Properties

Label 441.2.f.h.148.4
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(148,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("441.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.4
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.649936 - 1.12572i) q^{2} +(0.0514049 + 1.73129i) q^{3} +(0.155166 - 0.268756i) q^{4} +(-1.76292 + 3.05347i) q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(-2.99472 + 0.177994i) q^{9} +O(q^{10})\) \(q+(-0.649936 - 1.12572i) q^{2} +(0.0514049 + 1.73129i) q^{3} +(0.155166 - 0.268756i) q^{4} +(-1.76292 + 3.05347i) q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(-2.99472 + 0.177994i) q^{9} +4.58314 q^{10} +(-0.589267 - 1.02064i) q^{11} +(0.473270 + 0.254822i) q^{12} +(1.61030 - 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} +(1.64151 + 2.84319i) q^{16} -4.90317 q^{17} +(2.14674 + 3.25553i) q^{18} -6.86637 q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(2.14994 - 3.72380i) q^{23} +(-0.154376 - 5.19929i) q^{24} +(-3.71578 - 6.43592i) q^{25} -4.18637 q^{26} +(-0.462101 - 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(0.235596 + 7.93474i) q^{30} +(0.960401 - 1.66346i) q^{31} +(-0.869378 + 1.50581i) q^{32} +(1.73673 - 1.07266i) q^{33} +(3.18675 + 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} -9.76457 q^{37} +(4.46270 + 7.72962i) q^{38} +(4.91156 + 2.64452i) q^{39} +(5.29429 - 9.16998i) q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} -0.365738 q^{44} +(4.73595 - 9.45806i) q^{45} -5.58928 q^{46} +(-0.316609 - 0.548383i) q^{47} +(-4.83799 + 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(-0.252047 - 8.48880i) q^{51} +(-0.499729 - 0.865557i) q^{52} -2.22756 q^{53} +(-5.52591 + 3.88398i) q^{54} +4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} +(1.76965 - 3.06512i) q^{58} +(-4.10652 + 7.11270i) q^{59} +(-1.61243 + 0.995884i) q^{60} +(4.82958 + 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(5.67767 + 9.83402i) q^{65} +(-2.33628 - 1.25792i) q^{66} +(-2.66651 + 4.61852i) q^{67} +(-0.760807 + 1.31776i) q^{68} +(6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(8.99354 - 0.534539i) q^{72} +1.03807 q^{73} +(6.34635 + 10.9922i) q^{74} +(10.9514 - 6.76392i) q^{75} +(-1.06543 + 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +(-0.502039 - 0.869557i) q^{79} -11.5754 q^{80} +(8.93664 - 1.06608i) q^{81} +8.64864 q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(6.28411 - 10.8844i) q^{86} +(-4.01243 + 2.47820i) q^{87} +(1.76965 + 3.06512i) q^{88} +12.0429 q^{89} +(-13.7252 + 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(2.92930 + 1.57722i) q^{93} +(-0.411551 + 0.712828i) q^{94} +(12.1049 - 20.9662i) q^{95} +(-2.65168 - 1.42774i) q^{96} +(-5.46454 - 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.649936 1.12572i −0.459574 0.796006i 0.539364 0.842073i \(-0.318665\pi\)
−0.998938 + 0.0460668i \(0.985331\pi\)
\(3\) 0.0514049 + 1.73129i 0.0296787 + 0.999559i
\(4\) 0.155166 0.268756i 0.0775831 0.134378i
\(5\) −1.76292 + 3.05347i −0.788402 + 1.36555i 0.138543 + 0.990356i \(0.455758\pi\)
−0.926945 + 0.375196i \(0.877575\pi\)
\(6\) 1.91554 1.18309i 0.782016 0.482996i
\(7\) 0 0
\(8\) −3.00314 −1.06177
\(9\) −2.99472 + 0.177994i −0.998238 + 0.0593312i
\(10\) 4.58314 1.44932
\(11\) −0.589267 1.02064i −0.177671 0.307735i 0.763412 0.645912i \(-0.223523\pi\)
−0.941082 + 0.338178i \(0.890190\pi\)
\(12\) 0.473270 + 0.254822i 0.136621 + 0.0735608i
\(13\) 1.61030 2.78913i 0.446618 0.773564i −0.551546 0.834145i \(-0.685962\pi\)
0.998163 + 0.0605803i \(0.0192951\pi\)
\(14\) 0 0
\(15\) −5.37706 2.89516i −1.38835 0.747527i
\(16\) 1.64151 + 2.84319i 0.410379 + 0.710797i
\(17\) −4.90317 −1.18919 −0.594597 0.804024i \(-0.702688\pi\)
−0.594597 + 0.804024i \(0.702688\pi\)
\(18\) 2.14674 + 3.25553i 0.505993 + 0.767336i
\(19\) −6.86637 −1.57525 −0.787627 0.616153i \(-0.788690\pi\)
−0.787627 + 0.616153i \(0.788690\pi\)
\(20\) 0.547092 + 0.947591i 0.122333 + 0.211888i
\(21\) 0 0
\(22\) −0.765972 + 1.32670i −0.163306 + 0.282854i
\(23\) 2.14994 3.72380i 0.448293 0.776466i −0.549982 0.835176i \(-0.685366\pi\)
0.998275 + 0.0587106i \(0.0186989\pi\)
\(24\) −0.154376 5.19929i −0.0315119 1.06130i
\(25\) −3.71578 6.43592i −0.743156 1.28718i
\(26\) −4.18637 −0.821016
\(27\) −0.462101 5.17556i −0.0889314 0.996038i
\(28\) 0 0
\(29\) 1.36140 + 2.35802i 0.252806 + 0.437873i 0.964297 0.264822i \(-0.0853131\pi\)
−0.711491 + 0.702695i \(0.751980\pi\)
\(30\) 0.235596 + 7.93474i 0.0430138 + 1.44868i
\(31\) 0.960401 1.66346i 0.172493 0.298767i −0.766798 0.641889i \(-0.778151\pi\)
0.939291 + 0.343122i \(0.111484\pi\)
\(32\) −0.869378 + 1.50581i −0.153686 + 0.266192i
\(33\) 1.73673 1.07266i 0.302326 0.186726i
\(34\) 3.18675 + 5.51961i 0.546523 + 0.946606i
\(35\) 0 0
\(36\) −0.416842 + 0.832466i −0.0694737 + 0.138744i
\(37\) −9.76457 −1.60529 −0.802643 0.596460i \(-0.796573\pi\)
−0.802643 + 0.596460i \(0.796573\pi\)
\(38\) 4.46270 + 7.72962i 0.723946 + 1.25391i
\(39\) 4.91156 + 2.64452i 0.786479 + 0.423462i
\(40\) 5.29429 9.16998i 0.837101 1.44990i
\(41\) −3.32673 + 5.76206i −0.519547 + 0.899883i 0.480194 + 0.877162i \(0.340566\pi\)
−0.999742 + 0.0227205i \(0.992767\pi\)
\(42\) 0 0
\(43\) 4.83441 + 8.37344i 0.737240 + 1.27694i 0.953734 + 0.300653i \(0.0972047\pi\)
−0.216493 + 0.976284i \(0.569462\pi\)
\(44\) −0.365738 −0.0551370
\(45\) 4.73595 9.45806i 0.705993 1.40992i
\(46\) −5.58928 −0.824095
\(47\) −0.316609 0.548383i −0.0461822 0.0799899i 0.842010 0.539461i \(-0.181372\pi\)
−0.888192 + 0.459472i \(0.848039\pi\)
\(48\) −4.83799 + 2.98809i −0.698304 + 0.431293i
\(49\) 0 0
\(50\) −4.83004 + 8.36587i −0.683071 + 1.18311i
\(51\) −0.252047 8.48880i −0.0352937 1.18867i
\(52\) −0.499729 0.865557i −0.0693000 0.120031i
\(53\) −2.22756 −0.305978 −0.152989 0.988228i \(-0.548890\pi\)
−0.152989 + 0.988228i \(0.548890\pi\)
\(54\) −5.52591 + 3.88398i −0.751981 + 0.528543i
\(55\) 4.15533 0.560304
\(56\) 0 0
\(57\) −0.352965 11.8877i −0.0467514 1.57456i
\(58\) 1.76965 3.06512i 0.232366 0.402471i
\(59\) −4.10652 + 7.11270i −0.534623 + 0.925995i 0.464558 + 0.885543i \(0.346213\pi\)
−0.999181 + 0.0404521i \(0.987120\pi\)
\(60\) −1.61243 + 0.995884i −0.208164 + 0.128568i
\(61\) 4.82958 + 8.36508i 0.618364 + 1.07104i 0.989784 + 0.142573i \(0.0455376\pi\)
−0.371420 + 0.928465i \(0.621129\pi\)
\(62\) −2.49680 −0.317093
\(63\) 0 0
\(64\) 8.82622 1.10328
\(65\) 5.67767 + 9.83402i 0.704229 + 1.21976i
\(66\) −2.33628 1.25792i −0.287576 0.154839i
\(67\) −2.66651 + 4.61852i −0.325766 + 0.564242i −0.981667 0.190604i \(-0.938955\pi\)
0.655901 + 0.754847i \(0.272289\pi\)
\(68\) −0.760807 + 1.31776i −0.0922614 + 0.159801i
\(69\) 6.55748 + 3.53074i 0.789428 + 0.425051i
\(70\) 0 0
\(71\) −3.27719 −0.388931 −0.194466 0.980909i \(-0.562297\pi\)
−0.194466 + 0.980909i \(0.562297\pi\)
\(72\) 8.99354 0.534539i 1.05990 0.0629960i
\(73\) 1.03807 0.121497 0.0607486 0.998153i \(-0.480651\pi\)
0.0607486 + 0.998153i \(0.480651\pi\)
\(74\) 6.34635 + 10.9922i 0.737748 + 1.27782i
\(75\) 10.9514 6.76392i 1.26456 0.781031i
\(76\) −1.06543 + 1.84538i −0.122213 + 0.211679i
\(77\) 0 0
\(78\) −0.215200 7.24782i −0.0243666 0.820654i
\(79\) −0.502039 0.869557i −0.0564838 0.0978328i 0.836401 0.548118i \(-0.184656\pi\)
−0.892885 + 0.450285i \(0.851322\pi\)
\(80\) −11.5754 −1.29417
\(81\) 8.93664 1.06608i 0.992960 0.118453i
\(82\) 8.64864 0.955082
\(83\) −3.65598 6.33234i −0.401296 0.695064i 0.592587 0.805506i \(-0.298107\pi\)
−0.993883 + 0.110442i \(0.964773\pi\)
\(84\) 0 0
\(85\) 8.64391 14.9717i 0.937563 1.62391i
\(86\) 6.28411 10.8844i 0.677633 1.17369i
\(87\) −4.01243 + 2.47820i −0.430177 + 0.265690i
\(88\) 1.76965 + 3.06512i 0.188645 + 0.326743i
\(89\) 12.0429 1.27654 0.638271 0.769812i \(-0.279650\pi\)
0.638271 + 0.769812i \(0.279650\pi\)
\(90\) −13.7252 + 0.815770i −1.44676 + 0.0859897i
\(91\) 0 0
\(92\) −0.667195 1.15562i −0.0695599 0.120481i
\(93\) 2.92930 + 1.57722i 0.303755 + 0.163550i
\(94\) −0.411551 + 0.712828i −0.0424483 + 0.0735226i
\(95\) 12.1049 20.9662i 1.24193 2.15109i
\(96\) −2.65168 1.42774i −0.270636 0.145718i
\(97\) −5.46454 9.46487i −0.554840 0.961012i −0.997916 0.0645275i \(-0.979446\pi\)
0.443076 0.896484i \(-0.353887\pi\)
\(98\) 0 0
\(99\) 1.94636 + 2.95164i 0.195616 + 0.296651i
\(100\) −2.30626 −0.230626
\(101\) 0.797546 + 1.38139i 0.0793588 + 0.137453i 0.902973 0.429696i \(-0.141379\pi\)
−0.823615 + 0.567150i \(0.808046\pi\)
\(102\) −9.39222 + 5.80092i −0.929969 + 0.574376i
\(103\) −1.16778 + 2.02265i −0.115065 + 0.199298i −0.917806 0.397030i \(-0.870041\pi\)
0.802741 + 0.596328i \(0.203374\pi\)
\(104\) −4.83596 + 8.37613i −0.474205 + 0.821347i
\(105\) 0 0
\(106\) 1.44777 + 2.50761i 0.140620 + 0.243561i
\(107\) −2.22362 −0.214966 −0.107483 0.994207i \(-0.534279\pi\)
−0.107483 + 0.994207i \(0.534279\pi\)
\(108\) −1.46267 0.678881i −0.140745 0.0653253i
\(109\) −0.919564 −0.0880782 −0.0440391 0.999030i \(-0.514023\pi\)
−0.0440391 + 0.999030i \(0.514023\pi\)
\(110\) −2.70070 4.67774i −0.257501 0.446005i
\(111\) −0.501947 16.9053i −0.0476427 1.60458i
\(112\) 0 0
\(113\) 1.19327 2.06681i 0.112254 0.194429i −0.804425 0.594054i \(-0.797526\pi\)
0.916679 + 0.399625i \(0.130860\pi\)
\(114\) −13.1528 + 8.12356i −1.23187 + 0.760841i
\(115\) 7.58033 + 13.1295i 0.706870 + 1.22433i
\(116\) 0.844976 0.0784540
\(117\) −4.32595 + 8.63926i −0.399934 + 0.798700i
\(118\) 10.6759 0.982796
\(119\) 0 0
\(120\) 16.1480 + 8.69456i 1.47411 + 0.793701i
\(121\) 4.80553 8.32342i 0.436866 0.756674i
\(122\) 6.27783 10.8735i 0.568368 0.984443i
\(123\) −10.1468 5.46332i −0.914906 0.492611i
\(124\) −0.298044 0.516227i −0.0267651 0.0463585i
\(125\) 8.57330 0.766819
\(126\) 0 0
\(127\) −3.04170 −0.269907 −0.134954 0.990852i \(-0.543089\pi\)
−0.134954 + 0.990852i \(0.543089\pi\)
\(128\) −3.99772 6.92426i −0.353352 0.612024i
\(129\) −14.2483 + 8.80019i −1.25449 + 0.774813i
\(130\) 7.38025 12.7830i 0.647291 1.12114i
\(131\) 1.63088 2.82476i 0.142490 0.246801i −0.785943 0.618298i \(-0.787822\pi\)
0.928434 + 0.371498i \(0.121156\pi\)
\(132\) −0.0188007 0.633197i −0.00163639 0.0551127i
\(133\) 0 0
\(134\) 6.93223 0.598854
\(135\) 16.6181 + 7.71310i 1.43026 + 0.663838i
\(136\) 14.7249 1.26265
\(137\) −10.4669 18.1292i −0.894246 1.54888i −0.834734 0.550653i \(-0.814379\pi\)
−0.0595120 0.998228i \(-0.518954\pi\)
\(138\) −0.287317 9.67666i −0.0244580 0.823732i
\(139\) −8.31195 + 14.3967i −0.705010 + 1.22111i 0.261677 + 0.965155i \(0.415724\pi\)
−0.966688 + 0.255958i \(0.917609\pi\)
\(140\) 0 0
\(141\) 0.933134 0.576331i 0.0785840 0.0485358i
\(142\) 2.12997 + 3.68921i 0.178743 + 0.309592i
\(143\) −3.79559 −0.317404
\(144\) −5.42194 8.22235i −0.451828 0.685196i
\(145\) −9.60019 −0.797252
\(146\) −0.674681 1.16858i −0.0558370 0.0967124i
\(147\) 0 0
\(148\) −1.51513 + 2.62429i −0.124543 + 0.215715i
\(149\) −0.564221 + 0.977260i −0.0462228 + 0.0800602i −0.888211 0.459435i \(-0.848052\pi\)
0.841988 + 0.539496i \(0.181385\pi\)
\(150\) −14.7320 7.93214i −1.20286 0.647657i
\(151\) 9.81476 + 16.9997i 0.798714 + 1.38341i 0.920454 + 0.390851i \(0.127819\pi\)
−0.121740 + 0.992562i \(0.538847\pi\)
\(152\) 20.6206 1.67256
\(153\) 14.6836 0.872733i 1.18710 0.0705563i
\(154\) 0 0
\(155\) 3.38622 + 5.86511i 0.271988 + 0.471097i
\(156\) 1.47284 0.909669i 0.117921 0.0728318i
\(157\) −4.66619 + 8.08207i −0.372402 + 0.645020i −0.989935 0.141526i \(-0.954799\pi\)
0.617532 + 0.786545i \(0.288132\pi\)
\(158\) −0.652586 + 1.13031i −0.0519170 + 0.0899228i
\(159\) −0.114507 3.85654i −0.00908103 0.305844i
\(160\) −3.06529 5.30924i −0.242332 0.419732i
\(161\) 0 0
\(162\) −7.00835 9.36729i −0.550628 0.735964i
\(163\) 16.9011 1.32380 0.661899 0.749593i \(-0.269751\pi\)
0.661899 + 0.749593i \(0.269751\pi\)
\(164\) 1.03239 + 1.78815i 0.0806162 + 0.139631i
\(165\) 0.213604 + 7.19407i 0.0166291 + 0.560057i
\(166\) −4.75230 + 8.23123i −0.368850 + 0.638867i
\(167\) 2.57319 4.45689i 0.199119 0.344885i −0.749124 0.662430i \(-0.769525\pi\)
0.948243 + 0.317545i \(0.102859\pi\)
\(168\) 0 0
\(169\) 1.31385 + 2.27566i 0.101066 + 0.175051i
\(170\) −22.4719 −1.72352
\(171\) 20.5628 1.22217i 1.57248 0.0934616i
\(172\) 3.00055 0.228790
\(173\) −4.86834 8.43222i −0.370133 0.641090i 0.619453 0.785034i \(-0.287355\pi\)
−0.989586 + 0.143945i \(0.954021\pi\)
\(174\) 5.39758 + 2.90621i 0.409190 + 0.220319i
\(175\) 0 0
\(176\) 1.93458 3.35079i 0.145825 0.252576i
\(177\) −12.5252 6.74394i −0.941454 0.506905i
\(178\) −7.82710 13.5569i −0.586666 1.01613i
\(179\) 1.37598 0.102846 0.0514228 0.998677i \(-0.483624\pi\)
0.0514228 + 0.998677i \(0.483624\pi\)
\(180\) −1.80705 2.74039i −0.134689 0.204256i
\(181\) −5.66560 −0.421120 −0.210560 0.977581i \(-0.567529\pi\)
−0.210560 + 0.977581i \(0.567529\pi\)
\(182\) 0 0
\(183\) −14.2341 + 8.79140i −1.05221 + 0.649879i
\(184\) −6.45655 + 11.1831i −0.475983 + 0.824427i
\(185\) 17.2142 29.8158i 1.26561 2.19210i
\(186\) −0.128348 4.32267i −0.00941091 0.316954i
\(187\) 2.88928 + 5.00438i 0.211285 + 0.365956i
\(188\) −0.196508 −0.0143318
\(189\) 0 0
\(190\) −31.4696 −2.28304
\(191\) 12.5065 + 21.6618i 0.904936 + 1.56740i 0.821003 + 0.570925i \(0.193415\pi\)
0.0839339 + 0.996471i \(0.473252\pi\)
\(192\) 0.453711 + 15.2807i 0.0327438 + 1.10279i
\(193\) −8.76688 + 15.1847i −0.631054 + 1.09302i 0.356282 + 0.934378i \(0.384044\pi\)
−0.987337 + 0.158640i \(0.949289\pi\)
\(194\) −7.10321 + 12.3031i −0.509981 + 0.883312i
\(195\) −16.7337 + 10.3352i −1.19832 + 0.740119i
\(196\) 0 0
\(197\) −19.7540 −1.40741 −0.703707 0.710490i \(-0.748473\pi\)
−0.703707 + 0.710490i \(0.748473\pi\)
\(198\) 2.05772 4.10943i 0.146236 0.292045i
\(199\) −19.0222 −1.34845 −0.674224 0.738527i \(-0.735522\pi\)
−0.674224 + 0.738527i \(0.735522\pi\)
\(200\) 11.1590 + 19.3279i 0.789060 + 1.36669i
\(201\) −8.13307 4.37907i −0.573662 0.308876i
\(202\) 1.03671 1.79563i 0.0729425 0.126340i
\(203\) 0 0
\(204\) −2.32053 1.24944i −0.162469 0.0874781i
\(205\) −11.7295 20.3161i −0.819225 1.41894i
\(206\) 3.03593 0.211523
\(207\) −5.77563 + 11.5344i −0.401434 + 0.801696i
\(208\) 10.5733 0.733129
\(209\) 4.04613 + 7.00810i 0.279876 + 0.484760i
\(210\) 0 0
\(211\) 3.71809 6.43993i 0.255964 0.443343i −0.709193 0.705015i \(-0.750940\pi\)
0.965157 + 0.261672i \(0.0842738\pi\)
\(212\) −0.345642 + 0.598669i −0.0237388 + 0.0411168i
\(213\) −0.168464 5.67376i −0.0115430 0.388760i
\(214\) 1.44521 + 2.50318i 0.0987927 + 0.171114i
\(215\) −34.0907 −2.32497
\(216\) 1.38775 + 15.5429i 0.0944246 + 1.05756i
\(217\) 0 0
\(218\) 0.597658 + 1.03517i 0.0404785 + 0.0701108i
\(219\) 0.0533620 + 1.79720i 0.00360587 + 0.121444i
\(220\) 0.644767 1.11677i 0.0434702 0.0752925i
\(221\) −7.89559 + 13.6756i −0.531115 + 0.919918i
\(222\) −18.7044 + 11.5524i −1.25536 + 0.775347i
\(223\) 1.64565 + 2.85034i 0.110201 + 0.190873i 0.915851 0.401518i \(-0.131517\pi\)
−0.805650 + 0.592391i \(0.798184\pi\)
\(224\) 0 0
\(225\) 12.2733 + 18.6124i 0.818217 + 1.24082i
\(226\) −3.10221 −0.206356
\(227\) 9.00847 + 15.6031i 0.597913 + 1.03562i 0.993129 + 0.117028i \(0.0373366\pi\)
−0.395215 + 0.918589i \(0.629330\pi\)
\(228\) −3.24965 1.74970i −0.215213 0.115877i
\(229\) −2.12746 + 3.68486i −0.140586 + 0.243503i −0.927718 0.373283i \(-0.878232\pi\)
0.787131 + 0.616785i \(0.211565\pi\)
\(230\) 9.85347 17.0667i 0.649718 1.12535i
\(231\) 0 0
\(232\) −4.08848 7.08146i −0.268422 0.464920i
\(233\) −14.7055 −0.963390 −0.481695 0.876339i \(-0.659979\pi\)
−0.481695 + 0.876339i \(0.659979\pi\)
\(234\) 12.5370 0.745148i 0.819569 0.0487118i
\(235\) 2.23263 0.145641
\(236\) 1.27439 + 2.20730i 0.0829555 + 0.143683i
\(237\) 1.47965 0.913873i 0.0961133 0.0593624i
\(238\) 0 0
\(239\) 7.08187 12.2662i 0.458088 0.793432i −0.540772 0.841169i \(-0.681868\pi\)
0.998860 + 0.0477377i \(0.0152011\pi\)
\(240\) −0.595035 20.0404i −0.0384093 1.29360i
\(241\) −3.96752 6.87194i −0.255570 0.442661i 0.709480 0.704726i \(-0.248930\pi\)
−0.965050 + 0.262065i \(0.915597\pi\)
\(242\) −12.4931 −0.803090
\(243\) 2.30508 + 15.4171i 0.147871 + 0.989007i
\(244\) 2.99755 0.191899
\(245\) 0 0
\(246\) 0.444583 + 14.9733i 0.0283456 + 0.954662i
\(247\) −11.0569 + 19.1512i −0.703536 + 1.21856i
\(248\) −2.88422 + 4.99561i −0.183148 + 0.317221i
\(249\) 10.7752 6.65506i 0.682848 0.421747i
\(250\) −5.57210 9.65115i −0.352410 0.610392i
\(251\) 8.05097 0.508173 0.254087 0.967181i \(-0.418225\pi\)
0.254087 + 0.967181i \(0.418225\pi\)
\(252\) 0 0
\(253\) −5.06755 −0.318594
\(254\) 1.97691 + 3.42411i 0.124042 + 0.214848i
\(255\) 26.3646 + 14.1955i 1.65102 + 0.888955i
\(256\) 3.62969 6.28681i 0.226856 0.392926i
\(257\) 8.77687 15.2020i 0.547486 0.948273i −0.450960 0.892544i \(-0.648918\pi\)
0.998446 0.0557293i \(-0.0177484\pi\)
\(258\) 19.1671 + 10.3201i 1.19329 + 0.642501i
\(259\) 0 0
\(260\) 3.52393 0.218545
\(261\) −4.49673 6.81928i −0.278340 0.422103i
\(262\) −4.23986 −0.261940
\(263\) 11.6743 + 20.2205i 0.719867 + 1.24685i 0.961052 + 0.276367i \(0.0891306\pi\)
−0.241185 + 0.970479i \(0.577536\pi\)
\(264\) −5.21564 + 3.22134i −0.321001 + 0.198260i
\(265\) 3.92701 6.80177i 0.241234 0.417830i
\(266\) 0 0
\(267\) 0.619063 + 20.8497i 0.0378861 + 1.27598i
\(268\) 0.827504 + 1.43328i 0.0505478 + 0.0875514i
\(269\) 0.538488 0.0328322 0.0164161 0.999865i \(-0.494774\pi\)
0.0164161 + 0.999865i \(0.494774\pi\)
\(270\) −2.11788 23.7204i −0.128890 1.44357i
\(271\) −14.4150 −0.875648 −0.437824 0.899061i \(-0.644251\pi\)
−0.437824 + 0.899061i \(0.644251\pi\)
\(272\) −8.04863 13.9406i −0.488020 0.845275i
\(273\) 0 0
\(274\) −13.6056 + 23.5656i −0.821945 + 1.42365i
\(275\) −4.37918 + 7.58495i −0.264074 + 0.457390i
\(276\) 1.96641 1.21451i 0.118364 0.0731050i
\(277\) −10.9533 18.9717i −0.658121 1.13990i −0.981101 0.193494i \(-0.938018\pi\)
0.322980 0.946406i \(-0.395315\pi\)
\(278\) 21.6089 1.29602
\(279\) −2.58004 + 5.15254i −0.154463 + 0.308475i
\(280\) 0 0
\(281\) −0.776622 1.34515i −0.0463294 0.0802449i 0.841931 0.539586i \(-0.181419\pi\)
−0.888260 + 0.459341i \(0.848086\pi\)
\(282\) −1.25527 0.675871i −0.0747500 0.0402475i
\(283\) 1.32571 2.29619i 0.0788051 0.136495i −0.823930 0.566692i \(-0.808223\pi\)
0.902735 + 0.430198i \(0.141556\pi\)
\(284\) −0.508510 + 0.880765i −0.0301745 + 0.0522638i
\(285\) 36.9208 + 19.8792i 2.18700 + 1.17754i
\(286\) 2.46689 + 4.27279i 0.145870 + 0.252655i
\(287\) 0 0
\(288\) 2.33552 4.66421i 0.137622 0.274841i
\(289\) 7.04111 0.414183
\(290\) 6.23951 + 10.8071i 0.366396 + 0.634617i
\(291\) 16.1055 9.94724i 0.944121 0.583118i
\(292\) 0.161074 0.278988i 0.00942613 0.0163265i
\(293\) −5.19314 + 8.99478i −0.303386 + 0.525481i −0.976901 0.213694i \(-0.931451\pi\)
0.673514 + 0.739174i \(0.264784\pi\)
\(294\) 0 0
\(295\) −14.4789 25.0783i −0.842996 1.46011i
\(296\) 29.3243 1.70444
\(297\) −5.01009 + 3.52143i −0.290715 + 0.204334i
\(298\) 1.46683 0.0849712
\(299\) −6.92409 11.9929i −0.400431 0.693566i
\(300\) −0.118553 3.99279i −0.00684466 0.230524i
\(301\) 0 0
\(302\) 12.7579 22.0974i 0.734137 1.27156i
\(303\) −2.35059 + 1.45179i −0.135038 + 0.0834033i
\(304\) −11.2712 19.5224i −0.646450 1.11968i
\(305\) −34.0567 −1.95008
\(306\) −10.5259 15.9624i −0.601723 0.912512i
\(307\) −10.6425 −0.607400 −0.303700 0.952768i \(-0.598222\pi\)
−0.303700 + 0.952768i \(0.598222\pi\)
\(308\) 0 0
\(309\) −3.56182 1.91779i −0.202625 0.109099i
\(310\) 4.40165 7.62389i 0.249997 0.433008i
\(311\) 6.85479 11.8728i 0.388699 0.673247i −0.603576 0.797306i \(-0.706258\pi\)
0.992275 + 0.124059i \(0.0395912\pi\)
\(312\) −14.7501 7.94186i −0.835059 0.449619i
\(313\) −10.6090 18.3752i −0.599653 1.03863i −0.992872 0.119185i \(-0.961972\pi\)
0.393219 0.919445i \(-0.371362\pi\)
\(314\) 12.1309 0.684586
\(315\) 0 0
\(316\) −0.311598 −0.0175288
\(317\) −1.78521 3.09208i −0.100268 0.173669i 0.811527 0.584315i \(-0.198637\pi\)
−0.911795 + 0.410646i \(0.865303\pi\)
\(318\) −4.26697 + 2.63541i −0.239280 + 0.147786i
\(319\) 1.60446 2.77901i 0.0898326 0.155595i
\(320\) −15.5599 + 26.9506i −0.869826 + 1.50658i
\(321\) −0.114305 3.84973i −0.00637989 0.214871i
\(322\) 0 0
\(323\) 33.6670 1.87328
\(324\) 1.10015 2.56719i 0.0611194 0.142622i
\(325\) −23.9341 −1.32763
\(326\) −10.9846 19.0260i −0.608383 1.05375i
\(327\) −0.0472701 1.59203i −0.00261404 0.0880394i
\(328\) 9.99062 17.3043i 0.551639 0.955468i
\(329\) 0 0
\(330\) 7.95969 4.91614i 0.438167 0.270625i
\(331\) 11.9728 + 20.7375i 0.658085 + 1.13984i 0.981111 + 0.193446i \(0.0619666\pi\)
−0.323026 + 0.946390i \(0.604700\pi\)
\(332\) −2.26914 −0.124535
\(333\) 29.2421 1.73803i 1.60246 0.0952435i
\(334\) −6.68963 −0.366040
\(335\) −9.40168 16.2842i −0.513669 0.889700i
\(336\) 0 0
\(337\) −13.7468 + 23.8102i −0.748838 + 1.29703i 0.199542 + 0.979889i \(0.436055\pi\)
−0.948380 + 0.317137i \(0.897279\pi\)
\(338\) 1.70784 2.95806i 0.0928942 0.160897i
\(339\) 3.63959 + 1.95966i 0.197675 + 0.106434i
\(340\) −2.68249 4.64620i −0.145478 0.251976i
\(341\) −2.26373 −0.122588
\(342\) −14.7403 22.3537i −0.797066 1.20875i
\(343\) 0 0
\(344\) −14.5184 25.1466i −0.782779 1.35581i
\(345\) −22.3413 + 13.7987i −1.20282 + 0.742895i
\(346\) −6.32822 + 10.9608i −0.340207 + 0.589256i
\(347\) 2.56412 4.44119i 0.137649 0.238416i −0.788957 0.614448i \(-0.789379\pi\)
0.926606 + 0.376033i \(0.122712\pi\)
\(348\) 0.0434359 + 1.46290i 0.00232841 + 0.0784195i
\(349\) −7.56980 13.1113i −0.405202 0.701830i 0.589143 0.808029i \(-0.299465\pi\)
−0.994345 + 0.106198i \(0.966132\pi\)
\(350\) 0 0
\(351\) −15.1794 7.04537i −0.810218 0.376054i
\(352\) 2.04918 0.109222
\(353\) −16.4878 28.5578i −0.877559 1.51998i −0.854011 0.520254i \(-0.825837\pi\)
−0.0235477 0.999723i \(-0.507496\pi\)
\(354\) 0.548794 + 18.4831i 0.0291681 + 0.982363i
\(355\) 5.77743 10.0068i 0.306634 0.531106i
\(356\) 1.86865 3.23659i 0.0990381 0.171539i
\(357\) 0 0
\(358\) −0.894299 1.54897i −0.0472651 0.0818656i
\(359\) −24.0355 −1.26855 −0.634274 0.773109i \(-0.718701\pi\)
−0.634274 + 0.773109i \(0.718701\pi\)
\(360\) −14.2227 + 28.4038i −0.749602 + 1.49701i
\(361\) 28.1470 1.48142
\(362\) 3.68227 + 6.37789i 0.193536 + 0.335214i
\(363\) 14.6573 + 7.89189i 0.769307 + 0.414217i
\(364\) 0 0
\(365\) −1.83004 + 3.16972i −0.0957886 + 0.165911i
\(366\) 19.1479 + 10.3098i 1.00088 + 0.538901i
\(367\) 1.32751 + 2.29931i 0.0692952 + 0.120023i 0.898591 0.438787i \(-0.144592\pi\)
−0.829296 + 0.558810i \(0.811258\pi\)
\(368\) 14.1166 0.735879
\(369\) 8.93699 17.8479i 0.465241 0.929123i
\(370\) −44.7524 −2.32657
\(371\) 0 0
\(372\) 0.878416 0.542536i 0.0455438 0.0281292i
\(373\) 15.9592 27.6421i 0.826334 1.43125i −0.0745621 0.997216i \(-0.523756\pi\)
0.900896 0.434036i \(-0.142911\pi\)
\(374\) 3.75569 6.50505i 0.194202 0.336368i
\(375\) 0.440710 + 14.8428i 0.0227582 + 0.766481i
\(376\) 0.950821 + 1.64687i 0.0490348 + 0.0849308i
\(377\) 8.76909 0.451631
\(378\) 0 0
\(379\) 30.2681 1.55477 0.777384 0.629027i \(-0.216546\pi\)
0.777384 + 0.629027i \(0.216546\pi\)
\(380\) −3.75653 6.50651i −0.192706 0.333777i
\(381\) −0.156358 5.26606i −0.00801048 0.269788i
\(382\) 16.2568 28.1576i 0.831771 1.44067i
\(383\) −0.866526 + 1.50087i −0.0442774 + 0.0766907i −0.887315 0.461164i \(-0.847432\pi\)
0.843037 + 0.537855i \(0.180765\pi\)
\(384\) 11.7824 7.27715i 0.601267 0.371360i
\(385\) 0 0
\(386\) 22.7917 1.16006
\(387\) −15.9681 24.2156i −0.811704 1.23095i
\(388\) −3.39165 −0.172185
\(389\) 5.54175 + 9.59859i 0.280978 + 0.486668i 0.971626 0.236523i \(-0.0760079\pi\)
−0.690648 + 0.723191i \(0.742675\pi\)
\(390\) 22.5104 + 12.1202i 1.13986 + 0.613731i
\(391\) −10.5415 + 18.2584i −0.533107 + 0.923368i
\(392\) 0 0
\(393\) 4.97431 + 2.67831i 0.250921 + 0.135103i
\(394\) 12.8388 + 22.2375i 0.646811 + 1.12031i
\(395\) 3.54022 0.178128
\(396\) 1.09528 0.0650989i 0.0550399 0.00327134i
\(397\) 25.3391 1.27173 0.635867 0.771799i \(-0.280643\pi\)
0.635867 + 0.771799i \(0.280643\pi\)
\(398\) 12.3632 + 21.4137i 0.619712 + 1.07337i
\(399\) 0 0
\(400\) 12.1990 21.1293i 0.609951 1.05647i
\(401\) 17.4122 30.1588i 0.869524 1.50606i 0.00704089 0.999975i \(-0.497759\pi\)
0.862483 0.506085i \(-0.168908\pi\)
\(402\) 0.356351 + 12.0017i 0.0177732 + 0.598590i
\(403\) −3.09307 5.35736i −0.154077 0.266869i
\(404\) 0.495009 0.0246276
\(405\) −12.4993 + 29.1672i −0.621097 + 1.44933i
\(406\) 0 0
\(407\) 5.75394 + 9.96612i 0.285212 + 0.494002i
\(408\) 0.756933 + 25.4930i 0.0374738 + 1.26209i
\(409\) 9.12308 15.8016i 0.451107 0.781341i −0.547348 0.836905i \(-0.684362\pi\)
0.998455 + 0.0555643i \(0.0176958\pi\)
\(410\) −15.2469 + 26.4083i −0.752989 + 1.30422i
\(411\) 30.8488 19.0531i 1.52166 0.939821i
\(412\) 0.362400 + 0.627695i 0.0178541 + 0.0309243i
\(413\) 0 0
\(414\) 16.7383 0.994856i 0.822643 0.0488945i
\(415\) 25.7808 1.26553
\(416\) 2.79992 + 4.84961i 0.137278 + 0.237772i
\(417\) −25.3521 13.6503i −1.24150 0.668459i
\(418\) 5.25945 9.10963i 0.257248 0.445567i
\(419\) −4.20719 + 7.28708i −0.205535 + 0.355997i −0.950303 0.311326i \(-0.899227\pi\)
0.744768 + 0.667323i \(0.232560\pi\)
\(420\) 0 0
\(421\) 0.144291 + 0.249919i 0.00703230 + 0.0121803i 0.869520 0.493897i \(-0.164428\pi\)
−0.862488 + 0.506078i \(0.831095\pi\)
\(422\) −9.66609 −0.470538
\(423\) 1.04576 + 1.58590i 0.0508467 + 0.0771090i
\(424\) 6.68966 0.324878
\(425\) 18.2191 + 31.5564i 0.883757 + 1.53071i
\(426\) −6.27759 + 3.87723i −0.304150 + 0.187852i
\(427\) 0 0
\(428\) −0.345031 + 0.597612i −0.0166777 + 0.0288866i
\(429\) −0.195112 6.57127i −0.00942011 0.317264i
\(430\) 22.1568 + 38.3767i 1.06849 + 1.85069i
\(431\) −13.4959 −0.650075 −0.325037 0.945701i \(-0.605377\pi\)
−0.325037 + 0.945701i \(0.605377\pi\)
\(432\) 13.9565 9.80960i 0.671485 0.471965i
\(433\) −4.85211 −0.233177 −0.116589 0.993180i \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(434\) 0 0
\(435\) −0.493497 16.6207i −0.0236614 0.796901i
\(436\) −0.142685 + 0.247138i −0.00683339 + 0.0118358i
\(437\) −14.7623 + 25.5690i −0.706174 + 1.22313i
\(438\) 1.98847 1.22814i 0.0950127 0.0586827i
\(439\) −1.27397 2.20657i −0.0608031 0.105314i 0.834022 0.551732i \(-0.186033\pi\)
−0.894825 + 0.446418i \(0.852699\pi\)
\(440\) −12.4790 −0.594914
\(441\) 0 0
\(442\) 20.5265 0.976347
\(443\) 0.322753 + 0.559025i 0.0153345 + 0.0265601i 0.873591 0.486661i \(-0.161785\pi\)
−0.858256 + 0.513221i \(0.828452\pi\)
\(444\) −4.62128 2.48823i −0.219316 0.118086i
\(445\) −21.2306 + 36.7725i −1.00643 + 1.74319i
\(446\) 2.13913 3.70508i 0.101291 0.175441i
\(447\) −1.72092 0.926593i −0.0813968 0.0438264i
\(448\) 0 0
\(449\) −5.22658 −0.246658 −0.123329 0.992366i \(-0.539357\pi\)
−0.123329 + 0.992366i \(0.539357\pi\)
\(450\) 12.9755 25.9131i 0.611672 1.22156i
\(451\) 7.84133 0.369234
\(452\) −0.370312 0.641399i −0.0174180 0.0301689i
\(453\) −28.9268 + 17.8660i −1.35910 + 0.839420i
\(454\) 11.7099 20.2821i 0.549571 0.951885i
\(455\) 0 0
\(456\) 1.06000 + 35.7003i 0.0496392 + 1.67182i
\(457\) 1.43037 + 2.47748i 0.0669101 + 0.115892i 0.897540 0.440934i \(-0.145353\pi\)
−0.830630 + 0.556825i \(0.812019\pi\)
\(458\) 5.53084 0.258439
\(459\) 2.26576 + 25.3767i 0.105757 + 1.18448i
\(460\) 4.70485 0.219365
\(461\) 1.82624 + 3.16314i 0.0850566 + 0.147322i 0.905415 0.424527i \(-0.139560\pi\)
−0.820359 + 0.571849i \(0.806226\pi\)
\(462\) 0 0
\(463\) −15.4052 + 26.6825i −0.715939 + 1.24004i 0.246657 + 0.969103i \(0.420668\pi\)
−0.962596 + 0.270940i \(0.912666\pi\)
\(464\) −4.46953 + 7.74145i −0.207493 + 0.359388i
\(465\) −9.98012 + 6.16402i −0.462817 + 0.285850i
\(466\) 9.55764 + 16.5543i 0.442749 + 0.766864i
\(467\) 20.5770 0.952191 0.476096 0.879393i \(-0.342052\pi\)
0.476096 + 0.879393i \(0.342052\pi\)
\(468\) 1.65061 + 2.50315i 0.0762995 + 0.115708i
\(469\) 0 0
\(470\) −1.45107 2.51332i −0.0669327 0.115931i
\(471\) −14.2323 7.66305i −0.655788 0.353095i
\(472\) 12.3324 21.3604i 0.567647 0.983193i
\(473\) 5.69752 9.86839i 0.261972 0.453749i
\(474\) −1.99044 1.07171i −0.0914240 0.0492253i
\(475\) 25.5139 + 44.1914i 1.17066 + 2.02764i
\(476\) 0 0
\(477\) 6.67090 0.396491i 0.305439 0.0181541i
\(478\) −18.4110 −0.842102
\(479\) −12.5916 21.8093i −0.575325 0.996492i −0.996006 0.0892833i \(-0.971542\pi\)
0.420682 0.907208i \(-0.361791\pi\)
\(480\) 9.03425 5.57982i 0.412355 0.254683i
\(481\) −15.7239 + 27.2346i −0.716949 + 1.24179i
\(482\) −5.15726 + 8.93264i −0.234907 + 0.406871i
\(483\) 0 0
\(484\) −1.49131 2.58303i −0.0677869 0.117410i
\(485\) 38.5342 1.74975
\(486\) 15.8572 12.6150i 0.719297 0.572228i
\(487\) −32.7615 −1.48456 −0.742282 0.670088i \(-0.766256\pi\)
−0.742282 + 0.670088i \(0.766256\pi\)
\(488\) −14.5039 25.1215i −0.656560 1.13720i
\(489\) 0.868801 + 29.2607i 0.0392886 + 1.32321i
\(490\) 0 0
\(491\) 1.76000 3.04841i 0.0794278 0.137573i −0.823575 0.567207i \(-0.808024\pi\)
0.903003 + 0.429634i \(0.141357\pi\)
\(492\) −3.04274 + 1.87929i −0.137177 + 0.0847248i
\(493\) −6.67520 11.5618i −0.300636 0.520716i
\(494\) 28.7452 1.29331
\(495\) −12.4440 + 0.739621i −0.559317 + 0.0332435i
\(496\) 6.30605 0.283150
\(497\) 0 0
\(498\) −14.4949 7.80448i −0.649533 0.349727i
\(499\) −7.82082 + 13.5461i −0.350108 + 0.606405i −0.986268 0.165152i \(-0.947188\pi\)
0.636160 + 0.771557i \(0.280522\pi\)
\(500\) 1.33029 2.30412i 0.0594922 0.103044i
\(501\) 7.84844 + 4.22582i 0.350642 + 0.188796i
\(502\) −5.23262 9.06316i −0.233543 0.404509i
\(503\) −36.5427 −1.62936 −0.814678 0.579913i \(-0.803086\pi\)
−0.814678 + 0.579913i \(0.803086\pi\)
\(504\) 0 0
\(505\) −5.62404 −0.250267
\(506\) 3.29358 + 5.70465i 0.146418 + 0.253603i
\(507\) −3.87228 + 2.39164i −0.171974 + 0.106216i
\(508\) −0.471969 + 0.817474i −0.0209402 + 0.0362696i
\(509\) 18.8229 32.6023i 0.834311 1.44507i −0.0602789 0.998182i \(-0.519199\pi\)
0.894590 0.446888i \(-0.147468\pi\)
\(510\) −1.15517 38.9054i −0.0511518 1.72276i
\(511\) 0 0
\(512\) −25.4272 −1.12373
\(513\) 3.17296 + 35.5373i 0.140089 + 1.56901i
\(514\) −22.8176 −1.00644
\(515\) −4.11740 7.13155i −0.181434 0.314254i
\(516\) 0.154243 + 5.19481i 0.00679017 + 0.228689i
\(517\) −0.373135 + 0.646289i −0.0164105 + 0.0284237i
\(518\) 0 0
\(519\) 14.3483 8.86196i 0.629822 0.388997i
\(520\) −17.0508 29.5329i −0.747728 1.29510i
\(521\) −14.3423 −0.628347 −0.314174 0.949366i \(-0.601727\pi\)
−0.314174 + 0.949366i \(0.601727\pi\)
\(522\) −4.75403 + 9.49416i −0.208078 + 0.415548i
\(523\) 10.4844 0.458453 0.229226 0.973373i \(-0.426380\pi\)
0.229226 + 0.973373i \(0.426380\pi\)
\(524\) −0.506114 0.876616i −0.0221097 0.0382951i
\(525\) 0 0
\(526\) 15.1751 26.2840i 0.661665 1.14604i
\(527\) −4.70901 + 8.15625i −0.205128 + 0.355292i
\(528\) 5.90063 + 3.17707i 0.256792 + 0.138264i
\(529\) 2.25555 + 3.90673i 0.0980674 + 0.169858i
\(530\) −10.2092 −0.443460
\(531\) 11.0318 22.0314i 0.478741 0.956083i
\(532\) 0 0
\(533\) 10.7141 + 18.5573i 0.464078 + 0.803807i
\(534\) 23.0686 14.2479i 0.998276 0.616565i
\(535\) 3.92007 6.78976i 0.169479 0.293547i
\(536\) 8.00788 13.8701i 0.345888 0.599095i
\(537\) 0.0707321 + 2.38222i 0.00305232 + 0.102800i
\(538\) −0.349983 0.606188i −0.0150888 0.0261346i
\(539\) 0 0
\(540\) 4.65150 3.26939i 0.200169 0.140692i
\(541\) −46.0922 −1.98166 −0.990830 0.135118i \(-0.956859\pi\)
−0.990830 + 0.135118i \(0.956859\pi\)
\(542\) 9.36882 + 16.2273i 0.402425 + 0.697021i
\(543\) −0.291240 9.80878i −0.0124983 0.420935i
\(544\) 4.26271 7.38323i 0.182762 0.316554i
\(545\) 1.62112 2.80786i 0.0694411 0.120275i
\(546\) 0 0
\(547\) −12.1793 21.0951i −0.520747 0.901961i −0.999709 0.0241250i \(-0.992320\pi\)
0.478962 0.877836i \(-0.341013\pi\)
\(548\) −6.49643 −0.277514
\(549\) −15.9521 24.1914i −0.680821 1.03246i
\(550\) 11.3847 0.485447
\(551\) −9.34790 16.1910i −0.398234 0.689761i
\(552\) −19.6930 10.6033i −0.838191 0.451306i
\(553\) 0 0
\(554\) −14.2379 + 24.6608i −0.604911 + 1.04774i
\(555\) 52.5046 + 28.2700i 2.22870 + 1.19999i
\(556\) 2.57947 + 4.46777i 0.109394 + 0.189476i
\(557\) 30.5775 1.29561 0.647806 0.761805i \(-0.275687\pi\)
0.647806 + 0.761805i \(0.275687\pi\)
\(558\) 7.47719 0.444414i 0.316535 0.0188135i
\(559\) 31.1394 1.31706
\(560\) 0 0
\(561\) −8.51550 + 5.25943i −0.359525 + 0.222053i
\(562\) −1.00951 + 1.74852i −0.0425836 + 0.0737570i
\(563\) −4.41357 + 7.64452i −0.186010 + 0.322178i −0.943916 0.330185i \(-0.892889\pi\)
0.757907 + 0.652363i \(0.226222\pi\)
\(564\) −0.0101015 0.340212i −0.000425350 0.0143255i
\(565\) 4.20730 + 7.28725i 0.177002 + 0.306577i
\(566\) −3.44650 −0.144867
\(567\) 0 0
\(568\) 9.84186 0.412955
\(569\) −3.56027 6.16658i −0.149254 0.258516i 0.781698 0.623658i \(-0.214354\pi\)
−0.930952 + 0.365141i \(0.881021\pi\)
\(570\) −1.61769 54.4829i −0.0677576 2.28204i
\(571\) −3.33181 + 5.77086i −0.139432 + 0.241503i −0.927282 0.374364i \(-0.877861\pi\)
0.787850 + 0.615867i \(0.211194\pi\)
\(572\) −0.588948 + 1.02009i −0.0246252 + 0.0426520i
\(573\) −36.8600 + 22.7658i −1.53985 + 0.951056i
\(574\) 0 0
\(575\) −31.9548 −1.33261
\(576\) −26.4320 + 1.57101i −1.10133 + 0.0654587i
\(577\) 7.91259 0.329405 0.164703 0.986343i \(-0.447334\pi\)
0.164703 + 0.986343i \(0.447334\pi\)
\(578\) −4.57627 7.92633i −0.190348 0.329692i
\(579\) −26.7397 14.3974i −1.11127 0.598337i
\(580\) −1.48963 + 2.58011i −0.0618533 + 0.107133i
\(581\) 0 0
\(582\) −21.6654 11.6653i −0.898059 0.483540i
\(583\) 1.31263 + 2.27354i 0.0543634 + 0.0941602i
\(584\) −3.11747 −0.129002
\(585\) −18.7534 28.4395i −0.775358 1.17583i
\(586\) 13.5008 0.557714
\(587\) −9.13891 15.8291i −0.377203 0.653335i 0.613451 0.789733i \(-0.289781\pi\)
−0.990654 + 0.136398i \(0.956447\pi\)
\(588\) 0 0
\(589\) −6.59447 + 11.4220i −0.271720 + 0.470633i
\(590\) −18.8208 + 32.5985i −0.774839 + 1.34206i
\(591\) −1.01545 34.1999i −0.0417702 1.40679i
\(592\) −16.0287 27.7625i −0.658775 1.14103i
\(593\) −28.3816 −1.16549 −0.582745 0.812655i \(-0.698022\pi\)
−0.582745 + 0.812655i \(0.698022\pi\)
\(594\) 7.22039 + 3.35127i 0.296256 + 0.137504i
\(595\) 0 0
\(596\) 0.175096 + 0.303275i 0.00717222 + 0.0124226i
\(597\) −0.977835 32.9329i −0.0400201 1.34785i
\(598\) −9.00044 + 15.5892i −0.368055 + 0.637490i
\(599\) −4.69451 + 8.13113i −0.191813 + 0.332229i −0.945851 0.324601i \(-0.894770\pi\)
0.754038 + 0.656830i \(0.228103\pi\)
\(600\) −32.8886 + 20.3130i −1.34267 + 0.829274i
\(601\) −6.31432 10.9367i −0.257566 0.446118i 0.708023 0.706189i \(-0.249587\pi\)
−0.965589 + 0.260071i \(0.916254\pi\)
\(602\) 0 0
\(603\) 7.16336 14.3058i 0.291714 0.582577i
\(604\) 6.09168 0.247867
\(605\) 16.9435 + 29.3471i 0.688853 + 1.19313i
\(606\) 3.16205 + 1.70254i 0.128449 + 0.0691608i
\(607\) −12.0133 + 20.8076i −0.487604 + 0.844554i −0.999898 0.0142555i \(-0.995462\pi\)
0.512295 + 0.858810i \(0.328796\pi\)
\(608\) 5.96947 10.3394i 0.242094 0.419319i
\(609\) 0 0
\(610\) 22.1347 + 38.3383i 0.896206 + 1.55227i
\(611\) −2.03935 −0.0825031
\(612\) 2.04385 4.08172i 0.0826177 0.164994i
\(613\) −28.5415 −1.15278 −0.576390 0.817175i \(-0.695539\pi\)
−0.576390 + 0.817175i \(0.695539\pi\)
\(614\) 6.91695 + 11.9805i 0.279145 + 0.483494i
\(615\) 34.5701 21.3515i 1.39400 0.860976i
\(616\) 0 0
\(617\) −6.05549 + 10.4884i −0.243785 + 0.422248i −0.961789 0.273791i \(-0.911722\pi\)
0.718004 + 0.696039i \(0.245056\pi\)
\(618\) 0.156062 + 5.25606i 0.00627772 + 0.211430i
\(619\) 13.2870 + 23.0137i 0.534048 + 0.924998i 0.999209 + 0.0397721i \(0.0126632\pi\)
−0.465161 + 0.885226i \(0.654003\pi\)
\(620\) 2.10171 0.0844067
\(621\) −20.2662 9.40636i −0.813256 0.377464i
\(622\) −17.8207 −0.714545
\(623\) 0 0
\(624\) 0.543522 + 18.3055i 0.0217583 + 0.732806i
\(625\) 3.46486 6.00131i 0.138594 0.240052i
\(626\) −13.7903 + 23.8855i −0.551170 + 0.954655i
\(627\) −11.9250 + 7.36526i −0.476240 + 0.294140i
\(628\) 1.44807 + 2.50813i 0.0577843 + 0.100085i
\(629\) 47.8774 1.90900
\(630\) 0 0
\(631\) 3.30962 0.131754 0.0658770 0.997828i \(-0.479015\pi\)
0.0658770 + 0.997828i \(0.479015\pi\)
\(632\) 1.50769 + 2.61140i 0.0599727 + 0.103876i
\(633\) 11.3405 + 6.10604i 0.450744 + 0.242693i
\(634\) −2.32055 + 4.01931i −0.0921608 + 0.159627i
\(635\) 5.36227 9.28773i 0.212795 0.368572i
\(636\) −1.05424 0.567631i −0.0418032 0.0225080i
\(637\) 0 0
\(638\) −4.17119 −0.165139
\(639\) 9.81426 0.583319i 0.388246 0.0230757i
\(640\) 28.1907 1.11433
\(641\) −16.2922 28.2189i −0.643503 1.11458i −0.984645 0.174568i \(-0.944147\pi\)
0.341142 0.940012i \(-0.389186\pi\)
\(642\) −4.25944 + 2.63075i −0.168107 + 0.103828i
\(643\) 21.5327 37.2957i 0.849166 1.47080i −0.0327873 0.999462i \(-0.510438\pi\)
0.881953 0.471337i \(-0.156228\pi\)
\(644\) 0 0
\(645\) −1.75243 59.0208i −0.0690019 2.32394i
\(646\) −21.8814 37.8997i −0.860912 1.49114i
\(647\) 46.1975 1.81621 0.908106 0.418739i \(-0.137528\pi\)
0.908106 + 0.418739i \(0.137528\pi\)
\(648\) −26.8379 + 3.20158i −1.05429 + 0.125770i
\(649\) 9.67935 0.379948
\(650\) 15.5556 + 26.9432i 0.610143 + 1.05680i
\(651\) 0 0
\(652\) 2.62248 4.54228i 0.102704 0.177889i
\(653\) −16.0002 + 27.7132i −0.626138 + 1.08450i 0.362182 + 0.932107i \(0.382032\pi\)
−0.988320 + 0.152395i \(0.951301\pi\)
\(654\) −1.76146 + 1.08793i −0.0688786 + 0.0425414i
\(655\) 5.75022 + 9.95967i 0.224680 + 0.389156i
\(656\) −21.8435 −0.852845
\(657\) −3.10873 + 0.184770i −0.121283 + 0.00720857i
\(658\) 0 0
\(659\) 19.2070 + 33.2674i 0.748197 + 1.29591i 0.948686 + 0.316219i \(0.102413\pi\)
−0.200490 + 0.979696i \(0.564253\pi\)
\(660\) 1.96659 + 1.05887i 0.0765495 + 0.0412164i
\(661\) −14.0130 + 24.2712i −0.545043 + 0.944042i 0.453561 + 0.891225i \(0.350153\pi\)
−0.998604 + 0.0528170i \(0.983180\pi\)
\(662\) 15.5631 26.9561i 0.604878 1.04768i
\(663\) −24.0822 12.9666i −0.935276 0.503579i
\(664\) 10.9794 + 19.0169i 0.426083 + 0.737998i
\(665\) 0 0
\(666\) −20.9620 31.7889i −0.812263 1.23179i
\(667\) 11.7077 0.453325
\(668\) −0.798544 1.38312i −0.0308966 0.0535145i
\(669\) −4.85017 + 2.99561i −0.187518 + 0.115817i
\(670\) −12.2210 + 21.1674i −0.472138 + 0.817766i
\(671\) 5.69183 9.85853i 0.219730 0.380584i
\(672\) 0 0
\(673\) 0.796281 + 1.37920i 0.0306944 + 0.0531642i 0.880965 0.473182i \(-0.156895\pi\)
−0.850270 + 0.526347i \(0.823561\pi\)
\(674\) 35.7383 1.37659
\(675\) −31.5925 + 22.2053i −1.21599 + 0.854683i
\(676\) 0.815462 0.0313639
\(677\) 21.0167 + 36.4020i 0.807737 + 1.39904i 0.914428 + 0.404749i \(0.132641\pi\)
−0.106691 + 0.994292i \(0.534025\pi\)
\(678\) −0.159469 5.37082i −0.00612437 0.206265i
\(679\) 0 0
\(680\) −25.9588 + 44.9620i −0.995476 + 1.72421i
\(681\) −26.5504 + 16.3983i −1.01741 + 0.628386i
\(682\) 1.47128 + 2.54833i 0.0563382 + 0.0975807i
\(683\) 35.7289 1.36713 0.683565 0.729890i \(-0.260429\pi\)
0.683565 + 0.729890i \(0.260429\pi\)
\(684\) 2.86219 5.71602i 0.109439 0.218557i
\(685\) 73.8092 2.82010
\(686\) 0 0
\(687\) −6.48892 3.49382i −0.247568 0.133298i
\(688\) −15.8715 + 27.4902i −0.605095 + 1.04806i
\(689\) −3.58704 + 6.21294i −0.136655 + 0.236694i
\(690\) 30.0539 + 16.1819i 1.14413 + 0.616033i
\(691\) 25.5675 + 44.2841i 0.972632 + 1.68465i 0.687538 + 0.726149i \(0.258692\pi\)
0.285094 + 0.958499i \(0.407975\pi\)
\(692\) −3.02161 −0.114864
\(693\) 0 0
\(694\) −6.66606 −0.253040
\(695\) −29.3066 50.7606i −1.11166 1.92546i
\(696\) 12.0499 7.44236i 0.456749 0.282102i
\(697\) 16.3115 28.2524i 0.617843 1.07014i
\(698\) −9.83977 + 17.0430i −0.372441 + 0.645086i
\(699\) −0.755936 25.4595i −0.0285921 0.962965i
\(700\) 0 0
\(701\) −24.5761 −0.928226 −0.464113 0.885776i \(-0.653627\pi\)
−0.464113 + 0.885776i \(0.653627\pi\)
\(702\) 1.93453 + 21.6668i 0.0730141 + 0.817763i
\(703\) 67.0472 2.52873
\(704\) −5.20100 9.00840i −0.196020 0.339517i
\(705\) 0.114768 + 3.86532i 0.00432242 + 0.145576i
\(706\) −21.4321 + 37.1215i −0.806607 + 1.39708i
\(707\) 0 0
\(708\) −3.75597 + 2.31980i −0.141158 + 0.0871833i
\(709\) −15.4488 26.7581i −0.580192 1.00492i −0.995456 0.0952206i \(-0.969644\pi\)
0.415265 0.909701i \(-0.363689\pi\)
\(710\) −15.0198 −0.563685
\(711\) 1.65824 + 2.51471i 0.0621888 + 0.0943092i
\(712\) −36.1664 −1.35539
\(713\) −4.12960 7.15268i −0.154655 0.267870i
\(714\) 0 0
\(715\) 6.69133 11.5897i 0.250242 0.433431i
\(716\) 0.213506 0.369803i 0.00797908 0.0138202i
\(717\) 21.6003 + 11.6302i 0.806677 + 0.434338i
\(718\) 15.6216 + 27.0573i 0.582992 + 1.00977i
\(719\) −6.11380 −0.228006 −0.114003 0.993480i \(-0.536367\pi\)
−0.114003 + 0.993480i \(0.536367\pi\)
\(720\) 34.6651 2.06035i 1.29189 0.0767848i
\(721\) 0 0
\(722\) −18.2938 31.6857i −0.680823 1.17922i
\(723\) 11.6934 7.22216i 0.434881 0.268595i
\(724\) −0.879109 + 1.52266i −0.0326718 + 0.0565893i
\(725\) 10.1174 17.5238i 0.375749 0.650816i
\(726\) −0.642209 21.6292i −0.0238346 0.802736i
\(727\) −22.2492 38.5367i −0.825176 1.42925i −0.901785 0.432186i \(-0.857743\pi\)
0.0766087 0.997061i \(-0.475591\pi\)
\(728\) 0 0
\(729\) −26.5729 + 4.78327i −0.984182 + 0.177158i
\(730\) 4.75763 0.176088
\(731\) −23.7039 41.0564i −0.876722 1.51853i
\(732\) 0.154089 + 5.18962i 0.00569529 + 0.191814i
\(733\) 4.91854 8.51916i 0.181670 0.314662i −0.760779 0.649011i \(-0.775183\pi\)
0.942449 + 0.334349i \(0.108516\pi\)
\(734\) 1.72559 2.98881i 0.0636926 0.110319i
\(735\) 0 0
\(736\) 3.73821 + 6.47478i 0.137792 + 0.238663i
\(737\) 6.28514 0.231516
\(738\) −25.9002 + 1.53940i −0.953400 + 0.0566662i
\(739\) 14.8493 0.546239 0.273120 0.961980i \(-0.411944\pi\)
0.273120 + 0.961980i \(0.411944\pi\)
\(740\) −5.34212 9.25282i −0.196380 0.340140i
\(741\) −33.7246 18.1583i −1.23890 0.667061i
\(742\) 0 0
\(743\) −3.04201 + 5.26892i −0.111601 + 0.193298i −0.916416 0.400228i \(-0.868931\pi\)
0.804815 + 0.593525i \(0.202264\pi\)
\(744\) −8.79710 4.73661i −0.322517 0.173652i
\(745\) −1.98935 3.44566i −0.0728843 0.126239i
\(746\) −41.4897 −1.51905
\(747\) 12.0757 + 18.3128i 0.441828 + 0.670031i
\(748\) 1.79328 0.0655686
\(749\) 0 0
\(750\) 16.4225 10.1430i 0.599665 0.370371i
\(751\) −11.1005 + 19.2266i −0.405063 + 0.701590i −0.994329 0.106349i \(-0.966084\pi\)
0.589266 + 0.807939i \(0.299417\pi\)
\(752\) 1.03944 1.80036i 0.0379044 0.0656523i
\(753\) 0.413860 + 13.9386i 0.0150819 + 0.507949i
\(754\) −5.69934 9.87156i −0.207558 0.359501i
\(755\) −69.2106 −2.51883
\(756\) 0 0
\(757\) 25.0464 0.910329 0.455164 0.890407i \(-0.349581\pi\)
0.455164 + 0.890407i \(0.349581\pi\)
\(758\) −19.6723 34.0735i −0.714531 1.23760i
\(759\) −0.260497 8.77338i −0.00945544 0.318454i
\(760\) −36.3526 + 62.9645i −1.31865 + 2.28396i
\(761\) 3.37632 5.84796i 0.122392 0.211988i −0.798319 0.602235i \(-0.794277\pi\)
0.920710 + 0.390247i \(0.127610\pi\)
\(762\) −5.82649 + 3.59862i −0.211072 + 0.130364i
\(763\) 0 0
\(764\) 7.76233 0.280831
\(765\) −23.2212 + 46.3745i −0.839563 + 1.67667i
\(766\) 2.25275 0.0813950
\(767\) 13.2255 + 22.9072i 0.477544 + 0.827131i
\(768\) 11.0709 + 5.96087i 0.399485 + 0.215094i
\(769\) −21.0805 + 36.5125i −0.760182 + 1.31667i 0.182575 + 0.983192i \(0.441557\pi\)
−0.942757 + 0.333482i \(0.891776\pi\)
\(770\) 0 0
\(771\) 26.7702 + 14.4138i 0.964104 + 0.519101i
\(772\) 2.72065 + 4.71230i 0.0979183 + 0.169600i
\(773\) −3.29852 −0.118639 −0.0593197 0.998239i \(-0.518893\pi\)
−0.0593197 + 0.998239i \(0.518893\pi\)
\(774\) −16.8818 + 33.7142i −0.606803 + 1.21183i
\(775\) −14.2746 −0.512757
\(776\) 16.4108 + 28.4243i 0.589112 + 1.02037i
\(777\) 0 0
\(778\) 7.20356 12.4769i 0.258260 0.447320i
\(779\) 22.8425 39.5644i 0.818419 1.41754i
\(780\) 0.181148 + 6.10094i 0.00648612 + 0.218449i
\(781\) 1.93114 + 3.34484i 0.0691017 + 0.119688i
\(782\) 27.4052 0.980009
\(783\) 11.5750 8.13567i 0.413656 0.290745i
\(784\) 0 0
\(785\) −16.4522 28.4961i −0.587205 1.01707i
\(786\) −0.217950 7.34043i −0.00777402 0.261824i
\(787\) 3.36455 5.82757i 0.119933 0.207731i −0.799808 0.600256i \(-0.795065\pi\)
0.919741 + 0.392526i \(0.128399\pi\)
\(788\) −3.06515 + 5.30900i −0.109192 + 0.189125i
\(789\) −34.4073 + 21.2510i −1.22493 + 0.756555i
\(790\) −2.30092 3.98530i −0.0818629 0.141791i
\(791\) 0 0
\(792\) −5.84517 8.86419i −0.207699 0.314975i
\(793\) 31.1083 1.10469
\(794\) −16.4688 28.5248i −0.584456 1.01231i
\(795\) 11.9777 + 6.44913i 0.424805 + 0.228727i
\(796\) −2.95160 + 5.11233i −0.104617 + 0.181202i
\(797\) −8.86302 + 15.3512i −0.313944 + 0.543767i −0.979213 0.202837i \(-0.934984\pi\)
0.665268 + 0.746604i \(0.268317\pi\)
\(798\) 0 0
\(799\) 1.55239 + 2.68882i 0.0549196 + 0.0951235i
\(800\) 12.9217 0.456850
\(801\) −36.0650 + 2.14355i −1.27429 + 0.0757387i
\(802\) −45.2673 −1.59844
\(803\) −0.611702 1.05950i −0.0215865 0.0373889i
\(804\) −2.43888 + 1.50632i −0.0860126 + 0.0531240i
\(805\) 0 0
\(806\) −4.02060 + 6.96388i −0.141620 + 0.245292i
\(807\) 0.0276809 + 0.932277i 0.000974415 + 0.0328177i
\(808\) −2.39514 4.14850i −0.0842607 0.145944i
\(809\) 39.0857 1.37418 0.687089 0.726573i \(-0.258888\pi\)
0.687089 + 0.726573i \(0.258888\pi\)
\(810\) 40.9579 4.88600i 1.43911 0.171676i
\(811\) −13.9559 −0.490058 −0.245029 0.969516i \(-0.578797\pi\)
−0.245029 + 0.969516i \(0.578797\pi\)
\(812\) 0 0
\(813\) −0.741002 24.9565i −0.0259881 0.875263i
\(814\) 7.47939 12.9547i 0.262152 0.454061i
\(815\) −29.7953 + 51.6070i −1.04369 + 1.80772i
\(816\) 23.7215 14.6511i 0.830419 0.512892i
\(817\) −33.1948 57.4951i −1.16134 2.01150i
\(818\) −23.7177 −0.829269
\(819\) 0 0
\(820\) −7.28010 −0.254232
\(821\) 22.4983 + 38.9682i 0.785196 + 1.36000i 0.928882 + 0.370376i \(0.120771\pi\)
−0.143685 + 0.989623i \(0.545895\pi\)
\(822\) −41.4983 22.3438i −1.44742 0.779331i
\(823\) 27.6232 47.8449i 0.962886 1.66777i 0.247694 0.968838i \(-0.420327\pi\)
0.715191 0.698929i \(-0.246340\pi\)
\(824\) 3.50700 6.07430i 0.122172 0.211608i
\(825\) −13.3569 7.19171i −0.465026 0.250383i
\(826\) 0 0
\(827\) −13.8901 −0.483005 −0.241502 0.970400i \(-0.577640\pi\)
−0.241502 + 0.970400i \(0.577640\pi\)
\(828\) 2.20375 + 3.34198i 0.0765857 + 0.116142i
\(829\) 38.9792 1.35381 0.676903 0.736073i \(-0.263322\pi\)
0.676903 + 0.736073i \(0.263322\pi\)
\(830\) −16.7559 29.0220i −0.581605 1.00737i
\(831\) 32.2824 19.9386i 1.11987 0.691662i
\(832\) 14.2129 24.6174i 0.492743 0.853456i
\(833\) 0 0
\(834\) 1.11081 + 37.4113i 0.0384641 + 1.29545i
\(835\) 9.07266 + 15.7143i 0.313972 + 0.543816i
\(836\) 2.51129 0.0868548
\(837\) −9.05316 4.20193i −0.312923 0.145240i
\(838\) 10.9376 0.377834
\(839\) 19.4708 + 33.7244i 0.672206 + 1.16429i 0.977277 + 0.211965i \(0.0679862\pi\)
−0.305072 + 0.952329i \(0.598680\pi\)
\(840\) 0 0
\(841\) 10.7932 18.6943i 0.372178 0.644631i
\(842\) 0.187560 0.324863i 0.00646373 0.0111955i
\(843\) 2.28892 1.41370i 0.0788345 0.0486906i
\(844\) −1.15385 1.99852i −0.0397170 0.0687918i
\(845\) −9.26487 −0.318721
\(846\) 1.10560 2.20797i 0.0380113 0.0759116i
\(847\) 0 0
\(848\) −3.65657 6.33336i −0.125567 0.217488i
\(849\) 4.04352 + 2.17715i 0.138773 + 0.0747194i
\(850\) 23.6825 41.0193i 0.812304 1.40695i
\(851\) −20.9932 + 36.3613i −0.719638 + 1.24645i
\(852\) −1.55100 0.835101i −0.0531363 0.0286101i
\(853\) 3.83890 + 6.64916i 0.131441 + 0.227663i 0.924232 0.381830i \(-0.124706\pi\)
−0.792791 + 0.609493i \(0.791373\pi\)
\(854\) 0 0
\(855\) −32.5188 + 64.9425i −1.11212 + 2.22099i
\(856\) 6.67784 0.228244
\(857\) −7.98194 13.8251i −0.272658 0.472258i 0.696884 0.717184i \(-0.254569\pi\)
−0.969542 + 0.244927i \(0.921236\pi\)
\(858\) −7.27061 + 4.49055i −0.248215 + 0.153305i
\(859\) 24.1645 41.8542i 0.824483 1.42805i −0.0778308 0.996967i \(-0.524799\pi\)
0.902314 0.431080i \(-0.141867\pi\)
\(860\) −5.28973 + 9.16208i −0.180378 + 0.312424i
\(861\) 0 0
\(862\) 8.77148 + 15.1926i 0.298758 + 0.517463i
\(863\) −34.3052 −1.16776 −0.583881 0.811839i \(-0.698467\pi\)
−0.583881 + 0.811839i \(0.698467\pi\)
\(864\) 8.19514 + 3.80369i 0.278804 + 0.129404i
\(865\) 34.3300 1.16726
\(866\) 3.15356 + 5.46212i 0.107162 + 0.185611i
\(867\) 0.361948 + 12.1902i 0.0122924 + 0.414001i
\(868\) 0 0
\(869\) −0.591670 + 1.02480i −0.0200710 + 0.0347640i
\(870\) −18.3895 + 11.3579i −0.623464 + 0.385070i
\(871\) 8.58776 + 14.8744i 0.290985 + 0.504001i
\(872\) 2.76158 0.0935188
\(873\) 18.0494 + 27.3719i 0.610881 + 0.926399i
\(874\) 38.3781 1.29816
\(875\) 0 0
\(876\) 0.491288 + 0.264524i 0.0165991 + 0.00893743i
\(877\) −7.09076 + 12.2816i −0.239438 + 0.414719i −0.960553 0.278097i \(-0.910296\pi\)
0.721115 + 0.692815i \(0.243630\pi\)
\(878\) −1.65599 + 2.86826i −0.0558870 + 0.0967992i
\(879\) −15.8395 8.52844i −0.534253 0.287657i
\(880\) 6.82103 + 11.8144i 0.229937 + 0.398262i
\(881\) 46.2822 1.55929 0.779643 0.626224i \(-0.215400\pi\)
0.779643 + 0.626224i \(0.215400\pi\)
\(882\) 0 0
\(883\) −4.37483 −0.147225 −0.0736124 0.997287i \(-0.523453\pi\)
−0.0736124 + 0.997287i \(0.523453\pi\)
\(884\) 2.45026 + 4.24397i 0.0824111 + 0.142740i
\(885\) 42.6734 26.3564i 1.43445 0.885959i
\(886\) 0.419538 0.726661i 0.0140946 0.0244126i
\(887\) −9.57208 + 16.5793i −0.321399 + 0.556679i −0.980777 0.195132i \(-0.937486\pi\)
0.659378 + 0.751812i \(0.270820\pi\)
\(888\) 1.50742 + 50.7689i 0.0505856 + 1.70369i
\(889\) 0 0
\(890\) 55.1942 1.85011
\(891\) −6.35415 8.49289i −0.212872 0.284523i
\(892\) 1.02139 0.0341988
\(893\) 2.17396 + 3.76540i 0.0727486 + 0.126004i
\(894\) 0.0754024 + 2.53951i 0.00252183 + 0.0849338i
\(895\) −2.42574 + 4.20151i −0.0810836 + 0.140441i
\(896\) 0 0
\(897\) 20.4072 12.6041i 0.681377 0.420838i
\(898\) 3.39694 + 5.88368i 0.113358 + 0.196341i
\(899\) 5.22997 0.174429
\(900\) 6.90658 0.410498i 0.230219 0.0136833i
\(901\) 10.9221 0.363868
\(902\) −5.09636 8.82715i −0.169690 0.293912i
\(903\) 0 0
\(904\) −3.58357 + 6.20692i −0.119188 + 0.206439i
\(905\) 9.98800 17.2997i 0.332012 0.575062i
\(906\) 38.9128 + 20.9517i 1.29279 + 0.696075i
\(907\) −19.9225 34.5068i −0.661515 1.14578i −0.980218 0.197923i \(-0.936580\pi\)
0.318702 0.947855i \(-0.396753\pi\)
\(908\) 5.59124 0.185552
\(909\) −2.63430 3.99491i −0.0873743 0.132503i
\(910\) 0 0
\(911\) 14.3727 + 24.8942i 0.476189 + 0.824783i 0.999628 0.0272803i \(-0.00868466\pi\)
−0.523439 + 0.852063i \(0.675351\pi\)
\(912\) 33.2194 20.5173i 1.10001 0.679396i
\(913\) −4.30870 + 7.46288i −0.142597 + 0.246985i
\(914\) 1.85930 3.22041i 0.0615003 0.106522i
\(915\) −1.75068 58.9619i −0.0578757 1.94922i
\(916\) 0.660219 + 1.14353i 0.0218142 + 0.0377834i
\(917\) 0 0
\(918\) 27.0945 19.0438i 0.894252 0.628540i
\(919\) −16.0269 −0.528680 −0.264340 0.964430i \(-0.585154\pi\)
−0.264340 + 0.964430i \(0.585154\pi\)
\(920\) −22.7648 39.4298i −0.750533 1.29996i
\(921\) −0.547078 18.4252i −0.0180268 0.607133i
\(922\) 2.37388 4.11168i 0.0781796 0.135411i
\(923\) −5.27727 + 9.14050i −0.173704 + 0.300863i
\(924\) 0 0
\(925\) 36.2830 + 62.8440i 1.19298 + 2.06630i
\(926\) 40.0495 1.31611
\(927\) 3.13714 6.26512i 0.103037 0.205774i
\(928\) −4.73430 −0.155411
\(929\) 7.00796 + 12.1381i 0.229924 + 0.398239i 0.957785 0.287485i \(-0.0928190\pi\)
−0.727862 + 0.685724i \(0.759486\pi\)
\(930\) 13.4254 + 7.22863i 0.440237 + 0.237036i
\(931\) 0 0
\(932\) −2.28180 + 3.95219i −0.0747428 + 0.129458i
\(933\) 20.9077 + 11.2573i 0.684486 + 0.368547i
\(934\) −13.3738 23.1640i −0.437603 0.757950i
\(935\) −20.3743 −0.666310
\(936\) 12.9914 25.9449i 0.424638 0.848035i
\(937\) −51.5307 −1.68344 −0.841718 0.539918i \(-0.818455\pi\)
−0.841718 + 0.539918i \(0.818455\pi\)
\(938\) 0 0
\(939\) 31.2675 19.3117i 1.02038 0.630214i
\(940\) 0.346429 0.600032i 0.0112993 0.0195709i
\(941\) −23.1564 + 40.1081i −0.754877 + 1.30749i 0.190558 + 0.981676i \(0.438970\pi\)
−0.945435 + 0.325809i \(0.894363\pi\)
\(942\) 0.623588 + 21.0021i 0.0203176 + 0.684284i
\(943\) 14.3045 + 24.7761i 0.465819 + 0.806821i
\(944\) −26.9636 −0.877592
\(945\) 0 0
\(946\) −14.8121 −0.481582
\(947\) −10.0041 17.3277i −0.325091 0.563073i 0.656440 0.754378i \(-0.272061\pi\)
−0.981531 + 0.191305i \(0.938728\pi\)
\(948\) −0.0160177 0.539466i −0.000520230 0.0175210i
\(949\) 1.67161 2.89531i 0.0542628 0.0939859i
\(950\) 33.1648 57.4432i 1.07601 1.86370i
\(951\) 5.26152 3.24967i 0.170616 0.105378i
\(952\) 0 0
\(953\) 30.0109 0.972148 0.486074 0.873918i \(-0.338429\pi\)
0.486074 + 0.873918i \(0.338429\pi\)
\(954\) −4.78200 7.25188i −0.154823 0.234788i
\(955\) −88.1917 −2.85382
\(956\) −2.19773 3.80659i −0.0710798 0.123114i
\(957\) 4.89374 + 2.63493i 0.158192 + 0.0851752i
\(958\) −16.3675 + 28.3493i −0.528809 + 0.915924i
\(959\) 0 0
\(960\) −47.4591 25.5533i −1.53173 0.824730i
\(961\) 13.6553 + 23.6516i 0.440492 + 0.762955i
\(962\) 40.8782 1.31796
\(963\) 6.65912 0.395790i 0.214587 0.0127542i
\(964\) −2.46250 −0.0793117
\(965\) −30.9106 53.5388i −0.995049 1.72348i
\(966\) 0 0
\(967\) 16.5721 28.7037i 0.532923 0.923050i −0.466338 0.884607i \(-0.654427\pi\)
0.999261 0.0384431i \(-0.0122398\pi\)
\(968\) −14.4317 + 24.9964i −0.463851 + 0.803414i
\(969\) 1.73065 + 58.2873i 0.0555965 + 1.87246i
\(970\) −25.0448 43.3788i −0.804140 1.39281i
\(971\) −41.6469 −1.33651 −0.668256 0.743932i \(-0.732959\pi\)
−0.668256 + 0.743932i \(0.732959\pi\)
\(972\) 4.50110 + 1.77271i 0.144373 + 0.0568597i
\(973\) 0 0
\(974\) 21.2928 + 36.8803i 0.682267 + 1.18172i
\(975\) −1.23033 41.4369i −0.0394022 1.32704i
\(976\) −15.8556 + 27.4628i −0.507527 + 0.879062i
\(977\) −18.7590 + 32.4916i −0.600154 + 1.03950i 0.392643 + 0.919691i \(0.371561\pi\)
−0.992797 + 0.119807i \(0.961772\pi\)
\(978\) 32.3748 19.9956i 1.03523 0.639389i
\(979\) −7.09647 12.2914i −0.226804 0.392836i
\(980\) 0 0
\(981\) 2.75383 0.163676i 0.0879231 0.00522578i
\(982\) −4.57556 −0.146012
\(983\) 24.0379 + 41.6349i 0.766690 + 1.32795i 0.939348 + 0.342964i \(0.111431\pi\)
−0.172658 + 0.984982i \(0.555236\pi\)
\(984\) 30.4722 + 16.4071i 0.971419 + 0.523039i
\(985\) 34.8247 60.3182i 1.10961 1.92190i
\(986\) −8.67690 + 15.0288i −0.276329 + 0.478616i
\(987\) 0 0
\(988\) 3.43133 + 5.94323i 0.109165 + 0.189079i
\(989\) 41.5747 1.32200
\(990\) 8.92042 + 13.5278i 0.283510 + 0.429942i
\(991\) −34.1286 −1.08413 −0.542065 0.840337i \(-0.682357\pi\)
−0.542065 + 0.840337i \(0.682357\pi\)
\(992\) 1.66990 + 2.89236i 0.0530195 + 0.0918324i
\(993\) −35.2871 + 21.7944i −1.11980 + 0.691624i
\(994\) 0 0
\(995\) 33.5346 58.0837i 1.06312 1.84138i
\(996\) −0.116645 3.92853i −0.00369603 0.124480i
\(997\) −22.0413 38.1767i −0.698056 1.20907i −0.969140 0.246512i \(-0.920715\pi\)
0.271084 0.962556i \(-0.412618\pi\)
\(998\) 20.3321 0.643602
\(999\) 4.51222 + 50.5372i 0.142760 + 1.59893i
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 441.2.f.h.148.4 yes 24
3.2 odd 2 1323.2.f.h.442.10 24
7.2 even 3 441.2.g.h.67.3 24
7.3 odd 6 441.2.h.h.373.9 24
7.4 even 3 441.2.h.h.373.10 24
7.5 odd 6 441.2.g.h.67.4 24
7.6 odd 2 inner 441.2.f.h.148.3 24
9.2 odd 6 1323.2.f.h.883.10 24
9.4 even 3 3969.2.a.bh.1.10 12
9.5 odd 6 3969.2.a.bi.1.3 12
9.7 even 3 inner 441.2.f.h.295.4 yes 24
21.2 odd 6 1323.2.g.h.361.10 24
21.5 even 6 1323.2.g.h.361.9 24
21.11 odd 6 1323.2.h.h.226.3 24
21.17 even 6 1323.2.h.h.226.4 24
21.20 even 2 1323.2.f.h.442.9 24
63.2 odd 6 1323.2.h.h.802.3 24
63.11 odd 6 1323.2.g.h.667.10 24
63.13 odd 6 3969.2.a.bh.1.9 12
63.16 even 3 441.2.h.h.214.10 24
63.20 even 6 1323.2.f.h.883.9 24
63.25 even 3 441.2.g.h.79.3 24
63.34 odd 6 inner 441.2.f.h.295.3 yes 24
63.38 even 6 1323.2.g.h.667.9 24
63.41 even 6 3969.2.a.bi.1.4 12
63.47 even 6 1323.2.h.h.802.4 24
63.52 odd 6 441.2.g.h.79.4 24
63.61 odd 6 441.2.h.h.214.9 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.h.148.3 24 7.6 odd 2 inner
441.2.f.h.148.4 yes 24 1.1 even 1 trivial
441.2.f.h.295.3 yes 24 63.34 odd 6 inner
441.2.f.h.295.4 yes 24 9.7 even 3 inner
441.2.g.h.67.3 24 7.2 even 3
441.2.g.h.67.4 24 7.5 odd 6
441.2.g.h.79.3 24 63.25 even 3
441.2.g.h.79.4 24 63.52 odd 6
441.2.h.h.214.9 24 63.61 odd 6
441.2.h.h.214.10 24 63.16 even 3
441.2.h.h.373.9 24 7.3 odd 6
441.2.h.h.373.10 24 7.4 even 3
1323.2.f.h.442.9 24 21.20 even 2
1323.2.f.h.442.10 24 3.2 odd 2
1323.2.f.h.883.9 24 63.20 even 6
1323.2.f.h.883.10 24 9.2 odd 6
1323.2.g.h.361.9 24 21.5 even 6
1323.2.g.h.361.10 24 21.2 odd 6
1323.2.g.h.667.9 24 63.38 even 6
1323.2.g.h.667.10 24 63.11 odd 6
1323.2.h.h.226.3 24 21.11 odd 6
1323.2.h.h.226.4 24 21.17 even 6
1323.2.h.h.802.3 24 63.2 odd 6
1323.2.h.h.802.4 24 63.47 even 6
3969.2.a.bh.1.9 12 63.13 odd 6
3969.2.a.bh.1.10 12 9.4 even 3
3969.2.a.bi.1.3 12 9.5 odd 6
3969.2.a.bi.1.4 12 63.41 even 6