Properties

Label 930.2.k.b.247.2
Level $930$
Weight $2$
Character 930.247
Analytic conductor $7.426$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(247,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.247");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.k (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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 247.2
Character \(\chi\) \(=\) 930.247
Dual form 930.2.k.b.433.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14949 + 0.616200i) q^{5} +1.00000i q^{6} +(0.0344550 + 0.0344550i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-2.14949 + 0.616200i) q^{5} +1.00000i q^{6} +(0.0344550 + 0.0344550i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.95564 + 1.08420i) q^{10} -0.241934i q^{11} +(0.707107 - 0.707107i) q^{12} +(3.88473 + 3.88473i) q^{13} -0.0487267i q^{14} +(1.95564 + 1.08420i) q^{15} -1.00000 q^{16} +(1.35699 - 1.35699i) q^{17} +(0.707107 - 0.707107i) q^{18} -8.10639i q^{19} +(-0.616200 - 2.14949i) q^{20} -0.0487267i q^{21} +(-0.171073 + 0.171073i) q^{22} +(-2.64257 - 2.64257i) q^{23} -1.00000 q^{24} +(4.24059 - 2.64903i) q^{25} -5.49384i q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.0344550 + 0.0344550i) q^{28} -8.54385 q^{29} +(-0.616200 - 2.14949i) q^{30} +(-3.04494 + 4.66137i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.171073 + 0.171073i) q^{33} -1.91907 q^{34} +(-0.0952917 - 0.0528294i) q^{35} -1.00000 q^{36} +(-4.54476 + 4.54476i) q^{37} +(-5.73208 + 5.73208i) q^{38} -5.49384i q^{39} +(-1.08420 + 1.95564i) q^{40} -1.46546 q^{41} +(-0.0344550 + 0.0344550i) q^{42} +(-0.329923 - 0.329923i) q^{43} +0.241934 q^{44} +(-0.616200 - 2.14949i) q^{45} +3.73716i q^{46} +(-2.81146 - 2.81146i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.99763i q^{49} +(-4.87170 - 1.12541i) q^{50} -1.91907 q^{51} +(-3.88473 + 3.88473i) q^{52} +(0.597357 + 0.597357i) q^{53} -1.00000 q^{54} +(0.149080 + 0.520034i) q^{55} +0.0487267 q^{56} +(-5.73208 + 5.73208i) q^{57} +(6.04141 + 6.04141i) q^{58} -13.6979i q^{59} +(-1.08420 + 1.95564i) q^{60} -11.6907i q^{61} +(5.44918 - 1.14299i) q^{62} +(-0.0344550 + 0.0344550i) q^{63} -1.00000i q^{64} +(-10.7440 - 5.95641i) q^{65} +0.241934 q^{66} +(-0.653315 - 0.653315i) q^{67} +(1.35699 + 1.35699i) q^{68} +3.73716i q^{69} +(0.0300254 + 0.104737i) q^{70} -4.44096 q^{71} +(0.707107 + 0.707107i) q^{72} +(8.64429 + 8.64429i) q^{73} +6.42726 q^{74} +(-4.87170 - 1.12541i) q^{75} +8.10639 q^{76} +(0.00833583 - 0.00833583i) q^{77} +(-3.88473 + 3.88473i) q^{78} -12.9046 q^{79} +(2.14949 - 0.616200i) q^{80} -1.00000 q^{81} +(1.03624 + 1.03624i) q^{82} +(-0.681471 - 0.681471i) q^{83} +0.0487267 q^{84} +(-2.08065 + 3.75301i) q^{85} +0.466581i q^{86} +(6.04141 + 6.04141i) q^{87} +(-0.171073 - 0.171073i) q^{88} -2.20446 q^{89} +(-1.08420 + 1.95564i) q^{90} +0.267697i q^{91} +(2.64257 - 2.64257i) q^{92} +(5.44918 - 1.14299i) q^{93} +3.97600i q^{94} +(4.99516 + 17.4246i) q^{95} -1.00000i q^{96} +(-5.06944 - 5.06944i) q^{97} +(-4.94807 + 4.94807i) q^{98} +0.241934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{7} + 4 q^{10} + 4 q^{15} - 32 q^{16} + 8 q^{17} - 4 q^{22} - 32 q^{24} + 8 q^{25} + 4 q^{28} + 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} + 4 q^{37} + 16 q^{38} - 16 q^{41} + 4 q^{42} - 16 q^{43} - 8 q^{44} - 8 q^{47} - 16 q^{50} - 24 q^{53} - 32 q^{54} - 28 q^{55} + 16 q^{57} + 20 q^{58} - 8 q^{62} + 4 q^{63} + 56 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 28 q^{70} + 16 q^{71} - 20 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 40 q^{77} - 56 q^{79} - 32 q^{81} + 16 q^{82} + 72 q^{83} - 32 q^{85} + 20 q^{87} - 4 q^{88} - 64 q^{89} - 8 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −2.14949 + 0.616200i −0.961280 + 0.275573i
\(6\) 1.00000i 0.408248i
\(7\) 0.0344550 + 0.0344550i 0.0130228 + 0.0130228i 0.713588 0.700565i \(-0.247069\pi\)
−0.700565 + 0.713588i \(0.747069\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.95564 + 1.08420i 0.618427 + 0.342853i
\(11\) 0.241934i 0.0729458i −0.999335 0.0364729i \(-0.988388\pi\)
0.999335 0.0364729i \(-0.0116123\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 3.88473 + 3.88473i 1.07743 + 1.07743i 0.996739 + 0.0806917i \(0.0257129\pi\)
0.0806917 + 0.996739i \(0.474287\pi\)
\(14\) 0.0487267i 0.0130228i
\(15\) 1.95564 + 1.08420i 0.504943 + 0.279939i
\(16\) −1.00000 −0.250000
\(17\) 1.35699 1.35699i 0.329118 0.329118i −0.523133 0.852251i \(-0.675237\pi\)
0.852251 + 0.523133i \(0.175237\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) 8.10639i 1.85973i −0.367898 0.929866i \(-0.619922\pi\)
0.367898 0.929866i \(-0.380078\pi\)
\(20\) −0.616200 2.14949i −0.137787 0.480640i
\(21\) 0.0487267i 0.0106330i
\(22\) −0.171073 + 0.171073i −0.0364729 + 0.0364729i
\(23\) −2.64257 2.64257i −0.551015 0.551015i 0.375719 0.926734i \(-0.377396\pi\)
−0.926734 + 0.375719i \(0.877396\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.24059 2.64903i 0.848119 0.529806i
\(26\) 5.49384i 1.07743i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.0344550 + 0.0344550i −0.00651138 + 0.00651138i
\(29\) −8.54385 −1.58655 −0.793277 0.608862i \(-0.791626\pi\)
−0.793277 + 0.608862i \(0.791626\pi\)
\(30\) −0.616200 2.14949i −0.112502 0.392441i
\(31\) −3.04494 + 4.66137i −0.546887 + 0.837207i
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.171073 + 0.171073i −0.0297800 + 0.0297800i
\(34\) −1.91907 −0.329118
\(35\) −0.0952917 0.0528294i −0.0161072 0.00892980i
\(36\) −1.00000 −0.166667
\(37\) −4.54476 + 4.54476i −0.747154 + 0.747154i −0.973944 0.226790i \(-0.927177\pi\)
0.226790 + 0.973944i \(0.427177\pi\)
\(38\) −5.73208 + 5.73208i −0.929866 + 0.929866i
\(39\) 5.49384i 0.879719i
\(40\) −1.08420 + 1.95564i −0.171427 + 0.309213i
\(41\) −1.46546 −0.228866 −0.114433 0.993431i \(-0.536505\pi\)
−0.114433 + 0.993431i \(0.536505\pi\)
\(42\) −0.0344550 + 0.0344550i −0.00531652 + 0.00531652i
\(43\) −0.329923 0.329923i −0.0503128 0.0503128i 0.681503 0.731816i \(-0.261327\pi\)
−0.731816 + 0.681503i \(0.761327\pi\)
\(44\) 0.241934 0.0364729
\(45\) −0.616200 2.14949i −0.0918577 0.320427i
\(46\) 3.73716i 0.551015i
\(47\) −2.81146 2.81146i −0.410093 0.410093i 0.471678 0.881771i \(-0.343649\pi\)
−0.881771 + 0.471678i \(0.843649\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 6.99763i 0.999661i
\(50\) −4.87170 1.12541i −0.688962 0.159156i
\(51\) −1.91907 −0.268724
\(52\) −3.88473 + 3.88473i −0.538715 + 0.538715i
\(53\) 0.597357 + 0.597357i 0.0820533 + 0.0820533i 0.746942 0.664889i \(-0.231521\pi\)
−0.664889 + 0.746942i \(0.731521\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0.149080 + 0.520034i 0.0201019 + 0.0701214i
\(56\) 0.0487267 0.00651138
\(57\) −5.73208 + 5.73208i −0.759233 + 0.759233i
\(58\) 6.04141 + 6.04141i 0.793277 + 0.793277i
\(59\) 13.6979i 1.78332i −0.452705 0.891660i \(-0.649541\pi\)
0.452705 0.891660i \(-0.350459\pi\)
\(60\) −1.08420 + 1.95564i −0.139969 + 0.252472i
\(61\) 11.6907i 1.49684i −0.663223 0.748421i \(-0.730812\pi\)
0.663223 0.748421i \(-0.269188\pi\)
\(62\) 5.44918 1.14299i 0.692047 0.145160i
\(63\) −0.0344550 + 0.0344550i −0.00434092 + 0.00434092i
\(64\) 1.00000i 0.125000i
\(65\) −10.7440 5.95641i −1.33262 0.738802i
\(66\) 0.241934 0.0297800
\(67\) −0.653315 0.653315i −0.0798151 0.0798151i 0.666072 0.745887i \(-0.267974\pi\)
−0.745887 + 0.666072i \(0.767974\pi\)
\(68\) 1.35699 + 1.35699i 0.164559 + 0.164559i
\(69\) 3.73716i 0.449902i
\(70\) 0.0300254 + 0.104737i 0.00358872 + 0.0125185i
\(71\) −4.44096 −0.527045 −0.263522 0.964653i \(-0.584884\pi\)
−0.263522 + 0.964653i \(0.584884\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 8.64429 + 8.64429i 1.01174 + 1.01174i 0.999930 + 0.0118067i \(0.00375829\pi\)
0.0118067 + 0.999930i \(0.496242\pi\)
\(74\) 6.42726 0.747154
\(75\) −4.87170 1.12541i −0.562535 0.129951i
\(76\) 8.10639 0.929866
\(77\) 0.00833583 0.00833583i 0.000949956 0.000949956i
\(78\) −3.88473 + 3.88473i −0.439859 + 0.439859i
\(79\) −12.9046 −1.45188 −0.725939 0.687759i \(-0.758595\pi\)
−0.725939 + 0.687759i \(0.758595\pi\)
\(80\) 2.14949 0.616200i 0.240320 0.0688933i
\(81\) −1.00000 −0.111111
\(82\) 1.03624 + 1.03624i 0.114433 + 0.114433i
\(83\) −0.681471 0.681471i −0.0748011 0.0748011i 0.668716 0.743518i \(-0.266844\pi\)
−0.743518 + 0.668716i \(0.766844\pi\)
\(84\) 0.0487267 0.00531652
\(85\) −2.08065 + 3.75301i −0.225679 + 0.407071i
\(86\) 0.466581i 0.0503128i
\(87\) 6.04141 + 6.04141i 0.647708 + 0.647708i
\(88\) −0.171073 0.171073i −0.0182365 0.0182365i
\(89\) −2.20446 −0.233672 −0.116836 0.993151i \(-0.537275\pi\)
−0.116836 + 0.993151i \(0.537275\pi\)
\(90\) −1.08420 + 1.95564i −0.114284 + 0.206142i
\(91\) 0.267697i 0.0280622i
\(92\) 2.64257 2.64257i 0.275507 0.275507i
\(93\) 5.44918 1.14299i 0.565054 0.118523i
\(94\) 3.97600i 0.410093i
\(95\) 4.99516 + 17.4246i 0.512493 + 1.78772i
\(96\) 1.00000i 0.102062i
\(97\) −5.06944 5.06944i −0.514724 0.514724i 0.401246 0.915970i \(-0.368577\pi\)
−0.915970 + 0.401246i \(0.868577\pi\)
\(98\) −4.94807 + 4.94807i −0.499830 + 0.499830i
\(99\) 0.241934 0.0243153
\(100\) 2.64903 + 4.24059i 0.264903 + 0.424059i
\(101\) −11.8507 −1.17919 −0.589593 0.807700i \(-0.700712\pi\)
−0.589593 + 0.807700i \(0.700712\pi\)
\(102\) 1.35699 + 1.35699i 0.134362 + 0.134362i
\(103\) −8.10157 + 8.10157i −0.798272 + 0.798272i −0.982823 0.184551i \(-0.940917\pi\)
0.184551 + 0.982823i \(0.440917\pi\)
\(104\) 5.49384 0.538715
\(105\) 0.0300254 + 0.104737i 0.00293018 + 0.0102213i
\(106\) 0.844790i 0.0820533i
\(107\) −10.2618 10.2618i −0.992044 0.992044i 0.00792440 0.999969i \(-0.497478\pi\)
−0.999969 + 0.00792440i \(0.997478\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 6.81387i 0.652651i −0.945258 0.326325i \(-0.894190\pi\)
0.945258 0.326325i \(-0.105810\pi\)
\(110\) 0.262304 0.473135i 0.0250097 0.0451116i
\(111\) 6.42726 0.610049
\(112\) −0.0344550 0.0344550i −0.00325569 0.00325569i
\(113\) 0.808734 0.808734i 0.0760793 0.0760793i −0.668043 0.744123i \(-0.732868\pi\)
0.744123 + 0.668043i \(0.232868\pi\)
\(114\) 8.10639 0.759233
\(115\) 7.30854 + 4.05183i 0.681525 + 0.377835i
\(116\) 8.54385i 0.793277i
\(117\) −3.88473 + 3.88473i −0.359144 + 0.359144i
\(118\) −9.68591 + 9.68591i −0.891660 + 0.891660i
\(119\) 0.0935101 0.00857205
\(120\) 2.14949 0.616200i 0.196220 0.0562511i
\(121\) 10.9415 0.994679
\(122\) −8.26659 + 8.26659i −0.748421 + 0.748421i
\(123\) 1.03624 + 1.03624i 0.0934342 + 0.0934342i
\(124\) −4.66137 3.04494i −0.418603 0.273443i
\(125\) −7.48277 + 8.30711i −0.669279 + 0.743011i
\(126\) 0.0487267 0.00434092
\(127\) 10.1076 10.1076i 0.896907 0.896907i −0.0982539 0.995161i \(-0.531326\pi\)
0.995161 + 0.0982539i \(0.0313257\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0.466581i 0.0410802i
\(130\) 3.38531 + 11.8089i 0.296911 + 1.03571i
\(131\) 7.31940 0.639499 0.319749 0.947502i \(-0.396401\pi\)
0.319749 + 0.947502i \(0.396401\pi\)
\(132\) −0.171073 0.171073i −0.0148900 0.0148900i
\(133\) 0.279305 0.279305i 0.0242189 0.0242189i
\(134\) 0.923926i 0.0798151i
\(135\) −1.08420 + 1.95564i −0.0933129 + 0.168314i
\(136\) 1.91907i 0.164559i
\(137\) −0.736104 + 0.736104i −0.0628896 + 0.0628896i −0.737852 0.674962i \(-0.764160\pi\)
0.674962 + 0.737852i \(0.264160\pi\)
\(138\) 2.64257 2.64257i 0.224951 0.224951i
\(139\) 4.32252 0.366631 0.183316 0.983054i \(-0.441317\pi\)
0.183316 + 0.983054i \(0.441317\pi\)
\(140\) 0.0528294 0.0952917i 0.00446490 0.00805362i
\(141\) 3.97600i 0.334840i
\(142\) 3.14023 + 3.14023i 0.263522 + 0.263522i
\(143\) 0.939849 0.939849i 0.0785941 0.0785941i
\(144\) 1.00000i 0.0833333i
\(145\) 18.3649 5.26472i 1.52512 0.437212i
\(146\) 12.2249i 1.01174i
\(147\) −4.94807 + 4.94807i −0.408110 + 0.408110i
\(148\) −4.54476 4.54476i −0.373577 0.373577i
\(149\) 15.8034i 1.29467i −0.762206 0.647334i \(-0.775884\pi\)
0.762206 0.647334i \(-0.224116\pi\)
\(150\) 2.64903 + 4.24059i 0.216292 + 0.346243i
\(151\) 3.30031i 0.268575i −0.990942 0.134288i \(-0.957125\pi\)
0.990942 0.134288i \(-0.0428746\pi\)
\(152\) −5.73208 5.73208i −0.464933 0.464933i
\(153\) 1.35699 + 1.35699i 0.109706 + 0.109706i
\(154\) −0.0117886 −0.000949956
\(155\) 3.67271 11.8958i 0.294999 0.955497i
\(156\) 5.49384 0.439859
\(157\) −4.79524 4.79524i −0.382702 0.382702i 0.489373 0.872075i \(-0.337226\pi\)
−0.872075 + 0.489373i \(0.837226\pi\)
\(158\) 9.12491 + 9.12491i 0.725939 + 0.725939i
\(159\) 0.844790i 0.0669962i
\(160\) −1.95564 1.08420i −0.154607 0.0857134i
\(161\) 0.182100i 0.0143515i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 12.0108 12.0108i 0.940756 0.940756i −0.0575847 0.998341i \(-0.518340\pi\)
0.998341 + 0.0575847i \(0.0183399\pi\)
\(164\) 1.46546i 0.114433i
\(165\) 0.262304 0.473135i 0.0204204 0.0368335i
\(166\) 0.963745i 0.0748011i
\(167\) 12.9307 12.9307i 1.00060 1.00060i 0.000604752 1.00000i \(-0.499808\pi\)
1.00000 0.000604752i \(-0.000192499\pi\)
\(168\) −0.0344550 0.0344550i −0.00265826 0.00265826i
\(169\) 17.1823i 1.32171i
\(170\) 4.12502 1.18253i 0.316375 0.0906961i
\(171\) 8.10639 0.619911
\(172\) 0.329923 0.329923i 0.0251564 0.0251564i
\(173\) −17.7387 + 17.7387i −1.34865 + 1.34865i −0.461511 + 0.887135i \(0.652692\pi\)
−0.887135 + 0.461511i \(0.847308\pi\)
\(174\) 8.54385i 0.647708i
\(175\) 0.237382 + 0.0548373i 0.0179444 + 0.00414531i
\(176\) 0.241934i 0.0182365i
\(177\) −9.68591 + 9.68591i −0.728037 + 0.728037i
\(178\) 1.55879 + 1.55879i 0.116836 + 0.116836i
\(179\) −7.57644 −0.566290 −0.283145 0.959077i \(-0.591378\pi\)
−0.283145 + 0.959077i \(0.591378\pi\)
\(180\) 2.14949 0.616200i 0.160213 0.0459289i
\(181\) 4.86746i 0.361795i 0.983502 + 0.180898i \(0.0579003\pi\)
−0.983502 + 0.180898i \(0.942100\pi\)
\(182\) 0.189290 0.189290i 0.0140311 0.0140311i
\(183\) −8.26659 + 8.26659i −0.611084 + 0.611084i
\(184\) −3.73716 −0.275507
\(185\) 6.96842 12.5694i 0.512329 0.924120i
\(186\) −4.66137 3.04494i −0.341788 0.223265i
\(187\) −0.328302 0.328302i −0.0240078 0.0240078i
\(188\) 2.81146 2.81146i 0.205047 0.205047i
\(189\) 0.0487267 0.00354435
\(190\) 8.78893 15.8531i 0.637616 1.15011i
\(191\) 18.8465 1.36368 0.681841 0.731500i \(-0.261180\pi\)
0.681841 + 0.731500i \(0.261180\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −6.30444 + 6.30444i −0.453803 + 0.453803i −0.896615 0.442811i \(-0.853981\pi\)
0.442811 + 0.896615i \(0.353981\pi\)
\(194\) 7.16927i 0.514724i
\(195\) 3.38531 + 11.8089i 0.242427 + 0.845656i
\(196\) 6.99763 0.499830
\(197\) 12.4152 12.4152i 0.884545 0.884545i −0.109448 0.993993i \(-0.534908\pi\)
0.993993 + 0.109448i \(0.0349082\pi\)
\(198\) −0.171073 0.171073i −0.0121576 0.0121576i
\(199\) −7.08879 −0.502511 −0.251255 0.967921i \(-0.580843\pi\)
−0.251255 + 0.967921i \(0.580843\pi\)
\(200\) 1.12541 4.87170i 0.0795782 0.344481i
\(201\) 0.923926i 0.0651687i
\(202\) 8.37970 + 8.37970i 0.589593 + 0.589593i
\(203\) −0.294378 0.294378i −0.0206613 0.0206613i
\(204\) 1.91907i 0.134362i
\(205\) 3.14998 0.903016i 0.220004 0.0630694i
\(206\) 11.4574 0.798272
\(207\) 2.64257 2.64257i 0.183672 0.183672i
\(208\) −3.88473 3.88473i −0.269358 0.269358i
\(209\) −1.96121 −0.135660
\(210\) 0.0528294 0.0952917i 0.00364557 0.00657576i
\(211\) 2.44965 0.168641 0.0843205 0.996439i \(-0.473128\pi\)
0.0843205 + 0.996439i \(0.473128\pi\)
\(212\) −0.597357 + 0.597357i −0.0410266 + 0.0410266i
\(213\) 3.14023 + 3.14023i 0.215165 + 0.215165i
\(214\) 14.5124i 0.992044i
\(215\) 0.912464 + 0.505866i 0.0622295 + 0.0344998i
\(216\) 1.00000i 0.0680414i
\(217\) −0.265521 + 0.0556942i −0.0180247 + 0.00378077i
\(218\) −4.81814 + 4.81814i −0.326325 + 0.326325i
\(219\) 12.2249i 0.826080i
\(220\) −0.520034 + 0.149080i −0.0350607 + 0.0100510i
\(221\) 10.5431 0.709204
\(222\) −4.54476 4.54476i −0.305024 0.305024i
\(223\) −15.8119 15.8119i −1.05884 1.05884i −0.998157 0.0606828i \(-0.980672\pi\)
−0.0606828 0.998157i \(-0.519328\pi\)
\(224\) 0.0487267i 0.00325569i
\(225\) 2.64903 + 4.24059i 0.176602 + 0.282706i
\(226\) −1.14372 −0.0760793
\(227\) 19.2620 + 19.2620i 1.27847 + 1.27847i 0.941526 + 0.336940i \(0.109392\pi\)
0.336940 + 0.941526i \(0.390608\pi\)
\(228\) −5.73208 5.73208i −0.379616 0.379616i
\(229\) −27.0642 −1.78845 −0.894226 0.447617i \(-0.852273\pi\)
−0.894226 + 0.447617i \(0.852273\pi\)
\(230\) −2.30284 8.03299i −0.151845 0.529680i
\(231\) −0.0117886 −0.000775636
\(232\) −6.04141 + 6.04141i −0.396638 + 0.396638i
\(233\) 9.02104 9.02104i 0.590988 0.590988i −0.346910 0.937898i \(-0.612769\pi\)
0.937898 + 0.346910i \(0.112769\pi\)
\(234\) 5.49384 0.359144
\(235\) 7.77561 + 4.31077i 0.507225 + 0.281204i
\(236\) 13.6979 0.891660
\(237\) 9.12491 + 9.12491i 0.592727 + 0.592727i
\(238\) −0.0661216 0.0661216i −0.00428603 0.00428603i
\(239\) 18.6644 1.20730 0.603651 0.797249i \(-0.293712\pi\)
0.603651 + 0.797249i \(0.293712\pi\)
\(240\) −1.95564 1.08420i −0.126236 0.0699847i
\(241\) 17.5955i 1.13343i 0.823915 + 0.566713i \(0.191785\pi\)
−0.823915 + 0.566713i \(0.808215\pi\)
\(242\) −7.73679 7.73679i −0.497339 0.497339i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 11.6907 0.748421
\(245\) 4.31194 + 15.0413i 0.275480 + 0.960954i
\(246\) 1.46546i 0.0934342i
\(247\) 31.4911 31.4911i 2.00373 2.00373i
\(248\) 1.14299 + 5.44918i 0.0725800 + 0.346023i
\(249\) 0.963745i 0.0610749i
\(250\) 11.1651 0.582899i 0.706145 0.0368658i
\(251\) 1.15940i 0.0731808i 0.999330 + 0.0365904i \(0.0116497\pi\)
−0.999330 + 0.0365904i \(0.988350\pi\)
\(252\) −0.0344550 0.0344550i −0.00217046 0.00217046i
\(253\) −0.639328 + 0.639328i −0.0401942 + 0.0401942i
\(254\) −14.2944 −0.896907
\(255\) 4.12502 1.18253i 0.258319 0.0740531i
\(256\) 1.00000 0.0625000
\(257\) −3.36262 3.36262i −0.209754 0.209754i 0.594409 0.804163i \(-0.297386\pi\)
−0.804163 + 0.594409i \(0.797386\pi\)
\(258\) 0.329923 0.329923i 0.0205401 0.0205401i
\(259\) −0.313179 −0.0194600
\(260\) 5.95641 10.7440i 0.369401 0.666312i
\(261\) 8.54385i 0.528851i
\(262\) −5.17559 5.17559i −0.319749 0.319749i
\(263\) 16.2256 + 16.2256i 1.00051 + 1.00051i 1.00000 0.000512751i \(0.000163214\pi\)
0.000512751 1.00000i \(0.499837\pi\)
\(264\) 0.241934i 0.0148900i
\(265\) −1.65210 0.915920i −0.101488 0.0562645i
\(266\) −0.394998 −0.0242189
\(267\) 1.55879 + 1.55879i 0.0953962 + 0.0953962i
\(268\) 0.653315 0.653315i 0.0399075 0.0399075i
\(269\) 0.853836 0.0520593 0.0260296 0.999661i \(-0.491714\pi\)
0.0260296 + 0.999661i \(0.491714\pi\)
\(270\) 2.14949 0.616200i 0.130814 0.0375008i
\(271\) 15.1304i 0.919103i −0.888151 0.459552i \(-0.848010\pi\)
0.888151 0.459552i \(-0.151990\pi\)
\(272\) −1.35699 + 1.35699i −0.0822795 + 0.0822795i
\(273\) 0.189290 0.189290i 0.0114564 0.0114564i
\(274\) 1.04101 0.0628896
\(275\) −0.640890 1.02594i −0.0386471 0.0618667i
\(276\) −3.73716 −0.224951
\(277\) −11.1206 + 11.1206i −0.668173 + 0.668173i −0.957293 0.289120i \(-0.906637\pi\)
0.289120 + 0.957293i \(0.406637\pi\)
\(278\) −3.05648 3.05648i −0.183316 0.183316i
\(279\) −4.66137 3.04494i −0.279069 0.182296i
\(280\) −0.104737 + 0.0300254i −0.00625926 + 0.00179436i
\(281\) −11.2075 −0.668581 −0.334290 0.942470i \(-0.608497\pi\)
−0.334290 + 0.942470i \(0.608497\pi\)
\(282\) 2.81146 2.81146i 0.167420 0.167420i
\(283\) 2.06960 2.06960i 0.123025 0.123025i −0.642914 0.765939i \(-0.722275\pi\)
0.765939 + 0.642914i \(0.222275\pi\)
\(284\) 4.44096i 0.263522i
\(285\) 8.78893 15.8531i 0.520611 0.939059i
\(286\) −1.32915 −0.0785941
\(287\) −0.0504923 0.0504923i −0.00298047 0.00298047i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 13.3172i 0.783362i
\(290\) −16.7087 9.26322i −0.981167 0.543955i
\(291\) 7.16927i 0.420270i
\(292\) −8.64429 + 8.64429i −0.505869 + 0.505869i
\(293\) −15.8821 + 15.8821i −0.927841 + 0.927841i −0.997566 0.0697252i \(-0.977788\pi\)
0.0697252 + 0.997566i \(0.477788\pi\)
\(294\) 6.99763 0.408110
\(295\) 8.44068 + 29.4436i 0.491435 + 1.71427i
\(296\) 6.42726i 0.373577i
\(297\) −0.171073 0.171073i −0.00992667 0.00992667i
\(298\) −11.1747 + 11.1747i −0.647334 + 0.647334i
\(299\) 20.5314i 1.18736i
\(300\) 1.12541 4.87170i 0.0649753 0.281268i
\(301\) 0.0227350i 0.00131042i
\(302\) −2.33367 + 2.33367i −0.134288 + 0.134288i
\(303\) 8.37970 + 8.37970i 0.481401 + 0.481401i
\(304\) 8.10639i 0.464933i
\(305\) 7.20382 + 25.1291i 0.412490 + 1.43889i
\(306\) 1.91907i 0.109706i
\(307\) 6.44243 + 6.44243i 0.367689 + 0.367689i 0.866634 0.498945i \(-0.166279\pi\)
−0.498945 + 0.866634i \(0.666279\pi\)
\(308\) 0.00833583 + 0.00833583i 0.000474978 + 0.000474978i
\(309\) 11.4574 0.651786
\(310\) −11.0086 + 5.81463i −0.625248 + 0.330249i
\(311\) 10.1552 0.575850 0.287925 0.957653i \(-0.407035\pi\)
0.287925 + 0.957653i \(0.407035\pi\)
\(312\) −3.88473 3.88473i −0.219930 0.219930i
\(313\) 15.3235 + 15.3235i 0.866136 + 0.866136i 0.992042 0.125906i \(-0.0401838\pi\)
−0.125906 + 0.992042i \(0.540184\pi\)
\(314\) 6.78150i 0.382702i
\(315\) 0.0528294 0.0952917i 0.00297660 0.00536908i
\(316\) 12.9046i 0.725939i
\(317\) 0.905319 + 0.905319i 0.0508478 + 0.0508478i 0.732073 0.681226i \(-0.238553\pi\)
−0.681226 + 0.732073i \(0.738553\pi\)
\(318\) −0.597357 + 0.597357i −0.0334981 + 0.0334981i
\(319\) 2.06705i 0.115732i
\(320\) 0.616200 + 2.14949i 0.0344467 + 0.120160i
\(321\) 14.5124i 0.810001i
\(322\) −0.128764 + 0.128764i −0.00717573 + 0.00717573i
\(323\) −11.0003 11.0003i −0.612072 0.612072i
\(324\) 1.00000i 0.0555556i
\(325\) 26.7643 + 6.18280i 1.48462 + 0.342960i
\(326\) −16.9858 −0.940756
\(327\) −4.81814 + 4.81814i −0.266444 + 0.266444i
\(328\) −1.03624 + 1.03624i −0.0572165 + 0.0572165i
\(329\) 0.193737i 0.0106811i
\(330\) −0.520034 + 0.149080i −0.0286269 + 0.00820657i
\(331\) 35.2620i 1.93818i −0.246715 0.969088i \(-0.579351\pi\)
0.246715 0.969088i \(-0.420649\pi\)
\(332\) 0.681471 0.681471i 0.0374006 0.0374006i
\(333\) −4.54476 4.54476i −0.249051 0.249051i
\(334\) −18.2867 −1.00060
\(335\) 1.80686 + 1.00172i 0.0987196 + 0.0547298i
\(336\) 0.0487267i 0.00265826i
\(337\) −5.38072 + 5.38072i −0.293107 + 0.293107i −0.838306 0.545200i \(-0.816454\pi\)
0.545200 + 0.838306i \(0.316454\pi\)
\(338\) 12.1497 12.1497i 0.660857 0.660857i
\(339\) −1.14372 −0.0621185
\(340\) −3.75301 2.08065i −0.203535 0.112839i
\(341\) 1.12774 + 0.736673i 0.0610707 + 0.0398931i
\(342\) −5.73208 5.73208i −0.309955 0.309955i
\(343\) 0.482288 0.482288i 0.0260411 0.0260411i
\(344\) −0.466581 −0.0251564
\(345\) −2.30284 8.03299i −0.123981 0.432482i
\(346\) 25.0863 1.34865
\(347\) −24.2354 + 24.2354i −1.30102 + 1.30102i −0.373320 + 0.927703i \(0.621781\pi\)
−0.927703 + 0.373320i \(0.878219\pi\)
\(348\) −6.04141 + 6.04141i −0.323854 + 0.323854i
\(349\) 10.3438i 0.553692i −0.960914 0.276846i \(-0.910711\pi\)
0.960914 0.276846i \(-0.0892892\pi\)
\(350\) −0.129079 0.206630i −0.00689954 0.0110448i
\(351\) 5.49384 0.293240
\(352\) 0.171073 0.171073i 0.00911823 0.00911823i
\(353\) −17.9124 17.9124i −0.953381 0.953381i 0.0455794 0.998961i \(-0.485487\pi\)
−0.998961 + 0.0455794i \(0.985487\pi\)
\(354\) 13.6979 0.728037
\(355\) 9.54578 2.73652i 0.506637 0.145239i
\(356\) 2.20446i 0.116836i
\(357\) −0.0661216 0.0661216i −0.00349953 0.00349953i
\(358\) 5.35735 + 5.35735i 0.283145 + 0.283145i
\(359\) 20.7844i 1.09696i 0.836165 + 0.548478i \(0.184793\pi\)
−0.836165 + 0.548478i \(0.815207\pi\)
\(360\) −1.95564 1.08420i −0.103071 0.0571422i
\(361\) −46.7135 −2.45861
\(362\) 3.44181 3.44181i 0.180898 0.180898i
\(363\) −7.73679 7.73679i −0.406076 0.406076i
\(364\) −0.267697 −0.0140311
\(365\) −23.9074 13.2542i −1.25137 0.693755i
\(366\) 11.6907 0.611084
\(367\) −18.3540 + 18.3540i −0.958073 + 0.958073i −0.999156 0.0410828i \(-0.986919\pi\)
0.0410828 + 0.999156i \(0.486919\pi\)
\(368\) 2.64257 + 2.64257i 0.137754 + 0.137754i
\(369\) 1.46546i 0.0762887i
\(370\) −13.8153 + 3.96048i −0.718224 + 0.205896i
\(371\) 0.0411639i 0.00213712i
\(372\) 1.14299 + 5.44918i 0.0592614 + 0.282527i
\(373\) 21.9349 21.9349i 1.13575 1.13575i 0.146542 0.989204i \(-0.453186\pi\)
0.989204 0.146542i \(-0.0468143\pi\)
\(374\) 0.464289i 0.0240078i
\(375\) 11.1651 0.582899i 0.576565 0.0301008i
\(376\) −3.97600 −0.205047
\(377\) −33.1906 33.1906i −1.70940 1.70940i
\(378\) −0.0344550 0.0344550i −0.00177217 0.00177217i
\(379\) 16.6229i 0.853861i −0.904284 0.426931i \(-0.859595\pi\)
0.904284 0.426931i \(-0.140405\pi\)
\(380\) −17.4246 + 4.99516i −0.893862 + 0.256246i
\(381\) −14.2944 −0.732322
\(382\) −13.3265 13.3265i −0.681841 0.681841i
\(383\) 12.1354 + 12.1354i 0.620088 + 0.620088i 0.945554 0.325466i \(-0.105521\pi\)
−0.325466 + 0.945554i \(0.605521\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.0127812 + 0.0230543i −0.000651391 + 0.00117496i
\(386\) 8.91582 0.453803
\(387\) 0.329923 0.329923i 0.0167709 0.0167709i
\(388\) 5.06944 5.06944i 0.257362 0.257362i
\(389\) 4.95801 0.251381 0.125691 0.992069i \(-0.459885\pi\)
0.125691 + 0.992069i \(0.459885\pi\)
\(390\) 5.95641 10.7440i 0.301615 0.544041i
\(391\) −7.17189 −0.362698
\(392\) −4.94807 4.94807i −0.249915 0.249915i
\(393\) −5.17559 5.17559i −0.261074 0.261074i
\(394\) −17.5577 −0.884545
\(395\) 27.7382 7.95181i 1.39566 0.400099i
\(396\) 0.241934i 0.0121576i
\(397\) −14.1182 14.1182i −0.708573 0.708573i 0.257662 0.966235i \(-0.417048\pi\)
−0.966235 + 0.257662i \(0.917048\pi\)
\(398\) 5.01253 + 5.01253i 0.251255 + 0.251255i
\(399\) −0.394998 −0.0197746
\(400\) −4.24059 + 2.64903i −0.212030 + 0.132452i
\(401\) 39.3985i 1.96747i 0.179637 + 0.983733i \(0.442508\pi\)
−0.179637 + 0.983733i \(0.557492\pi\)
\(402\) 0.653315 0.653315i 0.0325844 0.0325844i
\(403\) −29.9369 + 6.27941i −1.49126 + 0.312800i
\(404\) 11.8507i 0.589593i
\(405\) 2.14949 0.616200i 0.106809 0.0306192i
\(406\) 0.416314i 0.0206613i
\(407\) 1.09953 + 1.09953i 0.0545018 + 0.0545018i
\(408\) −1.35699 + 1.35699i −0.0671810 + 0.0671810i
\(409\) 10.0302 0.495959 0.247980 0.968765i \(-0.420233\pi\)
0.247980 + 0.968765i \(0.420233\pi\)
\(410\) −2.86590 1.58885i −0.141537 0.0784675i
\(411\) 1.04101 0.0513492
\(412\) −8.10157 8.10157i −0.399136 0.399136i
\(413\) 0.471962 0.471962i 0.0232238 0.0232238i
\(414\) −3.73716 −0.183672
\(415\) 1.88474 + 1.04489i 0.0925180 + 0.0512916i
\(416\) 5.49384i 0.269358i
\(417\) −3.05648 3.05648i −0.149677 0.149677i
\(418\) 1.38678 + 1.38678i 0.0678299 + 0.0678299i
\(419\) 8.39979i 0.410356i 0.978725 + 0.205178i \(0.0657774\pi\)
−0.978725 + 0.205178i \(0.934223\pi\)
\(420\) −0.104737 + 0.0300254i −0.00511066 + 0.00146509i
\(421\) −22.3492 −1.08923 −0.544616 0.838685i \(-0.683325\pi\)
−0.544616 + 0.838685i \(0.683325\pi\)
\(422\) −1.73217 1.73217i −0.0843205 0.0843205i
\(423\) 2.81146 2.81146i 0.136698 0.136698i
\(424\) 0.844790 0.0410266
\(425\) 2.15973 9.34914i 0.104762 0.453500i
\(426\) 4.44096i 0.215165i
\(427\) 0.402803 0.402803i 0.0194930 0.0194930i
\(428\) 10.2618 10.2618i 0.496022 0.496022i
\(429\) −1.32915 −0.0641718
\(430\) −0.287508 1.00291i −0.0138649 0.0483647i
\(431\) 0.528344 0.0254494 0.0127247 0.999919i \(-0.495949\pi\)
0.0127247 + 0.999919i \(0.495949\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 21.1562 + 21.1562i 1.01670 + 1.01670i 0.999858 + 0.0168458i \(0.00536245\pi\)
0.0168458 + 0.999858i \(0.494638\pi\)
\(434\) 0.227133 + 0.148370i 0.0109027 + 0.00712197i
\(435\) −16.7087 9.26322i −0.801119 0.444138i
\(436\) 6.81387 0.326325
\(437\) −21.4217 + 21.4217i −1.02474 + 1.02474i
\(438\) −8.64429 + 8.64429i −0.413040 + 0.413040i
\(439\) 23.1210i 1.10351i 0.834008 + 0.551753i \(0.186041\pi\)
−0.834008 + 0.551753i \(0.813959\pi\)
\(440\) 0.473135 + 0.262304i 0.0225558 + 0.0125049i
\(441\) 6.99763 0.333220
\(442\) −7.45508 7.45508i −0.354602 0.354602i
\(443\) 12.5636 12.5636i 0.596913 0.596913i −0.342577 0.939490i \(-0.611300\pi\)
0.939490 + 0.342577i \(0.111300\pi\)
\(444\) 6.42726i 0.305024i
\(445\) 4.73845 1.35839i 0.224624 0.0643937i
\(446\) 22.3613i 1.05884i
\(447\) −11.1747 + 11.1747i −0.528546 + 0.528546i
\(448\) 0.0344550 0.0344550i 0.00162785 0.00162785i
\(449\) 1.12394 0.0530420 0.0265210 0.999648i \(-0.491557\pi\)
0.0265210 + 0.999648i \(0.491557\pi\)
\(450\) 1.12541 4.87170i 0.0530521 0.229654i
\(451\) 0.354544i 0.0166948i
\(452\) 0.808734 + 0.808734i 0.0380397 + 0.0380397i
\(453\) −2.33367 + 2.33367i −0.109645 + 0.109645i
\(454\) 27.2406i 1.27847i
\(455\) −0.164955 0.575411i −0.00773320 0.0269757i
\(456\) 8.10639i 0.379616i
\(457\) 12.7413 12.7413i 0.596013 0.596013i −0.343236 0.939249i \(-0.611523\pi\)
0.939249 + 0.343236i \(0.111523\pi\)
\(458\) 19.1373 + 19.1373i 0.894226 + 0.894226i
\(459\) 1.91907i 0.0895746i
\(460\) −4.05183 + 7.30854i −0.188917 + 0.340762i
\(461\) 31.9605i 1.48855i 0.667875 + 0.744273i \(0.267204\pi\)
−0.667875 + 0.744273i \(0.732796\pi\)
\(462\) 0.00833583 + 0.00833583i 0.000387818 + 0.000387818i
\(463\) 6.70781 + 6.70781i 0.311738 + 0.311738i 0.845583 0.533844i \(-0.179253\pi\)
−0.533844 + 0.845583i \(0.679253\pi\)
\(464\) 8.54385 0.396638
\(465\) −11.0086 + 5.81463i −0.510513 + 0.269647i
\(466\) −12.7577 −0.590988
\(467\) 10.0801 + 10.0801i 0.466449 + 0.466449i 0.900762 0.434313i \(-0.143009\pi\)
−0.434313 + 0.900762i \(0.643009\pi\)
\(468\) −3.88473 3.88473i −0.179572 0.179572i
\(469\) 0.0450199i 0.00207883i
\(470\) −2.45001 8.54636i −0.113011 0.394214i
\(471\) 6.78150i 0.312475i
\(472\) −9.68591 9.68591i −0.445830 0.445830i
\(473\) −0.0798195 + 0.0798195i −0.00367011 + 0.00367011i
\(474\) 12.9046i 0.592727i
\(475\) −21.4741 34.3759i −0.985298 1.57727i
\(476\) 0.0935101i 0.00428603i
\(477\) −0.597357 + 0.597357i −0.0273511 + 0.0273511i
\(478\) −13.1978 13.1978i −0.603651 0.603651i
\(479\) 9.22871i 0.421671i 0.977522 + 0.210835i \(0.0676184\pi\)
−0.977522 + 0.210835i \(0.932382\pi\)
\(480\) 0.616200 + 2.14949i 0.0281256 + 0.0981102i
\(481\) −35.3104 −1.61001
\(482\) 12.4419 12.4419i 0.566713 0.566713i
\(483\) −0.128764 + 0.128764i −0.00585896 + 0.00585896i
\(484\) 10.9415i 0.497339i
\(485\) 14.0205 + 7.77291i 0.636638 + 0.352950i
\(486\) 1.00000i 0.0453609i
\(487\) 19.6425 19.6425i 0.890086 0.890086i −0.104444 0.994531i \(-0.533306\pi\)
0.994531 + 0.104444i \(0.0333064\pi\)
\(488\) −8.26659 8.26659i −0.374211 0.374211i
\(489\) −16.9858 −0.768124
\(490\) 7.58681 13.6848i 0.342737 0.618217i
\(491\) 1.10627i 0.0499255i −0.999688 0.0249627i \(-0.992053\pi\)
0.999688 0.0249627i \(-0.00794671\pi\)
\(492\) −1.03624 + 1.03624i −0.0467171 + 0.0467171i
\(493\) −11.5939 + 11.5939i −0.522163 + 0.522163i
\(494\) −44.5352 −2.00373
\(495\) −0.520034 + 0.149080i −0.0233738 + 0.00670064i
\(496\) 3.04494 4.66137i 0.136722 0.209302i
\(497\) −0.153013 0.153013i −0.00686358 0.00686358i
\(498\) 0.681471 0.681471i 0.0305374 0.0305374i
\(499\) −30.7515 −1.37663 −0.688313 0.725414i \(-0.741648\pi\)
−0.688313 + 0.725414i \(0.741648\pi\)
\(500\) −8.30711 7.48277i −0.371505 0.334640i
\(501\) −18.2867 −0.816990
\(502\) 0.819821 0.819821i 0.0365904 0.0365904i
\(503\) 8.46280 8.46280i 0.377337 0.377337i −0.492803 0.870141i \(-0.664028\pi\)
0.870141 + 0.492803i \(0.164028\pi\)
\(504\) 0.0487267i 0.00217046i
\(505\) 25.4729 7.30240i 1.13353 0.324952i
\(506\) 0.904147 0.0401942
\(507\) 12.1497 12.1497i 0.539588 0.539588i
\(508\) 10.1076 + 10.1076i 0.448454 + 0.448454i
\(509\) −20.4726 −0.907431 −0.453716 0.891147i \(-0.649902\pi\)
−0.453716 + 0.891147i \(0.649902\pi\)
\(510\) −3.75301 2.08065i −0.166186 0.0921329i
\(511\) 0.595677i 0.0263512i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −5.73208 5.73208i −0.253078 0.253078i
\(514\) 4.75546i 0.209754i
\(515\) 12.4220 22.4064i 0.547380 0.987345i
\(516\) −0.466581 −0.0205401
\(517\) −0.680187 + 0.680187i −0.0299146 + 0.0299146i
\(518\) 0.221451 + 0.221451i 0.00973001 + 0.00973001i
\(519\) 25.0863 1.10116
\(520\) −11.8089 + 3.38531i −0.517856 + 0.148456i
\(521\) −3.57424 −0.156590 −0.0782951 0.996930i \(-0.524948\pi\)
−0.0782951 + 0.996930i \(0.524948\pi\)
\(522\) −6.04141 + 6.04141i −0.264426 + 0.264426i
\(523\) −11.4759 11.4759i −0.501805 0.501805i 0.410194 0.911998i \(-0.365461\pi\)
−0.911998 + 0.410194i \(0.865461\pi\)
\(524\) 7.31940i 0.319749i
\(525\) −0.129079 0.206630i −0.00563345 0.00901808i
\(526\) 22.9464i 1.00051i
\(527\) 2.19348 + 10.4574i 0.0955496 + 0.455530i
\(528\) 0.171073 0.171073i 0.00744500 0.00744500i
\(529\) 9.03360i 0.392765i
\(530\) 0.520560 + 1.81587i 0.0226117 + 0.0788762i
\(531\) 13.6979 0.594440
\(532\) 0.279305 + 0.279305i 0.0121094 + 0.0121094i
\(533\) −5.69291 5.69291i −0.246587 0.246587i
\(534\) 2.20446i 0.0953962i
\(535\) 28.3809 + 15.7343i 1.22701 + 0.680252i
\(536\) −0.923926 −0.0399075
\(537\) 5.35735 + 5.35735i 0.231187 + 0.231187i
\(538\) −0.603753 0.603753i −0.0260296 0.0260296i
\(539\) −1.69296 −0.0729211
\(540\) −1.95564 1.08420i −0.0841572 0.0466564i
\(541\) 2.91694 0.125409 0.0627046 0.998032i \(-0.480027\pi\)
0.0627046 + 0.998032i \(0.480027\pi\)
\(542\) −10.6988 + 10.6988i −0.459552 + 0.459552i
\(543\) 3.44181 3.44181i 0.147702 0.147702i
\(544\) 1.91907 0.0822795
\(545\) 4.19871 + 14.6463i 0.179853 + 0.627380i
\(546\) −0.267697 −0.0114564
\(547\) −17.5259 17.5259i −0.749353 0.749353i 0.225005 0.974358i \(-0.427760\pi\)
−0.974358 + 0.225005i \(0.927760\pi\)
\(548\) −0.736104 0.736104i −0.0314448 0.0314448i
\(549\) 11.6907 0.498948
\(550\) −0.272274 + 1.17863i −0.0116098 + 0.0502569i
\(551\) 69.2597i 2.95056i
\(552\) 2.64257 + 2.64257i 0.112475 + 0.112475i
\(553\) −0.444627 0.444627i −0.0189075 0.0189075i
\(554\) 15.7269 0.668173
\(555\) −13.8153 + 3.96048i −0.586428 + 0.168113i
\(556\) 4.32252i 0.183316i
\(557\) 21.0848 21.0848i 0.893390 0.893390i −0.101451 0.994841i \(-0.532348\pi\)
0.994841 + 0.101451i \(0.0323484\pi\)
\(558\) 1.14299 + 5.44918i 0.0483867 + 0.230682i
\(559\) 2.56332i 0.108417i
\(560\) 0.0952917 + 0.0528294i 0.00402681 + 0.00223245i
\(561\) 0.464289i 0.0196023i
\(562\) 7.92487 + 7.92487i 0.334290 + 0.334290i
\(563\) −18.6518 + 18.6518i −0.786080 + 0.786080i −0.980849 0.194769i \(-0.937604\pi\)
0.194769 + 0.980849i \(0.437604\pi\)
\(564\) −3.97600 −0.167420
\(565\) −1.24002 + 2.23671i −0.0521681 + 0.0940990i
\(566\) −2.92685 −0.123025
\(567\) −0.0344550 0.0344550i −0.00144697 0.00144697i
\(568\) −3.14023 + 3.14023i −0.131761 + 0.131761i
\(569\) 44.2050 1.85317 0.926586 0.376084i \(-0.122730\pi\)
0.926586 + 0.376084i \(0.122730\pi\)
\(570\) −17.4246 + 4.99516i −0.729835 + 0.209224i
\(571\) 25.3388i 1.06040i −0.847874 0.530198i \(-0.822117\pi\)
0.847874 0.530198i \(-0.177883\pi\)
\(572\) 0.939849 + 0.939849i 0.0392970 + 0.0392970i
\(573\) −13.3265 13.3265i −0.556721 0.556721i
\(574\) 0.0714069i 0.00298047i
\(575\) −18.2063 4.20582i −0.759257 0.175395i
\(576\) 1.00000 0.0416667
\(577\) −15.7492 15.7492i −0.655648 0.655648i 0.298699 0.954347i \(-0.403447\pi\)
−0.954347 + 0.298699i \(0.903447\pi\)
\(578\) 9.41666 9.41666i 0.391681 0.391681i
\(579\) 8.91582 0.370529
\(580\) 5.26472 + 18.3649i 0.218606 + 0.762561i
\(581\) 0.0469601i 0.00194823i
\(582\) 5.06944 5.06944i 0.210135 0.210135i
\(583\) 0.144521 0.144521i 0.00598545 0.00598545i
\(584\) 12.2249 0.505869
\(585\) 5.95641 10.7440i 0.246267 0.444208i
\(586\) 22.4607 0.927841
\(587\) −22.8549 + 22.8549i −0.943325 + 0.943325i −0.998478 0.0551533i \(-0.982435\pi\)
0.0551533 + 0.998478i \(0.482435\pi\)
\(588\) −4.94807 4.94807i −0.204055 0.204055i
\(589\) 37.7869 + 24.6834i 1.55698 + 1.01706i
\(590\) 14.8513 26.7882i 0.611418 1.10285i
\(591\) −17.5577 −0.722228
\(592\) 4.54476 4.54476i 0.186789 0.186789i
\(593\) −9.77033 + 9.77033i −0.401219 + 0.401219i −0.878663 0.477443i \(-0.841564\pi\)
0.477443 + 0.878663i \(0.341564\pi\)
\(594\) 0.241934i 0.00992667i
\(595\) −0.200999 + 0.0576209i −0.00824014 + 0.00236223i
\(596\) 15.8034 0.647334
\(597\) 5.01253 + 5.01253i 0.205149 + 0.205149i
\(598\) −14.5179 + 14.5179i −0.593680 + 0.593680i
\(599\) 0.724583i 0.0296057i −0.999890 0.0148028i \(-0.995288\pi\)
0.999890 0.0148028i \(-0.00471206\pi\)
\(600\) −4.24059 + 2.64903i −0.173122 + 0.108146i
\(601\) 12.8455i 0.523978i −0.965071 0.261989i \(-0.915622\pi\)
0.965071 0.261989i \(-0.0843784\pi\)
\(602\) −0.0160761 + 0.0160761i −0.000655211 + 0.000655211i
\(603\) 0.653315 0.653315i 0.0266050 0.0266050i
\(604\) 3.30031 0.134288
\(605\) −23.5185 + 6.74214i −0.956165 + 0.274107i
\(606\) 11.8507i 0.481401i
\(607\) −7.27742 7.27742i −0.295381 0.295381i 0.543820 0.839202i \(-0.316977\pi\)
−0.839202 + 0.543820i \(0.816977\pi\)
\(608\) 5.73208 5.73208i 0.232467 0.232467i
\(609\) 0.416314i 0.0168699i
\(610\) 12.6750 22.8628i 0.513198 0.925688i
\(611\) 21.8435i 0.883694i
\(612\) −1.35699 + 1.35699i −0.0548530 + 0.0548530i
\(613\) 10.9037 + 10.9037i 0.440396 + 0.440396i 0.892145 0.451749i \(-0.149200\pi\)
−0.451749 + 0.892145i \(0.649200\pi\)
\(614\) 9.11097i 0.367689i
\(615\) −2.86590 1.58885i −0.115564 0.0640685i
\(616\) 0.0117886i 0.000474978i
\(617\) 20.7282 + 20.7282i 0.834486 + 0.834486i 0.988127 0.153641i \(-0.0490998\pi\)
−0.153641 + 0.988127i \(0.549100\pi\)
\(618\) −8.10157 8.10157i −0.325893 0.325893i
\(619\) −32.6126 −1.31081 −0.655406 0.755277i \(-0.727502\pi\)
−0.655406 + 0.755277i \(0.727502\pi\)
\(620\) 11.8958 + 3.67271i 0.477749 + 0.147500i
\(621\) −3.73716 −0.149967
\(622\) −7.18083 7.18083i −0.287925 0.287925i
\(623\) −0.0759545 0.0759545i −0.00304305 0.00304305i
\(624\) 5.49384i 0.219930i
\(625\) 10.9653 22.4669i 0.438611 0.898677i
\(626\) 21.6707i 0.866136i
\(627\) 1.38678 + 1.38678i 0.0553829 + 0.0553829i
\(628\) 4.79524 4.79524i 0.191351 0.191351i
\(629\) 12.3344i 0.491804i
\(630\) −0.104737 + 0.0300254i −0.00417284 + 0.00119624i
\(631\) 8.88412i 0.353671i 0.984240 + 0.176836i \(0.0565861\pi\)
−0.984240 + 0.176836i \(0.943414\pi\)
\(632\) −9.12491 + 9.12491i −0.362970 + 0.362970i
\(633\) −1.73217 1.73217i −0.0688474 0.0688474i
\(634\) 1.28031i 0.0508478i
\(635\) −15.4979 + 27.9546i −0.615016 + 1.10934i
\(636\) 0.844790 0.0334981
\(637\) 27.1839 27.1839i 1.07707 1.07707i
\(638\) 1.46162 1.46162i 0.0578662 0.0578662i
\(639\) 4.44096i 0.175682i
\(640\) 1.08420 1.95564i 0.0428567 0.0773033i
\(641\) 10.7525i 0.424697i 0.977194 + 0.212348i \(0.0681111\pi\)
−0.977194 + 0.212348i \(0.931889\pi\)
\(642\) 10.2618 10.2618i 0.405000 0.405000i
\(643\) −11.7446 11.7446i −0.463162 0.463162i 0.436529 0.899690i \(-0.356208\pi\)
−0.899690 + 0.436529i \(0.856208\pi\)
\(644\) 0.182100 0.00717573
\(645\) −0.287508 1.00291i −0.0113206 0.0394896i
\(646\) 15.5567i 0.612072i
\(647\) −5.34144 + 5.34144i −0.209994 + 0.209994i −0.804265 0.594271i \(-0.797441\pi\)
0.594271 + 0.804265i \(0.297441\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) −3.31400 −0.130086
\(650\) −14.5534 23.2971i −0.570829 0.913789i
\(651\) 0.227133 + 0.148370i 0.00890205 + 0.00581507i
\(652\) 12.0108 + 12.0108i 0.470378 + 0.470378i
\(653\) 25.5474 25.5474i 0.999745 0.999745i −0.000254663 1.00000i \(-0.500081\pi\)
1.00000 0.000254663i \(8.10619e-5\pi\)
\(654\) 6.81387 0.266444
\(655\) −15.7330 + 4.51022i −0.614737 + 0.176229i
\(656\) 1.46546 0.0572165
\(657\) −8.64429 + 8.64429i −0.337246 + 0.337246i
\(658\) −0.136993 + 0.136993i −0.00534054 + 0.00534054i
\(659\) 31.8901i 1.24226i −0.783706 0.621132i \(-0.786673\pi\)
0.783706 0.621132i \(-0.213327\pi\)
\(660\) 0.473135 + 0.262304i 0.0184168 + 0.0102102i
\(661\) −13.1832 −0.512767 −0.256383 0.966575i \(-0.582531\pi\)
−0.256383 + 0.966575i \(0.582531\pi\)
\(662\) −24.9340 + 24.9340i −0.969088 + 0.969088i
\(663\) −7.45508 7.45508i −0.289531 0.289531i
\(664\) −0.963745 −0.0374006
\(665\) −0.428255 + 0.772472i −0.0166070 + 0.0299552i
\(666\) 6.42726i 0.249051i
\(667\) 22.5778 + 22.5778i 0.874214 + 0.874214i
\(668\) 12.9307 + 12.9307i 0.500302 + 0.500302i
\(669\) 22.3613i 0.864539i
\(670\) −0.569324 1.98597i −0.0219949 0.0767247i
\(671\) −2.82838 −0.109188
\(672\) 0.0344550 0.0344550i 0.00132913 0.00132913i
\(673\) −25.9900 25.9900i −1.00184 1.00184i −0.999998 0.00184286i \(-0.999413\pi\)
−0.00184286 0.999998i \(-0.500587\pi\)
\(674\) 7.60949 0.293107
\(675\) 1.12541 4.87170i 0.0433169 0.187512i
\(676\) −17.1823 −0.660857
\(677\) −8.51300 + 8.51300i −0.327181 + 0.327181i −0.851514 0.524333i \(-0.824315\pi\)
0.524333 + 0.851514i \(0.324315\pi\)
\(678\) 0.808734 + 0.808734i 0.0310593 + 0.0310593i
\(679\) 0.349335i 0.0134063i
\(680\) 1.18253 + 4.12502i 0.0453481 + 0.158187i
\(681\) 27.2406i 1.04386i
\(682\) −0.276529 1.31834i −0.0105888 0.0504819i
\(683\) 7.75769 7.75769i 0.296840 0.296840i −0.542935 0.839775i \(-0.682687\pi\)
0.839775 + 0.542935i \(0.182687\pi\)
\(684\) 8.10639i 0.309955i
\(685\) 1.12866 2.03583i 0.0431239 0.0777852i
\(686\) −0.682058 −0.0260411
\(687\) 19.1373 + 19.1373i 0.730132 + 0.730132i
\(688\) 0.329923 + 0.329923i 0.0125782 + 0.0125782i
\(689\) 4.64114i 0.176813i
\(690\) −4.05183 + 7.30854i −0.154250 + 0.278231i
\(691\) 8.98563 0.341829 0.170915 0.985286i \(-0.445328\pi\)
0.170915 + 0.985286i \(0.445328\pi\)
\(692\) −17.7387 17.7387i −0.674323 0.674323i
\(693\) 0.00833583 + 0.00833583i 0.000316652 + 0.000316652i
\(694\) 34.2740 1.30102
\(695\) −9.29120 + 2.66354i −0.352435 + 0.101034i
\(696\) 8.54385 0.323854
\(697\) −1.98861 + 1.98861i −0.0753240 + 0.0753240i
\(698\) −7.31418 + 7.31418i −0.276846 + 0.276846i
\(699\) −12.7577 −0.482540
\(700\) −0.0548373 + 0.237382i −0.00207266 + 0.00897219i
\(701\) 21.0088 0.793491 0.396745 0.917929i \(-0.370140\pi\)
0.396745 + 0.917929i \(0.370140\pi\)
\(702\) −3.88473 3.88473i −0.146620 0.146620i
\(703\) 36.8416 + 36.8416i 1.38951 + 1.38951i
\(704\) −0.241934 −0.00911823
\(705\) −2.45001 8.54636i −0.0922728 0.321875i
\(706\) 25.3320i 0.953381i
\(707\) −0.408315 0.408315i −0.0153563 0.0153563i
\(708\) −9.68591 9.68591i −0.364019 0.364019i
\(709\) −28.8232 −1.08248 −0.541239 0.840869i \(-0.682045\pi\)
−0.541239 + 0.840869i \(0.682045\pi\)
\(710\) −8.68490 4.81488i −0.325938 0.180699i
\(711\) 12.9046i 0.483959i
\(712\) −1.55879 + 1.55879i −0.0584180 + 0.0584180i
\(713\) 20.3645 4.27155i 0.762656 0.159971i
\(714\) 0.0935101i 0.00349953i
\(715\) −1.44106 + 2.59933i −0.0538925 + 0.0972094i
\(716\) 7.57644i 0.283145i
\(717\) −13.1978 13.1978i −0.492879 0.492879i
\(718\) 14.6968 14.6968i 0.548478 0.548478i
\(719\) 19.4702 0.726116 0.363058 0.931767i \(-0.381733\pi\)
0.363058 + 0.931767i \(0.381733\pi\)
\(720\) 0.616200 + 2.14949i 0.0229644 + 0.0801067i
\(721\) −0.558279 −0.0207914
\(722\) 33.0314 + 33.0314i 1.22930 + 1.22930i
\(723\) 12.4419 12.4419i 0.462719 0.462719i
\(724\) −4.86746 −0.180898
\(725\) −36.2310 + 22.6329i −1.34559 + 0.840565i
\(726\) 10.9415i 0.406076i
\(727\) 23.8912 + 23.8912i 0.886075 + 0.886075i 0.994143 0.108068i \(-0.0344666\pi\)
−0.108068 + 0.994143i \(0.534467\pi\)
\(728\) 0.189290 + 0.189290i 0.00701556 + 0.00701556i
\(729\) 1.00000i 0.0370370i
\(730\) 7.53297 + 26.2772i 0.278808 + 0.972563i
\(731\) −0.895403 −0.0331177
\(732\) −8.26659 8.26659i −0.305542 0.305542i
\(733\) 27.0190 27.0190i 0.997968 0.997968i −0.00202986 0.999998i \(-0.500646\pi\)
0.999998 + 0.00202986i \(0.000646125\pi\)
\(734\) 25.9565 0.958073
\(735\) 7.58681 13.6848i 0.279844 0.504772i
\(736\) 3.73716i 0.137754i
\(737\) −0.158059 + 0.158059i −0.00582218 + 0.00582218i
\(738\) −1.03624 + 1.03624i −0.0381443 + 0.0381443i
\(739\) −35.9676 −1.32309 −0.661544 0.749906i \(-0.730099\pi\)
−0.661544 + 0.749906i \(0.730099\pi\)
\(740\) 12.5694 + 6.96842i 0.462060 + 0.256164i
\(741\) −44.5352 −1.63604
\(742\) 0.0291072 0.0291072i 0.00106856 0.00106856i
\(743\) −17.1623 17.1623i −0.629624 0.629624i 0.318349 0.947973i \(-0.396871\pi\)
−0.947973 + 0.318349i \(0.896871\pi\)
\(744\) 3.04494 4.66137i 0.111633 0.170894i
\(745\) 9.73809 + 33.9693i 0.356776 + 1.24454i
\(746\) −31.0206 −1.13575
\(747\) 0.681471 0.681471i 0.0249337 0.0249337i
\(748\) 0.328302 0.328302i 0.0120039 0.0120039i
\(749\) 0.707139i 0.0258383i
\(750\) −8.30711 7.48277i −0.303333 0.273232i
\(751\) −37.8302 −1.38044 −0.690222 0.723598i \(-0.742487\pi\)
−0.690222 + 0.723598i \(0.742487\pi\)
\(752\) 2.81146 + 2.81146i 0.102523 + 0.102523i
\(753\) 0.819821 0.819821i 0.0298759 0.0298759i
\(754\) 46.9385i 1.70940i
\(755\) 2.03365 + 7.09398i 0.0740122 + 0.258176i
\(756\) 0.0487267i 0.00177217i
\(757\) −15.9320 + 15.9320i −0.579059 + 0.579059i −0.934644 0.355585i \(-0.884282\pi\)
0.355585 + 0.934644i \(0.384282\pi\)
\(758\) −11.7542 + 11.7542i −0.426931 + 0.426931i
\(759\) 0.904147 0.0328185
\(760\) 15.8531 + 8.78893i 0.575054 + 0.318808i
\(761\) 46.0885i 1.67071i −0.549713 0.835354i \(-0.685263\pi\)
0.549713 0.835354i \(-0.314737\pi\)
\(762\) 10.1076 + 10.1076i 0.366161 + 0.366161i
\(763\) 0.234772 0.234772i 0.00849931 0.00849931i
\(764\) 18.8465i 0.681841i
\(765\) −3.75301 2.08065i −0.135690 0.0752262i
\(766\) 17.1620i 0.620088i
\(767\) 53.2128 53.2128i 1.92140 1.92140i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 11.2917i 0.407189i 0.979055 + 0.203594i \(0.0652624\pi\)
−0.979055 + 0.203594i \(0.934738\pi\)
\(770\) 0.0253395 0.00726417i 0.000913174 0.000261782i
\(771\) 4.75546i 0.171264i
\(772\) −6.30444 6.30444i −0.226902 0.226902i
\(773\) 5.24463 + 5.24463i 0.188636 + 0.188636i 0.795106 0.606470i \(-0.207415\pi\)
−0.606470 + 0.795106i \(0.707415\pi\)
\(774\) −0.466581 −0.0167709
\(775\) −0.564224 + 27.8331i −0.0202675 + 0.999795i
\(776\) −7.16927 −0.257362
\(777\) 0.221451 + 0.221451i 0.00794452 + 0.00794452i
\(778\) −3.50584 3.50584i −0.125691 0.125691i
\(779\) 11.8796i 0.425630i
\(780\) −11.8089 + 3.38531i −0.422828 + 0.121213i
\(781\) 1.07442i 0.0384457i
\(782\) 5.07129 + 5.07129i 0.181349 + 0.181349i
\(783\) −6.04141 + 6.04141i −0.215903 + 0.215903i
\(784\) 6.99763i 0.249915i
\(785\) 13.2621 + 7.35249i 0.473346 + 0.262421i
\(786\) 7.31940i 0.261074i
\(787\) −13.5398 + 13.5398i −0.482641 + 0.482641i −0.905974 0.423333i \(-0.860860\pi\)
0.423333 + 0.905974i \(0.360860\pi\)
\(788\) 12.4152 + 12.4152i 0.442273 + 0.442273i
\(789\) 22.9464i 0.816915i
\(790\) −25.2367 13.9911i −0.897880 0.497781i
\(791\) 0.0557299 0.00198153
\(792\) 0.171073 0.171073i 0.00607882 0.00607882i
\(793\) 45.4153 45.4153i 1.61274 1.61274i
\(794\) 19.9662i 0.708573i
\(795\) 0.520560 + 1.81587i 0.0184624 + 0.0644021i
\(796\) 7.08879i 0.251255i
\(797\) 9.78542 9.78542i 0.346618 0.346618i −0.512231 0.858848i \(-0.671181\pi\)
0.858848 + 0.512231i \(0.171181\pi\)
\(798\) 0.279305 + 0.279305i 0.00988731 + 0.00988731i
\(799\) −7.63023 −0.269938
\(800\) 4.87170 + 1.12541i 0.172241 + 0.0397891i
\(801\) 2.20446i 0.0778906i
\(802\) 27.8589 27.8589i 0.983733 0.983733i
\(803\) 2.09135 2.09135i 0.0738020 0.0738020i
\(804\) −0.923926 −0.0325844
\(805\) 0.112210 + 0.391421i 0.00395488 + 0.0137958i
\(806\) 25.6088 + 16.7284i 0.902032 + 0.589232i
\(807\) −0.603753 0.603753i −0.0212531 0.0212531i
\(808\) −8.37970 + 8.37970i −0.294797 + 0.294797i
\(809\) 13.6119 0.478568 0.239284 0.970950i \(-0.423087\pi\)
0.239284 + 0.970950i \(0.423087\pi\)
\(810\) −1.95564 1.08420i −0.0687141 0.0380948i
\(811\) 33.5786 1.17910 0.589551 0.807731i \(-0.299305\pi\)
0.589551 + 0.807731i \(0.299305\pi\)
\(812\) 0.294378 0.294378i 0.0103307 0.0103307i
\(813\) −10.6988 + 10.6988i −0.375222 + 0.375222i
\(814\) 1.55497i 0.0545018i
\(815\) −18.4160 + 33.2180i −0.645083 + 1.16358i
\(816\) 1.91907 0.0671810
\(817\) −2.67448 + 2.67448i −0.0935683 + 0.0935683i
\(818\) −7.09239 7.09239i −0.247980 0.247980i
\(819\) −0.267697 −0.00935408
\(820\) 0.903016 + 3.14998i 0.0315347 + 0.110002i
\(821\) 14.7572i 0.515031i −0.966274 0.257516i \(-0.917096\pi\)
0.966274 0.257516i \(-0.0829039\pi\)
\(822\) −0.736104 0.736104i −0.0256746 0.0256746i
\(823\) −9.22666 9.22666i −0.321621 0.321621i 0.527768 0.849389i \(-0.323029\pi\)
−0.849389 + 0.527768i \(0.823029\pi\)
\(824\) 11.4574i 0.399136i
\(825\) −0.272274 + 1.17863i −0.00947936 + 0.0410346i
\(826\) −0.667456 −0.0232238
\(827\) 19.7186 19.7186i 0.685683 0.685683i −0.275592 0.961275i \(-0.588874\pi\)
0.961275 + 0.275592i \(0.0888739\pi\)
\(828\) 2.64257 + 2.64257i 0.0918358 + 0.0918358i
\(829\) 30.2439 1.05041 0.525207 0.850974i \(-0.323988\pi\)
0.525207 + 0.850974i \(0.323988\pi\)
\(830\) −0.593860 2.07156i −0.0206132 0.0719048i
\(831\) 15.7269 0.545561
\(832\) 3.88473 3.88473i 0.134679 0.134679i
\(833\) −9.49570 9.49570i −0.329007 0.329007i
\(834\) 4.32252i 0.149677i
\(835\) −19.8264 + 35.7622i −0.686121 + 1.23760i
\(836\) 1.96121i 0.0678299i
\(837\) 1.14299 + 5.44918i 0.0395076 + 0.188351i
\(838\) 5.93955 5.93955i 0.205178 0.205178i
\(839\) 33.3839i 1.15254i −0.817260 0.576269i \(-0.804508\pi\)
0.817260 0.576269i \(-0.195492\pi\)
\(840\) 0.0952917 + 0.0528294i 0.00328788 + 0.00182279i
\(841\) 43.9974 1.51715
\(842\) 15.8033 + 15.8033i 0.544616 + 0.544616i
\(843\) 7.92487 + 7.92487i 0.272947 + 0.272947i
\(844\) 2.44965i 0.0843205i
\(845\) −10.5877 36.9331i −0.364229 1.27054i
\(846\) −3.97600 −0.136698
\(847\) 0.376988 + 0.376988i 0.0129535 + 0.0129535i
\(848\) −0.597357 0.597357i −0.0205133 0.0205133i
\(849\) −2.92685 −0.100449
\(850\) −8.13801 + 5.08368i −0.279131 + 0.174369i
\(851\) 24.0197 0.823386
\(852\) −3.14023 + 3.14023i −0.107583 + 0.107583i
\(853\) 28.2893 28.2893i 0.968608 0.968608i −0.0309136 0.999522i \(-0.509842\pi\)
0.999522 + 0.0309136i \(0.00984168\pi\)
\(854\) −0.569650 −0.0194930
\(855\) −17.4246 + 4.99516i −0.595908 + 0.170831i
\(856\) −14.5124 −0.496022
\(857\) 34.0629 + 34.0629i 1.16357 + 1.16357i 0.983689 + 0.179876i \(0.0575696\pi\)
0.179876 + 0.983689i \(0.442430\pi\)
\(858\) 0.939849 + 0.939849i 0.0320859 + 0.0320859i
\(859\) 31.7668 1.08387 0.541934 0.840421i \(-0.317692\pi\)
0.541934 + 0.840421i \(0.317692\pi\)
\(860\) −0.505866 + 0.912464i −0.0172499 + 0.0311148i
\(861\) 0.0714069i 0.00243354i
\(862\) −0.373596 0.373596i −0.0127247 0.0127247i
\(863\) −36.5834 36.5834i −1.24531 1.24531i −0.957767 0.287544i \(-0.907161\pi\)
−0.287544 0.957767i \(-0.592839\pi\)
\(864\) 1.00000 0.0340207
\(865\) 27.1985 49.0596i 0.924775 1.66808i
\(866\) 29.9194i 1.01670i
\(867\) 9.41666 9.41666i 0.319806 0.319806i
\(868\) −0.0556942 0.265521i −0.00189039 0.00901236i
\(869\) 3.12206i 0.105908i
\(870\) 5.26472 + 18.3649i 0.178491 + 0.622628i
\(871\) 5.07590i 0.171990i
\(872\) −4.81814 4.81814i −0.163163 0.163163i
\(873\) 5.06944 5.06944i 0.171575 0.171575i
\(874\) 30.2949 1.02474
\(875\) −0.544040 + 0.0284027i −0.0183919 + 0.000960188i
\(876\) 12.2249 0.413040
\(877\) −13.7222 13.7222i −0.463367 0.463367i 0.436390 0.899757i \(-0.356257\pi\)
−0.899757 + 0.436390i \(0.856257\pi\)
\(878\) 16.3490 16.3490i 0.551753 0.551753i
\(879\) 22.4607 0.757579
\(880\) −0.149080 0.520034i −0.00502548 0.0175303i
\(881\) 43.5538i 1.46736i 0.679493 + 0.733682i \(0.262200\pi\)
−0.679493 + 0.733682i \(0.737800\pi\)
\(882\) −4.94807 4.94807i −0.166610 0.166610i
\(883\) 30.3612 + 30.3612i 1.02174 + 1.02174i 0.999758 + 0.0219787i \(0.00699661\pi\)
0.0219787 + 0.999758i \(0.493003\pi\)
\(884\) 10.5431i 0.354602i
\(885\) 14.8513 26.7882i 0.499220 0.900476i
\(886\) −17.7676 −0.596913
\(887\) 15.7102 + 15.7102i 0.527498 + 0.527498i 0.919826 0.392327i \(-0.128330\pi\)
−0.392327 + 0.919826i \(0.628330\pi\)
\(888\) 4.54476 4.54476i 0.152512 0.152512i
\(889\) 0.696517 0.0233604
\(890\) −4.31112 2.39007i −0.144509 0.0801152i
\(891\) 0.241934i 0.00810509i
\(892\) 15.8119 15.8119i 0.529420 0.529420i
\(893\) −22.7908 + 22.7908i −0.762663 + 0.762663i
\(894\) 15.8034 0.528546
\(895\) 16.2855 4.66861i 0.544363 0.156054i
\(896\) −0.0487267 −0.00162785
\(897\) −14.5179 + 14.5179i −0.484738 + 0.484738i
\(898\) −0.794746 0.794746i −0.0265210 0.0265210i
\(899\) 26.0155 39.8260i 0.867664 1.32827i
\(900\) −4.24059 + 2.64903i −0.141353 + 0.0883010i
\(901\) 1.62121 0.0540105
\(902\) 0.250701 0.250701i 0.00834741 0.00834741i
\(903\) −0.0160761 + 0.0160761i −0.000534978 + 0.000534978i
\(904\) 1.14372i 0.0380397i
\(905\) −2.99933 10.4625i −0.0997011 0.347787i
\(906\) 3.30031 0.109645
\(907\) 22.6786 + 22.6786i 0.753032 + 0.753032i 0.975044 0.222012i \(-0.0712624\pi\)
−0.222012 + 0.975044i \(0.571262\pi\)
\(908\) −19.2620 + 19.2620i −0.639233 + 0.639233i
\(909\) 11.8507i 0.393062i
\(910\) −0.290236 + 0.523518i −0.00962124 + 0.0173544i
\(911\) 35.9909i 1.19243i 0.802824 + 0.596216i \(0.203330\pi\)
−0.802824 + 0.596216i \(0.796670\pi\)
\(912\) 5.73208 5.73208i 0.189808 0.189808i
\(913\) −0.164871 + 0.164871i −0.00545643 + 0.00545643i
\(914\) −18.0189 −0.596013
\(915\) 12.6750 22.8628i 0.419024 0.755821i
\(916\) 27.0642i 0.894226i
\(917\) 0.252190 + 0.252190i 0.00832804 + 0.00832804i
\(918\) −1.35699 + 1.35699i −0.0447873 + 0.0447873i
\(919\) 1.89965i 0.0626635i −0.999509 0.0313318i \(-0.990025\pi\)
0.999509 0.0313318i \(-0.00997484\pi\)
\(920\) 8.03299 2.30284i 0.264840 0.0759225i
\(921\) 9.11097i 0.300217i
\(922\) 22.5995 22.5995i 0.744273 0.744273i
\(923\) −17.2519 17.2519i −0.567854 0.567854i
\(924\) 0.0117886i 0.000387818i
\(925\) −7.23328 + 31.3117i −0.237829 + 1.02952i
\(926\) 9.48627i 0.311738i
\(927\) −8.10157 8.10157i −0.266091 0.266091i
\(928\) −6.04141 6.04141i −0.198319 0.198319i
\(929\) 23.8623 0.782896 0.391448 0.920200i \(-0.371974\pi\)
0.391448 + 0.920200i \(0.371974\pi\)
\(930\) 11.8958 + 3.67271i 0.390080 + 0.120433i
\(931\) −56.7255 −1.85910
\(932\) 9.02104 + 9.02104i 0.295494 + 0.295494i
\(933\) −7.18083 7.18083i −0.235090 0.235090i
\(934\) 14.2554i 0.466449i
\(935\) 0.907980 + 0.503381i 0.0296941 + 0.0164623i
\(936\) 5.49384i 0.179572i
\(937\) 32.3207 + 32.3207i 1.05587 + 1.05587i 0.998344 + 0.0575269i \(0.0183215\pi\)
0.0575269 + 0.998344i \(0.481678\pi\)
\(938\) −0.0318339 + 0.0318339i −0.00103941 + 0.00103941i
\(939\) 21.6707i 0.707197i
\(940\) −4.31077 + 7.77561i −0.140602 + 0.253612i
\(941\) 15.5412i 0.506627i 0.967384 + 0.253314i \(0.0815205\pi\)
−0.967384 + 0.253314i \(0.918480\pi\)
\(942\) 4.79524 4.79524i 0.156237 0.156237i
\(943\) 3.87258 + 3.87258i 0.126109 + 0.126109i
\(944\) 13.6979i 0.445830i
\(945\) −0.104737 + 0.0300254i −0.00340711 + 0.000976727i
\(946\) 0.112882 0.00367011
\(947\) 1.24213 1.24213i 0.0403639 0.0403639i −0.686637 0.727001i \(-0.740914\pi\)
0.727001 + 0.686637i \(0.240914\pi\)
\(948\) −9.12491 + 9.12491i −0.296363 + 0.296363i
\(949\) 67.1615i 2.18015i
\(950\) −9.12297 + 39.4919i −0.295988 + 1.28129i
\(951\) 1.28031i 0.0415170i
\(952\) 0.0661216 0.0661216i 0.00214301 0.00214301i
\(953\) 4.65276 + 4.65276i 0.150718 + 0.150718i 0.778439 0.627721i \(-0.216012\pi\)
−0.627721 + 0.778439i \(0.716012\pi\)
\(954\) 0.844790 0.0273511
\(955\) −40.5102 + 11.6132i −1.31088 + 0.375794i
\(956\) 18.6644i 0.603651i
\(957\) 1.46162 1.46162i 0.0472476 0.0472476i
\(958\) 6.52569 6.52569i 0.210835 0.210835i
\(959\) −0.0507249 −0.00163799
\(960\) 1.08420 1.95564i 0.0349923 0.0631179i
\(961\) −12.4567 28.3871i −0.401830 0.915714i
\(962\) 24.9682 + 24.9682i 0.805007 + 0.805007i
\(963\) 10.2618 10.2618i 0.330681 0.330681i
\(964\) −17.5955 −0.566713
\(965\) 9.66652 17.4361i 0.311176 0.561288i
\(966\) 0.182100 0.00585896
\(967\) −2.16898 + 2.16898i −0.0697498 + 0.0697498i −0.741121 0.671371i \(-0.765706\pi\)
0.671371 + 0.741121i \(0.265706\pi\)
\(968\) 7.73679 7.73679i 0.248670 0.248670i
\(969\) 15.5567i 0.499755i
\(970\) −4.41771 15.4103i −0.141844 0.494794i
\(971\) −20.3741 −0.653835 −0.326918 0.945053i \(-0.606010\pi\)
−0.326918 + 0.945053i \(0.606010\pi\)
\(972\) −0.707107 + 0.707107i −0.0226805 + 0.0226805i
\(973\) 0.148932 + 0.148932i 0.00477455 + 0.00477455i
\(974\) −27.7787 −0.890086
\(975\) −14.5534 23.2971i −0.466080 0.746106i
\(976\) 11.6907i 0.374211i
\(977\) −18.2867 18.2867i −0.585043 0.585043i 0.351242 0.936285i \(-0.385760\pi\)
−0.936285 + 0.351242i \(0.885760\pi\)
\(978\) 12.0108 + 12.0108i 0.384062 + 0.384062i
\(979\) 0.533333i 0.0170454i
\(980\) −15.0413 + 4.31194i −0.480477 + 0.137740i
\(981\) 6.81387 0.217550
\(982\) −0.782254 + 0.782254i −0.0249627 + 0.0249627i
\(983\) −15.5673 15.5673i −0.496519 0.496519i 0.413833 0.910353i \(-0.364190\pi\)
−0.910353 + 0.413833i \(0.864190\pi\)
\(984\) 1.46546 0.0467171
\(985\) −19.0360 + 34.3365i −0.606539 + 1.09405i
\(986\) 16.3963 0.522163
\(987\) −0.136993 + 0.136993i −0.00436054 + 0.00436054i
\(988\) 31.4911 + 31.4911i 1.00187 + 1.00187i
\(989\) 1.74369i 0.0554462i
\(990\) 0.473135 + 0.262304i 0.0150372 + 0.00833658i
\(991\) 45.9481i 1.45959i −0.683666 0.729795i \(-0.739615\pi\)
0.683666 0.729795i \(-0.260385\pi\)
\(992\) −5.44918 + 1.14299i −0.173012 + 0.0362900i
\(993\) −24.9340 + 24.9340i −0.791257 + 0.791257i
\(994\) 0.216393i 0.00686358i
\(995\) 15.2373 4.36811i 0.483054 0.138478i
\(996\) −0.963745 −0.0305374
\(997\) 43.3516 + 43.3516i 1.37296 + 1.37296i 0.856025 + 0.516935i \(0.172927\pi\)
0.516935 + 0.856025i \(0.327073\pi\)
\(998\) 21.7446 + 21.7446i 0.688313 + 0.688313i
\(999\) 6.42726i 0.203350i
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 930.2.k.b.247.2 yes 32
5.3 odd 4 930.2.k.a.433.2 yes 32
31.30 odd 2 930.2.k.a.247.2 32
155.123 even 4 inner 930.2.k.b.433.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.k.a.247.2 32 31.30 odd 2
930.2.k.a.433.2 yes 32 5.3 odd 4
930.2.k.b.247.2 yes 32 1.1 even 1 trivial
930.2.k.b.433.2 yes 32 155.123 even 4 inner