Properties

Label 240.2.bk.b.11.2
Level $240$
Weight $2$
Character 240.11
Analytic conductor $1.916$
Analytic rank $0$
Dimension $60$
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] = [240,2,Mod(11,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bk (of order \(4\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(30\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.2
Character \(\chi\) \(=\) 240.11
Dual form 240.2.bk.b.131.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38304 - 0.295312i) q^{2} +(-1.72570 + 0.148181i) q^{3} +(1.82558 + 0.816854i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.43047 + 0.304680i) q^{6} -1.12315 q^{7} +(-2.28362 - 1.66885i) q^{8} +(2.95608 - 0.511431i) q^{9} +O(q^{10})\) \(q+(-1.38304 - 0.295312i) q^{2} +(-1.72570 + 0.148181i) q^{3} +(1.82558 + 0.816854i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.43047 + 0.304680i) q^{6} -1.12315 q^{7} +(-2.28362 - 1.66885i) q^{8} +(2.95608 - 0.511431i) q^{9} +(1.18677 - 0.769138i) q^{10} +(-0.353925 - 0.353925i) q^{11} +(-3.27145 - 1.13913i) q^{12} +(0.745034 - 0.745034i) q^{13} +(1.55336 + 0.331680i) q^{14} +(1.11548 - 1.32503i) q^{15} +(2.66550 + 2.98247i) q^{16} -6.14478i q^{17} +(-4.23941 - 0.165639i) q^{18} +(-5.49163 - 5.49163i) q^{19} +(-1.86848 + 0.713278i) q^{20} +(1.93822 - 0.166429i) q^{21} +(0.384973 + 0.594009i) q^{22} -2.47584i q^{23} +(4.18814 + 2.54156i) q^{24} -1.00000i q^{25} +(-1.25043 + 0.810393i) q^{26} +(-5.02553 + 1.32061i) q^{27} +(-2.05041 - 0.917451i) q^{28} +(-4.49575 - 4.49575i) q^{29} +(-1.93404 + 1.50316i) q^{30} -4.31976i q^{31} +(-2.80573 - 4.91202i) q^{32} +(0.663213 + 0.558324i) q^{33} +(-1.81462 + 8.49845i) q^{34} +(0.794189 - 0.794189i) q^{35} +(5.81434 + 1.48103i) q^{36} +(5.07782 + 5.07782i) q^{37} +(5.97339 + 9.21687i) q^{38} +(-1.17531 + 1.39611i) q^{39} +(2.79482 - 0.434705i) q^{40} +10.5512 q^{41} +(-2.72978 - 0.342202i) q^{42} +(-1.60246 + 1.60246i) q^{43} +(-0.357014 - 0.935224i) q^{44} +(-1.72863 + 2.45190i) q^{45} +(-0.731146 + 3.42418i) q^{46} +3.71298 q^{47} +(-5.04180 - 4.75187i) q^{48} -5.73853 q^{49} +(-0.295312 + 1.38304i) q^{50} +(0.910537 + 10.6040i) q^{51} +(1.96871 - 0.751537i) q^{52} +(-3.09666 + 3.09666i) q^{53} +(7.34049 - 0.342356i) q^{54} +0.500525 q^{55} +(2.56485 + 1.87438i) q^{56} +(10.2907 + 8.66316i) q^{57} +(4.89014 + 7.54544i) q^{58} +(-2.03620 - 2.03620i) q^{59} +(3.11875 - 1.50778i) q^{60} +(0.543956 - 0.543956i) q^{61} +(-1.27568 + 5.97439i) q^{62} +(-3.32013 + 0.574415i) q^{63} +(2.42985 + 7.62206i) q^{64} +1.05364i q^{65} +(-0.752369 - 0.968037i) q^{66} +(-2.38268 - 2.38268i) q^{67} +(5.01939 - 11.2178i) q^{68} +(0.366872 + 4.27257i) q^{69} +(-1.33293 + 0.863859i) q^{70} +14.1420i q^{71} +(-7.60408 - 3.76536i) q^{72} -9.88440i q^{73} +(-5.52327 - 8.52235i) q^{74} +(0.148181 + 1.72570i) q^{75} +(-5.53956 - 14.5113i) q^{76} +(0.397512 + 0.397512i) q^{77} +(2.03778 - 1.58378i) q^{78} -8.16570i q^{79} +(-3.99372 - 0.224130i) q^{80} +(8.47688 - 3.02367i) q^{81} +(-14.5927 - 3.11589i) q^{82} +(-0.200632 + 0.200632i) q^{83} +(3.67434 + 1.27942i) q^{84} +(4.34501 + 4.34501i) q^{85} +(2.68949 - 1.74304i) q^{86} +(8.42451 + 7.09214i) q^{87} +(0.217581 + 1.39888i) q^{88} -17.1014 q^{89} +(3.11484 - 2.88059i) q^{90} +(-0.836787 + 0.836787i) q^{91} +(2.02240 - 4.51986i) q^{92} +(0.640106 + 7.45462i) q^{93} +(-5.13518 - 1.09649i) q^{94} +7.76634 q^{95} +(5.56971 + 8.06091i) q^{96} -13.3983 q^{97} +(7.93660 + 1.69465i) q^{98} +(-1.22724 - 0.865224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38304 0.295312i −0.977955 0.208817i
\(3\) −1.72570 + 0.148181i −0.996334 + 0.0855522i
\(4\) 1.82558 + 0.816854i 0.912791 + 0.408427i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 2.43047 + 0.304680i 0.992234 + 0.124385i
\(7\) −1.12315 −0.424512 −0.212256 0.977214i \(-0.568081\pi\)
−0.212256 + 0.977214i \(0.568081\pi\)
\(8\) −2.28362 1.66885i −0.807382 0.590029i
\(9\) 2.95608 0.511431i 0.985362 0.170477i
\(10\) 1.18677 0.769138i 0.375290 0.243223i
\(11\) −0.353925 0.353925i −0.106712 0.106712i 0.651735 0.758447i \(-0.274042\pi\)
−0.758447 + 0.651735i \(0.774042\pi\)
\(12\) −3.27145 1.13913i −0.944386 0.328838i
\(13\) 0.745034 0.745034i 0.206635 0.206635i −0.596200 0.802836i \(-0.703324\pi\)
0.802836 + 0.596200i \(0.203324\pi\)
\(14\) 1.55336 + 0.331680i 0.415153 + 0.0886452i
\(15\) 1.11548 1.32503i 0.288014 0.342122i
\(16\) 2.66550 + 2.98247i 0.666375 + 0.745617i
\(17\) 6.14478i 1.49033i −0.666882 0.745164i \(-0.732371\pi\)
0.666882 0.745164i \(-0.267629\pi\)
\(18\) −4.23941 0.165639i −0.999238 0.0390414i
\(19\) −5.49163 5.49163i −1.25987 1.25987i −0.951156 0.308711i \(-0.900102\pi\)
−0.308711 0.951156i \(-0.599898\pi\)
\(20\) −1.86848 + 0.713278i −0.417806 + 0.159494i
\(21\) 1.93822 0.166429i 0.422955 0.0363179i
\(22\) 0.384973 + 0.594009i 0.0820765 + 0.126643i
\(23\) 2.47584i 0.516249i −0.966112 0.258125i \(-0.916895\pi\)
0.966112 0.258125i \(-0.0831045\pi\)
\(24\) 4.18814 + 2.54156i 0.854900 + 0.518793i
\(25\) 1.00000i 0.200000i
\(26\) −1.25043 + 0.810393i −0.245229 + 0.158931i
\(27\) −5.02553 + 1.32061i −0.967164 + 0.254152i
\(28\) −2.05041 0.917451i −0.387490 0.173382i
\(29\) −4.49575 4.49575i −0.834840 0.834840i 0.153334 0.988174i \(-0.450999\pi\)
−0.988174 + 0.153334i \(0.950999\pi\)
\(30\) −1.93404 + 1.50316i −0.353106 + 0.274438i
\(31\) 4.31976i 0.775852i −0.921690 0.387926i \(-0.873192\pi\)
0.921690 0.387926i \(-0.126808\pi\)
\(32\) −2.80573 4.91202i −0.495987 0.868330i
\(33\) 0.663213 + 0.558324i 0.115451 + 0.0971917i
\(34\) −1.81462 + 8.49845i −0.311206 + 1.45747i
\(35\) 0.794189 0.794189i 0.134242 0.134242i
\(36\) 5.81434 + 1.48103i 0.969057 + 0.246838i
\(37\) 5.07782 + 5.07782i 0.834788 + 0.834788i 0.988167 0.153379i \(-0.0490157\pi\)
−0.153379 + 0.988167i \(0.549016\pi\)
\(38\) 5.97339 + 9.21687i 0.969011 + 1.49517i
\(39\) −1.17531 + 1.39611i −0.188200 + 0.223556i
\(40\) 2.79482 0.434705i 0.441900 0.0687329i
\(41\) 10.5512 1.64782 0.823909 0.566723i \(-0.191789\pi\)
0.823909 + 0.566723i \(0.191789\pi\)
\(42\) −2.72978 0.342202i −0.421215 0.0528030i
\(43\) −1.60246 + 1.60246i −0.244373 + 0.244373i −0.818657 0.574283i \(-0.805281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(44\) −0.357014 0.935224i −0.0538219 0.140990i
\(45\) −1.72863 + 2.45190i −0.257689 + 0.365508i
\(46\) −0.731146 + 3.42418i −0.107802 + 0.504868i
\(47\) 3.71298 0.541593 0.270797 0.962637i \(-0.412713\pi\)
0.270797 + 0.962637i \(0.412713\pi\)
\(48\) −5.04180 4.75187i −0.727721 0.685873i
\(49\) −5.73853 −0.819790
\(50\) −0.295312 + 1.38304i −0.0417634 + 0.195591i
\(51\) 0.910537 + 10.6040i 0.127501 + 1.48486i
\(52\) 1.96871 0.751537i 0.273010 0.104219i
\(53\) −3.09666 + 3.09666i −0.425359 + 0.425359i −0.887044 0.461685i \(-0.847245\pi\)
0.461685 + 0.887044i \(0.347245\pi\)
\(54\) 7.34049 0.342356i 0.998914 0.0465887i
\(55\) 0.500525 0.0674908
\(56\) 2.56485 + 1.87438i 0.342743 + 0.250474i
\(57\) 10.2907 + 8.66316i 1.36303 + 1.14746i
\(58\) 4.89014 + 7.54544i 0.642107 + 0.990765i
\(59\) −2.03620 2.03620i −0.265090 0.265090i 0.562028 0.827118i \(-0.310021\pi\)
−0.827118 + 0.562028i \(0.810021\pi\)
\(60\) 3.11875 1.50778i 0.402629 0.194653i
\(61\) 0.543956 0.543956i 0.0696464 0.0696464i −0.671426 0.741072i \(-0.734318\pi\)
0.741072 + 0.671426i \(0.234318\pi\)
\(62\) −1.27568 + 5.97439i −0.162011 + 0.758749i
\(63\) −3.32013 + 0.574415i −0.418298 + 0.0723695i
\(64\) 2.42985 + 7.62206i 0.303731 + 0.952758i
\(65\) 1.05364i 0.130688i
\(66\) −0.752369 0.968037i −0.0926102 0.119157i
\(67\) −2.38268 2.38268i −0.291090 0.291090i 0.546421 0.837511i \(-0.315990\pi\)
−0.837511 + 0.546421i \(0.815990\pi\)
\(68\) 5.01939 11.2178i 0.608690 1.36036i
\(69\) 0.366872 + 4.27257i 0.0441662 + 0.514357i
\(70\) −1.33293 + 0.863859i −0.159315 + 0.103251i
\(71\) 14.1420i 1.67835i 0.543865 + 0.839173i \(0.316960\pi\)
−0.543865 + 0.839173i \(0.683040\pi\)
\(72\) −7.60408 3.76536i −0.896150 0.443752i
\(73\) 9.88440i 1.15688i −0.815724 0.578441i \(-0.803661\pi\)
0.815724 0.578441i \(-0.196339\pi\)
\(74\) −5.52327 8.52235i −0.642067 0.990703i
\(75\) 0.148181 + 1.72570i 0.0171104 + 0.199267i
\(76\) −5.53956 14.5113i −0.635431 1.66456i
\(77\) 0.397512 + 0.397512i 0.0453007 + 0.0453007i
\(78\) 2.03778 1.58378i 0.230733 0.179328i
\(79\) 8.16570i 0.918713i −0.888252 0.459357i \(-0.848080\pi\)
0.888252 0.459357i \(-0.151920\pi\)
\(80\) −3.99372 0.224130i −0.446511 0.0250585i
\(81\) 8.47688 3.02367i 0.941875 0.335963i
\(82\) −14.5927 3.11589i −1.61149 0.344092i
\(83\) −0.200632 + 0.200632i −0.0220223 + 0.0220223i −0.718032 0.696010i \(-0.754957\pi\)
0.696010 + 0.718032i \(0.254957\pi\)
\(84\) 3.67434 + 1.27942i 0.400903 + 0.139596i
\(85\) 4.34501 + 4.34501i 0.471283 + 0.471283i
\(86\) 2.68949 1.74304i 0.290016 0.187957i
\(87\) 8.42451 + 7.09214i 0.903202 + 0.760357i
\(88\) 0.217581 + 1.39888i 0.0231942 + 0.149121i
\(89\) −17.1014 −1.81275 −0.906374 0.422477i \(-0.861161\pi\)
−0.906374 + 0.422477i \(0.861161\pi\)
\(90\) 3.11484 2.88059i 0.328333 0.303641i
\(91\) −0.836787 + 0.836787i −0.0877191 + 0.0877191i
\(92\) 2.02240 4.51986i 0.210850 0.471228i
\(93\) 0.640106 + 7.45462i 0.0663759 + 0.773008i
\(94\) −5.13518 1.09649i −0.529654 0.113094i
\(95\) 7.76634 0.796810
\(96\) 5.56971 + 8.06091i 0.568456 + 0.822714i
\(97\) −13.3983 −1.36039 −0.680195 0.733031i \(-0.738105\pi\)
−0.680195 + 0.733031i \(0.738105\pi\)
\(98\) 7.93660 + 1.69465i 0.801717 + 0.171186i
\(99\) −1.22724 0.865224i −0.123342 0.0869583i
\(100\) 0.816854 1.82558i 0.0816854 0.182558i
\(101\) −3.36893 + 3.36893i −0.335221 + 0.335221i −0.854565 0.519344i \(-0.826176\pi\)
0.519344 + 0.854565i \(0.326176\pi\)
\(102\) 1.87219 14.9347i 0.185375 1.47875i
\(103\) 15.6861 1.54560 0.772800 0.634650i \(-0.218856\pi\)
0.772800 + 0.634650i \(0.218856\pi\)
\(104\) −2.94473 + 0.458022i −0.288755 + 0.0449127i
\(105\) −1.25285 + 1.48822i −0.122265 + 0.145235i
\(106\) 5.19727 3.36831i 0.504804 0.327160i
\(107\) −3.35432 3.35432i −0.324274 0.324274i 0.526130 0.850404i \(-0.323643\pi\)
−0.850404 + 0.526130i \(0.823643\pi\)
\(108\) −10.2533 1.69424i −0.986621 0.163029i
\(109\) 0.0567858 0.0567858i 0.00543909 0.00543909i −0.704382 0.709821i \(-0.748776\pi\)
0.709821 + 0.704382i \(0.248776\pi\)
\(110\) −0.692245 0.147811i −0.0660030 0.0140932i
\(111\) −9.51523 8.01036i −0.903145 0.760309i
\(112\) −2.99376 3.34977i −0.282884 0.316523i
\(113\) 2.12147i 0.199571i −0.995009 0.0997857i \(-0.968184\pi\)
0.995009 0.0997857i \(-0.0318157\pi\)
\(114\) −11.6740 15.0204i −1.09337 1.40679i
\(115\) 1.75069 + 1.75069i 0.163252 + 0.163252i
\(116\) −4.53499 11.8797i −0.421063 1.10301i
\(117\) 1.82135 2.58342i 0.168384 0.238837i
\(118\) 2.21482 + 3.41745i 0.203891 + 0.314602i
\(119\) 6.90152i 0.632661i
\(120\) −4.75861 + 1.16431i −0.434400 + 0.106286i
\(121\) 10.7495i 0.977225i
\(122\) −0.912948 + 0.591675i −0.0826544 + 0.0535677i
\(123\) −18.2082 + 1.56348i −1.64178 + 0.140974i
\(124\) 3.52862 7.88608i 0.316879 0.708191i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 4.76150 + 0.186037i 0.424188 + 0.0165735i
\(127\) 20.4253i 1.81245i 0.422796 + 0.906225i \(0.361049\pi\)
−0.422796 + 0.906225i \(0.638951\pi\)
\(128\) −1.10968 11.2592i −0.0980832 0.995178i
\(129\) 2.52792 3.00283i 0.222571 0.264384i
\(130\) 0.311152 1.45722i 0.0272898 0.127807i
\(131\) 4.66794 4.66794i 0.407840 0.407840i −0.473145 0.880985i \(-0.656881\pi\)
0.880985 + 0.473145i \(0.156881\pi\)
\(132\) 0.754681 + 1.56101i 0.0656866 + 0.135869i
\(133\) 6.16794 + 6.16794i 0.534828 + 0.534828i
\(134\) 2.59170 + 3.99896i 0.223888 + 0.345458i
\(135\) 2.61978 4.48740i 0.225474 0.386214i
\(136\) −10.2547 + 14.0323i −0.879337 + 1.20326i
\(137\) 0.593951 0.0507446 0.0253723 0.999678i \(-0.491923\pi\)
0.0253723 + 0.999678i \(0.491923\pi\)
\(138\) 0.754341 6.01746i 0.0642138 0.512240i
\(139\) 11.7056 11.7056i 0.992854 0.992854i −0.00712063 0.999975i \(-0.502267\pi\)
0.999975 + 0.00712063i \(0.00226659\pi\)
\(140\) 2.09859 0.801120i 0.177363 0.0677070i
\(141\) −6.40749 + 0.550191i −0.539608 + 0.0463345i
\(142\) 4.17630 19.5589i 0.350467 1.64135i
\(143\) −0.527372 −0.0441011
\(144\) 9.40477 + 7.45321i 0.783731 + 0.621101i
\(145\) 6.35795 0.527999
\(146\) −2.91898 + 13.6705i −0.241576 + 1.13138i
\(147\) 9.90298 0.850339i 0.816784 0.0701348i
\(148\) 5.12214 + 13.4178i 0.421037 + 1.10294i
\(149\) −12.6860 + 12.6860i −1.03927 + 1.03927i −0.0400778 + 0.999197i \(0.512761\pi\)
−0.999197 + 0.0400778i \(0.987239\pi\)
\(150\) 0.304680 2.43047i 0.0248770 0.198447i
\(151\) −20.3694 −1.65764 −0.828818 0.559518i \(-0.810986\pi\)
−0.828818 + 0.559518i \(0.810986\pi\)
\(152\) 3.37607 + 21.7055i 0.273835 + 1.76055i
\(153\) −3.14263 18.1645i −0.254067 1.46851i
\(154\) −0.432383 0.667163i −0.0348424 0.0537615i
\(155\) 3.05453 + 3.05453i 0.245346 + 0.245346i
\(156\) −3.28603 + 1.58865i −0.263093 + 0.127194i
\(157\) 13.3188 13.3188i 1.06296 1.06296i 0.0650759 0.997880i \(-0.479271\pi\)
0.997880 0.0650759i \(-0.0207289\pi\)
\(158\) −2.41143 + 11.2935i −0.191843 + 0.898460i
\(159\) 4.88504 5.80277i 0.387409 0.460190i
\(160\) 5.45727 + 1.48937i 0.431435 + 0.117745i
\(161\) 2.78075i 0.219154i
\(162\) −12.6168 + 1.67852i −0.991266 + 0.131877i
\(163\) −5.17232 5.17232i −0.405127 0.405127i 0.474908 0.880035i \(-0.342481\pi\)
−0.880035 + 0.474908i \(0.842481\pi\)
\(164\) 19.2620 + 8.61877i 1.50411 + 0.673013i
\(165\) −0.863757 + 0.0741682i −0.0672434 + 0.00577399i
\(166\) 0.336731 0.218233i 0.0261354 0.0169382i
\(167\) 0.100449i 0.00777299i 0.999992 + 0.00388649i \(0.00123711\pi\)
−0.999992 + 0.00388649i \(0.998763\pi\)
\(168\) −4.70392 2.85455i −0.362915 0.220234i
\(169\) 11.8898i 0.914604i
\(170\) −4.72618 7.29245i −0.362482 0.559305i
\(171\) −19.0423 13.4251i −1.45620 1.02665i
\(172\) −4.23441 + 1.61645i −0.322871 + 0.123253i
\(173\) 8.07334 + 8.07334i 0.613805 + 0.613805i 0.943935 0.330130i \(-0.107093\pi\)
−0.330130 + 0.943935i \(0.607093\pi\)
\(174\) −9.55701 12.2965i −0.724515 0.932199i
\(175\) 1.12315i 0.0849023i
\(176\) 0.112183 1.99896i 0.00845611 0.150677i
\(177\) 3.81559 + 3.21214i 0.286798 + 0.241440i
\(178\) 23.6519 + 5.05025i 1.77278 + 0.378532i
\(179\) 9.73444 9.73444i 0.727586 0.727586i −0.242552 0.970138i \(-0.577985\pi\)
0.970138 + 0.242552i \(0.0779845\pi\)
\(180\) −5.15861 + 3.06411i −0.384500 + 0.228385i
\(181\) −8.76867 8.76867i −0.651770 0.651770i 0.301649 0.953419i \(-0.402463\pi\)
−0.953419 + 0.301649i \(0.902463\pi\)
\(182\) 1.40442 0.910194i 0.104103 0.0674681i
\(183\) −0.858101 + 1.01931i −0.0634327 + 0.0753495i
\(184\) −4.13182 + 5.65389i −0.304602 + 0.416810i
\(185\) −7.18112 −0.527966
\(186\) 1.31615 10.4990i 0.0965045 0.769827i
\(187\) −2.17479 + 2.17479i −0.159036 + 0.159036i
\(188\) 6.77834 + 3.03296i 0.494362 + 0.221201i
\(189\) 5.64444 1.48325i 0.410573 0.107890i
\(190\) −10.7411 2.29349i −0.779244 0.166387i
\(191\) 9.44638 0.683516 0.341758 0.939788i \(-0.388978\pi\)
0.341758 + 0.939788i \(0.388978\pi\)
\(192\) −5.32263 12.7933i −0.384128 0.923280i
\(193\) −8.02406 −0.577585 −0.288792 0.957392i \(-0.593254\pi\)
−0.288792 + 0.957392i \(0.593254\pi\)
\(194\) 18.5303 + 3.95667i 1.33040 + 0.284072i
\(195\) −0.156129 1.81826i −0.0111806 0.130209i
\(196\) −10.4762 4.68754i −0.748297 0.334824i
\(197\) −2.93926 + 2.93926i −0.209414 + 0.209414i −0.804018 0.594604i \(-0.797309\pi\)
0.594604 + 0.804018i \(0.297309\pi\)
\(198\) 1.44181 + 1.55906i 0.102465 + 0.110797i
\(199\) 11.4537 0.811930 0.405965 0.913889i \(-0.366936\pi\)
0.405965 + 0.913889i \(0.366936\pi\)
\(200\) −1.66885 + 2.28362i −0.118006 + 0.161476i
\(201\) 4.46485 + 3.75872i 0.314926 + 0.265120i
\(202\) 5.65424 3.66447i 0.397831 0.257831i
\(203\) 5.04942 + 5.04942i 0.354399 + 0.354399i
\(204\) −6.99970 + 20.1023i −0.490077 + 1.40744i
\(205\) −7.46081 + 7.46081i −0.521086 + 0.521086i
\(206\) −21.6945 4.63229i −1.51153 0.322747i
\(207\) −1.26622 7.31881i −0.0880086 0.508692i
\(208\) 4.20793 + 0.236152i 0.291767 + 0.0163742i
\(209\) 3.88725i 0.268887i
\(210\) 2.17222 1.68828i 0.149898 0.116502i
\(211\) 15.0006 + 15.0006i 1.03268 + 1.03268i 0.999448 + 0.0332334i \(0.0105805\pi\)
0.0332334 + 0.999448i \(0.489420\pi\)
\(212\) −8.18272 + 3.12369i −0.561992 + 0.214536i
\(213\) −2.09557 24.4048i −0.143586 1.67219i
\(214\) 3.64858 + 5.62972i 0.249412 + 0.384840i
\(215\) 2.26623i 0.154555i
\(216\) 13.6803 + 5.37111i 0.930828 + 0.365458i
\(217\) 4.85175i 0.329358i
\(218\) −0.0953063 + 0.0617673i −0.00645496 + 0.00418341i
\(219\) 1.46468 + 17.0575i 0.0989737 + 1.15264i
\(220\) 0.913750 + 0.408856i 0.0616050 + 0.0275651i
\(221\) −4.57807 4.57807i −0.307954 0.307954i
\(222\) 10.7944 + 13.8886i 0.724470 + 0.932140i
\(223\) 20.9105i 1.40027i 0.714009 + 0.700136i \(0.246877\pi\)
−0.714009 + 0.700136i \(0.753123\pi\)
\(224\) 3.15126 + 5.51694i 0.210552 + 0.368616i
\(225\) −0.511431 2.95608i −0.0340954 0.197072i
\(226\) −0.626496 + 2.93408i −0.0416739 + 0.195172i
\(227\) 9.05527 9.05527i 0.601019 0.601019i −0.339564 0.940583i \(-0.610279\pi\)
0.940583 + 0.339564i \(0.110279\pi\)
\(228\) 11.7099 + 24.2213i 0.775508 + 1.60409i
\(229\) 10.7014 + 10.7014i 0.707171 + 0.707171i 0.965939 0.258768i \(-0.0833167\pi\)
−0.258768 + 0.965939i \(0.583317\pi\)
\(230\) −1.90427 2.93826i −0.125564 0.193743i
\(231\) −0.744890 0.627083i −0.0490101 0.0412590i
\(232\) 2.76384 + 17.7694i 0.181455 + 1.16662i
\(233\) −1.04584 −0.0685151 −0.0342576 0.999413i \(-0.510907\pi\)
−0.0342576 + 0.999413i \(0.510907\pi\)
\(234\) −3.28191 + 3.03510i −0.214545 + 0.198410i
\(235\) −2.62547 + 2.62547i −0.171267 + 0.171267i
\(236\) −2.05397 5.38052i −0.133702 0.350242i
\(237\) 1.21000 + 14.0916i 0.0785979 + 0.915345i
\(238\) 2.03810 9.54506i 0.132110 0.618714i
\(239\) 22.0221 1.42449 0.712244 0.701932i \(-0.247679\pi\)
0.712244 + 0.701932i \(0.247679\pi\)
\(240\) 6.92517 0.205010i 0.447018 0.0132333i
\(241\) −17.6559 −1.13732 −0.568658 0.822574i \(-0.692537\pi\)
−0.568658 + 0.822574i \(0.692537\pi\)
\(242\) −3.17445 + 14.8669i −0.204061 + 0.955682i
\(243\) −14.1805 + 6.47405i −0.909680 + 0.415311i
\(244\) 1.43737 0.548704i 0.0920181 0.0351272i
\(245\) 4.05775 4.05775i 0.259240 0.259240i
\(246\) 25.6443 + 3.21474i 1.63502 + 0.204964i
\(247\) −8.18291 −0.520666
\(248\) −7.20906 + 9.86470i −0.457776 + 0.626409i
\(249\) 0.316502 0.375961i 0.0200575 0.0238256i
\(250\) −0.769138 1.18677i −0.0486445 0.0750580i
\(251\) 4.59329 + 4.59329i 0.289926 + 0.289926i 0.837051 0.547125i \(-0.184278\pi\)
−0.547125 + 0.837051i \(0.684278\pi\)
\(252\) −6.53039 1.66342i −0.411376 0.104786i
\(253\) −0.876263 + 0.876263i −0.0550902 + 0.0550902i
\(254\) 6.03182 28.2489i 0.378470 1.77249i
\(255\) −8.14204 6.85435i −0.509874 0.429236i
\(256\) −1.79023 + 15.8995i −0.111889 + 0.993721i
\(257\) 9.11566i 0.568620i 0.958732 + 0.284310i \(0.0917644\pi\)
−0.958732 + 0.284310i \(0.908236\pi\)
\(258\) −4.38298 + 3.40650i −0.272872 + 0.212079i
\(259\) −5.70316 5.70316i −0.354377 0.354377i
\(260\) −0.860668 + 1.92350i −0.0533764 + 0.119291i
\(261\) −15.5891 10.9906i −0.964941 0.680299i
\(262\) −7.83443 + 5.07744i −0.484013 + 0.313685i
\(263\) 24.4415i 1.50713i −0.657374 0.753564i \(-0.728333\pi\)
0.657374 0.753564i \(-0.271667\pi\)
\(264\) −0.582767 2.38181i −0.0358668 0.146590i
\(265\) 4.37934i 0.269021i
\(266\) −6.70902 10.3520i −0.411357 0.634719i
\(267\) 29.5119 2.53410i 1.80610 0.155084i
\(268\) −2.40347 6.29607i −0.146815 0.384594i
\(269\) −11.9844 11.9844i −0.730703 0.730703i 0.240056 0.970759i \(-0.422834\pi\)
−0.970759 + 0.240056i \(0.922834\pi\)
\(270\) −4.94843 + 5.43259i −0.301152 + 0.330617i
\(271\) 8.84453i 0.537267i 0.963242 + 0.268633i \(0.0865720\pi\)
−0.963242 + 0.268633i \(0.913428\pi\)
\(272\) 18.3266 16.3789i 1.11121 0.993117i
\(273\) 1.32005 1.56804i 0.0798930 0.0949021i
\(274\) −0.821456 0.175401i −0.0496260 0.0105963i
\(275\) −0.353925 + 0.353925i −0.0213425 + 0.0213425i
\(276\) −2.82031 + 8.09960i −0.169763 + 0.487539i
\(277\) −9.20943 9.20943i −0.553341 0.553341i 0.374062 0.927404i \(-0.377965\pi\)
−0.927404 + 0.374062i \(0.877965\pi\)
\(278\) −19.6460 + 12.7325i −1.17829 + 0.763642i
\(279\) −2.20926 12.7696i −0.132265 0.764495i
\(280\) −3.13901 + 0.488240i −0.187592 + 0.0291779i
\(281\) 10.0855 0.601649 0.300824 0.953680i \(-0.402738\pi\)
0.300824 + 0.953680i \(0.402738\pi\)
\(282\) 9.02427 + 1.13127i 0.537387 + 0.0673662i
\(283\) 2.04983 2.04983i 0.121850 0.121850i −0.643552 0.765402i \(-0.722540\pi\)
0.765402 + 0.643552i \(0.222540\pi\)
\(284\) −11.5519 + 25.8174i −0.685482 + 1.53198i
\(285\) −13.4024 + 1.15082i −0.793888 + 0.0681688i
\(286\) 0.729376 + 0.155739i 0.0431289 + 0.00920905i
\(287\) −11.8506 −0.699518
\(288\) −10.8061 13.0854i −0.636757 0.771065i
\(289\) −20.7583 −1.22108
\(290\) −8.79329 1.87758i −0.516360 0.110255i
\(291\) 23.1214 1.98537i 1.35540 0.116384i
\(292\) 8.07411 18.0448i 0.472502 1.05599i
\(293\) 13.6551 13.6551i 0.797741 0.797741i −0.184998 0.982739i \(-0.559228\pi\)
0.982739 + 0.184998i \(0.0592277\pi\)
\(294\) −13.9473 1.74842i −0.813423 0.101970i
\(295\) 2.87962 0.167658
\(296\) −3.12167 20.0699i −0.181443 1.16654i
\(297\) 2.24606 + 1.31126i 0.130330 + 0.0760873i
\(298\) 21.2915 13.7988i 1.23338 0.799345i
\(299\) −1.84459 1.84459i −0.106675 0.106675i
\(300\) −1.13913 + 3.27145i −0.0657677 + 0.188877i
\(301\) 1.79981 1.79981i 0.103739 0.103739i
\(302\) 28.1716 + 6.01532i 1.62109 + 0.346143i
\(303\) 5.31455 6.31297i 0.305313 0.362671i
\(304\) 1.74067 31.0166i 0.0998344 1.77892i
\(305\) 0.769270i 0.0440483i
\(306\) −1.01781 + 26.0502i −0.0581844 + 1.48919i
\(307\) 0.351696 + 0.351696i 0.0200724 + 0.0200724i 0.717072 0.696999i \(-0.245482\pi\)
−0.696999 + 0.717072i \(0.745482\pi\)
\(308\) 0.400981 + 1.05040i 0.0228480 + 0.0598520i
\(309\) −27.0695 + 2.32438i −1.53993 + 0.132229i
\(310\) −3.32249 5.12657i −0.188705 0.291170i
\(311\) 25.3543i 1.43771i −0.695159 0.718856i \(-0.744666\pi\)
0.695159 0.718856i \(-0.255334\pi\)
\(312\) 5.01385 1.22676i 0.283853 0.0694516i
\(313\) 21.4154i 1.21047i −0.796046 0.605236i \(-0.793079\pi\)
0.796046 0.605236i \(-0.206921\pi\)
\(314\) −22.3536 + 14.4872i −1.26149 + 0.817560i
\(315\) 1.94152 2.75386i 0.109392 0.155163i
\(316\) 6.67018 14.9072i 0.375227 0.838593i
\(317\) −14.6915 14.6915i −0.825156 0.825156i 0.161686 0.986842i \(-0.448307\pi\)
−0.986842 + 0.161686i \(0.948307\pi\)
\(318\) −8.46982 + 6.58284i −0.474964 + 0.369147i
\(319\) 3.18232i 0.178176i
\(320\) −7.10777 3.67145i −0.397337 0.205240i
\(321\) 6.28560 + 5.29151i 0.350828 + 0.295343i
\(322\) 0.821188 3.84588i 0.0457630 0.214323i
\(323\) −33.7449 + 33.7449i −1.87761 + 1.87761i
\(324\) 17.9451 + 1.40442i 0.996952 + 0.0780232i
\(325\) −0.745034 0.745034i −0.0413271 0.0413271i
\(326\) 5.62606 + 8.68096i 0.311599 + 0.480794i
\(327\) −0.0895807 + 0.106410i −0.00495382 + 0.00588447i
\(328\) −24.0949 17.6084i −1.33042 0.972260i
\(329\) −4.17024 −0.229913
\(330\) 1.21651 + 0.152500i 0.0669667 + 0.00839486i
\(331\) 13.6051 13.6051i 0.747806 0.747806i −0.226261 0.974067i \(-0.572650\pi\)
0.974067 + 0.226261i \(0.0726503\pi\)
\(332\) −0.530158 + 0.202383i −0.0290962 + 0.0111072i
\(333\) 17.6074 + 12.4135i 0.964880 + 0.680256i
\(334\) 0.0296638 0.138925i 0.00162313 0.00760163i
\(335\) 3.36961 0.184102
\(336\) 5.66271 + 5.33707i 0.308926 + 0.291161i
\(337\) 21.0315 1.14566 0.572830 0.819674i \(-0.305846\pi\)
0.572830 + 0.819674i \(0.305846\pi\)
\(338\) 3.51121 16.4441i 0.190985 0.894441i
\(339\) 0.314361 + 3.66103i 0.0170738 + 0.198840i
\(340\) 4.38294 + 11.4814i 0.237698 + 0.622667i
\(341\) −1.52887 + 1.52887i −0.0827931 + 0.0827931i
\(342\) 22.3716 + 24.1909i 1.20972 + 1.30809i
\(343\) 14.3073 0.772522
\(344\) 6.33370 0.985140i 0.341490 0.0531152i
\(345\) −3.28058 2.76174i −0.176620 0.148687i
\(346\) −8.78158 13.5499i −0.472101 0.728446i
\(347\) −0.769673 0.769673i −0.0413182 0.0413182i 0.686146 0.727464i \(-0.259301\pi\)
−0.727464 + 0.686146i \(0.759301\pi\)
\(348\) 9.58639 + 19.8289i 0.513884 + 1.06294i
\(349\) −8.62944 + 8.62944i −0.461923 + 0.461923i −0.899285 0.437362i \(-0.855913\pi\)
0.437362 + 0.899285i \(0.355913\pi\)
\(350\) 0.331680 1.55336i 0.0177290 0.0830306i
\(351\) −2.76029 + 4.72810i −0.147334 + 0.252367i
\(352\) −0.745468 + 2.73150i −0.0397336 + 0.145590i
\(353\) 8.64254i 0.459996i −0.973191 0.229998i \(-0.926128\pi\)
0.973191 0.229998i \(-0.0738720\pi\)
\(354\) −4.32852 5.56930i −0.230058 0.296005i
\(355\) −9.99990 9.99990i −0.530740 0.530740i
\(356\) −31.2201 13.9694i −1.65466 0.740375i
\(357\) −1.02267 11.9100i −0.0541255 0.630342i
\(358\) −16.3378 + 10.5884i −0.863479 + 0.559614i
\(359\) 6.55134i 0.345766i 0.984942 + 0.172883i \(0.0553083\pi\)
−0.984942 + 0.172883i \(0.944692\pi\)
\(360\) 8.03941 2.71438i 0.423714 0.143061i
\(361\) 41.3160i 2.17453i
\(362\) 9.53790 + 14.7169i 0.501301 + 0.773502i
\(363\) 1.59286 + 18.5504i 0.0836037 + 0.973642i
\(364\) −2.21116 + 0.844091i −0.115896 + 0.0442424i
\(365\) 6.98933 + 6.98933i 0.365838 + 0.365838i
\(366\) 1.48780 1.15633i 0.0777685 0.0604426i
\(367\) 6.93333i 0.361917i 0.983491 + 0.180958i \(0.0579200\pi\)
−0.983491 + 0.180958i \(0.942080\pi\)
\(368\) 7.38413 6.59936i 0.384924 0.344016i
\(369\) 31.1902 5.39620i 1.62370 0.280915i
\(370\) 9.93175 + 2.12067i 0.516327 + 0.110248i
\(371\) 3.47802 3.47802i 0.180570 0.180570i
\(372\) −4.92077 + 14.1319i −0.255130 + 0.732704i
\(373\) 13.3454 + 13.3454i 0.691000 + 0.691000i 0.962452 0.271452i \(-0.0875037\pi\)
−0.271452 + 0.962452i \(0.587504\pi\)
\(374\) 3.65006 2.36557i 0.188740 0.122321i
\(375\) −1.32503 1.11548i −0.0684245 0.0576029i
\(376\) −8.47903 6.19642i −0.437273 0.319556i
\(377\) −6.69898 −0.345015
\(378\) −8.24449 + 0.384517i −0.424051 + 0.0197774i
\(379\) 16.4779 16.4779i 0.846414 0.846414i −0.143270 0.989684i \(-0.545762\pi\)
0.989684 + 0.143270i \(0.0457616\pi\)
\(380\) 14.1781 + 6.34397i 0.727321 + 0.325439i
\(381\) −3.02663 35.2479i −0.155059 1.80580i
\(382\) −13.0647 2.78963i −0.668448 0.142730i
\(383\) −38.0542 −1.94448 −0.972239 0.233992i \(-0.924821\pi\)
−0.972239 + 0.233992i \(0.924821\pi\)
\(384\) 3.58337 + 19.2655i 0.182863 + 0.983138i
\(385\) −0.562166 −0.0286506
\(386\) 11.0976 + 2.36960i 0.564852 + 0.120609i
\(387\) −3.91747 + 5.55657i −0.199136 + 0.282456i
\(388\) −24.4597 10.9444i −1.24175 0.555620i
\(389\) 25.7169 25.7169i 1.30390 1.30390i 0.378157 0.925742i \(-0.376558\pi\)
0.925742 0.378157i \(-0.123442\pi\)
\(390\) −0.321023 + 2.56083i −0.0162556 + 0.129673i
\(391\) −15.2135 −0.769380
\(392\) 13.1046 + 9.57677i 0.661883 + 0.483700i
\(393\) −7.36377 + 8.74717i −0.371453 + 0.441236i
\(394\) 4.93311 3.19711i 0.248527 0.161068i
\(395\) 5.77402 + 5.77402i 0.290523 + 0.290523i
\(396\) −1.53367 2.58201i −0.0770696 0.129751i
\(397\) 20.5780 20.5780i 1.03278 1.03278i 0.0333335 0.999444i \(-0.489388\pi\)
0.999444 0.0333335i \(-0.0106123\pi\)
\(398\) −15.8409 3.38241i −0.794031 0.169545i
\(399\) −11.5580 9.73005i −0.578623 0.487112i
\(400\) 2.98247 2.66550i 0.149123 0.133275i
\(401\) 13.3882i 0.668575i 0.942471 + 0.334288i \(0.108496\pi\)
−0.942471 + 0.334288i \(0.891504\pi\)
\(402\) −5.06506 6.51697i −0.252622 0.325037i
\(403\) −3.21837 3.21837i −0.160319 0.160319i
\(404\) −8.90218 + 3.39833i −0.442900 + 0.169073i
\(405\) −3.85600 + 8.13211i −0.191606 + 0.404088i
\(406\) −5.49238 8.47468i −0.272582 0.420591i
\(407\) 3.59433i 0.178164i
\(408\) 15.6173 25.7352i 0.773171 1.27408i
\(409\) 22.2754i 1.10145i 0.834687 + 0.550724i \(0.185648\pi\)
−0.834687 + 0.550724i \(0.814352\pi\)
\(410\) 12.5218 8.11531i 0.618410 0.400787i
\(411\) −1.02498 + 0.0880120i −0.0505586 + 0.00434131i
\(412\) 28.6363 + 12.8133i 1.41081 + 0.631264i
\(413\) 2.28696 + 2.28696i 0.112534 + 0.112534i
\(414\) −0.410095 + 10.4961i −0.0201551 + 0.515856i
\(415\) 0.283737i 0.0139281i
\(416\) −5.74998 1.56926i −0.281916 0.0769392i
\(417\) −18.4658 + 21.9349i −0.904273 + 1.07415i
\(418\) 1.14795 5.37621i 0.0561481 0.262959i
\(419\) 7.19845 7.19845i 0.351667 0.351667i −0.509062 0.860730i \(-0.670008\pi\)
0.860730 + 0.509062i \(0.170008\pi\)
\(420\) −3.50283 + 1.69346i −0.170921 + 0.0826326i
\(421\) 6.77995 + 6.77995i 0.330434 + 0.330434i 0.852751 0.522317i \(-0.174932\pi\)
−0.522317 + 0.852751i \(0.674932\pi\)
\(422\) −16.3165 25.1762i −0.794274 1.22556i
\(423\) 10.9759 1.89893i 0.533665 0.0923292i
\(424\) 12.2395 1.90372i 0.594401 0.0924528i
\(425\) −6.14478 −0.298065
\(426\) −4.30879 + 34.3716i −0.208761 + 1.66531i
\(427\) −0.610945 + 0.610945i −0.0295657 + 0.0295657i
\(428\) −3.38360 8.86357i −0.163552 0.428437i
\(429\) 0.910087 0.0781464i 0.0439394 0.00377294i
\(430\) −0.669243 + 3.13427i −0.0322738 + 0.151148i
\(431\) −17.6060 −0.848053 −0.424027 0.905650i \(-0.639384\pi\)
−0.424027 + 0.905650i \(0.639384\pi\)
\(432\) −17.3342 11.4684i −0.833994 0.551774i
\(433\) 15.9610 0.767036 0.383518 0.923533i \(-0.374712\pi\)
0.383518 + 0.923533i \(0.374712\pi\)
\(434\) 1.43278 6.71015i 0.0687756 0.322098i
\(435\) −10.9719 + 0.942126i −0.526064 + 0.0451715i
\(436\) 0.150053 0.0572814i 0.00718622 0.00274328i
\(437\) −13.5964 + 13.5964i −0.650405 + 0.650405i
\(438\) 3.01158 24.0237i 0.143899 1.14790i
\(439\) −25.1878 −1.20215 −0.601075 0.799193i \(-0.705261\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(440\) −1.14301 0.835304i −0.0544909 0.0398216i
\(441\) −16.9636 + 2.93486i −0.807789 + 0.139755i
\(442\) 4.97968 + 7.68360i 0.236859 + 0.365471i
\(443\) 10.7728 + 10.7728i 0.511831 + 0.511831i 0.915087 0.403256i \(-0.132122\pi\)
−0.403256 + 0.915087i \(0.632122\pi\)
\(444\) −10.8275 22.3961i −0.513852 1.06287i
\(445\) 12.0925 12.0925i 0.573241 0.573241i
\(446\) 6.17512 28.9200i 0.292401 1.36940i
\(447\) 20.0124 23.7720i 0.946552 1.12438i
\(448\) −2.72909 8.56074i −0.128937 0.404457i
\(449\) 12.9034i 0.608947i 0.952521 + 0.304474i \(0.0984805\pi\)
−0.952521 + 0.304474i \(0.901519\pi\)
\(450\) −0.165639 + 4.23941i −0.00780828 + 0.199848i
\(451\) −3.73433 3.73433i −0.175843 0.175843i
\(452\) 1.73293 3.87292i 0.0815104 0.182167i
\(453\) 35.1515 3.01835i 1.65156 0.141814i
\(454\) −15.1979 + 9.84964i −0.713273 + 0.462267i
\(455\) 1.18340i 0.0554784i
\(456\) −9.04242 36.9570i −0.423450 1.73067i
\(457\) 2.30813i 0.107970i −0.998542 0.0539848i \(-0.982808\pi\)
0.998542 0.0539848i \(-0.0171922\pi\)
\(458\) −11.6402 17.9607i −0.543912 0.839250i
\(459\) 8.11486 + 30.8808i 0.378769 + 1.44139i
\(460\) 1.76597 + 4.62608i 0.0823386 + 0.215692i
\(461\) 15.7652 + 15.7652i 0.734257 + 0.734257i 0.971460 0.237203i \(-0.0762308\pi\)
−0.237203 + 0.971460i \(0.576231\pi\)
\(462\) 0.845025 + 1.08725i 0.0393141 + 0.0505836i
\(463\) 18.0736i 0.839953i 0.907535 + 0.419976i \(0.137962\pi\)
−0.907535 + 0.419976i \(0.862038\pi\)
\(464\) 1.42501 25.3919i 0.0661545 1.17879i
\(465\) −5.72383 4.81859i −0.265436 0.223457i
\(466\) 1.44643 + 0.308848i 0.0670047 + 0.0143071i
\(467\) −18.8540 + 18.8540i −0.872460 + 0.872460i −0.992740 0.120280i \(-0.961621\pi\)
0.120280 + 0.992740i \(0.461621\pi\)
\(468\) 5.43530 3.22846i 0.251247 0.149236i
\(469\) 2.67611 + 2.67611i 0.123571 + 0.123571i
\(470\) 4.40646 2.85579i 0.203255 0.131728i
\(471\) −21.0107 + 24.9579i −0.968121 + 1.15000i
\(472\) 1.25179 + 8.04803i 0.0576181 + 0.370440i
\(473\) 1.13430 0.0521554
\(474\) 2.48793 19.8465i 0.114274 0.911578i
\(475\) −5.49163 + 5.49163i −0.251973 + 0.251973i
\(476\) −5.63753 + 12.5993i −0.258396 + 0.577488i
\(477\) −7.57026 + 10.7377i −0.346618 + 0.491646i
\(478\) −30.4573 6.50337i −1.39309 0.297457i
\(479\) −10.6120 −0.484873 −0.242436 0.970167i \(-0.577947\pi\)
−0.242436 + 0.970167i \(0.577947\pi\)
\(480\) −9.63831 1.76155i −0.439926 0.0804033i
\(481\) 7.56630 0.344993
\(482\) 24.4187 + 5.21399i 1.11224 + 0.237491i
\(483\) −0.412054 4.79874i −0.0187491 0.218350i
\(484\) 8.78075 19.6240i 0.399125 0.892002i
\(485\) 9.47402 9.47402i 0.430193 0.430193i
\(486\) 21.5240 4.76619i 0.976349 0.216199i
\(487\) −27.2849 −1.23640 −0.618198 0.786022i \(-0.712137\pi\)
−0.618198 + 0.786022i \(0.712137\pi\)
\(488\) −2.14997 + 0.334406i −0.0973247 + 0.0151378i
\(489\) 9.69231 + 8.15944i 0.438302 + 0.368983i
\(490\) −6.81032 + 4.41372i −0.307659 + 0.199392i
\(491\) 5.25791 + 5.25791i 0.237286 + 0.237286i 0.815725 0.578439i \(-0.196338\pi\)
−0.578439 + 0.815725i \(0.696338\pi\)
\(492\) −34.5177 12.0192i −1.55618 0.541865i
\(493\) −27.6254 + 27.6254i −1.24419 + 1.24419i
\(494\) 11.3173 + 2.41651i 0.509188 + 0.108724i
\(495\) 1.47960 0.255984i 0.0665029 0.0115056i
\(496\) 12.8836 11.5143i 0.578489 0.517009i
\(497\) 15.8836i 0.712477i
\(498\) −0.548759 + 0.426502i −0.0245905 + 0.0191120i
\(499\) 10.4407 + 10.4407i 0.467391 + 0.467391i 0.901068 0.433677i \(-0.142784\pi\)
−0.433677 + 0.901068i \(0.642784\pi\)
\(500\) 0.713278 + 1.86848i 0.0318988 + 0.0835612i
\(501\) −0.0148846 0.173345i −0.000664996 0.00774449i
\(502\) −4.99623 7.70914i −0.222993 0.344076i
\(503\) 6.10431i 0.272178i −0.990697 0.136089i \(-0.956547\pi\)
0.990697 0.136089i \(-0.0434533\pi\)
\(504\) 8.54054 + 4.22908i 0.380426 + 0.188378i
\(505\) 4.76439i 0.212012i
\(506\) 1.47067 0.953133i 0.0653795 0.0423719i
\(507\) −1.76185 20.5183i −0.0782463 0.911250i
\(508\) −16.6845 + 37.2880i −0.740253 + 1.65439i
\(509\) 19.8126 + 19.8126i 0.878176 + 0.878176i 0.993346 0.115170i \(-0.0367413\pi\)
−0.115170 + 0.993346i \(0.536741\pi\)
\(510\) 9.23657 + 11.8843i 0.409002 + 0.526244i
\(511\) 11.1017i 0.491110i
\(512\) 7.17127 21.4610i 0.316928 0.948450i
\(513\) 34.8507 + 20.3461i 1.53870 + 0.898301i
\(514\) 2.69196 12.6073i 0.118737 0.556084i
\(515\) −11.0918 + 11.0918i −0.488761 + 0.488761i
\(516\) 7.06779 3.41697i 0.311142 0.150424i
\(517\) −1.31412 1.31412i −0.0577947 0.0577947i
\(518\) 6.20347 + 9.57189i 0.272565 + 0.420565i
\(519\) −15.1285 12.7359i −0.664067 0.559042i
\(520\) 1.75837 2.40611i 0.0771095 0.105515i
\(521\) 28.0649 1.22955 0.614773 0.788704i \(-0.289248\pi\)
0.614773 + 0.788704i \(0.289248\pi\)
\(522\) 18.3147 + 19.8040i 0.801611 + 0.866797i
\(523\) −3.10143 + 3.10143i −0.135616 + 0.135616i −0.771656 0.636040i \(-0.780571\pi\)
0.636040 + 0.771656i \(0.280571\pi\)
\(524\) 12.3347 4.70868i 0.538845 0.205700i
\(525\) −0.166429 1.93822i −0.00726358 0.0845911i
\(526\) −7.21787 + 33.8035i −0.314714 + 1.47390i
\(527\) −26.5440 −1.15627
\(528\) 0.102613 + 3.46622i 0.00446564 + 0.150848i
\(529\) 16.8702 0.733487
\(530\) −1.29327 + 6.05678i −0.0561760 + 0.263090i
\(531\) −7.06055 4.97780i −0.306402 0.216018i
\(532\) 6.22177 + 16.2984i 0.269748 + 0.706625i
\(533\) 7.86099 7.86099i 0.340497 0.340497i
\(534\) −41.5644 5.21047i −1.79867 0.225479i
\(535\) 4.74372 0.205089
\(536\) 1.46479 + 9.41747i 0.0632692 + 0.406773i
\(537\) −15.3563 + 18.2412i −0.662672 + 0.787165i
\(538\) 13.0358 + 20.1140i 0.562011 + 0.867178i
\(539\) 2.03101 + 2.03101i 0.0874817 + 0.0874817i
\(540\) 8.44817 6.05215i 0.363551 0.260443i
\(541\) 31.7579 31.7579i 1.36538 1.36538i 0.498473 0.866905i \(-0.333894\pi\)
0.866905 0.498473i \(-0.166106\pi\)
\(542\) 2.61189 12.2323i 0.112190 0.525423i
\(543\) 16.4314 + 13.8327i 0.705140 + 0.593620i
\(544\) −30.1832 + 17.2406i −1.29410 + 0.739183i
\(545\) 0.0803072i 0.00343998i
\(546\) −2.28874 + 1.77883i −0.0979489 + 0.0761269i
\(547\) 4.25767 + 4.25767i 0.182045 + 0.182045i 0.792246 0.610202i \(-0.208912\pi\)
−0.610202 + 0.792246i \(0.708912\pi\)
\(548\) 1.08431 + 0.485171i 0.0463192 + 0.0207255i
\(549\) 1.32978 1.88618i 0.0567538 0.0805000i
\(550\) 0.594009 0.384973i 0.0253286 0.0164153i
\(551\) 49.3780i 2.10358i
\(552\) 6.29250 10.3692i 0.267826 0.441342i
\(553\) 9.17133i 0.390004i
\(554\) 10.0173 + 15.4566i 0.425596 + 0.656689i
\(555\) 12.3925 1.06410i 0.526031 0.0451686i
\(556\) 30.9312 11.8077i 1.31178 0.500760i
\(557\) −4.91179 4.91179i −0.208119 0.208119i 0.595348 0.803468i \(-0.297014\pi\)
−0.803468 + 0.595348i \(0.797014\pi\)
\(558\) −0.715519 + 18.3132i −0.0302904 + 0.775261i
\(559\) 2.38778i 0.100992i
\(560\) 4.48555 + 0.251733i 0.189549 + 0.0106376i
\(561\) 3.43077 4.07530i 0.144847 0.172059i
\(562\) −13.9486 2.97836i −0.588385 0.125634i
\(563\) 16.0018 16.0018i 0.674394 0.674394i −0.284332 0.958726i \(-0.591772\pi\)
0.958726 + 0.284332i \(0.0917717\pi\)
\(564\) −12.1468 4.22956i −0.511473 0.178097i
\(565\) 1.50011 + 1.50011i 0.0631100 + 0.0631100i
\(566\) −3.44033 + 2.22965i −0.144608 + 0.0937193i
\(567\) −9.52082 + 3.39604i −0.399837 + 0.142620i
\(568\) 23.6009 32.2949i 0.990273 1.35507i
\(569\) −15.5844 −0.653333 −0.326666 0.945140i \(-0.605925\pi\)
−0.326666 + 0.945140i \(0.605925\pi\)
\(570\) 18.8758 + 2.36625i 0.790622 + 0.0991113i
\(571\) 16.9630 16.9630i 0.709878 0.709878i −0.256631 0.966509i \(-0.582612\pi\)
0.966509 + 0.256631i \(0.0826125\pi\)
\(572\) −0.962762 0.430786i −0.0402551 0.0180121i
\(573\) −16.3016 + 1.39977i −0.681010 + 0.0584763i
\(574\) 16.3898 + 3.49962i 0.684097 + 0.146071i
\(575\) −2.47584 −0.103250
\(576\) 11.0810 + 21.2888i 0.461708 + 0.887032i
\(577\) 7.83292 0.326089 0.163044 0.986619i \(-0.447869\pi\)
0.163044 + 0.986619i \(0.447869\pi\)
\(578\) 28.7095 + 6.13016i 1.19416 + 0.254981i
\(579\) 13.8471 1.18901i 0.575467 0.0494136i
\(580\) 11.6070 + 5.19352i 0.481953 + 0.215649i
\(581\) 0.225341 0.225341i 0.00934871 0.00934871i
\(582\) −32.5641 4.08219i −1.34983 0.169212i
\(583\) 2.19197 0.0907821
\(584\) −16.4956 + 22.5722i −0.682594 + 0.934045i
\(585\) 0.538863 + 3.11464i 0.0222792 + 0.128775i
\(586\) −22.9181 + 14.8530i −0.946737 + 0.613573i
\(587\) −25.8232 25.8232i −1.06584 1.06584i −0.997674 0.0681648i \(-0.978286\pi\)
−0.0681648 0.997674i \(-0.521714\pi\)
\(588\) 18.7733 + 6.53693i 0.774198 + 0.269578i
\(589\) −23.7226 + 23.7226i −0.977471 + 0.977471i
\(590\) −3.98262 0.850385i −0.163962 0.0350098i
\(591\) 4.63675 5.50783i 0.190730 0.226562i
\(592\) −1.60951 + 28.6793i −0.0661503 + 1.17871i
\(593\) 27.6730i 1.13640i −0.822892 0.568198i \(-0.807641\pi\)
0.822892 0.568198i \(-0.192359\pi\)
\(594\) −2.71915 2.47681i −0.111568 0.101625i
\(595\) −4.88011 4.88011i −0.200065 0.200065i
\(596\) −33.5218 + 12.7967i −1.37311 + 0.524173i
\(597\) −19.7656 + 1.69721i −0.808953 + 0.0694623i
\(598\) 2.00641 + 3.09586i 0.0820480 + 0.126599i
\(599\) 1.70952i 0.0698493i −0.999390 0.0349246i \(-0.988881\pi\)
0.999390 0.0349246i \(-0.0111191\pi\)
\(600\) 2.54156 4.18814i 0.103759 0.170980i
\(601\) 8.40978i 0.343042i 0.985180 + 0.171521i \(0.0548682\pi\)
−0.985180 + 0.171521i \(0.945132\pi\)
\(602\) −3.02071 + 1.95770i −0.123115 + 0.0797899i
\(603\) −8.26197 5.82482i −0.336453 0.237205i
\(604\) −37.1860 16.6388i −1.51308 0.677024i
\(605\) 7.60103 + 7.60103i 0.309026 + 0.309026i
\(606\) −9.21452 + 7.16162i −0.374314 + 0.290921i
\(607\) 29.2914i 1.18890i −0.804132 0.594451i \(-0.797369\pi\)
0.804132 0.594451i \(-0.202631\pi\)
\(608\) −11.5670 + 42.3830i −0.469102 + 1.71886i
\(609\) −9.46200 7.96555i −0.383420 0.322781i
\(610\) 0.227174 1.06393i 0.00919802 0.0430772i
\(611\) 2.76630 2.76630i 0.111912 0.111912i
\(612\) 9.10060 35.7278i 0.367870 1.44421i
\(613\) −0.0369270 0.0369270i −0.00149147 0.00149147i 0.706361 0.707852i \(-0.250336\pi\)
−0.707852 + 0.706361i \(0.750336\pi\)
\(614\) −0.382549 0.590269i −0.0154384 0.0238213i
\(615\) 11.7696 13.9807i 0.474595 0.563755i
\(616\) −0.244377 1.57115i −0.00984621 0.0633036i
\(617\) 2.44515 0.0984379 0.0492190 0.998788i \(-0.484327\pi\)
0.0492190 + 0.998788i \(0.484327\pi\)
\(618\) 38.1246 + 4.77925i 1.53360 + 0.192250i
\(619\) 1.89668 1.89668i 0.0762340 0.0762340i −0.667962 0.744196i \(-0.732833\pi\)
0.744196 + 0.667962i \(0.232833\pi\)
\(620\) 3.08119 + 8.07141i 0.123744 + 0.324156i
\(621\) 3.26963 + 12.4424i 0.131206 + 0.499298i
\(622\) −7.48743 + 35.0660i −0.300219 + 1.40602i
\(623\) 19.2075 0.769532
\(624\) −7.29662 + 0.216006i −0.292099 + 0.00864715i
\(625\) −1.00000 −0.0400000
\(626\) −6.32423 + 29.6183i −0.252767 + 1.18379i
\(627\) −0.576015 6.70823i −0.0230038 0.267901i
\(628\) 35.1941 13.4351i 1.40440 0.536117i
\(629\) 31.2021 31.2021i 1.24411 1.24411i
\(630\) −3.49844 + 3.23534i −0.139381 + 0.128899i
\(631\) 33.1646 1.32026 0.660132 0.751150i \(-0.270500\pi\)
0.660132 + 0.751150i \(0.270500\pi\)
\(632\) −13.6274 + 18.6474i −0.542068 + 0.741752i
\(633\) −28.1093 23.6637i −1.11724 0.940547i
\(634\) 15.9803 + 24.6574i 0.634659 + 0.979272i
\(635\) −14.4428 14.4428i −0.573147 0.573147i
\(636\) 13.6581 6.60307i 0.541577 0.261829i
\(637\) −4.27540 + 4.27540i −0.169398 + 0.169398i
\(638\) 0.939776 4.40126i 0.0372061 0.174248i
\(639\) 7.23265 + 41.8049i 0.286119 + 1.65378i
\(640\) 8.74609 + 7.17676i 0.345720 + 0.283686i
\(641\) 1.34629i 0.0531754i 0.999646 + 0.0265877i \(0.00846413\pi\)
−0.999646 + 0.0265877i \(0.991536\pi\)
\(642\) −7.13057 9.17456i −0.281421 0.362091i
\(643\) −21.5284 21.5284i −0.848999 0.848999i 0.141009 0.990008i \(-0.454965\pi\)
−0.990008 + 0.141009i \(0.954965\pi\)
\(644\) −2.27147 + 5.07649i −0.0895083 + 0.200042i
\(645\) 0.335811 + 3.91083i 0.0132225 + 0.153989i
\(646\) 56.6356 36.7051i 2.22830 1.44414i
\(647\) 8.62645i 0.339141i 0.985518 + 0.169570i \(0.0542380\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(648\) −24.4040 7.24177i −0.958681 0.284484i
\(649\) 1.44132i 0.0565769i
\(650\) 0.810393 + 1.25043i 0.0317862 + 0.0490458i
\(651\) −0.718936 8.37267i −0.0281773 0.328151i
\(652\) −5.21746 13.6675i −0.204332 0.535262i
\(653\) 21.4073 + 21.4073i 0.837732 + 0.837732i 0.988560 0.150828i \(-0.0481939\pi\)
−0.150828 + 0.988560i \(0.548194\pi\)
\(654\) 0.155317 0.120714i 0.00607339 0.00472031i
\(655\) 6.60147i 0.257941i
\(656\) 28.1242 + 31.4685i 1.09806 + 1.22864i
\(657\) −5.05519 29.2191i −0.197222 1.13995i
\(658\) 5.76759 + 1.23152i 0.224844 + 0.0480097i
\(659\) −8.86765 + 8.86765i −0.345435 + 0.345435i −0.858406 0.512971i \(-0.828545\pi\)
0.512971 + 0.858406i \(0.328545\pi\)
\(660\) −1.63744 0.570163i −0.0637374 0.0221936i
\(661\) −14.5233 14.5233i −0.564892 0.564892i 0.365801 0.930693i \(-0.380795\pi\)
−0.930693 + 0.365801i \(0.880795\pi\)
\(662\) −22.8342 + 14.7986i −0.887474 + 0.575166i
\(663\) 8.57876 + 7.22200i 0.333171 + 0.280479i
\(664\) 0.792994 0.123342i 0.0307742 0.00478660i
\(665\) −8.72278 −0.338255
\(666\) −20.6858 22.3680i −0.801560 0.866743i
\(667\) −11.1308 + 11.1308i −0.430986 + 0.430986i
\(668\) −0.0820523 + 0.183378i −0.00317470 + 0.00709511i
\(669\) −3.09854 36.0853i −0.119796 1.39514i
\(670\) −4.66030 0.995086i −0.180043 0.0384435i
\(671\) −0.385039 −0.0148643
\(672\) −6.25563 9.05363i −0.241316 0.349252i
\(673\) −30.7302 −1.18456 −0.592282 0.805731i \(-0.701773\pi\)
−0.592282 + 0.805731i \(0.701773\pi\)
\(674\) −29.0874 6.21085i −1.12040 0.239233i
\(675\) 1.32061 + 5.02553i 0.0508304 + 0.193433i
\(676\) −9.71227 + 21.7059i −0.373549 + 0.834842i
\(677\) 17.0398 17.0398i 0.654894 0.654894i −0.299274 0.954167i \(-0.596744\pi\)
0.954167 + 0.299274i \(0.0967443\pi\)
\(678\) 0.646371 5.15617i 0.0248237 0.198022i
\(679\) 15.0483 0.577502
\(680\) −2.67117 17.1736i −0.102435 0.658576i
\(681\) −14.2849 + 16.9685i −0.547397 + 0.650234i
\(682\) 2.56598 1.66299i 0.0982565 0.0636793i
\(683\) 21.2833 + 21.2833i 0.814381 + 0.814381i 0.985287 0.170906i \(-0.0546695\pi\)
−0.170906 + 0.985287i \(0.554670\pi\)
\(684\) −23.7969 40.0635i −0.909899 1.53187i
\(685\) −0.419987 + 0.419987i −0.0160469 + 0.0160469i
\(686\) −19.7875 4.22512i −0.755492 0.161316i
\(687\) −20.0532 16.8817i −0.765078 0.644078i
\(688\) −9.05066 0.507930i −0.345053 0.0193647i
\(689\) 4.61423i 0.175788i
\(690\) 3.72159 + 4.78839i 0.141678 + 0.182291i
\(691\) −16.5327 16.5327i −0.628932 0.628932i 0.318867 0.947799i \(-0.396698\pi\)
−0.947799 + 0.318867i \(0.896698\pi\)
\(692\) 8.14381 + 21.3333i 0.309581 + 0.810970i
\(693\) 1.37838 + 0.971778i 0.0523602 + 0.0369148i
\(694\) 0.837193 + 1.29178i 0.0317794 + 0.0490353i
\(695\) 16.5542i 0.627936i
\(696\) −7.40263 30.2550i −0.280596 1.14681i
\(697\) 64.8346i 2.45579i
\(698\) 14.4832 9.38646i 0.548197 0.355283i
\(699\) 1.80480 0.154973i 0.0682639 0.00586162i
\(700\) −0.917451 + 2.05041i −0.0346764 + 0.0774981i
\(701\) −12.4742 12.4742i −0.471145 0.471145i 0.431140 0.902285i \(-0.358111\pi\)
−0.902285 + 0.431140i \(0.858111\pi\)
\(702\) 5.21385 5.72398i 0.196784 0.216038i
\(703\) 55.7710i 2.10344i
\(704\) 1.83765 3.55762i 0.0692592 0.134083i
\(705\) 4.14173 4.91982i 0.155987 0.185291i
\(706\) −2.55224 + 11.9529i −0.0960549 + 0.449855i
\(707\) 3.78382 3.78382i 0.142305 0.142305i
\(708\) 4.34183 + 8.98082i 0.163176 + 0.337520i
\(709\) −9.13318 9.13318i −0.343004 0.343004i 0.514492 0.857495i \(-0.327981\pi\)
−0.857495 + 0.514492i \(0.827981\pi\)
\(710\) 10.8771 + 16.7833i 0.408212 + 0.629867i
\(711\) −4.17619 24.1385i −0.156619 0.905265i
\(712\) 39.0532 + 28.5398i 1.46358 + 1.06957i
\(713\) −10.6951 −0.400533
\(714\) −2.10276 + 16.7739i −0.0786937 + 0.627748i
\(715\) 0.372909 0.372909i 0.0139460 0.0139460i
\(716\) 25.7226 9.81941i 0.961300 0.366968i
\(717\) −38.0035 + 3.26324i −1.41927 + 0.121868i
\(718\) 1.93469 9.06074i 0.0722018 0.338144i
\(719\) 5.55155 0.207038 0.103519 0.994627i \(-0.466990\pi\)
0.103519 + 0.994627i \(0.466990\pi\)
\(720\) −11.9204 + 1.37996i −0.444247 + 0.0514281i
\(721\) −17.6179 −0.656125
\(722\) 12.2011 57.1416i 0.454078 2.12659i
\(723\) 30.4688 2.61626i 1.13315 0.0972998i
\(724\) −8.84520 23.1706i −0.328729 0.861130i
\(725\) −4.49575 + 4.49575i −0.166968 + 0.166968i
\(726\) 3.27515 26.1262i 0.121552 0.969636i
\(727\) −35.5686 −1.31917 −0.659584 0.751631i \(-0.729267\pi\)
−0.659584 + 0.751631i \(0.729267\pi\)
\(728\) 3.30738 0.514428i 0.122580 0.0190660i
\(729\) 23.5120 13.2736i 0.870814 0.491613i
\(730\) −7.60247 11.7305i −0.281380 0.434166i
\(731\) 9.84679 + 9.84679i 0.364197 + 0.364197i
\(732\) −2.39916 + 1.15989i −0.0886755 + 0.0428707i
\(733\) −7.46382 + 7.46382i −0.275683 + 0.275683i −0.831383 0.555700i \(-0.812450\pi\)
0.555700 + 0.831383i \(0.312450\pi\)
\(734\) 2.04749 9.58905i 0.0755744 0.353938i
\(735\) −6.40119 + 7.60375i −0.236111 + 0.280468i
\(736\) −12.1614 + 6.94654i −0.448275 + 0.256053i
\(737\) 1.68658i 0.0621259i
\(738\) −44.7307 1.74768i −1.64656 0.0643331i
\(739\) 14.2909 + 14.2909i 0.525698 + 0.525698i 0.919287 0.393589i \(-0.128767\pi\)
−0.393589 + 0.919287i \(0.628767\pi\)
\(740\) −13.1097 5.86592i −0.481923 0.215636i
\(741\) 14.1212 1.21255i 0.518757 0.0445441i
\(742\) −5.83733 + 3.78313i −0.214295 + 0.138883i
\(743\) 52.4964i 1.92591i −0.269668 0.962953i \(-0.586914\pi\)
0.269668 0.962953i \(-0.413086\pi\)
\(744\) 10.9789 18.0918i 0.402507 0.663276i
\(745\) 17.9407i 0.657295i
\(746\) −14.5162 22.3983i −0.531475 0.820060i
\(747\) −0.490477 + 0.695696i −0.0179456 + 0.0254542i
\(748\) −5.74674 + 2.19377i −0.210122 + 0.0802122i
\(749\) 3.76741 + 3.76741i 0.137658 + 0.137658i
\(750\) 1.50316 + 1.93404i 0.0548876 + 0.0706212i
\(751\) 6.70417i 0.244639i −0.992491 0.122319i \(-0.960967\pi\)
0.992491 0.122319i \(-0.0390332\pi\)
\(752\) 9.89694 + 11.0738i 0.360904 + 0.403821i
\(753\) −8.60728 7.24600i −0.313667 0.264059i
\(754\) 9.26494 + 1.97829i 0.337409 + 0.0720450i
\(755\) 14.4033 14.4033i 0.524191 0.524191i
\(756\) 11.5160 + 1.90289i 0.418832 + 0.0692075i
\(757\) −19.4878 19.4878i −0.708296 0.708296i 0.257881 0.966177i \(-0.416976\pi\)
−0.966177 + 0.257881i \(0.916976\pi\)
\(758\) −27.6557 + 17.9235i −1.00450 + 0.651009i
\(759\) 1.38232 1.64201i 0.0501751 0.0596013i
\(760\) −17.7354 12.9609i −0.643330 0.470141i
\(761\) 28.9450 1.04925 0.524627 0.851332i \(-0.324205\pi\)
0.524627 + 0.851332i \(0.324205\pi\)
\(762\) −6.22318 + 49.6429i −0.225442 + 1.79837i
\(763\) −0.0637791 + 0.0637791i −0.00230896 + 0.00230896i
\(764\) 17.2451 + 7.71632i 0.623908 + 0.279166i
\(765\) 15.0664 + 10.6221i 0.544727 + 0.384041i
\(766\) 52.6303 + 11.2378i 1.90161 + 0.406040i
\(767\) −3.03408 −0.109554
\(768\) 0.733391 27.7031i 0.0264640 0.999650i
\(769\) −14.7982 −0.533636 −0.266818 0.963747i \(-0.585972\pi\)
−0.266818 + 0.963747i \(0.585972\pi\)
\(770\) 0.777497 + 0.166014i 0.0280190 + 0.00598274i
\(771\) −1.35077 15.7309i −0.0486466 0.566535i
\(772\) −14.6486 6.55449i −0.527214 0.235901i
\(773\) −36.1821 + 36.1821i −1.30138 + 1.30138i −0.373917 + 0.927462i \(0.621986\pi\)
−0.927462 + 0.373917i \(0.878014\pi\)
\(774\) 7.05893 6.52807i 0.253728 0.234647i
\(775\) −4.31976 −0.155170
\(776\) 30.5966 + 22.3598i 1.09835 + 0.802670i
\(777\) 10.6870 + 8.99685i 0.383396 + 0.322760i
\(778\) −43.1619 + 27.9729i −1.54743 + 1.00288i
\(779\) −57.9432 57.9432i −2.07603 2.07603i
\(780\) 1.20023 3.44692i 0.0429751 0.123420i
\(781\) 5.00520 5.00520i 0.179100 0.179100i
\(782\) 21.0408 + 4.49273i 0.752419 + 0.160660i
\(783\) 28.5307 + 16.6564i 1.01960 + 0.595252i
\(784\) −15.2960 17.1150i −0.546287 0.611249i
\(785\) 18.8356i 0.672273i
\(786\) 12.7675 9.92305i 0.455402 0.353943i
\(787\) 22.3145 + 22.3145i 0.795426 + 0.795426i 0.982370 0.186945i \(-0.0598585\pi\)
−0.186945 + 0.982370i \(0.559858\pi\)
\(788\) −7.76682 + 2.96492i −0.276681 + 0.105621i
\(789\) 3.62176 + 42.1787i 0.128938 + 1.50160i
\(790\) −6.28055 9.69082i −0.223452 0.344784i
\(791\) 2.38274i 0.0847204i
\(792\) 1.35862 + 4.02393i 0.0482764 + 0.142984i
\(793\) 0.810532i 0.0287828i
\(794\) −34.5370 + 22.3832i −1.22567 + 0.794348i
\(795\) 0.648933 + 7.55742i 0.0230153 + 0.268034i
\(796\) 20.9096 + 9.35598i 0.741122 + 0.331614i
\(797\) 7.91987 + 7.91987i 0.280536 + 0.280536i 0.833323 0.552787i \(-0.186436\pi\)
−0.552787 + 0.833323i \(0.686436\pi\)
\(798\) 13.1117 + 16.8702i 0.464150 + 0.597199i
\(799\) 22.8154i 0.807151i
\(800\) −4.91202 + 2.80573i −0.173666 + 0.0991974i
\(801\) −50.5533 + 8.74620i −1.78621 + 0.309032i
\(802\) 3.95370 18.5164i 0.139610 0.653837i
\(803\) −3.49834 + 3.49834i −0.123454 + 0.123454i
\(804\) 5.08063 + 10.5090i 0.179180 + 0.370623i
\(805\) −1.96629 1.96629i −0.0693025 0.0693025i
\(806\) 3.50070 + 5.40155i 0.123307 + 0.190262i
\(807\) 22.4574 + 18.9057i 0.790537 + 0.665511i
\(808\) 13.3156 2.07110i 0.468442 0.0728611i
\(809\) 32.3002 1.13561 0.567807 0.823162i \(-0.307792\pi\)
0.567807 + 0.823162i \(0.307792\pi\)
\(810\) 7.73450 10.1083i 0.271763 0.355169i
\(811\) 0.250525 0.250525i 0.00879714 0.00879714i −0.702695 0.711492i \(-0.748020\pi\)
0.711492 + 0.702695i \(0.248020\pi\)
\(812\) 5.09349 + 13.3428i 0.178746 + 0.468239i
\(813\) −1.31059 15.2630i −0.0459643 0.535297i
\(814\) −1.06145 + 4.97109i −0.0372037 + 0.174237i
\(815\) 7.31476 0.256225
\(816\) −29.1992 + 30.9807i −1.02218 + 1.08454i
\(817\) 17.6003 0.615756
\(818\) 6.57819 30.8077i 0.230001 1.07717i
\(819\) −2.04565 + 2.90157i −0.0714810 + 0.101389i
\(820\) −19.7147 + 7.52593i −0.688468 + 0.262817i
\(821\) −21.7932 + 21.7932i −0.760589 + 0.760589i −0.976429 0.215839i \(-0.930751\pi\)
0.215839 + 0.976429i \(0.430751\pi\)
\(822\) 1.44358 + 0.180965i 0.0503505 + 0.00631188i
\(823\) 3.78296 0.131866 0.0659329 0.997824i \(-0.478998\pi\)
0.0659329 + 0.997824i \(0.478998\pi\)
\(824\) −35.8211 26.1779i −1.24789 0.911949i
\(825\) 0.558324 0.663213i 0.0194383 0.0230901i
\(826\) −2.48759 3.83832i −0.0865542 0.133552i
\(827\) 22.8419 + 22.8419i 0.794289 + 0.794289i 0.982188 0.187899i \(-0.0601678\pi\)
−0.187899 + 0.982188i \(0.560168\pi\)
\(828\) 3.66680 14.3954i 0.127430 0.500275i
\(829\) 25.8791 25.8791i 0.898819 0.898819i −0.0965129 0.995332i \(-0.530769\pi\)
0.995332 + 0.0965129i \(0.0307689\pi\)
\(830\) −0.0837908 + 0.392419i −0.00290842 + 0.0136211i
\(831\) 17.2574 + 14.5281i 0.598652 + 0.503973i
\(832\) 7.48902 + 3.86838i 0.259635 + 0.134112i
\(833\) 35.2620i 1.22176i
\(834\) 32.0165 24.8836i 1.10864 0.861647i
\(835\) −0.0710283 0.0710283i −0.00245804 0.00245804i
\(836\) −3.17532 + 7.09650i −0.109821 + 0.245437i
\(837\) 5.70473 + 21.7091i 0.197184 + 0.750377i
\(838\) −12.0815 + 7.82993i −0.417349 + 0.270481i
\(839\) 40.8189i 1.40923i 0.709592 + 0.704613i \(0.248879\pi\)
−0.709592 + 0.704613i \(0.751121\pi\)
\(840\) 5.34465 1.30770i 0.184408 0.0451198i
\(841\) 11.4236i 0.393917i
\(842\) −7.37472 11.3791i −0.254150 0.392150i
\(843\) −17.4045 + 1.49447i −0.599443 + 0.0514723i
\(844\) 15.1315 + 39.6380i 0.520847 + 1.36440i
\(845\) −8.40739 8.40739i −0.289223 0.289223i
\(846\) −15.7408 0.615012i −0.541180 0.0211446i
\(847\) 12.0733i 0.414843i
\(848\) −17.4898 0.981542i −0.600603 0.0337063i
\(849\) −3.23365 + 3.84114i −0.110979 + 0.131828i
\(850\) 8.49845 + 1.81462i 0.291495 + 0.0622411i
\(851\) 12.5719 12.5719i 0.430959 0.430959i
\(852\) 16.1096 46.2648i 0.551904 1.58501i
\(853\) −28.8336 28.8336i −0.987245 0.987245i 0.0126748 0.999920i \(-0.495965\pi\)
−0.999920 + 0.0126748i \(0.995965\pi\)
\(854\) 1.02538 0.664541i 0.0350878 0.0227401i
\(855\) 22.9580 3.97195i 0.785146 0.135838i
\(856\) 2.06212 + 13.2579i 0.0704819 + 0.453145i
\(857\) 15.9421 0.544571 0.272286 0.962216i \(-0.412220\pi\)
0.272286 + 0.962216i \(0.412220\pi\)
\(858\) −1.28176 0.160680i −0.0437586 0.00548552i
\(859\) −19.2238 + 19.2238i −0.655908 + 0.655908i −0.954409 0.298501i \(-0.903513\pi\)
0.298501 + 0.954409i \(0.403513\pi\)
\(860\) 1.85118 4.13718i 0.0631246 0.141077i
\(861\) 20.4506 1.75603i 0.696953 0.0598452i
\(862\) 24.3498 + 5.19927i 0.829358 + 0.177088i
\(863\) 9.61129 0.327172 0.163586 0.986529i \(-0.447694\pi\)
0.163586 + 0.986529i \(0.447694\pi\)
\(864\) 20.5871 + 20.9802i 0.700389 + 0.713762i
\(865\) −11.4174 −0.388204
\(866\) −22.0746 4.71346i −0.750126 0.160170i
\(867\) 35.8226 3.07598i 1.21660 0.104466i
\(868\) −3.96317 + 8.85727i −0.134519 + 0.300635i
\(869\) −2.89004 + 2.89004i −0.0980381 + 0.0980381i
\(870\) 15.4528 + 1.93714i 0.523899 + 0.0656753i
\(871\) −3.55035 −0.120299
\(872\) −0.224444 + 0.0349099i −0.00760064 + 0.00118220i
\(873\) −39.6065 + 6.85230i −1.34048 + 0.231915i
\(874\) 22.8195 14.7892i 0.771883 0.500251i
\(875\) −0.794189 0.794189i −0.0268485 0.0268485i
\(876\) −11.2596 + 32.3363i −0.380427 + 1.09254i
\(877\) −1.48744 + 1.48744i −0.0502272 + 0.0502272i −0.731774 0.681547i \(-0.761307\pi\)
0.681547 + 0.731774i \(0.261307\pi\)
\(878\) 34.8357 + 7.43826i 1.17565 + 0.251029i
\(879\) −21.5412 + 25.5881i −0.726568 + 0.863065i
\(880\) 1.33415 + 1.49280i 0.0449742 + 0.0503223i
\(881\) 53.3497i 1.79740i −0.438567 0.898699i \(-0.644514\pi\)
0.438567 0.898699i \(-0.355486\pi\)
\(882\) 24.3280 + 0.950522i 0.819165 + 0.0320057i
\(883\) −18.2721 18.2721i −0.614904 0.614904i 0.329316 0.944220i \(-0.393182\pi\)
−0.944220 + 0.329316i \(0.893182\pi\)
\(884\) −4.61803 12.0973i −0.155321 0.406875i
\(885\) −4.96936 + 0.426704i −0.167043 + 0.0143435i
\(886\) −11.7178 18.0805i −0.393669 0.607427i
\(887\) 13.1325i 0.440948i −0.975393 0.220474i \(-0.929240\pi\)
0.975393 0.220474i \(-0.0707604\pi\)
\(888\) 8.36104 + 34.1721i 0.280578 + 1.14674i
\(889\) 22.9407i 0.769406i
\(890\) −20.2955 + 13.1534i −0.680306 + 0.440901i
\(891\) −4.07033 1.93003i −0.136361 0.0646583i
\(892\) −17.0808 + 38.1739i −0.571909 + 1.27816i
\(893\) −20.3903 20.3903i −0.682335 0.682335i
\(894\) −34.6980 + 26.9676i −1.16047 + 0.901933i
\(895\) 13.7666i 0.460166i
\(896\) 1.24634 + 12.6457i 0.0416374 + 0.422465i
\(897\) 3.45654 + 2.90988i 0.115411 + 0.0971579i
\(898\) 3.81051 17.8458i 0.127158 0.595523i
\(899\) −19.4206 + 19.4206i −0.647713 + 0.647713i
\(900\) 1.48103 5.81434i 0.0493677 0.193811i
\(901\) 19.0283 + 19.0283i 0.633924 + 0.633924i
\(902\) 4.06192 + 6.26750i 0.135247 + 0.208685i
\(903\) −2.83924 + 3.37263i −0.0944839 + 0.112234i
\(904\) −3.54043 + 4.84464i −0.117753 + 0.161130i
\(905\) 12.4008 0.412215
\(906\) −49.5071 6.20615i −1.64476 0.206185i
\(907\) −17.9022 + 17.9022i −0.594433 + 0.594433i −0.938826 0.344393i \(-0.888085\pi\)
0.344393 + 0.938826i \(0.388085\pi\)
\(908\) 23.9280 9.13430i 0.794077 0.303133i
\(909\) −8.23587 + 11.6818i −0.273166 + 0.387461i
\(910\) −0.349471 + 1.63668i −0.0115848 + 0.0542554i
\(911\) −8.31540 −0.275501 −0.137751 0.990467i \(-0.543987\pi\)
−0.137751 + 0.990467i \(0.543987\pi\)
\(912\) 1.59217 + 53.7832i 0.0527222 + 1.78094i
\(913\) 0.142018 0.00470010
\(914\) −0.681616 + 3.19222i −0.0225459 + 0.105589i
\(915\) −0.113991 1.32753i −0.00376842 0.0438868i
\(916\) 10.7948 + 28.2779i 0.356672 + 0.934327i
\(917\) −5.24281 + 5.24281i −0.173133 + 0.173133i
\(918\) −2.10370 45.1057i −0.0694324 1.48871i
\(919\) 57.0505 1.88192 0.940961 0.338514i \(-0.109924\pi\)
0.940961 + 0.338514i \(0.109924\pi\)
\(920\) −1.07626 6.91955i −0.0354833 0.228131i
\(921\) −0.659037 0.554808i −0.0217160 0.0182815i
\(922\) −17.1482 26.4594i −0.564745 0.871395i
\(923\) 10.5363 + 10.5363i 0.346806 + 0.346806i
\(924\) −0.847622 1.75326i −0.0278847 0.0576779i
\(925\) 5.07782 5.07782i 0.166958 0.166958i
\(926\) 5.33735 24.9965i 0.175396 0.821436i
\(927\) 46.3695 8.02237i 1.52297 0.263489i
\(928\) −9.46936 + 34.6971i −0.310847 + 1.13899i
\(929\) 2.69835i 0.0885300i 0.999020 + 0.0442650i \(0.0140946\pi\)
−0.999020 + 0.0442650i \(0.985905\pi\)
\(930\) 6.49329 + 8.35460i 0.212923 + 0.273958i
\(931\) 31.5139 + 31.5139i 1.03283 + 1.03283i
\(932\) −1.90926 0.854297i −0.0625400 0.0279834i
\(933\) 3.75702 + 43.7540i 0.122999 + 1.43244i
\(934\) 31.6436 20.5080i 1.03541 0.671042i
\(935\) 3.07562i 0.100583i
\(936\) −8.47063 + 2.85998i −0.276871 + 0.0934813i
\(937\) 40.0708i 1.30906i 0.756037 + 0.654528i \(0.227133\pi\)
−0.756037 + 0.654528i \(0.772867\pi\)
\(938\) −2.91087 4.49144i −0.0950433 0.146651i
\(939\) 3.17335 + 36.9566i 0.103558 + 1.20603i
\(940\) −6.93764 + 2.64839i −0.226281 + 0.0863809i
\(941\) −15.1886 15.1886i −0.495135 0.495135i 0.414785 0.909920i \(-0.363857\pi\)
−0.909920 + 0.414785i \(0.863857\pi\)
\(942\) 36.4289 28.3129i 1.18692 0.922485i
\(943\) 26.1231i 0.850684i
\(944\) 0.645410 11.5004i 0.0210063 0.374306i
\(945\) −2.94241 + 5.04004i −0.0957165 + 0.163952i
\(946\) −1.56878 0.334973i −0.0510056 0.0108909i
\(947\) 1.64124 1.64124i 0.0533330 0.0533330i −0.679937 0.733270i \(-0.737993\pi\)
0.733270 + 0.679937i \(0.237993\pi\)
\(948\) −9.30179 + 26.7137i −0.302108 + 0.867620i
\(949\) −7.36422 7.36422i −0.239053 0.239053i
\(950\) 9.21687 5.97339i 0.299035 0.193802i
\(951\) 27.5301 + 23.1761i 0.892725 + 0.751537i
\(952\) 11.5176 15.7605i 0.373289 0.510799i
\(953\) 7.69106 0.249138 0.124569 0.992211i \(-0.460245\pi\)
0.124569 + 0.992211i \(0.460245\pi\)
\(954\) 13.6409 12.6151i 0.441641 0.408428i
\(955\) −6.67960 + 6.67960i −0.216147 + 0.216147i
\(956\) 40.2031 + 17.9888i 1.30026 + 0.581800i
\(957\) −0.471558 5.49173i −0.0152433 0.177522i
\(958\) 14.6767 + 3.13384i 0.474184 + 0.101250i
\(959\) −0.667097 −0.0215417
\(960\) 12.8099 + 5.28259i 0.413439 + 0.170495i
\(961\) 12.3396 0.398053
\(962\) −10.4645 2.23442i −0.337388 0.0720404i
\(963\) −11.6312 8.20015i −0.374809 0.264246i
\(964\) −32.2323 14.4223i −1.03813 0.464510i
\(965\) 5.67387 5.67387i 0.182648 0.182648i
\(966\) −0.847240 + 6.75852i −0.0272595 + 0.217452i
\(967\) 8.28040 0.266280 0.133140 0.991097i \(-0.457494\pi\)
0.133140 + 0.991097i \(0.457494\pi\)
\(968\) −17.9393 + 24.5477i −0.576591 + 0.788994i
\(969\) 53.2332 63.2338i 1.71010 2.03136i
\(970\) −15.9007 + 10.3051i −0.510541 + 0.330878i
\(971\) −17.0367 17.0367i −0.546734 0.546734i 0.378761 0.925495i \(-0.376350\pi\)
−0.925495 + 0.378761i \(0.876350\pi\)
\(972\) −31.1760 + 0.235516i −0.999971 + 0.00755418i
\(973\) −13.1471 + 13.1471i −0.421478 + 0.421478i
\(974\) 37.7360 + 8.05755i 1.20914 + 0.258180i
\(975\) 1.39611 + 1.17531i 0.0447112 + 0.0376399i
\(976\) 3.07225 + 0.172417i 0.0983402 + 0.00551893i
\(977\) 27.9191i 0.893210i 0.894731 + 0.446605i \(0.147367\pi\)
−0.894731 + 0.446605i \(0.852633\pi\)
\(978\) −10.9952 14.1471i −0.351589 0.452373i
\(979\) 6.05262 + 6.05262i 0.193443 + 0.193443i
\(980\) 10.7224 4.09317i 0.342513 0.130751i
\(981\) 0.138822 0.196906i 0.00443223 0.00628671i
\(982\) −5.71916 8.82460i −0.182506 0.281604i
\(983\) 10.3040i 0.328646i −0.986407 0.164323i \(-0.947456\pi\)
0.986407 0.164323i \(-0.0525439\pi\)
\(984\) 44.1898 + 26.8164i 1.40872 + 0.854876i
\(985\) 4.15675i 0.132445i
\(986\) 46.3650 30.0488i 1.47656 0.956950i
\(987\) 7.19658 0.617949i 0.229070 0.0196695i
\(988\) −14.9386 6.68424i −0.475259 0.212654i
\(989\) 3.96745 + 3.96745i 0.126158 + 0.126158i
\(990\) −2.12193 0.0829063i −0.0674394 0.00263494i
\(991\) 5.61753i 0.178447i −0.996012 0.0892233i \(-0.971562\pi\)
0.996012 0.0892233i \(-0.0284385\pi\)
\(992\) −21.2187 + 12.1201i −0.673696 + 0.384813i
\(993\) −21.4624 + 25.4944i −0.681088 + 0.809040i
\(994\) −4.69062 + 21.9676i −0.148777 + 0.696771i
\(995\) −8.09897 + 8.09897i −0.256755 + 0.256755i
\(996\) 0.884905 0.427812i 0.0280393 0.0135558i
\(997\) 33.8451 + 33.8451i 1.07189 + 1.07189i 0.997208 + 0.0746777i \(0.0237928\pi\)
0.0746777 + 0.997208i \(0.476207\pi\)
\(998\) −11.3566 17.5232i −0.359488 0.554687i
\(999\) −32.2246 18.8129i −1.01954 0.595214i
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 240.2.bk.b.11.2 60
3.2 odd 2 inner 240.2.bk.b.11.29 yes 60
4.3 odd 2 960.2.bk.b.911.30 60
12.11 even 2 960.2.bk.b.911.15 60
16.3 odd 4 inner 240.2.bk.b.131.29 yes 60
16.13 even 4 960.2.bk.b.431.15 60
48.29 odd 4 960.2.bk.b.431.30 60
48.35 even 4 inner 240.2.bk.b.131.2 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bk.b.11.2 60 1.1 even 1 trivial
240.2.bk.b.11.29 yes 60 3.2 odd 2 inner
240.2.bk.b.131.2 yes 60 48.35 even 4 inner
240.2.bk.b.131.29 yes 60 16.3 odd 4 inner
960.2.bk.b.431.15 60 16.13 even 4
960.2.bk.b.431.30 60 48.29 odd 4
960.2.bk.b.911.15 60 12.11 even 2
960.2.bk.b.911.30 60 4.3 odd 2