −225.677 225.677i −0.605033 0.605033i 0.336611 0.941644i \(-0.390719\pi\)
−0.941644 + 0.336611i \(0.890719\pi\)
\(374\) 176.816 256.847i 0.472771 0.686756i
\(375\) 0 0
\(376\) 318.656 + 522.699i 0.847488 + 1.39016i
\(377\) 40.8923i 0.108468i
\(378\) 0 0
\(379\) −157.180 + 157.180i −0.414724 + 0.414724i −0.883381 0.468656i \(-0.844738\pi\)
0.468656 + 0.883381i \(0.344738\pi\)
\(380\) 105.267 + 275.496i 0.277019 + 0.724988i
\(381\) 0 0
\(382\) −12.8112 69.4207i −0.0335372 0.181729i
\(383\) 703.356i 1.83644i 0.396072 + 0.918219i \(0.370373\pi\)
−0.396072 + 0.918219i \(0.629627\pi\)
\(384\) 0 0
\(385\) 109.212 0.283668
\(386\) 716.578 132.241i 1.85642 0.342592i
\(387\) 0 0
\(388\) 86.3168 32.9818i 0.222466 0.0850047i
\(389\) −10.7401 10.7401i −0.0276095 0.0276095i 0.693167 0.720777i \(-0.256215\pi\)
−0.720777 + 0.693167i \(0.756215\pi\)
\(390\) 0 0
\(391\) 491.095 1.25600
\(392\) 109.430 66.7124i 0.279158 0.170185i
\(393\) 0 0
\(394\) 304.222 + 209.431i 0.772138 + 0.531550i
\(395\) 7.01234 7.01234i 0.0177528 0.0177528i
\(396\) 0 0
\(397\) 365.020 365.020i 0.919446 0.919446i −0.0775433 0.996989i \(-0.524708\pi\)
0.996989 + 0.0775433i \(0.0247076\pi\)
\(398\) 25.0753 4.62750i 0.0630032 0.0116269i
\(399\) 0 0
\(400\) −205.118 229.220i −0.512796 0.573049i
\(401\) −341.735 −0.852207 −0.426104 0.904674i \(-0.640114\pi\)
−0.426104 + 0.904674i \(0.640114\pi\)
\(402\) 0 0
\(403\) −29.8770 29.8770i −0.0741364 0.0741364i
\(404\) −83.2558 37.2213i −0.206079 0.0921318i
\(405\) 0 0
\(406\) −13.8692 + 20.1467i −0.0341606 + 0.0496223i
\(407\) 309.947 0.761541
\(408\) 0 0
\(409\) 368.259i 0.900389i 0.892931 + 0.450194i \(0.148645\pi\)
−0.892931 + 0.450194i \(0.851355\pi\)
\(410\) −139.847 + 203.144i −0.341091 + 0.495474i
\(411\) 0 0
\(412\) −369.310 + 141.114i −0.896384 + 0.342510i
\(413\) −275.678 + 275.678i −0.667501 + 0.667501i
\(414\) 0 0
\(415\) 130.652i 0.314824i
\(416\) −77.8646 609.525i −0.187174 1.46520i
\(417\) 0 0
\(418\) 477.508 88.1215i 1.14236 0.210817i
\(419\) −407.140 407.140i −0.971694 0.971694i 0.0279165 0.999610i \(-0.491113\pi\)
−0.999610 + 0.0279165i \(0.991113\pi\)
\(420\) 0 0
\(421\) 57.5576 + 57.5576i 0.136716 + 0.136716i 0.772153 0.635437i \(-0.219180\pi\)
−0.635437 + 0.772153i \(0.719180\pi\)
\(422\) −20.0242 13.7849i −0.0474506 0.0326656i
\(423\) 0 0
\(424\) −621.376 150.695i −1.46551 0.355412i
\(425\) 378.772i 0.891229i
\(426\) 0 0
\(427\) 296.091 296.091i 0.693422 0.693422i
\(428\) −36.1683 + 80.9005i −0.0845053 + 0.189020i
\(429\) 0 0
\(430\) 143.313 26.4476i 0.333285 0.0615060i
\(431\) 796.565i 1.84818i −0.382177 0.924089i \(-0.624826\pi\)
0.382177 0.924089i \(-0.375174\pi\)
\(432\) 0 0
\(433\) −335.804 −0.775529 −0.387764 0.921758i \(-0.626753\pi\)
−0.387764 + 0.921758i \(0.626753\pi\)
\(434\) 4.58646 + 24.8529i 0.0105679 + 0.0572647i
\(435\) 0 0
\(436\) 195.540 437.380i 0.448487 1.00317i
\(437\) 540.746 + 540.746i 1.23741 + 1.23741i
\(438\) 0 0
\(439\) −285.630 −0.650638 −0.325319 0.945604i \(-0.605472\pi\)
−0.325319 + 0.945604i \(0.605472\pi\)
\(440\) 129.902 79.1927i 0.295232 0.179983i
\(441\) 0 0
\(442\) −429.059 + 623.259i −0.970722 + 1.41009i
\(443\) −111.596 + 111.596i −0.251909 + 0.251909i −0.821753 0.569844i \(-0.807004\pi\)
0.569844 + 0.821753i \(0.307004\pi\)
\(444\) 0 0
\(445\) −90.0358 + 90.0358i −0.202328 + 0.202328i
\(446\) −18.3625 99.5017i −0.0411715 0.223098i
\(447\) 0 0
\(448\) −168.367 + 326.707i −0.375820 + 0.729257i
\(449\) 99.6741 0.221991 0.110996 0.993821i \(-0.464596\pi\)
0.110996 + 0.993821i \(0.464596\pi\)
\(450\) 0 0
\(451\) 287.125 + 287.125i 0.636641 + 0.636641i
\(452\) −238.591 + 91.1659i −0.527855 + 0.201695i
\(453\) 0 0
\(454\) 73.8939 + 50.8695i 0.162762 + 0.112047i
\(455\) −265.012 −0.582445
\(456\) 0 0
\(457\) 32.1643i 0.0703813i −0.999381 0.0351907i \(-0.988796\pi\)
0.999381 0.0351907i \(-0.0112039\pi\)
\(458\) 395.652 + 272.372i 0.863870 + 0.594699i
\(459\) 0 0
\(460\) 218.739 + 97.7918i 0.475519 + 0.212591i
\(461\) −165.361 + 165.361i −0.358701 + 0.358701i −0.863334 0.504633i \(-0.831628\pi\)
0.504633 + 0.863334i \(0.331628\pi\)
\(462\) 0 0
\(463\) 923.215i 1.99398i −0.0774991 0.996992i \(-0.524693\pi\)
0.0774991 0.996992i \(-0.475307\pi\)
\(464\) −1.88778 + 34.0202i −0.00406849 + 0.0733195i
\(465\) 0 0
\(466\) −131.784 714.105i −0.282798 1.53241i
\(467\) −507.842 507.842i −1.08746 1.08746i −0.995790 0.0916660i \(-0.970781\pi\)
−0.0916660 0.995790i \(-0.529219\pi\)
\(468\) 0 0
\(469\) −364.349 364.349i −0.776864 0.776864i
\(470\) 208.551 302.945i 0.443727 0.644565i
\(471\) 0 0
\(472\) −128.002 + 527.805i −0.271191 + 1.11823i
\(473\) 239.940i 0.507272i
\(474\) 0 0
\(475\) −417.068 + 417.068i −0.878037 + 0.878037i
\(476\) 422.775 161.543i 0.888182 0.339376i
\(477\) 0 0
\(478\) 10.0279 + 54.3389i 0.0209789 + 0.113680i
\(479\) 52.3866i 0.109367i −0.998504 0.0546833i \(-0.982585\pi\)
0.998504 0.0546833i \(-0.0174149\pi\)
\(480\) 0 0
\(481\) −752.112 −1.56364
\(482\) −724.017 + 133.613i −1.50211 + 0.277206i
\(483\) 0 0
\(484\) 83.3489 + 218.132i 0.172208 + 0.450687i
\(485\) −39.2554 39.2554i −0.0809389 0.0809389i
\(486\) 0 0
\(487\) −715.733 −1.46968 −0.734839 0.678241i \(-0.762742\pi\)
−0.734839 + 0.678241i \(0.762742\pi\)
\(488\) 137.480 566.887i 0.281722 1.16165i
\(489\) 0 0
\(490\) −63.4234 43.6614i −0.129435 0.0891050i
\(491\) 22.3258 22.3258i 0.0454701 0.0454701i −0.684006 0.729476i \(-0.739764\pi\)
0.729476 + 0.684006i \(0.239764\pi\)
\(492\) 0 0
\(493\) 29.6680 29.6680i 0.0601784 0.0601784i
\(494\) −1158.71 + 213.834i −2.34557 + 0.432862i
\(495\) 0 0
\(496\) 23.4768 + 26.2353i 0.0473323 + 0.0528938i
\(497\) 249.729 0.502473
\(498\) 0 0
\(499\) 84.0984 + 84.0984i 0.168534 + 0.168534i 0.786335 0.617801i \(-0.211976\pi\)
−0.617801 + 0.786335i \(0.711976\pi\)
\(500\) −173.508 + 388.100i −0.347017 + 0.776200i
\(501\) 0 0
\(502\) 529.005 768.442i 1.05380 1.53076i
\(503\) −327.870 −0.651829 −0.325914 0.945399i \(-0.605672\pi\)
−0.325914 + 0.945399i \(0.605672\pi\)
\(504\) 0 0
\(505\) 54.7909i 0.108497i
\(506\) 223.693 324.940i 0.442081 0.642174i
\(507\) 0 0
\(508\) −52.6692 137.841i −0.103680 0.271340i
\(509\) −34.6224 + 34.6224i −0.0680205 + 0.0680205i −0.740299 0.672278i \(-0.765316\pi\)
0.672278 + 0.740299i \(0.265316\pi\)
\(510\) 0 0
\(511\) 424.963i 0.831630i
\(512\) 36.6407 + 510.687i 0.0715639 + 0.997436i
\(513\) 0 0
\(514\) 46.5661 8.59351i 0.0905954 0.0167189i
\(515\) 167.956 + 167.956i 0.326128 + 0.326128i
\(516\) 0 0
\(517\) −428.184 428.184i −0.828210 0.828210i
\(518\) 370.548 + 255.090i 0.715343 + 0.492451i
\(519\) 0 0
\(520\) −315.217 + 192.167i −0.606187 + 0.369553i
\(521\) 235.719i 0.452436i −0.974077 0.226218i \(-0.927364\pi\)
0.974077 0.226218i \(-0.0726362\pi\)
\(522\) 0 0
\(523\) −185.851 + 185.851i −0.355356 + 0.355356i −0.862098 0.506742i \(-0.830850\pi\)
0.506742 + 0.862098i \(0.330850\pi\)
\(524\) 208.706 + 93.3063i 0.398294 + 0.178066i
\(525\) 0 0
\(526\) 479.610 88.5093i 0.911805 0.168269i
\(527\) 43.3524i 0.0822626i
\(528\) 0 0
\(529\) 92.2900 0.174461
\(530\) 69.7139 + 377.762i 0.131536 + 0.712759i
\(531\) 0 0
\(532\) 643.394 + 287.643i 1.20939 + 0.540683i
\(533\) −696.732 696.732i −1.30719 1.30719i
\(534\) 0 0
\(535\) 53.2408 0.0995155
\(536\) −697.572 169.174i −1.30144 0.315623i
\(537\) 0 0
\(538\) 375.765 545.843i 0.698448 1.01458i
\(539\) −89.6428 + 89.6428i −0.166313 + 0.166313i
\(540\) 0 0
\(541\) −315.952 + 315.952i −0.584015 + 0.584015i −0.936004 0.351989i \(-0.885506\pi\)
0.351989 + 0.936004i \(0.385506\pi\)
\(542\) −11.2348 60.8786i −0.0207284 0.112322i
\(543\) 0 0
\(544\) 385.728 498.711i 0.709058 0.916749i
\(545\) −287.841 −0.528149
\(546\) 0 0
\(547\) −550.957 550.957i −1.00723 1.00723i −0.999974 0.00725954i \(-0.997689\pi\)
−0.00725954 0.999974i \(-0.502311\pi\)
\(548\) −361.929 947.204i −0.660454 1.72847i
\(549\) 0 0
\(550\) 250.620 + 172.530i 0.455673 + 0.313691i
\(551\) 65.3350 0.118575
\(552\) 0 0
\(553\) 23.6982i 0.0428539i
\(554\) 96.5631 + 66.4753i 0.174302 + 0.119992i
\(555\) 0 0
\(556\) 156.551 350.170i 0.281566 0.629802i
\(557\) −2.35545 + 2.35545i −0.00422882 + 0.00422882i −0.709218 0.704989i \(-0.750952\pi\)
0.704989 + 0.709218i \(0.250952\pi\)
\(558\) 0 0
\(559\) 582.233i 1.04156i
\(560\) 220.476 + 12.2342i 0.393708 + 0.0218468i
\(561\) 0 0
\(562\) 33.8994 + 183.692i 0.0603192 + 0.326855i
\(563\) −269.210 269.210i −0.478170 0.478170i 0.426376 0.904546i \(-0.359790\pi\)
−0.904546 + 0.426376i \(0.859790\pi\)
\(564\) 0 0
\(565\) 108.507 + 108.507i 0.192047 + 0.192047i
\(566\) −64.3106 + 93.4187i −0.113623 + 0.165051i
\(567\) 0 0
\(568\) 297.039 181.085i 0.522956 0.318812i
\(569\) 342.558i 0.602035i 0.953619 + 0.301018i \(0.0973263\pi\)
−0.953619 + 0.301018i \(0.902674\pi\)
\(570\) 0 0
\(571\) 153.948 153.948i 0.269610 0.269610i −0.559333 0.828943i \(-0.688943\pi\)
0.828943 + 0.559333i \(0.188943\pi\)
\(572\) 216.953 + 567.787i 0.379288 + 0.992634i
\(573\) 0 0
\(574\) 106.957 + 579.570i 0.186335 + 1.00970i
\(575\) 479.190i 0.833373i
\(576\) 0 0
\(577\) 563.693 0.976938 0.488469 0.872581i \(-0.337556\pi\)
0.488469 + 0.872581i \(0.337556\pi\)
\(578\) −195.071 + 35.9992i −0.337493 + 0.0622824i
\(579\) 0 0
\(580\) 19.1222 7.30664i 0.0329693 0.0125977i
\(581\) 220.769 + 220.769i 0.379981 + 0.379981i
\(582\) 0 0
\(583\) 632.465 1.08484
\(584\) 308.152 + 505.469i 0.527657 + 0.865530i
\(585\) 0 0
\(586\) 329.253 + 226.662i 0.561866 + 0.386796i
\(587\) −176.603 + 176.603i −0.300857 + 0.300857i −0.841349 0.540492i \(-0.818238\pi\)
0.540492 + 0.841349i \(0.318238\pi\)
\(588\) 0 0
\(589\) 47.7355 47.7355i 0.0810450 0.0810450i
\(590\) 320.876 59.2159i 0.543857 0.100366i
\(591\) 0 0
\(592\) 625.718 + 34.7210i 1.05696 + 0.0586504i
\(593\) 996.597 1.68060 0.840301 0.542120i \(-0.182378\pi\)
0.840301 + 0.542120i \(0.182378\pi\)
\(594\) 0 0
\(595\) −192.271 192.271i −0.323144 0.323144i
\(596\) 226.885 + 101.434i 0.380679 + 0.170191i
\(597\) 0 0
\(598\) −542.808 + 788.493i −0.907707 + 1.31855i
\(599\) 854.031 1.42576 0.712880 0.701286i \(-0.247390\pi\)
0.712880 + 0.701286i \(0.247390\pi\)
\(600\) 0 0
\(601\) 345.733i 0.575263i −0.957741 0.287631i \(-0.907132\pi\)
0.957741 0.287631i \(-0.0928678\pi\)
\(602\) 197.473 286.853i 0.328028 0.476499i
\(603\) 0 0
\(604\) −833.557 + 318.504i −1.38006 + 0.527325i
\(605\) 99.2029 99.2029i 0.163972 0.163972i
\(606\) 0 0
\(607\) 526.354i 0.867141i 0.901120 + 0.433570i \(0.142746\pi\)
−0.901120 + 0.433570i \(0.857254\pi\)
\(608\) 973.859 124.407i 1.60174 0.204617i
\(609\) 0 0
\(610\) −344.636 + 63.6007i −0.564977 + 0.104263i
\(611\) 1039.02 + 1039.02i 1.70053 + 1.70053i
\(612\) 0 0
\(613\) 410.567 + 410.567i 0.669767 + 0.669767i 0.957662 0.287895i \(-0.0929554\pi\)
−0.287895 + 0.957662i \(0.592955\pi\)
\(614\) 665.256 + 457.971i 1.08348 + 0.745881i
\(615\) 0 0
\(616\) 85.6859 353.318i 0.139100 0.573568i
\(617\) 514.755i 0.834287i −0.908841 0.417144i \(-0.863031\pi\)
0.908841 0.417144i \(-0.136969\pi\)
\(618\) 0 0
\(619\) 314.214 314.214i 0.507615 0.507615i −0.406179 0.913794i \(-0.633139\pi\)
0.913794 + 0.406179i \(0.133139\pi\)
\(620\) 8.63278 19.3096i 0.0139238 0.0311446i
\(621\) 0 0
\(622\) −718.772 + 132.645i −1.15558 + 0.213256i
\(623\) 304.276i 0.488404i
\(624\) 0 0
\(625\) −225.209 −0.360334
\(626\) −167.509 907.690i −0.267586 1.44998i
\(627\) 0 0
\(628\) −182.054 + 407.215i −0.289895 + 0.648431i
\(629\) −545.669 545.669i −0.867518 0.867518i
\(630\) 0 0
\(631\) −230.081 −0.364629 −0.182315 0.983240i \(-0.558359\pi\)
−0.182315 + 0.983240i \(0.558359\pi\)
\(632\) −17.1842 28.1877i −0.0271902 0.0446008i
\(633\) 0 0
\(634\) −511.967 + 743.692i −0.807519 + 1.17302i
\(635\) −62.6875 + 62.6875i −0.0987205 + 0.0987205i
\(636\) 0 0
\(637\) 217.526 217.526i 0.341484 0.341484i
\(638\) −6.11654 33.1440i −0.00958705 0.0519498i
\(639\) 0 0
\(640\) 271.116 145.321i 0.423618 0.227065i
\(641\) −746.825 −1.16509 −0.582547 0.812797i \(-0.697944\pi\)
−0.582547 + 0.812797i \(0.697944\pi\)
\(642\) 0 0
\(643\) 548.092 + 548.092i 0.852398 + 0.852398i 0.990428 0.138030i \(-0.0440772\pi\)
−0.138030 + 0.990428i \(0.544077\pi\)
\(644\) 534.858 204.370i 0.830524 0.317345i
\(645\) 0 0
\(646\) −995.803 685.523i −1.54149 1.06118i
\(647\) −1055.00 −1.63060 −0.815302 0.579036i \(-0.803429\pi\)
−0.815302 + 0.579036i \(0.803429\pi\)
\(648\) 0 0
\(649\) 537.223i 0.827771i
\(650\) −608.150 418.658i −0.935616 0.644090i
\(651\) 0 0
\(652\) 269.794 + 120.617i 0.413794 + 0.184995i
\(653\) 854.888 854.888i 1.30917 1.30917i 0.387155 0.922015i \(-0.373458\pi\)
0.922015 0.387155i \(-0.126542\pi\)
\(654\) 0 0
\(655\) 137.350i 0.209694i
\(656\) 547.480 + 611.809i 0.834574 + 0.932636i
\(657\) 0 0
\(658\) −159.502 864.302i −0.242405 1.31353i
\(659\) 768.766 + 768.766i 1.16656 + 1.16656i 0.983009 + 0.183556i \(0.0587607\pi\)
0.183556 + 0.983009i \(0.441239\pi\)
\(660\) 0 0
\(661\) 312.323 + 312.323i 0.472500 + 0.472500i 0.902723 0.430223i \(-0.141565\pi\)
−0.430223 + 0.902723i \(0.641565\pi\)
\(662\) 137.587 199.861i 0.207835 0.301904i
\(663\) 0 0
\(664\) 422.678 + 102.507i 0.636563 + 0.154378i
\(665\) 423.420i 0.636721i
\(666\) 0 0
\(667\) 37.5333 37.5333i 0.0562719 0.0562719i
\(668\) −360.649 + 137.805i −0.539894 + 0.206295i
\(669\) 0 0
\(670\) 78.2626 + 424.085i 0.116810 + 0.632963i
\(671\) 577.004i 0.859916i
\(672\) 0 0
\(673\) 740.565 1.10039 0.550197 0.835035i \(-0.314553\pi\)
0.550197 + 0.835035i \(0.314553\pi\)
\(674\) −507.936 + 93.7367i −0.753614 + 0.139075i
\(675\) 0 0
\(676\) −285.166 746.308i −0.421843 1.10401i
\(677\) 547.118 + 547.118i 0.808151 + 0.808151i 0.984354 0.176203i \(-0.0563814\pi\)
−0.176203 + 0.984354i \(0.556381\pi\)
\(678\) 0 0
\(679\) −132.664 −0.195381
\(680\) −368.115 89.2746i −0.541346 0.131286i
\(681\) 0 0
\(682\) −28.6848 19.7470i −0.0420598 0.0289545i
\(683\) 407.623 407.623i 0.596813 0.596813i −0.342650 0.939463i \(-0.611324\pi\)
0.939463 + 0.342650i \(0.111324\pi\)
\(684\) 0 0
\(685\) −430.772 + 430.772i −0.628864 + 0.628864i
\(686\) −734.396 + 135.529i −1.07055 + 0.197564i
\(687\) 0 0
\(688\) 26.8786 484.388i 0.0390678 0.704052i
\(689\) −1534.73 −2.22747
\(690\) 0 0
\(691\) 17.6037 + 17.6037i 0.0254757 + 0.0254757i 0.719730 0.694254i \(-0.244266\pi\)
−0.694254 + 0.719730i \(0.744266\pi\)
\(692\) 106.915 239.144i 0.154501 0.345584i
\(693\) 0 0
\(694\) 44.4640 64.5892i 0.0640692 0.0930680i
\(695\) −230.448 −0.331579
\(696\) 0 0
\(697\) 1010.98i 1.45047i
\(698\) −514.973 + 748.058i −0.737783 + 1.07172i
\(699\) 0 0
\(700\) 157.627 + 412.526i 0.225181 + 0.589323i
\(701\) −164.273 + 164.273i −0.234341 + 0.234341i −0.814502 0.580161i \(-0.802990\pi\)
0.580161 + 0.814502i \(0.302990\pi\)
\(702\) 0 0
\(703\) 1201.68i 1.70935i
\(704\) −154.281 482.385i −0.219150 0.685205i
\(705\) 0 0
\(706\) −474.710 + 87.6051i −0.672394 + 0.124087i
\(707\) 92.5829 + 92.5829i 0.130952 + 0.130952i
\(708\) 0 0
\(709\) 422.796 + 422.796i 0.596327 + 0.596327i 0.939333 0.343006i \(-0.111445\pi\)
−0.343006 + 0.939333i \(0.611445\pi\)
\(710\) −172.157 118.515i −0.242475 0.166923i
\(711\) 0 0
\(712\) 220.638 + 361.919i 0.309886 + 0.508313i
\(713\) 54.8457i 0.0769224i
\(714\) 0 0
\(715\) 258.220 258.220i 0.361146 0.361146i
\(716\) 483.085 + 215.973i 0.674699 + 0.301639i
\(717\) 0 0
\(718\) −715.559 + 132.052i −0.996601 + 0.183917i
\(719\) 1029.00i 1.43115i −0.698534 0.715577i \(-0.746164\pi\)
0.698534 0.715577i \(-0.253836\pi\)
\(720\) 0 0
\(721\) 567.607 0.787250
\(722\) −210.621 1141.30i −0.291719 1.58075i
\(723\) 0 0
\(724\) −598.074 267.381i −0.826068 0.369311i
\(725\) 28.9488 + 28.9488i 0.0399293 + 0.0399293i
\(726\) 0 0
\(727\) −475.001 −0.653372 −0.326686 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(728\) −207.924 + 857.354i −0.285609 + 1.17768i
\(729\) 0 0
\(730\) 201.677 292.960i 0.276270 0.401314i
\(731\) −422.419 + 422.419i −0.577865 + 0.577865i
\(732\) 0 0
\(733\) −344.939 + 344.939i −0.470586 + 0.470586i −0.902104 0.431519i \(-0.857978\pi\)
0.431519 + 0.902104i \(0.357978\pi\)
\(734\) 149.322 + 809.141i 0.203437 + 1.10237i
\(735\) 0 0
\(736\) 487.989 630.926i 0.663028 0.857237i
\(737\) 710.021 0.963393
\(738\) 0 0
\(739\) 363.340 + 363.340i 0.491665 + 0.491665i 0.908831 0.417166i \(-0.136976\pi\)
−0.417166 + 0.908831i \(0.636976\pi\)
\(740\) −134.388 351.706i −0.181605 0.475278i
\(741\) 0 0
\(742\) 756.123 + 520.525i 1.01903 + 0.701516i
\(743\) −271.667 −0.365636 −0.182818 0.983147i \(-0.558522\pi\)
−0.182818 + 0.983147i \(0.558522\pi\)
\(744\) 0 0
\(745\) 149.314i 0.200421i
\(746\) 525.771 + 361.948i 0.704787 + 0.485185i
\(747\) 0 0
\(748\) −254.536 + 569.340i −0.340288 + 0.761150i
\(749\) 89.9637 89.9637i 0.120112 0.120112i
\(750\) 0 0
\(751\) 1105.27i 1.47173i 0.677128 + 0.735866i \(0.263224\pi\)
−0.677128 + 0.735866i \(0.736776\pi\)
\(752\) −816.447 912.380i −1.08570 1.21327i
\(753\) 0 0
\(754\) 14.8423 + 80.4265i 0.0196847 + 0.106666i
\(755\) 379.087 + 379.087i 0.502102 + 0.502102i
\(756\) 0 0
\(757\) 554.565 + 554.565i 0.732583 + 0.732583i 0.971131 0.238548i \(-0.0766713\pi\)
−0.238548 + 0.971131i \(0.576671\pi\)
\(758\) 252.091 366.191i 0.332573 0.483102i
\(759\) 0 0
\(760\) −307.033 503.634i −0.403990 0.662676i
\(761\) 188.496i 0.247695i 0.992301 + 0.123847i \(0.0395234\pi\)
−0.992301 + 0.123847i \(0.960477\pi\)
\(762\) 0 0
\(763\) −486.380 + 486.380i −0.637457 + 0.637457i
\(764\) 50.3939 + 131.886i 0.0659605 + 0.172625i
\(765\) 0 0
\(766\) −255.290 1383.35i −0.333277 1.80594i
\(767\) 1303.62i 1.69963i
\(768\) 0 0
\(769\) −593.354 −0.771592 −0.385796 0.922584i \(-0.626073\pi\)
−0.385796 + 0.922584i \(0.626073\pi\)
\(770\) −214.798 + 39.6397i −0.278958 + 0.0514801i
\(771\) 0 0
\(772\) −1361.36 + 520.179i −1.76342 + 0.673807i
\(773\) −514.720 514.720i −0.665873 0.665873i 0.290885 0.956758i \(-0.406050\pi\)
−0.956758 + 0.290885i \(0.906050\pi\)
\(774\) 0 0
\(775\) 42.3015 0.0545826
\(776\) −157.796 + 96.1978i −0.203345 + 0.123966i
\(777\) 0 0
\(778\) 25.0218 + 17.2253i 0.0321616 + 0.0221405i
\(779\) 1113.19 1113.19i 1.42900 1.42900i
\(780\) 0 0
\(781\) −243.328 + 243.328i −0.311560 + 0.311560i
\(782\) −965.879 + 178.248i −1.23514 + 0.227938i
\(783\) 0 0
\(784\) −191.012 + 170.928i −0.243638 + 0.218020i
\(785\)