Properties

Label 48.3.l.a.19.2
Level 48
Weight 3
Character 48.19
Analytic conductor 1.308
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.2
Root \(1.80398 - 0.863518i\) of defining polynomial
Character \(\chi\) \(=\) 48.19
Dual form 48.3.l.a.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.80398 - 0.863518i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(2.50867 + 3.11554i) q^{4} +(6.49473 - 6.49473i) q^{5} +(3.26700 - 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 - 7.78664i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.80398 - 0.863518i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(2.50867 + 3.11554i) q^{4} +(6.49473 - 6.49473i) q^{5} +(3.26700 - 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 - 7.78664i) q^{8} -3.00000i q^{9} +(-17.3247 + 6.10803i) q^{10} +(4.31091 + 4.31091i) q^{11} +(-6.88822 - 0.743251i) q^{12} +(4.06281 + 4.06281i) q^{13} +(-7.11259 - 3.40462i) q^{14} +15.9088i q^{15} +(-3.41312 + 15.6317i) q^{16} -14.5538 q^{17} +(-2.59055 + 5.41193i) q^{18} +(4.94805 - 4.94805i) q^{19} +(36.5277 + 3.94140i) q^{20} +(-4.82883 + 4.82883i) q^{21} +(-4.05424 - 11.4993i) q^{22} -43.6717 q^{23} +(11.7844 + 7.28891i) q^{24} -59.3629i q^{25} +(-3.82091 - 10.8375i) q^{26} +(3.67423 + 3.67423i) q^{27} +(9.89101 + 12.2837i) q^{28} +(25.0979 + 25.0979i) q^{29} +(13.7375 - 28.6991i) q^{30} +32.5024i q^{31} +(19.6555 - 25.2520i) q^{32} -10.5595 q^{33} +(26.2547 + 12.5675i) q^{34} +(25.6069 - 25.6069i) q^{35} +(9.34661 - 7.52602i) q^{36} +(4.14345 - 4.14345i) q^{37} +(-13.1989 + 4.65344i) q^{38} -9.95180 q^{39} +(-62.4917 - 38.6525i) q^{40} +55.3348i q^{41} +(12.8809 - 4.54133i) q^{42} +(-16.1189 - 16.1189i) q^{43} +(-2.61613 + 24.2455i) q^{44} +(-19.4842 - 19.4842i) q^{45} +(78.7828 + 37.7113i) q^{46} -7.92420i q^{47} +(-14.9647 - 23.3251i) q^{48} -33.4549 q^{49} +(-51.2610 + 107.089i) q^{50} +(17.8247 - 17.8247i) q^{51} +(-2.46556 + 22.8501i) q^{52} +(-31.5748 + 31.5748i) q^{53} +(-3.45547 - 9.80101i) q^{54} +55.9964 q^{55} +(-7.23597 - 30.7006i) q^{56} +12.1202i q^{57} +(-23.6036 - 66.9485i) q^{58} +(-49.7172 - 49.7172i) q^{59} +(-49.5643 + 39.9099i) q^{60} +(44.4711 + 44.4711i) q^{61} +(28.0664 - 58.6336i) q^{62} -11.8282i q^{63} +(-57.2636 + 28.5812i) q^{64} +52.7736 q^{65} +(19.0492 + 9.11834i) q^{66} +(-1.64068 + 1.64068i) q^{67} +(-36.5107 - 45.3429i) q^{68} +(53.4867 - 53.4867i) q^{69} +(-68.3064 + 24.0823i) q^{70} +24.1145 q^{71} +(-23.3599 + 5.50581i) q^{72} +10.7741i q^{73} +(-11.0526 + 3.89675i) q^{74} +(72.7044 + 72.7044i) q^{75} +(27.8288 + 3.00278i) q^{76} +(16.9967 + 16.9967i) q^{77} +(17.9528 + 8.59356i) q^{78} -72.0517i q^{79} +(79.3565 + 123.691i) q^{80} -9.00000 q^{81} +(47.7826 - 99.8227i) q^{82} +(42.0499 - 42.0499i) q^{83} +(-27.1584 - 2.93044i) q^{84} +(-94.5229 + 94.5229i) q^{85} +(15.1592 + 42.9971i) q^{86} -61.4770 q^{87} +(25.6558 - 41.4792i) q^{88} -28.9853i q^{89} +(18.3241 + 51.9740i) q^{90} +(16.0185 + 16.0185i) q^{91} +(-109.558 - 136.061i) q^{92} +(-39.8071 - 39.8071i) q^{93} +(-6.84269 + 14.2951i) q^{94} -64.2724i q^{95} +(6.85432 + 55.0002i) q^{96} -54.2698 q^{97} +(60.3519 + 28.8889i) q^{98} +(12.9327 - 12.9327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80398 0.863518i −0.901989 0.431759i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.50867 + 3.11554i 0.627168 + 0.778884i
\(5\) 6.49473 6.49473i 1.29895 1.29895i 0.369856 0.929089i \(-0.379407\pi\)
0.929089 0.369856i \(-0.120593\pi\)
\(6\) 3.26700 1.15182i 0.544500 0.191971i
\(7\) 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
\(9\) 3.00000i 0.333333i
\(10\) −17.3247 + 6.10803i −1.73247 + 0.610803i
\(11\) 4.31091 + 4.31091i 0.391901 + 0.391901i 0.875364 0.483464i \(-0.160621\pi\)
−0.483464 + 0.875364i \(0.660621\pi\)
\(12\) −6.88822 0.743251i −0.574018 0.0619376i
\(13\) 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
\(15\) 15.9088i 1.06058i
\(16\) −3.41312 + 15.6317i −0.213320 + 0.976982i
\(17\) −14.5538 −0.856106 −0.428053 0.903754i \(-0.640800\pi\)
−0.428053 + 0.903754i \(0.640800\pi\)
\(18\) −2.59055 + 5.41193i −0.143920 + 0.300663i
\(19\) 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
\(21\) −4.82883 + 4.82883i −0.229945 + 0.229945i
\(22\) −4.05424 11.4993i −0.184284 0.522697i
\(23\) −43.6717 −1.89877 −0.949385 0.314115i \(-0.898292\pi\)
−0.949385 + 0.314115i \(0.898292\pi\)
\(24\) 11.7844 + 7.28891i 0.491016 + 0.303705i
\(25\) 59.3629i 2.37452i
\(26\) −3.82091 10.8375i −0.146958 0.416828i
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 9.89101 + 12.2837i 0.353250 + 0.438704i
\(29\) 25.0979 + 25.0979i 0.865445 + 0.865445i 0.991964 0.126519i \(-0.0403806\pi\)
−0.126519 + 0.991964i \(0.540381\pi\)
\(30\) 13.7375 28.6991i 0.457917 0.956635i
\(31\) 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
\(33\) −10.5595 −0.319986
\(34\) 26.2547 + 12.5675i 0.772198 + 0.369631i
\(35\) 25.6069 25.6069i 0.731627 0.731627i
\(36\) 9.34661 7.52602i 0.259628 0.209056i
\(37\) 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
\(39\) −9.95180 −0.255174
\(40\) −62.4917 38.6525i −1.56229 0.966313i
\(41\) 55.3348i 1.34963i 0.737987 + 0.674814i \(0.235776\pi\)
−0.737987 + 0.674814i \(0.764224\pi\)
\(42\) 12.8809 4.54133i 0.306688 0.108127i
\(43\) −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
\(45\) −19.4842 19.4842i −0.432982 0.432982i
\(46\) 78.7828 + 37.7113i 1.71267 + 0.819811i
\(47\) 7.92420i 0.168600i −0.996440 0.0843001i \(-0.973135\pi\)
0.996440 0.0843001i \(-0.0268654\pi\)
\(48\) −14.9647 23.3251i −0.311764 0.485939i
\(49\) −33.4549 −0.682753
\(50\) −51.2610 + 107.089i −1.02522 + 2.14179i
\(51\) 17.8247 17.8247i 0.349504 0.349504i
\(52\) −2.46556 + 22.8501i −0.0474147 + 0.439424i
\(53\) −31.5748 + 31.5748i −0.595750 + 0.595750i −0.939179 0.343429i \(-0.888412\pi\)
0.343429 + 0.939179i \(0.388412\pi\)
\(54\) −3.45547 9.80101i −0.0639902 0.181500i
\(55\) 55.9964 1.01812
\(56\) −7.23597 30.7006i −0.129214 0.548225i
\(57\) 12.1202i 0.212635i
\(58\) −23.6036 66.9485i −0.406958 1.15429i
\(59\) −49.7172 49.7172i −0.842665 0.842665i 0.146540 0.989205i \(-0.453186\pi\)
−0.989205 + 0.146540i \(0.953186\pi\)
\(60\) −49.5643 + 39.9099i −0.826072 + 0.665165i
\(61\) 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
\(63\) 11.8282i 0.187749i
\(64\) −57.2636 + 28.5812i −0.894743 + 0.446581i
\(65\) 52.7736 0.811902
\(66\) 19.0492 + 9.11834i 0.288624 + 0.138157i
\(67\) −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
\(69\) 53.4867 53.4867i 0.775170 0.775170i
\(70\) −68.3064 + 24.0823i −0.975805 + 0.344033i
\(71\) 24.1145 0.339641 0.169821 0.985475i \(-0.445681\pi\)
0.169821 + 0.985475i \(0.445681\pi\)
\(72\) −23.3599 + 5.50581i −0.324443 + 0.0764696i
\(73\) 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
\(75\) 72.7044 + 72.7044i 0.969392 + 0.969392i
\(76\) 27.8288 + 3.00278i 0.366169 + 0.0395103i
\(77\) 16.9967 + 16.9967i 0.220737 + 0.220737i
\(78\) 17.9528 + 8.59356i 0.230165 + 0.110174i
\(79\) 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
\(81\) −9.00000 −0.111111
\(82\) 47.7826 99.8227i 0.582714 1.21735i
\(83\) 42.0499 42.0499i 0.506625 0.506625i −0.406864 0.913489i \(-0.633378\pi\)
0.913489 + 0.406864i \(0.133378\pi\)
\(84\) −27.1584 2.93044i −0.323314 0.0348861i
\(85\) −94.5229 + 94.5229i −1.11203 + 1.11203i
\(86\) 15.1592 + 42.9971i 0.176269 + 0.499966i
\(87\) −61.4770 −0.706633
\(88\) 25.6558 41.4792i 0.291543 0.471354i
\(89\) 28.9853i 0.325677i −0.986653 0.162839i \(-0.947935\pi\)
0.986653 0.162839i \(-0.0520650\pi\)
\(90\) 18.3241 + 51.9740i 0.203601 + 0.577488i
\(91\) 16.0185 + 16.0185i 0.176028 + 0.176028i
\(92\) −109.558 136.061i −1.19085 1.47892i
\(93\) −39.8071 39.8071i −0.428034 0.428034i
\(94\) −6.84269 + 14.2951i −0.0727946 + 0.152075i
\(95\) 64.2724i 0.676552i
\(96\) 6.85432 + 55.0002i 0.0713992 + 0.572918i
\(97\) −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
\(99\) 12.9327 12.9327i 0.130634 0.130634i
\(100\) 184.947 148.922i 1.84947 1.48922i
\(101\) 57.0829 57.0829i 0.565177 0.565177i −0.365597 0.930773i \(-0.619135\pi\)
0.930773 + 0.365597i \(0.119135\pi\)
\(102\) −47.5473 + 16.7634i −0.466150 + 0.164347i
\(103\) 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
\(105\) 62.7239i 0.597371i
\(106\) 84.2255 29.6948i 0.794581 0.280140i
\(107\) 25.6981 + 25.6981i 0.240169 + 0.240169i 0.816920 0.576751i \(-0.195680\pi\)
−0.576751 + 0.816920i \(0.695680\pi\)
\(108\) −2.22975 + 20.6647i −0.0206459 + 0.191339i
\(109\) −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
\(111\) 10.1493i 0.0914355i
\(112\) −13.4570 + 61.6316i −0.120152 + 0.550282i
\(113\) 64.2927 0.568962 0.284481 0.958682i \(-0.408179\pi\)
0.284481 + 0.958682i \(0.408179\pi\)
\(114\) 10.4660 21.8645i 0.0918070 0.191794i
\(115\) −283.636 + 283.636i −2.46640 + 2.46640i
\(116\) −15.2310 + 141.156i −0.131301 + 1.21686i
\(117\) 12.1884 12.1884i 0.104175 0.104175i
\(118\) 46.7571 + 132.620i 0.396246 + 1.12390i
\(119\) −57.3816 −0.482199
\(120\) 123.876 29.1969i 1.03230 0.243307i
\(121\) 83.8321i 0.692827i
\(122\) −41.8233 118.627i −0.342814 0.972348i
\(123\) −67.7710 67.7710i −0.550984 0.550984i
\(124\) −101.262 + 81.5379i −0.816632 + 0.657563i
\(125\) −223.178 223.178i −1.78542 1.78542i
\(126\) −10.2138 + 21.3378i −0.0810623 + 0.169347i
\(127\) 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
\(129\) 39.4830 0.306070
\(130\) −95.2025 45.5710i −0.732327 0.350546i
\(131\) −118.504 + 118.504i −0.904613 + 0.904613i −0.995831 0.0912183i \(-0.970924\pi\)
0.0912183 + 0.995831i \(0.470924\pi\)
\(132\) −26.4904 32.8986i −0.200685 0.249232i
\(133\) 19.5088 19.5088i 0.146683 0.146683i
\(134\) 4.37651 1.54299i 0.0326605 0.0115149i
\(135\) 47.7263 0.353528
\(136\) 26.7102 + 113.325i 0.196398 + 0.833273i
\(137\) 157.472i 1.14943i 0.818353 + 0.574716i \(0.194888\pi\)
−0.818353 + 0.574716i \(0.805112\pi\)
\(138\) −142.676 + 50.3021i −1.03388 + 0.364508i
\(139\) −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
\(141\) 9.70513 + 9.70513i 0.0688307 + 0.0688307i
\(142\) −43.5021 20.8233i −0.306353 0.146643i
\(143\) 35.0288i 0.244957i
\(144\) 46.8952 + 10.2394i 0.325661 + 0.0711066i
\(145\) 326.008 2.24833
\(146\) 9.30367 19.4363i 0.0637238 0.133125i
\(147\) 40.9737 40.9737i 0.278733 0.278733i
\(148\) 23.3036 + 2.51450i 0.157457 + 0.0169899i
\(149\) 99.5402 99.5402i 0.668055 0.668055i −0.289210 0.957266i \(-0.593393\pi\)
0.957266 + 0.289210i \(0.0933927\pi\)
\(150\) −68.3756 193.939i −0.455837 1.29293i
\(151\) 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
\(153\) 43.6614i 0.285369i
\(154\) −15.9848 45.3387i −0.103797 0.294407i
\(155\) 211.094 + 211.094i 1.36190 + 1.36190i
\(156\) −24.9658 31.0052i −0.160037 0.198751i
\(157\) −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
\(159\) 77.3420i 0.486428i
\(160\) −36.3479 291.662i −0.227175 1.82288i
\(161\) −172.186 −1.06948
\(162\) 16.2358 + 7.77166i 0.100221 + 0.0479732i
\(163\) 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
\(165\) −68.5812 + 68.5812i −0.415644 + 0.415644i
\(166\) −112.168 + 39.5462i −0.675710 + 0.238230i
\(167\) 61.6774 0.369326 0.184663 0.982802i \(-0.440881\pi\)
0.184663 + 0.982802i \(0.440881\pi\)
\(168\) 46.4626 + 28.7382i 0.276563 + 0.171061i
\(169\) 135.987i 0.804658i
\(170\) 252.140 88.8950i 1.48317 0.522912i
\(171\) −14.8441 14.8441i −0.0868078 0.0868078i
\(172\) 9.78193 90.6560i 0.0568717 0.527069i
\(173\) 69.7012 + 69.7012i 0.402897 + 0.402897i 0.879253 0.476355i \(-0.158042\pi\)
−0.476355 + 0.879253i \(0.658042\pi\)
\(174\) 110.903 + 53.0865i 0.637375 + 0.305095i
\(175\) 234.052i 1.33744i
\(176\) −82.1006 + 52.6733i −0.466481 + 0.299280i
\(177\) 121.782 0.688033
\(178\) −25.0293 + 52.2888i −0.140614 + 0.293757i
\(179\) 43.6228 43.6228i 0.243703 0.243703i −0.574677 0.818380i \(-0.694872\pi\)
0.818380 + 0.574677i \(0.194872\pi\)
\(180\) 11.8242 109.583i 0.0656900 0.608795i
\(181\) −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
\(183\) −108.932 −0.595254
\(184\) 80.1494 + 340.056i 0.435595 + 1.84813i
\(185\) 53.8211i 0.290925i
\(186\) 37.4370 + 106.185i 0.201274 + 0.570889i
\(187\) −62.7401 62.7401i −0.335509 0.335509i
\(188\) 24.6881 19.8792i 0.131320 0.105741i
\(189\) 14.4865 + 14.4865i 0.0766482 + 0.0766482i
\(190\) −55.5004 + 115.946i −0.292107 + 0.610242i
\(191\) 171.759i 0.899263i 0.893214 + 0.449632i \(0.148445\pi\)
−0.893214 + 0.449632i \(0.851555\pi\)
\(192\) 35.1286 105.138i 0.182961 0.547593i
\(193\) −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
\(195\) −64.6342 + 64.6342i −0.331458 + 0.331458i
\(196\) −83.9274 104.230i −0.428201 0.531785i
\(197\) −18.3354 + 18.3354i −0.0930731 + 0.0930731i −0.752110 0.659037i \(-0.770964\pi\)
0.659037 + 0.752110i \(0.270964\pi\)
\(198\) −34.4980 + 12.1627i −0.174232 + 0.0614279i
\(199\) −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
\(201\) 4.01883i 0.0199942i
\(202\) −152.268 + 53.6842i −0.753804 + 0.265763i
\(203\) 98.9542 + 98.9542i 0.487459 + 0.487459i
\(204\) 100.250 + 10.8171i 0.491420 + 0.0530251i
\(205\) 359.384 + 359.384i 1.75309 + 1.75309i
\(206\) −70.9051 33.9404i −0.344199 0.164759i
\(207\) 131.015i 0.632923i
\(208\) −77.3755 + 49.6418i −0.371998 + 0.238663i
\(209\) 42.6612 0.204120
\(210\) 54.1632 113.153i 0.257920 0.538822i
\(211\) 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
\(213\) −29.5342 + 29.5342i −0.138658 + 0.138658i
\(214\) −24.1680 68.5496i −0.112935 0.320325i
\(215\) −209.375 −0.973839
\(216\) 21.8667 35.3532i 0.101235 0.163672i
\(217\) 128.148i 0.590544i
\(218\) 9.08609 + 25.7716i 0.0416793 + 0.118218i
\(219\) −13.1956 13.1956i −0.0602538 0.0602538i
\(220\) 140.477 + 174.459i 0.638530 + 0.792994i
\(221\) −59.1293 59.1293i −0.267553 0.267553i
\(222\) 8.76414 18.3092i 0.0394781 0.0824738i
\(223\) 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
\(225\) −178.089 −0.791506
\(226\) −115.983 55.5179i −0.513197 0.245654i
\(227\) −36.8204 + 36.8204i −0.162204 + 0.162204i −0.783543 0.621338i \(-0.786589\pi\)
0.621338 + 0.783543i \(0.286589\pi\)
\(228\) −37.7609 + 30.4056i −0.165618 + 0.133358i
\(229\) 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
\(231\) −41.6333 −0.180231
\(232\) 149.367 241.490i 0.643823 1.04090i
\(233\) 167.669i 0.719608i −0.933028 0.359804i \(-0.882844\pi\)
0.933028 0.359804i \(-0.117156\pi\)
\(234\) −32.5126 + 11.4627i −0.138943 + 0.0489860i
\(235\) −51.4655 51.4655i −0.219002 0.219002i
\(236\) 30.1715 279.620i 0.127845 1.18483i
\(237\) 88.2450 + 88.2450i 0.372342 + 0.372342i
\(238\) 103.515 + 49.5501i 0.434938 + 0.208194i
\(239\) 29.7509i 0.124481i −0.998061 0.0622403i \(-0.980175\pi\)
0.998061 0.0622403i \(-0.0198245\pi\)
\(240\) −248.681 54.2985i −1.03617 0.226244i
\(241\) −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
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) −26.9878 + 250.115i −0.110606 + 1.02506i
\(245\) −217.280 + 217.280i −0.886859 + 0.886859i
\(246\) 63.7359 + 180.779i 0.259089 + 0.734873i
\(247\) 40.2059 0.162777
\(248\) 253.084 59.6507i 1.02050 0.240527i
\(249\) 103.001i 0.413658i
\(250\) 209.890 + 595.326i 0.839559 + 2.38130i
\(251\) −342.946 342.946i −1.36632 1.36632i −0.865623 0.500697i \(-0.833077\pi\)
−0.500697 0.865623i \(-0.666923\pi\)
\(252\) 36.8511 29.6730i 0.146235 0.117750i
\(253\) −188.265 188.265i −0.744130 0.744130i
\(254\) 111.971 233.918i 0.440829 0.920938i
\(255\) 231.533i 0.907972i
\(256\) −232.701 106.706i −0.908989 0.416819i
\(257\) −393.565 −1.53138 −0.765691 0.643209i \(-0.777603\pi\)
−0.765691 + 0.643209i \(0.777603\pi\)
\(258\) −71.2265 34.0943i −0.276072 0.132149i
\(259\) 16.3365 16.3365i 0.0630753 0.0630753i
\(260\) 132.392 + 164.418i 0.509199 + 0.632377i
\(261\) 75.2937 75.2937i 0.288482 0.288482i
\(262\) 316.110 111.449i 1.20653 0.425376i
\(263\) 413.800 1.57338 0.786692 0.617346i \(-0.211792\pi\)
0.786692 + 0.617346i \(0.211792\pi\)
\(264\) 19.3796 + 82.2233i 0.0734076 + 0.311452i
\(265\) 410.139i 1.54769i
\(266\) −52.0396 + 18.3472i −0.195638 + 0.0689746i
\(267\) 35.4995 + 35.4995i 0.132957 + 0.132957i
\(268\) −9.22752 0.995666i −0.0344311 0.00371517i
\(269\) 165.389 + 165.389i 0.614830 + 0.614830i 0.944201 0.329371i \(-0.106837\pi\)
−0.329371 + 0.944201i \(0.606837\pi\)
\(270\) −86.0972 41.2125i −0.318878 0.152639i
\(271\) 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
\(273\) −39.2372 −0.143726
\(274\) 135.980 284.076i 0.496278 1.03678i
\(275\) 255.908 255.908i 0.930575 0.930575i
\(276\) 300.820 + 32.4590i 1.08993 + 0.117605i
\(277\) 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
\(279\) 97.5071 0.349488
\(280\) −246.388 152.396i −0.879956 0.544273i
\(281\) 411.141i 1.46313i −0.681769 0.731567i \(-0.738789\pi\)
0.681769 0.731567i \(-0.261211\pi\)
\(282\) −9.12729 25.8884i −0.0323663 0.0918028i
\(283\) 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
\(285\) 78.7173 + 78.7173i 0.276201 + 0.276201i
\(286\) 30.2480 63.1912i 0.105762 0.220948i
\(287\) 218.170i 0.760174i
\(288\) −75.7560 58.9664i −0.263042 0.204744i
\(289\) −77.1870 −0.267083
\(290\) −588.111 281.514i −2.02797 0.970737i
\(291\) 66.4667 66.4667i 0.228408 0.228408i
\(292\) −33.5672 + 27.0288i −0.114956 + 0.0925644i
\(293\) 35.1386 35.1386i 0.119927 0.119927i −0.644596 0.764523i \(-0.722975\pi\)
0.764523 + 0.644596i \(0.222975\pi\)
\(294\) −109.297 + 38.5341i −0.371759 + 0.131069i
\(295\) −645.799 −2.18915
\(296\) −39.8679 24.6592i −0.134689 0.0833081i
\(297\) 31.6786i 0.106662i
\(298\) −265.523 + 93.6136i −0.891017 + 0.314140i
\(299\) −177.430 177.430i −0.593410 0.593410i
\(300\) −44.1215 + 408.905i −0.147072 + 1.36302i
\(301\) −63.5524 63.5524i −0.211137 0.211137i
\(302\) −493.758 236.349i −1.63496 0.782613i
\(303\) 139.824i 0.461465i
\(304\) 60.4582 + 94.2347i 0.198876 + 0.309983i
\(305\) 577.655 1.89395
\(306\) 37.7024 78.7642i 0.123210 0.257399i
\(307\) −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
\(309\) −48.1384 + 48.1384i −0.155788 + 0.155788i
\(310\) −198.526 563.093i −0.640405 1.81643i
\(311\) 39.8016 0.127980 0.0639898 0.997951i \(-0.479618\pi\)
0.0639898 + 0.997951i \(0.479618\pi\)
\(312\) 18.2643 + 77.4911i 0.0585393 + 0.248369i
\(313\) 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
\(315\) −76.8208 76.8208i −0.243876 0.243876i
\(316\) 224.480 180.754i 0.710379 0.572007i
\(317\) 255.063 + 255.063i 0.804615 + 0.804615i 0.983813 0.179198i \(-0.0573503\pi\)
−0.179198 + 0.983813i \(0.557350\pi\)
\(318\) −66.7862 + 139.523i −0.210020 + 0.438753i
\(319\) 216.390i 0.678337i
\(320\) −186.284 + 557.538i −0.582138 + 1.74231i
\(321\) −62.9472 −0.196097
\(322\) 310.619 + 148.685i 0.964656 + 0.461756i
\(323\) −72.0128 + 72.0128i −0.222950 + 0.222950i
\(324\) −22.5781 28.0398i −0.0696854 0.0865426i
\(325\) 241.180 241.180i 0.742092 0.742092i
\(326\) −472.792 + 166.689i −1.45028 + 0.511316i
\(327\) 23.6653 0.0723710
\(328\) 430.872 101.554i 1.31363 0.309617i
\(329\) 31.2430i 0.0949635i
\(330\) 182.940 64.4979i 0.554364 0.195448i
\(331\) 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
\(333\) −12.4303 12.4303i −0.0373284 0.0373284i
\(334\) −111.265 53.2596i −0.333128 0.159460i
\(335\) 21.3115i 0.0636165i
\(336\) −59.0016 91.9644i −0.175600 0.273703i
\(337\) 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
\(339\) −78.7421 + 78.7421i −0.232278 + 0.232278i
\(340\) −531.617 57.3623i −1.56358 0.168713i
\(341\) −140.115 + 140.115i −0.410894 + 0.410894i
\(342\) 13.9603 + 39.5967i 0.0408196 + 0.115780i
\(343\) −325.097 −0.947805
\(344\) −95.9294 + 155.094i −0.278865 + 0.450856i
\(345\) 694.763i 2.01381i
\(346\) −65.5512 185.928i −0.189454 0.537363i
\(347\) 296.512 + 296.512i 0.854500 + 0.854500i 0.990684 0.136183i \(-0.0434836\pi\)
−0.136183 + 0.990684i \(0.543484\pi\)
\(348\) −154.226 191.534i −0.443178 0.550385i
\(349\) −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
\(351\) 29.8554i 0.0850581i
\(352\) 193.592 24.1261i 0.549977 0.0685402i
\(353\) 85.4490 0.242065 0.121033 0.992649i \(-0.461379\pi\)
0.121033 + 0.992649i \(0.461379\pi\)
\(354\) −219.692 105.161i −0.620598 0.297064i
\(355\) 156.617 156.617i 0.441176 0.441176i
\(356\) 90.3046 72.7145i 0.253665 0.204254i
\(357\) 70.2779 70.2779i 0.196857 0.196857i
\(358\) −116.364 + 41.0255i −0.325038 + 0.114596i
\(359\) −302.214 −0.841823 −0.420911 0.907102i \(-0.638290\pi\)
−0.420911 + 0.907102i \(0.638290\pi\)
\(360\) −115.958 + 187.475i −0.322104 + 0.520764i
\(361\) 312.034i 0.864359i
\(362\) 119.315 42.0659i 0.329599 0.116204i
\(363\) 102.673 + 102.673i 0.282846 + 0.282846i
\(364\) −9.72104 + 90.0916i −0.0267061 + 0.247504i
\(365\) 69.9751 + 69.9751i 0.191713 + 0.191713i
\(366\) 196.510 + 94.0643i 0.536913 + 0.257006i
\(367\) 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
\(369\) 166.004 0.449876
\(370\) −46.4755 + 97.0921i −0.125610 + 0.262411i
\(371\) −124.491 + 124.491i −0.335554 + 0.335554i
\(372\) 24.1574 223.884i 0.0649393 0.601838i
\(373\) −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
\(375\) 546.672 1.45779
\(376\) −61.7029 + 14.5431i −0.164104 + 0.0386784i
\(377\) 203.936i 0.540944i
\(378\) −13.6240 38.6427i −0.0360423 0.102229i
\(379\) −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
\(381\) −158.810 158.810i −0.416825 0.416825i
\(382\) 148.317 309.850i 0.388265 0.811126i
\(383\) 407.983i 1.06523i −0.846357 0.532615i \(-0.821209\pi\)
0.846357 0.532615i \(-0.178791\pi\)
\(384\) −154.160 + 159.332i −0.401458 + 0.414928i
\(385\) 220.778 0.573450
\(386\) 388.548 + 185.988i 1.00660 + 0.481834i
\(387\) −48.3566 + 48.3566i −0.124953 + 0.124953i
\(388\) −136.145 169.080i −0.350890 0.435772i
\(389\) 458.508 458.508i 1.17868 1.17868i 0.198605 0.980080i \(-0.436359\pi\)
0.980080 0.198605i \(-0.0636411\pi\)
\(390\) 172.412 60.7859i 0.442081 0.155861i
\(391\) 635.589 1.62555
\(392\) 61.3988 + 260.501i 0.156630 + 0.664544i
\(393\) 290.275i 0.738613i
\(394\) 48.9096 17.2437i 0.124136 0.0437658i
\(395\) −467.956 467.956i −1.18470 1.18470i
\(396\) 72.7364 + 7.84838i 0.183678 + 0.0198191i
\(397\) −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
\(399\) 47.7866i 0.119766i
\(400\) 927.944 + 202.613i 2.31986 + 0.506531i
\(401\) −499.197 −1.24488 −0.622441 0.782667i \(-0.713859\pi\)
−0.622441 + 0.782667i \(0.713859\pi\)
\(402\) −3.47033 + 7.24988i −0.00863266 + 0.0180345i
\(403\) −132.051 + 132.051i −0.327670 + 0.327670i
\(404\) 321.046 + 34.6414i 0.794668 + 0.0857461i
\(405\) −58.4525 + 58.4525i −0.144327 + 0.144327i
\(406\) −93.0624 263.960i −0.229218 0.650147i
\(407\) 35.7241 0.0877741
\(408\) −171.508 106.081i −0.420362 0.260003i
\(409\) 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
\(411\) −192.863 192.863i −0.469254 0.469254i
\(412\) 98.6030 + 122.456i 0.239328 + 0.297222i
\(413\) −196.021 196.021i −0.474628 0.474628i
\(414\) 113.134 236.348i 0.273270 0.570890i
\(415\) 546.205i 1.31616i
\(416\) 182.450 22.7376i 0.438582 0.0546577i
\(417\) 291.349 0.698679
\(418\) −76.9598 36.8387i −0.184114 0.0881308i
\(419\) −560.555 + 560.555i −1.33784 + 1.33784i −0.439693 + 0.898148i \(0.644913\pi\)
−0.898148 + 0.439693i \(0.855087\pi\)
\(420\) −195.419 + 157.354i −0.465282 + 0.374652i
\(421\) 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
\(423\) −23.7726 −0.0562000
\(424\) 303.810 + 187.913i 0.716532 + 0.443191i
\(425\) 863.956i 2.03284i
\(426\) 78.7823 27.7757i 0.184935 0.0652012i
\(427\) 175.337 + 175.337i 0.410626 + 0.410626i
\(428\) −15.5952 + 144.531i −0.0364374 + 0.337690i
\(429\) −42.9013 42.9013i −0.100003 0.100003i
\(430\) 377.709 + 180.799i 0.878392 + 0.420464i
\(431\) 662.874i 1.53799i −0.639255 0.768995i \(-0.720757\pi\)
0.639255 0.768995i \(-0.279243\pi\)
\(432\) −69.9752 + 44.8940i −0.161980 + 0.103921i
\(433\) −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
\(435\) −399.277 + 399.277i −0.917877 + 0.917877i
\(436\) 5.86309 54.3373i 0.0134475 0.124627i
\(437\) −216.090 + 216.090i −0.494484 + 0.494484i
\(438\) 12.4099 + 35.1992i 0.0283331 + 0.0803634i
\(439\) −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
\(441\) 100.365i 0.227584i
\(442\) 55.6087 + 157.727i 0.125812 + 0.356849i
\(443\) 421.096 + 421.096i 0.950555 + 0.950555i 0.998834 0.0482792i \(-0.0153737\pi\)
−0.0482792 + 0.998834i \(0.515374\pi\)
\(444\) −31.6206 + 25.4614i −0.0712176 + 0.0573454i
\(445\) −188.251 188.251i −0.423037 0.423037i
\(446\) −133.328 + 278.535i −0.298941 + 0.624518i
\(447\) 243.823i 0.545465i
\(448\) −225.775 + 112.688i −0.503961 + 0.251535i
\(449\) 492.636 1.09718 0.548592 0.836090i \(-0.315164\pi\)
0.548592 + 0.836090i \(0.315164\pi\)
\(450\) 321.268 + 153.783i 0.713929 + 0.341740i
\(451\) −238.543 + 238.543i −0.528921 + 0.528921i
\(452\) 161.289 + 200.306i 0.356835 + 0.443155i
\(453\) −335.219 + 335.219i −0.739997 + 0.739997i
\(454\) 98.2182 34.6281i 0.216340 0.0762733i
\(455\) 208.072 0.457301
\(456\) 94.3755 22.2438i 0.206964 0.0487803i
\(457\) 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
\(459\) −53.4741 53.4741i −0.116501 0.116501i
\(460\) −1595.23 172.128i −3.46788 0.374191i
\(461\) −27.5260 27.5260i −0.0597093 0.0597093i 0.676622 0.736331i \(-0.263443\pi\)
−0.736331 + 0.676622i \(0.763443\pi\)
\(462\) 75.1056 + 35.9511i 0.162566 + 0.0778163i
\(463\) 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
\(465\) −517.073 −1.11198
\(466\) −144.785 + 302.471i −0.310697 + 0.649079i
\(467\) 267.964 267.964i 0.573798 0.573798i −0.359390 0.933188i \(-0.617015\pi\)
0.933188 + 0.359390i \(0.117015\pi\)
\(468\) 68.5502 + 7.39669i 0.146475 + 0.0158049i
\(469\) −6.46875 + 6.46875i −0.0137926 + 0.0137926i
\(470\) 48.4013 + 137.284i 0.102981 + 0.292094i
\(471\) 185.865 0.394618
\(472\) −295.886 + 478.375i −0.626876 + 1.01351i
\(473\) 138.974i 0.293814i
\(474\) −82.9909 235.393i −0.175086 0.496610i
\(475\) −293.730 293.730i −0.618380 0.618380i
\(476\) −143.952 178.775i −0.302420 0.375577i
\(477\) 94.7243 + 94.7243i 0.198583 + 0.198583i
\(478\) −25.6904 + 53.6699i −0.0537456 + 0.112280i
\(479\) 419.084i 0.874915i −0.899239 0.437457i \(-0.855879\pi\)
0.899239 0.437457i \(-0.144121\pi\)
\(480\) 401.728 + 312.694i 0.836933 + 0.651446i
\(481\) 33.6681 0.0699960
\(482\) 193.699 + 92.7186i 0.401864 + 0.192362i
\(483\) 210.883 210.883i 0.436612 0.436612i
\(484\) 261.182 210.307i 0.539632 0.434519i
\(485\) −352.468 + 352.468i −0.726738 + 0.726738i
\(486\) −29.4030 + 10.3664i −0.0605000 + 0.0213301i
\(487\) −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
\(489\) 434.153i 0.887838i
\(490\) 579.595 204.344i 1.18285 0.417028i
\(491\) −301.955 301.955i −0.614979 0.614979i 0.329260 0.944239i \(-0.393201\pi\)
−0.944239 + 0.329260i \(0.893201\pi\)
\(492\) 41.1276 381.158i 0.0835927 0.774712i
\(493\) −365.270 365.270i −0.740912 0.740912i
\(494\) −72.5306 34.7185i −0.146823 0.0702804i
\(495\) 167.989i 0.339372i
\(496\) −508.068 110.934i −1.02433 0.223658i
\(497\) 95.0771 0.191302
\(498\) 88.9430 185.811i 0.178600 0.373115i
\(499\) 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
\(501\) −75.5391 + 75.5391i −0.150777 + 0.150777i
\(502\) 322.527 + 914.808i 0.642484 + 1.82233i
\(503\) 222.446 0.442239 0.221120 0.975247i \(-0.429029\pi\)
0.221120 + 0.975247i \(0.429029\pi\)
\(504\) −92.1018 + 21.7079i −0.182742 + 0.0430713i
\(505\) 741.475i 1.46827i
\(506\) 177.056 + 502.196i 0.349912 + 0.992482i
\(507\) 166.550 + 166.550i 0.328500 + 0.328500i
\(508\) −403.985 + 325.295i −0.795246 + 0.640344i
\(509\) 489.873 + 489.873i 0.962421 + 0.962421i 0.999319 0.0368976i \(-0.0117475\pi\)
−0.0368976 + 0.999319i \(0.511748\pi\)
\(510\) −199.933 + 417.680i −0.392025 + 0.818981i
\(511\) 42.4795i 0.0831302i
\(512\) 327.646 + 393.437i 0.639933 + 0.768431i
\(513\) 36.3606 0.0708783
\(514\) 709.983 + 339.850i 1.38129 + 0.661188i
\(515\) 255.274 255.274i 0.495678 0.495678i
\(516\) 99.0500 + 123.011i 0.191957 + 0.238393i
\(517\) 34.1605 34.1605i 0.0660745 0.0660745i
\(518\) −43.5775 + 15.3638i −0.0841265 + 0.0296599i
\(519\) −170.732 −0.328964
\(520\) −96.8539 410.929i −0.186257 0.790249i
\(521\) 197.152i 0.378412i −0.981937 0.189206i \(-0.939409\pi\)
0.981937 0.189206i \(-0.0605913\pi\)
\(522\) −200.846 + 70.8107i −0.384762 + 0.135653i
\(523\) 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
\(525\) 286.654 + 286.654i 0.546007 + 0.546007i
\(526\) −746.486 357.324i −1.41918 0.679323i
\(527\) 473.033i 0.897596i
\(528\) 36.0409 165.064i 0.0682593 0.312620i
\(529\) 1378.22 2.60533
\(530\) 354.162 739.881i 0.668231 1.39600i
\(531\) −149.152 + 149.152i −0.280888 + 0.280888i
\(532\) 109.722 + 11.8391i 0.206243 + 0.0222540i
\(533\) −224.815 + 224.815i −0.421791 + 0.421791i
\(534\) −33.3859 94.6949i −0.0625204 0.177331i
\(535\) 333.804 0.623933
\(536\) 15.7865 + 9.76429i 0.0294524 + 0.0182170i
\(537\) 106.854i 0.198983i
\(538\) −155.542 441.175i −0.289111 0.820028i
\(539\) −144.221 144.221i −0.267572 0.267572i
\(540\) 119.730 + 148.693i 0.221722 + 0.275357i
\(541\) 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
\(543\) 109.563i 0.201774i
\(544\) −286.062 + 367.512i −0.525848 + 0.675574i
\(545\) −125.495 −0.230267
\(546\) 70.7831 + 33.8821i 0.129639 + 0.0620551i
\(547\) −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
\(549\) 133.413 133.413i 0.243012 0.243012i
\(550\) −682.634 + 240.671i −1.24115 + 0.437584i
\(551\) 248.371 0.450764
\(552\) −514.644 318.319i −0.932327 0.576665i
\(553\) 284.080i 0.513708i
\(554\) −419.856 + 148.026i −0.757863 + 0.267194i
\(555\) 65.9172 + 65.9172i 0.118770 + 0.118770i
\(556\) 72.1818 668.959i 0.129823 1.20316i
\(557\) −351.991 351.991i −0.631941 0.631941i 0.316614 0.948554i \(-0.397454\pi\)
−0.948554 + 0.316614i \(0.897454\pi\)
\(558\) −175.901 84.1992i −0.315234 0.150895i
\(559\) 130.976i 0.234304i
\(560\) 312.881 + 487.680i 0.558716 + 0.870857i
\(561\) 153.681 0.273942
\(562\) −355.027 + 741.689i −0.631721 + 1.31973i
\(563\) −150.902 + 150.902i −0.268031 + 0.268031i −0.828307 0.560275i \(-0.810695\pi\)
0.560275 + 0.828307i \(0.310695\pi\)
\(564\) −5.88967 + 54.5837i −0.0104427 + 0.0967796i
\(565\) 417.563 417.563i 0.739050 0.739050i
\(566\) −323.068 916.341i −0.570791 1.61898i
\(567\) −35.4845 −0.0625830
\(568\) −44.2567 187.771i −0.0779168 0.330583i
\(569\) 113.300i 0.199121i −0.995032 0.0995603i \(-0.968256\pi\)
0.995032 0.0995603i \(-0.0317436\pi\)
\(570\) −74.0305 209.978i −0.129878 0.368383i
\(571\) −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
\(573\) −210.361 210.361i −0.367123 0.367123i
\(574\) 188.394 393.574i 0.328212 0.685669i
\(575\) 2592.48i 4.50866i
\(576\) 85.7436 + 171.791i 0.148860 + 0.298248i
\(577\) −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
\(579\) 263.790 263.790i 0.455596 0.455596i
\(580\) 817.847 + 1015.69i 1.41008 + 1.75119i
\(581\) 165.791 165.791i 0.285355 0.285355i
\(582\) −177.300 + 62.5093i −0.304639 + 0.107404i
\(583\) −272.232 −0.466950
\(584\) 83.8944 19.7735i 0.143655 0.0338587i
\(585\) 158.321i 0.270634i
\(586\) −93.7320 + 33.0464i −0.159952 + 0.0563932i
\(587\) −540.404 540.404i −0.920619 0.920619i 0.0764537 0.997073i \(-0.475640\pi\)
−0.997073 + 0.0764537i \(0.975640\pi\)
\(588\) 230.445 + 24.8654i 0.391913 + 0.0422881i
\(589\) 160.823 + 160.823i 0.273045 + 0.273045i
\(590\) 1165.01 + 557.659i 1.97459 + 0.945185i
\(591\) 44.9124i 0.0759939i
\(592\) 50.6272 + 78.9113i 0.0855189 + 0.133296i
\(593\) 411.176 0.693383 0.346692 0.937979i \(-0.387305\pi\)
0.346692 + 0.937979i \(0.387305\pi\)
\(594\) 27.3550 57.1475i 0.0460522 0.0962079i
\(595\) −372.678 + 372.678i −0.626350 + 0.626350i
\(596\) 559.835 + 60.4072i 0.939320 + 0.101354i
\(597\) 278.154 278.154i 0.465920 0.465920i
\(598\) 166.866 + 473.293i 0.279039 + 0.791460i
\(599\) −552.839 −0.922936 −0.461468 0.887157i \(-0.652677\pi\)
−0.461468 + 0.887157i \(0.652677\pi\)
\(600\) 432.691 699.556i 0.721152 1.16593i
\(601\) 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
\(603\) 4.92204 + 4.92204i 0.00816259 + 0.00816259i
\(604\) 686.637 + 852.738i 1.13682 + 1.41182i
\(605\) −544.467 544.467i −0.899945 0.899945i
\(606\) 120.740 252.239i 0.199242 0.416236i
\(607\) 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
\(609\) −242.387 −0.398009
\(610\) −1042.08 498.816i −1.70832 0.817731i
\(611\) 32.1945 32.1945i 0.0526915 0.0526915i
\(612\) −136.029 + 109.532i −0.222269 + 0.178974i
\(613\) −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
\(615\) −880.308 −1.43140
\(616\) 101.154 163.541i 0.164211 0.265489i
\(617\) 623.301i 1.01021i −0.863057 0.505106i \(-0.831453\pi\)
0.863057 0.505106i \(-0.168547\pi\)
\(618\) 128.409 45.2722i 0.207781 0.0732560i
\(619\) 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
\(621\) −160.460 160.460i −0.258390 0.258390i
\(622\) −71.8013 34.3694i −0.115436 0.0552563i
\(623\) 114.281i 0.183437i
\(624\) 33.9667 155.564i 0.0544338 0.249301i
\(625\) −1414.88 −2.26381
\(626\) −372.940 + 779.110i −0.595751 + 1.24458i
\(627\) −52.2490 + 52.2490i −0.0833318 + 0.0833318i
\(628\) 46.0482 426.760i 0.0733251 0.679555i
\(629\) −60.3029 + 60.3029i −0.0958711 + 0.0958711i
\(630\) 72.2469 + 204.919i 0.114678 + 0.325268i
\(631\) 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
\(633\) 465.908i 0.736031i
\(634\) −239.877 680.379i −0.378354 1.07315i
\(635\) 842.158 + 842.158i 1.32623 + 1.32623i
\(636\) 240.962 194.026i 0.378871 0.305072i
\(637\) −135.921 135.921i −0.213376 0.213376i
\(638\) 186.856 390.362i 0.292878 0.611853i
\(639\) 72.3436i 0.113214i
\(640\) 817.497 844.927i 1.27734 1.32020i
\(641\) −782.691 −1.22105 −0.610523 0.791998i \(-0.709041\pi\)
−0.610523 + 0.791998i \(0.709041\pi\)
\(642\) 113.555 + 54.3561i 0.176878 + 0.0846668i
\(643\) 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
\(645\) 256.431 256.431i 0.397568 0.397568i
\(646\) 192.094 67.7252i 0.297359 0.104838i
\(647\) 1226.09 1.89504 0.947520 0.319697i \(-0.103581\pi\)
0.947520 + 0.319697i \(0.103581\pi\)
\(648\) 16.5174 + 70.0798i 0.0254899 + 0.108148i
\(649\) 428.653i 0.660482i
\(650\) −643.347 + 226.820i −0.989764 + 0.348954i
\(651\) −156.949 156.949i −0.241089 0.241089i
\(652\) 996.846 + 107.561i 1.52891 + 0.164972i
\(653\) 326.300 + 326.300i 0.499694 + 0.499694i 0.911343 0.411649i \(-0.135047\pi\)
−0.411649 + 0.911343i \(0.635047\pi\)
\(654\) −42.6917 20.4354i −0.0652779 0.0312468i
\(655\) 1539.31i 2.35008i
\(656\) −864.978 188.864i −1.31856 0.287903i
\(657\) 32.3224 0.0491970
\(658\) −26.9789 + 56.3616i −0.0410013 + 0.0856560i
\(659\) −574.901 + 574.901i −0.872384 + 0.872384i −0.992732 0.120347i \(-0.961599\pi\)
0.120347 + 0.992732i \(0.461599\pi\)
\(660\) −385.715 41.6193i −0.584417 0.0630596i
\(661\) 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
\(663\) 144.837 0.218456
\(664\) −404.600 250.254i −0.609338 0.376889i
\(665\) 253.409i 0.381065i
\(666\) 11.6902 + 33.1579i 0.0175529 + 0.0497866i
\(667\) −1096.07 1096.07i −1.64328 1.64328i
\(668\) 154.729 + 192.158i 0.231630 + 0.287662i
\(669\) 189.101 + 189.101i 0.282663 + 0.282663i
\(670\) 18.4029 38.4455i 0.0274670 0.0573814i
\(671\) 383.422i 0.571419i
\(672\) 27.0247 + 216.851i 0.0402154 + 0.322694i
\(673\) 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
\(675\) 218.113 218.113i 0.323131 0.323131i
\(676\) 423.673 341.147i 0.626735 0.504656i
\(677\) 107.154 107.154i 0.158278 0.158278i −0.623525 0.781803i \(-0.714300\pi\)
0.781803 + 0.623525i \(0.214300\pi\)
\(678\) 210.044 74.0538i 0.309800 0.109224i
\(679\) −213.971 −0.315127
\(680\) 909.491 + 562.541i 1.33749 + 0.827266i
\(681\) 90.1911i 0.132439i
\(682\) 373.756 131.772i 0.548029 0.193215i
\(683\) 724.233 + 724.233i 1.06037 + 1.06037i 0.998057 + 0.0623142i \(0.0198481\pi\)
0.0623142 + 0.998057i \(0.480152\pi\)
\(684\) 9.00834 83.4865i 0.0131701 0.122056i
\(685\) 1022.74 + 1022.74i 1.49305 + 1.49305i
\(686\) 586.468 + 280.727i 0.854910 + 0.409223i
\(687\) 44.0155i 0.0640691i
\(688\) 306.981 196.950i 0.446194 0.286265i
\(689\) −256.564 −0.372372
\(690\) −599.940 + 1253.34i −0.869479 + 1.81643i
\(691\) 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
\(693\) 50.9902 50.9902i 0.0735790 0.0735790i
\(694\) −278.857 790.943i −0.401812 1.13969i
\(695\) −1545.00 −2.22302
\(696\) 112.827 + 478.700i 0.162108 + 0.687787i
\(697\) 805.331i 1.15543i
\(698\) 186.312 + 528.449i 0.266922 + 0.757090i
\(699\) 205.351 + 205.351i 0.293779 + 0.293779i
\(700\) 729.197 587.159i 1.04171 0.838799i
\(701\) −301.659 301.659i −0.430327 0.430327i 0.458412 0.888740i \(-0.348418\pi\)
−0.888740 + 0.458412i \(0.848418\pi\)
\(702\) 25.7807 53.8585i 0.0367246 0.0767215i
\(703\) 41.0040i 0.0583271i
\(704\) −370.069 123.647i −0.525666 0.175635i
\(705\) 126.064 0.178815
\(706\) −154.148 73.7867i −0.218340 0.104514i
\(707\) 225.062 225.062i 0.318334 0.318334i
\(708\) 305.511 + 379.415i 0.431512 + 0.535898i
\(709\) −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
\(711\) −216.155 −0.304016
\(712\) −225.698 + 53.1958i −0.316991 + 0.0747132i
\(713\) 1419.43i 1.99079i
\(714\) −187.466 + 66.0935i −0.262557 + 0.0925680i
\(715\) 227.502 + 227.502i 0.318185 + 0.318185i
\(716\) 245.344 + 26.4730i 0.342659 + 0.0369735i
\(717\) 36.4372 + 36.4372i 0.0508190 + 0.0508190i
\(718\) 545.188 + 260.968i 0.759315 + 0.363465i
\(719\) 145.542i 0.202422i 0.994865 + 0.101211i \(0.0322718\pi\)
−0.994865 + 0.101211i \(0.967728\pi\)
\(720\) 371.073 238.069i 0.515379 0.330652i
\(721\) 154.968 0.214935
\(722\) 269.447 562.902i 0.373195 0.779643i
\(723\) 131.505 131.505i 0.181887 0.181887i
\(724\) −251.566 27.1444i −0.347466 0.0374922i
\(725\) 1489.88 1489.88i 2.05501 2.05501i
\(726\) −96.5598 273.880i −0.133002 0.377245i
\(727\) −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
\(729\) 27.0000i 0.0370370i
\(730\) −65.8088 186.658i −0.0901490 0.255696i
\(731\) 234.591 + 234.591i 0.320918 + 0.320918i
\(732\) −273.274 339.380i −0.373325 0.463634i
\(733\) 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
\(735\) 532.226i 0.724117i
\(736\) −858.388 + 1102.80i −1.16629 + 1.49837i
\(737\) −14.1456 −0.0191935
\(738\) −299.468 143.348i −0.405783 0.194238i
\(739\) −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
\(741\) −49.2420 + 49.2420i −0.0664534 + 0.0664534i
\(742\) 332.078 117.078i 0.447545 0.157788i
\(743\) −1010.54 −1.36008 −0.680039 0.733176i \(-0.738037\pi\)
−0.680039 + 0.733176i \(0.738037\pi\)
\(744\) −236.907 + 383.021i −0.318423 + 0.514813i
\(745\) 1292.97i 1.73553i
\(746\) 1086.02 382.889i 1.45579 0.513256i
\(747\) −126.150 126.150i −0.168875 0.168875i
\(748\) 38.0746 352.863i 0.0509018 0.471743i
\(749\) 101.321 + 101.321i 0.135275 + 0.135275i
\(750\) −986.183 472.061i −1.31491 0.629414i
\(751\) 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
\(753\) 840.043 1.11560
\(754\) 176.102 367.896i 0.233557 0.487925i
\(755\) 1777.64 1777.64i 2.35449 2.35449i
\(756\) −8.79131 + 81.4751i −0.0116287 + 0.107771i
\(757\) 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
\(759\) 461.153 0.607579
\(760\) −500.466 + 117.957i −0.658508 + 0.155207i
\(761\) 1502.22i 1.97400i 0.160711 + 0.987001i \(0.448621\pi\)
−0.160711 + 0.987001i \(0.551379\pi\)
\(762\) 149.355 + 423.626i 0.196003 + 0.555939i
\(763\) −38.0920 38.0920i −0.0499239 0.0499239i
\(764\) −535.122 + 430.888i −0.700421 + 0.563989i
\(765\) 283.569 + 283.569i 0.370678 + 0.370678i
\(766\) −352.301 + 735.993i −0.459923 + 0.960827i
\(767\) 403.983i 0.526705i
\(768\) 415.687 154.312i 0.541259 0.200928i
\(769\) −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