Properties

Label 48.3.l.a.43.4
Level $48$
Weight $3$
Character 48.43
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 43.4
Root \(0.125358 + 1.99607i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +(-7.05755 + 6.22347i) q^{10} +(6.82458 - 6.82458i) q^{11} +(-4.24757 - 5.47340i) q^{12} +(4.29091 - 4.29091i) q^{13} +(0.506555 - 8.06588i) q^{14} +8.14895i q^{15} +(15.4991 + 3.97210i) q^{16} +30.1192 q^{17} +(-5.98820 - 0.376073i) q^{18} +(-19.7548 - 19.7548i) q^{19} +(-11.5377 - 14.8675i) q^{20} +(-4.94905 - 4.94905i) q^{21} +(12.7668 + 14.4778i) q^{22} -28.2345 q^{23} +(11.4577 - 7.79230i) q^{24} -2.86488i q^{25} +(8.02705 + 9.10285i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.0365 + 2.02224i) q^{28} +(-21.3607 + 21.3607i) q^{29} +(-16.2659 - 1.02153i) q^{30} +38.0396i q^{31} +(-9.87151 + 30.4393i) q^{32} +16.7167 q^{33} +(-3.77567 + 60.1200i) q^{34} +(-13.4432 - 13.4432i) q^{35} +(1.50133 - 11.9057i) q^{36} +(-42.8916 - 42.8916i) q^{37} +(41.9084 - 36.9556i) q^{38} +10.5105 q^{39} +(31.1229 - 21.1664i) q^{40} +48.2343i q^{41} +(10.4990 - 9.25824i) q^{42} +(32.6765 - 32.6765i) q^{43} +(-30.4991 + 23.6685i) q^{44} +(-9.98038 + 9.98038i) q^{45} +(3.53941 - 56.3580i) q^{46} -15.8305i q^{47} +(14.1177 + 23.8473i) q^{48} -32.6713 q^{49} +(5.71849 + 0.359134i) q^{50} +(36.8883 + 36.8883i) q^{51} +(-19.1761 + 14.8814i) q^{52} +(-0.476870 - 0.476870i) q^{53} +(-6.87343 - 7.79461i) q^{54} +45.4079 q^{55} +(-6.04682 + 31.7565i) q^{56} -48.3893i q^{57} +(-39.9596 - 45.3151i) q^{58} +(9.97719 - 9.97719i) q^{59} +(4.07809 - 32.3397i) q^{60} +(37.9455 - 37.9455i) q^{61} +(-75.9296 - 4.76855i) q^{62} -12.1226i q^{63} +(-59.5215 - 23.5200i) q^{64} +28.5500 q^{65} +(-2.09557 + 33.3677i) q^{66} +(20.0705 + 20.0705i) q^{67} +(-119.530 - 15.0730i) q^{68} +(-34.5801 - 34.5801i) q^{69} +(28.5187 - 25.1483i) q^{70} +40.0818 q^{71} +(23.5764 + 4.48923i) q^{72} +30.8095i q^{73} +(90.9912 - 80.2377i) q^{74} +(3.50874 - 3.50874i) q^{75} +(68.5123 + 88.2846i) q^{76} +(-27.5773 + 27.5773i) q^{77} +(-1.31758 + 20.9798i) q^{78} +130.125i q^{79} +(38.3480 + 64.7767i) q^{80} -9.00000 q^{81} +(-96.2789 - 6.04653i) q^{82} +(-2.26155 - 2.26155i) q^{83} +(17.1639 + 22.1174i) q^{84} +(100.200 + 100.200i) q^{85} +(61.1282 + 69.3207i) q^{86} -52.3228 q^{87} +(-43.4206 - 63.8454i) q^{88} -72.2232i q^{89} +(-18.6704 - 21.1726i) q^{90} +(-17.3391 + 17.3391i) q^{91} +(112.051 + 14.1298i) q^{92} +(-46.5888 + 46.5888i) q^{93} +(31.5986 + 1.98447i) q^{94} -131.441i q^{95} +(-49.3705 + 25.1903i) q^{96} -112.343 q^{97} +(4.09559 - 65.2140i) q^{98} +(20.4737 + 20.4737i) 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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.125358 + 1.99607i −0.0626788 + 0.998034i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) −3.96857 0.500444i −0.992143 0.125111i
\(5\) 3.32679 + 3.32679i 0.665359 + 0.665359i 0.956638 0.291279i \(-0.0940809\pi\)
−0.291279 + 0.956638i \(0.594081\pi\)
\(6\) −2.59820 + 2.29114i −0.433034 + 0.381857i
\(7\) −4.04088 −0.577269 −0.288635 0.957439i \(-0.593201\pi\)
−0.288635 + 0.957439i \(0.593201\pi\)
\(8\) 1.49641 7.85880i 0.187051 0.982350i
\(9\) 3.00000i 0.333333i
\(10\) −7.05755 + 6.22347i −0.705755 + 0.622347i
\(11\) 6.82458 6.82458i 0.620416 0.620416i −0.325222 0.945638i \(-0.605439\pi\)
0.945638 + 0.325222i \(0.105439\pi\)
\(12\) −4.24757 5.47340i −0.353964 0.456117i
\(13\) 4.29091 4.29091i 0.330070 0.330070i −0.522543 0.852613i \(-0.675017\pi\)
0.852613 + 0.522543i \(0.175017\pi\)
\(14\) 0.506555 8.06588i 0.0361825 0.576134i
\(15\) 8.14895i 0.543263i
\(16\) 15.4991 + 3.97210i 0.968694 + 0.248256i
\(17\) 30.1192 1.77172 0.885859 0.463954i \(-0.153570\pi\)
0.885859 + 0.463954i \(0.153570\pi\)
\(18\) −5.98820 0.376073i −0.332678 0.0208929i
\(19\) −19.7548 19.7548i −1.03973 1.03973i −0.999177 0.0405505i \(-0.987089\pi\)
−0.0405505 0.999177i \(-0.512911\pi\)
\(20\) −11.5377 14.8675i −0.576887 0.743375i
\(21\) −4.94905 4.94905i −0.235669 0.235669i
\(22\) 12.7668 + 14.4778i 0.580309 + 0.658083i
\(23\) −28.2345 −1.22759 −0.613794 0.789466i \(-0.710358\pi\)
−0.613794 + 0.789466i \(0.710358\pi\)
\(24\) 11.4577 7.79230i 0.477406 0.324679i
\(25\) 2.86488i 0.114595i
\(26\) 8.02705 + 9.10285i 0.308733 + 0.350109i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 16.0365 + 2.02224i 0.572733 + 0.0722227i
\(29\) −21.3607 + 21.3607i −0.736575 + 0.736575i −0.971914 0.235338i \(-0.924380\pi\)
0.235338 + 0.971914i \(0.424380\pi\)
\(30\) −16.2659 1.02153i −0.542195 0.0340511i
\(31\) 38.0396i 1.22708i 0.789662 + 0.613541i \(0.210256\pi\)
−0.789662 + 0.613541i \(0.789744\pi\)
\(32\) −9.87151 + 30.4393i −0.308485 + 0.951229i
\(33\) 16.7167 0.506568
\(34\) −3.77567 + 60.1200i −0.111049 + 1.76823i
\(35\) −13.4432 13.4432i −0.384091 0.384091i
\(36\) 1.50133 11.9057i 0.0417037 0.330714i
\(37\) −42.8916 42.8916i −1.15923 1.15923i −0.984641 0.174590i \(-0.944140\pi\)
−0.174590 0.984641i \(-0.555860\pi\)
\(38\) 41.9084 36.9556i 1.10285 0.972515i
\(39\) 10.5105 0.269501
\(40\) 31.1229 21.1664i 0.778072 0.529159i
\(41\) 48.2343i 1.17645i 0.808699 + 0.588223i \(0.200172\pi\)
−0.808699 + 0.588223i \(0.799828\pi\)
\(42\) 10.4990 9.25824i 0.249977 0.220434i
\(43\) 32.6765 32.6765i 0.759918 0.759918i −0.216389 0.976307i \(-0.569428\pi\)
0.976307 + 0.216389i \(0.0694281\pi\)
\(44\) −30.4991 + 23.6685i −0.693162 + 0.537921i
\(45\) −9.98038 + 9.98038i −0.221786 + 0.221786i
\(46\) 3.53941 56.3580i 0.0769437 1.22517i
\(47\) 15.8305i 0.336818i −0.985717 0.168409i \(-0.946137\pi\)
0.985717 0.168409i \(-0.0538630\pi\)
\(48\) 14.1177 + 23.8473i 0.294118 + 0.496818i
\(49\) −32.6713 −0.666760
\(50\) 5.71849 + 0.359134i 0.114370 + 0.00718268i
\(51\) 36.8883 + 36.8883i 0.723301 + 0.723301i
\(52\) −19.1761 + 14.8814i −0.368772 + 0.286181i
\(53\) −0.476870 0.476870i −0.00899755 0.00899755i 0.702594 0.711591i \(-0.252025\pi\)
−0.711591 + 0.702594i \(0.752025\pi\)
\(54\) −6.87343 7.79461i −0.127286 0.144345i
\(55\) 45.4079 0.825599
\(56\) −6.04682 + 31.7565i −0.107979 + 0.567080i
\(57\) 48.3893i 0.848934i
\(58\) −39.9596 45.3151i −0.688959 0.781295i
\(59\) 9.97719 9.97719i 0.169105 0.169105i −0.617481 0.786586i \(-0.711847\pi\)
0.786586 + 0.617481i \(0.211847\pi\)
\(60\) 4.07809 32.3397i 0.0679682 0.538995i
\(61\) 37.9455 37.9455i 0.622057 0.622057i −0.324000 0.946057i \(-0.605028\pi\)
0.946057 + 0.324000i \(0.105028\pi\)
\(62\) −75.9296 4.76855i −1.22467 0.0769121i
\(63\) 12.1226i 0.192423i
\(64\) −59.5215 23.5200i −0.930024 0.367500i
\(65\) 28.5500 0.439230
\(66\) −2.09557 + 33.3677i −0.0317510 + 0.505572i
\(67\) 20.0705 + 20.0705i 0.299559 + 0.299559i 0.840841 0.541282i \(-0.182061\pi\)
−0.541282 + 0.840841i \(0.682061\pi\)
\(68\) −119.530 15.0730i −1.75780 0.221662i
\(69\) −34.5801 34.5801i −0.501161 0.501161i
\(70\) 28.5187 25.1483i 0.407410 0.359261i
\(71\) 40.0818 0.564532 0.282266 0.959336i \(-0.408914\pi\)
0.282266 + 0.959336i \(0.408914\pi\)
\(72\) 23.5764 + 4.48923i 0.327450 + 0.0623505i
\(73\) 30.8095i 0.422049i 0.977481 + 0.211024i \(0.0676799\pi\)
−0.977481 + 0.211024i \(0.932320\pi\)
\(74\) 90.9912 80.2377i 1.22961 1.08429i
\(75\) 3.50874 3.50874i 0.0467833 0.0467833i
\(76\) 68.5123 + 88.2846i 0.901477 + 1.16164i
\(77\) −27.5773 + 27.5773i −0.358147 + 0.358147i
\(78\) −1.31758 + 20.9798i −0.0168920 + 0.268971i
\(79\) 130.125i 1.64716i 0.567203 + 0.823578i \(0.308025\pi\)
−0.567203 + 0.823578i \(0.691975\pi\)
\(80\) 38.3480 + 64.7767i 0.479350 + 0.809709i
\(81\) −9.00000 −0.111111
\(82\) −96.2789 6.04653i −1.17413 0.0737382i
\(83\) −2.26155 2.26155i −0.0272476 0.0272476i 0.693352 0.720599i \(-0.256133\pi\)
−0.720599 + 0.693352i \(0.756133\pi\)
\(84\) 17.1639 + 22.1174i 0.204333 + 0.263302i
\(85\) 100.200 + 100.200i 1.17883 + 1.17883i
\(86\) 61.1282 + 69.3207i 0.710793 + 0.806054i
\(87\) −52.3228 −0.601411
\(88\) −43.4206 63.8454i −0.493416 0.725516i
\(89\) 72.2232i 0.811496i −0.913985 0.405748i \(-0.867011\pi\)
0.913985 0.405748i \(-0.132989\pi\)
\(90\) −18.6704 21.1726i −0.207449 0.235252i
\(91\) −17.3391 + 17.3391i −0.190539 + 0.190539i
\(92\) 112.051 + 14.1298i 1.21794 + 0.153585i
\(93\) −46.5888 + 46.5888i −0.500955 + 0.500955i
\(94\) 31.5986 + 1.98447i 0.336156 + 0.0211113i
\(95\) 131.441i 1.38358i
\(96\) −49.3705 + 25.1903i −0.514276 + 0.262399i
\(97\) −112.343 −1.15817 −0.579085 0.815267i \(-0.696590\pi\)
−0.579085 + 0.815267i \(0.696590\pi\)
\(98\) 4.09559 65.2140i 0.0417917 0.665449i
\(99\) 20.4737 + 20.4737i 0.206805 + 0.206805i
\(100\) −1.43371 + 11.3695i −0.0143371 + 0.113695i
\(101\) −1.61933 1.61933i −0.0160330 0.0160330i 0.699045 0.715078i \(-0.253609\pi\)
−0.715078 + 0.699045i \(0.753609\pi\)
\(102\) −78.2559 + 69.0074i −0.767214 + 0.676543i
\(103\) 27.9974 0.271819 0.135910 0.990721i \(-0.456604\pi\)
0.135910 + 0.990721i \(0.456604\pi\)
\(104\) −27.3005 40.1424i −0.262504 0.385984i
\(105\) 32.9289i 0.313609i
\(106\) 1.01164 0.892086i 0.00954381 0.00841590i
\(107\) −40.3835 + 40.3835i −0.377416 + 0.377416i −0.870169 0.492753i \(-0.835990\pi\)
0.492753 + 0.870169i \(0.335990\pi\)
\(108\) 16.4202 12.7427i 0.152039 0.117988i
\(109\) 36.8336 36.8336i 0.337923 0.337923i −0.517662 0.855585i \(-0.673198\pi\)
0.855585 + 0.517662i \(0.173198\pi\)
\(110\) −5.69223 + 90.6373i −0.0517475 + 0.823976i
\(111\) 105.062i 0.946508i
\(112\) −62.6301 16.0508i −0.559197 0.143311i
\(113\) −55.5952 −0.491993 −0.245997 0.969271i \(-0.579115\pi\)
−0.245997 + 0.969271i \(0.579115\pi\)
\(114\) 96.5882 + 6.06596i 0.847265 + 0.0532102i
\(115\) −93.9305 93.9305i −0.816787 0.816787i
\(116\) 95.4612 74.0815i 0.822941 0.638634i
\(117\) 12.8727 + 12.8727i 0.110023 + 0.110023i
\(118\) 18.6644 + 21.1659i 0.158173 + 0.179372i
\(119\) −121.708 −1.02276
\(120\) 64.0410 + 12.1942i 0.533675 + 0.101618i
\(121\) 27.8503i 0.230167i
\(122\) 70.9850 + 80.4985i 0.581844 + 0.659824i
\(123\) −59.0747 + 59.0747i −0.480282 + 0.480282i
\(124\) 19.0367 150.963i 0.153522 1.21744i
\(125\) 92.7007 92.7007i 0.741606 0.741606i
\(126\) 24.1976 + 1.51967i 0.192045 + 0.0120608i
\(127\) 109.927i 0.865569i −0.901497 0.432785i \(-0.857531\pi\)
0.901497 0.432785i \(-0.142469\pi\)
\(128\) 54.4090 115.861i 0.425070 0.905160i
\(129\) 80.0407 0.620470
\(130\) −3.57895 + 56.9876i −0.0275304 + 0.438367i
\(131\) 75.6795 + 75.6795i 0.577706 + 0.577706i 0.934271 0.356565i \(-0.116052\pi\)
−0.356565 + 0.934271i \(0.616052\pi\)
\(132\) −66.3415 8.36579i −0.502587 0.0633772i
\(133\) 79.8270 + 79.8270i 0.600203 + 0.600203i
\(134\) −42.5780 + 37.5460i −0.317746 + 0.280194i
\(135\) −24.4468 −0.181088
\(136\) 45.0707 236.701i 0.331402 1.74045i
\(137\) 2.14751i 0.0156752i −0.999969 0.00783762i \(-0.997505\pi\)
0.999969 0.00783762i \(-0.00249482\pi\)
\(138\) 73.3591 64.6893i 0.531588 0.468763i
\(139\) −109.246 + 109.246i −0.785941 + 0.785941i −0.980826 0.194885i \(-0.937567\pi\)
0.194885 + 0.980826i \(0.437567\pi\)
\(140\) 46.6227 + 60.0778i 0.333019 + 0.429127i
\(141\) 19.3883 19.3883i 0.137505 0.137505i
\(142\) −5.02455 + 80.0059i −0.0353842 + 0.563422i
\(143\) 58.5673i 0.409562i
\(144\) −11.9163 + 46.4973i −0.0827520 + 0.322898i
\(145\) −142.125 −0.980174
\(146\) −61.4979 3.86221i −0.421219 0.0264535i
\(147\) −40.0140 40.0140i −0.272204 0.272204i
\(148\) 148.753 + 191.683i 1.00509 + 1.29516i
\(149\) 79.6950 + 79.6950i 0.534866 + 0.534866i 0.922016 0.387151i \(-0.126541\pi\)
−0.387151 + 0.922016i \(0.626541\pi\)
\(150\) 6.56384 + 7.44354i 0.0437589 + 0.0496236i
\(151\) 105.546 0.698982 0.349491 0.936940i \(-0.386355\pi\)
0.349491 + 0.936940i \(0.386355\pi\)
\(152\) −184.811 + 125.688i −1.21586 + 0.826894i
\(153\) 90.3576i 0.590573i
\(154\) −51.5892 58.5032i −0.334995 0.379891i
\(155\) −126.550 + 126.550i −0.816451 + 0.816451i
\(156\) −41.7118 5.25994i −0.267384 0.0337176i
\(157\) 190.060 190.060i 1.21057 1.21057i 0.239733 0.970839i \(-0.422940\pi\)
0.970839 0.239733i \(-0.0770598\pi\)
\(158\) −259.739 16.3122i −1.64392 0.103242i
\(159\) 1.16809i 0.00734647i
\(160\) −134.106 + 68.4250i −0.838162 + 0.427656i
\(161\) 114.092 0.708649
\(162\) 1.12822 17.9646i 0.00696431 0.110893i
\(163\) −59.4130 59.4130i −0.364497 0.364497i 0.500969 0.865465i \(-0.332977\pi\)
−0.865465 + 0.500969i \(0.832977\pi\)
\(164\) 24.1386 191.421i 0.147186 1.16720i
\(165\) 55.6131 + 55.6131i 0.337049 + 0.337049i
\(166\) 4.79772 4.23071i 0.0289019 0.0254862i
\(167\) 65.3894 0.391553 0.195777 0.980649i \(-0.437277\pi\)
0.195777 + 0.980649i \(0.437277\pi\)
\(168\) −46.2994 + 31.4878i −0.275592 + 0.187427i
\(169\) 132.176i 0.782107i
\(170\) −212.568 + 187.446i −1.25040 + 1.10262i
\(171\) 59.2645 59.2645i 0.346576 0.346576i
\(172\) −146.032 + 113.326i −0.849021 + 0.658873i
\(173\) −212.939 + 212.939i −1.23086 + 1.23086i −0.267228 + 0.963633i \(0.586108\pi\)
−0.963633 + 0.267228i \(0.913892\pi\)
\(174\) 6.55905 104.440i 0.0376957 0.600229i
\(175\) 11.5766i 0.0661522i
\(176\) 132.883 78.6670i 0.755016 0.446972i
\(177\) 24.4390 0.138074
\(178\) 144.162 + 9.05372i 0.809901 + 0.0508636i
\(179\) 196.852 + 196.852i 1.09973 + 1.09973i 0.994442 + 0.105289i \(0.0335768\pi\)
0.105289 + 0.994442i \(0.466423\pi\)
\(180\) 44.6025 34.6132i 0.247792 0.192296i
\(181\) −27.4330 27.4330i −0.151564 0.151564i 0.627252 0.778816i \(-0.284179\pi\)
−0.778816 + 0.627252i \(0.784179\pi\)
\(182\) −32.4364 36.7835i −0.178222 0.202107i
\(183\) 92.9471 0.507907
\(184\) −42.2505 + 221.890i −0.229622 + 1.20592i
\(185\) 285.383i 1.54261i
\(186\) −87.1541 98.8346i −0.468570 0.531369i
\(187\) 205.551 205.551i 1.09920 1.09920i
\(188\) −7.92226 + 62.8243i −0.0421397 + 0.334172i
\(189\) 14.8472 14.8472i 0.0785564 0.0785564i
\(190\) 262.364 + 16.4771i 1.38086 + 0.0867214i
\(191\) 244.409i 1.27963i 0.768530 + 0.639814i \(0.220989\pi\)
−0.768530 + 0.639814i \(0.779011\pi\)
\(192\) −44.0927 101.705i −0.229649 0.529712i
\(193\) 255.040 1.32145 0.660726 0.750627i \(-0.270249\pi\)
0.660726 + 0.750627i \(0.270249\pi\)
\(194\) 14.0830 224.243i 0.0725927 1.15589i
\(195\) 34.9664 + 34.9664i 0.179315 + 0.179315i
\(196\) 129.658 + 16.3501i 0.661522 + 0.0834191i
\(197\) −194.229 194.229i −0.985936 0.985936i 0.0139666 0.999902i \(-0.495554\pi\)
−0.999902 + 0.0139666i \(0.995554\pi\)
\(198\) −43.4335 + 38.3004i −0.219361 + 0.193436i
\(199\) −169.797 −0.853252 −0.426626 0.904428i \(-0.640298\pi\)
−0.426626 + 0.904428i \(0.640298\pi\)
\(200\) −22.5145 4.28703i −0.112573 0.0214352i
\(201\) 49.1624i 0.244589i
\(202\) 3.43529 3.02930i 0.0170064 0.0149965i
\(203\) 86.3160 86.3160i 0.425202 0.425202i
\(204\) −127.933 164.855i −0.627125 0.808111i
\(205\) −160.466 + 160.466i −0.782759 + 0.782759i
\(206\) −3.50969 + 55.8847i −0.0170373 + 0.271285i
\(207\) 84.7036i 0.409196i
\(208\) 83.5492 49.4614i 0.401679 0.237795i
\(209\) −269.637 −1.29013
\(210\) 65.7284 + 4.12789i 0.312992 + 0.0196566i
\(211\) −132.691 132.691i −0.628868 0.628868i 0.318915 0.947783i \(-0.396681\pi\)
−0.947783 + 0.318915i \(0.896681\pi\)
\(212\) 1.65385 + 2.13114i 0.00780116 + 0.0100525i
\(213\) 49.0899 + 49.0899i 0.230469 + 0.230469i
\(214\) −75.5458 85.6705i −0.353018 0.400330i
\(215\) 217.416 1.01124
\(216\) 23.3769 + 34.3732i 0.108226 + 0.159135i
\(217\) 153.713i 0.708357i
\(218\) 68.9050 + 78.1398i 0.316078 + 0.358439i
\(219\) −37.7338 + 37.7338i −0.172301 + 0.172301i
\(220\) −180.205 22.7241i −0.819112 0.103292i
\(221\) 129.239 129.239i 0.584791 0.584791i
\(222\) 209.712 + 13.1704i 0.944647 + 0.0593260i
\(223\) 26.3436i 0.118133i −0.998254 0.0590664i \(-0.981188\pi\)
0.998254 0.0590664i \(-0.0188124\pi\)
\(224\) 39.8896 123.002i 0.178079 0.549115i
\(225\) 8.59463 0.0381984
\(226\) 6.96928 110.972i 0.0308375 0.491026i
\(227\) −70.3362 70.3362i −0.309851 0.309851i 0.535001 0.844852i \(-0.320311\pi\)
−0.844852 + 0.535001i \(0.820311\pi\)
\(228\) −24.2161 + 192.036i −0.106211 + 0.842264i
\(229\) −215.607 215.607i −0.941516 0.941516i 0.0568658 0.998382i \(-0.481889\pi\)
−0.998382 + 0.0568658i \(0.981889\pi\)
\(230\) 199.266 175.717i 0.866376 0.763986i
\(231\) −67.5504 −0.292426
\(232\) 135.905 + 199.834i 0.585797 + 0.861352i
\(233\) 183.853i 0.789069i 0.918881 + 0.394534i \(0.129094\pi\)
−0.918881 + 0.394534i \(0.870906\pi\)
\(234\) −27.3085 + 24.0812i −0.116703 + 0.102911i
\(235\) 52.6647 52.6647i 0.224105 0.224105i
\(236\) −44.5882 + 34.6021i −0.188933 + 0.146619i
\(237\) −159.370 + 159.370i −0.672449 + 0.672449i
\(238\) 15.2570 242.938i 0.0641052 1.02075i
\(239\) 315.183i 1.31876i 0.751811 + 0.659379i \(0.229181\pi\)
−0.751811 + 0.659379i \(0.770819\pi\)
\(240\) −32.3684 + 126.301i −0.134868 + 0.526256i
\(241\) −327.804 −1.36018 −0.680090 0.733128i \(-0.738059\pi\)
−0.680090 + 0.733128i \(0.738059\pi\)
\(242\) −55.5910 3.49124i −0.229715 0.0144266i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) −169.579 + 131.600i −0.694996 + 0.539343i
\(245\) −108.691 108.691i −0.443635 0.443635i
\(246\) −110.512 125.323i −0.449234 0.509441i
\(247\) −169.532 −0.686366
\(248\) 298.945 + 56.9228i 1.20543 + 0.229528i
\(249\) 5.53965i 0.0222476i
\(250\) 173.416 + 196.658i 0.693665 + 0.786631i
\(251\) 219.813 219.813i 0.875747 0.875747i −0.117344 0.993091i \(-0.537438\pi\)
0.993091 + 0.117344i \(0.0374381\pi\)
\(252\) −6.06671 + 48.1096i −0.0240742 + 0.190911i
\(253\) −192.689 + 192.689i −0.761616 + 0.761616i
\(254\) 219.422 + 13.7802i 0.863867 + 0.0542528i
\(255\) 245.440i 0.962509i
\(256\) 224.445 + 123.128i 0.876738 + 0.480969i
\(257\) 150.042 0.583823 0.291911 0.956445i \(-0.405709\pi\)
0.291911 + 0.956445i \(0.405709\pi\)
\(258\) −10.0337 + 159.767i −0.0388903 + 0.619250i
\(259\) 173.320 + 173.320i 0.669188 + 0.669188i
\(260\) −113.303 14.2877i −0.435779 0.0549526i
\(261\) −64.0820 64.0820i −0.245525 0.245525i
\(262\) −160.548 + 141.574i −0.612780 + 0.540360i
\(263\) 14.8922 0.0566242 0.0283121 0.999599i \(-0.490987\pi\)
0.0283121 + 0.999599i \(0.490987\pi\)
\(264\) 25.0151 131.373i 0.0947542 0.497627i
\(265\) 3.17290i 0.0119732i
\(266\) −169.347 + 149.333i −0.636643 + 0.561403i
\(267\) 88.4550 88.4550i 0.331292 0.331292i
\(268\) −69.6069 89.6952i −0.259727 0.334684i
\(269\) 95.4169 95.4169i 0.354710 0.354710i −0.507149 0.861858i \(-0.669301\pi\)
0.861858 + 0.507149i \(0.169301\pi\)
\(270\) 3.06460 48.7976i 0.0113504 0.180732i
\(271\) 46.4991i 0.171583i −0.996313 0.0857917i \(-0.972658\pi\)
0.996313 0.0857917i \(-0.0273420\pi\)
\(272\) 466.821 + 119.636i 1.71625 + 0.439840i
\(273\) −42.4719 −0.155575
\(274\) 4.28657 + 0.269206i 0.0156444 + 0.000982505i
\(275\) −19.5516 19.5516i −0.0710967 0.0710967i
\(276\) 119.928 + 154.539i 0.434522 + 0.559924i
\(277\) 30.5071 + 30.5071i 0.110134 + 0.110134i 0.760026 0.649892i \(-0.225186\pi\)
−0.649892 + 0.760026i \(0.725186\pi\)
\(278\) −204.367 231.757i −0.735134 0.833657i
\(279\) −114.119 −0.409028
\(280\) −125.764 + 85.5308i −0.449157 + 0.305467i
\(281\) 217.239i 0.773093i 0.922270 + 0.386547i \(0.126332\pi\)
−0.922270 + 0.386547i \(0.873668\pi\)
\(282\) 36.2698 + 41.1307i 0.128616 + 0.145854i
\(283\) −136.055 + 136.055i −0.480760 + 0.480760i −0.905374 0.424614i \(-0.860410\pi\)
0.424614 + 0.905374i \(0.360410\pi\)
\(284\) −159.067 20.0587i −0.560096 0.0706292i
\(285\) 160.981 160.981i 0.564846 0.564846i
\(286\) 116.904 + 7.34186i 0.408756 + 0.0256708i
\(287\) 194.909i 0.679126i
\(288\) −91.3180 29.6145i −0.317076 0.102828i
\(289\) 618.167 2.13898
\(290\) 17.8165 283.691i 0.0614361 0.978246i
\(291\) −137.591 137.591i −0.472821 0.472821i
\(292\) 15.4185 122.270i 0.0528030 0.418732i
\(293\) −56.8362 56.8362i −0.193980 0.193980i 0.603433 0.797414i \(-0.293799\pi\)
−0.797414 + 0.603433i \(0.793799\pi\)
\(294\) 84.8866 74.8545i 0.288730 0.254607i
\(295\) 66.3841 0.225031
\(296\) −401.260 + 272.893i −1.35561 + 0.921935i
\(297\) 50.1502i 0.168856i
\(298\) −169.067 + 149.086i −0.567339 + 0.500289i
\(299\) −121.152 + 121.152i −0.405190 + 0.405190i
\(300\) −15.6806 + 12.1688i −0.0522688 + 0.0405626i
\(301\) −132.042 + 132.042i −0.438677 + 0.438677i
\(302\) −13.2310 + 210.677i −0.0438113 + 0.697608i
\(303\) 3.96654i 0.0130909i
\(304\) −227.714 384.650i −0.749060 1.26530i
\(305\) 252.474 0.827782
\(306\) −180.360 11.3270i −0.589411 0.0370164i
\(307\) 245.927 + 245.927i 0.801067 + 0.801067i 0.983262 0.182196i \(-0.0583205\pi\)
−0.182196 + 0.983262i \(0.558320\pi\)
\(308\) 123.243 95.6416i 0.400141 0.310525i
\(309\) 34.2897 + 34.2897i 0.110970 + 0.110970i
\(310\) −236.738 268.466i −0.763671 0.866019i
\(311\) −359.964 −1.15744 −0.578721 0.815526i \(-0.696448\pi\)
−0.578721 + 0.815526i \(0.696448\pi\)
\(312\) 15.7281 82.6003i 0.0504106 0.264744i
\(313\) 131.023i 0.418605i −0.977851 0.209303i \(-0.932881\pi\)
0.977851 0.209303i \(-0.0671194\pi\)
\(314\) 355.547 + 403.198i 1.13231 + 1.28407i
\(315\) 40.3296 40.3296i 0.128030 0.128030i
\(316\) 65.1205 516.412i 0.206077 1.63421i
\(317\) 89.0470 89.0470i 0.280905 0.280905i −0.552565 0.833470i \(-0.686351\pi\)
0.833470 + 0.552565i \(0.186351\pi\)
\(318\) 2.33158 + 0.146429i 0.00733202 + 0.000460468i
\(319\) 291.555i 0.913966i
\(320\) −119.770 276.262i −0.374280 0.863319i
\(321\) −98.9189 −0.308159
\(322\) −14.3024 + 227.736i −0.0444172 + 0.707255i
\(323\) −595.000 595.000i −1.84210 1.84210i
\(324\) 35.7171 + 4.50400i 0.110238 + 0.0139012i
\(325\) −12.2929 12.2929i −0.0378244 0.0378244i
\(326\) 126.040 111.144i 0.386626 0.340934i
\(327\) 90.2236 0.275913
\(328\) 379.064 + 72.1783i 1.15568 + 0.220056i
\(329\) 63.9690i 0.194435i
\(330\) −117.979 + 104.036i −0.357512 + 0.315261i
\(331\) 95.5992 95.5992i 0.288819 0.288819i −0.547794 0.836613i \(-0.684532\pi\)
0.836613 + 0.547794i \(0.184532\pi\)
\(332\) 7.84336 + 10.1069i 0.0236246 + 0.0304425i
\(333\) 128.675 128.675i 0.386410 0.386410i
\(334\) −8.19706 + 130.522i −0.0245421 + 0.390783i
\(335\) 133.541i 0.398629i
\(336\) −57.0478 96.3640i −0.169785 0.286798i
\(337\) 583.717 1.73210 0.866050 0.499958i \(-0.166651\pi\)
0.866050 + 0.499958i \(0.166651\pi\)
\(338\) −263.833 16.5693i −0.780570 0.0490215i
\(339\) −68.0900 68.0900i −0.200855 0.200855i
\(340\) −347.508 447.797i −1.02208 1.31705i
\(341\) 259.604 + 259.604i 0.761302 + 0.761302i
\(342\) 110.867 + 125.725i 0.324172 + 0.367617i
\(343\) 330.024 0.962169
\(344\) −207.900 305.695i −0.604362 0.888649i
\(345\) 230.082i 0.666904i
\(346\) −398.347 451.734i −1.15129 1.30559i
\(347\) 191.655 191.655i 0.552320 0.552320i −0.374790 0.927110i \(-0.622285\pi\)
0.927110 + 0.374790i \(0.122285\pi\)
\(348\) 207.647 + 26.1846i 0.596686 + 0.0752432i
\(349\) −19.4781 + 19.4781i −0.0558112 + 0.0558112i −0.734462 0.678650i \(-0.762565\pi\)
0.678650 + 0.734462i \(0.262565\pi\)
\(350\) −23.1077 1.45122i −0.0660221 0.00414634i
\(351\) 31.5316i 0.0898337i
\(352\) 140.367 + 275.105i 0.398769 + 0.781547i
\(353\) −82.9610 −0.235017 −0.117509 0.993072i \(-0.537491\pi\)
−0.117509 + 0.993072i \(0.537491\pi\)
\(354\) −3.06362 + 48.7819i −0.00865428 + 0.137802i
\(355\) 133.344 + 133.344i 0.375616 + 0.375616i
\(356\) −36.1437 + 286.623i −0.101527 + 0.805120i
\(357\) −149.061 149.061i −0.417539 0.417539i
\(358\) −417.606 + 368.253i −1.16650 + 1.02864i
\(359\) 357.792 0.996634 0.498317 0.866995i \(-0.333952\pi\)
0.498317 + 0.866995i \(0.333952\pi\)
\(360\) 63.4991 + 93.3686i 0.176386 + 0.259357i
\(361\) 419.507i 1.16207i
\(362\) 58.1971 51.3193i 0.160766 0.141766i
\(363\) −34.1095 + 34.1095i −0.0939655 + 0.0939655i
\(364\) 77.4886 60.1341i 0.212881 0.165204i
\(365\) −102.497 + 102.497i −0.280814 + 0.280814i
\(366\) −11.6516 + 185.529i −0.0318350 + 0.506909i
\(367\) 651.729i 1.77583i −0.460010 0.887914i \(-0.652154\pi\)
0.460010 0.887914i \(-0.347846\pi\)
\(368\) −437.610 112.150i −1.18916 0.304756i
\(369\) −144.703 −0.392149
\(370\) 569.643 + 35.7749i 1.53958 + 0.0966889i
\(371\) 1.92698 + 1.92698i 0.00519401 + 0.00519401i
\(372\) 208.206 161.576i 0.559693 0.434343i
\(373\) 199.720 + 199.720i 0.535442 + 0.535442i 0.922187 0.386745i \(-0.126401\pi\)
−0.386745 + 0.922187i \(0.626401\pi\)
\(374\) 384.526 + 436.061i 1.02814 + 1.16594i
\(375\) 227.069 0.605519
\(376\) −124.408 23.6889i −0.330873 0.0630023i
\(377\) 183.314i 0.486243i
\(378\) 27.7747 + 31.4971i 0.0734781 + 0.0833257i
\(379\) −330.204 + 330.204i −0.871251 + 0.871251i −0.992609 0.121358i \(-0.961275\pi\)
0.121358 + 0.992609i \(0.461275\pi\)
\(380\) −65.7787 + 521.631i −0.173102 + 1.37271i
\(381\) 134.633 134.633i 0.353367 0.353367i
\(382\) −487.857 30.6385i −1.27711 0.0802055i
\(383\) 174.284i 0.455049i −0.973772 0.227524i \(-0.926937\pi\)
0.973772 0.227524i \(-0.0730631\pi\)
\(384\) 208.537 75.2625i 0.543064 0.195996i
\(385\) −183.488 −0.476593
\(386\) −31.9712 + 509.077i −0.0828270 + 1.31885i
\(387\) 98.0294 + 98.0294i 0.253306 + 0.253306i
\(388\) 445.839 + 56.2212i 1.14907 + 0.144900i
\(389\) 207.835 + 207.835i 0.534279 + 0.534279i 0.921843 0.387564i \(-0.126683\pi\)
−0.387564 + 0.921843i \(0.626683\pi\)
\(390\) −74.1786 + 65.4120i −0.190202 + 0.167723i
\(391\) −850.402 −2.17494
\(392\) −48.8896 + 256.757i −0.124718 + 0.654992i
\(393\) 185.376i 0.471695i
\(394\) 412.043 363.347i 1.04579 0.922200i
\(395\) −432.900 + 432.900i −1.09595 + 1.09595i
\(396\) −71.0055 91.4974i −0.179307 0.231054i
\(397\) −37.2994 + 37.2994i −0.0939533 + 0.0939533i −0.752521 0.658568i \(-0.771162\pi\)
0.658568 + 0.752521i \(0.271162\pi\)
\(398\) 21.2854 338.927i 0.0534808 0.851574i
\(399\) 195.535i 0.490063i
\(400\) 11.3796 44.4031i 0.0284489 0.111008i
\(401\) −524.704 −1.30849 −0.654244 0.756284i \(-0.727013\pi\)
−0.654244 + 0.756284i \(0.727013\pi\)
\(402\) −98.1315 6.16288i −0.244108 0.0153305i
\(403\) 163.224 + 163.224i 0.405023 + 0.405023i
\(404\) 5.61605 + 7.23682i 0.0139011 + 0.0179129i
\(405\) −29.9411 29.9411i −0.0739288 0.0739288i
\(406\) 161.472 + 183.113i 0.397715 + 0.451017i
\(407\) −585.434 −1.43841
\(408\) 345.098 234.698i 0.845829 0.575240i
\(409\) 787.357i 1.92508i −0.271141 0.962540i \(-0.587401\pi\)
0.271141 0.962540i \(-0.412599\pi\)
\(410\) −300.184 340.416i −0.732157 0.830282i
\(411\) 2.63015 2.63015i 0.00639939 0.00639939i
\(412\) −111.110 14.0111i −0.269684 0.0340076i
\(413\) −40.3166 + 40.3166i −0.0976190 + 0.0976190i
\(414\) 169.074 + 10.6182i 0.408392 + 0.0256479i
\(415\) 15.0475i 0.0362589i
\(416\) 88.2548 + 172.970i 0.212151 + 0.415794i
\(417\) −267.596 −0.641718
\(418\) 33.8010 538.213i 0.0808637 1.28759i
\(419\) 30.1767 + 30.1767i 0.0720209 + 0.0720209i 0.742200 0.670179i \(-0.233783\pi\)
−0.670179 + 0.742200i \(0.733783\pi\)
\(420\) −16.4791 + 130.681i −0.0392360 + 0.311145i
\(421\) −261.021 261.021i −0.620003 0.620003i 0.325529 0.945532i \(-0.394458\pi\)
−0.945532 + 0.325529i \(0.894458\pi\)
\(422\) 281.494 248.227i 0.667048 0.588215i
\(423\) 47.4914 0.112273
\(424\) −4.46122 + 3.03403i −0.0105217 + 0.00715574i
\(425\) 86.2878i 0.203030i
\(426\) −104.141 + 91.8330i −0.244462 + 0.215571i
\(427\) −153.333 + 153.333i −0.359094 + 0.359094i
\(428\) 180.474 140.055i 0.421669 0.327231i
\(429\) 71.7300 71.7300i 0.167203 0.167203i
\(430\) −27.2547 + 433.977i −0.0633830 + 1.00925i
\(431\) 459.989i 1.06726i −0.845718 0.533630i \(-0.820828\pi\)
0.845718 0.533630i \(-0.179172\pi\)
\(432\) −71.5418 + 42.3530i −0.165606 + 0.0980392i
\(433\) −445.246 −1.02828 −0.514140 0.857706i \(-0.671889\pi\)
−0.514140 + 0.857706i \(0.671889\pi\)
\(434\) 306.822 + 19.2691i 0.706964 + 0.0443989i
\(435\) −174.067 174.067i −0.400154 0.400154i
\(436\) −164.610 + 127.744i −0.377546 + 0.292990i
\(437\) 557.768 + 557.768i 1.27636 + 1.27636i
\(438\) −70.5891 80.0495i −0.161162 0.182761i
\(439\) 356.467 0.811998 0.405999 0.913874i \(-0.366924\pi\)
0.405999 + 0.913874i \(0.366924\pi\)
\(440\) 67.9489 356.852i 0.154429 0.811027i
\(441\) 98.0138i 0.222253i
\(442\) 241.768 + 274.171i 0.546987 + 0.620295i
\(443\) 358.752 358.752i 0.809824 0.809824i −0.174783 0.984607i \(-0.555922\pi\)
0.984607 + 0.174783i \(0.0559224\pi\)
\(444\) −52.5779 + 416.948i −0.118419 + 0.939071i
\(445\) 240.272 240.272i 0.539936 0.539936i
\(446\) 52.5837 + 3.30237i 0.117901 + 0.00740442i
\(447\) 195.212i 0.436716i
\(448\) 240.519 + 95.0415i 0.536874 + 0.212146i
\(449\) −44.6564 −0.0994576 −0.0497288 0.998763i \(-0.515836\pi\)
−0.0497288 + 0.998763i \(0.515836\pi\)
\(450\) −1.07740 + 17.1555i −0.00239423 + 0.0381233i
\(451\) 329.179 + 329.179i 0.729886 + 0.729886i
\(452\) 220.634 + 27.8223i 0.488128 + 0.0615538i
\(453\) 129.267 + 129.267i 0.285358 + 0.285358i
\(454\) 149.213 131.579i 0.328663 0.289821i
\(455\) −115.367 −0.253554
\(456\) −380.282 72.4102i −0.833951 0.158794i
\(457\) 84.2332i 0.184318i −0.995744 0.0921589i \(-0.970623\pi\)
0.995744 0.0921589i \(-0.0293768\pi\)
\(458\) 457.394 403.338i 0.998678 0.880652i
\(459\) −110.665 + 110.665i −0.241100 + 0.241100i
\(460\) 325.763 + 419.777i 0.708180 + 0.912558i
\(461\) 205.347 205.347i 0.445438 0.445438i −0.448397 0.893835i \(-0.648005\pi\)
0.893835 + 0.448397i \(0.148005\pi\)
\(462\) 8.46795 134.835i 0.0183289 0.291851i
\(463\) 270.647i 0.584550i −0.956334 0.292275i \(-0.905588\pi\)
0.956334 0.292275i \(-0.0944123\pi\)
\(464\) −415.918 + 246.225i −0.896376 + 0.530657i
\(465\) −309.983 −0.666629
\(466\) −366.983 23.0474i −0.787517 0.0494579i
\(467\) 230.389 + 230.389i 0.493338 + 0.493338i 0.909356 0.416018i \(-0.136575\pi\)
−0.416018 + 0.909356i \(0.636575\pi\)
\(468\) −44.6443 57.5284i −0.0953937 0.122924i
\(469\) −81.1024 81.1024i −0.172926 0.172926i
\(470\) 98.5203 + 111.724i 0.209618 + 0.237711i
\(471\) 465.549 0.988428
\(472\) −63.4788 93.3387i −0.134489 0.197751i
\(473\) 446.006i 0.942931i
\(474\) −298.136 338.092i −0.628978 0.713275i
\(475\) −56.5952 + 56.5952i −0.119148 + 0.119148i
\(476\) 483.008 + 60.9082i 1.01472 + 0.127958i
\(477\) 1.43061 1.43061i 0.00299918 0.00299918i
\(478\) −629.127 39.5106i −1.31616 0.0826581i
\(479\) 575.911i 1.20232i −0.799129 0.601159i \(-0.794706\pi\)
0.799129 0.601159i \(-0.205294\pi\)
\(480\) −248.049 80.4424i −0.516768 0.167588i
\(481\) −368.088 −0.765255
\(482\) 41.0926 654.318i 0.0852545 1.35751i
\(483\) 139.734 + 139.734i 0.289305 + 0.289305i
\(484\) 13.9375 110.526i 0.0287965 0.228359i
\(485\) −373.740 373.740i −0.770599 0.770599i
\(486\) 23.3838 20.6203i 0.0481149 0.0424286i
\(487\) 600.355 1.23276 0.616381 0.787448i \(-0.288598\pi\)
0.616381 + 0.787448i \(0.288598\pi\)
\(488\) −241.424 354.988i −0.494721 0.727434i
\(489\) 145.531i 0.297610i
\(490\) 230.579 203.329i 0.470569 0.414956i
\(491\) 79.7182 79.7182i 0.162359 0.162359i −0.621252 0.783611i \(-0.713376\pi\)
0.783611 + 0.621252i \(0.213376\pi\)
\(492\) 264.006 204.879i 0.536597 0.416420i
\(493\) −643.367 + 643.367i −1.30500 + 1.30500i
\(494\) 21.2522 338.398i 0.0430206 0.685017i
\(495\) 136.224i 0.275200i
\(496\) −151.097 + 589.580i −0.304631 + 1.18867i
\(497\) −161.966 −0.325887
\(498\) 11.0575 + 0.694437i 0.0222039 + 0.00139445i
\(499\) −13.4912 13.4912i −0.0270365 0.0270365i 0.693459 0.720496i \(-0.256086\pi\)
−0.720496 + 0.693459i \(0.756086\pi\)
\(500\) −414.281 + 321.498i −0.828562 + 0.642996i
\(501\) 80.0853 + 80.0853i 0.159851 + 0.159851i
\(502\) 411.205 + 466.316i 0.819134 + 0.928916i
\(503\) 892.196 1.77375 0.886875 0.462009i \(-0.152871\pi\)
0.886875 + 0.462009i \(0.152871\pi\)
\(504\) −95.2695 18.1405i −0.189027 0.0359930i
\(505\) 10.7744i 0.0213354i
\(506\) −360.465 408.775i −0.712381 0.807855i
\(507\) −161.882 + 161.882i −0.319294 + 0.319294i
\(508\) −55.0125 + 436.254i −0.108292 + 0.858768i
\(509\) −44.9128 + 44.9128i −0.0882374 + 0.0882374i −0.749848 0.661610i \(-0.769873\pi\)
0.661610 + 0.749848i \(0.269873\pi\)
\(510\) −489.915 30.7677i −0.960617 0.0603289i
\(511\) 124.498i 0.243636i
\(512\) −273.908 + 432.572i −0.534976 + 0.844867i
\(513\) 145.168 0.282978
\(514\) −18.8090 + 299.495i −0.0365933 + 0.582675i
\(515\) 93.1416 + 93.1416i 0.180857 + 0.180857i
\(516\) −317.647 40.0559i −0.615595 0.0776277i
\(517\) −108.036 108.036i −0.208967 0.208967i
\(518\) −367.685 + 324.231i −0.709816 + 0.625929i
\(519\) −521.592 −1.00499
\(520\) 42.7225 224.368i 0.0821586 0.431478i
\(521\) 866.038i 1.66226i 0.556078 + 0.831130i \(0.312306\pi\)
−0.556078 + 0.831130i \(0.687694\pi\)
\(522\) 135.945 119.879i 0.260432 0.229653i
\(523\) 359.579 359.579i 0.687531 0.687531i −0.274155 0.961686i \(-0.588398\pi\)
0.961686 + 0.274155i \(0.0883981\pi\)
\(524\) −262.466 338.213i −0.500889 0.645444i
\(525\) −14.1784 + 14.1784i −0.0270065 + 0.0270065i
\(526\) −1.86684 + 29.7257i −0.00354913 + 0.0565128i
\(527\) 1145.72i 2.17405i
\(528\) 259.095 + 66.4005i 0.490709 + 0.125759i
\(529\) 268.189 0.506973
\(530\) 6.33332 + 0.397747i 0.0119497 + 0.000750466i
\(531\) 29.9316 + 29.9316i 0.0563683 + 0.0563683i
\(532\) −276.850 356.748i −0.520395 0.670579i
\(533\) 206.969 + 206.969i 0.388310 + 0.388310i
\(534\) 165.474 + 187.651i 0.309876 + 0.351406i
\(535\) −268.695 −0.502234
\(536\) 187.764 127.696i 0.350305 0.238239i
\(537\) 482.187i 0.897926i
\(538\) 178.497 + 202.420i 0.331779 + 0.376245i
\(539\) −222.968 + 222.968i −0.413669 + 0.413669i
\(540\) 97.0190 + 12.2343i 0.179665 + 0.0226561i
\(541\) −9.41176 + 9.41176i −0.0173970 + 0.0173970i −0.715752 0.698355i \(-0.753916\pi\)
0.698355 + 0.715752i \(0.253916\pi\)
\(542\) 92.8154 + 5.82902i 0.171246 + 0.0107546i
\(543\) 67.1970i 0.123751i
\(544\) −297.322 + 916.809i −0.546548 + 1.68531i
\(545\) 245.076 0.449680
\(546\) 5.32417 84.7767i 0.00975123 0.155269i
\(547\) −37.6377 37.6377i −0.0688075 0.0688075i 0.671866 0.740673i \(-0.265493\pi\)
−0.740673 + 0.671866i \(0.765493\pi\)
\(548\) −1.07471 + 8.52253i −0.00196115 + 0.0155521i
\(549\) 113.836 + 113.836i 0.207352 + 0.207352i
\(550\) 41.4772 36.5753i 0.0754131 0.0665006i
\(551\) 843.953 1.53168
\(552\) −323.504 + 220.012i −0.586058 + 0.398573i
\(553\) 525.821i 0.950852i
\(554\) −64.7186 + 57.0700i −0.116821 + 0.103014i
\(555\) 349.521 349.521i 0.629768 0.629768i
\(556\) 488.221 378.878i 0.878096 0.681436i
\(557\) 369.172 369.172i 0.662786 0.662786i −0.293250 0.956036i \(-0.594737\pi\)
0.956036 + 0.293250i \(0.0947369\pi\)
\(558\) 14.3056 227.789i 0.0256374 0.408223i
\(559\) 280.424i 0.501652i
\(560\) −154.960 261.755i −0.276714 0.467420i
\(561\) 503.495 0.897495
\(562\) −433.624 27.2326i −0.771573 0.0484565i
\(563\) −141.210 141.210i −0.250817 0.250817i 0.570489 0.821306i \(-0.306754\pi\)
−0.821306 + 0.570489i \(0.806754\pi\)
\(564\) −86.6464 + 67.2410i −0.153628 + 0.119222i
\(565\) −184.954 184.954i −0.327352 0.327352i
\(566\) −254.520 288.631i −0.449682 0.509949i
\(567\) 36.3679 0.0641410
\(568\) 59.9788 314.995i 0.105596 0.554568i
\(569\) 134.928i 0.237131i −0.992946 0.118566i \(-0.962170\pi\)
0.992946 0.118566i \(-0.0378296\pi\)
\(570\) 301.149 + 341.509i 0.528332 + 0.599139i
\(571\) −486.485 + 486.485i −0.851988 + 0.851988i −0.990378 0.138390i \(-0.955807\pi\)
0.138390 + 0.990378i \(0.455807\pi\)
\(572\) −29.3097 + 232.429i −0.0512407 + 0.406344i
\(573\) −299.339 + 299.339i −0.522406 + 0.522406i
\(574\) 389.052 + 24.4333i 0.677790 + 0.0425668i
\(575\) 80.8885i 0.140676i
\(576\) 70.5600 178.565i 0.122500 0.310008i
\(577\) −310.050 −0.537349 −0.268674 0.963231i \(-0.586586\pi\)
−0.268674 + 0.963231i \(0.586586\pi\)
\(578\) −77.4919 + 1233.90i −0.134069 + 2.13478i
\(579\) 312.359 + 312.359i 0.539480 + 0.539480i
\(580\) 564.034 + 71.1257i 0.972472 + 0.122631i
\(581\) 9.13868 + 9.13868i 0.0157292 + 0.0157292i
\(582\) 291.889 257.393i 0.501527 0.442255i
\(583\) −6.50888 −0.0111645
\(584\) 242.126 + 46.1037i 0.414599 + 0.0789448i
\(585\) 85.6499i 0.146410i
\(586\) 120.574 106.324i 0.205757 0.181440i
\(587\) −301.021 + 301.021i −0.512812 + 0.512812i −0.915387 0.402575i \(-0.868115\pi\)
0.402575 + 0.915387i \(0.368115\pi\)
\(588\) 138.773 + 178.823i 0.236009 + 0.304121i
\(589\) 751.465 751.465i 1.27583 1.27583i
\(590\) −8.32175 + 132.507i −0.0141047 + 0.224588i
\(591\) 475.763i 0.805013i
\(592\) −494.412 835.150i −0.835155 1.41073i
\(593\) 6.08782 0.0102661 0.00513307 0.999987i \(-0.498366\pi\)
0.00513307 + 0.999987i \(0.498366\pi\)
\(594\) −100.103 6.28671i −0.168524 0.0105837i
\(595\) −404.898 404.898i −0.680501 0.680501i
\(596\) −276.392 356.158i −0.463746 0.597581i
\(597\) −207.958 207.958i −0.348339 0.348339i
\(598\) −226.640 257.015i −0.378997 0.429790i
\(599\) −756.472 −1.26289 −0.631446 0.775420i \(-0.717538\pi\)
−0.631446 + 0.775420i \(0.717538\pi\)
\(600\) −22.3240 32.8250i −0.0372067 0.0547084i
\(601\) 753.072i 1.25303i 0.779409 + 0.626516i \(0.215520\pi\)
−0.779409 + 0.626516i \(0.784480\pi\)
\(602\) −247.012 280.117i −0.410319 0.465310i
\(603\) −60.2114 + 60.2114i −0.0998531 + 0.0998531i
\(604\) −418.868 52.8200i −0.693490 0.0874504i
\(605\) −92.6521 + 92.6521i −0.153144 + 0.153144i
\(606\) 7.91748 + 0.497235i 0.0130651 + 0.000820521i
\(607\) 47.1200i 0.0776277i −0.999246 0.0388139i \(-0.987642\pi\)
0.999246 0.0388139i \(-0.0123579\pi\)
\(608\) 796.334 406.314i 1.30976 0.668280i
\(609\) 211.430 0.347176
\(610\) −31.6495 + 503.954i −0.0518844 + 0.826155i
\(611\) −67.9271 67.9271i −0.111174 0.111174i
\(612\) 45.2190 358.591i 0.0738872 0.585932i
\(613\) 637.192 + 637.192i 1.03947 + 1.03947i 0.999189 + 0.0402769i \(0.0128240\pi\)
0.0402769 + 0.999189i \(0.487176\pi\)
\(614\) −521.717 + 460.059i −0.849701 + 0.749282i
\(615\) −393.059 −0.639120
\(616\) 175.458 + 257.992i 0.284834 + 0.418818i
\(617\) 514.635i 0.834092i −0.908885 0.417046i \(-0.863065\pi\)
0.908885 0.417046i \(-0.136935\pi\)
\(618\) −72.7430 + 64.1460i −0.117707 + 0.103796i
\(619\) 313.704 313.704i 0.506791 0.506791i −0.406749 0.913540i \(-0.633338\pi\)
0.913540 + 0.406749i \(0.133338\pi\)
\(620\) 565.553 438.891i 0.912182 0.707888i
\(621\) 103.740 103.740i 0.167054 0.167054i
\(622\) 45.1243 718.513i 0.0725471 1.15517i
\(623\) 291.845i 0.468452i
\(624\) 162.904 + 41.7489i 0.261064 + 0.0669053i
\(625\) 545.171 0.872273
\(626\) 261.532 + 16.4248i 0.417782 + 0.0262377i
\(627\) −330.236 330.236i −0.526693 0.526693i
\(628\) −849.380 + 659.151i −1.35252 + 1.04960i
\(629\) −1291.86 1291.86i −2.05383 2.05383i
\(630\) 75.4449 + 85.5561i 0.119754 + 0.135803i
\(631\) −1226.20 −1.94326 −0.971631 0.236502i \(-0.923999\pi\)
−0.971631 + 0.236502i \(0.923999\pi\)
\(632\) 1022.63 + 194.721i 1.61808 + 0.308103i
\(633\) 325.025i 0.513468i
\(634\) 166.581 + 188.906i 0.262746 + 0.297960i
\(635\) 365.706 365.706i 0.575914 0.575914i
\(636\) −0.584563 + 4.63564i −0.000919125 + 0.00728875i
\(637\) −140.189 + 140.189i −0.220078 + 0.220078i
\(638\) −581.964 36.5487i −0.912169 0.0572863i
\(639\) 120.245i 0.188177i
\(640\) 566.452 204.437i 0.885081 0.319432i
\(641\) 241.218 0.376314 0.188157 0.982139i \(-0.439749\pi\)
0.188157 + 0.982139i \(0.439749\pi\)
\(642\) 12.4002 197.449i 0.0193150 0.307553i
\(643\) −736.141 736.141i −1.14485 1.14485i −0.987550 0.157304i \(-0.949720\pi\)
−0.157304 0.987550i \(-0.550280\pi\)
\(644\) −452.784 57.0969i −0.703081 0.0886598i
\(645\) 266.279 + 266.279i 0.412835 + 0.412835i
\(646\) 1262.25 1113.07i 1.95394 1.72302i
\(647\) −680.082 −1.05113 −0.525565 0.850753i \(-0.676146\pi\)
−0.525565 + 0.850753i \(0.676146\pi\)
\(648\) −13.4677 + 70.7292i −0.0207835 + 0.109150i
\(649\) 136.180i 0.209831i
\(650\) 26.0785 22.9965i 0.0401208 0.0353793i
\(651\) 188.260 188.260i 0.289186 0.289186i
\(652\) 206.052 + 265.518i 0.316030 + 0.407235i
\(653\) −716.929 + 716.929i −1.09790 + 1.09790i −0.103244 + 0.994656i \(0.532922\pi\)
−0.994656 + 0.103244i \(0.967078\pi\)
\(654\) −11.3102 + 180.092i −0.0172939 + 0.275371i
\(655\) 503.540i 0.768763i
\(656\) −191.591 + 747.589i −0.292060 + 1.13962i
\(657\) −92.4286 −0.140683
\(658\) −127.686 8.01900i −0.194052 0.0121869i
\(659\) 276.868 + 276.868i 0.420133 + 0.420133i 0.885250 0.465116i \(-0.153988\pi\)
−0.465116 + 0.885250i \(0.653988\pi\)
\(660\) −192.873 248.536i −0.292232 0.376570i
\(661\) 251.780 + 251.780i 0.380907 + 0.380907i 0.871429 0.490522i \(-0.163194\pi\)
−0.490522 + 0.871429i \(0.663194\pi\)
\(662\) 178.838 + 202.807i 0.270149 + 0.306354i
\(663\) 316.569 0.477480
\(664\) −21.1573 + 14.3889i −0.0318634 + 0.0216700i
\(665\) 531.136i 0.798700i
\(666\) 240.713 + 272.974i 0.361431 + 0.409870i
\(667\) 603.109 603.109i 0.904211 0.904211i
\(668\) −259.502 32.7238i −0.388477 0.0489877i
\(669\) 32.2642 32.2642i 0.0482275 0.0482275i
\(670\) −266.556 16.7403i −0.397845 0.0249856i
\(671\) 517.924i 0.771869i
\(672\) 199.500 101.791i 0.296876 0.151475i
\(673\) 674.332 1.00198 0.500990 0.865453i \(-0.332969\pi\)
0.500990 + 0.865453i \(0.332969\pi\)
\(674\) −73.1734 + 1165.14i −0.108566 + 1.72869i
\(675\) 10.5262 + 10.5262i 0.0155944 + 0.0155944i
\(676\) 66.1468 524.550i 0.0978503 0.775962i
\(677\) 109.048 + 109.048i 0.161075 + 0.161075i 0.783043 0.621968i \(-0.213666\pi\)
−0.621968 + 0.783043i \(0.713666\pi\)
\(678\) 144.448 127.377i 0.213050 0.187871i
\(679\) 453.963 0.668576
\(680\) 937.396 637.514i 1.37852 0.937521i
\(681\) 172.288i 0.252992i
\(682\) −550.731 + 485.644i −0.807523 + 0.712088i
\(683\) −784.278 + 784.278i −1.14828 + 1.14828i −0.161394 + 0.986890i \(0.551599\pi\)
−0.986890 + 0.161394i \(0.948401\pi\)
\(684\) −264.854 + 205.537i −0.387213 + 0.300492i
\(685\) 7.14432 7.14432i 0.0104297 0.0104297i
\(686\) −41.3710 + 658.750i −0.0603076 + 0.960277i
\(687\) 528.128i 0.768745i
\(688\) 636.250 376.662i 0.924782 0.547474i
\(689\) −4.09241 −0.00593964
\(690\) 459.259 + 28.8425i 0.665592 + 0.0418007i
\(691\) −99.4915 99.4915i −0.143982 0.143982i 0.631442 0.775423i \(-0.282464\pi\)
−0.775423 + 0.631442i \(0.782464\pi\)
\(692\) 951.628 738.500i 1.37518 1.06720i
\(693\) −82.7320 82.7320i −0.119382 0.119382i
\(694\) 358.531 + 406.582i 0.516615 + 0.585853i
\(695\) −726.877 −1.04587
\(696\) −78.2964 + 411.194i −0.112495 + 0.590796i
\(697\) 1452.78i 2.08433i
\(698\) −36.4379 41.3213i −0.0522032 0.0591996i
\(699\) −225.173 + 225.173i −0.322136 + 0.322136i
\(700\) 5.79346 45.9427i 0.00827637 0.0656324i
\(701\) 177.909 177.909i 0.253794 0.253794i −0.568730 0.822524i \(-0.692565\pi\)
0.822524 + 0.568730i \(0.192565\pi\)
\(702\) −62.9393 3.95273i −0.0896571 0.00563067i
\(703\) 1694.63i 2.41057i
\(704\) −566.723 + 245.695i −0.805005 + 0.348999i
\(705\) 129.002 0.182981
\(706\) 10.3998 165.596i 0.0147306 0.234555i
\(707\) 6.54353 + 6.54353i 0.00925535 + 0.00925535i
\(708\) −96.9880 12.2304i −0.136989 0.0172745i
\(709\) −208.080 208.080i −0.293484 0.293484i 0.544971 0.838455i \(-0.316541\pi\)
−0.838455 + 0.544971i \(0.816541\pi\)
\(710\) −282.879 + 249.448i −0.398421 + 0.351335i
\(711\) −390.376 −0.549052
\(712\) −567.587 108.076i −0.797173 0.151791i
\(713\) 1074.03i 1.50635i
\(714\) 316.223 278.851i 0.442889 0.390547i
\(715\) 194.841 194.841i 0.272506 0.272506i
\(716\) −682.707 879.734i −0.953501 1.22868i
\(717\) −386.019 + 386.019i −0.538381 + 0.538381i
\(718\) −44.8519 + 714.176i −0.0624678 + 0.994674i
\(719\) 1013.84i 1.41007i 0.709171 + 0.705036i \(0.249069\pi\)
−0.709171 + 0.705036i \(0.750931\pi\)
\(720\) −194.330 + 115.044i −0.269903 + 0.159783i
\(721\) −113.134 −0.156913
\(722\) −837.364 52.5883i −1.15978 0.0728370i
\(723\) −401.476 401.476i −0.555291 0.555291i
\(724\) 95.1413 + 122.599i 0.131411 + 0.169335i
\(725\) 61.1957 + 61.1957i 0.0844079 + 0.0844079i
\(726\) −63.8089 72.3607i −0.0878911 0.0996703i
\(727\) 697.156 0.958949 0.479474 0.877556i \(-0.340827\pi\)
0.479474 + 0.877556i \(0.340827\pi\)
\(728\) 110.318 + 162.211i 0.151536 + 0.222817i
\(729\) 27.0000i 0.0370370i
\(730\) −191.742 217.440i −0.262661 0.297863i
\(731\) 984.189 984.189i 1.34636 1.34636i
\(732\) −368.867 46.5148i −0.503917 0.0635448i
\(733\) −39.9608 + 39.9608i −0.0545168 + 0.0545168i −0.733840 0.679323i \(-0.762274\pi\)
0.679323 + 0.733840i \(0.262274\pi\)
\(734\) 1300.89 + 81.6991i 1.77234 + 0.111307i
\(735\) 266.236i 0.362226i
\(736\) 278.717 859.441i 0.378692 1.16772i
\(737\) 273.945 0.371703
\(738\) 18.1396 288.837i 0.0245794 0.391378i
\(739\) −236.377 236.377i −0.319860 0.319860i 0.528853 0.848713i \(-0.322622\pi\)
−0.848713 + 0.528853i \(0.822622\pi\)
\(740\) −142.818 + 1132.56i −0.192998 + 1.53049i
\(741\) −207.634 207.634i −0.280208 0.280208i
\(742\) −4.08794 + 3.60481i −0.00550935 + 0.00485824i
\(743\) 804.248 1.08243 0.541217 0.840883i \(-0.317964\pi\)
0.541217 + 0.840883i \(0.317964\pi\)
\(744\) 296.416 + 435.848i 0.398409 + 0.585817i
\(745\) 530.258i 0.711755i
\(746\) −423.691 + 373.618i −0.567950 + 0.500828i
\(747\) 6.78466 6.78466i 0.00908255 0.00908255i
\(748\) −918.610 + 712.877i −1.22809 + 0.953043i
\(749\) 163.185 163.185i 0.217870 0.217870i
\(750\) −28.4649 + 453.246i −0.0379532 + 0.604328i
\(751\) 607.492i 0.808911i 0.914558 + 0.404456i \(0.132539\pi\)
−0.914558 + 0.404456i \(0.867461\pi\)
\(752\) 62.8801 245.358i 0.0836171 0.326274i
\(753\) 538.429 0.715045
\(754\) −365.906 22.9797i −0.485287 0.0304771i
\(755\) 351.131 + 351.131i 0.465074 + 0.465074i
\(756\) −66.3522 + 51.4918i −0.0877674 + 0.0681109i
\(757\) −11.6797 11.6797i −0.0154289 0.0154289i 0.699350 0.714779i \(-0.253473\pi\)
−0.714779 + 0.699350i \(0.753473\pi\)
\(758\) −617.716 700.503i −0.814929 0.924147i
\(759\) −471.989 −0.621857
\(760\) −1032.96 196.689i −1.35916 0.258801i
\(761\) 659.125i 0.866130i −0.901363 0.433065i \(-0.857432\pi\)
0.901363 0.433065i \(-0.142568\pi\)
\(762\) 251.859 + 285.614i 0.330524 + 0.374821i
\(763\) −148.840 + 148.840i −0.195073 + 0.195073i
\(764\) 122.313 969.954i 0.160096 1.26957i
\(765\) −300.601 + 300.601i −0.392943 + 0.392943i
\(766\) 347.882 + 21.8478i 0.454154 + 0.0285219i
\(767\) 85.6224i 0.111633i
\(768\) 124.087 + 425.688i 0.161572 + 0.554281i
\(769\) −178.802 −0.232512 −0.116256 0.993219i \(-0.537089\pi\)
−0.116256 + 0.993219i \(0.537089\pi\)
\(770\) 23.0016 366.255i 0.0298722 0.475656i
\(771\) 183.764 + 183.764i 0.238345 +