Properties

Label 152.2.o.c.107.12
Level $152$
Weight $2$
Character 152.107
Analytic conductor $1.214$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [152,2,Mod(27,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.o (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.12
Character \(\chi\) \(=\) 152.107
Dual form 152.2.o.c.27.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.14168 + 0.834605i) q^{2} +(-1.05104 + 0.606818i) q^{3} +(0.606869 + 1.90570i) q^{4} +(2.45005 - 1.41453i) q^{5} +(-1.70640 - 0.184411i) q^{6} +0.450769i q^{7} +(-0.897660 + 2.68220i) q^{8} +(-0.763544 + 1.32250i) q^{9} +O(q^{10})\) \(q+(1.14168 + 0.834605i) q^{2} +(-1.05104 + 0.606818i) q^{3} +(0.606869 + 1.90570i) q^{4} +(2.45005 - 1.41453i) q^{5} +(-1.70640 - 0.184411i) q^{6} +0.450769i q^{7} +(-0.897660 + 2.68220i) q^{8} +(-0.763544 + 1.32250i) q^{9} +(3.97775 + 0.429874i) q^{10} -2.15933 q^{11} +(-1.79426 - 1.63471i) q^{12} +(1.86406 - 3.22864i) q^{13} +(-0.376214 + 0.514634i) q^{14} +(-1.71673 + 2.97346i) q^{15} +(-3.26342 + 2.31303i) q^{16} +(-0.716566 - 1.24113i) q^{17} +(-1.97549 + 0.872612i) q^{18} +(-0.0305680 - 4.35879i) q^{19} +(4.18254 + 3.81063i) q^{20} +(-0.273535 - 0.473776i) q^{21} +(-2.46527 - 1.80219i) q^{22} +(1.12985 + 0.652319i) q^{23} +(-0.684132 - 3.36382i) q^{24} +(1.50182 - 2.60122i) q^{25} +(4.82280 - 2.13033i) q^{26} -5.49424i q^{27} +(-0.859032 + 0.273558i) q^{28} +(4.22992 - 7.32644i) q^{29} +(-4.44162 + 1.96195i) q^{30} +0.497284 q^{31} +(-5.65625 - 0.0829299i) q^{32} +(2.26955 - 1.31032i) q^{33} +(0.217763 - 2.01502i) q^{34} +(0.637628 + 1.10440i) q^{35} +(-2.98366 - 0.652507i) q^{36} -6.72997 q^{37} +(3.60297 - 5.00186i) q^{38} +4.52457i q^{39} +(1.59476 + 7.84129i) q^{40} +(-7.30919 + 4.21996i) q^{41} +(0.0831265 - 0.769194i) q^{42} +(2.90174 + 5.02595i) q^{43} +(-1.31043 - 4.11505i) q^{44} +4.32024i q^{45} +(0.745499 + 1.68772i) q^{46} +(0.567335 + 0.327551i) q^{47} +(2.02640 - 4.41138i) q^{48} +6.79681 q^{49} +(3.88559 - 1.71634i) q^{50} +(1.50628 + 0.869651i) q^{51} +(7.28408 + 1.59298i) q^{52} +(-3.86444 + 6.69340i) q^{53} +(4.58552 - 6.27266i) q^{54} +(-5.29047 + 3.05445i) q^{55} +(-1.20905 - 0.404637i) q^{56} +(2.67712 + 4.56271i) q^{57} +(10.9439 - 4.83414i) q^{58} +(-12.1090 + 6.99113i) q^{59} +(-6.70837 - 1.46708i) q^{60} +(2.13281 + 1.23138i) q^{61} +(0.567740 + 0.415036i) q^{62} +(-0.596141 - 0.344182i) q^{63} +(-6.38841 - 4.81541i) q^{64} -10.5471i q^{65} +(3.68470 + 0.398204i) q^{66} +(2.16651 + 1.25083i) q^{67} +(1.93036 - 2.11877i) q^{68} -1.58336 q^{69} +(-0.193774 + 1.79304i) q^{70} +(-8.35311 - 14.4680i) q^{71} +(-2.86180 - 3.23513i) q^{72} +(8.25523 + 14.2985i) q^{73} +(-7.68347 - 5.61686i) q^{74} +3.64532i q^{75} +(8.28802 - 2.70347i) q^{76} -0.973361i q^{77} +(-3.77623 + 5.16562i) q^{78} +(4.05535 + 7.02407i) q^{79} +(-4.72367 + 10.2832i) q^{80} +(1.04337 + 1.80717i) q^{81} +(-11.8668 - 1.28244i) q^{82} +11.8333 q^{83} +(0.736877 - 0.808796i) q^{84} +(-3.51124 - 2.02722i) q^{85} +(-0.881831 + 8.15984i) q^{86} +10.2672i q^{87} +(1.93835 - 5.79177i) q^{88} +(-6.95256 - 4.01406i) q^{89} +(-3.60569 + 4.93233i) q^{90} +(1.45537 + 0.840259i) q^{91} +(-0.557457 + 2.54903i) q^{92} +(-0.522665 + 0.301761i) q^{93} +(0.374340 + 0.847459i) q^{94} +(-6.24056 - 10.6360i) q^{95} +(5.99526 - 3.34515i) q^{96} +(-5.47310 + 3.15990i) q^{97} +(7.75978 + 5.67265i) q^{98} +(1.64875 - 2.85571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32} + 36 q^{33} - 12 q^{34} - 28 q^{35} - 8 q^{36} + 38 q^{38} - 48 q^{40} + 6 q^{41} + 14 q^{42} + 30 q^{43} + 5 q^{44} - 15 q^{48} - 68 q^{49} - 42 q^{51} + 36 q^{52} + 23 q^{54} - 26 q^{57} + 20 q^{58} - 18 q^{59} - 42 q^{60} + 22 q^{62} + 70 q^{64} - 27 q^{66} + 78 q^{67} + 4 q^{68} + 18 q^{70} - 24 q^{72} + 14 q^{73} + 4 q^{74} + 47 q^{76} - 30 q^{78} - 20 q^{80} + 6 q^{81} + 23 q^{82} - 32 q^{83} + 42 q^{86} - 18 q^{89} - 96 q^{90} - 12 q^{91} + 46 q^{92} + 50 q^{96} + 30 q^{97} + 15 q^{98} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14168 + 0.834605i 0.807290 + 0.590155i
\(3\) −1.05104 + 0.606818i −0.606818 + 0.350346i −0.771719 0.635964i \(-0.780603\pi\)
0.164901 + 0.986310i \(0.447269\pi\)
\(4\) 0.606869 + 1.90570i 0.303434 + 0.952852i
\(5\) 2.45005 1.41453i 1.09569 0.632599i 0.160607 0.987018i \(-0.448655\pi\)
0.935087 + 0.354419i \(0.115321\pi\)
\(6\) −1.70640 0.184411i −0.696637 0.0752853i
\(7\) 0.450769i 0.170375i 0.996365 + 0.0851873i \(0.0271489\pi\)
−0.996365 + 0.0851873i \(0.972851\pi\)
\(8\) −0.897660 + 2.68220i −0.317371 + 0.948302i
\(9\) −0.763544 + 1.32250i −0.254515 + 0.440832i
\(10\) 3.97775 + 0.429874i 1.25787 + 0.135938i
\(11\) −2.15933 −0.651064 −0.325532 0.945531i \(-0.605543\pi\)
−0.325532 + 0.945531i \(0.605543\pi\)
\(12\) −1.79426 1.63471i −0.517958 0.471901i
\(13\) 1.86406 3.22864i 0.516996 0.895464i −0.482809 0.875726i \(-0.660383\pi\)
0.999805 0.0197382i \(-0.00628328\pi\)
\(14\) −0.376214 + 0.514634i −0.100547 + 0.137542i
\(15\) −1.71673 + 2.97346i −0.443258 + 0.767745i
\(16\) −3.26342 + 2.31303i −0.815855 + 0.578257i
\(17\) −0.716566 1.24113i −0.173793 0.301018i 0.765950 0.642900i \(-0.222269\pi\)
−0.939743 + 0.341882i \(0.888936\pi\)
\(18\) −1.97549 + 0.872612i −0.465627 + 0.205677i
\(19\) −0.0305680 4.35879i −0.00701278 0.999975i
\(20\) 4.18254 + 3.81063i 0.935245 + 0.852082i
\(21\) −0.273535 0.473776i −0.0596901 0.103386i
\(22\) −2.46527 1.80219i −0.525597 0.384229i
\(23\) 1.12985 + 0.652319i 0.235590 + 0.136018i 0.613148 0.789968i \(-0.289903\pi\)
−0.377558 + 0.925986i \(0.623236\pi\)
\(24\) −0.684132 3.36382i −0.139648 0.686636i
\(25\) 1.50182 2.60122i 0.300363 0.520245i
\(26\) 4.82280 2.13033i 0.945828 0.417791i
\(27\) 5.49424i 1.05737i
\(28\) −0.859032 + 0.273558i −0.162342 + 0.0516975i
\(29\) 4.22992 7.32644i 0.785477 1.36049i −0.143237 0.989688i \(-0.545751\pi\)
0.928714 0.370797i \(-0.120915\pi\)
\(30\) −4.44162 + 1.96195i −0.810926 + 0.358202i
\(31\) 0.497284 0.0893149 0.0446575 0.999002i \(-0.485780\pi\)
0.0446575 + 0.999002i \(0.485780\pi\)
\(32\) −5.65625 0.0829299i −0.999893 0.0146601i
\(33\) 2.26955 1.31032i 0.395077 0.228098i
\(34\) 0.217763 2.01502i 0.0373460 0.345574i
\(35\) 0.637628 + 1.10440i 0.107779 + 0.186678i
\(36\) −2.98366 0.652507i −0.497277 0.108751i
\(37\) −6.72997 −1.10640 −0.553200 0.833049i \(-0.686593\pi\)
−0.553200 + 0.833049i \(0.686593\pi\)
\(38\) 3.60297 5.00186i 0.584479 0.811409i
\(39\) 4.52457i 0.724511i
\(40\) 1.59476 + 7.84129i 0.252154 + 1.23982i
\(41\) −7.30919 + 4.21996i −1.14150 + 0.659047i −0.946802 0.321815i \(-0.895707\pi\)
−0.194701 + 0.980863i \(0.562374\pi\)
\(42\) 0.0831265 0.769194i 0.0128267 0.118689i
\(43\) 2.90174 + 5.02595i 0.442511 + 0.766451i 0.997875 0.0651562i \(-0.0207546\pi\)
−0.555364 + 0.831607i \(0.687421\pi\)
\(44\) −1.31043 4.11505i −0.197555 0.620368i
\(45\) 4.32024i 0.644023i
\(46\) 0.745499 + 1.68772i 0.109918 + 0.248841i
\(47\) 0.567335 + 0.327551i 0.0827543 + 0.0477782i 0.540806 0.841147i \(-0.318119\pi\)
−0.458052 + 0.888925i \(0.651453\pi\)
\(48\) 2.02640 4.41138i 0.292485 0.636728i
\(49\) 6.79681 0.970972
\(50\) 3.88559 1.71634i 0.549505 0.242727i
\(51\) 1.50628 + 0.869651i 0.210921 + 0.121775i
\(52\) 7.28408 + 1.59298i 1.01012 + 0.220907i
\(53\) −3.86444 + 6.69340i −0.530821 + 0.919409i 0.468532 + 0.883446i \(0.344783\pi\)
−0.999353 + 0.0359626i \(0.988550\pi\)
\(54\) 4.58552 6.27266i 0.624010 0.853601i
\(55\) −5.29047 + 3.05445i −0.713367 + 0.411862i
\(56\) −1.20905 0.404637i −0.161567 0.0540719i
\(57\) 2.67712 + 4.56271i 0.354593 + 0.604346i
\(58\) 10.9439 4.83414i 1.43700 0.634753i
\(59\) −12.1090 + 6.99113i −1.57646 + 0.910168i −0.581109 + 0.813826i \(0.697381\pi\)
−0.995348 + 0.0963425i \(0.969286\pi\)
\(60\) −6.70837 1.46708i −0.866047 0.189399i
\(61\) 2.13281 + 1.23138i 0.273078 + 0.157662i 0.630286 0.776363i \(-0.282938\pi\)
−0.357208 + 0.934025i \(0.616271\pi\)
\(62\) 0.567740 + 0.415036i 0.0721030 + 0.0527096i
\(63\) −0.596141 0.344182i −0.0751067 0.0433629i
\(64\) −6.38841 4.81541i −0.798552 0.601926i
\(65\) 10.5471i 1.30821i
\(66\) 3.68470 + 0.398204i 0.453555 + 0.0490155i
\(67\) 2.16651 + 1.25083i 0.264681 + 0.152814i 0.626468 0.779447i \(-0.284500\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(68\) 1.93036 2.11877i 0.234091 0.256938i
\(69\) −1.58336 −0.190614
\(70\) −0.193774 + 1.79304i −0.0231604 + 0.214310i
\(71\) −8.35311 14.4680i −0.991332 1.71704i −0.609444 0.792829i \(-0.708607\pi\)
−0.381888 0.924209i \(-0.624726\pi\)
\(72\) −2.86180 3.23513i −0.337267 0.381264i
\(73\) 8.25523 + 14.2985i 0.966202 + 1.67351i 0.706351 + 0.707862i \(0.250340\pi\)
0.259851 + 0.965649i \(0.416327\pi\)
\(74\) −7.68347 5.61686i −0.893186 0.652947i
\(75\) 3.64532i 0.420925i
\(76\) 8.28802 2.70347i 0.950701 0.310109i
\(77\) 0.973361i 0.110925i
\(78\) −3.77623 + 5.16562i −0.427574 + 0.584891i
\(79\) 4.05535 + 7.02407i 0.456262 + 0.790269i 0.998760 0.0497881i \(-0.0158546\pi\)
−0.542498 + 0.840057i \(0.682521\pi\)
\(80\) −4.72367 + 10.2832i −0.528123 + 1.14970i
\(81\) 1.04337 + 1.80717i 0.115930 + 0.200796i
\(82\) −11.8668 1.28244i −1.31046 0.141621i
\(83\) 11.8333 1.29887 0.649435 0.760417i \(-0.275006\pi\)
0.649435 + 0.760417i \(0.275006\pi\)
\(84\) 0.736877 0.808796i 0.0803999 0.0882469i
\(85\) −3.51124 2.02722i −0.380848 0.219882i
\(86\) −0.881831 + 8.15984i −0.0950903 + 0.879898i
\(87\) 10.2672i 1.10076i
\(88\) 1.93835 5.79177i 0.206629 0.617405i
\(89\) −6.95256 4.01406i −0.736970 0.425490i 0.0839965 0.996466i \(-0.473232\pi\)
−0.820967 + 0.570976i \(0.806565\pi\)
\(90\) −3.60569 + 4.93233i −0.380073 + 0.519914i
\(91\) 1.45537 + 0.840259i 0.152564 + 0.0880831i
\(92\) −0.557457 + 2.54903i −0.0581189 + 0.265755i
\(93\) −0.522665 + 0.301761i −0.0541979 + 0.0312912i
\(94\) 0.374340 + 0.847459i 0.0386102 + 0.0874088i
\(95\) −6.24056 10.6360i −0.640267 1.09123i
\(96\) 5.99526 3.34515i 0.611889 0.341413i
\(97\) −5.47310 + 3.15990i −0.555709 + 0.320839i −0.751422 0.659822i \(-0.770632\pi\)
0.195712 + 0.980661i \(0.437298\pi\)
\(98\) 7.75978 + 5.67265i 0.783856 + 0.573024i
\(99\) 1.64875 2.85571i 0.165705 0.287010i
\(100\) 5.86857 + 1.28342i 0.586857 + 0.128342i
\(101\) 4.61075 + 2.66202i 0.458787 + 0.264881i 0.711534 0.702652i \(-0.248001\pi\)
−0.252747 + 0.967532i \(0.581334\pi\)
\(102\) 0.993875 + 2.25001i 0.0984083 + 0.222784i
\(103\) 17.9095 1.76468 0.882340 0.470613i \(-0.155967\pi\)
0.882340 + 0.470613i \(0.155967\pi\)
\(104\) 6.98658 + 7.89800i 0.685090 + 0.774463i
\(105\) −1.34034 0.773848i −0.130804 0.0755199i
\(106\) −9.99830 + 4.41645i −0.971120 + 0.428963i
\(107\) 0.909747i 0.0879485i 0.999033 + 0.0439743i \(0.0140020\pi\)
−0.999033 + 0.0439743i \(0.985998\pi\)
\(108\) 10.4704 3.33428i 1.00751 0.320841i
\(109\) 0.935166 + 1.61976i 0.0895727 + 0.155144i 0.907331 0.420418i \(-0.138117\pi\)
−0.817758 + 0.575562i \(0.804783\pi\)
\(110\) −8.58929 0.928242i −0.818957 0.0885044i
\(111\) 7.07346 4.08386i 0.671383 0.387623i
\(112\) −1.04264 1.47105i −0.0985202 0.139001i
\(113\) 2.34200i 0.220317i −0.993914 0.110159i \(-0.964864\pi\)
0.993914 0.110159i \(-0.0351359\pi\)
\(114\) −0.751646 + 7.44350i −0.0703981 + 0.697148i
\(115\) 3.69091 0.344179
\(116\) 16.5290 + 3.61479i 1.53468 + 0.335625i
\(117\) 2.84658 + 4.93042i 0.263166 + 0.455818i
\(118\) −19.6594 2.12459i −1.80980 0.195584i
\(119\) 0.559462 0.323006i 0.0512858 0.0296099i
\(120\) −6.43439 7.27378i −0.587377 0.664002i
\(121\) −6.33727 −0.576116
\(122\) 1.40727 + 3.18589i 0.127408 + 0.288437i
\(123\) 5.12150 8.87069i 0.461790 0.799843i
\(124\) 0.301786 + 0.947677i 0.0271012 + 0.0851039i
\(125\) 5.64786i 0.505160i
\(126\) −0.393346 0.890488i −0.0350421 0.0793310i
\(127\) 1.06604 1.84643i 0.0945955 0.163844i −0.814844 0.579680i \(-0.803178\pi\)
0.909440 + 0.415836i \(0.136511\pi\)
\(128\) −3.27456 10.8295i −0.289433 0.957198i
\(129\) −6.09968 3.52165i −0.537047 0.310064i
\(130\) 8.80266 12.0414i 0.772044 1.05610i
\(131\) −8.72441 15.1111i −0.762255 1.32026i −0.941686 0.336494i \(-0.890759\pi\)
0.179430 0.983771i \(-0.442575\pi\)
\(132\) 3.87441 + 3.52989i 0.337224 + 0.307237i
\(133\) 1.96481 0.0137791i 0.170370 0.00119480i
\(134\) 1.42951 + 3.23623i 0.123491 + 0.279568i
\(135\) −7.77179 13.4611i −0.668889 1.15855i
\(136\) 3.97219 0.807863i 0.340613 0.0692737i
\(137\) −4.28881 + 7.42843i −0.366417 + 0.634654i −0.989003 0.147898i \(-0.952749\pi\)
0.622585 + 0.782552i \(0.286082\pi\)
\(138\) −1.80769 1.32148i −0.153880 0.112492i
\(139\) −2.38145 + 4.12479i −0.201992 + 0.349860i −0.949170 0.314763i \(-0.898075\pi\)
0.747178 + 0.664624i \(0.231408\pi\)
\(140\) −1.71771 + 1.88536i −0.145173 + 0.159342i
\(141\) −0.795055 −0.0669557
\(142\) 2.53849 23.4894i 0.213026 1.97119i
\(143\) −4.02512 + 6.97172i −0.336598 + 0.583004i
\(144\) −0.567205 6.08196i −0.0472671 0.506830i
\(145\) 23.9335i 1.98757i
\(146\) −2.50875 + 23.2142i −0.207625 + 1.92122i
\(147\) −7.14371 + 4.12442i −0.589203 + 0.340177i
\(148\) −4.08421 12.8253i −0.335720 1.05424i
\(149\) −9.33207 + 5.38787i −0.764513 + 0.441392i −0.830914 0.556401i \(-0.812182\pi\)
0.0664008 + 0.997793i \(0.478848\pi\)
\(150\) −3.04240 + 4.16179i −0.248411 + 0.339809i
\(151\) 5.40642 0.439968 0.219984 0.975503i \(-0.429399\pi\)
0.219984 + 0.975503i \(0.429399\pi\)
\(152\) 11.7186 + 3.83072i 0.950504 + 0.310713i
\(153\) 2.18852 0.176931
\(154\) 0.812372 1.11127i 0.0654628 0.0895485i
\(155\) 1.21837 0.703426i 0.0978618 0.0565005i
\(156\) −8.62250 + 2.74582i −0.690352 + 0.219842i
\(157\) −13.3288 + 7.69539i −1.06375 + 0.614159i −0.926468 0.376373i \(-0.877171\pi\)
−0.137286 + 0.990531i \(0.543838\pi\)
\(158\) −1.23241 + 11.4039i −0.0980453 + 0.907242i
\(159\) 9.38003i 0.743885i
\(160\) −13.9754 + 7.79777i −1.10485 + 0.616468i
\(161\) −0.294045 + 0.509301i −0.0231740 + 0.0401386i
\(162\) −0.317077 + 2.93401i −0.0249119 + 0.230517i
\(163\) 0.534048 0.0418298 0.0209149 0.999781i \(-0.493342\pi\)
0.0209149 + 0.999781i \(0.493342\pi\)
\(164\) −12.4777 11.3682i −0.974346 0.887706i
\(165\) 3.70699 6.42070i 0.288589 0.499851i
\(166\) 13.5098 + 9.87610i 1.04856 + 0.766534i
\(167\) 6.81811 11.8093i 0.527601 0.913832i −0.471881 0.881662i \(-0.656425\pi\)
0.999482 0.0321697i \(-0.0102417\pi\)
\(168\) 1.51630 0.308385i 0.116985 0.0237924i
\(169\) −0.449417 0.778413i −0.0345705 0.0598779i
\(170\) −2.31679 5.24493i −0.177690 0.402268i
\(171\) 5.78783 + 3.28770i 0.442606 + 0.251417i
\(172\) −7.81701 + 8.57995i −0.596041 + 0.654215i
\(173\) −0.822987 1.42546i −0.0625706 0.108375i 0.833043 0.553208i \(-0.186597\pi\)
−0.895614 + 0.444833i \(0.853263\pi\)
\(174\) −8.56903 + 11.7218i −0.649616 + 0.888629i
\(175\) 1.17255 + 0.676972i 0.0886365 + 0.0511743i
\(176\) 7.04682 4.99460i 0.531174 0.376482i
\(177\) 8.48469 14.6959i 0.637748 1.10461i
\(178\) −4.58745 10.3854i −0.343844 0.778420i
\(179\) 7.67159i 0.573402i −0.958020 0.286701i \(-0.907441\pi\)
0.958020 0.286701i \(-0.0925586\pi\)
\(180\) −8.23310 + 2.62182i −0.613659 + 0.195419i
\(181\) 11.7649 20.3774i 0.874479 1.51464i 0.0171632 0.999853i \(-0.494537\pi\)
0.857316 0.514790i \(-0.172130\pi\)
\(182\) 0.960285 + 2.17397i 0.0711810 + 0.161145i
\(183\) −2.98889 −0.220945
\(184\) −2.76387 + 2.44492i −0.203755 + 0.180242i
\(185\) −16.4887 + 9.51977i −1.21228 + 0.699908i
\(186\) −0.848568 0.0917045i −0.0622200 0.00672410i
\(187\) 1.54731 + 2.68001i 0.113150 + 0.195982i
\(188\) −0.279918 + 1.27995i −0.0204151 + 0.0933502i
\(189\) 2.47663 0.180148
\(190\) 1.75214 17.3513i 0.127114 1.25880i
\(191\) 23.8645i 1.72678i −0.504540 0.863388i \(-0.668338\pi\)
0.504540 0.863388i \(-0.331662\pi\)
\(192\) 9.63655 + 1.18458i 0.695458 + 0.0854899i
\(193\) 16.5463 9.55301i 1.19103 0.687641i 0.232489 0.972599i \(-0.425313\pi\)
0.958540 + 0.284958i \(0.0919798\pi\)
\(194\) −8.88580 0.960286i −0.637963 0.0689445i
\(195\) 6.40016 + 11.0854i 0.458325 + 0.793843i
\(196\) 4.12477 + 12.9527i 0.294627 + 0.925193i
\(197\) 11.2480i 0.801385i 0.916213 + 0.400693i \(0.131230\pi\)
−0.916213 + 0.400693i \(0.868770\pi\)
\(198\) 4.26574 1.88426i 0.303153 0.133909i
\(199\) 9.91953 + 5.72704i 0.703177 + 0.405979i 0.808530 0.588456i \(-0.200264\pi\)
−0.105353 + 0.994435i \(0.533597\pi\)
\(200\) 5.62888 + 6.36319i 0.398022 + 0.449946i
\(201\) −3.03611 −0.214151
\(202\) 3.04227 + 6.88733i 0.214053 + 0.484591i
\(203\) 3.30253 + 1.90672i 0.231792 + 0.133825i
\(204\) −0.743183 + 3.39829i −0.0520332 + 0.237928i
\(205\) −11.9386 + 20.6782i −0.833825 + 1.44423i
\(206\) 20.4470 + 14.9474i 1.42461 + 1.04143i
\(207\) −1.72538 + 0.996149i −0.119922 + 0.0692371i
\(208\) 1.38473 + 14.8480i 0.0960138 + 1.02953i
\(209\) 0.0660065 + 9.41209i 0.00456577 + 0.651048i
\(210\) −0.884388 2.00215i −0.0610286 0.138161i
\(211\) −13.8288 + 7.98406i −0.952013 + 0.549645i −0.893706 0.448653i \(-0.851904\pi\)
−0.0583076 + 0.998299i \(0.518570\pi\)
\(212\) −15.1008 3.30246i −1.03713 0.226814i
\(213\) 17.5589 + 10.1376i 1.20312 + 0.694619i
\(214\) −0.759279 + 1.03864i −0.0519033 + 0.0710000i
\(215\) 14.2188 + 8.20921i 0.969712 + 0.559864i
\(216\) 14.7366 + 4.93196i 1.00270 + 0.335577i
\(217\) 0.224160i 0.0152170i
\(218\) −0.284195 + 2.62974i −0.0192481 + 0.178108i
\(219\) −17.3531 10.0188i −1.17262 0.677011i
\(220\) −9.03151 8.22842i −0.608904 0.554760i
\(221\) −5.34288 −0.359401
\(222\) 11.4840 + 1.24108i 0.770759 + 0.0832956i
\(223\) 8.06323 + 13.9659i 0.539954 + 0.935227i 0.998906 + 0.0467660i \(0.0148915\pi\)
−0.458952 + 0.888461i \(0.651775\pi\)
\(224\) 0.0373822 2.54966i 0.00249770 0.170356i
\(225\) 2.29341 + 3.97230i 0.152894 + 0.264820i
\(226\) 1.95465 2.67382i 0.130021 0.177860i
\(227\) 13.0282i 0.864715i 0.901702 + 0.432357i \(0.142318\pi\)
−0.901702 + 0.432357i \(0.857682\pi\)
\(228\) −7.07052 + 7.87077i −0.468257 + 0.521254i
\(229\) 12.7253i 0.840914i −0.907312 0.420457i \(-0.861870\pi\)
0.907312 0.420457i \(-0.138130\pi\)
\(230\) 4.21384 + 3.08045i 0.277853 + 0.203119i
\(231\) 0.590653 + 1.02304i 0.0388621 + 0.0673111i
\(232\) 15.8540 + 17.9222i 1.04086 + 1.17665i
\(233\) 5.77758 + 10.0071i 0.378502 + 0.655585i 0.990845 0.135008i \(-0.0431060\pi\)
−0.612343 + 0.790593i \(0.709773\pi\)
\(234\) −0.865069 + 8.00474i −0.0565513 + 0.523286i
\(235\) 1.85333 0.120898
\(236\) −20.6716 18.8335i −1.34561 1.22595i
\(237\) −8.52466 4.92171i −0.553736 0.319700i
\(238\) 0.908310 + 0.0981607i 0.0588770 + 0.00636282i
\(239\) 18.8301i 1.21802i 0.793163 + 0.609010i \(0.208433\pi\)
−0.793163 + 0.609010i \(0.791567\pi\)
\(240\) −1.27529 13.6745i −0.0823194 0.882685i
\(241\) −8.47571 4.89346i −0.545969 0.315215i 0.201526 0.979483i \(-0.435410\pi\)
−0.747494 + 0.664268i \(0.768743\pi\)
\(242\) −7.23514 5.28912i −0.465093 0.339998i
\(243\) 12.0812 + 6.97509i 0.775009 + 0.447452i
\(244\) −1.05231 + 4.81179i −0.0673670 + 0.308043i
\(245\) 16.6525 9.61432i 1.06389 0.614236i
\(246\) 13.2506 5.85307i 0.844830 0.373178i
\(247\) −14.1300 8.02634i −0.899068 0.510704i
\(248\) −0.446392 + 1.33382i −0.0283459 + 0.0846975i
\(249\) −12.4372 + 7.18063i −0.788177 + 0.455054i
\(250\) −4.71373 + 6.44805i −0.298123 + 0.407810i
\(251\) 8.19032 14.1861i 0.516969 0.895416i −0.482837 0.875710i \(-0.660394\pi\)
0.999806 0.0197059i \(-0.00627298\pi\)
\(252\) 0.294130 1.34494i 0.0185284 0.0847233i
\(253\) −2.43972 1.40858i −0.153384 0.0885564i
\(254\) 2.75812 1.21831i 0.173060 0.0764438i
\(255\) 4.92060 0.308140
\(256\) 5.29982 15.0968i 0.331239 0.943547i
\(257\) 7.56834 + 4.36958i 0.472100 + 0.272567i 0.717118 0.696951i \(-0.245461\pi\)
−0.245019 + 0.969518i \(0.578794\pi\)
\(258\) −4.02470 9.11142i −0.250567 0.567252i
\(259\) 3.03366i 0.188502i
\(260\) 20.0996 6.40070i 1.24653 0.396955i
\(261\) 6.45946 + 11.1881i 0.399831 + 0.692527i
\(262\) 2.65133 24.5335i 0.163800 1.51569i
\(263\) −24.1288 + 13.9308i −1.48785 + 0.859008i −0.999904 0.0138683i \(-0.995585\pi\)
−0.487942 + 0.872876i \(0.662252\pi\)
\(264\) 1.47727 + 7.26360i 0.0909197 + 0.447044i
\(265\) 21.8655i 1.34319i
\(266\) 2.25468 + 1.62411i 0.138243 + 0.0995804i
\(267\) 9.74322 0.596276
\(268\) −1.06893 + 4.88782i −0.0652955 + 0.298571i
\(269\) −11.8357 20.5001i −0.721638 1.24991i −0.960343 0.278822i \(-0.910056\pi\)
0.238704 0.971092i \(-0.423277\pi\)
\(270\) 2.36183 21.8547i 0.143736 1.33003i
\(271\) −15.9524 + 9.21013i −0.969041 + 0.559476i −0.898944 0.438064i \(-0.855664\pi\)
−0.0700969 + 0.997540i \(0.522331\pi\)
\(272\) 5.20922 + 2.39289i 0.315855 + 0.145090i
\(273\) −2.03954 −0.123438
\(274\) −11.0963 + 4.90144i −0.670349 + 0.296107i
\(275\) −3.24293 + 5.61691i −0.195556 + 0.338713i
\(276\) −0.960889 3.01741i −0.0578387 0.181627i
\(277\) 26.0321i 1.56412i −0.623203 0.782060i \(-0.714169\pi\)
0.623203 0.782060i \(-0.285831\pi\)
\(278\) −6.16143 + 2.72163i −0.369538 + 0.163232i
\(279\) −0.379699 + 0.657657i −0.0227320 + 0.0393729i
\(280\) −3.53461 + 0.718868i −0.211233 + 0.0429606i
\(281\) 18.1670 + 10.4887i 1.08375 + 0.625706i 0.931907 0.362698i \(-0.118144\pi\)
0.151848 + 0.988404i \(0.451478\pi\)
\(282\) −0.907699 0.663557i −0.0540527 0.0395143i
\(283\) −5.72882 9.92260i −0.340543 0.589837i 0.643991 0.765033i \(-0.277277\pi\)
−0.984534 + 0.175196i \(0.943944\pi\)
\(284\) 22.5025 24.6988i 1.33528 1.46560i
\(285\) 13.0132 + 7.39198i 0.770835 + 0.437863i
\(286\) −10.4140 + 4.60009i −0.615795 + 0.272009i
\(287\) −1.90223 3.29475i −0.112285 0.194483i
\(288\) 4.42847 7.41705i 0.260950 0.437054i
\(289\) 7.47307 12.9437i 0.439592 0.761396i
\(290\) 19.9750 27.3244i 1.17297 1.60454i
\(291\) 3.83496 6.64235i 0.224810 0.389382i
\(292\) −22.2388 + 24.4093i −1.30143 + 1.42845i
\(293\) −10.4003 −0.607590 −0.303795 0.952737i \(-0.598254\pi\)
−0.303795 + 0.952737i \(0.598254\pi\)
\(294\) −11.5981 1.25340i −0.676415 0.0731000i
\(295\) −19.7784 + 34.2572i −1.15154 + 1.99453i
\(296\) 6.04122 18.0511i 0.351139 1.04920i
\(297\) 11.8639i 0.688413i
\(298\) −15.1510 1.63736i −0.877673 0.0948499i
\(299\) 4.21221 2.43192i 0.243598 0.140642i
\(300\) −6.94690 + 2.21223i −0.401079 + 0.127723i
\(301\) −2.26554 + 1.30801i −0.130584 + 0.0753926i
\(302\) 6.17241 + 4.51223i 0.355182 + 0.259649i
\(303\) −6.46144 −0.371200
\(304\) 10.1818 + 14.1539i 0.583964 + 0.811780i
\(305\) 6.96731 0.398947
\(306\) 2.49859 + 1.82655i 0.142835 + 0.104417i
\(307\) −2.39992 + 1.38560i −0.136971 + 0.0790801i −0.566920 0.823773i \(-0.691865\pi\)
0.429949 + 0.902853i \(0.358532\pi\)
\(308\) 1.85494 0.590703i 0.105695 0.0336584i
\(309\) −18.8236 + 10.8678i −1.07084 + 0.618249i
\(310\) 1.97807 + 0.213770i 0.112347 + 0.0121413i
\(311\) 13.8001i 0.782530i −0.920278 0.391265i \(-0.872038\pi\)
0.920278 0.391265i \(-0.127962\pi\)
\(312\) −12.1358 4.06153i −0.687055 0.229939i
\(313\) 5.89194 10.2051i 0.333032 0.576829i −0.650073 0.759872i \(-0.725262\pi\)
0.983105 + 0.183043i \(0.0585949\pi\)
\(314\) −21.6398 2.33861i −1.22121 0.131975i
\(315\) −1.94743 −0.109725
\(316\) −10.9247 + 11.9910i −0.614564 + 0.674545i
\(317\) 8.86581 15.3560i 0.497953 0.862480i −0.502044 0.864842i \(-0.667418\pi\)
0.999997 + 0.00236177i \(0.000751775\pi\)
\(318\) 7.82862 10.7090i 0.439007 0.600531i
\(319\) −9.13381 + 15.8202i −0.511395 + 0.885763i
\(320\) −22.4635 2.76135i −1.25575 0.154364i
\(321\) −0.552051 0.956180i −0.0308125 0.0533687i
\(322\) −0.760771 + 0.336048i −0.0423961 + 0.0187272i
\(323\) −5.38792 + 3.16130i −0.299792 + 0.175900i
\(324\) −2.81074 + 3.08506i −0.156152 + 0.171392i
\(325\) −5.59894 9.69766i −0.310574 0.537929i
\(326\) 0.609712 + 0.445719i 0.0337688 + 0.0246861i
\(327\) −1.96579 1.13495i −0.108709 0.0627630i
\(328\) −4.75762 23.3928i −0.262696 1.29165i
\(329\) −0.147650 + 0.255737i −0.00814020 + 0.0140992i
\(330\) 9.59095 4.23652i 0.527965 0.233212i
\(331\) 27.3712i 1.50445i 0.658904 + 0.752227i \(0.271020\pi\)
−0.658904 + 0.752227i \(0.728980\pi\)
\(332\) 7.18124 + 22.5507i 0.394122 + 1.23763i
\(333\) 5.13863 8.90036i 0.281595 0.487737i
\(334\) 17.6402 7.79203i 0.965229 0.426361i
\(335\) 7.07739 0.386679
\(336\) 1.98851 + 0.913437i 0.108482 + 0.0498321i
\(337\) 10.7104 6.18363i 0.583430 0.336844i −0.179065 0.983837i \(-0.557307\pi\)
0.762495 + 0.646994i \(0.223974\pi\)
\(338\) 0.136577 1.26378i 0.00742880 0.0687408i
\(339\) 1.42117 + 2.46154i 0.0771873 + 0.133692i
\(340\) 1.73241 7.92164i 0.0939532 0.429611i
\(341\) −1.07380 −0.0581497
\(342\) 3.86392 + 8.58406i 0.208937 + 0.464173i
\(343\) 6.21917i 0.335804i
\(344\) −16.0854 + 3.27144i −0.867266 + 0.176384i
\(345\) −3.87929 + 2.23971i −0.208854 + 0.120582i
\(346\) 0.250104 2.31429i 0.0134457 0.124417i
\(347\) −5.69195 9.85874i −0.305560 0.529245i 0.671826 0.740709i \(-0.265510\pi\)
−0.977386 + 0.211464i \(0.932177\pi\)
\(348\) −19.5662 + 6.23082i −1.04886 + 0.334007i
\(349\) 2.93676i 0.157201i −0.996906 0.0786007i \(-0.974955\pi\)
0.996906 0.0786007i \(-0.0250452\pi\)
\(350\) 0.773674 + 1.75150i 0.0413546 + 0.0936218i
\(351\) −17.7389 10.2416i −0.946833 0.546655i
\(352\) 12.2137 + 0.179073i 0.650994 + 0.00954464i
\(353\) 19.1919 1.02148 0.510740 0.859735i \(-0.329371\pi\)
0.510740 + 0.859735i \(0.329371\pi\)
\(354\) 21.9521 9.69667i 1.16674 0.515372i
\(355\) −40.9310 23.6315i −2.17239 1.25423i
\(356\) 3.43033 15.6855i 0.181807 0.831332i
\(357\) −0.392011 + 0.678984i −0.0207474 + 0.0359356i
\(358\) 6.40275 8.75851i 0.338396 0.462901i
\(359\) 3.85728 2.22700i 0.203579 0.117537i −0.394745 0.918791i \(-0.629167\pi\)
0.598324 + 0.801254i \(0.295834\pi\)
\(360\) −11.5878 3.87811i −0.610728 0.204394i
\(361\) −18.9981 + 0.266479i −0.999902 + 0.0140252i
\(362\) 30.4389 13.4455i 1.59983 0.706678i
\(363\) 6.66072 3.84557i 0.349597 0.201840i
\(364\) −0.718066 + 3.28343i −0.0376369 + 0.172099i
\(365\) 40.4514 + 23.3546i 2.11732 + 1.22244i
\(366\) −3.41235 2.49454i −0.178367 0.130392i
\(367\) 16.5629 + 9.56259i 0.864576 + 0.499163i 0.865542 0.500837i \(-0.166974\pi\)
−0.000966198 1.00000i \(0.500308\pi\)
\(368\) −5.19601 + 0.484581i −0.270861 + 0.0252605i
\(369\) 12.8885i 0.670949i
\(370\) −26.7701 2.89304i −1.39171 0.150402i
\(371\) −3.01718 1.74197i −0.156644 0.0904384i
\(372\) −0.892257 0.812917i −0.0462614 0.0421478i
\(373\) −20.6810 −1.07082 −0.535411 0.844592i \(-0.679843\pi\)
−0.535411 + 0.844592i \(0.679843\pi\)
\(374\) −0.470223 + 4.35111i −0.0243146 + 0.224991i
\(375\) −3.42722 5.93612i −0.176981 0.306540i
\(376\) −1.38783 + 1.22768i −0.0715720 + 0.0633126i
\(377\) −15.7696 27.3138i −0.812177 1.40673i
\(378\) 2.82752 + 2.06701i 0.145432 + 0.106315i
\(379\) 2.56021i 0.131509i −0.997836 0.0657546i \(-0.979055\pi\)
0.997836 0.0657546i \(-0.0209454\pi\)
\(380\) 16.4819 18.3473i 0.845502 0.941197i
\(381\) 2.58756i 0.132565i
\(382\) 19.9175 27.2457i 1.01907 1.39401i
\(383\) 9.13650 + 15.8249i 0.466853 + 0.808613i 0.999283 0.0378608i \(-0.0120543\pi\)
−0.532430 + 0.846474i \(0.678721\pi\)
\(384\) 10.0132 + 9.39513i 0.510984 + 0.479443i
\(385\) −1.37685 2.38478i −0.0701709 0.121540i
\(386\) 26.8636 + 2.90314i 1.36732 + 0.147766i
\(387\) −8.86241 −0.450502
\(388\) −9.34329 8.51247i −0.474334 0.432155i
\(389\) 12.4317 + 7.17743i 0.630311 + 0.363910i 0.780872 0.624690i \(-0.214775\pi\)
−0.150562 + 0.988601i \(0.548108\pi\)
\(390\) −1.94500 + 17.9976i −0.0984887 + 0.911344i
\(391\) 1.86972i 0.0945558i
\(392\) −6.10122 + 18.2304i −0.308158 + 0.920775i
\(393\) 18.3394 + 10.5883i 0.925100 + 0.534107i
\(394\) −9.38762 + 12.8416i −0.472941 + 0.646950i
\(395\) 19.8716 + 11.4729i 0.999847 + 0.577262i
\(396\) 6.44272 + 1.40898i 0.323759 + 0.0708040i
\(397\) 22.8960 13.2190i 1.14912 0.663444i 0.200447 0.979705i \(-0.435761\pi\)
0.948673 + 0.316260i \(0.102427\pi\)
\(398\) 6.54512 + 14.8173i 0.328077 + 0.742726i
\(399\) −2.05673 + 1.20676i −0.102965 + 0.0604137i
\(400\) 1.11564 + 11.9626i 0.0557819 + 0.598131i
\(401\) −6.10144 + 3.52267i −0.304691 + 0.175914i −0.644549 0.764563i \(-0.722955\pi\)
0.339857 + 0.940477i \(0.389621\pi\)
\(402\) −3.46627 2.53396i −0.172882 0.126382i
\(403\) 0.926966 1.60555i 0.0461755 0.0799783i
\(404\) −2.27490 + 10.4022i −0.113180 + 0.517530i
\(405\) 5.11260 + 2.95176i 0.254047 + 0.146674i
\(406\) 2.17908 + 4.93317i 0.108146 + 0.244829i
\(407\) 14.5323 0.720337
\(408\) −3.68470 + 3.25949i −0.182420 + 0.161369i
\(409\) 17.6696 + 10.2015i 0.873705 + 0.504434i 0.868578 0.495553i \(-0.165035\pi\)
0.00512749 + 0.999987i \(0.498368\pi\)
\(410\) −30.8882 + 13.6439i −1.52546 + 0.673825i
\(411\) 10.4101i 0.513492i
\(412\) 10.8687 + 34.1303i 0.535465 + 1.68148i
\(413\) −3.15139 5.45836i −0.155070 0.268588i
\(414\) −2.80122 0.302727i −0.137673 0.0148782i
\(415\) 28.9920 16.7386i 1.42316 0.821664i
\(416\) −10.8113 + 18.1074i −0.530068 + 0.887789i
\(417\) 5.78043i 0.283069i
\(418\) −7.78002 + 10.8007i −0.380533 + 0.528279i
\(419\) −7.69306 −0.375831 −0.187915 0.982185i \(-0.560173\pi\)
−0.187915 + 0.982185i \(0.560173\pi\)
\(420\) 0.661313 3.02393i 0.0322688 0.147552i
\(421\) −3.05025 5.28319i −0.148660 0.257487i 0.782072 0.623188i \(-0.214163\pi\)
−0.930732 + 0.365701i \(0.880829\pi\)
\(422\) −22.4516 2.42634i −1.09293 0.118112i
\(423\) −0.866371 + 0.500199i −0.0421244 + 0.0243205i
\(424\) −14.4841 16.3736i −0.703410 0.795172i
\(425\) −4.30461 −0.208804
\(426\) 11.5857 + 26.2287i 0.561331 + 1.27078i
\(427\) −0.555067 + 0.961404i −0.0268616 + 0.0465256i
\(428\) −1.73371 + 0.552097i −0.0838020 + 0.0266866i
\(429\) 9.77007i 0.471703i
\(430\) 9.38185 + 21.2394i 0.452433 + 1.02425i
\(431\) −4.72335 + 8.18108i −0.227516 + 0.394069i −0.957071 0.289853i \(-0.906394\pi\)
0.729555 + 0.683922i \(0.239727\pi\)
\(432\) 12.7083 + 17.9300i 0.611429 + 0.862658i
\(433\) −14.9419 8.62669i −0.718061 0.414572i 0.0959778 0.995383i \(-0.469402\pi\)
−0.814038 + 0.580811i \(0.802736\pi\)
\(434\) −0.187085 + 0.255919i −0.00898038 + 0.0122845i
\(435\) 14.5233 + 25.1550i 0.696337 + 1.20609i
\(436\) −2.51925 + 2.76513i −0.120650 + 0.132426i
\(437\) 2.80879 4.94472i 0.134362 0.236538i
\(438\) −11.4500 25.9213i −0.547101 1.23857i
\(439\) −4.84656 8.39450i −0.231314 0.400647i 0.726881 0.686763i \(-0.240969\pi\)
−0.958195 + 0.286116i \(0.907636\pi\)
\(440\) −3.44362 16.9320i −0.164168 0.807200i
\(441\) −5.18966 + 8.98876i −0.247127 + 0.428036i
\(442\) −6.09986 4.45920i −0.290141 0.212102i
\(443\) 8.03408 13.9154i 0.381711 0.661142i −0.609596 0.792712i \(-0.708668\pi\)
0.991307 + 0.131570i \(0.0420018\pi\)
\(444\) 12.0753 + 11.0016i 0.573069 + 0.522111i
\(445\) −22.7121 −1.07666
\(446\) −2.45040 + 22.6742i −0.116030 + 1.07366i
\(447\) 6.53892 11.3257i 0.309280 0.535689i
\(448\) 2.17064 2.87970i 0.102553 0.136053i
\(449\) 12.4409i 0.587123i 0.955940 + 0.293562i \(0.0948406\pi\)
−0.955940 + 0.293562i \(0.905159\pi\)
\(450\) −0.696961 + 6.44918i −0.0328551 + 0.304017i
\(451\) 15.7830 9.11231i 0.743192 0.429082i
\(452\) 4.46317 1.42129i 0.209930 0.0668518i
\(453\) −5.68236 + 3.28071i −0.266981 + 0.154141i
\(454\) −10.8734 + 14.8741i −0.510315 + 0.698075i
\(455\) 4.75430 0.222885
\(456\) −14.6413 + 3.08481i −0.685640 + 0.144460i
\(457\) −23.5694 −1.10253 −0.551265 0.834330i \(-0.685855\pi\)
−0.551265 + 0.834330i \(0.685855\pi\)
\(458\) 10.6206 14.5283i 0.496270 0.678862i
\(459\) −6.81906 + 3.93698i −0.318286 + 0.183763i
\(460\) 2.23990 + 7.03379i 0.104436 + 0.327952i
\(461\) −0.956655 + 0.552325i −0.0445559 + 0.0257243i −0.522112 0.852877i \(-0.674856\pi\)
0.477557 + 0.878601i \(0.341523\pi\)
\(462\) −0.179498 + 1.66095i −0.00835100 + 0.0772743i
\(463\) 26.1205i 1.21392i −0.794731 0.606962i \(-0.792388\pi\)
0.794731 0.606962i \(-0.207612\pi\)
\(464\) 3.14223 + 33.6932i 0.145874 + 1.56417i
\(465\) −0.853703 + 1.47866i −0.0395895 + 0.0685711i
\(466\) −1.75579 + 16.2469i −0.0813356 + 0.752622i
\(467\) −18.4324 −0.852950 −0.426475 0.904499i \(-0.640245\pi\)
−0.426475 + 0.904499i \(0.640245\pi\)
\(468\) −7.66842 + 8.41686i −0.354473 + 0.389069i
\(469\) −0.563837 + 0.976594i −0.0260356 + 0.0450949i
\(470\) 2.11591 + 1.54680i 0.0975997 + 0.0713485i
\(471\) 9.33940 16.1763i 0.430337 0.745365i
\(472\) −7.88187 38.7544i −0.362792 1.78382i
\(473\) −6.26582 10.8527i −0.288103 0.499008i
\(474\) −5.62475 12.7337i −0.258353 0.584880i
\(475\) −11.3841 6.46659i −0.522338 0.296708i
\(476\) 0.955074 + 0.870148i 0.0437758 + 0.0398832i
\(477\) −5.90133 10.2214i −0.270204 0.468006i
\(478\) −15.7157 + 21.4980i −0.718820 + 0.983295i
\(479\) −26.2671 15.1653i −1.20018 0.692922i −0.239581 0.970876i \(-0.577010\pi\)
−0.960594 + 0.277955i \(0.910343\pi\)
\(480\) 9.95684 16.6763i 0.454465 0.761164i
\(481\) −12.5450 + 21.7287i −0.572005 + 0.990741i
\(482\) −5.59245 12.6606i −0.254729 0.576676i
\(483\) 0.713727i 0.0324757i
\(484\) −3.84589 12.0770i −0.174813 0.548953i
\(485\) −8.93957 + 15.4838i −0.405925 + 0.703083i
\(486\) 7.97143 + 18.0464i 0.361592 + 0.818599i
\(487\) 41.6132 1.88568 0.942838 0.333253i \(-0.108146\pi\)
0.942838 + 0.333253i \(0.108146\pi\)
\(488\) −5.21734 + 4.61526i −0.236178 + 0.208923i
\(489\) −0.561305 + 0.324070i −0.0253831 + 0.0146549i
\(490\) 27.0360 + 2.92177i 1.22136 + 0.131992i
\(491\) 15.3752 + 26.6306i 0.693873 + 1.20182i 0.970559 + 0.240863i \(0.0774304\pi\)
−0.276686 + 0.960960i \(0.589236\pi\)
\(492\) 20.0130 + 4.37671i 0.902255 + 0.197317i
\(493\) −12.1241 −0.546041
\(494\) −9.43307 20.9565i −0.424414 0.942875i
\(495\) 9.32884i 0.419300i
\(496\) −1.62285 + 1.15023i −0.0728680 + 0.0516469i
\(497\) 6.52173 3.76532i 0.292540 0.168898i
\(498\) −20.1923 2.18218i −0.904840 0.0977857i
\(499\) 12.0566 + 20.8826i 0.539728 + 0.934835i 0.998918 + 0.0464978i \(0.0148061\pi\)
−0.459191 + 0.888338i \(0.651861\pi\)
\(500\) −10.7631 + 3.42751i −0.481343 + 0.153283i
\(501\) 16.5494i 0.739373i
\(502\) 21.1905 9.36026i 0.945778 0.417769i
\(503\) 10.6337 + 6.13939i 0.474135 + 0.273742i 0.717969 0.696075i \(-0.245072\pi\)
−0.243834 + 0.969817i \(0.578405\pi\)
\(504\) 1.45830 1.29001i 0.0649577 0.0574617i
\(505\) 15.0621 0.670253
\(506\) −1.60978 3.64435i −0.0715635 0.162011i
\(507\) 0.944710 + 0.545429i 0.0419560 + 0.0242233i
\(508\) 4.16570 + 0.911011i 0.184823 + 0.0404196i
\(509\) 2.27630 3.94266i 0.100895 0.174755i −0.811159 0.584826i \(-0.801163\pi\)
0.912054 + 0.410071i \(0.134496\pi\)
\(510\) 5.61776 + 4.10676i 0.248758 + 0.181850i
\(511\) −6.44531 + 3.72120i −0.285124 + 0.164616i
\(512\) 18.6505 12.8124i 0.824245 0.566234i
\(513\) −23.9482 + 0.167948i −1.05734 + 0.00741507i
\(514\) 4.99375 + 11.3052i 0.220265 + 0.498653i
\(515\) 43.8792 25.3337i 1.93355 1.11633i
\(516\) 3.00952 13.7614i 0.132487 0.605810i
\(517\) −1.22507 0.707292i −0.0538784 0.0311067i
\(518\) 2.53191 3.46347i 0.111246 0.152176i
\(519\) 1.72998 + 0.998807i 0.0759379 + 0.0438428i
\(520\) 28.2894 + 9.46770i 1.24057 + 0.415186i
\(521\) 14.0347i 0.614871i −0.951569 0.307436i \(-0.900529\pi\)
0.951569 0.307436i \(-0.0994709\pi\)
\(522\) −1.96302 + 18.1644i −0.0859189 + 0.795032i
\(523\) −5.94814 3.43416i −0.260094 0.150165i 0.364283 0.931288i \(-0.381314\pi\)
−0.624378 + 0.781123i \(0.714647\pi\)
\(524\) 23.5028 25.7966i 1.02672 1.12693i
\(525\) −1.64320 −0.0717149
\(526\) −39.1741 4.23353i −1.70807 0.184591i
\(527\) −0.356337 0.617194i −0.0155223 0.0268854i
\(528\) −4.37567 + 9.52565i −0.190427 + 0.414551i
\(529\) −10.6490 18.4445i −0.462998 0.801936i
\(530\) −18.2491 + 24.9634i −0.792689 + 1.08434i
\(531\) 21.3522i 0.926605i
\(532\) 1.21864 + 3.73598i 0.0528347 + 0.161975i
\(533\) 31.4650i 1.36290i
\(534\) 11.1236 + 8.13174i 0.481367 + 0.351895i
\(535\) 1.28687 + 2.22892i 0.0556362 + 0.0963647i
\(536\) −5.29978 + 4.68819i −0.228915 + 0.202499i
\(537\) 4.65526 + 8.06314i 0.200889 + 0.347950i
\(538\) 3.59686 33.2828i 0.155072 1.43492i
\(539\) −14.6766 −0.632165
\(540\) 20.9365 22.9799i 0.900963 0.988896i
\(541\) 34.4443 + 19.8865i 1.48088 + 0.854985i 0.999765 0.0216733i \(-0.00689936\pi\)
0.481113 + 0.876659i \(0.340233\pi\)
\(542\) −25.8994 2.79894i −1.11247 0.120225i
\(543\) 28.5566i 1.22548i
\(544\) 3.95015 + 7.07956i 0.169361 + 0.303534i
\(545\) 4.58240 + 2.64565i 0.196289 + 0.113327i
\(546\) −2.32850 1.70221i −0.0996506 0.0728477i
\(547\) −9.78439 5.64902i −0.418350 0.241535i 0.276021 0.961152i \(-0.410984\pi\)
−0.694371 + 0.719617i \(0.744317\pi\)
\(548\) −16.7591 3.66511i −0.715915 0.156566i
\(549\) −3.25699 + 1.88042i −0.139005 + 0.0802545i
\(550\) −8.39029 + 3.70616i −0.357763 + 0.158031i
\(551\) −32.0637 18.2134i −1.36596 0.775916i
\(552\) 1.42132 4.24688i 0.0604952 0.180759i
\(553\) −3.16623 + 1.82802i −0.134642 + 0.0777355i
\(554\) 21.7266 29.7204i 0.923073 1.26270i
\(555\) 11.5535 20.0113i 0.490420 0.849433i
\(556\) −9.30587 2.03513i −0.394657 0.0863088i
\(557\) −20.8369 12.0302i −0.882888 0.509735i −0.0112782 0.999936i \(-0.503590\pi\)
−0.871609 + 0.490201i \(0.836923\pi\)
\(558\) −0.982379 + 0.433936i −0.0415874 + 0.0183700i
\(559\) 21.6360 0.915106
\(560\) −4.63537 2.12929i −0.195880 0.0899787i
\(561\) −3.25256 1.87787i −0.137323 0.0792836i
\(562\) 11.9870 + 27.1371i 0.505641 + 1.14471i
\(563\) 30.2137i 1.27336i 0.771130 + 0.636678i \(0.219692\pi\)
−0.771130 + 0.636678i \(0.780308\pi\)
\(564\) −0.482494 1.51514i −0.0203167 0.0637989i
\(565\) −3.31284 5.73801i −0.139372 0.241400i
\(566\) 1.74097 16.1097i 0.0731786 0.677143i
\(567\) −0.814614 + 0.470318i −0.0342106 + 0.0197515i
\(568\) 46.3044 9.41737i 1.94289 0.395144i
\(569\) 31.3114i 1.31264i −0.754482 0.656320i \(-0.772112\pi\)
0.754482 0.656320i \(-0.227888\pi\)
\(570\) 8.68752 + 19.3001i 0.363880 + 0.808394i
\(571\) −36.8938 −1.54396 −0.771978 0.635649i \(-0.780733\pi\)
−0.771978 + 0.635649i \(0.780733\pi\)
\(572\) −15.7288 3.43978i −0.657652 0.143824i
\(573\) 14.4814 + 25.0826i 0.604970 + 1.04784i
\(574\) 0.578083 5.34917i 0.0241287 0.223270i
\(575\) 3.39366 1.95933i 0.141525 0.0817096i
\(576\) 11.2462 4.77188i 0.468592 0.198828i
\(577\) −1.16074 −0.0483220 −0.0241610 0.999708i \(-0.507691\pi\)
−0.0241610 + 0.999708i \(0.507691\pi\)
\(578\) 19.3348 8.54055i 0.804220 0.355240i
\(579\) −11.5939 + 20.0812i −0.481825 + 0.834545i
\(580\) 45.6101 14.5245i 1.89386 0.603096i
\(581\) 5.33407i 0.221294i
\(582\) 9.92205 4.38277i 0.411282 0.181671i
\(583\) 8.34461 14.4533i 0.345598 0.598594i
\(584\) −45.7618 + 9.30702i −1.89364 + 0.385127i
\(585\) 13.9485 + 8.05317i 0.576700 + 0.332958i
\(586\) −11.8738 8.68011i −0.490501 0.358572i
\(587\) −0.751317 1.30132i −0.0310102 0.0537112i 0.850104 0.526615i \(-0.176539\pi\)
−0.881114 + 0.472904i \(0.843206\pi\)
\(588\) −12.1952 11.1108i −0.502923 0.458202i
\(589\) −0.0152010 2.16756i −0.000626346 0.0893127i
\(590\) −51.1718 + 22.6036i −2.10671 + 0.930576i
\(591\) −6.82547 11.8221i −0.280763 0.486295i
\(592\) 21.9627 15.5666i 0.902662 0.639783i
\(593\) 9.24084 16.0056i 0.379476 0.657271i −0.611510 0.791237i \(-0.709438\pi\)
0.990986 + 0.133965i \(0.0427710\pi\)
\(594\) −9.90167 + 13.5448i −0.406270 + 0.555749i
\(595\) 0.913806 1.58276i 0.0374624 0.0648868i
\(596\) −15.9310 14.5144i −0.652561 0.594534i
\(597\) −13.9011 −0.568934
\(598\) 6.83869 + 0.739055i 0.279655 + 0.0302222i
\(599\) −16.6212 + 28.7888i −0.679124 + 1.17628i 0.296121 + 0.955150i \(0.404307\pi\)
−0.975245 + 0.221127i \(0.929027\pi\)
\(600\) −9.77748 3.27226i −0.399164 0.133589i
\(601\) 11.1345i 0.454186i 0.973873 + 0.227093i \(0.0729221\pi\)
−0.973873 + 0.227093i \(0.927078\pi\)
\(602\) −3.67820 0.397502i −0.149912 0.0162010i
\(603\) −3.30845 + 1.91013i −0.134730 + 0.0777867i
\(604\) 3.28099 + 10.3030i 0.133502 + 0.419225i
\(605\) −15.5266 + 8.96429i −0.631247 + 0.364450i
\(606\) −7.37690 5.39275i −0.299666 0.219065i
\(607\) −11.2378 −0.456127 −0.228064 0.973646i \(-0.573239\pi\)
−0.228064 + 0.973646i \(0.573239\pi\)
\(608\) −0.188574 + 24.6569i −0.00764769 + 0.999971i
\(609\) −4.62812 −0.187541
\(610\) 7.95444 + 5.81495i 0.322066 + 0.235440i
\(611\) 2.11509 1.22115i 0.0855674 0.0494024i
\(612\) 1.32815 + 4.17067i 0.0536871 + 0.168589i
\(613\) 20.5664 11.8740i 0.830669 0.479587i −0.0234126 0.999726i \(-0.507453\pi\)
0.854082 + 0.520139i \(0.174120\pi\)
\(614\) −3.89637 0.421079i −0.157245 0.0169934i
\(615\) 28.9781i 1.16851i
\(616\) 2.61075 + 0.873747i 0.105190 + 0.0352043i
\(617\) −2.53920 + 4.39802i −0.102224 + 0.177058i −0.912601 0.408852i \(-0.865929\pi\)
0.810376 + 0.585910i \(0.199263\pi\)
\(618\) −30.5609 3.30271i −1.22934 0.132854i
\(619\) 45.0160 1.80935 0.904674 0.426105i \(-0.140115\pi\)
0.904674 + 0.426105i \(0.140115\pi\)
\(620\) 2.07991 + 1.89497i 0.0835313 + 0.0761036i
\(621\) 3.58400 6.20766i 0.143821 0.249105i
\(622\) 11.5176 15.7553i 0.461814 0.631728i
\(623\) 1.80941 3.13400i 0.0724927 0.125561i
\(624\) −10.4655 14.7656i −0.418953 0.591096i
\(625\) 15.4982 + 26.8436i 0.619927 + 1.07375i
\(626\) 15.2440 6.73357i 0.609272 0.269127i
\(627\) −5.78080 9.85242i −0.230863 0.393468i
\(628\) −22.7540 20.7307i −0.907982 0.827244i
\(629\) 4.82247 + 8.35276i 0.192284 + 0.333046i
\(630\) −2.22334 1.62533i −0.0885801 0.0647549i
\(631\) −20.6719 11.9349i −0.822936 0.475122i 0.0284918 0.999594i \(-0.490930\pi\)
−0.851428 + 0.524472i \(0.824263\pi\)
\(632\) −22.4803 + 4.57203i −0.894218 + 0.181866i
\(633\) 9.68974 16.7831i 0.385132 0.667069i
\(634\) 22.9381 10.1322i 0.910990 0.402402i
\(635\) 6.03179i 0.239364i
\(636\) 17.8756 5.69245i 0.708813 0.225720i
\(637\) 12.6696 21.9445i 0.501989 0.869471i
\(638\) −23.6315 + 10.4385i −0.935582 + 0.413265i
\(639\) 25.5119 1.00923
\(640\) −23.3415 21.9007i −0.922653 0.865701i
\(641\) −0.303877 + 0.175444i −0.0120024 + 0.00692960i −0.505989 0.862540i \(-0.668872\pi\)
0.493987 + 0.869469i \(0.335539\pi\)
\(642\) 0.167767 1.55240i 0.00662123 0.0612682i
\(643\) 7.67194 + 13.2882i 0.302552 + 0.524035i 0.976713 0.214549i \(-0.0688281\pi\)
−0.674161 + 0.738584i \(0.735495\pi\)
\(644\) −1.14902 0.251284i −0.0452779 0.00990198i
\(645\) −19.9260 −0.784585
\(646\) −8.78972 0.887588i −0.345827 0.0349217i
\(647\) 12.4035i 0.487632i 0.969821 + 0.243816i \(0.0783994\pi\)
−0.969821 + 0.243816i \(0.921601\pi\)
\(648\) −5.78378 + 1.17630i −0.227208 + 0.0462095i
\(649\) 26.1474 15.0962i 1.02637 0.592578i
\(650\) 1.70151 15.7445i 0.0667386 0.617551i
\(651\) −0.136024 0.235601i −0.00533122 0.00923394i
\(652\) 0.324097 + 1.01774i 0.0126926 + 0.0398577i
\(653\) 38.6270i 1.51159i 0.654808 + 0.755795i \(0.272750\pi\)
−0.654808 + 0.755795i \(0.727250\pi\)
\(654\) −1.29707 2.93641i −0.0507195 0.114823i
\(655\) −42.7504 24.6820i −1.67040 0.964404i
\(656\) 14.0921 30.6778i 0.550203 1.19777i
\(657\) −25.2129 −0.983650
\(658\) −0.382008 + 0.168741i −0.0148922 + 0.00657820i
\(659\) 0.427803 + 0.246992i 0.0166648 + 0.00962144i 0.508309 0.861175i \(-0.330271\pi\)
−0.491644 + 0.870796i \(0.663604\pi\)
\(660\) 14.4856 + 3.16791i 0.563852 + 0.123311i
\(661\) −12.5398 + 21.7195i −0.487740 + 0.844791i −0.999901 0.0140991i \(-0.995512\pi\)
0.512160 + 0.858890i \(0.328845\pi\)
\(662\) −22.8441 + 31.2491i −0.887861 + 1.21453i
\(663\) 5.61558 3.24216i 0.218091 0.125915i
\(664\) −10.6222 + 31.7392i −0.412223 + 1.23172i
\(665\) 4.79438 2.81305i 0.185918 0.109085i
\(666\) 13.2950 5.87265i 0.515169 0.227560i
\(667\) 9.55835 5.51852i 0.370101 0.213678i
\(668\) 26.6428 + 5.82660i 1.03084 + 0.225438i
\(669\) −16.9495 9.78582i −0.655307 0.378342i
\(670\) 8.08012 + 5.90683i 0.312162 + 0.228201i
\(671\) −4.60545 2.65896i −0.177791 0.102648i
\(672\) 1.50789 + 2.70248i 0.0581681 + 0.104250i
\(673\) 12.2784i 0.473296i 0.971595 + 0.236648i \(0.0760489\pi\)
−0.971595 + 0.236648i \(0.923951\pi\)
\(674\) 17.3887 + 1.87919i 0.669787 + 0.0723837i
\(675\) −14.2917 8.25134i −0.550089 0.317594i
\(676\) 1.21069 1.32885i 0.0465649 0.0511096i
\(677\) −6.28293 −0.241473 −0.120736 0.992685i \(-0.538526\pi\)
−0.120736 + 0.992685i \(0.538526\pi\)
\(678\) −0.431890 + 3.99640i −0.0165866 + 0.153481i
\(679\) −1.42438 2.46710i −0.0546628 0.0946788i
\(680\) 8.58930 7.59811i 0.329385 0.291374i
\(681\) −7.90577 13.6932i −0.302950 0.524724i
\(682\) −1.22594 0.896202i −0.0469437 0.0343173i
\(683\) 28.9958i 1.10949i 0.832020 + 0.554746i \(0.187185\pi\)
−0.832020 + 0.554746i \(0.812815\pi\)
\(684\) −2.75294 + 13.0251i −0.105261 + 0.498027i
\(685\) 24.2667i 0.927181i
\(686\) −5.19055 + 7.10031i −0.198176 + 0.271091i
\(687\) 7.72197 + 13.3748i 0.294611 + 0.510282i
\(688\) −21.0947 9.69001i −0.804230 0.369428i
\(689\) 14.4071 + 24.9538i 0.548865 + 0.950662i
\(690\) −6.29819 0.680643i −0.239768 0.0259116i
\(691\) 29.0538 1.10526 0.552629 0.833427i \(-0.313625\pi\)
0.552629 + 0.833427i \(0.313625\pi\)
\(692\) 2.21705 2.43344i 0.0842797 0.0925054i
\(693\) 1.28727 + 0.743204i 0.0488992 + 0.0282320i
\(694\) 1.72977 16.0061i 0.0656612 0.607582i
\(695\) 13.4746i 0.511120i
\(696\) −27.5386 9.21642i −1.04385 0.349348i
\(697\) 10.4750 + 6.04776i 0.396770 + 0.229075i
\(698\) 2.45104 3.35285i 0.0927731 0.126907i
\(699\) −12.1449 7.01188i −0.459363 0.265214i
\(700\) −0.578525 + 2.64537i −0.0218662 + 0.0999855i
\(701\) −21.1436 + 12.2073i −0.798584 + 0.461063i −0.842976 0.537952i \(-0.819198\pi\)
0.0443920 + 0.999014i \(0.485865\pi\)
\(702\) −11.7045 26.4976i −0.441758 1.00009i
\(703\) 0.205722 + 29.3345i 0.00775894 + 1.10637i
\(704\) 13.7947 + 10.3981i 0.519908 + 0.391893i
\(705\) −1.94792 + 1.12463i −0.0733630 + 0.0423561i
\(706\) 21.9110 + 16.0176i 0.824631 + 0.602832i
\(707\) −1.19995 + 2.07838i −0.0451289 + 0.0781656i
\(708\) 33.1552 + 7.25082i 1.24605 + 0.272502i
\(709\) −3.14824 1.81764i −0.118235 0.0682627i 0.439716 0.898137i \(-0.355079\pi\)
−0.557951 + 0.829874i \(0.688412\pi\)
\(710\) −27.0072 61.1409i −1.01356 2.29458i
\(711\) −12.3857 −0.464502
\(712\) 17.0076 15.0449i 0.637385 0.563832i
\(713\) 0.561857 + 0.324388i 0.0210417 + 0.0121484i
\(714\) −1.01423 + 0.448008i −0.0379568 + 0.0167663i
\(715\) 22.7747i 0.851726i
\(716\) 14.6198 4.65565i 0.546367 0.173990i
\(717\) −11.4265 19.7912i −0.426729 0.739116i
\(718\) 6.26244 + 0.676780i 0.233712 + 0.0252572i
\(719\) 34.9775 20.1943i 1.30444 0.753120i 0.323279 0.946304i \(-0.395215\pi\)
0.981163 + 0.193184i \(0.0618813\pi\)
\(720\) −9.99283 14.0988i −0.372411 0.525430i
\(721\) 8.07306i 0.300657i
\(722\) −21.9122 15.5517i −0.815488 0.578774i
\(723\) 11.8777 0.441738
\(724\) 45.9731 + 10.0540i 1.70858 + 0.373655i
\(725\) −12.7051 22.0059i −0.471857 0.817280i
\(726\) 10.8140 + 1.16866i 0.401343 + 0.0433730i
\(727\) −4.07642 + 2.35352i −0.151186 + 0.0872873i −0.573685 0.819076i \(-0.694486\pi\)
0.422499 + 0.906364i \(0.361153\pi\)
\(728\) −3.56017 + 3.14933i −0.131949 + 0.116722i
\(729\) −23.1906 −0.858912
\(730\) 26.6907 + 60.4245i 0.987867 + 2.23641i
\(731\) 4.15857 7.20286i 0.153810 0.266407i
\(732\) −1.81386 5.69594i −0.0670423 0.210528i
\(733\) 23.9315i 0.883930i −0.897032 0.441965i \(-0.854282\pi\)
0.897032 0.441965i \(-0.145718\pi\)
\(734\) 10.9285 + 24.7409i 0.403380 + 0.913203i
\(735\) −11.6683 + 20.2101i −0.430391 + 0.745459i
\(736\) −6.33661 3.78338i −0.233571 0.139457i
\(737\) −4.67821 2.70097i −0.172324 0.0994915i
\(738\) 10.7568 14.7146i 0.395964 0.541650i
\(739\) 1.44053 + 2.49507i 0.0529906 + 0.0917825i 0.891304 0.453406i \(-0.149791\pi\)
−0.838313 + 0.545189i \(0.816458\pi\)
\(740\) −28.1484 25.6454i −1.03475 0.942743i
\(741\) 19.7217 0.138307i 0.724494 0.00508084i
\(742\) −1.99080 4.50692i −0.0730844 0.165454i
\(743\) 17.8747 + 30.9598i 0.655758 + 1.13581i 0.981703 + 0.190418i \(0.0609843\pi\)
−0.325945 + 0.945389i \(0.605682\pi\)
\(744\) −0.340208 1.67277i −0.0124726 0.0613268i
\(745\) −15.2427 + 26.4011i −0.558448 + 0.967261i
\(746\) −23.6111 17.2605i −0.864463 0.631950i
\(747\) −9.03522 + 15.6495i −0.330581 + 0.572584i
\(748\) −4.16830 + 4.57513i −0.152408 + 0.167283i
\(749\) −0.410086 −0.0149842
\(750\) 1.04152 9.63753i 0.0380311 0.351913i
\(751\) 24.3250 42.1322i 0.887632 1.53742i 0.0449656 0.998989i \(-0.485682\pi\)
0.842667 0.538436i \(-0.180985\pi\)
\(752\) −2.60909 + 0.243324i −0.0951436 + 0.00887312i
\(753\) 19.8801i 0.724473i
\(754\) 4.79235 44.3450i 0.174527 1.61495i
\(755\) 13.2460 7.64757i 0.482071 0.278324i
\(756\) 1.50299 + 4.71973i 0.0546632 + 0.171655i
\(757\) −29.4372 + 16.9956i −1.06991 + 0.617716i −0.928158 0.372186i \(-0.878608\pi\)
−0.141757 + 0.989902i \(0.545275\pi\)
\(758\) 2.13676 2.92294i 0.0776108 0.106166i
\(759\) 3.41899 0.124102
\(760\) 34.1298 7.19092i 1.23802 0.260842i
\(761\) −34.2969 −1.24326 −0.621631 0.783310i \(-0.713530\pi\)
−0.621631 + 0.783310i \(0.713530\pi\)
\(762\) −2.15959 + 2.95417i −0.0782338 + 0.107018i
\(763\) −0.730135 + 0.421544i −0.0264327 + 0.0152609i
\(764\) 45.4787 14.4826i 1.64536 0.523964i
\(765\) 5.36198 3.09574i 0.193863 0.111927i
\(766\) −2.77656 + 25.6923i −0.100321 + 0.928301i
\(767\) 52.1275i 1.88221i
\(768\) 3.59066 + 19.0833i 0.129567 + 0.688609i
\(769\) −5.78344 + 10.0172i −0.208556 + 0.361230i −0.951260 0.308390i \(-0.900210\pi\)
0.742704 + 0.669620i \(0.233543\pi\)
\(770\) 0.418422 3.87178i 0.0150789 0.139529i
\(771\) −10.6062 −0.381971
\(772\) 28.2467 + 25.7349i 1.01662 + 0.926220i
\(773\) 11.6089 20.1073i 0.417545 0.723209i −0.578147 0.815933i \(-0.696224\pi\)
0.995692 + 0.0927238i \(0.0295574\pi\)
\(774\) −10.1180 7.39662i −0.363686 0.265866i
\(775\) 0.746830 1.29355i 0.0268269 0.0464656i
\(776\) −3.56250 17.5165i −0.127886 0.628805i
\(777\) 1.84088 + 3.18850i 0.0660412 + 0.114387i
\(778\) 8.20268 + 18.5699i 0.294080 + 0.665762i
\(779\) 18.6174 + 31.7302i 0.667036 + 1.13685i
\(780\) −17.2415 + 18.9242i −0.617343 + 0.677596i
\(781\) 18.0372 + 31.2413i 0.645421 + 1.11790i
\(782\) 1.56048 2.13462i 0.0558026 0.0763340i
\(783\) −40.2532 23.2402i −1.43853 0.830536i
\(784\) −22.1808 + 15.7212i −0.792173 + 0.561471i
\(785\) −21.7708 + 37.7081i −0.777033 + 1.34586i
\(786\) 12.1007 + 27.3946i 0.431618 + 0.977132i
\(787\) 33.9207i 1.20914i 0.796552 + 0.604571i \(0.206655\pi\)
−0.796552 + 0.604571i \(0.793345\pi\)
\(788\) −21.4353 + 6.82605i −0.763602 + 0.243168i
\(789\) 16.9069 29.2836i 0.601901 1.04252i
\(790\) 13.1117 + 29.6833i 0.466493 + 1.05608i
\(791\) 1.05570 0.0375364
\(792\) 6.17959 + 6.98573i 0.219582 + 0.248227i
\(793\) 7.95135 4.59072i 0.282361 0.163021i
\(794\) 37.1726 + 4.01723i 1.31921 + 0.142566i
\(795\) −13.2684 22.9815i −0.470581 0.815070i
\(796\) −4.89420 + 22.3793i −0.173470 + 0.793212i
\(797\) 12.2630 0.434378 0.217189 0.976130i \(-0.430311\pi\)
0.217189 + 0.976130i \(0.430311\pi\)
\(798\) −3.35530 0.338819i −0.118776 0.0119940i
\(799\) 0.938848i 0.0332141i
\(800\) −8.71037 + 14.5886i −0.307958 + 0.515785i
\(801\) 10.6172 6.12983i 0.375139 0.216587i
\(802\) −9.90594 1.07053i −0.349791 0.0378018i
\(803\) −17.8258 30.8752i −0.629059 1.08956i
\(804\) −1.84252 5.78593i −0.0649808 0.204054i
\(805\) 1.66375i 0.0586394i
\(806\) 2.39830 1.05938i 0.0844766 0.0373150i
\(807\) 24.8797 + 14.3643i 0.875806 + 0.505647i
\(808\) −11.2790 + 9.97737i −0.396792 + 0.351003i
\(809\) 35.6199 1.25233 0.626164 0.779691i \(-0.284624\pi\)
0.626164 + 0.779691i \(0.284624\pi\)
\(810\) 3.37340 + 7.63697i 0.118529 + 0.268336i
\(811\) 16.4875 + 9.51908i 0.578956 + 0.334260i 0.760718 0.649082i \(-0.224847\pi\)
−0.181763 + 0.983342i \(0.558180\pi\)
\(812\) −1.62944 + 7.45077i −0.0571820 + 0.261471i
\(813\) 11.1777 19.3604i 0.392021 0.679000i
\(814\) 16.5912 + 12.1287i 0.581521 + 0.425110i
\(815\) 1.30844 0.755429i 0.0458327 0.0264615i
\(816\) −6.92715 + 0.646027i −0.242499 + 0.0226155i
\(817\) 21.8184 12.8017i 0.763329 0.447875i
\(818\) 11.6588 + 26.3940i 0.407639 + 0.922846i
\(819\) −2.22248 + 1.28315i −0.0776597 + 0.0448369i
\(820\) −46.6517 10.2024i −1.62915 0.356284i
\(821\) 34.7173 + 20.0441i 1.21164 + 0.699543i 0.963117 0.269082i \(-0.0867204\pi\)
0.248526 + 0.968625i \(0.420054\pi\)
\(822\) 8.68832 11.8850i 0.303040 0.414537i
\(823\) −27.7423 16.0170i −0.967037 0.558319i −0.0687052 0.997637i \(-0.521887\pi\)
−0.898332 + 0.439318i \(0.855220\pi\)
\(824\) −16.0767 + 48.0370i −0.560058 + 1.67345i
\(825\) 7.87146i 0.274049i
\(826\) 0.957699 8.86187i 0.0333226 0.308344i
\(827\) −13.4637 7.77329i −0.468180 0.270304i 0.247298 0.968940i \(-0.420457\pi\)
−0.715477 + 0.698636i \(0.753791\pi\)
\(828\) −2.94545 2.68353i −0.102361 0.0932592i
\(829\) −5.94617 −0.206519 −0.103260 0.994654i \(-0.532927\pi\)
−0.103260 + 0.994654i \(0.532927\pi\)
\(830\) 47.0697 + 5.08681i 1.63381 + 0.176566i
\(831\) 15.7968 + 27.3608i 0.547984 + 0.949136i
\(832\) −27.4556 + 11.6497i −0.951852 + 0.403880i
\(833\) −4.87036 8.43572i −0.168748 0.292280i
\(834\) 4.82437 6.59940i 0.167054 0.228519i
\(835\) 38.5778i 1.33504i
\(836\) −17.8966 + 5.83769i −0.618967 + 0.201901i
\(837\) 2.73220i 0.0944386i
\(838\) −8.78302 6.42067i −0.303404 0.221798i
\(839\) −6.06590 10.5064i −0.209418 0.362723i 0.742113 0.670274i \(-0.233824\pi\)
−0.951531 + 0.307552i \(0.900490\pi\)
\(840\) 3.27879 2.90042i 0.113129 0.100074i
\(841\) −21.2845 36.8658i −0.733947 1.27123i
\(842\) 0.926964 8.57746i 0.0319453 0.295599i
\(843\) −25.4590 −0.876855
\(844\) −23.6075 21.5083i −0.812604 0.740347i
\(845\) −2.20218 1.27143i −0.0757575 0.0437386i
\(846\) −1.40659 0.152009i −0.0483595 0.00522619i
\(847\) 2.85665i 0.0981555i
\(848\) −2.87073 30.7819i −0.0985812 1.05706i
\(849\) 12.0424 + 6.95270i 0.413295 + 0.238616i
\(850\) −4.91449 3.59265i −0.168565 0.123227i
\(851\) −7.60385 4.39009i −0.260657 0.150490i
\(852\) −8.66339 + 39.6143i −0.296803 + 1.35716i
\(853\) 13.8144 7.97575i 0.472996 0.273085i −0.244497 0.969650i \(-0.578623\pi\)
0.717493 + 0.696565i \(0.245289\pi\)
\(854\) −1.43610 + 0.634354i −0.0491424 + 0.0217072i
\(855\) 18.8310 0.132061i 0.644007 0.00451639i
\(856\) −2.44012 0.816643i −0.0834017 0.0279123i
\(857\) 46.8936 27.0741i 1.60186 0.924832i 0.610740 0.791831i \(-0.290872\pi\)
0.991116 0.133001i \(-0.0424614\pi\)
\(858\) 8.15415 11.1543i 0.278378 0.380801i
\(859\) 10.3529 17.9317i 0.353236 0.611823i −0.633578 0.773678i \(-0.718415\pi\)
0.986814 + 0.161856i \(0.0517479\pi\)
\(860\) −7.01540 + 32.0787i −0.239223 + 1.09387i
\(861\) 3.99863 + 2.30861i 0.136273 + 0.0786773i
\(862\) −12.2205 + 5.39805i −0.416233 + 0.183858i
\(863\) 24.9184 0.848231 0.424115 0.905608i \(-0.360585\pi\)
0.424115 + 0.905608i \(0.360585\pi\)
\(864\) −0.455636 + 31.0768i −0.0155011 + 1.05725i
\(865\) −4.03271 2.32829i −0.137116 0.0791642i
\(866\) −9.85896 22.3195i −0.335021 0.758447i
\(867\) 18.1392i 0.616038i
\(868\) −0.427183 + 0.136036i −0.0144995 + 0.00461736i
\(869\) −8.75685 15.1673i −0.297056 0.514516i
\(870\) −4.41359 + 40.8402i −0.149635 + 1.38461i
\(871\) 8.07699 4.66325i 0.273678 0.158008i
\(872\) −5.18397 + 1.05431i −0.175551 + 0.0357036i
\(873\) 9.65089i 0.326633i
\(874\) 7.33362 3.30106i 0.248064 0.111660i
\(875\) −2.54588 −0.0860664
\(876\) 8.56187 39.1501i 0.289279 1.32276i
\(877\) −19.0653 33.0221i −0.643790 1.11508i −0.984580 0.174937i \(-0.944028\pi\)
0.340790 0.940140i \(-0.389306\pi\)
\(878\) 1.47286 13.6288i 0.0497066 0.459950i
\(879\) 10.9311 6.31106i 0.368696 0.212867i
\(880\) 10.2000 22.2050i 0.343842 0.748529i
\(881\) 16.6723 0.561702 0.280851 0.959751i \(-0.409383\pi\)
0.280851 + 0.959751i \(0.409383\pi\)
\(882\) −13.4270 + 5.93097i −0.452111 + 0.199706i
\(883\) 16.1610 27.9917i 0.543861 0.941994i −0.454817 0.890585i \(-0.650295\pi\)
0.998678 0.0514093i \(-0.0163713\pi\)
\(884\) −3.24243 10.1820i −0.109055 0.342456i
\(885\) 48.0076i 1.61376i
\(886\) 20.7862 9.18170i 0.698327 0.308465i
\(887\) −5.27663 + 9.13939i −0.177172 + 0.306871i −0.940911 0.338655i \(-0.890028\pi\)
0.763739 + 0.645525i \(0.223361\pi\)
\(888\) 4.60419 + 22.6384i 0.154506 + 0.759694i
\(889\) 0.832314 + 0.480537i 0.0279149 + 0.0161167i
\(890\) −25.9300 18.9557i −0.869175 0.635395i
\(891\) −2.25298 3.90228i −0.0754777 0.130731i
\(892\) −21.7216 + 23.8416i −0.727293 + 0.798276i
\(893\) 1.41038 2.48291i 0.0471967 0.0830874i
\(894\) 16.9179 7.47296i 0.565818 0.249933i
\(895\) −10.8517 18.7958i −0.362733 0.628273i
\(896\) 4.88158 1.47607i 0.163082 0.0493120i
\(897\) −2.95147 + 5.11209i −0.0985465 + 0.170688i
\(898\) −10.3833 + 14.2036i −0.346494 + 0.473979i
\(899\) 2.10347 3.64332i 0.0701548 0.121512i
\(900\) −6.17823 + 6.78122i −0.205941 + 0.226041i
\(901\) 11.0765 0.369012
\(902\) 25.6243 + 2.76921i 0.853196 + 0.0922046i
\(903\) 1.58745 2.74954i 0.0528270 0.0914991i
\(904\) 6.28172 + 2.10232i 0.208927 + 0.0699222i
\(905\) 66.5675i 2.21278i
\(906\) −9.22554 0.997001i −0.306498 0.0331231i
\(907\) −32.3892 + 18.6999i −1.07546 + 0.620920i −0.929669 0.368395i \(-0.879907\pi\)
−0.145795 + 0.989315i \(0.546574\pi\)
\(908\) −24.8280 + 7.90643i −0.823945 + 0.262384i
\(909\) −7.04102 + 4.06513i −0.233536 + 0.134832i
\(910\) 5.42789 + 3.96796i 0.179933 + 0.131537i
\(911\) −40.7900 −1.35143 −0.675717 0.737162i \(-0.736166\pi\)
−0.675717 + 0.737162i \(0.736166\pi\)
\(912\) −19.2902 8.69780i −0.638764 0.288013i
\(913\) −25.5520 −0.845647
\(914\) −26.9087 19.6711i −0.890062 0.650664i
\(915\) −7.32291 + 4.22789i −0.242088 + 0.139770i
\(916\) 24.2507 7.72262i 0.801267 0.255162i
\(917\) 6.81162 3.93269i 0.224940 0.129869i
\(918\) −11.0710 1.19644i −0.365398 0.0394884i
\(919\) 10.9991i 0.362826i −0.983407 0.181413i \(-0.941933\pi\)
0.983407 0.181413i \(-0.0580670\pi\)
\(920\) −3.31318 + 9.89977i −0.109232 + 0.326386i
\(921\) 1.68161 2.91263i 0.0554109 0.0959744i
\(922\) −1.55317 0.167850i −0.0511509 0.00552786i
\(923\) −62.2827 −2.05006
\(924\) −1.59116 + 1.74646i −0.0523455 + 0.0574544i
\(925\) −10.1072 + 17.5061i −0.332322 + 0.575599i
\(926\) 21.8003 29.8213i 0.716403 0.979988i
\(927\) −13.6747 + 23.6853i −0.449137 + 0.777928i
\(928\) −24.5331 + 41.0893i −0.805337 + 1.34882i
\(929\) 15.0117 + 26.0011i 0.492519 + 0.853067i 0.999963 0.00861738i \(-0.00274303\pi\)
−0.507444 + 0.861685i \(0.669410\pi\)
\(930\) −2.20875 + 0.975649i −0.0724278 + 0.0319928i
\(931\) −0.207765 29.6259i −0.00680921 0.970949i
\(932\) −15.5643 + 17.0833i −0.509825 + 0.559583i
\(933\) 8.37412 + 14.5044i 0.274156 + 0.474853i
\(934\) −21.0439 15.3838i −0.688578 0.503373i
\(935\) 7.58194 + 4.37744i 0.247956 + 0.143158i
\(936\) −15.7796 + 3.20926i −0.515774 + 0.104898i
\(937\) 20.0689 34.7604i 0.655623 1.13557i −0.326115 0.945330i \(-0.605740\pi\)
0.981737 0.190241i \(-0.0609271\pi\)
\(938\) −1.45879 + 0.644377i −0.0476312 + 0.0210397i
\(939\) 14.3013i 0.466706i
\(940\) 1.12473 + 3.53190i 0.0366846 + 0.115198i
\(941\) −0.433456 + 0.750768i −0.0141303 + 0.0244743i −0.873004 0.487713i \(-0.837831\pi\)
0.858874 + 0.512187i \(0.171165\pi\)
\(942\) 24.1634 10.6735i 0.787287 0.347761i
\(943\) −11.0110 −0.358569
\(944\) 23.3461 50.8234i 0.759850 1.65416i
\(945\) 6.06786 3.50328i 0.197387 0.113962i
\(946\) 1.90417 17.6198i 0.0619098 0.572870i
\(947\) −12.4598 21.5809i −0.404888 0.701286i 0.589421 0.807826i \(-0.299356\pi\)
−0.994308 + 0.106540i \(0.966023\pi\)
\(948\) 4.20598 19.2323i 0.136604 0.624637i
\(949\) 61.5529 1.99809
\(950\) −7.59995 16.8840i −0.246575 0.547790i
\(951\) 21.5197i 0.697825i
\(952\) 0.364160 + 1.79054i 0.0118025 + 0.0580318i
\(953\) −25.5317 + 14.7407i −0.827053 + 0.477499i −0.852843 0.522168i \(-0.825123\pi\)
0.0257895 + 0.999667i \(0.491790\pi\)
\(954\) 1.79340 16.5949i 0.0580635 0.537279i
\(955\) −33.7572 58.4692i −1.09236 1.89202i
\(956\) −35.8846 + 11.4274i −1.16059 + 0.369589i
\(957\) 22.1702i 0.716662i
\(958\) −17.3316 39.2366i −0.559959 1.26768i
\(959\) −3.34851 1.93326i −0.108129 0.0624282i
\(960\) 25.2856 10.7290i 0.816090 0.346275i
\(961\) −30.7527 −0.992023
\(962\) −32.4573 + 14.3370i −1.04646 + 0.462244i
\(963\) −1.20314 0.694632i −0.0387706 0.0223842i
\(964\) 4.18183 19.1219i 0.134688 0.615875i
\(965\) 27.0261 46.8106i 0.870002 1.50689i
\(966\) 0.595680 0.814849i 0.0191657 0.0262173i
\(967\) −50.5276 + 29.1722i −1.62486 + 0.938113i −0.639265 + 0.768986i \(0.720761\pi\)
−0.985594 + 0.169127i \(0.945905\pi\)
\(968\) 5.68872 16.9978i 0.182842 0.546331i
\(969\) 3.74458 6.59214i 0.120293 0.211770i
\(970\) −23.1290 + 10.2165i −0.742627 + 0.328033i
\(971\) −0.791582 + 0.457020i −0.0254031 + 0.0146665i −0.512648 0.858599i \(-0.671335\pi\)
0.487245 + 0.873265i \(0.338002\pi\)
\(972\) −5.96075 + 27.2562i −0.191191 + 0.874242i
\(973\) −1.85933 1.07348i −0.0596073 0.0344143i
\(974\) 47.5090 + 34.7306i 1.52229 + 1.11284i
\(975\) 11.7694 + 6.79508i 0.376923 + 0.217617i
\(976\) −9.80846 + 0.914739i −0.313961 + 0.0292801i
\(977\) 19.2494i 0.615841i 0.951412 + 0.307921i \(0.0996331\pi\)
−0.951412 + 0.307921i \(0.900367\pi\)
\(978\) −0.911301 0.0984840i −0.0291402 0.00314917i
\(979\) 15.0129 + 8.66771i 0.479815 + 0.277021i
\(980\) 28.4279 + 25.9001i 0.908097 + 0.827348i
\(981\) −2.85616 −0.0911903
\(982\) −4.67249 + 43.2359i −0.149105 + 1.37971i
\(983\) −10.4028 18.0182i −0.331799 0.574693i 0.651066 0.759021i \(-0.274322\pi\)
−0.982865 + 0.184329i \(0.940989\pi\)
\(984\) 19.1956 + 21.6998i 0.611934 + 0.691763i
\(985\) 15.9107 + 27.5581i 0.506956 + 0.878073i
\(986\) −13.8418 10.1188i −0.440813 0.322249i
\(987\) 0.358386i 0.0114076i
\(988\) 6.72081 31.7985i 0.213817 1.01164i
\(989\) 7.57143i 0.240758i
\(990\) 7.78590 10.6506i 0.247452 0.338497i
\(991\) −2.09378 3.62654i −0.0665113 0.115201i 0.830852 0.556493i \(-0.187853\pi\)
−0.897363 + 0.441292i \(0.854520\pi\)
\(992\) −2.81276 0.0412397i −0.0893053 0.00130936i
\(993\) −16.6093 28.7682i −0.527080 0.912930i
\(994\) 10.5883 + 1.14427i 0.335840 + 0.0362941i
\(995\) 32.4044 1.02729
\(996\) −21.2319 19.3440i −0.672760 0.612937i
\(997\) −4.65708 2.68877i −0.147491 0.0851542i 0.424438 0.905457i \(-0.360472\pi\)
−0.571930 + 0.820303i \(0.693805\pi\)
\(998\) −3.66397 + 33.9038i −0.115981 + 1.07321i
\(999\) 36.9760i 1.16987i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 152.2.o.c.107.12 yes 28
4.3 odd 2 608.2.s.c.335.10 28
8.3 odd 2 inner 152.2.o.c.107.8 yes 28
8.5 even 2 608.2.s.c.335.9 28
19.8 odd 6 inner 152.2.o.c.27.8 28
76.27 even 6 608.2.s.c.559.9 28
152.27 even 6 inner 152.2.o.c.27.12 yes 28
152.141 odd 6 608.2.s.c.559.10 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.o.c.27.8 28 19.8 odd 6 inner
152.2.o.c.27.12 yes 28 152.27 even 6 inner
152.2.o.c.107.8 yes 28 8.3 odd 2 inner
152.2.o.c.107.12 yes 28 1.1 even 1 trivial
608.2.s.c.335.9 28 8.5 even 2
608.2.s.c.335.10 28 4.3 odd 2
608.2.s.c.559.9 28 76.27 even 6
608.2.s.c.559.10 28 152.141 odd 6