Properties

Label 144.3.m.c.19.7
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 19.7
Root \(1.80398 - 0.863518i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +O(q^{10})\) \(q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +(-17.3247 + 6.10803i) q^{10} +(-4.31091 - 4.31091i) q^{11} +(4.06281 + 4.06281i) q^{13} +(7.11259 + 3.40462i) q^{14} +(-3.41312 + 15.6317i) q^{16} +14.5538 q^{17} +(4.94805 - 4.94805i) q^{19} +(-36.5277 - 3.94140i) q^{20} +(-4.05424 - 11.4993i) q^{22} +43.6717 q^{23} -59.3629i q^{25} +(3.82091 + 10.8375i) q^{26} +(9.89101 + 12.2837i) q^{28} +(-25.0979 - 25.0979i) q^{29} +32.5024i q^{31} +(-19.6555 + 25.2520i) q^{32} +(26.2547 + 12.5675i) q^{34} +(-25.6069 + 25.6069i) q^{35} +(4.14345 - 4.14345i) q^{37} +(13.1989 - 4.65344i) q^{38} +(-62.4917 - 38.6525i) q^{40} -55.3348i q^{41} +(-16.1189 - 16.1189i) q^{43} +(2.61613 - 24.2455i) q^{44} +(78.7828 + 37.7113i) q^{46} +7.92420i q^{47} -33.4549 q^{49} +(51.2610 - 107.089i) q^{50} +(-2.46556 + 22.8501i) q^{52} +(31.5748 - 31.5748i) q^{53} +55.9964 q^{55} +(7.23597 + 30.7006i) q^{56} +(-23.6036 - 66.9485i) q^{58} +(49.7172 + 49.7172i) q^{59} +(44.4711 + 44.4711i) q^{61} +(-28.0664 + 58.6336i) q^{62} +(-57.2636 + 28.5812i) q^{64} -52.7736 q^{65} +(-1.64068 + 1.64068i) q^{67} +(36.5107 + 45.3429i) q^{68} +(-68.3064 + 24.0823i) q^{70} -24.1145 q^{71} +10.7741i q^{73} +(11.0526 - 3.89675i) q^{74} +(27.8288 + 3.00278i) q^{76} +(-16.9967 - 16.9967i) q^{77} -72.0517i q^{79} +(-79.3565 - 123.691i) q^{80} +(47.7826 - 99.8227i) q^{82} +(-42.0499 + 42.0499i) q^{83} +(-94.5229 + 94.5229i) q^{85} +(-15.1592 - 42.9971i) q^{86} +(25.6558 - 41.4792i) q^{88} +28.9853i q^{89} +(16.0185 + 16.0185i) q^{91} +(109.558 + 136.061i) q^{92} +(-6.84269 + 14.2951i) q^{94} +64.2724i q^{95} -54.2698 q^{97} +(-60.3519 - 28.8889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.80398 + 0.863518i 0.901989 + 0.431759i
\(3\) 0 0
\(4\) 2.50867 + 3.11554i 0.627168 + 0.778884i
\(5\) −6.49473 + 6.49473i −1.29895 + 1.29895i −0.369856 + 0.929089i \(0.620593\pi\)
−0.929089 + 0.369856i \(0.879407\pi\)
\(6\) 0 0
\(7\) 3.94273 0.563247 0.281623 0.959525i \(-0.409127\pi\)
0.281623 + 0.959525i \(0.409127\pi\)
\(8\) 1.83527 + 7.78664i 0.229409 + 0.973330i
\(9\) 0 0
\(10\) −17.3247 + 6.10803i −1.73247 + 0.610803i
\(11\) −4.31091 4.31091i −0.391901 0.391901i 0.483464 0.875364i \(-0.339379\pi\)
−0.875364 + 0.483464i \(0.839379\pi\)
\(12\) 0 0
\(13\) 4.06281 + 4.06281i 0.312524 + 0.312524i 0.845887 0.533363i \(-0.179072\pi\)
−0.533363 + 0.845887i \(0.679072\pi\)
\(14\) 7.11259 + 3.40462i 0.508042 + 0.243187i
\(15\) 0 0
\(16\) −3.41312 + 15.6317i −0.213320 + 0.976982i
\(17\) 14.5538 0.856106 0.428053 0.903754i \(-0.359200\pi\)
0.428053 + 0.903754i \(0.359200\pi\)
\(18\) 0 0
\(19\) 4.94805 4.94805i 0.260423 0.260423i −0.564803 0.825226i \(-0.691048\pi\)
0.825226 + 0.564803i \(0.191048\pi\)
\(20\) −36.5277 3.94140i −1.82638 0.197070i
\(21\) 0 0
\(22\) −4.05424 11.4993i −0.184284 0.522697i
\(23\) 43.6717 1.89877 0.949385 0.314115i \(-0.101708\pi\)
0.949385 + 0.314115i \(0.101708\pi\)
\(24\) 0 0
\(25\) 59.3629i 2.37452i
\(26\) 3.82091 + 10.8375i 0.146958 + 0.416828i
\(27\) 0 0
\(28\) 9.89101 + 12.2837i 0.353250 + 0.438704i
\(29\) −25.0979 25.0979i −0.865445 0.865445i 0.126519 0.991964i \(-0.459619\pi\)
−0.991964 + 0.126519i \(0.959619\pi\)
\(30\) 0 0
\(31\) 32.5024i 1.04846i 0.851576 + 0.524232i \(0.175648\pi\)
−0.851576 + 0.524232i \(0.824352\pi\)
\(32\) −19.6555 + 25.2520i −0.614233 + 0.789125i
\(33\) 0 0
\(34\) 26.2547 + 12.5675i 0.772198 + 0.369631i
\(35\) −25.6069 + 25.6069i −0.731627 + 0.731627i
\(36\) 0 0
\(37\) 4.14345 4.14345i 0.111985 0.111985i −0.648894 0.760879i \(-0.724768\pi\)
0.760879 + 0.648894i \(0.224768\pi\)
\(38\) 13.1989 4.65344i 0.347339 0.122459i
\(39\) 0 0
\(40\) −62.4917 38.6525i −1.56229 0.966313i
\(41\) 55.3348i 1.34963i −0.737987 0.674814i \(-0.764224\pi\)
0.737987 0.674814i \(-0.235776\pi\)
\(42\) 0 0
\(43\) −16.1189 16.1189i −0.374858 0.374858i 0.494385 0.869243i \(-0.335393\pi\)
−0.869243 + 0.494385i \(0.835393\pi\)
\(44\) 2.61613 24.2455i 0.0594574 0.551033i
\(45\) 0 0
\(46\) 78.7828 + 37.7113i 1.71267 + 0.819811i
\(47\) 7.92420i 0.168600i 0.996440 + 0.0843001i \(0.0268654\pi\)
−0.996440 + 0.0843001i \(0.973135\pi\)
\(48\) 0 0
\(49\) −33.4549 −0.682753
\(50\) 51.2610 107.089i 1.02522 2.14179i
\(51\) 0 0
\(52\) −2.46556 + 22.8501i −0.0474147 + 0.439424i
\(53\) 31.5748 31.5748i 0.595750 0.595750i −0.343429 0.939179i \(-0.611588\pi\)
0.939179 + 0.343429i \(0.111588\pi\)
\(54\) 0 0
\(55\) 55.9964 1.01812
\(56\) 7.23597 + 30.7006i 0.129214 + 0.548225i
\(57\) 0 0
\(58\) −23.6036 66.9485i −0.406958 1.15429i
\(59\) 49.7172 + 49.7172i 0.842665 + 0.842665i 0.989205 0.146540i \(-0.0468137\pi\)
−0.146540 + 0.989205i \(0.546814\pi\)
\(60\) 0 0
\(61\) 44.4711 + 44.4711i 0.729035 + 0.729035i 0.970427 0.241393i \(-0.0776043\pi\)
−0.241393 + 0.970427i \(0.577604\pi\)
\(62\) −28.0664 + 58.6336i −0.452684 + 0.945703i
\(63\) 0 0
\(64\) −57.2636 + 28.5812i −0.894743 + 0.446581i
\(65\) −52.7736 −0.811902
\(66\) 0 0
\(67\) −1.64068 + 1.64068i −0.0244878 + 0.0244878i −0.719245 0.694757i \(-0.755512\pi\)
0.694757 + 0.719245i \(0.255512\pi\)
\(68\) 36.5107 + 45.3429i 0.536922 + 0.666807i
\(69\) 0 0
\(70\) −68.3064 + 24.0823i −0.975805 + 0.344033i
\(71\) −24.1145 −0.339641 −0.169821 0.985475i \(-0.554319\pi\)
−0.169821 + 0.985475i \(0.554319\pi\)
\(72\) 0 0
\(73\) 10.7741i 0.147591i 0.997273 + 0.0737955i \(0.0235112\pi\)
−0.997273 + 0.0737955i \(0.976489\pi\)
\(74\) 11.0526 3.89675i 0.149360 0.0526588i
\(75\) 0 0
\(76\) 27.8288 + 3.00278i 0.366169 + 0.0395103i
\(77\) −16.9967 16.9967i −0.220737 0.220737i
\(78\) 0 0
\(79\) 72.0517i 0.912047i −0.889968 0.456024i \(-0.849273\pi\)
0.889968 0.456024i \(-0.150727\pi\)
\(80\) −79.3565 123.691i −0.991956 1.54614i
\(81\) 0 0
\(82\) 47.7826 99.8227i 0.582714 1.21735i
\(83\) −42.0499 + 42.0499i −0.506625 + 0.506625i −0.913489 0.406864i \(-0.866622\pi\)
0.406864 + 0.913489i \(0.366622\pi\)
\(84\) 0 0
\(85\) −94.5229 + 94.5229i −1.11203 + 1.11203i
\(86\) −15.1592 42.9971i −0.176269 0.499966i
\(87\) 0 0
\(88\) 25.6558 41.4792i 0.291543 0.471354i
\(89\) 28.9853i 0.325677i 0.986653 + 0.162839i \(0.0520650\pi\)
−0.986653 + 0.162839i \(0.947935\pi\)
\(90\) 0 0
\(91\) 16.0185 + 16.0185i 0.176028 + 0.176028i
\(92\) 109.558 + 136.061i 1.19085 + 1.47892i
\(93\) 0 0
\(94\) −6.84269 + 14.2951i −0.0727946 + 0.152075i
\(95\) 64.2724i 0.676552i
\(96\) 0 0
\(97\) −54.2698 −0.559483 −0.279741 0.960075i \(-0.590249\pi\)
−0.279741 + 0.960075i \(0.590249\pi\)
\(98\) −60.3519 28.8889i −0.615836 0.294785i
\(99\) 0 0
\(100\) 184.947 148.922i 1.84947 1.48922i
\(101\) −57.0829 + 57.0829i −0.565177 + 0.565177i −0.930773 0.365597i \(-0.880865\pi\)
0.365597 + 0.930773i \(0.380865\pi\)
\(102\) 0 0
\(103\) 39.3048 0.381600 0.190800 0.981629i \(-0.438892\pi\)
0.190800 + 0.981629i \(0.438892\pi\)
\(104\) −24.1793 + 39.0920i −0.232493 + 0.375884i
\(105\) 0 0
\(106\) 84.2255 29.6948i 0.794581 0.280140i
\(107\) −25.6981 25.6981i −0.240169 0.240169i 0.576751 0.816920i \(-0.304320\pi\)
−0.816920 + 0.576751i \(0.804320\pi\)
\(108\) 0 0
\(109\) −9.66133 9.66133i −0.0886360 0.0886360i 0.661399 0.750035i \(-0.269963\pi\)
−0.750035 + 0.661399i \(0.769963\pi\)
\(110\) 101.016 + 48.3539i 0.918329 + 0.439581i
\(111\) 0 0
\(112\) −13.4570 + 61.6316i −0.120152 + 0.550282i
\(113\) −64.2927 −0.568962 −0.284481 0.958682i \(-0.591821\pi\)
−0.284481 + 0.958682i \(0.591821\pi\)
\(114\) 0 0
\(115\) −283.636 + 283.636i −2.46640 + 2.46640i
\(116\) 15.2310 141.156i 0.131301 1.21686i
\(117\) 0 0
\(118\) 46.7571 + 132.620i 0.396246 + 1.12390i
\(119\) 57.3816 0.482199
\(120\) 0 0
\(121\) 83.8321i 0.692827i
\(122\) 41.8233 + 118.627i 0.342814 + 0.972348i
\(123\) 0 0
\(124\) −101.262 + 81.5379i −0.816632 + 0.657563i
\(125\) 223.178 + 223.178i 1.78542 + 1.78542i
\(126\) 0 0
\(127\) 129.668i 1.02101i 0.859875 + 0.510504i \(0.170541\pi\)
−0.859875 + 0.510504i \(0.829459\pi\)
\(128\) −127.983 + 2.11172i −0.999864 + 0.0164978i
\(129\) 0 0
\(130\) −95.2025 45.5710i −0.732327 0.350546i
\(131\) 118.504 118.504i 0.904613 0.904613i −0.0912183 0.995831i \(-0.529076\pi\)
0.995831 + 0.0912183i \(0.0290761\pi\)
\(132\) 0 0
\(133\) 19.5088 19.5088i 0.146683 0.146683i
\(134\) −4.37651 + 1.54299i −0.0326605 + 0.0115149i
\(135\) 0 0
\(136\) 26.7102 + 113.325i 0.196398 + 0.833273i
\(137\) 157.472i 1.14943i −0.818353 0.574716i \(-0.805112\pi\)
0.818353 0.574716i \(-0.194888\pi\)
\(138\) 0 0
\(139\) −118.943 118.943i −0.855703 0.855703i 0.135125 0.990829i \(-0.456856\pi\)
−0.990829 + 0.135125i \(0.956856\pi\)
\(140\) −144.019 15.5399i −1.02871 0.110999i
\(141\) 0 0
\(142\) −43.5021 20.8233i −0.306353 0.146643i
\(143\) 35.0288i 0.244957i
\(144\) 0 0
\(145\) 326.008 2.24833
\(146\) −9.30367 + 19.4363i −0.0637238 + 0.133125i
\(147\) 0 0
\(148\) 23.3036 + 2.51450i 0.157457 + 0.0169899i
\(149\) −99.5402 + 99.5402i −0.668055 + 0.668055i −0.957266 0.289210i \(-0.906607\pi\)
0.289210 + 0.957266i \(0.406607\pi\)
\(150\) 0 0
\(151\) 273.705 1.81262 0.906308 0.422618i \(-0.138889\pi\)
0.906308 + 0.422618i \(0.138889\pi\)
\(152\) 47.6097 + 29.4477i 0.313221 + 0.193735i
\(153\) 0 0
\(154\) −15.9848 45.3387i −0.103797 0.294407i
\(155\) −211.094 211.094i −1.36190 1.36190i
\(156\) 0 0
\(157\) −75.8792 75.8792i −0.483307 0.483307i 0.422879 0.906186i \(-0.361019\pi\)
−0.906186 + 0.422879i \(0.861019\pi\)
\(158\) 62.2180 129.980i 0.393785 0.822657i
\(159\) 0 0
\(160\) −36.3479 291.662i −0.227175 1.82288i
\(161\) 172.186 1.06948
\(162\) 0 0
\(163\) 177.242 177.242i 1.08737 1.08737i 0.0915766 0.995798i \(-0.470809\pi\)
0.995798 0.0915766i \(-0.0291906\pi\)
\(164\) 172.397 138.817i 1.05120 0.846444i
\(165\) 0 0
\(166\) −112.168 + 39.5462i −0.675710 + 0.238230i
\(167\) −61.6774 −0.369326 −0.184663 0.982802i \(-0.559119\pi\)
−0.184663 + 0.982802i \(0.559119\pi\)
\(168\) 0 0
\(169\) 135.987i 0.804658i
\(170\) −252.140 + 88.8950i −1.48317 + 0.522912i
\(171\) 0 0
\(172\) 9.78193 90.6560i 0.0568717 0.527069i
\(173\) −69.7012 69.7012i −0.402897 0.402897i 0.476355 0.879253i \(-0.341958\pi\)
−0.879253 + 0.476355i \(0.841958\pi\)
\(174\) 0 0
\(175\) 234.052i 1.33744i
\(176\) 82.1006 52.6733i 0.466481 0.299280i
\(177\) 0 0
\(178\) −25.0293 + 52.2888i −0.140614 + 0.293757i
\(179\) −43.6228 + 43.6228i −0.243703 + 0.243703i −0.818380 0.574677i \(-0.805128\pi\)
0.574677 + 0.818380i \(0.305128\pi\)
\(180\) 0 0
\(181\) −44.7291 + 44.7291i −0.247122 + 0.247122i −0.819788 0.572666i \(-0.805909\pi\)
0.572666 + 0.819788i \(0.305909\pi\)
\(182\) 15.0648 + 42.7294i 0.0827736 + 0.234777i
\(183\) 0 0
\(184\) 80.1494 + 340.056i 0.435595 + 1.84813i
\(185\) 53.8211i 0.290925i
\(186\) 0 0
\(187\) −62.7401 62.7401i −0.335509 0.335509i
\(188\) −24.6881 + 19.8792i −0.131320 + 0.105741i
\(189\) 0 0
\(190\) −55.5004 + 115.946i −0.292107 + 0.610242i
\(191\) 171.759i 0.899263i −0.893214 0.449632i \(-0.851555\pi\)
0.893214 0.449632i \(-0.148445\pi\)
\(192\) 0 0
\(193\) −215.384 −1.11598 −0.557989 0.829848i \(-0.688427\pi\)
−0.557989 + 0.829848i \(0.688427\pi\)
\(194\) −97.9016 46.8630i −0.504647 0.241562i
\(195\) 0 0
\(196\) −83.9274 104.230i −0.428201 0.531785i
\(197\) 18.3354 18.3354i 0.0930731 0.0930731i −0.659037 0.752110i \(-0.729036\pi\)
0.752110 + 0.659037i \(0.229036\pi\)
\(198\) 0 0
\(199\) −227.112 −1.14127 −0.570634 0.821205i \(-0.693302\pi\)
−0.570634 + 0.821205i \(0.693302\pi\)
\(200\) 462.238 108.947i 2.31119 0.544735i
\(201\) 0 0
\(202\) −152.268 + 53.6842i −0.753804 + 0.265763i
\(203\) −98.9542 98.9542i −0.487459 0.487459i
\(204\) 0 0
\(205\) 359.384 + 359.384i 1.75309 + 1.75309i
\(206\) 70.9051 + 33.9404i 0.344199 + 0.164759i
\(207\) 0 0
\(208\) −77.3755 + 49.6418i −0.371998 + 0.238663i
\(209\) −42.6612 −0.204120
\(210\) 0 0
\(211\) 190.206 190.206i 0.901451 0.901451i −0.0941112 0.995562i \(-0.530001\pi\)
0.995562 + 0.0941112i \(0.0300009\pi\)
\(212\) 177.583 + 19.1615i 0.837656 + 0.0903845i
\(213\) 0 0
\(214\) −24.1680 68.5496i −0.112935 0.320325i
\(215\) 209.375 0.973839
\(216\) 0 0
\(217\) 128.148i 0.590544i
\(218\) −9.08609 25.7716i −0.0416793 0.118218i
\(219\) 0 0
\(220\) 140.477 + 174.459i 0.638530 + 0.792994i
\(221\) 59.1293 + 59.1293i 0.267553 + 0.267553i
\(222\) 0 0
\(223\) 154.401i 0.692379i −0.938165 0.346190i \(-0.887475\pi\)
0.938165 0.346190i \(-0.112525\pi\)
\(224\) −77.4961 + 99.5617i −0.345965 + 0.444472i
\(225\) 0 0
\(226\) −115.983 55.5179i −0.513197 0.245654i
\(227\) 36.8204 36.8204i 0.162204 0.162204i −0.621338 0.783543i \(-0.713411\pi\)
0.783543 + 0.621338i \(0.213411\pi\)
\(228\) 0 0
\(229\) 17.9692 17.9692i 0.0784683 0.0784683i −0.666783 0.745252i \(-0.732329\pi\)
0.745252 + 0.666783i \(0.232329\pi\)
\(230\) −756.597 + 266.748i −3.28955 + 1.15977i
\(231\) 0 0
\(232\) 149.367 241.490i 0.643823 1.04090i
\(233\) 167.669i 0.719608i 0.933028 + 0.359804i \(0.117156\pi\)
−0.933028 + 0.359804i \(0.882844\pi\)
\(234\) 0 0
\(235\) −51.4655 51.4655i −0.219002 0.219002i
\(236\) −30.1715 + 279.620i −0.127845 + 1.18483i
\(237\) 0 0
\(238\) 103.515 + 49.5501i 0.434938 + 0.208194i
\(239\) 29.7509i 0.124481i 0.998061 + 0.0622403i \(0.0198245\pi\)
−0.998061 + 0.0622403i \(0.980175\pi\)
\(240\) 0 0
\(241\) −107.373 −0.445531 −0.222766 0.974872i \(-0.571508\pi\)
−0.222766 + 0.974872i \(0.571508\pi\)
\(242\) 72.3905 151.231i 0.299134 0.624923i
\(243\) 0 0
\(244\) −26.9878 + 250.115i −0.110606 + 1.02506i
\(245\) 217.280 217.280i 0.886859 0.886859i
\(246\) 0 0
\(247\) 40.2059 0.162777
\(248\) −253.084 + 59.6507i −1.02050 + 0.240527i
\(249\) 0 0
\(250\) 209.890 + 595.326i 0.839559 + 2.38130i
\(251\) 342.946 + 342.946i 1.36632 + 1.36632i 0.865623 + 0.500697i \(0.166923\pi\)
0.500697 + 0.865623i \(0.333077\pi\)
\(252\) 0 0
\(253\) −188.265 188.265i −0.744130 0.744130i
\(254\) −111.971 + 233.918i −0.440829 + 0.920938i
\(255\) 0 0
\(256\) −232.701 106.706i −0.908989 0.416819i
\(257\) 393.565 1.53138 0.765691 0.643209i \(-0.222397\pi\)
0.765691 + 0.643209i \(0.222397\pi\)
\(258\) 0 0
\(259\) 16.3365 16.3365i 0.0630753 0.0630753i
\(260\) −132.392 164.418i −0.509199 0.632377i
\(261\) 0 0
\(262\) 316.110 111.449i 1.20653 0.425376i
\(263\) −413.800 −1.57338 −0.786692 0.617346i \(-0.788208\pi\)
−0.786692 + 0.617346i \(0.788208\pi\)
\(264\) 0 0
\(265\) 410.139i 1.54769i
\(266\) 52.0396 18.3472i 0.195638 0.0689746i
\(267\) 0 0
\(268\) −9.22752 0.995666i −0.0344311 0.00371517i
\(269\) −165.389 165.389i −0.614830 0.614830i 0.329371 0.944201i \(-0.393163\pi\)
−0.944201 + 0.329371i \(0.893163\pi\)
\(270\) 0 0
\(271\) 309.821i 1.14325i 0.820514 + 0.571626i \(0.193687\pi\)
−0.820514 + 0.571626i \(0.806313\pi\)
\(272\) −49.6738 + 227.501i −0.182624 + 0.836400i
\(273\) 0 0
\(274\) 135.980 284.076i 0.496278 1.03678i
\(275\) −255.908 + 255.908i −0.930575 + 0.930575i
\(276\) 0 0
\(277\) 157.397 157.397i 0.568221 0.568221i −0.363409 0.931630i \(-0.618387\pi\)
0.931630 + 0.363409i \(0.118387\pi\)
\(278\) −111.861 317.279i −0.402377 1.14129i
\(279\) 0 0
\(280\) −246.388 152.396i −0.879956 0.544273i
\(281\) 411.141i 1.46313i 0.681769 + 0.731567i \(0.261211\pi\)
−0.681769 + 0.731567i \(0.738789\pi\)
\(282\) 0 0
\(283\) 343.521 + 343.521i 1.21385 + 1.21385i 0.969748 + 0.244106i \(0.0784946\pi\)
0.244106 + 0.969748i \(0.421505\pi\)
\(284\) −60.4955 75.1297i −0.213012 0.264541i
\(285\) 0 0
\(286\) 30.2480 63.1912i 0.105762 0.220948i
\(287\) 218.170i 0.760174i
\(288\) 0 0
\(289\) −77.1870 −0.267083
\(290\) 588.111 + 281.514i 2.02797 + 0.970737i
\(291\) 0 0
\(292\) −33.5672 + 27.0288i −0.114956 + 0.0925644i
\(293\) −35.1386 + 35.1386i −0.119927 + 0.119927i −0.764523 0.644596i \(-0.777025\pi\)
0.644596 + 0.764523i \(0.277025\pi\)
\(294\) 0 0
\(295\) −645.799 −2.18915
\(296\) 39.8679 + 24.6592i 0.134689 + 0.0833081i
\(297\) 0 0
\(298\) −265.523 + 93.6136i −0.891017 + 0.314140i
\(299\) 177.430 + 177.430i 0.593410 + 0.593410i
\(300\) 0 0
\(301\) −63.5524 63.5524i −0.211137 0.211137i
\(302\) 493.758 + 236.349i 1.63496 + 0.782613i
\(303\) 0 0
\(304\) 60.4582 + 94.2347i 0.198876 + 0.309983i
\(305\) −577.655 −1.89395
\(306\) 0 0
\(307\) −16.4432 + 16.4432i −0.0535609 + 0.0535609i −0.733380 0.679819i \(-0.762058\pi\)
0.679819 + 0.733380i \(0.262058\pi\)
\(308\) 10.3147 95.5932i 0.0334892 0.310368i
\(309\) 0 0
\(310\) −198.526 563.093i −0.640405 1.81643i
\(311\) −39.8016 −0.127980 −0.0639898 0.997951i \(-0.520382\pi\)
−0.0639898 + 0.997951i \(0.520382\pi\)
\(312\) 0 0
\(313\) 431.885i 1.37982i −0.723894 0.689911i \(-0.757649\pi\)
0.723894 0.689911i \(-0.242351\pi\)
\(314\) −71.3613 202.407i −0.227265 0.644610i
\(315\) 0 0
\(316\) 224.480 180.754i 0.710379 0.572007i
\(317\) −255.063 255.063i −0.804615 0.804615i 0.179198 0.983813i \(-0.442650\pi\)
−0.983813 + 0.179198i \(0.942650\pi\)
\(318\) 0 0
\(319\) 216.390i 0.678337i
\(320\) 186.284 557.538i 0.582138 1.74231i
\(321\) 0 0
\(322\) 310.619 + 148.685i 0.964656 + 0.461756i
\(323\) 72.0128 72.0128i 0.222950 0.222950i
\(324\) 0 0
\(325\) 241.180 241.180i 0.742092 0.742092i
\(326\) 472.792 166.689i 1.45028 0.511316i
\(327\) 0 0
\(328\) 430.872 101.554i 1.31363 0.309617i
\(329\) 31.2430i 0.0949635i
\(330\) 0 0
\(331\) 205.897 + 205.897i 0.622045 + 0.622045i 0.946054 0.324009i \(-0.105031\pi\)
−0.324009 + 0.946054i \(0.605031\pi\)
\(332\) −236.497 25.5185i −0.712341 0.0768628i
\(333\) 0 0
\(334\) −111.265 53.2596i −0.333128 0.159460i
\(335\) 21.3115i 0.0636165i
\(336\) 0 0
\(337\) 45.7312 0.135701 0.0678504 0.997696i \(-0.478386\pi\)
0.0678504 + 0.997696i \(0.478386\pi\)
\(338\) 117.427 245.318i 0.347418 0.725793i
\(339\) 0 0
\(340\) −531.617 57.3623i −1.56358 0.168713i
\(341\) 140.115 140.115i 0.410894 0.410894i
\(342\) 0 0
\(343\) −325.097 −0.947805
\(344\) 95.9294 155.094i 0.278865 0.450856i
\(345\) 0 0
\(346\) −65.5512 185.928i −0.189454 0.537363i
\(347\) −296.512 296.512i −0.854500 0.854500i 0.136183 0.990684i \(-0.456516\pi\)
−0.990684 + 0.136183i \(0.956516\pi\)
\(348\) 0 0
\(349\) −198.107 198.107i −0.567641 0.567641i 0.363826 0.931467i \(-0.381470\pi\)
−0.931467 + 0.363826i \(0.881470\pi\)
\(350\) 202.108 422.224i 0.577451 1.20636i
\(351\) 0 0
\(352\) 193.592 24.1261i 0.549977 0.0685402i
\(353\) −85.4490 −0.242065 −0.121033 0.992649i \(-0.538621\pi\)
−0.121033 + 0.992649i \(0.538621\pi\)
\(354\) 0 0
\(355\) 156.617 156.617i 0.441176 0.441176i
\(356\) −90.3046 + 72.7145i −0.253665 + 0.204254i
\(357\) 0 0
\(358\) −116.364 + 41.0255i −0.325038 + 0.114596i
\(359\) 302.214 0.841823 0.420911 0.907102i \(-0.361710\pi\)
0.420911 + 0.907102i \(0.361710\pi\)
\(360\) 0 0
\(361\) 312.034i 0.864359i
\(362\) −119.315 + 42.0659i −0.329599 + 0.116204i
\(363\) 0 0
\(364\) −9.72104 + 90.0916i −0.0267061 + 0.247504i
\(365\) −69.9751 69.9751i −0.191713 0.191713i
\(366\) 0 0
\(367\) 372.554i 1.01513i 0.861612 + 0.507567i \(0.169455\pi\)
−0.861612 + 0.507567i \(0.830545\pi\)
\(368\) −149.057 + 682.664i −0.405045 + 1.85507i
\(369\) 0 0
\(370\) −46.4755 + 97.0921i −0.125610 + 0.262411i
\(371\) 124.491 124.491i 0.335554 0.335554i
\(372\) 0 0
\(373\) −407.130 + 407.130i −1.09150 + 1.09150i −0.0961318 + 0.995369i \(0.530647\pi\)
−0.995369 + 0.0961318i \(0.969353\pi\)
\(374\) −59.0046 167.359i −0.157766 0.447484i
\(375\) 0 0
\(376\) −61.7029 + 14.5431i −0.164104 + 0.0386784i
\(377\) 203.936i 0.540944i
\(378\) 0 0
\(379\) −117.854 117.854i −0.310961 0.310961i 0.534321 0.845282i \(-0.320567\pi\)
−0.845282 + 0.534321i \(0.820567\pi\)
\(380\) −200.243 + 161.238i −0.526955 + 0.424312i
\(381\) 0 0
\(382\) 148.317 309.850i 0.388265 0.811126i
\(383\) 407.983i 1.06523i 0.846357 + 0.532615i \(0.178791\pi\)
−0.846357 + 0.532615i \(0.821209\pi\)
\(384\) 0 0
\(385\) 220.778 0.573450
\(386\) −388.548 185.988i −1.00660 0.481834i
\(387\) 0 0
\(388\) −136.145 169.080i −0.350890 0.435772i
\(389\) −458.508 + 458.508i −1.17868 + 1.17868i −0.198605 + 0.980080i \(0.563641\pi\)
−0.980080 + 0.198605i \(0.936359\pi\)
\(390\) 0 0
\(391\) 635.589 1.62555
\(392\) −61.3988 260.501i −0.156630 0.664544i
\(393\) 0 0
\(394\) 48.9096 17.2437i 0.124136 0.0437658i
\(395\) 467.956 + 467.956i 1.18470 + 1.18470i
\(396\) 0 0
\(397\) −259.865 259.865i −0.654573 0.654573i 0.299518 0.954091i \(-0.403174\pi\)
−0.954091 + 0.299518i \(0.903174\pi\)
\(398\) −409.705 196.115i −1.02941 0.492752i
\(399\) 0 0
\(400\) 927.944 + 202.613i 2.31986 + 0.506531i
\(401\) 499.197 1.24488 0.622441 0.782667i \(-0.286141\pi\)
0.622441 + 0.782667i \(0.286141\pi\)
\(402\) 0 0
\(403\) −132.051 + 132.051i −0.327670 + 0.327670i
\(404\) −321.046 34.6414i −0.794668 0.0857461i
\(405\) 0 0
\(406\) −93.0624 263.960i −0.229218 0.650147i
\(407\) −35.7241 −0.0877741
\(408\) 0 0
\(409\) 494.949i 1.21014i 0.796171 + 0.605072i \(0.206856\pi\)
−0.796171 + 0.605072i \(0.793144\pi\)
\(410\) 337.986 + 958.656i 0.824357 + 2.33819i
\(411\) 0 0
\(412\) 98.6030 + 122.456i 0.239328 + 0.297222i
\(413\) 196.021 + 196.021i 0.474628 + 0.474628i
\(414\) 0 0
\(415\) 546.205i 1.31616i
\(416\) −182.450 + 22.7376i −0.438582 + 0.0546577i
\(417\) 0 0
\(418\) −76.9598 36.8387i −0.184114 0.0881308i
\(419\) 560.555 560.555i 1.33784 1.33784i 0.439693 0.898148i \(-0.355087\pi\)
0.898148 0.439693i \(-0.144913\pi\)
\(420\) 0 0
\(421\) 397.946 397.946i 0.945239 0.945239i −0.0533373 0.998577i \(-0.516986\pi\)
0.998577 + 0.0533373i \(0.0169858\pi\)
\(422\) 507.374 178.881i 1.20231 0.423889i
\(423\) 0 0
\(424\) 303.810 + 187.913i 0.716532 + 0.443191i
\(425\) 863.956i 2.03284i
\(426\) 0 0
\(427\) 175.337 + 175.337i 0.410626 + 0.410626i
\(428\) 15.5952 144.531i 0.0364374 0.337690i
\(429\) 0 0
\(430\) 377.709 + 180.799i 0.878392 + 0.420464i
\(431\) 662.874i 1.53799i 0.639255 + 0.768995i \(0.279243\pi\)
−0.639255 + 0.768995i \(0.720757\pi\)
\(432\) 0 0
\(433\) −338.800 −0.782448 −0.391224 0.920296i \(-0.627948\pi\)
−0.391224 + 0.920296i \(0.627948\pi\)
\(434\) −110.658 + 231.176i −0.254973 + 0.532664i
\(435\) 0 0
\(436\) 5.86309 54.3373i 0.0134475 0.124627i
\(437\) 216.090 216.090i 0.494484 0.494484i
\(438\) 0 0
\(439\) −234.566 −0.534319 −0.267160 0.963652i \(-0.586085\pi\)
−0.267160 + 0.963652i \(0.586085\pi\)
\(440\) 102.768 + 436.024i 0.233565 + 0.990963i
\(441\) 0 0
\(442\) 55.6087 + 157.727i 0.125812 + 0.356849i
\(443\) −421.096 421.096i −0.950555 0.950555i 0.0482792 0.998834i \(-0.484626\pi\)
−0.998834 + 0.0482792i \(0.984626\pi\)
\(444\) 0 0
\(445\) −188.251 188.251i −0.423037 0.423037i
\(446\) 133.328 278.535i 0.298941 0.624518i
\(447\) 0 0
\(448\) −225.775 + 112.688i −0.503961 + 0.251535i
\(449\) −492.636 −1.09718 −0.548592 0.836090i \(-0.684836\pi\)
−0.548592 + 0.836090i \(0.684836\pi\)
\(450\) 0 0
\(451\) −238.543 + 238.543i −0.528921 + 0.528921i
\(452\) −161.289 200.306i −0.356835 0.443155i
\(453\) 0 0
\(454\) 98.2182 34.6281i 0.216340 0.0762733i
\(455\) −208.072 −0.457301
\(456\) 0 0
\(457\) 516.831i 1.13092i 0.824775 + 0.565461i \(0.191302\pi\)
−0.824775 + 0.565461i \(0.808698\pi\)
\(458\) 47.9329 16.8994i 0.104657 0.0368981i
\(459\) 0 0
\(460\) −1595.23 172.128i −3.46788 0.374191i
\(461\) 27.5260 + 27.5260i 0.0597093 + 0.0597093i 0.736331 0.676622i \(-0.236557\pi\)
−0.676622 + 0.736331i \(0.736557\pi\)
\(462\) 0 0
\(463\) 122.111i 0.263740i −0.991267 0.131870i \(-0.957902\pi\)
0.991267 0.131870i \(-0.0420981\pi\)
\(464\) 477.985 306.661i 1.03014 0.660908i
\(465\) 0 0
\(466\) −144.785 + 302.471i −0.310697 + 0.649079i
\(467\) −267.964 + 267.964i −0.573798 + 0.573798i −0.933188 0.359390i \(-0.882985\pi\)
0.359390 + 0.933188i \(0.382985\pi\)
\(468\) 0 0
\(469\) −6.46875 + 6.46875i −0.0137926 + 0.0137926i
\(470\) −48.4013 137.284i −0.102981 0.292094i
\(471\) 0 0
\(472\) −295.886 + 478.375i −0.626876 + 1.01351i
\(473\) 138.974i 0.293814i
\(474\) 0 0
\(475\) −293.730 293.730i −0.618380 0.618380i
\(476\) 143.952 + 178.775i 0.302420 + 0.375577i
\(477\) 0 0
\(478\) −25.6904 + 53.6699i −0.0537456 + 0.112280i
\(479\) 419.084i 0.874915i 0.899239 + 0.437457i \(0.144121\pi\)
−0.899239 + 0.437457i \(0.855879\pi\)
\(480\) 0 0
\(481\) 33.6681 0.0699960
\(482\) −193.699 92.7186i −0.401864 0.192362i
\(483\) 0 0
\(484\) 261.182 210.307i 0.539632 0.434519i
\(485\) 352.468 352.468i 0.726738 0.726738i
\(486\) 0 0
\(487\) −57.2378 −0.117531 −0.0587657 0.998272i \(-0.518716\pi\)
−0.0587657 + 0.998272i \(0.518716\pi\)
\(488\) −264.664 + 427.897i −0.542344 + 0.876838i
\(489\) 0 0
\(490\) 579.595 204.344i 1.18285 0.417028i
\(491\) 301.955 + 301.955i 0.614979 + 0.614979i 0.944239 0.329260i \(-0.106799\pi\)
−0.329260 + 0.944239i \(0.606799\pi\)
\(492\) 0 0
\(493\) −365.270 365.270i −0.740912 0.740912i
\(494\) 72.5306 + 34.7185i 0.146823 + 0.0702804i
\(495\) 0 0
\(496\) −508.068 110.934i −1.02433 0.223658i
\(497\) −95.0771 −0.191302
\(498\) 0 0
\(499\) 619.990 619.990i 1.24247 1.24247i 0.283491 0.958975i \(-0.408507\pi\)
0.958975 0.283491i \(-0.0914925\pi\)
\(500\) −135.438 + 1255.20i −0.270876 + 2.51040i
\(501\) 0 0
\(502\) 322.527 + 914.808i 0.642484 + 1.82233i
\(503\) −222.446 −0.442239 −0.221120 0.975247i \(-0.570971\pi\)
−0.221120 + 0.975247i \(0.570971\pi\)
\(504\) 0 0
\(505\) 741.475i 1.46827i
\(506\) −177.056 502.196i −0.349912 0.992482i
\(507\) 0 0
\(508\) −403.985 + 325.295i −0.795246 + 0.640344i
\(509\) −489.873 489.873i −0.962421 0.962421i 0.0368976 0.999319i \(-0.488252\pi\)
−0.999319 + 0.0368976i \(0.988252\pi\)
\(510\) 0 0
\(511\) 42.4795i 0.0831302i
\(512\) −327.646 393.437i −0.639933 0.768431i
\(513\) 0 0
\(514\) 709.983 + 339.850i 1.38129 + 0.661188i
\(515\) −255.274 + 255.274i −0.495678 + 0.495678i
\(516\) 0 0
\(517\) 34.1605 34.1605i 0.0660745 0.0660745i
\(518\) 43.5775 15.3638i 0.0841265 0.0296599i
\(519\) 0 0
\(520\) −96.8539 410.929i −0.186257 0.790249i
\(521\) 197.152i 0.378412i 0.981937 + 0.189206i \(0.0605913\pi\)
−0.981937 + 0.189206i \(0.939409\pi\)
\(522\) 0 0
\(523\) 621.874 + 621.874i 1.18905 + 1.18905i 0.977330 + 0.211721i \(0.0679067\pi\)
0.211721 + 0.977330i \(0.432093\pi\)
\(524\) 666.493 + 71.9157i 1.27193 + 0.137244i
\(525\) 0 0
\(526\) −746.486 357.324i −1.41918 0.679323i
\(527\) 473.033i 0.897596i
\(528\) 0 0
\(529\) 1378.22 2.60533
\(530\) −354.162 + 739.881i −0.668231 + 1.39600i
\(531\) 0 0
\(532\) 109.722 + 11.8391i 0.206243 + 0.0222540i
\(533\) 224.815 224.815i 0.421791 0.421791i
\(534\) 0 0
\(535\) 333.804 0.623933
\(536\) −15.7865 9.76429i −0.0294524 0.0182170i
\(537\) 0 0
\(538\) −155.542 441.175i −0.289111 0.820028i
\(539\) 144.221 + 144.221i 0.267572 + 0.267572i
\(540\) 0 0
\(541\) 423.563 + 423.563i 0.782925 + 0.782925i 0.980323 0.197398i \(-0.0632492\pi\)
−0.197398 + 0.980323i \(0.563249\pi\)
\(542\) −267.536 + 558.911i −0.493609 + 1.03120i
\(543\) 0 0
\(544\) −286.062 + 367.512i −0.525848 + 0.675574i
\(545\) 125.495 0.230267
\(546\) 0 0
\(547\) −14.5553 + 14.5553i −0.0266093 + 0.0266093i −0.720286 0.693677i \(-0.755990\pi\)
0.693677 + 0.720286i \(0.255990\pi\)
\(548\) 490.610 395.046i 0.895274 0.720888i
\(549\) 0 0
\(550\) −682.634 + 240.671i −1.24115 + 0.437584i
\(551\) −248.371 −0.450764
\(552\) 0 0
\(553\) 284.080i 0.513708i
\(554\) 419.856 148.026i 0.757863 0.267194i
\(555\) 0 0
\(556\) 72.1818 668.959i 0.129823 1.20316i
\(557\) 351.991 + 351.991i 0.631941 + 0.631941i 0.948554 0.316614i \(-0.102546\pi\)
−0.316614 + 0.948554i \(0.602546\pi\)
\(558\) 0 0
\(559\) 130.976i 0.234304i
\(560\) −312.881 487.680i −0.558716 0.870857i
\(561\) 0 0
\(562\) −355.027 + 741.689i −0.631721 + 1.31973i
\(563\) 150.902 150.902i 0.268031 0.268031i −0.560275 0.828307i \(-0.689305\pi\)
0.828307 + 0.560275i \(0.189305\pi\)
\(564\) 0 0
\(565\) 417.563 417.563i 0.739050 0.739050i
\(566\) 323.068 + 916.341i 0.570791 + 1.61898i
\(567\) 0 0
\(568\) −44.2567 187.771i −0.0779168 0.330583i
\(569\) 113.300i 0.199121i 0.995032 + 0.0995603i \(0.0317436\pi\)
−0.995032 + 0.0995603i \(0.968256\pi\)
\(570\) 0 0
\(571\) −207.486 207.486i −0.363373 0.363373i 0.501680 0.865053i \(-0.332715\pi\)
−0.865053 + 0.501680i \(0.832715\pi\)
\(572\) 109.133 87.8758i 0.190793 0.153629i
\(573\) 0 0
\(574\) 188.394 393.574i 0.328212 0.685669i
\(575\) 2592.48i 4.50866i
\(576\) 0 0
\(577\) −484.715 −0.840061 −0.420031 0.907510i \(-0.637981\pi\)
−0.420031 + 0.907510i \(0.637981\pi\)
\(578\) −139.244 66.6524i −0.240906 0.115316i
\(579\) 0 0
\(580\) 817.847 + 1015.69i 1.41008 + 1.75119i
\(581\) −165.791 + 165.791i −0.285355 + 0.285355i
\(582\) 0 0
\(583\) −272.232 −0.466950
\(584\) −83.8944 + 19.7735i −0.143655 + 0.0338587i
\(585\) 0 0
\(586\) −93.7320 + 33.0464i −0.159952 + 0.0563932i
\(587\) 540.404 + 540.404i 0.920619 + 0.920619i 0.997073 0.0764537i \(-0.0243597\pi\)
−0.0764537 + 0.997073i \(0.524360\pi\)
\(588\) 0 0
\(589\) 160.823 + 160.823i 0.273045 + 0.273045i
\(590\) −1165.01 557.659i −1.97459 0.945185i
\(591\) 0 0
\(592\) 50.6272 + 78.9113i 0.0855189 + 0.133296i
\(593\) −411.176 −0.693383 −0.346692 0.937979i \(-0.612695\pi\)
−0.346692 + 0.937979i \(0.612695\pi\)
\(594\) 0 0
\(595\) −372.678 + 372.678i −0.626350 + 0.626350i
\(596\) −559.835 60.4072i −0.939320 0.101354i
\(597\) 0 0
\(598\) 166.866 + 473.293i 0.279039 + 0.791460i
\(599\) 552.839 0.922936 0.461468 0.887157i \(-0.347323\pi\)
0.461468 + 0.887157i \(0.347323\pi\)
\(600\) 0 0
\(601\) 881.159i 1.46615i 0.680145 + 0.733077i \(0.261917\pi\)
−0.680145 + 0.733077i \(0.738083\pi\)
\(602\) −59.7684 169.526i −0.0992831 0.281604i
\(603\) 0 0
\(604\) 686.637 + 852.738i 1.13682 + 1.41182i
\(605\) 544.467 + 544.467i 0.899945 + 0.899945i
\(606\) 0 0
\(607\) 1175.08i 1.93588i −0.251186 0.967939i \(-0.580820\pi\)
0.251186 0.967939i \(-0.419180\pi\)
\(608\) 27.6919 + 222.204i 0.0455459 + 0.365467i
\(609\) 0 0
\(610\) −1042.08 498.816i −1.70832 0.817731i
\(611\) −32.1945 + 32.1945i −0.0526915 + 0.0526915i
\(612\) 0 0
\(613\) −496.928 + 496.928i −0.810649 + 0.810649i −0.984731 0.174082i \(-0.944304\pi\)
0.174082 + 0.984731i \(0.444304\pi\)
\(614\) −43.8622 + 15.4642i −0.0714367 + 0.0251859i
\(615\) 0 0
\(616\) 101.154 163.541i 0.164211 0.265489i
\(617\) 623.301i 1.01021i 0.863057 + 0.505106i \(0.168547\pi\)
−0.863057 + 0.505106i \(0.831453\pi\)
\(618\) 0 0
\(619\) 7.45302 + 7.45302i 0.0120404 + 0.0120404i 0.713101 0.701061i \(-0.247290\pi\)
−0.701061 + 0.713101i \(0.747290\pi\)
\(620\) 128.105 1187.24i 0.206621 1.91490i
\(621\) 0 0
\(622\) −71.8013 34.3694i −0.115436 0.0552563i
\(623\) 114.281i 0.183437i
\(624\) 0 0
\(625\) −1414.88 −2.26381
\(626\) 372.940 779.110i 0.595751 1.24458i
\(627\) 0 0
\(628\) 46.0482 426.760i 0.0733251 0.679555i
\(629\) 60.3029 60.3029i 0.0958711 0.0958711i
\(630\) 0 0
\(631\) 147.833 0.234284 0.117142 0.993115i \(-0.462627\pi\)
0.117142 + 0.993115i \(0.462627\pi\)
\(632\) 561.041 132.234i 0.887723 0.209232i
\(633\) 0 0
\(634\) −239.877 680.379i −0.378354 1.07315i
\(635\) −842.158 842.158i −1.32623 1.32623i
\(636\) 0 0
\(637\) −135.921 135.921i −0.213376 0.213376i
\(638\) −186.856 + 390.362i −0.292878 + 0.611853i
\(639\) 0 0
\(640\) 817.497 844.927i 1.27734 1.32020i
\(641\) 782.691 1.22105 0.610523 0.791998i \(-0.290959\pi\)
0.610523 + 0.791998i \(0.290959\pi\)
\(642\) 0 0
\(643\) 126.760 126.760i 0.197138 0.197138i −0.601634 0.798772i \(-0.705483\pi\)
0.798772 + 0.601634i \(0.205483\pi\)
\(644\) 431.958 + 536.450i 0.670741 + 0.832998i
\(645\) 0 0
\(646\) 192.094 67.7252i 0.297359 0.104838i
\(647\) −1226.09 −1.89504 −0.947520 0.319697i \(-0.896419\pi\)
−0.947520 + 0.319697i \(0.896419\pi\)
\(648\) 0 0
\(649\) 428.653i 0.660482i
\(650\) 643.347 226.820i 0.989764 0.348954i
\(651\) 0 0
\(652\) 996.846 + 107.561i 1.52891 + 0.164972i
\(653\) −326.300 326.300i −0.499694 0.499694i 0.411649 0.911343i \(-0.364953\pi\)
−0.911343 + 0.411649i \(0.864953\pi\)
\(654\) 0 0
\(655\) 1539.31i 2.35008i
\(656\) 864.978 + 188.864i 1.31856 + 0.287903i
\(657\) 0 0
\(658\) −26.9789 + 56.3616i −0.0410013 + 0.0856560i
\(659\) 574.901 574.901i 0.872384 0.872384i −0.120347 0.992732i \(-0.538401\pi\)
0.992732 + 0.120347i \(0.0384009\pi\)
\(660\) 0 0
\(661\) 52.8795 52.8795i 0.0799993 0.0799993i −0.665975 0.745974i \(-0.731984\pi\)
0.745974 + 0.665975i \(0.231984\pi\)
\(662\) 193.638 + 549.229i 0.292504 + 0.829651i
\(663\) 0 0
\(664\) −404.600 250.254i −0.609338 0.376889i
\(665\) 253.409i 0.381065i
\(666\) 0 0
\(667\) −1096.07 1096.07i −1.64328 1.64328i
\(668\) −154.729 192.158i −0.231630 0.287662i
\(669\) 0 0
\(670\) 18.4029 38.4455i 0.0274670 0.0573814i
\(671\) 383.422i 0.571419i
\(672\) 0 0
\(673\) 342.318 0.508645 0.254322 0.967119i \(-0.418148\pi\)
0.254322 + 0.967119i \(0.418148\pi\)
\(674\) 82.4981 + 39.4897i 0.122401 + 0.0585901i
\(675\) 0 0
\(676\) 423.673 341.147i 0.626735 0.504656i
\(677\) −107.154 + 107.154i −0.158278 + 0.158278i −0.781803 0.623525i \(-0.785700\pi\)
0.623525 + 0.781803i \(0.285700\pi\)
\(678\) 0 0
\(679\) −213.971 −0.315127
\(680\) −909.491 562.541i −1.33749 0.827266i
\(681\) 0 0
\(682\) 373.756 131.772i 0.548029 0.193215i
\(683\) −724.233 724.233i −1.06037 1.06037i −0.998057 0.0623142i \(-0.980152\pi\)
−0.0623142 0.998057i \(-0.519848\pi\)
\(684\) 0 0
\(685\) 1022.74 + 1022.74i 1.49305 + 1.49305i
\(686\) −586.468 280.727i −0.854910 0.409223i
\(687\) 0 0
\(688\) 306.981 196.950i 0.446194 0.286265i
\(689\) 256.564 0.372372
\(690\) 0 0
\(691\) 162.528 162.528i 0.235207 0.235207i −0.579655 0.814862i \(-0.696813\pi\)
0.814862 + 0.579655i \(0.196813\pi\)
\(692\) 42.2990 392.014i 0.0611257 0.566495i
\(693\) 0 0
\(694\) −278.857 790.943i −0.401812 1.13969i
\(695\) 1545.00 2.22302
\(696\) 0 0
\(697\) 805.331i 1.15543i
\(698\) −186.312 528.449i −0.266922 0.757090i
\(699\) 0 0
\(700\) 729.197 587.159i 1.04171 0.838799i
\(701\) 301.659 + 301.659i 0.430327 + 0.430327i 0.888740 0.458412i \(-0.151582\pi\)
−0.458412 + 0.888740i \(0.651582\pi\)
\(702\) 0 0
\(703\) 41.0040i 0.0583271i
\(704\) 370.069 + 123.647i 0.525666 + 0.175635i
\(705\) 0 0
\(706\) −154.148 73.7867i −0.218340 0.104514i
\(707\) −225.062 + 225.062i −0.318334 + 0.318334i
\(708\) 0 0
\(709\) −629.100 + 629.100i −0.887306 + 0.887306i −0.994264 0.106958i \(-0.965889\pi\)
0.106958 + 0.994264i \(0.465889\pi\)
\(710\) 417.776 147.292i 0.588417 0.207454i
\(711\) 0 0
\(712\) −225.698 + 53.1958i −0.316991 + 0.0747132i
\(713\) 1419.43i 1.99079i
\(714\) 0 0
\(715\) 227.502 + 227.502i 0.318185 + 0.318185i
\(716\) −245.344 26.4730i −0.342659 0.0369735i
\(717\) 0 0
\(718\) 545.188 + 260.968i 0.759315 + 0.363465i
\(719\) 145.542i 0.202422i −0.994865 0.101211i \(-0.967728\pi\)
0.994865 0.101211i \(-0.0322718\pi\)
\(720\) 0 0
\(721\) 154.968 0.214935
\(722\) −269.447 + 562.902i −0.373195 + 0.779643i
\(723\) 0 0
\(724\) −251.566 27.1444i −0.347466 0.0374922i
\(725\) −1489.88 + 1489.88i −2.05501 + 2.05501i
\(726\) 0 0
\(727\) −938.214 −1.29053 −0.645264 0.763960i \(-0.723253\pi\)
−0.645264 + 0.763960i \(0.723253\pi\)
\(728\) −95.3322 + 154.129i −0.130951 + 0.211716i
\(729\) 0 0
\(730\) −65.8088 186.658i −0.0901490 0.255696i
\(731\) −234.591 234.591i −0.320918 0.320918i
\(732\) 0 0
\(733\) 692.101 + 692.101i 0.944203 + 0.944203i 0.998524 0.0543203i \(-0.0172992\pi\)
−0.0543203 + 0.998524i \(0.517299\pi\)
\(734\) −321.707 + 672.080i −0.438294 + 0.915640i
\(735\) 0 0
\(736\) −858.388 + 1102.80i −1.16629 + 1.49837i
\(737\) 14.1456 0.0191935
\(738\) 0 0
\(739\) −440.389 + 440.389i −0.595926 + 0.595926i −0.939226 0.343300i \(-0.888455\pi\)
0.343300 + 0.939226i \(0.388455\pi\)
\(740\) −167.682 + 135.020i −0.226597 + 0.182459i
\(741\) 0 0
\(742\) 332.078 117.078i 0.447545 0.157788i
\(743\) 1010.54 1.36008 0.680039 0.733176i \(-0.261963\pi\)
0.680039 + 0.733176i \(0.261963\pi\)
\(744\) 0 0
\(745\) 1292.97i 1.73553i
\(746\) −1086.02 + 382.889i −1.45579 + 0.513256i
\(747\) 0 0
\(748\) 38.0746 352.863i 0.0509018 0.471743i
\(749\) −101.321 101.321i −0.135275 0.135275i
\(750\) 0 0
\(751\) 776.971i 1.03458i 0.855810 + 0.517291i \(0.173060\pi\)
−0.855810 + 0.517291i \(0.826940\pi\)
\(752\) −123.869 27.0462i −0.164719 0.0359657i
\(753\) 0 0
\(754\) 176.102 367.896i 0.233557 0.487925i
\(755\) −1777.64 + 1777.64i −2.35449 + 2.35449i
\(756\) 0 0
\(757\) 375.481 375.481i 0.496012 0.496012i −0.414182 0.910194i \(-0.635932\pi\)
0.910194 + 0.414182i \(0.135932\pi\)
\(758\) −110.837 314.376i −0.146223 0.414744i
\(759\) 0 0
\(760\) −500.466 + 117.957i −0.658508 + 0.155207i
\(761\) 1502.22i 1.97400i −0.160711 0.987001i \(-0.551379\pi\)
0.160711 0.987001i \(-0.448621\pi\)
\(762\) 0 0
\(763\) −38.0920 38.0920i −0.0499239 0.0499239i
\(764\) 535.122 430.888i 0.700421 0.563989i
\(765\) 0 0
\(766\) −352.301 + 735.993i −0.459923 + 0.960827i
\(767\) 403.983i 0.526705i
\(768\) 0 0
\(769\) −293.930 −0.382223 −0.191112 0.981568i \(-0.561209\pi\)
−0.191112 + 0.981568i \(0.561209\pi\)
\(770\) 398.279 + 190.646i 0.517246 + 0.247592i
\(771\) 0 0
\(772\) −540.328 671.036i −0.699906 0.869218i
\(773\) 748.271 748.271i 0.968009 0.968009i −0.0314945 0.999504i \(-0.510027\pi\)
0.999504 + 0.0314945i \(0.0100267\pi\)
\(774\) 0 0
\(775\) 1929.44 2.48960
\(776\) −99.5999 422.580i −0.128350 0.544562i
\(777\) 0 0
\(778\) −1223.07 + 431.209i −1.57207 + 0.554253i
\(779\) −273.799 273.799i −0.351475 0.351475i
\(780\) 0 0
\(781\) 103.956 + 103.956i 0.133106 + 0.133106i
\(782\) 1146.59 + 548.843i 1.46623 + 0.701845i
\(783\) 0 0
\(784\) 114.185 522.958i 0.145645 0.667038i
\(785\) 985.629 1.25558
\(786\) 0 0
\(787\) −735.839 + 735.839i −0.934992 + 0.934992i