Properties

Label 144.3.m.c.19.1
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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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 19.1
Root \(-1.96679 + 0.362960i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.1

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 −0.856315 0.516454i \(-0.827252\pi\)
0.516454 + 0.856315i \(0.327252\pi\)
\(6\) 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 0.914125 0.405434i \(-0.132879\pi\)
−0.405434 + 0.914125i \(0.632879\pi\)
\(12\) 0 0
\(13\) −13.5782 13.5782i −1.04447 1.04447i −0.998964 0.0455110i \(-0.985508\pi\)
−0.0455110 0.998964i \(-0.514492\pi\)
\(14\) 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 −0.153687 + 0.988120i \(0.549115\pi\)
−0.988120 + 0.153687i \(0.950885\pi\)
\(20\) −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 0.680668 0.732592i \(-0.261690\pi\)
−0.732592 + 0.680668i \(0.761690\pi\)
\(30\) 0 0
\(31\) 2.20037i 0.0709796i −0.999370 0.0354898i \(-0.988701\pi\)
0.999370 0.0354898i \(-0.0112991\pi\)
\(32\) −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 −0.225673 0.974203i \(-0.572458\pi\)
0.974203 + 0.225673i \(0.0724580\pi\)
\(38\) 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 \(-0.784787\pi\)
0.780012 0.625764i \(-0.215213\pi\)
\(42\) 0 0
\(43\) 21.4400 + 21.4400i 0.498606 + 0.498606i 0.911004 0.412398i \(-0.135309\pi\)
−0.412398 + 0.911004i \(0.635309\pi\)
\(44\) 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 \(0.302747\pi\)
−0.580781 + 0.814060i \(0.697253\pi\)
\(48\) 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 0.0686712 0.997639i \(-0.478124\pi\)
0.997639 0.0686712i \(-0.0218759\pi\)
\(54\) 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 0.985176 0.171547i \(-0.0548767\pi\)
−0.171547 + 0.985176i \(0.554877\pi\)
\(60\) 0 0
\(61\) −51.5587 51.5587i −0.845224 0.845224i 0.144308 0.989533i \(-0.453904\pi\)
−0.989533 + 0.144308i \(0.953904\pi\)
\(62\) −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 −0.0517277 0.998661i \(-0.516473\pi\)
0.998661 + 0.0517277i \(0.0164728\pi\)
\(68\) −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 \(0.169188\pi\)
−0.862038 + 0.506844i \(0.830812\pi\)
\(74\) −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 \(-0.991686\pi\)
0.999659 0.0261177i \(-0.00831446\pi\)
\(80\) −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 −0.899692 0.436526i \(-0.856209\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(84\) 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 \(0.0962070\pi\)
−0.954671 + 0.297662i \(0.903793\pi\)
\(90\) 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 −0.782398 0.622779i \(-0.786004\pi\)
0.622779 + 0.782398i \(0.286004\pi\)
\(102\) 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 0.630104 0.776511i \(-0.283012\pi\)
−0.776511 + 0.630104i \(0.783012\pi\)
\(108\) 0 0
\(109\) 84.6938 + 84.6938i 0.777008 + 0.777008i 0.979321 0.202313i \(-0.0648459\pi\)
−0.202313 + 0.979321i \(0.564846\pi\)
\(110\) 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 \(0.0463944\pi\)
−0.989397 + 0.145237i \(0.953606\pi\)
\(128\) −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 −0.535827 0.844328i \(-0.680000\pi\)
0.844328 + 0.535827i \(0.180000\pi\)
\(132\) 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 \(0.376085\pi\)
−0.379531 + 0.925179i \(0.623915\pi\)
\(138\) 0 0
\(139\) 67.8065 + 67.8065i 0.487816 + 0.487816i 0.907617 0.419800i \(-0.137900\pi\)
−0.419800 + 0.907617i \(0.637900\pi\)
\(140\) 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 −0.544138 0.838996i \(-0.683143\pi\)
0.838996 + 0.544138i \(0.183143\pi\)
\(150\) 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 0.409889 0.912135i \(-0.365567\pi\)
−0.912135 + 0.409889i \(0.865567\pi\)
\(158\) −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 −0.528455 0.848961i \(-0.677228\pi\)
0.848961 + 0.528455i \(0.177228\pi\)
\(164\) 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 0.828162 0.560488i \(-0.189386\pi\)
−0.560488 + 0.828162i \(0.689386\pi\)
\(174\) 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 −0.395761 0.918353i \(-0.629519\pi\)
0.918353 + 0.395761i \(0.129519\pi\)
\(180\) 0 0
\(181\) −115.810 + 115.810i −0.639836 + 0.639836i −0.950515 0.310679i \(-0.899444\pi\)
0.310679 + 0.950515i \(0.399444\pi\)
\(182\) −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 \(-0.970546\pi\)
0.995722 0.0923991i \(-0.0294535\pi\)
\(192\) 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 −0.956051 0.293200i \(-0.905280\pi\)
0.293200 + 0.956051i \(0.405280\pi\)
\(198\) 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 −0.686446 0.727181i \(-0.740830\pi\)
0.727181 + 0.686446i \(0.240830\pi\)
\(212\) 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 \(-0.963815\pi\)
0.993546 0.113433i \(-0.0361846\pi\)
\(224\) 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 −0.773509 0.633785i \(-0.781501\pi\)
0.633785 + 0.773509i \(0.281501\pi\)
\(228\) 0 0
\(229\) −169.826 + 169.826i −0.741599 + 0.741599i −0.972886 0.231287i \(-0.925706\pi\)
0.231287 + 0.972886i \(0.425706\pi\)
\(230\) −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 \(-0.715654\pi\)
0.626844 0.779145i \(-0.284346\pi\)
\(234\) 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 \(0.0184084\pi\)
−0.998328 + 0.0577996i \(0.981592\pi\)
\(240\) 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 −0.918365 0.395734i \(-0.870490\pi\)
−0.395734 0.918365i \(-0.629510\pi\)
\(252\) 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 0.121603 0.992579i \(-0.461197\pi\)
−0.992579 + 0.121603i \(0.961197\pi\)
\(270\) 0 0
\(271\) 30.9533i 0.114219i −0.998368 0.0571094i \(-0.981812\pi\)
0.998368 0.0571094i \(-0.0181884\pi\)
\(272\) −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 −0.777953 0.628322i \(-0.783742\pi\)
0.628322 + 0.777953i \(0.283742\pi\)
\(278\) −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 \(0.0531455\pi\)
−0.986094 + 0.166187i \(0.946854\pi\)
\(282\) 0 0
\(283\) 40.0982 + 40.0982i 0.141690 + 0.141690i 0.774394 0.632704i \(-0.218055\pi\)
−0.632704 + 0.774394i \(0.718055\pi\)
\(284\) −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 −0.905878 0.423538i \(-0.860788\pi\)
0.423538 + 0.905878i \(0.360788\pi\)
\(294\) 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 −0.997713 0.0675885i \(-0.978470\pi\)
0.0675885 + 0.997713i \(0.478470\pi\)
\(308\) −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 \(-0.736132\pi\)
0.675638 0.737234i \(-0.263868\pi\)
\(314\) 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 0.999975 + 0.00701388i \(0.00223261\pi\)
0.00701388 + 0.999975i \(0.497767\pi\)
\(318\) 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 0.565544 0.824718i \(-0.308666\pi\)
−0.824718 + 0.565544i \(0.808666\pi\)
\(332\) −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 0.666030 0.745925i \(-0.267992\pi\)
−0.745925 + 0.666030i \(0.767992\pi\)
\(348\) 0 0
\(349\) 321.089 + 321.089i 0.920027 + 0.920027i 0.997031 0.0770037i \(-0.0245353\pi\)
−0.0770037 + 0.997031i \(0.524535\pi\)
\(350\) −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 \(0.189388\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(368\) −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 −0.941644 0.336611i \(-0.890719\pi\)
0.336611 + 0.941644i \(0.390719\pi\)
\(374\) 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 0.468656 0.883381i \(-0.344738\pi\)
−0.883381 + 0.468656i \(0.844738\pi\)
\(380\) 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 \(-0.629627\pi\)
0.396072 0.918219i \(-0.370373\pi\)
\(384\) 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 −0.720777 0.693167i \(-0.756215\pi\)
0.693167 + 0.720777i \(0.256215\pi\)
\(390\) 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 0.996989 0.0775433i \(-0.0247076\pi\)
−0.0775433 + 0.996989i \(0.524708\pi\)
\(398\) 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 \(-0.851355\pi\)
0.892931 0.450194i \(-0.148645\pi\)
\(410\) −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 −0.999610 0.0279165i \(-0.991113\pi\)
0.0279165 + 0.999610i \(0.491113\pi\)
\(420\) 0 0
\(421\) 57.5576 57.5576i 0.136716 0.136716i −0.635437 0.772153i \(-0.719180\pi\)
0.772153 + 0.635437i \(0.219180\pi\)
\(422\) −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 \(0.375174\pi\)
−0.382177 + 0.924089i \(0.624826\pi\)
\(432\) 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 0.569844 0.821753i \(-0.307004\pi\)
−0.821753 + 0.569844i \(0.807004\pi\)
\(444\) 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 \(0.0112039\pi\)
−0.999381 + 0.0351907i \(0.988796\pi\)
\(458\) 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 0.504633 0.863334i \(-0.331628\pi\)
−0.863334 + 0.504633i \(0.831628\pi\)
\(462\) 0 0
\(463\) 923.215i 1.99398i 0.0774991 + 0.996992i \(0.475307\pi\)
−0.0774991 + 0.996992i \(0.524693\pi\)
\(464\) −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 −0.0916660 + 0.995790i \(0.529219\pi\)
−0.995790 + 0.0916660i \(0.970781\pi\)
\(468\) 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 \(0.0174149\pi\)
−0.998504 + 0.0546833i \(0.982585\pi\)
\(480\) 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 0.729476 0.684006i \(-0.239764\pi\)
−0.684006 + 0.729476i \(0.739764\pi\)
\(492\) 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 −0.617801 0.786335i \(-0.711976\pi\)
0.786335 + 0.617801i \(0.211976\pi\)
\(500\) −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 0.672278 0.740299i \(-0.265316\pi\)
−0.740299 + 0.672278i \(0.765316\pi\)
\(510\) 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 \(0.0726362\pi\)
−0.974077 + 0.226218i \(0.927364\pi\)
\(522\) 0 0
\(523\) −185.851 185.851i −0.355356 0.355356i 0.506742 0.862098i \(-0.330850\pi\)
−0.862098 + 0.506742i \(0.830850\pi\)
\(524\) 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 0.351989 0.936004i \(-0.385506\pi\)
−0.936004 + 0.351989i \(0.885506\pi\)
\(542\) −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 −0.00725954 + 0.999974i \(0.502311\pi\)
−0.999974 + 0.00725954i \(0.997689\pi\)
\(548\) −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 0.704989 0.709218i \(-0.250952\pi\)
−0.709218 + 0.704989i \(0.750952\pi\)
\(558\) 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 −0.904546 0.426376i \(-0.859790\pi\)
0.426376 + 0.904546i \(0.359790\pi\)
\(564\) 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 \(-0.902674\pi\)
0.953619 0.301018i \(-0.0973263\pi\)
\(570\) 0 0
\(571\) 153.948 + 153.948i 0.269610 + 0.269610i 0.828943 0.559333i \(-0.188943\pi\)
−0.559333 + 0.828943i \(0.688943\pi\)
\(572\) 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 0.540492 0.841349i \(-0.318238\pi\)
−0.841349 + 0.540492i \(0.818238\pi\)
\(588\) 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 \(0.0928678\pi\)
−0.957741 + 0.287631i \(0.907132\pi\)
\(602\) 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 \(-0.857254\pi\)
0.901120 0.433570i \(-0.142746\pi\)
\(608\) 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 −0.287895 0.957662i \(-0.592955\pi\)
0.957662 + 0.287895i \(0.0929554\pi\)
\(614\) 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 \(0.136969\pi\)
−0.908841 + 0.417144i \(0.863031\pi\)
\(618\) 0 0
\(619\) 314.214 + 314.214i 0.507615 + 0.507615i 0.913794 0.406179i \(-0.133139\pi\)
−0.406179 + 0.913794i \(0.633139\pi\)
\(620\) 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 −0.138030 0.990428i \(-0.544077\pi\)
0.990428 + 0.138030i \(0.0440772\pi\)
\(644\) 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 0.922015 + 0.387155i \(0.126542\pi\)
0.387155 + 0.922015i \(0.373458\pi\)
\(654\) 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 0.183556 0.983009i \(-0.441239\pi\)
0.983009 0.183556i \(-0.0587607\pi\)
\(660\) 0 0
\(661\) 312.323 312.323i 0.472500 0.472500i −0.430223 0.902723i \(-0.641565\pi\)
0.902723 + 0.430223i \(0.141565\pi\)
\(662\) 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 −0.176203 0.984354i \(-0.556381\pi\)
0.984354 + 0.176203i \(0.0563814\pi\)
\(678\) 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 0.939463 0.342650i \(-0.111324\pi\)
−0.342650 + 0.939463i \(0.611324\pi\)
\(684\) 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 −0.694254 0.719730i \(-0.744266\pi\)
0.719730 + 0.694254i \(0.244266\pi\)
\(692\) 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 0.580161 0.814502i \(-0.302990\pi\)
−0.814502 + 0.580161i \(0.802990\pi\)
\(702\) 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 −0.343006 0.939333i \(-0.611445\pi\)
0.939333 + 0.343006i \(0.111445\pi\)
\(710\) −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 \(0.253836\pi\)
−0.698534 + 0.715577i \(0.746164\pi\)
\(720\) 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 0.431519 0.902104i \(-0.357978\pi\)
−0.902104 + 0.431519i \(0.857978\pi\)
\(734\) 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 −0.417166 0.908831i \(-0.636976\pi\)
0.908831 + 0.417166i \(0.136976\pi\)
\(740\) −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 \(-0.736776\pi\)
0.677128 0.735866i \(-0.263224\pi\)
\(752\) −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 −0.238548 0.971131i \(-0.576671\pi\)
0.971131 + 0.238548i \(0.0766713\pi\)
\(758\) 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 \(-0.960477\pi\)
0.992301 0.123847i \(-0.0395234\pi\)
\(762\) 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 −0.956758 0.290885i \(-0.906050\pi\)
0.290885 + 0.956758i \(0.406050\pi\)
\(774\) 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
\(785\) 267.989 0.341387
\(786\) 0 0
\(787\) 96.1835 96.1835i 0.122215 0.122215i